Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(287,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.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: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 863.11 | ||
Character | \(\chi\) | \(=\) | 1152.863 |
Dual form | 1152.4.l.b.287.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.22357 | − | 3.22357i | −0.288325 | − | 0.288325i | 0.548093 | − | 0.836418i | \(-0.315354\pi\) |
−0.836418 | + | 0.548093i | \(0.815354\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.1030 | −0.707497 | −0.353749 | − | 0.935341i | \(-0.615093\pi\) | ||||
−0.353749 | + | 0.935341i | \(0.615093\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.39235 | − | 3.39235i | 0.0929847 | − | 0.0929847i | −0.659084 | − | 0.752069i | \(-0.729056\pi\) |
0.752069 | + | 0.659084i | \(0.229056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.1435 | + | 54.1435i | 1.15513 | + | 1.15513i | 0.985509 | + | 0.169623i | \(0.0542550\pi\) |
0.169623 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 70.7730i | − | 1.00970i | −0.863206 | − | 0.504852i | \(-0.831547\pi\) | ||
0.863206 | − | 0.504852i | \(-0.168453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.5595 | + | 32.5595i | −0.393140 | + | 0.393140i | −0.875805 | − | 0.482665i | \(-0.839669\pi\) |
0.482665 | + | 0.875805i | \(0.339669\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.4197i | 0.148858i | 0.997226 | + | 0.0744291i | \(0.0237135\pi\) | ||||
−0.997226 | + | 0.0744291i | \(0.976287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 104.217i | − | 0.833738i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.0742 | + | 28.0742i | −0.179767 | + | 0.179767i | −0.791254 | − | 0.611487i | \(-0.790572\pi\) |
0.611487 | + | 0.791254i | \(0.290572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 174.864i | − | 1.01311i | −0.862207 | − | 0.506556i | \(-0.830918\pi\) | ||
0.862207 | − | 0.506556i | \(-0.169082\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.2385 | + | 42.2385i | 0.203989 | + | 0.203989i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −116.834 | + | 116.834i | −0.519117 | + | 0.519117i | −0.917304 | − | 0.398187i | \(-0.869640\pi\) |
0.398187 | + | 0.917304i | \(0.369640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19.6290 | −0.0747692 | −0.0373846 | − | 0.999301i | \(-0.511903\pi\) | ||||
−0.0373846 | + | 0.999301i | \(0.511903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −94.2456 | − | 94.2456i | −0.334240 | − | 0.334240i | 0.519954 | − | 0.854194i | \(-0.325949\pi\) |
−0.854194 | + | 0.519954i | \(0.825949\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −372.603 | −1.15638 | −0.578189 | − | 0.815903i | \(-0.696240\pi\) | ||||
−0.578189 | + | 0.815903i | \(0.696240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −171.310 | −0.499447 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 162.999 | + | 162.999i | 0.422445 | + | 0.422445i | 0.886045 | − | 0.463600i | \(-0.153442\pi\) |
−0.463600 | + | 0.886045i | \(0.653442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.8710 | −0.0536196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 610.346 | − | 610.346i | 1.34678 | − | 1.34678i | 0.457655 | − | 0.889130i | \(-0.348690\pi\) |
0.889130 | − | 0.457655i | \(-0.151310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 531.488 | + | 531.488i | 1.11557 | + | 1.11557i | 0.992383 | + | 0.123191i | \(0.0393128\pi\) |
0.123191 | + | 0.992383i | \(0.460687\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 349.071i | − | 0.666106i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −562.092 | + | 562.092i | −1.02493 | + | 1.02493i | −0.0252516 | + | 0.999681i | \(0.508039\pi\) |
−0.999681 | + | 0.0252516i | \(0.991961\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1166.76i | 1.95027i | 0.221612 | + | 0.975135i | \(0.428868\pi\) | ||||
−0.221612 | + | 0.975135i | \(0.571132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 308.564i | 0.494721i | 0.968923 | + | 0.247361i | \(0.0795633\pi\) | ||||
−0.968923 | + | 0.247361i | \(0.920437\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −44.4501 | + | 44.4501i | −0.0657865 | + | 0.0657865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1170.83i | 1.66746i | 0.552176 | + | 0.833728i | \(0.313798\pi\) | ||||
−0.552176 | + | 0.833728i | \(0.686202\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 469.366 | + | 469.366i | 0.620719 | + | 0.620719i | 0.945715 | − | 0.324996i | \(-0.105363\pi\) |
−0.324996 | + | 0.945715i | \(0.605363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −228.142 | + | 228.142i | −0.291123 | + | 0.291123i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1534.65 | 1.82778 | 0.913892 | − | 0.405957i | \(-0.133062\pi\) | ||||
0.913892 | + | 0.405957i | \(0.133062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −709.445 | − | 709.445i | −0.817253 | − | 0.817253i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 209.916 | 0.226704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −139.670 | −0.146200 | −0.0730998 | − | 0.997325i | \(-0.523289\pi\) | ||||
−0.0730998 | + | 0.997325i | \(0.523289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 525.800 | + | 525.800i | 0.518011 | + | 0.518011i | 0.916969 | − | 0.398958i | \(-0.130628\pi\) |
−0.398958 | + | 0.916969i | \(0.630628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −221.106 | −0.211517 | −0.105758 | − | 0.994392i | \(-0.533727\pi\) | ||||
−0.105758 | + | 0.994392i | \(0.533727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −824.395 | + | 824.395i | −0.744834 | + | 0.744834i | −0.973504 | − | 0.228670i | \(-0.926562\pi\) |
0.228670 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 675.079 | + | 675.079i | 0.593219 | + | 0.593219i | 0.938500 | − | 0.345281i | \(-0.112216\pi\) |
