Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(575,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("672.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.h (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.8 | ||
Root | \(-1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.575 |
Dual form | 672.2.h.e.575.5 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 1.58114i | 0.408248 | + | 0.912871i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.47214 | −1.34840 | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.16228 | −1.98646 | −0.993229 | − | 0.116171i | \(-0.962938\pi\) | ||||
−0.993229 | + | 0.116171i | \(0.962938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.23607 | + | 1.00000i | −0.577350 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.30056i | 1.77065i | 0.464976 | + | 0.885323i | \(0.346063\pi\) | ||||
−0.464976 | + | 0.885323i | \(0.653937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.837722i | − | 0.192187i | −0.995372 | − | 0.0960933i | \(-0.969365\pi\) | ||
0.995372 | − | 0.0960933i | \(-0.0306347\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.58114 | − | 0.707107i | 0.345033 | − | 0.154303i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.94975 | − | 1.58114i | −0.952579 | − | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.64371i | 0.305229i | 0.988286 | + | 0.152615i | \(0.0487693\pi\) | ||||
−0.988286 | + | 0.152615i | \(0.951231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32456i | − | 1.13592i | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||
0.823055 | − | 0.567962i | \(-0.192268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.16228 | − | 7.07107i | −0.550482 | − | 1.23091i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | 0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.32456 | 0.710953 | 0.355476 | − | 0.934685i | \(-0.384319\pi\) | ||||
0.355476 | + | 0.934685i | \(0.384319\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.06450 | − | 11.3246i | −0.810968 | − | 1.81338i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1290i | 1.58188i | 0.611892 | + | 0.790941i | \(0.290409\pi\) | ||||
−0.611892 | + | 0.790941i | \(0.709591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.32456i | 1.26948i | 0.772725 | + | 0.634741i | \(0.218893\pi\) | ||||
−0.772725 | + | 0.634741i | \(0.781107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.16228 | − | 2.82843i | −0.471405 | − | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.94427 | −1.30466 | −0.652328 | − | 0.757937i | \(-0.726208\pi\) | ||||
−0.652328 | + | 0.757937i | \(0.726208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.5432 | + | 5.16228i | −1.61637 | + | 0.722863i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.18472i | 0.162734i | 0.996684 | + | 0.0813668i | \(0.0259285\pi\) | ||||
−0.996684 | + | 0.0813668i | \(0.974071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.32456i | − | 0.852803i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.32456 | − | 0.592359i | 0.175442 | − | 0.0784599i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | −0.184115 | −0.0920575 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920575 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.16228 | 0.404888 | 0.202444 | − | 0.979294i | \(-0.435112\pi\) | ||||
0.202444 | + | 0.979294i | \(0.435112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.23607 | + | 2.00000i | 0.281718 | + | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.1290i | − | 1.25635i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.00000i | − | 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | + | 8.94427i | 0.481543 | + | 1.07676i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1290 | 1.20209 | 0.601045 | − | 0.799215i | \(-0.294751\pi\) | ||||
0.601045 | + | 0.799215i | \(0.294751\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.32456 | 0.506151 | 0.253075 | − | 0.967447i | \(-0.418558\pi\) | ||||
0.253075 | + | 0.967447i | \(0.418558\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.12132 | + | 4.74342i | 0.244949 | + | 0.547723i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.47214i | 0.509647i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.53006 | 0.826531 | 0.413266 | − | 0.910611i | \(-0.364388\pi\) | ||||
0.413266 | + | 0.910611i | \(0.364388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3246 | −1.11986 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.59893 | + | 1.16228i | −0.278635 | + | 0.124609i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.18472i | 0.125580i | 0.998027 | + | 0.0627899i | \(0.0199998\pi\) | ||||
−0.998027 | + | 0.0627899i | \(0.980000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.16228i | 0.750811i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0000 | − | 4.47214i | 1.03695 | − | 0.463739i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.18472 | 0.121550 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6491 | −1.08125 | −0.540627 | − | 0.841263i | \(-0.681813\pi\) | ||||
−0.540627 | + | 0.841263i | \(0.681813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.94427 | − | 10.0000i | 0.898933 | − | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.41421i | 0.140720i | 0.997522 | + | 0.0703598i | \(0.0224147\pi\) | ||||
−0.997522 | + | 0.0703598i | \(0.977585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | + | 2.23607i | 0.0975900 | + | 0.218218i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.67000 | 0.934834 | 0.467417 | − | 0.884037i | \(-0.345185\pi\) | ||||
0.467417 | + | 0.884037i | \(0.345185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.32456 | −0.414217 | −0.207109 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207109 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.05792 | + | 6.83772i | 0.290245 | + | 0.649008i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.84157i | 0.643601i | 0.946807 | + | 0.321801i | \(0.104288\pi\) | ||||
−0.946807 | + | 0.321801i | \(0.895712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000i | 0.746004i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.3246 | − | 16.0153i | 1.32431 | − | 1.48062i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.30056 | 0.669242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.0153 | + | 7.16228i | −1.44405 | + | 0.645801i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000i | 0.532414i | 0.963916 | + | 0.266207i | \(0.0857705\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1623 | + | 5.88635i | −1.15887 | + | 0.518264i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.70163 | 0.410783 | 0.205392 | − | 0.978680i | \(-0.434153\pi\) | ||||
