Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(883,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3822.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 883.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.883 |
Dual form | 3822.2.c.e.883.2 |
$q$-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 \(\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times\).
\(n\) | \(1471\) | \(2549\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | −0.974679 | − | 0.223607i | \(-0.928217\pi\) | ||
0.974679 | − | 0.223607i | \(-0.0717831\pi\) | |||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000i | 0.301511i | 0.988571 | + | 0.150756i | \(0.0481707\pi\) | ||||
−0.988571 | + | 0.150756i | \(0.951829\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.00000 | − | 2.00000i | −0.832050 | − | 0.554700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | −2.00000 | + | 3.00000i | −0.392232 | + | 0.588348i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | 1.67126 | 0.835629 | − | 0.549294i | \(-0.185103\pi\) | ||||
0.835629 | + | 0.549294i | \(0.185103\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 1.00000i | 0.171499i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 9.00000i | − | 1.47959i | −0.672832 | − | 0.739795i | \(-0.734922\pi\) | ||
0.672832 | − | 0.739795i | \(-0.265078\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −3.00000 | − | 2.00000i | −0.480384 | − | 0.320256i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − | 8.00000i | − | 1.24939i | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||
0.780869 | − | 0.624695i | \(-0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000 | 1.06749 | 0.533745 | − | 0.845645i | \(-0.320784\pi\) | ||||
0.533745 | + | 0.845645i | \(0.320784\pi\) | |||||||
\(44\) | − | 1.00000i | − | 0.150756i | ||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | − | 3.00000i | − | 0.442326i | ||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.00000i | − | 0.565685i | ||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 3.00000 | + | 2.00000i | 0.416025 | + | 0.277350i | ||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | − | 9.00000i | − | 1.18176i | ||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −11.0000 | −1.40841 | −0.704203 | − | 0.709999i | \(-0.748695\pi\) | ||||
−0.704203 | + | 0.709999i | \(0.748695\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.00000 | + | 3.00000i | −0.248069 | + | 0.372104i | ||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − | 11.0000i | − | 1.28745i | −0.765256 | − | 0.643726i | \(-0.777388\pi\) | ||
0.765256 | − | 0.643726i | \(-0.222612\pi\) | |||||||
\(74\) | −9.00000 | −1.04623 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | − | 1.00000i | − | 0.114708i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.00000 | + | 3.00000i | −0.226455 | + | 0.339683i | ||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.00000 | −0.883452 | ||||||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000i | 0.108465i | ||||||||
\(86\) | − | 7.00000i | − | 0.754829i | ||||||
\(87\) | 9.00000 | 0.964901 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | − | 12.0000i | − | 1.27200i | −0.771690 | − | 0.635999i | \(-0.780588\pi\) | ||
0.771690 | − | 0.635999i | \(-0.219412\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 1.00000i | 0.0990148i | ||||||||
\(103\) | 5.00000 | 0.492665 | 0.246332 | − | 0.969185i | \(-0.420775\pi\) | ||||
0.246332 | + | 0.969185i | \(0.420775\pi\) | |||||||
\(104\) | 2.00000 | − | 3.00000i | 0.196116 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000i | 0.971286i | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | − | 1.00000i | − | 0.0953463i | ||||||
\(111\) | − | 9.00000i | − | 0.854242i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | − | 3.00000i | − | 0.279751i | ||||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | −3.00000 | − | 2.00000i | −0.277350 | − | 0.184900i | ||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 10.0000 | 0.909091 | ||||||||
\(122\) | 11.0000i | 0.995893i | ||||||||
\(123\) | − | 8.00000i | − | 0.721336i | ||||||
\(124\) | − | 4.00000i | − | 0.359211i | ||||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 7.00000 | 0.616316 | ||||||||
\(130\) | 3.00000 | + | 2.00000i | 0.263117 | + | 0.175412i | ||||
\(131\) | 3.00000 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | − | 1.00000i | − | 0.0870388i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | − | 1.00000i | − | 0.0857493i | ||||||
\(137\) | − | 15.0000i | − | 1.28154i | −0.767734 | − | 0.640768i | \(-0.778616\pi\) | ||
0.767734 | − | 0.640768i | \(-0.221384\pi\) | |||||||
\(138\) | − | 3.00000i | − | 0.255377i | ||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.00000i | − | 0.673722i | ||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 2.00000 | − | 3.00000i | 0.167248 | − | 0.250873i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − | 9.00000i | − | 0.747409i | ||||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.00000i | 0.739795i | ||||||||
\(149\) | 6.00000i | 0.491539i | 0.969328 | + | 0.245770i | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | − | 4.00000i | − | 0.326599i | ||||||
\(151\) | 1.00000i | 0.0813788i | 0.999172 | + | 0.0406894i | \(0.0129554\pi\) | ||||
−0.999172 | + | 0.0406894i | \(0.987045\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 3.00000 | + | 2.00000i | 0.240192 | + | 0.160128i | ||||
\(157\) | 21.0000 | 1.67598 | 0.837991 | − | 0.545684i | \(-0.183730\pi\) | ||||
0.837991 | + | 0.545684i | \(0.183730\pi\) | |||||||
\(158\) | 12.0000i | 0.954669i | ||||||||
\(159\) | −10.0000 | −0.793052 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 20.0000i | − | 1.56652i | −0.621694 | − | 0.783260i | \(-0.713555\pi\) | ||
