Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1264,2,Mod(735,1264)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1264, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1264.735");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1264 = 2^{4} \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1264.n (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: | \(10.0930908155\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 767.8 | ||
Character | \(\chi\) | \(=\) | 1264.767 |
Dual form | 1264.2.n.i.735.8 |
$q$-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 \(\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times\).
\(n\) | \(159\) | \(161\) | \(949\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.143444 | + | 0.248452i | 0.0828172 | + | 0.143444i | 0.904459 | − | 0.426561i | \(-0.140275\pi\) |
−0.821642 | + | 0.570004i | \(0.806942\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.31050 | + | 2.26985i | −0.586073 | + | 1.01511i | 0.408668 | + | 0.912683i | \(0.365993\pi\) |
−0.994741 | + | 0.102425i | \(0.967340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.522039 | − | 0.904199i | 0.197312 | − | 0.341755i | −0.750344 | − | 0.661048i | \(-0.770112\pi\) |
0.947656 | + | 0.319293i | \(0.103445\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.45885 | − | 2.52680i | 0.486283 | − | 0.842266i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.34034 | + | 1.92855i | 1.00715 | + | 0.581479i | 0.910356 | − | 0.413825i | \(-0.135807\pi\) |
0.0967952 | + | 0.995304i | \(0.469141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0743559 | + | 0.128788i | 0.0206226 | + | 0.0357194i | 0.876153 | − | 0.482034i | \(-0.160102\pi\) |
−0.855530 | + | 0.517753i | \(0.826768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.751930 | −0.194148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.07112i | 0.502321i | 0.967945 | + | 0.251161i | \(0.0808123\pi\) | ||||
−0.967945 | + | 0.251161i | \(0.919188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.33400 | + | 1.92488i | 0.764871 | + | 0.441599i | 0.831042 | − | 0.556210i | \(-0.187745\pi\) |
−0.0661707 | + | 0.997808i | \(0.521078\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.299533 | 0.0653634 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.48230 | − | 3.16521i | −1.14314 | − | 0.659991i | −0.195932 | − | 0.980617i | \(-0.562773\pi\) |
−0.947206 | + | 0.320626i | \(0.896107\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.934814 | − | 1.61915i | −0.186963 | − | 0.323829i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.69771 | 0.326725 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.48579 | − | 2.58987i | −0.832990 | − | 0.480927i | 0.0218856 | − | 0.999760i | \(-0.493033\pi\) |
−0.854875 | + | 0.518834i | \(0.826366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.96760 | + | 4.60010i | 1.43102 | + | 0.826202i | 0.997199 | − | 0.0747955i | \(-0.0238304\pi\) |
0.433825 | + | 0.900997i | \(0.357164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.10655i | 0.192626i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.36826 | + | 2.36990i | 0.231279 | + | 0.400587i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.737560 | − | 0.425831i | 0.121254 | − | 0.0700061i | −0.438146 | − | 0.898904i | \(-0.644365\pi\) |
0.559400 | + | 0.828898i | \(0.311031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0213317 | + | 0.0369477i | −0.00341581 | + | 0.00591636i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.0287i | − | 1.56622i | −0.621881 | − | 0.783112i | \(-0.713631\pi\) | ||
0.621881 | − | 0.783112i | \(-0.286369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.84945 | + | 10.1315i | 0.892032 | + | 1.54505i | 0.837435 | + | 0.546537i | \(0.184054\pi\) |
0.0545975 | + | 0.998508i | \(0.482612\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.82364 | + | 6.62273i | 0.569994 | + | 0.987259i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.36826 | + | 2.36990i | −0.199582 | + | 0.345686i | −0.948393 | − | 0.317098i | \(-0.897292\pi\) |
0.748811 | + | 0.662784i | \(0.230625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.95495 | + | 5.11812i | 0.422136 | + | 0.731160i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.514574 | + | 0.297089i | −0.0720548 | + | 0.0416008i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.26082 | + | 3.03733i | 0.722629 | + | 0.417210i | 0.815720 | − | 0.578448i | \(-0.196341\pi\) |
−0.0930906 | + | 0.995658i | \(0.529675\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.75503 | + | 5.05472i | −1.18053 | + | 0.681578i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.10445i | 0.146288i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.30608 | + | 9.19039i | 0.690792 | + | 1.19649i | 0.971579 | + | 0.236717i | \(0.0760715\pi\) |
−0.280786 | + | 0.959770i | \(0.590595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.39920i | − | 0.819334i | −0.912235 | − | 0.409667i | \(-0.865645\pi\) | ||
0.912235 | − | 0.409667i | \(-0.134355\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.52315 | − | 2.63818i | −0.191899 | − | 0.332379i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.389773 | −0.0483454 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6644i | 1.42503i | 0.701656 | + | 0.712516i | \(0.252445\pi\) | ||||
−0.701656 | + | 0.712516i | \(0.747555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.81611i | − | 0.218634i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.93147 | −0.466579 | −0.233290 | − | 0.972407i | \(-0.574949\pi\) | ||||
−0.233290 | + | 0.972407i | \(0.574949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.04018 | + | 13.9260i | −0.941032 | + | 1.62992i | −0.177524 | + | 0.984116i | \(0.556809\pi\) |
−0.763508 | + | 0.645799i | \(0.776525\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.268186 | − | 0.464512i | 0.0309675 | − | 0.0536372i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.48758 | − | 2.01356i | 0.397447 | − | 0.229466i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.46822 | + | 7.00704i | 0.615223 | + | 0.788353i | ||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.13302 | − | 7.15860i | −0.459224 | − | 0.795400i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.05759 | + | 2.92000i | 0.555142 | + | 0.320512i | 0.751194 | − | 0.660082i | \(-0.229478\pi\) |
−0.196051 | + | 0.980594i | \(0.562812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.70114 | − | 2.71421i | −0.509910 | − | 0.294397i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.48600i | − | 0.159316i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.247488 | 0.0262337 | 0.0131169 | − | 0.999914i | \(-0.495825\pi\) | ||||
0.0131169 | + | 0.999914i | \(0.495825\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.155267 | 0.0162764 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.63942i | 0.273695i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.73840 | + | 5.04512i | −0.896541 | + | 0.517618i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.68782 | −0.882115 | −0.441057 | − | 0.897479i | \(-0.645396\pi\) | ||||
−0.441057 | + | 0.897479i | \(0.645396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.74611 | − | 5.62692i | 0.979521 | − | 0.565527i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.60721 | 0.756946 | 0.378473 | − | 0.925612i | \(-0.376449\pi\) | ||||
0.378473 | + | 0.925612i | \(0.376449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.38442 | + | 7.59404i | 0.432010 | + | 0.748263i | 0.997046 | − | 0.0768028i | \(-0.0244712\pi\) |
−0.565036 | + | 0.825066i | \(0.691138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.392537 | + | 0.679895i | −0.0383077 | + | 0.0663509i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.72723 | − | 13.3840i | −0.747020 | − | 1.29388i | −0.949245 | − | 0.314537i | \(-0.898151\pi\) |
