Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(67,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.3 | ||
Character | \(\chi\) | \(=\) | 441.79 |
Dual form | 441.2.g.h.67.3 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(-0.318665\pi\) |
−0.998938 | + | 0.0460668i | \(0.985331\pi\) | |||||||
\(3\) | −1.52504 | + | 0.821126i | −0.880483 | + | 0.474077i | ||||
\(4\) | 0.155166 | − | 0.268756i | 0.0775831 | − | 0.134378i | ||||
\(5\) | 3.52584 | 1.57680 | 0.788402 | − | 0.615160i | \(-0.210909\pi\) | ||||
0.788402 | + | 0.615160i | \(0.210909\pi\) | |||||||
\(6\) | 1.91554 | + | 1.18309i | 0.782016 | + | 0.482996i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00314 | −1.06177 | ||||||||
\(9\) | 1.65150 | − | 2.50450i | 0.550501 | − | 0.834834i | ||||
\(10\) | −2.29157 | − | 3.96912i | −0.724659 | − | 1.25515i | ||||
\(11\) | 1.17853 | 0.355342 | 0.177671 | − | 0.984090i | \(-0.443144\pi\) | ||||
0.177671 | + | 0.984090i | \(0.443144\pi\) | |||||||
\(12\) | −0.0159526 | + | 0.537275i | −0.00460513 | + | 0.155098i | ||||
\(13\) | 1.61030 | + | 2.78913i | 0.446618 | + | 0.773564i | 0.998163 | − | 0.0605803i | \(-0.0192951\pi\) |
−0.551546 | + | 0.834145i | \(0.685962\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.37706 | + | 2.89516i | −1.38835 | + | 0.747527i | ||||
\(16\) | 1.64151 | + | 2.84319i | 0.410379 | + | 0.710797i | ||||
\(17\) | 2.45159 | + | 4.24627i | 0.594597 | + | 1.02987i | 0.993604 | + | 0.112924i | \(0.0360218\pi\) |
−0.399006 | + | 0.916948i | \(0.630645\pi\) | |||||||
\(18\) | −3.89275 | − | 0.231369i | −0.917529 | − | 0.0545342i | ||||
\(19\) | 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 | ||||
\(23\) | −4.29987 | −0.896585 | −0.448293 | − | 0.893887i | \(-0.647968\pi\) | ||||
−0.448293 | + | 0.893887i | \(0.647968\pi\) | |||||||
\(24\) | 4.57991 | − | 2.46595i | 0.934870 | − | 0.503361i | ||||
\(25\) | 7.43156 | 1.48631 | ||||||||
\(26\) | 2.09319 | − | 3.62551i | 0.410508 | − | 0.711020i | ||||
\(27\) | −0.462101 | + | 5.17556i | −0.0889314 | + | 0.996038i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.36140 | − | 2.35802i | 0.252806 | − | 0.437873i | −0.711491 | − | 0.702695i | \(-0.751980\pi\) |
0.964297 | + | 0.264822i | \(0.0853131\pi\) | |||||||
\(30\) | 6.75389 | + | 4.17140i | 1.23309 | + | 0.761590i | ||||
\(31\) | 0.960401 | − | 1.66346i | 0.172493 | − | 0.298767i | −0.766798 | − | 0.641889i | \(-0.778151\pi\) |
0.939291 | + | 0.343122i | \(0.111484\pi\) | |||||||
\(32\) | −0.869378 | + | 1.50581i | −0.153686 | + | 0.266192i | ||||
\(33\) | −1.79731 | + | 0.967725i | −0.312872 | + | 0.168459i | ||||
\(34\) | 3.18675 | − | 5.51961i | 0.546523 | − | 0.946606i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.416842 | − | 0.832466i | −0.0694737 | − | 0.138744i | ||||
\(37\) | 4.88229 | − | 8.45637i | 0.802643 | − | 1.39022i | −0.115228 | − | 0.993339i | \(-0.536760\pi\) |
0.917871 | − | 0.396879i | \(-0.129907\pi\) | |||||||
\(38\) | −8.92540 | −1.44789 | ||||||||
\(39\) | −4.74600 | − | 2.93127i | −0.759969 | − | 0.469379i | ||||
\(40\) | −10.5886 | −1.67420 | ||||||||
\(41\) | −3.32673 | − | 5.76206i | −0.519547 | − | 0.899883i | −0.999742 | − | 0.0227205i | \(-0.992767\pi\) |
0.480194 | − | 0.877162i | \(-0.340566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.83441 | − | 8.37344i | 0.737240 | − | 1.27694i | −0.216493 | − | 0.976284i | \(-0.569462\pi\) |
0.953734 | − | 0.300653i | \(-0.0972047\pi\) | |||||||
\(44\) | 0.182869 | − | 0.316738i | 0.0275685 | − | 0.0477501i | ||||
\(45\) | 5.82294 | − | 8.83048i | 0.868033 | − | 1.31637i | ||||
\(46\) | 2.79464 | + | 4.84046i | 0.412047 | + | 0.713687i | ||||
\(47\) | −0.316609 | − | 0.548383i | −0.0461822 | − | 0.0799899i | 0.842010 | − | 0.539461i | \(-0.181372\pi\) |
−0.888192 | + | 0.459472i | \(0.848039\pi\) | |||||||
\(48\) | −4.83799 | − | 2.98809i | −0.698304 | − | 0.431293i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.83004 | − | 8.36587i | −0.683071 | − | 1.18311i | ||||
\(51\) | −7.22550 | − | 4.46268i | −1.01177 | − | 0.624900i | ||||
\(52\) | 0.999459 | 0.138600 | ||||||||
\(53\) | 1.11378 | + | 1.92912i | 0.152989 | + | 0.264985i | 0.932325 | − | 0.361621i | \(-0.117777\pi\) |
−0.779336 | + | 0.626606i | \(0.784443\pi\) | |||||||
\(54\) | 6.12658 | − | 2.84359i | 0.833722 | − | 0.386963i | ||||
\(55\) | 4.15533 | 0.560304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.352965 | + | 11.8877i | −0.0467514 | + | 1.57456i | ||||
\(58\) | −3.53930 | −0.464733 | ||||||||
\(59\) | −4.10652 | + | 7.11270i | −0.534623 | + | 0.925995i | 0.464558 | + | 0.885543i | \(0.346213\pi\) |
−0.999181 | + | 0.0404521i | \(0.987120\pi\) | |||||||
\(60\) | −0.0562464 | + | 1.89435i | −0.00726138 | + | 0.244559i | ||||
\(61\) | 4.82958 | + | 8.36508i | 0.618364 | + | 1.07104i | 0.989784 | + | 0.142573i | \(0.0455376\pi\) |
−0.371420 | + | 0.928465i | \(0.621129\pi\) | |||||||
\(62\) | −2.49680 | −0.317093 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.82622 | 1.10328 | ||||||||
\(65\) | 5.67767 | + | 9.83402i | 0.704229 | + | 1.21976i | ||||
\(66\) | 2.25753 | + | 1.39432i | 0.277883 | + | 0.171629i | ||||
\(67\) | −2.66651 | + | 4.61852i | −0.325766 | + | 0.564242i | −0.981667 | − | 0.190604i | \(-0.938955\pi\) |
0.655901 | + | 0.754847i | \(0.272289\pi\) | |||||||
\(68\) | 1.52161 | 0.184523 | ||||||||
\(69\) | 6.55748 | − | 3.53074i | 0.789428 | − | 0.425051i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.27719 | −0.388931 | −0.194466 | − | 0.980909i | \(-0.562297\pi\) | ||||
−0.194466 | + | 0.980909i | \(0.562297\pi\) | |||||||
\(72\) | −4.95969 | + | 7.52136i | −0.584506 | + | 0.886401i | ||||
\(73\) | −0.519036 | − | 0.898997i | −0.0607486 | − | 0.105220i | 0.834052 | − | 0.551686i | \(-0.186015\pi\) |
−0.894800 | + | 0.446467i | \(0.852682\pi\) | |||||||
\(74\) | −12.6927 | −1.47550 | ||||||||
\(75\) | −11.3334 | + | 6.10225i | −1.30867 | + | 0.704627i | ||||
\(76\) | −1.06543 | − | 1.84538i | −0.122213 | − | 0.211679i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.215200 | + | 7.24782i | −0.0243666 | + | 0.820654i | ||||
\(79\) | −0.502039 | − | 0.869557i | −0.0564838 | − | 0.0978328i | 0.836401 | − | 0.548118i | \(-0.184656\pi\) |
−0.892885 | + | 0.450285i | \(0.851322\pi\) | |||||||
\(80\) | 5.78772 | + | 10.0246i | 0.647087 | + | 1.12079i | ||||
\(81\) | −3.54507 | − | 8.27239i | −0.393896 | − | 0.919155i | ||||
\(82\) | −4.32432 | + | 7.48994i | −0.477541 | + | 0.827126i | ||||
\(83\) | −3.65598 | + | 6.33234i | −0.401296 | + | 0.695064i | −0.993883 | − | 0.110442i | \(-0.964773\pi\) |
0.592587 | + | 0.805506i | \(0.298107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.64391 | + | 14.9717i | 0.937563 | + | 1.62391i | ||||
\(86\) | −12.5682 | −1.35527 | ||||||||
\(87\) | −0.139966 | + | 4.71396i | −0.0150059 | + | 0.505390i | ||||
\(88\) | −3.53930 | −0.377291 | ||||||||
\(89\) | −6.02144 | + | 10.4294i | −0.638271 | + | 1.10552i | 0.347541 | + | 0.937665i | \(0.387017\pi\) |
−0.985812 | + | 0.167853i | \(0.946317\pi\) | |||||||
\(90\) | −13.7252 | − | 0.815770i | −1.44676 | − | 0.0859897i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.667195 | + | 1.15562i | −0.0695599 | + | 0.120481i | ||||
\(93\) | −0.0987387 | + | 3.32546i | −0.0102387 | + | 0.344834i | ||||
\(94\) | −0.411551 | + | 0.712828i | −0.0424483 | + | 0.0735226i | ||||
\(95\) | 12.1049 | − | 20.9662i | 1.24193 | − | 2.15109i | ||||
\(96\) | 0.0893807 | − | 3.01029i | 0.00912238 | − | 0.307236i | ||||
\(97\) | −5.46454 | + | 9.46487i | −0.554840 | + | 0.961012i | 0.443076 | + | 0.896484i | \(0.353887\pi\) |
−0.997916 | + | 0.0645275i | \(0.979446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.94636 | − | 2.95164i | 0.195616 | − | 0.296651i | ||||
\(100\) | 1.15313 | − | 1.99728i | 0.115313 | − | 0.199728i | ||||
\(101\) | −1.59509 | −0.158718 | −0.0793588 | − | 0.996846i | \(-0.525287\pi\) | ||||
−0.0793588 | + | 0.996846i | \(0.525287\pi\) | |||||||
\(102\) | −0.327629 | + | 11.0344i | −0.0324401 | + | 1.09256i | ||||
\(103\) | 2.33556 | 0.230129 | 0.115065 | − | 0.993358i | \(-0.463292\pi\) | ||||
0.115065 | + | 0.993358i | \(0.463292\pi\) | |||||||
\(104\) | −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 | \(-0.799054\pi\) |
0.914750 | + | 0.404021i | \(0.132388\pi\) | |||||||
\(108\) | 1.31926 | + | 0.927265i | 0.126946 | + | 0.0892262i | ||||
\(109\) | 0.459782 | + | 0.796366i | 0.0440391 | + | 0.0762780i | 0.887205 | − | 0.461376i | \(-0.152644\pi\) |
