Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1322,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1322");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.c (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: | \(10.5642081874\) |
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: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1322.6 | ||
Root | \(-1.65604 - 0.956115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1322 |
Dual form | 1323.2.c.d.1322.8 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.656620i | − 0.464301i | −0.972680 | − | 0.232150i | \(-0.925424\pi\) | ||||
0.972680 | − | 0.232150i | \(-0.0745761\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.56885 | 0.784425 | ||||||||
\(5\) | 3.31208 | 1.48121 | 0.740603 | − | 0.671943i | \(-0.234540\pi\) | ||||
0.740603 | + | 0.671943i | \(0.234540\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 2.34338i | − 0.828510i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 2.17478i | − 0.687725i | ||||||||
\(11\) | 2.34338i | 0.706556i | 0.935518 | + | 0.353278i | \(0.114933\pi\) | ||||
−0.935518 | + | 0.353278i | \(0.885067\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.58003i | − 0.438221i | −0.975700 | − | 0.219110i | \(-0.929685\pi\) | ||||
0.975700 | − | 0.219110i | \(-0.0703155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.59899 | 0.399747 | ||||||||
\(17\) | 1.13730 | 0.275836 | 0.137918 | − | 0.990444i | \(-0.455959\pi\) | ||||
0.137918 | + | 0.990444i | \(0.455959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.44938i | 1.02076i | 0.859950 | + | 0.510379i | \(0.170495\pi\) | ||||
−0.859950 | + | 0.510379i | \(0.829505\pi\) | |||||||
\(20\) | 5.19615 | 1.16190 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.53871 | 0.328054 | ||||||||
\(23\) | − 9.39331i | − 1.95864i | −0.202317 | − | 0.979320i | \(-0.564847\pi\) | ||||
0.202317 | − | 0.979320i | \(-0.435153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.96986 | 1.19397 | ||||||||
\(26\) | −1.03748 | −0.203466 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.65662i | − 0.679017i | −0.940603 | − | 0.339509i | \(-0.889739\pi\) | ||||
0.940603 | − | 0.339509i | \(-0.110261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.31873i | 1.31448i | 0.753680 | + | 0.657241i | \(0.228277\pi\) | ||||
−0.753680 | + | 0.657241i | \(0.771723\pi\) | |||||||
\(32\) | − 5.73669i | − 1.01411i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 0.746774i | − 0.128071i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.16784 | −0.849587 | −0.424794 | − | 0.905290i | \(-0.639653\pi\) | ||||
−0.424794 | + | 0.905290i | \(0.639653\pi\) | |||||||
\(38\) | 2.92155 | 0.473938 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 7.76146i | − 1.22719i | ||||||||
\(41\) | 9.64553 | 1.50638 | 0.753189 | − | 0.657804i | \(-0.228514\pi\) | ||||
0.753189 | + | 0.657804i | \(0.228514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.16784 | −0.330592 | −0.165296 | − | 0.986244i | \(-0.552858\pi\) | ||||
−0.165296 | + | 0.986244i | \(0.552858\pi\) | |||||||
\(44\) | 3.67641i | 0.554240i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.16784 | −0.909398 | ||||||||
\(47\) | −5.58668 | −0.814901 | −0.407450 | − | 0.913227i | \(-0.633582\pi\) | ||||
−0.407450 | + | 0.913227i | \(0.633582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 3.91993i | − 0.554362i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.47883i | − 0.343751i | ||||||||
\(53\) | 10.0499i | 1.38046i | 0.723588 | + | 0.690232i | \(0.242491\pi\) | ||||
−0.723588 | + | 0.690232i | \(0.757509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.76146i | 1.04655i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.40101 | −0.315268 | ||||||||
\(59\) | 2.17478 | 0.283132 | 0.141566 | − | 0.989929i | \(-0.454786\pi\) | ||||
0.141566 | + | 0.989929i | \(0.454786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00665i | 0.512999i | 0.966544 | + | 0.256500i | \(0.0825692\pi\) | ||||
−0.966544 | + | 0.256500i | \(0.917431\pi\) | |||||||
\(62\) | 4.80563 | 0.610315 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.568850 | −0.0711062 | ||||||||
\(65\) | − 5.23317i | − 0.649095i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7668 | −1.31538 | −0.657689 | − | 0.753290i | \(-0.728466\pi\) | ||||
−0.657689 | + | 0.753290i | \(0.728466\pi\) | |||||||
\(68\) | 1.78425 | 0.216372 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 6.39331i | − 0.758746i | −0.925244 | − | 0.379373i | \(-0.876140\pi\) | ||||
0.925244 | − | 0.379373i | \(-0.123860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6830i | 1.25035i | 0.780484 | + | 0.625176i | \(0.214973\pi\) | ||||
−0.780484 | + | 0.625176i | \(0.785027\pi\) | |||||||
\(74\) | 3.39331i | 0.394464i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.98041i | 0.800707i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.23317 | 0.138743 | 0.0693714 | − | 0.997591i | \(-0.477901\pi\) | ||||
0.0693714 | + | 0.997591i | \(0.477901\pi\) | |||||||
\(80\) | 5.29597 | 0.592108 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 6.33345i | − 0.699413i | ||||||||
\(83\) | −1.03748 | −0.113878 | −0.0569390 | − | 0.998378i | \(-0.518134\pi\) | ||||
−0.0569390 | + | 0.998378i | \(0.518134\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.76683 | 0.408570 | ||||||||
\(86\) | 1.42345i | 0.153494i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.49143 | 0.585388 | ||||||||
\(89\) | 7.47075 | 0.791898 | 0.395949 | − | 0.918272i | \(-0.370416\pi\) | ||||
0.395949 | + | 0.918272i | \(0.370416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 14.7367i | − 1.53641i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.66833i | 0.378359i | ||||||||
\(95\) | 14.7367i | 1.51195i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.5524i | − 1.37603i | −0.725695 | − | 0.688017i | \(-0.758482\pi\) | ||||
0.725695 | − | 0.688017i | \(-0.241518\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.36581 | 0.936581 | ||||||||
\(101\) | −13.7044 | −1.36364 | −0.681819 | − | 0.731521i | \(-0.738811\pi\) | ||||
−0.681819 | + | 0.731521i | \(0.738811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89211i | 0.482033i | 0.970521 | + | 0.241017i | \(0.0774809\pi\) | ||||
−0.970521 | + | 0.241017i | \(0.922519\pi\) | |||||||
\(104\) | −3.70260 | −0.363070 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.59899 | 0.640950 | ||||||||
