Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.2 | ||
Root | \(0.809017 - 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.165 |
Dual form | 637.2.h.f.471.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61803 | 1.85123 | 0.925615 | − | 0.378467i | \(-0.123549\pi\) | ||||
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | −1.30902 | − | 2.26728i | −0.755761 | − | 1.30902i | −0.944995 | − | 0.327085i | \(-0.893934\pi\) |
0.189234 | − | 0.981932i | \(-0.439400\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | 1.30902 | + | 2.26728i | 0.585410 | + | 1.01396i | 0.994824 | + | 0.101611i | \(0.0323999\pi\) |
−0.409414 | + | 0.912349i | \(0.634267\pi\) | |||||||
\(6\) | −3.42705 | − | 5.93583i | −1.39909 | − | 2.42329i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.47214 | 2.64180 | ||||||||
\(9\) | −1.92705 | + | 3.33775i | −0.642350 | + | 1.11258i | ||||
\(10\) | 3.42705 | + | 5.93583i | 1.08373 | + | 1.87707i | ||||
\(11\) | −0.927051 | − | 1.60570i | −0.279516 | − | 0.484137i | 0.691748 | − | 0.722139i | \(-0.256841\pi\) |
−0.971265 | + | 0.238002i | \(0.923507\pi\) | |||||||
\(12\) | −6.35410 | − | 11.0056i | −1.83427 | − | 3.17705i | ||||
\(13\) | 2.50000 | − | 2.59808i | 0.693375 | − | 0.720577i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.42705 | − | 5.93583i | 0.884861 | − | 1.53262i | ||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | 1.47214 | 0.357045 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(18\) | −5.04508 | + | 8.73834i | −1.18914 | + | 2.05965i | ||||
\(19\) | −0.927051 | + | 1.60570i | −0.212680 | + | 0.368373i | −0.952552 | − | 0.304375i | \(-0.901553\pi\) |
0.739872 | + | 0.672747i | \(0.234886\pi\) | |||||||
\(20\) | 6.35410 | + | 11.0056i | 1.42082 | + | 2.46093i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.42705 | − | 4.20378i | −0.517449 | − | 0.896248i | ||||
\(23\) | −4.47214 | −0.932505 | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | −9.78115 | − | 16.9415i | −1.99657 | − | 3.45816i | ||||
\(25\) | −0.927051 | + | 1.60570i | −0.185410 | + | 0.321140i | ||||
\(26\) | 6.54508 | − | 6.80185i | 1.28360 | − | 1.33395i | ||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54508 | + | 6.14027i | −0.658306 | + | 1.14022i | 0.322748 | + | 0.946485i | \(0.395393\pi\) |
−0.981054 | + | 0.193734i | \(0.937940\pi\) | |||||||
\(30\) | 8.97214 | − | 15.5402i | 1.63808 | − | 2.83724i | ||||
\(31\) | −2.35410 | + | 4.07742i | −0.422809 | + | 0.732327i | −0.996213 | − | 0.0869459i | \(-0.972289\pi\) |
0.573404 | + | 0.819273i | \(0.305623\pi\) | |||||||
\(32\) | 10.8541 | 1.91875 | ||||||||
\(33\) | −2.42705 | + | 4.20378i | −0.422495 | + | 0.731783i | ||||
\(34\) | 3.85410 | 0.660973 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.35410 | + | 16.2018i | −1.55902 | + | 2.70030i | ||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | −2.42705 | + | 4.20378i | −0.393720 | + | 0.681942i | ||||
\(39\) | −9.16312 | − | 2.26728i | −1.46727 | − | 0.363056i | ||||
\(40\) | 9.78115 | + | 16.9415i | 1.54654 | + | 2.67868i | ||||
\(41\) | 0.381966 | − | 0.661585i | 0.0596531 | − | 0.103322i | −0.834657 | − | 0.550771i | \(-0.814334\pi\) |
0.894310 | + | 0.447449i | \(0.147667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.28115 | − | 10.8793i | −0.957867 | − | 1.65907i | −0.727667 | − | 0.685931i | \(-0.759395\pi\) |
−0.230200 | − | 0.973143i | \(-0.573938\pi\) | |||||||
\(44\) | −4.50000 | − | 7.79423i | −0.678401 | − | 1.17502i | ||||
\(45\) | −10.0902 | −1.50415 | ||||||||
\(46\) | −11.7082 | −1.72628 | ||||||||
\(47\) | −1.11803 | − | 1.93649i | −0.163082 | − | 0.282466i | 0.772890 | − | 0.634539i | \(-0.218810\pi\) |
−0.935973 | + | 0.352073i | \(0.885477\pi\) | |||||||
\(48\) | −12.8992 | − | 22.3420i | −1.86184 | − | 3.22480i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.42705 | + | 4.20378i | −0.343237 | + | 0.594504i | ||||
\(51\) | −1.92705 | − | 3.33775i | −0.269841 | − | 0.467379i | ||||
\(52\) | 12.1353 | − | 12.6113i | 1.68286 | − | 1.74888i | ||||
\(53\) | −1.88197 | + | 3.25966i | −0.258508 | + | 0.447749i | −0.965842 | − | 0.259130i | \(-0.916564\pi\) |
0.707334 | + | 0.706879i | \(0.249897\pi\) | |||||||
\(54\) | 5.85410 | 0.796642 | ||||||||
\(55\) | 2.42705 | − | 4.20378i | 0.327263 | − | 0.566837i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.85410 | 0.642942 | ||||||||
\(58\) | −9.28115 | + | 16.0754i | −1.21868 | + | 2.11081i | ||||
\(59\) | 2.23607 | 0.291111 | 0.145556 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(60\) | 16.6353 | − | 28.8131i | 2.14760 | − | 3.71976i | ||||
\(61\) | −3.00000 | + | 5.19615i | −0.384111 | + | 0.665299i | −0.991645 | − | 0.128994i | \(-0.958825\pi\) |
0.607535 | + | 0.794293i | \(0.292159\pi\) | |||||||
\(62\) | −6.16312 | + | 10.6748i | −0.782717 | + | 1.35571i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 9.16312 | + | 2.26728i | 1.13655 | + | 0.281222i | ||||
\(66\) | −6.35410 | + | 11.0056i | −0.782136 | + | 1.35470i | ||||
\(67\) | 6.35410 | + | 11.0056i | 0.776277 | + | 1.34455i | 0.934074 | + | 0.357080i | \(0.116228\pi\) |
−0.157797 | + | 0.987472i | \(0.550439\pi\) | |||||||
\(68\) | 7.14590 | 0.866567 | ||||||||
\(69\) | 5.85410 | + | 10.1396i | 0.704751 | + | 1.22066i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.09017 | + | 12.2805i | 0.841448 | + | 1.45743i | 0.888670 | + | 0.458547i | \(0.151630\pi\) |
−0.0472218 | + | 0.998884i | \(0.515037\pi\) | |||||||
\(72\) | −14.3992 | + | 24.9401i | −1.69696 | + | 2.93922i | ||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 10.4721 | 1.21736 | ||||||||
\(75\) | 4.85410 | 0.560503 | ||||||||
\(76\) | −4.50000 | + | 7.79423i | −0.516185 | + | 0.894059i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −23.9894 | − | 5.93583i | −2.71626 | − | 0.672100i | ||||
\(79\) | −2.00000 | − | 3.46410i | −0.225018 | − | 0.389742i | 0.731307 | − | 0.682048i | \(-0.238911\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 12.8992 | + | 22.3420i | 1.44217 | + | 2.49792i | ||||
\(81\) | 2.85410 | + | 4.94345i | 0.317122 | + | 0.549272i | ||||
\(82\) | 1.00000 | − | 1.73205i | 0.110432 | − | 0.191273i | ||||
\(83\) | −6.70820 | −0.736321 | −0.368161 | − | 0.929762i | \(-0.620012\pi\) | ||||
−0.368161 | + | 0.929762i | \(0.620012\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.92705 | + | 3.33775i | 0.209018 | + | 0.362030i | ||||
\(86\) | −16.4443 | − | 28.4823i | −1.77323 | − | 3.07133i | ||||
\(87\) | 18.5623 | 1.99009 | ||||||||
\(88\) | −6.92705 | − | 11.9980i | −0.738426 | − | 1.27899i | ||||
\(89\) | −4.90983 | −0.520441 | −0.260220 | − | 0.965549i | \(-0.583795\pi\) | ||||
−0.260220 | + | 0.965549i | \(0.583795\pi\) | |||||||
\(90\) | −26.4164 | −2.78453 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.7082 | −2.26324 | ||||||||
\(93\) | 12.3262 | 1.27817 | ||||||||
\(94\) | −2.92705 | − | 5.06980i | −0.301902 | − | 0.522910i | ||||
\(95\) | −4.85410 | −0.498020 | ||||||||
\(96\) | −14.2082 | − | 24.6093i | −1.45012 | − | 2.51168i | ||||
\(97\) | 9.42705 | + | 16.3281i | 0.957172 | + | 1.65787i | 0.729318 | + | 0.684175i | \(0.239838\pi\) |
0.227854 | + | 0.973695i | \(0.426829\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.14590 | 0.718190 | ||||||||
\(100\) | −4.50000 | + | 7.79423i | −0.450000 | + | 0.779423i | ||||
\(101\) | −5.78115 | − | 10.0133i | −0.575246 | − | 0.996356i | −0.996015 | − | 0.0891877i | \(-0.971573\pi\) |
0.420769 | − | 0.907168i | \(-0.361760\pi\) | |||||||
\(102\) | −5.04508 | − | 8.73834i | −0.499538 | − | 0.865225i | ||||
\(103\) | −4.35410 | − | 7.54153i | −0.429022 | − | 0.743089i | 0.567764 | − | 0.823191i | \(-0.307809\pi\) |
−0.996787 | + | 0.0801026i | \(0.974475\pi\) | |||||||
\(104\) | 18.6803 | − | 19.4132i | 1.83176 | − | 1.90362i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.92705 | + | 8.53390i | −0.478557 | + | 0.828886i | ||||
\(107\) | −3.38197 | −0.326947 | −0.163473 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163473 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(108\) | 10.8541 | 1.04444 | ||||||||
\(109\) | 1.35410 | − | 2.34537i | 0.129699 | − | 0.224646i | −0.793861 | − | 0.608100i | \(-0.791932\pi\) |
0.923560 | + | 0.383454i | \(0.125265\pi\) | |||||||
\(110\) | 6.35410 | − | 11.0056i | 0.605840 | − | 1.04935i | ||||
\(111\) | −5.23607 | − | 9.06914i | −0.496986 | − | 0.860804i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.736068 | − | 1.27491i | −0.0692435 | − | 0.119933i | 0.829325 | − | 0.558766i | \(-0.188725\pi\) |
−0.898568 | + | 0.438833i | \(0.855392\pi\) | |||||||
\(114\) | 12.7082 | 1.19023 | ||||||||
\(115\) | −5.85410 | − | 10.1396i | −0.545898 | − | 0.945523i | ||||
\(116\) | −17.2082 | + | 29.8055i | −1.59774 | + | 2.76737i | ||||
\(117\) | 3.85410 | + | 13.3510i | 0.356312 | + | 1.23430i | ||||
\(118\) | 5.85410 | 0.538914 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 25.6074 | − | 44.3533i | 2.33762 | − | 4.04888i | ||||
\(121\) | 3.78115 | − | 6.54915i | 0.343741 | − | 0.595377i | ||||