0.202225 | − | 0.979339i | \(-0.435183\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.91549 | + | 4.57001i | −0.758166 | + | 0.437727i | −0.828637 | − | 0.559786i | \(-0.810883\pi\) |
0.0704708 | + | 0.997514i | \(0.477550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.211596 | + | 0.122165i | 0.0200838 | + | 0.0115954i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2401 | − | 5.91210i | 0.963304 | − | 0.556164i | 0.0661155 | − | 0.997812i | \(-0.478939\pi\) |
0.897188 | + | 0.441648i | \(0.145606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.3691 | − | 8.29600i | 1.33992 | − | 0.773606i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.433896 | 0.0401137 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.87271 | + | 1.08121i | 0.171671 | + | 0.0991142i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.93860 | + | 3.35775i | 0.176236 | + | 0.305250i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.49165 | − | 1.43856i | 0.224665 | − | 0.129710i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.20470 | −0.733850 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.12979 | − | 14.0812i | 0.721402 | − | 1.24951i | −0.239035 | − | 0.971011i | \(-0.576831\pi\) |
0.960438 | − | 0.278495i | \(-0.0898355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.67813 | + | 2.90661i | −0.147751 | + | 0.255913i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.8554i | − | 1.21056i | −0.796014 | − | 0.605278i | \(-0.793062\pi\) | ||
0.796014 | − | 0.605278i | \(-0.206938\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.48096 | − | 2.00973i | 0.301837 | − | 0.174266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.22485 | + | 3.85355i | −0.191484 | + | 0.331661i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.134464i | 0.0114880i | 0.999984 | + | 0.00574400i | \(0.00182838\pi\) | ||||
−0.999984 | + | 0.00574400i | \(0.998172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.19993 | − | 9.00655i | 0.441052 | − | 0.763925i | −0.556715 | − | 0.830703i | \(-0.687939\pi\) |
0.997768 | + | 0.0667781i | \(0.0212720\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.785075 | −0.0661152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.573596i | 0.0479665i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7572 | − | 6.78804i | 0.976385 | − | 0.563716i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.847737 | + | 1.46832i | −0.0699202 | + | 0.121105i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7110 | − | 7.33868i | −1.04132 | − | 0.601208i | −0.121115 | − | 0.992639i | \(-0.538647\pi\) |
−0.920208 | + | 0.391431i | \(0.871980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6546 | − | 8.46086i | −1.19258 | − | 0.688535i | −0.233687 | − | 0.972312i | \(-0.575079\pi\) |
−0.958890 | + | 0.283777i | \(0.908412\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.23331 | + | 3.02146i | 0.423088 | + | 0.244270i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.8831 | + | 12.0568i | −1.67737 | + | 0.968429i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.85502i | 0.307664i | 0.988097 | + | 0.153832i | \(0.0491614\pi\) | ||||
−0.988097 | + | 0.153832i | \(0.950839\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.74274i | 0.138209i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.72395 | + | 3.30472i | −0.451110 | + | 0.260449i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.62216 | + | 3.82331i | 0.518688 | + | 0.299465i | 0.736398 | − | 0.676549i | \(-0.236525\pi\) |
−0.217710 | + | 0.976014i | \(0.569859\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.51171 | − | 1.45013i | −0.195536 | − | 0.112893i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.182390 | − | 0.105303i | −0.0141137 | − | 0.00814858i | 0.492927 | − | 0.870071i | \(-0.335927\pi\) |
−0.507040 | + | 0.861922i | \(0.669260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48894 | − | 11.2392i | 0.499149 | − | 0.864552i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.72759 | − | 5.61623i | 0.743887 | − | 0.429484i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.25740i | 0.627798i | 0.949456 | + | 0.313899i | \(0.101635\pi\) | ||||
−0.949456 | + | 0.313899i | \(0.898365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.95204 | −0.147560 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.52224 | + | 2.63661i | −0.114419 | + | 0.198179i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.0994i | − | 1.27807i | −0.769179 | − | 0.639034i | \(-0.779334\pi\) | ||
0.769179 | − | 0.639034i | \(-0.220666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.28591 | − | 9.15546i | 0.392898 | − | 0.680520i | −0.599932 | − | 0.800051i | \(-0.704806\pi\) |
0.992830 | + | 0.119531i | \(0.0381391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.58989 | − | 0.917924i | 0.117528 | − | 0.0678549i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.23220i | 0.164115i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.99426 | + | 6.91827i | −0.292089 | + | 0.505914i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.886272 | − | 1.53507i | 0.0644668 | − | 0.111660i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.18928 | 0.375483 | 0.187742 | − | 0.982218i | \(-0.439883\pi\) | ||||
0.187742 | + | 0.982218i | \(0.439883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.96781 | − | 1.71347i | 0.213628 | − | 0.123338i | −0.389369 | − | 0.921082i | \(-0.627307\pi\) |
0.602996 | + | 0.797744i | \(0.293973\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0559105 | − | 0.0968397i | −0.00400383 | − | 0.00693484i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.83897 | + | 5.10318i | 0.629750 | + | 0.363587i | 0.780655 | − | 0.624962i | \(-0.214885\pi\) |
−0.150905 | + | 0.988548i | \(0.548219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.74146 | 0.194337 | 0.0971685 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971685 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.89804 | + | 1.67318i | −0.204412 | + | 0.118017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.68351 | + | 2.70403i | −0.328718 | + | 0.189786i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.7637 | + | 13.1426i | 1.58989 | + | 0.917921i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.9957 | + | 9.23511i | −1.11178 | + | 0.641884i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.42446 | + | 12.8595i | 0.513561 | + | 0.889514i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.58922 | − | 7.94876i | 0.315935 | − | 0.547215i | −0.663701 | − | 0.747998i | \(-0.731015\pi\) |
0.979636 | + | 0.200783i | \(0.0643485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.563943 | − | 0.976779i | −0.0386408 | − | 0.0669278i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.6628 | −2.09118 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.31880 | − | 4.80286i | 0.564717 | − | 0.326040i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.61325 | −0.311734 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.266736 | + | 0.154000i | −0.0179426 | + | 0.0103592i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.54495i | 0.304352i | 0.988353 | + | 0.152176i | \(0.0486281\pi\) | ||||
−0.988353 | + | 0.152176i | \(0.951372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.45501 | −0.363667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.97620 | −0.595772 | −0.297886 | − | 0.954602i | \(-0.596281\pi\) | ||||
−0.297886 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.4381i | − | 0.821934i | −0.911650 | − | 0.410967i | \(-0.865191\pi\) | ||
