Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(889,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 889.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.889 |
Dual form | 1110.2.d.g.889.2 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.707107 | − | 2.12132i | 0.316228 | − | 0.948683i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.41421i | 0.912487i | 0.889855 | + | 0.456243i | \(0.150805\pi\) | ||||
−0.889855 | + | 0.456243i | \(0.849195\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.12132 | + | 0.707107i | 0.670820 | + | 0.223607i | ||||
\(11\) | −6.41421 | −1.93396 | −0.966979 | − | 0.254856i | \(-0.917972\pi\) | ||||
−0.966979 | + | 0.254856i | \(0.917972\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 5.24264i | 1.45405i | 0.686613 | + | 0.727023i | \(0.259097\pi\) | ||||
−0.686613 | + | 0.727023i | \(0.740903\pi\) | |||||||
\(14\) | −2.41421 | −0.645226 | ||||||||
\(15\) | −2.12132 | − | 0.707107i | −0.547723 | − | 0.182574i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.58579i | − | 0.869681i | −0.900508 | − | 0.434840i | \(-0.856805\pi\) | ||
0.900508 | − | 0.434840i | \(-0.143195\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 2.17157 | 0.498193 | 0.249096 | − | 0.968479i | \(-0.419866\pi\) | ||||
0.249096 | + | 0.968479i | \(0.419866\pi\) | |||||||
\(20\) | −0.707107 | + | 2.12132i | −0.158114 | + | 0.474342i | ||||
\(21\) | 2.41421 | 0.526825 | ||||||||
\(22\) | − | 6.41421i | − | 1.36751i | ||||||
\(23\) | 3.00000i | 0.625543i | 0.949828 | + | 0.312772i | \(0.101257\pi\) | ||||
−0.949828 | + | 0.312772i | \(0.898743\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.00000 | − | 3.00000i | −0.800000 | − | 0.600000i | ||||
\(26\) | −5.24264 | −1.02817 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 2.41421i | − | 0.456243i | ||||||
\(29\) | −7.07107 | −1.31306 | −0.656532 | − | 0.754298i | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754298i | \(0.727977\pi\) | |||||||
\(30\) | 0.707107 | − | 2.12132i | 0.129099 | − | 0.387298i | ||||
\(31\) | −3.65685 | −0.656790 | −0.328395 | − | 0.944540i | \(-0.606508\pi\) | ||||
−0.328395 | + | 0.944540i | \(0.606508\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.41421i | 1.11657i | ||||||||
\(34\) | 3.58579 | 0.614957 | ||||||||
\(35\) | 5.12132 | + | 1.70711i | 0.865661 | + | 0.288554i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 2.17157i | 0.352276i | ||||||||
\(39\) | 5.24264 | 0.839494 | ||||||||
\(40\) | −2.12132 | − | 0.707107i | −0.335410 | − | 0.111803i | ||||
\(41\) | −6.58579 | −1.02853 | −0.514264 | − | 0.857632i | \(-0.671935\pi\) | ||||
−0.514264 | + | 0.857632i | \(0.671935\pi\) | |||||||
\(42\) | 2.41421i | 0.372521i | ||||||||
\(43\) | 10.4853i | 1.59899i | 0.600672 | + | 0.799495i | \(0.294900\pi\) | ||||
−0.600672 | + | 0.799495i | \(0.705100\pi\) | |||||||
\(44\) | 6.41421 | 0.966979 | ||||||||
\(45\) | −0.707107 | + | 2.12132i | −0.105409 | + | 0.316228i | ||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 11.8995i | 1.73572i | 0.496809 | + | 0.867860i | \(0.334505\pi\) | ||||
−0.496809 | + | 0.867860i | \(0.665495\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 1.17157 | 0.167368 | ||||||||
\(50\) | 3.00000 | − | 4.00000i | 0.424264 | − | 0.565685i | ||||
\(51\) | −3.58579 | −0.502111 | ||||||||
\(52\) | − | 5.24264i | − | 0.727023i | ||||||
\(53\) | − | 3.82843i | − | 0.525875i | −0.964813 | − | 0.262937i | \(-0.915309\pi\) | ||
0.964813 | − | 0.262937i | \(-0.0846913\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.53553 | + | 13.6066i | −0.611571 | + | 1.83471i | ||||
\(56\) | 2.41421 | 0.322613 | ||||||||
\(57\) | − | 2.17157i | − | 0.287632i | ||||||
\(58\) | − | 7.07107i | − | 0.928477i | ||||||
\(59\) | 13.0711 | 1.70171 | 0.850854 | − | 0.525402i | \(-0.176085\pi\) | ||||
0.850854 | + | 0.525402i | \(0.176085\pi\) | |||||||
\(60\) | 2.12132 | + | 0.707107i | 0.273861 | + | 0.0912871i | ||||
\(61\) | −6.48528 | −0.830355 | −0.415178 | − | 0.909740i | \(-0.636281\pi\) | ||||
−0.415178 | + | 0.909740i | \(0.636281\pi\) | |||||||
\(62\) | − | 3.65685i | − | 0.464421i | ||||||
\(63\) | − | 2.41421i | − | 0.304162i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 11.1213 | + | 3.70711i | 1.37943 | + | 0.459810i | ||||
\(66\) | −6.41421 | −0.789535 | ||||||||
\(67\) | 0.828427i | 0.101208i | 0.998719 | + | 0.0506042i | \(0.0161147\pi\) | ||||
−0.998719 | + | 0.0506042i | \(0.983885\pi\) | |||||||
\(68\) | 3.58579i | 0.434840i | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | −1.70711 | + | 5.12132i | −0.204038 | + | 0.612115i | ||||
\(71\) | −9.41421 | −1.11726 | −0.558631 | − | 0.829416i | \(-0.688673\pi\) | ||||
−0.558631 | + | 0.829416i | \(0.688673\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 2.17157i | 0.254163i | 0.991892 | + | 0.127082i | \(0.0405610\pi\) | ||||
−0.991892 | + | 0.127082i | \(0.959439\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | −3.00000 | + | 4.00000i | −0.346410 | + | 0.461880i | ||||
\(76\) | −2.17157 | −0.249096 | ||||||||
\(77\) | − | 15.4853i | − | 1.76471i | ||||||
\(78\) | 5.24264i | 0.593612i | ||||||||
\(79\) | −12.2426 | −1.37740 | −0.688702 | − | 0.725044i | \(-0.741819\pi\) | ||||
−0.688702 | + | 0.725044i | \(0.741819\pi\) | |||||||
\(80\) | 0.707107 | − | 2.12132i | 0.0790569 | − | 0.237171i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 6.58579i | − | 0.727278i | ||||||
\(83\) | 6.89949i | 0.757318i | 0.925536 | + | 0.378659i | \(0.123615\pi\) | ||||
−0.925536 | + | 0.378659i | \(0.876385\pi\) | |||||||
\(84\) | −2.41421 | −0.263412 | ||||||||
\(85\) | −7.60660 | − | 2.53553i | −0.825052 | − | 0.275017i | ||||
\(86\) | −10.4853 | −1.13066 | ||||||||
\(87\) | 7.07107i | 0.758098i | ||||||||
\(88\) | 6.41421i | 0.683757i | ||||||||
\(89\) | −2.89949 | −0.307346 | −0.153673 | − | 0.988122i | \(-0.549110\pi\) | ||||
−0.153673 | + | 0.988122i | \(0.549110\pi\) | |||||||
\(90\) | −2.12132 | − | 0.707107i | −0.223607 | − | 0.0745356i | ||||
\(91\) | −12.6569 | −1.32680 | ||||||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | 3.65685i | 0.379198i | ||||||||
\(94\) | −11.8995 | −1.22734 | ||||||||
\(95\) | 1.53553 | − | 4.60660i | 0.157542 | − | 0.472627i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.72792i | 0.683117i | 0.939861 | + | 0.341558i | \(0.110955\pi\) | ||||
−0.939861 | + | 0.341558i | \(0.889045\pi\) | |||||||
\(98\) | 1.17157i | 0.118347i | ||||||||
\(99\) | 6.41421 | 0.644653 | ||||||||
\(100\) | 4.00000 | + | 3.00000i | 0.400000 | + | 0.300000i | ||||
\(101\) | −5.31371 | −0.528734 | −0.264367 | − | 0.964422i | \(-0.585163\pi\) | ||||
−0.264367 | + | 0.964422i | \(0.585163\pi\) | |||||||
\(102\) | − | 3.58579i | − | 0.355046i | ||||||
\(103\) | − | 15.0711i | − | 1.48500i | −0.669848 | − | 0.742498i | \(-0.733641\pi\) | ||
0.669848 | − | 0.742498i | \(-0.266359\pi\) | |||||||
\(104\) | 5.24264 | 0.514083 | ||||||||
\(105\) | 1.70711 | − | 5.12132i | 0.166597 | − | 0.499790i | ||||
\(106\) | 3.82843 | 0.371850 | ||||||||
\(107\) | − | 16.0711i | − | 1.55365i | −0.629717 | − | 0.776824i | \(-0.716829\pi\) | ||
0.629717 | − | 0.776824i | \(-0.283171\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −4.75736 | −0.455672 | −0.227836 | − | 0.973699i | \(-0.573165\pi\) | ||||
−0.227836 | + | 0.973699i | \(0.573165\pi\) | |||||||
\(110\) | −13.6066 | − | 4.53553i | −1.29734 | − | 0.432446i | ||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 2.41421i | 0.228122i | ||||||||
\(113\) | − | 2.82843i | − | 0.266076i | −0.991111 | − | 0.133038i | \(-0.957527\pi\) | ||
0.991111 | − | 0.133038i | \(-0.0424732\pi\) | |||||||
\(114\) | 2.17157 | 0.203386 | ||||||||
\(115\) | 6.36396 | + | 2.12132i | 0.593442 | + | 0.197814i | ||||
\(116\) | 7.07107 | 0.656532 | ||||||||
\(117\) | − | 5.24264i | − | 0.484682i | ||||||
\(118\) | 13.0711i | 1.20329i | ||||||||
\(119\) | 8.65685 | 0.793573 | ||||||||
