Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.12 | ||
Character | \(\chi\) | \(=\) | 3150.1601 |
Dual form | 3150.2.bf.d.1151.12 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52781 | − | 2.16005i | −0.577458 | − | 0.816421i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29783 | − | 2.48135i | 1.29584 | − | 0.748156i | 0.316160 | − | 0.948706i | \(-0.397606\pi\) |
0.979683 | + | 0.200550i | \(0.0642729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.49388i | 1.52373i | 0.647737 | + | 0.761864i | \(0.275715\pi\) | ||||
−0.647737 | + | 0.761864i | \(0.724285\pi\) | |||||||
\(14\) | −0.243099 | − | 2.63456i | −0.0649709 | − | 0.704116i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.53712 | + | 2.66237i | 0.372806 | + | 0.645719i | 0.989996 | − | 0.141095i | \(-0.0450623\pi\) |
−0.617190 | + | 0.786814i | \(0.711729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.68622 | − | 1.55089i | −0.616261 | − | 0.355798i | 0.159151 | − | 0.987254i | \(-0.449124\pi\) |
−0.775412 | + | 0.631456i | \(0.782458\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.96270 | 1.05805 | ||||||||
\(23\) | 5.34875 | + | 3.08810i | 1.11529 | + | 0.643914i | 0.940195 | − | 0.340638i | \(-0.110643\pi\) |
0.175097 | + | 0.984551i | \(0.443976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.74694 | + | 4.75784i | −0.538719 | + | 0.933089i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.10675 | − | 2.40314i | 0.209156 | − | 0.454152i | ||||
\(29\) | − | 6.67885i | − | 1.24023i | −0.784510 | − | 0.620116i | \(-0.787086\pi\) | ||
0.784510 | − | 0.620116i | \(-0.212914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.01653 | + | 0.586893i | −0.182574 | + | 0.105409i | −0.588501 | − | 0.808496i | \(-0.700282\pi\) |
0.405928 | + | 0.913905i | \(0.366949\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.07424i | 0.527228i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.35400 | − | 9.27339i | 0.880192 | − | 1.52454i | 0.0290640 | − | 0.999578i | \(-0.490747\pi\) |
0.851128 | − | 0.524959i | \(-0.175919\pi\) | |||||||
\(38\) | −1.55089 | − | 2.68622i | −0.251587 | − | 0.435762i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.39427 | −1.31096 | −0.655482 | − | 0.755211i | \(-0.727534\pi\) | ||||
−0.655482 | + | 0.755211i | \(0.727534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.81025 | 1.34355 | 0.671776 | − | 0.740755i | \(-0.265532\pi\) | ||||
0.671776 | + | 0.740755i | \(0.265532\pi\) | |||||||
\(44\) | 4.29783 | + | 2.48135i | 0.647922 | + | 0.374078i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.08810 | + | 5.34875i | 0.455316 | + | 0.788630i | ||||
\(47\) | −2.07312 | + | 3.59075i | −0.302396 | + | 0.523765i | −0.976678 | − | 0.214709i | \(-0.931120\pi\) |
0.674282 | + | 0.738474i | \(0.264453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.33160 | + | 6.60028i | −0.333085 | + | 0.942897i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.75784 | + | 2.74694i | −0.659793 | + | 0.380932i | ||||
\(53\) | −3.85443 | + | 2.22536i | −0.529446 | + | 0.305676i | −0.740791 | − | 0.671736i | \(-0.765549\pi\) |
0.211345 | + | 0.977412i | \(0.432216\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.16005 | − | 1.52781i | 0.288648 | − | 0.204162i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.33943 | − | 5.78405i | 0.438488 | − | 0.759484i | ||||
\(59\) | 3.00381 | + | 5.20275i | 0.391062 | + | 0.677340i | 0.992590 | − | 0.121512i | \(-0.0387743\pi\) |
−0.601528 | + | 0.798852i | \(0.705441\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.05018 | + | 5.22512i | 1.15876 | + | 0.669008i | 0.951006 | − | 0.309173i | \(-0.100052\pi\) |
0.207751 | + | 0.978182i | \(0.433386\pi\) | |||||||
\(62\) | −1.17379 | −0.149071 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.97727 | + | 10.3529i | 0.730240 | + | 1.26481i | 0.956780 | + | 0.290811i | \(0.0939252\pi\) |
−0.226540 | + | 0.974002i | \(0.572741\pi\) | |||||||
\(68\) | −1.53712 | + | 2.66237i | −0.186403 | + | 0.322860i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.973522i | − | 0.115536i | −0.998330 | − | 0.0577679i | \(-0.981602\pi\) | ||
0.998330 | − | 0.0577679i | \(-0.0183983\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4612 | − | 8.34916i | 1.69255 | − | 0.977196i | 0.740106 | − | 0.672490i | \(-0.234775\pi\) |
0.952446 | − | 0.304706i | \(-0.0985582\pi\) | |||||||
\(74\) | 9.27339 | − | 5.35400i | 1.07801 | − | 0.622389i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.10178i | − | 0.355798i | ||||||
\(77\) | −11.9261 | − | 5.49247i | −1.35910 | − | 0.625925i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.12328 | − | 3.67763i | 0.238887 | − | 0.413765i | −0.721508 | − | 0.692406i | \(-0.756551\pi\) |
0.960395 | + | 0.278641i | \(0.0898840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.26965 | − | 4.19713i | −0.802798 | − | 0.463496i | ||||
\(83\) | 14.2841 | 1.56789 | 0.783944 | − | 0.620831i | \(-0.213205\pi\) | ||||
0.783944 | + | 0.620831i | \(0.213205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.62990 | + | 4.40513i | 0.822754 | + | 0.475017i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.48135 | + | 4.29783i | 0.264513 | + | 0.458150i | ||||
\(89\) | 7.38517 | − | 12.7915i | 0.782826 | − | 1.35590i | −0.147463 | − | 0.989068i | \(-0.547111\pi\) |
0.930289 | − | 0.366827i | \(-0.119556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8670 | − | 8.39360i | 1.24400 | − | 0.879888i | ||||
\(92\) | 6.17620i | 0.643914i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.59075 | + | 2.07312i | −0.370358 | + | 0.213826i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.41643i | − | 0.448420i | −0.974541 | − | 0.224210i | \(-0.928020\pi\) | ||
0.974541 | − | 0.224210i | \(-0.0719802\pi\) | |||||||
\(98\) | −5.31936 | + | 4.55021i | −0.537336 | + | 0.459641i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.19825 | + | 9.00364i | 0.517245 | + | 0.895895i | 0.999799 | + | 0.0200290i | \(0.00637586\pi\) |
−0.482554 | + | 0.875866i | \(0.660291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.86709 | + | 5.11942i | 0.873701 | + | 0.504431i | 0.868576 | − | 0.495556i | \(-0.165035\pi\) |
0.00512447 | + | 0.999987i | \(0.498369\pi\) | |||||||
\(104\) | −5.49388 | −0.538719 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.45071 | −0.432291 | ||||||||
\(107\) | 5.69797 | + | 3.28972i | 0.550844 | + | 0.318030i | 0.749462 | − | 0.662047i | \(-0.230312\pi\) |
−0.198619 | + | 0.980077i | \(0.563645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.34219 | − | 2.32474i | −0.128558 | − | 0.222669i | 0.794560 | − | 0.607186i | \(-0.207702\pi\) |
−0.923118 | + | 0.384516i | \(0.874368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.63456 | − | 0.243099i | 0.248942 | − | 0.0229707i | ||||
\(113\) | 3.55031i | 0.333985i | 0.985958 | + | 0.166992i | \(0.0534056\pi\) | ||||
−0.985958 | + | 0.166992i | \(0.946594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.78405 | − | 3.33943i | 0.537036 | − | 0.310058i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00761i | 0.553046i | ||||||||
\(119\) | 3.40241 | − | 7.38784i | 0.311899 | − | 0.677242i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.81421 | − | 11.8026i | 0.619474 | − | 1.07296i | ||||
\(122\) | 5.22512 | + | 9.05018i | 0.473060 | + | 0.819365i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.01653 | − | 0.586893i | −0.0912869 | − | 0.0527045i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.51567 | −0.489437 | −0.244719 | − | 0.969594i | \(-0.578696\pi\) | ||||
