Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(76,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.76");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.7 | ||
Root | \(-1.74681 + 3.02556i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.76 |
Dual form | 105.3.h.a.76.8 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.112974 | −0.0564869 | −0.0282435 | − | 0.999601i | \(-0.508991\pi\) | ||||
−0.0282435 | + | 0.999601i | \(0.508991\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −3.98724 | −0.996809 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0.195676i | 0.0326127i | ||||||||
\(7\) | −6.71303 | + | 1.98374i | −0.959004 | + | 0.283391i | ||||
\(8\) | 0.902349 | 0.112794 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0.252617i | 0.0252617i | ||||||||
\(11\) | −15.8613 | −1.44194 | −0.720970 | − | 0.692966i | \(-0.756303\pi\) | ||||
−0.720970 | + | 0.692966i | \(0.756303\pi\) | |||||||
\(12\) | 6.90610i | 0.575508i | ||||||||
\(13\) | − | 13.3044i | − | 1.02341i | −0.859160 | − | 0.511707i | \(-0.829013\pi\) | ||
0.859160 | − | 0.511707i | \(-0.170987\pi\) | |||||||
\(14\) | 0.758397 | − | 0.224110i | 0.0541712 | − | 0.0160079i | ||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | 15.8470 | 0.990438 | ||||||||
\(17\) | 15.6784i | 0.922257i | 0.887333 | + | 0.461129i | \(0.152555\pi\) | ||||
−0.887333 | + | 0.461129i | \(0.847445\pi\) | |||||||
\(18\) | 0.338921 | 0.0188290 | ||||||||
\(19\) | − | 30.8816i | − | 1.62535i | −0.582719 | − | 0.812673i | \(-0.698011\pi\) | ||
0.582719 | − | 0.812673i | \(-0.301989\pi\) | |||||||
\(20\) | 8.91573i | 0.445787i | ||||||||
\(21\) | 3.43593 | + | 11.6273i | 0.163616 | + | 0.553681i | ||||
\(22\) | 1.79192 | 0.0814507 | ||||||||
\(23\) | 3.63638 | 0.158104 | 0.0790518 | − | 0.996871i | \(-0.474811\pi\) | ||||
0.0790518 | + | 0.996871i | \(0.474811\pi\) | |||||||
\(24\) | − | 1.56291i | − | 0.0651214i | ||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 1.50305i | 0.0578095i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 26.7664 | − | 7.90963i | 0.955944 | − | 0.282487i | ||||
\(29\) | 14.5640 | 0.502208 | 0.251104 | − | 0.967960i | \(-0.419206\pi\) | ||||
0.251104 | + | 0.967960i | \(0.419206\pi\) | |||||||
\(30\) | 0.437546 | 0.0145849 | ||||||||
\(31\) | − | 11.3504i | − | 0.366142i | −0.983100 | − | 0.183071i | \(-0.941396\pi\) | ||
0.983100 | − | 0.183071i | \(-0.0586038\pi\) | |||||||
\(32\) | −5.39969 | −0.168740 | ||||||||
\(33\) | 27.4726i | 0.832504i | ||||||||
\(34\) | − | 1.77125i | − | 0.0520955i | ||||||
\(35\) | 4.43577 | + | 15.0108i | 0.126736 | + | 0.428880i | ||||
\(36\) | 11.9617 | 0.332270 | ||||||||
\(37\) | 17.3820 | 0.469784 | 0.234892 | − | 0.972021i | \(-0.424526\pi\) | ||||
0.234892 | + | 0.972021i | \(0.424526\pi\) | |||||||
\(38\) | 3.48881i | 0.0918108i | ||||||||
\(39\) | −23.0439 | −0.590869 | ||||||||
\(40\) | − | 2.01771i | − | 0.0504428i | ||||||
\(41\) | − | 27.9286i | − | 0.681186i | −0.940211 | − | 0.340593i | \(-0.889372\pi\) | ||
0.940211 | − | 0.340593i | \(-0.110628\pi\) | |||||||
\(42\) | −0.388171 | − | 1.31358i | −0.00924216 | − | 0.0312758i | ||||
\(43\) | −12.1944 | −0.283591 | −0.141796 | − | 0.989896i | \(-0.545288\pi\) | ||||
−0.141796 | + | 0.989896i | \(0.545288\pi\) | |||||||
\(44\) | 63.2429 | 1.43734 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | −0.410816 | −0.00893078 | ||||||||
\(47\) | 80.5893i | 1.71467i | 0.514762 | + | 0.857333i | \(0.327880\pi\) | ||||
−0.514762 | + | 0.857333i | \(0.672120\pi\) | |||||||
\(48\) | − | 27.4478i | − | 0.571830i | ||||||
\(49\) | 41.1296 | − | 26.6338i | 0.839379 | − | 0.543546i | ||||
\(50\) | 0.564869 | 0.0112974 | ||||||||
\(51\) | 27.1557 | 0.532465 | ||||||||
\(52\) | 53.0477i | 1.02015i | ||||||||
\(53\) | −55.9152 | −1.05500 | −0.527502 | − | 0.849554i | \(-0.676871\pi\) | ||||
−0.527502 | + | 0.849554i | \(0.676871\pi\) | |||||||
\(54\) | − | 0.587029i | − | 0.0108709i | ||||||
\(55\) | 35.4670i | 0.644855i | ||||||||
\(56\) | −6.05750 | + | 1.79002i | −0.108170 | + | 0.0319647i | ||||
\(57\) | −53.4885 | −0.938395 | ||||||||
\(58\) | −1.64536 | −0.0283682 | ||||||||
\(59\) | − | 79.5439i | − | 1.34820i | −0.738640 | − | 0.674101i | \(-0.764531\pi\) | ||
0.738640 | − | 0.674101i | \(-0.235469\pi\) | |||||||
\(60\) | 15.4425 | 0.257375 | ||||||||
\(61\) | − | 94.5743i | − | 1.55040i | −0.631717 | − | 0.775199i | \(-0.717650\pi\) | ||
0.631717 | − | 0.775199i | \(-0.282350\pi\) | |||||||
\(62\) | 1.28230i | 0.0206822i | ||||||||
\(63\) | 20.1391 | − | 5.95121i | 0.319668 | − | 0.0944637i | ||||
\(64\) | −62.7780 | −0.980906 | ||||||||
\(65\) | −29.7495 | −0.457685 | ||||||||
\(66\) | − | 3.10369i | − | 0.0470256i | ||||||
\(67\) | −103.457 | −1.54414 | −0.772068 | − | 0.635540i | \(-0.780778\pi\) | ||||
−0.772068 | + | 0.635540i | \(0.780778\pi\) | |||||||
\(68\) | − | 62.5134i | − | 0.919314i | ||||||
\(69\) | − | 6.29840i | − | 0.0912811i | ||||||
\(70\) | −0.501126 | − | 1.69583i | −0.00715894 | − | 0.0242261i | ||||
\(71\) | −113.803 | −1.60286 | −0.801431 | − | 0.598087i | \(-0.795928\pi\) | ||||
−0.801431 | + | 0.598087i | \(0.795928\pi\) | |||||||
\(72\) | −2.70705 | −0.0375979 | ||||||||
\(73\) | 20.3444i | 0.278690i | 0.990244 | + | 0.139345i | \(0.0444998\pi\) | ||||
−0.990244 | + | 0.139345i | \(0.955500\pi\) | |||||||
\(74\) | −1.96371 | −0.0265367 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 123.132i | 1.62016i | ||||||||
\(77\) | 106.478 | − | 31.4647i | 1.38283 | − | 0.408633i | ||||
\(78\) | 2.60336 | 0.0333763 | ||||||||
\(79\) | −1.27532 | −0.0161433 | −0.00807165 | − | 0.999967i | \(-0.502569\pi\) | ||||
−0.00807165 | + | 0.999967i | \(0.502569\pi\) | |||||||
\(80\) | − | 35.4350i | − | 0.442937i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 3.15520i | 0.0384781i | ||||||||
\(83\) | − | 19.7667i | − | 0.238153i | −0.992885 | − | 0.119076i | \(-0.962007\pi\) | ||
0.992885 | − | 0.119076i | \(-0.0379934\pi\) | |||||||
\(84\) | −13.6999 | − | 46.3608i | −0.163094 | − | 0.551915i | ||||
\(85\) | 35.0579 | 0.412446 | ||||||||
\(86\) | 1.37765 | 0.0160192 | ||||||||
\(87\) | − | 25.2257i | − | 0.289950i | ||||||
\(88\) | −14.3125 | −0.162642 | ||||||||
\(89\) | 131.258i | 1.47481i | 0.675450 | + | 0.737406i | \(0.263949\pi\) | ||||
−0.675450 | + | 0.737406i | \(0.736051\pi\) | |||||||
\(90\) | − | 0.757851i | − | 0.00842057i | ||||||
\(91\) | 26.3924 | + | 89.3128i | 0.290026 | + | 0.981459i | ||||
\(92\) | −14.4991 | −0.157599 | ||||||||
\(93\) | −19.6595 | −0.211392 | ||||||||
\(94\) | − | 9.10448i | − | 0.0968562i | ||||||
\(95\) | −69.0533 | −0.726877 | ||||||||
\(96\) | 9.35254i | 0.0974223i | ||||||||
\(97\) | − | 12.4236i | − | 0.128078i | −0.997947 | − | 0.0640391i | \(-0.979602\pi\) | ||
0.997947 | − | 0.0640391i | \(-0.0203982\pi\) | |||||||
\(98\) | −4.64657 | + | 3.00892i | −0.0474139 | + | 0.0307033i | ||||
\(99\) | 47.5840 | 0.480647 | ||||||||
\(100\) | 19.9362 | 0.199362 | ||||||||
\(101\) | 15.0668i | 0.149176i | 0.997214 | + | 0.0745882i | \(0.0237642\pi\) | ||||
−0.997214 | + | 0.0745882i | \(0.976236\pi\) | |||||||
\(102\) | −3.06789 | −0.0300773 | ||||||||
\(103\) | − | 69.5863i | − | 0.675595i | −0.941219 | − | 0.337798i | \(-0.890318\pi\) | ||
0.941219 | − | 0.337798i | \(-0.109682\pi\) | |||||||
\(104\) | − | 12.0052i | − | 0.115435i | ||||||
\(105\) | 25.9995 | − | 7.68298i | 0.247614 | − | 0.0731712i | ||||
\(106\) | 6.31696 | 0.0595939 | ||||||||
\(107\) | 104.493 | 0.976569 | 0.488285 | − | 0.872684i | \(-0.337623\pi\) | ||||
0.488285 | + | 0.872684i | \(0.337623\pi\) | |||||||
\(108\) | − | 20.7183i | − | 0.191836i | ||||||
\(109\) | −19.2137 | −0.176273 | −0.0881363 | − | 0.996108i | \(-0.528091\pi\) | ||||
−0.0881363 | + | 0.996108i | \(0.528091\pi\) | |||||||
\(110\) | − | 4.00685i | − | 0.0364259i | ||||||
\(111\) | − | 30.1065i | − | 0.271230i | ||||||
\(112\) | −106.381 | + | 31.4363i | −0.949834 | + | 0.280681i | ||||
\(113\) | 208.552 | 1.84559 | 0.922795 | − | 0.385291i | \(-0.125899\pi\) | ||||