\(107\) | − 2.45359i | − 0.237197i | −0.992942 | − | 0.118599i | \(-0.962160\pi\) | ||||
0.992942 | − | 0.118599i | \(-0.0378401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.33568 | 0.415282 | 0.207641 | − | 0.978205i | \(-0.433421\pi\) | ||||
0.207641 | + | 0.978205i | \(0.433421\pi\) | |||||||
\(110\) | 5.09633 | 0.485916 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 7.16013i | − 0.673569i | −0.941582 | − | 0.336784i | \(-0.890661\pi\) | ||||
0.941582 | − | 0.336784i | \(-0.109339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 31.1114i | − 2.90115i | ||||||||
\(116\) | − 5.73669i | − 0.532638i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1.42800i | − 0.131458i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50857 | 0.500779 | ||||||||
\(122\) | 2.63085 | 0.238186 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.4820i | 1.03111i | ||||||||
\(125\) | 3.21226 | 0.287313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.7065 | −1.57120 | −0.785601 | − | 0.618733i | \(-0.787646\pi\) | ||||
−0.785601 | + | 0.618733i | \(0.787646\pi\) | |||||||
\(128\) | − 11.0999i | − 0.981098i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.43621 | −0.301375 | ||||||||
\(131\) | −13.6046 | −1.18864 | −0.594318 | − | 0.804230i | \(-0.702578\pi\) | ||||
−0.594318 | + | 0.804230i | \(0.702578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.06972i | 0.610731i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 2.66513i | − 0.228533i | ||||||||
\(137\) | − 10.1601i | − 0.868039i | −0.900904 | − | 0.434019i | \(-0.857095\pi\) | ||||
0.900904 | − | 0.434019i | \(-0.142905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.85463i | 0.326945i | 0.986548 | + | 0.163473i | \(0.0522695\pi\) | ||||
−0.986548 | + | 0.163473i | \(0.947730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.19798 | −0.352286 | ||||||||
\(143\) | 3.70260 | 0.309627 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 12.1110i | − 1.00576i | ||||||||
\(146\) | 7.01468 | 0.580539 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.10756 | −0.666437 | ||||||||
\(149\) | 5.08007i | 0.416175i | 0.978110 | + | 0.208088i | \(0.0667239\pi\) | ||||
−0.978110 | + | 0.208088i | \(0.933276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3055 | 1.48968 | 0.744842 | − | 0.667241i | \(-0.232525\pi\) | ||||
0.744842 | + | 0.667241i | \(0.232525\pi\) | |||||||
\(152\) | 10.4266 | 0.845707 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.2402i | 1.94702i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.31208i | − 0.264333i | −0.991228 | − | 0.132166i | \(-0.957807\pi\) | ||||
0.991228 | − | 0.132166i | \(-0.0421933\pi\) | |||||||
\(158\) | − 0.809727i | − 0.0644184i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 19.0004i | − 1.50211i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.29345 | −0.179637 | −0.0898185 | − | 0.995958i | \(-0.528629\pi\) | ||||
−0.0898185 | + | 0.995958i | \(0.528629\pi\) | |||||||
\(164\) | 15.1324 | 1.18164 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.681229i | 0.0528737i | ||||||||
\(167\) | 2.66513 | 0.206234 | 0.103117 | − | 0.994669i | \(-0.467118\pi\) | ||||
0.103117 | + | 0.994669i | \(0.467118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5035 | 0.807963 | ||||||||
\(170\) | − 2.47338i | − 0.189699i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.40101 | −0.259325 | ||||||||
\(173\) | 2.56530 | 0.195036 | 0.0975182 | − | 0.995234i | \(-0.468910\pi\) | ||||
0.0975182 | + | 0.995234i | \(0.468910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.74704i | 0.282444i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 4.90545i | − 0.367679i | ||||||||
\(179\) | − 13.8365i | − 1.03419i | −0.855927 | − | 0.517096i | \(-0.827013\pi\) | ||||
0.855927 | − | 0.517096i | \(-0.172987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.74008i | − 0.352328i | −0.984361 | − | 0.176164i | \(-0.943631\pi\) | ||||
0.984361 | − | 0.176164i | \(-0.0563688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22.0121 | −1.62275 | ||||||||
\(185\) | −17.1163 | −1.25841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.66513i | 0.194893i | ||||||||
\(188\) | −8.76466 | −0.639228 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.67641 | 0.702001 | ||||||||
\(191\) | 8.34338i | 0.603706i | 0.953355 | + | 0.301853i | \(0.0976051\pi\) | ||||
−0.953355 | + | 0.301853i | \(0.902395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8442 | −1.28446 | −0.642229 | − | 0.766513i | \(-0.721990\pi\) | ||||
−0.642229 | + | 0.766513i | \(0.721990\pi\) | |||||||
\(194\) | −8.89876 | −0.638893 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1102i | 1.07656i | 0.842767 | + | 0.538279i | \(0.180925\pi\) | ||||
−0.842767 | + | 0.538279i | \(0.819075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.66025i | 0.613909i | 0.951724 | + | 0.306955i | \(0.0993100\pi\) | ||||
−0.951724 | + | 0.306955i | \(0.900690\pi\) | |||||||
\(200\) | − 13.9897i | − 0.989218i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.99858i | 0.633138i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.9468 | 2.23126 | ||||||||
\(206\) | 3.21226 | 0.223809 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.52645i | − 0.175177i | ||||||||
\(209\) | −10.4266 | −0.721222 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5809 | −1.00379 | −0.501897 | − | 0.864928i | \(-0.667364\pi\) | ||||
−0.501897 | + | 0.864928i | \(0.667364\pi\) | |||||||
\(212\) | 15.7668i | 1.08287i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.61107 | −0.110131 | ||||||||
\(215\) | −7.18005 | −0.489675 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 2.84689i | − 0.192816i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.1766i | 0.820943i | ||||||||
\(221\) | − 1.79696i | − 0.120877i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5832i | 0.708703i | 0.935112 | + | 0.354351i | \(0.115298\pi\) | ||||
−0.935112 | + | 0.354351i | \(0.884702\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.70149 | −0.312738 | ||||||||
\(227\) | −6.72398 | −0.446286 | −0.223143 | − | 0.974786i | \(-0.571632\pi\) | ||||
−0.223143 | + | 0.974786i | \(0.571632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 12.2630i | − 0.810364i | −0.914236 | − | 0.405182i | \(-0.867208\pi\) | ||||
0.914236 | − | 0.405182i | \(-0.132792\pi\) | |||||||
\(230\) | −20.4284 | −1.34701 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.56885 | −0.562573 | ||||||||
