Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [726,2,Mod(487,726)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(726, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("726.487");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 726 = 2 \cdot 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 726.e (of order \(5\), degree \(4\), 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: | \(5.79713918674\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 66) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 487.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 726.487 |
Dual form | 726.2.e.n.565.1 |
$q$-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 \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).
\(n\) | \(485\) | \(607\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | ||||
\(5\) | −2.30902 | − | 1.67760i | −1.03262 | − | 0.750245i | −0.0637916 | − | 0.997963i | \(-0.520319\pi\) |
−0.968832 | + | 0.247718i | \(0.920319\pi\) | |||||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | −1.42705 | + | 4.39201i | −0.539375 | + | 1.66002i | 0.194628 | + | 0.980877i | \(0.437650\pi\) |
−0.734002 | + | 0.679147i | \(0.762350\pi\) | |||||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −2.85410 | −0.902546 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.61803 | + | 1.90211i | −0.726112 | + | 0.527551i | −0.888331 | − | 0.459204i | \(-0.848135\pi\) |
0.162219 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(14\) | 1.42705 | + | 4.39201i | 0.381395 | + | 1.17381i | ||||
\(15\) | −0.881966 | + | 2.71441i | −0.227723 | + | 0.700858i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −2.00000 | − | 1.45309i | −0.485071 | − | 0.352425i | 0.318214 | − | 0.948019i | \(-0.396917\pi\) |
−0.803286 | + | 0.595594i | \(0.796917\pi\) | |||||||
\(18\) | −0.309017 | + | 0.951057i | −0.0728360 | + | 0.224166i | ||||
\(19\) | 1.00000 | + | 3.07768i | 0.229416 | + | 0.706069i | 0.997813 | + | 0.0660962i | \(0.0210544\pi\) |
−0.768398 | + | 0.639973i | \(0.778946\pi\) | |||||||
\(20\) | −2.30902 | + | 1.67760i | −0.516312 | + | 0.375123i | ||||
\(21\) | 4.61803 | 1.00774 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.23607 | −0.674767 | −0.337383 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(24\) | −0.809017 | + | 0.587785i | −0.165140 | + | 0.119981i | ||||
\(25\) | 0.972136 | + | 2.99193i | 0.194427 | + | 0.598385i | ||||
\(26\) | −1.00000 | + | 3.07768i | −0.196116 | + | 0.603583i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | 3.73607 | + | 2.71441i | 0.706050 | + | 0.512976i | ||||
\(29\) | 0.118034 | − | 0.363271i | 0.0219184 | − | 0.0674578i | −0.939499 | − | 0.342551i | \(-0.888709\pi\) |
0.961417 | + | 0.275094i | \(0.0887089\pi\) | |||||||
\(30\) | 0.881966 | + | 2.71441i | 0.161024 | + | 0.495582i | ||||
\(31\) | −6.97214 | + | 5.06555i | −1.25223 | + | 0.909800i | −0.998349 | − | 0.0574346i | \(-0.981708\pi\) |
−0.253883 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.47214 | −0.423968 | ||||||||
\(35\) | 10.6631 | − | 7.74721i | 1.80240 | − | 1.30952i | ||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | 0.472136 | − | 1.45309i | 0.0776187 | − | 0.238886i | −0.904717 | − | 0.426013i | \(-0.859918\pi\) |
0.982336 | + | 0.187127i | \(0.0599177\pi\) | |||||||
\(38\) | 2.61803 | + | 1.90211i | 0.424701 | + | 0.308563i | ||||
\(39\) | 2.61803 | + | 1.90211i | 0.419221 | + | 0.304582i | ||||
\(40\) | −0.881966 | + | 2.71441i | −0.139451 | + | 0.429186i | ||||
\(41\) | 1.00000 | + | 3.07768i | 0.156174 | + | 0.480653i | 0.998278 | − | 0.0586615i | \(-0.0186833\pi\) |
−0.842104 | + | 0.539315i | \(0.818683\pi\) | |||||||
\(42\) | 3.73607 | − | 2.71441i | 0.576488 | − | 0.418843i | ||||
\(43\) | 3.23607 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.85410 | 0.425464 | ||||||||
\(46\) | −2.61803 | + | 1.90211i | −0.386008 | + | 0.280451i | ||||
\(47\) | 0.763932 | + | 2.35114i | 0.111431 | + | 0.342949i | 0.991186 | − | 0.132478i | \(-0.0422935\pi\) |
−0.879755 | + | 0.475427i | \(0.842293\pi\) | |||||||
\(48\) | −0.309017 | + | 0.951057i | −0.0446028 | + | 0.137273i | ||||
\(49\) | −11.5902 | − | 8.42075i | −1.65574 | − | 1.20296i | ||||
\(50\) | 2.54508 | + | 1.84911i | 0.359929 | + | 0.261504i | ||||
\(51\) | −0.763932 | + | 2.35114i | −0.106972 | + | 0.329226i | ||||
\(52\) | 1.00000 | + | 3.07768i | 0.138675 | + | 0.426798i | ||||
\(53\) | 3.11803 | − | 2.26538i | 0.428295 | − | 0.311174i | −0.352672 | − | 0.935747i | \(-0.614727\pi\) |
0.780967 | + | 0.624573i | \(0.214727\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.61803 | 0.617111 | ||||||||
\(57\) | 2.61803 | − | 1.90211i | 0.346767 | − | 0.251941i | ||||
\(58\) | −0.118034 | − | 0.363271i | −0.0154986 | − | 0.0476999i | ||||
\(59\) | −1.19098 | + | 3.66547i | −0.155053 | + | 0.477203i | −0.998166 | − | 0.0605323i | \(-0.980720\pi\) |
0.843113 | + | 0.537736i | \(0.180720\pi\) | |||||||
\(60\) | 2.30902 | + | 1.67760i | 0.298093 | + | 0.216577i | ||||
\(61\) | −5.47214 | − | 3.97574i | −0.700635 | − | 0.509041i | 0.179504 | − | 0.983757i | \(-0.442551\pi\) |
−0.880139 | + | 0.474716i | \(0.842551\pi\) | |||||||
\(62\) | −2.66312 | + | 8.19624i | −0.338216 | + | 1.04092i | ||||
\(63\) | −1.42705 | − | 4.39201i | −0.179792 | − | 0.553341i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 9.23607 | 1.14559 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | −2.00000 | + | 1.45309i | −0.242536 | + | 0.176212i | ||||
\(69\) | 1.00000 | + | 3.07768i | 0.120386 | + | 0.370510i | ||||
\(70\) | 4.07295 | − | 12.5352i | 0.486811 | − | 1.49825i | ||||
\(71\) | −10.0902 | − | 7.33094i | −1.19748 | − | 0.870022i | −0.203448 | − | 0.979086i | \(-0.565215\pi\) |
−0.994035 | + | 0.109064i | \(0.965215\pi\) | |||||||
\(72\) | 0.809017 | + | 0.587785i | 0.0953436 | + | 0.0692712i | ||||
\(73\) | 3.50000 | − | 10.7719i | 0.409644 | − | 1.26075i | −0.507311 | − | 0.861763i | \(-0.669360\pi\) |
0.916955 | − | 0.398991i | \(-0.130640\pi\) | |||||||
\(74\) | −0.472136 | − | 1.45309i | −0.0548847 | − | 0.168918i | ||||
\(75\) | 2.54508 | − | 1.84911i | 0.293881 | − | 0.213517i | ||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.23607 | 0.366413 | ||||||||
\(79\) | −7.54508 | + | 5.48183i | −0.848888 | + | 0.616754i | −0.924839 | − | 0.380358i | \(-0.875801\pi\) |
0.0759509 | + | 0.997112i | \(0.475801\pi\) | |||||||
\(80\) | 0.881966 | + | 2.71441i | 0.0986068 | + | 0.303481i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 2.61803 | + | 1.90211i | 0.289113 | + | 0.210053i | ||||
\(83\) | −0.545085 | − | 0.396027i | −0.0598308 | − | 0.0434697i | 0.557468 | − | 0.830199i | \(-0.311773\pi\) |
−0.617299 | + | 0.786729i | \(0.711773\pi\) | |||||||
\(84\) | 1.42705 | − | 4.39201i | 0.155704 | − | 0.479208i | ||||
\(85\) | 2.18034 | + | 6.71040i | 0.236491 | + | 0.727845i | ||||
\(86\) | 2.61803 | − | 1.90211i | 0.282310 | − | 0.205110i | ||||
\(87\) | −0.381966 | −0.0409511 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7082 | −1.24107 | −0.620534 | − | 0.784180i | \(-0.713084\pi\) | ||||
−0.620534 | + | 0.784180i | \(0.713084\pi\) | |||||||
\(90\) | 2.30902 | − | 1.67760i | 0.243392 | − | 0.176834i | ||||
\(91\) | −4.61803 | − | 14.2128i | −0.484102 | − | 1.48991i | ||||
\(92\) | −1.00000 | + | 3.07768i | −0.104257 | + | 0.320871i | ||||
\(93\) | 6.97214 | + | 5.06555i | 0.722977 | + | 0.525273i | ||||
\(94\) | 2.00000 | + | 1.45309i | 0.206284 | + | 0.149874i | ||||
\(95\) | 2.85410 | − | 8.78402i | 0.292825 | − | 0.901222i | ||||
\(96\) | 0.309017 | + | 0.951057i | 0.0315389 | + | 0.0970668i | ||||
\(97\) | −9.16312 | + | 6.65740i | −0.930374 | + | 0.675956i | −0.946084 | − | 0.323920i | \(-0.894999\pi\) |
0.0157105 | + | 0.999877i | \(0.494999\pi\) | |||||||
\(98\) | −14.3262 | −1.44717 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.14590 | 0.314590 | ||||||||
\(101\) | −10.0172 | + | 7.27794i | −0.996751 | + | 0.724182i | −0.961389 | − | 0.275193i | \(-0.911258\pi\) |
−0.0353617 | + | 0.999375i | \(0.511258\pi\) | |||||||
\(102\) | 0.763932 | + | 2.35114i | 0.0756405 | + | 0.232798i | ||||
\(103\) | 3.71885 | − | 11.4454i | 0.366429 | − | 1.12775i | −0.582653 | − | 0.812721i | \(-0.697985\pi\) |
0.949081 | − | 0.315031i | \(-0.102015\pi\) | |||||||
\(104\) | 2.61803 | + | 1.90211i | 0.256719 | + | 0.186518i | ||||
\(105\) | −10.6631 | − | 7.74721i | −1.04061 | − | 0.756050i | ||||
\(106\) | 1.19098 | − | 3.66547i | 0.115678 | − | 0.356022i | ||||
\(107\) | −1.66312 | − | 5.11855i | −0.160780 | − | 0.494829i | 0.837921 | − | 0.545792i | \(-0.183771\pi\) |
−0.998701 | + | 0.0509626i | \(0.983771\pi\) | |||||||
\(108\) | 0.809017 | − | 0.587785i | 0.0778477 | − | 0.0565597i | ||||
\(109\) | −17.4164 | −1.66819 | −0.834095 | − | 0.551621i | \(-0.814009\pi\) | ||||
−0.834095 | + | 0.551621i | \(0.814009\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.52786 | −0.145018 | ||||||||
\(112\) | 3.73607 | − | 2.71441i | 0.353025 | − | 0.256488i | ||||
\(113\) | −3.85410 | − | 11.8617i | −0.362563 | − | 1.11586i | −0.951493 | − | 0.307671i | \(-0.900450\pi\) |
0.588929 | − | 0.808184i | \(-0.299550\pi\) | |||||||
\(114\) | 1.00000 | − | 3.07768i | 0.0936586 | − | 0.288251i | ||||
\(115\) | 7.47214 | + | 5.42882i | 0.696780 | + | 0.506240i | ||||
\(116\) | −0.309017 | − | 0.224514i | −0.0286915 | − | 0.0208456i | ||||
\(117\) | 1.00000 | − | 3.07768i | 0.0924500 | − | 0.284532i | ||||
\(118\) | 1.19098 | + | 3.66547i | 0.109639 | + | 0.337434i | ||||
\(119\) | 9.23607 | − | 6.71040i | 0.846669 | − | 0.615141i | ||||