0.621694 | − | 0.783260i | \(-0.286445\pi\) | |||||||
\(164\) | 8.00000i | 0.624695i | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | 11.0000i | 0.851206i | 0.904910 | + | 0.425603i | \(0.139938\pi\) | ||||
−0.904910 | + | 0.425603i | \(0.860062\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | + | 12.0000i | 0.384615 | + | 0.923077i | ||||
\(170\) | 1.00000 | 0.0766965 | ||||||||
\(171\) | 1.00000i | 0.0764719i | ||||||||
\(172\) | −7.00000 | −0.533745 | ||||||||
\(173\) | −14.0000 | −1.06440 | −0.532200 | − | 0.846619i | \(-0.678635\pi\) | ||||
−0.532200 | + | 0.846619i | \(0.678635\pi\) | |||||||
\(174\) | − | 9.00000i | − | 0.682288i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | −12.0000 | −0.899438 | ||||||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0000 | −0.813143 | ||||||||
\(184\) | 3.00000i | 0.221163i | ||||||||
\(185\) | −9.00000 | −0.661693 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | − | 1.00000i | − | 0.0731272i | ||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 1.00000i | − | 0.0725476i | ||||||
\(191\) | −11.0000 | −0.795932 | −0.397966 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397966 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − | 12.0000i | − | 0.863779i | −0.901927 | − | 0.431889i | \(-0.857847\pi\) | ||
0.901927 | − | 0.431889i | \(-0.142153\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | −2.00000 | + | 3.00000i | −0.143223 | + | 0.214834i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −5.00000 | −0.354441 | −0.177220 | − | 0.984171i | \(-0.556711\pi\) | ||||
−0.177220 | + | 0.984171i | \(0.556711\pi\) | |||||||
\(200\) | 4.00000i | 0.282843i | ||||||||
\(201\) | − | 12.0000i | − | 0.846415i | ||||||
\(202\) | − | 2.00000i | − | 0.140720i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −8.00000 | −0.558744 | ||||||||
\(206\) | − | 5.00000i | − | 0.348367i | ||||||
\(207\) | 3.00000 | 0.208514 | ||||||||
\(208\) | −3.00000 | − | 2.00000i | −0.208013 | − | 0.138675i | ||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 10.0000 | 0.686803 | ||||||||
\(213\) | 6.00000i | 0.411113i | ||||||||
\(214\) | 2.00000i | 0.136717i | ||||||||
\(215\) | − | 7.00000i | − | 0.477396i | ||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.00000 | 0.474100 | ||||||||
\(219\) | − | 11.0000i | − | 0.743311i | ||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 3.00000 | + | 2.00000i | 0.201802 | + | 0.134535i | ||||
\(222\) | −9.00000 | −0.604040 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 2.00000i | 0.133038i | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | − | 1.00000i | − | 0.0662266i | ||||||
\(229\) | − | 2.00000i | − | 0.132164i | −0.997814 | − | 0.0660819i | \(-0.978950\pi\) | ||
0.997814 | − | 0.0660819i | \(-0.0210498\pi\) | |||||||
\(230\) | −3.00000 | −0.197814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00000i | 0.590879i | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | −2.00000 | + | 3.00000i | −0.130744 | + | 0.196116i | ||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | − | 6.00000i | − | 0.390567i | ||||||
\(237\) | −12.0000 | −0.779484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.00000i | − | 0.517477i | −0.965947 | − | 0.258738i | \(-0.916693\pi\) | ||
0.965947 | − | 0.258738i | \(-0.0833068\pi\) | |||||||
\(240\) | − | 1.00000i | − | 0.0645497i | ||||||
\(241\) | − | 10.0000i | − | 0.644157i | −0.946713 | − | 0.322078i | \(-0.895619\pi\) | ||
0.946713 | − | 0.322078i | \(-0.104381\pi\) | |||||||
\(242\) | − | 10.0000i | − | 0.642824i | ||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.0000 | 0.704203 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.00000 | −0.510061 | ||||||||
\(247\) | 2.00000 | − | 3.00000i | 0.127257 | − | 0.190885i | ||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | − | 6.00000i | − | 0.380235i | ||||||
\(250\) | −9.00000 | −0.569210 | ||||||||
\(251\) | −11.0000 | −0.694314 | −0.347157 | − | 0.937807i | \(-0.612853\pi\) | ||||
−0.347157 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000i | 0.188608i | ||||||||
\(254\) | − | 16.0000i | − | 1.00393i | ||||||
\(255\) | 1.00000i | 0.0626224i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | − | 7.00000i | − | 0.435801i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.00000 | − | 3.00000i | 0.124035 | − | 0.186052i | ||||
\(261\) | 9.00000 | 0.557086 | ||||||||
\(262\) | − | 3.00000i | − | 0.185341i | ||||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 10.0000i | 0.614295i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.0000i | − | 0.734388i | ||||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | 20.0000 | 1.21942 | 0.609711 | − | 0.792624i | \(-0.291286\pi\) | ||||
0.609711 | + | 0.792624i | \(0.291286\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 4.00000i | 0.242983i | 0.992592 | + | 0.121491i | \(0.0387677\pi\) | ||||
−0.992592 | + | 0.121491i | \(0.961232\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | 4.00000i | 0.241209i | ||||||||
\(276\) | −3.00000 | −0.180579 | ||||||||
\(277\) | 16.0000 | 0.961347 | 0.480673 | − | 0.876900i | \(-0.340392\pi\) | ||||
0.480673 | + | 0.876900i | \(0.340392\pi\) | |||||||
\(278\) | − | 12.0000i | − | 0.719712i | ||||||
\(279\) | 4.00000i | 0.239474i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.0000i | − | 1.31241i | −0.754583 | − | 0.656205i | \(-0.772161\pi\) | ||
0.754583 | − | 0.656205i | \(-0.227839\pi\) | |||||||
\(282\) | −8.00000 | −0.476393 | ||||||||
\(283\) | 14.0000 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(284\) | − | 6.00000i | − | 0.356034i | ||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | −3.00000 | − | 2.00000i | −0.177394 | − | 0.118262i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −9.00000 | −0.528498 | ||||||||
