Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,3,Mod(10,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.10");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(0.899184872389\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.39744.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 12x^{2} + 4x + 22 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.2 | ||
Root | \(1.36603 + 3.21405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.10 |
Dual form | 33.3.c.a.10.3 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.35285i | − | 1.17642i | −0.808707 | − | 0.588212i | \(-0.799832\pi\) | ||
0.808707 | − | 0.588212i | \(-0.200168\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −1.53590 | −0.383975 | ||||||||
\(5\) | −4.19615 | −0.839230 | −0.419615 | − | 0.907702i | \(-0.637835\pi\) | ||||
−0.419615 | + | 0.907702i | \(0.637835\pi\) | |||||||
\(6\) | − | 4.07525i | − | 0.679209i | ||||||
\(7\) | 6.42810i | 0.918300i | 0.888359 | + | 0.459150i | \(0.151846\pi\) | ||||
−0.888359 | + | 0.459150i | \(0.848154\pi\) | |||||||
\(8\) | − | 5.79766i | − | 0.724707i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 9.87291i | 0.987291i | ||||||||
\(11\) | 3.26795 | + | 10.5034i | 0.297086 | + | 0.954851i | ||||
\(12\) | −2.66025 | −0.221688 | ||||||||
\(13\) | 7.68899i | 0.591461i | 0.955271 | + | 0.295730i | \(0.0955630\pi\) | ||||
−0.955271 | + | 0.295730i | \(0.904437\pi\) | |||||||
\(14\) | 15.1244 | 1.08031 | ||||||||
\(15\) | −7.26795 | −0.484530 | ||||||||
\(16\) | −19.7846 | −1.23654 | ||||||||
\(17\) | − | 8.15051i | − | 0.479442i | −0.970842 | − | 0.239721i | \(-0.922944\pi\) | ||
0.970842 | − | 0.239721i | \(-0.0770559\pi\) | |||||||
\(18\) | − | 7.05855i | − | 0.392141i | ||||||
\(19\) | − | 30.4181i | − | 1.60095i | −0.599364 | − | 0.800477i | \(-0.704580\pi\) | ||
0.599364 | − | 0.800477i | \(-0.295420\pi\) | |||||||
\(20\) | 6.44486 | 0.322243 | ||||||||
\(21\) | 11.1338i | 0.530181i | ||||||||
\(22\) | 24.7128 | − | 7.68899i | 1.12331 | − | 0.349500i | ||||
\(23\) | −31.6603 | −1.37653 | −0.688266 | − | 0.725458i | \(-0.741628\pi\) | ||||
−0.688266 | + | 0.725458i | \(0.741628\pi\) | |||||||
\(24\) | − | 10.0418i | − | 0.418410i | ||||||
\(25\) | −7.39230 | −0.295692 | ||||||||
\(26\) | 18.0910 | 0.695809 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 9.87291i | − | 0.352604i | ||||||
\(29\) | 6.88962i | 0.237573i | 0.992920 | + | 0.118787i | \(0.0379004\pi\) | ||||
−0.992920 | + | 0.118787i | \(0.962100\pi\) | |||||||
\(30\) | 17.1004i | 0.570013i | ||||||||
\(31\) | 51.1769 | 1.65087 | 0.825434 | − | 0.564498i | \(-0.190930\pi\) | ||||
0.825434 | + | 0.564498i | \(0.190930\pi\) | |||||||
\(32\) | 23.3596i | 0.729986i | ||||||||
\(33\) | 5.66025 | + | 18.1923i | 0.171523 | + | 0.551283i | ||||
\(34\) | −19.1769 | −0.564027 | ||||||||
\(35\) | − | 26.9733i | − | 0.770666i | ||||||
\(36\) | −4.60770 | −0.127992 | ||||||||
\(37\) | −19.4641 | −0.526057 | −0.263028 | − | 0.964788i | \(-0.584721\pi\) | ||||
−0.263028 | + | 0.964788i | \(0.584721\pi\) | |||||||
\(38\) | −71.5692 | −1.88340 | ||||||||
\(39\) | 13.3177i | 0.341480i | ||||||||
\(40\) | 24.3279i | 0.608197i | ||||||||
\(41\) | 47.9800i | 1.17024i | 0.810945 | + | 0.585122i | \(0.198953\pi\) | ||||
−0.810945 | + | 0.585122i | \(0.801047\pi\) | |||||||
\(42\) | 26.1962 | 0.623718 | ||||||||
\(43\) | − | 81.8429i | − | 1.90332i | −0.307147 | − | 0.951662i | \(-0.599374\pi\) | ||
0.307147 | − | 0.951662i | \(-0.400626\pi\) | |||||||
\(44\) | −5.01924 | − | 16.1321i | −0.114074 | − | 0.366638i | ||||
\(45\) | −12.5885 | −0.279743 | ||||||||
\(46\) | 74.4918i | 1.61939i | ||||||||
\(47\) | 30.1962 | 0.642471 | 0.321236 | − | 0.946999i | \(-0.395902\pi\) | ||||
0.321236 | + | 0.946999i | \(0.395902\pi\) | |||||||
\(48\) | −34.2679 | −0.713916 | ||||||||
\(49\) | 7.67949 | 0.156724 | ||||||||
\(50\) | 17.3930i | 0.347860i | ||||||||
\(51\) | − | 14.1171i | − | 0.276806i | ||||||
\(52\) | − | 11.8095i | − | 0.227106i | ||||||
\(53\) | 26.0526 | 0.491558 | 0.245779 | − | 0.969326i | \(-0.420956\pi\) | ||||
0.245779 | + | 0.969326i | \(0.420956\pi\) | |||||||
\(54\) | − | 12.2258i | − | 0.226403i | ||||||
\(55\) | −13.7128 | − | 44.0737i | −0.249324 | − | 0.801340i | ||||
\(56\) | 37.2679 | 0.665499 | ||||||||
\(57\) | − | 52.6857i | − | 0.924311i | ||||||
\(58\) | 16.2102 | 0.279487 | ||||||||
\(59\) | 82.7461 | 1.40248 | 0.701238 | − | 0.712927i | \(-0.252631\pi\) | ||||
0.701238 | + | 0.712927i | \(0.252631\pi\) | |||||||
\(60\) | 11.1628 | 0.186047 | ||||||||
\(61\) | 75.4148i | 1.23631i | 0.786057 | + | 0.618154i | \(0.212119\pi\) | ||||
−0.786057 | + | 0.618154i | \(0.787881\pi\) | |||||||
\(62\) | − | 120.412i | − | 1.94212i | ||||||
\(63\) | 19.2843i | 0.306100i | ||||||||
\(64\) | −24.1769 | −0.377764 | ||||||||
\(65\) | − | 32.2642i | − | 0.496372i | ||||||
\(66\) | 42.8038 | − | 13.3177i | 0.648543 | − | 0.201784i | ||||
\(67\) | −34.0000 | −0.507463 | −0.253731 | − | 0.967275i | \(-0.581658\pi\) | ||||
−0.253731 | + | 0.967275i | \(0.581658\pi\) | |||||||
\(68\) | 12.5184i | 0.184093i | ||||||||
\(69\) | −54.8372 | −0.794742 | ||||||||
\(70\) | −63.4641 | −0.906630 | ||||||||
\(71\) | −72.7321 | −1.02440 | −0.512198 | − | 0.858868i | \(-0.671168\pi\) | ||||
−0.512198 | + | 0.858868i | \(0.671168\pi\) | |||||||
\(72\) | − | 17.3930i | − | 0.241569i | ||||||
\(73\) | 54.8696i | 0.751639i | 0.926693 | + | 0.375819i | \(0.122639\pi\) | ||||
−0.926693 | + | 0.375819i | \(0.877361\pi\) | |||||||
\(74\) | 45.7961i | 0.618866i | ||||||||
\(75\) | −12.8038 | −0.170718 | ||||||||
\(76\) | 46.7191i | 0.614725i | ||||||||
\(77\) | −67.5167 | + | 21.0067i | −0.876840 | + | 0.272814i | ||||
\(78\) | 31.3346 | 0.401726 | ||||||||
\(79\) | 24.3279i | 0.307948i | 0.988075 | + | 0.153974i | \(0.0492071\pi\) | ||||
−0.988075 | + | 0.153974i | \(0.950793\pi\) | |||||||
\(80\) | 83.0192 | 1.03774 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 112.890 | 1.37670 | ||||||||
\(83\) | 0.923034i | 0.0111209i | 0.999985 | + | 0.00556045i | \(0.00176995\pi\) | ||||
−0.999985 | + | 0.00556045i | \(0.998230\pi\) | |||||||
\(84\) | − | 17.1004i | − | 0.203576i | ||||||
\(85\) | 34.2008i | 0.402362i | ||||||||
\(86\) | −192.564 | −2.23912 | ||||||||
\(87\) | 11.9332i | 0.137163i | ||||||||
\(88\) | 60.8949 | − | 18.9465i | 0.691987 | − | 0.215301i | ||||
\(89\) | 44.8231 | 0.503630 | 0.251815 | − | 0.967775i | \(-0.418973\pi\) | ||||
0.251815 | + | 0.967775i | \(0.418973\pi\) | |||||||
\(90\) | 29.6187i | 0.329097i | ||||||||
\(91\) | −49.4256 | −0.543139 | ||||||||
\(92\) | 48.6269 | 0.528554 | ||||||||
\(93\) | 88.6410 | 0.953129 | ||||||||
\(94\) | − | 71.0470i | − | 0.755819i | ||||||
\(95\) | 127.639i | 1.34357i | ||||||||
\(96\) | 40.4599i | 0.421458i | ||||||||
\(97\) | −21.2539 | −0.219112 | −0.109556 | − | 0.993981i | \(-0.534943\pi\) | ||||
−0.109556 | + | 0.993981i | \(0.534943\pi\) | |||||||
\(98\) | − | 18.0687i | − | 0.184374i | ||||||
\(99\) | 9.80385 | + | 31.5101i | 0.0990288 | + | 0.318284i | ||||
\(100\) | 11.3538 | 0.113538 | ||||||||
\(101\) | − | 52.3479i | − | 0.518296i | −0.965838 | − | 0.259148i | \(-0.916558\pi\) | ||
0.965838 | − | 0.259148i | \(-0.0834417\pi\) | |||||||
\(102\) | −33.2154 | −0.325641 | ||||||||
\(103\) | −4.74613 | −0.0460790 | −0.0230395 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230395 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(104\) | 44.5781 | 0.428636 | ||||||||
\(105\) | − | 46.7191i | − | 0.444944i | ||||||
\(106\) | − | 61.2977i | − | 0.578281i | ||||||
\(107\) | − | 147.723i | − | 1.38059i | −0.723530 | − | 0.690293i | \(-0.757482\pi\) | ||
0.723530 | − | 0.690293i | \(-0.242518\pi\) | |||||||
\(108\) | −7.98076 | −0.0738959 | ||||||||
\(109\) | 3.56847i | 0.0327383i | 0.999866 | + | 0.0163691i | \(0.00521069\pi\) | ||||
−0.999866 | + | 0.0163691i | \(0.994789\pi\) | |||||||
\(110\) | −103.699 | + | 32.2642i | −0.942716 | + | 0.293311i | ||||
\(111\) | −33.7128 | −0.303719 | ||||||||
