Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,3,Mod(374,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.374");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.2180099135\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 374.12 | ||
Character | \(\chi\) | \(=\) | 375.374 |
Dual form | 375.3.d.e.374.11 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67701 | −0.838504 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(3\) | −0.0488427 | + | 2.99960i | −0.0162809 | + | 0.999867i | ||||
\(4\) | −1.18764 | −0.296911 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0819097 | − | 5.03036i | 0.0136516 | − | 0.838393i | ||||
\(7\) | 0.986092i | 0.140870i | 0.997516 | + | 0.0704352i | \(0.0224388\pi\) | ||||
−0.997516 | + | 0.0704352i | \(0.977561\pi\) | |||||||
\(8\) | 8.69972 | 1.08747 | ||||||||
\(9\) | −8.99523 | − | 0.293018i | −0.999470 | − | 0.0325575i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.7308i | − | 0.975532i | −0.872975 | − | 0.487766i | \(-0.837812\pi\) | ||
0.872975 | − | 0.487766i | \(-0.162188\pi\) | |||||||
\(12\) | 0.0580078 | − | 3.56246i | 0.00483398 | − | 0.296872i | ||||
\(13\) | − | 8.72887i | − | 0.671452i | −0.941960 | − | 0.335726i | \(-0.891018\pi\) | ||
0.941960 | − | 0.335726i | \(-0.108982\pi\) | |||||||
\(14\) | − | 1.65368i | − | 0.118120i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.83892 | −0.614933 | ||||||||
\(17\) | 5.40271 | 0.317806 | 0.158903 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158903 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(18\) | 15.0851 | + | 0.491393i | 0.838059 | + | 0.0272996i | ||||
\(19\) | −21.2651 | −1.11921 | −0.559607 | − | 0.828758i | \(-0.689048\pi\) | ||||
−0.559607 | + | 0.828758i | \(0.689048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.95789 | − | 0.0481634i | −0.140852 | − | 0.00229350i | ||||
\(22\) | 17.9957i | 0.817987i | ||||||||
\(23\) | 33.8142 | 1.47018 | 0.735092 | − | 0.677968i | \(-0.237139\pi\) | ||||
0.735092 | + | 0.677968i | \(0.237139\pi\) | |||||||
\(24\) | −0.424918 | + | 26.0957i | −0.0177049 | + | 1.08732i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.6384i | 0.563015i | ||||||||
\(27\) | 1.31829 | − | 26.9678i | 0.0488255 | − | 0.998807i | ||||
\(28\) | − | 1.17113i | − | 0.0418260i | ||||||
\(29\) | − | 35.1451i | − | 1.21190i | −0.795503 | − | 0.605950i | \(-0.792793\pi\) | ||
0.795503 | − | 0.605950i | \(-0.207207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.9689 | 1.12803 | 0.564015 | − | 0.825765i | \(-0.309256\pi\) | ||||
0.564015 | + | 0.825765i | \(0.309256\pi\) | |||||||
\(32\) | −18.2989 | −0.571842 | ||||||||
\(33\) | 32.1883 | + | 0.524124i | 0.975402 | + | 0.0158825i | ||||
\(34\) | −9.06038 | −0.266482 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.6831 | + | 0.348001i | 0.296754 | + | 0.00966668i | ||||
\(37\) | 19.3152i | 0.522033i | 0.965334 | + | 0.261017i | \(0.0840578\pi\) | ||||
−0.965334 | + | 0.261017i | \(0.915942\pi\) | |||||||
\(38\) | 35.6617 | 0.938466 | ||||||||
\(39\) | 26.1831 | + | 0.426342i | 0.671363 | + | 0.0109318i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 52.7118i | 1.28565i | 0.766012 | + | 0.642827i | \(0.222238\pi\) | ||||
−0.766012 | + | 0.642827i | \(0.777762\pi\) | |||||||
\(42\) | 4.96040 | + | 0.0807705i | 0.118105 | + | 0.00192311i | ||||
\(43\) | 29.1674i | 0.678310i | 0.940730 | + | 0.339155i | \(0.110141\pi\) | ||||
−0.940730 | + | 0.339155i | \(0.889859\pi\) | |||||||
\(44\) | 12.7444i | 0.289646i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −56.7067 | −1.23275 | ||||||||
\(47\) | 52.7420 | 1.12217 | 0.561085 | − | 0.827758i | \(-0.310384\pi\) | ||||
0.561085 | + | 0.827758i | \(0.310384\pi\) | |||||||
\(48\) | 0.480560 | − | 29.5129i | 0.0100117 | − | 0.614851i | ||||
\(49\) | 48.0276 | 0.980156 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.263883 | + | 16.2060i | −0.00517418 | + | 0.317764i | ||||
\(52\) | 10.3668i | 0.199361i | ||||||||
\(53\) | 48.0164 | 0.905969 | 0.452985 | − | 0.891518i | \(-0.350359\pi\) | ||||
0.452985 | + | 0.891518i | \(0.350359\pi\) | |||||||
\(54\) | −2.21078 | + | 45.2252i | −0.0409404 | + | 0.837504i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.57873i | 0.153192i | ||||||||
\(57\) | 1.03864 | − | 63.7868i | 0.0182218 | − | 1.11907i | ||||
\(58\) | 58.9386i | 1.01618i | ||||||||
\(59\) | − | 93.9152i | − | 1.59178i | −0.605440 | − | 0.795891i | \(-0.707003\pi\) | ||
0.605440 | − | 0.795891i | \(-0.292997\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.9169 | 0.474048 | 0.237024 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237024 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(62\) | −58.6432 | −0.945857 | ||||||||
\(63\) | 0.288942 | − | 8.87013i | 0.00458639 | − | 0.140796i | ||||
\(64\) | 70.0431 | 1.09442 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −53.9800 | − | 0.878960i | −0.817879 | − | 0.0133176i | ||||
\(67\) | 90.9035i | 1.35677i | 0.734707 | + | 0.678384i | \(0.237320\pi\) | ||||
−0.734707 | + | 0.678384i | \(0.762680\pi\) | |||||||
\(68\) | −6.41649 | −0.0943602 | ||||||||
\(69\) | −1.65158 | + | 101.429i | −0.0239359 | + | 1.46999i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 127.604i | − | 1.79724i | −0.438730 | − | 0.898619i | \(-0.644571\pi\) | ||
0.438730 | − | 0.898619i | \(-0.355429\pi\) | |||||||
\(72\) | −78.2560 | − | 2.54917i | −1.08689 | − | 0.0354052i | ||||
\(73\) | − | 97.8731i | − | 1.34073i | −0.742032 | − | 0.670364i | \(-0.766138\pi\) | ||
0.742032 | − | 0.670364i | \(-0.233862\pi\) | |||||||
\(74\) | − | 32.3918i | − | 0.437727i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 25.2553 | 0.332307 | ||||||||
\(77\) | 10.5816 | 0.137423 | ||||||||
\(78\) | −43.9093 | − | 0.714979i | −0.562940 | − | 0.00916639i | ||||
\(79\) | 41.7927 | 0.529022 | 0.264511 | − | 0.964383i | \(-0.414789\pi\) | ||||
0.264511 | + | 0.964383i | \(0.414789\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.8283 | + | 5.27152i | 0.997880 | + | 0.0650805i | ||||
\(82\) | − | 88.3981i | − | 1.07803i | ||||||
\(83\) | −97.3060 | −1.17236 | −0.586181 | − | 0.810180i | \(-0.699369\pi\) | ||||
−0.586181 | + | 0.810180i | \(0.699369\pi\) | |||||||
\(84\) | 3.51292 | + | 0.0572010i | 0.0418204 | + | 0.000680965i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 48.9139i | − | 0.568766i | ||||||
\(87\) | 105.421 | + | 1.71658i | 1.21174 | + | 0.0197308i | ||||
\(88\) | − | 93.3554i | − | 1.06086i | ||||||
\(89\) | − | 87.7324i | − | 0.985757i | −0.870098 | − | 0.492879i | \(-0.835945\pi\) | ||
0.870098 | − | 0.492879i | \(-0.164055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.60747 | 0.0945876 | ||||||||
\(92\) | −40.1593 | −0.436514 | ||||||||
\(93\) | −1.70798 | + | 104.893i | −0.0183654 | + | 1.12788i | ||||
\(94\) | −88.4487 | −0.940944 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.893770 | − | 54.8895i | 0.00931010 | − | 0.571766i | ||||
\(97\) | 85.0442i | 0.876744i | 0.898794 | + | 0.438372i | \(0.144445\pi\) | ||||
−0.898794 | + | 0.438372i | \(0.855555\pi\) | |||||||
\(98\) | −80.5427 | −0.821864 | ||||||||
\(99\) | −3.14433 | + | 96.5264i | −0.0317609 | + | 0.975014i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 32.4214i | 0.321004i | 0.987035 | + | 0.160502i | \(0.0513114\pi\) | ||||
−0.987035 | + | 0.160502i | \(0.948689\pi\) | |||||||
\(102\) | 0.442534 | − | 27.1775i | 0.00433857 | − | 0.266447i | ||||
\(103\) | 37.0251i | 0.359467i | 0.983715 | + | 0.179733i | \(0.0575235\pi\) | ||||
−0.983715 | + | 0.179733i | \(0.942476\pi\) | |||||||
\(104\) | − | 75.9387i | − | 0.730180i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −80.5238 | −0.759659 | ||||||||
\(107\) | 115.551 | 1.07991 | 0.539957 | − | 0.841692i | \(-0.318440\pi\) | ||||
0.539957 | + | 0.841692i | \(0.318440\pi\) | |||||||
\(108\) | −1.56566 | + | 32.0281i | −0.0144968 | + | 0.296557i | ||||
\(109\) | −74.6098 | −0.684494 | −0.342247 | − | 0.939610i | \(-0.611188\pi\) | ||||
−0.342247 | + | 0.939610i | \(0.611188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −57.9380 | − | 0.943409i | −0.521964 | − | 0.00849918i | ||||
