Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [57,3,Mod(31,57)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(57, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("57.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55313750685\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.92607408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.500000 + 2.93068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 57.31 |
Dual form | 57.3.g.b.46.1 |
$q$-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 \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(40\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78805 | + | 1.03233i | −0.894023 | + | 0.516164i | −0.875256 | − | 0.483659i | \(-0.839307\pi\) |
−0.0187668 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.131406 | − | 0.227602i | 0.0328515 | − | 0.0569005i | ||||
\(5\) | −3.20750 | − | 5.55555i | −0.641500 | − | 1.11111i | −0.985098 | − | 0.171993i | \(-0.944979\pi\) |
0.343598 | − | 0.939117i | \(-0.388354\pi\) | |||||||
\(6\) | 1.78805 | − | 3.09699i | 0.298008 | − | 0.516164i | ||||
\(7\) | −2.26281 | −0.323259 | −0.161629 | − | 0.986852i | \(-0.551675\pi\) | ||||
−0.161629 | + | 0.986852i | \(0.551675\pi\) | |||||||
\(8\) | − | 7.71601i | − | 0.964502i | ||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 11.4703 | + | 6.62239i | 1.14703 | + | 0.662239i | ||||
\(11\) | −20.0928 | −1.82662 | −0.913309 | − | 0.407267i | \(-0.866482\pi\) | ||||
−0.913309 | + | 0.407267i | \(0.866482\pi\) | |||||||
\(12\) | 0.455204i | 0.0379337i | ||||||||
\(13\) | −0.135471 | − | 0.0782143i | −0.0104209 | − | 0.00601649i | 0.494781 | − | 0.869018i | \(-0.335248\pi\) |
−0.505201 | + | 0.863001i | \(0.668582\pi\) | |||||||
\(14\) | 4.04601 | − | 2.33597i | 0.289001 | − | 0.166855i | ||||
\(15\) | 9.62250 | + | 5.55555i | 0.641500 | + | 0.370370i | ||||
\(16\) | 8.49109 | + | 14.7070i | 0.530693 | + | 0.919187i | ||||
\(17\) | 12.3133 | + | 21.3272i | 0.724311 | + | 1.25454i | 0.959257 | + | 0.282534i | \(0.0911752\pi\) |
−0.234947 | + | 0.972008i | \(0.575492\pi\) | |||||||
\(18\) | 6.19397i | 0.344110i | ||||||||
\(19\) | −18.9317 | − | 1.60945i | −0.996406 | − | 0.0847081i | ||||
\(20\) | −1.68594 | −0.0842970 | ||||||||
\(21\) | 3.39422 | − | 1.95965i | 0.161629 | − | 0.0933168i | ||||
\(22\) | 35.9269 | − | 20.7424i | 1.63304 | − | 0.942836i | ||||
\(23\) | −2.62250 | + | 4.54230i | −0.114022 | + | 0.197491i | −0.917388 | − | 0.397994i | \(-0.869707\pi\) |
0.803367 | + | 0.595485i | \(0.203040\pi\) | |||||||
\(24\) | 6.68226 | + | 11.5740i | 0.278428 | + | 0.482251i | ||||
\(25\) | −8.07609 | + | 13.9882i | −0.323044 | + | 0.559528i | ||||
\(26\) | 0.322972 | 0.0124220 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −0.297347 | + | 0.515021i | −0.0106195 | + | 0.0183936i | ||||
\(29\) | −31.4573 | − | 18.1619i | −1.08474 | − | 0.626272i | −0.152566 | − | 0.988293i | \(-0.548754\pi\) |
−0.932170 | + | 0.362021i | \(0.882087\pi\) | |||||||
\(30\) | −22.9406 | −0.764687 | ||||||||
\(31\) | − | 17.1105i | − | 0.551952i | −0.961165 | − | 0.275976i | \(-0.910999\pi\) | ||
0.961165 | − | 0.275976i | \(-0.0890010\pi\) | |||||||
\(32\) | −3.63586 | − | 2.09917i | −0.113621 | − | 0.0655989i | ||||
\(33\) | 30.1392 | − | 17.4009i | 0.913309 | − | 0.527299i | ||||
\(34\) | −44.0334 | − | 25.4227i | −1.29510 | − | 0.747727i | ||||
\(35\) | 7.25797 | + | 12.5712i | 0.207370 | + | 0.359176i | ||||
\(36\) | −0.394218 | − | 0.682806i | −0.0109505 | − | 0.0189668i | ||||
\(37\) | − | 42.7124i | − | 1.15439i | −0.816607 | − | 0.577194i | \(-0.804148\pi\) | ||
0.816607 | − | 0.577194i | \(-0.195852\pi\) | |||||||
\(38\) | 35.5123 | − | 16.6660i | 0.934533 | − | 0.438578i | ||||
\(39\) | 0.270942 | 0.00694724 | ||||||||
\(40\) | −42.8667 | + | 24.7491i | −1.07167 | + | 0.618728i | ||||
\(41\) | 30.0928 | − | 17.3741i | 0.733971 | − | 0.423758i | −0.0859022 | − | 0.996304i | \(-0.527377\pi\) |
0.819873 | + | 0.572545i | \(0.194044\pi\) | |||||||
\(42\) | −4.04601 | + | 7.00790i | −0.0963336 | + | 0.166855i | ||||
\(43\) | 12.5553 | + | 21.7464i | 0.291984 | + | 0.505731i | 0.974279 | − | 0.225346i | \(-0.0723512\pi\) |
−0.682295 | + | 0.731077i | \(0.739018\pi\) | |||||||
\(44\) | −2.64032 | + | 4.57316i | −0.0600072 | + | 0.103936i | ||||
\(45\) | −19.2450 | −0.427666 | ||||||||
\(46\) | − | 10.8291i | − | 0.235415i | ||||||
\(47\) | −14.6778 | + | 25.4227i | −0.312294 | + | 0.540909i | −0.978859 | − | 0.204538i | \(-0.934431\pi\) |
0.666565 | + | 0.745447i | \(0.267764\pi\) | |||||||
\(48\) | −25.4733 | − | 14.7070i | −0.530693 | − | 0.306396i | ||||
\(49\) | −43.8797 | −0.895504 | ||||||||
\(50\) | − | 33.3487i | − | 0.666975i | ||||||
\(51\) | −36.9398 | − | 21.3272i | −0.724311 | − | 0.418181i | ||||
\(52\) | −0.0356035 | + | 0.0205557i | −0.000684682 | + | 0.000395301i | ||||
\(53\) | 48.4176 | + | 27.9539i | 0.913540 | + | 0.527433i | 0.881568 | − | 0.472056i | \(-0.156488\pi\) |
0.0319716 | + | 0.999489i | \(0.489821\pi\) | |||||||
\(54\) | −5.36414 | − | 9.29096i | −0.0993359 | − | 0.172055i | ||||
\(55\) | 64.4476 | + | 111.627i | 1.17178 | + | 2.02957i | ||||
\(56\) | 17.4599i | 0.311784i | ||||||||
\(57\) | 29.7914 | − | 13.9812i | 0.522656 | − | 0.245284i | ||||
\(58\) | 74.9962 | 1.29304 | ||||||||
\(59\) | −29.9269 | + | 17.2783i | −0.507235 | + | 0.292852i | −0.731696 | − | 0.681631i | \(-0.761271\pi\) |
0.224461 | + | 0.974483i | \(0.427938\pi\) | |||||||
\(60\) | 2.52891 | − | 1.46007i | 0.0421485 | − | 0.0243344i | ||||
\(61\) | 27.3805 | − | 47.4244i | 0.448860 | − | 0.777448i | −0.549452 | − | 0.835525i | \(-0.685164\pi\) |
0.998312 | + | 0.0580769i | \(0.0184968\pi\) | |||||||
\(62\) | 17.6637 | + | 30.5944i | 0.284898 | + | 0.493457i | ||||
\(63\) | −3.39422 | + | 5.87896i | −0.0538765 | + | 0.0933168i | ||||
\(64\) | −59.2606 | −0.925947 | ||||||||
\(65\) | 1.00349i | 0.0154383i | ||||||||
\(66\) | −35.9269 | + | 62.2272i | −0.544346 | + | 0.942836i | ||||
\(67\) | 66.0698 | + | 38.1454i | 0.986117 | + | 0.569335i | 0.904111 | − | 0.427297i | \(-0.140534\pi\) |
0.0820054 | + | 0.996632i | \(0.473868\pi\) | |||||||
\(68\) | 6.47216 | 0.0951788 | ||||||||
\(69\) | − | 9.08459i | − | 0.131661i | ||||||
\(70\) | −25.9552 | − | 14.9852i | −0.370788 | − | 0.214075i | ||||
\(71\) | 63.6080 | − | 36.7241i | 0.895887 | − | 0.517240i | 0.0200233 | − | 0.999800i | \(-0.493626\pi\) |
0.875863 | + | 0.482559i | \(0.160293\pi\) | |||||||
\(72\) | −20.0468 | − | 11.5740i | −0.278428 | − | 0.160750i | ||||
\(73\) | −45.9053 | − | 79.5103i | −0.628840 | − | 1.08918i | −0.987785 | − | 0.155824i | \(-0.950197\pi\) |
0.358945 | − | 0.933359i | \(-0.383137\pi\) | |||||||
\(74\) | 44.0932 | + | 76.3717i | 0.595854 | + | 1.03205i | ||||
\(75\) | − | 27.9764i | − | 0.373019i | ||||||
\(76\) | −2.85406 | + | 4.09740i | −0.0375534 | + | 0.0539132i | ||||
\(77\) | 45.4662 | 0.590471 | ||||||||
\(78\) | −0.484457 | + | 0.279702i | −0.00621099 | + | 0.00358592i | ||||
\(79\) | −53.1300 | + | 30.6746i | −0.672531 | + | 0.388286i | −0.797035 | − | 0.603933i | \(-0.793599\pi\) |
0.124504 | + | 0.992219i | \(0.460266\pi\) | |||||||
\(80\) | 54.4703 | − | 94.3453i | 0.680879 | − | 1.17932i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −35.8716 | + | 62.1313i | −0.437458 | + | 0.757699i | ||||
\(83\) | −148.793 | −1.79268 | −0.896342 | − | 0.443363i | \(-0.853785\pi\) | ||||
−0.896342 | + | 0.443363i | \(0.853785\pi\) | |||||||
\(84\) | − | 1.03004i | − | 0.0122624i | ||||||
\(85\) | 78.9897 | − | 136.814i | 0.929290 | − | 1.60958i | ||||
\(86\) | −44.8990 | − | 25.9224i | −0.522081 | − | 0.301424i | ||||
\(87\) | 62.9147 | 0.723157 | ||||||||
\(88\) | 155.036i | 1.76178i | ||||||||
\(89\) | −62.7829 | − | 36.2477i | −0.705426 | − | 0.407278i | 0.103939 | − | 0.994584i | \(-0.466855\pi\) |
−0.809365 | + | 0.587306i | \(0.800189\pi\) | |||||||
\(90\) | 34.4109 | − | 19.8672i | 0.382344 | − | 0.220746i | ||||
\(91\) | 0.306546 | + | 0.176984i | 0.00336864 | + | 0.00194488i | ||||
\(92\) | 0.689224 | + | 1.19377i | 0.00749156 | + | 0.0129758i | ||||
\(93\) | 14.8181 | + | 25.6657i | 0.159335 | + | 0.275976i | ||||
\(94\) | − | 60.6093i | − | 0.644780i | ||||||
\(95\) | 51.7820 | + | 110.338i | 0.545074 | + | 1.16146i | ||||
\(96\) | 7.27172 | 0.0757471 | ||||||||
\(97\) | −70.0326 | + | 40.4334i | −0.721986 | + | 0.416839i | −0.815483 | − | 0.578781i | \(-0.803529\pi\) |
0.0934972 | + | 0.995620i | \(0.470195\pi\) | |||||||
\(98\) | 78.4589 | − | 45.2983i | 0.800601 | − | 0.462227i | ||||
\(99\) | −30.1392 | + | 52.2026i | −0.304436 | + | 0.527299i | ||||
\(100\) | 2.12250 | + | 3.67627i | 0.0212250 | + | 0.0367627i | ||||
\(101\) | −76.6770 | + | 132.809i | −0.759178 | + | 1.31494i | 0.184092 | + | 0.982909i | \(0.441066\pi\) |
−0.943270 | + | 0.332027i | \(0.892268\pi\) | |||||||
\(102\) | 88.0669 | 0.863401 | ||||||||
\(103\) | − | 168.948i | − | 1.64027i | −0.572169 | − | 0.820136i | \(-0.693898\pi\) | ||
0.572169 | − | 0.820136i | \(-0.306102\pi\) | |||||||
\(104\) | −0.603503 | + | 1.04530i | −0.00580291 | + | 0.0100509i | ||||
\(105\) | −21.7739 | − | 12.5712i | −0.207370 | − | 0.119725i | ||||
\(106\) | −115.431 | −1.08897 | ||||||||
\(107\) | − | 139.060i | − | 1.29963i | −0.760093 | − | 0.649815i | \(-0.774846\pi\) | ||
0.760093 | − | 0.649815i | \(-0.225154\pi\) | |||||||
\(108\) | 1.18265 | + | 0.682806i | 0.0109505 | + | 0.00632228i | ||||
\(109\) | −9.15888 | + | 5.28788i | −0.0840264 | + | 0.0485127i | −0.541424 | − | 0.840749i | \(-0.682115\pi\) |
0.457398 | + | 0.889262i | \(0.348781\pi\) | |||||||
\(110\) | −230.471 | − | 133.062i | −2.09519 | − | 1.20966i | ||||
\(111\) | 36.9900 | + | 64.0685i | 0.333243 | + | 0.577194i | ||||