\(112\) | − | 127.178i | − | 1.13551i | ||||||
\(113\) | −62.3154 | −0.551463 | −0.275732 | − | 0.961235i | \(-0.588920\pi\) | ||||
−0.275732 | + | 0.961235i | \(0.588920\pi\) | |||||||
\(114\) | −123.962 | −1.08738 | ||||||||
\(115\) | 132.851 | 1.15523 | ||||||||
\(116\) | − | 10.5818i | − | 0.0912220i | ||||||
\(117\) | 23.0670i | 0.197154i | ||||||||
\(118\) | − | 194.689i | − | 1.64991i | ||||||
\(119\) | 52.3923 | 0.440271 | ||||||||
\(120\) | 42.1371i | 0.351142i | ||||||||
\(121\) | −99.6410 | + | 68.6489i | −0.823479 | + | 0.567346i | ||||
\(122\) | 177.440 | 1.45442 | ||||||||
\(123\) | 83.1038i | 0.675641i | ||||||||
\(124\) | −78.6025 | −0.633891 | ||||||||
\(125\) | 135.923 | 1.08738 | ||||||||
\(126\) | 45.3731 | 0.360104 | ||||||||
\(127\) | − | 28.0200i | − | 0.220630i | −0.993897 | − | 0.110315i | \(-0.964814\pi\) | ||
0.993897 | − | 0.110315i | \(-0.0351860\pi\) | |||||||
\(128\) | 150.323i | 1.17440i | ||||||||
\(129\) | − | 141.756i | − | 1.09888i | ||||||
\(130\) | −75.9127 | −0.583944 | ||||||||
\(131\) | 113.184i | 0.864001i | 0.901873 | + | 0.432000i | \(0.142192\pi\) | ||||
−0.901873 | + | 0.432000i | \(0.857808\pi\) | |||||||
\(132\) | −8.69358 | − | 27.9416i | −0.0658604 | − | 0.211679i | ||||
\(133\) | 195.531 | 1.47016 | ||||||||
\(134\) | 79.9969i | 0.596992i | ||||||||
\(135\) | −21.8038 | −0.161510 | ||||||||
\(136\) | −47.2539 | −0.347455 | ||||||||
\(137\) | −70.7846 | −0.516676 | −0.258338 | − | 0.966055i | \(-0.583175\pi\) | ||||
−0.258338 | + | 0.966055i | \(0.583175\pi\) | |||||||
\(138\) | 129.024i | 0.934953i | ||||||||
\(139\) | − | 130.499i | − | 0.938839i | −0.882975 | − | 0.469420i | \(-0.844463\pi\) | ||
0.882975 | − | 0.469420i | \(-0.155537\pi\) | |||||||
\(140\) | 41.4282i | 0.295916i | ||||||||
\(141\) | 52.3013 | 0.370931 | ||||||||
\(142\) | 171.128i | 1.20512i | ||||||||
\(143\) | −80.7602 | + | 25.1272i | −0.564757 | + | 0.175715i | ||||
\(144\) | −59.3538 | −0.412179 | ||||||||
\(145\) | − | 28.9099i | − | 0.199379i | ||||||
\(146\) | 129.100 | 0.884246 | ||||||||
\(147\) | 13.3013 | 0.0904848 | ||||||||
\(148\) | 29.8949 | 0.201992 | ||||||||
\(149\) | − | 125.793i | − | 0.844248i | −0.906538 | − | 0.422124i | \(-0.861285\pi\) | ||
0.906538 | − | 0.422124i | \(-0.138715\pi\) | |||||||
\(150\) | 30.1255i | 0.200837i | ||||||||
\(151\) | 275.238i | 1.82277i | 0.411556 | + | 0.911384i | \(0.364985\pi\) | ||||
−0.411556 | + | 0.911384i | \(0.635015\pi\) | |||||||
\(152\) | −176.354 | −1.16022 | ||||||||
\(153\) | − | 24.4515i | − | 0.159814i | ||||||
\(154\) | 49.4256 | + | 158.857i | 0.320946 | + | 1.03154i | ||||
\(155\) | −214.746 | −1.38546 | ||||||||
\(156\) | − | 20.4547i | − | 0.131120i | ||||||
\(157\) | −273.138 | −1.73974 | −0.869868 | − | 0.493285i | \(-0.835796\pi\) | ||||
−0.869868 | + | 0.493285i | \(0.835796\pi\) | |||||||
\(158\) | 57.2398 | 0.362277 | ||||||||
\(159\) | 45.1244 | 0.283801 | ||||||||
\(160\) | − | 98.0203i | − | 0.612627i | ||||||
\(161\) | − | 203.515i | − | 1.26407i | ||||||
\(162\) | − | 21.1756i | − | 0.130714i | ||||||
\(163\) | 62.0666 | 0.380777 | 0.190388 | − | 0.981709i | \(-0.439025\pi\) | ||||
0.190388 | + | 0.981709i | \(0.439025\pi\) | |||||||
\(164\) | − | 73.6924i | − | 0.449344i | ||||||
\(165\) | −23.7513 | − | 76.3379i | −0.143947 | − | 0.462654i | ||||
\(166\) | 2.17176 | 0.0130829 | ||||||||
\(167\) | 47.9800i | 0.287305i | 0.989628 | + | 0.143653i | \(0.0458848\pi\) | ||||
−0.989628 | + | 0.143653i | \(0.954115\pi\) | |||||||
\(168\) | 64.5500 | 0.384226 | ||||||||
\(169\) | 109.879 | 0.650174 | ||||||||
\(170\) | 80.4693 | 0.473349 | ||||||||
\(171\) | − | 91.2543i | − | 0.533651i | ||||||
\(172\) | 125.702i | 0.730828i | ||||||||
\(173\) | − | 143.017i | − | 0.826688i | −0.910575 | − | 0.413344i | \(-0.864361\pi\) | ||
0.910575 | − | 0.413344i | \(-0.135639\pi\) | |||||||
\(174\) | 28.0770 | 0.161362 | ||||||||
\(175\) | − | 47.5185i | − | 0.271534i | ||||||
\(176\) | −64.6551 | − | 207.805i | −0.367359 | − | 1.18071i | ||||
\(177\) | 143.321 | 0.809720 | ||||||||
\(178\) | − | 105.462i | − | 0.592483i | ||||||
\(179\) | 36.6025 | 0.204483 | 0.102242 | − | 0.994760i | \(-0.467398\pi\) | ||||
0.102242 | + | 0.994760i | \(0.467398\pi\) | |||||||
\(180\) | 19.3346 | 0.107414 | ||||||||
\(181\) | −84.1718 | −0.465037 | −0.232519 | − | 0.972592i | \(-0.574697\pi\) | ||||
−0.232519 | + | 0.972592i | \(0.574697\pi\) | |||||||
\(182\) | 116.291i | 0.638962i | ||||||||
\(183\) | 130.622i | 0.713783i | ||||||||
\(184\) | 183.555i | 0.997583i | ||||||||
\(185\) | 81.6743 | 0.441483 | ||||||||
\(186\) | − | 208.559i | − | 1.12128i | ||||||
\(187\) | 85.6077 | − | 26.6354i | 0.457795 | − | 0.142436i | ||||
\(188\) | −46.3782 | −0.246693 | ||||||||
\(189\) | 33.4014i | 0.176727i | ||||||||
\(190\) | 300.315 | 1.58061 | ||||||||
\(191\) | 44.2346 | 0.231595 | 0.115797 | − | 0.993273i | \(-0.463058\pi\) | ||||
0.115797 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(192\) | −41.8756 | −0.218102 | ||||||||
\(193\) | 136.127i | 0.705323i | 0.935751 | + | 0.352662i | \(0.114723\pi\) | ||||
−0.935751 | + | 0.352662i | \(0.885277\pi\) | |||||||
\(194\) | 50.0071i | 0.257769i | ||||||||
\(195\) | − | 55.8832i | − | 0.286580i | ||||||
\(196\) | −11.7949 | −0.0601782 | ||||||||
\(197\) | − | 5.96659i | − | 0.0302872i | −0.999885 | − | 0.0151436i | \(-0.995179\pi\) | ||
0.999885 | − | 0.0151436i | \(-0.00482055\pi\) | |||||||
\(198\) | 74.1384 | − | 23.0670i | 0.374437 | − | 0.116500i | ||||
\(199\) | −234.056 | −1.17616 | −0.588081 | − | 0.808802i | \(-0.700116\pi\) | ||||
−0.588081 | + | 0.808802i | \(0.700116\pi\) | |||||||
\(200\) | 42.8581i | 0.214290i | ||||||||
\(201\) | −58.8897 | −0.292984 | ||||||||
\(202\) | −123.167 | −0.609736 | ||||||||
\(203\) | −44.2872 | −0.218163 | ||||||||
\(204\) | 21.6824i | 0.106286i | ||||||||
\(205\) | − | 201.331i | − | 0.982105i | ||||||
\(206\) | 11.1669i | 0.0542084i | ||||||||
\(207\) | −94.9808 | −0.458844 | ||||||||
\(208\) | − | 152.124i | − | 0.731364i | ||||||
\(209\) | 319.492 | − | 99.4048i | 1.52867 | − | 0.475621i | ||||
\(210\) | −109.923 | −0.523443 | ||||||||
\(211\) | − | 167.469i | − | 0.793690i | −0.917886 | − | 0.396845i | \(-0.870105\pi\) | ||
0.917886 | − | 0.396845i | \(-0.129895\pi\) | |||||||
\(212\) | −40.0141 | −0.188746 | ||||||||
\(213\) | −125.976 | −0.591435 | ||||||||
\(214\) | −347.569 | −1.62416 | ||||||||
\(215\) | 343.425i | 1.59733i | ||||||||
\(216\) | − | 30.1255i | − | 0.139470i | ||||||
\(217\) | 328.970i | 1.51599i | ||||||||
\(218\) | 8.39608 | 0.0385141 | ||||||||
\(219\) | 95.0370i | 0.433959i | ||||||||
\(220\) | 21.0615 | + | 67.6927i | 0.0957340 | + | 0.307694i | ||||
\(221\) | 62.6692 | 0.283571 | ||||||||
\(222\) | 79.3212i | 0.357303i | ||||||||
\(223\) | 82.2872 | 0.369001 | 0.184500 | − | 0.982832i | \(-0.440933\pi\) | ||||
0.184500 | + | 0.982832i | \(0.440933\pi\) | |||||||
\(224\) | −150.158 | −0.670347 | ||||||||
\(225\) | −22.1769 | −0.0985641 | ||||||||
\(226\) | 146.619i | 0.648755i | ||||||||
\(227\) | − | 40.9999i | − | 0.180616i | −0.995914 | − | 0.0903081i | \(-0.971215\pi\) | ||
0.995914 | − | 0.0903081i | \(-0.0287852\pi\) | |||||||
\(228\) | 80.9199i | 0.354912i | ||||||||
\(229\) | 160.718 | 0.701825 | 0.350913 | − | 0.936408i | \(-0.385871\pi\) | ||||
0.350913 | + | 0.936408i | \(0.385871\pi\) | |||||||
\(230\) | − | 312.579i | − | 1.35904i | ||||||
\(231\) | −116.942 | + | 36.3847i | −0.506244 | + | 0.157510i | ||||
\(232\) | 39.9437 | 0.172171 | ||||||||
\(233\) | 407.954i | 1.75087i | 0.483332 | + | 0.875437i | \(0.339427\pi\) | ||||
−0.483332 | + | 0.875437i | \(0.660573\pi\) | |||||||
\(234\) | 54.2731 | 0.231936 | ||||||||
\(235\) | −126.708 | −0.539182 | ||||||||
\(236\) | −127.090 | −0.538515 | ||||||||
\(237\) | 42.1371i | 0.177794i | ||||||||
\(238\) | − | 123.271i | − | 0.517946i | ||||||
\(239\) | 202.254i | 0.846253i | 0.906071 | + | 0.423127i | \(0.139067\pi\) | ||||
−0.906071 | + | 0.423127i | \(0.860933\pi\) | |||||||