\(112\) | − | 9.70209i | − | 0.0866258i | ||||||
\(113\) | −162.240 | −1.43575 | −0.717876 | − | 0.696171i | \(-0.754885\pi\) | ||||
−0.717876 | + | 0.696171i | \(0.754885\pi\) | |||||||
\(114\) | −1.74181 | + | 106.971i | −0.0152791 | + | 0.938341i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 41.7399i | 0.359827i | ||||||||
\(117\) | −2.55771 | + | 78.5182i | −0.0218608 | + | 0.671096i | ||||
\(118\) | 157.496i | 1.33472i | ||||||||
\(119\) | 5.32757i | 0.0447695i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.84890 | 0.0483380 | ||||||||
\(122\) | −48.4939 | −0.397491 | ||||||||
\(123\) | −158.114 | − | 2.57459i | −1.28548 | − | 0.0209316i | ||||
\(124\) | −41.5306 | −0.334925 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.484559 | + | 14.8753i | −0.00384570 | + | 0.118058i | ||||
\(127\) | − | 233.536i | − | 1.83887i | −0.393244 | − | 0.919434i | \(-0.628647\pi\) | ||
0.393244 | − | 0.919434i | \(-0.371353\pi\) | |||||||
\(128\) | −44.2672 | −0.345838 | ||||||||
\(129\) | −87.4905 | − | 1.42461i | −0.678221 | − | 0.0110435i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 29.4351i | − | 0.224696i | −0.993669 | − | 0.112348i | \(-0.964163\pi\) | ||
0.993669 | − | 0.112348i | \(-0.0358371\pi\) | |||||||
\(132\) | −38.2282 | − | 0.622473i | −0.289608 | − | 0.00471570i | ||||
\(133\) | − | 20.9693i | − | 0.157664i | ||||||
\(134\) | − | 152.446i | − | 1.13766i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 47.0020 | 0.345603 | ||||||||
\(137\) | 55.3091 | 0.403716 | 0.201858 | − | 0.979415i | \(-0.435302\pi\) | ||||
0.201858 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(138\) | 2.76971 | − | 170.098i | 0.0200704 | − | 1.23259i | ||||
\(139\) | −183.499 | −1.32014 | −0.660069 | − | 0.751205i | \(-0.729473\pi\) | ||||
−0.660069 | + | 0.751205i | \(0.729473\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.57606 | + | 158.205i | −0.0182700 | + | 1.12202i | ||||
\(142\) | 213.993i | 1.50699i | ||||||||
\(143\) | −93.6682 | −0.655022 | ||||||||
\(144\) | 88.5034 | + | 2.88298i | 0.614607 | + | 0.0200207i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 164.134i | 1.12421i | ||||||||
\(147\) | −2.34580 | + | 144.064i | −0.0159578 | + | 0.980026i | ||||
\(148\) | − | 22.9396i | − | 0.154998i | ||||||
\(149\) | 69.5256i | 0.466615i | 0.972403 | + | 0.233307i | \(0.0749548\pi\) | ||||
−0.972403 | + | 0.233307i | \(0.925045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.62107 | −0.0637157 | −0.0318578 | − | 0.999492i | \(-0.510142\pi\) | ||||
−0.0318578 | + | 0.999492i | \(0.510142\pi\) | |||||||
\(152\) | −185.000 | −1.21711 | ||||||||
\(153\) | −48.5986 | − | 1.58309i | −0.317638 | − | 0.0103470i | ||||
\(154\) | −17.7454 | −0.115230 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −31.0963 | − | 0.506342i | −0.199335 | − | 0.00324579i | ||||
\(157\) | − | 231.458i | − | 1.47425i | −0.675755 | − | 0.737126i | \(-0.736182\pi\) | ||
0.675755 | − | 0.737126i | \(-0.263818\pi\) | |||||||
\(158\) | −70.0868 | −0.443587 | ||||||||
\(159\) | −2.34525 | + | 144.030i | −0.0147500 | + | 0.905849i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.3439i | 0.207105i | ||||||||
\(162\) | −135.550 | − | 8.84038i | −0.836726 | − | 0.0545703i | ||||
\(163\) | − | 237.273i | − | 1.45566i | −0.685757 | − | 0.727830i | \(-0.740529\pi\) | ||
0.685757 | − | 0.727830i | \(-0.259471\pi\) | |||||||
\(164\) | − | 62.6028i | − | 0.381725i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 163.183 | 0.983030 | ||||||||
\(167\) | 54.5204 | 0.326470 | 0.163235 | − | 0.986587i | \(-0.447807\pi\) | ||||
0.163235 | + | 0.986587i | \(0.447807\pi\) | |||||||
\(168\) | −25.7328 | − | 0.419009i | −0.153171 | − | 0.00249410i | ||||
\(169\) | 92.8068 | 0.549153 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 191.284 | + | 6.23104i | 1.11862 | + | 0.0364388i | ||||
\(172\) | − | 34.6404i | − | 0.201398i | ||||||
\(173\) | 207.155 | 1.19743 | 0.598713 | − | 0.800963i | \(-0.295679\pi\) | ||||
0.598713 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(174\) | −176.792 | − | 2.87872i | −1.01605 | − | 0.0165444i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 105.580i | 0.599886i | ||||||||
\(177\) | 281.708 | + | 4.58707i | 1.59157 | + | 0.0259157i | ||||
\(178\) | 147.128i | 0.826561i | ||||||||
\(179\) | − | 62.7827i | − | 0.350741i | −0.984502 | − | 0.175371i | \(-0.943888\pi\) | ||
0.984502 | − | 0.175371i | \(-0.0561124\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −139.836 | −0.772574 | −0.386287 | − | 0.922379i | \(-0.626242\pi\) | ||||
−0.386287 | + | 0.922379i | \(0.626242\pi\) | |||||||
\(182\) | −14.4348 | −0.0793121 | ||||||||
\(183\) | −1.41238 | + | 86.7392i | −0.00771793 | + | 0.473985i | ||||
\(184\) | 294.174 | 1.59877 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.86429 | − | 175.906i | 0.0153994 | − | 0.945732i | ||||
\(187\) | − | 57.9756i | − | 0.310030i | ||||||
\(188\) | −62.6387 | −0.333185 | ||||||||
\(189\) | 26.5927 | + | 1.29995i | 0.140702 | + | 0.00687806i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 163.827i | − | 0.857732i | −0.903368 | − | 0.428866i | \(-0.858913\pi\) | ||
0.903368 | − | 0.428866i | \(-0.141087\pi\) | |||||||
\(192\) | −3.42110 | + | 210.102i | −0.0178182 | + | 1.09428i | ||||
\(193\) | 312.575i | 1.61956i | 0.586732 | + | 0.809781i | \(0.300414\pi\) | ||||
−0.586732 | + | 0.809781i | \(0.699586\pi\) | |||||||
\(194\) | − | 142.620i | − | 0.735154i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −57.0397 | −0.291019 | ||||||||
\(197\) | 203.833 | 1.03469 | 0.517343 | − | 0.855778i | \(-0.326921\pi\) | ||||
0.517343 | + | 0.855778i | \(0.326921\pi\) | |||||||
\(198\) | 5.27306 | − | 161.876i | 0.0266316 | − | 0.817554i | ||||
\(199\) | 151.879 | 0.763212 | 0.381606 | − | 0.924325i | \(-0.375371\pi\) | ||||
0.381606 | + | 0.924325i | \(0.375371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −272.674 | − | 4.43998i | −1.35659 | − | 0.0220894i | ||||
\(202\) | − | 54.3710i | − | 0.269163i | ||||||
\(203\) | 34.6563 | 0.170721 | ||||||||
\(204\) | 0.313399 | − | 19.2469i | 0.00153627 | − | 0.0943477i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 62.0914i | − | 0.301414i | ||||||
\(207\) | −304.167 | − | 9.90816i | −1.46940 | − | 0.0478655i | ||||
\(208\) | 85.8827i | 0.412898i | ||||||||
\(209\) | 228.192i | 1.09183i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −220.231 | −1.04375 | −0.521875 | − | 0.853022i | \(-0.674767\pi\) | ||||
−0.521875 | + | 0.853022i | \(0.674767\pi\) | |||||||
\(212\) | −57.0264 | −0.268992 | ||||||||
\(213\) | 382.761 | + | 6.23252i | 1.79700 | + | 0.0292607i | ||||
\(214\) | −193.780 | −0.905513 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.4687 | − | 234.612i | 0.0530960 | − | 1.08617i | ||||
\(217\) | 34.4826i | 0.158906i | ||||||||
\(218\) | 125.121 | 0.573951 | ||||||||
\(219\) | 293.581 | + | 4.78039i | 1.34055 | + | 0.0218283i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 47.1595i | − | 0.213392i | ||||||
\(222\) | 97.1626 | + | 1.58210i | 0.437669 | + | 0.00712660i | ||||
\(223\) | − | 263.520i | − | 1.18170i | −0.806781 | − | 0.590851i | \(-0.798792\pi\) | ||
0.806781 | − | 0.590851i | \(-0.201208\pi\) | |||||||
\(224\) | − | 18.0444i | − | 0.0805555i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 272.078 | 1.20388 | ||||||||
\(227\) | −140.571 | −0.619257 | −0.309628 | − | 0.950858i | \(-0.600205\pi\) | ||||
−0.309628 | + | 0.950858i | \(0.600205\pi\) | |||||||
\(228\) | −1.23354 | + | 75.7560i | −0.00541026 | + | 0.332263i | ||||
\(229\) | 253.095 | 1.10522 | 0.552610 | − | 0.833440i | \(-0.313632\pi\) | ||||
0.552610 | + | 0.833440i | \(0.313632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.516835 | + | 31.7406i | −0.00223738 | + | 0.137405i | ||||
\(232\) | − | 305.753i | − | 1.31790i | ||||||
\(233\) | 316.754 | 1.35946 | 0.679730 | − | 0.733463i | \(-0.262097\pi\) | ||||
0.679730 | + | 0.733463i | \(0.262097\pi\) | |||||||
\(234\) | 4.28930 | − | 131.676i | 0.0183304 | − | 0.562716i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 111.538i | 0.472618i | ||||||||