−0.843166 | + | 0.537654i | \(0.819311\pi\) | |||||||
\(110\) | −2.70070 | − | 4.67774i | −0.257501 | − | 0.446005i | ||||
\(111\) | −0.501947 | + | 16.9053i | −0.0476427 | + | 1.60458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.19327 | + | 2.06681i | 0.112254 | + | 0.194429i | 0.916679 | − | 0.399625i | \(-0.130860\pi\) |
−0.804425 | + | 0.594054i | \(0.797526\pi\) | |||||||
\(114\) | 13.6116 | − | 7.32888i | 1.27484 | − | 0.686412i | ||||
\(115\) | −15.1607 | −1.41374 | ||||||||
\(116\) | −0.422488 | − | 0.731770i | −0.0392270 | − | 0.0679432i | ||||
\(117\) | 9.64479 | + | 0.573247i | 0.891662 | + | 0.0529967i | ||||
\(118\) | 10.6759 | 0.982796 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 16.1480 | − | 8.69456i | 1.47411 | − | 0.793701i | ||||
\(121\) | −9.61106 | −0.873732 | ||||||||
\(122\) | 6.27783 | − | 10.8735i | 0.568368 | − | 0.984443i | ||||
\(123\) | 9.80477 | + | 6.05572i | 0.884067 | + | 0.546026i | ||||
\(124\) | −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 | ||||
\(129\) | −0.497025 | + | 16.7395i | −0.0437606 | + | 1.47383i | ||||
\(130\) | 7.38025 | − | 12.7830i | 0.647291 | − | 1.12114i | ||||
\(131\) | −3.26176 | −0.284981 | −0.142490 | − | 0.989796i | \(-0.545511\pi\) | ||||
−0.142490 | + | 0.989796i | \(0.545511\pi\) | |||||||
\(132\) | −0.0188007 | + | 0.633197i | −0.00163639 | + | 0.0551127i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.93223 | 0.598854 | ||||||||
\(135\) | −1.62930 | + | 18.2482i | −0.140227 | + | 1.57056i | ||||
\(136\) | −7.36245 | − | 12.7521i | −0.631325 | − | 1.09349i | ||||
\(137\) | 20.9338 | 1.78849 | 0.894246 | − | 0.447575i | \(-0.147712\pi\) | ||||
0.894246 | + | 0.447575i | \(0.147712\pi\) | |||||||
\(138\) | −8.23657 | − | 5.08715i | −0.701144 | − | 0.433047i | ||||
\(139\) | −8.31195 | − | 14.3967i | −0.705010 | − | 1.22111i | −0.966688 | − | 0.255958i | \(-0.917609\pi\) |
0.261677 | − | 0.965155i | \(-0.415724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.933134 | + | 0.576331i | 0.0785840 | + | 0.0485358i | ||||
\(142\) | 2.12997 | + | 3.68921i | 0.178743 | + | 0.309592i | ||||
\(143\) | 1.89780 | + | 3.28708i | 0.158702 | + | 0.274880i | ||||
\(144\) | 9.83174 | + | 0.584358i | 0.819311 | + | 0.0486965i | ||||
\(145\) | 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 | \(-0.485282\pi\) | ||||
0.0462228 | + | 0.998931i | \(0.485282\pi\) | |||||||
\(150\) | 14.2354 | + | 8.79224i | 1.16232 | + | 0.717883i | ||||
\(151\) | −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 | ||||
\(153\) | 14.6836 | + | 0.872733i | 1.18710 | + | 0.0705563i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.38622 | − | 5.86511i | 0.271988 | − | 0.471097i | ||||
\(156\) | −1.52422 | + | 0.820681i | −0.122035 | + | 0.0657071i | ||||
\(157\) | −4.66619 | + | 8.08207i | −0.372402 | + | 0.645020i | −0.989935 | − | 0.141526i | \(-0.954799\pi\) |
0.617532 | + | 0.786545i | \(0.288132\pi\) | |||||||
\(158\) | −0.652586 | + | 1.13031i | −0.0519170 | + | 0.0899228i | ||||
\(159\) | −3.28261 | − | 2.02744i | −0.260328 | − | 0.160786i | ||||
\(160\) | −3.06529 | + | 5.30924i | −0.242332 | + | 0.419732i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.00835 | + | 9.36729i | −0.550628 | + | 0.735964i | ||||
\(163\) | −8.45056 | + | 14.6368i | −0.661899 | + | 1.14644i | 0.318217 | + | 0.948018i | \(0.396916\pi\) |
−0.980116 | + | 0.198425i | \(0.936417\pi\) | |||||||
\(164\) | −2.06478 | −0.161232 | ||||||||
\(165\) | −6.33705 | + | 3.41205i | −0.493338 | + | 0.265627i | ||||
\(166\) | 9.50460 | 0.737700 | ||||||||
\(167\) | 2.57319 | + | 4.45689i | 0.199119 | + | 0.344885i | 0.948243 | − | 0.317545i | \(-0.102859\pi\) |
−0.749124 | + | 0.662430i | \(0.769525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.31385 | − | 2.27566i | 0.101066 | − | 0.175051i | ||||
\(170\) | 11.2360 | − | 19.4613i | 0.861760 | − | 1.49261i | ||||
\(171\) | −9.22298 | − | 18.4190i | −0.705299 | − | 1.40854i | ||||
\(172\) | −1.50027 | − | 2.59855i | −0.114395 | − | 0.198138i | ||||
\(173\) | −4.86834 | − | 8.43222i | −0.370133 | − | 0.641090i | 0.619453 | − | 0.785034i | \(-0.287355\pi\) |
−0.989586 | + | 0.143945i | \(0.954021\pi\) | |||||||
\(174\) | 5.39758 | − | 2.90621i | 0.409190 | − | 0.220319i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.93458 | + | 3.35079i | 0.145825 | + | 0.252576i | ||||
\(177\) | 0.422191 | − | 14.2191i | 0.0317338 | − | 1.06878i | ||||
\(178\) | 15.6542 | 1.17333 | ||||||||
\(179\) | −0.687990 | − | 1.19163i | −0.0514228 | − | 0.0890668i | 0.839168 | − | 0.543872i | \(-0.183042\pi\) |
−0.890591 | + | 0.454805i | \(0.849709\pi\) | |||||||
\(180\) | −1.46972 | − | 2.93514i | −0.109546 | − | 0.218773i | ||||
\(181\) | −5.66560 | −0.421120 | −0.210560 | − | 0.977581i | \(-0.567529\pi\) | ||||
−0.210560 | + | 0.977581i | \(0.567529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2341 | − | 8.79140i | −1.05221 | − | 0.649879i | ||||
\(184\) | 12.9131 | 0.951967 | ||||||||
\(185\) | 17.2142 | − | 29.8158i | 1.26561 | − | 2.19210i | ||||
\(186\) | 3.80772 | − | 2.05018i | 0.279196 | − | 0.150327i | ||||
\(187\) | 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 | 0.821003 | + | 0.570925i | \(0.193415\pi\) |
0.0839339 | + | 0.996471i | \(0.473252\pi\) | |||||||
\(192\) | −13.4604 | + | 7.24744i | −0.971417 | + | 0.523039i | ||||
\(193\) | −8.76688 | + | 15.1847i | −0.631054 | + | 1.09302i | 0.356282 | + | 0.934378i | \(0.384044\pi\) |
−0.987337 | + | 0.158640i | \(0.949289\pi\) | |||||||
\(194\) | 14.2064 | 1.01996 | ||||||||
\(195\) | −16.7337 | − | 10.3352i | −1.19832 | − | 0.740119i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.7540 | −1.40741 | −0.703707 | − | 0.710490i | \(-0.748473\pi\) | ||||
−0.703707 | + | 0.710490i | \(0.748473\pi\) | |||||||
\(198\) | −4.58774 | − | 0.272676i | −0.326036 | − | 0.0193783i | ||||
\(199\) | 9.51110 | + | 16.4737i | 0.674224 | + | 1.16779i | 0.976695 | + | 0.214631i | \(0.0688550\pi\) |
−0.302471 | + | 0.953158i | \(0.597812\pi\) | |||||||
\(200\) | −22.3180 | −1.57812 | ||||||||
\(201\) | 0.274143 | − | 9.23298i | 0.0193366 | − | 0.651244i | ||||
\(202\) | 1.03671 | + | 1.79563i | 0.0729425 | + | 0.126340i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.32053 | + | 1.24944i | −0.162469 | + | 0.0874781i | ||||
\(205\) | −11.7295 | − | 20.3161i | −0.819225 | − | 1.41894i | ||||
\(206\) | −1.51796 | − | 2.62919i | −0.105761 | − | 0.183184i | ||||
\(207\) | −7.10126 | + | 10.7690i | −0.493572 | + | 0.748500i | ||||
\(208\) | −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 | 0.965157 | − | 0.261672i | \(-0.0842738\pi\) |
−0.709193 | + | 0.705015i | \(0.750940\pi\) | |||||||
\(212\) | 0.691283 | 0.0474775 | ||||||||
\(213\) | 4.99786 | − | 2.69099i | 0.342447 | − | 0.184383i | ||||
\(214\) | −2.89043 | −0.197585 | ||||||||
\(215\) | 17.0454 | − | 29.5234i | 1.16248 | − | 2.01348i | ||||
\(216\) | 1.38775 | − | 15.5429i | 0.0944246 | − | 1.05756i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.597658 | − | 1.03517i | 0.0404785 | − | 0.0701108i | ||||
\(219\) | 1.52974 | + | 0.944814i | 0.103370 | + | 0.0638446i | ||||
\(220\) | 0.644767 | − | 1.11677i | 0.0434702 | − | 0.0752925i | ||||
\(221\) | −7.89559 | + | 13.6756i | −0.531115 | + | 0.919918i | ||||
\(222\) | 19.3569 | − | 10.4223i | 1.29915 | − | 0.699499i | ||||
\(223\) | 1.64565 | − | 2.85034i | 0.110201 | − | 0.190873i | −0.805650 | − | 0.592391i | \(-0.798184\pi\) |
0.915851 | + | 0.401518i | \(0.131517\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2733 | − | 18.6124i | 0.818217 | − | 1.24082i | ||||
\(226\) | 1.55110 | − | 2.68659i | 0.103178 | − | 0.178709i | ||||
\(227\) | −18.0169 | −1.19583 | −0.597913 | − | 0.801561i | \(-0.704003\pi\) | ||||
−0.597913 | + | 0.801561i | \(0.704003\pi\) | |||||||
\(228\) | 3.14011 | + | 1.93943i | 0.207959 | + | 0.128442i | ||||
\(229\) | 4.25491 | 0.281173 | 0.140586 | − | 0.990068i | \(-0.455101\pi\) | ||||
0.140586 | + | 0.990068i | \(0.455101\pi\) | |||||||
\(230\) | 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 | \(-0.673355\pi\) |
0.999779 | + | 0.0210095i | \(0.00668801\pi\) | |||||||
\(234\) | −5.62318 | − | 11.2299i | −0.367599 | − | 0.734124i | ||||
\(235\) | −1.11631 | − | 1.93351i | −0.0728203 | − | 0.126128i | ||||
\(236\) | 1.27439 | + | 2.20730i | 0.0829555 | + | 0.143683i | ||||
\(237\) | 1.47965 | + | 0.913873i | 0.0961133 | + | 0.0593624i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.08187 | + | 12.2662i | 0.458088 | + | 0.793432i | 0.998860 | − | 0.0477377i | \(-0.0152011\pi\) |
