Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1161862439\) |
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: | \( x^{12} - 2x^{11} + 2x^{10} + 54x^{8} - 114x^{7} + 120x^{6} + 46x^{5} + 9x^{4} - 4x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 798) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.9 | ||
Root | \(0.382656 + 0.382656i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.b.1063.4 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.765312i | − | 0.342258i | −0.985249 | − | 0.171129i | \(-0.945259\pi\) | ||
0.985249 | − | 0.171129i | \(-0.0547415\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.29245 | − | 1.32086i | −0.866464 | − | 0.499240i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.765312 | 0.242013 | ||||||||
\(11\) | −4.09356 | −1.23426 | −0.617128 | − | 0.786863i | \(-0.711704\pi\) | ||||
−0.617128 | + | 0.786863i | \(0.711704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23469 | 0.342441 | 0.171220 | − | 0.985233i | \(-0.445229\pi\) | ||||
0.171220 | + | 0.985233i | \(0.445229\pi\) | |||||||
\(14\) | 1.32086 | − | 2.29245i | 0.353016 | − | 0.612682i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.96246i | 0.961039i | 0.876984 | + | 0.480519i | \(0.159552\pi\) | ||||
−0.876984 | + | 0.480519i | \(0.840448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.29983 | − | 2.84800i | 0.757034 | − | 0.653376i | ||||
\(20\) | 0.765312i | 0.171129i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.09356i | − | 0.872750i | ||||||
\(23\) | −2.23644 | −0.466331 | −0.233165 | − | 0.972437i | \(-0.574908\pi\) | ||||
−0.233165 | + | 0.972437i | \(0.574908\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41430 | 0.882859 | ||||||||
\(26\) | 1.23469i | 0.242142i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.29245 | + | 1.32086i | 0.433232 | + | 0.249620i | ||||
\(29\) | 3.54539i | 0.658363i | 0.944267 | + | 0.329182i | \(0.106773\pi\) | ||||
−0.944267 | + | 0.329182i | \(0.893227\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.42378 | −1.51296 | −0.756478 | − | 0.654020i | \(-0.773081\pi\) | ||||
−0.756478 | + | 0.654020i | \(0.773081\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.96246 | −0.679557 | ||||||||
\(35\) | −1.01087 | + | 1.75444i | −0.170869 | + | 0.296554i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.83888i | − | 0.959906i | −0.877294 | − | 0.479953i | \(-0.840654\pi\) | ||
0.877294 | − | 0.479953i | \(-0.159346\pi\) | |||||||
\(38\) | 2.84800 | + | 3.29983i | 0.462007 | + | 0.535304i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.765312 | −0.121006 | ||||||||
\(41\) | 5.62174 | 0.877968 | 0.438984 | − | 0.898495i | \(-0.355338\pi\) | ||||
0.438984 | + | 0.898495i | \(0.355338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3395 | 1.72926 | 0.864628 | − | 0.502413i | \(-0.167554\pi\) | ||||
0.864628 | + | 0.502413i | \(0.167554\pi\) | |||||||
\(44\) | 4.09356 | 0.617128 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 2.23644i | − | 0.329746i | ||||||
\(47\) | 10.9149i | 1.59210i | 0.605230 | + | 0.796051i | \(0.293081\pi\) | ||||
−0.605230 | + | 0.796051i | \(0.706919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.51063 | + | 6.05603i | 0.501519 | + | 0.865147i | ||||
\(50\) | 4.41430i | 0.624276i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.23469 | −0.171220 | ||||||||
\(53\) | − | 8.28090i | − | 1.13747i | −0.822521 | − | 0.568734i | \(-0.807433\pi\) | ||
0.822521 | − | 0.568734i | \(-0.192567\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.13285i | 0.422434i | ||||||||
\(56\) | −1.32086 | + | 2.29245i | −0.176508 | + | 0.306341i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.54539 | −0.465533 | ||||||||
\(59\) | −6.22487 | −0.810409 | −0.405204 | − | 0.914226i | \(-0.632800\pi\) | ||||
−0.405204 | + | 0.914226i | \(0.632800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.64349i | 0.722574i | 0.932455 | + | 0.361287i | \(0.117663\pi\) | ||||
−0.932455 | + | 0.361287i | \(0.882337\pi\) | |||||||
\(62\) | − | 8.42378i | − | 1.06982i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 0.944922i | − | 0.117203i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.7327i | 1.67772i | 0.544347 | + | 0.838860i | \(0.316777\pi\) | ||||
−0.544347 | + | 0.838860i | \(0.683223\pi\) | |||||||
\(68\) | − | 3.96246i | − | 0.480519i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.75444 | − | 1.01087i | −0.209695 | − | 0.120823i | ||||
\(71\) | 11.2414i | 1.33411i | 0.745009 | + | 0.667054i | \(0.232445\pi\) | ||||
−0.745009 | + | 0.667054i | \(0.767555\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.01653i | 1.05530i | 0.849460 | + | 0.527652i | \(0.176928\pi\) | ||||
−0.849460 | + | 0.527652i | \(0.823072\pi\) | |||||||
\(74\) | 5.83888 | 0.678756 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.29983 | + | 2.84800i | −0.378517 | + | 0.326688i | ||||
\(77\) | 9.38428 | + | 5.40704i | 1.06944 | + | 0.616190i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.21470i | 0.699208i | 0.936898 | + | 0.349604i | \(0.113684\pi\) | ||||
−0.936898 | + | 0.349604i | \(0.886316\pi\) | |||||||
\(80\) | − | 0.765312i | − | 0.0855645i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.62174i | 0.620817i | ||||||||
\(83\) | 2.03860i | 0.223765i | 0.993721 | + | 0.111883i | \(0.0356881\pi\) | ||||
−0.993721 | + | 0.111883i | \(0.964312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.03252 | 0.328923 | ||||||||
\(86\) | 11.3395i | 1.22277i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.09356i | 0.436375i | ||||||||
\(89\) | 16.3174 | 1.72964 | 0.864821 | − | 0.502080i | \(-0.167432\pi\) | ||||
0.864821 | + | 0.502080i | \(0.167432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.83046 | − | 1.63086i | −0.296713 | − | 0.170960i | ||||
\(92\) | 2.23644 | 0.233165 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.9149 | −1.12579 | ||||||||
\(95\) | −2.17961 | − | 2.52540i | −0.223623 | − | 0.259101i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.90563 | 0.193487 | 0.0967437 | − | 0.995309i | \(-0.469157\pi\) | ||||
0.0967437 | + | 0.995309i | \(0.469157\pi\) | |||||||
\(98\) | −6.05603 | + | 3.51063i | −0.611751 | + | 0.354627i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.41430 | −0.441430 | ||||||||
\(101\) | 11.8561i | 1.17973i | 0.807503 | + | 0.589863i | \(0.200818\pi\) | ||||
−0.807503 | + | 0.589863i | \(0.799182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.00772432 | 0.000761100 | 0.000380550 | − | 1.00000i | \(-0.499879\pi\) | ||||
0.000380550 | 1.00000i | \(0.499879\pi\) | ||||||||
\(104\) | − | 1.23469i | − | 0.121071i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.28090 | 0.804312 | ||||||||
\(107\) | − | 13.2084i | − | 1.27690i | −0.769662 | − | 0.638452i | \(-0.779575\pi\) | ||
0.769662 | − | 0.638452i | \(-0.220425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.93963i | − | 0.568914i | −0.958689 | − | 0.284457i | \(-0.908187\pi\) | ||
0.958689 | − | 0.284457i | \(-0.0918132\pi\) | |||||||
\(110\) | −3.13285 | −0.298706 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.29245 | − | 1.32086i | −0.216616 | − | 0.124810i | ||||
\(113\) | − | 4.56747i | − | 0.429671i | −0.976650 | − | 0.214836i | \(-0.931078\pi\) | ||