\(291\) | 2.00000i | 0.117242i | ||||||||
\(292\) | 11.0000i | 0.643726i | ||||||||
\(293\) | 26.0000i | 1.51894i | 0.650545 | + | 0.759468i | \(0.274541\pi\) | ||||
−0.650545 | + | 0.759468i | \(0.725459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 9.00000 | 0.523114 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −9.00000 | − | 6.00000i | −0.520483 | − | 0.346989i | ||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.00000 | 0.0575435 | ||||||||
\(303\) | 2.00000 | 0.114897 | ||||||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | 11.0000i | 0.629858i | ||||||||
\(306\) | 1.00000i | 0.0571662i | ||||||||
\(307\) | 8.00000i | 0.456584i | 0.973593 | + | 0.228292i | \(0.0733141\pi\) | ||||
−0.973593 | + | 0.228292i | \(0.926686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.00000 | 0.284440 | ||||||||
\(310\) | − | 4.00000i | − | 0.227185i | ||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 2.00000 | − | 3.00000i | 0.113228 | − | 0.169842i | ||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | − | 21.0000i | − | 1.18510i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | − | 12.0000i | − | 0.673987i | −0.941507 | − | 0.336994i | \(-0.890590\pi\) | ||
0.941507 | − | 0.336994i | \(-0.109410\pi\) | |||||||
\(318\) | 10.0000i | 0.560772i | ||||||||
\(319\) | 9.00000i | 0.503903i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.00000i | − | 0.0556415i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −12.0000 | − | 8.00000i | −0.665640 | − | 0.443760i | ||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | 7.00000i | 0.387101i | ||||||||
\(328\) | 8.00000 | 0.441726 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 1.00000i | − | 0.0550482i | ||||||
\(331\) | − | 8.00000i | − | 0.439720i | −0.975531 | − | 0.219860i | \(-0.929440\pi\) | ||
0.975531 | − | 0.219860i | \(-0.0705600\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | − | 9.00000i | − | 0.493197i | ||||||
\(334\) | 11.0000 | 0.601893 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0000 | 0.926049 | 0.463025 | − | 0.886345i | \(-0.346764\pi\) | ||||
0.463025 | + | 0.886345i | \(0.346764\pi\) | |||||||
\(338\) | 12.0000 | − | 5.00000i | 0.652714 | − | 0.271964i | ||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | − | 1.00000i | − | 0.0542326i | ||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.00000i | 0.377415i | ||||||||
\(345\) | − | 3.00000i | − | 0.161515i | ||||||
\(346\) | 14.0000i | 0.752645i | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | −9.00000 | −0.482451 | ||||||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.00000 | − | 2.00000i | −0.160128 | − | 0.106752i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 16.0000i | 0.851594i | 0.904819 | + | 0.425797i | \(0.140006\pi\) | ||||
−0.904819 | + | 0.425797i | \(0.859994\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | 6.00000 | 0.318447 | ||||||||
\(356\) | 12.0000i | 0.635999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.0000i | 0.951330i | ||||||||
\(359\) | 30.0000i | 1.58334i | 0.610949 | + | 0.791670i | \(0.290788\pi\) | ||||
−0.610949 | + | 0.791670i | \(0.709212\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | − | 2.00000i | − | 0.105118i | ||||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | 11.0000i | 0.574979i | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 3.00000 | 0.156386 | ||||||||
\(369\) | − | 8.00000i | − | 0.416463i | ||||||
\(370\) | 9.00000i | 0.467888i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | − | 9.00000i | − | 0.464758i | ||||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | −27.0000 | − | 18.0000i | −1.39057 | − | 0.927047i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | −1.00000 | −0.0512989 | ||||||||
\(381\) | 16.0000 | 0.819705 | ||||||||
\(382\) | 11.0000i | 0.562809i | ||||||||
\(383\) | − | 35.0000i | − | 1.78842i | −0.447651 | − | 0.894208i | \(-0.647739\pi\) | ||
0.447651 | − | 0.894208i | \(-0.352261\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.0000 | −0.610784 | ||||||||
\(387\) | 7.00000 | 0.355830 | ||||||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | 2.00000 | 0.101404 | 0.0507020 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507020 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(390\) | 3.00000 | + | 2.00000i | 0.151911 | + | 0.101274i | ||||
\(391\) | −3.00000 | −0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | 12.0000i | 0.603786i | ||||||||
\(396\) | − | 1.00000i | − | 0.0502519i | ||||||
\(397\) | − | 4.00000i | − | 0.200754i | −0.994949 | − | 0.100377i | \(-0.967995\pi\) | ||
0.994949 | − | 0.100377i | \(-0.0320049\pi\) | |||||||
\(398\) | 5.00000i | 0.250627i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 14.0000i | 0.699127i | 0.936913 | + | 0.349563i | \(0.113670\pi\) | ||||
−0.936913 | + | 0.349563i | \(0.886330\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | 8.00000 | − | 12.0000i | 0.398508 | − | 0.597763i | ||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.00000 | 0.446113 | ||||||||
\(408\) | − | 1.00000i | − | 0.0495074i | ||||||
\(409\) | − | 27.0000i | − | 1.33506i | −0.744581 | − | 0.667532i | \(-0.767351\pi\) | ||
0.744581 | − | 0.667532i | \(-0.232649\pi\) | |||||||
\(410\) | 8.00000i | 0.395092i | ||||||||
\(411\) | − | 15.0000i | − | 0.739895i | ||||||
\(412\) | −5.00000 | −0.246332 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 3.00000i | − | 0.147442i | ||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | −2.00000 | + | 3.00000i | −0.0980581 | + | 0.147087i | ||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 1.00000i | 0.0489116i | ||||||||
\(419\) | −23.0000 | −1.12362 | −0.561812 | − | 0.827265i | \(-0.689895\pi\) | ||||
