Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 22x^{10} + 179x^{8} + 641x^{6} + 869x^{4} + 67x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.9 | ||
Root | \(2.01887i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.f.1249.4 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.01887i | 1.42756i | 0.700372 | + | 0.713778i | \(0.253018\pi\) | ||||
−0.700372 | + | 0.713778i | \(0.746982\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −2.07584 | −1.03792 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.01887 | 0.824200 | ||||||||
\(7\) | − 1.01887i | − 0.385097i | −0.981287 | − | 0.192548i | \(-0.938325\pi\) | ||||
0.981287 | − | 0.192548i | \(-0.0616752\pi\) | |||||||
\(8\) | − 0.153106i | − 0.0541311i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.75961 | 1.43508 | 0.717538 | − | 0.696519i | \(-0.245269\pi\) | ||||
0.717538 | + | 0.696519i | \(0.245269\pi\) | |||||||
\(12\) | 2.07584i | 0.599243i | ||||||||
\(13\) | − 0.103837i | − 0.0287992i | −0.999896 | − | 0.0143996i | \(-0.995416\pi\) | ||||
0.999896 | − | 0.0143996i | \(-0.00458370\pi\) | |||||||
\(14\) | 2.05697 | 0.549748 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.84257 | −0.960643 | ||||||||
\(17\) | 5.83776i | 1.41587i | 0.706280 | + | 0.707933i | \(0.250372\pi\) | ||||
−0.706280 | + | 0.707933i | \(0.749628\pi\) | |||||||
\(18\) | − 2.01887i | − 0.475852i | ||||||||
\(19\) | 0.724404 | 0.166190 | 0.0830949 | − | 0.996542i | \(-0.473520\pi\) | ||||
0.0830949 | + | 0.996542i | \(0.473520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.01887 | −0.222336 | ||||||||
\(22\) | 9.60904i | 2.04865i | ||||||||
\(23\) | − 9.07152i | − 1.89154i | −0.324834 | − | 0.945771i | \(-0.605308\pi\) | ||||
0.324834 | − | 0.945771i | \(-0.394692\pi\) | |||||||
\(24\) | −0.153106 | −0.0312526 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.209634 | 0.0411126 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.11501i | 0.399699i | ||||||||
\(29\) | 3.98847 | 0.740641 | 0.370320 | − | 0.928904i | \(-0.379248\pi\) | ||||
0.370320 | + | 0.928904i | \(0.379248\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06662 | 0.191571 | 0.0957857 | − | 0.995402i | \(-0.469464\pi\) | ||||
0.0957857 | + | 0.995402i | \(0.469464\pi\) | |||||||
\(32\) | − 8.06387i | − 1.42550i | ||||||||
\(33\) | − 4.75961i | − 0.828542i | ||||||||
\(34\) | −11.7857 | −2.02123 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.07584 | 0.345973 | ||||||||
\(37\) | − 4.02621i | − 0.661905i | −0.943647 | − | 0.330953i | \(-0.892630\pi\) | ||||
0.943647 | − | 0.330953i | \(-0.107370\pi\) | |||||||
\(38\) | 1.46248i | 0.237245i | ||||||||
\(39\) | −0.103837 | −0.0166273 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.20977 | 1.12598 | 0.562988 | − | 0.826465i | \(-0.309652\pi\) | ||||
0.562988 | + | 0.826465i | \(0.309652\pi\) | |||||||
\(42\) | − 2.05697i | − 0.317397i | ||||||||
\(43\) | 8.62791i | 1.31574i | 0.753130 | + | 0.657872i | \(0.228543\pi\) | ||||
−0.753130 | + | 0.657872i | \(0.771457\pi\) | |||||||
\(44\) | −9.88018 | −1.48949 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.3142 | 2.70028 | ||||||||
\(47\) | 8.19797i | 1.19580i | 0.801572 | + | 0.597899i | \(0.203997\pi\) | ||||
−0.801572 | + | 0.597899i | \(0.796003\pi\) | |||||||
\(48\) | 3.84257i | 0.554628i | ||||||||
\(49\) | 5.96190 | 0.851700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.83776 | 0.817451 | ||||||||
\(52\) | 0.215549i | 0.0298913i | ||||||||
\(53\) | − 4.36719i | − 0.599880i | −0.953958 | − | 0.299940i | \(-0.903033\pi\) | ||||
0.953958 | − | 0.299940i | \(-0.0969667\pi\) | |||||||
\(54\) | −2.01887 | −0.274733 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.155995 | −0.0208457 | ||||||||
\(57\) | − 0.724404i | − 0.0959497i | ||||||||
\(58\) | 8.05221i | 1.05731i | ||||||||
\(59\) | 4.91285 | 0.639599 | 0.319799 | − | 0.947485i | \(-0.396384\pi\) | ||||
0.319799 | + | 0.947485i | \(0.396384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.96435 | 0.891694 | 0.445847 | − | 0.895109i | \(-0.352903\pi\) | ||||
0.445847 | + | 0.895109i | \(0.352903\pi\) | |||||||
\(62\) | 2.15338i | 0.273479i | ||||||||
\(63\) | 1.01887i | 0.128366i | ||||||||
\(64\) | 8.59476 | 1.07435 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.60904 | 1.18279 | ||||||||
\(67\) | 9.91998i | 1.21192i | 0.795496 | + | 0.605959i | \(0.207210\pi\) | ||||
−0.795496 | + | 0.605959i | \(0.792790\pi\) | |||||||
\(68\) | − 12.1183i | − 1.46955i | ||||||||
\(69\) | −9.07152 | −1.09208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7866 | −1.28013 | −0.640065 | − | 0.768320i | \(-0.721093\pi\) | ||||
−0.640065 | + | 0.768320i | \(0.721093\pi\) | |||||||
\(72\) | 0.153106i | 0.0180437i | ||||||||
\(73\) | 8.63115i | 1.01020i | 0.863061 | + | 0.505100i | \(0.168544\pi\) | ||||
−0.863061 | + | 0.505100i | \(0.831456\pi\) | |||||||
\(74\) | 8.12840 | 0.944907 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50375 | −0.172491 | ||||||||
\(77\) | − 4.84943i | − 0.552644i | ||||||||
\(78\) | − 0.209634i | − 0.0237363i | ||||||||
\(79\) | −2.48291 | −0.279350 | −0.139675 | − | 0.990197i | \(-0.544606\pi\) | ||||
−0.139675 | + | 0.990197i | \(0.544606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.5556i | 1.60740i | ||||||||
\(83\) | 4.24385i | 0.465823i | 0.972498 | + | 0.232911i | \(0.0748252\pi\) | ||||
−0.972498 | + | 0.232911i | \(0.925175\pi\) | |||||||
\(84\) | 2.11501 | 0.230766 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17.4186 | −1.87830 | ||||||||
\(87\) | − 3.98847i | − 0.427609i | ||||||||
\(88\) | − 0.728724i | − 0.0776823i | ||||||||
\(89\) | 18.3752 | 1.94777 | 0.973884 | − | 0.227047i | \(-0.0729072\pi\) | ||||
0.973884 | + | 0.227047i | \(0.0729072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.105797 | −0.0110905 | ||||||||
\(92\) | 18.8310i | 1.96327i | ||||||||
\(93\) | − 1.06662i | − 0.110604i | ||||||||
\(94\) | −16.5506 | −1.70707 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.06387 | −0.823015 | ||||||||
\(97\) | − 6.69876i | − 0.680156i | −0.940397 | − | 0.340078i | \(-0.889546\pi\) | ||||
0.940397 | − | 0.340078i | \(-0.110454\pi\) | |||||||
\(98\) | 12.0363i | 1.21585i | ||||||||
\(99\) | −4.75961 | −0.478359 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.66147 | 0.563337 | 0.281669 | − | 0.959512i | \(-0.409112\pi\) | ||||
0.281669 | + | 0.959512i | \(0.409112\pi\) | |||||||
\(102\) | 11.7857i | 1.16696i | ||||||||
\(103\) | 0.594489i | 0.0585767i | 0.999571 | + | 0.0292884i | \(0.00932411\pi\) | ||||
−0.999571 | + | 0.0292884i | \(0.990676\pi\) | |||||||
\(104\) | −0.0158981 | −0.00155893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.81680 | 0.856363 | ||||||||
\(107\) | − 1.38651i | − 0.134039i | −0.997752 | − | 0.0670193i | \(-0.978651\pi\) | ||||
0.997752 | − | 0.0670193i | \(-0.0213489\pi\) | |||||||
\(108\) | − 2.07584i | − 0.199748i | ||||||||
\(109\) | 8.85677 | 0.848325 | 0.424162 | − | 0.905586i | \(-0.360569\pi\) | ||||
0.424162 | + | 0.905586i | \(0.360569\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02621 | −0.382151 | ||||||||
\(112\) | 3.91508i | 0.369941i | ||||||||
\(113\) | 6.59039i | 0.619971i | 0.950741 | + | 0.309986i | \(0.100324\pi\) | ||||
