Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1925,2,Mod(1849,1925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1925.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1925 = 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1925.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.3712023891\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 385) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1925.1849 |
Dual form | 1925.2.b.n.1849.6 |
$q$-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 \(\left(\mathbb{Z}/1925\mathbb{Z}\right)^\times\).
\(n\) | \(276\) | \(1002\) | \(1751\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.67513i | − 1.89160i | −0.324745 | − | 0.945802i | \(-0.605279\pi\) | ||||
0.324745 | − | 0.945802i | \(-0.394721\pi\) | |||||||
\(3\) | 2.48119i | 1.43252i | 0.697834 | + | 0.716259i | \(0.254147\pi\) | ||||
−0.697834 | + | 0.716259i | \(0.745853\pi\) | |||||||
\(4\) | −5.15633 | −2.57816 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.63752 | 2.70976 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 8.44358i | 2.98526i | ||||||||
\(9\) | −3.15633 | −1.05211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − 12.7938i | − 3.69326i | ||||||||
\(13\) | − 5.83146i | − 1.61735i | −0.588252 | − | 0.808677i | \(-0.700184\pi\) | ||||
0.588252 | − | 0.808677i | \(-0.299816\pi\) | |||||||
\(14\) | −2.67513 | −0.714959 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2750 | 3.06876 | ||||||||
\(17\) | 5.44358i | 1.32026i | 0.751150 | + | 0.660131i | \(0.229499\pi\) | ||||
−0.751150 | + | 0.660131i | \(0.770501\pi\) | |||||||
\(18\) | 8.44358i | 1.99017i | ||||||||
\(19\) | 1.35026 | 0.309771 | 0.154886 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154886 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.48119 | 0.541441 | ||||||||
\(22\) | 2.67513i | 0.570340i | ||||||||
\(23\) | 3.19394i | 0.665982i | 0.942930 | + | 0.332991i | \(0.108058\pi\) | ||||
−0.942930 | + | 0.332991i | \(0.891942\pi\) | |||||||
\(24\) | −20.9502 | −4.27644 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −15.5999 | −3.05939 | ||||||||
\(27\) | − 0.387873i | − 0.0746462i | ||||||||
\(28\) | 5.15633i | 0.974454i | ||||||||
\(29\) | 3.61213 | 0.670755 | 0.335378 | − | 0.942084i | \(-0.391136\pi\) | ||||
0.335378 | + | 0.942084i | \(0.391136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.28726 | −0.949620 | −0.474810 | − | 0.880088i | \(-0.657483\pi\) | ||||
−0.474810 | + | 0.880088i | \(0.657483\pi\) | |||||||
\(32\) | − 15.9502i | − 2.81962i | ||||||||
\(33\) | − 2.48119i | − 0.431920i | ||||||||
\(34\) | 14.5623 | 2.49741 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.2750 | 2.71251 | ||||||||
\(37\) | − 8.54420i | − 1.40466i | −0.711853 | − | 0.702329i | \(-0.752144\pi\) | ||||
0.711853 | − | 0.702329i | \(-0.247856\pi\) | |||||||
\(38\) | − 3.61213i | − 0.585964i | ||||||||
\(39\) | 14.4690 | 2.31689 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.02539 | −0.784834 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(42\) | − 6.63752i | − 1.02419i | ||||||||
\(43\) | − 5.89446i | − 0.898897i | −0.893306 | − | 0.449448i | \(-0.851621\pi\) | ||||
0.893306 | − | 0.449448i | \(-0.148379\pi\) | |||||||
\(44\) | 5.15633 | 0.777345 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.54420 | 1.25977 | ||||||||
\(47\) | − 11.8315i | − 1.72580i | −0.505379 | − | 0.862898i | \(-0.668647\pi\) | ||||
0.505379 | − | 0.862898i | \(-0.331353\pi\) | |||||||
\(48\) | 30.4568i | 4.39605i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.5066 | −1.89130 | ||||||||
\(52\) | 30.0689i | 4.16980i | ||||||||
\(53\) | 0.231548i | 0.0318056i | 0.999874 | + | 0.0159028i | \(0.00506223\pi\) | ||||
−0.999874 | + | 0.0159028i | \(0.994938\pi\) | |||||||
\(54\) | −1.03761 | −0.141201 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.44358 | 1.12832 | ||||||||
\(57\) | 3.35026i | 0.443753i | ||||||||
\(58\) | − 9.66291i | − 1.26880i | ||||||||
\(59\) | −13.5999 | −1.77056 | −0.885279 | − | 0.465061i | \(-0.846032\pi\) | ||||
−0.885279 | + | 0.465061i | \(0.846032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41327 | −0.180950 | −0.0904751 | − | 0.995899i | \(-0.528839\pi\) | ||||
−0.0904751 | + | 0.995899i | \(0.528839\pi\) | |||||||
\(62\) | 14.1441i | 1.79630i | ||||||||
\(63\) | 3.15633i | 0.397660i | ||||||||
\(64\) | −18.1187 | −2.26484 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.63752 | −0.817022 | ||||||||
\(67\) | − 10.8568i | − 1.32638i | −0.748453 | − | 0.663188i | \(-0.769203\pi\) | ||||
0.748453 | − | 0.663188i | \(-0.230797\pi\) | |||||||
\(68\) | − 28.0689i | − 3.40385i | ||||||||
\(69\) | −7.92478 | −0.954031 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.5369 | −1.84389 | −0.921946 | − | 0.387319i | \(-0.873401\pi\) | ||||
−0.921946 | + | 0.387319i | \(0.873401\pi\) | |||||||
\(72\) | − 26.6507i | − 3.14081i | ||||||||
\(73\) | 11.3684i | 1.33057i | 0.746591 | + | 0.665283i | \(0.231689\pi\) | ||||
−0.746591 | + | 0.665283i | \(0.768311\pi\) | |||||||
\(74\) | −22.8568 | −2.65705 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.96239 | −0.798641 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | − 38.7064i | − 4.38264i | ||||||||
\(79\) | −1.96968 | −0.221607 | −0.110803 | − | 0.993842i | \(-0.535342\pi\) | ||||
−0.110803 | + | 0.993842i | \(0.535342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.50659 | −0.945176 | ||||||||
\(82\) | 13.4436i | 1.48460i | ||||||||
\(83\) | − 10.6253i | − 1.16628i | −0.812372 | − | 0.583139i | \(-0.801824\pi\) | ||||
0.812372 | − | 0.583139i | \(-0.198176\pi\) | |||||||
\(84\) | −12.7938 | −1.39592 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.7685 | −1.70036 | ||||||||
\(87\) | 8.96239i | 0.960869i | ||||||||
\(88\) | − 8.44358i | − 0.900089i | ||||||||
\(89\) | −7.22425 | −0.765769 | −0.382885 | − | 0.923796i | \(-0.625069\pi\) | ||||
−0.382885 | + | 0.923796i | \(0.625069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.83146 | −0.611303 | ||||||||
\(92\) | − 16.4690i | − 1.71701i | ||||||||
\(93\) | − 13.1187i | − 1.36035i | ||||||||
\(94\) | −31.6507 | −3.26452 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 39.5755 | 4.03915 | ||||||||
\(97\) | − 0.836381i | − 0.0849216i | −0.999098 | − | 0.0424608i | \(-0.986480\pi\) | ||||
0.999098 | − | 0.0424608i | \(-0.0135198\pi\) | |||||||
\(98\) | 2.67513i | 0.270229i | ||||||||
\(99\) | 3.15633 | 0.317223 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.41327 | 0.737648 | 0.368824 | − | 0.929499i | \(-0.379761\pi\) | ||||
0.368824 | + | 0.929499i | \(0.379761\pi\) | |||||||
\(102\) | 36.1319i | 3.57759i | ||||||||
\(103\) | − 4.21933i | − 0.415743i | −0.978156 | − | 0.207871i | \(-0.933346\pi\) | ||||
0.978156 | − | 0.207871i | \(-0.0666536\pi\) | |||||||
\(104\) | 49.2384 | 4.82822 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.619421 | 0.0601635 | ||||||||
\(107\) | − 11.5369i | − 1.11531i | −0.830071 | − | 0.557657i | \(-0.811700\pi\) | ||||
0.830071 | − | 0.557657i | \(-0.188300\pi\) | |||||||