−0.244719 | + | 0.969594i | \(0.578696\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3068 | + | 17.8519i | −0.900510 | + | 1.55973i | −0.0736773 | + | 0.997282i | \(0.523473\pi\) |
−0.826833 | + | 0.562447i | \(0.809860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.754039 | + | 8.17182i | 0.0653835 | + | 0.708586i | ||||
\(134\) | 11.9545i | 1.03272i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.66237 | + | 1.53712i | −0.228296 | + | 0.131807i | ||||
\(137\) | −9.92131 | + | 5.72807i | −0.847635 | + | 0.489382i | −0.859852 | − | 0.510543i | \(-0.829444\pi\) |
0.0122175 | + | 0.999925i | \(0.496111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.16700i | 0.0989840i | 0.998775 | + | 0.0494920i | \(0.0157602\pi\) | ||||
−0.998775 | + | 0.0494920i | \(0.984240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.486761 | − | 0.843095i | 0.0408481 | − | 0.0707509i | ||||
\(143\) | 13.6322 | + | 23.6117i | 1.13999 | + | 1.97451i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.6983 | 1.38196 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.7080 | 0.880192 | ||||||||
\(149\) | −13.3404 | − | 7.70205i | −1.09288 | − | 0.630977i | −0.158541 | − | 0.987352i | \(-0.550679\pi\) |
−0.934343 | + | 0.356375i | \(0.884012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.511281 | − | 0.885565i | −0.0416075 | − | 0.0720663i | 0.844472 | − | 0.535600i | \(-0.179915\pi\) |
−0.886079 | + | 0.463534i | \(0.846581\pi\) | |||||||
\(152\) | 1.55089 | − | 2.68622i | 0.125794 | − | 0.217881i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.58207 | − | 10.7197i | −0.610980 | − | 0.863815i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.64699 | − | 2.68294i | 0.370871 | − | 0.214122i | −0.302968 | − | 0.953001i | \(-0.597978\pi\) |
0.673839 | + | 0.738878i | \(0.264644\pi\) | |||||||
\(158\) | 3.67763 | − | 2.12328i | 0.292576 | − | 0.168919i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50143 | − | 16.2716i | −0.118329 | − | 1.28238i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.02108 | + | 8.69677i | −0.393282 | + | 0.681184i | −0.992880 | − | 0.119117i | \(-0.961994\pi\) |
0.599599 | + | 0.800301i | \(0.295327\pi\) | |||||||
\(164\) | −4.19713 | − | 7.26965i | −0.327741 | − | 0.567664i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.3704 | + | 7.14207i | 0.960131 | + | 0.554332i | ||||
\(167\) | −2.46005 | −0.190364 | −0.0951822 | − | 0.995460i | \(-0.530343\pi\) | ||||
−0.0951822 | + | 0.995460i | \(0.530343\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.1827 | −1.32175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.40513 | + | 7.62990i | 0.335888 | + | 0.581775i | ||||
\(173\) | −1.50042 | + | 2.59880i | −0.114075 | + | 0.197583i | −0.917410 | − | 0.397944i | \(-0.869724\pi\) |
0.803335 | + | 0.595528i | \(0.203057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.96270i | 0.374078i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.7915 | − | 7.38517i | 0.958763 | − | 0.553542i | ||||
\(179\) | 3.18036 | − | 1.83618i | 0.237711 | − | 0.137243i | −0.376413 | − | 0.926452i | \(-0.622843\pi\) |
0.614124 | + | 0.789209i | \(0.289509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.13560i | 0.456056i | 0.973655 | + | 0.228028i | \(0.0732278\pi\) | ||||
−0.973655 | + | 0.228028i | \(0.926772\pi\) | |||||||
\(182\) | 14.4739 | − | 1.33556i | 1.07288 | − | 0.0989980i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.08810 | + | 5.34875i | −0.227658 | + | 0.394315i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.2125 | + | 7.62827i | 0.966197 | + | 0.557834i | ||||
\(188\) | −4.14624 | −0.302396 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.95227 | − | 2.85920i | −0.358334 | − | 0.206884i | 0.310016 | − | 0.950731i | \(-0.399666\pi\) |
−0.668350 | + | 0.743847i | \(0.732999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.11665 | − | 5.39819i | −0.224341 | − | 0.388570i | 0.731780 | − | 0.681541i | \(-0.238690\pi\) |
−0.956122 | + | 0.292970i | \(0.905356\pi\) | |||||||
\(194\) | 2.20821 | − | 3.82474i | 0.158540 | − | 0.274600i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.88181 | + | 1.28092i | −0.491558 | + | 0.0914941i | ||||
\(197\) | − | 1.32234i | − | 0.0942128i | −0.998890 | − | 0.0471064i | \(-0.985000\pi\) | ||
0.998890 | − | 0.0471064i | \(-0.0150000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.27163 | + | 4.77563i | −0.586360 | + | 0.338535i | −0.763657 | − | 0.645622i | \(-0.776598\pi\) |
0.177297 | + | 0.984157i | \(0.443265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.3965i | 0.731495i | ||||||||
\(203\) | −14.4266 | + | 10.2040i | −1.01255 | + | 0.716181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.11942 | + | 8.86709i | 0.356687 | + | 0.617800i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.75784 | − | 2.74694i | −0.329897 | − | 0.190466i | ||||
\(209\) | −15.3932 | −1.06477 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0219 | 1.79142 | 0.895711 | − | 0.444636i | \(-0.146667\pi\) | ||||
0.895711 | + | 0.444636i | \(0.146667\pi\) | |||||||
\(212\) | −3.85443 | − | 2.22536i | −0.264723 | − | 0.152838i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.28972 | + | 5.69797i | 0.224881 | + | 0.389505i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.82078 | + | 1.29909i | 0.191487 | + | 0.0881878i | ||||
\(218\) | − | 2.68437i | − | 0.181809i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.6267 | + | 8.44475i | −0.983900 | + | 0.568055i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.25222i | − | 0.485644i | −0.970071 | − | 0.242822i | \(-0.921927\pi\) | ||
0.970071 | − | 0.242822i | \(-0.0780731\pi\) | |||||||
\(224\) | 2.40314 | + | 1.10675i | 0.160567 | + | 0.0739478i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.77515 | + | 3.07466i | −0.118081 | + | 0.204523i | ||||
\(227\) | −13.3604 | − | 23.1409i | −0.886762 | − | 1.53592i | −0.843680 | − | 0.536846i | \(-0.819616\pi\) |
−0.0430820 | − | 0.999072i | \(-0.513718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0473 | + | 12.1517i | 1.39085 | + | 0.803006i | 0.993409 | − | 0.114622i | \(-0.0365658\pi\) |
0.397439 | + | 0.917629i | \(0.369899\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.67885 | 0.438488 | ||||||||
\(233\) | −8.01573 | − | 4.62788i | −0.525128 | − | 0.303183i | 0.213902 | − | 0.976855i | \(-0.431383\pi\) |
−0.739030 | + | 0.673672i | \(0.764716\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00381 | + | 5.20275i | −0.195531 | + | 0.338670i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.64050 | − | 4.69685i | 0.430439 | − | 0.304452i | ||||
\(239\) | 0.253367i | 0.0163889i | 0.999966 | + | 0.00819446i | \(0.00260841\pi\) | ||||
−0.999966 | + | 0.00819446i | \(0.997392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.57538 | − | 1.48689i | 0.165895 | − | 0.0957792i | −0.414754 | − | 0.909934i | \(-0.636132\pi\) |
0.580649 | + | 0.814154i | \(0.302799\pi\) | |||||||
\(242\) | 11.8026 | − | 6.81421i | 0.758698 | − | 0.438034i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.4502i | 0.669008i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.52039 | − | 14.7578i | 0.542140 | − | 0.939013i | ||||
