Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), 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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.8 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.33 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.96663i | − | 1.24166i | −0.783946 | − | 0.620829i | \(-0.786796\pi\) | ||
0.783946 | − | 0.620829i | \(-0.213204\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −8.66741 | −0.541713 | ||||||||
\(5\) | 41.3974 | 1.65590 | 0.827948 | − | 0.560805i | \(-0.189508\pi\) | ||||
0.827948 | + | 0.560805i | \(0.189508\pi\) | |||||||
\(6\) | − | 25.8074i | − | 0.716871i | ||||||
\(7\) | 1.08721 | 0.0221880 | 0.0110940 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110940 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(8\) | − | 36.4182i | − | 0.569035i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 205.606i | − | 2.05606i | ||||||
\(11\) | 142.708i | 1.17941i | 0.807620 | + | 0.589704i | \(0.200756\pi\) | ||||
−0.807620 | + | 0.589704i | \(0.799244\pi\) | |||||||
\(12\) | −45.0372 | −0.312758 | ||||||||
\(13\) | − | 35.2627i | − | 0.208655i | −0.994543 | − | 0.104327i | \(-0.966731\pi\) | ||
0.994543 | − | 0.104327i | \(-0.0332690\pi\) | |||||||
\(14\) | − | 5.39978i | − | 0.0275499i | ||||||
\(15\) | 215.107 | 0.956032 | ||||||||
\(16\) | −319.555 | −1.24826 | ||||||||
\(17\) | 527.661 | 1.82581 | 0.912907 | − | 0.408167i | \(-0.133832\pi\) | ||||
0.912907 | + | 0.408167i | \(0.133832\pi\) | |||||||
\(18\) | − | 134.099i | − | 0.413886i | ||||||
\(19\) | 76.0375 | 0.210630 | 0.105315 | − | 0.994439i | \(-0.466415\pi\) | ||||
0.105315 | + | 0.994439i | \(0.466415\pi\) | |||||||
\(20\) | −358.808 | −0.897021 | ||||||||
\(21\) | 5.64932 | 0.0128103 | ||||||||
\(22\) | 708.780 | 1.46442 | ||||||||
\(23\) | − | 138.991i | − | 0.262744i | −0.991333 | − | 0.131372i | \(-0.958062\pi\) | ||
0.991333 | − | 0.131372i | \(-0.0419382\pi\) | |||||||
\(24\) | − | 189.235i | − | 0.328533i | ||||||
\(25\) | 1088.75 | 1.74199 | ||||||||
\(26\) | −175.137 | −0.259078 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | −9.42332 | −0.0120195 | ||||||||
\(29\) | −1044.28 | −1.24171 | −0.620857 | − | 0.783924i | \(-0.713215\pi\) | ||||
−0.620857 | + | 0.783924i | \(0.713215\pi\) | |||||||
\(30\) | − | 1068.36i | − | 1.18706i | ||||||
\(31\) | − | 1364.14i | − | 1.41950i | −0.704454 | − | 0.709749i | \(-0.748808\pi\) | ||
0.704454 | − | 0.709749i | \(-0.251192\pi\) | |||||||
\(32\) | 1004.42i | 0.980876i | ||||||||
\(33\) | 741.534i | 0.680931i | ||||||||
\(34\) | − | 2620.69i | − | 2.26704i | ||||||
\(35\) | 45.0078 | 0.0367410 | ||||||||
\(36\) | −234.020 | −0.180571 | ||||||||
\(37\) | 2076.33i | 1.51668i | 0.651860 | + | 0.758339i | \(0.273989\pi\) | ||||
−0.651860 | + | 0.758339i | \(0.726011\pi\) | |||||||
\(38\) | − | 377.650i | − | 0.261530i | ||||||
\(39\) | − | 183.230i | − | 0.120467i | ||||||
\(40\) | − | 1507.62i | − | 0.942263i | ||||||
\(41\) | −1604.49 | −0.954485 | −0.477242 | − | 0.878772i | \(-0.658364\pi\) | ||||
−0.477242 | + | 0.878772i | \(0.658364\pi\) | |||||||
\(42\) | − | 28.0581i | − | 0.0159059i | ||||||
\(43\) | − | 746.077i | − | 0.403503i | −0.979437 | − | 0.201751i | \(-0.935337\pi\) | ||
0.979437 | − | 0.201751i | \(-0.0646633\pi\) | |||||||
\(44\) | − | 1236.91i | − | 0.638901i | ||||||
\(45\) | 1117.73 | 0.551965 | ||||||||
\(46\) | −690.318 | −0.326237 | ||||||||
\(47\) | 613.862i | 0.277891i | 0.990300 | + | 0.138946i | \(0.0443713\pi\) | ||||
−0.990300 | + | 0.138946i | \(0.955629\pi\) | |||||||
\(48\) | −1660.45 | −0.720683 | ||||||||
\(49\) | −2399.82 | −0.999508 | ||||||||
\(50\) | − | 5407.39i | − | 2.16296i | ||||||
\(51\) | 2741.80 | 1.05413 | ||||||||
\(52\) | 305.636i | 0.113031i | ||||||||
\(53\) | −3306.58 | −1.17714 | −0.588569 | − | 0.808447i | \(-0.700308\pi\) | ||||
−0.588569 | + | 0.808447i | \(0.700308\pi\) | |||||||
\(54\) | − | 696.799i | − | 0.238957i | ||||||
\(55\) | 5907.75i | 1.95298i | ||||||||
\(56\) | − | 39.5944i | − | 0.0126258i | ||||||
\(57\) | 395.102 | 0.121607 | ||||||||
\(58\) | 5186.56i | 1.54178i | ||||||||
\(59\) | 330.884 | − | 3465.24i | 0.0950543 | − | 0.995472i | ||||
\(60\) | −1864.42 | −0.517895 | ||||||||
\(61\) | 3021.56i | 0.812028i | 0.913867 | + | 0.406014i | \(0.133082\pi\) | ||||
−0.913867 | + | 0.406014i | \(0.866918\pi\) | |||||||
\(62\) | −6775.17 | −1.76253 | ||||||||
\(63\) | 29.3547 | 0.00739600 | ||||||||
\(64\) | −124.304 | −0.0303476 | ||||||||
\(65\) | − | 1459.78i | − | 0.345511i | ||||||
\(66\) | 3682.93 | 0.845484 | ||||||||
\(67\) | − | 3679.74i | − | 0.819724i | −0.912148 | − | 0.409862i | \(-0.865577\pi\) | ||
0.912148 | − | 0.409862i | \(-0.134423\pi\) | |||||||
\(68\) | −4573.45 | −0.989068 | ||||||||
\(69\) | − | 722.220i | − | 0.151695i | ||||||
\(70\) | − | 223.537i | − | 0.0456198i | ||||||
\(71\) | 1827.67 | 0.362560 | 0.181280 | − | 0.983431i | \(-0.441976\pi\) | ||||
0.181280 | + | 0.983431i | \(0.441976\pi\) | |||||||
\(72\) | − | 983.293i | − | 0.189678i | ||||||
\(73\) | − | 2692.51i | − | 0.505256i | −0.967563 | − | 0.252628i | \(-0.918705\pi\) | ||
0.967563 | − | 0.252628i | \(-0.0812949\pi\) | |||||||
\(74\) | 10312.4 | 1.88320 | ||||||||
\(75\) | 5657.29 | 1.00574 | ||||||||
\(76\) | −659.048 | −0.114101 | ||||||||
\(77\) | 155.154i | 0.0261687i | ||||||||
\(78\) | −910.037 | −0.149579 | ||||||||
\(79\) | 3087.31 | 0.494682 | 0.247341 | − | 0.968928i | \(-0.420443\pi\) | ||||
0.247341 | + | 0.968928i | \(0.420443\pi\) | |||||||
\(80\) | −13228.7 | −2.06699 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 7968.90i | 1.18514i | ||||||||
\(83\) | − | 7955.09i | − | 1.15475i | −0.816478 | − | 0.577377i | \(-0.804076\pi\) | ||
0.816478 | − | 0.577377i | \(-0.195924\pi\) | |||||||
\(84\) | −48.9650 | −0.00693949 | ||||||||
\(85\) | 21843.8 | 3.02336 | ||||||||
\(86\) | −3705.49 | −0.501012 | ||||||||
\(87\) | −5426.25 | −0.716904 | ||||||||
\(88\) | 5197.19 | 0.671124 | ||||||||
\(89\) | 5141.10i | 0.649047i | 0.945878 | + | 0.324524i | \(0.105204\pi\) | ||||
−0.945878 | + | 0.324524i | \(0.894796\pi\) | |||||||
\(90\) | − | 5551.35i | − | 0.685352i | ||||||
\(91\) | − | 38.3380i | − | 0.00462964i | ||||||
\(92\) | 1204.70i | 0.142332i | ||||||||
\(93\) | − | 7088.27i | − | 0.819548i | ||||||
\(94\) | 3048.82 | 0.345046 | ||||||||
\(95\) | 3147.75 | 0.348782 | ||||||||
\(96\) | 5219.11i | 0.566309i | ||||||||
\(97\) | 13063.6i | 1.38842i | 0.719772 | + | 0.694210i | \(0.244246\pi\) | ||||
−0.719772 | + | 0.694210i | \(0.755754\pi\) | |||||||
\(98\) | 11919.0i | 1.24105i | ||||||||
\(99\) | 3853.13i | 0.393136i | ||||||||
\(100\) | −9436.60 | −0.943660 | ||||||||
\(101\) | − | 6212.97i | − | 0.609055i | −0.952504 | − | 0.304527i | \(-0.901502\pi\) | ||
0.952504 | − | 0.304527i | \(-0.0984985\pi\) | |||||||
\(102\) | − | 13617.5i | − | 1.30887i | ||||||
\(103\) | 12027.0i | 1.13366i | 0.823834 | + | 0.566831i | \(0.191831\pi\) | ||||
−0.823834 | + | 0.566831i | \(0.808169\pi\) | |||||||
\(104\) | −1284.21 | −0.118732 | ||||||||
\(105\) | 233.867 | 0.0212125 | ||||||||
\(106\) | 16422.6i | 1.46160i | ||||||||
\(107\) | −5915.89 | −0.516717 | −0.258359 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258359 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(108\) | −1216.00 | −0.104253 | ||||||||
\(109\) | 17887.0i | 1.50552i | 0.658298 | + | 0.752758i | \(0.271277\pi\) | ||||
−0.658298 | + | 0.752758i | \(0.728723\pi\) | |||||||
\(110\) | 29341.6 | 2.42493 | ||||||||
\(111\) | 10788.9i | 0.875655i | ||||||||