\(120\) | 2.85410 | 0.260543 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −6.76393 | −0.612378 | ||||||||
\(123\) | 2.61803 | − | 1.90211i | 0.236060 | − | 0.171508i | ||||
\(124\) | 2.66312 | + | 8.19624i | 0.239155 | + | 0.736044i | ||||
\(125\) | −1.63525 | + | 5.03280i | −0.146262 | + | 0.450147i | ||||
\(126\) | −3.73607 | − | 2.71441i | −0.332835 | − | 0.241819i | ||||
\(127\) | 9.70820 | + | 7.05342i | 0.861464 | + | 0.625890i | 0.928283 | − | 0.371875i | \(-0.121285\pi\) |
−0.0668190 | + | 0.997765i | \(0.521285\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | −1.00000 | − | 3.07768i | −0.0880451 | − | 0.270975i | ||||
\(130\) | 7.47214 | − | 5.42882i | 0.655350 | − | 0.476139i | ||||
\(131\) | 15.2705 | 1.33419 | 0.667095 | − | 0.744972i | \(-0.267537\pi\) | ||||
0.667095 | + | 0.744972i | \(0.267537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.9443 | −1.29583 | ||||||||
\(134\) | 3.23607 | − | 2.35114i | 0.279554 | − | 0.203108i | ||||
\(135\) | −0.881966 | − | 2.71441i | −0.0759075 | − | 0.233619i | ||||
\(136\) | −0.763932 | + | 2.35114i | −0.0655066 | + | 0.201609i | ||||
\(137\) | 18.7082 | + | 13.5923i | 1.59835 | + | 1.16127i | 0.890581 | + | 0.454825i | \(0.150298\pi\) |
0.707769 | + | 0.706444i | \(0.249702\pi\) | |||||||
\(138\) | 2.61803 | + | 1.90211i | 0.222862 | + | 0.161919i | ||||
\(139\) | −4.09017 | + | 12.5882i | −0.346924 | + | 1.06772i | 0.613622 | + | 0.789600i | \(0.289712\pi\) |
−0.960546 | + | 0.278122i | \(0.910288\pi\) | |||||||
\(140\) | −4.07295 | − | 12.5352i | −0.344227 | − | 1.05942i | ||||
\(141\) | 2.00000 | − | 1.45309i | 0.168430 | − | 0.122372i | ||||
\(142\) | −12.4721 | −1.04664 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.881966 | + | 0.640786i | −0.0732433 | + | 0.0532144i | ||||
\(146\) | −3.50000 | − | 10.7719i | −0.289662 | − | 0.891488i | ||||
\(147\) | −4.42705 | + | 13.6251i | −0.365137 | + | 1.12378i | ||||
\(148\) | −1.23607 | − | 0.898056i | −0.101604 | − | 0.0738197i | ||||
\(149\) | 1.11803 | + | 0.812299i | 0.0915929 | + | 0.0665461i | 0.632639 | − | 0.774447i | \(-0.281972\pi\) |
−0.541046 | + | 0.840993i | \(0.681972\pi\) | |||||||
\(150\) | 0.972136 | − | 2.99193i | 0.0793746 | − | 0.244290i | ||||
\(151\) | −2.88197 | − | 8.86978i | −0.234531 | − | 0.721812i | −0.997183 | − | 0.0750036i | \(-0.976103\pi\) |
0.762652 | − | 0.646809i | \(-0.223897\pi\) | |||||||
\(152\) | 2.61803 | − | 1.90211i | 0.212351 | − | 0.154282i | ||||
\(153\) | 2.47214 | 0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.5967 | 1.97566 | ||||||||
\(156\) | 2.61803 | − | 1.90211i | 0.209610 | − | 0.152291i | ||||
\(157\) | 1.38197 | + | 4.25325i | 0.110293 | + | 0.339447i | 0.990936 | − | 0.134333i | \(-0.0428892\pi\) |
−0.880643 | + | 0.473780i | \(0.842889\pi\) | |||||||
\(158\) | −2.88197 | + | 8.86978i | −0.229277 | + | 0.705642i | ||||
\(159\) | −3.11803 | − | 2.26538i | −0.247276 | − | 0.179657i | ||||
\(160\) | 2.30902 | + | 1.67760i | 0.182544 | + | 0.132626i | ||||
\(161\) | 4.61803 | − | 14.2128i | 0.363952 | − | 1.12013i | ||||
\(162\) | −0.309017 | − | 0.951057i | −0.0242787 | − | 0.0747221i | ||||
\(163\) | 10.8541 | − | 7.88597i | 0.850159 | − | 0.617677i | −0.0750310 | − | 0.997181i | \(-0.523906\pi\) |
0.925190 | + | 0.379505i | \(0.123906\pi\) | |||||||
\(164\) | 3.23607 | 0.252694 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.673762 | −0.0522941 | ||||||||
\(167\) | 5.85410 | − | 4.25325i | 0.453004 | − | 0.329127i | −0.337777 | − | 0.941226i | \(-0.609675\pi\) |
0.790781 | + | 0.612100i | \(0.209675\pi\) | |||||||
\(168\) | −1.42705 | − | 4.39201i | −0.110099 | − | 0.338851i | ||||
\(169\) | −0.781153 | + | 2.40414i | −0.0600887 | + | 0.184934i | ||||
\(170\) | 5.70820 | + | 4.14725i | 0.437799 | + | 0.318080i | ||||
\(171\) | −2.61803 | − | 1.90211i | −0.200206 | − | 0.145458i | ||||
\(172\) | 1.00000 | − | 3.07768i | 0.0762493 | − | 0.234671i | ||||
\(173\) | 1.28115 | + | 3.94298i | 0.0974043 | + | 0.299779i | 0.987873 | − | 0.155265i | \(-0.0496232\pi\) |
−0.890469 | + | 0.455045i | \(0.849623\pi\) | |||||||
\(174\) | −0.309017 | + | 0.224514i | −0.0234265 | + | 0.0170204i | ||||
\(175\) | −14.5279 | −1.09820 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.85410 | 0.289692 | ||||||||
\(178\) | −9.47214 | + | 6.88191i | −0.709967 | + | 0.515821i | ||||
\(179\) | −1.97214 | − | 6.06961i | −0.147404 | − | 0.453664i | 0.849908 | − | 0.526931i | \(-0.176657\pi\) |
−0.997312 | + | 0.0732671i | \(0.976657\pi\) | |||||||
\(180\) | 0.881966 | − | 2.71441i | 0.0657379 | − | 0.202320i | ||||
\(181\) | 13.3262 | + | 9.68208i | 0.990531 | + | 0.719663i | 0.960037 | − | 0.279872i | \(-0.0902919\pi\) |
0.0304941 | + | 0.999535i | \(0.490292\pi\) | |||||||
\(182\) | −12.0902 | − | 8.78402i | −0.896183 | − | 0.651115i | ||||
\(183\) | −2.09017 | + | 6.43288i | −0.154510 | + | 0.475532i | ||||
\(184\) | 1.00000 | + | 3.07768i | 0.0737210 | + | 0.226890i | ||||
\(185\) | −3.52786 | + | 2.56314i | −0.259374 | + | 0.188446i | ||||
\(186\) | 8.61803 | 0.631905 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.47214 | 0.180299 | ||||||||
\(189\) | −3.73607 | + | 2.71441i | −0.271759 | + | 0.197444i | ||||
\(190\) | −2.85410 | − | 8.78402i | −0.207058 | − | 0.637260i | ||||
\(191\) | 6.94427 | − | 21.3723i | 0.502470 | − | 1.54644i | −0.302513 | − | 0.953145i | \(-0.597826\pi\) |
0.804983 | − | 0.593298i | \(-0.202174\pi\) | |||||||
\(192\) | 0.809017 | + | 0.587785i | 0.0583858 | + | 0.0424197i | ||||
\(193\) | 0.263932 | + | 0.191758i | 0.0189982 | + | 0.0138030i | 0.597244 | − | 0.802060i | \(-0.296262\pi\) |
−0.578246 | + | 0.815863i | \(0.696262\pi\) | |||||||
\(194\) | −3.50000 | + | 10.7719i | −0.251285 | + | 0.773377i | ||||
\(195\) | −2.85410 | − | 8.78402i | −0.204386 | − | 0.629037i | ||||
\(196\) | −11.5902 | + | 8.42075i | −0.827869 | + | 0.601482i | ||||
\(197\) | −6.09017 | −0.433907 | −0.216953 | − | 0.976182i | \(-0.569612\pi\) | ||||
−0.216953 | + | 0.976182i | \(0.569612\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1459 | 0.931888 | 0.465944 | − | 0.884814i | \(-0.345715\pi\) | ||||
0.465944 | + | 0.884814i | \(0.345715\pi\) | |||||||
\(200\) | 2.54508 | − | 1.84911i | 0.179965 | − | 0.130752i | ||||
\(201\) | −1.23607 | − | 3.80423i | −0.0871855 | − | 0.268329i | ||||
\(202\) | −3.82624 | + | 11.7759i | −0.269213 | + | 0.828553i | ||||
\(203\) | 1.42705 | + | 1.03681i | 0.100159 | + | 0.0727700i | ||||
\(204\) | 2.00000 | + | 1.45309i | 0.140028 | + | 0.101736i | ||||
\(205\) | 2.85410 | − | 8.78402i | 0.199339 | − | 0.613503i | ||||
\(206\) | −3.71885 | − | 11.4454i | −0.259104 | − | 0.797441i | ||||
\(207\) | 2.61803 | − | 1.90211i | 0.181966 | − | 0.132206i | ||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −13.1803 | −0.909530 | ||||||||
\(211\) | −3.76393 | + | 2.73466i | −0.259120 | + | 0.188262i | −0.709759 | − | 0.704445i | \(-0.751196\pi\) |
0.450639 | + | 0.892706i | \(0.351196\pi\) | |||||||
\(212\) | −1.19098 | − | 3.66547i | −0.0817970 | − | 0.251745i | ||||
\(213\) | −3.85410 | + | 11.8617i | −0.264079 | + | 0.812751i | ||||
\(214\) | −4.35410 | − | 3.16344i | −0.297640 | − | 0.216248i | ||||
\(215\) | −7.47214 | − | 5.42882i | −0.509595 | − | 0.370243i | ||||
\(216\) | 0.309017 | − | 0.951057i | 0.0210259 | − | 0.0647112i | ||||
\(217\) | −12.2984 | − | 37.8505i | −0.834868 | − | 2.56946i | ||||
\(218\) | −14.0902 | + | 10.2371i | −0.954307 | + | 0.693344i | ||||
\(219\) | −11.3262 | −0.765356 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | −1.23607 | + | 0.898056i | −0.0829595 | + | 0.0602736i | ||||
\(223\) | −0.590170 | − | 1.81636i | −0.0395207 | − | 0.121632i | 0.929350 | − | 0.369201i | \(-0.120368\pi\) |
−0.968870 | + | 0.247568i | \(0.920368\pi\) | |||||||
\(224\) | 1.42705 | − | 4.39201i | 0.0953489 | − | 0.293454i | ||||
\(225\) | −2.54508 | − | 1.84911i | −0.169672 | − | 0.123274i | ||||
\(226\) | −10.0902 | − | 7.33094i | −0.671188 | − | 0.487647i | ||||
\(227\) | 2.20820 | − | 6.79615i | 0.146564 | − | 0.451077i | −0.850645 | − | 0.525740i | \(-0.823788\pi\) |
0.997209 | + | 0.0746638i | \(0.0237884\pi\) | |||||||
\(228\) | −1.00000 | − | 3.07768i | −0.0662266 | − | 0.203825i | ||||
\(229\) | −18.5623 | + | 13.4863i | −1.22663 | + | 0.891200i | −0.996633 | − | 0.0819909i | \(-0.973872\pi\) |
−0.229999 | + | 0.973191i | \(0.573872\pi\) | |||||||
\(230\) | 9.23607 | 0.609008 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.381966 | −0.0250773 | ||||||||
\(233\) | −7.23607 | + | 5.25731i | −0.474051 | + | 0.344418i | −0.799018 | − | 0.601307i | \(-0.794647\pi\) |
0.324967 | + | 0.945725i | \(0.394647\pi\) | |||||||
\(234\) | −1.00000 | − | 3.07768i | −0.0653720 | − | 0.201194i | ||||
\(235\) | 2.18034 | − | 6.71040i | 0.142230 | − | 0.437738i | ||||
\(236\) | 3.11803 | + | 2.26538i | 0.202967 | + | 0.147464i | ||||
\(237\) | 7.54508 | + | 5.48183i | 0.490106 | + | 0.356083i | ||||
\(238\) | 3.52786 | − | 10.8576i | 0.228677 | − | 0.703797i | ||||
\(239\) | 5.09017 | + | 15.6659i | 0.329256 | + | 1.01334i | 0.969483 | + | 0.245159i | \(0.0788402\pi\) |
−0.640227 | + | 0.768186i | \(0.721160\pi\) | |||||||
\(240\) | 2.30902 | − | 1.67760i | 0.149046 | − | 0.108289i | ||||
\(241\) | 2.43769 | 0.157026 | 0.0785128 | − | 0.996913i | \(-0.474983\pi\) | ||||
0.0785128 | + | 0.996913i | \(0.474983\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.47214 | + | 3.97574i | −0.350318 | + | 0.254521i | ||||
\(245\) | 12.6353 | + | 38.8873i | 0.807237 | + | 2.48442i | ||||
\(246\) | 1.00000 | − | 3.07768i | 0.0637577 | − | 0.196226i | ||||