0.205392 | + | 0.978680i | \(0.434153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.837722 | −0.0726397 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23607 | − | 7.00000i | 0.192450 | − | 0.602464i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.8885i | − | 1.52832i | −0.645026 | − | 0.764161i | \(-0.723153\pi\) | ||
0.645026 | − | 0.764161i | \(-0.276847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.16228i | 0.607496i | 0.952752 | + | 0.303748i | \(0.0982382\pi\) | ||||
−0.952752 | + | 0.303748i | \(0.901762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.32456 | − | 14.1421i | −0.532624 | − | 1.19098i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32.0307 | 2.67854 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.32456 | −0.193044 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.707107 | − | 1.58114i | −0.0583212 | − | 0.130410i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.47214i | − | 0.366372i | −0.983078 | − | 0.183186i | \(-0.941359\pi\) | ||
0.983078 | − | 0.183186i | \(-0.0586410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.3246 | − | 14.6011i | −1.31976 | − | 1.18043i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.94427 | 0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.4868 | −1.07637 | −0.538183 | − | 0.842828i | \(-0.680889\pi\) | ||||
−0.538183 | + | 0.842828i | \(0.680889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.87320 | + | 0.837722i | −0.148555 | + | 0.0664357i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.65685i | − | 0.445823i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.32456i | 0.338725i | 0.985554 | + | 0.169363i | \(0.0541709\pi\) | ||||
−0.985554 | + | 0.169363i | \(0.945829\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.0000 | − | 4.47214i | 0.778499 | − | 0.348155i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.458991 | 0.0355178 | 0.0177589 | − | 0.999842i | \(-0.494347\pi\) | ||||
0.0177589 | + | 0.999842i | \(0.494347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38.2982 | 2.94602 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.87320 | + | 1.67544i | 0.143247 | + | 0.128124i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.78365i | 0.287666i | 0.989602 | + | 0.143833i | \(0.0459427\pi\) | ||||
−0.989602 | + | 0.143833i | \(0.954057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.00000i | − | 0.226779i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | − | 2.23607i | −0.0751646 | − | 0.168073i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.5323 | −1.45991 | −0.729955 | − | 0.683496i | \(-0.760459\pi\) | ||||
−0.729955 | + | 0.683496i | \(0.760459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1359 | 1.34803 | 0.674017 | − | 0.738716i | \(-0.264567\pi\) | ||||
0.674017 | + | 0.738716i | \(0.264567\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.23607 | + | 5.00000i | 0.165295 | + | 0.369611i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.11584i | 0.449646i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 32.6491i | − | 2.38754i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.58114 | + | 4.94975i | −0.115011 | + | 0.360041i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4984 | −0.904354 | −0.452177 | − | 0.891928i | \(-0.649353\pi\) | ||||
−0.452177 | + | 0.891928i | \(0.649353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.0153 | − | 7.16228i | 1.14688 | − | 0.512901i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1290i | 0.721661i | 0.932631 | + | 0.360830i | \(0.117507\pi\) | ||||
−0.932631 | + | 0.360830i | \(0.882493\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.6491i | 1.74733i | 0.486529 | + | 0.873665i | \(0.338263\pi\) | ||||
−0.486529 | + | 0.873665i | \(0.661737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.16228 | − | 1.41421i | 0.223050 | − | 0.0997509i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.64371 | 0.115366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.3246 | −1.00047 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.3137 | + | 12.6491i | −0.786357 | + | 0.879174i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.74641i | 0.259144i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.35089i | 0.0929991i | 0.998918 | + | 0.0464995i | \(0.0148066\pi\) | ||||
−0.998918 | + | 0.0464995i | \(0.985193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.16228 | + | 16.0153i | 0.490751 | + | 1.09735i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.7727 | −0.802891 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.32456 | −0.429339 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.05792 | + | 6.83772i | 0.206635 | + | 0.462050i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 52.2887i | − | 3.51732i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.32456i | 0.155664i | 0.996966 | + | 0.0778319i | \(0.0247997\pi\) | ||||
−0.996966 | + | 0.0778319i | \(0.975200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 6.70820i | −0.400000 | + | 0.447214i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1869 | 0.875246 | 0.437623 | − | 0.899159i | \(-0.355820\pi\) | ||||
0.437623 | + | 0.899159i | \(0.355820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.81139 | 0.251864 | 0.125932 | − | 0.992039i | \(-0.459808\pi\) | ||||
0.125932 | + | 0.992039i | \(0.459808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.07107 | + | 3.16228i | −0.465242 | + | 0.208063i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65685i | 0.370593i | 0.982683 | + | 0.185296i | \(0.0593245\pi\) | ||||
−0.982683 | + | 0.185296i | \(0.940675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.6491i | − | 0.825137i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.32456 | − | 2.82843i | 0.410824 | − | 0.183726i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.9148 | −1.67629 | −0.838146 | − | 0.545446i | \(-0.816360\pi\) | ||||
−0.838146 | + | 0.545446i | \(0.816360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.4350 | − | 7.90569i | 0.861858 | − | 0.507151i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.41421i | − | 0.0903508i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.32456 | + | 11.9061i | 0.337430 | + | 0.754516i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8438 | 1.18941 | 0.594704 | − | 0.803945i | \(-0.297269\pi\) | ||||
0.594704 | + | 0.803945i | \(0.297269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.2982 | −1.59049 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.30056 | − | 16.3246i | −0.457179 | − | 1.02228i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 16.2448i | − | 1.01332i | −0.862144 | − | 0.506662i | \(-0.830879\pi\) | ||
