Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (of order \(6\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 737.9 | ||
Character | \(\chi\) | \(=\) | 1148.737 |
Dual form | 1148.2.r.a.81.9 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.48683 | + | 0.858424i | −0.858424 | + | 0.495612i | −0.863484 | − | 0.504376i | \(-0.831723\pi\) |
0.00505996 | + | 0.999987i | \(0.498389\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.14679 | − | 1.98629i | 0.512859 | − | 0.888297i | −0.487030 | − | 0.873385i | \(-0.661920\pi\) |
0.999889 | − | 0.0149121i | \(-0.00474685\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.58388 | − | 0.568830i | −0.976615 | − | 0.214997i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0262152 | + | 0.0454060i | −0.00873839 | + | 0.0151353i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.876249 | + | 0.505903i | −0.264199 | + | 0.152535i | −0.626249 | − | 0.779623i | \(-0.715410\pi\) |
0.362049 | + | 0.932159i | \(0.382077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.49899i | 1.52515i | 0.646903 | + | 0.762573i | \(0.276064\pi\) | ||||
−0.646903 | + | 0.762573i | \(0.723936\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.93772i | 1.01671i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.76985 | − | 2.17652i | 0.914322 | − | 0.527884i | 0.0325029 | − | 0.999472i | \(-0.489652\pi\) |
0.881819 | + | 0.471588i | \(0.156319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0236876 | + | 0.0136760i | 0.00543430 | + | 0.00313749i | 0.502715 | − | 0.864452i | \(-0.332335\pi\) |
−0.497280 | + | 0.867590i | \(0.665668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.33010 | − | 1.37231i | 0.944905 | − | 0.299462i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.62858 | − | 8.01694i | 0.965126 | − | 1.67165i | 0.255851 | − | 0.966716i | \(-0.417644\pi\) |
0.709275 | − | 0.704932i | \(-0.249022\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.130240 | − | 0.225582i | −0.0260480 | − | 0.0451165i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.24056i | − | 1.00855i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.46316i | − | 0.643093i | −0.946894 | − | 0.321547i | \(-0.895797\pi\) | ||
0.946894 | − | 0.321547i | \(-0.104203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.927599 | − | 1.60665i | −0.166602 | − | 0.288563i | 0.770621 | − | 0.637294i | \(-0.219946\pi\) |
−0.937223 | + | 0.348731i | \(0.886613\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.868559 | − | 1.50439i | 0.151197 | − | 0.261880i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.09302 | + | 4.48002i | −0.691847 | + | 0.757261i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.06145 | + | 1.83848i | −0.174501 | + | 0.302244i | −0.939988 | − | 0.341206i | \(-0.889165\pi\) |
0.765488 | + | 0.643451i | \(0.222498\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.72047 | − | 8.17609i | −0.755880 | − | 1.30922i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.247452 | − | 6.39834i | 0.0386455 | − | 0.999253i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.16986 | −1.24589 | −0.622946 | − | 0.782265i | \(-0.714064\pi\) | ||||
−0.622946 | + | 0.782265i | \(0.714064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0601264 | + | 0.104142i | 0.00896311 | + | 0.0155246i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1569 | − | 5.86411i | −1.48154 | − | 0.855369i | −0.481762 | − | 0.876302i | \(-0.660003\pi\) |
−0.999781 | + | 0.0209334i | \(0.993336\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.35287 | + | 2.93958i | 0.907552 | + | 0.419939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.73676 | + | 6.47226i | −0.523251 | + | 0.906297i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.98638 | − | 1.14684i | 0.272850 | − | 0.157530i | −0.357332 | − | 0.933977i | \(-0.616313\pi\) |
0.630182 | + | 0.776447i | \(0.282980\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.32065i | 0.312917i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0469593 | −0.00621991 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.40841 | − | 7.63559i | −0.573926 | − | 0.994069i | −0.996157 | − | 0.0875808i | \(-0.972086\pi\) |
0.422232 | − | 0.906488i | \(-0.361247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.35245 | − | 12.7348i | 0.941385 | − | 1.63053i | 0.178552 | − | 0.983930i | \(-0.442859\pi\) |
0.762833 | − | 0.646596i | \(-0.223808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0935651 | − | 0.102412i | 0.0117881 | − | 0.0129027i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.9226 | + | 6.30617i | 1.35478 | + | 0.782184i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.35625 | − | 3.66979i | 0.776540 | − | 0.448336i | −0.0586626 | − | 0.998278i | \(-0.518684\pi\) |
0.835203 | + | 0.549942i | \(0.185350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.8932i | 1.91331i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.23771i | − | 0.977637i | −0.872386 | − | 0.488818i | \(-0.837428\pi\) | ||
0.872386 | − | 0.488818i | \(-0.162572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.17947 | − | 8.97111i | −0.606211 | − | 1.04999i | −0.991859 | − | 0.127342i | \(-0.959355\pi\) |
0.385648 | − | 0.922646i | \(-0.373978\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.387291 | + | 0.223603i | 0.0447205 | + | 0.0258194i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.55190 | − | 0.808755i | 0.290815 | − | 0.0921662i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5262 | + | 6.65466i | 1.29680 | + | 0.748707i | 0.979850 | − | 0.199735i | \(-0.0640082\pi\) |
0.316949 | + | 0.948442i | \(0.397342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.41998 | + | 7.65563i | 0.491109 | + | 0.850626i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1779 | 1.33670 | 0.668348 | − | 0.743849i | \(-0.267002\pi\) | ||||
0.668348 | + | 0.743849i | \(0.267002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 9.98403i | − | 1.08292i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.97286 | + | 5.14915i | 0.318724 | + | 0.552047i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.364394 | + | 0.210383i | 0.0386257 | + | 0.0223006i | 0.519189 | − | 0.854660i | \(-0.326234\pi\) |
−0.480563 | + | 0.876960i | \(0.659568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.12799 | − | 14.2087i | 0.327902 | − | 1.48948i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.75837 | + | 1.59255i | 0.286030 | + | 0.165140i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0543292 | − | 0.0313670i | 0.00557406 | − | 0.00321818i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.28117i | − | 0.942360i | −0.882037 | − | 0.471180i | \(-0.843828\pi\) | ||
0.882037 | − | 0.471180i | \(-0.156172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.0530493i | − | 0.00533166i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.37577 | − | 0.794299i | 0.136894 | − | 0.0790357i | −0.429989 | − | 0.902834i | \(-0.641483\pi\) |
0.566883 | + | 0.823798i | \(0.308149\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.76840 | + | 15.1873i | −0.863976 | + | 1.49645i | 0.00408443 | + | 0.999992i | \(0.498700\pi\) |
−0.868060 | + | 0.496459i | \(0.834633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.23989 | − | 10.1746i | 0.218591 | − | 0.992938i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.941777 | − | 1.63121i | 0.0910450 | − | 0.157695i | −0.816906 | − | 0.576771i | \(-0.804313\pi\) |
0.907951 | + | 0.419076i | \(0.137646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.52823 | + | 4.92377i | −0.816856 | + | 0.471612i | −0.849331 | − | 0.527861i | \(-0.822994\pi\) |