−0.540772 | + | 0.841169i | \(0.681868\pi\) | |||||||
\(240\) | −17.0580 | − | 10.5355i | −1.10109 | − | 0.680065i | ||||
\(241\) | 7.93503 | 0.511140 | 0.255570 | − | 0.966791i | \(-0.417737\pi\) | ||||
0.255570 | + | 0.966791i | \(0.417737\pi\) | |||||||
\(242\) | 6.24657 | + | 10.8194i | 0.401545 | + | 0.695496i | ||||
\(243\) | 12.1991 | + | 9.70480i | 0.782569 | + | 0.622563i | ||||
\(244\) | 2.99755 | 0.191899 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.444583 | − | 14.9733i | 0.0283456 | − | 0.954662i | ||||
\(247\) | 22.1139 | 1.40707 | ||||||||
\(248\) | −2.88422 | + | 4.99561i | −0.183148 | + | 0.317221i | ||||
\(249\) | 0.375871 | − | 12.6591i | 0.0238198 | − | 0.802238i | ||||
\(250\) | −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 | ||||
\(255\) | −25.4760 | − | 15.7347i | −1.59537 | − | 0.985346i | ||||
\(256\) | 3.62969 | − | 6.28681i | 0.226856 | − | 0.392926i | ||||
\(257\) | −17.5537 | −1.09497 | −0.547486 | − | 0.836815i | \(-0.684415\pi\) | ||||
−0.547486 | + | 0.836815i | \(0.684415\pi\) | |||||||
\(258\) | 19.1671 | − | 10.3201i | 1.19329 | − | 0.642501i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.52393 | 0.218545 | ||||||||
\(261\) | −3.65730 | − | 7.30392i | −0.226381 | − | 0.452101i | ||||
\(262\) | 2.11993 | + | 3.67183i | 0.130970 | + | 0.226846i | ||||
\(263\) | −23.3486 | −1.43973 | −0.719867 | − | 0.694112i | \(-0.755797\pi\) | ||||
−0.719867 | + | 0.694112i | \(0.755797\pi\) | |||||||
\(264\) | 5.39758 | − | 2.90621i | 0.332198 | − | 0.178865i | ||||
\(265\) | 3.92701 | + | 6.80177i | 0.241234 | + | 0.417830i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.619063 | − | 20.8497i | 0.0378861 | − | 1.27598i | ||||
\(268\) | 0.827504 | + | 1.43328i | 0.0505478 | + | 0.0875514i | ||||
\(269\) | −0.269244 | − | 0.466344i | −0.0164161 | − | 0.0284335i | 0.857701 | − | 0.514149i | \(-0.171892\pi\) |
−0.874117 | + | 0.485716i | \(0.838559\pi\) | |||||||
\(270\) | 21.6014 | − | 10.0260i | 1.31462 | − | 0.610165i | ||||
\(271\) | 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 | ||||
\(275\) | 8.75835 | 0.528148 | ||||||||
\(276\) | 0.0685943 | − | 2.31021i | 0.00412889 | − | 0.139059i | ||||
\(277\) | 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 | ||||
\(279\) | −2.58004 | − | 5.15254i | −0.154463 | − | 0.308475i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.776622 | + | 1.34515i | −0.0463294 | + | 0.0802449i | −0.888260 | − | 0.459341i | \(-0.848086\pi\) |
0.841931 | + | 0.539586i | \(0.181419\pi\) | |||||||
\(282\) | 0.0423116 | − | 1.42503i | 0.00251962 | − | 0.0848592i | ||||
\(283\) | 1.32571 | − | 2.29619i | 0.0788051 | − | 0.136495i | −0.823930 | − | 0.566692i | \(-0.808223\pi\) |
0.902735 | + | 0.430198i | \(0.141556\pi\) | |||||||
\(284\) | −0.508510 | + | 0.880765i | −0.0301745 | + | 0.0522638i | ||||
\(285\) | −1.24450 | + | 41.9140i | −0.0737178 | + | 2.48277i | ||||
\(286\) | 2.46689 | − | 4.27279i | 0.145870 | − | 0.252655i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.33552 | + | 4.66421i | 0.137622 | + | 0.274841i | ||||
\(289\) | −3.52056 | + | 6.09778i | −0.207091 | + | 0.358693i | ||||
\(290\) | −12.4790 | −0.732793 | ||||||||
\(291\) | 0.561809 | − | 18.9214i | 0.0329338 | − | 1.10919i | ||||
\(292\) | −0.322148 | −0.0188523 | ||||||||
\(293\) | −5.19314 | − | 8.99478i | −0.303386 | − | 0.525481i | 0.673514 | − | 0.739174i | \(-0.264784\pi\) |
−0.976901 | + | 0.213694i | \(0.931451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4789 | + | 25.0783i | −0.842996 | + | 1.46011i | ||||
\(296\) | −14.6622 | + | 25.3956i | −0.852221 | + | 1.47609i | ||||
\(297\) | −0.544602 | + | 6.09958i | −0.0316010 | + | 0.353934i | ||||
\(298\) | −0.733415 | − | 1.27031i | −0.0424856 | − | 0.0735872i | ||||
\(299\) | −6.92409 | − | 11.9929i | −0.400431 | − | 0.693566i | ||||
\(300\) | −0.118553 | + | 3.99279i | −0.00684466 | + | 0.230524i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.7579 | + | 22.0974i | 0.734137 | + | 1.27156i | ||||
\(303\) | 2.43258 | − | 1.30977i | 0.139748 | − | 0.0752444i | ||||
\(304\) | 22.5425 | 1.29290 | ||||||||
\(305\) | 17.0283 | + | 29.4939i | 0.975039 | + | 1.68882i | ||||
\(306\) | −8.56095 | − | 17.0969i | −0.489397 | − | 0.977364i | ||||
\(307\) | −10.6425 | −0.607400 | −0.303700 | − | 0.952768i | \(-0.598222\pi\) | ||||
−0.303700 | + | 0.952768i | \(0.598222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.56182 | + | 1.91779i | −0.202625 | + | 0.109099i | ||||
\(310\) | −8.80331 | −0.499994 | ||||||||
\(311\) | 6.85479 | − | 11.8728i | 0.388699 | − | 0.673247i | −0.603576 | − | 0.797306i | \(-0.706258\pi\) |
0.992275 | + | 0.124059i | \(0.0395912\pi\) | |||||||
\(312\) | 14.2529 | + | 8.80301i | 0.806911 | + | 0.498372i | ||||
\(313\) | −10.6090 | − | 18.3752i | −0.599653 | − | 1.03863i | −0.992872 | − | 0.119185i | \(-0.961972\pi\) |
0.393219 | − | 0.919445i | \(-0.371362\pi\) | |||||||
\(314\) | 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 | \(-0.198637\pi\) |
−0.911795 | + | 0.410646i | \(0.865303\pi\) | |||||||
\(318\) | −0.148845 | + | 5.01301i | −0.00834681 | + | 0.281116i | ||||
\(319\) | 1.60446 | − | 2.77901i | 0.0898326 | − | 0.155595i | ||||
\(320\) | 31.1198 | 1.73965 | ||||||||
\(321\) | −0.114305 | + | 3.84973i | −0.00637989 | + | 0.214871i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.6670 | 1.87328 | ||||||||
\(324\) | −2.77333 | − | 0.330839i | −0.154074 | − | 0.0183800i | ||||
\(325\) | 11.9671 | + | 20.7276i | 0.663813 | + | 1.14976i | ||||
\(326\) | 21.9693 | 1.21677 | ||||||||
\(327\) | −1.35510 | − | 0.836952i | −0.0749374 | − | 0.0462835i | ||||
\(328\) | 9.99062 | + | 17.3043i | 0.551639 | + | 0.955468i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.95969 | + | 4.91614i | 0.438167 | + | 0.270625i | ||||
\(331\) | 11.9728 | + | 20.7375i | 0.658085 | + | 1.13984i | 0.981111 | + | 0.193446i | \(0.0619666\pi\) |
−0.323026 | + | 0.946390i | \(0.604700\pi\) | |||||||
\(332\) | 1.13457 | + | 1.96513i | 0.0622675 | + | 0.107851i | ||||
\(333\) | −13.1159 | − | 26.1934i | −0.718746 | − | 1.43539i | ||||
\(334\) | 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 | −0.948380 | − | 0.317137i | \(-0.897279\pi\) |
0.199542 | − | 0.979889i | \(-0.436055\pi\) | |||||||
\(338\) | −3.41568 | −0.185788 | ||||||||
\(339\) | −3.51691 | − | 2.17215i | −0.191012 | − | 0.117975i | ||||
\(340\) | 5.36497 | 0.290956 | ||||||||
\(341\) | 1.13187 | − | 1.96045i | 0.0612940 | − | 0.106164i | ||||
\(342\) | −14.7403 | + | 22.3537i | −0.797066 | + | 1.20875i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −14.5184 | + | 25.1466i | −0.782779 | + | 1.35581i | ||||
\(345\) | 23.1207 | − | 12.4488i | 1.24477 | − | 0.670222i | ||||
\(346\) | −6.32822 | + | 10.9608i | −0.340207 | + | 0.589256i | ||||
\(347\) | 2.56412 | − | 4.44119i | 0.137649 | − | 0.238416i | −0.788957 | − | 0.614448i | \(-0.789379\pi\) |
0.926606 | + | 0.376033i | \(0.122712\pi\) | |||||||
\(348\) | 1.24519 | + | 0.769065i | 0.0667490 | + | 0.0412262i | ||||
\(349\) | −7.56980 | + | 13.1113i | −0.405202 | + | 0.701830i | −0.994345 | − | 0.106198i | \(-0.966132\pi\) |
0.589143 | + | 0.808029i | \(0.299465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.1794 | + | 7.04537i | −0.810218 | + | 0.376054i | ||||
\(352\) | −1.02459 | + | 1.77465i | −0.0546110 | + | 0.0945889i | ||||
\(353\) | 32.9757 | 1.75512 | 0.877559 | − | 0.479468i | \(-0.159171\pi\) | ||||
0.877559 | + | 0.479468i | \(0.159171\pi\) | |||||||
\(354\) | −16.2812 | + | 8.76626i | −0.865336 | + | 0.465921i | ||||
\(355\) | −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 | −0.352395 | − | 0.935851i | \(-0.614633\pi\) |
0.986669 | − | 0.162743i | \(-0.0520341\pi\) | |||||||
\(360\) | −17.4871 | + | 26.5191i | −0.921651 | + | 1.39768i | ||||
\(361\) | −14.0735 | − | 24.3760i | −0.740711 | − | 1.28295i | ||||
\(362\) | 3.68227 | + | 6.37789i | 0.193536 | + | 0.335214i | ||||
\(363\) | 14.6573 | − | 7.89189i | 0.769307 | − | 0.414217i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.83004 | − | 3.16972i | −0.0957886 | − | 0.165911i | ||||
\(366\) | −0.645424 | + | 21.7375i | −0.0337368 | + | 1.13624i | ||||
\(367\) | −2.65501 | −0.138590 | −0.0692952 | − | 0.997596i | \(-0.522075\pi\) | ||||
−0.0692952 | + | 0.997596i | \(0.522075\pi\) | |||||||
\(368\) | −7.05830 | − | 12.2253i | −0.367939 | − | 0.637290i | ||||
\(369\) | −19.9252 | − | 1.18427i | −1.03726 | − | 0.0616507i | ||||
