Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(421,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.421");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.o (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: | \(6.58765816676\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.421 |
Dual form | 825.2.o.b.631.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.190983 | + | 0.587785i | 0.135045 | + | 0.415627i | 0.995597 | − | 0.0937362i | \(-0.0298810\pi\) |
−0.860552 | + | 0.509363i | \(0.829881\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 1.30902 | − | 0.951057i | 0.654508 | − | 0.475528i | ||||
\(5\) | 1.80902 | − | 1.31433i | 0.809017 | − | 0.587785i | ||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | −0.927051 | + | 2.85317i | −0.350392 | + | 1.07840i | 0.608241 | + | 0.793752i | \(0.291875\pi\) |
−0.958633 | + | 0.284644i | \(0.908125\pi\) | |||||||
\(8\) | 1.80902 | + | 1.31433i | 0.639584 | + | 0.464685i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 1.11803 | + | 0.812299i | 0.353553 | + | 0.256872i | ||||
\(11\) | 0.309017 | + | 3.30220i | 0.0931721 | + | 0.995650i | ||||
\(12\) | 0.500000 | + | 1.53884i | 0.144338 | + | 0.444225i | ||||
\(13\) | 1.00000 | + | 0.726543i | 0.277350 | + | 0.201507i | 0.717761 | − | 0.696290i | \(-0.245167\pi\) |
−0.440411 | + | 0.897796i | \(0.645167\pi\) | |||||||
\(14\) | −1.85410 | −0.495530 | ||||||||
\(15\) | 0.690983 | + | 2.12663i | 0.178411 | + | 0.549093i | ||||
\(16\) | 0.572949 | − | 1.76336i | 0.143237 | − | 0.440839i | ||||
\(17\) | −5.23607 | −1.26993 | −0.634967 | − | 0.772540i | \(-0.718986\pi\) | ||||
−0.634967 | + | 0.772540i | \(0.718986\pi\) | |||||||
\(18\) | 0.190983 | − | 0.587785i | 0.0450151 | − | 0.138542i | ||||
\(19\) | 2.92705 | + | 2.12663i | 0.671512 | + | 0.487882i | 0.870531 | − | 0.492114i | \(-0.163776\pi\) |
−0.199019 | + | 0.979996i | \(0.563776\pi\) | |||||||
\(20\) | 1.11803 | − | 3.44095i | 0.250000 | − | 0.769421i | ||||
\(21\) | −2.42705 | − | 1.76336i | −0.529626 | − | 0.384796i | ||||
\(22\) | −1.88197 | + | 0.812299i | −0.401237 | + | 0.173183i | ||||
\(23\) | −1.50000 | + | 4.61653i | −0.312772 | + | 0.962612i | 0.663890 | + | 0.747830i | \(0.268904\pi\) |
−0.976662 | + | 0.214782i | \(0.931096\pi\) | |||||||
\(24\) | −1.80902 | + | 1.31433i | −0.369264 | + | 0.268286i | ||||
\(25\) | 1.54508 | − | 4.75528i | 0.309017 | − | 0.951057i | ||||
\(26\) | −0.236068 | + | 0.726543i | −0.0462967 | + | 0.142487i | ||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 1.50000 | + | 4.61653i | 0.283473 | + | 0.872441i | ||||
\(29\) | 8.35410 | − | 6.06961i | 1.55132 | − | 1.12710i | 0.608614 | − | 0.793466i | \(-0.291726\pi\) |
0.942703 | − | 0.333632i | \(-0.108274\pi\) | |||||||
\(30\) | −1.11803 | + | 0.812299i | −0.204124 | + | 0.148305i | ||||
\(31\) | −1.78115 | + | 5.48183i | −0.319905 | + | 0.984565i | 0.653784 | + | 0.756681i | \(0.273181\pi\) |
−0.973688 | + | 0.227884i | \(0.926819\pi\) | |||||||
\(32\) | 5.61803 | 0.993137 | ||||||||
\(33\) | −3.23607 | − | 0.726543i | −0.563327 | − | 0.126475i | ||||
\(34\) | −1.00000 | − | 3.07768i | −0.171499 | − | 0.527818i | ||||
\(35\) | 2.07295 | + | 6.37988i | 0.350392 | + | 1.07840i | ||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | −2.14590 | −0.352783 | −0.176392 | − | 0.984320i | \(-0.556443\pi\) | ||||
−0.176392 | + | 0.984320i | \(0.556443\pi\) | |||||||
\(38\) | −0.690983 | + | 2.12663i | −0.112092 | + | 0.344984i | ||||
\(39\) | −1.00000 | + | 0.726543i | −0.160128 | + | 0.116340i | ||||
\(40\) | 5.00000 | 0.790569 | ||||||||
\(41\) | 8.97214 | − | 6.51864i | 1.40121 | − | 1.01804i | 0.406684 | − | 0.913569i | \(-0.366685\pi\) |
0.994528 | − | 0.104472i | \(-0.0333151\pi\) | |||||||
\(42\) | 0.572949 | − | 1.76336i | 0.0884080 | − | 0.272092i | ||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 3.54508 | + | 4.02874i | 0.534442 | + | 0.607355i | ||||
\(45\) | −2.23607 | −0.333333 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | −0.336881 | + | 1.03681i | −0.0491391 | + | 0.151235i | −0.972615 | − | 0.232421i | \(-0.925335\pi\) |
0.923476 | + | 0.383656i | \(0.125335\pi\) | |||||||
\(48\) | 1.50000 | + | 1.08981i | 0.216506 | + | 0.157301i | ||||
\(49\) | −1.61803 | − | 1.17557i | −0.231148 | − | 0.167939i | ||||
\(50\) | 3.09017 | 0.437016 | ||||||||
\(51\) | 1.61803 | − | 4.97980i | 0.226570 | − | 0.697311i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −11.2361 | −1.54339 | −0.771696 | − | 0.635991i | \(-0.780591\pi\) | ||||
−0.771696 | + | 0.635991i | \(0.780591\pi\) | |||||||
\(54\) | 0.500000 | + | 0.363271i | 0.0680414 | + | 0.0494350i | ||||
\(55\) | 4.89919 | + | 5.56758i | 0.660606 | + | 0.750733i | ||||
\(56\) | −5.42705 | + | 3.94298i | −0.725220 | + | 0.526903i | ||||
\(57\) | −2.92705 | + | 2.12663i | −0.387697 | + | 0.281679i | ||||
\(58\) | 5.16312 | + | 3.75123i | 0.677951 | + | 0.492560i | ||||
\(59\) | −14.4721 | −1.88411 | −0.942056 | − | 0.335456i | \(-0.891110\pi\) | ||||
−0.942056 | + | 0.335456i | \(0.891110\pi\) | |||||||
\(60\) | 2.92705 | + | 2.12663i | 0.377881 | + | 0.274546i | ||||
\(61\) | 3.80902 | − | 2.76741i | 0.487695 | − | 0.354331i | −0.316602 | − | 0.948558i | \(-0.602542\pi\) |
0.804297 | + | 0.594227i | \(0.202542\pi\) | |||||||
\(62\) | −3.56231 | −0.452413 | ||||||||
\(63\) | 2.42705 | − | 1.76336i | 0.305780 | − | 0.222162i | ||||
\(64\) | −0.0729490 | − | 0.224514i | −0.00911863 | − | 0.0280642i | ||||
\(65\) | 2.76393 | 0.342824 | ||||||||
\(66\) | −0.190983 | − | 2.04087i | −0.0235084 | − | 0.251214i | ||||
\(67\) | 2.42705 | − | 1.76336i | 0.296511 | − | 0.215428i | −0.429576 | − | 0.903031i | \(-0.641337\pi\) |
0.726087 | + | 0.687603i | \(0.241337\pi\) | |||||||
\(68\) | −6.85410 | + | 4.97980i | −0.831182 | + | 0.603889i | ||||
\(69\) | −3.92705 | − | 2.85317i | −0.472761 | − | 0.343481i | ||||
\(70\) | −3.35410 | + | 2.43690i | −0.400892 | + | 0.291265i | ||||
\(71\) | −3.59017 | − | 11.0494i | −0.426075 | − | 1.31132i | −0.901961 | − | 0.431817i | \(-0.857873\pi\) |
0.475887 | − | 0.879507i | \(-0.342127\pi\) | |||||||
\(72\) | −0.690983 | − | 2.12663i | −0.0814331 | − | 0.250625i | ||||
\(73\) | 9.35410 | + | 6.79615i | 1.09481 | + | 0.795430i | 0.980206 | − | 0.197981i | \(-0.0634385\pi\) |
0.114609 | + | 0.993411i | \(0.463438\pi\) | |||||||
\(74\) | −0.409830 | − | 1.26133i | −0.0476418 | − | 0.146626i | ||||
\(75\) | 4.04508 | + | 2.93893i | 0.467086 | + | 0.339358i | ||||
\(76\) | 5.85410 | 0.671512 | ||||||||
\(77\) | −9.70820 | − | 2.17963i | −1.10635 | − | 0.248392i | ||||
\(78\) | −0.618034 | − | 0.449028i | −0.0699786 | − | 0.0508424i | ||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | −1.28115 | − | 3.94298i | −0.143237 | − | 0.440839i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 5.54508 | + | 4.02874i | 0.612352 | + | 0.444900i | ||||
\(83\) | −7.61803 | −0.836188 | −0.418094 | − | 0.908404i | \(-0.637302\pi\) | ||||
−0.418094 | + | 0.908404i | \(0.637302\pi\) | |||||||
\(84\) | −4.85410 | −0.529626 | ||||||||
\(85\) | −9.47214 | + | 6.88191i | −1.02740 | + | 0.746448i | ||||
\(86\) | 1.14590 | + | 3.52671i | 0.123565 | + | 0.380295i | ||||
\(87\) | 3.19098 | + | 9.82084i | 0.342109 | + | 1.05290i | ||||
\(88\) | −3.78115 | + | 6.37988i | −0.403072 | + | 0.680098i | ||||
\(89\) | 0.690983 | − | 2.12663i | 0.0732441 | − | 0.225422i | −0.907732 | − | 0.419550i | \(-0.862188\pi\) |
0.980976 | + | 0.194128i | \(0.0621878\pi\) | |||||||
\(90\) | −0.427051 | − | 1.31433i | −0.0450151 | − | 0.138542i | ||||
\(91\) | −3.00000 | + | 2.17963i | −0.314485 | + | 0.228487i | ||||
\(92\) | 2.42705 | + | 7.46969i | 0.253038 | + | 0.778770i | ||||
\(93\) | −4.66312 | − | 3.38795i | −0.483543 | − | 0.351314i | ||||
\(94\) | −0.673762 | −0.0694933 | ||||||||
\(95\) | 8.09017 | 0.830034 | ||||||||
\(96\) | −1.73607 | + | 5.34307i | −0.177187 | + | 0.545325i | ||||
\(97\) | 11.4721 | 1.16482 | 0.582409 | − | 0.812896i | \(-0.302110\pi\) | ||||
0.582409 | + | 0.812896i | \(0.302110\pi\) | |||||||
\(98\) | 0.381966 | − | 1.17557i | 0.0385844 | − | 0.118751i | ||||
\(99\) | 1.69098 | − | 2.85317i | 0.169950 | − | 0.286754i | ||||
\(100\) | −2.50000 | − | 7.69421i | −0.250000 | − | 0.769421i | ||||
\(101\) | −9.28115 | + | 6.74315i | −0.923509 | + | 0.670969i | −0.944395 | − | 0.328813i | \(-0.893351\pi\) |
0.0208858 | + | 0.999782i | \(0.493351\pi\) | |||||||
\(102\) | 3.23607 | 0.320418 | ||||||||
\(103\) | 5.04508 | − | 3.66547i | 0.497107 | − | 0.361169i | −0.310804 | − | 0.950474i | \(-0.600598\pi\) |
0.807911 | + | 0.589305i | \(0.200598\pi\) | |||||||
\(104\) | 0.854102 | + | 2.62866i | 0.0837516 | + | 0.257761i | ||||
\(105\) | −6.70820 | −0.654654 | ||||||||
\(106\) | −2.14590 | − | 6.60440i | −0.208428 | − | 0.641476i | ||||
\(107\) | −2.40983 | − | 7.41669i | −0.232967 | − | 0.716999i | −0.997385 | − | 0.0722774i | \(-0.976973\pi\) |