\(108\) | 2.00000i | 0.192450i | ||||||||
\(109\) | 2.18664 | 0.209442 | 0.104721 | − | 0.994502i | \(-0.466605\pi\) | ||||
0.104721 | + | 0.994502i | \(0.466605\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1998 | 2.01220 | ||||||||
\(112\) | − 12.2750i | − 1.15988i | ||||||||
\(113\) | 9.35026i | 0.879599i | 0.898096 | + | 0.439799i | \(0.144950\pi\) | ||||
−0.898096 | + | 0.439799i | \(0.855050\pi\) | |||||||
\(114\) | 8.96239 | 0.839405 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.6253 | −1.72932 | ||||||||
\(117\) | 18.4060i | 1.70163i | ||||||||
\(118\) | 36.3815i | 3.34919i | ||||||||
\(119\) | 5.44358 | 0.499012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.78067i | 0.342286i | ||||||||
\(123\) | − 12.4690i | − 1.12429i | ||||||||
\(124\) | 27.2628 | 2.44827 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.44358 | 0.752214 | ||||||||
\(127\) | − 16.9624i | − 1.50517i | −0.658496 | − | 0.752584i | \(-0.728807\pi\) | ||||
0.658496 | − | 0.752584i | \(-0.271193\pi\) | |||||||
\(128\) | 16.5696i | 1.46456i | ||||||||
\(129\) | 14.6253 | 1.28769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.92478 | −0.867132 | −0.433566 | − | 0.901122i | \(-0.642745\pi\) | ||||
−0.433566 | + | 0.901122i | \(0.642745\pi\) | |||||||
\(132\) | 12.7938i | 1.11356i | ||||||||
\(133\) | − 1.35026i | − 0.117083i | ||||||||
\(134\) | −29.0435 | −2.50898 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −45.9633 | −3.94132 | ||||||||
\(137\) | − 10.9927i | − 0.939170i | −0.882887 | − | 0.469585i | \(-0.844404\pi\) | ||||
0.882887 | − | 0.469585i | \(-0.155596\pi\) | |||||||
\(138\) | 21.1998i | 1.80465i | ||||||||
\(139\) | −6.88717 | −0.584162 | −0.292081 | − | 0.956394i | \(-0.594348\pi\) | ||||
−0.292081 | + | 0.956394i | \(0.594348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.3561 | 2.47223 | ||||||||
\(142\) | 41.5633i | 3.48791i | ||||||||
\(143\) | 5.83146i | 0.487651i | ||||||||
\(144\) | −38.7440 | −3.22867 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 30.4119 | 2.51690 | ||||||||
\(147\) | − 2.48119i | − 0.204645i | ||||||||
\(148\) | 44.0567i | 3.62144i | ||||||||
\(149\) | −22.8119 | −1.86883 | −0.934414 | − | 0.356190i | \(-0.884076\pi\) | ||||
−0.934414 | + | 0.356190i | \(0.884076\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.24472 | −0.264052 | −0.132026 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132026 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(152\) | 11.4010i | 0.924747i | ||||||||
\(153\) | − 17.1817i | − 1.38906i | ||||||||
\(154\) | 2.67513 | 0.215568 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −74.6067 | −5.97332 | ||||||||
\(157\) | − 5.42548i | − 0.433001i | −0.976283 | − | 0.216500i | \(-0.930536\pi\) | ||||
0.976283 | − | 0.216500i | \(-0.0694643\pi\) | |||||||
\(158\) | 5.26916i | 0.419192i | ||||||||
\(159\) | −0.574515 | −0.0455620 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.19394 | 0.251717 | ||||||||
\(162\) | 22.7562i | 1.78790i | ||||||||
\(163\) | − 3.38058i | − 0.264787i | −0.991197 | − | 0.132394i | \(-0.957734\pi\) | ||||
0.991197 | − | 0.132394i | \(-0.0422663\pi\) | |||||||
\(164\) | 25.9126 | 2.02343 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −28.4241 | −2.20614 | ||||||||
\(167\) | 11.2750i | 0.872489i | 0.899828 | + | 0.436244i | \(0.143692\pi\) | ||||
−0.899828 | + | 0.436244i | \(0.856308\pi\) | |||||||
\(168\) | 20.9502i | 1.61634i | ||||||||
\(169\) | −21.0059 | −1.61584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.26187 | −0.325913 | ||||||||
\(172\) | 30.3938i | 2.31750i | ||||||||
\(173\) | 8.98049i | 0.682774i | 0.939923 | + | 0.341387i | \(0.110897\pi\) | ||||
−0.939923 | + | 0.341387i | \(0.889103\pi\) | |||||||
\(174\) | 23.9756 | 1.81758 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.2750 | −0.925266 | ||||||||
\(177\) | − 33.7440i | − 2.53636i | ||||||||
\(178\) | 19.3258i | 1.44853i | ||||||||
\(179\) | 26.2374 | 1.96108 | 0.980539 | − | 0.196326i | \(-0.0629010\pi\) | ||||
0.980539 | + | 0.196326i | \(0.0629010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1998 | −0.832476 | −0.416238 | − | 0.909256i | \(-0.636652\pi\) | ||||
−0.416238 | + | 0.909256i | \(0.636652\pi\) | |||||||
\(182\) | 15.5999i | 1.15634i | ||||||||
\(183\) | − 3.50659i | − 0.259214i | ||||||||
\(184\) | −26.9683 | −1.98813 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −35.0943 | −2.57324 | ||||||||
\(187\) | − 5.44358i | − 0.398074i | ||||||||
\(188\) | 61.0068i | 4.44938i | ||||||||
\(189\) | −0.387873 | −0.0282136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1998 | 0.810390 | 0.405195 | − | 0.914230i | \(-0.367204\pi\) | ||||
0.405195 | + | 0.914230i | \(0.367204\pi\) | |||||||
\(192\) | − 44.9560i | − 3.24442i | ||||||||
\(193\) | − 0.604833i | − 0.0435368i | −0.999763 | − | 0.0217684i | \(-0.993070\pi\) | ||||
0.999763 | − | 0.0217684i | \(-0.00692965\pi\) | |||||||
\(194\) | −2.23743 | −0.160638 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.15633 | 0.368309 | ||||||||
\(197\) | 15.3054i | 1.09046i | 0.838286 | + | 0.545231i | \(0.183558\pi\) | ||||
−0.838286 | + | 0.545231i | \(0.816442\pi\) | |||||||
\(198\) | − 8.44358i | − 0.600059i | ||||||||
\(199\) | 12.5623 | 0.890518 | 0.445259 | − | 0.895402i | \(-0.353112\pi\) | ||||
0.445259 | + | 0.895402i | \(0.353112\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.9380 | 1.90006 | ||||||||
\(202\) | − 19.8315i | − 1.39534i | ||||||||
\(203\) | − 3.61213i | − 0.253522i | ||||||||
\(204\) | 69.6444 | 4.87608 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2873 | −0.786421 | ||||||||
\(207\) | − 10.0811i | − 0.700685i | ||||||||
\(208\) | − 71.5814i | − 4.96327i | ||||||||
\(209\) | −1.35026 | −0.0933996 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.43866 | −0.305570 | −0.152785 | − | 0.988259i | \(-0.548824\pi\) | ||||
−0.152785 | + | 0.988259i | \(0.548824\pi\) | |||||||
\(212\) | − 1.19394i | − 0.0819999i | ||||||||
\(213\) | − 38.5501i | − 2.64141i | ||||||||
\(214\) | −30.8627 | −2.10973 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.27504 | 0.222838 | ||||||||
\(217\) | 5.28726i | 0.358922i | ||||||||
\(218\) | − 5.84955i | − 0.396182i | ||||||||
\(219\) | −28.2071 | −1.90606 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.7440 | 2.13533 | ||||||||
\(222\) | − 56.7123i | − 3.80628i | ||||||||
\(223\) | 7.78067i | 0.521032i | 0.965469 | + | 0.260516i | \(0.0838927\pi\) | ||||
−0.965469 | + | 0.260516i | \(0.916107\pi\) | |||||||
\(224\) | −15.9502 | −1.06572 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.0132 | 1.66385 | ||||||||
\(227\) | − 10.4485i | − 0.693492i | −0.937959 | − | 0.346746i | \(-0.887287\pi\) | ||||
0.937959 | − | 0.346746i | \(-0.112713\pi\) | |||||||
\(228\) | − 17.2750i | − 1.14407i | ||||||||
\(229\) | 29.4518 | 1.94623 | 0.973116 | − | 0.230316i | \(-0.0739759\pi\) | ||||
0.973116 | + | 0.230316i | \(0.0739759\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.48119 | −0.163251 | ||||||||
\(232\) | 30.4993i | 2.00238i | ||||||||
