Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(22,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.f (of order \(3\), 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: | \(0.726638658394\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 29.1 | ||
Root | \(0.809017 + 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.29 |
Dual form | 91.2.f.a.22.1 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30902 | − | 2.26728i | −0.925615 | − | 1.60321i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) |
−0.135045 | − | 0.990839i | \(-0.543118\pi\) | |||||||
\(3\) | 1.30902 | + | 2.26728i | 0.755761 | + | 1.30902i | 0.944995 | + | 0.327085i | \(0.106066\pi\) |
−0.189234 | + | 0.981932i | \(0.560600\pi\) | |||||||
\(4\) | −2.42705 | + | 4.20378i | −1.21353 | + | 2.10189i | ||||
\(5\) | 2.61803 | 1.17082 | 0.585410 | − | 0.810737i | \(-0.300933\pi\) | ||||
0.585410 | + | 0.810737i | \(0.300933\pi\) | |||||||
\(6\) | 3.42705 | − | 5.93583i | 1.39909 | − | 2.42329i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 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 | \(0.923507\pi\) | |||||||
\(12\) | −12.7082 | −3.66854 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | 2.61803 | 0.699699 | ||||||||
\(15\) | 3.42705 | + | 5.93583i | 0.884861 | + | 1.53262i | ||||
\(16\) | −4.92705 | − | 8.53390i | −1.23176 | − | 2.13348i | ||||
\(17\) | 0.736068 | − | 1.27491i | 0.178523 | − | 0.309210i | −0.762852 | − | 0.646573i | \(-0.776202\pi\) |
0.941375 | + | 0.337363i | \(0.109535\pi\) | |||||||
\(18\) | 10.0902 | 2.37828 | ||||||||
\(19\) | 0.927051 | − | 1.60570i | 0.212680 | − | 0.368373i | −0.739872 | − | 0.672747i | \(-0.765114\pi\) |
0.952552 | + | 0.304375i | \(0.0984475\pi\) | |||||||
\(20\) | −6.35410 | + | 11.0056i | −1.42082 | + | 2.46093i | ||||
\(21\) | −2.61803 | −0.571302 | ||||||||
\(22\) | −2.42705 | + | 4.20378i | −0.517449 | + | 0.896248i | ||||
\(23\) | 2.23607 | + | 3.87298i | 0.466252 | + | 0.807573i | 0.999257 | − | 0.0385394i | \(-0.0122705\pi\) |
−0.533005 | + | 0.846112i | \(0.678937\pi\) | |||||||
\(24\) | 9.78115 | + | 16.9415i | 1.99657 | + | 3.45816i | ||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | −2.61803 | + | 9.06914i | −0.513439 | + | 1.77860i | ||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −2.42705 | − | 4.20378i | −0.458670 | − | 0.794439i | ||||
\(29\) | −3.54508 | − | 6.14027i | −0.658306 | − | 1.14022i | −0.981054 | − | 0.193734i | \(-0.937940\pi\) |
0.322748 | − | 0.946485i | \(-0.395393\pi\) | |||||||
\(30\) | 8.97214 | − | 15.5402i | 1.63808 | − | 2.83724i | ||||
\(31\) | −4.70820 | −0.845618 | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||||
−0.422809 | + | 0.906219i | \(0.638956\pi\) | |||||||
\(32\) | −5.42705 | + | 9.39993i | −0.959376 | + | 1.66169i | ||||
\(33\) | 2.42705 | − | 4.20378i | 0.422495 | − | 0.731783i | ||||
\(34\) | −3.85410 | −0.660973 | ||||||||
\(35\) | −1.30902 | + | 2.26728i | −0.221264 | + | 0.383241i | ||||
\(36\) | −9.35410 | − | 16.2018i | −1.55902 | − | 2.70030i | ||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | −4.85410 | −0.787439 | ||||||||
\(39\) | 2.61803 | − | 9.06914i | 0.419221 | − | 1.45222i | ||||
\(40\) | 19.5623 | 3.09307 | ||||||||
\(41\) | −0.381966 | − | 0.661585i | −0.0596531 | − | 0.103322i | 0.834657 | − | 0.550771i | \(-0.185666\pi\) |
−0.894310 | + | 0.447449i | \(0.852333\pi\) | |||||||
\(42\) | 3.42705 | + | 5.93583i | 0.528805 | + | 0.915918i | ||||
\(43\) | −6.28115 | + | 10.8793i | −0.957867 | + | 1.65907i | −0.230200 | + | 0.973143i | \(0.573938\pi\) |
−0.727667 | + | 0.685931i | \(0.759395\pi\) | |||||||
\(44\) | 9.00000 | 1.35680 | ||||||||
\(45\) | −5.04508 | + | 8.73834i | −0.752077 | + | 1.30264i | ||||
\(46\) | 5.85410 | − | 10.1396i | 0.863140 | − | 1.49500i | ||||
\(47\) | −2.23607 | −0.326164 | −0.163082 | − | 0.986613i | \(-0.552144\pi\) | ||||
−0.163082 | + | 0.986613i | \(0.552144\pi\) | |||||||
\(48\) | 12.8992 | − | 22.3420i | 1.86184 | − | 3.22480i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −2.42705 | − | 4.20378i | −0.343237 | − | 0.594504i | ||||
\(51\) | 3.85410 | 0.539682 | ||||||||
\(52\) | 16.9894 | − | 4.20378i | 2.35600 | − | 0.582959i | ||||
\(53\) | 3.76393 | 0.517016 | 0.258508 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258508 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(54\) | 2.92705 | + | 5.06980i | 0.398321 | + | 0.689913i | ||||
\(55\) | −2.42705 | − | 4.20378i | −0.327263 | − | 0.566837i | ||||
\(56\) | −3.73607 | + | 6.47106i | −0.499253 | + | 0.864732i | ||||
\(57\) | 4.85410 | 0.642942 | ||||||||
\(58\) | −9.28115 | + | 16.0754i | −1.21868 | + | 2.11081i | ||||
\(59\) | 1.11803 | − | 1.93649i | 0.145556 | − | 0.252110i | −0.784024 | − | 0.620730i | \(-0.786836\pi\) |
0.929580 | + | 0.368620i | \(0.120170\pi\) | |||||||
\(60\) | −33.2705 | −4.29520 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 6.16312 | + | 10.6748i | 0.782717 | + | 1.35571i | ||||
\(63\) | −1.92705 | − | 3.33775i | −0.242786 | − | 0.420517i | ||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | −6.54508 | − | 6.80185i | −0.811818 | − | 0.843666i | ||||
\(66\) | −12.7082 | −1.56427 | ||||||||
\(67\) | 6.35410 | + | 11.0056i | 0.776277 | + | 1.34455i | 0.934074 | + | 0.357080i | \(0.116228\pi\) |
−0.157797 | + | 0.987472i | \(0.550439\pi\) | |||||||
\(68\) | 3.57295 | + | 6.18853i | 0.433284 | + | 0.750469i | ||||
\(69\) | −5.85410 | + | 10.1396i | −0.704751 | + | 1.22066i | ||||
\(70\) | 6.85410 | 0.819222 | ||||||||
\(71\) | 7.09017 | − | 12.2805i | 0.841448 | − | 1.45743i | −0.0472218 | − | 0.998884i | \(-0.515037\pi\) |
0.888670 | − | 0.458547i | \(-0.151630\pi\) | |||||||
\(72\) | −14.3992 | + | 24.9401i | −1.69696 | + | 2.93922i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | −5.23607 | + | 9.06914i | −0.608681 | + | 1.05427i | ||||
\(75\) | 2.42705 | + | 4.20378i | 0.280252 | + | 0.485410i | ||||
\(76\) | 4.50000 | + | 7.79423i | 0.516185 | + | 0.894059i | ||||
\(77\) | 1.85410 | 0.211295 | ||||||||
\(78\) | −23.9894 | + | 5.93583i | −2.71626 | + | 0.672100i | ||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −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 | \(-0.379988\pi\) | ||||
0.368161 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(84\) | 6.35410 | − | 11.0056i | 0.693289 | − | 1.20081i | ||||
\(85\) | 1.92705 | − | 3.33775i | 0.209018 | − | 0.362030i | ||||
\(86\) | 32.8885 | 3.54646 | ||||||||
\(87\) | 9.28115 | − | 16.0754i | 0.995044 | − | 1.72347i | ||||
\(88\) | −6.92705 | − | 11.9980i | −0.738426 | − | 1.27899i | ||||
\(89\) | −2.45492 | − | 4.25204i | −0.260220 | − | 0.450715i | 0.706080 | − | 0.708132i | \(-0.250462\pi\) |
−0.966300 | + | 0.257417i | \(0.917129\pi\) | |||||||
\(90\) | 26.4164 | 2.78453 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | −21.7082 | −2.26324 | ||||||||
\(93\) | −6.16312 | − | 10.6748i | −0.639086 | − | 1.10693i | ||||
\(94\) | 2.92705 | + | 5.06980i | 0.301902 | + | 0.522910i | ||||
\(95\) | 2.42705 | − | 4.20378i | 0.249010 | − | 0.431298i | ||||
\(96\) | −28.4164 | −2.90024 | ||||||||
\(97\) | −9.42705 | + | 16.3281i | −0.957172 | + | 1.65787i | −0.227854 | + | 0.973695i | \(0.573171\pi\) |
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(98\) | −1.30902 | + | 2.26728i | −0.132231 | + | 0.229030i | ||||
\(99\) | 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 | \(0.0284271\pi\) |
−0.420769 | + | 0.907168i | \(0.638240\pi\) | |||||||
\(102\) | −5.04508 | − | 8.73834i | −0.499538 | − | 0.865225i | ||||
\(103\) | −8.70820 | −0.858045 | −0.429022 | − | 0.903294i | \(-0.641142\pi\) | ||||
−0.429022 | + | 0.903294i | \(0.641142\pi\) | |||||||
\(104\) | −18.6803 | − | 19.4132i | −1.83176 | − | 1.90362i | ||||
\(105\) | −6.85410 | −0.668892 | ||||||||
\(106\) | −4.92705 | − | 8.53390i | −0.478557 | − | 0.828886i | ||||
\(107\) | 1.69098 | + | 2.92887i | 0.163473 | + | 0.283144i | 0.936112 | − | 0.351702i | \(-0.114397\pi\) |
−0.772639 | + | 0.634846i | \(0.781064\pi\) | |||||||
\(108\) | 5.42705 | − | 9.39993i | 0.522218 | − | 0.904508i | ||||
\(109\) | −2.70820 | −0.259399 | −0.129699 | − | 0.991553i | \(-0.541401\pi\) | ||||
−0.129699 | + | 0.991553i | \(0.541401\pi\) | |||||||
\(110\) | −6.35410 | + | 11.0056i | −0.605840 | + | 1.04935i | ||||
\(111\) | 5.23607 | − | 9.06914i | 0.496986 | − | 0.860804i | ||||
\(112\) | 9.85410 | 0.931125 | ||||||||
\(113\) | −0.736068 | + | 1.27491i | −0.0692435 | + | 0.119933i | −0.898568 | − | 0.438833i | \(-0.855392\pi\) |
0.829325 | + | 0.558766i | \(0.188725\pi\) | |||||||
\(114\) | −6.35410 | − | 11.0056i | −0.595116 | − | 1.03077i | ||||
\(115\) | 5.85410 | + | 10.1396i | 0.545898 | + | 0.945523i | ||||
\(116\) | 34.4164 | 3.19548 | ||||||||
\(117\) | 13.4894 | − | 3.33775i | 1.24709 | − | 0.308575i | ||||
\(118\) | −5.85410 | −0.538914 | ||||||||
\(119\) | 0.736068 | + | 1.27491i | 0.0674752 | + | 0.116871i | ||||
\(120\) | 25.6074 | + | 44.3533i | 2.33762 | + | 4.04888i | ||||
