Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(449,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4337012736.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 8x^{6} + 4x^{5} + 12x^{4} - 40x^{3} + 72x^{2} + 24x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(-0.153548 + 0.153548i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.449 |
Dual form | 525.3.f.a.449.4 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30710 | −0.653548 | −0.326774 | − | 0.945103i | \(-0.605962\pi\) | ||||
−0.326774 | + | 0.945103i | \(0.605962\pi\) | |||||||
\(3\) | 2.38267 | − | 1.82288i | 0.794224 | − | 0.607625i | ||||
\(4\) | −2.29150 | −0.572876 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.11438 | + | 2.38267i | −0.519063 | + | 0.397112i | ||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 8.22359 | 1.02795 | ||||||||
\(9\) | 2.35425 | − | 8.68663i | 0.261583 | − | 0.965181i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.61419i | − | 0.237654i | −0.992915 | − | 0.118827i | \(-0.962087\pi\) | ||
0.992915 | − | 0.118827i | \(-0.0379133\pi\) | |||||||
\(12\) | −5.45990 | + | 4.17712i | −0.454992 | + | 0.348094i | ||||
\(13\) | − | 6.35425i | − | 0.488788i | −0.969676 | − | 0.244394i | \(-0.921411\pi\) | ||
0.969676 | − | 0.244394i | \(-0.0785891\pi\) | |||||||
\(14\) | − | 3.45825i | − | 0.247018i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.58301 | −0.0989378 | ||||||||
\(17\) | −12.1449 | −0.714405 | −0.357202 | − | 0.934027i | \(-0.616269\pi\) | ||||
−0.357202 | + | 0.934027i | \(0.616269\pi\) | |||||||
\(18\) | −3.07723 | + | 11.3542i | −0.170957 | + | 0.630792i | ||||
\(19\) | 10.2288 | 0.538356 | 0.269178 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269178 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82288 | + | 6.30396i | 0.229661 | + | 0.300188i | ||||
\(22\) | 3.41699i | 0.155318i | ||||||||
\(23\) | −4.30231 | −0.187057 | −0.0935284 | − | 0.995617i | \(-0.529815\pi\) | ||||
−0.0935284 | + | 0.995617i | \(0.529815\pi\) | |||||||
\(24\) | 19.5941 | − | 14.9906i | 0.816422 | − | 0.624608i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.30561i | 0.319446i | ||||||||
\(27\) | −10.2252 | − | 24.9889i | −0.378713 | − | 0.925514i | ||||
\(28\) | − | 6.06275i | − | 0.216527i | ||||||
\(29\) | − | 17.3733i | − | 0.599078i | −0.954084 | − | 0.299539i | \(-0.903167\pi\) | ||
0.954084 | − | 0.299539i | \(-0.0968328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.2915 | 1.26747 | 0.633734 | − | 0.773551i | \(-0.281521\pi\) | ||||
0.633734 | + | 0.773551i | \(0.281521\pi\) | |||||||
\(32\) | −30.8252 | −0.963288 | ||||||||
\(33\) | −4.76534 | − | 6.22876i | −0.144404 | − | 0.188750i | ||||
\(34\) | 15.8745 | 0.466897 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.39477 | + | 19.9054i | −0.149855 | + | 0.552929i | ||||
\(37\) | − | 41.0405i | − | 1.10920i | −0.832116 | − | 0.554602i | \(-0.812871\pi\) | ||
0.832116 | − | 0.554602i | \(-0.187129\pi\) | |||||||
\(38\) | −13.3700 | −0.351841 | ||||||||
\(39\) | −11.5830 | − | 15.1401i | −0.297000 | − | 0.388207i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 30.2802i | − | 0.738541i | −0.929322 | − | 0.369270i | \(-0.879608\pi\) | ||
0.929322 | − | 0.369270i | \(-0.120392\pi\) | |||||||
\(42\) | −6.30396 | − | 8.23987i | −0.150094 | − | 0.196187i | ||||
\(43\) | − | 55.8745i | − | 1.29941i | −0.760188 | − | 0.649704i | \(-0.774893\pi\) | ||
0.760188 | − | 0.649704i | \(-0.225107\pi\) | |||||||
\(44\) | 5.99042i | 0.136146i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.62352 | 0.122251 | ||||||||
\(47\) | −39.9749 | −0.850530 | −0.425265 | − | 0.905069i | \(-0.639819\pi\) | ||||
−0.425265 | + | 0.905069i | \(0.639819\pi\) | |||||||
\(48\) | −3.77178 | + | 2.88562i | −0.0785788 | + | 0.0601171i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28.9373 | + | 22.1386i | −0.567397 | + | 0.434090i | ||||
\(52\) | 14.5608i | 0.280015i | ||||||||
\(53\) | −105.002 | −1.98116 | −0.990581 | − | 0.136928i | \(-0.956277\pi\) | ||||
−0.990581 | + | 0.136928i | \(0.956277\pi\) | |||||||
\(54\) | 13.3654 | + | 32.6628i | 0.247507 | + | 0.604868i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21.7576i | 0.388528i | ||||||||
\(57\) | 24.3718 | − | 18.6458i | 0.427575 | − | 0.327118i | ||||
\(58\) | 22.7085i | 0.391526i | ||||||||
\(59\) | − | 41.3640i | − | 0.701085i | −0.936547 | − | 0.350542i | \(-0.885997\pi\) | ||
0.936547 | − | 0.350542i | \(-0.114003\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20.4797 | −0.335733 | −0.167867 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167867 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(62\) | −51.3577 | −0.828350 | ||||||||
\(63\) | 22.9827 | + | 6.22876i | 0.364804 | + | 0.0988692i | ||||
\(64\) | 46.6235 | 0.728493 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.22876 | + | 8.14158i | 0.0943751 | + | 0.123357i | ||||
\(67\) | 27.1660i | 0.405463i | 0.979234 | + | 0.202731i | \(0.0649818\pi\) | ||||
−0.979234 | + | 0.202731i | \(0.935018\pi\) | |||||||
\(68\) | 27.8300 | 0.409265 | ||||||||
\(69\) | −10.2510 | + | 7.84257i | −0.148565 | + | 0.113660i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 67.8049i | − | 0.954999i | −0.878632 | − | 0.477499i | \(-0.841543\pi\) | ||
0.878632 | − | 0.477499i | \(-0.158457\pi\) | |||||||
\(72\) | 19.3604 | − | 71.4353i | 0.268894 | − | 0.992157i | ||||
\(73\) | 60.7895i | 0.832733i | 0.909197 | + | 0.416367i | \(0.136697\pi\) | ||||
−0.909197 | + | 0.416367i | \(0.863303\pi\) | |||||||
\(74\) | 53.6439i | 0.724917i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.4392 | −0.308411 | ||||||||
\(77\) | 6.91650 | 0.0898246 | ||||||||
\(78\) | 15.1401 | + | 19.7895i | 0.194104 | + | 0.253712i | ||||
\(79\) | 63.2470 | 0.800596 | 0.400298 | − | 0.916385i | \(-0.368907\pi\) | ||||
0.400298 | + | 0.916385i | \(0.368907\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69.9150 | − | 40.9010i | −0.863148 | − | 0.504950i | ||||
\(82\) | 39.5791i | 0.482672i | ||||||||
\(83\) | −89.9435 | −1.08366 | −0.541828 | − | 0.840489i | \(-0.682268\pi\) | ||||
−0.541828 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(84\) | −11.0516 | − | 14.4455i | −0.131567 | − | 0.171971i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 73.0333i | 0.849224i | ||||||||
\(87\) | −31.6693 | − | 41.3948i | −0.364015 | − | 0.475802i | ||||
\(88\) | − | 21.4980i | − | 0.244296i | ||||||
\(89\) | − | 63.1745i | − | 0.709826i | −0.934899 | − | 0.354913i | \(-0.884510\pi\) | ||
0.934899 | − | 0.354913i | \(-0.115490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.8118 | 0.184745 | ||||||||
\(92\) | 9.85875 | 0.107160 | ||||||||
\(93\) | 93.6188 | − | 71.6235i | 1.00665 | − | 0.770145i | ||||
\(94\) | 52.2510 | 0.555862 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −73.4464 | + | 56.1906i | −0.765067 | + | 0.585318i | ||||
\(97\) | − | 19.1660i | − | 0.197588i | −0.995108 | − | 0.0987939i | \(-0.968502\pi\) | ||
0.995108 | − | 0.0987939i | \(-0.0314984\pi\) | |||||||
\(98\) | 9.14967 | 0.0933639 | ||||||||
\(99\) | −22.7085 | − | 6.15445i | −0.229379 | − | 0.0621662i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 98.7122i | − | 0.977348i | −0.872466 | − | 0.488674i | \(-0.837481\pi\) | ||
0.872466 | − | 0.488674i | \(-0.162519\pi\) | |||||||
\(102\) | 37.8237 | − | 28.9373i | 0.370821 | − | 0.283699i | ||||
\(103\) | − | 56.2510i | − | 0.546126i | −0.961996 | − | 0.273063i | \(-0.911963\pi\) | ||
0.961996 | − | 0.273063i | \(-0.0880368\pi\) | |||||||
\(104\) | − | 52.2547i | − | 0.502449i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 137.247 | 1.29478 | ||||||||
\(107\) | 123.137 | 1.15081 | 0.575406 | − | 0.817868i | \(-0.304844\pi\) | ||||
0.575406 | + | 0.817868i | \(0.304844\pi\) | |||||||
\(108\) | 23.4312 | + | 57.2621i | 0.216955 | + | 0.530205i | ||||
\(109\) | −164.539 | −1.50953 | −0.754764 | − | 0.655996i | \(-0.772249\pi\) | ||||
−0.754764 | + | 0.655996i | \(0.772249\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74.8118 | − | 97.7861i | −0.673980 | − | 0.880956i | ||||
\(112\) | − | 4.18824i | − | 0.0373950i | ||||||
\(113\) | 144.050 | 1.27478 | 0.637391 | − | 0.770540i | \(-0.280014\pi\) | ||||
0.637391 | + | 0.770540i | \(0.280014\pi\) | |||||||