\(112\) | −19.2137 | − | 33.2792i | −0.171551 | − | 0.297135i | ||||
\(113\) | 69.1581i | 0.612018i | 0.952029 | + | 0.306009i | \(0.0989938\pi\) | ||||
−0.952029 | + | 0.306009i | \(0.901006\pi\) | |||||||
\(114\) | −38.8352 | + | 55.7535i | −0.340660 | + | 0.489066i | ||||
\(115\) | 33.6466 | 0.292579 | ||||||||
\(116\) | −8.26737 | + | 4.77317i | −0.0712704 | + | 0.0411480i | ||||
\(117\) | −0.406413 | + | 0.234643i | −0.00347362 | + | 0.00200550i | ||||
\(118\) | 35.6737 | − | 61.7887i | 0.302320 | − | 0.523633i | ||||
\(119\) | −27.8626 | − | 48.2595i | −0.234140 | − | 0.405542i | ||||
\(120\) | 42.8667 | − | 74.2473i | 0.357223 | − | 0.618728i | ||||
\(121\) | 282.721 | 2.33654 | ||||||||
\(122\) | 113.063i | 0.926742i | ||||||||
\(123\) | −30.0928 | + | 52.1223i | −0.244657 | + | 0.423758i | ||||
\(124\) | −3.89438 | − | 2.24842i | −0.0314063 | − | 0.0181324i | ||||
\(125\) | −56.7587 | −0.454070 | ||||||||
\(126\) | − | 14.0158i | − | 0.111236i | ||||||
\(127\) | −25.6547 | − | 14.8118i | −0.202006 | − | 0.116628i | 0.395585 | − | 0.918429i | \(-0.370542\pi\) |
−0.597591 | + | 0.801801i | \(0.703875\pi\) | |||||||
\(128\) | 120.504 | − | 69.5731i | 0.941438 | − | 0.543540i | ||||
\(129\) | −37.6659 | − | 21.7464i | −0.291984 | − | 0.168577i | ||||
\(130\) | −1.03593 | − | 1.79428i | −0.00796870 | − | 0.0138022i | ||||
\(131\) | −28.6526 | − | 49.6278i | −0.218722 | − | 0.378838i | 0.735695 | − | 0.677313i | \(-0.236856\pi\) |
−0.954418 | + | 0.298474i | \(0.903522\pi\) | |||||||
\(132\) | − | 9.14633i | − | 0.0692903i | ||||||
\(133\) | 42.8389 | + | 3.64189i | 0.322097 | + | 0.0273826i | ||||
\(134\) | −157.514 | −1.17548 | ||||||||
\(135\) | 28.8675 | − | 16.6667i | 0.213833 | − | 0.123457i | ||||
\(136\) | 164.561 | − | 95.0094i | 1.21001 | − | 0.698599i | ||||
\(137\) | 47.4499 | − | 82.1856i | 0.346349 | − | 0.599895i | −0.639249 | − | 0.769000i | \(-0.720755\pi\) |
0.985598 | + | 0.169105i | \(0.0540879\pi\) | |||||||
\(138\) | 9.37829 | + | 16.2437i | 0.0679586 | + | 0.117708i | ||||
\(139\) | −91.2747 | + | 158.092i | −0.656652 | + | 1.13736i | 0.324824 | + | 0.945774i | \(0.394695\pi\) |
−0.981477 | + | 0.191581i | \(0.938639\pi\) | |||||||
\(140\) | 3.81496 | 0.0272497 | ||||||||
\(141\) | − | 50.8454i | − | 0.360606i | ||||||
\(142\) | −75.8226 | + | 131.329i | −0.533962 | + | 0.924850i | ||||
\(143\) | 2.72200 | + | 1.57155i | 0.0190349 | + | 0.0109898i | ||||
\(144\) | 50.9465 | 0.353795 | ||||||||
\(145\) | 233.017i | 1.60701i | ||||||||
\(146\) | 164.162 | + | 94.7788i | 1.12439 | + | 0.649170i | ||||
\(147\) | 65.8195 | − | 38.0009i | 0.447752 | − | 0.258510i | ||||
\(148\) | −9.72142 | − | 5.61266i | −0.0656852 | − | 0.0379234i | ||||
\(149\) | −5.50439 | − | 9.53389i | −0.0369422 | − | 0.0639858i | 0.846963 | − | 0.531652i | \(-0.178428\pi\) |
−0.883905 | + | 0.467666i | \(0.845095\pi\) | |||||||
\(150\) | 28.8809 | + | 50.0231i | 0.192539 | + | 0.333487i | ||||
\(151\) | 238.846i | 1.58176i | 0.611968 | + | 0.790882i | \(0.290378\pi\) | ||||
−0.611968 | + | 0.790882i | \(0.709622\pi\) | |||||||
\(152\) | −12.4186 | + | 146.077i | −0.0817011 | + | 0.961035i | ||||
\(153\) | 73.8797 | 0.482874 | ||||||||
\(154\) | −81.2957 | + | 46.9361i | −0.527894 | + | 0.304780i | ||||
\(155\) | −95.0582 | + | 54.8819i | −0.613279 | + | 0.354077i | ||||
\(156\) | 0.0356035 | − | 0.0616670i | 0.000228227 | − | 0.000395301i | ||||
\(157\) | 22.8125 | + | 39.5124i | 0.145303 | + | 0.251671i | 0.929486 | − | 0.368858i | \(-0.120251\pi\) |
−0.784183 | + | 0.620529i | \(0.786918\pi\) | |||||||
\(158\) | 63.3326 | − | 109.695i | 0.400839 | − | 0.694273i | ||||
\(159\) | −96.8353 | −0.609027 | ||||||||
\(160\) | 26.9323i | 0.168327i | ||||||||
\(161\) | 5.93421 | − | 10.2784i | 0.0368585 | − | 0.0638407i | ||||
\(162\) | 16.0924 | + | 9.29096i | 0.0993359 | + | 0.0573516i | ||||
\(163\) | 5.89159 | 0.0361447 | 0.0180724 | − | 0.999837i | \(-0.494247\pi\) | ||||
0.0180724 | + | 0.999837i | \(0.494247\pi\) | |||||||
\(164\) | − | 9.13224i | − | 0.0556844i | ||||||
\(165\) | −193.343 | − | 111.627i | −1.17178 | − | 0.676525i | ||||
\(166\) | 266.048 | − | 153.603i | 1.60270 | − | 0.925320i | ||||
\(167\) | 142.140 | + | 82.0646i | 0.851138 | + | 0.491405i | 0.861035 | − | 0.508546i | \(-0.169817\pi\) |
−0.00989689 | + | 0.999951i | \(0.503150\pi\) | |||||||
\(168\) | −15.1207 | − | 26.1898i | −0.0900042 | − | 0.155892i | ||||
\(169\) | −84.4878 | − | 146.337i | −0.499928 | − | 0.865900i | ||||
\(170\) | 326.173i | 1.91867i | ||||||||
\(171\) | −32.5790 | + | 46.7718i | −0.190521 | + | 0.273520i | ||||
\(172\) | 6.59938 | 0.0383685 | ||||||||
\(173\) | 234.355 | − | 135.305i | 1.35465 | − | 0.782109i | 0.365755 | − | 0.930711i | \(-0.380811\pi\) |
0.988897 | + | 0.148603i | \(0.0474775\pi\) | |||||||
\(174\) | −112.494 | + | 64.9486i | −0.646519 | + | 0.373268i | ||||
\(175\) | 18.2747 | − | 31.6527i | 0.104427 | − | 0.180872i | ||||
\(176\) | −170.610 | − | 295.505i | −0.969374 | − | 1.67900i | ||||
\(177\) | 29.9269 | − | 51.8349i | 0.169078 | − | 0.292852i | ||||
\(178\) | 149.678 | 0.840890 | ||||||||
\(179\) | − | 186.439i | − | 1.04156i | −0.853691 | − | 0.520779i | \(-0.825641\pi\) | ||
0.853691 | − | 0.520779i | \(-0.174359\pi\) | |||||||
\(180\) | −2.52891 | + | 4.38020i | −0.0140495 | + | 0.0243344i | ||||
\(181\) | −40.1939 | − | 23.2059i | −0.222066 | − | 0.128210i | 0.384841 | − | 0.922983i | \(-0.374256\pi\) |
−0.606906 | + | 0.794773i | \(0.707590\pi\) | |||||||
\(182\) | −0.730824 | −0.00401552 | ||||||||
\(183\) | 94.8487i | 0.518299i | ||||||||
\(184\) | 35.0484 | + | 20.2352i | 0.190481 | + | 0.109974i | ||||
\(185\) | −237.291 | + | 137.000i | −1.28265 | + | 0.740539i | ||||
\(186\) | −52.9910 | − | 30.5944i | −0.284898 | − | 0.164486i | ||||
\(187\) | −247.408 | − | 428.524i | −1.32304 | − | 2.29157i | ||||
\(188\) | 3.85751 | + | 6.68140i | 0.0205187 | + | 0.0355393i | ||||
\(189\) | − | 11.7579i | − | 0.0622112i | ||||||
\(190\) | −206.494 | − | 143.834i | −1.08681 | − | 0.757021i | ||||
\(191\) | −36.7222 | −0.192263 | −0.0961315 | − | 0.995369i | \(-0.530647\pi\) | ||||
−0.0961315 | + | 0.995369i | \(0.530647\pi\) | |||||||
\(192\) | 88.8909 | − | 51.3212i | 0.462973 | − | 0.267298i | ||||
\(193\) | −173.472 | + | 100.154i | −0.898817 | + | 0.518932i | −0.876816 | − | 0.480826i | \(-0.840337\pi\) |
−0.0220009 | + | 0.999758i | \(0.507004\pi\) | |||||||
\(194\) | 83.4811 | − | 144.593i | 0.430315 | − | 0.745327i | ||||
\(195\) | −0.869047 | − | 1.50523i | −0.00445665 | − | 0.00771915i | ||||
\(196\) | −5.76606 | + | 9.98710i | −0.0294187 | + | 0.0509546i | ||||
\(197\) | −171.512 | −0.870620 | −0.435310 | − | 0.900281i | \(-0.643361\pi\) | ||||
−0.435310 | + | 0.900281i | \(0.643361\pi\) | |||||||
\(198\) | − | 124.454i | − | 0.628557i | ||||||
\(199\) | −43.7500 | + | 75.7772i | −0.219849 | + | 0.380790i | −0.954762 | − | 0.297372i | \(-0.903890\pi\) |
0.734913 | + | 0.678162i | \(0.237223\pi\) | |||||||
\(200\) | 107.933 | + | 62.3152i | 0.539666 | + | 0.311576i | ||||
\(201\) | −132.140 | −0.657411 | ||||||||
\(202\) | − | 316.624i | − | 1.56744i | ||||||
\(203\) | 71.1820 | + | 41.0970i | 0.350650 | + | 0.202448i | ||||
\(204\) | −9.70824 | + | 5.60505i | −0.0475894 | + | 0.0274758i | ||||
\(205\) | −193.045 | − | 111.455i | −0.941684 | − | 0.543682i | ||||
\(206\) | 174.410 | + | 302.087i | 0.846650 | + | 1.46644i | ||||
\(207\) | 7.86749 | + | 13.6269i | 0.0380072 | + | 0.0658304i | ||||
\(208\) | − | 2.65650i | − | 0.0127716i | ||||||
\(209\) | 380.391 | + | 32.3384i | 1.82005 | + | 0.154729i | ||||
\(210\) | 51.9103 | 0.247192 | ||||||||
\(211\) | 16.3950 | − | 9.46566i | 0.0777014 | − | 0.0448609i | −0.460646 | − | 0.887584i | \(-0.652382\pi\) |
0.538347 | + | 0.842723i | \(0.319049\pi\) | |||||||
\(212\) | 12.7247 | − | 7.34663i | 0.0600224 | − | 0.0346539i | ||||
\(213\) | −63.6080 | + | 110.172i | −0.298629 | + | 0.517240i | ||||
\(214\) | 143.556 | + | 248.646i | 0.670823 | + | 1.16190i | ||||
\(215\) | 80.5423 | − | 139.503i | 0.374615 | − | 0.648853i | ||||
\(216\) | 40.0936 | 0.185618 | ||||||||
\(217\) | 38.7178i | 0.178423i | ||||||||
\(218\) | 10.9177 | − | 18.9100i | 0.0500810 | − | 0.0867429i | ||||
\(219\) | 137.716 | + | 79.5103i | 0.628840 | + | 0.363061i | ||||
\(220\) | 33.8752 | 0.153978 | ||||||||
\(221\) | − | 3.85230i | − | 0.0174312i | ||||||
\(222\) | −132.280 | − | 76.3717i | −0.595854 | − | 0.344016i | ||||
\(223\) | −224.162 | + | 129.420i | −1.00521 | + | 0.580358i | −0.909786 | − | 0.415078i | \(-0.863754\pi\) |
−0.0954244 | + | 0.995437i | \(0.530421\pi\) | |||||||
\(224\) | 8.22727 | + | 4.75002i | 0.0367289 | + | 0.0212054i | ||||
\(225\) | 24.2283 | + | 41.9646i | 0.107681 | + | 0.186509i | ||||
\(226\) | −71.3939 | − | 123.658i | −0.315902 | − | 0.547159i | ||||
\(227\) | − | 129.054i | − | 0.568522i | −0.958747 | − | 0.284261i | \(-0.908252\pi\) | ||
0.958747 | − | 0.284261i | \(-0.0917482\pi\) | |||||||
\(228\) | 0.732630 | − | 8.61779i | 0.00321329 | − | 0.0377973i | ||||
\(229\) | −98.8946 | −0.431854 | −0.215927 | − | 0.976409i | \(-0.569277\pi\) | ||||
−0.215927 | + | 0.976409i | \(0.569277\pi\) | |||||||
\(230\) | −60.1617 | + | 34.7344i | −0.261572 | + | 0.151019i | ||||
\(231\) | −68.1994 | + | 39.3749i | −0.295235 | + | 0.170454i | ||||
\(232\) | −140.137 | + | 242.725i | −0.604041 | + | 1.04623i | ||||
\(233\) | 174.731 | + | 302.644i | 0.749920 | + | 1.29890i | 0.947861 | + | 0.318685i | \(0.103241\pi\) |
−0.197941 | + | 0.980214i | \(0.563425\pi\) | |||||||
\(234\) | 0.484457 | − | 0.839105i | 0.00207033 | − | 0.00358592i | ||||
\(235\) | 188.316 | 0.801346 | ||||||||
\(236\) | 9.08189i | 0.0384826i | ||||||||
