Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(111,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([7, 0, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.bb (of order \(14\), degree \(6\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 111.5 | ||
Character | \(\chi\) | \(=\) | 784.111 |
Dual form | 784.2.bb.b.671.5 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{11}{14}\right)\) |
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 | ||||||||
\(3\) | −1.31050 | − | 1.64332i | −0.756618 | − | 0.948769i | 0.243157 | − | 0.969987i | \(-0.421817\pi\) |
−0.999775 | + | 0.0212178i | \(0.993246\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.883194 | + | 0.704324i | −0.394977 | + | 0.314983i | −0.800759 | − | 0.598986i | \(-0.795570\pi\) |
0.405783 | + | 0.913970i | \(0.366999\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18004 | + | 1.49914i | 0.823979 | + | 0.566621i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.315513 | + | 1.38235i | −0.105171 | + | 0.460784i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.37781 | − | 0.314477i | 0.415427 | − | 0.0948184i | −0.00969862 | − | 0.999953i | \(-0.503087\pi\) |
0.425125 | + | 0.905135i | \(0.360230\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.18274 | + | 1.18293i | −1.43743 | + | 0.328085i | −0.869069 | − | 0.494691i | \(-0.835281\pi\) |
−0.568365 | + | 0.822776i | \(0.692424\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.31485 | + | 0.528350i | 0.597693 | + | 0.136419i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.36325 | + | 6.98386i | −0.815708 | + | 1.69384i | −0.100486 | + | 0.994939i | \(0.532040\pi\) |
−0.715223 | + | 0.698897i | \(0.753675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00755 | 0.460565 | 0.230282 | − | 0.973124i | \(-0.426035\pi\) | ||||
0.230282 | + | 0.973124i | \(0.426035\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.393391 | − | 5.54712i | −0.0858450 | − | 1.21048i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.914165 | − | 1.89828i | −0.190617 | − | 0.395820i | 0.783655 | − | 0.621196i | \(-0.213353\pi\) |
−0.974272 | + | 0.225377i | \(0.927639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.828645 | + | 3.63053i | −0.165729 | + | 0.726106i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.99606 | + | 1.44283i | −0.576593 | + | 0.277672i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94415 | + | 2.38098i | 0.918106 | + | 0.442137i | 0.832395 | − | 0.554183i | \(-0.186969\pi\) |
0.0857115 | + | 0.996320i | \(0.472684\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.76273 | 1.75344 | 0.876719 | − | 0.481003i | \(-0.159727\pi\) | ||||
0.876719 | + | 0.481003i | \(0.159727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.32241 | − | 1.85206i | −0.404280 | − | 0.322403i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.98128 | + | 0.211427i | −0.503928 | + | 0.0357376i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.81066 | + | 1.35354i | 0.462070 | + | 0.222521i | 0.650411 | − | 0.759582i | \(-0.274597\pi\) |
−0.188341 | + | 0.982104i | \(0.560311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.73591 | + | 6.96666i | 1.39887 | + | 1.11556i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.681339 | + | 0.543349i | −0.106407 | + | 0.0848569i | −0.675248 | − | 0.737591i | \(-0.735963\pi\) |
0.568841 | + | 0.822448i | \(0.307392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.89477 | − | 3.10598i | −0.593947 | − | 0.473657i | 0.279786 | − | 0.960062i | \(-0.409736\pi\) |
−0.873733 | + | 0.486405i | \(0.838308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.694965 | − | 1.44311i | −0.103599 | − | 0.215126i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.75189 | + | 12.0568i | 0.401404 | + | 1.75866i | 0.621723 | + | 0.783237i | \(0.286433\pi\) |
−0.220319 | + | 0.975428i | \(0.570710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.50517 | + | 6.53637i | 0.357882 | + | 0.933767i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.8842 | − | 3.62547i | 2.22424 | − | 0.507668i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.52933 | − | 2.66278i | 0.759511 | − | 0.365761i | −0.0137031 | − | 0.999906i | \(-0.504362\pi\) |
0.773214 | + | 0.634145i | \(0.218648\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.995384 | + | 1.24817i | −0.134218 | + | 0.168303i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.63090 | − | 3.29905i | −0.348472 | − | 0.436970i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.75057 | + | 2.19514i | −0.227904 | + | 0.285783i | −0.882615 | − | 0.470097i | \(-0.844219\pi\) |
0.654711 | + | 0.755880i | \(0.272790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.33760 | − | 4.85407i | 0.299298 | − | 0.621500i | −0.696034 | − | 0.718009i | \(-0.745054\pi\) |
0.995332 | + | 0.0965096i | \(0.0307678\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.76017 | + | 2.54059i | −0.347749 | + | 0.320084i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.74420 | − | 4.69508i | 0.464411 | − | 0.582353i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.28419i | 0.767736i | 0.923388 | + | 0.383868i | \(0.125408\pi\) | ||||
−0.923388 | + | 0.383868i | \(0.874592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.92147 | + | 3.98997i | −0.231317 | + | 0.480336i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.36050 | − | 2.82510i | −0.161461 | − | 0.335278i | 0.804505 | − | 0.593946i | \(-0.202431\pi\) |
−0.965966 | + | 0.258668i | \(0.916716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.8418 | + | 2.93106i | 1.50302 | + | 0.343055i | 0.893264 | − | 0.449533i | \(-0.148409\pi\) |
0.609758 | + | 0.792588i | \(0.291267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.05205 | − | 3.39609i | 0.814301 | − | 0.392146i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.47514 | + | 1.37996i | 0.396029 | + | 0.157261i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.3351i | − | 1.16279i | −0.813622 | − | 0.581395i | \(-0.802507\pi\) | ||
0.813622 | − | 0.581395i | \(-0.197493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1298 | + | 4.87827i | 1.12554 | + | 0.542030i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.14760 | + | 9.40925i | −0.235730 | + | 1.03280i | 0.709067 | + | 0.705141i | \(0.249116\pi\) |
−0.944796 | + | 0.327658i | \(0.893741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.94850 | − | 8.53693i | −0.211344 | − | 0.925960i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.56662 | − | 11.2451i | −0.275170 | − | 1.20560i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.5995 | − | 3.10399i | −1.44154 | − | 0.329023i | −0.570933 | − | 0.820997i | \(-0.693418\pi\) |
−0.870610 | + | 0.491974i | \(0.836275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0720 | − | 5.19081i | −1.37031 | − | 0.544145i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.7941 | − | 16.0433i | −1.32668 | − | 1.66361i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.77306 | + | 1.41397i | −0.181912 | + | 0.145070i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89447i | 0.496958i | 0.968637 | + | 0.248479i | \(0.0799308\pi\) | ||||
−0.968637 | + | 0.248479i | \(0.920069\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00385i | 0.201394i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.9356 | + | 10.3158i | −1.28714 | + | 1.02646i | −0.289544 | + | 0.957165i | \(0.593504\pi\) |
−0.997596 | + | 0.0692955i | \(0.977925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.29632 | + | 4.13345i | 0.324796 | + | 0.407281i | 0.917243 | − | 0.398328i | \(-0.130410\pi\) |
−0.592447 | + | 0.805609i | \(0.701838\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.25441 | + | 4.62211i | 0.415188 | + | 0.451072i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0461 | − | 2.74945i | −1.16454 | − | 0.265800i | −0.403797 | − | 0.914848i | \(-0.632310\pi\) |
−0.760747 | + | 0.649049i | \(0.775167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.990406 | + | 4.33925i | 0.0948637 | + | 0.415625i | 0.999954 | − | 0.00959447i | \(-0.00305406\pi\) |