\(247\) | −8.47214 | − | 6.15537i | −0.539069 | − | 0.391657i | ||||
\(248\) | 6.97214 | + | 5.06555i | 0.442731 | + | 0.321663i | ||||
\(249\) | −0.208204 | + | 0.640786i | −0.0131944 | + | 0.0406082i | ||||
\(250\) | 1.63525 | + | 5.03280i | 0.103423 | + | 0.318302i | ||||
\(251\) | 15.6353 | − | 11.3597i | 0.986889 | − | 0.717016i | 0.0276510 | − | 0.999618i | \(-0.491197\pi\) |
0.959238 | + | 0.282601i | \(0.0911973\pi\) | |||||||
\(252\) | −4.61803 | −0.290909 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 5.70820 | − | 4.14725i | 0.357462 | − | 0.259711i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −0.562306 | + | 1.73060i | −0.0350757 | + | 0.107952i | −0.967061 | − | 0.254543i | \(-0.918075\pi\) |
0.931986 | + | 0.362495i | \(0.118075\pi\) | |||||||
\(258\) | −2.61803 | − | 1.90211i | −0.162992 | − | 0.118420i | ||||
\(259\) | 5.70820 | + | 4.14725i | 0.354691 | + | 0.257698i | ||||
\(260\) | 2.85410 | − | 8.78402i | 0.177004 | − | 0.544762i | ||||
\(261\) | 0.118034 | + | 0.363271i | 0.00730612 | + | 0.0224859i | ||||
\(262\) | 12.3541 | − | 8.97578i | 0.763239 | − | 0.554526i | ||||
\(263\) | −7.70820 | −0.475308 | −0.237654 | − | 0.971350i | \(-0.576378\pi\) | ||||
−0.237654 | + | 0.971350i | \(0.576378\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0000 | −0.675725 | ||||||||
\(266\) | −12.0902 | + | 8.78402i | −0.741296 | + | 0.538583i | ||||
\(267\) | 3.61803 | + | 11.1352i | 0.221420 | + | 0.681461i | ||||
\(268\) | 1.23607 | − | 3.80423i | 0.0755049 | − | 0.232380i | ||||
\(269\) | 2.38197 | + | 1.73060i | 0.145231 | + | 0.105517i | 0.658028 | − | 0.752993i | \(-0.271391\pi\) |
−0.512797 | + | 0.858510i | \(0.671391\pi\) | |||||||
\(270\) | −2.30902 | − | 1.67760i | −0.140522 | − | 0.102095i | ||||
\(271\) | −7.23607 | + | 22.2703i | −0.439560 | + | 1.35283i | 0.448781 | + | 0.893642i | \(0.351858\pi\) |
−0.888341 | + | 0.459184i | \(0.848142\pi\) | |||||||
\(272\) | 0.763932 | + | 2.35114i | 0.0463202 | + | 0.142559i | ||||
\(273\) | −12.0902 | + | 8.78402i | −0.731730 | + | 0.531633i | ||||
\(274\) | 23.1246 | 1.39701 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.23607 | 0.194788 | ||||||||
\(277\) | 9.00000 | − | 6.53888i | 0.540758 | − | 0.392883i | −0.283609 | − | 0.958940i | \(-0.591532\pi\) |
0.824366 | + | 0.566057i | \(0.191532\pi\) | |||||||
\(278\) | 4.09017 | + | 12.5882i | 0.245312 | + | 0.754993i | ||||
\(279\) | 2.66312 | − | 8.19624i | 0.159437 | − | 0.490696i | ||||
\(280\) | −10.6631 | − | 7.74721i | −0.637243 | − | 0.462984i | ||||
\(281\) | 18.7082 | + | 13.5923i | 1.11604 | + | 0.810849i | 0.983604 | − | 0.180343i | \(-0.0577207\pi\) |
0.132434 | + | 0.991192i | \(0.457721\pi\) | |||||||
\(282\) | 0.763932 | − | 2.35114i | 0.0454915 | − | 0.140008i | ||||
\(283\) | 7.38197 | + | 22.7194i | 0.438812 | + | 1.35053i | 0.889129 | + | 0.457657i | \(0.151311\pi\) |
−0.450317 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(284\) | −10.0902 | + | 7.33094i | −0.598741 | + | 0.435011i | ||||
\(285\) | −9.23607 | −0.547097 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.9443 | −0.882132 | ||||||||
\(288\) | 0.809017 | − | 0.587785i | 0.0476718 | − | 0.0346356i | ||||
\(289\) | −3.36475 | − | 10.3556i | −0.197926 | − | 0.609154i | ||||
\(290\) | −0.336881 | + | 1.03681i | −0.0197823 | + | 0.0608838i | ||||
\(291\) | 9.16312 | + | 6.65740i | 0.537152 | + | 0.390263i | ||||
\(292\) | −9.16312 | − | 6.65740i | −0.536231 | − | 0.389595i | ||||
\(293\) | −7.10081 | + | 21.8541i | −0.414834 | + | 1.27673i | 0.497565 | + | 0.867426i | \(0.334227\pi\) |
−0.912399 | + | 0.409301i | \(0.865773\pi\) | |||||||
\(294\) | 4.42705 | + | 13.6251i | 0.258191 | + | 0.794630i | ||||
\(295\) | 8.89919 | − | 6.46564i | 0.518131 | − | 0.376444i | ||||
\(296\) | −1.52786 | −0.0888053 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.38197 | 0.0800551 | ||||||||
\(299\) | 8.47214 | − | 6.15537i | 0.489956 | − | 0.355974i | ||||
\(300\) | −0.972136 | − | 2.99193i | −0.0561263 | − | 0.172739i | ||||
\(301\) | −4.61803 | + | 14.2128i | −0.266179 | + | 0.819215i | ||||
\(302\) | −7.54508 | − | 5.48183i | −0.434171 | − | 0.315444i | ||||
\(303\) | 10.0172 | + | 7.27794i | 0.575474 | + | 0.418107i | ||||
\(304\) | 1.00000 | − | 3.07768i | 0.0573539 | − | 0.176517i | ||||
\(305\) | 5.96556 | + | 18.3601i | 0.341587 | + | 1.05130i | ||||
\(306\) | 2.00000 | − | 1.45309i | 0.114332 | − | 0.0830673i | ||||
\(307\) | 16.6525 | 0.950407 | 0.475203 | − | 0.879876i | \(-0.342374\pi\) | ||||
0.475203 | + | 0.879876i | \(0.342374\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0344 | −0.684615 | ||||||||
\(310\) | 19.8992 | − | 14.4576i | 1.13020 | − | 0.821137i | ||||
\(311\) | −7.38197 | − | 22.7194i | −0.418593 | − | 1.28830i | −0.908997 | − | 0.416802i | \(-0.863151\pi\) |
0.490405 | − | 0.871495i | \(-0.336849\pi\) | |||||||
\(312\) | 1.00000 | − | 3.07768i | 0.0566139 | − | 0.174240i | ||||
\(313\) | −12.2533 | − | 8.90254i | −0.692597 | − | 0.503201i | 0.184916 | − | 0.982754i | \(-0.440799\pi\) |
−0.877513 | + | 0.479553i | \(0.840799\pi\) | |||||||
\(314\) | 3.61803 | + | 2.62866i | 0.204177 | + | 0.148344i | ||||
\(315\) | −4.07295 | + | 12.5352i | −0.229485 | + | 0.706281i | ||||
\(316\) | 2.88197 | + | 8.86978i | 0.162123 | + | 0.498964i | ||||
\(317\) | 16.0902 | − | 11.6902i | 0.903714 | − | 0.656587i | −0.0357033 | − | 0.999362i | \(-0.511367\pi\) |
0.939417 | + | 0.342776i | \(0.111367\pi\) | |||||||
\(318\) | −3.85410 | −0.216127 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.85410 | 0.159549 | ||||||||
\(321\) | −4.35410 | + | 3.16344i | −0.243022 | + | 0.176566i | ||||
\(322\) | −4.61803 | − | 14.2128i | −0.257353 | − | 0.792051i | ||||
\(323\) | 2.47214 | − | 7.60845i | 0.137553 | − | 0.423346i | ||||
\(324\) | −0.809017 | − | 0.587785i | −0.0449454 | − | 0.0326547i | ||||
\(325\) | −8.23607 | − | 5.98385i | −0.456855 | − | 0.331924i | ||||
\(326\) | 4.14590 | − | 12.7598i | 0.229620 | − | 0.706698i | ||||
\(327\) | 5.38197 | + | 16.5640i | 0.297623 | + | 0.915991i | ||||
\(328\) | 2.61803 | − | 1.90211i | 0.144557 | − | 0.105027i | ||||
\(329\) | −11.4164 | −0.629407 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94427 | 0.491622 | 0.245811 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245811 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(332\) | −0.545085 | + | 0.396027i | −0.0299154 | + | 0.0217348i | ||||
\(333\) | 0.472136 | + | 1.45309i | 0.0258729 | + | 0.0796286i | ||||
\(334\) | 2.23607 | − | 6.88191i | 0.122352 | − | 0.376561i | ||||
\(335\) | −9.23607 | − | 6.71040i | −0.504620 | − | 0.366628i | ||||
\(336\) | −3.73607 | − | 2.71441i | −0.203819 | − | 0.148083i | ||||
\(337\) | −2.14590 | + | 6.60440i | −0.116895 | + | 0.359764i | −0.992337 | − | 0.123557i | \(-0.960570\pi\) |
0.875443 | + | 0.483321i | \(0.160570\pi\) | |||||||
\(338\) | 0.781153 | + | 2.40414i | 0.0424891 | + | 0.130768i | ||||
\(339\) | −10.0902 | + | 7.33094i | −0.548023 | + | 0.398162i | ||||
\(340\) | 7.05573 | 0.382651 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −3.23607 | −0.174987 | ||||||||
\(343\) | 27.3713 | − | 19.8864i | 1.47791 | − | 1.07377i | ||||
\(344\) | −1.00000 | − | 3.07768i | −0.0539164 | − | 0.165938i | ||||
\(345\) | 2.85410 | − | 8.78402i | 0.153660 | − | 0.472916i | ||||
\(346\) | 3.35410 | + | 2.43690i | 0.180318 | + | 0.131008i | ||||
\(347\) | 9.59017 | + | 6.96767i | 0.514827 | + | 0.374044i | 0.814652 | − | 0.579950i | \(-0.196928\pi\) |
−0.299824 | + | 0.953994i | \(0.596928\pi\) | |||||||
\(348\) | −0.118034 | + | 0.363271i | −0.00632729 | + | 0.0194734i | ||||
\(349\) | 4.09017 | + | 12.5882i | 0.218942 | + | 0.673834i | 0.998850 | + | 0.0479399i | \(0.0152656\pi\) |
−0.779908 | + | 0.625894i | \(0.784734\pi\) | |||||||
\(350\) | −11.7533 | + | 8.53926i | −0.628240 | + | 0.456443i | ||||
\(351\) | −3.23607 | −0.172729 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.5967 | −1.14948 | −0.574739 | − | 0.818336i | \(-0.694897\pi\) | ||||
−0.574739 | + | 0.818336i | \(0.694897\pi\) | |||||||
\(354\) | 3.11803 | − | 2.26538i | 0.165722 | − | 0.120404i | ||||
\(355\) | 11.0000 | + | 33.8545i | 0.583819 | + | 1.79681i | ||||
\(356\) | −3.61803 | + | 11.1352i | −0.191755 | + | 0.590162i | ||||
\(357\) | −9.23607 | − | 6.71040i | −0.488825 | − | 0.355152i | ||||
\(358\) | −5.16312 | − | 3.75123i | −0.272879 | − | 0.198258i | ||||
\(359\) | −3.94427 | + | 12.1392i | −0.208171 | + | 0.640684i | 0.791398 | + | 0.611302i | \(0.209354\pi\) |
−0.999568 | + | 0.0293817i | \(0.990646\pi\) | |||||||
\(360\) | −0.881966 | − | 2.71441i | −0.0464837 | − | 0.143062i | ||||
\(361\) | 6.89919 | − | 5.01255i | 0.363115 | − | 0.263819i | ||||
\(362\) | 16.4721 | 0.865756 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.9443 | −0.783293 | ||||||||
\(365\) | −26.1525 | + | 19.0009i | −1.36888 | + | 0.994552i | ||||
\(366\) | 2.09017 | + | 6.43288i | 0.109255 | + | 0.336252i | ||||
\(367\) | −11.5902 | + | 35.6709i | −0.605002 | + | 1.86200i | −0.108225 | + | 0.994126i | \(0.534517\pi\) |
−0.496777 | + | 0.867878i | \(0.665483\pi\) | |||||||
\(368\) | 2.61803 | + | 1.90211i | 0.136474 | + | 0.0991545i | ||||
\(369\) | −2.61803 | − | 1.90211i | −0.136289 | − | 0.0990200i | ||||
\(370\) | −1.34752 | + | 4.14725i | −0.0700544 | + | 0.215605i | ||||
\(371\) | 5.50000 | + | 16.9273i | 0.285546 | + | 0.878820i | ||||
\(372\) | 6.97214 | − | 5.06555i | 0.361488 | − | 0.262637i | ||||
\(373\) | 9.52786 | 0.493334 | 0.246667 | − | 0.969100i | \(-0.420665\pi\) | ||||
0.246667 | + | 0.969100i | \(0.420665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.29180 | 0.273267 | ||||||||