0.764418 | − | 0.644722i | \(-0.223027\pi\) | |||||||
\(108\) | 0.500000 | − | 1.53884i | 0.0481125 | − | 0.148075i | ||||
\(109\) | −0.527864 | − | 1.62460i | −0.0505602 | − | 0.155608i | 0.922589 | − | 0.385785i | \(-0.126069\pi\) |
−0.973149 | + | 0.230177i | \(0.926069\pi\) | |||||||
\(110\) | −2.33688 | + | 3.94298i | −0.222813 | + | 0.375949i | ||||
\(111\) | 0.663119 | − | 2.04087i | 0.0629405 | − | 0.193711i | ||||
\(112\) | 4.50000 | + | 3.26944i | 0.425210 | + | 0.308933i | ||||
\(113\) | −9.85410 | + | 7.15942i | −0.926996 | + | 0.673502i | −0.945255 | − | 0.326331i | \(-0.894187\pi\) |
0.0182595 | + | 0.999833i | \(0.494187\pi\) | |||||||
\(114\) | −1.80902 | − | 1.31433i | −0.169430 | − | 0.123098i | ||||
\(115\) | 3.35410 | + | 10.3229i | 0.312772 | + | 0.962612i | ||||
\(116\) | 5.16312 | − | 15.8904i | 0.479384 | − | 1.47539i | ||||
\(117\) | −0.381966 | − | 1.17557i | −0.0353128 | − | 0.108682i | ||||
\(118\) | −2.76393 | − | 8.50651i | −0.254441 | − | 0.783088i | ||||
\(119\) | 4.85410 | − | 14.9394i | 0.444975 | − | 1.36949i | ||||
\(120\) | −1.54508 | + | 4.75528i | −0.141046 | + | 0.434096i | ||||
\(121\) | −10.8090 | + | 2.04087i | −0.982638 | + | 0.185534i | ||||
\(122\) | 2.35410 | + | 1.71036i | 0.213130 | + | 0.154848i | ||||
\(123\) | 3.42705 | + | 10.5474i | 0.309007 | + | 0.951025i | ||||
\(124\) | 2.88197 | + | 8.86978i | 0.258808 | + | 0.796530i | ||||
\(125\) | −3.45492 | − | 10.6331i | −0.309017 | − | 0.951057i | ||||
\(126\) | 1.50000 | + | 1.08981i | 0.133631 | + | 0.0970883i | ||||
\(127\) | 13.2812 | − | 9.64932i | 1.17851 | − | 0.856239i | 0.186509 | − | 0.982453i | \(-0.440283\pi\) |
0.992003 | + | 0.126214i | \(0.0402827\pi\) | |||||||
\(128\) | 9.20820 | − | 6.69015i | 0.813898 | − | 0.591331i | ||||
\(129\) | −1.85410 | + | 5.70634i | −0.163245 | + | 0.502415i | ||||
\(130\) | 0.527864 | + | 1.62460i | 0.0462967 | + | 0.142487i | ||||
\(131\) | −12.8992 | + | 9.37181i | −1.12701 | + | 0.818819i | −0.985256 | − | 0.171084i | \(-0.945273\pi\) |
−0.141751 | + | 0.989902i | \(0.545273\pi\) | |||||||
\(132\) | −4.92705 | + | 2.12663i | −0.428845 | + | 0.185099i | ||||
\(133\) | −8.78115 | + | 6.37988i | −0.761423 | + | 0.553206i | ||||
\(134\) | 1.50000 | + | 1.08981i | 0.129580 | + | 0.0941456i | ||||
\(135\) | 0.690983 | − | 2.12663i | 0.0594703 | − | 0.183031i | ||||
\(136\) | −9.47214 | − | 6.88191i | −0.812229 | − | 0.590119i | ||||
\(137\) | 4.33688 | − | 13.3475i | 0.370525 | − | 1.14036i | −0.575924 | − | 0.817503i | \(-0.695358\pi\) |
0.946449 | − | 0.322855i | \(-0.104642\pi\) | |||||||
\(138\) | 0.927051 | − | 2.85317i | 0.0789158 | − | 0.242878i | ||||
\(139\) | −3.19098 | − | 2.31838i | −0.270656 | − | 0.196643i | 0.444176 | − | 0.895940i | \(-0.353497\pi\) |
−0.714831 | + | 0.699297i | \(0.753497\pi\) | |||||||
\(140\) | 8.78115 | + | 6.37988i | 0.742143 | + | 0.539198i | ||||
\(141\) | −0.881966 | − | 0.640786i | −0.0742749 | − | 0.0539639i | ||||
\(142\) | 5.80902 | − | 4.22050i | 0.487482 | − | 0.354176i | ||||
\(143\) | −2.09017 | + | 3.52671i | −0.174789 | + | 0.294918i | ||||
\(144\) | −1.50000 | + | 1.08981i | −0.125000 | + | 0.0908178i | ||||
\(145\) | 7.13525 | − | 21.9601i | 0.592551 | − | 1.82368i | ||||
\(146\) | −2.20820 | + | 6.79615i | −0.182752 | + | 0.562454i | ||||
\(147\) | 1.61803 | − | 1.17557i | 0.133453 | − | 0.0969594i | ||||
\(148\) | −2.80902 | + | 2.04087i | −0.230900 | + | 0.167759i | ||||
\(149\) | 5.16312 | + | 3.75123i | 0.422979 | + | 0.307312i | 0.778835 | − | 0.627228i | \(-0.215811\pi\) |
−0.355856 | + | 0.934541i | \(0.615811\pi\) | |||||||
\(150\) | −0.954915 | + | 2.93893i | −0.0779685 | + | 0.239962i | ||||
\(151\) | 1.20820 | + | 3.71847i | 0.0983222 | + | 0.302605i | 0.988105 | − | 0.153779i | \(-0.0491444\pi\) |
−0.889783 | + | 0.456384i | \(0.849144\pi\) | |||||||
\(152\) | 2.50000 | + | 7.69421i | 0.202777 | + | 0.624083i | ||||
\(153\) | 4.23607 | + | 3.07768i | 0.342466 | + | 0.248816i | ||||
\(154\) | −0.572949 | − | 6.12261i | −0.0461695 | − | 0.493374i | ||||
\(155\) | 3.98278 | + | 12.2577i | 0.319905 | + | 0.984565i | ||||
\(156\) | −0.618034 | + | 1.90211i | −0.0494823 | + | 0.152291i | ||||
\(157\) | −1.71885 | − | 5.29007i | −0.137179 | − | 0.422193i | 0.858744 | − | 0.512405i | \(-0.171245\pi\) |
−0.995923 | + | 0.0902121i | \(0.971245\pi\) | |||||||
\(158\) | −0.954915 | − | 2.93893i | −0.0759690 | − | 0.233808i | ||||
\(159\) | 3.47214 | − | 10.6861i | 0.275358 | − | 0.847466i | ||||
\(160\) | 10.1631 | − | 7.38394i | 0.803465 | − | 0.583752i | ||||
\(161\) | −11.7812 | − | 8.55951i | −0.928485 | − | 0.674584i | ||||
\(162\) | −0.500000 | + | 0.363271i | −0.0392837 | + | 0.0285413i | ||||
\(163\) | −10.9721 | − | 7.97172i | −0.859404 | − | 0.624394i | 0.0683187 | − | 0.997664i | \(-0.478237\pi\) |
−0.927723 | + | 0.373270i | \(0.878237\pi\) | |||||||
\(164\) | 5.54508 | − | 17.0660i | 0.432998 | − | 1.33263i | ||||
\(165\) | −6.80902 | + | 2.93893i | −0.530081 | + | 0.228795i | ||||
\(166\) | −1.45492 | − | 4.47777i | −0.112923 | − | 0.347542i | ||||
\(167\) | 6.89919 | − | 21.2335i | 0.533875 | − | 1.64310i | −0.212192 | − | 0.977228i | \(-0.568060\pi\) |
0.746067 | − | 0.665871i | \(-0.231940\pi\) | |||||||
\(168\) | −2.07295 | − | 6.37988i | −0.159931 | − | 0.492219i | ||||
\(169\) | −3.54508 | − | 10.9106i | −0.272699 | − | 0.839281i | ||||
\(170\) | −5.85410 | − | 4.25325i | −0.448989 | − | 0.326210i | ||||
\(171\) | −1.11803 | − | 3.44095i | −0.0854982 | − | 0.263136i | ||||
\(172\) | 7.85410 | − | 5.70634i | 0.598870 | − | 0.435104i | ||||
\(173\) | 5.47214 | 0.416039 | 0.208019 | − | 0.978125i | \(-0.433298\pi\) | ||||
0.208019 | + | 0.978125i | \(0.433298\pi\) | |||||||
\(174\) | −5.16312 | + | 3.75123i | −0.391415 | + | 0.284380i | ||||
\(175\) | 12.1353 | + | 8.81678i | 0.917339 | + | 0.666486i | ||||
\(176\) | 6.00000 | + | 1.34708i | 0.452267 | + | 0.101540i | ||||
\(177\) | 4.47214 | − | 13.7638i | 0.336146 | − | 1.03455i | ||||
\(178\) | 1.38197 | 0.103583 | ||||||||
\(179\) | 6.80902 | − | 20.9560i | 0.508930 | − | 1.56632i | −0.285132 | − | 0.958488i | \(-0.592038\pi\) |
0.794062 | − | 0.607837i | \(-0.207962\pi\) | |||||||
\(180\) | −2.92705 | + | 2.12663i | −0.218169 | + | 0.158509i | ||||
\(181\) | 12.5279 | 0.931189 | 0.465594 | − | 0.884998i | \(-0.345841\pi\) | ||||
0.465594 | + | 0.884998i | \(0.345841\pi\) | |||||||
\(182\) | −1.85410 | − | 1.34708i | −0.137435 | − | 0.0998525i | ||||
\(183\) | 1.45492 | + | 4.47777i | 0.107550 | + | 0.331006i | ||||
\(184\) | −8.78115 | + | 6.37988i | −0.647355 | + | 0.470331i | ||||
\(185\) | −3.88197 | + | 2.82041i | −0.285408 | + | 0.207361i | ||||
\(186\) | 1.10081 | − | 3.38795i | 0.0807155 | − | 0.248417i | ||||
\(187\) | −1.61803 | − | 17.2905i | −0.118322 | − | 1.26441i | ||||
\(188\) | 0.545085 | + | 1.67760i | 0.0397544 | + | 0.122351i | ||||
\(189\) | 0.927051 | + | 2.85317i | 0.0674330 | + | 0.207538i | ||||
\(190\) | 1.54508 | + | 4.75528i | 0.112092 | + | 0.344984i | ||||
\(191\) | 0.618034 | 0.0447194 | 0.0223597 | − | 0.999750i | \(-0.492882\pi\) | ||||
0.0223597 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(192\) | 0.236068 | 0.0170367 | ||||||||
\(193\) | −7.61803 | − | 5.53483i | −0.548358 | − | 0.398405i | 0.278822 | − | 0.960343i | \(-0.410056\pi\) |
−0.827180 | + | 0.561937i | \(0.810056\pi\) | |||||||
\(194\) | 2.19098 | + | 6.74315i | 0.157303 | + | 0.484130i | ||||
\(195\) | −0.854102 | + | 2.62866i | −0.0611635 | + | 0.188242i | ||||
\(196\) | −3.23607 | −0.231148 | ||||||||
\(197\) | −7.89919 | − | 5.73910i | −0.562794 | − | 0.408894i | 0.269687 | − | 0.962948i | \(-0.413080\pi\) |
−0.832480 | + | 0.554055i | \(0.813080\pi\) | |||||||
\(198\) | 2.00000 | + | 0.449028i | 0.142134 | + | 0.0319110i | ||||
\(199\) | 14.7984 | 1.04903 | 0.524514 | − | 0.851402i | \(-0.324247\pi\) | ||||
0.524514 | + | 0.851402i | \(0.324247\pi\) | |||||||
\(200\) | 9.04508 | − | 6.57164i | 0.639584 | − | 0.464685i | ||||
\(201\) | 0.927051 | + | 2.85317i | 0.0653891 | + | 0.201247i | ||||
\(202\) | −5.73607 | − | 4.16750i | −0.403588 | − | 0.293224i | ||||
\(203\) | 9.57295 | + | 29.4625i | 0.671889 | + | 2.06786i | ||||
\(204\) | −2.61803 | − | 8.05748i | −0.183299 | − | 0.564136i | ||||
\(205\) | 7.66312 | − | 23.5847i | 0.535215 | − | 1.64722i | ||||
\(206\) | 3.11803 | + | 2.26538i | 0.217244 | + | 0.157837i | ||||
\(207\) | 3.92705 | − | 2.85317i | 0.272949 | − | 0.198309i | ||||
\(208\) | 1.85410 | − | 1.34708i | 0.128559 | − | 0.0934035i | ||||
\(209\) | −6.11803 | + | 10.3229i | −0.423193 | + | 0.714047i | ||||
\(210\) | −1.28115 | − | 3.94298i | −0.0884080 | − | 0.272092i | ||||
\(211\) | 7.69098 | + | 23.6704i | 0.529469 | + | 1.62954i | 0.755305 | + | 0.655373i | \(0.227489\pi\) |
−0.225836 | + | 0.974165i | \(0.572511\pi\) | |||||||
\(212\) | −14.7082 | + | 10.6861i | −1.01016 | + | 0.733927i | ||||
\(213\) | 11.6180 | 0.796055 | ||||||||