0.976650 | − | 0.214836i | \(-0.0689216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.71158i | 0.159605i | ||||||||
\(116\) | − | 3.54539i | − | 0.329182i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.22487i | − | 0.573046i | ||||||
\(119\) | 5.23388 | − | 9.08374i | 0.479789 | − | 0.832705i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.75725 | 0.523386 | ||||||||
\(122\) | −5.64349 | −0.510937 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.42378 | 0.756478 | ||||||||
\(125\) | − | 7.20488i | − | 0.644424i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.92024i | 0.259129i | 0.991571 | + | 0.129565i | \(0.0413580\pi\) | ||||
−0.991571 | + | 0.129565i | \(0.958642\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.944922 | 0.0828751 | ||||||||
\(131\) | 10.9795i | 0.959280i | 0.877465 | + | 0.479640i | \(0.159233\pi\) | ||||
−0.877465 | + | 0.479640i | \(0.840767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3265 | + | 2.17026i | −0.982134 | + | 0.188185i | ||||
\(134\) | −13.7327 | −1.18633 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.96246 | 0.339779 | ||||||||
\(137\) | 16.2479 | 1.38815 | 0.694075 | − | 0.719902i | \(-0.255813\pi\) | ||||
0.694075 | + | 0.719902i | \(0.255813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.75338i | 0.148720i | 0.997231 | + | 0.0743600i | \(0.0236914\pi\) | ||||
−0.997231 | + | 0.0743600i | \(0.976309\pi\) | |||||||
\(140\) | 1.01087 | − | 1.75444i | 0.0854344 | − | 0.148277i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.2414 | −0.943357 | ||||||||
\(143\) | −5.05427 | −0.422659 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.71333 | 0.225330 | ||||||||
\(146\) | −9.01653 | −0.746213 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.83888i | 0.479953i | ||||||||
\(149\) | 13.3695 | 1.09527 | 0.547636 | − | 0.836716i | \(-0.315528\pi\) | ||||
0.547636 | + | 0.836716i | \(0.315528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0410i | 1.14264i | 0.820728 | + | 0.571320i | \(0.193568\pi\) | ||||
−0.820728 | + | 0.571320i | \(0.806432\pi\) | |||||||
\(152\) | −2.84800 | − | 3.29983i | −0.231003 | − | 0.267652i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.40704 | + | 9.38428i | −0.435712 | + | 0.756207i | ||||
\(155\) | 6.44682i | 0.517821i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2233i | 1.61399i | 0.590557 | + | 0.806996i | \(0.298908\pi\) | ||||
−0.590557 | + | 0.806996i | \(0.701092\pi\) | |||||||
\(158\) | −6.21470 | −0.494415 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.765312 | 0.0605032 | ||||||||
\(161\) | 5.12693 | + | 2.95404i | 0.404059 | + | 0.232811i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1471 | 1.10809 | 0.554045 | − | 0.832487i | \(-0.313084\pi\) | ||||
0.554045 | + | 0.832487i | \(0.313084\pi\) | |||||||
\(164\) | −5.62174 | −0.438984 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.03860 | −0.158226 | ||||||||
\(167\) | 3.09425 | 0.239441 | 0.119720 | − | 0.992808i | \(-0.461800\pi\) | ||||
0.119720 | + | 0.992808i | \(0.461800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4755 | −0.882734 | ||||||||
\(170\) | 3.03252i | 0.232584i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.3395 | −0.864628 | ||||||||
\(173\) | −13.7442 | −1.04495 | −0.522477 | − | 0.852653i | \(-0.674992\pi\) | ||||
−0.522477 | + | 0.852653i | \(0.674992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1195 | − | 5.83069i | −0.764966 | − | 0.440759i | ||||
\(176\) | −4.09356 | −0.308564 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.3174i | 1.22304i | ||||||||
\(179\) | − | 18.6774i | − | 1.39602i | −0.716089 | − | 0.698009i | \(-0.754070\pi\) | ||
0.716089 | − | 0.698009i | \(-0.245930\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.23590 | 0.612169 | 0.306085 | − | 0.952004i | \(-0.400981\pi\) | ||||
0.306085 | + | 0.952004i | \(0.400981\pi\) | |||||||
\(182\) | 1.63086 | − | 2.83046i | 0.120887 | − | 0.209807i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.23644i | 0.164873i | ||||||||
\(185\) | −4.46857 | −0.328536 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.2206i | − | 1.18617i | ||||||
\(188\) | − | 10.9149i | − | 0.796051i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.52540 | − | 2.17961i | 0.183212 | − | 0.158125i | ||||
\(191\) | −3.13660 | −0.226956 | −0.113478 | − | 0.993541i | \(-0.536199\pi\) | ||||
−0.113478 | + | 0.993541i | \(0.536199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3387i | 1.24807i | 0.781398 | + | 0.624033i | \(0.214507\pi\) | ||||
−0.781398 | + | 0.624033i | \(0.785493\pi\) | |||||||
\(194\) | 1.90563i | 0.136816i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.51063 | − | 6.05603i | −0.250759 | − | 0.432573i | ||||
\(197\) | −21.1245 | −1.50505 | −0.752527 | − | 0.658561i | \(-0.771165\pi\) | ||||
−0.752527 | + | 0.658561i | \(0.771165\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.25847i | 0.301875i | 0.988543 | + | 0.150937i | \(0.0482292\pi\) | ||||
−0.988543 | + | 0.150937i | \(0.951771\pi\) | |||||||
\(200\) | − | 4.41430i | − | 0.312138i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.8561 | −0.834192 | ||||||||
\(203\) | 4.68299 | − | 8.12763i | 0.328681 | − | 0.570448i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.30238i | − | 0.300492i | ||||||
\(206\) | 0.00772432i | 0.000538179i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.23469 | 0.0856102 | ||||||||
\(209\) | −13.5081 | + | 11.6585i | −0.934373 | + | 0.806433i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.9211i | − | 1.71564i | −0.513953 | − | 0.857818i | \(-0.671819\pi\) | ||
0.513953 | − | 0.857818i | \(-0.328181\pi\) | |||||||
\(212\) | 8.28090i | 0.568734i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.2084 | 0.902907 | ||||||||
\(215\) | − | 8.67825i | − | 0.591852i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.3111 | + | 11.1267i | 1.31092 | + | 0.755328i | ||||
\(218\) | 5.93963 | 0.402283 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 3.13285i | − | 0.211217i | ||||||
\(221\) | 4.89241i | 0.329099i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.6895 | −0.715821 | −0.357910 | − | 0.933756i | \(-0.616511\pi\) | ||||
−0.357910 | + | 0.933756i | \(0.616511\pi\) | |||||||
\(224\) | 1.32086 | − | 2.29245i | 0.0882540 | − | 0.153171i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.56747 | 0.303823 | ||||||||
\(227\) | −18.2992 | −1.21456 | −0.607280 | − | 0.794488i | \(-0.707739\pi\) | ||||
−0.607280 | + | 0.794488i | \(0.707739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3769i | − | 0.685725i | −0.939386 | − | 0.342863i | \(-0.888603\pi\) | ||
0.939386 | − | 0.342863i | \(-0.111397\pi\) | |||||||
\(230\) | −1.71158 | −0.112858 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.54539 | 0.232767 | ||||||||
\(233\) | −1.50567 | −0.0986397 | −0.0493198 | − | 0.998783i | \(-0.515705\pi\) | ||||
−0.0493198 | + | 0.998783i | \(0.515705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.35331 | 0.544910 | ||||||||
\(236\) | 6.22487 | 0.405204 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.08374 | + | 5.23388i | 0.588812 | + | 0.339262i | ||||
\(239\) | 8.59215 | 0.555780 | 0.277890 | − | 0.960613i | \(-0.410365\pi\) | ||||