\(237\) | 53.1300 | − | 92.0238i | 0.224177 | − | 0.388286i | ||||
\(238\) | 99.6394 | + | 57.5268i | 0.418653 | + | 0.241709i | ||||
\(239\) | 301.091 | 1.25979 | 0.629897 | − | 0.776679i | \(-0.283097\pi\) | ||||
0.629897 | + | 0.776679i | \(0.283097\pi\) | |||||||
\(240\) | 188.691i | 0.786211i | ||||||||
\(241\) | 110.242 | + | 63.6485i | 0.457438 | + | 0.264102i | 0.710966 | − | 0.703226i | \(-0.248258\pi\) |
−0.253529 | + | 0.967328i | \(0.581591\pi\) | |||||||
\(242\) | −505.518 | + | 291.861i | −2.08892 | + | 1.20604i | ||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −7.19592 | − | 12.4637i | −0.0294915 | − | 0.0510807i | ||||
\(245\) | 140.744 | + | 243.776i | 0.574465 | + | 0.995003i | ||||
\(246\) | − | 124.263i | − | 0.505133i | ||||||
\(247\) | 2.43882 | + | 1.69877i | 0.00987376 | + | 0.00687759i | ||||
\(248\) | −132.025 | −0.532358 | ||||||||
\(249\) | 223.189 | − | 128.858i | 0.896342 | − | 0.517503i | ||||
\(250\) | 101.487 | − | 58.5937i | 0.405949 | − | 0.234375i | ||||
\(251\) | 177.023 | − | 306.613i | 0.705271 | − | 1.22157i | −0.261322 | − | 0.965252i | \(-0.584159\pi\) |
0.966594 | − | 0.256314i | \(-0.0825081\pi\) | |||||||
\(252\) | 0.892042 | + | 1.54506i | 0.00353985 | + | 0.00613120i | ||||
\(253\) | 52.6933 | − | 91.2675i | 0.208274 | − | 0.360741i | ||||
\(254\) | 61.1625 | 0.240797 | ||||||||
\(255\) | 273.628i | 1.07305i | ||||||||
\(256\) | −25.1234 | + | 43.5151i | −0.0981384 | + | 0.169981i | ||||
\(257\) | −236.669 | − | 136.641i | −0.920889 | − | 0.531676i | −0.0369706 | − | 0.999316i | \(-0.511771\pi\) |
−0.883919 | + | 0.467641i | \(0.845104\pi\) | |||||||
\(258\) | 89.7979 | 0.348054 | ||||||||
\(259\) | 96.6500i | 0.373166i | ||||||||
\(260\) | 0.228396 | + | 0.131865i | 0.000878447 | + | 0.000507171i | ||||
\(261\) | −94.3720 | + | 54.4857i | −0.361579 | + | 0.208757i | ||||
\(262\) | 102.464 | + | 59.1579i | 0.391086 | + | 0.225793i | ||||
\(263\) | −75.5642 | − | 130.881i | −0.287316 | − | 0.497646i | 0.685852 | − | 0.727741i | \(-0.259430\pi\) |
−0.973168 | + | 0.230095i | \(0.926096\pi\) | |||||||
\(264\) | −134.265 | − | 232.555i | −0.508581 | − | 0.880889i | ||||
\(265\) | − | 358.649i | − | 1.35339i | ||||||
\(266\) | −80.3576 | + | 37.7120i | −0.302096 | + | 0.141774i | ||||
\(267\) | 125.566 | 0.470284 | ||||||||
\(268\) | 17.3639 | − | 10.0251i | 0.0647909 | − | 0.0374070i | ||||
\(269\) | 58.9364 | − | 34.0269i | 0.219094 | − | 0.126494i | −0.386437 | − | 0.922316i | \(-0.626294\pi\) |
0.605531 | + | 0.795822i | \(0.292961\pi\) | |||||||
\(270\) | −34.4109 | + | 59.6015i | −0.127448 | + | 0.220746i | ||||
\(271\) | 56.8991 | + | 98.5521i | 0.209960 | + | 0.363661i | 0.951702 | − | 0.307025i | \(-0.0993334\pi\) |
−0.741742 | + | 0.670685i | \(0.766000\pi\) | |||||||
\(272\) | −209.106 | + | 362.183i | −0.768773 | + | 1.33155i | ||||
\(273\) | −0.613092 | −0.00224576 | ||||||||
\(274\) | 195.935i | 0.715093i | ||||||||
\(275\) | 162.271 | − | 281.062i | 0.590078 | − | 1.02204i | ||||
\(276\) | −2.06767 | − | 1.19377i | −0.00749156 | − | 0.00432526i | ||||
\(277\) | 440.910 | 1.59173 | 0.795867 | − | 0.605472i | \(-0.207016\pi\) | ||||
0.795867 | + | 0.605472i | \(0.207016\pi\) | |||||||
\(278\) | − | 376.902i | − | 1.35576i | ||||||
\(279\) | −44.4544 | − | 25.6657i | −0.159335 | − | 0.0919919i | ||||
\(280\) | 96.9993 | − | 56.0026i | 0.346426 | − | 0.200009i | ||||
\(281\) | 78.0928 | + | 45.0869i | 0.277910 | + | 0.160452i | 0.632477 | − | 0.774579i | \(-0.282038\pi\) |
−0.354567 | + | 0.935031i | \(0.615372\pi\) | |||||||
\(282\) | 52.4892 | + | 90.9140i | 0.186132 | + | 0.322390i | ||||
\(283\) | 34.5331 | + | 59.8131i | 0.122025 | + | 0.211354i | 0.920566 | − | 0.390587i | \(-0.127728\pi\) |
−0.798541 | + | 0.601940i | \(0.794394\pi\) | |||||||
\(284\) | − | 19.3031i | − | 0.0679685i | ||||||
\(285\) | −173.229 | − | 120.663i | −0.607821 | − | 0.423379i | ||||
\(286\) | −6.48941 | −0.0226902 | ||||||||
\(287\) | −68.0944 | + | 39.3143i | −0.237263 | + | 0.136984i | ||||
\(288\) | −10.9076 | + | 6.29750i | −0.0378736 | + | 0.0218663i | ||||
\(289\) | −158.734 | + | 274.935i | −0.549252 | + | 0.951332i | ||||
\(290\) | −240.550 | − | 416.645i | −0.829484 | − | 1.43671i | ||||
\(291\) | 70.0326 | − | 121.300i | 0.240662 | − | 0.416839i | ||||
\(292\) | −24.1289 | −0.0826334 | ||||||||
\(293\) | 410.238i | 1.40013i | 0.714079 | + | 0.700065i | \(0.246846\pi\) | ||||
−0.714079 | + | 0.700065i | \(0.753154\pi\) | |||||||
\(294\) | −78.4589 | + | 135.895i | −0.266867 | + | 0.462227i | ||||
\(295\) | 191.981 | + | 110.840i | 0.650782 | + | 0.375729i | ||||
\(296\) | −329.569 | −1.11341 | ||||||||
\(297\) | − | 104.405i | − | 0.351533i | ||||||
\(298\) | 19.6842 | + | 11.3647i | 0.0660544 | + | 0.0381365i | ||||
\(299\) | 0.710545 | − | 0.410233i | 0.00237640 | − | 0.00137202i | ||||
\(300\) | −6.36749 | − | 3.67627i | −0.0212250 | − | 0.0122542i | ||||
\(301\) | −28.4103 | − | 49.2081i | −0.0943864 | − | 0.163482i | ||||
\(302\) | −246.568 | − | 427.068i | −0.816451 | − | 1.41413i | ||||
\(303\) | − | 265.617i | − | 0.876624i | ||||||
\(304\) | −137.081 | − | 292.095i | −0.450923 | − | 0.960838i | ||||
\(305\) | −351.291 | −1.15177 | ||||||||
\(306\) | −132.100 | + | 76.2681i | −0.431700 | + | 0.249242i | ||||
\(307\) | −201.882 | + | 116.556i | −0.657595 | + | 0.379663i | −0.791360 | − | 0.611350i | \(-0.790627\pi\) |
0.133765 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(308\) | 5.97454 | − | 10.3482i | 0.0193979 | − | 0.0335981i | ||||
\(309\) | 146.313 | + | 253.422i | 0.473506 | + | 0.820136i | ||||
\(310\) | 113.312 | − | 196.263i | 0.365524 | − | 0.633106i | ||||
\(311\) | −441.280 | −1.41891 | −0.709454 | − | 0.704752i | \(-0.751058\pi\) | ||||
−0.709454 | + | 0.704752i | \(0.751058\pi\) | |||||||
\(312\) | − | 2.09059i | − | 0.00670062i | ||||||
\(313\) | −60.6339 | + | 105.021i | −0.193719 | + | 0.335530i | −0.946480 | − | 0.322763i | \(-0.895388\pi\) |
0.752761 | + | 0.658294i | \(0.228722\pi\) | |||||||
\(314\) | −81.5796 | − | 47.1000i | −0.259808 | − | 0.150000i | ||||
\(315\) | 43.5478 | 0.138247 | ||||||||
\(316\) | 16.1233i | 0.0510232i | ||||||||
\(317\) | 286.409 | + | 165.358i | 0.903499 | + | 0.521635i | 0.878334 | − | 0.478048i | \(-0.158656\pi\) |
0.0251649 | + | 0.999683i | \(0.491989\pi\) | |||||||
\(318\) | 173.146 | − | 99.9658i | 0.544484 | − | 0.314358i | ||||
\(319\) | 632.066 | + | 364.924i | 1.98140 | + | 1.14396i | ||||
\(320\) | 190.078 | + | 329.225i | 0.593995 | + | 1.02883i | ||||
\(321\) | 120.430 | + | 208.591i | 0.375171 | + | 0.649815i | ||||
\(322\) | 24.5042i | 0.0761001i | ||||||||
\(323\) | −198.786 | − | 423.579i | −0.615437 | − | 1.31139i | ||||
\(324\) | −2.36531 | −0.00730034 | ||||||||
\(325\) | 2.18816 | − | 1.26333i | 0.00673279 | − | 0.00388718i | ||||
\(326\) | −10.5344 | + | 6.08206i | −0.0323142 | + | 0.0186566i | ||||
\(327\) | 9.15888 | − | 15.8636i | 0.0280088 | − | 0.0485127i | ||||
\(328\) | −134.059 | − | 232.197i | −0.408716 | − | 0.707916i | ||||
\(329\) | 33.2131 | − | 57.5268i | 0.100952 | − | 0.174854i | ||||
\(330\) | 460.941 | 1.39679 | ||||||||
\(331\) | − | 436.308i | − | 1.31815i | −0.752077 | − | 0.659075i | \(-0.770948\pi\) | ||
0.752077 | − | 0.659075i | \(-0.229052\pi\) | |||||||
\(332\) | −19.5523 | + | 33.8655i | −0.0588924 | + | 0.102005i | ||||
\(333\) | −110.970 | − | 64.0685i | −0.333243 | − | 0.192398i | ||||
\(334\) | −338.870 | −1.01458 | ||||||||
\(335\) | − | 489.406i | − | 1.46091i | ||||||
\(336\) | 57.6412 | + | 33.2792i | 0.171551 | + | 0.0990452i | ||||
\(337\) | −217.027 | + | 125.301i | −0.643997 | + | 0.371812i | −0.786153 | − | 0.618033i | \(-0.787930\pi\) |
0.142156 | + | 0.989844i | \(0.454597\pi\) | |||||||
\(338\) | 302.136 | + | 174.438i | 0.893894 | + | 0.516090i | ||||
\(339\) | −59.8927 | − | 103.737i | −0.176675 | − | 0.306009i | ||||
\(340\) | −20.7594 | − | 35.9564i | −0.0610572 | − | 0.105754i | ||||
\(341\) | 343.798i | 1.00821i | ||||||||
\(342\) | 9.96891 | − | 117.263i | 0.0291489 | − | 0.342873i | ||||
\(343\) | 210.169 | 0.612738 | ||||||||
\(344\) | 167.796 | − | 96.8770i | 0.487779 | − | 0.281619i | ||||
\(345\) | −50.4699 | + | 29.1388i | −0.146290 | + | 0.0844603i | ||||
\(346\) | −279.358 | + | 483.862i | −0.807393 | + | 1.39845i | ||||
\(347\) | −83.6670 | − | 144.915i | −0.241115 | − | 0.417624i | 0.719917 | − | 0.694060i | \(-0.244180\pi\) |
−0.961032 | + | 0.276436i | \(0.910846\pi\) | |||||||
\(348\) | 8.26737 | − | 14.3195i | 0.0237568 | − | 0.0411480i | ||||
\(349\) | −486.776 | −1.39477 | −0.697387 | − | 0.716695i | \(-0.745654\pi\) | ||||
−0.697387 | + | 0.716695i | \(0.745654\pi\) | |||||||
\(350\) | 75.4619i | 0.215605i | ||||||||
\(351\) | 0.406413 | − | 0.703929i | 0.00115787 | − | 0.00200550i | ||||
\(352\) | 73.0547 | + | 42.1781i | 0.207542 | + | 0.119824i | ||||
\(353\) | 30.1507 | 0.0854128 | 0.0427064 | − | 0.999088i | \(-0.486402\pi\) | ||||
0.0427064 | + | 0.999088i | \(0.486402\pi\) | |||||||
\(354\) | 123.577i | 0.349089i | ||||||||
\(355\) | −408.045 | − | 235.585i | −1.14942 | − | 0.663619i | ||||
\(356\) | −16.5001 | + | 9.52635i | −0.0463486 | + | 0.0267594i | ||||
\(357\) | 83.5879 | + | 48.2595i | 0.234140 | + | 0.135181i | ||||
\(358\) | 192.466 | + | 333.361i | 0.537615 | + | 0.931177i | ||||
\(359\) | −75.0088 | − | 129.919i | −0.208938 | − | 0.361891i | 0.742442 | − | 0.669910i | \(-0.233667\pi\) |
−0.951380 | + | 0.308019i | \(0.900334\pi\) | |||||||
\(360\) | 148.495i | 0.412485i | ||||||||
\(361\) | 355.819 | + | 60.9394i | 0.985649 | + | 0.168807i | ||||
\(362\) | 95.8247 | 0.264709 | ||||||||
\(363\) | −424.081 | + | 244.843i | −1.16827 | + | 0.674500i | ||||