\(240\) | 143.794 | 0.599140 | ||||||||
\(241\) | 26.8828i | 0.111547i | 0.998443 | + | 0.0557734i | \(0.0177624\pi\) | ||||
−0.998443 | + | 0.0557734i | \(0.982238\pi\) | |||||||
\(242\) | 161.520 | + | 234.440i | 0.667440 | + | 0.968761i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 115.830i | − | 0.474711i | ||||||
\(245\) | −32.2243 | −0.131528 | ||||||||
\(246\) | 195.531 | 0.794840 | ||||||||
\(247\) | 233.885 | 0.946901 | ||||||||
\(248\) | − | 296.706i | − | 1.19640i | ||||||
\(249\) | 1.59874i | 0.00642065i | ||||||||
\(250\) | − | 319.806i | − | 1.27923i | ||||||
\(251\) | 398.277 | 1.58676 | 0.793380 | − | 0.608726i | \(-0.208319\pi\) | ||||
0.793380 | + | 0.608726i | \(0.208319\pi\) | |||||||
\(252\) | − | 29.6187i | − | 0.117535i | ||||||
\(253\) | −103.464 | − | 332.539i | −0.408949 | − | 1.31438i | ||||
\(254\) | −65.9268 | −0.259554 | ||||||||
\(255\) | 59.2375i | 0.232304i | ||||||||
\(256\) | 256.979 | 1.00383 | ||||||||
\(257\) | −337.818 | −1.31447 | −0.657233 | − | 0.753687i | \(-0.728273\pi\) | ||||
−0.657233 | + | 0.753687i | \(0.728273\pi\) | |||||||
\(258\) | −333.531 | −1.29275 | ||||||||
\(259\) | − | 125.117i | − | 0.483078i | ||||||
\(260\) | 49.5545i | 0.190594i | ||||||||
\(261\) | 20.6689i | 0.0791910i | ||||||||
\(262\) | 266.305 | 1.01643 | ||||||||
\(263\) | 134.529i | 0.511516i | 0.966741 | + | 0.255758i | \(0.0823250\pi\) | ||||
−0.966741 | + | 0.255758i | \(0.917675\pi\) | |||||||
\(264\) | 105.473 | − | 32.8162i | 0.399519 | − | 0.124304i | ||||
\(265\) | −109.321 | −0.412530 | ||||||||
\(266\) | − | 460.054i | − | 1.72953i | ||||||
\(267\) | 77.6359 | 0.290771 | ||||||||
\(268\) | 52.2205 | 0.194853 | ||||||||
\(269\) | −341.870 | −1.27089 | −0.635447 | − | 0.772144i | \(-0.719184\pi\) | ||||
−0.635447 | + | 0.772144i | \(0.719184\pi\) | |||||||
\(270\) | 51.3012i | 0.190004i | ||||||||
\(271\) | − | 213.298i | − | 0.787077i | −0.919308 | − | 0.393538i | \(-0.871251\pi\) | ||
0.919308 | − | 0.393538i | \(-0.128749\pi\) | |||||||
\(272\) | 161.255i | 0.592848i | ||||||||
\(273\) | −85.6077 | −0.313581 | ||||||||
\(274\) | 166.545i | 0.607830i | ||||||||
\(275\) | −24.1577 | − | 77.6440i | −0.0878461 | − | 0.282342i | ||||
\(276\) | 84.2243 | 0.305161 | ||||||||
\(277\) | 84.5789i | 0.305339i | 0.988277 | + | 0.152669i | \(0.0487870\pi\) | ||||
−0.988277 | + | 0.152669i | \(0.951213\pi\) | |||||||
\(278\) | −307.044 | −1.10447 | ||||||||
\(279\) | 153.531 | 0.550289 | ||||||||
\(280\) | −156.382 | −0.558507 | ||||||||
\(281\) | − | 351.148i | − | 1.24964i | −0.780771 | − | 0.624818i | \(-0.785173\pi\) | ||
0.780771 | − | 0.624818i | \(-0.214827\pi\) | |||||||
\(282\) | − | 123.057i | − | 0.436372i | ||||||
\(283\) | − | 285.943i | − | 1.01040i | −0.863002 | − | 0.505201i | \(-0.831419\pi\) | ||
0.863002 | − | 0.505201i | \(-0.168581\pi\) | |||||||
\(284\) | 111.709 | 0.393342 | ||||||||
\(285\) | 221.077i | 0.775710i | ||||||||
\(286\) | 59.1206 | + | 190.017i | 0.206715 | + | 0.664394i | ||||
\(287\) | −308.420 | −1.07464 | ||||||||
\(288\) | 70.0787i | 0.243329i | ||||||||
\(289\) | 222.569 | 0.770136 | ||||||||
\(290\) | −68.0206 | −0.234554 | ||||||||
\(291\) | −36.8128 | −0.126504 | ||||||||
\(292\) | − | 84.2742i | − | 0.288610i | ||||||
\(293\) | 393.927i | 1.34446i | 0.740342 | + | 0.672231i | \(0.234664\pi\) | ||||
−0.740342 | + | 0.672231i | \(0.765336\pi\) | |||||||
\(294\) | − | 31.2959i | − | 0.106449i | ||||||
\(295\) | −347.215 | −1.17700 | ||||||||
\(296\) | 112.846i | 0.381237i | ||||||||
\(297\) | 16.9808 | + | 54.5770i | 0.0571743 | + | 0.183761i | ||||
\(298\) | −295.972 | −0.993194 | ||||||||
\(299\) | − | 243.435i | − | 0.814165i | ||||||
\(300\) | 19.6654 | 0.0655514 | ||||||||
\(301\) | 526.095 | 1.74782 | ||||||||
\(302\) | 647.594 | 2.14435 | ||||||||
\(303\) | − | 90.6691i | − | 0.299238i | ||||||
\(304\) | 601.810i | 1.97964i | ||||||||
\(305\) | − | 316.452i | − | 1.03755i | ||||||
\(306\) | −57.5307 | −0.188009 | ||||||||
\(307\) | 58.2239i | 0.189654i | 0.995494 | + | 0.0948272i | \(0.0302299\pi\) | ||||
−0.995494 | + | 0.0948272i | \(0.969770\pi\) | |||||||
\(308\) | 103.699 | − | 32.2642i | 0.336684 | − | 0.104754i | ||||
\(309\) | −8.22055 | −0.0266037 | ||||||||
\(310\) | 505.265i | 1.62989i | ||||||||
\(311\) | 207.611 | 0.667561 | 0.333780 | − | 0.942651i | \(-0.391676\pi\) | ||||
0.333780 | + | 0.942651i | \(0.391676\pi\) | |||||||
\(312\) | 77.2116 | 0.247473 | ||||||||
\(313\) | −376.697 | −1.20351 | −0.601753 | − | 0.798682i | \(-0.705531\pi\) | ||||
−0.601753 | + | 0.798682i | \(0.705531\pi\) | |||||||
\(314\) | 642.654i | 2.04667i | ||||||||
\(315\) | − | 80.9199i | − | 0.256889i | ||||||
\(316\) | − | 37.3651i | − | 0.118244i | ||||||
\(317\) | 246.809 | 0.778577 | 0.389289 | − | 0.921116i | \(-0.372721\pi\) | ||||
0.389289 | + | 0.921116i | \(0.372721\pi\) | |||||||
\(318\) | − | 106.171i | − | 0.333870i | ||||||
\(319\) | −72.3641 | + | 22.5149i | −0.226847 | + | 0.0705797i | ||||
\(320\) | 101.450 | 0.317031 | ||||||||
\(321\) | − | 255.863i | − | 0.797082i | ||||||
\(322\) | −478.841 | −1.48708 | ||||||||
\(323\) | −247.923 | −0.767564 | ||||||||
\(324\) | −13.8231 | −0.0426638 | ||||||||
\(325\) | − | 56.8394i | − | 0.174890i | ||||||
\(326\) | − | 146.033i | − | 0.447955i | ||||||
\(327\) | 6.18078i | 0.0189015i | ||||||||
\(328\) | 278.172 | 0.848085 | ||||||||
\(329\) | 194.104i | 0.589982i | ||||||||
\(330\) | −179.611 | + | 55.8832i | −0.544277 | + | 0.169343i | ||||
\(331\) | 146.431 | 0.442389 | 0.221195 | − | 0.975230i | \(-0.429004\pi\) | ||||
0.221195 | + | 0.975230i | \(0.429004\pi\) | |||||||
\(332\) | − | 1.41769i | − | 0.00427014i | ||||||
\(333\) | −58.3923 | −0.175352 | ||||||||
\(334\) | 112.890 | 0.337993 | ||||||||
\(335\) | 142.669 | 0.425878 | ||||||||
\(336\) | − | 220.278i | − | 0.655589i | ||||||
\(337\) | 354.007i | 1.05047i | 0.850958 | + | 0.525233i | \(0.176022\pi\) | ||||
−0.850958 | + | 0.525233i | \(0.823978\pi\) | |||||||
\(338\) | − | 258.530i | − | 0.764881i | ||||||
\(339\) | −107.933 | −0.318387 | ||||||||
\(340\) | − | 52.5289i | − | 0.154497i | ||||||
\(341\) | 167.244 | + | 537.529i | 0.490450 | + | 1.57633i | ||||
\(342\) | −214.708 | −0.627800 | ||||||||
\(343\) | 364.342i | 1.06222i | ||||||||
\(344\) | −474.497 | −1.37935 | ||||||||
\(345\) | 230.105 | 0.666971 | ||||||||
\(346\) | −336.497 | −0.972536 | ||||||||
\(347\) | − | 529.807i | − | 1.52682i | −0.645913 | − | 0.763411i | \(-0.723523\pi\) | ||
0.645913 | − | 0.763411i | \(-0.276477\pi\) | |||||||
\(348\) | − | 18.3281i | − | 0.0526671i | ||||||
\(349\) | − | 342.873i | − | 0.982445i | −0.871034 | − | 0.491223i | \(-0.836550\pi\) | ||
0.871034 | − | 0.491223i | \(-0.163450\pi\) | |||||||
\(350\) | −111.804 | −0.319440 | ||||||||
\(351\) | 39.9532i | 0.113827i | ||||||||
\(352\) | −245.354 | + | 76.3379i | −0.697028 | + | 0.216869i | ||||
\(353\) | 191.990 | 0.543880 | 0.271940 | − | 0.962314i | \(-0.412335\pi\) | ||||
0.271940 | + | 0.962314i | \(0.412335\pi\) | |||||||
\(354\) | − | 337.212i | − | 0.952575i | ||||||
\(355\) | 305.195 | 0.859704 | ||||||||
\(356\) | −68.8437 | −0.193381 | ||||||||
\(357\) | 90.7461 | 0.254191 | ||||||||
\(358\) | − | 86.1203i | − | 0.240559i | ||||||
\(359\) | − | 601.654i | − | 1.67592i | −0.545735 | − | 0.837958i | \(-0.683750\pi\) | ||
0.545735 | − | 0.837958i | \(-0.316250\pi\) | |||||||
\(360\) | 72.9836i | 0.202732i | ||||||||
\(361\) | −564.261 | −1.56305 | ||||||||
\(362\) | 198.043i | 0.547081i | ||||||||
\(363\) | −172.583 | + | 118.903i | −0.475436 | + | 0.327557i | ||||
\(364\) | 75.9127 | 0.208551 | ||||||||
\(365\) | − | 230.241i | − | 0.630798i | ||||||
\(366\) | 307.335 | 0.839712 | ||||||||
\(367\) | −139.415 | −0.379878 | −0.189939 | − | 0.981796i | \(-0.560829\pi\) | ||||
−0.189939 | + | 0.981796i | \(0.560829\pi\) | |||||||
\(368\) | 626.386 | 1.70214 | ||||||||
\(369\) | 143.940i | 0.390081i | ||||||||
\(370\) | − | 192.167i | − | 0.519371i | ||||||
\(371\) | 167.469i | 0.451398i | ||||||||