\(214\) | 3.89919 | − | 2.83293i | 0.266543 | − | 0.193655i | ||||
\(215\) | 10.8541 | − | 7.88597i | 0.740244 | − | 0.537818i | ||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −13.9894 | − | 10.1639i | −0.949659 | − | 0.689968i | ||||
\(218\) | 0.854102 | − | 0.620541i | 0.0578471 | − | 0.0420284i | ||||
\(219\) | −9.35410 | + | 6.79615i | −0.632092 | + | 0.459241i | ||||
\(220\) | 11.7082 | + | 2.62866i | 0.789367 | + | 0.177224i | ||||
\(221\) | −5.23607 | − | 3.80423i | −0.352216 | − | 0.255900i | ||||
\(222\) | 1.32624 | 0.0890113 | ||||||||
\(223\) | −22.4164 | −1.50111 | −0.750557 | − | 0.660806i | \(-0.770215\pi\) | ||||
−0.750557 | + | 0.660806i | \(0.770215\pi\) | |||||||
\(224\) | −5.20820 | + | 16.0292i | −0.347988 | + | 1.07100i | ||||
\(225\) | −4.04508 | + | 2.93893i | −0.269672 | + | 0.195928i | ||||
\(226\) | −6.09017 | − | 4.42477i | −0.405112 | − | 0.294331i | ||||
\(227\) | −10.6631 | − | 7.74721i | −0.707736 | − | 0.514200i | 0.174706 | − | 0.984621i | \(-0.444102\pi\) |
−0.882443 | + | 0.470420i | \(0.844102\pi\) | |||||||
\(228\) | −1.80902 | + | 5.56758i | −0.119805 | + | 0.368722i | ||||
\(229\) | −25.0000 | −1.65205 | −0.826023 | − | 0.563636i | \(-0.809402\pi\) | ||||
−0.826023 | + | 0.563636i | \(0.809402\pi\) | |||||||
\(230\) | −5.42705 | + | 3.94298i | −0.357849 | + | 0.259993i | ||||
\(231\) | 5.07295 | − | 8.55951i | 0.333776 | − | 0.563174i | ||||
\(232\) | 23.0902 | 1.51594 | ||||||||
\(233\) | −0.708204 | + | 2.17963i | −0.0463960 | + | 0.142792i | −0.971571 | − | 0.236749i | \(-0.923918\pi\) |
0.925175 | + | 0.379541i | \(0.123918\pi\) | |||||||
\(234\) | 0.618034 | − | 0.449028i | 0.0404021 | − | 0.0293539i | ||||
\(235\) | 0.753289 | + | 2.31838i | 0.0491391 | + | 0.151235i | ||||
\(236\) | −18.9443 | + | 13.7638i | −1.23317 | + | 0.895948i | ||||
\(237\) | 1.54508 | − | 4.75528i | 0.100364 | − | 0.308889i | ||||
\(238\) | 9.70820 | 0.629289 | ||||||||
\(239\) | 10.5279 | 0.680991 | 0.340495 | − | 0.940246i | \(-0.389405\pi\) | ||||
0.340495 | + | 0.940246i | \(0.389405\pi\) | |||||||
\(240\) | 4.14590 | 0.267617 | ||||||||
\(241\) | −0.173762 | − | 0.534785i | −0.0111930 | − | 0.0344485i | 0.945304 | − | 0.326191i | \(-0.105765\pi\) |
−0.956497 | + | 0.291742i | \(0.905765\pi\) | |||||||
\(242\) | −3.26393 | − | 5.96361i | −0.209813 | − | 0.383355i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.35410 | − | 7.24518i | 0.150706 | − | 0.463825i | ||||
\(245\) | −4.47214 | −0.285714 | ||||||||
\(246\) | −5.54508 | + | 4.02874i | −0.353542 | + | 0.256863i | ||||
\(247\) | 1.38197 | + | 4.25325i | 0.0879324 | + | 0.270628i | ||||
\(248\) | −10.4271 | + | 7.57570i | −0.662118 | + | 0.481057i | ||||
\(249\) | 2.35410 | − | 7.24518i | 0.149185 | − | 0.459145i | ||||
\(250\) | 5.59017 | − | 4.06150i | 0.353553 | − | 0.256872i | ||||
\(251\) | 19.1353 | − | 13.9026i | 1.20781 | − | 0.877523i | 0.212777 | − | 0.977101i | \(-0.431749\pi\) |
0.995030 | + | 0.0995780i | \(0.0317493\pi\) | |||||||
\(252\) | 1.50000 | − | 4.61653i | 0.0944911 | − | 0.290814i | ||||
\(253\) | −15.7082 | − | 3.52671i | −0.987566 | − | 0.221722i | ||||
\(254\) | 8.20820 | + | 5.96361i | 0.515029 | + | 0.374190i | ||||
\(255\) | −3.61803 | − | 11.1352i | −0.226570 | − | 0.697311i | ||||
\(256\) | 5.30902 | + | 3.85723i | 0.331814 | + | 0.241077i | ||||
\(257\) | −5.56231 | + | 17.1190i | −0.346967 | + | 1.06785i | 0.613555 | + | 0.789652i | \(0.289739\pi\) |
−0.960522 | + | 0.278203i | \(0.910261\pi\) | |||||||
\(258\) | −3.70820 | −0.230863 | ||||||||
\(259\) | 1.98936 | − | 6.12261i | 0.123613 | − | 0.380441i | ||||
\(260\) | 3.61803 | − | 2.62866i | 0.224381 | − | 0.163022i | ||||
\(261\) | −10.3262 | −0.639178 | ||||||||
\(262\) | −7.97214 | − | 5.79210i | −0.492520 | − | 0.357837i | ||||
\(263\) | 1.52786 | + | 4.70228i | 0.0942121 | + | 0.289955i | 0.987048 | − | 0.160428i | \(-0.0512874\pi\) |
−0.892835 | + | 0.450383i | \(0.851287\pi\) | |||||||
\(264\) | −4.89919 | − | 5.56758i | −0.301524 | − | 0.342661i | ||||
\(265\) | −20.3262 | + | 14.7679i | −1.24863 | + | 0.907183i | ||||
\(266\) | −5.42705 | − | 3.94298i | −0.332754 | − | 0.241760i | ||||
\(267\) | 1.80902 | + | 1.31433i | 0.110710 | + | 0.0804356i | ||||
\(268\) | 1.50000 | − | 4.61653i | 0.0916271 | − | 0.281999i | ||||
\(269\) | 10.5279 | 0.641895 | 0.320948 | − | 0.947097i | \(-0.395999\pi\) | ||||
0.320948 | + | 0.947097i | \(0.395999\pi\) | |||||||
\(270\) | 1.38197 | 0.0841038 | ||||||||
\(271\) | −14.7082 | + | 10.6861i | −0.893460 | + | 0.649137i | −0.936778 | − | 0.349925i | \(-0.886207\pi\) |
0.0433180 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(272\) | −3.00000 | + | 9.23305i | −0.181902 | + | 0.559836i | ||||
\(273\) | −1.14590 | − | 3.52671i | −0.0693529 | − | 0.213446i | ||||
\(274\) | 8.67376 | 0.524001 | ||||||||
\(275\) | 16.1803 | + | 3.63271i | 0.975711 | + | 0.219061i | ||||
\(276\) | −7.85410 | −0.472761 | ||||||||
\(277\) | 6.24671 | + | 19.2254i | 0.375328 | + | 1.15514i | 0.943257 | + | 0.332064i | \(0.107745\pi\) |
−0.567928 | + | 0.823078i | \(0.692255\pi\) | |||||||
\(278\) | 0.753289 | − | 2.31838i | 0.0451793 | − | 0.139047i | ||||
\(279\) | 4.66312 | − | 3.38795i | 0.279174 | − | 0.202832i | ||||
\(280\) | −4.63525 | + | 14.2658i | −0.277009 | + | 0.852547i | ||||
\(281\) | −25.3607 | −1.51289 | −0.756446 | − | 0.654057i | \(-0.773066\pi\) | ||||
−0.756446 | + | 0.654057i | \(0.773066\pi\) | |||||||
\(282\) | 0.208204 | − | 0.640786i | 0.0123984 | − | 0.0381582i | ||||
\(283\) | 0.472136 | + | 0.343027i | 0.0280656 | + | 0.0203908i | 0.601730 | − | 0.798700i | \(-0.294478\pi\) |
−0.573664 | + | 0.819091i | \(0.694478\pi\) | |||||||
\(284\) | −15.2082 | − | 11.0494i | −0.902441 | − | 0.655662i | ||||
\(285\) | −2.50000 | + | 7.69421i | −0.148087 | + | 0.455766i | ||||
\(286\) | −2.47214 | − | 0.555029i | −0.146180 | − | 0.0328196i | ||||
\(287\) | 10.2812 | + | 31.6421i | 0.606877 | + | 1.86778i | ||||
\(288\) | −4.54508 | − | 3.30220i | −0.267822 | − | 0.194584i | ||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 14.2705 | 0.837993 | ||||||||
\(291\) | −3.54508 | + | 10.9106i | −0.207817 | + | 0.639594i | ||||
\(292\) | 18.7082 | 1.09481 | ||||||||
\(293\) | −1.86475 | + | 5.73910i | −0.108940 | + | 0.335282i | −0.990635 | − | 0.136538i | \(-0.956403\pi\) |
0.881695 | + | 0.471819i | \(0.156403\pi\) | |||||||
\(294\) | 1.00000 | + | 0.726543i | 0.0583212 | + | 0.0423728i | ||||
\(295\) | −26.1803 | + | 19.0211i | −1.52428 | + | 1.10745i | ||||
\(296\) | −3.88197 | − | 2.82041i | −0.225635 | − | 0.163933i | ||||
\(297\) | 2.19098 | + | 2.48990i | 0.127134 | + | 0.144479i | ||||
\(298\) | −1.21885 | + | 3.75123i | −0.0706059 | + | 0.217303i | ||||
\(299\) | −4.85410 | + | 3.52671i | −0.280720 | + | 0.203955i | ||||
\(300\) | 8.09017 | 0.467086 | ||||||||
\(301\) | −5.56231 | + | 17.1190i | −0.320606 | + | 0.986724i | ||||
\(302\) | −1.95492 | + | 1.42033i | −0.112493 | + | 0.0817307i | ||||
\(303\) | −3.54508 | − | 10.9106i | −0.203660 | − | 0.626800i | ||||
\(304\) | 5.42705 | − | 3.94298i | 0.311263 | − | 0.226146i | ||||
\(305\) | 3.25329 | − | 10.0126i | 0.186283 | − | 0.573319i | ||||
\(306\) | −1.00000 | + | 3.07768i | −0.0571662 | + | 0.175939i | ||||
\(307\) | 1.67376 | 0.0955266 | 0.0477633 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477633 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(308\) | −14.7812 | + | 6.37988i | −0.842234 | + | 0.363527i | ||||
\(309\) | 1.92705 | + | 5.93085i | 0.109626 | + | 0.337394i | ||||
\(310\) | −6.44427 | + | 4.68204i | −0.366010 | + | 0.265922i | ||||
\(311\) | 8.38197 | 0.475298 | 0.237649 | − | 0.971351i | \(-0.423623\pi\) | ||||
0.237649 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(312\) | −2.76393 | −0.156477 | ||||||||
\(313\) | 3.43769 | − | 10.5801i | 0.194310 | − | 0.598025i | −0.805674 | − | 0.592359i | \(-0.798197\pi\) |
0.999984 | − | 0.00566537i | \(-0.00180335\pi\) | |||||||
\(314\) | 2.78115 | − | 2.02063i | 0.156950 | − | 0.114031i | ||||
\(315\) | 2.07295 | − | 6.37988i | 0.116797 | − | 0.359466i | ||||
\(316\) | −6.54508 | + | 4.75528i | −0.368190 | + | 0.267506i | ||||
\(317\) | 5.29180 | − | 16.2865i | 0.297217 | − | 0.914739i | −0.685251 | − | 0.728307i | \(-0.740307\pi\) |
0.982468 | − | 0.186432i | \(-0.0596925\pi\) | |||||||
\(318\) | 6.94427 | 0.389415 | ||||||||
\(319\) | 22.6246 | + | 25.7113i | 1.26674 | + | 1.43956i | ||||
\(320\) | −0.427051 | − | 0.310271i | −0.0238729 | − | 0.0173447i | ||||
\(321\) | 7.79837 | 0.435263 | ||||||||
\(322\) | 2.78115 | − | 8.55951i | 0.154988 | − | 0.477003i | ||||
\(323\) | −15.3262 | − | 11.1352i | −0.852775 | − | 0.619577i | ||||
\(324\) | 1.30902 | + | 0.951057i | 0.0727232 | + | 0.0528365i | ||||
\(325\) | 5.00000 | − | 3.63271i | 0.277350 | − | 0.201507i | ||||
\(326\) | 2.59017 | − | 7.97172i | 0.143456 | − | 0.441513i | ||||
\(327\) | 1.70820 | 0.0944639 | ||||||||
\(328\) | 24.7984 | 1.36926 | ||||||||