\(121\) | 3.78115 | − | 6.54915i | 0.343741 | − | 0.595377i | ||||
\(122\) | −15.7082 | −1.42215 | ||||||||
\(123\) | 1.00000 | − | 1.73205i | 0.0901670 | − | 0.156174i | ||||
\(124\) | 11.4271 | − | 19.7922i | 1.02618 | − | 1.77739i | ||||
\(125\) | −8.23607 | −0.736656 | ||||||||
\(126\) | −5.04508 | + | 8.73834i | −0.449452 | + | 0.778474i | ||||
\(127\) | 10.4271 | + | 18.0602i | 0.925251 | + | 1.60258i | 0.791157 | + | 0.611613i | \(0.209479\pi\) |
0.134094 | + | 0.990969i | \(0.457187\pi\) | |||||||
\(128\) | −0.545085 | − | 0.944115i | −0.0481792 | − | 0.0834488i | ||||
\(129\) | −32.8885 | −2.89567 | ||||||||
\(130\) | −6.85410 | + | 23.7433i | −0.601145 | + | 2.08243i | ||||
\(131\) | −15.3262 | −1.33906 | −0.669530 | − | 0.742785i | \(-0.733504\pi\) | ||||
−0.669530 | + | 0.742785i | \(0.733504\pi\) | |||||||
\(132\) | 11.7812 | + | 20.4056i | 1.02542 | + | 1.77608i | ||||
\(133\) | 0.927051 | + | 1.60570i | 0.0803855 | + | 0.139232i | ||||
\(134\) | 16.6353 | − | 28.8131i | 1.43707 | − | 2.48907i | ||||
\(135\) | −5.85410 | −0.503841 | ||||||||
\(136\) | 5.50000 | − | 9.52628i | 0.471621 | − | 0.816872i | ||||
\(137\) | 1.30902 | − | 2.26728i | 0.111837 | − | 0.193707i | −0.804674 | − | 0.593717i | \(-0.797660\pi\) |
0.916511 | + | 0.400010i | \(0.130993\pi\) | |||||||
\(138\) | 30.6525 | 2.60931 | ||||||||
\(139\) | −2.28115 | + | 3.95107i | −0.193485 | + | 0.335126i | −0.946403 | − | 0.322989i | \(-0.895312\pi\) |
0.752918 | + | 0.658114i | \(0.228646\pi\) | |||||||
\(140\) | −6.35410 | − | 11.0056i | −0.537020 | − | 0.930145i | ||||
\(141\) | −2.92705 | − | 5.06980i | −0.246502 | − | 0.426954i | ||||
\(142\) | −37.1246 | −3.11543 | ||||||||
\(143\) | −1.85410 | + | 6.42280i | −0.155048 | + | 0.537101i | ||||
\(144\) | 37.9787 | 3.16489 | ||||||||
\(145\) | −9.28115 | − | 16.0754i | −0.770758 | − | 1.33499i | ||||
\(146\) | 2.61803 | + | 4.53457i | 0.216670 | + | 0.375284i | ||||
\(147\) | 1.30902 | − | 2.26728i | 0.107966 | − | 0.187002i | ||||
\(148\) | 19.4164 | 1.59602 | ||||||||
\(149\) | −0.927051 | + | 1.60570i | −0.0759470 | + | 0.131544i | −0.901498 | − | 0.432784i | \(-0.857531\pi\) |
0.825551 | + | 0.564328i | \(0.190865\pi\) | |||||||
\(150\) | 6.35410 | − | 11.0056i | 0.518810 | − | 0.898606i | ||||
\(151\) | −1.29180 | −0.105125 | −0.0525624 | − | 0.998618i | \(-0.516739\pi\) | ||||
−0.0525624 | + | 0.998618i | \(0.516739\pi\) | |||||||
\(152\) | 6.92705 | − | 11.9980i | 0.561858 | − | 0.973167i | ||||
\(153\) | 2.83688 | + | 4.91362i | 0.229348 | + | 0.397243i | ||||
\(154\) | −2.42705 | − | 4.20378i | −0.195577 | − | 0.338750i | ||||
\(155\) | −12.3262 | −0.990067 | ||||||||
\(156\) | 31.7705 | + | 33.0169i | 2.54368 | + | 2.64347i | ||||
\(157\) | 14.8541 | 1.18549 | 0.592743 | − | 0.805392i | \(-0.298045\pi\) | ||||
0.592743 | + | 0.805392i | \(0.298045\pi\) | |||||||
\(158\) | −5.23607 | − | 9.06914i | −0.416559 | − | 0.721502i | ||||
\(159\) | 4.92705 | + | 8.53390i | 0.390741 | + | 0.676783i | ||||
\(160\) | −14.2082 | + | 24.6093i | −1.12326 | + | 1.94554i | ||||
\(161\) | −4.47214 | −0.352454 | ||||||||
\(162\) | 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 | \(0.120276\pi\) | |||||||
\(164\) | 3.70820 | 0.289562 | ||||||||
\(165\) | 6.35410 | − | 11.0056i | 0.494666 | − | 0.856787i | ||||
\(166\) | −8.78115 | − | 15.2094i | −0.681550 | − | 1.18048i | ||||
\(167\) | −7.11803 | − | 12.3288i | −0.550810 | − | 0.954031i | −0.998216 | − | 0.0597001i | \(-0.980986\pi\) |
0.447406 | − | 0.894331i | \(-0.352348\pi\) | |||||||
\(168\) | −19.5623 | −1.50926 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | −10.0902 | −0.773881 | ||||||||
\(171\) | 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 | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | −48.5967 | −3.68411 | ||||||||
\(175\) | −0.927051 | + | 1.60570i | −0.0700785 | + | 0.121379i | ||||
\(176\) | −9.13525 | + | 15.8227i | −0.688596 | + | 1.19268i | ||||
\(177\) | 5.85410 | 0.440021 | ||||||||
\(178\) | −6.42705 | + | 11.1320i | −0.481728 | + | 0.834377i | ||||
\(179\) | 4.50000 | + | 7.79423i | 0.336346 | + | 0.582568i | 0.983742 | − | 0.179585i | \(-0.0574756\pi\) |
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(180\) | −24.4894 | − | 42.4168i | −1.82533 | − | 3.16156i | ||||
\(181\) | 9.70820 | 0.721605 | 0.360803 | − | 0.932642i | \(-0.382503\pi\) | ||||
0.360803 | + | 0.932642i | \(0.382503\pi\) | |||||||
\(182\) | −6.54508 | − | 6.80185i | −0.485154 | − | 0.504187i | ||||
\(183\) | 15.7082 | 1.16118 | ||||||||
\(184\) | 16.7082 | + | 28.9395i | 1.23175 | + | 2.13345i | ||||
\(185\) | −5.23607 | − | 9.06914i | −0.384963 | − | 0.666776i | ||||
\(186\) | −16.1353 | + | 27.9471i | −1.18309 | + | 2.04918i | ||||
\(187\) | −2.72949 | −0.199600 | ||||||||
\(188\) | 5.42705 | − | 9.39993i | 0.395808 | − | 0.685560i | ||||
\(189\) | 1.11803 | − | 1.93649i | 0.0813250 | − | 0.140859i | ||||
\(190\) | −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 | \(0.764050\pi\) | |||||||
\(194\) | 49.3607 | 3.54389 | ||||||||
\(195\) | 6.85410 | − | 23.7433i | 0.490832 | − | 1.70029i | ||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | 8.39919 | + | 14.5478i | 0.598417 | + | 1.03649i | 0.993055 | + | 0.117652i | \(0.0375368\pi\) |
−0.394638 | + | 0.918837i | \(0.629130\pi\) | |||||||
\(198\) | −9.35410 | − | 16.2018i | −0.664767 | − | 1.15141i | ||||
\(199\) | 12.2082 | − | 21.1452i | 0.865417 | − | 1.49895i | −0.00121626 | − | 0.999999i | \(-0.500387\pi\) |
0.866633 | − | 0.498946i | \(-0.166280\pi\) | |||||||
\(200\) | 13.8541 | 0.979633 | ||||||||
\(201\) | −16.6353 | + | 28.8131i | −1.17336 | + | 2.03232i | ||||
\(202\) | 15.1353 | − | 26.2150i | 1.06491 | − | 1.84448i | ||||
\(203\) | 7.09017 | 0.497632 | ||||||||
\(204\) | −9.35410 | + | 16.2018i | −0.654918 | + | 1.13435i | ||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | 11.3992 | + | 19.7440i | 0.794219 | + | 1.37563i | ||||
\(207\) | −17.2361 | −1.19799 | ||||||||
\(208\) | −9.85410 | + | 34.1356i | −0.683259 | + | 2.36688i | ||||
\(209\) | −3.43769 | −0.237790 | ||||||||
\(210\) | 8.97214 | + | 15.5402i | 0.619136 | + | 1.07238i | ||||
\(211\) | −2.35410 | − | 4.07742i | −0.162063 | − | 0.280701i | 0.773545 | − | 0.633741i | \(-0.218481\pi\) |
−0.935608 | + | 0.353039i | \(0.885148\pi\) | |||||||
\(212\) | −9.13525 | + | 15.8227i | −0.627412 | + | 1.08671i | ||||
\(213\) | 37.1246 | 2.54374 | ||||||||
\(214\) | 4.42705 | − | 7.66788i | 0.302627 | − | 0.524165i | ||||
\(215\) | −16.4443 | + | 28.4823i | −1.12149 | + | 1.94248i | ||||
\(216\) | −16.7082 | −1.13685 | ||||||||
\(217\) | 2.35410 | − | 4.07742i | 0.159807 | − | 0.276794i | ||||
\(218\) | 3.54508 | + | 6.14027i | 0.240103 | + | 0.415871i | ||||
\(219\) | −2.61803 | − | 4.53457i | −0.176910 | − | 0.306418i | ||||
\(220\) | 23.5623 | 1.58857 | ||||||||
\(221\) | −5.15248 | + | 1.27491i | −0.346593 | + | 0.0857595i | ||||
\(222\) | −27.4164 | −1.84007 | ||||||||
\(223\) | −10.1353 | − | 17.5548i | −0.678707 | − | 1.17555i | −0.975371 | − | 0.220573i | \(-0.929207\pi\) |
0.296664 | − | 0.954982i | \(-0.404126\pi\) | |||||||
\(224\) | −5.42705 | − | 9.39993i | −0.362610 | − | 0.628059i | ||||
\(225\) | −3.57295 | + | 6.18853i | −0.238197 | + | 0.412569i | ||||
\(226\) | 3.85410 | 0.256371 | ||||||||
\(227\) | −0.736068 | + | 1.27491i | −0.0488545 | + | 0.0846186i | −0.889419 | − | 0.457094i | \(-0.848890\pi\) |
0.840564 | + | 0.541712i | \(0.182224\pi\) | |||||||
\(228\) | −11.7812 | + | 20.4056i | −0.780226 | + | 1.35139i | ||||
\(229\) | −13.1246 | −0.867299 | −0.433649 | − | 0.901082i | \(-0.642774\pi\) | ||||
−0.433649 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(230\) | 15.3262 | − | 26.5458i | 1.01058 | − | 1.75038i | ||||
\(231\) | 2.42705 | + | 4.20378i | 0.159688 | + | 0.276588i | ||||
\(232\) | −26.4894 | − | 45.8809i | −1.73911 | − | 3.01223i | ||||
\(233\) | 2.61803 | 0.171513 | 0.0857566 | − | 0.996316i | \(-0.472669\pi\) | ||||
0.0857566 | + | 0.996316i | \(0.472669\pi\) | |||||||
\(234\) | −25.2254 | − | 26.2150i | −1.64904 | − | 1.71373i | ||||
\(235\) | −5.85410 | −0.381880 | ||||||||
\(236\) | 5.42705 | + | 9.39993i | 0.353271 | + | 0.611883i | ||||
\(237\) | 5.23607 | + | 9.06914i | 0.340119 | + | 0.589104i | ||||
\(238\) | 1.92705 | − | 3.33775i | 0.124912 | − | 0.216354i | ||||
\(239\) | −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 | ||||
\(241\) | −12.2812 | + | 21.2716i | −0.791099 | + | 1.37022i | 0.134189 | + | 0.990956i | \(0.457157\pi\) |
−0.925287 | + | 0.379267i | \(0.876176\pi\) | |||||||
\(242\) | −19.7984 | −1.27269 | ||||||||
\(243\) | −10.8262 | + | 18.7516i | −0.694503 | + | 1.20292i | ||||
\(244\) | 14.5623 | + | 25.2227i | 0.932256 | + | 1.61471i | ||||
\(245\) | −1.30902 | − | 2.26728i | −0.0836300 | − | 0.144851i | ||||
\(246\) | −5.23607 | −0.333840 | ||||||||
\(247\) | −6.48936 | + | 1.60570i | −0.412908 | + | 0.102168i | ||||
\(248\) | −35.1803 | −2.23395 | ||||||||