0.911650 | − | 0.410967i | \(-0.134809\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00054 | + | 0.577663i | 0.0658309 | + | 0.0380075i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.7408 | − | 7.93324i | −0.900188 | − | 0.519724i | −0.0229269 | − | 0.999737i | \(-0.507298\pi\) |
−0.877261 | + | 0.480013i | \(0.840632\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.58622 | − | 6.21151i | −0.233939 | − | 0.405194i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.956528 | + | 2.36370i | −0.0621331 | + | 0.153539i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3607 | + | 7.71378i | −0.864229 | + | 0.498963i | −0.865426 | − | 0.501037i | \(-0.832952\pi\) |
0.00119740 | + | 0.999999i | \(0.499619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.23424 | + | 10.7980i | −0.401583 | + | 0.695562i | −0.993917 | − | 0.110130i | \(-0.964873\pi\) |
0.592334 | + | 0.805692i | \(0.298206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.73228 | − | 6.46449i | 0.239426 | − | 0.414697i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.4898 | −0.989609 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.572506i | 0.0364277i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.67542i | 0.106175i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2210 | 0.771380 | 0.385690 | − | 0.922628i | \(-0.373963\pi\) | ||||
0.385690 | + | 0.922628i | \(0.373963\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.2085 | − | 21.1457i | −0.767542 | − | 1.32942i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.55734i | − | 0.0975245i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.8767 | − | 24.0352i | −0.865606 | − | 1.49927i | −0.866444 | − | 0.499274i | \(-0.833600\pi\) |
0.000838460 | − | 1.00000i | \(-0.499733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.889201i | − | 0.0552523i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0882 | + | 7.55645i | −0.810137 | + | 0.467733i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.0931 | − | 15.0649i | −1.60897 | − | 0.928940i | −0.989601 | − | 0.143841i | \(-0.954055\pi\) |
−0.619370 | − | 0.785099i | \(-0.712612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.7886 | + | 7.96085i | −0.847026 | + | 0.489031i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0355006 | + | 0.0614888i | 0.00217260 | + | 0.00376306i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.60650 | + | 4.51458i | −0.158921 | + | 0.275259i | −0.934480 | − | 0.356016i | \(-0.884135\pi\) |
0.775559 | + | 0.631275i | \(0.217468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.19956 | + | 10.7380i | 0.376596 | + | 0.652284i | 0.990565 | − | 0.137047i | \(-0.0437610\pi\) |
−0.613968 | + | 0.789331i | \(0.710428\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0222720 | + | 0.0385763i | 0.00134796 | + | 0.00233474i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 7.21134i | − | 0.434860i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.87674 | − | 6.71471i | 0.232931 | − | 0.403448i | −0.725739 | − | 0.687971i | \(-0.758502\pi\) |
0.958669 | + | 0.284523i | \(0.0918351\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.2470 | − | 13.4217i | 1.39176 | − | 0.803535i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.06094 | + | 13.9620i | 0.480875 | + | 0.832900i | 0.999759 | − | 0.0219443i | \(-0.00698565\pi\) |
−0.518884 | + | 0.854845i | \(0.673652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.25774i | − | 0.0747647i | −0.999301 | − | 0.0373823i | \(-0.988098\pi\) | ||
0.999301 | − | 0.0373823i | \(-0.0119019\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.50693 | − | 1.44738i | −0.148498 | − | 0.0857353i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.06796 | − | 5.23539i | −0.535265 | − | 0.309035i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7104 | 0.747673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.24621 | − | 2.15850i | −0.0730542 | − | 0.126534i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.2857 | + | 7.67048i | 0.776157 | + | 0.448114i | 0.835066 | − | 0.550149i | \(-0.185429\pi\) |
−0.0589099 | + | 0.998263i | \(0.518762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.8144 | −1.61942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.67094 | + | 3.27412i | 0.329061 | + | 0.189984i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 0.941407i | − | 0.0544430i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2146 | 0.704036 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.09121 | + | 1.89002i | 0.0626881 | + | 0.108579i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.5252 | + | 8.38615i | 0.831712 | + | 0.480189i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3818 | − | 17.9819i | 0.592523 | − | 1.02628i | −0.401369 | − | 0.915917i | \(-0.631465\pi\) |
0.993891 | − | 0.110363i | \(-0.0352013\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.25783 | + | 2.17863i | −0.0715557 | + | 0.123938i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.7085 | − | 23.7438i | 0.777339 | − | 1.34639i | −0.156132 | − | 0.987736i | \(-0.549903\pi\) |
0.933471 | − | 0.358654i | \(-0.116764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.38681 | − | 9.33023i | −0.304480 | − | 0.527376i | 0.672665 | − | 0.739947i | \(-0.265149\pi\) |
−0.977146 | + | 0.212572i | \(0.931816\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.98436 | 0.449868 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.86194 | −0.273074 | −0.136537 | − | 0.990635i | \(-0.543597\pi\) | ||||
−0.136537 | + | 0.990635i | \(0.543597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.98938 | − | 17.3021i | −0.559298 | − | 0.968732i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.21684 | − | 3.83969i | 0.123732 | − | 0.214310i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98667 | + | 6.90512i | −0.221824 | + | 0.384211i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.139018 | − | 0.240786i | 0.00771132 | − | 0.0133564i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.27085 | − | 1.31108i | −0.125578 | − | 0.0725027i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.42858 | + | 2.47437i | 0.0787599 | + | 0.136416i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.4317 | −0.848201 | −0.424101 | − | 0.905615i | \(-0.639410\pi\) | ||||
−0.424101 | + | 0.905615i | \(0.639410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.48489i | − | 0.136171i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.4764 | − | 15.2862i | −1.44656 | − | 0.835173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.71194 | 0.529043 | 0.264522 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264522 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.93774 | + | 1.69611i | 0.159556 | + | 0.0921198i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.7430 | + | 30.7318i | 0.960838 | + | 1.66422i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4790 | 0.727795 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.12231 | + | 2.38001i | 0.221937 | + | 0.128136i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.56059 | + | 4.36511i | 0.405874 | + | 0.234331i | 0.689015 | − | 0.724747i | \(-0.258043\pi\) |
−0.283141 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.8346i | 0.901135i | 0.892742 | + | 0.450567i | \(0.148778\pi\) | ||||
−0.892742 | + | 0.450567i | \(0.851222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.126235 | + | 0.218645i | 0.00673791 | + | 0.0116704i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.3640 | − | 6.56099i | 0.604843 | − | 0.349206i | −0.166101 | − | 0.986109i | \(-0.553118\pi\) |
0.770944 | + | 0.636902i | \(0.219785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.15218 | − | 8.92384i | 0.273449 | − | 0.473628i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.620370i | 0.0328334i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.14249 | − | 5.44295i | −0.165854 | − | 0.287268i | 0.771104 | − | 0.636709i | \(-0.219705\pi\) |