−0.345281 | + | 0.938500i | \(0.612216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1052.43i | − | 0.876141i | −0.898941 | − | 0.438070i | \(-0.855662\pi\) | ||
0.898941 | − | 0.438070i | \(-0.144338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 52.9300 | − | 52.9300i | 0.0429195 | − | 0.0429195i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 927.341i | 0.714363i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1307.98i | 0.982708i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −738.897 | + | 738.897i | −0.528712 | + | 0.528712i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 103.084i | 0.0720254i | 0.999351 | + | 0.0360127i | \(0.0114657\pi\) | ||||
−0.999351 | + | 0.0360127i | \(0.988534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −535.858 | − | 535.858i | −0.357390 | − | 0.357390i | 0.505460 | − | 0.862850i | \(-0.331323\pi\) |
−0.862850 | + | 0.505460i | \(0.831323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 426.628 | − | 426.628i | 0.278146 | − | 0.278146i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2093.02 | 1.30525 | 0.652625 | − | 0.757681i | \(-0.273668\pi\) | ||||
0.652625 | + | 0.757681i | \(0.273668\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1367.29 | − | 1367.29i | −0.834331 | − | 0.834331i | 0.153775 | − | 0.988106i | \(-0.450857\pi\) |
−0.988106 | + | 0.153775i | \(0.950857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 367.348 | 0.214819 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 180.998 | 0.103663 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −713.205 | − | 713.205i | −0.392135 | − | 0.392135i | 0.483313 | − | 0.875448i | \(-0.339433\pi\) |
−0.875448 | + | 0.483313i | \(0.839433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3184.13 | −1.71603 | −0.858017 | − | 0.513622i | \(-0.828304\pi\) | ||||
−0.858017 | + | 0.513622i | \(0.828304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −563.686 | + | 563.686i | −0.292105 | + | 0.292105i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1517.94 | + | 1517.94i | 0.771622 | + | 0.771622i | 0.978390 | − | 0.206768i | \(-0.0662945\pi\) |
−0.206768 | + | 0.978390i | \(0.566294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 215.148i | − | 0.105317i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1433.43 | + | 1433.43i | −0.688802 | + | 0.688802i | −0.961967 | − | 0.273165i | \(-0.911930\pi\) |
0.273165 | + | 0.961967i | \(0.411930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1574.93i | 0.729771i | 0.931052 | + | 0.364886i | \(0.118892\pi\) | ||||
−0.931052 | + | 0.364886i | \(0.881108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3666.05i | 1.66866i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2323.05 | − | 2323.05i | 1.02092 | − | 1.02092i | 0.0211385 | − | 0.999777i | \(-0.493271\pi\) |
0.999777 | − | 0.0211385i | \(-0.00672911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1365.56i | 0.589867i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2499.16 | + | 2499.16i | 1.04355 | + | 1.04355i | 0.999007 | + | 0.0445458i | \(0.0141841\pi\) |
0.0445458 | + | 0.999007i | \(0.485816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1207.94 | + | 1207.94i | −0.496053 | + | 0.496053i | −0.910207 | − | 0.414154i | \(-0.864078\pi\) |
0.414154 | + | 0.910207i | \(0.364078\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 753.243 | 0.299349 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −240.087 | − | 240.087i | −0.0938871 | − | 0.0938871i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1303.81 | 0.493930 | 0.246965 | − | 0.969024i | \(-0.420567\pi\) | ||||
0.246965 | + | 0.969024i | \(0.420567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3208.56 | 1.19667 | 0.598335 | − | 0.801246i | \(-0.295829\pi\) | ||||
0.598335 | + | 0.801246i | \(0.295829\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1476.04 | + | 1476.04i | 0.533824 | + | 0.533824i | 0.921708 | − | 0.387884i | \(-0.126794\pi\) |
−0.387884 | + | 0.921708i | \(0.626794\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1698.58 | −0.605072 | −0.302536 | − | 0.953138i | \(-0.597833\pi\) | ||||
−0.302536 | + | 0.953138i | \(0.597833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 367.857 | − | 367.857i | 0.127185 | − | 0.127185i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 63.2755 | + | 63.2755i | 0.0215578 | + | 0.0215578i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 220.907i | 0.0731121i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3141.93 | + | 3141.93i | −1.02511 | + | 1.02511i | −0.0254381 | + | 0.999676i | \(0.508098\pi\) |
−0.999676 | + | 0.0254381i | \(0.991902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 607.614i | 0.192739i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2291.25i | 0.716774i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3831.90 | − | 3831.90i | 1.16634 | − | 1.16634i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 869.633i | − | 0.261143i | −0.991439 | − | 0.130572i | \(-0.958319\pi\) | ||
0.991439 | − | 0.130572i | \(-0.0416812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1203.65 | + | 1203.65i | 0.351935 | + | 0.351935i | 0.860829 | − | 0.508894i | \(-0.169945\pi\) |
−0.508894 | + | 0.860829i | \(0.669945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3001.80 | + | 3001.80i | −0.866220 | + | 0.866220i | −0.992052 | − | 0.125832i | \(-0.959840\pi\) |
0.125832 | + | 0.992052i | \(0.459840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5006.57 | −1.40769 | −0.703844 | − | 0.710355i | \(-0.748534\pi\) | ||||
