Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(176,525)]
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, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.176");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.c (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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.65856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 14x^{2} + 21 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.3 | ||
Root | \(1.30710i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.176 |
Dual form | 525.3.c.a.176.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30710i | 0.653548i | 0.945103 | + | 0.326774i | \(0.105962\pi\) | ||||
−0.945103 | + | 0.326774i | \(0.894038\pi\) | |||||||
\(3\) | 1.82288 | + | 2.38267i | 0.607625 | + | 0.794224i | ||||
\(4\) | 2.29150 | 0.572876 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.11438 | + | 2.38267i | −0.519063 | + | 0.397112i | ||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 8.22359i | 1.02795i | ||||||||
\(9\) | −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 | \(-0.0379133\pi\) | |||||||
\(12\) | 4.17712 | + | 5.45990i | 0.348094 | + | 0.454992i | ||||
\(13\) | 6.35425 | 0.488788 | 0.244394 | − | 0.969676i | \(-0.421411\pi\) | ||||
0.244394 | + | 0.969676i | \(0.421411\pi\) | |||||||
\(14\) | 3.45825i | 0.247018i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.58301 | −0.0989378 | ||||||||
\(17\) | 12.1449i | 0.714405i | 0.934027 | + | 0.357202i | \(0.116269\pi\) | ||||
−0.934027 | + | 0.357202i | \(0.883731\pi\) | |||||||
\(18\) | −11.3542 | − | 3.07723i | −0.630792 | − | 0.170957i | ||||
\(19\) | −10.2288 | −0.538356 | −0.269178 | − | 0.963090i | \(-0.586752\pi\) | ||||
−0.269178 | + | 0.963090i | \(0.586752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82288 | + | 6.30396i | 0.229661 | + | 0.300188i | ||||
\(22\) | 3.41699 | 0.155318 | ||||||||
\(23\) | − | 4.30231i | − | 0.187057i | −0.995617 | − | 0.0935284i | \(-0.970185\pi\) | ||
0.995617 | − | 0.0935284i | \(-0.0298146\pi\) | |||||||
\(24\) | −19.5941 | + | 14.9906i | −0.816422 | + | 0.624608i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.30561i | 0.319446i | ||||||||
\(27\) | −24.9889 | + | 10.2252i | −0.925514 | + | 0.378713i | ||||
\(28\) | 6.06275 | 0.216527 | ||||||||
\(29\) | 17.3733i | 0.599078i | 0.954084 | + | 0.299539i | \(0.0968328\pi\) | ||||
−0.954084 | + | 0.299539i | \(0.903167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.2915 | 1.26747 | 0.633734 | − | 0.773551i | \(-0.281521\pi\) | ||||
0.633734 | + | 0.773551i | \(0.281521\pi\) | |||||||
\(32\) | 30.8252i | 0.963288i | ||||||||
\(33\) | 6.22876 | − | 4.76534i | 0.188750 | − | 0.144404i | ||||
\(34\) | −15.8745 | −0.466897 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.39477 | + | 19.9054i | −0.149855 | + | 0.552929i | ||||
\(37\) | −41.0405 | −1.10920 | −0.554602 | − | 0.832116i | \(-0.687129\pi\) | ||||
−0.554602 | + | 0.832116i | \(0.687129\pi\) | |||||||
\(38\) | − | 13.3700i | − | 0.351841i | ||||||
\(39\) | 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 | \(-0.120392\pi\) | |||||||
\(42\) | −8.23987 | + | 6.30396i | −0.196187 | + | 0.150094i | ||||
\(43\) | 55.8745 | 1.29941 | 0.649704 | − | 0.760188i | \(-0.274893\pi\) | ||||
0.649704 | + | 0.760188i | \(0.274893\pi\) | |||||||
\(44\) | − | 5.99042i | − | 0.136146i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.62352 | 0.122251 | ||||||||
\(47\) | 39.9749i | 0.850530i | 0.905069 | + | 0.425265i | \(0.139819\pi\) | ||||
−0.905069 | + | 0.425265i | \(0.860181\pi\) | |||||||
\(48\) | −2.88562 | − | 3.77178i | −0.0601171 | − | 0.0785788i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28.9373 | + | 22.1386i | −0.567397 | + | 0.434090i | ||||
\(52\) | 14.5608 | 0.280015 | ||||||||
\(53\) | − | 105.002i | − | 1.98116i | −0.136928 | − | 0.990581i | \(-0.543723\pi\) | ||
0.136928 | − | 0.990581i | \(-0.456277\pi\) | |||||||
\(54\) | −13.3654 | − | 32.6628i | −0.247507 | − | 0.604868i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21.7576i | 0.388528i | ||||||||
\(57\) | −18.6458 | − | 24.3718i | −0.327118 | − | 0.427575i | ||||
\(58\) | −22.7085 | −0.391526 | ||||||||
\(59\) | 41.3640i | 0.701085i | 0.936547 | + | 0.350542i | \(0.114003\pi\) | ||||
−0.936547 | + | 0.350542i | \(0.885997\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20.4797 | −0.335733 | −0.167867 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167867 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(62\) | 51.3577i | 0.828350i | ||||||||
\(63\) | −6.22876 | + | 22.9827i | −0.0988692 | + | 0.364804i | ||||
\(64\) | −46.6235 | −0.728493 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.22876 | + | 8.14158i | 0.0943751 | + | 0.123357i | ||||
\(67\) | 27.1660 | 0.405463 | 0.202731 | − | 0.979234i | \(-0.435018\pi\) | ||||
0.202731 | + | 0.979234i | \(0.435018\pi\) | |||||||
\(68\) | 27.8300i | 0.409265i | ||||||||
\(69\) | 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 | \(-0.158457\pi\) | |||||||
\(72\) | −71.4353 | − | 19.3604i | −0.992157 | − | 0.268894i | ||||
\(73\) | −60.7895 | −0.832733 | −0.416367 | − | 0.909197i | \(-0.636697\pi\) | ||||
−0.416367 | + | 0.909197i | \(0.636697\pi\) | |||||||
\(74\) | − | 53.6439i | − | 0.724917i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.4392 | −0.308411 | ||||||||
\(77\) | − | 6.91650i | − | 0.0898246i | ||||||
\(78\) | −19.7895 | + | 15.1401i | −0.253712 | + | 0.194104i | ||||
\(79\) | −63.2470 | −0.800596 | −0.400298 | − | 0.916385i | \(-0.631093\pi\) | ||||
−0.400298 | + | 0.916385i | \(0.631093\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69.9150 | − | 40.9010i | −0.863148 | − | 0.504950i | ||||
\(82\) | 39.5791 | 0.482672 | ||||||||
\(83\) | − | 89.9435i | − | 1.08366i | −0.840489 | − | 0.541828i | \(-0.817732\pi\) | ||
0.840489 | − | 0.541828i | \(-0.182268\pi\) | |||||||
\(84\) | 11.0516 | + | 14.4455i | 0.131567 | + | 0.171971i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 73.0333i | 0.849224i | ||||||||
\(87\) | −41.3948 | + | 31.6693i | −0.475802 | + | 0.364015i | ||||
\(88\) | 21.4980 | 0.244296 | ||||||||
\(89\) | 63.1745i | 0.709826i | 0.934899 | + | 0.354913i | \(0.115490\pi\) | ||||
−0.934899 | + | 0.354913i | \(0.884510\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.8118 | 0.184745 | ||||||||
\(92\) | − | 9.85875i | − | 0.107160i | ||||||
\(93\) | 71.6235 | + | 93.6188i | 0.770145 | + | 1.00665i | ||||
\(94\) | −52.2510 | −0.555862 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −73.4464 | + | 56.1906i | −0.765067 | + | 0.585318i | ||||
\(97\) | −19.1660 | −0.197588 | −0.0987939 | − | 0.995108i | \(-0.531498\pi\) | ||||
−0.0987939 | + | 0.995108i | \(0.531498\pi\) | |||||||
\(98\) | 9.14967i | 0.0933639i | ||||||||
\(99\) | 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 | \(-0.162519\pi\) | |||||||
\(102\) | −28.9373 | − | 37.8237i | −0.283699 | − | 0.370821i | ||||
\(103\) | 56.2510 | 0.546126 | 0.273063 | − | 0.961996i | \(-0.411963\pi\) | ||||
0.273063 | + | 0.961996i | \(0.411963\pi\) | |||||||
\(104\) | 52.2547i | 0.502449i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 137.247 | 1.29478 | ||||||||
\(107\) | − | 123.137i | − | 1.15081i | −0.817868 | − | 0.575406i | \(-0.804844\pi\) | ||
0.817868 | − | 0.575406i | \(-0.195156\pi\) | |||||||
\(108\) | −57.2621 | + | 23.4312i | −0.530205 | + | 0.216955i | ||||
\(109\) | 164.539 | 1.50953 | 0.754764 | − | 0.655996i | \(-0.227751\pi\) | ||||
0.754764 | + | 0.655996i | \(0.227751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74.8118 | − | 97.7861i | −0.673980 | − | 0.880956i | ||||
\(112\) | −4.18824 | −0.0373950 | ||||||||
\(113\) | 144.050i | 1.27478i | 0.770540 | + | 0.637391i | \(0.219986\pi\) | ||||
−0.770540 | + | 0.637391i | \(0.780014\pi\) | |||||||
\(114\) | 31.8562 | − | 24.3718i | 0.279441 | − | 0.213787i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 39.8109i | 0.343197i | ||||||||