\(114\) | −31.8562 | + | 24.3718i | −0.279441 | + | 0.213787i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 39.8109i | 0.343197i | ||||||||
\(117\) | −55.1970 | − | 14.9595i | −0.471769 | − | 0.127859i | ||||
\(118\) | 54.0667i | 0.458192i | ||||||||
\(119\) | − | 32.1323i | − | 0.270020i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.166 | 0.943521 | ||||||||
\(122\) | 26.7690 | 0.219418 | ||||||||
\(123\) | −55.1970 | − | 72.1477i | −0.448756 | − | 0.586567i | ||||
\(124\) | −90.0366 | −0.726101 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −30.0405 | − | 8.14158i | −0.238417 | − | 0.0646157i | ||||
\(127\) | 36.5830i | 0.288055i | 0.989574 | + | 0.144028i | \(0.0460054\pi\) | ||||
−0.989574 | + | 0.144028i | \(0.953995\pi\) | |||||||
\(128\) | 62.3595 | 0.487184 | ||||||||
\(129\) | −101.852 | − | 133.131i | −0.789553 | − | 1.03202i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 33.6855i | 0.257141i | 0.991700 | + | 0.128570i | \(0.0410389\pi\) | ||||
−0.991700 | + | 0.128570i | \(0.958961\pi\) | |||||||
\(132\) | 10.9198 | + | 14.2732i | 0.0827257 | + | 0.108130i | ||||
\(133\) | 27.0627i | 0.203479i | ||||||||
\(134\) | − | 35.5086i | − | 0.264989i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −99.8745 | −0.734371 | ||||||||
\(137\) | 39.9749 | 0.291788 | 0.145894 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145894 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(138\) | 13.3990 | − | 10.2510i | 0.0970943 | − | 0.0742825i | ||||
\(139\) | 194.642 | 1.40030 | 0.700150 | − | 0.713995i | \(-0.253116\pi\) | ||||
0.700150 | + | 0.713995i | \(0.253116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −95.2470 | + | 72.8693i | −0.675511 | + | 0.516803i | ||||
\(142\) | 88.6275i | 0.624137i | ||||||||
\(143\) | −16.6112 | −0.116162 | ||||||||
\(144\) | −3.72679 | + | 13.7510i | −0.0258805 | + | 0.0954929i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 79.4577i | − | 0.544231i | ||||||
\(147\) | −16.6787 | + | 12.7601i | −0.113461 | + | 0.0868036i | ||||
\(148\) | 94.0445i | 0.635436i | ||||||||
\(149\) | 203.685i | 1.36701i | 0.729945 | + | 0.683506i | \(0.239546\pi\) | ||||
−0.729945 | + | 0.683506i | \(0.760454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 165.749 | 1.09768 | 0.548838 | − | 0.835929i | \(-0.315070\pi\) | ||||
0.548838 | + | 0.835929i | \(0.315070\pi\) | |||||||
\(152\) | 84.1171 | 0.553402 | ||||||||
\(153\) | −28.5921 | + | 105.498i | −0.186876 | + | 0.689530i | ||||
\(154\) | −9.04052 | −0.0587047 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 26.5425 | + | 34.6936i | 0.170144 | + | 0.222395i | ||||
\(157\) | 302.723i | 1.92817i | 0.265592 | + | 0.964086i | \(0.414433\pi\) | ||||
−0.265592 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(158\) | −82.6699 | −0.523227 | ||||||||
\(159\) | −250.184 | + | 191.405i | −1.57349 | + | 1.20380i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.3828i | − | 0.0707008i | ||||||
\(162\) | 91.3856 | + | 53.4615i | 0.564109 | + | 0.330009i | ||||
\(163\) | − | 145.041i | − | 0.889819i | −0.895576 | − | 0.444910i | \(-0.853236\pi\) | ||
0.895576 | − | 0.444910i | \(-0.146764\pi\) | |||||||
\(164\) | 69.3871i | 0.423092i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 117.565 | 0.708221 | ||||||||
\(167\) | 19.6594 | 0.117721 | 0.0588604 | − | 0.998266i | \(-0.481253\pi\) | ||||
0.0588604 | + | 0.998266i | \(0.481253\pi\) | |||||||
\(168\) | 39.6614 | + | 51.8412i | 0.236080 | + | 0.308578i | ||||
\(169\) | 128.624 | 0.761086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.0810 | − | 88.8534i | 0.140825 | − | 0.519611i | ||||
\(172\) | 128.037i | 0.744399i | ||||||||
\(173\) | −19.6884 | −0.113806 | −0.0569030 | − | 0.998380i | \(-0.518123\pi\) | ||||
−0.0569030 | + | 0.998380i | \(0.518123\pi\) | |||||||
\(174\) | 41.3948 | + | 54.1069i | 0.237901 | + | 0.310959i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.13828i | 0.0235129i | ||||||||
\(177\) | −75.4014 | − | 98.5568i | −0.425997 | − | 0.556818i | ||||
\(178\) | 82.5751i | 0.463905i | ||||||||
\(179\) | 341.745i | 1.90919i | 0.297910 | + | 0.954594i | \(0.403711\pi\) | ||||
−0.297910 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 215.889 | 1.19276 | 0.596378 | − | 0.802704i | \(-0.296606\pi\) | ||||
0.596378 | + | 0.802704i | \(0.296606\pi\) | |||||||
\(182\) | −21.9746 | −0.120739 | ||||||||
\(183\) | −48.7965 | + | 37.3320i | −0.266648 | + | 0.204000i | ||||
\(184\) | −35.3804 | −0.192285 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −122.369 | + | 93.6188i | −0.657896 | + | 0.503327i | ||||
\(187\) | 31.7490i | 0.169781i | ||||||||
\(188\) | 91.6026 | 0.487248 | ||||||||
\(189\) | 66.1144 | − | 27.0534i | 0.349812 | − | 0.143140i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 44.7112i | 0.234090i | 0.993127 | + | 0.117045i | \(0.0373422\pi\) | ||||
−0.993127 | + | 0.117045i | \(0.962658\pi\) | |||||||
\(192\) | 111.089 | − | 84.9889i | 0.578586 | − | 0.442650i | ||||
\(193\) | − | 145.122i | − | 0.751925i | −0.926635 | − | 0.375963i | \(-0.877312\pi\) | ||
0.926635 | − | 0.375963i | \(-0.122688\pi\) | |||||||
\(194\) | 25.0518i | 0.129133i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.0405 | 0.0818394 | ||||||||
\(197\) | 87.4643 | 0.443981 | 0.221991 | − | 0.975049i | \(-0.428745\pi\) | ||||
0.221991 | + | 0.975049i | \(0.428745\pi\) | |||||||
\(198\) | 29.6822 | + | 8.04446i | 0.149910 | + | 0.0406286i | ||||
\(199\) | −65.4170 | −0.328729 | −0.164364 | − | 0.986400i | \(-0.552557\pi\) | ||||
−0.164364 | + | 0.986400i | \(0.552557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.5203 | + | 64.7277i | 0.246369 | + | 0.322028i | ||||
\(202\) | 129.026i | 0.638743i | ||||||||
\(203\) | 45.9653 | 0.226430 | ||||||||
\(204\) | 66.3098 | − | 50.7307i | 0.325048 | − | 0.248680i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 73.5254i | 0.356919i | ||||||||
\(207\) | −10.1287 | + | 37.3725i | −0.0489309 | + | 0.180544i | ||||
\(208\) | 10.0588i | 0.0483597i | ||||||||
\(209\) | − | 26.7399i | − | 0.127942i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40.5830 | 0.192337 | 0.0961683 | − | 0.995365i | \(-0.469341\pi\) | ||||
0.0961683 | + | 0.995365i | \(0.469341\pi\) | |||||||
\(212\) | 240.611 | 1.13496 | ||||||||
\(213\) | −123.600 | − | 161.557i | −0.580281 | − | 0.758483i | ||||
\(214\) | −160.952 | −0.752110 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −84.0882 | − | 205.498i | −0.389297 | − | 0.951381i | ||||
\(217\) | 103.956i | 0.479058i | ||||||||
\(218\) | 215.068 | 0.986548 | ||||||||
\(219\) | 110.812 | + | 144.842i | 0.505990 | + | 0.661377i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 77.1716i | 0.349193i | ||||||||
\(222\) | 97.7861 | + | 127.816i | 0.440478 | + | 0.575746i | ||||
\(223\) | 100.959i | 0.452733i | 0.974042 | + | 0.226367i | \(0.0726847\pi\) | ||||
−0.974042 | + | 0.226367i | \(0.927315\pi\) | |||||||
\(224\) | − | 81.5559i | − | 0.364089i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −188.288 | −0.833131 | ||||||||
\(227\) | −391.279 | −1.72370 | −0.861849 | − | 0.507166i | \(-0.830693\pi\) | ||||
−0.861849 | + | 0.507166i | \(0.830693\pi\) | |||||||
\(228\) | −55.8480 | + | 42.7268i | −0.244947 | + | 0.187398i | ||||
\(229\) | 6.81176 | 0.0297457 | 0.0148728 | − | 0.999889i | \(-0.495266\pi\) | ||||
0.0148728 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4797 | − | 12.6079i | 0.0713409 | − | 0.0545797i | ||||
\(232\) | − | 142.871i | − | 0.615821i | ||||||
\(233\) | −116.877 | −0.501616 | −0.250808 | − | 0.968037i | \(-0.580696\pi\) | ||||
−0.250808 | + | 0.968037i | \(0.580696\pi\) | |||||||
\(234\) | 72.1477 | + | 19.5535i | 0.308324 | + | 0.0835618i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 94.7857i | 0.401634i | ||||||||
\(237\) | 150.697 | − | 115.292i | 0.635852 | − | 0.486462i | ||||
\(238\) | 42.0000i | 0.176471i | ||||||||
\(239\) | 59.9623i | 0.250888i | 0.992101 | + | 0.125444i | \(0.0400356\pi\) | ||||
−0.992101 | + | 0.125444i | \(0.959964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 134.753 | 0.559141 | 0.279570 | − | 0.960125i | \(-0.409808\pi\) | ||||
0.279570 | + | 0.960125i | \(0.409808\pi\) | |||||||
\(242\) | −149.226 | −0.616636 | ||||||||
\(243\) | −241.142 | + | 29.9928i | −0.992354 | + | 0.123427i | ||||