0.922795 | + | 0.385291i | \(0.125899\pi\) | |||||||
\(114\) | 6.04280 | 0.0530070 | ||||||||
\(115\) | − | 8.13119i | − | 0.0707060i | ||||||
\(116\) | −58.0703 | −0.500606 | ||||||||
\(117\) | 39.9132i | 0.341138i | ||||||||
\(118\) | 8.98637i | 0.0761557i | ||||||||
\(119\) | −31.1018 | − | 105.249i | −0.261359 | − | 0.884449i | ||||
\(120\) | −3.49478 | −0.0291232 | ||||||||
\(121\) | 130.582 | 1.07919 | ||||||||
\(122\) | 10.6844i | 0.0875772i | ||||||||
\(123\) | −48.3738 | −0.393283 | ||||||||
\(124\) | 45.2567i | 0.364974i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −2.27519 | + | 0.672331i | −0.0180571 | + | 0.00533596i | ||||
\(127\) | 65.1002 | 0.512600 | 0.256300 | − | 0.966597i | \(-0.417496\pi\) | ||||
0.256300 | + | 0.966597i | \(0.417496\pi\) | |||||||
\(128\) | 28.6910 | 0.224149 | ||||||||
\(129\) | 21.1213i | 0.163731i | ||||||||
\(130\) | 3.36092 | 0.0258532 | ||||||||
\(131\) | − | 160.360i | − | 1.22412i | −0.790812 | − | 0.612060i | \(-0.790341\pi\) | ||
0.790812 | − | 0.612060i | \(-0.209659\pi\) | |||||||
\(132\) | − | 109.540i | − | 0.829848i | ||||||
\(133\) | 61.2610 | + | 207.309i | 0.460609 | + | 1.55871i | ||||
\(134\) | 11.6879 | 0.0872235 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | 14.1474i | 0.104025i | ||||||||
\(137\) | 158.451 | 1.15658 | 0.578289 | − | 0.815832i | \(-0.303721\pi\) | ||||
0.578289 | + | 0.815832i | \(0.303721\pi\) | |||||||
\(138\) | 0.711554i | 0.00515619i | ||||||||
\(139\) | 243.471i | 1.75159i | 0.482684 | + | 0.875794i | \(0.339662\pi\) | ||||
−0.482684 | + | 0.875794i | \(0.660338\pi\) | |||||||
\(140\) | −17.6865 | − | 59.8516i | −0.126332 | − | 0.427511i | ||||
\(141\) | 139.585 | 0.989963 | ||||||||
\(142\) | 12.8568 | 0.0905408 | ||||||||
\(143\) | 211.025i | 1.47570i | ||||||||
\(144\) | −47.5410 | −0.330146 | ||||||||
\(145\) | − | 32.5662i | − | 0.224594i | ||||||
\(146\) | − | 2.29838i | − | 0.0157424i | ||||||
\(147\) | −46.1311 | − | 71.2385i | −0.313817 | − | 0.484616i | ||||
\(148\) | −69.3062 | −0.468285 | ||||||||
\(149\) | −134.390 | −0.901948 | −0.450974 | − | 0.892537i | \(-0.648923\pi\) | ||||
−0.450974 | + | 0.892537i | \(0.648923\pi\) | |||||||
\(150\) | − | 0.978382i | − | 0.00652255i | ||||||
\(151\) | 1.60056 | 0.0105997 | 0.00529987 | − | 0.999986i | \(-0.498313\pi\) | ||||
0.00529987 | + | 0.999986i | \(0.498313\pi\) | |||||||
\(152\) | − | 27.8660i | − | 0.183329i | ||||||
\(153\) | − | 47.0351i | − | 0.307419i | ||||||
\(154\) | −12.0292 | + | 3.55469i | −0.0781116 | + | 0.0230824i | ||||
\(155\) | −25.3803 | −0.163744 | ||||||||
\(156\) | 91.8814 | 0.588983 | ||||||||
\(157\) | − | 252.462i | − | 1.60804i | −0.594602 | − | 0.804020i | \(-0.702690\pi\) | ||
0.594602 | − | 0.804020i | \(-0.297310\pi\) | |||||||
\(158\) | 0.144078 | 0.000911885 | ||||||||
\(159\) | 96.8480i | 0.609107i | ||||||||
\(160\) | 12.0741i | 0.0754630i | ||||||||
\(161\) | −24.4111 | + | 7.21362i | −0.151622 | + | 0.0448051i | ||||
\(162\) | −1.01676 | −0.00627632 | ||||||||
\(163\) | −239.023 | −1.46640 | −0.733199 | − | 0.680014i | \(-0.761974\pi\) | ||||
−0.733199 | + | 0.680014i | \(0.761974\pi\) | |||||||
\(164\) | 111.358i | 0.679013i | ||||||||
\(165\) | 61.4307 | 0.372307 | ||||||||
\(166\) | 2.23312i | 0.0134525i | ||||||||
\(167\) | − | 170.456i | − | 1.02070i | −0.859968 | − | 0.510348i | \(-0.829517\pi\) | ||
0.859968 | − | 0.510348i | \(-0.170483\pi\) | |||||||
\(168\) | 3.10041 | + | 10.4919i | 0.0184548 | + | 0.0624517i | ||||
\(169\) | −8.00675 | −0.0473772 | ||||||||
\(170\) | −3.96063 | −0.0232978 | ||||||||
\(171\) | 92.6448i | 0.541782i | ||||||||
\(172\) | 48.6220 | 0.282686 | ||||||||
\(173\) | 269.554i | 1.55812i | 0.626952 | + | 0.779058i | \(0.284302\pi\) | ||||
−0.626952 | + | 0.779058i | \(0.715698\pi\) | |||||||
\(174\) | 2.84984i | 0.0163784i | ||||||||
\(175\) | 33.5652 | − | 9.91868i | 0.191801 | − | 0.0566782i | ||||
\(176\) | −251.355 | −1.42815 | ||||||||
\(177\) | −137.774 | −0.778384 | ||||||||
\(178\) | − | 14.8287i | − | 0.0833076i | ||||||
\(179\) | 132.675 | 0.741199 | 0.370599 | − | 0.928793i | \(-0.379152\pi\) | ||||
0.370599 | + | 0.928793i | \(0.379152\pi\) | |||||||
\(180\) | − | 26.7472i | − | 0.148596i | ||||||
\(181\) | − | 231.384i | − | 1.27836i | −0.769056 | − | 0.639182i | \(-0.779273\pi\) | ||
0.769056 | − | 0.639182i | \(-0.220727\pi\) | |||||||
\(182\) | −2.98165 | − | 10.0900i | −0.0163827 | − | 0.0554396i | ||||
\(183\) | −163.807 | −0.895123 | ||||||||
\(184\) | 3.28128 | 0.0178331 | ||||||||
\(185\) | − | 38.8674i | − | 0.210094i | ||||||
\(186\) | 2.22101 | 0.0119409 | ||||||||
\(187\) | − | 248.680i | − | 1.32984i | ||||||
\(188\) | − | 321.329i | − | 1.70920i | ||||||
\(189\) | −10.3078 | − | 34.8819i | −0.0545386 | − | 0.184560i | ||||
\(190\) | 7.80122 | 0.0410591 | ||||||||
\(191\) | −304.129 | −1.59230 | −0.796150 | − | 0.605099i | \(-0.793133\pi\) | ||||
−0.796150 | + | 0.605099i | \(0.793133\pi\) | |||||||
\(192\) | 108.735i | 0.566326i | ||||||||
\(193\) | 138.227 | 0.716202 | 0.358101 | − | 0.933683i | \(-0.383424\pi\) | ||||
0.358101 | + | 0.933683i | \(0.383424\pi\) | |||||||
\(194\) | 1.40354i | 0.00723474i | ||||||||
\(195\) | 51.5277i | 0.264244i | ||||||||
\(196\) | −163.993 | + | 106.195i | −0.836701 | + | 0.541812i | ||||
\(197\) | −26.9115 | −0.136607 | −0.0683034 | − | 0.997665i | \(-0.521759\pi\) | ||||
−0.0683034 | + | 0.997665i | \(0.521759\pi\) | |||||||
\(198\) | −5.37575 | −0.0271502 | ||||||||
\(199\) | − | 251.997i | − | 1.26632i | −0.774023 | − | 0.633158i | \(-0.781759\pi\) | ||
0.774023 | − | 0.633158i | \(-0.218241\pi\) | |||||||
\(200\) | −4.51174 | −0.0225587 | ||||||||
\(201\) | 179.193i | 0.891507i | ||||||||
\(202\) | − | 1.70216i | − | 0.00842651i | ||||||
\(203\) | −97.7689 | + | 28.8912i | −0.481620 | + | 0.142321i | ||||
\(204\) | −108.276 | −0.530766 | ||||||||
\(205\) | −62.4503 | −0.304636 | ||||||||
\(206\) | 7.86143i | 0.0381623i | ||||||||
\(207\) | −10.9091 | −0.0527012 | ||||||||
\(208\) | − | 210.835i | − | 1.01363i | ||||||
\(209\) | 489.823i | 2.34365i | ||||||||
\(210\) | −2.93726 | + | 0.867976i | −0.0139869 | + | 0.00413322i | ||||
\(211\) | 235.692 | 1.11702 | 0.558511 | − | 0.829497i | \(-0.311373\pi\) | ||||
0.558511 | + | 0.829497i | \(0.311373\pi\) | |||||||
\(212\) | 222.947 | 1.05164 | ||||||||
\(213\) | 197.113i | 0.925413i | ||||||||
\(214\) | −11.8050 | −0.0551634 | ||||||||
\(215\) | 27.2675i | 0.126826i | ||||||||
\(216\) | 4.68874i | 0.0217071i | ||||||||
\(217\) | 22.5162 | + | 76.1956i | 0.103761 | + | 0.351132i | ||||
\(218\) | 2.17065 | 0.00995709 | ||||||||
\(219\) | 35.2375 | 0.160902 | ||||||||
\(220\) | − | 141.415i | − | 0.642797i | ||||||
\(221\) | 208.591 | 0.943851 | ||||||||
\(222\) | 3.40125i | 0.0153210i | ||||||||
\(223\) | − | 142.790i | − | 0.640314i | −0.947365 | − | 0.320157i | \(-0.896264\pi\) | ||
0.947365 | − | 0.320157i | \(-0.103736\pi\) | |||||||
\(224\) | 36.2483 | − | 10.7116i | 0.161823 | − | 0.0478195i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −23.5609 | −0.104252 | ||||||||
\(227\) | 30.6210i | 0.134894i | 0.997723 | + | 0.0674472i | \(0.0214854\pi\) | ||||
−0.997723 | + | 0.0674472i | \(0.978515\pi\) | |||||||
\(228\) | 213.271 | 0.935400 | ||||||||
\(229\) | − | 210.682i | − | 0.920007i | −0.887917 | − | 0.460004i | \(-0.847848\pi\) | ||
0.887917 | − | 0.460004i | \(-0.152152\pi\) | |||||||
\(230\) | 0.918612i | 0.00399397i | ||||||||
\(231\) | −54.4985 | − | 184.425i | −0.235924 | − | 0.798375i | ||||
\(232\) | 13.1418 | 0.0566459 | ||||||||
\(233\) | −182.891 | −0.784940 | −0.392470 | − | 0.919765i | \(-0.628379\pi\) | ||||
−0.392470 | + | 0.919765i | \(0.628379\pi\) | |||||||
\(234\) | − | 4.50914i | − | 0.0192698i | ||||||
\(235\) | 180.203 | 0.766822 | ||||||||
\(236\) | 317.160i | 1.34390i | ||||||||
\(237\) | 2.20892i | 0.00932034i | ||||||||
\(238\) | 3.51369 | + | 11.8904i | 0.0147634 | + | 0.0499598i | ||||
\(239\) | 122.511 | 0.512597 | 0.256299 | − | 0.966598i | \(-0.417497\pi\) | ||||
