Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,3,Mod(379,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.379");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.g (of order \(2\), degree \(1\), 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: | \(13.7330053238\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.3 | ||
Root | \(1.37098 + 1.45617i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.379 |
Dual form | 504.3.g.b.379.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37098 | − | 1.45617i | −0.685489 | − | 0.728083i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.240837 | + | 3.99274i | −0.0602092 | + | 0.998186i | ||||
\(5\) | − | 6.26788i | − | 1.25358i | −0.779190 | − | 0.626788i | \(-0.784369\pi\) | ||
0.779190 | − | 0.626788i | \(-0.215631\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 6.14428 | − | 5.12327i | 0.768035 | − | 0.640408i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.12707 | + | 8.59313i | −0.912707 | + | 0.859313i | ||||
\(11\) | −9.80688 | −0.891535 | −0.445767 | − | 0.895149i | \(-0.647069\pi\) | ||||
−0.445767 | + | 0.895149i | \(0.647069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41653i | 0.185887i | 0.995671 | + | 0.0929434i | \(0.0296276\pi\) | ||||
−0.995671 | + | 0.0929434i | \(0.970372\pi\) | |||||||
\(14\) | −3.85265 | + | 3.62727i | −0.275189 | + | 0.259091i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.8840 | − | 1.92320i | −0.992750 | − | 0.120200i | ||||
\(17\) | −6.89452 | −0.405560 | −0.202780 | − | 0.979224i | \(-0.564998\pi\) | ||||
−0.202780 | + | 0.979224i | \(0.564998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.77637 | 0.146125 | 0.0730624 | − | 0.997327i | \(-0.476723\pi\) | ||||
0.0730624 | + | 0.997327i | \(0.476723\pi\) | |||||||
\(20\) | 25.0260 | + | 1.50954i | 1.25130 | + | 0.0754769i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.4450 | + | 14.2804i | 0.611137 | + | 0.649111i | ||||
\(23\) | − | 42.8332i | − | 1.86231i | −0.364617 | − | 0.931157i | \(-0.618800\pi\) | ||
0.364617 | − | 0.931157i | \(-0.381200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.2863 | −0.571453 | ||||||||
\(26\) | 3.51887 | − | 3.31301i | 0.135341 | − | 0.127423i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.5638 | + | 0.637195i | 0.377279 | + | 0.0227570i | ||||
\(29\) | 37.3505i | 1.28795i | 0.765048 | + | 0.643974i | \(0.222715\pi\) | ||||
−0.765048 | + | 0.643974i | \(0.777285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.16835i | − | 0.231237i | −0.993294 | − | 0.115619i | \(-0.963115\pi\) | ||
0.993294 | − | 0.115619i | \(-0.0368850\pi\) | |||||||
\(32\) | 18.9761 | + | 25.7664i | 0.593004 | + | 0.805200i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.45224 | + | 10.0396i | 0.278007 | + | 0.295281i | ||||
\(35\) | −16.5833 | −0.473807 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.202653i | − | 0.00547709i | −0.999996 | − | 0.00273855i | \(-0.999128\pi\) | ||
0.999996 | − | 0.00273855i | \(-0.000871708\pi\) | |||||||
\(38\) | −3.80634 | − | 4.04285i | −0.100167 | − | 0.106391i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −32.1120 | − | 38.5116i | −0.802800 | − | 0.962790i | ||||
\(41\) | −63.5494 | −1.54999 | −0.774993 | − | 0.631970i | \(-0.782247\pi\) | ||||
−0.774993 | + | 0.631970i | \(0.782247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −35.3384 | −0.821823 | −0.410911 | − | 0.911675i | \(-0.634789\pi\) | ||||
−0.410911 | + | 0.911675i | \(0.634789\pi\) | |||||||
\(44\) | 2.36186 | − | 39.1564i | 0.0536786 | − | 0.889917i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −62.3723 | + | 58.7234i | −1.35592 | + | 1.27660i | ||||
\(47\) | 37.9129i | 0.806657i | 0.915055 | + | 0.403329i | \(0.132147\pi\) | ||||
−0.915055 | + | 0.403329i | \(0.867853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 19.5862 | + | 20.8032i | 0.391725 | + | 0.416065i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.64858 | − | 0.581989i | −0.185550 | − | 0.0111921i | ||||
\(53\) | 54.6651i | 1.03142i | 0.856764 | + | 0.515709i | \(0.172471\pi\) | ||||
−0.856764 | + | 0.515709i | \(0.827529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 61.4684i | 1.11761i | ||||||||
\(56\) | −13.5549 | − | 16.2562i | −0.242052 | − | 0.290290i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 54.3885 | − | 51.2067i | 0.937732 | − | 0.882874i | ||||
\(59\) | −104.795 | −1.77619 | −0.888093 | − | 0.459665i | \(-0.847970\pi\) | ||||
−0.888093 | + | 0.459665i | \(0.847970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.7668i | 0.717489i | 0.933436 | + | 0.358745i | \(0.116795\pi\) | ||||
−0.933436 | + | 0.358745i | \(0.883205\pi\) | |||||||
\(62\) | −10.4383 | + | 9.82765i | −0.168360 | + | 0.158511i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.5043 | − | 62.9575i | 0.179755 | − | 0.983711i | ||||
\(65\) | 15.1465 | 0.233023 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31.1021 | 0.464210 | 0.232105 | − | 0.972691i | \(-0.425439\pi\) | ||||
0.232105 | + | 0.972691i | \(0.425439\pi\) | |||||||
\(68\) | 1.66046 | − | 27.5281i | 0.0244185 | − | 0.404824i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 22.7353 | + | 24.1480i | 0.324790 | + | 0.344971i | ||||
\(71\) | − | 23.1294i | − | 0.325766i | −0.986645 | − | 0.162883i | \(-0.947921\pi\) | ||
0.986645 | − | 0.162883i | \(-0.0520794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −69.2275 | −0.948322 | −0.474161 | − | 0.880438i | \(-0.657249\pi\) | ||||
−0.474161 | + | 0.880438i | \(0.657249\pi\) | |||||||
\(74\) | −0.295096 | + | 0.277832i | −0.00398778 | + | 0.00375449i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.668652 | + | 11.0853i | −0.00879806 | + | 0.145860i | ||||
\(77\) | 25.9466i | 0.336968i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.9328i | 0.252315i | 0.992010 | + | 0.126157i | \(0.0402644\pi\) | ||||
−0.992010 | + | 0.126157i | \(0.959736\pi\) | |||||||
\(80\) | −12.0544 | + | 99.5590i | −0.150680 | + | 1.24449i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87.1249 | + | 92.5385i | 1.06250 | + | 1.12852i | ||||
\(83\) | 5.11617 | 0.0616406 | 0.0308203 | − | 0.999525i | \(-0.490188\pi\) | ||||
0.0308203 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43.2140i | 0.508400i | ||||||||
\(86\) | 48.4482 | + | 51.4585i | 0.563351 | + | 0.598355i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −60.2562 | + | 50.2433i | −0.684730 | + | 0.570946i | ||||
\(89\) | 17.9889 | 0.202122 | 0.101061 | − | 0.994880i | \(-0.467776\pi\) | ||||
0.101061 | + | 0.994880i | \(0.467776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.39353 | 0.0702586 | ||||||||
\(92\) | 171.022 | + | 10.3158i | 1.85894 | + | 0.112129i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 55.2075 | − | 51.9778i | 0.587313 | − | 0.552955i | ||||
\(95\) | − | 17.4019i | − | 0.183178i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4864 | 0.128726 | 0.0643629 | − | 0.997927i | \(-0.479498\pi\) | ||||
0.0643629 | + | 0.997927i | \(0.479498\pi\) | |||||||
\(98\) | 9.59685 | + | 10.1932i | 0.0979270 | + | 0.104012i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.44067 | − | 57.0416i | 0.0344067 | − | 0.570416i | ||||
\(101\) | 68.0753i | 0.674013i | 0.941502 | + | 0.337006i | \(0.109414\pi\) | ||||
−0.941502 | + | 0.337006i | \(0.890586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 58.2931i | − | 0.565952i | −0.959127 | − | 0.282976i | \(-0.908678\pi\) | ||
0.959127 | − | 0.282976i | \(-0.0913217\pi\) | |||||||
\(104\) | 12.3805 | + | 14.8478i | 0.119043 | + | 0.142768i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79.6015 | − | 74.9447i | 0.750957 | − | 0.707026i | ||||
\(107\) | −135.868 | −1.26979 | −0.634897 | − | 0.772597i | \(-0.718957\pi\) | ||||
−0.634897 | + | 0.772597i | \(0.718957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 44.4981i | 0.408239i | 0.978946 | + | 0.204120i | \(0.0654332\pi\) | ||||
−0.978946 | + | 0.204120i | \(0.934567\pi\) | |||||||
\(110\) | 89.5081 | − | 84.2718i | 0.813710 | − | 0.766107i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.08831 | + | 42.0251i | −0.0454313 | + | 0.375224i | ||||
\(113\) | 133.391 | 1.18045 | 0.590224 | − | 0.807240i | \(-0.299039\pi\) | ||||
