Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(226,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.3 | ||
Character | \(\chi\) | \(=\) | 1323.226 |
Dual form | 1323.2.h.h.802.3 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29987 | −0.919148 | −0.459574 | − | 0.888139i | \(-0.651998\pi\) | ||||
−0.459574 | + | 0.888139i | \(0.651998\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.310333 | −0.155166 | ||||||||
\(5\) | 1.76292 | + | 3.05347i | 0.788402 | + | 1.36555i | 0.926945 | + | 0.375196i | \(0.122425\pi\) |
−0.138543 | + | 0.990356i | \(0.544242\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00314 | 1.06177 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.29157 | − | 3.96912i | −0.724659 | − | 1.25515i | ||||
\(11\) | 0.589267 | − | 1.02064i | 0.177671 | − | 0.307735i | −0.763412 | − | 0.645912i | \(-0.776477\pi\) |
0.941082 | + | 0.338178i | \(0.109810\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.61030 | − | 2.78913i | 0.446618 | − | 0.773564i | −0.551546 | − | 0.834145i | \(-0.685962\pi\) |
0.998163 | + | 0.0605803i | \(0.0192951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.28303 | −0.820757 | ||||||||
\(17\) | −2.45159 | − | 4.24627i | −0.594597 | − | 1.02987i | −0.993604 | − | 0.112924i | \(-0.963978\pi\) |
0.399006 | − | 0.916948i | \(-0.369355\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.43318 | − | 5.94645i | 0.787627 | − | 1.36421i | −0.139791 | − | 0.990181i | \(-0.544643\pi\) |
0.927417 | − | 0.374028i | \(-0.122024\pi\) | |||||||
\(20\) | −0.547092 | − | 0.947591i | −0.122333 | − | 0.211888i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.765972 | + | 1.32670i | −0.163306 | + | 0.282854i | ||||
\(23\) | −2.14994 | − | 3.72380i | −0.448293 | − | 0.776466i | 0.549982 | − | 0.835176i | \(-0.314634\pi\) |
−0.998275 | + | 0.0587106i | \(0.981301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.71578 | + | 6.43592i | −0.743156 | + | 1.28718i | ||||
\(26\) | −2.09319 | + | 3.62551i | −0.410508 | + | 0.711020i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.36140 | − | 2.35802i | −0.252806 | − | 0.437873i | 0.711491 | − | 0.702695i | \(-0.248020\pi\) |
−0.964297 | + | 0.264822i | \(0.914687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.92080 | −0.344986 | −0.172493 | − | 0.985011i | \(-0.555182\pi\) | ||||
−0.172493 | + | 0.985011i | \(0.555182\pi\) | |||||||
\(32\) | −1.73876 | −0.307372 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.18675 | + | 5.51961i | 0.546523 | + | 0.946606i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.88229 | − | 8.45637i | 0.802643 | − | 1.39022i | −0.115228 | − | 0.993339i | \(-0.536760\pi\) |
0.917871 | − | 0.396879i | \(-0.129907\pi\) | |||||||
\(38\) | −4.46270 | + | 7.72962i | −0.723946 | + | 1.25391i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.29429 | + | 9.16998i | 0.837101 | + | 1.44990i | ||||
\(41\) | 3.32673 | − | 5.76206i | 0.519547 | − | 0.899883i | −0.480194 | − | 0.877162i | \(-0.659434\pi\) |
0.999742 | − | 0.0227205i | \(-0.00723278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.83441 | + | 8.37344i | 0.737240 | + | 1.27694i | 0.953734 | + | 0.300653i | \(0.0972047\pi\) |
−0.216493 | + | 0.976284i | \(0.569462\pi\) | |||||||
\(44\) | −0.182869 | + | 0.316738i | −0.0275685 | + | 0.0477501i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.79464 | + | 4.84046i | 0.412047 | + | 0.713687i | ||||
\(47\) | −0.633218 | −0.0923644 | −0.0461822 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461822 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.83004 | − | 8.36587i | 0.683071 | − | 1.18311i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.499729 | + | 0.865557i | −0.0693000 | + | 0.120031i | ||||
\(53\) | −1.11378 | − | 1.92912i | −0.152989 | − | 0.264985i | 0.779336 | − | 0.626606i | \(-0.215557\pi\) |
−0.932325 | + | 0.361621i | \(0.882223\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.15533 | 0.560304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.76965 | + | 3.06512i | 0.232366 | + | 0.402471i | ||||
\(59\) | −8.21304 | −1.06925 | −0.534623 | − | 0.845091i | \(-0.679546\pi\) | ||||
−0.534623 | + | 0.845091i | \(0.679546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.65916 | −1.23673 | −0.618364 | − | 0.785892i | \(-0.712204\pi\) | ||||
−0.618364 | + | 0.785892i | \(0.712204\pi\) | |||||||
\(62\) | 2.49680 | 0.317093 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.82622 | 1.10328 | ||||||||
\(65\) | 11.3553 | 1.40846 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.33301 | 0.651531 | 0.325766 | − | 0.945451i | \(-0.394378\pi\) | ||||
0.325766 | + | 0.945451i | \(0.394378\pi\) | |||||||
\(68\) | 0.760807 | + | 1.31776i | 0.0922614 | + | 0.159801i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.27719 | 0.388931 | 0.194466 | − | 0.980909i | \(-0.437703\pi\) | ||||
0.194466 | + | 0.980909i | \(0.437703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.519036 | − | 0.898997i | −0.0607486 | − | 0.105220i | 0.834052 | − | 0.551686i | \(-0.186015\pi\) |
−0.894800 | + | 0.446467i | \(0.852682\pi\) | |||||||
\(74\) | −6.34635 | + | 10.9922i | −0.737748 | + | 1.27782i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.06543 | + | 1.84538i | −0.122213 | + | 0.211679i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00408 | 0.112968 | 0.0564838 | − | 0.998404i | \(-0.482011\pi\) | ||||
0.0564838 | + | 0.998404i | \(0.482011\pi\) | |||||||
\(80\) | −5.78772 | − | 10.0246i | −0.647087 | − | 1.12079i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.32432 | + | 7.48994i | −0.477541 | + | 0.827126i | ||||
\(83\) | 3.65598 | + | 6.33234i | 0.401296 | + | 0.695064i | 0.993883 | − | 0.110442i | \(-0.0352267\pi\) |
−0.592587 | + | 0.805506i | \(0.701893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.64391 | − | 14.9717i | 0.937563 | − | 1.62391i | ||||
\(86\) | −6.28411 | − | 10.8844i | −0.677633 | − | 1.17369i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.76965 | − | 3.06512i | 0.188645 | − | 0.326743i | ||||
\(89\) | 6.02144 | − | 10.4294i | 0.638271 | − | 1.10552i | −0.347541 | − | 0.937665i | \(-0.612983\pi\) |
0.985812 | − | 0.167853i | \(-0.0536834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.667195 | + | 1.15562i | 0.0695599 | + | 0.120481i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.823103 | 0.0848966 | ||||||||
\(95\) | 24.2097 | 2.48387 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.46454 | − | 9.46487i | −0.554840 | − | 0.961012i | −0.997916 | − | 0.0645275i | \(-0.979446\pi\) |
0.443076 | − | 0.896484i | \(-0.353887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.15313 | − | 1.99728i | 0.115313 | − | 0.199728i | ||||
\(101\) | −0.797546 | + | 1.38139i | −0.0793588 | + | 0.137453i | −0.902973 | − | 0.429696i | \(-0.858621\pi\) |
0.823615 | + | 0.567150i | \(0.191954\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.16778 | − | 2.02265i | −0.115065 | − | 0.199298i | 0.802741 | − | 0.596328i | \(-0.203374\pi\) |
−0.917806 | + | 0.397030i | \(0.870041\pi\) | |||||||
\(104\) | 4.83596 | − | 8.37613i | 0.474205 | − | 0.821347i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.44777 | + | 2.50761i | 0.140620 | + | 0.243561i | ||||
\(107\) | −1.11181 | + | 1.92571i | −0.107483 | + | 0.186166i | −0.914750 | − | 0.404021i | \(-0.867612\pi\) |
0.807267 | + | 0.590186i | \(0.200946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.459782 | + | 0.796366i | 0.0440391 | + | 0.0762780i | 0.887205 | − | 0.461376i | \(-0.152644\pi\) |
−0.843166 | + | 0.537654i | \(0.819311\pi\) | |||||||
\(110\) | −5.40139 | −0.515003 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.19327 | + | 2.06681i | −0.112254 | + | 0.194429i | −0.916679 | − | 0.399625i | \(-0.869140\pi\) |
