Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 223.1 | ||
Root | \(1.80398 - 0.863518i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.223 |
Dual form | 384.3.l.b.31.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.49473 | + | 6.49473i | −1.29895 | + | 1.29895i | −0.369856 | + | 0.929089i | \(0.620593\pi\) |
−0.929089 | + | 0.369856i | \(0.879407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.94273 | −0.563247 | −0.281623 | − | 0.959525i | \(-0.590873\pi\) | ||||
−0.281623 | + | 0.959525i | \(0.590873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.31091 | + | 4.31091i | 0.391901 | + | 0.391901i | 0.875364 | − | 0.483464i | \(-0.160621\pi\) |
−0.483464 | + | 0.875364i | \(0.660621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.06281 | − | 4.06281i | −0.312524 | − | 0.312524i | 0.533363 | − | 0.845887i | \(-0.320928\pi\) |
−0.845887 | + | 0.533363i | \(0.820928\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 15.9088i | − | 1.06058i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.5538 | −0.856106 | −0.428053 | − | 0.903754i | \(-0.640800\pi\) | ||||
−0.428053 | + | 0.903754i | \(0.640800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.94805 | − | 4.94805i | 0.260423 | − | 0.260423i | −0.564803 | − | 0.825226i | \(-0.691048\pi\) |
0.825226 | + | 0.564803i | \(0.191048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82883 | − | 4.82883i | 0.229945 | − | 0.229945i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 43.6717 | 1.89877 | 0.949385 | − | 0.314115i | \(-0.101708\pi\) | ||||
0.949385 | + | 0.314115i | \(0.101708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 59.3629i | − | 2.37452i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.0979 | − | 25.0979i | −0.865445 | − | 0.865445i | 0.126519 | − | 0.991964i | \(-0.459619\pi\) |
−0.991964 | + | 0.126519i | \(0.959619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 32.5024i | − | 1.04846i | −0.851576 | − | 0.524232i | \(-0.824352\pi\) | ||
0.851576 | − | 0.524232i | \(-0.175648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.5595 | −0.319986 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.6069 | − | 25.6069i | 0.731627 | − | 0.731627i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.14345 | + | 4.14345i | −0.111985 | + | 0.111985i | −0.760879 | − | 0.648894i | \(-0.775232\pi\) |
0.648894 | + | 0.760879i | \(0.275232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.95180 | 0.255174 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 55.3348i | 1.34963i | 0.737987 | + | 0.674814i | \(0.235776\pi\) | ||||
−0.737987 | + | 0.674814i | \(0.764224\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16.1189 | − | 16.1189i | −0.374858 | − | 0.374858i | 0.494385 | − | 0.869243i | \(-0.335393\pi\) |
−0.869243 | + | 0.494385i | \(0.835393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.4842 | + | 19.4842i | 0.432982 | + | 0.432982i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.92420i | 0.168600i | 0.996440 | + | 0.0843001i | \(0.0268654\pi\) | ||||
−0.996440 | + | 0.0843001i | \(0.973135\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.4549 | −0.682753 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.8247 | − | 17.8247i | 0.349504 | − | 0.349504i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 31.5748 | − | 31.5748i | 0.595750 | − | 0.595750i | −0.343429 | − | 0.939179i | \(-0.611588\pi\) |
0.939179 | + | 0.343429i | \(0.111588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −55.9964 | −1.01812 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.1202i | 0.212635i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −49.7172 | − | 49.7172i | −0.842665 | − | 0.842665i | 0.146540 | − | 0.989205i | \(-0.453186\pi\) |
−0.989205 | + | 0.146540i | \(0.953186\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −44.4711 | − | 44.4711i | −0.729035 | − | 0.729035i | 0.241393 | − | 0.970427i | \(-0.422396\pi\) |
−0.970427 | + | 0.241393i | \(0.922396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.8282i | 0.187749i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 52.7736 | 0.811902 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.64068 | + | 1.64068i | −0.0244878 | + | 0.0244878i | −0.719245 | − | 0.694757i | \(-0.755512\pi\) |
0.694757 | + | 0.719245i | \(0.255512\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −53.4867 | + | 53.4867i | −0.775170 | + | 0.775170i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24.1145 | −0.339641 | −0.169821 | − | 0.985475i | \(-0.554319\pi\) | ||||
−0.169821 | + | 0.985475i | \(0.554319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7741i | 0.147591i | 0.997273 | + | 0.0737955i | \(0.0235112\pi\) | ||||
−0.997273 | + | 0.0737955i | \(0.976489\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 72.7044 | + | 72.7044i | 0.969392 | + | 0.969392i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.9967 | − | 16.9967i | −0.220737 | − | 0.220737i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 72.0517i | 0.912047i | 0.889968 | + | 0.456024i | \(0.150727\pi\) | ||||
−0.889968 | + | 0.456024i | \(0.849273\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 42.0499 | − | 42.0499i | 0.506625 | − | 0.506625i | −0.406864 | − | 0.913489i | \(-0.633378\pi\) |
0.913489 | + | 0.406864i | \(0.133378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 94.5229 | − | 94.5229i | 1.11203 | − | 1.11203i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 61.4770 | 0.706633 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 28.9853i | − | 0.325677i | −0.986653 | − | 0.162839i | \(-0.947935\pi\) | ||
0.986653 | − | 0.162839i | \(-0.0520650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0185 | + | 16.0185i | 0.176028 | + | 0.176028i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 39.8071 | + | 39.8071i | 0.428034 | + | 0.428034i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 64.2724i | 0.676552i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −54.2698 | −0.559483 | −0.279741 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279741 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.9327 | − | 12.9327i | 0.130634 | − | 0.130634i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −57.0829 | + | 57.0829i | −0.565177 | + | 0.565177i | −0.930773 | − | 0.365597i | \(-0.880865\pi\) |
0.365597 | + | 0.930773i | \(0.380865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −39.3048 | −0.381600 | −0.190800 | − | 0.981629i | \(-0.561108\pi\) | ||||
−0.190800 | + | 0.981629i | \(0.561108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 62.7239i | 0.597371i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 25.6981 | + | 25.6981i | 0.240169 | + | 0.240169i | 0.816920 | − | 0.576751i | \(-0.195680\pi\) |
−0.576751 | + | 0.816920i | \(0.695680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.66133 | + | 9.66133i | 0.0886360 | + | 0.0886360i | 0.750035 | − | 0.661399i | \(-0.230037\pi\) |
−0.661399 | + | 0.750035i | \(0.730037\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 10.1493i | − | 0.0914355i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 64.2927 | 0.568962 | 0.284481 | − | 0.958682i | \(-0.408179\pi\) | ||||