\(249\) | 8.78115 | + | 15.2094i | 0.556483 | + | 0.963857i | ||||
\(250\) | 10.7812 | + | 18.6735i | 0.681860 | + | 1.18102i | ||||
\(251\) | −0.381966 | + | 0.661585i | −0.0241095 | + | 0.0417588i | −0.877828 | − | 0.478975i | \(-0.841008\pi\) |
0.853719 | + | 0.520734i | \(0.174342\pi\) | |||||||
\(252\) | 18.7082 | 1.17851 | ||||||||
\(253\) | 4.14590 | − | 7.18091i | 0.260650 | − | 0.451460i | ||||
\(254\) | 27.2984 | − | 47.2822i | 1.71285 | − | 2.96675i | ||||
\(255\) | 10.0902 | 0.631871 | ||||||||
\(256\) | 7.28115 | − | 12.6113i | 0.455072 | − | 0.788208i | ||||
\(257\) | −8.37132 | − | 14.4996i | −0.522189 | − | 0.904457i | −0.999667 | − | 0.0258138i | \(-0.991782\pi\) |
0.477478 | − | 0.878644i | \(-0.341551\pi\) | |||||||
\(258\) | 43.0517 | + | 74.5677i | 2.68028 | + | 4.64238i | ||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 44.4787 | − | 11.0056i | 2.75845 | − | 0.682540i | ||||
\(261\) | 27.3262 | 1.69145 | ||||||||
\(262\) | 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 | ||||||||
\(266\) | 2.42705 | − | 4.20378i | 0.148812 | − | 0.257750i | ||||
\(267\) | 6.42705 | − | 11.1320i | 0.393329 | − | 0.681266i | ||||
\(268\) | −61.6869 | −3.76813 | ||||||||
\(269\) | 14.3713 | − | 24.8919i | 0.876235 | − | 1.51768i | 0.0207937 | − | 0.999784i | \(-0.493381\pi\) |
0.855441 | − | 0.517900i | \(-0.173286\pi\) | |||||||
\(270\) | 7.66312 | + | 13.2729i | 0.466363 | + | 0.807764i | ||||
\(271\) | 4.20820 | + | 7.28882i | 0.255630 | + | 0.442764i | 0.965066 | − | 0.262005i | \(-0.0843837\pi\) |
−0.709436 | + | 0.704770i | \(0.751050\pi\) | |||||||
\(272\) | −14.5066 | −0.879590 | ||||||||
\(273\) | 6.54508 | + | 6.80185i | 0.396127 | + | 0.411667i | ||||
\(274\) | −6.85410 | −0.414071 | ||||||||
\(275\) | −1.71885 | − | 2.97713i | −0.103650 | − | 0.179528i | ||||
\(276\) | −28.4164 | − | 49.2187i | −1.71047 | − | 2.96262i | ||||
\(277\) | 2.50000 | − | 4.33013i | 0.150210 | − | 0.260172i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
0.931305 | + | 0.364241i | \(0.118672\pi\) | |||||||
\(278\) | 11.9443 | 0.716370 | ||||||||
\(279\) | 9.07295 | − | 15.7148i | 0.543183 | − | 0.940821i | ||||
\(280\) | −9.78115 | + | 16.9415i | −0.584536 | + | 1.01245i | ||||
\(281\) | 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 | 0.594812 | − | 0.803865i | \(-0.297226\pi\) |
−0.993573 | + | 0.113190i | \(0.963893\pi\) | |||||||
\(284\) | 34.4164 | + | 59.6110i | 2.04224 | + | 3.53726i | ||||
\(285\) | 12.7082 | 0.752769 | ||||||||
\(286\) | 16.9894 | − | 4.20378i | 1.00460 | − | 0.248574i | ||||
\(287\) | 0.763932 | 0.0450935 | ||||||||
\(288\) | −20.9164 | − | 36.2283i | −1.23251 | − | 2.13477i | ||||
\(289\) | 7.41641 | + | 12.8456i | 0.436259 | + | 0.755623i | ||||
\(290\) | −24.2984 | + | 42.0860i | −1.42685 | + | 2.47138i | ||||
\(291\) | −49.3607 | −2.89357 | ||||||||
\(292\) | 4.85410 | − | 8.40755i | 0.284065 | − | 0.492015i | ||||
\(293\) | 3.38197 | − | 5.85774i | 0.197577 | − | 0.342213i | −0.750166 | − | 0.661250i | \(-0.770026\pi\) |
0.947742 | + | 0.319037i | \(0.103360\pi\) | |||||||
\(294\) | −6.85410 | −0.399739 | ||||||||
\(295\) | 2.92705 | − | 5.06980i | 0.170419 | − | 0.295175i | ||||
\(296\) | −14.9443 | − | 25.8842i | −0.868618 | − | 1.50449i | ||||
\(297\) | 2.07295 | + | 3.59045i | 0.120285 | + | 0.208339i | ||||
\(298\) | 4.85410 | 0.281191 | ||||||||
\(299\) | 4.47214 | − | 15.4919i | 0.258630 | − | 0.895922i | ||||
\(300\) | −23.5623 | −1.36037 | ||||||||
\(301\) | −6.28115 | − | 10.8793i | −0.362040 | − | 0.627071i | ||||
\(302\) | 1.69098 | + | 2.92887i | 0.0973051 | + | 0.168537i | ||||
\(303\) | −15.1353 | + | 26.2150i | −0.869498 | + | 1.50601i | ||||
\(304\) | −18.2705 | −1.04789 | ||||||||
\(305\) | 7.85410 | − | 13.6037i | 0.449725 | − | 0.778946i | ||||
\(306\) | 7.42705 | − | 12.8640i | 0.424576 | − | 0.735388i | ||||
\(307\) | −4.85410 | −0.277038 | −0.138519 | − | 0.990360i | \(-0.544234\pi\) | ||||
−0.138519 | + | 0.990360i | \(0.544234\pi\) | |||||||
\(308\) | −4.50000 | + | 7.79423i | −0.256411 | + | 0.444117i | ||||
\(309\) | −11.3992 | − | 19.7440i | −0.648477 | − | 1.12320i | ||||
\(310\) | 16.1353 | + | 27.9471i | 0.916421 | + | 1.58729i | ||||
\(311\) | 3.32624 | 0.188614 | 0.0943068 | − | 0.995543i | \(-0.469937\pi\) | ||||
0.0943068 | + | 0.995543i | \(0.469937\pi\) | |||||||
\(312\) | 19.5623 | − | 67.7658i | 1.10750 | − | 3.83648i | ||||
\(313\) | 25.1246 | 1.42013 | 0.710064 | − | 0.704138i | \(-0.248666\pi\) | ||||
0.710064 | + | 0.704138i | \(0.248666\pi\) | |||||||
\(314\) | −19.4443 | − | 33.6785i | −1.09730 | − | 1.90059i | ||||
\(315\) | −5.04508 | − | 8.73834i | −0.284258 | − | 0.492350i | ||||
\(316\) | −9.70820 | + | 16.8151i | −0.546129 | + | 0.945923i | ||||
\(317\) | 26.2361 | 1.47356 | 0.736782 | − | 0.676130i | \(-0.236344\pi\) | ||||
0.736782 | + | 0.676130i | \(0.236344\pi\) | |||||||
\(318\) | 12.8992 | − | 22.3420i | 0.723350 | − | 1.25288i | ||||
\(319\) | −6.57295 | + | 11.3847i | −0.368014 | + | 0.637420i | ||||
\(320\) | 22.7984 | 1.27447 | ||||||||
\(321\) | −4.42705 | + | 7.66788i | −0.247094 | + | 0.427979i | ||||
\(322\) | 5.85410 | + | 10.1396i | 0.326236 | + | 0.565058i | ||||
\(323\) | −1.36475 | − | 2.36381i | −0.0759364 | − | 0.131526i | ||||
\(324\) | −27.7082 | −1.53934 | ||||||||
\(325\) | −4.63525 | − | 4.81710i | −0.257118 | − | 0.267205i | ||||
\(326\) | −9.70820 | −0.537688 | ||||||||
\(327\) | −3.54508 | − | 6.14027i | −0.196044 | − | 0.339558i | ||||
\(328\) | −2.85410 | − | 4.94345i | −0.157591 | − | 0.272956i | ||||
\(329\) | 1.11803 | − | 1.93649i | 0.0616392 | − | 0.106762i | ||||
\(330\) | −33.2705 | −1.83148 | ||||||||
\(331\) | 5.07295 | − | 8.78661i | 0.278834 | − | 0.482956i | −0.692261 | − | 0.721647i | \(-0.743385\pi\) |
0.971095 | + | 0.238692i | \(0.0767186\pi\) | |||||||
\(332\) | −16.2812 | + | 28.1998i | −0.893544 | + | 1.54766i | ||||
\(333\) | 15.4164 | 0.844814 | ||||||||
\(334\) | −18.6353 | + | 32.2772i | −1.01968 | + | 1.76613i | ||||
\(335\) | 16.6353 | + | 28.8131i | 0.908881 | + | 1.57423i | ||||
\(336\) | 12.8992 | + | 22.3420i | 0.703708 | + | 1.21886i | ||||
\(337\) | −11.5623 | −0.629839 | −0.314919 | − | 0.949118i | \(-0.601978\pi\) | ||||
−0.314919 | + | 0.949118i | \(0.601978\pi\) | |||||||
\(338\) | 30.1074 | − | 15.8710i | 1.63763 | − | 0.863268i | ||||
\(339\) | −3.85410 | −0.209326 | ||||||||
\(340\) | 9.35410 | + | 16.2018i | 0.507297 | + | 0.878665i | ||||
\(341\) | 4.36475 | + | 7.55996i | 0.236364 | + | 0.409395i | ||||
\(342\) | 9.35410 | − | 16.2018i | 0.505812 | − | 0.876092i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −46.9336 | + | 81.2914i | −2.53049 | + | 4.38294i | ||||
\(345\) | −15.3262 | + | 26.5458i | −0.825137 | + | 1.42918i | ||||
\(346\) | −23.5623 | −1.26672 | ||||||||
\(347\) | −15.3820 | + | 26.6423i | −0.825747 | + | 1.43024i | 0.0755997 | + | 0.997138i | \(0.475913\pi\) |
−0.901347 | + | 0.433098i | \(0.857420\pi\) | |||||||
\(348\) | 45.0517 | + | 78.0318i | 2.41502 | + | 4.18294i | ||||
\(349\) | −10.3541 | − | 17.9338i | −0.554242 | − | 0.959976i | −0.997962 | − | 0.0638103i | \(-0.979675\pi\) |
0.443720 | − | 0.896166i | \(-0.353659\pi\) | |||||||
\(350\) | 4.85410 | 0.259463 | ||||||||
\(351\) | 5.59017 | + | 5.80948i | 0.298381 | + | 0.310087i | ||||
\(352\) | 20.1246 | 1.07265 | ||||||||
\(353\) | −11.0729 | − | 19.1789i | −0.589354 | − | 1.02079i | −0.994317 | − | 0.106458i | \(-0.966049\pi\) |
0.404964 | − | 0.914333i | \(-0.367284\pi\) | |||||||
\(354\) | −7.66312 | − | 13.2729i | −0.407290 | − | 0.705447i | ||||
\(355\) | 18.5623 | − | 32.1509i | 0.985185 | − | 1.70639i | ||||
\(356\) | 23.8328 | 1.26314 | ||||||||
\(357\) | −1.92705 | + | 3.33775i | −0.101990 | + | 0.176652i | ||||
\(358\) | 11.7812 | − | 20.4056i | 0.622653 | − | 1.07847i | ||||
\(359\) | −22.0902 | −1.16587 | −0.582937 | − | 0.812517i | \(-0.698097\pi\) | ||||
−0.582937 | + | 0.812517i | \(0.698097\pi\) | |||||||
\(360\) | −37.6976 | + | 65.2941i | −1.98684 | + | 3.44130i | ||||
\(361\) | 7.78115 | + | 13.4774i | 0.409534 | + | 0.709334i | ||||
\(362\) | −12.7082 | − | 22.0113i | −0.667928 | − | 1.15689i | ||||
\(363\) | 19.7984 | 1.03915 | ||||||||
\(364\) | −4.85410 | + | 16.8151i | −0.254424 | + | 0.881351i | ||||
\(365\) | −5.23607 | −0.274068 | ||||||||
\(366\) | −20.5623 | − | 35.6150i | −1.07481 | − | 1.86162i | ||||
\(367\) | 0.708204 | + | 1.22665i | 0.0369679 | + | 0.0640304i | 0.883917 | − | 0.467643i | \(-0.154897\pi\) |
−0.846949 | + | 0.531673i | \(0.821563\pi\) | |||||||
\(368\) | 22.0344 | − | 38.1648i | 1.14862 | − | 1.98948i | ||||
\(369\) | 2.94427 | 0.153273 | ||||||||
\(370\) | −13.7082 | + | 23.7433i | −0.712656 | + | 1.23436i | ||||
\(371\) | −1.88197 | + | 3.25966i | −0.0977068 | + | 0.169233i | ||||
\(372\) | 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 | ||||
\(376\) | −16.7082 | −0.861660 | ||||||||
\(377\) | −7.09017 | + | 24.5611i | −0.365162 | + | 1.26496i | ||||