\(237\) | −2.04127 | + | 125.362i | −0.00861296 | + | 0.528952i | ||||
\(238\) | − | 8.93438i | − | 0.0375394i | ||||||
\(239\) | 65.1454i | 0.272575i | 0.990669 | + | 0.136287i | \(0.0435171\pi\) | ||||
−0.990669 | + | 0.136287i | \(0.956483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 177.015 | 0.734501 | 0.367250 | − | 0.930122i | \(-0.380299\pi\) | ||||
0.367250 | + | 0.930122i | \(0.380299\pi\) | |||||||
\(242\) | −9.80865 | −0.0405316 | ||||||||
\(243\) | −19.7603 | + | 242.195i | −0.0813183 | + | 0.996688i | ||||
\(244\) | −34.3430 | −0.140750 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 265.159 | + | 4.31760i | 1.07788 | + | 0.0175512i | ||||
\(247\) | 185.620i | 0.751498i | ||||||||
\(248\) | 304.220 | 1.22669 | ||||||||
\(249\) | 4.75269 | − | 291.879i | 0.0190871 | − | 1.17221i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 480.997i | − | 1.91632i | −0.286227 | − | 0.958162i | \(-0.592401\pi\) | ||
0.286227 | − | 0.958162i | \(-0.407599\pi\) | |||||||
\(252\) | −0.343161 | + | 10.5346i | −0.00136175 | + | 0.0418038i | ||||
\(253\) | − | 362.855i | − | 1.43421i | ||||||
\(254\) | 391.642i | 1.54190i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −205.936 | −0.804438 | ||||||||
\(257\) | 228.740 | 0.890037 | 0.445019 | − | 0.895521i | \(-0.353197\pi\) | ||||
0.445019 | + | 0.895521i | \(0.353197\pi\) | |||||||
\(258\) | 146.722 | + | 2.38909i | 0.568691 | + | 0.00926003i | ||||
\(259\) | −19.0466 | −0.0735390 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.2981 | + | 316.138i | −0.0394564 | + | 1.21126i | ||||
\(262\) | 49.3630i | 0.188408i | ||||||||
\(263\) | −161.703 | −0.614839 | −0.307419 | − | 0.951574i | \(-0.599465\pi\) | ||||
−0.307419 | + | 0.951574i | \(0.599465\pi\) | |||||||
\(264\) | 280.029 | + | 4.55973i | 1.06072 | + | 0.0172717i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 35.1657i | 0.132202i | ||||||||
\(267\) | 263.162 | + | 4.28509i | 0.985627 | + | 0.0160490i | ||||
\(268\) | − | 107.961i | − | 0.402840i | ||||||
\(269\) | − | 27.1313i | − | 0.100860i | −0.998728 | − | 0.0504299i | \(-0.983941\pi\) | ||
0.998728 | − | 0.0504299i | \(-0.0160591\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −46.0453 | −0.169909 | −0.0849544 | − | 0.996385i | \(-0.527074\pi\) | ||||
−0.0849544 | + | 0.996385i | \(0.527074\pi\) | |||||||
\(272\) | −53.1568 | −0.195430 | ||||||||
\(273\) | −0.420413 | + | 25.8190i | −0.00153997 | + | 0.0945751i | ||||
\(274\) | −92.7537 | −0.338517 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.96149 | − | 120.462i | 0.00710684 | − | 0.436456i | ||||
\(277\) | − | 93.7155i | − | 0.338323i | −0.985588 | − | 0.169162i | \(-0.945894\pi\) | ||
0.985588 | − | 0.169162i | \(-0.0541060\pi\) | |||||||
\(278\) | 307.730 | 1.10694 | ||||||||
\(279\) | −314.553 | − | 10.2465i | −1.12743 | − | 0.0367258i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 194.543i | 0.692325i | 0.938175 | + | 0.346162i | \(0.112515\pi\) | ||||
−0.938175 | + | 0.346162i | \(0.887485\pi\) | |||||||
\(282\) | 4.32008 | − | 265.311i | 0.0153194 | − | 0.940819i | ||||
\(283\) | 201.513i | 0.712061i | 0.934474 | + | 0.356031i | \(0.115870\pi\) | ||||
−0.934474 | + | 0.356031i | \(0.884130\pi\) | |||||||
\(284\) | 151.548i | 0.533620i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 157.082 | 0.549239 | ||||||||
\(287\) | −51.9787 | −0.181110 | ||||||||
\(288\) | 164.603 | + | 5.36191i | 0.571538 | + | 0.0186177i | ||||
\(289\) | −259.811 | −0.898999 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −255.099 | − | 4.15379i | −0.876628 | − | 0.0142742i | ||||
\(292\) | 116.238i | 0.398077i | ||||||||
\(293\) | 401.132 | 1.36905 | 0.684526 | − | 0.728988i | \(-0.260009\pi\) | ||||
0.684526 | + | 0.728988i | \(0.260009\pi\) | |||||||
\(294\) | 3.93393 | − | 241.596i | 0.0133807 | − | 0.821755i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 168.037i | 0.567693i | ||||||||
\(297\) | −289.387 | − | 14.1463i | −0.974368 | − | 0.0476308i | ||||
\(298\) | − | 116.595i | − | 0.391258i | ||||||
\(299\) | − | 295.160i | − | 0.987157i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.7617 | −0.0955538 | ||||||||
\(302\) | 16.1346 | 0.0534259 | ||||||||
\(303\) | −97.2514 | − | 1.58355i | −0.320962 | − | 0.00522624i | ||||
\(304\) | 209.225 | 0.688242 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 81.5002 | + | 2.65485i | 0.266341 | + | 0.00867598i | ||||
\(307\) | 305.937i | 0.996538i | 0.867023 | + | 0.498269i | \(0.166031\pi\) | ||||
−0.867023 | + | 0.498269i | \(0.833969\pi\) | |||||||
\(308\) | −12.5672 | −0.0408026 | ||||||||
\(309\) | −111.061 | − | 1.80841i | −0.359419 | − | 0.00585245i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 248.920i | 0.800387i | 0.916431 | + | 0.400193i | \(0.131057\pi\) | ||||
−0.916431 | + | 0.400193i | \(0.868943\pi\) | |||||||
\(312\) | 227.786 | + | 3.70906i | 0.730083 | + | 0.0118880i | ||||
\(313\) | − | 40.3421i | − | 0.128889i | −0.997921 | − | 0.0644443i | \(-0.979473\pi\) | ||
0.997921 | − | 0.0644443i | \(-0.0205275\pi\) | |||||||
\(314\) | 388.156i | 1.23617i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −49.6349 | −0.157072 | ||||||||
\(317\) | −302.546 | −0.954405 | −0.477203 | − | 0.878793i | \(-0.658349\pi\) | ||||
−0.477203 | + | 0.878793i | \(0.658349\pi\) | |||||||
\(318\) | 3.93300 | − | 241.539i | 0.0123679 | − | 0.759558i | ||||
\(319\) | −377.137 | −1.18225 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.64382 | + | 346.607i | −0.0175820 | + | 1.07977i | ||||
\(322\) | − | 55.9181i | − | 0.173659i | ||||||
\(323\) | −114.889 | −0.355693 | ||||||||
\(324\) | −95.9952 | − | 6.26069i | −0.296282 | − | 0.0193231i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 397.908i | 1.22058i | ||||||||
\(327\) | 3.64415 | − | 223.800i | 0.0111442 | − | 0.684403i | ||||
\(328\) | 458.578i | 1.39810i | ||||||||
\(329\) | 52.0085i | 0.158080i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.13884 | −0.0215675 | −0.0107837 | − | 0.999942i | \(-0.503433\pi\) | ||||
−0.0107837 | + | 0.999942i | \(0.503433\pi\) | |||||||
\(332\) | 115.565 | 0.348087 | ||||||||
\(333\) | 5.65970 | − | 173.745i | 0.0169961 | − | 0.521757i | ||||
\(334\) | −91.4312 | −0.273746 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 29.1024 | + | 0.473877i | 0.0866143 | + | 0.00141035i | ||||
\(337\) | 65.3823i | 0.194013i | 0.995284 | + | 0.0970064i | \(0.0309267\pi\) | ||||
−0.995284 | + | 0.0970064i | \(0.969073\pi\) | |||||||
\(338\) | −155.638 | −0.460467 | ||||||||
\(339\) | 7.92424 | − | 486.655i | 0.0233753 | − | 1.43556i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 375.246i | − | 1.10043i | ||||||
\(342\) | −320.785 | − | 10.4495i | −0.937968 | − | 0.0305541i | ||||
\(343\) | 95.6782i | 0.278945i | ||||||||
\(344\) | 253.748i | 0.737639i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −347.400 | −1.00405 | ||||||||
\(347\) | −110.933 | −0.319691 | −0.159845 | − | 0.987142i | \(-0.551100\pi\) | ||||
−0.159845 | + | 0.987142i | \(0.551100\pi\) | |||||||
\(348\) | −125.203 | − | 2.03869i | −0.359779 | − | 0.00585830i | ||||
\(349\) | −0.246730 | −0.000706961 | −0.000353481 | − | 1.00000i | \(-0.500113\pi\) | ||||
−0.000353481 | 1.00000i | \(0.500113\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −235.398 | − | 11.5072i | −0.670651 | − | 0.0327839i | ||||
\(352\) | 196.363i | 0.557849i | ||||||||
\(353\) | 85.7892 | 0.243029 | 0.121515 | − | 0.992590i | \(-0.461225\pi\) | ||||
0.121515 | + | 0.992590i | \(0.461225\pi\) | |||||||
\(354\) | −472.427 | − | 7.69256i | −1.33454 | − | 0.0217304i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 104.195i | 0.292682i | ||||||||
\(357\) | −15.9806 | − | 0.260213i | −0.0447636 | − | 0.000728888i | ||||
\(358\) | 105.287i | 0.294098i | ||||||||
\(359\) | 638.603i | 1.77884i | 0.457091 | + | 0.889420i | \(0.348891\pi\) | ||||
−0.457091 | + | 0.889420i | \(0.651109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 91.2034 | 0.252641 | ||||||||
\(362\) | 234.506 | 0.647806 | ||||||||
\(363\) | −0.285676 | + | 17.5444i | −0.000786987 | + | 0.0483316i | ||||