0.284481 | + | 0.958682i | \(0.408179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −283.636 | + | 283.636i | −2.46640 | + | 2.46640i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.1884 | + | 12.1884i | −0.104175 | + | 0.104175i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 57.3816 | 0.482199 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 83.8321i | − | 0.692827i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −67.7710 | − | 67.7710i | −0.550984 | − | 0.550984i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 223.178 | + | 223.178i | 1.78542 | + | 1.78542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 129.668i | − | 1.02101i | −0.859875 | − | 0.510504i | \(-0.829459\pi\) | ||
0.859875 | − | 0.510504i | \(-0.170541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 39.4830 | 0.306070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −118.504 | + | 118.504i | −0.904613 | + | 0.904613i | −0.995831 | − | 0.0912183i | \(-0.970924\pi\) |
0.0912183 | + | 0.995831i | \(0.470924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.5088 | + | 19.5088i | −0.146683 | + | 0.146683i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −47.7263 | −0.353528 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 157.472i | 1.14943i | 0.818353 | + | 0.574716i | \(0.194888\pi\) | ||||
−0.818353 | + | 0.574716i | \(0.805112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −118.943 | − | 118.943i | −0.855703 | − | 0.855703i | 0.135125 | − | 0.990829i | \(-0.456856\pi\) |
−0.990829 | + | 0.135125i | \(0.956856\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.70513 | − | 9.70513i | −0.0688307 | − | 0.0688307i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 35.0288i | − | 0.244957i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 326.008 | 2.24833 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 40.9737 | − | 40.9737i | 0.278733 | − | 0.278733i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −99.5402 | + | 99.5402i | −0.668055 | + | 0.668055i | −0.957266 | − | 0.289210i | \(-0.906607\pi\) |
0.289210 | + | 0.957266i | \(0.406607\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −273.705 | −1.81262 | −0.906308 | − | 0.422618i | \(-0.861111\pi\) | ||||
−0.906308 | + | 0.422618i | \(0.861111\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 43.6614i | 0.285369i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 211.094 | + | 211.094i | 1.36190 | + | 1.36190i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 75.8792 | + | 75.8792i | 0.483307 | + | 0.483307i | 0.906186 | − | 0.422879i | \(-0.138981\pi\) |
−0.422879 | + | 0.906186i | \(0.638981\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 77.3420i | 0.486428i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −172.186 | −1.06948 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 177.242 | − | 177.242i | 1.08737 | − | 1.08737i | 0.0915766 | − | 0.995798i | \(-0.470809\pi\) |
0.995798 | − | 0.0915766i | \(-0.0291906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 68.5812 | − | 68.5812i | 0.415644 | − | 0.415644i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −61.6774 | −0.369326 | −0.184663 | − | 0.982802i | \(-0.559119\pi\) | ||||
−0.184663 | + | 0.982802i | \(0.559119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 135.987i | − | 0.804658i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.8441 | − | 14.8441i | −0.0868078 | − | 0.0868078i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −69.7012 | − | 69.7012i | −0.402897 | − | 0.402897i | 0.476355 | − | 0.879253i | \(-0.341958\pi\) |
−0.879253 | + | 0.476355i | \(0.841958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 234.052i | 1.33744i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 121.782 | 0.688033 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 43.6228 | − | 43.6228i | 0.243703 | − | 0.243703i | −0.574677 | − | 0.818380i | \(-0.694872\pi\) |
0.818380 | + | 0.574677i | \(0.194872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 44.7291 | − | 44.7291i | 0.247122 | − | 0.247122i | −0.572666 | − | 0.819788i | \(-0.694091\pi\) |
0.819788 | + | 0.572666i | \(0.194091\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 108.932 | 0.595254 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 53.8211i | − | 0.290925i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −62.7401 | − | 62.7401i | −0.335509 | − | 0.335509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.4865 | − | 14.4865i | −0.0766482 | − | 0.0766482i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 171.759i | − | 0.899263i | −0.893214 | − | 0.449632i | \(-0.851555\pi\) | ||
0.893214 | − | 0.449632i | \(-0.148445\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −215.384 | −1.11598 | −0.557989 | − | 0.829848i | \(-0.688427\pi\) | ||||
−0.557989 | + | 0.829848i | \(0.688427\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −64.6342 | + | 64.6342i | −0.331458 | + | 0.331458i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3354 | − | 18.3354i | 0.0930731 | − | 0.0930731i | −0.659037 | − | 0.752110i | \(-0.729036\pi\) |
0.752110 | + | 0.659037i | \(0.229036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 227.112 | 1.14127 | 0.570634 | − | 0.821205i | \(-0.306698\pi\) | ||||
0.570634 | + | 0.821205i | \(0.306698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.01883i | − | 0.0199942i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 98.9542 | + | 98.9542i | 0.487459 | + | 0.487459i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −359.384 | − | 359.384i | −1.75309 | − | 1.75309i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 131.015i | − | 0.632923i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42.6612 | 0.204120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 190.206 | − | 190.206i | 0.901451 | − | 0.901451i | −0.0941112 | − | 0.995562i | \(-0.530001\pi\) |
0.995562 | + | 0.0941112i | \(0.0300009\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.5342 | − | 29.5342i | 0.138658 | − | 0.138658i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 209.375 | 0.973839 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 128.148i | 0.590544i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.1956 | − | 13.1956i | −0.0602538 | − | 0.0602538i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 59.1293 | + | 59.1293i | 0.267553 | + | 0.267553i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 154.401i | 0.692379i | 0.938165 | + | 0.346190i | \(0.112525\pi\) | ||||
−0.938165 | + | 0.346190i | \(0.887475\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −178.089 | −0.791506 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −36.8204 | + | 36.8204i | −0.162204 | + | 0.162204i | −0.783543 | − | 0.621338i | \(-0.786589\pi\) |
0.621338 | + | 0.783543i | \(0.286589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9692 | + | 17.9692i | −0.0784683 | + | 0.0784683i | −0.745252 | − | 0.666783i | \(-0.767671\pi\) |
0.666783 | + | 0.745252i | \(0.267671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 41.6333 | 0.180231 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 167.669i | − | 0.719608i | −0.933028 | − | 0.359804i | \(-0.882844\pi\) | ||
0.933028 | − | 0.359804i | \(-0.117156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −51.4655 | − | 51.4655i | −0.219002 | − | 0.219002i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −88.2450 | − | 88.2450i | −0.372342 | − | 0.372342i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.7509i | 0.124481i | 0.998061 | + | 0.0622403i | \(0.0198245\pi\) | ||||
−0.998061 | + | 0.0622403i | \(0.980175\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −107.373 | −0.445531 | −0.222766 | − | 0.974872i | \(-0.571508\pi\) | ||||
