Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(683,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.683");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.b (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 683.8 | ||
Character | \(\chi\) | \(=\) | 684.683 |
Dual form | 684.3.b.a.683.6 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90361 | + | 0.613402i | −0.951806 | + | 0.306701i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.24748 | − | 2.33536i | 0.811869 | − | 0.583840i | ||||
\(5\) | − | 6.64226i | − | 1.32845i | −0.747531 | − | 0.664226i | \(-0.768761\pi\) | ||
0.747531 | − | 0.664226i | \(-0.231239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.470842i | − | 0.0672631i | −0.999434 | − | 0.0336316i | \(-0.989293\pi\) | ||
0.999434 | − | 0.0336316i | \(-0.0107073\pi\) | |||||||
\(8\) | −4.74942 | + | 6.43762i | −0.593678 | + | 0.804703i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.07438 | + | 12.6443i | 0.407438 | + | 1.26443i | ||||
\(11\) | −10.1736 | −0.924875 | −0.462437 | − | 0.886652i | \(-0.653025\pi\) | ||||
−0.462437 | + | 0.886652i | \(0.653025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.45114i | 0.265472i | 0.991151 | + | 0.132736i | \(0.0423763\pi\) | ||||
−0.991151 | + | 0.132736i | \(0.957624\pi\) | |||||||
\(14\) | 0.288815 | + | 0.896300i | 0.0206297 | + | 0.0640214i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.09220 | − | 15.1680i | 0.318263 | − | 0.948003i | ||||
\(17\) | − | 14.2737i | − | 0.839629i | −0.907610 | − | 0.419814i | \(-0.862095\pi\) | ||
0.907610 | − | 0.419814i | \(-0.137905\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.6293 | + | 13.2379i | −0.717332 | + | 0.696731i | ||||
\(20\) | −15.5121 | − | 21.5706i | −0.775603 | − | 1.07853i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 19.3666 | − | 6.24052i | 0.880301 | − | 0.283660i | ||||
\(23\) | −25.5501 | −1.11087 | −0.555437 | − | 0.831558i | \(-0.687449\pi\) | ||||
−0.555437 | + | 0.831558i | \(0.687449\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.1197 | −0.764787 | ||||||||
\(26\) | −2.11694 | − | 6.56963i | −0.0814206 | − | 0.252678i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.09958 | − | 1.52905i | −0.0392709 | − | 0.0546088i | ||||
\(29\) | −14.1589 | −0.488238 | −0.244119 | − | 0.969745i | \(-0.578499\pi\) | ||||
−0.244119 | + | 0.969745i | \(0.578499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.3243 | 0.623364 | 0.311682 | − | 0.950187i | \(-0.399108\pi\) | ||||
0.311682 | + | 0.950187i | \(0.399108\pi\) | |||||||
\(32\) | −0.389466 | + | 31.9976i | −0.0121708 | + | 0.999926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.75551 | + | 27.1716i | 0.257515 | + | 0.799164i | ||||
\(35\) | −3.12746 | −0.0893559 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0832i | 0.813059i | 0.913638 | + | 0.406529i | \(0.133261\pi\) | ||||
−0.913638 | + | 0.406529i | \(0.866739\pi\) | |||||||
\(38\) | 17.8248 | − | 33.5601i | 0.469073 | − | 0.883160i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 42.7604 | + | 31.5469i | 1.06901 | + | 0.788673i | ||||
\(41\) | 25.6549 | 0.625728 | 0.312864 | − | 0.949798i | \(-0.398712\pi\) | ||||
0.312864 | + | 0.949798i | \(0.398712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38.5869i | 0.897370i | 0.893690 | + | 0.448685i | \(0.148107\pi\) | ||||
−0.893690 | + | 0.448685i | \(0.851893\pi\) | |||||||
\(44\) | −33.0386 | + | 23.7591i | −0.750877 | + | 0.539979i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 48.6375 | − | 15.6725i | 1.05734 | − | 0.340706i | ||||
\(47\) | 16.5047 | 0.351164 | 0.175582 | − | 0.984465i | \(-0.443819\pi\) | ||||
0.175582 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.7783 | 0.995476 | ||||||||
\(50\) | 36.3964 | − | 11.7280i | 0.727929 | − | 0.234561i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.05965 | + | 11.2075i | 0.154993 | + | 0.215529i | ||||
\(53\) | −41.6477 | −0.785805 | −0.392903 | − | 0.919580i | \(-0.628529\pi\) | ||||
−0.392903 | + | 0.919580i | \(0.628529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 67.5759i | 1.22865i | ||||||||
\(56\) | 3.03110 | + | 2.23623i | 0.0541268 | + | 0.0399326i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 26.9530 | − | 8.68510i | 0.464708 | − | 0.149743i | ||||
\(59\) | 31.3349i | 0.531099i | 0.964097 | + | 0.265550i | \(0.0855534\pi\) | ||||
−0.964097 | + | 0.265550i | \(0.914447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.53469 | −0.0579457 | −0.0289728 | − | 0.999580i | \(-0.509224\pi\) | ||||
−0.0289728 | + | 0.999580i | \(0.509224\pi\) | |||||||
\(62\) | −36.7859 | + | 11.8535i | −0.593321 | + | 0.191186i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −18.8860 | − | 61.1500i | −0.295094 | − | 0.955468i | ||||
\(65\) | 22.9234 | 0.352667 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9620 | 0.208388 | 0.104194 | − | 0.994557i | \(-0.466774\pi\) | ||||
0.104194 | + | 0.994557i | \(0.466774\pi\) | |||||||
\(68\) | −33.3342 | − | 46.3535i | −0.490209 | − | 0.681669i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.95346 | − | 1.91839i | 0.0850494 | − | 0.0274055i | ||||
\(71\) | 128.352i | 1.80777i | 0.427773 | + | 0.903886i | \(0.359298\pi\) | ||||
−0.427773 | + | 0.903886i | \(0.640702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −71.6376 | −0.981337 | −0.490668 | − | 0.871346i | \(-0.663247\pi\) | ||||
−0.490668 | + | 0.871346i | \(0.663247\pi\) | |||||||
\(74\) | −18.4531 | − | 57.2667i | −0.249366 | − | 0.773874i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.3456 | + | 74.8191i | −0.175600 | + | 0.984462i | ||||
\(77\) | 4.79017i | 0.0622100i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −100.177 | −1.26807 | −0.634034 | − | 0.773305i | \(-0.718602\pi\) | ||||
−0.634034 | + | 0.773305i | \(0.718602\pi\) | |||||||
\(80\) | −100.750 | − | 33.8237i | −1.25938 | − | 0.422797i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −48.8369 | + | 15.7367i | −0.595572 | + | 0.191912i | ||||
\(83\) | 58.6257 | 0.706333 | 0.353167 | − | 0.935560i | \(-0.385105\pi\) | ||||
0.353167 | + | 0.935560i | \(0.385105\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −94.8096 | −1.11541 | ||||||||
\(86\) | −23.6693 | − | 73.4545i | −0.275224 | − | 0.854122i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 48.3188 | − | 65.4940i | 0.549077 | − | 0.744250i | ||||
\(89\) | −108.060 | −1.21415 | −0.607077 | − | 0.794643i | \(-0.707658\pi\) | ||||
−0.607077 | + | 0.794643i | \(0.707658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.62494 | 0.0178565 | ||||||||
\(92\) | −82.9734 | + | 59.6687i | −0.901885 | + | 0.648573i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −31.4186 | + | 10.1240i | −0.334240 | + | 0.107702i | ||||
\(95\) | 87.9296 | + | 90.5295i | 0.925575 | + | 0.952942i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 124.227i | − | 1.28069i | −0.768087 | − | 0.640346i | \(-0.778791\pi\) | ||
0.768087 | − | 0.640346i | \(-0.221209\pi\) | |||||||
\(98\) | −92.8550 | + | 29.9207i | −0.947500 | + | 0.305313i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −62.0907 | + | 44.6513i | −0.620907 | + | 0.446513i | ||||
\(101\) | 16.1661i | 0.160060i | 0.996792 | + | 0.0800301i | \(0.0255016\pi\) | ||||
−0.996792 | + | 0.0800301i | \(0.974498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.61325 | 0.0836238 | 0.0418119 | − | 0.999126i | \(-0.486687\pi\) | ||||
0.0418119 | + | 0.999126i | \(0.486687\pi\) | |||||||
\(104\) | −22.2171 | − | 16.3909i | −0.213626 | − | 0.157605i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79.2810 | − | 25.5468i | 0.747934 | − | 0.241007i | ||||
\(107\) | 192.384i | 1.79798i | 0.437972 | + | 0.898989i | \(0.355697\pi\) | ||||
−0.437972 | + | 0.898989i | \(0.644303\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 31.7667i | − | 0.291438i | −0.989326 | − | 0.145719i | \(-0.953450\pi\) | ||
0.989326 | − | 0.145719i | \(-0.0465495\pi\) | |||||||
\(110\) | −41.4512 | − | 128.638i | −0.376829 | − | 1.16944i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.14175 | − | 2.39762i | −0.0637656 | − | 0.0214073i | ||||