\(248\) | −0.586893 | − | 1.01653i | −0.0372677 | − | 0.0645496i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.0800 | −0.825599 | −0.412800 | − | 0.910822i | \(-0.635449\pi\) | ||||
−0.412800 | + | 0.910822i | \(0.635449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.6507 | 1.92699 | ||||||||
\(254\) | −4.77671 | − | 2.75784i | −0.299718 | − | 0.173042i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.29797 | + | 10.9084i | −0.392856 | + | 0.680447i | −0.992825 | − | 0.119576i | \(-0.961846\pi\) |
0.599969 | + | 0.800023i | \(0.295180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.2108 | + | 2.60310i | −1.75294 | + | 0.161749i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.8519 | + | 10.3068i | −1.10290 | + | 0.636757i | ||||
\(263\) | −14.4383 | + | 8.33594i | −0.890302 | + | 0.514016i | −0.874041 | − | 0.485852i | \(-0.838510\pi\) |
−0.0162609 | + | 0.999868i | \(0.505176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.43289 | + | 7.45402i | −0.210484 | + | 0.457035i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.97727 | + | 10.3529i | −0.365120 | + | 0.632407i | ||||
\(269\) | −10.0035 | − | 17.3265i | −0.609923 | − | 1.05642i | −0.991253 | − | 0.131978i | \(-0.957867\pi\) |
0.381330 | − | 0.924439i | \(-0.375466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4684 | − | 8.93068i | −0.939638 | − | 0.542500i | −0.0497914 | − | 0.998760i | \(-0.515856\pi\) |
−0.889847 | + | 0.456259i | \(0.849189\pi\) | |||||||
\(272\) | −3.07424 | −0.186403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.4561 | −0.692091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.07406 | − | 15.7167i | −0.545207 | − | 0.944327i | −0.998594 | − | 0.0530128i | \(-0.983118\pi\) |
0.453386 | − | 0.891314i | \(-0.350216\pi\) | |||||||
\(278\) | −0.583502 | + | 1.01066i | −0.0349961 | + | 0.0606151i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.5129i | − | 0.925425i | −0.886508 | − | 0.462713i | \(-0.846876\pi\) | ||
0.886508 | − | 0.462713i | \(-0.153124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2813 | + | 8.82268i | −0.908381 | + | 0.524454i | −0.879910 | − | 0.475141i | \(-0.842397\pi\) |
−0.0284708 | + | 0.999595i | \(0.509064\pi\) | |||||||
\(284\) | 0.843095 | − | 0.486761i | 0.0500285 | − | 0.0288840i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.2645i | 1.61218i | ||||||||
\(287\) | 12.8248 | + | 18.1320i | 0.757026 | + | 1.07030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.77453 | − | 6.53767i | 0.222031 | − | 0.384569i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.4612 | + | 8.34916i | 0.846276 | + | 0.488598i | ||||
\(293\) | 10.4489 | 0.610432 | 0.305216 | − | 0.952283i | \(-0.401271\pi\) | ||||
0.305216 | + | 0.952283i | \(0.401271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.27339 | + | 5.35400i | 0.539005 | + | 0.311195i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.70205 | − | 13.3404i | −0.446168 | − | 0.772786i | ||||
\(299\) | −16.9657 | + | 29.3854i | −0.981149 | + | 1.69940i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4604 | − | 19.0306i | −0.775844 | − | 1.09690i | ||||
\(302\) | − | 1.02256i | − | 0.0588419i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.68622 | − | 1.55089i | 0.154065 | − | 0.0889496i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.724648i | 0.0413579i | 0.999786 | + | 0.0206789i | \(0.00658278\pi\) | ||||
−0.999786 | + | 0.0206789i | \(0.993417\pi\) | |||||||
\(308\) | −1.20643 | − | 13.0745i | −0.0687426 | − | 0.744991i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1225 | − | 24.4609i | −0.800813 | − | 1.38705i | −0.919081 | − | 0.394068i | \(-0.871068\pi\) |
0.118268 | − | 0.992982i | \(-0.462266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7797 | − | 10.2651i | −1.00497 | − | 0.580218i | −0.0952528 | − | 0.995453i | \(-0.530366\pi\) |
−0.909714 | + | 0.415235i | \(0.863699\pi\) | |||||||
\(314\) | 5.36589 | 0.302815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.24656 | 0.238887 | ||||||||
\(317\) | 1.96890 | + | 1.13674i | 0.110584 | + | 0.0638459i | 0.554272 | − | 0.832336i | \(-0.312997\pi\) |
−0.443688 | + | 0.896181i | \(0.646330\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.5726 | − | 28.7045i | −0.927886 | − | 1.60715i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.83551 | − | 14.8423i | 0.380928 | − | 0.827130i | ||||
\(323\) | − | 9.53560i | − | 0.530575i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.69677 | + | 5.02108i | −0.481670 | + | 0.278092i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.39427i | − | 0.463496i | ||||||
\(329\) | 10.9235 | − | 1.00795i | 0.602233 | − | 0.0555699i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0646 | − | 31.2889i | 0.992922 | − | 1.71979i | 0.393605 | − | 0.919280i | \(-0.371228\pi\) |
0.599317 | − | 0.800512i | \(-0.295439\pi\) | |||||||
\(332\) | 7.14207 | + | 12.3704i | 0.391972 | + | 0.678915i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.13047 | − | 1.23003i | −0.116574 | − | 0.0673040i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.76361 | −0.205017 | −0.102508 | − | 0.994732i | \(-0.532687\pi\) | ||||
−0.102508 | + | 0.994732i | \(0.532687\pi\) | |||||||
\(338\) | −14.8806 | − | 8.59134i | −0.809400 | − | 0.467308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.91258 | + | 5.04473i | −0.157725 | + | 0.273187i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8191 | − | 5.04761i | 0.962143 | − | 0.272546i | ||||
\(344\) | 8.81025i | 0.475017i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.59880 | + | 1.50042i | −0.139713 | + | 0.0806631i | ||||
\(347\) | −3.50549 | + | 2.02389i | −0.188184 | + | 0.108648i | −0.591132 | − | 0.806575i | \(-0.701319\pi\) |
0.402948 | + | 0.915223i | \(0.367986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.9364i | − | 1.28129i | −0.767838 | − | 0.640644i | \(-0.778667\pi\) | ||
0.767838 | − | 0.640644i | \(-0.221333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.48135 | + | 4.29783i | −0.132256 | + | 0.229075i | ||||
\(353\) | 12.7409 | + | 22.0679i | 0.678129 | + | 1.17455i | 0.975544 | + | 0.219805i | \(0.0705422\pi\) |
−0.297415 | + | 0.954748i | \(0.596124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.7703 | 0.782826 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.67236 | 0.194091 | ||||||||
\(359\) | 15.4893 | + | 8.94277i | 0.817496 | + | 0.471981i | 0.849552 | − | 0.527505i | \(-0.176872\pi\) |
−0.0320565 | + | 0.999486i | \(0.510206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.68949 | − | 8.12243i | −0.246815 | − | 0.427496i | ||||
\(362\) | −3.06780 | + | 5.31359i | −0.161240 | + | 0.279276i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.2026 | + | 6.08035i | 0.692003 | + | 0.318697i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.57004 | + | 2.63851i | −0.238554 | + | 0.137729i | −0.614512 | − | 0.788907i | \(-0.710647\pi\) |
0.375958 | + | 0.926637i | \(0.377314\pi\) | |||||||
\(368\) | −5.34875 | + | 3.08810i | −0.278823 | + | 0.160978i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6957 | + | 4.92582i | 0.555293 | + | 0.255736i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.27390 | + | 12.5988i | −0.376628 | + | 0.652339i | −0.990569 | − | 0.137013i | \(-0.956250\pi\) |
0.613941 | + | 0.789352i | \(0.289583\pi\) | |||||||
\(374\) | 7.62827 | + | 13.2125i | 0.394448 | + | 0.683205i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.59075 | − | 2.07312i | −0.185179 | − | 0.106913i | ||||