0.0324751 | + | 0.999473i | \(0.489661\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.64469i | − | 0.345939i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.77649 | 0.637478 | 0.318739 | − | 0.947842i | \(-0.396741\pi\) | ||||
0.318739 | + | 0.947842i | \(0.396741\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6160 | − | 18.3874i | −0.989947 | − | 1.71464i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.249687 | − | 0.144157i | −0.0230836 | − | 0.0133273i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.9789 | + | 3.47947i | −1.00643 | + | 0.318962i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.98812 | + | 8.63969i | −0.453466 | + | 0.785426i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.12457 | + | 9.72569i | 0.462067 | + | 0.876936i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8704 | 0.972282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.228661 | −0.0202904 | −0.0101452 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101452 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1472 | − | 7.01321i | 1.06950 | − | 0.617478i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.06690 | + | 10.5082i | −0.530068 | + | 0.918104i | 0.469317 | + | 0.883030i | \(0.344500\pi\) |
−0.999385 | + | 0.0350745i | \(0.988833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0534265 | − | 0.0488114i | −0.00463266 | − | 0.00423248i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.4093 | − | 6.00981i | −0.895889 | − | 0.517242i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.78538 | + | 5.07224i | −0.750586 | + | 0.433351i | −0.825905 | − | 0.563809i | \(-0.809336\pi\) |
0.0753199 | + | 0.997159i | \(0.476002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6427 | 1.75089 | 0.875447 | − | 0.483313i | \(-0.160567\pi\) | ||||
0.875447 | + | 0.483313i | \(0.160567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.1356 | 1.69572 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.78195 | − | 4.81849i | −0.232639 | − | 0.402942i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.87885 | − | 3.97151i | −0.571258 | − | 0.329816i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.9691 | + | 1.08279i | −0.987192 | + | 0.0893072i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.52383 | + | 3.18919i | 0.452530 | + | 0.261268i | 0.708898 | − | 0.705311i | \(-0.249193\pi\) |
−0.256368 | + | 0.966579i | \(0.582526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.92964 | − | 4.57818i | 0.645305 | − | 0.372567i | −0.141350 | − | 0.989960i | \(-0.545144\pi\) |
0.786655 | + | 0.617393i | \(0.211811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.228231i | 0.0184514i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.25504 | −0.341773 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.19772 | + | 1.26886i | −0.175397 | + | 0.101266i | −0.585128 | − | 0.810941i | \(-0.698956\pi\) |
0.409731 | + | 0.912206i | \(0.365623\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.96895 | + | 3.41032i | −0.156148 | + | 0.270456i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.5200 | + | 18.0819i | −1.30196 | + | 1.42506i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.6290 | + | 18.4100i | −0.832530 | + | 1.44198i | 0.0634965 | + | 0.997982i | \(0.479775\pi\) |
−0.896026 | + | 0.444001i | \(0.853559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.99210 | − | 3.45042i | −0.155085 | − | 0.268615i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.6811i | − | 1.60035i | −0.599766 | − | 0.800175i | \(-0.704740\pi\) | ||
0.599766 | − | 0.800175i | \(-0.295260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.2389 | −1.32607 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.00124195 | 0.000717038i | −9.49740e−5 | 5.48333e-5i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.51697 | − | 14.7518i | 0.647533 | − | 1.12156i | −0.336177 | − | 0.941799i | \(-0.609134\pi\) |
0.983710 | − | 0.179762i | \(-0.0575326\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.208207 | + | 0.656962i | 0.0157389 | + | 0.0496617i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.1091 | + | 7.56857i | 0.985344 | + | 0.568889i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.32902 | + | 4.80876i | −0.622540 | + | 0.359424i | −0.777857 | − | 0.628441i | \(-0.783693\pi\) |
0.155317 | + | 0.987865i | \(0.450360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.0178i | − | 0.818944i | −0.912323 | − | 0.409472i | \(-0.865713\pi\) | ||
0.912323 | − | 0.409472i | \(-0.134287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.2461i | 1.86624i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.43451 | + | 4.21669i | 0.178989 | + | 0.310017i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.20222 | + | 3.81435i | −0.161042 | + | 0.278933i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.98099 | + | 13.5410i | −0.216835 | + | 0.984961i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3580 | + | 10.5990i | 1.32834 | + | 0.766917i | 0.985043 | − | 0.172311i | \(-0.0551233\pi\) |
0.343296 | + | 0.939227i | \(0.388457\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.79448 | − | 3.34544i | 0.417096 | − | 0.240810i | −0.276738 | − | 0.960945i | \(-0.589253\pi\) |
0.693834 | + | 0.720135i | \(0.255920\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.6535 | −1.55064 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.8608 | −1.13003 | −0.565017 | − | 0.825080i | \(-0.691130\pi\) | ||||
−0.565017 | + | 0.825080i | \(0.691130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8162 | − | 8.55412i | 1.05029 | − | 0.606385i | 0.127560 | − | 0.991831i | \(-0.459286\pi\) |
0.922731 | + | 0.385445i | \(0.125952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.30047 | + | 10.9127i | −0.444401 | + | 0.769725i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.96995 | + | 8.94839i | −0.138263 | + | 0.628054i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4252 | − | 7.82905i | −0.867814 | − | 0.546804i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.242678 | + | 0.420331i | 0.0168673 | + | 0.0292150i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0276750 | −0.00191432 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.40556i | 0.647506i | 0.946142 | + | 0.323753i | \(0.104945\pi\) | ||||
−0.946142 | + | 0.323753i | \(0.895055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.07145 | + | 12.2481i | 0.484528 | + | 0.839227i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.36909 | + | 16.2277i | −0.638966 | + | 1.10672i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.48290 | + | 4.67903i | 0.100665 | + | 0.317634i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.4020 | + | 8.89237i | 1.04077 | + | 0.600891i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.9687 | + | 20.7303i | 0.805100 | + | 1.39447i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.24919 | −0.619371 | −0.309686 | − | 0.950839i | \(-0.600224\pi\) | ||||
−0.309686 | + | 0.950839i | \(0.600224\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0136571 | 0.000910471 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.8955 | + | 8.02258i | −0.922278 | + | 0.532477i | −0.884361 | − | 0.466803i | \(-0.845406\pi\) |
−0.0379169 | + | 0.999281i | \(0.512072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97763 | − | 4.02854i | −0.461095 | − | 0.266213i | 0.251410 | − | 0.967881i | \(-0.419106\pi\) |
−0.712505 | + | 0.701667i | \(0.752439\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.09999 | + | 3.39309i | −0.203964 | + | 0.223249i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9946 | − | 8.65715i | −0.982330 | − | 0.567149i | −0.0793574 | − | 0.996846i | \(-0.525287\pi\) |
−0.902973 | + | 0.429698i | \(0.858620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.2957 | + | 13.4498i | −1.51964 | + | 0.877367i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.8501 | −1.48427 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.4320i | − | 1.19227i | −0.802884 | − | 0.596135i | \(-0.796702\pi\) | ||