−0.561812 | + | 0.827265i | \(0.689895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000i | 1.07221i | 0.844150 | + | 0.536107i | \(0.180106\pi\) | ||||
−0.844150 | + | 0.536107i | \(0.819894\pi\) | |||||||
\(422\) | 5.00000i | 0.243396i | ||||||||
\(423\) | − | 8.00000i | − | 0.388973i | ||||||
\(424\) | − | 10.0000i | − | 0.485643i | ||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | 2.00000 | − | 3.00000i | 0.0965609 | − | 0.144841i | ||||
\(430\) | −7.00000 | −0.337570 | ||||||||
\(431\) | − | 18.0000i | − | 0.867029i | −0.901146 | − | 0.433515i | \(-0.857273\pi\) | ||
0.901146 | − | 0.433515i | \(-0.142727\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 9.00000i | − | 0.431517i | ||||||
\(436\) | − | 7.00000i | − | 0.335239i | ||||||
\(437\) | 3.00000i | 0.143509i | ||||||||
\(438\) | −11.0000 | −0.525600 | ||||||||
\(439\) | 33.0000 | 1.57500 | 0.787502 | − | 0.616312i | \(-0.211374\pi\) | ||||
0.787502 | + | 0.616312i | \(0.211374\pi\) | |||||||
\(440\) | 1.00000i | 0.0476731i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | − | 3.00000i | 0.0951303 | − | 0.142695i | ||||
\(443\) | −6.00000 | −0.285069 | −0.142534 | − | 0.989790i | \(-0.545525\pi\) | ||||
−0.142534 | + | 0.989790i | \(0.545525\pi\) | |||||||
\(444\) | 9.00000i | 0.427121i | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | 8.00000 | 0.378811 | ||||||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.0000i | − | 0.707894i | −0.935266 | − | 0.353947i | \(-0.884839\pi\) | ||
0.935266 | − | 0.353947i | \(-0.115161\pi\) | |||||||
\(450\) | − | 4.00000i | − | 0.188562i | ||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 2.00000 | 0.0940721 | ||||||||
\(453\) | 1.00000i | 0.0469841i | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 4.00000i | 0.187112i | 0.995614 | + | 0.0935561i | \(0.0298234\pi\) | ||||
−0.995614 | + | 0.0935561i | \(0.970177\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 3.00000i | 0.139876i | ||||||||
\(461\) | − | 3.00000i | − | 0.139724i | −0.997557 | − | 0.0698620i | \(-0.977744\pi\) | ||
0.997557 | − | 0.0698620i | \(-0.0222559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0000i | 1.34774i | 0.738848 | + | 0.673872i | \(0.235370\pi\) | ||||
−0.738848 | + | 0.673872i | \(0.764630\pi\) | |||||||
\(464\) | 9.00000 | 0.417815 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 18.0000i | 0.833834i | ||||||||
\(467\) | 37.0000 | 1.71216 | 0.856078 | − | 0.516847i | \(-0.172894\pi\) | ||||
0.856078 | + | 0.516847i | \(0.172894\pi\) | |||||||
\(468\) | 3.00000 | + | 2.00000i | 0.138675 | + | 0.0924500i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.00000i | 0.369012i | ||||||||
\(471\) | 21.0000 | 0.967629 | ||||||||
\(472\) | −6.00000 | −0.276172 | ||||||||
\(473\) | 7.00000i | 0.321860i | ||||||||
\(474\) | 12.0000i | 0.551178i | ||||||||
\(475\) | 4.00000i | 0.183533i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.0000 | −0.457869 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | − | 39.0000i | − | 1.78196i | −0.454047 | − | 0.890978i | \(-0.650020\pi\) | ||
0.454047 | − | 0.890978i | \(-0.349980\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −18.0000 | + | 27.0000i | −0.820729 | + | 1.23109i | ||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | − | 11.0000i | − | 0.497947i | ||||||
\(489\) | − | 20.0000i | − | 0.904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 8.00000i | 0.360668i | ||||||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | −3.00000 | − | 2.00000i | −0.134976 | − | 0.0899843i | ||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 4.00000i | 0.179605i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.00000 | −0.268866 | ||||||||
\(499\) | − | 10.0000i | − | 0.447661i | −0.974628 | − | 0.223831i | \(-0.928144\pi\) | ||
0.974628 | − | 0.223831i | \(-0.0718563\pi\) | |||||||
\(500\) | 9.00000i | 0.402492i | ||||||||
\(501\) | 11.0000i | 0.491444i | ||||||||
\(502\) | 11.0000i | 0.490954i | ||||||||
\(503\) | 38.0000 | 1.69434 | 0.847168 | − | 0.531325i | \(-0.178306\pi\) | ||||
0.847168 | + | 0.531325i | \(0.178306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.00000i | − | 0.0889988i | ||||||
\(506\) | 3.00000 | 0.133366 | ||||||||
\(507\) | 5.00000 | + | 12.0000i | 0.222058 | + | 0.532939i | ||||
\(508\) | −16.0000 | −0.709885 | ||||||||
\(509\) | 37.0000i | 1.64000i | 0.572366 | + | 0.819998i | \(0.306026\pi\) | ||||
−0.572366 | + | 0.819998i | \(0.693974\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 14.0000i | 0.617514i | ||||||||
\(515\) | − | 5.00000i | − | 0.220326i | ||||||
\(516\) | −7.00000 | −0.308158 | ||||||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | −3.00000 | − | 2.00000i | −0.131559 | − | 0.0877058i | ||||
\(521\) | 31.0000 | 1.35813 | 0.679067 | − | 0.734076i | \(-0.262384\pi\) | ||||
0.679067 | + | 0.734076i | \(0.262384\pi\) | |||||||
\(522\) | − | 9.00000i | − | 0.393919i | ||||||
\(523\) | 36.0000 | 1.57417 | 0.787085 | − | 0.616844i | \(-0.211589\pi\) | ||||
0.787085 | + | 0.616844i | \(0.211589\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 16.0000i | − | 0.697633i | ||||||
\(527\) | − | 4.00000i | − | 0.174243i | ||||||
\(528\) | 1.00000i | 0.0435194i | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 10.0000 | 0.434372 | ||||||||
\(531\) | 6.00000i | 0.260378i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.0000 | + | 24.0000i | −0.693037 | + | 1.03956i | ||||
\(534\) | −12.0000 | −0.519291 | ||||||||
\(535\) | 2.00000i | 0.0864675i | ||||||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | −18.0000 | −0.776757 | ||||||||
\(538\) | − | 20.0000i | − | 0.862261i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 41.0000i | 1.76273i | 0.472438 | + | 0.881364i | \(0.343374\pi\) | ||||
−0.472438 | + | 0.881364i | \(0.656626\pi\) | |||||||