\(122\) | −7.85410 | + | 13.6037i | −0.711077 | + | 1.23162i | ||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | −11.4271 | + | 19.7922i | −1.02618 | + | 1.77739i | ||||
\(125\) | 8.23607 | 0.736656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4271 | − | 18.0602i | 0.925251 | − | 1.60258i | 0.134094 | − | 0.990969i | \(-0.457187\pi\) |
0.791157 | − | 0.611613i | \(-0.209479\pi\) | |||||||
\(128\) | 1.09017 | 0.0963583 | ||||||||
\(129\) | −16.4443 | + | 28.4823i | −1.44784 | + | 2.50773i | ||||
\(130\) | 23.9894 | + | 5.93583i | 2.10401 | + | 0.520606i | ||||
\(131\) | −7.66312 | − | 13.2729i | −0.669530 | − | 1.15966i | −0.978036 | − | 0.208437i | \(-0.933162\pi\) |
0.308506 | − | 0.951222i | \(-0.400171\pi\) | |||||||
\(132\) | −11.7812 | + | 20.4056i | −1.02542 | + | 1.77608i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.6353 | + | 28.8131i | 1.43707 | + | 2.48907i | ||||
\(135\) | 2.92705 | + | 5.06980i | 0.251920 | + | 0.436339i | ||||
\(136\) | 11.0000 | 0.943242 | ||||||||
\(137\) | −2.61803 | −0.223674 | −0.111837 | − | 0.993727i | \(-0.535673\pi\) | ||||
−0.111837 | + | 0.993727i | \(0.535673\pi\) | |||||||
\(138\) | 15.3262 | + | 26.5458i | 1.30466 | + | 2.25973i | ||||
\(139\) | 2.28115 | + | 3.95107i | 0.193485 | + | 0.335126i | 0.946403 | − | 0.322989i | \(-0.104688\pi\) |
−0.752918 | + | 0.658114i | \(0.771354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.92705 | + | 5.06980i | −0.246502 | + | 0.426954i | ||||
\(142\) | 18.5623 | + | 32.1509i | 1.55771 | + | 2.69804i | ||||
\(143\) | −6.48936 | − | 1.60570i | −0.542667 | − | 0.134275i | ||||
\(144\) | −18.9894 | + | 32.8905i | −1.58245 | + | 2.74088i | ||||
\(145\) | −18.5623 | −1.54152 | ||||||||
\(146\) | −2.61803 | + | 4.53457i | −0.216670 | + | 0.375284i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.4164 | 1.59602 | ||||||||
\(149\) | −0.927051 | + | 1.60570i | −0.0759470 | + | 0.131544i | −0.901498 | − | 0.432784i | \(-0.857531\pi\) |
0.825551 | + | 0.564328i | \(0.190865\pi\) | |||||||
\(150\) | 12.7082 | 1.03762 | ||||||||
\(151\) | 0.645898 | − | 1.11873i | 0.0525624 | − | 0.0910408i | −0.838547 | − | 0.544829i | \(-0.816594\pi\) |
0.891109 | + | 0.453788i | \(0.149928\pi\) | |||||||
\(152\) | −6.92705 | + | 11.9980i | −0.561858 | + | 0.973167i | ||||
\(153\) | −2.83688 | + | 4.91362i | −0.229348 | + | 0.397243i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3262 | −0.990067 | ||||||||
\(156\) | −44.4787 | − | 11.0056i | −3.56115 | − | 0.881155i | ||||
\(157\) | 7.42705 | − | 12.8640i | 0.592743 | − | 1.02666i | −0.401118 | − | 0.916026i | \(-0.631378\pi\) |
0.993861 | − | 0.110635i | \(-0.0352884\pi\) | |||||||
\(158\) | −5.23607 | − | 9.06914i | −0.416559 | − | 0.721502i | ||||
\(159\) | 9.85410 | 0.781481 | ||||||||
\(160\) | 14.2082 | + | 24.6093i | 1.12326 | + | 1.94554i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.47214 | + | 12.9421i | 0.587066 | + | 1.01683i | ||||
\(163\) | 1.85410 | − | 3.21140i | 0.145224 | − | 0.251536i | −0.784232 | − | 0.620467i | \(-0.786943\pi\) |
0.929457 | + | 0.368931i | \(0.120276\pi\) | |||||||
\(164\) | 1.85410 | − | 3.21140i | 0.144781 | − | 0.250768i | ||||
\(165\) | −12.7082 | −0.989332 | ||||||||
\(166\) | −17.5623 | −1.36310 | ||||||||
\(167\) | 7.11803 | − | 12.3288i | 0.550810 | − | 0.954031i | −0.447406 | − | 0.894331i | \(-0.647652\pi\) |
0.998216 | − | 0.0597001i | \(-0.0190144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 5.04508 | + | 8.73834i | 0.386940 | + | 0.670200i | ||||
\(171\) | −3.57295 | − | 6.18853i | −0.273230 | − | 0.473249i | ||||
\(172\) | −30.4894 | − | 52.8091i | −2.32479 | − | 4.02666i | ||||
\(173\) | −4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | 48.5967 | 3.68411 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.13525 | − | 15.8227i | −0.688596 | − | 1.19268i | ||||
\(177\) | −2.92705 | − | 5.06980i | −0.220011 | − | 0.381070i | ||||
\(178\) | −12.8541 | −0.963456 | ||||||||
\(179\) | 4.50000 | + | 7.79423i | 0.336346 | + | 0.582568i | 0.983742 | − | 0.179585i | \(-0.0574756\pi\) |
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(180\) | −48.9787 | −3.65066 | ||||||||
\(181\) | −9.70820 | −0.721605 | −0.360803 | − | 0.932642i | \(-0.617497\pi\) | ||||
−0.360803 | + | 0.932642i | \(0.617497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7082 | 1.16118 | ||||||||
\(184\) | −33.4164 | −2.46349 | ||||||||
\(185\) | 5.23607 | + | 9.06914i | 0.384963 | + | 0.666776i | ||||
\(186\) | 32.2705 | 2.36619 | ||||||||
\(187\) | −1.36475 | − | 2.36381i | −0.0998000 | − | 0.172859i | ||||
\(188\) | −5.42705 | − | 9.39993i | −0.395808 | − | 0.685560i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.7082 | −0.921950 | ||||||||
\(191\) | −10.6910 | + | 18.5173i | −0.773572 | + | 1.33987i | 0.162021 | + | 0.986787i | \(0.448199\pi\) |
−0.935593 | + | 0.353079i | \(0.885135\pi\) | |||||||
\(192\) | −11.3992 | − | 19.7440i | −0.822665 | − | 1.42490i | ||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | 24.6803 | + | 42.7476i | 1.77195 | + | 3.06910i | ||||
\(195\) | −6.85410 | − | 23.7433i | −0.490832 | − | 1.70029i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.39919 | − | 14.5478i | 0.598417 | − | 1.03649i | −0.394638 | − | 0.918837i | \(-0.629130\pi\) |
0.993055 | − | 0.117652i | \(-0.0375368\pi\) | |||||||
\(198\) | 18.7082 | 1.32953 | ||||||||
\(199\) | 24.4164 | 1.73083 | 0.865417 | − | 0.501053i | \(-0.167054\pi\) | ||||
0.865417 | + | 0.501053i | \(0.167054\pi\) | |||||||
\(200\) | −6.92705 | + | 11.9980i | −0.489816 | + | 0.848387i | ||||
\(201\) | 16.6353 | − | 28.8131i | 1.17336 | − | 2.03232i | ||||
\(202\) | −15.1353 | − | 26.2150i | −1.06491 | − | 1.84448i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.35410 | − | 16.2018i | −0.654918 | − | 1.13435i | ||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | −11.3992 | − | 19.7440i | −0.794219 | − | 1.37563i | ||||
\(207\) | 8.61803 | − | 14.9269i | 0.598995 | − | 1.03749i | ||||
\(208\) | 24.6353 | − | 25.6017i | 1.70815 | − | 1.77516i | ||||
\(209\) | 3.43769 | 0.237790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.35410 | + | 4.07742i | −0.162063 | + | 0.280701i | −0.935608 | − | 0.353039i | \(-0.885148\pi\) |
0.773545 | + | 0.633741i | \(0.218481\pi\) | |||||||
\(212\) | −9.13525 | + | 15.8227i | −0.627412 | + | 1.08671i | ||||
\(213\) | 18.5623 | − | 32.1509i | 1.27187 | − | 2.20294i | ||||
\(214\) | −8.85410 | −0.605254 | ||||||||
\(215\) | 16.4443 | − | 28.4823i | 1.12149 | − | 1.94248i | ||||
\(216\) | 16.7082 | 1.13685 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.54508 | − | 6.14027i | 0.240103 | − | 0.415871i | ||||
\(219\) | 5.23607 | 0.353821 | ||||||||
\(220\) | 11.7812 | − | 20.4056i | 0.794285 | − | 1.37574i | ||||
\(221\) | 3.68034 | − | 3.82472i | 0.247566 | − | 0.257279i | ||||
\(222\) | −13.7082 | − | 23.7433i | −0.920034 | − | 1.59355i | ||||
\(223\) | 10.1353 | − | 17.5548i | 0.678707 | − | 1.17555i | −0.296664 | − | 0.954982i | \(-0.595874\pi\) |
0.975371 | − | 0.220573i | \(-0.0707926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.57295 | − | 6.18853i | −0.238197 | − | 0.412569i | ||||
\(226\) | −1.92705 | − | 3.33775i | −0.128186 | − | 0.222024i | ||||
\(227\) | −1.47214 | −0.0977091 | −0.0488545 | − | 0.998806i | \(-0.515557\pi\) | ||||
−0.0488545 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(228\) | 23.5623 | 1.56045 | ||||||||
\(229\) | −6.56231 | − | 11.3662i | −0.433649 | − | 0.751103i | 0.563535 | − | 0.826092i | \(-0.309441\pi\) |
−0.997184 | + | 0.0749895i | \(0.976108\pi\) | |||||||
\(230\) | −15.3262 | − | 26.5458i | −1.01058 | − | 1.75038i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −26.4894 | + | 45.8809i | −1.73911 | + | 3.01223i | ||||
\(233\) | −1.30902 | − | 2.26728i | −0.0857566 | − | 0.148535i | 0.819957 | − | 0.572425i | \(-0.193997\pi\) |
−0.905713 | + | 0.423891i | \(0.860664\pi\) | |||||||
\(234\) | 10.0902 | + | 34.9534i | 0.659615 | + | 2.28497i | ||||
\(235\) | 2.92705 | − | 5.06980i | 0.190940 | − | 0.330717i | ||||
\(236\) | 10.8541 | 0.706542 | ||||||||
\(237\) | −5.23607 | + | 9.06914i | −0.340119 | + | 0.589104i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.7082 | −1.59824 | −0.799120 | − | 0.601171i | \(-0.794701\pi\) | ||||
−0.799120 | + | 0.601171i | \(0.794701\pi\) | |||||||
\(240\) | 33.7705 | − | 58.4922i | 2.17988 | − | 3.77566i | ||||
\(241\) | −24.5623 | −1.58220 | −0.791099 | − | 0.611689i | \(-0.790491\pi\) | ||||
−0.791099 | + | 0.611689i | \(0.790491\pi\) | |||||||
\(242\) | 9.89919 | − | 17.1459i | 0.636344 | − | 1.10218i | ||||
\(243\) | 10.8262 | − | 18.7516i | 0.694503 | − | 1.20292i | ||||
\(244\) | −14.5623 | + | 25.2227i | −0.932256 | + | 1.61471i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.23607 | −0.333840 | ||||||||
\(247\) | 1.85410 | + | 6.42280i | 0.117974 | + | 0.408673i | ||||
\(248\) | −17.5902 | + | 30.4671i | −1.11698 | + | 1.93466i | ||||
\(249\) | 8.78115 | + | 15.2094i | 0.556483 | + | 0.963857i | ||||
\(250\) | 21.5623 | 1.36372 | ||||||||