\(112\) | −347.424 | −0.0276964 | ||||||||
\(113\) | 24933.1i | 1.95262i | 0.216368 | + | 0.976312i | \(0.430579\pi\) | ||||
−0.216368 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(114\) | − | 1962.33i | − | 0.150995i | ||||||
\(115\) | − | 5753.88i | − | 0.435076i | ||||||
\(116\) | 9051.23 | 0.672653 | ||||||||
\(117\) | − | 952.093i | − | 0.0695517i | ||||||
\(118\) | −17210.6 | − | 1643.38i | −1.23604 | − | 0.118025i | ||||
\(119\) | 573.679 | 0.0405112 | ||||||||
\(120\) | − | 7833.83i | − | 0.544016i | ||||||
\(121\) | −5724.67 | −0.391003 | ||||||||
\(122\) | 15007.0 | 1.00826 | ||||||||
\(123\) | −8337.17 | −0.551072 | ||||||||
\(124\) | 11823.6i | 0.768962i | ||||||||
\(125\) | 19197.8 | 1.22866 | ||||||||
\(126\) | − | 145.794i | − | 0.00918330i | ||||||
\(127\) | 22413.1 | 1.38961 | 0.694806 | − | 0.719197i | \(-0.255490\pi\) | ||||
0.694806 | + | 0.719197i | \(0.255490\pi\) | |||||||
\(128\) | 16688.0i | 1.01856i | ||||||||
\(129\) | − | 3876.73i | − | 0.232963i | ||||||
\(130\) | −7250.21 | −0.429006 | ||||||||
\(131\) | − | 17802.3i | − | 1.03737i | −0.854965 | − | 0.518685i | \(-0.826422\pi\) | ||
0.854965 | − | 0.518685i | \(-0.173578\pi\) | |||||||
\(132\) | − | 6427.18i | − | 0.368870i | ||||||
\(133\) | 82.6689 | 0.00467346 | ||||||||
\(134\) | −18275.9 | −1.01782 | ||||||||
\(135\) | 5807.89 | 0.318677 | ||||||||
\(136\) | − | 19216.5i | − | 1.03895i | ||||||
\(137\) | −11891.9 | −0.633595 | −0.316797 | − | 0.948493i | \(-0.602607\pi\) | ||||
−0.316797 | + | 0.948493i | \(0.602607\pi\) | |||||||
\(138\) | −3587.00 | −0.188353 | ||||||||
\(139\) | −24841.5 | −1.28572 | −0.642862 | − | 0.765982i | \(-0.722253\pi\) | ||||
−0.642862 | + | 0.765982i | \(0.722253\pi\) | |||||||
\(140\) | −390.101 | −0.0199031 | ||||||||
\(141\) | 3189.72i | 0.160441i | ||||||||
\(142\) | − | 9077.34i | − | 0.450176i | ||||||
\(143\) | 5032.28 | 0.246089 | ||||||||
\(144\) | −8627.97 | −0.416087 | ||||||||
\(145\) | −43230.6 | −2.05615 | ||||||||
\(146\) | −13372.7 | −0.627355 | ||||||||
\(147\) | −12469.8 | −0.577066 | ||||||||
\(148\) | − | 17996.4i | − | 0.821605i | ||||||
\(149\) | 26032.6i | 1.17259i | 0.810099 | + | 0.586293i | \(0.199413\pi\) | ||||
−0.810099 | + | 0.586293i | \(0.800587\pi\) | |||||||
\(150\) | − | 28097.6i | − | 1.24878i | ||||||
\(151\) | 12278.3i | 0.538497i | 0.963071 | + | 0.269249i | \(0.0867753\pi\) | ||||
−0.963071 | + | 0.269249i | \(0.913225\pi\) | |||||||
\(152\) | − | 2769.15i | − | 0.119856i | ||||||
\(153\) | 14246.8 | 0.608605 | ||||||||
\(154\) | 770.594 | 0.0324926 | ||||||||
\(155\) | − | 56471.8i | − | 2.35054i | ||||||
\(156\) | 1588.13i | 0.0652586i | ||||||||
\(157\) | − | 21189.6i | − | 0.859655i | −0.902911 | − | 0.429827i | \(-0.858574\pi\) | ||
0.902911 | − | 0.429827i | \(-0.141426\pi\) | |||||||
\(158\) | − | 15333.5i | − | 0.614226i | ||||||
\(159\) | −17181.5 | −0.679621 | ||||||||
\(160\) | 41580.3i | 1.62423i | ||||||||
\(161\) | − | 151.113i | − | 0.00582976i | ||||||
\(162\) | − | 3620.67i | − | 0.137962i | ||||||
\(163\) | 22822.0 | 0.858970 | 0.429485 | − | 0.903074i | \(-0.358695\pi\) | ||||
0.429485 | + | 0.903074i | \(0.358695\pi\) | |||||||
\(164\) | 13906.8 | 0.517057 | ||||||||
\(165\) | 30697.6i | 1.12755i | ||||||||
\(166\) | −39510.0 | −1.43381 | ||||||||
\(167\) | −28368.2 | −1.01718 | −0.508592 | − | 0.861008i | \(-0.669834\pi\) | ||||
−0.508592 | + | 0.861008i | \(0.669834\pi\) | |||||||
\(168\) | − | 205.738i | − | 0.00728948i | ||||||
\(169\) | 27317.5 | 0.956463 | ||||||||
\(170\) | − | 108490.i | − | 3.75398i | ||||||
\(171\) | 2053.01 | 0.0702100 | ||||||||
\(172\) | 6466.56i | 0.218583i | ||||||||
\(173\) | − | 7580.94i | − | 0.253297i | −0.991948 | − | 0.126649i | \(-0.959578\pi\) | ||
0.991948 | − | 0.126649i | \(-0.0404221\pi\) | |||||||
\(174\) | 26950.2i | 0.890150i | ||||||||
\(175\) | 1183.70 | 0.0386513 | ||||||||
\(176\) | − | 45603.1i | − | 1.47221i | ||||||
\(177\) | 1719.32 | − | 18005.9i | 0.0548796 | − | 0.574736i | ||||
\(178\) | 25533.9 | 0.805894 | ||||||||
\(179\) | 34939.2i | 1.09045i | 0.838289 | + | 0.545226i | \(0.183556\pi\) | ||||
−0.838289 | + | 0.545226i | \(0.816444\pi\) | |||||||
\(180\) | −9687.83 | −0.299007 | ||||||||
\(181\) | 37840.7 | 1.15505 | 0.577527 | − | 0.816372i | \(-0.304018\pi\) | ||||
0.577527 | + | 0.816372i | \(0.304018\pi\) | |||||||
\(182\) | −190.411 | −0.00574843 | ||||||||
\(183\) | 15700.5i | 0.468825i | ||||||||
\(184\) | −5061.82 | −0.149510 | ||||||||
\(185\) | 85954.8i | 2.51146i | ||||||||
\(186\) | −35204.8 | −1.01760 | ||||||||
\(187\) | 75301.6i | 2.15338i | ||||||||
\(188\) | − | 5320.59i | − | 0.150537i | ||||||
\(189\) | 152.532 | 0.00427008 | ||||||||
\(190\) | − | 15633.7i | − | 0.433067i | ||||||
\(191\) | 3569.74i | 0.0978521i | 0.998802 | + | 0.0489261i | \(0.0155799\pi\) | ||||
−0.998802 | + | 0.0489261i | \(0.984420\pi\) | |||||||
\(192\) | −645.901 | −0.0175212 | ||||||||
\(193\) | 24451.4 | 0.656430 | 0.328215 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328215 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(194\) | 64882.3 | 1.72394 | ||||||||
\(195\) | − | 7585.26i | − | 0.199481i | ||||||
\(196\) | 20800.2 | 0.541447 | ||||||||
\(197\) | −29706.3 | −0.765449 | −0.382724 | − | 0.923863i | \(-0.625014\pi\) | ||||
−0.382724 | + | 0.923863i | \(0.625014\pi\) | |||||||
\(198\) | 19137.0 | 0.488140 | ||||||||
\(199\) | −22181.5 | −0.560125 | −0.280062 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280062 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(200\) | − | 39650.2i | − | 0.991255i | ||||||
\(201\) | − | 19120.5i | − | 0.473268i | ||||||
\(202\) | −30857.5 | −0.756237 | ||||||||
\(203\) | −1135.36 | −0.0275512 | ||||||||
\(204\) | −23764.4 | −0.571039 | ||||||||
\(205\) | −66421.7 | −1.58053 | ||||||||
\(206\) | 59733.8 | 1.40762 | ||||||||
\(207\) | − | 3752.77i | − | 0.0875812i | ||||||
\(208\) | 11268.4i | 0.260456i | ||||||||
\(209\) | 10851.2i | 0.248419i | ||||||||
\(210\) | − | 1161.53i | − | 0.0263386i | ||||||
\(211\) | − | 81724.8i | − | 1.83565i | −0.396989 | − | 0.917824i | \(-0.629945\pi\) | ||
0.396989 | − | 0.917824i | \(-0.370055\pi\) | |||||||
\(212\) | 28659.5 | 0.637671 | ||||||||
\(213\) | 9496.83 | 0.209324 | ||||||||
\(214\) | 29382.1i | 0.641586i | ||||||||
\(215\) | − | 30885.6i | − | 0.668159i | ||||||
\(216\) | − | 5109.34i | − | 0.109511i | ||||||
\(217\) | − | 1483.11i | − | 0.0314959i | ||||||
\(218\) | 88838.3 | 1.86933 | ||||||||
\(219\) | − | 13990.7i | − | 0.291710i | ||||||
\(220\) | − | 51205.0i | − | 1.05795i | ||||||
\(221\) | − | 18606.7i | − | 0.380965i | ||||||
\(222\) | 53584.7 | 1.08726 | ||||||||
\(223\) | −54373.6 | −1.09340 | −0.546699 | − | 0.837329i | \(-0.684116\pi\) | ||||
−0.546699 | + | 0.837329i | \(0.684116\pi\) | |||||||
\(224\) | 1092.02i | 0.0217637i | ||||||||
\(225\) | 29396.1 | 0.580664 | ||||||||
\(226\) | 123833. | 2.42449 | ||||||||
\(227\) | 55801.8i | 1.08292i | 0.840726 | + | 0.541460i | \(0.182128\pi\) | ||||
−0.840726 | + | 0.541460i | \(0.817872\pi\) | |||||||
\(228\) | −3424.51 | −0.0658763 | ||||||||
\(229\) | − | 102771.i | − | 1.95975i | −0.199624 | − | 0.979873i | \(-0.563972\pi\) | ||
0.199624 | − | 0.979873i | \(-0.436028\pi\) | |||||||
\(230\) | −28577.4 | −0.540215 | ||||||||
\(231\) | 806.205i | 0.0151085i | ||||||||
\(232\) | 38030.9i | 0.706579i | ||||||||
\(233\) | − | 60636.1i | − | 1.11691i | −0.829534 | − | 0.558457i | \(-0.811394\pi\) | ||
0.829534 | − | 0.558457i | \(-0.188606\pi\) | |||||||
\(234\) | −4728.69 | −0.0863593 | ||||||||