\(244\) | 46.9294 | 0.192334 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 72.1477 | + | 94.3039i | 0.293283 | + | 0.383349i | ||||
\(247\) | − | 64.9961i | − | 0.263142i | ||||||
\(248\) | 323.117 | 1.30289 | ||||||||
\(249\) | −214.306 | + | 163.956i | −0.860666 | + | 0.658457i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 268.248i | 1.06872i | 0.845257 | + | 0.534359i | \(0.179447\pi\) | ||||
−0.845257 | + | 0.534359i | \(0.820553\pi\) | |||||||
\(252\) | −52.6648 | − | 14.2732i | −0.208987 | − | 0.0566397i | ||||
\(253\) | 11.2470i | 0.0444547i | ||||||||
\(254\) | − | 47.8175i | − | 0.188258i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −268.004 | −1.04689 | ||||||||
\(257\) | 234.129 | 0.911007 | 0.455504 | − | 0.890234i | \(-0.349459\pi\) | ||||
0.455504 | + | 0.890234i | \(0.349459\pi\) | |||||||
\(258\) | 133.131 | + | 174.014i | 0.516010 | + | 0.674474i | ||||
\(259\) | 108.583 | 0.419239 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −150.915 | − | 40.9010i | −0.578218 | − | 0.156709i | ||||
\(262\) | − | 44.0301i | − | 0.168054i | ||||||
\(263\) | −250.142 | −0.951111 | −0.475555 | − | 0.879686i | \(-0.657753\pi\) | ||||
−0.475555 | + | 0.879686i | \(0.657753\pi\) | |||||||
\(264\) | −39.1882 | − | 51.2228i | −0.148440 | − | 0.194026i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 35.3736i | − | 0.132983i | ||||||
\(267\) | −115.159 | − | 150.524i | −0.431308 | − | 0.563761i | ||||
\(268\) | − | 62.2510i | − | 0.232280i | ||||||
\(269\) | − | 340.684i | − | 1.26648i | −0.773955 | − | 0.633241i | \(-0.781724\pi\) | ||
0.773955 | − | 0.633241i | \(-0.218276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.2994 | −0.0785955 | −0.0392977 | − | 0.999228i | \(-0.512512\pi\) | ||||
−0.0392977 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(272\) | 19.2254 | 0.0706816 | ||||||||
\(273\) | 40.0569 | − | 30.6458i | 0.146729 | − | 0.112255i | ||||
\(274\) | −52.2510 | −0.190697 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 23.4902 | − | 17.9713i | 0.0851093 | − | 0.0651133i | ||||
\(277\) | 226.915i | 0.819188i | 0.912268 | + | 0.409594i | \(0.134330\pi\) | ||||
−0.912268 | + | 0.409594i | \(0.865670\pi\) | |||||||
\(278\) | −254.415 | −0.915163 | ||||||||
\(279\) | 92.5020 | − | 341.311i | 0.331548 | − | 1.22334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 235.489i | − | 0.838039i | −0.907977 | − | 0.419019i | \(-0.862374\pi\) | ||
0.907977 | − | 0.419019i | \(-0.137626\pi\) | |||||||
\(282\) | 124.497 | − | 95.2470i | 0.441479 | − | 0.337755i | ||||
\(283\) | 368.634i | 1.30259i | 0.758823 | + | 0.651297i | \(0.225775\pi\) | ||||
−0.758823 | + | 0.651297i | \(0.774225\pi\) | |||||||
\(284\) | 155.375i | 0.547096i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.7124 | 0.0759176 | ||||||||
\(287\) | 80.1138 | 0.279142 | ||||||||
\(288\) | −72.5703 | + | 267.767i | −0.251980 | + | 0.929748i | ||||
\(289\) | −141.502 | −0.489626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.9373 | − | 45.6663i | −0.120059 | − | 0.156929i | ||||
\(292\) | − | 139.299i | − | 0.477053i | ||||||
\(293\) | 531.625 | 1.81442 | 0.907211 | − | 0.420677i | \(-0.138207\pi\) | ||||
0.907211 | + | 0.420677i | \(0.138207\pi\) | |||||||
\(294\) | 21.8006 | − | 16.6787i | 0.0741519 | − | 0.0567303i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 337.500i | − | 1.14020i | ||||||
\(297\) | −65.3257 | + | 26.7307i | −0.219952 | + | 0.0900024i | ||||
\(298\) | − | 266.235i | − | 0.893407i | ||||||
\(299\) | 27.3379i | 0.0914312i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 147.830 | 0.491130 | ||||||||
\(302\) | −216.650 | −0.717383 | ||||||||
\(303\) | −179.940 | − | 235.199i | −0.593861 | − | 0.776233i | ||||
\(304\) | −16.1922 | −0.0532637 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 37.3725 | − | 137.896i | 0.122132 | − | 0.450640i | ||||
\(307\) | − | 567.763i | − | 1.84939i | −0.380706 | − | 0.924696i | \(-0.624319\pi\) | ||
0.380706 | − | 0.924696i | \(-0.375681\pi\) | |||||||
\(308\) | −15.8492 | −0.0514583 | ||||||||
\(309\) | −102.539 | − | 134.028i | −0.331840 | − | 0.433746i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 42.7531i | 0.137470i | 0.997635 | + | 0.0687349i | \(0.0218963\pi\) | ||||
−0.997635 | + | 0.0687349i | \(0.978104\pi\) | |||||||
\(312\) | −95.2539 | − | 124.506i | −0.305301 | − | 0.399057i | ||||
\(313\) | − | 158.118i | − | 0.505168i | −0.967575 | − | 0.252584i | \(-0.918720\pi\) | ||
0.967575 | − | 0.252584i | \(-0.0812804\pi\) | |||||||
\(314\) | − | 395.688i | − | 1.26015i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −144.931 | −0.458642 | ||||||||
\(317\) | −140.944 | −0.444619 | −0.222309 | − | 0.974976i | \(-0.571359\pi\) | ||||
−0.222309 | + | 0.974976i | \(0.571359\pi\) | |||||||
\(318\) | 327.015 | − | 250.184i | 1.02835 | − | 0.786743i | ||||
\(319\) | −45.4170 | −0.142373 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 293.395 | − | 224.463i | 0.914002 | − | 0.699262i | ||||
\(322\) | 14.8784i | 0.0462064i | ||||||||
\(323\) | −124.227 | −0.384604 | ||||||||
\(324\) | 160.210 | + | 93.7247i | 0.494477 | + | 0.289274i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 189.582i | 0.581539i | ||||||||
\(327\) | −392.041 | + | 299.933i | −1.19890 | + | 0.917227i | ||||
\(328\) | − | 249.012i | − | 0.759182i | ||||||
\(329\) | − | 105.764i | − | 0.321470i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −258.369 | −0.780570 | −0.390285 | − | 0.920694i | \(-0.627623\pi\) | ||||
−0.390285 | + | 0.920694i | \(0.627623\pi\) | |||||||
\(332\) | 206.106 | 0.620801 | ||||||||
\(333\) | −356.504 | − | 96.6196i | −1.07058 | − | 0.290149i | ||||
\(334\) | −25.6967 | −0.0769362 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.63464 | − | 9.97920i | −0.0227221 | − | 0.0297000i | ||||
\(337\) | − | 328.959i | − | 0.976141i | −0.872804 | − | 0.488070i | \(-0.837701\pi\) | ||
0.872804 | − | 0.488070i | \(-0.162299\pi\) | |||||||
\(338\) | −168.123 | −0.497406 | ||||||||
\(339\) | 343.225 | − | 262.586i | 1.01246 | − | 0.774590i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 102.715i | − | 0.301218i | ||||||
\(342\) | −31.4762 | + | 116.140i | −0.0920357 | + | 0.339590i | ||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | − | 459.489i | − | 1.33572i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.7347 | 0.0743776 | ||||||||
\(347\) | 128.635 | 0.370707 | 0.185353 | − | 0.982672i | \(-0.440657\pi\) | ||||
0.185353 | + | 0.982672i | \(0.440657\pi\) | |||||||
\(348\) | 72.5703 | + | 94.8562i | 0.208535 | + | 0.272575i | ||||
\(349\) | 73.4837 | 0.210555 | 0.105277 | − | 0.994443i | \(-0.466427\pi\) | ||||
0.105277 | + | 0.994443i | \(0.466427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −158.786 | + | 64.9737i | −0.452381 | + | 0.185110i | ||||
\(352\) | 80.5830i | 0.228929i | ||||||||
\(353\) | 239.685 | 0.678995 | 0.339498 | − | 0.940607i | \(-0.389743\pi\) | ||||
0.339498 | + | 0.940607i | \(0.389743\pi\) | |||||||
\(354\) | 98.5568 | + | 128.823i | 0.278409 | + | 0.363907i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 144.765i | 0.406642i | ||||||||
\(357\) | −58.5732 | − | 76.5608i | −0.164071 | − | 0.214456i | ||||
\(358\) | − | 446.693i | − | 1.24775i | ||||||
\(359\) | − | 180.215i | − | 0.501992i | −0.967988 | − | 0.250996i | \(-0.919242\pi\) | ||
0.967988 | − | 0.250996i | \(-0.0807581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −256.373 | −0.710173 | ||||||||
\(362\) | −282.187 | −0.779523 | ||||||||
\(363\) | 272.020 | − | 208.110i | 0.749367 | − | 0.573307i | ||||
\(364\) | −38.5242 | −0.105836 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 63.7817 | − | 48.7965i | 0.174267 | − | 0.133324i | ||||
\(367\) | − | 229.786i | − | 0.626119i | −0.949734 | − | 0.313059i | \(-0.898646\pi\) | ||
0.949734 | − | 0.313059i | \(-0.101354\pi\) | |||||||
\(368\) | 6.81057 | 0.0185070 | ||||||||
\(369\) | −263.033 | − | 71.2871i | −0.712826 | − | 0.193190i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 277.808i | − | 0.748809i | ||||||
\(372\) | −214.528 | + | 164.125i | −0.576687 | + | 0.441198i | ||||
\(373\) | 441.749i | 1.18431i | 0.805823 | + | 0.592157i | \(0.201723\pi\) | ||||
−0.805823 | + | 0.592157i | \(0.798277\pi\) | |||||||