0.802884 | − | 0.596135i | \(-0.203298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2748 | − | 22.9926i | −0.855104 | − | 1.48108i | −0.876549 | − | 0.481313i | \(-0.840160\pi\) |
0.0214453 | − | 0.999770i | \(-0.493173\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.471819 | + | 0.272405i | 0.0302672 | + | 0.0174748i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.1242 | − | 9.24759i | 0.838477 | − | 0.590807i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0752043 | + | 0.130258i | −0.00478513 | + | 0.00828810i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.1065 | + | 10.4538i | −1.14745 | + | 0.662482i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.44527 | 0.343703 | 0.171851 | − | 0.985123i | \(-0.445025\pi\) | ||||
0.171851 | + | 0.985123i | \(0.445025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.36646i | 0.588864i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.57053 | + | 14.8446i | 0.536708 | + | 0.929605i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.69005 | − | 3.28515i | −0.354935 | − | 0.204922i | 0.311921 | − | 0.950108i | \(-0.399027\pi\) |
−0.666857 | + | 0.745186i | \(0.732361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.78843 | − | 4.14663i | 0.235402 | − | 0.257659i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.157248 | + | 0.0907873i | 0.00973342 | + | 0.00561960i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.2079 | + | 6.47086i | −0.691106 | + | 0.399010i | −0.804026 | − | 0.594594i | \(-0.797313\pi\) |
0.112920 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.26071i | − | 0.323163i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.722392 | −0.0442097 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5290 | + | 23.4329i | 0.824876 | + | 1.42873i | 0.902014 | + | 0.431706i | \(0.142088\pi\) |
−0.0771385 | + | 0.997020i | \(0.524578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.20052 | − | 5.54346i | 0.194418 | − | 0.336741i | −0.752292 | − | 0.658830i | \(-0.771052\pi\) |
0.946709 | + | 0.322089i | \(0.104385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.54631 | + | 23.8112i | 0.456724 | + | 1.44112i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.228246 | + | 0.131778i | 0.0137637 | + | 0.00794649i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.02681 | + | 8.70669i | 0.302032 | + | 0.523134i | 0.976596 | − | 0.215082i | \(-0.0690018\pi\) |
−0.674564 | + | 0.738216i | \(0.735668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0972687 | 0.00582332 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.01572i | − | 0.418523i | −0.977860 | − | 0.209262i | \(-0.932894\pi\) | ||
0.977860 | − | 0.209262i | \(-0.0671060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.46189 | + | 4.26411i | 0.146344 | + | 0.253475i | 0.929874 | − | 0.367879i | \(-0.119916\pi\) |
−0.783530 | + | 0.621354i | \(0.786583\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0538523 | + | 0.0932750i | −0.00318994 | + | 0.00552513i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.27895 | + | 16.3918i | −0.252579 | + | 0.967576i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.974496 | − | 1.68788i | 0.0573233 | − | 0.0992868i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.96718 | + | 13.7996i | 0.467044 | + | 0.808945i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 28.2933i | − | 1.65291i | −0.563003 | − | 0.826455i | \(-0.690354\pi\) | ||
0.563003 | − | 0.826455i | \(-0.309646\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.2220 | −1.17737 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.65121 | + | 4.59204i | 0.153839 | + | 0.266457i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.0851 | + | 25.4525i | 2.54951 | + | 1.47196i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.1099 | + | 4.64726i | 1.21676 | + | 0.267864i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.36369 | + | 2.36198i | −0.0783420 | + | 0.135692i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.8634 | − | 29.2082i | −0.965595 | − | 1.67246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.2351 | −1.78268 | −0.891342 | − | 0.453331i | \(-0.850235\pi\) | ||||
−0.891342 | + | 0.453331i | \(0.850235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 30.1080i | − | 1.71279i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7231 | − | 10.8098i | 1.06169 | − | 0.612968i | 0.135792 | − | 0.990737i | \(-0.456642\pi\) |
0.925900 | + | 0.377769i | \(0.123309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3229 | − | 11.7334i | −1.14872 | − | 0.663213i | −0.200144 | − | 0.979766i | \(-0.564141\pi\) |
−0.948575 | + | 0.316553i | \(0.897474\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0961203 | − | 0.303292i | −0.00541577 | − | 0.0170886i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48989 | + | 4.90164i | 0.476840 | + | 0.275304i | 0.719099 | − | 0.694908i | \(-0.244555\pi\) |
−0.242259 | + | 0.970212i | \(0.577888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.75202 | + | 3.03459i | 0.0980945 | + | 0.169905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.23378i | 0.180492i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.119065 | 0.00662493 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.24048 | − | 0.716189i | 0.0688092 | − | 0.0397270i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.45338 | − | 14.6417i | 0.467473 | − | 0.809686i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.9086 | + | 20.9297i | 1.26299 | + | 1.15389i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8968 | + | 11.4874i | 1.09363 | + | 0.631406i | 0.934540 | − | 0.355858i | \(-0.115811\pi\) |
0.159088 | + | 0.987264i | \(0.449145\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0556520 | − | 0.0963921i | −0.00304971 | − | 0.00528226i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 16.8338i | − | 0.919731i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.18581 | 0.228016 | 0.114008 | − | 0.993480i | \(-0.463631\pi\) | ||||
0.114008 | + | 0.993480i | \(0.463631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0755 | + | 5.81710i | −0.547227 | + | 0.315942i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.62562 | + | 0.938550i | 0.0880321 | + | 0.0508254i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.7429 | − | 11.2092i | −0.796043 | − | 0.605240i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.5685 | + | 18.2261i | 1.69959 | + | 0.981258i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.77971 | − | 4.49162i | 0.417637 | − | 0.241123i | −0.276429 | − | 0.961034i | \(-0.589151\pi\) |
0.694066 | + | 0.719912i | \(0.255818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.4024 | 1.19918 | 0.599588 | − | 0.800309i | \(-0.295331\pi\) | ||||
0.599588 | + | 0.800309i | \(0.295331\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.8178 | 1.53818 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.6767 | + | 21.9567i | 0.674712 | + | 1.16864i | 0.976553 | + | 0.215277i | \(0.0690655\pi\) |
−0.301841 | + | 0.953358i | \(0.597601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.3625 | − | 9.44690i | −0.868432 | − | 0.501389i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.3369 | − | 14.5980i | 0.705866 | − | 0.772605i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.32664 | + | 14.4222i | −0.439463 | + | 0.761173i | −0.997648 | − | 0.0685440i | \(-0.978165\pi\) |