0.804425 | + | 0.594054i | \(0.202474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.58033 | − | 13.1295i | 0.706870 | − | 1.22433i | ||||
\(116\) | 0.422488 | + | 0.731770i | 0.0392270 | + | 0.0679432i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.6759 | 0.982796 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.80553 | + | 8.32342i | 0.436866 | + | 0.756674i | ||||
\(122\) | 12.5557 | 1.13674 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.596087 | 0.0535302 | ||||||||
\(125\) | −8.57330 | −0.766819 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04170 | −0.269907 | −0.134954 | − | 0.990852i | \(-0.543089\pi\) | ||||
−0.134954 | + | 0.990852i | \(0.543089\pi\) | |||||||
\(128\) | −7.99544 | −0.706704 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.7605 | −1.29458 | ||||||||
\(131\) | −1.63088 | − | 2.82476i | −0.142490 | − | 0.246801i | 0.785943 | − | 0.618298i | \(-0.212178\pi\) |
−0.928434 | + | 0.371498i | \(0.878844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.93223 | −0.598854 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.36245 | − | 12.7521i | −0.631325 | − | 1.09349i | ||||
\(137\) | 10.4669 | − | 18.1292i | 0.894246 | − | 1.54888i | 0.0595120 | − | 0.998228i | \(-0.481046\pi\) |
0.834734 | − | 0.550653i | \(-0.185621\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.31195 | + | 14.3967i | −0.705010 | + | 1.22111i | 0.261677 | + | 0.965155i | \(0.415724\pi\) |
−0.966688 | + | 0.255958i | \(0.917609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.25993 | −0.357486 | ||||||||
\(143\) | −1.89780 | − | 3.28708i | −0.158702 | − | 0.274880i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.80009 | − | 8.31401i | 0.398626 | − | 0.690441i | ||||
\(146\) | 0.674681 | + | 1.16858i | 0.0558370 | + | 0.0967124i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.51513 | + | 2.62429i | −0.124543 | + | 0.215715i | ||||
\(149\) | 0.564221 | + | 0.977260i | 0.0462228 | + | 0.0800602i | 0.888211 | − | 0.459435i | \(-0.151948\pi\) |
−0.841988 | + | 0.539496i | \(0.818615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.81476 | − | 16.9997i | 0.798714 | − | 1.38341i | −0.121740 | − | 0.992562i | \(-0.538847\pi\) |
0.920454 | − | 0.390851i | \(-0.127819\pi\) | |||||||
\(152\) | 10.3103 | − | 17.8580i | 0.836278 | − | 1.44848i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.38622 | − | 5.86511i | −0.271988 | − | 0.471097i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.33237 | 0.744804 | 0.372402 | − | 0.928071i | \(-0.378534\pi\) | ||||
0.372402 | + | 0.928071i | \(0.378534\pi\) | |||||||
\(158\) | −1.30517 | −0.103834 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.06529 | − | 5.30924i | −0.242332 | − | 0.419732i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.45056 | + | 14.6368i | −0.661899 | + | 1.14644i | 0.318217 | + | 0.948018i | \(0.396916\pi\) |
−0.980116 | + | 0.198425i | \(0.936417\pi\) | |||||||
\(164\) | −1.03239 | + | 1.78815i | −0.0806162 | + | 0.139631i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.75230 | − | 8.23123i | −0.368850 | − | 0.638867i | ||||
\(167\) | −2.57319 | + | 4.45689i | −0.199119 | + | 0.344885i | −0.948243 | − | 0.317545i | \(-0.897141\pi\) |
0.749124 | + | 0.662430i | \(0.230475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.31385 | + | 2.27566i | 0.101066 | + | 0.175051i | ||||
\(170\) | −11.2360 | + | 19.4613i | −0.861760 | + | 1.49261i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.50027 | − | 2.59855i | −0.114395 | − | 0.198138i | ||||
\(173\) | −9.73669 | −0.740266 | −0.370133 | − | 0.928979i | \(-0.620688\pi\) | ||||
−0.370133 | + | 0.928979i | \(0.620688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.93458 | + | 3.35079i | −0.145825 | + | 0.252576i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.82710 | + | 13.5569i | −0.586666 | + | 1.01613i | ||||
\(179\) | 0.687990 | + | 1.19163i | 0.0514228 | + | 0.0890668i | 0.890591 | − | 0.454805i | \(-0.150291\pi\) |
−0.839168 | + | 0.543872i | \(0.816958\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.66560 | −0.421120 | −0.210560 | − | 0.977581i | \(-0.567529\pi\) | ||||
−0.210560 | + | 0.977581i | \(0.567529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.45655 | − | 11.1831i | −0.475983 | − | 0.824427i | ||||
\(185\) | 34.4283 | 2.53122 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.77856 | −0.422570 | ||||||||
\(188\) | 0.196508 | 0.0143318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −31.4696 | −2.28304 | ||||||||
\(191\) | 25.0129 | 1.80987 | 0.904936 | − | 0.425547i | \(-0.139918\pi\) | ||||
0.904936 | + | 0.425547i | \(0.139918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5338 | 1.26211 | 0.631054 | − | 0.775739i | \(-0.282623\pi\) | ||||
0.631054 | + | 0.775739i | \(0.282623\pi\) | |||||||
\(194\) | 7.10321 | + | 12.3031i | 0.509981 | + | 0.883312i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7540 | 1.40741 | 0.703707 | − | 0.710490i | \(-0.251527\pi\) | ||||
0.703707 | + | 0.710490i | \(0.251527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.51110 | + | 16.4737i | 0.674224 | + | 1.16779i | 0.976695 | + | 0.214631i | \(0.0688550\pi\) |
−0.302471 | + | 0.953158i | \(0.597812\pi\) | |||||||
\(200\) | −11.1590 | + | 19.3279i | −0.789060 | + | 1.36669i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.03671 | − | 1.79563i | 0.0729425 | − | 0.126340i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.4590 | 1.63845 | ||||||||
\(206\) | 1.51796 | + | 2.62919i | 0.105761 | + | 0.183184i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.28667 | + | 9.15678i | −0.366565 | + | 0.634908i | ||||
\(209\) | −4.04613 | − | 7.00810i | −0.279876 | − | 0.484760i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.71809 | − | 6.43993i | 0.255964 | − | 0.443343i | −0.709193 | − | 0.705015i | \(-0.750940\pi\) |
0.965157 | + | 0.261672i | \(0.0842738\pi\) | |||||||
\(212\) | 0.345642 | + | 0.598669i | 0.0237388 | + | 0.0411168i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.44521 | − | 2.50318i | 0.0987927 | − | 0.171114i | ||||
\(215\) | −17.0454 | + | 29.5234i | −1.16248 | + | 2.01348i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.597658 | − | 1.03517i | −0.0404785 | − | 0.0701108i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.28953 | −0.0869403 | ||||||||
\(221\) | −15.7912 | −1.06223 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.64565 | + | 2.85034i | 0.110201 | + | 0.190873i | 0.915851 | − | 0.401518i | \(-0.131517\pi\) |
−0.805650 | + | 0.592391i | \(0.798184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.55110 | − | 2.68659i | 0.103178 | − | 0.178709i | ||||
\(227\) | −9.00847 | + | 15.6031i | −0.597913 | + | 1.03562i | 0.395215 | + | 0.918589i | \(0.370670\pi\) |
−0.993129 | + | 0.117028i | \(0.962663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.12746 | − | 3.68486i | −0.140586 | − | 0.243503i | 0.787131 | − | 0.616785i | \(-0.211565\pi\) |
−0.927718 | + | 0.373283i | \(0.878232\pi\) | |||||||
\(230\) | −9.85347 | + | 17.0667i | −0.649718 | + | 1.12535i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.08848 | − | 7.08146i | −0.268422 | − | 0.464920i | ||||
\(233\) | −7.35275 | + | 12.7353i | −0.481695 | + | 0.834320i | −0.999779 | − | 0.0210095i | \(-0.993312\pi\) |
0.518084 | + | 0.855330i | \(0.326645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.11631 | − | 1.93351i | −0.0728203 | − | 0.126128i | ||||
\(236\) | 2.54877 | 0.165911 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.08187 | + | 12.2662i | −0.458088 | + | 0.793432i | −0.998860 | − | 0.0477377i | \(-0.984799\pi\) |
0.540772 | + | 0.841169i | \(0.318132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.96752 | + | 6.87194i | −0.255570 | + | 0.442661i | −0.965050 | − | 0.262065i | \(-0.915597\pi\) |
0.709480 | + | 0.704726i | \(0.248930\pi\) | |||||||