\(374\) | − | 41.4990i | − | 0.110960i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −328.737 | −0.874301 | ||||||||
\(377\) | −110.394 | −0.292822 | ||||||||
\(378\) | −86.4178 | + | 35.3614i | −0.228618 | + | 0.0935487i | ||||
\(379\) | 421.203 | 1.11135 | 0.555676 | − | 0.831399i | \(-0.312459\pi\) | ||||
0.555676 | + | 0.831399i | \(0.312459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 66.6863 | + | 87.1653i | 0.175030 | + | 0.228780i | ||||
\(382\) | − | 58.4418i | − | 0.152989i | ||||||
\(383\) | −595.591 | −1.55507 | −0.777534 | − | 0.628841i | \(-0.783530\pi\) | ||||
−0.777534 | + | 0.628841i | \(0.783530\pi\) | |||||||
\(384\) | 148.582 | − | 113.674i | 0.386933 | − | 0.296025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 189.688i | 0.491419i | ||||||||
\(387\) | −485.361 | − | 131.542i | −1.25416 | − | 0.339903i | ||||
\(388\) | 43.9190i | 0.113193i | ||||||||
\(389\) | 367.347i | 0.944336i | 0.881509 | + | 0.472168i | \(0.156528\pi\) | ||||
−0.881509 | + | 0.472168i | \(0.843472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.2510 | 0.133634 | ||||||||
\(392\) | −57.5651 | −0.146850 | ||||||||
\(393\) | 61.4044 | + | 80.2614i | 0.156245 | + | 0.204227i | ||||
\(394\) | −114.324 | −0.290163 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 52.0366 | + | 14.1029i | 0.131406 | + | 0.0356135i | ||||
\(397\) | − | 408.346i | − | 1.02858i | −0.857616 | − | 0.514290i | \(-0.828055\pi\) | ||
0.857616 | − | 0.514290i | \(-0.171945\pi\) | |||||||
\(398\) | 85.5062 | 0.214840 | ||||||||
\(399\) | 49.3320 | + | 64.4816i | 0.123639 | + | 0.161608i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 238.817i | − | 0.595555i | −0.954635 | − | 0.297777i | \(-0.903755\pi\) | ||
0.954635 | − | 0.297777i | \(-0.0962453\pi\) | |||||||
\(402\) | −64.7277 | − | 84.6052i | −0.161014 | − | 0.210461i | ||||
\(403\) | − | 249.668i | − | 0.619524i | ||||||
\(404\) | 226.199i | 0.559899i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −60.0810 | −0.147983 | ||||||||
\(407\) | −107.288 | −0.263606 | ||||||||
\(408\) | −237.968 | + | 182.059i | −0.583255 | + | 0.446223i | ||||
\(409\) | 649.365 | 1.58769 | 0.793844 | − | 0.608121i | \(-0.208076\pi\) | ||||
0.793844 | + | 0.608121i | \(0.208076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 95.2470 | − | 72.8693i | 0.231745 | − | 0.177297i | ||||
\(412\) | 128.899i | 0.312862i | ||||||||
\(413\) | 109.439 | 0.264985 | ||||||||
\(414\) | 13.2392 | − | 48.8495i | 0.0319787 | − | 0.117994i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 195.871i | 0.470844i | ||||||||
\(417\) | 463.768 | − | 354.808i | 1.11215 | − | 0.850858i | ||||
\(418\) | 34.9516i | 0.0836163i | ||||||||
\(419\) | 11.5178i | 0.0274888i | 0.999906 | + | 0.0137444i | \(0.00437512\pi\) | ||||
−0.999906 | + | 0.0137444i | \(0.995625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −83.9921 | −0.199506 | −0.0997531 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997531 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(422\) | −53.0458 | −0.125701 | ||||||||
\(423\) | −94.1108 | + | 347.247i | −0.222484 | + | 0.820915i | ||||
\(424\) | −863.490 | −2.03653 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 161.557 | + | 211.170i | 0.379241 | + | 0.495705i | ||||
\(427\) | − | 54.1843i | − | 0.126895i | ||||||
\(428\) | −282.168 | −0.659272 | ||||||||
\(429\) | −39.5791 | + | 30.2802i | −0.0922589 | + | 0.0705832i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 694.004i | 1.61022i | 0.593127 | + | 0.805109i | \(0.297893\pi\) | ||||
−0.593127 | + | 0.805109i | \(0.702107\pi\) | |||||||
\(432\) | 16.1866 | + | 39.5575i | 0.0374690 | + | 0.0915684i | ||||
\(433\) | 116.834i | 0.269824i | 0.990858 | + | 0.134912i | \(0.0430752\pi\) | ||||
−0.990858 | + | 0.134912i | \(0.956925\pi\) | |||||||
\(434\) | − | 135.880i | − | 0.313087i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 377.041 | 0.864772 | ||||||||
\(437\) | −44.0072 | −0.100703 | ||||||||
\(438\) | −144.842 | − | 189.322i | −0.330688 | − | 0.432241i | ||||
\(439\) | 528.073 | 1.20290 | 0.601450 | − | 0.798910i | \(-0.294590\pi\) | ||||
0.601450 | + | 0.798910i | \(0.294590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.4797 | + | 60.8064i | −0.0373690 | + | 0.137883i | ||||
\(442\) | − | 100.871i | − | 0.228214i | ||||||
\(443\) | −272.252 | −0.614564 | −0.307282 | − | 0.951619i | \(-0.599419\pi\) | ||||
−0.307282 | + | 0.951619i | \(0.599419\pi\) | |||||||
\(444\) | 171.431 | + | 224.077i | 0.386107 | + | 0.504678i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 131.964i | − | 0.295883i | ||||||
\(447\) | 371.292 | + | 485.314i | 0.830631 | + | 1.08571i | ||||
\(448\) | 123.354i | 0.275344i | ||||||||
\(449\) | 525.770i | 1.17098i | 0.810680 | + | 0.585490i | \(0.199098\pi\) | ||||
−0.810680 | + | 0.585490i | \(0.800902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −79.1581 | −0.175517 | ||||||||
\(452\) | −330.092 | −0.730292 | ||||||||
\(453\) | 394.925 | − | 302.140i | 0.871800 | − | 0.666975i | ||||
\(454\) | 511.439 | 1.12652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 200.423 | − | 153.335i | 0.439525 | − | 0.336261i | ||||
\(457\) | 513.786i | 1.12426i | 0.827050 | + | 0.562129i | \(0.190017\pi\) | ||||
−0.827050 | + | 0.562129i | \(0.809983\pi\) | |||||||
\(458\) | −8.90362 | −0.0194402 | ||||||||
\(459\) | 124.184 | + | 303.487i | 0.270554 | + | 0.661192i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 687.879i | 1.49214i | 0.665865 | + | 0.746072i | \(0.268063\pi\) | ||||
−0.665865 | + | 0.746072i | \(0.731937\pi\) | |||||||
\(462\) | −21.5406 | + | 16.4797i | −0.0466246 | + | 0.0356704i | ||||
\(463\) | 781.061i | 1.68696i | 0.537162 | + | 0.843479i | \(0.319496\pi\) | ||||
−0.537162 | + | 0.843479i | \(0.680504\pi\) | |||||||
\(464\) | 27.5020i | 0.0592715i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 152.769 | 0.327830 | ||||||||
\(467\) | 163.353 | 0.349792 | 0.174896 | − | 0.984587i | \(-0.444041\pi\) | ||||
0.174896 | + | 0.984587i | \(0.444041\pi\) | |||||||
\(468\) | 126.484 | + | 34.2797i | 0.270265 | + | 0.0732472i | ||||
\(469\) | −71.8745 | −0.153251 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 551.826 | + | 721.289i | 1.17161 | + | 1.53140i | ||||
\(472\) | − | 340.161i | − | 0.720679i | ||||||
\(473\) | −146.067 | −0.308809 | ||||||||
\(474\) | −196.975 | + | 150.697i | −0.415560 | + | 0.317926i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 73.6313i | 0.154688i | ||||||||
\(477\) | −247.200 | + | 912.110i | −0.518239 | + | 1.91218i | ||||
\(478\) | − | 78.3765i | − | 0.163968i | ||||||
\(479\) | − | 700.159i | − | 1.46171i | −0.682533 | − | 0.730855i | \(-0.739122\pi\) | ||
0.682533 | − | 0.730855i | \(-0.260878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −260.782 | −0.542166 | ||||||||
\(482\) | −176.135 | −0.365425 | ||||||||
\(483\) | −20.7495 | − | 27.1216i | −0.0429596 | − | 0.0561523i | ||||
\(484\) | −261.612 | −0.540520 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 315.195 | − | 39.2035i | 0.648550 | − | 0.0806656i | ||||
\(487\) | − | 86.5909i | − | 0.177805i | −0.996040 | − | 0.0889023i | \(-0.971664\pi\) | ||
0.996040 | − | 0.0889023i | \(-0.0283359\pi\) | |||||||
\(488\) | −168.417 | −0.345117 | ||||||||
\(489\) | −264.391 | − | 345.584i | −0.540677 | − | 0.706716i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 741.494i | − | 1.51017i | −0.655627 | − | 0.755085i | \(-0.727596\pi\) | ||
0.655627 | − | 0.755085i | \(-0.272404\pi\) | |||||||
\(492\) | 126.484 | + | 165.327i | 0.257081 | + | 0.336030i | ||||
\(493\) | 210.996i | 0.427984i | ||||||||
\(494\) | 84.9560i | 0.171976i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −62.1987 | −0.125401 | ||||||||
\(497\) | 179.395 | 0.360956 | ||||||||
\(498\) | 280.118 | − | 214.306i | 0.562486 | − | 0.430333i | ||||
\(499\) | −379.814 | −0.761151 | −0.380575 | − | 0.924750i | \(-0.624274\pi\) | ||||
−0.380575 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.8419 | − | 35.8366i | 0.0934967 | − | 0.0715302i | ||||
\(502\) | − | 350.626i | − | 0.698458i | ||||||
\(503\) | 465.808 | 0.926059 | 0.463029 | − | 0.886343i | \(-0.346762\pi\) | ||||
0.463029 | + | 0.886343i | \(0.346762\pi\) | |||||||