\(329\) | −2.64590 | − | 1.92236i | −0.145873 | − | 0.105983i | ||||
\(330\) | −3.02786 | − | 3.44095i | −0.166678 | − | 0.189418i | ||||
\(331\) | 5.45492 | − | 3.96323i | 0.299829 | − | 0.217839i | −0.427691 | − | 0.903925i | \(-0.640673\pi\) |
0.727520 | + | 0.686086i | \(0.240673\pi\) | |||||||
\(332\) | −9.97214 | + | 7.24518i | −0.547292 | + | 0.397631i | ||||
\(333\) | 1.73607 | + | 1.26133i | 0.0951359 | + | 0.0691203i | ||||
\(334\) | 13.7984 | 0.755013 | ||||||||
\(335\) | 2.07295 | − | 6.37988i | 0.113257 | − | 0.348570i | ||||
\(336\) | −4.50000 | + | 3.26944i | −0.245495 | + | 0.178363i | ||||
\(337\) | 8.90983 | 0.485349 | 0.242675 | − | 0.970108i | \(-0.421975\pi\) | ||||
0.242675 | + | 0.970108i | \(0.421975\pi\) | |||||||
\(338\) | 5.73607 | − | 4.16750i | 0.312001 | − | 0.226682i | ||||
\(339\) | −3.76393 | − | 11.5842i | −0.204429 | − | 0.629167i | ||||
\(340\) | −5.85410 | + | 18.0171i | −0.317483 | + | 0.977113i | ||||
\(341\) | −18.6525 | − | 4.18774i | −1.01009 | − | 0.226779i | ||||
\(342\) | 1.80902 | − | 1.31433i | 0.0978204 | − | 0.0710707i | ||||
\(343\) | −12.1353 | + | 8.81678i | −0.655242 | + | 0.476061i | ||||
\(344\) | 10.8541 | + | 7.88597i | 0.585214 | + | 0.425183i | ||||
\(345\) | −10.8541 | −0.584365 | ||||||||
\(346\) | 1.04508 | + | 3.21644i | 0.0561841 | + | 0.172917i | ||||
\(347\) | −5.17376 | − | 15.9232i | −0.277742 | − | 0.854802i | −0.988481 | − | 0.151346i | \(-0.951639\pi\) |
0.710739 | − | 0.703456i | \(-0.248361\pi\) | |||||||
\(348\) | 13.5172 | + | 9.82084i | 0.724599 | + | 0.526452i | ||||
\(349\) | −1.44427 | − | 4.44501i | −0.0773101 | − | 0.237936i | 0.904931 | − | 0.425558i | \(-0.139922\pi\) |
−0.982241 | + | 0.187622i | \(0.939922\pi\) | |||||||
\(350\) | −2.86475 | + | 8.81678i | −0.153127 | + | 0.471277i | ||||
\(351\) | 1.23607 | 0.0659764 | ||||||||
\(352\) | 1.73607 | + | 18.5519i | 0.0925327 | + | 0.988817i | ||||
\(353\) | 23.1353 | + | 16.8087i | 1.23137 | + | 0.894639i | 0.996992 | − | 0.0775073i | \(-0.0246961\pi\) |
0.234374 | + | 0.972147i | \(0.424696\pi\) | |||||||
\(354\) | 8.94427 | 0.475383 | ||||||||
\(355\) | −21.0172 | − | 15.2699i | −1.11548 | − | 0.810442i | ||||
\(356\) | −1.11803 | − | 3.44095i | −0.0592557 | − | 0.182370i | ||||
\(357\) | 12.7082 | + | 9.23305i | 0.672589 | + | 0.488665i | ||||
\(358\) | 13.6180 | 0.719735 | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | −4.04508 | − | 2.93893i | −0.213195 | − | 0.154895i | ||||
\(361\) | −1.82624 | − | 5.62058i | −0.0961178 | − | 0.295820i | ||||
\(362\) | 2.39261 | + | 7.36369i | 0.125753 | + | 0.387027i | ||||
\(363\) | 1.39919 | − | 10.9106i | 0.0734383 | − | 0.572661i | ||||
\(364\) | −1.85410 | + | 5.70634i | −0.0971813 | + | 0.299093i | ||||
\(365\) | 25.8541 | 1.35327 | ||||||||
\(366\) | −2.35410 | + | 1.71036i | −0.123051 | + | 0.0894017i | ||||
\(367\) | −6.12868 | − | 18.8621i | −0.319914 | − | 0.984595i | −0.973684 | − | 0.227902i | \(-0.926814\pi\) |
0.653770 | − | 0.756693i | \(-0.273186\pi\) | |||||||
\(368\) | 7.28115 | + | 5.29007i | 0.379556 | + | 0.275764i | ||||
\(369\) | −11.0902 | −0.577331 | ||||||||
\(370\) | −2.39919 | − | 1.74311i | −0.124728 | − | 0.0906200i | ||||
\(371\) | 10.4164 | − | 32.0584i | 0.540793 | − | 1.66439i | ||||
\(372\) | −9.32624 | −0.483543 | ||||||||
\(373\) | −5.87132 | + | 18.0701i | −0.304006 | + | 0.935633i | 0.676041 | + | 0.736864i | \(0.263694\pi\) |
−0.980046 | + | 0.198769i | \(0.936306\pi\) | |||||||
\(374\) | 9.85410 | − | 4.25325i | 0.509543 | − | 0.219931i | ||||
\(375\) | 11.1803 | 0.577350 | ||||||||
\(376\) | −1.97214 | + | 1.43284i | −0.101705 | + | 0.0738931i | ||||
\(377\) | 12.7639 | 0.657376 | ||||||||
\(378\) | −1.50000 | + | 1.08981i | −0.0771517 | + | 0.0560540i | ||||
\(379\) | −9.83688 | − | 30.2748i | −0.505287 | − | 1.55511i | −0.800288 | − | 0.599616i | \(-0.795320\pi\) |
0.295002 | − | 0.955497i | \(-0.404680\pi\) | |||||||
\(380\) | 10.5902 | − | 7.69421i | 0.543264 | − | 0.394705i | ||||
\(381\) | 5.07295 | + | 15.6129i | 0.259895 | + | 0.799875i | ||||
\(382\) | 0.118034 | + | 0.363271i | 0.00603914 | + | 0.0185866i | ||||
\(383\) | 0.572949 | − | 1.76336i | 0.0292763 | − | 0.0901033i | −0.935351 | − | 0.353722i | \(-0.884916\pi\) |
0.964627 | + | 0.263618i | \(0.0849160\pi\) | |||||||
\(384\) | 3.51722 | + | 10.8249i | 0.179487 | + | 0.552406i | ||||
\(385\) | −20.4271 | + | 8.81678i | −1.04106 | + | 0.449345i | ||||
\(386\) | 1.79837 | − | 5.53483i | 0.0915348 | − | 0.281715i | ||||
\(387\) | −4.85410 | − | 3.52671i | −0.246748 | − | 0.179273i | ||||
\(388\) | 15.0172 | − | 10.9106i | 0.762384 | − | 0.553904i | ||||
\(389\) | 7.92705 | + | 5.75934i | 0.401917 | + | 0.292010i | 0.770322 | − | 0.637656i | \(-0.220096\pi\) |
−0.368404 | + | 0.929666i | \(0.620096\pi\) | |||||||
\(390\) | −1.70820 | −0.0864983 | ||||||||
\(391\) | 7.85410 | − | 24.1724i | 0.397199 | − | 1.22245i | ||||
\(392\) | −1.38197 | − | 4.25325i | −0.0697998 | − | 0.214822i | ||||
\(393\) | −4.92705 | − | 15.1639i | −0.248537 | − | 0.764918i | ||||
\(394\) | 1.86475 | − | 5.73910i | 0.0939445 | − | 0.289131i | ||||
\(395\) | −9.04508 | + | 6.57164i | −0.455108 | + | 0.330655i | ||||
\(396\) | −0.500000 | − | 5.34307i | −0.0251259 | − | 0.268499i | ||||
\(397\) | 9.92705 | + | 7.21242i | 0.498224 | + | 0.361981i | 0.808338 | − | 0.588718i | \(-0.200367\pi\) |
−0.310114 | + | 0.950699i | \(0.600367\pi\) | |||||||
\(398\) | 2.82624 | + | 8.69827i | 0.141667 | + | 0.436005i | ||||
\(399\) | −3.35410 | − | 10.3229i | −0.167915 | − | 0.516790i | ||||
\(400\) | −7.50000 | − | 5.44907i | −0.375000 | − | 0.272453i | ||||
\(401\) | 8.11803 | + | 5.89810i | 0.405395 | + | 0.294537i | 0.771735 | − | 0.635944i | \(-0.219389\pi\) |
−0.366340 | + | 0.930481i | \(0.619389\pi\) | |||||||
\(402\) | −1.50000 | + | 1.08981i | −0.0748132 | + | 0.0543550i | ||||
\(403\) | −5.76393 | + | 4.18774i | −0.287122 | + | 0.208606i | ||||
\(404\) | −5.73607 | + | 17.6538i | −0.285380 | + | 0.878309i | ||||
\(405\) | 1.80902 | + | 1.31433i | 0.0898908 | + | 0.0653095i | ||||
\(406\) | −15.4894 | + | 11.2537i | −0.768724 | + | 0.558511i | ||||
\(407\) | −0.663119 | − | 7.08618i | −0.0328696 | − | 0.351249i | ||||
\(408\) | 9.47214 | − | 6.88191i | 0.468941 | − | 0.340705i | ||||
\(409\) | 4.20820 | + | 3.05744i | 0.208082 | + | 0.151181i | 0.686946 | − | 0.726709i | \(-0.258951\pi\) |
−0.478863 | + | 0.877889i | \(0.658951\pi\) | |||||||
\(410\) | 15.3262 | 0.756909 | ||||||||
\(411\) | 11.3541 | + | 8.24924i | 0.560057 | + | 0.406905i | ||||
\(412\) | 3.11803 | − | 9.59632i | 0.153615 | − | 0.472777i | ||||
\(413\) | 13.4164 | − | 41.2915i | 0.660178 | − | 2.03182i | ||||
\(414\) | 2.42705 | + | 1.76336i | 0.119283 | + | 0.0866642i | ||||
\(415\) | −13.7812 | + | 10.0126i | −0.676490 | + | 0.491499i | ||||
\(416\) | 5.61803 | + | 4.08174i | 0.275447 | + | 0.200124i | ||||
\(417\) | 3.19098 | − | 2.31838i | 0.156263 | − | 0.113532i | ||||
\(418\) | −7.23607 | − | 1.62460i | −0.353928 | − | 0.0794617i | ||||
\(419\) | −17.2984 | + | 12.5680i | −0.845081 | + | 0.613987i | −0.923785 | − | 0.382911i | \(-0.874922\pi\) |
0.0787045 | + | 0.996898i | \(0.474922\pi\) | |||||||
\(420\) | −8.78115 | + | 6.37988i | −0.428476 | + | 0.311306i | ||||
\(421\) | 4.66312 | − | 14.3516i | 0.227267 | − | 0.699454i | −0.770787 | − | 0.637093i | \(-0.780137\pi\) |
0.998054 | − | 0.0623616i | \(-0.0198632\pi\) | |||||||
\(422\) | −12.4443 | + | 9.04129i | −0.605778 | + | 0.440123i | ||||
\(423\) | 0.881966 | − | 0.640786i | 0.0428827 | − | 0.0311561i | ||||
\(424\) | −20.3262 | − | 14.7679i | −0.987129 | − | 0.717191i | ||||
\(425\) | −8.09017 | + | 24.8990i | −0.392431 | + | 1.20778i | ||||
\(426\) | 2.21885 | + | 6.82891i | 0.107503 | + | 0.330862i | ||||
\(427\) | 4.36475 | + | 13.4333i | 0.211225 | + | 0.650083i | ||||
\(428\) | −10.2082 | − | 7.41669i | −0.493432 | − | 0.358499i | ||||
\(429\) | −2.70820 | − | 3.07768i | −0.130753 | − | 0.148592i | ||||
\(430\) | 6.70820 | + | 4.87380i | 0.323498 | + | 0.235035i | ||||
\(431\) | −7.30902 | + | 22.4948i | −0.352063 | + | 1.08354i | 0.605630 | + | 0.795746i | \(0.292921\pi\) |
−0.957693 | + | 0.287792i | \(0.907079\pi\) | |||||||
\(432\) | −0.572949 | − | 1.76336i | −0.0275660 | − | 0.0848395i | ||||
\(433\) | 8.43769 | + | 25.9686i | 0.405490 | + | 1.24797i | 0.920486 | + | 0.390776i | \(0.127793\pi\) |
−0.514996 | + | 0.857193i | \(0.672207\pi\) | |||||||
\(434\) | 3.30244 | − | 10.1639i | 0.158522 | − | 0.487881i | ||||
\(435\) | 18.6803 | + | 13.5721i | 0.895654 | + | 0.650731i | ||||
\(436\) | −2.23607 | − | 1.62460i | −0.107088 | − | 0.0778042i | ||||
\(437\) | −14.2082 | + | 10.3229i | −0.679671 | + | 0.493810i | ||||
\(438\) | −5.78115 | − | 4.20025i | −0.276234 | − | 0.200696i | ||||
\(439\) | −8.84346 | + | 27.2174i | −0.422075 | + | 1.29901i | 0.483692 | + | 0.875238i | \(0.339296\pi\) |
−0.905767 | + | 0.423776i | \(0.860704\pi\) | |||||||