\(378\) | −5.85410 | −0.301103 | ||||||||
\(379\) | 3.07295 | + | 5.32250i | 0.157847 | + | 0.273399i | 0.934092 | − | 0.357032i | \(-0.116211\pi\) |
−0.776245 | + | 0.630431i | \(0.782878\pi\) | |||||||
\(380\) | 11.7812 | + | 20.4056i | 0.604360 | + | 1.04678i | ||||
\(381\) | −27.2984 | + | 47.2822i | −1.39854 | + | 2.42234i | ||||
\(382\) | 55.9787 | 2.86412 | ||||||||
\(383\) | 10.9894 | − | 19.0341i | 0.561530 | − | 0.972598i | −0.435833 | − | 0.900027i | \(-0.643546\pi\) |
0.997363 | − | 0.0725709i | \(-0.0231204\pi\) | |||||||
\(384\) | 1.42705 | − | 2.47172i | 0.0728239 | − | 0.126135i | ||||
\(385\) | 4.85410 | 0.247388 | ||||||||
\(386\) | 7.85410 | − | 13.6037i | 0.399763 | − | 0.692410i | ||||
\(387\) | −24.2082 | − | 41.9298i | −1.23057 | − | 2.13141i | ||||
\(388\) | −45.7599 | − | 79.2584i | −2.32311 | − | 4.02374i | ||||
\(389\) | −11.8885 | −0.602773 | −0.301387 | − | 0.953502i | \(-0.597449\pi\) | ||||
−0.301387 | + | 0.953502i | \(0.597449\pi\) | |||||||
\(390\) | −62.8050 | + | 15.5402i | −3.18025 | + | 0.786908i | ||||
\(391\) | 6.58359 | 0.332947 | ||||||||
\(392\) | −3.73607 | − | 6.47106i | −0.188700 | − | 0.326838i | ||||
\(393\) | −20.0623 | − | 34.7489i | −1.01201 | − | 1.75285i | ||||
\(394\) | 21.9894 | − | 38.0867i | 1.10781 | − | 1.91878i | ||||
\(395\) | 10.4721 | 0.526910 | ||||||||
\(396\) | −17.3435 | + | 30.0398i | −0.871542 | + | 1.50955i | ||||
\(397\) | −0.708204 | + | 1.22665i | −0.0355437 | + | 0.0615636i | −0.883250 | − | 0.468902i | \(-0.844650\pi\) |
0.847706 | + | 0.530466i | \(0.177983\pi\) | |||||||
\(398\) | −63.9230 | −3.20417 | ||||||||
\(399\) | −2.42705 | + | 4.20378i | −0.121505 | + | 0.210452i | ||||
\(400\) | −9.13525 | − | 15.8227i | −0.456763 | − | 0.791136i | ||||
\(401\) | −17.7254 | − | 30.7013i | −0.885165 | − | 1.53315i | −0.845524 | − | 0.533938i | \(-0.820712\pi\) |
−0.0396416 | − | 0.999214i | \(-0.512622\pi\) | |||||||
\(402\) | 87.1033 | 4.34432 | ||||||||
\(403\) | 11.7705 | + | 12.2323i | 0.586331 | + | 0.609333i | ||||
\(404\) | −56.1246 | −2.79230 | ||||||||
\(405\) | 7.47214 | + | 12.9421i | 0.371293 | + | 0.643099i | ||||
\(406\) | −9.28115 | − | 16.0754i | −0.460616 | − | 0.797810i | ||||
\(407\) | −3.70820 | + | 6.42280i | −0.183809 | + | 0.318366i | ||||
\(408\) | 28.7984 | 1.42573 | ||||||||
\(409\) | −7.21885 | + | 12.5034i | −0.356949 | + | 0.618254i | −0.987450 | − | 0.157935i | \(-0.949516\pi\) |
0.630500 | + | 0.776189i | \(0.282850\pi\) | |||||||
\(410\) | −2.61803 | + | 4.53457i | −0.129295 | + | 0.223946i | ||||
\(411\) | 6.85410 | 0.338088 | ||||||||
\(412\) | 21.1353 | − | 36.6073i | 1.04126 | − | 1.80351i | ||||
\(413\) | 1.11803 | + | 1.93649i | 0.0550149 | + | 0.0952885i | ||||
\(414\) | 22.5623 | + | 39.0791i | 1.10888 | + | 1.92063i | ||||
\(415\) | 17.5623 | 0.862100 | ||||||||
\(416\) | 37.9894 | − | 9.39993i | 1.86258 | − | 0.460869i | ||||
\(417\) | −11.9443 | −0.584914 | ||||||||
\(418\) | 4.50000 | + | 7.79423i | 0.220102 | + | 0.381228i | ||||
\(419\) | 5.97214 | + | 10.3440i | 0.291758 | + | 0.505340i | 0.974226 | − | 0.225576i | \(-0.0724265\pi\) |
−0.682468 | + | 0.730916i | \(0.739093\pi\) | |||||||
\(420\) | 16.6353 | − | 28.8131i | 0.811717 | − | 1.40594i | ||||
\(421\) | 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 | ||||
\(423\) | 4.30902 | − | 7.46344i | 0.209512 | − | 0.362885i | ||||
\(424\) | 28.1246 | 1.36585 | ||||||||
\(425\) | 1.36475 | − | 2.36381i | 0.0661999 | − | 0.114662i | ||||
\(426\) | −48.5967 | − | 84.1720i | −2.35452 | − | 4.07815i | ||||
\(427\) | 3.00000 | + | 5.19615i | 0.145180 | + | 0.251459i | ||||
\(428\) | −16.4164 | −0.793517 | ||||||||
\(429\) | −16.9894 | + | 4.20378i | −0.820254 | + | 0.202960i | ||||
\(430\) | 86.1033 | 4.15227 | ||||||||
\(431\) | −3.89919 | − | 6.75359i | −0.187817 | − | 0.325309i | 0.756705 | − | 0.653756i | \(-0.226808\pi\) |
−0.944522 | + | 0.328448i | \(0.893475\pi\) | |||||||
\(432\) | 11.0172 | + | 19.0824i | 0.530066 | + | 0.918102i | ||||
\(433\) | −0.500000 | + | 0.866025i | −0.0240285 | + | 0.0416185i | −0.877790 | − | 0.479046i | \(-0.840983\pi\) |
0.853761 | + | 0.520665i | \(0.174316\pi\) | |||||||
\(434\) | −12.3262 | −0.591678 | ||||||||
\(435\) | 24.2984 | − | 42.0860i | 1.16502 | − | 2.01787i | ||||
\(436\) | 6.57295 | − | 11.3847i | 0.314787 | − | 0.545227i | ||||
\(437\) | 8.29180 | 0.396650 | ||||||||
\(438\) | −6.85410 | + | 11.8717i | −0.327502 | + | 0.567250i | ||||
\(439\) | −7.42705 | − | 12.8640i | −0.354474 | − | 0.613967i | 0.632554 | − | 0.774516i | \(-0.282007\pi\) |
−0.987028 | + | 0.160550i | \(0.948673\pi\) | |||||||
\(440\) | −18.1353 | − | 31.4112i | −0.864564 | − | 1.49747i | ||||
\(441\) | 3.85410 | 0.183529 | ||||||||
\(442\) | 9.63525 | + | 10.0133i | 0.458302 | + | 0.476282i | ||||
\(443\) | −5.23607 | −0.248773 | −0.124387 | − | 0.992234i | \(-0.539696\pi\) | ||||
−0.124387 | + | 0.992234i | \(0.539696\pi\) | |||||||
\(444\) | 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 | ||||||||
\(448\) | −4.35410 | + | 7.54153i | −0.205712 | + | 0.356304i | ||||
\(449\) | −9.76393 | + | 16.9116i | −0.460788 | + | 0.798109i | −0.999000 | − | 0.0447005i | \(-0.985767\pi\) |
0.538212 | + | 0.842809i | \(0.319100\pi\) | |||||||
\(450\) | 18.7082 | 0.881913 | ||||||||
\(451\) | −0.708204 | + | 1.22665i | −0.0333480 | + | 0.0577605i | ||||
\(452\) | −3.57295 | − | 6.18853i | −0.168057 | − | 0.291084i | ||||
\(453\) | −1.69098 | − | 2.92887i | −0.0794493 | − | 0.137610i | ||||
\(454\) | 3.85410 | 0.180882 | ||||||||
\(455\) | 9.16312 | − | 2.26728i | 0.429574 | − | 0.106292i | ||||
\(456\) | 36.2705 | 1.69852 | ||||||||
\(457\) | −7.70820 | − | 13.3510i | −0.360575 | − | 0.624533i | 0.627481 | − | 0.778632i | \(-0.284086\pi\) |
−0.988055 | + | 0.154098i | \(0.950753\pi\) | |||||||
\(458\) | 17.1803 | + | 29.7572i | 0.802785 | + | 1.39046i | ||||
\(459\) | −1.64590 | + | 2.85078i | −0.0768239 | + | 0.133063i | ||||
\(460\) | −56.8328 | −2.64984 | ||||||||
\(461\) | 6.10739 | − | 10.5783i | 0.284450 | − | 0.492681i | −0.688026 | − | 0.725686i | \(-0.741523\pi\) |
0.972476 | + | 0.233005i | \(0.0748558\pi\) | |||||||
\(462\) | 6.35410 | − | 11.0056i | 0.295620 | − | 0.512028i | ||||
\(463\) | 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 | ||||
\(467\) | 2.34752 | 0.108630 | 0.0543152 | − | 0.998524i | \(-0.482702\pi\) | ||||
0.0543152 | + | 0.998524i | \(0.482702\pi\) | |||||||
\(468\) | −18.7082 | + | 64.8071i | −0.864787 | + | 2.99571i | ||||
\(469\) | −12.7082 | −0.586810 | ||||||||
\(470\) | 7.66312 | + | 13.2729i | 0.353473 | + | 0.612234i | ||||
\(471\) | 19.4443 | + | 33.6785i | 0.895945 | + | 1.55182i | ||||
\(472\) | 8.35410 | − | 14.4697i | 0.384529 | − | 0.666023i | ||||
\(473\) | 23.2918 | 1.07096 | ||||||||
\(474\) | 13.7082 | − | 23.7433i | 0.629639 | − | 1.09057i | ||||
\(475\) | 1.71885 | − | 2.97713i | 0.0788661 | − | 0.136600i | ||||
\(476\) | −7.14590 | −0.327532 | ||||||||
\(477\) | −7.25329 | + | 12.5631i | −0.332105 | + | 0.575223i | ||||
\(478\) | 32.3435 | + | 56.0205i | 1.47936 | + | 2.56232i | ||||
\(479\) | −12.4894 | − | 21.6322i | −0.570653 | − | 0.988400i | −0.996499 | − | 0.0836047i | \(-0.973357\pi\) |
0.425846 | − | 0.904796i | \(-0.359977\pi\) | |||||||
\(480\) | −74.3951 | −3.39566 | ||||||||
\(481\) | −4.00000 | + | 13.8564i | −0.182384 | + | 0.631798i | ||||
\(482\) | 64.3050 | 2.92901 | ||||||||
\(483\) | −5.85410 | − | 10.1396i | −0.266371 | − | 0.461368i | ||||
\(484\) | 18.3541 | + | 31.7902i | 0.834277 | + | 1.44501i | ||||
\(485\) | −24.6803 | + | 42.7476i | −1.12068 | + | 1.94107i | ||||
\(486\) | 56.6869 | 2.57137 | ||||||||
\(487\) | −14.9894 | + | 25.9623i | −0.679233 | + | 1.17647i | 0.295980 | + | 0.955194i | \(0.404354\pi\) |
−0.975212 | + | 0.221271i | \(0.928979\pi\) | |||||||
\(488\) | 22.4164 | − | 38.8264i | 1.01474 | − | 1.75759i | ||||
\(489\) | 9.70820 | 0.439020 | ||||||||
\(490\) | −3.42705 | + | 5.93583i | −0.154818 | + | 0.268153i | ||||
\(491\) | −6.19098 | − | 10.7231i | −0.279395 | − | 0.483927i | 0.691839 | − | 0.722051i | \(-0.256801\pi\) |
−0.971235 | + | 0.238125i | \(0.923467\pi\) | |||||||
\(492\) | 4.85410 | + | 8.40755i | 0.218840 | + | 0.379042i | ||||
\(493\) | −10.4377 | −0.470090 | ||||||||
\(494\) | 12.1353 | + | 12.6113i | 0.545991 | + | 0.567410i | ||||
\(495\) | 18.7082 | 0.840871 | ||||||||
\(496\) | 23.1976 | + | 40.1794i | 1.04160 | + | 1.80411i | ||||
\(497\) | 7.09017 | + | 12.2805i | 0.318038 | + | 0.550857i | ||||
\(498\) | 22.9894 | − | 39.8187i | 1.03018 | − | 1.78432i | ||||
\(499\) | 14.8541 | 0.664961 | 0.332480 | − | 0.943110i | \(-0.392114\pi\) | ||||
0.332480 | + | 0.943110i | \(0.392114\pi\) | |||||||
\(500\) | 19.9894 | − | 34.6226i | 0.893951 | − | 1.54837i | ||||
\(501\) | 18.6353 | − | 32.2772i | 0.832562 | − | 1.44204i | ||||
\(502\) | 2.00000 | 0.0892644 | ||||||||
\(503\) | −13.3090 | + | 23.0519i | −0.593420 | + | 1.02783i | 0.400348 | + | 0.916363i | \(0.368889\pi\) |