\(120\) | −0.707107 | + | 2.12132i | −0.0645497 | + | 0.193649i | ||||
\(121\) | 30.1421 | 2.74019 | ||||||||
\(122\) | − | 6.48528i | − | 0.587150i | ||||||
\(123\) | 6.58579i | 0.593820i | ||||||||
\(124\) | 3.65685 | 0.328395 | ||||||||
\(125\) | −9.19239 | + | 6.36396i | −0.822192 | + | 0.569210i | ||||
\(126\) | 2.41421 | 0.215075 | ||||||||
\(127\) | − | 9.58579i | − | 0.850601i | −0.905052 | − | 0.425300i | \(-0.860168\pi\) | ||
0.905052 | − | 0.425300i | \(-0.139832\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 10.4853 | 0.923178 | ||||||||
\(130\) | −3.70711 | + | 11.1213i | −0.325135 | + | 0.975404i | ||||
\(131\) | 1.89949 | 0.165960 | 0.0829798 | − | 0.996551i | \(-0.473556\pi\) | ||||
0.0829798 | + | 0.996551i | \(0.473556\pi\) | |||||||
\(132\) | − | 6.41421i | − | 0.558286i | ||||||
\(133\) | 5.24264i | 0.454595i | ||||||||
\(134\) | −0.828427 | −0.0715652 | ||||||||
\(135\) | 2.12132 | + | 0.707107i | 0.182574 | + | 0.0608581i | ||||
\(136\) | −3.58579 | −0.307479 | ||||||||
\(137\) | − | 17.5563i | − | 1.49994i | −0.661472 | − | 0.749970i | \(-0.730068\pi\) | ||
0.661472 | − | 0.749970i | \(-0.269932\pi\) | |||||||
\(138\) | 3.00000i | 0.255377i | ||||||||
\(139\) | 2.48528 | 0.210799 | 0.105399 | − | 0.994430i | \(-0.466388\pi\) | ||||
0.105399 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(140\) | −5.12132 | − | 1.70711i | −0.432831 | − | 0.144277i | ||||
\(141\) | 11.8995 | 1.00212 | ||||||||
\(142\) | − | 9.41421i | − | 0.790023i | ||||||
\(143\) | − | 33.6274i | − | 2.81207i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −5.00000 | + | 15.0000i | −0.415227 | + | 1.24568i | ||||
\(146\) | −2.17157 | −0.179721 | ||||||||
\(147\) | − | 1.17157i | − | 0.0966297i | ||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −3.51472 | −0.287937 | −0.143968 | − | 0.989582i | \(-0.545986\pi\) | ||||
−0.143968 | + | 0.989582i | \(0.545986\pi\) | |||||||
\(150\) | −4.00000 | − | 3.00000i | −0.326599 | − | 0.244949i | ||||
\(151\) | 2.41421 | 0.196466 | 0.0982330 | − | 0.995163i | \(-0.468681\pi\) | ||||
0.0982330 | + | 0.995163i | \(0.468681\pi\) | |||||||
\(152\) | − | 2.17157i | − | 0.176138i | ||||||
\(153\) | 3.58579i | 0.289894i | ||||||||
\(154\) | 15.4853 | 1.24784 | ||||||||
\(155\) | −2.58579 | + | 7.75736i | −0.207695 | + | 0.623086i | ||||
\(156\) | −5.24264 | −0.419747 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | − | 12.2426i | − | 0.973972i | ||||||
\(159\) | −3.82843 | −0.303614 | ||||||||
\(160\) | 2.12132 | + | 0.707107i | 0.167705 | + | 0.0559017i | ||||
\(161\) | −7.24264 | −0.570800 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 15.1421i | 1.18602i | 0.805194 | + | 0.593012i | \(0.202061\pi\) | ||||
−0.805194 | + | 0.593012i | \(0.797939\pi\) | |||||||
\(164\) | 6.58579 | 0.514264 | ||||||||
\(165\) | 13.6066 | + | 4.53553i | 1.05927 | + | 0.353091i | ||||
\(166\) | −6.89949 | −0.535505 | ||||||||
\(167\) | 18.6569i | 1.44371i | 0.692044 | + | 0.721855i | \(0.256710\pi\) | ||||
−0.692044 | + | 0.721855i | \(0.743290\pi\) | |||||||
\(168\) | − | 2.41421i | − | 0.186261i | ||||||
\(169\) | −14.4853 | −1.11425 | ||||||||
\(170\) | 2.53553 | − | 7.60660i | 0.194467 | − | 0.583400i | ||||
\(171\) | −2.17157 | −0.166064 | ||||||||
\(172\) | − | 10.4853i | − | 0.799495i | ||||||
\(173\) | 0.656854i | 0.0499397i | 0.999688 | + | 0.0249699i | \(0.00794898\pi\) | ||||
−0.999688 | + | 0.0249699i | \(0.992051\pi\) | |||||||
\(174\) | −7.07107 | −0.536056 | ||||||||
\(175\) | 7.24264 | − | 9.65685i | 0.547492 | − | 0.729990i | ||||
\(176\) | −6.41421 | −0.483490 | ||||||||
\(177\) | − | 13.0711i | − | 0.982482i | ||||||
\(178\) | − | 2.89949i | − | 0.217326i | ||||||
\(179\) | 18.8284 | 1.40730 | 0.703651 | − | 0.710545i | \(-0.251552\pi\) | ||||
0.703651 | + | 0.710545i | \(0.251552\pi\) | |||||||
\(180\) | 0.707107 | − | 2.12132i | 0.0527046 | − | 0.158114i | ||||
\(181\) | 20.5858 | 1.53013 | 0.765065 | − | 0.643953i | \(-0.222707\pi\) | ||||
0.765065 | + | 0.643953i | \(0.222707\pi\) | |||||||
\(182\) | − | 12.6569i | − | 0.938188i | ||||||
\(183\) | 6.48528i | 0.479406i | ||||||||
\(184\) | 3.00000 | 0.221163 | ||||||||
\(185\) | 2.12132 | + | 0.707107i | 0.155963 | + | 0.0519875i | ||||
\(186\) | −3.65685 | −0.268134 | ||||||||
\(187\) | 23.0000i | 1.68193i | ||||||||
\(188\) | − | 11.8995i | − | 0.867860i | ||||||
\(189\) | −2.41421 | −0.175608 | ||||||||
\(190\) | 4.60660 | + | 1.53553i | 0.334198 | + | 0.111399i | ||||
\(191\) | 8.65685 | 0.626388 | 0.313194 | − | 0.949689i | \(-0.398601\pi\) | ||||
0.313194 | + | 0.949689i | \(0.398601\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 9.31371i | − | 0.670415i | −0.942144 | − | 0.335208i | \(-0.891194\pi\) | ||
0.942144 | − | 0.335208i | \(-0.108806\pi\) | |||||||
\(194\) | −6.72792 | −0.483037 | ||||||||
\(195\) | 3.70711 | − | 11.1213i | 0.265471 | − | 0.796414i | ||||
\(196\) | −1.17157 | −0.0836838 | ||||||||
\(197\) | − | 15.1421i | − | 1.07883i | −0.842039 | − | 0.539416i | \(-0.818645\pi\) | ||
0.842039 | − | 0.539416i | \(-0.181355\pi\) | |||||||
\(198\) | 6.41421i | 0.455838i | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | −3.00000 | + | 4.00000i | −0.212132 | + | 0.282843i | ||||
\(201\) | 0.828427 | 0.0584327 | ||||||||
\(202\) | − | 5.31371i | − | 0.373871i | ||||||
\(203\) | − | 17.0711i | − | 1.19815i | ||||||
\(204\) | 3.58579 | 0.251055 | ||||||||
\(205\) | −4.65685 | + | 13.9706i | −0.325249 | + | 0.975746i | ||||
\(206\) | 15.0711 | 1.05005 | ||||||||
\(207\) | − | 3.00000i | − | 0.208514i | ||||||
\(208\) | 5.24264i | 0.363512i | ||||||||
\(209\) | −13.9289 | −0.963484 | ||||||||
\(210\) | 5.12132 | + | 1.70711i | 0.353405 | + | 0.117802i | ||||
\(211\) | 10.3848 | 0.714917 | 0.357459 | − | 0.933929i | \(-0.383643\pi\) | ||||
0.357459 | + | 0.933929i | \(0.383643\pi\) | |||||||
\(212\) | 3.82843i | 0.262937i | ||||||||
\(213\) | 9.41421i | 0.645051i | ||||||||
\(214\) | 16.0711 | 1.09860 | ||||||||
\(215\) | 22.2426 | + | 7.41421i | 1.51694 | + | 0.505645i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − | 8.82843i | − | 0.599313i | ||||||
\(218\) | − | 4.75736i | − | 0.322209i | ||||||
\(219\) | 2.17157 | 0.146741 | ||||||||
\(220\) | 4.53553 | − | 13.6066i | 0.305786 | − | 0.917357i | ||||
\(221\) | 18.7990 | 1.26456 | ||||||||
\(222\) | 1.00000i | 0.0671156i | ||||||||
\(223\) | 9.65685i | 0.646671i | 0.946284 | + | 0.323335i | \(0.104804\pi\) | ||||
−0.946284 | + | 0.323335i | \(0.895196\pi\) | |||||||
\(224\) | −2.41421 | −0.161306 | ||||||||
\(225\) | 4.00000 | + | 3.00000i | 0.266667 | + | 0.200000i | ||||
\(226\) | 2.82843 | 0.188144 | ||||||||
\(227\) | − | 12.0000i | − | 0.796468i | −0.917284 | − | 0.398234i | \(-0.869623\pi\) | ||
0.917284 | − | 0.398234i | \(-0.130377\pi\) | |||||||
\(228\) | 2.17157i | 0.143816i | ||||||||
\(229\) | −18.7279 | −1.23758 | −0.618788 | − | 0.785558i | \(-0.712376\pi\) | ||||
−0.618788 | + | 0.785558i | \(0.712376\pi\) | |||||||
\(230\) | −2.12132 | + | 6.36396i | −0.139876 | + | 0.419627i | ||||
\(231\) | −15.4853 | −1.01886 | ||||||||
\(232\) | 7.07107i | 0.464238i | ||||||||
\(233\) | − | 2.48528i | − | 0.162816i | −0.996681 | − | 0.0814081i | \(-0.974058\pi\) | ||
0.996681 | − | 0.0814081i | \(-0.0259417\pi\) | |||||||
\(234\) | 5.24264 | 0.342722 | ||||||||
\(235\) | 25.2426 | + | 8.41421i | 1.64665 | + | 0.548883i | ||||
\(236\) | −13.0711 | −0.850854 | ||||||||
\(237\) | 12.2426i | 0.795245i | ||||||||
\(238\) | 8.65685i | 0.561141i | ||||||||
\(239\) | −20.6274 | −1.33428 | −0.667138 | − | 0.744934i | \(-0.732481\pi\) | ||||
−0.667138 | + | 0.744934i | \(0.732481\pi\) | |||||||
\(240\) | −2.12132 | − | 0.707107i | −0.136931 | − | 0.0456435i | ||||
\(241\) | 2.58579 | 0.166565 | 0.0832826 | − | 0.996526i | \(-0.473460\pi\) | ||||
0.0832826 | + | 0.996526i | \(0.473460\pi\) | |||||||
\(242\) | 30.1421i | 1.93761i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.48528 | 0.415178 | ||||||||