−0.222766 | + | 0.974872i | \(0.571508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 217.280 | − | 217.280i | 0.886859 | − | 0.886859i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −40.2059 | −0.162777 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 103.001i | 0.413658i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −342.946 | − | 342.946i | −1.36632 | − | 1.36632i | −0.865623 | − | 0.500697i | \(-0.833077\pi\) |
−0.500697 | − | 0.865623i | \(-0.666923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 188.265 | + | 188.265i | 0.744130 | + | 0.744130i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 231.533i | 0.907972i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −393.565 | −1.53138 | −0.765691 | − | 0.643209i | \(-0.777603\pi\) | ||||
−0.765691 | + | 0.643209i | \(0.777603\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.3365 | − | 16.3365i | 0.0630753 | − | 0.0630753i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −75.2937 | + | 75.2937i | −0.288482 | + | 0.288482i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −413.800 | −1.57338 | −0.786692 | − | 0.617346i | \(-0.788208\pi\) | ||||
−0.786692 | + | 0.617346i | \(0.788208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 410.139i | 1.54769i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.4995 | + | 35.4995i | 0.132957 | + | 0.132957i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −165.389 | − | 165.389i | −0.614830 | − | 0.614830i | 0.329371 | − | 0.944201i | \(-0.393163\pi\) |
−0.944201 | + | 0.329371i | \(0.893163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 309.821i | − | 1.14325i | −0.820514 | − | 0.571626i | \(-0.806313\pi\) | ||
0.820514 | − | 0.571626i | \(-0.193687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −39.2372 | −0.143726 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 255.908 | − | 255.908i | 0.930575 | − | 0.930575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −157.397 | + | 157.397i | −0.568221 | + | 0.568221i | −0.931630 | − | 0.363409i | \(-0.881613\pi\) |
0.363409 | + | 0.931630i | \(0.381613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −97.5071 | −0.349488 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 411.141i | − | 1.46313i | −0.681769 | − | 0.731567i | \(-0.738789\pi\) | ||
0.681769 | − | 0.731567i | \(-0.261211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 343.521 | + | 343.521i | 1.21385 | + | 1.21385i | 0.969748 | + | 0.244106i | \(0.0784946\pi\) |
0.244106 | + | 0.969748i | \(0.421505\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −78.7173 | − | 78.7173i | −0.276201 | − | 0.276201i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 218.170i | − | 0.760174i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −77.1870 | −0.267083 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 66.4667 | − | 66.4667i | 0.228408 | − | 0.228408i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −35.1386 | + | 35.1386i | −0.119927 | + | 0.119927i | −0.764523 | − | 0.644596i | \(-0.777025\pi\) |
0.644596 | + | 0.764523i | \(0.277025\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 645.799 | 2.18915 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.6786i | 0.106662i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −177.430 | − | 177.430i | −0.593410 | − | 0.593410i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 63.5524 | + | 63.5524i | 0.211137 | + | 0.211137i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 139.824i | − | 0.461465i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 577.655 | 1.89395 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.4432 | + | 16.4432i | −0.0535609 | + | 0.0535609i | −0.733380 | − | 0.679819i | \(-0.762058\pi\) |
0.679819 | + | 0.733380i | \(0.262058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 48.1384 | − | 48.1384i | 0.155788 | − | 0.155788i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −39.8016 | −0.127980 | −0.0639898 | − | 0.997951i | \(-0.520382\pi\) | ||||
−0.0639898 | + | 0.997951i | \(0.520382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 431.885i | − | 1.37982i | −0.723894 | − | 0.689911i | \(-0.757649\pi\) | ||
0.723894 | − | 0.689911i | \(-0.242351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −76.8208 | − | 76.8208i | −0.243876 | − | 0.243876i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −255.063 | − | 255.063i | −0.804615 | − | 0.804615i | 0.179198 | − | 0.983813i | \(-0.442650\pi\) |
−0.983813 | + | 0.179198i | \(0.942650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 216.390i | − | 0.678337i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −62.9472 | −0.196097 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −72.0128 | + | 72.0128i | −0.222950 | + | 0.222950i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −241.180 | + | 241.180i | −0.742092 | + | 0.742092i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.6653 | −0.0723710 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 31.2430i | − | 0.0949635i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 205.897 | + | 205.897i | 0.622045 | + | 0.622045i | 0.946054 | − | 0.324009i | \(-0.105031\pi\) |
−0.324009 | + | 0.946054i | \(0.605031\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4303 | + | 12.4303i | 0.0373284 | + | 0.0373284i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 21.3115i | − | 0.0636165i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 45.7312 | 0.135701 | 0.0678504 | − | 0.997696i | \(-0.478386\pi\) | ||||
0.0678504 | + | 0.997696i | \(0.478386\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −78.7421 | + | 78.7421i | −0.232278 | + | 0.232278i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 140.115 | − | 140.115i | 0.410894 | − | 0.410894i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 325.097 | 0.947805 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 694.763i | − | 2.01381i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 296.512 | + | 296.512i | 0.854500 | + | 0.854500i | 0.990684 | − | 0.136183i | \(-0.0434836\pi\) |
−0.136183 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 198.107 | + | 198.107i | 0.567641 | + | 0.567641i | 0.931467 | − | 0.363826i | \(-0.118530\pi\) |
−0.363826 | + | 0.931467i | \(0.618530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 29.8554i | − | 0.0850581i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 85.4490 | 0.242065 | 0.121033 | − | 0.992649i | \(-0.461379\pi\) | ||||
0.121033 | + | 0.992649i | \(0.461379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 156.617 | − | 156.617i | 0.441176 | − | 0.441176i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −70.2779 | + | 70.2779i | −0.196857 | + | 0.196857i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 302.214 | 0.841823 | 0.420911 | − | 0.907102i | \(-0.361710\pi\) | ||||
0.420911 | + | 0.907102i | \(0.361710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 312.034i | 0.864359i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 102.673 | + | 102.673i | 0.282846 | + | 0.282846i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −69.9751 | − | 69.9751i | −0.191713 | − | 0.191713i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 372.554i | − | 1.01513i | −0.861612 | − | 0.507567i | \(-0.830545\pi\) | ||
0.861612 | − | 0.507567i | \(-0.169455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 166.004 | 0.449876 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −124.491 | + | 124.491i | −0.335554 | + | 0.335554i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 407.130 | − | 407.130i | 1.09150 | − | 1.09150i | 0.0961318 | − | 0.995369i | \(-0.469353\pi\) |