0.590224 | + | 0.807240i | \(0.299039\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −268.474 | −2.33455 | ||||||||
\(116\) | −149.131 | − | 8.99537i | −1.28561 | − | 0.0775463i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 143.672 | + | 152.599i | 1.21756 | + | 1.29321i | ||||
\(119\) | 18.2412i | 0.153287i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.8251 | −0.205166 | ||||||||
\(122\) | 63.7318 | − | 60.0034i | 0.522392 | − | 0.491831i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 28.6214 | + | 1.72640i | 0.230818 | + | 0.0139226i | ||||
\(125\) | − | 67.1521i | − | 0.537217i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 130.977i | − | 1.03131i | −0.856795 | − | 0.515657i | \(-0.827548\pi\) | ||
0.856795 | − | 0.515657i | \(-0.172452\pi\) | |||||||
\(128\) | −107.449 | + | 69.5612i | −0.839443 | + | 0.543447i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −20.7655 | − | 22.0558i | −0.159735 | − | 0.169660i | ||||
\(131\) | 53.3311 | 0.407108 | 0.203554 | − | 0.979064i | \(-0.434751\pi\) | ||||
0.203554 | + | 0.979064i | \(0.434751\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 7.34558i | − | 0.0552299i | ||||||
\(134\) | −42.6403 | − | 45.2898i | −0.318211 | − | 0.337983i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −42.3619 | + | 35.3225i | −0.311484 | + | 0.259724i | ||||
\(137\) | 57.7179 | 0.421299 | 0.210649 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210649 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −172.422 | −1.24045 | −0.620224 | − | 0.784425i | \(-0.712958\pi\) | ||||
−0.620224 | + | 0.784425i | \(0.712958\pi\) | |||||||
\(140\) | 3.99386 | − | 66.2127i | 0.0285276 | − | 0.472948i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −33.6803 | + | 31.7099i | −0.237185 | + | 0.223309i | ||||
\(143\) | − | 23.6986i | − | 0.165725i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 234.108 | 1.61454 | ||||||||
\(146\) | 94.9094 | + | 100.807i | 0.650065 | + | 0.690457i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.809139 | + | 0.0488062i | 0.00546716 | + | 0.000329772i | ||||
\(149\) | − | 219.529i | − | 1.47335i | −0.676249 | − | 0.736673i | \(-0.736396\pi\) | ||
0.676249 | − | 0.736673i | \(-0.263604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 185.668i | − | 1.22959i | −0.788687 | − | 0.614795i | \(-0.789239\pi\) | ||
0.788687 | − | 0.614795i | \(-0.210761\pi\) | |||||||
\(152\) | 17.0588 | − | 14.2241i | 0.112229 | − | 0.0935795i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 37.7825 | − | 35.5722i | 0.245341 | − | 0.230988i | ||||
\(155\) | −44.9304 | −0.289873 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 188.182i | − | 1.19861i | −0.800521 | − | 0.599305i | \(-0.795444\pi\) | ||
0.800521 | − | 0.599305i | \(-0.204556\pi\) | |||||||
\(158\) | 29.0255 | − | 27.3275i | 0.183706 | − | 0.172959i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 161.501 | − | 118.940i | 1.00938 | − | 0.743375i | ||||
\(161\) | −113.326 | −0.703889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 54.5154 | 0.334450 | 0.167225 | − | 0.985919i | \(-0.446519\pi\) | ||||
0.167225 | + | 0.985919i | \(0.446519\pi\) | |||||||
\(164\) | 15.3050 | − | 253.736i | 0.0933235 | − | 1.54717i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.01416 | − | 7.45000i | −0.0422540 | − | 0.0448795i | ||||
\(167\) | − | 266.435i | − | 1.59542i | −0.603042 | − | 0.797709i | \(-0.706045\pi\) | ||
0.603042 | − | 0.797709i | \(-0.293955\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.160 | 0.965446 | ||||||||
\(170\) | 62.9268 | − | 59.2455i | 0.370158 | − | 0.348503i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.51079 | − | 141.097i | 0.0494813 | − | 0.820332i | ||||
\(173\) | − | 114.835i | − | 0.663786i | −0.943317 | − | 0.331893i | \(-0.892313\pi\) | ||
0.943317 | − | 0.331893i | \(-0.107687\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 37.7980i | 0.215989i | ||||||||
\(176\) | 155.772 | + | 18.8606i | 0.885071 | + | 0.107162i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24.6624 | − | 26.1948i | −0.138553 | − | 0.147162i | ||||
\(179\) | −112.849 | −0.630439 | −0.315220 | − | 0.949019i | \(-0.602078\pi\) | ||||
−0.315220 | + | 0.949019i | \(0.602078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 60.9470i | 0.336724i | 0.985725 | + | 0.168362i | \(0.0538477\pi\) | ||||
−0.985725 | + | 0.168362i | \(0.946152\pi\) | |||||||
\(182\) | −8.76539 | − | 9.31004i | −0.0481615 | − | 0.0511541i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −219.446 | − | 263.179i | −1.19264 | − | 1.43032i | ||||
\(185\) | −1.27020 | −0.00686595 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 67.6138 | 0.361571 | ||||||||
\(188\) | −151.376 | − | 9.13083i | −0.805194 | − | 0.0485682i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.3401 | + | 23.8577i | −0.133369 | + | 0.125567i | ||||
\(191\) | 178.459i | 0.934342i | 0.884167 | + | 0.467171i | \(0.154727\pi\) | ||||
−0.884167 | + | 0.467171i | \(0.845273\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 221.588 | 1.14812 | 0.574062 | − | 0.818812i | \(-0.305367\pi\) | ||||
0.574062 | + | 0.818812i | \(0.305367\pi\) | |||||||
\(194\) | −17.1186 | − | 18.1823i | −0.0882402 | − | 0.0937231i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.68586 | − | 27.9492i | 0.00860132 | − | 0.142598i | ||||
\(197\) | 242.298i | 1.22994i | 0.788550 | + | 0.614970i | \(0.210832\pi\) | ||||
−0.788550 | + | 0.614970i | \(0.789168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 297.047i | − | 1.49270i | −0.665555 | − | 0.746349i | \(-0.731805\pi\) | ||
0.665555 | − | 0.746349i | \(-0.268195\pi\) | |||||||
\(200\) | −87.7791 | + | 73.1926i | −0.438895 | + | 0.365963i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 99.1289 | − | 93.3297i | 0.490737 | − | 0.462028i | ||||
\(203\) | 98.8201 | 0.486798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 398.320i | 1.94302i | ||||||||
\(206\) | −84.8844 | + | 79.9186i | −0.412060 | + | 0.387954i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.64747 | − | 38.3841i | 0.0223436 | − | 0.184539i | ||||
\(209\) | −27.2275 | −0.130275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −141.020 | −0.668341 | −0.334171 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334171 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(212\) | −218.264 | − | 13.1654i | −1.02955 | − | 0.0621009i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 186.272 | + | 197.846i | 0.870430 | + | 0.924515i | ||||
\(215\) | 221.497i | 1.03022i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.9657 | −0.0873994 | ||||||||
\(218\) | 64.7966 | − | 61.0059i | 0.297232 | − | 0.279844i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −245.427 | − | 14.8039i | −1.11558 | − | 0.0672902i | ||||
\(221\) | − | 16.6608i | − | 0.0753883i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 40.8267i | − | 0.183079i | −0.995801 | − | 0.0915396i | \(-0.970821\pi\) | ||
0.995801 | − | 0.0915396i | \(-0.0291788\pi\) | |||||||
\(224\) | 68.1715 | − | 50.2061i | 0.304337 | − | 0.224134i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −182.876 | − | 194.239i | −0.809184 | − | 0.859464i | ||||
\(227\) | −8.18598 | −0.0360616 | −0.0180308 | − | 0.999837i | \(-0.505740\pi\) | ||||
−0.0180308 | + | 0.999837i | \(0.505740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 332.252i | − | 1.45088i | −0.688285 | − | 0.725440i | \(-0.741636\pi\) | ||
0.688285 | − | 0.725440i | \(-0.258364\pi\) | |||||||
\(230\) | 368.071 | + | 390.942i | 1.60031 | + | 1.69975i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 191.356 | + | 229.492i | 0.824812 | + | 0.989188i | ||||
\(233\) | −329.260 | −1.41314 | −0.706568 | − | 0.707646i | \(-0.749757\pi\) | ||||
−0.706568 | + | 0.707646i | \(0.749757\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 237.633 | 1.01121 | ||||||||
\(236\) | 25.2385 | − | 418.419i | 0.106943 | − | 1.77296i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.5622 | − | 25.0083i | 0.111606 | − | 0.105077i | ||||
\(239\) | − | 137.719i | − | 0.576230i | −0.957596 | − | 0.288115i | \(-0.906971\pi\) | ||
0.957596 | − | 0.288115i | \(-0.0930286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 201.854 | 0.837567 | 0.418783 | − | 0.908086i | \(-0.362457\pi\) | ||||