\(377\) | 36.6928 | 1.88977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.66669 | 0.188345 | 0.0941726 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941726 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.85920 | − | 4.95227i | −0.146289 | − | 0.253380i | ||||
\(383\) | −9.76247 | + | 16.9091i | −0.498839 | + | 0.864015i | −0.999999 | − | 0.00134002i | \(-0.999573\pi\) |
0.501160 | + | 0.865355i | \(0.332907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.23330i | − | 0.317266i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.82474 | − | 2.20821i | 0.194172 | − | 0.112105i | ||||
\(389\) | −14.9711 | + | 8.64356i | −0.759064 | + | 0.438246i | −0.828960 | − | 0.559309i | \(-0.811067\pi\) |
0.0698956 | + | 0.997554i | \(0.477733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9871i | 0.960220i | ||||||||
\(392\) | −6.60028 | − | 2.33160i | −0.333364 | − | 0.117763i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.661170 | − | 1.14518i | 0.0333092 | − | 0.0576933i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9755 | + | 13.8423i | 1.20330 | + | 0.694724i | 0.961287 | − | 0.275549i | \(-0.0888598\pi\) |
0.242011 | + | 0.970274i | \(0.422193\pi\) | |||||||
\(398\) | −9.55125 | −0.478761 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.7521 | + | 18.9095i | 1.63556 | + | 0.944293i | 0.982335 | + | 0.187132i | \(0.0599194\pi\) |
0.653229 | + | 0.757161i | \(0.273414\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.22432 | − | 5.58468i | −0.160615 | − | 0.278193i | ||||
\(404\) | −5.19825 | + | 9.00364i | −0.258623 | + | 0.447948i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5958 | + | 1.62362i | −0.873266 | + | 0.0805790i | ||||
\(407\) | − | 53.1406i | − | 2.63408i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.6028 | − | 18.2459i | 1.56266 | − | 0.902202i | 0.565673 | − | 0.824630i | \(-0.308617\pi\) |
0.996987 | − | 0.0775719i | \(-0.0247167\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.2388i | 0.504431i | ||||||||
\(413\) | 6.64893 | − | 14.4372i | 0.327172 | − | 0.710407i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.74694 | − | 4.75784i | −0.134680 | − | 0.233272i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.3309 | − | 7.69660i | −0.652036 | − | 0.376453i | ||||
\(419\) | −21.6669 | −1.05850 | −0.529249 | − | 0.848466i | \(-0.677526\pi\) | ||||
−0.529249 | + | 0.848466i | \(0.677526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.84193 | −0.430929 | −0.215465 | − | 0.976512i | \(-0.569127\pi\) | ||||
−0.215465 | + | 0.976512i | \(0.569127\pi\) | |||||||
\(422\) | 22.5356 | + | 13.0110i | 1.09702 | + | 0.633363i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.22536 | − | 3.85443i | −0.108073 | − | 0.187188i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.54044 | − | 27.5318i | −0.122941 | − | 1.33236i | ||||
\(428\) | 6.57945i | 0.318030i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7481 | + | 14.8656i | −1.24024 | + | 0.716053i | −0.969143 | − | 0.246499i | \(-0.920720\pi\) |
−0.271097 | + | 0.962552i | \(0.587386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.5666i | 1.27671i | 0.769741 | + | 0.638356i | \(0.220385\pi\) | ||||
−0.769741 | + | 0.638356i | \(0.779615\pi\) | |||||||
\(434\) | 1.79332 | + | 2.53543i | 0.0860822 | + | 0.121705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.34219 | − | 2.32474i | 0.0642791 | − | 0.111335i | ||||
\(437\) | −9.57860 | − | 16.5906i | −0.458207 | − | 0.793637i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4067 | + | 8.31774i | 0.687597 | + | 0.396984i | 0.802711 | − | 0.596368i | \(-0.203390\pi\) |
−0.115114 | + | 0.993352i | \(0.536723\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.8895 | −0.803351 | ||||||||
\(443\) | 2.83428 | + | 1.63637i | 0.134661 | + | 0.0777464i | 0.565817 | − | 0.824531i | \(-0.308561\pi\) |
−0.431156 | + | 0.902277i | \(0.641894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.62611 | − | 6.28060i | 0.171701 | − | 0.297395i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.52781 | + | 2.16005i | 0.0721822 | + | 0.102053i | ||||
\(449\) | 10.4322i | 0.492324i | 0.969229 | + | 0.246162i | \(0.0791695\pi\) | ||||
−0.969229 | + | 0.246162i | \(0.920831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.0771 | + | 20.8291i | −1.69880 | + | 0.980805i | ||||
\(452\) | −3.07466 | + | 1.77515i | −0.144620 | + | 0.0834962i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 26.7208i | − | 1.25407i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.5394 | + | 28.6471i | −0.773680 | + | 1.34005i | 0.161853 | + | 0.986815i | \(0.448253\pi\) |
−0.935533 | + | 0.353238i | \(0.885080\pi\) | |||||||
\(458\) | 12.1517 | + | 21.0473i | 0.567811 | + | 0.983478i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5639 | −0.538585 | −0.269293 | − | 0.963058i | \(-0.586790\pi\) | ||||
−0.269293 | + | 0.963058i | \(0.586790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6061 | −1.79418 | −0.897090 | − | 0.441848i | \(-0.854323\pi\) | ||||
−0.897090 | + | 0.441848i | \(0.854323\pi\) | |||||||
\(464\) | 5.78405 | + | 3.33943i | 0.268518 | + | 0.155029i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.62788 | − | 8.01573i | −0.214383 | − | 0.371322i | ||||
\(467\) | −2.35692 | + | 4.08230i | −0.109065 | + | 0.188906i | −0.915392 | − | 0.402564i | \(-0.868119\pi\) |
0.806327 | + | 0.591471i | \(0.201452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.2307 | − | 28.7285i | 0.610937 | − | 1.32656i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.20275 | + | 3.00381i | −0.239476 | + | 0.138261i | ||||
\(473\) | 37.8649 | − | 21.8613i | 1.74103 | − | 1.00519i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.09926 | − | 0.747344i | 0.371229 | − | 0.0342545i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.126683 | + | 0.219422i | −0.00579436 | + | 0.0100361i | ||||
\(479\) | −10.0096 | − | 17.3371i | −0.457349 | − | 0.792152i | 0.541471 | − | 0.840720i | \(-0.317868\pi\) |
−0.998820 | + | 0.0485678i | \(0.984534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.9469 | + | 29.4142i | 2.32298 | + | 1.34117i | ||||
\(482\) | 2.97379 | 0.135452 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.6284 | 0.619474 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.36544 | − | 4.09706i | −0.107188 | − | 0.185656i | 0.807442 | − | 0.589947i | \(-0.200851\pi\) |
−0.914630 | + | 0.404292i | \(0.867518\pi\) | |||||||
\(488\) | −5.22512 | + | 9.05018i | −0.236530 | + | 0.409682i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.0027i | − | 0.722190i | −0.932529 | − | 0.361095i | \(-0.882403\pi\) | ||
0.932529 | − | 0.361095i | \(-0.117597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.7816 | − | 10.2662i | 0.800841 | − | 0.462366i | ||||
\(494\) | 14.7578 | − | 8.52039i | 0.663983 | − | 0.383351i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.17379i | − | 0.0527045i | ||||||
\(497\) | −2.10285 | + | 1.48736i | −0.0943258 | + | 0.0667170i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.18097 | + | 5.50961i | −0.142400 | + | 0.246644i | −0.928400 | − | 0.371583i | \(-0.878815\pi\) |
0.786000 | + | 0.618227i | \(0.212149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.3276 | − | 6.53998i | −0.505574 | − | 0.291893i | ||||
\(503\) | 36.3826 | 1.62222 | 0.811109 | − | 0.584895i | \(-0.198864\pi\) | ||||