\(233\) | 8.73084i | 0.571976i | 0.958233 | + | 0.285988i | \(0.0923218\pi\) | ||||
−0.958233 | + | 0.285988i | \(0.907678\pi\) | |||||||
\(234\) | 49.2384 | 3.21881 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 70.1255 | 4.56478 | ||||||||
\(237\) | − 4.88717i | − 0.317456i | ||||||||
\(238\) | − 14.5623i | − 0.943933i | ||||||||
\(239\) | 21.2144 | 1.37225 | 0.686123 | − | 0.727486i | \(-0.259311\pi\) | ||||
0.686123 | + | 0.727486i | \(0.259311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.33804 | −0.601516 | −0.300758 | − | 0.953700i | \(-0.597240\pi\) | ||||
−0.300758 | + | 0.953700i | \(0.597240\pi\) | |||||||
\(242\) | − 2.67513i | − 0.171964i | ||||||||
\(243\) | − 22.2701i | − 1.42863i | ||||||||
\(244\) | 7.28726 | 0.466519 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −33.3561 | −2.12671 | ||||||||
\(247\) | − 7.87399i | − 0.501010i | ||||||||
\(248\) | − 44.6434i | − 2.83486i | ||||||||
\(249\) | 26.3634 | 1.67071 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.87636 | 0.118435 | 0.0592174 | − | 0.998245i | \(-0.481139\pi\) | ||||
0.0592174 | + | 0.998245i | \(0.481139\pi\) | |||||||
\(252\) | − 16.2750i | − 1.02523i | ||||||||
\(253\) | − 3.19394i | − 0.200801i | ||||||||
\(254\) | −45.3766 | −2.84718 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.08840 | 0.505525 | ||||||||
\(257\) | 27.1392i | 1.69290i | 0.532472 | + | 0.846448i | \(0.321263\pi\) | ||||
−0.532472 | + | 0.846448i | \(0.678737\pi\) | |||||||
\(258\) | − 39.1246i | − 2.43579i | ||||||||
\(259\) | −8.54420 | −0.530911 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4010 | −0.705707 | ||||||||
\(262\) | 26.5501i | 1.64027i | ||||||||
\(263\) | − 12.8119i | − 0.790018i | −0.918677 | − | 0.395009i | \(-0.870741\pi\) | ||||
0.918677 | − | 0.395009i | \(-0.129259\pi\) | |||||||
\(264\) | 20.9502 | 1.28939 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.61213 | −0.221474 | ||||||||
\(267\) | − 17.9248i | − 1.09698i | ||||||||
\(268\) | 55.9814i | 3.41961i | ||||||||
\(269\) | 6.26187 | 0.381793 | 0.190896 | − | 0.981610i | \(-0.438861\pi\) | ||||
0.190896 | + | 0.981610i | \(0.438861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.73813 | −0.348567 | −0.174283 | − | 0.984696i | \(-0.555761\pi\) | ||||
−0.174283 | + | 0.984696i | \(0.555761\pi\) | |||||||
\(272\) | 66.8202i | 4.05157i | ||||||||
\(273\) | − 14.4690i | − 0.875702i | ||||||||
\(274\) | −29.4069 | −1.77654 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 40.8627 | 2.45965 | ||||||||
\(277\) | − 8.35756i | − 0.502157i | −0.967967 | − | 0.251078i | \(-0.919215\pi\) | ||||
0.967967 | − | 0.251078i | \(-0.0807852\pi\) | |||||||
\(278\) | 18.4241i | 1.10500i | ||||||||
\(279\) | 16.6883 | 0.999103 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.44851 | −0.503996 | −0.251998 | − | 0.967728i | \(-0.581088\pi\) | ||||
−0.251998 | + | 0.967728i | \(0.581088\pi\) | |||||||
\(282\) | − 78.5315i | − 4.67648i | ||||||||
\(283\) | − 0.836381i | − 0.0497177i | −0.999691 | − | 0.0248588i | \(-0.992086\pi\) | ||||
0.999691 | − | 0.0248588i | \(-0.00791363\pi\) | |||||||
\(284\) | 80.1133 | 4.75385 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.5999 | 0.922442 | ||||||||
\(287\) | 5.02539i | 0.296640i | ||||||||
\(288\) | 50.3439i | 2.96654i | ||||||||
\(289\) | −12.6326 | −0.743094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.07522 | 0.121652 | ||||||||
\(292\) | − 58.6190i | − 3.43042i | ||||||||
\(293\) | 2.71862i | 0.158824i | 0.996842 | + | 0.0794118i | \(0.0253042\pi\) | ||||
−0.996842 | + | 0.0794118i | \(0.974696\pi\) | |||||||
\(294\) | −6.63752 | −0.387108 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 72.1436 | 4.19326 | ||||||||
\(297\) | 0.387873i | 0.0225067i | ||||||||
\(298\) | 61.0249i | 3.53508i | ||||||||
\(299\) | 18.6253 | 1.07713 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.89446 | −0.339751 | ||||||||
\(302\) | 8.68006i | 0.499481i | ||||||||
\(303\) | 18.3938i | 1.05669i | ||||||||
\(304\) | 16.5745 | 0.950614 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −45.9633 | −2.62755 | ||||||||
\(307\) | − 8.36344i | − 0.477326i | −0.971102 | − | 0.238663i | \(-0.923291\pi\) | ||||
0.971102 | − | 0.238663i | \(-0.0767092\pi\) | |||||||
\(308\) | − 5.15633i | − 0.293809i | ||||||||
\(309\) | 10.4690 | 0.595559 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.43629 | 0.251559 | 0.125779 | − | 0.992058i | \(-0.459857\pi\) | ||||
0.125779 | + | 0.992058i | \(0.459857\pi\) | |||||||
\(312\) | 122.170i | 6.91651i | ||||||||
\(313\) | − 29.7889i | − 1.68377i | −0.539658 | − | 0.841885i | \(-0.681446\pi\) | ||||
0.539658 | − | 0.841885i | \(-0.318554\pi\) | |||||||
\(314\) | −14.5139 | −0.819066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.1563 | 0.571338 | ||||||||
\(317\) | 15.4010i | 0.865009i | 0.901632 | + | 0.432504i | \(0.142370\pi\) | ||||
−0.901632 | + | 0.432504i | \(0.857630\pi\) | |||||||
\(318\) | 1.53690i | 0.0861853i | ||||||||
\(319\) | −3.61213 | −0.202240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.6253 | 1.59771 | ||||||||
\(322\) | − 8.54420i | − 0.476150i | ||||||||
\(323\) | 7.35026i | 0.408980i | ||||||||
\(324\) | 43.8627 | 2.43682 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.04349 | −0.500873 | ||||||||
\(327\) | 5.42548i | 0.300030i | ||||||||
\(328\) | − 42.4323i | − 2.34293i | ||||||||
\(329\) | −11.8315 | −0.652289 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.26187 | 0.344183 | 0.172092 | − | 0.985081i | \(-0.444947\pi\) | ||||
0.172092 | + | 0.985081i | \(0.444947\pi\) | |||||||
\(332\) | 54.7875i | 3.00685i | ||||||||
\(333\) | 26.9683i | 1.47785i | ||||||||
\(334\) | 30.1622 | 1.65040 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 30.4568 | 1.66155 | ||||||||
\(337\) | − 15.8700i | − 0.864495i | −0.901755 | − | 0.432248i | \(-0.857721\pi\) | ||||
0.901755 | − | 0.432248i | \(-0.142279\pi\) | |||||||
\(338\) | 56.1935i | 3.05652i | ||||||||
\(339\) | −23.1998 | −1.26004 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.28726 | 0.286321 | ||||||||
\(342\) | 11.4010i | 0.616498i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 49.7704 | 2.68344 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0240 | 1.29154 | ||||||||
\(347\) | 6.79147i | 0.364585i | 0.983244 | + | 0.182293i | \(0.0583519\pi\) | ||||
−0.983244 | + | 0.182293i | \(0.941648\pi\) | |||||||
\(348\) | − 46.2130i | − 2.47728i | ||||||||
\(349\) | −26.7489 | −1.43184 | −0.715919 | − | 0.698183i | \(-0.753992\pi\) | ||||
−0.715919 | + | 0.698183i | \(0.753992\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.26187 | −0.120729 | ||||||||
\(352\) | 15.9502i | 0.850147i | ||||||||
\(353\) | 16.8627i | 0.897512i | 0.893654 | + | 0.448756i | \(0.148133\pi\) | ||||
−0.893654 | + | 0.448756i | \(0.851867\pi\) | |||||||
\(354\) | −90.2697 | −4.79778 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 37.2506 | 1.97428 | ||||||||
\(357\) | 13.5066i | 0.714844i | ||||||||
\(358\) | − 70.1886i | − 3.70958i | ||||||||
\(359\) | 3.79289 | 0.200181 | 0.100091 | − | 0.994978i | \(-0.468087\pi\) | ||||