\(364\) | 0.0805640 | − | 0.0465136i | 0.000221330 | − | 0.000127785i | ||||
\(365\) | −294.482 | + | 510.058i | −0.806801 | + | 1.39742i | ||||
\(366\) | −97.9151 | − | 169.594i | −0.267527 | − | 0.463371i | ||||
\(367\) | 248.090 | − | 429.704i | 0.675994 | − | 1.17086i | −0.300183 | − | 0.953882i | \(-0.597048\pi\) |
0.976177 | − | 0.216975i | \(-0.0696189\pi\) | |||||||
\(368\) | −89.0714 | −0.242042 | ||||||||
\(369\) | − | 104.245i | − | 0.282506i | ||||||
\(370\) | 282.858 | − | 489.924i | 0.764480 | − | 1.32412i | ||||
\(371\) | −109.560 | − | 63.2545i | −0.295310 | − | 0.170497i | ||||
\(372\) | 7.78877 | 0.0209375 | ||||||||
\(373\) | 449.613i | 1.20540i | 0.797969 | + | 0.602698i | \(0.205908\pi\) | ||||
−0.797969 | + | 0.602698i | \(0.794092\pi\) | |||||||
\(374\) | 884.755 | + | 510.814i | 2.36566 | + | 1.36581i | ||||
\(375\) | 85.1381 | − | 49.1545i | 0.227035 | − | 0.131079i | ||||
\(376\) | 196.162 | + | 113.254i | 0.521707 | + | 0.301208i | ||||
\(377\) | 2.84104 | + | 4.92083i | 0.00753592 | + | 0.0130526i | ||||
\(378\) | 12.1380 | + | 21.0237i | 0.0321112 | + | 0.0556182i | ||||
\(379\) | − | 471.336i | − | 1.24363i | −0.783163 | − | 0.621816i | \(-0.786395\pi\) | ||
0.783163 | − | 0.621816i | \(-0.213605\pi\) | |||||||
\(380\) | 31.9177 | + | 2.71344i | 0.0839940 | + | 0.00714064i | ||||
\(381\) | 51.3095 | 0.134670 | ||||||||
\(382\) | 65.6611 | − | 37.9094i | 0.171888 | − | 0.0992393i | ||||
\(383\) | −23.4258 | + | 13.5249i | −0.0611641 | + | 0.0353131i | −0.530270 | − | 0.847829i | \(-0.677910\pi\) |
0.469106 | + | 0.883142i | \(0.344576\pi\) | |||||||
\(384\) | −120.504 | + | 208.719i | −0.313813 | + | 0.543540i | ||||
\(385\) | −145.833 | − | 252.590i | −0.378787 | − | 0.656078i | ||||
\(386\) | 206.784 | − | 358.160i | 0.535709 | − | 0.927875i | ||||
\(387\) | 75.3319 | 0.194656 | ||||||||
\(388\) | 21.2528i | 0.0547752i | ||||||||
\(389\) | 177.144 | − | 306.822i | 0.455382 | − | 0.788745i | −0.543328 | − | 0.839520i | \(-0.682836\pi\) |
0.998710 | + | 0.0507758i | \(0.0161694\pi\) | |||||||
\(390\) | 3.10779 | + | 1.79428i | 0.00796870 | + | 0.00460073i | ||||
\(391\) | −129.166 | −0.330348 | ||||||||
\(392\) | 338.576i | 0.863715i | ||||||||
\(393\) | 85.9579 | + | 49.6278i | 0.218722 | + | 0.126279i | ||||
\(394\) | 306.672 | − | 177.057i | 0.778354 | − | 0.449383i | ||||
\(395\) | 340.829 | + | 196.777i | 0.862857 | + | 0.498171i | ||||
\(396\) | 7.92095 | + | 13.7195i | 0.0200024 | + | 0.0346452i | ||||
\(397\) | −79.5105 | − | 137.716i | −0.200278 | − | 0.346892i | 0.748340 | − | 0.663316i | \(-0.230851\pi\) |
−0.948618 | + | 0.316423i | \(0.897518\pi\) | |||||||
\(398\) | − | 180.657i | − | 0.453913i | ||||||
\(399\) | −67.4123 | + | 31.6367i | −0.168953 | + | 0.0792901i | ||||
\(400\) | −274.299 | −0.685748 | ||||||||
\(401\) | −277.534 | + | 160.234i | −0.692105 | + | 0.399587i | −0.804400 | − | 0.594088i | \(-0.797513\pi\) |
0.112295 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(402\) | 236.272 | − | 136.412i | 0.587741 | − | 0.339332i | ||||
\(403\) | −1.33829 | + | 2.31798i | −0.00332081 | + | 0.00575181i | ||||
\(404\) | 20.1517 | + | 34.9037i | 0.0498803 | + | 0.0863953i | ||||
\(405\) | −28.8675 | + | 50.0000i | −0.0712777 | + | 0.123457i | ||||
\(406\) | −169.702 | −0.417986 | ||||||||
\(407\) | 858.211i | 2.10863i | ||||||||
\(408\) | −164.561 | + | 285.028i | −0.403336 | + | 0.698599i | ||||
\(409\) | −251.776 | − | 145.363i | −0.615590 | − | 0.355411i | 0.159560 | − | 0.987188i | \(-0.448992\pi\) |
−0.775150 | + | 0.631777i | \(0.782326\pi\) | |||||||
\(410\) | 460.232 | 1.12252 | ||||||||
\(411\) | 164.371i | 0.399930i | ||||||||
\(412\) | −38.4529 | − | 22.2008i | −0.0933323 | − | 0.0538854i | ||||
\(413\) | 67.7189 | − | 39.0975i | 0.163968 | − | 0.0946671i | ||||
\(414\) | −28.1349 | − | 16.2437i | −0.0679586 | − | 0.0392359i | ||||
\(415\) | 477.253 | + | 826.626i | 1.15001 | + | 1.99187i | ||||
\(416\) | 0.328370 | + | 0.568753i | 0.000789350 | + | 0.00136719i | ||||
\(417\) | − | 316.185i | − | 0.758237i | ||||||
\(418\) | −713.541 | + | 334.866i | −1.70704 | + | 0.801115i | ||||
\(419\) | −141.846 | −0.338535 | −0.169267 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169267 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(420\) | −5.72245 | + | 3.30386i | −0.0136249 | + | 0.00786632i | ||||
\(421\) | 98.6666 | − | 56.9652i | 0.234362 | − | 0.135309i | −0.378220 | − | 0.925716i | \(-0.623464\pi\) |
0.612583 | + | 0.790406i | \(0.290131\pi\) | |||||||
\(422\) | −19.5433 | + | 33.8501i | −0.0463112 | + | 0.0802134i | ||||
\(423\) | 44.0334 | + | 76.2681i | 0.104098 | + | 0.180303i | ||||
\(424\) | 215.693 | − | 373.591i | 0.508710 | − | 0.881111i | ||||
\(425\) | −397.773 | −0.935936 | ||||||||
\(426\) | − | 262.657i | − | 0.616567i | ||||||
\(427\) | −61.9568 | + | 107.312i | −0.145098 | + | 0.251317i | ||||
\(428\) | −31.6504 | − | 18.2734i | −0.0739496 | − | 0.0426948i | ||||
\(429\) | −5.44399 | −0.0126900 | ||||||||
\(430\) | 332.585i | 0.773453i | ||||||||
\(431\) | 229.263 | + | 132.365i | 0.531932 | + | 0.307111i | 0.741803 | − | 0.670618i | \(-0.233971\pi\) |
−0.209871 | + | 0.977729i | \(0.567304\pi\) | |||||||
\(432\) | −76.4198 | + | 44.1210i | −0.176898 | + | 0.102132i | ||||
\(433\) | −631.333 | − | 364.500i | −1.45804 | − | 0.841802i | −0.459129 | − | 0.888369i | \(-0.651839\pi\) |
−0.998915 | + | 0.0465669i | \(0.985172\pi\) | |||||||
\(434\) | −39.9695 | − | 69.2293i | −0.0920957 | − | 0.159514i | ||||
\(435\) | −201.799 | − | 349.526i | −0.463905 | − | 0.803507i | ||||
\(436\) | 2.77944i | 0.00637486i | ||||||||
\(437\) | 56.9589 | − | 81.7726i | 0.130341 | − | 0.187123i | ||||
\(438\) | −328.323 | −0.749596 | ||||||||
\(439\) | 319.591 | − | 184.516i | 0.727998 | − | 0.420310i | −0.0896911 | − | 0.995970i | \(-0.528588\pi\) |
0.817689 | + | 0.575660i | \(0.195255\pi\) | |||||||
\(440\) | 861.312 | − | 497.279i | 1.95753 | − | 1.13018i | ||||
\(441\) | −65.8195 | + | 114.003i | −0.149251 | + | 0.258510i | ||||
\(442\) | 3.97684 | + | 6.88809i | 0.00899738 | + | 0.0155839i | ||||
\(443\) | −291.547 | + | 504.975i | −0.658120 | + | 1.13990i | 0.322982 | + | 0.946405i | \(0.395315\pi\) |
−0.981102 | + | 0.193492i | \(0.938019\pi\) | |||||||
\(444\) | 19.4428 | 0.0437902 | ||||||||
\(445\) | 465.058i | 1.04507i | ||||||||
\(446\) | 267.208 | − | 462.818i | 0.599121 | − | 1.03771i | ||||
\(447\) | 16.5132 | + | 9.53389i | 0.0369422 | + | 0.0213286i | ||||
\(448\) | 134.096 | 0.299321 | ||||||||
\(449\) | − | 314.423i | − | 0.700273i | −0.936699 | − | 0.350137i | \(-0.886135\pi\) | ||
0.936699 | − | 0.350137i | \(-0.113865\pi\) | |||||||
\(450\) | −86.6426 | − | 50.0231i | −0.192539 | − | 0.111162i | ||||
\(451\) | −604.649 | + | 349.094i | −1.34068 | + | 0.774045i | ||||
\(452\) | 15.7405 | + | 9.08779i | 0.0348242 | + | 0.0201057i | ||||
\(453\) | −206.847 | − | 358.270i | −0.456616 | − | 0.790882i | ||||
\(454\) | 133.227 | + | 230.755i | 0.293451 | + | 0.508272i | ||||
\(455\) | − | 2.27071i | − | 0.00499057i | ||||||
\(456\) | −107.879 | − | 229.871i | −0.236576 | − | 0.504103i | ||||
\(457\) | 505.253 | 1.10559 | 0.552793 | − | 0.833319i | \(-0.313562\pi\) | ||||
0.552793 | + | 0.833319i | \(0.313562\pi\) | |||||||
\(458\) | 176.828 | − | 102.092i | 0.386088 | − | 0.222908i | ||||
\(459\) | −110.820 | + | 63.9817i | −0.241437 | + | 0.139394i | ||||
\(460\) | 4.42137 | − | 7.65803i | 0.00961167 | − | 0.0166479i | ||||
\(461\) | 136.902 | + | 237.122i | 0.296968 | + | 0.514364i | 0.975441 | − | 0.220262i | \(-0.0706912\pi\) |
−0.678473 | + | 0.734626i | \(0.737358\pi\) | |||||||
\(462\) | 81.2957 | − | 140.808i | 0.175965 | − | 0.304780i | ||||
\(463\) | 319.780 | 0.690669 | 0.345334 | − | 0.938480i | \(-0.387765\pi\) | ||||
0.345334 | + | 0.938480i | \(0.387765\pi\) | |||||||
\(464\) | − | 616.857i | − | 1.32943i | ||||||
\(465\) | 95.0582 | − | 164.646i | 0.204426 | − | 0.354077i | ||||
\(466\) | −624.855 | − | 360.760i | −1.34089 | − | 0.774164i | ||||
\(467\) | −295.510 | −0.632785 | −0.316392 | − | 0.948628i | \(-0.602472\pi\) | ||||
−0.316392 | + | 0.948628i | \(0.602472\pi\) | |||||||
\(468\) | 0.123334i | 0.000263534i | ||||||||
\(469\) | −149.504 | − | 86.3159i | −0.318771 | − | 0.184042i | ||||
\(470\) | −336.718 | + | 194.404i | −0.716421 | + | 0.413626i | ||||
\(471\) | −68.4375 | − | 39.5124i | −0.145303 | − | 0.0838905i | ||||
\(472\) | 133.319 | + | 230.916i | 0.282457 | + | 0.489229i | ||||
\(473\) | −252.271 | − | 436.947i | −0.533344 | − | 0.923778i | ||||
\(474\) | 219.390i | 0.462849i | ||||||||
\(475\) | 175.408 | − | 251.822i | 0.369279 | − | 0.530153i | ||||
\(476\) | −14.6453 | −0.0307674 | ||||||||
\(477\) | 145.253 | − | 83.8618i | 0.304513 | − | 0.175811i | ||||
\(478\) | −538.364 | + | 310.825i | −1.12629 | + | 0.650261i | ||||
\(479\) | 204.559 | − | 354.306i | 0.427054 | − | 0.739679i | −0.569556 | − | 0.821953i | \(-0.692885\pi\) |
0.996610 | + | 0.0822735i | \(0.0262181\pi\) | |||||||
\(480\) | −23.3240 | − | 40.3984i | −0.0485917 | − | 0.0841634i | ||||
\(481\) | −3.34072 | + | 5.78629i | −0.00694536 | + | 0.0120297i | ||||
\(482\) | −262.825 | −0.545280 | ||||||||
\(483\) | 20.5567i | 0.0425605i | ||||||||
\(484\) | 37.1512 | − | 64.3478i | 0.0767588 | − | 0.132950i | ||||
\(485\) | 449.259 | + | 259.380i | 0.926308 | + | 0.534804i | ||||
\(486\) | −32.1848 | −0.0662239 | ||||||||
\(487\) | − | 638.208i | − | 1.31049i | −0.755417 | − | 0.655244i | \(-0.772566\pi\) | ||
0.755417 | − | 0.655244i | \(-0.227434\pi\) | |||||||
\(488\) | −365.927 | − | 211.268i | −0.749850 | − | 0.432926i | ||||
\(489\) | −8.83738 | + | 5.10227i | −0.0180724 | + | 0.0104341i | ||||