\(372\) | −136.144 | −0.365977 | ||||||||
\(373\) | − | 303.629i | − | 0.814019i | −0.913424 | − | 0.407009i | \(-0.866572\pi\) | ||
0.913424 | − | 0.407009i | \(-0.133428\pi\) | |||||||
\(374\) | −62.6692 | − | 201.422i | −0.167565 | − | 0.538561i | ||||
\(375\) | 235.426 | 0.627802 | ||||||||
\(376\) | − | 175.067i | − | 0.465604i | ||||||
\(377\) | −52.9742 | −0.140515 | ||||||||
\(378\) | 78.5885 | 0.207906 | ||||||||
\(379\) | 690.046 | 1.82070 | 0.910351 | − | 0.413837i | \(-0.135812\pi\) | ||||
0.910351 | + | 0.413837i | \(0.135812\pi\) | |||||||
\(380\) | − | 196.041i | − | 0.515896i | ||||||
\(381\) | − | 48.5321i | − | 0.127381i | ||||||
\(382\) | − | 104.077i | − | 0.272454i | ||||||
\(383\) | −53.2576 | −0.139054 | −0.0695269 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695269 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(384\) | 260.367i | 0.678039i | ||||||||
\(385\) | 283.310 | − | 88.1474i | 0.735871 | − | 0.228954i | ||||
\(386\) | 320.287 | 0.829760 | ||||||||
\(387\) | − | 245.529i | − | 0.634441i | ||||||
\(388\) | 32.6438 | 0.0841334 | ||||||||
\(389\) | −587.027 | −1.50907 | −0.754533 | − | 0.656262i | \(-0.772137\pi\) | ||||
−0.754533 | + | 0.656262i | \(0.772137\pi\) | |||||||
\(390\) | −131.485 | −0.337140 | ||||||||
\(391\) | 258.047i | 0.659967i | ||||||||
\(392\) | − | 44.5231i | − | 0.113579i | ||||||
\(393\) | 196.041i | 0.498831i | ||||||||
\(394\) | −14.0385 | −0.0356306 | ||||||||
\(395\) | − | 102.083i | − | 0.258439i | ||||||
\(396\) | −15.0577 | − | 48.3963i | −0.0380245 | − | 0.122213i | ||||
\(397\) | 485.797 | 1.22367 | 0.611835 | − | 0.790985i | \(-0.290431\pi\) | ||||
0.611835 | + | 0.790985i | \(0.290431\pi\) | |||||||
\(398\) | 550.699i | 1.38367i | ||||||||
\(399\) | 338.669 | 0.848795 | ||||||||
\(400\) | 146.254 | 0.365635 | ||||||||
\(401\) | −166.469 | −0.415135 | −0.207568 | − | 0.978221i | \(-0.566555\pi\) | ||||
−0.207568 | + | 0.978221i | \(0.566555\pi\) | |||||||
\(402\) | 138.559i | 0.344673i | ||||||||
\(403\) | 393.499i | 0.976424i | ||||||||
\(404\) | 80.4010i | 0.199012i | ||||||||
\(405\) | −37.7654 | −0.0932478 | ||||||||
\(406\) | 104.201i | 0.256653i | ||||||||
\(407\) | −63.6077 | − | 204.438i | −0.156284 | − | 0.502306i | ||||
\(408\) | −81.8461 | −0.200603 | ||||||||
\(409\) | 270.161i | 0.660541i | 0.943886 | + | 0.330271i | \(0.107140\pi\) | ||||
−0.943886 | + | 0.330271i | \(0.892860\pi\) | |||||||
\(410\) | −473.703 | −1.15537 | ||||||||
\(411\) | −122.603 | −0.298303 | ||||||||
\(412\) | 7.28958 | 0.0176932 | ||||||||
\(413\) | 531.901i | 1.28790i | ||||||||
\(414\) | 223.475i | 0.539796i | ||||||||
\(415\) | − | 3.87319i | − | 0.00933299i | ||||||
\(416\) | −179.611 | −0.431758 | ||||||||
\(417\) | − | 226.030i | − | 0.542039i | ||||||
\(418\) | −233.885 | − | 751.717i | −0.559532 | − | 1.79837i | ||||
\(419\) | −356.631 | −0.851147 | −0.425574 | − | 0.904924i | \(-0.639928\pi\) | ||||
−0.425574 | + | 0.904924i | \(0.639928\pi\) | |||||||
\(420\) | 71.7558i | 0.170847i | ||||||||
\(421\) | −462.238 | −1.09795 | −0.548977 | − | 0.835838i | \(-0.684982\pi\) | ||||
−0.548977 | + | 0.835838i | \(0.684982\pi\) | |||||||
\(422\) | −394.028 | −0.933716 | ||||||||
\(423\) | 90.5885 | 0.214157 | ||||||||
\(424\) | − | 151.044i | − | 0.356236i | ||||||
\(425\) | 60.2510i | 0.141767i | ||||||||
\(426\) | 296.402i | 0.695778i | ||||||||
\(427\) | −484.774 | −1.13530 | ||||||||
\(428\) | 226.887i | 0.530110i | ||||||||
\(429\) | −139.881 | + | 43.5216i | −0.326062 | + | 0.101449i | ||||
\(430\) | 808.028 | 1.87914 | ||||||||
\(431\) | − | 199.552i | − | 0.462997i | −0.972835 | − | 0.231498i | \(-0.925637\pi\) | ||
0.972835 | − | 0.231498i | \(-0.0743628\pi\) | |||||||
\(432\) | −102.804 | −0.237972 | ||||||||
\(433\) | −45.3693 | −0.104779 | −0.0523895 | − | 0.998627i | \(-0.516684\pi\) | ||||
−0.0523895 | + | 0.998627i | \(0.516684\pi\) | |||||||
\(434\) | 774.018 | 1.78345 | ||||||||
\(435\) | − | 50.0734i | − | 0.115111i | ||||||
\(436\) | − | 5.48081i | − | 0.0125707i | ||||||
\(437\) | 963.045i | 2.20376i | ||||||||
\(438\) | 223.608 | 0.510520 | ||||||||
\(439\) | − | 484.630i | − | 1.10394i | −0.833864 | − | 0.551970i | \(-0.813876\pi\) | ||
0.833864 | − | 0.551970i | \(-0.186124\pi\) | |||||||
\(440\) | −255.524 | + | 79.5022i | −0.580737 | + | 0.180687i | ||||
\(441\) | 23.0385 | 0.0522414 | ||||||||
\(442\) | − | 147.451i | − | 0.333600i | ||||||
\(443\) | 375.538 | 0.847716 | 0.423858 | − | 0.905729i | \(-0.360676\pi\) | ||||
0.423858 | + | 0.905729i | \(0.360676\pi\) | |||||||
\(444\) | 51.7795 | 0.116620 | ||||||||
\(445\) | −188.084 | −0.422662 | ||||||||
\(446\) | − | 193.609i | − | 0.434102i | ||||||
\(447\) | − | 217.880i | − | 0.487427i | ||||||
\(448\) | − | 155.412i | − | 0.346901i | ||||||
\(449\) | −385.636 | −0.858877 | −0.429439 | − | 0.903096i | \(-0.641289\pi\) | ||||
−0.429439 | + | 0.903096i | \(0.641289\pi\) | |||||||
\(450\) | 52.1789i | 0.115953i | ||||||||
\(451\) | −503.951 | + | 156.796i | −1.11741 | + | 0.347664i | ||||
\(452\) | 95.7101 | 0.211748 | ||||||||
\(453\) | 476.726i | 1.05238i | ||||||||
\(454\) | −96.4665 | −0.212481 | ||||||||
\(455\) | 207.397 | 0.455819 | ||||||||
\(456\) | −305.454 | −0.669855 | ||||||||
\(457\) | 378.368i | 0.827939i | 0.910291 | + | 0.413970i | \(0.135858\pi\) | ||||
−0.910291 | + | 0.413970i | \(0.864142\pi\) | |||||||
\(458\) | − | 378.145i | − | 0.825644i | ||||||
\(459\) | − | 42.3513i | − | 0.0922686i | ||||||
\(460\) | −204.046 | −0.443578 | ||||||||
\(461\) | − | 224.522i | − | 0.487033i | −0.969897 | − | 0.243516i | \(-0.921699\pi\) | ||
0.969897 | − | 0.243516i | \(-0.0783010\pi\) | |||||||
\(462\) | 85.6077 | + | 275.148i | 0.185298 | + | 0.595557i | ||||
\(463\) | −52.3820 | −0.113136 | −0.0565680 | − | 0.998399i | \(-0.518016\pi\) | ||||
−0.0565680 | + | 0.998399i | \(0.518016\pi\) | |||||||
\(464\) | − | 136.308i | − | 0.293768i | ||||||
\(465\) | −371.951 | −0.799895 | ||||||||
\(466\) | 959.854 | 2.05977 | ||||||||
\(467\) | 513.387 | 1.09933 | 0.549665 | − | 0.835385i | \(-0.314755\pi\) | ||||
0.549665 | + | 0.835385i | \(0.314755\pi\) | |||||||
\(468\) | − | 35.4285i | − | 0.0757020i | ||||||
\(469\) | − | 218.556i | − | 0.466003i | ||||||
\(470\) | 298.124i | 0.634306i | ||||||||
\(471\) | −473.090 | −1.00444 | ||||||||
\(472\) | − | 479.734i | − | 1.01639i | ||||||
\(473\) | 859.626 | − | 267.459i | 1.81739 | − | 0.565451i | ||||
\(474\) | 99.1422 | 0.209161 | ||||||||
\(475\) | 224.860i | 0.473389i | ||||||||
\(476\) | −80.4693 | −0.169053 | ||||||||
\(477\) | 78.1577 | 0.163853 | ||||||||
\(478\) | 475.874 | 0.995553 | ||||||||
\(479\) | 238.730i | 0.498392i | 0.968453 | + | 0.249196i | \(0.0801663\pi\) | ||||
−0.968453 | + | 0.249196i | \(0.919834\pi\) | |||||||
\(480\) | − | 169.776i | − | 0.353700i | ||||||
\(481\) | − | 149.659i | − | 0.311142i | ||||||
\(482\) | 63.2511 | 0.131226 | ||||||||
\(483\) | − | 352.499i | − | 0.729812i | ||||||
\(484\) | 153.038 | − | 105.438i | 0.316195 | − | 0.217846i | ||||
\(485\) | 89.1845 | 0.183885 | ||||||||
\(486\) | − | 36.6773i | − | 0.0754677i | ||||||
\(487\) | 593.251 | 1.21817 | 0.609087 | − | 0.793103i | \(-0.291536\pi\) | ||||
0.609087 | + | 0.793103i | \(0.291536\pi\) | |||||||
\(488\) | 437.229 | 0.895962 | ||||||||
\(489\) | 107.503 | 0.219842 | ||||||||
\(490\) | 75.8190i | 0.154733i | ||||||||
\(491\) | 858.935i | 1.74936i | 0.484703 | + | 0.874679i | \(0.338928\pi\) | ||||
−0.484703 | + | 0.874679i | \(0.661072\pi\) | |||||||
\(492\) | − | 127.639i | − | 0.259429i | ||||||
\(493\) | 56.1539 | 0.113902 | ||||||||
\(494\) | − | 550.295i | − | 1.11396i | ||||||
\(495\) | −41.1384 | − | 132.221i | −0.0831080 | − | 0.267113i | ||||
\(496\) | −1012.52 | −2.04136 | ||||||||
\(497\) | − | 467.529i | − | 0.940702i | ||||||
\(498\) | 3.76160 | 0.00755341 | ||||||||
\(499\) | −803.692 | −1.61061 | −0.805303 | − | 0.592864i | \(-0.797997\pi\) | ||||
−0.805303 | + | 0.592864i | \(0.797997\pi\) | |||||||
\(500\) | −208.764 | −0.417528 | ||||||||
