Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.1 | ||
Root | \(0.535233 + 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.421 |
Dual form | 462.2.j.g.169.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −2.26728 | − | 1.64728i | −1.01396 | − | 0.736685i | −0.0489242 | − | 0.998802i | \(-0.515579\pi\) |
−0.965036 | + | 0.262117i | \(0.915579\pi\) | |||||||
\(6\) | 0.809017 | + | 0.587785i | 0.330280 | + | 0.239962i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −2.80252 | −0.886234 | ||||||||
\(11\) | 3.31485 | + | 0.108436i | 0.999465 | + | 0.0326948i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 5.56036 | − | 4.03984i | 1.54217 | − | 1.12045i | 0.593208 | − | 0.805049i | \(-0.297861\pi\) |
0.948959 | − | 0.315400i | \(-0.102139\pi\) | |||||||
\(14\) | −0.309017 | − | 0.951057i | −0.0825883 | − | 0.254181i | ||||
\(15\) | 0.866025 | − | 2.66535i | 0.223607 | − | 0.688191i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.68448 | − | 1.22385i | −0.408547 | − | 0.296827i | 0.364466 | − | 0.931217i | \(-0.381251\pi\) |
−0.773013 | + | 0.634390i | \(0.781251\pi\) | |||||||
\(18\) | −0.309017 | + | 0.951057i | −0.0728360 | + | 0.224166i | ||||
\(19\) | −2.10570 | − | 6.48068i | −0.483081 | − | 1.48677i | −0.834742 | − | 0.550642i | \(-0.814383\pi\) |
0.351661 | − | 0.936127i | \(-0.385617\pi\) | |||||||
\(20\) | −2.26728 | + | 1.64728i | −0.506980 | + | 0.368343i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 2.74551 | − | 1.86069i | 0.585344 | − | 0.396701i | ||||
\(23\) | −1.57448 | −0.328302 | −0.164151 | − | 0.986435i | \(-0.552489\pi\) | ||||
−0.164151 | + | 0.986435i | \(0.552489\pi\) | |||||||
\(24\) | 0.809017 | − | 0.587785i | 0.165140 | − | 0.119981i | ||||
\(25\) | 0.881966 | + | 2.71441i | 0.176393 | + | 0.542882i | ||||
\(26\) | 2.12387 | − | 6.53660i | 0.416525 | − | 1.28193i | ||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | −0.809017 | − | 0.587785i | −0.152890 | − | 0.111081i | ||||
\(29\) | −2.16672 | + | 6.66849i | −0.402351 | + | 1.23831i | 0.520736 | + | 0.853717i | \(0.325657\pi\) |
−0.923087 | + | 0.384591i | \(0.874343\pi\) | |||||||
\(30\) | −0.866025 | − | 2.66535i | −0.158114 | − | 0.486624i | ||||
\(31\) | 3.70378 | − | 2.69095i | 0.665218 | − | 0.483309i | −0.203203 | − | 0.979137i | \(-0.565135\pi\) |
0.868421 | + | 0.495828i | \(0.165135\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.921216 | + | 3.18612i | 0.160363 | + | 0.554632i | ||||
\(34\) | −2.08214 | −0.357083 | ||||||||
\(35\) | −2.26728 | + | 1.64728i | −0.383241 | + | 0.278441i | ||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | −3.36201 | + | 10.3472i | −0.552711 | + | 1.70107i | 0.149203 | + | 0.988807i | \(0.452329\pi\) |
−0.701914 | + | 0.712262i | \(0.747671\pi\) | |||||||
\(38\) | −5.51279 | − | 4.00528i | −0.894293 | − | 0.649742i | ||||
\(39\) | 5.56036 | + | 4.03984i | 0.890370 | + | 0.646892i | ||||
\(40\) | −0.866025 | + | 2.66535i | −0.136931 | + | 0.421429i | ||||
\(41\) | −0.0475677 | − | 0.146398i | −0.00742883 | − | 0.0228636i | 0.947273 | − | 0.320426i | \(-0.103826\pi\) |
−0.954702 | + | 0.297563i | \(0.903826\pi\) | |||||||
\(42\) | 0.809017 | − | 0.587785i | 0.124834 | − | 0.0906972i | ||||
\(43\) | 7.20419 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(44\) | 1.12747 | − | 3.11910i | 0.169973 | − | 0.470222i | ||||
\(45\) | 2.80252 | 0.417775 | ||||||||
\(46\) | −1.27378 | + | 0.925458i | −0.187809 | + | 0.136451i | ||||
\(47\) | 1.91541 | + | 5.89503i | 0.279391 | + | 0.859878i | 0.988024 | + | 0.154301i | \(0.0493124\pi\) |
−0.708633 | + | 0.705578i | \(0.750688\pi\) | |||||||
\(48\) | 0.309017 | − | 0.951057i | 0.0446028 | − | 0.137273i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 2.30902 | + | 1.67760i | 0.326544 | + | 0.237248i | ||||
\(51\) | 0.643415 | − | 1.98023i | 0.0900962 | − | 0.277287i | ||||
\(52\) | −2.12387 | − | 6.53660i | −0.294528 | − | 0.906463i | ||||
\(53\) | 3.49283 | − | 2.53769i | 0.479778 | − | 0.348579i | −0.321462 | − | 0.946923i | \(-0.604174\pi\) |
0.801240 | + | 0.598344i | \(0.204174\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −7.33708 | − | 5.70634i | −0.989332 | − | 0.769443i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.51279 | − | 4.00528i | 0.730187 | − | 0.530512i | ||||
\(58\) | 2.16672 | + | 6.66849i | 0.284505 | + | 0.875616i | ||||
\(59\) | −2.89878 | + | 8.92151i | −0.377388 | + | 1.16148i | 0.564465 | + | 0.825457i | \(0.309083\pi\) |
−0.941853 | + | 0.336025i | \(0.890917\pi\) | |||||||
\(60\) | −2.26728 | − | 1.64728i | −0.292705 | − | 0.212663i | ||||
\(61\) | 5.96630 | + | 4.33477i | 0.763907 | + | 0.555011i | 0.900106 | − | 0.435671i | \(-0.143489\pi\) |
−0.136199 | + | 0.990681i | \(0.543489\pi\) | |||||||
\(62\) | 1.41472 | − | 4.35405i | 0.179669 | − | 0.552965i | ||||
\(63\) | 0.309017 | + | 0.951057i | 0.0389325 | + | 0.119822i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −19.2617 | −2.38911 | ||||||||
\(66\) | 2.61803 | + | 2.03615i | 0.322258 | + | 0.250632i | ||||
\(67\) | −6.66465 | −0.814217 | −0.407109 | − | 0.913380i | \(-0.633463\pi\) | ||||
−0.407109 | + | 0.913380i | \(0.633463\pi\) | |||||||
\(68\) | −1.68448 | + | 1.22385i | −0.204274 | + | 0.148413i | ||||
\(69\) | −0.486542 | − | 1.49742i | −0.0585728 | − | 0.180269i | ||||
\(70\) | −0.866025 | + | 2.66535i | −0.103510 | + | 0.318571i | ||||
\(71\) | 4.26662 | + | 3.09988i | 0.506354 | + | 0.367888i | 0.811439 | − | 0.584437i | \(-0.198685\pi\) |
−0.305084 | + | 0.952325i | \(0.598685\pi\) | |||||||
\(72\) | 0.809017 | + | 0.587785i | 0.0953436 | + | 0.0692712i | ||||
\(73\) | −1.23494 | + | 3.80077i | −0.144539 | + | 0.444846i | −0.996951 | − | 0.0780241i | \(-0.975139\pi\) |
0.852412 | + | 0.522871i | \(0.175139\pi\) | |||||||
\(74\) | 3.36201 | + | 10.3472i | 0.390826 | + | 1.20284i | ||||
\(75\) | −2.30902 | + | 1.67760i | −0.266622 | + | 0.193712i | ||||
\(76\) | −6.81419 | −0.781641 | ||||||||
\(77\) | 1.12747 | − | 3.11910i | 0.128488 | − | 0.355455i | ||||
\(78\) | 6.87298 | 0.778212 | ||||||||
\(79\) | −7.97106 | + | 5.79131i | −0.896814 | + | 0.651574i | −0.937646 | − | 0.347592i | \(-0.886999\pi\) |
0.0408315 | + | 0.999166i | \(0.486999\pi\) | |||||||
\(80\) | 0.866025 | + | 2.66535i | 0.0968246 | + | 0.297995i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −0.124534 | − | 0.0904792i | −0.0137525 | − | 0.00999175i | ||||
\(83\) | −7.00985 | − | 5.09296i | −0.769431 | − | 0.559024i | 0.132357 | − | 0.991202i | \(-0.457745\pi\) |
−0.901789 | + | 0.432178i | \(0.857745\pi\) | |||||||
\(84\) | 0.309017 | − | 0.951057i | 0.0337165 | − | 0.103769i | ||||
\(85\) | 1.80318 | + | 5.54962i | 0.195583 | + | 0.601941i | ||||
\(86\) | 5.82831 | − | 4.23451i | 0.628483 | − | 0.456619i | ||||
\(87\) | −7.01167 | −0.751730 | ||||||||
\(88\) | −0.921216 | − | 3.18612i | −0.0982020 | − | 0.339642i | ||||
\(89\) | −1.48514 | −0.157424 | −0.0787120 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787120 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(90\) | 2.26728 | − | 1.64728i | 0.238993 | − | 0.173638i | ||||
\(91\) | −2.12387 | − | 6.53660i | −0.222642 | − | 0.685221i | ||||
\(92\) | −0.486542 | + | 1.49742i | −0.0507255 | + | 0.156117i | ||||
\(93\) | 3.70378 | + | 2.69095i | 0.384064 | + | 0.279039i | ||||
\(94\) | 5.01461 | + | 3.64333i | 0.517218 | + | 0.375781i | ||||
\(95\) | −5.90126 | + | 18.1622i | −0.605456 | + | 1.86340i | ||||
\(96\) | −0.309017 | − | 0.951057i | −0.0315389 | − | 0.0970668i | ||||
\(97\) | 4.74190 | − | 3.44519i | 0.481467 | − | 0.349806i | −0.320426 | − | 0.947273i | \(-0.603826\pi\) |
0.801893 | + | 0.597467i | \(0.203826\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −2.74551 | + | 1.86069i | −0.275934 | + | 0.187007i | ||||
\(100\) | 2.85410 | 0.285410 | ||||||||
\(101\) | 9.35745 | − | 6.79859i | 0.931101 | − | 0.676485i | −0.0151608 | − | 0.999885i | \(-0.504826\pi\) |
0.946262 | + | 0.323400i | \(0.104826\pi\) | |||||||
\(102\) | −0.643415 | − | 1.98023i | −0.0637076 | − | 0.196072i | ||||
\(103\) | 3.89046 | − | 11.9736i | 0.383338 | − | 1.17979i | −0.554340 | − | 0.832290i | \(-0.687029\pi\) |
0.937679 | − | 0.347504i | \(-0.112971\pi\) | |||||||
\(104\) | −5.56036 | − | 4.03984i | −0.545238 | − | 0.396139i | ||||
\(105\) | −2.26728 | − | 1.64728i | −0.221264 | − | 0.160758i | ||||
\(106\) | 1.33414 | − | 4.10607i | 0.129584 | − | 0.398817i | ||||
\(107\) | −4.29822 | − | 13.2286i | −0.415524 | − | 1.27885i | −0.911781 | − | 0.410677i | \(-0.865293\pi\) |
0.496257 | − | 0.868176i | \(-0.334707\pi\) | |||||||
\(108\) | −0.809017 | + | 0.587785i | −0.0778477 | + | 0.0565597i | ||||
\(109\) | 19.0440 | 1.82408 | 0.912040 | − | 0.410101i | \(-0.134506\pi\) | ||||
0.912040 | + | 0.410101i | \(0.134506\pi\) | |||||||
\(110\) | −9.28993 | − | 0.303895i | −0.885760 | − | 0.0289752i | ||||
\(111\) | −10.8797 | −1.03265 | ||||||||
\(112\) | −0.809017 | + | 0.587785i | −0.0764449 | + | 0.0555405i | ||||
\(113\) | 1.35436 | + | 4.16828i | 0.127407 | + | 0.392119i | 0.994332 | − | 0.106320i | \(-0.0339068\pi\) |
−0.866925 | + | 0.498439i | \(0.833907\pi\) | |||||||
\(114\) | 2.10570 | − | 6.48068i | 0.197217 | − | 0.606971i | ||||
\(115\) | 3.56980 | + | 2.59361i | 0.332886 | + | 0.241856i | ||||
\(116\) | 5.67256 | + | 4.12136i | 0.526684 | + | 0.382658i | ||||
\(117\) | −2.12387 | + | 6.53660i | −0.196352 | + | 0.604308i | ||||
\(118\) | 2.89878 | + | 8.92151i | 0.266854 | + | 0.821292i | ||||
\(119\) | −1.68448 | + | 1.22385i | −0.154416 | + | 0.112190i | ||||
\(120\) | −2.80252 | −0.255834 | ||||||||
\(121\) | 10.9765 | + | 0.718901i | 0.997862 | + | 0.0653547i | ||||
\(122\) | 7.37475 | 0.667679 | ||||||||
\(123\) | 0.124534 | − | 0.0904792i | 0.0112288 | − | 0.00815823i | ||||
\(124\) | −1.41472 | − | 4.35405i | −0.127045 | − | 0.391005i | ||||
\(125\) | −1.85840 | + | 5.71957i | −0.166221 | + | 0.511574i | ||||
