Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(739,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.739");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 739.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.739 |
Dual form | 3330.2.e.b.739.2 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.00000i | − | 1.13389i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||
0.823754 | − | 0.566947i | \(-0.191875\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | − | 1.00000i | −0.632456 | − | 0.316228i | ||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | − | 3.00000i | − | 0.801784i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.00000 | −1.69775 | −0.848875 | − | 0.528594i | \(-0.822719\pi\) | ||||
−0.848875 | + | 0.528594i | \(0.822719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.00000i | − | 0.566947i | ||||||
\(29\) | − | 9.00000i | − | 1.67126i | −0.549294 | − | 0.835629i | \(-0.685103\pi\) | ||
0.549294 | − | 0.835629i | \(-0.314897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000i | 0.898027i | 0.893525 | + | 0.449013i | \(0.148224\pi\) | ||||
−0.893525 | + | 0.449013i | \(0.851776\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.00000 | −1.20049 | ||||||||
\(35\) | −3.00000 | + | 6.00000i | −0.507093 | + | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | + | 1.00000i | 0.986394 | + | 0.164399i | ||||
\(38\) | 4.00000i | 0.648886i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | − | 1.00000i | −0.316228 | − | 0.158114i | ||||
\(41\) | −7.00000 | −1.09322 | −0.546608 | − | 0.837389i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837389i | \(0.684081\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 3.00000 | + | 4.00000i | 0.424264 | + | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | 1.00000i | 0.137361i | 0.997639 | + | 0.0686803i | \(0.0218788\pi\) | ||||
−0.997639 | + | 0.0686803i | \(0.978121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | − | 3.00000i | −0.809040 | − | 0.404520i | ||||
\(56\) | − | 3.00000i | − | 0.400892i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 9.00000i | − | 1.18176i | ||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000i | 0.640184i | 0.947386 | + | 0.320092i | \(0.103714\pi\) | ||||
−0.947386 | + | 0.320092i | \(0.896286\pi\) | |||||||
\(62\) | 5.00000i | 0.635001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.00000 | + | 4.00000i | 0.992278 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | −7.00000 | −0.848875 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | + | 6.00000i | −0.358569 | + | 0.717137i | ||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 6.00000 | + | 1.00000i | 0.697486 | + | 0.116248i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000i | 0.458831i | ||||||||
\(77\) | − | 9.00000i | − | 1.02565i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.00000 | −0.773021 | ||||||||
\(83\) | − | 14.0000i | − | 1.53670i | −0.640030 | − | 0.768350i | \(-0.721078\pi\) | ||
0.640030 | − | 0.768350i | \(-0.278922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0000 | + | 7.00000i | 1.51851 | + | 0.759257i | ||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000i | 1.25794i | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000i | 0.825137i | ||||||||
\(95\) | 4.00000 | − | 8.00000i | 0.410391 | − | 0.820783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | −2.00000 | −0.202031 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000i | 0.0971286i | ||||||||
\(107\) | 18.0000i | 1.74013i | 0.492941 | + | 0.870063i | \(0.335922\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.0000i | − | 1.05361i | −0.849987 | − | 0.526804i | \(-0.823390\pi\) | ||
0.849987 | − | 0.526804i | \(-0.176610\pi\) | |||||||
\(110\) | −6.00000 | − | 3.00000i | −0.572078 | − | 0.286039i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 3.00000i | − | 0.283473i | ||||||
\(113\) | −1.00000 | −0.0940721 | −0.0470360 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470360 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | + | 6.00000i | 1.11901 | + | 0.559503i | ||||
\(116\) | − | 9.00000i | − | 0.835629i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 21.0000i | 1.92507i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 5.00000i | 0.452679i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.00000i | 0.449013i | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.00000 | + | 4.00000i | 0.701646 | + | 0.350823i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | 1.04053 | ||||||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.00000 | −0.600245 | ||||||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0000 | −1.27228 | −0.636142 | − | 0.771572i | \(-0.719471\pi\) | ||||
−0.636142 | + | 0.771572i | \(0.719471\pi\) | |||||||
\(140\) | −3.00000 | + | 6.00000i | −0.253546 | + | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | + | 18.0000i | −0.747409 | + | 1.49482i | ||||
\(146\) | 4.00000i | 0.331042i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | + | 1.00000i | 0.493197 | + | 0.0821995i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 4.00000i | 0.324443i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 9.00000i | − | 0.725241i | ||||||
\(155\) | 5.00000 | − | 10.0000i | 0.401610 | − | 0.803219i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000i | 0.558661i | 0.960195 | + | 0.279330i | \(0.0901125\pi\) | ||||
−0.960195 | + | 0.279330i | \(0.909888\pi\) | |||||||
\(158\) | 4.00000i | 0.318223i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 18.0000i | 1.41860i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.00000 | −0.704934 | −0.352467 | − | 0.935824i | \(-0.614657\pi\) | ||||