0.558185 | + | 0.829717i | \(0.311498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49963 | − | 16.4538i | −0.499980 | − | 0.865991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.1277i | − | 0.898972i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.7590 | −1.24360 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.83457 | − | 11.8378i | −0.356762 | − | 0.617929i | 0.630656 | − | 0.776062i | \(-0.282786\pi\) |
−0.987418 | + | 0.158133i | \(0.949453\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.284036 | + | 0.178969i | 0.0147863 | + | 0.00931677i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.78492 | + | 1.83338i | −0.300338 | + | 0.0951842i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3549 | − | 17.9352i | 0.536157 | − | 0.928651i | −0.462949 | − | 0.886385i | \(-0.653209\pi\) |
0.999106 | − | 0.0422664i | \(-0.0134578\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.1625 | + | 9.33145i | −0.834630 | + | 0.481874i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.0439 | 0.980810 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.44098 | −0.125385 | −0.0626923 | − | 0.998033i | \(-0.519969\pi\) | ||||
−0.0626923 | + | 0.998033i | \(0.519969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.339981 | − | 0.196288i | 0.0174178 | − | 0.0100562i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.631121 | + | 0.364378i | 0.0322488 | + | 0.0186188i | 0.516038 | − | 0.856566i | \(-0.327406\pi\) |
−0.483789 | + | 0.875185i | \(0.660740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.32006 | − | 5.99628i | 0.0672763 | − | 0.305599i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.214174 | − | 0.370961i | 0.0108871 | − | 0.0188570i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.87641 | + | 8.44619i | 0.247244 | + | 0.428239i | 0.962760 | − | 0.270357i | \(-0.0871418\pi\) |
−0.715516 | + | 0.698596i | \(0.753808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 40.2969i | − | 2.03790i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.8319i | − | 1.05083i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.4362 | − | 15.2629i | 1.33015 | − | 0.767962i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.84743 | − | 5.10806i | −0.444040 | − | 0.256366i | 0.261270 | − | 0.965266i | \(-0.415859\pi\) |
−0.705310 | + | 0.708899i | \(0.749192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.121337 | + | 0.0267119i | 0.00607446 | + | 0.00133727i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.43352 | + | 11.1432i | −0.321275 | + | 0.556464i | −0.980751 | − | 0.195261i | \(-0.937445\pi\) |
0.659477 | + | 0.751725i | \(0.270778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.83495 | − | 5.10086i | 0.440100 | − | 0.254092i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.2751 | 1.00748 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.14796i | − | 0.106470i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.20473 | − | 2.08665i | −0.0595700 | − | 0.103178i | 0.834702 | − | 0.550701i | \(-0.185640\pi\) |
−0.894272 | + | 0.447523i | \(0.852306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.70827 | − | 15.0832i | 0.429547 | − | 0.743998i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.04745 | + | 22.2371i | 0.346782 | + | 1.09421i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9654 | − | 24.1888i | 0.685536 | − | 1.18738i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.6923 | + | 17.7202i | −1.50301 | + | 0.867764i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.1047 | −1.17759 | −0.588795 | − | 0.808283i | \(-0.700397\pi\) | ||||
−0.588795 | + | 0.808283i | \(0.700397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3312i | 0.990883i | 0.868641 | + | 0.495441i | \(0.164994\pi\) | ||||
−0.868641 | + | 0.495441i | \(0.835006\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.532532 | − | 0.307457i | 0.0258926 | − | 0.0149491i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.981970 | − | 0.566941i | −0.0476326 | − | 0.0275007i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.2418 | + | 28.7229i | −1.26993 | + | 1.39000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.27261 | + | 4.77619i | 0.399405 | + | 0.230597i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.12872 | − | 7.15115i | −0.198873 | − | 0.344459i | 0.749290 | − | 0.662242i | \(-0.230395\pi\) |
−0.948163 | + | 0.317783i | \(0.897062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.4302 | −0.693472 | −0.346736 | − | 0.937963i | \(-0.612710\pi\) | ||||
−0.346736 | + | 0.937963i | \(0.612710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.6370 | 0.653842 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.219280 | − | 0.126601i | 0.0104896 | − | 0.00605616i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.82678 | + | 2.20939i | 0.182642 | + | 0.105449i | 0.588533 | − | 0.808473i | \(-0.299706\pi\) |
−0.405891 | + | 0.913921i | \(0.633039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.300016 | + | 0.211397i | −0.0142865 | + | 0.0100665i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.35249 | + | 11.0028i | −0.301816 | + | 0.522761i | −0.976547 | − | 0.215303i | \(-0.930926\pi\) |
0.674731 | + | 0.738063i | \(0.264259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.835765 | − | 0.482529i | 0.0396190 | − | 0.0228741i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9507 | −0.517950 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.96485 | −0.0927271 | −0.0463636 | − | 0.998925i | \(-0.514763\pi\) | ||||
−0.0463636 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02011 | + | 5.73173i | 0.142211 | + | 0.269897i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.86004 | + | 13.6140i | −0.369297 | + | 0.639641i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.6356 | − | 22.5075i | −1.15493 | − | 1.05517i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.14173 | − | 1.81388i | −0.146964 | − | 0.0848497i | 0.424715 | − | 0.905327i | \(-0.360374\pi\) |
−0.571679 | + | 0.820477i | \(0.693708\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.4062 | − | 19.7561i | −0.532396 | − | 0.922136i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.5514 | 0.491427 | 0.245713 | − | 0.969343i | \(-0.420978\pi\) | ||||
0.245713 | + | 0.969343i | \(0.420978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4984i | 0.720273i | 0.932900 | + | 0.360137i | \(0.117270\pi\) | ||||
−0.932900 | + | 0.360137i | \(0.882730\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.32653 | − | 3.65263i | 0.293386 | − | 0.169386i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4487 | + | 18.0976i | −0.483507 | + | 0.837459i | −0.999821 | − | 0.0189410i | \(-0.993971\pi\) |
0.516314 | + | 0.856400i | \(0.327304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.5113 | + | 5.86666i | −0.854771 | + | 0.270897i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17843 | − | 3.77316i | 0.100377 | − | 0.173858i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.15883 | − | 4.13316i | 0.329164 | − | 0.190043i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.00712467i | − | 0.000326902i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.120258i | 0.00550624i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.4879 | + | 16.4475i | −1.30164 | + | 0.751504i | −0.980686 | − | 0.195589i | \(-0.937338\pi\) |
−0.320958 | + | 0.947093i | \(0.604005\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1098 | − | 5.83689i | −0.460966 | − | 0.266139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.04050 | − | 41.0660i | 0.411357 | − | 1.86857i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.4351 | − | 10.6435i | −0.837096 | − | 0.483297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.3327 | − | 23.0929i | −0.604163 | − | 1.04644i | −0.992183 | − | 0.124790i | \(-0.960174\pi\) |