\(126\) | 0.809017 | + | 0.587785i | 0.0720730 | + | 0.0523641i | ||||
\(127\) | 8.64383 | + | 6.28011i | 0.767016 | + | 0.557269i | 0.901054 | − | 0.433707i | \(-0.142795\pi\) |
−0.134039 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | 2.22622 | + | 6.85159i | 0.196007 | + | 0.603249i | ||||
\(130\) | −15.5830 | + | 11.3217i | −1.36672 | + | 0.992980i | ||||
\(131\) | −16.0292 | −1.40048 | −0.700240 | − | 0.713908i | \(-0.746924\pi\) | ||||
−0.700240 | + | 0.713908i | \(0.746924\pi\) | |||||||
\(132\) | 3.31485 | + | 0.108436i | 0.288521 | + | 0.00943818i | ||||
\(133\) | −6.81419 | −0.590865 | ||||||||
\(134\) | −5.39182 | + | 3.91738i | −0.465782 | + | 0.338411i | ||||
\(135\) | 0.866025 | + | 2.66535i | 0.0745356 | + | 0.229397i | ||||
\(136\) | −0.643415 | + | 1.98023i | −0.0551724 | + | 0.169803i | ||||
\(137\) | −7.51863 | − | 5.46260i | −0.642360 | − | 0.466702i | 0.218300 | − | 0.975882i | \(-0.429949\pi\) |
−0.860660 | + | 0.509180i | \(0.829949\pi\) | |||||||
\(138\) | −1.27378 | − | 0.925458i | −0.108432 | − | 0.0787802i | ||||
\(139\) | −4.01056 | + | 12.3432i | −0.340172 | + | 1.04694i | 0.623947 | + | 0.781467i | \(0.285528\pi\) |
−0.964118 | + | 0.265474i | \(0.914472\pi\) | |||||||
\(140\) | 0.866025 | + | 2.66535i | 0.0731925 | + | 0.225263i | ||||
\(141\) | −5.01461 | + | 3.64333i | −0.422306 | + | 0.306824i | ||||
\(142\) | 5.27383 | 0.442570 | ||||||||
\(143\) | 18.8698 | − | 12.7885i | 1.57797 | − | 1.06943i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 15.8974 | − | 11.5502i | 1.32021 | − | 0.959189i | ||||
\(146\) | 1.23494 | + | 3.80077i | 0.102205 | + | 0.314554i | ||||
\(147\) | 0.309017 | − | 0.951057i | 0.0254873 | − | 0.0784418i | ||||
\(148\) | 8.80185 | + | 6.39492i | 0.723508 | + | 0.525659i | ||||
\(149\) | 1.23607 | + | 0.898056i | 0.101263 | + | 0.0735716i | 0.637264 | − | 0.770645i | \(-0.280066\pi\) |
−0.536002 | + | 0.844217i | \(0.680066\pi\) | |||||||
\(150\) | −0.881966 | + | 2.71441i | −0.0720122 | + | 0.221631i | ||||
\(151\) | 1.58434 | + | 4.87608i | 0.128931 | + | 0.396810i | 0.994597 | − | 0.103813i | \(-0.0331043\pi\) |
−0.865665 | + | 0.500623i | \(0.833104\pi\) | |||||||
\(152\) | −5.51279 | + | 4.00528i | −0.447147 | + | 0.324871i | ||||
\(153\) | 2.08214 | 0.168331 | ||||||||
\(154\) | −0.921216 | − | 3.18612i | −0.0742337 | − | 0.256745i | ||||
\(155\) | −12.8303 | −1.03055 | ||||||||
\(156\) | 5.56036 | − | 4.03984i | 0.445185 | − | 0.323446i | ||||
\(157\) | 5.14093 | + | 15.8222i | 0.410291 | + | 1.26275i | 0.916396 | + | 0.400274i | \(0.131085\pi\) |
−0.506104 | + | 0.862472i | \(0.668915\pi\) | |||||||
\(158\) | −3.04467 | + | 9.37054i | −0.242221 | + | 0.745480i | ||||
\(159\) | 3.49283 | + | 2.53769i | 0.277000 | + | 0.201252i | ||||
\(160\) | 2.26728 | + | 1.64728i | 0.179245 | + | 0.130229i | ||||
\(161\) | −0.486542 | + | 1.49742i | −0.0383449 | + | 0.118013i | ||||
\(162\) | −0.309017 | − | 0.951057i | −0.0242787 | − | 0.0747221i | ||||
\(163\) | 6.85410 | − | 4.97980i | 0.536855 | − | 0.390048i | −0.286061 | − | 0.958211i | \(-0.592346\pi\) |
0.822916 | + | 0.568164i | \(0.192346\pi\) | |||||||
\(164\) | −0.153932 | −0.0120201 | ||||||||
\(165\) | 3.15977 | − | 8.74134i | 0.245988 | − | 0.680512i | ||||
\(166\) | −8.66465 | −0.672508 | ||||||||
\(167\) | −3.31444 | + | 2.40808i | −0.256479 | + | 0.186343i | −0.708593 | − | 0.705617i | \(-0.750670\pi\) |
0.452114 | + | 0.891960i | \(0.350670\pi\) | |||||||
\(168\) | −0.309017 | − | 0.951057i | −0.0238412 | − | 0.0733756i | ||||
\(169\) | 10.5801 | − | 32.5622i | 0.813853 | − | 2.50478i | ||||
\(170\) | 4.72079 | + | 3.42986i | 0.362068 | + | 0.263058i | ||||
\(171\) | 5.51279 | + | 4.00528i | 0.421574 | + | 0.306291i | ||||
\(172\) | 2.22622 | − | 6.85159i | 0.169747 | − | 0.522429i | ||||
\(173\) | 4.95107 | + | 15.2378i | 0.376423 | + | 1.15851i | 0.942514 | + | 0.334168i | \(0.108455\pi\) |
−0.566090 | + | 0.824343i | \(0.691545\pi\) | |||||||
\(174\) | −5.67256 | + | 4.12136i | −0.430036 | + | 0.312439i | ||||
\(175\) | 2.85410 | 0.215750 | ||||||||
\(176\) | −2.61803 | − | 2.03615i | −0.197342 | − | 0.153480i | ||||
\(177\) | −9.38064 | −0.705092 | ||||||||
\(178\) | −1.20150 | + | 0.872941i | −0.0900562 | + | 0.0654297i | ||||
\(179\) | −2.03344 | − | 6.25830i | −0.151987 | − | 0.467767i | 0.845856 | − | 0.533411i | \(-0.179090\pi\) |
−0.997843 | + | 0.0656435i | \(0.979090\pi\) | |||||||
\(180\) | 0.866025 | − | 2.66535i | 0.0645497 | − | 0.198664i | ||||
\(181\) | −12.0949 | − | 8.78748i | −0.899009 | − | 0.653168i | 0.0392023 | − | 0.999231i | \(-0.487518\pi\) |
−0.938211 | + | 0.346063i | \(0.887518\pi\) | |||||||
\(182\) | −5.56036 | − | 4.03984i | −0.412161 | − | 0.299453i | ||||
\(183\) | −2.27892 | + | 7.01381i | −0.168463 | + | 0.518476i | ||||
\(184\) | 0.486542 | + | 1.49742i | 0.0358684 | + | 0.110391i | ||||
\(185\) | 24.6673 | − | 17.9219i | 1.81358 | − | 1.31764i | ||||
\(186\) | 4.57812 | 0.335684 | ||||||||
\(187\) | −5.45110 | − | 4.23954i | −0.398624 | − | 0.310026i | ||||
\(188\) | 6.19840 | 0.452065 | ||||||||
\(189\) | −0.809017 | + | 0.587785i | −0.0588473 | + | 0.0427551i | ||||
\(190\) | 5.90126 | + | 18.1622i | 0.428122 | + | 1.31762i | ||||
\(191\) | 3.97892 | − | 12.2459i | 0.287904 | − | 0.886079i | −0.697609 | − | 0.716479i | \(-0.745753\pi\) |
0.985513 | − | 0.169600i | \(-0.0542475\pi\) | |||||||
\(192\) | −0.809017 | − | 0.587785i | −0.0583858 | − | 0.0424197i | ||||
\(193\) | 5.90817 | + | 4.29254i | 0.425279 | + | 0.308984i | 0.779759 | − | 0.626080i | \(-0.215342\pi\) |
−0.354479 | + | 0.935064i | \(0.615342\pi\) | |||||||
\(194\) | 1.81125 | − | 5.57444i | 0.130040 | − | 0.400222i | ||||
\(195\) | −5.95218 | − | 18.3189i | −0.426244 | − | 1.31185i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | 17.3388 | 1.23534 | 0.617670 | − | 0.786437i | \(-0.288077\pi\) | ||||
0.617670 | + | 0.786437i | \(0.288077\pi\) | |||||||
\(198\) | −1.12747 | + | 3.11910i | −0.0801261 | + | 0.221665i | ||||
\(199\) | −20.7862 | −1.47349 | −0.736747 | − | 0.676168i | \(-0.763639\pi\) | ||||
−0.736747 | + | 0.676168i | \(0.763639\pi\) | |||||||
\(200\) | 2.30902 | − | 1.67760i | 0.163272 | − | 0.118624i | ||||
\(201\) | −2.05949 | − | 6.33846i | −0.145265 | − | 0.447081i | ||||
\(202\) | 3.57423 | − | 11.0003i | 0.251482 | − | 0.773982i | ||||
\(203\) | 5.67256 | + | 4.12136i | 0.398136 | + | 0.289262i | ||||
\(204\) | −1.68448 | − | 1.22385i | −0.117937 | − | 0.0856865i | ||||
\(205\) | −0.133309 | + | 0.410284i | −0.00931073 | + | 0.0286555i | ||||
\(206\) | −3.89046 | − | 11.9736i | −0.271061 | − | 0.834240i | ||||
\(207\) | 1.27378 | − | 0.925458i | 0.0885341 | − | 0.0643238i | ||||
\(208\) | −6.87298 | −0.476556 | ||||||||
\(209\) | −6.27734 | − | 21.7108i | −0.434213 | − | 1.50177i | ||||
\(210\) | −2.80252 | −0.193392 | ||||||||
\(211\) | −18.0471 | + | 13.1120i | −1.24241 | + | 0.902667i | −0.997757 | − | 0.0669430i | \(-0.978675\pi\) |
−0.244657 | + | 0.969610i | \(0.578675\pi\) | |||||||
\(212\) | −1.33414 | − | 4.10607i | −0.0916294 | − | 0.282006i | ||||
\(213\) | −1.62970 | + | 5.01571i | −0.111665 | + | 0.343671i | ||||
\(214\) | −11.2529 | − | 8.17569i | −0.769231 | − | 0.558879i | ||||
\(215\) | −16.3339 | − | 11.8673i | −1.11397 | − | 0.809343i | ||||
\(216\) | −0.309017 | + | 0.951057i | −0.0210259 | + | 0.0647112i | ||||
\(217\) | −1.41472 | − | 4.35405i | −0.0960372 | − | 0.295572i | ||||
\(218\) | 15.4069 | − | 11.1938i | 1.04349 | − | 0.758137i | ||||
\(219\) | −3.99637 | −0.270049 | ||||||||
\(220\) | −7.69433 | + | 5.21463i | −0.518752 | + | 0.351570i | ||||
\(221\) | −14.3105 | −0.962627 | ||||||||
\(222\) | −8.80185 | + | 6.39492i | −0.590742 | + | 0.429199i | ||||
\(223\) | 1.94394 | + | 5.98283i | 0.130176 | + | 0.400640i | 0.994809 | − | 0.101765i | \(-0.0324488\pi\) |
−0.864633 | + | 0.502405i | \(0.832449\pi\) | |||||||
\(224\) | −0.309017 | + | 0.951057i | −0.0206471 | + | 0.0635451i | ||||
\(225\) | −2.30902 | − | 1.67760i | −0.153934 | − | 0.111840i | ||||
\(226\) | 3.54575 | + | 2.57614i | 0.235860 | + | 0.171362i | ||||
\(227\) | −4.21455 | + | 12.9710i | −0.279729 | + | 0.860918i | 0.708200 | + | 0.706012i | \(0.249508\pi\) |
−0.987929 | + | 0.154906i | \(0.950492\pi\) | |||||||
\(228\) | −2.10570 | − | 6.48068i | −0.139453 | − | 0.429193i | ||||
\(229\) | −18.2635 | + | 13.2692i | −1.20688 | + | 0.876853i | −0.994944 | − | 0.100430i | \(-0.967978\pi\) |
−0.211940 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(230\) | 4.41252 | 0.290953 | ||||||||
\(231\) | 3.31485 | + | 0.108436i | 0.218101 | + | 0.00713459i | ||||
\(232\) | 7.01167 | 0.460339 | ||||||||
\(233\) | 1.43864 | − | 1.04524i | 0.0942487 | − | 0.0684757i | −0.539663 | − | 0.841881i | \(-0.681448\pi\) |
0.633912 | + | 0.773406i | \(0.281448\pi\) | |||||||
\(234\) | 2.12387 | + | 6.53660i | 0.138842 | + | 0.427311i | ||||
\(235\) | 5.36797 | − | 16.5209i | 0.350168 | − | 1.07771i | ||||
\(236\) | 7.58909 | + | 5.51380i | 0.494008 | + | 0.358918i | ||||
\(237\) | −7.97106 | − | 5.79131i | −0.517776 | − | 0.376186i | ||||
\(238\) | −0.643415 | + | 1.98023i | −0.0417064 | + | 0.128359i | ||||
\(239\) | 7.98426 | + | 24.5730i | 0.516459 | + | 1.58950i | 0.780611 | + | 0.625017i | \(0.214908\pi\) |
−0.264152 | + | 0.964481i | \(0.585092\pi\) | |||||||
\(240\) | −2.26728 | + | 1.64728i | −0.146353 | + | 0.106331i | ||||
\(241\) | 14.9321 | 0.961861 | 0.480930 | − | 0.876759i | \(-0.340299\pi\) | ||||
0.480930 | + | 0.876759i | \(0.340299\pi\) | |||||||
\(242\) | 9.30272 | − | 5.87021i | 0.598002 | − | 0.377351i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.96630 | − | 4.33477i | 0.381953 | − | 0.277505i | ||||
\(245\) | 0.866025 | + | 2.66535i | 0.0553283 | + | 0.170283i | ||||
\(246\) | 0.0475677 | − | 0.146398i | 0.00303281 | − | 0.00933402i | ||||
\(247\) | −37.8893 | − | 27.5282i | −2.41084 | − | 1.75158i | ||||