\(376\) | 2.00000 | − | 1.45309i | 0.103142 | − | 0.0749371i | ||||
\(377\) | 0.381966 | + | 1.17557i | 0.0196723 | + | 0.0605450i | ||||
\(378\) | −1.42705 | + | 4.39201i | −0.0733996 | + | 0.225901i | ||||
\(379\) | −3.00000 | − | 2.17963i | −0.154100 | − | 0.111960i | 0.508064 | − | 0.861320i | \(-0.330361\pi\) |
−0.662163 | + | 0.749360i | \(0.730361\pi\) | |||||||
\(380\) | −7.47214 | − | 5.42882i | −0.383312 | − | 0.278493i | ||||
\(381\) | 3.70820 | − | 11.4127i | 0.189977 | − | 0.584689i | ||||
\(382\) | −6.94427 | − | 21.3723i | −0.355300 | − | 1.09350i | ||||
\(383\) | −10.7082 | + | 7.77997i | −0.547164 | + | 0.397538i | −0.826739 | − | 0.562586i | \(-0.809806\pi\) |
0.279575 | + | 0.960124i | \(0.409806\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.326238 | 0.0166051 | ||||||||
\(387\) | −2.61803 | + | 1.90211i | −0.133082 | + | 0.0966898i | ||||
\(388\) | 3.50000 | + | 10.7719i | 0.177686 | + | 0.546860i | ||||
\(389\) | 12.0344 | − | 37.0382i | 0.610170 | − | 1.87791i | 0.153855 | − | 0.988093i | \(-0.450831\pi\) |
0.456316 | − | 0.889818i | \(-0.349169\pi\) | |||||||
\(390\) | −7.47214 | − | 5.42882i | −0.378366 | − | 0.274899i | ||||
\(391\) | 6.47214 | + | 4.70228i | 0.327310 | + | 0.237805i | ||||
\(392\) | −4.42705 | + | 13.6251i | −0.223600 | + | 0.688170i | ||||
\(393\) | −4.71885 | − | 14.5231i | −0.238034 | − | 0.732594i | ||||
\(394\) | −4.92705 | + | 3.57971i | −0.248221 | + | 0.180343i | ||||
\(395\) | 26.6180 | 1.33930 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.88854 | 0.496292 | 0.248146 | − | 0.968723i | \(-0.420179\pi\) | ||||
0.248146 | + | 0.968723i | \(0.420179\pi\) | |||||||
\(398\) | 10.6353 | − | 7.72696i | 0.533097 | − | 0.387318i | ||||
\(399\) | 4.61803 | + | 14.2128i | 0.231191 | + | 0.711532i | ||||
\(400\) | 0.972136 | − | 2.99193i | 0.0486068 | − | 0.149596i | ||||
\(401\) | −8.32624 | − | 6.04937i | −0.415792 | − | 0.302091i | 0.360150 | − | 0.932894i | \(-0.382725\pi\) |
−0.775943 | + | 0.630803i | \(0.782725\pi\) | |||||||
\(402\) | −3.23607 | − | 2.35114i | −0.161400 | − | 0.117264i | ||||
\(403\) | 8.61803 | − | 26.5236i | 0.429295 | − | 1.32123i | ||||
\(404\) | 3.82624 | + | 11.7759i | 0.190362 | + | 0.585875i | ||||
\(405\) | −2.30902 | + | 1.67760i | −0.114736 | + | 0.0833606i | ||||
\(406\) | 1.76393 | 0.0875425 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.47214 | 0.122389 | ||||||||
\(409\) | −9.78115 | + | 7.10642i | −0.483647 | + | 0.351390i | −0.802736 | − | 0.596335i | \(-0.796623\pi\) |
0.319089 | + | 0.947725i | \(0.396623\pi\) | |||||||
\(410\) | −2.85410 | − | 8.78402i | −0.140954 | − | 0.433812i | ||||
\(411\) | 7.14590 | − | 21.9928i | 0.352481 | − | 1.08483i | ||||
\(412\) | −9.73607 | − | 7.07367i | −0.479662 | − | 0.348495i | ||||
\(413\) | −14.3992 | − | 10.4616i | −0.708538 | − | 0.514783i | ||||
\(414\) | 1.00000 | − | 3.07768i | 0.0491473 | − | 0.151260i | ||||
\(415\) | 0.594235 | + | 1.82887i | 0.0291699 | + | 0.0897756i | ||||
\(416\) | 2.61803 | − | 1.90211i | 0.128360 | − | 0.0932588i | ||||
\(417\) | 13.2361 | 0.648173 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.9787 | −0.878318 | −0.439159 | − | 0.898409i | \(-0.644723\pi\) | ||||
−0.439159 | + | 0.898409i | \(0.644723\pi\) | |||||||
\(420\) | −10.6631 | + | 7.74721i | −0.520307 | + | 0.378025i | ||||
\(421\) | 10.8541 | + | 33.4055i | 0.528997 | + | 1.62808i | 0.756275 | + | 0.654254i | \(0.227017\pi\) |
−0.227278 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(422\) | −1.43769 | + | 4.42477i | −0.0699859 | + | 0.215394i | ||||
\(423\) | −2.00000 | − | 1.45309i | −0.0972433 | − | 0.0706514i | ||||
\(424\) | −3.11803 | − | 2.26538i | −0.151425 | − | 0.110017i | ||||
\(425\) | 2.40325 | − | 7.39645i | 0.116575 | − | 0.358781i | ||||
\(426\) | 3.85410 | + | 11.8617i | 0.186732 | + | 0.574702i | ||||
\(427\) | 25.2705 | − | 18.3601i | 1.22293 | − | 0.888508i | ||||
\(428\) | −5.38197 | −0.260147 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.23607 | −0.445403 | ||||||||
\(431\) | −5.85410 | + | 4.25325i | −0.281982 | + | 0.204872i | −0.719782 | − | 0.694201i | \(-0.755758\pi\) |
0.437799 | + | 0.899073i | \(0.355758\pi\) | |||||||
\(432\) | −0.309017 | − | 0.951057i | −0.0148676 | − | 0.0457577i | ||||
\(433\) | 3.80902 | − | 11.7229i | 0.183050 | − | 0.563369i | −0.816860 | − | 0.576836i | \(-0.804287\pi\) |
0.999909 | + | 0.0134675i | \(0.00428697\pi\) | |||||||
\(434\) | −32.1976 | − | 23.3929i | −1.54553 | − | 1.12290i | ||||
\(435\) | 0.881966 | + | 0.640786i | 0.0422870 | + | 0.0307233i | ||||
\(436\) | −5.38197 | + | 16.5640i | −0.257749 | + | 0.793271i | ||||
\(437\) | −3.23607 | − | 9.95959i | −0.154802 | − | 0.476432i | ||||
\(438\) | −9.16312 | + | 6.65740i | −0.437831 | + | 0.318103i | ||||
\(439\) | −16.0344 | −0.765282 | −0.382641 | − | 0.923897i | \(-0.624985\pi\) | ||||
−0.382641 | + | 0.923897i | \(0.624985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.3262 | 0.682202 | ||||||||
\(442\) | 6.47214 | − | 4.70228i | 0.307848 | − | 0.223665i | ||||
\(443\) | −0.517221 | − | 1.59184i | −0.0245739 | − | 0.0756307i | 0.938017 | − | 0.346588i | \(-0.112660\pi\) |
−0.962591 | + | 0.270957i | \(0.912660\pi\) | |||||||
\(444\) | −0.472136 | + | 1.45309i | −0.0224066 | + | 0.0689604i | ||||
\(445\) | 27.0344 | + | 19.6417i | 1.28156 | + | 0.931105i | ||||
\(446\) | −1.54508 | − | 1.12257i | −0.0731619 | − | 0.0531552i | ||||
\(447\) | 0.427051 | − | 1.31433i | 0.0201988 | − | 0.0621656i | ||||
\(448\) | −1.42705 | − | 4.39201i | −0.0674218 | − | 0.207503i | ||||
\(449\) | −29.0344 | + | 21.0948i | −1.37022 | + | 0.995523i | −0.372500 | + | 0.928032i | \(0.621499\pi\) |
−0.997720 | + | 0.0674910i | \(0.978501\pi\) | |||||||
\(450\) | −3.14590 | −0.148299 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.4721 | −0.586640 | ||||||||
\(453\) | −7.54508 | + | 5.48183i | −0.354499 | + | 0.257559i | ||||
\(454\) | −2.20820 | − | 6.79615i | −0.103636 | − | 0.318959i | ||||
\(455\) | −13.1803 | + | 40.5649i | −0.617904 | + | 1.90171i | ||||
\(456\) | −2.61803 | − | 1.90211i | −0.122601 | − | 0.0890746i | ||||
\(457\) | −17.7812 | − | 12.9188i | −0.831767 | − | 0.604314i | 0.0882915 | − | 0.996095i | \(-0.471859\pi\) |
−0.920059 | + | 0.391780i | \(0.871859\pi\) | |||||||
\(458\) | −7.09017 | + | 21.8213i | −0.331302 | + | 1.01964i | ||||
\(459\) | −0.763932 | − | 2.35114i | −0.0356573 | − | 0.109742i | ||||
\(460\) | 7.47214 | − | 5.42882i | 0.348390 | − | 0.253120i | ||||
\(461\) | −40.8328 | −1.90177 | −0.950887 | − | 0.309538i | \(-0.899825\pi\) | ||||
−0.950887 | + | 0.309538i | \(0.899825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0902 | 0.887195 | 0.443598 | − | 0.896226i | \(-0.353702\pi\) | ||||
0.443598 | + | 0.896226i | \(0.353702\pi\) | |||||||
\(464\) | −0.309017 | + | 0.224514i | −0.0143458 | + | 0.0104228i | ||||
\(465\) | −7.60081 | − | 23.3929i | −0.352479 | − | 1.08482i | ||||
\(466\) | −2.76393 | + | 8.50651i | −0.128037 | + | 0.394056i | ||||
\(467\) | −15.8262 | − | 11.4984i | −0.732351 | − | 0.532084i | 0.157955 | − | 0.987446i | \(-0.449510\pi\) |
−0.890306 | + | 0.455362i | \(0.849510\pi\) | |||||||
\(468\) | −2.61803 | − | 1.90211i | −0.121019 | − | 0.0879252i | ||||
\(469\) | −5.70820 | + | 17.5680i | −0.263580 | + | 0.811217i | ||||
\(470\) | −2.18034 | − | 6.71040i | −0.100572 | − | 0.309527i | ||||
\(471\) | 3.61803 | − | 2.62866i | 0.166710 | − | 0.121122i | ||||
\(472\) | 3.85410 | 0.177399 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.32624 | 0.428368 | ||||||||
\(475\) | −8.23607 | + | 5.98385i | −0.377897 | + | 0.274558i | ||||
\(476\) | −3.52786 | − | 10.8576i | −0.161699 | − | 0.497660i | ||||
\(477\) | −1.19098 | + | 3.66547i | −0.0545314 | + | 0.167830i | ||||
\(478\) | 13.3262 | + | 9.68208i | 0.609528 | + | 0.442848i | ||||
\(479\) | −5.85410 | − | 4.25325i | −0.267481 | − | 0.194336i | 0.445958 | − | 0.895054i | \(-0.352863\pi\) |
−0.713438 | + | 0.700718i | \(0.752863\pi\) | |||||||
\(480\) | 0.881966 | − | 2.71441i | 0.0402561 | − | 0.123895i | ||||
\(481\) | 1.52786 | + | 4.70228i | 0.0696646 | + | 0.214406i | ||||
\(482\) | 1.97214 | − | 1.43284i | 0.0898283 | − | 0.0652641i | ||||
\(483\) | −14.9443 | −0.679988 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.3262 | 1.46786 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 7.71885 | + | 23.7562i | 0.349774 | + | 1.07649i | 0.958978 | + | 0.283481i | \(0.0914892\pi\) |
−0.609204 | + | 0.793014i | \(0.708511\pi\) | |||||||
\(488\) | −2.09017 | + | 6.43288i | −0.0946175 | + | 0.291203i | ||||
\(489\) | −10.8541 | − | 7.88597i | −0.490839 | − | 0.356616i | ||||
\(490\) | 33.0795 | + | 24.0337i | 1.49438 | + | 1.08573i | ||||
\(491\) | −13.0557 | + | 40.1814i | −0.589197 | + | 1.81336i | −0.00747678 | + | 0.999972i | \(0.502380\pi\) |
−0.581720 | + | 0.813389i | \(0.697620\pi\) | |||||||
\(492\) | −1.00000 | − | 3.07768i | −0.0450835 | − | 0.138753i | ||||
\(493\) | −0.763932 | + | 0.555029i | −0.0344058 | + | 0.0249973i | ||||
\(494\) | −10.4721 | −0.471164 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.61803 | 0.386961 | ||||||||
\(497\) | 46.5967 | − | 33.8545i | 2.09015 | − | 1.51858i | ||||
\(498\) | 0.208204 | + | 0.640786i | 0.00932984 | + | 0.0287143i | ||||
\(499\) | −2.29180 | + | 7.05342i | −0.102595 | + | 0.315755i | −0.989158 | − | 0.146852i | \(-0.953086\pi\) |
0.886564 | + | 0.462607i | \(0.153086\pi\) | |||||||
\(500\) | 4.28115 | + | 3.11044i | 0.191459 | + | 0.139103i | ||||
\(501\) | −5.85410 | − | 4.25325i | −0.261542 | − | 0.190021i | ||||