\(113\) | −157.215 | −1.39128 | −0.695640 | − | 0.718391i | \(-0.744879\pi\) | ||||
−0.695640 | + | 0.718391i | \(0.744879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 169.711i | 1.47574i | ||||||||
\(116\) | −45.9807 | + | 33.0661i | −0.396385 | + | 0.285053i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.2209 | − | 59.6494i | −0.162889 | − | 0.505504i | ||||
\(119\) | −6.72065 | −0.0564761 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.4974 | −0.144607 | ||||||||
\(122\) | 6.72867 | − | 2.16818i | 0.0551530 | − | 0.0177720i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 62.7551 | − | 45.1291i | 0.506090 | − | 0.363944i | ||||
\(125\) | − | 39.0587i | − | 0.312470i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −118.218 | −0.930851 | −0.465425 | − | 0.885087i | \(-0.654099\pi\) | ||||
−0.465425 | + | 0.885087i | \(0.654099\pi\) | |||||||
\(128\) | 73.4612 | + | 104.821i | 0.573915 | + | 0.818915i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −43.6372 | + | 14.0612i | −0.335671 | + | 0.108163i | ||||
\(131\) | 126.719 | 0.967322 | 0.483661 | − | 0.875255i | \(-0.339307\pi\) | ||||
0.483661 | + | 0.875255i | \(0.339307\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.23295 | + | 6.41725i | 0.0468643 | + | 0.0482500i | ||||
\(134\) | −26.5783 | + | 8.56433i | −0.198345 | + | 0.0639129i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 91.8887 | + | 67.7918i | 0.675652 | + | 0.498469i | ||||
\(137\) | 20.4018i | 0.148918i | 0.997224 | + | 0.0744590i | \(0.0237230\pi\) | ||||
−0.997224 | + | 0.0744590i | \(0.976277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 106.578i | 0.766746i | 0.923594 | + | 0.383373i | \(0.125238\pi\) | ||||
−0.923594 | + | 0.383373i | \(0.874762\pi\) | |||||||
\(140\) | −10.1563 | + | 7.30373i | −0.0725453 | + | 0.0521695i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −78.7313 | − | 244.332i | −0.554446 | − | 1.72065i | ||||
\(143\) | − | 35.1106i | − | 0.245529i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 94.0471i | 0.648601i | ||||||||
\(146\) | 136.370 | − | 43.9426i | 0.934042 | − | 0.300977i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 70.2550 | + | 97.6944i | 0.474696 | + | 0.660097i | ||||
\(149\) | 187.048i | 1.25535i | 0.778474 | + | 0.627677i | \(0.215994\pi\) | ||||
−0.778474 | + | 0.627677i | \(0.784006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −280.997 | −1.86091 | −0.930454 | − | 0.366409i | \(-0.880587\pi\) | ||||
−0.930454 | + | 0.366409i | \(0.880587\pi\) | |||||||
\(152\) | −20.4893 | − | 150.613i | −0.134798 | − | 0.990873i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.93830 | − | 9.11862i | −0.0190799 | − | 0.0592118i | ||||
\(155\) | − | 128.357i | − | 0.828109i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −191.202 | −1.21785 | −0.608923 | − | 0.793230i | \(-0.708398\pi\) | ||||
−0.608923 | + | 0.793230i | \(0.708398\pi\) | |||||||
\(158\) | 190.699 | − | 61.4490i | 1.20695 | − | 0.388918i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 212.537 | + | 2.58693i | 1.32835 | + | 0.0161683i | ||||
\(161\) | 12.0301i | 0.0747209i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 177.569i | 1.08938i | 0.838637 | + | 0.544691i | \(0.183353\pi\) | ||||
−0.838637 | + | 0.544691i | \(0.816647\pi\) | |||||||
\(164\) | 83.3136 | − | 59.9133i | 0.508009 | − | 0.365325i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −111.601 | + | 35.9611i | −0.672292 | + | 0.216633i | ||||
\(167\) | − | 101.127i | − | 0.605550i | −0.953062 | − | 0.302775i | \(-0.902087\pi\) | ||
0.953062 | − | 0.302775i | \(-0.0979131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 157.090 | 0.929525 | ||||||||
\(170\) | 180.481 | − | 58.1564i | 1.06165 | − | 0.342097i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 90.1143 | + | 125.310i | 0.523920 | + | 0.728547i | ||||
\(173\) | 178.731 | 1.03313 | 0.516565 | − | 0.856248i | \(-0.327211\pi\) | ||||
0.516565 | + | 0.856248i | \(0.327211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.00234i | 0.0514419i | ||||||||
\(176\) | −51.8061 | + | 154.314i | −0.294353 | + | 0.876784i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 205.704 | − | 66.2840i | 1.15564 | − | 0.372382i | ||||
\(179\) | − | 149.034i | − | 0.832591i | −0.909229 | − | 0.416296i | \(-0.863328\pi\) | ||
0.909229 | − | 0.416296i | \(-0.136672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 40.0902i | 0.221493i | 0.993849 | + | 0.110746i | \(0.0353242\pi\) | ||||
−0.993849 | + | 0.110746i | \(0.964676\pi\) | |||||||
\(182\) | −3.09326 | + | 0.996742i | −0.0169959 | + | 0.00547660i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 121.348 | − | 164.482i | 0.659501 | − | 0.893924i | ||||
\(185\) | 199.820 | 1.08011 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 145.215i | 0.776552i | ||||||||
\(188\) | 53.5987 | − | 38.5444i | 0.285099 | − | 0.205024i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −222.915 | − | 118.397i | −1.17324 | − | 0.623141i | ||||
\(191\) | −12.1725 | −0.0637301 | −0.0318651 | − | 0.999492i | \(-0.510145\pi\) | ||||
−0.0318651 | + | 0.999492i | \(0.510145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 268.517i | − | 1.39128i | −0.718390 | − | 0.695641i | \(-0.755121\pi\) | ||
0.718390 | − | 0.695641i | \(-0.244879\pi\) | |||||||
\(194\) | 76.2012 | + | 236.480i | 0.392790 | + | 1.21897i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 158.406 | − | 113.915i | 0.808196 | − | 0.581198i | ||||
\(197\) | 67.3589i | 0.341923i | 0.985278 | + | 0.170962i | \(0.0546874\pi\) | ||||
−0.985278 | + | 0.170962i | \(0.945313\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 347.506i | − | 1.74626i | −0.487485 | − | 0.873131i | \(-0.662086\pi\) | ||
0.487485 | − | 0.873131i | \(-0.337914\pi\) | |||||||
\(200\) | 90.8073 | − | 123.085i | 0.454037 | − | 0.615426i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.91630 | − | 30.7739i | −0.0490906 | − | 0.152346i | ||||
\(203\) | 6.66660i | 0.0328404i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 170.406i | − | 0.831251i | ||||||
\(206\) | −16.3963 | + | 5.28338i | −0.0795936 | + | 0.0256475i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 52.3470 | + | 17.5739i | 0.251668 | + | 0.0844899i | ||||
\(209\) | 138.659 | − | 134.677i | 0.663442 | − | 0.644389i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 130.187 | 0.616998 | 0.308499 | − | 0.951225i | \(-0.400173\pi\) | ||||
0.308499 | + | 0.951225i | \(0.400173\pi\) | |||||||
\(212\) | −135.250 | + | 97.2623i | −0.637971 | + | 0.458784i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −118.008 | − | 366.224i | −0.551442 | − | 1.71133i | ||||
\(215\) | 256.304 | 1.19211 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.09867i | − | 0.0419294i | ||||||
\(218\) | 19.4858 | + | 60.4715i | 0.0893843 | + | 0.277392i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 157.814 | + | 219.451i | 0.717336 | + | 0.997505i | ||||
\(221\) | 49.2605 | 0.222898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −375.296 | −1.68294 | −0.841470 | − | 0.540303i | \(-0.818309\pi\) | ||||
−0.841470 | + | 0.540303i | \(0.818309\pi\) | |||||||
\(224\) | 15.0658 | + | 0.183377i | 0.0672581 | + | 0.000818646i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 299.275 | − | 96.4357i | 1.32423 | − | 0.426707i | ||||
\(227\) | − | 151.029i | − | 0.665326i | −0.943046 | − | 0.332663i | \(-0.892053\pi\) | ||
0.943046 | − | 0.332663i | \(-0.107947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 239.645 | 1.04649 | 0.523243 | − | 0.852183i | \(-0.324722\pi\) | ||||
0.523243 | + | 0.852183i | \(0.324722\pi\) | |||||||
\(230\) | −104.101 | − | 323.063i | −0.452612 | − | 1.40462i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 67.2466 | − | 91.1497i | 0.289856 | − | 0.392887i | ||||
\(233\) | 285.201i | 1.22404i | 0.790844 | + | 0.612018i | \(0.209642\pi\) | ||||
−0.790844 | + | 0.612018i | \(0.790358\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 109.629i | − | 0.466505i | ||||||
\(236\) | 73.1781 | + | 101.759i | 0.310077 | + | 0.431183i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.7935 | − | 4.12246i | 0.0537542 | − | 0.0173213i | ||||