\(248\) | −3.70378 | − | 2.69095i | −0.235190 | − | 0.170876i | ||||
\(249\) | 2.67753 | − | 8.24058i | 0.169681 | − | 0.522225i | ||||
\(250\) | 1.85840 | + | 5.71957i | 0.117536 | + | 0.361738i | ||||
\(251\) | 4.59734 | − | 3.34016i | 0.290181 | − | 0.210829i | −0.433165 | − | 0.901315i | \(-0.642603\pi\) |
0.723346 | + | 0.690486i | \(0.242603\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −5.21918 | − | 0.170731i | −0.328127 | − | 0.0107338i | ||||
\(254\) | 10.6844 | 0.670396 | ||||||||
\(255\) | −4.72079 | + | 3.42986i | −0.295628 | + | 0.214786i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 7.87145 | − | 24.2258i | 0.491007 | − | 1.51117i | −0.332080 | − | 0.943251i | \(-0.607750\pi\) |
0.823088 | − | 0.567914i | \(-0.192250\pi\) | |||||||
\(258\) | 5.82831 | + | 4.23451i | 0.362855 | + | 0.263629i | ||||
\(259\) | 8.80185 | + | 6.39492i | 0.546920 | + | 0.397361i | ||||
\(260\) | −5.95218 | + | 18.3189i | −0.369138 | + | 1.13609i | ||||
\(261\) | −2.16672 | − | 6.66849i | −0.134117 | − | 0.412769i | ||||
\(262\) | −12.9679 | + | 9.42174i | −0.801160 | + | 0.582077i | ||||
\(263\) | 20.3518 | 1.25495 | 0.627474 | − | 0.778638i | \(-0.284089\pi\) | ||||
0.627474 | + | 0.778638i | \(0.284089\pi\) | |||||||
\(264\) | 2.74551 | − | 1.86069i | 0.168974 | − | 0.114518i | ||||
\(265\) | −12.0995 | −0.743269 | ||||||||
\(266\) | −5.51279 | + | 4.00528i | −0.338011 | + | 0.245579i | ||||
\(267\) | −0.458932 | − | 1.41245i | −0.0280862 | − | 0.0864404i | ||||
\(268\) | −2.05949 | + | 6.33846i | −0.125803 | + | 0.387183i | ||||
\(269\) | 2.23019 | + | 1.62033i | 0.135977 | + | 0.0987930i | 0.653694 | − | 0.756759i | \(-0.273218\pi\) |
−0.517718 | + | 0.855552i | \(0.673218\pi\) | |||||||
\(270\) | 2.26728 | + | 1.64728i | 0.137983 | + | 0.100250i | ||||
\(271\) | 5.79668 | − | 17.8404i | 0.352123 | − | 1.08372i | −0.605535 | − | 0.795818i | \(-0.707041\pi\) |
0.957659 | − | 0.287906i | \(-0.0929590\pi\) | |||||||
\(272\) | 0.643415 | + | 1.98023i | 0.0390128 | + | 0.120069i | ||||
\(273\) | 5.56036 | − | 4.03984i | 0.336528 | − | 0.244502i | ||||
\(274\) | −9.29353 | −0.561443 | ||||||||
\(275\) | 2.62925 | + | 9.09351i | 0.158549 | + | 0.548359i | ||||
\(276\) | −1.57448 | −0.0947728 | ||||||||
\(277\) | 2.51594 | − | 1.82794i | 0.151168 | − | 0.109830i | −0.509630 | − | 0.860394i | \(-0.670218\pi\) |
0.660798 | + | 0.750563i | \(0.270218\pi\) | |||||||
\(278\) | 4.01056 | + | 12.3432i | 0.240538 | + | 0.740299i | ||||
\(279\) | −1.41472 | + | 4.35405i | −0.0846969 | + | 0.260670i | ||||
\(280\) | 2.26728 | + | 1.64728i | 0.135496 | + | 0.0984437i | ||||
\(281\) | 2.32135 | + | 1.68656i | 0.138480 | + | 0.100612i | 0.654869 | − | 0.755743i | \(-0.272724\pi\) |
−0.516388 | + | 0.856354i | \(0.672724\pi\) | |||||||
\(282\) | −1.91541 | + | 5.89503i | −0.114061 | + | 0.351044i | ||||
\(283\) | 0.686429 | + | 2.11261i | 0.0408039 | + | 0.125582i | 0.969383 | − | 0.245552i | \(-0.0789692\pi\) |
−0.928579 | + | 0.371134i | \(0.878969\pi\) | |||||||
\(284\) | 4.26662 | − | 3.09988i | 0.253177 | − | 0.183944i | ||||
\(285\) | −19.0969 | −1.13120 | ||||||||
\(286\) | 7.74911 | − | 21.4375i | 0.458215 | − | 1.26763i | ||||
\(287\) | −0.153932 | −0.00908634 | ||||||||
\(288\) | 0.809017 | − | 0.587785i | 0.0476718 | − | 0.0346356i | ||||
\(289\) | −3.91361 | − | 12.0449i | −0.230212 | − | 0.708521i | ||||
\(290\) | 6.07228 | − | 18.6886i | 0.356577 | − | 1.09743i | ||||
\(291\) | 4.74190 | + | 3.44519i | 0.277975 | + | 0.201961i | ||||
\(292\) | 3.23313 | + | 2.34900i | 0.189204 | + | 0.137465i | ||||
\(293\) | −8.26463 | + | 25.4359i | −0.482825 | + | 1.48598i | 0.352282 | + | 0.935894i | \(0.385406\pi\) |
−0.835107 | + | 0.550088i | \(0.814594\pi\) | |||||||
\(294\) | −0.309017 | − | 0.951057i | −0.0180222 | − | 0.0554667i | ||||
\(295\) | 21.2686 | − | 15.4525i | 1.23830 | − | 0.899680i | ||||
\(296\) | 10.8797 | 0.632369 | ||||||||
\(297\) | −2.61803 | − | 2.03615i | −0.151914 | − | 0.118149i | ||||
\(298\) | 1.52786 | 0.0885068 | ||||||||
\(299\) | −8.75470 | + | 6.36066i | −0.506297 | + | 0.367846i | ||||
\(300\) | 0.881966 | + | 2.71441i | 0.0509203 | + | 0.156717i | ||||
\(301\) | 2.22622 | − | 6.85159i | 0.128317 | − | 0.394919i | ||||
\(302\) | 4.14784 | + | 3.01358i | 0.238682 | + | 0.173412i | ||||
\(303\) | 9.35745 | + | 6.79859i | 0.537572 | + | 0.390569i | ||||
\(304\) | −2.10570 | + | 6.48068i | −0.120770 | + | 0.371692i | ||||
\(305\) | −6.38672 | − | 19.6563i | −0.365703 | − | 1.12552i | ||||
\(306\) | 1.68448 | − | 1.22385i | 0.0962955 | − | 0.0699628i | ||||
\(307\) | −5.34430 | −0.305015 | −0.152508 | − | 0.988302i | \(-0.548735\pi\) | ||||
−0.152508 | + | 0.988302i | \(0.548735\pi\) | |||||||
\(308\) | −2.61803 | − | 2.03615i | −0.149176 | − | 0.116020i | ||||
\(309\) | 12.5898 | 0.716208 | ||||||||
\(310\) | −10.3799 | + | 7.54143i | −0.589538 | + | 0.428325i | ||||
\(311\) | −10.6981 | − | 32.9255i | −0.606636 | − | 1.86703i | −0.485127 | − | 0.874444i | \(-0.661227\pi\) |
−0.121509 | − | 0.992590i | \(-0.538773\pi\) | |||||||
\(312\) | 2.12387 | − | 6.53660i | 0.120240 | − | 0.370062i | ||||
\(313\) | 16.9007 | + | 12.2791i | 0.955285 | + | 0.694055i | 0.952051 | − | 0.305939i | \(-0.0989705\pi\) |
0.00323427 | + | 0.999995i | \(0.498970\pi\) | |||||||
\(314\) | 13.4591 | + | 9.77863i | 0.759543 | + | 0.551840i | ||||
\(315\) | 0.866025 | − | 2.66535i | 0.0487950 | − | 0.150176i | ||||
\(316\) | 3.04467 | + | 9.37054i | 0.171276 | + | 0.527134i | ||||
\(317\) | 1.15575 | − | 0.839701i | 0.0649134 | − | 0.0471623i | −0.554855 | − | 0.831947i | \(-0.687226\pi\) |
0.619769 | + | 0.784785i | \(0.287226\pi\) | |||||||
\(318\) | 4.31738 | 0.242107 | ||||||||
\(319\) | −7.90548 | + | 21.8701i | −0.442622 | + | 1.22449i | ||||
\(320\) | 2.80252 | 0.156665 | ||||||||
\(321\) | 11.2529 | − | 8.17569i | 0.628074 | − | 0.456323i | ||||
\(322\) | 0.486542 | + | 1.49742i | 0.0271139 | + | 0.0834481i | ||||
\(323\) | −4.38435 | + | 13.4936i | −0.243952 | + | 0.750807i | ||||
\(324\) | −0.809017 | − | 0.587785i | −0.0449454 | − | 0.0326547i | ||||
\(325\) | 15.8698 | + | 11.5301i | 0.880300 | + | 0.639575i | ||||
\(326\) | 2.61803 | − | 8.05748i | 0.144999 | − | 0.446263i | ||||
\(327\) | 5.88491 | + | 18.1119i | 0.325436 | + | 1.00159i | ||||
\(328\) | −0.124534 | + | 0.0904792i | −0.00687623 | + | 0.00499588i | ||||
\(329\) | 6.19840 | 0.341729 | ||||||||
\(330\) | −2.58172 | − | 8.92916i | −0.142119 | − | 0.491534i | ||||
\(331\) | −22.6880 | −1.24704 | −0.623522 | − | 0.781805i | \(-0.714299\pi\) | ||||
−0.623522 | + | 0.781805i | \(0.714299\pi\) | |||||||
\(332\) | −7.00985 | + | 5.09296i | −0.384716 | + | 0.279512i | ||||
\(333\) | −3.36201 | − | 10.3472i | −0.184237 | − | 0.567023i | ||||
\(334\) | −1.26600 | + | 3.89636i | −0.0692726 | + | 0.213199i | ||||
\(335\) | 15.1107 | + | 10.9785i | 0.825584 | + | 0.599822i | ||||
\(336\) | −0.809017 | − | 0.587785i | −0.0441355 | − | 0.0320663i | ||||
\(337\) | 8.01569 | − | 24.6697i | 0.436642 | − | 1.34385i | −0.454752 | − | 0.890618i | \(-0.650272\pi\) |
0.891394 | − | 0.453229i | \(-0.149728\pi\) | |||||||
\(338\) | −10.5801 | − | 32.5622i | −0.575481 | − | 1.77115i | ||||
\(339\) | −3.54575 | + | 2.57614i | −0.192579 | + | 0.139917i | ||||
\(340\) | 5.83522 | 0.316459 | ||||||||
\(341\) | 12.5693 | − | 8.51848i | 0.680664 | − | 0.461301i | ||||
\(342\) | 6.81419 | 0.368469 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | −2.22622 | − | 6.85159i | −0.120030 | − | 0.369413i | ||||
\(345\) | −1.36354 | + | 4.19655i | −0.0734107 | + | 0.225935i | ||||
\(346\) | 12.9621 | + | 9.41750i | 0.696846 | + | 0.506288i | ||||
\(347\) | 24.1786 | + | 17.5668i | 1.29798 | + | 0.943036i | 0.999934 | − | 0.0115162i | \(-0.00366579\pi\) |
0.298044 | + | 0.954552i | \(0.403666\pi\) | |||||||
\(348\) | −2.16672 | + | 6.66849i | −0.116149 | + | 0.357469i | ||||
\(349\) | 6.14427 | + | 18.9101i | 0.328895 | + | 1.01223i | 0.969652 | + | 0.244491i | \(0.0786208\pi\) |
−0.640757 | + | 0.767744i | \(0.721379\pi\) | |||||||
\(350\) | 2.30902 | − | 1.67760i | 0.123422 | − | 0.0896714i | ||||
\(351\) | −6.87298 | −0.366853 | ||||||||
\(352\) | −3.31485 | − | 0.108436i | −0.176682 | − | 0.00577968i | ||||
\(353\) | −2.87886 | −0.153227 | −0.0766133 | − | 0.997061i | \(-0.524411\pi\) | ||||
−0.0766133 | + | 0.997061i | \(0.524411\pi\) | |||||||
\(354\) | −7.58909 | + | 5.51380i | −0.403356 | + | 0.293055i | ||||
\(355\) | −4.56727 | − | 14.0566i | −0.242406 | − | 0.746048i | ||||
\(356\) | −0.458932 | + | 1.41245i | −0.0243234 | + | 0.0748596i | ||||
\(357\) | −1.68448 | − | 1.22385i | −0.0891523 | − | 0.0647729i | ||||
\(358\) | −5.32363 | − | 3.86784i | −0.281362 | − | 0.204422i | ||||
\(359\) | 5.21416 | − | 16.0475i | 0.275193 | − | 0.846957i | −0.713975 | − | 0.700171i | \(-0.753107\pi\) |
0.989168 | − | 0.146786i | \(-0.0468929\pi\) | |||||||
\(360\) | −0.866025 | − | 2.66535i | −0.0456435 | − | 0.140476i | ||||
\(361\) | −22.1939 | + | 16.1248i | −1.16810 | + | 0.848673i | ||||
\(362\) | −14.9502 | −0.785763 | ||||||||
\(363\) | 2.70820 | + | 10.6614i | 0.142144 | + | 0.559579i | ||||
\(364\) | −6.87298 | −0.360242 | ||||||||
\(365\) | 9.06089 | − | 6.58312i | 0.474269 | − | 0.344577i | ||||
\(366\) | 2.27892 | + | 7.01381i | 0.119121 | + | 0.366618i | ||||
\(367\) | 1.48518 | − | 4.57092i | 0.0775259 | − | 0.238600i | −0.904781 | − | 0.425876i | \(-0.859966\pi\) |
0.982307 | + | 0.187276i | \(0.0599659\pi\) | |||||||
\(368\) | 1.27378 | + | 0.925458i | 0.0664006 | + | 0.0482428i | ||||
\(369\) | 0.124534 | + | 0.0904792i | 0.00648298 | + | 0.00471016i | ||||
\(370\) | 9.42209 | − | 28.9982i | 0.489831 | − | 1.50754i | ||||
\(371\) | −1.33414 | − | 4.10607i | −0.0692653 | − | 0.213177i | ||||
\(372\) | 3.70378 | − | 2.69095i | 0.192032 | − | 0.139519i | ||||
\(373\) | −30.8275 | −1.59619 | −0.798094 | − | 0.602533i | \(-0.794158\pi\) | ||||