−0.905090 | + | 0.425219i | \(0.860197\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.45908 | − | 6.39263i | −0.138489 | − | 0.606762i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.554152 | + | 2.42790i | −0.0521303 | + | 0.228398i | −0.994282 | − | 0.106790i | \(-0.965943\pi\) |
0.942151 | + | 0.335188i | \(0.108800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14439 | + | 1.03269i | 0.199966 | + | 0.0962984i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7.53761i | − | 0.696852i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.8018 | + | 10.1831i | −1.63189 | + | 0.933487i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.11118 | + | 3.90614i | −0.737380 | + | 0.355104i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.78579 | + | 0.407595i | 0.161019 | + | 0.0367516i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.27589 | − | 8.87899i | −0.382448 | − | 0.794161i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.39015 | − | 11.1928i | 0.478299 | − | 0.993197i | −0.512605 | − | 0.858624i | \(-0.671320\pi\) |
0.990904 | − | 0.134573i | \(-0.0429662\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4707i | 0.921896i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.01964 | − | 7.54838i | 0.525938 | − | 0.659505i | −0.445920 | − | 0.895073i | \(-0.647123\pi\) |
0.971858 | + | 0.235567i | \(0.0756948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.37656 | + | 3.00960i | 0.379496 | + | 0.260965i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.62989 | − | 3.38450i | 0.140278 | − | 0.291291i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.75603 | + | 8.47179i | −0.577206 | + | 0.723794i | −0.981634 | − | 0.190776i | \(-0.938899\pi\) |
0.404427 | + | 0.914570i | \(0.367471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.06030 | − | 8.85333i | −0.598846 | − | 0.750930i | 0.386351 | − | 0.922352i | \(-0.373735\pi\) |
−0.985198 | + | 0.171422i | \(0.945164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.2068 | − | 20.3227i | 1.36486 | − | 1.71148i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.76885 | + | 3.25971i | −0.566040 | + | 0.272590i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.04363 | + | 1.37942i | −0.501896 | + | 0.114554i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.45829 | − | 12.6827i | 0.615149 | − | 1.04605i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.64512 | + | 11.5890i | 0.216697 | + | 0.949410i | 0.959900 | + | 0.280344i | \(0.0904485\pi\) |
−0.743203 | + | 0.669066i | \(0.766694\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.130043 | − | 0.270038i | −0.0105828 | − | 0.0219754i | 0.895610 | − | 0.444839i | \(-0.146739\pi\) |
−0.906193 | + | 0.422864i | \(0.861025\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.59301 | − | 6.85270i | −0.694704 | − | 0.554008i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.62239 | + | 6.87613i | −0.692567 | + | 0.552304i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.39102 | + | 1.10930i | 0.111016 | + | 0.0885321i | 0.677424 | − | 0.735592i | \(-0.263096\pi\) |
−0.566409 | + | 0.824125i | \(0.691668\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6220 | − | 5.59685i | −0.921683 | − | 0.443859i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.852869 | − | 5.50880i | 0.0672155 | − | 0.434154i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.68761 | + | 2.14330i | 0.210510 | + | 0.167876i | 0.723069 | − | 0.690776i | \(-0.242731\pi\) |
−0.512559 | + | 0.858652i | \(0.671302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.35559 | 0.261233 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.87138 | − | 3.30908i | −0.531724 | − | 0.256065i | 0.148702 | − | 0.988882i | \(-0.452491\pi\) |
−0.680425 | + | 0.732817i | \(0.738205\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7489 | − | 6.62112i | 1.05761 | − | 0.509317i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.633410 | + | 2.77515i | −0.0484381 | + | 0.212221i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.15031 | − | 14.8478i | −0.543628 | − | 1.12885i | −0.974072 | − | 0.226238i | \(-0.927357\pi\) |
0.430444 | − | 0.902617i | \(-0.358357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.24914 | + | 6.67246i | −0.547984 | + | 0.504390i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.90143 | 0.443578 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.55426 | + | 13.6101i | −0.489888 | + | 1.01726i | 0.498722 | + | 0.866762i | \(0.333803\pi\) |
−0.988610 | + | 0.150501i | \(0.951911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0580 | − | 3.89337i | −1.26791 | − | 0.289392i | −0.464902 | − | 0.885362i | \(-0.653910\pi\) |
−0.803007 | + | 0.595970i | \(0.796768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0402 | + | 2.51985i | −0.816114 | + | 0.186273i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.43570 | + | 0.784175i | −0.252597 | + | 0.0576537i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.43767 | + | 10.6801i | −0.178260 | + | 0.781008i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.69454 | − | 1.34608i | −0.632435 | − | 0.0979132i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.384152 | + | 0.306351i | −0.0277963 | + | 0.0221668i | −0.637289 | − | 0.770625i | \(-0.719944\pi\) |
0.609493 | + | 0.792791i | \(0.291373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.60979 | + | 4.52653i | 0.259838 | + | 0.325827i | 0.894589 | − | 0.446890i | \(-0.147469\pi\) |
−0.634751 | + | 0.772717i | \(0.718897\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.6223 | −0.903901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3913 | 1.31033 | 0.655163 | − | 0.755488i | \(-0.272600\pi\) | ||||
0.655163 | + | 0.755488i | \(0.272600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6929 | − | 17.1704i | −0.970665 | − | 1.21717i | −0.976129 | − | 0.217190i | \(-0.930311\pi\) |
0.00546475 | − | 0.999985i | \(-0.498261\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3269 | − | 8.23543i | 0.728404 | − | 0.580883i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.20905 | + | 12.6026i | 0.505976 | + | 0.884529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.219060 | − | 0.959766i | 0.0152998 | − | 0.0670330i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.91253 | − | 0.664766i | 0.202435 | − | 0.0462044i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.76604 | − | 0.631330i | 0.191331 | − | 0.0436700i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3607 | + | 5.56018i | 1.67706 | + | 0.382779i | 0.952047 | − | 0.305953i | \(-0.0989751\pi\) |
0.725016 | + | 0.688732i | \(0.241832\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.85960 | + | 5.93802i | −0.195937 | + | 0.406867i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.62746 | 0.383789 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.2832 | + | 14.6357i | 1.44480 | + | 0.993534i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0126 | − | 24.9443i | −0.811734 | − | 1.68558i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.16946 | − | 40.1740i | 0.616805 | − | 2.70240i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4983 | − | 7.46358i | 1.03784 | − | 0.499798i | 0.164230 | − | 0.986422i | \(-0.447486\pi\) |
0.873612 | + | 0.486624i | \(0.161772\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.75723 | − | 2.29096i | −0.317148 | − | 0.152731i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.767670 | −0.0509521 | −0.0254760 | − | 0.999675i | \(-0.508110\pi\) | ||||
−0.0254760 | + | 0.999675i | \(0.508110\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4532 | + | 11.5260i | 0.955092 | + | 0.761660i | 0.971214 | − | 0.238210i | \(-0.0765606\pi\) |
−0.0161221 | + | 0.999870i | \(0.505132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.28646 | − | 7.51919i | −0.150438 | − | 0.494726i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6669 | − | 7.06322i | −0.960862 | − | 0.462727i | −0.113380 | − | 0.993552i | \(-0.536168\pi\) |