−0.993768 | + | 0.111470i | \(0.964444\pi\) | |||||||
\(504\) | −14.3992 | − | 24.9401i | −0.641391 | − | 1.11092i | ||||
\(505\) | 15.1353 | + | 26.2150i | 0.673510 | + | 1.16655i | ||||
\(506\) | −21.7082 | −0.965047 | ||||||||
\(507\) | −30.1074 | + | 15.8710i | −1.33712 | + | 0.704855i | ||||
\(508\) | −101.228 | −4.49126 | ||||||||
\(509\) | 9.29837 | + | 16.1053i | 0.412143 | + | 0.713853i | 0.995124 | − | 0.0986331i | \(-0.0314470\pi\) |
−0.582981 | + | 0.812486i | \(0.698114\pi\) | |||||||
\(510\) | −13.2082 | − | 22.8773i | −0.584869 | − | 1.01302i | ||||
\(511\) | 1.00000 | − | 1.73205i | 0.0442374 | − | 0.0766214i | ||||
\(512\) | −40.3050 | −1.78124 | ||||||||
\(513\) | −2.07295 | + | 3.59045i | −0.0915229 | + | 0.158522i | ||||
\(514\) | −21.9164 | + | 37.9603i | −0.966691 | + | 1.67436i | ||||
\(515\) | −22.7984 | −1.00462 | ||||||||
\(516\) | 79.8222 | − | 138.256i | 3.51398 | − | 6.08638i | ||||
\(517\) | 2.07295 | + | 3.59045i | 0.0911682 | + | 0.157908i | ||||
\(518\) | −5.23607 | − | 9.06914i | −0.230060 | − | 0.398475i | ||||
\(519\) | 23.5623 | 1.03427 | ||||||||
\(520\) | −48.9058 | − | 50.8244i | −2.14466 | − | 2.22880i | ||||
\(521\) | 18.6525 | 0.817180 | 0.408590 | − | 0.912718i | \(-0.366021\pi\) | ||||
0.408590 | + | 0.912718i | \(0.366021\pi\) | |||||||
\(522\) | −35.7705 | − | 61.9563i | −1.56563 | − | 2.71176i | ||||
\(523\) | −0.562306 | − | 0.973942i | −0.0245879 | − | 0.0425875i | 0.853470 | − | 0.521143i | \(-0.174494\pi\) |
−0.878058 | + | 0.478555i | \(0.841161\pi\) | |||||||
\(524\) | 37.1976 | − | 64.4281i | 1.62498 | − | 2.81455i | ||||
\(525\) | −4.85410 | −0.211850 | ||||||||
\(526\) | −11.7812 | + | 20.4056i | −0.513683 | + | 0.889724i | ||||
\(527\) | −3.46556 | + | 6.00252i | −0.150962 | + | 0.261474i | ||||
\(528\) | −47.8328 | −2.08166 | ||||||||
\(529\) | 1.50000 | − | 2.59808i | 0.0652174 | − | 0.112960i | ||||
\(530\) | −12.8992 | − | 22.3420i | −0.560305 | − | 0.970477i | ||||
\(531\) | 4.30902 | + | 7.46344i | 0.186995 | + | 0.323886i | ||||
\(532\) | −9.00000 | −0.390199 | ||||||||
\(533\) | −0.763932 | + | 2.64634i | −0.0330896 | + | 0.114626i | ||||
\(534\) | −33.6525 | −1.45629 | ||||||||
\(535\) | 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 | ||||||||
\(539\) | −0.927051 | + | 1.60570i | −0.0399309 | + | 0.0691624i | ||||
\(540\) | 14.2082 | − | 24.6093i | 0.611424 | − | 1.05902i | ||||
\(541\) | 35.2705 | 1.51640 | 0.758199 | − | 0.652023i | \(-0.226080\pi\) | ||||
0.758199 | + | 0.652023i | \(0.226080\pi\) | |||||||
\(542\) | 11.0172 | − | 19.0824i | 0.473230 | − | 0.819659i | ||||
\(543\) | 12.7082 | + | 22.0113i | 0.545361 | + | 0.944593i | ||||
\(544\) | 7.98936 | + | 13.8380i | 0.342541 | + | 0.593298i | ||||
\(545\) | −7.09017 | −0.303710 | ||||||||
\(546\) | 6.85410 | − | 23.7433i | 0.293328 | − | 1.01612i | ||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | 6.35410 | + | 11.0056i | 0.271434 | + | 0.470137i | ||||
\(549\) | 11.5623 | + | 20.0265i | 0.493467 | + | 0.854710i | ||||
\(550\) | −4.50000 | + | 7.79423i | −0.191881 | + | 0.332347i | ||||
\(551\) | −13.1459 | −0.560034 | ||||||||
\(552\) | −43.7426 | + | 75.7645i | −1.86181 | + | 3.22475i | ||||
\(553\) | −2.00000 | + | 3.46410i | −0.0850487 | + | 0.147309i | ||||
\(554\) | −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 | \(0.631376\pi\) | |||||||
\(558\) | −47.5066 | −2.01111 | ||||||||
\(559\) | 43.9681 | − | 10.8793i | 1.85965 | − | 0.460144i | ||||
\(560\) | 25.7984 | 1.09018 | ||||||||
\(561\) | −3.57295 | − | 6.18853i | −0.150850 | − | 0.261280i | ||||
\(562\) | −26.4164 | − | 45.7546i | −1.11431 | − | 1.93004i | ||||
\(563\) | 10.5279 | − | 18.2348i | 0.443697 | − | 0.768505i | −0.554264 | − | 0.832341i | \(-0.687000\pi\) |
0.997960 | + | 0.0638360i | \(0.0203335\pi\) | |||||||
\(564\) | 28.4164 | 1.19655 | ||||||||
\(565\) | −1.92705 | + | 3.33775i | −0.0810716 | + | 0.140420i | ||||
\(566\) | −17.5623 | + | 30.4188i | −0.738199 | + | 1.27860i | ||||
\(567\) | −5.70820 | −0.239722 | ||||||||
\(568\) | 52.9787 | − | 91.7618i | 2.22294 | − | 3.85024i | ||||
\(569\) | −7.47214 | − | 12.9421i | −0.313248 | − | 0.542562i | 0.665815 | − | 0.746117i | \(-0.268084\pi\) |
−0.979064 | + | 0.203555i | \(0.934751\pi\) | |||||||
\(570\) | −16.6353 | − | 28.8131i | −0.696774 | − | 1.20685i | ||||
\(571\) | 24.6869 | 1.03312 | 0.516558 | − | 0.856252i | \(-0.327213\pi\) | ||||
0.516558 | + | 0.856252i | \(0.327213\pi\) | |||||||
\(572\) | −22.5000 | − | 23.3827i | −0.940772 | − | 0.977679i | ||||
\(573\) | −55.9787 | −2.33854 | ||||||||
\(574\) | −1.00000 | − | 1.73205i | −0.0417392 | − | 0.0722944i | ||||
\(575\) | 4.14590 | + | 7.18091i | 0.172896 | + | 0.299464i | ||||
\(576\) | −16.7812 | + | 29.0658i | −0.699215 | + | 1.21108i | ||||
\(577\) | −43.8328 | −1.82478 | −0.912392 | − | 0.409318i | \(-0.865767\pi\) | ||||
−0.912392 | + | 0.409318i | \(0.865767\pi\) | |||||||
\(578\) | 19.4164 | − | 33.6302i | 0.807616 | − | 1.39883i | ||||
\(579\) | −7.85410 | + | 13.6037i | −0.326405 | + | 0.565351i | ||||
\(580\) | 90.1033 | 3.74134 | ||||||||
\(581\) | −3.35410 | + | 5.80948i | −0.139152 | + | 0.241018i | ||||
\(582\) | 64.6140 | + | 111.915i | 2.67834 | + | 4.63901i | ||||
\(583\) | −3.48936 | − | 6.04374i | −0.144514 | − | 0.250306i | ||||
\(584\) | −14.9443 | −0.618398 | ||||||||
\(585\) | 35.3156 | − | 8.73834i | 1.46012 | − | 0.361286i | ||||
\(586\) | −17.7082 | −0.731519 | ||||||||
\(587\) | 9.95492 | + | 17.2424i | 0.410883 | + | 0.711671i | 0.994987 | − | 0.100009i | \(-0.0318870\pi\) |
−0.584103 | + | 0.811679i | \(0.698554\pi\) | |||||||
\(588\) | 6.35410 | + | 11.0056i | 0.262039 | + | 0.453864i | ||||
\(589\) | −4.36475 | + | 7.55996i | −0.179846 | + | 0.311503i | ||||
\(590\) | −15.3262 | −0.630971 | ||||||||
\(591\) | −21.9894 | + | 38.0867i | −0.904521 | + | 1.56668i | ||||
\(592\) | −19.7082 | + | 34.1356i | −0.810002 | + | 1.40296i | ||||
\(593\) | 43.7984 | 1.79858 | 0.899292 | − | 0.437349i | \(-0.144083\pi\) | ||||
0.899292 | + | 0.437349i | \(0.144083\pi\) | |||||||
\(594\) | 5.42705 | − | 9.39993i | 0.222675 | − | 0.385684i | ||||
\(595\) | 1.92705 | + | 3.33775i | 0.0790014 | + | 0.136834i | ||||
\(596\) | −4.50000 | − | 7.79423i | −0.184327 | − | 0.319264i | ||||
\(597\) | 63.9230 | 2.61619 | ||||||||
\(598\) | −40.9787 | + | 10.1396i | −1.67574 | + | 0.414639i | ||||
\(599\) | 29.5066 | 1.20561 | 0.602803 | − | 0.797890i | \(-0.294050\pi\) | ||||
0.602803 | + | 0.797890i | \(0.294050\pi\) | |||||||
\(600\) | 18.1353 | + | 31.4112i | 0.740369 | + | 1.28236i | ||||
\(601\) | −20.1976 | − | 34.9832i | −0.823876 | − | 1.42699i | −0.902776 | − | 0.430112i | \(-0.858474\pi\) |
0.0788998 | − | 0.996883i | \(-0.474859\pi\) | |||||||
\(602\) | −16.4443 | + | 28.4823i | −0.670218 | + | 1.16085i | ||||
\(603\) | −48.9787 | −1.99457 | ||||||||
\(604\) | 3.13525 | − | 5.43042i | 0.127572 | − | 0.220961i | ||||
\(605\) | 9.89919 | − | 17.1459i | 0.402459 | − | 0.697080i | ||||
\(606\) | 79.2492 | 3.21928 | ||||||||
\(607\) | 11.5000 | − | 19.9186i | 0.466771 | − | 0.808470i | −0.532509 | − | 0.846424i | \(-0.678751\pi\) |
0.999279 | + | 0.0379540i | \(0.0120840\pi\) | |||||||
\(608\) | 10.0623 | + | 17.4284i | 0.408080 | + | 0.706816i | ||||
\(609\) | 9.28115 | + | 16.0754i | 0.376091 | + | 0.651409i | ||||
\(610\) | −41.1246 | −1.66509 | ||||||||
\(611\) | 5.59017 | + | 5.80948i | 0.226154 | + | 0.235026i | ||||
\(612\) | −27.5410 | −1.11328 | ||||||||
\(613\) | −17.2812 | − | 29.9318i | −0.697979 | − | 1.20894i | −0.969166 | − | 0.246409i | \(-0.920749\pi\) |
0.271187 | − | 0.962527i | \(-0.412584\pi\) | |||||||
\(614\) | 6.35410 | + | 11.0056i | 0.256431 | + | 0.444151i | ||||
\(615\) | 2.61803 | − | 4.53457i | 0.105569 | − | 0.182851i | ||||
\(616\) | 13.8541 | 0.558198 | ||||||||
\(617\) | −0.0278640 | + | 0.0482619i | −0.00112176 | + | 0.00194295i | −0.866586 | − | 0.499028i | \(-0.833690\pi\) |
0.865464 | + | 0.500971i | \(0.167024\pi\) | |||||||
\(618\) | −29.8435 | + | 51.6904i | −1.20048 | + | 2.07929i | ||||
\(619\) | 9.41641 | 0.378477 | 0.189239 | − | 0.981931i | \(-0.439398\pi\) | ||||
0.189239 | + | 0.981931i | \(0.439398\pi\) | |||||||
\(620\) | 29.9164 | − | 51.8167i | 1.20147 | − | 2.08101i | ||||
\(621\) | −5.00000 | − | 8.66025i | −0.200643 | − | 0.347524i | ||||
\(622\) | −4.35410 | − | 7.54153i | −0.174584 | − | 0.302388i | ||||
\(623\) | 4.90983 | 0.196708 | ||||||||
\(624\) | −90.2943 | + | 22.3420i | −3.61467 | + | 0.894398i | ||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | −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 | ||||||||
\(630\) | −13.2082 | + | 22.8773i | −0.526227 | + | 0.911453i | ||||
\(631\) | −17.1976 | + | 29.7870i | −0.684624 | + | 1.18580i | 0.288931 | + | 0.957350i | \(0.406700\pi\) |
−0.973555 | + | 0.228454i | \(0.926633\pi\) | |||||||
\(632\) | 29.8885 | 1.18890 | ||||||||
\(633\) | 6.16312 | − | 10.6748i | 0.244962 | − | 0.424287i | ||||
\(634\) | −34.3435 | − | 59.4846i | −1.36395 | − | 2.36244i | ||||