0.862144 | − | 0.506662i | \(-0.169121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.32456i | − | 0.268715i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.67544 | − | 3.28742i | −0.227504 | − | 0.203486i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.10270 | −0.129658 | −0.0648290 | − | 0.997896i | \(-0.520650\pi\) | ||||
−0.0648290 | + | 0.997896i | \(0.520650\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.67544 | −0.102922 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.87320 | + | 0.837722i | −0.114638 | + | 0.0512678i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.61208i | − | 0.403145i | −0.979474 | − | 0.201573i | \(-0.935395\pi\) | ||
0.979474 | − | 0.201573i | \(-0.0646052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.67544i | − | 0.101776i | −0.998704 | − | 0.0508880i | \(-0.983795\pi\) | ||
0.998704 | − | 0.0508880i | \(-0.0162052\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.3246 | + | 5.06450i | −0.685393 | + | 0.306517i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.4164 | −0.809040 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.1421 | + | 12.6491i | 0.846668 | + | 0.757282i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.5454i | 1.40460i | 0.711881 | + | 0.702300i | \(0.247844\pi\) | ||||
−0.711881 | + | 0.702300i | \(0.752156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.51317i | − | 0.387168i | −0.981084 | − | 0.193584i | \(-0.937989\pi\) | ||
0.981084 | − | 0.193584i | \(-0.0620111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.837722 | + | 1.87320i | 0.0496224 | + | 0.110959i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1290 | 0.597895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.2982 | −2.13519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.53006 | − | 16.8377i | −0.441420 | − | 0.987045i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.1312i | 1.29292i | 0.762949 | + | 0.646459i | \(0.223751\pi\) | ||||
−0.762949 | + | 0.646459i | \(0.776249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.00000i | − | 0.116445i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.1359 | + | 7.07107i | 1.28446 | + | 0.410305i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −40.5160 | −2.34310 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.32456 | 0.479819 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.23607 | + | 1.00000i | −0.128459 | + | 0.0574485i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.47214i | 0.256074i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.51317i | 0.143434i | 0.997425 | + | 0.0717170i | \(0.0228478\pi\) | ||||
−0.997425 | + | 0.0717170i | \(0.977152\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.6491 | + | 5.65685i | −0.719583 | + | 0.321807i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.4296 | −0.988339 | −0.494170 | − | 0.869365i | \(-0.664528\pi\) | ||||
−0.494170 | + | 0.869365i | \(0.664528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.97367 | −0.281128 | −0.140564 | − | 0.990072i | \(-0.544892\pi\) | ||||
−0.140564 | + | 0.990072i | \(0.544892\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.82843 | + | 3.16228i | −0.159364 | + | 0.178174i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.75955i | 0.435820i | 0.975969 | + | 0.217910i | \(0.0699239\pi\) | ||||
−0.975969 | + | 0.217910i | \(0.930076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.35089i | − | 0.411571i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.83772 | + | 15.2896i | 0.381644 | + | 0.853383i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.11584 | 0.340295 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.4868 | −1.19188 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.05792 | − | 6.83772i | −0.169103 | − | 0.378127i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.94427i | 0.493114i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 28.9737i | − | 1.59254i | −0.604944 | − | 0.796268i | \(-0.706804\pi\) | ||
0.604944 | − | 0.796268i | \(-0.293196\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.64911 | + | 9.67000i | −0.473968 | + | 0.529913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.82843 | 0.154533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.35089 | −0.400428 | −0.200214 | − | 0.979752i | \(-0.564164\pi\) | ||||
−0.200214 | + | 0.979752i | \(0.564164\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.8175 | + | 4.83772i | −0.587525 | + | 0.262749i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.2843i | 1.53168i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.6491 | + | 5.65685i | −0.681005 | + | 0.304555i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.4427 | 1.15110 | 0.575552 | − | 0.817765i | \(-0.304787\pi\) | ||||
0.575552 | + | 0.817765i | \(0.304787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8377 | −0.901303 | −0.450651 | − | 0.892700i | \(-0.648808\pi\) | ||||
−0.450651 | + | 0.892700i | \(0.648808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.4515 | + | 11.3246i | 1.89226 | + | 0.604460i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.9574i | − | 0.689654i | −0.938666 | − | 0.344827i | \(-0.887938\pi\) | ||
0.938666 | − | 0.344827i | \(-0.112062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.3246i | 0.760268i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.16228 | + | 11.5432i | 0.273217 | + | 0.610931i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.2317 | −0.645564 | −0.322782 | − | 0.946473i | \(-0.604618\pi\) | ||||
−0.322782 | + | 0.946473i | \(0.604618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.2982 | 0.963064 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.36396 | + | 14.2302i | 0.334021 | + | 0.746894i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.11584i | 0.320118i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3246i | 0.956534i | 0.878214 | + | 0.478267i | \(0.158735\pi\) | ||||
−0.878214 | + | 0.478267i | \(0.841265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.6491 | − | 20.2580i | −1.17907 | − | 1.05459i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.18472 | 0.0615075 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.6491 | 1.58695 | 0.793475 | − | 0.608602i | \(-0.208270\pi\) | ||||
0.793475 | + | 0.608602i | \(0.208270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.8885 | + | 8.00000i | −0.923760 | + | 0.413118i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.7727i | − | 0.606325i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.3246i | − | 1.24947i | −0.780837 | − | 0.624734i | \(-0.785207\pi\) | ||
0.780837 | − | 0.624734i | \(-0.214793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.48683 | + | 4.24264i | −0.486025 | + | 0.217357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6274 | −1.15621 | −0.578103 | − | 0.815963i | \(-0.696207\pi\) | ||||