\(233\) | − 5.62648i | − 0.368603i | −0.982870 | − | 0.184302i | \(-0.940998\pi\) | ||||
0.982870 | − | 0.184302i | \(-0.0590023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5035 | −1.20704 | ||||||||
\(236\) | 3.41190 | 0.222096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.9595i | 1.03234i | 0.856488 | + | 0.516168i | \(0.172642\pi\) | ||||
−0.856488 | + | 0.516168i | \(0.827358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.58806i | 0.295543i | 0.989022 | + | 0.147771i | \(0.0472100\pi\) | ||||
−0.989022 | + | 0.147771i | \(0.952790\pi\) | |||||||
\(242\) | − 3.61704i | − 0.232512i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.28583i | 0.402409i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.03014 | 0.447317 | ||||||||
\(248\) | 17.1506 | 1.08906 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 2.10923i | − 0.133400i | ||||||||
\(251\) | −13.8042 | −0.871314 | −0.435657 | − | 0.900113i | \(-0.643484\pi\) | ||||
−0.435657 | + | 0.900113i | \(0.643484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0121 | 1.38389 | ||||||||
\(254\) | 11.6265i | 0.729510i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.42609 | −0.526631 | ||||||||
\(257\) | 8.96430 | 0.559178 | 0.279589 | − | 0.960120i | \(-0.409802\pi\) | ||||
0.279589 | + | 0.960120i | \(0.409802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 8.21006i | − 0.509166i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.93303i | 0.551885i | ||||||||
\(263\) | 28.5534i | 1.76068i | 0.474343 | + | 0.880340i | \(0.342686\pi\) | ||||
−0.474343 | + | 0.880340i | \(0.657314\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.2861i | 2.04475i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.8915 | −1.03181 | ||||||||
\(269\) | −23.9313 | −1.45912 | −0.729559 | − | 0.683918i | \(-0.760275\pi\) | ||||
−0.729559 | + | 0.683918i | \(0.760275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6032i | 0.887080i | 0.896255 | + | 0.443540i | \(0.146278\pi\) | ||||
−0.896255 | + | 0.443540i | \(0.853722\pi\) | |||||||
\(272\) | 1.81853 | 0.110265 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.67135 | −0.403031 | ||||||||
\(275\) | 13.9897i | 0.843608i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3830 | 1.34486 | 0.672431 | − | 0.740160i | \(-0.265250\pi\) | ||||
0.672431 | + | 0.740160i | \(0.265250\pi\) | |||||||
\(278\) | 2.53103 | 0.151801 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6067i | 0.692397i | 0.938161 | + | 0.346199i | \(0.112528\pi\) | ||||
−0.938161 | + | 0.346199i | \(0.887472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9937i | 0.891283i | 0.895211 | + | 0.445642i | \(0.147024\pi\) | ||||
−0.895211 | + | 0.445642i | \(0.852976\pi\) | |||||||
\(284\) | − 10.0301i | − 0.595179i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 2.43121i | − 0.143760i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7065 | −0.923915 | ||||||||
\(290\) | −7.95234 | −0.466977 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.7600i | 0.980807i | ||||||||
\(293\) | −16.3352 | −0.954314 | −0.477157 | − | 0.878818i | \(-0.658333\pi\) | ||||
−0.477157 | + | 0.878818i | \(0.658333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.20304 | 0.419377 | ||||||||
\(296\) | 12.1102i | 0.703891i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.33568 | 0.193231 | ||||||||
\(299\) | −14.8417 | −0.858317 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 12.0198i | − 0.691661i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.11450i | 0.408045i | ||||||||
\(305\) | 13.2703i | 0.759857i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.17340i | − 0.181115i | −0.995891 | − | 0.0905577i | \(-0.971135\pi\) | ||||
0.995891 | − | 0.0905577i | \(-0.0288650\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.9166 | 0.904003 | ||||||||
\(311\) | −25.1342 | −1.42523 | −0.712614 | − | 0.701556i | \(-0.752489\pi\) | ||||
−0.712614 | + | 0.701556i | \(0.752489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 18.6441i | − 1.05383i | −0.849919 | − | 0.526914i | \(-0.823349\pi\) | ||||
0.849919 | − | 0.526914i | \(-0.176651\pi\) | |||||||
\(314\) | −2.17478 | −0.122730 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.93466 | 0.108833 | ||||||||
\(317\) | 7.98965i | 0.448744i | 0.974504 | + | 0.224372i | \(0.0720330\pi\) | ||||
−0.974504 | + | 0.224372i | \(0.927967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.56885 | 0.479763 | ||||||||
\(320\) | −1.88407 | −0.105323 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.06028i | 0.281561i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 9.43254i | − 0.523223i | ||||||||
\(326\) | 1.50593i | 0.0834056i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 22.6031i | − 1.24805i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.93466 | −0.491094 | −0.245547 | − | 0.969385i | \(-0.578967\pi\) | ||||
−0.245547 | + | 0.969385i | \(0.578967\pi\) | |||||||
\(332\) | −1.62765 | −0.0893287 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 1.74998i | − 0.0957544i | ||||||||
\(335\) | −35.6606 | −1.94835 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.24526 | 0.231254 | 0.115627 | − | 0.993293i | \(-0.463112\pi\) | ||||
0.115627 | + | 0.993293i | \(0.463112\pi\) | |||||||
\(338\) | − 6.89682i | − 0.375138i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.90958 | 0.320492 | ||||||||
\(341\) | −17.1506 | −0.928755 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.08007i | 0.273899i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 1.68443i | − 0.0905556i | ||||||||
\(347\) | − 2.62648i | − 0.140997i | −0.997512 | − | 0.0704985i | \(-0.977541\pi\) | ||||
0.997512 | − | 0.0704985i | \(-0.0224590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 32.4918i | − 1.73924i | −0.493718 | − | 0.869622i | \(-0.664363\pi\) | ||||
0.493718 | − | 0.869622i | \(-0.335637\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.4432 | 0.716527 | ||||||||
\(353\) | 23.3842 | 1.24461 | 0.622307 | − | 0.782773i | \(-0.286195\pi\) | ||||
0.622307 | + | 0.782773i | \(0.286195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 21.1751i | − 1.12386i | ||||||||
\(356\) | 11.7205 | 0.621185 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.08536 | −0.480176 | ||||||||
\(359\) | 21.3504i | 1.12683i | 0.826174 | + | 0.563416i | \(0.190513\pi\) | ||||
−0.826174 | + | 0.563416i | \(0.809487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.796965 | −0.0419455 | ||||||||
