Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (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 | 361.9 | ||
Character | \(\chi\) | \(=\) | 1323.361 |
Dual form | 1323.2.g.h.667.9 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.649936 | − | 1.12572i | 0.459574 | − | 0.796006i | −0.539364 | − | 0.842073i | \(-0.681335\pi\) |
0.998938 | + | 0.0460668i | \(0.0146687\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.155166 | + | 0.268756i | 0.0775831 | + | 0.134378i | ||||
\(5\) | 3.52584 | 1.57680 | 0.788402 | − | 0.615160i | \(-0.210909\pi\) | ||||
0.788402 | + | 0.615160i | \(0.210909\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00314 | 1.06177 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.29157 | − | 3.96912i | 0.724659 | − | 1.25515i | ||||
\(11\) | −1.17853 | −0.355342 | −0.177671 | − | 0.984090i | \(-0.556856\pi\) | ||||
−0.177671 | + | 0.984090i | \(0.556856\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.61030 | + | 2.78913i | −0.446618 | + | 0.773564i | −0.998163 | − | 0.0605803i | \(-0.980705\pi\) |
0.551546 | + | 0.834145i | \(0.314038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.64151 | − | 2.84319i | 0.410379 | − | 0.710797i | ||||
\(17\) | 2.45159 | − | 4.24627i | 0.594597 | − | 1.02987i | −0.399006 | − | 0.916948i | \(-0.630645\pi\) |
0.993604 | − | 0.112924i | \(-0.0360218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.43318 | − | 5.94645i | −0.787627 | − | 1.36421i | −0.927417 | − | 0.374028i | \(-0.877976\pi\) |
0.139791 | − | 0.990181i | \(-0.455357\pi\) | |||||||
\(20\) | 0.547092 | + | 0.947591i | 0.122333 | + | 0.211888i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.765972 | + | 1.32670i | −0.163306 | + | 0.282854i | ||||
\(23\) | 4.29987 | 0.896585 | 0.448293 | − | 0.893887i | \(-0.352032\pi\) | ||||
0.448293 | + | 0.893887i | \(0.352032\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.43156 | 1.48631 | ||||||||
\(26\) | 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 | ||||||||
\(31\) | −0.960401 | − | 1.66346i | −0.172493 | − | 0.298767i | 0.766798 | − | 0.641889i | \(-0.221849\pi\) |
−0.939291 | + | 0.343122i | \(0.888516\pi\) | |||||||
\(32\) | 0.869378 | + | 1.50581i | 0.153686 | + | 0.266192i | ||||
\(33\) | 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 | 0.917871 | + | 0.396879i | \(0.129907\pi\) |
−0.115228 | + | 0.993339i | \(0.536760\pi\) | |||||||
\(38\) | −8.92540 | −1.44789 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10.5886 | 1.67420 | ||||||||
\(41\) | −3.32673 | + | 5.76206i | −0.519547 | + | 0.899883i | 0.480194 | + | 0.877162i | \(0.340566\pi\) |
−0.999742 | + | 0.0227205i | \(0.992767\pi\) | |||||||
\(42\) | 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 | ||||
\(47\) | −0.316609 | + | 0.548383i | −0.0461822 | + | 0.0799899i | −0.888192 | − | 0.459472i | \(-0.848039\pi\) |
0.842010 | + | 0.539461i | \(0.181372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.83004 | − | 8.36587i | 0.683071 | − | 1.18311i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.999459 | −0.138600 | ||||||||
\(53\) | −1.11378 | + | 1.92912i | −0.152989 | + | 0.264985i | −0.932325 | − | 0.361621i | \(-0.882223\pi\) |
0.779336 | + | 0.626606i | \(0.215557\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.15533 | −0.560304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.53930 | −0.464733 | ||||||||
\(59\) | −4.10652 | − | 7.11270i | −0.534623 | − | 0.925995i | −0.999181 | − | 0.0404521i | \(-0.987120\pi\) |
0.464558 | − | 0.885543i | \(-0.346213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.82958 | + | 8.36508i | −0.618364 | + | 1.07104i | 0.371420 | + | 0.928465i | \(0.378871\pi\) |
−0.989784 | + | 0.142573i | \(0.954462\pi\) | |||||||
\(62\) | −2.49680 | −0.317093 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.82622 | 1.10328 | ||||||||
\(65\) | −5.67767 | + | 9.83402i | −0.704229 | + | 1.21976i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.66651 | − | 4.61852i | −0.325766 | − | 0.564242i | 0.655901 | − | 0.754847i | \(-0.272289\pi\) |
−0.981667 | + | 0.190604i | \(0.938955\pi\) | |||||||
\(68\) | 1.52161 | 0.184523 | ||||||||
\(69\) | 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 | \(-0.813985\pi\) |
0.894800 | + | 0.446467i | \(0.147318\pi\) | |||||||
\(74\) | 12.6927 | 1.47550 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.06543 | − | 1.84538i | 0.122213 | − | 0.211679i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.502039 | + | 0.869557i | −0.0564838 | + | 0.0978328i | −0.892885 | − | 0.450285i | \(-0.851322\pi\) |
0.836401 | + | 0.548118i | \(0.184656\pi\) | |||||||
\(80\) | 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 | 0.592587 | − | 0.805506i | \(-0.298107\pi\) |
−0.993883 | + | 0.110442i | \(0.964773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.64391 | − | 14.9717i | 0.937563 | − | 1.62391i | ||||
\(86\) | 12.5682 | 1.35527 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.53930 | −0.377291 | ||||||||
\(89\) | −6.02144 | − | 10.4294i | −0.638271 | − | 1.10552i | −0.985812 | − | 0.167853i | \(-0.946317\pi\) |
0.347541 | − | 0.937665i | \(-0.387017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.667195 | + | 1.15562i | 0.0695599 | + | 0.120481i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.411551 | + | 0.712828i | 0.0424483 | + | 0.0735226i | ||||
\(95\) | −12.1049 | − | 20.9662i | −1.24193 | − | 2.15109i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.46454 | + | 9.46487i | 0.554840 | + | 0.961012i | 0.997916 | + | 0.0645275i | \(0.0205540\pi\) |
−0.443076 | + | 0.896484i | \(0.646113\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.15313 | + | 1.99728i | 0.115313 | + | 0.199728i | ||||
\(101\) | −1.59509 | −0.158718 | −0.0793588 | − | 0.996846i | \(-0.525287\pi\) | ||||
−0.0793588 | + | 0.996846i | \(0.525287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.33556 | −0.230129 | −0.115065 | − | 0.993358i | \(-0.536708\pi\) | ||||
−0.115065 | + | 0.993358i | \(0.536708\pi\) | |||||||
\(104\) | −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 | 0.807267 | − | 0.590186i | \(-0.200946\pi\) |
−0.914750 | + | 0.404021i | \(0.867612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.459782 | − | 0.796366i | 0.0440391 | − | 0.0762780i | −0.843166 | − | 0.537654i | \(-0.819311\pi\) |