\(251\) | 0.381966 | + | 0.661585i | 0.0241095 | + | 0.0417588i | 0.877828 | − | 0.478975i | \(-0.158992\pi\) |
−0.853719 | + | 0.520734i | \(0.825658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.14590 | + | 7.18091i | 0.260650 | + | 0.451460i | ||||
\(254\) | 27.2984 | − | 47.2822i | 1.71285 | − | 2.96675i | ||||
\(255\) | 5.04508 | − | 8.73834i | 0.315935 | − | 0.547216i | ||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | −16.7426 | −1.04438 | −0.522189 | − | 0.852830i | \(-0.674884\pi\) | ||||
−0.522189 | + | 0.852830i | \(0.674884\pi\) | |||||||
\(258\) | −43.0517 | + | 74.5677i | −2.68028 | + | 4.64238i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 44.4787 | + | 11.0056i | 2.75845 | + | 0.682540i | ||||
\(261\) | −13.6631 | − | 23.6652i | −0.845726 | − | 1.46484i | ||||
\(262\) | −20.0623 | − | 34.7489i | −1.23945 | − | 2.14680i | ||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | −18.1353 | + | 31.4112i | −1.11615 | + | 1.93322i | ||||
\(265\) | −9.85410 | −0.605333 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.42705 | + | 11.1320i | 0.393329 | + | 0.681266i | ||||
\(268\) | 30.8435 | + | 53.4224i | 1.88406 | + | 3.26329i | ||||
\(269\) | 28.7426 | 1.75247 | 0.876235 | − | 0.481884i | \(-0.160047\pi\) | ||||
0.876235 | + | 0.481884i | \(0.160047\pi\) | |||||||
\(270\) | 7.66312 | + | 13.2729i | 0.466363 | + | 0.807764i | ||||
\(271\) | 8.41641 | 0.511260 | 0.255630 | − | 0.966775i | \(-0.417717\pi\) | ||||
0.255630 | + | 0.966775i | \(0.417717\pi\) | |||||||
\(272\) | 14.5066 | 0.879590 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.85410 | −0.414071 | ||||||||
\(275\) | 3.43769 | 0.207301 | ||||||||
\(276\) | 28.4164 | + | 49.2187i | 1.71047 | + | 2.96262i | ||||
\(277\) | −5.00000 | −0.300421 | −0.150210 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150210 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(278\) | 5.97214 | + | 10.3440i | 0.358185 | + | 0.620394i | ||||
\(279\) | −9.07295 | − | 15.7148i | −0.543183 | − | 0.940821i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1803 | 1.20386 | 0.601929 | − | 0.798550i | \(-0.294399\pi\) | ||||
0.601929 | + | 0.798550i | \(0.294399\pi\) | |||||||
\(282\) | −7.66312 | + | 13.2729i | −0.456332 | + | 0.790390i | ||||
\(283\) | 6.70820 | + | 11.6190i | 0.398761 | + | 0.690675i | 0.993573 | − | 0.113190i | \(-0.0361069\pi\) |
−0.594812 | + | 0.803865i | \(0.702774\pi\) | |||||||
\(284\) | 34.4164 | + | 59.6110i | 2.04224 | + | 3.53726i | ||||
\(285\) | 6.35410 | + | 11.0056i | 0.376385 | + | 0.651917i | ||||
\(286\) | −16.9894 | − | 4.20378i | −1.00460 | − | 0.248574i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −20.9164 | + | 36.2283i | −1.23251 | + | 2.13477i | ||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | −48.5967 | −2.85370 | ||||||||
\(291\) | 24.6803 | − | 42.7476i | 1.44679 | − | 2.50591i | ||||
\(292\) | −4.85410 | + | 8.40755i | −0.284065 | + | 0.492015i | ||||
\(293\) | −3.38197 | − | 5.85774i | −0.197577 | − | 0.342213i | 0.750166 | − | 0.661250i | \(-0.229974\pi\) |
−0.947742 | + | 0.319037i | \(0.896640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.92705 | + | 5.06980i | 0.170419 | + | 0.295175i | ||||
\(296\) | 29.8885 | 1.73724 | ||||||||
\(297\) | −2.07295 | − | 3.59045i | −0.120285 | − | 0.208339i | ||||
\(298\) | −2.42705 | + | 4.20378i | −0.140595 | + | 0.243518i | ||||
\(299\) | −11.1803 | + | 11.6190i | −0.646576 | + | 0.671941i | ||||
\(300\) | 23.5623 | 1.36037 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.69098 | − | 2.92887i | 0.0973051 | − | 0.168537i | ||||
\(303\) | −15.1353 | + | 26.2150i | −0.869498 | + | 1.50601i | ||||
\(304\) | −9.13525 | + | 15.8227i | −0.523943 | + | 0.907496i | ||||
\(305\) | −15.7082 | −0.899449 | ||||||||
\(306\) | −7.42705 | + | 12.8640i | −0.424576 | + | 0.735388i | ||||
\(307\) | 4.85410 | 0.277038 | 0.138519 | − | 0.990360i | \(-0.455766\pi\) | ||||
0.138519 | + | 0.990360i | \(0.455766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3992 | + | 19.7440i | −0.648477 | + | 1.12320i | ||||
\(310\) | −32.2705 | −1.83284 | ||||||||
\(311\) | 1.66312 | − | 2.88061i | 0.0943068 | − | 0.163344i | −0.815012 | − | 0.579444i | \(-0.803270\pi\) |
0.909319 | + | 0.416099i | \(0.136603\pi\) | |||||||
\(312\) | −68.4681 | − | 16.9415i | −3.87624 | − | 0.959121i | ||||
\(313\) | 12.5623 | + | 21.7586i | 0.710064 | + | 1.22987i | 0.964833 | + | 0.262864i | \(0.0846671\pi\) |
−0.254769 | + | 0.967002i | \(0.582000\pi\) | |||||||
\(314\) | 19.4443 | − | 33.6785i | 1.09730 | − | 1.90059i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.70820 | − | 16.8151i | −0.546129 | − | 0.945923i | ||||
\(317\) | −13.1180 | − | 22.7211i | −0.736782 | − | 1.27614i | −0.953937 | − | 0.300007i | \(-0.903011\pi\) |
0.217155 | − | 0.976137i | \(-0.430322\pi\) | |||||||
\(318\) | 25.7984 | 1.44670 | ||||||||
\(319\) | 13.1459 | 0.736029 | ||||||||
\(320\) | 11.3992 | + | 19.7440i | 0.637234 | + | 1.10372i | ||||
\(321\) | 4.42705 | + | 7.66788i | 0.247094 | + | 0.427979i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.36475 | + | 2.36381i | −0.0759364 | + | 0.131526i | ||||
\(324\) | 13.8541 | + | 23.9960i | 0.769672 | + | 1.33311i | ||||
\(325\) | 1.85410 | + | 6.42280i | 0.102847 | + | 0.356273i | ||||
\(326\) | 4.85410 | − | 8.40755i | 0.268844 | − | 0.465651i | ||||
\(327\) | −7.09017 | −0.392087 | ||||||||
\(328\) | 2.85410 | − | 4.94345i | 0.157591 | − | 0.272956i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −33.2705 | −1.83148 | ||||||||
\(331\) | 5.07295 | − | 8.78661i | 0.278834 | − | 0.482956i | −0.692261 | − | 0.721647i | \(-0.743385\pi\) |
0.971095 | + | 0.238692i | \(0.0767186\pi\) | |||||||
\(332\) | −32.5623 | −1.78709 | ||||||||
\(333\) | −7.70820 | + | 13.3510i | −0.422407 | + | 0.731630i | ||||
\(334\) | 18.6353 | − | 32.2772i | 1.01968 | − | 1.76613i | ||||
\(335\) | −16.6353 | + | 28.8131i | −0.908881 | + | 1.57423i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5623 | −0.629839 | −0.314919 | − | 0.949118i | \(-0.601978\pi\) | ||||
−0.314919 | + | 0.949118i | \(0.601978\pi\) | |||||||
\(338\) | −1.30902 | − | 34.0093i | −0.0712011 | − | 1.84986i | ||||
\(339\) | −1.92705 | + | 3.33775i | −0.104663 | + | 0.181282i | ||||
\(340\) | 9.35410 | + | 16.2018i | 0.507297 | + | 0.878665i | ||||
\(341\) | 8.72949 | 0.472728 | ||||||||
\(342\) | −9.35410 | − | 16.2018i | −0.505812 | − | 0.876092i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −46.9336 | − | 81.2914i | −2.53049 | − | 4.38294i | ||||
\(345\) | −15.3262 | + | 26.5458i | −0.825137 | + | 1.42918i | ||||
\(346\) | −11.7812 | + | 20.4056i | −0.633359 | + | 1.09701i | ||||
\(347\) | 30.7639 | 1.65149 | 0.825747 | − | 0.564040i | \(-0.190754\pi\) | ||||
0.825747 | + | 0.564040i | \(0.190754\pi\) | |||||||
\(348\) | 90.1033 | 4.83005 | ||||||||
\(349\) | 10.3541 | − | 17.9338i | 0.554242 | − | 0.959976i | −0.443720 | − | 0.896166i | \(-0.646341\pi\) |
0.997962 | − | 0.0638103i | \(-0.0203253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.59017 | − | 5.80948i | 0.298381 | − | 0.310087i | ||||
\(352\) | −10.0623 | − | 17.4284i | −0.536323 | − | 0.928938i | ||||
\(353\) | 11.0729 | + | 19.1789i | 0.589354 | + | 1.02079i | 0.994317 | + | 0.106458i | \(0.0339508\pi\) |
−0.404964 | + | 0.914333i | \(0.632716\pi\) | |||||||
\(354\) | −7.66312 | − | 13.2729i | −0.407290 | − | 0.705447i | ||||
\(355\) | −18.5623 | + | 32.1509i | −0.985185 | + | 1.70639i | ||||
\(356\) | −23.8328 | −1.26314 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.7812 | + | 20.4056i | 0.622653 | + | 1.07847i | ||||
\(359\) | 11.0451 | + | 19.1306i | 0.582937 | + | 1.00968i | 0.995129 | + | 0.0985799i | \(0.0314300\pi\) |
−0.412192 | + | 0.911097i | \(0.635237\pi\) | |||||||
\(360\) | −75.3951 | −3.97367 | ||||||||
\(361\) | 7.78115 | + | 13.4774i | 0.409534 | + | 0.709334i | ||||
\(362\) | −25.4164 | −1.33586 | ||||||||
\(363\) | −19.7984 | −1.03915 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.23607 | −0.274068 | ||||||||
\(366\) | 41.1246 | 2.14962 | ||||||||
\(367\) | −0.708204 | − | 1.22665i | −0.0369679 | − | 0.0640304i | 0.846949 | − | 0.531673i | \(-0.178437\pi\) |
−0.883917 | + | 0.467643i | \(0.845103\pi\) | |||||||
\(368\) | −44.0689 | −2.29725 | ||||||||
\(369\) | 1.47214 | + | 2.54981i | 0.0766363 | + | 0.132738i | ||||
\(370\) | 13.7082 | + | 23.7433i | 0.712656 | + | 1.23436i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 59.8328 | 3.10219 | ||||||||
\(373\) | 10.2812 | − | 17.8075i | 0.532338 | − | 0.922036i | −0.466949 | − | 0.884284i | \(-0.654647\pi\) |
0.999287 | − | 0.0377522i | \(-0.0120198\pi\) | |||||||
\(374\) | −3.57295 | − | 6.18853i | −0.184753 | − | 0.320001i | ||||
\(375\) | −10.7812 | − | 18.6735i | −0.556736 | − | 0.964296i | ||||
\(376\) | −8.35410 | − | 14.4697i | −0.430830 | − | 0.746219i | ||||
\(377\) | 7.09017 | + | 24.5611i | 0.365162 | + | 1.26496i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.07295 | − | 5.32250i | 0.157847 | − | 0.273399i | −0.776245 | − | 0.630431i | \(-0.782878\pi\) |