0.418783 | + | 0.908086i | \(0.362457\pi\) | |||||||
\(242\) | 34.0346 | + | 36.1494i | 0.140639 | + | 0.149378i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −174.750 | − | 10.5407i | −0.716188 | − | 0.0431995i | ||||
\(245\) | 43.8752i | 0.179082i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.70917i | 0.0271627i | ||||||||
\(248\) | −36.7254 | − | 44.0443i | −0.148086 | − | 0.177598i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −97.7846 | + | 92.0640i | −0.391138 | + | 0.368256i | ||||
\(251\) | 269.203 | 1.07252 | 0.536261 | − | 0.844052i | \(-0.319836\pi\) | ||||
0.536261 | + | 0.844052i | \(0.319836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 420.061i | 1.66032i | ||||||||
\(254\) | −190.724 | + | 179.566i | −0.750881 | + | 0.706954i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 248.603 | + | 61.0962i | 0.971104 | + | 0.238657i | ||||
\(257\) | 242.359 | 0.943032 | 0.471516 | − | 0.881858i | \(-0.343707\pi\) | ||||
0.471516 | + | 0.881858i | \(0.343707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.536168 | −0.00207015 | ||||||||
\(260\) | −3.64784 | + | 60.4761i | −0.0140302 | + | 0.232600i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −73.1158 | − | 77.6589i | −0.279068 | − | 0.296408i | ||||
\(263\) | 33.8470i | 0.128696i | 0.997928 | + | 0.0643479i | \(0.0204967\pi\) | ||||
−0.997928 | + | 0.0643479i | \(0.979503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 342.634 | 1.29296 | ||||||||
\(266\) | −10.6964 | + | 10.0706i | −0.0402120 | + | 0.0378595i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.49053 | + | 124.183i | −0.0279497 | + | 0.463368i | ||||
\(269\) | 165.598i | 0.615606i | 0.951450 | + | 0.307803i | \(0.0995938\pi\) | ||||
−0.951450 | + | 0.307803i | \(0.900406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 148.308i | − | 0.547263i | −0.961835 | − | 0.273632i | \(-0.911775\pi\) | ||
0.961835 | − | 0.273632i | \(-0.0882249\pi\) | |||||||
\(272\) | 109.513 | + | 13.2595i | 0.402620 | + | 0.0487483i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −79.1300 | − | 84.0468i | −0.288796 | − | 0.306740i | ||||
\(275\) | 140.104 | 0.509470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 478.358i | 1.72693i | 0.504413 | + | 0.863463i | \(0.331709\pi\) | ||||
−0.504413 | + | 0.863463i | \(0.668291\pi\) | |||||||
\(278\) | 236.387 | + | 251.075i | 0.850314 | + | 0.903149i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −101.892 | + | 84.9604i | −0.363900 | + | 0.303430i | ||||
\(281\) | 226.066 | 0.804506 | 0.402253 | − | 0.915528i | \(-0.368227\pi\) | ||||
0.402253 | + | 0.915528i | \(0.368227\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −254.628 | −0.899745 | −0.449873 | − | 0.893093i | \(-0.648531\pi\) | ||||
−0.449873 | + | 0.893093i | \(0.648531\pi\) | |||||||
\(284\) | 92.3498 | + | 5.57042i | 0.325175 | + | 0.0196142i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −34.5091 | + | 32.4903i | −0.120661 | + | 0.113602i | ||||
\(287\) | 168.136i | 0.585840i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −241.466 | −0.835521 | ||||||||
\(290\) | −320.957 | − | 340.900i | −1.10675 | − | 1.17552i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.6725 | − | 276.408i | 0.0570978 | − | 0.946602i | ||||
\(293\) | − | 149.558i | − | 0.510437i | −0.966883 | − | 0.255218i | \(-0.917853\pi\) | ||
0.966883 | − | 0.255218i | \(-0.0821474\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 656.842i | 2.22658i | ||||||||
\(296\) | −1.03824 | − | 1.24515i | −0.00350758 | − | 0.00420660i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −319.670 | + | 300.969i | −1.07272 | + | 1.00996i | ||||
\(299\) | 103.508 | 0.346180 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 93.4966i | 0.310620i | ||||||||
\(302\) | −270.363 | + | 254.547i | −0.895243 | + | 0.842870i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −44.0998 | − | 5.33951i | −0.145065 | − | 0.0175642i | ||||
\(305\) | 274.325 | 0.899427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 271.779 | 0.885272 | 0.442636 | − | 0.896701i | \(-0.354043\pi\) | ||||
0.442636 | + | 0.896701i | \(0.354043\pi\) | |||||||
\(308\) | −103.598 | − | 6.24889i | −0.336357 | − | 0.0202886i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 61.5985 | + | 65.4260i | 0.198705 | + | 0.211052i | ||||
\(311\) | − | 534.180i | − | 1.71762i | −0.512293 | − | 0.858811i | \(-0.671204\pi\) | ||
0.512293 | − | 0.858811i | \(-0.328796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −556.232 | −1.77710 | −0.888550 | − | 0.458780i | \(-0.848287\pi\) | ||||
−0.888550 | + | 0.458780i | \(0.848287\pi\) | |||||||
\(314\) | −274.024 | + | 257.993i | −0.872688 | + | 0.821634i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −79.5867 | − | 4.80057i | −0.251857 | − | 0.0151917i | ||||
\(317\) | 387.459i | 1.22227i | 0.791527 | + | 0.611134i | \(0.209286\pi\) | ||||
−0.791527 | + | 0.611134i | \(0.790714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 366.292i | − | 1.14825i | ||||||
\(320\) | −394.610 | − | 72.1076i | −1.23316 | − | 0.225336i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 155.368 | + | 165.022i | 0.482508 | + | 0.512489i | ||||
\(323\) | −19.1417 | −0.0592624 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 34.5233i | − | 0.106225i | ||||||
\(326\) | −74.7394 | − | 79.3834i | −0.229262 | − | 0.243507i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −390.465 | + | 325.581i | −1.19044 | + | 0.992624i | ||||
\(329\) | 100.308 | 0.304888 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −383.205 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(332\) | −1.23216 | + | 20.4276i | −0.00371134 | + | 0.0615288i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −387.973 | + | 365.276i | −1.16160 | + | 1.09364i | ||||
\(335\) | − | 194.944i | − | 0.581923i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 563.726 | 1.67278 | 0.836388 | − | 0.548138i | \(-0.184663\pi\) | ||||
0.836388 | + | 0.548138i | \(0.184663\pi\) | |||||||
\(338\) | −223.689 | − | 237.589i | −0.661803 | − | 0.702925i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −172.543 | − | 10.4075i | −0.507478 | − | 0.0306104i | ||||
\(341\) | 70.2992i | 0.206156i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | −217.129 | + | 181.048i | −0.631188 | + | 0.526302i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −167.219 | + | 157.436i | −0.483291 | + | 0.455018i | ||||
\(347\) | −51.5890 | −0.148671 | −0.0743357 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743357 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 586.383i | − | 1.68018i | −0.542447 | − | 0.840090i | \(-0.682502\pi\) | ||
0.542447 | − | 0.840090i | \(-0.317498\pi\) | |||||||
\(350\) | 55.0402 | − | 51.8203i | 0.157258 | − | 0.148058i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −186.097 | − | 252.688i | −0.528683 | − | 0.717864i | ||||
\(353\) | −303.844 | −0.860746 | −0.430373 | − | 0.902651i | \(-0.641618\pi\) | ||||
−0.430373 | + | 0.902651i | \(0.641618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −144.972 | −0.408373 | ||||||||
\(356\) | −4.33239 | + | 71.8250i | −0.0121696 | + | 0.201756i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 154.713 | + | 164.326i | 0.432159 | + | 0.459012i | ||||
\(359\) | − | 116.130i | − | 0.323481i | −0.986833 | − | 0.161741i | \(-0.948289\pi\) | ||
0.986833 | − | 0.161741i | \(-0.0517108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −353.292 | −0.978648 | ||||||||
\(362\) | 88.7489 | − | 83.5570i | 0.245163 | − | 0.230820i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.53980 | + | 25.5277i | −0.00423022 | + | 0.0701311i | ||||
\(365\) | 433.910i | 1.18879i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 476.288i | − | 1.29779i | −0.760879 | − | 0.648894i | \(-0.775232\pi\) | ||
0.760879 | − | 0.648894i | \(-0.224768\pi\) | |||||||
\(368\) | −82.3769 | + | 680.363i | −0.223850 | + | 1.84881i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.74142 | + | 1.84962i | 0.00470654 | + | 0.00499898i | ||||
\(371\) | 144.630 | 0.389839 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 49.2857i | 0.132133i | 0.997815 | + | 0.0660666i | \(0.0210450\pi\) | ||||