\(635\) | 27.2984 | + | 47.2822i | 1.08330 | + | 1.87634i | ||||
\(636\) | −47.8328 | −1.89669 | ||||||||
\(637\) | −1.00000 | + | 3.46410i | −0.0396214 | + | 0.137253i | ||||
\(638\) | 34.4164 | 1.36256 | ||||||||
\(639\) | 27.3262 | + | 47.3304i | 1.08101 | + | 1.87236i | ||||
\(640\) | −1.42705 | − | 2.47172i | −0.0564091 | − | 0.0977035i | ||||
\(641\) | 23.7533 | − | 41.1419i | 0.938199 | − | 1.62501i | 0.169370 | − | 0.985553i | \(-0.445827\pi\) |
0.768829 | − | 0.639455i | \(-0.220840\pi\) | |||||||
\(642\) | 23.1803 | 0.914855 | ||||||||
\(643\) | 3.50000 | − | 6.06218i | 0.138027 | − | 0.239069i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
0.926750 | + | 0.375680i | \(0.122591\pi\) | |||||||
\(644\) | 10.8541 | − | 18.7999i | 0.427712 | − | 0.740818i | ||||
\(645\) | −86.1033 | −3.39032 | ||||||||
\(646\) | −3.57295 | + | 6.18853i | −0.140576 | + | 0.243484i | ||||
\(647\) | −12.3820 | − | 21.4462i | −0.486785 | − | 0.843137i | 0.513099 | − | 0.858329i | \(-0.328497\pi\) |
−0.999885 | + | 0.0151924i | \(0.995164\pi\) | |||||||
\(648\) | 21.3262 | + | 36.9381i | 0.837774 | + | 1.45107i | ||||
\(649\) | −4.14590 | −0.162741 | ||||||||
\(650\) | −4.85410 | + | 16.8151i | −0.190394 | + | 0.659543i | ||||
\(651\) | 12.3262 | 0.483103 | ||||||||
\(652\) | 9.00000 | + | 15.5885i | 0.352467 | + | 0.610491i | ||||
\(653\) | 0.190983 | + | 0.330792i | 0.00747374 | + | 0.0129449i | 0.869738 | − | 0.493514i | \(-0.164288\pi\) |
−0.862264 | + | 0.506458i | \(0.830954\pi\) | |||||||
\(654\) | −9.28115 | + | 16.0754i | −0.362922 | + | 0.628599i | ||||
\(655\) | −40.1246 | −1.56780 | ||||||||
\(656\) | −3.76393 | + | 6.51932i | −0.146957 | + | 0.254537i | ||||
\(657\) | 3.85410 | − | 6.67550i | 0.150363 | − | 0.260436i | ||||
\(658\) | −5.85410 | −0.228217 | ||||||||
\(659\) | 11.9443 | − | 20.6881i | 0.465283 | − | 0.805893i | −0.533931 | − | 0.845528i | \(-0.679286\pi\) |
0.999214 | + | 0.0396343i | \(0.0126193\pi\) | |||||||
\(660\) | 30.8435 | + | 53.4224i | 1.20058 | + | 2.07947i | ||||
\(661\) | 24.2705 | + | 42.0378i | 0.944013 | + | 1.63508i | 0.757715 | + | 0.652586i | \(0.226316\pi\) |
0.186299 | + | 0.982493i | \(0.440351\pi\) | |||||||
\(662\) | −26.5623 | −1.03237 | ||||||||
\(663\) | −9.63525 | − | 10.0133i | −0.374202 | − | 0.388882i | ||||
\(664\) | 50.1246 | 1.94521 | ||||||||
\(665\) | 2.42705 | + | 4.20378i | 0.0941170 | + | 0.163015i | ||||
\(666\) | −20.1803 | − | 34.9534i | −0.781972 | − | 1.35442i | ||||
\(667\) | 15.8541 | − | 27.4601i | 0.613873 | − | 1.06326i | ||||
\(668\) | 69.1033 | 2.67369 | ||||||||
\(669\) | 26.5344 | − | 45.9590i | 1.02588 | − | 1.77688i | ||||
\(670\) | 43.5517 | − | 75.4337i | 1.68255 | − | 2.91426i | ||||
\(671\) | −11.1246 | −0.429461 | ||||||||
\(672\) | 14.2082 | − | 24.6093i | 0.548093 | − | 0.949326i | ||||
\(673\) | 19.6246 | + | 33.9908i | 0.756473 | + | 1.31025i | 0.944639 | + | 0.328113i | \(0.106413\pi\) |
−0.188165 | + | 0.982137i | \(0.560254\pi\) | |||||||
\(674\) | 15.1353 | + | 26.2150i | 0.582988 | + | 1.00977i | ||||
\(675\) | −4.14590 | −0.159576 | ||||||||
\(676\) | −53.3951 | − | 33.6302i | −2.05366 | − | 1.29347i | ||||
\(677\) | 43.7426 | 1.68117 | 0.840583 | − | 0.541682i | \(-0.182212\pi\) | ||||
0.840583 | + | 0.541682i | \(0.182212\pi\) | |||||||
\(678\) | 5.04508 | + | 8.73834i | 0.193755 | + | 0.335594i | ||||
\(679\) | −9.42705 | − | 16.3281i | −0.361777 | − | 0.626616i | ||||
\(680\) | 14.3992 | − | 24.9401i | 0.552184 | − | 0.956410i | ||||
\(681\) | −3.85410 | −0.147690 | ||||||||
\(682\) | 11.4271 | − | 19.7922i | 0.437564 | − | 0.757884i | ||||
\(683\) | −0.736068 | + | 1.27491i | −0.0281649 | + | 0.0487830i | −0.879764 | − | 0.475410i | \(-0.842300\pi\) |
0.851599 | + | 0.524193i | \(0.175633\pi\) | |||||||
\(684\) | −34.6869 | −1.32629 | ||||||||
\(685\) | 3.42705 | − | 5.93583i | 0.130941 | − | 0.226796i | ||||
\(686\) | −1.30902 | − | 2.26728i | −0.0499785 | − | 0.0865653i | ||||
\(687\) | −17.1803 | − | 29.7572i | −0.655471 | − | 1.13531i | ||||
\(688\) | 123.790 | 4.71946 | ||||||||
\(689\) | −9.40983 | − | 9.77898i | −0.358486 | − | 0.372550i | ||||
\(690\) | 80.2492 | 3.05504 | ||||||||
\(691\) | 2.92705 | + | 5.06980i | 0.111350 | + | 0.192864i | 0.916315 | − | 0.400458i | \(-0.131149\pi\) |
−0.804965 | + | 0.593323i | \(0.797816\pi\) | |||||||
\(692\) | 21.8435 | + | 37.8340i | 0.830364 | + | 1.43823i | ||||
\(693\) | −3.57295 | + | 6.18853i | −0.135725 | + | 0.235083i | ||||
\(694\) | 80.5410 | 3.05730 | ||||||||
\(695\) | −5.97214 | + | 10.3440i | −0.226536 | + | 0.392372i | ||||
\(696\) | 69.3500 | − | 120.118i | 2.62871 | − | 4.55305i | ||||
\(697\) | −1.12461 | −0.0425977 | ||||||||
\(698\) | −27.1074 | + | 46.9514i | −1.02603 | + | 1.77714i | ||||
\(699\) | 3.42705 | + | 5.93583i | 0.129623 | + | 0.224514i | ||||
\(700\) | −4.50000 | − | 7.79423i | −0.170084 | − | 0.294594i | ||||
\(701\) | 11.2361 | 0.424380 | 0.212190 | − | 0.977228i | \(-0.431940\pi\) | ||||
0.212190 | + | 0.977228i | \(0.431940\pi\) | |||||||
\(702\) | 5.85410 | − | 20.2792i | 0.220949 | − | 0.765389i | ||||
\(703\) | −7.41641 | −0.279715 | ||||||||
\(704\) | −8.07295 | − | 13.9828i | −0.304261 | − | 0.526995i | ||||
\(705\) | −7.66312 | − | 13.2729i | −0.288610 | − | 0.499887i | ||||
\(706\) | −28.9894 | + | 50.2110i | −1.09103 | + | 1.88972i | ||||
\(707\) | −11.5623 | −0.434845 | ||||||||
\(708\) | −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 | \(0.312557\pi\) | |||||||
\(710\) | −97.1935 | −3.64761 | ||||||||
\(711\) | −7.70820 | + | 13.3510i | −0.289080 | + | 0.500702i | ||||
\(712\) | −18.3435 | − | 31.7718i | −0.687450 | − | 1.19070i | ||||
\(713\) | −10.5279 | − | 18.2348i | −0.394272 | − | 0.682898i | ||||
\(714\) | 10.0902 | 0.377615 | ||||||||
\(715\) | −4.85410 | + | 16.8151i | −0.181533 | + | 0.628849i | ||||
\(716\) | −43.6869 | −1.63266 | ||||||||
\(717\) | −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 | −0.931779 | − | 0.363027i | \(-0.881743\pi\) |
0.780280 | + | 0.625430i | \(0.215077\pi\) | |||||||
\(720\) | 99.4296 | 3.70552 | ||||||||
\(721\) | 4.35410 | − | 7.54153i | 0.162155 | − | 0.280861i | ||||
\(722\) | 20.3713 | − | 35.2842i | 0.758142 | − | 1.31314i | ||||
\(723\) | −64.3050 | −2.39153 | ||||||||
\(724\) | −23.5623 | + | 40.8111i | −0.875686 | + | 1.51673i | ||||
\(725\) | −6.57295 | − | 11.3847i | −0.244113 | − | 0.422816i | ||||
\(726\) | −25.9164 | − | 44.8885i | −0.961848 | − | 1.66597i | ||||
\(727\) | −30.7082 | −1.13890 | −0.569452 | − | 0.822025i | \(-0.692845\pi\) | ||||
−0.569452 | + | 0.822025i | \(0.692845\pi\) | |||||||
\(728\) | 26.1525 | − | 6.47106i | 0.969275 | − | 0.239833i | ||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 6.85410 | + | 11.8717i | 0.253682 | + | 0.439390i | ||||
\(731\) | 9.24671 | + | 16.0158i | 0.342002 | + | 0.592365i | ||||
\(732\) | −38.1246 | + | 66.0338i | −1.40913 | + | 2.44068i | ||||
\(733\) | −32.2705 | −1.19194 | −0.595969 | − | 0.803007i | \(-0.703232\pi\) | ||||
−0.595969 | + | 0.803007i | \(0.703232\pi\) | |||||||
\(734\) | 1.85410 | − | 3.21140i | 0.0684362 | − | 0.118535i | ||||
\(735\) | 3.42705 | − | 5.93583i | 0.126409 | − | 0.218946i | ||||
\(736\) | −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 | \(0.792973\pi\) | |||||||
\(740\) | 50.8328 | 1.86865 | ||||||||
\(741\) | −12.1353 | − | 12.6113i | −0.445800 | − | 0.463289i | ||||
\(742\) | 9.85410 | 0.361755 | ||||||||
\(743\) | −19.6631 | − | 34.0575i | −0.721370 | − | 1.24945i | −0.960451 | − | 0.278450i | \(-0.910179\pi\) |
0.239081 | − | 0.971000i | \(-0.423154\pi\) | |||||||
\(744\) | −46.0517 | − | 79.7638i | −1.68834 | − | 2.92428i | ||||
\(745\) | −2.42705 | + | 4.20378i | −0.0889203 | + | 0.154014i | ||||
\(746\) | −53.8328 | −1.97096 | ||||||||
\(747\) | −12.9271 | + | 22.3903i | −0.472976 | + | 0.819219i | ||||
\(748\) | 6.62461 | − | 11.4742i | 0.242220 | − | 0.419537i | ||||
\(749\) | −3.38197 | −0.123574 | ||||||||
\(750\) | −28.2254 | + | 48.8879i | −1.03065 | + | 1.78513i | ||||
\(751\) | −11.3541 | − | 19.6659i | −0.414317 | − | 0.717618i | 0.581039 | − | 0.813875i | \(-0.302646\pi\) |
−0.995356 | + | 0.0962572i | \(0.969313\pi\) | |||||||
\(752\) | 11.0172 | + | 19.0824i | 0.401757 | + | 0.695863i | ||||
\(753\) | −2.00000 | −0.0728841 | ||||||||
\(754\) | 64.9681 | − | 16.0754i | 2.36600 | − | 0.585433i | ||||
\(755\) | −3.38197 | −0.123082 | ||||||||
\(756\) | 5.42705 | + | 9.39993i | 0.197380 | + | 0.341872i | ||||
\(757\) | −14.0000 | − | 24.2487i | −0.508839 | − | 0.881334i | −0.999948 | − | 0.0102362i | \(-0.996742\pi\) |
0.491109 | − | 0.871098i | \(-0.336592\pi\) | |||||||
\(758\) | 8.04508 | − | 13.9345i | 0.292211 | − | 0.506124i | ||||
\(759\) | 21.7082 | 0.787958 | ||||||||
\(760\) | 18.1353 | − | 31.4112i | 0.657835 | − | 1.13940i | ||||
\(761\) | 14.4271 | − | 24.9884i | 0.522980 | − | 0.905828i | −0.476662 | − | 0.879087i | \(-0.658154\pi\) |
0.999642 | − | 0.0267417i | \(-0.00851317\pi\) | |||||||