0.934092 | + | 0.357032i | \(0.116211\pi\) | |||||||
\(380\) | −23.5623 | −1.20872 | ||||||||
\(381\) | −54.5967 | −2.79708 | ||||||||
\(382\) | −27.9894 | + | 48.4790i | −1.43206 | + | 2.48040i | ||||
\(383\) | −10.9894 | + | 19.0341i | −0.561530 | + | 0.972598i | 0.435833 | + | 0.900027i | \(0.356454\pi\) |
−0.997363 | + | 0.0725709i | \(0.976880\pi\) | |||||||
\(384\) | −1.42705 | − | 2.47172i | −0.0728239 | − | 0.126135i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.85410 | + | 13.6037i | 0.399763 | + | 0.692410i | ||||
\(387\) | 48.4164 | 2.46114 | ||||||||
\(388\) | 45.7599 | + | 79.2584i | 2.32311 | + | 4.02374i | ||||
\(389\) | 5.94427 | − | 10.2958i | 0.301387 | − | 0.522017i | −0.675064 | − | 0.737759i | \(-0.735884\pi\) |
0.976450 | + | 0.215743i | \(0.0692172\pi\) | |||||||
\(390\) | −17.9443 | − | 62.1608i | −0.908644 | − | 3.14763i | ||||
\(391\) | −6.58359 | −0.332947 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.0623 | + | 34.7489i | −1.01201 | + | 1.75285i | ||||
\(394\) | 21.9894 | − | 38.0867i | 1.10781 | − | 1.91878i | ||||
\(395\) | 5.23607 | − | 9.06914i | 0.263455 | − | 0.456318i | ||||
\(396\) | 34.6869 | 1.74308 | ||||||||
\(397\) | 0.708204 | − | 1.22665i | 0.0355437 | − | 0.0615636i | −0.847706 | − | 0.530466i | \(-0.822017\pi\) |
0.883250 | + | 0.468902i | \(0.155350\pi\) | |||||||
\(398\) | 63.9230 | 3.20417 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.13525 | + | 15.8227i | −0.456763 | + | 0.791136i | ||||
\(401\) | 35.4508 | 1.77033 | 0.885165 | − | 0.465276i | \(-0.154045\pi\) | ||||
0.885165 | + | 0.465276i | \(0.154045\pi\) | |||||||
\(402\) | 43.5517 | − | 75.4337i | 2.17216 | − | 3.76229i | ||||
\(403\) | 4.70820 | + | 16.3097i | 0.234532 | + | 0.812444i | ||||
\(404\) | −28.0623 | − | 48.6053i | −1.39615 | − | 2.41821i | ||||
\(405\) | −7.47214 | + | 12.9421i | −0.371293 | + | 0.643099i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.70820 | − | 6.42280i | −0.183809 | − | 0.318366i | ||||
\(408\) | −14.3992 | − | 24.9401i | −0.712866 | − | 1.23472i | ||||
\(409\) | −14.4377 | −0.713898 | −0.356949 | − | 0.934124i | \(-0.616183\pi\) | ||||
−0.356949 | + | 0.934124i | \(0.616183\pi\) | |||||||
\(410\) | 5.23607 | 0.258591 | ||||||||
\(411\) | 3.42705 | + | 5.93583i | 0.169044 | + | 0.292793i | ||||
\(412\) | −21.1353 | − | 36.6073i | −1.04126 | − | 1.80351i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 22.5623 | − | 39.0791i | 1.10888 | − | 1.92063i | ||||
\(415\) | −8.78115 | − | 15.2094i | −0.431050 | − | 0.746600i | ||||
\(416\) | 27.1353 | − | 28.1998i | 1.33042 | − | 1.38261i | ||||
\(417\) | 5.97214 | − | 10.3440i | 0.292457 | − | 0.506550i | ||||
\(418\) | 9.00000 | 0.440204 | ||||||||
\(419\) | −5.97214 | + | 10.3440i | −0.291758 | + | 0.505340i | −0.974226 | − | 0.225576i | \(-0.927574\pi\) |
0.682468 | + | 0.730916i | \(0.260907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.41641 | 0.0690315 | 0.0345157 | − | 0.999404i | \(-0.489011\pi\) | ||||
0.0345157 | + | 0.999404i | \(0.489011\pi\) | |||||||
\(422\) | −6.16312 | + | 10.6748i | −0.300016 | + | 0.519643i | ||||
\(423\) | 8.61803 | 0.419023 | ||||||||
\(424\) | −14.0623 | + | 24.3566i | −0.682926 | + | 1.18286i | ||||
\(425\) | −1.36475 | + | 2.36381i | −0.0661999 | + | 0.114662i | ||||
\(426\) | 48.5967 | − | 84.1720i | 2.35452 | − | 4.07815i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.4164 | −0.793517 | ||||||||
\(429\) | 4.85410 | + | 16.8151i | 0.234358 | + | 0.811841i | ||||
\(430\) | 43.0517 | − | 74.5677i | 2.07614 | − | 3.59597i | ||||
\(431\) | −3.89919 | − | 6.75359i | −0.187817 | − | 0.325309i | 0.756705 | − | 0.653756i | \(-0.226808\pi\) |
−0.944522 | + | 0.328448i | \(0.893475\pi\) | |||||||
\(432\) | 22.0344 | 1.06013 | ||||||||
\(433\) | 0.500000 | + | 0.866025i | 0.0240285 | + | 0.0416185i | 0.877790 | − | 0.479046i | \(-0.159017\pi\) |
−0.853761 | + | 0.520665i | \(0.825684\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.2984 | + | 42.0860i | 1.16502 | + | 2.01787i | ||||
\(436\) | 6.57295 | − | 11.3847i | 0.314787 | − | 0.545227i | ||||
\(437\) | 4.14590 | − | 7.18091i | 0.198325 | − | 0.343509i | ||||
\(438\) | 13.7082 | 0.655003 | ||||||||
\(439\) | −14.8541 | −0.708948 | −0.354474 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354474 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(440\) | 18.1353 | − | 31.4112i | 0.864564 | − | 1.49747i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.63525 | − | 10.0133i | 0.458302 | − | 0.476282i | ||||
\(443\) | 2.61803 | + | 4.53457i | 0.124387 | + | 0.215444i | 0.921493 | − | 0.388395i | \(-0.126970\pi\) |
−0.797106 | + | 0.603839i | \(0.793637\pi\) | |||||||
\(444\) | −25.4164 | − | 44.0225i | −1.20621 | − | 2.08922i | ||||
\(445\) | −6.42705 | − | 11.1320i | −0.304671 | − | 0.527706i | ||||
\(446\) | 26.5344 | − | 45.9590i | 1.25644 | − | 2.17622i | ||||
\(447\) | 4.85410 | 0.229591 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.76393 | − | 16.9116i | −0.460788 | − | 0.798109i | 0.538212 | − | 0.842809i | \(-0.319100\pi\) |
−0.999000 | + | 0.0447005i | \(0.985767\pi\) | |||||||
\(450\) | −9.35410 | − | 16.2018i | −0.440957 | − | 0.763759i | ||||
\(451\) | −1.41641 | −0.0666960 | ||||||||
\(452\) | −3.57295 | − | 6.18853i | −0.168057 | − | 0.291084i | ||||
\(453\) | −3.38197 | −0.158899 | ||||||||
\(454\) | −3.85410 | −0.180882 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 36.2705 | 1.69852 | ||||||||
\(457\) | 15.4164 | 0.721149 | 0.360575 | − | 0.932730i | \(-0.382581\pi\) | ||||
0.360575 | + | 0.932730i | \(0.382581\pi\) | |||||||
\(458\) | −17.1803 | − | 29.7572i | −0.802785 | − | 1.39046i | ||||
\(459\) | 3.29180 | 0.153648 | ||||||||
\(460\) | −28.4164 | − | 49.2187i | −1.32492 | − | 2.29483i | ||||
\(461\) | −6.10739 | − | 10.5783i | −0.284450 | − | 0.492681i | 0.688026 | − | 0.725686i | \(-0.258477\pi\) |
−0.972476 | + | 0.233005i | \(0.925144\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.70820 | 0.311757 | 0.155878 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155878 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(464\) | −34.9336 | + | 60.5068i | −1.62175 | + | 2.80896i | ||||
\(465\) | 16.1353 | + | 27.9471i | 0.748255 | + | 1.29601i | ||||
\(466\) | −3.42705 | − | 5.93583i | −0.158755 | − | 0.274972i | ||||
\(467\) | 1.17376 | + | 2.03302i | 0.0543152 | + | 0.0940767i | 0.891905 | − | 0.452224i | \(-0.149369\pi\) |
−0.837589 | + | 0.546300i | \(0.816036\pi\) | |||||||
\(468\) | 18.7082 | + | 64.8071i | 0.864787 | + | 2.99571i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.66312 | − | 13.2729i | 0.353473 | − | 0.612234i | ||||
\(471\) | −38.8885 | −1.79189 | ||||||||
\(472\) | 16.7082 | 0.769057 | ||||||||
\(473\) | −11.6459 | + | 20.1713i | −0.535479 | + | 0.927477i | ||||
\(474\) | −13.7082 | + | 23.7433i | −0.629639 | + | 1.09057i | ||||
\(475\) | −1.71885 | − | 2.97713i | −0.0788661 | − | 0.136600i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.25329 | − | 12.5631i | −0.332105 | − | 0.575223i | ||||
\(478\) | −64.6869 | −2.95871 | ||||||||
\(479\) | 12.4894 | + | 21.6322i | 0.570653 | + | 0.988400i | 0.996499 | + | 0.0836047i | \(0.0266433\pi\) |
−0.425846 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(480\) | 37.1976 | − | 64.4281i | 1.69783 | − | 2.94073i | ||||
\(481\) | 10.0000 | − | 10.3923i | 0.455961 | − | 0.473848i | ||||
\(482\) | −64.3050 | −2.92901 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.3541 | − | 31.7902i | 0.834277 | − | 1.44501i | ||||
\(485\) | −24.6803 | + | 42.7476i | −1.12068 | + | 1.94107i | ||||
\(486\) | 28.3435 | − | 49.0923i | 1.28569 | − | 2.22687i | ||||
\(487\) | 29.9787 | 1.35847 | 0.679233 | − | 0.733923i | \(-0.262313\pi\) | ||||
0.679233 | + | 0.733923i | \(0.262313\pi\) | |||||||
\(488\) | −22.4164 | + | 38.8264i | −1.01474 | + | 1.75759i | ||||
\(489\) | −9.70820 | −0.439020 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.19098 | + | 10.7231i | −0.279395 | + | 0.483927i | −0.971235 | − | 0.238125i | \(-0.923467\pi\) |
0.691839 | + | 0.722051i | \(0.256801\pi\) | |||||||
\(492\) | −9.70820 | −0.437680 | ||||||||
\(493\) | −5.21885 | + | 9.03931i | −0.235045 | + | 0.407110i | ||||
\(494\) | 4.85410 | + | 16.8151i | 0.218396 | + | 0.756547i | ||||
\(495\) | 9.35410 | + | 16.2018i | 0.420436 | + | 0.728216i | ||||
\(496\) | −23.1976 | + | 40.1794i | −1.04160 | + | 1.80411i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 22.9894 | + | 39.8187i | 1.03018 | + | 1.78432i | ||||
\(499\) | −7.42705 | − | 12.8640i | −0.332480 | − | 0.575873i | 0.650517 | − | 0.759492i | \(-0.274552\pi\) |
−0.982998 | + | 0.183619i | \(0.941219\pi\) | |||||||
\(500\) | 39.9787 | 1.78790 | ||||||||
\(501\) | −37.2705 | −1.66512 | ||||||||
\(502\) | 1.00000 | + | 1.73205i | 0.0446322 | + | 0.0773052i | ||||
\(503\) | 13.3090 | + | 23.0519i | 0.593420 | + | 1.02783i | 0.993768 | + | 0.111470i | \(0.0355559\pi\) |