0.256299 | + | 0.966598i | \(0.417497\pi\) | |||||||
\(240\) | −61.3752 | −0.255730 | ||||||||
\(241\) | 149.941i | 0.622160i | 0.950384 | + | 0.311080i | \(0.100691\pi\) | ||||
−0.950384 | + | 0.311080i | \(0.899309\pi\) | |||||||
\(242\) | −14.7524 | −0.0609601 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 377.090i | 1.54545i | ||||||||
\(245\) | −59.5549 | − | 91.9685i | −0.243081 | − | 0.375382i | ||||
\(246\) | 5.46497 | 0.0222153 | ||||||||
\(247\) | −410.861 | −1.66340 | ||||||||
\(248\) | − | 10.2420i | − | 0.0412985i | ||||||
\(249\) | −34.2369 | −0.137498 | ||||||||
\(250\) | − | 1.26309i | − | 0.00505234i | ||||||
\(251\) | − | 229.388i | − | 0.913896i | −0.889493 | − | 0.456948i | \(-0.848942\pi\) | ||
0.889493 | − | 0.456948i | \(-0.151058\pi\) | |||||||
\(252\) | −80.2993 | + | 23.7289i | −0.318648 | + | 0.0941622i | ||||
\(253\) | −57.6779 | −0.227976 | ||||||||
\(254\) | −7.35462 | −0.0289552 | ||||||||
\(255\) | − | 60.7221i | − | 0.238126i | ||||||
\(256\) | 247.871 | 0.968245 | ||||||||
\(257\) | − | 48.6524i | − | 0.189309i | −0.995510 | − | 0.0946545i | \(-0.969825\pi\) | ||
0.995510 | − | 0.0946545i | \(-0.0301746\pi\) | |||||||
\(258\) | − | 2.38616i | − | 0.00924868i | ||||||
\(259\) | −116.686 | + | 34.4814i | −0.450525 | + | 0.133133i | ||||
\(260\) | 118.618 | 0.456225 | ||||||||
\(261\) | −43.6921 | −0.167403 | ||||||||
\(262\) | 18.1164i | 0.0691467i | ||||||||
\(263\) | −37.6942 | −0.143324 | −0.0716620 | − | 0.997429i | \(-0.522830\pi\) | ||||
−0.0716620 | + | 0.997429i | \(0.522830\pi\) | |||||||
\(264\) | 24.7899i | 0.0939012i | ||||||||
\(265\) | 125.030i | 0.471812i | ||||||||
\(266\) | −6.92088 | − | 23.4205i | −0.0260184 | − | 0.0880470i | ||||
\(267\) | 227.346 | 0.851483 | ||||||||
\(268\) | 412.508 | 1.53921 | ||||||||
\(269\) | − | 291.724i | − | 1.08448i | −0.840225 | − | 0.542238i | \(-0.817577\pi\) | ||
0.840225 | − | 0.542238i | \(-0.182423\pi\) | |||||||
\(270\) | −1.31264 | −0.00486162 | ||||||||
\(271\) | − | 102.880i | − | 0.379631i | −0.981820 | − | 0.189815i | \(-0.939211\pi\) | ||
0.981820 | − | 0.189815i | \(-0.0607890\pi\) | |||||||
\(272\) | 248.455i | 0.913438i | ||||||||
\(273\) | 154.694 | − | 45.7130i | 0.566646 | − | 0.167447i | ||||
\(274\) | −17.9008 | −0.0653316 | ||||||||
\(275\) | 79.3067 | 0.288388 | ||||||||
\(276\) | 25.1132i | 0.0909898i | ||||||||
\(277\) | 381.417 | 1.37696 | 0.688479 | − | 0.725256i | \(-0.258279\pi\) | ||||
0.688479 | + | 0.725256i | \(0.258279\pi\) | |||||||
\(278\) | − | 27.5058i | − | 0.0989418i | ||||||
\(279\) | 34.0512i | 0.122047i | ||||||||
\(280\) | 4.00261 | + | 13.5450i | 0.0142950 | + | 0.0483749i | ||||
\(281\) | 17.4853 | 0.0622251 | 0.0311126 | − | 0.999516i | \(-0.490095\pi\) | ||||
0.0311126 | + | 0.999516i | \(0.490095\pi\) | |||||||
\(282\) | −15.7694 | −0.0559200 | ||||||||
\(283\) | 343.358i | 1.21328i | 0.794977 | + | 0.606640i | \(0.207483\pi\) | ||||
−0.794977 | + | 0.606640i | \(0.792517\pi\) | |||||||
\(284\) | 453.760 | 1.59775 | ||||||||
\(285\) | 119.604i | 0.419663i | ||||||||
\(286\) | − | 23.8403i | − | 0.0833579i | ||||||
\(287\) | 55.4031 | + | 187.486i | 0.193042 | + | 0.653260i | ||||
\(288\) | 16.1991 | 0.0562468 | ||||||||
\(289\) | 43.1887 | 0.149442 | ||||||||
\(290\) | 3.67913i | 0.0126866i | ||||||||
\(291\) | −21.5183 | −0.0739460 | ||||||||
\(292\) | − | 81.1179i | − | 0.277801i | ||||||
\(293\) | − | 244.504i | − | 0.834486i | −0.908795 | − | 0.417243i | \(-0.862996\pi\) | ||
0.908795 | − | 0.417243i | \(-0.137004\pi\) | |||||||
\(294\) | 5.21160 | + | 8.04809i | 0.0177265 | + | 0.0273744i | ||||
\(295\) | −177.865 | −0.602934 | ||||||||
\(296\) | 15.6846 | 0.0529887 | ||||||||
\(297\) | − | 82.4179i | − | 0.277501i | ||||||
\(298\) | 15.1826 | 0.0509482 | ||||||||
\(299\) | − | 48.3798i | − | 0.161805i | ||||||
\(300\) | − | 34.5305i | − | 0.115102i | ||||||
\(301\) | 81.8615 | − | 24.1905i | 0.271965 | − | 0.0803672i | ||||
\(302\) | −0.180822 | −0.000598747 | ||||||||
\(303\) | 26.0965 | 0.0861270 | ||||||||
\(304\) | − | 489.381i | − | 1.60981i | ||||||
\(305\) | −211.475 | −0.693359 | ||||||||
\(306\) | 5.31374i | 0.0173652i | ||||||||
\(307\) | 347.793i | 1.13287i | 0.824105 | + | 0.566437i | \(0.191679\pi\) | ||||
−0.824105 | + | 0.566437i | \(0.808321\pi\) | |||||||
\(308\) | −424.552 | + | 125.457i | −1.37841 | + | 0.407329i | ||||
\(309\) | −120.527 | −0.390055 | ||||||||
\(310\) | 2.86731 | 0.00924938 | ||||||||
\(311\) | 105.360i | 0.338778i | 0.985549 | + | 0.169389i | \(0.0541794\pi\) | ||||
−0.985549 | + | 0.169389i | \(0.945821\pi\) | |||||||
\(312\) | −20.7936 | −0.0666462 | ||||||||
\(313\) | − | 165.880i | − | 0.529967i | −0.964253 | − | 0.264984i | \(-0.914633\pi\) | ||
0.964253 | − | 0.264984i | \(-0.0853666\pi\) | |||||||
\(314\) | 28.5216i | 0.0908333i | ||||||||
\(315\) | −13.3073 | − | 45.0324i | −0.0422454 | − | 0.142960i | ||||
\(316\) | 5.08500 | 0.0160918 | ||||||||
\(317\) | −96.7933 | −0.305342 | −0.152671 | − | 0.988277i | \(-0.548787\pi\) | ||||
−0.152671 | + | 0.988277i | \(0.548787\pi\) | |||||||
\(318\) | − | 10.9413i | − | 0.0344066i | ||||||
\(319\) | −231.005 | −0.724154 | ||||||||
\(320\) | 140.376i | 0.438675i | ||||||||
\(321\) | − | 180.987i | − | 0.563823i | ||||||
\(322\) | 2.75782 | − | 0.814951i | 0.00856466 | − | 0.00253090i | ||||
\(323\) | 484.173 | 1.49899 | ||||||||
\(324\) | −35.8851 | −0.110757 | ||||||||
\(325\) | 66.5219i | 0.204683i | ||||||||
\(326\) | 27.0033 | 0.0828323 | ||||||||
\(327\) | 33.2791i | 0.101771i | ||||||||
\(328\) | − | 25.2014i | − | 0.0768334i | ||||||
\(329\) | −159.868 | − | 540.999i | −0.485921 | − | 1.64437i | ||||
\(330\) | −6.94006 | −0.0210305 | ||||||||
\(331\) | −193.682 | −0.585141 | −0.292571 | − | 0.956244i | \(-0.594511\pi\) | ||||
−0.292571 | + | 0.956244i | \(0.594511\pi\) | |||||||
\(332\) | 78.8145i | 0.237393i | ||||||||
\(333\) | −52.1461 | −0.156595 | ||||||||
\(334\) | 19.2571i | 0.0576559i | ||||||||
\(335\) | 231.337i | 0.690559i | ||||||||
\(336\) | 54.4493 | + | 184.258i | 0.162051 | + | 0.548387i | ||||
\(337\) | −238.742 | −0.708433 | −0.354216 | − | 0.935163i | \(-0.615252\pi\) | ||||
−0.354216 | + | 0.935163i | \(0.615252\pi\) | |||||||
\(338\) | 0.904554 | 0.00267619 | ||||||||
\(339\) | − | 361.222i | − | 1.06555i | ||||||
\(340\) | −139.784 | −0.411130 | ||||||||
\(341\) | 180.033i | 0.527955i | ||||||||
\(342\) | − | 10.4664i | − | 0.0306036i | ||||||
\(343\) | −223.270 | + | 260.384i | −0.650932 | + | 0.759136i | ||||
\(344\) | −11.0036 | −0.0319873 | ||||||||
\(345\) | −14.0836 | −0.0408222 | ||||||||
\(346\) | − | 30.4526i | − | 0.0880132i | ||||||
\(347\) | −533.787 | −1.53829 | −0.769145 | − | 0.639074i | \(-0.779318\pi\) | ||||
−0.769145 | + | 0.639074i | \(0.779318\pi\) | |||||||
\(348\) | 100.581i | 0.289025i | ||||||||
\(349\) | 230.498i | 0.660454i | 0.943902 | + | 0.330227i | \(0.107125\pi\) | ||||
−0.943902 | + | 0.330227i | \(0.892875\pi\) | |||||||
\(350\) | −3.79198 | + | 1.12055i | −0.0108342 | + | 0.00320158i | ||||
\(351\) | 69.1316 | 0.196956 | ||||||||
\(352\) | 85.6463 | 0.243313 | ||||||||
\(353\) | − | 12.3883i | − | 0.0350944i | −0.999846 | − | 0.0175472i | \(-0.994414\pi\) | ||
0.999846 | − | 0.0175472i | \(-0.00558574\pi\) | |||||||
\(354\) | 15.5649 | 0.0439685 | ||||||||
\(355\) | 254.472i | 0.716822i | ||||||||
\(356\) | − | 523.358i | − | 1.47011i | ||||||
\(357\) | −182.297 | + | 53.8698i | −0.510637 | + | 0.150896i | ||||
\(358\) | −14.9888 | −0.0418680 | ||||||||
\(359\) | −442.447 | −1.23244 | −0.616222 | − | 0.787572i | \(-0.711338\pi\) | ||||
−0.616222 | + | 0.787572i | \(0.711338\pi\) | |||||||
\(360\) | 6.05314i | 0.0168143i | ||||||||
\(361\) | −592.673 | −1.64175 | ||||||||
\(362\) | 26.1403i | 0.0722108i | ||||||||
\(363\) | − | 226.175i | − | 0.623071i | ||||||
\(364\) | −105.233 | − | 356.111i | −0.289101 | − | 0.978327i | ||||
\(365\) | 45.4915 | 0.124634 | ||||||||
\(366\) | 18.5060 | 0.0505627 | ||||||||
\(367\) | 567.114i | 1.54527i | 0.634851 | + | 0.772635i | \(0.281062\pi\) | ||||