−0.936958 | + | 0.349441i | \(0.886371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.08964 | − | 3.61937i | −0.109981 | − | 0.190493i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.556159 | + | 0.963295i | −0.0291908 | + | 0.0505599i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0733 | − | 36.5000i | −1.10303 | − | 1.91050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.3513 | − | 11.1725i | 1.01013 | − | 0.583199i | 0.0989004 | − | 0.995097i | \(-0.468467\pi\) |
0.911230 | + | 0.411898i | \(0.135134\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.3406 | − | 14.6304i | −1.31918 | − | 0.761628i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.49271 | − | 3.17122i | 0.285167 | − | 0.164641i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8708i | 1.28776i | 0.765125 | + | 0.643881i | \(0.222677\pi\) | ||||
−0.765125 | + | 0.643881i | \(0.777323\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.17691 | − | 2.03847i | −0.0607754 | − | 0.105266i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.770288i | − | 0.0396719i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.87089 | − | 13.6328i | −0.404300 | − | 0.700269i | 0.589939 | − | 0.807447i | \(-0.299152\pi\) |
−0.994240 | + | 0.107179i | \(0.965818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.66466 | 0.238978 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.01323i | 0.102871i | 0.998676 | + | 0.0514355i | \(0.0163797\pi\) | ||||
−0.998676 | + | 0.0514355i | \(0.983620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.5551i | 0.537935i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.1338 | 1.73512 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.29928 | + | 3.98248i | −0.116578 | + | 0.201920i | −0.918410 | − | 0.395631i | \(-0.870526\pi\) |
0.801831 | + | 0.597551i | \(0.203859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.55553 | − | 11.3545i | 0.331528 | − | 0.574223i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.44241 | − | 1.98747i | 0.173646 | − | 0.100255i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.0710 | + | 3.22933i | −1.16083 | + | 0.162485i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2267 | − | 33.3015i | −0.964958 | − | 1.67136i | −0.709728 | − | 0.704476i | \(-0.751182\pi\) |
−0.255230 | − | 0.966880i | \(-0.582151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.998641 | + | 0.576566i | 0.0499946 | + | 0.0288644i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.12521 | − | 3.53639i | −0.305878 | − | 0.176599i | 0.339202 | − | 0.940713i | \(-0.389843\pi\) |
−0.645081 | + | 0.764115i | \(0.723176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.36818i | 0.0681538i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.6653 | 1.07656 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.28494 | 0.162828 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.5919i | − | 1.31489i | −0.753504 | − | 0.657444i | \(-0.771638\pi\) | ||
0.753504 | − | 0.657444i | \(-0.228362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0334077 | + | 0.0192879i | −0.00164788 | + | 0.000951403i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.0799 | 0.545207 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.2559 | + | 7.65331i | −0.650708 | + | 0.375686i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.98359 | 0.146107 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.93143 | + | 13.7376i | 0.387476 | + | 0.671128i | 0.992109 | − | 0.125376i | \(-0.0400137\pi\) |
−0.604633 | + | 0.796504i | \(0.706680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0224 | + | 24.2875i | −0.683409 | + | 1.18370i | 0.290526 | + | 0.956867i | \(0.406170\pi\) |
−0.973934 | + | 0.226831i | \(0.927163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.99218 | + | 6.91466i | 0.194106 | + | 0.336202i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.35345 | − | 1.93612i | 0.162666 | − | 0.0939154i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.78615 | − | 3.34064i | −0.280012 | − | 0.161665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.142511 | + | 0.0822786i | −0.00688048 | + | 0.00397245i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.3303 | + | 19.2433i | −1.60546 | + | 0.926915i | −0.615096 | + | 0.788452i | \(0.710883\pi\) |
−0.990368 | + | 0.138462i | \(0.955784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4070 | −1.12487 | −0.562435 | − | 0.826842i | \(-0.690135\pi\) | ||||
−0.562435 | + | 0.826842i | \(0.690135\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.37300 | + | 1.94740i | 0.161723 | + | 0.0933708i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.1853 | − | 21.1056i | −0.582902 | − | 1.00962i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.366674 | − | 0.211699i | 0.0175004 | − | 0.0101038i | −0.491224 | − | 0.871033i | \(-0.663450\pi\) |
0.508725 | + | 0.860929i | \(0.330117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.2433 | 0.821109 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.4892 | + | 30.2922i | −0.830938 | + | 1.43923i | 0.0663577 | + | 0.997796i | \(0.478862\pi\) |
−0.897295 | + | 0.441431i | \(0.854471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.324333 | + | 0.561761i | −0.0153749 | + | 0.0266300i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.21074i | − | 0.199161i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.4024 | + | 18.1302i | −1.48197 | + | 0.855615i | −0.999791 | − | 0.0204579i | \(-0.993488\pi\) |
−0.482178 | + | 0.876073i | \(0.660154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.3409 | − | 33.4994i | 0.910727 | − | 1.57743i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.85462i | − | 0.228090i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.203477 | + | 0.352432i | −0.00953915 | + | 0.0165223i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9743 | −0.887580 | −0.443790 | − | 0.896131i | \(-0.646366\pi\) | ||||
−0.443790 | + | 0.896131i | \(0.646366\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.51617i | 0.164121i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.40097 | − | 3.11825i | 0.251548 | − | 0.145232i | −0.368925 | − | 0.929459i | \(-0.620274\pi\) |
0.620473 | + | 0.784228i | \(0.286941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3933 | + | 18.0018i | −0.483019 | + | 0.836614i | −0.999810 | − | 0.0194977i | \(-0.993793\pi\) |
0.516790 | + | 0.856112i | \(0.327127\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.99108 | − | 3.45895i | −0.277830 | − | 0.160405i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5119 | + | 7.80111i | 0.625257 | + | 0.360992i | 0.778913 | − | 0.627132i | \(-0.215771\pi\) |
−0.153656 | + | 0.988124i | \(0.549105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.5469 | + | 6.08927i | 0.487012 | + | 0.281177i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.957785 | + | 0.552977i | −0.0441324 | + | 0.0254798i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.1238i | 2.07479i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.19763i | − | 0.330250i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3495 | − | 8.86202i | 0.702804 | − | 0.405764i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.91564 | + | 1.68334i | 0.133219 | + | 0.0769139i | 0.565128 | − | 0.825003i | \(-0.308827\pi\) |
−0.431909 | + | 0.901917i | \(0.642160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.109684 | + | 0.0633260i | 0.00500115 | + | 0.00288742i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.64213 | − | 0.948083i | −0.0747194 | − | 0.0431393i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.3854 | − | 19.7201i | 0.516983 | − | 0.895442i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1944 | − | 9.34985i | 0.733839 | − | 0.423682i | −0.0859861 | − | 0.996296i | \(-0.527404\pi\) |
