Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.14 | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.f.379.16 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.847808 | − | 1.13191i | 0.599491 | − | 0.800382i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.562443 | − | 1.91929i | −0.281221 | − | 0.959643i | ||||
\(5\) | − | 2.55248i | − | 1.14150i | −0.821123 | − | 0.570751i | \(-0.806652\pi\) | ||
0.821123 | − | 0.570751i | \(-0.193348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.08957i | − | 1.16775i | −0.811845 | − | 0.583873i | \(-0.801537\pi\) | ||
0.811845 | − | 0.583873i | \(-0.198463\pi\) | |||||||
\(8\) | −2.64930 | − | 0.990551i | −0.936670 | − | 0.350213i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.88918 | − | 2.16401i | −0.913637 | − | 0.684320i | ||||
\(11\) | 5.76753 | 1.73898 | 0.869488 | − | 0.493953i | \(-0.164449\pi\) | ||||
0.869488 | + | 0.493953i | \(0.164449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95212 | 0.541421 | 0.270711 | − | 0.962661i | \(-0.412741\pi\) | ||||
0.270711 | + | 0.962661i | \(0.412741\pi\) | |||||||
\(14\) | −3.49711 | − | 2.61936i | −0.934642 | − | 0.700053i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.36732 | + | 2.15898i | −0.841829 | + | 0.539744i | ||||
\(17\) | 1.39823 | 0.339120 | 0.169560 | − | 0.985520i | \(-0.445765\pi\) | ||||
0.169560 | + | 0.985520i | \(0.445765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.64002 | − | 2.39796i | 0.835079 | − | 0.550131i | ||||
\(20\) | −4.89893 | + | 1.43562i | −1.09543 | + | 0.321015i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.88976 | − | 6.52833i | 1.04250 | − | 1.39185i | ||||
\(23\) | − | 1.59083i | − | 0.331711i | −0.986150 | − | 0.165855i | \(-0.946962\pi\) | ||
0.986150 | − | 0.165855i | \(-0.0530385\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.51514 | −0.303028 | ||||||||
\(26\) | 1.65503 | − | 2.20963i | 0.324577 | − | 0.433344i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.92976 | + | 1.73770i | −1.12062 | + | 0.328395i | ||||
\(29\) | −7.86770 | −1.46100 | −0.730498 | − | 0.682915i | \(-0.760712\pi\) | ||||
−0.730498 | + | 0.682915i | \(0.760712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.85075 | −0.871221 | −0.435611 | − | 0.900135i | \(-0.643468\pi\) | ||||
−0.435611 | + | 0.900135i | \(0.643468\pi\) | |||||||
\(32\) | −0.411070 | + | 5.64190i | −0.0726676 | + | 0.997356i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.18543 | − | 1.58267i | 0.203300 | − | 0.271426i | ||||
\(35\) | −7.88604 | −1.33298 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2538 | 1.85011 | 0.925057 | − | 0.379828i | \(-0.124017\pi\) | ||||
0.925057 | + | 0.379828i | \(0.124017\pi\) | |||||||
\(38\) | 0.371761 | − | 6.15319i | 0.0603077 | − | 0.998180i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.52836 | + | 6.76229i | −0.399769 | + | 1.06921i | ||||
\(41\) | 6.86000i | 1.07135i | 0.844423 | + | 0.535676i | \(0.179943\pi\) | ||||
−0.844423 | + | 0.535676i | \(0.820057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37466 | −1.27712 | −0.638562 | − | 0.769571i | \(-0.720470\pi\) | ||||
−0.638562 | + | 0.769571i | \(0.720470\pi\) | |||||||
\(44\) | −3.24391 | − | 11.0695i | −0.489037 | − | 1.66880i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.80068 | − | 1.34872i | −0.265495 | − | 0.198857i | ||||
\(47\) | 8.93785i | 1.30372i | 0.758340 | + | 0.651859i | \(0.226011\pi\) | ||||
−0.758340 | + | 0.651859i | \(0.773989\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.54541 | −0.363631 | ||||||||
\(50\) | −1.28455 | + | 1.71500i | −0.181662 | + | 0.242538i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.09796 | − | 3.74668i | −0.152259 | − | 0.519571i | ||||
\(53\) | −10.5972 | −1.45564 | −0.727820 | − | 0.685769i | \(-0.759466\pi\) | ||||
−0.727820 | + | 0.685769i | \(0.759466\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.7215i | − | 1.98505i | ||||||
\(56\) | −3.06037 | + | 8.18520i | −0.408960 | + | 1.09379i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.67030 | + | 8.90553i | −0.875853 | + | 1.16935i | ||||
\(59\) | 12.8365i | 1.67118i | 0.549357 | + | 0.835588i | \(0.314873\pi\) | ||||
−0.549357 | + | 0.835588i | \(0.685127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.56497i | − | 0.840559i | −0.907395 | − | 0.420279i | \(-0.861932\pi\) | ||
0.907395 | − | 0.420279i | \(-0.138068\pi\) | |||||||
\(62\) | −4.11251 | + | 5.49062i | −0.522289 | + | 0.697309i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.03762 | + | 5.24854i | 0.754702 | + | 0.656068i | ||||
\(65\) | − | 4.98275i | − | 0.618034i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.2220i | 1.98183i | 0.134477 | + | 0.990917i | \(0.457064\pi\) | ||||
−0.134477 | + | 0.990917i | \(0.542936\pi\) | |||||||
\(68\) | −0.786424 | − | 2.68360i | −0.0953679 | − | 0.325434i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.68585 | + | 8.92630i | −0.799112 | + | 1.06690i | ||||
\(71\) | 4.47647 | 0.531259 | 0.265629 | − | 0.964075i | \(-0.414420\pi\) | ||||
0.265629 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.48486 | 0.407872 | 0.203936 | − | 0.978984i | \(-0.434627\pi\) | ||||
0.203936 | + | 0.978984i | \(0.434627\pi\) | |||||||
\(74\) | 9.54107 | − | 12.7383i | 1.10913 | − | 1.48080i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.64968 | − | 5.63753i | −0.762771 | − | 0.646669i | ||||
\(77\) | − | 17.8192i | − | 2.03068i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.99879 | 1.01244 | 0.506222 | − | 0.862403i | \(-0.331042\pi\) | ||||
0.506222 | + | 0.862403i | \(0.331042\pi\) | |||||||
\(80\) | 5.51074 | + | 8.59500i | 0.616119 | + | 0.960950i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.76491 | + | 5.81597i | 0.857491 | + | 0.642266i | ||||
\(83\) | −8.73861 | −0.959187 | −0.479594 | − | 0.877491i | \(-0.659216\pi\) | ||||
−0.479594 | + | 0.877491i | \(0.659216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.56895i | − | 0.387107i | ||||||
\(86\) | −7.10010 | + | 9.47936i | −0.765624 | + | 1.02219i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.2799 | − | 5.71304i | −1.62885 | − | 0.609012i | ||||
\(89\) | − | 9.05528i | − | 0.959858i | −0.877307 | − | 0.479929i | \(-0.840662\pi\) | ||
0.877307 | − | 0.479929i | \(-0.159338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.03121i | − | 0.632243i | ||||||
\(92\) | −3.05325 | + | 0.894750i | −0.318324 | + | 0.0932841i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.1168 | + | 7.57758i | 1.04347 | + | 0.781568i | ||||
\(95\) | −6.12075 | − | 9.29108i | −0.627975 | − | 0.953244i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.6873i | − | 1.49126i | −0.666358 | − | 0.745632i | \(-0.732148\pi\) | ||
0.666358 | − | 0.745632i | \(-0.267852\pi\) | |||||||
\(98\) | −2.15802 | + | 2.88118i | −0.217993 | + | 0.291043i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.852178 | + | 2.90798i | 0.0852178 | + | 0.290798i | ||||
\(101\) | 9.05794i | 0.901299i | 0.892701 | + | 0.450649i | \(0.148808\pi\) | ||||
−0.892701 | + | 0.450649i | \(0.851192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8596 | 1.16856 | 0.584280 | − | 0.811552i | \(-0.301377\pi\) | ||||
0.584280 | + | 0.811552i | \(0.301377\pi\) | |||||||
\(104\) | −5.17176 | − | 1.93368i | −0.507133 | − | 0.189613i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.98440 | + | 11.9951i | −0.872642 | + | 1.16507i | ||||
\(107\) | − | 0.428357i | − | 0.0414108i | −0.999786 | − | 0.0207054i | \(-0.993409\pi\) | ||
0.999786 | − | 0.0207054i | \(-0.00659121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65128 | 0.349729 | 0.174865 | − | 0.984592i | \(-0.444051\pi\) | ||||
0.174865 | + | 0.984592i | \(0.444051\pi\) | |||||||
\(110\) | −16.6634 | − | 12.4810i | −1.58879 | − | 1.19002i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.67030 | + | 10.4035i | 0.630284 | + | 0.983043i | ||||
\(113\) | − | 6.97033i | − | 0.655714i | −0.944727 | − | 0.327857i | \(-0.893674\pi\) | ||
0.944727 | − | 0.327857i | \(-0.106326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.06055 | −0.378648 | ||||||||