−0.400348 | + | 0.916363i | \(0.631111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.1353 | − | 26.2150i | 0.673510 | − | 1.16655i | ||||
\(506\) | 10.8541 | + | 18.7999i | 0.482524 | + | 0.835756i | ||||
\(507\) | −28.7984 | + | 18.1383i | −1.27898 | + | 0.805549i | ||||
\(508\) | 50.6140 | − | 87.6660i | 2.24563 | − | 3.88955i | ||||
\(509\) | 18.5967 | 0.824286 | 0.412143 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412143 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(510\) | 13.2082 | − | 22.8773i | 0.584869 | − | 1.01302i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −40.3050 | −1.78124 | ||||||||
\(513\) | −2.07295 | + | 3.59045i | −0.0915229 | + | 0.158522i | ||||
\(514\) | −43.8328 | −1.93338 | ||||||||
\(515\) | 11.3992 | − | 19.7440i | 0.502308 | − | 0.870023i | ||||
\(516\) | −79.8222 | + | 138.256i | −3.51398 | + | 6.08638i | ||||
\(517\) | −2.07295 | + | 3.59045i | −0.0911682 | + | 0.157908i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.5623 | 1.03427 | ||||||||
\(520\) | 68.4681 | + | 16.9415i | 3.00252 | + | 0.742932i | ||||
\(521\) | 9.32624 | − | 16.1535i | 0.408590 | − | 0.707698i | −0.586142 | − | 0.810208i | \(-0.699354\pi\) |
0.994732 | + | 0.102510i | \(0.0326873\pi\) | |||||||
\(522\) | −35.7705 | − | 61.9563i | −1.56563 | − | 2.71176i | ||||
\(523\) | −1.12461 | −0.0491758 | −0.0245879 | − | 0.999698i | \(-0.507827\pi\) | ||||
−0.0245879 | + | 0.999698i | \(0.507827\pi\) | |||||||
\(524\) | −37.1976 | − | 64.4281i | −1.62498 | − | 2.81455i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.7812 | − | 20.4056i | −0.513683 | − | 0.889724i | ||||
\(527\) | −3.46556 | + | 6.00252i | −0.150962 | + | 0.261474i | ||||
\(528\) | −23.9164 | + | 41.4244i | −1.04083 | + | 1.80277i | ||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | −25.7984 | −1.12061 | ||||||||
\(531\) | −4.30902 | + | 7.46344i | −0.186995 | + | 0.323886i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.763932 | − | 2.64634i | −0.0330896 | − | 0.114626i | ||||
\(534\) | 16.8262 | + | 29.1439i | 0.728143 | + | 1.26118i | ||||
\(535\) | −4.42705 | − | 7.66788i | −0.191398 | − | 0.331511i | ||||
\(536\) | 47.4787 | + | 82.2355i | 2.05077 | + | 3.55203i | ||||
\(537\) | 11.7812 | − | 20.4056i | 0.508394 | − | 0.880565i | ||||
\(538\) | 75.2492 | 3.24422 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14.2082 | + | 24.6093i | 0.611424 | + | 1.05902i | ||||
\(541\) | −17.6353 | − | 30.5452i | −0.758199 | − | 1.31324i | −0.943768 | − | 0.330608i | \(-0.892746\pi\) |
0.185569 | − | 0.982631i | \(-0.440587\pi\) | |||||||
\(542\) | 22.0344 | 0.946460 | ||||||||
\(543\) | 12.7082 | + | 22.0113i | 0.545361 | + | 0.944593i | ||||
\(544\) | 15.9787 | 0.685082 | ||||||||
\(545\) | 7.09017 | 0.303710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | −12.7082 | −0.542868 | ||||||||
\(549\) | −11.5623 | − | 20.0265i | −0.493467 | − | 0.854710i | ||||
\(550\) | 9.00000 | 0.383761 | ||||||||
\(551\) | −6.57295 | − | 11.3847i | −0.280017 | − | 0.485004i | ||||
\(552\) | 43.7426 | + | 75.7645i | 1.86181 | + | 3.22475i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.0902 | −0.556148 | ||||||||
\(555\) | 13.7082 | − | 23.7433i | 0.581881 | − | 1.00785i | ||||
\(556\) | 11.0729 | + | 19.1789i | 0.469598 | + | 0.813367i | ||||
\(557\) | 13.9894 | + | 24.2303i | 0.592748 | + | 1.02667i | 0.993860 | + | 0.110641i | \(0.0352904\pi\) |
−0.401112 | + | 0.916029i | \(0.631376\pi\) | |||||||
\(558\) | −23.7533 | − | 41.1419i | −1.00556 | − | 1.74168i | ||||
\(559\) | −43.9681 | − | 10.8793i | −1.85965 | − | 0.460144i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.57295 | + | 6.18853i | −0.150850 | + | 0.261280i | ||||
\(562\) | 52.8328 | 2.22862 | ||||||||
\(563\) | 21.0557 | 0.887393 | 0.443697 | − | 0.896177i | \(-0.353667\pi\) | ||||
0.443697 | + | 0.896177i | \(0.353667\pi\) | |||||||
\(564\) | −14.2082 | + | 24.6093i | −0.598273 | + | 1.03624i | ||||
\(565\) | 1.92705 | − | 3.33775i | 0.0810716 | − | 0.140420i | ||||
\(566\) | 17.5623 | + | 30.4188i | 0.738199 | + | 1.27860i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 52.9787 | + | 91.7618i | 2.22294 | + | 3.85024i | ||||
\(569\) | 14.9443 | 0.626496 | 0.313248 | − | 0.949671i | \(-0.398583\pi\) | ||||
0.313248 | + | 0.949671i | \(0.398583\pi\) | |||||||
\(570\) | 16.6353 | + | 28.8131i | 0.696774 | + | 1.20685i | ||||
\(571\) | −12.3435 | + | 21.3795i | −0.516558 | + | 0.894704i | 0.483257 | + | 0.875478i | \(0.339453\pi\) |
−0.999815 | + | 0.0192259i | \(0.993880\pi\) | |||||||
\(572\) | −31.5000 | − | 7.79423i | −1.31708 | − | 0.325893i | ||||
\(573\) | 55.9787 | 2.33854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.14590 | − | 7.18091i | 0.172896 | − | 0.299464i | ||||
\(576\) | −16.7812 | + | 29.0658i | −0.699215 | + | 1.21108i | ||||
\(577\) | −21.9164 | + | 37.9603i | −0.912392 | + | 1.58031i | −0.101717 | + | 0.994813i | \(0.532433\pi\) |
−0.810675 | + | 0.585496i | \(0.800900\pi\) | |||||||
\(578\) | −38.8328 | −1.61523 | ||||||||
\(579\) | 7.85410 | − | 13.6037i | 0.326405 | − | 0.565351i | ||||
\(580\) | −90.1033 | −3.74134 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 64.6140 | − | 111.915i | 2.67834 | − | 4.63901i | ||||
\(583\) | 6.97871 | 0.289029 | ||||||||
\(584\) | −7.47214 | + | 12.9421i | −0.309199 | + | 0.535549i | ||||
\(585\) | −25.2254 | + | 26.2150i | −1.04294 | + | 1.08386i | ||||
\(586\) | −8.85410 | − | 15.3358i | −0.365760 | − | 0.633514i | ||||
\(587\) | −9.95492 | + | 17.2424i | −0.410883 | + | 0.711671i | −0.994987 | − | 0.100009i | \(-0.968113\pi\) |
0.584103 | + | 0.811679i | \(0.301446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.36475 | − | 7.55996i | −0.179846 | − | 0.311503i | ||||
\(590\) | 7.66312 | + | 13.2729i | 0.315486 | + | 0.546437i | ||||
\(591\) | −43.9787 | −1.80904 | ||||||||
\(592\) | 39.4164 | 1.62000 | ||||||||
\(593\) | 21.8992 | + | 37.9305i | 0.899292 | + | 1.55762i | 0.828401 | + | 0.560135i | \(0.189251\pi\) |
0.0708905 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(594\) | −5.42705 | − | 9.39993i | −0.222675 | − | 0.385684i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.50000 | + | 7.79423i | −0.184327 | + | 0.319264i | ||||
\(597\) | −31.9615 | − | 55.3589i | −1.30810 | − | 2.26569i | ||||
\(598\) | −29.2705 | + | 30.4188i | −1.19696 | + | 1.24392i | ||||
\(599\) | −14.7533 | + | 25.5534i | −0.602803 | + | 1.04409i | 0.389592 | + | 0.920988i | \(0.372616\pi\) |
−0.992395 | + | 0.123098i | \(0.960717\pi\) | |||||||
\(600\) | 36.2705 | 1.48074 | ||||||||
\(601\) | 20.1976 | − | 34.9832i | 0.823876 | − | 1.42699i | −0.0788998 | − | 0.996883i | \(-0.525141\pi\) |
0.902776 | − | 0.430112i | \(-0.141526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48.9787 | −1.99457 | ||||||||
\(604\) | 3.13525 | − | 5.43042i | 0.127572 | − | 0.220961i | ||||
\(605\) | 19.7984 | 0.804918 | ||||||||
\(606\) | −39.6246 | + | 68.6318i | −1.60964 | + | 2.78798i | ||||
\(607\) | −11.5000 | + | 19.9186i | −0.466771 | + | 0.808470i | −0.999279 | − | 0.0379540i | \(-0.987916\pi\) |
0.532509 | + | 0.846424i | \(0.321249\pi\) | |||||||
\(608\) | −10.0623 | + | 17.4284i | −0.408080 | + | 0.706816i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −41.1246 | −1.66509 | ||||||||
\(611\) | −7.82624 | − | 1.93649i | −0.316616 | − | 0.0783421i | ||||
\(612\) | −13.7705 | + | 23.8512i | −0.556640 | + | 0.964129i | ||||
\(613\) | −17.2812 | − | 29.9318i | −0.697979 | − | 1.20894i | −0.969166 | − | 0.246409i | \(-0.920749\pi\) |
0.271187 | − | 0.962527i | \(-0.412584\pi\) | |||||||
\(614\) | 12.7082 | 0.512861 | ||||||||
\(615\) | −2.61803 | − | 4.53457i | −0.105569 | − | 0.182851i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.0278640 | − | 0.0482619i | −0.00112176 | − | 0.00194295i | 0.865464 | − | 0.500971i | \(-0.167024\pi\) |
−0.866586 | + | 0.499028i | \(0.833690\pi\) | |||||||
\(618\) | −29.8435 | + | 51.6904i | −1.20048 | + | 2.07929i | ||||
\(619\) | 4.70820 | − | 8.15485i | 0.189239 | − | 0.327771i | −0.755758 | − | 0.654851i | \(-0.772731\pi\) |
0.944997 | + | 0.327080i | \(0.106065\pi\) | |||||||
\(620\) | −59.8328 | −2.40294 | ||||||||
\(621\) | −10.0000 | −0.401286 | ||||||||
\(622\) | 4.35410 | − | 7.54153i | 0.174584 | − | 0.302388i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −90.2943 | − | 22.3420i | −3.61467 | − | 0.894398i | ||||
\(625\) | 15.4164 | + | 26.7020i | 0.616656 | + | 1.06808i | ||||
\(626\) | 32.8885 | + | 56.9646i | 1.31449 | + | 2.27676i | ||||
\(627\) | −4.50000 | − | 7.79423i | −0.179713 | − | 0.311272i | ||||
\(628\) | 36.0517 | − | 62.4433i | 1.43862 | − | 2.49176i | ||||
\(629\) | 5.88854 | 0.234792 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.1976 | − | 29.7870i | −0.684624 | − | 1.18580i | −0.973555 | − | 0.228454i | \(-0.926633\pi\) |
0.288931 | − | 0.957350i | \(-0.406700\pi\) | |||||||
\(632\) | −14.9443 | − | 25.8842i | −0.594451 | − | 1.02962i | ||||
\(633\) | 12.3262 | 0.489924 | ||||||||
\(634\) | −34.3435 | − | 59.4846i | −1.36395 | − | 2.36244i | ||||
\(635\) | 54.5967 | 2.16661 | ||||||||