\(245\) | 0.828427 | − | 2.48528i | 0.0529263 | − | 0.158779i | ||||
\(246\) | −6.58579 | −0.419894 | ||||||||
\(247\) | 11.3848i | 0.724396i | ||||||||
\(248\) | 3.65685i | 0.232210i | ||||||||
\(249\) | 6.89949 | 0.437238 | ||||||||
\(250\) | −6.36396 | − | 9.19239i | −0.402492 | − | 0.581378i | ||||
\(251\) | 4.82843 | 0.304768 | 0.152384 | − | 0.988321i | \(-0.451305\pi\) | ||||
0.152384 | + | 0.988321i | \(0.451305\pi\) | |||||||
\(252\) | 2.41421i | 0.152081i | ||||||||
\(253\) | − | 19.2426i | − | 1.20977i | ||||||
\(254\) | 9.58579 | 0.601466 | ||||||||
\(255\) | −2.53553 | + | 7.60660i | −0.158781 | + | 0.476344i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.58579i | 0.597945i | 0.954262 | + | 0.298972i | \(0.0966439\pi\) | ||||
−0.954262 | + | 0.298972i | \(0.903356\pi\) | |||||||
\(258\) | 10.4853i | 0.652785i | ||||||||
\(259\) | −2.41421 | −0.150012 | ||||||||
\(260\) | −11.1213 | − | 3.70711i | −0.689715 | − | 0.229905i | ||||
\(261\) | 7.07107 | 0.437688 | ||||||||
\(262\) | 1.89949i | 0.117351i | ||||||||
\(263\) | 31.4142i | 1.93708i | 0.248851 | + | 0.968542i | \(0.419947\pi\) | ||||
−0.248851 | + | 0.968542i | \(0.580053\pi\) | |||||||
\(264\) | 6.41421 | 0.394768 | ||||||||
\(265\) | −8.12132 | − | 2.70711i | −0.498889 | − | 0.166296i | ||||
\(266\) | −5.24264 | −0.321447 | ||||||||
\(267\) | 2.89949i | 0.177446i | ||||||||
\(268\) | − | 0.828427i | − | 0.0506042i | ||||||
\(269\) | 25.6274 | 1.56253 | 0.781266 | − | 0.624199i | \(-0.214574\pi\) | ||||
0.781266 | + | 0.624199i | \(0.214574\pi\) | |||||||
\(270\) | −0.707107 | + | 2.12132i | −0.0430331 | + | 0.129099i | ||||
\(271\) | −6.82843 | −0.414797 | −0.207399 | − | 0.978256i | \(-0.566500\pi\) | ||||
−0.207399 | + | 0.978256i | \(0.566500\pi\) | |||||||
\(272\) | − | 3.58579i | − | 0.217420i | ||||||
\(273\) | 12.6569i | 0.766028i | ||||||||
\(274\) | 17.5563 | 1.06062 | ||||||||
\(275\) | 25.6569 | + | 19.2426i | 1.54717 | + | 1.16037i | ||||
\(276\) | −3.00000 | −0.180579 | ||||||||
\(277\) | 2.89949i | 0.174214i | 0.996199 | + | 0.0871069i | \(0.0277622\pi\) | ||||
−0.996199 | + | 0.0871069i | \(0.972238\pi\) | |||||||
\(278\) | 2.48528i | 0.149057i | ||||||||
\(279\) | 3.65685 | 0.218930 | ||||||||
\(280\) | 1.70711 | − | 5.12132i | 0.102019 | − | 0.306057i | ||||
\(281\) | −13.3848 | −0.798469 | −0.399234 | − | 0.916849i | \(-0.630724\pi\) | ||||
−0.399234 | + | 0.916849i | \(0.630724\pi\) | |||||||
\(282\) | 11.8995i | 0.708605i | ||||||||
\(283\) | − | 18.7990i | − | 1.11748i | −0.829342 | − | 0.558742i | \(-0.811284\pi\) | ||
0.829342 | − | 0.558742i | \(-0.188716\pi\) | |||||||
\(284\) | 9.41421 | 0.558631 | ||||||||
\(285\) | −4.60660 | − | 1.53553i | −0.272872 | − | 0.0909572i | ||||
\(286\) | 33.6274 | 1.98843 | ||||||||
\(287\) | − | 15.8995i | − | 0.938518i | ||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 4.14214 | 0.243655 | ||||||||
\(290\) | −15.0000 | − | 5.00000i | −0.880830 | − | 0.293610i | ||||
\(291\) | 6.72792 | 0.394398 | ||||||||
\(292\) | − | 2.17157i | − | 0.127082i | ||||||
\(293\) | − | 8.65685i | − | 0.505739i | −0.967500 | − | 0.252869i | \(-0.918626\pi\) | ||
0.967500 | − | 0.252869i | \(-0.0813743\pi\) | |||||||
\(294\) | 1.17157 | 0.0683275 | ||||||||
\(295\) | 9.24264 | − | 27.7279i | 0.538127 | − | 1.61438i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | − | 6.41421i | − | 0.372190i | ||||||
\(298\) | − | 3.51472i | − | 0.203602i | ||||||
\(299\) | −15.7279 | −0.909569 | ||||||||
\(300\) | 3.00000 | − | 4.00000i | 0.173205 | − | 0.230940i | ||||
\(301\) | −25.3137 | −1.45906 | ||||||||
\(302\) | 2.41421i | 0.138922i | ||||||||
\(303\) | 5.31371i | 0.305265i | ||||||||
\(304\) | 2.17157 | 0.124548 | ||||||||
\(305\) | −4.58579 | + | 13.7574i | −0.262581 | + | 0.787744i | ||||
\(306\) | −3.58579 | −0.204986 | ||||||||
\(307\) | 13.8995i | 0.793286i | 0.917973 | + | 0.396643i | \(0.129825\pi\) | ||||
−0.917973 | + | 0.396643i | \(0.870175\pi\) | |||||||
\(308\) | 15.4853i | 0.882356i | ||||||||
\(309\) | −15.0711 | −0.857363 | ||||||||
\(310\) | −7.75736 | − | 2.58579i | −0.440588 | − | 0.146863i | ||||
\(311\) | −12.8284 | −0.727433 | −0.363717 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363717 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(312\) | − | 5.24264i | − | 0.296806i | ||||||
\(313\) | − | 2.72792i | − | 0.154191i | −0.997024 | − | 0.0770956i | \(-0.975435\pi\) | ||
0.997024 | − | 0.0770956i | \(-0.0245647\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.12132 | − | 1.70711i | −0.288554 | − | 0.0961846i | ||||
\(316\) | 12.2426 | 0.688702 | ||||||||
\(317\) | − | 21.1716i | − | 1.18911i | −0.804053 | − | 0.594557i | \(-0.797327\pi\) | ||
0.804053 | − | 0.594557i | \(-0.202673\pi\) | |||||||
\(318\) | − | 3.82843i | − | 0.214688i | ||||||
\(319\) | 45.3553 | 2.53941 | ||||||||
\(320\) | −0.707107 | + | 2.12132i | −0.0395285 | + | 0.118585i | ||||
\(321\) | −16.0711 | −0.897000 | ||||||||
\(322\) | − | 7.24264i | − | 0.403617i | ||||||
\(323\) | − | 7.78680i | − | 0.433269i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 15.7279 | − | 20.9706i | 0.872428 | − | 1.16324i | ||||
\(326\) | −15.1421 | −0.838645 | ||||||||
\(327\) | 4.75736i | 0.263083i | ||||||||
\(328\) | 6.58579i | 0.363639i | ||||||||
\(329\) | −28.7279 | −1.58382 | ||||||||
\(330\) | −4.53553 | + | 13.6066i | −0.249673 | + | 0.749019i | ||||
\(331\) | 23.4558 | 1.28925 | 0.644625 | − | 0.764499i | \(-0.277014\pi\) | ||||
0.644625 | + | 0.764499i | \(0.277014\pi\) | |||||||
\(332\) | − | 6.89949i | − | 0.378659i | ||||||
\(333\) | − | 1.00000i | − | 0.0547997i | ||||||
\(334\) | −18.6569 | −1.02086 | ||||||||
\(335\) | 1.75736 | + | 0.585786i | 0.0960148 | + | 0.0320049i | ||||
\(336\) | 2.41421 | 0.131706 | ||||||||
\(337\) | − | 27.9706i | − | 1.52365i | −0.647781 | − | 0.761827i | \(-0.724303\pi\) | ||
0.647781 | − | 0.761827i | \(-0.275697\pi\) | |||||||
\(338\) | − | 14.4853i | − | 0.787895i | ||||||
\(339\) | −2.82843 | −0.153619 | ||||||||
\(340\) | 7.60660 | + | 2.53553i | 0.412526 | + | 0.137509i | ||||
\(341\) | 23.4558 | 1.27021 | ||||||||
\(342\) | − | 2.17157i | − | 0.117425i | ||||||
\(343\) | 19.7279i | 1.06521i | ||||||||
\(344\) | 10.4853 | 0.565328 | ||||||||
\(345\) | 2.12132 | − | 6.36396i | 0.114208 | − | 0.342624i | ||||
\(346\) | −0.656854 | −0.0353127 | ||||||||
\(347\) | 23.5563i | 1.26457i | 0.774735 | + | 0.632286i | \(0.217883\pi\) | ||||
−0.774735 | + | 0.632286i | \(0.782117\pi\) | |||||||
\(348\) | − | 7.07107i | − | 0.379049i | ||||||
\(349\) | −28.0416 | −1.50103 | −0.750517 | − | 0.660851i | \(-0.770195\pi\) | ||||
−0.750517 | + | 0.660851i | \(0.770195\pi\) | |||||||
\(350\) | 9.65685 | + | 7.24264i | 0.516181 | + | 0.387135i | ||||
\(351\) | −5.24264 | −0.279831 | ||||||||
\(352\) | − | 6.41421i | − | 0.341879i | ||||||
\(353\) | 16.1421i | 0.859159i | 0.903029 | + | 0.429580i | \(0.141338\pi\) | ||||
−0.903029 | + | 0.429580i | \(0.858662\pi\) | |||||||
\(354\) | 13.0711 | 0.694719 | ||||||||
\(355\) | −6.65685 | + | 19.9706i | −0.353309 | + | 1.05993i | ||||
\(356\) | 2.89949 | 0.153673 | ||||||||
\(357\) | − | 8.65685i | − | 0.458169i | ||||||
\(358\) | 18.8284i | 0.995113i | ||||||||
\(359\) | −29.0711 | −1.53431 | −0.767156 | − | 0.641460i | \(-0.778329\pi\) | ||||
−0.767156 | + | 0.641460i | \(0.778329\pi\) | |||||||
\(360\) | 2.12132 | + | 0.707107i | 0.111803 | + | 0.0372678i | ||||
\(361\) | −14.2843 | −0.751804 | ||||||||
\(362\) | 20.5858i | 1.08196i | ||||||||
\(363\) | − | 30.1421i | − | 1.58205i | ||||||
\(364\) | 12.6569 | 0.663399 | ||||||||
\(365\) | 4.60660 | + | 1.53553i | 0.241121 | + | 0.0803735i | ||||
\(366\) | −6.48528 | −0.338991 | ||||||||
\(367\) | − | 15.2426i | − | 0.795659i | −0.917459 | − | 0.397830i | \(-0.869763\pi\) | ||
0.917459 | − | 0.397830i | \(-0.130237\pi\) | |||||||
\(368\) | 3.00000i | 0.156386i | ||||||||
\(369\) | 6.58579 | 0.342842 | ||||||||