\(542\) | 4.00000 | 0.171815 | ||||||||
\(543\) | 2.00000 | 0.0858282 | ||||||||
\(544\) | 1.00000i | 0.0428746i | ||||||||
\(545\) | 7.00000 | 0.299847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 15.0000i | 0.640768i | ||||||||
\(549\) | −11.0000 | −0.469469 | ||||||||
\(550\) | 4.00000 | 0.170561 | ||||||||
\(551\) | 9.00000i | 0.383413i | ||||||||
\(552\) | 3.00000i | 0.127688i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 16.0000i | − | 0.679775i | ||||||
\(555\) | −9.00000 | −0.382029 | ||||||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | − | 2.00000i | − | 0.0847427i | −0.999102 | − | 0.0423714i | \(-0.986509\pi\) | ||
0.999102 | − | 0.0423714i | \(-0.0134913\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | −21.0000 | − | 14.0000i | −0.888205 | − | 0.592137i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.00000i | − | 0.0422200i | ||||||
\(562\) | −22.0000 | −0.928014 | ||||||||
\(563\) | −11.0000 | −0.463595 | −0.231797 | − | 0.972764i | \(-0.574461\pi\) | ||||
−0.231797 | + | 0.972764i | \(0.574461\pi\) | |||||||
\(564\) | 8.00000i | 0.336861i | ||||||||
\(565\) | 2.00000i | 0.0841406i | ||||||||
\(566\) | − | 14.0000i | − | 0.588464i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | − | 1.00000i | − | 0.0418854i | ||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | −2.00000 | + | 3.00000i | −0.0836242 | + | 0.125436i | ||||
\(573\) | −11.0000 | −0.459532 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | 16.0000i | 0.665512i | ||||||||
\(579\) | − | 12.0000i | − | 0.498703i | ||||||
\(580\) | 9.00000i | 0.373705i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | − | 10.0000i | − | 0.414158i | ||||||
\(584\) | 11.0000 | 0.455183 | ||||||||
\(585\) | −2.00000 | + | 3.00000i | −0.0826898 | + | 0.124035i | ||||
\(586\) | 26.0000 | 1.07405 | ||||||||
\(587\) | 16.0000i | 0.660391i | 0.943913 | + | 0.330195i | \(0.107115\pi\) | ||||
−0.943913 | + | 0.330195i | \(0.892885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | − | 6.00000i | − | 0.247016i | ||||||
\(591\) | − | 2.00000i | − | 0.0822690i | ||||||
\(592\) | − | 9.00000i | − | 0.369898i | ||||||
\(593\) | 28.0000i | 1.14982i | 0.818216 | + | 0.574911i | \(0.194963\pi\) | ||||
−0.818216 | + | 0.574911i | \(0.805037\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.00000i | − | 0.245770i | ||||||
\(597\) | −5.00000 | −0.204636 | ||||||||
\(598\) | −6.00000 | + | 9.00000i | −0.245358 | + | 0.368037i | ||||
\(599\) | 39.0000 | 1.59350 | 0.796748 | − | 0.604311i | \(-0.206552\pi\) | ||||
0.796748 | + | 0.604311i | \(0.206552\pi\) | |||||||
\(600\) | 4.00000i | 0.163299i | ||||||||
\(601\) | 16.0000 | 0.652654 | 0.326327 | − | 0.945257i | \(-0.394189\pi\) | ||||
0.326327 | + | 0.945257i | \(0.394189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | − | 1.00000i | − | 0.0406894i | ||||||
\(605\) | − | 10.0000i | − | 0.406558i | ||||||
\(606\) | − | 2.00000i | − | 0.0812444i | ||||||
\(607\) | −1.00000 | −0.0405887 | −0.0202944 | − | 0.999794i | \(-0.506460\pi\) | ||||
−0.0202944 | + | 0.999794i | \(0.506460\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.0000 | 0.445377 | ||||||||
\(611\) | −16.0000 | + | 24.0000i | −0.647291 | + | 0.970936i | ||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | − | 17.0000i | − | 0.686624i | −0.939222 | − | 0.343312i | \(-0.888451\pi\) | ||
0.939222 | − | 0.343312i | \(-0.111549\pi\) | |||||||
\(614\) | 8.00000 | 0.322854 | ||||||||
\(615\) | −8.00000 | −0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.0000i | − | 0.764911i | −0.923974 | − | 0.382456i | \(-0.875078\pi\) | ||
0.923974 | − | 0.382456i | \(-0.124922\pi\) | |||||||
\(618\) | − | 5.00000i | − | 0.201129i | ||||||
\(619\) | − | 21.0000i | − | 0.844061i | −0.906582 | − | 0.422031i | \(-0.861317\pi\) | ||
0.906582 | − | 0.422031i | \(-0.138683\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | 3.00000 | 0.120386 | ||||||||
\(622\) | 8.00000i | 0.320771i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | − | 2.00000i | −0.120096 | − | 0.0800641i | ||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | − | 14.0000i | − | 0.559553i | ||||||
\(627\) | −1.00000 | −0.0399362 | ||||||||
\(628\) | −21.0000 | −0.837991 | ||||||||
\(629\) | 9.00000i | 0.358854i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000i | 1.15447i | 0.816577 | + | 0.577236i | \(0.195869\pi\) | ||||
−0.816577 | + | 0.577236i | \(0.804131\pi\) | |||||||
\(632\) | − | 12.0000i | − | 0.477334i | ||||||
\(633\) | −5.00000 | −0.198732 | ||||||||
\(634\) | −12.0000 | −0.476581 | ||||||||
\(635\) | − | 16.0000i | − | 0.634941i | ||||||
\(636\) | 10.0000 | 0.396526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | 6.00000i | 0.237356i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −44.0000 | −1.73790 | −0.868948 | − | 0.494904i | \(-0.835203\pi\) | ||||
−0.868948 | + | 0.494904i | \(0.835203\pi\) | |||||||
\(642\) | 2.00000i | 0.0789337i | ||||||||
\(643\) | 19.0000i | 0.749287i | 0.927169 | + | 0.374643i | \(0.122235\pi\) | ||||
−0.927169 | + | 0.374643i | \(0.877765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.00000i | − | 0.275625i | ||||||
\(646\) | −1.00000 | −0.0393445 | ||||||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | −8.00000 | + | 12.0000i | −0.313786 | + | 0.470679i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.0000i | 0.783260i | ||||||||
\(653\) | −13.0000 | −0.508729 | −0.254365 | − | 0.967108i | \(-0.581866\pi\) | ||||
−0.254365 | + | 0.967108i | \(0.581866\pi\) | |||||||
\(654\) | 7.00000 | 0.273722 | ||||||||
\(655\) | − | 3.00000i | − | 0.117220i | ||||||
\(656\) | − | 8.00000i | − | 0.312348i | ||||||
\(657\) | − | 11.0000i | − | 0.429151i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | −1.00000 | −0.0389249 | ||||||||