\(636\) | 47.8328 | 1.89669 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.4164 | 1.36256 | ||||||||
\(639\) | −54.6525 | −2.16202 | ||||||||
\(640\) | 1.42705 | + | 2.47172i | 0.0564091 | + | 0.0977035i | ||||
\(641\) | −47.5066 | −1.87640 | −0.938199 | − | 0.346098i | \(-0.887507\pi\) | ||||
−0.938199 | + | 0.346098i | \(0.887507\pi\) | |||||||
\(642\) | 11.5902 | + | 20.0748i | 0.457428 | + | 0.792288i | ||||
\(643\) | −3.50000 | − | 6.06218i | −0.138027 | − | 0.239069i | 0.788723 | − | 0.614749i | \(-0.210743\pi\) |
−0.926750 | + | 0.375680i | \(0.877409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −86.1033 | −3.39032 | ||||||||
\(646\) | −3.57295 | + | 6.18853i | −0.140576 | + | 0.243484i | ||||
\(647\) | 12.3820 | + | 21.4462i | 0.486785 | + | 0.843137i | 0.999885 | − | 0.0151924i | \(-0.00483607\pi\) |
−0.513099 | + | 0.858329i | \(0.671503\pi\) | |||||||
\(648\) | 21.3262 | + | 36.9381i | 0.837774 | + | 1.45107i | ||||
\(649\) | −2.07295 | − | 3.59045i | −0.0813704 | − | 0.140938i | ||||
\(650\) | 4.85410 | + | 16.8151i | 0.190394 | + | 0.659543i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.00000 | − | 15.5885i | 0.352467 | − | 0.610491i | ||||
\(653\) | −0.381966 | −0.0149475 | −0.00747374 | − | 0.999972i | \(-0.502379\pi\) | ||||
−0.00747374 | + | 0.999972i | \(0.502379\pi\) | |||||||
\(654\) | −18.5623 | −0.725844 | ||||||||
\(655\) | 20.0623 | − | 34.7489i | 0.783899 | − | 1.35775i | ||||
\(656\) | 3.76393 | − | 6.51932i | 0.146957 | − | 0.254537i | ||||
\(657\) | −3.85410 | − | 6.67550i | −0.150363 | − | 0.260436i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.9443 | + | 20.6881i | 0.465283 | + | 0.805893i | 0.999214 | − | 0.0396343i | \(-0.0126193\pi\) |
−0.533931 | + | 0.845528i | \(0.679286\pi\) | |||||||
\(660\) | −61.6869 | −2.40116 | ||||||||
\(661\) | −24.2705 | − | 42.0378i | −0.944013 | − | 1.63508i | −0.757715 | − | 0.652586i | \(-0.773684\pi\) |
−0.186299 | − | 0.982493i | \(-0.559649\pi\) | |||||||
\(662\) | 13.2812 | − | 23.0036i | 0.516187 | − | 0.894062i | ||||
\(663\) | −13.4894 | − | 3.33775i | −0.523883 | − | 0.129627i | ||||
\(664\) | −50.1246 | −1.94521 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.1803 | + | 34.9534i | −0.781972 | + | 1.35442i | ||||
\(667\) | 15.8541 | − | 27.4601i | 0.613873 | − | 1.06326i | ||||
\(668\) | 34.5517 | − | 59.8452i | 1.33684 | − | 2.31548i | ||||
\(669\) | −53.0689 | −2.05176 | ||||||||
\(670\) | −43.5517 | + | 75.4337i | −1.68255 | + | 2.91426i | ||||
\(671\) | 11.1246 | 0.429461 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6246 | − | 33.9908i | 0.756473 | − | 1.31025i | −0.188165 | − | 0.982137i | \(-0.560254\pi\) |
0.944639 | − | 0.328113i | \(-0.106413\pi\) | |||||||
\(674\) | −30.2705 | −1.16598 | ||||||||
\(675\) | −2.07295 | + | 3.59045i | −0.0797878 | + | 0.138197i | ||||
\(676\) | −2.42705 | − | 63.0566i | −0.0933481 | − | 2.42526i | ||||
\(677\) | 21.8713 | + | 37.8822i | 0.840583 | + | 1.45593i | 0.889402 | + | 0.457125i | \(0.151121\pi\) |
−0.0488191 | + | 0.998808i | \(0.515546\pi\) | |||||||
\(678\) | −5.04508 | + | 8.73834i | −0.193755 | + | 0.335594i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.3992 | + | 24.9401i | 0.552184 | + | 0.956410i | ||||
\(681\) | 1.92705 | + | 3.33775i | 0.0738448 | + | 0.127903i | ||||
\(682\) | 22.8541 | 0.875129 | ||||||||
\(683\) | 1.47214 | 0.0563297 | 0.0281649 | − | 0.999603i | \(-0.491034\pi\) | ||||
0.0281649 | + | 0.999603i | \(0.491034\pi\) | |||||||
\(684\) | −17.3435 | − | 30.0398i | −0.663144 | − | 1.14860i | ||||
\(685\) | −3.42705 | − | 5.93583i | −0.130941 | − | 0.226796i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.1803 | + | 29.7572i | −0.655471 | + | 1.13531i | ||||
\(688\) | −61.8951 | − | 107.205i | −2.35973 | − | 4.08717i | ||||
\(689\) | 3.76393 | + | 13.0386i | 0.143394 | + | 0.496733i | ||||
\(690\) | −40.1246 | + | 69.4979i | −1.52752 | + | 2.64574i | ||||
\(691\) | 5.85410 | 0.222701 | 0.111350 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111350 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(692\) | −21.8435 | + | 37.8340i | −0.830364 | + | 1.43823i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 80.5410 | 3.05730 | ||||||||
\(695\) | −5.97214 | + | 10.3440i | −0.226536 | + | 0.392372i | ||||
\(696\) | 138.700 | 5.25741 | ||||||||
\(697\) | 0.562306 | − | 0.973942i | 0.0212989 | − | 0.0368907i | ||||
\(698\) | 27.1074 | − | 46.9514i | 1.02603 | − | 1.77714i | ||||
\(699\) | −3.42705 | + | 5.93583i | −0.129623 | + | 0.224514i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2361 | 0.424380 | 0.212190 | − | 0.977228i | \(-0.431940\pi\) | ||||
0.212190 | + | 0.977228i | \(0.431940\pi\) | |||||||
\(702\) | 14.6353 | − | 15.2094i | 0.552372 | − | 0.574042i | ||||
\(703\) | −3.70820 | + | 6.42280i | −0.139858 | + | 0.242240i | ||||
\(704\) | −8.07295 | − | 13.9828i | −0.304261 | − | 0.526995i | ||||
\(705\) | −15.3262 | −0.577220 | ||||||||
\(706\) | 28.9894 | + | 50.2110i | 1.09103 | + | 1.88972i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.2082 | − | 24.6093i | −0.533977 | − | 0.924875i | ||||
\(709\) | −11.7812 | + | 20.4056i | −0.442450 | + | 0.766347i | −0.997871 | − | 0.0652231i | \(-0.979224\pi\) |
0.555420 | + | 0.831570i | \(0.312557\pi\) | |||||||
\(710\) | −48.5967 | + | 84.1720i | −1.82380 | + | 3.15892i | ||||
\(711\) | 15.4164 | 0.578160 | ||||||||
\(712\) | −36.6869 | −1.37490 | ||||||||
\(713\) | 10.5279 | − | 18.2348i | 0.394272 | − | 0.682898i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.85410 | − | 16.8151i | −0.181533 | − | 0.628849i | ||||
\(716\) | 21.8435 | + | 37.8340i | 0.816328 | + | 1.41392i | ||||
\(717\) | 32.3435 | + | 56.0205i | 1.20789 | + | 2.09212i | ||||
\(718\) | 28.9164 | + | 50.0847i | 1.07915 | + | 1.86914i | ||||
\(719\) | 4.06231 | − | 7.03612i | 0.151498 | − | 0.262403i | −0.780280 | − | 0.625430i | \(-0.784923\pi\) |
0.931779 | + | 0.363027i | \(0.118257\pi\) | |||||||
\(720\) | −99.4296 | −3.70552 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.3713 | + | 35.2842i | 0.758142 | + | 1.31314i | ||||
\(723\) | 32.1525 | + | 55.6897i | 1.19576 | + | 2.07112i | ||||
\(724\) | −47.1246 | −1.75137 | ||||||||
\(725\) | −6.57295 | − | 11.3847i | −0.244113 | − | 0.422816i | ||||
\(726\) | −51.8328 | −1.92370 | ||||||||
\(727\) | 30.7082 | 1.13890 | 0.569452 | − | 0.822025i | \(-0.307155\pi\) | ||||
0.569452 | + | 0.822025i | \(0.307155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | −13.7082 | −0.507363 | ||||||||
\(731\) | −9.24671 | − | 16.0158i | −0.342002 | − | 0.592365i | ||||
\(732\) | 76.2492 | 2.81825 | ||||||||
\(733\) | −16.1353 | − | 27.9471i | −0.595969 | − | 1.03225i | −0.993409 | − | 0.114621i | \(-0.963435\pi\) |
0.397440 | − | 0.917628i | \(-0.369899\pi\) | |||||||
\(734\) | −1.85410 | − | 3.21140i | −0.0684362 | − | 0.118535i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −48.5410 | −1.78925 | ||||||||
\(737\) | 11.7812 | − | 20.4056i | 0.433964 | − | 0.751648i | ||||
\(738\) | 3.85410 | + | 6.67550i | 0.141871 | + | 0.245729i | ||||
\(739\) | 3.43769 | + | 5.95426i | 0.126458 | + | 0.219031i | 0.922302 | − | 0.386470i | \(-0.126306\pi\) |
−0.795844 | + | 0.605502i | \(0.792973\pi\) | |||||||
\(740\) | 25.4164 | + | 44.0225i | 0.934326 | + | 1.61830i | ||||
\(741\) | 12.1353 | − | 12.6113i | 0.445800 | − | 0.463289i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.6631 | + | 34.0575i | −0.721370 | + | 1.24945i | 0.239081 | + | 0.971000i | \(0.423154\pi\) |
−0.960451 | + | 0.278450i | \(0.910179\pi\) | |||||||
\(744\) | 92.1033 | 3.37667 | ||||||||
\(745\) | −4.85410 | −0.177841 | ||||||||
\(746\) | 26.9164 | − | 46.6206i | 0.985480 | − | 1.70690i | ||||
\(747\) | 12.9271 | − | 22.3903i | 0.472976 | − | 0.819219i | ||||
\(748\) | −6.62461 | − | 11.4742i | −0.242220 | − | 0.419537i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −28.2254 | − | 48.8879i | −1.03065 | − | 1.78513i | ||||
\(751\) | 22.7082 | 0.828634 | 0.414317 | − | 0.910133i | \(-0.364020\pi\) | ||||
0.414317 | + | 0.910133i | \(0.364020\pi\) | |||||||
\(752\) | −11.0172 | − | 19.0824i | −0.401757 | − | 0.695863i | ||||
\(753\) | 1.00000 | − | 1.73205i | 0.0364420 | − | 0.0631194i | ||||
\(754\) | 18.5623 | + | 64.3017i | 0.675999 | + | 2.34173i | ||||
\(755\) | 3.38197 | 0.123082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | + | 24.2487i | −0.508839 | + | 0.881334i | 0.491109 | + | 0.871098i | \(0.336592\pi\) |
−0.999948 | + | 0.0102362i | \(0.996742\pi\) | |||||||
\(758\) | 8.04508 | − | 13.9345i | 0.292211 | − | 0.506124i | ||||
\(759\) | 10.8541 | − | 18.7999i | 0.393979 | − | 0.682392i | ||||
\(760\) | −36.2705 | −1.31567 | ||||||||
\(761\) | −14.4271 | + | 24.9884i | −0.522980 | + | 0.905828i | 0.476662 | + | 0.879087i | \(0.341846\pi\) |
−0.999642 | + | 0.0267417i | \(0.991487\pi\) | |||||||
\(762\) | −142.936 | −5.17803 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −51.8951 | + | 89.8850i | −1.87750 | + | 3.25192i | ||||
\(765\) | −14.8541 | −0.537051 | ||||||||