−0.703844 | + | 0.710355i | \(0.748534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1201.11 | + | 1201.11i | 0.333412 | + | 0.333412i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 659.973 | 0.178620 | 0.0893098 | − | 0.996004i | \(-0.471534\pi\) | ||||
0.0893098 | + | 0.996004i | \(0.471534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1088.72 | −0.290998 | −0.145499 | − | 0.989358i | \(-0.546479\pi\) | ||||
−0.145499 | + | 0.989358i | \(0.546479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 552.231 | + | 552.231i | 0.144003 | + | 0.144003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3525.77 | −0.908258 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3317.58 | + | 3317.58i | −0.834277 | + | 0.834277i | −0.988099 | − | 0.153821i | \(-0.950842\pi\) |
0.153821 | + | 0.988099i | \(0.450842\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 55.7013 | + | 55.7013i | 0.0138415 | + | 0.0138415i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7233.11i | 1.75560i | 0.479028 | + | 0.877800i | \(0.340989\pi\) | ||||
−0.479028 | + | 0.877800i | \(0.659011\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1530.88 | − | 1530.88i | 0.367274 | − | 0.367274i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7081.78i | − | 1.66039i | −0.557476 | − | 0.830193i | \(-0.688230\pi\) | ||
0.557476 | − | 0.830193i | \(-0.311770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1050.88i | − | 0.243603i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1277.73 | − | 1277.73i | 0.289607 | − | 0.289607i | −0.547318 | − | 0.836925i | \(-0.684351\pi\) |
0.836925 | + | 0.547318i | \(0.184351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5785.88i | − | 1.29693i | −0.761246 | − | 0.648463i | \(-0.775412\pi\) | ||
0.761246 | − | 0.648463i | \(-0.224588\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −353.541 | − | 353.541i | −0.0775249 | − | 0.0775249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2243.55 | + | 2243.55i | −0.486648 | + | 0.486648i | −0.907247 | − | 0.420598i | \(-0.861820\pi\) |
0.420598 | + | 0.907247i | \(0.361820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 645.762 | 0.137092 | 0.0685461 | − | 0.997648i | \(-0.478164\pi\) | ||||
0.0685461 | + | 0.997648i | \(0.478164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4732.85 | + | 4732.85i | 0.994130 | + | 0.994130i | 0.999983 | − | 0.00585324i | \(-0.00186315\pi\) |
−0.00585324 | + | 0.999983i | \(0.501863\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 257.200 | 0.0528990 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95.8192 | −0.0195032 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 648.055 | + | 648.055i | 0.129214 | + | 0.129214i | 0.768756 | − | 0.639542i | \(-0.220876\pi\) |
−0.639542 | + | 0.768756i | \(0.720876\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3934.99 | −0.776623 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −889.020 | + | 889.020i | −0.171951 | + | 0.171951i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1234.90 | + | 1234.90i | 0.236474 | + | 0.236474i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3426.57i | − | 0.643295i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3406.50 | + | 3406.50i | −0.633288 | + | 0.633288i | −0.948891 | − | 0.315604i | \(-0.897793\pi\) |
0.315604 | + | 0.948891i | \(0.397793\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7811.27i | 1.42423i | 0.702061 | + | 0.712117i | \(0.252263\pi\) | ||||
−0.702061 | + | 0.712117i | \(0.747737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3161.73i | − | 0.570963i | −0.958384 | − | 0.285481i | \(-0.907847\pi\) | ||
0.958384 | − | 0.285481i | \(-0.0921535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −318.480 | + | 318.480i | −0.0564278 | + | 0.0564278i | −0.734758 | − | 0.678330i | \(-0.762704\pi\) |
0.678330 | + | 0.734758i | \(0.262704\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 190.475i | 0.0334312i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2304.33 | + | 2304.33i | 0.396955 | + | 0.396955i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5642.69 | − | 5642.69i | 0.963077 | − | 0.963077i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4882.23 | 0.818134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2065.35 | − | 2065.35i | −0.342966 | − | 0.342966i | 0.514515 | − | 0.857481i | \(-0.327972\pi\) |
−0.857481 | + | 0.514515i | \(0.827972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3623.89 | 0.591027 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6794.49 | 1.09828 | 0.549138 | − | 0.835731i | \(-0.314956\pi\) | ||||
0.549138 | + | 0.835731i | \(0.314956\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −593.199 | − | 593.199i | −0.0942040 | − | 0.0942040i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6739.03 | 1.06086 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3999.59 | + | 3999.59i | −0.618759 | + | 0.618759i | −0.945213 | − | 0.326454i | \(-0.894146\pi\) |
0.326454 | + | 0.945213i | \(0.394146\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1482.98 | − | 1482.98i | −0.227456 | − | 0.227456i | 0.584173 | − | 0.811629i | \(-0.301419\pi\) |
−0.811629 | + | 0.584173i | \(0.801419\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6753.68i | − | 1.01831i | −0.860676 | − | 0.509153i | \(-0.829959\pi\) | ||
0.860676 | − | 0.509153i | \(-0.170041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3761.14 | − | 3761.14i | 0.562311 | − | 0.562311i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8234.72i | − | 1.21062i | −0.795991 | − | 0.605309i | \(-0.793050\pi\) | ||
0.795991 | − | 0.605309i | \(-0.206950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4738.76i | 0.690882i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 994.677 | − | 994.677i | 0.142640 | − | 0.142640i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5584.58i | 0.794312i | 0.917751 | + | 0.397156i | \(0.130003\pi\) | ||||