\(364\) | −10.2226 | −0.0280841 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.36857 | − | 145.462i | 0.00647151 | − | 0.397438i | ||||
\(367\) | − | 254.118i | − | 0.692419i | −0.938157 | − | 0.346209i | \(-0.887469\pi\) | ||
0.938157 | − | 0.346209i | \(-0.112531\pi\) | |||||||
\(368\) | −332.695 | −0.904064 | ||||||||
\(369\) | 15.4455 | − | 474.155i | 0.0418577 | − | 1.28497i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.3486i | 0.127624i | ||||||||
\(372\) | 2.02847 | − | 124.575i | 0.00545288 | − | 0.334880i | ||||
\(373\) | 436.515i | 1.17028i | 0.810932 | + | 0.585141i | \(0.198961\pi\) | ||||
−0.810932 | + | 0.585141i | \(0.801039\pi\) | |||||||
\(374\) | 97.2256i | 0.259961i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 458.841 | 1.22032 | ||||||||
\(377\) | −306.777 | −0.813732 | ||||||||
\(378\) | −44.5962 | − | 2.18003i | −0.117979 | − | 0.00576728i | ||||
\(379\) | 269.326 | 0.710624 | 0.355312 | − | 0.934748i | \(-0.384375\pi\) | ||||
0.355312 | + | 0.934748i | \(0.384375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 700.516 | + | 11.4065i | 1.83862 | + | 0.0299384i | ||||
\(382\) | 274.739i | 0.719211i | ||||||||
\(383\) | −630.454 | −1.64609 | −0.823047 | − | 0.567974i | \(-0.807727\pi\) | ||||
−0.823047 | + | 0.567974i | \(0.807727\pi\) | |||||||
\(384\) | 2.16213 | − | 132.784i | 0.00563055 | − | 0.345792i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 524.191i | − | 1.35801i | ||||||
\(387\) | 8.54655 | − | 262.367i | 0.0220841 | − | 0.677951i | ||||
\(388\) | − | 101.002i | − | 0.260315i | ||||||
\(389\) | 61.9695i | 0.159305i | 0.996823 | + | 0.0796523i | \(0.0253810\pi\) | ||||
−0.996823 | + | 0.0796523i | \(0.974619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 182.688 | 0.467233 | ||||||||
\(392\) | 417.827 | 1.06588 | ||||||||
\(393\) | 88.2937 | + | 1.43769i | 0.224666 | + | 0.00365825i | ||||
\(394\) | −341.830 | −0.867588 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.73434 | − | 114.639i | 0.00943016 | − | 0.289493i | ||||
\(397\) | 511.967i | 1.28959i | 0.764356 | + | 0.644794i | \(0.223057\pi\) | ||||
−0.764356 | + | 0.644794i | \(0.776943\pi\) | |||||||
\(398\) | −254.703 | −0.639956 | ||||||||
\(399\) | 62.8997 | + | 1.02420i | 0.157643 | + | 0.00256692i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 403.443i | − | 1.00609i | −0.864260 | − | 0.503046i | \(-0.832213\pi\) | ||
0.864260 | − | 0.503046i | \(-0.167787\pi\) | |||||||
\(402\) | 457.277 | + | 7.44588i | 1.13751 | + | 0.0185221i | ||||
\(403\) | − | 305.239i | − | 0.757417i | ||||||
\(404\) | − | 38.5051i | − | 0.0953097i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −58.1189 | −0.143150 | ||||||||
\(407\) | 207.269 | 0.509260 | ||||||||
\(408\) | −2.29571 | + | 140.987i | −0.00562674 | + | 0.345557i | ||||
\(409\) | −203.296 | −0.497057 | −0.248528 | − | 0.968625i | \(-0.579947\pi\) | ||||
−0.248528 | + | 0.968625i | \(0.579947\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.70145 | + | 165.905i | −0.00657286 | + | 0.403662i | ||||
\(412\) | − | 43.9726i | − | 0.106730i | ||||||
\(413\) | 92.6090 | 0.224235 | ||||||||
\(414\) | 510.090 | + | 16.6161i | 1.23210 | + | 0.0401354i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 159.729i | 0.383964i | ||||||||
\(417\) | 8.96260 | − | 550.424i | 0.0214930 | − | 1.31996i | ||||
\(418\) | − | 382.680i | − | 0.915503i | ||||||
\(419\) | − | 63.4056i | − | 0.151326i | −0.997133 | − | 0.0756630i | \(-0.975893\pi\) | ||
0.997133 | − | 0.0756630i | \(-0.0241073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −666.311 | −1.58269 | −0.791344 | − | 0.611371i | \(-0.790618\pi\) | ||||
−0.791344 | + | 0.611371i | \(0.790618\pi\) | |||||||
\(422\) | 369.329 | 0.875188 | ||||||||
\(423\) | −474.426 | − | 15.4543i | −1.12158 | − | 0.0365351i | ||||
\(424\) | 417.729 | 0.985210 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −641.893 | − | 10.4520i | −1.50679 | − | 0.0245352i | ||||
\(427\) | 28.5147i | 0.0667793i | ||||||||
\(428\) | −137.233 | −0.320639 | ||||||||
\(429\) | 4.57501 | − | 280.967i | 0.0106644 | − | 0.654935i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 582.760i | − | 1.35211i | −0.736851 | − | 0.676055i | \(-0.763688\pi\) | ||
0.736851 | − | 0.676055i | \(-0.236312\pi\) | |||||||
\(432\) | −12.9705 | + | 265.334i | −0.0300244 | + | 0.614199i | ||||
\(433\) | − | 756.314i | − | 1.74668i | −0.487109 | − | 0.873341i | \(-0.661949\pi\) | ||
0.487109 | − | 0.873341i | \(-0.338051\pi\) | |||||||
\(434\) | − | 57.8276i | − | 0.133243i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 88.6099 | 0.203234 | ||||||||
\(437\) | −719.062 | −1.64545 | ||||||||
\(438\) | −492.337 | − | 8.01676i | −1.12406 | − | 0.0183031i | ||||
\(439\) | 243.610 | 0.554921 | 0.277461 | − | 0.960737i | \(-0.410507\pi\) | ||||
0.277461 | + | 0.960737i | \(0.410507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −432.019 | − | 14.0729i | −0.979636 | − | 0.0319114i | ||||
\(442\) | 79.0869i | 0.178930i | ||||||||
\(443\) | −719.320 | −1.62375 | −0.811874 | − | 0.583833i | \(-0.801552\pi\) | ||||
−0.811874 | + | 0.583833i | \(0.801552\pi\) | |||||||
\(444\) | 68.8098 | + | 1.12043i | 0.154977 | + | 0.00252350i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 441.924i | 0.990862i | ||||||||
\(447\) | −208.549 | − | 3.39582i | −0.466553 | − | 0.00759692i | ||||
\(448\) | 69.0690i | 0.154172i | ||||||||
\(449\) | 509.284i | 1.13426i | 0.823628 | + | 0.567131i | \(0.191947\pi\) | ||||
−0.823628 | + | 0.567131i | \(0.808053\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 565.642 | 1.25420 | ||||||||
\(452\) | 192.683 | 0.426290 | ||||||||
\(453\) | 0.469919 | − | 28.8594i | 0.00103735 | − | 0.0637073i | ||||
\(454\) | 235.739 | 0.519249 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.03592 | − | 554.927i | 0.0198156 | − | 1.21695i | ||||
\(457\) | 220.079i | 0.481573i | 0.970578 | + | 0.240786i | \(0.0774053\pi\) | ||||
−0.970578 | + | 0.240786i | \(0.922595\pi\) | |||||||
\(458\) | −424.443 | −0.926731 | ||||||||
\(459\) | 7.12232 | − | 145.699i | 0.0155170 | − | 0.317427i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 75.3071i | − | 0.163356i | −0.996659 | − | 0.0816779i | \(-0.973972\pi\) | ||
0.996659 | − | 0.0816779i | \(-0.0260279\pi\) | |||||||
\(462\) | 0.866736 | − | 53.2293i | 0.00187605 | − | 0.115215i | ||||
\(463\) | 832.748i | 1.79859i | 0.437342 | + | 0.899295i | \(0.355920\pi\) | ||||
−0.437342 | + | 0.899295i | \(0.644080\pi\) | |||||||
\(464\) | 345.790i | 0.745237i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −531.199 | −1.13991 | ||||||||
\(467\) | −322.907 | −0.691451 | −0.345725 | − | 0.938336i | \(-0.612367\pi\) | ||||
−0.345725 | + | 0.938336i | \(0.612367\pi\) | |||||||
\(468\) | 3.03765 | − | 93.2517i | 0.00649071 | − | 0.199256i | ||||
\(469\) | −89.6393 | −0.191129 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 694.281 | + | 11.3050i | 1.47406 | + | 0.0240022i | ||||
\(472\) | − | 817.036i | − | 1.73101i | ||||||
\(473\) | 312.990 | 0.661713 | ||||||||
\(474\) | 3.42323 | − | 210.232i | 0.00722200 | − | 0.443528i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.32726i | − | 0.0132926i | ||||||
\(477\) | −431.918 | − | 14.0696i | −0.905489 | − | 0.0294961i | ||||
\(478\) | − | 109.249i | − | 0.228555i | ||||||
\(479\) | − | 12.5420i | − | 0.0261836i | −0.999914 | − | 0.0130918i | \(-0.995833\pi\) | ||
0.999914 | − | 0.0130918i | \(-0.00416737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 168.600 | 0.350520 | ||||||||
\(482\) | −296.855 | −0.615882 | ||||||||
\(483\) | −100.019 | − | 1.62861i | −0.207078 | − | 0.00337186i | ||||
\(484\) | −6.94641 | −0.0143521 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 33.1382 | − | 406.163i | 0.0681857 | − | 0.835727i | ||||
\(487\) | 391.799i | 0.804515i | 0.915526 | + | 0.402258i | \(0.131774\pi\) | ||||
−0.915526 | + | 0.402258i | \(0.868226\pi\) | |||||||
\(488\) | 251.569 | 0.515510 | ||||||||
\(489\) | 711.724 | + | 11.5890i | 1.45547 | + | 0.0236995i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 501.930i | 1.02226i | 0.859503 | + | 0.511130i | \(0.170773\pi\) | ||||