\(766\) | −28.7705 | + | 49.8320i | −1.03952 | + | 1.80050i | ||||
\(767\) | 5.59017 | − | 5.80948i | 0.201849 | − | 0.209768i | ||||
\(768\) | 19.0623 | + | 33.0169i | 0.687852 | + | 1.19139i | ||||
\(769\) | −9.20820 | + | 15.9491i | −0.332056 | + | 0.575138i | −0.982915 | − | 0.184061i | \(-0.941076\pi\) |
0.650859 | + | 0.759199i | \(0.274409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.9164 | + | 37.9603i | 0.789300 | + | 1.36711i | ||||
\(772\) | 14.5623 | + | 25.2227i | 0.524109 | + | 0.907783i | ||||
\(773\) | −25.3607 | −0.912160 | −0.456080 | − | 0.889939i | \(-0.650747\pi\) | ||||
−0.456080 | + | 0.889939i | \(0.650747\pi\) | |||||||
\(774\) | 126.756 | 4.55614 | ||||||||
\(775\) | −4.36475 | − | 7.55996i | −0.156786 | − | 0.271562i | ||||
\(776\) | 70.4402 | + | 122.006i | 2.52866 | + | 4.37976i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.5623 | − | 26.9547i | 0.557936 | − | 0.966373i | ||||
\(779\) | 0.708204 | + | 1.22665i | 0.0253740 | + | 0.0439491i | ||||
\(780\) | −33.2705 | − | 115.252i | −1.19128 | − | 4.12670i | ||||
\(781\) | 13.1459 | − | 22.7694i | 0.470397 | − | 0.814752i | ||||
\(782\) | −17.2361 | −0.616361 | ||||||||
\(783\) | −7.92705 | + | 13.7301i | −0.283290 | + | 0.490672i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.8885 | 1.38799 | ||||||||
\(786\) | −52.5238 | + | 90.9739i | −1.87346 | + | 3.24493i | ||||
\(787\) | −2.58359 | −0.0920951 | −0.0460476 | − | 0.998939i | \(-0.514663\pi\) | ||||
−0.0460476 | + | 0.998939i | \(0.514663\pi\) | |||||||
\(788\) | 40.7705 | − | 70.6166i | 1.45239 | − | 2.51561i | ||||
\(789\) | −11.7812 | + | 20.4056i | −0.419420 | + | 0.726457i | ||||
\(790\) | 13.7082 | − | 23.7433i | 0.487716 | − | 0.844749i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 53.3951 | 1.89731 | ||||||||
\(793\) | 6.00000 | + | 20.7846i | 0.213066 | + | 0.738083i | ||||
\(794\) | 1.85410 | − | 3.21140i | 0.0657996 | − | 0.113968i | ||||
\(795\) | 12.8992 | + | 22.3420i | 0.457487 | + | 0.792391i | ||||
\(796\) | 118.520 | 4.20082 | ||||||||
\(797\) | −4.09017 | − | 7.08438i | −0.144881 | − | 0.250942i | 0.784447 | − | 0.620195i | \(-0.212947\pi\) |
−0.929329 | + | 0.369254i | \(0.879613\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.64590 | − | 2.85078i | −0.0582277 | − | 0.100853i | ||||
\(800\) | −10.0623 | + | 17.4284i | −0.355756 | + | 0.616188i | ||||
\(801\) | 9.46149 | − | 16.3878i | 0.334305 | − | 0.579034i | ||||
\(802\) | 92.8115 | 3.27729 | ||||||||
\(803\) | 3.70820 | 0.130860 | ||||||||
\(804\) | 80.7492 | − | 139.862i | 2.84781 | − | 4.93254i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.3262 | + | 42.6993i | 0.434173 | + | 1.50402i | ||||
\(807\) | −37.6246 | − | 65.1677i | −1.32445 | − | 2.29401i | ||||
\(808\) | −43.1976 | − | 74.8204i | −1.51968 | − | 2.63217i | ||||
\(809\) | 2.20820 | + | 3.82472i | 0.0776363 | + | 0.134470i | 0.902230 | − | 0.431256i | \(-0.141929\pi\) |
−0.824593 | + | 0.565726i | \(0.808596\pi\) | |||||||
\(810\) | −19.5623 | + | 33.8829i | −0.687349 | + | 1.19052i | ||||
\(811\) | −39.2705 | −1.37897 | −0.689487 | − | 0.724298i | \(-0.742164\pi\) | ||||
−0.689487 | + | 0.724298i | \(0.742164\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0172 | − | 19.0824i | −0.386391 | − | 0.669249i | ||||
\(814\) | −9.70820 | − | 16.8151i | −0.340272 | − | 0.589369i | ||||
\(815\) | 9.70820 | 0.340064 | ||||||||
\(816\) | −18.9894 | − | 32.8905i | −0.664760 | − | 1.15140i | ||||
\(817\) | 23.2918 | 0.814877 | ||||||||
\(818\) | −37.7984 | −1.32159 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.70820 | 0.339025 | ||||||||
\(821\) | −7.36068 | −0.256889 | −0.128445 | − | 0.991717i | \(-0.540998\pi\) | ||||
−0.128445 | + | 0.991717i | \(0.540998\pi\) | |||||||
\(822\) | 8.97214 | + | 15.5402i | 0.312939 | + | 0.542027i | ||||
\(823\) | −38.4164 | −1.33911 | −0.669556 | − | 0.742762i | \(-0.733516\pi\) | ||||
−0.669556 | + | 0.742762i | \(0.733516\pi\) | |||||||
\(824\) | −32.5344 | − | 56.3513i | −1.13339 | − | 1.96309i | ||||
\(825\) | −4.50000 | − | 7.79423i | −0.156670 | − | 0.271360i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.9787 | 0.555634 | 0.277817 | − | 0.960634i | \(-0.410389\pi\) | ||||
0.277817 | + | 0.960634i | \(0.410389\pi\) | |||||||
\(828\) | 41.8328 | − | 72.4566i | 1.45379 | − | 2.51804i | ||||
\(829\) | 3.78115 | + | 6.54915i | 0.131325 | + | 0.227461i | 0.924188 | − | 0.381939i | \(-0.124744\pi\) |
−0.792863 | + | 0.609400i | \(0.791410\pi\) | |||||||
\(830\) | −22.9894 | − | 39.8187i | −0.797972 | − | 1.38213i | ||||
\(831\) | 6.54508 | + | 11.3364i | 0.227046 | + | 0.393256i | ||||
\(832\) | 21.7705 | − | 22.6246i | 0.754757 | − | 0.784366i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.6353 | − | 27.0811i | 0.541405 | − | 0.937740i | ||||
\(835\) | 37.2705 | 1.28980 | ||||||||
\(836\) | 16.6869 | 0.577129 | ||||||||
\(837\) | −5.26393 | + | 9.11740i | −0.181948 | + | 0.315143i | ||||
\(838\) | −15.6353 | + | 27.0811i | −0.540111 | + | 0.935500i | ||||
\(839\) | 6.87132 | + | 11.9015i | 0.237224 | + | 0.410885i | 0.959917 | − | 0.280285i | \(-0.0904290\pi\) |
−0.722692 | + | 0.691170i | \(0.757096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6353 | − | 18.4208i | −0.366733 | − | 0.635200i | ||||
\(842\) | 3.70820 | 0.127793 | ||||||||
\(843\) | −26.4164 | − | 45.7546i | −0.909829 | − | 1.57587i | ||||
\(844\) | −11.4271 | + | 19.7922i | −0.393335 | + | 0.681277i | ||||
\(845\) | 28.7984 | − | 18.1383i | 0.990694 | − | 0.623976i | ||||
\(846\) | 22.5623 | 0.775708 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.5451 | + | 32.1210i | −0.636841 | + | 1.10304i | ||||
\(849\) | 17.5623 | − | 30.4188i | 0.602737 | − | 1.04397i | ||||
\(850\) | −3.57295 | + | 6.18853i | −0.122551 | + | 0.212265i | ||||
\(851\) | −17.8885 | −0.613211 | ||||||||
\(852\) | 90.1033 | − | 156.064i | 3.08689 | − | 5.34665i | ||||
\(853\) | −14.1246 | −0.483617 | −0.241809 | − | 0.970324i | \(-0.577741\pi\) | ||||
−0.241809 | + | 0.970324i | \(0.577741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.35410 | − | 16.2018i | 0.319904 | − | 0.554089i | ||||
\(856\) | −25.2705 | −0.863728 | ||||||||
\(857\) | −13.2254 | + | 22.9071i | −0.451772 | + | 0.782492i | −0.998496 | − | 0.0548208i | \(-0.982541\pi\) |
0.546724 | + | 0.837313i | \(0.315875\pi\) | |||||||
\(858\) | 12.7082 | + | 44.0225i | 0.433851 | + | 1.50290i | ||||
\(859\) | −22.1246 | − | 38.3210i | −0.754882 | − | 1.30749i | −0.945433 | − | 0.325817i | \(-0.894361\pi\) |
0.190551 | − | 0.981677i | \(-0.438973\pi\) | |||||||
\(860\) | 79.8222 | − | 138.256i | 2.72191 | − | 4.71449i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.2082 | − | 17.6811i | −0.347693 | − | 0.602222i | ||||
\(863\) | −5.94427 | − | 10.2958i | −0.202345 | − | 0.350472i | 0.746938 | − | 0.664893i | \(-0.231523\pi\) |
−0.949284 | + | 0.314421i | \(0.898190\pi\) | |||||||
\(864\) | 24.2705 | 0.825700 | ||||||||
\(865\) | −23.5623 | −0.801142 | ||||||||
\(866\) | 1.30902 | + | 2.26728i | 0.0444822 | + | 0.0770454i | ||||
\(867\) | 19.4164 | + | 33.6302i | 0.659416 | + | 1.14214i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.70820 | + | 6.42280i | −0.125792 | + | 0.217878i | ||||
\(870\) | 63.6140 | + | 110.183i | 2.15672 | + | 3.73554i | ||||
\(871\) | 44.4787 | + | 11.0056i | 1.50710 | + | 0.372911i | ||||
\(872\) | 10.1180 | − | 17.5249i | 0.342640 | − | 0.593470i | ||||
\(873\) | −72.6656 | −2.45936 | ||||||||
\(874\) | 10.8541 | − | 18.7999i | 0.367145 | − | 0.635915i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 25.4164 | 0.858741 | ||||||||
\(877\) | −0.354102 | + | 0.613323i | −0.0119572 | + | 0.0207104i | −0.871942 | − | 0.489609i | \(-0.837140\pi\) |
0.859985 | + | 0.510319i | \(0.170473\pi\) | |||||||
\(878\) | −38.8885 | −1.31242 | ||||||||
\(879\) | −8.85410 | + | 15.3358i | −0.298641 | + | 0.517262i | ||||
\(880\) | 23.9164 | − | 41.4244i | 0.806222 | − | 1.39642i | ||||
\(881\) | −18.2984 | + | 31.6937i | −0.616488 | + | 1.06779i | 0.373634 | + | 0.927576i | \(0.378112\pi\) |
−0.990122 | + | 0.140212i | \(0.955222\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 17.8647 | − | 18.5656i | 0.600856 | − | 0.624428i | ||||
\(885\) | 7.66312 | − | 13.2729i | 0.257593 | − | 0.446164i | ||||
\(886\) | 6.85410 | + | 11.8717i | 0.230268 | + | 0.398836i | ||||
\(887\) | −54.6525 | −1.83505 | −0.917525 | − | 0.397677i | \(-0.869816\pi\) | ||||
−0.917525 | + | 0.397677i | \(0.869816\pi\) | |||||||
\(888\) | −39.1246 | − | 67.7658i | −1.31294 | − | 2.27407i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.8262 | − | 29.1439i | −0.564017 | − | 0.976906i | ||||
\(891\) | 5.29180 | − | 9.16566i | 0.177282 | − | 0.307061i | ||||
\(892\) | 49.1976 | − | 85.2127i | 1.64726 | − | 2.85313i | ||||
\(893\) | 4.14590 | 0.138737 | ||||||||
\(894\) | 12.7082 | 0.425026 | ||||||||
\(895\) | −11.7812 | + | 20.4056i | −0.393801 | + | 0.682082i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.9787 | + | 10.1396i | 1.36824 | + | 0.338551i | ||||