−0.917751 | + | 0.397156i | \(0.869997\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2135.78 | − | 2135.78i | −0.298879 | − | 0.298879i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3202.91 | − | 3202.91i | 0.444613 | − | 0.444613i | −0.448946 | − | 0.893559i | \(-0.648200\pi\) |
0.893559 | + | 0.448946i | \(0.148200\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3040.08 | −0.415310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6142 | + | 21.6142i | 0.00292941 | + | 0.00292941i | 0.708570 | − | 0.705641i | \(-0.249341\pi\) |
−0.705641 | + | 0.708570i | \(0.749341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4947.98 | −0.660131 | −0.330065 | − | 0.943958i | \(-0.607071\pi\) | ||||
−0.330065 | + | 0.943958i | \(0.607071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 286.576 | 0.0379357 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4708.60 | − | 4708.60i | −0.613716 | − | 0.613716i | 0.330196 | − | 0.943912i | \(-0.392885\pi\) |
−0.943912 | + | 0.330196i | \(0.892885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1162.07 | 0.150303 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3774.26 | − | 3774.26i | 0.480769 | − | 0.480769i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7418.04 | − | 7418.04i | −0.937786 | − | 0.937786i | 0.0603890 | − | 0.998175i | \(-0.480766\pi\) |
−0.998175 | + | 0.0603890i | \(0.980766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13363.8i | 1.66423i | 0.554600 | + | 0.832117i | \(0.312871\pi\) | ||||
−0.554600 | + | 0.832117i | \(0.687129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9467.75 | − | 9467.75i | 1.17028 | − | 1.17028i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 792.682i | 0.0965400i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1784.64i | − | 0.215758i | −0.994164 | − | 0.107879i | \(-0.965594\pi\) | ||
0.994164 | − | 0.107879i | \(-0.0344059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7997.39 | + | 7997.39i | −0.952847 | + | 0.952847i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3026.07i | − | 0.357937i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10663.3 | − | 10663.3i | −1.24328 | − | 1.24328i | −0.958632 | − | 0.284650i | \(-0.908123\pi\) |
−0.284650 | − | 0.958632i | \(-0.591877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1980.40 | + | 1980.40i | −0.229261 | + | 0.229261i | −0.812384 | − | 0.583123i | \(-0.801831\pi\) |
0.583123 | + | 0.812384i | \(0.301831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7375.77 | −0.841829 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6964.10 | − | 6964.10i | −0.789266 | − | 0.789266i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3750.79 | −0.419186 | −0.209593 | − | 0.977789i | \(-0.567214\pi\) | ||||
−0.209593 | + | 0.977789i | \(0.567214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14507.9 | −1.61017 | −0.805086 | − | 0.593159i | \(-0.797881\pi\) | ||||
−0.805086 | + | 0.593159i | \(0.797881\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −534.617 | − | 534.617i | −0.0585222 | − | 0.0585222i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13109.7 | 1.42526 | 0.712632 | − | 0.701538i | \(-0.247503\pi\) | ||||
0.712632 | + | 0.701538i | \(0.247503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9118.69 | − | 9118.69i | 0.977973 | − | 0.977973i | −0.0217894 | − | 0.999763i | \(-0.506936\pi\) |
0.999763 | + | 0.0217894i | \(0.00693635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4947.06 | − | 4947.06i | −0.526995 | − | 0.526995i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3154.04i | − | 0.331511i | −0.986167 | − | 0.165756i | \(-0.946994\pi\) | ||
0.986167 | − | 0.165756i | \(-0.0530063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −66.5885 | + | 66.5885i | −0.00695240 | + | 0.00695240i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4573.89i | 0.471268i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14705.8i | − | 1.50527i | −0.658440 | − | 0.752633i | \(-0.728783\pi\) | ||
0.658440 | − | 0.752633i | \(-0.271217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9633.21 | + | 9633.21i | −0.973240 | + | 0.973240i | −0.999651 | − | 0.0264114i | \(-0.991592\pi\) |
0.0264114 | + | 0.999651i | \(0.491592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13731.1i | 1.37827i | 0.724632 | + | 0.689136i | \(0.242010\pi\) | ||||
−0.724632 | + | 0.689136i | \(0.757990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1307.20 | − | 1307.20i | −0.129529 | − | 0.129529i | 0.639370 | − | 0.768899i | \(-0.279195\pi\) |
−0.768899 | + | 0.639370i | \(0.779195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7365.11 | − | 7365.11i | 0.725137 | − | 0.725137i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −639.428 | −0.0621584 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3393.26 | + | 3393.26i | 0.327776 | + | 0.327776i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5950.85 | 0.567644 | 0.283822 | − | 0.958877i | \(-0.408398\pi\) | ||||
0.283822 | + | 0.958877i | \(0.408398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12651.6 | −1.19930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 450.237 | + | 450.237i | 0.0421530 | + | 0.0421530i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13651.9 | 1.27028 | 0.635141 | − | 0.772396i | \(-0.280942\pi\) | ||||
0.635141 | + | 0.772396i | \(0.280942\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9699.69 | − | 9699.69i | 0.891530 | − | 0.891530i | −0.103137 | − | 0.994667i | \(-0.532888\pi\) |