−0.634851 | + | 0.772635i | \(0.718938\pi\) | |||||||
\(368\) | 57.6257 | 0.156592 | ||||||||
\(369\) | 83.7859i | 0.227062i | ||||||||
\(370\) | 4.39100i | 0.0118676i | ||||||||
\(371\) | 375.361 | − | 110.921i | 1.01175 | − | 0.298979i | ||||
\(372\) | 78.3870 | 0.210718 | ||||||||
\(373\) | −106.146 | −0.284574 | −0.142287 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(374\) | 28.0943i | 0.0751185i | ||||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | 72.7197i | 0.193403i | ||||||||
\(377\) | − | 193.766i | − | 0.513967i | ||||||
\(378\) | 1.16451 | + | 3.94075i | 0.00308072 | + | 0.0104253i | ||||
\(379\) | 715.733 | 1.88848 | 0.944239 | − | 0.329262i | \(-0.106800\pi\) | ||||
0.944239 | + | 0.329262i | \(0.106800\pi\) | |||||||
\(380\) | 275.332 | 0.724558 | ||||||||
\(381\) | − | 112.757i | − | 0.295950i | ||||||
\(382\) | 34.3587 | 0.0899441 | ||||||||
\(383\) | − | 571.840i | − | 1.49305i | −0.665355 | − | 0.746527i | \(-0.731720\pi\) | ||
0.665355 | − | 0.746527i | \(-0.268280\pi\) | |||||||
\(384\) | − | 49.6943i | − | 0.129412i | ||||||
\(385\) | −70.3573 | − | 238.091i | −0.182746 | − | 0.618419i | ||||
\(386\) | −15.6160 | −0.0404560 | ||||||||
\(387\) | 36.5832 | 0.0945304 | ||||||||
\(388\) | 49.5358i | 0.127670i | ||||||||
\(389\) | −12.6584 | −0.0325409 | −0.0162705 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162705 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(390\) | − | 5.82128i | − | 0.0149264i | ||||||
\(391\) | 57.0125i | 0.145812i | ||||||||
\(392\) | 37.1132 | − | 24.0330i | 0.0946766 | − | 0.0613086i | ||||
\(393\) | −277.751 | −0.706745 | ||||||||
\(394\) | 3.04030 | 0.00771650 | ||||||||
\(395\) | 2.85170i | 0.00721950i | ||||||||
\(396\) | −189.729 | −0.479113 | ||||||||
\(397\) | − | 29.1232i | − | 0.0733582i | −0.999327 | − | 0.0366791i | \(-0.988322\pi\) | ||
0.999327 | − | 0.0366791i | \(-0.0116779\pi\) | |||||||
\(398\) | 28.4690i | 0.0715302i | ||||||||
\(399\) | 359.070 | − | 106.107i | 0.899925 | − | 0.265933i | ||||
\(400\) | −79.2350 | −0.198088 | ||||||||
\(401\) | 144.012 | 0.359133 | 0.179567 | − | 0.983746i | \(-0.442530\pi\) | ||||
0.179567 | + | 0.983746i | \(0.442530\pi\) | |||||||
\(402\) | − | 20.2441i | − | 0.0503585i | ||||||
\(403\) | −151.010 | −0.374715 | ||||||||
\(404\) | − | 60.0749i | − | 0.148700i | ||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | 11.0453 | − | 3.26395i | 0.0272052 | − | 0.00803929i | ||||
\(407\) | −275.702 | −0.677401 | ||||||||
\(408\) | 24.5039 | 0.0600587 | ||||||||
\(409\) | 338.914i | 0.828641i | 0.910131 | + | 0.414320i | \(0.135981\pi\) | ||||
−0.910131 | + | 0.414320i | \(0.864019\pi\) | |||||||
\(410\) | 7.05525 | 0.0172079 | ||||||||
\(411\) | − | 274.446i | − | 0.667751i | ||||||
\(412\) | 277.457i | 0.673440i | ||||||||
\(413\) | 157.794 | + | 533.980i | 0.382068 | + | 1.29293i | ||||
\(414\) | 1.23245 | 0.00297693 | ||||||||
\(415\) | −44.1997 | −0.106505 | ||||||||
\(416\) | 71.8396i | 0.172691i | ||||||||
\(417\) | 421.704 | 1.01128 | ||||||||
\(418\) | − | 55.3372i | − | 0.132386i | ||||||
\(419\) | − | 101.585i | − | 0.242446i | −0.992625 | − | 0.121223i | \(-0.961318\pi\) | ||
0.992625 | − | 0.121223i | \(-0.0386816\pi\) | |||||||
\(420\) | −103.666 | + | 30.6339i | −0.246824 | + | 0.0729378i | ||||
\(421\) | −145.700 | −0.346081 | −0.173041 | − | 0.984915i | \(-0.555359\pi\) | ||||
−0.173041 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(422\) | −26.6270 | −0.0630972 | ||||||||
\(423\) | − | 241.768i | − | 0.571555i | ||||||
\(424\) | −50.4550 | −0.118998 | ||||||||
\(425\) | − | 78.3919i | − | 0.184451i | ||||||
\(426\) | − | 22.2686i | − | 0.0522737i | ||||||
\(427\) | 187.610 | + | 634.880i | 0.439369 | + | 1.48684i | ||||
\(428\) | −416.638 | −0.973453 | ||||||||
\(429\) | 365.507 | 0.851997 | ||||||||
\(430\) | − | 3.08052i | − | 0.00716400i | ||||||
\(431\) | 497.669 | 1.15468 | 0.577342 | − | 0.816502i | \(-0.304090\pi\) | ||||
0.577342 | + | 0.816502i | \(0.304090\pi\) | |||||||
\(432\) | 82.3435i | 0.190610i | ||||||||
\(433\) | − | 605.000i | − | 1.39723i | −0.715499 | − | 0.698614i | \(-0.753801\pi\) | ||
0.715499 | − | 0.698614i | \(-0.246199\pi\) | |||||||
\(434\) | −2.54374 | − | 8.60811i | −0.00586116 | − | 0.0198344i | ||||
\(435\) | −56.4063 | −0.129670 | ||||||||
\(436\) | 76.6096 | 0.175710 | ||||||||
\(437\) | − | 112.297i | − | 0.256973i | ||||||
\(438\) | −3.98092 | −0.00908886 | ||||||||
\(439\) | 211.605i | 0.482015i | 0.970523 | + | 0.241008i | \(0.0774779\pi\) | ||||
−0.970523 | + | 0.241008i | \(0.922522\pi\) | |||||||
\(440\) | 32.0036i | 0.0727355i | ||||||||
\(441\) | −123.389 | + | 79.9013i | −0.279793 | + | 0.181182i | ||||
\(442\) | −23.5653 | −0.0533152 | ||||||||
\(443\) | 794.013 | 1.79235 | 0.896177 | − | 0.443697i | \(-0.146334\pi\) | ||||
0.896177 | + | 0.443697i | \(0.146334\pi\) | |||||||
\(444\) | 120.042i | 0.270365i | ||||||||
\(445\) | 293.502 | 0.659556 | ||||||||
\(446\) | 16.1315i | 0.0361693i | ||||||||
\(447\) | 232.771i | 0.520740i | ||||||||
\(448\) | 421.431 | − | 124.535i | 0.940693 | − | 0.277980i | ||||
\(449\) | −486.171 | −1.08279 | −0.541393 | − | 0.840769i | \(-0.682103\pi\) | ||||
−0.541393 | + | 0.840769i | \(0.682103\pi\) | |||||||
\(450\) | −1.69461 | −0.00376579 | ||||||||
\(451\) | 442.985i | 0.982229i | ||||||||
\(452\) | −831.545 | −1.83970 | ||||||||
\(453\) | − | 2.77226i | − | 0.00611977i | ||||||
\(454\) | − | 3.45938i | − | 0.00761977i | ||||||
\(455\) | 199.709 | − | 59.0152i | 0.438922 | − | 0.129704i | ||||
\(456\) | −48.2653 | −0.105845 | ||||||||
\(457\) | 114.609 | 0.250786 | 0.125393 | − | 0.992107i | \(-0.459981\pi\) | ||||
0.125393 | + | 0.992107i | \(0.459981\pi\) | |||||||
\(458\) | 23.8015i | 0.0519684i | ||||||||
\(459\) | −81.4672 | −0.177488 | ||||||||
\(460\) | 32.4210i | 0.0704804i | ||||||||
\(461\) | 352.184i | 0.763957i | 0.924171 | + | 0.381978i | \(0.124757\pi\) | ||||
−0.924171 | + | 0.381978i | \(0.875243\pi\) | |||||||
\(462\) | 6.15690 | + | 20.8352i | 0.0133266 | + | 0.0450978i | ||||
\(463\) | −226.624 | −0.489468 | −0.244734 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244734 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(464\) | 230.796 | 0.497406 | ||||||||
\(465\) | 43.9599i | 0.0945375i | ||||||||
\(466\) | 20.6619 | 0.0443388 | ||||||||
\(467\) | 405.655i | 0.868641i | 0.900758 | + | 0.434320i | \(0.143011\pi\) | ||||
−0.900758 | + | 0.434320i | \(0.856989\pi\) | |||||||
\(468\) | − | 159.143i | − | 0.340050i | ||||||
\(469\) | 694.511 | − | 205.232i | 1.48083 | − | 0.437594i | ||||
\(470\) | −20.3582 | −0.0433154 | ||||||||
\(471\) | −437.278 | −0.928403 | ||||||||
\(472\) | − | 71.7763i | − | 0.152068i | ||||||
\(473\) | 193.420 | 0.408921 | ||||||||
\(474\) | − | 0.249550i | − | 0.000526477i | ||||||
\(475\) | 154.408i | 0.325069i | ||||||||
\(476\) | 124.010 | + | 419.654i | 0.260525 | + | 0.881627i | ||||
\(477\) | 167.746 | 0.351668 | ||||||||
\(478\) | −13.8405 | −0.0289550 | ||||||||
\(479\) | − | 900.420i | − | 1.87979i | −0.341463 | − | 0.939895i | \(-0.610922\pi\) | ||
0.341463 | − | 0.939895i | \(-0.389078\pi\) | |||||||
\(480\) | 20.9129 | 0.0435686 | ||||||||
\(481\) | − | 231.257i | − | 0.480784i | ||||||
\(482\) | − | 16.9394i | − | 0.0351439i | ||||||
\(483\) | 12.4944 | + | 42.2813i | 0.0258682 | + | 0.0875390i | ||||
\(484\) | −520.661 | −1.07575 | ||||||||
\(485\) | −27.7800 | −0.0572783 | ||||||||
\(486\) | 1.76109i | 0.00362364i | ||||||||
\(487\) | 55.4219 | 0.113803 | 0.0569014 | − | 0.998380i | \(-0.481878\pi\) | ||||
0.0569014 | + | 0.998380i | \(0.481878\pi\) | |||||||
\(488\) | − | 85.3390i | − | 0.174875i | ||||||
\(489\) | 414.000i | 0.846625i | ||||||||
\(490\) | 6.72815 | + | 10.3900i | 0.0137309 | + | 0.0212042i | ||||
\(491\) | 616.592 | 1.25579 | 0.627894 | − | 0.778299i | \(-0.283917\pi\) | ||||
0.627894 | + | 0.778299i | \(0.283917\pi\) | |||||||
\(492\) | 192.878 | 0.392028 | ||||||||
\(493\) | 228.340i | 0.463165i | ||||||||