0.819825 | + | 0.572614i | \(0.194071\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.19371i | 0.0992032i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0613 | 1.22126 | 0.610630 | − | 0.791916i | \(-0.290916\pi\) | ||||
0.610630 | + | 0.791916i | \(0.290916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.36394 | − | 9.29062i | 0.241580 | − | 0.418429i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.4963i | 1.32576i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.05238 | + | 3.55483i | −0.0920618 | + | 0.159456i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4927 | + | 6.05797i | −0.469718 | + | 0.271192i | −0.716122 | − | 0.697975i | \(-0.754084\pi\) |
0.246404 | + | 0.969167i | \(0.420751\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 0.0604200i | − | 0.00269937i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.65090 | − | 4.59149i | 0.118198 | − | 0.204724i | −0.800856 | − | 0.598857i | \(-0.795622\pi\) |
0.919053 | + | 0.394133i | \(0.128955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.96924 | + | 17.2672i | −0.443625 | + | 0.768382i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.72319 | 0.165353 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.8558 | − | 19.5466i | 1.50063 | − | 0.866390i | 0.500631 | − | 0.865661i | \(-0.333101\pi\) |
1.00000 | 0.000729200i | \(-0.000232111\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.39458 | + | 14.5398i | 0.371354 | + | 0.643205i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.66016 | + | 3.26790i | 0.249902 | + | 0.144281i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.9831 | −1.01276 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.14094 | + | 5.27753i | −0.402018 | + | 0.232105i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.05156 | + | 1.18447i | −0.0900536 | + | 0.0519925i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2815 | + | 7.66809i | 0.581874 | + | 0.335945i | 0.761878 | − | 0.647721i | \(-0.224278\pi\) |
−0.180004 | + | 0.983666i | \(0.557611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6932 | + | 10.7925i | −0.817397 | + | 0.471924i | −0.849518 | − | 0.527560i | \(-0.823107\pi\) |
0.0321209 | + | 0.999484i | \(0.489774\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.280007 | − | 0.484987i | −0.0122205 | − | 0.0211666i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.52737 | + | 16.5019i | −0.415019 | + | 0.718834i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.53705 | + | 14.7866i | 0.371176 | + | 0.642896i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.9630 | 1.34368 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.29158 | − | 0.745695i | 0.0559446 | − | 0.0322996i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.5061 | 1.75123 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.24837 | − | 2.45280i | 0.183331 | − | 0.105846i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.7951i | 0.981853i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.189401 | −0.00814298 | −0.00407149 | − | 0.999992i | \(-0.501296\pi\) | ||||
−0.00407149 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.03292 | 0.130155 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 23.9560i | − | 1.02616i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.13519 | + | 0.655400i | 0.0485371 | + | 0.0280229i | 0.524072 | − | 0.851674i | \(-0.324412\pi\) |
−0.475535 | + | 0.879697i | \(0.657746\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.1695 | − | 9.33546i | −0.690097 | − | 0.398428i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.97040 | − | 17.2692i | −0.424753 | − | 0.735694i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.19038 | − | 1.28641i | 0.390815 | − | 0.0547037i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.554594 | + | 0.320195i | −0.0235412 | + | 0.0135915i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.5233 | + | 35.5473i | −0.869598 | + | 1.50619i | −0.00719035 | + | 0.999974i | \(0.502289\pi\) |
−0.862408 | + | 0.506214i | \(0.831045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.869882 | + | 1.50668i | −0.0367921 | + | 0.0637258i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.29181 | −0.0967601 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.9162i | 1.38725i | 0.720335 | + | 0.693627i | \(0.243988\pi\) | ||||
−0.720335 | + | 0.693627i | \(0.756012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.9912i | 1.30381i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.63039 | −0.362442 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.39794 | − | 5.88540i | −0.142449 | − | 0.246729i | 0.785969 | − | 0.618266i | \(-0.212164\pi\) |
−0.928418 | + | 0.371537i | \(0.878831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.46019i | 0.354048i | 0.984207 | + | 0.177024i | \(0.0566470\pi\) | ||||
−0.984207 | + | 0.177024i | \(0.943353\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.744369 | + | 1.28929i | 0.0310965 | + | 0.0538607i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.8355i | 0.493575i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.23698 | + | 1.86887i | −0.134757 | + | 0.0778020i | −0.565863 | − | 0.824499i | \(-0.691457\pi\) |
0.431106 | + | 0.902301i | \(0.358124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.851426 | + | 0.491571i | 0.0353841 | + | 0.0204290i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.28052 | − | 3.04871i | 0.219073 | − | 0.126482i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7153 | + | 20.2915i | 0.485198 | + | 0.840387i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.568620 | + | 0.984878i | −0.0235095 | + | 0.0407197i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.7362 | − | 18.5956i | −0.443130 | − | 0.767524i | 0.554790 | − | 0.831991i | \(-0.312799\pi\) |
−0.997920 | + | 0.0644666i | \(0.979465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.7093 | + | 30.6734i | 0.729699 | + | 1.26388i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.92807i | 0.120445i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6239 | − | 28.7935i | 0.682664 | − | 1.18241i | −0.291501 | − | 0.956570i | \(-0.594155\pi\) |
0.974165 | − | 0.225838i | \(-0.0725119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.90836 | + | 2.83384i | −0.201223 | + | 0.116176i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.393245 | + | 0.681120i | 0.0160944 | + | 0.0278764i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 20.2184i | − | 0.826103i | −0.910708 | − | 0.413051i | \(-0.864463\pi\) | ||
0.910708 | − | 0.413051i | \(-0.135537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.1708 | − | 22.0379i | −1.55702 | − | 0.898946i | −0.997540 | − | 0.0701013i | \(-0.977668\pi\) |
−0.559479 | − | 0.828844i | \(-0.688999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.4736 | + | 17.0166i | 1.20026 | + | 0.692969i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.1621 | −0.413149 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.7616 | − | 25.5679i | −0.599156 | − | 1.03777i | −0.992946 | − | 0.118569i | \(-0.962169\pi\) |
0.393789 | − | 0.919201i | \(-0.371164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.34364 | − | 0.775751i | −0.0544470 | − | 0.0314350i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.406954 | −0.0164636 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3742 | − | 14.0725i | −0.984466 | − | 0.568382i | −0.0808509 | − | 0.996726i | \(-0.525764\pi\) |
−0.903616 | + | 0.428344i | \(0.859097\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.54090i | 0.304079i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.1730 | 1.77834 | 0.889170 | − | 0.457577i | \(-0.151283\pi\) | ||||