−0.352467 | + | 0.935824i | \(0.614657\pi\) | |||||||
\(164\) | −7.00000 | −0.546608 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.0000i | − | 1.08661i | ||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 14.0000 | + | 7.00000i | 1.07375 | + | 0.536875i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | − | 9.00000i | − | 0.684257i | −0.939653 | − | 0.342129i | \(-0.888852\pi\) | ||
0.939653 | − | 0.342129i | \(-0.111148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0000 | − | 9.00000i | 0.907115 | − | 0.680336i | ||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | − | 4.00000i | − | 0.298974i | −0.988764 | − | 0.149487i | \(-0.952238\pi\) | ||
0.988764 | − | 0.149487i | \(-0.0477622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 12.0000i | 0.889499i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −11.0000 | − | 8.00000i | −0.808736 | − | 0.588172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0000 | −1.53567 | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | − | 8.00000i | 0.290191 | − | 0.580381i | ||||
\(191\) | − | 15.0000i | − | 1.08536i | −0.839939 | − | 0.542681i | \(-0.817409\pi\) | ||
0.839939 | − | 0.542681i | \(-0.182591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 7.00000 | 0.502571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | −0.142857 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.0000i | − | 1.13421i | −0.823646 | − | 0.567105i | \(-0.808063\pi\) | ||
0.823646 | − | 0.567105i | \(-0.191937\pi\) | |||||||
\(200\) | 3.00000 | + | 4.00000i | 0.212132 | + | 0.282843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | −27.0000 | −1.89503 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0000 | + | 7.00000i | 0.977802 | + | 0.488901i | ||||
\(206\) | −14.0000 | −0.975426 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 12.0000i | 0.830057i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 1.00000i | 0.0686803i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000i | 1.23045i | ||||||||
\(215\) | −2.00000 | − | 1.00000i | −0.136399 | − | 0.0681994i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0000 | 1.01827 | ||||||||
\(218\) | − | 11.0000i | − | 0.745014i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | − | 3.00000i | −0.404520 | − | 0.202260i | ||||
\(221\) | 28.0000 | 1.88348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.0000i | − | 0.736614i | −0.929704 | − | 0.368307i | \(-0.879937\pi\) | ||
0.929704 | − | 0.368307i | \(-0.120063\pi\) | |||||||
\(224\) | − | 3.00000i | − | 0.200446i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.00000 | −0.0665190 | ||||||||
\(227\) | 13.0000 | 0.862840 | 0.431420 | − | 0.902151i | \(-0.358013\pi\) | ||||
0.431420 | + | 0.902151i | \(0.358013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 12.0000 | + | 6.00000i | 0.791257 | + | 0.395628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 9.00000i | − | 0.590879i | ||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | − | 16.0000i | 0.521862 | − | 1.04372i | ||||
\(236\) | 6.00000i | 0.390567i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21.0000i | 1.36123i | ||||||||
\(239\) | − | 9.00000i | − | 0.582162i | −0.956698 | − | 0.291081i | \(-0.905985\pi\) | ||
0.956698 | − | 0.291081i | \(-0.0940149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.00000i | 0.320092i | ||||||||
\(245\) | 4.00000 | + | 2.00000i | 0.255551 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 16.0000i | − | 1.01806i | ||||||
\(248\) | 5.00000i | 0.317500i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.00000 | − | 11.0000i | −0.126491 | − | 0.695701i | ||||
\(251\) | 20.0000i | 1.26239i | 0.775625 | + | 0.631194i | \(0.217435\pi\) | ||||
−0.775625 | + | 0.631194i | \(0.782565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | − | 8.00000i | − | 0.501965i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | − | 18.0000i | 0.186411 | − | 1.11847i | ||||
\(260\) | 8.00000 | + | 4.00000i | 0.496139 | + | 0.248069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.0000i | 1.91154i | 0.294112 | + | 0.955771i | \(0.404976\pi\) | ||||
−0.294112 | + | 0.955771i | \(0.595024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | − | 2.00000i | 0.0614295 | − | 0.122859i | ||||
\(266\) | 12.0000 | 0.735767 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000i | 0.122169i | ||||||||
\(269\) | −20.0000 | −1.21942 | −0.609711 | − | 0.792624i | \(-0.708714\pi\) | ||||
−0.609711 | + | 0.792624i | \(0.708714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0000 | 1.33640 | 0.668202 | − | 0.743980i | \(-0.267064\pi\) | ||||
0.668202 | + | 0.743980i | \(0.267064\pi\) | |||||||
\(272\) | −7.00000 | −0.424437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 12.0000i | − | 0.724947i | ||||||
\(275\) | 9.00000 | + | 12.0000i | 0.542720 | + | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.0000 | −1.68236 | −0.841178 | − | 0.540758i | \(-0.818138\pi\) | ||||
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | −15.0000 | −0.899640 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | + | 6.00000i | −0.179284 | + | 0.358569i | ||||
\(281\) | − | 30.0000i | − | 1.78965i | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||
0.446417 | − | 0.894825i | \(-0.352700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | 21.0000i | 1.23959i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | −9.00000 | + | 18.0000i | −0.528498 | + | 1.05700i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00000i | 0.234082i | ||||||||
\(293\) | − | 29.0000i | − | 1.69420i | −0.531435 | − | 0.847099i | \(-0.678347\pi\) | ||
0.531435 | − | 0.847099i | \(-0.321653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 12.0000i | 0.349334 | − | 0.698667i | ||||