\(501\) | 83.1038i | 0.165876i | ||||||||
\(502\) | − | 937.085i | − | 1.86670i | ||||||
\(503\) | − | 752.302i | − | 1.49563i | −0.663907 | − | 0.747815i | \(-0.731103\pi\) | ||
0.663907 | − | 0.747815i | \(-0.268897\pi\) | |||||||
\(504\) | 111.804 | 0.221833 | ||||||||
\(505\) | 219.660i | 0.434969i | ||||||||
\(506\) | −782.414 | + | 243.435i | −1.54627 | + | 0.481098i | ||||
\(507\) | 190.317 | 0.375378 | ||||||||
\(508\) | 43.0359i | 0.0847163i | ||||||||
\(509\) | −249.268 | −0.489721 | −0.244860 | − | 0.969558i | \(-0.578742\pi\) | ||||
−0.244860 | + | 0.969558i | \(0.578742\pi\) | |||||||
\(510\) | 139.377 | 0.273288 | ||||||||
\(511\) | −352.708 | −0.690230 | ||||||||
\(512\) | − | 3.34215i | − | 0.00652764i | ||||||
\(513\) | − | 158.057i | − | 0.308104i | ||||||
\(514\) | 794.835i | 1.54637i | ||||||||
\(515\) | 19.9155 | 0.0386709 | ||||||||
\(516\) | 217.723i | 0.421944i | ||||||||
\(517\) | 98.6795 | + | 317.161i | 0.190869 | + | 0.613464i | ||||
\(518\) | −294.382 | −0.568305 | ||||||||
\(519\) | − | 247.713i | − | 0.477288i | ||||||
\(520\) | −187.057 | −0.359724 | ||||||||
\(521\) | 475.864 | 0.913367 | 0.456683 | − | 0.889629i | \(-0.349037\pi\) | ||||
0.456683 | + | 0.889629i | \(0.349037\pi\) | |||||||
\(522\) | 48.6307 | 0.0931623 | ||||||||
\(523\) | 362.833i | 0.693754i | 0.937911 | + | 0.346877i | \(0.112758\pi\) | ||||
−0.937911 | + | 0.346877i | \(0.887242\pi\) | |||||||
\(524\) | − | 173.839i | − | 0.331754i | ||||||
\(525\) | − | 82.3045i | − | 0.156770i | ||||||
\(526\) | 316.526 | 0.601760 | ||||||||
\(527\) | − | 417.118i | − | 0.791495i | ||||||
\(528\) | −111.986 | − | 359.929i | −0.212095 | − | 0.681683i | ||||
\(529\) | 473.372 | 0.894843 | ||||||||
\(530\) | 257.215i | 0.485311i | ||||||||
\(531\) | 248.238 | 0.467492 | ||||||||
\(532\) | −300.315 | −0.564503 | ||||||||
\(533\) | −368.918 | −0.692154 | ||||||||
\(534\) | − | 182.665i | − | 0.342070i | ||||||
\(535\) | 619.867i | 1.15863i | ||||||||
\(536\) | 197.120i | 0.367762i | ||||||||
\(537\) | 63.3975 | 0.118059 | ||||||||
\(538\) | 804.370i | 1.49511i | ||||||||
\(539\) | 25.0962 | + | 80.6604i | 0.0465606 | + | 0.149648i | ||||
\(540\) | 33.4885 | 0.0620157 | ||||||||
\(541\) | − | 830.667i | − | 1.53543i | −0.640792 | − | 0.767715i | \(-0.721394\pi\) | ||
0.640792 | − | 0.767715i | \(-0.278606\pi\) | |||||||
\(542\) | −501.857 | −0.925936 | ||||||||
\(543\) | −145.790 | −0.268489 | ||||||||
\(544\) | 190.392 | 0.349986 | ||||||||
\(545\) | − | 14.9739i | − | 0.0274750i | ||||||
\(546\) | 201.422i | 0.368905i | ||||||||
\(547\) | 456.091i | 0.833804i | 0.908952 | + | 0.416902i | \(0.136884\pi\) | ||||
−0.908952 | + | 0.416902i | \(0.863116\pi\) | |||||||
\(548\) | 108.718 | 0.198390 | ||||||||
\(549\) | 226.244i | 0.412103i | ||||||||
\(550\) | −182.685 | + | 56.8394i | −0.332154 | + | 0.103344i | ||||
\(551\) | 209.569 | 0.380343 | ||||||||
\(552\) | 317.927i | 0.575955i | ||||||||
\(553\) | −156.382 | −0.282788 | ||||||||
\(554\) | 199.001 | 0.359208 | ||||||||
\(555\) | 141.464 | 0.254890 | ||||||||
\(556\) | 200.433i | 0.360490i | ||||||||
\(557\) | − | 338.810i | − | 0.608277i | −0.952628 | − | 0.304138i | \(-0.901631\pi\) | ||
0.952628 | − | 0.304138i | \(-0.0983686\pi\) | |||||||
\(558\) | − | 361.235i | − | 0.647374i | ||||||
\(559\) | 629.290 | 1.12574 | ||||||||
\(560\) | 533.656i | 0.952958i | ||||||||
\(561\) | 148.277 | − | 46.1339i | 0.264308 | − | 0.0822352i | ||||
\(562\) | −826.197 | −1.47010 | ||||||||
\(563\) | 447.041i | 0.794034i | 0.917811 | + | 0.397017i | \(0.129955\pi\) | ||||
−0.917811 | + | 0.397017i | \(0.870045\pi\) | |||||||
\(564\) | −80.3294 | −0.142428 | ||||||||
\(565\) | 261.485 | 0.462805 | ||||||||
\(566\) | −672.782 | −1.18866 | ||||||||
\(567\) | 57.8529i | 0.102033i | ||||||||
\(568\) | 421.676i | 0.742387i | ||||||||
\(569\) | − | 522.893i | − | 0.918969i | −0.888186 | − | 0.459485i | \(-0.848034\pi\) | ||
0.888186 | − | 0.459485i | \(-0.151966\pi\) | |||||||
\(570\) | 520.161 | 0.912564 | ||||||||
\(571\) | 904.574i | 1.58419i | 0.610396 | + | 0.792096i | \(0.291010\pi\) | ||||
−0.610396 | + | 0.792096i | \(0.708990\pi\) | |||||||
\(572\) | 124.039 | − | 38.5929i | 0.216852 | − | 0.0674701i | ||||
\(573\) | 76.6166 | 0.133711 | ||||||||
\(574\) | 725.667i | 1.26423i | ||||||||
\(575\) | 234.042 | 0.407030 | ||||||||
\(576\) | −72.5307 | −0.125921 | ||||||||
\(577\) | 237.674 | 0.411914 | 0.205957 | − | 0.978561i | \(-0.433969\pi\) | ||||
0.205957 | + | 0.978561i | \(0.433969\pi\) | |||||||
\(578\) | − | 523.672i | − | 0.906007i | ||||||
\(579\) | 235.780i | 0.407219i | ||||||||
\(580\) | 44.4027i | 0.0765563i | ||||||||
\(581\) | −5.93336 | −0.0102123 | ||||||||
\(582\) | 86.6149i | 0.148823i | ||||||||
\(583\) | 85.1384 | + | 273.639i | 0.146035 | + | 0.469364i | ||||
\(584\) | 318.115 | 0.544718 | ||||||||
\(585\) | − | 96.7925i | − | 0.165457i | ||||||
\(586\) | 926.851 | 1.58166 | ||||||||
\(587\) | −578.515 | −0.985546 | −0.492773 | − | 0.870158i | \(-0.664017\pi\) | ||||
−0.492773 | + | 0.870158i | \(0.664017\pi\) | |||||||
\(588\) | −20.4294 | −0.0347439 | ||||||||
\(589\) | − | 1556.71i | − | 2.64296i | ||||||
\(590\) | 816.945i | 1.38465i | ||||||||
\(591\) | − | 10.3344i | − | 0.0174863i | ||||||
\(592\) | 385.090 | 0.650489 | ||||||||
\(593\) | − | 333.857i | − | 0.562997i | −0.959562 | − | 0.281499i | \(-0.909169\pi\) | ||
0.959562 | − | 0.281499i | \(-0.0908314\pi\) | |||||||
\(594\) | 128.412 | − | 39.9532i | 0.216181 | − | 0.0672612i | ||||
\(595\) | −219.846 | −0.369489 | ||||||||
\(596\) | 193.205i | 0.324170i | ||||||||
\(597\) | −405.397 | −0.679058 | ||||||||
\(598\) | −572.767 | −0.957804 | ||||||||
\(599\) | −846.483 | −1.41316 | −0.706580 | − | 0.707633i | \(-0.749763\pi\) | ||||
−0.706580 | + | 0.707633i | \(0.749763\pi\) | |||||||
\(600\) | 74.2323i | 0.123721i | ||||||||
\(601\) | − | 455.011i | − | 0.757089i | −0.925583 | − | 0.378545i | \(-0.876425\pi\) | ||
0.925583 | − | 0.378545i | \(-0.123575\pi\) | |||||||
\(602\) | − | 1237.82i | − | 2.05618i | ||||||
\(603\) | −102.000 | −0.169154 | ||||||||
\(604\) | − | 422.738i | − | 0.699897i | ||||||
\(605\) | 418.109 | − | 288.061i | 0.691089 | − | 0.476134i | ||||
\(606\) | −213.331 | −0.352031 | ||||||||
\(607\) | − | 726.557i | − | 1.19696i | −0.801137 | − | 0.598482i | \(-0.795771\pi\) | ||
0.801137 | − | 0.598482i | \(-0.204229\pi\) | |||||||
\(608\) | 710.554 | 1.16867 | ||||||||
\(609\) | −76.7077 | −0.125957 | ||||||||
\(610\) | −744.564 | −1.22060 | ||||||||
\(611\) | 232.178i | 0.379997i | ||||||||
\(612\) | 37.5551i | 0.0613645i | ||||||||
\(613\) | − | 574.532i | − | 0.937247i | −0.883398 | − | 0.468624i | \(-0.844750\pi\) | ||
0.883398 | − | 0.468624i | \(-0.155250\pi\) | |||||||
\(614\) | 136.992 | 0.223114 | ||||||||
\(615\) | − | 348.716i | − | 0.567018i | ||||||
\(616\) | 121.790 | + | 391.439i | 0.197711 | + | 0.635452i | ||||
\(617\) | −278.946 | −0.452101 | −0.226050 | − | 0.974116i | \(-0.572581\pi\) | ||||
−0.226050 | + | 0.974116i | \(0.572581\pi\) | |||||||
\(618\) | 19.3417i | 0.0312973i | ||||||||
\(619\) | −593.061 | −0.958096 | −0.479048 | − | 0.877789i | \(-0.659018\pi\) | ||||
−0.479048 | + | 0.877789i | \(0.659018\pi\) | |||||||
\(620\) | 329.828 | 0.531981 | ||||||||
\(621\) | −164.512 | −0.264914 | ||||||||
\(622\) | − | 488.478i | − | 0.785335i | ||||||
\(623\) | 288.127i | 0.462484i | ||||||||
\(624\) | − | 263.486i | − | 0.422253i | ||||||
\(625\) | −385.546 | −0.616874 | ||||||||
\(626\) | 886.312i | 1.41583i | ||||||||
\(627\) | 553.377 | − | 172.174i | 0.882579 | − | 0.274600i | ||||
\(628\) | 419.513 | 0.668014 | ||||||||
\(629\) | 158.642i | 0.252214i | ||||||||
\(630\) | −190.392 | −0.302210 | ||||||||
\(631\) | −361.664 | −0.573160 | −0.286580 | − | 0.958056i | \(-0.592518\pi\) | ||||
−0.286580 | + | 0.958056i | \(0.592518\pi\) | |||||||
\(632\) | 141.045 | 0.223172 | ||||||||
\(633\) | − | 290.064i | − | 0.458237i | ||||||
\(634\) | − | 580.704i | − | 0.915937i | ||||||