\(490\) | −503.314 | − | 290.588i | −1.02717 | − | 0.593037i | ||||
\(491\) | −173.278 | − | 300.126i | −0.352908 | − | 0.611255i | 0.633850 | − | 0.773456i | \(-0.281474\pi\) |
−0.986758 | + | 0.162202i | \(0.948141\pi\) | |||||||
\(492\) | 7.90876 | + | 13.6984i | 0.0160747 | + | 0.0278422i | ||||
\(493\) | − | 894.530i | − | 1.81446i | ||||||
\(494\) | −6.11440 | − | 0.519808i | −0.0123773 | − | 0.00105224i | ||||
\(495\) | 386.686 | 0.781184 | ||||||||
\(496\) | 251.644 | − | 145.287i | 0.507347 | − | 0.292917i | ||||
\(497\) | −143.933 | + | 83.0997i | −0.289603 | + | 0.167203i | ||||
\(498\) | −266.048 | + | 460.809i | −0.534234 | + | 0.925320i | ||||
\(499\) | −40.3510 | − | 69.8900i | −0.0808638 | − | 0.140060i | 0.822757 | − | 0.568393i | \(-0.192435\pi\) |
−0.903621 | + | 0.428333i | \(0.859101\pi\) | |||||||
\(500\) | −7.45844 | + | 12.9184i | −0.0149169 | + | 0.0258368i | ||||
\(501\) | −284.280 | −0.567425 | ||||||||
\(502\) | 730.984i | 1.45614i | ||||||||
\(503\) | −247.050 | + | 427.903i | −0.491153 | + | 0.850701i | −0.999948 | − | 0.0101862i | \(-0.996758\pi\) |
0.508796 | + | 0.860887i | \(0.330091\pi\) | |||||||
\(504\) | 45.3621 | + | 26.1898i | 0.0900042 | + | 0.0519640i | ||||
\(505\) | 983.766 | 1.94805 | ||||||||
\(506\) | 217.587i | 0.430014i | ||||||||
\(507\) | 253.463 | + | 146.337i | 0.499928 | + | 0.288633i | ||||
\(508\) | −6.74237 | + | 3.89271i | −0.0132724 | + | 0.00766282i | ||||
\(509\) | 63.9084 | + | 36.8975i | 0.125557 | + | 0.0724902i | 0.561463 | − | 0.827502i | \(-0.310239\pi\) |
−0.435906 | + | 0.899992i | \(0.643572\pi\) | |||||||
\(510\) | −282.474 | − | 489.260i | −0.553871 | − | 0.959333i | ||||
\(511\) | 103.875 | + | 179.917i | 0.203278 | + | 0.352088i | ||||
\(512\) | 452.842i | 0.884457i | ||||||||
\(513\) | 8.36297 | − | 98.3721i | 0.0163021 | − | 0.191758i | ||||
\(514\) | 564.232 | 1.09773 | ||||||||
\(515\) | −938.599 | + | 541.900i | −1.82252 | + | 1.05223i | ||||
\(516\) | −9.89907 | + | 5.71523i | −0.0191842 | + | 0.0110760i | ||||
\(517\) | 294.918 | − | 510.814i | 0.570442 | − | 0.988034i | ||||
\(518\) | −99.7746 | − | 172.815i | −0.192615 | − | 0.333619i | ||||
\(519\) | −234.355 | + | 405.914i | −0.451551 | + | 0.782109i | ||||
\(520\) | 7.74294 | 0.0148903 | ||||||||
\(521\) | − | 357.582i | − | 0.686337i | −0.939274 | − | 0.343169i | \(-0.888500\pi\) | ||
0.939274 | − | 0.343169i | \(-0.111500\pi\) | |||||||
\(522\) | 112.494 | − | 194.846i | 0.215506 | − | 0.373268i | ||||
\(523\) | 382.935 | + | 221.088i | 0.732190 | + | 0.422730i | 0.819223 | − | 0.573475i | \(-0.194405\pi\) |
−0.0870328 | + | 0.996205i | \(0.527739\pi\) | |||||||
\(524\) | −15.0605 | −0.0287415 | ||||||||
\(525\) | 63.3053i | 0.120582i | ||||||||
\(526\) | 270.225 | + | 156.014i | 0.513735 | + | 0.296605i | ||||
\(527\) | 364.919 | − | 210.686i | 0.692447 | − | 0.399784i | ||||
\(528\) | 511.829 | + | 295.505i | 0.969374 | + | 0.559668i | ||||
\(529\) | 250.745 | + | 434.303i | 0.473998 | + | 0.820989i | ||||
\(530\) | 370.243 | + | 641.281i | 0.698573 | + | 1.20996i | ||||
\(531\) | 103.670i | 0.195235i | ||||||||
\(532\) | 6.45819 | − | 9.27165i | 0.0121395 | − | 0.0174279i | ||||
\(533\) | −5.43561 | −0.0101981 | ||||||||
\(534\) | −224.518 | + | 129.625i | −0.420445 | + | 0.242744i | ||||
\(535\) | −772.557 | + | 446.036i | −1.44403 | + | 0.833712i | ||||
\(536\) | 294.331 | − | 509.796i | 0.549124 | − | 0.951111i | ||||
\(537\) | 161.461 | + | 279.658i | 0.300672 | + | 0.520779i | ||||
\(538\) | −70.2539 | + | 121.683i | −0.130584 | + | 0.226177i | ||||
\(539\) | 881.666 | 1.63574 | ||||||||
\(540\) | − | 8.76040i | − | 0.0162230i | ||||||
\(541\) | −487.737 | + | 844.785i | −0.901547 | + | 1.56152i | −0.0760596 | + | 0.997103i | \(0.524234\pi\) |
−0.825487 | + | 0.564421i | \(0.809099\pi\) | |||||||
\(542\) | −203.476 | − | 117.477i | −0.375418 | − | 0.216747i | ||||
\(543\) | 80.3877 | 0.148044 | ||||||||
\(544\) | − | 103.390i | − | 0.190056i | ||||||
\(545\) | 58.7542 | + | 33.9217i | 0.107806 | + | 0.0622417i | ||||
\(546\) | 1.09624 | − | 0.632912i | 0.00200776 | − | 0.00115918i | ||||
\(547\) | 350.050 | + | 202.102i | 0.639945 | + | 0.369473i | 0.784594 | − | 0.620010i | \(-0.212872\pi\) |
−0.144648 | + | 0.989483i | \(0.546205\pi\) | |||||||
\(548\) | −12.4704 | − | 21.5994i | −0.0227562 | − | 0.0394149i | ||||
\(549\) | −82.1414 | − | 142.273i | −0.149620 | − | 0.259149i | ||||
\(550\) | 670.070i | 1.21831i | ||||||||
\(551\) | 566.310 | + | 394.465i | 1.02779 | + | 0.715907i | ||||
\(552\) | −70.0968 | −0.126987 | ||||||||
\(553\) | 120.223 | − | 69.4109i | 0.217402 | − | 0.125517i | ||||
\(554\) | −788.368 | + | 455.164i | −1.42305 | + | 0.821596i | ||||
\(555\) | 237.291 | − | 410.999i | 0.427551 | − | 0.740539i | ||||
\(556\) | 23.9881 | + | 41.5486i | 0.0431441 | + | 0.0747277i | ||||
\(557\) | −29.9352 | + | 51.8492i | −0.0537435 | + | 0.0930866i | −0.891646 | − | 0.452734i | \(-0.850449\pi\) |
0.837902 | + | 0.545821i | \(0.183782\pi\) | |||||||
\(558\) | 105.982 | 0.189932 | ||||||||
\(559\) | − | 3.92802i | − | 0.00702687i | ||||||
\(560\) | −123.256 | + | 213.486i | −0.220100 | + | 0.381225i | ||||
\(561\) | 742.225 | + | 428.524i | 1.32304 | + | 0.763857i | ||||
\(562\) | −186.178 | −0.331278 | ||||||||
\(563\) | 247.579i | 0.439749i | 0.975528 | + | 0.219874i | \(0.0705648\pi\) | ||||
−0.975528 | + | 0.219874i | \(0.929435\pi\) | |||||||
\(564\) | −11.5725 | − | 6.68140i | −0.0205187 | − | 0.0118464i | ||||
\(565\) | 384.211 | − | 221.824i | 0.680020 | − | 0.392610i | ||||
\(566\) | −123.494 | − | 71.2990i | −0.218186 | − | 0.125970i | ||||
\(567\) | 10.1827 | + | 17.6369i | 0.0179588 | + | 0.0311056i | ||||
\(568\) | −283.363 | − | 490.800i | −0.498879 | − | 0.864084i | ||||
\(569\) | − | 76.4991i | − | 0.134445i | −0.997738 | − | 0.0672224i | \(-0.978586\pi\) | ||
0.997738 | − | 0.0672224i | \(-0.0214137\pi\) | |||||||
\(570\) | 434.305 | + | 36.9219i | 0.761939 | + | 0.0647752i | ||||
\(571\) | −624.523 | −1.09373 | −0.546867 | − | 0.837219i | \(-0.684180\pi\) | ||||
−0.546867 | + | 0.837219i | \(0.684180\pi\) | |||||||
\(572\) | 0.715374 | − | 0.413021i | 0.00125065 | − | 0.000722065i | ||||
\(573\) | 55.0834 | − | 31.8024i | 0.0961315 | − | 0.0555016i | ||||
\(574\) | 81.1706 | − | 140.592i | 0.141412 | − | 0.244933i | ||||
\(575\) | −42.3590 | − | 73.3680i | −0.0736679 | − | 0.127597i | ||||
\(576\) | −88.8909 | + | 153.964i | −0.154324 | + | 0.267298i | ||||
\(577\) | 185.550 | 0.321577 | 0.160789 | − | 0.986989i | \(-0.448596\pi\) | ||||
0.160789 | + | 0.986989i | \(0.448596\pi\) | |||||||
\(578\) | − | 655.462i | − | 1.13402i | ||||||
\(579\) | 173.472 | − | 300.462i | 0.299606 | − | 0.518932i | ||||
\(580\) | 53.0352 | + | 30.6199i | 0.0914399 | + | 0.0527929i | ||||
\(581\) | 336.690 | 0.579501 | ||||||||
\(582\) | 289.187i | 0.496885i | ||||||||
\(583\) | −972.846 | − | 561.673i | −1.66869 | − | 0.963418i | ||||
\(584\) | −613.503 | + | 354.206i | −1.05052 | + | 0.606517i | ||||
\(585\) | 2.60714 | + | 1.50523i | 0.00445665 | + | 0.00257305i | ||||
\(586\) | −423.501 | − | 733.525i | −0.722698 | − | 1.25175i | ||||
\(587\) | −130.891 | − | 226.710i | −0.222983 | − | 0.386218i | 0.732729 | − | 0.680520i | \(-0.238246\pi\) |
−0.955712 | + | 0.294302i | \(0.904913\pi\) | |||||||
\(588\) | − | 19.9742i | − | 0.0339697i | ||||||
\(589\) | −27.5386 | + | 323.931i | −0.0467548 | + | 0.549968i | ||||
\(590\) | −457.694 | −0.775752 | ||||||||
\(591\) | 257.268 | − | 148.534i | 0.435310 | − | 0.251326i | ||||
\(592\) | 628.170 | − | 362.674i | 1.06110 | − | 0.612626i | ||||
\(593\) | −124.254 | + | 215.215i | −0.209535 | + | 0.362925i | −0.951568 | − | 0.307438i | \(-0.900528\pi\) |
0.742033 | + | 0.670363i | \(0.233862\pi\) | |||||||
\(594\) | 107.781 | + | 186.681i | 0.181449 | + | 0.314279i | ||||
\(595\) | −178.739 | + | 309.585i | −0.300401 | + | 0.520310i | ||||
\(596\) | −2.89324 | −0.00485443 | ||||||||
\(597\) | − | 151.554i | − | 0.253860i | ||||||
\(598\) | −0.846992 | + | 1.46703i | −0.00141637 | + | 0.00245323i | ||||
\(599\) | −167.646 | − | 96.7905i | −0.279877 | − | 0.161587i | 0.353491 | − | 0.935438i | \(-0.384995\pi\) |
−0.633368 | + | 0.773851i | \(0.718328\pi\) | |||||||
\(600\) | −215.866 | −0.359777 | ||||||||
\(601\) | − | 675.975i | − | 1.12475i | −0.826882 | − | 0.562375i | \(-0.809888\pi\) | ||
0.826882 | − | 0.562375i | \(-0.190112\pi\) | |||||||
\(602\) | 101.598 | + | 58.6576i | 0.168767 | + | 0.0974378i | ||||
\(603\) | 198.209 | − | 114.436i | 0.328706 | − | 0.189778i | ||||
\(604\) | 54.3619 | + | 31.3859i | 0.0900032 | + | 0.0519634i | ||||
\(605\) | −906.827 | − | 1570.67i | −1.49889 | − | 2.59615i | ||||
\(606\) | 274.204 | + | 474.935i | 0.452482 | + | 0.783722i | ||||
\(607\) | 383.052i | 0.631057i | 0.948916 | + | 0.315528i | \(0.102182\pi\) | ||||
−0.948916 | + | 0.315528i | \(0.897818\pi\) | |||||||
\(608\) | 65.4546 | + | 45.5925i | 0.107656 | + | 0.0749877i | ||||
\(609\) | −142.364 | −0.233767 | ||||||||
\(610\) | 628.125 | − | 362.648i | 1.02971 | − | 0.594505i | ||||
\(611\) | 3.97684 | − | 2.29603i | 0.00650874 | − | 0.00375782i | ||||
\(612\) | 9.70824 | − | 16.8152i | 0.0158631 | − | 0.0274758i | ||||
\(613\) | −27.5410 | − | 47.7025i | −0.0449283 | − | 0.0778180i | 0.842687 | − | 0.538404i | \(-0.180973\pi\) |
−0.887615 | + | 0.460586i | \(0.847639\pi\) | |||||||
\(614\) | 240.649 | − | 416.817i | 0.391937 | − | 0.678854i | ||||
\(615\) | 386.091 | 0.627789 | ||||||||
\(616\) | − | 350.818i | − | 0.569510i | ||||||
\(617\) | −51.7851 | + | 89.6944i | −0.0839305 | + | 0.145372i | −0.904935 | − | 0.425550i | \(-0.860081\pi\) |
0.821004 | + | 0.570922i | \(0.193414\pi\) | |||||||