\(494\) | 46.4165 | 0.0939605 | ||||||||
\(495\) | − | 106.401i | − | 0.214952i | ||||||
\(496\) | − | 179.870i | − | 0.362641i | ||||||
\(497\) | 763.965 | − | 225.756i | 1.53715 | − | 0.454237i | ||||
\(498\) | 3.86788 | 0.00776682 | ||||||||
\(499\) | 624.620 | 1.25174 | 0.625872 | − | 0.779926i | \(-0.284743\pi\) | ||||
0.625872 | + | 0.779926i | \(0.284743\pi\) | |||||||
\(500\) | − | 44.5787i | − | 0.0891573i | ||||||
\(501\) | −295.239 | −0.589299 | ||||||||
\(502\) | 25.9148i | 0.0516232i | ||||||||
\(503\) | − | 226.444i | − | 0.450187i | −0.974337 | − | 0.225093i | \(-0.927731\pi\) | ||
0.974337 | − | 0.225093i | \(-0.0722687\pi\) | |||||||
\(504\) | 18.1725 | − | 5.37007i | 0.0360565 | − | 0.0106549i | ||||
\(505\) | 33.6904 | 0.0667137 | ||||||||
\(506\) | 6.51609 | 0.0128776 | ||||||||
\(507\) | 13.8681i | 0.0273533i | ||||||||
\(508\) | −259.570 | −0.510965 | ||||||||
\(509\) | 468.169i | 0.919781i | 0.887976 | + | 0.459891i | \(0.152111\pi\) | ||||
−0.887976 | + | 0.459891i | \(0.847889\pi\) | |||||||
\(510\) | 6.86000i | 0.0134510i | ||||||||
\(511\) | −40.3579 | − | 136.573i | −0.0789783 | − | 0.267265i | ||||
\(512\) | −142.767 | −0.278842 | ||||||||
\(513\) | 160.465 | 0.312798 | ||||||||
\(514\) | 5.49645i | 0.0106935i | ||||||||
\(515\) | −155.600 | −0.302135 | ||||||||
\(516\) | − | 84.2158i | − | 0.163209i | ||||||
\(517\) | − | 1278.25i | − | 2.47245i | ||||||
\(518\) | 13.1825 | − | 3.89549i | 0.0254488 | − | 0.00752025i | ||||
\(519\) | 466.881 | 0.899579 | ||||||||
\(520\) | −26.8444 | −0.0516239 | ||||||||
\(521\) | 458.100i | 0.879271i | 0.898176 | + | 0.439635i | \(0.144892\pi\) | ||||
−0.898176 | + | 0.439635i | \(0.855108\pi\) | |||||||
\(522\) | 4.93607 | 0.00945607 | ||||||||
\(523\) | 256.863i | 0.491135i | 0.969380 | + | 0.245567i | \(0.0789742\pi\) | ||||
−0.969380 | + | 0.245567i | \(0.921026\pi\) | |||||||
\(524\) | 639.392i | 1.22021i | ||||||||
\(525\) | −17.1797 | − | 58.1366i | −0.0327232 | − | 0.110736i | ||||
\(526\) | 4.25846 | 0.00809593 | ||||||||
\(527\) | 177.956 | 0.337677 | ||||||||
\(528\) | 435.359i | 0.824544i | ||||||||
\(529\) | −515.777 | −0.975003 | ||||||||
\(530\) | − | 14.1251i | − | 0.0266512i | ||||||
\(531\) | 238.632i | 0.449400i | ||||||||
\(532\) | −244.262 | − | 826.590i | −0.459139 | − | 1.55374i | ||||
\(533\) | −371.573 | −0.697136 | ||||||||
\(534\) | −25.6841 | −0.0480976 | ||||||||
\(535\) | − | 233.653i | − | 0.436735i | ||||||
\(536\) | −93.3544 | −0.174169 | ||||||||
\(537\) | − | 229.799i | − | 0.427931i | ||||||
\(538\) | 32.9572i | 0.0612587i | ||||||||
\(539\) | −652.370 | + | 422.447i | −1.21033 | + | 0.783761i | ||||
\(540\) | −46.3275 | −0.0857917 | ||||||||
\(541\) | −57.7912 | −0.106823 | −0.0534115 | − | 0.998573i | \(-0.517009\pi\) | ||||
−0.0534115 | + | 0.998573i | \(0.517009\pi\) | |||||||
\(542\) | 11.6227i | 0.0214442i | ||||||||
\(543\) | −400.768 | −0.738063 | ||||||||
\(544\) | − | 84.6584i | − | 0.155622i | ||||||
\(545\) | 42.9632i | 0.0788315i | ||||||||
\(546\) | −17.4764 | + | 5.16437i | −0.0320081 | + | 0.00945856i | ||||
\(547\) | 658.275 | 1.20343 | 0.601714 | − | 0.798712i | \(-0.294485\pi\) | ||||
0.601714 | + | 0.798712i | \(0.294485\pi\) | |||||||
\(548\) | −631.783 | −1.15289 | ||||||||
\(549\) | 283.723i | 0.516799i | ||||||||
\(550\) | −8.95958 | −0.0162901 | ||||||||
\(551\) | − | 449.761i | − | 0.816263i | ||||||
\(552\) | − | 5.68335i | − | 0.0102959i | ||||||
\(553\) | 8.56126 | − | 2.52990i | 0.0154815 | − | 0.00457486i | ||||
\(554\) | −43.0902 | −0.0777801 | ||||||||
\(555\) | −67.3203 | −0.121298 | ||||||||
\(556\) | − | 970.776i | − | 1.74600i | ||||||
\(557\) | −782.705 | −1.40521 | −0.702607 | − | 0.711578i | \(-0.747981\pi\) | ||||
−0.702607 | + | 0.711578i | \(0.747981\pi\) | |||||||
\(558\) | − | 3.84690i | − | 0.00689408i | ||||||
\(559\) | 162.239i | 0.290231i | ||||||||
\(560\) | 70.2937 | + | 237.876i | 0.125524 | + | 0.424779i | ||||
\(561\) | −430.726 | −0.767783 | ||||||||
\(562\) | −1.97538 | −0.00351491 | ||||||||
\(563\) | 632.083i | 1.12271i | 0.827577 | + | 0.561353i | \(0.189719\pi\) | ||||
−0.827577 | + | 0.561353i | \(0.810281\pi\) | |||||||
\(564\) | −556.558 | −0.986804 | ||||||||
\(565\) | − | 466.336i | − | 0.825373i | ||||||
\(566\) | − | 38.7905i | − | 0.0685345i | ||||||
\(567\) | −60.4173 | + | 17.8536i | −0.106556 | + | 0.0314879i | ||||
\(568\) | −102.690 | −0.180793 | ||||||||
\(569\) | −603.746 | −1.06107 | −0.530533 | − | 0.847665i | \(-0.678008\pi\) | ||||
−0.530533 | + | 0.847665i | \(0.678008\pi\) | |||||||
\(570\) | − | 13.5121i | − | 0.0237055i | ||||||
\(571\) | −638.070 | −1.11746 | −0.558730 | − | 0.829349i | \(-0.688711\pi\) | ||||
−0.558730 | + | 0.829349i | \(0.688711\pi\) | |||||||
\(572\) | − | 841.408i | − | 1.47099i | ||||||
\(573\) | 526.767i | 0.919315i | ||||||||
\(574\) | −6.25909 | − | 21.1810i | −0.0109043 | − | 0.0369007i | ||||
\(575\) | −18.1819 | −0.0316207 | ||||||||
\(576\) | 188.334 | 0.326969 | ||||||||
\(577\) | − | 449.363i | − | 0.778792i | −0.921070 | − | 0.389396i | \(-0.872684\pi\) | ||
0.921070 | − | 0.389396i | \(-0.127316\pi\) | |||||||
\(578\) | −4.87919 | −0.00844151 | ||||||||
\(579\) | − | 239.416i | − | 0.413499i | ||||||
\(580\) | 129.849i | 0.223878i | ||||||||
\(581\) | 39.2119 | + | 132.694i | 0.0674904 | + | 0.228390i | ||||
\(582\) | 2.43100 | 0.00417698 | ||||||||
\(583\) | 886.890 | 1.52125 | ||||||||
\(584\) | 18.3577i | 0.0314345i | ||||||||
\(585\) | 89.2486 | 0.152562 | ||||||||
\(586\) | 27.6226i | 0.0471375i | ||||||||
\(587\) | 133.202i | 0.226920i | 0.993543 | + | 0.113460i | \(0.0361935\pi\) | ||||
−0.993543 | + | 0.113460i | \(0.963807\pi\) | |||||||
\(588\) | 183.935 | + | 284.045i | 0.312815 | + | 0.483069i | ||||
\(589\) | −350.519 | −0.595108 | ||||||||
\(590\) | 20.0941 | 0.0340579 | ||||||||
\(591\) | 46.6122i | 0.0788700i | ||||||||
\(592\) | 275.453 | 0.465292 | ||||||||
\(593\) | 444.341i | 0.749310i | 0.927164 | + | 0.374655i | \(0.122239\pi\) | ||||
−0.927164 | + | 0.374655i | \(0.877761\pi\) | |||||||
\(594\) | 9.31107i | 0.0156752i | ||||||||
\(595\) | −235.345 | + | 69.5457i | −0.395537 | + | 0.116883i | ||||
\(596\) | 535.846 | 0.899070 | ||||||||
\(597\) | −436.471 | −0.731107 | ||||||||
\(598\) | 5.46565i | 0.00913989i | ||||||||
\(599\) | −230.917 | −0.385504 | −0.192752 | − | 0.981247i | \(-0.561741\pi\) | ||||
−0.192752 | + | 0.981247i | \(0.561741\pi\) | |||||||
\(600\) | 7.81457i | 0.0130243i | ||||||||
\(601\) | − | 147.957i | − | 0.246185i | −0.992395 | − | 0.123092i | \(-0.960719\pi\) | ||
0.992395 | − | 0.123092i | \(-0.0392812\pi\) | |||||||
\(602\) | −9.24821 | + | 2.73289i | −0.0153625 | + | 0.00453969i | ||||
\(603\) | 310.371 | 0.514712 | ||||||||
\(604\) | −6.38182 | −0.0105659 | ||||||||
\(605\) | − | 291.990i | − | 0.482629i | ||||||
\(606\) | −2.94822 | −0.00486505 | ||||||||
\(607\) | 1036.13i | 1.70697i | 0.521119 | + | 0.853484i | \(0.325515\pi\) | ||||
−0.521119 | + | 0.853484i | \(0.674485\pi\) | |||||||
\(608\) | 166.751i | 0.274262i | ||||||||
\(609\) | 50.0411 | + | 169.341i | 0.0821692 | + | 0.278063i | ||||
\(610\) | 23.8911 | 0.0391657 | ||||||||
\(611\) | 1072.19 | 1.75481 | ||||||||
\(612\) | 187.540i | 0.306438i | ||||||||
\(613\) | −175.987 | −0.287091 | −0.143545 | − | 0.989644i | \(-0.545850\pi\) | ||||
−0.143545 | + | 0.989644i | \(0.545850\pi\) | |||||||
\(614\) | − | 39.2915i | − | 0.0639926i | ||||||
\(615\) | 108.167i | 0.175881i | ||||||||
\(616\) | 96.0800 | − | 28.3922i | 0.155974 | − | 0.0460912i | ||||
\(617\) | −635.690 | −1.03029 | −0.515146 | − | 0.857103i | \(-0.672262\pi\) | ||||
−0.515146 | + | 0.857103i | \(0.672262\pi\) | |||||||
\(618\) | 13.6164 | 0.0220330 | ||||||||
\(619\) | − | 581.258i | − | 0.939027i | −0.882925 | − | 0.469514i | \(-0.844429\pi\) | ||
0.882925 | − | 0.469514i | \(-0.155571\pi\) | |||||||
\(620\) | 101.197 | 0.163221 | ||||||||
\(621\) | 18.8952i | 0.0304270i | ||||||||
\(622\) | − | 11.9029i | − | 0.0191365i | ||||||
\(623\) | −260.382 | − | 881.141i | −0.417948 | − | 1.41435i | ||||