0.811109 | + | 0.584895i | \(0.198864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.5443 | + | 15.3253i | 1.18004 | + | 0.681294i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.75784 | − | 4.77671i | −0.122359 | − | 0.211932i | ||||
\(509\) | 8.55353 | − | 14.8151i | 0.379128 | − | 0.656670i | −0.611807 | − | 0.791007i | \(-0.709557\pi\) |
0.990936 | + | 0.134337i | \(0.0428905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.1285 | − | 18.4809i | −1.77518 | − | 0.817546i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.9084 | + | 6.29797i | −0.481149 | + | 0.277791i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.5766i | 0.904956i | ||||||||
\(518\) | −25.7329 | − | 11.8511i | −1.13064 | − | 0.520706i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2375 | − | 35.0524i | −0.886622 | − | 1.53567i | −0.843843 | − | 0.536590i | \(-0.819712\pi\) |
−0.0427789 | − | 0.999085i | \(-0.513621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.8314 | − | 21.8420i | −1.65425 | − | 0.955083i | −0.975295 | − | 0.220905i | \(-0.929099\pi\) |
−0.678957 | − | 0.734178i | \(-0.737568\pi\) | |||||||
\(524\) | −20.6136 | −0.900510 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.6719 | −0.726929 | ||||||||
\(527\) | −3.12505 | − | 1.80425i | −0.136129 | − | 0.0785943i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.57274 | + | 13.1164i | 0.329250 | + | 0.570277i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.69998 | + | 4.73893i | −0.290481 | + | 0.205458i | ||||
\(533\) | − | 46.1171i | − | 1.99755i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.3529 | + | 5.97727i | −0.447179 | + | 0.258179i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 20.0069i | − | 0.862561i | ||||||
\(539\) | 6.35681 | + | 34.1524i | 0.273807 | + | 1.47105i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.85601 | − | 10.1429i | 0.251770 | − | 0.436078i | −0.712243 | − | 0.701933i | \(-0.752321\pi\) |
0.964013 | + | 0.265855i | \(0.0856541\pi\) | |||||||
\(542\) | −8.93068 | − | 15.4684i | −0.383606 | − | 0.664425i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.66237 | − | 1.53712i | −0.114148 | − | 0.0659035i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6501 | 1.48153 | 0.740765 | − | 0.671764i | \(-0.234463\pi\) | ||||
0.740765 | + | 0.671764i | \(0.234463\pi\) | |||||||
\(548\) | −9.92131 | − | 5.72807i | −0.423817 | − | 0.244691i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3582 | + | 17.9409i | −0.441272 | + | 0.764306i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1878 | + | 1.03233i | −0.475754 | + | 0.0438993i | ||||
\(554\) | − | 18.1481i | − | 0.771040i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.01066 | + | 0.583502i | −0.0428613 | + | 0.0247460i | ||||
\(557\) | −30.5822 | + | 17.6567i | −1.29581 | + | 0.748137i | −0.979678 | − | 0.200578i | \(-0.935718\pi\) |
−0.316134 | + | 0.948715i | \(0.602385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.4025i | 2.04721i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.75647 | − | 13.4346i | 0.327187 | − | 0.566705i | ||||
\(563\) | −19.3495 | − | 33.5143i | −0.815483 | − | 1.41246i | −0.908981 | − | 0.416839i | \(-0.863138\pi\) |
0.0934975 | − | 0.995620i | \(-0.470195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.6454 | −0.741690 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.973522 | 0.0408481 | ||||||||
\(569\) | 6.20799 | + | 3.58419i | 0.260253 | + | 0.150257i | 0.624450 | − | 0.781065i | \(-0.285323\pi\) |
−0.364197 | + | 0.931322i | \(0.618657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7717 | + | 18.6571i | 0.450781 | + | 0.780776i | 0.998435 | − | 0.0559290i | \(-0.0178121\pi\) |
−0.547653 | + | 0.836705i | \(0.684479\pi\) | |||||||
\(572\) | −13.6322 | + | 23.6117i | −0.569993 | + | 0.987256i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.04064 | + | 22.1152i | 0.0851746 | + | 0.923070i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.6179 | + | 7.86230i | −0.566921 | + | 0.327312i | −0.755919 | − | 0.654666i | \(-0.772809\pi\) |
0.188998 | + | 0.981978i | \(0.439476\pi\) | |||||||
\(578\) | 6.53767 | − | 3.77453i | 0.271931 | − | 0.157000i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8234 | − | 30.8544i | −0.905389 | − | 1.28006i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.0438 | + | 19.1284i | −0.457387 | + | 0.792217i | ||||
\(584\) | 8.34916 | + | 14.4612i | 0.345491 | + | 0.598408i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.04902 | + | 5.22446i | 0.373812 | + | 0.215820i | ||||
\(587\) | 4.59252 | 0.189554 | 0.0947769 | − | 0.995499i | \(-0.469786\pi\) | ||||
0.0947769 | + | 0.995499i | \(0.469786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.64082 | 0.150017 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.35400 | + | 9.27339i | 0.220048 | + | 0.381134i | ||||
\(593\) | −1.91286 | + | 3.31317i | −0.0785516 | + | 0.136055i | −0.902625 | − | 0.430427i | \(-0.858363\pi\) |
0.824074 | + | 0.566483i | \(0.191696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 15.4041i | − | 0.630977i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −29.3854 | + | 16.9657i | −1.20166 | + | 0.693777i | ||||
\(599\) | −13.6589 | + | 7.88600i | −0.558089 | + | 0.322213i | −0.752378 | − | 0.658731i | \(-0.771093\pi\) |
0.194289 | + | 0.980944i | \(0.437760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.39673i | 0.0569740i | 0.999594 | + | 0.0284870i | \(0.00906892\pi\) | ||||
−0.999594 | + | 0.0284870i | \(0.990931\pi\) | |||||||
\(602\) | −2.14176 | − | 23.2111i | −0.0872918 | − | 0.946015i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.511281 | − | 0.885565i | 0.0208037 | − | 0.0360331i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.94920 | − | 5.16682i | −0.363237 | − | 0.209715i | 0.307263 | − | 0.951625i | \(-0.400587\pi\) |
−0.670500 | + | 0.741910i | \(0.733920\pi\) | |||||||
\(608\) | 3.10178 | 0.125794 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7271 | − | 11.3895i | −0.798075 | − | 0.460769i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.14772 | − | 10.6482i | −0.248304 | − | 0.430075i | 0.714751 | − | 0.699379i | \(-0.246540\pi\) |
−0.963055 | + | 0.269303i | \(0.913207\pi\) | |||||||
\(614\) | −0.362324 | + | 0.627564i | −0.0146222 | + | 0.0253264i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.49247 | − | 11.9261i | 0.221298 | − | 0.480516i | ||||
\(617\) | 8.10935i | 0.326470i | 0.986587 | + | 0.163235i | \(0.0521929\pi\) | ||||
−0.986587 | + | 0.163235i | \(0.947807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.03506 | − | 4.06170i | 0.282763 | − | 0.163253i | −0.351911 | − | 0.936034i | \(-0.614468\pi\) |
0.634674 | + | 0.772780i | \(0.281135\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 28.2450i | − | 1.13252i | ||||||
\(623\) | −38.9133 | + | 3.59065i | −1.55903 | + | 0.143857i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.2651 | − | 17.7797i | −0.410276 | − | 0.710619i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.64699 | + | 2.68294i | 0.185435 | + | 0.107061i | ||||
\(629\) | 32.9189 | 1.31256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.6011 | −1.61630 | −0.808151 | − | 0.588975i | \(-0.799532\pi\) | ||||
−0.808151 | + | 0.588975i | \(0.799532\pi\) | |||||||
\(632\) | 3.67763 | + | 2.12328i | 0.146288 | + | 0.0844595i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.13674 | + | 1.96890i | 0.0451459 | + | 0.0781950i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.2611 | − | 12.8095i | −1.43672 | − | 0.507531i | ||||