−0.798094 | + | 0.602533i | \(0.794158\pi\) | |||||||
\(374\) | −6.90197 | − | 0.225779i | −0.356892 | − | 0.0116748i | ||||
\(375\) | −6.01392 | −0.310557 | ||||||||
\(376\) | 5.01461 | − | 3.64333i | 0.258609 | − | 0.187890i | ||||
\(377\) | 14.8919 | + | 45.8324i | 0.766970 | + | 2.36049i | ||||
\(378\) | −0.309017 | + | 0.951057i | −0.0158941 | + | 0.0489171i | ||||
\(379\) | −9.34714 | − | 6.79110i | −0.480131 | − | 0.348835i | 0.321246 | − | 0.946996i | \(-0.395898\pi\) |
−0.801376 | + | 0.598161i | \(0.795898\pi\) | |||||||
\(380\) | 15.4497 | + | 11.2249i | 0.792553 | + | 0.575823i | ||||
\(381\) | −3.30165 | + | 10.1614i | −0.169149 | + | 0.520586i | ||||
\(382\) | −3.97892 | − | 12.2459i | −0.203579 | − | 0.626552i | ||||
\(383\) | 16.7962 | − | 12.2032i | 0.858247 | − | 0.623553i | −0.0691606 | − | 0.997606i | \(-0.522032\pi\) |
0.927407 | + | 0.374053i | \(0.122032\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −7.69433 | + | 5.21463i | −0.392140 | + | 0.265762i | ||||
\(386\) | 7.30290 | 0.371708 | ||||||||
\(387\) | −5.82831 | + | 4.23451i | −0.296270 | + | 0.215252i | ||||
\(388\) | −1.81125 | − | 5.57444i | −0.0919521 | − | 0.282999i | ||||
\(389\) | 1.04480 | − | 3.21557i | 0.0529736 | − | 0.163036i | −0.921070 | − | 0.389398i | \(-0.872683\pi\) |
0.974043 | + | 0.226362i | \(0.0726832\pi\) | |||||||
\(390\) | −15.5830 | − | 11.3217i | −0.789076 | − | 0.573297i | ||||
\(391\) | 2.65219 | + | 1.92693i | 0.134127 | + | 0.0974490i | ||||
\(392\) | −0.309017 | + | 0.951057i | −0.0156077 | + | 0.0480356i | ||||
\(393\) | −4.95330 | − | 15.2447i | −0.249861 | − | 0.768993i | ||||
\(394\) | 14.0274 | − | 10.1915i | 0.706690 | − | 0.513441i | ||||
\(395\) | 27.6126 | 1.38934 | ||||||||
\(396\) | 0.921216 | + | 3.18612i | 0.0462929 | + | 0.160109i | ||||
\(397\) | −2.73835 | −0.137434 | −0.0687168 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687168 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(398\) | −16.8164 | + | 12.2178i | −0.842929 | + | 0.612424i | ||||
\(399\) | −2.10570 | − | 6.48068i | −0.105417 | − | 0.324440i | ||||
\(400\) | 0.881966 | − | 2.71441i | 0.0440983 | − | 0.135721i | ||||
\(401\) | 21.1692 | + | 15.3803i | 1.05714 | + | 0.768055i | 0.973557 | − | 0.228446i | \(-0.0733644\pi\) |
0.0835807 | + | 0.996501i | \(0.473364\pi\) | |||||||
\(402\) | −5.39182 | − | 3.91738i | −0.268919 | − | 0.195381i | ||||
\(403\) | 9.72332 | − | 29.9253i | 0.484353 | − | 1.49069i | ||||
\(404\) | −3.57423 | − | 11.0003i | −0.177825 | − | 0.547288i | ||||
\(405\) | −2.26728 | + | 1.64728i | −0.112662 | + | 0.0818539i | ||||
\(406\) | 7.01167 | 0.347983 | ||||||||
\(407\) | −12.2666 | + | 33.9349i | −0.608031 | + | 1.68209i | ||||
\(408\) | −2.08214 | −0.103081 | ||||||||
\(409\) | −30.9685 | + | 22.5000i | −1.53130 | + | 1.11255i | −0.575782 | + | 0.817604i | \(0.695302\pi\) |
−0.955513 | + | 0.294947i | \(0.904698\pi\) | |||||||
\(410\) | 0.133309 | + | 0.410284i | 0.00658368 | + | 0.0202625i | ||||
\(411\) | 2.87186 | − | 8.83868i | 0.141658 | − | 0.435980i | ||||
\(412\) | −10.1854 | − | 7.40009i | −0.501796 | − | 0.364576i | ||||
\(413\) | 7.58909 | + | 5.51380i | 0.373435 | + | 0.271316i | ||||
\(414\) | 0.486542 | − | 1.49742i | 0.0239122 | − | 0.0735943i | ||||
\(415\) | 7.50381 | + | 23.0944i | 0.368348 | + | 1.13366i | ||||
\(416\) | −5.56036 | + | 4.03984i | −0.272619 | + | 0.198069i | ||||
\(417\) | −12.9785 | −0.635558 | ||||||||
\(418\) | −17.8398 | − | 13.8747i | −0.872572 | − | 0.678633i | ||||
\(419\) | 1.43586 | 0.0701461 | 0.0350731 | − | 0.999385i | \(-0.488834\pi\) | ||||
0.0350731 | + | 0.999385i | \(0.488834\pi\) | |||||||
\(420\) | −2.26728 | + | 1.64728i | −0.110632 | + | 0.0803789i | ||||
\(421\) | 6.18853 | + | 19.0463i | 0.301610 | + | 0.928262i | 0.980920 | + | 0.194410i | \(0.0622792\pi\) |
−0.679310 | + | 0.733852i | \(0.737721\pi\) | |||||||
\(422\) | −6.89338 | + | 21.2156i | −0.335565 | + | 1.03276i | ||||
\(423\) | −5.01461 | − | 3.64333i | −0.243819 | − | 0.177145i | ||||
\(424\) | −3.49283 | − | 2.53769i | −0.169627 | − | 0.123241i | ||||
\(425\) | 1.83637 | − | 5.65177i | 0.0890772 | − | 0.274151i | ||||
\(426\) | 1.62970 | + | 5.01571i | 0.0789594 | + | 0.243012i | ||||
\(427\) | 5.96630 | − | 4.33477i | 0.288730 | − | 0.209774i | ||||
\(428\) | −13.9093 | −0.672332 | ||||||||
\(429\) | 17.9937 | + | 13.9944i | 0.868744 | + | 0.675656i | ||||
\(430\) | −20.1899 | −0.973641 | ||||||||
\(431\) | −6.08789 | + | 4.42311i | −0.293244 | + | 0.213054i | −0.724673 | − | 0.689093i | \(-0.758009\pi\) |
0.431430 | + | 0.902147i | \(0.358009\pi\) | |||||||
\(432\) | 0.309017 | + | 0.951057i | 0.0148676 | + | 0.0457577i | ||||
\(433\) | −4.20237 | + | 12.9336i | −0.201953 | + | 0.621547i | 0.797872 | + | 0.602827i | \(0.205959\pi\) |
−0.999825 | + | 0.0187202i | \(0.994041\pi\) | |||||||
\(434\) | −3.70378 | − | 2.69095i | −0.177787 | − | 0.129170i | ||||
\(435\) | 15.8974 | + | 11.5502i | 0.762224 | + | 0.553788i | ||||
\(436\) | 5.88491 | − | 18.1119i | 0.281836 | − | 0.867402i | ||||
\(437\) | 3.31539 | + | 10.2037i | 0.158597 | + | 0.488110i | ||||
\(438\) | −3.23313 | + | 2.34900i | −0.154485 | + | 0.112240i | ||||
\(439\) | −3.22895 | −0.154109 | −0.0770547 | − | 0.997027i | \(-0.524552\pi\) | ||||
−0.0770547 | + | 0.997027i | \(0.524552\pi\) | |||||||
\(440\) | −3.15977 | + | 8.74134i | −0.150636 | + | 0.416727i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −11.5774 | + | 8.41149i | −0.550682 | + | 0.400094i | ||||
\(443\) | −0.0401986 | − | 0.123719i | −0.00190989 | − | 0.00587805i | 0.950097 | − | 0.311955i | \(-0.100984\pi\) |
−0.952007 | + | 0.306076i | \(0.900984\pi\) | |||||||
\(444\) | −3.36201 | + | 10.3472i | −0.159554 | + | 0.491056i | ||||
\(445\) | 3.36722 | + | 2.44643i | 0.159622 | + | 0.115972i | ||||
\(446\) | 5.08930 | + | 3.69759i | 0.240985 | + | 0.175086i | ||||
\(447\) | −0.472136 | + | 1.45309i | −0.0223313 | + | 0.0687286i | ||||
\(448\) | 0.309017 | + | 0.951057i | 0.0145997 | + | 0.0449332i | ||||
\(449\) | −2.52451 | + | 1.83416i | −0.119139 | + | 0.0865595i | −0.645759 | − | 0.763541i | \(-0.723459\pi\) |
0.526620 | + | 0.850101i | \(0.323459\pi\) | |||||||
\(450\) | −2.85410 | −0.134544 | ||||||||
\(451\) | −0.141805 | − | 0.490447i | −0.00667734 | − | 0.0230942i | ||||
\(452\) | 4.38279 | 0.206149 | ||||||||
\(453\) | −4.14784 | + | 3.01358i | −0.194883 | + | 0.141591i | ||||
\(454\) | 4.21455 | + | 12.9710i | 0.197798 | + | 0.608761i | ||||
\(455\) | −5.95218 | + | 18.3189i | −0.279042 | + | 0.858804i | ||||
\(456\) | −5.51279 | − | 4.00528i | −0.258160 | − | 0.187564i | ||||
\(457\) | 6.18448 | + | 4.49329i | 0.289298 | + | 0.210187i | 0.722963 | − | 0.690887i | \(-0.242780\pi\) |
−0.433665 | + | 0.901074i | \(0.642780\pi\) | |||||||
\(458\) | −6.97603 | + | 21.4700i | −0.325968 | + | 1.00323i | ||||
\(459\) | 0.643415 | + | 1.98023i | 0.0300321 | + | 0.0924292i | ||||
\(460\) | 3.56980 | − | 2.59361i | 0.166443 | − | 0.120928i | ||||
\(461\) | −34.7136 | −1.61677 | −0.808386 | − | 0.588652i | \(-0.799659\pi\) | ||||
−0.808386 | + | 0.588652i | \(0.799659\pi\) | |||||||
\(462\) | 2.74551 | − | 1.86069i | 0.127733 | − | 0.0865673i | ||||
\(463\) | 3.56322 | 0.165597 | 0.0827985 | − | 0.996566i | \(-0.473614\pi\) | ||||
0.0827985 | + | 0.996566i | \(0.473614\pi\) | |||||||
\(464\) | 5.67256 | − | 4.12136i | 0.263342 | − | 0.191329i | ||||
\(465\) | −3.96477 | − | 12.2023i | −0.183862 | − | 0.565868i | ||||
\(466\) | 0.549513 | − | 1.69123i | 0.0254557 | − | 0.0783446i | ||||
\(467\) | −0.0512496 | − | 0.0372350i | −0.00237155 | − | 0.00172303i | 0.586599 | − | 0.809878i | \(-0.300467\pi\) |
−0.588970 | + | 0.808155i | \(0.700467\pi\) | |||||||
\(468\) | 5.56036 | + | 4.03984i | 0.257028 | + | 0.186742i | ||||
\(469\) | −2.05949 | + | 6.33846i | −0.0950985 | + | 0.292683i | ||||
\(470\) | −5.36797 | − | 16.5209i | −0.247606 | − | 0.762053i | ||||
\(471\) | −13.4591 | + | 9.77863i | −0.620164 | + | 0.450576i | ||||
\(472\) | 9.38064 | 0.431779 | ||||||||
\(473\) | 23.8808 | + | 0.781196i | 1.09804 | + | 0.0359194i | ||||
\(474\) | −9.85277 | −0.452553 | ||||||||
\(475\) | 15.7341 | − | 11.4315i | 0.721929 | − | 0.524512i | ||||
\(476\) | 0.643415 | + | 1.98023i | 0.0294909 | + | 0.0907636i | ||||
\(477\) | −1.33414 | + | 4.10607i | −0.0610863 | + | 0.188004i | ||||
\(478\) | 20.9031 | + | 15.1870i | 0.956084 | + | 0.694636i | ||||
\(479\) | −26.8864 | − | 19.5341i | −1.22847 | − | 0.892536i | −0.231696 | − | 0.972788i | \(-0.574427\pi\) |
−0.996775 | + | 0.0802521i | \(0.974427\pi\) | |||||||
\(480\) | −0.866025 | + | 2.66535i | −0.0395285 | + | 0.121656i | ||||
\(481\) | 23.1070 | + | 71.1161i | 1.05359 | + | 3.24262i | ||||
\(482\) | 12.0803 | − | 8.77686i | 0.550243 | − | 0.399775i | ||||
\(483\) | −1.57448 | −0.0716415 | ||||||||
\(484\) | 4.07564 | − | 10.2171i | 0.185256 | − | 0.464414i | ||||
\(485\) | −16.4264 | −0.745886 | ||||||||
\(486\) | 0.809017 | − | 0.587785i | 0.0366978 | − | 0.0266625i | ||||
\(487\) | −2.82706 | − | 8.70079i | −0.128106 | − | 0.394270i | 0.866348 | − | 0.499441i | \(-0.166461\pi\) |
−0.994454 | + | 0.105170i | \(0.966461\pi\) | |||||||
\(488\) | 2.27892 | − | 7.01381i | 0.103162 | − | 0.317500i | ||||
\(489\) | 6.85410 | + | 4.97980i | 0.309953 | + | 0.225194i | ||||
\(490\) | 2.26728 | + | 1.64728i | 0.102425 | + | 0.0744164i | ||||
\(491\) | −5.91539 | + | 18.2057i | −0.266958 | + | 0.821612i | 0.724278 | + | 0.689508i | \(0.242173\pi\) |
−0.991236 | + | 0.132104i | \(0.957827\pi\) | |||||||
\(492\) | −0.0475677 | − | 0.146398i | −0.00214452 | − | 0.00660015i | ||||
\(493\) | 11.8110 | − | 8.58122i | 0.531942 | − | 0.386479i | ||||
\(494\) | −46.8338 | −2.10715 | ||||||||
\(495\) | 9.28993 | + | 0.303895i | 0.417551 | + | 0.0136591i | ||||
\(496\) | −4.57812 | −0.205564 | ||||||||