\(296\) | 6.00000 | + | 1.00000i | 0.348743 | + | 0.0581238i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3.00000i | − | 0.172917i | ||||||
\(302\) | 2.00000 | 0.115087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000i | 0.229416i | ||||||||
\(305\) | 5.00000 | − | 10.0000i | 0.286299 | − | 0.572598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | − | 9.00000i | − | 0.512823i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.00000 | − | 10.0000i | 0.283981 | − | 0.567962i | ||||
\(311\) | 15.0000i | 0.850572i | 0.905059 | + | 0.425286i | \(0.139826\pi\) | ||||
−0.905059 | + | 0.425286i | \(0.860174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 7.00000i | 0.395033i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000i | 0.225018i | ||||||||
\(317\) | − | 27.0000i | − | 1.51647i | −0.651981 | − | 0.758236i | \(-0.726062\pi\) | ||
0.651981 | − | 0.758236i | \(-0.273938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27.0000i | − | 1.51171i | ||||||
\(320\) | −2.00000 | − | 1.00000i | −0.111803 | − | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.0000i | 1.00310i | ||||||||
\(323\) | − | 28.0000i | − | 1.55796i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | − | 16.0000i | −0.665640 | − | 0.887520i | ||||
\(326\) | −9.00000 | −0.498464 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.00000 | −0.386510 | ||||||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000i | 1.09930i | 0.835395 | + | 0.549650i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549650i | \(0.814761\pi\) | |||||||
\(332\) | − | 14.0000i | − | 0.768350i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 2.00000 | − | 4.00000i | 0.109272 | − | 0.218543i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.0000i | − | 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | 3.00000 | 0.163178 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.0000 | + | 7.00000i | 0.759257 | + | 0.379628i | ||||
\(341\) | 15.0000i | 0.812296i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 9.00000i | − | 0.483843i | ||||||
\(347\) | 28.0000 | 1.50312 | 0.751559 | − | 0.659665i | \(-0.229302\pi\) | ||||
0.751559 | + | 0.659665i | \(0.229302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 12.0000 | − | 9.00000i | 0.641427 | − | 0.481070i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | −31.0000 | −1.64996 | −0.824982 | − | 0.565159i | \(-0.808815\pi\) | ||||
−0.824982 | + | 0.565159i | \(0.808815\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.0000 | + | 12.0000i | 1.27379 | + | 0.636894i | ||||
\(356\) | 6.00000i | 0.317999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 4.00000i | − | 0.211407i | ||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −18.0000 | −0.946059 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0000i | 0.628971i | ||||||||
\(365\) | 4.00000 | − | 8.00000i | 0.209370 | − | 0.418739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.0000i | − | 1.20059i | −0.799779 | − | 0.600295i | \(-0.795050\pi\) | ||
0.799779 | − | 0.600295i | \(-0.204950\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.0000 | − | 8.00000i | −0.571863 | − | 0.415900i | ||||
\(371\) | 3.00000 | 0.155752 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000i | 0.724893i | 0.932005 | + | 0.362446i | \(0.118058\pi\) | ||||
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | −21.0000 | −1.08588 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00000i | 0.412568i | ||||||||
\(377\) | 36.0000i | 1.85409i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 4.00000 | − | 8.00000i | 0.205196 | − | 0.410391i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 15.0000i | − | 0.767467i | ||||||
\(383\) | −6.00000 | −0.306586 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | + | 18.0000i | −0.458682 | + | 0.917365i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.00000 | 0.355371 | ||||||||
\(389\) | 31.0000i | 1.57176i | 0.618378 | + | 0.785881i | \(0.287790\pi\) | ||||
−0.618378 | + | 0.785881i | \(0.712210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.0000 | 2.12403 | ||||||||
\(392\) | −2.00000 | −0.101015 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.0000i | 0.906827i | ||||||||
\(395\) | 4.00000 | − | 8.00000i | 0.201262 | − | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 38.0000i | − | 1.90717i | −0.301131 | − | 0.953583i | \(-0.597364\pi\) | ||
0.301131 | − | 0.953583i | \(-0.402636\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | − | 10.0000i | − | 0.499376i | −0.968326 | − | 0.249688i | \(-0.919672\pi\) | ||
0.968326 | − | 0.249688i | \(-0.0803281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.0000i | − | 0.996271i | ||||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.0000 | −1.33999 | ||||||||
\(407\) | 18.0000 | + | 3.00000i | 0.892227 | + | 0.148704i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000i | 0.692255i | 0.938187 | + | 0.346128i | \(0.112504\pi\) | ||||
−0.938187 | + | 0.346128i | \(0.887496\pi\) | |||||||
\(410\) | 14.0000 | + | 7.00000i | 0.691411 | + | 0.345705i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.0000 | −0.689730 | ||||||||
\(413\) | 18.0000 | 0.885722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0000 | + | 28.0000i | −0.687233 | + | 1.37447i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.0000i | 0.586939i | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.0000i | − | 1.46211i | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||
0.682318 | − | 0.731055i | \(-0.260972\pi\) | |||||||
\(422\) | −13.0000 | −0.632830 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.00000i | 0.0485643i | ||||||||