\(635\) | 117.576i | 0.185159i | ||||||||
\(636\) | −69.3064 | −0.108972 | ||||||||
\(637\) | 59.0475i | 0.0926963i | ||||||||
\(638\) | 52.9742 | + | 170.262i | 0.0830317 | + | 0.266868i | ||||
\(639\) | −218.196 | −0.341465 | ||||||||
\(640\) | − | 630.778i | − | 0.985590i | ||||||
\(641\) | 784.382 | 1.22368 | 0.611842 | − | 0.790980i | \(-0.290429\pi\) | ||||
0.611842 | + | 0.790980i | \(0.290429\pi\) | |||||||
\(642\) | −602.008 | −0.937706 | ||||||||
\(643\) | 362.764 | 0.564174 | 0.282087 | − | 0.959389i | \(-0.408973\pi\) | ||||
0.282087 | + | 0.959389i | \(0.408973\pi\) | |||||||
\(644\) | 312.579i | 0.485371i | ||||||||
\(645\) | 594.830i | 0.922217i | ||||||||
\(646\) | 583.325i | 0.902981i | ||||||||
\(647\) | 921.727 | 1.42462 | 0.712308 | − | 0.701867i | \(-0.247650\pi\) | ||||
0.712308 | + | 0.701867i | \(0.247650\pi\) | |||||||
\(648\) | − | 52.1789i | − | 0.0805230i | ||||||
\(649\) | 270.410 | + | 869.112i | 0.416657 | + | 1.33916i | ||||
\(650\) | −133.734 | −0.205745 | ||||||||
\(651\) | 569.794i | 0.875259i | ||||||||
\(652\) | −95.3281 | −0.146209 | ||||||||
\(653\) | 26.8653 | 0.0411414 | 0.0205707 | − | 0.999788i | \(-0.493452\pi\) | ||||
0.0205707 | + | 0.999788i | \(0.493452\pi\) | |||||||
\(654\) | 14.5424 | 0.0222361 | ||||||||
\(655\) | − | 474.938i | − | 0.725096i | ||||||
\(656\) | − | 949.266i | − | 1.44705i | ||||||
\(657\) | 164.609i | 0.250546i | ||||||||
\(658\) | 456.697 | 0.694069 | ||||||||
\(659\) | 320.820i | 0.486828i | 0.969922 | + | 0.243414i | \(0.0782674\pi\) | ||||
−0.969922 | + | 0.243414i | \(0.921733\pi\) | |||||||
\(660\) | 36.4796 | + | 117.247i | 0.0552721 | + | 0.177647i | ||||
\(661\) | 331.969 | 0.502222 | 0.251111 | − | 0.967958i | \(-0.419204\pi\) | ||||
0.251111 | + | 0.967958i | \(0.419204\pi\) | |||||||
\(662\) | − | 344.530i | − | 0.520437i | ||||||
\(663\) | 108.546 | 0.163720 | ||||||||
\(664\) | 5.35144 | 0.00805939 | ||||||||
\(665\) | −820.477 | −1.23380 | ||||||||
\(666\) | 137.388i | 0.206289i | ||||||||
\(667\) | − | 218.127i | − | 0.327027i | ||||||
\(668\) | − | 73.6924i | − | 0.110318i | ||||||
\(669\) | 142.526 | 0.213043 | ||||||||
\(670\) | − | 335.679i | − | 0.501013i | ||||||
\(671\) | −792.109 | + | 246.452i | −1.18049 | + | 0.367290i | ||||
\(672\) | −260.081 | −0.387025 | ||||||||
\(673\) | − | 797.019i | − | 1.18428i | −0.805836 | − | 0.592139i | \(-0.798284\pi\) | ||
0.805836 | − | 0.592139i | \(-0.201716\pi\) | |||||||
\(674\) | 832.925 | 1.23579 | ||||||||
\(675\) | −38.4115 | −0.0569060 | ||||||||
\(676\) | −168.764 | −0.249650 | ||||||||
\(677\) | 534.175i | 0.789033i | 0.918889 | + | 0.394516i | \(0.129088\pi\) | ||||
−0.918889 | + | 0.394516i | \(0.870912\pi\) | |||||||
\(678\) | 253.951i | 0.374559i | ||||||||
\(679\) | − | 136.622i | − | 0.201211i | ||||||
\(680\) | 198.284 | 0.291595 | ||||||||
\(681\) | − | 71.0139i | − | 0.104279i | ||||||
\(682\) | 1264.73 | − | 393.499i | 1.85444 | − | 0.576978i | ||||
\(683\) | −843.097 | −1.23440 | −0.617201 | − | 0.786805i | \(-0.711734\pi\) | ||||
−0.617201 | + | 0.786805i | \(0.711734\pi\) | |||||||
\(684\) | 140.157i | 0.204908i | ||||||||
\(685\) | 297.023 | 0.433610 | ||||||||
\(686\) | 857.241 | 1.24962 | ||||||||
\(687\) | 278.372 | 0.405199 | ||||||||
\(688\) | 1619.23i | 2.35353i | ||||||||
\(689\) | 200.318i | 0.290737i | ||||||||
\(690\) | − | 541.403i | − | 0.784641i | ||||||
\(691\) | −193.615 | −0.280196 | −0.140098 | − | 0.990138i | \(-0.544742\pi\) | ||||
−0.140098 | + | 0.990138i | \(0.544742\pi\) | |||||||
\(692\) | 219.660i | 0.317427i | ||||||||
\(693\) | −202.550 | + | 63.0201i | −0.292280 | + | 0.0909382i | ||||
\(694\) | −1246.56 | −1.79619 | ||||||||
\(695\) | 547.592i | 0.787903i | ||||||||
\(696\) | 69.1845 | 0.0994030 | ||||||||
\(697\) | 391.061 | 0.561064 | ||||||||
\(698\) | −806.729 | −1.15577 | ||||||||
\(699\) | 706.597i | 1.01087i | ||||||||
\(700\) | 72.9836i | 0.104262i | ||||||||
\(701\) | 448.863i | 0.640318i | 0.947364 | + | 0.320159i | \(0.103736\pi\) | ||||
−0.947364 | + | 0.320159i | \(0.896264\pi\) | |||||||
\(702\) | 94.0038 | 0.133909 | ||||||||
\(703\) | 592.061i | 0.842192i | ||||||||
\(704\) | −79.0089 | − | 253.939i | −0.112229 | − | 0.360708i | ||||
\(705\) | −219.464 | −0.311297 | ||||||||
\(706\) | − | 451.723i | − | 0.639834i | ||||||
\(707\) | 336.497 | 0.475951 | ||||||||
\(708\) | −220.126 | −0.310912 | ||||||||
\(709\) | −311.031 | −0.438689 | −0.219345 | − | 0.975647i | \(-0.570392\pi\) | ||||
−0.219345 | + | 0.975647i | \(0.570392\pi\) | |||||||
\(710\) | − | 718.077i | − | 1.01138i | ||||||
\(711\) | 72.9836i | 0.102649i | ||||||||
\(712\) | − | 259.869i | − | 0.364985i | ||||||
\(713\) | −1620.27 | −2.27247 | ||||||||
\(714\) | − | 213.512i | − | 0.299036i | ||||||
\(715\) | 338.882 | − | 105.438i | 0.473961 | − | 0.147465i | ||||
\(716\) | −56.2178 | −0.0785165 | ||||||||
\(717\) | 350.315i | 0.488584i | ||||||||
\(718\) | −1415.60 | −1.97159 | ||||||||
\(719\) | 486.014 | 0.675958 | 0.337979 | − | 0.941154i | \(-0.390257\pi\) | ||||
0.337979 | + | 0.941154i | \(0.390257\pi\) | |||||||
\(720\) | 249.058 | 0.345913 | ||||||||
\(721\) | − | 30.5086i | − | 0.0423143i | ||||||
\(722\) | 1327.62i | 1.83881i | ||||||||
\(723\) | 46.5623i | 0.0644016i | ||||||||
\(724\) | 129.279 | 0.178563 | ||||||||
\(725\) | − | 50.9302i | − | 0.0702485i | ||||||
\(726\) | 279.762 | + | 406.062i | 0.385347 | + | 0.559315i | ||||
\(727\) | 38.8616 | 0.0534547 | 0.0267273 | − | 0.999643i | \(-0.491491\pi\) | ||||
0.0267273 | + | 0.999643i | \(0.491491\pi\) | |||||||
\(728\) | 286.553i | 0.393617i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −541.723 | −0.742086 | ||||||||
\(731\) | −667.061 | −0.912533 | ||||||||
\(732\) | − | 200.623i | − | 0.274075i | ||||||
\(733\) | − | 175.562i | − | 0.239511i | −0.992803 | − | 0.119756i | \(-0.961789\pi\) | ||
0.992803 | − | 0.119756i | \(-0.0382111\pi\) | |||||||
\(734\) | 328.023i | 0.446898i | ||||||||
\(735\) | −55.8142 | −0.0759376 | ||||||||
\(736\) | − | 739.570i | − | 1.00485i | ||||||
\(737\) | −111.110 | − | 357.114i | −0.150760 | − | 0.484551i | ||||
\(738\) | 338.669 | 0.458901 | ||||||||
\(739\) | 494.527i | 0.669184i | 0.942363 | + | 0.334592i | \(0.108598\pi\) | ||||
−0.942363 | + | 0.334592i | \(0.891402\pi\) | |||||||
\(740\) | −125.443 | −0.169518 | ||||||||
\(741\) | 405.100 | 0.546694 | ||||||||
\(742\) | 394.028 | 0.531035 | ||||||||
\(743\) | − | 1150.84i | − | 1.54892i | −0.632625 | − | 0.774458i | \(-0.718023\pi\) | ||
0.632625 | − | 0.774458i | \(-0.281977\pi\) | |||||||
\(744\) | − | 513.910i | − | 0.690740i | ||||||
\(745\) | 527.846i | 0.708519i | ||||||||
\(746\) | −714.393 | −0.957632 | ||||||||
\(747\) | 2.76910i | 0.00370696i | ||||||||
\(748\) | −131.485 | + | 40.9093i | −0.175782 | + | 0.0546916i | ||||
\(749\) | 949.577 | 1.26779 | ||||||||
\(750\) | − | 553.921i | − | 0.738561i | ||||||
\(751\) | 1343.73 | 1.78926 | 0.894628 | − | 0.446813i | \(-0.147441\pi\) | ||||
0.894628 | + | 0.446813i | \(0.147441\pi\) | |||||||
\(752\) | −597.419 | −0.794440 | ||||||||
\(753\) | 689.836 | 0.916117 | ||||||||
\(754\) | 124.640i | 0.165306i | ||||||||
\(755\) | − | 1154.94i | − | 1.52972i | ||||||
\(756\) | − | 51.3012i | − | 0.0678587i | ||||||
\(757\) | 1034.58 | 1.36669 | 0.683343 | − | 0.730097i | \(-0.260525\pi\) | ||||
0.683343 | + | 0.730097i | \(0.260525\pi\) | |||||||
\(758\) | − | 1623.57i | − | 2.14192i | ||||||
\(759\) | −179.205 | − | 575.974i | −0.236107 | − | 0.758859i | ||||
\(760\) | 740.008 | 0.973694 | ||||||||
\(761\) | 798.527i | 1.04931i | 0.851314 | + | 0.524656i | \(0.175806\pi\) | ||||
−0.851314 | + | 0.524656i | \(0.824194\pi\) | |||||||
\(762\) | −114.189 | −0.149854 | ||||||||
\(763\) | −22.9385 | −0.0300636 | ||||||||
\(764\) | −67.9399 | −0.0889266 | ||||||||
\(765\) | 102.602i | 0.134121i | ||||||||
\(766\) | 125.307i | 0.163586i | ||||||||
\(767\) | 636.234i | 0.829510i | ||||||||
\(768\) | 445.101 | 0.579559 | ||||||||
\(769\) | 261.311i | 0.339806i | 0.985461 | + | 0.169903i | \(0.0543455\pi\) | ||||