\(661\) | − | 26.0000i | − | 1.01128i | −0.862744 | − | 0.505641i | \(-0.831256\pi\) | ||
0.862744 | − | 0.505641i | \(-0.168744\pi\) | |||||||
\(662\) | −8.00000 | −0.310929 | ||||||||
\(663\) | 3.00000 | + | 2.00000i | 0.116510 | + | 0.0776736i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.00000 | −0.348743 | ||||||||
\(667\) | 27.0000 | 1.04544 | ||||||||
\(668\) | − | 11.0000i | − | 0.425603i | ||||||
\(669\) | 8.00000i | 0.309298i | ||||||||
\(670\) | 12.0000i | 0.463600i | ||||||||
\(671\) | − | 11.0000i | − | 0.424650i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0000 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311211\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311211\pi\) | |||||||
\(674\) | − | 17.0000i | − | 0.654816i | ||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | −5.00000 | − | 12.0000i | −0.192308 | − | 0.461538i | ||||
\(677\) | −32.0000 | −1.22986 | −0.614930 | − | 0.788582i | \(-0.710816\pi\) | ||||
−0.614930 | + | 0.788582i | \(0.710816\pi\) | |||||||
\(678\) | 2.00000i | 0.0768095i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | 12.0000i | 0.459841i | ||||||||
\(682\) | 4.00000i | 0.153168i | ||||||||
\(683\) | 19.0000i | 0.727015i | 0.931591 | + | 0.363507i | \(0.118421\pi\) | ||||
−0.931591 | + | 0.363507i | \(0.881579\pi\) | |||||||
\(684\) | − | 1.00000i | − | 0.0382360i | ||||||
\(685\) | −15.0000 | −0.573121 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.00000i | − | 0.0763048i | ||||||
\(688\) | 7.00000 | 0.266872 | ||||||||
\(689\) | 30.0000 | + | 20.0000i | 1.14291 | + | 0.761939i | ||||
\(690\) | −3.00000 | −0.114208 | ||||||||
\(691\) | 40.0000i | 1.52167i | 0.648944 | + | 0.760836i | \(0.275211\pi\) | ||||
−0.648944 | + | 0.760836i | \(0.724789\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 12.0000i | − | 0.455186i | ||||||
\(696\) | 9.00000i | 0.341144i | ||||||||
\(697\) | 8.00000i | 0.303022i | ||||||||
\(698\) | 4.00000 | 0.151402 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | −2.00000 | + | 3.00000i | −0.0754851 | + | 0.113228i | ||||
\(703\) | 9.00000 | 0.339441 | ||||||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 16.0000 | 0.602168 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | − | 14.0000i | − | 0.525781i | −0.964826 | − | 0.262891i | \(-0.915324\pi\) | ||
0.964826 | − | 0.262891i | \(-0.0846758\pi\) | |||||||
\(710\) | − | 6.00000i | − | 0.225176i | ||||||
\(711\) | −12.0000 | −0.450035 | ||||||||
\(712\) | 12.0000 | 0.449719 | ||||||||
\(713\) | 12.0000i | 0.449404i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | − | 2.00000i | −0.112194 | − | 0.0747958i | ||||
\(716\) | 18.0000 | 0.672692 | ||||||||
\(717\) | − | 8.00000i | − | 0.298765i | ||||||
\(718\) | 30.0000 | 1.11959 | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.0000i | − | 0.669891i | ||||||
\(723\) | − | 10.0000i | − | 0.371904i | ||||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | 36.0000 | 1.33701 | ||||||||
\(726\) | − | 10.0000i | − | 0.371135i | ||||||
\(727\) | −23.0000 | −0.853023 | −0.426511 | − | 0.904482i | \(-0.640258\pi\) | ||||
−0.426511 | + | 0.904482i | \(0.640258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.0000i | 0.407128i | ||||||||
\(731\) | −7.00000 | −0.258904 | ||||||||
\(732\) | 11.0000 | 0.406572 | ||||||||
\(733\) | 40.0000i | 1.47743i | 0.674016 | + | 0.738717i | \(0.264568\pi\) | ||||
−0.674016 | + | 0.738717i | \(0.735432\pi\) | |||||||
\(734\) | − | 8.00000i | − | 0.295285i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.00000i | − | 0.110581i | ||||||
\(737\) | 12.0000 | 0.442026 | ||||||||
\(738\) | −8.00000 | −0.294484 | ||||||||
\(739\) | 8.00000i | 0.294285i | 0.989115 | + | 0.147142i | \(0.0470076\pi\) | ||||
−0.989115 | + | 0.147142i | \(0.952992\pi\) | |||||||
\(740\) | 9.00000 | 0.330847 | ||||||||
\(741\) | 2.00000 | − | 3.00000i | 0.0734718 | − | 0.110208i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 36.0000i | − | 1.32071i | −0.750953 | − | 0.660356i | \(-0.770405\pi\) | ||
0.750953 | − | 0.660356i | \(-0.229595\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 14.0000i | 0.512576i | ||||||||
\(747\) | − | 6.00000i | − | 0.219529i | ||||||
\(748\) | 1.00000i | 0.0365636i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.00000 | −0.328634 | ||||||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | −11.0000 | −0.400862 | ||||||||
\(754\) | −18.0000 | + | 27.0000i | −0.655521 | + | 0.983282i | ||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 16.0000 | 0.581146 | ||||||||
\(759\) | 3.00000i | 0.108893i | ||||||||
\(760\) | 1.00000i | 0.0362738i | ||||||||
\(761\) | 42.0000i | 1.52250i | 0.648459 | + | 0.761249i | \(0.275414\pi\) | ||||
−0.648459 | + | 0.761249i | \(0.724586\pi\) | |||||||
\(762\) | − | 16.0000i | − | 0.579619i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.0000 | 0.397966 | ||||||||
\(765\) | 1.00000i | 0.0361551i | ||||||||
\(766\) | −35.0000 | −1.26460 | ||||||||
\(767\) | 12.0000 | − | 18.0000i | 0.433295 | − | 0.649942i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − | 31.0000i | − | 1.11789i | −0.829205 | − | 0.558944i | \(-0.811207\pi\) | ||
0.829205 | − | 0.558944i | \(-0.188793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 12.0000i | 0.431889i | ||||||||
\(773\) | − | 19.0000i | − | 0.683383i | −0.939812 | − | 0.341691i | \(-0.889000\pi\) | ||
0.939812 | − | 0.341691i | \(-0.111000\pi\) | |||||||
\(774\) | − | 7.00000i | − | 0.251610i | ||||||
\(775\) | 16.0000i | 0.574737i | ||||||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 2.00000i | − | 0.0717035i | ||||||
\(779\) | 8.00000 | 0.286630 | ||||||||