\(425\) | −21.0000 | − | 28.0000i | −1.01865 | − | 1.35820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.0000 | 0.725901 | ||||||||
\(428\) | 18.0000i | 0.870063i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.00000 | − | 1.00000i | −0.0964486 | − | 0.0482243i | ||||
\(431\) | − | 25.0000i | − | 1.20421i | −0.798418 | − | 0.602104i | \(-0.794329\pi\) | ||
0.798418 | − | 0.602104i | \(-0.205671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0000i | 1.63394i | 0.576683 | + | 0.816968i | \(0.304347\pi\) | ||||
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(434\) | 15.0000 | 0.720023 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 11.0000i | − | 0.526804i | ||||||
\(437\) | − | 24.0000i | − | 1.14808i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.00000i | 0.429547i | 0.976664 | + | 0.214773i | \(0.0689013\pi\) | ||||
−0.976664 | + | 0.214773i | \(0.931099\pi\) | |||||||
\(440\) | −6.00000 | − | 3.00000i | −0.286039 | − | 0.143019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.0000 | 1.33182 | ||||||||
\(443\) | 36.0000i | 1.71041i | 0.518289 | + | 0.855206i | \(0.326569\pi\) | ||||
−0.518289 | + | 0.855206i | \(0.673431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 12.0000i | 0.284427 | − | 0.568855i | ||||
\(446\) | − | 11.0000i | − | 0.520865i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.00000i | − | 0.141737i | ||||||
\(449\) | 6.00000i | 0.283158i | 0.989927 | + | 0.141579i | \(0.0452178\pi\) | ||||
−0.989927 | + | 0.141579i | \(0.954782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.0000 | −0.988851 | ||||||||
\(452\) | −1.00000 | −0.0470360 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.0000 | 0.610120 | ||||||||
\(455\) | 12.0000 | − | 24.0000i | 0.562569 | − | 1.12514i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0000 | −0.608114 | −0.304057 | − | 0.952654i | \(-0.598341\pi\) | ||||
−0.304057 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(458\) | 10.0000 | 0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0000 | + | 6.00000i | 0.559503 | + | 0.279751i | ||||
\(461\) | 25.0000i | 1.16437i | 0.813058 | + | 0.582183i | \(0.197801\pi\) | ||||
−0.813058 | + | 0.582183i | \(0.802199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | − | 9.00000i | − | 0.417815i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000i | 0.277945i | ||||||||
\(467\) | 23.0000 | 1.06431 | 0.532157 | − | 0.846646i | \(-0.321382\pi\) | ||||
0.532157 | + | 0.846646i | \(0.321382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000 | 0.277054 | ||||||||
\(470\) | 8.00000 | − | 16.0000i | 0.369012 | − | 0.738025i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000i | 0.276172i | ||||||||
\(473\) | 3.00000 | 0.137940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | + | 12.0000i | −0.734130 | + | 0.550598i | ||||
\(476\) | 21.0000i | 0.962533i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 9.00000i | − | 0.411650i | ||||||
\(479\) | − | 24.0000i | − | 1.09659i | −0.836286 | − | 0.548294i | \(-0.815277\pi\) | ||
0.836286 | − | 0.548294i | \(-0.184723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | − | 4.00000i | −1.09431 | − | 0.182384i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | −14.0000 | − | 7.00000i | −0.635707 | − | 0.317854i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 5.00000i | 0.226339i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.00000 | + | 2.00000i | 0.180702 | + | 0.0903508i | ||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 63.0000i | 2.83738i | ||||||||
\(494\) | − | 16.0000i | − | 0.719874i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000i | 0.224507i | ||||||||
\(497\) | 36.0000i | 1.61482i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0000i | 1.07439i | 0.843459 | + | 0.537194i | \(0.180516\pi\) | ||||
−0.843459 | + | 0.537194i | \(0.819484\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.0000i | 0.892644i | ||||||||
\(503\) | 14.0000 | 0.624229 | 0.312115 | − | 0.950044i | \(-0.398963\pi\) | ||||
0.312115 | + | 0.950044i | \(0.398963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | + | 2.00000i | 0.177998 | + | 0.0889988i | ||||
\(506\) | −18.0000 | −0.800198 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | 10.0000 | 0.443242 | 0.221621 | − | 0.975133i | \(-0.428865\pi\) | ||||
0.221621 | + | 0.975133i | \(0.428865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 28.0000 | + | 14.0000i | 1.23383 | + | 0.616914i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000i | 1.05552i | ||||||||
\(518\) | 3.00000 | − | 18.0000i | 0.131812 | − | 0.790875i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.00000 | + | 4.00000i | 0.350823 | + | 0.175412i | ||||
\(521\) | −37.0000 | −1.62100 | −0.810500 | − | 0.585739i | \(-0.800804\pi\) | ||||
−0.810500 | + | 0.585739i | \(0.800804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.0000i | 1.35166i | ||||||||
\(527\) | − | 35.0000i | − | 1.52462i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 1.00000 | − | 2.00000i | 0.0434372 | − | 0.0868744i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | 0.520266 | ||||||||
\(533\) | 28.0000 | 1.21281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | − | 36.0000i | 0.778208 | − | 1.55642i | ||||
\(536\) | 2.00000i | 0.0863868i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.0000 | −0.862261 | ||||||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.0000i | − | 1.28980i | −0.764267 | − | 0.644900i | \(-0.776899\pi\) | ||
0.764267 | − | 0.644900i | \(-0.223101\pi\) | |||||||
\(542\) | 22.0000 | 0.944981 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.00000 | −0.300123 | ||||||||