\(370\) | −44.7524 | −2.32657 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.878416 | + | 0.542536i | 0.0455438 | + | 0.0281292i | ||||
\(373\) | −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 | ||||
\(375\) | −13.0746 | + | 7.03976i | −0.675171 | + | 0.363531i | ||||
\(376\) | 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 | ||||
\(381\) | 4.63872 | − | 2.49762i | 0.237649 | − | 0.127957i | ||||
\(382\) | 16.2568 | − | 28.1576i | 0.831771 | − | 1.44067i | ||||
\(383\) | 1.73305 | 0.0885548 | 0.0442774 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442774 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(384\) | 11.7824 | + | 7.27715i | 0.601267 | + | 0.371360i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.7917 | 1.16006 | ||||||||
\(387\) | −12.9873 | − | 25.9366i | −0.660179 | − | 1.31843i | ||||
\(388\) | 1.69583 | + | 2.93726i | 0.0860925 | + | 0.149117i | ||||
\(389\) | −11.0835 | −0.561956 | −0.280978 | − | 0.959714i | \(-0.590659\pi\) | ||||
−0.280978 | + | 0.959714i | \(0.590659\pi\) | |||||||
\(390\) | −0.758762 | + | 25.5547i | −0.0384214 | + | 1.29401i | ||||
\(391\) | −10.5415 | − | 18.2584i | −0.533107 | − | 0.923368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.97431 | − | 2.67831i | 0.250921 | − | 0.135103i | ||||
\(394\) | 12.8388 | + | 22.2375i | 0.646811 | + | 1.12031i | ||||
\(395\) | −1.77011 | − | 3.06592i | −0.0890639 | − | 0.154263i | ||||
\(396\) | −0.491263 | − | 0.981090i | −0.0246869 | − | 0.0493016i | ||||
\(397\) | −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 | ||||
\(401\) | −34.8244 | −1.73905 | −0.869524 | − | 0.493890i | \(-0.835575\pi\) | ||||
−0.869524 | + | 0.493890i | \(0.835575\pi\) | |||||||
\(402\) | −10.5719 | + | 5.69224i | −0.527281 | + | 0.283903i | ||||
\(403\) | 6.18614 | 0.308154 | ||||||||
\(404\) | −0.247505 | + | 0.428690i | −0.0123138 | + | 0.0213281i | ||||
\(405\) | −12.4993 | − | 29.1672i | −0.621097 | − | 1.44933i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.75394 | − | 9.96612i | 0.285212 | − | 0.494002i | ||||
\(408\) | 21.6992 | + | 13.4020i | 1.07427 | + | 0.663500i | ||||
\(409\) | 9.12308 | − | 15.8016i | 0.451107 | − | 0.781341i | −0.547348 | − | 0.836905i | \(-0.684362\pi\) |
0.998455 | + | 0.0555643i | \(0.0176958\pi\) | |||||||
\(410\) | −15.2469 | + | 26.4083i | −0.752989 | + | 1.30422i | ||||
\(411\) | −31.9249 | + | 17.1893i | −1.57474 | + | 0.847884i | ||||
\(412\) | 0.362400 | − | 0.627695i | 0.0178541 | − | 0.0309243i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.7383 | + | 0.994856i | 0.822643 | + | 0.0488945i | ||||
\(415\) | −12.8904 | + | 22.3268i | −0.632765 | + | 1.09598i | ||||
\(416\) | −5.59985 | −0.274555 | ||||||||
\(417\) | 24.4976 | + | 15.1304i | 1.19965 | + | 0.740941i | ||||
\(418\) | −10.5189 | −0.514496 | ||||||||
\(419\) | −4.20719 | − | 7.28708i | −0.205535 | − | 0.355997i | 0.744768 | − | 0.667323i | \(-0.232560\pi\) |
−0.950303 | + | 0.311326i | \(0.899227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.144291 | − | 0.249919i | 0.00703230 | − | 0.0121803i | −0.862488 | − | 0.506078i | \(-0.831095\pi\) |
0.869520 | + | 0.493897i | \(0.164428\pi\) | |||||||
\(422\) | 4.83304 | − | 8.37108i | 0.235269 | − | 0.407498i | ||||
\(423\) | −1.89631 | − | 0.112709i | −0.0922017 | − | 0.00548009i | ||||
\(424\) | −3.34483 | − | 5.79341i | −0.162439 | − | 0.281353i | ||||
\(425\) | 18.2191 | + | 31.5564i | 0.883757 | + | 1.53071i | ||||
\(426\) | −6.27759 | − | 3.87723i | −0.304150 | − | 0.187852i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.345031 | − | 0.597612i | −0.0166777 | − | 0.0288866i | ||||
\(429\) | −5.59333 | − | 3.45461i | −0.270048 | − | 0.166790i | ||||
\(430\) | −44.3136 | −2.13699 | ||||||||
\(431\) | 6.74795 | + | 11.6878i | 0.325037 | + | 0.562981i | 0.981520 | − | 0.191360i | \(-0.0612898\pi\) |
−0.656482 | + | 0.754341i | \(0.727956\pi\) | |||||||
\(432\) | −15.4736 | + | 7.18192i | −0.744476 | + | 0.345540i | ||||
\(433\) | −4.85211 | −0.233177 | −0.116589 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116589 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.493497 | + | 16.6207i | −0.0236614 | + | 0.796901i | ||||
\(436\) | 0.285371 | 0.0136668 | ||||||||
\(437\) | −14.7623 | + | 25.5690i | −0.706174 | + | 1.22313i | ||||
\(438\) | 0.0693638 | − | 2.33613i | 0.00331433 | − | 0.111625i | ||||
\(439\) | −1.27397 | − | 2.20657i | −0.0608031 | − | 0.105314i | 0.834022 | − | 0.551732i | \(-0.186033\pi\) |
−0.894825 | + | 0.446418i | \(0.852699\pi\) | |||||||
\(440\) | −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 | \(-0.161785\pi\) |
−0.858256 | + | 0.513221i | \(0.828452\pi\) | |||||||
\(444\) | 4.46551 | + | 2.75803i | 0.211924 | + | 0.130890i | ||||
\(445\) | −21.2306 | + | 36.7725i | −1.00643 | + | 1.74319i | ||||
\(446\) | −4.27826 | −0.202581 | ||||||||
\(447\) | −1.72092 | + | 0.926593i | −0.0813968 | + | 0.0438264i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.22658 | −0.246658 | −0.123329 | − | 0.992366i | \(-0.539357\pi\) | ||||
−0.123329 | + | 0.992366i | \(0.539357\pi\) | |||||||
\(450\) | −28.9292 | − | 1.71943i | −1.36373 | − | 0.0810548i | ||||
\(451\) | −3.92066 | − | 6.79079i | −0.184617 | − | 0.319766i | ||||
\(452\) | 0.740624 | 0.0348360 | ||||||||
\(453\) | 29.9358 | − | 16.1183i | 1.40651 | − | 0.757304i | ||||
\(454\) | 11.7099 | + | 20.2821i | 0.549571 | + | 0.951885i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.06000 | − | 35.7003i | 0.0496392 | − | 1.67182i | ||||
\(457\) | 1.43037 | + | 2.47748i | 0.0669101 | + | 0.115892i | 0.897540 | − | 0.440934i | \(-0.145353\pi\) |
−0.830630 | + | 0.556825i | \(0.812019\pi\) | |||||||
\(458\) | −2.76542 | − | 4.78985i | −0.129220 | − | 0.223815i | ||||
\(459\) | −23.1097 | + | 10.7261i | −1.07867 | + | 0.500653i | ||||
\(460\) | −2.35242 | + | 4.07452i | −0.109682 | + | 0.189975i | ||||
\(461\) | 1.82624 | − | 3.16314i | 0.0850566 | − | 0.147322i | −0.820359 | − | 0.571849i | \(-0.806226\pi\) |
0.905415 | + | 0.424527i | \(0.139560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4052 | − | 26.6825i | −0.715939 | − | 1.24004i | −0.962596 | − | 0.270940i | \(-0.912666\pi\) |
0.246657 | − | 0.969103i | \(-0.420668\pi\) | |||||||
\(464\) | 8.93905 | 0.414985 | ||||||||
\(465\) | −0.348137 | + | 11.7250i | −0.0161445 | + | 0.543736i | ||||
\(466\) | −19.1153 | −0.885498 | ||||||||
\(467\) | −10.2885 | + | 17.8202i | −0.476096 | + | 0.824622i | −0.999625 | − | 0.0273858i | \(-0.991282\pi\) |
0.523529 | + | 0.852008i | \(0.324615\pi\) | |||||||
\(468\) | 1.65061 | − | 2.50315i | 0.0762995 | − | 0.115708i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.45107 | + | 2.51332i | −0.0669327 | + | 0.115931i | ||||
\(471\) | 0.479730 | − | 16.1570i | 0.0221048 | − | 0.744476i | ||||
\(472\) | 12.3324 | − | 21.3604i | 0.567647 | − | 0.983193i | ||||
\(473\) | 5.69752 | − | 9.86839i | 0.261972 | − | 0.453749i | ||||
\(474\) | 0.0670923 | − | 2.25963i | 0.00308165 | − | 0.103788i | ||||
\(475\) | 25.5139 | − | 44.1914i | 1.17066 | − | 2.02764i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.67090 | + | 0.396491i | 0.305439 | + | 0.0181541i | ||||
\(478\) | 9.20552 | − | 15.9444i | 0.421051 | − | 0.729281i | ||||
\(479\) | 25.1832 | 1.15065 | 0.575325 | − | 0.817925i | \(-0.304876\pi\) | ||||
0.575325 | + | 0.817925i | \(0.304876\pi\) | |||||||
\(480\) | 0.315142 | − | 10.6138i | 0.0143842 | − | 0.484451i | ||||
\(481\) | 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 | ||||
\(486\) | 2.99631 | − | 20.0402i | 0.135915 | − | 0.909044i | ||||
\(487\) | 16.3807 | + | 28.3723i | 0.742282 | + | 1.28567i | 0.951454 | + | 0.307791i | \(0.0995896\pi\) |
−0.209173 | + | 0.977879i | \(0.567077\pi\) | |||||||
\(488\) | −14.5039 | − | 25.1215i | −0.656560 | − | 1.13720i | ||||
\(489\) | 0.868801 | − | 29.2607i | 0.0392886 | − | 1.32321i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.76000 | + | 3.04841i | 0.0794278 | + | 0.137573i | 0.903003 | − | 0.429634i | \(-0.141357\pi\) |
−0.823575 | + | 0.567207i | \(0.808024\pi\) | |||||||
\(492\) | 3.14888 | − | 1.69545i | 0.141962 | − | 0.0764367i | ||||
\(493\) | 13.3504 | 0.601272 | ||||||||
\(494\) | −14.3726 | − | 24.8941i | −0.646654 | − | 1.12004i | ||||
\(495\) | 6.86254 | − | 10.4070i | 0.308448 | − | 0.467761i | ||||
\(496\) | 6.30605 | 0.283150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.4949 | + | 7.80448i | −0.649533 | + | 0.349727i | ||||