\(440\) | 1.54508 | + | 16.5110i | 0.0736590 | + | 0.787130i | ||||
\(441\) | 0.618034 | + | 1.90211i | 0.0294302 | + | 0.0905768i | ||||
\(442\) | 1.23607 | − | 3.80423i | 0.0587938 | − | 0.180949i | ||||
\(443\) | 6.59017 | + | 20.2825i | 0.313108 | + | 0.963649i | 0.976526 | + | 0.215399i | \(0.0691053\pi\) |
−0.663418 | + | 0.748249i | \(0.730895\pi\) | |||||||
\(444\) | −1.07295 | − | 3.30220i | −0.0509199 | − | 0.156715i | ||||
\(445\) | −1.54508 | − | 4.75528i | −0.0732441 | − | 0.225422i | ||||
\(446\) | −4.28115 | − | 13.1760i | −0.202718 | − | 0.623903i | ||||
\(447\) | −5.16312 | + | 3.75123i | −0.244207 | + | 0.177427i | ||||
\(448\) | 0.708204 | 0.0334595 | ||||||||
\(449\) | −16.6074 | + | 12.0660i | −0.783751 | + | 0.569429i | −0.906102 | − | 0.423058i | \(-0.860957\pi\) |
0.122351 | + | 0.992487i | \(0.460957\pi\) | |||||||
\(450\) | −2.50000 | − | 1.81636i | −0.117851 | − | 0.0856239i | ||||
\(451\) | 24.2984 | + | 27.6134i | 1.14417 | + | 1.30026i | ||||
\(452\) | −6.09017 | + | 18.7436i | −0.286457 | + | 0.881626i | ||||
\(453\) | −3.90983 | −0.183700 | ||||||||
\(454\) | 2.51722 | − | 7.74721i | 0.118139 | − | 0.363595i | ||||
\(455\) | −2.56231 | + | 7.88597i | −0.120123 | + | 0.369700i | ||||
\(456\) | −8.09017 | −0.378857 | ||||||||
\(457\) | −6.78115 | − | 4.92680i | −0.317209 | − | 0.230466i | 0.417775 | − | 0.908551i | \(-0.362810\pi\) |
−0.734984 | + | 0.678085i | \(0.762810\pi\) | |||||||
\(458\) | −4.77458 | − | 14.6946i | −0.223101 | − | 0.686635i | ||||
\(459\) | −4.23607 | + | 3.07768i | −0.197723 | + | 0.143654i | ||||
\(460\) | 14.2082 | + | 10.3229i | 0.662461 | + | 0.481306i | ||||
\(461\) | 3.07953 | − | 9.47781i | 0.143428 | − | 0.441426i | −0.853378 | − | 0.521293i | \(-0.825450\pi\) |
0.996805 | + | 0.0798677i | \(0.0254498\pi\) | |||||||
\(462\) | 6.00000 | + | 1.34708i | 0.279145 | + | 0.0626720i | ||||
\(463\) | −8.47214 | − | 26.0746i | −0.393734 | − | 1.21179i | −0.929943 | − | 0.367703i | \(-0.880144\pi\) |
0.536210 | − | 0.844085i | \(-0.319856\pi\) | |||||||
\(464\) | −5.91641 | − | 18.2088i | −0.274662 | − | 0.845324i | ||||
\(465\) | −12.8885 | −0.597692 | ||||||||
\(466\) | −1.41641 | −0.0656138 | ||||||||
\(467\) | −19.0557 | −0.881794 | −0.440897 | − | 0.897558i | \(-0.645340\pi\) | ||||
−0.440897 | + | 0.897558i | \(0.645340\pi\) | |||||||
\(468\) | −1.61803 | − | 1.17557i | −0.0747936 | − | 0.0543408i | ||||
\(469\) | 2.78115 | + | 8.55951i | 0.128422 | + | 0.395241i | ||||
\(470\) | −1.21885 | + | 0.885544i | −0.0562212 | + | 0.0408471i | ||||
\(471\) | 5.56231 | 0.256298 | ||||||||
\(472\) | −26.1803 | − | 19.0211i | −1.20505 | − | 0.875518i | ||||
\(473\) | 1.85410 | + | 19.8132i | 0.0852517 | + | 0.911011i | ||||
\(474\) | 3.09017 | 0.141936 | ||||||||
\(475\) | 14.6353 | − | 10.6331i | 0.671512 | − | 0.487882i | ||||
\(476\) | −7.85410 | − | 24.1724i | −0.359992 | − | 1.10794i | ||||
\(477\) | 9.09017 | + | 6.60440i | 0.416210 | + | 0.302394i | ||||
\(478\) | 2.01064 | + | 6.18812i | 0.0919647 | + | 0.283038i | ||||
\(479\) | 4.04508 | + | 12.4495i | 0.184825 | + | 0.568832i | 0.999945 | − | 0.0104594i | \(-0.00332941\pi\) |
−0.815121 | + | 0.579291i | \(0.803329\pi\) | |||||||
\(480\) | 3.88197 | + | 11.9475i | 0.177187 | + | 0.545325i | ||||
\(481\) | −2.14590 | − | 1.55909i | −0.0978445 | − | 0.0710882i | ||||
\(482\) | 0.281153 | − | 0.204270i | 0.0128062 | − | 0.00930422i | ||||
\(483\) | 11.7812 | − | 8.55951i | 0.536061 | − | 0.389471i | ||||
\(484\) | −12.2082 | + | 12.9515i | −0.554918 | + | 0.588705i | ||||
\(485\) | 20.7533 | − | 15.0781i | 0.942358 | − | 0.684663i | ||||
\(486\) | −0.190983 | − | 0.587785i | −0.00866317 | − | 0.0266625i | ||||
\(487\) | 2.85410 | − | 2.07363i | 0.129332 | − | 0.0939650i | −0.521239 | − | 0.853411i | \(-0.674530\pi\) |
0.650570 | + | 0.759446i | \(0.274530\pi\) | |||||||
\(488\) | 10.5279 | 0.476574 | ||||||||
\(489\) | 10.9721 | − | 7.97172i | 0.496177 | − | 0.360494i | ||||
\(490\) | −0.854102 | − | 2.62866i | −0.0385844 | − | 0.118751i | ||||
\(491\) | 17.4508 | 0.787546 | 0.393773 | − | 0.919208i | \(-0.371170\pi\) | ||||
0.393773 | + | 0.919208i | \(0.371170\pi\) | |||||||
\(492\) | 14.5172 | + | 10.5474i | 0.654487 | + | 0.475513i | ||||
\(493\) | −43.7426 | + | 31.7809i | −1.97007 | + | 1.43134i | ||||
\(494\) | −2.23607 | + | 1.62460i | −0.100605 | + | 0.0730941i | ||||
\(495\) | −0.690983 | − | 7.38394i | −0.0310574 | − | 0.331883i | ||||
\(496\) | 8.64590 | + | 6.28161i | 0.388212 | + | 0.282053i | ||||
\(497\) | 34.8541 | 1.56342 | ||||||||
\(498\) | 4.70820 | 0.210980 | ||||||||
\(499\) | 7.76393 | − | 23.8949i | 0.347561 | − | 1.06968i | −0.612637 | − | 0.790364i | \(-0.709891\pi\) |
0.960198 | − | 0.279319i | \(-0.0901088\pi\) | |||||||
\(500\) | −14.6353 | − | 10.6331i | −0.654508 | − | 0.475528i | ||||
\(501\) | 18.0623 | + | 13.1230i | 0.806964 | + | 0.586294i | ||||
\(502\) | 11.8262 | + | 8.59226i | 0.527831 | + | 0.383492i | ||||
\(503\) | −6.33688 | + | 19.5029i | −0.282548 | + | 0.869592i | 0.704575 | + | 0.709629i | \(0.251137\pi\) |
−0.987123 | + | 0.159963i | \(0.948863\pi\) | |||||||
\(504\) | 6.70820 | 0.298807 | ||||||||
\(505\) | −7.92705 | + | 24.3970i | −0.352749 | + | 1.08565i | ||||
\(506\) | −0.927051 | − | 9.90659i | −0.0412124 | − | 0.440402i | ||||
\(507\) | 11.4721 | 0.509495 | ||||||||
\(508\) | 8.20820 | − | 25.2623i | 0.364180 | − | 1.12083i | ||||
\(509\) | 17.8262 | − | 12.9515i | 0.790134 | − | 0.574066i | −0.117869 | − | 0.993029i | \(-0.537606\pi\) |
0.908003 | + | 0.418963i | \(0.137606\pi\) | |||||||
\(510\) | 5.85410 | − | 4.25325i | 0.259224 | − | 0.188337i | ||||
\(511\) | −28.0623 | + | 20.3885i | −1.24140 | + | 0.901932i | ||||
\(512\) | 5.78115 | − | 17.7926i | 0.255493 | − | 0.786327i | ||||
\(513\) | 3.61803 | 0.159740 | ||||||||
\(514\) | −11.1246 | −0.490686 | ||||||||
\(515\) | 4.30902 | − | 13.2618i | 0.189878 | − | 0.584384i | ||||
\(516\) | 3.00000 | + | 9.23305i | 0.132068 | + | 0.406462i | ||||
\(517\) | −3.52786 | − | 0.792055i | −0.155155 | − | 0.0348345i | ||||
\(518\) | 3.97871 | 0.174815 | ||||||||
\(519\) | −1.69098 | + | 5.20431i | −0.0742259 | + | 0.228444i | ||||
\(520\) | 5.00000 | + | 3.63271i | 0.219265 | + | 0.159305i | ||||
\(521\) | −25.4615 | + | 18.4989i | −1.11549 | + | 0.810450i | −0.983519 | − | 0.180804i | \(-0.942130\pi\) |
−0.131969 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(522\) | −1.97214 | − | 6.06961i | −0.0863180 | − | 0.265660i | ||||
\(523\) | −16.9894 | + | 12.3435i | −0.742893 | + | 0.539743i | −0.893616 | − | 0.448833i | \(-0.851840\pi\) |
0.150723 | + | 0.988576i | \(0.451840\pi\) | |||||||
\(524\) | −7.97214 | + | 24.5357i | −0.348264 | + | 1.07185i | ||||
\(525\) | −12.1353 | + | 8.81678i | −0.529626 | + | 0.384796i | ||||
\(526\) | −2.47214 | + | 1.79611i | −0.107790 | + | 0.0783142i | ||||
\(527\) | 9.32624 | − | 28.7032i | 0.406257 | − | 1.25033i | ||||
\(528\) | −3.13525 | + | 5.29007i | −0.136444 | + | 0.230221i | ||||
\(529\) | −0.454915 | − | 0.330515i | −0.0197789 | − | 0.0143702i | ||||
\(530\) | −12.5623 | − | 9.12705i | −0.545672 | − | 0.396454i | ||||
\(531\) | 11.7082 | + | 8.50651i | 0.508093 | + | 0.369151i | ||||
\(532\) | −5.42705 | + | 16.7027i | −0.235293 | + | 0.724156i | ||||
\(533\) | 13.7082 | 0.593768 | ||||||||
\(534\) | −0.427051 | + | 1.31433i | −0.0184803 | + | 0.0568765i | ||||
\(535\) | −14.1074 | − | 10.2496i | −0.609916 | − | 0.443130i | ||||
\(536\) | 6.70820 | 0.289750 | ||||||||
\(537\) | 17.8262 | + | 12.9515i | 0.769259 | + | 0.558899i | ||||
\(538\) | 2.01064 | + | 6.18812i | 0.0866850 | + | 0.266789i | ||||
\(539\) | 3.38197 | − | 5.70634i | 0.145672 | − | 0.245789i | ||||
\(540\) | −1.11803 | − | 3.44095i | −0.0481125 | − | 0.148075i | ||||
\(541\) | 9.50000 | + | 6.90215i | 0.408437 | + | 0.296747i | 0.772969 | − | 0.634444i | \(-0.218771\pi\) |
−0.364532 | + | 0.931191i | \(0.618771\pi\) | |||||||
\(542\) | −9.09017 | − | 6.60440i | −0.390456 | − | 0.283683i | ||||
\(543\) | −3.87132 | + | 11.9147i | −0.166134 | + | 0.511309i | ||||
\(544\) | −29.4164 | −1.26122 | ||||||||
\(545\) | −3.09017 | − | 2.24514i | −0.132368 | − | 0.0961712i | ||||
\(546\) | 1.85410 | − | 1.34708i | 0.0793482 | − | 0.0576499i | ||||
\(547\) | −7.10739 | + | 21.8743i | −0.303890 | + | 0.935278i | 0.676199 | + | 0.736719i | \(0.263626\pi\) |
−0.980089 | + | 0.198558i | \(0.936374\pi\) | |||||||
\(548\) | −7.01722 | − | 21.5968i | −0.299761 | − | 0.922569i | ||||
\(549\) | −4.70820 | −0.200941 | ||||||||
\(550\) | 0.954915 | + | 10.2044i | 0.0407177 | + | 0.435115i | ||||
\(551\) | 37.3607 | 1.59162 | ||||||||
\(552\) | −3.35410 | − | 10.3229i | −0.142760 | − | 0.439370i | ||||
\(553\) | 4.63525 | − | 14.2658i | 0.197111 | − | 0.606646i | ||||
\(554\) | −10.1074 | + | 7.34345i | −0.429422 | + | 0.311993i | ||||
\(555\) | −1.48278 | − | 4.56352i | −0.0629405 | − | 0.193711i | ||||