\(545\) | −11.0000 | + | 22.0000i | −0.471188 | + | 0.942376i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0000 | −0.983409 | −0.491704 | − | 0.870762i | \(-0.663626\pi\) | ||||
−0.491704 | + | 0.870762i | \(0.663626\pi\) | |||||||
\(548\) | − | 12.0000i | − | 0.512615i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.00000 | + | 12.0000i | 0.383761 | + | 0.511682i | ||||
\(551\) | 36.0000 | 1.53365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | 0.510292 | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.0000 | −0.636142 | ||||||||
\(557\) | −12.0000 | −0.508456 | −0.254228 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | −3.00000 | + | 6.00000i | −0.126773 | + | 0.253546i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 30.0000i | − | 1.26547i | ||||||
\(563\) | −21.0000 | −0.885044 | −0.442522 | − | 0.896758i | \(-0.645916\pi\) | ||||
−0.442522 | + | 0.896758i | \(0.645916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | + | 1.00000i | 0.0841406 | + | 0.0420703i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | − | 24.0000i | − | 1.00613i | −0.864248 | − | 0.503066i | \(-0.832205\pi\) | ||
0.864248 | − | 0.503066i | \(-0.167795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0000 | −1.38101 | −0.690504 | − | 0.723329i | \(-0.742611\pi\) | ||||
−0.690504 | + | 0.723329i | \(0.742611\pi\) | |||||||
\(572\) | −12.0000 | −0.501745 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 21.0000i | 0.876523i | ||||||||
\(575\) | −18.0000 | − | 24.0000i | −0.750652 | − | 1.00087i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 32.0000 | 1.33102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.00000 | + | 18.0000i | −0.373705 | + | 0.747409i | ||||
\(581\) | −42.0000 | −1.74245 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000i | 0.124247i | ||||||||
\(584\) | 4.00000i | 0.165521i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 29.0000i | − | 1.19798i | ||||||
\(587\) | −47.0000 | −1.93990 | −0.969949 | − | 0.243309i | \(-0.921767\pi\) | ||||
−0.969949 | + | 0.243309i | \(0.921767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0000 | −0.824086 | ||||||||
\(590\) | 6.00000 | − | 12.0000i | 0.247016 | − | 0.494032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | + | 1.00000i | 0.246598 | + | 0.0410997i | ||||
\(593\) | 46.0000i | 1.88899i | 0.328521 | + | 0.944497i | \(0.393450\pi\) | ||||
−0.328521 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0000 | − | 42.0000i | 0.860916 | − | 1.72183i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.0000 | 0.981433 | ||||||||
\(599\) | 30.0000 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.0000 | −0.938190 | −0.469095 | − | 0.883148i | \(-0.655420\pi\) | ||||
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | − | 3.00000i | − | 0.122271i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | 4.00000 | + | 2.00000i | 0.162623 | + | 0.0813116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 4.00000i | 0.162221i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.00000 | − | 10.0000i | 0.202444 | − | 0.404888i | ||||
\(611\) | − | 32.0000i | − | 1.29458i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 31.0000i | − | 1.25208i | −0.779792 | − | 0.626039i | \(-0.784675\pi\) | ||
0.779792 | − | 0.626039i | \(-0.215325\pi\) | |||||||
\(614\) | − | 18.0000i | − | 0.726421i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 9.00000i | − | 0.362620i | ||||||
\(617\) | 8.00000i | 0.322068i | 0.986949 | + | 0.161034i | \(0.0514829\pi\) | ||||
−0.986949 | + | 0.161034i | \(0.948517\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0000 | 1.00483 | 0.502417 | − | 0.864625i | \(-0.332444\pi\) | ||||
0.502417 | + | 0.864625i | \(0.332444\pi\) | |||||||
\(620\) | 5.00000 | − | 10.0000i | 0.200805 | − | 0.401610i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0000i | 0.601445i | ||||||||
\(623\) | 18.0000 | 0.721155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 6.00000 | 0.239808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.00000i | 0.279330i | ||||||||
\(629\) | −42.0000 | − | 7.00000i | −1.67465 | − | 0.279108i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0000i | 0.995234i | 0.867397 | + | 0.497617i | \(0.165792\pi\) | ||||
−0.867397 | + | 0.497617i | \(0.834208\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 27.0000i | − | 1.07231i | ||||||
\(635\) | −8.00000 | + | 16.0000i | −0.317470 | + | 0.634941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.00000 | 0.316972 | ||||||||
\(638\) | − | 27.0000i | − | 1.06894i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.00000 | − | 1.00000i | −0.0790569 | − | 0.0395285i | ||||
\(641\) | −17.0000 | −0.671460 | −0.335730 | − | 0.941958i | \(-0.608983\pi\) | ||||
−0.335730 | + | 0.941958i | \(0.608983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.0000 | 1.22252 | 0.611260 | − | 0.791430i | \(-0.290663\pi\) | ||||
0.611260 | + | 0.791430i | \(0.290663\pi\) | |||||||
\(644\) | 18.0000i | 0.709299i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 28.0000i | − | 1.10165i | ||||||
\(647\) | 48.0000 | 1.88707 | 0.943537 | − | 0.331266i | \(-0.107476\pi\) | ||||
0.943537 | + | 0.331266i | \(0.107476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000i | 0.706562i | ||||||||
\(650\) | −12.0000 | − | 16.0000i | −0.470679 | − | 0.627572i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.00000 | −0.352467 | ||||||||
\(653\) | −36.0000 | −1.40879 | −0.704394 | − | 0.709809i | \(-0.748781\pi\) | ||||
−0.704394 | + | 0.709809i | \(0.748781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.00000 | −0.273304 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | 20.0000 | 0.779089 | 0.389545 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389545 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.0000i | 1.36134i | 0.732589 | + | 0.680671i | \(0.238312\pi\) | ||||