−0.859503 | + | 0.511130i | \(0.829227\pi\) | |||||||
\(492\) | 187.784 | + | 3.05769i | 0.381674 | + | 0.00621482i | ||||
\(493\) | − | 189.879i | − | 0.385149i | ||||||
\(494\) | − | 311.286i | − | 0.630134i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −344.057 | −0.693662 | ||||||||
\(497\) | 125.829 | 0.253178 | ||||||||
\(498\) | −7.97030 | + | 489.484i | −0.0160046 | + | 0.982900i | ||||
\(499\) | 444.402 | 0.890585 | 0.445293 | − | 0.895385i | \(-0.353100\pi\) | ||||
0.445293 | + | 0.895385i | \(0.353100\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.66293 | + | 163.540i | −0.00531522 | + | 0.326426i | ||||
\(502\) | 806.636i | 1.60685i | ||||||||
\(503\) | −624.696 | −1.24194 | −0.620971 | − | 0.783834i | \(-0.713261\pi\) | ||||
−0.620971 | + | 0.783834i | \(0.713261\pi\) | |||||||
\(504\) | 2.51372 | − | 77.1676i | 0.00498754 | − | 0.153110i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 608.511i | 1.20259i | ||||||||
\(507\) | −4.53294 | + | 278.384i | −0.00894071 | + | 0.549080i | ||||
\(508\) | 277.358i | 0.545980i | ||||||||
\(509\) | − | 127.740i | − | 0.250962i | −0.992096 | − | 0.125481i | \(-0.959953\pi\) | ||
0.992096 | − | 0.125481i | \(-0.0400474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 96.5120 | 0.188869 | ||||||||
\(512\) | 522.425 | 1.02036 | ||||||||
\(513\) | −28.0335 | + | 573.472i | −0.0546462 | + | 1.11788i | ||||
\(514\) | −383.598 | −0.746300 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 103.908 | + | 1.69193i | 0.201371 | + | 0.00327894i | ||||
\(517\) | − | 565.966i | − | 1.09471i | ||||||
\(518\) | 31.9413 | 0.0616628 | ||||||||
\(519\) | −10.1180 | + | 621.382i | −0.0194952 | + | 1.19727i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 813.374i | − | 1.56118i | −0.625044 | − | 0.780589i | \(-0.714919\pi\) | ||
0.625044 | − | 0.780589i | \(-0.285081\pi\) | |||||||
\(522\) | 17.2700 | − | 530.166i | 0.0330844 | − | 1.01564i | ||||
\(523\) | 170.814i | 0.326605i | 0.986576 | + | 0.163303i | \(0.0522147\pi\) | ||||
−0.986576 | + | 0.163303i | \(0.947785\pi\) | |||||||
\(524\) | 34.9585i | 0.0667146i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 271.177 | 0.515545 | ||||||||
\(527\) | 188.927 | 0.358495 | ||||||||
\(528\) | −316.698 | − | 5.15682i | −0.599807 | − | 0.00976670i | ||||
\(529\) | 614.401 | 1.16144 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.5188 | + | 844.788i | −0.0518245 | + | 1.59094i | ||||
\(532\) | 24.9041i | 0.0468122i | ||||||||
\(533\) | 460.114 | 0.863254 | ||||||||
\(534\) | −441.325 | − | 7.18613i | −0.826452 | − | 0.0134572i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 790.835i | 1.47544i | ||||||||
\(537\) | 188.323 | + | 3.06648i | 0.350695 | + | 0.00571038i | ||||
\(538\) | 45.4993i | 0.0845713i | ||||||||
\(539\) | − | 515.377i | − | 0.956173i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 418.188 | 0.772990 | 0.386495 | − | 0.922291i | \(-0.373686\pi\) | ||||
0.386495 | + | 0.922291i | \(0.373686\pi\) | |||||||
\(542\) | 77.2183 | 0.142469 | ||||||||
\(543\) | 6.82996 | − | 419.452i | 0.0125782 | − | 0.772471i | ||||
\(544\) | −98.8637 | −0.181735 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.705035 | − | 43.2987i | 0.00129127 | − | 0.0793016i | ||||
\(547\) | − | 515.125i | − | 0.941728i | −0.882206 | − | 0.470864i | \(-0.843942\pi\) | ||
0.882206 | − | 0.470864i | \(-0.156058\pi\) | |||||||
\(548\) | −65.6875 | −0.119868 | ||||||||
\(549\) | −260.114 | − | 8.47316i | −0.473796 | − | 0.0154338i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 747.363i | 1.35638i | ||||||||
\(552\) | −14.3683 | + | 882.406i | −0.0260295 | + | 1.59856i | ||||
\(553\) | 41.2115i | 0.0745235i | ||||||||
\(554\) | 157.162i | 0.283685i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 217.932 | 0.391963 | ||||||||
\(557\) | −688.047 | −1.23527 | −0.617637 | − | 0.786464i | \(-0.711910\pi\) | ||||
−0.617637 | + | 0.786464i | \(0.711910\pi\) | |||||||
\(558\) | 527.509 | + | 17.1835i | 0.945356 | + | 0.0307948i | ||||
\(559\) | 254.598 | 0.455453 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 173.904 | + | 2.83169i | 0.309989 | + | 0.00504757i | ||||
\(562\) | − | 326.251i | − | 0.580517i | ||||||
\(563\) | −523.680 | −0.930159 | −0.465079 | − | 0.885269i | \(-0.653974\pi\) | ||||
−0.465079 | + | 0.885269i | \(0.653974\pi\) | |||||||
\(564\) | 3.05945 | − | 187.891i | 0.00542455 | − | 0.333141i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 337.939i | − | 0.597066i | ||||||
\(567\) | −5.19821 | + | 79.7042i | −0.00916791 | + | 0.140572i | ||||
\(568\) | − | 1110.12i | − | 1.95443i | ||||||
\(569\) | 1008.79i | 1.77291i | 0.462811 | + | 0.886457i | \(0.346841\pi\) | ||||
−0.462811 | + | 0.886457i | \(0.653159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −142.897 | −0.250257 | −0.125129 | − | 0.992141i | \(-0.539934\pi\) | ||||
−0.125129 | + | 0.992141i | \(0.539934\pi\) | |||||||
\(572\) | 111.244 | 0.194483 | ||||||||
\(573\) | 491.415 | + | 8.00175i | 0.857618 | + | 0.0139647i | ||||
\(574\) | 87.1687 | 0.151862 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −630.054 | − | 20.5239i | −1.09384 | − | 0.0356317i | ||||
\(577\) | − | 175.636i | − | 0.304394i | −0.988350 | − | 0.152197i | \(-0.951365\pi\) | ||
0.988350 | − | 0.152197i | \(-0.0486349\pi\) | |||||||
\(578\) | 435.705 | 0.753814 | ||||||||
\(579\) | −937.602 | − | 15.2670i | −1.61935 | − | 0.0263679i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 95.9527i | − | 0.165151i | ||||||
\(582\) | 427.803 | + | 6.96594i | 0.735056 | + | 0.0119690i | ||||
\(583\) | − | 515.256i | − | 0.883802i | ||||||
\(584\) | − | 851.469i | − | 1.45799i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −672.702 | −1.14796 | ||||||||
\(587\) | −523.786 | −0.892311 | −0.446155 | − | 0.894955i | \(-0.647207\pi\) | ||||
−0.446155 | + | 0.894955i | \(0.647207\pi\) | |||||||
\(588\) | 2.78598 | − | 171.096i | 0.00473805 | − | 0.290980i | ||||
\(589\) | −743.617 | −1.26251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.95576 | + | 611.418i | −0.0168456 | + | 1.03455i | ||||
\(592\) | − | 190.041i | − | 0.321016i | ||||||
\(593\) | 649.656 | 1.09554 | 0.547771 | − | 0.836629i | \(-0.315477\pi\) | ||||
0.547771 | + | 0.836629i | \(0.315477\pi\) | |||||||
\(594\) | 485.305 | + | 23.7235i | 0.817012 | + | 0.0399386i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 82.5717i | − | 0.138543i | ||||||
\(597\) | −7.41819 | + | 455.577i | −0.0124258 | + | 0.763111i | ||||
\(598\) | 494.985i | 0.827735i | ||||||||
\(599\) | − | 26.1406i | − | 0.0436405i | −0.999762 | − | 0.0218202i | \(-0.993054\pi\) | ||
0.999762 | − | 0.0218202i | \(-0.00694614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 233.697 | 0.388847 | 0.194423 | − | 0.980918i | \(-0.437716\pi\) | ||||
0.194423 | + | 0.980918i | \(0.437716\pi\) | |||||||
\(602\) | 48.2336 | 0.0801223 | ||||||||
\(603\) | 26.6363 | − | 817.698i | 0.0441730 | − | 1.35605i | ||||
\(604\) | 11.4264 | 0.0189179 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 163.091 | + | 2.65563i | 0.269128 | + | 0.00438223i | ||||
\(607\) | 623.998i | 1.02800i | 0.857789 | + | 0.514001i | \(0.171837\pi\) | ||||
−0.857789 | + | 0.514001i | \(0.828163\pi\) | |||||||
\(608\) | 389.128 | 0.640013 | ||||||||
\(609\) | −1.69271 | + | 103.955i | −0.00277949 | + | 0.170698i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 460.378i | − | 0.753483i | ||||||
\(612\) | 57.7178 | + | 1.88015i | 0.0943102 | + | 0.00307213i | ||||
\(613\) | 947.803i | 1.54617i | 0.634302 | + | 0.773086i | \(0.281288\pi\) | ||||
−0.634302 | + | 0.773086i | \(0.718712\pi\) | |||||||
\(614\) | − | 513.059i | − | 0.835601i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 92.0570 | 0.149443 | ||||||||
\(617\) | 429.729 | 0.696482 | 0.348241 | − | 0.937405i | \(-0.386779\pi\) | ||||
0.348241 | + | 0.937405i | \(0.386779\pi\) | |||||||
\(618\) | 186.249 | + | 3.03271i | 0.301374 | + | 0.00490730i | ||||
\(619\) | −687.130 | −1.11006 | −0.555032 | − | 0.831829i | \(-0.687294\pi\) | ||||