\(638\) | − | 33.1452i | − | 1.31223i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.0260 | − | 18.4902i | 1.26495 | − | 0.730319i | 0.290922 | − | 0.956747i | \(-0.406038\pi\) |
0.974028 | + | 0.226427i | \(0.0727046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.86696i | 0.191934i | 0.995385 | + | 0.0959671i | \(0.0305944\pi\) | ||||
−0.995385 | + | 0.0959671i | \(0.969406\pi\) | |||||||
\(644\) | 13.3409 | − | 9.43606i | 0.525704 | − | 0.371833i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.76780 | − | 8.25808i | 0.187587 | − | 0.324910i | ||||
\(647\) | −12.4833 | − | 21.6217i | −0.490769 | − | 0.850037i | 0.509175 | − | 0.860663i | \(-0.329951\pi\) |
−0.999944 | + | 0.0106266i | \(0.996617\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.8197 | + | 14.9070i | 1.01351 | + | 0.585151i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0422 | −0.393282 | ||||||||
\(653\) | −12.6352 | − | 7.29496i | −0.494455 | − | 0.285474i | 0.231966 | − | 0.972724i | \(-0.425484\pi\) |
−0.726421 | + | 0.687250i | \(0.758818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.19713 | − | 7.26965i | 0.163870 | − | 0.283832i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.96402 | + | 4.58885i | 0.388438 | + | 0.178892i | ||||
\(659\) | 33.8468i | 1.31848i | 0.751931 | + | 0.659242i | \(0.229123\pi\) | ||||
−0.751931 | + | 0.659242i | \(0.770877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9053 | + | 8.60557i | −0.579749 | + | 0.334718i | −0.761034 | − | 0.648713i | \(-0.775308\pi\) |
0.181285 | + | 0.983431i | \(0.441974\pi\) | |||||||
\(662\) | 31.2889 | − | 18.0646i | 1.21608 | − | 0.702102i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.2841i | 0.554332i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.6250 | − | 35.7235i | 0.798602 | − | 1.38322i | ||||
\(668\) | −1.23003 | − | 2.13047i | −0.0475911 | − | 0.0824302i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.8615 | 2.00209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.47971 | −0.0570387 | −0.0285193 | − | 0.999593i | \(-0.509079\pi\) | ||||
−0.0285193 | + | 0.999593i | \(0.509079\pi\) | |||||||
\(674\) | −3.25938 | − | 1.88181i | −0.125547 | − | 0.0724844i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.59134 | − | 14.8806i | −0.330436 | − | 0.572333i | ||||
\(677\) | −5.92549 | + | 10.2632i | −0.227735 | + | 0.394448i | −0.957136 | − | 0.289637i | \(-0.906465\pi\) |
0.729402 | + | 0.684086i | \(0.239799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.53968 | + | 6.74746i | −0.366099 | + | 0.258944i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.04473 | + | 2.91258i | −0.193173 | + | 0.111528i | ||||
\(683\) | −9.11732 | + | 5.26389i | −0.348865 | + | 0.201417i | −0.664185 | − | 0.747568i | \(-0.731221\pi\) |
0.315320 | + | 0.948985i | \(0.397888\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.9556 | + | 4.53821i | 0.685549 | + | 0.173270i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.40513 | + | 7.62990i | −0.167944 | + | 0.290887i | ||||
\(689\) | −12.2258 | − | 21.1758i | −0.465767 | − | 0.806732i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.61628 | + | 3.81991i | 0.251695 | + | 0.145316i | 0.620540 | − | 0.784175i | \(-0.286913\pi\) |
−0.368845 | + | 0.929491i | \(0.620247\pi\) | |||||||
\(692\) | −3.00084 | −0.114075 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.04779 | −0.153652 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9030 | − | 22.3486i | −0.488736 | − | 0.846515i | ||||
\(698\) | 11.9682 | − | 20.7296i | 0.453004 | − | 0.784626i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.2007i | − | 1.32951i | −0.747060 | − | 0.664757i | \(-0.768535\pi\) | ||
0.747060 | − | 0.664757i | \(-0.231465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.7640 | + | 16.6069i | −1.08485 | + | 0.626341i | ||||
\(704\) | −4.29783 | + | 2.48135i | −0.161980 | + | 0.0935195i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.4818i | 0.959019i | ||||||||
\(707\) | 11.5063 | − | 24.9843i | 0.432740 | − | 0.939631i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1846 | − | 31.4966i | 0.682936 | − | 1.18288i | −0.291145 | − | 0.956679i | \(-0.594036\pi\) |
0.974081 | − | 0.226201i | \(-0.0726306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.7915 | + | 7.38517i | 0.479381 | + | 0.276771i | ||||
\(713\) | −7.24954 | −0.271497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.18036 | + | 1.83618i | 0.118856 | + | 0.0686214i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.94277 | + | 15.4893i | 0.333741 | + | 0.578057i | ||||
\(719\) | 0.772550 | − | 1.33810i | 0.0288113 | − | 0.0499026i | −0.851260 | − | 0.524744i | \(-0.824161\pi\) |
0.880072 | + | 0.474841i | \(0.157494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.48905 | − | 26.9748i | −0.0926971 | − | 1.00460i | ||||
\(722\) | − | 9.37898i | − | 0.349049i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.31359 | + | 3.06780i | −0.197478 | + | 0.114014i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.1857i | 1.26788i | 0.773383 | + | 0.633939i | \(0.218563\pi\) | ||||
−0.773383 | + | 0.633939i | \(0.781437\pi\) | |||||||
\(728\) | 8.39360 | + | 11.8670i | 0.311087 | + | 0.439821i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5424 | + | 23.4561i | 0.500884 | + | 0.867557i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.9485 | − | 21.9095i | −1.40166 | − | 0.809248i | −0.407095 | − | 0.913386i | \(-0.633458\pi\) |
−0.994563 | + | 0.104138i | \(0.966792\pi\) | |||||||
\(734\) | −5.27703 | −0.194779 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.17620 | −0.227658 | ||||||||
\(737\) | 51.3786 | + | 29.6634i | 1.89255 | + | 1.09267i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.86403 | + | 11.8888i | 0.252497 | + | 0.437338i | 0.964213 | − | 0.265130i | \(-0.0854148\pi\) |
−0.711715 | + | 0.702468i | \(0.752081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.79984 | + | 9.61374i | 0.249630 | + | 0.352931i | ||||
\(743\) | 20.8393i | 0.764520i | 0.924055 | + | 0.382260i | \(0.124854\pi\) | ||||
−0.924055 | + | 0.382260i | \(0.875146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.5988 | + | 7.27390i | −0.461274 | + | 0.266316i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.2565i | 0.557834i | ||||||||
\(749\) | −1.59946 | − | 17.3339i | −0.0584429 | − | 0.633369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8346 | − | 37.8186i | 0.796755 | − | 1.38002i | −0.124964 | − | 0.992161i | \(-0.539881\pi\) |
0.921719 | − | 0.387859i | \(-0.126785\pi\) | |||||||
\(752\) | −2.07312 | − | 3.59075i | −0.0755989 | − | 0.130941i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 31.7769 | + | 18.3464i | 1.15725 | + | 0.668136i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.4115 | −1.46878 | −0.734391 | − | 0.678727i | \(-0.762532\pi\) | ||||
−0.734391 | + | 0.678727i | \(0.762532\pi\) | |||||||
\(758\) | 3.17545 | + | 1.83335i | 0.115337 | + | 0.0665901i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3292 | + | 31.7471i | −0.664432 | + | 1.15083i | 0.315007 | + | 0.949089i | \(0.397993\pi\) |
−0.979439 | + | 0.201741i | \(0.935340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.97093 | + | 6.45094i | −0.107555 | + | 0.233540i | ||||