−0.578103 | + | 0.815963i | \(0.696207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.32456 | −0.322329 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.6143 | − | 16.6491i | −0.946217 | − | 0.846322i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.38258i | − | 0.323610i | −0.986823 | − | 0.161805i | \(-0.948268\pi\) | ||
0.986823 | − | 0.161805i | \(-0.0517315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.2982i | 2.08854i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.32456 | + | 7.43393i | 0.167702 | + | 0.374992i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | 0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1623 | 1.16248 | 0.581241 | − | 0.813732i | \(-0.302567\pi\) | ||||
0.581241 | + | 0.813732i | \(0.302567\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.592359 | − | 1.32456i | −0.0296550 | − | 0.0663107i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 21.4427i | − | 1.07080i | −0.844599 | − | 0.535399i | \(-0.820161\pi\) | ||
0.844599 | − | 0.535399i | \(-0.179839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.2982i | 2.25647i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.6491 | − | 1.41421i | 0.628539 | − | 0.0702728i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.3400 | −0.958648 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.6754 | −0.577314 | −0.288657 | − | 0.957433i | \(-0.593209\pi\) | ||||
−0.288657 | + | 0.957433i | \(0.593209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.2843 | − | 12.6491i | 1.39516 | − | 0.623935i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.41421i | 0.0695889i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6491i | 0.522744i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3246 | + | 5.06450i | −0.554566 | + | 0.248009i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.7880 | −1.35753 | −0.678767 | − | 0.734353i | \(-0.737485\pi\) | ||||
−0.678767 | + | 0.734353i | \(0.737485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.6491 | −1.10385 | −0.551925 | − | 0.833894i | \(-0.686107\pi\) | ||||
−0.551925 | + | 0.833894i | \(0.686107\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.8885 | − | 20.0000i | 0.869771 | − | 0.972433i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.9017i | 1.06239i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.16228i | − | 0.153033i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.6491 | + | 50.6450i | 1.09351 | + | 2.44516i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.6011 | −0.703311 | −0.351656 | − | 0.936129i | \(-0.614381\pi\) | ||||
−0.351656 | + | 0.936129i | \(0.614381\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.00000 | 0.288342 | 0.144171 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144171 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.64371 | − | 3.67544i | −0.0788098 | − | 0.176224i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.73887i | − | 0.226691i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.649111i | − | 0.0309804i | −0.999880 | − | 0.0154902i | \(-0.995069\pi\) | ||
0.999880 | − | 0.0154902i | \(-0.00493087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | − | 2.23607i | 0.0952381 | − | 0.106479i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.01315 | −0.190670 | −0.0953351 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953351 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.67544 | −0.0794237 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.07107 | − | 3.16228i | 0.334450 | − | 0.149571i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9706i | 0.800890i | 0.916321 | + | 0.400445i | \(0.131145\pi\) | ||||
−0.916321 | + | 0.400445i | \(0.868855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 45.2982i | − | 2.13301i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.8114 | − | 7.07107i | 0.742884 | − | 0.332228i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.1290 | −0.474854 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6491 | 1.15304 | 0.576518 | − | 0.817084i | \(-0.304411\pi\) | ||||
0.576518 | + | 0.817084i | \(0.304411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.5432 | − | 36.1359i | 0.538791 | − | 1.68668i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.9859i | − | 1.53631i | −0.640266 | − | 0.768153i | \(-0.721176\pi\) | ||
0.640266 | − | 0.768153i | \(-0.278824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.6491i | − | 1.88912i | −0.328333 | − | 0.944562i | \(-0.606487\pi\) | ||
0.328333 | − | 0.944562i | \(-0.393513\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.32456 | + | 14.1421i | 0.293294 | + | 0.655826i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.3290 | −1.26464 | −0.632319 | − | 0.774708i | \(-0.717897\pi\) | ||||
−0.632319 | + | 0.774708i | \(0.717897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.53663 | − | 21.3246i | −0.439425 | − | 0.982584i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 37.2285i | − | 1.71177i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.51317i | − | 0.115312i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.64911 | − | 2.36944i | −0.121294 | − | 0.108489i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.65685 | −0.258468 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.9737 | −1.41228 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.94427 | − | 4.00000i | 0.406978 | − | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 15.0601i | − | 0.683845i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.2982i | − | 1.05574i | −0.849324 | − | 0.527872i | \(-0.822990\pi\) | ||
0.849324 | − | 0.527872i | \(-0.177010\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.83772 | + | 3.05792i | −0.309212 | + | 0.138284i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.9280 | −1.35063 | −0.675315 | − | 0.737529i | \(-0.735992\pi\) | ||||
−0.675315 | + | 0.737529i | \(0.735992\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.1421 | + | 12.6491i | 0.635642 | + | 0.568535i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 10.1290i | − | 0.454347i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000i | 0.0895323i | 0.998997 | + | 0.0447661i | \(0.0142543\pi\) | ||||
−0.998997 | + | 0.0447661i | \(0.985746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.324555 | + | 0.725728i | 0.0145001 | + | 0.0324231i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7727 | 0.524919 | 0.262459 | − | 0.964943i | \(-0.415466\pi\) | ||||
0.262459 | + | 0.964943i | \(0.415466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00000 | −0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.0809 | + | 60.5548i | 1.20271 | + | 2.68933i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.70163i | 0.208396i | 0.994557 | + | 0.104198i | \(0.0332276\pi\) | ||||