−0.847481 | + | 0.530825i | \(0.821882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9223 | − | 8.71028i | −0.712495 | − | 0.568196i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9838 | + | 13.5442i | −1.10322 | + | 0.879788i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.56441 | + | 4.43747i | 0.359932 | + | 0.287036i | 0.786713 | − | 0.617319i | \(-0.211781\pi\) |
−0.426781 | + | 0.904355i | \(0.640353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.257898 | + | 0.535531i | 0.0166127 | + | 0.0344966i | 0.909110 | − | 0.416556i | \(-0.136763\pi\) |
−0.892497 | + | 0.451053i | \(0.851049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.03871 | − | 13.3135i | −0.194934 | − | 0.854060i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.81628 | − | 4.00843i | −0.435476 | − | 0.256089i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4046 | + | 2.37479i | −0.662031 | + | 0.151104i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.2768 | − | 8.80165i | 1.15825 | − | 0.557782i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.97401 | − | 11.2531i | 0.566434 | − | 0.710286i | −0.413298 | − | 0.910596i | \(-0.635623\pi\) |
0.979733 | + | 0.200309i | \(0.0641947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.85652 | − | 2.32800i | −0.116718 | − | 0.146360i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.4754 | + | 14.3896i | −0.718615 | + | 0.901115i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.68198 | − | 15.9518i | 0.479189 | − | 0.995046i | −0.511549 | − | 0.859254i | \(-0.670928\pi\) |
0.990737 | − | 0.135791i | \(-0.0433577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.09822 | + | 7.16435i | 0.254651 | + | 0.445171i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.85130 | + | 6.08334i | −0.300288 | + | 0.376549i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.63281i | 0.100683i | 0.998732 | + | 0.0503416i | \(0.0160310\pi\) | ||||
−0.998732 | + | 0.0503416i | \(0.983969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00801 | + | 6.24619i | −0.184780 | + | 0.383700i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7213 | + | 26.4160i | 0.778531 | + | 1.61664i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.36730 | + | 0.540321i | 0.144337 | + | 0.0329439i | 0.294079 | − | 0.955781i | \(-0.404987\pi\) |
−0.149742 | + | 0.988725i | \(0.547844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.12411 | − | 0.541345i | 0.0682850 | − | 0.0328843i | −0.399430 | − | 0.916764i | \(-0.630792\pi\) |
0.467715 | + | 0.883880i | \(0.345078\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.60069 | + | 28.2840i | 0.520537 | + | 1.71182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.26278i | 0.317358i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.4147 | + | 11.2759i | 1.40685 | + | 0.677505i | 0.974539 | − | 0.224219i | \(-0.0719829\pi\) |
0.432314 | + | 0.901723i | \(0.357697\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.08027 | + | 13.4955i | −0.184411 | + | 0.807957i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.26857 | − | 9.93924i | −0.135331 | − | 0.592925i | −0.996425 | − | 0.0844793i | \(-0.973077\pi\) |
0.861094 | − | 0.508446i | \(-0.169780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.40148 | + | 10.5216i | 0.142753 | + | 0.625442i | 0.994789 | + | 0.101958i | \(0.0325107\pi\) |
−0.852036 | + | 0.523484i | \(0.824632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.64720 | + | 1.06069i | 0.275276 | + | 0.0628300i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.29990 | + | 0.163105i | −0.135759 | + | 0.00962777i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.8635 | − | 33.6858i | −1.58021 | − | 1.98152i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.04317 | − | 6.41421i | 0.471499 | − | 0.376008i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.437380i | 0.0255520i | 0.999918 | + | 0.0127760i | \(0.00406684\pi\) | ||||
−0.999918 | + | 0.0127760i | \(0.995933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.17170i | − | 0.184664i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.67428 | + | 2.93014i | −0.213203 | + | 0.170024i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.98342 | + | 8.75693i | 0.403861 | + | 0.506426i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.83448 | − | 12.6100i | −0.221016 | − | 0.726826i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.9042 | + | 7.73842i | 1.94775 | + | 0.444561i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.35428 | + | 5.93351i | 0.0775461 | + | 0.339752i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.56510 | − | 28.7636i | −0.374690 | − | 1.64162i | −0.713417 | − | 0.700739i | \(-0.752854\pi\) |
0.338727 | − | 0.940885i | \(-0.390004\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.47274 | − | 10.8338i | 0.140669 | − | 0.616312i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3742 | − | 9.81170i | −1.15531 | − | 0.556370i | −0.244689 | − | 0.969602i | \(-0.578686\pi\) |
−0.910626 | + | 0.413231i | \(0.864400\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.98244i | − | 0.507717i | −0.967241 | − | 0.253859i | \(-0.918300\pi\) | ||
0.967241 | − | 0.253859i | \(-0.0816998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.648367 | − | 4.18789i | 0.0365313 | − | 0.235961i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.5066 | + | 8.43074i | −0.983270 | + | 0.473518i | −0.855228 | − | 0.518251i | \(-0.826583\pi\) |
−0.128041 | + | 0.991769i | \(0.540869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.56089 | + | 1.72572i | 0.423328 | + | 0.0966219i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.2683 | + | 23.3988i | 0.628933 | + | 1.30599i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.75191 | + | 14.0205i | −0.375686 | + | 0.780121i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 19.7963i | − | 1.09810i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.83284 | − | 7.31415i | 0.322557 | − | 0.404473i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0756 | + | 30.4098i | −0.665748 | + | 1.67655i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.66278 | + | 3.45280i | −0.0913946 | + | 0.189783i | −0.941655 | − | 0.336579i | \(-0.890730\pi\) |
0.850261 | + | 0.526362i | \(0.176444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.75788 | + | 3.45827i | −0.151131 | + | 0.189512i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.42610 | − | 5.55016i | −0.241824 | − | 0.303238i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.2172 | + | 17.8278i | −0.774462 | + | 0.971144i | −0.999995 | − | 0.00309116i | \(-0.999016\pi\) |
0.225534 | + | 0.974235i | \(0.427587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.71603 | − | 2.27112i | 0.256139 | − | 0.123350i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4512 | − | 3.07016i | 0.728425 | − | 0.166258i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.33753 | + | 18.0052i | −0.234205 | + | 0.972187i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.11320 | − | 4.87725i | −0.0599327 | − | 0.262582i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.473626 | + | 0.983495i | 0.0254256 | + | 0.0527968i | 0.913295 | − | 0.407299i | \(-0.133529\pi\) |
−0.887869 | + | 0.460096i | \(0.847815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3887 | + | 12.2721i | 0.823741 | + | 0.656911i | 0.941829 | − | 0.336092i | \(-0.109105\pi\) |
−0.118088 | + | 0.993003i | \(0.537677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8211 | − | 11.0219i | 0.737714 | − | 0.588307i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4385 | + | 20.2865i | 1.35396 | + | 1.07974i | 0.988872 | + | 0.148769i | \(0.0475310\pi\) |
0.365084 | + | 0.930975i | \(0.381040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.19137 | + | 1.53688i | 0.169380 | + | 0.0815692i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 40.0634 | + | 15.9090i | 2.12038 | + | 0.841992i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.6266 | + | 18.8416i | 1.24697 | + | 0.994422i | 0.999675 | + | 0.0254811i | \(0.00811177\pi\) |