0.388020 | − | 0.921651i | \(-0.373159\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.4969i | − | 1.65045i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.3066 | 0.961554 | 0.480777 | − | 0.876843i | \(-0.340355\pi\) | ||||
0.480777 | + | 0.876843i | \(0.340355\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.53765 | − | 13.0556i | −0.339479 | − | 0.587994i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.105371 | − | 0.0608362i | −0.00473609 | − | 0.00273439i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.68586 | + | 21.2853i | −0.210189 | + | 0.954774i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6019 | + | 11.8945i | 0.922266 | + | 0.532471i | 0.884357 | − | 0.466810i | \(-0.154597\pi\) |
0.0379090 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7531 | + | 30.7494i | 0.793152 | + | 1.37378i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.3595i | 1.17531i | 0.809111 | + | 0.587656i | \(0.199949\pi\) | ||||
−0.809111 | + | 0.587656i | \(0.800051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.64356i | − | 0.162137i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.6314 | − | 14.7983i | 1.13833 | − | 0.657214i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.9992 | + | 12.1239i | 0.930773 | + | 0.537382i | 0.887056 | − | 0.461662i | \(-0.152747\pi\) |
0.0437171 | + | 0.999044i | \(0.486080\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.28010 | + | 26.1265i | 0.366290 | + | 1.15577i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0716700 | − | 0.124136i | 0.00316431 | − | 0.00548074i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.1110 | + | 34.8332i | 0.886195 | + | 1.53493i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.8667 | 0.521896 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.2447i | 1.28370i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5413 | + | 7.24075i | −0.549446 | + | 0.317223i | −0.748899 | − | 0.662685i | \(-0.769417\pi\) |
0.199452 | + | 0.979908i | \(0.436084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4025 | − | 24.9458i | 0.629776 | − | 1.09080i | −0.357821 | − | 0.933790i | \(-0.616480\pi\) |
0.987596 | − | 0.157013i | \(-0.0501866\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.873521 | − | 0.798065i | −0.0381236 | − | 0.0348304i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.99382 | − | 4.03788i | −0.304655 | − | 0.175893i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.3476 | − | 54.2956i | −1.36294 | − | 2.36068i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.462269 | 0.0200607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.1844 | + | 1.36074i | 1.52401 | + | 0.0589400i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.16003 | − | 3.74129i | −0.0933864 | − | 0.161750i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.25592 | − | 14.2997i | 0.356269 | − | 0.617076i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.05383 | + | 0.638132i | −0.303830 | + | 0.0274863i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0565 | − | 19.1505i | 0.475358 | − | 0.823344i | −0.524244 | − | 0.851568i | \(-0.675652\pi\) |
0.999602 | + | 0.0282240i | \(0.00898518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.45792 | + | 16.3816i | 0.405878 | + | 0.703002i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.5861i | 0.967481i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.1752i | 1.11917i | 0.828772 | + | 0.559586i | \(0.189040\pi\) | ||||
−0.828772 | + | 0.559586i | \(0.810960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.385491 | + | 0.667691i | 0.0164524 | + | 0.0284963i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0473623 | − | 0.0820339i | 0.00201770 | − | 0.00349476i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.9970 | − | 23.7513i | −1.10550 | − | 1.01001i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.23942 | − | 4.17968i | −0.307296 | − | 0.177418i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.9931 | + | 20.7806i | −1.52507 | + | 0.880502i | −0.525516 | + | 0.850784i | \(0.676128\pi\) |
−0.999558 | + | 0.0297187i | \(0.990539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 44.9260i | − | 1.90017i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 7.56175i | − | 0.319257i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.57560 | − | 4.95112i | 0.361418 | − | 0.208665i | −0.308284 | − | 0.951294i | \(-0.599755\pi\) |
0.669703 | + | 0.742629i | \(0.266422\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.77119 | − | 13.4601i | 0.326936 | − | 0.566270i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.06595 | − | 22.2954i | −0.296742 | − | 0.936321i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.2764 | − | 26.4595i | 0.640420 | − | 1.10924i | −0.344920 | − | 0.938632i | \(-0.612094\pi\) |
0.985339 | − | 0.170607i | \(-0.0545729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.2741 | + | 14.0146i | −1.01584 | + | 0.586495i | −0.912896 | − | 0.408193i | \(-0.866159\pi\) |
−0.102943 | + | 0.994687i | \(0.532826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.3938 | −1.52037 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.41131 | −0.100559 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.97252 | + | 3.44823i | −0.248639 | + | 0.143552i | −0.619141 | − | 0.785280i | \(-0.712519\pi\) |
0.370502 | + | 0.928832i | \(0.379186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.74362 | + | 9.94825i | −0.238697 | + | 0.413435i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.4662 | − | 6.92714i | −1.30544 | − | 0.287386i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.16038 | + | 2.00983i | −0.0480579 | + | 0.0832387i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.572676 | + | 0.330634i | −0.0236772 | + | 0.0136700i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.20050i | 0.379745i | 0.981809 | + | 0.189873i | \(0.0608075\pi\) | ||||
−0.981809 | + | 0.189873i | \(0.939193\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.0507435i | − | 0.00209085i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.5823 | − | 13.6153i | 0.970048 | − | 0.560057i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5149 | + | 12.9990i | 0.924578 | + | 0.533805i | 0.885093 | − | 0.465415i | \(-0.154095\pi\) |
0.0394854 | + | 0.999220i | \(0.487428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.67921 | + | 25.7975i | −0.232825 | + | 1.05760i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.6861 | + | 25.4371i | −0.601063 | + | 1.04107i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.8871 | − | 34.4455i | −0.812565 | − | 1.40740i | −0.911063 | − | 0.412266i | \(-0.864737\pi\) |
0.0984989 | − | 0.995137i | \(-0.468596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2196i | 0.783986i | 0.919968 | + | 0.391993i | \(0.128214\pi\) | ||||
−0.919968 | + | 0.391993i | \(0.871786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.384816i | 0.0156709i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.4406 | + | 19.8158i | 0.465128 | + | 0.805625i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.84464 | + | 3.19502i | −0.0748718 | + | 0.129682i | −0.901031 | − | 0.433756i | \(-0.857188\pi\) |
0.826159 | + | 0.563437i | \(0.190521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.75253 | − | 14.9958i | −0.192582 | − | 0.607662i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.2467 | − | 55.8529i | 1.30456 | − | 2.25957i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.49271 | + | 4.31750i | 0.100680 | + | 0.174382i | 0.911965 | − | 0.410268i | \(-0.134565\pi\) |
−0.811285 | + | 0.584650i | \(0.801232\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 25.1949 | + | 0.974396i | 1.01596 | + | 0.0392915i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.67816 | −0.268852 | −0.134426 | − | 0.990924i | \(-0.542919\pi\) | ||||