\(502\) | 5.97214 | − | 18.3803i | 0.266549 | − | 0.820355i | ||||
\(503\) | −1.34752 | − | 4.14725i | −0.0600831 | − | 0.184917i | 0.916510 | − | 0.400012i | \(-0.130994\pi\) |
−0.976593 | + | 0.215095i | \(0.930994\pi\) | |||||||
\(504\) | −3.73607 | + | 2.71441i | −0.166418 | + | 0.120910i | ||||
\(505\) | 35.3394 | 1.57258 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.52786 | 0.112266 | ||||||||
\(508\) | 9.70820 | − | 7.05342i | 0.430732 | − | 0.312945i | ||||
\(509\) | 0.989357 | + | 3.04493i | 0.0438525 | + | 0.134964i | 0.970586 | − | 0.240756i | \(-0.0773954\pi\) |
−0.926733 | + | 0.375720i | \(0.877395\pi\) | |||||||
\(510\) | 2.18034 | − | 6.71040i | 0.0965471 | − | 0.297141i | ||||
\(511\) | 42.3156 | + | 30.7441i | 1.87193 | + | 1.36004i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −1.00000 | + | 3.07768i | −0.0441511 | + | 0.135883i | ||||
\(514\) | 0.562306 | + | 1.73060i | 0.0248022 | + | 0.0763335i | ||||
\(515\) | −27.7877 | + | 20.1890i | −1.22447 | + | 0.889632i | ||||
\(516\) | −3.23607 | −0.142460 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.05573 | 0.310011 | ||||||||
\(519\) | 3.35410 | − | 2.43690i | 0.147229 | − | 0.106968i | ||||
\(520\) | −2.85410 | − | 8.78402i | −0.125161 | − | 0.385205i | ||||
\(521\) | 9.70820 | − | 29.8788i | 0.425324 | − | 1.30901i | −0.477359 | − | 0.878708i | \(-0.658406\pi\) |
0.902684 | − | 0.430305i | \(-0.141594\pi\) | |||||||
\(522\) | 0.309017 | + | 0.224514i | 0.0135253 | + | 0.00982671i | ||||
\(523\) | 15.8541 | + | 11.5187i | 0.693251 | + | 0.503677i | 0.877727 | − | 0.479160i | \(-0.159059\pi\) |
−0.184476 | + | 0.982837i | \(0.559059\pi\) | |||||||
\(524\) | 4.71885 | − | 14.5231i | 0.206144 | − | 0.634445i | ||||
\(525\) | 4.48936 | + | 13.8168i | 0.195932 | + | 0.603015i | ||||
\(526\) | −6.23607 | + | 4.53077i | −0.271905 | + | 0.197551i | ||||
\(527\) | 21.3050 | 0.928058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | −8.89919 | + | 6.46564i | −0.386556 | + | 0.280849i | ||||
\(531\) | −1.19098 | − | 3.66547i | −0.0516843 | − | 0.159068i | ||||
\(532\) | −4.61803 | + | 14.2128i | −0.200217 | + | 0.616205i | ||||
\(533\) | −8.47214 | − | 6.15537i | −0.366969 | − | 0.266619i | ||||
\(534\) | 9.47214 | + | 6.88191i | 0.409899 | + | 0.297809i | ||||
\(535\) | −4.74671 | + | 14.6089i | −0.205218 | + | 0.631597i | ||||
\(536\) | −1.23607 | − | 3.80423i | −0.0533900 | − | 0.164318i | ||||
\(537\) | −5.16312 | + | 3.75123i | −0.222805 | + | 0.161877i | ||||
\(538\) | 2.94427 | 0.126937 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.85410 | −0.122821 | ||||||||
\(541\) | 6.09017 | − | 4.42477i | 0.261837 | − | 0.190236i | −0.449120 | − | 0.893472i | \(-0.648262\pi\) |
0.710956 | + | 0.703236i | \(0.248262\pi\) | |||||||
\(542\) | 7.23607 | + | 22.2703i | 0.310816 | + | 0.956592i | ||||
\(543\) | 5.09017 | − | 15.6659i | 0.218440 | − | 0.672290i | ||||
\(544\) | 2.00000 | + | 1.45309i | 0.0857493 | + | 0.0623005i | ||||
\(545\) | 40.2148 | + | 29.2177i | 1.72261 | + | 1.25155i | ||||
\(546\) | −4.61803 | + | 14.2128i | −0.197634 | + | 0.608254i | ||||
\(547\) | −5.61803 | − | 17.2905i | −0.240210 | − | 0.739290i | −0.996387 | − | 0.0849234i | \(-0.972935\pi\) |
0.756178 | − | 0.654366i | \(-0.227065\pi\) | |||||||
\(548\) | 18.7082 | − | 13.5923i | 0.799175 | − | 0.580635i | ||||
\(549\) | 6.76393 | 0.288678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.23607 | 0.0526583 | ||||||||
\(552\) | 2.61803 | − | 1.90211i | 0.111431 | − | 0.0809593i | ||||
\(553\) | −13.3090 | − | 40.9609i | −0.565957 | − | 1.74184i | ||||
\(554\) | 3.43769 | − | 10.5801i | 0.146054 | − | 0.449507i | ||||
\(555\) | 3.52786 | + | 2.56314i | 0.149749 | + | 0.108799i | ||||
\(556\) | 10.7082 | + | 7.77997i | 0.454129 | + | 0.329944i | ||||
\(557\) | 12.9894 | − | 39.9771i | 0.550377 | − | 1.69389i | −0.157474 | − | 0.987523i | \(-0.550335\pi\) |
0.707851 | − | 0.706362i | \(-0.249665\pi\) | |||||||
\(558\) | −2.66312 | − | 8.19624i | −0.112739 | − | 0.346974i | ||||
\(559\) | −8.47214 | + | 6.15537i | −0.358333 | + | 0.260344i | ||||
\(560\) | −13.1803 | −0.556971 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.1246 | 0.975453 | ||||||||
\(563\) | −37.8885 | + | 27.5276i | −1.59681 | + | 1.16015i | −0.703519 | + | 0.710677i | \(0.748389\pi\) |
−0.893293 | + | 0.449475i | \(0.851611\pi\) | |||||||
\(564\) | −0.763932 | − | 2.35114i | −0.0321673 | − | 0.0990009i | ||||
\(565\) | −11.0000 | + | 33.8545i | −0.462773 | + | 1.42427i | ||||
\(566\) | 19.3262 | + | 14.0413i | 0.812342 | + | 0.590201i | ||||
\(567\) | 3.73607 | + | 2.71441i | 0.156900 | + | 0.113995i | ||||
\(568\) | −3.85410 | + | 11.8617i | −0.161715 | + | 0.497706i | ||||
\(569\) | −11.3820 | − | 35.0301i | −0.477157 | − | 1.46854i | −0.843027 | − | 0.537872i | \(-0.819228\pi\) |
0.365870 | − | 0.930666i | \(-0.380772\pi\) | |||||||
\(570\) | −7.47214 | + | 5.42882i | −0.312973 | + | 0.227388i | ||||
\(571\) | −9.59675 | −0.401611 | −0.200806 | − | 0.979631i | \(-0.564356\pi\) | ||||
−0.200806 | + | 0.979631i | \(0.564356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.4721 | −0.938787 | ||||||||
\(574\) | −12.0902 | + | 8.78402i | −0.504634 | + | 0.366638i | ||||
\(575\) | −3.14590 | − | 9.68208i | −0.131193 | − | 0.403771i | ||||
\(576\) | 0.309017 | − | 0.951057i | 0.0128757 | − | 0.0396274i | ||||
\(577\) | −5.73607 | − | 4.16750i | −0.238796 | − | 0.173495i | 0.461951 | − | 0.886905i | \(-0.347150\pi\) |
−0.700747 | + | 0.713410i | \(0.747150\pi\) | |||||||
\(578\) | −8.80902 | − | 6.40013i | −0.366407 | − | 0.266210i | ||||
\(579\) | 0.100813 | − | 0.310271i | 0.00418965 | − | 0.0128944i | ||||
\(580\) | 0.336881 | + | 1.03681i | 0.0139882 | + | 0.0430513i | ||||
\(581\) | 2.51722 | − | 1.82887i | 0.104432 | − | 0.0758742i | ||||
\(582\) | 11.3262 | 0.469488 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −11.3262 | −0.468683 | ||||||||
\(585\) | −7.47214 | + | 5.42882i | −0.308935 | + | 0.224454i | ||||
\(586\) | 7.10081 | + | 21.8541i | 0.293332 | + | 0.902783i | ||||
\(587\) | −7.44427 | + | 22.9111i | −0.307258 | + | 0.945643i | 0.671567 | + | 0.740944i | \(0.265622\pi\) |
−0.978825 | + | 0.204699i | \(0.934378\pi\) | |||||||
\(588\) | 11.5902 | + | 8.42075i | 0.477971 | + | 0.347266i | ||||
\(589\) | −22.5623 | − | 16.3925i | −0.929664 | − | 0.675440i | ||||
\(590\) | 3.39919 | − | 10.4616i | 0.139942 | − | 0.430698i | ||||
\(591\) | 1.88197 | + | 5.79210i | 0.0774137 | + | 0.238255i | ||||
\(592\) | −1.23607 | + | 0.898056i | −0.0508021 | + | 0.0369099i | ||||
\(593\) | −24.4721 | −1.00495 | −0.502475 | − | 0.864592i | \(-0.667577\pi\) | ||||
−0.502475 | + | 0.864592i | \(0.667577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.5836 | −1.33580 | ||||||||
\(596\) | 1.11803 | − | 0.812299i | 0.0457965 | − | 0.0332731i | ||||
\(597\) | −4.06231 | − | 12.5025i | −0.166259 | − | 0.511693i | ||||
\(598\) | 3.23607 | − | 9.95959i | 0.132333 | − | 0.407278i | ||||
\(599\) | −6.76393 | − | 4.91428i | −0.276367 | − | 0.200792i | 0.440964 | − | 0.897525i | \(-0.354637\pi\) |
−0.717331 | + | 0.696732i | \(0.754637\pi\) | |||||||
\(600\) | −2.54508 | − | 1.84911i | −0.103903 | − | 0.0754897i | ||||
\(601\) | 7.33688 | − | 22.5806i | 0.299278 | − | 0.921082i | −0.682473 | − | 0.730911i | \(-0.739096\pi\) |
0.981751 | − | 0.190171i | \(-0.0609043\pi\) | |||||||
\(602\) | 4.61803 | + | 14.2128i | 0.188217 | + | 0.579272i | ||||
\(603\) | −3.23607 | + | 2.35114i | −0.131783 | + | 0.0957459i | ||||
\(604\) | −9.32624 | −0.379479 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.3820 | 0.502983 | ||||||||
\(607\) | 19.2361 | − | 13.9758i | 0.780768 | − | 0.567261i | −0.124441 | − | 0.992227i | \(-0.539714\pi\) |
0.905209 | + | 0.424966i | \(0.139714\pi\) | |||||||
\(608\) | −1.00000 | − | 3.07768i | −0.0405554 | − | 0.124817i | ||||
\(609\) | 0.545085 | − | 1.67760i | 0.0220880 | − | 0.0679797i | ||||
\(610\) | 15.6180 | + | 11.3472i | 0.632356 | + | 0.459433i | ||||
\(611\) | −6.47214 | − | 4.70228i | −0.261835 | − | 0.190234i | ||||
\(612\) | 0.763932 | − | 2.35114i | 0.0308801 | − | 0.0950392i | ||||
\(613\) | 4.41641 | + | 13.5923i | 0.178377 | + | 0.548988i | 0.999772 | − | 0.0213723i | \(-0.00680355\pi\) |
−0.821395 | + | 0.570360i | \(0.806804\pi\) | |||||||
\(614\) | 13.4721 | − | 9.78808i | 0.543691 | − | 0.395015i | ||||
\(615\) | −9.23607 | −0.372434 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2918 | −1.21950 | −0.609751 | − | 0.792593i | \(-0.708731\pi\) | ||||
−0.609751 | + | 0.792593i | \(0.708731\pi\) | |||||||
\(618\) | −9.73607 | + | 7.07367i | −0.391642 | + | 0.284545i | ||||
\(619\) | −7.81966 | − | 24.0664i | −0.314299 | − | 0.967312i | −0.976042 | − | 0.217582i | \(-0.930183\pi\) |
0.661743 | − | 0.749730i | \(-0.269817\pi\) | |||||||
\(620\) | 7.60081 | − | 23.3929i | 0.305256 | − | 0.939481i | ||||
\(621\) | −2.61803 | − | 1.90211i | −0.105058 | − | 0.0763292i | ||||
\(622\) | −19.3262 | − | 14.0413i | −0.774912 | − | 0.563006i | ||||
\(623\) | 16.7082 | − | 51.4226i | 0.669400 | − | 2.06020i | ||||
\(624\) | −1.00000 | − | 3.07768i | −0.0400320 | − | 0.123206i | ||||
\(625\) | 24.9443 | − | 18.1231i | 0.997771 | − | 0.724923i | ||||
\(626\) | −15.1459 | −0.605352 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.47214 | 0.178458 | ||||||||
\(629\) | −3.05573 | + | 2.22012i | −0.121840 | + | 0.0885218i | ||||
\(630\) | 4.07295 | + | 12.5352i | 0.162270 | + | 0.499416i | ||||
\(631\) | −5.29837 | + | 16.3067i | −0.210925 | + | 0.649160i | 0.788493 | + | 0.615044i | \(0.210862\pi\) |