\(504\) | 189.000 | + | 51.2228i | 0.375000 | + | 0.101632i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 14.7010i | − | 0.0290533i | ||||||
\(507\) | 306.468 | − | 234.465i | 0.604473 | − | 0.462455i | ||||
\(508\) | − | 83.8301i | − | 0.165020i | ||||||
\(509\) | 750.503i | 1.47447i | 0.675639 | + | 0.737233i | \(0.263868\pi\) | ||||
−0.675639 | + | 0.737233i | \(0.736132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −160.834 | −0.314744 | ||||||||
\(512\) | 100.868 | 0.197009 | ||||||||
\(513\) | −104.592 | − | 255.605i | −0.203882 | − | 0.498256i | ||||
\(514\) | −306.029 | −0.595387 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 233.395 | + | 305.069i | 0.452315 | + | 0.591219i | ||||
\(517\) | 104.502i | 0.202131i | ||||||||
\(518\) | −141.928 | −0.273993 | ||||||||
\(519\) | −46.9111 | + | 35.8896i | −0.0903875 | + | 0.0691514i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 726.946i | − | 1.39529i | −0.716443 | − | 0.697645i | \(-0.754231\pi\) | ||
0.716443 | − | 0.697645i | \(-0.245769\pi\) | |||||||
\(522\) | 197.260 | + | 53.4615i | 0.377893 | + | 0.102417i | ||||
\(523\) | − | 624.707i | − | 1.19447i | −0.802067 | − | 0.597234i | \(-0.796266\pi\) | ||
0.802067 | − | 0.597234i | \(-0.203734\pi\) | |||||||
\(524\) | − | 77.1903i | − | 0.147310i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 326.959 | 0.621596 | ||||||||
\(527\) | −477.190 | −0.905485 | ||||||||
\(528\) | 7.54356 | + | 9.86015i | 0.0142871 | + | 0.0186745i | ||||
\(529\) | −510.490 | −0.965010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −359.314 | − | 97.3812i | −0.676674 | − | 0.183392i | ||||
\(532\) | − | 62.0144i | − | 0.116568i | ||||||
\(533\) | −192.408 | −0.360990 | ||||||||
\(534\) | 150.524 | + | 196.749i | 0.281881 | + | 0.368445i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 223.402i | 0.416795i | ||||||||
\(537\) | 622.958 | + | 814.265i | 1.16007 | + | 1.51632i | ||||
\(538\) | 445.306i | 0.827706i | ||||||||
\(539\) | 18.2993i | 0.0339505i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −291.757 | −0.539292 | −0.269646 | − | 0.962960i | \(-0.586907\pi\) | ||||
−0.269646 | + | 0.962960i | \(0.586907\pi\) | |||||||
\(542\) | 27.8403 | 0.0513659 | ||||||||
\(543\) | 514.392 | − | 393.539i | 0.947315 | − | 0.724749i | ||||
\(544\) | 374.369 | 0.688178 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −52.3582 | + | 40.0569i | −0.0958941 | + | 0.0733643i | ||||
\(547\) | − | 204.952i | − | 0.374683i | −0.982295 | − | 0.187342i | \(-0.940013\pi\) | ||
0.982295 | − | 0.187342i | \(-0.0599871\pi\) | |||||||
\(548\) | −91.6026 | −0.167158 | ||||||||
\(549\) | −48.2144 | + | 177.900i | −0.0878222 | + | 0.324044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 177.707i | − | 0.322517i | ||||||
\(552\) | −84.2999 | + | 64.4941i | −0.152717 | + | 0.116837i | ||||
\(553\) | 167.336i | 0.302597i | ||||||||
\(554\) | − | 296.599i | − | 0.535378i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −446.022 | −0.802198 | ||||||||
\(557\) | 503.883 | 0.904637 | 0.452318 | − | 0.891857i | \(-0.350597\pi\) | ||||
0.452318 | + | 0.891857i | \(0.350597\pi\) | |||||||
\(558\) | −120.909 | + | 446.125i | −0.216683 | + | 0.799508i | ||||
\(559\) | −355.041 | −0.635135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.8745 | + | 75.6475i | 0.103163 | + | 0.134844i | ||||
\(562\) | 307.806i | 0.547698i | ||||||||
\(563\) | 108.735 | 0.193135 | 0.0965674 | − | 0.995326i | \(-0.469214\pi\) | ||||
0.0965674 | + | 0.995326i | \(0.469214\pi\) | |||||||
\(564\) | 218.259 | − | 166.980i | 0.386984 | − | 0.296064i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 481.840i | − | 0.851307i | ||||||
\(567\) | 108.214 | − | 184.978i | 0.190853 | − | 0.326239i | ||||
\(568\) | − | 557.600i | − | 0.981690i | ||||||
\(569\) | − | 434.871i | − | 0.764273i | −0.924106 | − | 0.382136i | \(-0.875188\pi\) | ||
0.924106 | − | 0.382136i | \(-0.124812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 119.122 | 0.208619 | 0.104310 | − | 0.994545i | \(-0.466737\pi\) | ||||
0.104310 | + | 0.994545i | \(0.466737\pi\) | |||||||
\(572\) | 38.0646 | 0.0665466 | ||||||||
\(573\) | 81.5029 | + | 106.532i | 0.142239 | + | 0.185920i | ||||
\(574\) | −104.716 | −0.182433 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 109.763 | − | 405.001i | 0.190561 | − | 0.703127i | ||||
\(577\) | 655.417i | 1.13590i | 0.823061 | + | 0.567952i | \(0.192264\pi\) | ||||
−0.823061 | + | 0.567952i | \(0.807736\pi\) | |||||||
\(578\) | 184.957 | 0.319994 | ||||||||
\(579\) | −264.539 | − | 345.777i | −0.456889 | − | 0.597197i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 237.968i | − | 0.409584i | ||||||
\(582\) | 45.6663 | + | 59.6902i | 0.0784645 | + | 0.102560i | ||||
\(583\) | 274.494i | 0.470830i | ||||||||
\(584\) | 499.908i | 0.856007i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −694.885 | −1.18581 | ||||||||
\(587\) | −736.236 | −1.25424 | −0.627118 | − | 0.778925i | \(-0.715765\pi\) | ||||
−0.627118 | + | 0.778925i | \(0.715765\pi\) | |||||||
\(588\) | 38.2193 | − | 29.2399i | 0.0649988 | − | 0.0497277i | ||||
\(589\) | 401.903 | 0.682348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 208.399 | − | 159.437i | 0.352620 | − | 0.269774i | ||||
\(592\) | 64.9674i | 0.109742i | ||||||||
\(593\) | 832.884 | 1.40453 | 0.702263 | − | 0.711917i | \(-0.252173\pi\) | ||||
0.702263 | + | 0.711917i | \(0.252173\pi\) | |||||||
\(594\) | 85.3869 | − | 34.9396i | 0.143749 | − | 0.0588209i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 466.744i | − | 0.783127i | ||||||
\(597\) | −155.867 | + | 119.247i | −0.261084 | + | 0.199744i | ||||
\(598\) | − | 35.7333i | − | 0.0597546i | ||||||
\(599\) | 69.3290i | 0.115741i | 0.998324 | + | 0.0578706i | \(0.0184311\pi\) | ||||
−0.998324 | + | 0.0578706i | \(0.981569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −161.720 | −0.269085 | −0.134543 | − | 0.990908i | \(-0.542957\pi\) | ||||
−0.134543 | + | 0.990908i | \(0.542957\pi\) | |||||||
\(602\) | −193.228 | −0.320977 | ||||||||
\(603\) | 235.981 | + | 63.9555i | 0.391345 | + | 0.106062i | ||||
\(604\) | −379.814 | −0.628832 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 235.199 | + | 307.427i | 0.388117 | + | 0.507305i | ||||
\(607\) | − | 929.608i | − | 1.53148i | −0.643151 | − | 0.765740i | \(-0.722373\pi\) | ||
0.643151 | − | 0.765740i | \(-0.277627\pi\) | |||||||
\(608\) | −315.304 | −0.518592 | ||||||||
\(609\) | 109.520 | − | 83.7891i | 0.179836 | − | 0.137585i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 254.010i | 0.415729i | ||||||||
\(612\) | 65.5188 | − | 241.749i | 0.107057 | − | 0.395015i | ||||
\(613\) | 297.940i | 0.486036i | 0.970022 | + | 0.243018i | \(0.0781373\pi\) | ||||
−0.970022 | + | 0.243018i | \(0.921863\pi\) | |||||||
\(614\) | 742.121i | 1.20867i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 56.8784 | 0.0923351 | ||||||||
\(617\) | 975.575 | 1.58116 | 0.790579 | − | 0.612360i | \(-0.209780\pi\) | ||||
0.790579 | + | 0.612360i | \(0.209780\pi\) | |||||||
\(618\) | 134.028 | + | 175.187i | 0.216873 | + | 0.283474i | ||||
\(619\) | −357.034 | −0.576792 | −0.288396 | − | 0.957511i | \(-0.593122\pi\) | ||||
−0.288396 | + | 0.957511i | \(0.593122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.9921 | + | 107.510i | 0.0708408 | + | 0.173124i | ||||
\(622\) | − | 55.8824i | − | 0.0898431i | ||||||
\(623\) | 167.144 | 0.268289 | ||||||||
\(624\) | 18.3360 | + | 23.9668i | 0.0293845 | + | 0.0384084i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 206.675i | 0.330151i | ||||||||
\(627\) | −48.7435 | − | 63.7124i | −0.0777409 | − | 0.101615i | ||||
\(628\) | − | 693.690i | − | 1.10460i | ||||||
\(629\) | 498.432i | 0.792420i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −813.223 | −1.28879 | −0.644393 | − | 0.764695i | \(-0.722890\pi\) | ||||
−0.644393 | + | 0.764695i | \(0.722890\pi\) | |||||||
\(632\) | 520.118 | 0.822971 | ||||||||
\(633\) | 96.6960 | − | 73.9778i | 0.152758 | − | 0.116869i | ||||
\(634\) | 184.227 | 0.290579 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 573.298 | − | 438.605i | 0.901412 | − | 0.689630i | ||||
\(637\) | 44.4797i | 0.0698269i | ||||||||
\(638\) | 59.3643 | 0.0930475 | ||||||||