\(117\) | −14.9595 | + | 55.1970i | −0.127859 | + | 0.471769i | ||||
\(118\) | −54.0667 | −0.458192 | ||||||||
\(119\) | 32.1323i | 0.270020i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.166 | 0.943521 | ||||||||
\(122\) | − | 26.7690i | − | 0.219418i | ||||||
\(123\) | 72.1477 | − | 55.1970i | 0.586567 | − | 0.448756i | ||||
\(124\) | 90.0366 | 0.726101 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −30.0405 | − | 8.14158i | −0.238417 | − | 0.0646157i | ||||
\(127\) | 36.5830 | 0.288055 | 0.144028 | − | 0.989574i | \(-0.453995\pi\) | ||||
0.144028 | + | 0.989574i | \(0.453995\pi\) | |||||||
\(128\) | 62.3595i | 0.487184i | ||||||||
\(129\) | 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 | \(0.958961\pi\) | |||||||
\(132\) | 14.2732 | − | 10.9198i | 0.108130 | − | 0.0827257i | ||||
\(133\) | −27.0627 | −0.203479 | ||||||||
\(134\) | 35.5086i | 0.264989i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −99.8745 | −0.734371 | ||||||||
\(137\) | − | 39.9749i | − | 0.291788i | −0.989300 | − | 0.145894i | \(-0.953394\pi\) | ||
0.989300 | − | 0.145894i | \(-0.0466058\pi\) | |||||||
\(138\) | 10.2510 | + | 13.3990i | 0.0742825 | + | 0.0970943i | ||||
\(139\) | −194.642 | −1.40030 | −0.700150 | − | 0.713995i | \(-0.746884\pi\) | ||||
−0.700150 | + | 0.713995i | \(0.746884\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −95.2470 | + | 72.8693i | −0.675511 | + | 0.516803i | ||||
\(142\) | 88.6275 | 0.624137 | ||||||||
\(143\) | − | 16.6112i | − | 0.116162i | ||||||
\(144\) | 3.72679 | − | 13.7510i | 0.0258805 | − | 0.0954929i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 79.4577i | − | 0.544231i | ||||||
\(147\) | 12.7601 | + | 16.6787i | 0.0868036 | + | 0.113461i | ||||
\(148\) | −94.0445 | −0.635436 | ||||||||
\(149\) | − | 203.685i | − | 1.36701i | −0.729945 | − | 0.683506i | \(-0.760454\pi\) | ||
0.729945 | − | 0.683506i | \(-0.239546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 165.749 | 1.09768 | 0.548838 | − | 0.835929i | \(-0.315070\pi\) | ||||
0.548838 | + | 0.835929i | \(0.315070\pi\) | |||||||
\(152\) | − | 84.1171i | − | 0.553402i | ||||||
\(153\) | −105.498 | − | 28.5921i | −0.689530 | − | 0.186876i | ||||
\(154\) | 9.04052 | 0.0587047 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 26.5425 | + | 34.6936i | 0.170144 | + | 0.222395i | ||||
\(157\) | 302.723 | 1.92817 | 0.964086 | − | 0.265592i | \(-0.0855674\pi\) | ||||
0.964086 | + | 0.265592i | \(0.0855674\pi\) | |||||||
\(158\) | − | 82.6699i | − | 0.523227i | ||||||
\(159\) | 250.184 | − | 191.405i | 1.57349 | − | 1.20380i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.3828i | − | 0.0707008i | ||||||
\(162\) | 53.4615 | − | 91.3856i | 0.330009 | − | 0.564109i | ||||
\(163\) | 145.041 | 0.889819 | 0.444910 | − | 0.895576i | \(-0.353236\pi\) | ||||
0.444910 | + | 0.895576i | \(0.353236\pi\) | |||||||
\(164\) | − | 69.3871i | − | 0.423092i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 117.565 | 0.708221 | ||||||||
\(167\) | − | 19.6594i | − | 0.117721i | −0.998266 | − | 0.0588604i | \(-0.981253\pi\) | ||
0.998266 | − | 0.0588604i | \(-0.0187467\pi\) | |||||||
\(168\) | −51.8412 | + | 39.6614i | −0.308578 | + | 0.236080i | ||||
\(169\) | −128.624 | −0.761086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.0810 | − | 88.8534i | 0.140825 | − | 0.519611i | ||||
\(172\) | 128.037 | 0.744399 | ||||||||
\(173\) | − | 19.6884i | − | 0.113806i | −0.998380 | − | 0.0569030i | \(-0.981877\pi\) | ||
0.998380 | − | 0.0569030i | \(-0.0181226\pi\) | |||||||
\(174\) | −41.3948 | − | 54.1069i | −0.237901 | − | 0.310959i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.13828i | 0.0235129i | ||||||||
\(177\) | −98.5568 | + | 75.4014i | −0.556818 | + | 0.425997i | ||||
\(178\) | −82.5751 | −0.463905 | ||||||||
\(179\) | − | 341.745i | − | 1.90919i | −0.297910 | − | 0.954594i | \(-0.596289\pi\) | ||
0.297910 | − | 0.954594i | \(-0.403711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 215.889 | 1.19276 | 0.596378 | − | 0.802704i | \(-0.296606\pi\) | ||||
0.596378 | + | 0.802704i | \(0.296606\pi\) | |||||||
\(182\) | 21.9746i | 0.120739i | ||||||||
\(183\) | −37.3320 | − | 48.7965i | −0.204000 | − | 0.266648i | ||||
\(184\) | 35.3804 | 0.192285 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −122.369 | + | 93.6188i | −0.657896 | + | 0.503327i | ||||
\(187\) | 31.7490 | 0.169781 | ||||||||
\(188\) | 91.6026i | 0.487248i | ||||||||
\(189\) | −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 | \(0.962658\pi\) | |||||||
\(192\) | −84.9889 | − | 111.089i | −0.442650 | − | 0.578586i | ||||
\(193\) | 145.122 | 0.751925 | 0.375963 | − | 0.926635i | \(-0.377312\pi\) | ||||
0.375963 | + | 0.926635i | \(0.377312\pi\) | |||||||
\(194\) | − | 25.0518i | − | 0.129133i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.0405 | 0.0818394 | ||||||||
\(197\) | − | 87.4643i | − | 0.443981i | −0.975049 | − | 0.221991i | \(-0.928745\pi\) | ||
0.975049 | − | 0.221991i | \(-0.0712554\pi\) | |||||||
\(198\) | −8.04446 | + | 29.6822i | −0.0406286 | + | 0.149910i | ||||
\(199\) | 65.4170 | 0.328729 | 0.164364 | − | 0.986400i | \(-0.447443\pi\) | ||||
0.164364 | + | 0.986400i | \(0.447443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.5203 | + | 64.7277i | 0.246369 | + | 0.322028i | ||||
\(202\) | 129.026 | 0.638743 | ||||||||
\(203\) | 45.9653i | 0.226430i | ||||||||
\(204\) | −66.3098 | + | 50.7307i | −0.325048 | + | 0.248680i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 73.5254i | 0.356919i | ||||||||
\(207\) | 37.3725 | + | 10.1287i | 0.180544 | + | 0.0489309i | ||||
\(208\) | −10.0588 | −0.0483597 | ||||||||
\(209\) | 26.7399i | 0.127942i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40.5830 | 0.192337 | 0.0961683 | − | 0.995365i | \(-0.469341\pi\) | ||||
0.0961683 | + | 0.995365i | \(0.469341\pi\) | |||||||
\(212\) | − | 240.611i | − | 1.13496i | ||||||
\(213\) | 161.557 | − | 123.600i | 0.758483 | − | 0.580281i | ||||
\(214\) | 160.952 | 0.752110 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −84.0882 | − | 205.498i | −0.389297 | − | 0.951381i | ||||
\(217\) | 103.956 | 0.479058 | ||||||||
\(218\) | 215.068i | 0.986548i | ||||||||
\(219\) | −110.812 | − | 144.842i | −0.505990 | − | 0.661377i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 77.1716i | 0.349193i | ||||||||
\(222\) | 127.816 | − | 97.7861i | 0.575746 | − | 0.440478i | ||||
\(223\) | −100.959 | −0.452733 | −0.226367 | − | 0.974042i | \(-0.572685\pi\) | ||||
−0.226367 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(224\) | 81.5559i | 0.364089i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −188.288 | −0.833131 | ||||||||
\(227\) | 391.279i | 1.72370i | 0.507166 | + | 0.861849i | \(0.330693\pi\) | ||||
−0.507166 | + | 0.861849i | \(0.669307\pi\) | |||||||
\(228\) | −42.7268 | − | 55.8480i | −0.187398 | − | 0.244947i | ||||
\(229\) | −6.81176 | −0.0297457 | −0.0148728 | − | 0.999889i | \(-0.504734\pi\) | ||||
−0.0148728 | + | 0.999889i | \(0.504734\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4797 | − | 12.6079i | 0.0713409 | − | 0.0545797i | ||||
\(232\) | −142.871 | −0.615821 | ||||||||
\(233\) | − | 116.877i | − | 0.501616i | −0.968037 | − | 0.250808i | \(-0.919304\pi\) | ||
0.968037 | − | 0.250808i | \(-0.0806963\pi\) | |||||||
\(234\) | −72.1477 | − | 19.5535i | −0.308324 | − | 0.0835618i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 94.7857i | 0.401634i | ||||||||
\(237\) | −115.292 | − | 150.697i | −0.486462 | − | 0.635852i | ||||
\(238\) | −42.0000 | −0.176471 | ||||||||
\(239\) | − | 59.9623i | − | 0.250888i | −0.992101 | − | 0.125444i | \(-0.959964\pi\) | ||
0.992101 | − | 0.125444i | \(-0.0400356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 134.753 | 0.559141 | 0.279570 | − | 0.960125i | \(-0.409808\pi\) | ||||