\(780\) | 2.00000 | − | 3.00000i | 0.0716115 | − | 0.107417i | ||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | 3.00000i | 0.107280i | ||||||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 21.0000i | − | 0.749522i | ||||||
\(786\) | − | 3.00000i | − | 0.107006i | ||||||
\(787\) | − | 53.0000i | − | 1.88925i | −0.328158 | − | 0.944623i | \(-0.606428\pi\) | ||
0.328158 | − | 0.944623i | \(-0.393572\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | 16.0000 | 0.569615 | ||||||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 33.0000 | + | 22.0000i | 1.17186 | + | 0.781243i | ||||
\(794\) | −4.00000 | −0.141955 | ||||||||
\(795\) | 10.0000i | 0.354663i | ||||||||
\(796\) | 5.00000 | 0.177220 | ||||||||
\(797\) | −2.00000 | −0.0708436 | −0.0354218 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354218 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | − | 4.00000i | − | 0.141421i | ||||||
\(801\) | − | 12.0000i | − | 0.423999i | ||||||
\(802\) | 14.0000 | 0.494357 | ||||||||
\(803\) | 11.0000 | 0.388182 | ||||||||
\(804\) | 12.0000i | 0.423207i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | − | 8.00000i | −0.422682 | − | 0.281788i | ||||
\(807\) | 20.0000 | 0.704033 | ||||||||
\(808\) | 2.00000i | 0.0703598i | ||||||||
\(809\) | −4.00000 | −0.140633 | −0.0703163 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703163 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 21.0000i | 0.737410i | 0.929547 | + | 0.368705i | \(0.120199\pi\) | ||||
−0.929547 | + | 0.368705i | \(0.879801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000i | 0.140286i | ||||||||
\(814\) | − | 9.00000i | − | 0.315450i | ||||||
\(815\) | −20.0000 | −0.700569 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 7.00000i | 0.244899i | ||||||||
\(818\) | −27.0000 | −0.944033 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | 36.0000i | 1.25641i | 0.778048 | + | 0.628204i | \(0.216210\pi\) | ||||
−0.778048 | + | 0.628204i | \(0.783790\pi\) | |||||||
\(822\) | −15.0000 | −0.523185 | ||||||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | 5.00000i | 0.174183i | ||||||||
\(825\) | 4.00000i | 0.139262i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.00000i | − | 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | −3.00000 | −0.104257 | ||||||||
\(829\) | −25.0000 | −0.868286 | −0.434143 | − | 0.900844i | \(-0.642949\pi\) | ||||
−0.434143 | + | 0.900844i | \(0.642949\pi\) | |||||||
\(830\) | 6.00000i | 0.208263i | ||||||||
\(831\) | 16.0000 | 0.555034 | ||||||||
\(832\) | 3.00000 | + | 2.00000i | 0.104006 | + | 0.0693375i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 12.0000i | − | 0.415526i | ||||||
\(835\) | 11.0000 | 0.380671 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | 23.0000i | 0.794522i | ||||||||
\(839\) | − | 52.0000i | − | 1.79524i | −0.440771 | − | 0.897620i | \(-0.645295\pi\) | ||
0.440771 | − | 0.897620i | \(-0.354705\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 22.0000 | 0.758170 | ||||||||
\(843\) | − | 22.0000i | − | 0.757720i | ||||||
\(844\) | 5.00000 | 0.172107 | ||||||||
\(845\) | 12.0000 | − | 5.00000i | 0.412813 | − | 0.172005i | ||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0000 | −0.343401 | ||||||||
\(849\) | 14.0000 | 0.480479 | ||||||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | − | 27.0000i | − | 0.925548i | ||||||
\(852\) | − | 6.00000i | − | 0.205557i | ||||||
\(853\) | 56.0000i | 1.91740i | 0.284413 | + | 0.958702i | \(0.408201\pi\) | ||||
−0.284413 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | − | 2.00000i | − | 0.0683586i | ||||||
\(857\) | 22.0000 | 0.751506 | 0.375753 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375753 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(858\) | −3.00000 | − | 2.00000i | −0.102418 | − | 0.0682789i | ||||
\(859\) | −10.0000 | −0.341196 | −0.170598 | − | 0.985341i | \(-0.554570\pi\) | ||||
−0.170598 | + | 0.985341i | \(0.554570\pi\) | |||||||
\(860\) | 7.00000i | 0.238698i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.0000 | −0.613082 | ||||||||
\(863\) | 48.0000i | 1.63394i | 0.576681 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 14.0000i | 0.476014i | ||||||||
\(866\) | 4.00000i | 0.135926i | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 12.0000i | − | 0.407072i | ||||||
\(870\) | −9.00000 | −0.305129 | ||||||||
\(871\) | −24.0000 | + | 36.0000i | −0.813209 | + | 1.21981i | ||||
\(872\) | −7.00000 | −0.237050 | ||||||||
\(873\) | 2.00000i | 0.0676897i | ||||||||
\(874\) | 3.00000 | 0.101477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.0000i | 0.371656i | ||||||||
\(877\) | − | 22.0000i | − | 0.742887i | −0.928456 | − | 0.371444i | \(-0.878863\pi\) | ||
0.928456 | − | 0.371444i | \(-0.121137\pi\) | |||||||
\(878\) | − | 33.0000i | − | 1.11370i | ||||||
\(879\) | 26.0000i | 0.876958i | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 59.0000 | 1.98776 | 0.993880 | − | 0.110463i | \(-0.0352333\pi\) | ||||
0.993880 | + | 0.110463i | \(0.0352333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0000 | 1.04323 | 0.521617 | − | 0.853180i | \(-0.325329\pi\) | ||||
0.521617 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(884\) | −3.00000 | − | 2.00000i | −0.100901 | − | 0.0672673i | ||||
\(885\) | 6.00000 | 0.201688 | ||||||||
\(886\) | 6.00000i | 0.201574i | ||||||||
\(887\) | −2.00000 | −0.0671534 | −0.0335767 | − | 0.999436i | \(-0.510690\pi\) | ||||
−0.0335767 | + | 0.999436i | \(0.510690\pi\) | |||||||
\(888\) | 9.00000 | 0.302020 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000i | 0.402241i | ||||||||
\(891\) | 1.00000i | 0.0335013i | ||||||||
\(892\) | − | 8.00000i | − | 0.267860i | ||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 6.00000 | 0.200670 | ||||||||
\(895\) | 18.0000i | 0.601674i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.00000 | − | 6.00000i | −0.300501 | − | 0.200334i | ||||