\(762\) | 142.936 | 5.17803 | ||||||||
\(763\) | 1.35410 | − | 2.34537i | 0.0490218 | − | 0.0849082i | ||||
\(764\) | −51.8951 | − | 89.8850i | −1.87750 | − | 3.25192i | ||||
\(765\) | 7.42705 | + | 12.8640i | 0.268526 | + | 0.465100i | ||||
\(766\) | −57.5410 | −2.07904 | ||||||||
\(767\) | −7.82624 | + | 1.93649i | −0.282589 | + | 0.0699227i | ||||
\(768\) | 38.1246 | 1.37570 | ||||||||
\(769\) | 9.20820 | + | 15.9491i | 0.332056 | + | 0.575138i | 0.982915 | − | 0.184061i | \(-0.0589243\pi\) |
−0.650859 | + | 0.759199i | \(0.725591\pi\) | |||||||
\(770\) | −6.35410 | − | 11.0056i | −0.228986 | − | 0.396615i | ||||
\(771\) | 21.9164 | − | 37.9603i | 0.789300 | − | 1.36711i | ||||
\(772\) | −29.1246 | −1.04822 | ||||||||
\(773\) | −12.6803 | + | 21.9630i | −0.456080 | + | 0.789954i | −0.998750 | − | 0.0499924i | \(-0.984080\pi\) |
0.542669 | + | 0.839946i | \(0.317414\pi\) | |||||||
\(774\) | −63.3779 | + | 109.774i | −2.27807 | + | 3.94574i | ||||
\(775\) | −8.72949 | −0.313573 | ||||||||
\(776\) | −70.4402 | + | 122.006i | −2.52866 | + | 4.37976i | ||||
\(777\) | 5.23607 | + | 9.06914i | 0.187843 | + | 0.325353i | ||||
\(778\) | 15.5623 | + | 26.9547i | 0.557936 | + | 0.966373i | ||||
\(779\) | −1.41641 | −0.0507481 | ||||||||
\(780\) | 83.1763 | + | 86.4393i | 2.97819 | + | 3.09502i | ||||
\(781\) | −26.2918 | −0.940794 | ||||||||
\(782\) | −8.61803 | − | 14.9269i | −0.308180 | − | 0.533784i | ||||
\(783\) | 7.92705 | + | 13.7301i | 0.283290 | + | 0.490672i | ||||
\(784\) | −4.92705 | + | 8.53390i | −0.175966 | + | 0.304782i | ||||
\(785\) | 38.8885 | 1.38799 | ||||||||
\(786\) | −52.5238 | + | 90.9739i | −1.87346 | + | 3.24493i | ||||
\(787\) | −1.29180 | + | 2.23746i | −0.0460476 | + | 0.0797567i | −0.888131 | − | 0.459591i | \(-0.847996\pi\) |
0.842083 | + | 0.539348i | \(0.181329\pi\) | |||||||
\(788\) | −81.5410 | −2.90478 | ||||||||
\(789\) | 11.7812 | − | 20.4056i | 0.419420 | − | 0.726457i | ||||
\(790\) | −13.7082 | − | 23.7433i | −0.487716 | − | 0.844749i | ||||
\(791\) | −0.736068 | − | 1.27491i | −0.0261716 | − | 0.0453305i | ||||
\(792\) | 53.3951 | 1.89731 | ||||||||
\(793\) | −21.0000 | + | 5.19615i | −0.745732 | + | 0.184521i | ||||
\(794\) | 3.70820 | 0.131599 | ||||||||
\(795\) | 12.8992 | + | 22.3420i | 0.457487 | + | 0.792391i | ||||
\(796\) | 59.2599 | + | 102.641i | 2.10041 | + | 3.63802i | ||||
\(797\) | 4.09017 | − | 7.08438i | 0.144881 | − | 0.250942i | −0.784447 | − | 0.620195i | \(-0.787053\pi\) |
0.929329 | + | 0.369254i | \(0.120387\pi\) | |||||||
\(798\) | 12.7082 | 0.449866 | ||||||||
\(799\) | −1.64590 | + | 2.85078i | −0.0582277 | + | 0.100853i | ||||
\(800\) | −10.0623 | + | 17.4284i | −0.355756 | + | 0.616188i | ||||
\(801\) | 18.9230 | 0.668611 | ||||||||
\(802\) | −46.4058 | + | 80.3771i | −1.63864 | + | 2.83822i | ||||
\(803\) | 1.85410 | + | 3.21140i | 0.0654298 | + | 0.113328i | ||||
\(804\) | −80.7492 | − | 139.862i | −2.84781 | − | 4.93254i | ||||
\(805\) | −11.7082 | −0.412660 | ||||||||
\(806\) | 12.3262 | − | 42.6993i | 0.434173 | − | 1.50402i | ||||
\(807\) | 75.2492 | 2.64890 | ||||||||
\(808\) | 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 | \(-0.257836\pi\) | ||||
0.689487 | + | 0.724298i | \(0.257836\pi\) | |||||||
\(812\) | −17.2082 | + | 29.8055i | −0.603890 | + | 1.04597i | ||||
\(813\) | −11.0172 | + | 19.0824i | −0.386391 | + | 0.669249i | ||||
\(814\) | 19.4164 | 0.680545 | ||||||||
\(815\) | 4.85410 | − | 8.40755i | 0.170032 | − | 0.294504i | ||||
\(816\) | −18.9894 | − | 32.8905i | −0.664760 | − | 1.15140i | ||||
\(817\) | 11.6459 | + | 20.1713i | 0.407438 | + | 0.705704i | ||||
\(818\) | 37.7984 | 1.32159 | ||||||||
\(819\) | −3.85410 | + | 13.3510i | −0.134673 | + | 0.466522i | ||||
\(820\) | 9.70820 | 0.339025 | ||||||||
\(821\) | 3.68034 | + | 6.37454i | 0.128445 | + | 0.222473i | 0.923074 | − | 0.384622i | \(-0.125668\pi\) |
−0.794629 | + | 0.607095i | \(0.792335\pi\) | |||||||
\(822\) | −8.97214 | − | 15.5402i | −0.312939 | − | 0.542027i | ||||
\(823\) | 19.2082 | − | 33.2696i | 0.669556 | − | 1.15970i | −0.308473 | − | 0.951233i | \(-0.599818\pi\) |
0.978028 | − | 0.208472i | \(-0.0668489\pi\) | |||||||
\(824\) | −65.0689 | −2.26678 | ||||||||
\(825\) | 4.50000 | − | 7.79423i | 0.156670 | − | 0.271360i | ||||
\(826\) | 2.92705 | − | 5.06980i | 0.101845 | − | 0.176401i | ||||
\(827\) | 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 | 0.792863 | − | 0.609400i | \(-0.208590\pi\) |
−0.924188 | + | 0.381939i | \(0.875256\pi\) | |||||||
\(830\) | −22.9894 | − | 39.8187i | −0.797972 | − | 1.38213i | ||||
\(831\) | 13.0902 | 0.454093 | ||||||||
\(832\) | −21.7705 | − | 22.6246i | −0.754757 | − | 0.784366i | ||||
\(833\) | −1.47214 | −0.0510065 | ||||||||
\(834\) | 15.6353 | + | 27.0811i | 0.541405 | + | 0.937740i | ||||
\(835\) | −18.6353 | − | 32.2772i | −0.644900 | − | 1.11700i | ||||
\(836\) | 8.34346 | − | 14.4513i | 0.288565 | − | 0.499808i | ||||
\(837\) | 10.5279 | 0.363896 | ||||||||
\(838\) | 15.6353 | − | 27.0811i | 0.540111 | − | 0.935500i | ||||
\(839\) | −6.87132 | + | 11.9015i | −0.237224 | + | 0.410885i | −0.959917 | − | 0.280285i | \(-0.909571\pi\) |
0.722692 | + | 0.691170i | \(0.242904\pi\) | |||||||
\(840\) | −51.2148 | −1.76708 | ||||||||
\(841\) | −10.6353 | + | 18.4208i | −0.366733 | + | 0.635200i | ||||
\(842\) | −1.85410 | − | 3.21140i | −0.0638966 | − | 0.110672i | ||||
\(843\) | 26.4164 | + | 45.7546i | 0.909829 | + | 1.57587i | ||||
\(844\) | 22.8541 | 0.786671 | ||||||||
\(845\) | −1.30902 | + | 34.0093i | −0.0450316 | + | 1.16995i | ||||
\(846\) | −22.5623 | −0.775708 | ||||||||
\(847\) | 3.78115 | + | 6.54915i | 0.129922 | + | 0.225031i | ||||
\(848\) | −18.5451 | − | 32.1210i | −0.636841 | − | 1.10304i | ||||
\(849\) | 17.5623 | − | 30.4188i | 0.602737 | − | 1.04397i | ||||
\(850\) | −7.14590 | −0.245102 | ||||||||
\(851\) | 8.94427 | − | 15.4919i | 0.306606 | − | 0.531057i | ||||
\(852\) | −90.1033 | + | 156.064i | −3.08689 | + | 5.34665i | ||||
\(853\) | 14.1246 | 0.483617 | 0.241809 | − | 0.970324i | \(-0.422259\pi\) | ||||
0.241809 | + | 0.970324i | \(0.422259\pi\) | |||||||
\(854\) | 7.85410 | − | 13.6037i | 0.268762 | − | 0.465509i | ||||
\(855\) | 9.35410 | + | 16.2018i | 0.319904 | + | 0.554089i | ||||
\(856\) | 12.6353 | + | 21.8849i | 0.431864 | + | 0.748011i | ||||
\(857\) | −26.4508 | −0.903544 | −0.451772 | − | 0.892133i | \(-0.649208\pi\) | ||||
−0.451772 | + | 0.892133i | \(0.649208\pi\) | |||||||
\(858\) | 31.7705 | + | 33.0169i | 1.08463 | + | 1.12718i | ||||
\(859\) | −44.2492 | −1.50976 | −0.754882 | − | 0.655861i | \(-0.772306\pi\) | ||||
−0.754882 | + | 0.655861i | \(0.772306\pi\) | |||||||
\(860\) | −79.8222 | − | 138.256i | −2.72191 | − | 4.71449i | ||||
\(861\) | 1.00000 | + | 1.73205i | 0.0340799 | + | 0.0590281i | ||||
\(862\) | −10.2082 | + | 17.6811i | −0.347693 | + | 0.602222i | ||||
\(863\) | 11.8885 | 0.404691 | 0.202345 | − | 0.979314i | \(-0.435144\pi\) | ||||
0.202345 | + | 0.979314i | \(0.435144\pi\) | |||||||
\(864\) | 12.1353 | − | 21.0189i | 0.412850 | − | 0.715077i | ||||
\(865\) | 11.7812 | − | 20.4056i | 0.400571 | − | 0.693810i | ||||
\(866\) | 2.61803 | 0.0889644 | ||||||||
\(867\) | −19.4164 | + | 33.6302i | −0.659416 | + | 1.14214i | ||||
\(868\) | 11.4271 | + | 19.7922i | 0.387859 | + | 0.671792i | ||||
\(869\) | −3.70820 | − | 6.42280i | −0.125792 | − | 0.217878i | ||||
\(870\) | −127.228 | −4.31343 | ||||||||
\(871\) | 12.7082 | − | 44.0225i | 0.430601 | − | 1.49165i | ||||
\(872\) | −20.2361 | −0.685280 | ||||||||
\(873\) | −36.3328 | − | 62.9303i | −1.22968 | − | 2.12987i | ||||
\(874\) | −10.8541 | − | 18.7999i | −0.367145 | − | 0.635915i | ||||
\(875\) | 4.11803 | − | 7.13264i | 0.139215 | − | 0.241127i | ||||
\(876\) | 25.4164 | 0.858741 | ||||||||
\(877\) | −0.354102 | + | 0.613323i | −0.0119572 | + | 0.0207104i | −0.871942 | − | 0.489609i | \(-0.837140\pi\) |
0.859985 | + | 0.510319i | \(0.170473\pi\) | |||||||
\(878\) | −19.4443 | + | 33.6785i | −0.656212 | + | 1.13659i | ||||
\(879\) | 17.7082 | 0.597283 | ||||||||
\(880\) | −23.9164 | + | 41.4244i | −0.806222 | + | 1.39642i | ||||
\(881\) | 18.2984 | + | 31.6937i | 0.616488 | + | 1.06779i | 0.990122 | + | 0.140212i | \(0.0447784\pi\) |
−0.373634 | + | 0.927576i | \(0.621888\pi\) | |||||||
\(882\) | −5.04508 | − | 8.73834i | −0.169877 | − | 0.294235i | ||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 7.14590 | − | 24.7541i | 0.240343 | − | 0.832571i | ||||
\(885\) | 15.3262 | 0.515186 | ||||||||
\(886\) | 6.85410 | + | 11.8717i | 0.230268 | + | 0.398836i | ||||
\(887\) | −27.3262 | − | 47.3304i | −0.917525 | − | 1.58920i | −0.803161 | − | 0.595761i | \(-0.796850\pi\) |
−0.114364 | − | 0.993439i | \(-0.536483\pi\) | |||||||
\(888\) | 39.1246 | − | 67.7658i | 1.31294 | − | 2.27407i | ||||
\(889\) | −20.8541 | −0.699424 | ||||||||
\(890\) | −16.8262 | + | 29.1439i | −0.564017 | + | 0.976906i | ||||
\(891\) | 5.29180 | − | 9.16566i | 0.177282 | − | 0.307061i | ||||