0.279570 | + | 0.960125i | \(0.409808\pi\) | |||||||
\(242\) | 149.226i | 0.616636i | ||||||||
\(243\) | −29.9928 | − | 241.142i | −0.123427 | − | 0.992354i | ||||
\(244\) | −46.9294 | −0.192334 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 72.1477 | + | 94.3039i | 0.293283 | + | 0.383349i | ||||
\(247\) | −64.9961 | −0.263142 | ||||||||
\(248\) | 323.117i | 1.30289i | ||||||||
\(249\) | 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 | \(0.820553\pi\) | |||||||
\(252\) | −14.2732 | + | 52.6648i | −0.0566397 | + | 0.208987i | ||||
\(253\) | −11.2470 | −0.0444547 | ||||||||
\(254\) | 47.8175i | 0.188258i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −268.004 | −1.04689 | ||||||||
\(257\) | − | 234.129i | − | 0.911007i | −0.890234 | − | 0.455504i | \(-0.849459\pi\) | ||
0.890234 | − | 0.455504i | \(-0.150541\pi\) | |||||||
\(258\) | −174.014 | + | 133.131i | −0.674474 | + | 0.516010i | ||||
\(259\) | −108.583 | −0.419239 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −150.915 | − | 40.9010i | −0.578218 | − | 0.156709i | ||||
\(262\) | −44.0301 | −0.168054 | ||||||||
\(263\) | − | 250.142i | − | 0.951111i | −0.879686 | − | 0.475555i | \(-0.842247\pi\) | ||
0.879686 | − | 0.475555i | \(-0.157753\pi\) | |||||||
\(264\) | 39.1882 | + | 51.2228i | 0.148440 | + | 0.194026i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 35.3736i | − | 0.132983i | ||||||
\(267\) | −150.524 | + | 115.159i | −0.563761 | + | 0.431308i | ||||
\(268\) | 62.2510 | 0.232280 | ||||||||
\(269\) | 340.684i | 1.26648i | 0.773955 | + | 0.633241i | \(0.218276\pi\) | ||||
−0.773955 | + | 0.633241i | \(0.781724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.2994 | −0.0785955 | −0.0392977 | − | 0.999228i | \(-0.512512\pi\) | ||||
−0.0392977 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(272\) | − | 19.2254i | − | 0.0706816i | ||||||
\(273\) | 30.6458 | + | 40.0569i | 0.112255 | + | 0.146729i | ||||
\(274\) | 52.2510 | 0.190697 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 23.4902 | − | 17.9713i | 0.0851093 | − | 0.0651133i | ||||
\(277\) | 226.915 | 0.819188 | 0.409594 | − | 0.912268i | \(-0.365670\pi\) | ||||
0.409594 | + | 0.912268i | \(0.365670\pi\) | |||||||
\(278\) | − | 254.415i | − | 0.915163i | ||||||
\(279\) | −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 | \(-0.137626\pi\) | |||||||
\(282\) | −95.2470 | − | 124.497i | −0.337755 | − | 0.441479i | ||||
\(283\) | −368.634 | −1.30259 | −0.651297 | − | 0.758823i | \(-0.725775\pi\) | ||||
−0.651297 | + | 0.758823i | \(0.725775\pi\) | |||||||
\(284\) | − | 155.375i | − | 0.547096i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.7124 | 0.0759176 | ||||||||
\(287\) | − | 80.1138i | − | 0.279142i | ||||||
\(288\) | −267.767 | − | 72.5703i | −0.929748 | − | 0.251980i | ||||
\(289\) | 141.502 | 0.489626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.9373 | − | 45.6663i | −0.120059 | − | 0.156929i | ||||
\(292\) | −139.299 | −0.477053 | ||||||||
\(293\) | 531.625i | 1.81442i | 0.420677 | + | 0.907211i | \(0.361793\pi\) | ||||
−0.420677 | + | 0.907211i | \(0.638207\pi\) | |||||||
\(294\) | −21.8006 | + | 16.6787i | −0.0741519 | + | 0.0567303i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 337.500i | − | 1.14020i | ||||||
\(297\) | 26.7307 | + | 65.3257i | 0.0900024 | + | 0.219952i | ||||
\(298\) | 266.235 | 0.893407 | ||||||||
\(299\) | − | 27.3379i | − | 0.0914312i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 147.830 | 0.491130 | ||||||||
\(302\) | 216.650i | 0.717383i | ||||||||
\(303\) | 235.199 | − | 179.940i | 0.776233 | − | 0.593861i | ||||
\(304\) | 16.1922 | 0.0532637 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 37.3725 | − | 137.896i | 0.122132 | − | 0.450640i | ||||
\(307\) | −567.763 | −1.84939 | −0.924696 | − | 0.380706i | \(-0.875681\pi\) | ||||
−0.924696 | + | 0.380706i | \(0.875681\pi\) | |||||||
\(308\) | − | 15.8492i | − | 0.0514583i | ||||||
\(309\) | 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 | \(0.978104\pi\) | |||||||
\(312\) | −124.506 | + | 95.2539i | −0.399057 | + | 0.305301i | ||||
\(313\) | 158.118 | 0.505168 | 0.252584 | − | 0.967575i | \(-0.418720\pi\) | ||||
0.252584 | + | 0.967575i | \(0.418720\pi\) | |||||||
\(314\) | 395.688i | 1.26015i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −144.931 | −0.458642 | ||||||||
\(317\) | 140.944i | 0.444619i | 0.974976 | + | 0.222309i | \(0.0713595\pi\) | ||||
−0.974976 | + | 0.222309i | \(0.928641\pi\) | |||||||
\(318\) | 250.184 | + | 327.015i | 0.786743 | + | 1.02835i | ||||
\(319\) | 45.4170 | 0.142373 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 293.395 | − | 224.463i | 0.914002 | − | 0.699262i | ||||
\(322\) | 14.8784 | 0.0462064 | ||||||||
\(323\) | − | 124.227i | − | 0.384604i | ||||||
\(324\) | −160.210 | − | 93.7247i | −0.494477 | − | 0.289274i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 189.582i | 0.581539i | ||||||||
\(327\) | 299.933 | + | 392.041i | 0.917227 | + | 1.19890i | ||||
\(328\) | 249.012 | 0.759182 | ||||||||
\(329\) | 105.764i | 0.321470i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −258.369 | −0.780570 | −0.390285 | − | 0.920694i | \(-0.627623\pi\) | ||||
−0.390285 | + | 0.920694i | \(0.627623\pi\) | |||||||
\(332\) | − | 206.106i | − | 0.620801i | ||||||
\(333\) | 96.6196 | − | 356.504i | 0.290149 | − | 1.07058i | ||||
\(334\) | 25.6967 | 0.0769362 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.63464 | − | 9.97920i | −0.0227221 | − | 0.0297000i | ||||
\(337\) | −328.959 | −0.976141 | −0.488070 | − | 0.872804i | \(-0.662299\pi\) | ||||
−0.488070 | + | 0.872804i | \(0.662299\pi\) | |||||||
\(338\) | − | 168.123i | − | 0.497406i | ||||||
\(339\) | −343.225 | + | 262.586i | −1.01246 | + | 0.774590i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 102.715i | − | 0.301218i | ||||||
\(342\) | 116.140 | + | 31.4762i | 0.339590 | + | 0.0920357i | ||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | 459.489i | 1.33572i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.7347 | 0.0743776 | ||||||||
\(347\) | − | 128.635i | − | 0.370707i | −0.982672 | − | 0.185353i | \(-0.940657\pi\) | ||
0.982672 | − | 0.185353i | \(-0.0593430\pi\) | |||||||
\(348\) | −94.8562 | + | 72.5703i | −0.272575 | + | 0.208535i | ||||
\(349\) | −73.4837 | −0.210555 | −0.105277 | − | 0.994443i | \(-0.533573\pi\) | ||||
−0.105277 | + | 0.994443i | \(0.533573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −158.786 | + | 64.9737i | −0.452381 | + | 0.185110i | ||||
\(352\) | 80.5830 | 0.228929 | ||||||||
\(353\) | 239.685i | 0.678995i | 0.940607 | + | 0.339498i | \(0.110257\pi\) | ||||
−0.940607 | + | 0.339498i | \(0.889743\pi\) | |||||||
\(354\) | −98.5568 | − | 128.823i | −0.278409 | − | 0.363907i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 144.765i | 0.406642i | ||||||||
\(357\) | −76.5608 | + | 58.5732i | −0.214456 | + | 0.164071i | ||||
\(358\) | 446.693 | 1.24775 | ||||||||
\(359\) | 180.215i | 0.501992i | 0.967988 | + | 0.250996i | \(0.0807581\pi\) | ||||
−0.967988 | + | 0.250996i | \(0.919242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −256.373 | −0.710173 | ||||||||
\(362\) | 282.187i | 0.779523i | ||||||||
\(363\) | 208.110 | + | 272.020i | 0.573307 | + | 0.749367i | ||||
\(364\) | 38.5242 | 0.105836 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 63.7817 | − | 48.7965i | 0.174267 | − | 0.133324i | ||||
\(367\) | −229.786 | −0.626119 | −0.313059 | − | 0.949734i | \(-0.601354\pi\) | ||||
−0.313059 | + | 0.949734i | \(0.601354\pi\) | |||||||
\(368\) | 6.81057i | 0.0185070i | ||||||||
\(369\) | 263.033 | + | 71.2871i | 0.712826 | + | 0.193190i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 277.808i | − | 0.748809i | ||||||
\(372\) | 164.125 | + | 214.528i | 0.441198 | + | 0.576687i | ||||
\(373\) | −441.749 | −1.18431 | −0.592157 | − | 0.805823i | \(-0.701723\pi\) | ||||
−0.592157 | + | 0.805823i | \(0.701723\pi\) | |||||||