\(242\) | −6.24657 | − | 10.8194i | −0.401545 | − | 0.695496i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.99755 | 0.191899 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.0569 | − | 19.1512i | −0.703536 | − | 1.21856i | ||||
\(248\) | −5.76843 | −0.366296 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.1442 | 0.704821 | ||||||||
\(251\) | −8.05097 | −0.508173 | −0.254087 | − | 0.967181i | \(-0.581775\pi\) | ||||
−0.254087 | + | 0.967181i | \(0.581775\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.06755 | −0.318594 | ||||||||
\(254\) | 3.95382 | 0.248085 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.25938 | −0.453712 | ||||||||
\(257\) | −8.77687 | − | 15.2020i | −0.547486 | − | 0.948273i | −0.998446 | − | 0.0557293i | \(-0.982252\pi\) |
0.450960 | − | 0.892544i | \(-0.351082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.52393 | −0.218545 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.11993 | + | 3.67183i | 0.130970 | + | 0.226846i | ||||
\(263\) | −11.6743 | + | 20.2205i | −0.719867 | + | 1.24685i | 0.241185 | + | 0.970479i | \(0.422464\pi\) |
−0.961052 | + | 0.276367i | \(0.910869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.92701 | − | 6.80177i | 0.241234 | − | 0.417830i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.65501 | −0.101096 | ||||||||
\(269\) | 0.269244 | + | 0.466344i | 0.0164161 | + | 0.0284335i | 0.874117 | − | 0.485716i | \(-0.161441\pi\) |
−0.857701 | + | 0.514149i | \(0.828108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.20749 | − | 12.4837i | 0.437824 | − | 0.758334i | −0.559697 | − | 0.828697i | \(-0.689083\pi\) |
0.997521 | + | 0.0703635i | \(0.0224159\pi\) | |||||||
\(272\) | 8.04863 | + | 13.9406i | 0.488020 | + | 0.845275i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6056 | + | 23.5656i | −0.821945 | + | 1.42365i | ||||
\(275\) | 4.37918 | + | 7.58495i | 0.264074 | + | 0.457390i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9533 | + | 18.9717i | −0.658121 | + | 1.13990i | 0.322980 | + | 0.946406i | \(0.395315\pi\) |
−0.981101 | + | 0.193494i | \(0.938018\pi\) | |||||||
\(278\) | 10.8045 | − | 18.7139i | 0.648009 | − | 1.12238i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.776622 | + | 1.34515i | 0.0463294 | + | 0.0802449i | 0.888260 | − | 0.459341i | \(-0.151914\pi\) |
−0.841931 | + | 0.539586i | \(0.818581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.65142 | −0.157610 | −0.0788051 | − | 0.996890i | \(-0.525110\pi\) | ||||
−0.0788051 | + | 0.996890i | \(0.525110\pi\) | |||||||
\(284\) | −1.01702 | −0.0603490 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.46689 | + | 4.27279i | 0.145870 | + | 0.252655i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.52056 | + | 6.09778i | −0.207091 | + | 0.358693i | ||||
\(290\) | −6.23951 | + | 10.8071i | −0.366396 | + | 0.634617i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.161074 | + | 0.278988i | 0.00942613 | + | 0.0163265i | ||||
\(293\) | 5.19314 | − | 8.99478i | 0.303386 | − | 0.525481i | −0.673514 | − | 0.739174i | \(-0.735216\pi\) |
0.976901 | + | 0.213694i | \(0.0685494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4789 | − | 25.0783i | −0.842996 | − | 1.46011i | ||||
\(296\) | 14.6622 | − | 25.3956i | 0.852221 | − | 1.47609i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.733415 | − | 1.27031i | −0.0424856 | − | 0.0735872i | ||||
\(299\) | −13.8482 | −0.800861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.7579 | + | 22.0974i | −0.734137 | + | 1.27156i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.2712 | + | 19.5224i | −0.646450 | + | 1.11968i | ||||
\(305\) | −17.0283 | − | 29.4939i | −0.975039 | − | 1.68882i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6425 | −0.607400 | −0.303700 | − | 0.952768i | \(-0.598222\pi\) | ||||
−0.303700 | + | 0.952768i | \(0.598222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.40165 | + | 7.62389i | 0.249997 | + | 0.433008i | ||||
\(311\) | 13.7096 | 0.777399 | 0.388699 | − | 0.921365i | \(-0.372925\pi\) | ||||
0.388699 | + | 0.921365i | \(0.372925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2179 | 1.19931 | 0.599653 | − | 0.800260i | \(-0.295305\pi\) | ||||
0.599653 | + | 0.800260i | \(0.295305\pi\) | |||||||
\(314\) | −12.1309 | −0.684586 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.311598 | −0.0175288 | ||||||||
\(317\) | −3.57043 | −0.200535 | −0.100268 | − | 0.994961i | \(-0.531970\pi\) | ||||
−0.100268 | + | 0.994961i | \(0.531970\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.20892 | −0.179665 | ||||||||
\(320\) | 15.5599 | + | 26.9506i | 0.869826 | + | 1.50658i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.6670 | −1.87328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.9671 | + | 20.7276i | 0.663813 | + | 1.14976i | ||||
\(326\) | 10.9846 | − | 19.0260i | 0.608383 | − | 1.05375i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.99062 | − | 17.3043i | 0.551639 | − | 0.955468i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.9456 | −1.31617 | −0.658085 | − | 0.752944i | \(-0.728633\pi\) | ||||
−0.658085 | + | 0.752944i | \(0.728633\pi\) | |||||||
\(332\) | −1.13457 | − | 1.96513i | −0.0622675 | − | 0.107851i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.34482 | − | 5.79339i | 0.183020 | − | 0.317000i | ||||
\(335\) | 9.40168 | + | 16.2842i | 0.513669 | + | 0.889700i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7468 | + | 23.8102i | −0.748838 | + | 1.29703i | 0.199542 | + | 0.979889i | \(0.436055\pi\) |
−0.948380 | + | 0.317137i | \(0.897279\pi\) | |||||||
\(338\) | −1.70784 | − | 2.95806i | −0.0928942 | − | 0.160897i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.68249 | + | 4.64620i | −0.145478 | + | 0.251976i | ||||
\(341\) | −1.13187 | + | 1.96045i | −0.0612940 | + | 0.106164i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.5184 | + | 25.1466i | 0.782779 | + | 1.35581i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.6564 | 0.680415 | ||||||||
\(347\) | 5.12824 | 0.275299 | 0.137649 | − | 0.990481i | \(-0.456045\pi\) | ||||
0.137649 | + | 0.990481i | \(0.456045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.56980 | − | 13.1113i | −0.405202 | − | 0.701830i | 0.589143 | − | 0.808029i | \(-0.299465\pi\) |
−0.994345 | + | 0.106198i | \(0.966132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.02459 | + | 1.77465i | −0.0546110 | + | 0.0945889i | ||||
\(353\) | 16.4878 | − | 28.5578i | 0.877559 | − | 1.51998i | 0.0235477 | − | 0.999723i | \(-0.492504\pi\) |
0.854011 | − | 0.520254i | \(-0.174163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.77743 | + | 10.0068i | 0.306634 | + | 0.531106i | ||||
\(356\) | −1.86865 | + | 3.23659i | −0.0990381 | + | 0.171539i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.894299 | − | 1.54897i | −0.0472651 | − | 0.0818656i | ||||
\(359\) | −12.0178 | + | 20.8154i | −0.634274 | + | 1.09859i | 0.352395 | + | 0.935851i | \(0.385367\pi\) |
−0.986669 | + | 0.162743i | \(0.947966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0735 | − | 24.3760i | −0.740711 | − | 1.28295i | ||||
\(362\) | 7.36455 | 0.387072 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.83004 | − | 3.16972i | 0.0957886 | − | 0.165911i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.32751 | − | 2.29931i | 0.0692952 | − | 0.120023i | −0.829296 | − | 0.558810i | \(-0.811258\pi\) |
0.898591 | + | 0.438787i | \(0.144592\pi\) | |||||||
\(368\) | 7.05830 | + | 12.2253i | 0.367939 | + | 0.637290i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −44.7524 | −2.32657 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.9592 | + | 27.6421i | 0.826334 | + | 1.43125i | 0.900896 | + | 0.434036i | \(0.142911\pi\) |
−0.0745621 | + | 0.997216i | \(0.523756\pi\) | |||||||
\(374\) | 7.51139 | 0.388405 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.90164 | −0.0980697 | ||||||||