−0.950741 | + | 0.309986i | \(0.899676\pi\) | |||||||
\(114\) | 1.46248 | 0.136974 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.27942 | −0.768725 | ||||||||
\(117\) | 0.103837i | 0.00959975i | ||||||||
\(118\) | 9.91841i | 0.913064i | ||||||||
\(119\) | 5.94793 | 0.545245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6539 | 1.05945 | ||||||||
\(122\) | 14.0601i | 1.27294i | ||||||||
\(123\) | − 7.20977i | − 0.650083i | ||||||||
\(124\) | −2.21414 | −0.198836 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.05697 | −0.183249 | ||||||||
\(127\) | 7.29144i | 0.647011i | 0.946226 | + | 0.323505i | \(0.104861\pi\) | ||||
−0.946226 | + | 0.323505i | \(0.895139\pi\) | |||||||
\(128\) | 1.22397i | 0.108184i | ||||||||
\(129\) | 8.62791 | 0.759645 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.55386 | −0.834725 | −0.417362 | − | 0.908740i | \(-0.637045\pi\) | ||||
−0.417362 | + | 0.908740i | \(0.637045\pi\) | |||||||
\(132\) | 9.88018i | 0.859959i | ||||||||
\(133\) | − 0.738074i | − 0.0639991i | ||||||||
\(134\) | −20.0271 | −1.73008 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.893796 | 0.0766424 | ||||||||
\(137\) | 6.19984i | 0.529688i | 0.964291 | + | 0.264844i | \(0.0853205\pi\) | ||||
−0.964291 | + | 0.264844i | \(0.914680\pi\) | |||||||
\(138\) | − 18.3142i | − 1.55901i | ||||||||
\(139\) | 0.906531 | 0.0768910 | 0.0384455 | − | 0.999261i | \(-0.487759\pi\) | ||||
0.0384455 | + | 0.999261i | \(0.487759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.19797 | 0.690394 | ||||||||
\(142\) | − 21.7767i | − 1.82746i | ||||||||
\(143\) | − 0.494225i | − 0.0413291i | ||||||||
\(144\) | 3.84257 | 0.320214 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.4252 | −1.44212 | ||||||||
\(147\) | − 5.96190i | − 0.491729i | ||||||||
\(148\) | 8.35776i | 0.687004i | ||||||||
\(149\) | 4.89808 | 0.401267 | 0.200633 | − | 0.979666i | \(-0.435700\pi\) | ||||
0.200633 | + | 0.979666i | \(0.435700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2626 | −0.835161 | −0.417581 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(152\) | − 0.110911i | − 0.00899603i | ||||||||
\(153\) | − 5.83776i | − 0.471955i | ||||||||
\(154\) | 9.79036 | 0.788930 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.215549 | 0.0172577 | ||||||||
\(157\) | 8.89537i | 0.709928i | 0.934880 | + | 0.354964i | \(0.115507\pi\) | ||||
−0.934880 | + | 0.354964i | \(0.884493\pi\) | |||||||
\(158\) | − 5.01268i | − 0.398788i | ||||||||
\(159\) | −4.36719 | −0.346341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.24270 | −0.728427 | ||||||||
\(162\) | 2.01887i | 0.158617i | ||||||||
\(163\) | 11.7791i | 0.922607i | 0.887242 | + | 0.461304i | \(0.152618\pi\) | ||||
−0.887242 | + | 0.461304i | \(0.847382\pi\) | |||||||
\(164\) | −14.9663 | −1.16867 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.56778 | −0.664989 | ||||||||
\(167\) | − 17.3762i | − 1.34461i | −0.740274 | − | 0.672306i | \(-0.765304\pi\) | ||||
0.740274 | − | 0.672306i | \(-0.234696\pi\) | |||||||
\(168\) | 0.155995i | 0.0120353i | ||||||||
\(169\) | 12.9892 | 0.999171 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.724404 | −0.0553966 | ||||||||
\(172\) | − 17.9101i | − 1.36564i | ||||||||
\(173\) | − 12.9596i | − 0.985298i | −0.870228 | − | 0.492649i | \(-0.836029\pi\) | ||||
0.870228 | − | 0.492649i | \(-0.163971\pi\) | |||||||
\(174\) | 8.05221 | 0.610436 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.2892 | −1.37860 | ||||||||
\(177\) | − 4.91285i | − 0.369273i | ||||||||
\(178\) | 37.0971i | 2.78055i | ||||||||
\(179\) | −1.09897 | −0.0821409 | −0.0410704 | − | 0.999156i | \(-0.513077\pi\) | ||||
−0.0410704 | + | 0.999156i | \(0.513077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9797 | −1.11343 | −0.556716 | − | 0.830703i | \(-0.687939\pi\) | ||||
−0.556716 | + | 0.830703i | \(0.687939\pi\) | |||||||
\(182\) | − 0.213590i | − 0.0158323i | ||||||||
\(183\) | − 6.96435i | − 0.514820i | ||||||||
\(184\) | −1.38890 | −0.102391 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.15338 | 0.157893 | ||||||||
\(187\) | 27.7855i | 2.03188i | ||||||||
\(188\) | − 17.0177i | − 1.24114i | ||||||||
\(189\) | 1.01887 | 0.0741119 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7404 | −0.921862 | −0.460931 | − | 0.887436i | \(-0.652484\pi\) | ||||
−0.460931 | + | 0.887436i | \(0.652484\pi\) | |||||||
\(192\) | − 8.59476i | − 0.620273i | ||||||||
\(193\) | − 4.38386i | − 0.315557i | −0.987475 | − | 0.157779i | \(-0.949567\pi\) | ||||
0.987475 | − | 0.157779i | \(-0.0504332\pi\) | |||||||
\(194\) | 13.5239 | 0.970962 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.3759 | −0.883996 | ||||||||
\(197\) | − 3.22165i | − 0.229533i | −0.993392 | − | 0.114767i | \(-0.963388\pi\) | ||||
0.993392 | − | 0.114767i | \(-0.0366120\pi\) | |||||||
\(198\) | − 9.60904i | − 0.682885i | ||||||||
\(199\) | 2.70518 | 0.191765 | 0.0958825 | − | 0.995393i | \(-0.469433\pi\) | ||||
0.0958825 | + | 0.995393i | \(0.469433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.91998 | 0.699701 | ||||||||
\(202\) | 11.4298i | 0.804196i | ||||||||
\(203\) | − 4.06374i | − 0.285218i | ||||||||
\(204\) | −12.1183 | −0.848447 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.20020 | −0.0836216 | ||||||||
\(207\) | 9.07152i | 0.630514i | ||||||||
\(208\) | 0.399002i | 0.0276658i | ||||||||
\(209\) | 3.44788 | 0.238495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4435 | 1.82044 | 0.910222 | − | 0.414122i | \(-0.135911\pi\) | ||||
0.910222 | + | 0.414122i | \(0.135911\pi\) | |||||||
\(212\) | 9.06559i | 0.622627i | ||||||||
\(213\) | 10.7866i | 0.739084i | ||||||||
\(214\) | 2.79918 | 0.191348 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.153106 | 0.0104175 | ||||||||
\(217\) | − 1.08675i | − 0.0737736i | ||||||||
\(218\) | 17.8807i | 1.21103i | ||||||||
\(219\) | 8.63115 | 0.583239 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.606177 | 0.0407759 | ||||||||
\(222\) | − 8.12840i | − 0.545543i | ||||||||
\(223\) | − 8.03245i | − 0.537893i | −0.963155 | − | 0.268946i | \(-0.913325\pi\) | ||||
0.963155 | − | 0.268946i | \(-0.0866755\pi\) | |||||||
\(224\) | −8.21604 | −0.548957 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3051 | −0.885044 | ||||||||
\(227\) | − 16.4576i | − 1.09233i | −0.837677 | − | 0.546166i | \(-0.816087\pi\) | ||||
0.837677 | − | 0.546166i | \(-0.183913\pi\) | |||||||
\(228\) | 1.50375i | 0.0995880i | ||||||||
\(229\) | −0.409285 | −0.0270463 | −0.0135231 | − | 0.999909i | \(-0.504305\pi\) | ||||
−0.0135231 | + | 0.999909i | \(0.504305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.84943 | −0.319069 | ||||||||
\(232\) | − 0.610658i | − 0.0400917i | ||||||||
\(233\) | − 18.4641i | − 1.20962i | −0.796369 | − | 0.604811i | \(-0.793249\pi\) | ||||
0.796369 | − | 0.604811i | \(-0.206751\pi\) | |||||||
\(234\) | −0.209634 | −0.0137042 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.1983 | −0.663852 | ||||||||
\(237\) | 2.48291i | 0.161283i | ||||||||
\(238\) | 12.0081i | 0.778369i | ||||||||
\(239\) | 4.61682 | 0.298637 | 0.149319 | − | 0.988789i | \(-0.452292\pi\) | ||||