\(362\) | −3.11243 | −0.163586 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.3830i | 1.85203i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 15.5229i | − 0.810289i | −0.914253 | − | 0.405145i | \(-0.867221\pi\) | ||||
0.914253 | − | 0.405145i | \(-0.132779\pi\) | |||||||
\(368\) | − 15.0198i | − 0.782961i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.2389i | 0.584283i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3528 | −1.20916 | −0.604582 | − | 0.796543i | \(-0.706660\pi\) | ||||
−0.604582 | + | 0.796543i | \(0.706660\pi\) | |||||||
\(374\) | 1.74998 | 0.0904891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.0917i | 0.675153i | ||||||||
\(377\) | −5.77756 | −0.297559 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.53871 | 0.130405 | 0.0652024 | − | 0.997872i | \(-0.479231\pi\) | ||||
0.0652024 | + | 0.997872i | \(0.479231\pi\) | |||||||
\(380\) | 23.1196i | 1.18601i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.47843 | 0.280301 | ||||||||
\(383\) | 16.2041 | 0.827993 | 0.413996 | − | 0.910278i | \(-0.364133\pi\) | ||||
0.413996 | + | 0.910278i | \(0.364133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.7169i | 0.596374i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 21.2616i | − 1.07939i | ||||||||
\(389\) | − 22.3330i | − 1.13233i | −0.824292 | − | 0.566165i | \(-0.808427\pi\) | ||||
0.824292 | − | 0.566165i | \(-0.191573\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 10.6830i | − 0.540263i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.92167 | 0.499847 | ||||||||
\(395\) | 4.08437 | 0.205507 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.6914i | 1.64073i | 0.571837 | + | 0.820367i | \(0.306231\pi\) | ||||
−0.571837 | + | 0.820367i | \(0.693769\pi\) | |||||||
\(398\) | 5.68650 | 0.285038 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.54574 | 0.477287 | ||||||||
\(401\) | − 28.9270i | − 1.44454i | −0.691609 | − | 0.722272i | \(-0.743098\pi\) | ||||
0.691609 | − | 0.722272i | \(-0.256902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5638 | 0.576033 | ||||||||
\(404\) | −21.5001 | −1.06967 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 12.1102i | − 0.600281i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 1.05082i | − 0.0519598i | −0.999662 | − | 0.0259799i | \(-0.991729\pi\) | ||||
0.999662 | − | 0.0259799i | \(-0.00827059\pi\) | |||||||
\(410\) | − 20.9769i | − 1.03597i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.67498i | 0.378119i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.43621 | −0.168677 | ||||||||
\(416\) | −9.06412 | −0.444405 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.84631i | 0.334864i | ||||||||
\(419\) | 3.12120 | 0.152480 | 0.0762402 | − | 0.997089i | \(-0.475708\pi\) | ||||
0.0762402 | + | 0.997089i | \(0.475708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.70655 | −0.424331 | −0.212166 | − | 0.977234i | \(-0.568052\pi\) | ||||
−0.212166 | + | 0.977234i | \(0.568052\pi\) | |||||||
\(422\) | 9.57414i | 0.466062i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.5508 | 1.14373 | ||||||||
\(425\) | 6.78952 | 0.329340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 3.84931i | − 0.186063i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.71457i | 0.227357i | ||||||||
\(431\) | 27.2831i | 1.31418i | 0.753812 | + | 0.657090i | \(0.228213\pi\) | ||||
−0.753812 | + | 0.657090i | \(0.771787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 12.8711i | − 0.618547i | −0.950973 | − | 0.309274i | \(-0.899914\pi\) | ||||
0.950973 | − | 0.309274i | \(-0.100086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.80202 | 0.325758 | ||||||||
\(437\) | 41.7944 | 1.99930 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.4445i | 0.880306i | 0.897923 | + | 0.440153i | \(0.145076\pi\) | ||||
−0.897923 | + | 0.440153i | \(0.854924\pi\) | |||||||
\(440\) | 18.1880 | 0.867081 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.17992 | −0.0561233 | ||||||||
\(443\) | 2.87000i | 0.136358i | 0.997673 | + | 0.0681790i | \(0.0217189\pi\) | ||||
−0.997673 | + | 0.0681790i | \(0.978281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.7437 | 1.17296 | ||||||||
\(446\) | 6.94914 | 0.329051 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.81675i | 0.0857380i | 0.999081 | + | 0.0428690i | \(0.0136498\pi\) | ||||
−0.999081 | + | 0.0428690i | \(0.986350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6031i | 1.06434i | ||||||||
\(452\) | − 11.2332i | − 0.528364i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.41510i | 0.207211i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.15575 | 0.287954 | 0.143977 | − | 0.989581i | \(-0.454011\pi\) | ||||
0.143977 | + | 0.989581i | \(0.454011\pi\) | |||||||
\(458\) | −8.05216 | −0.376253 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 48.8091i | − 2.27573i | ||||||||
\(461\) | 17.0507 | 0.794132 | 0.397066 | − | 0.917790i | \(-0.370028\pi\) | ||||
0.397066 | + | 0.917790i | \(0.370028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4131 | 1.36694 | 0.683471 | − | 0.729977i | \(-0.260469\pi\) | ||||
0.683471 | + | 0.729977i | \(0.260469\pi\) | |||||||
\(464\) | − 5.84689i | − 0.271435i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.69446 | −0.171143 | ||||||||
\(467\) | −27.1181 | −1.25487 | −0.627437 | − | 0.778667i | \(-0.715896\pi\) | ||||
−0.627437 | + | 0.778667i | \(0.715896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.1498i | 0.560428i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 5.09633i | − 0.234578i | ||||||||
\(473\) | − 5.08007i | − 0.233582i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.5622i | 1.21876i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.4793 | 0.479314 | ||||||||
\(479\) | −21.5569 | −0.984960 | −0.492480 | − | 0.870324i | \(-0.663910\pi\) | ||||
−0.492480 | + | 0.870324i | \(0.663910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.16532i | 0.372307i | ||||||||
\(482\) | 3.01261 | 0.137221 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.64212 | 0.392824 | ||||||||
\(485\) | − 44.8865i | − 2.03819i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5809 | −0.660725 | −0.330363 | − | 0.943854i | \(-0.607171\pi\) | ||||
−0.330363 | + | 0.943854i | \(0.607171\pi\) | |||||||
\(488\) | 9.38910 | 0.425025 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.283102i | 0.0127762i | 0.999980 | + | 0.00638811i | \(0.00203341\pi\) | ||||