0.995369 | − | 0.0961318i | \(-0.0306470\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −546.672 | −1.45779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 203.936i | 0.540944i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −117.854 | − | 117.854i | −0.310961 | − | 0.310961i | 0.534321 | − | 0.845282i | \(-0.320567\pi\) |
−0.845282 | + | 0.534321i | \(0.820567\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 158.810 | + | 158.810i | 0.416825 | + | 0.416825i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 407.983i | 1.06523i | 0.846357 | + | 0.532615i | \(0.178791\pi\) | ||||
−0.846357 | + | 0.532615i | \(0.821209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 220.778 | 0.573450 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −48.3566 | + | 48.3566i | −0.124953 | + | 0.124953i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −458.508 | + | 458.508i | −1.17868 | + | 1.17868i | −0.198605 | + | 0.980080i | \(0.563641\pi\) |
−0.980080 | + | 0.198605i | \(0.936359\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −635.589 | −1.62555 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 290.275i | − | 0.738613i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −467.956 | − | 467.956i | −1.18470 | − | 1.18470i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 259.865 | + | 259.865i | 0.654573 | + | 0.654573i | 0.954091 | − | 0.299518i | \(-0.0968259\pi\) |
−0.299518 | + | 0.954091i | \(0.596826\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 47.7866i | − | 0.119766i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −499.197 | −1.24488 | −0.622441 | − | 0.782667i | \(-0.713859\pi\) | ||||
−0.622441 | + | 0.782667i | \(0.713859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −132.051 | + | 132.051i | −0.327670 | + | 0.327670i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 58.4525 | − | 58.4525i | 0.144327 | − | 0.144327i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.7241 | −0.0877741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 494.949i | 1.21014i | 0.796171 | + | 0.605072i | \(0.206856\pi\) | ||||
−0.796171 | + | 0.605072i | \(0.793144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −192.863 | − | 192.863i | −0.469254 | − | 0.469254i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 196.021 | + | 196.021i | 0.474628 | + | 0.474628i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 546.205i | 1.31616i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 291.349 | 0.698679 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −560.555 | + | 560.555i | −1.33784 | + | 1.33784i | −0.439693 | + | 0.898148i | \(0.644913\pi\) |
−0.898148 | + | 0.439693i | \(0.855087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −397.946 | + | 397.946i | −0.945239 | + | 0.945239i | −0.998577 | − | 0.0533373i | \(-0.983014\pi\) |
0.0533373 | + | 0.998577i | \(0.483014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.7726 | 0.0562000 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 863.956i | 2.03284i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 175.337 | + | 175.337i | 0.410626 | + | 0.410626i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.9013 | + | 42.9013i | 0.100003 | + | 0.100003i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 662.874i | 1.53799i | 0.639255 | + | 0.768995i | \(0.279243\pi\) | ||||
−0.639255 | + | 0.768995i | \(0.720757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −338.800 | −0.782448 | −0.391224 | − | 0.920296i | \(-0.627948\pi\) | ||||
−0.391224 | + | 0.920296i | \(0.627948\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −399.277 | + | 399.277i | −0.917877 | + | 0.917877i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 216.090 | − | 216.090i | 0.494484 | − | 0.494484i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 234.566 | 0.534319 | 0.267160 | − | 0.963652i | \(-0.413915\pi\) | ||||
0.267160 | + | 0.963652i | \(0.413915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 100.365i | 0.227584i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 421.096 | + | 421.096i | 0.950555 | + | 0.950555i | 0.998834 | − | 0.0482792i | \(-0.0153737\pi\) |
−0.0482792 | + | 0.998834i | \(0.515374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 188.251 | + | 188.251i | 0.423037 | + | 0.423037i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 243.823i | − | 0.545465i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 492.636 | 1.09718 | 0.548592 | − | 0.836090i | \(-0.315164\pi\) | ||||
0.548592 | + | 0.836090i | \(0.315164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −238.543 | + | 238.543i | −0.528921 | + | 0.528921i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 335.219 | − | 335.219i | 0.739997 | − | 0.739997i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −208.072 | −0.457301 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 516.831i | 1.13092i | 0.824775 | + | 0.565461i | \(0.191302\pi\) | ||||
−0.824775 | + | 0.565461i | \(0.808698\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −53.4741 | − | 53.4741i | −0.116501 | − | 0.116501i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5260 | + | 27.5260i | 0.0597093 | + | 0.0597093i | 0.736331 | − | 0.676622i | \(-0.236557\pi\) |
−0.676622 | + | 0.736331i | \(0.736557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 122.111i | 0.263740i | 0.991267 | + | 0.131870i | \(0.0420981\pi\) | ||||
−0.991267 | + | 0.131870i | \(0.957902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −517.073 | −1.11198 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 267.964 | − | 267.964i | 0.573798 | − | 0.573798i | −0.359390 | − | 0.933188i | \(-0.617015\pi\) |
0.933188 | + | 0.359390i | \(0.117015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.46875 | − | 6.46875i | 0.0137926 | − | 0.0137926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −185.865 | −0.394618 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 138.974i | − | 0.293814i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −293.730 | − | 293.730i | −0.618380 | − | 0.618380i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −94.7243 | − | 94.7243i | −0.198583 | − | 0.198583i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 419.084i | 0.874915i | 0.899239 | + | 0.437457i | \(0.144121\pi\) | ||||
−0.899239 | + | 0.437457i | \(0.855879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.6681 | 0.0699960 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 210.883 | − | 210.883i | 0.436612 | − | 0.436612i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 352.468 | − | 352.468i | 0.726738 | − | 0.726738i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 57.2378 | 0.117531 | 0.0587657 | − | 0.998272i | \(-0.481284\pi\) | ||||
0.0587657 | + | 0.998272i | \(0.481284\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 434.153i | 0.887838i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −301.955 | − | 301.955i | −0.614979 | − | 0.614979i | 0.329260 | − | 0.944239i | \(-0.393201\pi\) |
−0.944239 | + | 0.329260i | \(0.893201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 365.270 | + | 365.270i | 0.740912 | + | 0.740912i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 167.989i | 0.339372i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 95.0771 | 0.191302 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 619.990 | − | 619.990i | 1.24247 | − | 1.24247i | 0.283491 | − | 0.958975i | \(-0.408507\pi\) |