\(239\) | −30.9287 | −0.129409 | −0.0647045 | − | 0.997904i | \(-0.520610\pi\) | ||||
−0.0647045 | + | 0.997904i | \(0.520610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 81.9792i | 0.340162i | 0.985430 | + | 0.170081i | \(0.0544030\pi\) | ||||
−0.985430 | + | 0.170081i | \(0.945597\pi\) | |||||||
\(242\) | 33.3082 | − | 10.7329i | 0.137637 | − | 0.0443510i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.4788 | + | 8.25476i | −0.0470443 | + | 0.0338310i | ||||
\(245\) | − | 323.998i | − | 1.32244i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.6858 | − | 47.0366i | −0.184963 | − | 0.190432i | ||||
\(248\) | −91.7791 | + | 124.402i | −0.370077 | + | 0.501623i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23.9587 | + | 74.3526i | 0.0958347 | + | 0.297410i | ||||
\(251\) | 68.9014 | 0.274508 | 0.137254 | − | 0.990536i | \(-0.456172\pi\) | ||||
0.137254 | + | 0.990536i | \(0.456172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 259.937 | 1.02742 | ||||||||
\(254\) | 225.041 | − | 72.5152i | 0.885989 | − | 0.285493i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −204.139 | − | 154.477i | −0.797418 | − | 0.603427i | ||||
\(257\) | −432.173 | −1.68161 | −0.840803 | − | 0.541342i | \(-0.817917\pi\) | ||||
−0.840803 | + | 0.541342i | \(0.817917\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.1644 | 0.0546889 | ||||||||
\(260\) | 74.4431 | − | 53.5343i | 0.286320 | − | 0.205901i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −241.224 | + | 77.7298i | −0.920703 | + | 0.296679i | ||||
\(263\) | −440.010 | −1.67304 | −0.836522 | − | 0.547934i | \(-0.815415\pi\) | ||||
−0.836522 | + | 0.547934i | \(0.815415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 276.635i | 1.04391i | ||||||||
\(266\) | −15.8015 | − | 8.39264i | −0.0594041 | − | 0.0315513i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 45.3413 | − | 32.6063i | 0.169184 | − | 0.121665i | ||||
\(269\) | 217.732 | 0.809413 | 0.404706 | − | 0.914447i | \(-0.367374\pi\) | ||||
0.404706 | + | 0.914447i | \(0.367374\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 301.510i | − | 1.11258i | −0.830987 | − | 0.556291i | \(-0.812224\pi\) | ||
0.830987 | − | 0.556291i | \(-0.187776\pi\) | |||||||
\(272\) | −216.504 | − | 72.6845i | −0.795970 | − | 0.267222i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.5145 | − | 38.8370i | −0.0456733 | − | 0.141741i | ||||
\(275\) | 194.516 | 0.707332 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 99.8731 | 0.360553 | 0.180276 | − | 0.983616i | \(-0.442301\pi\) | ||||
0.180276 | + | 0.983616i | \(0.442301\pi\) | |||||||
\(278\) | −65.3750 | − | 202.883i | −0.235162 | − | 0.729794i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.8536 | − | 20.1334i | 0.0530486 | − | 0.0719049i | ||||
\(281\) | 530.591 | 1.88822 | 0.944112 | − | 0.329625i | \(-0.106922\pi\) | ||||
0.944112 | + | 0.329625i | \(0.106922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 135.855i | − | 0.480052i | −0.970766 | − | 0.240026i | \(-0.922844\pi\) | ||
0.970766 | − | 0.240026i | \(-0.0771560\pi\) | |||||||
\(284\) | 299.748 | + | 416.819i | 1.05545 | + | 1.46767i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.5369 | + | 66.8369i | 0.0753039 | + | 0.233696i | ||||
\(287\) | − | 12.0794i | − | 0.0420884i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 85.2617 | 0.295023 | ||||||||
\(290\) | −57.6887 | − | 179.029i | −0.198927 | − | 0.617342i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −232.641 | + | 167.299i | −0.796717 | + | 0.572943i | ||||
\(293\) | −96.2009 | −0.328331 | −0.164165 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164165 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 208.134 | 0.705540 | ||||||||
\(296\) | −193.664 | − | 142.878i | −0.654271 | − | 0.482695i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −114.735 | − | 356.066i | −0.385018 | − | 1.19485i | ||||
\(299\) | − | 88.1770i | − | 0.294906i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.1683 | 0.0603599 | ||||||||
\(302\) | 534.909 | − | 172.364i | 1.77122 | − | 0.570742i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 131.390 | + | 274.140i | 0.432203 | + | 0.901776i | ||||
\(305\) | 23.4783i | 0.0769781i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 368.613 | 1.20070 | 0.600348 | − | 0.799739i | \(-0.295029\pi\) | ||||
0.600348 | + | 0.799739i | \(0.295029\pi\) | |||||||
\(308\) | 11.1868 | + | 15.5560i | 0.0363206 | + | 0.0505063i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 78.7344 | + | 244.342i | 0.253982 | + | 0.788199i | ||||
\(311\) | 69.9477 | 0.224912 | 0.112456 | − | 0.993657i | \(-0.464128\pi\) | ||||
0.112456 | + | 0.993657i | \(0.464128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −465.161 | −1.48614 | −0.743068 | − | 0.669216i | \(-0.766630\pi\) | ||||
−0.743068 | + | 0.669216i | \(0.766630\pi\) | |||||||
\(314\) | 363.974 | − | 117.284i | 1.15915 | − | 0.373514i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −325.323 | + | 233.950i | −1.02950 | + | 0.740348i | ||||
\(317\) | −477.532 | −1.50641 | −0.753205 | − | 0.657786i | \(-0.771493\pi\) | ||||
−0.753205 | + | 0.657786i | \(0.771493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 144.047 | 0.451559 | ||||||||
\(320\) | −406.174 | + | 125.446i | −1.26929 | + | 0.392019i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.37927 | − | 22.9006i | −0.0229170 | − | 0.0711198i | ||||
\(323\) | 188.954 | + | 194.541i | 0.584996 | + | 0.602293i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 65.9846i | − | 0.203030i | ||||||
\(326\) | −108.921 | − | 338.023i | −0.334115 | − | 1.03688i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −121.846 | + | 165.156i | −0.371481 | + | 0.503526i | ||||
\(329\) | − | 7.77111i | − | 0.0236204i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −158.883 | −0.480009 | −0.240004 | − | 0.970772i | \(-0.577149\pi\) | ||||
−0.240004 | + | 0.970772i | \(0.577149\pi\) | |||||||
\(332\) | 190.385 | − | 136.912i | 0.573450 | − | 0.412385i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62.0315 | + | 192.506i | 0.185723 | + | 0.576366i | ||||
\(335\) | − | 92.7395i | − | 0.276834i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 611.695i | 1.81512i | 0.419922 | + | 0.907560i | \(0.362057\pi\) | ||||
−0.419922 | + | 0.907560i | \(0.637943\pi\) | |||||||
\(338\) | −299.038 | + | 96.3591i | −0.884727 | + | 0.285086i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −307.892 | + | 221.414i | −0.905565 | + | 0.651219i | ||||
\(341\) | −196.598 | −0.576533 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 46.0381i | − | 0.134222i | ||||||
\(344\) | −248.408 | − | 183.265i | −0.722116 | − | 0.532748i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −340.235 | + | 109.634i | −0.983339 | + | 0.316862i | ||||
\(347\) | −332.664 | −0.958685 | −0.479343 | − | 0.877628i | \(-0.659125\pi\) | ||||
−0.479343 | + | 0.877628i | \(0.659125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.3612 | −0.0984562 | −0.0492281 | − | 0.998788i | \(-0.515676\pi\) | ||||
−0.0492281 | + | 0.998788i | \(0.515676\pi\) | |||||||
\(350\) | −5.52205 | − | 17.1370i | −0.0157773 | − | 0.0489627i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.96228 | − | 325.532i | 0.0112565 | − | 0.924806i | ||||
\(353\) | − | 66.4096i | − | 0.188129i | −0.995566 | − | 0.0940646i | \(-0.970014\pi\) | ||
0.995566 | − | 0.0940646i | \(-0.0299860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 852.547 | 2.40154 | ||||||||
\(356\) | −350.921 | + | 252.358i | −0.985733 | + | 0.708871i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 91.4177 | + | 283.703i | 0.255357 | + | 0.792465i | ||||
\(359\) | 423.674 | 1.18015 | 0.590076 | − | 0.807348i | \(-0.299098\pi\) | ||||
0.590076 | + | 0.807348i | \(0.299098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.5162 | − | 360.847i | 0.0291308 | − | 0.999576i | ||||
\(362\) | −24.5914 | − | 76.3162i | −0.0679321 | − | 0.210818i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.27695 | − | 3.79482i | 0.0144971 | − | 0.0104253i | ||||