\(377\) | −8.76909 | −0.451631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2681 | 1.55477 | 0.777384 | − | 0.629027i | \(-0.216546\pi\) | ||||
0.777384 | + | 0.629027i | \(0.216546\pi\) | |||||||
\(380\) | −7.51307 | −0.385412 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.5136 | −1.66354 | ||||||||
\(383\) | 0.866526 | + | 1.50087i | 0.0442774 | + | 0.0766907i | 0.887315 | − | 0.461164i | \(-0.152568\pi\) |
−0.843037 | + | 0.537855i | \(0.819235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.7917 | −1.16006 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.69583 | + | 2.93726i | 0.0860925 | + | 0.149117i | ||||
\(389\) | −5.54175 | + | 9.59859i | −0.280978 | + | 0.486668i | −0.971626 | − | 0.236523i | \(-0.923992\pi\) |
0.690648 | + | 0.723191i | \(0.257325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5415 | + | 18.2584i | −0.533107 | + | 0.923368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.6777 | −1.29362 | ||||||||
\(395\) | 1.77011 | + | 3.06592i | 0.0890639 | + | 0.154263i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.6696 | + | 21.9443i | −0.635867 | + | 1.10135i | 0.350464 | + | 0.936576i | \(0.386024\pi\) |
−0.986331 | + | 0.164777i | \(0.947310\pi\) | |||||||
\(398\) | −12.3632 | − | 21.4137i | −0.619712 | − | 1.07337i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.1990 | − | 21.1293i | 0.609951 | − | 1.05647i | ||||
\(401\) | −17.4122 | − | 30.1588i | −0.869524 | − | 1.50606i | −0.862483 | − | 0.506085i | \(-0.831092\pi\) |
−0.00704089 | − | 0.999975i | \(-0.502241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.09307 | + | 5.35736i | −0.154077 | + | 0.266869i | ||||
\(404\) | 0.247505 | − | 0.428690i | 0.0123138 | − | 0.0213281i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.75394 | − | 9.96612i | −0.285212 | − | 0.494002i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.2462 | −0.902215 | −0.451107 | − | 0.892470i | \(-0.648971\pi\) | ||||
−0.451107 | + | 0.892470i | \(0.648971\pi\) | |||||||
\(410\) | −30.4937 | −1.50598 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.362400 | + | 0.627695i | 0.0178541 | + | 0.0309243i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8904 | + | 22.3268i | −0.632765 | + | 1.09598i | ||||
\(416\) | −2.79992 | + | 4.84961i | −0.137278 | + | 0.237772i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.25945 | + | 9.10963i | 0.257248 | + | 0.445567i | ||||
\(419\) | 4.20719 | − | 7.28708i | 0.205535 | − | 0.355997i | −0.744768 | − | 0.667323i | \(-0.767440\pi\) |
0.950303 | + | 0.311326i | \(0.100773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.144291 | + | 0.249919i | 0.00703230 | + | 0.0121803i | 0.869520 | − | 0.493897i | \(-0.164428\pi\) |
−0.862488 | + | 0.506078i | \(0.831095\pi\) | |||||||
\(422\) | −4.83304 | + | 8.37108i | −0.235269 | + | 0.407498i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.34483 | − | 5.79341i | −0.162439 | − | 0.281353i | ||||
\(425\) | 36.4382 | 1.76751 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.345031 | − | 0.597612i | 0.0166777 | − | 0.0288866i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.1568 | − | 38.3767i | 1.06849 | − | 1.85069i | ||||
\(431\) | −6.74795 | − | 11.6878i | −0.325037 | − | 0.562981i | 0.656482 | − | 0.754341i | \(-0.272044\pi\) |
−0.981520 | + | 0.191360i | \(0.938710\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.85211 | −0.233177 | −0.116589 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116589 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.142685 | − | 0.247138i | −0.00683339 | − | 0.0118358i | ||||
\(437\) | −29.5245 | −1.41235 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.54793 | 0.121606 | 0.0608031 | − | 0.998150i | \(-0.480634\pi\) | ||||
0.0608031 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(440\) | 12.4790 | 0.594914 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.5265 | 0.976347 | ||||||||
\(443\) | 0.645506 | 0.0306689 | 0.0153345 | − | 0.999882i | \(-0.495119\pi\) | ||||
0.0153345 | + | 0.999882i | \(0.495119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.4613 | 2.01286 | ||||||||
\(446\) | −2.13913 | − | 3.70508i | −0.101291 | − | 0.175441i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.22658 | 0.246658 | 0.123329 | − | 0.992366i | \(-0.460643\pi\) | ||||
0.123329 | + | 0.992366i | \(0.460643\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.92066 | − | 6.79079i | −0.184617 | − | 0.319766i | ||||
\(452\) | 0.370312 | − | 0.641399i | 0.0174180 | − | 0.0301689i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.7099 | − | 20.2821i | 0.549571 | − | 0.951885i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.86075 | −0.133820 | −0.0669101 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669101 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(458\) | 2.76542 | + | 4.78985i | 0.129220 | + | 0.223815i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.35242 | + | 4.07452i | −0.109682 | + | 0.189975i | ||||
\(461\) | −1.82624 | − | 3.16314i | −0.0850566 | − | 0.147322i | 0.820359 | − | 0.571849i | \(-0.193774\pi\) |
−0.905415 | + | 0.424527i | \(0.860440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4052 | + | 26.6825i | −0.715939 | + | 1.24004i | 0.246657 | + | 0.969103i | \(0.420668\pi\) |
−0.962596 | + | 0.270940i | \(0.912666\pi\) | |||||||
\(464\) | 4.46953 | + | 7.74145i | 0.207493 | + | 0.359388i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.55764 | − | 16.5543i | 0.442749 | − | 0.766864i | ||||
\(467\) | 10.2885 | − | 17.8202i | 0.476096 | − | 0.824622i | −0.523529 | − | 0.852008i | \(-0.675385\pi\) |
0.999625 | + | 0.0273858i | \(0.00871825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.45107 | + | 2.51332i | 0.0669327 | + | 0.115931i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −24.6649 | −1.13529 | ||||||||
\(473\) | 11.3950 | 0.523944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.5139 | + | 44.1914i | 1.17066 | + | 2.02764i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.20552 | − | 15.9444i | 0.421051 | − | 0.729281i | ||||
\(479\) | 12.5916 | − | 21.8093i | 0.575325 | − | 0.996492i | −0.420682 | − | 0.907208i | \(-0.638209\pi\) |
0.996006 | − | 0.0892833i | \(-0.0284577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7239 | − | 27.2346i | −0.716949 | − | 1.24179i | ||||
\(482\) | 5.15726 | − | 8.93264i | 0.234907 | − | 0.406871i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.49131 | − | 2.58303i | −0.0677869 | − | 0.117410i | ||||
\(485\) | 19.2671 | − | 33.3716i | 0.874875 | − | 1.51533i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3807 | + | 28.3723i | 0.742282 | + | 1.28567i | 0.951454 | + | 0.307791i | \(0.0995896\pi\) |
−0.209173 | + | 0.977879i | \(0.567077\pi\) | |||||||
\(488\) | −29.0078 | −1.31312 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.76000 | + | 3.04841i | −0.0794278 | + | 0.137573i | −0.903003 | − | 0.429634i | \(-0.858643\pi\) |
0.823575 | + | 0.567207i | \(0.191976\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.67520 | + | 11.5618i | −0.300636 | + | 0.520716i | ||||
\(494\) | 14.3726 | + | 24.8941i | 0.646654 | + | 1.12004i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.30605 | 0.283150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.82082 | − | 13.5461i | −0.350108 | − | 0.606405i | 0.636160 | − | 0.771557i | \(-0.280522\pi\) |
−0.986268 | + | 0.165152i | \(0.947188\pi\) | |||||||
\(500\) | 2.66057 | 0.118984 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.4652 | 0.467086 | ||||||||
\(503\) | 36.5427 | 1.62936 | 0.814678 | − | 0.579913i | \(-0.196914\pi\) | ||||
0.814678 | + | 0.579913i | \(0.196914\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.62404 | −0.250267 | ||||||||