\(370\) | −0.707107 | + | 2.12132i | −0.0367607 | + | 0.110282i | ||||
\(371\) | 9.24264 | 0.479854 | ||||||||
\(372\) | − | 3.65685i | − | 0.189599i | ||||||
\(373\) | 1.75736i | 0.0909926i | 0.998965 | + | 0.0454963i | \(0.0144869\pi\) | ||||
−0.998965 | + | 0.0454963i | \(0.985513\pi\) | |||||||
\(374\) | −23.0000 | −1.18930 | ||||||||
\(375\) | 6.36396 | + | 9.19239i | 0.328634 | + | 0.474693i | ||||
\(376\) | 11.8995 | 0.613670 | ||||||||
\(377\) | − | 37.0711i | − | 1.90926i | ||||||
\(378\) | − | 2.41421i | − | 0.124174i | ||||||
\(379\) | 28.7279 | 1.47565 | 0.737827 | − | 0.674990i | \(-0.235852\pi\) | ||||
0.737827 | + | 0.674990i | \(0.235852\pi\) | |||||||
\(380\) | −1.53553 | + | 4.60660i | −0.0787712 | + | 0.236314i | ||||
\(381\) | −9.58579 | −0.491095 | ||||||||
\(382\) | 8.65685i | 0.442923i | ||||||||
\(383\) | − | 14.6569i | − | 0.748930i | −0.927241 | − | 0.374465i | \(-0.877826\pi\) | ||
0.927241 | − | 0.374465i | \(-0.122174\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −32.8492 | − | 10.9497i | −1.67415 | − | 0.558051i | ||||
\(386\) | 9.31371 | 0.474055 | ||||||||
\(387\) | − | 10.4853i | − | 0.532997i | ||||||
\(388\) | − | 6.72792i | − | 0.341558i | ||||||
\(389\) | 22.9706 | 1.16465 | 0.582327 | − | 0.812955i | \(-0.302142\pi\) | ||||
0.582327 | + | 0.812955i | \(0.302142\pi\) | |||||||
\(390\) | 11.1213 | + | 3.70711i | 0.563150 | + | 0.187717i | ||||
\(391\) | 10.7574 | 0.544023 | ||||||||
\(392\) | − | 1.17157i | − | 0.0591734i | ||||||
\(393\) | − | 1.89949i | − | 0.0958168i | ||||||
\(394\) | 15.1421 | 0.762850 | ||||||||
\(395\) | −8.65685 | + | 25.9706i | −0.435574 | + | 1.30672i | ||||
\(396\) | −6.41421 | −0.322326 | ||||||||
\(397\) | 8.48528i | 0.425864i | 0.977067 | + | 0.212932i | \(0.0683013\pi\) | ||||
−0.977067 | + | 0.212932i | \(0.931699\pi\) | |||||||
\(398\) | − | 20.0000i | − | 1.00251i | ||||||
\(399\) | 5.24264 | 0.262460 | ||||||||
\(400\) | −4.00000 | − | 3.00000i | −0.200000 | − | 0.150000i | ||||
\(401\) | −15.0416 | −0.751143 | −0.375572 | − | 0.926793i | \(-0.622554\pi\) | ||||
−0.375572 | + | 0.926793i | \(0.622554\pi\) | |||||||
\(402\) | 0.828427i | 0.0413182i | ||||||||
\(403\) | − | 19.1716i | − | 0.955004i | ||||||
\(404\) | 5.31371 | 0.264367 | ||||||||
\(405\) | 0.707107 | − | 2.12132i | 0.0351364 | − | 0.105409i | ||||
\(406\) | 17.0711 | 0.847223 | ||||||||
\(407\) | − | 6.41421i | − | 0.317941i | ||||||
\(408\) | 3.58579i | 0.177523i | ||||||||
\(409\) | −32.3848 | −1.60132 | −0.800662 | − | 0.599116i | \(-0.795519\pi\) | ||||
−0.800662 | + | 0.599116i | \(0.795519\pi\) | |||||||
\(410\) | −13.9706 | − | 4.65685i | −0.689957 | − | 0.229986i | ||||
\(411\) | −17.5563 | −0.865991 | ||||||||
\(412\) | 15.0711i | 0.742498i | ||||||||
\(413\) | 31.5563i | 1.55279i | ||||||||
\(414\) | 3.00000 | 0.147442 | ||||||||
\(415\) | 14.6360 | + | 4.87868i | 0.718455 | + | 0.239485i | ||||
\(416\) | −5.24264 | −0.257042 | ||||||||
\(417\) | − | 2.48528i | − | 0.121705i | ||||||
\(418\) | − | 13.9289i | − | 0.681286i | ||||||
\(419\) | 27.7279 | 1.35460 | 0.677299 | − | 0.735708i | \(-0.263150\pi\) | ||||
0.677299 | + | 0.735708i | \(0.263150\pi\) | |||||||
\(420\) | −1.70711 | + | 5.12132i | −0.0832983 | + | 0.249895i | ||||
\(421\) | −13.4558 | −0.655798 | −0.327899 | − | 0.944713i | \(-0.606341\pi\) | ||||
−0.327899 | + | 0.944713i | \(0.606341\pi\) | |||||||
\(422\) | 10.3848i | 0.505523i | ||||||||
\(423\) | − | 11.8995i | − | 0.578573i | ||||||
\(424\) | −3.82843 | −0.185925 | ||||||||
\(425\) | −10.7574 | + | 14.3431i | −0.521809 | + | 0.695745i | ||||
\(426\) | −9.41421 | −0.456120 | ||||||||
\(427\) | − | 15.6569i | − | 0.757688i | ||||||
\(428\) | 16.0711i | 0.776824i | ||||||||
\(429\) | −33.6274 | −1.62355 | ||||||||
\(430\) | −7.41421 | + | 22.2426i | −0.357545 | + | 1.07264i | ||||
\(431\) | 29.8284 | 1.43678 | 0.718392 | − | 0.695638i | \(-0.244878\pi\) | ||||
0.718392 | + | 0.695638i | \(0.244878\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 23.4853i | 1.12863i | 0.825559 | + | 0.564315i | \(0.190860\pi\) | ||||
−0.825559 | + | 0.564315i | \(0.809140\pi\) | |||||||
\(434\) | 8.82843 | 0.423778 | ||||||||
\(435\) | 15.0000 | + | 5.00000i | 0.719195 | + | 0.239732i | ||||
\(436\) | 4.75736 | 0.227836 | ||||||||
\(437\) | 6.51472i | 0.311641i | ||||||||
\(438\) | 2.17157i | 0.103762i | ||||||||
\(439\) | −24.7279 | −1.18020 | −0.590100 | − | 0.807330i | \(-0.700912\pi\) | ||||
−0.590100 | + | 0.807330i | \(0.700912\pi\) | |||||||
\(440\) | 13.6066 | + | 4.53553i | 0.648669 | + | 0.216223i | ||||
\(441\) | −1.17157 | −0.0557892 | ||||||||
\(442\) | 18.7990i | 0.894177i | ||||||||
\(443\) | 23.6569i | 1.12397i | 0.827147 | + | 0.561986i | \(0.189962\pi\) | ||||
−0.827147 | + | 0.561986i | \(0.810038\pi\) | |||||||
\(444\) | −1.00000 | −0.0474579 | ||||||||
\(445\) | −2.05025 | + | 6.15076i | −0.0971913 | + | 0.291574i | ||||
\(446\) | −9.65685 | −0.457265 | ||||||||
\(447\) | 3.51472i | 0.166240i | ||||||||
\(448\) | − | 2.41421i | − | 0.114061i | ||||||
\(449\) | 13.7990 | 0.651215 | 0.325607 | − | 0.945505i | \(-0.394431\pi\) | ||||
0.325607 | + | 0.945505i | \(0.394431\pi\) | |||||||
\(450\) | −3.00000 | + | 4.00000i | −0.141421 | + | 0.188562i | ||||
\(451\) | 42.2426 | 1.98913 | ||||||||
\(452\) | 2.82843i | 0.133038i | ||||||||
\(453\) | − | 2.41421i | − | 0.113430i | ||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | −8.94975 | + | 26.8492i | −0.419571 | + | 1.25871i | ||||
\(456\) | −2.17157 | −0.101693 | ||||||||
\(457\) | − | 0.970563i | − | 0.0454010i | −0.999742 | − | 0.0227005i | \(-0.992774\pi\) | ||
0.999742 | − | 0.0227005i | \(-0.00722642\pi\) | |||||||
\(458\) | − | 18.7279i | − | 0.875098i | ||||||
\(459\) | 3.58579 | 0.167370 | ||||||||
\(460\) | −6.36396 | − | 2.12132i | −0.296721 | − | 0.0989071i | ||||
\(461\) | 20.8284 | 0.970077 | 0.485038 | − | 0.874493i | \(-0.338806\pi\) | ||||
0.485038 | + | 0.874493i | \(0.338806\pi\) | |||||||
\(462\) | − | 15.4853i | − | 0.720440i | ||||||
\(463\) | 29.8995i | 1.38955i | 0.719228 | + | 0.694774i | \(0.244495\pi\) | ||||
−0.719228 | + | 0.694774i | \(0.755505\pi\) | |||||||
\(464\) | −7.07107 | −0.328266 | ||||||||
\(465\) | 7.75736 | + | 2.58579i | 0.359739 | + | 0.119913i | ||||
\(466\) | 2.48528 | 0.115128 | ||||||||
\(467\) | − | 40.2426i | − | 1.86221i | −0.364755 | − | 0.931104i | \(-0.618847\pi\) | ||
0.364755 | − | 0.931104i | \(-0.381153\pi\) | |||||||
\(468\) | 5.24264i | 0.242341i | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | −8.41421 | + | 25.2426i | −0.388119 | + | 1.16436i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 13.0711i | − | 0.601645i | ||||||
\(473\) | − | 67.2548i | − | 3.09238i | ||||||
\(474\) | −12.2426 | −0.562323 | ||||||||
\(475\) | −8.68629 | − | 6.51472i | −0.398554 | − | 0.298916i | ||||
\(476\) | −8.65685 | −0.396786 | ||||||||
\(477\) | 3.82843i | 0.175292i | ||||||||
\(478\) | − | 20.6274i | − | 0.943476i | ||||||
\(479\) | −6.17157 | −0.281986 | −0.140993 | − | 0.990011i | \(-0.545030\pi\) | ||||
−0.140993 | + | 0.990011i | \(0.545030\pi\) | |||||||
\(480\) | 0.707107 | − | 2.12132i | 0.0322749 | − | 0.0968246i | ||||
\(481\) | −5.24264 | −0.239044 | ||||||||
\(482\) | 2.58579i | 0.117779i | ||||||||
\(483\) | 7.24264i | 0.329552i | ||||||||
\(484\) | −30.1421 | −1.37010 | ||||||||
\(485\) | 14.2721 | + | 4.75736i | 0.648062 | + | 0.216021i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 30.0000i | − | 1.35943i | −0.733476 | − | 0.679715i | \(-0.762104\pi\) | ||
0.733476 | − | 0.679715i | \(-0.237896\pi\) | |||||||
\(488\) | 6.48528i | 0.293575i | ||||||||
\(489\) | 15.1421 | 0.684751 | ||||||||
\(490\) | 2.48528 | + | 0.828427i | 0.112274 | + | 0.0374245i | ||||
\(491\) | −16.4142 | −0.740763 | −0.370382 | − | 0.928880i | \(-0.620773\pi\) | ||||
−0.370382 | + | 0.928880i | \(0.620773\pi\) | |||||||
\(492\) | − | 6.58579i | − | 0.296910i | ||||||