\(624\) | −365.176 | −0.585219 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 18.7401i | 0.0299362i | ||||||||
\(627\) | 848.399 | 1.35311 | ||||||||
\(628\) | 1006.63i | 1.60291i | ||||||||
\(629\) | 272.522i | 0.433262i | ||||||||
\(630\) | 1.50338 | + | 5.08748i | 0.00238631 | + | 0.00807537i | ||||
\(631\) | −550.845 | −0.872972 | −0.436486 | − | 0.899711i | \(-0.643777\pi\) | ||||
−0.436486 | + | 0.899711i | \(0.643777\pi\) | |||||||
\(632\) | −1.15078 | −0.00182086 | ||||||||
\(633\) | − | 408.230i | − | 0.644913i | ||||||
\(634\) | 10.9351 | 0.0172478 | ||||||||
\(635\) | − | 145.569i | − | 0.229242i | ||||||
\(636\) | − | 386.156i | − | 0.607163i | ||||||
\(637\) | −354.346 | − | 547.204i | −0.556273 | − | 0.859033i | ||||
\(638\) | 26.0975 | 0.0409052 | ||||||||
\(639\) | 341.410 | 0.534287 | ||||||||
\(640\) | − | 64.1551i | − | 0.100242i | ||||||
\(641\) | −64.8667 | −0.101196 | −0.0505981 | − | 0.998719i | \(-0.516113\pi\) | ||||
−0.0505981 | + | 0.998719i | \(0.516113\pi\) | |||||||
\(642\) | 20.4468i | 0.0318486i | ||||||||
\(643\) | − | 812.068i | − | 1.26294i | −0.775402 | − | 0.631468i | \(-0.782453\pi\) | ||
0.775402 | − | 0.631468i | \(-0.217547\pi\) | |||||||
\(644\) | 97.3330 | − | 28.7624i | 0.151138 | − | 0.0446621i | ||||
\(645\) | 47.2288 | 0.0732229 | ||||||||
\(646\) | −54.6989 | −0.0846732 | ||||||||
\(647\) | − | 618.282i | − | 0.955613i | −0.878465 | − | 0.477807i | \(-0.841432\pi\) | ||
0.878465 | − | 0.477807i | \(-0.158568\pi\) | |||||||
\(648\) | 8.12114 | 0.0125326 | ||||||||
\(649\) | 1261.67i | 1.94402i | ||||||||
\(650\) | − | 7.51524i | − | 0.0115619i | ||||||
\(651\) | 131.975 | − | 38.9992i | 0.202726 | − | 0.0599066i | ||||
\(652\) | 953.041 | 1.46172 | ||||||||
\(653\) | −694.281 | −1.06322 | −0.531609 | − | 0.846990i | \(-0.678412\pi\) | ||||
−0.531609 | + | 0.846990i | \(0.678412\pi\) | |||||||
\(654\) | − | 3.75967i | − | 0.00574873i | ||||||
\(655\) | −358.575 | −0.547443 | ||||||||
\(656\) | − | 442.585i | − | 0.674672i | ||||||
\(657\) | − | 61.0332i | − | 0.0928968i | ||||||
\(658\) | 18.0609 | + | 61.1187i | 0.0274482 | + | 0.0928855i | ||||
\(659\) | 514.683 | 0.781007 | 0.390503 | − | 0.920601i | \(-0.372301\pi\) | ||||
0.390503 | + | 0.920601i | \(0.372301\pi\) | |||||||
\(660\) | −244.939 | −0.371119 | ||||||||
\(661\) | 347.998i | 0.526472i | 0.964731 | + | 0.263236i | \(0.0847899\pi\) | ||||
−0.964731 | + | 0.263236i | \(0.915210\pi\) | |||||||
\(662\) | 21.8810 | 0.0330528 | ||||||||
\(663\) | − | 361.290i | − | 0.544933i | ||||||
\(664\) | − | 17.8364i | − | 0.0268621i | ||||||
\(665\) | 463.557 | − | 136.984i | 0.697079 | − | 0.205990i | ||||
\(666\) | 5.89114 | 0.00884556 | ||||||||
\(667\) | 52.9604 | 0.0794009 | ||||||||
\(668\) | 679.649i | 1.01744i | ||||||||
\(669\) | −247.319 | −0.369685 | ||||||||
\(670\) | − | 26.1350i | − | 0.0390075i | ||||||
\(671\) | 1500.07i | 2.23558i | ||||||||
\(672\) | −18.5530 | − | 62.7839i | −0.0276086 | − | 0.0934284i | ||||
\(673\) | 478.656 | 0.711227 | 0.355614 | − | 0.934633i | \(-0.384272\pi\) | ||||
0.355614 | + | 0.934633i | \(0.384272\pi\) | |||||||
\(674\) | 26.9716 | 0.0400172 | ||||||||
\(675\) | − | 25.9808i | − | 0.0384900i | ||||||
\(676\) | 31.9248 | 0.0472261 | ||||||||
\(677\) | − | 276.403i | − | 0.408277i | −0.978942 | − | 0.204138i | \(-0.934561\pi\) | ||
0.978942 | − | 0.204138i | \(-0.0654393\pi\) | |||||||
\(678\) | 40.8087i | 0.0601898i | ||||||||
\(679\) | 24.6451 | + | 83.3999i | 0.0362962 | + | 0.122828i | ||||
\(680\) | 31.6345 | 0.0465213 | ||||||||
\(681\) | 53.0372 | 0.0778814 | ||||||||
\(682\) | − | 20.3390i | − | 0.0298225i | ||||||
\(683\) | 311.395 | 0.455922 | 0.227961 | − | 0.973670i | \(-0.426794\pi\) | ||||
0.227961 | + | 0.973670i | \(0.426794\pi\) | |||||||
\(684\) | − | 369.397i | − | 0.540054i | ||||||
\(685\) | − | 354.308i | − | 0.517238i | ||||||
\(686\) | 25.2236 | − | 29.4165i | 0.0367691 | − | 0.0428812i | ||||
\(687\) | −364.911 | −0.531166 | ||||||||
\(688\) | −193.245 | −0.280879 | ||||||||
\(689\) | 743.918i | 1.07971i | ||||||||
\(690\) | 1.59108 | 0.00230592 | ||||||||
\(691\) | 569.213i | 0.823752i | 0.911240 | + | 0.411876i | \(0.135126\pi\) | ||||
−0.911240 | + | 0.411876i | \(0.864874\pi\) | |||||||
\(692\) | − | 1074.78i | − | 1.55314i | ||||||
\(693\) | −319.433 | + | 94.3942i | −0.460942 | + | 0.136211i | ||||
\(694\) | 60.3039 | 0.0868933 | ||||||||
\(695\) | 544.417 | 0.783334 | ||||||||
\(696\) | − | 22.7623i | − | 0.0327045i | ||||||
\(697\) | 437.875 | 0.628229 | ||||||||
\(698\) | − | 26.0403i | − | 0.0373070i | ||||||
\(699\) | 316.776i | 0.453185i | ||||||||
\(700\) | −133.832 | + | 39.5481i | −0.191189 | + | 0.0564973i | ||||
\(701\) | −446.061 | −0.636321 | −0.318160 | − | 0.948037i | \(-0.603065\pi\) | ||||
−0.318160 | + | 0.948037i | \(0.603065\pi\) | |||||||
\(702\) | −7.81007 | −0.0111254 | ||||||||
\(703\) | − | 536.785i | − | 0.763563i | ||||||
\(704\) | 995.743 | 1.41441 | ||||||||
\(705\) | − | 312.121i | − | 0.442725i | ||||||
\(706\) | 1.39956i | 0.00198238i | ||||||||
\(707\) | −29.8886 | − | 101.144i | −0.0422752 | − | 0.143061i | ||||
\(708\) | 549.338 | 0.775901 | ||||||||
\(709\) | −480.480 | −0.677686 | −0.338843 | − | 0.940843i | \(-0.610036\pi\) | ||||
−0.338843 | + | 0.940843i | \(0.610036\pi\) | |||||||
\(710\) | − | 28.7486i | − | 0.0404911i | ||||||
\(711\) | 3.82596 | 0.00538110 | ||||||||
\(712\) | 118.441i | 0.166349i | ||||||||
\(713\) | − | 41.2744i | − | 0.0578883i | ||||||
\(714\) | 20.5948 | − | 6.08588i | 0.0288443 | − | 0.00852364i | ||||
\(715\) | 471.867 | 0.659954 | ||||||||
\(716\) | −529.005 | −0.738834 | ||||||||
\(717\) | − | 212.195i | − | 0.295948i | ||||||
\(718\) | 49.9850 | 0.0696170 | ||||||||
\(719\) | − | 330.338i | − | 0.459441i | −0.973257 | − | 0.229721i | \(-0.926219\pi\) | ||
0.973257 | − | 0.229721i | \(-0.0737813\pi\) | |||||||
\(720\) | 106.305i | 0.147646i | ||||||||
\(721\) | 138.041 | + | 467.135i | 0.191458 | + | 0.647899i | ||||
\(722\) | 66.9565 | 0.0927375 | ||||||||
\(723\) | 259.705 | 0.359204 | ||||||||
\(724\) | 922.582i | 1.27428i | ||||||||
\(725\) | −72.8202 | −0.100442 | ||||||||
\(726\) | 25.5518i | 0.0351953i | ||||||||
\(727\) | − | 327.774i | − | 0.450858i | −0.974260 | − | 0.225429i | \(-0.927622\pi\) | ||
0.974260 | − | 0.225429i | \(-0.0723783\pi\) | |||||||
\(728\) | 23.8152 | + | 80.5913i | 0.0327131 | + | 0.110702i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −5.13934 | −0.00704020 | ||||||||
\(731\) | − | 191.189i | − | 0.261544i | ||||||
\(732\) | 653.139 | 0.892267 | ||||||||
\(733\) | − | 124.845i | − | 0.170320i | −0.996367 | − | 0.0851601i | \(-0.972860\pi\) | ||
0.996367 | − | 0.0851601i | \(-0.0271402\pi\) | |||||||
\(734\) | − | 64.0690i | − | 0.0872875i | ||||||
\(735\) | −159.294 | + | 103.152i | −0.216727 | + | 0.140343i | ||||
\(736\) | −19.6353 | −0.0266784 | ||||||||
\(737\) | 1640.97 | 2.22655 | ||||||||
\(738\) | − | 9.46561i | − | 0.0128260i | ||||||
\(739\) | 759.049 | 1.02713 | 0.513565 | − | 0.858051i | \(-0.328325\pi\) | ||||
0.513565 | + | 0.858051i | \(0.328325\pi\) | |||||||
\(740\) | 154.973i | 0.209424i | ||||||||
\(741\) | 711.632i | 0.960367i | ||||||||
\(742\) | −42.4059 | + | 12.5312i | −0.0571508 | + | 0.0168884i | ||||
\(743\) | 658.165 | 0.885820 | 0.442910 | − | 0.896566i | \(-0.353946\pi\) | ||||
0.442910 | + | 0.896566i | \(0.353946\pi\) | |||||||
\(744\) | −17.7397 | −0.0238437 | ||||||||
\(745\) | 300.506i | 0.403363i | ||||||||
\(746\) | 11.9917 | 0.0160747 | ||||||||
\(747\) | 59.3001i | 0.0793843i | ||||||||
\(748\) | 991.546i | 1.32560i | ||||||||
\(749\) | −701.464 | + | 207.286i | −0.936534 | + | 0.276751i | ||||
\(750\) | −2.18773 | −0.00291697 | ||||||||
\(751\) | −15.4050 | −0.0205127 | −0.0102564 | − | 0.999947i | \(-0.503265\pi\) | ||||
−0.0102564 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(752\) | 1277.10i | 1.69827i | ||||||||
\(753\) | −397.312 | −0.527638 | ||||||||
\(754\) | 21.8904i | 0.0290324i | ||||||||