\(365\) | 475.836i | 1.30366i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 280.945i | − | 0.765517i | −0.923848 | − | 0.382759i | \(-0.874974\pi\) | ||
0.923848 | − | 0.382759i | \(-0.125026\pi\) | |||||||
\(368\) | −130.106 | + | 387.545i | −0.353550 | + | 1.05311i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −380.380 | + | 122.570i | −1.02806 | + | 0.331271i | ||||
\(371\) | 19.6095i | 0.0528557i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 72.2157i | 0.193608i | 0.995303 | + | 0.0968038i | \(0.0308619\pi\) | ||||
−0.995303 | + | 0.0968038i | \(0.969138\pi\) | |||||||
\(374\) | −89.0753 | − | 276.433i | −0.238169 | − | 0.739126i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −78.3878 | + | 106.251i | −0.208478 | + | 0.282583i | ||||
\(377\) | − | 48.8643i | − | 0.129614i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −84.5932 | −0.223201 | −0.111601 | − | 0.993753i | \(-0.535598\pi\) | ||||
−0.111601 | + | 0.993753i | \(0.535598\pi\) | |||||||
\(380\) | 496.968 | + | 88.6452i | 1.30781 | + | 0.233277i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.1716 | − | 7.46661i | 0.0606587 | − | 0.0195461i | ||||
\(383\) | − | 60.9941i | − | 0.159254i | −0.996825 | − | 0.0796268i | \(-0.974627\pi\) | ||
0.996825 | − | 0.0796268i | \(-0.0253729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.8176 | 0.0826430 | ||||||||
\(386\) | 164.709 | + | 511.153i | 0.426707 | + | 1.32423i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −290.115 | − | 403.425i | −0.747719 | − | 1.03975i | ||||
\(389\) | − | 147.820i | − | 0.380001i | −0.981784 | − | 0.190001i | \(-0.939151\pi\) | ||
0.981784 | − | 0.190001i | \(-0.0608490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 364.695i | 0.932723i | ||||||||
\(392\) | −231.669 | + | 314.016i | −0.590992 | + | 0.801062i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −41.3181 | − | 128.225i | −0.104868 | − | 0.325445i | ||||
\(395\) | 665.404i | 1.68457i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −116.017 | −0.292234 | −0.146117 | − | 0.989267i | \(-0.546678\pi\) | ||||
−0.146117 | + | 0.989267i | \(0.546678\pi\) | |||||||
\(398\) | 213.161 | + | 661.517i | 0.535580 | + | 1.66210i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −97.3612 | + | 290.008i | −0.243403 | + | 0.725020i | ||||
\(401\) | −145.033 | −0.361678 | −0.180839 | − | 0.983513i | \(-0.557881\pi\) | ||||
−0.180839 | + | 0.983513i | \(0.557881\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 66.6907i | 0.165486i | ||||||||
\(404\) | 37.7536 | + | 52.4989i | 0.0934495 | + | 0.129948i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.08931 | − | 12.6906i | −0.0100722 | − | 0.0312577i | ||||
\(407\) | − | 306.055i | − | 0.751978i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 197.143i | 0.482012i | 0.970524 | + | 0.241006i | \(0.0774773\pi\) | ||||
−0.970524 | + | 0.241006i | \(0.922523\pi\) | |||||||
\(410\) | 104.528 | + | 324.388i | 0.254945 | + | 0.791189i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 27.9713 | − | 20.1150i | 0.0678915 | − | 0.0488229i | ||||
\(413\) | 14.7538 | 0.0357234 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 389.407i | − | 0.938331i | ||||||
\(416\) | −110.428 | − | 1.34410i | −0.265453 | − | 0.00323101i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −181.342 | + | 341.427i | −0.433834 | + | 0.816812i | ||||
\(419\) | −659.596 | −1.57421 | −0.787107 | − | 0.616816i | \(-0.788422\pi\) | ||||
−0.787107 | + | 0.616816i | \(0.788422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 714.982i | − | 1.69830i | −0.528155 | − | 0.849148i | \(-0.677116\pi\) | ||
0.528155 | − | 0.849148i | \(-0.322884\pi\) | |||||||
\(422\) | −247.825 | + | 79.8568i | −0.587263 | + | 0.189234i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 197.802 | − | 268.112i | 0.466515 | − | 0.632340i | ||||
\(425\) | 272.908i | 0.642137i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.66428i | 0.00389761i | ||||||||
\(428\) | 449.285 | + | 624.761i | 1.04973 | + | 1.45972i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −487.904 | + | 157.218i | −1.13466 | + | 0.365622i | ||||
\(431\) | − | 534.659i | − | 1.24051i | −0.784401 | − | 0.620255i | \(-0.787029\pi\) | ||
0.784401 | − | 0.620255i | \(-0.212971\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 482.402i | − | 1.11409i | −0.830482 | − | 0.557046i | \(-0.811935\pi\) | ||
0.830482 | − | 0.557046i | \(-0.188065\pi\) | |||||||
\(434\) | 5.58115 | + | 17.3203i | 0.0128598 | + | 0.0399086i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −74.1867 | − | 103.162i | −0.170153 | − | 0.236609i | ||||
\(437\) | 348.231 | − | 338.230i | 0.796866 | − | 0.773981i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 376.488 | 0.857603 | 0.428802 | − | 0.903399i | \(-0.358936\pi\) | ||||
0.428802 | + | 0.903399i | \(0.358936\pi\) | |||||||
\(440\) | −435.028 | − | 320.946i | −0.988701 | − | 0.729423i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −93.7729 | + | 30.2165i | −0.212156 | + | 0.0683631i | ||||
\(443\) | −828.172 | −1.86946 | −0.934731 | − | 0.355356i | \(-0.884360\pi\) | ||||
−0.934731 | + | 0.355356i | \(0.884360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 717.761i | 1.61295i | ||||||||
\(446\) | 714.417 | − | 230.207i | 1.60183 | − | 0.516160i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −28.7920 | + | 8.89233i | −0.0642678 | + | 0.0198489i | ||||
\(449\) | 484.547 | 1.07917 | 0.539585 | − | 0.841931i | \(-0.318581\pi\) | ||||
0.539585 | + | 0.841931i | \(0.318581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −261.003 | −0.578720 | ||||||||
\(452\) | −510.551 | + | 367.152i | −1.12954 | + | 0.812284i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 92.6415 | + | 287.501i | 0.204056 | + | 0.633261i | ||||
\(455\) | − | 10.7933i | − | 0.0237215i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5377 | 0.0318113 | 0.0159056 | − | 0.999873i | \(-0.494937\pi\) | ||||
0.0159056 | + | 0.999873i | \(0.494937\pi\) | |||||||
\(458\) | −456.192 | + | 146.999i | −0.996052 | + | 0.320958i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 396.335 | + | 551.131i | 0.861598 | + | 1.19811i | ||||
\(461\) | − | 822.917i | − | 1.78507i | −0.450979 | − | 0.892534i | \(-0.648925\pi\) | ||
0.450979 | − | 0.892534i | \(-0.351075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.5543i | − | 0.0292750i | −0.999893 | − | 0.0146375i | \(-0.995341\pi\) | ||
0.999893 | − | 0.0146375i | \(-0.00465943\pi\) | |||||||
\(464\) | −72.1000 | + | 214.763i | −0.155388 | + | 0.462851i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −174.943 | − | 542.911i | −0.375413 | − | 1.16505i | ||||
\(467\) | −335.258 | −0.717897 | −0.358948 | − | 0.933357i | \(-0.616865\pi\) | ||||
−0.358948 | + | 0.933357i | \(0.616865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.57390i | − | 0.0140169i | ||||||
\(470\) | 67.2465 | + | 208.690i | 0.143078 | + | 0.444022i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −201.722 | − | 148.822i | −0.427377 | − | 0.315302i | ||||
\(473\) | − | 392.569i | − | 0.829955i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 260.588 | − | 253.104i | 0.548606 | − | 0.532851i | ||||
\(476\) | −21.8252 | + | 15.6951i | −0.0458512 | + | 0.0329730i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 58.8763 | − | 18.9717i | 0.123172 | − | 0.0396899i | ||||
\(479\) | −760.782 | −1.58827 | −0.794136 | − | 0.607740i | \(-0.792076\pi\) | ||||
−0.794136 | + | 0.607740i | \(0.792076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −103.821 | −0.215845 | ||||||||
\(482\) | −50.2862 | − | 156.057i | −0.104328 | − | 0.323769i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −56.8223 | + | 40.8627i | −0.117402 | + | 0.0844270i | ||||
\(485\) | −825.149 | −1.70134 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −687.736 | −1.41219 | −0.706095 | − | 0.708117i | \(-0.749545\pi\) | ||||
−0.706095 | + | 0.708117i | \(0.749545\pi\) | |||||||
\(488\) | 16.7877 | − | 22.7550i | 0.0344010 | − | 0.0466291i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 198.741 | + | 616.767i | 0.405594 | + | 1.25871i | ||||
\(491\) | −276.744 | −0.563634 | −0.281817 | − | 0.959468i | \(-0.590937\pi\) | ||||