−0.555032 | + | 0.831829i | \(0.687294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.5769 | − | 911.895i | 0.0717824 | − | 1.46843i | ||||
\(622\) | − | 417.441i | − | 0.671128i | ||||||
\(623\) | 86.5123 | 0.138864 | ||||||||
\(624\) | −257.614 | − | 4.19475i | −0.412843 | − | 0.00672235i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 67.6541i | 0.108074i | ||||||||
\(627\) | −684.486 | − | 11.1455i | −1.09168 | − | 0.0177760i | ||||
\(628\) | 274.889i | 0.437722i | ||||||||
\(629\) | 104.355i | 0.165906i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1137.47 | −1.80265 | −0.901326 | − | 0.433141i | \(-0.857405\pi\) | ||||
−0.901326 | + | 0.433141i | \(0.857405\pi\) | |||||||
\(632\) | 363.585 | 0.575293 | ||||||||
\(633\) | 10.7567 | − | 660.606i | 0.0169932 | − | 1.04361i | ||||
\(634\) | 507.373 | 0.800273 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.78532 | − | 171.056i | 0.00437944 | − | 0.268957i | ||||
\(637\) | − | 419.227i | − | 0.658127i | ||||||
\(638\) | 632.461 | 0.991319 | ||||||||
\(639\) | −37.3902 | + | 1147.83i | −0.0585136 | + | 1.79629i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 344.531i | 0.537490i | 0.963211 | + | 0.268745i | \(0.0866089\pi\) | ||||
−0.963211 | + | 0.268745i | \(0.913391\pi\) | |||||||
\(642\) | 9.46473 | − | 581.262i | 0.0147426 | − | 0.905393i | ||||
\(643\) | 444.434i | 0.691189i | 0.938384 | + | 0.345594i | \(0.112323\pi\) | ||||
−0.938384 | + | 0.345594i | \(0.887677\pi\) | |||||||
\(644\) | − | 39.6007i | − | 0.0614918i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 192.670 | 0.298250 | ||||||||
\(647\) | −203.910 | −0.315162 | −0.157581 | − | 0.987506i | \(-0.550370\pi\) | ||||
−0.157581 | + | 0.987506i | \(0.550370\pi\) | |||||||
\(648\) | 703.183 | + | 45.8608i | 1.08516 | + | 0.0707728i | ||||
\(649\) | −1007.79 | −1.55283 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −103.434 | − | 1.68422i | −0.158885 | − | 0.00258713i | ||||
\(652\) | 281.796i | 0.432202i | ||||||||
\(653\) | 587.575 | 0.899809 | 0.449904 | − | 0.893077i | \(-0.351458\pi\) | ||||
0.449904 | + | 0.893077i | \(0.351458\pi\) | |||||||
\(654\) | −6.11127 | + | 375.314i | −0.00934444 | + | 0.573875i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 518.627i | − | 0.790590i | ||||||
\(657\) | −28.6786 | + | 880.391i | −0.0436508 | + | 1.34002i | ||||
\(658\) | − | 87.2186i | − | 0.132551i | ||||||
\(659\) | − | 1001.62i | − | 1.51991i | −0.649977 | − | 0.759954i | \(-0.725221\pi\) | ||
0.649977 | − | 0.759954i | \(-0.274779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 809.420 | 1.22454 | 0.612269 | − | 0.790650i | \(-0.290257\pi\) | ||||
0.612269 | + | 0.790650i | \(0.290257\pi\) | |||||||
\(662\) | 11.9719 | 0.0180844 | ||||||||
\(663\) | 141.460 | + | 2.30340i | 0.213363 | + | 0.00347421i | ||||
\(664\) | −846.535 | −1.27490 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.49137 | + | 291.372i | −0.0142513 | + | 0.437495i | ||||
\(667\) | − | 1188.40i | − | 1.78172i | ||||||
\(668\) | −64.7509 | −0.0969325 | ||||||||
\(669\) | 790.454 | + | 12.8710i | 1.18155 | + | 0.0192392i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 310.303i | − | 0.462449i | ||||||
\(672\) | 54.1261 | + | 0.881340i | 0.0805448 | + | 0.00131152i | ||||
\(673\) | 627.941i | 0.933047i | 0.884509 | + | 0.466523i | \(0.154494\pi\) | ||||
−0.884509 | + | 0.466523i | \(0.845506\pi\) | |||||||
\(674\) | − | 109.647i | − | 0.162680i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −110.221 | −0.163050 | ||||||||
\(677\) | 592.236 | 0.874794 | 0.437397 | − | 0.899268i | \(-0.355900\pi\) | ||||
0.437397 | + | 0.899268i | \(0.355900\pi\) | |||||||
\(678\) | −13.2890 | + | 816.125i | −0.0196003 | + | 1.20372i | ||||
\(679\) | −83.8615 | −0.123507 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.86588 | − | 421.658i | 0.0100821 | − | 0.619175i | ||||
\(682\) | 629.291i | 0.922714i | ||||||||
\(683\) | 668.583 | 0.978891 | 0.489446 | − | 0.872034i | \(-0.337199\pi\) | ||||
0.489446 | + | 0.872034i | \(0.337199\pi\) | |||||||
\(684\) | −227.178 | − | 7.40026i | −0.332131 | − | 0.0108191i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 160.453i | − | 0.233897i | ||||||
\(687\) | −12.3619 | + | 759.185i | −0.0179940 | + | 1.10507i | ||||
\(688\) | − | 286.975i | − | 0.417115i | ||||||
\(689\) | − | 419.129i | − | 0.608314i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 754.280 | 1.09158 | 0.545789 | − | 0.837923i | \(-0.316230\pi\) | ||||
0.545789 | + | 0.837923i | \(0.316230\pi\) | |||||||
\(692\) | −246.026 | −0.355529 | ||||||||
\(693\) | −95.1840 | − | 3.10060i | −0.137351 | − | 0.00447417i | ||||
\(694\) | 186.035 | 0.268062 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 917.136 | + | 14.9338i | 1.31772 | + | 0.0214566i | ||||
\(697\) | 284.786i | 0.408589i | ||||||||
\(698\) | 0.413767 | 0.000592790 | ||||||||
\(699\) | −15.4711 | + | 950.136i | −0.0221332 | + | 1.35928i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 682.125i | − | 0.973074i | −0.873660 | − | 0.486537i | \(-0.838260\pi\) | ||
0.873660 | − | 0.486537i | \(-0.161740\pi\) | |||||||
\(702\) | 394.765 | + | 19.2976i | 0.562343 | + | 0.0274895i | ||||
\(703\) | − | 410.740i | − | 0.584267i | ||||||
\(704\) | − | 751.622i | − | 1.06765i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −143.869 | −0.203781 | ||||||||
\(707\) | −31.9705 | −0.0452200 | ||||||||
\(708\) | −334.569 | − | 5.44781i | −0.472555 | − | 0.00769465i | ||||
\(709\) | 106.898 | 0.150773 | 0.0753867 | − | 0.997154i | \(-0.475981\pi\) | ||||
0.0753867 | + | 0.997154i | \(0.475981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −375.935 | − | 12.2460i | −0.528742 | − | 0.0172236i | ||||
\(712\) | − | 763.247i | − | 1.07198i | ||||||
\(713\) | 1182.45 | 1.65841 | ||||||||
\(714\) | 26.7996 | + | 0.436379i | 0.0375344 | + | 0.000611175i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 74.5635i | 0.104139i | ||||||||
\(717\) | −195.410 | − | 3.18188i | −0.272539 | − | 0.00443777i | ||||
\(718\) | − | 1070.94i | − | 1.49156i | ||||||
\(719\) | − | 172.195i | − | 0.239492i | −0.992805 | − | 0.119746i | \(-0.961792\pi\) | ||
0.992805 | − | 0.119746i | \(-0.0382081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.5102 | −0.0506382 | ||||||||
\(722\) | −152.949 | −0.211841 | ||||||||
\(723\) | −8.64588 | + | 530.974i | −0.0119583 | + | 0.734404i | ||||
\(724\) | 166.075 | 0.229386 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.479081 | − | 29.4221i | 0.000659892 | − | 0.0405263i | ||||
\(727\) | − | 501.862i | − | 0.690319i | −0.938544 | − | 0.345160i | \(-0.887825\pi\) | ||
0.938544 | − | 0.345160i | \(-0.112175\pi\) | |||||||
\(728\) | 74.8826 | 0.102861 | ||||||||
\(729\) | −725.524 | − | 71.1026i | −0.995232 | − | 0.0975345i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 157.583i | 0.215571i | ||||||||
\(732\) | 1.67741 | − | 103.015i | 0.00229154 | − | 0.140731i | ||||
\(733\) | − | 102.508i | − | 0.139847i | −0.997552 | − | 0.0699237i | \(-0.977724\pi\) | ||
0.997552 | − | 0.0699237i | \(-0.0222756\pi\) | |||||||
\(734\) | 426.157i | 0.580596i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −618.764 | −0.840712 | ||||||||
\(737\) | 975.472 | 1.32357 | ||||||||
\(738\) | −25.9022 | + | 795.161i | −0.0350978 | + | 1.07745i | ||||
\(739\) | 228.683 | 0.309449 | 0.154724 | − | 0.987958i | \(-0.450551\pi\) | ||||
0.154724 | + | 0.987958i | \(0.450551\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −556.786 | − | 9.06619i | −0.751399 | − | 0.0122351i | ||||
\(742\) | − | 79.4039i | − | 0.107013i | ||||||
\(743\) | 597.078 | 0.803605 | 0.401802 | − | 0.915726i | \(-0.368384\pi\) | ||||
0.401802 | + | 0.915726i | \(0.368384\pi\) | |||||||
\(744\) | −14.8589 | + | 912.539i | −0.0199717 | + | 1.22653i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 732.040i | − | 0.981286i | ||||||
\(747\) | 875.290 | + | 28.5124i | 1.17174 | + | 0.0381692i | ||||
\(748\) | 68.8544i | 0.0920514i | ||||||||
\(749\) | 113.944i | 0.152128i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 339.769 | 0.452422 | 0.226211 | − | 0.974078i | \(-0.427366\pi\) | ||||