\(755\) | − | 3.57897i | − | 0.00474035i | ||||||
\(756\) | 41.0996 | + | 139.083i | 0.0543646 | + | 0.183972i | ||||
\(757\) | −732.280 | −0.967345 | −0.483673 | − | 0.875249i | \(-0.660697\pi\) | ||||
−0.483673 | + | 0.875249i | \(0.660697\pi\) | |||||||
\(758\) | −80.8591 | −0.106674 | ||||||||
\(759\) | 99.9010i | 0.131622i | ||||||||
\(760\) | −62.3102 | −0.0819871 | ||||||||
\(761\) | − | 969.037i | − | 1.27337i | −0.771123 | − | 0.636686i | \(-0.780305\pi\) | ||
0.771123 | − | 0.636686i | \(-0.219695\pi\) | |||||||
\(762\) | 12.7386i | 0.0167173i | ||||||||
\(763\) | 128.982 | − | 38.1149i | 0.169046 | − | 0.0499541i | ||||
\(764\) | 1212.64 | 1.58722 | ||||||||
\(765\) | −105.174 | −0.137482 | ||||||||
\(766\) | 64.6029i | 0.0843380i | ||||||||
\(767\) | −1058.28 | −1.37977 | ||||||||
\(768\) | − | 429.325i | − | 0.559016i | ||||||
\(769\) | − | 1090.28i | − | 1.41778i | −0.705317 | − | 0.708892i | \(-0.749195\pi\) | ||
0.705317 | − | 0.708892i | \(-0.250805\pi\) | |||||||
\(770\) | 7.94853 | + | 26.8981i | 0.0103228 | + | 0.0349326i | ||||
\(771\) | −84.2685 | −0.109298 | ||||||||
\(772\) | −551.144 | −0.713917 | ||||||||
\(773\) | − | 1490.66i | − | 1.92841i | −0.265155 | − | 0.964206i | \(-0.585423\pi\) | ||
0.265155 | − | 0.964206i | \(-0.414577\pi\) | |||||||
\(774\) | −4.13295 | −0.00533973 | ||||||||
\(775\) | 56.7520i | 0.0732284i | ||||||||
\(776\) | − | 11.2104i | − | 0.0144464i | ||||||
\(777\) | 59.7235 | + | 202.106i | 0.0768642 | + | 0.260111i | ||||
\(778\) | 1.43007 | 0.00183814 | ||||||||
\(779\) | −862.481 | −1.10716 | ||||||||
\(780\) | − | 205.453i | − | 0.263401i | ||||||
\(781\) | 1805.07 | 2.31123 | ||||||||
\(782\) | − | 6.44092i | − | 0.00823647i | ||||||
\(783\) | 75.6770i | 0.0966500i | ||||||||
\(784\) | 651.781 | − | 422.066i | 0.831353 | − | 0.538349i | ||||
\(785\) | −564.523 | −0.719138 | ||||||||
\(786\) | 31.3786 | 0.0399219 | ||||||||
\(787\) | 290.045i | 0.368545i | 0.982875 | + | 0.184272i | \(0.0589928\pi\) | ||||
−0.982875 | + | 0.184272i | \(0.941007\pi\) | |||||||
\(788\) | 107.303 | 0.136171 | ||||||||
\(789\) | 65.2883i | 0.0827481i | ||||||||
\(790\) | − | 0.322168i | − | 0.000407807i | ||||||
\(791\) | −1400.01 | + | 413.712i | −1.76993 | + | 0.523024i | ||||
\(792\) | 42.9374 | 0.0542139 | ||||||||
\(793\) | −1258.25 | −1.58670 | ||||||||
\(794\) | 3.29016i | 0.00414378i | ||||||||
\(795\) | 216.559 | 0.272401 | ||||||||
\(796\) | 1004.77i | 1.26227i | ||||||||
\(797\) | 1089.39i | 1.36686i | 0.730016 | + | 0.683430i | \(0.239512\pi\) | ||||
−0.730016 | + | 0.683430i | \(0.760488\pi\) | |||||||
\(798\) | −40.5655 | + | 11.9873i | −0.0508340 | + | 0.0150217i | ||||
\(799\) | −1263.51 | −1.58136 | ||||||||
\(800\) | 26.9985 | 0.0337481 | ||||||||
\(801\) | − | 393.775i | − | 0.491604i | ||||||
\(802\) | −16.2696 | −0.0202863 | ||||||||
\(803\) | − | 322.689i | − | 0.401855i | ||||||
\(804\) | − | 714.485i | − | 0.888663i | ||||||
\(805\) | 16.1302 | + | 54.5850i | 0.0200375 | + | 0.0678074i | ||||
\(806\) | 17.0602 | 0.0211665 | ||||||||
\(807\) | −505.281 | −0.626123 | ||||||||
\(808\) | 13.5955i | 0.0168261i | ||||||||
\(809\) | 1396.14 | 1.72576 | 0.862880 | − | 0.505408i | \(-0.168658\pi\) | ||||
0.862880 | + | 0.505408i | \(0.168658\pi\) | |||||||
\(810\) | 2.27355i | 0.00280686i | ||||||||
\(811\) | − | 1199.88i | − | 1.47950i | −0.672881 | − | 0.739751i | \(-0.734943\pi\) | ||
0.672881 | − | 0.739751i | \(-0.265057\pi\) | |||||||
\(812\) | 389.828 | − | 115.196i | 0.480083 | − | 0.141867i | ||||
\(813\) | −178.193 | −0.219180 | ||||||||
\(814\) | 31.1471 | 0.0382643 | ||||||||
\(815\) | 534.472i | 0.655793i | ||||||||
\(816\) | 430.337 | 0.527374 | ||||||||
\(817\) | 376.583i | 0.460934i | ||||||||
\(818\) | − | 38.2884i | − | 0.0468073i | ||||||
\(819\) | −79.1772 | − | 267.938i | −0.0966755 | − | 0.327153i | ||||
\(820\) | 249.004 | 0.303664 | ||||||||
\(821\) | −720.125 | −0.877131 | −0.438565 | − | 0.898699i | \(-0.644513\pi\) | ||||
−0.438565 | + | 0.898699i | \(0.644513\pi\) | |||||||
\(822\) | 31.0052i | 0.0377192i | ||||||||
\(823\) | −136.641 | −0.166027 | −0.0830137 | − | 0.996548i | \(-0.526455\pi\) | ||||
−0.0830137 | + | 0.996548i | \(0.526455\pi\) | |||||||
\(824\) | − | 62.7911i | − | 0.0762028i | ||||||
\(825\) | − | 137.363i | − | 0.166501i | ||||||
\(826\) | −17.8266 | − | 60.3258i | −0.0215818 | − | 0.0730337i | ||||
\(827\) | −732.193 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(828\) | 43.4973 | 0.0525330 | ||||||||
\(829\) | 478.689i | 0.577430i | 0.957415 | + | 0.288715i | \(0.0932280\pi\) | ||||
−0.957415 | + | 0.288715i | \(0.906772\pi\) | |||||||
\(830\) | 4.99341 | 0.00601615 | ||||||||
\(831\) | − | 660.634i | − | 0.794987i | ||||||
\(832\) | 835.223i | 1.00387i | ||||||||
\(833\) | 417.574 | + | 644.845i | 0.501290 | + | 0.774123i | ||||
\(834\) | −47.6415 | −0.0571241 | ||||||||
\(835\) | −381.151 | −0.456469 | ||||||||
\(836\) | − | 1953.04i | − | 2.33617i | ||||||
\(837\) | 58.9784 | 0.0704641 | ||||||||
\(838\) | 11.4764i | 0.0136950i | ||||||||
\(839\) | − | 1156.58i | − | 1.37852i | −0.724516 | − | 0.689258i | \(-0.757936\pi\) | ||
0.724516 | − | 0.689258i | \(-0.242064\pi\) | |||||||
\(840\) | 23.4606 | − | 6.93273i | 0.0279293 | − | 0.00825325i | ||||
\(841\) | −628.889 | −0.747787 | ||||||||
\(842\) | 16.4603 | 0.0195491 | ||||||||
\(843\) | − | 30.2854i | − | 0.0359257i | ||||||
\(844\) | −939.759 | −1.11346 | ||||||||
\(845\) | 17.9036i | 0.0211877i | ||||||||
\(846\) | 27.3135i | 0.0322854i | ||||||||
\(847\) | −876.601 | + | 259.040i | −1.03495 | + | 0.305833i | ||||
\(848\) | −886.089 | −1.04492 | ||||||||
\(849\) | 594.714 | 0.700488 | ||||||||
\(850\) | 8.85623i | 0.0104191i | ||||||||
\(851\) | 63.2077 | 0.0742746 | ||||||||
\(852\) | − | 785.936i | − | 0.922460i | ||||||
\(853\) | 338.541i | 0.396883i | 0.980113 | + | 0.198441i | \(0.0635880\pi\) | ||||
−0.980113 | + | 0.198441i | \(0.936412\pi\) | |||||||
\(854\) | −21.1951 | − | 71.7248i | −0.0248186 | − | 0.0839869i | ||||
\(855\) | 207.160 | 0.242292 | ||||||||
\(856\) | 94.2890 | 0.110151 | ||||||||
\(857\) | − | 884.607i | − | 1.03221i | −0.856524 | − | 0.516107i | \(-0.827381\pi\) | ||
0.856524 | − | 0.516107i | \(-0.172619\pi\) | |||||||
\(858\) | −41.2927 | −0.0481267 | ||||||||
\(859\) | 87.7088i | 0.102106i | 0.998696 | + | 0.0510528i | \(0.0162577\pi\) | ||||
−0.998696 | + | 0.0510528i | \(0.983742\pi\) | |||||||
\(860\) | − | 108.722i | − | 0.126421i | ||||||
\(861\) | 324.735 | − | 95.9609i | 0.377160 | − | 0.111453i | ||||
\(862\) | −56.2236 | −0.0652246 | ||||||||
\(863\) | −1419.95 | −1.64537 | −0.822683 | − | 0.568501i | \(-0.807524\pi\) | ||||
−0.822683 | + | 0.568501i | \(0.807524\pi\) | |||||||
\(864\) | − | 28.0576i | − | 0.0324741i | ||||||
\(865\) | 602.741 | 0.696811 | ||||||||
\(866\) | 68.3491i | 0.0789251i | ||||||||
\(867\) | − | 74.8050i | − | 0.0862803i | ||||||
\(868\) | −89.7775 | − | 303.810i | −0.103430 | − | 0.350011i | ||||
\(869\) | 20.2283 | 0.0232777 | ||||||||
\(870\) | 6.37243 | 0.00732464 | ||||||||
\(871\) | 1376.43i | 1.58029i | ||||||||
\(872\) | −17.3375 | −0.0198824 | ||||||||
\(873\) | 37.2708i | 0.0426927i | ||||||||
\(874\) | 12.6866i | 0.0145156i | ||||||||
\(875\) | −22.1789 | − | 75.0540i | −0.0253473 | − | 0.0857760i | ||||
\(876\) | −140.500 | −0.160389 | ||||||||
\(877\) | −831.389 | −0.947992 | −0.473996 | − | 0.880527i | \(-0.657189\pi\) | ||||
−0.473996 | + | 0.880527i | \(0.657189\pi\) | |||||||
\(878\) | − | 23.9058i | − | 0.0272276i | ||||||
\(879\) | −423.494 | −0.481791 | ||||||||
\(880\) | 562.046i | 0.638689i | ||||||||
\(881\) | − | 782.236i | − | 0.887895i | −0.896053 | − | 0.443948i | \(-0.853578\pi\) | ||
0.896053 | − | 0.443948i | \(-0.146422\pi\) | |||||||
\(882\) | 13.9397 | − | 9.02676i | 0.0158046 | − | 0.0102344i | ||||
\(883\) | 10.4243 | 0.0118056 | 0.00590278 | − | 0.999983i | \(-0.498121\pi\) | ||||
0.00590278 | + | 0.999983i | \(0.498121\pi\) | |||||||
\(884\) | −831.702 | −0.940840 | ||||||||
\(885\) | 308.072i | 0.348104i | ||||||||