\(499\) | 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 | ||||
\(501\) | −7.58389 | − | 4.68404i | −0.338823 | − | 0.209267i | ||||
\(502\) | −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 | ||||
\(507\) | −0.135077 | + | 4.54931i | −0.00599898 | + | 0.202042i | ||||
\(508\) | −0.471969 | + | 0.817474i | −0.0209402 | + | 0.0362696i | ||||
\(509\) | −37.6458 | −1.66862 | −0.834311 | − | 0.551294i | \(-0.814134\pi\) | ||||
−0.834311 | + | 0.551294i | \(0.814134\pi\) | |||||||
\(510\) | −1.15517 | + | 38.9054i | −0.0511518 | + | 1.72276i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −25.4272 | −1.12373 | ||||||||
\(513\) | 29.1898 | + | 20.5165i | 1.28876 | + | 0.905827i | ||||
\(514\) | 11.4088 | + | 19.7606i | 0.503221 | + | 0.871604i | ||||
\(515\) | 8.23480 | 0.362869 | ||||||||
\(516\) | 4.42172 | + | 2.73098i | 0.194655 | + | 0.120225i | ||||
\(517\) | −0.373135 | − | 0.646289i | −0.0164105 | − | 0.0284237i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.3483 | + | 8.86196i | 0.629822 | + | 0.388997i | ||||
\(520\) | −17.0508 | − | 29.5329i | −0.747728 | − | 1.29510i | ||||
\(521\) | 7.17115 | + | 12.4208i | 0.314174 | + | 0.544165i | 0.979262 | − | 0.202600i | \(-0.0649392\pi\) |
−0.665088 | + | 0.746765i | \(0.731606\pi\) | |||||||
\(522\) | −5.84517 | + | 8.86419i | −0.255836 | + | 0.387975i | ||||
\(523\) | −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 | ||||
\(527\) | 9.41802 | 0.410256 | ||||||||
\(528\) | −5.70174 | − | 3.52156i | −0.248136 | − | 0.153256i | ||||
\(529\) | −4.51110 | −0.196135 | ||||||||
\(530\) | 5.10461 | − | 8.84144i | 0.221730 | − | 0.384047i | ||||
\(531\) | 11.0318 | + | 22.0314i | 0.478741 | + | 0.956083i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7141 | − | 18.5573i | 0.464078 | − | 0.803807i | ||||
\(534\) | −23.8733 | + | 12.8541i | −1.03310 | + | 0.556250i | ||||
\(535\) | 3.92007 | − | 6.78976i | 0.169479 | − | 0.293547i | ||||
\(536\) | 8.00788 | − | 13.8701i | 0.345888 | − | 0.599095i | ||||
\(537\) | 2.02769 | + | 1.25236i | 0.0875014 | + | 0.0540435i | ||||
\(538\) | −0.349983 | + | 0.606188i | −0.0150888 | + | 0.0261346i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.65150 | + | 3.26939i | 0.200169 | + | 0.140692i | ||||
\(541\) | 23.0461 | − | 39.9170i | 0.990830 | − | 1.71617i | 0.378399 | − | 0.925643i | \(-0.376475\pi\) |
0.612430 | − | 0.790524i | \(-0.290192\pi\) | |||||||
\(542\) | −18.7376 | −0.804851 | ||||||||
\(543\) | 8.64027 | − | 4.65217i | 0.370789 | − | 0.199644i | ||||
\(544\) | −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 | 0.478962 | + | 0.877836i | \(0.341013\pi\) |
−0.999709 | + | 0.0241250i | \(0.992320\pi\) | |||||||
\(548\) | 3.24822 | − | 5.62607i | 0.138757 | − | 0.240334i | ||||
\(549\) | 28.9264 | + | 1.71927i | 1.23455 | + | 0.0733765i | ||||
\(550\) | −5.69237 | − | 9.85947i | −0.242723 | − | 0.420409i | ||||
\(551\) | −9.34790 | − | 16.1910i | −0.398234 | − | 0.689761i | ||||
\(552\) | −19.6930 | + | 10.6033i | −0.838191 | + | 0.451306i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2379 | − | 24.6608i | −0.604911 | − | 1.04774i | ||||
\(555\) | −1.76979 | + | 59.6054i | −0.0751233 | + | 2.53011i | ||||
\(556\) | −5.15894 | −0.218788 | ||||||||
\(557\) | −15.2888 | − | 26.4809i | −0.647806 | − | 1.12203i | −0.983646 | − | 0.180114i | \(-0.942353\pi\) |
0.335840 | − | 0.941919i | \(-0.390980\pi\) | |||||||
\(558\) | −4.12347 | + | 6.25323i | −0.174560 | + | 0.264720i | ||||
\(559\) | 31.1394 | 1.31706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.51550 | − | 5.25943i | −0.359525 | − | 0.222053i | ||||
\(562\) | 2.01902 | 0.0851672 | ||||||||
\(563\) | −4.41357 | + | 7.64452i | −0.186010 | + | 0.322178i | −0.943916 | − | 0.330185i | \(-0.892889\pi\) |
0.757907 | + | 0.652363i | \(0.226222\pi\) | |||||||
\(564\) | 0.299683 | − | 0.161358i | 0.0126189 | − | 0.00679440i | ||||
\(565\) | 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 | \(-0.214354\pi\) |
−0.930952 | + | 0.365141i | \(0.881021\pi\) | |||||||
\(570\) | 47.9924 | − | 25.8405i | 2.01018 | − | 1.08234i | ||||
\(571\) | −3.33181 | + | 5.77086i | −0.139432 | + | 0.241503i | −0.927282 | − | 0.374364i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(572\) | 1.17790 | 0.0492503 | ||||||||
\(573\) | −36.8600 | − | 22.7658i | −1.53985 | − | 0.951056i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.9548 | −1.33261 | ||||||||
\(576\) | 14.5765 | − | 22.1053i | 0.607356 | − | 0.921054i | ||||
\(577\) | −3.95629 | − | 6.85250i | −0.164703 | − | 0.285273i | 0.771847 | − | 0.635808i | \(-0.219333\pi\) |
−0.936550 | + | 0.350535i | \(0.886000\pi\) | |||||||
\(578\) | 9.15254 | 0.380696 | ||||||||
\(579\) | 0.901323 | − | 30.3560i | 0.0374577 | − | 1.26155i | ||||
\(580\) | −1.48963 | − | 2.58011i | −0.0618533 | − | 0.107133i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.6654 | + | 11.6653i | −0.898059 | + | 0.483540i | ||||
\(583\) | 1.31263 | + | 2.27354i | 0.0543634 | + | 0.0941602i | ||||
\(584\) | 1.55874 | + | 2.69981i | 0.0645010 | + | 0.111719i | ||||
\(585\) | 34.0060 | + | 2.02118i | 1.40598 | + | 0.0835654i | ||||
\(586\) | −6.75042 | + | 11.6921i | −0.278857 | + | 0.482995i | ||||
\(587\) | −9.13891 | + | 15.8291i | −0.377203 | + | 0.653335i | −0.990654 | − | 0.136398i | \(-0.956447\pi\) |
0.613451 | + | 0.789733i | \(0.289781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.59447 | − | 11.4220i | −0.271720 | − | 0.470633i | ||||
\(590\) | 37.6415 | 1.54968 | ||||||||
\(591\) | 30.1257 | − | 16.2205i | 1.23920 | − | 0.667223i | ||||
\(592\) | 32.0574 | 1.31755 | ||||||||
\(593\) | 14.1908 | − | 24.5792i | 0.582745 | − | 1.00934i | −0.412407 | − | 0.911000i | \(-0.635312\pi\) |
0.995152 | − | 0.0983450i | \(-0.0313549\pi\) | |||||||
\(594\) | 7.22039 | − | 3.35127i | 0.296256 | − | 0.137504i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.175096 | − | 0.303275i | 0.00717222 | − | 0.0124226i | ||||
\(597\) | −28.0318 | − | 17.3133i | −1.14727 | − | 0.708585i | ||||
\(598\) | −9.00044 | + | 15.5892i | −0.368055 | + | 0.637490i | ||||
\(599\) | −4.69451 | + | 8.13113i | −0.191813 | + | 0.332229i | −0.945851 | − | 0.324601i | \(-0.894770\pi\) |
0.754038 | + | 0.656830i | \(0.228103\pi\) | |||||||
\(600\) | 34.0359 | − | 18.3259i | 1.38951 | − | 0.748151i | ||||
\(601\) | −6.31432 | + | 10.9367i | −0.257566 | + | 0.446118i | −0.965589 | − | 0.260071i | \(-0.916254\pi\) |
0.708023 | + | 0.706189i | \(0.249587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.16336 | + | 14.3058i | 0.291714 | + | 0.582577i | ||||
\(604\) | −3.04584 | + | 5.27555i | −0.123934 | + | 0.214659i | ||||
\(605\) | −33.8871 | −1.37771 | ||||||||
\(606\) | −3.05546 | − | 1.88714i | −0.124120 | − | 0.0766600i | ||||
\(607\) | 24.0265 | 0.975207 | 0.487604 | − | 0.873065i | \(-0.337871\pi\) | ||||
0.487604 | + | 0.873065i | \(0.337871\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 2.51295 | − | 3.81089i | 0.101580 | − | 0.154046i | ||||
\(613\) | 14.2708 | + | 24.7177i | 0.576390 | + | 0.998337i | 0.995889 | + | 0.0905814i | \(0.0288725\pi\) |
−0.419499 | + | 0.907756i | \(0.637794\pi\) | |||||||
\(614\) | 6.91695 | + | 11.9805i | 0.279145 | + | 0.483494i | ||||
\(615\) | 34.5701 | + | 21.3515i | 1.39400 | + | 0.860976i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.05549 | − | 10.4884i | −0.243785 | − | 0.422248i | 0.718004 | − | 0.696039i | \(-0.245056\pi\) |
−0.961789 | + | 0.273791i | \(0.911722\pi\) | |||||||
\(618\) | 4.47385 | + | 2.76318i | 0.179965 | + | 0.111152i | ||||
\(619\) | −26.5739 | −1.06810 | −0.534048 | − | 0.845454i | \(-0.679330\pi\) | ||||
−0.534048 | + | 0.845454i | \(0.679330\pi\) | |||||||
\(620\) | −1.05085 | − | 1.82013i | −0.0422033 | − | 0.0730983i | ||||
\(621\) | 1.98698 | − | 22.2543i | 0.0797346 | − | 0.893033i | ||||
\(622\) | −17.8207 | −0.714545 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.543522 | − | 18.3055i | 0.0217583 | − | 0.732806i | ||||
\(625\) | −6.92971 | −0.277188 | ||||||||
\(626\) | −13.7903 | + | 23.8855i | −0.551170 | + | 0.954655i | ||||
\(627\) | −0.415982 | + | 14.0100i | −0.0166127 | + | 0.559506i | ||||
\(628\) | 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 | ||||
\(633\) | −10.9582 | − | 6.76813i | −0.435551 | − | 0.269009i | ||||
\(634\) | −2.32055 | + | 4.01931i | −0.0921608 | + | 0.159627i | ||||
\(635\) | −10.7245 | −0.425591 | ||||||||
\(636\) | −1.05424 | + | 0.567631i | −0.0418032 | + | 0.0225080i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.17119 | −0.165139 | ||||||||