−0.997815 | + | 0.0660666i | \(0.978955\pi\) | |||||||
\(374\) | −92.6970 | − | 98.4568i | −0.247853 | − | 0.263254i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 194.238 | + | 232.947i | 0.516590 | + | 0.619541i | ||||
\(377\) | −90.2585 | −0.239412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 167.511 | 0.441983 | 0.220991 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220991 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(380\) | 69.4815 | + | 4.19103i | 0.182846 | + | 0.0110290i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 259.866 | − | 244.664i | 0.680278 | − | 0.640481i | ||||
\(383\) | 513.207i | 1.33997i | 0.742376 | + | 0.669983i | \(0.233699\pi\) | ||||
−0.742376 | + | 0.669983i | \(0.766301\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 162.630 | 0.422416 | ||||||||
\(386\) | −303.792 | − | 322.668i | −0.787026 | − | 0.835929i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.00719 | + | 49.8550i | −0.00775049 | + | 0.128492i | ||||
\(389\) | − | 709.398i | − | 1.82365i | −0.410584 | − | 0.911823i | \(-0.634675\pi\) | ||
0.410584 | − | 0.911823i | \(-0.365325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 295.315i | 0.755281i | ||||||||
\(392\) | −43.0099 | + | 35.8629i | −0.109719 | + | 0.0914869i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 352.826 | − | 332.186i | 0.895498 | − | 0.843111i | ||||
\(395\) | 124.937 | 0.316295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 309.404i | 0.779355i | 0.920951 | + | 0.389677i | \(0.127413\pi\) | ||||
−0.920951 | + | 0.389677i | \(0.872587\pi\) | |||||||
\(398\) | −432.549 | + | 407.245i | −1.08681 | + | 1.02323i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 226.924 | + | 27.4754i | 0.567309 | + | 0.0686886i | ||||
\(401\) | 528.073 | 1.31689 | 0.658445 | − | 0.752629i | \(-0.271215\pi\) | ||||
0.658445 | + | 0.752629i | \(0.271215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.3225 | 0.0429839 | ||||||||
\(404\) | −271.807 | − | 16.3950i | −0.672790 | − | 0.0405818i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −135.480 | − | 143.898i | −0.333695 | − | 0.354429i | ||||
\(407\) | 1.98739i | 0.00488302i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −612.830 | −1.49836 | −0.749181 | − | 0.662366i | \(-0.769552\pi\) | ||||
−0.749181 | + | 0.662366i | \(0.769552\pi\) | |||||||
\(410\) | 580.020 | − | 546.088i | 1.41468 | − | 1.33192i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 232.749 | + | 14.0391i | 0.564926 | + | 0.0340756i | ||||
\(413\) | 277.261i | 0.671335i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 32.0676i | − | 0.0772712i | ||||||
\(416\) | −62.2652 | + | 45.8563i | −0.149676 | + | 0.110232i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 37.3283 | + | 39.6478i | 0.0893023 | + | 0.0948512i | ||||
\(419\) | 237.642 | 0.567165 | 0.283583 | − | 0.958948i | \(-0.408477\pi\) | ||||
0.283583 | + | 0.958948i | \(0.408477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 394.516i | − | 0.937092i | −0.883439 | − | 0.468546i | \(-0.844778\pi\) | ||
0.883439 | − | 0.468546i | \(-0.155222\pi\) | |||||||
\(422\) | 193.335 | + | 205.348i | 0.458141 | + | 0.486608i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 280.064 | + | 335.878i | 0.660528 | + | 0.792164i | ||||
\(425\) | 98.4973 | 0.231758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 115.796 | 0.271185 | ||||||||
\(428\) | 32.7220 | − | 542.486i | 0.0764533 | − | 1.26749i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 322.536 | − | 303.667i | 0.750084 | − | 0.706203i | ||||
\(431\) | 363.359i | 0.843059i | 0.906815 | + | 0.421530i | \(0.138507\pi\) | ||||
−0.906815 | + | 0.421530i | \(0.861493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 119.733 | 0.276520 | 0.138260 | − | 0.990396i | \(-0.455849\pi\) | ||||
0.138260 | + | 0.990396i | \(0.455849\pi\) | |||||||
\(434\) | 26.0015 | + | 27.6172i | 0.0599113 | + | 0.0636340i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −177.669 | − | 10.7168i | −0.407499 | − | 0.0245798i | ||||
\(437\) | − | 118.921i | − | 0.272130i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 871.477i | 1.98514i | 0.121672 | + | 0.992570i | \(0.461174\pi\) | ||||
−0.121672 | + | 0.992570i | \(0.538826\pi\) | |||||||
\(440\) | 314.919 | + | 377.679i | 0.715724 | + | 0.858361i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.2609 | + | 22.8416i | −0.0548889 | + | 0.0516778i | ||||
\(443\) | 343.956 | 0.776424 | 0.388212 | − | 0.921570i | \(-0.373093\pi\) | ||||
0.388212 | + | 0.921570i | \(0.373093\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 112.752i | − | 0.253376i | ||||||
\(446\) | −59.4504 | + | 55.9725i | −0.133297 | + | 0.125499i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −166.570 | − | 30.4375i | −0.371808 | − | 0.0679409i | ||||
\(449\) | 242.849 | 0.540866 | 0.270433 | − | 0.962739i | \(-0.412833\pi\) | ||||
0.270433 | + | 0.962739i | \(0.412833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 623.222 | 1.38187 | ||||||||
\(452\) | −32.1254 | + | 532.594i | −0.0710739 | + | 1.17831i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.2228 | + | 11.9201i | 0.0247198 | + | 0.0262558i | ||||
\(455\) | − | 40.0739i | − | 0.0880745i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.2571 | −0.0924662 | −0.0462331 | − | 0.998931i | \(-0.514722\pi\) | ||||
−0.0462331 | + | 0.998931i | \(0.514722\pi\) | |||||||
\(458\) | −483.814 | + | 455.510i | −1.05636 | + | 0.994563i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 64.6584 | − | 1071.95i | 0.140562 | − | 2.33032i | ||||
\(461\) | − | 816.370i | − | 1.77087i | −0.464766 | − | 0.885434i | \(-0.653861\pi\) | ||
0.464766 | − | 0.885434i | \(-0.346139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 115.161i | 0.248727i | 0.992237 | + | 0.124363i | \(0.0396889\pi\) | ||||
−0.992237 | + | 0.124363i | \(0.960311\pi\) | |||||||
\(464\) | 71.8324 | − | 593.275i | 0.154811 | − | 1.27861i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 451.409 | + | 479.458i | 0.968689 | + | 1.02888i | ||||
\(467\) | −603.424 | −1.29213 | −0.646064 | − | 0.763283i | \(-0.723586\pi\) | ||||
−0.646064 | + | 0.763283i | \(0.723586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 82.2884i | − | 0.175455i | ||||||
\(470\) | −325.790 | − | 346.034i | −0.693171 | − | 0.736242i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −643.889 | + | 536.892i | −1.36417 | + | 1.13748i | ||||
\(473\) | 346.559 | 0.732684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.6641 | −0.0835034 | ||||||||
\(476\) | −72.8324 | − | 4.39315i | −0.153009 | − | 0.00922931i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −200.542 | + | 188.810i | −0.419543 | + | 0.395000i | ||||
\(479\) | − | 158.595i | − | 0.331097i | −0.986202 | − | 0.165548i | \(-0.947061\pi\) | ||
0.986202 | − | 0.165548i | \(-0.0529394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.489715 | 0.00101812 | ||||||||
\(482\) | −276.737 | − | 293.932i | −0.574143 | − | 0.609818i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.97880 | − | 99.1201i | 0.0123529 | − | 0.204794i | ||||
\(485\) | − | 78.2633i | − | 0.161368i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 106.987i | − | 0.219687i | −0.993949 | − | 0.109843i | \(-0.964965\pi\) | ||
0.993949 | − | 0.109843i | \(-0.0350349\pi\) | |||||||
\(488\) | 224.229 | + | 268.916i | 0.459486 | + | 0.551057i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 63.8895 | − | 60.1519i | 0.130387 | − | 0.122759i | ||||
\(491\) | −616.591 | −1.25579 | −0.627893 | − | 0.778299i | \(-0.716083\pi\) | ||||
−0.627893 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 257.514i | − | 0.522340i | ||||||
\(494\) | 9.76967 | − | 9.19813i | 0.0197767 | − | 0.0186197i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.7862 | + | 113.862i | −0.0277947 | + | 0.229561i | ||||
\(497\) | −61.1947 | −0.123128 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 554.090 | 1.11040 | 0.555200 | − | 0.831717i | \(-0.312642\pi\) | ||||
0.555200 | + | 0.831717i | \(0.312642\pi\) | |||||||
\(500\) | 268.121 | + | 16.1727i | 0.536242 | + | 0.0323454i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −369.072 | − | 392.004i | −0.735202 | − | 0.780885i | ||||