\(898\) | −15.0000 | −0.500556 | ||||||||
\(899\) | 36.0000i | 1.20067i | ||||||||
\(900\) | −4.00000 | −0.133333 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | − | 8.00000i | − | 0.266371i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.00000i | − | 0.0665190i | ||||||
\(905\) | − | 2.00000i | − | 0.0664822i | ||||||
\(906\) | 1.00000 | 0.0332228 | ||||||||
\(907\) | −12.0000 | −0.398453 | −0.199227 | − | 0.979953i | \(-0.563843\pi\) | ||||
−0.199227 | + | 0.979953i | \(0.563843\pi\) | |||||||
\(908\) | − | 12.0000i | − | 0.398234i | ||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.0000 | −0.960813 | −0.480406 | − | 0.877046i | \(-0.659511\pi\) | ||||
−0.480406 | + | 0.877046i | \(0.659511\pi\) | |||||||
\(912\) | 1.00000i | 0.0331133i | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 4.00000 | 0.132308 | ||||||||
\(915\) | 11.0000i | 0.363649i | ||||||||
\(916\) | 2.00000i | 0.0660819i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.00000i | 0.0330049i | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 3.00000 | 0.0989071 | ||||||||
\(921\) | 8.00000i | 0.263609i | ||||||||
\(922\) | −3.00000 | −0.0987997 | ||||||||
\(923\) | 12.0000 | − | 18.0000i | 0.394985 | − | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 36.0000i | − | 1.18367i | ||||||
\(926\) | 29.0000 | 0.952999 | ||||||||
\(927\) | 5.00000 | 0.164222 | ||||||||
\(928\) | − | 9.00000i | − | 0.295439i | ||||||
\(929\) | 26.0000i | 0.853032i | 0.904480 | + | 0.426516i | \(0.140259\pi\) | ||||
−0.904480 | + | 0.426516i | \(0.859741\pi\) | |||||||
\(930\) | − | 4.00000i | − | 0.131165i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | − | 37.0000i | − | 1.21068i | ||||||
\(935\) | −1.00000 | −0.0327035 | ||||||||
\(936\) | 2.00000 | − | 3.00000i | 0.0653720 | − | 0.0980581i | ||||
\(937\) | 20.0000 | 0.653372 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 8.00000 | 0.260931 | ||||||||
\(941\) | 30.0000i | 0.977972i | 0.872292 | + | 0.488986i | \(0.162633\pi\) | ||||
−0.872292 | + | 0.488986i | \(0.837367\pi\) | |||||||
\(942\) | − | 21.0000i | − | 0.684217i | ||||||
\(943\) | − | 24.0000i | − | 0.781548i | ||||||
\(944\) | 6.00000i | 0.195283i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.00000 | 0.227590 | ||||||||
\(947\) | − | 35.0000i | − | 1.13735i | −0.822563 | − | 0.568674i | \(-0.807457\pi\) | ||
0.822563 | − | 0.568674i | \(-0.192543\pi\) | |||||||
\(948\) | 12.0000 | 0.389742 | ||||||||
\(949\) | −22.0000 | + | 33.0000i | −0.714150 | + | 1.07123i | ||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | − | 12.0000i | − | 0.389127i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.0000 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | 10.0000i | 0.323762i | ||||||||
\(955\) | 11.0000i | 0.355952i | ||||||||
\(956\) | 8.00000i | 0.258738i | ||||||||
\(957\) | 9.00000i | 0.290929i | ||||||||
\(958\) | −39.0000 | −1.26003 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 27.0000 | + | 18.0000i | 0.870515 | + | 0.580343i | ||||
\(963\) | −2.00000 | −0.0644491 | ||||||||
\(964\) | 10.0000i | 0.322078i | ||||||||
\(965\) | −12.0000 | −0.386294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.00000i | 0.289420i | 0.989474 | + | 0.144710i | \(0.0462250\pi\) | ||||
−0.989474 | + | 0.144710i | \(0.953775\pi\) | |||||||
\(968\) | 10.0000i | 0.321412i | ||||||||
\(969\) | − | 1.00000i | − | 0.0321246i | ||||||
\(970\) | − | 2.00000i | − | 0.0642161i | ||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | −12.0000 | − | 8.00000i | −0.384308 | − | 0.256205i | ||||
\(976\) | −11.0000 | −0.352101 | ||||||||
\(977\) | − | 39.0000i | − | 1.24772i | −0.781536 | − | 0.623860i | \(-0.785563\pi\) | ||
0.781536 | − | 0.623860i | \(-0.214437\pi\) | |||||||
\(978\) | −20.0000 | −0.639529 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.00000i | 0.223493i | ||||||||
\(982\) | − | 12.0000i | − | 0.382935i | ||||||
\(983\) | 9.00000i | 0.287055i | 0.989646 | + | 0.143528i | \(0.0458446\pi\) | ||||
−0.989646 | + | 0.143528i | \(0.954155\pi\) | |||||||
\(984\) | 8.00000 | 0.255031 | ||||||||
\(985\) | −2.00000 | −0.0637253 | ||||||||
\(986\) | 9.00000i | 0.286618i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | + | 3.00000i | −0.0636285 | + | 0.0954427i | ||||
\(989\) | 21.0000 | 0.667761 | ||||||||
\(990\) | − | 1.00000i | − | 0.0317821i | ||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.00000i | 0.158511i | ||||||||
\(996\) | 6.00000i | 0.190117i | ||||||||
\(997\) | 14.0000 | 0.443384 | 0.221692 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221692 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(998\) | −10.0000 | −0.316544 | ||||||||
\(999\) | − | 9.00000i | − | 0.284747i |
(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 | 3822.2.c.e.883.1 | 2 | ||
7.6 | odd | 2 | 546.2.c.a.337.1 | ✓ | 2 | ||
13.12 | even | 2 | inner | 3822.2.c.e.883.2 | 2 | ||
21.20 | even | 2 | 1638.2.c.f.883.2 | 2 | |||
28.27 | even | 2 | 4368.2.h.k.337.2 | 2 | |||
91.34 | even | 4 | 7098.2.a.s.1.1 | 1 | |||
91.83 | even | 4 | 7098.2.a.d.1.1 | 1 | |||
91.90 | odd | 2 | 546.2.c.a.337.2 | yes | 2 | ||
273.272 | even | 2 | 1638.2.c.f.883.1 | 2 | |||
364.363 | even | 2 | 4368.2.h.k.337.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.c.a.337.1 | ✓ | 2 | 7.6 | odd | 2 | ||
546.2.c.a.337.2 | yes | 2 | 91.90 | odd | 2 | ||
1638.2.c.f.883.1 | 2 | 273.272 | even | 2 | |||
1638.2.c.f.883.2 | 2 | 21.20 | even | 2 | |||
3822.2.c.e.883.1 | 2 | 1.1 | even | 1 | trivial | ||
3822.2.c.e.883.2 | 2 | 13.12 | even | 2 | inner | ||
4368.2.h.k.337.1 | 2 | 364.363 | even | 2 | |||
4368.2.h.k.337.2 | 2 | 28.27 | even | 2 | |||
7098.2.a.d.1.1 | 1 | 91.83 | even | 4 | |||
7098.2.a.s.1.1 | 1 | 91.34 | even | 4 |