0.994667 | + | 0.103137i | \(0.0328882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1986.90 | + | 1986.90i | 0.181512 | + | 0.181512i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15288.1i | − | 1.37981i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9376.88 | − | 9376.88i | 0.841216 | − | 0.841216i | −0.147801 | − | 0.989017i | \(-0.547220\pi\) |
0.989017 | + | 0.147801i | \(0.0472195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9495.92i | − | 0.841753i | −0.907118 | − | 0.420877i | \(-0.861723\pi\) | ||
0.907118 | − | 0.420877i | \(-0.138277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3389.91i | − | 0.298711i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5671.64 | + | 5671.64i | −0.493892 | + | 0.493892i | −0.909530 | − | 0.415638i | \(-0.863558\pi\) |
0.415638 | + | 0.909530i | \(0.363558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4043.12i | − | 0.350014i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 712.750 | + | 712.750i | 0.0609855 | + | 0.0609855i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1264.00 | + | 1264.00i | −0.107525 | + | 0.107525i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11983.5 | 1.00769 | 0.503846 | − | 0.863794i | \(-0.331918\pi\) | ||||
0.503846 | + | 0.863794i | \(0.331918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1886.67 | + | 1886.67i | 0.157741 | + | 0.157741i | 0.781565 | − | 0.623824i | \(-0.214422\pi\) |
−0.623824 | + | 0.781565i | \(0.714422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12375.6 | −1.02294 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11897.4 | 0.977841 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1062.78 | − | 1062.78i | −0.0863683 | − | 0.0863683i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5314.99 | 0.429508 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −581.145 | + | 581.145i | −0.0464410 | + | 0.0464410i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2569.34 | + | 2569.34i | 0.204186 | + | 0.204186i | 0.801791 | − | 0.597605i | \(-0.203881\pi\) |
−0.597605 | + | 0.801791i | \(0.703881\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4352.33i | − | 0.342079i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10127.9 | + | 10127.9i | −0.791662 | + | 0.791662i | −0.981764 | − | 0.190102i | \(-0.939118\pi\) |
0.190102 | + | 0.981764i | \(0.439118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1828.17i | − | 0.141348i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15341.5i | − | 1.17972i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11050.4 | + | 11050.4i | −0.840612 | + | 0.840612i | −0.988938 | − | 0.148327i | \(-0.952611\pi\) |
0.148327 | + | 0.988938i | \(0.452611\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10205.6i | − | 0.772183i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3100.96 | + | 3100.96i | 0.232131 | + | 0.232131i | 0.813582 | − | 0.581450i | \(-0.197515\pi\) |
−0.581450 | + | 0.813582i | \(0.697515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3392.57 | + | 3392.57i | −0.252613 | + | 0.252613i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12626.6 | −0.930288 | −0.465144 | − | 0.885235i | \(-0.653997\pi\) | ||||
−0.465144 | + | 0.885235i | \(0.653997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5777.87 | + | 5777.87i | 0.423461 | + | 0.423461i | 0.886394 | − | 0.462932i | \(-0.153203\pi\) |
−0.462932 | + | 0.886394i | \(0.653203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1711.21 | 0.124109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9644.17 | −0.695827 | −0.347913 | − | 0.937527i | \(-0.613110\pi\) | ||||
−0.347913 | + | 0.937527i | \(0.613110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6150.13 | − | 6150.13i | −0.439157 | − | 0.439157i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1105.90 | 0.0785619 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6832.33 | − | 6832.33i | 0.480410 | − | 0.480410i | −0.424853 | − | 0.905262i | \(-0.639674\pi\) |
0.905262 | + | 0.424853i | \(0.139674\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5693.48 | + | 5693.48i | 0.398295 | + | 0.398295i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3807.51i | 0.263669i | 0.991272 | + | 0.131835i | \(0.0420868\pi\) | ||||
−0.991272 | + | 0.131835i | \(0.957913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2989.35 | − | 2989.35i | 0.205969 | − | 0.205969i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1731.22i | − | 0.118090i | −0.998255 | − | 0.0590449i | \(-0.981194\pi\) | ||
0.998255 | − | 0.0590449i | \(-0.0188055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21704.9i | − | 1.47315i | −0.676356 | − | 0.736575i | \(-0.736442\pi\) | ||
0.676356 | − | 0.736575i | \(-0.263558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4216.38 | − | 4216.38i | 0.283339 | − | 0.283339i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19231.2i | − | 1.28595i | −0.765888 | − | 0.642974i | \(-0.777700\pi\) | ||
0.765888 | − | 0.642974i | \(-0.222300\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20174.1 | − | 20174.1i | −1.33577 | − | 1.33577i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9854.85 | − | 9854.85i | 0.649321 | − | 0.649321i | −0.303508 | − | 0.952829i | \(-0.598158\pi\) |
0.952829 | + | 0.303508i | \(0.0981579\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17948.8 | −1.17114 | −0.585569 | − | 0.810622i | \(-0.699129\pi\) | ||||
−0.585569 | + | 0.810622i | \(0.699129\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6084.79 | + | 6084.79i | 0.395102 | + | 0.395102i | 0.876501 | − | 0.481399i | \(-0.159871\pi\) |
−0.481399 | + | 0.876501i | \(0.659871\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20108.6 | −1.29315 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8263.38 | −0.528856 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8268.68 | + | 8268.68i | 0.524155 | + | 0.524155i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10974.2 | 0.692352 | 0.346176 | − | 0.938170i | \(-0.387480\pi\) | ||||