\(374\) | 41.4990i | 0.110960i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −328.737 | −0.874301 | ||||||||
\(377\) | 110.394i | 0.292822i | ||||||||
\(378\) | −35.3614 | − | 86.4178i | −0.0935487 | − | 0.228618i | ||||
\(379\) | −421.203 | −1.11135 | −0.555676 | − | 0.831399i | \(-0.687541\pi\) | ||||
−0.555676 | + | 0.831399i | \(0.687541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 66.6863 | + | 87.1653i | 0.175030 | + | 0.228780i | ||||
\(382\) | −58.4418 | −0.152989 | ||||||||
\(383\) | − | 595.591i | − | 1.55507i | −0.628841 | − | 0.777534i | \(-0.716470\pi\) | ||
0.628841 | − | 0.777534i | \(-0.283530\pi\) | |||||||
\(384\) | −148.582 | + | 113.674i | −0.386933 | + | 0.296025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 189.688i | 0.491419i | ||||||||
\(387\) | −131.542 | + | 485.361i | −0.339903 | + | 1.25416i | ||||
\(388\) | −43.9190 | −0.113193 | ||||||||
\(389\) | − | 367.347i | − | 0.944336i | −0.881509 | − | 0.472168i | \(-0.843472\pi\) | ||
0.881509 | − | 0.472168i | \(-0.156528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.2510 | 0.133634 | ||||||||
\(392\) | 57.5651i | 0.146850i | ||||||||
\(393\) | −80.2614 | + | 61.4044i | −0.204227 | + | 0.156245i | ||||
\(394\) | 114.324 | 0.290163 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 52.0366 | + | 14.1029i | 0.131406 | + | 0.0356135i | ||||
\(397\) | −408.346 | −1.02858 | −0.514290 | − | 0.857616i | \(-0.671945\pi\) | ||||
−0.514290 | + | 0.857616i | \(0.671945\pi\) | |||||||
\(398\) | 85.5062i | 0.214840i | ||||||||
\(399\) | −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 | \(-0.0962453\pi\) | |||||||
\(402\) | −84.6052 | + | 64.7277i | −0.210461 | + | 0.161014i | ||||
\(403\) | 249.668 | 0.619524 | ||||||||
\(404\) | − | 226.199i | − | 0.559899i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −60.0810 | −0.147983 | ||||||||
\(407\) | 107.288i | 0.263606i | ||||||||
\(408\) | −182.059 | − | 237.968i | −0.446223 | − | 0.583255i | ||||
\(409\) | −649.365 | −1.58769 | −0.793844 | − | 0.608121i | \(-0.791924\pi\) | ||||
−0.793844 | + | 0.608121i | \(0.791924\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 95.2470 | − | 72.8693i | 0.231745 | − | 0.177297i | ||||
\(412\) | 128.899 | 0.312862 | ||||||||
\(413\) | 109.439i | 0.264985i | ||||||||
\(414\) | −13.2392 | + | 48.8495i | −0.0319787 | + | 0.117994i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 195.871i | 0.470844i | ||||||||
\(417\) | −354.808 | − | 463.768i | −0.850858 | − | 1.11215i | ||||
\(418\) | −34.9516 | −0.0836163 | ||||||||
\(419\) | − | 11.5178i | − | 0.0274888i | −0.999906 | − | 0.0137444i | \(-0.995625\pi\) | ||
0.999906 | − | 0.0137444i | \(-0.00437512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −83.9921 | −0.199506 | −0.0997531 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997531 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(422\) | 53.0458i | 0.125701i | ||||||||
\(423\) | −347.247 | − | 94.1108i | −0.820915 | − | 0.222484i | ||||
\(424\) | 863.490 | 2.03653 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 161.557 | + | 211.170i | 0.379241 | + | 0.495705i | ||||
\(427\) | −54.1843 | −0.126895 | ||||||||
\(428\) | − | 282.168i | − | 0.659272i | ||||||
\(429\) | 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 | \(0.702107\pi\) | |||||||
\(432\) | 39.5575 | − | 16.1866i | 0.0915684 | − | 0.0374690i | ||||
\(433\) | −116.834 | −0.269824 | −0.134912 | − | 0.990858i | \(-0.543075\pi\) | ||||
−0.134912 | + | 0.990858i | \(0.543075\pi\) | |||||||
\(434\) | 135.880i | 0.313087i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 377.041 | 0.864772 | ||||||||
\(437\) | 44.0072i | 0.100703i | ||||||||
\(438\) | 189.322 | − | 144.842i | 0.432241 | − | 0.330688i | ||||
\(439\) | −528.073 | −1.20290 | −0.601450 | − | 0.798910i | \(-0.705410\pi\) | ||||
−0.601450 | + | 0.798910i | \(0.705410\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.4797 | + | 60.8064i | −0.0373690 | + | 0.137883i | ||||
\(442\) | −100.871 | −0.228214 | ||||||||
\(443\) | − | 272.252i | − | 0.614564i | −0.951619 | − | 0.307282i | \(-0.900581\pi\) | ||
0.951619 | − | 0.307282i | \(-0.0994194\pi\) | |||||||
\(444\) | −171.431 | − | 224.077i | −0.386107 | − | 0.504678i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 131.964i | − | 0.295883i | ||||||
\(447\) | 485.314 | − | 371.292i | 1.08571 | − | 0.830631i | ||||
\(448\) | −123.354 | −0.275344 | ||||||||
\(449\) | − | 525.770i | − | 1.17098i | −0.810680 | − | 0.585490i | \(-0.800902\pi\) | ||
0.810680 | − | 0.585490i | \(-0.199098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −79.1581 | −0.175517 | ||||||||
\(452\) | 330.092i | 0.730292i | ||||||||
\(453\) | 302.140 | + | 394.925i | 0.666975 | + | 0.871800i | ||||
\(454\) | −511.439 | −1.12652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 200.423 | − | 153.335i | 0.439525 | − | 0.336261i | ||||
\(457\) | 513.786 | 1.12426 | 0.562129 | − | 0.827050i | \(-0.309983\pi\) | ||||
0.562129 | + | 0.827050i | \(0.309983\pi\) | |||||||
\(458\) | − | 8.90362i | − | 0.0194402i | ||||||
\(459\) | −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 | \(0.731937\pi\) | |||||||
\(462\) | 16.4797 | + | 21.5406i | 0.0356704 | + | 0.0466246i | ||||
\(463\) | −781.061 | −1.68696 | −0.843479 | − | 0.537162i | \(-0.819496\pi\) | ||||
−0.843479 | + | 0.537162i | \(0.819496\pi\) | |||||||
\(464\) | − | 27.5020i | − | 0.0592715i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 152.769 | 0.327830 | ||||||||
\(467\) | − | 163.353i | − | 0.349792i | −0.984587 | − | 0.174896i | \(-0.944041\pi\) | ||
0.984587 | − | 0.174896i | \(-0.0559589\pi\) | |||||||
\(468\) | −34.2797 | + | 126.484i | −0.0732472 | + | 0.270265i | ||||
\(469\) | 71.8745 | 0.153251 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 551.826 | + | 721.289i | 1.17161 | + | 1.53140i | ||||
\(472\) | −340.161 | −0.720679 | ||||||||
\(473\) | − | 146.067i | − | 0.308809i | ||||||
\(474\) | 196.975 | − | 150.697i | 0.415560 | − | 0.317926i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 73.6313i | 0.154688i | ||||||||
\(477\) | 912.110 | + | 247.200i | 1.91218 | + | 0.518239i | ||||
\(478\) | 78.3765 | 0.163968 | ||||||||
\(479\) | 700.159i | 1.46171i | 0.682533 | + | 0.730855i | \(0.260878\pi\) | ||||
−0.682533 | + | 0.730855i | \(0.739122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −260.782 | −0.542166 | ||||||||
\(482\) | 176.135i | 0.365425i | ||||||||
\(483\) | 27.1216 | − | 20.7495i | 0.0561523 | − | 0.0429596i | ||||
\(484\) | 261.612 | 0.540520 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 315.195 | − | 39.2035i | 0.648550 | − | 0.0806656i | ||||
\(487\) | −86.5909 | −0.177805 | −0.0889023 | − | 0.996040i | \(-0.528336\pi\) | ||||
−0.0889023 | + | 0.996040i | \(0.528336\pi\) | |||||||
\(488\) | − | 168.417i | − | 0.345117i | ||||||
\(489\) | 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 | \(-0.272404\pi\) | |||||||
\(492\) | 165.327 | − | 126.484i | 0.336030 | − | 0.257081i | ||||
\(493\) | −210.996 | −0.427984 | ||||||||
\(494\) | − | 84.9560i | − | 0.171976i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −62.1987 | −0.125401 | ||||||||
\(497\) | − | 179.395i | − | 0.360956i | ||||||
\(498\) | 214.306 | + | 280.118i | 0.430333 | + | 0.562486i | ||||
\(499\) | 379.814 | 0.761151 | 0.380575 | − | 0.924750i | \(-0.375726\pi\) | ||||
0.380575 | + | 0.924750i | \(0.375726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.8419 | − | 35.8366i | 0.0934967 | − | 0.0715302i | ||||
\(502\) | −350.626 | −0.698458 | ||||||||
\(503\) | 465.808i | 0.926059i | 0.886343 | + | 0.463029i | \(0.153238\pi\) | ||||
−0.886343 | + | 0.463029i | \(0.846762\pi\) | |||||||
\(504\) | −189.000 | − | 51.2228i | −0.375000 | − | 0.101632i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 14.7010i | − | 0.0290533i | ||||||