0.226211 | + | 0.974078i | \(0.427366\pi\) | |||||||
\(752\) | −518.924 | −0.690059 | ||||||||
\(753\) | 1442.80 | + | 23.4932i | 1.91607 | + | 0.0311995i | ||||
\(754\) | 514.468 | 0.682318 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −31.5827 | − | 1.54388i | −0.0417761 | − | 0.00204217i | ||||
\(757\) | 244.894i | 0.323506i | 0.986831 | + | 0.161753i | \(0.0517148\pi\) | ||||
−0.986831 | + | 0.161753i | \(0.948285\pi\) | |||||||
\(758\) | −451.662 | −0.595861 | ||||||||
\(759\) | 1088.42 | + | 17.7228i | 1.43402 | + | 0.0233502i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 551.072i | − | 0.724142i | −0.932151 | − | 0.362071i | \(-0.882070\pi\) | ||
0.932151 | − | 0.362071i | \(-0.117930\pi\) | |||||||
\(762\) | −1174.77 | − | 19.1289i | −1.54169 | − | 0.0251035i | ||||
\(763\) | − | 73.5722i | − | 0.0964249i | ||||||
\(764\) | 194.568i | 0.254670i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1057.28 | 1.38026 | ||||||||
\(767\) | −819.773 | −1.06880 | ||||||||
\(768\) | 10.0585 | − | 617.727i | 0.0130970 | − | 0.804331i | ||||
\(769\) | 903.877 | 1.17539 | 0.587696 | − | 0.809082i | \(-0.300035\pi\) | ||||
0.587696 | + | 0.809082i | \(0.300035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.1723 | + | 686.128i | −0.0144906 | + | 0.889919i | ||||
\(772\) | − | 371.228i | − | 0.480866i | ||||||
\(773\) | −438.057 | −0.566697 | −0.283349 | − | 0.959017i | \(-0.591445\pi\) | ||||
−0.283349 | + | 0.959017i | \(0.591445\pi\) | |||||||
\(774\) | −14.3326 | + | 439.992i | −0.0185176 | + | 0.568465i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 739.861i | 0.953429i | ||||||||
\(777\) | 0.930289 | − | 57.1323i | 0.00119728 | − | 0.0735293i | ||||
\(778\) | − | 103.923i | − | 0.133578i | ||||||
\(779\) | − | 1120.92i | − | 1.43892i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1369.30 | −1.75326 | ||||||||
\(782\) | −306.370 | −0.391777 | ||||||||
\(783\) | −947.786 | − | 46.3314i | −1.21045 | − | 0.0591716i | ||||
\(784\) | −472.540 | −0.602730 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −148.069 | − | 2.41102i | −0.188383 | − | 0.00306746i | ||||
\(787\) | 678.254i | 0.861822i | 0.902394 | + | 0.430911i | \(0.141808\pi\) | ||||
−0.902394 | + | 0.430911i | \(0.858192\pi\) | |||||||
\(788\) | −242.081 | −0.307210 | ||||||||
\(789\) | 7.89800 | − | 485.043i | 0.0100101 | − | 0.614757i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 159.984i | − | 0.202255i | ||||||
\(792\) | −27.3548 | + | 839.753i | −0.0345388 | + | 1.06029i | ||||
\(793\) | − | 252.412i | − | 0.318300i | ||||||
\(794\) | − | 858.572i | − | 1.08133i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −180.378 | −0.226606 | ||||||||
\(797\) | −1248.06 | −1.56595 | −0.782973 | − | 0.622056i | \(-0.786298\pi\) | ||||
−0.782973 | + | 0.622056i | \(0.786298\pi\) | |||||||
\(798\) | −105.483 | − | 1.71759i | −0.132184 | − | 0.00215237i | ||||
\(799\) | 284.950 | 0.356633 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.7071 | + | 789.173i | −0.0320938 | + | 0.985235i | ||||
\(802\) | 676.577i | 0.843612i | ||||||||
\(803\) | −1050.26 | −1.30792 | ||||||||
\(804\) | 323.840 | + | 5.27311i | 0.402786 | + | 0.00655860i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 511.889i | 0.635098i | ||||||||
\(807\) | 81.3830 | + | 1.32517i | 0.100846 | + | 0.00164209i | ||||
\(808\) | 282.057i | 0.349081i | ||||||||
\(809\) | − | 351.882i | − | 0.434959i | −0.976065 | − | 0.217479i | \(-0.930216\pi\) | ||
0.976065 | − | 0.217479i | \(-0.0697835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −715.833 | −0.882654 | −0.441327 | − | 0.897346i | \(-0.645492\pi\) | ||||
−0.441327 | + | 0.897346i | \(0.645492\pi\) | |||||||
\(812\) | −41.1594 | −0.0506889 | ||||||||
\(813\) | 2.24898 | − | 138.118i | 0.00276627 | − | 0.169886i | ||||
\(814\) | −347.592 | −0.427017 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.59632 | − | 159.449i | 0.00318177 | − | 0.195404i | ||||
\(817\) | − | 620.246i | − | 0.759175i | ||||||
\(818\) | 340.929 | 0.416784 | ||||||||
\(819\) | −77.4262 | − | 2.52214i | −0.0945375 | − | 0.00307954i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1391.14i | 1.69445i | 0.531238 | + | 0.847223i | \(0.321727\pi\) | ||||
−0.531238 | + | 0.847223i | \(0.678273\pi\) | |||||||
\(822\) | 4.53035 | − | 278.224i | 0.00551137 | − | 0.338472i | ||||
\(823\) | 140.224i | 0.170382i | 0.996365 | + | 0.0851910i | \(0.0271501\pi\) | ||||
−0.996365 | + | 0.0851910i | \(0.972850\pi\) | |||||||
\(824\) | 322.108i | 0.390908i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −155.306 | −0.188022 | ||||||||
\(827\) | 926.931 | 1.12084 | 0.560418 | − | 0.828210i | \(-0.310641\pi\) | ||||
0.560418 | + | 0.828210i | \(0.310641\pi\) | |||||||
\(828\) | 361.242 | + | 11.7674i | 0.436282 | + | 0.0142118i | ||||
\(829\) | 1423.22 | 1.71679 | 0.858394 | − | 0.512991i | \(-0.171463\pi\) | ||||
0.858394 | + | 0.512991i | \(0.171463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 281.109 | + | 4.57732i | 0.338278 | + | 0.00550821i | ||||
\(832\) | − | 611.398i | − | 0.734853i | ||||||
\(833\) | 259.479 | 0.311500 | ||||||||
\(834\) | −15.0304 | + | 923.066i | −0.0180220 | + | 1.10679i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 271.011i | − | 0.324176i | ||||||
\(837\) | 46.0991 | − | 943.035i | 0.0550766 | − | 1.12668i | ||||
\(838\) | 106.332i | 0.126888i | ||||||||
\(839\) | − | 24.8412i | − | 0.0296081i | −0.999890 | − | 0.0148040i | \(-0.995288\pi\) | ||
0.999890 | − | 0.0148040i | \(-0.00471244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −394.178 | −0.468702 | ||||||||
\(842\) | 1117.41 | 1.32709 | ||||||||
\(843\) | −583.552 | − | 9.50202i | −0.692233 | − | 0.0112717i | ||||
\(844\) | 261.556 | 0.309901 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 795.617 | + | 25.9170i | 0.940445 | + | 0.0306348i | ||||
\(847\) | 5.76756i | 0.00680939i | ||||||||
\(848\) | −472.429 | −0.557110 | ||||||||
\(849\) | −604.460 | − | 9.84246i | −0.711967 | − | 0.0115930i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 653.130i | 0.767485i | ||||||||
\(852\) | −454.584 | − | 7.40202i | −0.533549 | − | 0.00868782i | ||||
\(853\) | − | 559.803i | − | 0.656275i | −0.944630 | − | 0.328138i | \(-0.893579\pi\) | ||
0.944630 | − | 0.328138i | \(-0.106421\pi\) | |||||||
\(854\) | − | 47.8195i | − | 0.0559947i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1005.26 | 1.17437 | ||||||||
\(857\) | 733.960 | 0.856429 | 0.428214 | − | 0.903677i | \(-0.359143\pi\) | ||||
0.428214 | + | 0.903677i | \(0.359143\pi\) | |||||||
\(858\) | −7.67233 | + | 471.184i | −0.00894211 | + | 0.549166i | ||||
\(859\) | 359.689 | 0.418730 | 0.209365 | − | 0.977838i | \(-0.432860\pi\) | ||||
0.209365 | + | 0.977838i | \(0.432860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.53878 | − | 155.915i | 0.00294864 | − | 0.181086i | ||||
\(862\) | 977.292i | 1.13375i | ||||||||
\(863\) | −867.952 | −1.00574 | −0.502869 | − | 0.864362i | \(-0.667722\pi\) | ||||
−0.502869 | + | 0.864362i | \(0.667722\pi\) | |||||||
\(864\) | −24.1233 | + | 493.482i | −0.0279204 | + | 0.571159i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1268.34i | 1.46460i | ||||||||
\(867\) | 12.6899 | − | 779.329i | 0.0146365 | − | 0.898880i | ||||
\(868\) | − | 40.9530i | − | 0.0471809i | ||||||
\(869\) | − | 448.472i | − | 0.516078i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 793.485 | 0.911005 | ||||||||
\(872\) | −649.085 | −0.744363 | ||||||||
\(873\) | 24.9194 | − | 764.992i | 0.0285446 | − | 0.876280i | ||||
\(874\) | 1205.87 | 1.37972 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −348.669 | − | 5.67740i | −0.398024 | − | 0.00648106i | ||||
\(877\) | 441.711i | 0.503661i | 0.967771 | + | 0.251831i | \(0.0810326\pi\) | ||||
−0.967771 | + | 0.251831i | \(0.918967\pi\) | |||||||
\(878\) | −408.537 | −0.465304 | ||||||||
\(879\) | −19.5924 | + | 1203.24i | −0.0222894 | + | 1.36887i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 610.857i | − | 0.693368i | −0.937982 | − | 0.346684i | \(-0.887308\pi\) | ||