\(493\) | 25.3553i | 1.14195i | ||||||||
\(494\) | −11.3848 | −0.512225 | ||||||||
\(495\) | 4.53553 | − | 13.6066i | 0.203857 | − | 0.611571i | ||||
\(496\) | −3.65685 | −0.164198 | ||||||||
\(497\) | − | 22.7279i | − | 1.01949i | ||||||
\(498\) | 6.89949i | 0.309174i | ||||||||
\(499\) | −7.48528 | −0.335087 | −0.167544 | − | 0.985865i | \(-0.553583\pi\) | ||||
−0.167544 | + | 0.985865i | \(0.553583\pi\) | |||||||
\(500\) | 9.19239 | − | 6.36396i | 0.411096 | − | 0.284605i | ||||
\(501\) | 18.6569 | 0.833527 | ||||||||
\(502\) | 4.82843i | 0.215503i | ||||||||
\(503\) | 23.6569i | 1.05481i | 0.849615 | + | 0.527403i | \(0.176834\pi\) | ||||
−0.849615 | + | 0.527403i | \(0.823166\pi\) | |||||||
\(504\) | −2.41421 | −0.107538 | ||||||||
\(505\) | −3.75736 | + | 11.2721i | −0.167200 | + | 0.501601i | ||||
\(506\) | 19.2426 | 0.855440 | ||||||||
\(507\) | 14.4853i | 0.643314i | ||||||||
\(508\) | 9.58579i | 0.425300i | ||||||||
\(509\) | 30.3137 | 1.34363 | 0.671816 | − | 0.740718i | \(-0.265515\pi\) | ||||
0.671816 | + | 0.740718i | \(0.265515\pi\) | |||||||
\(510\) | −7.60660 | − | 2.53553i | −0.336826 | − | 0.112275i | ||||
\(511\) | −5.24264 | −0.231921 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.17157i | 0.0958773i | ||||||||
\(514\) | −9.58579 | −0.422811 | ||||||||
\(515\) | −31.9706 | − | 10.6569i | −1.40879 | − | 0.469597i | ||||
\(516\) | −10.4853 | −0.461589 | ||||||||
\(517\) | − | 76.3259i | − | 3.35681i | ||||||
\(518\) | − | 2.41421i | − | 0.106074i | ||||||
\(519\) | 0.656854 | 0.0288327 | ||||||||
\(520\) | 3.70711 | − | 11.1213i | 0.162567 | − | 0.487702i | ||||
\(521\) | −16.0416 | −0.702797 | −0.351398 | − | 0.936226i | \(-0.614294\pi\) | ||||
−0.351398 | + | 0.936226i | \(0.614294\pi\) | |||||||
\(522\) | 7.07107i | 0.309492i | ||||||||
\(523\) | 34.0000i | 1.48672i | 0.668894 | + | 0.743358i | \(0.266768\pi\) | ||||
−0.668894 | + | 0.743358i | \(0.733232\pi\) | |||||||
\(524\) | −1.89949 | −0.0829798 | ||||||||
\(525\) | −9.65685 | − | 7.24264i | −0.421460 | − | 0.316095i | ||||
\(526\) | −31.4142 | −1.36972 | ||||||||
\(527\) | 13.1127i | 0.571198i | ||||||||
\(528\) | 6.41421i | 0.279143i | ||||||||
\(529\) | 14.0000 | 0.608696 | ||||||||
\(530\) | 2.70711 | − | 8.12132i | 0.117589 | − | 0.352768i | ||||
\(531\) | −13.0711 | −0.567236 | ||||||||
\(532\) | − | 5.24264i | − | 0.227297i | ||||||
\(533\) | − | 34.5269i | − | 1.49553i | ||||||
\(534\) | −2.89949 | −0.125473 | ||||||||
\(535\) | −34.0919 | − | 11.3640i | −1.47392 | − | 0.491307i | ||||
\(536\) | 0.828427 | 0.0357826 | ||||||||
\(537\) | − | 18.8284i | − | 0.812507i | ||||||
\(538\) | 25.6274i | 1.10488i | ||||||||
\(539\) | −7.51472 | −0.323682 | ||||||||
\(540\) | −2.12132 | − | 0.707107i | −0.0912871 | − | 0.0304290i | ||||
\(541\) | 36.2132 | 1.55693 | 0.778464 | − | 0.627690i | \(-0.215999\pi\) | ||||
0.778464 | + | 0.627690i | \(0.215999\pi\) | |||||||
\(542\) | − | 6.82843i | − | 0.293306i | ||||||
\(543\) | − | 20.5858i | − | 0.883421i | ||||||
\(544\) | 3.58579 | 0.153739 | ||||||||
\(545\) | −3.36396 | + | 10.0919i | −0.144096 | + | 0.432289i | ||||
\(546\) | −12.6569 | −0.541663 | ||||||||
\(547\) | 0.372583i | 0.0159305i | 0.999968 | + | 0.00796525i | \(0.00253544\pi\) | ||||
−0.999968 | + | 0.00796525i | \(0.997465\pi\) | |||||||
\(548\) | 17.5563i | 0.749970i | ||||||||
\(549\) | 6.48528 | 0.276785 | ||||||||
\(550\) | −19.2426 | + | 25.6569i | −0.820509 | + | 1.09401i | ||||
\(551\) | −15.3553 | −0.654159 | ||||||||
\(552\) | − | 3.00000i | − | 0.127688i | ||||||
\(553\) | − | 29.5563i | − | 1.25686i | ||||||
\(554\) | −2.89949 | −0.123188 | ||||||||
\(555\) | 0.707107 | − | 2.12132i | 0.0300150 | − | 0.0900450i | ||||
\(556\) | −2.48528 | −0.105399 | ||||||||
\(557\) | 37.5563i | 1.59131i | 0.605748 | + | 0.795657i | \(0.292874\pi\) | ||||
−0.605748 | + | 0.795657i | \(0.707126\pi\) | |||||||
\(558\) | 3.65685i | 0.154807i | ||||||||
\(559\) | −54.9706 | −2.32501 | ||||||||
\(560\) | 5.12132 | + | 1.70711i | 0.216415 | + | 0.0721384i | ||||
\(561\) | 23.0000 | 0.971061 | ||||||||
\(562\) | − | 13.3848i | − | 0.564603i | ||||||
\(563\) | 16.5858i | 0.699008i | 0.936935 | + | 0.349504i | \(0.113650\pi\) | ||||
−0.936935 | + | 0.349504i | \(0.886350\pi\) | |||||||
\(564\) | −11.8995 | −0.501059 | ||||||||
\(565\) | −6.00000 | − | 2.00000i | −0.252422 | − | 0.0841406i | ||||
\(566\) | 18.7990 | 0.790180 | ||||||||
\(567\) | 2.41421i | 0.101387i | ||||||||
\(568\) | 9.41421i | 0.395012i | ||||||||
\(569\) | −37.0416 | −1.55287 | −0.776433 | − | 0.630200i | \(-0.782973\pi\) | ||||
−0.776433 | + | 0.630200i | \(0.782973\pi\) | |||||||
\(570\) | 1.53553 | − | 4.60660i | 0.0643164 | − | 0.192949i | ||||
\(571\) | −28.0416 | −1.17351 | −0.586753 | − | 0.809766i | \(-0.699594\pi\) | ||||
−0.586753 | + | 0.809766i | \(0.699594\pi\) | |||||||
\(572\) | 33.6274i | 1.40603i | ||||||||
\(573\) | − | 8.65685i | − | 0.361645i | ||||||
\(574\) | 15.8995 | 0.663632 | ||||||||
\(575\) | 9.00000 | − | 12.0000i | 0.375326 | − | 0.500435i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 9.51472i | − | 0.396103i | −0.980192 | − | 0.198051i | \(-0.936539\pi\) | ||
0.980192 | − | 0.198051i | \(-0.0634613\pi\) | |||||||
\(578\) | 4.14214i | 0.172290i | ||||||||
\(579\) | −9.31371 | −0.387065 | ||||||||
\(580\) | 5.00000 | − | 15.0000i | 0.207614 | − | 0.622841i | ||||
\(581\) | −16.6569 | −0.691043 | ||||||||
\(582\) | 6.72792i | 0.278881i | ||||||||
\(583\) | 24.5563i | 1.01702i | ||||||||
\(584\) | 2.17157 | 0.0898603 | ||||||||
\(585\) | −11.1213 | − | 3.70711i | −0.459810 | − | 0.153270i | ||||
\(586\) | 8.65685 | 0.357611 | ||||||||
\(587\) | 2.82843i | 0.116742i | 0.998295 | + | 0.0583708i | \(0.0185906\pi\) | ||||
−0.998295 | + | 0.0583708i | \(0.981409\pi\) | |||||||
\(588\) | 1.17157i | 0.0483149i | ||||||||
\(589\) | −7.94113 | −0.327208 | ||||||||
\(590\) | 27.7279 | + | 9.24264i | 1.14154 | + | 0.380513i | ||||
\(591\) | −15.1421 | −0.622864 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 4.97056i | 0.204117i | 0.994778 | + | 0.102058i | \(0.0325428\pi\) | ||||
−0.994778 | + | 0.102058i | \(0.967457\pi\) | |||||||
\(594\) | 6.41421 | 0.263178 | ||||||||
\(595\) | 6.12132 | − | 18.3640i | 0.250950 | − | 0.752849i | ||||
\(596\) | 3.51472 | 0.143968 | ||||||||
\(597\) | 20.0000i | 0.818546i | ||||||||
\(598\) | − | 15.7279i | − | 0.643163i | ||||||
\(599\) | −32.8701 | −1.34303 | −0.671517 | − | 0.740989i | \(-0.734357\pi\) | ||||
−0.671517 | + | 0.740989i | \(0.734357\pi\) | |||||||
\(600\) | 4.00000 | + | 3.00000i | 0.163299 | + | 0.122474i | ||||
\(601\) | 9.97056 | 0.406708 | 0.203354 | − | 0.979105i | \(-0.434816\pi\) | ||||
0.203354 | + | 0.979105i | \(0.434816\pi\) | |||||||
\(602\) | − | 25.3137i | − | 1.03171i | ||||||
\(603\) | − | 0.828427i | − | 0.0337362i | ||||||
\(604\) | −2.41421 | −0.0982330 | ||||||||
\(605\) | 21.3137 | − | 63.9411i | 0.866525 | − | 2.59958i | ||||
\(606\) | −5.31371 | −0.215855 | ||||||||
\(607\) | 11.8579i | 0.481296i | 0.970612 | + | 0.240648i | \(0.0773599\pi\) | ||||
−0.970612 | + | 0.240648i | \(0.922640\pi\) | |||||||
\(608\) | 2.17157i | 0.0880689i | ||||||||
\(609\) | −17.0711 | −0.691755 | ||||||||
\(610\) | −13.7574 | − | 4.58579i | −0.557019 | − | 0.185673i | ||||
\(611\) | −62.3848 | −2.52382 | ||||||||
\(612\) | − | 3.58579i | − | 0.144947i | ||||||
\(613\) | 1.31371i | 0.0530602i | 0.999648 | + | 0.0265301i | \(0.00844578\pi\) | ||||
−0.999648 | + | 0.0265301i | \(0.991554\pi\) | |||||||
\(614\) | −13.8995 | −0.560938 | ||||||||
\(615\) | 13.9706 | + | 4.65685i | 0.563347 | + | 0.187782i | ||||
\(616\) | −15.4853 | −0.623920 | ||||||||
\(617\) | 35.6985i | 1.43717i | 0.695441 | + | 0.718583i | \(0.255209\pi\) | ||||
−0.695441 | + | 0.718583i | \(0.744791\pi\) | |||||||
\(618\) | − | 15.0711i | − | 0.606247i | ||||||
\(619\) | 7.21320 | 0.289923 | 0.144962 | − | 0.989437i | \(-0.453694\pi\) | ||||