0.149319 | + | 0.988789i | \(0.452292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.2022 | −1.88108 | −0.940540 | − | 0.339682i | \(-0.889681\pi\) | ||||
−0.940540 | + | 0.339682i | \(0.889681\pi\) | |||||||
\(242\) | 23.5277i | 1.51242i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −14.4569 | −0.925506 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.5556 | 0.928030 | ||||||||
\(247\) | − 0.0752201i | − 0.00478614i | ||||||||
\(248\) | − 0.163307i | − 0.0103700i | ||||||||
\(249\) | 4.24385 | 0.268943 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.389664 | 0.0245954 | 0.0122977 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122977 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(252\) | − 2.11501i | − 0.133233i | ||||||||
\(253\) | − 43.1769i | − 2.71451i | ||||||||
\(254\) | −14.7205 | −0.923645 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.7185 | 0.919906 | ||||||||
\(257\) | − 8.03324i | − 0.501100i | −0.968104 | − | 0.250550i | \(-0.919389\pi\) | ||||
0.968104 | − | 0.250550i | \(-0.0806114\pi\) | |||||||
\(258\) | 17.4186i | 1.08444i | ||||||||
\(259\) | −4.10219 | −0.254898 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.98847 | −0.246880 | ||||||||
\(262\) | − 19.2880i | − 1.19162i | ||||||||
\(263\) | − 24.2131i | − 1.49304i | −0.665360 | − | 0.746522i | \(-0.731722\pi\) | ||||
0.665360 | − | 0.746522i | \(-0.268278\pi\) | |||||||
\(264\) | −0.728724 | −0.0448499 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.49008 | 0.0913624 | ||||||||
\(267\) | − 18.3752i | − 1.12454i | ||||||||
\(268\) | − 20.5923i | − 1.25787i | ||||||||
\(269\) | −26.4063 | −1.61002 | −0.805009 | − | 0.593263i | \(-0.797839\pi\) | ||||
−0.805009 | + | 0.593263i | \(0.797839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4088 | −0.632287 | −0.316144 | − | 0.948711i | \(-0.602388\pi\) | ||||
−0.316144 | + | 0.948711i | \(0.602388\pi\) | |||||||
\(272\) | − 22.4320i | − 1.36014i | ||||||||
\(273\) | 0.105797i | 0.00640310i | ||||||||
\(274\) | −12.5167 | −0.756160 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.8310 | 1.13349 | ||||||||
\(277\) | 24.5207i | 1.47330i | 0.676272 | + | 0.736652i | \(0.263595\pi\) | ||||
−0.676272 | + | 0.736652i | \(0.736405\pi\) | |||||||
\(278\) | 1.83017i | 0.109766i | ||||||||
\(279\) | −1.06662 | −0.0638572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4228 | −0.860393 | −0.430197 | − | 0.902735i | \(-0.641556\pi\) | ||||
−0.430197 | + | 0.902735i | \(0.641556\pi\) | |||||||
\(282\) | 16.5506i | 0.985576i | ||||||||
\(283\) | 2.14925i | 0.127760i | 0.997958 | + | 0.0638798i | \(0.0203474\pi\) | ||||
−0.997958 | + | 0.0638798i | \(0.979653\pi\) | |||||||
\(284\) | 22.3912 | 1.32867 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.997775 | 0.0589997 | ||||||||
\(287\) | − 7.34582i | − 0.433610i | ||||||||
\(288\) | 8.06387i | 0.475168i | ||||||||
\(289\) | −17.0795 | −1.00468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.69876 | −0.392688 | ||||||||
\(292\) | − 17.9169i | − 1.04851i | ||||||||
\(293\) | − 9.02970i | − 0.527521i | −0.964588 | − | 0.263760i | \(-0.915037\pi\) | ||||
0.964588 | − | 0.263760i | \(-0.0849628\pi\) | |||||||
\(294\) | 12.0363 | 0.701972 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.616437 | −0.0358297 | ||||||||
\(297\) | 4.75961i | 0.276181i | ||||||||
\(298\) | 9.88860i | 0.572831i | ||||||||
\(299\) | −0.941960 | −0.0544750 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.79072 | 0.506689 | ||||||||
\(302\) | − 20.7189i | − 1.19224i | ||||||||
\(303\) | − 5.66147i | − 0.325243i | ||||||||
\(304\) | −2.78358 | −0.159649 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.7857 | 0.673743 | ||||||||
\(307\) | − 5.03454i | − 0.287336i | −0.989626 | − | 0.143668i | \(-0.954110\pi\) | ||||
0.989626 | − | 0.143668i | \(-0.0458898\pi\) | |||||||
\(308\) | 10.0666i | 0.573599i | ||||||||
\(309\) | 0.594489 | 0.0338193 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.89158 | −0.277376 | −0.138688 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138688 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(312\) | 0.0158981i | 0 0.000900051i | ||||||||
\(313\) | − 3.17282i | − 0.179338i | −0.995972 | − | 0.0896691i | \(-0.971419\pi\) | ||||
0.995972 | − | 0.0896691i | \(-0.0285810\pi\) | |||||||
\(314\) | −17.9586 | −1.01346 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.15413 | 0.289942 | ||||||||
\(317\) | 19.9953i | 1.12305i | 0.827461 | + | 0.561524i | \(0.189785\pi\) | ||||
−0.827461 | + | 0.561524i | \(0.810215\pi\) | |||||||
\(318\) | − 8.81680i | − 0.494422i | ||||||||
\(319\) | 18.9836 | 1.06288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.38651 | −0.0773872 | ||||||||
\(322\) | − 18.6598i | − 1.03987i | ||||||||
\(323\) | 4.22890i | 0.235302i | ||||||||
\(324\) | −2.07584 | −0.115324 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.7804 | −1.31707 | ||||||||
\(327\) | − 8.85677i | − 0.489780i | ||||||||
\(328\) | − 1.10386i | − 0.0609503i | ||||||||
\(329\) | 8.35267 | 0.460498 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.01724 | 0.330738 | 0.165369 | − | 0.986232i | \(-0.447119\pi\) | ||||
0.165369 | + | 0.986232i | \(0.447119\pi\) | |||||||
\(332\) | − 8.80954i | − 0.483486i | ||||||||
\(333\) | 4.02621i | 0.220635i | ||||||||
\(334\) | 35.0803 | 1.91951 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.91508 | 0.213585 | ||||||||
\(337\) | − 22.8136i | − 1.24274i | −0.783518 | − | 0.621369i | \(-0.786577\pi\) | ||||
0.783518 | − | 0.621369i | \(-0.213423\pi\) | |||||||
\(338\) | 26.2235i | 1.42637i | ||||||||
\(339\) | 6.59039 | 0.357941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.07672 | 0.274920 | ||||||||
\(342\) | − 1.46248i | − 0.0790818i | ||||||||
\(343\) | − 13.2065i | − 0.713084i | ||||||||
\(344\) | 1.32098 | 0.0712227 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.1637 | 1.40657 | ||||||||
\(347\) | − 9.79068i | − 0.525591i | −0.964852 | − | 0.262796i | \(-0.915356\pi\) | ||||
0.964852 | − | 0.262796i | \(-0.0846445\pi\) | |||||||
\(348\) | 8.27942i | 0.443823i | ||||||||
\(349\) | 1.28648 | 0.0688639 | 0.0344320 | − | 0.999407i | \(-0.489038\pi\) | ||||
0.0344320 | + | 0.999407i | \(0.489038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.103837 | 0.00554242 | ||||||||
\(352\) | − 38.3809i | − 2.04571i | ||||||||
\(353\) | 1.16422i | 0.0619654i | 0.999520 | + | 0.0309827i | \(0.00986368\pi\) | ||||
−0.999520 | + | 0.0309827i | \(0.990136\pi\) | |||||||
\(354\) | 9.91841 | 0.527158 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −38.1439 | −2.02162 | ||||||||
\(357\) | − 5.94793i | − 0.314798i | ||||||||
\(358\) | − 2.21868i | − 0.117261i | ||||||||
\(359\) | −19.0504 | −1.00544 | −0.502720 | − | 0.864449i | \(-0.667667\pi\) | ||||
−0.502720 | + | 0.864449i | \(0.667667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4752 | −0.972381 | ||||||||
\(362\) | − 30.2421i | − 1.58949i | ||||||||
\(363\) | − 11.6539i | − 0.611671i | ||||||||
\(364\) | 0.219617 | 0.0115110 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0601 | 0.734935 | ||||||||
\(367\) | − 16.7694i | − 0.875357i | −0.899131 | − | 0.437679i | \(-0.855801\pi\) | ||||
0.899131 | − | 0.437679i | \(-0.144199\pi\) | |||||||