−0.999418 | + | 0.0341164i | \(0.989138\pi\) | |||||||
\(632\) | 7.54508 | + | 5.48183i | 0.300127 | + | 0.218055i | ||||
\(633\) | 3.76393 | + | 2.73466i | 0.149603 | + | 0.108693i | ||||
\(634\) | 6.14590 | − | 18.9151i | 0.244085 | − | 0.751216i | ||||
\(635\) | −10.5836 | − | 32.5729i | −0.419997 | − | 1.29262i | ||||
\(636\) | −3.11803 | + | 2.26538i | −0.123638 | + | 0.0898283i | ||||
\(637\) | 46.3607 | 1.83688 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.4721 | 0.493390 | ||||||||
\(640\) | 2.30902 | − | 1.67760i | 0.0912719 | − | 0.0663129i | ||||
\(641\) | 14.5623 | + | 44.8182i | 0.575177 | + | 1.77021i | 0.635578 | + | 0.772037i | \(0.280762\pi\) |
−0.0604010 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(642\) | −1.66312 | + | 5.11855i | −0.0656381 | + | 0.202013i | ||||
\(643\) | −8.85410 | − | 6.43288i | −0.349172 | − | 0.253688i | 0.399350 | − | 0.916799i | \(-0.369236\pi\) |
−0.748521 | + | 0.663111i | \(0.769236\pi\) | |||||||
\(644\) | −12.0902 | − | 8.78402i | −0.476419 | − | 0.346139i | ||||
\(645\) | −2.85410 | + | 8.78402i | −0.112380 | + | 0.345871i | ||||
\(646\) | −2.47214 | − | 7.60845i | −0.0972649 | − | 0.299351i | ||||
\(647\) | 2.32624 | − | 1.69011i | 0.0914538 | − | 0.0664451i | −0.541119 | − | 0.840946i | \(-0.681999\pi\) |
0.632573 | + | 0.774501i | \(0.281999\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −10.1803 | −0.399306 | ||||||||
\(651\) | −32.1976 | + | 23.3929i | −1.26192 | + | 0.916840i | ||||
\(652\) | −4.14590 | − | 12.7598i | −0.162366 | − | 0.499711i | ||||
\(653\) | −6.53444 | + | 20.1109i | −0.255712 | + | 0.787002i | 0.737976 | + | 0.674827i | \(0.235782\pi\) |
−0.993688 | + | 0.112175i | \(0.964218\pi\) | |||||||
\(654\) | 14.0902 | + | 10.2371i | 0.550969 | + | 0.400303i | ||||
\(655\) | −35.2599 | − | 25.6178i | −1.37772 | − | 1.00097i | ||||
\(656\) | 1.00000 | − | 3.07768i | 0.0390434 | − | 0.120163i | ||||
\(657\) | 3.50000 | + | 10.7719i | 0.136548 | + | 0.420252i | ||||
\(658\) | −9.23607 | + | 6.71040i | −0.360059 | + | 0.261598i | ||||
\(659\) | −43.1459 | −1.68073 | −0.840363 | − | 0.542024i | \(-0.817658\pi\) | ||||
−0.840363 | + | 0.542024i | \(0.817658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.81966 | 0.226359 | 0.113179 | − | 0.993575i | \(-0.463897\pi\) | ||||
0.113179 | + | 0.993575i | \(0.463897\pi\) | |||||||
\(662\) | 7.23607 | − | 5.25731i | 0.281238 | − | 0.204331i | ||||
\(663\) | −2.47214 | − | 7.60845i | −0.0960098 | − | 0.295488i | ||||
\(664\) | −0.208204 | + | 0.640786i | −0.00807988 | + | 0.0248673i | ||||
\(665\) | 34.5066 | + | 25.0705i | 1.33811 | + | 0.972192i | ||||
\(666\) | 1.23607 | + | 0.898056i | 0.0478967 | + | 0.0347990i | ||||
\(667\) | −0.381966 | + | 1.17557i | −0.0147898 | + | 0.0455183i | ||||
\(668\) | −2.23607 | − | 6.88191i | −0.0865161 | − | 0.266269i | ||||
\(669\) | −1.54508 | + | 1.12257i | −0.0597364 | + | 0.0434011i | ||||
\(670\) | −11.4164 | −0.441054 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.61803 | −0.178145 | ||||||||
\(673\) | −5.63525 | + | 4.09425i | −0.217223 | + | 0.157822i | −0.691076 | − | 0.722782i | \(-0.742863\pi\) |
0.473853 | + | 0.880604i | \(0.342863\pi\) | |||||||
\(674\) | 2.14590 | + | 6.60440i | 0.0826569 | + | 0.254392i | ||||
\(675\) | −0.972136 | + | 2.99193i | −0.0374175 | + | 0.115159i | ||||
\(676\) | 2.04508 | + | 1.48584i | 0.0786571 | + | 0.0571477i | ||||
\(677\) | −32.7705 | − | 23.8092i | −1.25947 | − | 0.915061i | −0.260741 | − | 0.965409i | \(-0.583967\pi\) |
−0.998732 | + | 0.0503480i | \(0.983967\pi\) | |||||||
\(678\) | −3.85410 | + | 11.8617i | −0.148016 | + | 0.455546i | ||||
\(679\) | −16.1631 | − | 49.7450i | −0.620284 | − | 1.90904i | ||||
\(680\) | 5.70820 | − | 4.14725i | 0.218900 | − | 0.159040i | ||||
\(681\) | −7.14590 | −0.273831 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.7426 | 1.75029 | 0.875147 | − | 0.483857i | \(-0.160765\pi\) | ||||
0.875147 | + | 0.483857i | \(0.160765\pi\) | |||||||
\(684\) | −2.61803 | + | 1.90211i | −0.100103 | + | 0.0727291i | ||||
\(685\) | −20.3951 | − | 62.7697i | −0.779258 | − | 2.39831i | ||||
\(686\) | 10.4549 | − | 32.1769i | 0.399171 | − | 1.22852i | ||||
\(687\) | 18.5623 | + | 13.4863i | 0.708196 | + | 0.514535i | ||||
\(688\) | −2.61803 | − | 1.90211i | −0.0998116 | − | 0.0725174i | ||||
\(689\) | −3.85410 | + | 11.8617i | −0.146830 | + | 0.451895i | ||||
\(690\) | −2.85410 | − | 8.78402i | −0.108654 | − | 0.334402i | ||||
\(691\) | 0.236068 | − | 0.171513i | 0.00898045 | − | 0.00652468i | −0.583286 | − | 0.812267i | \(-0.698233\pi\) |
0.592266 | + | 0.805742i | \(0.298233\pi\) | |||||||
\(692\) | 4.14590 | 0.157603 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.8541 | 0.449976 | ||||||||
\(695\) | 30.5623 | − | 22.2048i | 1.15929 | − | 0.842277i | ||||
\(696\) | 0.118034 | + | 0.363271i | 0.00447407 | + | 0.0137698i | ||||
\(697\) | 2.47214 | − | 7.60845i | 0.0936388 | − | 0.288191i | ||||
\(698\) | 10.7082 | + | 7.77997i | 0.405311 | + | 0.294476i | ||||
\(699\) | 7.23607 | + | 5.25731i | 0.273693 | + | 0.198850i | ||||
\(700\) | −4.48936 | + | 13.8168i | −0.169682 | + | 0.522227i | ||||
\(701\) | −0.326238 | − | 1.00406i | −0.0123218 | − | 0.0379227i | 0.944707 | − | 0.327917i | \(-0.106347\pi\) |
−0.957028 | + | 0.289994i | \(0.906347\pi\) | |||||||
\(702\) | −2.61803 | + | 1.90211i | −0.0988113 | + | 0.0717906i | ||||
\(703\) | 4.94427 | 0.186477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.05573 | −0.265734 | ||||||||
\(706\) | −17.4721 | + | 12.6942i | −0.657573 | + | 0.477754i | ||||
\(707\) | −17.6697 | − | 54.3817i | −0.664537 | − | 2.04524i | ||||
\(708\) | 1.19098 | − | 3.66547i | 0.0447599 | − | 0.137757i | ||||
\(709\) | −28.3262 | − | 20.5802i | −1.06381 | − | 0.772906i | −0.0890239 | − | 0.996029i | \(-0.528375\pi\) |
−0.974790 | + | 0.223123i | \(0.928375\pi\) | |||||||
\(710\) | 28.7984 | + | 20.9232i | 1.08078 | + | 0.785235i | ||||
\(711\) | 2.88197 | − | 8.86978i | 0.108082 | − | 0.332643i | ||||
\(712\) | 3.61803 | + | 11.1352i | 0.135592 | + | 0.417308i | ||||
\(713\) | 22.5623 | − | 16.3925i | 0.844965 | − | 0.613903i | ||||
\(714\) | −11.4164 | −0.427248 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.38197 | −0.238505 | ||||||||
\(717\) | 13.3262 | − | 9.68208i | 0.497677 | − | 0.361584i | ||||
\(718\) | 3.94427 | + | 12.1392i | 0.147199 | + | 0.453032i | ||||
\(719\) | 3.38197 | − | 10.4086i | 0.126126 | − | 0.388176i | −0.867979 | − | 0.496602i | \(-0.834581\pi\) |
0.994105 | + | 0.108426i | \(0.0345810\pi\) | |||||||
\(720\) | −2.30902 | − | 1.67760i | −0.0860520 | − | 0.0625204i | ||||
\(721\) | 44.9615 | + | 32.6664i | 1.67445 | + | 1.21656i | ||||
\(722\) | 2.63525 | − | 8.11048i | 0.0980740 | − | 0.301841i | ||||
\(723\) | −0.753289 | − | 2.31838i | −0.0280151 | − | 0.0862217i | ||||
\(724\) | 13.3262 | − | 9.68208i | 0.495266 | − | 0.359832i | ||||
\(725\) | 1.20163 | 0.0446273 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.41641 | 0.126708 | 0.0633538 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633538 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(728\) | −12.0902 | + | 8.78402i | −0.448092 | + | 0.325558i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −9.98936 | + | 30.7441i | −0.369723 | + | 1.13789i | ||||
\(731\) | −6.47214 | − | 4.70228i | −0.239381 | − | 0.173920i | ||||
\(732\) | 5.47214 | + | 3.97574i | 0.202256 | + | 0.146948i | ||||
\(733\) | 13.5066 | − | 41.5690i | 0.498877 | − | 1.53539i | −0.311950 | − | 0.950099i | \(-0.600982\pi\) |
0.810827 | − | 0.585286i | \(-0.199018\pi\) | |||||||
\(734\) | 11.5902 | + | 35.6709i | 0.427801 | + | 1.31664i | ||||
\(735\) | 33.0795 | − | 24.0337i | 1.22016 | − | 0.886496i | ||||
\(736\) | 3.23607 | 0.119283 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.23607 | −0.119121 | ||||||||
\(739\) | 12.1803 | − | 8.84953i | 0.448061 | − | 0.325535i | −0.340769 | − | 0.940147i | \(-0.610687\pi\) |
0.788830 | + | 0.614612i | \(0.210687\pi\) | |||||||
\(740\) | 1.34752 | + | 4.14725i | 0.0495360 | + | 0.152456i | ||||
\(741\) | −3.23607 | + | 9.95959i | −0.118880 | + | 0.365875i | ||||
\(742\) | 14.3992 | + | 10.4616i | 0.528611 | + | 0.384058i | ||||
\(743\) | −30.5623 | − | 22.2048i | −1.12122 | − | 0.814616i | −0.136828 | − | 0.990595i | \(-0.543691\pi\) |
−0.984394 | + | 0.175979i | \(0.943691\pi\) | |||||||
\(744\) | 2.66312 | − | 8.19624i | 0.0976347 | − | 0.300489i | ||||
\(745\) | −1.21885 | − | 3.75123i | −0.0446551 | − | 0.137434i | ||||
\(746\) | 7.70820 | − | 5.60034i | 0.282217 | − | 0.205043i | ||||
\(747\) | 0.673762 | 0.0246517 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.8541 | 0.908149 | ||||||||
\(750\) | 4.28115 | − | 3.11044i | 0.156326 | − | 0.113577i | ||||
\(751\) | −3.12461 | − | 9.61657i | −0.114019 | − | 0.350913i | 0.877722 | − | 0.479169i | \(-0.159062\pi\) |
−0.991741 | + | 0.128256i | \(0.959062\pi\) | |||||||
\(752\) | 0.763932 | − | 2.35114i | 0.0278577 | − | 0.0857373i | ||||
\(753\) | −15.6353 | − | 11.3597i | −0.569780 | − | 0.413970i | ||||
\(754\) | 1.00000 | + | 0.726543i | 0.0364179 | + | 0.0264591i | ||||
\(755\) | −8.22542 | + | 25.3153i | −0.299354 | + | 0.921316i | ||||
\(756\) | 1.42705 | + | 4.39201i | 0.0519013 | + | 0.159736i | ||||
\(757\) | 24.7082 | − | 17.9516i | 0.898035 | − | 0.652461i | −0.0399256 | − | 0.999203i | \(-0.512712\pi\) |
0.937961 | + | 0.346742i | \(0.112712\pi\) | |||||||
\(758\) | −3.70820 | −0.134688 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.23607 | −0.335027 | ||||||||