0.277890 | + | 0.960613i | \(0.410365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.4908 | −1.06226 | −0.531132 | − | 0.847289i | \(-0.678233\pi\) | ||||
−0.531132 | + | 0.847289i | \(0.678233\pi\) | |||||||
\(242\) | 5.75725i | 0.370090i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.64349i | − | 0.361287i | ||||||
\(245\) | 4.63475 | − | 2.68673i | 0.296103 | − | 0.171649i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07426 | − | 3.51639i | 0.259239 | − | 0.223743i | ||||
\(248\) | 8.42378i | 0.534910i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.20488 | 0.455676 | ||||||||
\(251\) | 1.47028i | 0.0928031i | 0.998923 | + | 0.0464016i | \(0.0147754\pi\) | ||||
−0.998923 | + | 0.0464016i | \(0.985225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.15502 | 0.575571 | ||||||||
\(254\) | −2.92024 | −0.183232 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2597 | 1.20139 | 0.600693 | − | 0.799480i | \(-0.294891\pi\) | ||||
0.600693 | + | 0.799480i | \(0.294891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.71237 | + | 13.3853i | −0.479224 | + | 0.831724i | ||||
\(260\) | 0.944922i | 0.0586016i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.9795 | −0.678313 | ||||||||
\(263\) | −2.32602 | −0.143429 | −0.0717144 | − | 0.997425i | \(-0.522847\pi\) | ||||
−0.0717144 | + | 0.997425i | \(0.522847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.33747 | −0.389308 | ||||||||
\(266\) | −2.17026 | − | 11.3265i | −0.133067 | − | 0.694473i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 13.7327i | − | 0.838860i | ||||||
\(269\) | 26.1715 | 1.59571 | 0.797854 | − | 0.602851i | \(-0.205969\pi\) | ||||
0.797854 | + | 0.602851i | \(0.205969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.5470i | 1.49113i | 0.666436 | + | 0.745563i | \(0.267819\pi\) | ||||
−0.666436 | + | 0.745563i | \(0.732181\pi\) | |||||||
\(272\) | 3.96246i | 0.240260i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.2479i | 0.981571i | ||||||||
\(275\) | −18.0702 | −1.08967 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.5064 | −1.47244 | −0.736222 | − | 0.676740i | \(-0.763392\pi\) | ||||
−0.736222 | + | 0.676740i | \(0.763392\pi\) | |||||||
\(278\) | −1.75338 | −0.105161 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.75444 | + | 1.01087i | 0.104848 | + | 0.0604113i | ||||
\(281\) | − | 0.686453i | − | 0.0409503i | −0.999790 | − | 0.0204752i | \(-0.993482\pi\) | ||
0.999790 | − | 0.0204752i | \(-0.00651790\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.7294i | 1.23224i | 0.787654 | + | 0.616118i | \(0.211295\pi\) | ||||
−0.787654 | + | 0.616118i | \(0.788705\pi\) | |||||||
\(284\) | − | 11.2414i | − | 0.667054i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5.05427i | − | 0.298865i | ||||||
\(287\) | −12.8875 | − | 7.42556i | −0.760727 | − | 0.438317i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.29887 | 0.0764043 | ||||||||
\(290\) | 2.71333i | 0.159332i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 9.01653i | − | 0.527652i | ||||||
\(293\) | −2.43374 | −0.142181 | −0.0710903 | − | 0.997470i | \(-0.522648\pi\) | ||||
−0.0710903 | + | 0.997470i | \(0.522648\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.76397i | 0.277369i | ||||||||
\(296\) | −5.83888 | −0.339378 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.3695i | 0.774475i | ||||||||
\(299\) | −2.76131 | −0.159691 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.9952 | − | 14.9779i | −1.49834 | − | 0.863313i | ||||
\(302\) | −14.0410 | −0.807968 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.29983 | − | 2.84800i | 0.189258 | − | 0.163344i | ||||
\(305\) | 4.31903 | 0.247307 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1689 | 0.922807 | 0.461404 | − | 0.887190i | \(-0.347346\pi\) | ||||
0.461404 | + | 0.887190i | \(0.347346\pi\) | |||||||
\(308\) | −9.38428 | − | 5.40704i | −0.534719 | − | 0.308095i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.44682 | −0.366155 | ||||||||
\(311\) | − | 32.0665i | − | 1.81832i | −0.416445 | − | 0.909161i | \(-0.636724\pi\) | ||
0.416445 | − | 0.909161i | \(-0.363276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.1690i | − | 1.53568i | −0.640641 | − | 0.767841i | \(-0.721331\pi\) | ||
0.640641 | − | 0.767841i | \(-0.278669\pi\) | |||||||
\(314\) | −20.2233 | −1.14126 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 6.21470i | − | 0.349604i | ||||||
\(317\) | 23.6041i | 1.32574i | 0.748736 | + | 0.662869i | \(0.230661\pi\) | ||||
−0.748736 | + | 0.662869i | \(0.769339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.5133i | − | 0.812588i | ||||||
\(320\) | 0.765312i | 0.0427823i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.95404 | + | 5.12693i | −0.164622 | + | 0.285713i | ||||
\(323\) | 11.2851 | + | 13.0755i | 0.627920 | + | 0.727539i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.45028 | 0.302327 | ||||||||
\(326\) | 14.1471i | 0.783538i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.62174i | − | 0.310409i | ||||||
\(329\) | 14.4171 | − | 25.0218i | 0.794841 | − | 1.37950i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 0.995116i | − | 0.0546965i | −0.999626 | − | 0.0273483i | \(-0.991294\pi\) | ||
0.999626 | − | 0.0273483i | \(-0.00870631\pi\) | |||||||
\(332\) | − | 2.03860i | − | 0.111883i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.09425i | 0.169310i | ||||||||
\(335\) | 10.5098 | 0.574213 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.5073i | − | 1.49842i | −0.662335 | − | 0.749208i | \(-0.730434\pi\) | ||
0.662335 | − | 0.749208i | \(-0.269566\pi\) | |||||||
\(338\) | − | 11.4755i | − | 0.624187i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.03252 | −0.164462 | ||||||||
\(341\) | 34.4833 | 1.86737 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.0487486 | − | 18.5202i | −0.00263218 | − | 0.999997i | ||||
\(344\) | − | 11.3395i | − | 0.611384i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 13.7442i | − | 0.738895i | ||||||
\(347\) | −7.19341 | −0.386162 | −0.193081 | − | 0.981183i | \(-0.561848\pi\) | ||||
−0.193081 | + | 0.981183i | \(0.561848\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.0586i | 1.93017i | 0.261932 | + | 0.965086i | \(0.415640\pi\) | ||||
−0.261932 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(350\) | 5.83069 | − | 10.1195i | 0.311663 | − | 0.540912i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.09356i | − | 0.218188i | ||||||
\(353\) | 6.51821i | 0.346930i | 0.984840 | + | 0.173465i | \(0.0554963\pi\) | ||||
−0.984840 | + | 0.173465i | \(0.944504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.60318 | 0.456609 | ||||||||
\(356\) | −16.3174 | −0.864821 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.6774 | 0.987133 | ||||||||
\(359\) | −31.9680 | −1.68721 | −0.843604 | − | 0.536966i | \(-0.819570\pi\) | ||||
−0.843604 | + | 0.536966i | \(0.819570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.77779 | − | 18.7958i | 0.146199 | − | 0.989255i | ||||
\(362\) | 8.23590i | 0.432869i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.83046 | + | 1.63086i | 0.148356 | + | 0.0854801i | ||||
\(365\) | 6.90046 | 0.361186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.2110i | − | 1.26380i | −0.775049 | − | 0.631901i | \(-0.782275\pi\) | ||