\(368\) | 34.8580i | 1.81710i | ||||||||
\(369\) | −7.20977 | −0.375326 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.44960 | −0.231012 | ||||||||
\(372\) | 2.21414i | 0.114798i | ||||||||
\(373\) | − 17.0520i | − 0.882920i | −0.897281 | − | 0.441460i | \(-0.854461\pi\) | ||||
0.897281 | − | 0.441460i | \(-0.145539\pi\) | |||||||
\(374\) | −56.0953 | −2.90062 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.25516 | 0.0647298 | ||||||||
\(377\) | − 0.414152i | − 0.0213299i | ||||||||
\(378\) | 2.05697i | 0.105799i | ||||||||
\(379\) | −1.66611 | −0.0855825 | −0.0427913 | − | 0.999084i | \(-0.513625\pi\) | ||||
−0.0427913 | + | 0.999084i | \(0.513625\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.29144 | 0.373552 | ||||||||
\(382\) | − 25.7212i | − 1.31601i | ||||||||
\(383\) | 3.05361i | 0.156032i | 0.996952 | + | 0.0780162i | \(0.0248586\pi\) | ||||
−0.996952 | + | 0.0780162i | \(0.975141\pi\) | |||||||
\(384\) | 1.22397 | 0.0624603 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.85045 | 0.450476 | ||||||||
\(387\) | − 8.62791i | − 0.438581i | ||||||||
\(388\) | 13.9055i | 0.705947i | ||||||||
\(389\) | −28.2725 | −1.43347 | −0.716737 | − | 0.697343i | \(-0.754365\pi\) | ||||
−0.716737 | + | 0.697343i | \(0.754365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.9574 | 2.67817 | ||||||||
\(392\) | − 0.912802i | − 0.0461035i | ||||||||
\(393\) | 9.55386i | 0.481928i | ||||||||
\(394\) | 6.50410 | 0.327672 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.88018 | 0.496498 | ||||||||
\(397\) | 20.4783i | 1.02778i | 0.857858 | + | 0.513888i | \(0.171795\pi\) | ||||
−0.857858 | + | 0.513888i | \(0.828205\pi\) | |||||||
\(398\) | 5.46140i | 0.273755i | ||||||||
\(399\) | −0.738074 | −0.0369499 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.5952 | 1.27816 | 0.639081 | − | 0.769139i | \(-0.279315\pi\) | ||||
0.639081 | + | 0.769139i | \(0.279315\pi\) | |||||||
\(402\) | 20.0271i | 0.998863i | ||||||||
\(403\) | − 0.110755i | − 0.00551711i | ||||||||
\(404\) | −11.7523 | −0.584698 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.20416 | 0.407165 | ||||||||
\(407\) | − 19.1632i | − 0.949885i | ||||||||
\(408\) | − 0.893796i | − 0.0442495i | ||||||||
\(409\) | 12.0402 | 0.595349 | 0.297675 | − | 0.954667i | \(-0.403789\pi\) | ||||
0.297675 | + | 0.954667i | \(0.403789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.19984 | 0.305816 | ||||||||
\(412\) | − 1.23406i | − 0.0607979i | ||||||||
\(413\) | − 5.00556i | − 0.246307i | ||||||||
\(414\) | −18.3142 | −0.900095 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.837329 | −0.0410534 | ||||||||
\(417\) | − 0.906531i | − 0.0443930i | ||||||||
\(418\) | 6.96083i | 0.340465i | ||||||||
\(419\) | 34.6045 | 1.69054 | 0.845270 | − | 0.534340i | \(-0.179440\pi\) | ||||
0.845270 | + | 0.534340i | \(0.179440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9525 | −0.728738 | −0.364369 | − | 0.931255i | \(-0.618715\pi\) | ||||
−0.364369 | + | 0.931255i | \(0.618715\pi\) | |||||||
\(422\) | 53.3859i | 2.59879i | ||||||||
\(423\) | − 8.19797i | − 0.398599i | ||||||||
\(424\) | −0.668643 | −0.0324722 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −21.7767 | −1.05508 | ||||||||
\(427\) | − 7.09577i | − 0.343389i | ||||||||
\(428\) | 2.87816i | 0.139121i | ||||||||
\(429\) | −0.494225 | −0.0238614 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.81107 | 0.231741 | 0.115871 | − | 0.993264i | \(-0.463034\pi\) | ||||
0.115871 | + | 0.993264i | \(0.463034\pi\) | |||||||
\(432\) | − 3.84257i | − 0.184876i | ||||||||
\(433\) | 10.3435i | 0.497077i | 0.968622 | + | 0.248538i | \(0.0799502\pi\) | ||||
−0.968622 | + | 0.248538i | \(0.920050\pi\) | |||||||
\(434\) | 2.19401 | 0.105316 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.3852 | −0.880492 | ||||||||
\(437\) | − 6.57145i | − 0.314355i | ||||||||
\(438\) | 17.4252i | 0.832607i | ||||||||
\(439\) | −30.7640 | −1.46829 | −0.734143 | − | 0.678995i | \(-0.762416\pi\) | ||||
−0.734143 | + | 0.678995i | \(0.762416\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.96190 | −0.283900 | ||||||||
\(442\) | 1.22379i | 0.0582099i | ||||||||
\(443\) | − 17.7545i | − 0.843543i | −0.906702 | − | 0.421772i | \(-0.861408\pi\) | ||||
0.906702 | − | 0.421772i | \(-0.138592\pi\) | |||||||
\(444\) | 8.35776 | 0.396642 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.2165 | 0.767873 | ||||||||
\(447\) | − 4.89808i | − 0.231671i | ||||||||
\(448\) | − 8.75695i | − 0.413727i | ||||||||
\(449\) | 37.2184 | 1.75645 | 0.878223 | − | 0.478251i | \(-0.158729\pi\) | ||||
0.878223 | + | 0.478251i | \(0.158729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.3157 | 1.61586 | ||||||||
\(452\) | − 13.6806i | − 0.643480i | ||||||||
\(453\) | 10.2626i | 0.482181i | ||||||||
\(454\) | 33.2258 | 1.55937 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.110911 | −0.00519386 | ||||||||
\(457\) | 27.6987i | 1.29569i | 0.761772 | + | 0.647846i | \(0.224330\pi\) | ||||
−0.761772 | + | 0.647846i | \(0.775670\pi\) | |||||||
\(458\) | − 0.826293i | − 0.0386101i | ||||||||
\(459\) | −5.83776 | −0.272484 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.81742 | 0.457243 | 0.228621 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228621 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(462\) | − 9.79036i | − 0.455489i | ||||||||
\(463\) | − 3.72732i | − 0.173223i | −0.996242 | − | 0.0866115i | \(-0.972396\pi\) | ||||
0.996242 | − | 0.0866115i | \(-0.0276039\pi\) | |||||||
\(464\) | −15.3260 | −0.711492 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.2766 | 1.72680 | ||||||||
\(467\) | 7.09925i | 0.328514i | 0.986418 | + | 0.164257i | \(0.0525227\pi\) | ||||
−0.986418 | + | 0.164257i | \(0.947477\pi\) | |||||||
\(468\) | − 0.215549i | − 0.00996376i | ||||||||
\(469\) | 10.1072 | 0.466706 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.89537 | 0.409877 | ||||||||
\(472\) | − 0.752186i | − 0.0346222i | ||||||||
\(473\) | 41.0655i | 1.88819i | ||||||||
\(474\) | −5.01268 | −0.230240 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.3469 | −0.565920 | ||||||||
\(477\) | 4.36719i | 0.199960i | ||||||||
\(478\) | 9.32076i | 0.426322i | ||||||||
\(479\) | 28.4451 | 1.29969 | 0.649845 | − | 0.760066i | \(-0.274834\pi\) | ||||
0.649845 | + | 0.760066i | \(0.274834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.418070 | −0.0190624 | ||||||||
\(482\) | − 58.9555i | − 2.68535i | ||||||||
\(483\) | 9.24270i | 0.420557i | ||||||||
\(484\) | −24.1916 | −1.09962 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.01887 | 0.0915778 | ||||||||
\(487\) | 14.7384i | 0.667860i | 0.942598 | + | 0.333930i | \(0.108375\pi\) | ||||
−0.942598 | + | 0.333930i | \(0.891625\pi\) | |||||||
\(488\) | − 1.06628i | − 0.0482684i | ||||||||
\(489\) | 11.7791 | 0.532668 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.4014 | −1.28174 | −0.640869 | − | 0.767650i | \(-0.721426\pi\) | ||||
−0.640869 | + | 0.767650i | \(0.721426\pi\) | |||||||
\(492\) | 14.9663i | 0.674733i | ||||||||
\(493\) | 23.2838i | 1.04865i | ||||||||
\(494\) | 0.151860 | 0.00683248 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.09858 | −0.184032 | ||||||||