\(898\) | −25.5623 | − | 44.2752i | −0.853025 | − | 1.47748i | ||||
\(899\) | −16.6910 | − | 28.9096i | −0.556675 | − | 0.964190i | ||||
\(900\) | −17.3435 | − | 30.0398i | −0.578115 | − | 1.00133i | ||||
\(901\) | −2.77051 | + | 4.79866i | −0.0922991 | + | 0.159867i | ||||
\(902\) | −3.70820 | −0.123470 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.50000 | − | 9.52628i | −0.182927 | − | 0.316839i | ||||
\(905\) | −12.7082 | − | 22.0113i | −0.422435 | − | 0.731679i | ||||
\(906\) | −8.85410 | −0.294158 | ||||||||
\(907\) | 12.0000 | + | 20.7846i | 0.398453 | + | 0.690142i | 0.993535 | − | 0.113523i | \(-0.0362137\pi\) |
−0.595082 | + | 0.803665i | \(0.702880\pi\) | |||||||
\(908\) | −7.14590 | −0.237145 | ||||||||
\(909\) | 44.5623 | 1.47804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6869 | −0.751651 | −0.375826 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375826 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(912\) | 47.8328 | 1.58390 | ||||||||
\(913\) | 6.21885 | + | 10.7714i | 0.205814 | + | 0.356480i | ||||
\(914\) | 40.3607 | 1.33501 | ||||||||
\(915\) | 20.5623 | + | 35.6150i | 0.679769 | + | 1.17739i | ||||
\(916\) | −31.8541 | − | 55.1729i | −1.05249 | − | 1.82296i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.61803 | 0.284438 | ||||||||
\(919\) | 15.0000 | − | 25.9808i | 0.494804 | − | 0.857026i | −0.505178 | − | 0.863015i | \(-0.668573\pi\) |
0.999982 | + | 0.00598907i | \(0.00190639\pi\) | |||||||
\(920\) | −43.7426 | − | 75.7645i | −1.44215 | − | 2.49788i | ||||
\(921\) | −6.35410 | − | 11.0056i | −0.209375 | − | 0.362648i | ||||
\(922\) | −15.9894 | − | 27.6944i | −0.526581 | − | 0.912066i | ||||
\(923\) | 49.6312 | + | 12.2805i | 1.63363 | + | 0.404219i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.70820 | + | 6.42280i | −0.121925 | + | 0.211180i | ||||
\(926\) | 17.5623 | 0.577133 | ||||||||
\(927\) | 33.5623 | 1.10233 | ||||||||
\(928\) | −38.4787 | + | 66.6471i | −1.26313 | + | 2.18780i | ||||
\(929\) | 5.53444 | − | 9.58593i | 0.181579 | − | 0.314504i | −0.760839 | − | 0.648940i | \(-0.775212\pi\) |
0.942418 | + | 0.334436i | \(0.108546\pi\) | |||||||
\(930\) | 42.2426 | + | 73.1664i | 1.38519 | + | 2.39922i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.35410 | − | 11.0056i | −0.208136 | − | 0.360501i | ||||
\(933\) | −8.70820 | −0.285094 | ||||||||
\(934\) | 3.07295 | + | 5.32250i | 0.100550 | + | 0.174158i | ||||
\(935\) | 3.57295 | − | 6.18853i | 0.116848 | − | 0.202387i | ||||
\(936\) | 28.7984 | + | 99.7605i | 0.941304 | + | 3.26077i | ||||
\(937\) | 15.8754 | 0.518626 | 0.259313 | − | 0.965793i | \(-0.416504\pi\) | ||||
0.259313 | + | 0.965793i | \(0.416504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.8885 | − | 56.9646i | 1.07328 | − | 1.85897i | ||||
\(940\) | 14.2082 | − | 24.6093i | 0.463421 | − | 0.802668i | ||||
\(941\) | 10.1738 | − | 17.6215i | 0.331655 | − | 0.574444i | −0.651181 | − | 0.758922i | \(-0.725726\pi\) |
0.982837 | + | 0.184479i | \(0.0590596\pi\) | |||||||
\(942\) | −101.812 | −3.31720 | ||||||||
\(943\) | −1.70820 | + | 2.95870i | −0.0556268 | + | 0.0963484i | ||||
\(944\) | 22.0344 | 0.717160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.4894 | + | 52.8091i | −0.991294 | + | 1.71697i | ||||
\(947\) | −36.8673 | −1.19802 | −0.599012 | − | 0.800740i | \(-0.704440\pi\) | ||||
−0.599012 | + | 0.800740i | \(0.704440\pi\) | |||||||
\(948\) | −25.4164 | + | 44.0225i | −0.825487 | + | 1.42978i | ||||
\(949\) | 2.00000 | + | 6.92820i | 0.0649227 | + | 0.224899i | ||||
\(950\) | −4.50000 | − | 7.79423i | −0.145999 | − | 0.252878i | ||||
\(951\) | −34.3435 | + | 59.4846i | −1.11366 | + | 1.92892i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.3885 | − | 23.1896i | −0.433697 | − | 0.751186i | 0.563491 | − | 0.826122i | \(-0.309458\pi\) |
−0.997188 | + | 0.0749362i | \(0.976125\pi\) | |||||||
\(954\) | −18.9894 | − | 32.8905i | −0.614803 | − | 1.06487i | ||||
\(955\) | −55.9787 | −1.81143 | ||||||||
\(956\) | −119.936 | −3.87901 | ||||||||
\(957\) | −17.2082 | − | 29.8055i | −0.556262 | − | 0.963474i | ||||
\(958\) | 32.6976 | + | 56.6338i | 1.05641 | + | 1.82976i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 29.8435 | − | 51.6904i | 0.963193 | − | 1.66830i | ||||
\(961\) | 4.41641 | + | 7.64944i | 0.142465 | + | 0.246756i | ||||
\(962\) | 26.1803 | − | 27.2074i | 0.844088 | − | 0.877202i | ||||
\(963\) | 6.51722 | − | 11.2882i | 0.210015 | − | 0.363756i | ||||
\(964\) | −119.228 | −3.84007 | ||||||||
\(965\) | −7.85410 | + | 13.6037i | −0.252832 | + | 0.437919i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.0000 | −1.25416 | −0.627078 | − | 0.778957i | \(-0.715749\pi\) | ||||
−0.627078 | + | 0.778957i | \(0.715749\pi\) | |||||||
\(968\) | 28.2533 | − | 48.9361i | 0.908095 | − | 1.57287i | ||||
\(969\) | 7.14590 | 0.229559 | ||||||||
\(970\) | −64.6140 | + | 111.915i | −2.07463 | + | 3.59336i | ||||
\(971\) | 15.7918 | − | 27.3522i | 0.506783 | − | 0.877774i | −0.493186 | − | 0.869924i | \(-0.664168\pi\) |
0.999969 | − | 0.00784995i | \(-0.00249874\pi\) | |||||||
\(972\) | 52.5517 | − | 91.0221i | 1.68560 | − | 2.91954i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 78.4853 | 2.51483 | ||||||||
\(975\) | 12.1353 | − | 12.6113i | 0.388639 | − | 0.403886i | ||||
\(976\) | −29.5623 | + | 51.2034i | −0.946266 | + | 1.63898i | ||||
\(977\) | 11.2639 | + | 19.5097i | 0.360365 | + | 0.624171i | 0.988021 | − | 0.154320i | \(-0.0493188\pi\) |
−0.627656 | + | 0.778491i | \(0.715985\pi\) | |||||||
\(978\) | −25.4164 | −0.812727 | ||||||||
\(979\) | 4.55166 | + | 7.88371i | 0.145472 | + | 0.251965i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.21885 | + | 9.03931i | 0.166625 | + | 0.288603i | ||||
\(982\) | −16.2082 | + | 28.0734i | −0.517225 | + | 0.895859i | ||||
\(983\) | 9.19098 | − | 15.9192i | 0.293147 | − | 0.507745i | −0.681405 | − | 0.731906i | \(-0.738631\pi\) |
0.974552 | + | 0.224161i | \(0.0719642\pi\) | |||||||
\(984\) | −14.9443 | −0.476406 | ||||||||
\(985\) | 43.9787 | 1.40128 | ||||||||
\(986\) | −13.6631 | + | 23.6652i | −0.435122 | + | 0.753654i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.00000 | + | 31.1769i | 0.286328 | + | 0.991870i | ||||
\(989\) | 28.0902 | + | 48.6536i | 0.893215 | + | 1.54709i | ||||
\(990\) | 24.4894 | + | 42.4168i | 0.778323 | + | 1.34809i | ||||
\(991\) | 8.07295 | + | 13.9828i | 0.256446 | + | 0.444177i | 0.965287 | − | 0.261191i | \(-0.0841152\pi\) |
−0.708842 | + | 0.705368i | \(0.750782\pi\) | |||||||
\(992\) | −25.5517 | + | 44.2568i | −0.811266 | + | 1.40515i | ||||
\(993\) | −26.5623 | −0.842929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.9615 | + | 55.3589i | 1.01325 | + | 1.75500i | ||||
\(996\) | 42.6246 | + | 73.8280i | 1.35061 | + | 2.33933i | ||||
\(997\) | −49.0000 | −1.55185 | −0.775923 | − | 0.630828i | \(-0.782715\pi\) | ||||
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | −19.4443 | − | 33.6785i | −0.615498 | − | 1.06607i | ||||
\(999\) | 8.94427 | 0.282984 |
(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 | 637.2.h.f.165.2 | 4 | ||
7.2 | even | 3 | 637.2.g.c.373.1 | 4 | |||
7.3 | odd | 6 | 91.2.f.a.22.1 | ✓ | 4 | ||
7.4 | even | 3 | 637.2.f.c.295.1 | 4 | |||
7.5 | odd | 6 | 637.2.g.b.373.1 | 4 | |||
7.6 | odd | 2 | 637.2.h.g.165.2 | 4 | |||
13.3 | even | 3 | 637.2.g.c.263.1 | 4 | |||
21.17 | even | 6 | 819.2.o.c.568.2 | 4 | |||
28.3 | even | 6 | 1456.2.s.h.113.1 | 4 | |||
91.3 | odd | 6 | 91.2.f.a.29.1 | yes | 4 | ||
91.4 | even | 6 | 8281.2.a.n.1.1 | 2 | |||
91.16 | even | 3 | inner | 637.2.h.f.471.2 | 4 | ||
91.17 | odd | 6 | 1183.2.a.c.1.1 | 2 | |||
91.45 | even | 12 | 1183.2.c.c.337.1 | 4 | |||
91.55 | odd | 6 | 637.2.g.b.263.1 | 4 | |||
91.59 | even | 12 | 1183.2.c.c.337.4 | 4 | |||
91.68 | odd | 6 | 637.2.h.g.471.2 | 4 | |||
91.74 | even | 3 | 8281.2.a.bb.1.2 | 2 | |||
91.81 | even | 3 | 637.2.f.c.393.1 | 4 | |||
91.87 | odd | 6 | 1183.2.a.g.1.2 | 2 | |||
273.185 | even | 6 | 819.2.o.c.757.2 | 4 | |||
364.3 | even | 6 | 1456.2.s.h.1121.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.1 | ✓ | 4 | 7.3 | odd | 6 | ||
91.2.f.a.29.1 | yes | 4 | 91.3 | odd | 6 | ||
637.2.f.c.295.1 | 4 | 7.4 | even | 3 | |||
637.2.f.c.393.1 | 4 | 91.81 | even | 3 | |||
637.2.g.b.263.1 | 4 | 91.55 | odd | 6 | |||
637.2.g.b.373.1 | 4 | 7.5 | odd | 6 | |||
637.2.g.c.263.1 | 4 | 13.3 | even | 3 | |||
637.2.g.c.373.1 | 4 | 7.2 | even | 3 | |||
637.2.h.f.165.2 | 4 | 1.1 | even | 1 | trivial | ||
637.2.h.f.471.2 | 4 | 91.16 | even | 3 | inner | ||
637.2.h.g.165.2 | 4 | 7.6 | odd | 2 | |||
637.2.h.g.471.2 | 4 | 91.68 | odd | 6 | |||
819.2.o.c.568.2 | 4 | 21.17 | even | 6 | |||
819.2.o.c.757.2 | 4 | 273.185 | even | 6 | |||
1183.2.a.c.1.1 | 2 | 91.17 | odd | 6 | |||
1183.2.a.g.1.2 | 2 | 91.87 | odd | 6 | |||
1183.2.c.c.337.1 | 4 | 91.45 | even | 12 | |||
1183.2.c.c.337.4 | 4 | 91.59 | even | 12 | |||
1456.2.s.h.113.1 | 4 | 28.3 | even | 6 | |||
1456.2.s.h.1121.1 | 4 | 364.3 | even | 6 | |||
8281.2.a.n.1.1 | 2 | 91.4 | even | 6 | |||
8281.2.a.bb.1.2 | 2 | 91.74 | even | 3 |