0.346176 | + | 0.938170i | \(0.387480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 332.298 | − | 332.298i | 0.0207667 | − | 0.0207667i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9275.36 | − | 9275.36i | −0.576928 | − | 0.576928i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2520.18i | 0.155290i | 0.996981 | + | 0.0776451i | \(0.0247401\pi\) | ||||
−0.996981 | + | 0.0776451i | \(0.975260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9626.14 | − | 9626.14i | 0.590386 | − | 0.590386i | −0.347350 | − | 0.937736i | \(-0.612918\pi\) |
0.937736 | + | 0.347350i | \(0.112918\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1795.90i | − | 0.109126i | −0.998510 | − | 0.0545628i | \(-0.982623\pi\) | ||
0.998510 | − | 0.0545628i | \(-0.0173765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4141.02i | − | 0.250461i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2175.09 | + | 2175.09i | −0.130349 | + | 0.130349i | −0.769271 | − | 0.638922i | \(-0.779380\pi\) |
0.638922 | + | 0.769271i | \(0.279380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3454.75i | 0.206089i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16223.9 | + | 16223.9i | 0.959017 | + | 0.959017i | 0.999193 | − | 0.0401752i | \(-0.0127916\pi\) |
−0.0401752 | + | 0.999193i | \(0.512792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2953.68 | − | 2953.68i | 0.173805 | − | 0.173805i | −0.614844 | − | 0.788649i | \(-0.710781\pi\) |
0.788649 | + | 0.614844i | \(0.210781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2750.53 | −0.160393 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −460.970 | − | 460.970i | −0.0267598 | − | 0.0267598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3605.99 | 0.207463 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13136.0 | 0.752385 | 0.376193 | − | 0.926542i | \(-0.377233\pi\) | ||||
0.376193 | + | 0.926542i | \(0.377233\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2954.97 | − | 2954.97i | −0.167753 | − | 0.167753i | 0.618238 | − | 0.785991i | \(-0.287847\pi\) |
−0.785991 | + | 0.618238i | \(0.787847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1830.10 | 0.103436 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6641.03 | + | 6641.03i | −0.372053 | + | 0.372053i | −0.868224 | − | 0.496172i | \(-0.834739\pi\) |
0.496172 | + | 0.868224i | \(0.334739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6747.01 | − | 6747.01i | −0.376336 | − | 0.376336i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17650.7i | 0.975960i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17821.2 | − | 17821.2i | 0.981115 | − | 0.981115i | −0.0187097 | − | 0.999825i | \(-0.505956\pi\) |
0.999825 | + | 0.0187097i | \(0.00595583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8815.11i | 0.481117i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1389.20i | 0.0754948i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19022.9 | − | 19022.9i | 1.02494 | − | 1.02494i | 0.0252614 | − | 0.999681i | \(-0.491958\pi\) |
0.999681 | − | 0.0252614i | \(-0.00804182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7608.10i | − | 0.408172i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6889.58 | − | 6889.58i | −0.366491 | − | 0.366491i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15338.6 | + | 15338.6i | −0.812485 | + | 0.812485i | −0.985006 | − | 0.172521i | \(-0.944809\pi\) |
0.172521 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2871.21 | 0.150810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1184.17 | − | 1184.17i | −0.0619377 | − | 0.0619377i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24937.9 | −1.29350 | −0.646751 | − | 0.762701i | \(-0.723873\pi\) | ||||
−0.646751 | + | 0.762701i | \(0.723873\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2897.16 | 0.149647 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2925.82 | + | 2925.82i | 0.149879 | + | 0.149879i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4479.75 | 0.228535 | 0.114267 | − | 0.993450i | \(-0.463548\pi\) | ||||
0.114267 | + | 0.993450i | \(0.463548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6670.05 | + | 6670.05i | −0.337484 | + | 0.337484i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7481.44 | − | 7481.44i | −0.376989 | − | 0.376989i | 0.493025 | − | 0.870015i | \(-0.335891\pi\) |
−0.870015 | + | 0.493025i | \(0.835891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3813.63i | 0.190606i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24827.3 | + | 24827.3i | −1.23584 | + | 1.23584i | −0.274160 | + | 0.961684i | \(0.588400\pi\) |
−0.961684 | + | 0.274160i | \(0.911600\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16682.5i | − | 0.823716i | −0.911248 | − | 0.411858i | \(-0.864880\pi\) | ||
0.911248 | − | 0.411858i | \(-0.135120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4598.13i | 0.226124i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10802.1 | − | 10802.1i | 0.526968 | − | 0.526968i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21972.3i | 1.06762i | 0.845605 | + | 0.533809i | \(0.179240\pi\) | ||||
−0.845605 | + | 0.533809i | \(0.820760\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10264.3 | + | 10264.3i | 0.494775 | + | 0.494775i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13715.8 | − | 13715.8i | 0.658530 | − | 0.658530i | −0.296502 | − | 0.955032i | \(-0.595820\pi\) |
0.955032 | + | 0.296502i | \(0.0958201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3346.07 | −0.159389 | −0.0796944 | − | 0.996819i | \(-0.525394\pi\) | ||||