0.247291 | + | 0.968941i | \(0.420460\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9697 | −0.787880 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.0487 | + | 8.21024i | 0.894827 | + | 0.430926i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.4062 | + | 6.45611i | −0.701715 | + | 0.337928i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.409354 | + | 1.79350i | −0.0213681 | + | 0.0936198i | −0.984488 | − | 0.175454i | \(-0.943861\pi\) |
0.963119 | + | 0.269074i | \(0.0867177\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.536130 | − | 1.11328i | −0.0279098 | − | 0.0579553i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.0460 | + | 2.48424i | 0.833069 | + | 0.128975i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0289 | −1.14061 | −0.570307 | − | 0.821432i | \(-0.693176\pi\) | ||||
−0.570307 | + | 0.821432i | \(0.693176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.98742 | + | 18.6626i | −0.464108 | + | 0.963731i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.4408 | − | 6.49143i | −1.46478 | − | 0.334325i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0539 | − | 3.43596i | 0.773267 | − | 0.176493i | 0.182359 | − | 0.983232i | \(-0.441627\pi\) |
0.590908 | + | 0.806739i | \(0.298770\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.4571 | + | 5.81041i | −1.30420 | + | 0.297676i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.04751 | − | 4.58942i | 0.0535251 | − | 0.234509i | −0.941089 | − | 0.338160i | \(-0.890195\pi\) |
0.994614 | + | 0.103651i | \(0.0330526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.04116 | + | 1.22885i | −0.205957 | + | 0.0626280i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.52241 | − | 4.40397i | 0.280720 | − | 0.223867i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.63767 | − | 9.57733i | −0.387245 | − | 0.485590i | 0.549554 | − | 0.835458i | \(-0.314798\pi\) |
−0.936799 | + | 0.349868i | \(0.886226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3319 | 0.825941 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.2931 | −1.02365 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.27926 | + | 9.12790i | 0.366259 | + | 0.459275i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.5331 | + | 10.7923i | −0.679205 | + | 0.541648i | −0.901202 | − | 0.433399i | \(-0.857314\pi\) |
0.221997 | + | 0.975047i | \(0.428743\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.789755 | − | 11.1362i | −0.0395372 | − | 0.557505i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.64332 | + | 11.5811i | −0.132001 | + | 0.578334i | 0.865056 | + | 0.501675i | \(0.167283\pi\) |
−0.997057 | + | 0.0766593i | \(0.975575\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.5977 | + | 11.5486i | −2.52045 | + | 0.575277i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.3825 | + | 2.82622i | −0.615291 | + | 0.140436i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.29823 | + | 0.981043i | 0.213055 | + | 0.0486285i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.21686 | + | 19.1390i | −0.455744 | + | 0.946363i | 0.538838 | + | 0.842410i | \(0.318864\pi\) |
−0.994582 | + | 0.103953i | \(0.966851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.7756 | 1.12344 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.10712 | + | 2.16116i | −0.349719 | + | 0.106344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.73041 | − | 9.82280i | −0.232207 | − | 0.482182i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.29630 | + | 23.2046i | −0.259361 | + | 1.13633i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1126 | − | 4.86999i | 0.494034 | − | 0.237914i | −0.170241 | − | 0.985402i | \(-0.554455\pi\) |
0.664275 | + | 0.747488i | \(0.268740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2597 | + | 5.90397i | 0.597502 | + | 0.287742i | 0.708087 | − | 0.706125i | \(-0.249558\pi\) |
−0.110586 | + | 0.993867i | \(0.535273\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.5350 | −0.852581 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.5682 | − | 17.9975i | −1.09472 | − | 0.873008i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3730 | − | 7.07770i | 0.598770 | − | 0.342514i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.2273 | + | 6.85152i | 0.686901 | + | 0.330794i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.95681 | − | 1.56050i | −0.0942562 | − | 0.0751668i | 0.575228 | − | 0.817993i | \(-0.304913\pi\) |
−0.669484 | + | 0.742826i | \(0.733485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.0486 | − | 23.1655i | 1.39599 | − | 1.11326i | 0.417102 | − | 0.908860i | \(-0.363046\pi\) |
0.978887 | − | 0.204404i | \(-0.0655257\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.1870 | + | 8.12386i | 0.488429 | + | 0.389509i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.83524 | − | 3.81091i | −0.0877913 | − | 0.182301i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.98456 | − | 39.3639i | −0.428810 | − | 1.87874i | −0.475308 | − | 0.879819i | \(-0.657664\pi\) |
0.0464989 | − | 0.998918i | \(-0.485194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.82598 | + | 1.40072i | −0.467904 | + | 0.0667012i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.3401 | + | 7.38141i | −1.53652 | + | 0.350702i | −0.905257 | − | 0.424864i | \(-0.860322\pi\) |
−0.631267 | + | 0.775566i | \(0.717465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1972 | − | 6.83701i | 0.673012 | − | 0.324105i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5780 | − | 19.5342i | 0.736814 | − | 0.923936i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.7080 | + | 13.4274i | 0.505340 | + | 0.633677i | 0.967425 | − | 0.253159i | \(-0.0814697\pi\) |
−0.462084 | + | 0.886836i | \(0.652898\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.767887 | + | 0.962900i | −0.0361584 | + | 0.0453412i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.273336 | + | 0.567588i | −0.0128424 | + | 0.0266676i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.2011 | − | 4.62241i | 0.712639 | − | 0.216702i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.5001 | − | 28.2142i | 1.05251 | − | 1.31980i | 0.106982 | − | 0.994261i | \(-0.465881\pi\) |
0.945527 | − | 0.325544i | \(-0.105547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 25.7767i | − | 1.20315i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.28244 | + | 15.1222i | −0.339177 | + | 0.704309i | −0.998885 | − | 0.0472136i | \(-0.984966\pi\) |
0.659708 | + | 0.751522i | \(0.270680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.38682 | − | 2.87977i | −0.0644511 | − | 0.133834i | 0.866255 | − | 0.499602i | \(-0.166521\pi\) |
−0.930706 | + | 0.365768i | \(0.880806\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.5993 | + | 5.15814i | 1.04802 | + | 0.239203i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.30490 | − | 0.628409i | 0.0603838 | − | 0.0290793i | −0.403448 | − | 0.915002i | \(-0.632188\pi\) |
0.463832 | + | 0.885923i | \(0.346474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.42086 | + | 13.6998i | −0.435015 | + | 0.632598i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 3.73964i | − | 0.172313i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.34303 | − | 3.05464i | −0.291653 | − | 0.140453i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.66355 | + | 7.28849i | −0.0763289 | + | 0.334419i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.93633 | + | 8.48362i | 0.0886585 | + | 0.388438i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.39019 | + | 23.6160i | 0.246284 | + | 1.07904i | 0.935178 | + | 0.354179i | \(0.115239\pi\) |
−0.688894 | + | 0.724862i | \(0.741903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1681 | − | 3.69026i | −0.737201 | − | 0.168261i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.1704 | + | 5.81776i | −0.462769 | + | 0.264717i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.44729 | − | 4.32277i | −0.156534 | − | 0.196287i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2132 | − | 26.4866i | 1.50503 | − | 1.20022i | 0.583383 | − | 0.812197i | \(-0.301729\pi\) |