\(639\) | −5.41230 | + | 8.20774i | −0.214107 | + | 0.324693i | ||||
\(640\) | −14.0953 | − | 24.4138i | −0.557167 | − | 0.965041i | ||||
\(641\) | 32.5844 | 1.28701 | 0.643503 | − | 0.765443i | \(-0.277480\pi\) | ||||
0.643503 | + | 0.765443i | \(0.277480\pi\) | |||||||
\(642\) | 4.40802 | − | 2.37340i | 0.173971 | − | 0.0936707i | ||||
\(643\) | 21.5327 | + | 37.2957i | 0.849166 | + | 1.47080i | 0.881953 | + | 0.471337i | \(0.156228\pi\) |
−0.0327873 | + | 0.999462i | \(0.510438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.75243 | + | 59.0208i | −0.0690019 | + | 2.32394i | ||||
\(646\) | −21.8814 | − | 37.8997i | −0.860912 | − | 1.49114i | ||||
\(647\) | −23.0988 | − | 40.0082i | −0.908106 | − | 1.57289i | −0.816692 | − | 0.577074i | \(-0.804195\pi\) |
−0.0914143 | − | 0.995813i | \(-0.529139\pi\) | |||||||
\(648\) | 10.6463 | + | 24.8431i | 0.418227 | + | 0.975930i | ||||
\(649\) | −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 | \(-0.284635\pi\) | ||||
0.626138 | + | 0.779713i | \(0.284635\pi\) | |||||||
\(654\) | −0.0614451 | + | 2.06943i | −0.00240269 | + | 0.0809213i | ||||
\(655\) | −11.5004 | −0.449359 | ||||||||
\(656\) | 10.9217 | − | 18.9170i | 0.426422 | − | 0.738585i | ||||
\(657\) | −3.10873 | − | 0.184770i | −0.121283 | − | 0.00720857i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2070 | − | 33.2674i | 0.748197 | − | 1.29591i | −0.200490 | − | 0.979696i | \(-0.564253\pi\) |
0.948686 | − | 0.316219i | \(-0.102413\pi\) | |||||||
\(660\) | −0.0662884 | + | 2.23255i | −0.00258027 | + | 0.0869020i | ||||
\(661\) | −14.0130 | + | 24.2712i | −0.545043 | + | 0.944042i | 0.453561 | + | 0.891225i | \(0.350153\pi\) |
−0.998604 | + | 0.0528170i | \(0.983180\pi\) | |||||||
\(662\) | 15.5631 | − | 26.9561i | 0.604878 | − | 1.04768i | ||||
\(663\) | 0.811745 | − | 27.3391i | 0.0315256 | − | 1.06176i | ||||
\(664\) | 10.9794 | − | 19.0169i | 0.426083 | − | 0.737998i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.9620 | + | 31.7889i | −0.812263 | + | 1.23179i | ||||
\(667\) | −5.85386 | + | 10.1392i | −0.226662 | + | 0.392591i | ||||
\(668\) | 1.59709 | 0.0617932 | ||||||||
\(669\) | −0.169189 | + | 5.69817i | −0.00654121 | + | 0.220304i | ||||
\(670\) | 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 | −0.850270 | − | 0.526347i | \(-0.823561\pi\) |
0.880965 | + | 0.473182i | \(0.156895\pi\) | |||||||
\(674\) | −17.8691 | + | 30.9503i | −0.688293 | + | 1.19216i | ||||
\(675\) | −3.43413 | + | 38.4625i | −0.132180 | + | 1.48042i | ||||
\(676\) | −0.407731 | − | 0.706211i | −0.0156820 | − | 0.0271619i | ||||
\(677\) | 21.0167 | + | 36.4020i | 0.807737 | + | 1.39904i | 0.914428 | + | 0.404749i | \(0.132641\pi\) |
−0.106691 | + | 0.994292i | \(0.534025\pi\) | |||||||
\(678\) | −0.159469 | + | 5.37082i | −0.00612437 | + | 0.206265i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −25.9588 | − | 44.9620i | −0.995476 | − | 1.72421i | ||||
\(681\) | 27.4766 | − | 14.7942i | 1.05291 | − | 0.566914i | ||||
\(682\) | −2.94256 | −0.112676 | ||||||||
\(683\) | −17.8645 | − | 30.9422i | −0.683565 | − | 1.18397i | −0.973886 | − | 0.227039i | \(-0.927095\pi\) |
0.290321 | − | 0.956929i | \(-0.406238\pi\) | |||||||
\(684\) | −6.38131 | − | 0.379279i | −0.243996 | − | 0.0145021i | ||||
\(685\) | 73.8092 | 2.82010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.48892 | + | 3.49382i | −0.247568 | + | 0.133298i | ||||
\(688\) | 31.7430 | 1.21019 | ||||||||
\(689\) | −3.58704 | + | 6.21294i | −0.136655 | + | 0.236694i | ||||
\(690\) | −29.0409 | − | 17.9365i | −1.10557 | − | 0.682831i | ||||
\(691\) | 25.5675 | + | 44.2841i | 0.972632 | + | 1.68465i | 0.687538 | + | 0.726149i | \(0.258692\pi\) |
0.285094 | + | 0.958499i | \(0.407975\pi\) | |||||||
\(692\) | −3.02161 | −0.114864 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.66606 | −0.253040 | ||||||||
\(695\) | −29.3066 | − | 50.7606i | −1.11166 | − | 1.92546i | ||||
\(696\) | 0.420336 | − | 14.1567i | 0.0159328 | − | 0.536607i | ||||
\(697\) | 16.3115 | − | 28.2524i | 0.617843 | − | 1.07014i | ||||
\(698\) | 19.6795 | 0.744881 | ||||||||
\(699\) | −0.755936 | + | 25.4595i | −0.0285921 | + | 0.962965i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5761 | −0.928226 | −0.464113 | − | 0.885776i | \(-0.653627\pi\) | ||||
−0.464113 | + | 0.885776i | \(0.653627\pi\) | |||||||
\(702\) | 17.7968 | + | 12.5088i | 0.671696 | + | 0.472113i | ||||
\(703\) | −33.5236 | − | 58.0645i | −1.26437 | − | 2.18995i | ||||
\(704\) | 10.4020 | 0.392040 | ||||||||
\(705\) | 3.29008 | + | 2.03205i | 0.123912 | + | 0.0765315i | ||||
\(706\) | −21.4321 | − | 37.1215i | −0.806607 | − | 1.39708i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.75597 | − | 2.31980i | −0.141158 | − | 0.0871833i | ||||
\(709\) | −15.4488 | − | 26.7581i | −0.580192 | − | 1.00492i | −0.995456 | − | 0.0952206i | \(-0.969644\pi\) |
0.415265 | − | 0.909701i | \(-0.363689\pi\) | |||||||
\(710\) | 7.50992 | + | 13.0076i | 0.281842 | + | 0.488165i | ||||
\(711\) | −3.00693 | − | 0.178719i | −0.112769 | − | 0.00670250i | ||||
\(712\) | 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 | ||||||||
\(717\) | −20.8722 | − | 12.8913i | −0.779487 | − | 0.481434i | ||||
\(718\) | −31.2431 | −1.16598 | ||||||||
\(719\) | 3.05690 | − | 5.29471i | 0.114003 | − | 0.197459i | −0.803378 | − | 0.595470i | \(-0.796966\pi\) |
0.917381 | + | 0.398011i | \(0.130299\pi\) | |||||||
\(720\) | 34.6651 | + | 2.06035i | 1.29189 | + | 0.0767848i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.2938 | + | 31.6857i | −0.680823 | + | 1.17922i | ||||
\(723\) | −12.1013 | + | 6.51566i | −0.450051 | + | 0.242320i | ||||
\(724\) | −0.879109 | + | 1.52266i | −0.0326718 | + | 0.0565893i | ||||
\(725\) | 10.1174 | − | 17.5238i | 0.375749 | − | 0.650816i | ||||
\(726\) | −18.4104 | − | 11.3708i | −0.683272 | − | 0.422009i | ||||
\(727\) | −22.2492 | + | 38.5367i | −0.825176 | + | 1.42925i | 0.0766087 | + | 0.997061i | \(0.475591\pi\) |
−0.901785 | + | 0.432186i | \(0.857743\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5729 | − | 4.78327i | −0.984182 | − | 0.177158i | ||||
\(730\) | −2.37882 | + | 4.12023i | −0.0880440 | + | 0.152497i | ||||
\(731\) | 47.4079 | 1.75344 | ||||||||
\(732\) | −4.57139 | + | 2.46137i | −0.168963 | + | 0.0909747i | ||||
\(733\) | −9.83708 | −0.363341 | −0.181670 | − | 0.983359i | \(-0.558150\pi\) | ||||
−0.181670 | + | 0.983359i | \(0.558150\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | 11.6169 | + | 23.1999i | 0.427626 | + | 0.854002i | ||||
\(739\) | −7.42464 | − | 12.8598i | −0.273120 | − | 0.473057i | 0.696539 | − | 0.717519i | \(-0.254722\pi\) |
−0.969659 | + | 0.244461i | \(0.921389\pi\) | |||||||
\(740\) | −5.34212 | − | 9.25282i | −0.196380 | − | 0.340140i | ||||
\(741\) | −33.7246 | + | 18.1583i | −1.23890 | + | 0.667061i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.04201 | − | 5.26892i | −0.111601 | − | 0.193298i | 0.804815 | − | 0.593525i | \(-0.202264\pi\) |
−0.916416 | + | 0.400228i | \(0.868931\pi\) | |||||||
\(744\) | 0.296526 | − | 9.98681i | 0.0108712 | − | 0.366134i | ||||
\(745\) | 3.97871 | 0.145769 | ||||||||
\(746\) | 20.7449 | + | 35.9311i | 0.759523 | + | 1.31553i | ||||
\(747\) | 9.82149 | + | 19.6143i | 0.359350 | + | 0.717649i | ||||
\(748\) | 1.79328 | 0.0655686 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 16.4225 | + | 10.1430i | 0.599665 | + | 0.370371i | ||||
\(751\) | 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 | ||||
\(753\) | −12.2781 | + | 6.61086i | −0.447438 | + | 0.240913i | ||||
\(754\) | −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 | ||||
\(759\) | 7.72822 | − | 4.16110i | 0.280517 | − | 0.151038i | ||||
\(760\) | −36.3526 | + | 62.9645i | −1.31865 | + | 2.28396i | ||||
\(761\) | −6.75264 | −0.244783 | −0.122392 | − | 0.992482i | \(-0.539056\pi\) | ||||
−0.122392 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(762\) | −5.82649 | − | 3.59862i | −0.211072 | − | 0.130364i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.76233 | 0.280831 | ||||||||
\(765\) | 51.7721 | + | 3.07712i | 1.87182 | + | 0.111253i | ||||
\(766\) | −1.12637 | − | 1.95094i | −0.0406975 | − | 0.0704902i | ||||
\(767\) | −26.4510 | −0.955089 | ||||||||
\(768\) | −0.373168 | + | 12.5681i | −0.0134656 | + | 0.453512i | ||||
\(769\) | −21.0805 | − | 36.5125i | −0.760182 | − | 1.31667i | −0.942757 | − | 0.333482i | \(-0.891776\pi\) |