0.937982 | − | 0.346684i | \(-0.112692\pi\) | |||||||
\(882\) | 724.500 | + | 23.6004i | 0.821429 | + | 0.0267579i | ||||
\(883\) | 145.758i | 0.165071i | 0.996588 | + | 0.0825356i | \(0.0263018\pi\) | ||||
−0.996588 | + | 0.0825356i | \(0.973698\pi\) | |||||||
\(884\) | 56.0087i | 0.0633583i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1206.31 | 1.36152 | ||||||||
\(887\) | 1104.66 | 1.24539 | 0.622693 | − | 0.782466i | \(-0.286039\pi\) | ||||
0.622693 | + | 0.782466i | \(0.286039\pi\) | |||||||
\(888\) | −504.045 | − | 8.20740i | −0.567618 | − | 0.00924256i | ||||
\(889\) | 230.288 | 0.259042 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 56.5679 | − | 867.356i | 0.0634881 | − | 0.973464i | ||||
\(892\) | 312.967i | 0.350860i | ||||||||
\(893\) | −1121.56 | −1.25595 | ||||||||
\(894\) | 349.739 | + | 5.69482i | 0.391207 | + | 0.00637004i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 43.6516i | − | 0.0487183i | ||||||
\(897\) | 885.362 | + | 14.4164i | 0.987026 | + | 0.0160718i | ||||
\(898\) | − | 854.073i | − | 0.951083i | ||||||
\(899\) | − | 1228.99i | − | 1.36706i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 259.418 | 0.287923 | ||||||||
\(902\) | −948.586 | −1.05165 | ||||||||
\(903\) | 1.40480 | − | 86.2737i | 0.00155570 | − | 0.0955412i | ||||
\(904\) | −1411.44 | −1.56133 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.788059 | + | 48.3974i | −0.000869822 | + | 0.0534188i | ||||
\(907\) | 438.512i | 0.483475i | 0.970342 | + | 0.241737i | \(0.0777172\pi\) | ||||
−0.970342 | + | 0.241737i | \(0.922283\pi\) | |||||||
\(908\) | 166.949 | 0.183864 | ||||||||
\(909\) | 9.50005 | − | 291.638i | 0.0104511 | − | 0.320834i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 870.840i | 0.955917i | 0.878383 | + | 0.477958i | \(0.158623\pi\) | ||||
−0.878383 | + | 0.477958i | \(0.841377\pi\) | |||||||
\(912\) | −10.2191 | + | 627.593i | −0.0112052 | + | 0.688150i | ||||
\(913\) | 1044.18i | 1.14368i | ||||||||
\(914\) | − | 369.074i | − | 0.403801i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −300.587 | −0.328152 | ||||||||
\(917\) | 29.0258 | 0.0316530 | ||||||||
\(918\) | −11.9442 | + | 244.339i | −0.0130111 | + | 0.266164i | ||||
\(919\) | −916.817 | −0.997625 | −0.498812 | − | 0.866710i | \(-0.666230\pi\) | ||||
−0.498812 | + | 0.866710i | \(0.666230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −917.689 | − | 14.9428i | −0.996406 | − | 0.0162245i | ||||
\(922\) | 126.291i | 0.136975i | ||||||||
\(923\) | −1113.84 | −1.20676 | ||||||||
\(924\) | 0.613816 | − | 37.6966i | 0.000664303 | − | 0.0407971i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1396.52i | − | 1.50813i | ||||||
\(927\) | 10.8490 | − | 333.049i | 0.0117033 | − | 0.359276i | ||||
\(928\) | 643.118i | 0.693015i | ||||||||
\(929\) | 237.632i | 0.255793i | 0.991788 | + | 0.127896i | \(0.0408225\pi\) | ||||
−0.991788 | + | 0.127896i | \(0.959177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1021.31 | −1.09700 | ||||||||
\(932\) | −376.191 | −0.403639 | ||||||||
\(933\) | −746.662 | − | 12.1580i | −0.800281 | − | 0.0130310i | ||||
\(934\) | 541.518 | 0.579784 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.2514 | + | 683.086i | −0.0237728 | + | 0.729793i | ||||
\(937\) | − | 649.421i | − | 0.693085i | −0.938034 | − | 0.346542i | \(-0.887356\pi\) | ||
0.938034 | − | 0.346542i | \(-0.112644\pi\) | |||||||
\(938\) | 150.326 | 0.160262 | ||||||||
\(939\) | 121.010 | + | 1.97042i | 0.128872 | + | 0.00209842i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 87.3770i | − | 0.0928555i | −0.998922 | − | 0.0464277i | \(-0.985216\pi\) | ||
0.998922 | − | 0.0464277i | \(-0.0147837\pi\) | |||||||
\(942\) | −1164.31 | − | 18.9586i | −1.23600 | − | 0.0201259i | ||||
\(943\) | 1782.41i | 1.89015i | ||||||||
\(944\) | 924.024i | 0.978839i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −524.887 | −0.554849 | ||||||||
\(947\) | −152.556 | −0.161094 | −0.0805470 | − | 0.996751i | \(-0.525667\pi\) | ||||
−0.0805470 | + | 0.996751i | \(0.525667\pi\) | |||||||
\(948\) | 2.42430 | − | 148.885i | 0.00255728 | − | 0.157052i | ||||
\(949\) | −854.322 | −0.900234 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.7772 | − | 907.519i | 0.0155386 | − | 0.954279i | ||||
\(952\) | 46.3484i | 0.0486853i | ||||||||
\(953\) | −940.275 | −0.986647 | −0.493323 | − | 0.869846i | \(-0.664218\pi\) | ||||
−0.493323 | + | 0.869846i | \(0.664218\pi\) | |||||||
\(954\) | 724.330 | + | 23.5949i | 0.759256 | + | 0.0247326i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 77.3695i | − | 0.0809305i | ||||||
\(957\) | 18.4204 | − | 1131.26i | 0.0192481 | − | 1.18209i | ||||
\(958\) | 21.0330i | 0.0219551i | ||||||||
\(959\) | 54.5399i | 0.0568716i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 261.826 | 0.272451 | ||||||||
\(962\) | −282.744 | −0.293913 | ||||||||
\(963\) | −1039.41 | − | 33.8584i | −1.07934 | − | 0.0351593i | ||||
\(964\) | −210.231 | −0.218081 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 167.732 | + | 2.73119i | 0.173636 | + | 0.00282732i | ||||
\(967\) | 569.336i | 0.588765i | 0.955688 | + | 0.294383i | \(0.0951140\pi\) | ||||
−0.955688 | + | 0.294383i | \(0.904886\pi\) | |||||||
\(968\) | 50.8838 | 0.0525659 | ||||||||
\(969\) | 5.61149 | − | 344.621i | 0.00579101 | − | 0.355646i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 733.809i | − | 0.755725i | −0.925862 | − | 0.377862i | \(-0.876659\pi\) | ||
0.925862 | − | 0.377862i | \(-0.123341\pi\) | |||||||
\(972\) | 23.4683 | − | 287.642i | 0.0241443 | − | 0.295928i | ||||
\(973\) | − | 180.947i | − | 0.185968i | ||||||
\(974\) | − | 657.050i | − | 0.674589i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −284.511 | −0.291507 | ||||||||
\(977\) | 917.699 | 0.939303 | 0.469652 | − | 0.882852i | \(-0.344379\pi\) | ||||
0.469652 | + | 0.882852i | \(0.344379\pi\) | |||||||
\(978\) | −1193.57 | − | 19.4349i | −1.22042 | − | 0.0198721i | ||||
\(979\) | −941.443 | −0.961637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 671.133 | + | 21.8620i | 0.684131 | + | 0.0222854i | ||||
\(982\) | − | 841.740i | − | 0.857169i | ||||||
\(983\) | 629.515 | 0.640402 | 0.320201 | − | 0.947350i | \(-0.396250\pi\) | ||||
0.320201 | + | 0.947350i | \(0.396250\pi\) | |||||||
\(984\) | −1375.55 | − | 22.3982i | −1.39792 | − | 0.0227624i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 318.428i | 0.322949i | ||||||||
\(987\) | −156.005 | − | 2.54024i | −0.158060 | − | 0.00257369i | ||||
\(988\) | − | 220.451i | − | 0.223128i | ||||||
\(989\) | 986.271i | 0.997241i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −367.381 | −0.370717 | −0.185359 | − | 0.982671i | \(-0.559345\pi\) | ||||
−0.185359 | + | 0.982671i | \(0.559345\pi\) | |||||||
\(992\) | −639.894 | −0.645054 | ||||||||
\(993\) | 0.348680 | − | 21.4137i | 0.000351138 | − | 0.0215646i | ||||
\(994\) | −211.017 | −0.212290 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.64451 | + | 346.649i | −0.00566718 | + | 0.348041i | ||||
\(997\) | 1777.46i | 1.78281i | 0.453212 | + | 0.891403i | \(0.350278\pi\) | ||||
−0.453212 | + | 0.891403i | \(0.649722\pi\) | |||||||
\(998\) | −745.266 | −0.746759 | ||||||||
\(999\) | 520.889 | + | 25.4630i | 0.521411 | + | 0.0254885i |
(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 | 375.3.d.e.374.12 | 32 | ||
3.2 | odd | 2 | inner | 375.3.d.e.374.22 | 32 | ||
5.2 | odd | 4 | 375.3.c.c.251.12 | yes | 32 | ||
5.3 | odd | 4 | 375.3.c.c.251.21 | yes | 32 | ||
5.4 | even | 2 | inner | 375.3.d.e.374.21 | 32 | ||
15.2 | even | 4 | 375.3.c.c.251.22 | yes | 32 | ||
15.8 | even | 4 | 375.3.c.c.251.11 | ✓ | 32 | ||
15.14 | odd | 2 | inner | 375.3.d.e.374.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
375.3.c.c.251.11 | ✓ | 32 | 15.8 | even | 4 | ||
375.3.c.c.251.12 | yes | 32 | 5.2 | odd | 4 | ||
375.3.c.c.251.21 | yes | 32 | 5.3 | odd | 4 | ||
375.3.c.c.251.22 | yes | 32 | 15.2 | even | 4 | ||
375.3.d.e.374.11 | 32 | 15.14 | odd | 2 | inner | ||
375.3.d.e.374.12 | 32 | 1.1 | even | 1 | trivial | ||
375.3.d.e.374.21 | 32 | 5.4 | even | 2 | inner | ||
375.3.d.e.374.22 | 32 | 3.2 | odd | 2 | inner |