\(497\) | 10.9901i | 0.492974i | ||||||||
\(498\) | 8.56778i | 0.383931i | ||||||||
\(499\) | −26.3842 | −1.18112 | −0.590559 | − | 0.806995i | \(-0.701093\pi\) | ||||
−0.590559 | + | 0.806995i | \(0.701093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3762 | −0.776312 | ||||||||
\(502\) | 0.786682i | 0.0351113i | ||||||||
\(503\) | 16.6592i | 0.742795i | 0.928474 | + | 0.371398i | \(0.121121\pi\) | ||||
−0.928474 | + | 0.371398i | \(0.878879\pi\) | |||||||
\(504\) | 0.155995 | 0.00694857 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 87.1686 | 3.87512 | ||||||||
\(507\) | − 12.9892i | − 0.576871i | ||||||||
\(508\) | − 15.1358i | − 0.671544i | ||||||||
\(509\) | 31.7760 | 1.40845 | 0.704223 | − | 0.709979i | \(-0.251296\pi\) | ||||
0.704223 | + | 0.709979i | \(0.251296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.79403 | 0.389025 | ||||||||
\(512\) | 32.1627i | 1.42140i | ||||||||
\(513\) | 0.724404i | 0.0319832i | ||||||||
\(514\) | 16.2181 | 0.715349 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −17.9101 | −0.788450 | ||||||||
\(517\) | 39.0192i | 1.71606i | ||||||||
\(518\) | − 8.28179i | − 0.363881i | ||||||||
\(519\) | −12.9596 | −0.568862 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.592363 | −0.0259519 | −0.0129759 | − | 0.999916i | \(-0.504130\pi\) | ||||
−0.0129759 | + | 0.999916i | \(0.504130\pi\) | |||||||
\(522\) | − 8.05221i | − 0.352436i | ||||||||
\(523\) | − 17.2298i | − 0.753405i | −0.926334 | − | 0.376703i | \(-0.877058\pi\) | ||||
0.926334 | − | 0.376703i | \(-0.122942\pi\) | |||||||
\(524\) | 19.8323 | 0.866376 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.8832 | 2.13141 | ||||||||
\(527\) | 6.22670i | 0.271240i | ||||||||
\(528\) | 18.2892i | 0.795934i | ||||||||
\(529\) | −59.2924 | −2.57793 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.91285 | −0.213200 | ||||||||
\(532\) | 1.53212i | 0.0664259i | ||||||||
\(533\) | − 0.748642i | − 0.0324273i | ||||||||
\(534\) | 37.0971 | 1.60535 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.51881 | 0.0656025 | ||||||||
\(537\) | 1.09897i | 0.0474241i | ||||||||
\(538\) | − 53.3108i | − 2.29839i | ||||||||
\(539\) | 28.3763 | 1.22226 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7990 | 0.636258 | 0.318129 | − | 0.948047i | \(-0.396945\pi\) | ||||
0.318129 | + | 0.948047i | \(0.396945\pi\) | |||||||
\(542\) | − 21.0139i | − 0.902626i | ||||||||
\(543\) | 14.9797i | 0.642840i | ||||||||
\(544\) | 47.0750 | 2.01832 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.213590 | −0.00914079 | ||||||||
\(547\) | − 6.50806i | − 0.278264i | −0.990274 | − | 0.139132i | \(-0.955569\pi\) | ||||
0.990274 | − | 0.139132i | \(-0.0444313\pi\) | |||||||
\(548\) | − 12.8699i | − 0.549773i | ||||||||
\(549\) | −6.96435 | −0.297231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.88927 | 0.123087 | ||||||||
\(552\) | 1.38890i | 0.0591156i | ||||||||
\(553\) | 2.52977i | 0.107577i | ||||||||
\(554\) | −49.5041 | −2.10323 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.88181 | −0.0798066 | ||||||||
\(557\) | 6.67224i | 0.282712i | 0.989959 | + | 0.141356i | \(0.0451462\pi\) | ||||
−0.989959 | + | 0.141356i | \(0.954854\pi\) | |||||||
\(558\) | − 2.15338i | − 0.0911597i | ||||||||
\(559\) | 0.895898 | 0.0378924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.7855 | 1.17310 | ||||||||
\(562\) | − 29.1178i | − 1.22826i | ||||||||
\(563\) | 20.0663i | 0.845694i | 0.906201 | + | 0.422847i | \(0.138969\pi\) | ||||
−0.906201 | + | 0.422847i | \(0.861031\pi\) | |||||||
\(564\) | −17.0177 | −0.716573 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.33906 | −0.182384 | ||||||||
\(567\) | − 1.01887i | − 0.0427885i | ||||||||
\(568\) | 1.65149i | 0.0692949i | ||||||||
\(569\) | 21.5938 | 0.905261 | 0.452631 | − | 0.891698i | \(-0.350486\pi\) | ||||
0.452631 | + | 0.891698i | \(0.350486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.3338 | −1.10203 | −0.551017 | − | 0.834494i | \(-0.685760\pi\) | ||||
−0.551017 | + | 0.834494i | \(0.685760\pi\) | |||||||
\(572\) | 1.02593i | 0.0428963i | ||||||||
\(573\) | 12.7404i | 0.532237i | ||||||||
\(574\) | 14.8303 | 0.619003 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.59476 | −0.358115 | ||||||||
\(577\) | 9.18240i | 0.382268i | 0.981564 | + | 0.191134i | \(0.0612165\pi\) | ||||
−0.981564 | + | 0.191134i | \(0.938783\pi\) | |||||||
\(578\) | − 34.4813i | − 1.43423i | ||||||||
\(579\) | −4.38386 | −0.182187 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.32393 | 0.179387 | ||||||||
\(582\) | − 13.5239i | − 0.560585i | ||||||||
\(583\) | − 20.7861i | − 0.860874i | ||||||||
\(584\) | 1.32148 | 0.0546832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.2298 | 0.753066 | ||||||||
\(587\) | − 39.9771i | − 1.65003i | −0.565108 | − | 0.825017i | \(-0.691166\pi\) | ||||
0.565108 | − | 0.825017i | \(-0.308834\pi\) | |||||||
\(588\) | 12.3759i | 0.510375i | ||||||||
\(589\) | 0.772668 | 0.0318372 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.22165 | −0.132521 | ||||||||
\(592\) | 15.4710i | 0.635855i | ||||||||
\(593\) | − 41.6331i | − 1.70967i | −0.518902 | − | 0.854834i | \(-0.673659\pi\) | ||||
0.518902 | − | 0.854834i | \(-0.326341\pi\) | |||||||
\(594\) | −9.60904 | −0.394264 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.1676 | −0.416482 | ||||||||
\(597\) | − 2.70518i | − 0.110716i | ||||||||
\(598\) | − 1.90170i | − 0.0777661i | ||||||||
\(599\) | −39.0726 | −1.59646 | −0.798232 | − | 0.602350i | \(-0.794231\pi\) | ||||
−0.798232 | + | 0.602350i | \(0.794231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.46965 | 0.223112 | 0.111556 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111556 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(602\) | 17.7473i | 0.723327i | ||||||||
\(603\) | − 9.91998i | − 0.403973i | ||||||||
\(604\) | 21.3036 | 0.866829 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.4298 | 0.464303 | ||||||||
\(607\) | − 42.3108i | − 1.71734i | −0.512527 | − | 0.858671i | \(-0.671291\pi\) | ||||
0.512527 | − | 0.858671i | \(-0.328709\pi\) | |||||||
\(608\) | − 5.84150i | − 0.236904i | ||||||||
\(609\) | −4.06374 | −0.164671 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.851254 | 0.0344380 | ||||||||
\(612\) | 12.1183i | 0.489851i | ||||||||
\(613\) | − 34.0064i | − 1.37351i | −0.726891 | − | 0.686753i | \(-0.759035\pi\) | ||||
0.726891 | − | 0.686753i | \(-0.240965\pi\) | |||||||
\(614\) | 10.1641 | 0.410189 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.742476 | −0.0299152 | ||||||||
\(617\) | − 23.3173i | − 0.938717i | −0.883008 | − | 0.469359i | \(-0.844485\pi\) | ||||
0.883008 | − | 0.469359i | \(-0.155515\pi\) | |||||||
\(618\) | 1.20020i | 0.0482790i | ||||||||
\(619\) | −35.2998 | −1.41882 | −0.709409 | − | 0.704797i | \(-0.751038\pi\) | ||||
−0.709409 | + | 0.704797i | \(0.751038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.07152 | 0.364027 | ||||||||
\(622\) | − 9.87547i | − 0.395970i | ||||||||
\(623\) | − 18.7219i | − 0.750079i | ||||||||
\(624\) | 0.399002 | 0.0159729 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.40551 | 0.256016 | ||||||||
\(627\) | − 3.44788i | − 0.137695i | ||||||||