\(764\) | − | 5.71839i | − | 0.206884i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.9091 | + | 9.76247i | −0.610951 | + | 0.352732i | ||||
\(767\) | −28.5833 | + | 16.5025i | −1.03208 | + | 0.595872i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.4304i | 0.736738i | 0.929680 | + | 0.368369i | \(0.120084\pi\) | ||||
−0.929680 | + | 0.368369i | \(0.879916\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.11665 | − | 5.39819i | 0.112171 | − | 0.194285i | ||||
\(773\) | −6.84657 | − | 11.8586i | −0.246254 | − | 0.426525i | 0.716229 | − | 0.697865i | \(-0.245866\pi\) |
−0.962483 | + | 0.271340i | \(0.912533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.41643 | 0.158540 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.2871 | −0.619773 | ||||||||
\(779\) | 22.5488 | + | 13.0186i | 0.807896 | + | 0.466439i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.41565 | − | 4.18403i | −0.0864388 | − | 0.149716i | ||||
\(782\) | −9.49356 | + | 16.4433i | −0.339489 | + | 0.588012i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.55021 | − | 5.31936i | −0.162507 | − | 0.189977i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6169 | + | 6.70701i | −0.414097 | + | 0.239079i | −0.692549 | − | 0.721371i | \(-0.743512\pi\) |
0.278451 | + | 0.960450i | \(0.410179\pi\) | |||||||
\(788\) | 1.14518 | − | 0.661170i | 0.0407953 | − | 0.0235532i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.66883 | − | 5.42419i | 0.272672 | − | 0.192862i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.7062 | + | 49.7206i | −1.01939 | + | 1.76563i | ||||
\(794\) | 13.8423 | + | 23.9755i | 0.491244 | + | 0.850860i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.27163 | − | 4.77563i | −0.293180 | − | 0.169268i | ||||
\(797\) | −53.8858 | −1.90873 | −0.954367 | − | 0.298636i | \(-0.903468\pi\) | ||||
−0.954367 | + | 0.298636i | \(0.903468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7465 | −0.450940 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.9095 | + | 32.7521i | 0.667716 | + | 1.15652i | ||||
\(803\) | 41.4344 | − | 71.7665i | 1.46219 | − | 2.53259i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.44864i | − | 0.227144i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.00364 | + | 5.19825i | −0.316747 | + | 0.182874i | ||||
\(809\) | 10.1762 | − | 5.87522i | 0.357775 | − | 0.206562i | −0.310329 | − | 0.950629i | \(-0.600439\pi\) |
0.668104 | + | 0.744068i | \(0.267106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.8579i | 0.802649i | 0.915936 | + | 0.401325i | \(0.131450\pi\) | ||||
−0.915936 | + | 0.401325i | \(0.868550\pi\) | |||||||
\(812\) | −16.0502 | − | 7.39182i | −0.563253 | − | 0.259402i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26.5703 | − | 46.0211i | 0.931288 | − | 1.61304i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.6663 | − | 13.6637i | −0.827978 | − | 0.478033i | ||||
\(818\) | 36.4918 | 1.27591 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.58876 | + | 5.53607i | 0.334650 | + | 0.193210i | 0.657904 | − | 0.753102i | \(-0.271443\pi\) |
−0.323254 | + | 0.946312i | \(0.604777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.353401 | + | 0.612108i | 0.0123188 | + | 0.0213368i | 0.872119 | − | 0.489294i | \(-0.162745\pi\) |
−0.859800 | + | 0.510630i | \(0.829412\pi\) | |||||||
\(824\) | −5.11942 | + | 8.86709i | −0.178343 | + | 0.308900i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9767 | − | 9.17849i | 0.451518 | − | 0.319361i | ||||
\(827\) | 18.8230i | 0.654540i | 0.944931 | + | 0.327270i | \(0.106129\pi\) | ||||
−0.944931 | + | 0.327270i | \(0.893871\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.7423 | + | 15.4397i | −0.928800 | + | 0.536243i | −0.886432 | − | 0.462859i | \(-0.846824\pi\) |
−0.0423683 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.49388i | − | 0.190466i | ||||||
\(833\) | −21.1563 | + | 3.93785i | −0.733023 | + | 0.136438i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.69660 | − | 13.3309i | −0.266193 | − | 0.461059i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.7641 | − | 10.8335i | −0.648195 | − | 0.374236i | ||||
\(839\) | −20.9932 | −0.724766 | −0.362383 | − | 0.932029i | \(-0.618037\pi\) | ||||
−0.362383 | + | 0.932029i | \(0.618037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6071 | −0.538174 | ||||||||
\(842\) | −7.65733 | − | 4.42096i | −0.263889 | − | 0.152356i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.0110 | + | 22.5356i | 0.447856 | + | 0.775709i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.9049 | + | 3.31306i | −1.23371 | + | 0.113838i | ||||
\(848\) | − | 4.45071i | − | 0.152838i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.2744 | − | 33.0674i | 1.96334 | − | 1.13353i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2167i | 0.623729i | 0.950127 | + | 0.311864i | \(0.100953\pi\) | ||||
−0.950127 | + | 0.311864i | \(0.899047\pi\) | |||||||
\(854\) | 11.5658 | − | 25.1135i | 0.395774 | − | 0.859365i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.28972 | + | 5.69797i | −0.112440 | + | 0.194753i | ||||
\(857\) | −6.19973 | − | 10.7382i | −0.211779 | − | 0.366812i | 0.740493 | − | 0.672065i | \(-0.234592\pi\) |
−0.952271 | + | 0.305253i | \(0.901259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.67438 | + | 3.85345i | 0.227727 | + | 0.131478i | 0.609523 | − | 0.792768i | \(-0.291361\pi\) |
−0.381796 | + | 0.924247i | \(0.624694\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.7313 | −1.01265 | ||||||||
\(863\) | 6.54406 | + | 3.77821i | 0.222762 | + | 0.128612i | 0.607229 | − | 0.794527i | \(-0.292281\pi\) |
−0.384466 | + | 0.923139i | \(0.625615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.2833 | + | 23.0074i | −0.451386 | + | 0.781823i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.285346 | + | 3.09241i | 0.00968528 | + | 0.104963i | ||||
\(869\) | − | 21.0744i | − | 0.714900i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.8778 | + | 32.8384i | −1.92723 | + | 1.11269i | ||||
\(872\) | 2.32474 | − | 1.34219i | 0.0787255 | − | 0.0454522i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 19.1572i | − | 0.648002i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0598 | − | 26.0843i | 0.508532 | − | 0.880803i | −0.491420 | − | 0.870923i | \(-0.663522\pi\) |
0.999951 | − | 0.00987971i | \(-0.00314486\pi\) | |||||||
\(878\) | 8.31774 | + | 14.4067i | 0.280710 | + | 0.486204i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6642 | −0.999411 | −0.499706 | − | 0.866195i | \(-0.666558\pi\) | ||||
−0.499706 | + | 0.866195i | \(0.666558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.9643 | 1.31125 | 0.655626 | − | 0.755086i | \(-0.272405\pi\) | ||||
0.655626 | + | 0.755086i | \(0.272405\pi\) | |||||||
\(884\) | −14.6267 | − | 8.44475i | −0.491950 | − | 0.284028i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.63637 | + | 2.83428i | 0.0549750 | + | 0.0952195i | ||||
\(887\) | 10.3423 | − | 17.9134i | 0.347260 | − | 0.601472i | −0.638502 | − | 0.769620i | \(-0.720446\pi\) |
0.985762 | + | 0.168149i | \(0.0537789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.42690 | + | 11.9141i | 0.282629 | + | 0.399586i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.28060 | − | 3.62611i | 0.210290 | − | 0.121411i | ||||
\(893\) | 11.1377 | − | 6.43036i | 0.372709 | − | 0.215184i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.243099 | + | 2.63456i | 0.00812137 | + | 0.0880144i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.21608 | + | 9.03451i | −0.174063 | + | 0.301485i | ||||