0.144962 | + | 0.989437i | \(0.453694\pi\) | |||||||
\(620\) | 2.58579 | − | 7.75736i | 0.103848 | − | 0.311543i | ||||
\(621\) | −3.00000 | −0.120386 | ||||||||
\(622\) | − | 12.8284i | − | 0.514373i | ||||||
\(623\) | − | 7.00000i | − | 0.280449i | ||||||
\(624\) | 5.24264 | 0.209874 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 2.72792 | 0.109030 | ||||||||
\(627\) | 13.9289i | 0.556268i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.58579 | 0.142975 | ||||||||
\(630\) | 1.70711 | − | 5.12132i | 0.0680128 | − | 0.204038i | ||||
\(631\) | 7.51472 | 0.299156 | 0.149578 | − | 0.988750i | \(-0.452208\pi\) | ||||
0.149578 | + | 0.988750i | \(0.452208\pi\) | |||||||
\(632\) | 12.2426i | 0.486986i | ||||||||
\(633\) | − | 10.3848i | − | 0.412758i | ||||||
\(634\) | 21.1716 | 0.840831 | ||||||||
\(635\) | −20.3345 | − | 6.77817i | −0.806951 | − | 0.268984i | ||||
\(636\) | 3.82843 | 0.151807 | ||||||||
\(637\) | 6.14214i | 0.243360i | ||||||||
\(638\) | 45.3553i | 1.79564i | ||||||||
\(639\) | 9.41421 | 0.372421 | ||||||||
\(640\) | −2.12132 | − | 0.707107i | −0.0838525 | − | 0.0279508i | ||||
\(641\) | −26.8284 | −1.05966 | −0.529830 | − | 0.848104i | \(-0.677744\pi\) | ||||
−0.529830 | + | 0.848104i | \(0.677744\pi\) | |||||||
\(642\) | − | 16.0711i | − | 0.634274i | ||||||
\(643\) | − | 18.4558i | − | 0.727827i | −0.931433 | − | 0.363914i | \(-0.881440\pi\) | ||
0.931433 | − | 0.363914i | \(-0.118560\pi\) | |||||||
\(644\) | 7.24264 | 0.285400 | ||||||||
\(645\) | 7.41421 | − | 22.2426i | 0.291934 | − | 0.875803i | ||||
\(646\) | 7.78680 | 0.306367 | ||||||||
\(647\) | 21.0000i | 0.825595i | 0.910823 | + | 0.412798i | \(0.135448\pi\) | ||||
−0.910823 | + | 0.412798i | \(0.864552\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −83.8406 | −3.29103 | ||||||||
\(650\) | 20.9706 | + | 15.7279i | 0.822533 | + | 0.616900i | ||||
\(651\) | −8.82843 | −0.346013 | ||||||||
\(652\) | − | 15.1421i | − | 0.593012i | ||||||
\(653\) | 20.4853i | 0.801651i | 0.916154 | + | 0.400826i | \(0.131277\pi\) | ||||
−0.916154 | + | 0.400826i | \(0.868723\pi\) | |||||||
\(654\) | −4.75736 | −0.186027 | ||||||||
\(655\) | 1.34315 | − | 4.02944i | 0.0524810 | − | 0.157443i | ||||
\(656\) | −6.58579 | −0.257132 | ||||||||
\(657\) | − | 2.17157i | − | 0.0847211i | ||||||
\(658\) | − | 28.7279i | − | 1.11993i | ||||||
\(659\) | −51.1127 | −1.99107 | −0.995534 | − | 0.0944035i | \(-0.969906\pi\) | ||||
−0.995534 | + | 0.0944035i | \(0.969906\pi\) | |||||||
\(660\) | −13.6066 | − | 4.53553i | −0.529636 | − | 0.176545i | ||||
\(661\) | 25.2426 | 0.981825 | 0.490912 | − | 0.871209i | \(-0.336663\pi\) | ||||
0.490912 | + | 0.871209i | \(0.336663\pi\) | |||||||
\(662\) | 23.4558i | 0.911637i | ||||||||
\(663\) | − | 18.7990i | − | 0.730092i | ||||||
\(664\) | 6.89949 | 0.267752 | ||||||||
\(665\) | 11.1213 | + | 3.70711i | 0.431266 | + | 0.143755i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | − | 21.2132i | − | 0.821379i | ||||||
\(668\) | − | 18.6569i | − | 0.721855i | ||||||
\(669\) | 9.65685 | 0.373356 | ||||||||
\(670\) | −0.585786 | + | 1.75736i | −0.0226309 | + | 0.0678927i | ||||
\(671\) | 41.5980 | 1.60587 | ||||||||
\(672\) | 2.41421i | 0.0931303i | ||||||||
\(673\) | 0.0294373i | 0.00113472i | 1.00000 | 0.000567361i | \(0.000180597\pi\) | |||||
−1.00000 | 0.000567361i | \(0.999819\pi\) | ||||||||
\(674\) | 27.9706 | 1.07739 | ||||||||
\(675\) | 3.00000 | − | 4.00000i | 0.115470 | − | 0.153960i | ||||
\(676\) | 14.4853 | 0.557126 | ||||||||
\(677\) | − | 1.20101i | − | 0.0461586i | −0.999734 | − | 0.0230793i | \(-0.992653\pi\) | ||
0.999734 | − | 0.0230793i | \(-0.00734702\pi\) | |||||||
\(678\) | − | 2.82843i | − | 0.108625i | ||||||
\(679\) | −16.2426 | −0.623335 | ||||||||
\(680\) | −2.53553 | + | 7.60660i | −0.0972333 | + | 0.291700i | ||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 23.4558i | 0.898171i | ||||||||
\(683\) | − | 16.9289i | − | 0.647768i | −0.946097 | − | 0.323884i | \(-0.895011\pi\) | ||
0.946097 | − | 0.323884i | \(-0.104989\pi\) | |||||||
\(684\) | 2.17157 | 0.0830322 | ||||||||
\(685\) | −37.2426 | − | 12.4142i | −1.42297 | − | 0.474323i | ||||
\(686\) | −19.7279 | −0.753216 | ||||||||
\(687\) | 18.7279i | 0.714515i | ||||||||
\(688\) | 10.4853i | 0.399748i | ||||||||
\(689\) | 20.0711 | 0.764647 | ||||||||
\(690\) | 6.36396 | + | 2.12132i | 0.242272 | + | 0.0807573i | ||||
\(691\) | 30.5858 | 1.16354 | 0.581769 | − | 0.813354i | \(-0.302361\pi\) | ||||
0.581769 | + | 0.813354i | \(0.302361\pi\) | |||||||
\(692\) | − | 0.656854i | − | 0.0249699i | ||||||
\(693\) | 15.4853i | 0.588237i | ||||||||
\(694\) | −23.5563 | −0.894187 | ||||||||
\(695\) | 1.75736 | − | 5.27208i | 0.0666604 | − | 0.199981i | ||||
\(696\) | 7.07107 | 0.268028 | ||||||||
\(697\) | 23.6152i | 0.894490i | ||||||||
\(698\) | − | 28.0416i | − | 1.06139i | ||||||
\(699\) | −2.48528 | −0.0940020 | ||||||||
\(700\) | −7.24264 | + | 9.65685i | −0.273746 | + | 0.364995i | ||||
\(701\) | 14.6274 | 0.552470 | 0.276235 | − | 0.961090i | \(-0.410913\pi\) | ||||
0.276235 | + | 0.961090i | \(0.410913\pi\) | |||||||
\(702\) | − | 5.24264i | − | 0.197871i | ||||||
\(703\) | 2.17157i | 0.0819024i | ||||||||
\(704\) | 6.41421 | 0.241745 | ||||||||
\(705\) | 8.41421 | − | 25.2426i | 0.316898 | − | 0.950693i | ||||
\(706\) | −16.1421 | −0.607517 | ||||||||
\(707\) | − | 12.8284i | − | 0.482463i | ||||||
\(708\) | 13.0711i | 0.491241i | ||||||||
\(709\) | −44.0711 | −1.65512 | −0.827562 | − | 0.561375i | \(-0.810273\pi\) | ||||
−0.827562 | + | 0.561375i | \(0.810273\pi\) | |||||||
\(710\) | −19.9706 | − | 6.65685i | −0.749482 | − | 0.249827i | ||||
\(711\) | 12.2426 | 0.459135 | ||||||||
\(712\) | 2.89949i | 0.108663i | ||||||||
\(713\) | − | 10.9706i | − | 0.410851i | ||||||
\(714\) | 8.65685 | 0.323975 | ||||||||
\(715\) | −71.3345 | − | 23.7782i | −2.66776 | − | 0.889253i | ||||
\(716\) | −18.8284 | −0.703651 | ||||||||
\(717\) | 20.6274i | 0.770345i | ||||||||
\(718\) | − | 29.0711i | − | 1.08492i | ||||||
\(719\) | −1.41421 | −0.0527413 | −0.0263706 | − | 0.999652i | \(-0.508395\pi\) | ||||
−0.0263706 | + | 0.999652i | \(0.508395\pi\) | |||||||
\(720\) | −0.707107 | + | 2.12132i | −0.0263523 | + | 0.0790569i | ||||
\(721\) | 36.3848 | 1.35504 | ||||||||
\(722\) | − | 14.2843i | − | 0.531606i | ||||||
\(723\) | − | 2.58579i | − | 0.0961664i | ||||||
\(724\) | −20.5858 | −0.765065 | ||||||||
\(725\) | 28.2843 | + | 21.2132i | 1.05045 | + | 0.787839i | ||||
\(726\) | 30.1421 | 1.11868 | ||||||||
\(727\) | − | 20.3848i | − | 0.756030i | −0.925800 | − | 0.378015i | \(-0.876607\pi\) | ||
0.925800 | − | 0.378015i | \(-0.123393\pi\) | |||||||
\(728\) | 12.6569i | 0.469094i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.53553 | + | 4.60660i | −0.0568327 | + | 0.170498i | ||||
\(731\) | 37.5980 | 1.39061 | ||||||||
\(732\) | − | 6.48528i | − | 0.239703i | ||||||
\(733\) | − | 10.9706i | − | 0.405207i | −0.979261 | − | 0.202603i | \(-0.935060\pi\) | ||
0.979261 | − | 0.202603i | \(-0.0649403\pi\) | |||||||
\(734\) | 15.2426 | 0.562616 | ||||||||
\(735\) | −2.48528 | − | 0.828427i | −0.0916710 | − | 0.0305570i | ||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | − | 5.31371i | − | 0.195733i | ||||||
\(738\) | 6.58579i | 0.242426i | ||||||||
\(739\) | 10.0000 | 0.367856 | 0.183928 | − | 0.982940i | \(-0.441119\pi\) | ||||
0.183928 | + | 0.982940i | \(0.441119\pi\) | |||||||
\(740\) | −2.12132 | − | 0.707107i | −0.0779813 | − | 0.0259938i | ||||
\(741\) | 11.3848 | 0.418230 | ||||||||
\(742\) | 9.24264i | 0.339308i | ||||||||
\(743\) | 51.3553i | 1.88404i | 0.335550 | + | 0.942022i | \(0.391078\pi\) | ||||
−0.335550 | + | 0.942022i | \(0.608922\pi\) | |||||||
\(744\) | 3.65685 | 0.134067 | ||||||||
\(745\) | −2.48528 | + | 7.45584i | −0.0910537 | + | 0.273161i | ||||
\(746\) | −1.75736 | −0.0643415 | ||||||||
\(747\) | − | 6.89949i | − | 0.252439i | ||||||
\(748\) | − | 23.0000i | − | 0.840963i | ||||||