\(235\) | 25412.3i | 0.460159i | ||||||||
\(236\) | −2867.91 | + | 30034.7i | −0.0514922 | + | 0.539261i | ||||
\(237\) | 16042.1 | 0.285605 | ||||||||
\(238\) | − | 2849.25i | − | 0.0503010i | ||||||
\(239\) | 12138.8 | 0.212510 | 0.106255 | − | 0.994339i | \(-0.466114\pi\) | ||||
0.106255 | + | 0.994339i | \(0.466114\pi\) | |||||||
\(240\) | −68738.5 | −1.19338 | ||||||||
\(241\) | −13471.2 | −0.231938 | −0.115969 | − | 0.993253i | \(-0.536997\pi\) | ||||
−0.115969 | + | 0.993253i | \(0.536997\pi\) | |||||||
\(242\) | 28432.3i | 0.485491i | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 26189.1i | − | 0.439886i | ||||||
\(245\) | −99346.2 | −1.65508 | ||||||||
\(246\) | 41407.6i | 0.684243i | ||||||||
\(247\) | − | 2681.29i | − | 0.0439490i | ||||||
\(248\) | −49679.5 | −0.807745 | ||||||||
\(249\) | − | 41335.9i | − | 0.666697i | ||||||
\(250\) | − | 95348.6i | − | 1.52558i | ||||||
\(251\) | −20999.2 | −0.333315 | −0.166657 | − | 0.986015i | \(-0.553297\pi\) | ||||
−0.166657 | + | 0.986015i | \(0.553297\pi\) | |||||||
\(252\) | −254.430 | −0.00400651 | ||||||||
\(253\) | 19835.2 | 0.309882 | ||||||||
\(254\) | − | 111317.i | − | 1.72542i | ||||||
\(255\) | 113504. | 1.74554 | ||||||||
\(256\) | 80894.5 | 1.23435 | ||||||||
\(257\) | −39315.0 | −0.595240 | −0.297620 | − | 0.954684i | \(-0.596193\pi\) | ||||
−0.297620 | + | 0.954684i | \(0.596193\pi\) | |||||||
\(258\) | −19254.3 | −0.289260 | ||||||||
\(259\) | 2257.42i | 0.0336521i | ||||||||
\(260\) | 12652.5i | 0.187168i | ||||||||
\(261\) | −28195.6 | −0.413905 | ||||||||
\(262\) | −88417.5 | −1.28806 | ||||||||
\(263\) | 37861.6 | 0.547378 | 0.273689 | − | 0.961818i | \(-0.411756\pi\) | ||||
0.273689 | + | 0.961818i | \(0.411756\pi\) | |||||||
\(264\) | 27005.4 | 0.387474 | ||||||||
\(265\) | −136884. | −1.94922 | ||||||||
\(266\) | − | 410.586i | − | 0.00580284i | ||||||
\(267\) | 26713.9i | 0.374727i | ||||||||
\(268\) | 31893.8i | 0.444055i | ||||||||
\(269\) | 123756.i | 1.71026i | 0.518413 | + | 0.855130i | \(0.326523\pi\) | ||||
−0.518413 | + | 0.855130i | \(0.673477\pi\) | |||||||
\(270\) | − | 28845.7i | − | 0.395688i | ||||||
\(271\) | 4855.26 | 0.0661110 | 0.0330555 | − | 0.999454i | \(-0.489476\pi\) | ||||
0.0330555 | + | 0.999454i | \(0.489476\pi\) | |||||||
\(272\) | −168616. | −2.27909 | ||||||||
\(273\) | − | 199.210i | − | 0.00267292i | ||||||
\(274\) | 59062.9i | 0.786707i | ||||||||
\(275\) | 155373.i | 2.05452i | ||||||||
\(276\) | 6259.78i | 0.0821752i | ||||||||
\(277\) | 97089.7 | 1.26536 | 0.632680 | − | 0.774414i | \(-0.281955\pi\) | ||||
0.632680 | + | 0.774414i | \(0.281955\pi\) | |||||||
\(278\) | 123378.i | 1.59643i | ||||||||
\(279\) | − | 36831.7i | − | 0.473166i | ||||||
\(280\) | − | 1639.10i | − | 0.0209069i | ||||||
\(281\) | −108342. | −1.37209 | −0.686045 | − | 0.727559i | \(-0.740655\pi\) | ||||
−0.686045 | + | 0.727559i | \(0.740655\pi\) | |||||||
\(282\) | 15842.2 | 0.199212 | ||||||||
\(283\) | 67893.8i | 0.847729i | 0.905726 | + | 0.423864i | \(0.139327\pi\) | ||||
−0.905726 | + | 0.423864i | \(0.860673\pi\) | |||||||
\(284\) | −15841.1 | −0.196404 | ||||||||
\(285\) | 16356.2 | 0.201369 | ||||||||
\(286\) | − | 24993.5i | − | 0.305559i | ||||||
\(287\) | −1744.42 | −0.0211781 | ||||||||
\(288\) | 27119.3i | 0.326959i | ||||||||
\(289\) | 194905. | 2.33360 | ||||||||
\(290\) | 214710.i | 2.55304i | ||||||||
\(291\) | 67880.7i | 0.801605i | ||||||||
\(292\) | 23337.1i | 0.273704i | ||||||||
\(293\) | 51965.3 | 0.605311 | 0.302655 | − | 0.953100i | \(-0.402127\pi\) | ||||
0.302655 | + | 0.953100i | \(0.402127\pi\) | |||||||
\(294\) | 61933.0i | 0.716518i | ||||||||
\(295\) | 13697.7 | − | 143452.i | 0.157400 | − | 1.64840i | ||||
\(296\) | 75616.4 | 0.863043 | ||||||||
\(297\) | 20021.4i | 0.226977i | ||||||||
\(298\) | 129294. | 1.45595 | ||||||||
\(299\) | −4901.21 | −0.0548227 | ||||||||
\(300\) | −49034.0 | −0.544823 | ||||||||
\(301\) | − | 811.144i | − | 0.00895293i | ||||||
\(302\) | 60981.7 | 0.668629 | ||||||||
\(303\) | − | 32283.5i | − | 0.351638i | ||||||
\(304\) | −24298.1 | −0.262921 | ||||||||
\(305\) | 125085.i | 1.34463i | ||||||||
\(306\) | − | 70758.8i | − | 0.755679i | ||||||
\(307\) | 122608. | 1.30089 | 0.650445 | − | 0.759553i | \(-0.274582\pi\) | ||||
0.650445 | + | 0.759553i | \(0.274582\pi\) | |||||||
\(308\) | − | 1344.79i | − | 0.0141759i | ||||||
\(309\) | 62494.2i | 0.654520i | ||||||||
\(310\) | −280475. | −2.91857 | ||||||||
\(311\) | −159419. | −1.64823 | −0.824117 | − | 0.566420i | \(-0.808328\pi\) | ||||
−0.824117 | + | 0.566420i | \(0.808328\pi\) | |||||||
\(312\) | −6672.93 | −0.0685499 | ||||||||
\(313\) | 17723.3i | 0.180907i | 0.995901 | + | 0.0904534i | \(0.0288316\pi\) | ||||
−0.995901 | + | 0.0904534i | \(0.971168\pi\) | |||||||
\(314\) | −105241. | −1.06740 | ||||||||
\(315\) | 1215.21 | 0.0122470 | ||||||||
\(316\) | −26759.0 | −0.267976 | ||||||||
\(317\) | −112577. | −1.12029 | −0.560145 | − | 0.828394i | \(-0.689255\pi\) | ||||
−0.560145 | + | 0.828394i | \(0.689255\pi\) | |||||||
\(318\) | 85334.1i | 0.843856i | ||||||||
\(319\) | − | 149028.i | − | 1.46449i | ||||||
\(320\) | −5145.85 | −0.0502524 | ||||||||
\(321\) | −30739.9 | −0.298327 | ||||||||
\(322\) | −750.523 | −0.00723856 | ||||||||
\(323\) | 40122.0 | 0.384572 | ||||||||
\(324\) | −6318.54 | −0.0601904 | ||||||||
\(325\) | − | 38392.1i | − | 0.363475i | ||||||
\(326\) | − | 113348.i | − | 1.06655i | ||||||
\(327\) | 92943.7i | 0.869210i | ||||||||
\(328\) | 58432.7i | 0.543135i | ||||||||
\(329\) | 667.398i | 0.00616585i | ||||||||
\(330\) | 152464. | 1.40003 | ||||||||
\(331\) | −126890. | −1.15817 | −0.579083 | − | 0.815268i | \(-0.696589\pi\) | ||||
−0.579083 | + | 0.815268i | \(0.696589\pi\) | |||||||
\(332\) | 68950.1i | 0.625545i | ||||||||
\(333\) | 56061.0i | 0.505560i | ||||||||
\(334\) | 140895.i | 1.26299i | ||||||||
\(335\) | − | 152332.i | − | 1.35738i | ||||||
\(336\) | −1805.27 | −0.0159905 | ||||||||
\(337\) | − | 145883.i | − | 1.28454i | −0.766480 | − | 0.642268i | \(-0.777994\pi\) | ||
0.766480 | − | 0.642268i | \(-0.222006\pi\) | |||||||
\(338\) | − | 135676.i | − | 1.18760i | ||||||
\(339\) | 129556.i | 1.12735i | ||||||||
\(340\) | −189329. | −1.63779 | ||||||||
\(341\) | 194674. | 1.67417 | ||||||||
\(342\) | − | 10196.5i | − | 0.0871768i | ||||||
\(343\) | −5219.51 | −0.0443651 | ||||||||
\(344\) | −27170.8 | −0.229607 | ||||||||
\(345\) | − | 29898.0i | − | 0.251191i | ||||||
\(346\) | −37651.7 | −0.314509 | ||||||||
\(347\) | 118230.i | 0.981905i | 0.871186 | + | 0.490953i | \(0.163351\pi\) | ||||
−0.871186 | + | 0.490953i | \(0.836649\pi\) | |||||||
\(348\) | 47031.5 | 0.388357 | ||||||||
\(349\) | − | 24509.0i | − | 0.201222i | −0.994926 | − | 0.100611i | \(-0.967920\pi\) | ||
0.994926 | − | 0.100611i | \(-0.0320797\pi\) | |||||||
\(350\) | − | 5878.99i | − | 0.0479917i | ||||||
\(351\) | − | 4947.22i | − | 0.0401557i | ||||||
\(352\) | −143339. | −1.15685 | ||||||||
\(353\) | − | 38007.7i | − | 0.305015i | −0.988302 | − | 0.152508i | \(-0.951265\pi\) | ||
0.988302 | − | 0.152508i | \(-0.0487349\pi\) | |||||||
\(354\) | −89428.7 | − | 8539.24i | −0.713625 | − | 0.0681417i | ||||
\(355\) | 75660.7 | 0.600362 | ||||||||
\(356\) | − | 44560.1i | − | 0.351597i | ||||||
\(357\) | 2980.92 | 0.0233892 | ||||||||
\(358\) | 173530. | 1.35397 | ||||||||
\(359\) | 192503. | 1.49365 | 0.746826 | − | 0.665020i | \(-0.231577\pi\) | ||||
0.746826 | + | 0.665020i | \(0.231577\pi\) | |||||||
\(360\) | − | 40705.8i | − | 0.314088i | ||||||