\(556\) | −6.38197 | −0.270656 | ||||||||
\(557\) | −5.17376 | + | 15.9232i | −0.219219 | + | 0.674688i | 0.779608 | + | 0.626268i | \(0.215418\pi\) |
−0.998827 | + | 0.0484196i | \(0.984582\pi\) | |||||||
\(558\) | 2.88197 | + | 2.09387i | 0.122003 | + | 0.0886406i | ||||
\(559\) | 6.00000 | + | 4.35926i | 0.253773 | + | 0.184377i | ||||
\(560\) | 12.4377 | 0.525589 | ||||||||
\(561\) | 16.9443 | + | 3.80423i | 0.715388 | + | 0.160615i | ||||
\(562\) | −4.84346 | − | 14.9066i | −0.204309 | − | 0.628798i | ||||
\(563\) | 27.9336 | + | 20.2950i | 1.17726 | + | 0.855331i | 0.991860 | − | 0.127332i | \(-0.0406413\pi\) |
0.185402 | + | 0.982663i | \(0.440641\pi\) | |||||||
\(564\) | −1.76393 | −0.0742749 | ||||||||
\(565\) | −8.41641 | + | 25.9030i | −0.354081 | + | 1.08975i | ||||
\(566\) | −0.111456 | + | 0.343027i | −0.00468485 | + | 0.0144185i | ||||
\(567\) | −3.00000 | −0.125988 | ||||||||
\(568\) | 8.02786 | − | 24.7072i | 0.336842 | − | 1.03669i | ||||
\(569\) | 18.6803 | + | 13.5721i | 0.783121 | + | 0.568970i | 0.905914 | − | 0.423462i | \(-0.139185\pi\) |
−0.122793 | + | 0.992432i | \(0.539185\pi\) | |||||||
\(570\) | −5.00000 | −0.209427 | ||||||||
\(571\) | 21.8992 | + | 15.9107i | 0.916452 | + | 0.665842i | 0.942638 | − | 0.333815i | \(-0.108336\pi\) |
−0.0261860 | + | 0.999657i | \(0.508336\pi\) | |||||||
\(572\) | 0.618034 | + | 6.60440i | 0.0258413 | + | 0.276144i | ||||
\(573\) | −0.190983 | + | 0.587785i | −0.00797843 | + | 0.0245551i | ||||
\(574\) | −16.6353 | + | 12.0862i | −0.694342 | + | 0.504469i | ||||
\(575\) | 19.6353 | + | 14.2658i | 0.818847 | + | 0.594927i | ||||
\(576\) | −0.0729490 | + | 0.224514i | −0.00303954 | + | 0.00935475i | ||||
\(577\) | 3.80902 | − | 2.76741i | 0.158571 | − | 0.115209i | −0.505670 | − | 0.862727i | \(-0.668755\pi\) |
0.664241 | + | 0.747518i | \(0.268755\pi\) | |||||||
\(578\) | 1.98936 | + | 6.12261i | 0.0827463 | + | 0.254667i | ||||
\(579\) | 7.61803 | − | 5.53483i | 0.316595 | − | 0.230020i | ||||
\(580\) | −11.5451 | − | 35.5321i | −0.479384 | − | 1.47539i | ||||
\(581\) | 7.06231 | − | 21.7355i | 0.292994 | − | 0.901742i | ||||
\(582\) | −7.09017 | −0.293897 | ||||||||
\(583\) | −3.47214 | − | 37.1037i | −0.143801 | − | 1.53668i | ||||
\(584\) | 7.98936 | + | 24.5887i | 0.330602 | + | 1.01749i | ||||
\(585\) | −2.23607 | − | 1.62460i | −0.0924500 | − | 0.0671689i | ||||
\(586\) | −3.72949 | −0.154064 | ||||||||
\(587\) | 2.72949 | 0.112658 | 0.0563291 | − | 0.998412i | \(-0.482060\pi\) | ||||
0.0563291 | + | 0.998412i | \(0.482060\pi\) | |||||||
\(588\) | 1.00000 | − | 3.07768i | 0.0412393 | − | 0.126922i | ||||
\(589\) | −16.8713 | + | 12.2577i | −0.695171 | + | 0.505071i | ||||
\(590\) | −16.1803 | − | 11.7557i | −0.666134 | − | 0.483975i | ||||
\(591\) | 7.89919 | − | 5.73910i | 0.324929 | − | 0.236075i | ||||
\(592\) | −1.22949 | + | 3.78398i | −0.0505317 | + | 0.155521i | ||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | −1.04508 | + | 1.76336i | −0.0428804 | + | 0.0723514i | ||||
\(595\) | −10.8541 | − | 33.4055i | −0.444975 | − | 1.36949i | ||||
\(596\) | 10.3262 | 0.422979 | ||||||||
\(597\) | −4.57295 | + | 14.0741i | −0.187158 | + | 0.576014i | ||||
\(598\) | −3.00000 | − | 2.17963i | −0.122679 | − | 0.0891316i | ||||
\(599\) | 2.33688 | + | 1.69784i | 0.0954824 | + | 0.0693720i | 0.634502 | − | 0.772921i | \(-0.281205\pi\) |
−0.539020 | + | 0.842293i | \(0.681205\pi\) | |||||||
\(600\) | 3.45492 | + | 10.6331i | 0.141046 | + | 0.434096i | ||||
\(601\) | 3.48278 | − | 10.7189i | 0.142066 | − | 0.437233i | −0.854556 | − | 0.519359i | \(-0.826171\pi\) |
0.996622 | + | 0.0821258i | \(0.0261709\pi\) | |||||||
\(602\) | −11.1246 | −0.453405 | ||||||||
\(603\) | −3.00000 | −0.122169 | ||||||||
\(604\) | 5.11803 | + | 3.71847i | 0.208250 | + | 0.151302i | ||||
\(605\) | −16.8713 | + | 17.8986i | −0.685917 | + | 0.727680i | ||||
\(606\) | 5.73607 | − | 4.16750i | 0.233012 | − | 0.169293i | ||||
\(607\) | 25.2533 | − | 18.3476i | 1.02500 | − | 0.744706i | 0.0576977 | − | 0.998334i | \(-0.481624\pi\) |
0.967302 | + | 0.253628i | \(0.0816241\pi\) | |||||||
\(608\) | 16.4443 | + | 11.9475i | 0.666903 | + | 0.484534i | ||||
\(609\) | −30.9787 | −1.25532 | ||||||||
\(610\) | 6.50658 | 0.263444 | ||||||||
\(611\) | −1.09017 | + | 0.792055i | −0.0441036 | + | 0.0320431i | ||||
\(612\) | 8.47214 | 0.342466 | ||||||||
\(613\) | 26.1246 | − | 18.9806i | 1.05516 | − | 0.766621i | 0.0819757 | − | 0.996634i | \(-0.473877\pi\) |
0.973187 | + | 0.230013i | \(0.0738770\pi\) | |||||||
\(614\) | 0.319660 | + | 0.983813i | 0.0129004 | + | 0.0397034i | ||||
\(615\) | 20.0623 | + | 14.5761i | 0.808990 | + | 0.587766i | ||||
\(616\) | −14.6976 | − | 16.7027i | −0.592182 | − | 0.672973i | ||||
\(617\) | −22.2082 | + | 16.1352i | −0.894069 | + | 0.649579i | −0.936936 | − | 0.349502i | \(-0.886351\pi\) |
0.0428670 | + | 0.999081i | \(0.486351\pi\) | |||||||
\(618\) | −3.11803 | + | 2.26538i | −0.125426 | + | 0.0911271i | ||||
\(619\) | −32.4615 | − | 23.5847i | −1.30474 | − | 0.947947i | −0.304748 | − | 0.952433i | \(-0.598572\pi\) |
−0.999990 | + | 0.00448582i | \(0.998572\pi\) | |||||||
\(620\) | 16.8713 | + | 12.2577i | 0.677569 | + | 0.492282i | ||||
\(621\) | 1.50000 | + | 4.61653i | 0.0601929 | + | 0.185255i | ||||
\(622\) | 1.60081 | + | 4.92680i | 0.0641868 | + | 0.197547i | ||||
\(623\) | 5.42705 | + | 3.94298i | 0.217430 | + | 0.157972i | ||||
\(624\) | 0.708204 | + | 2.17963i | 0.0283508 | + | 0.0872549i | ||||
\(625\) | −20.2254 | − | 14.6946i | −0.809017 | − | 0.587785i | ||||
\(626\) | 6.87539 | 0.274796 | ||||||||
\(627\) | −7.92705 | − | 9.00854i | −0.316576 | − | 0.359766i | ||||
\(628\) | −7.28115 | − | 5.29007i | −0.290550 | − | 0.211097i | ||||
\(629\) | 11.2361 | 0.448011 | ||||||||
\(630\) | 4.14590 | 0.165177 | ||||||||
\(631\) | −0.274575 | − | 0.845055i | −0.0109307 | − | 0.0336411i | 0.945442 | − | 0.325789i | \(-0.105630\pi\) |
−0.956373 | + | 0.292148i | \(0.905630\pi\) | |||||||
\(632\) | −9.04508 | − | 6.57164i | −0.359794 | − | 0.261406i | ||||
\(633\) | −24.8885 | −0.989231 | ||||||||
\(634\) | 10.5836 | 0.420328 | ||||||||
\(635\) | 11.3435 | − | 34.9116i | 0.450151 | − | 1.38542i | ||||
\(636\) | −5.61803 | − | 17.2905i | −0.222770 | − | 0.685614i | ||||
\(637\) | −0.763932 | − | 2.35114i | −0.0302681 | − | 0.0931556i | ||||
\(638\) | −10.7918 | + | 18.2088i | −0.427251 | + | 0.720895i | ||||
\(639\) | −3.59017 | + | 11.0494i | −0.142025 | + | 0.437108i | ||||
\(640\) | 7.86475 | − | 24.2052i | 0.310881 | − | 0.956794i | ||||
\(641\) | 37.2877 | − | 27.0911i | 1.47278 | − | 1.07003i | 0.492980 | − | 0.870041i | \(-0.335908\pi\) |
0.979797 | − | 0.199994i | \(-0.0640923\pi\) | |||||||
\(642\) | 1.48936 | + | 4.58377i | 0.0587802 | + | 0.180907i | ||||
\(643\) | 32.2426 | + | 23.4257i | 1.27153 | + | 0.923818i | 0.999262 | − | 0.0384051i | \(-0.0122277\pi\) |
0.272264 | + | 0.962223i | \(0.412228\pi\) | |||||||
\(644\) | −23.5623 | −0.928485 | ||||||||
\(645\) | 4.14590 | + | 12.7598i | 0.163245 | + | 0.502415i | ||||
\(646\) | 3.61803 | − | 11.1352i | 0.142350 | − | 0.438107i | ||||
\(647\) | −10.0344 | −0.394495 | −0.197247 | − | 0.980354i | \(-0.563200\pi\) | ||||
−0.197247 | + | 0.980354i | \(0.563200\pi\) | |||||||
\(648\) | −0.690983 | + | 2.12663i | −0.0271444 | + | 0.0835418i | ||||
\(649\) | −4.47214 | − | 47.7899i | −0.175547 | − | 1.87592i | ||||
\(650\) | 3.09017 | + | 2.24514i | 0.121206 | + | 0.0880616i | ||||
\(651\) | 13.9894 | − | 10.1639i | 0.548286 | − | 0.398353i | ||||
\(652\) | −21.9443 | −0.859404 | ||||||||
\(653\) | −0.708204 | + | 0.514540i | −0.0277142 | + | 0.0201355i | −0.601556 | − | 0.798831i | \(-0.705452\pi\) |
0.573842 | + | 0.818966i | \(0.305452\pi\) | |||||||
\(654\) | 0.326238 | + | 1.00406i | 0.0127569 | + | 0.0392617i | ||||
\(655\) | −11.0172 | + | 33.9075i | −0.430478 | + | 1.32488i | ||||
\(656\) | −6.35410 | − | 19.5559i | −0.248086 | − | 0.763530i | ||||
\(657\) | −3.57295 | − | 10.9964i | −0.139394 | − | 0.429011i | ||||
\(658\) | 0.624612 | − | 1.92236i | 0.0243499 | − | 0.0749413i | ||||
\(659\) | 9.96149 | + | 30.6583i | 0.388045 | + | 1.19428i | 0.934247 | + | 0.356626i | \(0.116073\pi\) |
−0.546203 | + | 0.837653i | \(0.683927\pi\) | |||||||
\(660\) | −6.11803 | + | 10.3229i | −0.238144 | + | 0.401817i | ||||
\(661\) | −12.7984 | + | 39.3893i | −0.497799 | + | 1.53207i | 0.314750 | + | 0.949175i | \(0.398079\pi\) |
−0.812549 | + | 0.582893i | \(0.801921\pi\) | |||||||
\(662\) | 3.37132 | + | 2.44941i | 0.131030 | + | 0.0951990i | ||||
\(663\) | 5.23607 | − | 3.80423i | 0.203352 | − | 0.147744i | ||||
\(664\) | −13.7812 | − | 10.0126i | −0.534812 | − | 0.388564i | ||||
\(665\) | −7.50000 | + | 23.0826i | −0.290838 | + | 0.895106i | ||||
\(666\) | −0.409830 | + | 1.26133i | −0.0158806 | + | 0.0488754i | ||||
\(667\) | 15.4894 | + | 47.6713i | 0.599750 | + | 1.84584i | ||||
\(668\) | −11.1631 | − | 34.3565i | −0.431914 | − | 1.32929i | ||||