\(506\) | 6.58716 | 0.292835 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.943938 | 0.0418805 | ||||||||
\(509\) | −18.8229 | − | 32.6023i | −0.834311 | − | 1.44507i | −0.894590 | − | 0.446888i | \(-0.852532\pi\) |
0.0602789 | − | 0.998182i | \(-0.480801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.4272 | 1.12373 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.4088 | + | 19.7606i | 0.503221 | + | 0.871604i | ||||
\(515\) | 4.11740 | − | 7.13155i | 0.181434 | − | 0.314254i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.373135 | + | 0.646289i | −0.0164105 | + | 0.0284237i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 34.1017 | 1.49546 | ||||||||
\(521\) | −7.17115 | − | 12.4208i | −0.314174 | − | 0.544165i | 0.665088 | − | 0.746765i | \(-0.268394\pi\) |
−0.979262 | + | 0.202600i | \(0.935061\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.24222 | + | 9.07980i | −0.229226 | + | 0.397032i | −0.957579 | − | 0.288171i | \(-0.906953\pi\) |
0.728353 | + | 0.685202i | \(0.240286\pi\) | |||||||
\(524\) | 0.506114 | + | 0.876616i | 0.0221097 | + | 0.0382951i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.1751 | − | 26.2840i | 0.661665 | − | 1.14604i | ||||
\(527\) | 4.70901 | + | 8.15625i | 0.205128 | + | 0.355292i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.25555 | − | 3.90673i | 0.0980674 | − | 0.169858i | ||||
\(530\) | −5.10461 | + | 8.84144i | −0.221730 | + | 0.384047i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.7141 | − | 18.5573i | −0.464078 | − | 0.803807i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.84014 | −0.338959 | ||||||||
\(536\) | 16.0158 | 0.691776 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.349983 | − | 0.606188i | −0.0150888 | − | 0.0261346i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0461 | − | 39.9170i | 0.990830 | − | 1.71617i | 0.378399 | − | 0.925643i | \(-0.376475\pi\) |
0.612430 | − | 0.790524i | \(-0.290192\pi\) | |||||||
\(542\) | −9.36882 | + | 16.2273i | −0.402425 | + | 0.697021i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.26271 | + | 7.38323i | 0.182762 | + | 0.316554i | ||||
\(545\) | −1.62112 | + | 2.80786i | −0.0694411 | + | 0.120275i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1793 | − | 21.0951i | −0.520747 | − | 0.901961i | −0.999709 | − | 0.0241250i | \(-0.992320\pi\) |
0.478962 | − | 0.877836i | \(-0.341013\pi\) | |||||||
\(548\) | −3.24822 | + | 5.62607i | −0.138757 | + | 0.240334i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.69237 | − | 9.85947i | −0.242723 | − | 0.420409i | ||||
\(551\) | −18.6958 | −0.796468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.2379 | − | 24.6608i | 0.604911 | − | 1.04774i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.57947 | − | 4.46777i | 0.109394 | − | 0.189476i | ||||
\(557\) | 15.2888 | + | 26.4809i | 0.647806 | + | 1.12203i | 0.983646 | + | 0.180114i | \(0.0576466\pi\) |
−0.335840 | + | 0.941919i | \(0.609020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.1394 | 1.31706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.00951 | − | 1.74852i | −0.0425836 | − | 0.0737570i | ||||
\(563\) | −8.82714 | −0.372019 | −0.186010 | − | 0.982548i | \(-0.559556\pi\) | ||||
−0.186010 | + | 0.982548i | \(0.559556\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.41459 | −0.354005 | ||||||||
\(566\) | 3.44650 | 0.144867 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.84186 | 0.412955 | ||||||||
\(569\) | −7.12055 | −0.298509 | −0.149254 | − | 0.988799i | \(-0.547687\pi\) | ||||
−0.149254 | + | 0.988799i | \(0.547687\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.66361 | 0.278863 | 0.139432 | − | 0.990232i | \(-0.455472\pi\) | ||||
0.139432 | + | 0.990232i | \(0.455472\pi\) | |||||||
\(572\) | 0.588948 | + | 1.02009i | 0.0246252 | + | 0.0426520i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.9548 | 1.33261 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.95629 | − | 6.85250i | −0.164703 | − | 0.285273i | 0.771847 | − | 0.635808i | \(-0.219333\pi\) |
−0.936550 | + | 0.350535i | \(0.886000\pi\) | |||||||
\(578\) | 4.57627 | − | 7.92633i | 0.190348 | − | 0.329692i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.48963 | + | 2.58011i | −0.0618533 | + | 0.107133i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.62525 | −0.108727 | ||||||||
\(584\) | −1.55874 | − | 2.69981i | −0.0645010 | − | 0.111719i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.75042 | + | 11.6921i | −0.278857 | + | 0.482995i | ||||
\(587\) | 9.13891 | + | 15.8291i | 0.377203 | + | 0.653335i | 0.990654 | − | 0.136398i | \(-0.0435525\pi\) |
−0.613451 | + | 0.789733i | \(0.710219\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.59447 | + | 11.4220i | −0.271720 | + | 0.470633i | ||||
\(590\) | 18.8208 | + | 32.5985i | 0.774839 | + | 1.34206i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0287 | + | 27.7625i | −0.658775 | + | 1.14103i | ||||
\(593\) | −14.1908 | + | 24.5792i | −0.582745 | + | 1.00934i | 0.412407 | + | 0.911000i | \(0.364688\pi\) |
−0.995152 | + | 0.0983450i | \(0.968645\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.175096 | − | 0.303275i | −0.00717222 | − | 0.0124226i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.0009 | 0.736111 | ||||||||
\(599\) | −9.38902 | −0.383625 | −0.191813 | − | 0.981432i | \(-0.561437\pi\) | ||||
−0.191813 | + | 0.981432i | \(0.561437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.31432 | − | 10.9367i | −0.257566 | − | 0.446118i | 0.708023 | − | 0.706189i | \(-0.249587\pi\) |
−0.965589 | + | 0.260071i | \(0.916254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.04584 | + | 5.27555i | −0.123934 | + | 0.214659i | ||||
\(605\) | −16.9435 | + | 29.3471i | −0.688853 | + | 1.19313i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0133 | − | 20.8076i | −0.487604 | − | 0.844554i | 0.512295 | − | 0.858810i | \(-0.328796\pi\) |
−0.999898 | + | 0.0142555i | \(0.995462\pi\) | |||||||
\(608\) | −5.96947 | + | 10.3394i | −0.242094 | + | 0.419319i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.1347 | + | 38.3383i | 0.896206 | + | 1.55227i | ||||
\(611\) | −1.01967 | + | 1.76613i | −0.0412516 | + | 0.0714498i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.2708 | + | 24.7177i | 0.576390 | + | 0.998337i | 0.995889 | + | 0.0905814i | \(0.0288725\pi\) |
−0.419499 | + | 0.907756i | \(0.637794\pi\) | |||||||
\(614\) | 13.8339 | 0.558291 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.05549 | − | 10.4884i | 0.243785 | − | 0.422248i | −0.718004 | − | 0.696039i | \(-0.754944\pi\) |
0.961789 | + | 0.273791i | \(0.0882776\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2870 | − | 23.0137i | 0.534048 | − | 0.924998i | −0.465161 | − | 0.885226i | \(-0.654003\pi\) |
0.999209 | − | 0.0397721i | \(-0.0126632\pi\) | |||||||
\(620\) | 1.05085 | + | 1.82013i | 0.0422033 | + | 0.0730983i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.8207 | −0.714545 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.46486 | + | 6.00131i | 0.138594 | + | 0.240052i | ||||
\(626\) | −27.5806 | −1.10234 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.89614 | −0.115569 | ||||||||
\(629\) | −47.8774 | −1.90900 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.30962 | 0.131754 | 0.0658770 | − | 0.997828i | \(-0.479015\pi\) | ||||
0.0658770 | + | 0.997828i | \(0.479015\pi\) | |||||||
\(632\) | 3.01538 | 0.119945 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.64110 | 0.184322 | ||||||||
\(635\) | −5.36227 | − | 9.28773i | −0.212795 | − | 0.368572i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.17119 | 0.165139 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.0953 | − | 24.4138i | −0.557167 | − | 0.965041i | ||||
\(641\) | 16.2922 | − | 28.2189i | 0.643503 | − | 1.11458i | −0.341142 | − | 0.940012i | \(-0.610814\pi\) |