\(503\) | − | 148.158i | − | 0.294548i | −0.989096 | − | 0.147274i | \(-0.952950\pi\) | ||
0.989096 | − | 0.147274i | \(-0.0470499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 426.688 | 0.844926 | ||||||||
\(506\) | 611.678 | − | 575.894i | 1.20885 | − | 1.13813i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 522.957 | + | 31.5440i | 1.02944 | + | 0.0620946i | ||||
\(509\) | 182.889i | 0.359310i | 0.983730 | + | 0.179655i | \(0.0574981\pi\) | ||||
−0.983730 | + | 0.179655i | \(0.942502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 183.159i | 0.358432i | ||||||||
\(512\) | −251.863 | − | 445.768i | −0.491919 | − | 0.870641i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −332.269 | − | 352.915i | −0.646438 | − | 0.686605i | ||||
\(515\) | −365.374 | −0.709464 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 371.807i | − | 0.719163i | ||||||
\(518\) | 0.735075 | + | 0.780750i | 0.00141906 | + | 0.00150724i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 93.0644 | − | 77.5996i | 0.178970 | − | 0.149230i | ||||
\(521\) | −98.2461 | −0.188572 | −0.0942861 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942861 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −574.764 | −1.09898 | −0.549488 | − | 0.835502i | \(-0.685177\pi\) | ||||
−0.549488 | + | 0.835502i | \(0.685177\pi\) | |||||||
\(524\) | −12.8441 | + | 212.937i | −0.0245116 | + | 0.406369i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.2868 | − | 46.4035i | 0.0937012 | − | 0.0882196i | ||||
\(527\) | 49.4223i | 0.0937805i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1305.69 | −2.46822 | ||||||||
\(530\) | −469.744 | − | 498.933i | −0.886310 | − | 0.941382i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 29.3290 | + | 1.76909i | 0.0551297 | + | 0.00332535i | ||||
\(533\) | − | 153.569i | − | 0.288122i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 851.604i | 1.59178i | ||||||||
\(536\) | 191.100 | − | 159.344i | 0.356529 | − | 0.297284i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 241.138 | − | 227.031i | 0.448212 | − | 0.421991i | ||||
\(539\) | 68.6482 | 0.127362 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 370.654i | − | 0.685128i | −0.939495 | − | 0.342564i | \(-0.888705\pi\) | ||
0.939495 | − | 0.342564i | \(-0.111295\pi\) | |||||||
\(542\) | −215.962 | + | 203.328i | −0.398453 | + | 0.375143i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −130.831 | − | 177.647i | −0.240499 | − | 0.326557i | ||||
\(545\) | 278.909 | 0.511759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −56.5966 | −0.103467 | −0.0517336 | − | 0.998661i | \(-0.516475\pi\) | ||||
−0.0517336 | + | 0.998661i | \(0.516475\pi\) | |||||||
\(548\) | −13.9006 | + | 230.453i | −0.0253661 | + | 0.420534i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −192.080 | − | 204.015i | −0.349236 | − | 0.370936i | ||||
\(551\) | 103.699i | 0.188201i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 52.7374 | 0.0953659 | ||||||||
\(554\) | 696.569 | − | 655.819i | 1.25734 | − | 1.18379i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 41.5257 | − | 688.438i | 0.0746864 | − | 1.23820i | ||||
\(557\) | 151.525i | 0.272037i | 0.990706 | + | 0.136019i | \(0.0434307\pi\) | ||||
−0.990706 | + | 0.136019i | \(0.956569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 85.3962i | − | 0.152766i | ||||||
\(560\) | 263.408 | + | 31.8929i | 0.470372 | + | 0.0569516i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −309.932 | − | 329.190i | −0.551480 | − | 0.585747i | ||||
\(563\) | 318.048 | 0.564917 | 0.282458 | − | 0.959280i | \(-0.408850\pi\) | ||||
0.282458 | + | 0.959280i | \(0.408850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 836.076i | − | 1.47978i | ||||||
\(566\) | 349.089 | + | 370.780i | 0.616766 | + | 0.655089i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −118.498 | − | 142.114i | −0.208624 | − | 0.250200i | ||||
\(569\) | −356.654 | −0.626808 | −0.313404 | − | 0.949620i | \(-0.601469\pi\) | ||||
−0.313404 | + | 0.949620i | \(0.601469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 831.014 | 1.45537 | 0.727683 | − | 0.685914i | \(-0.240597\pi\) | ||||
0.727683 | + | 0.685914i | \(0.240597\pi\) | |||||||
\(572\) | 94.6224 | + | 5.70750i | 0.165424 | + | 0.00997815i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 244.834 | − | 230.511i | 0.426540 | − | 0.401587i | ||||
\(575\) | 611.929i | 1.06422i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 771.483 | 1.33706 | 0.668530 | − | 0.743685i | \(-0.266924\pi\) | ||||
0.668530 | + | 0.743685i | \(0.266924\pi\) | |||||||
\(578\) | 331.044 | + | 351.614i | 0.572741 | + | 0.608328i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −56.3819 | + | 934.734i | −0.0972102 | + | 1.61161i | ||||
\(581\) | − | 13.5361i | − | 0.0232980i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 536.094i | − | 0.919544i | ||||||
\(584\) | −425.353 | + | 354.671i | −0.728344 | + | 0.607313i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −217.781 | + | 205.041i | −0.371640 | + | 0.349899i | ||||
\(587\) | −144.376 | −0.245956 | −0.122978 | − | 0.992409i | \(-0.539244\pi\) | ||||
−0.122978 | + | 0.992409i | \(0.539244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 19.9020i | − | 0.0337894i | ||||||
\(590\) | 956.471 | − | 900.516i | 1.62114 | − | 1.52630i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.389741 | + | 3.21893i | −0.000658347 | + | 0.00543738i | ||||
\(593\) | −838.926 | −1.41471 | −0.707357 | − | 0.706856i | \(-0.750113\pi\) | ||||
−0.707357 | + | 0.706856i | \(0.750113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 114.334 | 0.192157 | ||||||||
\(596\) | 876.521 | + | 52.8706i | 1.47067 | + | 0.0887090i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −141.907 | − | 150.724i | −0.237302 | − | 0.252048i | ||||
\(599\) | − | 711.341i | − | 1.18755i | −0.804632 | − | 0.593774i | \(-0.797637\pi\) | ||
0.804632 | − | 0.593774i | \(-0.202363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −356.394 | −0.593002 | −0.296501 | − | 0.955033i | \(-0.595820\pi\) | ||||
−0.296501 | + | 0.955033i | \(0.595820\pi\) | |||||||
\(602\) | 136.147 | − | 128.182i | 0.226157 | − | 0.212927i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 741.324 | + | 44.7157i | 1.22736 | + | 0.0740326i | ||||
\(605\) | 155.601i | 0.257191i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 60.3719i | 0.0994595i | 0.998763 | + | 0.0497298i | \(0.0158360\pi\) | ||||
−0.998763 | + | 0.0497298i | \(0.984164\pi\) | |||||||
\(608\) | 52.6847 | + | 71.5370i | 0.0866525 | + | 0.117660i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −376.094 | − | 399.463i | −0.616548 | − | 0.654858i | ||||
\(611\) | −91.6176 | −0.149947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 482.989i | 0.787911i | 0.919130 | + | 0.393955i | \(0.128894\pi\) | ||||
−0.919130 | + | 0.393955i | \(0.871106\pi\) | |||||||
\(614\) | −372.603 | − | 395.755i | −0.606845 | − | 0.644552i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 132.931 | + | 159.423i | 0.215797 | + | 0.258803i | ||||
\(617\) | −712.490 | −1.15476 | −0.577382 | − | 0.816474i | \(-0.695926\pi\) | ||||
−0.577382 | + | 0.816474i | \(0.695926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −93.0817 | −0.150374 | −0.0751872 | − | 0.997169i | \(-0.523955\pi\) | ||||
−0.0751872 | + | 0.997169i | \(0.523955\pi\) | |||||||
\(620\) | 10.8209 | − | 179.395i | 0.0174530 | − | 0.289347i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −777.855 | + | 732.350i | −1.25057 | + | 1.17741i | ||||
\(623\) | − | 47.5941i | − | 0.0763951i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −778.059 | −1.24489 | ||||||||
\(626\) | 762.582 | + | 809.966i | 1.21818 | + | 1.29388i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 751.362 | + | 45.3211i | 1.19644 | + | 0.0721674i | ||||
\(629\) | 1.39719i | 0.00222129i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 610.573i | 0.967628i | 0.875171 | + | 0.483814i | \(0.160749\pi\) | ||||
−0.875171 | + | 0.483814i | \(0.839251\pi\) | |||||||
\(632\) | 102.121 | + | 122.473i | 0.161584 | + | 0.193786i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 564.205 | − | 531.198i | 0.889912 | − | 0.837852i | ||||