\(507\) | −234.465 | − | 306.468i | −0.462455 | − | 0.604473i | ||||
\(508\) | 83.8301 | 0.165020 | ||||||||
\(509\) | − | 750.503i | − | 1.47447i | −0.675639 | − | 0.737233i | \(-0.736132\pi\) | ||
0.675639 | − | 0.737233i | \(-0.263868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −160.834 | −0.314744 | ||||||||
\(512\) | − | 100.868i | − | 0.197009i | ||||||
\(513\) | 255.605 | − | 104.592i | 0.498256 | − | 0.203882i | ||||
\(514\) | 306.029 | 0.595387 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 233.395 | + | 305.069i | 0.452315 | + | 0.591219i | ||||
\(517\) | 104.502 | 0.202131 | ||||||||
\(518\) | − | 141.928i | − | 0.273993i | ||||||
\(519\) | 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 | \(-0.245769\pi\) | |||||||
\(522\) | 53.4615 | − | 197.260i | 0.102417 | − | 0.377893i | ||||
\(523\) | 624.707 | 1.19447 | 0.597234 | − | 0.802067i | \(-0.296266\pi\) | ||||
0.597234 | + | 0.802067i | \(0.296266\pi\) | |||||||
\(524\) | 77.1903i | 0.147310i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 326.959 | 0.621596 | ||||||||
\(527\) | 477.190i | 0.905485i | ||||||||
\(528\) | −9.86015 | + | 7.54356i | −0.0186745 | + | 0.0142871i | ||||
\(529\) | 510.490 | 0.965010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −359.314 | − | 97.3812i | −0.676674 | − | 0.183392i | ||||
\(532\) | −62.0144 | −0.116568 | ||||||||
\(533\) | − | 192.408i | − | 0.360990i | ||||||
\(534\) | −150.524 | − | 196.749i | −0.281881 | − | 0.368445i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 223.402i | 0.416795i | ||||||||
\(537\) | 814.265 | − | 622.958i | 1.51632 | − | 1.16007i | ||||
\(538\) | −445.306 | −0.827706 | ||||||||
\(539\) | − | 18.2993i | − | 0.0339505i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −291.757 | −0.539292 | −0.269646 | − | 0.962960i | \(-0.586907\pi\) | ||||
−0.269646 | + | 0.962960i | \(0.586907\pi\) | |||||||
\(542\) | − | 27.8403i | − | 0.0513659i | ||||||
\(543\) | 393.539 | + | 514.392i | 0.724749 | + | 0.947315i | ||||
\(544\) | −374.369 | −0.688178 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −52.3582 | + | 40.0569i | −0.0958941 | + | 0.0733643i | ||||
\(547\) | −204.952 | −0.374683 | −0.187342 | − | 0.982295i | \(-0.559987\pi\) | ||||
−0.187342 | + | 0.982295i | \(0.559987\pi\) | |||||||
\(548\) | − | 91.6026i | − | 0.167158i | ||||||
\(549\) | 48.2144 | − | 177.900i | 0.0878222 | − | 0.324044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 177.707i | − | 0.322517i | ||||||
\(552\) | 64.4941 | + | 84.2999i | 0.116837 | + | 0.152717i | ||||
\(553\) | −167.336 | −0.302597 | ||||||||
\(554\) | 296.599i | 0.535378i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −446.022 | −0.802198 | ||||||||
\(557\) | − | 503.883i | − | 0.904637i | −0.891857 | − | 0.452318i | \(-0.850597\pi\) | ||
0.891857 | − | 0.452318i | \(-0.149403\pi\) | |||||||
\(558\) | −446.125 | − | 120.909i | −0.799508 | − | 0.216683i | ||||
\(559\) | 355.041 | 0.635135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.8745 | + | 75.6475i | 0.103163 | + | 0.134844i | ||||
\(562\) | 307.806 | 0.547698 | ||||||||
\(563\) | 108.735i | 0.193135i | 0.995326 | + | 0.0965674i | \(0.0307863\pi\) | ||||
−0.995326 | + | 0.0965674i | \(0.969214\pi\) | |||||||
\(564\) | −218.259 | + | 166.980i | −0.386984 | + | 0.296064i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 481.840i | − | 0.851307i | ||||||
\(567\) | −184.978 | − | 108.214i | −0.326239 | − | 0.190853i | ||||
\(568\) | 557.600 | 0.981690 | ||||||||
\(569\) | 434.871i | 0.764273i | 0.924106 | + | 0.382136i | \(0.124812\pi\) | ||||
−0.924106 | + | 0.382136i | \(0.875188\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 119.122 | 0.208619 | 0.104310 | − | 0.994545i | \(-0.466737\pi\) | ||||
0.104310 | + | 0.994545i | \(0.466737\pi\) | |||||||
\(572\) | − | 38.0646i | − | 0.0665466i | ||||||
\(573\) | −106.532 | + | 81.5029i | −0.185920 | + | 0.142239i | ||||
\(574\) | 104.716 | 0.182433 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 109.763 | − | 405.001i | 0.190561 | − | 0.703127i | ||||
\(577\) | 655.417 | 1.13590 | 0.567952 | − | 0.823061i | \(-0.307736\pi\) | ||||
0.567952 | + | 0.823061i | \(0.307736\pi\) | |||||||
\(578\) | 184.957i | 0.319994i | ||||||||
\(579\) | 264.539 | + | 345.777i | 0.456889 | + | 0.597197i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 237.968i | − | 0.409584i | ||||||
\(582\) | 59.6902 | − | 45.6663i | 0.102560 | − | 0.0784645i | ||||
\(583\) | −274.494 | −0.470830 | ||||||||
\(584\) | − | 499.908i | − | 0.856007i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −694.885 | −1.18581 | ||||||||
\(587\) | 736.236i | 1.25424i | 0.778925 | + | 0.627118i | \(0.215765\pi\) | ||||
−0.778925 | + | 0.627118i | \(0.784235\pi\) | |||||||
\(588\) | 29.2399 | + | 38.2193i | 0.0497277 | + | 0.0649988i | ||||
\(589\) | −401.903 | −0.682348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 208.399 | − | 159.437i | 0.352620 | − | 0.269774i | ||||
\(592\) | 64.9674 | 0.109742 | ||||||||
\(593\) | 832.884i | 1.40453i | 0.711917 | + | 0.702263i | \(0.247827\pi\) | ||||
−0.711917 | + | 0.702263i | \(0.752173\pi\) | |||||||
\(594\) | −85.3869 | + | 34.9396i | −0.143749 | + | 0.0588209i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 466.744i | − | 0.783127i | ||||||
\(597\) | 119.247 | + | 155.867i | 0.199744 | + | 0.261084i | ||||
\(598\) | 35.7333 | 0.0597546 | ||||||||
\(599\) | − | 69.3290i | − | 0.115741i | −0.998324 | − | 0.0578706i | \(-0.981569\pi\) | ||
0.998324 | − | 0.0578706i | \(-0.0184311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −161.720 | −0.269085 | −0.134543 | − | 0.990908i | \(-0.542957\pi\) | ||||
−0.134543 | + | 0.990908i | \(0.542957\pi\) | |||||||
\(602\) | 193.228i | 0.320977i | ||||||||
\(603\) | −63.9555 | + | 235.981i | −0.106062 | + | 0.391345i | ||||
\(604\) | 379.814 | 0.628832 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 235.199 | + | 307.427i | 0.388117 | + | 0.507305i | ||||
\(607\) | −929.608 | −1.53148 | −0.765740 | − | 0.643151i | \(-0.777627\pi\) | ||||
−0.765740 | + | 0.643151i | \(0.777627\pi\) | |||||||
\(608\) | − | 315.304i | − | 0.518592i | ||||||
\(609\) | −109.520 | + | 83.7891i | −0.179836 | + | 0.137585i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 254.010i | 0.415729i | ||||||||
\(612\) | −241.749 | − | 65.5188i | −0.395015 | − | 0.107057i | ||||
\(613\) | −297.940 | −0.486036 | −0.243018 | − | 0.970022i | \(-0.578137\pi\) | ||||
−0.243018 | + | 0.970022i | \(0.578137\pi\) | |||||||
\(614\) | − | 742.121i | − | 1.20867i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 56.8784 | 0.0923351 | ||||||||
\(617\) | − | 975.575i | − | 1.58116i | −0.612360 | − | 0.790579i | \(-0.709780\pi\) | ||
0.612360 | − | 0.790579i | \(-0.290220\pi\) | |||||||
\(618\) | −175.187 | + | 134.028i | −0.283474 | + | 0.216873i | ||||
\(619\) | 357.034 | 0.576792 | 0.288396 | − | 0.957511i | \(-0.406878\pi\) | ||||
0.288396 | + | 0.957511i | \(0.406878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.9921 | + | 107.510i | 0.0708408 | + | 0.173124i | ||||
\(622\) | −55.8824 | −0.0898431 | ||||||||
\(623\) | 167.144i | 0.268289i | ||||||||
\(624\) | −18.3360 | − | 23.9668i | −0.0293845 | − | 0.0384084i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 206.675i | 0.330151i | ||||||||
\(627\) | −63.7124 | + | 48.7435i | −0.101615 | + | 0.0777409i | ||||
\(628\) | 693.690 | 1.10460 | ||||||||
\(629\) | − | 498.432i | − | 0.792420i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −813.223 | −1.28879 | −0.644393 | − | 0.764695i | \(-0.722890\pi\) | ||||
−0.644393 | + | 0.764695i | \(0.722890\pi\) | |||||||
\(632\) | − | 520.118i | − | 0.822971i | ||||||
\(633\) | 73.9778 | + | 96.6960i | 0.116869 | + | 0.152758i | ||||
\(634\) | −184.227 | −0.290579 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 573.298 | − | 438.605i | 0.901412 | − | 0.689630i | ||||
\(637\) | 44.4797 | 0.0698269 | ||||||||