0.984645 | − | 0.174568i | \(-0.0558530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5327 | − | 37.2957i | 0.849166 | − | 1.47080i | −0.0327873 | − | 0.999462i | \(-0.510438\pi\) |
0.881953 | − | 0.471337i | \(-0.156228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 43.7628 | 1.72182 | ||||||||
\(647\) | 23.0988 | + | 40.0082i | 0.908106 | + | 1.57289i | 0.816692 | + | 0.577074i | \(0.195805\pi\) |
0.0914143 | + | 0.995813i | \(0.470861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.83968 | + | 8.38256i | −0.189974 | + | 0.329044i | ||||
\(650\) | −15.5556 | − | 26.9432i | −0.610143 | − | 1.05680i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.62248 | − | 4.54228i | 0.102704 | − | 0.177889i | ||||
\(653\) | 16.0002 | + | 27.7132i | 0.626138 | + | 1.08450i | 0.988320 | + | 0.152395i | \(0.0486985\pi\) |
−0.362182 | + | 0.932107i | \(0.617968\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.75022 | − | 9.95967i | 0.224680 | − | 0.389156i | ||||
\(656\) | −10.9217 | + | 18.9170i | −0.426422 | + | 0.738585i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.2070 | − | 33.2674i | −0.748197 | − | 1.29591i | −0.948686 | − | 0.316219i | \(-0.897587\pi\) |
0.200490 | − | 0.979696i | \(-0.435747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.0260 | 1.09009 | 0.545043 | − | 0.838408i | \(-0.316513\pi\) | ||||
0.545043 | + | 0.838408i | \(0.316513\pi\) | |||||||
\(662\) | 31.1262 | 1.20976 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.9794 | + | 19.0169i | 0.426083 | + | 0.737998i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.85386 | + | 10.1392i | −0.226662 | + | 0.392591i | ||||
\(668\) | 0.798544 | − | 1.38312i | 0.0308966 | − | 0.0535145i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.2210 | − | 21.1674i | −0.472138 | − | 0.817766i | ||||
\(671\) | −5.69183 | + | 9.85853i | −0.219730 | + | 0.380584i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.796281 | + | 1.37920i | 0.0306944 | + | 0.0531642i | 0.880965 | − | 0.473182i | \(-0.156895\pi\) |
−0.850270 | + | 0.526347i | \(0.823561\pi\) | |||||||
\(674\) | 17.8691 | − | 30.9503i | 0.688293 | − | 1.19216i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.407731 | − | 0.706211i | −0.0156820 | − | 0.0271619i | ||||
\(677\) | 42.0334 | 1.61547 | 0.807737 | − | 0.589543i | \(-0.200692\pi\) | ||||
0.807737 | + | 0.589543i | \(0.200692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 25.9588 | − | 44.9620i | 0.995476 | − | 1.72421i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.47128 | − | 2.54833i | 0.0563382 | − | 0.0975807i | ||||
\(683\) | 17.8645 | + | 30.9422i | 0.683565 | + | 1.18397i | 0.973886 | + | 0.227039i | \(0.0729046\pi\) |
−0.290321 | + | 0.956929i | \(0.593762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 73.8092 | 2.82010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.8715 | − | 27.4902i | −0.605095 | − | 1.04806i | ||||
\(689\) | −7.17408 | −0.273311 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.1349 | −1.94526 | −0.972632 | − | 0.232351i | \(-0.925358\pi\) | ||||
−0.972632 | + | 0.232351i | \(0.925358\pi\) | |||||||
\(692\) | 3.02161 | 0.114864 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.66606 | −0.253040 | ||||||||
\(695\) | −58.6132 | −2.22333 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.6230 | −1.23569 | ||||||||
\(698\) | 9.83977 | + | 17.0430i | 0.372441 | + | 0.645086i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.5761 | 0.928226 | 0.464113 | − | 0.885776i | \(-0.346373\pi\) | ||||
0.464113 | + | 0.885776i | \(0.346373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.5236 | − | 58.0645i | −1.26437 | − | 2.18995i | ||||
\(704\) | 5.20100 | − | 9.00840i | 0.196020 | − | 0.339517i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.4321 | + | 37.1215i | −0.806607 | + | 1.39708i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8976 | 1.16038 | 0.580192 | − | 0.814480i | \(-0.302978\pi\) | ||||
0.580192 | + | 0.814480i | \(0.302978\pi\) | |||||||
\(710\) | −7.50992 | − | 13.0076i | −0.281842 | − | 0.488165i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.0832 | − | 31.3210i | 0.677697 | − | 1.17380i | ||||
\(713\) | 4.12960 | + | 7.15268i | 0.154655 | + | 0.267870i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.69133 | − | 11.5897i | 0.250242 | − | 0.433431i | ||||
\(716\) | −0.213506 | − | 0.369803i | −0.00797908 | − | 0.0138202i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.6216 | − | 27.0573i | 0.582992 | − | 1.00977i | ||||
\(719\) | −3.05690 | + | 5.29471i | −0.114003 | + | 0.197459i | −0.917381 | − | 0.398011i | \(-0.869701\pi\) |
0.803378 | + | 0.595470i | \(0.203034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.2938 | + | 31.6857i | 0.680823 | + | 1.17922i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.75822 | 0.0653437 | ||||||||
\(725\) | 20.2347 | 0.751498 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2492 | − | 38.5367i | −0.825176 | − | 1.42925i | −0.901785 | − | 0.432186i | \(-0.857743\pi\) |
0.0766087 | − | 0.997061i | \(-0.475591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.37882 | + | 4.12023i | −0.0880440 | + | 0.152497i | ||||
\(731\) | 23.7039 | − | 41.0564i | 0.876722 | − | 1.51853i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.91854 | + | 8.51916i | 0.181670 | + | 0.314662i | 0.942449 | − | 0.334349i | \(-0.108516\pi\) |
−0.760779 | + | 0.649011i | \(0.775183\pi\) | |||||||
\(734\) | −1.72559 | + | 2.98881i | −0.0636926 | + | 0.110319i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.73821 | + | 6.47478i | 0.137792 | + | 0.238663i | ||||
\(737\) | 3.14257 | − | 5.44309i | 0.115758 | − | 0.200499i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.42464 | − | 12.8598i | −0.273120 | − | 0.473057i | 0.696539 | − | 0.717519i | \(-0.254722\pi\) |
−0.969659 | + | 0.244461i | \(0.921389\pi\) | |||||||
\(740\) | −10.6842 | −0.392760 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.04201 | − | 5.26892i | 0.111601 | − | 0.193298i | −0.804815 | − | 0.593525i | \(-0.797736\pi\) |
0.916416 | + | 0.400228i | \(0.131069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.98935 | + | 3.44566i | −0.0728843 | + | 0.126239i | ||||
\(746\) | −20.7449 | − | 35.9311i | −0.759523 | − | 1.31553i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.79328 | 0.0655686 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1005 | − | 19.2266i | −0.405063 | − | 0.701590i | 0.589266 | − | 0.807939i | \(-0.299417\pi\) |
−0.994329 | + | 0.106349i | \(0.966084\pi\) | |||||||
\(752\) | 2.07887 | 0.0758087 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.3987 | 0.415116 | ||||||||
\(755\) | 69.2106 | 2.51883 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0464 | 0.910329 | 0.455164 | − | 0.890407i | \(-0.349581\pi\) | ||||
0.455164 | + | 0.890407i | \(0.349581\pi\) | |||||||
\(758\) | −39.3446 | −1.42906 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 72.7051 | 2.63729 | ||||||||
\(761\) | −3.37632 | − | 5.84796i | −0.122392 | − | 0.211988i | 0.798319 | − | 0.602235i | \(-0.205723\pi\) |
−0.920710 | + | 0.390247i | \(0.872390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.76233 | −0.280831 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.12637 | − | 1.95094i | −0.0406975 | − | 0.0704902i | ||||
\(767\) | −13.2255 | + | 22.9072i | −0.477544 | + | 0.827131i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0805 | + | 36.5125i | −0.760182 | + | 1.31667i | 0.182575 | + | 0.983192i | \(0.441557\pi\) |
−0.942757 | + | 0.333482i | \(0.891776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.44130 | −0.195837 | ||||||||
\(773\) | −1.64926 | − | 2.85660i | −0.0593197 | − | 0.102745i | 0.834841 | − | 0.550492i | \(-0.185560\pi\) |
−0.894160 | + | 0.447747i | \(0.852226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.13728 | − | 12.3621i | 0.256379 | − | 0.444061i | ||||