0.887205 | + | 0.461376i | \(0.152644\pi\) | |||||||
\(110\) | −2.70070 | + | 4.67774i | −0.257501 | + | 0.446005i | ||||
\(111\) | 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 | ||||||||
\(115\) | 15.1607 | 1.41374 | ||||||||
\(116\) | 0.422488 | − | 0.731770i | 0.0392270 | − | 0.0679432i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.6759 | −0.982796 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.61106 | −0.873732 | ||||||||
\(122\) | 6.27783 | + | 10.8735i | 0.568368 | + | 0.984443i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.298044 | − | 0.516227i | 0.0267651 | − | 0.0463585i | ||||
\(125\) | 8.57330 | 0.766819 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04170 | −0.269907 | −0.134954 | − | 0.990852i | \(-0.543089\pi\) | ||||
−0.134954 | + | 0.990852i | \(0.543089\pi\) | |||||||
\(128\) | 3.99772 | − | 6.92426i | 0.353352 | − | 0.612024i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.38025 | + | 12.7830i | 0.647291 | + | 1.12114i | ||||
\(131\) | −3.26176 | −0.284981 | −0.142490 | − | 0.989796i | \(-0.545511\pi\) | ||||
−0.142490 | + | 0.989796i | \(0.545511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.93223 | −0.598854 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.36245 | − | 12.7521i | 0.631325 | − | 1.09349i | ||||
\(137\) | −20.9338 | −1.78849 | −0.894246 | − | 0.447575i | \(-0.852288\pi\) | ||||
−0.894246 | + | 0.447575i | \(0.852288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.31195 | − | 14.3967i | 0.705010 | − | 1.22111i | −0.261677 | − | 0.965155i | \(-0.584276\pi\) |
0.966688 | − | 0.255958i | \(-0.0823910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.12997 | − | 3.68921i | 0.178743 | − | 0.309592i | ||||
\(143\) | 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 | ||||
\(149\) | −1.12844 | −0.0924456 | −0.0462228 | − | 0.998931i | \(-0.514718\pi\) | ||||
−0.0462228 | + | 0.998931i | \(0.514718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.6295 | −1.59743 | −0.798714 | − | 0.601711i | \(-0.794486\pi\) | ||||
−0.798714 | + | 0.601711i | \(0.794486\pi\) | |||||||
\(152\) | −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 | ||||||||
\(157\) | 4.66619 | + | 8.08207i | 0.372402 | + | 0.645020i | 0.989935 | − | 0.141526i | \(-0.0452009\pi\) |
−0.617532 | + | 0.786545i | \(0.711868\pi\) | |||||||
\(158\) | 0.652586 | + | 1.13031i | 0.0519170 | + | 0.0899228i | ||||
\(159\) | 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 | −0.980116 | − | 0.198425i | \(-0.936417\pi\) |
0.318217 | − | 0.948018i | \(-0.396916\pi\) | |||||||
\(164\) | −2.06478 | −0.161232 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.50460 | −0.737700 | ||||||||
\(167\) | 2.57319 | − | 4.45689i | 0.199119 | − | 0.344885i | −0.749124 | − | 0.662430i | \(-0.769525\pi\) |
0.948243 | + | 0.317545i | \(0.102859\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −4.86834 | + | 8.43222i | −0.370133 | + | 0.641090i | −0.989586 | − | 0.143945i | \(-0.954021\pi\) |
0.619453 | + | 0.785034i | \(0.287355\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.93458 | + | 3.35079i | −0.145825 | + | 0.252576i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.6542 | −1.17333 | ||||||||
\(179\) | 0.687990 | − | 1.19163i | 0.0514228 | − | 0.0890668i | −0.839168 | − | 0.543872i | \(-0.816958\pi\) |
0.890591 | + | 0.454805i | \(0.150291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.66560 | 0.421120 | 0.210560 | − | 0.977581i | \(-0.432471\pi\) | ||||
0.210560 | + | 0.977581i | \(0.432471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.9131 | 0.951967 | ||||||||
\(185\) | 17.2142 | + | 29.8158i | 1.26561 | + | 2.19210i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.88928 | + | 5.00438i | −0.211285 | + | 0.365956i | ||||
\(188\) | −0.196508 | −0.0143318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −31.4696 | −2.28304 | ||||||||
\(191\) | −12.5065 | + | 21.6618i | −0.904936 | + | 1.56740i | −0.0839339 | + | 0.996471i | \(0.526748\pi\) |
−0.821003 | + | 0.570925i | \(0.806585\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.76688 | − | 15.1847i | −0.631054 | − | 1.09302i | −0.987337 | − | 0.158640i | \(-0.949289\pi\) |
0.356282 | − | 0.934378i | \(-0.384044\pi\) | |||||||
\(194\) | 14.2064 | 1.01996 | ||||||||
\(195\) | 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 | 0.302471 | + | 0.953158i | \(0.402188\pi\) |
−0.976695 | + | 0.214631i | \(0.931145\pi\) | |||||||
\(200\) | 22.3180 | 1.57812 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.03671 | + | 1.79563i | −0.0729425 | + | 0.126340i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.7295 | + | 20.3161i | −0.819225 | + | 1.41894i | ||||
\(206\) | −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 | \(0.0842738\pi\) | |||||||
\(212\) | −0.691283 | −0.0474775 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.89043 | −0.197585 | ||||||||
\(215\) | 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 | ||||||||
\(220\) | −0.644767 | − | 1.11677i | −0.0434702 | − | 0.0752925i | ||||
\(221\) | 7.89559 | + | 13.6756i | 0.531115 | + | 0.919918i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.64565 | − | 2.85034i | −0.110201 | − | 0.190873i | 0.805650 | − | 0.592391i | \(-0.201816\pi\) |
−0.915851 | + | 0.401518i | \(0.868483\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.55110 | + | 2.68659i | 0.103178 | + | 0.178709i | ||||
\(227\) | −18.0169 | −1.19583 | −0.597913 | − | 0.801561i | \(-0.704003\pi\) | ||||
−0.597913 | + | 0.801561i | \(0.704003\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.25491 | −0.281173 | −0.140586 | − | 0.990068i | \(-0.544899\pi\) | ||||
−0.140586 | + | 0.990068i | \(0.544899\pi\) | |||||||
\(230\) | 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 | 0.518084 | − | 0.855330i | \(-0.326645\pi\) |
−0.999779 | + | 0.0210095i | \(0.993312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.11631 | + | 1.93351i | −0.0728203 | + | 0.126128i | ||||
\(236\) | 1.27439 | − | 2.20730i | 0.0829555 | − | 0.143683i | ||||
\(237\) | 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 | ||||||||
\(241\) | −7.93503 | −0.511140 | −0.255570 | − | 0.966791i | \(-0.582263\pi\) | ||||
−0.255570 | + | 0.966791i | \(0.582263\pi\) | |||||||