−0.994557 | + | 0.104198i | \(0.966772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.32456i | − | 0.191307i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.32456 | + | 4.14651i | −0.0584805 | + | 0.183073i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3137 | −0.498542 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.0000 | 1.75920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.98248 | + | 2.67544i | −0.262602 | + | 0.117439i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.10270i | − | 0.0921209i | −0.998939 | − | 0.0460605i | \(-0.985333\pi\) | ||
0.998939 | − | 0.0460605i | \(-0.0146667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.8114i | 1.74083i | 0.492318 | + | 0.870415i | \(0.336150\pi\) | ||||
−0.492318 | + | 0.870415i | \(0.663850\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.74342 | − | 2.12132i | 0.207020 | − | 0.0925820i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.1728 | 2.01132 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.82843 | − | 3.16228i | 0.122743 | − | 0.137231i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 72.5466i | − | 3.14234i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6754i | 0.591241i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.8114 | − | 30.8832i | −0.596005 | − | 1.33271i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.47214 | 0.192629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.8240 | + | 28.6754i | 0.550333 | + | 1.23058i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.11584i | − | 0.261974i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.3246i | 1.55313i | 0.630040 | + | 0.776563i | \(0.283039\pi\) | ||||
−0.630040 | + | 0.776563i | \(0.716961\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.32456 | + | 7.07107i | −0.269925 | + | 0.301786i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.37697 | 0.0586610 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.67000 | + | 4.32456i | −0.410469 | + | 0.183567i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.7564i | 1.38793i | 0.720007 | + | 0.693967i | \(0.244139\pi\) | ||||
−0.720007 | + | 0.693967i | \(0.755861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 59.6228i | − | 2.52177i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.6228 | − | 23.0864i | 2.17952 | − | 0.974709i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.1312 | 0.932718 | 0.466359 | − | 0.884595i | \(-0.345565\pi\) | ||||
0.466359 | + | 0.884595i | \(0.345565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.67544 | −0.407049 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.94427 | + | 1.00000i | −0.375624 | + | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 29.4690i | − | 1.23540i | −0.786412 | − | 0.617702i | \(-0.788064\pi\) | ||
0.786412 | − | 0.617702i | \(-0.211936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.3246i | − | 0.515767i | −0.966176 | − | 0.257883i | \(-0.916975\pi\) | ||
0.966176 | − | 0.257883i | \(-0.0830250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.83772 | − | 19.7617i | −0.369201 | − | 0.825559i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706 | 0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.2982 | 1.46948 | 0.734742 | − | 0.678347i | \(-0.237303\pi\) | ||||
0.734742 | + | 0.678347i | \(0.237303\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3137 | + | 25.2982i | 0.470182 | + | 1.05136i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 7.53006i | − | 0.312399i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.29822i | − | 0.219430i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.6491 | + | 20.2580i | 0.936425 | + | 0.837564i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.44050 | −0.389651 | −0.194826 | − | 0.980838i | \(-0.562414\pi\) | ||||
−0.194826 | + | 0.980838i | \(0.562414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.29822 | −0.218309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0153 | + | 7.16228i | −0.658783 | + | 0.294617i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.2711i | 0.996696i | 0.866977 | + | 0.498348i | \(0.166060\pi\) | ||||
−0.866977 | + | 0.498348i | \(0.833940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3246i | 0.423266i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.9737 | + | 17.4296i | −1.59509 | + | 0.713344i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.7301 | 1.01045 | 0.505223 | − | 0.862989i | \(-0.331410\pi\) | ||||
0.505223 | + | 0.862989i | \(0.331410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.6228 | −1.20834 | −0.604169 | − | 0.796856i | \(-0.706495\pi\) | ||||
−0.604169 | + | 0.796856i | \(0.706495\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.47214 | + | 4.00000i | 0.182119 | + | 0.162893i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.7279i | 0.517464i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.6754i | − | 0.717424i | −0.933448 | − | 0.358712i | \(-0.883216\pi\) | ||
0.933448 | − | 0.358712i | \(-0.116784\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.16228 | + | 2.59893i | 0.0470979 | + | 0.105314i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.0614 | 2.59165 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6754 | 0.794684 | 0.397342 | − | 0.917671i | \(-0.369933\pi\) | ||||
0.397342 | + | 0.917671i | \(0.369933\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.1290 | − | 22.6491i | −0.408440 | − | 0.913300i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.0996i | 1.09099i | 0.838115 | + | 0.545493i | \(0.183658\pi\) | ||||
−0.838115 | + | 0.545493i | \(0.816342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.18861i | − | 0.329128i | −0.986366 | − | 0.164564i | \(-0.947378\pi\) | ||
0.986366 | − | 0.164564i | \(-0.0526217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.0000 | − | 8.94427i | −1.12360 | − | 0.358921i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.18472 | 0.0474647 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.92359 | + | 2.64911i | −0.236565 | + | 0.105795i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.5717i | 1.25885i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.9473i | 1.51066i | 0.655345 | + | 0.755330i | \(0.272523\pi\) | ||||
−0.655345 | + | 0.755330i | \(0.727477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.13594 | + | 0.955223i | −0.0848961 | + | 0.0379667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.48528 | −0.336728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.16228 | 0.283780 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.2580 | + | 22.6491i | −0.801393 | + | 0.895985i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.4984i | − | 0.493658i | −0.969059 | − | 0.246829i | \(-0.920611\pi\) | ||