\(776\) | −16.4108 | − | 28.4243i | −0.589112 | − | 1.02037i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.20356 | − | 12.4769i | 0.258260 | − | 0.447320i | ||||
\(779\) | −22.8425 | − | 39.5644i | −0.818419 | − | 1.41754i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.93114 | − | 3.34484i | 0.0691017 | − | 0.119688i | ||||
\(782\) | 13.7026 | − | 23.7336i | 0.490004 | − | 0.848713i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4522 | + | 28.4961i | 0.587205 | + | 1.01707i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.72910 | −0.239867 | −0.119933 | − | 0.992782i | \(-0.538268\pi\) | ||||
−0.119933 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(788\) | −6.13031 | −0.218383 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.30092 | − | 3.98530i | −0.0818629 | − | 0.141791i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.5542 | + | 26.9406i | −0.552345 | + | 0.956689i | ||||
\(794\) | 16.4688 | − | 28.5248i | 0.584456 | − | 1.01231i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.95160 | − | 5.11233i | −0.104617 | − | 0.181202i | ||||
\(797\) | 8.86302 | − | 15.3512i | 0.313944 | − | 0.543767i | −0.665268 | − | 0.746604i | \(-0.731683\pi\) |
0.979213 | + | 0.202837i | \(0.0650162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.55239 | + | 2.68882i | 0.0549196 | + | 0.0951235i | ||||
\(800\) | 6.46084 | − | 11.1905i | 0.228425 | − | 0.395644i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.6336 | + | 39.2026i | 0.799222 | + | 1.38429i | ||||
\(803\) | −1.22340 | −0.0431730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.02060 | − | 6.96388i | 0.141620 | − | 0.245292i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.39514 | + | 4.14850i | −0.0842607 | + | 0.145944i | ||||
\(809\) | 19.5428 | + | 33.8492i | 0.687089 | + | 1.19007i | 0.972775 | + | 0.231751i | \(0.0744453\pi\) |
−0.285686 | + | 0.958323i | \(0.592221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.9559 | −0.490058 | −0.245029 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245029 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.47939 | + | 12.9547i | 0.262152 | + | 0.454061i | ||||
\(815\) | −59.5907 | −2.08737 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.3896 | 2.32268 | ||||||||
\(818\) | 23.7177 | 0.829269 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.28010 | −0.254232 | ||||||||
\(821\) | 44.9966 | 1.57039 | 0.785196 | − | 0.619247i | \(-0.212562\pi\) | ||||
0.785196 | + | 0.619247i | \(0.212562\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.2465 | −1.92577 | −0.962886 | − | 0.269909i | \(-0.913006\pi\) | ||||
−0.962886 | + | 0.269909i | \(0.913006\pi\) | |||||||
\(824\) | −3.50700 | − | 6.07430i | −0.122172 | − | 0.211608i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8901 | 0.483005 | 0.241502 | − | 0.970400i | \(-0.422360\pi\) | ||||
0.241502 | + | 0.970400i | \(0.422360\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.4896 | − | 33.7570i | −0.676903 | − | 1.17243i | −0.975909 | − | 0.218179i | \(-0.929988\pi\) |
0.299006 | − | 0.954251i | \(-0.403345\pi\) | |||||||
\(830\) | 16.7559 | − | 29.0220i | 0.581605 | − | 1.00737i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.2129 | − | 24.6174i | 0.492743 | − | 0.853456i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.1453 | −0.627944 | ||||||||
\(836\) | 1.25564 | + | 2.17484i | 0.0434274 | + | 0.0752184i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.46882 | + | 9.47227i | −0.188917 | + | 0.327214i | ||||
\(839\) | −19.4708 | − | 33.7244i | −0.672206 | − | 1.16429i | −0.977277 | − | 0.211965i | \(-0.932014\pi\) |
0.305072 | − | 0.952329i | \(-0.401320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7932 | − | 18.6943i | 0.372178 | − | 0.644631i | ||||
\(842\) | −0.187560 | − | 0.324863i | −0.00646373 | − | 0.0111955i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.15385 | + | 1.99852i | −0.0397170 | + | 0.0687918i | ||||
\(845\) | −4.63243 | + | 8.02361i | −0.159361 | + | 0.276021i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.65657 | + | 6.33336i | 0.125567 | + | 0.217488i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.3650 | −1.62461 | ||||||||
\(851\) | −41.9864 | −1.43928 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.83890 | + | 6.64916i | 0.131441 | + | 0.227663i | 0.924232 | − | 0.381830i | \(-0.124706\pi\) |
−0.792791 | + | 0.609493i | \(0.791373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.33892 | + | 5.78318i | −0.114122 | + | 0.197665i | ||||
\(857\) | 7.98194 | − | 13.8251i | 0.272658 | − | 0.472258i | −0.696884 | − | 0.717184i | \(-0.745431\pi\) |
0.969542 | + | 0.244927i | \(0.0787639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1645 | + | 41.8542i | 0.824483 | + | 1.42805i | 0.902314 | + | 0.431080i | \(0.141867\pi\) |
−0.0778308 | + | 0.996967i | \(0.524799\pi\) | |||||||
\(860\) | 5.28973 | − | 9.16208i | 0.180378 | − | 0.312424i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.77148 | + | 15.1926i | 0.298758 | + | 0.517463i | ||||
\(863\) | −17.1526 | + | 29.7092i | −0.583881 | + | 1.01131i | 0.411133 | + | 0.911576i | \(0.365133\pi\) |
−0.995014 | + | 0.0997366i | \(0.968200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1650 | − | 29.7307i | −0.583628 | − | 1.01087i | ||||
\(866\) | 6.30712 | 0.214325 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.591670 | − | 1.02480i | 0.0200710 | − | 0.0347640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.58776 | − | 14.8744i | 0.290985 | − | 0.504001i | ||||
\(872\) | 1.38079 | + | 2.39159i | 0.0467594 | + | 0.0809896i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.3781 | 1.29816 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.09076 | − | 12.2816i | −0.239438 | − | 0.414719i | 0.721115 | − | 0.692815i | \(-0.243630\pi\) |
−0.960553 | + | 0.278097i | \(0.910296\pi\) | |||||||
\(878\) | −3.31198 | −0.111774 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.6421 | −0.459874 | ||||||||
\(881\) | −46.2822 | −1.55929 | −0.779643 | − | 0.626224i | \(-0.784600\pi\) | ||||
−0.779643 | + | 0.626224i | \(0.784600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.37483 | −0.147225 | −0.0736124 | − | 0.997287i | \(-0.523453\pi\) | ||||
−0.0736124 | + | 0.997287i | \(0.523453\pi\) | |||||||
\(884\) | 4.90052 | 0.164822 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.839076 | −0.0281893 | ||||||||
\(887\) | 9.57208 | + | 16.5793i | 0.321399 | + | 0.556679i | 0.980777 | − | 0.195132i | \(-0.0625136\pi\) |
−0.659378 | + | 0.751812i | \(0.729180\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −55.1942 | −1.85011 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.510697 | − | 0.884554i | −0.0170994 | − | 0.0296171i | ||||
\(893\) | −2.17396 | + | 3.76540i | −0.0727486 | + | 0.126004i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.42574 | + | 4.20151i | −0.0810836 | + | 0.140441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.79389 | −0.226715 | ||||||||
\(899\) | 2.61499 | + | 4.52929i | 0.0872147 | + | 0.151060i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.46105 | + | 9.45881i | −0.181934 | + | 0.315119i | ||||
\(902\) | 5.09636 | + | 8.82715i | 0.169690 | + | 0.293912i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.58357 | + | 6.20692i | −0.119188 | + | 0.206439i | ||||
\(905\) | −9.98800 | − | 17.2997i | −0.332012 | − | 0.575062i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9225 | + | 34.5068i | −0.661515 | + | 1.14578i | 0.318702 | + | 0.947855i | \(0.396753\pi\) |
−0.980218 | + | 0.197923i | \(0.936580\pi\) | |||||||
\(908\) | 2.79562 | − | 4.84216i | 0.0927760 | − | 0.160693i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.3727 | − | 24.8942i | −0.476189 | − | 0.824783i | 0.523439 | − | 0.852063i | \(-0.324649\pi\) |