0.775049 | − | 0.631901i | \(-0.217725\pi\) | |||||||
\(368\) | −2.23644 | −0.116583 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 4.46857i | − | 0.232310i | ||||||
\(371\) | −10.9379 | + | 18.9835i | −0.567870 | + | 0.985575i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.25956i | 0.375886i | 0.982180 | + | 0.187943i | \(0.0601820\pi\) | ||||
−0.982180 | + | 0.187943i | \(0.939818\pi\) | |||||||
\(374\) | 16.2206 | 0.838747 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.9149 | 0.562893 | ||||||||
\(377\) | 4.37745i | 0.225450i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.8834i | − | 0.918608i | −0.888279 | − | 0.459304i | \(-0.848099\pi\) | ||
0.888279 | − | 0.459304i | \(-0.151901\pi\) | |||||||
\(380\) | 2.17961 | + | 2.52540i | 0.111812 | + | 0.129550i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3.13660i | − | 0.160482i | ||||||
\(383\) | 5.90529 | 0.301746 | 0.150873 | − | 0.988553i | \(-0.451791\pi\) | ||||
0.150873 | + | 0.988553i | \(0.451791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.13808 | − | 7.18190i | 0.210896 | − | 0.366024i | ||||
\(386\) | −17.3387 | −0.882515 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.90563 | −0.0967437 | ||||||||
\(389\) | 26.0156 | 1.31904 | 0.659521 | − | 0.751686i | \(-0.270759\pi\) | ||||
0.659521 | + | 0.751686i | \(0.270759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.86183i | − | 0.448162i | ||||||
\(392\) | 6.05603 | − | 3.51063i | 0.305876 | − | 0.177314i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 21.1245i | − | 1.06423i | ||||||
\(395\) | 4.75618 | 0.239310 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3829i | 1.02299i | 0.859286 | + | 0.511495i | \(0.170908\pi\) | ||||
−0.859286 | + | 0.511495i | \(0.829092\pi\) | |||||||
\(398\) | −4.25847 | −0.213458 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.41430 | 0.220715 | ||||||||
\(401\) | 6.26305i | 0.312762i | 0.987697 | + | 0.156381i | \(0.0499827\pi\) | ||||
−0.987697 | + | 0.156381i | \(0.950017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.4007 | −0.518098 | ||||||||
\(404\) | − | 11.8561i | − | 0.589863i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.12763 | + | 4.68299i | 0.403368 | + | 0.232413i | ||||
\(407\) | 23.9018i | 1.18477i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.08055 | 0.449004 | 0.224502 | − | 0.974474i | \(-0.427924\pi\) | ||||
0.224502 | + | 0.974474i | \(0.427924\pi\) | |||||||
\(410\) | 4.30238 | 0.212480 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.00772432 | −0.000380550 | ||||||||
\(413\) | 14.2702 | + | 8.22221i | 0.702190 | + | 0.404589i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.56016 | 0.0765854 | ||||||||
\(416\) | 1.23469i | 0.0605355i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.6585 | − | 13.5081i | −0.570234 | − | 0.660701i | ||||
\(419\) | 20.3578i | 0.994544i | 0.867595 | + | 0.497272i | \(0.165665\pi\) | ||||
−0.867595 | + | 0.497272i | \(0.834335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.6067i | − | 0.711888i | −0.934507 | − | 0.355944i | \(-0.884159\pi\) | ||
0.934507 | − | 0.355944i | \(-0.115841\pi\) | |||||||
\(422\) | 24.9211 | 1.21314 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.28090 | −0.402156 | ||||||||
\(425\) | 17.4915i | 0.848462i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.45428 | − | 12.9374i | 0.360738 | − | 0.626084i | ||||
\(428\) | 13.2084i | 0.638452i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.67825 | 0.418502 | ||||||||
\(431\) | − | 1.86831i | − | 0.0899933i | −0.998987 | − | 0.0449966i | \(-0.985672\pi\) | ||
0.998987 | − | 0.0449966i | \(-0.0143277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.0009 | −1.48981 | −0.744903 | − | 0.667172i | \(-0.767504\pi\) | ||||
−0.744903 | + | 0.667172i | \(0.767504\pi\) | |||||||
\(434\) | −11.1267 | + | 19.3111i | −0.534097 | + | 0.926961i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.93963i | 0.284457i | ||||||||
\(437\) | −7.37989 | + | 6.36939i | −0.353028 | + | 0.304689i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8712 | 1.28249 | 0.641246 | − | 0.767336i | \(-0.278418\pi\) | ||||
0.641246 | + | 0.767336i | \(0.278418\pi\) | |||||||
\(440\) | 3.13285 | 0.149353 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.89241 | −0.232708 | ||||||||
\(443\) | 8.07575 | 0.383690 | 0.191845 | − | 0.981425i | \(-0.438553\pi\) | ||||
0.191845 | + | 0.981425i | \(0.438553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.4879i | − | 0.591984i | ||||||
\(446\) | − | 10.6895i | − | 0.506162i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.29245 | + | 1.32086i | 0.108308 | + | 0.0624050i | ||||
\(449\) | 7.13077i | 0.336522i | 0.985742 | + | 0.168261i | \(0.0538151\pi\) | ||||
−0.985742 | + | 0.168261i | \(0.946185\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.0129 | −1.08364 | ||||||||
\(452\) | 4.56747i | 0.214836i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 18.2992i | − | 0.858823i | ||||||
\(455\) | −1.24811 | + | 2.16618i | −0.0585125 | + | 0.101552i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.94992 | −0.231547 | −0.115774 | − | 0.993276i | \(-0.536935\pi\) | ||||
−0.115774 | + | 0.993276i | \(0.536935\pi\) | |||||||
\(458\) | 10.3769 | 0.484881 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 1.71158i | − | 0.0798027i | ||||||
\(461\) | − | 12.3884i | − | 0.576983i | −0.957482 | − | 0.288492i | \(-0.906846\pi\) | ||
0.957482 | − | 0.288492i | \(-0.0931537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.203161 | 0.00944167 | 0.00472084 | − | 0.999989i | \(-0.498497\pi\) | ||||
0.00472084 | + | 0.999989i | \(0.498497\pi\) | |||||||
\(464\) | 3.54539i | 0.164591i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 1.50567i | − | 0.0697488i | ||||||
\(467\) | − | 39.7312i | − | 1.83854i | −0.393629 | − | 0.919269i | \(-0.628780\pi\) | ||
0.393629 | − | 0.919269i | \(-0.371220\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.1391 | − | 31.4816i | 0.837585 | − | 1.45368i | ||||
\(470\) | 8.35331i | 0.385309i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.22487i | 0.286523i | ||||||||
\(473\) | −46.4189 | −2.13434 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.5664 | − | 12.5719i | 0.668354 | − | 0.576839i | ||||
\(476\) | −5.23388 | + | 9.08374i | −0.239895 | + | 0.416353i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.59215i | 0.392996i | ||||||||
\(479\) | 42.8715i | 1.95885i | 0.201813 | + | 0.979424i | \(0.435317\pi\) | ||||
−0.201813 | + | 0.979424i | \(0.564683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.20920i | − | 0.328711i | ||||||
\(482\) | − | 16.4908i | − | 0.751135i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.75725 | −0.261693 | ||||||||
\(485\) | − | 1.45840i | − | 0.0662226i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.8373i | 1.17080i | 0.810744 | + | 0.585400i | \(0.199063\pi\) | ||||
−0.810744 | + | 0.585400i | \(0.800937\pi\) | |||||||
\(488\) | 5.64349 | 0.255469 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.68673 | + | 4.63475i | 0.121374 | + | 0.209377i | ||||
\(491\) | 0.388503 | 0.0175329 | 0.00876645 | − | 0.999962i | \(-0.497210\pi\) | ||||