0.969059 | − | 0.246829i | \(-0.0793886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.83772i | 0.190781i | 0.995440 | + | 0.0953906i | \(0.0304100\pi\) | ||||
−0.995440 | + | 0.0953906i | \(0.969590\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.32456 | − | 18.6143i | −0.327779 | − | 0.732936i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.2242 | 0.519895 | 0.259948 | − | 0.965623i | \(-0.416295\pi\) | ||||
0.259948 | + | 0.965623i | \(0.416295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.32456 | 0.248261 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.47214 | − | 10.0000i | −0.175277 | − | 0.391931i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47.8165i | − | 1.87121i | −0.353055 | − | 0.935603i | \(-0.614857\pi\) | ||
0.353055 | − | 0.935603i | \(-0.385143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.64911i | 0.259802i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.64911 | + | 9.67000i | −0.337434 | + | 0.377263i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.7038 | −0.650689 | −0.325344 | − | 0.945596i | \(-0.605480\pi\) | ||||
−0.325344 | + | 0.945596i | \(0.605480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5132 | 0.875661 | 0.437830 | − | 0.899058i | \(-0.355747\pi\) | ||||
0.437830 | + | 0.899058i | \(0.355747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 82.6756 | − | 36.9737i | 3.21086 | − | 1.43594i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.18472i | − | 0.0459414i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.29822i | 0.360029i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.67544 | + | 1.64371i | −0.142101 | + | 0.0635495i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1421 | −0.545951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.2982 | 1.05227 | 0.526135 | − | 0.850401i | \(-0.323641\pi\) | ||||
0.526135 | + | 0.850401i | \(0.323641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.8492 | − | 4.74342i | −0.571548 | − | 0.182574i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8.44804i | − | 0.324685i | −0.986735 | − | 0.162342i | \(-0.948095\pi\) | ||
0.986735 | − | 0.162342i | \(-0.0519049\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6491i | 0.408675i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.32456 | + | 20.8503i | 0.357318 | + | 0.798987i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 51.1039 | 1.95544 | 0.977719 | − | 0.209918i | \(-0.0673197\pi\) | ||||
0.977719 | + | 0.209918i | \(0.0673197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.2982 | 0.966595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.69506 | + | 6.02633i | 0.102823 | + | 0.229919i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.48528i | − | 0.323263i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1623i | 0.576800i | 0.957510 | + | 0.288400i | \(0.0931233\pi\) | ||||
−0.957510 | + | 0.288400i | \(0.906877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.0000 | − | 8.94427i | −0.379869 | − | 0.339765i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1290 | −0.384214 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −73.9473 | −2.80095 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.94427 | + | 4.00000i | −0.338303 | + | 0.151294i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.6406i | 1.00620i | 0.864228 | + | 0.503100i | \(0.167807\pi\) | ||||
−0.864228 | + | 0.503100i | \(0.832193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.62278i | − | 0.136636i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.0000 | − | 8.94427i | 0.753244 | − | 0.336861i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.41421 | 0.0531870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.02633 | −0.113656 | −0.0568282 | − | 0.998384i | \(-0.518099\pi\) | ||||
−0.0568282 | + | 0.998384i | \(0.518099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.94427 | + | 8.00000i | 0.335436 | + | 0.300023i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 35.7771i | − | 1.33986i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.2982i | 1.69406i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.3246 | − | 40.9750i | −0.684343 | − | 1.53024i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.2317 | 0.456165 | 0.228083 | − | 0.973642i | \(-0.426754\pi\) | ||||
0.228083 | + | 0.973642i | \(0.426754\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.89949 | + | 22.1359i | 0.368166 | + | 0.823245i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.93113i | 0.183137i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6491i | 0.617481i | 0.951146 | + | 0.308741i | \(0.0999075\pi\) | ||||
−0.951146 | + | 0.308741i | \(0.900092\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.7739 | −2.24781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.1359 | 1.70407 | 0.852035 | − | 0.523485i | \(-0.175368\pi\) | ||||
0.852035 | + | 0.523485i | \(0.175368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.23607 | − | 1.00000i | 0.0824786 | − | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.94427i | 0.329466i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.9737i | 1.21296i | 0.795100 | + | 0.606478i | \(0.207418\pi\) | ||||
−0.795100 | + | 0.606478i | \(0.792582\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.48683 | + | 4.24264i | −0.348508 | + | 0.155857i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5454 | 0.863797 | 0.431898 | − | 0.901922i | \(-0.357844\pi\) | ||||
0.431898 | + | 0.901922i | \(0.357844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.32456 | 0.231714 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.0601 | + | 16.8377i | −0.551021 | + | 0.616060i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 9.67000i | − | 0.353334i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3509i | 0.633143i | 0.948569 | + | 0.316571i | \(0.102532\pi\) | ||||
−0.948569 | + | 0.316571i | \(0.897468\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.3246 | + | 29.7946i | 0.485574 | + | 1.08578i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1421 | 0.514685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3246 | −0.738709 | −0.369354 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369354 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.8885 | − | 40.0000i | −0.649313 | − | 1.45191i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.47214i | − | 0.162115i | −0.996709 | − | 0.0810574i | \(-0.974170\pi\) | ||