\(669\) | 6.92705 | − | 21.3193i | 0.267815 | − | 0.824251i | ||||
\(670\) | 4.14590 | 0.160170 | ||||||||
\(671\) | 10.3156 | + | 11.7229i | 0.398229 | + | 0.452559i | ||||
\(672\) | −13.6353 | − | 9.90659i | −0.525991 | − | 0.382155i | ||||
\(673\) | −13.4721 | − | 41.4630i | −0.519313 | − | 1.59828i | −0.775295 | − | 0.631599i | \(-0.782399\pi\) |
0.255983 | − | 0.966681i | \(-0.417601\pi\) | |||||||
\(674\) | 1.70163 | + | 5.23707i | 0.0655442 | + | 0.201724i | ||||
\(675\) | −1.54508 | − | 4.75528i | −0.0594703 | − | 0.183031i | ||||
\(676\) | −15.0172 | − | 10.9106i | −0.577585 | − | 0.419640i | ||||
\(677\) | −7.14590 | + | 5.19180i | −0.274639 | + | 0.199537i | −0.716576 | − | 0.697509i | \(-0.754292\pi\) |
0.441937 | + | 0.897046i | \(0.354292\pi\) | |||||||
\(678\) | 6.09017 | − | 4.42477i | 0.233892 | − | 0.169932i | ||||
\(679\) | −10.6353 | + | 32.7319i | −0.408144 | + | 1.25614i | ||||
\(680\) | −26.1803 | −1.00397 | ||||||||
\(681\) | 10.6631 | − | 7.74721i | 0.408612 | − | 0.296874i | ||||
\(682\) | −1.10081 | − | 11.7634i | −0.0421523 | − | 0.450445i | ||||
\(683\) | 21.3262 | − | 15.4944i | 0.816026 | − | 0.592877i | −0.0995455 | − | 0.995033i | \(-0.531739\pi\) |
0.915571 | + | 0.402156i | \(0.131739\pi\) | |||||||
\(684\) | −4.73607 | − | 3.44095i | −0.181088 | − | 0.131568i | ||||
\(685\) | −9.69756 | − | 29.8460i | −0.370525 | − | 1.14036i | ||||
\(686\) | −7.50000 | − | 5.44907i | −0.286351 | − | 0.208046i | ||||
\(687\) | 7.72542 | − | 23.7764i | 0.294743 | − | 0.907127i | ||||
\(688\) | 3.43769 | − | 10.5801i | 0.131061 | − | 0.403364i | ||||
\(689\) | −11.2361 | − | 8.16348i | −0.428060 | − | 0.311004i | ||||
\(690\) | −2.07295 | − | 6.37988i | −0.0789158 | − | 0.242878i | ||||
\(691\) | −13.1631 | − | 9.56357i | −0.500749 | − | 0.363815i | 0.308554 | − | 0.951207i | \(-0.400155\pi\) |
−0.809303 | + | 0.587392i | \(0.800155\pi\) | |||||||
\(692\) | 7.16312 | − | 5.20431i | 0.272301 | − | 0.197838i | ||||
\(693\) | 6.57295 | + | 7.46969i | 0.249686 | + | 0.283750i | ||||
\(694\) | 8.37132 | − | 6.08212i | 0.317771 | − | 0.230874i | ||||
\(695\) | −8.81966 | −0.334549 | ||||||||
\(696\) | −7.13525 | + | 21.9601i | −0.270461 | + | 0.832394i | ||||
\(697\) | −46.9787 | + | 34.1320i | −1.77945 | + | 1.29284i | ||||
\(698\) | 2.33688 | − | 1.69784i | 0.0884523 | − | 0.0642643i | ||||
\(699\) | −1.85410 | − | 1.34708i | −0.0701286 | − | 0.0509514i | ||||
\(700\) | 24.2705 | 0.917339 | ||||||||
\(701\) | 0.517221 | + | 1.59184i | 0.0195352 | + | 0.0601231i | 0.960349 | − | 0.278801i | \(-0.0899370\pi\) |
−0.940814 | + | 0.338924i | \(0.889937\pi\) | |||||||
\(702\) | 0.236068 | + | 0.726543i | 0.00890981 | + | 0.0274216i | ||||
\(703\) | −6.28115 | − | 4.56352i | −0.236898 | − | 0.172117i | ||||
\(704\) | 0.718847 | − | 0.310271i | 0.0270926 | − | 0.0116938i | ||||
\(705\) | −2.43769 | −0.0918089 | ||||||||
\(706\) | −5.46149 | + | 16.8087i | −0.205546 | + | 0.632606i | ||||
\(707\) | −10.6353 | − | 32.7319i | −0.399980 | − | 1.23101i | ||||
\(708\) | −7.23607 | − | 22.2703i | −0.271948 | − | 0.836970i | ||||
\(709\) | 8.12868 | − | 25.0175i | 0.305279 | − | 0.939552i | −0.674294 | − | 0.738463i | \(-0.735552\pi\) |
0.979573 | − | 0.201089i | \(-0.0644480\pi\) | |||||||
\(710\) | 4.96149 | − | 15.2699i | 0.186202 | − | 0.573069i | ||||
\(711\) | 4.04508 | + | 2.93893i | 0.151703 | + | 0.110218i | ||||
\(712\) | 4.04508 | − | 2.93893i | 0.151596 | − | 0.110141i | ||||
\(713\) | −22.6353 | − | 16.4455i | −0.847697 | − | 0.615888i | ||||
\(714\) | −3.00000 | + | 9.23305i | −0.112272 | + | 0.345538i | ||||
\(715\) | 0.854102 | + | 9.12705i | 0.0319416 | + | 0.341332i | ||||
\(716\) | −11.0172 | − | 33.9075i | −0.411733 | − | 1.26718i | ||||
\(717\) | −3.25329 | + | 10.0126i | −0.121496 | + | 0.373927i | ||||
\(718\) | −2.56231 | − | 7.88597i | −0.0956244 | − | 0.294302i | ||||
\(719\) | −5.52786 | − | 17.0130i | −0.206155 | − | 0.634478i | −0.999664 | − | 0.0259205i | \(-0.991748\pi\) |
0.793509 | − | 0.608558i | \(-0.208252\pi\) | |||||||
\(720\) | −1.28115 | + | 3.94298i | −0.0477458 | + | 0.146946i | ||||
\(721\) | 5.78115 | + | 17.7926i | 0.215301 | + | 0.662630i | ||||
\(722\) | 2.95492 | − | 2.14687i | 0.109971 | − | 0.0798983i | ||||
\(723\) | 0.562306 | 0.0209124 | ||||||||
\(724\) | 16.3992 | − | 11.9147i | 0.609471 | − | 0.442807i | ||||
\(725\) | −15.9549 | − | 49.1042i | −0.592551 | − | 1.82368i | ||||
\(726\) | 6.68034 | − | 1.26133i | 0.247931 | − | 0.0468122i | ||||
\(727\) | −8.75329 | + | 26.9399i | −0.324642 | + | 0.999144i | 0.646961 | + | 0.762523i | \(0.276040\pi\) |
−0.971602 | + | 0.236620i | \(0.923960\pi\) | |||||||
\(728\) | −8.29180 | −0.307314 | ||||||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 4.93769 | + | 15.1967i | 0.182752 | + | 0.562454i | ||||
\(731\) | −31.4164 | −1.16198 | ||||||||
\(732\) | 6.16312 | + | 4.47777i | 0.227795 | + | 0.165503i | ||||
\(733\) | 6.26393 | + | 19.2784i | 0.231364 | + | 0.712064i | 0.997583 | + | 0.0694849i | \(0.0221356\pi\) |
−0.766219 | + | 0.642579i | \(0.777864\pi\) | |||||||
\(734\) | 9.91641 | − | 7.20469i | 0.366021 | − | 0.265930i | ||||
\(735\) | 1.38197 | − | 4.25325i | 0.0509746 | − | 0.156884i | ||||
\(736\) | −8.42705 | + | 25.9358i | −0.310625 | + | 0.956006i | ||||
\(737\) | 6.57295 | + | 7.46969i | 0.242118 | + | 0.275150i | ||||
\(738\) | −2.11803 | − | 6.51864i | −0.0779659 | − | 0.239954i | ||||
\(739\) | −0.489357 | − | 1.50609i | −0.0180013 | − | 0.0554023i | 0.941652 | − | 0.336587i | \(-0.109273\pi\) |
−0.959654 | + | 0.281185i | \(0.909273\pi\) | |||||||
\(740\) | −2.39919 | + | 7.38394i | −0.0881959 | + | 0.271439i | ||||
\(741\) | −4.47214 | −0.164288 | ||||||||
\(742\) | 20.8328 | 0.764797 | ||||||||
\(743\) | 25.3713 | + | 18.4333i | 0.930784 | + | 0.676254i | 0.946185 | − | 0.323628i | \(-0.104902\pi\) |
−0.0154010 | + | 0.999881i | \(0.504902\pi\) | |||||||
\(744\) | −3.98278 | − | 12.2577i | −0.146016 | − | 0.449390i | ||||
\(745\) | 14.2705 | 0.522831 | ||||||||
\(746\) | −11.7426 | −0.429929 | ||||||||
\(747\) | 6.16312 | + | 4.47777i | 0.225497 | + | 0.163833i | ||||
\(748\) | −18.5623 | − | 21.0948i | −0.678705 | − | 0.771301i | ||||
\(749\) | 23.3951 | 0.854839 | ||||||||
\(750\) | 2.13525 | + | 6.57164i | 0.0779685 | + | 0.239962i | ||||
\(751\) | 11.4336 | + | 35.1891i | 0.417219 | + | 1.28407i | 0.910251 | + | 0.414057i | \(0.135889\pi\) |
−0.493032 | + | 0.870011i | \(0.664111\pi\) | |||||||
\(752\) | 1.63525 | + | 1.18808i | 0.0596316 | + | 0.0433249i | ||||
\(753\) | 7.30902 | + | 22.4948i | 0.266355 | + | 0.819758i | ||||
\(754\) | 2.43769 | + | 7.50245i | 0.0887756 | + | 0.273223i | ||||
\(755\) | 7.07295 | + | 5.13880i | 0.257411 | + | 0.187020i | ||||
\(756\) | 3.92705 | + | 2.85317i | 0.142825 | + | 0.103769i | ||||
\(757\) | −23.5902 | + | 17.1393i | −0.857399 | + | 0.622937i | −0.927176 | − | 0.374626i | \(-0.877771\pi\) |
0.0697769 | + | 0.997563i | \(0.477771\pi\) | |||||||
\(758\) | 15.9164 | − | 11.5639i | 0.578110 | − | 0.420021i | ||||
\(759\) | 8.20820 | − | 13.8496i | 0.297939 | − | 0.502708i | ||||
\(760\) | 14.6353 | + | 10.6331i | 0.530876 | + | 0.385704i | ||||
\(761\) | 7.36475 | + | 22.6664i | 0.266972 | + | 0.821655i | 0.991233 | + | 0.132129i | \(0.0421812\pi\) |
−0.724261 | + | 0.689526i | \(0.757819\pi\) | |||||||
\(762\) | −8.20820 | + | 5.96361i | −0.297352 | + | 0.216039i | ||||
\(763\) | 5.12461 | 0.185523 | ||||||||
\(764\) | 0.809017 | − | 0.587785i | 0.0292692 | − | 0.0212653i | ||||
\(765\) | 11.7082 | 0.423311 | ||||||||
\(766\) | 1.14590 | 0.0414030 | ||||||||
\(767\) | −14.4721 | − | 10.5146i | −0.522559 | − | 0.379661i | ||||
\(768\) | −5.30902 | + | 3.85723i | −0.191573 | + | 0.139186i | ||||
\(769\) | 5.00000 | − | 3.63271i | 0.180305 | − | 0.130999i | −0.493972 | − | 0.869478i | \(-0.664456\pi\) |
0.674277 | + | 0.738479i | \(0.264456\pi\) | |||||||
\(770\) | −9.08359 | − | 10.3229i | −0.327350 | − | 0.372010i | ||||
\(771\) | −14.5623 | − | 10.5801i | −0.524449 | − | 0.381034i | ||||
\(772\) | −15.2361 | −0.548358 | ||||||||
\(773\) | −32.8673 | −1.18215 | −0.591077 | − | 0.806615i | \(-0.701297\pi\) | ||||
−0.591077 | + | 0.806615i | \(0.701297\pi\) | |||||||
\(774\) | 1.14590 | − | 3.52671i | 0.0411885 | − | 0.126765i | ||||
\(775\) | 23.3156 | + | 16.9398i | 0.837521 | + | 0.608495i | ||||
\(776\) | 20.7533 | + | 15.0781i | 0.745000 | + | 0.541274i | ||||
\(777\) | 5.20820 | + | 3.78398i | 0.186843 | + | 0.135750i | ||||
\(778\) | −1.87132 | + | 5.75934i | −0.0670902 | + | 0.206482i | ||||
\(779\) | 40.1246 | 1.43761 | ||||||||
\(780\) | 1.38197 | + | 4.25325i | 0.0494823 | + | 0.152291i | ||||
\(781\) | 35.3779 | − | 15.2699i | 1.26592 | − | 0.546400i | ||||
\(782\) | 15.7082 | 0.561724 | ||||||||
\(783\) | 3.19098 | − | 9.82084i | 0.114036 | − | 0.350968i | ||||
\(784\) | −3.00000 | + | 2.17963i | −0.107143 | + | 0.0778438i | ||||