\(116\) | 4.42513 | + | 15.1004i | 0.410863 | + | 1.40203i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.5298 | + | 10.8829i | 1.33758 | + | 1.00185i | ||||
\(119\) | − | 4.31992i | − | 0.396006i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.2645 | 2.02404 | ||||||||
\(122\) | −7.43096 | − | 5.56584i | −0.672768 | − | 0.503907i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.72827 | + | 9.30998i | 0.245006 | + | 0.836061i | ||||
\(125\) | − | 8.89503i | − | 0.795596i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.50237 | −0.133313 | −0.0666567 | − | 0.997776i | \(-0.521233\pi\) | ||||
−0.0666567 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(128\) | 11.0596 | − | 2.38428i | 0.977542 | − | 0.210743i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.64002 | − | 4.22441i | −0.494663 | − | 0.370506i | ||||
\(131\) | −13.8282 | −1.20818 | −0.604088 | − | 0.796918i | \(-0.706462\pi\) | ||||
−0.604088 | + | 0.796918i | \(0.706462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.40867 | − | 11.2461i | −0.642413 | − | 0.975160i | ||||
\(134\) | 18.3619 | + | 13.7531i | 1.58622 | + | 1.18809i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.70433 | − | 1.38502i | −0.317644 | − | 0.118764i | ||||
\(137\) | 9.45889 | 0.808128 | 0.404064 | − | 0.914731i | \(-0.367597\pi\) | ||||
0.404064 | + | 0.914731i | \(0.367597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.4049 | 0.967354 | 0.483677 | − | 0.875247i | \(-0.339301\pi\) | ||||
0.483677 | + | 0.875247i | \(0.339301\pi\) | |||||||
\(140\) | 4.43545 | + | 15.1356i | 0.374864 | + | 1.27919i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.79518 | − | 5.06696i | 0.318485 | − | 0.425210i | ||||
\(143\) | 11.2589 | 0.941519 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.0821i | 1.66773i | ||||||||
\(146\) | 2.95449 | − | 3.94455i | 0.244516 | − | 0.326453i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.32962 | − | 21.5993i | −0.520292 | − | 1.77545i | ||||
\(149\) | 12.2961i | 1.00734i | 0.863897 | + | 0.503669i | \(0.168017\pi\) | ||||
−0.863897 | + | 0.503669i | \(0.831983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.39539 | −0.276313 | −0.138156 | − | 0.990410i | \(-0.544118\pi\) | ||||
−0.138156 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(152\) | −12.0188 | + | 2.74730i | −0.974856 | + | 0.222836i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20.1697 | − | 15.1072i | −1.62532 | − | 1.21738i | ||||
\(155\) | 12.3814i | 0.994501i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.95479i | − | 0.315626i | −0.987469 | − | 0.157813i | \(-0.949556\pi\) | ||
0.987469 | − | 0.157813i | \(-0.0504444\pi\) | |||||||
\(158\) | 7.62925 | − | 10.1858i | 0.606950 | − | 0.810341i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.4008 | + | 1.04925i | 1.13848 | + | 0.0829502i | ||||
\(161\) | −4.91497 | −0.387354 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.24977 | 0.646172 | 0.323086 | − | 0.946370i | \(-0.395280\pi\) | ||||
0.323086 | + | 0.946370i | \(0.395280\pi\) | |||||||
\(164\) | 13.1663 | − | 3.85836i | 1.02812 | − | 0.301287i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.40867 | + | 9.89132i | −0.575024 | + | 0.767716i | ||||
\(167\) | 4.47647 | 0.346399 | 0.173200 | − | 0.984887i | \(-0.444589\pi\) | ||||
0.173200 | + | 0.984887i | \(0.444589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.18922 | −0.706863 | ||||||||
\(170\) | −4.03973 | − | 3.02578i | −0.309833 | − | 0.232067i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.71026 | + | 16.0734i | 0.359154 | + | 1.22558i | ||||
\(173\) | 1.64428 | 0.125012 | 0.0625061 | − | 0.998045i | \(-0.480091\pi\) | ||||
0.0625061 | + | 0.998045i | \(0.480091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68112i | 0.353859i | ||||||||
\(176\) | −19.4211 | + | 12.4520i | −1.46392 | + | 0.938603i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.2498 | − | 7.67714i | −0.768253 | − | 0.575426i | ||||
\(179\) | − | 10.3671i | − | 0.774874i | −0.921896 | − | 0.387437i | \(-0.873361\pi\) | ||
0.921896 | − | 0.387437i | \(-0.126639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7461 | −1.09607 | −0.548035 | − | 0.836455i | \(-0.684624\pi\) | ||||
−0.548035 | + | 0.836455i | \(0.684624\pi\) | |||||||
\(182\) | −6.82679 | − | 5.11331i | −0.506035 | − | 0.379024i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.57580 | + | 4.21459i | −0.116169 | + | 0.310703i | ||||
\(185\) | − | 28.7251i | − | 2.11191i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.06433 | 0.589722 | ||||||||
\(188\) | 17.1543 | − | 5.02703i | 1.25110 | − | 0.366634i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.7059 | − | 0.948912i | −1.13942 | − | 0.0688413i | ||||
\(191\) | − | 6.54828i | − | 0.473817i | −0.971532 | − | 0.236909i | \(-0.923866\pi\) | ||
0.971532 | − | 0.236909i | \(-0.0761342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.3619i | − | 0.889828i | −0.895573 | − | 0.444914i | \(-0.853234\pi\) | ||
0.895573 | − | 0.444914i | \(-0.146766\pi\) | |||||||
\(194\) | −16.6247 | − | 12.4520i | −1.19358 | − | 0.893999i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.43165 | + | 4.88538i | 0.102261 | + | 0.348956i | ||||
\(197\) | − | 8.35148i | − | 0.595019i | −0.954719 | − | 0.297509i | \(-0.903844\pi\) | ||
0.954719 | − | 0.297509i | \(-0.0961559\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.04833i | − | 0.286978i | −0.989652 | − | 0.143489i | \(-0.954168\pi\) | ||
0.989652 | − | 0.143489i | \(-0.0458322\pi\) | |||||||
\(200\) | 4.01406 | + | 1.50082i | 0.283837 | + | 0.106124i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.2528 | + | 7.67940i | 0.721383 | + | 0.540320i | ||||
\(203\) | 24.3078i | 1.70607i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.5100 | 1.22295 | ||||||||
\(206\) | 10.0547 | − | 13.4240i | 0.700541 | − | 0.935294i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.57341 | + | 4.21459i | −0.455784 | + | 0.292229i | ||||
\(209\) | 20.9940 | − | 13.8303i | 1.45218 | − | 0.956664i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5474i | 1.27685i | 0.769683 | + | 0.638427i | \(0.220414\pi\) | ||||
−0.769683 | + | 0.638427i | \(0.779586\pi\) | |||||||
\(212\) | 5.96033 | + | 20.3391i | 0.409357 | + | 1.39689i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.484862 | − | 0.363165i | −0.0331445 | − | 0.0248254i | ||||
\(215\) | 21.3761i | 1.45784i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.9867i | 1.01737i | ||||||||
\(218\) | 3.09559 | − | 4.13292i | 0.209660 | − | 0.279917i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −28.2548 | + | 8.28000i | −1.90494 | + | 0.558237i | ||||
\(221\) | 2.72951 | 0.183607 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.94886 | 0.599260 | 0.299630 | − | 0.954056i | \(-0.403137\pi\) | ||||
0.299630 | + | 0.954056i | \(0.403137\pi\) | |||||||
\(224\) | 17.4310 | + | 1.27003i | 1.16466 | + | 0.0848573i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.88979 | − | 5.90951i | −0.524821 | − | 0.393094i | ||||
\(227\) | 15.6679i | 1.03991i | 0.854193 | + | 0.519957i | \(0.174052\pi\) | ||||
−0.854193 | + | 0.519957i | \(0.825948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.56895i | 0.235843i | 0.993023 | + | 0.117921i | \(0.0376231\pi\) | ||||
−0.993023 | + | 0.117921i | \(0.962377\pi\) | |||||||
\(230\) | −3.44257 | + | 4.59618i | −0.226996 | + | 0.303063i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.8439 | + | 7.79336i | 1.36847 | + | 0.511659i | ||||
\(233\) | 14.3739 | 0.941663 | 0.470831 | − | 0.882223i | \(-0.343954\pi\) | ||||
0.470831 | + | 0.882223i | \(0.343954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.8136 | 1.48820 | ||||||||
\(236\) | 24.6370 | − | 7.21982i | 1.60373 | − | 0.469970i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.88976 | − | 3.66246i | −0.316956 | − | 0.237402i | ||||
\(239\) | 23.5188i | 1.52131i | 0.649158 | + | 0.760654i | \(0.275122\pi\) | ||||
−0.649158 | + | 0.760654i | \(0.724878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4573i | 1.12452i | 0.826960 | + | 0.562261i | \(0.190069\pi\) | ||||