\(361\) | −124539. | −0.955635 | ||||||||
\(362\) | − | 187941.i | − | 1.43418i | ||||||
\(363\) | −29746.3 | −0.225745 | ||||||||
\(364\) | 332.292i | 0.00250794i | ||||||||
\(365\) | − | 111463.i | − | 0.836652i | ||||||
\(366\) | 77978.4 | 0.582120 | ||||||||
\(367\) | − | 18295.0i | − | 0.135831i | −0.997691 | − | 0.0679157i | \(-0.978365\pi\) | ||
0.997691 | − | 0.0679157i | \(-0.0216349\pi\) | |||||||
\(368\) | 44415.3i | 0.327972i | ||||||||
\(369\) | −43321.2 | −0.318162 | ||||||||
\(370\) | 426906. | 3.11838 | ||||||||
\(371\) | −3594.96 | −0.0261183 | ||||||||
\(372\) | 61437.0i | 0.443960i | ||||||||
\(373\) | 57630.7 | 0.414225 | 0.207112 | − | 0.978317i | \(-0.433593\pi\) | ||||
0.207112 | + | 0.978317i | \(0.433593\pi\) | |||||||
\(374\) | 373995. | 2.67376 | ||||||||
\(375\) | 99754.9 | 0.709368 | ||||||||
\(376\) | 22355.8 | 0.158130 | ||||||||
\(377\) | 36824.2i | 0.259090i | ||||||||
\(378\) | − | 757.569i | − | 0.00530198i | ||||||
\(379\) | 170818. | 1.18920 | 0.594599 | − | 0.804023i | \(-0.297311\pi\) | ||||
0.594599 | + | 0.804023i | \(0.297311\pi\) | |||||||
\(380\) | −27282.9 | −0.188940 | ||||||||
\(381\) | 116462. | 0.802293 | ||||||||
\(382\) | 17729.6 | 0.121499 | ||||||||
\(383\) | −221122. | −1.50742 | −0.753709 | − | 0.657208i | \(-0.771737\pi\) | ||||
−0.753709 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(384\) | 86713.6i | 0.588065i | ||||||||
\(385\) | 6422.99i | 0.0433327i | ||||||||
\(386\) | − | 121441.i | − | 0.815061i | ||||||
\(387\) | − | 20144.1i | − | 0.134501i | ||||||
\(388\) | − | 113228.i | − | 0.752126i | ||||||
\(389\) | 87151.4 | 0.575937 | 0.287969 | − | 0.957640i | \(-0.407020\pi\) | ||||
0.287969 | + | 0.957640i | \(0.407020\pi\) | |||||||
\(390\) | −37673.2 | −0.247687 | ||||||||
\(391\) | − | 73340.2i | − | 0.479721i | ||||||
\(392\) | 87397.2i | 0.568755i | ||||||||
\(393\) | − | 92503.6i | − | 0.598926i | ||||||
\(394\) | 147540.i | 0.950425i | ||||||||
\(395\) | 127807. | 0.819143 | ||||||||
\(396\) | − | 33396.6i | − | 0.212967i | ||||||
\(397\) | − | 126155.i | − | 0.800431i | −0.916421 | − | 0.400216i | \(-0.868935\pi\) | ||
0.916421 | − | 0.400216i | \(-0.131065\pi\) | |||||||
\(398\) | 110167.i | 0.695483i | ||||||||
\(399\) | 429.560 | 0.00269823 | ||||||||
\(400\) | −347913. | −2.17446 | ||||||||
\(401\) | 27343.9i | 0.170048i | 0.996379 | + | 0.0850242i | \(0.0270967\pi\) | ||||
−0.996379 | + | 0.0850242i | \(0.972903\pi\) | |||||||
\(402\) | −94964.4 | −0.587637 | ||||||||
\(403\) | −48103.2 | −0.296185 | ||||||||
\(404\) | 53850.4i | 0.329933i | ||||||||
\(405\) | 30178.7 | 0.183988 | ||||||||
\(406\) | 5638.90i | 0.0342091i | ||||||||
\(407\) | −296310. | −1.78878 | ||||||||
\(408\) | − | 99851.7i | − | 0.599840i | ||||||
\(409\) | 104932.i | 0.627282i | 0.949542 | + | 0.313641i | \(0.101549\pi\) | ||||
−0.949542 | + | 0.313641i | \(0.898451\pi\) | |||||||
\(410\) | 329892.i | 1.96247i | ||||||||
\(411\) | −61792.3 | −0.365806 | ||||||||
\(412\) | − | 104243.i | − | 0.614120i | ||||||
\(413\) | 359.741 | − | 3767.45i | 0.00210907 | − | 0.0220875i | ||||
\(414\) | −18638.6 | −0.108746 | ||||||||
\(415\) | − | 329320.i | − | 1.91215i | ||||||
\(416\) | 35418.5 | 0.204665 | ||||||||
\(417\) | −129080. | −0.742313 | ||||||||
\(418\) | 53893.8 | 0.308451 | ||||||||
\(419\) | − | 203320.i | − | 1.15812i | −0.815286 | − | 0.579058i | \(-0.803420\pi\) | ||
0.815286 | − | 0.579058i | \(-0.196580\pi\) | |||||||
\(420\) | −2027.02 | −0.0114911 | ||||||||
\(421\) | 7915.89i | 0.0446617i | 0.999751 | + | 0.0223309i | \(0.00710872\pi\) | ||||
−0.999751 | + | 0.0223309i | \(0.992891\pi\) | |||||||
\(422\) | −405897. | −2.27924 | ||||||||
\(423\) | 16574.3i | 0.0926304i | ||||||||
\(424\) | 120420.i | 0.669833i | ||||||||
\(425\) | 574488. | 3.18056 | ||||||||
\(426\) | − | 47167.3i | − | 0.259909i | ||||||
\(427\) | 3285.07i | 0.0180173i | ||||||||
\(428\) | 51275.5 | 0.279913 | ||||||||
\(429\) | 26148.5 | 0.142080 | ||||||||
\(430\) | −153398. | −0.829625 | ||||||||
\(431\) | − | 166950.i | − | 0.898734i | −0.893347 | − | 0.449367i | \(-0.851650\pi\) | ||
0.893347 | − | 0.449367i | \(-0.148350\pi\) | |||||||
\(432\) | −44832.3 | −0.240228 | ||||||||
\(433\) | −47184.7 | −0.251666 | −0.125833 | − | 0.992051i | \(-0.540160\pi\) | ||||
−0.125833 | + | 0.992051i | \(0.540160\pi\) | |||||||
\(434\) | −7366.05 | −0.0391071 | ||||||||
\(435\) | −224633. | −1.18712 | ||||||||
\(436\) | − | 155034.i | − | 0.815558i | ||||||
\(437\) | − | 10568.5i | − | 0.0553417i | ||||||
\(438\) | −69486.6 | −0.362204 | ||||||||
\(439\) | 168825. | 0.876010 | 0.438005 | − | 0.898973i | \(-0.355685\pi\) | ||||
0.438005 | + | 0.898973i | \(0.355685\pi\) | |||||||
\(440\) | 215150. | 1.11131 | ||||||||
\(441\) | −64795.1 | −0.333169 | ||||||||
\(442\) | −92412.7 | −0.473028 | ||||||||
\(443\) | − | 307500.i | − | 1.56689i | −0.621462 | − | 0.783444i | \(-0.713461\pi\) | ||
0.621462 | − | 0.783444i | \(-0.286539\pi\) | |||||||
\(444\) | − | 93512.2i | − | 0.474354i | ||||||
\(445\) | 212828.i | 1.07475i | ||||||||
\(446\) | 270053.i | 1.35763i | ||||||||
\(447\) | 135269.i | 0.676993i | ||||||||
\(448\) | −135.145 | −0.000673352 | ||||||||
\(449\) | −243616. | −1.20841 | −0.604203 | − | 0.796830i | \(-0.706509\pi\) | ||||
−0.604203 | + | 0.796830i | \(0.706509\pi\) | |||||||
\(450\) | − | 146000.i | − | 0.720986i | ||||||
\(451\) | − | 228974.i | − | 1.12573i | ||||||
\(452\) | − | 216105.i | − | 1.05776i | ||||||
\(453\) | 63799.8i | 0.310902i | ||||||||
\(454\) | 277147. | 1.34462 | ||||||||
\(455\) | − | 1587.10i | − | 0.00766620i | ||||||
\(456\) | − | 14388.9i | − | 0.0691988i | ||||||
\(457\) | − | 240817.i | − | 1.15307i | −0.817073 | − | 0.576535i | \(-0.804405\pi\) | ||
0.817073 | − | 0.576535i | \(-0.195595\pi\) | |||||||
\(458\) | −510426. | −2.43333 | ||||||||
\(459\) | 74028.7 | 0.351378 | ||||||||
\(460\) | 49871.3i | 0.235686i | ||||||||
\(461\) | 105419. | 0.496043 | 0.248021 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248021 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(462\) | 4004.12 | 0.0187596 | ||||||||
\(463\) | 177261.i | 0.826895i | 0.910528 | + | 0.413447i | \(0.135675\pi\) | ||||
−0.910528 | + | 0.413447i | \(0.864325\pi\) | |||||||
\(464\) | 333705. | 1.54998 | ||||||||
\(465\) | − | 293436.i | − | 1.35709i | ||||||
\(466\) | −301157. | −1.38682 | ||||||||
\(467\) | − | 387563.i | − | 1.77709i | −0.458792 | − | 0.888544i | \(-0.651718\pi\) | ||
0.458792 | − | 0.888544i | \(-0.348282\pi\) | |||||||
\(468\) | 8252.18i | 0.0376771i | ||||||||
\(469\) | − | 4000.66i | − | 0.0181880i | ||||||
\(470\) | 126213. | 0.571360 | ||||||||
\(471\) | − | 110105.i | − | 0.496322i | ||||||
\(472\) | −126198. | − | 12050.2i | −0.566459 | − | 0.0540892i | ||||
\(473\) | 106471. | 0.475894 | ||||||||
\(474\) | − | 79675.4i | − | 0.354624i | ||||||
\(475\) | 82785.4 | 0.366916 | ||||||||
\(476\) | −4972.31 | −0.0219455 | ||||||||
\(477\) | −89277.7 | −0.392379 | ||||||||
\(478\) | − | 60288.8i | − | 0.263865i | ||||||
\(479\) | 346182. | 1.50881 | 0.754404 | − | 0.656411i | \(-0.227926\pi\) | ||||
0.754404 | + | 0.656411i | \(0.227926\pi\) | |||||||
\(480\) | 216057.i | 0.937749i | ||||||||
\(481\) | 73217.1 | 0.316463 | ||||||||
\(482\) | 66906.3i | 0.287987i | ||||||||
\(483\) | − | 785.207i | − | 0.00336581i | ||||||
\(484\) | 49618.1 | 0.211811 | ||||||||
\(485\) | 540801.i | 2.29908i | ||||||||
\(486\) | − | 18813.6i | − | 0.0796524i | ||||||
\(487\) | −204643. | −0.862855 | −0.431428 | − | 0.902148i | \(-0.641990\pi\) | ||||