\(635\) | −820.947 | −1.29283 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 16.9157i | − | 0.0265553i | ||||||
\(638\) | −533.381 | + | 502.178i | −0.836021 | + | 0.787113i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 436.002 | + | 673.476i | 0.681252 | + | 1.05231i | ||||
\(641\) | −590.153 | −0.920676 | −0.460338 | − | 0.887744i | \(-0.652272\pi\) | ||||
−0.460338 | + | 0.887744i | \(0.652272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −257.971 | −0.401199 | −0.200600 | − | 0.979673i | \(-0.564289\pi\) | ||||
−0.200600 | + | 0.979673i | \(0.564289\pi\) | |||||||
\(644\) | 27.2931 | − | 452.482i | 0.0423806 | − | 0.702612i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.2429 | + | 27.8735i | 0.0406237 | + | 0.0431479i | ||||
\(647\) | − | 379.964i | − | 0.587271i | −0.955918 | − | 0.293635i | \(-0.905135\pi\) | ||
0.955918 | − | 0.293635i | \(-0.0948651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1027.71 | 1.58353 | ||||||||
\(650\) | −50.2716 | + | 47.3307i | −0.0773410 | + | 0.0728164i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.1293 | + | 217.666i | −0.0201370 | + | 0.333843i | ||||
\(653\) | 952.773i | 1.45907i | 0.683943 | + | 0.729535i | \(0.260264\pi\) | ||||
−0.683943 | + | 0.729535i | \(0.739736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 334.273i | − | 0.510340i | ||||||
\(656\) | 1009.42 | + | 122.218i | 1.53875 | + | 0.186308i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −137.520 | − | 146.065i | −0.208997 | − | 0.221984i | ||||
\(659\) | 963.119 | 1.46149 | 0.730743 | − | 0.682653i | \(-0.239174\pi\) | ||||
0.730743 | + | 0.682653i | \(0.239174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 71.6817i | 0.108444i | 0.998529 | + | 0.0542222i | \(0.0172679\pi\) | ||||
−0.998529 | + | 0.0542222i | \(0.982732\pi\) | |||||||
\(662\) | 525.366 | + | 558.010i | 0.793604 | + | 0.842915i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.4352 | − | 26.2115i | 0.0473422 | − | 0.0394752i | ||||
\(665\) | −46.0412 | −0.0692349 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1599.84 | 2.39856 | ||||||||
\(668\) | 1063.81 | + | 64.1674i | 1.59252 | + | 0.0960589i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −283.871 | + | 267.264i | −0.423688 | + | 0.398902i | ||||
\(671\) | − | 429.216i | − | 0.639667i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −712.783 | −1.05911 | −0.529556 | − | 0.848275i | \(-0.677642\pi\) | ||||
−0.529556 | + | 0.848275i | \(0.677642\pi\) | |||||||
\(674\) | −772.856 | − | 820.878i | −1.14667 | − | 1.21792i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −39.2951 | + | 651.458i | −0.0581288 | + | 0.963695i | ||||
\(677\) | − | 767.527i | − | 1.13372i | −0.823815 | − | 0.566859i | \(-0.808159\pi\) | ||
0.823815 | − | 0.566859i | \(-0.191841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 33.0359i | − | 0.0486538i | ||||||
\(680\) | 221.397 | + | 265.519i | 0.325584 | + | 0.390469i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 102.367 | − | 96.3786i | 0.150099 | − | 0.141318i | ||||
\(683\) | 484.354 | 0.709156 | 0.354578 | − | 0.935026i | \(-0.384625\pi\) | ||||
0.354578 | + | 0.935026i | \(0.384625\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 361.769i | − | 0.528130i | ||||||
\(686\) | 26.9686 | − | 25.3909i | 0.0393128 | − | 0.0370129i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 561.315 | + | 67.9628i | 0.815864 | + | 0.0987831i | ||||
\(689\) | −132.100 | −0.191727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −574.851 | −0.831912 | −0.415956 | − | 0.909385i | \(-0.636553\pi\) | ||||
−0.415956 | + | 0.909385i | \(0.636553\pi\) | |||||||
\(692\) | 458.507 | + | 27.6565i | 0.662582 | + | 0.0399661i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 70.7274 | + | 75.1221i | 0.101913 | + | 0.108245i | ||||
\(695\) | 1080.72i | 1.55500i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 438.143 | 0.628612 | ||||||||
\(698\) | −853.871 | + | 803.918i | −1.22331 | + | 1.15175i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −150.918 | − | 9.10317i | −0.215597 | − | 0.0130045i | ||||
\(701\) | 143.138i | 0.204191i | 0.994775 | + | 0.102096i | \(0.0325548\pi\) | ||||
−0.994775 | + | 0.102096i | \(0.967445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.562638i | − | 0.000800339i | ||||||
\(704\) | −112.821 | + | 617.417i | −0.160258 | + | 0.877013i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 416.563 | + | 442.446i | 0.590032 | + | 0.626695i | ||||
\(707\) | 180.110 | 0.254753 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 255.311i | 0.360101i | 0.983657 | + | 0.180050i | \(0.0576261\pi\) | ||||
−0.983657 | + | 0.180050i | \(0.942374\pi\) | |||||||
\(710\) | 198.754 | + | 211.104i | 0.279935 | + | 0.297329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 110.529 | − | 92.1618i | 0.155237 | − | 0.129441i | ||||
\(713\) | −307.044 | −0.430636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −148.540 | −0.207748 | ||||||||
\(716\) | 27.1781 | − | 450.576i | 0.0379583 | − | 0.629296i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −169.104 | + | 159.211i | −0.235521 | + | 0.221743i | ||||
\(719\) | 415.630i | 0.578067i | 0.957319 | + | 0.289034i | \(0.0933340\pi\) | ||||
−0.957319 | + | 0.289034i | \(0.906666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −154.229 | −0.213910 | ||||||||
\(722\) | 484.355 | + | 514.451i | 0.670852 | + | 0.712537i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −243.346 | − | 14.6783i | −0.336113 | − | 0.0202739i | ||||
\(725\) | − | 533.601i | − | 0.736001i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 896.838i | − | 1.23361i | −0.787114 | − | 0.616807i | \(-0.788426\pi\) | ||
0.787114 | − | 0.616807i | \(-0.211574\pi\) | |||||||
\(728\) | 39.2836 | − | 32.7558i | 0.0539610 | − | 0.0449942i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 631.845 | − | 594.881i | 0.865541 | − | 0.814905i | ||||
\(731\) | 243.641 | 0.333299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 509.059i | 0.694487i | 0.937775 | + | 0.347244i | \(0.112882\pi\) | ||||
−0.937775 | + | 0.347244i | \(0.887118\pi\) | |||||||
\(734\) | −693.555 | + | 652.981i | −0.944898 | + | 0.889620i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1103.66 | − | 812.808i | 1.49954 | − | 1.10436i | ||||
\(737\) | −305.014 | −0.413859 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 741.427 | 1.00328 | 0.501642 | − | 0.865075i | \(-0.332729\pi\) | ||||
0.501642 | + | 0.865075i | \(0.332729\pi\) | |||||||
\(740\) | 0.305911 | − | 5.07159i | 0.000413394 | − | 0.00685350i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −198.285 | − | 210.606i | −0.267231 | − | 0.283835i | ||||
\(743\) | 1344.98i | 1.81021i | 0.425191 | + | 0.905104i | \(0.360207\pi\) | ||||
−0.425191 | + | 0.905104i | \(0.639793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1375.98 | −1.84695 | ||||||||
\(746\) | 71.7681 | − | 67.5696i | 0.0962039 | − | 0.0905759i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.2839 | + | 269.964i | −0.0217699 | + | 0.360915i | ||||
\(749\) | 359.473i | 0.479937i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27.6931i | − | 0.0368749i | −0.999830 | − | 0.0184375i | \(-0.994131\pi\) | ||
0.999830 | − | 0.0184375i | \(-0.00586916\pi\) | |||||||
\(752\) | 72.9141 | − | 602.208i | 0.0969602 | − | 0.800809i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 123.742 | + | 131.431i | 0.164115 | + | 0.174312i | ||||
\(755\) | −1163.74 | −1.54138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1341.69i | − | 1.77238i | −0.463318 | − | 0.886192i | \(-0.653341\pi\) | ||
0.463318 | − | 0.886192i | \(-0.346659\pi\) | |||||||
\(758\) | −229.654 | − | 243.924i | −0.302974 | − | 0.321800i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −89.1548 | − | 106.922i | −0.117309 | − | 0.140687i | ||||
\(761\) | 112.001 | 0.147176 | 0.0735881 | − | 0.997289i | \(-0.476555\pi\) | ||||
0.0735881 | + | 0.997289i | \(0.476555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 117.731 | 0.154300 | ||||||||
\(764\) | −712.542 | − | 42.9796i | −0.932647 | − | 0.0562560i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 747.314 | − | 703.596i | 0.975606 | − | 0.918532i | ||||