−0.985461 | + | 0.169903i | \(0.945655\pi\) | |||||||
\(770\) | −207.397 | − | 666.586i | −0.269347 | − | 0.865696i | ||||
\(771\) | −585.118 | −0.758908 | ||||||||
\(772\) | − | 209.078i | − | 0.270826i | ||||||
\(773\) | −327.734 | −0.423977 | −0.211989 | − | 0.977272i | \(-0.567994\pi\) | ||||
−0.211989 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(774\) | −577.692 | −0.746372 | ||||||||
\(775\) | −378.315 | −0.488149 | ||||||||
\(776\) | 123.223i | 0.158792i | ||||||||
\(777\) | − | 216.709i | − | 0.278905i | ||||||
\(778\) | 1381.19i | 1.77530i | ||||||||
\(779\) | 1459.46 | 1.87351 | ||||||||
\(780\) | 85.8309i | 0.110040i | ||||||||
\(781\) | −237.685 | − | 763.931i | −0.304334 | − | 0.978144i | ||||
\(782\) | 607.146 | 0.776402 | ||||||||
\(783\) | 35.7995i | 0.0457210i | ||||||||
\(784\) | −151.936 | −0.193796 | ||||||||
\(785\) | 1146.13 | 1.46004 | ||||||||
\(786\) | 461.254 | 0.586837 | ||||||||
\(787\) | 289.388i | 0.367711i | 0.982953 | + | 0.183855i | \(0.0588578\pi\) | ||||
−0.982953 | + | 0.183855i | \(0.941142\pi\) | |||||||
\(788\) | 9.16407i | 0.0116295i | ||||||||
\(789\) | 233.010i | 0.295324i | ||||||||
\(790\) | −240.187 | −0.304034 | ||||||||
\(791\) | − | 400.570i | − | 0.506409i | ||||||
\(792\) | 182.685 | − | 56.8394i | 0.230662 | − | 0.0717669i | ||||
\(793\) | −579.864 | −0.731228 | ||||||||
\(794\) | − | 1143.01i | − | 1.43956i | ||||||
\(795\) | −189.349 | −0.238174 | ||||||||
\(796\) | 359.487 | 0.451617 | ||||||||
\(797\) | 113.681 | 0.142636 | 0.0713180 | − | 0.997454i | \(-0.477279\pi\) | ||||
0.0713180 | + | 0.997454i | \(0.477279\pi\) | |||||||
\(798\) | − | 796.837i | − | 0.998543i | ||||||
\(799\) | − | 246.114i | − | 0.308028i | ||||||
\(800\) | − | 172.681i | − | 0.215851i | ||||||
\(801\) | 134.469 | 0.167877 | ||||||||
\(802\) | 391.677i | 0.488375i | ||||||||
\(803\) | −576.315 | + | 179.311i | −0.717703 | + | 0.223302i | ||||
\(804\) | 90.4486 | 0.112498 | ||||||||
\(805\) | 853.982i | 1.06085i | ||||||||
\(806\) | 925.843 | 1.14869 | ||||||||
\(807\) | −592.137 | −0.733751 | ||||||||
\(808\) | −303.495 | −0.375613 | ||||||||
\(809\) | 854.163i | 1.05583i | 0.849299 | + | 0.527913i | \(0.177025\pi\) | ||||
−0.849299 | + | 0.527913i | \(0.822975\pi\) | |||||||
\(810\) | 88.8562i | 0.109699i | ||||||||
\(811\) | − | 486.533i | − | 0.599917i | −0.953952 | − | 0.299959i | \(-0.903027\pi\) | ||
0.953952 | − | 0.299959i | \(-0.0969729\pi\) | |||||||
\(812\) | 68.0206 | 0.0837692 | ||||||||
\(813\) | − | 369.443i | − | 0.454419i | ||||||
\(814\) | −481.013 | + | 149.659i | −0.590925 | + | 0.183857i | ||||
\(815\) | −260.441 | −0.319560 | ||||||||
\(816\) | 279.301i | 0.342281i | ||||||||
\(817\) | −2489.51 | −3.04713 | ||||||||
\(818\) | 635.649 | 0.777077 | ||||||||
\(819\) | −148.277 | −0.181046 | ||||||||
\(820\) | 309.225i | 0.377103i | ||||||||
\(821\) | − | 527.104i | − | 0.642027i | −0.947075 | − | 0.321014i | \(-0.895976\pi\) | ||
0.947075 | − | 0.321014i | \(-0.104024\pi\) | |||||||
\(822\) | 288.465i | 0.350931i | ||||||||
\(823\) | −314.805 | −0.382509 | −0.191255 | − | 0.981540i | \(-0.561256\pi\) | ||||
−0.191255 | + | 0.981540i | \(0.561256\pi\) | |||||||
\(824\) | 27.5165i | 0.0333938i | ||||||||
\(825\) | −41.8423 | − | 134.483i | −0.0507180 | − | 0.163010i | ||||
\(826\) | 1251.48 | 1.51511 | ||||||||
\(827\) | 111.652i | 0.135008i | 0.997719 | + | 0.0675040i | \(0.0215035\pi\) | ||||
−0.997719 | + | 0.0675040i | \(0.978496\pi\) | |||||||
\(828\) | 145.881 | 0.176185 | ||||||||
\(829\) | −695.395 | −0.838836 | −0.419418 | − | 0.907793i | \(-0.637766\pi\) | ||||
−0.419418 | + | 0.907793i | \(0.637766\pi\) | |||||||
\(830\) | −9.11303 | −0.0109796 | ||||||||
\(831\) | 146.495i | 0.176288i | ||||||||
\(832\) | − | 185.896i | − | 0.223433i | ||||||
\(833\) | − | 62.5918i | − | 0.0751402i | ||||||
\(834\) | −531.815 | −0.637668 | ||||||||
\(835\) | − | 201.331i | − | 0.241116i | ||||||
\(836\) | −490.708 | + | 152.676i | −0.586971 | + | 0.182626i | ||||
\(837\) | 265.923 | 0.317710 | ||||||||
\(838\) | 839.098i | 1.00131i | ||||||||
\(839\) | −383.968 | −0.457650 | −0.228825 | − | 0.973468i | \(-0.573488\pi\) | ||||
−0.228825 | + | 0.973468i | \(0.573488\pi\) | |||||||
\(840\) | −270.862 | −0.322454 | ||||||||
\(841\) | 793.533 | 0.943559 | ||||||||
\(842\) | 1087.58i | 1.29166i | ||||||||
\(843\) | − | 608.205i | − | 0.721477i | ||||||
\(844\) | 257.215i | 0.304757i | ||||||||
\(845\) | −461.071 | −0.545646 | ||||||||
\(846\) | − | 213.141i | − | 0.251940i | ||||||
\(847\) | −441.282 | − | 640.503i | −0.520994 | − | 0.756202i | ||||
\(848\) | −515.440 | −0.607830 | ||||||||
\(849\) | − | 495.269i | − | 0.583355i | ||||||
\(850\) | 141.762 | 0.166778 | ||||||||
\(851\) | 616.238 | 0.724134 | ||||||||
\(852\) | 193.486 | 0.227096 | ||||||||
\(853\) | 570.527i | 0.668847i | 0.942423 | + | 0.334424i | \(0.108542\pi\) | ||||
−0.942423 | + | 0.334424i | \(0.891458\pi\) | |||||||
\(854\) | 1140.60i | 1.33560i | ||||||||
\(855\) | 382.917i | 0.447856i | ||||||||
\(856\) | −856.446 | −1.00052 | ||||||||
\(857\) | 315.553i | 0.368207i | 0.982907 | + | 0.184103i | \(0.0589382\pi\) | ||||
−0.982907 | + | 0.184103i | \(0.941062\pi\) | |||||||
\(858\) | 102.400 | + | 329.118i | 0.119347 | + | 0.383588i | ||||
\(859\) | −107.923 | −0.125638 | −0.0628190 | − | 0.998025i | \(-0.520009\pi\) | ||||
−0.0628190 | + | 0.998025i | \(0.520009\pi\) | |||||||
\(860\) | − | 527.467i | − | 0.613333i | ||||||
\(861\) | −534.200 | −0.620441 | ||||||||
\(862\) | −469.515 | −0.544681 | ||||||||
\(863\) | 1431.55 | 1.65881 | 0.829403 | − | 0.558651i | \(-0.188681\pi\) | ||||
0.829403 | + | 0.558651i | \(0.188681\pi\) | |||||||
\(864\) | 121.380i | 0.140486i | ||||||||
\(865\) | 600.121i | 0.693782i | ||||||||
\(866\) | 106.747i | 0.123265i | ||||||||
\(867\) | 385.501 | 0.444638 | ||||||||
\(868\) | − | 505.265i | − | 0.582103i | ||||||
\(869\) | −255.524 | + | 79.5022i | −0.294044 | + | 0.0914870i | ||||
\(870\) | −117.815 | −0.135420 | ||||||||
\(871\) | − | 261.426i | − | 0.300144i | ||||||
\(872\) | 20.6888 | 0.0237257 | ||||||||
\(873\) | −63.7616 | −0.0730373 | ||||||||
\(874\) | 2265.90 | 2.59256 | ||||||||
\(875\) | 873.727i | 0.998546i | ||||||||
\(876\) | − | 145.967i | − | 0.166629i | ||||||
\(877\) | − | 567.758i | − | 0.647386i | −0.946162 | − | 0.323693i | \(-0.895075\pi\) | ||
0.946162 | − | 0.323693i | \(-0.104925\pi\) | |||||||
\(878\) | −1140.26 | −1.29870 | ||||||||
\(879\) | 682.302i | 0.776225i | ||||||||
\(880\) | 271.303 | + | 871.981i | 0.308298 | + | 0.990887i | ||||
\(881\) | 488.641 | 0.554644 | 0.277322 | − | 0.960777i | \(-0.410553\pi\) | ||||
0.277322 | + | 0.960777i | \(0.410553\pi\) | |||||||
\(882\) | − | 54.2061i | − | 0.0614581i | ||||||
\(883\) | 840.144 | 0.951465 | 0.475732 | − | 0.879590i | \(-0.342183\pi\) | ||||
0.475732 | + | 0.879590i | \(0.342183\pi\) | |||||||
\(884\) | −96.2535 | −0.108884 | ||||||||
\(885\) | −601.395 | −0.679542 | ||||||||
\(886\) | − | 883.585i | − | 0.997274i | ||||||
\(887\) | − | 981.439i | − | 1.10647i | −0.833025 | − | 0.553235i | \(-0.813393\pi\) | ||
0.833025 | − | 0.553235i | \(-0.186607\pi\) | |||||||
\(888\) | 195.455i | 0.220107i | ||||||||
\(889\) | 180.115 | 0.202605 | ||||||||
\(890\) | 442.534i | 0.497230i | ||||||||
\(891\) | 29.4115 | + | 94.5302i | 0.0330096 | + | 0.106095i | ||||
\(892\) | −126.385 | −0.141687 | ||||||||
\(893\) | − | 918.510i | − | 1.02857i | ||||||
\(894\) | −512.638 | −0.573421 | ||||||||
\(895\) | −153.590 | −0.171609 | ||||||||
\(896\) | −966.291 | −1.07845 | ||||||||
\(897\) | − | 421.642i | − | 0.470059i | ||||||
\(898\) | 907.343i | 1.01040i | ||||||||
\(899\) | 352.589i | 0.392202i | ||||||||
\(900\) | 34.0615 | 0.0378461 | ||||||||
\(901\) | − | 212.342i | − | 0.235673i | ||||||
\(902\) | 368.918 | + | 1185.72i | 0.409000 | + | 1.31455i | ||||
\(903\) | 911.223 | 1.00911 | ||||||||
\(904\) | 361.283i | 0.399650i | ||||||||
\(905\) | 353.198 | 0.390274 | ||||||||
\(906\) | 1121.67 | 1.23804 | ||||||||