−0.826960 | + | 0.562261i | \(0.809931\pi\) | |||||||
\(242\) | 18.8760 | − | 25.2014i | 1.21339 | − | 1.62001i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.6001 | + | 3.69242i | −0.806636 | + | 0.236383i | ||||
\(245\) | 6.49711i | 0.415085i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.10577 | − | 4.68112i | 0.452129 | − | 0.297852i | ||||
\(248\) | 12.8511 | + | 4.80492i | 0.816047 | + | 0.305113i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.0684 | − | 7.54128i | −0.636780 | − | 0.476952i | ||||
\(251\) | 2.97108 | 0.187533 | 0.0937663 | − | 0.995594i | \(-0.470109\pi\) | ||||
0.0937663 | + | 0.995594i | \(0.470109\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.17516i | − | 0.576837i | ||||||
\(254\) | −1.27372 | + | 1.70054i | −0.0799202 | + | 0.106702i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.67764 | − | 14.5399i | 0.417352 | − | 0.908745i | ||||
\(257\) | 0.856714i | 0.0534404i | 0.999643 | + | 0.0267202i | \(0.00850631\pi\) | ||||
−0.999643 | + | 0.0267202i | \(0.991494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 34.7694i | − | 2.16046i | ||||||
\(260\) | −9.56332 | + | 2.80251i | −0.593092 | + | 0.173804i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.7237 | + | 15.6523i | −0.724290 | + | 0.967001i | ||||
\(263\) | 22.8813i | 1.41092i | 0.708749 | + | 0.705461i | \(0.249260\pi\) | ||||
−0.708749 | + | 0.705461i | \(0.750740\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.0491i | 1.66162i | ||||||||
\(266\) | −19.0107 | − | 1.14858i | −1.16562 | − | 0.0704240i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 31.1347 | − | 9.12395i | 1.90185 | − | 0.557334i | ||||
\(269\) | 8.42674 | 0.513788 | 0.256894 | − | 0.966440i | \(-0.417301\pi\) | ||||
0.256894 | + | 0.966440i | \(0.417301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.72235i | 0.226117i | 0.993588 | + | 0.113058i | \(0.0360647\pi\) | ||||
−0.993588 | + | 0.113058i | \(0.963935\pi\) | |||||||
\(272\) | −4.70828 | + | 3.01874i | −0.285481 | + | 0.183038i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.01933 | − | 10.7066i | 0.484465 | − | 0.646810i | ||||
\(275\) | −8.73861 | −0.526958 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.9232i | − | 1.13699i | −0.822688 | − | 0.568493i | \(-0.807526\pi\) | ||
0.822688 | − | 0.568493i | \(-0.192474\pi\) | |||||||
\(278\) | 9.66919 | − | 12.9094i | 0.579920 | − | 0.774252i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20.8925 | + | 7.81153i | 1.24857 | + | 0.466828i | ||||
\(281\) | 0.154199i | 0.00919871i | 0.999989 | + | 0.00459936i | \(0.00146403\pi\) | ||||
−0.999989 | + | 0.00459936i | \(0.998536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.6244 | −1.82043 | −0.910217 | − | 0.414132i | \(-0.864085\pi\) | ||||
−0.910217 | + | 0.414132i | \(0.864085\pi\) | |||||||
\(284\) | −2.51776 | − | 8.59162i | −0.149401 | − | 0.509819i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.54541 | − | 12.7441i | 0.564432 | − | 0.753575i | ||||
\(287\) | 21.1944 | 1.25107 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0450 | −0.884997 | ||||||||
\(290\) | 22.7312 | + | 17.0258i | 1.33482 | + | 0.999789i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.96004 | − | 6.68845i | −0.114702 | − | 0.391412i | ||||
\(293\) | −17.3797 | −1.01533 | −0.507666 | − | 0.861554i | \(-0.669492\pi\) | ||||
−0.507666 | + | 0.861554i | \(0.669492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.7650 | 1.90765 | ||||||||
\(296\) | −29.8147 | − | 11.1475i | −1.73295 | − | 0.647934i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.9181 | + | 10.4247i | 0.806254 | + | 0.603889i | ||||
\(299\) | − | 3.10549i | − | 0.179595i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.8740i | 1.49136i | ||||||||
\(302\) | −2.87864 | + | 3.84327i | −0.165647 | + | 0.221155i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.07996 | + | 15.9334i | −0.406064 | + | 0.913845i | ||||
\(305\) | −16.7569 | −0.959500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.3433i | − | 1.33227i | −0.745830 | − | 0.666136i | \(-0.767947\pi\) | ||
0.745830 | − | 0.666136i | \(-0.232053\pi\) | |||||||
\(308\) | −34.2001 | + | 10.0223i | −1.94873 | + | 0.571072i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.0147 | + | 10.4971i | 0.795980 | + | 0.596194i | ||||
\(311\) | − | 20.4917i | − | 1.16198i | −0.813911 | − | 0.580990i | \(-0.802665\pi\) | ||
0.813911 | − | 0.580990i | \(-0.197335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6888 | −0.604164 | −0.302082 | − | 0.953282i | \(-0.597682\pi\) | ||||
−0.302082 | + | 0.953282i | \(0.597682\pi\) | |||||||
\(314\) | −4.47647 | − | 3.35290i | −0.252622 | − | 0.189215i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.06130 | − | 17.2713i | −0.284721 | − | 0.971584i | ||||
\(317\) | 4.37379 | 0.245657 | 0.122828 | − | 0.992428i | \(-0.460804\pi\) | ||||
0.122828 | + | 0.992428i | \(0.460804\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.3772 | −2.54064 | ||||||||
\(320\) | 13.3968 | − | 15.4109i | 0.748903 | − | 0.861494i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.16695 | + | 5.56330i | −0.232215 | + | 0.310031i | ||||
\(323\) | 5.08959 | − | 3.35290i | 0.283192 | − | 0.186560i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.95773 | −0.164066 | ||||||||
\(326\) | 6.99422 | − | 9.33800i | 0.387374 | − | 0.517184i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.79518 | − | 18.1742i | 0.375201 | − | 1.00350i | ||||
\(329\) | 27.6141 | 1.52241 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.03121i | 0.331505i | 0.986167 | + | 0.165753i | \(0.0530053\pi\) | ||||
−0.986167 | + | 0.165753i | \(0.946995\pi\) | |||||||
\(332\) | 4.91497 | + | 16.7719i | 0.269744 | + | 0.920477i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.79518 | − | 5.06696i | 0.207663 | − | 0.277252i | ||||
\(335\) | 41.4063 | 2.26227 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.6740i | − | 1.61644i | −0.588878 | − | 0.808222i | \(-0.700430\pi\) | ||
0.588878 | − | 0.808222i | \(-0.299570\pi\) | |||||||
\(338\) | −7.79069 | + | 10.4014i | −0.423758 | + | 0.565760i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.84983 | + | 2.00733i | −0.371484 | + | 0.108863i | ||||
\(341\) | −27.9769 | −1.51503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.7627i | − | 0.743118i | ||||||
\(344\) | 22.1870 | + | 8.29553i | 1.19624 | + | 0.447265i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.39403 | − | 1.86118i | 0.0749437 | − | 0.100058i | ||||
\(347\) | 2.97108 | 0.159496 | 0.0797479 | − | 0.996815i | \(-0.474588\pi\) | ||||
0.0797479 | + | 0.996815i | \(0.474588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6537i | 1.10557i | 0.833325 | + | 0.552783i | \(0.186434\pi\) | ||||
−0.833325 | + | 0.552783i | \(0.813566\pi\) | |||||||
\(350\) | 5.29861 | + | 3.96869i | 0.283222 | + | 0.212135i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.37086 | + | 32.5398i | −0.126367 | + | 1.73438i | ||||
\(353\) | 23.8328 | 1.26849 | 0.634245 | − | 0.773132i | \(-0.281311\pi\) | ||||
0.634245 | + | 0.773132i | \(0.281311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.4261i | − | 0.606433i | ||||||
\(356\) | −17.3797 | + | 5.09308i | −0.921121 | + | 0.269933i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.7346 | − | 8.78931i | −0.620195 | − | 0.464530i | ||||
\(359\) | 8.30031i | 0.438074i | 0.975717 | + | 0.219037i | \(0.0702915\pi\) | ||||
−0.975717 | + | 0.219037i | \(0.929709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.49954 | − | 17.4573i | 0.394713 | − | 0.918805i | ||||
\(362\) | −12.5019 | + | 16.6913i | −0.657084 | + | 0.877275i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.5756 | + | 3.39221i | −0.606727 | + | 0.177800i | ||||
\(365\) | − | 8.89503i | − | 0.465587i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.63988i | 0.294399i | 0.989107 | + | 0.147200i | \(0.0470260\pi\) | ||||
−0.989107 | + | 0.147200i | \(0.952974\pi\) | |||||||
\(368\) | 3.43456 | + | 5.35682i | 0.179039 | + | 0.279244i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −32.5142 | − | 24.3534i | −1.69033 | − | 1.26607i | ||||