−0.0796944 | + | 0.996819i | \(0.525394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8845.59 | − | 8845.59i | −0.419701 | − | 0.419701i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 66092.6 | 3.11143 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18053.3 | 0.846578 | 0.423289 | − | 0.905995i | \(-0.360876\pi\) | ||||
0.423289 | + | 0.905995i | \(0.360876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8674.66 | + | 8674.66i | 0.403630 | + | 0.403630i | 0.879510 | − | 0.475880i | \(-0.157870\pi\) |
−0.475880 | + | 0.879510i | \(0.657870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18223.8 | −0.844670 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 639.111 | − | 639.111i | 0.0293948 | − | 0.0293948i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3958.07 | + | 3958.07i | 0.181345 | + | 0.181345i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9786.36i | − | 0.444956i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6512.95 | + | 6512.95i | −0.294996 | + | 0.294996i | −0.839050 | − | 0.544054i | \(-0.816889\pi\) |
0.544054 | + | 0.839050i | \(0.316889\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13790.0i | 0.619867i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57553.3i | 2.57727i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10831.9 | + | 10831.9i | −0.481413 | + | 0.481413i | −0.905583 | − | 0.424169i | \(-0.860566\pi\) |
0.424169 | + | 0.905583i | \(0.360566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26370.2i | 1.16760i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1046.76 | + | 1046.76i | 0.0460015 | + | 0.0460015i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −693.543 | + | 693.543i | −0.0303654 | + | 0.0303654i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18515.3 | 0.804651 | 0.402326 | − | 0.915497i | \(-0.368202\pi\) | ||||
0.402326 | + | 0.915497i | \(0.368202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15062.3 | + | 15062.3i | 0.652167 | + | 0.652167i | 0.953514 | − | 0.301347i | \(-0.0974364\pi\) |
−0.301347 | + | 0.953514i | \(0.597436\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9241.51 | 0.397197 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6137.18 | 0.262806 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24601.7 | − | 24601.7i | −1.04580 | − | 1.04580i | −0.998899 | − | 0.0469030i | \(-0.985065\pi\) |
−0.0469030 | − | 0.998899i | \(-0.514935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24417.7 | −1.03420 | −0.517101 | − | 0.855924i | \(-0.672989\pi\) | ||||
−0.517101 | + | 0.855924i | \(0.672989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26807.5 | + | 26807.5i | −1.12719 | + | 1.12719i | −0.136560 | + | 0.990632i | \(0.543604\pi\) |
−0.990632 | + | 0.136560i | \(0.956396\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3214.77 | + | 3214.77i | 0.134685 | + | 0.134685i | 0.771235 | − | 0.636550i | \(-0.219639\pi\) |
−0.636550 | + | 0.771235i | \(0.719639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12124.2i | 0.504294i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5076.90 | − | 5076.90i | 0.210411 | − | 0.210411i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 40899.9i | − | 1.68298i | −0.540271 | − | 0.841491i | \(-0.681678\pi\) | ||
0.540271 | − | 0.841491i | \(-0.318322\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22812.7i | 0.935367i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11817.8 | − | 11817.8i | 0.481116 | − | 0.481116i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 17138.6i | − | 0.695263i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1918.37 | − | 1918.37i | −0.0772749 | − | 0.0772749i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21139.7 | + | 21139.7i | −0.848545 | + | 0.848545i | −0.989952 | − | 0.141407i | \(-0.954837\pi\) |
0.141407 | + | 0.989952i | \(0.454837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2133.86 | 0.0850540 | 0.0425270 | − | 0.999095i | \(-0.486459\pi\) | ||||
0.0425270 | + | 0.999095i | \(0.486459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14755.9 | + | 14755.9i | 0.586107 | + | 0.586107i | 0.936575 | − | 0.350468i | \(-0.113977\pi\) |
−0.350468 | + | 0.936575i | \(0.613977\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13261.8 | 0.523101 | 0.261550 | − | 0.965190i | \(-0.415766\pi\) | ||||
0.261550 | + | 0.965190i | \(0.415766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14977.0 | −0.588710 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3971.88 | + | 3971.88i | 0.155048 | + | 0.155048i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60867.3 | −2.36787 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9681.80 | − | 9681.80i | 0.374062 | − | 0.374062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17125.7 | − | 17125.7i | −0.659399 | − | 0.659399i | 0.295839 | − | 0.955238i | \(-0.404401\pi\) |
−0.955238 | + | 0.295839i | \(0.904401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34029.0i | 1.30132i | 0.759368 | + | 0.650662i | \(0.225508\pi\) | ||||
−0.759368 | + | 0.650662i | \(0.774492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7536.29 | + | 7536.29i | −0.287221 | + | 0.287221i | −0.835981 | − | 0.548759i | \(-0.815100\pi\) |
0.548759 | + | 0.835981i | \(0.315100\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11775.4i | 0.445749i | 0.974847 | + | 0.222875i | \(0.0715441\pi\) | ||||
−0.974847 | + | 0.222875i | \(0.928456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1350.71i | − | 0.0509578i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12131.8 | − | 12131.8i | 0.454619 | − | 0.454619i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 16112.4i | − | 0.601764i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4909.17 | + | 4909.17i | 0.182124 | + | 0.182124i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11535.9 | − | 11535.9i | 0.426545 | − | 0.426545i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7787.77 | 0.286049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24197.1 | − | 24197.1i | −0.885833 | − | 0.885833i | 0.108287 | − | 0.994120i | \(-0.465463\pi\) |