\(618\) | −523.230 | − | 302.087i | −0.846650 | − | 0.488814i | ||||
\(619\) | −263.102 | −0.425043 | −0.212521 | − | 0.977156i | \(-0.568168\pi\) | ||||
−0.212521 | + | 0.977156i | \(0.568168\pi\) | |||||||
\(620\) | 28.8473i | 0.0465278i | ||||||||
\(621\) | −23.6025 | − | 13.6269i | −0.0380072 | − | 0.0219435i | ||||
\(622\) | 789.030 | − | 455.547i | 1.26854 | − | 0.732390i | ||||
\(623\) | 142.066 | + | 82.0218i | 0.228035 | + | 0.131656i | ||||
\(624\) | 2.30060 | + | 3.98475i | 0.00368685 | + | 0.00638581i | ||||
\(625\) | 383.956 | + | 665.031i | 0.614329 | + | 1.06405i | ||||
\(626\) | − | 250.377i | − | 0.399963i | ||||||
\(627\) | −598.593 | + | 280.921i | −0.954693 | + | 0.448039i | ||||
\(628\) | 11.9908 | 0.0190936 | ||||||||
\(629\) | 910.936 | − | 525.929i | 1.44823 | − | 0.836135i | ||||
\(630\) | −77.8655 | + | 44.9557i | −0.123596 | + | 0.0713582i | ||||
\(631\) | 72.5474 | − | 125.656i | 0.114972 | − | 0.199137i | −0.802797 | − | 0.596253i | \(-0.796655\pi\) |
0.917769 | + | 0.397116i | \(0.129989\pi\) | |||||||
\(632\) | 236.686 | + | 409.952i | 0.374503 | + | 0.648658i | ||||
\(633\) | −16.3950 | + | 28.3970i | −0.0259005 | + | 0.0448609i | ||||
\(634\) | −682.817 | −1.07700 | ||||||||
\(635\) | 190.035i | 0.299267i | ||||||||
\(636\) | −12.7247 | + | 22.0399i | −0.0200075 | + | 0.0346539i | ||||
\(637\) | 5.94443 | + | 3.43202i | 0.00933192 | + | 0.00538779i | ||||
\(638\) | −1506.88 | −2.36189 | ||||||||
\(639\) | − | 220.344i | − | 0.344827i | ||||||
\(640\) | −773.034 | − | 446.311i | −1.20787 | − | 0.697361i | ||||
\(641\) | −583.796 | + | 337.055i | −0.910758 | + | 0.525826i | −0.880675 | − | 0.473721i | \(-0.842911\pi\) |
−0.0300832 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(642\) | −430.668 | − | 248.646i | −0.670823 | − | 0.387300i | ||||
\(643\) | 0.719856 | + | 1.24683i | 0.00111953 | + | 0.00193908i | 0.866585 | − | 0.499030i | \(-0.166310\pi\) |
−0.865465 | + | 0.500969i | \(0.832977\pi\) | |||||||
\(644\) | −1.55958 | − | 2.70128i | −0.00242171 | − | 0.00419453i | ||||
\(645\) | 279.007i | 0.432569i | ||||||||
\(646\) | 792.711 | + | 552.165i | 1.22711 | + | 0.854745i | ||||
\(647\) | −614.044 | −0.949063 | −0.474532 | − | 0.880239i | \(-0.657383\pi\) | ||||
−0.474532 | + | 0.880239i | \(0.657383\pi\) | |||||||
\(648\) | −60.1404 | + | 34.7221i | −0.0928092 | + | 0.0535834i | ||||
\(649\) | 601.315 | − | 347.169i | 0.926525 | − | 0.534929i | ||||
\(650\) | −2.60835 | + | 4.51779i | −0.00401284 | + | 0.00695045i | ||||
\(651\) | −33.5306 | − | 58.0768i | −0.0515064 | − | 0.0892116i | ||||
\(652\) | 0.774191 | − | 1.34094i | 0.00118741 | − | 0.00205665i | ||||
\(653\) | 822.374 | 1.25938 | 0.629689 | − | 0.776847i | \(-0.283182\pi\) | ||||
0.629689 | + | 0.776847i | \(0.283182\pi\) | |||||||
\(654\) | 37.8199i | 0.0578286i | ||||||||
\(655\) | −183.807 | + | 318.362i | −0.280621 | + | 0.486049i | ||||
\(656\) | 511.041 | + | 295.050i | 0.779027 | + | 0.449771i | ||||
\(657\) | −275.432 | −0.419227 | ||||||||
\(658\) | 137.147i | 0.208431i | ||||||||
\(659\) | −549.386 | − | 317.188i | −0.833666 | − | 0.481317i | 0.0214404 | − | 0.999770i | \(-0.493175\pi\) |
−0.855106 | + | 0.518453i | \(0.826508\pi\) | |||||||
\(660\) | −50.8129 | + | 29.3368i | −0.0769892 | + | 0.0444497i | ||||
\(661\) | −818.470 | − | 472.544i | −1.23823 | − | 0.714893i | −0.269498 | − | 0.963001i | \(-0.586858\pi\) |
−0.968732 | + | 0.248108i | \(0.920191\pi\) | |||||||
\(662\) | 450.413 | + | 780.138i | 0.680382 | + | 1.17846i | ||||
\(663\) | 3.33619 | + | 5.77845i | 0.00503196 | + | 0.00871561i | ||||
\(664\) | 1148.09i | 1.72905i | ||||||||
\(665\) | −117.173 | − | 249.675i | −0.176200 | − | 0.375451i | ||||
\(666\) | 264.559 | 0.397236 | ||||||||
\(667\) | 164.993 | − | 95.2590i | 0.247366 | − | 0.142817i | ||||
\(668\) | 37.3561 | − | 21.5676i | 0.0559223 | − | 0.0322868i | ||||
\(669\) | 224.162 | − | 388.260i | 0.335070 | − | 0.580358i | ||||
\(670\) | 505.228 | + | 875.080i | 0.754071 | + | 1.30609i | ||||
\(671\) | −550.150 | + | 952.888i | −0.819896 | + | 1.42010i | ||||
\(672\) | −16.4545 | −0.0244859 | ||||||||
\(673\) | − | 570.803i | − | 0.848147i | −0.905628 | − | 0.424074i | \(-0.860600\pi\) | ||
0.905628 | − | 0.424074i | \(-0.139400\pi\) | |||||||
\(674\) | 258.703 | − | 448.086i | 0.383832 | − | 0.664817i | ||||
\(675\) | −72.6848 | − | 41.9646i | −0.107681 | − | 0.0621698i | ||||
\(676\) | −44.4088 | −0.0656935 | ||||||||
\(677\) | − | 275.976i | − | 0.407646i | −0.979008 | − | 0.203823i | \(-0.934663\pi\) | ||
0.979008 | − | 0.203823i | \(-0.0653367\pi\) | |||||||
\(678\) | 214.182 | + | 123.658i | 0.315902 | + | 0.182386i | ||||
\(679\) | 158.471 | − | 91.4931i | 0.233388 | − | 0.134747i | ||||
\(680\) | −1055.66 | − | 609.485i | −1.55244 | − | 0.896302i | ||||
\(681\) | 111.764 | + | 193.582i | 0.164118 | + | 0.284261i | ||||
\(682\) | −354.913 | − | 614.727i | −0.520400 | − | 0.901359i | ||||
\(683\) | 106.224i | 0.155525i | 0.996972 | + | 0.0777627i | \(0.0247776\pi\) | ||||
−0.996972 | + | 0.0777627i | \(0.975222\pi\) | |||||||
\(684\) | 6.36428 | + | 13.5612i | 0.00930450 | + | 0.0198263i | ||||
\(685\) | −608.781 | −0.888732 | ||||||||
\(686\) | −375.792 | + | 216.964i | −0.547802 | + | 0.316274i | ||||
\(687\) | 148.342 | − | 85.6453i | 0.215927 | − | 0.124666i | ||||
\(688\) | −213.217 | + | 369.302i | −0.309908 | + | 0.536776i | ||||
\(689\) | −4.37279 | − | 7.57390i | −0.00634658 | − | 0.0109926i | ||||
\(690\) | 60.1617 | − | 104.203i | 0.0871908 | − | 0.151019i | ||||
\(691\) | 244.177 | 0.353367 | 0.176684 | − | 0.984268i | \(-0.443463\pi\) | ||||
0.176684 | + | 0.984268i | \(0.443463\pi\) | |||||||
\(692\) | − | 71.1195i | − | 0.102774i | ||||||
\(693\) | 68.1994 | − | 118.125i | 0.0984118 | − | 0.170454i | ||||
\(694\) | 299.201 | + | 172.744i | 0.431125 | + | 0.248910i | ||||
\(695\) | 1171.05 | 1.68497 | ||||||||
\(696\) | − | 485.450i | − | 0.697486i | ||||||
\(697\) | 741.082 | + | 427.864i | 1.06325 | + | 0.613865i | ||||
\(698\) | 870.378 | − | 502.513i | 1.24696 | − | 0.719932i | ||||
\(699\) | −524.194 | − | 302.644i | −0.749920 | − | 0.432966i | ||||
\(700\) | −4.80281 | − | 8.31871i | −0.00686115 | − | 0.0118839i | ||||
\(701\) | 143.276 | + | 248.161i | 0.204388 | + | 0.354010i | 0.949938 | − | 0.312440i | \(-0.101146\pi\) |
−0.745550 | + | 0.666450i | \(0.767813\pi\) | |||||||
\(702\) | 1.67821i | 0.00239061i | ||||||||
\(703\) | −68.7436 | + | 808.618i | −0.0977860 | + | 1.15024i | ||||
\(704\) | 1190.71 | 1.69135 | ||||||||
\(705\) | −282.474 | + | 163.087i | −0.400673 | + | 0.231329i | ||||
\(706\) | −53.9108 | + | 31.1254i | −0.0763610 | + | 0.0440870i | ||||
\(707\) | 173.506 | − | 300.521i | 0.245411 | − | 0.425065i | ||||
\(708\) | −7.86514 | − | 13.6228i | −0.0111090 | − | 0.0192413i | ||||
\(709\) | −5.70585 | + | 9.88282i | −0.00804774 | + | 0.0139391i | −0.870021 | − | 0.493014i | \(-0.835895\pi\) |
0.861973 | + | 0.506953i | \(0.169228\pi\) | |||||||
\(710\) | 972.804 | 1.37015 | ||||||||
\(711\) | 184.048i | 0.258857i | ||||||||
\(712\) | −279.688 | + | 484.434i | −0.392820 | + | 0.680385i | ||||
\(713\) | 77.7209 | + | 44.8722i | 0.109006 | + | 0.0629344i | ||||
\(714\) | −199.279 | −0.279102 | ||||||||
\(715\) | − | 20.1629i | − | 0.0281999i | ||||||
\(716\) | −42.4339 | − | 24.4992i | −0.0592652 | − | 0.0342168i | ||||
\(717\) | −451.636 | + | 260.752i | −0.629897 | + | 0.363671i | ||||
\(718\) | 268.238 | + | 154.867i | 0.373591 | + | 0.215693i | ||||
\(719\) | 438.491 | + | 759.488i | 0.609862 | + | 1.05631i | 0.991263 | + | 0.131902i | \(0.0421084\pi\) |
−0.381401 | + | 0.924410i | \(0.624558\pi\) | |||||||
\(720\) | −163.411 | − | 283.036i | −0.226960 | − | 0.393106i | ||||
\(721\) | 382.298i | 0.530232i | ||||||||
\(722\) | −699.131 | + | 258.360i | −0.968325 | + | 0.357839i | ||||
\(723\) | −220.485 | −0.304958 | ||||||||
\(724\) | −10.5634 | + | 6.09880i | −0.0145904 | + | 0.00842376i | ||||
\(725\) | 508.105 | − | 293.354i | 0.700834 | − | 0.404627i | ||||
\(726\) | 505.518 | − | 875.583i | 0.696306 | − | 1.20604i | ||||
\(727\) | −360.167 | − | 623.827i | −0.495415 | − | 0.858084i | 0.504571 | − | 0.863370i | \(-0.331651\pi\) |
−0.999986 | + | 0.00528653i | \(0.998317\pi\) | |||||||
\(728\) | 1.36561 | − | 2.36531i | 0.00187584 | − | 0.00324905i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | − | 1216.01i | − | 1.66577i | ||||||
\(731\) | −309.194 | + | 535.540i | −0.422974 | + | 0.732613i | ||||
\(732\) | 21.5878 | + | 12.4637i | 0.0294915 | + | 0.0170269i | ||||
\(733\) | −170.651 | −0.232812 | −0.116406 | − | 0.993202i | \(-0.537137\pi\) | ||||
−0.116406 | + | 0.993202i | \(0.537137\pi\) | |||||||
\(734\) | 1024.44i | 1.39570i | ||||||||
\(735\) | −422.232 | − | 243.776i | −0.574465 | − | 0.331668i | ||||
\(736\) | 19.0701 | − | 11.0101i | 0.0259104 | − | 0.0149594i | ||||
\(737\) | −1327.53 | − | 766.449i | −1.80126 | − | 1.03996i | ||||
\(738\) | 107.615 | + | 186.394i | 0.145819 | + | 0.252566i | ||||
\(739\) | 530.334 | + | 918.566i | 0.717637 | + | 1.24298i | 0.961933 | + | 0.273284i | \(0.0881098\pi\) |
−0.244296 | + | 0.969701i | \(0.578557\pi\) | |||||||
\(740\) | 72.0104i | 0.0973114i | ||||||||
\(741\) | −5.12940 | − | 0.436069i | −0.00692227 | − | 0.000588487i | ||||
\(742\) | 261.198 | 0.352019 | ||||||||
\(743\) | 290.537 | − | 167.742i | 0.391033 | − | 0.225763i | −0.291575 | − | 0.956548i | \(-0.594179\pi\) |
0.682607 | + | 0.730785i | \(0.260846\pi\) | |||||||
\(744\) | 198.037 | − | 114.337i | 0.266179 | − | 0.153679i | ||||
\(745\) | −35.3107 | + | 61.1599i | −0.0473969 | + | 0.0820938i | ||||
\(746\) | −464.148 | − | 803.928i | −0.622182 | − | 1.07765i | ||||