\(497\) | 4.26662 | − | 3.09988i | 0.191384 | − | 0.139049i | ||||
\(498\) | −2.67753 | − | 8.24058i | −0.119983 | − | 0.369269i | ||||
\(499\) | −7.20825 | + | 22.1847i | −0.322686 | + | 0.993124i | 0.649789 | + | 0.760115i | \(0.274857\pi\) |
−0.972474 | + | 0.233009i | \(0.925143\pi\) | |||||||
\(500\) | 4.86536 | + | 3.53489i | 0.217586 | + | 0.158085i | ||||
\(501\) | −3.31444 | − | 2.40808i | −0.148078 | − | 0.107585i | ||||
\(502\) | 1.75603 | − | 5.40449i | 0.0783753 | − | 0.241214i | ||||
\(503\) | −7.46034 | − | 22.9606i | −0.332640 | − | 1.02376i | −0.967873 | − | 0.251440i | \(-0.919096\pi\) |
0.635233 | − | 0.772321i | \(-0.280904\pi\) | |||||||
\(504\) | 0.809017 | − | 0.587785i | 0.0360365 | − | 0.0261820i | ||||
\(505\) | −32.4152 | −1.44246 | ||||||||
\(506\) | −4.32276 | + | 2.92963i | −0.192170 | + | 0.130238i | ||||
\(507\) | 34.2379 | 1.52056 | ||||||||
\(508\) | 8.64383 | − | 6.28011i | 0.383508 | − | 0.278635i | ||||
\(509\) | −0.355304 | − | 1.09351i | −0.0157486 | − | 0.0484692i | 0.942873 | − | 0.333151i | \(-0.108112\pi\) |
−0.958622 | + | 0.284682i | \(0.908112\pi\) | |||||||
\(510\) | −1.80318 | + | 5.54962i | −0.0798463 | + | 0.245742i | ||||
\(511\) | 3.23313 | + | 2.34900i | 0.143025 | + | 0.103914i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −2.10570 | + | 6.48068i | −0.0929689 | + | 0.286129i | ||||
\(514\) | −7.87145 | − | 24.2258i | −0.347195 | − | 1.06856i | ||||
\(515\) | −28.5446 | + | 20.7389i | −1.25783 | + | 0.913864i | ||||
\(516\) | 7.20419 | 0.317147 | ||||||||
\(517\) | 5.71007 | + | 19.7488i | 0.251128 | + | 0.868553i | ||||
\(518\) | 10.8797 | 0.478026 | ||||||||
\(519\) | −12.9621 | + | 9.41750i | −0.568972 | + | 0.413382i | ||||
\(520\) | 5.95218 | + | 18.3189i | 0.261020 | + | 0.803338i | ||||
\(521\) | 8.06420 | − | 24.8191i | 0.353299 | − | 1.08734i | −0.603690 | − | 0.797219i | \(-0.706304\pi\) |
0.956989 | − | 0.290124i | \(-0.0936965\pi\) | |||||||
\(522\) | −5.67256 | − | 4.12136i | −0.248281 | − | 0.180387i | ||||
\(523\) | −7.63269 | − | 5.54547i | −0.333754 | − | 0.242487i | 0.408268 | − | 0.912862i | \(-0.366133\pi\) |
−0.742022 | + | 0.670376i | \(0.766133\pi\) | |||||||
\(524\) | −4.95330 | + | 15.2447i | −0.216386 | + | 0.665968i | ||||
\(525\) | 0.881966 | + | 2.71441i | 0.0384922 | + | 0.118467i | ||||
\(526\) | 16.4650 | − | 11.9625i | 0.717907 | − | 0.521590i | ||||
\(527\) | −9.53226 | −0.415232 | ||||||||
\(528\) | 1.12747 | − | 3.11910i | 0.0490670 | − | 0.135742i | ||||
\(529\) | −20.5210 | −0.892217 | ||||||||
\(530\) | −9.78873 | + | 7.11193i | −0.425195 | + | 0.308922i | ||||
\(531\) | −2.89878 | − | 8.92151i | −0.125796 | − | 0.387161i | ||||
\(532\) | −2.10570 | + | 6.48068i | −0.0912936 | + | 0.280973i | ||||
\(533\) | −0.855919 | − | 0.621862i | −0.0370740 | − | 0.0269358i | ||||
\(534\) | −1.20150 | − | 0.872941i | −0.0519940 | − | 0.0377758i | ||||
\(535\) | −12.0458 | + | 37.0732i | −0.520786 | + | 1.60282i | ||||
\(536\) | 2.05949 | + | 6.33846i | 0.0889565 | + | 0.273780i | ||||
\(537\) | 5.32363 | − | 3.86784i | 0.229731 | − | 0.166910i | ||||
\(538\) | 2.75666 | 0.118848 | ||||||||
\(539\) | −2.61803 | − | 2.03615i | −0.112767 | − | 0.0877031i | ||||
\(540\) | 2.80252 | 0.120601 | ||||||||
\(541\) | −5.70299 | + | 4.14346i | −0.245191 | + | 0.178141i | −0.703593 | − | 0.710604i | \(-0.748422\pi\) |
0.458402 | + | 0.888745i | \(0.348422\pi\) | |||||||
\(542\) | −5.79668 | − | 17.8404i | −0.248989 | − | 0.766309i | ||||
\(543\) | 4.61985 | − | 14.2184i | 0.198257 | − | 0.610172i | ||||
\(544\) | 1.68448 | + | 1.22385i | 0.0722216 | + | 0.0524721i | ||||
\(545\) | −43.1781 | − | 31.3707i | −1.84954 | − | 1.34377i | ||||
\(546\) | 2.12387 | − | 6.53660i | 0.0908932 | − | 0.279740i | ||||
\(547\) | −10.6940 | − | 32.9126i | −0.457240 | − | 1.40724i | −0.868485 | − | 0.495716i | \(-0.834906\pi\) |
0.411244 | − | 0.911525i | \(-0.365094\pi\) | |||||||
\(548\) | −7.51863 | + | 5.46260i | −0.321180 | + | 0.233351i | ||||
\(549\) | −7.37475 | −0.314747 | ||||||||
\(550\) | 7.47214 | + | 5.81137i | 0.318613 | + | 0.247798i | ||||
\(551\) | 47.7788 | 2.03545 | ||||||||
\(552\) | −1.27378 | + | 0.925458i | −0.0542158 | + | 0.0393901i | ||||
\(553\) | 3.04467 | + | 9.37054i | 0.129473 | + | 0.398476i | ||||
\(554\) | 0.961004 | − | 2.95767i | 0.0408291 | − | 0.125659i | ||||
\(555\) | 24.6673 | + | 17.9219i | 1.04707 | + | 0.760741i | ||||
\(556\) | 10.4998 | + | 7.62855i | 0.445290 | + | 0.323522i | ||||
\(557\) | −2.67325 | + | 8.22743i | −0.113269 | + | 0.348607i | −0.991582 | − | 0.129479i | \(-0.958669\pi\) |
0.878313 | + | 0.478087i | \(0.158669\pi\) | |||||||
\(558\) | 1.41472 | + | 4.35405i | 0.0598897 | + | 0.184322i | ||||
\(559\) | 40.0579 | − | 29.1037i | 1.69427 | − | 1.23096i | ||||
\(560\) | 2.80252 | 0.118428 | ||||||||
\(561\) | 2.34756 | − | 6.49439i | 0.0991139 | − | 0.274194i | ||||
\(562\) | 2.86935 | 0.121036 | ||||||||
\(563\) | 16.9889 | − | 12.3432i | 0.715999 | − | 0.520204i | −0.169105 | − | 0.985598i | \(-0.554088\pi\) |
0.885103 | + | 0.465395i | \(0.154088\pi\) | |||||||
\(564\) | 1.91541 | + | 5.89503i | 0.0806533 | + | 0.248225i | ||||
\(565\) | 3.79561 | − | 11.6817i | 0.159682 | − | 0.491452i | ||||
\(566\) | 1.79709 | + | 1.30566i | 0.0755375 | + | 0.0548812i | ||||
\(567\) | −0.809017 | − | 0.587785i | −0.0339755 | − | 0.0246847i | ||||
\(568\) | 1.62970 | − | 5.01571i | 0.0683808 | − | 0.210455i | ||||
\(569\) | −6.73197 | − | 20.7189i | −0.282219 | − | 0.868581i | −0.987218 | − | 0.159373i | \(-0.949053\pi\) |
0.705000 | − | 0.709208i | \(-0.250947\pi\) | |||||||
\(570\) | −15.4497 | + | 11.2249i | −0.647117 | + | 0.470158i | ||||
\(571\) | −9.04130 | −0.378367 | −0.189183 | − | 0.981942i | \(-0.560584\pi\) | ||||
−0.189183 | + | 0.981942i | \(0.560584\pi\) | |||||||
\(572\) | −6.33150 | − | 21.8981i | −0.264733 | − | 0.915608i | ||||
\(573\) | 12.8761 | 0.537905 | ||||||||
\(574\) | −0.124534 | + | 0.0904792i | −0.00519794 | + | 0.00377653i | ||||
\(575\) | −1.38864 | − | 4.27380i | −0.0579103 | − | 0.178230i | ||||
\(576\) | 0.309017 | − | 0.951057i | 0.0128757 | − | 0.0396274i | ||||
\(577\) | −1.83125 | − | 1.33048i | −0.0762359 | − | 0.0553887i | 0.549014 | − | 0.835813i | \(-0.315003\pi\) |
−0.625250 | + | 0.780424i | \(0.715003\pi\) | |||||||
\(578\) | −10.2460 | − | 7.44413i | −0.426176 | − | 0.309635i | ||||
\(579\) | −2.25672 | + | 6.94547i | −0.0937861 | + | 0.288644i | ||||
\(580\) | −6.07228 | − | 18.6886i | −0.252138 | − | 0.776001i | ||||
\(581\) | −7.00985 | + | 5.09296i | −0.290818 | + | 0.211291i | ||||
\(582\) | 5.86131 | 0.242959 | ||||||||
\(583\) | 11.8534 | − | 8.03333i | 0.490918 | − | 0.332706i | ||||
\(584\) | 3.99637 | 0.165371 | ||||||||
\(585\) | 15.5830 | − | 11.3217i | 0.644278 | − | 0.468095i | ||||
\(586\) | 8.26463 | + | 25.4359i | 0.341409 | + | 1.05075i | ||||
\(587\) | −1.45187 | + | 4.46838i | −0.0599249 | + | 0.184430i | −0.976538 | − | 0.215346i | \(-0.930912\pi\) |
0.916613 | + | 0.399776i | \(0.130912\pi\) | |||||||
\(588\) | −0.809017 | − | 0.587785i | −0.0333633 | − | 0.0242399i | ||||
\(589\) | −25.2382 | − | 18.3366i | −1.03992 | − | 0.755548i | ||||
\(590\) | 8.12387 | − | 25.0027i | 0.334454 | − | 1.02934i | ||||
\(591\) | 5.35799 | + | 16.4902i | 0.220398 | + | 0.678316i | ||||
\(592\) | 8.80185 | − | 6.39492i | 0.361754 | − | 0.262830i | ||||
\(593\) | 22.3415 | 0.917457 | 0.458729 | − | 0.888576i | \(-0.348305\pi\) | ||||
0.458729 | + | 0.888576i | \(0.348305\pi\) | |||||||
\(594\) | −3.31485 | − | 0.108436i | −0.136010 | − | 0.00444920i | ||||
\(595\) | 5.83522 | 0.239221 | ||||||||
\(596\) | 1.23607 | − | 0.898056i | 0.0506313 | − | 0.0367858i | ||||
\(597\) | −6.42329 | − | 19.7688i | −0.262888 | − | 0.809085i | ||||
\(598\) | −3.34400 | + | 10.2918i | −0.136746 | + | 0.420861i | ||||
\(599\) | −25.9900 | − | 18.8829i | −1.06192 | − | 0.771533i | −0.0874802 | − | 0.996166i | \(-0.527881\pi\) |
−0.974443 | + | 0.224634i | \(0.927881\pi\) | |||||||
\(600\) | 2.30902 | + | 1.67760i | 0.0942652 | + | 0.0684877i | ||||
\(601\) | −4.51123 | + | 13.8841i | −0.184017 | + | 0.566346i | −0.999930 | − | 0.0118288i | \(-0.996235\pi\) |
0.815913 | + | 0.578174i | \(0.196235\pi\) | |||||||
\(602\) | −2.22622 | − | 6.85159i | −0.0907338 | − | 0.279250i | ||||
\(603\) | 5.39182 | − | 3.91738i | 0.219572 | − | 0.159528i | ||||
\(604\) | 5.12702 | 0.208615 | ||||||||
\(605\) | −23.7026 | − | 19.7113i | −0.963647 | − | 0.801377i | ||||
\(606\) | 11.5664 | 0.469855 | ||||||||
\(607\) | 9.37117 | − | 6.80855i | 0.380364 | − | 0.276351i | −0.381132 | − | 0.924521i | \(-0.624466\pi\) |
0.761495 | + | 0.648170i | \(0.224466\pi\) | |||||||
\(608\) | 2.10570 | + | 6.48068i | 0.0853974 | + | 0.262826i | ||||
\(609\) | −2.16672 | + | 6.66849i | −0.0878001 | + | 0.270221i | ||||
\(610\) | −16.7207 | − | 12.1483i | −0.677000 | − | 0.491869i | ||||
\(611\) | 34.4653 | + | 25.0405i | 1.39432 | + | 1.01303i | ||||
\(612\) | 0.643415 | − | 1.98023i | 0.0260085 | − | 0.0800460i | ||||
\(613\) | −0.0992174 | − | 0.305360i | −0.00400735 | − | 0.0123334i | 0.949033 | − | 0.315177i | \(-0.102064\pi\) |
−0.953040 | + | 0.302844i | \(0.902064\pi\) | |||||||
\(614\) | −4.32363 | + | 3.14130i | −0.174487 | + | 0.126773i | ||||
\(615\) | −0.431398 | −0.0173957 | ||||||||
\(616\) | −3.31485 | − | 0.108436i | −0.133559 | − | 0.00436903i | ||||
\(617\) | −34.5805 | −1.39216 | −0.696080 | − | 0.717965i | \(-0.745074\pi\) | ||||
−0.696080 | + | 0.717965i | \(0.745074\pi\) | |||||||
\(618\) | 10.1854 | − | 7.40009i | 0.409715 | − | 0.297675i | ||||
\(619\) | 2.85228 | + | 8.77842i | 0.114643 | + | 0.352835i | 0.991872 | − | 0.127237i | \(-0.0406108\pi\) |
−0.877229 | + | 0.480071i | \(0.840611\pi\) | |||||||
\(620\) | −3.96477 | + | 12.2023i | −0.159229 | + | 0.490056i | ||||
\(621\) | 1.27378 | + | 0.925458i | 0.0511152 | + | 0.0371374i | ||||