0.182575 | − | 0.983192i | \(-0.441557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.7702 | − | 14.4138i | 0.964104 | − | 0.519101i | ||||
\(772\) | 2.72065 | + | 4.71230i | 0.0979183 | + | 0.169600i | ||||
\(773\) | 1.64926 | + | 2.85660i | 0.0593197 | + | 0.102745i | 0.894160 | − | 0.447747i | \(-0.147774\pi\) |
−0.834841 | + | 0.550492i | \(0.814440\pi\) | |||||||
\(774\) | −20.7565 | + | 31.4771i | −0.746076 | + | 1.13142i | ||||
\(775\) | 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 | ||||||||
\(780\) | −5.37414 | + | 2.89359i | −0.192425 | + | 0.103607i | ||||
\(781\) | −3.86229 | −0.138203 | ||||||||
\(782\) | −13.7026 | + | 23.7336i | −0.490004 | + | 0.848713i | ||||
\(783\) | 11.5750 | + | 8.13567i | 0.413656 | + | 0.290745i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.4522 | + | 28.4961i | −0.587205 | + | 1.01707i | ||||
\(786\) | −6.24802 | − | 3.85896i | −0.222860 | − | 0.137645i | ||||
\(787\) | 3.36455 | − | 5.82757i | 0.119933 | − | 0.207731i | −0.799808 | − | 0.600256i | \(-0.795065\pi\) |
0.919741 | + | 0.392526i | \(0.128399\pi\) | |||||||
\(788\) | −3.06515 | + | 5.30900i | −0.109192 | + | 0.189125i | ||||
\(789\) | 35.6075 | − | 19.1721i | 1.26766 | − | 0.682545i | ||||
\(790\) | −2.30092 | + | 3.98530i | −0.0818629 | + | 0.141791i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.84517 | + | 8.86419i | −0.207699 | + | 0.314975i | ||||
\(793\) | −15.5542 | + | 26.9406i | −0.552345 | + | 0.956689i | ||||
\(794\) | 32.9376 | 1.16891 | ||||||||
\(795\) | −11.5740 | − | 7.14842i | −0.410486 | − | 0.253528i | ||||
\(796\) | 5.90321 | 0.209234 | ||||||||
\(797\) | −8.86302 | − | 15.3512i | −0.313944 | − | 0.543767i | 0.665268 | − | 0.746604i | \(-0.268317\pi\) |
−0.979213 | + | 0.202837i | \(0.934984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.55239 | − | 2.68882i | 0.0549196 | − | 0.0951235i | ||||
\(800\) | −6.46084 | + | 11.1905i | −0.228425 | + | 0.395644i | ||||
\(801\) | 16.1761 | + | 32.3050i | 0.571555 | + | 1.14144i | ||||
\(802\) | 22.6336 | + | 39.2026i | 0.799222 | + | 1.38429i | ||||
\(803\) | −0.611702 | − | 1.05950i | −0.0215865 | − | 0.0373889i | ||||
\(804\) | −2.43888 | − | 1.50632i | −0.0860126 | − | 0.0531240i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.02060 | − | 6.96388i | −0.141620 | − | 0.245292i | ||||
\(807\) | 0.793535 | + | 0.490111i | 0.0279338 | + | 0.0172527i | ||||
\(808\) | 4.79028 | 0.168521 | ||||||||
\(809\) | −19.5428 | − | 33.8492i | −0.687089 | − | 1.19007i | −0.972775 | − | 0.231751i | \(-0.925555\pi\) |
0.285686 | − | 0.958323i | \(-0.407779\pi\) | |||||||
\(810\) | −24.7103 | + | 33.0276i | −0.868233 | + | 1.16047i | ||||
\(811\) | −13.9559 | −0.490058 | −0.245029 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245029 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.741002 | + | 24.9565i | −0.0259881 | + | 0.875263i | ||||
\(814\) | −14.9588 | −0.524305 | ||||||||
\(815\) | −29.7953 | + | 51.6070i | −1.04369 | + | 1.80772i | ||||
\(816\) | 0.827479 | − | 27.8690i | 0.0289676 | − | 0.975610i | ||||
\(817\) | −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 | 0.928882 | + | 0.370376i | \(0.120771\pi\) |
−0.143685 | + | 0.989623i | \(0.545895\pi\) | |||||||
\(822\) | 40.0995 | + | 24.7666i | 1.39863 | + | 0.863835i | ||||
\(823\) | 27.6232 | − | 47.8449i | 0.962886 | − | 1.66777i | 0.247694 | − | 0.968838i | \(-0.420327\pi\) |
0.715191 | − | 0.698929i | \(-0.246340\pi\) | |||||||
\(824\) | −7.01400 | −0.244344 | ||||||||
\(825\) | −13.3569 | + | 7.19171i | −0.465026 | + | 0.250383i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.8901 | −0.483005 | −0.241502 | − | 0.970400i | \(-0.577640\pi\) | ||||
−0.241502 | + | 0.970400i | \(0.577640\pi\) | |||||||
\(828\) | 1.79237 | + | 3.57950i | 0.0622891 | + | 0.124396i | ||||
\(829\) | −19.4896 | − | 33.7570i | −0.676903 | − | 1.17243i | −0.975909 | − | 0.218179i | \(-0.929988\pi\) |
0.299006 | − | 0.954251i | \(-0.403345\pi\) | |||||||
\(830\) | 33.5117 | 1.16321 | ||||||||
\(831\) | −33.4085 | + | 17.9881i | −1.15893 | + | 0.624001i | ||||
\(832\) | 14.2129 | + | 24.6174i | 0.492743 | + | 0.853456i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.11081 | − | 37.4113i | 0.0384641 | − | 1.29545i | ||||
\(835\) | 9.07266 | + | 15.7143i | 0.313972 | + | 0.543816i | ||||
\(836\) | −1.25564 | − | 2.17484i | −0.0434274 | − | 0.0752184i | ||||
\(837\) | 8.16556 | + | 5.73930i | 0.282243 | + | 0.198379i | ||||
\(838\) | −5.46882 | + | 9.47227i | −0.188917 | + | 0.327214i | ||||
\(839\) | 19.4708 | − | 33.7244i | 0.672206 | − | 1.16429i | −0.305072 | − | 0.952329i | \(-0.598680\pi\) |
0.977277 | − | 0.211965i | \(-0.0679862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7932 | + | 18.6943i | 0.372178 | + | 0.644631i | ||||
\(842\) | −0.375119 | −0.0129275 | ||||||||
\(843\) | 0.0798445 | − | 2.68911i | 0.00274999 | − | 0.0926180i | ||||
\(844\) | 2.30769 | 0.0794340 | ||||||||
\(845\) | 4.63243 | − | 8.02361i | 0.159361 | − | 0.276021i | ||||
\(846\) | 1.10560 | + | 2.20797i | 0.0380113 | + | 0.0759116i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.65657 | + | 6.33336i | −0.125567 | + | 0.217488i | ||||
\(849\) | −0.136296 | + | 4.59036i | −0.00467766 | + | 0.157541i | ||||
\(850\) | 23.6825 | − | 41.0193i | 0.812304 | − | 1.40695i | ||||
\(851\) | −20.9932 | + | 36.3613i | −0.719638 | + | 1.24645i | ||||
\(852\) | 0.0522798 | − | 1.76075i | 0.00179108 | − | 0.0603224i | ||||
\(853\) | 3.83890 | − | 6.64916i | 0.131441 | − | 0.227663i | −0.792791 | − | 0.609493i | \(-0.791373\pi\) |
0.924232 | + | 0.381830i | \(0.124706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.5188 | − | 64.9425i | −1.11212 | − | 2.22099i | ||||
\(856\) | −3.33892 | + | 5.78318i | −0.114122 | + | 0.197665i | ||||
\(857\) | 15.9639 | 0.545316 | 0.272658 | − | 0.962111i | \(-0.412097\pi\) | ||||
0.272658 | + | 0.962111i | \(0.412097\pi\) | |||||||
\(858\) | −0.253621 | + | 8.54181i | −0.00865848 | + | 0.291612i | ||||
\(859\) | −48.3291 | −1.64897 | −0.824483 | − | 0.565887i | \(-0.808534\pi\) | ||||
−0.824483 | + | 0.565887i | \(0.808534\pi\) | |||||||
\(860\) | −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 | \(-0.634867\pi\) |
0.995014 | − | 0.0997366i | \(-0.0318000\pi\) | |||||||
\(864\) | −7.39166 | − | 5.19536i | −0.251469 | − | 0.176750i | ||||
\(865\) | −17.1650 | − | 29.7307i | −0.583628 | − | 1.01087i | ||||
\(866\) | 3.15356 | + | 5.46212i | 0.107162 | + | 0.185611i | ||||
\(867\) | 0.361948 | − | 12.1902i | 0.0122924 | − | 0.414001i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.591670 | − | 1.02480i | −0.0200710 | − | 0.0347640i | ||||
\(870\) | 19.0310 | − | 10.2468i | 0.645212 | − | 0.347400i | ||||
\(871\) | −17.1755 | −0.581970 | ||||||||
\(872\) | −1.38079 | − | 2.39159i | −0.0467594 | − | 0.0809896i | ||||
\(873\) | 14.6801 | + | 29.3172i | 0.496845 | + | 0.992238i | ||||
\(874\) | 38.3781 | 1.29816 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.491288 | − | 0.264524i | 0.0165991 | − | 0.00893743i | ||||
\(877\) | 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 | ||||
\(879\) | 15.3056 | + | 9.45319i | 0.516245 | + | 0.318848i | ||||
\(880\) | 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 | ||||
\(885\) | 1.48858 | − | 50.1344i | 0.0500380 | − | 1.68525i | ||||
\(886\) | 0.419538 | − | 0.726661i | 0.0140946 | − | 0.0244126i | ||||
\(887\) | 19.1442 | 0.642798 | 0.321399 | − | 0.946944i | \(-0.395847\pi\) | ||||
0.321399 | + | 0.946944i | \(0.395847\pi\) | |||||||
\(888\) | 1.50742 | − | 50.7689i | 0.0505856 | − | 1.70369i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 55.1942 | 1.85011 | ||||||||
\(891\) | −4.17798 | − | 9.74930i | −0.139968 | − | 0.326614i | ||||
\(892\) | −0.510697 | − | 0.884554i | −0.0170994 | − | 0.0296171i | ||||
\(893\) | −4.34791 | −0.145497 | ||||||||
\(894\) | 2.16158 | + | 1.33505i | 0.0722939 | + | 0.0446509i | ||||
\(895\) | −2.42574 | − | 4.20151i | −0.0810836 | − | 0.140441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.4072 | + | 12.6041i | 0.681377 | + | 0.420838i | ||||
\(898\) | 3.39694 | + | 5.88368i | 0.113358 | + | 0.196341i | ||||
\(899\) | −2.61499 | − | 4.52929i | −0.0872147 | − | 0.151060i | ||||
\(900\) | −3.09779 | − | 6.18652i | −0.103260 | − | 0.206217i | ||||
\(901\) | −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 | ||||||||
\(906\) | −37.6011 | − | 23.2236i | −1.24921 | − | 0.771552i | ||||
\(907\) | 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 | ||||