0.100091 | + | 0.994978i | \(0.468087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1768 | −0.904042 | ||||||||
\(362\) | 29.9610i | 1.57471i | ||||||||
\(363\) | 2.48119i | 0.130229i | ||||||||
\(364\) | 30.0689 | 1.57604 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.38058 | −0.490331 | ||||||||
\(367\) | − 6.36977i | − 0.332500i | −0.986084 | − | 0.166250i | \(-0.946834\pi\) | ||||
0.986084 | − | 0.166250i | \(-0.0531658\pi\) | |||||||
\(368\) | 39.2057i | 2.04374i | ||||||||
\(369\) | 15.8618 | 0.825731 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.231548 | 0.0120214 | ||||||||
\(372\) | 67.6444i | 3.50720i | ||||||||
\(373\) | 21.3317i | 1.10451i | 0.833674 | + | 0.552257i | \(0.186233\pi\) | ||||
−0.833674 | + | 0.552257i | \(0.813767\pi\) | |||||||
\(374\) | −14.5623 | −0.752998 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 99.8999 | 5.15194 | ||||||||
\(377\) | − 21.0640i | − 1.08485i | ||||||||
\(378\) | 1.03761i | 0.0533690i | ||||||||
\(379\) | −24.7875 | −1.27325 | −0.636624 | − | 0.771174i | \(-0.719670\pi\) | ||||
−0.636624 | + | 0.771174i | \(0.719670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.0870 | 2.15618 | ||||||||
\(382\) | − 29.9610i | − 1.53294i | ||||||||
\(383\) | 5.45817i | 0.278900i | 0.990229 | + | 0.139450i | \(0.0445334\pi\) | ||||
−0.990229 | + | 0.139450i | \(0.955467\pi\) | |||||||
\(384\) | −41.1124 | −2.09801 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.61801 | −0.0823544 | ||||||||
\(387\) | 18.6048i | 0.945737i | ||||||||
\(388\) | 4.31265i | 0.218942i | ||||||||
\(389\) | 13.7235 | 0.695811 | 0.347906 | − | 0.937530i | \(-0.386893\pi\) | ||||
0.347906 | + | 0.937530i | \(0.386893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.3865 | −0.879271 | ||||||||
\(392\) | − 8.44358i | − 0.426465i | ||||||||
\(393\) | − 24.6253i | − 1.24218i | ||||||||
\(394\) | 40.9438 | 2.06272 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.2750 | −0.817851 | ||||||||
\(397\) | 2.11142i | 0.105969i | 0.998595 | + | 0.0529846i | \(0.0168734\pi\) | ||||
−0.998595 | + | 0.0529846i | \(0.983127\pi\) | |||||||
\(398\) | − 33.6058i | − 1.68451i | ||||||||
\(399\) | 3.35026 | 0.167723 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.1490 | 0.956257 | 0.478128 | − | 0.878290i | \(-0.341315\pi\) | ||||
0.478128 | + | 0.878290i | \(0.341315\pi\) | |||||||
\(402\) | − 72.0625i | − 3.59415i | ||||||||
\(403\) | 30.8324i | 1.53587i | ||||||||
\(404\) | −38.2252 | −1.90178 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.66291 | −0.479562 | ||||||||
\(407\) | 8.54420i | 0.423520i | ||||||||
\(408\) | − 114.044i | − 5.64602i | ||||||||
\(409\) | 18.6883 | 0.924077 | 0.462039 | − | 0.886860i | \(-0.347118\pi\) | ||||
0.462039 | + | 0.886860i | \(0.347118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.2750 | 1.34538 | ||||||||
\(412\) | 21.7562i | 1.07185i | ||||||||
\(413\) | 13.5999i | 0.669208i | ||||||||
\(414\) | −26.9683 | −1.32542 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −93.0127 | −4.56032 | ||||||||
\(417\) | − 17.0884i | − 0.836822i | ||||||||
\(418\) | 3.61213i | 0.176675i | ||||||||
\(419\) | 0.773377 | 0.0377819 | 0.0188910 | − | 0.999822i | \(-0.493986\pi\) | ||||
0.0188910 | + | 0.999822i | \(0.493986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5198 | −0.512702 | −0.256351 | − | 0.966584i | \(-0.582520\pi\) | ||||
−0.256351 | + | 0.966584i | \(0.582520\pi\) | |||||||
\(422\) | 11.8740i | 0.578017i | ||||||||
\(423\) | 37.3439i | 1.81572i | ||||||||
\(424\) | −1.95509 | −0.0949478 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −103.127 | −4.99650 | ||||||||
\(427\) | 1.41327i | 0.0683927i | ||||||||
\(428\) | 59.4880i | 2.87546i | ||||||||
\(429\) | −14.4690 | −0.698569 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7308 | −1.19124 | −0.595621 | − | 0.803265i | \(-0.703094\pi\) | ||||
−0.595621 | + | 0.803265i | \(0.703094\pi\) | |||||||
\(432\) | − 4.76116i | − 0.229071i | ||||||||
\(433\) | 18.5599i | 0.891933i | 0.895050 | + | 0.445967i | \(0.147140\pi\) | ||||
−0.895050 | + | 0.445967i | \(0.852860\pi\) | |||||||
\(434\) | 14.1441 | 0.678939 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.2750 | −0.539976 | ||||||||
\(437\) | 4.31265i | 0.206302i | ||||||||
\(438\) | 75.4577i | 3.60551i | ||||||||
\(439\) | 1.42548 | 0.0680347 | 0.0340173 | − | 0.999421i | \(-0.489170\pi\) | ||||
0.0340173 | + | 0.999421i | \(0.489170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15633 | 0.150301 | ||||||||
\(442\) | − 84.9194i | − 4.03920i | ||||||||
\(443\) | − 40.1925i | − 1.90960i | −0.297242 | − | 0.954802i | \(-0.596067\pi\) | ||||
0.297242 | − | 0.954802i | \(-0.403933\pi\) | |||||||
\(444\) | −109.313 | −5.18777 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.8143 | 0.985586 | ||||||||
\(447\) | − 56.6009i | − 2.67713i | ||||||||
\(448\) | 18.1187i | 0.856029i | ||||||||
\(449\) | −12.6556 | −0.597256 | −0.298628 | − | 0.954370i | \(-0.596529\pi\) | ||||
−0.298628 | + | 0.954370i | \(0.596529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.02539 | 0.236636 | ||||||||
\(452\) | − 48.2130i | − 2.26775i | ||||||||
\(453\) | − 8.05079i | − 0.378259i | ||||||||
\(454\) | −27.9511 | −1.31181 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.2882 | −1.32472 | ||||||||
\(457\) | − 0.544198i | − 0.0254565i | −0.999919 | − | 0.0127283i | \(-0.995948\pi\) | ||||
0.999919 | − | 0.0127283i | \(-0.00405164\pi\) | |||||||
\(458\) | − 78.7875i | − 3.68150i | ||||||||
\(459\) | 2.11142 | 0.0985526 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5755 | −0.539123 | −0.269562 | − | 0.962983i | \(-0.586879\pi\) | ||||
−0.269562 | + | 0.962983i | \(0.586879\pi\) | |||||||
\(462\) | 6.63752i | 0.308805i | ||||||||
\(463\) | − 23.7948i | − 1.10584i | −0.833235 | − | 0.552919i | \(-0.813514\pi\) | ||||
0.833235 | − | 0.552919i | \(-0.186486\pi\) | |||||||
\(464\) | 44.3390 | 2.05839 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.3561 | 1.08195 | ||||||||
\(467\) | − 2.66784i | − 0.123453i | −0.998093 | − | 0.0617264i | \(-0.980339\pi\) | ||||
0.998093 | − | 0.0617264i | \(-0.0196606\pi\) | |||||||
\(468\) | − 94.9072i | − 4.38709i | ||||||||
\(469\) | −10.8568 | −0.501323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4617 | 0.620282 | ||||||||
\(472\) | − 114.832i | − 5.28557i | ||||||||
\(473\) | 5.89446i | 0.271028i | ||||||||
\(474\) | −13.0738 | −0.600500 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −28.0689 | −1.28654 | ||||||||
\(477\) | − 0.730841i | − 0.0334629i | ||||||||
\(478\) | − 56.7513i | − 2.59574i | ||||||||
\(479\) | 10.7104 | 0.489369 | 0.244685 | − | 0.969603i | \(-0.421316\pi\) | ||||
0.244685 | + | 0.969603i | \(0.421316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.8251 | −2.27183 | ||||||||
\(482\) | 24.9805i | 1.13783i | ||||||||
\(483\) | 7.92478i | 0.360590i | ||||||||
\(484\) | −5.15633 | −0.234378 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −59.5755 | −2.70240 | ||||||||
\(487\) | 17.4314i | 0.789891i | 0.918705 | + | 0.394945i | \(0.129236\pi\) | ||||