0.00876645 | + | 0.999962i | \(0.497210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.0485 | −0.632713 | ||||||||
\(494\) | 3.51639 | + | 4.07426i | 0.158210 | + | 0.183310i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.42378 | −0.378239 | ||||||||
\(497\) | 14.8484 | − | 25.7703i | 0.666040 | − | 1.15596i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.56308 | 0.159505 | 0.0797527 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797527 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(500\) | 7.20488i | 0.322212i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.47028 | −0.0656217 | ||||||||
\(503\) | 8.38590i | 0.373909i | 0.982369 | + | 0.186954i | \(0.0598617\pi\) | ||||
−0.982369 | + | 0.186954i | \(0.940138\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.07362 | 0.403771 | ||||||||
\(506\) | 9.15502i | 0.406990i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 2.92024i | − | 0.129565i | ||||||
\(509\) | 27.1248 | 1.20229 | 0.601143 | − | 0.799141i | \(-0.294712\pi\) | ||||
0.601143 | + | 0.799141i | \(0.294712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9096 | − | 20.6699i | 0.526850 | − | 0.914383i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.2597i | 0.849508i | ||||||||
\(515\) | − | 0.00591152i | − | 0.000260493i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 44.6808i | − | 1.96506i | ||||||
\(518\) | −13.3853 | − | 7.71237i | −0.588118 | − | 0.338862i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.944922 | −0.0414376 | ||||||||
\(521\) | −6.02707 | −0.264051 | −0.132025 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132025 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.5396 | 0.810681 | 0.405341 | − | 0.914166i | \(-0.367153\pi\) | ||||
0.405341 | + | 0.914166i | \(0.367153\pi\) | |||||||
\(524\) | − | 10.9795i | − | 0.479640i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 2.32602i | − | 0.101420i | ||||||
\(527\) | − | 33.3789i | − | 1.45401i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9983 | −0.782536 | ||||||||
\(530\) | − | 6.33747i | − | 0.275282i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.3265 | − | 2.17026i | 0.491067 | − | 0.0940926i | ||||
\(533\) | 6.94109 | 0.300652 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.1085 | −0.437030 | ||||||||
\(536\) | 13.7327 | 0.593164 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.1715i | 1.12834i | ||||||||
\(539\) | −14.3710 | − | 24.7907i | −0.619002 | − | 1.06781i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8956 | −0.597421 | −0.298710 | − | 0.954344i | \(-0.596556\pi\) | ||||
−0.298710 | + | 0.954344i | \(0.596556\pi\) | |||||||
\(542\) | −24.5470 | −1.05438 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.96246 | −0.169889 | ||||||||
\(545\) | −4.54567 | −0.194715 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.6550i | − | 0.712118i | −0.934463 | − | 0.356059i | \(-0.884120\pi\) | ||
0.934463 | − | 0.356059i | \(-0.115880\pi\) | |||||||
\(548\) | −16.2479 | −0.694075 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 18.0702i | − | 0.770516i | ||||||
\(551\) | 10.0973 | + | 11.6992i | 0.430159 | + | 0.498403i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.20877 | − | 14.2469i | 0.349073 | − | 0.605838i | ||||
\(554\) | − | 24.5064i | − | 1.04118i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 1.75338i | − | 0.0743600i | ||||||
\(557\) | 34.7999 | 1.47452 | 0.737259 | − | 0.675610i | \(-0.236120\pi\) | ||||
0.737259 | + | 0.675610i | \(0.236120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0007 | 0.592168 | ||||||||
\(560\) | −1.01087 | + | 1.75444i | −0.0427172 | + | 0.0741385i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.686453 | 0.0289563 | ||||||||
\(563\) | 7.55182 | 0.318271 | 0.159136 | − | 0.987257i | \(-0.449129\pi\) | ||||
0.159136 | + | 0.987257i | \(0.449129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.49554 | −0.147058 | ||||||||
\(566\) | −20.7294 | −0.871322 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.2414 | 0.471678 | ||||||||
\(569\) | − | 26.5621i | − | 1.11354i | −0.830666 | − | 0.556770i | \(-0.812040\pi\) | ||
0.830666 | − | 0.556770i | \(-0.187960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.69844 | −0.364018 | −0.182009 | − | 0.983297i | \(-0.558260\pi\) | ||||
−0.182009 | + | 0.983297i | \(0.558260\pi\) | |||||||
\(572\) | 5.05427 | 0.211330 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.42556 | − | 12.8875i | 0.309937 | − | 0.537915i | ||||
\(575\) | −9.87233 | −0.411704 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.5019i | 1.14492i | 0.819933 | + | 0.572460i | \(0.194011\pi\) | ||||
−0.819933 | + | 0.572460i | \(0.805989\pi\) | |||||||
\(578\) | 1.29887i | 0.0540260i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.71333 | −0.112665 | ||||||||
\(581\) | 2.69271 | − | 4.67338i | 0.111713 | − | 0.193884i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8984i | 1.40393i | ||||||||
\(584\) | 9.01653 | 0.373106 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 2.43374i | − | 0.100537i | ||||||
\(587\) | 0.132209i | 0.00545686i | 0.999996 | + | 0.00272843i | \(0.000868488\pi\) | ||||
−0.999996 | + | 0.00272843i | \(0.999132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.7971 | + | 23.9909i | −1.14536 | + | 0.988529i | ||||
\(590\) | −4.76397 | −0.196129 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 5.83888i | − | 0.239977i | ||||||
\(593\) | 9.08659i | 0.373142i | 0.982442 | + | 0.186571i | \(0.0597374\pi\) | ||||
−0.982442 | + | 0.186571i | \(0.940263\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.95190 | − | 4.00555i | −0.285000 | − | 0.164212i | ||||
\(596\) | −13.3695 | −0.547636 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 2.76131i | − | 0.112918i | ||||||
\(599\) | − | 1.77247i | − | 0.0724213i | −0.999344 | − | 0.0362106i | \(-0.988471\pi\) | ||
0.999344 | − | 0.0362106i | \(-0.0115287\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.71929 | 0.192504 | 0.0962520 | − | 0.995357i | \(-0.469315\pi\) | ||||
0.0962520 | + | 0.995357i | \(0.469315\pi\) | |||||||
\(602\) | 14.9779 | − | 25.9952i | 0.610455 | − | 1.05948i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 14.0410i | − | 0.571320i | ||||||
\(605\) | − | 4.40609i | − | 0.179133i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.5330 | 1.64519 | 0.822593 | − | 0.568631i | \(-0.192527\pi\) | ||||
0.822593 | + | 0.568631i | \(0.192527\pi\) | |||||||
\(608\) | 2.84800 | + | 3.29983i | 0.115502 | + | 0.133826i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.31903i | 0.174872i | ||||||||
\(611\) | 13.4765i | 0.545201i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.97167 | 0.200804 | 0.100402 | − | 0.994947i | \(-0.467987\pi\) | ||||
0.100402 | + | 0.994947i | \(0.467987\pi\) | |||||||
\(614\) | 16.1689i | 0.652523i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.40704 | − | 9.38428i | 0.217856 | − | 0.378103i | ||||
\(617\) | −11.0803 | −0.446078 | −0.223039 | − | 0.974810i | \(-0.571598\pi\) | ||||
−0.223039 | + | 0.974810i | \(0.571598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.7817i | 1.47838i | 0.673497 | + | 0.739190i | \(0.264791\pi\) | ||||
−0.673497 | + | 0.739190i | \(0.735209\pi\) | |||||||