\(747\) | −223.189 | + | 386.575i | −0.298781 | + | 0.517503i | ||||
\(748\) | −130.044 | −0.173855 | ||||||||
\(749\) | 314.668i | 0.420117i | ||||||||
\(750\) | −101.487 | + | 175.781i | −0.135316 | + | 0.234375i | ||||
\(751\) | −1128.41 | − | 651.490i | −1.50255 | − | 0.867497i | −0.999996 | − | 0.00295120i | \(-0.999061\pi\) |
−0.502554 | − | 0.864546i | \(-0.667606\pi\) | |||||||
\(752\) | −498.522 | −0.662929 | ||||||||
\(753\) | 613.226i | 0.814377i | ||||||||
\(754\) | −10.1598 | − | 5.86578i | −0.0134746 | − | 0.00777955i | ||||
\(755\) | 1326.92 | − | 766.100i | 1.75751 | − | 1.01470i | ||||
\(756\) | −2.67613 | − | 1.54506i | −0.00353985 | − | 0.00204373i | ||||
\(757\) | −60.1511 | − | 104.185i | −0.0794598 | − | 0.137628i | 0.823557 | − | 0.567233i | \(-0.191986\pi\) |
−0.903017 | + | 0.429605i | \(0.858653\pi\) | |||||||
\(758\) | 486.574 | + | 842.771i | 0.641919 | + | 1.11184i | ||||
\(759\) | 182.535i | 0.240494i | ||||||||
\(760\) | 851.373 | − | 399.551i | 1.12023 | − | 0.525725i | ||||
\(761\) | 1346.45 | 1.76932 | 0.884658 | − | 0.466240i | \(-0.154392\pi\) | ||||
0.884658 | + | 0.466240i | \(0.154392\pi\) | |||||||
\(762\) | −91.7437 | + | 52.9682i | −0.120399 | + | 0.0695121i | ||||
\(763\) | 20.7248 | − | 11.9655i | 0.0271623 | − | 0.0156822i | ||||
\(764\) | −4.82553 | + | 8.35805i | −0.00631613 | + | 0.0109399i | ||||
\(765\) | −236.969 | − | 410.442i | −0.309763 | − | 0.536526i | ||||
\(766\) | 27.9243 | − | 48.3663i | 0.0364547 | − | 0.0631414i | ||||
\(767\) | 5.40564 | 0.00704777 | ||||||||
\(768\) | − | 87.0301i | − | 0.113320i | ||||||
\(769\) | 109.016 | − | 188.821i | 0.141763 | − | 0.245541i | −0.786398 | − | 0.617721i | \(-0.788056\pi\) |
0.928161 | + | 0.372180i | \(0.121390\pi\) | |||||||
\(770\) | 521.512 | + | 301.095i | 0.677288 | + | 0.391033i | ||||
\(771\) | 473.337 | 0.613926 | ||||||||
\(772\) | 52.6433i | 0.0681909i | ||||||||
\(773\) | −48.6422 | − | 28.0836i | −0.0629266 | − | 0.0363307i | 0.468207 | − | 0.883619i | \(-0.344900\pi\) |
−0.531133 | + | 0.847288i | \(0.678234\pi\) | |||||||
\(774\) | −134.697 | + | 77.7673i | −0.174027 | + | 0.100475i | ||||
\(775\) | 239.345 | + | 138.186i | 0.308832 | + | 0.178304i | ||||
\(776\) | 311.984 | + | 540.373i | 0.402042 | + | 0.696357i | ||||
\(777\) | −83.7014 | − | 144.975i | −0.107724 | − | 0.186583i | ||||
\(778\) | 731.482i | 0.940208i | ||||||||
\(779\) | −597.671 | + | 280.488i | −0.767229 | + | 0.360062i | ||||
\(780\) | −0.456792 | −0.000585631 | ||||||||
\(781\) | −1278.06 | + | 737.890i | −1.63644 | + | 0.944801i | ||||
\(782\) | 230.955 | − | 133.342i | 0.295339 | − | 0.170514i | ||||
\(783\) | 94.3720 | − | 163.457i | 0.120526 | − | 0.208757i | ||||
\(784\) | −372.586 | − | 645.338i | −0.475238 | − | 0.823136i | ||||
\(785\) | 146.342 | − | 253.472i | 0.186423 | − | 0.322894i | ||||
\(786\) | −204.929 | −0.260724 | ||||||||
\(787\) | − | 170.104i | − | 0.216142i | −0.994143 | − | 0.108071i | \(-0.965533\pi\) | ||
0.994143 | − | 0.108071i | \(-0.0344674\pi\) | |||||||
\(788\) | −22.5377 | + | 39.0365i | −0.0286012 | + | 0.0495387i | ||||
\(789\) | 226.693 | + | 130.881i | 0.287316 | + | 0.165882i | ||||
\(790\) | −812.556 | −1.02855 | ||||||||
\(791\) | − | 156.492i | − | 0.197840i | ||||||
\(792\) | 402.796 | + | 232.555i | 0.508581 | + | 0.293630i | ||||
\(793\) | −7.41853 | + | 4.28309i | −0.00935501 | + | 0.00540112i | ||||
\(794\) | 284.337 | + | 164.162i | 0.358107 | + | 0.206753i | ||||
\(795\) | 310.599 | + | 537.973i | 0.390690 | + | 0.676696i | ||||
\(796\) | 11.4980 | + | 19.9152i | 0.0144448 | + | 0.0250190i | ||||
\(797\) | 740.226i | 0.928765i | 0.885635 | + | 0.464383i | \(0.153724\pi\) | ||||
−0.885635 | + | 0.464383i | \(0.846276\pi\) | |||||||
\(798\) | 87.8768 | − | 126.160i | 0.110121 | − | 0.158095i | ||||
\(799\) | −722.928 | −0.904791 | ||||||||
\(800\) | 58.7271 | − | 33.9061i | 0.0734089 | − | 0.0423826i | ||||
\(801\) | −188.349 | + | 108.743i | −0.235142 | + | 0.135759i | ||||
\(802\) | 330.829 | − | 573.013i | 0.412505 | − | 0.714480i | ||||
\(803\) | 922.366 | + | 1597.59i | 1.14865 | + | 1.98952i | ||||
\(804\) | −17.3639 | + | 30.0752i | −0.0215970 | + | 0.0374070i | ||||
\(805\) | −76.1359 | −0.0945788 | ||||||||
\(806\) | − | 5.52620i | − | 0.00685633i | ||||||
\(807\) | −58.9364 | + | 102.081i | −0.0730314 | + | 0.126494i | ||||
\(808\) | 1024.75 | + | 591.641i | 1.26826 | + | 0.732229i | ||||
\(809\) | −1489.01 | −1.84056 | −0.920280 | − | 0.391260i | \(-0.872039\pi\) | ||||
−0.920280 | + | 0.391260i | \(0.872039\pi\) | |||||||
\(810\) | − | 119.203i | − | 0.147164i | ||||||
\(811\) | 823.672 | + | 475.547i | 1.01563 | + | 0.586372i | 0.912834 | − | 0.408331i | \(-0.133889\pi\) |
0.102792 | + | 0.994703i | \(0.467223\pi\) | |||||||
\(812\) | 18.7075 | − | 10.8008i | 0.0230388 | − | 0.0133015i | ||||
\(813\) | −170.697 | − | 98.5521i | −0.209960 | − | 0.121220i | ||||
\(814\) | −885.956 | − | 1534.52i | −1.08840 | − | 1.88516i | ||||
\(815\) | −18.8973 | − | 32.7310i | −0.0231868 | − | 0.0401608i | ||||
\(816\) | − | 724.366i | − | 0.887703i | ||||||
\(817\) | −202.694 | − | 431.905i | −0.248095 | − | 0.528647i | ||||
\(818\) | 600.250 | 0.733802 | ||||||||
\(819\) | 0.919637 | − | 0.530953i | 0.00112288 | − | 0.000648294i | ||||
\(820\) | −50.7346 | + | 29.2917i | −0.0618715 | + | 0.0357215i | ||||
\(821\) | 790.459 | − | 1369.12i | 0.962801 | − | 1.66762i | 0.247390 | − | 0.968916i | \(-0.420427\pi\) |
0.715411 | − | 0.698704i | \(-0.246240\pi\) | |||||||
\(822\) | −169.685 | − | 293.903i | −0.206430 | − | 0.357546i | ||||
\(823\) | 734.523 | − | 1272.23i | 0.892494 | − | 1.54585i | 0.0556192 | − | 0.998452i | \(-0.482287\pi\) |
0.836875 | − | 0.547394i | \(-0.184380\pi\) | |||||||
\(824\) | −1303.61 | −1.58204 | ||||||||
\(825\) | 562.124i | 0.681363i | ||||||||
\(826\) | −80.7230 | + | 139.816i | −0.0977276 | + | 0.169269i | ||||
\(827\) | −13.7499 | − | 7.93854i | −0.0166263 | − | 0.00959920i | 0.491664 | − | 0.870785i | \(-0.336389\pi\) |
−0.508290 | + | 0.861186i | \(0.669722\pi\) | |||||||
\(828\) | 4.13534 | 0.00499437 | ||||||||
\(829\) | 460.891i | 0.555960i | 0.960587 | + | 0.277980i | \(0.0896649\pi\) | ||||
−0.960587 | + | 0.277980i | \(0.910335\pi\) | |||||||
\(830\) | −1706.70 | − | 985.363i | −2.05626 | − | 1.18718i | ||||
\(831\) | −661.365 | + | 381.839i | −0.795867 | + | 0.459494i | ||||
\(832\) | 8.02810 | + | 4.63503i | 0.00964916 | + | 0.00557095i | ||||
\(833\) | −540.303 | − | 935.832i | −0.648623 | − | 1.12345i | ||||
\(834\) | 326.407 | + | 565.353i | 0.391375 | + | 0.677881i | ||||
\(835\) | − | 1052.89i | − | 1.26094i | ||||||
\(836\) | 57.3460 | − | 82.3283i | 0.0685957 | − | 0.0984789i | ||||
\(837\) | 88.9088 | 0.106223 | ||||||||
\(838\) | 253.627 | − | 146.432i | 0.302658 | − | 0.174740i | ||||
\(839\) | −11.1163 | + | 6.41800i | −0.0132495 | + | 0.00764959i | −0.506610 | − | 0.862175i | \(-0.669102\pi\) |
0.493361 | + | 0.869825i | \(0.335768\pi\) | |||||||
\(840\) | −96.9993 | + | 168.008i | −0.115475 | + | 0.200009i | ||||
\(841\) | 239.209 | + | 414.323i | 0.284434 | + | 0.492655i | ||||
\(842\) | −117.614 | + | 203.713i | −0.139684 | + | 0.241939i | ||||
\(843\) | −156.186 | −0.185274 | ||||||||
\(844\) | − | 4.97538i | − | 0.00589500i | ||||||
\(845\) | −541.989 | + | 938.752i | −0.641407 | + | 1.11095i | ||||
\(846\) | −157.468 | − | 90.9140i | −0.186132 | − | 0.107463i | ||||
\(847\) | −639.744 | −0.755306 | ||||||||
\(848\) | 949.437i | 1.11962i | ||||||||
\(849\) | −103.599 | − | 59.8131i | −0.122025 | − | 0.0704512i | ||||
\(850\) | 711.236 | − | 410.632i | 0.836748 | − | 0.483097i | ||||
\(851\) | 194.012 | + | 112.013i | 0.227981 | + | 0.131625i | ||||
\(852\) | 16.7169 | + | 28.9546i | 0.0196208 | + | 0.0339843i | ||||
\(853\) | 321.717 | + | 557.231i | 0.377160 | + | 0.653260i | 0.990648 | − | 0.136444i | \(-0.0435674\pi\) |
−0.613488 | + | 0.789704i | \(0.710234\pi\) | |||||||
\(854\) | − | 255.839i | − | 0.299578i | ||||||
\(855\) | 364.341 | + | 30.9739i | 0.426129 | + | 0.0362268i | ||||
\(856\) | −1072.99 | −1.25350 | ||||||||
\(857\) | −115.805 | + | 66.8603i | −0.135129 | + | 0.0780167i | −0.566040 | − | 0.824377i | \(-0.691525\pi\) |
0.430912 | + | 0.902394i | \(0.358192\pi\) | |||||||
\(858\) | 9.73411 | − | 5.61999i | 0.0113451 | − | 0.00655011i | ||||
\(859\) | −49.3229 | + | 85.4297i | −0.0574189 | + | 0.0994525i | −0.893306 | − | 0.449449i | \(-0.851620\pi\) |
0.835887 | + | 0.548901i | \(0.184954\pi\) | |||||||
\(860\) | −21.1675 | − | 36.6632i | −0.0246134 | − | 0.0426316i | ||||
\(861\) | 68.0944 | − | 117.943i | 0.0790875 | − | 0.136984i | ||||
\(862\) | −546.576 | −0.634079 | ||||||||
\(863\) | − | 829.585i | − | 0.961280i | −0.876918 | − | 0.480640i | \(-0.840404\pi\) | ||
0.876918 | − | 0.480640i | \(-0.159596\pi\) | |||||||
\(864\) | 10.9076 | − | 18.8925i | 0.0126245 | − | 0.0218663i | ||||
\(865\) | −1503.39 | − | 867.980i | −1.73802 | − | 1.00344i | ||||
\(866\) | 1505.14 | 1.73803 | ||||||||
\(867\) | − | 549.870i | − | 0.634221i | ||||||
\(868\) | 8.81226 | + | 5.08776i | 0.0101524 | + | 0.00586147i | ||||
\(869\) | 1067.53 | − | 616.339i | 1.22846 | − | 0.709251i | ||||
\(870\) | 721.651 | + | 416.645i | 0.829484 | + | 0.478903i | ||||
\(871\) | −5.96704 | − | 10.3352i | −0.00685079 | − | 0.0118659i | ||||
\(872\) | 40.8014 | + | 70.6700i | 0.0467906 | + | 0.0810436i | ||||
\(873\) | 242.600i | 0.277893i | ||||||||
\(874\) | −17.4290 | + | 205.014i | −0.0199416 | + | 0.234569i | ||||
\(875\) | 128.434 | 0.146782 | ||||||||
\(876\) | 36.1934 | − | 20.8963i | 0.0413167 | − | 0.0238542i | ||||
\(877\) | 157.383 | − | 90.8649i | 0.179456 | − | 0.103609i | −0.407581 | − | 0.913169i | \(-0.633628\pi\) |