\(892\) | 98.3951 | 3.29451 | ||||||||
\(893\) | −2.07295 | + | 3.59045i | −0.0693686 | + | 0.120150i | ||||
\(894\) | 6.35410 | + | 11.0056i | 0.212513 | + | 0.368083i | ||||
\(895\) | 11.7812 | + | 20.4056i | 0.393801 | + | 0.682082i | ||||
\(896\) | 1.09017 | 0.0364200 | ||||||||
\(897\) | 40.9787 | − | 10.1396i | 1.36824 | − | 0.338551i | ||||
\(898\) | 51.1246 | 1.70605 | ||||||||
\(899\) | 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 | ||||||||
\(903\) | 16.4443 | − | 28.4823i | 0.547231 | − | 0.947832i | ||||
\(904\) | −5.50000 | + | 9.52628i | −0.182927 | + | 0.316839i | ||||
\(905\) | 25.4164 | 0.844870 | ||||||||
\(906\) | −4.42705 | + | 7.66788i | −0.147079 | + | 0.254748i | ||||
\(907\) | 12.0000 | + | 20.7846i | 0.398453 | + | 0.690142i | 0.993535 | − | 0.113523i | \(-0.0362137\pi\) |
−0.595082 | + | 0.803665i | \(0.702880\pi\) | |||||||
\(908\) | −3.57295 | − | 6.18853i | −0.118572 | − | 0.205374i | ||||
\(909\) | −44.5623 | −1.47804 | ||||||||
\(910\) | −17.1353 | − | 17.8075i | −0.568028 | − | 0.590312i | ||||
\(911\) | −22.6869 | −0.751651 | −0.375826 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375826 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(912\) | −23.9164 | − | 41.4244i | −0.791951 | − | 1.37170i | ||||
\(913\) | −6.21885 | − | 10.7714i | −0.205814 | − | 0.356480i | ||||
\(914\) | −20.1803 | + | 34.9534i | −0.667506 | + | 1.15615i | ||||
\(915\) | 41.1246 | 1.35954 | ||||||||
\(916\) | 31.8541 | − | 55.1729i | 1.05249 | − | 1.82296i | ||||
\(917\) | 7.66312 | − | 13.2729i | 0.253058 | − | 0.438310i | ||||
\(918\) | 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 | ||||
\(922\) | −31.9787 | −1.05316 | ||||||||
\(923\) | −49.6312 | + | 12.2805i | −1.63363 | + | 0.404219i | ||||
\(924\) | −23.5623 | −0.775143 | ||||||||
\(925\) | −3.70820 | − | 6.42280i | −0.121925 | − | 0.211180i | ||||
\(926\) | −8.78115 | − | 15.2094i | −0.288567 | − | 0.499812i | ||||
\(927\) | 16.7812 | − | 29.0658i | 0.551165 | − | 0.954646i | ||||
\(928\) | 76.9574 | 2.52625 | ||||||||
\(929\) | −5.53444 | + | 9.58593i | −0.181579 | + | 0.314504i | −0.942418 | − | 0.334436i | \(-0.891454\pi\) |
0.760839 | + | 0.648940i | \(0.224788\pi\) | |||||||
\(930\) | −42.2426 | + | 73.1664i | −1.38519 | + | 2.39922i | ||||
\(931\) | −1.85410 | −0.0607657 | ||||||||
\(932\) | −6.35410 | + | 11.0056i | −0.208136 | + | 0.360501i | ||||
\(933\) | 4.35410 | + | 7.54153i | 0.142547 | + | 0.246898i | ||||
\(934\) | −3.07295 | − | 5.32250i | −0.100550 | − | 0.174158i | ||||
\(935\) | −7.14590 | −0.233696 | ||||||||
\(936\) | 100.794 | − | 24.9401i | 3.29457 | − | 0.815193i | ||||
\(937\) | −15.8754 | −0.518626 | −0.259313 | − | 0.965793i | \(-0.583496\pi\) | ||||
−0.259313 | + | 0.965793i | \(0.583496\pi\) | |||||||
\(938\) | 16.6353 | + | 28.8131i | 0.543160 | + | 0.940781i | ||||
\(939\) | 32.8885 | + | 56.9646i | 1.07328 | + | 1.85897i | ||||
\(940\) | 14.2082 | − | 24.6093i | 0.463421 | − | 0.802668i | ||||
\(941\) | 20.3475 | 0.663310 | 0.331655 | − | 0.943401i | \(-0.392393\pi\) | ||||
0.331655 | + | 0.943401i | \(0.392393\pi\) | |||||||
\(942\) | 50.9058 | − | 88.1714i | 1.65860 | − | 2.87278i | ||||
\(943\) | 1.70820 | − | 2.95870i | 0.0556268 | − | 0.0963484i | ||||
\(944\) | −22.0344 | −0.717160 | ||||||||
\(945\) | 2.92705 | − | 5.06980i | 0.0952170 | − | 0.164921i | ||||
\(946\) | −30.4894 | − | 52.8091i | −0.991294 | − | 1.71697i | ||||
\(947\) | 18.4336 | + | 31.9280i | 0.599012 | + | 1.03752i | 0.992967 | + | 0.118390i | \(0.0377733\pi\) |
−0.393955 | + | 0.919130i | \(0.628893\pi\) | |||||||
\(948\) | −50.8328 | −1.65097 | ||||||||
\(949\) | 5.00000 | + | 5.19615i | 0.162307 | + | 0.168674i | ||||
\(950\) | −9.00000 | −0.291999 | ||||||||
\(951\) | 34.3435 | + | 59.4846i | 1.11366 | + | 1.92892i | ||||
\(952\) | 5.50000 | + | 9.52628i | 0.178256 | + | 0.308748i | ||||
\(953\) | −13.3885 | + | 23.1896i | −0.433697 | + | 0.751186i | −0.997188 | − | 0.0749362i | \(-0.976125\pi\) |
0.563491 | + | 0.826122i | \(0.309458\pi\) | |||||||
\(954\) | 37.9787 | 1.22961 | ||||||||
\(955\) | −27.9894 | + | 48.4790i | −0.905714 | + | 1.56874i | ||||
\(956\) | 59.9681 | − | 103.868i | 1.93951 | − | 3.35932i | ||||
\(957\) | −34.4164 | −1.11252 | ||||||||
\(958\) | −32.6976 | + | 56.6338i | −1.05641 | + | 1.82976i | ||||
\(959\) | 1.30902 | + | 2.26728i | 0.0422704 | + | 0.0732144i | ||||
\(960\) | 29.8435 | + | 51.6904i | 0.963193 | + | 1.66830i | ||||
\(961\) | −8.83282 | −0.284930 | ||||||||
\(962\) | 36.6525 | − | 9.06914i | 1.18172 | − | 0.292401i | ||||
\(963\) | −13.0344 | −0.420029 | ||||||||
\(964\) | −59.6140 | − | 103.254i | −1.92004 | − | 3.32560i | ||||
\(965\) | 7.85410 | + | 13.6037i | 0.252832 | + | 0.437919i | ||||
\(966\) | −15.3262 | + | 26.5458i | −0.493114 | + | 0.854098i | ||||
\(967\) | −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 | ||||
\(969\) | 3.57295 | − | 6.18853i | 0.114780 | − | 0.198804i | ||||
\(970\) | 129.228 | 4.14926 | ||||||||
\(971\) | −15.7918 | + | 27.3522i | −0.506783 | + | 0.877774i | 0.493186 | + | 0.869924i | \(0.335832\pi\) |
−0.999969 | + | 0.00784995i | \(0.997501\pi\) | |||||||
\(972\) | −52.5517 | − | 91.0221i | −1.68560 | − | 2.91954i | ||||
\(973\) | −2.28115 | − | 3.95107i | −0.0731304 | − | 0.126666i | ||||
\(974\) | 78.4853 | 2.51483 | ||||||||
\(975\) | 4.85410 | − | 16.8151i | 0.155456 | − | 0.538514i | ||||
\(976\) | −59.1246 | −1.89253 | ||||||||
\(977\) | 11.2639 | + | 19.5097i | 0.360365 | + | 0.624171i | 0.988021 | − | 0.154320i | \(-0.0493188\pi\) |
−0.627656 | + | 0.778491i | \(0.715985\pi\) | |||||||
\(978\) | −12.7082 | − | 22.0113i | −0.406364 | − | 0.703842i | ||||
\(979\) | −4.55166 | + | 7.88371i | −0.145472 | + | 0.251965i | ||||
\(980\) | 12.7082 | 0.405949 | ||||||||
\(981\) | 5.21885 | − | 9.03931i | 0.166625 | − | 0.288603i | ||||
\(982\) | −16.2082 | + | 28.0734i | −0.517225 | + | 0.895859i | ||||
\(983\) | 18.3820 | 0.586294 | 0.293147 | − | 0.956067i | \(-0.405298\pi\) | ||||
0.293147 | + | 0.956067i | \(0.405298\pi\) | |||||||
\(984\) | 7.47214 | − | 12.9421i | 0.238203 | − | 0.412580i | ||||
\(985\) | 21.9894 | + | 38.0867i | 0.700639 | + | 1.21354i | ||||
\(986\) | 13.6631 | + | 23.6652i | 0.435122 | + | 0.753654i | ||||
\(987\) | 5.85410 | 0.186338 | ||||||||
\(988\) | 9.00000 | − | 31.1769i | 0.286328 | − | 0.991870i | ||||
\(989\) | −56.1803 | −1.78643 | ||||||||
\(990\) | −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 | ||||||||
\(994\) | 18.5623 | − | 32.1509i | 0.588761 | − | 1.01976i | ||||
\(995\) | 31.9615 | − | 55.3589i | 1.01325 | − | 1.75500i | ||||
\(996\) | −85.2492 | −2.70123 | ||||||||
\(997\) | −24.5000 | + | 42.4352i | −0.775923 | + | 1.34394i | 0.158352 | + | 0.987383i | \(0.449382\pi\) |
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | −19.4443 | − | 33.6785i | −0.615498 | − | 1.06607i | ||||
\(999\) | 4.47214 | + | 7.74597i | 0.141492 | + | 0.245072i |
(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 | 91.2.f.a.29.1 | yes | 4 | |
3.2 | odd | 2 | 819.2.o.c.757.2 | 4 | |||
4.3 | odd | 2 | 1456.2.s.h.1121.1 | 4 | |||
7.2 | even | 3 | 637.2.g.b.263.1 | 4 | |||
7.3 | odd | 6 | 637.2.h.f.471.2 | 4 | |||
7.4 | even | 3 | 637.2.h.g.471.2 | 4 | |||
7.5 | odd | 6 | 637.2.g.c.263.1 | 4 | |||
7.6 | odd | 2 | 637.2.f.c.393.1 | 4 | |||
13.2 | odd | 12 | 1183.2.c.c.337.1 | 4 | |||
13.3 | even | 3 | 1183.2.a.g.1.2 | 2 | |||
13.9 | even | 3 | inner | 91.2.f.a.22.1 | ✓ | 4 | |
13.10 | even | 6 | 1183.2.a.c.1.1 | 2 | |||
13.11 | odd | 12 | 1183.2.c.c.337.4 | 4 | |||
39.35 | odd | 6 | 819.2.o.c.568.2 | 4 | |||
52.35 | odd | 6 | 1456.2.s.h.113.1 | 4 | |||
91.9 | even | 3 | 637.2.h.g.165.2 | 4 | |||
91.48 | odd | 6 | 637.2.f.c.295.1 | 4 | |||
91.55 | odd | 6 | 8281.2.a.bb.1.2 | 2 | |||
91.61 | odd | 6 | 637.2.h.f.165.2 | 4 | |||
91.62 | odd | 6 | 8281.2.a.n.1.1 | 2 | |||
91.74 | even | 3 | 637.2.g.b.373.1 | 4 | |||
91.87 | odd | 6 | 637.2.g.c.373.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.1 | ✓ | 4 | 13.9 | even | 3 | inner | |
91.2.f.a.29.1 | yes | 4 | 1.1 | even | 1 | trivial | |
637.2.f.c.295.1 | 4 | 91.48 | odd | 6 | |||
637.2.f.c.393.1 | 4 | 7.6 | odd | 2 | |||
637.2.g.b.263.1 | 4 | 7.2 | even | 3 | |||
637.2.g.b.373.1 | 4 | 91.74 | even | 3 | |||
637.2.g.c.263.1 | 4 | 7.5 | odd | 6 | |||
637.2.g.c.373.1 | 4 | 91.87 | odd | 6 | |||
637.2.h.f.165.2 | 4 | 91.61 | odd | 6 | |||
637.2.h.f.471.2 | 4 | 7.3 | odd | 6 | |||
637.2.h.g.165.2 | 4 | 91.9 | even | 3 | |||
637.2.h.g.471.2 | 4 | 7.4 | even | 3 | |||
819.2.o.c.568.2 | 4 | 39.35 | odd | 6 | |||
819.2.o.c.757.2 | 4 | 3.2 | odd | 2 | |||
1183.2.a.c.1.1 | 2 | 13.10 | even | 6 | |||
1183.2.a.g.1.2 | 2 | 13.3 | even | 3 | |||
1183.2.c.c.337.1 | 4 | 13.2 | odd | 12 | |||
1183.2.c.c.337.4 | 4 | 13.11 | odd | 12 | |||
1456.2.s.h.113.1 | 4 | 52.35 | odd | 6 | |||
1456.2.s.h.1121.1 | 4 | 4.3 | odd | 2 | |||
8281.2.a.n.1.1 | 2 | 91.62 | odd | 6 | |||
8281.2.a.bb.1.2 | 2 | 91.55 | odd | 6 |