\(620\) | − | 6.44682i | − | 0.258911i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.0665 | 1.28575 | ||||||||
\(623\) | −37.4068 | − | 21.5531i | −1.49867 | − | 0.863507i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5575 | 0.662300 | ||||||||
\(626\) | 27.1690 | 1.08589 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 20.2233i | − | 0.806996i | ||||||
\(629\) | 23.1364 | 0.922507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.31188 | 0.0522251 | 0.0261126 | − | 0.999659i | \(-0.491687\pi\) | ||||
0.0261126 | + | 0.999659i | \(0.491687\pi\) | |||||||
\(632\) | 6.21470 | 0.247207 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.6041 | −0.937438 | ||||||||
\(635\) | 2.23489 | 0.0886891 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.33453 | + | 7.47730i | 0.171741 | + | 0.296261i | ||||
\(638\) | 14.5133 | 0.574587 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.765312 | −0.0302516 | ||||||||
\(641\) | − | 31.5076i | − | 1.24447i | −0.782829 | − | 0.622237i | \(-0.786224\pi\) | ||
0.782829 | − | 0.622237i | \(-0.213776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.6317i | 1.08969i | 0.838538 | + | 0.544844i | \(0.183411\pi\) | ||||
−0.838538 | + | 0.544844i | \(0.816589\pi\) | |||||||
\(644\) | −5.12693 | − | 2.95404i | −0.202029 | − | 0.116405i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.0755 | + | 11.2851i | −0.514448 | + | 0.444006i | ||||
\(647\) | 2.13843i | 0.0840705i | 0.999116 | + | 0.0420353i | \(0.0133842\pi\) | ||||
−0.999116 | + | 0.0420353i | \(0.986616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.4819 | 1.00025 | ||||||||
\(650\) | 5.45028i | 0.213778i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.1471 | −0.554045 | ||||||||
\(653\) | −22.8181 | −0.892942 | −0.446471 | − | 0.894798i | \(-0.647319\pi\) | ||||
−0.446471 | + | 0.894798i | \(0.647319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.40271 | 0.328321 | ||||||||
\(656\) | 5.62174 | 0.219492 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25.0218 | + | 14.4171i | 0.975453 | + | 0.562037i | ||||
\(659\) | − | 14.4903i | − | 0.564463i | −0.959346 | − | 0.282231i | \(-0.908925\pi\) | ||
0.959346 | − | 0.282231i | \(-0.0910746\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.7242 | −0.494915 | −0.247458 | − | 0.968899i | \(-0.579595\pi\) | ||||
−0.247458 | + | 0.968899i | \(0.579595\pi\) | |||||||
\(662\) | 0.995116 | 0.0386763 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.03860 | 0.0791130 | ||||||||
\(665\) | 1.66093 | + | 8.66832i | 0.0644079 | + | 0.336143i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.92907i | − | 0.307015i | ||||||
\(668\) | −3.09425 | −0.119720 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.5098i | 0.406030i | ||||||||
\(671\) | − | 23.1020i | − | 0.891841i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.9711i | 1.23239i | 0.787592 | + | 0.616197i | \(0.211328\pi\) | ||||
−0.787592 | + | 0.616197i | \(0.788672\pi\) | |||||||
\(674\) | 27.5073 | 1.05954 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.4755 | 0.441367 | ||||||||
\(677\) | 1.23340 | 0.0474035 | 0.0237018 | − | 0.999719i | \(-0.492455\pi\) | ||||
0.0237018 | + | 0.999719i | \(0.492455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.36856 | − | 2.51708i | −0.167650 | − | 0.0965967i | ||||
\(680\) | − | 3.03252i | − | 0.116292i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 34.4833i | 1.32043i | ||||||||
\(683\) | 15.2483i | 0.583460i | 0.956501 | + | 0.291730i | \(0.0942308\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.4347i | − | 0.475106i | ||||||
\(686\) | 18.5202 | − | 0.0487486i | 0.707104 | − | 0.00186123i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.3395 | 0.432314 | ||||||||
\(689\) | − | 10.2243i | − | 0.389516i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.6678i | − | 1.54708i | −0.633750 | − | 0.773538i | \(-0.718485\pi\) | ||
0.633750 | − | 0.773538i | \(-0.281515\pi\) | |||||||
\(692\) | 13.7442 | 0.522477 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 7.19341i | − | 0.273058i | ||||||
\(695\) | 1.34189 | 0.0509006 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2759i | 0.843761i | ||||||||
\(698\) | −36.0586 | −1.36484 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.1195 | + | 5.83069i | 0.382483 | + | 0.220379i | ||||
\(701\) | 10.6740 | 0.403151 | 0.201576 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201576 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6291 | − | 19.2673i | −0.627180 | − | 0.726681i | ||||
\(704\) | 4.09356 | 0.154282 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.51821 | −0.245316 | ||||||||
\(707\) | 15.6603 | − | 27.1795i | 0.588966 | − | 1.02219i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0499 | 1.31633 | 0.658163 | − | 0.752876i | \(-0.271334\pi\) | ||||
0.658163 | + | 0.752876i | \(0.271334\pi\) | |||||||
\(710\) | 8.60318i | 0.322871i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 16.3174i | − | 0.611521i | ||||||
\(713\) | 18.8393 | 0.705537 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.86810i | 0.144659i | ||||||||
\(716\) | 18.6774i | 0.698009i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 31.9680i | − | 1.19304i | ||||||
\(719\) | − | 17.5697i | − | 0.655240i | −0.944810 | − | 0.327620i | \(-0.893753\pi\) | ||
0.944810 | − | 0.327620i | \(-0.106247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0177076 | − | 0.0102028i | −0.000659466 | − | 0.000379972i | ||||
\(722\) | 18.7958 | + | 2.77779i | 0.699509 | + | 0.103379i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.23590 | −0.306085 | ||||||||
\(725\) | 15.6504i | 0.581242i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.00613i | 0.148579i | 0.997237 | + | 0.0742896i | \(0.0236689\pi\) | ||||
−0.997237 | + | 0.0742896i | \(0.976331\pi\) | |||||||
\(728\) | −1.63086 | + | 2.83046i | −0.0604435 | + | 0.104904i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.90046i | 0.255397i | ||||||||
\(731\) | 44.9323i | 1.66188i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6070i | 0.650328i | 0.945658 | + | 0.325164i | \(0.105420\pi\) | ||||
−0.945658 | + | 0.325164i | \(0.894580\pi\) | |||||||
\(734\) | 24.2110 | 0.893643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.23644i | − | 0.0824364i | ||||||
\(737\) | − | 56.2158i | − | 2.07073i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3500 | −0.932514 | −0.466257 | − | 0.884649i | \(-0.654398\pi\) | ||||
−0.466257 | + | 0.884649i | \(0.654398\pi\) | |||||||
\(740\) | 4.46857 | 0.164268 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.9835 | − | 10.9379i | −0.696907 | − | 0.401545i | ||||
\(743\) | − | 1.29589i | − | 0.0475416i | −0.999717 | − | 0.0237708i | \(-0.992433\pi\) | ||
0.999717 | − | 0.0237708i | \(-0.00756719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10.2318i | − | 0.374866i | ||||||
\(746\) | −7.25956 | −0.265792 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.2206i | 0.593084i | ||||||||
\(749\) | −17.4465 | + | 30.2795i | −0.637481 | + | 1.10639i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.84765i | − | 0.176893i | −0.996081 | − | 0.0884466i | \(-0.971810\pi\) | ||
0.996081 | − | 0.0884466i | \(-0.0281903\pi\) | |||||||