\(622\) | −28.0081 | − | 20.3491i | −1.12302 | − | 0.815924i | ||||
\(623\) | −0.458932 | + | 1.41245i | −0.0183867 | + | 0.0565885i | ||||
\(624\) | −2.12387 | − | 6.53660i | −0.0850228 | − | 0.261673i | ||||
\(625\) | 25.1803 | − | 18.2946i | 1.00721 | − | 0.731784i | ||||
\(626\) | 20.8904 | 0.834950 | ||||||||
\(627\) | 18.7084 | − | 12.6791i | 0.747142 | − | 0.506355i | ||||
\(628\) | 16.6364 | 0.663865 | ||||||||
\(629\) | 18.3266 | − | 13.3151i | 0.730731 | − | 0.530907i | ||||
\(630\) | −0.866025 | − | 2.66535i | −0.0345033 | − | 0.106190i | ||||
\(631\) | −12.0626 | + | 37.1249i | −0.480205 | + | 1.47792i | 0.358602 | + | 0.933491i | \(0.383254\pi\) |
−0.838807 | + | 0.544429i | \(0.816746\pi\) | |||||||
\(632\) | 7.97106 | + | 5.79131i | 0.317072 | + | 0.230366i | ||||
\(633\) | −18.0471 | − | 13.1120i | −0.717308 | − | 0.521155i | ||||
\(634\) | 0.441457 | − | 1.35867i | 0.0175325 | − | 0.0539595i | ||||
\(635\) | −9.25292 | − | 28.4776i | −0.367191 | − | 1.13010i | ||||
\(636\) | 3.49283 | − | 2.53769i | 0.138500 | − | 0.100626i | ||||
\(637\) | −6.87298 | −0.272318 | ||||||||
\(638\) | 6.45926 | + | 22.3400i | 0.255725 | + | 0.884450i | ||||
\(639\) | −5.27383 | −0.208630 | ||||||||
\(640\) | 2.26728 | − | 1.64728i | 0.0896223 | − | 0.0651144i | ||||
\(641\) | 6.71245 | + | 20.6588i | 0.265126 | + | 0.815974i | 0.991664 | + | 0.128848i | \(0.0411279\pi\) |
−0.726538 | + | 0.687126i | \(0.758872\pi\) | |||||||
\(642\) | 4.29822 | − | 13.2286i | 0.169637 | − | 0.522089i | ||||
\(643\) | 22.5572 | + | 16.3887i | 0.889568 | + | 0.646309i | 0.935765 | − | 0.352624i | \(-0.114710\pi\) |
−0.0461975 | + | 0.998932i | \(0.514710\pi\) | |||||||
\(644\) | 1.27378 | + | 0.925458i | 0.0501941 | + | 0.0364682i | ||||
\(645\) | 6.23901 | − | 19.2017i | 0.245661 | − | 0.756066i | ||||
\(646\) | 4.38435 | + | 13.4936i | 0.172500 | + | 0.530900i | ||||
\(647\) | 2.78069 | − | 2.02029i | 0.109320 | − | 0.0794259i | −0.531782 | − | 0.846881i | \(-0.678477\pi\) |
0.641102 | + | 0.767455i | \(0.278477\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.5764 | + | 29.2592i | −0.415161 | + | 1.14852i | ||||
\(650\) | 19.6162 | 0.769410 | ||||||||
\(651\) | 3.70378 | − | 2.69095i | 0.145162 | − | 0.105467i | ||||
\(652\) | −2.61803 | − | 8.05748i | −0.102530 | − | 0.315555i | ||||
\(653\) | −0.158819 | + | 0.488794i | −0.00621506 | + | 0.0191280i | −0.954116 | − | 0.299437i | \(-0.903201\pi\) |
0.947901 | + | 0.318565i | \(0.103201\pi\) | |||||||
\(654\) | 15.4069 | + | 11.1938i | 0.602457 | + | 0.437711i | ||||
\(655\) | 36.3428 | + | 26.4046i | 1.42003 | + | 1.03171i | ||||
\(656\) | −0.0475677 | + | 0.146398i | −0.00185721 | + | 0.00571590i | ||||
\(657\) | −1.23494 | − | 3.80077i | −0.0481798 | − | 0.148282i | ||||
\(658\) | 5.01461 | − | 3.64333i | 0.195490 | − | 0.142032i | ||||
\(659\) | −31.2923 | −1.21897 | −0.609487 | − | 0.792796i | \(-0.708625\pi\) | ||||
−0.609487 | + | 0.792796i | \(0.708625\pi\) | |||||||
\(660\) | −7.33708 | − | 5.70634i | −0.285596 | − | 0.222119i | ||||
\(661\) | 2.53548 | 0.0986189 | 0.0493094 | − | 0.998784i | \(-0.484298\pi\) | ||||
0.0493094 | + | 0.998784i | \(0.484298\pi\) | |||||||
\(662\) | −18.3550 | + | 13.3357i | −0.713386 | + | 0.518305i | ||||
\(663\) | −4.42218 | − | 13.6101i | −0.171743 | − | 0.528572i | ||||
\(664\) | −2.67753 | + | 8.24058i | −0.103908 | + | 0.319796i | ||||
\(665\) | 15.4497 | + | 11.2249i | 0.599113 | + | 0.435281i | ||||
\(666\) | −8.80185 | − | 6.39492i | −0.341065 | − | 0.247798i | ||||
\(667\) | 3.41147 | − | 10.4994i | 0.132093 | − | 0.406540i | ||||
\(668\) | 1.26600 | + | 3.89636i | 0.0489832 | + | 0.150755i | ||||
\(669\) | −5.08930 | + | 3.69759i | −0.196764 | + | 0.142957i | ||||
\(670\) | 18.6778 | 0.721587 | ||||||||
\(671\) | 19.3074 | + | 15.0161i | 0.745352 | + | 0.579690i | ||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 17.0843 | − | 12.4125i | 0.658551 | − | 0.478465i | −0.207622 | − | 0.978209i | \(-0.566573\pi\) |
0.866173 | + | 0.499744i | \(0.166573\pi\) | |||||||
\(674\) | −8.01569 | − | 24.6697i | −0.308753 | − | 0.950243i | ||||
\(675\) | 0.881966 | − | 2.71441i | 0.0339469 | − | 0.104478i | ||||
\(676\) | −27.6990 | − | 20.1245i | −1.06535 | − | 0.774020i | ||||
\(677\) | 32.9614 | + | 23.9479i | 1.26681 | + | 0.920391i | 0.999071 | − | 0.0431002i | \(-0.0137235\pi\) |
0.267739 | + | 0.963491i | \(0.413723\pi\) | |||||||
\(678\) | −1.35436 | + | 4.16828i | −0.0520137 | + | 0.160082i | ||||
\(679\) | −1.81125 | − | 5.57444i | −0.0695092 | − | 0.213927i | ||||
\(680\) | 4.72079 | − | 3.42986i | 0.181034 | − | 0.131529i | ||||
\(681\) | −13.6386 | −0.522631 | ||||||||
\(682\) | 5.16171 | − | 14.2796i | 0.197652 | − | 0.546795i | ||||
\(683\) | −23.0021 | −0.880153 | −0.440076 | − | 0.897960i | \(-0.645049\pi\) | ||||
−0.440076 | + | 0.897960i | \(0.645049\pi\) | |||||||
\(684\) | 5.51279 | − | 4.00528i | 0.210787 | − | 0.153146i | ||||
\(685\) | 8.04844 | + | 24.7705i | 0.307515 | + | 0.946434i | ||||
\(686\) | −0.309017 | + | 0.951057i | −0.0117983 | + | 0.0363115i | ||||
\(687\) | −18.2635 | − | 13.2692i | −0.696795 | − | 0.506251i | ||||
\(688\) | −5.82831 | − | 4.23451i | −0.222202 | − | 0.161439i | ||||
\(689\) | 9.16955 | − | 28.2210i | 0.349332 | − | 1.07513i | ||||
\(690\) | 1.36354 | + | 4.19655i | 0.0519092 | + | 0.159760i | ||||
\(691\) | 4.88043 | − | 3.54584i | 0.185660 | − | 0.134890i | −0.491073 | − | 0.871119i | \(-0.663395\pi\) |
0.676733 | + | 0.736228i | \(0.263395\pi\) | |||||||
\(692\) | 16.0220 | 0.609065 | ||||||||
\(693\) | 0.921216 | + | 3.18612i | 0.0349941 | + | 0.121031i | ||||
\(694\) | 29.8864 | 1.13447 | ||||||||
\(695\) | 29.4258 | − | 21.3791i | 1.11619 | − | 0.810957i | ||||
\(696\) | 2.16672 | + | 6.66849i | 0.0821295 | + | 0.252769i | ||||
\(697\) | −0.0990424 | + | 0.304821i | −0.00375150 | + | 0.0115459i | ||||
\(698\) | 16.0859 | + | 11.6871i | 0.608860 | + | 0.442363i | ||||
\(699\) | 1.43864 | + | 1.04524i | 0.0544145 | + | 0.0395345i | ||||
\(700\) | 0.881966 | − | 2.71441i | 0.0333352 | − | 0.102595i | ||||
\(701\) | −7.63704 | − | 23.5044i | −0.288447 | − | 0.887749i | −0.985344 | − | 0.170578i | \(-0.945437\pi\) |
0.696897 | − | 0.717171i | \(-0.254563\pi\) | |||||||
\(702\) | −5.56036 | + | 4.03984i | −0.209862 | + | 0.152474i | ||||
\(703\) | 74.1362 | 2.79610 | ||||||||
\(704\) | −2.74551 | + | 1.86069i | −0.103475 | + | 0.0701275i | ||||
\(705\) | 17.3711 | 0.654234 | ||||||||
\(706\) | −2.32905 | + | 1.69215i | −0.0876550 | + | 0.0636851i | ||||
\(707\) | −3.57423 | − | 11.0003i | −0.134423 | − | 0.413711i | ||||
\(708\) | −2.89878 | + | 8.92151i | −0.108943 | + | 0.335291i | ||||
\(709\) | −31.6416 | − | 22.9890i | −1.18833 | − | 0.863369i | −0.195240 | − | 0.980756i | \(-0.562548\pi\) |
−0.993086 | + | 0.117386i | \(0.962548\pi\) | |||||||
\(710\) | −11.9573 | − | 8.68747i | −0.448748 | − | 0.326035i | ||||
\(711\) | 3.04467 | − | 9.37054i | 0.114184 | − | 0.351423i | ||||
\(712\) | 0.458932 | + | 1.41245i | 0.0171992 | + | 0.0529337i | ||||
\(713\) | −5.83153 | + | 4.23686i | −0.218393 | + | 0.158672i | ||||
\(714\) | −2.08214 | −0.0779220 | ||||||||
\(715\) | −63.8495 | − | 2.08867i | −2.38784 | − | 0.0781116i | ||||
\(716\) | −6.58036 | −0.245920 | ||||||||
\(717\) | −20.9031 | + | 15.1870i | −0.780640 | + | 0.567168i | ||||
\(718\) | −5.21416 | − | 16.0475i | −0.194591 | − | 0.598889i | ||||
\(719\) | 0.341829 | − | 1.05204i | 0.0127481 | − | 0.0392345i | −0.944480 | − | 0.328568i | \(-0.893434\pi\) |
0.957228 | + | 0.289334i | \(0.0934338\pi\) | |||||||
\(720\) | −2.26728 | − | 1.64728i | −0.0844967 | − | 0.0613904i | ||||
\(721\) | −10.1854 | − | 7.40009i | −0.379322 | − | 0.275594i | ||||
\(722\) | −8.47731 | + | 26.0905i | −0.315493 | + | 0.970986i | ||||
\(723\) | 4.61427 | + | 14.2013i | 0.171607 | + | 0.528151i | ||||
\(724\) | −12.0949 | + | 8.78748i | −0.449504 | + | 0.326584i | ||||
\(725\) | −20.0120 | −0.743228 | ||||||||
\(726\) | 8.45760 | + | 7.03342i | 0.313891 | + | 0.261035i | ||||
\(727\) | −25.1214 | −0.931700 | −0.465850 | − | 0.884864i | \(-0.654251\pi\) | ||||
−0.465850 | + | 0.884864i | \(0.654251\pi\) | |||||||
\(728\) | −5.56036 | + | 4.03984i | −0.206081 | + | 0.149726i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 3.46095 | − | 10.6517i | 0.128096 | − | 0.394238i | ||||
\(731\) | −12.1353 | − | 8.81683i | −0.448841 | − | 0.326102i | ||||
\(732\) | 5.96630 | + | 4.33477i | 0.220521 | + | 0.160218i | ||||
\(733\) | 9.38033 | − | 28.8697i | 0.346471 | − | 1.06633i | −0.614321 | − | 0.789056i | \(-0.710570\pi\) |
0.960792 | − | 0.277271i | \(-0.0894299\pi\) | |||||||
\(734\) | −1.48518 | − | 4.57092i | −0.0548191 | − | 0.168716i | ||||
\(735\) | −2.26728 | + | 1.64728i | −0.0836300 | + | 0.0607608i | ||||
\(736\) | 1.57448 | 0.0580362 | ||||||||
\(737\) | −22.0923 | − | 0.722691i | −0.813782 | − | 0.0266207i | ||||
\(738\) | 0.153932 | 0.00566633 | ||||||||
\(739\) | −7.58119 | + | 5.50805i | −0.278878 | + | 0.202617i | −0.718428 | − | 0.695601i | \(-0.755138\pi\) |
0.439550 | + | 0.898218i | \(0.355138\pi\) | |||||||
\(740\) | −9.42209 | − | 28.9982i | −0.346363 | − | 1.06599i | ||||
\(741\) | 14.4724 | − | 44.5416i | 0.531658 | − | 1.63628i | ||||
\(742\) | −3.49283 | − | 2.53769i | −0.128226 | − | 0.0931616i | ||||
\(743\) | −27.8194 | − | 20.2120i | −1.02060 | − | 0.741507i | −0.0541912 | − | 0.998531i | \(-0.517258\pi\) |
−0.966405 | + | 0.257024i | \(0.917258\pi\) | |||||||
\(744\) | 1.41472 | − | 4.35405i | 0.0518660 | − | 0.159627i | ||||
\(745\) | −1.32317 | − | 4.07230i | −0.0484772 | − | 0.149197i | ||||
\(746\) | −24.9400 | + | 18.1200i | −0.913117 | + | 0.663419i | ||||
\(747\) | 8.66465 | 0.317023 | ||||||||
\(748\) | −5.71652 | + | 3.87422i | −0.209017 | + | 0.141655i | ||||
\(749\) | −13.9093 | −0.508236 | ||||||||
\(750\) | −4.86536 | + | 3.53489i | −0.177658 | + | 0.129076i | ||||