\(767\) | − | 253.240i | − | 0.330169i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 140.749 | 0.183028 | 0.0915142 | − | 0.995804i | \(-0.470829\pi\) | ||||
0.0915142 | + | 0.995804i | \(0.470829\pi\) | |||||||
\(770\) | −222.962 | − | 236.816i | −0.289561 | − | 0.307553i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −53.3665 | + | 884.743i | −0.0691276 | + | 1.14604i | ||||
\(773\) | − | 1325.14i | − | 1.71428i | −0.515087 | − | 0.857138i | \(-0.672240\pi\) | ||
0.515087 | − | 0.857138i | \(-0.327760\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 102.409i | 0.132141i | ||||||||
\(776\) | 76.7200 | − | 63.9712i | 0.0988660 | − | 0.0824371i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1033.00 | + | 972.570i | −1.32777 | + | 1.25009i | ||||
\(779\) | −176.437 | −0.226491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 226.827i | 0.290432i | ||||||||
\(782\) | 430.027 | − | 404.870i | 0.549907 | − | 0.517737i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 111.188 | + | 13.4624i | 0.141821 | + | 0.0171714i | ||||
\(785\) | −1179.50 | −1.50255 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −327.801 | −0.416519 | −0.208260 | − | 0.978074i | \(-0.566780\pi\) | ||||
−0.208260 | + | 0.978074i | \(0.566780\pi\) | |||||||
\(788\) | −967.434 | − | 58.3544i | −1.22771 | − | 0.0740538i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −171.285 | − | 181.929i | −0.216817 | − | 0.230289i | ||||
\(791\) | − | 352.918i | − | 0.446167i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −105.764 | −0.133372 | ||||||||
\(794\) | 450.543 | − | 424.186i | 0.567435 | − | 0.534239i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1186.03 | + | 71.5399i | 1.48999 | + | 0.0898742i | ||||
\(797\) | 393.650i | 0.493915i | 0.969026 | + | 0.246958i | \(0.0794308\pi\) | ||||
−0.969026 | + | 0.246958i | \(0.920569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 261.391i | − | 0.327148i | ||||||
\(800\) | −271.099 | − | 368.107i | −0.338873 | − | 0.460134i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −723.976 | − | 768.961i | −0.902713 | − | 0.958804i | ||||
\(803\) | 678.906 | 0.845462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 710.314i | 0.882378i | ||||||||
\(806\) | −23.7488 | − | 25.2245i | −0.0294650 | − | 0.0312959i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 348.768 | + | 418.273i | 0.431643 | + | 0.517665i | ||||
\(809\) | −416.641 | −0.515008 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −748.707 | −0.923190 | −0.461595 | − | 0.887091i | \(-0.652723\pi\) | ||||
−0.461595 | + | 0.887091i | \(0.652723\pi\) | |||||||
\(812\) | −23.7995 | + | 394.563i | −0.0293098 | + | 0.485915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.89397 | − | 2.72467i | 0.00355524 | − | 0.00334726i | ||||
\(815\) | − | 341.696i | − | 0.419259i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −98.1124 | −0.120089 | ||||||||
\(818\) | 840.176 | + | 892.382i | 1.02711 | + | 1.09093i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1590.39 | − | 95.9302i | −1.93950 | − | 0.116988i | ||||
\(821\) | 554.169i | 0.674993i | 0.941327 | + | 0.337496i | \(0.109580\pi\) | ||||
−0.941327 | + | 0.337496i | \(0.890420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 121.452i | − | 0.147572i | −0.997274 | − | 0.0737861i | \(-0.976492\pi\) | ||
0.997274 | − | 0.0737861i | \(-0.0235082\pi\) | |||||||
\(824\) | −298.651 | − | 358.169i | −0.362441 | − | 0.434671i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 403.738 | − | 380.119i | 0.488787 | − | 0.460193i | ||||
\(827\) | 1516.61 | 1.83386 | 0.916932 | − | 0.399043i | \(-0.130657\pi\) | ||||
0.916932 | + | 0.399043i | \(0.130657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 325.042i | 0.392089i | 0.980595 | + | 0.196044i | \(0.0628097\pi\) | ||||
−0.980595 | + | 0.196044i | \(0.937190\pi\) | |||||||
\(830\) | −46.6957 | + | 43.9639i | −0.0562599 | + | 0.0529686i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 152.139 | + | 27.8005i | 0.182859 | + | 0.0334140i | ||||
\(833\) | 48.2617 | 0.0579372 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1669.98 | −1.99998 | ||||||||
\(836\) | 6.55740 | − | 108.713i | 0.00784377 | − | 0.130039i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −325.802 | − | 346.046i | −0.388785 | − | 0.412943i | ||||
\(839\) | − | 1165.70i | − | 1.38939i | −0.719303 | − | 0.694696i | \(-0.755539\pi\) | ||
0.719303 | − | 0.694696i | \(-0.244461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −554.058 | −0.658808 | ||||||||
\(842\) | −574.480 | + | 540.872i | −0.682280 | + | 0.642366i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.9628 | − | 563.057i | 0.0402403 | − | 0.667129i | ||||
\(845\) | − | 1022.67i | − | 1.21026i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 65.6810i | 0.0775454i | ||||||||
\(848\) | 105.132 | − | 868.301i | 0.123976 | − | 1.02394i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −135.038 | − | 143.428i | −0.158868 | − | 0.168739i | ||||
\(851\) | −8.68026 | −0.0102001 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 151.949i | 0.178134i | 0.996026 | + | 0.0890672i | \(0.0283886\pi\) | ||||
−0.996026 | + | 0.0890672i | \(0.971611\pi\) | |||||||
\(854\) | −158.754 | − | 168.618i | −0.185895 | − | 0.197445i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −834.810 | + | 696.087i | −0.975246 | + | 0.813186i | ||||
\(857\) | −412.018 | −0.480768 | −0.240384 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240384 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 159.993 | 0.186255 | 0.0931274 | − | 0.995654i | \(-0.470314\pi\) | ||||
0.0931274 | + | 0.995654i | \(0.470314\pi\) | |||||||
\(860\) | −884.380 | − | 53.3446i | −1.02835 | − | 0.0620286i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 529.110 | − | 498.157i | 0.613817 | − | 0.577908i | ||||
\(863\) | 992.910i | 1.15053i | 0.817966 | + | 0.575266i | \(0.195102\pi\) | ||||
−0.817966 | + | 0.575266i | \(0.804898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −719.772 | −0.832107 | ||||||||
\(866\) | −164.152 | − | 174.352i | −0.189552 | − | 0.201330i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.56763 | − | 75.7250i | 0.00526225 | − | 0.0872408i | ||||
\(869\) | − | 195.479i | − | 0.224947i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 75.1590i | 0.0862905i | ||||||||
\(872\) | 227.975 | + | 273.409i | 0.261440 | + | 0.313542i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −173.169 | + | 163.038i | −0.198133 | + | 0.186542i | ||||
\(875\) | −177.668 | −0.203049 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 825.096i | 0.940817i | 0.882449 | + | 0.470408i | \(0.155893\pi\) | ||||
−0.882449 | + | 0.470408i | \(0.844107\pi\) | |||||||
\(878\) | 1269.01 | − | 1194.78i | 1.44535 | − | 1.36079i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 118.216 | − | 976.363i | 0.134336 | − | 1.10950i | ||||
\(881\) | −1352.83 | −1.53556 | −0.767780 | − | 0.640714i | \(-0.778639\pi\) | ||||
−0.767780 | + | 0.640714i | \(0.778639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1013.40 | −1.14768 | −0.573838 | − | 0.818969i | \(-0.694546\pi\) | ||||
−0.573838 | + | 0.818969i | \(0.694546\pi\) | |||||||
\(884\) | 66.5223 | + | 4.01254i | 0.0752515 | + | 0.00453907i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −471.556 | − | 500.857i | −0.532230 | − | 0.565301i | ||||
\(887\) | − | 233.760i | − | 0.263540i | −0.991280 | − | 0.131770i | \(-0.957934\pi\) | ||
0.991280 | − | 0.131770i | \(-0.0420661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −346.532 | −0.389800 | ||||||||
\(890\) | −164.186 | + | 154.581i | −0.184478 | + | 0.173686i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 163.010 | + | 9.83257i | 0.182747 | + | 0.0110231i | ||||
\(893\) | 105.260i | 0.117873i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 707.322i | 0.790304i | ||||||||
\(896\) | 184.042 | + | 284.283i | 0.205404 | + | 0.317280i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −332.941 | − | 353.628i | −0.370758 | − | 0.393795i | ||||
\(899\) | 267.741 | 0.297821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 376.890i | − | 0.418302i | ||||||