\(639\) | −588.996 | − | 159.630i | −0.921747 | − | 0.249812i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 646.727i | − | 1.00893i | −0.863431 | − | 0.504467i | \(-0.831689\pi\) | ||
0.863431 | − | 0.504467i | \(-0.168311\pi\) | |||||||
\(642\) | −383.495 | + | 293.395i | −0.597344 | + | 0.457001i | ||||
\(643\) | 144.561i | 0.224822i | 0.993662 | + | 0.112411i | \(0.0358574\pi\) | ||||
−0.993662 | + | 0.112411i | \(0.964143\pi\) | |||||||
\(644\) | 26.0838i | 0.0405028i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 162.376 | 0.251357 | ||||||||
\(647\) | 716.654 | 1.10766 | 0.553828 | − | 0.832631i | \(-0.313166\pi\) | ||||
0.553828 | + | 0.832631i | \(0.313166\pi\) | |||||||
\(648\) | −574.953 | − | 336.353i | −0.887273 | − | 0.519063i | ||||
\(649\) | −108.133 | −0.166615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 189.498 | + | 247.692i | 0.291088 | + | 0.380479i | ||||
\(652\) | 332.361i | 0.509756i | ||||||||
\(653\) | 378.999 | 0.580397 | 0.290199 | − | 0.956966i | \(-0.406279\pi\) | ||||
0.290199 | + | 0.956966i | \(0.406279\pi\) | |||||||
\(654\) | 512.435 | − | 392.041i | 0.783540 | − | 0.599452i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 47.9337i | 0.0730696i | ||||||||
\(657\) | 528.056 | + | 143.114i | 0.803738 | + | 0.217829i | ||||
\(658\) | 138.243i | 0.210096i | ||||||||
\(659\) | − | 710.721i | − | 1.07848i | −0.842151 | − | 0.539242i | \(-0.818711\pi\) | ||
0.842151 | − | 0.539242i | \(-0.181289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 91.5045 | 0.138433 | 0.0692167 | − | 0.997602i | \(-0.477950\pi\) | ||||
0.0692167 | + | 0.997602i | \(0.477950\pi\) | |||||||
\(662\) | 337.712 | 0.510139 | ||||||||
\(663\) | 140.674 | + | 183.875i | 0.212178 | + | 0.277337i | ||||
\(664\) | −739.659 | −1.11394 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 465.984 | + | 126.291i | 0.699676 | + | 0.189626i | ||||
\(667\) | 74.7451i | 0.112062i | ||||||||
\(668\) | −45.0495 | −0.0674394 | ||||||||
\(669\) | 184.037 | + | 240.553i | 0.275092 | + | 0.359571i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 53.5379i | 0.0797883i | ||||||||
\(672\) | −148.666 | − | 194.321i | −0.221230 | − | 0.289168i | ||||
\(673\) | 645.806i | 0.959594i | 0.877380 | + | 0.479797i | \(0.159290\pi\) | ||||
−0.877380 | + | 0.479797i | \(0.840710\pi\) | |||||||
\(674\) | 429.981i | 0.637954i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −294.741 | −0.436008 | ||||||||
\(677\) | 335.571 | 0.495674 | 0.247837 | − | 0.968802i | \(-0.420280\pi\) | ||||
0.247837 | + | 0.968802i | \(0.420280\pi\) | |||||||
\(678\) | −448.627 | + | 343.225i | −0.661692 | + | 0.506231i | ||||
\(679\) | 50.7085 | 0.0746811 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −932.290 | + | 713.254i | −1.36900 | + | 1.04736i | ||||
\(682\) | 134.259i | 0.196860i | ||||||||
\(683\) | −113.336 | −0.165939 | −0.0829694 | − | 0.996552i | \(-0.526440\pi\) | ||||
−0.0829694 | + | 0.996552i | \(0.526440\pi\) | |||||||
\(684\) | −55.1818 | + | 203.608i | −0.0806751 | + | 0.297672i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.2077i | 0.0352882i | ||||||||
\(687\) | 16.2302 | − | 12.4170i | 0.0236247 | − | 0.0180742i | ||||
\(688\) | 88.4496i | 0.128561i | ||||||||
\(689\) | 667.206i | 0.968369i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 565.667 | 0.818620 | 0.409310 | − | 0.912395i | \(-0.365769\pi\) | ||||
0.409310 | + | 0.912395i | \(0.365769\pi\) | |||||||
\(692\) | 45.1161 | 0.0651967 | ||||||||
\(693\) | 16.2832 | − | 60.0810i | 0.0234966 | − | 0.0866970i | ||||
\(694\) | −168.138 | −0.242274 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −260.435 | − | 340.414i | −0.374189 | − | 0.489100i | ||||
\(697\) | 367.749i | 0.527617i | ||||||||
\(698\) | −96.0501 | −0.137608 | ||||||||
\(699\) | −278.478 | + | 213.051i | −0.398395 | + | 0.304794i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 872.955i | 1.24530i | 0.782501 | + | 0.622650i | \(0.213944\pi\) | ||||
−0.782501 | + | 0.622650i | \(0.786056\pi\) | |||||||
\(702\) | 207.548 | − | 84.9268i | 0.295652 | − | 0.120978i | ||||
\(703\) | − | 419.793i | − | 0.597146i | ||||||
\(704\) | − | 121.883i | − | 0.173129i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −313.292 | −0.443756 | ||||||||
\(707\) | 261.168 | 0.369403 | ||||||||
\(708\) | 172.783 | + | 225.843i | 0.244043 | + | 0.318988i | ||||
\(709\) | −1092.04 | −1.54025 | −0.770125 | − | 0.637894i | \(-0.779806\pi\) | ||||
−0.770125 | + | 0.637894i | \(0.779806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 148.899 | − | 549.404i | 0.209422 | − | 0.772720i | ||||
\(712\) | − | 519.522i | − | 0.729665i | ||||||
\(713\) | −169.044 | −0.237088 | ||||||||
\(714\) | 76.5608 | + | 100.072i | 0.107228 | + | 0.140157i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 783.109i | − | 1.09373i | ||||||
\(717\) | 109.304 | + | 142.871i | 0.152446 | + | 0.199262i | ||||
\(718\) | 235.558i | 0.328076i | ||||||||
\(719\) | − | 901.769i | − | 1.25420i | −0.778939 | − | 0.627099i | \(-0.784242\pi\) | ||
0.778939 | − | 0.627099i | \(-0.215758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 148.826 | 0.206416 | ||||||||
\(722\) | 335.103 | 0.464132 | ||||||||
\(723\) | 321.072 | − | 245.638i | 0.444083 | − | 0.339748i | ||||
\(724\) | −494.710 | −0.683301 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −355.556 | + | 272.020i | −0.489747 | + | 0.374683i | ||||
\(727\) | − | 297.506i | − | 0.409224i | −0.978843 | − | 0.204612i | \(-0.934407\pi\) | ||
0.978843 | − | 0.204612i | \(-0.0655933\pi\) | |||||||
\(728\) | 138.253 | 0.189908 | ||||||||
\(729\) | −519.889 | + | 511.035i | −0.713153 | + | 0.701008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 678.589i | 0.928302i | ||||||||
\(732\) | 111.817 | − | 85.5464i | 0.152756 | − | 0.116867i | ||||
\(733\) | 456.966i | 0.623419i | 0.950177 | + | 0.311709i | \(0.100902\pi\) | ||||
−0.950177 | + | 0.311709i | \(0.899098\pi\) | |||||||
\(734\) | 300.352i | 0.409198i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 132.620 | 0.180190 | ||||||||
\(737\) | 71.0171 | 0.0963597 | ||||||||
\(738\) | 343.809 | + | 93.1790i | 0.465865 | + | 0.126259i | ||||
\(739\) | 332.199 | 0.449525 | 0.224762 | − | 0.974414i | \(-0.427839\pi\) | ||||
0.224762 | + | 0.974414i | \(0.427839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −118.480 | − | 154.864i | −0.159892 | − | 0.208994i | ||||
\(742\) | 363.122i | 0.489382i | ||||||||
\(743\) | 64.5346 | 0.0868568 | 0.0434284 | − | 0.999057i | \(-0.486172\pi\) | ||||
0.0434284 | + | 0.999057i | \(0.486172\pi\) | |||||||
\(744\) | 769.882 | − | 589.003i | 1.03479 | − | 0.791670i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 577.408i | − | 0.774005i | ||||||
\(747\) | −211.749 | + | 781.306i | −0.283466 | + | 1.04592i | ||||
\(748\) | − | 72.7530i | − | 0.0972633i | ||||||
\(749\) | 325.790i | 0.434966i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −611.668 | −0.814471 | −0.407236 | − | 0.913323i | \(-0.633507\pi\) | ||||
−0.407236 | + | 0.913323i | \(0.633507\pi\) | |||||||
\(752\) | 63.2805 | 0.0841496 | ||||||||
\(753\) | 488.983 | + | 639.148i | 0.649380 | + | 0.848802i | ||||
\(754\) | 144.295 | 0.191373 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −151.501 | + | 61.9930i | −0.200399 | + | 0.0820014i | ||||
\(757\) | 207.357i | 0.273919i | 0.990577 | + | 0.136960i | \(0.0437330\pi\) | ||||
−0.990577 | + | 0.136960i | \(0.956267\pi\) | |||||||
\(758\) | −550.552 | −0.726322 | ||||||||
\(759\) | 20.5020 | + | 26.7980i | 0.0270118 | + | 0.0353070i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 337.770i | 0.443851i | 0.975064 | + | 0.221925i | \(0.0712341\pi\) | ||||
−0.975064 | + | 0.221925i | \(0.928766\pi\) | |||||||
\(762\) | −87.1653 | − | 113.933i | −0.114390 | − | 0.149519i | ||||
\(763\) | − | 435.328i | − | 0.570548i | ||||||
\(764\) | − | 102.456i | − | 0.134104i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 778.494 | 1.01631 | ||||||||
\(767\) | −262.837 | −0.342682 | ||||||||
\(768\) | −638.565 | + | 488.538i | −0.831465 | + | 0.636117i | ||||
\(769\) | 1042.22 | 1.35529 | 0.677646 | − | 0.735388i | \(-0.263000\pi\) | ||||
0.677646 | + | 0.735388i | \(0.263000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 557.852 | − | 426.788i | 0.723544 | − | 0.553551i | ||||
\(772\) | 332.546i | 0.430760i | ||||||||