\(638\) | 59.3643i | 0.0930475i | ||||||||
\(639\) | 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 | \(-0.168311\pi\) | |||||||
\(642\) | 293.395 | + | 383.495i | 0.457001 | + | 0.597344i | ||||
\(643\) | −144.561 | −0.224822 | −0.112411 | − | 0.993662i | \(-0.535857\pi\) | ||||
−0.112411 | + | 0.993662i | \(0.535857\pi\) | |||||||
\(644\) | − | 26.0838i | − | 0.0405028i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 162.376 | 0.251357 | ||||||||
\(647\) | − | 716.654i | − | 1.10766i | −0.832631 | − | 0.553828i | \(-0.813166\pi\) | ||
0.832631 | − | 0.553828i | \(-0.186834\pi\) | |||||||
\(648\) | 336.353 | − | 574.953i | 0.519063 | − | 0.887273i | ||||
\(649\) | 108.133 | 0.166615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 189.498 | + | 247.692i | 0.291088 | + | 0.380479i | ||||
\(652\) | 332.361 | 0.509756 | ||||||||
\(653\) | 378.999i | 0.580397i | 0.956966 | + | 0.290199i | \(0.0937214\pi\) | ||||
−0.956966 | + | 0.290199i | \(0.906279\pi\) | |||||||
\(654\) | −512.435 | + | 392.041i | −0.783540 | + | 0.599452i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 47.9337i | 0.0730696i | ||||||||
\(657\) | 143.114 | − | 528.056i | 0.217829 | − | 0.803738i | ||||
\(658\) | −138.243 | −0.210096 | ||||||||
\(659\) | 710.721i | 1.07848i | 0.842151 | + | 0.539242i | \(0.181289\pi\) | ||||
−0.842151 | + | 0.539242i | \(0.818711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 91.5045 | 0.138433 | 0.0692167 | − | 0.997602i | \(-0.477950\pi\) | ||||
0.0692167 | + | 0.997602i | \(0.477950\pi\) | |||||||
\(662\) | − | 337.712i | − | 0.510139i | ||||||
\(663\) | −183.875 | + | 140.674i | −0.277337 | + | 0.212178i | ||||
\(664\) | 739.659 | 1.11394 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 465.984 | + | 126.291i | 0.699676 | + | 0.189626i | ||||
\(667\) | 74.7451 | 0.112062 | ||||||||
\(668\) | − | 45.0495i | − | 0.0674394i | ||||||
\(669\) | −184.037 | − | 240.553i | −0.275092 | − | 0.359571i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 53.5379i | 0.0797883i | ||||||||
\(672\) | −194.321 | + | 148.666i | −0.289168 | + | 0.221230i | ||||
\(673\) | −645.806 | −0.959594 | −0.479797 | − | 0.877380i | \(-0.659290\pi\) | ||||
−0.479797 | + | 0.877380i | \(0.659290\pi\) | |||||||
\(674\) | − | 429.981i | − | 0.637954i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −294.741 | −0.436008 | ||||||||
\(677\) | − | 335.571i | − | 0.495674i | −0.968802 | − | 0.247837i | \(-0.920280\pi\) | ||
0.968802 | − | 0.247837i | \(-0.0797198\pi\) | |||||||
\(678\) | −343.225 | − | 448.627i | −0.506231 | − | 0.661692i | ||||
\(679\) | −50.7085 | −0.0746811 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −932.290 | + | 713.254i | −1.36900 | + | 1.04736i | ||||
\(682\) | 134.259 | 0.196860 | ||||||||
\(683\) | − | 113.336i | − | 0.165939i | −0.996552 | − | 0.0829694i | \(-0.973560\pi\) | ||
0.996552 | − | 0.0829694i | \(-0.0264404\pi\) | |||||||
\(684\) | 55.1818 | − | 203.608i | 0.0806751 | − | 0.297672i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.2077i | 0.0352882i | ||||||||
\(687\) | −12.4170 | − | 16.2302i | −0.0180742 | − | 0.0236247i | ||||
\(688\) | −88.4496 | −0.128561 | ||||||||
\(689\) | − | 667.206i | − | 0.968369i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 565.667 | 0.818620 | 0.409310 | − | 0.912395i | \(-0.365769\pi\) | ||||
0.409310 | + | 0.912395i | \(0.365769\pi\) | |||||||
\(692\) | − | 45.1161i | − | 0.0651967i | ||||||
\(693\) | 60.0810 | + | 16.2832i | 0.0866970 | + | 0.0234966i | ||||
\(694\) | 168.138 | 0.242274 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −260.435 | − | 340.414i | −0.374189 | − | 0.489100i | ||||
\(697\) | 367.749 | 0.527617 | ||||||||
\(698\) | − | 96.0501i | − | 0.137608i | ||||||
\(699\) | 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 | \(0.786056\pi\) | |||||||
\(702\) | −84.9268 | − | 207.548i | −0.120978 | − | 0.295652i | ||||
\(703\) | 419.793 | 0.597146 | ||||||||
\(704\) | 121.883i | 0.173129i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −313.292 | −0.443756 | ||||||||
\(707\) | − | 261.168i | − | 0.369403i | ||||||
\(708\) | −225.843 | + | 172.783i | −0.318988 | + | 0.244043i | ||||
\(709\) | 1092.04 | 1.54025 | 0.770125 | − | 0.637894i | \(-0.220194\pi\) | ||||
0.770125 | + | 0.637894i | \(0.220194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 148.899 | − | 549.404i | 0.209422 | − | 0.772720i | ||||
\(712\) | −519.522 | −0.729665 | ||||||||
\(713\) | − | 169.044i | − | 0.237088i | ||||||
\(714\) | −76.5608 | − | 100.072i | −0.107228 | − | 0.140157i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 783.109i | − | 1.09373i | ||||||
\(717\) | 142.871 | − | 109.304i | 0.199262 | − | 0.152446i | ||||
\(718\) | −235.558 | −0.328076 | ||||||||
\(719\) | 901.769i | 1.25420i | 0.778939 | + | 0.627099i | \(0.215758\pi\) | ||||
−0.778939 | + | 0.627099i | \(0.784242\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 148.826 | 0.206416 | ||||||||
\(722\) | − | 335.103i | − | 0.464132i | ||||||
\(723\) | 245.638 | + | 321.072i | 0.339748 | + | 0.444083i | ||||
\(724\) | 494.710 | 0.683301 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −355.556 | + | 272.020i | −0.489747 | + | 0.374683i | ||||
\(727\) | −297.506 | −0.409224 | −0.204612 | − | 0.978843i | \(-0.565593\pi\) | ||||
−0.204612 | + | 0.978843i | \(0.565593\pi\) | |||||||
\(728\) | 138.253i | 0.189908i | ||||||||
\(729\) | 519.889 | − | 511.035i | 0.713153 | − | 0.701008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 678.589i | 0.928302i | ||||||||
\(732\) | −85.5464 | − | 111.817i | −0.116867 | − | 0.152756i | ||||
\(733\) | −456.966 | −0.623419 | −0.311709 | − | 0.950177i | \(-0.600902\pi\) | ||||
−0.311709 | + | 0.950177i | \(0.600902\pi\) | |||||||
\(734\) | − | 300.352i | − | 0.409198i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 132.620 | 0.180190 | ||||||||
\(737\) | − | 71.0171i | − | 0.0963597i | ||||||
\(738\) | −93.1790 | + | 343.809i | −0.126259 | + | 0.465865i | ||||
\(739\) | −332.199 | −0.449525 | −0.224762 | − | 0.974414i | \(-0.572161\pi\) | ||||
−0.224762 | + | 0.974414i | \(0.572161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −118.480 | − | 154.864i | −0.159892 | − | 0.208994i | ||||
\(742\) | 363.122 | 0.489382 | ||||||||
\(743\) | 64.5346i | 0.0868568i | 0.999057 | + | 0.0434284i | \(0.0138280\pi\) | ||||
−0.999057 | + | 0.0434284i | \(0.986172\pi\) | |||||||
\(744\) | −769.882 | + | 589.003i | −1.03479 | + | 0.791670i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 577.408i | − | 0.774005i | ||||||
\(747\) | 781.306 | + | 211.749i | 1.04592 | + | 0.283466i | ||||
\(748\) | 72.7530 | 0.0972633 | ||||||||
\(749\) | − | 325.790i | − | 0.434966i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −611.668 | −0.814471 | −0.407236 | − | 0.913323i | \(-0.633507\pi\) | ||||
−0.407236 | + | 0.913323i | \(0.633507\pi\) | |||||||
\(752\) | − | 63.2805i | − | 0.0841496i | ||||||
\(753\) | −639.148 | + | 488.983i | −0.848802 | + | 0.649380i | ||||
\(754\) | −144.295 | −0.191373 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −151.501 | + | 61.9930i | −0.200399 | + | 0.0820014i | ||||
\(757\) | 207.357 | 0.273919 | 0.136960 | − | 0.990577i | \(-0.456267\pi\) | ||||
0.136960 | + | 0.990577i | \(0.456267\pi\) | |||||||
\(758\) | − | 550.552i | − | 0.726322i | ||||||
\(759\) | −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 | \(0.928766\pi\) | |||||||
\(762\) | −113.933 | + | 87.1653i | −0.149519 | + | 0.114390i | ||||
\(763\) | 435.328 | 0.570548 | ||||||||
\(764\) | 102.456i | 0.134104i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 778.494 | 1.01631 | ||||||||
\(767\) | 262.837i | 0.342682i | ||||||||
\(768\) | −488.538 | − | 638.565i | −0.636117 | − | 0.831465i | ||||
\(769\) | −1042.22 | −1.35529 | −0.677646 | − | 0.735388i | \(-0.737000\pi\) | ||||