0.889170 | + | 0.457577i | \(0.151283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.8865 | + | 37.9085i | 0.879691 | + | 1.52367i | 0.851680 | + | 0.524063i | \(0.175584\pi\) |
0.0280118 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.30735 | − | 5.37360i | −0.373491 | − | 0.215635i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.129199 | − | 0.223779i | 0.00517623 | − | 0.00896550i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.4263 | − | 26.7192i | 0.617053 | − | 1.06877i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.12998 | + | 3.68924i | −0.0850633 | + | 0.147334i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.881948 | + | 1.52758i | 0.0351656 | + | 0.0609085i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4255 | 0.653888 | 0.326944 | − | 0.945044i | \(-0.393981\pi\) | ||||
0.326944 | + | 0.945044i | \(0.393981\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.63318 | 0.104659 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.3082 | + | 36.9068i | 0.845589 | + | 1.46460i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.439436 | + | 0.761125i | −0.0174111 | + | 0.0301569i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.73541 | + | 9.93402i | −0.226889 | + | 0.392984i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.2264 | − | 28.1050i | 0.640906 | − | 1.11008i | −0.344325 | − | 0.938850i | \(-0.611892\pi\) |
0.985231 | − | 0.171231i | \(-0.0547744\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.96359 | − | 5.75248i | −0.392925 | − | 0.226856i | 0.290501 | − | 0.956875i | \(-0.406178\pi\) |
−0.683427 | + | 0.730019i | \(0.739511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.39838 | − | 7.61821i | −0.173186 | − | 0.299967i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.26667 | 0.167740 | 0.0838701 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838701 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.9321i | 1.60673i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.38656 | + | 1.37788i | 0.0935366 | + | 0.0540034i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.8468 | −0.581000 | −0.290500 | − | 0.956875i | \(-0.593822\pi\) | ||||
−0.290500 | + | 0.956875i | \(0.593822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.4498 | + | 18.1575i | 1.22884 | + | 0.709474i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.4588 | + | 40.6318i | 0.915215 | + | 1.58520i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.6690 | −1.38947 | −0.694734 | − | 0.719267i | \(-0.744478\pi\) | ||||
−0.694734 | + | 0.719267i | \(0.744478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7966 | − | 9.69753i | −0.653312 | − | 0.377190i | 0.136412 | − | 0.990652i | \(-0.456443\pi\) |
−0.789724 | + | 0.613462i | \(0.789776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0765232 | − | 0.0441807i | −0.00297192 | − | 0.00171584i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5350i | 0.408530i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.3949 | + | 28.3969i | 0.634815 | + | 1.09953i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.12920 | + | 0.651943i | −0.0436574 | + | 0.0252056i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3412 | − | 21.3755i | 0.476426 | − | 0.825194i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.61221i | − | 0.100693i | −0.998732 | − | 0.0503467i | \(-0.983967\pi\) | ||
0.998732 | − | 0.0503467i | \(-0.0160326\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.58704 | − | 2.74884i | −0.0610853 | − | 0.105803i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.08332 | + | 5.34046i | 0.118502 | + | 0.205251i | 0.919174 | − | 0.393852i | \(-0.128858\pi\) |
−0.800673 | + | 0.599102i | \(0.795524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.53539 | + | 7.85552i | −0.174052 | + | 0.301467i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.28758 | − | 2.23015i | −0.0493401 | − | 0.0854596i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.8278 | + | 19.5305i | −1.29439 | + | 0.747314i | −0.979428 | − | 0.201792i | \(-0.935323\pi\) |
−0.314957 | + | 0.949106i | \(0.601990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.305212 | − | 0.176214i | −0.0116616 | − | 0.00673280i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.09027 | − | 1.78417i | 0.117901 | − | 0.0680703i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.903375i | 0.0344158i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3895 | − | 31.8516i | −0.699571 | − | 1.21169i | −0.968615 | − | 0.248565i | \(-0.920041\pi\) |
0.269044 | − | 0.963128i | \(-0.413292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 11.7499i | − | 0.446341i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6290 | + | 23.6061i | 0.516978 | + | 0.895432i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.7707 | 0.786748 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 4.55189i | − | 0.172168i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.47104i | 0.319947i | 0.987121 | + | 0.159973i | \(0.0511409\pi\) | ||||
−0.987121 | + | 0.159973i | \(0.948859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.27870 | 0.123658 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.02884 | − | 1.78200i | 0.0387483 | − | 0.0671141i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.97126 | − | 6.87843i | 0.149355 | − | 0.258690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1034 | − | 14.4935i | 0.942778 | − | 0.544313i | 0.0519481 | − | 0.998650i | \(-0.483457\pi\) |
0.890830 | + | 0.454337i | \(0.150124\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.6827 | − | 3.59489i | 0.963175 | − | 0.134819i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.1205 | − | 50.4382i | −1.09057 | − | 1.88893i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.30198 | − | 0.751697i | −0.0486912 | − | 0.0281119i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.83300 | − | 2.21298i | −0.143146 | − | 0.0826454i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.5467i | 1.54943i | 0.632311 | + | 0.774714i | \(0.282106\pi\) | ||||
−0.632311 | + | 0.774714i | \(0.717894\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.15537 | 0.340964 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.57705 | −0.133032 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.68419i | 0.359662i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3262 | − | 8.27126i | 0.531331 | − | 0.306764i | −0.210227 | − | 0.977653i | \(-0.567420\pi\) |
0.741558 | + | 0.670889i | \(0.234087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.6566 | −0.839134 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.9837 | + | 12.1149i | −0.776109 | + | 0.448087i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.8192 | 0.695105 | 0.347552 | − | 0.937661i | \(-0.387013\pi\) | ||||
0.347552 | + | 0.937661i | \(0.387013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.22192 | − | 3.84847i | −0.0819566 | − | 0.141953i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.4954 | + | 38.9631i | −0.828627 | + | 1.43522i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.37826 | − | 5.85131i | −0.124271 | − | 0.215244i | 0.797177 | − | 0.603746i | \(-0.206326\pi\) |
−0.921448 | + | 0.388502i | \(0.872993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.142240 | + | 0.0821223i | −0.00522532 | + | 0.00301684i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.9054 | + | 20.1527i | 1.28056 | + | 0.739329i | 0.976950 | − | 0.213468i | \(-0.0684761\pi\) |