−0.999980 | + | 0.00638811i | \(0.997967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.15867i | − 0.187297i | ||||||||
\(494\) | − 4.61613i | − 0.207690i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.7026i | 0.525461i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3055 | 0.550871 | 0.275436 | − | 0.961319i | \(-0.411178\pi\) | ||||
0.275436 | + | 0.961319i | \(0.411178\pi\) | |||||||
\(500\) | 5.03955 | 0.225375 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.06412i | 0.404552i | ||||||||
\(503\) | 1.78425 | 0.0795559 | 0.0397779 | − | 0.999209i | \(-0.487335\pi\) | ||||
0.0397779 | + | 0.999209i | \(0.487335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.3900 | −2.01983 | ||||||||
\(506\) | − 14.4536i | − 0.642540i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −27.7789 | −1.23249 | ||||||||
\(509\) | 39.0725 | 1.73186 | 0.865928 | − | 0.500168i | \(-0.166728\pi\) | ||||
0.865928 | + | 0.500168i | \(0.166728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 16.6670i | − 0.736583i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 5.88614i | − 0.259627i | ||||||||
\(515\) | 16.2030i | 0.713991i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 13.0917i | − 0.575773i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.2633 | −0.537782 | ||||||||
\(521\) | −20.3628 | −0.892111 | −0.446056 | − | 0.895005i | \(-0.647172\pi\) | ||||
−0.446056 | + | 0.895005i | \(0.647172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.43259i | 0.0626426i | 0.999509 | + | 0.0313213i | \(0.00997151\pi\) | ||||
−0.999509 | + | 0.0313213i | \(0.990028\pi\) | |||||||
\(524\) | −21.3435 | −0.932396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7488 | 0.817485 | ||||||||
\(527\) | 8.32359i | 0.362581i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −65.2342 | −2.83627 | ||||||||
\(530\) | 21.8564 | 0.949380 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 15.2402i | − 0.660126i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 8.12647i | − 0.351338i | ||||||||
\(536\) | 25.2308i | 1.08980i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.7138i | 0.677470i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0904 | −0.433821 | −0.216910 | − | 0.976192i | \(-0.569598\pi\) | ||||
−0.216910 | + | 0.976192i | \(0.569598\pi\) | |||||||
\(542\) | 9.58875 | 0.411872 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 6.52433i | − 0.279729i | ||||||||
\(545\) | 14.3601 | 0.615119 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.30048 | 0.312146 | 0.156073 | − | 0.987746i | \(-0.450117\pi\) | ||||
0.156073 | + | 0.987746i | \(0.450117\pi\) | |||||||
\(548\) | − 15.9397i | − 0.680911i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.18589 | 0.391688 | ||||||||
\(551\) | 16.2697 | 0.693112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 14.6971i | − 0.624420i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.04733i | 0.256464i | ||||||||
\(557\) | − 22.8597i | − 0.968595i | −0.874903 | − | 0.484297i | \(-0.839075\pi\) | ||||
0.874903 | − | 0.484297i | \(-0.160925\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.42524i | 0.144872i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.62119 | 0.321481 | ||||||||
\(563\) | −21.1096 | −0.889663 | −0.444832 | − | 0.895614i | \(-0.646736\pi\) | ||||
−0.444832 | + | 0.895614i | \(0.646736\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 23.7149i | − 0.997694i | ||||||||
\(566\) | 9.84517 | 0.413824 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.9819 | −0.628629 | ||||||||
\(569\) | − 26.4536i | − 1.10899i | −0.832186 | − | 0.554496i | \(-0.812911\pi\) | ||||
0.832186 | − | 0.554496i | \(-0.187089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0301 | 0.503446 | 0.251723 | − | 0.967799i | \(-0.419003\pi\) | ||||
0.251723 | + | 0.967799i | \(0.419003\pi\) | |||||||
\(572\) | 5.80883 | 0.242879 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 56.0767i | − 2.33856i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.8413i | 1.53372i | 0.641812 | + | 0.766862i | \(0.278183\pi\) | ||||
−0.641812 | + | 0.766862i | \(0.721817\pi\) | |||||||
\(578\) | 10.3132i | 0.428974i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 19.0004i | − 0.788947i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5508 | −0.975374 | ||||||||
\(584\) | 25.0343 | 1.03593 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.7260i | 0.443089i | ||||||||
\(587\) | 28.7712 | 1.18752 | 0.593758 | − | 0.804644i | \(-0.297644\pi\) | ||||
0.593758 | + | 0.804644i | \(0.297644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.5638 | −1.34177 | ||||||||
\(590\) | − 4.72966i | − 0.194717i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.26331 | −0.339620 | ||||||||
\(593\) | 10.5832 | 0.434599 | 0.217300 | − | 0.976105i | \(-0.430275\pi\) | ||||
0.217300 | + | 0.976105i | \(0.430275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.96986i | 0.326458i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.74535i | 0.398517i | ||||||||
\(599\) | 18.1927i | 0.743333i | 0.928366 | + | 0.371666i | \(0.121214\pi\) | ||||
−0.928366 | + | 0.371666i | \(0.878786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.4101i | 1.07729i | 0.842532 | + | 0.538646i | \(0.181064\pi\) | ||||
−0.842532 | + | 0.538646i | \(0.818936\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.7186 | 1.16854 | ||||||||
\(605\) | 18.2448 | 0.741757 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.9776i | − 1.01381i | −0.862003 | − | 0.506904i | \(-0.830790\pi\) | ||||
0.862003 | − | 0.506904i | \(-0.169210\pi\) | |||||||
\(608\) | 25.5247 | 1.03516 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.71358 | 0.352802 | ||||||||
\(611\) | 8.82710i | 0.357106i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1126 | −0.570003 | −0.285002 | − | 0.958527i | \(-0.591994\pi\) | ||||
−0.285002 | + | 0.958527i | \(0.591994\pi\) | |||||||
\(614\) | −2.08372 | −0.0840920 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 14.6265i | − 0.588840i | −0.955676 | − | 0.294420i | \(-0.904874\pi\) | ||||
0.955676 | − | 0.294420i | \(-0.0951264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.5442i | 1.06690i | 0.845831 | + | 0.533452i | \(0.179105\pi\) | ||||
−0.845831 | + | 0.533452i | \(0.820895\pi\) | |||||||
\(620\) | 38.0292i | 1.52729i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.5036i | 0.661734i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.2101 | −0.768403 | ||||||||