\(242\) | −6.24657 | + | 10.8194i | −0.401545 | + | 0.695496i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.99755 | −0.191899 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.1139 | 1.40707 | ||||||||
\(248\) | −2.88422 | − | 4.99561i | −0.183148 | − | 0.317221i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.57210 | − | 9.65115i | 0.352410 | − | 0.610392i | ||||
\(251\) | 8.05097 | 0.508173 | 0.254087 | − | 0.967181i | \(-0.418225\pi\) | ||||
0.254087 | + | 0.967181i | \(0.418225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.06755 | −0.318594 | ||||||||
\(254\) | −1.97691 | + | 3.42411i | −0.124042 | + | 0.214848i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.62969 | + | 6.28681i | 0.226856 | + | 0.392926i | ||||
\(257\) | −17.5537 | −1.09497 | −0.547486 | − | 0.836815i | \(-0.684415\pi\) | ||||
−0.547486 | + | 0.836815i | \(0.684415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.52393 | −0.218545 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.11993 | + | 3.67183i | −0.130970 | + | 0.226846i | ||||
\(263\) | 23.3486 | 1.43973 | 0.719867 | − | 0.694112i | \(-0.244203\pi\) | ||||
0.719867 | + | 0.694112i | \(0.244203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.92701 | + | 6.80177i | −0.241234 | + | 0.417830i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.827504 | − | 1.43328i | 0.0505478 | − | 0.0875514i | ||||
\(269\) | −0.269244 | + | 0.466344i | −0.0164161 | + | 0.0284335i | −0.874117 | − | 0.485716i | \(-0.838559\pi\) |
0.857701 | + | 0.514149i | \(0.171892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.20749 | − | 12.4837i | −0.437824 | − | 0.758334i | 0.559697 | − | 0.828697i | \(-0.310917\pi\) |
−0.997521 | + | 0.0703635i | \(0.977584\pi\) | |||||||
\(272\) | −8.04863 | − | 13.9406i | −0.488020 | − | 0.845275i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6056 | + | 23.5656i | −0.821945 | + | 1.42365i | ||||
\(275\) | −8.75835 | −0.528148 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.9066 | 1.31624 | 0.658121 | − | 0.752912i | \(-0.271351\pi\) | ||||
0.658121 | + | 0.752912i | \(0.271351\pi\) | |||||||
\(278\) | −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 | ||||||||
\(283\) | −1.32571 | − | 2.29619i | −0.0788051 | − | 0.136495i | 0.823930 | − | 0.566692i | \(-0.191777\pi\) |
−0.902735 | + | 0.430198i | \(0.858444\pi\) | |||||||
\(284\) | 0.508510 | + | 0.880765i | 0.0301745 | + | 0.0522638i | ||||
\(285\) | 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 | ||||
\(290\) | −12.4790 | −0.732793 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.322148 | 0.0188523 | ||||||||
\(293\) | −5.19314 | + | 8.99478i | −0.303386 | + | 0.525481i | −0.976901 | − | 0.213694i | \(-0.931451\pi\) |
0.673514 | + | 0.739174i | \(0.264784\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | −6.92409 | + | 11.9929i | −0.400431 | + | 0.693566i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.7579 | + | 22.0974i | −0.734137 | + | 1.27156i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.5425 | −1.29290 | ||||||||
\(305\) | −17.0283 | + | 29.4939i | −0.975039 | + | 1.68882i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6425 | 0.607400 | 0.303700 | − | 0.952768i | \(-0.401778\pi\) | ||||
0.303700 | + | 0.952768i | \(0.401778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.80331 | −0.499994 | ||||||||
\(311\) | 6.85479 | + | 11.8728i | 0.388699 | + | 0.673247i | 0.992275 | − | 0.124059i | \(-0.0395912\pi\) |
−0.603576 | + | 0.797306i | \(0.706258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6090 | − | 18.3752i | 0.599653 | − | 1.03863i | −0.393219 | − | 0.919445i | \(-0.628638\pi\) |
0.992872 | − | 0.119185i | \(-0.0380282\pi\) | |||||||
\(314\) | 12.1309 | 0.684586 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.311598 | −0.0175288 | ||||||||
\(317\) | 1.78521 | − | 3.09208i | 0.100268 | − | 0.173669i | −0.811527 | − | 0.584315i | \(-0.801363\pi\) |
0.911795 | + | 0.410646i | \(0.134697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.60446 | + | 2.77901i | 0.0898326 | + | 0.155595i | ||||
\(320\) | 31.1198 | 1.73965 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.6670 | −1.87328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9671 | + | 20.7276i | −0.663813 | + | 1.14976i | ||||
\(326\) | −21.9693 | −1.21677 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.99062 | + | 17.3043i | −0.551639 | + | 0.955468i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9728 | − | 20.7375i | 0.658085 | − | 1.13984i | −0.323026 | − | 0.946390i | \(-0.604700\pi\) |
0.981111 | − | 0.193446i | \(-0.0619666\pi\) | |||||||
\(332\) | 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 | \(0.897279\pi\) | |||||||
\(338\) | 3.41568 | 0.185788 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.36497 | 0.290956 | ||||||||
\(341\) | 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 | ||||||||
\(346\) | 6.32822 | + | 10.9608i | 0.340207 | + | 0.589256i | ||||
\(347\) | −2.56412 | − | 4.44119i | −0.137649 | − | 0.238416i | 0.788957 | − | 0.614448i | \(-0.210621\pi\) |
−0.926606 | + | 0.376033i | \(0.877288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.56980 | + | 13.1113i | 0.405202 | + | 0.701830i | 0.994345 | − | 0.106198i | \(-0.0338679\pi\) |
−0.589143 | + | 0.808029i | \(0.700535\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.02459 | − | 1.77465i | −0.0546110 | − | 0.0945889i | ||||
\(353\) | 32.9757 | 1.75512 | 0.877559 | − | 0.479468i | \(-0.159171\pi\) | ||||
0.877559 | + | 0.479468i | \(0.159171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.5549 | 0.613269 | ||||||||
\(356\) | 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 | −0.986669 | − | 0.162743i | \(-0.947966\pi\) |
0.352395 | − | 0.935851i | \(-0.385367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0735 | + | 24.3760i | −0.740711 | + | 1.28295i | ||||
\(362\) | 3.68227 | − | 6.37789i | 0.193536 | − | 0.335214i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.83004 | − | 3.16972i | 0.0957886 | − | 0.165911i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.65501 | 0.138590 | 0.0692952 | − | 0.997596i | \(-0.477925\pi\) | ||||
0.0692952 | + | 0.997596i | \(0.477925\pi\) | |||||||