−0.732589 | + | 0.680671i | \(0.761688\pi\) | |||||||
\(662\) | 20.0000i | 0.777322i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.0000i | − | 0.543305i | ||||||
\(665\) | −24.0000 | − | 12.0000i | −0.930680 | − | 0.465340i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.0000i | 2.09089i | ||||||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.00000 | − | 4.00000i | 0.0772667 | − | 0.154533i | ||||
\(671\) | 15.0000i | 0.579069i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.0000i | − | 1.00223i | −0.865382 | − | 0.501113i | \(-0.832924\pi\) | ||
0.865382 | − | 0.501113i | \(-0.167076\pi\) | |||||||
\(674\) | − | 18.0000i | − | 0.693334i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | − | 42.0000i | − | 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 21.0000i | − | 0.805906i | ||||||
\(680\) | 14.0000 | + | 7.00000i | 0.536875 | + | 0.268438i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.0000i | 0.574380i | ||||||||
\(683\) | −1.00000 | −0.0382639 | −0.0191320 | − | 0.999817i | \(-0.506090\pi\) | ||||
−0.0191320 | + | 0.999817i | \(0.506090\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | + | 24.0000i | −0.458496 | + | 0.916993i | ||||
\(686\) | − | 15.0000i | − | 0.572703i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | − | 4.00000i | − | 0.152388i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.0000 | −1.63580 | −0.817899 | − | 0.575362i | \(-0.804861\pi\) | ||||
−0.817899 | + | 0.575362i | \(0.804861\pi\) | |||||||
\(692\) | − | 9.00000i | − | 0.342129i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | 30.0000 | + | 15.0000i | 1.13796 | + | 0.568982i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.0000 | 1.85601 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.0000 | − | 9.00000i | 0.453557 | − | 0.340168i | ||||
\(701\) | − | 10.0000i | − | 0.377695i | −0.982006 | − | 0.188847i | \(-0.939525\pi\) | ||
0.982006 | − | 0.188847i | \(-0.0604752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | + | 24.0000i | −0.150863 | + | 0.905177i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.0000 | −1.16670 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 11.0000i | − | 0.413114i | −0.978435 | − | 0.206557i | \(-0.933774\pi\) | ||
0.978435 | − | 0.206557i | \(-0.0662258\pi\) | |||||||
\(710\) | 24.0000 | + | 12.0000i | 0.900704 | + | 0.450352i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000i | 0.224860i | ||||||||
\(713\) | − | 30.0000i | − | 1.12351i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | + | 12.0000i | 0.897549 | + | 0.448775i | ||||
\(716\) | − | 4.00000i | − | 0.149487i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.0000 | −1.86469 | −0.932343 | − | 0.361576i | \(-0.882239\pi\) | ||||
−0.932343 | + | 0.361576i | \(0.882239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.0000i | 1.56416i | ||||||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.0000 | −0.668965 | ||||||||
\(725\) | 36.0000 | − | 27.0000i | 1.33701 | − | 1.00275i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 12.0000i | 0.444750i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.00000 | − | 8.00000i | 0.148047 | − | 0.296093i | ||||
\(731\) | −7.00000 | −0.258904 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11.0000i | − | 0.406294i | −0.979148 | − | 0.203147i | \(-0.934883\pi\) | ||
0.979148 | − | 0.203147i | \(-0.0651170\pi\) | |||||||
\(734\) | − | 23.0000i | − | 0.848945i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 6.00000i | 0.221013i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | 0.183928 | 0.0919640 | − | 0.995762i | \(-0.470686\pi\) | ||||
0.0919640 | + | 0.995762i | \(0.470686\pi\) | |||||||
\(740\) | −11.0000 | − | 8.00000i | −0.404368 | − | 0.294086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | 51.0000i | 1.87101i | 0.353315 | + | 0.935504i | \(0.385054\pi\) | ||||
−0.353315 | + | 0.935504i | \(0.614946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.0000i | 0.512576i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.0000 | −0.767836 | ||||||||
\(749\) | 54.0000 | 1.97312 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0000 | −0.656829 | −0.328415 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328415 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(752\) | 8.00000i | 0.291730i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 36.0000i | 1.31104i | ||||||||
\(755\) | −4.00000 | − | 2.00000i | −0.145575 | − | 0.0727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 20.0000 | 0.726433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.00000 | − | 8.00000i | 0.145095 | − | 0.290191i | ||||
\(761\) | 13.0000 | 0.471250 | 0.235625 | − | 0.971844i | \(-0.424286\pi\) | ||||
0.235625 | + | 0.971844i | \(0.424286\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.0000 | −1.19468 | ||||||||
\(764\) | − | 15.0000i | − | 0.542681i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.00000 | −0.216789 | ||||||||
\(767\) | − | 24.0000i | − | 0.866590i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26.0000i | − | 0.937584i | −0.883309 | − | 0.468792i | \(-0.844689\pi\) | ||
0.883309 | − | 0.468792i | \(-0.155311\pi\) | |||||||
\(770\) | −9.00000 | + | 18.0000i | −0.324337 | + | 0.648675i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.0000 | −0.503871 | ||||||||
\(773\) | 11.0000i | 0.395643i | 0.980238 | + | 0.197821i | \(0.0633866\pi\) | ||||
−0.980238 | + | 0.197821i | \(0.936613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.0000 | + | 15.0000i | −0.718421 | + | 0.538816i | ||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.0000i | 1.11140i | ||||||||