0.958975 | − | 0.283491i | \(-0.0914925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 75.5391 | − | 75.5391i | 0.150777 | − | 0.150777i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −222.446 | −0.442239 | −0.221120 | − | 0.975247i | \(-0.570971\pi\) | ||||
−0.221120 | + | 0.975247i | \(0.570971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 741.475i | − | 1.46827i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 166.550 | + | 166.550i | 0.328500 | + | 0.328500i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −489.873 | − | 489.873i | −0.962421 | − | 0.962421i | 0.0368976 | − | 0.999319i | \(-0.488252\pi\) |
−0.999319 | + | 0.0368976i | \(0.988252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 42.4795i | − | 0.0831302i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.3606 | 0.0708783 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 255.274 | − | 255.274i | 0.495678 | − | 0.495678i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.1605 | + | 34.1605i | −0.0660745 | + | 0.0660745i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 170.732 | 0.328964 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 197.152i | − | 0.378412i | −0.981937 | − | 0.189206i | \(-0.939409\pi\) | ||
0.981937 | − | 0.189206i | \(-0.0605913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 621.874 | + | 621.874i | 1.18905 | + | 1.18905i | 0.977330 | + | 0.211721i | \(0.0679067\pi\) |
0.211721 | + | 0.977330i | \(0.432093\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −286.654 | − | 286.654i | −0.546007 | − | 0.546007i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 473.033i | 0.897596i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1378.22 | 2.60533 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −149.152 | + | 149.152i | −0.280888 | + | 0.280888i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 224.815 | − | 224.815i | 0.421791 | − | 0.421791i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −333.804 | −0.623933 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 106.854i | 0.198983i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −144.221 | − | 144.221i | −0.267572 | − | 0.267572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −423.563 | − | 423.563i | −0.782925 | − | 0.782925i | 0.197398 | − | 0.980323i | \(-0.436751\pi\) |
−0.980323 | + | 0.197398i | \(0.936751\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 109.563i | 0.201774i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −125.495 | −0.230267 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5553 | + | 14.5553i | −0.0266093 | + | 0.0266093i | −0.720286 | − | 0.693677i | \(-0.755990\pi\) |
0.693677 | + | 0.720286i | \(0.255990\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −133.413 | + | 133.413i | −0.243012 | + | 0.243012i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −248.371 | −0.450764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 284.080i | − | 0.513708i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 65.9172 | + | 65.9172i | 0.118770 | + | 0.118770i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 351.991 | + | 351.991i | 0.631941 | + | 0.631941i | 0.948554 | − | 0.316614i | \(-0.102546\pi\) |
−0.316614 | + | 0.948554i | \(0.602546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 130.976i | 0.234304i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 153.681 | 0.273942 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −150.902 | + | 150.902i | −0.268031 | + | 0.268031i | −0.828307 | − | 0.560275i | \(-0.810695\pi\) |
0.560275 | + | 0.828307i | \(0.310695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −417.563 | + | 417.563i | −0.739050 | + | 0.739050i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 35.4845 | 0.0625830 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 113.300i | − | 0.199121i | −0.995032 | − | 0.0995603i | \(-0.968256\pi\) | ||
0.995032 | − | 0.0995603i | \(-0.0317436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −207.486 | − | 207.486i | −0.363373 | − | 0.363373i | 0.501680 | − | 0.865053i | \(-0.332715\pi\) |
−0.865053 | + | 0.501680i | \(0.832715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 210.361 | + | 210.361i | 0.367123 | + | 0.367123i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2592.48i | − | 4.50866i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −484.715 | −0.840061 | −0.420031 | − | 0.907510i | \(-0.637981\pi\) | ||||
−0.420031 | + | 0.907510i | \(0.637981\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 263.790 | − | 263.790i | 0.455596 | − | 0.455596i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −165.791 | + | 165.791i | −0.285355 | + | 0.285355i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 272.232 | 0.466950 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 158.321i | − | 0.270634i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −540.404 | − | 540.404i | −0.920619 | − | 0.920619i | 0.0764537 | − | 0.997073i | \(-0.475640\pi\) |
−0.997073 | + | 0.0764537i | \(0.975640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −160.823 | − | 160.823i | −0.273045 | − | 0.273045i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44.9124i | 0.0759939i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 411.176 | 0.693383 | 0.346692 | − | 0.937979i | \(-0.387305\pi\) | ||||
0.346692 | + | 0.937979i | \(0.387305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −372.678 | + | 372.678i | −0.626350 | + | 0.626350i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −278.154 | + | 278.154i | −0.465920 | + | 0.465920i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 552.839 | 0.922936 | 0.461468 | − | 0.887157i | \(-0.347323\pi\) | ||||
0.461468 | + | 0.887157i | \(0.347323\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 881.159i | 1.46615i | 0.680145 | + | 0.733077i | \(0.261917\pi\) | ||||
−0.680145 | + | 0.733077i | \(0.738083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.92204 | + | 4.92204i | 0.00816259 | + | 0.00816259i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 544.467 | + | 544.467i | 0.899945 | + | 0.899945i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1175.08i | 1.93588i | 0.251186 | + | 0.967939i | \(0.419180\pi\) | ||||
−0.251186 | + | 0.967939i | \(0.580820\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −242.387 | −0.398009 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.1945 | − | 32.1945i | 0.0526915 | − | 0.0526915i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 496.928 | − | 496.928i | 0.810649 | − | 0.810649i | −0.174082 | − | 0.984731i | \(-0.555696\pi\) |
0.984731 | + | 0.174082i | \(0.0556959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 880.308 | 1.43140 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 623.301i | − | 1.01021i | −0.863057 | − | 0.505106i | \(-0.831453\pi\) | ||
0.863057 | − | 0.505106i | \(-0.168547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.45302 | + | 7.45302i | 0.0120404 | + | 0.0120404i | 0.713101 | − | 0.701061i | \(-0.247290\pi\) |
−0.701061 | + | 0.713101i | \(0.747290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 160.460 | + | 160.460i | 0.258390 | + | 0.258390i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 114.281i | 0.183437i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1414.88 | −2.26381 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −52.2490 | + | 52.2490i | −0.0833318 | + | 0.0833318i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60.3029 | − | 60.3029i | 0.0958711 | − | 0.0958711i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −147.833 | −0.234284 | −0.117142 | − | 0.993115i | \(-0.537373\pi\) | ||||