\(368\) | 7.05830 | − | 12.2253i | 0.367939 | − | 0.637290i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 44.7524 | 2.32657 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.9183 | −1.65267 | −0.826334 | − | 0.563181i | \(-0.809577\pi\) | ||||
−0.826334 | + | 0.563181i | \(0.809577\pi\) | |||||||
\(374\) | 3.75569 | + | 6.50505i | 0.194202 | + | 0.336368i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.950821 | + | 1.64687i | −0.0490348 | + | 0.0849308i | ||||
\(377\) | 8.76909 | 0.451631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2681 | 1.55477 | 0.777384 | − | 0.629027i | \(-0.216546\pi\) | ||||
0.777384 | + | 0.629027i | \(0.216546\pi\) | |||||||
\(380\) | 3.75653 | − | 6.50651i | 0.192706 | − | 0.333777i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.2568 | + | 28.1576i | 0.831771 | + | 1.44067i | ||||
\(383\) | 1.73305 | 0.0885548 | 0.0442774 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442774 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.7917 | −1.16006 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.69583 | + | 2.93726i | −0.0860925 | + | 0.149117i | ||||
\(389\) | 11.0835 | 0.561956 | 0.280978 | − | 0.959714i | \(-0.409341\pi\) | ||||
0.280978 | + | 0.959714i | \(0.409341\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5415 | − | 18.2584i | 0.533107 | − | 0.923368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.8388 | − | 22.2375i | 0.646811 | − | 1.12031i | ||||
\(395\) | −1.77011 | + | 3.06592i | −0.0890639 | + | 0.154263i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.6696 | + | 21.9443i | 0.635867 | + | 1.10135i | 0.986331 | + | 0.164777i | \(0.0526905\pi\) |
−0.350464 | + | 0.936576i | \(0.613976\pi\) | |||||||
\(398\) | 12.3632 | + | 21.4137i | 0.619712 | + | 1.07337i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.1990 | − | 21.1293i | 0.609951 | − | 1.05647i | ||||
\(401\) | 34.8244 | 1.73905 | 0.869524 | − | 0.493890i | \(-0.164425\pi\) | ||||
0.869524 | + | 0.493890i | \(0.164425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.18614 | 0.308154 | ||||||||
\(404\) | −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 | ||||||||
\(409\) | −9.12308 | − | 15.8016i | −0.451107 | − | 0.781341i | 0.547348 | − | 0.836905i | \(-0.315638\pi\) |
−0.998455 | + | 0.0555643i | \(0.982304\pi\) | |||||||
\(410\) | 15.2469 | + | 26.4083i | 0.752989 | + | 1.30422i | ||||
\(411\) | 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 | ||||
\(416\) | −5.59985 | −0.274555 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.5189 | 0.514496 | ||||||||
\(419\) | −4.20719 | + | 7.28708i | −0.205535 | + | 0.355997i | −0.950303 | − | 0.311326i | \(-0.899227\pi\) |
0.744768 | + | 0.667323i | \(0.232560\pi\) | |||||||
\(420\) | 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 | ||||
\(425\) | 18.2191 | − | 31.5564i | 0.883757 | − | 1.53071i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.345031 | − | 0.597612i | 0.0166777 | − | 0.0288866i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 44.3136 | 2.13699 | ||||||||
\(431\) | −6.74795 | + | 11.6878i | −0.325037 | + | 0.562981i | −0.981520 | − | 0.191360i | \(-0.938710\pi\) |
0.656482 | + | 0.754341i | \(0.272044\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.85211 | 0.233177 | 0.116589 | − | 0.993180i | \(-0.462804\pi\) | ||||
0.116589 | + | 0.993180i | \(0.462804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.285371 | 0.0136668 | ||||||||
\(437\) | −14.7623 | − | 25.5690i | −0.706174 | − | 1.22313i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.27397 | − | 2.20657i | 0.0608031 | − | 0.105314i | −0.834022 | − | 0.551732i | \(-0.813967\pi\) |
0.894825 | + | 0.446418i | \(0.147301\pi\) | |||||||
\(440\) | −12.4790 | −0.594914 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.5265 | 0.976347 | ||||||||
\(443\) | −0.322753 | + | 0.559025i | −0.0153345 | + | 0.0265601i | −0.873591 | − | 0.486661i | \(-0.838215\pi\) |
0.858256 | + | 0.513221i | \(0.171548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.2306 | − | 36.7725i | −1.00643 | − | 1.74319i | ||||
\(446\) | −4.27826 | −0.202581 | ||||||||
\(447\) | 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 | ||||
\(452\) | −0.740624 | −0.0348360 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.7099 | + | 20.2821i | −0.549571 | + | 0.951885i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.43037 | − | 2.47748i | 0.0669101 | − | 0.115892i | −0.830630 | − | 0.556825i | \(-0.812019\pi\) |
0.897540 | + | 0.440934i | \(0.145353\pi\) | |||||||
\(458\) | −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 | 0.905415 | − | 0.424527i | \(-0.139560\pi\) |
−0.820359 | + | 0.571849i | \(0.806226\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4052 | + | 26.6825i | −0.715939 | + | 1.24004i | 0.246657 | + | 0.969103i | \(0.420668\pi\) |
−0.962596 | + | 0.270940i | \(0.912666\pi\) | |||||||
\(464\) | −8.93905 | −0.414985 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.1153 | −0.885498 | ||||||||
\(467\) | −10.2885 | − | 17.8202i | −0.476096 | − | 0.824622i | 0.523529 | − | 0.852008i | \(-0.324615\pi\) |
−0.999625 | + | 0.0273858i | \(0.991282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.45107 | + | 2.51332i | 0.0669327 | + | 0.115931i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.3324 | − | 21.3604i | −0.567647 | − | 0.983193i | ||||
\(473\) | −5.69752 | − | 9.86839i | −0.261972 | − | 0.453749i | ||||
\(474\) | 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 | ||||
\(479\) | 25.1832 | 1.15065 | 0.575325 | − | 0.817925i | \(-0.304876\pi\) | ||||
0.575325 | + | 0.817925i | \(0.304876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.4478 | −1.43390 | ||||||||
\(482\) | −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 | −0.209173 | − | 0.977879i | \(-0.567077\pi\) |
0.951454 | − | 0.307791i | \(-0.0995896\pi\) | |||||||
\(488\) | −14.5039 | + | 25.1215i | −0.656560 | + | 1.13720i | ||||
\(489\) | 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 | ||||||||
\(493\) | −13.3504 | −0.601272 | ||||||||
\(494\) | 14.3726 | − | 24.8941i | 0.646654 | − | 1.12004i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.30605 | −0.283150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6416 | 0.700216 | 0.350108 | − | 0.936709i | \(-0.386145\pi\) | ||||
0.350108 | + | 0.936709i | \(0.386145\pi\) | |||||||