\(752\) | 10.9149i | 0.398025i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.37745 | −0.159418 | ||||||||
\(755\) | 10.7457 | 0.391077 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6530 | 0.532572 | 0.266286 | − | 0.963894i | \(-0.414203\pi\) | ||||
0.266286 | + | 0.963894i | \(0.414203\pi\) | |||||||
\(758\) | 17.8834 | 0.649554 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.52540 | + | 2.17961i | −0.0916060 | + | 0.0790627i | ||||
\(761\) | 33.0860i | 1.19937i | 0.800237 | + | 0.599684i | \(0.204707\pi\) | ||||
−0.800237 | + | 0.599684i | \(0.795293\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.84545 | + | 13.6163i | −0.284024 | + | 0.492943i | ||||
\(764\) | 3.13660 | 0.113478 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.90529i | 0.213367i | ||||||||
\(767\) | −7.68577 | −0.277517 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.2141i | 0.404391i | 0.979345 | + | 0.202195i | \(0.0648076\pi\) | ||||
−0.979345 | + | 0.202195i | \(0.935192\pi\) | |||||||
\(770\) | 7.18190 | + | 4.13808i | 0.258818 | + | 0.149126i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 17.3387i | − | 0.624033i | ||||||
\(773\) | −45.7715 | −1.64629 | −0.823144 | − | 0.567833i | \(-0.807782\pi\) | ||||
−0.823144 | + | 0.567833i | \(0.807782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.1851 | −1.33573 | ||||||||
\(776\) | − | 1.90563i | − | 0.0684081i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.0156i | 0.932703i | ||||||||
\(779\) | 18.5508 | − | 16.0107i | 0.664651 | − | 0.573643i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 46.0173i | − | 1.64663i | ||||||
\(782\) | 8.86183 | 0.316898 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.51063 | + | 6.05603i | 0.125380 | + | 0.216287i | ||||
\(785\) | 15.4771 | 0.552402 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.9600 | 0.497621 | 0.248810 | − | 0.968552i | \(-0.419960\pi\) | ||||
0.248810 | + | 0.968552i | \(0.419960\pi\) | |||||||
\(788\) | 21.1245 | 0.752527 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.75618i | 0.169217i | ||||||||
\(791\) | −6.03301 | + | 10.4707i | −0.214509 | + | 0.372294i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.96794i | 0.247439i | ||||||||
\(794\) | −20.3829 | −0.723363 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 4.25847i | − | 0.150937i | ||||||
\(797\) | −13.9410 | −0.493815 | −0.246907 | − | 0.969039i | \(-0.579414\pi\) | ||||
−0.246907 | + | 0.969039i | \(0.579414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.2499 | −1.53007 | ||||||||
\(800\) | 4.41430i | 0.156069i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.26305 | −0.221156 | ||||||||
\(803\) | − | 36.9097i | − | 1.30252i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.26076 | − | 3.92370i | 0.0796814 | − | 0.138292i | ||||
\(806\) | − | 10.4007i | − | 0.366350i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.8561 | 0.417096 | ||||||||
\(809\) | −6.97307 | −0.245160 | −0.122580 | − | 0.992459i | \(-0.539117\pi\) | ||||
−0.122580 | + | 0.992459i | \(0.539117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.17371 | 0.287018 | 0.143509 | − | 0.989649i | \(-0.454161\pi\) | ||||
0.143509 | + | 0.989649i | \(0.454161\pi\) | |||||||
\(812\) | −4.68299 | + | 8.12763i | −0.164341 | + | 0.285224i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.9018 | −0.837759 | ||||||||
\(815\) | − | 10.8270i | − | 0.379253i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.4184 | − | 32.2949i | 1.30910 | − | 1.12985i | ||||
\(818\) | 9.08055i | 0.317494i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.30238i | 0.150246i | ||||||||
\(821\) | −16.3649 | −0.571138 | −0.285569 | − | 0.958358i | \(-0.592183\pi\) | ||||
−0.285569 | + | 0.958358i | \(0.592183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7362 | 0.966822 | 0.483411 | − | 0.875394i | \(-0.339398\pi\) | ||||
0.483411 | + | 0.875394i | \(0.339398\pi\) | |||||||
\(824\) | − | 0.00772432i | − | 0.000269090i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.22221 | + | 14.2702i | −0.286087 | + | 0.496523i | ||||
\(827\) | − | 46.1901i | − | 1.60619i | −0.595852 | − | 0.803094i | \(-0.703186\pi\) | ||
0.595852 | − | 0.803094i | \(-0.296814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.51500 | 0.191544 | 0.0957719 | − | 0.995403i | \(-0.469468\pi\) | ||||
0.0957719 | + | 0.995403i | \(0.469468\pi\) | |||||||
\(830\) | 1.56016i | 0.0541541i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.23469 | −0.0428051 | ||||||||
\(833\) | −23.9968 | + | 13.9108i | −0.831440 | + | 0.481979i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.36807i | − | 0.0819505i | ||||||
\(836\) | 13.5081 | − | 11.6585i | 0.467186 | − | 0.403216i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.3578 | −0.703249 | ||||||||
\(839\) | −31.9140 | −1.10179 | −0.550896 | − | 0.834574i | \(-0.685714\pi\) | ||||
−0.550896 | + | 0.834574i | \(0.685714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4302 | 0.566558 | ||||||||
\(842\) | 14.6067 | 0.503380 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.9211i | 0.857818i | ||||||||
\(845\) | 8.78238i | 0.302123i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.1982 | − | 7.60455i | −0.453495 | − | 0.261295i | ||||
\(848\) | − | 8.28090i | − | 0.284367i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.4915 | −0.599953 | ||||||||
\(851\) | 13.0583i | 0.447634i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6794i | 0.742289i | 0.928575 | + | 0.371145i | \(0.121035\pi\) | ||||
−0.928575 | + | 0.371145i | \(0.878965\pi\) | |||||||
\(854\) | 12.9374 | + | 7.45428i | 0.442709 | + | 0.255080i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.2084 | −0.451453 | ||||||||
\(857\) | −39.9212 | −1.36368 | −0.681841 | − | 0.731501i | \(-0.738820\pi\) | ||||
−0.681841 | + | 0.731501i | \(0.738820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.68934i | 0.159998i | 0.996795 | + | 0.0799991i | \(0.0254918\pi\) | ||||
−0.996795 | + | 0.0799991i | \(0.974508\pi\) | |||||||
\(860\) | 8.67825i | 0.295926i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.86831 | 0.0636349 | ||||||||
\(863\) | 44.3151i | 1.50850i | 0.656585 | + | 0.754252i | \(0.272000\pi\) | ||||
−0.656585 | + | 0.754252i | \(0.728000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5186i | 0.357644i | ||||||||
\(866\) | − | 31.0009i | − | 1.05345i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.3111 | − | 11.1267i | −0.655460 | − | 0.377664i | ||||
\(869\) | − | 25.4402i | − | 0.863001i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9556i | 0.574520i | ||||||||
\(872\) | −5.93963 | −0.201141 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.36939 | − | 7.37989i | −0.215448 | − | 0.249628i | ||||
\(875\) | −9.51667 | + | 16.5168i | −0.321722 | + | 0.558370i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.3577i | 1.86930i | 0.355572 | + | 0.934649i | \(0.384286\pi\) | ||||
−0.355572 | + | 0.934649i | \(0.615714\pi\) | |||||||
\(878\) | 26.8712i | 0.906858i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.13285i | 0.105608i | ||||||||
\(881\) | − | 11.5455i | − | 0.388977i | −0.980905 | − | 0.194488i | \(-0.937695\pi\) | ||