\(626\) | −12.2421 | −0.489293 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 5.19615i | − 0.207349i | ||||||||
\(629\) | −5.87738 | −0.234347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.20304 | −0.326558 | −0.163279 | − | 0.986580i | \(-0.552207\pi\) | ||||
−0.163279 | + | 0.986580i | \(0.552207\pi\) | |||||||
\(632\) | − 2.88979i | − 0.114950i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.24617 | 0.208352 | ||||||||
\(635\) | −58.6455 | −2.32727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 5.62648i | − 0.222755i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 36.7636i | − 1.45321i | ||||||||
\(641\) | 16.0499i | 0.633934i | 0.948437 | + | 0.316967i | \(0.102664\pi\) | ||||
−0.948437 | + | 0.316967i | \(0.897336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 26.4101i | − 1.04151i | −0.853705 | − | 0.520757i | \(-0.825650\pi\) | ||||
0.853705 | − | 0.520757i | \(-0.174350\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.32268 | 0.130729 | ||||||||
\(647\) | 31.7015 | 1.24632 | 0.623158 | − | 0.782096i | \(-0.285849\pi\) | ||||
0.623158 | + | 0.782096i | \(0.285849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.09633i | 0.200048i | ||||||||
\(650\) | −6.19360 | −0.242933 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.59808 | −0.140912 | ||||||||
\(653\) | 13.2901i | 0.520083i | 0.965597 | + | 0.260041i | \(0.0837362\pi\) | ||||
−0.965597 | + | 0.260041i | \(0.916264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.0594 | −1.76062 | ||||||||
\(656\) | 15.4231 | 0.602171 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 36.2125i | − 1.41064i | −0.708890 | − | 0.705319i | \(-0.750804\pi\) | ||||
0.708890 | − | 0.705319i | \(-0.249196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 50.7930i | − 1.97562i | −0.155674 | − | 0.987809i | \(-0.549755\pi\) | ||||
0.155674 | − | 0.987809i | \(-0.450245\pi\) | |||||||
\(662\) | 5.86668i | 0.228015i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.43121i | 0.0943491i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.3478 | −1.32995 | ||||||||
\(668\) | 4.18118 | 0.161775 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.4155i | 0.904618i | ||||||||
\(671\) | −9.38910 | −0.362462 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.32865 | 0.128310 | 0.0641550 | − | 0.997940i | \(-0.479565\pi\) | ||||
0.0641550 | + | 0.997940i | \(0.479565\pi\) | |||||||
\(674\) | − 2.78752i | − 0.107371i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.4784 | 0.633786 | ||||||||
\(677\) | 19.9380 | 0.766280 | 0.383140 | − | 0.923690i | \(-0.374843\pi\) | ||||
0.383140 | + | 0.923690i | \(0.374843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 8.82710i | − 0.338504i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.2614i | 0.431222i | ||||||||
\(683\) | − 28.6636i | − 1.09678i | −0.836221 | − | 0.548392i | \(-0.815240\pi\) | ||||
0.836221 | − | 0.548392i | \(-0.184760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 33.6512i | − 1.28574i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.46635 | −0.132153 | ||||||||
\(689\) | 15.8792 | 0.604948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 20.3674i | − 0.774812i | −0.921909 | − | 0.387406i | \(-0.873371\pi\) | ||||
0.921909 | − | 0.387406i | \(-0.126629\pi\) | |||||||
\(692\) | 4.02458 | 0.152991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.72460 | −0.0654650 | ||||||||
\(695\) | 12.7668i | 0.484273i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9699 | 0.415513 | ||||||||
\(698\) | −21.3347 | −0.807532 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.1172i | 1.85513i | 0.373659 | + | 0.927566i | \(0.378103\pi\) | ||||
−0.373659 | + | 0.927566i | \(0.621897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 22.9937i | − 0.867222i | ||||||||
\(704\) | − 1.33303i | − 0.0502405i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 15.3545i | − 0.577876i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3658 | 0.877522 | 0.438761 | − | 0.898604i | \(-0.355418\pi\) | ||||
0.438761 | + | 0.898604i | \(0.355418\pi\) | |||||||
\(710\) | −13.9040 | −0.521809 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 17.5068i | − 0.656095i | ||||||||
\(713\) | 68.7471 | 2.57460 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.2633 | 0.458622 | ||||||||
\(716\) | − 21.7075i | − 0.811246i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.0191 | 0.523189 | ||||||||
\(719\) | 12.6669 | 0.472396 | 0.236198 | − | 0.971705i | \(-0.424099\pi\) | ||||
0.236198 | + | 0.971705i | \(0.424099\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.523303i | 0.0194753i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 7.43648i | − 0.276374i | ||||||||
\(725\) | − 21.8295i | − 0.810728i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.70398i | − 0.100285i | −0.998742 | − | 0.0501426i | \(-0.984032\pi\) | ||||
0.998742 | − | 0.0501426i | \(-0.0159676\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23.2332 | 0.859898 | ||||||||
\(731\) | −2.46548 | −0.0911891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.8087i | 0.805524i | 0.915305 | + | 0.402762i | \(0.131950\pi\) | ||||
−0.915305 | + | 0.402762i | \(0.868050\pi\) | |||||||
\(734\) | −10.1927 | −0.376218 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.8865 | −1.98628 | ||||||||
\(737\) | − 25.2308i | − 0.929387i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.1267 | 1.18180 | 0.590899 | − | 0.806745i | \(-0.298773\pi\) | ||||
0.590899 | + | 0.806745i | \(0.298773\pi\) | |||||||
\(740\) | −26.8529 | −0.987131 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 41.2728i | − 1.51415i | −0.653328 | − | 0.757075i | \(-0.726628\pi\) | ||||
0.653328 | − | 0.757075i | \(-0.273372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.8256i | 0.616442i | ||||||||
\(746\) | 15.3339i | 0.561415i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.18118i | 0.152879i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.8091 | 1.67160 | 0.835798 | − | 0.549037i | \(-0.185005\pi\) | ||||
0.835798 | + | 0.549037i | \(0.185005\pi\) | |||||||
\(752\) | −8.93303 | −0.325754 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.79366i | 0.138157i | ||||||||
\(755\) | 60.6294 | 2.20653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.3427 | 1.82974 | 0.914868 | − | 0.403752i | \(-0.132294\pi\) | ||||
0.914868 | + | 0.403752i | \(0.132294\pi\) | |||||||
\(758\) | − 1.66697i | − 0.0605471i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 34.5337 | 1.25267 | ||||||||