−0.994120 | + | 0.108287i | \(0.965463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15777.4 | 0.573798 | 0.286899 | − | 0.957961i | \(-0.407376\pi\) | ||||
0.286899 | + | 0.957961i | \(0.407376\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3184.51 | 0.115435 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7021.37 | + | 7021.37i | 0.252853 | + | 0.252853i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24261.8 | 0.870863 | 0.435432 | − | 0.900222i | \(-0.356596\pi\) | ||||
0.435432 | + | 0.900222i | \(0.356596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −63172.6 | + | 63172.6i | −2.25282 | + | 2.25282i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12176.1 | + | 12176.1i | 0.432808 | + | 0.432808i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19578.0i | − | 0.691423i | −0.938341 | − | 0.345712i | \(-0.887638\pi\) | ||
0.938341 | − | 0.345712i | \(-0.112362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5577.79 | − | 5577.79i | 0.196353 | − | 0.196353i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1547.87i | 0.0541400i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23706.5i | 0.826530i | 0.910611 | + | 0.413265i | \(0.135612\pi\) | ||||
−0.910611 | + | 0.413265i | \(0.864388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 516.925 | − | 516.925i | 0.0179078 | − | 0.0179078i | −0.698096 | − | 0.716004i | \(-0.745969\pi\) |
0.716004 | + | 0.698096i | \(0.245969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 322.302i | − | 0.0111300i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9551.64 | + | 9551.64i | 0.327758 | + | 0.327758i | 0.851733 | − | 0.523976i | \(-0.175552\pi\) |
−0.523976 | + | 0.851733i | \(0.675552\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16706.7 | + | 16706.7i | −0.571469 | + | 0.571469i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12241.2 | 0.416089 | 0.208044 | − | 0.978119i | \(-0.433290\pi\) | ||||
0.208044 | + | 0.978119i | \(0.433290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4202.94 | − | 4202.94i | −0.142412 | − | 0.142412i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27425.0 | −0.923461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −786.360 | −0.0263959 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10343.0 | − | 10343.0i | −0.345030 | − | 0.345030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12983.6 | −0.431773 | −0.215886 | − | 0.976418i | \(-0.569264\pi\) | ||||
−0.215886 | + | 0.976418i | \(0.569264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35022.4 | − | 35022.4i | 1.15749 | − | 1.15749i | 0.172477 | − | 0.985014i | \(-0.444823\pi\) |
0.985014 | − | 0.172477i | \(-0.0551771\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17915.7 | + | 17915.7i | 0.590287 | + | 0.590287i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 43174.5i | − | 1.41379i | −0.707317 | − | 0.706897i | \(-0.750095\pi\) | ||
0.707317 | − | 0.706897i | \(-0.249905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5206.08 | − | 5206.08i | 0.169956 | − | 0.169956i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43699.4i | 1.41790i | 0.705260 | + | 0.708949i | \(0.250830\pi\) | ||||
−0.705260 | + | 0.708949i | \(0.749170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9516.21i | − | 0.307829i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1547.48 | − | 1547.48i | 0.0497544 | − | 0.0497544i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 8324.37i | − | 0.266834i | −0.991060 | − | 0.133417i | \(-0.957405\pi\) | ||
0.991060 | − | 0.133417i | \(-0.0425949\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5475.50 | + | 5475.50i | 0.174457 | + | 0.174457i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 563.783 | − | 563.783i | 0.0179089 | − | 0.0179089i | −0.698096 | − | 0.716005i | \(-0.745969\pi\) |
0.716005 | + | 0.698096i | \(0.245969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1152.4.l.b.863.11 | 48 | ||
3.2 | odd | 2 | inner | 1152.4.l.b.863.14 | 48 | ||
4.3 | odd | 2 | 1152.4.l.a.863.11 | 48 | |||
8.3 | odd | 2 | 576.4.l.a.431.14 | 48 | |||
8.5 | even | 2 | 144.4.l.a.35.8 | ✓ | 48 | ||
12.11 | even | 2 | 1152.4.l.a.863.14 | 48 | |||
16.3 | odd | 4 | 144.4.l.a.107.17 | yes | 48 | ||
16.5 | even | 4 | 1152.4.l.a.287.14 | 48 | |||
16.11 | odd | 4 | inner | 1152.4.l.b.287.14 | 48 | ||
16.13 | even | 4 | 576.4.l.a.143.11 | 48 | |||
24.5 | odd | 2 | 144.4.l.a.35.17 | yes | 48 | ||
24.11 | even | 2 | 576.4.l.a.431.11 | 48 | |||
48.5 | odd | 4 | 1152.4.l.a.287.11 | 48 | |||
48.11 | even | 4 | inner | 1152.4.l.b.287.11 | 48 | ||
48.29 | odd | 4 | 576.4.l.a.143.14 | 48 | |||
48.35 | even | 4 | 144.4.l.a.107.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.4.l.a.35.8 | ✓ | 48 | 8.5 | even | 2 | ||
144.4.l.a.35.17 | yes | 48 | 24.5 | odd | 2 | ||
144.4.l.a.107.8 | yes | 48 | 48.35 | even | 4 | ||
144.4.l.a.107.17 | yes | 48 | 16.3 | odd | 4 | ||
576.4.l.a.143.11 | 48 | 16.13 | even | 4 | |||
576.4.l.a.143.14 | 48 | 48.29 | odd | 4 | |||
576.4.l.a.431.11 | 48 | 24.11 | even | 2 | |||
576.4.l.a.431.14 | 48 | 8.3 | odd | 2 | |||
1152.4.l.a.287.11 | 48 | 48.5 | odd | 4 | |||
1152.4.l.a.287.14 | 48 | 16.5 | even | 4 | |||
1152.4.l.a.863.11 | 48 | 4.3 | odd | 2 | |||
1152.4.l.a.863.14 | 48 | 12.11 | even | 2 | |||
1152.4.l.b.287.11 | 48 | 48.11 | even | 4 | inner | ||
1152.4.l.b.287.14 | 48 | 16.11 | odd | 4 | inner | ||
1152.4.l.b.863.11 | 48 | 1.1 | even | 1 | trivial | ||
1152.4.l.b.863.14 | 48 | 3.2 | odd | 2 | inner |