−0.999628 | + | 0.0272803i | \(0.991315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.61739 | 0.285194 | ||||||||
\(914\) | 3.71861 | 0.123001 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.660219 | + | 1.14353i | 0.0218142 | + | 0.0377834i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.01347 | − | 13.8797i | 0.264340 | − | 0.457850i | −0.703051 | − | 0.711140i | \(-0.748179\pi\) |
0.967390 | + | 0.253290i | \(0.0815126\pi\) | |||||||
\(920\) | 22.7648 | − | 39.4298i | 0.750533 | − | 1.29996i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.37388 | + | 4.11168i | 0.0781796 | + | 0.135411i | ||||
\(923\) | 5.27727 | − | 9.14050i | 0.173704 | − | 0.300863i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.2830 | + | 62.8440i | 1.19298 | + | 2.06630i | ||||
\(926\) | 20.0247 | − | 34.6839i | 0.658054 | − | 1.13978i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.36715 | + | 4.10002i | 0.0777055 | + | 0.134590i | ||||
\(929\) | 14.0159 | 0.459847 | 0.229924 | − | 0.973209i | \(-0.426152\pi\) | ||||
0.229924 | + | 0.973209i | \(0.426152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.28180 | − | 3.95219i | 0.0747428 | − | 0.129458i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.3738 | + | 23.1640i | −0.437603 | + | 0.757950i | ||||
\(935\) | −10.1871 | − | 17.6447i | −0.333155 | − | 0.577042i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.5307 | −1.68344 | −0.841718 | − | 0.539918i | \(-0.818455\pi\) | ||||
−0.841718 | + | 0.539918i | \(0.818455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.346429 | + | 0.600032i | 0.0112993 | + | 0.0195709i | ||||
\(941\) | −46.3128 | −1.50975 | −0.754877 | − | 0.655866i | \(-0.772303\pi\) | ||||
−0.754877 | + | 0.655866i | \(0.772303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.6090 | −0.931637 | ||||||||
\(944\) | 26.9636 | 0.877592 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.8121 | −0.481582 | ||||||||
\(947\) | −20.0083 | −0.650181 | −0.325091 | − | 0.945683i | \(-0.605395\pi\) | ||||
−0.325091 | + | 0.945683i | \(0.605395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.34322 | −0.108526 | ||||||||
\(950\) | −33.1648 | − | 57.4432i | −1.07601 | − | 1.86370i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.0109 | −0.972148 | −0.486074 | − | 0.873918i | \(-0.661571\pi\) | ||||
−0.486074 | + | 0.873918i | \(0.661571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.0958 | + | 76.3762i | 1.42691 | + | 2.47148i | ||||
\(956\) | 2.19773 | − | 3.80659i | 0.0710798 | − | 0.123114i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.3675 | + | 28.3493i | −0.528809 | + | 0.915924i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.3105 | −0.880985 | ||||||||
\(962\) | 20.4391 | + | 35.4015i | 0.658982 | + | 1.14139i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.23125 | − | 2.13259i | 0.0396559 | − | 0.0686860i | ||||
\(965\) | 30.9106 | + | 53.5388i | 0.995049 | + | 1.72348i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5721 | − | 28.7037i | 0.532923 | − | 0.923050i | −0.466338 | − | 0.884607i | \(-0.654427\pi\) |
0.999261 | − | 0.0384431i | \(-0.0122398\pi\) | |||||||
\(968\) | 14.4317 | + | 24.9964i | 0.463851 | + | 0.803414i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.0448 | + | 43.3788i | −0.804140 | + | 1.39281i | ||||
\(971\) | −20.8234 | + | 36.0672i | −0.668256 | + | 1.15745i | 0.310136 | + | 0.950692i | \(0.399625\pi\) |
−0.978392 | + | 0.206761i | \(0.933708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −21.2928 | − | 36.8803i | −0.682267 | − | 1.18172i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.7113 | 1.01505 | ||||||||
\(977\) | −37.5181 | −1.20031 | −0.600154 | − | 0.799884i | \(-0.704894\pi\) | ||||
−0.600154 | + | 0.799884i | \(0.704894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.09647 | − | 12.2914i | −0.226804 | − | 0.392836i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.28778 | − | 3.96255i | 0.0730059 | − | 0.126450i | ||||
\(983\) | −24.0379 | + | 41.6349i | −0.766690 | + | 1.32795i | 0.172658 | + | 0.984982i | \(0.444764\pi\) |
−0.939348 | + | 0.342964i | \(0.888569\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.8247 | + | 60.3182i | 1.10961 | + | 1.92190i | ||||
\(986\) | 8.67690 | − | 15.0288i | 0.276329 | − | 0.478616i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.43133 | + | 5.94323i | 0.109165 | + | 0.189079i | ||||
\(989\) | 20.7873 | − | 36.0047i | 0.660999 | − | 1.14488i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.0643 | + | 29.5562i | 0.542065 | + | 0.938884i | 0.998785 | + | 0.0492737i | \(0.0156907\pi\) |
−0.456720 | + | 0.889610i | \(0.650976\pi\) | |||||||
\(992\) | 3.33981 | 0.106039 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.5346 | + | 58.0837i | −1.06312 | + | 1.84138i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0413 | + | 38.1767i | −0.698056 | + | 1.20907i | 0.271084 | + | 0.962556i | \(0.412618\pi\) |
−0.969140 | + | 0.246512i | \(0.920715\pi\) | |||||||
\(998\) | 10.1661 | + | 17.6081i | 0.321801 | + | 0.557376i | ||||
\(999\) | 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 | 1323.2.h.h.226.3 | 24 | ||
3.2 | odd | 2 | 441.2.h.h.373.10 | 24 | |||
7.2 | even | 3 | 1323.2.f.h.442.10 | 24 | |||
7.3 | odd | 6 | 1323.2.g.h.361.9 | 24 | |||
7.4 | even | 3 | 1323.2.g.h.361.10 | 24 | |||
7.5 | odd | 6 | 1323.2.f.h.442.9 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.h.h.226.4 | 24 | ||
9.2 | odd | 6 | 441.2.g.h.79.3 | 24 | |||
9.7 | even | 3 | 1323.2.g.h.667.10 | 24 | |||
21.2 | odd | 6 | 441.2.f.h.148.4 | yes | 24 | ||
21.5 | even | 6 | 441.2.f.h.148.3 | ✓ | 24 | ||
21.11 | odd | 6 | 441.2.g.h.67.3 | 24 | |||
21.17 | even | 6 | 441.2.g.h.67.4 | 24 | |||
21.20 | even | 2 | 441.2.h.h.373.9 | 24 | |||
63.2 | odd | 6 | 441.2.f.h.295.4 | yes | 24 | ||
63.5 | even | 6 | 3969.2.a.bh.1.9 | 12 | |||
63.11 | odd | 6 | 441.2.h.h.214.10 | 24 | |||
63.16 | even | 3 | 1323.2.f.h.883.10 | 24 | |||
63.20 | even | 6 | 441.2.g.h.79.4 | 24 | |||
63.23 | odd | 6 | 3969.2.a.bh.1.10 | 12 | |||
63.25 | even | 3 | inner | 1323.2.h.h.802.3 | 24 | ||
63.34 | odd | 6 | 1323.2.g.h.667.9 | 24 | |||
63.38 | even | 6 | 441.2.h.h.214.9 | 24 | |||
63.40 | odd | 6 | 3969.2.a.bi.1.4 | 12 | |||
63.47 | even | 6 | 441.2.f.h.295.3 | yes | 24 | ||
63.52 | odd | 6 | inner | 1323.2.h.h.802.4 | 24 | ||
63.58 | even | 3 | 3969.2.a.bi.1.3 | 12 | |||
63.61 | odd | 6 | 1323.2.f.h.883.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.3 | ✓ | 24 | 21.5 | even | 6 | ||
441.2.f.h.148.4 | yes | 24 | 21.2 | odd | 6 | ||
441.2.f.h.295.3 | yes | 24 | 63.47 | even | 6 | ||
441.2.f.h.295.4 | yes | 24 | 63.2 | odd | 6 | ||
441.2.g.h.67.3 | 24 | 21.11 | odd | 6 | |||
441.2.g.h.67.4 | 24 | 21.17 | even | 6 | |||
441.2.g.h.79.3 | 24 | 9.2 | odd | 6 | |||
441.2.g.h.79.4 | 24 | 63.20 | even | 6 | |||
441.2.h.h.214.9 | 24 | 63.38 | even | 6 | |||
441.2.h.h.214.10 | 24 | 63.11 | odd | 6 | |||
441.2.h.h.373.9 | 24 | 21.20 | even | 2 | |||
441.2.h.h.373.10 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.442.9 | 24 | 7.5 | odd | 6 | |||
1323.2.f.h.442.10 | 24 | 7.2 | even | 3 | |||
1323.2.f.h.883.9 | 24 | 63.61 | odd | 6 | |||
1323.2.f.h.883.10 | 24 | 63.16 | even | 3 | |||
1323.2.g.h.361.9 | 24 | 7.3 | odd | 6 | |||
1323.2.g.h.361.10 | 24 | 7.4 | even | 3 | |||
1323.2.g.h.667.9 | 24 | 63.34 | odd | 6 | |||
1323.2.g.h.667.10 | 24 | 9.7 | even | 3 | |||
1323.2.h.h.226.3 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.h.h.226.4 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.802.3 | 24 | 63.25 | even | 3 | inner | ||
1323.2.h.h.802.4 | 24 | 63.52 | odd | 6 | inner | ||
3969.2.a.bh.1.9 | 12 | 63.5 | even | 6 | |||
3969.2.a.bh.1.10 | 12 | 63.23 | odd | 6 | |||
3969.2.a.bi.1.3 | 12 | 63.58 | even | 3 | |||
3969.2.a.bi.1.4 | 12 | 63.40 | odd | 6 |