\(773\) | −291.448 | −0.377035 | −0.188517 | − | 0.982070i | \(-0.560368\pi\) | ||||
−0.188517 | + | 0.982070i | \(0.560368\pi\) | |||||||
\(774\) | 634.413 | + | 171.939i | 0.819655 | + | 0.222143i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 157.613i | − | 0.203110i | ||||||
\(777\) | 258.718 | − | 197.933i | 0.332970 | − | 0.254740i | ||||
\(778\) | − | 480.157i | − | 0.617168i | ||||||
\(779\) | − | 309.729i | − | 0.397598i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −177.255 | −0.226959 | ||||||||
\(782\) | −68.2970 | −0.0873363 | ||||||||
\(783\) | −434.138 | + | 177.646i | −0.554455 | + | 0.226878i | ||||
\(784\) | 11.0810 | 0.0141340 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −80.2614 | − | 104.909i | −0.102114 | − | 0.133472i | ||||
\(787\) | − | 293.889i | − | 0.373429i | −0.982414 | − | 0.186715i | \(-0.940216\pi\) | ||
0.982414 | − | 0.186715i | \(-0.0597840\pi\) | |||||||
\(788\) | −200.425 | −0.254346 | ||||||||
\(789\) | −596.006 | + | 455.978i | −0.755395 | + | 0.577919i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 381.122i | 0.481822i | ||||||||
\(792\) | −186.745 | − | 50.6117i | −0.235790 | − | 0.0639037i | ||||
\(793\) | 130.133i | 0.164103i | ||||||||
\(794\) | 533.748i | 0.672226i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 149.903 | 0.188321 | ||||||||
\(797\) | −568.764 | −0.713631 | −0.356816 | − | 0.934175i | \(-0.616138\pi\) | ||||
−0.356816 | + | 0.934175i | \(0.616138\pi\) | |||||||
\(798\) | −64.4816 | − | 84.2836i | −0.0808041 | − | 0.105619i | ||||
\(799\) | 485.490 | 0.607622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −548.774 | − | 148.729i | −0.685111 | − | 0.185679i | ||||
\(802\) | 312.157i | 0.389223i | ||||||||
\(803\) | 158.915 | 0.197902 | ||||||||
\(804\) | −113.476 | − | 148.324i | −0.141139 | − | 0.184482i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 326.340i | 0.404888i | ||||||||
\(807\) | −621.024 | − | 811.737i | −0.769546 | − | 1.00587i | ||||
\(808\) | − | 811.768i | − | 1.00466i | ||||||
\(809\) | 183.697i | 0.227067i | 0.993534 | + | 0.113534i | \(0.0362169\pi\) | ||||
−0.993534 | + | 0.113534i | \(0.963783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −544.663 | −0.671594 | −0.335797 | − | 0.941934i | \(-0.609006\pi\) | ||||
−0.335797 | + | 0.941934i | \(0.609006\pi\) | |||||||
\(812\) | −105.330 | −0.129716 | ||||||||
\(813\) | −50.7494 | + | 38.8261i | −0.0624224 | + | 0.0477566i | ||||
\(814\) | 140.235 | 0.172279 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 45.8078 | − | 35.0455i | 0.0561370 | − | 0.0429479i | ||||
\(817\) | − | 571.527i | − | 0.699543i | ||||||
\(818\) | −848.781 | −1.03763 | ||||||||
\(819\) | 39.5791 | − | 146.038i | 0.0483261 | − | 0.178312i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1188.78i | 1.44797i | 0.689818 | + | 0.723983i | \(0.257691\pi\) | ||||
−0.689818 | + | 0.723983i | \(0.742309\pi\) | |||||||
\(822\) | −124.497 | + | 95.2470i | −0.151456 | + | 0.115872i | ||||
\(823\) | 1265.15i | 1.53724i | 0.639704 | + | 0.768621i | \(0.279057\pi\) | ||||
−0.639704 | + | 0.768621i | \(0.720943\pi\) | |||||||
\(824\) | − | 462.585i | − | 0.561390i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −143.047 | −0.173180 | ||||||||
\(827\) | −790.941 | −0.956398 | −0.478199 | − | 0.878252i | \(-0.658710\pi\) | ||||
−0.478199 | + | 0.878252i | \(0.658710\pi\) | |||||||
\(828\) | 23.2099 | − | 85.6393i | 0.0280313 | − | 0.103429i | ||||
\(829\) | −99.1961 | −0.119658 | −0.0598288 | − | 0.998209i | \(-0.519055\pi\) | ||||
−0.0598288 | + | 0.998209i | \(0.519055\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 413.638 | + | 540.664i | 0.497759 | + | 0.650619i | ||||
\(832\) | − | 296.257i | − | 0.356079i | ||||||
\(833\) | 85.0141 | 0.102058 | ||||||||
\(834\) | −606.188 | + | 463.768i | −0.726844 | + | 0.556076i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 61.2746i | 0.0732950i | ||||||||
\(837\) | −401.765 | − | 981.851i | −0.480006 | − | 1.17306i | ||||
\(838\) | − | 15.0549i | − | 0.0179652i | ||||||
\(839\) | − | 243.824i | − | 0.290612i | −0.989387 | − | 0.145306i | \(-0.953583\pi\) | ||
0.989387 | − | 0.145306i | \(-0.0464167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 539.170 | 0.641106 | ||||||||
\(842\) | 109.786 | 0.130387 | ||||||||
\(843\) | −429.267 | − | 561.093i | −0.509214 | − | 0.665591i | ||||
\(844\) | −92.9961 | −0.110185 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 123.012 | − | 453.885i | 0.145404 | − | 0.536507i | ||||
\(847\) | 302.055i | 0.356617i | ||||||||
\(848\) | 166.218 | 0.196012 | ||||||||
\(849\) | 671.974 | + | 878.334i | 0.791489 | + | 1.03455i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 176.569i | 0.207484i | ||||||||
\(852\) | 283.230 | + | 370.208i | 0.332429 | + | 0.434516i | ||||
\(853\) | − | 1122.06i | − | 1.31543i | −0.753268 | − | 0.657713i | \(-0.771524\pi\) | ||
0.753268 | − | 0.657713i | \(-0.228476\pi\) | |||||||
\(854\) | 70.8240i | 0.0829321i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1012.63 | 1.18298 | ||||||||
\(857\) | −871.489 | −1.01691 | −0.508453 | − | 0.861090i | \(-0.669783\pi\) | ||||
−0.508453 | + | 0.861090i | \(0.669783\pi\) | |||||||
\(858\) | 51.7336 | − | 39.5791i | 0.0602956 | − | 0.0461295i | ||||
\(859\) | 1674.92 | 1.94985 | 0.974925 | − | 0.222533i | \(-0.0714324\pi\) | ||||
0.974925 | + | 0.222533i | \(0.0714324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 190.885 | − | 146.038i | 0.221701 | − | 0.169614i | ||||
\(862\) | − | 907.129i | − | 1.05235i | ||||||
\(863\) | 1320.74 | 1.53041 | 0.765205 | − | 0.643787i | \(-0.222638\pi\) | ||||
0.765205 | + | 0.643787i | \(0.222638\pi\) | |||||||
\(864\) | 315.195 | + | 770.288i | 0.364810 | + | 0.891537i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 152.713i | − | 0.176343i | ||||||
\(867\) | −337.153 | + | 257.940i | −0.388873 | + | 0.297509i | ||||
\(868\) | − | 238.214i | − | 0.274441i | ||||||
\(869\) | − | 165.340i | − | 0.190264i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 172.620 | 0.198186 | ||||||||
\(872\) | −1353.10 | −1.55172 | ||||||||
\(873\) | −166.488 | − | 45.1216i | −0.190708 | − | 0.0516856i | ||||
\(874\) | 57.5217 | 0.0658142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −253.925 | − | 331.905i | −0.289869 | − | 0.378887i | ||||
\(877\) | 344.790i | 0.393147i | 0.980489 | + | 0.196573i | \(0.0629814\pi\) | ||||
−0.980489 | + | 0.196573i | \(0.937019\pi\) | |||||||
\(878\) | −690.242 | −0.786152 | ||||||||
\(879\) | 1266.69 | − | 969.087i | 1.44106 | − | 1.10249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 518.737i | 0.588805i | 0.955682 | + | 0.294403i | \(0.0951206\pi\) | ||||
−0.955682 | + | 0.294403i | \(0.904879\pi\) | |||||||
\(882\) | 21.5406 | − | 79.4797i | 0.0244224 | − | 0.0901131i | ||||
\(883\) | − | 584.008i | − | 0.661391i | −0.943738 | − | 0.330695i | \(-0.892717\pi\) | ||
0.943738 | − | 0.330695i | \(-0.107283\pi\) | |||||||
\(884\) | − | 176.839i | − | 0.200044i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 355.859 | 0.401646 | ||||||||
\(887\) | 263.213 | 0.296745 | 0.148373 | − | 0.988932i | \(-0.452597\pi\) | ||||
0.148373 | + | 0.988932i | \(0.452597\pi\) | |||||||
\(888\) | −615.221 | − | 804.153i | −0.692817 | − | 0.905577i | ||||
\(889\) | −96.7895 | −0.108875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −106.923 | + | 182.771i | −0.120003 | + | 0.205130i | ||||
\(892\) | − | 231.349i | − | 0.259360i | ||||||
\(893\) | −408.893 | −0.457887 | ||||||||
\(894\) | −485.314 | − | 634.351i | −0.542857 | − | 0.709565i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 164.988i | 0.184138i | ||||||||
\(897\) | 49.8336 | + | 65.1373i | 0.0555559 | + | 0.0726168i | ||||
\(898\) | − | 687.231i | − | 0.765291i | ||||||
\(899\) | − | 682.621i | − | 0.759312i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1275.23 | 1.41535 | ||||||||
\(902\) | 103.467 | 0.114709 | ||||||||
\(903\) | 352.230 | − | 269.476i | 0.390067 | − | 0.298423i | ||||
\(904\) | 1184.61 | 1.31041 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −516.205 | + | 394.925i | −0.569763 | + | 0.435900i | ||||
\(907\) | 1501.72i | 1.65570i | 0.560951 | + | 0.827849i | \(0.310435\pi\) | ||||