0.996709 | − | 0.0810574i | \(-0.0258297\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.32456i | 0.156559i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.6491 | − | 23.0864i | 0.746570 | − | 0.834691i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.1290 | 0.365737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.2982 | −0.984399 | −0.492200 | − | 0.870482i | \(-0.663807\pi\) | ||||
−0.492200 | + | 0.870482i | \(0.663807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.6853 | − | 11.4868i | 0.925035 | − | 0.413688i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 45.6766i | − | 1.64287i | −0.570300 | − | 0.821436i | \(-0.693173\pi\) | ||
0.570300 | − | 0.821436i | \(-0.306827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 18.9737i | − | 0.681554i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.83772 | − | 3.05792i | 0.245302 | − | 0.109702i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.48528 | 0.304017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.2982 | −1.62090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.59893 | − | 8.13594i | 0.0928782 | − | 0.290755i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 19.0733i | − | 0.680754i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 39.1623i | − | 1.39598i | −0.716105 | − | 0.697992i | \(-0.754077\pi\) | ||
0.716105 | − | 0.697992i | \(-0.245923\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.48683 | − | 3.32466i | −0.0529327 | − | 0.118361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.84157 | 0.243258 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.6491 | −0.804294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.18472 | − | 2.64911i | −0.0420176 | − | 0.0939543i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.9258i | 0.634964i | 0.948264 | + | 0.317482i | \(0.102837\pi\) | ||||
−0.948264 | + | 0.317482i | \(0.897163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 65.2982i | − | 2.31009i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.64911 | − | 2.36944i | −0.0936017 | − | 0.0837199i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.3400 | −0.682494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.4546 | − | 4.67544i | 0.368020 | − | 0.164583i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.9881i | 1.58170i | 0.612012 | + | 0.790849i | \(0.290360\pi\) | ||||
−0.612012 | + | 0.790849i | \(0.709640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.4868i | 1.17588i | 0.808904 | + | 0.587941i | \(0.200061\pi\) | ||||
−0.808904 | + | 0.587941i | \(0.799939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.64911 | − | 1.18472i | 0.0929084 | − | 0.0415499i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.11584 | −0.214229 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.97367 | 0.243978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.0153 | − | 14.3246i | −0.559621 | − | 0.500540i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3607i | 0.780393i | 0.920732 | + | 0.390197i | \(0.127593\pi\) | ||||
−0.920732 | + | 0.390197i | \(0.872407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.9473i | − | 0.765036i | −0.923948 | − | 0.382518i | \(-0.875057\pi\) | ||
0.923948 | − | 0.382518i | \(-0.124943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.48683 | − | 21.2132i | −0.330289 | − | 0.738549i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.93113 | −0.171472 | −0.0857360 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857360 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.1623 | 1.22124 | 0.610618 | − | 0.791925i | \(-0.290921\pi\) | ||||
0.610618 | + | 0.791925i | \(0.290921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | + | 3.16228i | 0.0490585 | + | 0.109698i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 7.30056i | − | 0.252950i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.649111i | 0.0224634i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0000 | + | 31.3050i | −0.345651 | + | 1.08206i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.0012 | −1.69171 | −0.845855 | − | 0.533412i | \(-0.820909\pi\) | ||||
−0.845855 | + | 0.533412i | \(0.820909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.2982 | 0.906835 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.2285 | + | 16.6491i | −1.28222 | + | 0.573426i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 54.1619i | 1.86322i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.00000i | − | 0.309244i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.2982 | − | 4.60550i | 0.353434 | − | 0.158061i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.4634 | 0.838594 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.1359 | −0.894878 | −0.447439 | − | 0.894315i | \(-0.647664\pi\) | ||||
−0.447439 | + | 0.894315i | \(0.647664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.36944 | + | 2.64911i | −0.0810330 | + | 0.0905977i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.0733i | − | 0.651530i | −0.945451 | − | 0.325765i | \(-0.894378\pi\) | ||
0.945451 | − | 0.325765i | \(-0.105622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 48.4605i | − | 1.65345i | −0.562606 | − | 0.826725i | \(-0.690201\pi\) | ||
0.562606 | − | 0.826725i | \(-0.309799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.16228 | + | 16.0153i | 0.244090 | + | 0.545801i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0470 | −0.376043 | −0.188022 | − | 0.982165i | \(-0.560208\pi\) | ||||
−0.188022 | + | 0.982165i | \(0.560208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.35089 | −0.181936 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.6667 | − | 57.3925i | −0.871687 | − | 1.94915i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8885i | 0.606827i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3246i | 0.485369i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.2982 | − | 23.8121i | 0.720836 | − | 0.805919i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137 | 0.382473 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.9737 | 1.38358 | 0.691791 | − | 0.722098i | \(-0.256822\pi\) | ||||
0.691791 | + | 0.722098i | \(0.256822\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −34.9925 | + | 15.6491i | −1.18027 | + | 0.527831i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.2711i | 0.817715i | 0.912598 | + | 0.408858i | \(0.134073\pi\) | ||||
−0.912598 | + | 0.408858i | \(0.865927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.0000i | − | 0.605748i | −0.953031 | − | 0.302874i | \(-0.902054\pi\) | ||
0.953031 | − | 0.302874i | \(-0.0979462\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.16228 | − | 1.41421i | 0.106299 | − | 0.0475383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.5116 | 0.554404 | 0.277202 | − | 0.960812i | \(-0.410593\pi\) | ||||