\(371\) | 32.7408i | 1.69982i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.45005 | 0.333971 | 0.166985 | − | 0.985959i | \(-0.446597\pi\) | ||||
0.166985 | + | 0.985959i | \(0.446597\pi\) | |||||||
\(374\) | 6.83701 | − | 9.12810i | 0.353533 | − | 0.472003i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.85340 | − | 23.6791i | 0.456579 | − | 1.22115i | ||||
\(377\) | −15.3587 | −0.791014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | −14.3897 | + | 16.9732i | −0.738174 | + | 0.870705i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.41207 | − | 5.55169i | −0.379234 | − | 0.284049i | ||||
\(383\) | −22.5179 | −1.15061 | −0.575305 | − | 0.817939i | \(-0.695116\pi\) | ||||
−0.575305 | + | 0.817939i | \(0.695116\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −45.4830 | −2.31803 | ||||||||
\(386\) | −13.9926 | − | 10.4805i | −0.712202 | − | 0.533444i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.1890 | + | 8.26074i | −1.43108 | + | 0.419375i | ||||
\(389\) | 3.25894i | 0.165235i | 0.996581 | + | 0.0826173i | \(0.0263279\pi\) | ||||
−0.996581 | + | 0.0826173i | \(0.973672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.22434i | − | 0.112490i | ||||||
\(392\) | 6.74357 | + | 2.52136i | 0.340602 | + | 0.127348i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.45313 | − | 7.08046i | −0.476242 | − | 0.356708i | ||||
\(395\) | − | 22.9692i | − | 1.15571i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 36.0080i | − | 1.80719i | −0.428390 | − | 0.903594i | \(-0.640919\pi\) | ||
0.428390 | − | 0.903594i | \(-0.359081\pi\) | |||||||
\(398\) | −4.58235 | − | 3.43221i | −0.229692 | − | 0.172041i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.10195 | − | 3.27115i | 0.255097 | − | 0.163557i | ||||
\(401\) | 20.6903i | 1.03323i | 0.856219 | + | 0.516613i | \(0.172807\pi\) | ||||
−0.856219 | + | 0.516613i | \(0.827193\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.46927 | −0.471698 | ||||||||
\(404\) | 17.3848 | − | 5.09457i | 0.864925 | − | 0.253465i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.5142 | + | 20.6083i | 1.36551 | + | 1.02277i | ||||
\(407\) | 64.9067 | 3.21731 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.8522i | − | 1.12997i | −0.825102 | − | 0.564983i | \(-0.808883\pi\) | ||
0.825102 | − | 0.564983i | \(-0.191117\pi\) | |||||||
\(410\) | 14.8451 | − | 19.8198i | 0.733148 | − | 0.978828i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.67034 | − | 22.7620i | −0.328624 | − | 1.12140i | ||||
\(413\) | 39.6593 | 1.95151 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3051i | 1.09491i | ||||||||
\(416\) | −0.802459 | + | 11.0137i | −0.0393438 | + | 0.539990i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.14415 | − | 35.4888i | 0.104874 | − | 1.73581i | ||||
\(419\) | −21.7142 | −1.06081 | −0.530405 | − | 0.847744i | \(-0.677960\pi\) | ||||
−0.530405 | + | 0.847744i | \(0.677960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3672 | −1.67496 | −0.837478 | − | 0.546472i | \(-0.815971\pi\) | ||||
−0.837478 | + | 0.546472i | \(0.815971\pi\) | |||||||
\(422\) | 20.9940 | + | 15.7246i | 1.02197 | + | 0.765462i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.0752 | + | 10.4971i | 1.36345 | + | 0.509783i | ||||
\(425\) | −2.11851 | −0.102763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.2829 | −0.981559 | ||||||||
\(428\) | −0.822140 | + | 0.240926i | −0.0397396 | + | 0.0116456i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.1959 | + | 18.1228i | 1.16683 | + | 0.873961i | ||||
\(431\) | −9.93549 | −0.478576 | −0.239288 | − | 0.970949i | \(-0.576914\pi\) | ||||
−0.239288 | + | 0.970949i | \(0.576914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.2167i | − | 0.587097i | −0.955944 | − | 0.293548i | \(-0.905164\pi\) | ||
0.955944 | − | 0.293548i | \(-0.0948361\pi\) | |||||||
\(434\) | 16.9636 | + | 12.7059i | 0.814280 | + | 0.609901i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.05364 | − | 7.00785i | −0.0983514 | − | 0.335615i | ||||
\(437\) | −3.81475 | − | 5.79065i | −0.182484 | − | 0.277004i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.90069 | −0.233897 | −0.116949 | − | 0.993138i | \(-0.537311\pi\) | ||||
−0.116949 | + | 0.993138i | \(0.537311\pi\) | |||||||
\(440\) | −14.5824 | + | 39.0017i | −0.695189 | + | 1.85933i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.31410 | − | 3.08957i | 0.110071 | − | 0.146956i | ||||
\(443\) | 2.97108 | 0.141160 | 0.0705800 | − | 0.997506i | \(-0.477515\pi\) | ||||
0.0705800 | + | 0.997506i | \(0.477515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.1134 | −1.09568 | ||||||||
\(446\) | 7.58691 | − | 10.1293i | 0.359251 | − | 0.479637i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.2157 | − | 18.6536i | 0.766120 | − | 0.881300i | ||||
\(449\) | − | 24.5422i | − | 1.15822i | −0.815250 | − | 0.579109i | \(-0.803400\pi\) | ||
0.815250 | − | 0.579109i | \(-0.196600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.5653i | 1.86306i | ||||||||
\(452\) | −13.3781 | + | 3.92041i | −0.629251 | + | 0.184401i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.7346 | + | 13.2834i | 0.832328 | + | 0.623419i | ||||
\(455\) | −15.3945 | −0.721706 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.7640 | 1.11163 | 0.555816 | − | 0.831305i | \(-0.312406\pi\) | ||||
0.555816 | + | 0.831305i | \(0.312406\pi\) | |||||||
\(458\) | 4.03973 | + | 3.02578i | 0.188764 | + | 0.141386i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.28383 | + | 7.79336i | 0.106484 | + | 0.363367i | ||||
\(461\) | − | 24.1617i | − | 1.12532i | −0.826687 | − | 0.562662i | \(-0.809777\pi\) | ||
0.826687 | − | 0.562662i | \(-0.190223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.4913i | 1.55647i | 0.627971 | + | 0.778237i | \(0.283886\pi\) | ||||
−0.627971 | + | 0.778237i | \(0.716114\pi\) | |||||||
\(464\) | 26.4930 | − | 16.9862i | 1.22991 | − | 0.788564i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.1863 | − | 16.2699i | 0.564518 | − | 0.753690i | ||||
\(467\) | 17.6518 | 0.816830 | 0.408415 | − | 0.912796i | \(-0.366082\pi\) | ||||
0.408415 | + | 0.912796i | \(0.366082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.1189 | 2.31428 | ||||||||
\(470\) | 19.3416 | − | 25.8230i | 0.892161 | − | 1.19113i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.7153 | − | 34.0079i | 0.585267 | − | 1.56534i | ||||
\(473\) | −48.3011 | −2.22089 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.51514 | + | 3.63325i | −0.253052 | + | 0.166705i | ||||
\(476\) | −8.29116 | + | 2.42971i | −0.380025 | + | 0.111365i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.6212 | + | 19.9395i | 1.21763 | + | 0.912010i | ||||
\(479\) | 18.6470i | 0.852004i | 0.904722 | + | 0.426002i | \(0.140078\pi\) | ||||
−0.904722 | + | 0.426002i | \(0.859922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.9688 | 1.00169 | ||||||||
\(482\) | 19.7601 | + | 14.8004i | 0.900047 | + | 0.674141i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5225 | − | 42.7318i | −0.569204 | − | 1.94236i | ||||
\(485\) | −37.4889 | −1.70228 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.8025 | 0.625453 | 0.312727 | − | 0.949843i | \(-0.398758\pi\) | ||||
0.312727 | + | 0.949843i | \(0.398758\pi\) | |||||||
\(488\) | −6.50294 | + | 17.3926i | −0.294374 | + | 0.787326i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.35415 | + | 5.50830i | 0.332227 | + | 0.248840i | ||||
\(491\) | 3.47441 | 0.156798 | 0.0783989 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0783989 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.0008 | −0.495453 | ||||||||
\(494\) | 0.725724 | − | 12.0118i | 0.0326519 | − | 0.540436i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.3340 | − | 10.4727i | 0.733419 | − | 0.470237i | ||||
\(497\) | − | 13.8303i | − | 0.620375i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7834 | −0.796093 | −0.398046 | − | 0.917365i | \(-0.630312\pi\) | ||||
−0.398046 | + | 0.917365i | \(0.630312\pi\) | |||||||