\(749\) | 38.7990 | 1.41768 | ||||||||
\(750\) | −9.19239 | + | 6.36396i | −0.335659 | + | 0.232379i | ||||
\(751\) | −35.1127 | −1.28128 | −0.640640 | − | 0.767841i | \(-0.721331\pi\) | ||||
−0.640640 | + | 0.767841i | \(0.721331\pi\) | |||||||
\(752\) | 11.8995i | 0.433930i | ||||||||
\(753\) | − | 4.82843i | − | 0.175958i | ||||||
\(754\) | 37.0711 | 1.35005 | ||||||||
\(755\) | 1.70711 | − | 5.12132i | 0.0621280 | − | 0.186384i | ||||
\(756\) | 2.41421 | 0.0878041 | ||||||||
\(757\) | 16.2132i | 0.589279i | 0.955608 | + | 0.294639i | \(0.0951995\pi\) | ||||
−0.955608 | + | 0.294639i | \(0.904800\pi\) | |||||||
\(758\) | 28.7279i | 1.04345i | ||||||||
\(759\) | −19.2426 | −0.698464 | ||||||||
\(760\) | −4.60660 | − | 1.53553i | −0.167099 | − | 0.0556997i | ||||
\(761\) | 25.3137 | 0.917621 | 0.458811 | − | 0.888534i | \(-0.348276\pi\) | ||||
0.458811 | + | 0.888534i | \(0.348276\pi\) | |||||||
\(762\) | − | 9.58579i | − | 0.347256i | ||||||
\(763\) | − | 11.4853i | − | 0.415795i | ||||||
\(764\) | −8.65685 | −0.313194 | ||||||||
\(765\) | 7.60660 | + | 2.53553i | 0.275017 | + | 0.0916724i | ||||
\(766\) | 14.6569 | 0.529574 | ||||||||
\(767\) | 68.5269i | 2.47436i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 19.5563 | 0.705220 | 0.352610 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352610 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(770\) | 10.9497 | − | 32.8492i | 0.394602 | − | 1.18380i | ||||
\(771\) | 9.58579 | 0.345224 | ||||||||
\(772\) | 9.31371i | 0.335208i | ||||||||
\(773\) | 14.6569i | 0.527170i | 0.964636 | + | 0.263585i | \(0.0849050\pi\) | ||||
−0.964636 | + | 0.263585i | \(0.915095\pi\) | |||||||
\(774\) | 10.4853 | 0.376886 | ||||||||
\(775\) | 14.6274 | + | 10.9706i | 0.525432 | + | 0.394074i | ||||
\(776\) | 6.72792 | 0.241518 | ||||||||
\(777\) | 2.41421i | 0.0866094i | ||||||||
\(778\) | 22.9706i | 0.823535i | ||||||||
\(779\) | −14.3015 | −0.512405 | ||||||||
\(780\) | −3.70711 | + | 11.1213i | −0.132736 | + | 0.398207i | ||||
\(781\) | 60.3848 | 2.16074 | ||||||||
\(782\) | 10.7574i | 0.384682i | ||||||||
\(783\) | − | 7.07107i | − | 0.252699i | ||||||
\(784\) | 1.17157 | 0.0418419 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.89949 | 0.0677527 | ||||||||
\(787\) | 38.4853i | 1.37185i | 0.727671 | + | 0.685926i | \(0.240603\pi\) | ||||
−0.727671 | + | 0.685926i | \(0.759397\pi\) | |||||||
\(788\) | 15.1421i | 0.539416i | ||||||||
\(789\) | 31.4142 | 1.11838 | ||||||||
\(790\) | −25.9706 | − | 8.65685i | −0.923991 | − | 0.307997i | ||||
\(791\) | 6.82843 | 0.242791 | ||||||||
\(792\) | − | 6.41421i | − | 0.227919i | ||||||
\(793\) | − | 34.0000i | − | 1.20738i | ||||||
\(794\) | −8.48528 | −0.301131 | ||||||||
\(795\) | −2.70711 | + | 8.12132i | −0.0960112 | + | 0.288034i | ||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | 50.8701i | 1.80191i | 0.433913 | + | 0.900955i | \(0.357133\pi\) | ||||
−0.433913 | + | 0.900955i | \(0.642867\pi\) | |||||||
\(798\) | 5.24264i | 0.185587i | ||||||||
\(799\) | 42.6690 | 1.50952 | ||||||||
\(800\) | 3.00000 | − | 4.00000i | 0.106066 | − | 0.141421i | ||||
\(801\) | 2.89949 | 0.102449 | ||||||||
\(802\) | − | 15.0416i | − | 0.531138i | ||||||
\(803\) | − | 13.9289i | − | 0.491541i | ||||||
\(804\) | −0.828427 | −0.0292164 | ||||||||
\(805\) | −5.12132 | + | 15.3640i | −0.180503 | + | 0.541508i | ||||
\(806\) | 19.1716 | 0.675290 | ||||||||
\(807\) | − | 25.6274i | − | 0.902128i | ||||||
\(808\) | 5.31371i | 0.186936i | ||||||||
\(809\) | −11.7868 | −0.414402 | −0.207201 | − | 0.978298i | \(-0.566435\pi\) | ||||
−0.207201 | + | 0.978298i | \(0.566435\pi\) | |||||||
\(810\) | 2.12132 | + | 0.707107i | 0.0745356 | + | 0.0248452i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 17.0711i | 0.599077i | ||||||||
\(813\) | 6.82843i | 0.239483i | ||||||||
\(814\) | 6.41421 | 0.224818 | ||||||||
\(815\) | 32.1213 | + | 10.7071i | 1.12516 | + | 0.375054i | ||||
\(816\) | −3.58579 | −0.125528 | ||||||||
\(817\) | 22.7696i | 0.796606i | ||||||||
\(818\) | − | 32.3848i | − | 1.13231i | ||||||
\(819\) | 12.6569 | 0.442266 | ||||||||
\(820\) | 4.65685 | − | 13.9706i | 0.162624 | − | 0.487873i | ||||
\(821\) | −51.2843 | −1.78983 | −0.894917 | − | 0.446233i | \(-0.852765\pi\) | ||||
−0.894917 | + | 0.446233i | \(0.852765\pi\) | |||||||
\(822\) | − | 17.5563i | − | 0.612348i | ||||||
\(823\) | 7.72792i | 0.269378i | 0.990888 | + | 0.134689i | \(0.0430036\pi\) | ||||
−0.990888 | + | 0.134689i | \(0.956996\pi\) | |||||||
\(824\) | −15.0711 | −0.525026 | ||||||||
\(825\) | 19.2426 | − | 25.6569i | 0.669943 | − | 0.893257i | ||||
\(826\) | −31.5563 | −1.09799 | ||||||||
\(827\) | 7.07107i | 0.245885i | 0.992414 | + | 0.122943i | \(0.0392331\pi\) | ||||
−0.992414 | + | 0.122943i | \(0.960767\pi\) | |||||||
\(828\) | 3.00000i | 0.104257i | ||||||||
\(829\) | 19.2426 | 0.668325 | 0.334162 | − | 0.942516i | \(-0.391547\pi\) | ||||
0.334162 | + | 0.942516i | \(0.391547\pi\) | |||||||
\(830\) | −4.87868 | + | 14.6360i | −0.169341 | + | 0.508024i | ||||
\(831\) | 2.89949 | 0.100582 | ||||||||
\(832\) | − | 5.24264i | − | 0.181756i | ||||||
\(833\) | − | 4.20101i | − | 0.145556i | ||||||
\(834\) | 2.48528 | 0.0860583 | ||||||||
\(835\) | 39.5772 | + | 13.1924i | 1.36962 | + | 0.456541i | ||||
\(836\) | 13.9289 | 0.481742 | ||||||||
\(837\) | − | 3.65685i | − | 0.126399i | ||||||
\(838\) | 27.7279i | 0.957845i | ||||||||
\(839\) | −21.2132 | −0.732361 | −0.366181 | − | 0.930544i | \(-0.619335\pi\) | ||||
−0.366181 | + | 0.930544i | \(0.619335\pi\) | |||||||
\(840\) | −5.12132 | − | 1.70711i | −0.176702 | − | 0.0589008i | ||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | − | 13.4558i | − | 0.463719i | ||||||
\(843\) | 13.3848i | 0.460996i | ||||||||
\(844\) | −10.3848 | −0.357459 | ||||||||
\(845\) | −10.2426 | + | 30.7279i | −0.352358 | + | 1.05707i | ||||
\(846\) | 11.8995 | 0.409113 | ||||||||
\(847\) | 72.7696i | 2.50039i | ||||||||
\(848\) | − | 3.82843i | − | 0.131469i | ||||||
\(849\) | −18.7990 | −0.645180 | ||||||||
\(850\) | −14.3431 | − | 10.7574i | −0.491966 | − | 0.368974i | ||||
\(851\) | −3.00000 | −0.102839 | ||||||||
\(852\) | − | 9.41421i | − | 0.322526i | ||||||
\(853\) | 42.8406i | 1.46683i | 0.679779 | + | 0.733417i | \(0.262076\pi\) | ||||
−0.679779 | + | 0.733417i | \(0.737924\pi\) | |||||||
\(854\) | 15.6569 | 0.535767 | ||||||||
\(855\) | −1.53553 | + | 4.60660i | −0.0525142 | + | 0.157542i | ||||
\(856\) | −16.0711 | −0.549298 | ||||||||
\(857\) | − | 56.4975i | − | 1.92992i | −0.262403 | − | 0.964958i | \(-0.584515\pi\) | ||
0.262403 | − | 0.964958i | \(-0.415485\pi\) | |||||||
\(858\) | − | 33.6274i | − | 1.14802i | ||||||
\(859\) | 23.4853 | 0.801307 | 0.400654 | − | 0.916230i | \(-0.368783\pi\) | ||||
0.400654 | + | 0.916230i | \(0.368783\pi\) | |||||||
\(860\) | −22.2426 | − | 7.41421i | −0.758468 | − | 0.252823i | ||||
\(861\) | −15.8995 | −0.541853 | ||||||||
\(862\) | 29.8284i | 1.01596i | ||||||||
\(863\) | 25.5563i | 0.869948i | 0.900443 | + | 0.434974i | \(0.143242\pi\) | ||||
−0.900443 | + | 0.434974i | \(0.856758\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 1.39340 | + | 0.464466i | 0.0473770 | + | 0.0157923i | ||||
\(866\) | −23.4853 | −0.798062 | ||||||||
\(867\) | − | 4.14214i | − | 0.140674i | ||||||
\(868\) | 8.82843i | 0.299656i | ||||||||
\(869\) | 78.5269 | 2.66384 | ||||||||
\(870\) | −5.00000 | + | 15.0000i | −0.169516 | + | 0.508548i | ||||
\(871\) | −4.34315 | −0.147162 | ||||||||
\(872\) | 4.75736i | 0.161105i | ||||||||
\(873\) | − | 6.72792i | − | 0.227706i | ||||||
\(874\) | −6.51472 | −0.220364 | ||||||||
\(875\) | −15.3640 | − | 22.1924i | −0.519397 | − | 0.750240i | ||||
\(876\) | −2.17157 | −0.0733706 | ||||||||
\(877\) | 40.2426i | 1.35890i | 0.733723 | + | 0.679449i | \(0.237781\pi\) | ||||
−0.733723 | + | 0.679449i | \(0.762219\pi\) | |||||||
\(878\) | − | 24.7279i | − | 0.834527i | ||||||