\(500\) | 1.33029 | + | 2.30412i | 0.0594922 | + | 0.103044i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.23262 | − | 9.06316i | 0.233543 | − | 0.404509i | ||||
\(503\) | −36.5427 | −1.62936 | −0.814678 | − | 0.579913i | \(-0.803086\pi\) | ||||
−0.814678 | + | 0.579913i | \(0.803086\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.62404 | −0.250267 | ||||||||
\(506\) | −3.29358 | + | 5.70465i | −0.146418 | + | 0.253603i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.471969 | − | 0.817474i | −0.0209402 | − | 0.0362696i | ||||
\(509\) | −37.6458 | −1.66862 | −0.834311 | − | 0.551294i | \(-0.814134\pi\) | ||||
−0.834311 | + | 0.551294i | \(0.814134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.4272 | 1.12373 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.4088 | + | 19.7606i | −0.503221 | + | 0.871604i | ||||
\(515\) | −8.23480 | −0.362869 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.373135 | − | 0.646289i | 0.0164105 | − | 0.0284237i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.0508 | + | 29.5329i | −0.747728 | + | 1.29510i | ||||
\(521\) | 7.17115 | − | 12.4208i | 0.314174 | − | 0.544165i | −0.665088 | − | 0.746765i | \(-0.731606\pi\) |
0.979262 | + | 0.202600i | \(0.0649392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.24222 | + | 9.07980i | 0.229226 | + | 0.397032i | 0.957579 | − | 0.288171i | \(-0.0930471\pi\) |
−0.728353 | + | 0.685202i | \(0.759714\pi\) | |||||||
\(524\) | −0.506114 | − | 0.876616i | −0.0221097 | − | 0.0382951i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.1751 | − | 26.2840i | 0.661665 | − | 1.14604i | ||||
\(527\) | −9.41802 | −0.410256 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.51110 | −0.196135 | ||||||||
\(530\) | 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 | ||||||||
\(535\) | −3.92007 | − | 6.78976i | −0.169479 | − | 0.293547i | ||||
\(536\) | −8.00788 | − | 13.8701i | −0.345888 | − | 0.599095i | ||||
\(537\) | 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 | 0.612430 | + | 0.790524i | \(0.290192\pi\) |
0.378399 | + | 0.925643i | \(0.376475\pi\) | |||||||
\(542\) | −18.7376 | −0.804851 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.52542 | 0.365525 | ||||||||
\(545\) | 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 | ||||
\(551\) | −9.34790 | + | 16.1910i | −0.398234 | + | 0.689761i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.2379 | − | 24.6608i | 0.604911 | − | 1.04774i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.15894 | 0.218788 | ||||||||
\(557\) | 15.2888 | − | 26.4809i | 0.647806 | − | 1.12203i | −0.335840 | − | 0.941919i | \(-0.609020\pi\) |
0.983646 | − | 0.180114i | \(-0.0576466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.1394 | −1.31706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.01902 | 0.0851672 | ||||||||
\(563\) | −4.41357 | − | 7.64452i | −0.186010 | − | 0.322178i | 0.757907 | − | 0.652363i | \(-0.226222\pi\) |
−0.943916 | + | 0.330185i | \(0.892889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.20730 | + | 7.28725i | −0.177002 | + | 0.306577i | ||||
\(566\) | −3.44650 | −0.144867 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.84186 | 0.412955 | ||||||||
\(569\) | 3.56027 | − | 6.16658i | 0.149254 | − | 0.258516i | −0.781698 | − | 0.623658i | \(-0.785646\pi\) |
0.930952 | + | 0.365141i | \(0.118979\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.33181 | − | 5.77086i | −0.139432 | − | 0.241503i | 0.787850 | − | 0.615867i | \(-0.211194\pi\) |
−0.927282 | + | 0.374364i | \(0.877861\pi\) | |||||||
\(572\) | 1.17790 | 0.0492503 | ||||||||
\(573\) | 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 | \(-0.780667\pi\) |
0.936550 | + | 0.350535i | \(0.114000\pi\) | |||||||
\(578\) | −9.15254 | −0.380696 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.48963 | − | 2.58011i | 0.0618533 | − | 0.107133i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.31263 | − | 2.27354i | 0.0543634 | − | 0.0941602i | ||||
\(584\) | 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 | 0.613451 | − | 0.789733i | \(-0.289781\pi\) |
−0.990654 | + | 0.136398i | \(0.956447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.59447 | + | 11.4220i | −0.271720 | + | 0.470633i | ||||
\(590\) | −37.6415 | −1.54968 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 32.0574 | 1.31755 | ||||||||
\(593\) | 14.1908 | + | 24.5792i | 0.582745 | + | 1.00934i | 0.995152 | + | 0.0983450i | \(0.0313549\pi\) |
−0.412407 | + | 0.911000i | \(0.635312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.175096 | − | 0.303275i | −0.00717222 | − | 0.0124226i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.00044 | + | 15.5892i | 0.368055 | + | 0.637490i | ||||
\(599\) | 4.69451 | + | 8.13113i | 0.191813 | + | 0.332229i | 0.945851 | − | 0.324601i | \(-0.105230\pi\) |
−0.754038 | + | 0.656830i | \(0.771897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.31432 | + | 10.9367i | 0.257566 | + | 0.446118i | 0.965589 | − | 0.260071i | \(-0.0837460\pi\) |
−0.708023 | + | 0.706189i | \(0.750413\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.04584 | − | 5.27555i | −0.123934 | − | 0.214659i | ||||
\(605\) | −33.8871 | −1.37771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0265 | −0.975207 | −0.487604 | − | 0.873065i | \(-0.662129\pi\) | ||||
−0.487604 | + | 0.873065i | \(0.662129\pi\) | |||||||
\(608\) | 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 | −0.419499 | − | 0.907756i | \(-0.637794\pi\) |
0.995889 | − | 0.0905814i | \(-0.0288725\pi\) | |||||||
\(614\) | 6.91695 | − | 11.9805i | 0.279145 | − | 0.483494i | ||||
\(615\) | 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 | ||||||||
\(619\) | 26.5739 | 1.06810 | 0.534048 | − | 0.845454i | \(-0.320670\pi\) | ||||
0.534048 | + | 0.845454i | \(0.320670\pi\) | |||||||
\(620\) | 1.05085 | − | 1.82013i | 0.0422033 | − | 0.0730983i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.8207 | 0.714545 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.92971 | −0.277188 | ||||||||
\(626\) | −13.7903 | − | 23.8855i | −0.551170 | − | 0.954655i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.44807 | + | 2.50813i | −0.0577843 | + | 0.100085i | ||||
\(629\) | 47.8774 | 1.90900 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.30962 | 0.131754 | 0.0658770 | − | 0.997828i | \(-0.479015\pi\) | ||||