−0.918705 | + | 0.394945i | \(0.870764\pi\) | |||||||
\(488\) | − 11.9330i | − 0.540183i | ||||||||
\(489\) | 8.38787 | 0.379313 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.3693 | −1.28029 | −0.640145 | − | 0.768254i | \(-0.721126\pi\) | ||||
−0.640145 | + | 0.768254i | \(0.721126\pi\) | |||||||
\(492\) | 64.2941i | 2.89860i | ||||||||
\(493\) | 19.6629i | 0.885573i | ||||||||
\(494\) | −21.0640 | −0.947712 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −64.9013 | −2.91415 | ||||||||
\(497\) | 15.5369i | 0.696925i | ||||||||
\(498\) | − 70.5256i | − 3.16033i | ||||||||
\(499\) | −27.4763 | −1.23001 | −0.615003 | − | 0.788524i | \(-0.710845\pi\) | ||||
−0.615003 | + | 0.788524i | \(0.710845\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.9756 | −1.24986 | ||||||||
\(502\) | − 5.01951i | − 0.224032i | ||||||||
\(503\) | − 20.2981i | − 0.905046i | −0.891753 | − | 0.452523i | \(-0.850524\pi\) | ||||
0.891753 | − | 0.452523i | \(-0.149476\pi\) | |||||||
\(504\) | −26.6507 | −1.18712 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.54420 | −0.379836 | ||||||||
\(507\) | − 52.1197i | − 2.31472i | ||||||||
\(508\) | 87.4636i | 3.88057i | ||||||||
\(509\) | 24.2619 | 1.07539 | 0.537694 | − | 0.843140i | \(-0.319296\pi\) | ||||
0.537694 | + | 0.843140i | \(0.319296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.3684 | 0.502907 | ||||||||
\(512\) | 11.5017i | 0.508306i | ||||||||
\(513\) | − 0.523730i | − 0.0231233i | ||||||||
\(514\) | 72.6009 | 3.20229 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −75.4128 | −3.31986 | ||||||||
\(517\) | 11.8315i | 0.520347i | ||||||||
\(518\) | 22.8568i | 1.00427i | ||||||||
\(519\) | −22.2823 | −0.978086 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.20123 | 0.0964377 | 0.0482188 | − | 0.998837i | \(-0.484646\pi\) | ||||
0.0482188 | + | 0.998837i | \(0.484646\pi\) | |||||||
\(522\) | 30.4993i | 1.33492i | ||||||||
\(523\) | 22.1378i | 0.968017i | 0.875063 | + | 0.484008i | \(0.160820\pi\) | ||||
−0.875063 | + | 0.484008i | \(0.839180\pi\) | |||||||
\(524\) | 51.1754 | 2.23561 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.2736 | −1.49440 | ||||||||
\(527\) | − 28.7816i | − 1.25375i | ||||||||
\(528\) | − 30.4568i | − 1.32546i | ||||||||
\(529\) | 12.7988 | 0.556468 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.9257 | 1.86282 | ||||||||
\(532\) | 6.96239i | 0.301858i | ||||||||
\(533\) | 29.3054i | 1.26936i | ||||||||
\(534\) | −47.9511 | −2.07505 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 91.6707 | 3.95957 | ||||||||
\(537\) | 65.1002i | 2.80928i | ||||||||
\(538\) | − 16.7513i | − 0.722200i | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0640 | 0.991597 | 0.495799 | − | 0.868438i | \(-0.334875\pi\) | ||||
0.495799 | + | 0.868438i | \(0.334875\pi\) | |||||||
\(542\) | 15.3503i | 0.659350i | ||||||||
\(543\) | − 27.7889i | − 1.19254i | ||||||||
\(544\) | 86.8261 | 3.72264 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −38.7064 | −1.65648 | ||||||||
\(547\) | 21.3766i | 0.913998i | 0.889467 | + | 0.456999i | \(0.151076\pi\) | ||||
−0.889467 | + | 0.456999i | \(0.848924\pi\) | |||||||
\(548\) | 56.6820i | 2.42133i | ||||||||
\(549\) | 4.46073 | 0.190379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.87732 | 0.207781 | ||||||||
\(552\) | − 66.9135i | − 2.84803i | ||||||||
\(553\) | 1.96968i | 0.0837594i | ||||||||
\(554\) | −22.3576 | −0.949882 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.5125 | 1.50606 | ||||||||
\(557\) | − 9.19394i | − 0.389560i | −0.980847 | − | 0.194780i | \(-0.937601\pi\) | ||||
0.980847 | − | 0.194780i | \(-0.0623992\pi\) | |||||||
\(558\) | − 44.6434i | − 1.88991i | ||||||||
\(559\) | −34.3733 | −1.45384 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5066 | 0.570249 | ||||||||
\(562\) | 22.6009i | 0.953360i | ||||||||
\(563\) | 9.79877i | 0.412969i | 0.978450 | + | 0.206484i | \(0.0662023\pi\) | ||||
−0.978450 | + | 0.206484i | \(0.933798\pi\) | |||||||
\(564\) | −151.370 | −6.37382 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.23743 | −0.0940461 | ||||||||
\(567\) | 8.50659i | 0.357243i | ||||||||
\(568\) | − 131.187i | − 5.50449i | ||||||||
\(569\) | 33.5125 | 1.40492 | 0.702458 | − | 0.711725i | \(-0.252086\pi\) | ||||
0.702458 | + | 0.711725i | \(0.252086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.1392 | 1.80532 | 0.902659 | − | 0.430356i | \(-0.141612\pi\) | ||||
0.902659 | + | 0.430356i | \(0.141612\pi\) | |||||||
\(572\) | − 30.0689i | − 1.25724i | ||||||||
\(573\) | 27.7889i | 1.16090i | ||||||||
\(574\) | 13.4436 | 0.561124 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 57.1886 | 2.38286 | ||||||||
\(577\) | − 14.8510i | − 0.618254i | −0.951021 | − | 0.309127i | \(-0.899963\pi\) | ||||
0.951021 | − | 0.309127i | \(-0.100037\pi\) | |||||||
\(578\) | 33.7938i | 1.40564i | ||||||||
\(579\) | 1.50071 | 0.0623673 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.6253 | −0.440812 | ||||||||
\(582\) | − 5.55149i | − 0.230117i | ||||||||
\(583\) | − 0.231548i | − 0.00958974i | ||||||||
\(584\) | −95.9897 | −3.97208 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.27267 | 0.300431 | ||||||||
\(587\) | 14.7938i | 0.610607i | 0.952255 | + | 0.305304i | \(0.0987580\pi\) | ||||
−0.952255 | + | 0.305304i | \(0.901242\pi\) | |||||||
\(588\) | 12.7938i | 0.527609i | ||||||||
\(589\) | −7.13918 | −0.294165 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.9756 | −1.56211 | ||||||||
\(592\) | − 104.880i | − 4.31056i | ||||||||
\(593\) | 27.4191i | 1.12597i | 0.826467 | + | 0.562985i | \(0.190347\pi\) | ||||
−0.826467 | + | 0.562985i | \(0.809653\pi\) | |||||||
\(594\) | 1.03761 | 0.0425737 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 117.626 | 4.81814 | ||||||||
\(597\) | 31.1695i | 1.27568i | ||||||||
\(598\) | − 49.8251i | − 2.03750i | ||||||||
\(599\) | −11.3258 | −0.462761 | −0.231380 | − | 0.972863i | \(-0.574324\pi\) | ||||
−0.231380 | + | 0.972863i | \(0.574324\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5393 | 0.633860 | 0.316930 | − | 0.948449i | \(-0.397348\pi\) | ||||
0.316930 | + | 0.948449i | \(0.397348\pi\) | |||||||
\(602\) | 15.7685i | 0.642674i | ||||||||
\(603\) | 34.2677i | 1.39549i | ||||||||
\(604\) | 16.7308 | 0.680768 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 49.2057 | 1.99884 | ||||||||
\(607\) | 17.7235i | 0.719377i | 0.933073 | + | 0.359688i | \(0.117117\pi\) | ||||
−0.933073 | + | 0.359688i | \(0.882883\pi\) | |||||||
\(608\) | − 21.5369i | − 0.873437i | ||||||||
\(609\) | 8.96239 | 0.363174 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −68.9946 | −2.79122 | ||||||||
\(612\) | 88.5945i | 3.58122i | ||||||||
\(613\) | − 22.2941i | − 0.900450i | −0.892915 | − | 0.450225i | \(-0.851344\pi\) | ||||
0.892915 | − | 0.450225i | \(-0.148656\pi\) | |||||||
\(614\) | −22.3733 | −0.902912 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.44358 | −0.340202 | ||||||||
\(617\) | − 30.9438i | − 1.24575i | −0.782321 | − | 0.622876i | \(-0.785964\pi\) | ||||