−0.117142 | + | 0.993115i | \(0.537373\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 465.908i | 0.736031i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 842.158 | + | 842.158i | 1.32623 | + | 1.32623i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 135.921 | + | 135.921i | 0.213376 | + | 0.213376i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 72.3436i | 0.113214i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −782.691 | −1.22105 | −0.610523 | − | 0.791998i | \(-0.709041\pi\) | ||||
−0.610523 | + | 0.791998i | \(0.709041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 126.760 | − | 126.760i | 0.197138 | − | 0.197138i | −0.601634 | − | 0.798772i | \(-0.705483\pi\) |
0.798772 | + | 0.601634i | \(0.205483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −256.431 | + | 256.431i | −0.397568 | + | 0.397568i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1226.09 | −1.89504 | −0.947520 | − | 0.319697i | \(-0.896419\pi\) | ||||
−0.947520 | + | 0.319697i | \(0.896419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 428.653i | − | 0.660482i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −156.949 | − | 156.949i | −0.241089 | − | 0.241089i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −326.300 | − | 326.300i | −0.499694 | − | 0.499694i | 0.411649 | − | 0.911343i | \(-0.364953\pi\) |
−0.911343 | + | 0.411649i | \(0.864953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1539.31i | − | 2.35008i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.3224 | 0.0491970 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −574.901 | + | 574.901i | −0.872384 | + | 0.872384i | −0.992732 | − | 0.120347i | \(-0.961599\pi\) |
0.120347 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −52.8795 | + | 52.8795i | −0.0799993 | + | 0.0799993i | −0.745974 | − | 0.665975i | \(-0.768016\pi\) |
0.665975 | + | 0.745974i | \(0.268016\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −144.837 | −0.218456 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 253.409i | − | 0.381065i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1096.07 | − | 1096.07i | −1.64328 | − | 1.64328i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −189.101 | − | 189.101i | −0.282663 | − | 0.282663i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 383.422i | − | 0.571419i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 342.318 | 0.508645 | 0.254322 | − | 0.967119i | \(-0.418148\pi\) | ||||
0.254322 | + | 0.967119i | \(0.418148\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 218.113 | − | 218.113i | 0.323131 | − | 0.323131i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −107.154 | + | 107.154i | −0.158278 | + | 0.158278i | −0.781803 | − | 0.623525i | \(-0.785700\pi\) |
0.623525 | + | 0.781803i | \(0.285700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 213.971 | 0.315127 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 90.1911i | − | 0.132439i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 724.233 | + | 724.233i | 1.06037 | + | 1.06037i | 0.998057 | + | 0.0623142i | \(0.0198481\pi\) |
0.0623142 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1022.74 | − | 1022.74i | −1.49305 | − | 1.49305i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 44.0155i | − | 0.0640691i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −256.564 | −0.372372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 162.528 | − | 162.528i | 0.235207 | − | 0.235207i | −0.579655 | − | 0.814862i | \(-0.696813\pi\) |
0.814862 | + | 0.579655i | \(0.196813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −50.9902 | + | 50.9902i | −0.0735790 | + | 0.0735790i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1545.00 | 2.22302 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 805.331i | − | 1.15543i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 205.351 | + | 205.351i | 0.293779 | + | 0.293779i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 301.659 | + | 301.659i | 0.430327 | + | 0.430327i | 0.888740 | − | 0.458412i | \(-0.151582\pi\) |
−0.458412 | + | 0.888740i | \(0.651582\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.0040i | 0.0583271i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 126.064 | 0.178815 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 225.062 | − | 225.062i | 0.318334 | − | 0.318334i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 629.100 | − | 629.100i | 0.887306 | − | 0.887306i | −0.106958 | − | 0.994264i | \(-0.534111\pi\) |
0.994264 | + | 0.106958i | \(0.0341109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 216.155 | 0.304016 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1419.43i | − | 1.99079i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 227.502 | + | 227.502i | 0.318185 | + | 0.318185i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36.4372 | − | 36.4372i | −0.0508190 | − | 0.0508190i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 145.542i | − | 0.202422i | −0.994865 | − | 0.101211i | \(-0.967728\pi\) | ||
0.994865 | − | 0.101211i | \(-0.0322718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 154.968 | 0.214935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 131.505 | − | 131.505i | 0.181887 | − | 0.181887i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1489.88 | + | 1489.88i | −2.05501 | + | 2.05501i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 938.214 | 1.29053 | 0.645264 | − | 0.763960i | \(-0.276747\pi\) | ||||
0.645264 | + | 0.763960i | \(0.276747\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 234.591 | + | 234.591i | 0.320918 | + | 0.320918i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −692.101 | − | 692.101i | −0.944203 | − | 0.944203i | 0.0543203 | − | 0.998524i | \(-0.482701\pi\) |
−0.998524 | + | 0.0543203i | \(0.982701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 532.226i | 0.724117i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.1456 | −0.0191935 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −440.389 | + | 440.389i | −0.595926 | + | 0.595926i | −0.939226 | − | 0.343300i | \(-0.888455\pi\) |
0.343300 | + | 0.939226i | \(0.388455\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49.2420 | − | 49.2420i | 0.0664534 | − | 0.0664534i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1010.54 | 1.36008 | 0.680039 | − | 0.733176i | \(-0.261963\pi\) | ||||
0.680039 | + | 0.733176i | \(0.261963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1292.97i | − | 1.73553i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −126.150 | − | 126.150i | −0.168875 | − | 0.168875i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −101.321 | − | 101.321i | −0.135275 | − | 0.135275i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 776.971i | − | 1.03458i | −0.855810 | − | 0.517291i | \(-0.826940\pi\) | ||
0.855810 | − | 0.517291i | \(-0.173060\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 840.043 | 1.11560 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1777.64 | − | 1777.64i | 2.35449 | − | 2.35449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −375.481 | + | 375.481i | −0.496012 | + | 0.496012i | −0.910194 | − | 0.414182i | \(-0.864068\pi\) |
0.414182 | + | 0.910194i | \(0.364068\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −461.153 | −0.607579 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1502.22i | 1.97400i | 0.160711 | + | 0.987001i | \(0.448621\pi\) | ||||