\(500\) | −17.0721 | + | 5.00294i | −0.763488 | + | 0.223738i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.51890 | − | 3.36299i | 0.112424 | − | 0.150098i | ||||
\(503\) | − | 23.2001i | − | 1.03444i | −0.855852 | − | 0.517220i | \(-0.826967\pi\) | ||
0.855852 | − | 0.517220i | \(-0.173033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.1202 | 1.02883 | ||||||||
\(506\) | −10.3855 | − | 7.77877i | −0.461690 | − | 0.345809i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.844995 | + | 2.88347i | 0.0374906 | + | 0.127933i | ||||
\(509\) | −22.2797 | −0.987529 | −0.493764 | − | 0.869596i | \(-0.664379\pi\) | ||||
−0.493764 | + | 0.869596i | \(0.664379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.7667i | − | 0.476291i | ||||||
\(512\) | −10.7965 | − | 19.8855i | −0.477144 | − | 0.878825i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.969724 | + | 0.726329i | 0.0427727 | + | 0.0320370i | ||||
\(515\) | − | 30.2713i | − | 1.33391i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.5493i | 2.26714i | ||||||||
\(518\) | −39.3558 | − | 29.4778i | −1.72920 | − | 1.29518i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.93567 | + | 13.2008i | −0.216443 | + | 0.578894i | ||||
\(521\) | 15.8179i | 0.692996i | 0.938051 | + | 0.346498i | \(0.112629\pi\) | ||||
−0.938051 | + | 0.346498i | \(0.887371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2532i | 0.973065i | 0.873662 | + | 0.486533i | \(0.161739\pi\) | ||||
−0.873662 | + | 0.486533i | \(0.838261\pi\) | |||||||
\(524\) | 7.77757 | + | 26.5403i | 0.339765 | + | 1.15942i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.8996 | + | 19.3990i | 1.12928 | + | 0.845835i | ||||
\(527\) | −6.78247 | −0.295449 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4693 | 0.889968 | ||||||||
\(530\) | 30.6172 | + | 22.9325i | 1.32993 | + | 0.996123i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.4175 | + | 20.5446i | −0.755145 | + | 0.890723i | ||||
\(533\) | 13.3916i | 0.580053i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.09337 | −0.0472706 | ||||||||
\(536\) | 16.0687 | − | 42.9770i | 0.694063 | − | 1.85632i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.14426 | − | 9.53832i | 0.308011 | − | 0.411226i | ||||
\(539\) | −14.6808 | −0.632345 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.3188i | 1.43249i | 0.697851 | + | 0.716243i | \(0.254140\pi\) | ||||
−0.697851 | + | 0.716243i | \(0.745860\pi\) | |||||||
\(542\) | 4.21337 | + | 3.15584i | 0.180980 | + | 0.135555i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.574770 | + | 7.88867i | −0.0246431 | + | 0.338224i | ||||
\(545\) | − | 9.31981i | − | 0.399217i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.88601i | 0.251668i | 0.992051 | + | 0.125834i | \(0.0401606\pi\) | ||||
−0.992051 | + | 0.125834i | \(0.959839\pi\) | |||||||
\(548\) | −5.32008 | − | 18.1543i | −0.227263 | − | 0.775514i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.40867 | + | 9.89132i | −0.315907 | + | 0.421768i | ||||
\(551\) | −28.6386 | + | 18.8665i | −1.22005 | + | 0.803738i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 27.8024i | − | 1.18228i | ||||||
\(554\) | −21.4194 | − | 16.0433i | −0.910023 | − | 0.681613i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.41462 | − | 21.8893i | −0.272041 | − | 0.928314i | ||||
\(557\) | 17.6854i | 0.749353i | 0.927156 | + | 0.374677i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374677i | \(0.877754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.3484 | −0.691462 | ||||||||
\(560\) | 26.5548 | − | 17.0258i | 1.12215 | − | 0.719471i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.174539 | + | 0.130731i | 0.00736248 | + | 0.00551454i | ||||
\(563\) | − | 26.4633i | − | 1.11530i | −0.830077 | − | 0.557648i | \(-0.811704\pi\) | ||
0.830077 | − | 0.557648i | \(-0.188296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.7916 | −0.748499 | ||||||||
\(566\) | −25.9636 | + | 34.6641i | −1.09133 | + | 1.45704i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.8595 | − | 4.43417i | −0.497614 | − | 0.186054i | ||||
\(569\) | − | 24.0165i | − | 1.00682i | −0.864047 | − | 0.503412i | \(-0.832078\pi\) | ||
0.864047 | − | 0.503412i | \(-0.167922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.1807 | 1.22118 | 0.610588 | − | 0.791948i | \(-0.290933\pi\) | ||||
0.610588 | + | 0.791948i | \(0.290933\pi\) | |||||||
\(572\) | −6.33250 | − | 21.6091i | −0.264775 | − | 0.903522i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.9688 | − | 23.9902i | 0.750004 | − | 1.00133i | ||||
\(575\) | 2.41032i | 0.100517i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.91629 | −0.163037 | −0.0815186 | − | 0.996672i | \(-0.525977\pi\) | ||||
−0.0815186 | + | 0.996672i | \(0.525977\pi\) | |||||||
\(578\) | −12.7552 | + | 17.0295i | −0.530548 | + | 0.708336i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 38.5433 | − | 11.2950i | 1.60042 | − | 0.469001i | ||||
\(581\) | 26.9985i | 1.12009i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −61.1198 | −2.53132 | ||||||||
\(584\) | −9.23246 | − | 3.45193i | −0.382042 | − | 0.142842i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.7346 | + | 19.6722i | −0.608682 | + | 0.812653i | ||||
\(587\) | −30.9562 | −1.27770 | −0.638849 | − | 0.769332i | \(-0.720589\pi\) | ||||
−0.638849 | + | 0.769332i | \(0.720589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.6569 | + | 11.6319i | −0.727538 | + | 0.479285i | ||||
\(590\) | 27.7784 | − | 37.0870i | 1.14362 | − | 1.52685i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −37.8951 | + | 24.2967i | −1.55748 | + | 0.998589i | ||||
\(593\) | 12.2130 | 0.501528 | 0.250764 | − | 0.968048i | \(-0.419318\pi\) | ||||
0.250764 | + | 0.968048i | \(0.419318\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.0265 | −0.452042 | ||||||||
\(596\) | 23.5998 | − | 6.91586i | 0.966684 | − | 0.283285i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.51514 | − | 2.63286i | −0.143745 | − | 0.107666i | ||||
\(599\) | −6.64694 | −0.271586 | −0.135793 | − | 0.990737i | \(-0.543358\pi\) | ||||
−0.135793 | + | 0.990737i | \(0.543358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.6045i | 1.08522i | 0.839985 | + | 0.542609i | \(0.182564\pi\) | ||||
−0.839985 | + | 0.542609i | \(0.817436\pi\) | |||||||
\(602\) | 29.2871 | + | 21.9362i | 1.19365 | + | 0.894054i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.90971 | + | 6.51672i | 0.0777050 | + | 0.265161i | ||||
\(605\) | − | 56.8295i | − | 2.31045i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.9143 | −0.605351 | −0.302676 | − | 0.953094i | \(-0.597880\pi\) | ||||
−0.302676 | + | 0.953094i | \(0.597880\pi\) | |||||||
\(608\) | 12.0328 | + | 21.5224i | 0.487993 | + | 0.872848i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2067 | + | 18.9674i | −0.575211 | + | 0.767966i | ||||
\(611\) | 17.4478i | 0.705861i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.0944i | 1.25589i | 0.778257 | + | 0.627946i | \(0.216104\pi\) | ||||
−0.778257 | + | 0.627946i | \(0.783896\pi\) | |||||||
\(614\) | −26.4225 | − | 19.7906i | −1.06633 | − | 0.798685i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.6508 | + | 47.2084i | −0.711171 | + | 1.90208i | ||||
\(617\) | 45.1554 | 1.81789 | 0.908944 | − | 0.416917i | \(-0.136890\pi\) | ||||
0.908944 | + | 0.416917i | \(0.136890\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.22041 | −0.169633 | −0.0848163 | − | 0.996397i | \(-0.527030\pi\) | ||||
−0.0848163 | + | 0.996397i | \(0.527030\pi\) | |||||||
\(620\) | 23.7635 | − | 6.96385i | 0.954366 | − | 0.279675i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.1948 | − | 17.3731i | −0.930028 | − | 0.696597i | ||||
\(623\) | −27.9769 | −1.12087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2800 | −1.21120 | ||||||||
\(626\) | −9.06202 | + | 12.0987i | −0.362191 | + | 0.483562i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.59037 | + | 2.22434i | −0.302889 | + | 0.0887609i | ||||
\(629\) | 15.7354 | 0.627411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4026i | 0.772406i | 0.922414 | + | 0.386203i | \(0.126214\pi\) | ||||