0.782321 | − | 0.622876i | \(-0.214036\pi\) | |||||||
\(618\) | − 28.0059i | − 1.12656i | ||||||||
\(619\) | −32.4119 | −1.30274 | −0.651371 | − | 0.758759i | \(-0.725806\pi\) | ||||
−0.651371 | + | 0.758759i | \(0.725806\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.23884 | 0.0497130 | ||||||||
\(622\) | − 11.8677i | − 0.475850i | ||||||||
\(623\) | 7.22425i | 0.289434i | ||||||||
\(624\) | 177.607 | 7.10998 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −79.6893 | −3.18502 | ||||||||
\(627\) | − 3.35026i | − 0.133797i | ||||||||
\(628\) | 27.9756i | 1.11635i | ||||||||
\(629\) | 46.5111 | 1.85452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.3258 | −1.08782 | −0.543912 | − | 0.839142i | \(-0.683057\pi\) | ||||
−0.543912 | + | 0.839142i | \(0.683057\pi\) | |||||||
\(632\) | − 16.6312i | − 0.661553i | ||||||||
\(633\) | − 11.0132i | − 0.437734i | ||||||||
\(634\) | 41.1998 | 1.63625 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.96239 | 0.117466 | ||||||||
\(637\) | 5.83146i | 0.231051i | ||||||||
\(638\) | 9.66291i | 0.382558i | ||||||||
\(639\) | 49.0395 | 1.93997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4460 | 0.768069 | 0.384034 | − | 0.923319i | \(-0.374534\pi\) | ||||
0.384034 | + | 0.923319i | \(0.374534\pi\) | |||||||
\(642\) | − 76.5764i | − 3.02223i | ||||||||
\(643\) | − 5.29314i | − 0.208741i | −0.994538 | − | 0.104370i | \(-0.966717\pi\) | ||||
0.994538 | − | 0.104370i | \(-0.0332828\pi\) | |||||||
\(644\) | −16.4690 | −0.648969 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.6629 | 0.773627 | ||||||||
\(647\) | 35.0966i | 1.37979i | 0.723909 | + | 0.689896i | \(0.242344\pi\) | ||||
−0.723909 | + | 0.689896i | \(0.757656\pi\) | |||||||
\(648\) | − 71.8261i | − 2.82159i | ||||||||
\(649\) | 13.5999 | 0.533843 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.1187 | −0.514163 | ||||||||
\(652\) | 17.4314i | 0.682665i | ||||||||
\(653\) | − 27.7988i | − 1.08785i | −0.839134 | − | 0.543925i | \(-0.816938\pi\) | ||||
0.839134 | − | 0.543925i | \(-0.183062\pi\) | |||||||
\(654\) | 14.5139 | 0.567538 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −61.6869 | −2.40847 | ||||||||
\(657\) | − 35.8822i | − 1.39990i | ||||||||
\(658\) | 31.6507i | 1.23387i | ||||||||
\(659\) | −19.6180 | −0.764209 | −0.382105 | − | 0.924119i | \(-0.624801\pi\) | ||||
−0.382105 | + | 0.924119i | \(0.624801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.5633 | 0.838713 | 0.419357 | − | 0.907822i | \(-0.362256\pi\) | ||||
0.419357 | + | 0.907822i | \(0.362256\pi\) | |||||||
\(662\) | − 16.7513i | − 0.651058i | ||||||||
\(663\) | 78.7631i | 3.05890i | ||||||||
\(664\) | 89.7156 | 3.48164 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 72.1436 | 2.79551 | ||||||||
\(667\) | 11.5369i | 0.446711i | ||||||||
\(668\) | − 58.1378i | − 2.24942i | ||||||||
\(669\) | −19.3054 | −0.746388 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.41327 | 0.0545585 | ||||||||
\(672\) | − 39.5755i | − 1.52666i | ||||||||
\(673\) | 21.0679i | 0.812109i | 0.913849 | + | 0.406054i | \(0.133096\pi\) | ||||
−0.913849 | + | 0.406054i | \(0.866904\pi\) | |||||||
\(674\) | −42.4544 | −1.63528 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 108.313 | 4.16589 | ||||||||
\(677\) | 34.5174i | 1.32661i | 0.748349 | + | 0.663306i | \(0.230847\pi\) | ||||
−0.748349 | + | 0.663306i | \(0.769153\pi\) | |||||||
\(678\) | 62.0625i | 2.38350i | ||||||||
\(679\) | −0.836381 | −0.0320973 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9248 | 0.993440 | ||||||||
\(682\) | − 14.1441i | − 0.541606i | ||||||||
\(683\) | − 33.7802i | − 1.29256i | −0.763099 | − | 0.646282i | \(-0.776323\pi\) | ||||
0.763099 | − | 0.646282i | \(-0.223677\pi\) | |||||||
\(684\) | 21.9756 | 0.840257 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.67513 | 0.102137 | ||||||||
\(687\) | 73.0757i | 2.78801i | ||||||||
\(688\) | − 72.3547i | − 2.75850i | ||||||||
\(689\) | 1.35026 | 0.0514409 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.8618 | −0.527327 | −0.263663 | − | 0.964615i | \(-0.584931\pi\) | ||||
−0.263663 | + | 0.964615i | \(0.584931\pi\) | |||||||
\(692\) | − 46.3063i | − 1.76030i | ||||||||
\(693\) | − 3.15633i | − 0.119899i | ||||||||
\(694\) | 18.1681 | 0.689651 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −75.6747 | −2.86844 | ||||||||
\(697\) | − 27.3561i | − 1.03619i | ||||||||
\(698\) | 71.5569i | 2.70847i | ||||||||
\(699\) | −21.6629 | −0.819367 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.5256 | 1.53063 | 0.765316 | − | 0.643655i | \(-0.222583\pi\) | ||||
0.765316 | + | 0.643655i | \(0.222583\pi\) | |||||||
\(702\) | 6.05079i | 0.228372i | ||||||||
\(703\) | − 11.5369i | − 0.435123i | ||||||||
\(704\) | 18.1187 | 0.682875 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.1100 | 1.69774 | ||||||||
\(707\) | − 7.41327i | − 0.278805i | ||||||||
\(708\) | 173.995i | 6.53914i | ||||||||
\(709\) | 0.850969 | 0.0319588 | 0.0159794 | − | 0.999872i | \(-0.494913\pi\) | ||||
0.0159794 | + | 0.999872i | \(0.494913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.21696 | 0.233154 | ||||||||
\(712\) | − 60.9986i | − 2.28602i | ||||||||
\(713\) | − 16.8872i | − 0.632429i | ||||||||
\(714\) | 36.1319 | 1.35220 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −135.289 | −5.05598 | ||||||||
\(717\) | 52.6371i | 1.96577i | ||||||||
\(718\) | − 10.1465i | − 0.378663i | ||||||||
\(719\) | −22.5769 | −0.841976 | −0.420988 | − | 0.907066i | \(-0.638317\pi\) | ||||
−0.420988 | + | 0.907066i | \(0.638317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.21933 | −0.157136 | ||||||||
\(722\) | 45.9502i | 1.71009i | ||||||||
\(723\) | − 23.1695i | − 0.861683i | ||||||||
\(724\) | 57.7499 | 2.14626 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.63752 | 0.246341 | ||||||||
\(727\) | 12.5174i | 0.464244i | 0.972687 | + | 0.232122i | \(0.0745669\pi\) | ||||
−0.972687 | + | 0.232122i | \(0.925433\pi\) | |||||||
\(728\) | − 49.2384i | − 1.82490i | ||||||||
\(729\) | 29.7367 | 1.10136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0870 | 1.18678 | ||||||||
\(732\) | 18.0811i | 0.668297i | ||||||||
\(733\) | − 16.6678i | − 0.615641i | −0.951445 | − | 0.307820i | \(-0.900400\pi\) | ||||
0.951445 | − | 0.307820i | \(-0.0995996\pi\) | |||||||
\(734\) | −17.0400 | −0.628957 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 50.9438 | 1.87781 | ||||||||
\(737\) | 10.8568i | 0.399917i | ||||||||
\(738\) | − 42.4323i | − 1.56196i | ||||||||
\(739\) | −42.7005 | −1.57076 | −0.785382 | − | 0.619011i | \(-0.787533\pi\) | ||||
−0.785382 | + | 0.619011i | \(0.787533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.5369 | 0.717706 | ||||||||
\(742\) | − 0.619421i | − 0.0227397i | ||||||||
\(743\) | 19.6873i | 0.722259i | 0.932516 | + | 0.361129i | \(0.117609\pi\) | ||||
−0.932516 | + | 0.361129i | \(0.882391\pi\) | |||||||
\(744\) | 110.769 | 4.06099 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 57.0651 | 2.08930 | ||||||||
\(747\) | 33.5369i | 1.22705i | ||||||||
\(748\) | 28.0689i | 1.02630i | ||||||||