0.921649 | − | 0.388025i | \(-0.126843\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.22539i | − | 0.326743i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.14568i | 0.367610i | 0.982963 | + | 0.183805i | \(0.0588414\pi\) | ||||
−0.982963 | + | 0.183805i | \(0.941159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.2569 | + | 26.5215i | −1.49781 | + | 1.19447i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.41136 | − | 1.76979i | −0.0634358 | − | 0.0795460i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.26927 | − | 8.19841i | 0.0569347 | − | 0.367749i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6155 | + | 6.53130i | 1.28101 | + | 0.292381i | 0.808264 | − | 0.588820i | \(-0.200407\pi\) |
0.472742 | + | 0.881201i | \(0.343264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.56708 | + | 15.6284i | 0.159366 | + | 0.698226i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.94965 | − | 17.3046i | −0.176106 | − | 0.771572i | −0.983404 | − | 0.181428i | \(-0.941928\pi\) |
0.807298 | − | 0.590144i | \(-0.200929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.15899 | − | 18.2217i | 0.185072 | − | 0.810855i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.8986 | − | 13.9168i | −1.28343 | − | 0.618067i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.45317i | − | 0.108735i | −0.998521 | − | 0.0543674i | \(-0.982686\pi\) | ||
0.998521 | − | 0.0543674i | \(-0.0173142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.6017 | + | 25.6415i | 1.04408 | + | 1.13431i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.01476 | + | 2.89656i | −0.265558 | + | 0.127886i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.82257 | − | 1.32896i | −0.256573 | − | 0.0585612i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.58317 | + | 15.7466i | 0.333508 | + | 0.692536i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0291 | + | 31.2082i | −0.659704 | + | 1.36989i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.1331i | − | 1.75827i | −0.476577 | − | 0.879133i | \(-0.658123\pi\) | ||
0.476577 | − | 0.879133i | \(-0.341877\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6480 | − | 18.3680i | 0.640511 | − | 0.803175i | −0.350556 | − | 0.936542i | \(-0.614007\pi\) |
0.991067 | + | 0.133367i | \(0.0425788\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.4650 | + | 3.16837i | 0.893165 | + | 0.138279i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.8345 | + | 68.1816i | −1.43029 | + | 2.97004i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5725 | − | 14.5114i | 0.503151 | − | 0.630932i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.48213 | − | 3.11250i | −0.107715 | − | 0.135071i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.88846 | − | 3.62201i | 0.125113 | − | 0.156887i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5756 | − | 6.05608i | 0.543690 | − | 0.261827i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.9550 | − | 7.06528i | 1.33581 | − | 0.304889i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.50720 | + | 8.21808i | 0.237212 | + | 0.353978i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.919204 | + | 4.02730i | 0.0395197 | + | 0.173147i | 0.990836 | − | 0.135068i | \(-0.0431254\pi\) |
−0.951317 | + | 0.308215i | \(0.900268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.9564 | + | 33.1339i | 0.684757 | + | 1.42191i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.93096 | − | 3.13484i | −0.168384 | − | 0.134282i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.03753 | + | 1.62488i | −0.0871185 | + | 0.0694747i | −0.666081 | − | 0.745880i | \(-0.732029\pi\) |
0.578962 | + | 0.815354i | \(0.303458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.97249 | + | 4.76290i | 0.254900 | + | 0.203276i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.92566 | + | 4.77995i | 0.422847 | + | 0.203633i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.4937 | − | 22.5310i | 0.658861 | − | 0.958114i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.79113 | + | 4.61827i | 0.245820 | + | 0.196035i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.6655 | 1.38408 | 0.692040 | − | 0.721859i | \(-0.256712\pi\) | ||||
0.692040 | + | 0.721859i | \(0.256712\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.8597 | + | 11.4902i | 1.00916 | + | 0.485986i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.7454 | − | 9.99046i | 0.875871 | − | 0.421797i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.32661 | + | 40.8626i | −0.393070 | + | 1.72215i | 0.260666 | + | 0.965429i | \(0.416058\pi\) |
−0.653736 | + | 0.756723i | \(0.726799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.22060 | − | 2.53461i | −0.0513512 | − | 0.106632i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.7703 | + | 25.8208i | 0.620293 | + | 1.08437i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.88304 | 0.204708 | 0.102354 | − | 0.994748i | \(-0.467363\pi\) | ||||
0.102354 | + | 0.994748i | \(0.467363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.54974 | + | 7.37110i | −0.148552 | + | 0.308471i | −0.961945 | − | 0.273243i | \(-0.911904\pi\) |
0.813393 | + | 0.581714i | \(0.197618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.00686 | + | 0.229810i | 0.0420623 | + | 0.00960046i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.64930 | − | 1.74590i | 0.318998 | − | 0.0728091i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.9450 | + | 2.72637i | −0.497278 | + | 0.113500i | −0.463802 | − | 0.885939i | \(-0.653515\pi\) |
−0.0334761 | + | 0.999440i | \(0.510658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.70789 | − | 11.8640i | 0.112536 | − | 0.493053i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.7876 | + | 17.2930i | −0.779442 | + | 0.717435i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.78100 | − | 5.40767i | 0.280840 | − | 0.223963i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.30892 | + | 6.65717i | 0.219497 | + | 0.275240i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.7289 | −1.68106 | −0.840532 | − | 0.541762i | \(-0.817757\pi\) | ||||
−0.840532 | + | 0.541762i | \(0.817757\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.5992 | 0.807572 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.1018 | − | 30.2227i | −0.991416 | − | 1.24320i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.10605 | + | 2.47699i | −0.127550 | + | 0.101718i | −0.685187 | − | 0.728367i | \(-0.740280\pi\) |
0.557637 | + | 0.830085i | \(0.311708\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.55022 | − | 21.5319i | 0.350525 | − | 0.882723i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.2718 | + | 45.0036i | −0.420396 | + | 1.84187i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.26110 | − | 0.516081i | 0.0923860 | − | 0.0210865i | −0.176078 | − | 0.984376i | \(-0.556341\pi\) |
0.268464 | + | 0.963290i | \(0.413484\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.5657 | − | 7.20466i | 1.28759 | − | 0.293884i | 0.476692 | − | 0.879070i | \(-0.341836\pi\) |
0.810899 | + | 0.585186i | \(0.198979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.68697 | − | 1.98274i | −0.353761 | − | 0.0807435i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.41256 | − | 9.16278i | 0.179396 | − | 0.372520i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.78007 | 0.112839 | 0.0564197 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564197 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.2626 | − | 28.3625i | 0.456383 | − | 1.14931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.5246 | − | 59.2320i | −1.15398 | − | 2.39627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49305 | − | 6.54148i | 0.0603037 | − | 0.264208i | −0.935784 | − | 0.352573i | \(-0.885307\pi\) |
0.996088 | + | 0.0883647i | \(0.0281641\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.86428 | + | 0.897789i | −0.0751750 | + | 0.0362024i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.3188 | − | 17.4902i | −1.46214 | − | 0.704130i | −0.477485 | − | 0.878640i | \(-0.658452\pi\) |