−0.922414 | + | 0.386203i | \(0.873786\pi\) | |||||||
\(632\) | −23.8405 | − | 8.91376i | −0.948325 | − | 0.354571i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.70814 | − | 4.95074i | 0.147269 | − | 0.196619i | ||||
\(635\) | 3.83475i | 0.152178i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.96896 | −0.196877 | ||||||||
\(638\) | −38.4712 | + | 51.3630i | −1.52309 | + | 2.03348i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.08583 | − | 28.2294i | −0.240564 | − | 1.11587i | ||||
\(641\) | − | 15.0489i | − | 0.594398i | −0.954816 | − | 0.297199i | \(-0.903948\pi\) | ||
0.954816 | − | 0.297199i | \(-0.0960524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.99622 | 0.236468 | 0.118234 | − | 0.992986i | \(-0.462277\pi\) | ||||
0.118234 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(644\) | 2.76439 | + | 9.43323i | 0.108932 | + | 0.371721i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.519808 | − | 8.60357i | 0.0204516 | − | 0.338503i | ||||
\(647\) | − | 0.565602i | − | 0.0222361i | −0.999938 | − | 0.0111181i | \(-0.996461\pi\) | ||
0.999938 | − | 0.0111181i | \(-0.00353906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 74.0352i | 2.90614i | ||||||||
\(650\) | −2.50759 | + | 3.34789i | −0.0983558 | + | 0.131315i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.64002 | − | 15.8337i | −0.181717 | − | 0.620094i | ||||
\(653\) | 8.32237i | 0.325679i | 0.986653 | + | 0.162840i | \(0.0520653\pi\) | ||||
−0.986653 | + | 0.162840i | \(0.947935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.2962i | 1.37913i | ||||||||
\(656\) | −14.8106 | − | 23.0998i | −0.578256 | − | 0.901896i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23.4114 | − | 31.2566i | 0.912672 | − | 1.21851i | ||||
\(659\) | 39.9756i | 1.55723i | 0.627502 | + | 0.778615i | \(0.284077\pi\) | ||||
−0.627502 | + | 0.778615i | \(0.715923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1669 | 1.36783 | 0.683916 | − | 0.729561i | \(-0.260275\pi\) | ||||
0.683916 | + | 0.729561i | \(0.260275\pi\) | |||||||
\(662\) | 6.82679 | + | 5.11331i | 0.265331 | + | 0.198734i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.1512 | + | 8.65604i | 0.898442 | + | 0.335920i | ||||
\(665\) | −28.7054 | + | 18.9104i | −1.11315 | + | 0.733316i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.5162i | 0.484628i | ||||||||
\(668\) | −2.51776 | − | 8.59162i | −0.0974149 | − | 0.332420i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.1046 | − | 46.8682i | 1.35621 | − | 1.81068i | ||||
\(671\) | − | 37.8637i | − | 1.46171i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 27.3486i | − | 1.05421i | −0.849800 | − | 0.527106i | \(-0.823277\pi\) | ||
0.849800 | − | 0.527106i | \(-0.176723\pi\) | |||||||
\(674\) | −33.5883 | − | 25.1578i | −1.29377 | − | 0.969044i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.16841 | + | 17.6367i | 0.198785 | + | 0.678336i | ||||
\(677\) | 7.86770 | 0.302380 | 0.151190 | − | 0.988505i | \(-0.451689\pi\) | ||||
0.151190 | + | 0.988505i | \(0.451689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.3772 | −1.74142 | ||||||||
\(680\) | −3.53523 | + | 9.45522i | −0.135570 | + | 0.362591i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −23.7190 | + | 31.6673i | −0.908249 | + | 1.21261i | ||||
\(683\) | 17.3813i | 0.665077i | 0.943090 | + | 0.332539i | \(0.107905\pi\) | ||||
−0.943090 | + | 0.332539i | \(0.892095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 24.1436i | − | 0.922480i | ||||||
\(686\) | −15.5782 | − | 11.6682i | −0.594778 | − | 0.445492i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.2001 | − | 18.0807i | 1.07512 | − | 0.689320i | ||||
\(689\) | −20.6871 | −0.788114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.6547 | 1.12812 | 0.564059 | − | 0.825734i | \(-0.309239\pi\) | ||||
0.564059 | + | 0.825734i | \(0.309239\pi\) | |||||||
\(692\) | −0.924813 | − | 3.15584i | −0.0351561 | − | 0.119967i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.51890 | − | 3.36299i | 0.0956162 | − | 0.127657i | ||||
\(695\) | − | 29.1108i | − | 1.10424i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.59185i | 0.363317i | ||||||||
\(698\) | 23.3781 | + | 17.5104i | 0.884875 | + | 0.662777i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.98440 | − | 2.63286i | 0.339579 | − | 0.0995128i | ||||
\(701\) | − | 24.3454i | − | 0.919513i | −0.888045 | − | 0.459757i | \(-0.847937\pi\) | ||
0.888045 | − | 0.459757i | \(-0.152063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.9641 | − | 26.9862i | 1.54499 | − | 1.01780i | ||||
\(704\) | 34.8222 | + | 30.2711i | 1.31241 | + | 1.14089i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.2056 | − | 26.9765i | 0.760448 | − | 1.01528i | ||||
\(707\) | 27.9851 | 1.05249 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.9431i | 1.72543i | 0.505690 | + | 0.862715i | \(0.331238\pi\) | ||||
−0.505690 | + | 0.862715i | \(0.668762\pi\) | |||||||
\(710\) | −12.9333 | − | 9.68712i | −0.485378 | − | 0.363551i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.96972 | + | 23.9902i | −0.336155 | + | 0.899071i | ||||
\(713\) | 7.71672i | 0.288993i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 28.7382i | − | 1.07475i | ||||||
\(716\) | −19.8974 | + | 5.83090i | −0.743602 | + | 0.217911i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.39521 | + | 7.03707i | 0.350626 | + | 0.262621i | ||||
\(719\) | − | 29.9952i | − | 1.11863i | −0.828955 | − | 0.559316i | \(-0.811064\pi\) | ||
0.828955 | − | 0.559316i | \(-0.188936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 36.6410i | − | 1.36458i | ||||||
\(722\) | −13.4019 | − | 23.2892i | −0.498768 | − | 0.866736i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.29385 | + | 28.3020i | 0.308238 | + | 1.05184i | ||||
\(725\) | 11.9207 | 0.442722 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.4851i | 0.648486i | 0.945974 | + | 0.324243i | \(0.105110\pi\) | ||||
−0.945974 | + | 0.324243i | \(0.894890\pi\) | |||||||
\(728\) | −5.97422 | + | 15.9785i | −0.221419 | + | 0.592203i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.0684 | − | 7.54128i | −0.372647 | − | 0.279115i | ||||
\(731\) | −11.7097 | −0.433098 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.90958i | 0.292147i | 0.989274 | + | 0.146073i | \(0.0466636\pi\) | ||||
−0.989274 | + | 0.146073i | \(0.953336\pi\) | |||||||
\(734\) | 6.38384 | + | 4.78154i | 0.235632 | + | 0.176490i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.97529 | + | 0.653942i | 0.330834 | + | 0.0241046i | ||||
\(737\) | 93.5610i | 3.44636i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.55631 | 0.314749 | 0.157375 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157375 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(740\) | −55.1316 | + | 16.1562i | −2.02668 | + | 0.593914i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 37.0596 | + | 27.7579i | 1.36050 | + | 1.01902i | ||||
\(743\) | −39.2358 | −1.43942 | −0.719711 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719711 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.3856 | 1.14988 | ||||||||
\(746\) | 5.46841 | − | 7.30088i | 0.200213 | − | 0.267304i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.53573 | − | 15.4778i | −0.165843 | − | 0.565923i | ||||
\(749\) | −1.32344 | −0.0483574 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0599 | −0.403583 | −0.201792 | − | 0.979428i | \(-0.564676\pi\) | ||||
−0.201792 | + | 0.979428i | \(0.564676\pi\) | |||||||
\(752\) | −19.2966 | − | 30.0966i | −0.703675 | − | 1.09751i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.0212 | + | 17.3847i | −0.474206 | + | 0.633113i | ||||
\(755\) | 8.66664i | 0.315411i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 17.6577i | − | 0.641778i | −0.947117 | − | 0.320889i | \(-0.896018\pi\) | ||
0.947117 | − | 0.320889i | \(-0.103982\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.01243 | + | 30.6778i | 0.254367 | + | 1.11280i | ||||
\(761\) | 0.635615 | 0.0230410 | 0.0115205 | − | 0.999934i | \(-0.496333\pi\) | ||||