−0.160711 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.0920 | − | 38.0920i | −0.0499239 | − | 0.0499239i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −283.569 | − | 283.569i | −0.370678 | − | 0.370678i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 403.983i | 0.526705i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −293.930 | −0.382223 | −0.191112 | − | 0.981568i | \(-0.561209\pi\) | ||||
−0.191112 | + | 0.981568i | \(0.561209\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 482.017 | − | 482.017i | 0.625184 | − | 0.625184i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 748.271 | − | 748.271i | 0.968009 | − | 0.968009i | −0.0314945 | − | 0.999504i | \(-0.510027\pi\) |
0.999504 | + | 0.0314945i | \(0.0100267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1929.44 | −2.48960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 40.0161i | 0.0515007i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 273.799 | + | 273.799i | 0.351475 | + | 0.351475i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −103.956 | − | 103.956i | −0.133106 | − | 0.133106i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 184.431i | − | 0.235544i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −985.629 | −1.25558 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −735.839 | + | 735.839i | −0.934992 | + | 0.934992i | −0.998012 | − | 0.0630203i | \(-0.979927\pi\) |
0.0630203 | + | 0.998012i | \(0.479927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 506.799 | − | 506.799i | 0.642331 | − | 0.642331i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −253.488 | −0.320466 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 361.355i | 0.455681i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −502.315 | − | 502.315i | −0.631843 | − | 0.631843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −212.043 | − | 212.043i | −0.266051 | − | 0.266051i | 0.561455 | − | 0.827507i | \(-0.310242\pi\) |
−0.827507 | + | 0.561455i | \(0.810242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 115.327i | − | 0.144340i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −86.9558 | −0.108559 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.4464 | + | 46.4464i | −0.0578411 | + | 0.0578411i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1118.30 | − | 1118.30i | 1.38919 | − | 1.38919i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 405.119 | 0.502006 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 827.491i | 1.02286i | 0.859326 | + | 0.511428i | \(0.170883\pi\) | ||||
−0.859326 | + | 0.511428i | \(0.829117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 112.908 | + | 112.908i | 0.139221 | + | 0.139221i | 0.773283 | − | 0.634062i | \(-0.218613\pi\) |
−0.634062 | + | 0.773283i | \(0.718613\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 379.452 | + | 379.452i | 0.466731 | + | 0.466731i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2302.28i | 2.82488i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −159.514 | −0.195243 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 48.0556 | − | 48.0556i | 0.0586760 | − | 0.0586760i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −555.298 | + | 555.298i | −0.676368 | + | 0.676368i | −0.959176 | − | 0.282808i | \(-0.908734\pi\) |
0.282808 | + | 0.959176i | \(0.408734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −763.799 | −0.928067 | −0.464034 | − | 0.885818i | \(-0.653598\pi\) | ||||
−0.464034 | + | 0.885818i | \(0.653598\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 626.844i | 0.759812i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 116.947 | + | 116.947i | 0.141411 | + | 0.141411i | 0.774268 | − | 0.632858i | \(-0.218118\pi\) |
−0.632858 | + | 0.774268i | \(0.718118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −181.419 | − | 181.419i | −0.218841 | − | 0.218841i | 0.589169 | − | 0.808010i | \(-0.299455\pi\) |
−0.808010 | + | 0.589169i | \(0.799455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 385.543i | − | 0.463950i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 486.896 | 0.584509 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 400.578 | − | 400.578i | 0.479734 | − | 0.479734i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 119.421 | − | 119.421i | 0.142678 | − | 0.142678i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −521.472 | −0.621540 | −0.310770 | − | 0.950485i | \(-0.600587\pi\) | ||||
−0.310770 | + | 0.950485i | \(0.600587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 418.809i | 0.497989i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 503.542 | + | 503.542i | 0.597322 | + | 0.597322i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 883.200 | + | 883.200i | 1.04521 | + | 1.04521i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 330.527i | 0.390233i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −841.451 | −0.991108 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −180.952 | + | 180.952i | −0.212634 | + | 0.212634i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 644.278 | − | 644.278i | 0.755309 | − | 0.755309i | −0.220156 | − | 0.975465i | \(-0.570657\pi\) |
0.975465 | + | 0.220156i | \(0.0706566\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 192.817 | 0.225517 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 757.190i | 0.883536i | 0.897129 | + | 0.441768i | \(0.145649\pi\) | ||||
−0.897129 | + | 0.441768i | \(0.854351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1011.32 | − | 1011.32i | −1.17732 | − | 1.17732i | −0.980425 | − | 0.196894i | \(-0.936915\pi\) |
−0.196894 | − | 0.980425i | \(-0.563085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 267.203 | + | 267.203i | 0.310340 | + | 0.310340i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 598.188i | − | 0.693149i | −0.938022 | − | 0.346575i | \(-0.887345\pi\) | ||
0.938022 | − | 0.346575i | \(-0.112655\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 905.381 | 1.04668 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 94.5344 | − | 94.5344i | 0.109036 | − | 0.109036i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −310.609 | + | 310.609i | −0.357432 | + | 0.357432i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.3315 | 0.0153060 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 162.810i | 0.186494i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −879.929 | − | 879.929i | −1.00563 | − | 1.00563i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 664.587 | + | 664.587i | 0.757796 | + | 0.757796i | 0.975921 | − | 0.218125i | \(-0.0699939\pi\) |
−0.218125 | + | 0.975921i | \(0.569994\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 86.0716i | − | 0.0979199i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 772.898 | 0.877296 | 0.438648 | − | 0.898659i | \(-0.355458\pi\) | ||||
0.438648 | + | 0.898659i | \(0.355458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −321.603 | + | 321.603i | −0.364216 | + | 0.364216i | −0.865363 | − | 0.501146i | \(-0.832912\pi\) |
0.501146 | + | 0.865363i | \(0.332912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −790.939 | + | 790.939i | −0.893717 | + | 0.893717i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −762.665 | −0.859825 | −0.429912 | − | 0.902871i | \(-0.641456\pi\) | ||||