−0.984655 | + | 0.174510i | \(0.944166\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.8051 | 0.956807 | 0.478404 | − | 0.878140i | \(-0.341216\pi\) | ||||
0.478404 | + | 0.878140i | \(0.341216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.47780 | + | 4.36840i | 0.219816 | + | 0.175298i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.9941 | − | 27.1543i | −1.00137 | − | 1.08792i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.74544 | − | 3.24843i | −0.269818 | − | 0.129937i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.66237 | − | 3.71812i | −0.186197 | − | 0.148487i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.9059 | + | 15.0770i | −0.753829 | + | 0.601158i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.9141 | + | 11.0961i | 0.553912 | + | 0.441730i | 0.860015 | − | 0.510268i | \(-0.170454\pi\) |
−0.306104 | + | 0.951998i | \(0.599025\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.7876 | − | 47.3190i | −0.905728 | − | 1.88076i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.12278 | + | 13.6818i | 0.123924 | + | 0.542946i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.7157 | − | 30.9129i | −0.820786 | − | 1.22481i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.33454 | − | 0.989331i | 0.171472 | − | 0.0391373i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7689 | − | 11.4465i | 0.938815 | − | 0.452109i | 0.0990637 | − | 0.995081i | \(-0.468415\pi\) |
0.839751 | + | 0.542972i | \(0.182701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.3736 | + | 31.8175i | −1.00064 | + | 1.25476i | −0.0337830 | + | 0.999429i | \(0.510756\pi\) |
−0.966854 | + | 0.255330i | \(0.917816\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.37479 | − | 9.24769i | −0.290382 | − | 0.364127i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.9231 | − | 28.7447i | 0.901200 | − | 1.13007i | −0.0897665 | − | 0.995963i | \(-0.528612\pi\) |
0.990967 | − | 0.134107i | \(-0.0428165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72163 | + | 3.57501i | −0.0675800 | + | 0.140331i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.84057 | − | 54.1551i | −0.150524 | − | 2.12250i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.3146 | − | 34.2514i | 1.06890 | − | 1.34036i | 0.131812 | − | 0.991275i | \(-0.457920\pi\) |
0.937090 | − | 0.349087i | \(-0.113508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.9065i | 0.426151i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.10353 | + | 16.8271i | −0.316149 | + | 0.656490i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.57366 | − | 15.7269i | −0.295028 | − | 0.612632i | 0.699785 | − | 0.714354i | \(-0.253279\pi\) |
−0.994813 | + | 0.101722i | \(0.967565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.6580 | + | 4.71504i | 0.803501 | + | 0.183394i | 0.604500 | − | 0.796605i | \(-0.293373\pi\) |
0.199001 | + | 0.979999i | \(0.436230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −78.0352 | + | 37.5798i | −3.03064 | + | 1.45948i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.98508 | + | 0.424451i | −0.232092 | + | 0.0164595i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.5620i | − | 0.447683i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.5755 | − | 15.6876i | −1.25944 | − | 0.606516i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.69428 | − | 7.42312i | 0.0654069 | − | 0.286566i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.41507 | + | 23.7250i | 0.208736 | + | 0.914531i | 0.965410 | + | 0.260738i | \(0.0839659\pi\) |
−0.756674 | + | 0.653792i | \(0.773177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.75556 | − | 12.0729i | −0.106061 | − | 0.464686i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.1885 | + | 7.34681i | 1.23710 | + | 0.282361i | 0.790551 | − | 0.612397i | \(-0.209794\pi\) |
0.446552 | + | 0.894757i | \(0.352652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.33749 | + | 10.6702i | −0.281587 | + | 0.409483i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00603 | + | 1.26153i | 0.0385513 | + | 0.0483418i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.4240 | + | 17.8825i | −0.858029 | + | 0.684255i | −0.950252 | − | 0.311483i | \(-0.899174\pi\) |
0.0922227 | + | 0.995738i | \(0.470603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.2407i | − | 0.467692i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 38.8560i | − | 1.48245i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.5072 | + | 20.3413i | −0.971747 | + | 0.774942i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.792354 | + | 0.993581i | 0.0301426 | + | 0.0377976i | 0.796674 | − | 0.604409i | \(-0.206591\pi\) |
−0.766532 | + | 0.642206i | \(0.778019\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.00404 | + | 4.36847i | −0.114114 | + | 0.165945i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4712 | + | 2.84648i | 0.473061 | + | 0.107973i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.50316 | − | 6.58580i | −0.0569364 | − | 0.249455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.61392 | + | 33.3587i | 0.287985 | + | 1.26174i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.34281 | + | 36.5522i | −0.315104 | + | 1.38056i | 0.530924 | + | 0.847420i | \(0.321845\pi\) |
−0.846027 | + | 0.533140i | \(0.821012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.64256 | + | 2.71731i | 0.212813 | + | 0.102485i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.3637i | 1.10590i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.6650 | + | 3.09664i | −1.64219 | + | 0.116461i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.97338 | − | 4.80293i | 0.374558 | − | 0.180378i | −0.237128 | − | 0.971479i | \(-0.576206\pi\) |
0.611686 | + | 0.791101i | \(0.290492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.2868 | + | 3.26086i | 0.535795 | + | 0.122292i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.92475 | − | 18.5324i | −0.334235 | − | 0.694045i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.68232 | − | 7.64642i | 0.137711 | − | 0.285960i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 14.9594i | − | 0.558669i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.2653 | + | 21.6501i | −0.643889 | + | 0.807411i | −0.991483 | − | 0.130234i | \(-0.958427\pi\) |
0.347594 | + | 0.937645i | \(0.386999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.989501 | + | 13.9527i | 0.0368509 | + | 0.519627i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.542072 | − | 1.12562i | 0.0201599 | − | 0.0418624i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.7412 | + | 15.9769i | −0.473195 | + | 0.593367i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4938 | − | 24.4445i | −0.722987 | − | 0.906597i | 0.275516 | − | 0.961296i | \(-0.411151\pi\) |
−0.998503 | + | 0.0546997i | \(0.982580\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.13416 | − | 3.93011i | 0.116080 | − | 0.145560i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.7908 | − | 16.7544i | 1.28678 | − | 0.619683i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.0375 | + | 4.80167i | −0.777037 | + | 0.177354i | −0.592607 | − | 0.805492i | \(-0.701901\pi\) |
−0.184430 | + | 0.982846i | \(0.559044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.34562 | + | 16.4544i | 0.0865195 | + | 0.606928i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.97623 | + | 8.65844i | 0.0727955 | + | 0.318938i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9905 | − | 33.2047i | −0.588221 | − | 1.22145i | −0.956499 | − | 0.291737i | \(-0.905767\pi\) |
0.368278 | − | 0.929716i | \(-0.379948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.5378 | + | 13.9859i | 0.644268 | + | 0.513787i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.5773 | − | 23.5871i | 1.08509 | − | 0.865328i | 0.0936102 | − | 0.995609i | \(-0.470159\pi\) |