\(761\) | −30.3646 | −1.10072 | −0.550358 | − | 0.834929i | \(-0.685509\pi\) | ||||
−0.550358 | + | 0.834929i | \(0.685509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.0895i | 0.473562i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 10.6400i | − 0.384438i | ||||||||
\(767\) | − 3.43621i | − 0.124074i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.3383i | 1.49070i | 0.666675 | + | 0.745349i | \(0.267717\pi\) | ||||
−0.666675 | + | 0.745349i | \(0.732283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.9949 | −1.00756 | ||||||||
\(773\) | −13.9951 | −0.503368 | −0.251684 | − | 0.967809i | \(-0.580984\pi\) | ||||
−0.251684 | + | 0.967809i | \(0.580984\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.6918i | 1.56946i | ||||||||
\(776\) | −31.7583 | −1.14006 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.6643 | −0.525741 | ||||||||
\(779\) | 42.9166i | 1.53765i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9819 | 0.536096 | ||||||||
\(782\) | −7.01468 | −0.250845 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 10.9699i | − 0.391531i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.4868i | − 0.480753i | −0.970680 | − | 0.240377i | \(-0.922729\pi\) | ||||
0.970680 | − | 0.240377i | \(-0.0772709\pi\) | |||||||
\(788\) | 23.7056i | 0.844478i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 2.68188i | − 0.0954170i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.33062 | 0.224807 | ||||||||
\(794\) | 21.4658 | 0.761794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.5866i | 0.481566i | ||||||||
\(797\) | 8.31735 | 0.294616 | 0.147308 | − | 0.989091i | \(-0.452939\pi\) | ||||
0.147308 | + | 0.989091i | \(0.452939\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.35373 | −0.224779 | ||||||||
\(800\) | − 34.2472i | − 1.21082i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.9940 | −0.670703 | ||||||||
\(803\) | −25.0343 | −0.883443 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 7.59302i | − 0.267453i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.1146i | 1.12979i | ||||||||
\(809\) | − 14.5440i | − 0.511340i | −0.966764 | − | 0.255670i | \(-0.917704\pi\) | ||||
0.966764 | − | 0.255670i | \(-0.0822960\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 41.8287i | − 1.46880i | −0.678715 | − | 0.734401i | \(-0.737463\pi\) | ||||
0.678715 | − | 0.734401i | \(-0.262537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.95181 | −0.278711 | ||||||||
\(815\) | −7.59609 | −0.266079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 9.64553i | − 0.337454i | ||||||||
\(818\) | −0.689991 | −0.0241250 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.1196 | 1.75025 | ||||||||
\(821\) | − 46.4828i | − 1.62226i | −0.584865 | − | 0.811131i | \(-0.698852\pi\) | ||||
0.584865 | − | 0.811131i | \(-0.301148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.73669 | 0.269684 | 0.134842 | − | 0.990867i | \(-0.456947\pi\) | ||||
0.134842 | + | 0.990867i | \(0.456947\pi\) | |||||||
\(824\) | 11.4641 | 0.399369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 20.8898i | − 0.726409i | −0.931709 | − | 0.363205i | \(-0.881683\pi\) | ||||
0.931709 | − | 0.363205i | \(-0.118317\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 47.6062i | − 1.65343i | −0.562619 | − | 0.826716i | \(-0.690206\pi\) | ||||
0.562619 | − | 0.826716i | \(-0.309794\pi\) | |||||||
\(830\) | 2.25628i | 0.0783168i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.898798i | 0.0311602i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.82710 | 0.305475 | ||||||||
\(836\) | −16.3577 | −0.565744 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 2.04944i | − 0.0707968i | ||||||||
\(839\) | 22.4035 | 0.773455 | 0.386727 | − | 0.922194i | \(-0.373605\pi\) | ||||
0.386727 | + | 0.922194i | \(0.373605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6291 | 0.538935 | ||||||||
\(842\) | 5.71690i | 0.197017i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.8753 | −0.787400 | ||||||||
\(845\) | 34.7885 | 1.19676 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.0697i | 0.551836i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 4.45814i | − 0.152913i | ||||||||
\(851\) | 48.5431i | 1.66404i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.4273i | 1.65812i | 0.559160 | + | 0.829060i | \(0.311124\pi\) | ||||
−0.559160 | + | 0.829060i | \(0.688876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.74968 | −0.196520 | ||||||||
\(857\) | 49.0655 | 1.67605 | 0.838023 | − | 0.545636i | \(-0.183712\pi\) | ||||
0.838023 | + | 0.545636i | \(0.183712\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 12.0245i | − 0.410272i | −0.978733 | − | 0.205136i | \(-0.934236\pi\) | ||||
0.978733 | − | 0.205136i | \(-0.0657636\pi\) | |||||||
\(860\) | −11.2644 | −0.384113 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.9146 | 0.610175 | ||||||||
\(863\) | 46.0499i | 1.56756i | 0.621040 | + | 0.783779i | \(0.286710\pi\) | ||||
−0.621040 | + | 0.783779i | \(0.713290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.49649 | 0.288889 | ||||||||
\(866\) | −8.45145 | −0.287192 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.88979i | 0.0980296i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0119i | 0.576426i | ||||||||
\(872\) | − 10.1601i | − 0.344066i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 27.4430i | − 0.928275i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4734 | 0.454964 | 0.227482 | − | 0.973782i | \(-0.426951\pi\) | ||||
0.227482 | + | 0.973782i | \(0.426951\pi\) | |||||||
\(878\) | 12.1110 | 0.408727 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.4105i | 0.418357i | ||||||||
\(881\) | −25.5247 | −0.859949 | −0.429974 | − | 0.902841i | \(-0.641477\pi\) | ||||
−0.429974 | + | 0.902841i | \(0.641477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.45532 | 0.217239 | 0.108619 | − | 0.994083i | \(-0.465357\pi\) | ||||
0.108619 | + | 0.994083i | \(0.465357\pi\) | |||||||
\(884\) | − 2.81917i | − 0.0948189i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.88450 | 0.0633111 | ||||||||
\(887\) | 33.1208 | 1.11209 | 0.556043 | − | 0.831153i | \(-0.312319\pi\) | ||||
0.556043 | + | 0.831153i | \(0.312319\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 16.2472i | − 0.544608i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.6034i | 0.555924i | ||||||||