0.277202 | + | 0.960812i | \(0.410593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.00000 | 0.201234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.47214 | + | 40.0000i | 0.149822 | + | 1.34005i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.49282i | 0.250738i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 27.6228i | − | 0.923328i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.6491 | − | 64.0614i | −0.956566 | − | 2.13895i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.3957 | 0.346717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.64911 | −0.288144 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.88635 | + | 13.1623i | 0.195885 | + | 0.438013i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.6481i | 0.852572i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27.9473i | − | 0.927976i | −0.885842 | − | 0.463988i | \(-0.846418\pi\) | ||
0.885842 | − | 0.463988i | \(-0.153582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.16228 | − | 2.82843i | −0.104886 | − | 0.0938130i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.6831 | 0.453343 | 0.226671 | − | 0.973971i | \(-0.427216\pi\) | ||||
0.226671 | + | 0.973971i | \(0.427216\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.6754 | −1.11449 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.07107 | + | 3.16228i | −0.233762 | + | 0.104542i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.70163i | − | 0.155262i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.6491i | 0.681151i | 0.940217 | + | 0.340576i | \(0.110622\pi\) | ||||
−0.940217 | + | 0.340576i | \(0.889378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.97367 | + | 1.77708i | −0.130937 | + | 0.0585567i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −72.5466 | −2.38790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.9737 | 0.426572 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.8885 | − | 16.0000i | −0.587537 | − | 0.525509i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.0777i | 1.41333i | 0.707547 | + | 0.706666i | \(0.249802\pi\) | ||||
−0.707547 | + | 0.706666i | \(0.750198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.837722i | 0.0274552i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3246 | − | 27.5585i | −0.403488 | − | 0.902226i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.1728 | 1.51001 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.67544 | −0.250746 | −0.125373 | − | 0.992110i | \(-0.540013\pi\) | ||||
−0.125373 | + | 0.992110i | \(0.540013\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.51691 | − | 7.86406i | −0.114770 | − | 0.256634i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 23.0492i | − | 0.751381i | −0.926745 | − | 0.375691i | \(-0.877406\pi\) | ||
0.926745 | − | 0.375691i | \(-0.122594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.2982i | 1.86589i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.00000 | − | 2.23607i | −0.227710 | − | 0.0727393i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.47214 | −0.145325 | −0.0726624 | − | 0.997357i | \(-0.523150\pi\) | ||||
−0.0726624 | + | 0.997357i | \(0.523150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.9737 | −1.00545 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.2689 | + | 5.48683i | −0.397847 | + | 0.177923i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.8328i | − | 0.869200i | −0.900624 | − | 0.434600i | \(-0.856890\pi\) | ||
0.900624 | − | 0.434600i | \(-0.143110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 17.6754i | − | 0.571964i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.6228 | − | 5.19786i | 0.375711 | − | 0.168023i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.8885 | −0.577651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.3400 | + | 21.6228i | −0.623223 | + | 0.696784i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.6274i | 0.728402i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.6491i | − | 1.11424i | −0.830432 | − | 0.557120i | \(-0.811906\pi\) | ||
0.830432 | − | 0.557120i | \(-0.188094\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.32456 | + | 9.67000i | 0.138925 | + | 0.310645i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.8406 | 1.40691 | 0.703456 | − | 0.710739i | \(-0.251639\pi\) | ||||
0.703456 | + | 0.710739i | \(0.251639\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.16228 | 0.229612 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.1935 | − | 33.9737i | −0.486581 | − | 1.08803i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.4602i | 1.58237i | 0.611575 | + | 0.791187i | \(0.290536\pi\) | ||||
−0.611575 | + | 0.791187i | \(0.709464\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.29822i | − | 0.169332i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.64911 | − | 9.67000i | 0.276145 | − | 0.308739i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.5116 | −0.526637 | −0.263319 | − | 0.964709i | \(-0.584817\pi\) | ||||
−0.263319 | + | 0.964709i | \(0.584817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.3246 | −0.456418 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.1421 | + | 6.32456i | −0.450149 | + | 0.201313i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.0908i | 1.49740i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.5964i | 1.48018i | 0.672505 | + | 0.740092i | \(0.265218\pi\) | ||||
−0.672505 | + | 0.740092i | \(0.734782\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.8114 | − | 20.4875i | 1.45378 | − | 0.650150i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.8591 | −1.10511 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.4868 | −0.807176 | −0.403588 | − | 0.914941i | \(-0.632237\pi\) | ||||
−0.403588 | + | 0.914941i | \(0.632237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.4055 | − | 6.83772i | −0.677239 | − | 0.216336i |
(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 | 672.2.h.e.575.8 | yes | 8 | |
3.2 | odd | 2 | inner | 672.2.h.e.575.3 | yes | 8 | |
4.3 | odd | 2 | inner | 672.2.h.e.575.2 | ✓ | 8 | |
8.3 | odd | 2 | 1344.2.h.f.575.7 | 8 | |||
8.5 | even | 2 | 1344.2.h.f.575.1 | 8 | |||
12.11 | even | 2 | inner | 672.2.h.e.575.5 | yes | 8 | |
24.5 | odd | 2 | 1344.2.h.f.575.6 | 8 | |||
24.11 | even | 2 | 1344.2.h.f.575.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.h.e.575.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
672.2.h.e.575.3 | yes | 8 | 3.2 | odd | 2 | inner | |
672.2.h.e.575.5 | yes | 8 | 12.11 | even | 2 | inner | |
672.2.h.e.575.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1344.2.h.f.575.1 | 8 | 8.5 | even | 2 | |||
1344.2.h.f.575.4 | 8 | 24.11 | even | 2 | |||
1344.2.h.f.575.6 | 8 | 24.5 | odd | 2 | |||
1344.2.h.f.575.7 | 8 | 8.3 | odd | 2 |