−0.431428 | + | 0.902148i | \(0.641990\pi\) | |||||||
\(488\) | 110040. | 0.462072 | ||||||||
\(489\) | 118586. | 0.495927 | ||||||||
\(490\) | 493416.i | 2.05504i | ||||||||
\(491\) | −124429. | −0.516128 | −0.258064 | − | 0.966128i | \(-0.583085\pi\) | ||||
−0.258064 | + | 0.966128i | \(0.583085\pi\) | |||||||
\(492\) | 72261.7 | 0.298523 | ||||||||
\(493\) | −551026. | −2.26714 | ||||||||
\(494\) | −13317.0 | −0.0545696 | ||||||||
\(495\) | 159509.i | 0.650992i | ||||||||
\(496\) | 435917.i | 1.77190i | ||||||||
\(497\) | 1987.06 | 0.00804449 | ||||||||
\(498\) | −205300. | −0.827809 | ||||||||
\(499\) | −410778. | −1.64970 | −0.824851 | − | 0.565350i | \(-0.808741\pi\) | ||||
−0.824851 | + | 0.565350i | \(0.808741\pi\) | |||||||
\(500\) | −166396. | −0.665583 | ||||||||
\(501\) | −147406. | −0.587271 | ||||||||
\(502\) | 104295.i | 0.413863i | ||||||||
\(503\) | − | 245979.i | − | 0.972213i | −0.873899 | − | 0.486107i | \(-0.838417\pi\) | ||
0.873899 | − | 0.486107i | \(-0.161583\pi\) | |||||||
\(504\) | − | 1069.05i | − | 0.00420859i | ||||||
\(505\) | − | 257201.i | − | 1.00853i | ||||||
\(506\) | − | 98514.2i | − | 0.384767i | ||||||
\(507\) | 141946. | 0.552214 | ||||||||
\(508\) | −194263. | −0.752771 | ||||||||
\(509\) | − | 32679.0i | − | 0.126134i | −0.998009 | − | 0.0630672i | \(-0.979912\pi\) | ||
0.998009 | − | 0.0630672i | \(-0.0200882\pi\) | |||||||
\(510\) | − | 563730.i | − | 2.16736i | ||||||
\(511\) | − | 2927.33i | − | 0.0112106i | ||||||
\(512\) | − | 134764.i | − | 0.514085i | ||||||
\(513\) | 10667.8 | 0.0405358 | ||||||||
\(514\) | 195263.i | 0.739084i | ||||||||
\(515\) | 497887.i | 1.87723i | ||||||||
\(516\) | 33601.2i | 0.126199i | ||||||||
\(517\) | −87603.2 | −0.327747 | ||||||||
\(518\) | 11211.7 | 0.0417844 | ||||||||
\(519\) | − | 39391.7i | − | 0.146241i | ||||||
\(520\) | −53162.8 | −0.196608 | ||||||||
\(521\) | −113050. | −0.416479 | −0.208240 | − | 0.978078i | \(-0.566773\pi\) | ||||
−0.208240 | + | 0.978078i | \(0.566773\pi\) | |||||||
\(522\) | 140037.i | 0.513928i | ||||||||
\(523\) | 237542. | 0.868435 | 0.434218 | − | 0.900808i | \(-0.357025\pi\) | ||||
0.434218 | + | 0.900808i | \(0.357025\pi\) | |||||||
\(524\) | 154300.i | 0.561957i | ||||||||
\(525\) | 6150.67 | 0.0223154 | ||||||||
\(526\) | − | 188044.i | − | 0.679656i | ||||||
\(527\) | − | 719802.i | − | 2.59174i | ||||||
\(528\) | − | 236961.i | − | 0.849979i | ||||||
\(529\) | 260522. | 0.930966 | ||||||||
\(530\) | 679851.i | 2.42026i | ||||||||
\(531\) | 8933.87 | − | 93561.4i | 0.0316848 | − | 0.331824i | ||||
\(532\) | −716.525 | −0.00253168 | ||||||||
\(533\) | 56578.6i | 0.199158i | ||||||||
\(534\) | 132678. | 0.465283 | ||||||||
\(535\) | −244903. | −0.855630 | ||||||||
\(536\) | −134010. | −0.466452 | ||||||||
\(537\) | 181549.i | 0.629573i | ||||||||
\(538\) | 614651. | 2.12356 | ||||||||
\(539\) | − | 342474.i | − | 1.17883i | ||||||
\(540\) | −50339.4 | −0.172632 | ||||||||
\(541\) | − | 203519.i | − | 0.695360i | −0.937613 | − | 0.347680i | \(-0.886970\pi\) | ||
0.937613 | − | 0.347680i | \(-0.113030\pi\) | |||||||
\(542\) | − | 24114.3i | − | 0.0820873i | ||||||
\(543\) | 196626. | 0.666871 | ||||||||
\(544\) | 529991.i | 1.79090i | ||||||||
\(545\) | 740477.i | 2.49298i | ||||||||
\(546\) | −989.404 | −0.00331886 | ||||||||
\(547\) | −388812. | −1.29947 | −0.649733 | − | 0.760163i | \(-0.725119\pi\) | ||||
−0.649733 | + | 0.760163i | \(0.725119\pi\) | |||||||
\(548\) | 103072. | 0.343227 | ||||||||
\(549\) | 81582.0i | 0.270676i | ||||||||
\(550\) | 771680. | 2.55101 | ||||||||
\(551\) | −79404.6 | −0.261543 | ||||||||
\(552\) | −26302.0 | −0.0863198 | ||||||||
\(553\) | 3356.57 | 0.0109760 | ||||||||
\(554\) | − | 482209.i | − | 1.57114i | ||||||
\(555\) | 446634.i | 1.44999i | ||||||||
\(556\) | 215311. | 0.696493 | ||||||||
\(557\) | 307150. | 0.990011 | 0.495006 | − | 0.868890i | \(-0.335166\pi\) | ||||
0.495006 | + | 0.868890i | \(0.335166\pi\) | |||||||
\(558\) | −182930. | −0.587511 | ||||||||
\(559\) | −26308.7 | −0.0841929 | ||||||||
\(560\) | −14382.4 | −0.0458624 | ||||||||
\(561\) | 391278.i | 1.24325i | ||||||||
\(562\) | 538093.i | 1.70367i | ||||||||
\(563\) | − | 224936.i | − | 0.709647i | −0.934933 | − | 0.354824i | \(-0.884541\pi\) | ||
0.934933 | − | 0.354824i | \(-0.115459\pi\) | |||||||
\(564\) | − | 27646.6i | − | 0.0869128i | ||||||
\(565\) | 1.03216e6i | 3.23334i | ||||||||
\(566\) | 337203. | 1.05259 | ||||||||
\(567\) | 792.578 | 0.00246533 | ||||||||
\(568\) | − | 66560.4i | − | 0.206310i | ||||||
\(569\) | 48390.1i | 0.149463i | 0.997204 | + | 0.0747313i | \(0.0238099\pi\) | ||||
−0.997204 | + | 0.0747313i | \(0.976190\pi\) | |||||||
\(570\) | − | 81235.2i | − | 0.250032i | ||||||
\(571\) | 344185.i | 1.05565i | 0.849353 | + | 0.527825i | \(0.176992\pi\) | ||||
−0.849353 | + | 0.527825i | \(0.823008\pi\) | |||||||
\(572\) | −43616.8 | −0.133310 | ||||||||
\(573\) | 18548.9i | 0.0564949i | ||||||||
\(574\) | 8663.89i | 0.0262960i | ||||||||
\(575\) | − | 151326.i | − | 0.457697i | ||||||
\(576\) | −3356.20 | −0.0101159 | ||||||||
\(577\) | 68280.6 | 0.205091 | 0.102545 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102545 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(578\) | − | 968019.i | − | 2.89753i | ||||||
\(579\) | 127053. | 0.378990 | ||||||||
\(580\) | 374697. | 1.11384 | ||||||||
\(581\) | − | 8648.88i | − | 0.0256217i | ||||||
\(582\) | 337138. | 0.995319 | ||||||||
\(583\) | − | 471876.i | − | 1.38833i | ||||||
\(584\) | −98056.5 | −0.287509 | ||||||||
\(585\) | − | 39414.2i | − | 0.115170i | ||||||
\(586\) | − | 258093.i | − | 0.751589i | ||||||
\(587\) | 275118.i | 0.798441i | 0.916855 | + | 0.399220i | \(0.130719\pi\) | ||||
−0.916855 | + | 0.399220i | \(0.869281\pi\) | |||||||
\(588\) | 108081. | 0.312604 | ||||||||
\(589\) | − | 103726.i | − | 0.298989i | ||||||
\(590\) | −712472. | − | 68031.6i | −2.04675 | − | 0.195437i | ||||
\(591\) | −154359. | −0.441932 | ||||||||
\(592\) | − | 663502.i | − | 1.89321i | ||||||
\(593\) | 84870.1 | 0.241349 | 0.120674 | − | 0.992692i | \(-0.461494\pi\) | ||||
0.120674 | + | 0.992692i | \(0.461494\pi\) | |||||||
\(594\) | 99439.0 | 0.281828 | ||||||||
\(595\) | 23748.8 | 0.0670823 | ||||||||
\(596\) | − | 225635.i | − | 0.635206i | ||||||
\(597\) | −115258. | −0.323388 | ||||||||
\(598\) | 24342.5i | 0.0680711i | ||||||||
\(599\) | −75105.1 | −0.209322 | −0.104661 | − | 0.994508i | \(-0.533376\pi\) | ||||
−0.104661 | + | 0.994508i | \(0.533376\pi\) | |||||||
\(600\) | − | 206028.i | − | 0.572301i | ||||||
\(601\) | 94230.3i | 0.260880i | 0.991456 | + | 0.130440i | \(0.0416391\pi\) | ||||
−0.991456 | + | 0.130440i | \(0.958361\pi\) | |||||||
\(602\) | −4028.65 | −0.0111165 | ||||||||
\(603\) | − | 99353.0i | − | 0.273241i | ||||||
\(604\) | − | 106421.i | − | 0.291711i | ||||||
\(605\) | −236986. | −0.647460 | ||||||||
\(606\) | −160340. | −0.436614 | ||||||||
\(607\) | 247136. | 0.670747 | 0.335374 | − | 0.942085i | \(-0.391137\pi\) | ||||
0.335374 | + | 0.942085i | \(0.391137\pi\) | |||||||
\(608\) | 76373.4i | 0.206602i | ||||||||
\(609\) | −5899.49 | −0.0159067 | ||||||||
\(610\) | 621249. | 1.66957 | ||||||||
\(611\) | 21646.4 | 0.0579834 | ||||||||
\(612\) | −123483. | −0.329689 | ||||||||
\(613\) | 349727.i | 0.930696i | 0.885128 | + | 0.465348i | \(0.154071\pi\) | ||||
−0.885128 | + | 0.465348i | \(0.845929\pi\) | |||||||
\(614\) | − | 608947.i | − | 1.61526i | ||||||
\(615\) | −345137. | −0.912518 | ||||||||
\(616\) | 5650.45 | 0.0148909 | ||||||||