\(899\) | 3.91977 | + | 6.78924i | 0.130732 | + | 0.226434i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.8494 | − | 6.84127i | −0.394762 | − | 0.227916i | ||||
\(902\) | −41.6583 | −1.38707 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.55031 | −0.118081 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.06658 | + | 10.5076i | 0.201437 | + | 0.348900i | 0.948992 | − | 0.315301i | \(-0.102105\pi\) |
−0.747554 | + | 0.664201i | \(0.768772\pi\) | |||||||
\(908\) | 13.3604 | − | 23.1409i | 0.443381 | − | 0.767959i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5869i | 0.814600i | 0.913294 | + | 0.407300i | \(0.133530\pi\) | ||||
−0.913294 | + | 0.407300i | \(0.866470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 61.3908 | − | 35.4440i | 2.03174 | − | 1.17302i | ||||
\(914\) | −28.6471 | + | 16.5394i | −0.947561 | + | 0.547074i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.3034i | 0.803006i | ||||||||
\(917\) | 54.3078 | − | 5.01115i | 1.79340 | − | 0.165483i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.5230 | − | 19.9585i | 0.380110 | − | 0.658369i | −0.610968 | − | 0.791655i | \(-0.709220\pi\) |
0.991078 | + | 0.133286i | \(0.0425529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0146 | − | 5.78196i | −0.329815 | − | 0.190419i | ||||
\(923\) | 5.34841 | 0.176045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.4339 | − | 19.3031i | −1.09871 | − | 0.634338i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.33943 | + | 5.78405i | 0.109622 | + | 0.189871i | ||||
\(929\) | 20.1685 | − | 34.9328i | 0.661706 | − | 1.14611i | −0.318461 | − | 0.947936i | \(-0.603166\pi\) |
0.980167 | − | 0.198173i | \(-0.0635007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.4995 | − | 14.1137i | 0.540748 | − | 0.462559i | ||||
\(932\) | − | 9.25577i | − | 0.303183i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.08230 | + | 2.35692i | −0.133577 | + | 0.0771207i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.4861i | 1.35529i | 0.735389 | + | 0.677646i | \(0.237000\pi\) | ||||
−0.735389 | + | 0.677646i | \(0.763000\pi\) | |||||||
\(938\) | 25.8224 | − | 18.2643i | 0.843130 | − | 0.596350i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.37786 | + | 16.2429i | 0.305710 | + | 0.529505i | 0.977419 | − | 0.211310i | \(-0.0677730\pi\) |
−0.671709 | + | 0.740815i | \(0.734440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.8988 | − | 25.9223i | −1.46211 | − | 0.844148i | ||||
\(944\) | −6.00761 | −0.195531 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 43.7227 | 1.42155 | ||||||||
\(947\) | −37.5699 | − | 21.6910i | −1.22086 | − | 0.704862i | −0.255756 | − | 0.966741i | \(-0.582324\pi\) |
−0.965101 | + | 0.261879i | \(0.915658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.8693 | + | 79.4479i | 1.48898 | + | 2.57899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.38784 | + | 3.40241i | 0.239441 | + | 0.110273i | ||||
\(953\) | − | 18.1672i | − | 0.588492i | −0.955730 | − | 0.294246i | \(-0.904931\pi\) | ||
0.955730 | − | 0.294246i | \(-0.0950685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.219422 | + | 0.126683i | −0.00709661 | + | 0.00409723i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 20.0191i | − | 0.646789i | ||||||
\(959\) | 27.5308 | + | 12.6791i | 0.889015 | + | 0.409429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.8111 | + | 25.6536i | −0.477778 | + | 0.827536i | ||||
\(962\) | 29.4142 | + | 50.9469i | 0.948352 | + | 1.64259i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.57538 | + | 1.48689i | 0.0829473 | + | 0.0478896i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.7712 | 0.957378 | 0.478689 | − | 0.877985i | \(-0.341112\pi\) | ||||
0.478689 | + | 0.877985i | \(0.341112\pi\) | |||||||
\(968\) | 11.8026 | + | 6.81421i | 0.379349 | + | 0.219017i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5472 | + | 32.1247i | −0.595209 | + | 1.03093i | 0.398309 | + | 0.917251i | \(0.369597\pi\) |
−0.993517 | + | 0.113680i | \(0.963736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.52078 | − | 1.78296i | 0.0808126 | − | 0.0571591i | ||||
\(974\) | − | 4.73088i | − | 0.151587i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.05018 | + | 5.22512i | −0.289689 | + | 0.167252i | ||||
\(977\) | 0.874971 | − | 0.505165i | 0.0279928 | − | 0.0161617i | −0.485938 | − | 0.873993i | \(-0.661522\pi\) |
0.513931 | + | 0.857831i | \(0.328189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 73.3008i | − | 2.34270i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.00133 | − | 13.8587i | 0.255333 | − | 0.442249i | ||||
\(983\) | 12.6799 | + | 21.9623i | 0.404427 | + | 0.700487i | 0.994255 | − | 0.107042i | \(-0.0341378\pi\) |
−0.589828 | + | 0.807529i | \(0.700804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.5324 | 0.653884 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.0408 | 0.542140 | ||||||||
\(989\) | 47.1238 | + | 27.2070i | 1.49845 | + | 0.865131i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3875 | + | 37.0442i | 0.679396 | + | 1.17675i | 0.975163 | + | 0.221488i | \(0.0710914\pi\) |
−0.295767 | + | 0.955260i | \(0.595575\pi\) | |||||||
\(992\) | 0.586893 | − | 1.01653i | 0.0186339 | − | 0.0322748i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.56480 | + | 0.236662i | −0.0813506 | + | 0.00750647i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.9808 | + | 12.6906i | −0.696139 | + | 0.401916i | −0.805908 | − | 0.592041i | \(-0.798322\pi\) |
0.109769 | + | 0.993957i | \(0.464989\pi\) | |||||||
\(998\) | −5.50961 | + | 3.18097i | −0.174404 | + | 0.100692i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bf.d.1601.12 | yes | 24 | |
3.2 | odd | 2 | inner | 3150.2.bf.d.1601.1 | yes | 24 | |
5.2 | odd | 4 | 3150.2.bp.g.1349.9 | 24 | |||
5.3 | odd | 4 | 3150.2.bp.h.1349.4 | 24 | |||
5.4 | even | 2 | 3150.2.bf.e.1601.1 | yes | 24 | ||
7.3 | odd | 6 | inner | 3150.2.bf.d.1151.1 | ✓ | 24 | |
15.2 | even | 4 | 3150.2.bp.h.1349.9 | 24 | |||
15.8 | even | 4 | 3150.2.bp.g.1349.4 | 24 | |||
15.14 | odd | 2 | 3150.2.bf.e.1601.12 | yes | 24 | ||
21.17 | even | 6 | inner | 3150.2.bf.d.1151.12 | yes | 24 | |
35.3 | even | 12 | 3150.2.bp.h.899.9 | 24 | |||
35.17 | even | 12 | 3150.2.bp.g.899.4 | 24 | |||
35.24 | odd | 6 | 3150.2.bf.e.1151.12 | yes | 24 | ||
105.17 | odd | 12 | 3150.2.bp.h.899.4 | 24 | |||
105.38 | odd | 12 | 3150.2.bp.g.899.9 | 24 | |||
105.59 | even | 6 | 3150.2.bf.e.1151.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.1 | ✓ | 24 | 7.3 | odd | 6 | inner | |
3150.2.bf.d.1151.12 | yes | 24 | 21.17 | even | 6 | inner | |
3150.2.bf.d.1601.1 | yes | 24 | 3.2 | odd | 2 | inner | |
3150.2.bf.d.1601.12 | yes | 24 | 1.1 | even | 1 | trivial | |
3150.2.bf.e.1151.1 | yes | 24 | 105.59 | even | 6 | ||
3150.2.bf.e.1151.12 | yes | 24 | 35.24 | odd | 6 | ||
3150.2.bf.e.1601.1 | yes | 24 | 5.4 | even | 2 | ||
3150.2.bf.e.1601.12 | yes | 24 | 15.14 | odd | 2 | ||
3150.2.bp.g.899.4 | 24 | 35.17 | even | 12 | |||
3150.2.bp.g.899.9 | 24 | 105.38 | odd | 12 | |||
3150.2.bp.g.1349.4 | 24 | 15.8 | even | 4 | |||
3150.2.bp.g.1349.9 | 24 | 5.2 | odd | 4 | |||
3150.2.bp.h.899.4 | 24 | 105.17 | odd | 12 | |||
3150.2.bp.h.899.9 | 24 | 35.3 | even | 12 | |||
3150.2.bp.h.1349.4 | 24 | 5.3 | odd | 4 | |||
3150.2.bp.h.1349.9 | 24 | 15.2 | even | 4 |