−0.560951 | + | 0.827849i | \(0.689565\pi\) | |||||||
\(908\) | 896.618 | 0.987464 | ||||||||
\(909\) | −857.476 | − | 232.393i | −0.943318 | − | 0.255658i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 879.178i | 0.965069i | 0.875877 | + | 0.482534i | \(0.160284\pi\) | ||||
−0.875877 | + | 0.482534i | \(0.839716\pi\) | |||||||
\(912\) | −38.5806 | + | 29.5163i | −0.0423033 | + | 0.0323644i | ||||
\(913\) | 235.129i | 0.257535i | ||||||||
\(914\) | − | 671.567i | − | 0.734756i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.6092 | −0.0170406 | ||||||||
\(917\) | −89.1234 | −0.0971901 | ||||||||
\(918\) | −162.321 | − | 396.686i | −0.176820 | − | 0.432120i | ||||
\(919\) | −76.9882 | −0.0837739 | −0.0418869 | − | 0.999122i | \(-0.513337\pi\) | ||||
−0.0418869 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1034.96 | − | 1352.79i | −1.12374 | − | 1.46883i | ||||
\(922\) | − | 899.123i | − | 0.975188i | ||||||
\(923\) | −430.849 | −0.466792 | ||||||||
\(924\) | −37.7634 | + | 28.8911i | −0.0408694 | + | 0.0312674i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1020.92i | − | 1.10251i | ||||||
\(927\) | −488.631 | − | 132.429i | −0.527110 | − | 0.142857i | ||||
\(928\) | 535.535i | 0.577085i | ||||||||
\(929\) | − | 1629.76i | − | 1.75431i | −0.480204 | − | 0.877157i | \(-0.659437\pi\) | ||
0.480204 | − | 0.877157i | \(-0.340563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −71.6013 | −0.0769079 | ||||||||
\(932\) | 267.823 | 0.287364 | ||||||||
\(933\) | 77.9336 | + | 101.867i | 0.0835301 | + | 0.109182i | ||||
\(934\) | −213.517 | −0.228605 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −453.918 | − | 123.021i | −0.484955 | − | 0.131432i | ||||
\(937\) | 497.720i | 0.531185i | 0.964085 | + | 0.265592i | \(0.0855676\pi\) | ||||
−0.964085 | + | 0.265592i | \(0.914432\pi\) | |||||||
\(938\) | 93.9468 | 0.100157 | ||||||||
\(939\) | −288.229 | − | 376.742i | −0.306953 | − | 0.401217i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 238.894i | − | 0.253873i | −0.991911 | − | 0.126936i | \(-0.959486\pi\) | ||
0.991911 | − | 0.126936i | \(-0.0405144\pi\) | |||||||
\(942\) | −721.289 | − | 942.793i | −0.765700 | − | 1.00084i | ||||
\(943\) | 130.275i | 0.138149i | ||||||||
\(944\) | 65.4794i | 0.0693638i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 190.923 | 0.201821 | ||||||||
\(947\) | −667.910 | −0.705291 | −0.352645 | − | 0.935757i | \(-0.614718\pi\) | ||||
−0.352645 | + | 0.935757i | \(0.614718\pi\) | |||||||
\(948\) | −345.322 | + | 264.191i | −0.364264 | + | 0.278682i | ||||
\(949\) | 386.272 | 0.407030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −335.824 | + | 256.924i | −0.353127 | + | 0.270162i | ||||
\(952\) | − | 264.243i | − | 0.277566i | ||||||
\(953\) | 11.3247 | 0.0118832 | 0.00594162 | − | 0.999982i | \(-0.498109\pi\) | ||||
0.00594162 | + | 0.999982i | \(0.498109\pi\) | |||||||
\(954\) | 323.114 | − | 1192.21i | 0.338694 | − | 1.24970i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 137.404i | − | 0.143728i | ||||||
\(957\) | −108.214 | + | 82.7895i | −0.113076 | + | 0.0865094i | ||||
\(958\) | 915.174i | 0.955296i | ||||||||
\(959\) | 105.764i | 0.110285i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 582.822 | 0.606475 | ||||||||
\(962\) | 340.866 | 0.354331 | ||||||||
\(963\) | 289.895 | − | 1069.64i | 0.301033 | − | 1.11074i | ||||
\(964\) | −308.787 | −0.320318 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 27.1216 | + | 35.4504i | 0.0280761 | + | 0.0366982i | ||||
\(967\) | − | 830.324i | − | 0.858660i | −0.903148 | − | 0.429330i | \(-0.858750\pi\) | ||
0.903148 | − | 0.429330i | \(-0.141250\pi\) | |||||||
\(968\) | 938.855 | 0.969891 | ||||||||
\(969\) | −295.992 | + | 226.450i | −0.305461 | + | 0.233695i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1217.58i | − | 1.25394i | −0.779044 | − | 0.626970i | \(-0.784295\pi\) | ||
0.779044 | − | 0.626970i | \(-0.215705\pi\) | |||||||
\(972\) | 552.577 | − | 68.7286i | 0.568495 | − | 0.0707085i | ||||
\(973\) | 514.974i | 0.529264i | ||||||||
\(974\) | 113.183i | 0.116204i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.4195 | 0.0332167 | ||||||||
\(977\) | 424.579 | 0.434574 | 0.217287 | − | 0.976108i | \(-0.430279\pi\) | ||||
0.217287 | + | 0.976108i | \(0.430279\pi\) | |||||||
\(978\) | 345.584 | + | 451.711i | 0.353358 | + | 0.461872i | ||||
\(979\) | −165.150 | −0.168693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −387.365 | + | 1429.29i | −0.394867 | + | 1.45697i | ||||
\(982\) | 969.203i | 0.986968i | ||||||||
\(983\) | −76.7273 | −0.0780542 | −0.0390271 | − | 0.999238i | \(-0.512426\pi\) | ||||
−0.0390271 | + | 0.999238i | \(0.512426\pi\) | |||||||
\(984\) | −453.918 | − | 593.313i | −0.461298 | − | 0.602961i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 275.792i | − | 0.279708i | ||||||
\(987\) | −192.794 | − | 252.000i | −0.195333 | − | 0.255319i | ||||
\(988\) | 148.939i | 0.150748i | ||||||||
\(989\) | 240.389i | 0.243063i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 181.271 | 0.182917 | 0.0914585 | − | 0.995809i | \(-0.470847\pi\) | ||||
0.0914585 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(992\) | −1211.17 | −1.22094 | ||||||||
\(993\) | −615.608 | + | 470.974i | −0.619947 | + | 0.474294i | ||||
\(994\) | −234.486 | −0.235902 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 491.082 | − | 375.705i | 0.493055 | − | 0.377214i | ||||
\(997\) | 1184.43i | 1.18800i | 0.804466 | + | 0.593998i | \(0.202451\pi\) | ||||
−0.804466 | + | 0.593998i | \(0.797549\pi\) | |||||||
\(998\) | 496.453 | 0.497448 | ||||||||
\(999\) | −1025.56 | + | 419.649i | −1.02658 | + | 0.420069i |
(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 | 525.3.f.a.449.3 | 8 | ||
3.2 | odd | 2 | inner | 525.3.f.a.449.5 | 8 | ||
5.2 | odd | 4 | 21.3.b.a.8.2 | ✓ | 4 | ||
5.3 | odd | 4 | 525.3.c.a.176.3 | 4 | |||
5.4 | even | 2 | inner | 525.3.f.a.449.6 | 8 | ||
15.2 | even | 4 | 21.3.b.a.8.3 | yes | 4 | ||
15.8 | even | 4 | 525.3.c.a.176.2 | 4 | |||
15.14 | odd | 2 | inner | 525.3.f.a.449.4 | 8 | ||
20.7 | even | 4 | 336.3.d.c.113.4 | 4 | |||
35.2 | odd | 12 | 147.3.h.e.116.2 | 8 | |||
35.12 | even | 12 | 147.3.h.c.116.2 | 8 | |||
35.17 | even | 12 | 147.3.h.c.128.3 | 8 | |||
35.27 | even | 4 | 147.3.b.f.50.2 | 4 | |||
35.32 | odd | 12 | 147.3.h.e.128.3 | 8 | |||
40.27 | even | 4 | 1344.3.d.b.449.1 | 4 | |||
40.37 | odd | 4 | 1344.3.d.f.449.4 | 4 | |||
45.2 | even | 12 | 567.3.r.c.134.3 | 8 | |||
45.7 | odd | 12 | 567.3.r.c.134.2 | 8 | |||
45.22 | odd | 12 | 567.3.r.c.512.3 | 8 | |||
45.32 | even | 12 | 567.3.r.c.512.2 | 8 | |||
60.47 | odd | 4 | 336.3.d.c.113.3 | 4 | |||
105.2 | even | 12 | 147.3.h.e.116.3 | 8 | |||
105.17 | odd | 12 | 147.3.h.c.128.2 | 8 | |||
105.32 | even | 12 | 147.3.h.e.128.2 | 8 | |||
105.47 | odd | 12 | 147.3.h.c.116.3 | 8 | |||
105.62 | odd | 4 | 147.3.b.f.50.3 | 4 | |||
120.77 | even | 4 | 1344.3.d.f.449.3 | 4 | |||
120.107 | odd | 4 | 1344.3.d.b.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.b.a.8.2 | ✓ | 4 | 5.2 | odd | 4 | ||
21.3.b.a.8.3 | yes | 4 | 15.2 | even | 4 | ||
147.3.b.f.50.2 | 4 | 35.27 | even | 4 | |||
147.3.b.f.50.3 | 4 | 105.62 | odd | 4 | |||
147.3.h.c.116.2 | 8 | 35.12 | even | 12 | |||
147.3.h.c.116.3 | 8 | 105.47 | odd | 12 | |||
147.3.h.c.128.2 | 8 | 105.17 | odd | 12 | |||
147.3.h.c.128.3 | 8 | 35.17 | even | 12 | |||
147.3.h.e.116.2 | 8 | 35.2 | odd | 12 | |||
147.3.h.e.116.3 | 8 | 105.2 | even | 12 | |||
147.3.h.e.128.2 | 8 | 105.32 | even | 12 | |||
147.3.h.e.128.3 | 8 | 35.32 | odd | 12 | |||
336.3.d.c.113.3 | 4 | 60.47 | odd | 4 | |||
336.3.d.c.113.4 | 4 | 20.7 | even | 4 | |||
525.3.c.a.176.2 | 4 | 15.8 | even | 4 | |||
525.3.c.a.176.3 | 4 | 5.3 | odd | 4 | |||
525.3.f.a.449.3 | 8 | 1.1 | even | 1 | trivial | ||
525.3.f.a.449.4 | 8 | 15.14 | odd | 2 | inner | ||
525.3.f.a.449.5 | 8 | 3.2 | odd | 2 | inner | ||
525.3.f.a.449.6 | 8 | 5.4 | even | 2 | inner | ||
567.3.r.c.134.2 | 8 | 45.7 | odd | 12 | |||
567.3.r.c.134.3 | 8 | 45.2 | even | 12 | |||
567.3.r.c.512.2 | 8 | 45.32 | even | 12 | |||
567.3.r.c.512.3 | 8 | 45.22 | odd | 12 | |||
1344.3.d.b.449.1 | 4 | 40.27 | even | 4 | |||
1344.3.d.b.449.2 | 4 | 120.107 | odd | 4 | |||
1344.3.d.f.449.3 | 4 | 120.77 | even | 4 | |||
1344.3.d.f.449.4 | 4 | 40.37 | odd | 4 |