\(617\) | −645133. | −1.69465 | −0.847323 | − | 0.531078i | \(-0.821787\pi\) | ||||
−0.847323 | + | 0.531078i | \(0.821787\pi\) | |||||||
\(618\) | 310386. | 0.812690 | ||||||||
\(619\) | −473269. | −1.23517 | −0.617585 | − | 0.786504i | \(-0.711889\pi\) | ||||
−0.617585 | + | 0.786504i | \(0.711889\pi\) | |||||||
\(620\) | 489464.i | 1.27332i | ||||||||
\(621\) | − | 19499.9i | − | 0.0505650i | ||||||
\(622\) | 791774.i | 2.04654i | ||||||||
\(623\) | 5589.47i | 0.0144011i | ||||||||
\(624\) | 58552.1i | 0.150374i | ||||||||
\(625\) | 114275. | 0.292544 | ||||||||
\(626\) | 88024.9 | 0.224624 | ||||||||
\(627\) | 56384.4i | 0.143425i | ||||||||
\(628\) | 183659.i | 0.465687i | ||||||||
\(629\) | 1.09560e6i | 2.76917i | ||||||||
\(630\) | − | 6035.50i | − | 0.0152066i | ||||||
\(631\) | 775739. | 1.94831 | 0.974153 | − | 0.225891i | \(-0.0725294\pi\) | ||||
0.974153 | + | 0.225891i | \(0.0725294\pi\) | |||||||
\(632\) | − | 112435.i | − | 0.281492i | ||||||
\(633\) | − | 424655.i | − | 1.05981i | ||||||
\(634\) | 559128.i | 1.39102i | ||||||||
\(635\) | 927842. | 2.30105 | ||||||||
\(636\) | 148919. | 0.368160 | ||||||||
\(637\) | 84624.0i | 0.208552i | ||||||||
\(638\) | −740166. | −1.81839 | ||||||||
\(639\) | 49347.0 | 0.120853 | ||||||||
\(640\) | 690842.i | 1.68663i | ||||||||
\(641\) | 368716. | 0.897380 | 0.448690 | − | 0.893688i | \(-0.351891\pi\) | ||||
0.448690 | + | 0.893688i | \(0.351891\pi\) | |||||||
\(642\) | 152674.i | 0.370420i | ||||||||
\(643\) | −81254.3 | −0.196528 | −0.0982640 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982640 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(644\) | 1309.76i | 0.00315806i | ||||||||
\(645\) | − | 160487.i | − | 0.385762i | ||||||
\(646\) | − | 199271.i | − | 0.477506i | ||||||
\(647\) | −176909. | −0.422612 | −0.211306 | − | 0.977420i | \(-0.567772\pi\) | ||||
−0.211306 | + | 0.977420i | \(0.567772\pi\) | |||||||
\(648\) | − | 26548.9i | − | 0.0632261i | ||||||
\(649\) | 494518. | + | 47219.9i | 1.17407 | + | 0.112108i | ||||
\(650\) | −190679. | −0.451312 | ||||||||
\(651\) | − | 7706.46i | − | 0.0181841i | ||||||
\(652\) | −197807. | −0.465316 | ||||||||
\(653\) | 467222. | 1.09571 | 0.547857 | − | 0.836572i | \(-0.315444\pi\) | ||||
0.547857 | + | 0.836572i | \(0.315444\pi\) | |||||||
\(654\) | 461617. | 1.07926 | ||||||||
\(655\) | − | 736970.i | − | 1.71778i | ||||||
\(656\) | 512722. | 1.19145 | ||||||||
\(657\) | − | 72697.8i | − | 0.168419i | ||||||
\(658\) | 3314.72 | 0.00765588 | ||||||||
\(659\) | 41300.9i | 0.0951018i | 0.998869 | + | 0.0475509i | \(0.0151416\pi\) | ||||
−0.998869 | + | 0.0475509i | \(0.984858\pi\) | |||||||
\(660\) | − | 266069.i | − | 0.610810i | ||||||
\(661\) | −298921. | −0.684153 | −0.342077 | − | 0.939672i | \(-0.611130\pi\) | ||||
−0.342077 | + | 0.939672i | \(0.611130\pi\) | |||||||
\(662\) | 630215.i | 1.43805i | ||||||||
\(663\) | − | 96683.4i | − | 0.219950i | ||||||
\(664\) | −289711. | −0.657095 | ||||||||
\(665\) | 3422.28 | 0.00773877 | ||||||||
\(666\) | 278434. | 0.627732 | ||||||||
\(667\) | 145146.i | 0.326253i | ||||||||
\(668\) | 245879. | 0.551022 | ||||||||
\(669\) | −282533. | −0.631274 | ||||||||
\(670\) | −756575. | −1.68540 | ||||||||
\(671\) | −431201. | −0.957712 | ||||||||
\(672\) | 5674.28i | 0.0125653i | ||||||||
\(673\) | 814423.i | 1.79812i | 0.437821 | + | 0.899062i | \(0.355751\pi\) | ||||
−0.437821 | + | 0.899062i | \(0.644249\pi\) | |||||||
\(674\) | −724549. | −1.59495 | ||||||||
\(675\) | 152747. | 0.335247 | ||||||||
\(676\) | −236772. | −0.518129 | ||||||||
\(677\) | −345729. | −0.754324 | −0.377162 | − | 0.926147i | \(-0.623100\pi\) | ||||
−0.377162 | + | 0.926147i | \(0.623100\pi\) | |||||||
\(678\) | 643456. | 1.39978 | ||||||||
\(679\) | 14203.0i | 0.0308063i | ||||||||
\(680\) | − | 795512.i | − | 1.72040i | ||||||
\(681\) | 289955.i | 0.625225i | ||||||||
\(682\) | − | 966873.i | − | 2.07874i | ||||||
\(683\) | 239945.i | 0.514363i | 0.966363 | + | 0.257181i | \(0.0827938\pi\) | ||||
−0.966363 | + | 0.257181i | \(0.917206\pi\) | |||||||
\(684\) | −17794.3 | −0.0380337 | ||||||||
\(685\) | −492295. | −1.04917 | ||||||||
\(686\) | 25923.4i | 0.0550863i | ||||||||
\(687\) | − | 534014.i | − | 1.13146i | ||||||
\(688\) | 238412.i | 0.503677i | ||||||||
\(689\) | 116599.i | 0.245616i | ||||||||
\(690\) | −148492. | −0.311893 | ||||||||
\(691\) | − | 695558.i | − | 1.45672i | −0.685193 | − | 0.728362i | \(-0.740282\pi\) | ||
0.685193 | − | 0.728362i | \(-0.259718\pi\) | |||||||
\(692\) | 65707.1i | 0.137215i | ||||||||
\(693\) | 4189.17i | 0.00872290i | ||||||||
\(694\) | 587206. | 1.21919 | ||||||||
\(695\) | −1.02837e6 | −2.12902 | ||||||||
\(696\) | 197614.i | 0.407944i | ||||||||
\(697\) | −846626. | −1.74271 | ||||||||
\(698\) | −121727. | −0.249848 | ||||||||
\(699\) | − | 315075.i | − | 0.644850i | ||||||
\(700\) | −10259.6 | −0.0209379 | ||||||||
\(701\) | 839756.i | 1.70890i | 0.519533 | + | 0.854451i | \(0.326106\pi\) | ||||
−0.519533 | + | 0.854451i | \(0.673894\pi\) | |||||||
\(702\) | −24571.0 | −0.0498596 | ||||||||
\(703\) | 157879.i | 0.319458i | ||||||||
\(704\) | − | 17739.2i | − | 0.0357922i | ||||||
\(705\) | 132046.i | 0.265673i | ||||||||
\(706\) | −188770. | −0.378725 | ||||||||
\(707\) | − | 6754.82i | − | 0.0135137i | ||||||
\(708\) | −14902.1 | + | 156065.i | −0.0297290 | + | 0.311342i | ||||
\(709\) | 340569. | 0.677505 | 0.338753 | − | 0.940875i | \(-0.389995\pi\) | ||||
0.338753 | + | 0.940875i | \(0.389995\pi\) | |||||||
\(710\) | − | 375778.i | − | 0.745444i | ||||||
\(711\) | 83357.5 | 0.164894 | ||||||||
\(712\) | 187230. | 0.369331 | ||||||||
\(713\) | −189603. | −0.372964 | ||||||||
\(714\) | − | 14805.1i | − | 0.0290413i | ||||||
\(715\) | 208323. | 0.407498 | ||||||||
\(716\) | − | 302832.i | − | 0.590712i | ||||||
\(717\) | 63075.0 | 0.122693 | ||||||||
\(718\) | − | 956093.i | − | 1.85460i | ||||||
\(719\) | 155487.i | 0.300770i | 0.988627 | + | 0.150385i | \(0.0480514\pi\) | ||||
−0.988627 | + | 0.150385i | \(0.951949\pi\) | |||||||
\(720\) | −357176. | −0.688996 | ||||||||
\(721\) | 13075.9i | 0.0251537i | ||||||||
\(722\) | 618541.i | 1.18657i | ||||||||
\(723\) | −69998.2 | −0.133909 | ||||||||
\(724\) | −327981. | −0.625708 | ||||||||
\(725\) | −1.13696e6 | −2.16306 | ||||||||
\(726\) | 147739.i | 0.280299i | ||||||||
\(727\) | −61349.1 | −0.116075 | −0.0580376 | − | 0.998314i | \(-0.518484\pi\) | ||||
−0.0580376 | + | 0.998314i | \(0.518484\pi\) | |||||||
\(728\) | −1396.20 | −0.00263443 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −553595. | −1.03884 | ||||||||
\(731\) | − | 393675.i | − | 0.736722i | ||||||
\(732\) | − | 136082.i | − | 0.253969i | ||||||
\(733\) | 39246.3 | 0.0730451 | 0.0365225 | − | 0.999333i | \(-0.488372\pi\) | ||||
0.0365225 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(734\) | −90864.4 | −0.168656 | ||||||||
\(735\) | −516218. | −0.955561 | ||||||||
\(736\) | 139605. | 0.257719 | ||||||||
\(737\) | 525130. | 0.966789 | ||||||||
\(738\) | 215160.i | 0.395048i | ||||||||
\(739\) | − | 856850.i | − | 1.56898i | −0.620144 | − | 0.784488i | \(-0.712926\pi\) | ||
0.620144 | − | 0.784488i | \(-0.287074\pi\) | |||||||
\(740\) | − | 745006.i | − | 1.36049i | ||||||
\(741\) | − | 13932.4i | − | 0.0253740i | ||||||
\(742\) | 17854.8i | 0.0324300i | ||||||||
\(743\) | 598825. | 1.08473 | 0.542366 | − | 0.840143i | \(-0.317529\pi\) | ||||
0.542366 | + | 0.840143i | \(0.317529\pi\) | |||||||
\(744\) | −258142. | −0.466352 | ||||||||
\(745\) | 1.07768e6i | 1.94168i | ||||||||
\(746\) | − | 286230.i | − | 0.514325i | ||||||