0.0115205 | + | 0.999934i | \(0.496333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11.2809i | − | 0.408395i | ||||||
\(764\) | −12.5680 | + | 3.68303i | −0.454695 | + | 0.133247i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.0908 | + | 25.4882i | −0.689780 | + | 0.920926i | ||||
\(767\) | 25.0585i | 0.904810i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.8236 | −1.61638 | −0.808191 | − | 0.588921i | \(-0.799553\pi\) | ||||
−0.808191 | + | 0.588921i | \(0.799553\pi\) | |||||||
\(770\) | −38.5609 | + | 51.4827i | −1.38964 | + | 1.85531i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.7260 | + | 6.95285i | −0.853917 | + | 0.250239i | ||||
\(773\) | 31.2326 | 1.12336 | 0.561679 | − | 0.827355i | \(-0.310156\pi\) | ||||
0.561679 | + | 0.827355i | \(0.310156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.34956 | 0.264004 | ||||||||
\(776\) | −14.5485 | + | 38.9110i | −0.522260 | + | 1.39682i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.68882 | + | 2.76295i | 0.132251 | + | 0.0990566i | ||||
\(779\) | 16.4500 | + | 24.9706i | 0.589384 | + | 0.894664i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8182 | 0.923847 | ||||||||
\(782\) | −2.51776 | − | 1.88582i | −0.0900348 | − | 0.0674366i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.57121 | − | 5.49549i | 0.306115 | − | 0.196267i | ||||
\(785\) | −10.0945 | −0.360288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 22.1080i | − | 0.788066i | −0.919096 | − | 0.394033i | \(-0.871080\pi\) | ||
0.919096 | − | 0.394033i | \(-0.128920\pi\) | |||||||
\(788\) | −16.0289 | + | 4.69723i | −0.571005 | + | 0.167332i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.9991 | − | 19.4735i | −0.925006 | − | 0.692835i | ||||
\(791\) | −21.5353 | −0.765707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.8156i | − | 0.455096i | ||||||
\(794\) | −40.7578 | − | 30.5278i | −1.44644 | − | 1.08339i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.76990 | + | 2.27695i | −0.275397 | + | 0.0807045i | ||||
\(797\) | −33.6741 | −1.19280 | −0.596399 | − | 0.802688i | \(-0.703402\pi\) | ||||
−0.596399 | + | 0.802688i | \(0.703402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4972i | 0.442118i | ||||||||
\(800\) | 0.622828 | − | 8.54826i | 0.0220203 | − | 0.302226i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.4196 | + | 17.5414i | 0.826975 | + | 0.619410i | ||||
\(803\) | 20.0991 | 0.709280 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.5453i | 0.442165i | ||||||||
\(806\) | −8.02812 | + | 10.7184i | −0.282778 | + | 0.377538i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.97236 | − | 23.9972i | 0.315646 | − | 0.844220i | ||||
\(809\) | 3.10336 | 0.109108 | 0.0545542 | − | 0.998511i | \(-0.482626\pi\) | ||||
0.0545542 | + | 0.998511i | \(0.482626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.4885i | − | 0.824793i | −0.911005 | − | 0.412396i | \(-0.864692\pi\) | ||
0.911005 | − | 0.412396i | \(-0.135308\pi\) | |||||||
\(812\) | 46.6536 | − | 13.6717i | 1.63722 | − | 0.479784i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 55.0284 | − | 73.4686i | 1.92875 | − | 2.57507i | ||||
\(815\) | − | 21.0573i | − | 0.737607i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.4839 | + | 20.0821i | −1.06650 | + | 0.702584i | ||||
\(818\) | −25.8666 | − | 19.3742i | −0.904404 | − | 0.677405i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.84837 | − | 33.6067i | −0.343920 | − | 1.17360i | ||||
\(821\) | 15.4088i | 0.537773i | 0.963172 | + | 0.268886i | \(0.0866556\pi\) | ||||
−0.963172 | + | 0.268886i | \(0.913344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.9991i | 0.383406i | 0.981453 | + | 0.191703i | \(0.0614010\pi\) | ||||
−0.981453 | + | 0.191703i | \(0.938599\pi\) | |||||||
\(824\) | −31.4197 | − | 11.7475i | −1.09456 | − | 0.409245i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.6235 | − | 44.8908i | 1.16991 | − | 1.56195i | ||||
\(827\) | − | 44.7336i | − | 1.55554i | −0.628550 | − | 0.777770i | \(-0.716351\pi\) | ||
0.628550 | − | 0.777770i | \(-0.283649\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.9618 | −1.14481 | −0.572405 | − | 0.819971i | \(-0.693989\pi\) | ||||
−0.572405 | + | 0.819971i | \(0.693989\pi\) | |||||||
\(830\) | 25.2474 | + | 18.9104i | 0.876349 | + | 0.656391i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.7862 | + | 10.2458i | 0.408612 | + | 0.355209i | ||||
\(833\) | −3.55907 | −0.123315 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 11.4261i | − | 0.395416i | ||||||
\(836\) | −38.3523 | − | 32.5146i | −1.32644 | − | 1.12454i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.4095 | + | 24.5786i | −0.635946 | + | 0.849053i | ||||
\(839\) | −15.5301 | −0.536157 | −0.268078 | − | 0.963397i | \(-0.586389\pi\) | ||||
−0.268078 | + | 0.963397i | \(0.586389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.9007 | 1.13451 | ||||||||
\(842\) | −29.1368 | + | 38.9006i | −1.00412 | + | 1.34060i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.5977 | − | 10.4318i | 1.22532 | − | 0.359078i | ||||
\(845\) | 23.4553i | 0.806886i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 68.7875i | − | 2.36357i | ||||||
\(848\) | 35.6842 | − | 22.8791i | 1.22540 | − | 0.785673i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.79609 | + | 2.39796i | −0.0616054 | + | 0.0822495i | ||||
\(851\) | − | 17.9029i | − | 0.613703i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.1160i | − | 1.23659i | −0.785947 | − | 0.618295i | \(-0.787824\pi\) | ||
0.785947 | − | 0.618295i | \(-0.212176\pi\) | |||||||
\(854\) | −17.1960 | + | 22.9584i | −0.588436 | + | 0.785622i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.424310 | + | 1.13485i | −0.0145026 | + | 0.0387883i | ||||
\(857\) | − | 27.3297i | − | 0.933564i | −0.884372 | − | 0.466782i | \(-0.845413\pi\) | ||
0.884372 | − | 0.466782i | \(-0.154587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.97350 | 0.101455 | 0.0507273 | − | 0.998713i | \(-0.483846\pi\) | ||||
0.0507273 | + | 0.998713i | \(0.483846\pi\) | |||||||
\(860\) | 41.0269 | − | 12.0228i | 1.39900 | − | 0.409975i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.42339 | + | 11.2461i | −0.286902 | + | 0.383043i | ||||
\(863\) | −5.66437 | −0.192818 | −0.0964088 | − | 0.995342i | \(-0.530736\pi\) | ||||
−0.0964088 | + | 0.995342i | \(0.530736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 4.19699i | − | 0.142702i | ||||||
\(866\) | −13.8282 | − | 10.3574i | −0.469901 | − | 0.351959i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.7638 | − | 8.42917i | 0.976307 | − | 0.286105i | ||||
\(869\) | 51.9008 | 1.76062 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6673i | 1.07301i | ||||||||
\(872\) | −9.67335 | − | 3.61678i | −0.327581 | − | 0.122480i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.78867 | − | 0.591409i | −0.331107 | − | 0.0200047i | ||||
\(875\) | −27.4818 | −0.929054 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7638 | −0.532307 | −0.266154 | − | 0.963931i | \(-0.585753\pi\) | ||||
−0.266154 | + | 0.963931i | \(0.585753\pi\) | |||||||
\(878\) | −4.15484 | + | 5.54714i | −0.140219 | + | 0.187207i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 31.7834 | + | 49.5719i | 1.07142 | + | 1.67107i | ||||
\(881\) | −20.3160 | −0.684464 | −0.342232 | − | 0.939616i | \(-0.611183\pi\) | ||||
−0.342232 | + | 0.939616i | \(0.611183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.2744 | −1.59091 | −0.795456 | − | 0.606012i | \(-0.792768\pi\) | ||||
−0.795456 | + | 0.606012i | \(0.792768\pi\) | |||||||
\(884\) | −1.53520 | − | 5.23872i | −0.0516342 | − | 0.176197i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.51890 | − | 3.36299i | 0.0846242 | − | 0.112982i | ||||
\(887\) | −7.97037 | −0.267619 | −0.133809 | − | 0.991007i | \(-0.542721\pi\) | ||||
−0.133809 | + | 0.991007i | \(0.542721\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.64166i | 0.155676i | ||||||||
\(890\) | −19.5957 | + | 26.1623i | −0.656850 | + | 0.876962i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.03322 | − | 17.1754i | −0.168525 | − | 0.575076i | ||||