\(907\) | 438.610 | 0.483583 | 0.241792 | − | 0.970328i | \(-0.422265\pi\) | ||||
0.241792 | + | 0.970328i | \(0.422265\pi\) | |||||||
\(908\) | 62.9716i | 0.0693520i | ||||||||
\(909\) | − | 157.044i | − | 0.172765i | ||||||
\(910\) | − | 487.975i | − | 0.536236i | ||||||
\(911\) | −170.042 | −0.186654 | −0.0933272 | − | 0.995635i | \(-0.529750\pi\) | ||||
−0.0933272 | + | 0.995635i | \(0.529750\pi\) | |||||||
\(912\) | 1042.37i | 1.14295i | ||||||||
\(913\) | −9.69496 | + | 3.01643i | −0.0106188 | + | 0.00330386i | ||||
\(914\) | 890.243 | 0.974008 | ||||||||
\(915\) | − | 548.111i | − | 0.599029i | ||||||
\(916\) | −246.846 | −0.269483 | ||||||||
\(917\) | −727.559 | −0.793412 | ||||||||
\(918\) | −99.6462 | −0.108547 | ||||||||
\(919\) | − | 1089.73i | − | 1.18578i | −0.805285 | − | 0.592888i | \(-0.797988\pi\) | ||
0.805285 | − | 0.592888i | \(-0.202012\pi\) | |||||||
\(920\) | − | 770.226i | − | 0.837202i | ||||||
\(921\) | 100.847i | 0.109497i | ||||||||
\(922\) | −528.267 | −0.572957 | ||||||||
\(923\) | − | 559.236i | − | 0.605890i | ||||||
\(924\) | 179.611 | − | 55.8832i | 0.194385 | − | 0.0604796i | ||||
\(925\) | 143.885 | 0.155551 | ||||||||
\(926\) | 123.247i | 0.133096i | ||||||||
\(927\) | −14.2384 | −0.0153597 | ||||||||
\(928\) | −160.939 | −0.173425 | ||||||||
\(929\) | 769.446 | 0.828252 | 0.414126 | − | 0.910220i | \(-0.364087\pi\) | ||||
0.414126 | + | 0.910220i | \(0.364087\pi\) | |||||||
\(930\) | 875.145i | 0.941016i | ||||||||
\(931\) | − | 233.596i | − | 0.250908i | ||||||
\(932\) | − | 626.576i | − | 0.672291i | ||||||
\(933\) | 359.594 | 0.385417 | ||||||||
\(934\) | − | 1207.92i | − | 1.29328i | ||||||
\(935\) | −359.223 | + | 111.766i | −0.384196 | + | 0.119536i | ||||
\(936\) | 133.734 | 0.142879 | ||||||||
\(937\) | 1606.78i | 1.71481i | 0.514641 | + | 0.857406i | \(0.327925\pi\) | ||||
−0.514641 | + | 0.857406i | \(0.672075\pi\) | |||||||
\(938\) | −514.228 | −0.548218 | ||||||||
\(939\) | −652.459 | −0.694844 | ||||||||
\(940\) | 194.610 | 0.207032 | ||||||||
\(941\) | − | 1279.34i | − | 1.35955i | −0.733419 | − | 0.679777i | \(-0.762077\pi\) | ||
0.733419 | − | 0.679777i | \(-0.237923\pi\) | |||||||
\(942\) | 1113.11i | 1.18164i | ||||||||
\(943\) | − | 1519.06i | − | 1.61088i | ||||||
\(944\) | −1637.10 | −1.73422 | ||||||||
\(945\) | − | 140.157i | − | 0.148315i | ||||||
\(946\) | −629.290 | − | 2022.57i | −0.665211 | − | 2.13802i | ||||
\(947\) | −985.800 | −1.04097 | −0.520486 | − | 0.853870i | \(-0.674249\pi\) | ||||
−0.520486 | + | 0.853870i | \(0.674249\pi\) | |||||||
\(948\) | − | 64.7183i | − | 0.0682682i | ||||||
\(949\) | −421.892 | −0.444565 | ||||||||
\(950\) | 529.061 | 0.556907 | ||||||||
\(951\) | 427.486 | 0.449512 | ||||||||
\(952\) | − | 303.753i | − | 0.319068i | ||||||
\(953\) | 761.038i | 0.798571i | 0.916827 | + | 0.399285i | \(0.130742\pi\) | ||||
−0.916827 | + | 0.399285i | \(0.869258\pi\) | |||||||
\(954\) | − | 183.893i | − | 0.192760i | ||||||
\(955\) | −185.615 | −0.194362 | ||||||||
\(956\) | − | 310.642i | − | 0.324940i | ||||||
\(957\) | −125.338 | + | 38.9970i | −0.130970 | + | 0.0407492i | ||||
\(958\) | 561.695 | 0.586320 | ||||||||
\(959\) | − | 455.011i | − | 0.474464i | ||||||
\(960\) | 175.717 | 0.183038 | ||||||||
\(961\) | 1658.08 | 1.72537 | ||||||||
\(962\) | −352.126 | −0.366035 | ||||||||
\(963\) | − | 443.168i | − | 0.460195i | ||||||
\(964\) | − | 41.2892i | − | 0.0428311i | ||||||
\(965\) | − | 571.211i | − | 0.591929i | ||||||
\(966\) | −829.377 | −0.858568 | ||||||||
\(967\) | 702.938i | 0.726926i | 0.931609 | + | 0.363463i | \(0.118406\pi\) | ||||
−0.931609 | + | 0.363463i | \(0.881594\pi\) | |||||||
\(968\) | 398.003 | + | 577.685i | 0.411160 | + | 0.596782i | ||||
\(969\) | −429.415 | −0.443153 | ||||||||
\(970\) | − | 209.838i | − | 0.216327i | ||||||
\(971\) | −1289.42 | −1.32793 | −0.663963 | − | 0.747766i | \(-0.731127\pi\) | ||||
−0.663963 | + | 0.747766i | \(0.731127\pi\) | |||||||
\(972\) | −23.9423 | −0.0246320 | ||||||||
\(973\) | 838.859 | 0.862136 | ||||||||
\(974\) | − | 1395.83i | − | 1.43309i | ||||||
\(975\) | − | 98.4487i | − | 0.100973i | ||||||
\(976\) | − | 1492.05i | − | 1.52874i | ||||||
\(977\) | −690.526 | −0.706782 | −0.353391 | − | 0.935476i | \(-0.614971\pi\) | ||||
−0.353391 | + | 0.935476i | \(0.614971\pi\) | |||||||
\(978\) | − | 252.937i | − | 0.258627i | ||||||
\(979\) | 146.480 | + | 470.793i | 0.149622 | + | 0.480892i | ||||
\(980\) | 49.4933 | 0.0505033 | ||||||||
\(981\) | 10.7054i | 0.0109128i | ||||||||
\(982\) | 2020.94 | 2.05799 | ||||||||
\(983\) | 1080.40 | 1.09908 | 0.549540 | − | 0.835467i | \(-0.314803\pi\) | ||||
0.549540 | + | 0.835467i | \(0.314803\pi\) | |||||||
\(984\) | 481.808 | 0.489642 | ||||||||
\(985\) | 25.0367i | 0.0254180i | ||||||||
\(986\) | − | 132.122i | − | 0.133998i | ||||||
\(987\) | 336.198i | 0.340626i | ||||||||
\(988\) | −359.223 | −0.363586 | ||||||||
\(989\) | 2591.17i | 2.61999i | ||||||||
\(990\) | −311.096 | + | 96.7925i | −0.314239 | + | 0.0977702i | ||||
\(991\) | −686.561 | −0.692796 | −0.346398 | − | 0.938088i | \(-0.612595\pi\) | ||||
−0.346398 | + | 0.938088i | \(0.612595\pi\) | |||||||
\(992\) | 1195.47i | 1.20511i | ||||||||
\(993\) | 253.626 | 0.255413 | ||||||||
\(994\) | −1100.03 | −1.10667 | ||||||||
\(995\) | 982.136 | 0.987071 | ||||||||
\(996\) | − | 2.45551i | − | 0.00246537i | ||||||
\(997\) | 1413.50i | 1.41775i | 0.705333 | + | 0.708876i | \(0.250797\pi\) | ||||
−0.705333 | + | 0.708876i | \(0.749203\pi\) | |||||||
\(998\) | 1890.97i | 1.89476i | ||||||||
\(999\) | −101.138 | −0.101240 |
(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 | 33.3.c.a.10.2 | ✓ | 4 | |
3.2 | odd | 2 | 99.3.c.b.10.3 | 4 | |||
4.3 | odd | 2 | 528.3.j.c.241.1 | 4 | |||
5.2 | odd | 4 | 825.3.h.a.274.5 | 8 | |||
5.3 | odd | 4 | 825.3.h.a.274.4 | 8 | |||
5.4 | even | 2 | 825.3.b.a.76.3 | 4 | |||
8.3 | odd | 2 | 2112.3.j.d.769.3 | 4 | |||
8.5 | even | 2 | 2112.3.j.a.769.2 | 4 | |||
11.2 | odd | 10 | 363.3.g.e.40.3 | 16 | |||
11.3 | even | 5 | 363.3.g.e.112.2 | 16 | |||
11.4 | even | 5 | 363.3.g.e.94.3 | 16 | |||
11.5 | even | 5 | 363.3.g.e.118.3 | 16 | |||
11.6 | odd | 10 | 363.3.g.e.118.2 | 16 | |||
11.7 | odd | 10 | 363.3.g.e.94.2 | 16 | |||
11.8 | odd | 10 | 363.3.g.e.112.3 | 16 | |||
11.9 | even | 5 | 363.3.g.e.40.2 | 16 | |||
11.10 | odd | 2 | inner | 33.3.c.a.10.3 | yes | 4 | |
12.11 | even | 2 | 1584.3.j.f.1297.3 | 4 | |||
33.32 | even | 2 | 99.3.c.b.10.2 | 4 | |||
44.43 | even | 2 | 528.3.j.c.241.2 | 4 | |||
55.32 | even | 4 | 825.3.h.a.274.3 | 8 | |||
55.43 | even | 4 | 825.3.h.a.274.6 | 8 | |||
55.54 | odd | 2 | 825.3.b.a.76.2 | 4 | |||
88.21 | odd | 2 | 2112.3.j.a.769.1 | 4 | |||
88.43 | even | 2 | 2112.3.j.d.769.4 | 4 | |||
132.131 | odd | 2 | 1584.3.j.f.1297.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.c.a.10.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
33.3.c.a.10.3 | yes | 4 | 11.10 | odd | 2 | inner | |
99.3.c.b.10.2 | 4 | 33.32 | even | 2 | |||
99.3.c.b.10.3 | 4 | 3.2 | odd | 2 | |||
363.3.g.e.40.2 | 16 | 11.9 | even | 5 | |||
363.3.g.e.40.3 | 16 | 11.2 | odd | 10 | |||
363.3.g.e.94.2 | 16 | 11.7 | odd | 10 | |||
363.3.g.e.94.3 | 16 | 11.4 | even | 5 | |||
363.3.g.e.112.2 | 16 | 11.3 | even | 5 | |||
363.3.g.e.112.3 | 16 | 11.8 | odd | 10 | |||
363.3.g.e.118.2 | 16 | 11.6 | odd | 10 | |||
363.3.g.e.118.3 | 16 | 11.5 | even | 5 | |||
528.3.j.c.241.1 | 4 | 4.3 | odd | 2 | |||
528.3.j.c.241.2 | 4 | 44.43 | even | 2 | |||
825.3.b.a.76.2 | 4 | 55.54 | odd | 2 | |||
825.3.b.a.76.3 | 4 | 5.4 | even | 2 | |||
825.3.h.a.274.3 | 8 | 55.32 | even | 4 | |||
825.3.h.a.274.4 | 8 | 5.3 | odd | 4 | |||
825.3.h.a.274.5 | 8 | 5.2 | odd | 4 | |||
825.3.h.a.274.6 | 8 | 55.43 | even | 4 | |||
1584.3.j.f.1297.3 | 4 | 12.11 | even | 2 | |||
1584.3.j.f.1297.4 | 4 | 132.131 | odd | 2 | |||
2112.3.j.a.769.1 | 4 | 88.21 | odd | 2 | |||
2112.3.j.a.769.2 | 4 | 8.5 | even | 2 | |||
2112.3.j.d.769.3 | 4 | 8.3 | odd | 2 | |||
2112.3.j.d.769.4 | 4 | 88.43 | even | 2 |