−0.134426 | + | 0.990924i | \(0.542919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.9535 | − | 20.7041i | −0.480454 | − | 0.832170i | 0.519295 | − | 0.854595i | \(-0.326195\pi\) |
−0.999749 | + | 0.0224251i | \(0.992861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −42.0133 | − | 24.2564i | −1.68593 | − | 0.973375i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.821878 | − | 0.750883i | −0.0329279 | − | 0.0300835i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.1173 | − | 22.7198i | 0.524691 | − | 0.908792i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0411481 | − | 0.0237569i | 0.00164330 | − | 0.000948757i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.24105i | 0.368465i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.2373 | 1.80087 | 0.900435 | − | 0.434991i | \(-0.143248\pi\) | ||||
0.900435 | + | 0.434991i | \(0.143248\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.07397 | − | 13.9845i | −0.320911 | − | 0.555835i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.262226 | + | 0.454188i | −0.0104061 | + | 0.0180239i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.1647 | + | 34.9343i | −0.640468 | + | 1.38415i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.374042 | + | 0.215953i | 0.0147969 | + | 0.00854297i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.8816 | − | 7.43721i | 0.508794 | − | 0.293752i | −0.223544 | − | 0.974694i | \(-0.571763\pi\) |
0.732338 | + | 0.680942i | \(0.238429\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.47902i | − | 0.294944i | −0.989066 | − | 0.147472i | \(-0.952886\pi\) | ||
0.989066 | − | 0.147472i | \(-0.0471136\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 32.1706i | − | 1.26672i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.41876 | + | 2.45737i | 0.0557773 | + | 0.0966092i | 0.892566 | − | 0.450917i | \(-0.148903\pi\) |
−0.836789 | + | 0.547526i | \(0.815570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.72573 | + | 4.46045i | 0.303261 | + | 0.175088i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.22142 | − | 5.68400i | −0.243837 | − | 0.222773i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5235 | + | 12.4266i | 0.842280 | + | 0.486290i | 0.858039 | − | 0.513585i | \(-0.171683\pi\) |
−0.0157587 | + | 0.999876i | \(0.505016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9149 | + | 24.1013i | 0.543700 | + | 0.941715i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.543123 | 0.0211892 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 17.3630i | − | 0.676366i | −0.941080 | − | 0.338183i | \(-0.890188\pi\) | ||
0.941080 | − | 0.338183i | \(-0.109812\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0085 | + | 20.7993i | 0.467076 | + | 0.808999i | 0.999293 | − | 0.0376093i | \(-0.0119742\pi\) |
−0.532217 | + | 0.846608i | \(0.678641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.5909 | − | 20.5484i | −1.38223 | − | 0.798034i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.158222 | + | 0.0501444i | −0.00613560 | + | 0.00194452i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.7640 | − | 16.0295i | −1.07503 | − | 0.620666i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.7520 | − | 7.93973i | 0.531683 | − | 0.306968i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.8785i | 0.574378i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 45.8308i | − | 1.76665i | −0.468764 | − | 0.883323i | \(-0.655301\pi\) | ||
0.468764 | − | 0.883323i | \(-0.344699\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.18218 | + | 0.682531i | −0.0455021 | + | 0.0262706i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.21947 | − | 5.57628i | 0.123734 | − | 0.214314i | −0.797503 | − | 0.603315i | \(-0.793846\pi\) |
0.921237 | + | 0.389001i | \(0.127180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.27940 | + | 23.9814i | −0.202605 | + | 0.920322i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.7736 | − | 23.8565i | 0.527804 | − | 0.914183i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.1415 | − | 13.3608i | 0.885486 | − | 0.511236i | 0.0130227 | − | 0.999915i | \(-0.495855\pi\) |
0.872463 | + | 0.488680i | \(0.162521\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.2671i | 0.888991i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8328 | 0.527754 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.30645 | + | 10.9231i | 0.240256 | + | 0.416136i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8343 | + | 9.71927i | 0.640406 | + | 0.369738i | 0.784771 | − | 0.619786i | \(-0.212781\pi\) |
−0.144365 | + | 0.989524i | \(0.546114\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0301760 | + | 0.137073i | −0.00114629 | + | 0.00520697i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.6728 | − | 41.0025i | 0.897962 | − | 1.55532i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9933 | − | 24.6593i | −0.492155 | − | 0.934039i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.7260 | 1.12434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.47798 | 0.131362 | 0.0656808 | − | 0.997841i | \(-0.479078\pi\) | ||||
0.0656808 | + | 0.997841i | \(0.479078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0502862 | + | 0.0290327i | −0.00189658 | + | 0.00109499i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.0912 | − | 39.9952i | 0.869666 | − | 1.50631i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.00663 | + | 1.26980i | −0.150685 | + | 0.0477556i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.6247 | + | 25.1867i | 1.63836 | + | 0.945907i | 0.981398 | + | 0.191983i | \(0.0614919\pi\) |
0.656961 | + | 0.753924i | \(0.271841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.604323 | + | 0.348906i | −0.0226639 | + | 0.0130850i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.1739 | −0.643167 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.7612 | −0.477243 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.8225 | + | 27.4054i | 0.590903 | + | 1.02347i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.2592 | − | 19.7796i | −1.27765 | − | 0.737653i | −0.301237 | − | 0.953549i | \(-0.597399\pi\) |
−0.976416 | + | 0.215896i | \(0.930733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.2955 | − | 34.2545i | 1.16550 | − | 1.27570i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.4748 | + | 22.7908i | 1.46808 | + | 0.847598i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.781229 | + | 0.451043i | −0.0290141 | + | 0.0167513i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.91826i | − | 0.182408i | −0.995832 | − | 0.0912042i | \(-0.970928\pi\) | ||
0.995832 | − | 0.0912042i | \(-0.0290716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.4552 | −1.01686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.7991 | + | 17.7819i | −1.13915 | + | 0.657687i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1875 | + | 21.1094i | −0.450156 | + | 0.779692i | −0.998395 | − | 0.0566289i | \(-0.981965\pi\) |
0.548240 | + | 0.836321i | \(0.315298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.5752 | + | 25.0158i | −0.426958 | + | 0.922722i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.71311 | + | 6.43130i | −0.136774 | + | 0.236900i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.07210 | − | 13.9813i | −0.296937 | − | 0.514310i | 0.678497 | − | 0.734604i | \(-0.262632\pi\) |
−0.975434 | + | 0.220294i | \(0.929298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.258229i | − | 0.00948627i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.5746 | 1.19504 | 0.597522 | − | 0.801852i | \(-0.296152\pi\) | ||||