\(749\) | −11.5369 | −0.421549 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.85940 | −0.213813 | −0.106906 | − | 0.994269i | \(-0.534094\pi\) | ||||
−0.106906 | + | 0.994269i | \(0.534094\pi\) | |||||||
\(752\) | − 145.232i | − 5.29605i | ||||||||
\(753\) | 4.65562i | 0.169660i | ||||||||
\(754\) | −56.3488 | −2.05210 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | − 40.5863i | − 1.47513i | −0.675274 | − | 0.737567i | \(-0.735975\pi\) | ||||
0.675274 | − | 0.737567i | \(-0.264025\pi\) | |||||||
\(758\) | 66.3098i | 2.40848i | ||||||||
\(759\) | 7.92478 | 0.287651 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.8472 | 0.791960 | 0.395980 | − | 0.918259i | \(-0.370405\pi\) | ||||
0.395980 | + | 0.918259i | \(0.370405\pi\) | |||||||
\(762\) | − 112.588i | − 4.07864i | ||||||||
\(763\) | − 2.18664i | − 0.0791618i | ||||||||
\(764\) | −57.7499 | −2.08932 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.6013 | 0.527567 | ||||||||
\(767\) | 79.3073i | 2.86362i | ||||||||
\(768\) | 20.0689i | 0.724173i | ||||||||
\(769\) | −45.2892 | −1.63317 | −0.816585 | − | 0.577226i | \(-0.804135\pi\) | ||||
−0.816585 | + | 0.577226i | \(0.804135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −67.3376 | −2.42510 | ||||||||
\(772\) | 3.11871i | 0.112245i | ||||||||
\(773\) | 33.8153i | 1.21625i | 0.793841 | + | 0.608125i | \(0.208078\pi\) | ||||
−0.793841 | + | 0.608125i | \(0.791922\pi\) | |||||||
\(774\) | 49.7704 | 1.78896 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.06205 | 0.253513 | ||||||||
\(777\) | − 21.1998i | − 0.760539i | ||||||||
\(778\) | − 36.7123i | − 1.31620i | ||||||||
\(779\) | −6.78560 | −0.243119 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.5369 | 0.555954 | ||||||||
\(782\) | 46.5111i | 1.66323i | ||||||||
\(783\) | − 1.40105i | − 0.0500693i | ||||||||
\(784\) | −12.2750 | −0.438394 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −65.8759 | −2.34972 | ||||||||
\(787\) | 1.27504i | 0.0454502i | 0.999742 | + | 0.0227251i | \(0.00723425\pi\) | ||||
−0.999742 | + | 0.0227251i | \(0.992766\pi\) | |||||||
\(788\) | − 78.9194i | − 2.81139i | ||||||||
\(789\) | 31.7889 | 1.13172 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.35026 | 0.332457 | ||||||||
\(792\) | 26.6507i | 0.946991i | ||||||||
\(793\) | 8.24140i | 0.292661i | ||||||||
\(794\) | 5.64832 | 0.200452 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −64.7753 | −2.29590 | ||||||||
\(797\) | − 42.5256i | − 1.50634i | −0.657829 | − | 0.753168i | \(-0.728525\pi\) | ||||
0.657829 | − | 0.753168i | \(-0.271475\pi\) | |||||||
\(798\) | − 8.96239i | − 0.317265i | ||||||||
\(799\) | 64.4055 | 2.27850 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.8021 | 0.805672 | ||||||||
\(802\) | − 51.2262i | − 1.80886i | ||||||||
\(803\) | − 11.3684i | − 0.401181i | ||||||||
\(804\) | −138.901 | −4.89865 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 82.4807 | 2.90526 | ||||||||
\(807\) | 15.5369i | 0.546925i | ||||||||
\(808\) | 62.5945i | 2.20207i | ||||||||
\(809\) | 14.7151 | 0.517356 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.7743 | 1.81804 | 0.909021 | − | 0.416750i | \(-0.136831\pi\) | ||||
0.909021 | + | 0.416750i | \(0.136831\pi\) | |||||||
\(812\) | 18.6253i | 0.653620i | ||||||||
\(813\) | − 14.2374i | − 0.499328i | ||||||||
\(814\) | 22.8568 | 0.801132 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −165.794 | −5.80395 | ||||||||
\(817\) | − 7.95906i | − 0.278452i | ||||||||
\(818\) | − 49.9937i | − 1.74799i | ||||||||
\(819\) | 18.4060 | 0.643157 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.64974 | 0.0924765 | 0.0462383 | − | 0.998930i | \(-0.485277\pi\) | ||||
0.0462383 | + | 0.998930i | \(0.485277\pi\) | |||||||
\(822\) | − 72.9643i | − 2.54492i | ||||||||
\(823\) | − 5.76845i | − 0.201076i | −0.994933 | − | 0.100538i | \(-0.967944\pi\) | ||||
0.994933 | − | 0.100538i | \(-0.0320563\pi\) | |||||||
\(824\) | 35.6263 | 1.24110 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.3815 | 1.26588 | ||||||||
\(827\) | − 13.4920i | − 0.469163i | −0.972096 | − | 0.234581i | \(-0.924628\pi\) | ||||
0.972096 | − | 0.234581i | \(-0.0753719\pi\) | |||||||
\(828\) | 51.9814i | 1.80648i | ||||||||
\(829\) | 4.70052 | 0.163256 | 0.0816280 | − | 0.996663i | \(-0.473988\pi\) | ||||
0.0816280 | + | 0.996663i | \(0.473988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.7367 | 0.719349 | ||||||||
\(832\) | 105.658i | 3.66305i | ||||||||
\(833\) | − 5.44358i | − 0.188609i | ||||||||
\(834\) | −45.7137 | −1.58294 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.96239 | 0.240799 | ||||||||
\(837\) | 2.05079i | 0.0708855i | ||||||||
\(838\) | − 2.06888i | − 0.0714684i | ||||||||
\(839\) | 38.8045 | 1.33968 | 0.669839 | − | 0.742506i | \(-0.266363\pi\) | ||||
0.669839 | + | 0.742506i | \(0.266363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9525 | −0.550088 | ||||||||
\(842\) | 28.1417i | 0.969828i | ||||||||
\(843\) | − 20.9624i | − 0.721983i | ||||||||
\(844\) | 22.8872 | 0.787809 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 99.8999 | 3.43463 | ||||||||
\(847\) | − 1.00000i | − 0.0343604i | ||||||||
\(848\) | 2.84226i | 0.0976036i | ||||||||
\(849\) | 2.07522 | 0.0712215 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.2896 | 0.935476 | ||||||||
\(852\) | 198.777i | 6.80998i | ||||||||
\(853\) | − 20.6824i | − 0.708153i | −0.935217 | − | 0.354076i | \(-0.884795\pi\) | ||||
0.935217 | − | 0.354076i | \(-0.115205\pi\) | |||||||
\(854\) | 3.78067 | 0.129372 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 97.4128 | 3.32950 | ||||||||
\(857\) | 26.3453i | 0.899940i | 0.893044 | + | 0.449970i | \(0.148565\pi\) | ||||
−0.893044 | + | 0.449970i | \(0.851435\pi\) | |||||||
\(858\) | 38.7064i | 1.32141i | ||||||||
\(859\) | 8.51151 | 0.290409 | 0.145205 | − | 0.989402i | \(-0.453616\pi\) | ||||
0.145205 | + | 0.989402i | \(0.453616\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.4690 | −0.424942 | ||||||||
\(862\) | 66.1582i | 2.25336i | ||||||||
\(863\) | − 7.56722i | − 0.257591i | −0.991671 | − | 0.128796i | \(-0.958889\pi\) | ||||
0.991671 | − | 0.128796i | \(-0.0411111\pi\) | |||||||
\(864\) | −6.18664 | −0.210474 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 49.6502 | 1.68718 | ||||||||
\(867\) | − 31.3439i | − 1.06450i | ||||||||
\(868\) | − 27.2628i | − 0.925360i | ||||||||
\(869\) | 1.96968 | 0.0668169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −63.3112 | −2.14522 | ||||||||
\(872\) | 18.4631i | 0.625239i | ||||||||
\(873\) | 2.63989i | 0.0893467i | ||||||||
\(874\) | 11.5369 | 0.390242 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 145.445 | 4.91413 | ||||||||
\(877\) | 17.2955i | 0.584028i | 0.956414 | + | 0.292014i | \(0.0943254\pi\) | ||||
−0.956414 | + | 0.292014i | \(0.905675\pi\) | |||||||
\(878\) | − 3.81336i | − 0.128695i | ||||||||
\(879\) | −6.74543 | −0.227518 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.4504 | 0.688992 | 0.344496 | − | 0.938788i | \(-0.388050\pi\) | ||||
0.344496 | + | 0.938788i | \(0.388050\pi\) | |||||||