\(893\) | 21.4326 | + | 32.5340i | 0.717216 | + | 1.08871i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.4618 | −0.884520 | ||||||||
\(896\) | −7.36640 | − | 34.1694i | −0.246094 | − | 1.14152i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.7796 | − | 20.8071i | −0.927017 | − | 0.694342i | ||||
\(899\) | 38.1643 | 1.27285 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8173 | −0.493637 | ||||||||
\(902\) | 44.7844 | + | 33.5438i | 1.49116 | + | 1.11689i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.90447 | + | 18.4665i | −0.229639 | + | 0.614188i | ||||
\(905\) | 37.6391i | 1.25117i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5029i | 0.913218i | 0.889667 | + | 0.456609i | \(0.150936\pi\) | ||||
−0.889667 | + | 0.456609i | \(0.849064\pi\) | |||||||
\(908\) | 30.0711 | − | 8.81228i | 0.997946 | − | 0.292446i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.0516 | + | 17.4252i | −0.432656 | + | 0.577640i | ||||
\(911\) | −32.3178 | −1.07074 | −0.535369 | − | 0.844618i | \(-0.679827\pi\) | ||||
−0.535369 | + | 0.844618i | \(0.679827\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.4002 | −1.66800 | ||||||||
\(914\) | 20.1473 | − | 26.8987i | 0.666414 | − | 0.889730i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.84983 | − | 2.00733i | 0.226325 | − | 0.0663240i | ||||
\(917\) | 42.7231i | 1.41084i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9942i | 0.692534i | 0.938136 | + | 0.346267i | \(0.112551\pi\) | ||||
−0.938136 | + | 0.346267i | \(0.887449\pi\) | |||||||
\(920\) | 10.7576 | + | 4.02219i | 0.354669 | + | 0.132608i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.3489 | − | 20.4845i | −0.900688 | − | 0.674621i | ||||
\(923\) | 8.73861 | 0.287635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0511 | −0.560636 | ||||||||
\(926\) | 37.9092 | + | 28.3942i | 1.24577 | + | 0.933092i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.23417 | − | 44.3888i | 0.106167 | − | 1.45713i | ||||
\(929\) | 54.6143 | 1.79184 | 0.895919 | − | 0.444218i | \(-0.146518\pi\) | ||||
0.895919 | + | 0.444218i | \(0.146518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.26537 | + | 6.10381i | −0.303660 | + | 0.200044i | ||||
\(932\) | −8.08447 | − | 27.5875i | −0.264816 | − | 0.903660i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.9654 | − | 19.9803i | 0.489682 | − | 0.653775i | ||||
\(935\) | − | 20.5840i | − | 0.673170i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.8557 | 0.517984 | 0.258992 | − | 0.965879i | \(-0.416610\pi\) | ||||
0.258992 | + | 0.965879i | \(0.416610\pi\) | |||||||
\(938\) | 42.4912 | − | 56.7302i | 1.38739 | − | 1.85231i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.8314 | − | 43.7859i | −0.418513 | − | 1.42814i | ||||
\(941\) | −52.1390 | −1.69968 | −0.849842 | − | 0.527038i | \(-0.823303\pi\) | ||||
−0.849842 | + | 0.527038i | \(0.823303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9131 | 0.355379 | ||||||||
\(944\) | −27.7138 | − | 43.2247i | −0.902007 | − | 1.40684i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.9501 | + | 54.6725i | −1.33140 | + | 1.77756i | ||||
\(947\) | 18.2398 | 0.592715 | 0.296357 | − | 0.955077i | \(-0.404228\pi\) | ||||
0.296357 | + | 0.955077i | \(0.404228\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.80288 | 0.220831 | ||||||||
\(950\) | −0.563270 | + | 9.32294i | −0.0182749 | + | 0.302476i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.27910 | + | 11.4448i | −0.138687 | + | 0.370927i | ||||
\(953\) | 45.0119i | 1.45808i | 0.684472 | + | 0.729039i | \(0.260033\pi\) | ||||
−0.684472 | + | 0.729039i | \(0.739967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.7143 | −0.540863 | ||||||||
\(956\) | 45.1394 | − | 13.2280i | 1.45991 | − | 0.427824i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.1068 | + | 15.8091i | 0.681929 | + | 0.510769i | ||||
\(959\) | − | 29.2239i | − | 0.943688i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.47018 | −0.240974 | ||||||||
\(962\) | 18.6253 | − | 24.8667i | 0.600505 | − | 0.801735i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33.5055 | − | 9.81872i | 1.07914 | − | 0.316240i | ||||
\(965\) | −31.5534 | −1.01574 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 42.3405i | − | 1.36158i | −0.732479 | − | 0.680789i | \(-0.761637\pi\) | ||
0.732479 | − | 0.680789i | \(-0.238363\pi\) | |||||||
\(968\) | −58.9853 | − | 22.0541i | −1.89586 | − | 0.708845i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.7834 | + | 42.4340i | −1.02050 | + | 1.36248i | ||||
\(971\) | − | 26.2556i | − | 0.842584i | −0.906925 | − | 0.421292i | \(-0.861577\pi\) | ||
0.906925 | − | 0.421292i | \(-0.138423\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 35.2363i | − | 1.12962i | ||||||
\(974\) | 11.7019 | − | 15.6232i | 0.374953 | − | 0.500601i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1736 | + | 22.1063i | 0.453687 | + | 0.707607i | ||||
\(977\) | − | 6.63934i | − | 0.212411i | −0.994344 | − | 0.106206i | \(-0.966130\pi\) | ||
0.994344 | − | 0.106206i | \(-0.0338702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 52.2267i | − | 1.66917i | ||||||
\(980\) | 12.4698 | − | 3.65425i | 0.398334 | − | 0.116731i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.94563 | − | 3.93272i | 0.0939988 | − | 0.125498i | ||||
\(983\) | 49.1713 | 1.56832 | 0.784161 | − | 0.620558i | \(-0.213094\pi\) | ||||
0.784161 | + | 0.620558i | \(0.213094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.3170 | −0.679215 | ||||||||
\(986\) | −9.32661 | + | 12.4520i | −0.297020 | + | 0.396552i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.9810 | − | 11.0051i | −0.412980 | − | 0.350120i | ||||
\(989\) | 13.3226i | 0.423635i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.1910 | 1.53084 | 0.765419 | − | 0.643532i | \(-0.222532\pi\) | ||||
0.765419 | + | 0.643532i | \(0.222532\pi\) | |||||||
\(992\) | 1.99400 | − | 27.3675i | 0.0633095 | − | 0.868918i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.6547 | − | 11.7255i | −0.496537 | − | 0.371909i | ||||
\(995\) | −10.3333 | −0.327587 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.53168i | − | 0.0485089i | −0.999706 | − | 0.0242545i | \(-0.992279\pi\) | ||
0.999706 | − | 0.0242545i | \(-0.00772120\pi\) | |||||||
\(998\) | −15.0769 | + | 20.1292i | −0.477250 | + | 0.637178i | ||||
\(999\) | 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 | 1368.2.e.f.379.14 | yes | 24 | |
3.2 | odd | 2 | inner | 1368.2.e.f.379.11 | yes | 24 | |
4.3 | odd | 2 | 5472.2.e.f.5167.7 | 24 | |||
8.3 | odd | 2 | inner | 1368.2.e.f.379.10 | yes | 24 | |
8.5 | even | 2 | 5472.2.e.f.5167.2 | 24 | |||
12.11 | even | 2 | 5472.2.e.f.5167.22 | 24 | |||
19.18 | odd | 2 | inner | 1368.2.e.f.379.12 | yes | 24 | |
24.5 | odd | 2 | 5472.2.e.f.5167.13 | 24 | |||
24.11 | even | 2 | inner | 1368.2.e.f.379.15 | yes | 24 | |
57.56 | even | 2 | inner | 1368.2.e.f.379.13 | yes | 24 | |
76.75 | even | 2 | 5472.2.e.f.5167.1 | 24 | |||
152.37 | odd | 2 | 5472.2.e.f.5167.8 | 24 | |||
152.75 | even | 2 | inner | 1368.2.e.f.379.16 | yes | 24 | |
228.227 | odd | 2 | 5472.2.e.f.5167.14 | 24 | |||
456.227 | odd | 2 | inner | 1368.2.e.f.379.9 | ✓ | 24 | |
456.341 | even | 2 | 5472.2.e.f.5167.21 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.e.f.379.9 | ✓ | 24 | 456.227 | odd | 2 | inner | |
1368.2.e.f.379.10 | yes | 24 | 8.3 | odd | 2 | inner | |
1368.2.e.f.379.11 | yes | 24 | 3.2 | odd | 2 | inner | |
1368.2.e.f.379.12 | yes | 24 | 19.18 | odd | 2 | inner | |
1368.2.e.f.379.13 | yes | 24 | 57.56 | even | 2 | inner | |
1368.2.e.f.379.14 | yes | 24 | 1.1 | even | 1 | trivial | |
1368.2.e.f.379.15 | yes | 24 | 24.11 | even | 2 | inner | |
1368.2.e.f.379.16 | yes | 24 | 152.75 | even | 2 | inner | |
5472.2.e.f.5167.1 | 24 | 76.75 | even | 2 | |||
5472.2.e.f.5167.2 | 24 | 8.5 | even | 2 | |||
5472.2.e.f.5167.7 | 24 | 4.3 | odd | 2 | |||
5472.2.e.f.5167.8 | 24 | 152.37 | odd | 2 | |||
5472.2.e.f.5167.13 | 24 | 24.5 | odd | 2 | |||
5472.2.e.f.5167.14 | 24 | 228.227 | odd | 2 | |||
5472.2.e.f.5167.21 | 24 | 456.341 | even | 2 | |||
5472.2.e.f.5167.22 | 24 | 12.11 | even | 2 |