0.991477 | + | 0.130281i | \(0.0415878\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.4986 | − | 8.37234i | −0.384638 | − | 0.306739i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.3293 | − | 5.93748i | −0.451106 | − | 0.217241i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.1393 | − | 24.0527i | −0.808952 | − | 0.878868i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.74296 | − | 7.76975i | −0.355526 | − | 0.283522i | 0.429397 | − | 0.903116i | \(-0.358726\pi\) |
−0.784923 | + | 0.619593i | \(0.787298\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.2528 | −1.10247 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.305048 | + | 0.146903i | 0.0111018 | + | 0.00534636i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.2906 | + | 8.80828i | −0.664783 | + | 0.320142i | −0.735668 | − | 0.677342i | \(-0.763132\pi\) |
0.0708857 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.39267 | + | 6.10169i | −0.0505507 | + | 0.221477i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.74795 | − | 16.0888i | −0.280863 | − | 0.583218i | 0.712041 | − | 0.702138i | \(-0.247771\pi\) |
−0.992904 | + | 0.118920i | \(0.962057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.34601 | + | 10.9445i | −0.157336 | + | 0.396218i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.4158 | 0.448895 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.47604 | − | 13.4476i | 0.233836 | − | 0.485566i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.18332 | − | 1.86779i | −0.295098 | − | 0.0673542i | 0.0724088 | − | 0.997375i | \(-0.476931\pi\) |
−0.367507 | + | 0.930021i | \(0.619789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.2811 | + | 8.28092i | −1.30663 | + | 0.298230i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.9293 | − | 8.65712i | 1.36422 | − | 0.311375i | 0.523124 | − | 0.852257i | \(-0.324767\pi\) |
0.841099 | + | 0.540882i | \(0.181909\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.08984 | + | 35.4439i | −0.290595 | + | 1.27318i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.40258 | − | 16.1236i | 0.229691 | − | 0.578430i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.36782 | + | 1.09080i | −0.0490074 | + | 0.0390821i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.76294 | − | 3.46462i | −0.0988658 | − | 0.123974i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.2483 | −0.652142 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00985 | −0.0717347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.49660 | − | 4.38460i | −0.124640 | − | 0.156294i | 0.715596 | − | 0.698514i | \(-0.246155\pi\) |
−0.840236 | + | 0.542220i | \(0.817584\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.68322 | − | 2.13979i | 0.0955251 | − | 0.0761787i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.84783 | + | 4.46218i | −0.172369 | + | 0.158657i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.37315 | + | 27.9226i | −0.226317 | + | 0.991560i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.2065 | − | 3.24253i | 0.503851 | − | 0.115001i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.7879 | − | 6.57065i | 1.01972 | − | 0.232744i | 0.320194 | − | 0.947352i | \(-0.396252\pi\) |
0.699526 | + | 0.714608i | \(0.253395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −93.4583 | − | 21.3312i | −3.30632 | − | 0.754645i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.58163 | − | 17.8199i | 0.303217 | − | 0.629636i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.6154 | 0.656923 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.12673 | + | 5.46604i | 0.110203 | + | 0.192653i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.21443 | − | 4.59831i | −0.0779517 | − | 0.161868i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.60772 | − | 28.9503i | 0.232315 | − | 1.01784i | −0.715399 | − | 0.698716i | \(-0.753755\pi\) |
0.947714 | − | 0.319122i | \(-0.103388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.6795 | + | 5.62456i | −0.410123 | + | 0.197505i | −0.627558 | − | 0.778570i | \(-0.715945\pi\) |
0.217435 | + | 0.976075i | \(0.430231\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.36275 | − | 1.13784i | −0.0828654 | − | 0.0399059i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.88326 | −0.136025 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.81897 | − | 6.23542i | −0.273551 | − | 0.218150i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2999 | − | 16.4323i | 0.394851 | − | 0.574191i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.6957 | + | 13.3375i | 0.966586 | + | 0.465483i | 0.849471 | − | 0.527635i | \(-0.176921\pi\) |
0.117115 | + | 0.993118i | \(0.462635\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.34299 | − | 1.86847i | −0.0816716 | − | 0.0651309i | 0.581803 | − | 0.813330i | \(-0.302347\pi\) |
−0.663475 | + | 0.748199i | \(0.730919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.64842 | − | 6.89689i | 0.301099 | − | 0.240119i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.7832 | − | 19.7639i | −0.861796 | − | 0.687260i | 0.0893499 | − | 0.996000i | \(-0.471521\pi\) |
−0.951146 | + | 0.308741i | \(0.900092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.41687 | + | 5.01868i | 0.0839413 | + | 0.174306i | 0.938714 | − | 0.344696i | \(-0.112018\pi\) |
−0.854773 | + | 0.519002i | \(0.826304\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.1551 | − | 53.2549i | −0.421655 | − | 1.84739i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −54.0746 | − | 4.48766i | −1.87357 | − | 0.155488i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.39944 | − | 1.91712i | 0.290674 | − | 0.0663445i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.2498 | + | 14.0859i | −1.01102 | + | 0.486881i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.7727 | − | 41.0956i | 1.13144 | − | 1.41878i | 0.237045 | − | 0.971499i | \(-0.423821\pi\) |
0.894394 | − | 0.447281i | \(-0.147607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.694385 | + | 0.870731i | 0.0239443 | + | 0.0300252i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.3604 | + | 16.7534i | −0.460155 | + | 0.577016i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.47954 | + | 15.5314i | −0.257304 | + | 0.534297i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.5386 | − | 3.64423i | −0.808795 | − | 0.125217i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.1431 | − | 17.7349i | 0.485390 | − | 0.608660i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.57280i | − | 0.225313i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.94410 | − | 12.3430i | 0.203522 | − | 0.422618i | −0.774078 | − | 0.633091i | \(-0.781786\pi\) |
0.977600 | + | 0.210473i | \(0.0675003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.39518 | − | 2.89712i | −0.0477142 | − | 0.0990795i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.8488 | + | 10.4647i | 1.56616 | + | 0.357467i | 0.915634 | − | 0.402013i | \(-0.131689\pi\) |
0.650531 | + | 0.759480i | \(0.274547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.7777 | − | 8.07973i | 0.572449 | − | 0.275677i | −0.125182 | − | 0.992134i | \(-0.539952\pi\) |
0.697631 | + | 0.716457i | \(0.254237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.28206 | + | 3.56572i | 0.111852 | + | 0.121519i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 20.5249i | − | 0.698676i | −0.936997 | − | 0.349338i | \(-0.886406\pi\) | ||
0.936997 | − | 0.349338i | \(-0.113594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7727 | + | 8.07733i | 0.570290 | + | 0.274637i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.1518 | + | 88.2906i | −0.684390 | + | 2.99851i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.25015 | − | 14.2398i | −0.110254 | − | 0.483054i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.43373 | − | 32.5693i | −0.251882 | − | 1.10357i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.76589 | − | 1.54427i | −0.228991 | − | 0.0522656i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.98919 | − | 25.7667i | 0.134859 | − | 0.871074i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.4794 | − | 38.2199i | −1.02922 | − | 1.29060i | −0.956027 | − | 0.293277i | \(-0.905254\pi\) |