−0.677646 | + | 0.735388i | \(0.737000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 557.852 | − | 426.788i | 0.723544 | − | 0.553551i | ||||
\(772\) | 332.546 | 0.430760 | ||||||||
\(773\) | − | 291.448i | − | 0.377035i | −0.982070 | − | 0.188517i | \(-0.939632\pi\) | ||
0.982070 | − | 0.188517i | \(-0.0603682\pi\) | |||||||
\(774\) | −634.413 | − | 171.939i | −0.819655 | − | 0.222143i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 157.613i | − | 0.203110i | ||||||
\(777\) | −197.933 | − | 258.718i | −0.254740 | − | 0.332970i | ||||
\(778\) | 480.157 | 0.617168 | ||||||||
\(779\) | 309.729i | 0.397598i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −177.255 | −0.226959 | ||||||||
\(782\) | 68.2970i | 0.0873363i | ||||||||
\(783\) | −177.646 | − | 434.138i | −0.226878 | − | 0.554455i | ||||
\(784\) | −11.0810 | −0.0141340 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −80.2614 | − | 104.909i | −0.102114 | − | 0.133472i | ||||
\(787\) | −293.889 | −0.373429 | −0.186715 | − | 0.982414i | \(-0.559784\pi\) | ||||
−0.186715 | + | 0.982414i | \(0.559784\pi\) | |||||||
\(788\) | − | 200.425i | − | 0.254346i | ||||||
\(789\) | 596.006 | − | 455.978i | 0.755395 | − | 0.577919i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 381.122i | 0.481822i | ||||||||
\(792\) | −50.6117 | + | 186.745i | −0.0639037 | + | 0.235790i | ||||
\(793\) | −130.133 | −0.164103 | ||||||||
\(794\) | − | 533.748i | − | 0.672226i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 149.903 | 0.188321 | ||||||||
\(797\) | 568.764i | 0.713631i | 0.934175 | + | 0.356816i | \(0.116138\pi\) | ||||
−0.934175 | + | 0.356816i | \(0.883862\pi\) | |||||||
\(798\) | 84.2836 | − | 64.4816i | 0.105619 | − | 0.0808041i | ||||
\(799\) | −485.490 | −0.607622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −548.774 | − | 148.729i | −0.685111 | − | 0.185679i | ||||
\(802\) | 312.157 | 0.389223 | ||||||||
\(803\) | 158.915i | 0.197902i | ||||||||
\(804\) | 113.476 | + | 148.324i | 0.141139 | + | 0.184482i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 326.340i | 0.404888i | ||||||||
\(807\) | −811.737 | + | 621.024i | −1.00587 | + | 0.769546i | ||||
\(808\) | 811.768 | 1.00466 | ||||||||
\(809\) | − | 183.697i | − | 0.227067i | −0.993534 | − | 0.113534i | \(-0.963783\pi\) | ||
0.993534 | − | 0.113534i | \(-0.0362169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −544.663 | −0.671594 | −0.335797 | − | 0.941934i | \(-0.609006\pi\) | ||||
−0.335797 | + | 0.941934i | \(0.609006\pi\) | |||||||
\(812\) | 105.330i | 0.129716i | ||||||||
\(813\) | −38.8261 | − | 50.7494i | −0.0477566 | − | 0.0624224i | ||||
\(814\) | −140.235 | −0.172279 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 45.8078 | − | 35.0455i | 0.0561370 | − | 0.0429479i | ||||
\(817\) | −571.527 | −0.699543 | ||||||||
\(818\) | − | 848.781i | − | 1.03763i | ||||||
\(819\) | −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 | \(0.742309\pi\) | |||||||
\(822\) | 95.2470 | + | 124.497i | 0.115872 | + | 0.151456i | ||||
\(823\) | −1265.15 | −1.53724 | −0.768621 | − | 0.639704i | \(-0.779057\pi\) | ||||
−0.768621 | + | 0.639704i | \(0.779057\pi\) | |||||||
\(824\) | 462.585i | 0.561390i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −143.047 | −0.173180 | ||||||||
\(827\) | 790.941i | 0.956398i | 0.878252 | + | 0.478199i | \(0.158710\pi\) | ||||
−0.878252 | + | 0.478199i | \(0.841290\pi\) | |||||||
\(828\) | 85.6393 | + | 23.2099i | 0.103429 | + | 0.0280313i | ||||
\(829\) | 99.1961 | 0.119658 | 0.0598288 | − | 0.998209i | \(-0.480945\pi\) | ||||
0.0598288 | + | 0.998209i | \(0.480945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 413.638 | + | 540.664i | 0.497759 | + | 0.650619i | ||||
\(832\) | −296.257 | −0.356079 | ||||||||
\(833\) | 85.0141i | 0.102058i | ||||||||
\(834\) | 606.188 | − | 463.768i | 0.726844 | − | 0.556076i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 61.2746i | 0.0732950i | ||||||||
\(837\) | −981.851 | + | 401.765i | −1.17306 | + | 0.480006i | ||||
\(838\) | 15.0549 | 0.0179652 | ||||||||
\(839\) | 243.824i | 0.290612i | 0.989387 | + | 0.145306i | \(0.0464167\pi\) | ||||
−0.989387 | + | 0.145306i | \(0.953583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 539.170 | 0.641106 | ||||||||
\(842\) | − | 109.786i | − | 0.130387i | ||||||
\(843\) | 561.093 | − | 429.267i | 0.665591 | − | 0.509214i | ||||
\(844\) | 92.9961 | 0.110185 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 123.012 | − | 453.885i | 0.145404 | − | 0.536507i | ||||
\(847\) | 302.055 | 0.356617 | ||||||||
\(848\) | 166.218i | 0.196012i | ||||||||
\(849\) | −671.974 | − | 878.334i | −0.791489 | − | 1.03455i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 176.569i | 0.207484i | ||||||||
\(852\) | 370.208 | − | 283.230i | 0.434516 | − | 0.332429i | ||||
\(853\) | 1122.06 | 1.31543 | 0.657713 | − | 0.753268i | \(-0.271524\pi\) | ||||
0.657713 | + | 0.753268i | \(0.271524\pi\) | |||||||
\(854\) | − | 70.8240i | − | 0.0829321i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1012.63 | 1.18298 | ||||||||
\(857\) | 871.489i | 1.01691i | 0.861090 | + | 0.508453i | \(0.169783\pi\) | ||||
−0.861090 | + | 0.508453i | \(0.830217\pi\) | |||||||
\(858\) | 39.5791 | + | 51.7336i | 0.0461295 | + | 0.0602956i | ||||
\(859\) | −1674.92 | −1.94985 | −0.974925 | − | 0.222533i | \(-0.928568\pi\) | ||||
−0.974925 | + | 0.222533i | \(0.928568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 190.885 | − | 146.038i | 0.221701 | − | 0.169614i | ||||
\(862\) | −907.129 | −1.05235 | ||||||||
\(863\) | 1320.74i | 1.53041i | 0.643787 | + | 0.765205i | \(0.277362\pi\) | ||||
−0.643787 | + | 0.765205i | \(0.722638\pi\) | |||||||
\(864\) | −315.195 | − | 770.288i | −0.364810 | − | 0.891537i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 152.713i | − | 0.176343i | ||||||
\(867\) | 257.940 | + | 337.153i | 0.297509 | + | 0.388873i | ||||
\(868\) | 238.214 | 0.274441 | ||||||||
\(869\) | 165.340i | 0.190264i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 172.620 | 0.198186 | ||||||||
\(872\) | 1353.10i | 1.55172i | ||||||||
\(873\) | 45.1216 | − | 166.488i | 0.0516856 | − | 0.190708i | ||||
\(874\) | −57.5217 | −0.0658142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −253.925 | − | 331.905i | −0.289869 | − | 0.378887i | ||||
\(877\) | 344.790 | 0.393147 | 0.196573 | − | 0.980489i | \(-0.437019\pi\) | ||||
0.196573 | + | 0.980489i | \(0.437019\pi\) | |||||||
\(878\) | − | 690.242i | − | 0.786152i | ||||||
\(879\) | −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 | \(0.904879\pi\) | |||||||
\(882\) | −79.4797 | − | 21.5406i | −0.0901131 | − | 0.0244224i | ||||
\(883\) | 584.008 | 0.661391 | 0.330695 | − | 0.943738i | \(-0.392717\pi\) | ||||
0.330695 | + | 0.943738i | \(0.392717\pi\) | |||||||
\(884\) | 176.839i | 0.200044i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 355.859 | 0.401646 | ||||||||
\(887\) | − | 263.213i | − | 0.296745i | −0.988932 | − | 0.148373i | \(-0.952597\pi\) | ||
0.988932 | − | 0.148373i | \(-0.0474035\pi\) | |||||||
\(888\) | 804.153 | − | 615.221i | 0.905577 | − | 0.692817i | ||||
\(889\) | 96.7895 | 0.108875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −106.923 | + | 182.771i | −0.120003 | + | 0.205130i | ||||
\(892\) | −231.349 | −0.259360 | ||||||||
\(893\) | − | 408.893i | − | 0.457887i | ||||||
\(894\) | 485.314 | + | 634.351i | 0.542857 | + | 0.709565i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 164.988i | 0.184138i | ||||||||
\(897\) | 65.1373 | − | 49.8336i | 0.0726168 | − | 0.0555559i | ||||
\(898\) | 687.231 | 0.765291 | ||||||||
\(899\) | 682.621i | 0.759312i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1275.23 | 1.41535 | ||||||||
\(902\) | − | 103.467i | − | 0.114709i | ||||||
\(903\) | 269.476 | + | 352.230i | 0.298423 | + | 0.390067i | ||||
\(904\) | −1184.61 | −1.31041 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −516.205 | + | 394.925i | −0.569763 | + | 0.435900i | ||||