\(628\) | − 18.4653i | − 0.736847i | ||||||||
\(629\) | 23.5041 | 0.937169 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.50433 | −0.139505 | −0.0697526 | − | 0.997564i | \(-0.522221\pi\) | ||||
−0.0697526 | + | 0.997564i | \(0.522221\pi\) | |||||||
\(632\) | 0.380149i | 0.0151215i | ||||||||
\(633\) | − 26.4435i | − 1.05103i | ||||||||
\(634\) | −40.3679 | −1.60321 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.06559 | 0.359474 | ||||||||
\(637\) | − 0.619067i | − 0.0245283i | ||||||||
\(638\) | 38.3254i | 1.51732i | ||||||||
\(639\) | 10.7866 | 0.426710 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.28841 | −0.366870 | −0.183435 | − | 0.983032i | \(-0.558722\pi\) | ||||
−0.183435 | + | 0.983032i | \(0.558722\pi\) | |||||||
\(642\) | − 2.79918i | − 0.110475i | ||||||||
\(643\) | − 0.0291680i | − 0.00115028i | −1.00000 | 0.000575138i | \(-0.999817\pi\) | |||||
1.00000 | 0.000575138i | \(-0.000183072\pi\) | ||||||||
\(644\) | 19.1863 | 0.756048 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.53760 | −0.335908 | ||||||||
\(647\) | 0.844100i | 0.0331850i | 0.999862 | + | 0.0165925i | \(0.00528180\pi\) | ||||
−0.999862 | + | 0.0165925i | \(0.994718\pi\) | |||||||
\(648\) | − 0.153106i | − 0.00601457i | ||||||||
\(649\) | 23.3833 | 0.917874 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.08675 | −0.0425932 | ||||||||
\(652\) | − 24.4514i | − 0.957591i | ||||||||
\(653\) | 38.0711i | 1.48984i | 0.667156 | + | 0.744918i | \(0.267511\pi\) | ||||
−0.667156 | + | 0.744918i | \(0.732489\pi\) | |||||||
\(654\) | 17.8807 | 0.699189 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.7041 | −1.08166 | ||||||||
\(657\) | − 8.63115i | − 0.336733i | ||||||||
\(658\) | 16.8630i | 0.657387i | ||||||||
\(659\) | −37.8343 | −1.47382 | −0.736908 | − | 0.675993i | \(-0.763715\pi\) | ||||
−0.736908 | + | 0.675993i | \(0.763715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.5614 | −0.721956 | −0.360978 | − | 0.932574i | \(-0.617557\pi\) | ||||
−0.360978 | + | 0.932574i | \(0.617557\pi\) | |||||||
\(662\) | 12.1480i | 0.472147i | ||||||||
\(663\) | − 0.606177i | − 0.0235420i | ||||||||
\(664\) | 0.649758 | 0.0252155 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.12840 | −0.314969 | ||||||||
\(667\) | − 36.1815i | − 1.40095i | ||||||||
\(668\) | 36.0702i | 1.39560i | ||||||||
\(669\) | −8.03245 | −0.310553 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.1476 | 1.27965 | ||||||||
\(672\) | 8.21604i | 0.316941i | ||||||||
\(673\) | 18.1607i | 0.700044i | 0.936742 | + | 0.350022i | \(0.113826\pi\) | ||||
−0.936742 | + | 0.350022i | \(0.886174\pi\) | |||||||
\(674\) | 46.0578 | 1.77408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.9635 | −1.03706 | ||||||||
\(677\) | 5.64312i | 0.216883i | 0.994103 | + | 0.108441i | \(0.0345860\pi\) | ||||
−0.994103 | + | 0.108441i | \(0.965414\pi\) | |||||||
\(678\) | 13.3051i | 0.510981i | ||||||||
\(679\) | −6.82517 | −0.261926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.4576 | −0.630658 | ||||||||
\(682\) | 10.2492i | 0.392464i | ||||||||
\(683\) | 30.4468i | 1.16502i | 0.812825 | + | 0.582508i | \(0.197929\pi\) | ||||
−0.812825 | + | 0.582508i | \(0.802071\pi\) | |||||||
\(684\) | 1.50375 | 0.0574971 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.6622 | 1.01797 | ||||||||
\(687\) | 0.409285i | 0.0156152i | ||||||||
\(688\) | − 33.1534i | − 1.26396i | ||||||||
\(689\) | −0.453477 | −0.0172761 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.22470 | −0.350924 | −0.175462 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175462 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(692\) | 26.9020i | 1.02266i | ||||||||
\(693\) | 4.84943i | 0.184215i | ||||||||
\(694\) | 19.7661 | 0.750311 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.610658 | −0.0231469 | ||||||||
\(697\) | 42.0889i | 1.59423i | ||||||||
\(698\) | 2.59724i | 0.0983071i | ||||||||
\(699\) | −18.4641 | −0.698375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9822 | −0.754717 | −0.377358 | − | 0.926067i | \(-0.623168\pi\) | ||||
−0.377358 | + | 0.926067i | \(0.623168\pi\) | |||||||
\(702\) | 0.209634i | 0.00791212i | ||||||||
\(703\) | − 2.91661i | − 0.110002i | ||||||||
\(704\) | 40.9077 | 1.54177 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.35042 | −0.0884591 | ||||||||
\(707\) | − 5.76830i | − 0.216939i | ||||||||
\(708\) | 10.1983i | 0.383275i | ||||||||
\(709\) | 26.8259 | 1.00747 | 0.503734 | − | 0.863859i | \(-0.331959\pi\) | ||||
0.503734 | + | 0.863859i | \(0.331959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.48291 | 0.0931166 | ||||||||
\(712\) | − 2.81335i | − 0.105435i | ||||||||
\(713\) | − 9.67591i | − 0.362366i | ||||||||
\(714\) | 12.0081 | 0.449391 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.28128 | 0.0852556 | ||||||||
\(717\) | − 4.61682i | − 0.172418i | ||||||||
\(718\) | − 38.4602i | − 1.43532i | ||||||||
\(719\) | −38.8224 | −1.44783 | −0.723915 | − | 0.689889i | \(-0.757659\pi\) | ||||
−0.723915 | + | 0.689889i | \(0.757659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.605707 | 0.0225577 | ||||||||
\(722\) | − 37.2991i | − 1.38813i | ||||||||
\(723\) | 29.2022i | 1.08604i | ||||||||
\(724\) | 31.0954 | 1.15565 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.5277 | 0.873196 | ||||||||
\(727\) | − 29.5764i | − 1.09693i | −0.836174 | − | 0.548465i | \(-0.815213\pi\) | ||||
0.836174 | − | 0.548465i | \(-0.184787\pi\) | |||||||
\(728\) | 0.0161981i | 0 0.000600341i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.3677 | −1.86292 | ||||||||
\(732\) | 14.4569i | 0.534341i | ||||||||
\(733\) | − 48.8782i | − 1.80536i | −0.430315 | − | 0.902679i | \(-0.641598\pi\) | ||||
0.430315 | − | 0.902679i | \(-0.358402\pi\) | |||||||
\(734\) | 33.8553 | 1.24962 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −73.1515 | −2.69640 | ||||||||
\(737\) | 47.2152i | 1.73920i | ||||||||
\(738\) | − 14.5556i | − 0.535799i | ||||||||
\(739\) | −21.7603 | −0.800466 | −0.400233 | − | 0.916413i | \(-0.631071\pi\) | ||||
−0.400233 | + | 0.916413i | \(0.631071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0752201 | −0.00276328 | ||||||||
\(742\) | − 8.98317i | − 0.329783i | ||||||||
\(743\) | − 9.75724i | − 0.357959i | −0.983853 | − | 0.178979i | \(-0.942720\pi\) | ||||
0.983853 | − | 0.178979i | \(-0.0572795\pi\) | |||||||
\(744\) | −0.163307 | −0.00598711 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34.4258 | 1.26042 | ||||||||
\(747\) | − 4.24385i | − 0.155274i | ||||||||
\(748\) | − 57.6782i | − 2.10892i | ||||||||
\(749\) | −1.41267 | −0.0516178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6413 | −0.643741 | −0.321871 | − | 0.946784i | \(-0.604312\pi\) | ||||
−0.321871 | + | 0.946784i | \(0.604312\pi\) | |||||||
\(752\) | − 31.5013i | − 1.14873i | ||||||||
\(753\) | − 0.389664i | − 0.0142002i | ||||||||
\(754\) | 0.836118 | 0.0304496 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.11501 | −0.0769221 | ||||||||
\(757\) | 44.2551i | 1.60848i | 0.594305 | + | 0.804240i | \(0.297427\pi\) | ||||
−0.594305 | + | 0.804240i | \(0.702573\pi\) | |||||||
\(758\) | − 3.36367i | − 0.122174i | ||||||||