0.587037 | + | 0.809560i | \(0.300294\pi\) | |||||||
\(878\) | −380.963 | + | 659.847i | −0.433898 | + | 0.751534i | ||||
\(879\) | −355.277 | − | 615.358i | −0.404183 | − | 0.700065i | ||||
\(880\) | −1094.46 | + | 1895.66i | −1.24371 | + | 2.15416i | ||||
\(881\) | −517.816 | −0.587759 | −0.293880 | − | 0.955842i | \(-0.594946\pi\) | ||||
−0.293880 | + | 0.955842i | \(0.594946\pi\) | |||||||
\(882\) | − | 271.790i | − | 0.308151i | ||||||
\(883\) | 782.367 | − | 1355.10i | 0.886033 | − | 1.53465i | 0.0415084 | − | 0.999138i | \(-0.486784\pi\) |
0.844525 | − | 0.535516i | \(-0.179883\pi\) | |||||||
\(884\) | −0.876791 | − | 0.506216i | −0.000991845 | − | 0.000572642i | ||||
\(885\) | −383.961 | −0.433855 | ||||||||
\(886\) | − | 1203.89i | − | 1.35879i | ||||||
\(887\) | −620.266 | − | 358.111i | −0.699285 | − | 0.403732i | 0.107796 | − | 0.994173i | \(-0.465621\pi\) |
−0.807081 | + | 0.590441i | \(0.798954\pi\) | |||||||
\(888\) | 494.354 | − | 285.415i | 0.556705 | − | 0.321414i | ||||
\(889\) | 58.0518 | + | 33.5162i | 0.0653001 | + | 0.0377011i | ||||
\(890\) | −480.093 | − | 831.546i | −0.539431 | − | 0.934321i | ||||
\(891\) | 90.4176 | + | 156.608i | 0.101479 | + | 0.175766i | ||||
\(892\) | 68.0262i | 0.0762626i | ||||||||
\(893\) | 318.793 | − | 457.672i | 0.356991 | − | 0.512511i | ||||
\(894\) | −39.3684 | −0.0440363 | ||||||||
\(895\) | −1035.77 | + | 598.003i | −1.15729 | + | 0.668159i | ||||
\(896\) | −272.678 | + | 157.431i | −0.304328 | + | 0.175704i | ||||
\(897\) | −0.710545 | + | 1.23070i | −0.000792135 | + | 0.00137202i | ||||
\(898\) | 324.588 | + | 562.202i | 0.361456 | + | 0.626061i | ||||
\(899\) | −310.759 | + | 538.251i | −0.345672 | + | 0.598722i | ||||
\(900\) | 12.7350 | 0.0141500 | ||||||||
\(901\) | 1376.82i | 1.52810i | ||||||||
\(902\) | 720.760 | − | 1248.39i | 0.799069 | − | 1.38403i | ||||
\(903\) | 85.2309 | + | 49.2081i | 0.0943864 | + | 0.0544940i | ||||
\(904\) | 533.625 | 0.590293 | ||||||||
\(905\) | 297.732i | 0.328986i | ||||||||
\(906\) | 739.704 | + | 427.068i | 0.816451 | + | 0.471378i | ||||
\(907\) | 240.379 | − | 138.783i | 0.265026 | − | 0.153013i | −0.361599 | − | 0.932334i | \(-0.617769\pi\) |
0.626625 | + | 0.779321i | \(0.284436\pi\) | |||||||
\(908\) | −29.3731 | − | 16.9585i | −0.0323492 | − | 0.0186768i | ||||
\(909\) | 230.031 | + | 398.426i | 0.253059 | + | 0.438312i | ||||
\(910\) | 2.34412 | + | 4.06013i | 0.00257595 | + | 0.00446168i | ||||
\(911\) | − | 1630.56i | − | 1.78986i | −0.446207 | − | 0.894930i | \(-0.647226\pi\) | ||
0.446207 | − | 0.894930i | \(-0.352774\pi\) | |||||||
\(912\) | 458.582 | + | 319.427i | 0.502831 | + | 0.350249i | ||||
\(913\) | 2989.66 | 3.27455 | ||||||||
\(914\) | −903.415 | + | 521.587i | −0.988419 | + | 0.570664i | ||||
\(915\) | 526.937 | − | 304.227i | 0.575887 | − | 0.332489i | ||||
\(916\) | −12.9954 | + | 22.5086i | −0.0141871 | + | 0.0245727i | ||||
\(917\) | 64.8355 | + | 112.298i | 0.0707040 | + | 0.122463i | ||||
\(918\) | 132.100 | − | 228.804i | 0.143900 | − | 0.249242i | ||||
\(919\) | −48.0409 | −0.0522752 | −0.0261376 | − | 0.999658i | \(-0.508321\pi\) | ||||
−0.0261376 | + | 0.999658i | \(0.508321\pi\) | |||||||
\(920\) | − | 259.618i | − | 0.282193i | ||||||
\(921\) | 201.882 | − | 349.669i | 0.219198 | − | 0.379663i | ||||
\(922\) | −489.575 | − | 282.656i | −0.530993 | − | 0.306569i | ||||
\(923\) | −11.4894 | −0.0124479 | ||||||||
\(924\) | 20.6964i | 0.0223987i | ||||||||
\(925\) | 597.469 | + | 344.949i | 0.645912 | + | 0.372918i | ||||
\(926\) | −571.781 | + | 330.118i | −0.617474 | + | 0.356499i | ||||
\(927\) | −438.940 | − | 253.422i | −0.473506 | − | 0.273379i | ||||
\(928\) | 76.2497 | + | 132.068i | 0.0821656 | + | 0.142315i | ||||
\(929\) | −641.727 | − | 1111.50i | −0.690772 | − | 1.19645i | −0.971585 | − | 0.236690i | \(-0.923937\pi\) |
0.280813 | − | 0.959763i | \(-0.409396\pi\) | |||||||
\(930\) | 392.525i | 0.422070i | ||||||||
\(931\) | 830.717 | + | 70.6223i | 0.892285 | + | 0.0758564i | ||||
\(932\) | 91.8430 | 0.0985440 | ||||||||
\(933\) | 661.921 | − | 382.160i | 0.709454 | − | 0.409604i | ||||
\(934\) | 528.386 | − | 305.064i | 0.565724 | − | 0.326621i | ||||
\(935\) | −1587.12 | + | 2748.98i | −1.69746 | + | 2.94008i | ||||
\(936\) | 1.81051 | + | 3.13589i | 0.00193430 | + | 0.00335031i | ||||
\(937\) | −769.568 | + | 1332.93i | −0.821311 | + | 1.42255i | 0.0833953 | + | 0.996517i | \(0.473424\pi\) |
−0.904706 | + | 0.426036i | \(0.859910\pi\) | |||||||
\(938\) | 356.426 | 0.379985 | ||||||||
\(939\) | − | 210.042i | − | 0.223687i | ||||||
\(940\) | 24.7459 | − | 42.8611i | 0.0263254 | − | 0.0455970i | ||||
\(941\) | −1281.05 | − | 739.617i | −1.36138 | − | 0.785990i | −0.371568 | − | 0.928406i | \(-0.621180\pi\) |
−0.989807 | + | 0.142415i | \(0.954513\pi\) | |||||||
\(942\) | 163.159 | 0.173205 | ||||||||
\(943\) | 182.254i | 0.193270i | ||||||||
\(944\) | −508.223 | − | 293.423i | −0.538372 | − | 0.310829i | ||||
\(945\) | −65.3217 | + | 37.7135i | −0.0691235 | + | 0.0399085i | ||||
\(946\) | 902.146 | + | 520.854i | 0.953643 | + | 0.550586i | ||||
\(947\) | 349.924 | + | 606.086i | 0.369508 | + | 0.640006i | 0.989489 | − | 0.144611i | \(-0.0461930\pi\) |
−0.619981 | + | 0.784617i | \(0.712860\pi\) | |||||||
\(948\) | −13.9632 | − | 24.1850i | −0.0147291 | − | 0.0255116i | ||||
\(949\) | 14.3618i | 0.0151336i | ||||||||
\(950\) | −53.6733 | + | 631.349i | −0.0564982 | + | 0.664577i | ||||
\(951\) | −572.818 | −0.602332 | ||||||||
\(952\) | −372.371 | + | 214.989i | −0.391146 | + | 0.225828i | ||||
\(953\) | −354.907 | + | 204.906i | −0.372411 | + | 0.215011i | −0.674511 | − | 0.738265i | \(-0.735646\pi\) |
0.302100 | + | 0.953276i | \(0.402312\pi\) | |||||||
\(954\) | −173.146 | + | 299.898i | −0.181495 | + | 0.314358i | ||||
\(955\) | 117.787 | + | 204.012i | 0.123337 | + | 0.213625i | ||||
\(956\) | 39.5652 | − | 68.5289i | 0.0413862 | − | 0.0716829i | ||||
\(957\) | −1264.13 | −1.32093 | ||||||||
\(958\) | 844.688i | 0.881720i | ||||||||
\(959\) | −107.370 | + | 185.971i | −0.111960 | + | 0.193921i | ||||
\(960\) | −570.235 | − | 329.225i | −0.593995 | − | 0.342943i | ||||
\(961\) | 668.231 | 0.695349 | ||||||||
\(962\) | − | 13.7949i | − | 0.0143398i | ||||||
\(963\) | −361.289 | − | 208.591i | −0.375171 | − | 0.216605i | ||||
\(964\) | 28.9731 | − | 16.7276i | 0.0300550 | − | 0.0173523i | ||||
\(965\) | 1112.82 | + | 642.487i | 1.15318 | + | 0.665790i | ||||
\(966\) | −21.2213 | − | 36.7564i | −0.0219682 | − | 0.0380501i | ||||
\(967\) | 92.4602 | + | 160.146i | 0.0956155 | + | 0.165611i | 0.909865 | − | 0.414904i | \(-0.136185\pi\) |
−0.814250 | + | 0.580515i | \(0.802851\pi\) | |||||||
\(968\) | − | 2181.48i | − | 2.25359i | ||||||
\(969\) | 665.009 | + | 463.214i | 0.686284 | + | 0.478033i | ||||
\(970\) | −1071.06 | −1.10419 | ||||||||
\(971\) | 218.148 | − | 125.948i | 0.224663 | − | 0.129709i | −0.383445 | − | 0.923564i | \(-0.625262\pi\) |
0.608107 | + | 0.793855i | \(0.291929\pi\) | |||||||
\(972\) | 3.54796 | − | 2.04842i | 0.00365017 | − | 0.00210743i | ||||
\(973\) | 206.537 | − | 357.733i | 0.212269 | − | 0.367660i | ||||
\(974\) | 658.840 | + | 1141.14i | 0.676427 | + | 1.17161i | ||||
\(975\) | −2.18816 | + | 3.79000i | −0.00224426 | + | 0.00388718i | ||||
\(976\) | 929.960 | 0.952828 | ||||||||
\(977\) | − | 372.639i | − | 0.381411i | −0.981647 | − | 0.190706i | \(-0.938922\pi\) | ||
0.981647 | − | 0.190706i | \(-0.0610776\pi\) | |||||||
\(978\) | 10.5344 | − | 18.2462i | 0.0107714 | − | 0.0186566i | ||||
\(979\) | 1261.49 | + | 728.319i | 1.28854 | + | 0.743942i | ||||
\(980\) | 73.9785 | 0.0754882 | ||||||||
\(981\) | 31.7273i | 0.0323418i | ||||||||
\(982\) | 619.658 | + | 357.760i | 0.631016 | + | 0.364317i | ||||
\(983\) | 137.328 | − | 79.2861i | 0.139702 | − | 0.0806573i | −0.428520 | − | 0.903532i | \(-0.640965\pi\) |
0.568222 | + | 0.822875i | \(0.307631\pi\) | |||||||
\(984\) | 402.176 | + | 232.197i | 0.408716 | + | 0.235972i | ||||
\(985\) | 550.125 | + | 952.844i | 0.558503 | + | 0.967355i | ||||
\(986\) | 923.450 | + | 1599.46i | 0.936561 | + | 1.62217i | ||||
\(987\) | 115.054i | 0.116569i | ||||||||
\(988\) | 0.707118 | − | 0.331852i | 0.000715706 | − | 0.000335882i | ||||
\(989\) | −131.705 | −0.133170 | ||||||||
\(990\) | −691.412 | + | 399.187i | −0.698396 | + | 0.403219i | ||||
\(991\) | 1489.96 | − | 860.227i | 1.50349 | − | 0.868039i | 0.503496 | − | 0.863998i | \(-0.332047\pi\) |
0.999992 | − | 0.00404127i | \(-0.00128638\pi\) | |||||||
\(992\) | −35.9178 | + | 62.2114i | −0.0362074 | + | 0.0627131i | ||||
\(993\) | 377.854 | + | 654.462i | 0.380517 | + | 0.659075i | ||||
\(994\) | 171.572 | − | 297.172i | 0.172608 | − | 0.298966i | ||||
\(995\) | 561.312 | 0.564132 | ||||||||
\(996\) | − | 67.7311i | − | 0.0680031i | ||||||
\(997\) | −261.532 | + | 452.987i | −0.262319 | + | 0.454350i | −0.966858 | − | 0.255316i | \(-0.917821\pi\) |
0.704539 | + | 0.709666i | \(0.251154\pi\) | |||||||
\(998\) | 144.299 | + | 83.3111i | 0.144588 | + | 0.0834780i | ||||
\(999\) | 221.940 | 0.222162 |
(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 | 57.3.g.b.31.1 | ✓ | 6 | |
3.2 | odd | 2 | 171.3.p.c.145.3 | 6 | |||
4.3 | odd | 2 | 912.3.be.f.145.1 | 6 | |||
19.8 | odd | 6 | inner | 57.3.g.b.46.1 | yes | 6 | |
57.8 | even | 6 | 171.3.p.c.46.3 | 6 | |||
76.27 | even | 6 | 912.3.be.f.673.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.g.b.31.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
57.3.g.b.46.1 | yes | 6 | 19.8 | odd | 6 | inner | |
171.3.p.c.46.3 | 6 | 57.8 | even | 6 | |||
171.3.p.c.145.3 | 6 | 3.2 | odd | 2 | |||
912.3.be.f.145.1 | 6 | 4.3 | odd | 2 | |||
912.3.be.f.673.1 | 6 | 76.27 | even | 6 |