\(761\) | 8.32624 | − | 6.04937i | 0.301826 | − | 0.219289i | −0.426555 | − | 0.904461i | \(-0.640273\pi\) |
0.728381 | + | 0.685172i | \(0.240273\pi\) | |||||||
\(762\) | −3.70820 | − | 11.4127i | −0.134334 | − | 0.413438i | ||||
\(763\) | 24.8541 | − | 76.4931i | 0.899779 | − | 2.76923i | ||||
\(764\) | −18.1803 | − | 13.2088i | −0.657742 | − | 0.477877i | ||||
\(765\) | −5.70820 | − | 4.14725i | −0.206381 | − | 0.149944i | ||||
\(766\) | −4.09017 | + | 12.5882i | −0.147784 | + | 0.454832i | ||||
\(767\) | −3.85410 | − | 11.8617i | −0.139164 | − | 0.428301i | ||||
\(768\) | 0.809017 | − | 0.587785i | 0.0291929 | − | 0.0212099i | ||||
\(769\) | 4.27051 | 0.153999 | 0.0769993 | − | 0.997031i | \(-0.475466\pi\) | ||||
0.0769993 | + | 0.997031i | \(0.475466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.81966 | 0.0655335 | ||||||||
\(772\) | 0.263932 | − | 0.191758i | 0.00949912 | − | 0.00690152i | ||||
\(773\) | 2.93769 | + | 9.04129i | 0.105662 | + | 0.325193i | 0.989885 | − | 0.141871i | \(-0.0453118\pi\) |
−0.884224 | + | 0.467064i | \(0.845312\pi\) | |||||||
\(774\) | −1.00000 | + | 3.07768i | −0.0359443 | + | 0.110625i | ||||
\(775\) | −21.9336 | − | 15.9357i | −0.787879 | − | 0.572428i | ||||
\(776\) | 9.16312 | + | 6.65740i | 0.328937 | + | 0.238987i | ||||
\(777\) | 2.18034 | − | 6.71040i | 0.0782193 | − | 0.240734i | ||||
\(778\) | −12.0344 | − | 37.0382i | −0.431456 | − | 1.32788i | ||||
\(779\) | −8.47214 | + | 6.15537i | −0.303546 | + | 0.220539i | ||||
\(780\) | −9.23607 | −0.330704 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.00000 | 0.286079 | ||||||||
\(783\) | 0.309017 | − | 0.224514i | 0.0110434 | − | 0.00802348i | ||||
\(784\) | 4.42705 | + | 13.6251i | 0.158109 | + | 0.486609i | ||||
\(785\) | 3.94427 | − | 12.1392i | 0.140777 | − | 0.433267i | ||||
\(786\) | −12.3541 | − | 8.97578i | −0.440656 | − | 0.320155i | ||||
\(787\) | −30.3262 | − | 22.0333i | −1.08101 | − | 0.785402i | −0.103154 | − | 0.994665i | \(-0.532894\pi\) |
−0.977859 | + | 0.209263i | \(0.932894\pi\) | |||||||
\(788\) | −1.88197 | + | 5.79210i | −0.0670423 | + | 0.206335i | ||||
\(789\) | 2.38197 | + | 7.33094i | 0.0848002 | + | 0.260988i | ||||
\(790\) | 21.5344 | − | 15.6457i | 0.766161 | − | 0.556649i | ||||
\(791\) | 57.5967 | 2.04790 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.8885 | 0.777285 | ||||||||
\(794\) | 8.00000 | − | 5.81234i | 0.283909 | − | 0.206272i | ||||
\(795\) | 3.39919 | + | 10.4616i | 0.120557 | + | 0.371035i | ||||
\(796\) | 4.06231 | − | 12.5025i | 0.143985 | − | 0.443139i | ||||
\(797\) | 18.2984 | + | 13.2945i | 0.648162 | + | 0.470917i | 0.862644 | − | 0.505811i | \(-0.168807\pi\) |
−0.214483 | + | 0.976728i | \(0.568807\pi\) | |||||||
\(798\) | 12.0902 | + | 8.78402i | 0.427987 | + | 0.310951i | ||||
\(799\) | 1.88854 | − | 5.81234i | 0.0668119 | − | 0.205626i | ||||
\(800\) | −0.972136 | − | 2.99193i | −0.0343702 | − | 0.105781i | ||||
\(801\) | 9.47214 | − | 6.88191i | 0.334681 | − | 0.243160i | ||||
\(802\) | −10.2918 | −0.363416 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | −34.5066 | + | 25.0705i | −1.21620 | + | 0.883619i | ||||
\(806\) | −8.61803 | − | 26.5236i | −0.303557 | − | 0.934253i | ||||
\(807\) | 0.909830 | − | 2.80017i | 0.0320275 | − | 0.0985706i | ||||
\(808\) | 10.0172 | + | 7.27794i | 0.352405 | + | 0.256037i | ||||
\(809\) | 24.4721 | + | 17.7800i | 0.860394 | + | 0.625113i | 0.927992 | − | 0.372599i | \(-0.121533\pi\) |
−0.0675978 | + | 0.997713i | \(0.521533\pi\) | |||||||
\(810\) | −0.881966 | + | 2.71441i | −0.0309891 | + | 0.0953747i | ||||
\(811\) | 12.5967 | + | 38.7688i | 0.442332 | + | 1.36136i | 0.885384 | + | 0.464861i | \(0.153896\pi\) |
−0.443052 | + | 0.896496i | \(0.646104\pi\) | |||||||
\(812\) | 1.42705 | − | 1.03681i | 0.0500797 | − | 0.0363850i | ||||
\(813\) | 23.4164 | 0.821249 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.2918 | −1.34130 | ||||||||
\(816\) | 2.00000 | − | 1.45309i | 0.0700140 | − | 0.0508682i | ||||
\(817\) | 3.23607 | + | 9.95959i | 0.113216 | + | 0.348442i | ||||
\(818\) | −3.73607 | + | 11.4984i | −0.130629 | + | 0.402033i | ||||
\(819\) | 12.0902 | + | 8.78402i | 0.422465 | + | 0.306939i | ||||
\(820\) | −7.47214 | − | 5.42882i | −0.260938 | − | 0.189583i | ||||
\(821\) | −6.51722 | + | 20.0579i | −0.227453 | + | 0.700027i | 0.770581 | + | 0.637342i | \(0.219966\pi\) |
−0.998033 | + | 0.0626847i | \(0.980034\pi\) | |||||||
\(822\) | −7.14590 | − | 21.9928i | −0.249242 | − | 0.767087i | ||||
\(823\) | 2.60081 | − | 1.88960i | 0.0906586 | − | 0.0658674i | −0.541533 | − | 0.840680i | \(-0.682156\pi\) |
0.632191 | + | 0.774812i | \(0.282156\pi\) | |||||||
\(824\) | −12.0344 | −0.419240 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.7984 | −0.619285 | ||||||||
\(827\) | 8.64590 | − | 6.28161i | 0.300647 | − | 0.218433i | −0.427226 | − | 0.904145i | \(-0.640509\pi\) |
0.727873 | + | 0.685712i | \(0.240509\pi\) | |||||||
\(828\) | −1.00000 | − | 3.07768i | −0.0347524 | − | 0.106957i | ||||
\(829\) | 2.25735 | − | 6.94742i | 0.0784012 | − | 0.241294i | −0.904173 | − | 0.427167i | \(-0.859511\pi\) |
0.982574 | + | 0.185874i | \(0.0595115\pi\) | |||||||
\(830\) | 1.55573 | + | 1.13030i | 0.0540001 | + | 0.0392334i | ||||
\(831\) | −9.00000 | − | 6.53888i | −0.312207 | − | 0.226831i | ||||
\(832\) | 1.00000 | − | 3.07768i | 0.0346688 | − | 0.106699i | ||||
\(833\) | 10.9443 | + | 33.6830i | 0.379197 | + | 1.16705i | ||||
\(834\) | 10.7082 | − | 7.77997i | 0.370795 | − | 0.269398i | ||||
\(835\) | −20.6525 | −0.714708 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.61803 | −0.297883 | ||||||||
\(838\) | −14.5451 | + | 10.5676i | −0.502452 | + | 0.365052i | ||||
\(839\) | −0.965558 | − | 2.97168i | −0.0333348 | − | 0.102594i | 0.933005 | − | 0.359864i | \(-0.117177\pi\) |
−0.966339 | + | 0.257270i | \(0.917177\pi\) | |||||||
\(840\) | −4.07295 | + | 12.5352i | −0.140530 | + | 0.432507i | ||||
\(841\) | 23.3435 | + | 16.9600i | 0.804947 | + | 0.584828i | ||||
\(842\) | 28.4164 | + | 20.6457i | 0.979294 | + | 0.711499i | ||||
\(843\) | 7.14590 | − | 21.9928i | 0.246118 | − | 0.757473i | ||||
\(844\) | 1.43769 | + | 4.42477i | 0.0494875 | + | 0.152307i | ||||
\(845\) | 5.83688 | − | 4.24074i | 0.200795 | − | 0.145886i | ||||
\(846\) | −2.47214 | −0.0849938 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.85410 | −0.132350 | ||||||||
\(849\) | 19.3262 | − | 14.0413i | 0.663275 | − | 0.481897i | ||||
\(850\) | −2.40325 | − | 7.39645i | −0.0824309 | − | 0.253696i | ||||
\(851\) | −1.52786 | + | 4.70228i | −0.0523745 | + | 0.161192i | ||||
\(852\) | 10.0902 | + | 7.33094i | 0.345684 | + | 0.251154i | ||||
\(853\) | 12.1803 | + | 8.84953i | 0.417047 | + | 0.303002i | 0.776449 | − | 0.630181i | \(-0.217019\pi\) |
−0.359402 | + | 0.933183i | \(0.617019\pi\) | |||||||
\(854\) | 9.65248 | − | 29.7073i | 0.330301 | − | 1.01656i | ||||
\(855\) | 2.85410 | + | 8.78402i | 0.0976082 | + | 0.300407i | ||||
\(856\) | −4.35410 | + | 3.16344i | −0.148820 | + | 0.108124i | ||||
\(857\) | −8.76393 | −0.299370 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.40325 | 0.150237 | 0.0751185 | − | 0.997175i | \(-0.476066\pi\) | ||||
0.0751185 | + | 0.997175i | \(0.476066\pi\) | |||||||
\(860\) | −7.47214 | + | 5.42882i | −0.254798 | + | 0.185121i | ||||
\(861\) | 4.61803 | + | 14.2128i | 0.157382 | + | 0.484373i | ||||
\(862\) | −2.23607 | + | 6.88191i | −0.0761608 | + | 0.234399i | ||||
\(863\) | −2.23607 | − | 1.62460i | −0.0761166 | − | 0.0553020i | 0.549076 | − | 0.835772i | \(-0.314980\pi\) |
−0.625193 | + | 0.780470i | \(0.714980\pi\) | |||||||
\(864\) | −0.809017 | − | 0.587785i | −0.0275233 | − | 0.0199969i | ||||
\(865\) | 3.65654 | − | 11.2537i | 0.124326 | − | 0.382636i | ||||
\(866\) | −3.80902 | − | 11.7229i | −0.129436 | − | 0.398362i | ||||
\(867\) | −8.80902 | + | 6.40013i | −0.299170 | + | 0.217360i | ||||
\(868\) | −39.7984 | −1.35084 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.09017 | 0.0369602 | ||||||||
\(871\) | −10.4721 | + | 7.60845i | −0.354835 | + | 0.257803i | ||||
\(872\) | 5.38197 | + | 16.5640i | 0.182256 | + | 0.560927i | ||||
\(873\) | 3.50000 | − | 10.7719i | 0.118457 | − | 0.364573i | ||||
\(874\) | −8.47214 | − | 6.15537i | −0.286574 | − | 0.208208i | ||||
\(875\) | −19.7705 | − | 14.3641i | −0.668365 | − | 0.485596i | ||||
\(876\) | −3.50000 | + | 10.7719i | −0.118254 | + | 0.363949i | ||||
\(877\) | 9.38197 | + | 28.8747i | 0.316806 | + | 0.975030i | 0.975004 | + | 0.222185i | \(0.0713190\pi\) |
−0.658198 | + | 0.752845i | \(0.728681\pi\) | |||||||
\(878\) | −12.9721 | + | 9.42481i | −0.437788 | + | 0.318072i | ||||
\(879\) | 22.9787 | 0.775053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.2918 | −0.414121 | −0.207061 | − | 0.978328i | \(-0.566390\pi\) | ||||
−0.207061 | + | 0.978328i | \(0.566390\pi\) | |||||||
\(882\) | 11.5902 | − | 8.42075i | 0.390261 | − | 0.283541i | ||||
\(883\) | 8.59675 | + | 26.4581i | 0.289304 | + | 0.890385i | 0.985076 | + | 0.172122i | \(0.0550624\pi\) |
−0.695772 | + | 0.718263i | \(0.744938\pi\) | |||||||
\(884\) | 2.47214 | − | 7.60845i | 0.0831469 | − | 0.255900i | ||||
\(885\) | −8.89919 | − | 6.46564i | −0.299143 | − | 0.217340i | ||||
\(886\) | −1.35410 | − | 0.983813i | −0.0454919 | − | 0.0330518i | ||||
\(887\) | 8.81966 | − | 27.1441i | 0.296135 | − | 0.911410i | −0.686703 | − | 0.726938i | \(-0.740943\pi\) |
0.982838 | − | 0.184472i | \(-0.0590575\pi\) | |||||||
\(888\) | 0.472136 | + | 1.45309i | 0.0158438 | + | 0.0487623i | ||||
\(889\) | −44.8328 | + | 32.5729i | −1.50364 | + | 1.09246i | ||||