−0.281817 | + | 0.959468i | \(0.590937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 202.100i | 0.409939i | ||||||||
\(494\) | 115.820 | + | 61.5157i | 0.234454 | + | 0.124526i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 98.4031 | − | 293.111i | 0.198393 | − | 0.590950i | ||||
\(497\) | 60.4334 | 0.121596 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 75.2973i | 0.150896i | 0.997150 | + | 0.0754482i | \(0.0240388\pi\) | ||||
−0.997150 | + | 0.0754482i | \(0.975961\pi\) | |||||||
\(500\) | −91.2161 | − | 126.842i | −0.182432 | − | 0.253684i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −131.162 | + | 42.2643i | −0.261278 | + | 0.0841917i | ||||
\(503\) | 379.172 | 0.753820 | 0.376910 | − | 0.926250i | \(-0.376987\pi\) | ||||
0.376910 | + | 0.926250i | \(0.376987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 107.379 | 0.212632 | ||||||||
\(506\) | −494.820 | + | 159.446i | −0.977905 | + | 0.315111i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −383.910 | + | 276.081i | −0.755729 | + | 0.543467i | ||||
\(509\) | 565.844 | 1.11168 | 0.555839 | − | 0.831290i | \(-0.312397\pi\) | ||||
0.555839 | + | 0.831290i | \(0.312397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.7300i | 0.0660078i | ||||||||
\(512\) | 483.358 | + | 168.846i | 0.944059 | + | 0.329777i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 822.689 | − | 265.096i | 1.60056 | − | 0.515750i | ||||
\(515\) | − | 57.2115i | − | 0.111090i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −167.913 | −0.324783 | ||||||||
\(518\) | −26.9636 | + | 8.68848i | −0.0520532 | + | 0.0167731i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −108.873 | + | 147.572i | −0.209371 | + | 0.283792i | ||||
\(521\) | −324.637 | −0.623103 | −0.311552 | − | 0.950229i | \(-0.600849\pi\) | ||||
−0.311552 | + | 0.950229i | \(0.600849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 271.054 | 0.518268 | 0.259134 | − | 0.965841i | \(-0.416563\pi\) | ||||
0.259134 | + | 0.965841i | \(0.416563\pi\) | |||||||
\(524\) | 411.518 | − | 295.935i | 0.785339 | − | 0.564761i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 837.609 | − | 269.903i | 1.59241 | − | 0.513124i | ||||
\(527\) | − | 275.829i | − | 0.523394i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 123.809 | 0.234043 | ||||||||
\(530\) | −169.688 | − | 526.605i | −0.320167 | − | 0.993595i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 35.2279 | + | 6.28368i | 0.0662179 | + | 0.0118114i | ||||
\(533\) | 88.5385i | 0.166113i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1277.86 | 2.38853 | ||||||||
\(536\) | −66.3115 | + | 89.8823i | −0.123716 | + | 0.167691i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −414.477 | + | 133.557i | −0.770404 | + | 0.248248i | ||||
\(539\) | −496.252 | −0.920690 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.97150 | 0.00918947 | 0.00459473 | − | 0.999989i | \(-0.498537\pi\) | ||||
0.00459473 | + | 0.999989i | \(0.498537\pi\) | |||||||
\(542\) | 184.947 | + | 573.958i | 0.341230 | + | 1.05896i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 456.724 | + | 5.55911i | 0.839567 | + | 0.0102190i | ||||
\(545\) | −211.003 | −0.387161 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 148.968 | 0.272337 | 0.136168 | − | 0.990686i | \(-0.456521\pi\) | ||||
0.136168 | + | 0.990686i | \(0.456521\pi\) | |||||||
\(548\) | 47.6454 | + | 66.2542i | 0.0869442 | + | 0.120902i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −370.284 | + | 119.317i | −0.673243 | + | 0.216939i | ||||
\(551\) | 192.976 | − | 187.434i | 0.350229 | − | 0.340171i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.1677i | 0.0852942i | ||||||||
\(554\) | −190.120 | + | 61.2624i | −0.343176 | + | 0.110582i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 248.897 | + | 346.109i | 0.447657 | + | 0.622498i | ||||
\(557\) | 507.393i | 0.910940i | 0.890251 | + | 0.455470i | \(0.150529\pi\) | ||||
−0.890251 | + | 0.455470i | \(0.849471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −133.169 | −0.238227 | ||||||||
\(560\) | −15.9256 | + | 47.4374i | −0.0284386 | + | 0.0847096i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1010.04 | + | 325.466i | −1.79722 | + | 0.579120i | ||||
\(563\) | 430.982i | 0.765510i | 0.923850 | + | 0.382755i | \(0.125025\pi\) | ||||
−0.923850 | + | 0.382755i | \(0.874975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1044.26i | 1.84825i | ||||||||
\(566\) | 83.3336 | + | 258.615i | 0.147232 | + | 0.456917i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −826.281 | − | 609.597i | −1.45472 | − | 1.07323i | ||||
\(569\) | −607.193 | −1.06712 | −0.533561 | − | 0.845761i | \(-0.679147\pi\) | ||||
−0.533561 | + | 0.845761i | \(0.679147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 248.126i | 0.434547i | 0.976111 | + | 0.217274i | \(0.0697164\pi\) | ||||
−0.976111 | + | 0.217274i | \(0.930284\pi\) | |||||||
\(572\) | −81.9958 | − | 114.021i | −0.143349 | − | 0.199337i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.40952 | + | 22.9945i | 0.0129086 | + | 0.0400600i | ||||
\(575\) | 488.510 | 0.849582 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 958.765 | 1.66164 | 0.830818 | − | 0.556543i | \(-0.187873\pi\) | ||||
0.830818 | + | 0.556543i | \(0.187873\pi\) | |||||||
\(578\) | −162.305 | + | 52.2997i | −0.280805 | + | 0.0904839i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 219.634 | + | 305.416i | 0.378679 | + | 0.526579i | ||||
\(581\) | − | 27.6034i | − | 0.0475102i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 423.708 | 0.726772 | ||||||||
\(584\) | 340.237 | − | 461.176i | 0.582597 | − | 0.789685i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 183.129 | − | 59.0098i | 0.312507 | − | 0.100699i | ||||
\(587\) | −702.884 | −1.19742 | −0.598708 | − | 0.800967i | \(-0.704319\pi\) | ||||
−0.598708 | + | 0.800967i | \(0.704319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −263.377 | + | 255.813i | −0.447159 | + | 0.434317i | ||||
\(590\) | −396.207 | + | 127.670i | −0.671538 | + | 0.216390i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 456.303 | + | 153.190i | 0.770782 | + | 0.258766i | ||||
\(593\) | − | 266.340i | − | 0.449141i | −0.974458 | − | 0.224570i | \(-0.927902\pi\) | ||
0.974458 | − | 0.224570i | \(-0.0720979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 44.6403i | 0.0750258i | ||||||||
\(596\) | 436.824 | + | 607.433i | 0.732926 | + | 1.01918i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 54.0880 | + | 167.855i | 0.0904481 | + | 0.280694i | ||||
\(599\) | − | 929.881i | − | 1.55239i | −0.630493 | − | 0.776195i | \(-0.717147\pi\) | ||
0.630493 | − | 0.776195i | \(-0.282853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 666.868i | 1.10960i | 0.831985 | + | 0.554798i | \(0.187205\pi\) | ||||
−0.831985 | + | 0.554798i | \(0.812795\pi\) | |||||||
\(602\) | −34.5854 | + | 11.1445i | −0.0574509 | + | 0.0185124i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −912.531 | + | 656.229i | −1.51081 | + | 1.08647i | ||||
\(605\) | 116.222i | 0.192103i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 146.368 | 0.241134 | 0.120567 | − | 0.992705i | \(-0.461529\pi\) | ||||
0.120567 | + | 0.992705i | \(0.461529\pi\) | |||||||
\(608\) | −418.273 | − | 441.261i | −0.687949 | − | 0.725759i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.4016 | − | 44.6936i | −0.0236093 | − | 0.0732682i | ||||
\(611\) | 56.9601i | 0.0932243i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.51007 | 0.0138827 | 0.00694133 | − | 0.999976i | \(-0.497790\pi\) | ||||
0.00694133 | + | 0.999976i | \(0.497790\pi\) | |||||||
\(614\) | −701.697 | + | 226.108i | −1.14283 | + | 0.368254i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.8373 | − | 22.7505i | −0.0500605 | − | 0.0369327i | ||||
\(617\) | − | 1036.99i | − | 1.68069i | −0.542052 | − | 0.840345i | \(-0.682352\pi\) | ||
0.542052 | − | 0.840345i | \(-0.317648\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1128.03i | − | 1.82234i | −0.412035 | − | 0.911168i | \(-0.635182\pi\) | ||
0.412035 | − | 0.911168i | \(-0.364818\pi\) | |||||||