\(879\) | −8.65685 | −0.291988 | ||||||||
\(880\) | −4.53553 | + | 13.6066i | −0.152893 | + | 0.458678i | ||||
\(881\) | 18.6274 | 0.627574 | 0.313787 | − | 0.949493i | \(-0.398402\pi\) | ||||
0.313787 | + | 0.949493i | \(0.398402\pi\) | |||||||
\(882\) | − | 1.17157i | − | 0.0394489i | ||||||
\(883\) | 22.0294i | 0.741350i | 0.928763 | + | 0.370675i | \(0.120874\pi\) | ||||
−0.928763 | + | 0.370675i | \(0.879126\pi\) | |||||||
\(884\) | −18.7990 | −0.632278 | ||||||||
\(885\) | −27.7279 | − | 9.24264i | −0.932064 | − | 0.310688i | ||||
\(886\) | −23.6569 | −0.794768 | ||||||||
\(887\) | 20.1421i | 0.676307i | 0.941091 | + | 0.338153i | \(0.109802\pi\) | ||||
−0.941091 | + | 0.338153i | \(0.890198\pi\) | |||||||
\(888\) | − | 1.00000i | − | 0.0335578i | ||||||
\(889\) | 23.1421 | 0.776162 | ||||||||
\(890\) | −6.15076 | − | 2.05025i | −0.206174 | − | 0.0687246i | ||||
\(891\) | −6.41421 | −0.214884 | ||||||||
\(892\) | − | 9.65685i | − | 0.323335i | ||||||
\(893\) | 25.8406i | 0.864723i | ||||||||
\(894\) | −3.51472 | −0.117550 | ||||||||
\(895\) | 13.3137 | − | 39.9411i | 0.445028 | − | 1.33508i | ||||
\(896\) | 2.41421 | 0.0806532 | ||||||||
\(897\) | 15.7279i | 0.525140i | ||||||||
\(898\) | 13.7990i | 0.460478i | ||||||||
\(899\) | 25.8579 | 0.862408 | ||||||||
\(900\) | −4.00000 | − | 3.00000i | −0.133333 | − | 0.100000i | ||||
\(901\) | −13.7279 | −0.457343 | ||||||||
\(902\) | 42.2426i | 1.40653i | ||||||||
\(903\) | 25.3137i | 0.842387i | ||||||||
\(904\) | −2.82843 | −0.0940721 | ||||||||
\(905\) | 14.5563 | − | 43.6690i | 0.483869 | − | 1.45161i | ||||
\(906\) | 2.41421 | 0.0802069 | ||||||||
\(907\) | 2.79899i | 0.0929389i | 0.998920 | + | 0.0464695i | \(0.0147970\pi\) | ||||
−0.998920 | + | 0.0464695i | \(0.985203\pi\) | |||||||
\(908\) | 12.0000i | 0.398234i | ||||||||
\(909\) | 5.31371 | 0.176245 | ||||||||
\(910\) | −26.8492 | − | 8.94975i | −0.890044 | − | 0.296681i | ||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | − | 2.17157i | − | 0.0719080i | ||||||
\(913\) | − | 44.2548i | − | 1.46462i | ||||||
\(914\) | 0.970563 | 0.0321034 | ||||||||
\(915\) | 13.7574 | + | 4.58579i | 0.454804 | + | 0.151601i | ||||
\(916\) | 18.7279 | 0.618788 | ||||||||
\(917\) | 4.58579i | 0.151436i | ||||||||
\(918\) | 3.58579i | 0.118349i | ||||||||
\(919\) | −16.2426 | −0.535795 | −0.267898 | − | 0.963447i | \(-0.586329\pi\) | ||||
−0.267898 | + | 0.963447i | \(0.586329\pi\) | |||||||
\(920\) | 2.12132 | − | 6.36396i | 0.0699379 | − | 0.209814i | ||||
\(921\) | 13.8995 | 0.458004 | ||||||||
\(922\) | 20.8284i | 0.685948i | ||||||||
\(923\) | − | 49.3553i | − | 1.62455i | ||||||
\(924\) | 15.4853 | 0.509428 | ||||||||
\(925\) | 3.00000 | − | 4.00000i | 0.0986394 | − | 0.131519i | ||||
\(926\) | −29.8995 | −0.982558 | ||||||||
\(927\) | 15.0711i | 0.494999i | ||||||||
\(928\) | − | 7.07107i | − | 0.232119i | ||||||
\(929\) | −2.48528 | −0.0815394 | −0.0407697 | − | 0.999169i | \(-0.512981\pi\) | ||||
−0.0407697 | + | 0.999169i | \(0.512981\pi\) | |||||||
\(930\) | −2.58579 | + | 7.75736i | −0.0847913 | + | 0.254374i | ||||
\(931\) | 2.54416 | 0.0833813 | ||||||||
\(932\) | 2.48528i | 0.0814081i | ||||||||
\(933\) | 12.8284i | 0.419984i | ||||||||
\(934\) | 40.2426 | 1.31678 | ||||||||
\(935\) | 48.7904 | + | 16.2635i | 1.59562 | + | 0.531872i | ||||
\(936\) | −5.24264 | −0.171361 | ||||||||
\(937\) | 49.9411i | 1.63151i | 0.578401 | + | 0.815753i | \(0.303677\pi\) | ||||
−0.578401 | + | 0.815753i | \(0.696323\pi\) | |||||||
\(938\) | − | 2.00000i | − | 0.0653023i | ||||||
\(939\) | −2.72792 | −0.0890224 | ||||||||
\(940\) | −25.2426 | − | 8.41421i | −0.823324 | − | 0.274441i | ||||
\(941\) | −37.6569 | −1.22758 | −0.613789 | − | 0.789470i | \(-0.710356\pi\) | ||||
−0.613789 | + | 0.789470i | \(0.710356\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19.7574i | − | 0.643388i | ||||||
\(944\) | 13.0711 | 0.425427 | ||||||||
\(945\) | −1.70711 | + | 5.12132i | −0.0555322 | + | 0.166597i | ||||
\(946\) | 67.2548 | 2.18664 | ||||||||
\(947\) | 28.0416i | 0.911231i | 0.890177 | + | 0.455615i | \(0.150581\pi\) | ||||
−0.890177 | + | 0.455615i | \(0.849419\pi\) | |||||||
\(948\) | − | 12.2426i | − | 0.397622i | ||||||
\(949\) | −11.3848 | −0.369565 | ||||||||
\(950\) | 6.51472 | − | 8.68629i | 0.211365 | − | 0.281821i | ||||
\(951\) | −21.1716 | −0.686535 | ||||||||
\(952\) | − | 8.65685i | − | 0.280570i | ||||||
\(953\) | − | 0.585786i | − | 0.0189755i | −0.999955 | − | 0.00948774i | \(-0.996980\pi\) | ||
0.999955 | − | 0.00948774i | \(-0.00302009\pi\) | |||||||
\(954\) | −3.82843 | −0.123950 | ||||||||
\(955\) | 6.12132 | − | 18.3640i | 0.198081 | − | 0.594244i | ||||
\(956\) | 20.6274 | 0.667138 | ||||||||
\(957\) | − | 45.3553i | − | 1.46613i | ||||||
\(958\) | − | 6.17157i | − | 0.199394i | ||||||
\(959\) | 42.3848 | 1.36868 | ||||||||
\(960\) | 2.12132 | + | 0.707107i | 0.0684653 | + | 0.0228218i | ||||
\(961\) | −17.6274 | −0.568626 | ||||||||
\(962\) | − | 5.24264i | − | 0.169030i | ||||||
\(963\) | 16.0711i | 0.517883i | ||||||||
\(964\) | −2.58579 | −0.0832826 | ||||||||
\(965\) | −19.7574 | − | 6.58579i | −0.636012 | − | 0.212004i | ||||
\(966\) | −7.24264 | −0.233028 | ||||||||
\(967\) | − | 59.8995i | − | 1.92624i | −0.269076 | − | 0.963119i | \(-0.586718\pi\) | ||
0.269076 | − | 0.963119i | \(-0.413282\pi\) | |||||||
\(968\) | − | 30.1421i | − | 0.968805i | ||||||
\(969\) | −7.78680 | −0.250148 | ||||||||
\(970\) | −4.75736 | + | 14.2721i | −0.152750 | + | 0.458249i | ||||
\(971\) | 10.9706 | 0.352062 | 0.176031 | − | 0.984385i | \(-0.443674\pi\) | ||||
0.176031 | + | 0.984385i | \(0.443674\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 6.00000i | 0.192351i | ||||||||
\(974\) | 30.0000 | 0.961262 | ||||||||
\(975\) | −20.9706 | − | 15.7279i | −0.671595 | − | 0.503697i | ||||
\(976\) | −6.48528 | −0.207589 | ||||||||
\(977\) | − | 38.6985i | − | 1.23807i | −0.785362 | − | 0.619037i | \(-0.787523\pi\) | ||
0.785362 | − | 0.619037i | \(-0.212477\pi\) | |||||||
\(978\) | 15.1421i | 0.484192i | ||||||||
\(979\) | 18.5980 | 0.594394 | ||||||||
\(980\) | −0.828427 | + | 2.48528i | −0.0264631 | + | 0.0793894i | ||||
\(981\) | 4.75736 | 0.151891 | ||||||||
\(982\) | − | 16.4142i | − | 0.523799i | ||||||
\(983\) | 25.1127i | 0.800971i | 0.916303 | + | 0.400485i | \(0.131158\pi\) | ||||
−0.916303 | + | 0.400485i | \(0.868842\pi\) | |||||||
\(984\) | 6.58579 | 0.209947 | ||||||||
\(985\) | −32.1213 | − | 10.7071i | −1.02347 | − | 0.341157i | ||||
\(986\) | −25.3553 | −0.807478 | ||||||||
\(987\) | 28.7279i | 0.914420i | ||||||||
\(988\) | − | 11.3848i | − | 0.362198i | ||||||
\(989\) | −31.4558 | −1.00024 | ||||||||
\(990\) | 13.6066 | + | 4.53553i | 0.432446 | + | 0.144149i | ||||
\(991\) | 14.6274 | 0.464655 | 0.232328 | − | 0.972638i | \(-0.425366\pi\) | ||||
0.232328 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(992\) | − | 3.65685i | − | 0.116105i | ||||||
\(993\) | − | 23.4558i | − | 0.744349i | ||||||
\(994\) | 22.7279 | 0.720886 | ||||||||
\(995\) | −14.1421 | + | 42.4264i | −0.448336 | + | 1.34501i | ||||
\(996\) | −6.89949 | −0.218619 | ||||||||
\(997\) | − | 52.2132i | − | 1.65361i | −0.562490 | − | 0.826804i | \(-0.690156\pi\) | ||
0.562490 | − | 0.826804i | \(-0.309844\pi\) | |||||||
\(998\) | − | 7.48528i | − | 0.236942i | ||||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 1110.2.d.g.889.4 | yes | 4 | |
3.2 | odd | 2 | 3330.2.d.k.1999.1 | 4 | |||
5.2 | odd | 4 | 5550.2.a.bs.1.1 | 2 | |||
5.3 | odd | 4 | 5550.2.a.cb.1.2 | 2 | |||
5.4 | even | 2 | inner | 1110.2.d.g.889.2 | ✓ | 4 | |
15.14 | odd | 2 | 3330.2.d.k.1999.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.d.g.889.2 | ✓ | 4 | 5.4 | even | 2 | inner | |
1110.2.d.g.889.4 | yes | 4 | 1.1 | even | 1 | trivial | |
3330.2.d.k.1999.1 | 4 | 3.2 | odd | 2 | |||
3330.2.d.k.1999.3 | 4 | 15.14 | odd | 2 | |||
5550.2.a.bs.1.1 | 2 | 5.2 | odd | 4 | |||
5550.2.a.cb.1.2 | 2 | 5.3 | odd | 4 |