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.6693 | − | 7.31463i | 0.464168 | − | 0.267987i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.319245 | + | 0.552949i | −0.0116806 | + | 0.0202313i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.36132 | + | 3.67913i | −0.122820 | + | 0.134432i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13907 | + | 1.23499i | 0.0780558 | + | 0.0450656i | 0.538520 | − | 0.842613i | \(-0.318984\pi\) |
−0.460464 | + | 0.887678i | \(0.652317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.09622 | + | 4.67436i | −0.295043 | + | 0.170343i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 21.0008i | − | 0.764297i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.24953i | 0.190797i | 0.995439 | + | 0.0953987i | \(0.0304126\pi\) | ||||
−0.995439 | + | 0.0953987i | \(0.969587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.04039 | − | 13.9264i | −0.291848 | − | 0.505495i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.17769 | − | 12.4321i | 0.260191 | − | 0.450664i | −0.706101 | − | 0.708111i | \(-0.749548\pi\) |
0.966293 | + | 0.257446i | \(0.0828811\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.8367 | − | 7.87133i | 0.899149 | − | 0.284961i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.453335 | + | 0.261733i | 0.0163903 | + | 0.00946297i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.9880 | − | 24.2418i | 1.51610 | − | 0.875320i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.8461 | −0.535365 | −0.267682 | − | 0.963507i | \(-0.586258\pi\) | ||||
−0.267682 | + | 0.963507i | \(0.586258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2802 | 0.406247 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.30467 | + | 4.21735i | −0.262731 | + | 0.151688i | −0.625580 | − | 0.780160i | \(-0.715137\pi\) |
0.362849 | + | 0.931848i | \(0.381804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.241621 | + | 0.418500i | −0.00867929 | + | 0.0150330i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.07321 | + | 9.41744i | −0.0743759 | + | 0.337849i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0933654 | − | 0.148177i | 0.00334516 | − | 0.00530899i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.16748 | + | 7.21829i | 0.149124 | + | 0.258291i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.1489 | −0.648589 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.82043i | 0.207740i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6135 | − | 20.1152i | −0.413976 | − | 0.717028i | 0.581344 | − | 0.813658i | \(-0.302527\pi\) |
−0.995320 | + | 0.0966299i | \(0.969194\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.1095 | − | 19.2422i | 0.395508 | − | 0.685041i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.5096 | − | 3.85467i | −0.622571 | − | 0.137056i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 70.0286 | + | 40.4310i | 2.48679 | + | 1.43575i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.51592 | + | 7.82181i | 0.160163 | + | 0.277411i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.0982 | −1.10156 | −0.550778 | − | 0.834652i | \(-0.685669\pi\) | ||||
−0.550778 | + | 0.834652i | \(0.685669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.0535 | −1.80614 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0191053 | + | 0.0110304i | −0.000675053 | + | 0.000389742i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.07702 | + | 5.24062i | 0.320321 | + | 0.184937i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.9711 | + | 53.5496i | 0.598154 | + | 1.88738i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.2307 | − | 23.2272i | −1.41619 | − | 0.817636i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.7653 | + | 24.6905i | −1.50355 | + | 0.868073i | −0.503555 | + | 0.863963i | \(0.667975\pi\) |
−0.999992 | + | 0.00411023i | \(0.998692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14547 | −0.0402230 | −0.0201115 | − | 0.999798i | \(-0.506402\pi\) | ||||
−0.0201115 | + | 0.999798i | \(0.506402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.9896i | 0.385423i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.3785 | + | 42.2247i | 0.853940 | + | 1.47907i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.193524 | − | 0.111731i | −0.00677055 | − | 0.00390898i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.563160 | + | 0.514513i | 0.0196784 | + | 0.0179786i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.1621 | + | 22.7974i | −0.459361 | + | 0.795636i | −0.998927 | − | 0.0463067i | \(-0.985255\pi\) |
0.539566 | + | 0.841943i | \(0.318588\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.1597 | − | 23.7635i | 1.43474 | − | 0.828345i | 0.437259 | − | 0.899336i | \(-0.355949\pi\) |
0.997477 | + | 0.0709909i | \(0.0226161\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.452485 | −0.0157535 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.2082i | − | 0.633160i | −0.948566 | − | 0.316580i | \(-0.897465\pi\) | ||
0.948566 | − | 0.316580i | \(-0.102535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4581 | + | 23.3101i | 0.467419 | + | 0.809594i | 0.999307 | − | 0.0372211i | \(-0.0118506\pi\) |
−0.531888 | + | 0.846815i | \(0.678517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9481 | − | 8.63027i | −0.518543 | − | 0.299381i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.3474 | − | 2.74540i | 1.05147 | − | 0.0951226i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.0787 | − | 23.7168i | −1.42159 | − | 0.820754i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.41974 | + | 4.86114i | −0.291029 | + | 0.168026i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.5300i | 1.19211i | 0.802944 | + | 0.596054i | \(0.203266\pi\) | ||||
−0.802944 | + | 0.596054i | \(0.796734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0065 | 0.586431 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.02247 | + | 10.4312i | 0.207425 | + | 0.359270i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.7693 | + | 34.2415i | −0.680085 | + | 1.17794i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.8032 | − | 19.4865i | 0.611726 | − | 0.669564i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.32083 | − | 4.22668i | −0.251250 | − | 0.145059i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.82599 | + | 17.0191i | 0.336831 | + | 0.583408i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.5341 | −0.874271 | −0.437136 | − | 0.899396i | \(-0.644007\pi\) | ||||
−0.437136 | + | 0.899396i | \(0.644007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.00328916i | 0.000112487i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.9384 | − | 48.3907i | −0.954358 | − | 1.65300i | −0.735831 | − | 0.677166i | \(-0.763208\pi\) |
−0.218527 | − | 0.975831i | \(-0.570125\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.44029 | − | 9.42285i | 0.185620 | − | 0.321504i | −0.758165 | − | 0.652063i | \(-0.773904\pi\) |
0.943785 | + | 0.330559i | \(0.107237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.70901 | − | 28.0450i | −0.262722 | − | 0.955772i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.39835 | + | 2.42201i | −0.0476003 | + | 0.0824462i | −0.888844 | − | 0.458210i | \(-0.848491\pi\) |
0.841244 | + | 0.540656i | \(0.181824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5343 | − | 33.8344i | −0.664186 | − | 1.15040i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.34612i | 0.113640i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.4664 | −0.456818 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.1801 | + | 34.9530i | 0.683777 | + | 1.18434i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.421421 | + | 0.243307i | 0.0142629 | + | 0.00823470i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.0879 | − | 6.18343i | −0.949544 | − | 0.209038i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.76745 | + | 13.4536i | −0.262288 | + | 0.454296i | −0.966850 | − | 0.255347i | \(-0.917810\pi\) |