\(620\) | −299.759 | − | 416.836i | −0.483483 | − | 0.672316i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −133.153 | + | 42.9061i | −0.214073 | + | 0.0689808i | ||||
\(623\) | 50.8790i | 0.0816677i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −737.430 | −1.17989 | ||||||||
\(626\) | 885.485 | − | 285.330i | 1.41451 | − | 0.455799i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −620.923 | + | 446.525i | −0.988731 | + | 0.711026i | ||||
\(629\) | 429.398 | 0.682668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 73.3862i | 0.116301i | 0.998308 | + | 0.0581507i | \(0.0185204\pi\) | ||||
−0.998308 | + | 0.0581507i | \(0.981480\pi\) | |||||||
\(632\) | 475.784 | − | 644.904i | 0.752823 | − | 1.02042i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 909.036 | − | 292.919i | 1.43381 | − | 0.462017i | ||||
\(635\) | 785.235i | 1.23659i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 168.341i | 0.264271i | ||||||||
\(638\) | −274.210 | + | 88.3589i | −0.429796 | + | 0.138494i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 696.249 | − | 487.948i | 1.08789 | − | 0.762419i | ||||
\(641\) | 458.489 | 0.715271 | 0.357635 | − | 0.933861i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933861i | \(0.383583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 691.411i | 1.07529i | 0.843172 | + | 0.537645i | \(0.180686\pi\) | ||||
−0.843172 | + | 0.537645i | \(0.819314\pi\) | |||||||
\(644\) | 28.0945 | + | 39.0673i | 0.0436250 | + | 0.0606636i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −479.026 | − | 254.425i | −0.741526 | − | 0.393847i | ||||
\(647\) | 504.684 | 0.780037 | 0.390018 | − | 0.920807i | \(-0.372469\pi\) | ||||
0.390018 | + | 0.920807i | \(0.372469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 318.789i | − | 0.491200i | ||||||
\(650\) | 40.4751 | + | 125.609i | 0.0622694 | + | 0.193245i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 414.688 | + | 576.652i | 0.636025 | + | 0.884436i | ||||
\(653\) | 251.132i | 0.384581i | 0.981338 | + | 0.192291i | \(0.0615916\pi\) | ||||
−0.981338 | + | 0.192291i | \(0.938408\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 841.702i | − | 1.28504i | ||||||
\(656\) | 130.640 | − | 389.134i | 0.199146 | − | 0.593192i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.76682 | + | 14.7932i | 0.00724440 | + | 0.0224820i | ||||
\(659\) | − | 785.619i | − | 1.19214i | −0.802933 | − | 0.596069i | \(-0.796729\pi\) | ||
0.802933 | − | 0.596069i | \(-0.203271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1136.79i | − | 1.71981i | −0.510455 | − | 0.859905i | \(-0.670523\pi\) | ||
0.510455 | − | 0.859905i | \(-0.329477\pi\) | |||||||
\(662\) | 302.451 | − | 97.4591i | 0.456875 | − | 0.147219i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −278.438 | + | 377.410i | −0.419334 | + | 0.568389i | ||||
\(665\) | 42.6251 | − | 41.4009i | 0.0640978 | − | 0.0622570i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 361.762 | 0.542371 | ||||||||
\(668\) | −236.168 | − | 328.407i | −0.353544 | − | 0.491628i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 56.8866 | + | 176.540i | 0.0849053 | + | 0.263492i | ||||
\(671\) | 35.9606 | 0.0535925 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 196.852i | 0.292499i | 0.989248 | + | 0.146250i | \(0.0467202\pi\) | ||||
−0.989248 | + | 0.146250i | \(0.953280\pi\) | |||||||
\(674\) | −375.215 | − | 1164.43i | −0.556699 | − | 1.72764i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 510.145 | − | 366.861i | 0.754652 | − | 0.542693i | ||||
\(677\) | 1186.26 | 1.75223 | 0.876117 | − | 0.482099i | \(-0.160125\pi\) | ||||
0.876117 | + | 0.482099i | \(0.160125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −58.4913 | −0.0861433 | ||||||||
\(680\) | 450.291 | − | 610.349i | 0.662192 | − | 0.897572i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 374.246 | − | 120.594i | 0.548748 | − | 0.176823i | ||||
\(683\) | 777.354i | 1.13815i | 0.822287 | + | 0.569073i | \(0.192698\pi\) | ||||
−0.822287 | + | 0.569073i | \(0.807302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 135.514 | 0.197831 | ||||||||
\(686\) | 28.2399 | + | 87.6387i | 0.0411660 | + | 0.127753i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 585.288 | + | 196.492i | 0.850709 | + | 0.285599i | ||||
\(689\) | − | 143.732i | − | 0.208609i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 531.659i | 0.769405i | 0.923041 | + | 0.384702i | \(0.125696\pi\) | ||||
−0.923041 | + | 0.384702i | \(0.874304\pi\) | |||||||
\(692\) | 580.426 | − | 417.402i | 0.838766 | − | 0.603182i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 633.263 | − | 204.057i | 0.912482 | − | 0.294030i | ||||
\(695\) | 707.918 | 1.01859 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 366.190i | − | 0.525380i | ||||||
\(698\) | 65.4104 | − | 21.0772i | 0.0937112 | − | 0.0301966i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.0237 | + | 29.2349i | 0.0300338 | + | 0.0417641i | ||||
\(701\) | 609.856i | 0.869980i | 0.900435 | + | 0.434990i | \(0.143248\pi\) | ||||
−0.900435 | + | 0.434990i | \(0.856752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −398.238 | − | 410.013i | −0.566484 | − | 0.583233i | ||||
\(704\) | 192.139 | + | 622.117i | 0.272925 | + | 0.883689i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.7358 | + | 126.418i | 0.0576994 | + | 0.179063i | ||||
\(707\) | 7.61166 | 0.0107661 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 963.066 | 1.35834 | 0.679172 | − | 0.733979i | \(-0.262339\pi\) | ||||
0.679172 | + | 0.733979i | \(0.262339\pi\) | |||||||
\(710\) | −1622.92 | + | 522.954i | −2.28580 | + | 0.736555i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 513.221 | − | 695.647i | 0.720816 | − | 0.977033i | ||||
\(713\) | −493.737 | −0.692479 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −233.214 | −0.326173 | ||||||||
\(716\) | −348.048 | − | 483.984i | −0.486100 | − | 0.675955i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −806.511 | + | 259.883i | −1.12327 | + | 0.361954i | ||||
\(719\) | 1180.47 | 1.64182 | 0.820910 | − | 0.571057i | \(-0.193466\pi\) | ||||
0.820910 | + | 0.571057i | \(0.193466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.05548i | − | 0.00562479i | ||||||
\(722\) | 201.325 | + | 693.363i | 0.278844 | + | 0.960336i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 93.6250 | + | 130.192i | 0.129316 | + | 0.179823i | ||||
\(725\) | 270.713 | 0.373398 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 86.0390i | 0.118348i | 0.998248 | + | 0.0591740i | \(0.0188467\pi\) | ||||
−0.998248 | + | 0.0591740i | \(0.981153\pi\) | |||||||
\(728\) | −7.71752 | + | 10.4608i | −0.0106010 | + | 0.0143692i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −291.879 | − | 905.806i | −0.399834 | − | 1.24083i | ||||
\(731\) | 550.778 | 0.753458 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −824.526 | −1.12486 | −0.562432 | − | 0.826843i | \(-0.690134\pi\) | ||||
−0.562432 | + | 0.826843i | \(0.690134\pi\) | |||||||
\(734\) | 172.332 | + | 534.810i | 0.234785 | + | 0.728624i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.95089 | − | 817.543i | 0.0135202 | − | 1.11079i | ||||
\(737\) | −142.044 | −0.192733 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1108.68i | − | 1.50024i | −0.661300 | − | 0.750121i | \(-0.729995\pi\) | ||
0.661300 | − | 0.750121i | \(-0.270005\pi\) | |||||||
\(740\) | 648.912 | − | 466.652i | 0.876908 | − | 0.630611i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0285 | − | 37.3288i | −0.0162109 | − | 0.0503084i | ||||
\(743\) | − | 1014.11i | − | 1.36488i | −0.730941 | − | 0.682441i | \(-0.760919\pi\) | ||
0.730941 | − | 0.682441i | \(-0.239081\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1242.42 | 1.66768 | ||||||||
\(746\) | −44.2972 | − | 137.471i | −0.0593797 | − | 0.184277i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 339.129 | + | 471.583i | 0.453382 | + | 0.630458i | ||||
\(749\) | 90.5822 | 0.120938 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1425.08 | −1.89758 | −0.948788 | − | 0.315915i | \(-0.897689\pi\) | ||||