\(759\) | −43.1769 | −1.56722 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.8755 | 1.44549 | 0.722743 | − | 0.691117i | \(-0.242881\pi\) | ||||
0.722743 | + | 0.691117i | \(0.242881\pi\) | |||||||
\(762\) | 14.7205i | 0.533266i | ||||||||
\(763\) | − 9.02390i | − 0.326687i | ||||||||
\(764\) | 26.4470 | 0.956818 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.16485 | −0.222745 | ||||||||
\(767\) | − 0.510137i | − 0.0184200i | ||||||||
\(768\) | − 14.7185i | − 0.531108i | ||||||||
\(769\) | −35.2667 | −1.27175 | −0.635876 | − | 0.771792i | \(-0.719361\pi\) | ||||
−0.635876 | + | 0.771792i | \(0.719361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.03324 | −0.289310 | ||||||||
\(772\) | 9.10018i | 0.327523i | ||||||||
\(773\) | − 23.2417i | − 0.835946i | −0.908459 | − | 0.417973i | \(-0.862741\pi\) | ||||
0.908459 | − | 0.417973i | \(-0.137259\pi\) | |||||||
\(774\) | 17.4186 | 0.626100 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.02562 | −0.0368176 | ||||||||
\(777\) | 4.10219i | 0.147165i | ||||||||
\(778\) | − 57.0786i | − 2.04637i | ||||||||
\(779\) | 5.22279 | 0.187126 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.3399 | −1.83709 | ||||||||
\(782\) | 106.914i | 3.82324i | ||||||||
\(783\) | 3.98847i | 0.142536i | ||||||||
\(784\) | −22.9091 | −0.818180 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.2880 | −0.687980 | ||||||||
\(787\) | − 6.83095i | − 0.243497i | −0.992561 | − | 0.121749i | \(-0.961150\pi\) | ||||
0.992561 | − | 0.121749i | \(-0.0388502\pi\) | |||||||
\(788\) | 6.68762i | 0.238237i | ||||||||
\(789\) | −24.2131 | −0.862010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.71475 | 0.238749 | ||||||||
\(792\) | 0.728724i | 0.0258941i | ||||||||
\(793\) | − 0.723159i | − 0.0256801i | ||||||||
\(794\) | −41.3430 | −1.46721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.61551 | −0.199036 | ||||||||
\(797\) | − 53.9287i | − 1.91025i | −0.296198 | − | 0.955126i | \(-0.595719\pi\) | ||||
0.296198 | − | 0.955126i | \(-0.404281\pi\) | |||||||
\(798\) | − 1.49008i | − 0.0527481i | ||||||||
\(799\) | −47.8578 | −1.69309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3752 | −0.649256 | ||||||||
\(802\) | 51.6734i | 1.82465i | ||||||||
\(803\) | 41.0809i | 1.44971i | ||||||||
\(804\) | −20.5923 | −0.726233 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.223601 | 0.00787599 | ||||||||
\(807\) | 26.4063i | 0.929544i | ||||||||
\(808\) | − 0.866804i | − 0.0304941i | ||||||||
\(809\) | 18.4104 | 0.647275 | 0.323637 | − | 0.946181i | \(-0.395094\pi\) | ||||
0.323637 | + | 0.946181i | \(0.395094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.7910 | −0.414040 | −0.207020 | − | 0.978337i | \(-0.566376\pi\) | ||||
−0.207020 | + | 0.978337i | \(0.566376\pi\) | |||||||
\(812\) | 8.43565i | 0.296033i | ||||||||
\(813\) | 10.4088i | 0.365051i | ||||||||
\(814\) | 38.6880 | 1.35601 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −22.4320 | −0.785279 | ||||||||
\(817\) | 6.25009i | 0.218663i | ||||||||
\(818\) | 24.3076i | 0.849895i | ||||||||
\(819\) | 0.105797 | 0.00369683 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3261 | −0.430185 | −0.215093 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215093 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(822\) | 12.5167i | 0.436569i | ||||||||
\(823\) | 2.81852i | 0.0982475i | 0.998793 | + | 0.0491237i | \(0.0156429\pi\) | ||||
−0.998793 | + | 0.0491237i | \(0.984357\pi\) | |||||||
\(824\) | 0.0910197 | 0.00317082 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.1056 | 0.351618 | ||||||||
\(827\) | 37.4251i | 1.30140i | 0.759335 | + | 0.650700i | \(0.225524\pi\) | ||||
−0.759335 | + | 0.650700i | \(0.774476\pi\) | |||||||
\(828\) | − 18.8310i | − 0.654422i | ||||||||
\(829\) | −30.9434 | −1.07471 | −0.537355 | − | 0.843356i | \(-0.680576\pi\) | ||||
−0.537355 | + | 0.843356i | \(0.680576\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.5207 | 0.850613 | ||||||||
\(832\) | − 0.892455i | − 0.0309403i | ||||||||
\(833\) | 34.8042i | 1.20589i | ||||||||
\(834\) | 1.83017 | 0.0633736 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.15724 | −0.247538 | ||||||||
\(837\) | 1.06662i | 0.0368679i | ||||||||
\(838\) | 69.8620i | 2.41334i | ||||||||
\(839\) | 26.6975 | 0.921701 | 0.460851 | − | 0.887478i | \(-0.347544\pi\) | ||||
0.460851 | + | 0.887478i | \(0.347544\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0921 | −0.451451 | ||||||||
\(842\) | − 30.1871i | − 1.04032i | ||||||||
\(843\) | 14.4228i | 0.496748i | ||||||||
\(844\) | −54.8923 | −1.88947 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.5506 | 0.569023 | ||||||||
\(847\) | − 11.8738i | − 0.407989i | ||||||||
\(848\) | 16.7813i | 0.576271i | ||||||||
\(849\) | 2.14925 | 0.0737620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.5239 | −1.25202 | ||||||||
\(852\) | − 22.3912i | − 0.767109i | ||||||||
\(853\) | 29.2600i | 1.00184i | 0.865493 | + | 0.500921i | \(0.167005\pi\) | ||||
−0.865493 | + | 0.500921i | \(0.832995\pi\) | |||||||
\(854\) | 14.3254 | 0.490207 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.212282 | −0.00725566 | ||||||||
\(857\) | 33.5284i | 1.14531i | 0.819797 | + | 0.572654i | \(0.194086\pi\) | ||||
−0.819797 | + | 0.572654i | \(0.805914\pi\) | |||||||
\(858\) | − 0.997775i | − 0.0340635i | ||||||||
\(859\) | 25.8243 | 0.881115 | 0.440557 | − | 0.897725i | \(-0.354781\pi\) | ||||
0.440557 | + | 0.897725i | \(0.354781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.34582 | −0.250345 | ||||||||
\(862\) | 9.71293i | 0.330824i | ||||||||
\(863\) | − 28.8886i | − 0.983378i | −0.870771 | − | 0.491689i | \(-0.836380\pi\) | ||||
0.870771 | − | 0.491689i | \(-0.163620\pi\) | |||||||
\(864\) | 8.06387 | 0.274338 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.8822 | −0.709605 | ||||||||
\(867\) | 17.0795i | 0.580050i | ||||||||
\(868\) | 2.25592i | 0.0765710i | ||||||||
\(869\) | −11.8177 | −0.400888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.03006 | 0.0349023 | ||||||||
\(872\) | − 1.35602i | − 0.0459207i | ||||||||
\(873\) | 6.69876i | 0.226719i | ||||||||
\(874\) | 13.2669 | 0.448759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.9169 | −0.605355 | ||||||||
\(877\) | 15.1004i | 0.509905i | 0.966954 | + | 0.254953i | \(0.0820598\pi\) | ||||
−0.966954 | + | 0.254953i | \(0.917940\pi\) | |||||||
\(878\) | − 62.1086i | − 2.09606i | ||||||||
\(879\) | −9.02970 | −0.304564 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.6216 | 1.23381 | 0.616906 | − | 0.787037i | \(-0.288386\pi\) | ||||
0.616906 | + | 0.787037i | \(0.288386\pi\) | |||||||
\(882\) | − 12.0363i | − 0.405284i | ||||||||
\(883\) | − 34.5459i | − 1.16256i | −0.813703 | − | 0.581281i | \(-0.802552\pi\) | ||||
0.813703 | − | 0.581281i | \(-0.197448\pi\) | |||||||
\(884\) | −1.25832 | −0.0423220 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.8441 | 1.20421 | ||||||||
\(887\) | − 33.0360i | − 1.10924i | −0.832104 | − | 0.554620i | \(-0.812864\pi\) | ||||
0.832104 | − | 0.554620i | \(-0.187136\pi\) | |||||||
\(888\) | 0.616437i | 0.0206863i | ||||||||
\(889\) | 7.42903 | 0.249162 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.75961 | 0.159453 | ||||||||