\(882\) | − 8.44358i | − 0.284310i | ||||||||
\(883\) | 49.6589i | 1.67116i | 0.549371 | + | 0.835578i | \(0.314867\pi\) | ||||
−0.549371 | + | 0.835578i | \(0.685133\pi\) | |||||||
\(884\) | −163.682 | −5.50524 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −107.520 | −3.61221 | ||||||||
\(887\) | − 47.1100i | − 1.58180i | −0.611946 | − | 0.790900i | \(-0.709613\pi\) | ||||
0.611946 | − | 0.790900i | \(-0.290387\pi\) | |||||||
\(888\) | 179.002i | 6.00693i | ||||||||
\(889\) | −16.9624 | −0.568900 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.50659 | 0.284981 | ||||||||
\(892\) | − 40.1197i | − 1.34331i | ||||||||
\(893\) | − 15.9756i | − 0.534602i | ||||||||
\(894\) | −151.415 | −5.06407 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.5696 | 0.553551 | ||||||||
\(897\) | 46.2130i | 1.54301i | ||||||||
\(898\) | 33.8554i | 1.12977i | ||||||||
\(899\) | −19.0982 | −0.636962 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.26045 | −0.0419917 | ||||||||
\(902\) | − 13.4436i | − 0.447622i | ||||||||
\(903\) | − 14.6253i | − 0.486700i | ||||||||
\(904\) | −78.9497 | −2.62583 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.5369 | −0.715516 | ||||||||
\(907\) | 14.4591i | 0.480107i | 0.970760 | + | 0.240054i | \(0.0771651\pi\) | ||||
−0.970760 | + | 0.240054i | \(0.922835\pi\) | |||||||
\(908\) | 53.8759i | 1.78793i | ||||||||
\(909\) | −23.3987 | −0.776085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.5369 | −1.04486 | −0.522432 | − | 0.852681i | \(-0.674975\pi\) | ||||
−0.522432 | + | 0.852681i | \(0.674975\pi\) | |||||||
\(912\) | 41.1246i | 1.36177i | ||||||||
\(913\) | 10.6253i | 0.351646i | ||||||||
\(914\) | −1.45580 | −0.0481536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −151.863 | −5.01770 | ||||||||
\(917\) | 9.92478i | 0.327745i | ||||||||
\(918\) | − 5.64832i | − 0.186422i | ||||||||
\(919\) | −5.26328 | −0.173620 | −0.0868098 | − | 0.996225i | \(-0.527667\pi\) | ||||
−0.0868098 | + | 0.996225i | \(0.527667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.7513 | 0.683779 | ||||||||
\(922\) | 30.9659i | 1.01981i | ||||||||
\(923\) | 90.6028i | 2.98223i | ||||||||
\(924\) | 12.7938 | 0.420887 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −63.6542 | −2.09181 | ||||||||
\(927\) | 13.3176i | 0.437407i | ||||||||
\(928\) | − 57.6140i | − 1.89127i | ||||||||
\(929\) | −26.0508 | −0.854699 | −0.427349 | − | 0.904087i | \(-0.640553\pi\) | ||||
−0.427349 | + | 0.904087i | \(0.640553\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.35026 | −0.0442530 | ||||||||
\(932\) | − 45.0191i | − 1.47465i | ||||||||
\(933\) | 11.0073i | 0.360363i | ||||||||
\(934\) | −7.13681 | −0.233524 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −155.412 | −5.07981 | ||||||||
\(937\) | − 29.3439i | − 0.958624i | −0.877645 | − | 0.479312i | \(-0.840886\pi\) | ||||
0.877645 | − | 0.479312i | \(-0.159114\pi\) | |||||||
\(938\) | 29.0435i | 0.948304i | ||||||||
\(939\) | 73.9121 | 2.41203 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.6375 | −0.933556 | −0.466778 | − | 0.884374i | \(-0.654585\pi\) | ||||
−0.466778 | + | 0.884374i | \(0.654585\pi\) | |||||||
\(942\) | − 36.0118i | − 1.17333i | ||||||||
\(943\) | − 16.0508i | − 0.522685i | ||||||||
\(944\) | −166.939 | −5.43341 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.7685 | 0.512677 | ||||||||
\(947\) | − 52.8178i | − 1.71635i | −0.513358 | − | 0.858174i | \(-0.671599\pi\) | ||||
0.513358 | − | 0.858174i | \(-0.328401\pi\) | |||||||
\(948\) | 25.1998i | 0.818452i | ||||||||
\(949\) | 66.2941 | 2.15200 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.2130 | −1.23914 | ||||||||
\(952\) | 45.9633i | 1.48968i | ||||||||
\(953\) | − 37.1939i | − 1.20483i | −0.798183 | − | 0.602415i | \(-0.794205\pi\) | ||||
0.798183 | − | 0.602415i | \(-0.205795\pi\) | |||||||
\(954\) | −1.95509 | −0.0632985 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −109.388 | −3.53787 | ||||||||
\(957\) | − 8.96239i | − 0.289713i | ||||||||
\(958\) | − 28.6516i | − 0.925693i | ||||||||
\(959\) | −10.9927 | −0.354973 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.04491 | −0.0982228 | ||||||||
\(962\) | 133.289i | 4.29740i | ||||||||
\(963\) | 36.4142i | 1.17343i | ||||||||
\(964\) | 48.1500 | 1.55081 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 21.1998 | 0.682093 | ||||||||
\(967\) | 4.07125i | 0.130923i | 0.997855 | + | 0.0654613i | \(0.0208519\pi\) | ||||
−0.997855 | + | 0.0654613i | \(0.979148\pi\) | |||||||
\(968\) | 8.44358i | 0.271387i | ||||||||
\(969\) | −18.2374 | −0.585871 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.773377 | 0.0248188 | 0.0124094 | − | 0.999923i | \(-0.496050\pi\) | ||||
0.0124094 | + | 0.999923i | \(0.496050\pi\) | |||||||
\(972\) | 114.832i | 3.68324i | ||||||||
\(973\) | 6.88717i | 0.220792i | ||||||||
\(974\) | 46.6312 | 1.49416 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.3479 | −0.555292 | ||||||||
\(977\) | − 37.8740i | − 1.21170i | −0.795580 | − | 0.605848i | \(-0.792834\pi\) | ||||
0.795580 | − | 0.605848i | \(-0.207166\pi\) | |||||||
\(978\) | − 22.4387i | − 0.717509i | ||||||||
\(979\) | 7.22425 | 0.230888 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.90175 | −0.220356 | ||||||||
\(982\) | 75.8916i | 2.42180i | ||||||||
\(983\) | 15.5794i | 0.496907i | 0.968644 | + | 0.248453i | \(0.0799223\pi\) | ||||
−0.968644 | + | 0.248453i | \(0.920078\pi\) | |||||||
\(984\) | 105.283 | 3.35629 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 52.6009 | 1.67515 | ||||||||
\(987\) | − 29.3561i | − 0.934416i | ||||||||
\(988\) | 40.6009i | 1.29169i | ||||||||
\(989\) | 18.8265 | 0.598649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0982 | 0.860804 | 0.430402 | − | 0.902637i | \(-0.358372\pi\) | ||||
0.430402 | + | 0.902637i | \(0.358372\pi\) | |||||||
\(992\) | 84.3327i | 2.67756i | ||||||||
\(993\) | 15.5369i | 0.493049i | ||||||||
\(994\) | 41.5633 | 1.31831 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −135.938 | −4.30737 | ||||||||
\(997\) | 50.4060i | 1.59637i | 0.602410 | + | 0.798187i | \(0.294207\pi\) | ||||
−0.602410 | + | 0.798187i | \(0.705793\pi\) | |||||||
\(998\) | 73.5026i | 2.32668i | ||||||||
\(999\) | −3.31406 | −0.104852 |
(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 | 1925.2.b.n.1849.1 | 6 | ||
5.2 | odd | 4 | 1925.2.a.v.1.3 | 3 | |||
5.3 | odd | 4 | 385.2.a.f.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 1925.2.b.n.1849.6 | 6 | ||
15.8 | even | 4 | 3465.2.a.bh.1.3 | 3 | |||
20.3 | even | 4 | 6160.2.a.bn.1.3 | 3 | |||
35.13 | even | 4 | 2695.2.a.g.1.1 | 3 | |||
55.43 | even | 4 | 4235.2.a.q.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.a.f.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
1925.2.a.v.1.3 | 3 | 5.2 | odd | 4 | |||
1925.2.b.n.1849.1 | 6 | 1.1 | even | 1 | trivial | ||
1925.2.b.n.1849.6 | 6 | 5.4 | even | 2 | inner | ||
2695.2.a.g.1.1 | 3 | 35.13 | even | 4 | |||
3465.2.a.bh.1.3 | 3 | 15.8 | even | 4 | |||
4235.2.a.q.1.3 | 3 | 55.43 | even | 4 | |||
6160.2.a.bn.1.3 | 3 | 20.3 | even | 4 |