\(751\) | −8.18769 | − | 25.1991i | −0.298773 | − | 0.919529i | −0.981928 | − | 0.189255i | \(-0.939393\pi\) |
0.683155 | − | 0.730273i | \(-0.260607\pi\) | |||||||
\(752\) | 1.91541 | − | 5.89503i | 0.0698478 | − | 0.214970i | ||||
\(753\) | 4.59734 | + | 3.34016i | 0.167536 | + | 0.121722i | ||||
\(754\) | 38.9874 | + | 28.3260i | 1.41984 | + | 1.03157i | ||||
\(755\) | 4.44013 | − | 13.6653i | 0.161593 | − | 0.497331i | ||||
\(756\) | 0.309017 | + | 0.951057i | 0.0112388 | + | 0.0345896i | ||||
\(757\) | 14.7811 | − | 10.7391i | 0.537227 | − | 0.390319i | −0.285827 | − | 0.958281i | \(-0.592268\pi\) |
0.823054 | + | 0.567963i | \(0.192268\pi\) | |||||||
\(758\) | −11.5537 | −0.419649 | ||||||||
\(759\) | −1.45044 | − | 5.01649i | −0.0526476 | − | 0.182087i | ||||
\(760\) | 19.0969 | 0.692716 | ||||||||
\(761\) | −20.1463 | + | 14.6371i | −0.730303 | + | 0.530596i | −0.889659 | − | 0.456625i | \(-0.849058\pi\) |
0.159356 | + | 0.987221i | \(0.449058\pi\) | |||||||
\(762\) | 3.30165 | + | 10.1614i | 0.119606 | + | 0.368110i | ||||
\(763\) | 5.88491 | − | 18.1119i | 0.213048 | − | 0.655694i | ||||
\(764\) | −10.4169 | − | 7.56835i | −0.376872 | − | 0.273813i | ||||
\(765\) | −4.72079 | − | 3.42986i | −0.170681 | − | 0.124007i | ||||
\(766\) | 6.41559 | − | 19.7451i | 0.231805 | − | 0.713421i | ||||
\(767\) | 19.9232 | + | 61.3174i | 0.719386 | + | 2.21404i | ||||
\(768\) | −0.809017 | + | 0.587785i | −0.0291929 | + | 0.0212099i | ||||
\(769\) | 23.7581 | 0.856739 | 0.428370 | − | 0.903604i | \(-0.359088\pi\) | ||||
0.428370 | + | 0.903604i | \(0.359088\pi\) | |||||||
\(770\) | −3.15977 | + | 8.74134i | −0.113870 | + | 0.315016i | ||||
\(771\) | 25.4725 | 0.917371 | ||||||||
\(772\) | 5.90817 | − | 4.29254i | 0.212640 | − | 0.154492i | ||||
\(773\) | −10.7657 | − | 33.1333i | −0.387214 | − | 1.19172i | −0.934861 | − | 0.355013i | \(-0.884476\pi\) |
0.547647 | − | 0.836710i | \(-0.315524\pi\) | |||||||
\(774\) | −2.22622 | + | 6.85159i | −0.0800197 | + | 0.246275i | ||||
\(775\) | 10.5710 | + | 7.68025i | 0.379720 | + | 0.275883i | ||||
\(776\) | −4.74190 | − | 3.44519i | −0.170224 | − | 0.123675i | ||||
\(777\) | −3.36201 | + | 10.3472i | −0.120611 | + | 0.371204i | ||||
\(778\) | −1.04480 | − | 3.21557i | −0.0374580 | − | 0.115284i | ||||
\(779\) | −0.848597 | + | 0.616542i | −0.0304042 | + | 0.0220899i | ||||
\(780\) | −19.2617 | −0.689678 | ||||||||
\(781\) | 13.8071 | + | 10.7383i | 0.494056 | + | 0.384247i | ||||
\(782\) | 3.27829 | 0.117231 | ||||||||
\(783\) | 5.67256 | − | 4.12136i | 0.202721 | − | 0.147285i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | 14.4076 | − | 44.3419i | 0.514228 | − | 1.58263i | ||||
\(786\) | −12.9679 | − | 9.42174i | −0.462550 | − | 0.336062i | ||||
\(787\) | −24.2935 | − | 17.6502i | −0.865969 | − | 0.629163i | 0.0635331 | − | 0.997980i | \(-0.479763\pi\) |
−0.929502 | + | 0.368816i | \(0.879763\pi\) | |||||||
\(788\) | 5.35799 | − | 16.4902i | 0.190871 | − | 0.587439i | ||||
\(789\) | 6.28906 | + | 19.3557i | 0.223896 | + | 0.689082i | ||||
\(790\) | 22.3390 | − | 16.2303i | 0.794787 | − | 0.577447i | ||||
\(791\) | 4.38279 | 0.155834 | ||||||||
\(792\) | 2.61803 | + | 2.03615i | 0.0930278 | + | 0.0723514i | ||||
\(793\) | 50.6866 | 1.79993 | ||||||||
\(794\) | −2.21537 | + | 1.60956i | −0.0786205 | + | 0.0571211i | ||||
\(795\) | −3.73896 | − | 11.5073i | −0.132607 | − | 0.408123i | ||||
\(796\) | −6.42329 | + | 19.7688i | −0.227667 | + | 0.700688i | ||||
\(797\) | 17.7889 | + | 12.9244i | 0.630113 | + | 0.457804i | 0.856440 | − | 0.516247i | \(-0.172671\pi\) |
−0.226326 | + | 0.974052i | \(0.572671\pi\) | |||||||
\(798\) | −5.51279 | − | 4.00528i | −0.195151 | − | 0.141785i | ||||
\(799\) | 3.98814 | − | 12.2742i | 0.141090 | − | 0.434232i | ||||
\(800\) | −0.881966 | − | 2.71441i | −0.0311822 | − | 0.0959690i | ||||
\(801\) | 1.20150 | − | 0.872941i | 0.0424529 | − | 0.0308439i | ||||
\(802\) | 26.1665 | 0.923972 | ||||||||
\(803\) | −4.50580 | + | 12.4651i | −0.159006 | + | 0.439883i | ||||
\(804\) | −6.66465 | −0.235044 | ||||||||
\(805\) | 3.56980 | − | 2.59361i | 0.125819 | − | 0.0914128i | ||||
\(806\) | −9.72332 | − | 29.9253i | −0.342489 | − | 1.05407i | ||||
\(807\) | −0.851855 | + | 2.62174i | −0.0299867 | + | 0.0922897i | ||||
\(808\) | −9.35745 | − | 6.79859i | −0.329194 | − | 0.239173i | ||||
\(809\) | −6.84719 | − | 4.97478i | −0.240734 | − | 0.174904i | 0.460876 | − | 0.887465i | \(-0.347535\pi\) |
−0.701610 | + | 0.712561i | \(0.747535\pi\) | |||||||
\(810\) | −0.866025 | + | 2.66535i | −0.0304290 | + | 0.0936509i | ||||
\(811\) | −7.45464 | − | 22.9430i | −0.261768 | − | 0.805639i | −0.992420 | − | 0.122889i | \(-0.960784\pi\) |
0.730652 | − | 0.682750i | \(-0.239216\pi\) | |||||||
\(812\) | 5.67256 | − | 4.12136i | 0.199068 | − | 0.144631i | ||||
\(813\) | 18.7585 | 0.657888 | ||||||||
\(814\) | 10.0225 | + | 34.6640i | 0.351290 | + | 1.21497i | ||||
\(815\) | −23.7433 | −0.831692 | ||||||||
\(816\) | −1.68448 | + | 1.22385i | −0.0589687 | + | 0.0428433i | ||||
\(817\) | −15.1699 | − | 46.6880i | −0.530726 | − | 1.63341i | ||||
\(818\) | −11.8289 | + | 36.4057i | −0.413589 | + | 1.27289i | ||||
\(819\) | 5.56036 | + | 4.03984i | 0.194295 | + | 0.141163i | ||||
\(820\) | 0.349008 | + | 0.253569i | 0.0121879 | + | 0.00885503i | ||||
\(821\) | −14.7713 | + | 45.4612i | −0.515520 | + | 1.58661i | 0.266813 | + | 0.963748i | \(0.414029\pi\) |
−0.782333 | + | 0.622860i | \(0.785971\pi\) | |||||||
\(822\) | −2.87186 | − | 8.83868i | −0.100168 | − | 0.308284i | ||||
\(823\) | −4.87038 | + | 3.53854i | −0.169771 | + | 0.123346i | −0.669426 | − | 0.742879i | \(-0.733460\pi\) |
0.499655 | + | 0.866224i | \(0.333460\pi\) | |||||||
\(824\) | −12.5898 | −0.438586 | ||||||||
\(825\) | −7.83596 | + | 5.31061i | −0.272813 | + | 0.184892i | ||||
\(826\) | 9.38064 | 0.326394 | ||||||||
\(827\) | 33.9387 | − | 24.6579i | 1.18016 | − | 0.857440i | 0.187975 | − | 0.982174i | \(-0.439808\pi\) |
0.992190 | + | 0.124734i | \(0.0398077\pi\) | |||||||
\(828\) | −0.486542 | − | 1.49742i | −0.0169085 | − | 0.0520390i | ||||
\(829\) | 0.816640 | − | 2.51336i | 0.0283631 | − | 0.0872926i | −0.935873 | − | 0.352338i | \(-0.885387\pi\) |
0.964236 | + | 0.265045i | \(0.0853869\pi\) | |||||||
\(830\) | 19.6452 | + | 14.2731i | 0.681896 | + | 0.495426i | ||||
\(831\) | 2.51594 | + | 1.82794i | 0.0872770 | + | 0.0634105i | ||||
\(832\) | −2.12387 | + | 6.53660i | −0.0736319 | + | 0.226616i | ||||
\(833\) | 0.643415 | + | 1.98023i | 0.0222930 | + | 0.0686109i | ||||
\(834\) | −10.4998 | + | 7.62855i | −0.363578 | + | 0.264155i | ||||
\(835\) | 11.4816 | 0.397336 | ||||||||
\(836\) | −22.5880 | − | 0.738906i | −0.781223 | − | 0.0255556i | ||||
\(837\) | −4.57812 | −0.158243 | ||||||||
\(838\) | 1.16163 | − | 0.843975i | 0.0401279 | − | 0.0291546i | ||||
\(839\) | −14.1275 | − | 43.4800i | −0.487736 | − | 1.50110i | −0.827979 | − | 0.560759i | \(-0.810510\pi\) |
0.340244 | − | 0.940337i | \(-0.389490\pi\) | |||||||
\(840\) | −0.866025 | + | 2.66535i | −0.0298807 | + | 0.0919634i | ||||
\(841\) | −16.3126 | − | 11.8518i | −0.562504 | − | 0.408683i | ||||
\(842\) | 16.2018 | + | 11.7713i | 0.558350 | + | 0.405665i | ||||
\(843\) | −0.886677 | + | 2.72891i | −0.0305388 | + | 0.0939887i | ||||
\(844\) | 6.89338 | + | 21.2156i | 0.237280 | + | 0.730273i | ||||
\(845\) | −77.6270 | + | 56.3993i | −2.67045 | + | 1.94020i | ||||
\(846\) | −6.19840 | −0.213105 | ||||||||
\(847\) | 4.07564 | − | 10.2171i | 0.140040 | − | 0.351064i | ||||
\(848\) | −4.31738 | −0.148259 | ||||||||
\(849\) | −1.79709 | + | 1.30566i | −0.0616761 | + | 0.0448103i | ||||
\(850\) | −1.83637 | − | 5.65177i | −0.0629871 | − | 0.193854i | ||||
\(851\) | 5.29343 | − | 16.2915i | 0.181456 | − | 0.558465i | ||||
\(852\) | 4.26662 | + | 3.09988i | 0.146172 | + | 0.106200i | ||||
\(853\) | 19.0804 | + | 13.8627i | 0.653300 | + | 0.474650i | 0.864394 | − | 0.502816i | \(-0.167702\pi\) |
−0.211094 | + | 0.977466i | \(0.567702\pi\) | |||||||
\(854\) | 2.27892 | − | 7.01381i | 0.0779832 | − | 0.240008i | ||||
\(855\) | −5.90126 | − | 18.1622i | −0.201819 | − | 0.621134i | ||||
\(856\) | −11.2529 | + | 8.17569i | −0.384615 | + | 0.279439i | ||||
\(857\) | −27.7693 | −0.948581 | −0.474291 | − | 0.880368i | \(-0.657295\pi\) | ||||
−0.474291 | + | 0.880368i | \(0.657295\pi\) | |||||||
\(858\) | 22.7829 | + | 0.745282i | 0.777796 | + | 0.0254435i | ||||
\(859\) | −31.8564 | −1.08693 | −0.543463 | − | 0.839433i | \(-0.682887\pi\) | ||||
−0.543463 | + | 0.839433i | \(0.682887\pi\) | |||||||
\(860\) | −16.3339 | + | 11.8673i | −0.556983 | + | 0.404672i | ||||
\(861\) | −0.0475677 | − | 0.146398i | −0.00162110 | − | 0.00498924i | ||||
\(862\) | −2.32537 | + | 7.15675i | −0.0792024 | + | 0.243760i | ||||
\(863\) | −22.9205 | − | 16.6528i | −0.780225 | − | 0.566866i | 0.124822 | − | 0.992179i | \(-0.460164\pi\) |
−0.905046 | + | 0.425313i | \(0.860164\pi\) | |||||||
\(864\) | 0.809017 | + | 0.587785i | 0.0275233 | + | 0.0199969i | ||||
\(865\) | 13.8755 | − | 42.7043i | 0.471780 | − | 1.45199i | ||||
\(866\) | 4.20237 | + | 12.9336i | 0.142802 | + | 0.439500i | ||||
\(867\) | 10.2460 | − | 7.44413i | 0.347971 | − | 0.252816i | ||||
\(868\) | −4.57812 | −0.155391 | ||||||||
\(869\) | −27.0509 | + | 18.3330i | −0.917638 | + | 0.621904i | ||||
\(870\) | 19.6503 | 0.666208 | ||||||||
\(871\) | −37.0579 | + | 26.9241i | −1.25566 | + | 0.912289i | ||||
\(872\) | −5.88491 | − | 18.1119i | −0.199288 | − | 0.613346i | ||||
\(873\) | −1.81125 | + | 5.57444i | −0.0613014 | + | 0.188666i | ||||
\(874\) | 8.67980 | + | 6.30624i | 0.293599 | + | 0.213312i | ||||
\(875\) | 4.86536 | + | 3.53489i | 0.164479 | + | 0.119501i | ||||
\(876\) | −1.23494 | + | 3.80077i | −0.0417249 | + | 0.128416i | ||||
\(877\) | 12.5399 | + | 38.5938i | 0.423442 | + | 1.30322i | 0.904478 | + | 0.426519i | \(0.140260\pi\) |
−0.481037 | + | 0.876700i | \(0.659740\pi\) | |||||||