\(907\) | 1501.72 | 1.65570 | 0.827849 | − | 0.560951i | \(-0.189565\pi\) | ||||
0.827849 | + | 0.560951i | \(0.189565\pi\) | |||||||
\(908\) | 896.618i | 0.987464i | ||||||||
\(909\) | 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 | \(0.839716\pi\) | |||||||
\(912\) | 29.5163 | + | 38.5806i | 0.0323644 | + | 0.0423033i | ||||
\(913\) | −235.129 | −0.257535 | ||||||||
\(914\) | 671.567i | 0.734756i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.6092 | −0.0170406 | ||||||||
\(917\) | 89.1234i | 0.0971901i | ||||||||
\(918\) | 396.686 | − | 162.321i | 0.432120 | − | 0.176820i | ||||
\(919\) | 76.9882 | 0.0837739 | 0.0418869 | − | 0.999122i | \(-0.486663\pi\) | ||||
0.0418869 | + | 0.999122i | \(0.486663\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1034.96 | − | 1352.79i | −1.12374 | − | 1.46883i | ||||
\(922\) | −899.123 | −0.975188 | ||||||||
\(923\) | − | 430.849i | − | 0.466792i | ||||||
\(924\) | 37.7634 | − | 28.8911i | 0.0408694 | − | 0.0312674i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1020.92i | − | 1.10251i | ||||||
\(927\) | −132.429 | + | 488.631i | −0.142857 | + | 0.527110i | ||||
\(928\) | −535.535 | −0.577085 | ||||||||
\(929\) | 1629.76i | 1.75431i | 0.480204 | + | 0.877157i | \(0.340563\pi\) | ||||
−0.480204 | + | 0.877157i | \(0.659437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −71.6013 | −0.0769079 | ||||||||
\(932\) | − | 267.823i | − | 0.287364i | ||||||
\(933\) | −101.867 | + | 77.9336i | −0.109182 | + | 0.0835301i | ||||
\(934\) | 213.517 | 0.228605 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −453.918 | − | 123.021i | −0.484955 | − | 0.131432i | ||||
\(937\) | 497.720 | 0.531185 | 0.265592 | − | 0.964085i | \(-0.414432\pi\) | ||||
0.265592 | + | 0.964085i | \(0.414432\pi\) | |||||||
\(938\) | 93.9468i | 0.100157i | ||||||||
\(939\) | 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 | \(-0.0405144\pi\) | |||||||
\(942\) | −942.793 | + | 721.289i | −1.00084 | + | 0.765700i | ||||
\(943\) | −130.275 | −0.138149 | ||||||||
\(944\) | − | 65.4794i | − | 0.0693638i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 190.923 | 0.201821 | ||||||||
\(947\) | 667.910i | 0.705291i | 0.935757 | + | 0.352645i | \(0.114718\pi\) | ||||
−0.935757 | + | 0.352645i | \(0.885282\pi\) | |||||||
\(948\) | −264.191 | − | 345.322i | −0.278682 | − | 0.364264i | ||||
\(949\) | −386.272 | −0.407030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −335.824 | + | 256.924i | −0.353127 | + | 0.270162i | ||||
\(952\) | −264.243 | −0.277566 | ||||||||
\(953\) | 11.3247i | 0.0118832i | 0.999982 | + | 0.00594162i | \(0.00189129\pi\) | ||||
−0.999982 | + | 0.00594162i | \(0.998109\pi\) | |||||||
\(954\) | −323.114 | + | 1192.21i | −0.338694 | + | 1.24970i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 137.404i | − | 0.143728i | ||||||
\(957\) | 82.7895 | + | 108.214i | 0.0865094 | + | 0.113076i | ||||
\(958\) | −915.174 | −0.955296 | ||||||||
\(959\) | − | 105.764i | − | 0.110285i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 582.822 | 0.606475 | ||||||||
\(962\) | − | 340.866i | − | 0.354331i | ||||||
\(963\) | 1069.64 | + | 289.895i | 1.11074 | + | 0.301033i | ||||
\(964\) | 308.787 | 0.320318 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 27.1216 | + | 35.4504i | 0.0280761 | + | 0.0366982i | ||||
\(967\) | −830.324 | −0.858660 | −0.429330 | − | 0.903148i | \(-0.641250\pi\) | ||||
−0.429330 | + | 0.903148i | \(0.641250\pi\) | |||||||
\(968\) | 938.855i | 0.969891i | ||||||||
\(969\) | 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 | \(-0.215705\pi\) | |||||||
\(972\) | −68.7286 | − | 552.577i | −0.0707085 | − | 0.568495i | ||||
\(973\) | −514.974 | −0.529264 | ||||||||
\(974\) | − | 113.183i | − | 0.116204i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.4195 | 0.0332167 | ||||||||
\(977\) | − | 424.579i | − | 0.434574i | −0.976108 | − | 0.217287i | \(-0.930279\pi\) | ||
0.976108 | − | 0.217287i | \(-0.0697207\pi\) | |||||||
\(978\) | −451.711 | + | 345.584i | −0.461872 | + | 0.353358i | ||||
\(979\) | 165.150 | 0.168693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −387.365 | + | 1429.29i | −0.394867 | + | 1.45697i | ||||
\(982\) | 969.203 | 0.986968 | ||||||||
\(983\) | − | 76.7273i | − | 0.0780542i | −0.999238 | − | 0.0390271i | \(-0.987574\pi\) | ||
0.999238 | − | 0.0390271i | \(-0.0124259\pi\) | |||||||
\(984\) | 453.918 | + | 593.313i | 0.461298 | + | 0.602961i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 275.792i | − | 0.279708i | ||||||
\(987\) | −252.000 | + | 192.794i | −0.255319 | + | 0.195333i | ||||
\(988\) | −148.939 | −0.150748 | ||||||||
\(989\) | − | 240.389i | − | 0.243063i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 181.271 | 0.182917 | 0.0914585 | − | 0.995809i | \(-0.470847\pi\) | ||||
0.0914585 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(992\) | 1211.17i | 1.22094i | ||||||||
\(993\) | −470.974 | − | 615.608i | −0.474294 | − | 0.619947i | ||||
\(994\) | 234.486 | 0.235902 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 491.082 | − | 375.705i | 0.493055 | − | 0.377214i | ||||
\(997\) | 1184.43 | 1.18800 | 0.593998 | − | 0.804466i | \(-0.297549\pi\) | ||||
0.593998 | + | 0.804466i | \(0.297549\pi\) | |||||||
\(998\) | 496.453i | 0.497448i | ||||||||
\(999\) | 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.c.a.176.3 | 4 | ||
3.2 | odd | 2 | inner | 525.3.c.a.176.2 | 4 | ||
5.2 | odd | 4 | 525.3.f.a.449.3 | 8 | |||
5.3 | odd | 4 | 525.3.f.a.449.6 | 8 | |||
5.4 | even | 2 | 21.3.b.a.8.2 | ✓ | 4 | ||
15.2 | even | 4 | 525.3.f.a.449.5 | 8 | |||
15.8 | even | 4 | 525.3.f.a.449.4 | 8 | |||
15.14 | odd | 2 | 21.3.b.a.8.3 | yes | 4 | ||
20.19 | odd | 2 | 336.3.d.c.113.4 | 4 | |||
35.4 | even | 6 | 147.3.h.e.128.3 | 8 | |||
35.9 | even | 6 | 147.3.h.e.116.2 | 8 | |||
35.19 | odd | 6 | 147.3.h.c.116.2 | 8 | |||
35.24 | odd | 6 | 147.3.h.c.128.3 | 8 | |||
35.34 | odd | 2 | 147.3.b.f.50.2 | 4 | |||
40.19 | odd | 2 | 1344.3.d.b.449.1 | 4 | |||
40.29 | even | 2 | 1344.3.d.f.449.4 | 4 | |||
45.4 | even | 6 | 567.3.r.c.512.3 | 8 | |||
45.14 | odd | 6 | 567.3.r.c.512.2 | 8 | |||
45.29 | odd | 6 | 567.3.r.c.134.3 | 8 | |||
45.34 | even | 6 | 567.3.r.c.134.2 | 8 | |||
60.59 | even | 2 | 336.3.d.c.113.3 | 4 | |||
105.44 | odd | 6 | 147.3.h.e.116.3 | 8 | |||
105.59 | even | 6 | 147.3.h.c.128.2 | 8 | |||
105.74 | odd | 6 | 147.3.h.e.128.2 | 8 | |||
105.89 | even | 6 | 147.3.h.c.116.3 | 8 | |||
105.104 | even | 2 | 147.3.b.f.50.3 | 4 | |||
120.29 | odd | 2 | 1344.3.d.f.449.3 | 4 | |||
120.59 | even | 2 | 1344.3.d.b.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.b.a.8.2 | ✓ | 4 | 5.4 | even | 2 | ||
21.3.b.a.8.3 | yes | 4 | 15.14 | odd | 2 | ||
147.3.b.f.50.2 | 4 | 35.34 | odd | 2 | |||
147.3.b.f.50.3 | 4 | 105.104 | even | 2 | |||
147.3.h.c.116.2 | 8 | 35.19 | odd | 6 | |||
147.3.h.c.116.3 | 8 | 105.89 | even | 6 | |||
147.3.h.c.128.2 | 8 | 105.59 | even | 6 | |||
147.3.h.c.128.3 | 8 | 35.24 | odd | 6 | |||
147.3.h.e.116.2 | 8 | 35.9 | even | 6 | |||
147.3.h.e.116.3 | 8 | 105.44 | odd | 6 | |||
147.3.h.e.128.2 | 8 | 105.74 | odd | 6 | |||
147.3.h.e.128.3 | 8 | 35.4 | even | 6 | |||
336.3.d.c.113.3 | 4 | 60.59 | even | 2 | |||
336.3.d.c.113.4 | 4 | 20.19 | odd | 2 | |||
525.3.c.a.176.2 | 4 | 3.2 | odd | 2 | inner | ||
525.3.c.a.176.3 | 4 | 1.1 | even | 1 | trivial | ||
525.3.f.a.449.3 | 8 | 5.2 | odd | 4 | |||
525.3.f.a.449.4 | 8 | 15.8 | even | 4 | |||
525.3.f.a.449.5 | 8 | 15.2 | even | 4 | |||
525.3.f.a.449.6 | 8 | 5.3 | odd | 4 | |||
567.3.r.c.134.2 | 8 | 45.34 | even | 6 | |||
567.3.r.c.134.3 | 8 | 45.29 | odd | 6 | |||
567.3.r.c.512.2 | 8 | 45.14 | odd | 6 | |||
567.3.r.c.512.3 | 8 | 45.4 | even | 6 | |||
1344.3.d.b.449.1 | 4 | 40.19 | odd | 2 | |||
1344.3.d.b.449.2 | 4 | 120.59 | even | 2 | |||
1344.3.d.f.449.3 | 4 | 120.29 | odd | 2 | |||
1344.3.d.f.449.4 | 4 | 40.29 | even | 2 |