0.704561 | + | 0.709643i | \(0.251144\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.2876 | + | 42.0674i | 0.819201 | + | 1.41890i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.58885 | −0.188293 | −0.0941465 | − | 0.995558i | \(-0.530012\pi\) | ||||
−0.0941465 | + | 0.995558i | \(0.530012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.5523i | − | 0.456070i | −0.973653 | − | 0.228035i | \(-0.926770\pi\) | ||
0.973653 | − | 0.228035i | \(-0.0732300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.0668 | − | 17.3591i | 1.01068 | − | 0.583519i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.04877 | + | 0.605507i | 0.0352142 | + | 0.0203309i | 0.517504 | − | 0.855681i | \(-0.326861\pi\) |
−0.482290 | + | 0.876012i | \(0.660195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.590833 | + | 0.130069i | 0.0198159 | + | 0.00436238i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.74601 | − | 4.47216i | −0.259501 | − | 0.149823i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.160395 | − | 0.277813i | −0.00536743 | − | 0.00929666i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0585i | 0.737334i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −87.3963 | −2.91808 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.56409 | + | 3.21243i | −0.185573 | + | 0.107140i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.99223 | − | 8.64680i | 0.166315 | − | 0.288067i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.3763 | + | 11.2116i | −1.17725 | + | 0.373098i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.8845 | − | 12.6350i | −0.727466 | − | 0.420003i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.99985 | − | 10.3921i | −0.199222 | − | 0.345062i | 0.749054 | − | 0.662508i | \(-0.230508\pi\) |
−0.948276 | + | 0.317446i | \(0.897175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0832907i | 0.00276258i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5560 | 0.449130 | 0.224565 | − | 0.974459i | \(-0.427904\pi\) | ||||
0.224565 | + | 0.974459i | \(0.427904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.6709 | + | 6.16083i | −0.353154 | + | 0.203894i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 50.1461 | + | 28.9519i | 1.65778 | + | 0.957120i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.6535 | − | 23.7008i | 0.715062 | − | 0.782671i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.2218 | + | 15.1392i | 0.864978 | + | 0.499395i | 0.865676 | − | 0.500605i | \(-0.166889\pi\) |
−0.000698268 | 1.00000i | \(0.500222\pi\) | ||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.4415 | − | 26.8130i | 1.53030 | − | 0.883519i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.2991 | 1.49104 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.552972 | 0.0181816 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.459730 | − | 0.796276i | −0.0150995 | − | 0.0261531i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.8118 | − | 10.8610i | −0.617197 | − | 0.356339i | 0.158580 | − | 0.987346i | \(-0.449308\pi\) |
−0.775777 | + | 0.631007i | \(0.782642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.110282 | + | 0.156513i | 0.00361435 | + | 0.00512952i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.5588 | + | 32.1448i | −0.607588 | + | 1.05237i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.05095 | + | 8.74850i | 0.165184 | + | 0.286106i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0546i | 1.21052i | 0.796027 | + | 0.605261i | \(0.206931\pi\) | ||||
−0.796027 | + | 0.605261i | \(0.793069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.2891 | 1.31478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.6032 | − | 37.4179i | −0.704245 | − | 1.21979i | −0.966963 | − | 0.254916i | \(-0.917952\pi\) |
0.262718 | − | 0.964873i | \(-0.415381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.1498 | − | 31.5991i | −1.63310 | − | 1.02901i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.4778 | + | 21.4497i | 0.763733 | + | 0.697760i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.9431 | + | 31.0783i | −0.583072 | + | 1.00991i | 0.412041 | + | 0.911165i | \(0.364816\pi\) |
−0.995113 | + | 0.0987443i | \(0.968517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.3320 | − | 28.4819i | 1.60138 | − | 0.924560i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8307 | −0.545774 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.40033 | 0.272113 | 0.136057 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136057 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.1054 | − | 24.3096i | 1.36250 | − | 0.786640i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.20994 | − | 3.00796i | −0.168413 | − | 0.0972335i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.5856 | − | 8.10867i | 0.826202 | − | 0.261843i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.7791 | − | 23.8661i | 0.444488 | − | 0.769875i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0493777 | + | 0.0855246i | 0.00159117 | + | 0.00275599i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 15.3460i | − | 0.494007i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.5090i | 1.81721i | 0.417660 | + | 0.908603i | \(0.362850\pi\) | ||||
−0.417660 | + | 0.908603i | \(0.637150\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.177029 | + | 0.102208i | −0.00568700 | + | 0.00328339i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.9521 | + | 10.9420i | 0.608202 | + | 0.351146i | 0.772262 | − | 0.635305i | \(-0.219125\pi\) |
−0.164059 | + | 0.986450i | \(0.552459\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −53.3384 | − | 11.7422i | −1.70995 | − | 0.376438i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.22959 | + | 2.12971i | −0.0393783 | + | 0.0682053i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.2467 | − | 10.5347i | 0.583764 | − | 0.337036i | −0.178864 | − | 0.983874i | \(-0.557242\pi\) |
0.762628 | + | 0.646838i | \(0.223909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.425734 | −0.0136065 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.516310i | − | 0.0164845i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.6247 | − | 18.4024i | −0.338874 | − | 0.586947i | 0.645347 | − | 0.763889i | \(-0.276713\pi\) |
−0.984221 | + | 0.176942i | \(0.943379\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1889 | + | 31.5041i | −0.579547 | + | 1.00381i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −52.0279 | − | 11.4537i | −1.65607 | − | 0.364576i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.8149 | + | 65.4973i | −1.20244 | + | 2.08269i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.9587 | + | 23.0702i | −1.26933 | + | 0.732848i | −0.974861 | − | 0.222813i | \(-0.928476\pi\) |
−0.294469 | + | 0.955661i | \(0.595143\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.4444 | −1.25173 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 39.2390i | − | 1.24396i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5535 | − | 11.8665i | 0.650935 | − | 0.375817i | −0.137880 | − | 0.990449i | \(-0.544029\pi\) |
0.788814 | + | 0.614632i | \(0.210695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.63467 | + | 5.56258i | 0.304827 | + | 0.175992i |
(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 | 1148.2.r.a.737.9 | yes | 56 | |
7.4 | even | 3 | inner | 1148.2.r.a.81.20 | yes | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.737.20 | yes | 56 | |
287.81 | even | 6 | inner | 1148.2.r.a.81.9 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.9 | ✓ | 56 | 287.81 | even | 6 | inner | |
1148.2.r.a.81.20 | yes | 56 | 7.4 | even | 3 | inner | |
1148.2.r.a.737.9 | yes | 56 | 1.1 | even | 1 | trivial | |
1148.2.r.a.737.20 | yes | 56 | 41.40 | even | 2 | inner |