\(886\) | −89.7026 | −0.101245 | ||||||||
\(887\) | 691.076i | 0.779116i | 0.921002 | + | 0.389558i | \(0.127372\pi\) | ||||
−0.921002 | + | 0.389558i | \(0.872628\pi\) | |||||||
\(888\) | − | 27.1666i | − | 0.0305930i | ||||||
\(889\) | −437.020 | + | 129.142i | −0.491586 | + | 0.145266i | ||||
\(890\) | −33.1581 | −0.0372563 | ||||||||
\(891\) | −142.752 | −0.160216 | ||||||||
\(892\) | 569.337i | 0.638271i | ||||||||
\(893\) | 2488.73 | 2.78693 | ||||||||
\(894\) | − | 26.2970i | − | 0.0294150i | ||||||
\(895\) | − | 296.669i | − | 0.331474i | ||||||
\(896\) | −192.604 | + | 56.9155i | −0.214960 | + | 0.0635217i | ||||
\(897\) | −83.7963 | −0.0934184 | ||||||||
\(898\) | 54.9246 | 0.0611633 | ||||||||
\(899\) | − | 165.308i | − | 0.183880i | ||||||
\(900\) | −59.8086 | −0.0664539 | ||||||||
\(901\) | − | 876.660i | − | 0.972985i | ||||||
\(902\) | − | 50.0458i | − | 0.0554831i | ||||||
\(903\) | −41.8992 | − | 141.788i | −0.0464000 | − | 0.157019i | ||||
\(904\) | 188.186 | 0.208171 | ||||||||
\(905\) | −517.390 | −0.571701 | ||||||||
\(906\) | 0.313192i | 0.000345687i | ||||||||
\(907\) | 704.064 | 0.776256 | 0.388128 | − | 0.921606i | \(-0.373122\pi\) | ||||
0.388128 | + | 0.921606i | \(0.373122\pi\) | |||||||
\(908\) | − | 122.093i | − | 0.134464i | ||||||
\(909\) | − | 45.2004i | − | 0.0497255i | ||||||
\(910\) | −22.5619 | + | 6.66717i | −0.0247933 | + | 0.00732657i | ||||
\(911\) | 1359.34 | 1.49214 | 0.746071 | − | 0.665867i | \(-0.231938\pi\) | ||||
0.746071 | + | 0.665867i | \(0.231938\pi\) | |||||||
\(912\) | −847.632 | −0.929421 | ||||||||
\(913\) | 313.526i | 0.343402i | ||||||||
\(914\) | −12.9479 | −0.0141662 | ||||||||
\(915\) | 366.285i | 0.400311i | ||||||||
\(916\) | 840.038i | 0.917072i | ||||||||
\(917\) | 318.111 | + | 1076.50i | 0.346904 | + | 1.17394i | ||||
\(918\) | 9.20366 | 0.0100258 | ||||||||
\(919\) | 1475.83 | 1.60591 | 0.802953 | − | 0.596043i | \(-0.203261\pi\) | ||||
0.802953 | + | 0.596043i | \(0.203261\pi\) | |||||||
\(920\) | − | 7.33717i | − | 0.00797519i | ||||||
\(921\) | 602.394 | 0.654065 | ||||||||
\(922\) | − | 39.7876i | − | 0.0431536i | ||||||
\(923\) | 1514.08i | 1.64039i | ||||||||
\(924\) | 217.298 | + | 735.345i | 0.235171 | + | 0.795828i | ||||
\(925\) | −86.9101 | −0.0939569 | ||||||||
\(926\) | 25.6025 | 0.0276485 | ||||||||
\(927\) | 208.759i | 0.225198i | ||||||||
\(928\) | −78.6413 | −0.0847428 | ||||||||
\(929\) | − | 795.306i | − | 0.856088i | −0.903758 | − | 0.428044i | \(-0.859203\pi\) | ||
0.903758 | − | 0.428044i | \(-0.140797\pi\) | |||||||
\(930\) | − | 4.96632i | − | 0.00534013i | ||||||
\(931\) | −822.493 | − | 1270.15i | −0.883452 | − | 1.36428i | ||||
\(932\) | 729.229 | 0.782435 | ||||||||
\(933\) | 182.489 | 0.195594 | ||||||||
\(934\) | − | 45.8284i | − | 0.0490668i | ||||||
\(935\) | −556.065 | −0.594722 | ||||||||
\(936\) | 36.0156i | 0.0384782i | ||||||||
\(937\) | 199.954i | 0.213398i | 0.994291 | + | 0.106699i | \(0.0340281\pi\) | ||||
−0.994291 | + | 0.106699i | \(0.965972\pi\) | |||||||
\(938\) | −78.4616 | + | 23.1858i | −0.0836477 | + | 0.0247183i | ||||
\(939\) | −287.312 | −0.305977 | ||||||||
\(940\) | −718.513 | −0.764375 | ||||||||
\(941\) | 1488.22i | 1.58153i | 0.612119 | + | 0.790765i | \(0.290317\pi\) | ||||
−0.612119 | + | 0.790765i | \(0.709683\pi\) | |||||||
\(942\) | 49.4009 | 0.0524426 | ||||||||
\(943\) | − | 101.559i | − | 0.107698i | ||||||
\(944\) | − | 1260.53i | − | 1.33531i | ||||||
\(945\) | −77.9984 | + | 23.0489i | −0.0825380 | + | 0.0243904i | ||||
\(946\) | −21.8514 | −0.0230987 | ||||||||
\(947\) | 1232.27 | 1.30124 | 0.650620 | − | 0.759404i | \(-0.274509\pi\) | ||||
0.650620 | + | 0.759404i | \(0.274509\pi\) | |||||||
\(948\) | − | 8.80749i | − | 0.00929060i | ||||||
\(949\) | 270.670 | 0.285216 | ||||||||
\(950\) | − | 17.4441i | − | 0.0183622i | ||||||
\(951\) | 167.651i | 0.176289i | ||||||||
\(952\) | −28.0646 | − | 94.9717i | −0.0294797 | − | 0.0997601i | ||||
\(953\) | −2.73670 | −0.00287167 | −0.00143584 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143584 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(954\) | −18.9509 | −0.0198646 | ||||||||
\(955\) | 680.054i | 0.712098i | ||||||||
\(956\) | −488.479 | −0.510961 | ||||||||
\(957\) | 400.113i | 0.418091i | ||||||||
\(958\) | 101.724i | 0.106184i | ||||||||
\(959\) | −1063.69 | + | 314.326i | −1.10916 | + | 0.327764i | ||||
\(960\) | 243.138 | 0.253269 | ||||||||
\(961\) | 832.168 | 0.865940 | ||||||||
\(962\) | 26.1260i | 0.0271580i | ||||||||
\(963\) | −313.479 | −0.325523 | ||||||||
\(964\) | − | 597.849i | − | 0.620175i | ||||||
\(965\) | − | 309.085i | − | 0.320295i | ||||||
\(966\) | −1.41154 | − | 4.77668i | −0.00146122 | − | 0.00494481i | ||||
\(967\) | 831.688 | 0.860070 | 0.430035 | − | 0.902812i | \(-0.358501\pi\) | ||||
0.430035 | + | 0.902812i | \(0.358501\pi\) | |||||||
\(968\) | 117.831 | 0.121726 | ||||||||
\(969\) | − | 838.612i | − | 0.865441i | ||||||
\(970\) | 3.13841 | 0.00323548 | ||||||||
\(971\) | 1800.97i | 1.85476i | 0.374118 | + | 0.927381i | \(0.377945\pi\) | ||||
−0.374118 | + | 0.927381i | \(0.622055\pi\) | |||||||
\(972\) | 62.1549i | 0.0639453i | ||||||||
\(973\) | −482.982 | − | 1634.43i | −0.496384 | − | 1.67978i | ||||
\(974\) | −6.26123 | −0.00642837 | ||||||||
\(975\) | 115.219 | 0.118174 | ||||||||
\(976\) | − | 1498.72i | − | 1.53557i | ||||||
\(977\) | −681.141 | −0.697176 | −0.348588 | − | 0.937276i | \(-0.613339\pi\) | ||||
−0.348588 | + | 0.937276i | \(0.613339\pi\) | |||||||
\(978\) | − | 46.7711i | − | 0.0478233i | ||||||
\(979\) | − | 2081.93i | − | 2.12659i | ||||||
\(980\) | 237.460 | + | 366.700i | 0.242306 | + | 0.374184i | ||||
\(981\) | 57.6411 | 0.0587575 | ||||||||
\(982\) | −69.6587 | −0.0709356 | ||||||||
\(983\) | − | 1188.81i | − | 1.20937i | −0.796465 | − | 0.604684i | \(-0.793299\pi\) | ||
0.796465 | − | 0.604684i | \(-0.206701\pi\) | |||||||
\(984\) | −43.6500 | −0.0443598 | ||||||||
\(985\) | 60.1761i | 0.0610924i | ||||||||
\(986\) | − | 25.7965i | − | 0.0261628i | ||||||
\(987\) | −937.037 | + | 276.900i | −0.949379 | + | 0.280547i | ||||
\(988\) | 1638.20 | 1.65810 | ||||||||
\(989\) | −44.3435 | −0.0448367 | ||||||||
\(990\) | 12.0205i | 0.0121420i | ||||||||
\(991\) | −325.271 | −0.328225 | −0.164113 | − | 0.986442i | \(-0.552476\pi\) | ||||
−0.164113 | + | 0.986442i | \(0.552476\pi\) | |||||||
\(992\) | 61.2887i | 0.0617829i | ||||||||
\(993\) | 335.467i | 0.337831i | ||||||||
\(994\) | −86.3080 | + | 25.5045i | −0.0868290 | + | 0.0256584i | ||||
\(995\) | −563.482 | −0.566313 | ||||||||
\(996\) | 136.511 | 0.137059 | ||||||||
\(997\) | − | 17.2566i | − | 0.0173085i | −0.999963 | − | 0.00865426i | \(-0.997245\pi\) | ||
0.999963 | − | 0.00865426i | \(-0.00275477\pi\) | |||||||
\(998\) | −70.5657 | −0.0707071 | ||||||||
\(999\) | 90.3196i | 0.0904100i |
(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 | 105.3.h.a.76.7 | ✓ | 12 | |
3.2 | odd | 2 | 315.3.h.d.181.6 | 12 | |||
4.3 | odd | 2 | 1680.3.s.c.1441.9 | 12 | |||
5.2 | odd | 4 | 525.3.e.c.349.5 | 24 | |||
5.3 | odd | 4 | 525.3.e.c.349.18 | 24 | |||
5.4 | even | 2 | 525.3.h.d.76.6 | 12 | |||
7.6 | odd | 2 | inner | 105.3.h.a.76.8 | yes | 12 | |
21.20 | even | 2 | 315.3.h.d.181.5 | 12 | |||
28.27 | even | 2 | 1680.3.s.c.1441.6 | 12 | |||
35.13 | even | 4 | 525.3.e.c.349.6 | 24 | |||
35.27 | even | 4 | 525.3.e.c.349.17 | 24 | |||
35.34 | odd | 2 | 525.3.h.d.76.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.7 | ✓ | 12 | 1.1 | even | 1 | trivial | |
105.3.h.a.76.8 | yes | 12 | 7.6 | odd | 2 | inner | |
315.3.h.d.181.5 | 12 | 21.20 | even | 2 | |||
315.3.h.d.181.6 | 12 | 3.2 | odd | 2 | |||
525.3.e.c.349.5 | 24 | 5.2 | odd | 4 | |||
525.3.e.c.349.6 | 24 | 35.13 | even | 4 | |||
525.3.e.c.349.17 | 24 | 35.27 | even | 4 | |||
525.3.e.c.349.18 | 24 | 5.3 | odd | 4 | |||
525.3.h.d.76.5 | 12 | 35.34 | odd | 2 | |||
525.3.h.d.76.6 | 12 | 5.4 | even | 2 | |||
1680.3.s.c.1441.6 | 12 | 28.27 | even | 2 | |||
1680.3.s.c.1441.9 | 12 | 4.3 | odd | 2 |