−0.429912 | + | 0.902871i | \(0.641456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 511.245i | 0.575079i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.7982 | − | 38.7982i | −0.0435445 | − | 0.0435445i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.2093 | + | 39.2093i | 0.0439074 | + | 0.0439074i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 566.637i | 0.633114i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 434.612 | 0.484518 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −815.741 | + | 815.741i | −0.907388 | + | 0.907388i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −459.533 | + | 459.533i | −0.510025 | + | 0.510025i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −155.671 | −0.172393 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 581.006i | 0.641996i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −729.007 | − | 729.007i | −0.803756 | − | 0.803756i | 0.179924 | − | 0.983680i | \(-0.442415\pi\) |
−0.983680 | + | 0.179924i | \(0.942415\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 171.249 | + | 171.249i | 0.188392 | + | 0.188392i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 885.541i | − | 0.972054i | −0.873944 | − | 0.486027i | \(-0.838446\pi\) | ||
0.873944 | − | 0.486027i | \(-0.161554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 362.546 | 0.397094 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −707.480 | + | 707.480i | −0.773203 | + | 0.773203i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 467.230 | − | 467.230i | 0.509520 | − | 0.509520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −714.964 | −0.777980 | −0.388990 | − | 0.921242i | \(-0.627176\pi\) | ||||
−0.388990 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 40.2774i | − | 0.0437323i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 97.9727 | + | 97.9727i | 0.106146 | + | 0.106146i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 245.967 | + | 245.967i | 0.265911 | + | 0.265911i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 117.914i | 0.127200i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 585.585 | 0.630339 | 0.315170 | − | 0.949035i | \(-0.397939\pi\) | ||||
0.315170 | + | 0.949035i | \(0.397939\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −165.536 | + | 165.536i | −0.177805 | + | 0.177805i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 48.7468 | − | 48.7468i | 0.0522474 | − | 0.0522474i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 814.960 | 0.871614 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1423.91i | − | 1.51965i | −0.650129 | − | 0.759824i | \(-0.725285\pi\) | ||
0.650129 | − | 0.759824i | \(-0.274715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 528.948 | + | 528.948i | 0.563310 | + | 0.563310i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −142.471 | − | 142.471i | −0.151404 | − | 0.151404i | 0.627341 | − | 0.778745i | \(-0.284143\pi\) |
−0.778745 | + | 0.627341i | \(0.784143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2416.56i | 2.56264i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 188.172 | 0.199124 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 174.352 | − | 174.352i | 0.184110 | − | 0.184110i | −0.609034 | − | 0.793144i | \(-0.708443\pi\) |
0.793144 | + | 0.609034i | \(0.208443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.7733 | − | 43.7733i | 0.0461257 | − | 0.0461257i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 624.774 | 0.656965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 66.9080i | − | 0.0702078i | −0.999384 | − | 0.0351039i | \(-0.988824\pi\) | ||
0.999384 | − | 0.0351039i | \(-0.0111762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1115.53 | + | 1115.53i | 1.16809 | + | 1.16809i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 265.022 | + | 265.022i | 0.276930 | + | 0.276930i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 620.870i | − | 0.647414i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −95.4048 | −0.0992766 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 77.0943 | − | 77.0943i | 0.0800564 | − | 0.0800564i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1398.86 | − | 1398.86i | 1.44959 | − | 1.44959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 128.892 | 0.133290 | 0.0666451 | − | 0.997777i | \(-0.478770\pi\) | ||||
0.0666451 | + | 0.997777i | \(0.478770\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 176.395i | − | 0.182038i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −801.089 | − | 801.089i | −0.825015 | − | 0.825015i | 0.161808 | − | 0.986822i | \(-0.448268\pi\) |
−0.986822 | + | 0.161808i | \(0.948268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 468.959 | + | 468.959i | 0.481972 | + | 0.481972i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 590.768i | − | 0.605916i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1591.49 | −1.62896 | −0.814479 | − | 0.580194i | \(-0.802977\pi\) | ||||
−0.814479 | + | 0.580194i | \(0.802977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 124.953 | − | 124.953i | 0.127633 | − | 0.127633i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.9840 | − | 28.9840i | 0.0295453 | − | 0.0295453i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1699.86 | 1.72926 | 0.864631 | − | 0.502408i | \(-0.167552\pi\) | ||||
0.864631 | + | 0.502408i | \(0.167552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 238.167i | 0.241794i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 38.2647 | + | 38.2647i | 0.0387687 | + | 0.0387687i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −703.939 | − | 703.939i | −0.711769 | − | 0.711769i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 228.875i | 0.230954i | 0.993310 | + | 0.115477i | \(0.0368397\pi\) | ||||
−0.993310 | + | 0.115477i | \(0.963160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −504.342 | −0.507898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1475.03 | + | 1475.03i | −1.48244 | + | 1.48244i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1020.63 | + | 1020.63i | −1.02370 | + | 1.02370i | −0.0239926 | + | 0.999712i | \(0.507638\pi\) |
−0.999712 | + | 0.0239926i | \(0.992362\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.4480 | −0.0304785 |
(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 | 384.3.l.b.223.1 | 16 | ||
3.2 | odd | 2 | 1152.3.m.c.991.8 | 16 | |||
4.3 | odd | 2 | 384.3.l.a.223.5 | 16 | |||
8.3 | odd | 2 | 48.3.l.a.19.2 | ✓ | 16 | ||
8.5 | even | 2 | 192.3.l.a.175.8 | 16 | |||
12.11 | even | 2 | 1152.3.m.f.991.8 | 16 | |||
16.3 | odd | 4 | 192.3.l.a.79.8 | 16 | |||
16.5 | even | 4 | 384.3.l.a.31.5 | 16 | |||
16.11 | odd | 4 | inner | 384.3.l.b.31.1 | 16 | ||
16.13 | even | 4 | 48.3.l.a.43.2 | yes | 16 | ||
24.5 | odd | 2 | 576.3.m.c.559.1 | 16 | |||
24.11 | even | 2 | 144.3.m.c.19.7 | 16 | |||
48.5 | odd | 4 | 1152.3.m.f.415.8 | 16 | |||
48.11 | even | 4 | 1152.3.m.c.415.8 | 16 | |||
48.29 | odd | 4 | 144.3.m.c.91.7 | 16 | |||
48.35 | even | 4 | 576.3.m.c.271.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.2 | ✓ | 16 | 8.3 | odd | 2 | ||
48.3.l.a.43.2 | yes | 16 | 16.13 | even | 4 | ||
144.3.m.c.19.7 | 16 | 24.11 | even | 2 | |||
144.3.m.c.91.7 | 16 | 48.29 | odd | 4 | |||
192.3.l.a.79.8 | 16 | 16.3 | odd | 4 | |||
192.3.l.a.175.8 | 16 | 8.5 | even | 2 | |||
384.3.l.a.31.5 | 16 | 16.5 | even | 4 | |||
384.3.l.a.223.5 | 16 | 4.3 | odd | 2 | |||
384.3.l.b.31.1 | 16 | 16.11 | odd | 4 | inner | ||
384.3.l.b.223.1 | 16 | 1.1 | even | 1 | trivial | ||
576.3.m.c.271.1 | 16 | 48.35 | even | 4 | |||
576.3.m.c.559.1 | 16 | 24.5 | odd | 2 | |||
1152.3.m.c.415.8 | 16 | 48.11 | even | 4 | |||
1152.3.m.c.991.8 | 16 | 3.2 | odd | 2 | |||
1152.3.m.f.415.8 | 16 | 48.5 | odd | 4 | |||
1152.3.m.f.991.8 | 16 | 12.11 | even | 2 |