\(892\) | 16.6741i | 0.558289i | ||||||||
\(893\) | 5.93864i | 0.198729i | ||||||||
\(894\) | 9.88860 | 0.330724 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.24706 | 0.0416614 | ||||||||
\(897\) | 0.941960i | 0.0314511i | ||||||||
\(898\) | 75.1392i | 2.50743i | ||||||||
\(899\) | 4.25420 | 0.141886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4947 | 0.849350 | ||||||||
\(902\) | 69.2789i | 2.30674i | ||||||||
\(903\) | − 8.79072i | − 0.292537i | ||||||||
\(904\) | 1.00903 | 0.0335597 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20.7189 | −0.688340 | ||||||||
\(907\) | 44.2708i | 1.46999i | 0.678074 | + | 0.734994i | \(0.262815\pi\) | ||||
−0.678074 | + | 0.734994i | \(0.737185\pi\) | |||||||
\(908\) | 34.1634i | 1.13375i | ||||||||
\(909\) | −5.66147 | −0.187779 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.8844 | −1.28830 | −0.644148 | − | 0.764901i | \(-0.722788\pi\) | ||||
−0.644148 | + | 0.764901i | \(0.722788\pi\) | |||||||
\(912\) | 2.78358i | 0.0921734i | ||||||||
\(913\) | 20.1991i | 0.668492i | ||||||||
\(914\) | −55.9201 | −1.84967 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.849608 | 0.0280719 | ||||||||
\(917\) | 9.73414i | 0.321450i | ||||||||
\(918\) | − 11.7857i | − 0.388986i | ||||||||
\(919\) | 28.5303 | 0.941127 | 0.470563 | − | 0.882366i | \(-0.344051\pi\) | ||||
0.470563 | + | 0.882366i | \(0.344051\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.03454 | −0.165894 | ||||||||
\(922\) | 19.8201i | 0.652740i | ||||||||
\(923\) | 1.12005i | 0.0368668i | ||||||||
\(924\) | 10.0666 | 0.331168 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.52497 | 0.247286 | ||||||||
\(927\) | − 0.594489i | − 0.0195256i | ||||||||
\(928\) | − 32.1625i | − 1.05579i | ||||||||
\(929\) | −36.3886 | −1.19387 | −0.596936 | − | 0.802289i | \(-0.703615\pi\) | ||||
−0.596936 | + | 0.802289i | \(0.703615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.31883 | 0.141544 | ||||||||
\(932\) | 38.3284i | 1.25549i | ||||||||
\(933\) | 4.89158i | 0.160143i | ||||||||
\(934\) | −14.3325 | −0.468973 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0158981 | 0.000519645 0 | ||||||||
\(937\) | 47.3354i | 1.54638i | 0.634175 | + | 0.773189i | \(0.281340\pi\) | ||||
−0.634175 | + | 0.773189i | \(0.718660\pi\) | |||||||
\(938\) | 20.4051i | 0.666249i | ||||||||
\(939\) | −3.17282 | −0.103541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.9254 | 1.72532 | 0.862659 | − | 0.505787i | \(-0.168798\pi\) | ||||
0.862659 | + | 0.505787i | \(0.168798\pi\) | |||||||
\(942\) | 17.9586i | 0.585123i | ||||||||
\(943\) | − 65.4035i | − 2.12983i | ||||||||
\(944\) | −18.8780 | −0.614426 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −82.9059 | −2.69550 | ||||||||
\(947\) | − 18.9330i | − 0.615239i | −0.951509 | − | 0.307619i | \(-0.900468\pi\) | ||||
0.951509 | − | 0.307619i | \(-0.0995324\pi\) | |||||||
\(948\) | − 5.15413i | − 0.167398i | ||||||||
\(949\) | 0.896234 | 0.0290930 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9953 | 0.648392 | ||||||||
\(952\) | − 0.910662i | − 0.0295147i | ||||||||
\(953\) | − 11.4499i | − 0.370899i | −0.982654 | − | 0.185450i | \(-0.940626\pi\) | ||||
0.982654 | − | 0.185450i | \(-0.0593742\pi\) | |||||||
\(954\) | −8.81680 | −0.285454 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.58377 | −0.309961 | ||||||||
\(957\) | − 18.9836i | − 0.613652i | ||||||||
\(958\) | 57.4270i | 1.85538i | ||||||||
\(959\) | 6.31683 | 0.203981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8623 | −0.963300 | ||||||||
\(962\) | − 0.844030i | − 0.0272126i | ||||||||
\(963\) | 1.38651i | 0.0446795i | ||||||||
\(964\) | 60.6191 | 1.95241 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.6598 | −0.600370 | ||||||||
\(967\) | 36.9926i | 1.18960i | 0.803873 | + | 0.594801i | \(0.202769\pi\) | ||||
−0.803873 | + | 0.594801i | \(0.797231\pi\) | |||||||
\(968\) | − 1.78428i | − 0.0573490i | ||||||||
\(969\) | 4.22890 | 0.135852 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.2897 | −0.972043 | −0.486022 | − | 0.873947i | \(-0.661552\pi\) | ||||
−0.486022 | + | 0.873947i | \(0.661552\pi\) | |||||||
\(972\) | 2.07584i | 0.0665825i | ||||||||
\(973\) | − 0.923638i | − 0.0296105i | ||||||||
\(974\) | −29.7549 | −0.953408 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.7610 | −0.856600 | ||||||||
\(977\) | − 16.6410i | − 0.532394i | −0.963919 | − | 0.266197i | \(-0.914233\pi\) | ||||
0.963919 | − | 0.266197i | \(-0.0857672\pi\) | |||||||
\(978\) | 23.7804i | 0.760413i | ||||||||
\(979\) | 87.4588 | 2.79520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.85677 | −0.282775 | ||||||||
\(982\) | − 57.3388i | − 1.82975i | ||||||||
\(983\) | 26.1897i | 0.835320i | 0.908603 | + | 0.417660i | \(0.137150\pi\) | ||||
−0.908603 | + | 0.417660i | \(0.862850\pi\) | |||||||
\(984\) | −1.10386 | −0.0351897 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −47.0069 | −1.49700 | ||||||||
\(987\) | − 8.35267i | − 0.265868i | ||||||||
\(988\) | 0.156145i | 0.00496762i | ||||||||
\(989\) | 78.2682 | 2.48878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.8373 | −0.788982 | −0.394491 | − | 0.918900i | \(-0.629079\pi\) | ||||
−0.394491 | + | 0.918900i | \(0.629079\pi\) | |||||||
\(992\) | − 8.60112i | − 0.273086i | ||||||||
\(993\) | − 6.01724i | − 0.190951i | ||||||||
\(994\) | −22.1876 | −0.703749 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.80954 | −0.279141 | ||||||||
\(997\) | − 25.0863i | − 0.794490i | −0.917713 | − | 0.397245i | \(-0.869966\pi\) | ||||
0.917713 | − | 0.397245i | \(-0.130034\pi\) | |||||||
\(998\) | − 53.2662i | − 1.68611i | ||||||||
\(999\) | 4.02621 | 0.127384 |
(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 | 1875.2.b.f.1249.9 | 12 | ||
5.2 | odd | 4 | 1875.2.a.j.1.2 | 6 | |||
5.3 | odd | 4 | 1875.2.a.k.1.5 | 6 | |||
5.4 | even | 2 | inner | 1875.2.b.f.1249.4 | 12 | ||
15.2 | even | 4 | 5625.2.a.p.1.5 | 6 | |||
15.8 | even | 4 | 5625.2.a.q.1.2 | 6 | |||
25.3 | odd | 20 | 375.2.g.c.76.1 | 12 | |||
25.4 | even | 10 | 375.2.i.d.49.2 | 24 | |||
25.6 | even | 5 | 375.2.i.d.199.2 | 24 | |||
25.8 | odd | 20 | 375.2.g.c.301.1 | 12 | |||
25.17 | odd | 20 | 75.2.g.c.61.3 | yes | 12 | ||
25.19 | even | 10 | 375.2.i.d.199.5 | 24 | |||
25.21 | even | 5 | 375.2.i.d.49.5 | 24 | |||
25.22 | odd | 20 | 75.2.g.c.16.3 | ✓ | 12 | ||
75.17 | even | 20 | 225.2.h.d.136.1 | 12 | |||
75.47 | even | 20 | 225.2.h.d.91.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.3 | ✓ | 12 | 25.22 | odd | 20 | ||
75.2.g.c.61.3 | yes | 12 | 25.17 | odd | 20 | ||
225.2.h.d.91.1 | 12 | 75.47 | even | 20 | |||
225.2.h.d.136.1 | 12 | 75.17 | even | 20 | |||
375.2.g.c.76.1 | 12 | 25.3 | odd | 20 | |||
375.2.g.c.301.1 | 12 | 25.8 | odd | 20 | |||
375.2.i.d.49.2 | 24 | 25.4 | even | 10 | |||
375.2.i.d.49.5 | 24 | 25.21 | even | 5 | |||
375.2.i.d.199.2 | 24 | 25.6 | even | 5 | |||
375.2.i.d.199.5 | 24 | 25.19 | even | 10 | |||
1875.2.a.j.1.2 | 6 | 5.2 | odd | 4 | |||
1875.2.a.k.1.5 | 6 | 5.3 | odd | 4 | |||
1875.2.b.f.1249.4 | 12 | 5.4 | even | 2 | inner | ||
1875.2.b.f.1249.9 | 12 | 1.1 | even | 1 | trivial | ||
5625.2.a.p.1.5 | 6 | 15.2 | even | 4 | |||
5625.2.a.q.1.2 | 6 | 15.8 | even | 4 |