−0.0731879 | − | 0.997318i | \(-0.523317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.718753 | − | 0.573186i | 0.0242429 | − | 0.0193331i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 34.7822i | − | 1.17184i | −0.810369 | − | 0.585920i | \(-0.800733\pi\) | ||
0.810369 | − | 0.585920i | \(-0.199267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.3737i | 1.08946i | 0.838611 | + | 0.544730i | \(0.183368\pi\) | ||||
−0.838611 | + | 0.544730i | \(0.816632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.21211 | + | 4.15652i | −0.175203 | + | 0.139720i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.6918 | + | 32.2165i | 0.862646 | + | 1.08172i | 0.995884 | + | 0.0906399i | \(0.0288912\pi\) |
−0.133238 | + | 0.991084i | \(0.542537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.5303 | − | 16.3201i | 0.956874 | − | 0.547360i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4911 | + | 3.53575i | 0.518972 | + | 0.118452i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.52456 | + | 24.2047i | 0.184872 | + | 0.809979i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.79721 | − | 16.6366i | −0.126927 | − | 0.556102i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.23863 | − | 22.9519i | 0.174913 | − | 0.766342i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.2684 | + | 23.2449i | 1.60984 | + | 0.775259i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.5716i | 1.58484i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.6971 | + | 22.8266i | −0.522366 | + | 0.759623i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.8077 | − | 8.57573i | 0.591948 | − | 0.285067i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.6377 | + | 3.56920i | 0.519241 | + | 0.118513i | 0.474106 | − | 0.880468i | \(-0.342771\pi\) |
0.0451346 | + | 0.998981i | \(0.485628\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.1787 | − | 21.1363i | −0.337607 | − | 0.701048i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.87288 | − | 12.1952i | 0.194577 | − | 0.404044i | −0.780739 | − | 0.624858i | \(-0.785157\pi\) |
0.975316 | + | 0.220814i | \(0.0708713\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6396i | 0.451404i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.97584 | − | 10.0014i | 0.263673 | − | 0.330636i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.4391 | − | 7.43154i | 0.807051 | − | 0.245411i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.5941 | + | 24.0755i | −0.382455 | + | 0.794176i | 0.617516 | + | 0.786559i | \(0.288139\pi\) |
−0.999971 | + | 0.00761797i | \(0.997575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.6641 | + | 48.4832i | −1.27403 | + | 1.59758i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3930 | + | 13.0324i | 0.342089 | + | 0.428967i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.24312 | + | 9.08259i | −0.238152 | + | 0.298634i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.75392 | + | 3.25252i | −0.221828 | + | 0.106827i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.85528 | + | 1.79292i | −0.257723 | + | 0.0588237i | −0.349430 | − | 0.936962i | \(-0.613625\pi\) |
0.0917069 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.02927 | + | 13.1221i | 0.164828 | + | 0.430060i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.5767 | + | 46.3395i | 0.346265 | + | 1.51709i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.36933 | − | 11.1495i | −0.175596 | − | 0.364629i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3113 | − | 12.2103i | −0.500197 | − | 0.398894i | 0.340630 | − | 0.940197i | \(-0.389360\pi\) |
−0.840827 | + | 0.541304i | \(0.817931\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.7610 | + | 11.7715i | −0.481707 | + | 0.384148i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.7957 | + | 32.5335i | 1.32990 | + | 1.06056i | 0.992887 | + | 0.119060i | \(0.0379882\pi\) |
0.337013 | + | 0.941500i | \(0.390583\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.65429 | + | 0.796663i | 0.0538710 | + | 0.0259429i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.62705 | − | 4.93492i | 0.280638 | − | 0.160533i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.84969 | + | 7.85486i | 0.320072 | + | 0.255249i | 0.770324 | − | 0.637653i | \(-0.220094\pi\) |
−0.450252 | + | 0.892901i | \(0.648666\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −70.0231 | −2.27305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.7968 | + | 17.7204i | 1.19322 | + | 0.574624i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.2346 | + | 10.2260i | −0.687857 | + | 0.331254i | −0.744955 | − | 0.667114i | \(-0.767529\pi\) |
0.0570989 | + | 0.998369i | \(0.481815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.123511 | − | 0.541135i | 0.00399671 | − | 0.0175107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.07264 | − | 14.6865i | −0.228626 | − | 0.474747i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.4288 | + | 8.34065i | −0.885722 | + | 0.269334i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.3109 | 2.07455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.60143 | − | 15.7845i | 0.244953 | − | 0.508649i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.37629 | − | 1.45535i | −0.205260 | − | 0.0468492i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.8548 | − | 12.0638i | 1.69970 | − | 0.387945i | 0.740805 | − | 0.671720i | \(-0.234444\pi\) |
0.958891 | + | 0.283775i | \(0.0915870\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.8885 | − | 7.27834i | 1.02441 | − | 0.233814i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.22785 | + | 18.5234i | −0.135678 | + | 0.594445i | 0.860678 | + | 0.509150i | \(0.170040\pi\) |
−0.996356 | + | 0.0852945i | \(0.972817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.11939 | − | 29.8850i | −0.0679444 | − | 0.958069i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.5316 | + | 25.9431i | −1.04185 | + | 0.830844i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.5013 | − | 36.9934i | −0.943830 | − | 1.18353i | −0.982872 | − | 0.184288i | \(-0.941002\pi\) |
0.0390426 | − | 0.999238i | \(-0.487569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.7137 | −0.630052 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.31087 | −0.201490 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.3534 | + | 23.0145i | 0.585383 | + | 0.734047i | 0.983021 | − | 0.183495i | \(-0.0587412\pi\) |
−0.397637 | + | 0.917543i | \(0.630170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.2431 | + | 12.9534i | −0.517548 | + | 0.412730i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 65.7980 | − | 20.0081i | 2.09437 | − | 0.636864i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.33556 | + | 10.2328i | −0.0742665 | + | 0.325383i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.30957 | + | 1.89661i | −0.263962 | + | 0.0602476i | −0.352454 | − | 0.935829i | \(-0.614653\pi\) |
0.0884914 | + | 0.996077i | \(0.471795\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.85311 | − | 1.79242i | 0.249211 | − | 0.0568808i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.1870 | + | 5.52052i | 0.766779 | + | 0.175012i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.724419 | − | 1.50427i | 0.0229426 | − | 0.0476408i | −0.889183 | − | 0.457552i | \(-0.848726\pi\) |
0.912125 | + | 0.409912i | \(0.134440\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.3739 | −0.328214 |
(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 | 784.2.bb.b.111.5 | ✓ | 120 | |
4.3 | odd | 2 | inner | 784.2.bb.b.111.16 | yes | 120 | |
49.34 | odd | 14 | inner | 784.2.bb.b.671.16 | yes | 120 | |
196.83 | even | 14 | inner | 784.2.bb.b.671.5 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.bb.b.111.5 | ✓ | 120 | 1.1 | even | 1 | trivial | |
784.2.bb.b.111.16 | yes | 120 | 4.3 | odd | 2 | inner | |
784.2.bb.b.671.5 | yes | 120 | 196.83 | even | 14 | inner | |
784.2.bb.b.671.16 | yes | 120 | 49.34 | odd | 14 | inner |