\(747\) | − | 214788.i | − | 0.384918i | ||||||
\(748\) | − | 652670.i | − | 1.16651i | ||||||
\(749\) | −6431.83 | −0.0114649 | ||||||||
\(750\) | − | 495446.i | − | 0.880792i | ||||||
\(751\) | − | 332338.i | − | 0.589250i | −0.955613 | − | 0.294625i | \(-0.904805\pi\) | ||
0.955613 | − | 0.294625i | \(-0.0951947\pi\) | |||||||
\(752\) | − | 196162.i | − | 0.346880i | ||||||
\(753\) | −109115. | −0.192439 | ||||||||
\(754\) | 182892. | 0.321701 | ||||||||
\(755\) | 508289.i | 0.891696i | ||||||||
\(756\) | −1322.06 | −0.00231316 | ||||||||
\(757\) | 824719. | 1.43918 | 0.719588 | − | 0.694401i | \(-0.244331\pi\) | ||||
0.719588 | + | 0.694401i | \(0.244331\pi\) | |||||||
\(758\) | − | 848387.i | − | 1.47658i | ||||||
\(759\) | 103067. | 0.178910 | ||||||||
\(760\) | − | 114636.i | − | 0.198469i | ||||||
\(761\) | 1.09768e6 | 1.89542 | 0.947711 | − | 0.319130i | \(-0.103391\pi\) | ||||
0.947711 | + | 0.319130i | \(0.103391\pi\) | |||||||
\(762\) | − | 578422.i | − | 0.996173i | ||||||
\(763\) | 19447.0i | 0.0334044i | ||||||||
\(764\) | − | 30940.4i | − | 0.0530078i | ||||||
\(765\) | 589782. | 1.00779 | ||||||||
\(766\) | 1.09823e6i | 1.87170i | ||||||||
\(767\) | −122194. | − | 11667.9i | −0.207710 | − | 0.0198336i | ||||
\(768\) | 420340. | 0.712654 | ||||||||
\(769\) | − | 237713.i | − | 0.401976i | −0.979594 | − | 0.200988i | \(-0.935585\pi\) | ||
0.979594 | − | 0.200988i | \(-0.0644153\pi\) | |||||||
\(770\) | 31900.6 | 0.0538043 | ||||||||
\(771\) | −204287. | −0.343662 | ||||||||
\(772\) | −211930. | −0.355597 | ||||||||
\(773\) | − | 998180.i | − | 1.67051i | −0.549860 | − | 0.835257i | \(-0.685319\pi\) | ||
0.549860 | − | 0.835257i | \(-0.314681\pi\) | |||||||
\(774\) | −100048. | −0.167004 | ||||||||
\(775\) | − | 1.48520e6i | − | 2.47276i | ||||||
\(776\) | 475755. | 0.790060 | ||||||||
\(777\) | 11729.9i | 0.0194290i | ||||||||
\(778\) | − | 432849.i | − | 0.715117i | ||||||
\(779\) | −122001. | −0.201043 | ||||||||
\(780\) | 65744.6i | 0.108061i | ||||||||
\(781\) | 260823.i | 0.427606i | ||||||||
\(782\) | −364254. | −0.595649 | ||||||||
\(783\) | −146509. | −0.238968 | ||||||||
\(784\) | 766873. | 1.24765 | ||||||||
\(785\) | − | 877196.i | − | 1.42350i | ||||||
\(786\) | −459431. | −0.743661 | ||||||||
\(787\) | −292759. | −0.472673 | −0.236337 | − | 0.971671i | \(-0.575947\pi\) | ||||
−0.236337 | + | 0.971671i | \(0.575947\pi\) | |||||||
\(788\) | 257477. | 0.414654 | ||||||||
\(789\) | 196734. | 0.316029 | ||||||||
\(790\) | − | 634769.i | − | 1.01709i | ||||||
\(791\) | 27107.5i | 0.0433248i | ||||||||
\(792\) | 140324. | 0.223708 | ||||||||
\(793\) | 106548. | 0.169434 | ||||||||
\(794\) | −626566. | −0.993861 | ||||||||
\(795\) | −711269. | −1.12538 | ||||||||
\(796\) | 192256. | 0.303427 | ||||||||
\(797\) | − | 105074.i | − | 0.165416i | −0.996574 | − | 0.0827079i | \(-0.973643\pi\) | ||
0.996574 | − | 0.0827079i | \(-0.0263569\pi\) | |||||||
\(798\) | − | 2133.47i | − | 0.00335027i | ||||||
\(799\) | 323911.i | 0.507378i | ||||||||
\(800\) | 1.09355e6i | 1.70868i | ||||||||
\(801\) | 138810.i | 0.216349i | ||||||||
\(802\) | 135807. | 0.211142 | ||||||||
\(803\) | 384244. | 0.595903 | ||||||||
\(804\) | 165725.i | 0.256375i | ||||||||
\(805\) | − | 6255.69i | − | 0.00965347i | ||||||
\(806\) | 238911.i | 0.367761i | ||||||||
\(807\) | 643056.i | 0.987419i | ||||||||
\(808\) | −226265. | −0.346573 | ||||||||
\(809\) | 526375.i | 0.804263i | 0.915582 | + | 0.402131i | \(0.131731\pi\) | ||||
−0.915582 | + | 0.402131i | \(0.868269\pi\) | |||||||
\(810\) | − | 149886.i | − | 0.228451i | ||||||
\(811\) | − | 725298.i | − | 1.10274i | −0.834260 | − | 0.551372i | \(-0.814105\pi\) | ||
0.834260 | − | 0.551372i | \(-0.185895\pi\) | |||||||
\(812\) | 9840.61 | 0.0149248 | ||||||||
\(813\) | 25228.7 | 0.0381692 | ||||||||
\(814\) | 1.47166e6i | 2.22106i | ||||||||
\(815\) | 944770. | 1.42237 | ||||||||
\(816\) | −876156. | −1.31583 | ||||||||
\(817\) | − | 56729.8i | − | 0.0849899i | ||||||
\(818\) | 521160. | 0.778869 | ||||||||
\(819\) | − | 1035.13i | − | 0.00154321i | ||||||
\(820\) | 575704. | 0.856193 | ||||||||
\(821\) | 299805.i | 0.444787i | 0.974957 | + | 0.222393i | \(0.0713870\pi\) | ||||
−0.974957 | + | 0.222393i | \(0.928613\pi\) | |||||||
\(822\) | 306900.i | 0.454206i | ||||||||
\(823\) | − | 416111.i | − | 0.614341i | −0.951655 | − | 0.307170i | \(-0.900618\pi\) | ||
0.951655 | − | 0.307170i | \(-0.0993821\pi\) | |||||||
\(824\) | 438003. | 0.645094 | ||||||||
\(825\) | 807342.i | 1.18618i | ||||||||
\(826\) | −18711.5 | − | 1786.70i | −0.0274252 | − | 0.00261874i | ||||
\(827\) | 1.32953e6 | 1.94396 | 0.971982 | − | 0.235057i | \(-0.0755277\pi\) | ||||
0.971982 | + | 0.235057i | \(0.0755277\pi\) | |||||||
\(828\) | 32526.8i | 0.0474439i | ||||||||
\(829\) | 212633. | 0.309401 | 0.154700 | − | 0.987961i | \(-0.450559\pi\) | ||||
0.154700 | + | 0.987961i | \(0.450559\pi\) | |||||||
\(830\) | −1.63561e6 | −2.37424 | ||||||||
\(831\) | 504493. | 0.730555 | ||||||||
\(832\) | 4383.28i | 0.00633217i | ||||||||
\(833\) | −1.26629e6 | −1.82492 | ||||||||
\(834\) | 641093.i | 0.921698i | ||||||||
\(835\) | −1.17437e6 | −1.68435 | ||||||||
\(836\) | − | 94051.7i | − | 0.134572i | ||||||
\(837\) | − | 191383.i | − | 0.273183i | ||||||
\(838\) | −1.00982e6 | −1.43798 | ||||||||
\(839\) | 916109.i | 1.30144i | 0.759319 | + | 0.650719i | \(0.225532\pi\) | ||||
−0.759319 | + | 0.650719i | \(0.774468\pi\) | |||||||
\(840\) | − | 8517.04i | − | 0.0120706i | ||||||
\(841\) | 383244. | 0.541856 | ||||||||
\(842\) | 39315.3 | 0.0554546 | ||||||||
\(843\) | −562960. | −0.792177 | ||||||||
\(844\) | 708343.i | 0.994394i | ||||||||
\(845\) | 1.13088e6 | 1.58380 | ||||||||
\(846\) | 82318.2 | 0.115015 | ||||||||
\(847\) | −6223.93 | −0.00867557 | ||||||||
\(848\) | 1.05663e6 | 1.46937 | ||||||||
\(849\) | 352786.i | 0.489437i | ||||||||
\(850\) | − | 2.85327e6i | − | 3.94916i | ||||||
\(851\) | 288592. | 0.398497 | ||||||||
\(852\) | −82313.0 | −0.113394 | ||||||||
\(853\) | 1.10136e6 | 1.51367 | 0.756833 | − | 0.653609i | \(-0.226746\pi\) | ||||
0.756833 | + | 0.653609i | \(0.226746\pi\) | |||||||
\(854\) | 16315.7 | 0.0223713 | ||||||||
\(855\) | 84989.4 | 0.116261 | ||||||||
\(856\) | 215446.i | 0.294030i | ||||||||
\(857\) | − | 1.13182e6i | − | 1.54105i | −0.637410 | − | 0.770525i | \(-0.719994\pi\) | ||
0.637410 | − | 0.770525i | \(-0.280006\pi\) | |||||||
\(858\) | − | 129870.i | − | 0.176414i | ||||||
\(859\) | 574395.i | 0.778439i | 0.921145 | + | 0.389220i | \(0.127255\pi\) | ||||
−0.921145 | + | 0.389220i | \(0.872745\pi\) | |||||||
\(860\) | 267699.i | 0.361951i | ||||||||
\(861\) | −9064.28 | −0.0122272 | ||||||||
\(862\) | −829178. | −1.11592 | ||||||||
\(863\) | − | 792718.i | − | 1.06438i | −0.846625 | − | 0.532190i | \(-0.821369\pi\) | ||
0.846625 | − | 0.532190i | \(-0.178631\pi\) | |||||||
\(864\) | 140916.i | 0.188770i | ||||||||
\(865\) | − | 313831.i | − | 0.419434i | ||||||
\(866\) | 234349.i | 0.312483i | ||||||||
\(867\) | 1.01275e6 | 1.34730 | ||||||||
\(868\) | 12854.7i | 0.0170617i | ||||||||
\(869\) | 440585.i | 0.583432i | ||||||||
\(870\) | 1.11567e6i | 1.47400i | ||||||||
\(871\) | −129758. | −0.171039 | ||||||||
\(872\) | 651414. | 0.856691 | ||||||||
\(873\) | 352719.i | 0.462807i | ||||||||
\(874\) | −52490.1 | −0.0687154 | ||||||||
\(875\) | 20872.1 | 0.0272616 | ||||||||
\(876\) | 121263.i | 0.158023i | ||||||||
\(877\) | −17892.2 | −0.0232629 | −0.0116314 | − | 0.999932i | \(-0.503702\pi\) | ||||
−0.0116314 | + | 0.999932i | \(0.503702\pi\) | |||||||