\(779\) | − | 28.0000i | − | 1.00320i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 42.0000 | 1.50192 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.00000 | −0.0714286 | ||||||||
\(785\) | 7.00000 | − | 14.0000i | 0.249841 | − | 0.499681i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.0000i | − | 0.998092i | −0.866575 | − | 0.499046i | \(-0.833684\pi\) | ||
0.866575 | − | 0.499046i | \(-0.166316\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.00000 | − | 8.00000i | 0.142314 | − | 0.284627i | ||||
\(791\) | 3.00000i | 0.106668i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 20.0000i | − | 0.710221i | ||||||
\(794\) | − | 38.0000i | − | 1.34857i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 16.0000i | − | 0.567105i | ||||||
\(797\) | 28.0000 | 0.991811 | 0.495905 | − | 0.868377i | \(-0.334836\pi\) | ||||
0.495905 | + | 0.868377i | \(0.334836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 56.0000i | − | 1.98114i | ||||||
\(800\) | 3.00000 | + | 4.00000i | 0.106066 | + | 0.141421i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 10.0000i | − | 0.353112i | ||||||
\(803\) | 12.0000i | 0.423471i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0000 | − | 36.0000i | 0.634417 | − | 1.26883i | ||||
\(806\) | − | 20.0000i | − | 0.704470i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.00000 | −0.0703598 | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | −27.0000 | −0.947514 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.0000 | + | 3.00000i | 0.630900 | + | 0.105150i | ||||
\(815\) | 18.0000 | + | 9.00000i | 0.630512 | + | 0.315256i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000i | 0.139942i | ||||||||
\(818\) | 14.0000i | 0.489499i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.0000 | + | 7.00000i | 0.488901 | + | 0.244451i | ||||
\(821\) | −52.0000 | −1.81481 | −0.907406 | − | 0.420255i | \(-0.861941\pi\) | ||||
−0.907406 | + | 0.420255i | \(0.861941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 16.0000i | − | 0.557725i | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||
0.960331 | − | 0.278862i | \(-0.0899574\pi\) | |||||||
\(824\) | −14.0000 | −0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0000 | 0.626300 | ||||||||
\(827\) | 33.0000 | 1.14752 | 0.573761 | − | 0.819023i | \(-0.305484\pi\) | ||||
0.573761 | + | 0.819023i | \(0.305484\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0000i | 0.659897i | 0.943999 | + | 0.329949i | \(0.107031\pi\) | ||||
−0.943999 | + | 0.329949i | \(0.892969\pi\) | |||||||
\(830\) | −14.0000 | + | 28.0000i | −0.485947 | + | 0.971894i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | 14.0000 | 0.485071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0000 | + | 12.0000i | 0.830554 | + | 0.415277i | ||||
\(836\) | 12.0000i | 0.415029i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52.0000 | −1.79310 | ||||||||
\(842\) | − | 30.0000i | − | 1.03387i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0000 | −0.447478 | ||||||||
\(845\) | −6.00000 | − | 3.00000i | −0.206406 | − | 0.103203i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00000i | 0.206162i | ||||||||
\(848\) | 1.00000i | 0.0343401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −21.0000 | − | 28.0000i | −0.720294 | − | 0.960392i | ||||
\(851\) | −36.0000 | − | 6.00000i | −1.23406 | − | 0.205677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 15.0000 | 0.513289 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000i | 0.615227i | ||||||||
\(857\) | 43.0000 | 1.46885 | 0.734426 | − | 0.678689i | \(-0.237451\pi\) | ||||
0.734426 | + | 0.678689i | \(0.237451\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 36.0000i | − | 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | −2.00000 | − | 1.00000i | −0.0681994 | − | 0.0340997i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 25.0000i | − | 0.851503i | ||||||
\(863\) | − | 49.0000i | − | 1.66798i | −0.551780 | − | 0.833990i | \(-0.686051\pi\) | ||
0.551780 | − | 0.833990i | \(-0.313949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.00000 | + | 18.0000i | −0.306009 | + | 0.612018i | ||||
\(866\) | 34.0000i | 1.15537i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.0000 | 0.509133 | ||||||||
\(869\) | 12.0000i | 0.407072i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.00000i | − | 0.271070i | ||||||
\(872\) | − | 11.0000i | − | 0.372507i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 24.0000i | − | 0.811812i | ||||||
\(875\) | −33.0000 | + | 6.00000i | −1.11560 | + | 0.202837i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0000i | 0.911725i | 0.890050 | + | 0.455863i | \(0.150669\pi\) | ||||
−0.890050 | + | 0.455863i | \(0.849331\pi\) | |||||||
\(878\) | 9.00000i | 0.303735i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | − | 3.00000i | −0.202260 | − | 0.101130i | ||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | 28.0000 | 0.941742 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000i | 1.20944i | ||||||||
\(887\) | − | 27.0000i | − | 0.906571i | −0.891365 | − | 0.453286i | \(-0.850252\pi\) | ||
0.891365 | − | 0.453286i | \(-0.149748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | −0.804934 | ||||||||
\(890\) | 6.00000 | − | 12.0000i | 0.201120 | − | 0.402241i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 11.0000i | − | 0.368307i | ||||||
\(893\) | −32.0000 | −1.07084 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | + | 8.00000i | −0.133705 | + | 0.267411i | ||||
\(896\) | − | 3.00000i | − | 0.100223i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000i | 0.200223i | ||||||||