\(902\) | −854.423 | − | 907.514i | −0.947254 | − | 1.00611i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 819.589 | − | 683.396i | 0.906625 | − | 0.755968i | ||||
\(905\) | 382.008 | 0.422109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −203.590 | −0.224465 | −0.112233 | − | 0.993682i | \(-0.535800\pi\) | ||||
−0.112233 | + | 0.993682i | \(0.535800\pi\) | |||||||
\(908\) | 1.97149 | − | 32.6845i | 0.00217124 | − | 0.0359961i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −58.3542 | + | 54.9404i | −0.0641255 | + | 0.0603741i | ||||
\(911\) | 712.022i | 0.781583i | 0.920479 | + | 0.390792i | \(0.127799\pi\) | ||||
−0.920479 | + | 0.390792i | \(0.872201\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.1737 | −0.0549548 | ||||||||
\(914\) | 57.9335 | + | 61.5333i | 0.0633846 | + | 0.0673231i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1326.60 | + | 80.0185i | 1.44825 | + | 0.0873564i | ||||
\(917\) | − | 141.101i | − | 0.153872i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 786.783i | 0.856129i | 0.903748 | + | 0.428065i | \(0.140804\pi\) | ||||
−0.903748 | + | 0.428065i | \(0.859196\pi\) | |||||||
\(920\) | −1649.58 | + | 1375.46i | −1.79302 | + | 1.49507i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1188.77 | + | 1119.23i | −1.28934 | + | 1.21391i | ||||
\(923\) | 55.8929 | 0.0605557 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.89516i | 0.00312990i | ||||||||
\(926\) | 167.693 | − | 157.883i | 0.181094 | − | 0.170500i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −962.387 | + | 708.767i | −1.03705 | + | 0.763757i | ||||
\(929\) | 1657.99 | 1.78471 | 0.892353 | − | 0.451338i | \(-0.149053\pi\) | ||||
0.892353 | + | 0.451338i | \(0.149053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.4346 | −0.0208750 | ||||||||
\(932\) | 79.2981 | − | 1314.65i | 0.0850838 | − | 1.41057i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 827.281 | + | 878.685i | 0.885740 | + | 0.940776i | ||||
\(935\) | − | 423.795i | − | 0.453257i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 333.736 | 0.356175 | 0.178088 | − | 0.984015i | \(-0.443009\pi\) | ||||
0.178088 | + | 0.984015i | \(0.443009\pi\) | |||||||
\(938\) | −119.825 | + | 112.816i | −0.127746 | + | 0.120272i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −57.2309 | + | 948.809i | −0.0608840 | + | 1.00937i | ||||
\(941\) | 543.324i | 0.577390i | 0.957421 | + | 0.288695i | \(0.0932214\pi\) | ||||
−0.957421 | + | 0.288695i | \(0.906779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2722.03i | 2.88656i | ||||||||
\(944\) | 1664.56 | + | 201.542i | 1.76331 | + | 0.213497i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −475.125 | − | 504.648i | −0.502247 | − | 0.533454i | ||||
\(947\) | 359.728 | 0.379861 | 0.189930 | − | 0.981798i | \(-0.439174\pi\) | ||||
0.189930 | + | 0.981798i | \(0.439174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 167.290i | − | 0.176281i | ||||||
\(950\) | 54.3786 | + | 57.7575i | 0.0572406 | + | 0.0607974i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 93.4545 | + | 112.079i | 0.0981665 | + | 0.117730i | ||||
\(953\) | 904.225 | 0.948820 | 0.474410 | − | 0.880304i | \(-0.342661\pi\) | ||||
0.474410 | + | 0.880304i | \(0.342661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1118.56 | 1.17127 | ||||||||
\(956\) | 549.877 | + | 33.1678i | 0.575185 | + | 0.0346944i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −230.941 | + | 217.431i | −0.241066 | + | 0.226963i | ||||
\(959\) | − | 152.707i | − | 0.159236i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 909.615 | 0.946529 | ||||||||
\(962\) | −0.671389 | − | 0.713107i | −0.000697910 | − | 0.000741275i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −48.6138 | + | 805.949i | −0.0504293 | + | 0.836047i | ||||
\(965\) | − | 1388.89i | − | 1.43926i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 920.961i | 0.952390i | 0.879340 | + | 0.476195i | \(0.157984\pi\) | ||||
−0.879340 | + | 0.476195i | \(0.842016\pi\) | |||||||
\(968\) | −152.532 | + | 127.185i | −0.157575 | + | 0.131390i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −113.964 | + | 107.297i | −0.117489 | + | 0.110616i | ||||
\(971\) | −1327.31 | −1.36695 | −0.683476 | − | 0.729973i | \(-0.739532\pi\) | ||||
−0.683476 | + | 0.729973i | \(0.739532\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 456.186i | 0.468845i | ||||||||
\(974\) | −155.791 | + | 146.677i | −0.159950 | + | 0.150593i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 84.1724 | − | 695.192i | 0.0862422 | − | 0.712287i | ||||
\(977\) | 688.490 | 0.704698 | 0.352349 | − | 0.935869i | \(-0.385383\pi\) | ||||
0.352349 | + | 0.935869i | \(0.385383\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −176.415 | −0.180199 | ||||||||
\(980\) | −175.182 | − | 10.5668i | −0.178757 | − | 0.0107824i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 845.333 | + | 897.859i | 0.860828 | + | 0.914317i | ||||
\(983\) | 1687.08i | 1.71625i | 0.513438 | + | 0.858127i | \(0.328372\pi\) | ||||
−0.513438 | + | 0.858127i | \(0.671628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1518.70 | 1.54182 | ||||||||
\(986\) | −374.983 | + | 353.046i | −0.380307 | + | 0.358058i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −26.7880 | − | 1.61582i | −0.0271134 | − | 0.00163544i | ||||
\(989\) | 1513.66i | 1.53049i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1139.22i | − | 1.14957i | −0.818304 | − | 0.574785i | \(-0.805086\pi\) | ||
0.818304 | − | 0.574785i | \(-0.194914\pi\) | |||||||
\(992\) | 184.703 | − | 136.027i | 0.186192 | − | 0.137124i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 83.8966 | + | 89.1096i | 0.0844030 | + | 0.0896475i | ||||
\(995\) | −1861.85 | −1.87121 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 206.085i | 0.206705i | 0.994645 | + | 0.103353i | \(0.0329570\pi\) | ||||
−0.994645 | + | 0.103353i | \(0.967043\pi\) | |||||||
\(998\) | −759.645 | − | 806.847i | −0.761168 | − | 0.808464i | ||||
\(999\) | 0 | 0 |
(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 | 504.3.g.b.379.3 | 8 | ||
3.2 | odd | 2 | 56.3.g.b.43.6 | yes | 8 | ||
4.3 | odd | 2 | 2016.3.g.b.1135.1 | 8 | |||
8.3 | odd | 2 | inner | 504.3.g.b.379.4 | 8 | ||
8.5 | even | 2 | 2016.3.g.b.1135.8 | 8 | |||
12.11 | even | 2 | 224.3.g.b.15.8 | 8 | |||
21.2 | odd | 6 | 392.3.k.o.67.6 | 16 | |||
21.5 | even | 6 | 392.3.k.n.67.6 | 16 | |||
21.11 | odd | 6 | 392.3.k.o.275.1 | 16 | |||
21.17 | even | 6 | 392.3.k.n.275.1 | 16 | |||
21.20 | even | 2 | 392.3.g.m.99.6 | 8 | |||
24.5 | odd | 2 | 224.3.g.b.15.7 | 8 | |||
24.11 | even | 2 | 56.3.g.b.43.5 | ✓ | 8 | ||
48.5 | odd | 4 | 1792.3.d.j.1023.15 | 16 | |||
48.11 | even | 4 | 1792.3.d.j.1023.1 | 16 | |||
48.29 | odd | 4 | 1792.3.d.j.1023.2 | 16 | |||
48.35 | even | 4 | 1792.3.d.j.1023.16 | 16 | |||
84.83 | odd | 2 | 1568.3.g.m.687.1 | 8 | |||
168.11 | even | 6 | 392.3.k.o.275.6 | 16 | |||
168.59 | odd | 6 | 392.3.k.n.275.6 | 16 | |||
168.83 | odd | 2 | 392.3.g.m.99.5 | 8 | |||
168.107 | even | 6 | 392.3.k.o.67.1 | 16 | |||
168.125 | even | 2 | 1568.3.g.m.687.2 | 8 | |||
168.131 | odd | 6 | 392.3.k.n.67.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.5 | ✓ | 8 | 24.11 | even | 2 | ||
56.3.g.b.43.6 | yes | 8 | 3.2 | odd | 2 | ||
224.3.g.b.15.7 | 8 | 24.5 | odd | 2 | |||
224.3.g.b.15.8 | 8 | 12.11 | even | 2 | |||
392.3.g.m.99.5 | 8 | 168.83 | odd | 2 | |||
392.3.g.m.99.6 | 8 | 21.20 | even | 2 | |||
392.3.k.n.67.1 | 16 | 168.131 | odd | 6 | |||
392.3.k.n.67.6 | 16 | 21.5 | even | 6 | |||
392.3.k.n.275.1 | 16 | 21.17 | even | 6 | |||
392.3.k.n.275.6 | 16 | 168.59 | odd | 6 | |||
392.3.k.o.67.1 | 16 | 168.107 | even | 6 | |||
392.3.k.o.67.6 | 16 | 21.2 | odd | 6 | |||
392.3.k.o.275.1 | 16 | 21.11 | odd | 6 | |||
392.3.k.o.275.6 | 16 | 168.11 | even | 6 | |||
504.3.g.b.379.3 | 8 | 1.1 | even | 1 | trivial | ||
504.3.g.b.379.4 | 8 | 8.3 | odd | 2 | inner | ||
1568.3.g.m.687.1 | 8 | 84.83 | odd | 2 | |||
1568.3.g.m.687.2 | 8 | 168.125 | even | 2 | |||
1792.3.d.j.1023.1 | 16 | 48.11 | even | 4 | |||
1792.3.d.j.1023.2 | 16 | 48.29 | odd | 4 | |||
1792.3.d.j.1023.15 | 16 | 48.5 | odd | 4 | |||
1792.3.d.j.1023.16 | 16 | 48.35 | even | 4 | |||
2016.3.g.b.1135.1 | 8 | 4.3 | odd | 2 | |||
2016.3.g.b.1135.8 | 8 | 8.5 | even | 2 |