\(893\) | − 24.8572i | − 0.831816i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 45.8277i | − 1.53185i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.19292 | 0.0398082 | ||||||||
\(899\) | 26.7618 | 0.892556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4298i | 0.380781i | ||||||||
\(902\) | 14.8417 | 0.494174 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.7789 | −0.558058 | ||||||||
\(905\) | − 15.6995i | − 0.521870i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.21512 | 0.206370 | 0.103185 | − | 0.994662i | \(-0.467097\pi\) | ||||
0.103185 | + | 0.994662i | \(0.467097\pi\) | |||||||
\(908\) | −10.5489 | −0.350078 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 18.0475i | − 0.597941i | −0.954262 | − | 0.298970i | \(-0.903357\pi\) | ||||
0.954262 | − | 0.298970i | \(-0.0966432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2.43121i | − 0.0804611i | ||||||||
\(914\) | − 4.04199i | − 0.133697i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 19.2389i | − 0.635670i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.25825 | −0.272415 | −0.136207 | − | 0.990680i | \(-0.543491\pi\) | ||||
−0.136207 | + | 0.990680i | \(0.543491\pi\) | |||||||
\(920\) | −72.9057 | −2.40363 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 11.1959i | − 0.368716i | ||||||||
\(923\) | −10.1016 | −0.332498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.8513 | −1.01438 | ||||||||
\(926\) | − 19.3132i | − 0.634672i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.9769 | −0.688600 | ||||||||
\(929\) | 34.7709 | 1.14080 | 0.570399 | − | 0.821368i | \(-0.306789\pi\) | ||||
0.570399 | + | 0.821368i | \(0.306789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 8.82710i | − 0.289141i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.8063i | 0.582639i | ||||||||
\(935\) | 8.82710i | 0.288677i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.0703i | 1.66839i | 0.551466 | + | 0.834197i | \(0.314069\pi\) | ||||
−0.551466 | + | 0.834197i | \(0.685931\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −29.0292 | −0.946829 | ||||||||
\(941\) | −3.47744 | −0.113361 | −0.0566807 | − | 0.998392i | \(-0.518052\pi\) | ||||
−0.0566807 | + | 0.998392i | \(0.518052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 90.6034i | − 2.95045i | ||||||||
\(944\) | 3.47744 | 0.113181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.33568 | −0.108452 | ||||||||
\(947\) | − 14.3401i | − 0.465989i | −0.972478 | − | 0.232995i | \(-0.925148\pi\) | ||||
0.972478 | − | 0.232995i | \(-0.0748525\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8794 | 0.547930 | ||||||||
\(950\) | 17.4413 | 0.565869 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 7.53697i | − 0.244147i | −0.992521 | − | 0.122073i | \(-0.961046\pi\) | ||||
0.992521 | − | 0.122073i | \(-0.0389543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.6339i | 0.894213i | ||||||||
\(956\) | 25.0381i | 0.809789i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.1547i | 0.457318i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5638 | −0.727864 | ||||||||
\(962\) | 5.36152 | 0.172862 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.19797i | 0.231831i | ||||||||
\(965\) | −59.1015 | −1.90255 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6161 | −0.373550 | −0.186775 | − | 0.982403i | \(-0.559803\pi\) | ||||
−0.186775 | + | 0.982403i | \(0.559803\pi\) | |||||||
\(968\) | − 12.9087i | − 0.414901i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.4734 | −0.946333 | ||||||||
\(971\) | 35.4952 | 1.13910 | 0.569548 | − | 0.821958i | \(-0.307118\pi\) | ||||
0.569548 | + | 0.821958i | \(0.307118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.57414i | 0.306775i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.40659i | 0.205070i | ||||||||
\(977\) | − 32.0094i | − 1.02407i | −0.858964 | − | 0.512036i | \(-0.828891\pi\) | ||||
0.858964 | − | 0.512036i | \(-0.171109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5068i | 0.559520i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.185891 | 0.00593201 | ||||||||
\(983\) | −49.4648 | −1.57768 | −0.788841 | − | 0.614598i | \(-0.789318\pi\) | ||||
−0.788841 | + | 0.614598i | \(0.789318\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.0462i | 1.59460i | ||||||||
\(986\) | −2.73067 | −0.0869623 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.0292 | 0.350887 | ||||||||
\(989\) | 20.3632i | 0.647511i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.9518 | 0.570258 | 0.285129 | − | 0.958489i | \(-0.407964\pi\) | ||||
0.285129 | + | 0.958489i | \(0.407964\pi\) | |||||||
\(992\) | 41.9853 | 1.33303 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.6834i | 0.909326i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.5037i | 1.06107i | 0.847662 | + | 0.530537i | \(0.178010\pi\) | ||||
−0.847662 | + | 0.530537i | \(0.821990\pi\) | |||||||
\(998\) | − 8.08007i | − 0.255770i | ||||||||
\(999\) | 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 | 1323.2.c.d.1322.6 | 12 | ||
3.2 | odd | 2 | inner | 1323.2.c.d.1322.7 | 12 | ||
7.2 | even | 3 | 189.2.p.d.80.3 | yes | 12 | ||
7.3 | odd | 6 | 189.2.p.d.26.4 | yes | 12 | ||
7.6 | odd | 2 | inner | 1323.2.c.d.1322.5 | 12 | ||
21.2 | odd | 6 | 189.2.p.d.80.4 | yes | 12 | ||
21.17 | even | 6 | 189.2.p.d.26.3 | ✓ | 12 | ||
21.20 | even | 2 | inner | 1323.2.c.d.1322.8 | 12 | ||
63.2 | odd | 6 | 567.2.s.f.458.3 | 12 | |||
63.16 | even | 3 | 567.2.s.f.458.4 | 12 | |||
63.23 | odd | 6 | 567.2.i.f.269.4 | 12 | |||
63.31 | odd | 6 | 567.2.s.f.26.3 | 12 | |||
63.38 | even | 6 | 567.2.i.f.215.4 | 12 | |||
63.52 | odd | 6 | 567.2.i.f.215.3 | 12 | |||
63.58 | even | 3 | 567.2.i.f.269.3 | 12 | |||
63.59 | even | 6 | 567.2.s.f.26.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.3 | ✓ | 12 | 21.17 | even | 6 | ||
189.2.p.d.26.4 | yes | 12 | 7.3 | odd | 6 | ||
189.2.p.d.80.3 | yes | 12 | 7.2 | even | 3 | ||
189.2.p.d.80.4 | yes | 12 | 21.2 | odd | 6 | ||
567.2.i.f.215.3 | 12 | 63.52 | odd | 6 | |||
567.2.i.f.215.4 | 12 | 63.38 | even | 6 | |||
567.2.i.f.269.3 | 12 | 63.58 | even | 3 | |||
567.2.i.f.269.4 | 12 | 63.23 | odd | 6 | |||
567.2.s.f.26.3 | 12 | 63.31 | odd | 6 | |||
567.2.s.f.26.4 | 12 | 63.59 | even | 6 | |||
567.2.s.f.458.3 | 12 | 63.2 | odd | 6 | |||
567.2.s.f.458.4 | 12 | 63.16 | even | 3 | |||
1323.2.c.d.1322.5 | 12 | 7.6 | odd | 2 | inner | ||
1323.2.c.d.1322.6 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.c.d.1322.7 | 12 | 3.2 | odd | 2 | inner | ||
1323.2.c.d.1322.8 | 12 | 21.20 | even | 2 | inner |