0.0658770 | + | 0.997828i | \(0.479015\pi\) | |||||||
\(632\) | −1.50769 | + | 2.61140i | −0.0599727 | + | 0.103876i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.32055 | − | 4.01931i | −0.0921608 | − | 0.159627i | ||||
\(635\) | −10.7245 | −0.425591 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.17119 | 0.165139 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.0953 | − | 24.4138i | 0.557167 | − | 0.965041i | ||||
\(641\) | −32.5844 | −1.28701 | −0.643503 | − | 0.765443i | \(-0.722520\pi\) | ||||
−0.643503 | + | 0.765443i | \(0.722520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.5327 | + | 37.2957i | −0.849166 | + | 1.47080i | 0.0327873 | + | 0.999462i | \(0.489562\pi\) |
−0.881953 | + | 0.471337i | \(0.843772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.8814 | + | 37.8997i | −0.860912 | + | 1.49114i | ||||
\(647\) | −23.0988 | + | 40.0082i | −0.908106 | + | 1.57289i | −0.0914143 | + | 0.995813i | \(0.529139\pi\) |
−0.816692 | + | 0.577074i | \(0.804195\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | −32.0005 | −1.25228 | −0.626138 | − | 0.779713i | \(-0.715365\pi\) | ||||
−0.626138 | + | 0.779713i | \(0.715365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.5004 | −0.449359 | ||||||||
\(656\) | 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 | ||||||||
\(661\) | 14.0130 | + | 24.2712i | 0.545043 | + | 0.944042i | 0.998604 | + | 0.0528170i | \(0.0168200\pi\) |
−0.453561 | + | 0.891225i | \(0.649847\pi\) | |||||||
\(662\) | −15.5631 | − | 26.9561i | −0.604878 | − | 1.04768i | ||||
\(663\) | 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 | ||||
\(668\) | 1.59709 | 0.0617932 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.4420 | −0.944275 | ||||||||
\(671\) | 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 | ||||
\(677\) | 21.0167 | − | 36.4020i | 0.807737 | − | 1.39904i | −0.106691 | − | 0.994292i | \(-0.534025\pi\) |
0.914428 | − | 0.404749i | \(-0.132641\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 25.9588 | − | 44.9620i | 0.995476 | − | 1.72421i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.94256 | 0.112676 | ||||||||
\(683\) | 17.8645 | − | 30.9422i | 0.683565 | − | 1.18397i | −0.290321 | − | 0.956929i | \(-0.593762\pi\) |
0.973886 | − | 0.227039i | \(-0.0729046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −73.8092 | −2.82010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.7430 | 1.21019 | ||||||||
\(689\) | −3.58704 | − | 6.21294i | −0.136655 | − | 0.236694i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.5675 | + | 44.2841i | −0.972632 | + | 1.68465i | −0.285094 | + | 0.958499i | \(0.592025\pi\) |
−0.687538 | + | 0.726149i | \(0.741308\pi\) | |||||||
\(692\) | −3.02161 | −0.114864 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.66606 | −0.253040 | ||||||||
\(695\) | 29.3066 | − | 50.7606i | 1.11166 | − | 1.92546i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.3115 | + | 28.2524i | 0.617843 | + | 1.07014i | ||||
\(698\) | 19.6795 | 0.744881 | ||||||||
\(699\) | 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 | ||||
\(704\) | −10.4020 | −0.392040 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.4321 | − | 37.1215i | 0.806607 | − | 1.39708i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.4488 | + | 26.7581i | −0.580192 | + | 1.00492i | 0.415265 | + | 0.909701i | \(0.363689\pi\) |
−0.995456 | + | 0.0952206i | \(0.969644\pi\) | |||||||
\(710\) | 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 | ||||
\(716\) | 0.427011 | 0.0159582 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.2431 | −1.16598 | ||||||||
\(719\) | 3.05690 | + | 5.29471i | 0.114003 | + | 0.197459i | 0.917381 | − | 0.398011i | \(-0.130299\pi\) |
−0.803378 | + | 0.595470i | \(0.796966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.2938 | + | 31.6857i | 0.680823 | + | 1.17922i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.879109 | + | 1.52266i | 0.0326718 | + | 0.0565893i | ||||
\(725\) | −10.1174 | − | 17.5238i | −0.375749 | − | 0.650816i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2492 | + | 38.5367i | 0.825176 | + | 1.42925i | 0.901785 | + | 0.432186i | \(0.142257\pi\) |
−0.0766087 | + | 0.997061i | \(0.524409\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.37882 | − | 4.12023i | −0.0880440 | − | 0.152497i | ||||
\(731\) | 47.4079 | 1.75344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.83708 | 0.363341 | 0.181670 | − | 0.983359i | \(-0.441850\pi\) | ||||
0.181670 | + | 0.983359i | \(0.441850\pi\) | |||||||
\(734\) | 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 | −0.969659 | − | 0.244461i | \(-0.921389\pi\) |
0.696539 | + | 0.717519i | \(0.254722\pi\) | |||||||
\(740\) | −5.34212 | + | 9.25282i | −0.196380 | + | 0.340140i | ||||
\(741\) | 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 | ||||||||
\(745\) | −3.97871 | −0.145769 | ||||||||
\(746\) | −20.7449 | + | 35.9311i | −0.759523 | + | 1.31553i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.79328 | −0.0655686 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2010 | 0.810127 | 0.405063 | − | 0.914289i | \(-0.367249\pi\) | ||||
0.405063 | + | 0.914289i | \(0.367249\pi\) | |||||||
\(752\) | 1.03944 | + | 1.80036i | 0.0379044 | + | 0.0656523i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.69934 | − | 9.87156i | 0.207558 | − | 0.359501i | ||||
\(755\) | −69.2106 | −2.51883 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0464 | 0.910329 | 0.455164 | − | 0.890407i | \(-0.349581\pi\) | ||||
0.455164 | + | 0.890407i | \(0.349581\pi\) | |||||||
\(758\) | 19.6723 | − | 34.0735i | 0.714531 | − | 1.23760i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.3526 | − | 62.9645i | −1.31865 | − | 2.28396i | ||||
\(761\) | −6.75264 | −0.244783 | −0.122392 | − | 0.992482i | \(-0.539056\pi\) | ||||
−0.122392 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.76233 | −0.280831 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.12637 | − | 1.95094i | 0.0406975 | − | 0.0704902i | ||||
\(767\) | 26.4510 | 0.955089 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.0805 | − | 36.5125i | 0.760182 | − | 1.31667i | −0.182575 | − | 0.983192i | \(-0.558443\pi\) |
0.942757 | − | 0.333482i | \(-0.108224\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.72065 | − | 4.71230i | 0.0979183 | − | 0.169600i | ||||