−0.948788 | + | 0.315915i | \(0.897689\pi\) | |||||||
\(752\) | 84.0453 | − | 250.344i | 0.111762 | − | 0.332905i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29.9735 | + | 93.0187i | 0.0397526 | + | 0.123367i | ||||
\(755\) | 1866.46i | 2.47213i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 354.171 | 0.467861 | 0.233931 | − | 0.972253i | \(-0.424841\pi\) | ||||
0.233931 | + | 0.972253i | \(0.424841\pi\) | |||||||
\(758\) | 161.033 | − | 51.8896i | 0.212444 | − | 0.0684560i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1000.41 | + | 136.095i | −1.31633 | + | 0.179073i | ||||
\(761\) | 1284.03i | 1.68729i | 0.536899 | + | 0.843647i | \(0.319596\pi\) | ||||
−0.536899 | + | 0.843647i | \(0.680404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9571 | −0.0196030 | ||||||||
\(764\) | −39.5298 | + | 28.4270i | −0.0517405 | + | 0.0372082i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.4139 | + | 116.109i | 0.0488432 | + | 0.151578i | ||||
\(767\) | −108.141 | −0.140992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 203.965 | 0.265233 | 0.132617 | − | 0.991167i | \(-0.457662\pi\) | ||||
0.132617 | + | 0.991167i | \(0.457662\pi\) | |||||||
\(770\) | −60.5683 | + | 19.5170i | −0.0786601 | + | 0.0253467i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −627.084 | − | 872.004i | −0.812285 | − | 1.12954i | ||||
\(773\) | −528.359 | −0.683518 | −0.341759 | − | 0.939788i | \(-0.611023\pi\) | ||||
−0.341759 | + | 0.939788i | \(0.611023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −369.474 | −0.476740 | ||||||||
\(776\) | 799.728 | + | 590.007i | 1.03058 | + | 0.760318i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 90.6734 | + | 281.393i | 0.116547 | + | 0.361687i | ||||
\(779\) | −349.658 | + | 339.616i | −0.448855 | + | 0.435965i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1305.80i | − | 1.67196i | ||||||
\(782\) | −223.704 | − | 694.237i | −0.286067 | − | 0.887771i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 248.389 | − | 739.871i | 0.316823 | − | 0.943714i | ||||
\(785\) | 1270.01i | 1.61785i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.60697 | −0.0122071 | −0.00610354 | − | 0.999981i | \(-0.501943\pi\) | ||||
−0.00610354 | + | 0.999981i | \(0.501943\pi\) | |||||||
\(788\) | 157.307 | + | 218.746i | 0.199628 | + | 0.277597i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −408.160 | − | 1266.67i | −0.516659 | − | 1.60338i | ||||
\(791\) | 74.0232i | 0.0935818i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.1987i | − | 0.0153830i | ||||||
\(794\) | 220.852 | − | 71.1651i | 0.278151 | − | 0.0896286i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −811.552 | − | 1128.52i | −1.01954 | − | 1.41774i | ||||
\(797\) | −1086.28 | −1.36296 | −0.681481 | − | 0.731836i | \(-0.738664\pi\) | ||||
−0.681481 | + | 0.731836i | \(0.738664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 235.583i | − | 0.294848i | ||||||
\(800\) | 7.44646 | − | 611.784i | 0.00930807 | − | 0.764730i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 276.087 | − | 88.9636i | 0.344248 | − | 0.110927i | ||||
\(803\) | 728.814 | 0.907614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 79.9069 | 0.0992632 | ||||||||
\(806\) | −40.9082 | − | 126.953i | −0.0507546 | − | 0.157510i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −104.071 | − | 76.7795i | −0.128801 | − | 0.0950241i | ||||
\(809\) | − | 2.98547i | − | 0.00369032i | −0.999998 | − | 0.00184516i | \(-0.999413\pi\) | ||
0.999998 | − | 0.00184516i | \(-0.000587334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1009.04 | −1.24419 | −0.622094 | − | 0.782942i | \(-0.713718\pi\) | ||||
−0.622094 | + | 0.782942i | \(0.713718\pi\) | |||||||
\(812\) | 15.5689 | + | 21.6496i | 0.0191735 | + | 0.0266621i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 187.735 | + | 582.610i | 0.230632 | + | 0.715737i | ||||
\(815\) | 1179.46 | 1.44719 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −510.809 | − | 525.913i | −0.625226 | − | 0.643712i | ||||
\(818\) | −120.928 | − | 375.284i | −0.147834 | − | 0.458782i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −397.960 | − | 553.391i | −0.485317 | − | 0.674867i | ||||
\(821\) | 815.300i | 0.993057i | 0.868020 | + | 0.496528i | \(0.165392\pi\) | ||||
−0.868020 | + | 0.496528i | \(0.834608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1406.52i | 1.70901i | 0.519442 | + | 0.854505i | \(0.326140\pi\) | ||||
−0.519442 | + | 0.854505i | \(0.673860\pi\) | |||||||
\(824\) | −40.9079 | + | 55.4489i | −0.0496455 | + | 0.0672923i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0854 | + | 9.04999i | −0.0340017 | + | 0.0109564i | ||||
\(827\) | − | 212.808i | − | 0.257326i | −0.991688 | − | 0.128663i | \(-0.958932\pi\) | ||
0.991688 | − | 0.128663i | \(-0.0410685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 683.402i | 0.824369i | 0.911100 | + | 0.412185i | \(0.135234\pi\) | ||||
−0.911100 | + | 0.412185i | \(0.864766\pi\) | |||||||
\(830\) | 238.863 | + | 741.280i | 0.287787 | + | 0.893109i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 211.037 | − | 65.1783i | 0.253650 | − | 0.0783393i | ||||
\(833\) | − | 696.247i | − | 0.835830i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −671.712 | −0.804445 | ||||||||
\(836\) | 135.773 | − | 761.181i | 0.162408 | − | 0.910504i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1255.61 | − | 404.597i | 1.49835 | − | 0.482813i | ||||
\(839\) | − | 629.634i | − | 0.750458i | −0.926932 | − | 0.375229i | \(-0.877564\pi\) | ||
0.926932 | − | 0.375229i | \(-0.122436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −640.526 | −0.761624 | ||||||||
\(842\) | 438.572 | + | 1361.05i | 0.520869 | + | 1.61645i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 422.778 | − | 304.033i | 0.500922 | − | 0.360228i | ||||
\(845\) | − | 1043.43i | − | 1.23483i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.23850i | 0.00972668i | ||||||||
\(848\) | −212.078 | + | 631.714i | −0.250092 | + | 0.744946i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −167.402 | − | 519.511i | −0.196944 | − | 0.611190i | ||||
\(851\) | − | 768.629i | − | 0.903207i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1223.56 | −1.43443 | −0.717213 | − | 0.696854i | \(-0.754582\pi\) | ||||
−0.717213 | + | 0.696854i | \(0.754582\pi\) | |||||||
\(854\) | −1.02087 | − | 3.16814i | −0.00119540 | − | 0.00370976i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1238.49 | − | 913.711i | −1.44684 | − | 1.06742i | ||||
\(857\) | 549.572 | 0.641274 | 0.320637 | − | 0.947202i | \(-0.396103\pi\) | ||||
0.320637 | + | 0.947202i | \(0.396103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1063.96i | 1.23861i | 0.785151 | + | 0.619304i | \(0.212585\pi\) | ||||
−0.785151 | + | 0.619304i | \(0.787415\pi\) | |||||||
\(860\) | 832.342 | − | 598.563i | 0.967840 | − | 0.696003i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 327.961 | + | 1017.78i | 0.380465 | + | 1.18072i | ||||
\(863\) | 696.514i | 0.807084i | 0.914961 | + | 0.403542i | \(0.132221\pi\) | ||||
−0.914961 | + | 0.403542i | \(0.867779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1187.18i | − | 1.37246i | ||||||
\(866\) | 295.906 | + | 918.305i | 0.341693 | + | 1.06040i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −21.2487 | − | 29.5477i | −0.0244800 | − | 0.0340412i | ||||
\(869\) | 1019.17 | 1.17280 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.1849i | 0.0553213i | ||||||||
\(872\) | 204.502 | + | 150.874i | 0.234521 | + | 0.173020i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −455.425 | + | 857.464i | −0.521081 | + | 0.981080i | ||||
\(875\) | −18.3905 | −0.0210177 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 372.892i | − | 0.425190i | −0.977140 | − | 0.212595i | \(-0.931808\pi\) | ||
0.977140 | − | 0.212595i | \(-0.0681915\pi\) | |||||||
\(878\) | −716.687 | + | 230.938i | −0.816272 | + | 0.263028i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1024.99 | + | 344.110i | 1.16477 | + | 0.391034i | ||||
\(881\) | 1643.37i | 1.86534i | 0.360725 | + | 0.932672i | \(0.382529\pi\) | ||||