\(878\) | − | 838494.i | − | 1.08770i | ||||||
\(879\) | 270020. | 0.349476 | ||||||||
\(880\) | − | 1.88785e6i | − | 2.43782i | ||||||
\(881\) | − | 1.36036e6i | − | 1.75268i | −0.481697 | − | 0.876338i | \(-0.659979\pi\) | ||
0.481697 | − | 0.876338i | \(-0.340021\pi\) | |||||||
\(882\) | 321813.i | 0.413682i | ||||||||
\(883\) | 125594. | 0.161082 | 0.0805408 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805408 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(884\) | 161272.i | 0.206374i | ||||||||
\(885\) | 71175.5 | − | 745398.i | 0.0908750 | − | 0.951703i | ||||
\(886\) | −1.52724e6 | −1.94554 | ||||||||
\(887\) | 1.43325e6i | 1.82169i | 0.412750 | + | 0.910844i | \(0.364568\pi\) | ||||
−0.412750 | + | 0.910844i | \(0.635432\pi\) | |||||||
\(888\) | 392914. | 0.498278 | ||||||||
\(889\) | 24367.8 | 0.0308327 | ||||||||
\(890\) | 1.05704e6 | 1.33448 | ||||||||
\(891\) | 104034.i | 0.131045i | ||||||||
\(892\) | 471278. | 0.592308 | ||||||||
\(893\) | 46676.5i | 0.0585323i | ||||||||
\(894\) | 671833. | 0.840594 | ||||||||
\(895\) | 1.44639e6i | 1.80567i | ||||||||
\(896\) | 18143.5i | 0.0225998i | ||||||||
\(897\) | −25467.4 | −0.0316519 | ||||||||
\(898\) | 1.20995e6i | 1.50043i | ||||||||
\(899\) | 1.42455e6i | 1.76261i | ||||||||
\(900\) | −254788. | −0.314553 | ||||||||
\(901\) | −1.74475e6 | −2.14924 | ||||||||
\(902\) | −1.13723e6 | −1.39777 | ||||||||
\(903\) | − | 4214.83i | − | 0.00516898i | ||||||
\(904\) | 908018. | 1.11111 | ||||||||
\(905\) | 1.56651e6 | 1.91265 | ||||||||
\(906\) | 316870. | 0.386033 | ||||||||
\(907\) | 780561. | 0.948838 | 0.474419 | − | 0.880299i | \(-0.342658\pi\) | ||||
0.474419 | + | 0.880299i | \(0.342658\pi\) | |||||||
\(908\) | − | 483657.i | − | 0.586633i | ||||||
\(909\) | − | 167750.i | − | 0.203018i | ||||||
\(910\) | −7882.51 | −0.00951880 | ||||||||
\(911\) | 414587. | 0.499550 | 0.249775 | − | 0.968304i | \(-0.419643\pi\) | ||||
0.249775 | + | 0.968304i | \(0.419643\pi\) | |||||||
\(912\) | −126257. | −0.151798 | ||||||||
\(913\) | 1.13526e6 | 1.36192 | ||||||||
\(914\) | −1.19605e6 | −1.43172 | ||||||||
\(915\) | 649959.i | 0.776325i | ||||||||
\(916\) | 890759.i | 1.06162i | ||||||||
\(917\) | − | 19354.9i | − | 0.0230172i | ||||||
\(918\) | − | 367673.i | − | 0.436291i | ||||||
\(919\) | − | 56347.3i | − | 0.0667179i | −0.999443 | − | 0.0333590i | \(-0.989380\pi\) | ||
0.999443 | − | 0.0333590i | \(-0.0106205\pi\) | |||||||
\(920\) | −209546. | −0.247573 | ||||||||
\(921\) | 637088. | 0.751069 | ||||||||
\(922\) | − | 523580.i | − | 0.615915i | ||||||
\(923\) | − | 64448.4i | − | 0.0756500i | ||||||
\(924\) | − | 6987.72i | − | 0.00818448i | ||||||
\(925\) | 2.26060e6i | 2.64204i | ||||||||
\(926\) | 880388. | 1.02672 | ||||||||
\(927\) | 324730.i | 0.377887i | ||||||||
\(928\) | − | 1.04890e6i | − | 1.21797i | ||||||
\(929\) | − | 1.10326e6i | − | 1.27834i | −0.769067 | − | 0.639168i | \(-0.779279\pi\) | ||
0.769067 | − | 0.639168i | \(-0.220721\pi\) | |||||||
\(930\) | −1.45739e6 | −1.68504 | ||||||||
\(931\) | −182476. | −0.210526 | ||||||||
\(932\) | 525558.i | 0.605047i | ||||||||
\(933\) | −828364. | −0.951608 | ||||||||
\(934\) | −1.92488e6 | −2.20653 | ||||||||
\(935\) | 3.11729e6i | 3.56577i | ||||||||
\(936\) | −34673.5 | −0.0395773 | ||||||||
\(937\) | − | 912935.i | − | 1.03983i | −0.854219 | − | 0.519913i | \(-0.825964\pi\) | ||
0.854219 | − | 0.519913i | \(-0.174036\pi\) | |||||||
\(938\) | −19869.8 | −0.0225833 | ||||||||
\(939\) | 92092.8i | 0.104447i | ||||||||
\(940\) | − | 220259.i | − | 0.249274i | ||||||
\(941\) | − | 1.63562e6i | − | 1.84716i | −0.383409 | − | 0.923579i | \(-0.625250\pi\) | ||
0.383409 | − | 0.923579i | \(-0.374750\pi\) | |||||||
\(942\) | −546849. | −0.616262 | ||||||||
\(943\) | 223010.i | 0.250785i | ||||||||
\(944\) | −105735. | + | 1.10733e6i | −0.118652 | + | 1.24261i | ||||
\(945\) | 6314.42 | 0.00707082 | ||||||||
\(946\) | − | 528804.i | − | 0.590898i | ||||||
\(947\) | −927647. | −1.03439 | −0.517193 | − | 0.855869i | \(-0.673023\pi\) | ||||
−0.517193 | + | 0.855869i | \(0.673023\pi\) | |||||||
\(948\) | −139044. | −0.154716 | ||||||||
\(949\) | −94945.2 | −0.105424 | ||||||||
\(950\) | − | 411165.i | − | 0.455584i | ||||||
\(951\) | −584967. | −0.646800 | ||||||||
\(952\) | − | 20892.4i | − | 0.0230523i | ||||||
\(953\) | −1.38318e6 | −1.52297 | −0.761487 | − | 0.648180i | \(-0.775530\pi\) | ||||
−0.761487 | + | 0.648180i | \(0.775530\pi\) | |||||||
\(954\) | 443409.i | 0.487201i | ||||||||
\(955\) | 147778.i | 0.162033i | ||||||||
\(956\) | −105212. | −0.115119 | ||||||||
\(957\) | − | 774371.i | − | 0.845523i | ||||||
\(958\) | − | 1.71936e6i | − | 1.87342i | ||||||
\(959\) | −12929.1 | −0.0140582 | ||||||||
\(960\) | −26738.6 | −0.0290133 | ||||||||
\(961\) | −937353. | −1.01498 | ||||||||
\(962\) | − | 363642.i | − | 0.392938i | ||||||
\(963\) | −159729. | −0.172239 | ||||||||
\(964\) | 116760. | 0.125644 | ||||||||
\(965\) | 1.01222e6 | 1.08698 | ||||||||
\(966\) | −3899.83 | −0.00417918 | ||||||||
\(967\) | − | 671415.i | − | 0.718023i | −0.933333 | − | 0.359011i | \(-0.883114\pi\) | ||
0.933333 | − | 0.359011i | \(-0.116886\pi\) | |||||||
\(968\) | 208482.i | 0.222494i | ||||||||
\(969\) | 208480. | 0.222033 | ||||||||
\(970\) | 2.68596e6 | 2.85467 | ||||||||
\(971\) | −819673. | −0.869365 | −0.434683 | − | 0.900584i | \(-0.643139\pi\) | ||||
−0.434683 | + | 0.900584i | \(0.643139\pi\) | |||||||
\(972\) | −32832.1 | −0.0347509 | ||||||||
\(973\) | −27007.9 | −0.0285276 | ||||||||
\(974\) | 1.01638e6i | 1.07137i | ||||||||
\(975\) | − | 199491.i | − | 0.209853i | ||||||
\(976\) | − | 965552.i | − | 1.01362i | ||||||
\(977\) | − | 209664.i | − | 0.219651i | −0.993951 | − | 0.109826i | \(-0.964971\pi\) | ||
0.993951 | − | 0.109826i | \(-0.0350293\pi\) | |||||||
\(978\) | − | 588975.i | − | 0.615771i | ||||||
\(979\) | −733678. | −0.765491 | ||||||||
\(980\) | 861075. | 0.896579 | ||||||||
\(981\) | 482950.i | 0.501839i | ||||||||
\(982\) | 617991.i | 0.640854i | ||||||||
\(983\) | 777728.i | 0.804861i | 0.915451 | + | 0.402431i | \(0.131835\pi\) | ||||
−0.915451 | + | 0.402431i | \(0.868165\pi\) | |||||||
\(984\) | 303625.i | 0.313579i | ||||||||
\(985\) | −1.22976e6 | −1.26750 | ||||||||
\(986\) | 2.73674e6i | 2.81501i | ||||||||
\(987\) | 3467.90i | 0.00355986i | ||||||||
\(988\) | 23239.8i | 0.0238078i | ||||||||
\(989\) | −103698. | −0.106018 | ||||||||
\(990\) | 792224. | 0.808309 | ||||||||
\(991\) | 1.67117e6i | 1.70166i | 0.525442 | + | 0.850829i | \(0.323900\pi\) | ||||
−0.525442 | + | 0.850829i | \(0.676100\pi\) | |||||||
\(992\) | 1.37016e6 | 1.39235 | ||||||||
\(993\) | −659339. | −0.668668 | ||||||||
\(994\) | − | 9869.00i | − | 0.00998850i | ||||||
\(995\) | −918257. | −0.927509 | ||||||||
\(996\) | 358275.i | 0.361159i | ||||||||
\(997\) | 43262.3 | 0.0435230 | 0.0217615 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217615 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(998\) | 2.04018e6i | 2.04837i | ||||||||
\(999\) | 291301.i | 0.291885i |
(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 | 177.5.c.a.58.8 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.33 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.33 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.8 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.8 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.33 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.8 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.33 | 40 | 3.2 | odd | 2 |