\(773\) | 1.64926 | − | 2.85660i | 0.0593197 | − | 0.102745i | −0.834841 | − | 0.550492i | \(-0.814440\pi\) |
0.894160 | + | 0.447747i | \(0.147774\pi\) | |||||||
\(774\) | 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 | ||||
\(779\) | 45.6851 | 1.63684 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.86229 | −0.138203 | ||||||||
\(782\) | −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 | ||||||||
\(787\) | −3.36455 | − | 5.82757i | −0.119933 | − | 0.207731i | 0.799808 | − | 0.600256i | \(-0.204935\pi\) |
−0.919741 | + | 0.392526i | \(0.871601\pi\) | |||||||
\(788\) | 3.06515 | + | 5.30900i | 0.109192 | + | 0.189125i | ||||
\(789\) | 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 | ||||
\(794\) | 32.9376 | 1.16891 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.90321 | −0.209234 | ||||||||
\(797\) | −8.86302 | + | 15.3512i | −0.313944 | + | 0.543767i | −0.979213 | − | 0.202837i | \(-0.934984\pi\) |
0.665268 | + | 0.746604i | \(0.268317\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | −0.611702 | + | 1.05950i | −0.0215865 | + | 0.0373889i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.02060 | − | 6.96388i | 0.141620 | − | 0.245292i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.79028 | −0.168521 | ||||||||
\(809\) | 19.5428 | − | 33.8492i | 0.687089 | − | 1.19007i | −0.285686 | − | 0.958323i | \(-0.592221\pi\) |
0.972775 | − | 0.231751i | \(-0.0744453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9559 | 0.490058 | 0.245029 | − | 0.969516i | \(-0.421203\pi\) | ||||
0.245029 | + | 0.969516i | \(0.421203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.9588 | −0.524305 | ||||||||
\(815\) | −29.7953 | − | 51.6070i | −1.04369 | − | 1.80772i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.1948 | − | 57.4951i | 1.16134 | − | 2.01150i | ||||
\(818\) | −23.7177 | −0.829269 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.28010 | −0.254232 | ||||||||
\(821\) | −22.4983 | + | 38.9682i | −0.785196 | + | 1.36000i | 0.143685 | + | 0.989623i | \(0.454105\pi\) |
−0.928882 | + | 0.370376i | \(0.879229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6232 | + | 47.8449i | 0.962886 | + | 1.66777i | 0.715191 | + | 0.698929i | \(0.246340\pi\) |
0.247694 | + | 0.968838i | \(0.420327\pi\) | |||||||
\(824\) | −7.01400 | −0.244344 | ||||||||
\(825\) | 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 | −0.299006 | − | 0.954251i | \(-0.596655\pi\) |
0.975909 | − | 0.218179i | \(-0.0700115\pi\) | |||||||
\(830\) | −33.5117 | −1.16321 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.2129 | + | 24.6174i | −0.492743 | + | 0.853456i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.07266 | − | 15.7143i | 0.313972 | − | 0.543816i | ||||
\(836\) | −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 | \(0.0679862\pi\) |
−0.305072 | + | 0.952329i | \(0.598680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7932 | − | 18.6943i | 0.372178 | − | 0.644631i | ||||
\(842\) | 0.375119 | 0.0129275 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.30769 | 0.0794340 | ||||||||
\(845\) | 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 | ||||||||
\(850\) | −23.6825 | − | 41.0193i | −0.812304 | − | 1.40695i | ||||
\(851\) | 20.9932 | + | 36.3613i | 0.719638 | + | 1.24645i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.83890 | − | 6.64916i | −0.131441 | − | 0.227663i | 0.792791 | − | 0.609493i | \(-0.208627\pi\) |
−0.924232 | + | 0.381830i | \(0.875294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.33892 | − | 5.78318i | −0.114122 | − | 0.197665i | ||||
\(857\) | 15.9639 | 0.545316 | 0.272658 | − | 0.962111i | \(-0.412097\pi\) | ||||
0.272658 | + | 0.962111i | \(0.412097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.3291 | 1.64897 | 0.824483 | − | 0.565887i | \(-0.191466\pi\) | ||||
0.824483 | + | 0.565887i | \(0.191466\pi\) | |||||||
\(860\) | −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 | −0.995014 | − | 0.0997366i | \(-0.968200\pi\) |
0.411133 | − | 0.911576i | \(-0.365133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1650 | + | 29.7307i | −0.583628 | + | 1.01087i | ||||
\(866\) | 3.15356 | − | 5.46212i | 0.107162 | − | 0.185611i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.591670 | − | 1.02480i | 0.0200710 | − | 0.0347640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.1755 | 0.581970 | ||||||||
\(872\) | 1.38079 | − | 2.39159i | 0.0467594 | − | 0.0809896i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −38.3781 | −1.29816 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1815 | 0.478876 | 0.239438 | − | 0.970912i | \(-0.423037\pi\) | ||||
0.239438 | + | 0.970912i | \(0.423037\pi\) | |||||||
\(878\) | −1.65599 | − | 2.86826i | −0.0558870 | − | 0.0967992i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.82103 | + | 11.8144i | −0.229937 | + | 0.398262i | ||||
\(881\) | 46.2822 | 1.55929 | 0.779643 | − | 0.626224i | \(-0.215400\pi\) | ||||
0.779643 | + | 0.626224i | \(0.215400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.37483 | −0.147225 | −0.0736124 | − | 0.997287i | \(-0.523453\pi\) | ||||
−0.0736124 | + | 0.997287i | \(0.523453\pi\) | |||||||
\(884\) | −2.45026 | + | 4.24397i | −0.0824111 | + | 0.142740i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.419538 | + | 0.726661i | 0.0140946 | + | 0.0244126i | ||||
\(887\) | 19.1442 | 0.642798 | 0.321399 | − | 0.946944i | \(-0.395847\pi\) | ||||
0.321399 | + | 0.946944i | \(0.395847\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −55.1942 | −1.85011 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.510697 | − | 0.884554i | 0.0170994 | − | 0.0296171i | ||||
\(893\) | 4.34791 | 0.145497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.42574 | − | 4.20151i | 0.0810836 | − | 0.140441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.39694 | − | 5.88368i | 0.113358 | − | 0.196341i | ||||
\(899\) | −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 | ||||
\(905\) | 19.9760 | 0.664024 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.8450 | 1.32303 | 0.661515 | − | 0.749932i | \(-0.269914\pi\) | ||||
0.661515 | + | 0.749932i | \(0.269914\pi\) | |||||||
\(908\) | −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 | ||||||||