0.303606 | + | 0.952798i | \(0.401809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.3154 | − | 19.2347i | 1.22058 | − | 0.704703i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.7565 | − | 8.51967i | 0.539912 | − | 0.311719i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.1357 | −0.589585 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.89270 | − | 3.97950i | −0.251518 | − | 0.145214i | 0.368941 | − | 0.929453i | \(-0.379720\pi\) |
−0.620459 | + | 0.784239i | \(0.713054\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.75302 | + | 3.03632i | 0.0638835 | + | 0.110650i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.4098 | − | 22.1759i | 1.39787 | − | 0.807063i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1997 | −0.588787 | −0.294393 | − | 0.955684i | \(-0.595118\pi\) | ||||
−0.294393 | + | 0.955684i | \(0.595118\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.50246 | − | 6.06644i | 0.127131 | − | 0.220198i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.40363 | + | 16.2876i | −0.340881 | + | 0.590424i | −0.984597 | − | 0.174841i | \(-0.944059\pi\) |
0.643715 | + | 0.765265i | \(0.277392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.54290i | 0.345476i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.7165 | + | 7.91923i | −0.495921 | + | 0.286320i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.789076 | + | 1.36672i | −0.0284919 | + | 0.0493494i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 42.4637i | − | 1.53128i | −0.643269 | − | 0.765640i | \(-0.722422\pi\) | ||
0.643269 | − | 0.765640i | \(-0.277578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.98105 | − | 6.89538i | 0.143374 | − | 0.248331i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.1939 | −0.978098 | −0.489049 | − | 0.872256i | \(-0.662656\pi\) | ||||
−0.489049 | + | 0.872256i | \(0.662656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 17.2009i | − | 0.617876i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.220923 | − | 0.127550i | 0.00792558 | − | 0.00457584i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.3041 | − | 33.4357i | 0.691642 | − | 1.19796i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1324 | − | 7.58202i | −0.469916 | − | 0.271306i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.61557 | − | 4.39685i | −0.272158 | − | 0.157131i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.75031 | − | 5.05199i | −0.312312 | − | 0.180313i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.2502 | − | 24.3932i | 1.50606 | − | 0.869522i | 0.506082 | − | 0.862486i | \(-0.331093\pi\) |
0.999975 | − | 0.00703669i | \(-0.00223987\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 8.64383i | − | 0.307729i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 12.3454i | − | 0.438952i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.824142 | − | 0.475818i | 0.0292661 | − | 0.0168968i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.95577 | − | 2.28386i | −0.140297 | − | 0.0810003i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4351 | + | 8.33409i | 0.511317 | + | 0.295209i | 0.733375 | − | 0.679825i | \(-0.237944\pi\) |
−0.222058 | + | 0.975033i | \(0.571277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.90836 | − | 2.83384i | −0.173645 | − | 0.100254i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.361048 | − | 0.625353i | 0.0127570 | − | 0.0220958i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −53.7139 | + | 31.0118i | −1.89552 | + | 1.09438i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 17.3233i | − | 0.610568i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.49554 | −0.0526455 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0642072 | − | 0.111210i | 0.00225741 | − | 0.00390994i | −0.864894 | − | 0.501954i | \(-0.832615\pi\) |
0.867152 | + | 0.498044i | \(0.165948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.32647i | − | 0.151923i | −0.997111 | − | 0.0759614i | \(-0.975797\pi\) | ||
0.997111 | − | 0.0759614i | \(-0.0242026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.77857 | + | 3.08058i | −0.0623773 | + | 0.108041i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.3567 | + | 10.0209i | −0.607978 | + | 0.351016i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.0380i | 1.57568i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.226511 | − | 0.392328i | 0.00791492 | − | 0.0137091i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2204 | − | 17.7022i | 0.356693 | − | 0.617810i | −0.630713 | − | 0.776016i | \(-0.717238\pi\) |
0.987406 | + | 0.158206i | \(0.0505709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.2987 | 0.358991 | 0.179495 | − | 0.983759i | \(-0.442553\pi\) | ||||
0.179495 | + | 0.983759i | \(0.442553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.79167 | − | 1.03442i | 0.0623778 | − | 0.0360139i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9104 | + | 20.6294i | 0.414166 | + | 0.717356i | 0.995340 | − | 0.0964228i | \(-0.0307401\pi\) |
−0.581175 | + | 0.813779i | \(0.697407\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.8812 | + | 23.0254i | 1.38513 | + | 0.799707i | 0.992762 | − | 0.120100i | \(-0.0383216\pi\) |
0.392371 | + | 0.919807i | \(0.371655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.22437 | 0.0771626 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.6003 | + | 6.12007i | −0.367278 | + | 0.212048i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.478043 | − | 0.275998i | 0.0165434 | − | 0.00955132i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.5267 | + | 7.80963i | 0.467551 | + | 0.269940i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.7797 | − | 21.8121i | 1.30430 | − | 0.753037i | 0.323161 | − | 0.946344i | \(-0.395255\pi\) |
0.981138 | + | 0.193307i | \(0.0619212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.08515 | − | 1.87953i | −0.0374189 | − | 0.0648114i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.31258 | + | 4.00550i | −0.0796495 | + | 0.137957i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.0075 | + | 29.4579i | 0.585076 | + | 1.01338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.04810 | 0.139094 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.312487 | − | 0.180414i | 0.0107245 | − | 0.00619180i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.39136 | −0.184814 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.9886 | − | 23.0874i | 1.36918 | − | 0.790498i | 0.378359 | − | 0.925659i | \(-0.376488\pi\) |
0.990824 | + | 0.135161i | \(0.0431550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.4402i | 1.00683i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.19449 | 0.177440 | 0.0887202 | − | 0.996057i | \(-0.471722\pi\) | ||||
0.0887202 | + | 0.996057i | \(0.471722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.9763 | −1.12514 | −0.562569 | − | 0.826751i | \(-0.690187\pi\) | ||||
−0.562569 | + | 0.826751i | \(0.690187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 3.00393i | − | 0.102374i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.78297 | − | 5.64820i | −0.333016 | − | 0.192267i | 0.324163 | − | 0.946001i | \(-0.394917\pi\) |
−0.657179 | + | 0.753734i | \(0.728251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7431 | − | 10.8213i | −0.637283 | − | 0.367935i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.82323 | + | 3.15793i | 0.0619202 | + | 0.107249i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.75233 | + | 33.9516i | 0.161212 | + | 1.15173i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.50224 | + | 0.867317i | −0.0509013 | + | 0.0293879i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.6742 | + | 21.9524i | −0.428957 | + | 0.742975i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.28318 | + | 7.41868i | −0.144798 | + | 0.250797i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.9467 | −0.876156 | −0.438078 | − | 0.898937i | \(-0.644341\pi\) | ||||