\(878\) | −2.61228 | + | 1.89793i | −0.0881600 | + | 0.0640520i | ||||
\(879\) | −26.7449 | −0.902083 | ||||||||
\(880\) | 2.58172 | + | 8.92916i | 0.0870299 | + | 0.301002i | ||||
\(881\) | 22.8128 | 0.768583 | 0.384291 | − | 0.923212i | \(-0.374446\pi\) | ||||
0.384291 | + | 0.923212i | \(0.374446\pi\) | |||||||
\(882\) | 0.809017 | − | 0.587785i | 0.0272410 | − | 0.0197918i | ||||
\(883\) | −1.75245 | − | 5.39348i | −0.0589746 | − | 0.181505i | 0.917229 | − | 0.398359i | \(-0.130420\pi\) |
−0.976204 | + | 0.216854i | \(0.930420\pi\) | |||||||
\(884\) | −4.42218 | + | 13.6101i | −0.148734 | + | 0.457756i | ||||
\(885\) | 21.2686 | + | 15.4525i | 0.714935 | + | 0.519431i | ||||
\(886\) | −0.105241 | − | 0.0764623i | −0.00353565 | − | 0.00256880i | ||||
\(887\) | −17.6891 | + | 54.4415i | −0.593942 | + | 1.82797i | −0.0340206 | + | 0.999421i | \(0.510831\pi\) |
−0.559922 | + | 0.828546i | \(0.689169\pi\) | |||||||
\(888\) | 3.36201 | + | 10.3472i | 0.112822 | + | 0.347229i | ||||
\(889\) | 8.64383 | − | 6.28011i | 0.289905 | − | 0.210628i | ||||
\(890\) | 4.16212 | 0.139515 | ||||||||
\(891\) | 1.12747 | − | 3.11910i | 0.0377718 | − | 0.104494i | ||||
\(892\) | 6.29072 | 0.210629 | ||||||||
\(893\) | 34.1705 | − | 24.8263i | 1.14347 | − | 0.830781i | ||||
\(894\) | 0.472136 | + | 1.45309i | 0.0157906 | + | 0.0485984i | ||||
\(895\) | −5.69876 | + | 17.5390i | −0.190489 | + | 0.586264i | ||||
\(896\) | 0.809017 | + | 0.587785i | 0.0270274 | + | 0.0196365i | ||||
\(897\) | −8.75470 | − | 6.36066i | −0.292311 | − | 0.212376i | ||||
\(898\) | −0.964277 | + | 2.96774i | −0.0321783 | + | 0.0990347i | ||||
\(899\) | 9.91952 | + | 30.5292i | 0.330835 | + | 1.01820i | ||||
\(900\) | −2.30902 | + | 1.67760i | −0.0769672 | + | 0.0559200i | ||||
\(901\) | −8.98937 | −0.299479 | ||||||||
\(902\) | −0.403000 | − | 0.313429i | −0.0134184 | − | 0.0104360i | ||||
\(903\) | 7.20419 | 0.239740 | ||||||||
\(904\) | 3.54575 | − | 2.57614i | 0.117930 | − | 0.0856811i | ||||
\(905\) | 12.9472 | + | 39.8474i | 0.430380 | + | 1.32457i | ||||
\(906\) | −1.58434 | + | 4.87608i | −0.0526360 | + | 0.161997i | ||||
\(907\) | −6.01515 | − | 4.37026i | −0.199730 | − | 0.145112i | 0.483425 | − | 0.875386i | \(-0.339393\pi\) |
−0.683155 | + | 0.730274i | \(0.739393\pi\) | |||||||
\(908\) | 11.0338 | + | 8.01654i | 0.366170 | + | 0.266038i | ||||
\(909\) | −3.57423 | + | 11.0003i | −0.118550 | + | 0.364858i | ||||
\(910\) | 5.95218 | + | 18.3189i | 0.197313 | + | 0.607266i | ||||
\(911\) | 19.1558 | − | 13.9175i | 0.634661 | − | 0.461108i | −0.223351 | − | 0.974738i | \(-0.571700\pi\) |
0.858012 | + | 0.513630i | \(0.171700\pi\) | |||||||
\(912\) | −6.81419 | −0.225640 | ||||||||
\(913\) | −22.6844 | − | 17.6425i | −0.750743 | − | 0.583882i | ||||
\(914\) | 7.64444 | 0.252856 | ||||||||
\(915\) | 16.7207 | − | 12.1483i | 0.552768 | − | 0.401609i | ||||
\(916\) | 6.97603 | + | 21.4700i | 0.230494 | + | 0.709389i | ||||
\(917\) | −4.95330 | + | 15.2447i | −0.163572 | + | 0.503424i | ||||
\(918\) | 1.68448 | + | 1.22385i | 0.0555962 | + | 0.0403930i | ||||
\(919\) | 5.44110 | + | 3.95319i | 0.179485 | + | 0.130404i | 0.673900 | − | 0.738822i | \(-0.264618\pi\) |
−0.494415 | + | 0.869226i | \(0.664618\pi\) | |||||||
\(920\) | 1.36354 | − | 4.19655i | 0.0449547 | − | 0.138356i | ||||
\(921\) | −1.65148 | − | 5.08273i | −0.0544181 | − | 0.167482i | ||||
\(922\) | −28.0839 | + | 20.4041i | −0.924893 | + | 0.671974i | ||||
\(923\) | 36.2470 | 1.19308 | ||||||||
\(924\) | 1.12747 | − | 3.11910i | 0.0370912 | − | 0.102611i | ||||
\(925\) | −31.0517 | −1.02097 | ||||||||
\(926\) | 2.88271 | − | 2.09441i | 0.0947316 | − | 0.0688266i | ||||
\(927\) | 3.89046 | + | 11.9736i | 0.127779 | + | 0.393265i | ||||
\(928\) | 2.16672 | − | 6.66849i | 0.0711262 | − | 0.218904i | ||||
\(929\) | 11.3745 | + | 8.26403i | 0.373184 | + | 0.271134i | 0.758530 | − | 0.651638i | \(-0.225918\pi\) |
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(930\) | −10.3799 | − | 7.54143i | −0.340370 | − | 0.247293i | ||||
\(931\) | −2.10570 | + | 6.48068i | −0.0690115 | + | 0.212396i | ||||
\(932\) | −0.549513 | − | 1.69123i | −0.0179999 | − | 0.0553980i | ||||
\(933\) | 28.0081 | − | 20.3491i | 0.916944 | − | 0.666199i | ||||
\(934\) | −0.0633480 | −0.00207281 | ||||||||
\(935\) | 5.37550 | + | 18.5917i | 0.175798 | + | 0.608014i | ||||
\(936\) | 6.87298 | 0.224650 | ||||||||
\(937\) | 5.55706 | − | 4.03744i | 0.181541 | − | 0.131897i | −0.493303 | − | 0.869857i | \(-0.664211\pi\) |
0.674844 | + | 0.737960i | \(0.264211\pi\) | |||||||
\(938\) | 2.05949 | + | 6.33846i | 0.0672448 | + | 0.206958i | ||||
\(939\) | −6.45550 | + | 19.8680i | −0.210667 | + | 0.648367i | ||||
\(940\) | −14.0535 | − | 10.2105i | −0.458376 | − | 0.333029i | ||||
\(941\) | −40.4795 | − | 29.4101i | −1.31959 | − | 0.958741i | −0.999937 | − | 0.0112078i | \(-0.996432\pi\) |
−0.319657 | − | 0.947533i | \(-0.603568\pi\) | |||||||
\(942\) | −5.14093 | + | 15.8222i | −0.167501 | + | 0.515514i | ||||
\(943\) | 0.0748946 | + | 0.230502i | 0.00243890 | + | 0.00750617i | ||||
\(944\) | 7.58909 | − | 5.51380i | 0.247004 | − | 0.179459i | ||||
\(945\) | 2.80252 | 0.0911659 | ||||||||
\(946\) | 19.7792 | − | 13.4048i | 0.643076 | − | 0.435827i | ||||
\(947\) | 54.9241 | 1.78479 | 0.892397 | − | 0.451250i | \(-0.149022\pi\) | ||||
0.892397 | + | 0.451250i | \(0.149022\pi\) | |||||||
\(948\) | −7.97106 | + | 5.79131i | −0.258888 | + | 0.188093i | ||||
\(949\) | 8.48775 | + | 26.1226i | 0.275524 | + | 0.847976i | ||||
\(950\) | 6.00988 | − | 18.4965i | 0.194986 | − | 0.600106i | ||||
\(951\) | 1.15575 | + | 0.839701i | 0.0374778 | + | 0.0272292i | ||||
\(952\) | 1.68448 | + | 1.22385i | 0.0545944 | + | 0.0396652i | ||||
\(953\) | −7.66413 | + | 23.5878i | −0.248266 | + | 0.764083i | 0.746817 | + | 0.665030i | \(0.231581\pi\) |
−0.995082 | + | 0.0990529i | \(0.968419\pi\) | |||||||
\(954\) | 1.33414 | + | 4.10607i | 0.0431945 | + | 0.132939i | ||||
\(955\) | −29.1937 | + | 21.2104i | −0.944685 | + | 0.686354i | ||||
\(956\) | 25.8376 | 0.835648 | ||||||||
\(957\) | −23.2426 | − | 0.760320i | −0.751328 | − | 0.0245777i | ||||
\(958\) | −33.2334 | −1.07372 | ||||||||
\(959\) | −7.51863 | + | 5.46260i | −0.242789 | + | 0.176397i | ||||
\(960\) | 0.866025 | + | 2.66535i | 0.0279508 | + | 0.0860239i | ||||
\(961\) | −3.10279 | + | 9.54940i | −0.100090 | + | 0.308045i | ||||
\(962\) | 60.4950 | + | 43.9522i | 1.95044 | + | 1.41708i | ||||
\(963\) | 11.2529 | + | 8.17569i | 0.362619 | + | 0.263458i | ||||
\(964\) | 4.61427 | − | 14.2013i | 0.148616 | − | 0.457392i | ||||
\(965\) | −6.32450 | − | 19.4648i | −0.203593 | − | 0.626594i | ||||
\(966\) | −1.27378 | + | 0.925458i | −0.0409833 | + | 0.0297761i | ||||
\(967\) | 19.1238 | 0.614981 | 0.307490 | − | 0.951551i | \(-0.400511\pi\) | ||||
0.307490 | + | 0.951551i | \(0.400511\pi\) | |||||||
\(968\) | −2.70820 | − | 10.6614i | −0.0870450 | − | 0.342671i | ||||
\(969\) | −14.1881 | −0.455786 | ||||||||
\(970\) | −13.2893 | + | 9.65521i | −0.426693 | + | 0.310010i | ||||
\(971\) | −4.46349 | − | 13.7372i | −0.143240 | − | 0.440848i | 0.853540 | − | 0.521027i | \(-0.174451\pi\) |
−0.996780 | + | 0.0801790i | \(0.974451\pi\) | |||||||
\(972\) | 0.309017 | − | 0.951057i | 0.00991172 | − | 0.0305052i | ||||
\(973\) | 10.4998 | + | 7.62855i | 0.336608 | + | 0.244560i | ||||
\(974\) | −7.40133 | − | 5.37738i | −0.237154 | − | 0.172303i | ||||
\(975\) | −6.06174 | + | 18.6561i | −0.194131 | + | 0.597474i | ||||
\(976\) | −2.27892 | − | 7.01381i | −0.0729466 | − | 0.224507i | ||||
\(977\) | −21.7263 | + | 15.7851i | −0.695086 | + | 0.505009i | −0.878328 | − | 0.478058i | \(-0.841341\pi\) |
0.183242 | + | 0.983068i | \(0.441341\pi\) | |||||||
\(978\) | 8.47214 | 0.270909 | ||||||||
\(979\) | −4.92300 | − | 0.161043i | −0.157340 | − | 0.00514695i | ||||
\(980\) | 2.80252 | 0.0895231 | ||||||||
\(981\) | −15.4069 | + | 11.1938i | −0.491904 | + | 0.357389i | ||||
\(982\) | 5.91539 | + | 18.2057i | 0.188768 | + | 0.580967i | ||||
\(983\) | −10.6710 | + | 32.8420i | −0.340352 | + | 1.04750i | 0.623673 | + | 0.781685i | \(0.285640\pi\) |
−0.964025 | + | 0.265811i | \(0.914360\pi\) | |||||||
\(984\) | −0.124534 | − | 0.0904792i | −0.00397000 | − | 0.00288437i | ||||
\(985\) | −39.3120 | − | 28.5619i | −1.25259 | − | 0.910057i | ||||
\(986\) | 4.51142 | − | 13.8847i | 0.143673 | − | 0.442179i | ||||
\(987\) | 1.91541 | + | 5.89503i | 0.0609682 | + | 0.187641i | ||||
\(988\) | −37.8893 | + | 27.5282i | −1.20542 | + | 0.875789i | ||||
\(989\) | −11.3429 | −0.360682 | ||||||||
\(990\) | 7.69433 | − | 5.21463i | 0.244542 | − | 0.165732i | ||||
\(991\) | 29.8475 | 0.948137 | 0.474068 | − | 0.880488i | \(-0.342785\pi\) | ||||
0.474068 | + | 0.880488i | \(0.342785\pi\) | |||||||
\(992\) | −3.70378 | + | 2.69095i | −0.117595 | + | 0.0854378i | ||||
\(993\) | −7.01098 | − | 21.5776i | −0.222487 | − | 0.684743i | ||||
\(994\) | 1.62970 | − | 5.01571i | 0.0516911 | − | 0.159089i | ||||
\(995\) | 47.1282 | + | 34.2406i | 1.49406 | + | 1.08550i | ||||
\(996\) | −7.00985 | − | 5.09296i | −0.222116 | − | 0.161376i | ||||
\(997\) | 10.2947 | − | 31.6837i | 0.326035 | − | 1.00343i | −0.644936 | − | 0.764236i | \(-0.723116\pi\) |
0.970971 | − | 0.239196i | \(-0.0768840\pi\) | |||||||
\(998\) | 7.20825 | + | 22.1847i | 0.228173 | + | 0.702245i | ||||
\(999\) | 8.80185 | − | 6.39492i | 0.278478 | − | 0.202326i |
(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 | 462.2.j.g.421.1 | yes | 8 | |
11.2 | odd | 10 | 5082.2.a.ce.1.4 | 4 | |||
11.4 | even | 5 | inner | 462.2.j.g.169.1 | ✓ | 8 | |
11.9 | even | 5 | 5082.2.a.bz.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.g.169.1 | ✓ | 8 | 11.4 | even | 5 | inner | |
462.2.j.g.421.1 | yes | 8 | 1.1 | even | 1 | trivial | |
5082.2.a.bz.1.4 | 4 | 11.9 | even | 5 | |||
5082.2.a.ce.1.4 | 4 | 11.2 | odd | 10 |