\(913\) | 4.30870 | + | 7.46288i | 0.142597 | + | 0.246985i | ||||
\(914\) | −1.85930 | − | 3.22041i | −0.0615003 | − | 0.106522i | ||||
\(915\) | 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 | 0.967390 | − | 0.253290i | \(-0.0815126\pi\) |
−0.703051 | + | 0.711140i | \(0.748179\pi\) | |||||||
\(920\) | 45.5296 | 1.50107 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.74776 | 0.156359 | ||||||||
\(923\) | −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 | ||||
\(929\) | 7.00796 | − | 12.1381i | 0.229924 | − | 0.398239i | −0.727862 | − | 0.685724i | \(-0.759486\pi\) |
0.957785 | + | 0.287485i | \(0.0928190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.28180 | − | 3.95219i | 0.0747428 | − | 0.129458i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.7475 | −0.875205 | ||||||||
\(935\) | −10.1871 | + | 17.6447i | −0.333155 | + | 0.577042i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.5307 | 1.68344 | 0.841718 | − | 0.539918i | \(-0.181545\pi\) | ||||
0.841718 | + | 0.539918i | \(0.181545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.692857 | −0.0225985 | ||||||||
\(941\) | −23.1564 | − | 40.1081i | −0.754877 | − | 1.30749i | −0.945435 | − | 0.325809i | \(-0.894363\pi\) |
0.190558 | − | 0.981676i | \(-0.438970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.3045 | + | 24.7761i | −0.465819 | + | 0.806821i | ||||
\(944\) | −26.9636 | −0.877592 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.8121 | −0.481582 | ||||||||
\(947\) | 10.0041 | − | 17.3277i | 0.325091 | − | 0.563073i | −0.656440 | − | 0.754378i | \(-0.727939\pi\) |
0.981531 | + | 0.191305i | \(0.0612719\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.67161 | + | 2.89531i | 0.0542628 | + | 0.0939859i | ||||
\(950\) | −66.3297 | −2.15202 | ||||||||
\(951\) | 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 | ||||
\(956\) | −4.39547 | −0.142160 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.3675 | − | 28.3493i | 0.528809 | − | 0.915924i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6553 | − | 23.6516i | 0.440492 | − | 0.762955i | ||||
\(962\) | −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 | \(-0.0122398\pi\) | |||||||
\(968\) | −28.8633 | −0.927702 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 50.0896 | 1.60828 | ||||||||
\(971\) | 20.8234 | + | 36.0672i | 0.668256 | + | 1.15745i | 0.978392 | + | 0.206761i | \(0.0662921\pi\) |
−0.310136 | + | 0.950692i | \(0.600375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −21.2928 | − | 36.8803i | −0.682267 | − | 1.18172i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.8556 | + | 27.4628i | 0.507527 | + | 0.879062i | ||||
\(977\) | 18.7590 | + | 32.4916i | 0.600154 | + | 1.03950i | 0.992797 | + | 0.119807i | \(0.0382276\pi\) |
−0.392643 | + | 0.919691i | \(0.628439\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | −48.0758 | −1.53338 | −0.766690 | − | 0.642017i | \(-0.778098\pi\) | ||||
−0.766690 | + | 0.642017i | \(0.778098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 69.6495 | 2.21922 | ||||||||
\(986\) | −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 | −0.456720 | − | 0.889610i | \(-0.650976\pi\) |
0.998785 | − | 0.0492737i | \(-0.0156907\pi\) | |||||||
\(992\) | 1.66990 | − | 2.89236i | 0.0530195 | − | 0.0918324i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.5346 | + | 58.0837i | −1.06312 | + | 1.84138i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0827 | −1.39611 | −0.698056 | − | 0.716043i | \(-0.745951\pi\) | ||||
−0.698056 | + | 0.716043i | \(0.745951\pi\) | |||||||
\(998\) | 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.g.h.361.9 | 24 | ||
3.2 | odd | 2 | 441.2.g.h.67.4 | 24 | |||
7.2 | even | 3 | 1323.2.h.h.226.4 | 24 | |||
7.3 | odd | 6 | 1323.2.f.h.442.10 | 24 | |||
7.4 | even | 3 | 1323.2.f.h.442.9 | 24 | |||
7.5 | odd | 6 | 1323.2.h.h.226.3 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.g.h.361.10 | 24 | ||
9.2 | odd | 6 | 441.2.h.h.214.9 | 24 | |||
9.7 | even | 3 | 1323.2.h.h.802.4 | 24 | |||
21.2 | odd | 6 | 441.2.h.h.373.9 | 24 | |||
21.5 | even | 6 | 441.2.h.h.373.10 | 24 | |||
21.11 | odd | 6 | 441.2.f.h.148.3 | ✓ | 24 | ||
21.17 | even | 6 | 441.2.f.h.148.4 | yes | 24 | ||
21.20 | even | 2 | 441.2.g.h.67.3 | 24 | |||
63.2 | odd | 6 | 441.2.g.h.79.4 | 24 | |||
63.4 | even | 3 | 3969.2.a.bi.1.4 | 12 | |||
63.11 | odd | 6 | 441.2.f.h.295.3 | yes | 24 | ||
63.16 | even | 3 | inner | 1323.2.g.h.667.9 | 24 | ||
63.20 | even | 6 | 441.2.h.h.214.10 | 24 | |||
63.25 | even | 3 | 1323.2.f.h.883.9 | 24 | |||
63.31 | odd | 6 | 3969.2.a.bi.1.3 | 12 | |||
63.32 | odd | 6 | 3969.2.a.bh.1.9 | 12 | |||
63.34 | odd | 6 | 1323.2.h.h.802.3 | 24 | |||
63.38 | even | 6 | 441.2.f.h.295.4 | yes | 24 | ||
63.47 | even | 6 | 441.2.g.h.79.3 | 24 | |||
63.52 | odd | 6 | 1323.2.f.h.883.10 | 24 | |||
63.59 | even | 6 | 3969.2.a.bh.1.10 | 12 | |||
63.61 | odd | 6 | inner | 1323.2.g.h.667.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.3 | ✓ | 24 | 21.11 | odd | 6 | ||
441.2.f.h.148.4 | yes | 24 | 21.17 | even | 6 | ||
441.2.f.h.295.3 | yes | 24 | 63.11 | odd | 6 | ||
441.2.f.h.295.4 | yes | 24 | 63.38 | even | 6 | ||
441.2.g.h.67.3 | 24 | 21.20 | even | 2 | |||
441.2.g.h.67.4 | 24 | 3.2 | odd | 2 | |||
441.2.g.h.79.3 | 24 | 63.47 | even | 6 | |||
441.2.g.h.79.4 | 24 | 63.2 | odd | 6 | |||
441.2.h.h.214.9 | 24 | 9.2 | odd | 6 | |||
441.2.h.h.214.10 | 24 | 63.20 | even | 6 | |||
441.2.h.h.373.9 | 24 | 21.2 | odd | 6 | |||
441.2.h.h.373.10 | 24 | 21.5 | even | 6 | |||
1323.2.f.h.442.9 | 24 | 7.4 | even | 3 | |||
1323.2.f.h.442.10 | 24 | 7.3 | odd | 6 | |||
1323.2.f.h.883.9 | 24 | 63.25 | even | 3 | |||
1323.2.f.h.883.10 | 24 | 63.52 | odd | 6 | |||
1323.2.g.h.361.9 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.g.h.361.10 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.g.h.667.9 | 24 | 63.16 | even | 3 | inner | ||
1323.2.g.h.667.10 | 24 | 63.61 | odd | 6 | inner | ||
1323.2.h.h.226.3 | 24 | 7.5 | odd | 6 | |||
1323.2.h.h.226.4 | 24 | 7.2 | even | 3 | |||
1323.2.h.h.802.3 | 24 | 63.34 | odd | 6 | |||
1323.2.h.h.802.4 | 24 | 9.7 | even | 3 | |||
3969.2.a.bh.1.9 | 12 | 63.32 | odd | 6 | |||
3969.2.a.bh.1.10 | 12 | 63.59 | even | 6 | |||
3969.2.a.bi.1.3 | 12 | 63.31 | odd | 6 | |||
3969.2.a.bi.1.4 | 12 | 63.4 | even | 3 |