\(899\) | 45.0000 | 1.50083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.00000i | − | 0.233204i | ||||||
\(902\) | −21.0000 | −0.699224 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.00000 | −0.0332595 | ||||||||
\(905\) | 36.0000 | + | 18.0000i | 1.19668 | + | 0.598340i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0000 | −0.929725 | −0.464862 | − | 0.885383i | \(-0.653896\pi\) | ||||
−0.464862 | + | 0.885383i | \(0.653896\pi\) | |||||||
\(908\) | 13.0000 | 0.431420 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | − | 24.0000i | 0.397796 | − | 0.795592i | ||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 42.0000i | − | 1.39000i | ||||||
\(914\) | −13.0000 | −0.430002 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000i | 0.791687i | 0.918318 | + | 0.395843i | \(0.129548\pi\) | ||||
−0.918318 | + | 0.395843i | \(0.870452\pi\) | |||||||
\(920\) | 12.0000 | + | 6.00000i | 0.395628 | + | 0.197814i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.0000i | 0.823331i | ||||||||
\(923\) | 48.0000 | 1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | + | 27.0000i | 0.460317 | + | 0.887755i | ||||
\(926\) | 26.0000 | 0.854413 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 9.00000i | − | 0.295439i | ||||||
\(929\) | 5.00000 | 0.164045 | 0.0820223 | − | 0.996630i | \(-0.473862\pi\) | ||||
0.0820223 | + | 0.996630i | \(0.473862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.00000i | − | 0.262189i | ||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.0000 | 0.752583 | ||||||||
\(935\) | 42.0000 | + | 21.0000i | 1.37355 | + | 0.686773i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.0000i | 0.392023i | 0.980602 | + | 0.196011i | \(0.0627990\pi\) | ||||
−0.980602 | + | 0.196011i | \(0.937201\pi\) | |||||||
\(938\) | 6.00000 | 0.195907 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.00000 | − | 16.0000i | 0.260931 | − | 0.521862i | ||||
\(941\) | −12.0000 | −0.391189 | −0.195594 | − | 0.980685i | \(-0.562664\pi\) | ||||
−0.195594 | + | 0.980685i | \(0.562664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.0000 | 1.36771 | ||||||||
\(944\) | 6.00000i | 0.195283i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | −27.0000 | −0.877382 | −0.438691 | − | 0.898638i | \(-0.644558\pi\) | ||||
−0.438691 | + | 0.898638i | \(0.644558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 16.0000i | − | 0.519382i | ||||||
\(950\) | −16.0000 | + | 12.0000i | −0.519109 | + | 0.389331i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.0000i | 0.680614i | ||||||||
\(953\) | 16.0000i | 0.518291i | 0.965838 | + | 0.259145i | \(0.0834409\pi\) | ||||
−0.965838 | + | 0.259145i | \(0.916559\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0000 | + | 30.0000i | −0.485389 | + | 0.970777i | ||||
\(956\) | − | 9.00000i | − | 0.291081i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 24.0000i | − | 0.775405i | ||||||
\(959\) | −36.0000 | −1.16250 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.00000 | 0.193548 | ||||||||
\(962\) | −24.0000 | − | 4.00000i | −0.773791 | − | 0.128965i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.0000 | + | 14.0000i | 0.901352 | + | 0.450676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0000 | − | 7.00000i | −0.449513 | − | 0.224756i | ||||
\(971\) | −57.0000 | −1.82922 | −0.914609 | − | 0.404341i | \(-0.867501\pi\) | ||||
−0.914609 | + | 0.404341i | \(0.867501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.0000i | 1.44263i | ||||||||
\(974\) | 22.0000 | 0.704925 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.00000i | 0.160046i | ||||||||
\(977\) | 3.00000 | 0.0959785 | 0.0479893 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479893 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000i | 0.575282i | ||||||||
\(980\) | 4.00000 | + | 2.00000i | 0.127775 | + | 0.0638877i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.00000 | 0.255290 | ||||||||
\(983\) | − | 19.0000i | − | 0.606006i | −0.952990 | − | 0.303003i | \(-0.902011\pi\) | ||
0.952990 | − | 0.303003i | \(-0.0979892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | − | 36.0000i | 0.573528 | − | 1.14706i | ||||
\(986\) | 63.0000i | 2.00633i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 16.0000i | − | 0.509028i | ||||||
\(989\) | −6.00000 | −0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 25.0000i | − | 0.794151i | −0.917786 | − | 0.397076i | \(-0.870025\pi\) | ||
0.917786 | − | 0.397076i | \(-0.129975\pi\) | |||||||
\(992\) | 5.00000i | 0.158750i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.0000i | 1.14185i | ||||||||
\(995\) | −16.0000 | + | 32.0000i | −0.507234 | + | 1.01447i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.0000 | 1.33015 | 0.665077 | − | 0.746775i | \(-0.268399\pi\) | ||||
0.665077 | + | 0.746775i | \(0.268399\pi\) | |||||||
\(998\) | 24.0000i | 0.759707i | ||||||||
\(999\) | 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 | 3330.2.e.b.739.1 | 2 | ||
3.2 | odd | 2 | 1110.2.e.a.739.2 | yes | 2 | ||
5.4 | even | 2 | 3330.2.e.a.739.1 | 2 | |||
15.14 | odd | 2 | 1110.2.e.b.739.1 | yes | 2 | ||
37.36 | even | 2 | 3330.2.e.a.739.2 | 2 | |||
111.110 | odd | 2 | 1110.2.e.b.739.2 | yes | 2 | ||
185.184 | even | 2 | inner | 3330.2.e.b.739.2 | 2 | ||
555.554 | odd | 2 | 1110.2.e.a.739.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.e.a.739.1 | ✓ | 2 | 555.554 | odd | 2 | ||
1110.2.e.a.739.2 | yes | 2 | 3.2 | odd | 2 | ||
1110.2.e.b.739.1 | yes | 2 | 15.14 | odd | 2 | ||
1110.2.e.b.739.2 | yes | 2 | 111.110 | odd | 2 | ||
3330.2.e.a.739.1 | 2 | 5.4 | even | 2 | |||
3330.2.e.a.739.2 | 2 | 37.36 | even | 2 | |||
3330.2.e.b.739.1 | 2 | 1.1 | even | 1 | trivial | ||
3330.2.e.b.739.2 | 2 | 185.184 | even | 2 | inner |