−0.360725 | + | 0.932672i | \(0.617471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1613.97i | 1.82783i | 0.405911 | + | 0.913913i | \(0.366954\pi\) | ||||
−0.405911 | + | 0.913913i | \(0.633046\pi\) | |||||||
\(884\) | 159.972 | − | 115.041i | 0.180964 | − | 0.130137i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1576.52 | − | 508.002i | 1.77937 | − | 0.573366i | ||||
\(887\) | − | 1163.22i | − | 1.31141i | −0.755019 | − | 0.655703i | \(-0.772372\pi\) | ||
0.755019 | − | 0.655703i | \(-0.227628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.6620i | 0.0626119i | ||||||||
\(890\) | −440.276 | − | 1366.34i | −0.494692 | − | 1.53521i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1218.76 | + | 876.450i | −1.36633 | + | 0.982567i | ||||
\(893\) | −224.948 | + | 218.488i | −0.251901 | + | 0.244667i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −989.922 | −1.10606 | ||||||||
\(896\) | 49.3541 | − | 34.5886i | 0.0550828 | − | 0.0386033i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −922.390 | + | 297.222i | −1.02716 | + | 0.330983i | ||||
\(899\) | −273.610 | −0.304350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 594.466i | 0.659785i | ||||||||
\(902\) | 496.848 | − | 160.100i | 0.550830 | − | 0.177494i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 746.678 | − | 1012.09i | 0.825971 | − | 1.11957i | ||||
\(905\) | 266.290 | 0.294243 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −798.239 | −0.880087 | −0.440043 | − | 0.897976i | \(-0.645037\pi\) | ||||
−0.440043 | + | 0.897976i | \(0.645037\pi\) | |||||||
\(908\) | −352.707 | − | 490.463i | −0.388444 | − | 0.540158i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.62062 | + | 20.5462i | 0.00727541 | + | 0.0225783i | ||||
\(911\) | − | 509.410i | − | 0.559177i | −0.960120 | − | 0.279588i | \(-0.909802\pi\) | ||
0.960120 | − | 0.279588i | \(-0.0901980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −596.435 | −0.653270 | ||||||||
\(914\) | −27.6742 | + | 8.91748i | −0.0302781 | + | 0.00975655i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 778.243 | − | 559.658i | 0.849610 | − | 0.610980i | ||||
\(917\) | − | 59.6647i | − | 0.0650651i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1415.52i | 1.54028i | 0.637873 | + | 0.770141i | \(0.279814\pi\) | ||||
−0.637873 | + | 0.770141i | \(0.720186\pi\) | |||||||
\(920\) | −1092.53 | − | 806.027i | −1.18754 | − | 0.876116i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 504.779 | + | 1566.51i | 0.547482 | + | 1.69904i | ||||
\(923\) | −442.960 | −0.479913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 575.180i | − | 0.621817i | ||||||
\(926\) | 8.31425 | + | 25.8022i | 0.00897867 | + | 0.0278641i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.51441 | − | 453.051i | 0.00594225 | − | 0.488202i | ||||
\(929\) | − | 1201.56i | − | 1.29339i | −0.762749 | − | 0.646695i | \(-0.776151\pi\) | ||
0.762749 | − | 0.646695i | \(-0.223849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −664.815 | + | 645.722i | −0.714087 | + | 0.693579i | ||||
\(932\) | 666.046 | + | 926.182i | 0.714641 | + | 0.993758i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 638.201 | − | 205.648i | 0.683298 | − | 0.220180i | ||||
\(935\) | 964.557 | 1.03161 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −834.064 | −0.890143 | −0.445071 | − | 0.895495i | \(-0.646822\pi\) | ||||
−0.445071 | + | 0.895495i | \(0.646822\pi\) | |||||||
\(938\) | 4.03245 | + | 12.5142i | 0.00429898 | + | 0.0133413i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −256.022 | − | 356.017i | −0.272364 | − | 0.378741i | ||||
\(941\) | 104.743 | 0.111310 | 0.0556551 | − | 0.998450i | \(-0.482275\pi\) | ||||
0.0556551 | + | 0.998450i | \(0.482275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −655.485 | −0.695106 | ||||||||
\(944\) | 475.289 | + | 159.563i | 0.503484 | + | 0.169029i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 240.802 | + | 747.298i | 0.254548 | + | 0.789956i | ||||
\(947\) | 659.420 | 0.696325 | 0.348162 | − | 0.937434i | \(-0.386806\pi\) | ||||
0.348162 | + | 0.937434i | \(0.386806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 247.231i | − | 0.260518i | ||||||
\(950\) | −340.804 | + | 641.657i | −0.358741 | + | 0.675429i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 31.9192 | − | 43.2650i | 0.0335286 | − | 0.0454465i | ||||
\(953\) | −840.251 | −0.881690 | −0.440845 | − | 0.897583i | \(-0.645321\pi\) | ||||
−0.440845 | + | 0.897583i | \(0.645321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 80.8526i | 0.0846625i | ||||||||
\(956\) | −100.440 | + | 72.2297i | −0.105063 | + | 0.0755541i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1448.23 | − | 466.665i | 1.51173 | − | 0.487124i | ||||
\(959\) | 9.60600 | 0.0100167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −587.573 | −0.611418 | ||||||||
\(962\) | 197.635 | − | 63.6841i | 0.205442 | − | 0.0661997i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 191.451 | + | 266.225i | 0.198600 | + | 0.276167i | ||||
\(965\) | −1783.56 | −1.84825 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 247.792i | − | 0.256249i | −0.991758 | − | 0.128124i | \(-0.959104\pi\) | ||
0.991758 | − | 0.128124i | \(-0.0408956\pi\) | |||||||
\(968\) | 83.1024 | − | 112.642i | 0.0858496 | − | 0.116365i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1570.76 | − | 506.148i | 1.61934 | − | 0.521802i | ||||
\(971\) | 1373.60i | 1.41463i | 0.706900 | + | 0.707314i | \(0.250093\pi\) | ||||
−0.706900 | + | 0.707314i | \(0.749907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.1813 | 0.0515738 | ||||||||
\(974\) | 1309.18 | − | 421.859i | 1.34413 | − | 0.433120i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.9993 | + | 53.6143i | −0.0184419 | + | 0.0549326i | ||||
\(977\) | 1414.12 | 1.44741 | 0.723704 | − | 0.690111i | \(-0.242438\pi\) | ||||
0.723704 | + | 0.690111i | \(0.242438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1099.36 | 1.12294 | ||||||||
\(980\) | −756.652 | − | 1052.18i | −0.772094 | − | 1.07365i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 526.813 | − | 169.755i | 0.536470 | − | 0.172867i | ||||
\(983\) | 1125.03i | 1.14448i | 0.820085 | + | 0.572242i | \(0.193926\pi\) | ||||
−0.820085 | + | 0.572242i | \(0.806074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 447.416 | 0.454229 | ||||||||
\(986\) | −123.968 | − | 384.719i | −0.125729 | − | 0.390182i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −258.211 | − | 46.0576i | −0.261347 | − | 0.0466170i | ||||
\(989\) | − | 985.900i | − | 0.996865i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −975.022 | −0.983877 | −0.491939 | − | 0.870630i | \(-0.663712\pi\) | ||||
−0.491939 | + | 0.870630i | \(0.663712\pi\) | |||||||
\(992\) | −7.52614 | + | 618.331i | −0.00758684 | + | 0.623317i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −115.042 | + | 37.0700i | −0.115736 | + | 0.0372937i | ||||
\(995\) | −2308.23 | −2.31983 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 200.568 | 0.201172 | 0.100586 | − | 0.994928i | \(-0.467928\pi\) | ||||
0.100586 | + | 0.994928i | \(0.467928\pi\) | |||||||
\(998\) | −46.1875 | − | 143.337i | −0.0462801 | − | 0.143624i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.3.b.a.683.8 | yes | 80 | |
3.2 | odd | 2 | inner | 684.3.b.a.683.73 | yes | 80 | |
4.3 | odd | 2 | inner | 684.3.b.a.683.5 | ✓ | 80 | |
12.11 | even | 2 | inner | 684.3.b.a.683.76 | yes | 80 | |
19.18 | odd | 2 | inner | 684.3.b.a.683.74 | yes | 80 | |
57.56 | even | 2 | inner | 684.3.b.a.683.7 | yes | 80 | |
76.75 | even | 2 | inner | 684.3.b.a.683.75 | yes | 80 | |
228.227 | odd | 2 | inner | 684.3.b.a.683.6 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.b.a.683.5 | ✓ | 80 | 4.3 | odd | 2 | inner | |
684.3.b.a.683.6 | yes | 80 | 228.227 | odd | 2 | inner | |
684.3.b.a.683.7 | yes | 80 | 57.56 | even | 2 | inner | |
684.3.b.a.683.8 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.b.a.683.73 | yes | 80 | 3.2 | odd | 2 | inner | |
684.3.b.a.683.74 | yes | 80 | 19.18 | odd | 2 | inner | |
684.3.b.a.683.75 | yes | 80 | 76.75 | even | 2 | inner | |
684.3.b.a.683.76 | yes | 80 | 12.11 | even | 2 | inner |