−0.438078 | + | 0.898937i | \(0.644341\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.40112i | 0.148446i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.6966i | − | 0.798360i | −0.916873 | − | 0.399180i | \(-0.869295\pi\) | ||
0.916873 | − | 0.399180i | \(-0.130705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.635140 | −0.0213742 | −0.0106871 | − | 0.999943i | \(-0.503402\pi\) | ||||
−0.0106871 | + | 0.999943i | \(0.503402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.98980 | − | 6.91054i | −0.134116 | − | 0.232295i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 53.7876i | − | 1.80601i | −0.429630 | − | 0.903005i | \(-0.641356\pi\) | ||
0.429630 | − | 0.903005i | \(-0.358644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.48814 | − | 14.7019i | −0.284683 | − | 0.493086i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 31.8829i | − | 1.06812i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.12358 | + | 5.26750i | −0.305309 | + | 0.176270i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.8130 | + | 22.4087i | 1.29738 | + | 0.749041i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.233894 | − | 0.135039i | 0.00780949 | − | 0.00450881i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.8273 | − | 41.2701i | −0.794685 | − | 1.37644i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.29070 | + | 10.8958i | −0.209574 | + | 0.362992i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.75210 | + | 3.03473i | 0.0583063 | + | 0.100989i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.8543 | + | 23.9964i | 0.460534 | + | 0.797668i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0116i | 0.531657i | 0.964020 | + | 0.265828i | \(0.0856455\pi\) | ||||
−0.964020 | + | 0.265828i | \(0.914355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0978 | − | 19.2219i | 0.368090 | − | 0.637550i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0598 | + | 5.80801i | −0.333295 | + | 0.192428i | −0.657303 | − | 0.753626i | \(-0.728303\pi\) |
0.324008 | + | 0.946054i | \(0.394970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.2627 | + | 19.5076i | 0.372742 | + | 0.645608i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.81176i | 0.159072i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.5281 | − | 7.23309i | −0.413713 | − | 0.238858i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5658 | + | 7.25486i | 0.414507 | + | 0.239316i | 0.692725 | − | 0.721202i | \(-0.256410\pi\) |
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.95683 | 0.196284 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.292328 | − | 0.506326i | −0.00962208 | − | 0.0166659i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.37896 | − | 0.796145i | −0.0453400 | − | 0.0261771i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.5848 | 0.840316 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.2264 | − | 8.21361i | −0.466753 | − | 0.269480i | 0.248127 | − | 0.968728i | \(-0.420185\pi\) |
−0.714879 | + | 0.699248i | \(0.753518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.7517i | 0.745658i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.86559 | 0.257508 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.4690 | − | 18.1328i | −0.342371 | − | 0.593005i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.8188 | + | 11.4424i | 0.647451 | + | 0.373806i | 0.787479 | − | 0.616341i | \(-0.211386\pi\) |
−0.140028 | + | 0.990148i | \(0.544719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.54541 | − | 2.67672i | 0.0504324 | − | 0.0873515i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.3415 | + | 23.1081i | −0.434920 | + | 0.753304i | −0.997289 | − | 0.0735825i | \(-0.976557\pi\) |
0.562369 | + | 0.826886i | \(0.309890\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.7430 | + | 54.9805i | −1.03369 | + | 1.79041i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.32292 | + | 4.02341i | 0.0755645 | + | 0.130882i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.5018 | −1.25114 | −0.625570 | − | 0.780168i | \(-0.715133\pi\) | ||||
−0.625570 | + | 0.780168i | \(0.715133\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.39134 | −0.0776262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.697415 | − | 1.20796i | −0.0226152 | − | 0.0391707i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.6779 | − | 37.5473i | 0.702217 | − | 1.21628i | −0.265469 | − | 0.964119i | \(-0.585527\pi\) |
0.967686 | − | 0.252157i | \(-0.0811398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.80055 | + | 11.7789i | −0.220061 | + | 0.381156i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.86582 | − | 4.96375i | 0.0926389 | − | 0.160455i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.121582 | + | 0.0701952i | 0.00392608 | + | 0.00226672i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.8218 | + | 46.4567i | 0.865219 | + | 1.49860i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.0914 | −1.45305 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.98198i | 0.289140i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.7752 | + | 17.1907i | 0.957507 | + | 0.552817i | 0.895405 | − | 0.445253i | \(-0.146886\pi\) |
0.0621023 | + | 0.998070i | \(0.480219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.28745 | −0.0734835 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.7681 | − | 15.4546i | −0.859029 | − | 0.495961i | 0.00465805 | − | 0.999989i | \(-0.498517\pi\) |
−0.863687 | + | 0.504029i | \(0.831851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.42914 | − | 9.40354i | −0.174050 | − | 0.301464i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0797649 | 0.00255452 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.3148 | − | 16.3475i | −0.905870 | − | 0.523004i | −0.0267700 | − | 0.999642i | \(-0.508522\pi\) |
−0.879100 | + | 0.476637i | \(0.841856\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.826696 | + | 0.477293i | 0.0264213 | + | 0.0152544i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.6678i | 0.851437i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0359291 | − | 0.0622311i | −0.00114596 | − | 0.00198486i | 0.865452 | − | 0.500992i | \(-0.167031\pi\) |
−0.866598 | + | 0.499007i | \(0.833698\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.1669 | + | 13.3754i | −0.738159 | + | 0.426176i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.409840 | + | 0.709864i | −0.0130453 | + | 0.0225952i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 74.0588i | − | 2.35493i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.6008 | − | 47.8059i | −0.876767 | − | 1.51860i | −0.854869 | − | 0.518844i | \(-0.826362\pi\) |
−0.0218982 | − | 0.999760i | \(-0.506971\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.21357 | − | 3.83402i | −0.0702456 | − | 0.121669i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.59268 | + | 6.22271i | −0.113896 | + | 0.197273i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9425 | − | 31.0774i | −0.568245 | − | 0.984230i | −0.996740 | − | 0.0806854i | \(-0.974289\pi\) |
0.428494 | − | 0.903545i | \(-0.359044\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.25216 | − | 0.722937i | 0.0396167 | − | 0.0228727i |
(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 | 1264.2.n.i.767.8 | yes | 28 | |
4.3 | odd | 2 | inner | 1264.2.n.i.767.7 | yes | 28 | |
79.24 | odd | 6 | inner | 1264.2.n.i.735.7 | ✓ | 28 | |
316.103 | even | 6 | inner | 1264.2.n.i.735.8 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1264.2.n.i.735.7 | ✓ | 28 | 79.24 | odd | 6 | inner | |
1264.2.n.i.735.8 | yes | 28 | 316.103 | even | 6 | inner | |
1264.2.n.i.767.7 | yes | 28 | 4.3 | odd | 2 | inner | |
1264.2.n.i.767.8 | yes | 28 | 1.1 | even | 1 | trivial |