\(909\) | −2.63430 | + | 3.99491i | −0.0873743 | + | 0.132503i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.3727 | − | 24.8942i | 0.476189 | − | 0.824783i | −0.523439 | − | 0.852063i | \(-0.675351\pi\) |
0.999628 | + | 0.0272803i | \(0.00868466\pi\) | |||||||
\(912\) | −34.3782 | + | 18.5102i | −1.13838 | + | 0.612935i | ||||
\(913\) | −4.30870 | + | 7.46288i | −0.142597 | + | 0.246985i | ||||
\(914\) | 1.85930 | − | 3.22041i | 0.0615003 | − | 0.106522i | ||||
\(915\) | −50.1871 | − | 30.9971i | −1.65914 | − | 1.02473i | ||||
\(916\) | 0.660219 | − | 1.14353i | 0.0218142 | − | 0.0377834i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 27.0945 | + | 19.0438i | 0.894252 | + | 0.628540i | ||||
\(919\) | 8.01347 | − | 13.8797i | 0.264340 | − | 0.457850i | −0.703051 | − | 0.711140i | \(-0.748179\pi\) |
0.967390 | + | 0.253290i | \(0.0815126\pi\) | |||||||
\(920\) | 45.5296 | 1.50107 | ||||||||
\(921\) | 16.2303 | − | 8.73884i | 0.534806 | − | 0.287955i | ||||
\(922\) | −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 | ||||
\(927\) | 3.85718 | − | 5.84941i | 0.126686 | − | 0.192120i | ||||
\(928\) | 2.36715 | + | 4.10002i | 0.0777055 | + | 0.134590i | ||||
\(929\) | 7.00796 | + | 12.1381i | 0.229924 | + | 0.398239i | 0.957785 | − | 0.287485i | \(-0.0928190\pi\) |
−0.727862 | + | 0.685724i | \(0.759486\pi\) | |||||||
\(930\) | 13.4254 | − | 7.22863i | 0.440237 | − | 0.237036i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.28180 | − | 3.95219i | −0.0747428 | − | 0.129458i | ||||
\(933\) | −0.704740 | + | 23.7352i | −0.0230721 | + | 0.777056i | ||||
\(934\) | 26.7475 | 0.875205 | ||||||||
\(935\) | 10.1871 | + | 17.6447i | 0.333155 | + | 0.577042i | ||||
\(936\) | −28.9646 | − | 1.72154i | −0.946739 | − | 0.0562703i | ||||
\(937\) | −51.5307 | −1.68344 | −0.841718 | − | 0.539918i | \(-0.818455\pi\) | ||||
−0.841718 | + | 0.539918i | \(0.818455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.2675 | + | 19.3117i | 1.02038 | + | 0.630214i | ||||
\(940\) | −0.692857 | −0.0225985 | ||||||||
\(941\) | −23.1564 | + | 40.1081i | −0.754877 | + | 1.30749i | 0.190558 | + | 0.981676i | \(0.438970\pi\) |
−0.945435 | + | 0.325809i | \(0.894363\pi\) | |||||||
\(942\) | −18.5001 | + | 9.96099i | −0.602766 | + | 0.324547i | ||||
\(943\) | 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 | \(-0.272061\pi\) |
−0.981531 | + | 0.191305i | \(0.938728\pi\) | |||||||
\(948\) | 0.475200 | − | 0.255861i | 0.0154338 | − | 0.00830998i | ||||
\(949\) | 1.67161 | − | 2.89531i | 0.0542628 | − | 0.0939859i | ||||
\(950\) | −66.3297 | −2.15202 | ||||||||
\(951\) | 5.26152 | + | 3.24967i | 0.170616 | + | 0.105378i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0109 | 0.972148 | 0.486074 | − | 0.873918i | \(-0.338429\pi\) | ||||
0.486074 | + | 0.873918i | \(0.338429\pi\) | |||||||
\(954\) | −3.88932 | − | 7.76727i | −0.125921 | − | 0.251475i | ||||
\(955\) | 44.0958 | + | 76.3762i | 1.42691 | + | 2.47148i | ||||
\(956\) | 4.39547 | 0.142160 | ||||||||
\(957\) | −0.164954 | + | 5.55557i | −0.00533222 | + | 0.179586i | ||||
\(958\) | −16.3675 | − | 28.3493i | −0.528809 | − | 0.915924i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −47.4591 | + | 25.5533i | −1.53173 | + | 0.824730i | ||||
\(961\) | 13.6553 | + | 23.6516i | 0.440492 | + | 0.762955i | ||||
\(962\) | −20.4391 | − | 35.4015i | −0.658982 | − | 1.14139i | ||||
\(963\) | −2.98679 | − | 5.96486i | −0.0962481 | − | 0.192215i | ||||
\(964\) | 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 | 0.999261 | + | 0.0384431i | \(0.0122398\pi\) |
−0.466338 | + | 0.884607i | \(0.654427\pi\) | |||||||
\(968\) | 28.8633 | 0.927702 | ||||||||
\(969\) | −51.3436 | + | 27.6448i | −1.64939 | + | 0.888080i | ||||
\(970\) | 50.0896 | 1.60828 | ||||||||
\(971\) | 20.8234 | − | 36.0672i | 0.668256 | − | 1.15745i | −0.310136 | − | 0.950692i | \(-0.600375\pi\) |
0.978392 | − | 0.206761i | \(-0.0662921\pi\) | |||||||
\(972\) | 4.50110 | − | 1.77271i | 0.144373 | − | 0.0568597i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.2928 | − | 36.8803i | 0.682267 | − | 1.18172i | ||||
\(975\) | −35.2702 | − | 21.7839i | −1.12955 | − | 0.697644i | ||||
\(976\) | −15.8556 | + | 27.4628i | −0.507527 | + | 0.879062i | ||||
\(977\) | −18.7590 | + | 32.4916i | −0.600154 | + | 1.03950i | 0.392643 | + | 0.919691i | \(0.371561\pi\) |
−0.992797 | + | 0.119807i | \(0.961772\pi\) | |||||||
\(978\) | −33.5041 | + | 18.0396i | −1.07134 | + | 0.576842i | ||||
\(979\) | −7.09647 | + | 12.2914i | −0.226804 | + | 0.392836i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.75383 | + | 0.163676i | 0.0879231 | + | 0.00522578i | ||||
\(982\) | 2.28778 | − | 3.96255i | 0.0730059 | − | 0.126450i | ||||
\(983\) | −48.0758 | −1.53338 | −0.766690 | − | 0.642017i | \(-0.778098\pi\) | ||||
−0.766690 | + | 0.642017i | \(0.778098\pi\) | |||||||
\(984\) | −29.4451 | − | 18.1862i | −0.938675 | − | 0.579753i | ||||
\(985\) | −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 | ||||
\(990\) | −16.1756 | − | 0.961413i | −0.514095 | − | 0.0305557i | ||||
\(991\) | 17.0643 | + | 29.5562i | 0.542065 | + | 0.938884i | 0.998785 | + | 0.0492737i | \(0.0156907\pi\) |
−0.456720 | + | 0.889610i | \(0.650976\pi\) | |||||||
\(992\) | 1.66990 | + | 2.89236i | 0.0530195 | + | 0.0918324i | ||||
\(993\) | −35.2871 | − | 21.7944i | −1.11980 | − | 0.691624i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.5346 | + | 58.0837i | 1.06312 | + | 1.84138i | ||||
\(996\) | −3.34388 | − | 2.06528i | −0.105955 | − | 0.0654410i | ||||
\(997\) | 44.0827 | 1.39611 | 0.698056 | − | 0.716043i | \(-0.254049\pi\) | ||||
0.698056 | + | 0.716043i | \(0.254049\pi\) | |||||||
\(998\) | −10.1661 | − | 17.6081i | −0.321801 | − | 0.557376i | ||||
\(999\) | 41.5104 | + | 29.1763i | 1.31333 | + | 0.923097i |
(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 | 441.2.g.h.79.3 | 24 | ||
3.2 | odd | 2 | 1323.2.g.h.667.10 | 24 | |||
7.2 | even | 3 | 441.2.f.h.295.4 | yes | 24 | ||
7.3 | odd | 6 | 441.2.h.h.214.9 | 24 | |||
7.4 | even | 3 | 441.2.h.h.214.10 | 24 | |||
7.5 | odd | 6 | 441.2.f.h.295.3 | yes | 24 | ||
7.6 | odd | 2 | inner | 441.2.g.h.79.4 | 24 | ||
9.4 | even | 3 | 441.2.h.h.373.10 | 24 | |||
9.5 | odd | 6 | 1323.2.h.h.226.3 | 24 | |||
21.2 | odd | 6 | 1323.2.f.h.883.10 | 24 | |||
21.5 | even | 6 | 1323.2.f.h.883.9 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.802.3 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.802.4 | 24 | |||
21.20 | even | 2 | 1323.2.g.h.667.9 | 24 | |||
63.2 | odd | 6 | 3969.2.a.bi.1.3 | 12 | |||
63.4 | even | 3 | inner | 441.2.g.h.67.3 | 24 | ||
63.5 | even | 6 | 1323.2.f.h.442.9 | 24 | |||
63.13 | odd | 6 | 441.2.h.h.373.9 | 24 | |||
63.16 | even | 3 | 3969.2.a.bh.1.10 | 12 | |||
63.23 | odd | 6 | 1323.2.f.h.442.10 | 24 | |||
63.31 | odd | 6 | inner | 441.2.g.h.67.4 | 24 | ||
63.32 | odd | 6 | 1323.2.g.h.361.10 | 24 | |||
63.40 | odd | 6 | 441.2.f.h.148.3 | ✓ | 24 | ||
63.41 | even | 6 | 1323.2.h.h.226.4 | 24 | |||
63.47 | even | 6 | 3969.2.a.bi.1.4 | 12 | |||
63.58 | even | 3 | 441.2.f.h.148.4 | yes | 24 | ||
63.59 | even | 6 | 1323.2.g.h.361.9 | 24 | |||
63.61 | odd | 6 | 3969.2.a.bh.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.3 | ✓ | 24 | 63.40 | odd | 6 | ||
441.2.f.h.148.4 | yes | 24 | 63.58 | even | 3 | ||
441.2.f.h.295.3 | yes | 24 | 7.5 | odd | 6 | ||
441.2.f.h.295.4 | yes | 24 | 7.2 | even | 3 | ||
441.2.g.h.67.3 | 24 | 63.4 | even | 3 | inner | ||
441.2.g.h.67.4 | 24 | 63.31 | odd | 6 | inner | ||
441.2.g.h.79.3 | 24 | 1.1 | even | 1 | trivial | ||
441.2.g.h.79.4 | 24 | 7.6 | odd | 2 | inner | ||
441.2.h.h.214.9 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.214.10 | 24 | 7.4 | even | 3 | |||
441.2.h.h.373.9 | 24 | 63.13 | odd | 6 | |||
441.2.h.h.373.10 | 24 | 9.4 | even | 3 | |||
1323.2.f.h.442.9 | 24 | 63.5 | even | 6 | |||
1323.2.f.h.442.10 | 24 | 63.23 | odd | 6 | |||
1323.2.f.h.883.9 | 24 | 21.5 | even | 6 | |||
1323.2.f.h.883.10 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.361.9 | 24 | 63.59 | even | 6 | |||
1323.2.g.h.361.10 | 24 | 63.32 | odd | 6 | |||
1323.2.g.h.667.9 | 24 | 21.20 | even | 2 | |||
1323.2.g.h.667.10 | 24 | 3.2 | odd | 2 | |||
1323.2.h.h.226.3 | 24 | 9.5 | odd | 6 | |||
1323.2.h.h.226.4 | 24 | 63.41 | even | 6 | |||
1323.2.h.h.802.3 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.802.4 | 24 | 21.17 | even | 6 | |||
3969.2.a.bh.1.9 | 12 | 63.61 | odd | 6 | |||
3969.2.a.bh.1.10 | 12 | 63.16 | even | 3 | |||
3969.2.a.bi.1.3 | 12 | 63.2 | odd | 6 | |||
3969.2.a.bi.1.4 | 12 | 63.47 | even | 6 |