0.980905 | − | 0.194488i | \(-0.0623047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.5239 | −1.86853 | −0.934264 | − | 0.356582i | \(-0.883942\pi\) | ||||
−0.934264 | + | 0.356582i | \(0.883942\pi\) | |||||||
\(884\) | − | 4.89241i | − | 0.164549i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.07575i | 0.271310i | ||||||||
\(887\) | −14.8432 | −0.498386 | −0.249193 | − | 0.968454i | \(-0.580165\pi\) | ||||
−0.249193 | + | 0.968454i | \(0.580165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.85724 | − | 6.69449i | 0.129368 | − | 0.224526i | ||||
\(890\) | 12.4879 | 0.418596 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.6895 | 0.357910 | ||||||||
\(893\) | 31.0856 | + | 36.0173i | 1.04024 | + | 1.20527i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2941 | −0.477798 | ||||||||
\(896\) | −1.32086 | + | 2.29245i | −0.0441270 | + | 0.0765853i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.13077 | −0.237957 | ||||||||
\(899\) | − | 29.8656i | − | 0.996074i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.8128 | 1.09315 | ||||||||
\(902\) | − | 23.0129i | − | 0.766247i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.56747 | −0.151912 | ||||||||
\(905\) | − | 6.30303i | − | 0.209520i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.44122i | 0.114264i | 0.998367 | + | 0.0571320i | \(0.0181956\pi\) | ||||
−0.998367 | + | 0.0571320i | \(0.981804\pi\) | |||||||
\(908\) | 18.2992 | 0.607280 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.16618 | − | 1.24811i | −0.0718083 | − | 0.0413746i | ||||
\(911\) | 31.1234i | 1.03116i | 0.856840 | + | 0.515582i | \(0.172424\pi\) | ||||
−0.856840 | + | 0.515582i | \(0.827576\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.34513i | − | 0.276183i | ||||||
\(914\) | − | 4.94992i | − | 0.163729i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.3769i | 0.342863i | ||||||||
\(917\) | 14.5024 | − | 25.1698i | 0.478911 | − | 0.831181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.282023 | −0.00930306 | −0.00465153 | − | 0.999989i | \(-0.501481\pi\) | ||||
−0.00465153 | + | 0.999989i | \(0.501481\pi\) | |||||||
\(920\) | 1.71158 | 0.0564290 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.3884 | 0.407989 | ||||||||
\(923\) | 13.8796i | 0.456853i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 25.7746i | − | 0.847462i | ||||||
\(926\) | 0.203161i | 0.00667627i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.54539 | −0.116383 | ||||||||
\(929\) | 22.0598i | 0.723758i | 0.932225 | + | 0.361879i | \(0.117865\pi\) | ||||
−0.932225 | + | 0.361879i | \(0.882135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.8321 | + | 9.98559i | 0.944933 | + | 0.327265i | ||||
\(932\) | 1.50567 | 0.0493198 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.7312 | 1.30004 | ||||||||
\(935\) | −12.4138 | −0.405975 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.59462i | 0.150100i | 0.997180 | + | 0.0750499i | \(0.0239116\pi\) | ||||
−0.997180 | + | 0.0750499i | \(0.976088\pi\) | |||||||
\(938\) | 31.4816 | + | 18.1391i | 1.02791 | + | 0.592262i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.35331 | −0.272455 | ||||||||
\(941\) | 20.2344 | 0.659623 | 0.329812 | − | 0.944047i | \(-0.393015\pi\) | ||||
0.329812 | + | 0.944047i | \(0.393015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.5727 | −0.409423 | ||||||||
\(944\) | −6.22487 | −0.202602 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 46.4189i | − | 1.50921i | ||||||
\(947\) | 13.6923 | 0.444941 | 0.222470 | − | 0.974939i | \(-0.428588\pi\) | ||||
0.222470 | + | 0.974939i | \(0.428588\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1326i | 0.361379i | ||||||||
\(950\) | 12.5719 | + | 14.5664i | 0.407887 | + | 0.472598i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.08374 | − | 5.23388i | −0.294406 | − | 0.169631i | ||||
\(953\) | − | 23.1598i | − | 0.750218i | −0.926981 | − | 0.375109i | \(-0.877605\pi\) | ||
0.926981 | − | 0.375109i | \(-0.122395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.40048i | 0.0776776i | ||||||||
\(956\) | −8.59215 | −0.277890 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −42.8715 | −1.38511 | ||||||||
\(959\) | −37.2474 | − | 21.4613i | −1.20278 | − | 0.693020i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.9600 | 1.28903 | ||||||||
\(962\) | 7.20920 | 0.232434 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.4908 | 0.531132 | ||||||||
\(965\) | 13.2695 | 0.427160 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9102 | −0.704584 | −0.352292 | − | 0.935890i | \(-0.614598\pi\) | ||||
−0.352292 | + | 0.935890i | \(0.614598\pi\) | |||||||
\(968\) | − | 5.75725i | − | 0.185045i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.45840 | 0.0468265 | ||||||||
\(971\) | −20.8725 | −0.669831 | −0.334915 | − | 0.942248i | \(-0.608708\pi\) | ||||
−0.334915 | + | 0.942248i | \(0.608708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.31598 | − | 4.01954i | 0.0742470 | − | 0.128861i | ||||
\(974\) | −25.8373 | −0.827881 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.64349i | 0.180644i | ||||||||
\(977\) | 10.9734i | 0.351069i | 0.984473 | + | 0.175535i | \(0.0561654\pi\) | ||||
−0.984473 | + | 0.175535i | \(0.943835\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −66.7963 | −2.13482 | ||||||||
\(980\) | −4.63475 | + | 2.68673i | −0.148052 | + | 0.0858244i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.388503i | 0.0123976i | ||||||||
\(983\) | −48.0126 | −1.53136 | −0.765682 | − | 0.643219i | \(-0.777598\pi\) | ||||
−0.765682 | + | 0.643219i | \(0.777598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.1668i | 0.515117i | ||||||||
\(986\) | − | 14.0485i | − | 0.447395i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.07426 | + | 3.51639i | −0.129620 | + | 0.111871i | ||||
\(989\) | −25.3601 | −0.806405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.0953i | − | 0.447752i | −0.974618 | − | 0.223876i | \(-0.928129\pi\) | ||
0.974618 | − | 0.223876i | \(-0.0718710\pi\) | |||||||
\(992\) | − | 8.42378i | − | 0.267455i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.7703 | + | 14.8484i | 0.817385 | + | 0.470961i | ||||
\(995\) | 3.25906 | 0.103319 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.3893i | 0.550726i | 0.961340 | + | 0.275363i | \(0.0887980\pi\) | ||||
−0.961340 | + | 0.275363i | \(0.911202\pi\) | |||||||
\(998\) | 3.56308i | 0.112787i | ||||||||
\(999\) | 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 | 2394.2.e.b.1063.9 | 12 | ||
3.2 | odd | 2 | 798.2.e.b.265.4 | yes | 12 | ||
7.6 | odd | 2 | 2394.2.e.a.1063.10 | 12 | |||
19.18 | odd | 2 | 2394.2.e.a.1063.3 | 12 | |||
21.20 | even | 2 | 798.2.e.a.265.3 | ✓ | 12 | ||
57.56 | even | 2 | 798.2.e.a.265.10 | yes | 12 | ||
133.132 | even | 2 | inner | 2394.2.e.b.1063.4 | 12 | ||
399.398 | odd | 2 | 798.2.e.b.265.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.e.a.265.3 | ✓ | 12 | 21.20 | even | 2 | ||
798.2.e.a.265.10 | yes | 12 | 57.56 | even | 2 | ||
798.2.e.b.265.4 | yes | 12 | 3.2 | odd | 2 | ||
798.2.e.b.265.9 | yes | 12 | 399.398 | odd | 2 | ||
2394.2.e.a.1063.3 | 12 | 19.18 | odd | 2 | |||
2394.2.e.a.1063.10 | 12 | 7.6 | odd | 2 | |||
2394.2.e.b.1063.4 | 12 | 133.132 | even | 2 | inner | ||
2394.2.e.b.1063.9 | 12 | 1.1 | even | 1 | trivial |