\(890\) | 33.4164 | 1.12012 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.90983 | −0.0639458 | ||||||||
\(893\) | −6.47214 | + | 4.70228i | −0.216582 | + | 0.157356i | ||||
\(894\) | −0.427051 | − | 1.31433i | −0.0142827 | − | 0.0439577i | ||||
\(895\) | −5.62868 | + | 17.3233i | −0.188146 | + | 0.579054i | ||||
\(896\) | −3.73607 | − | 2.71441i | −0.124813 | − | 0.0906821i | ||||
\(897\) | −8.47214 | − | 6.15537i | −0.282876 | − | 0.205522i | ||||
\(898\) | −11.0902 | + | 34.1320i | −0.370084 | + | 1.13900i | ||||
\(899\) | 1.01722 | + | 3.13068i | 0.0339262 | + | 0.104414i | ||||
\(900\) | −2.54508 | + | 1.84911i | −0.0848362 | + | 0.0616371i | ||||
\(901\) | −9.52786 | −0.317419 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.9443 | 0.497314 | ||||||||
\(904\) | −10.0902 | + | 7.33094i | −0.335594 | + | 0.243823i | ||||
\(905\) | −14.5279 | − | 44.7122i | −0.482923 | − | 1.48628i | ||||
\(906\) | −2.88197 | + | 8.86978i | −0.0957469 | + | 0.294679i | ||||
\(907\) | 6.61803 | + | 4.80828i | 0.219748 | + | 0.159656i | 0.692213 | − | 0.721693i | \(-0.256636\pi\) |
−0.472465 | + | 0.881349i | \(0.656636\pi\) | |||||||
\(908\) | −5.78115 | − | 4.20025i | −0.191854 | − | 0.139390i | ||||
\(909\) | 3.82624 | − | 11.7759i | 0.126908 | − | 0.390584i | ||||
\(910\) | 13.1803 | + | 40.5649i | 0.436924 | + | 1.34471i | ||||
\(911\) | −35.3607 | + | 25.6910i | −1.17155 | + | 0.851182i | −0.991194 | − | 0.132419i | \(-0.957726\pi\) |
−0.180358 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(912\) | −3.23607 | −0.107157 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −21.9787 | −0.726991 | ||||||||
\(915\) | 15.6180 | − | 11.3472i | 0.516316 | − | 0.375126i | ||||
\(916\) | 7.09017 | + | 21.8213i | 0.234266 | + | 0.720996i | ||||
\(917\) | −21.7918 | + | 67.0683i | −0.719629 | + | 2.21479i | ||||
\(918\) | −2.00000 | − | 1.45309i | −0.0660098 | − | 0.0479590i | ||||
\(919\) | 40.6697 | + | 29.5483i | 1.34157 | + | 0.974707i | 0.999385 | + | 0.0350746i | \(0.0111669\pi\) |
0.342185 | + | 0.939633i | \(0.388833\pi\) | |||||||
\(920\) | 2.85410 | − | 8.78402i | 0.0940970 | − | 0.289601i | ||||
\(921\) | −5.14590 | − | 15.8374i | −0.169563 | − | 0.521862i | ||||
\(922\) | −33.0344 | + | 24.0009i | −1.08793 | + | 0.790428i | ||||
\(923\) | 40.3607 | 1.32849 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.80650 | 0.158037 | ||||||||
\(926\) | 15.4443 | − | 11.2209i | 0.507530 | − | 0.368742i | ||||
\(927\) | 3.71885 | + | 11.4454i | 0.122143 | + | 0.375917i | ||||
\(928\) | −0.118034 | + | 0.363271i | −0.00387466 | + | 0.0119250i | ||||
\(929\) | 18.7082 | + | 13.5923i | 0.613796 | + | 0.445949i | 0.850749 | − | 0.525572i | \(-0.176149\pi\) |
−0.236953 | + | 0.971521i | \(0.576149\pi\) | |||||||
\(930\) | −19.8992 | − | 14.4576i | −0.652520 | − | 0.474084i | ||||
\(931\) | 14.3262 | − | 44.0916i | 0.469523 | − | 1.44504i | ||||
\(932\) | 2.76393 | + | 8.50651i | 0.0905356 | + | 0.278640i | ||||
\(933\) | −19.3262 | + | 14.0413i | −0.632713 | + | 0.459693i | ||||
\(934\) | −19.5623 | −0.640098 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.23607 | −0.105774 | ||||||||
\(937\) | 22.2082 | − | 16.1352i | 0.725510 | − | 0.527114i | −0.162630 | − | 0.986687i | \(-0.551998\pi\) |
0.888140 | + | 0.459573i | \(0.151998\pi\) | |||||||
\(938\) | 5.70820 | + | 17.5680i | 0.186379 | + | 0.573617i | ||||
\(939\) | −4.68034 | + | 14.4046i | −0.152737 | + | 0.470077i | ||||
\(940\) | −5.70820 | − | 4.14725i | −0.186181 | − | 0.135268i | ||||
\(941\) | −7.14590 | − | 5.19180i | −0.232950 | − | 0.169248i | 0.465187 | − | 0.885213i | \(-0.345987\pi\) |
−0.698136 | + | 0.715965i | \(0.745987\pi\) | |||||||
\(942\) | 1.38197 | − | 4.25325i | 0.0450269 | − | 0.138579i | ||||
\(943\) | −3.23607 | − | 9.95959i | −0.105381 | − | 0.324329i | ||||
\(944\) | 3.11803 | − | 2.26538i | 0.101483 | − | 0.0737320i | ||||
\(945\) | 13.1803 | 0.428756 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.32624 | 0.0755926 | 0.0377963 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377963 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(948\) | 7.54508 | − | 5.48183i | 0.245053 | − | 0.178041i | ||||
\(949\) | 11.3262 | + | 34.8586i | 0.367665 | + | 1.13156i | ||||
\(950\) | −3.14590 | + | 9.68208i | −0.102066 | + | 0.314128i | ||||
\(951\) | −16.0902 | − | 11.6902i | −0.521760 | − | 0.379080i | ||||
\(952\) | −9.23607 | − | 6.71040i | −0.299343 | − | 0.217485i | ||||
\(953\) | −15.0557 | + | 46.3368i | −0.487703 | + | 1.50100i | 0.340325 | + | 0.940308i | \(0.389463\pi\) |
−0.828028 | + | 0.560687i | \(0.810537\pi\) | |||||||
\(954\) | 1.19098 | + | 3.66547i | 0.0385595 | + | 0.118674i | ||||
\(955\) | −51.8885 | + | 37.6992i | −1.67907 | + | 1.21992i | ||||
\(956\) | 16.4721 | 0.532747 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.23607 | −0.233787 | ||||||||
\(959\) | −86.3951 | + | 62.7697i | −2.78984 | + | 2.02694i | ||||
\(960\) | −0.881966 | − | 2.71441i | −0.0284653 | − | 0.0876073i | ||||
\(961\) | 13.3713 | − | 41.1527i | 0.431333 | − | 1.32751i | ||||
\(962\) | 4.00000 | + | 2.90617i | 0.128965 | + | 0.0936987i | ||||
\(963\) | 4.35410 | + | 3.16344i | 0.140309 | + | 0.101940i | ||||
\(964\) | 0.753289 | − | 2.31838i | 0.0242618 | − | 0.0746701i | ||||
\(965\) | −0.287731 | − | 0.885544i | −0.00926238 | − | 0.0285067i | ||||
\(966\) | −12.0902 | + | 8.78402i | −0.388995 | + | 0.282621i | ||||
\(967\) | −13.6869 | −0.440142 | −0.220071 | − | 0.975484i | \(-0.570629\pi\) | ||||
−0.220071 | + | 0.975484i | \(0.570629\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 26.1525 | − | 19.0009i | 0.839705 | − | 0.610082i | ||||
\(971\) | −2.87539 | − | 8.84953i | −0.0922756 | − | 0.283995i | 0.894258 | − | 0.447551i | \(-0.147704\pi\) |
−0.986534 | + | 0.163556i | \(0.947704\pi\) | |||||||
\(972\) | −0.309017 | + | 0.951057i | −0.00991172 | + | 0.0305052i | ||||
\(973\) | −49.4508 | − | 35.9281i | −1.58532 | − | 1.15180i | ||||
\(974\) | 20.2082 | + | 14.6821i | 0.647513 | + | 0.470445i | ||||
\(975\) | −3.14590 | + | 9.68208i | −0.100749 | + | 0.310075i | ||||
\(976\) | 2.09017 | + | 6.43288i | 0.0669047 | + | 0.205912i | ||||
\(977\) | 29.7426 | − | 21.6093i | 0.951552 | − | 0.691343i | 0.000378218 | − | 1.00000i | \(-0.499880\pi\) |
0.951173 | + | 0.308657i | \(0.0998796\pi\) | |||||||
\(978\) | −13.4164 | −0.429009 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 40.8885 | 1.30614 | ||||||||
\(981\) | 14.0902 | − | 10.2371i | 0.449865 | − | 0.326846i | ||||
\(982\) | 13.0557 | + | 40.1814i | 0.416625 | + | 1.28224i | ||||
\(983\) | −2.81966 | + | 8.67802i | −0.0899332 | + | 0.276786i | −0.985900 | − | 0.167335i | \(-0.946484\pi\) |
0.895967 | + | 0.444121i | \(0.146484\pi\) | |||||||
\(984\) | −2.61803 | − | 1.90211i | −0.0834599 | − | 0.0606371i | ||||
\(985\) | 14.0623 | + | 10.2169i | 0.448062 | + | 0.325536i | ||||
\(986\) | −0.291796 | + | 0.898056i | −0.00929268 | + | 0.0285999i | ||||
\(987\) | 3.52786 | + | 10.8576i | 0.112293 | + | 0.345603i | ||||
\(988\) | −8.47214 | + | 6.15537i | −0.269535 | + | 0.195828i | ||||
\(989\) | −10.4721 | −0.332995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.6869 | −1.45129 | −0.725646 | − | 0.688068i | \(-0.758459\pi\) | ||||
−0.725646 | + | 0.688068i | \(0.758459\pi\) | |||||||
\(992\) | 6.97214 | − | 5.06555i | 0.221366 | − | 0.160831i | ||||
\(993\) | −2.76393 | − | 8.50651i | −0.0877107 | − | 0.269946i | ||||
\(994\) | 17.7984 | − | 54.7778i | 0.564530 | − | 1.73745i | ||||
\(995\) | −30.3541 | − | 22.0535i | −0.962290 | − | 0.699144i | ||||
\(996\) | 0.545085 | + | 0.396027i | 0.0172717 | + | 0.0125486i | ||||
\(997\) | −17.9098 | + | 55.1208i | −0.567210 | + | 1.74569i | 0.0940821 | + | 0.995564i | \(0.470008\pi\) |
−0.661292 | + | 0.750128i | \(0.729992\pi\) | |||||||
\(998\) | 2.29180 | + | 7.05342i | 0.0725455 | + | 0.223272i | ||||
\(999\) | 1.23607 | − | 0.898056i | 0.0391075 | − | 0.0284132i |
(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 | 726.2.e.n.487.1 | 4 | ||
11.2 | odd | 10 | 726.2.a.l.1.2 | 2 | |||
11.3 | even | 5 | 726.2.e.r.511.1 | 4 | |||
11.4 | even | 5 | inner | 726.2.e.n.565.1 | 4 | ||
11.5 | even | 5 | 726.2.e.r.493.1 | 4 | |||
11.6 | odd | 10 | 66.2.e.a.31.1 | ✓ | 4 | ||
11.7 | odd | 10 | 726.2.e.f.565.1 | 4 | |||
11.8 | odd | 10 | 66.2.e.a.49.1 | yes | 4 | ||
11.9 | even | 5 | 726.2.a.j.1.2 | 2 | |||
11.10 | odd | 2 | 726.2.e.f.487.1 | 4 | |||
33.2 | even | 10 | 2178.2.a.t.1.1 | 2 | |||
33.8 | even | 10 | 198.2.f.c.181.1 | 4 | |||
33.17 | even | 10 | 198.2.f.c.163.1 | 4 | |||
33.20 | odd | 10 | 2178.2.a.bb.1.1 | 2 | |||
44.19 | even | 10 | 528.2.y.d.49.1 | 4 | |||
44.31 | odd | 10 | 5808.2.a.cg.1.2 | 2 | |||
44.35 | even | 10 | 5808.2.a.cb.1.2 | 2 | |||
44.39 | even | 10 | 528.2.y.d.97.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
66.2.e.a.31.1 | ✓ | 4 | 11.6 | odd | 10 | ||
66.2.e.a.49.1 | yes | 4 | 11.8 | odd | 10 | ||
198.2.f.c.163.1 | 4 | 33.17 | even | 10 | |||
198.2.f.c.181.1 | 4 | 33.8 | even | 10 | |||
528.2.y.d.49.1 | 4 | 44.19 | even | 10 | |||
528.2.y.d.97.1 | 4 | 44.39 | even | 10 | |||
726.2.a.j.1.2 | 2 | 11.9 | even | 5 | |||
726.2.a.l.1.2 | 2 | 11.2 | odd | 10 | |||
726.2.e.f.487.1 | 4 | 11.10 | odd | 2 | |||
726.2.e.f.565.1 | 4 | 11.7 | odd | 10 | |||
726.2.e.n.487.1 | 4 | 1.1 | even | 1 | trivial | ||
726.2.e.n.565.1 | 4 | 11.4 | even | 5 | inner | ||
726.2.e.r.493.1 | 4 | 11.5 | even | 5 | |||
726.2.e.r.511.1 | 4 | 11.3 | even | 5 | |||
2178.2.a.t.1.1 | 2 | 33.2 | even | 10 | |||
2178.2.a.bb.1.1 | 2 | 33.20 | odd | 10 | |||
5808.2.a.cb.1.2 | 2 | 44.35 | even | 10 | |||
5808.2.a.cg.1.2 | 2 | 44.31 | odd | 10 |