\(785\) | −10.0623 | − | 7.31069i | −0.359139 | − | 0.260930i | ||||
\(786\) | 7.97214 | − | 5.79210i | 0.284357 | − | 0.206597i | ||||
\(787\) | −1.41641 | + | 4.35926i | −0.0504895 | + | 0.155391i | −0.973122 | − | 0.230289i | \(-0.926033\pi\) |
0.922633 | + | 0.385679i | \(0.126033\pi\) | |||||||
\(788\) | −15.7984 | −0.562794 | ||||||||
\(789\) | −4.94427 | −0.176021 | ||||||||
\(790\) | −5.59017 | − | 4.06150i | −0.198889 | − | 0.144502i | ||||
\(791\) | −11.2918 | − | 34.7526i | −0.401490 | − | 1.23566i | ||||
\(792\) | 6.80902 | − | 2.93893i | 0.241948 | − | 0.104430i | ||||
\(793\) | 5.81966 | 0.206662 | ||||||||
\(794\) | −2.34346 | + | 7.21242i | −0.0831662 | + | 0.255959i | ||||
\(795\) | −7.76393 | − | 23.8949i | −0.275358 | − | 0.847466i | ||||
\(796\) | 19.3713 | − | 14.0741i | 0.686598 | − | 0.498843i | ||||
\(797\) | 3.87132 | + | 11.9147i | 0.137129 | + | 0.422041i | 0.995915 | − | 0.0902942i | \(-0.0287807\pi\) |
−0.858786 | + | 0.512335i | \(0.828781\pi\) | |||||||
\(798\) | 5.42705 | − | 3.94298i | 0.192116 | − | 0.139580i | ||||
\(799\) | 1.76393 | − | 5.42882i | 0.0624034 | − | 0.192058i | ||||
\(800\) | 8.68034 | − | 26.7153i | 0.306896 | − | 0.944530i | ||||
\(801\) | −1.80902 | + | 1.31433i | −0.0639185 | + | 0.0464395i | ||||
\(802\) | −1.91641 | + | 5.89810i | −0.0676707 | + | 0.208269i | ||||
\(803\) | −19.5517 | + | 32.9892i | −0.689963 | + | 1.16416i | ||||
\(804\) | 3.92705 | + | 2.85317i | 0.138496 | + | 0.100624i | ||||
\(805\) | −32.5623 | −1.14767 | ||||||||
\(806\) | −3.56231 | − | 2.58817i | −0.125477 | − | 0.0911643i | ||||
\(807\) | −3.25329 | + | 10.0126i | −0.114521 | + | 0.352460i | ||||
\(808\) | −25.6525 | −0.902451 | ||||||||
\(809\) | 12.0344 | − | 37.0382i | 0.423108 | − | 1.30219i | −0.481685 | − | 0.876344i | \(-0.659975\pi\) |
0.904794 | − | 0.425850i | \(-0.140025\pi\) | |||||||
\(810\) | −0.427051 | + | 1.31433i | −0.0150050 | + | 0.0461808i | ||||
\(811\) | 22.4508 | 0.788356 | 0.394178 | − | 0.919034i | \(-0.371029\pi\) | ||||
0.394178 | + | 0.919034i | \(0.371029\pi\) | |||||||
\(812\) | 40.5517 | + | 29.4625i | 1.42308 | + | 1.03393i | ||||
\(813\) | −5.61803 | − | 17.2905i | −0.197033 | − | 0.606405i | ||||
\(814\) | 4.03851 | − | 1.74311i | 0.141550 | − | 0.0610960i | ||||
\(815\) | −30.3262 | −1.06228 | ||||||||
\(816\) | −7.85410 | − | 5.70634i | −0.274949 | − | 0.199762i | ||||
\(817\) | 17.5623 | + | 12.7598i | 0.614427 | + | 0.446408i | ||||
\(818\) | −0.993422 | + | 3.05744i | −0.0347342 | + | 0.106901i | ||||
\(819\) | 3.70820 | 0.129575 | ||||||||
\(820\) | −12.3992 | − | 38.1608i | −0.432998 | − | 1.33263i | ||||
\(821\) | 36.2705 | − | 26.3521i | 1.26585 | − | 0.919694i | 0.266820 | − | 0.963746i | \(-0.414027\pi\) |
0.999029 | + | 0.0440528i | \(0.0140270\pi\) | |||||||
\(822\) | −2.68034 | + | 8.24924i | −0.0934876 | + | 0.287725i | ||||
\(823\) | −1.01064 | − | 3.11044i | −0.0352288 | − | 0.108423i | 0.931896 | − | 0.362726i | \(-0.118154\pi\) |
−0.967125 | + | 0.254303i | \(0.918154\pi\) | |||||||
\(824\) | 13.9443 | 0.485772 | ||||||||
\(825\) | −8.45492 | + | 14.2658i | −0.294362 | + | 0.496673i | ||||
\(826\) | 26.8328 | 0.933633 | ||||||||
\(827\) | −10.9656 | − | 33.7485i | −0.381310 | − | 1.17355i | −0.939122 | − | 0.343584i | \(-0.888359\pi\) |
0.557812 | − | 0.829967i | \(-0.311641\pi\) | |||||||
\(828\) | 2.42705 | − | 7.46969i | 0.0843459 | − | 0.259590i | ||||
\(829\) | −28.8435 | + | 20.9560i | −1.00177 | + | 0.727832i | −0.962468 | − | 0.271395i | \(-0.912515\pi\) |
−0.0393067 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(830\) | −8.51722 | − | 6.18812i | −0.295637 | − | 0.214793i | ||||
\(831\) | −20.2148 | −0.701243 | ||||||||
\(832\) | 0.0901699 | − | 0.277515i | 0.00312608 | − | 0.00962109i | ||||
\(833\) | 8.47214 | + | 6.15537i | 0.293542 | + | 0.213271i | ||||
\(834\) | 1.97214 | + | 1.43284i | 0.0682895 | + | 0.0496152i | ||||
\(835\) | −15.4271 | − | 47.4796i | −0.533875 | − | 1.64310i | ||||
\(836\) | 1.80902 | + | 19.3314i | 0.0625662 | + | 0.668590i | ||||
\(837\) | 1.78115 | + | 5.48183i | 0.0615657 | + | 0.189480i | ||||
\(838\) | −10.6910 | − | 7.76745i | −0.369314 | − | 0.268322i | ||||
\(839\) | 53.8673 | 1.85970 | 0.929852 | − | 0.367933i | \(-0.119935\pi\) | ||||
0.929852 | + | 0.367933i | \(0.119935\pi\) | |||||||
\(840\) | −12.1353 | − | 8.81678i | −0.418706 | − | 0.304208i | ||||
\(841\) | 23.9894 | − | 73.8316i | 0.827219 | − | 2.54592i | ||||
\(842\) | 9.32624 | 0.321403 | ||||||||
\(843\) | 7.83688 | − | 24.1194i | 0.269917 | − | 0.830718i | ||||
\(844\) | 32.5795 | + | 23.6704i | 1.12143 | + | 0.814769i | ||||
\(845\) | −20.7533 | − | 15.0781i | −0.713935 | − | 0.518704i | ||||
\(846\) | 0.545085 | + | 0.396027i | 0.0187404 | + | 0.0136157i | ||||
\(847\) | 4.19756 | − | 32.7319i | 0.144230 | − | 1.12468i | ||||
\(848\) | −6.43769 | + | 19.8132i | −0.221071 | + | 0.680388i | ||||
\(849\) | −0.472136 | + | 0.343027i | −0.0162037 | + | 0.0117727i | ||||
\(850\) | −16.1803 | −0.554981 | ||||||||
\(851\) | 3.21885 | − | 9.90659i | 0.110341 | − | 0.339594i | ||||
\(852\) | 15.2082 | − | 11.0494i | 0.521024 | − | 0.378546i | ||||
\(853\) | 2.70820 | + | 8.33499i | 0.0927271 | + | 0.285385i | 0.986655 | − | 0.162827i | \(-0.0520611\pi\) |
−0.893928 | + | 0.448211i | \(0.852061\pi\) | |||||||
\(854\) | −7.06231 | + | 5.13107i | −0.241667 | + | 0.175581i | ||||
\(855\) | −6.54508 | − | 4.75528i | −0.223837 | − | 0.162627i | ||||
\(856\) | 5.38854 | − | 16.5842i | 0.184177 | − | 0.566837i | ||||
\(857\) | 10.4164 | 0.355818 | 0.177909 | − | 0.984047i | \(-0.443067\pi\) | ||||
0.177909 | + | 0.984047i | \(0.443067\pi\) | |||||||
\(858\) | 1.29180 | − | 2.17963i | 0.0441012 | − | 0.0744113i | ||||
\(859\) | 6.18034 | + | 19.0211i | 0.210870 | + | 0.648993i | 0.999421 | + | 0.0340227i | \(0.0108319\pi\) |
−0.788551 | + | 0.614970i | \(0.789168\pi\) | |||||||
\(860\) | 6.70820 | − | 20.6457i | 0.228748 | − | 0.704014i | ||||
\(861\) | −33.2705 | −1.13386 | ||||||||
\(862\) | −14.6180 | −0.497892 | ||||||||
\(863\) | −8.10739 | + | 24.9520i | −0.275979 | + | 0.849375i | 0.712980 | + | 0.701184i | \(0.247345\pi\) |
−0.988959 | + | 0.148191i | \(0.952655\pi\) | |||||||
\(864\) | 4.54508 | − | 3.30220i | 0.154627 | − | 0.112343i | ||||
\(865\) | 9.89919 | − | 7.19218i | 0.336582 | − | 0.244541i | ||||
\(866\) | −13.6525 | + | 9.91910i | −0.463930 | + | 0.337065i | ||||
\(867\) | −3.21885 | + | 9.90659i | −0.109318 | + | 0.336446i | ||||
\(868\) | −27.9787 | −0.949659 | ||||||||
\(869\) | −1.54508 | − | 16.5110i | −0.0524134 | − | 0.560097i | ||||
\(870\) | −4.40983 | + | 13.5721i | −0.149507 | + | 0.460136i | ||||
\(871\) | 3.70820 | 0.125648 | ||||||||
\(872\) | 1.18034 | − | 3.63271i | 0.0399714 | − | 0.123019i | ||||
\(873\) | −9.28115 | − | 6.74315i | −0.314119 | − | 0.228221i | ||||
\(874\) | −8.78115 | − | 6.37988i | −0.297027 | − | 0.215803i | ||||
\(875\) | 33.5410 | 1.13389 | ||||||||
\(876\) | −5.78115 | + | 17.7926i | −0.195327 | + | 0.601155i | ||||
\(877\) | −13.9787 | −0.472028 | −0.236014 | − | 0.971750i | \(-0.575841\pi\) | ||||
−0.236014 | + | 0.971750i | \(0.575841\pi\) | |||||||
\(878\) | −17.6869 | −0.596905 | ||||||||
\(879\) | −4.88197 | − | 3.54696i | −0.164665 | − | 0.119636i | ||||
\(880\) | 12.6246 | − | 5.44907i | 0.425576 | − | 0.183688i | ||||
\(881\) | −23.1631 | + | 16.8290i | −0.780385 | + | 0.566983i | −0.905095 | − | 0.425210i | \(-0.860200\pi\) |
0.124709 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(882\) | −1.00000 | + | 0.726543i | −0.0336718 | + | 0.0244640i | ||||
\(883\) | 12.8090 | + | 9.30630i | 0.431058 | + | 0.313182i | 0.782072 | − | 0.623188i | \(-0.214163\pi\) |
−0.351014 | + | 0.936370i | \(0.614163\pi\) | |||||||
\(884\) | −10.4721 | −0.352216 | ||||||||
\(885\) | −10.0000 | − | 30.7768i | −0.336146 | − | 1.03455i | ||||
\(886\) | −10.6631 | + | 7.74721i | −0.358234 | + | 0.260273i | ||||
\(887\) | −47.3951 | −1.59137 | −0.795686 | − | 0.605709i | \(-0.792890\pi\) | ||||
−0.795686 | + | 0.605709i | \(0.792890\pi\) | |||||||
\(888\) | 3.88197 | − | 2.82041i | 0.130270 | − | 0.0946469i | ||||
\(889\) | 15.2188 | + | 46.8388i | 0.510424 | + | 1.57092i | ||||
\(890\) | 2.50000 | − | 1.81636i | 0.0838002 | − | 0.0608844i | ||||
\(891\) | −3.04508 | + | 1.31433i | −0.102014 | + | 0.0440316i | ||||
\(892\) | −29.3435 | + | 21.3193i | −0.982492 | + | 0.713822i | ||||
\(893\) | −3.19098 | + | 2.31838i | −0.106782 | + | 0.0775818i | ||||
\(894\) | −3.19098 | − | 2.31838i | −0.106722 | − | 0.0775384i | ||||
\(895\) | −15.2254 | − | 46.8590i | −0.508930 | − | 1.56632i | ||||
\(896\) | 10.5517 | + | 32.4747i | 0.352506 | + | 1.08490i | ||||
\(897\) | −1.85410 | − | 5.70634i | −0.0619067 | − | 0.190529i | ||||
\(898\) | −10.2639 | − | 7.45718i | −0.342512 | − | 0.248849i | ||||
\(899\) | 18.3926 | + | 56.6066i | 0.613428 | + | 1.88794i | ||||
\(900\) | −2.50000 | + | 7.69421i | −0.0833333 | + | 0.256474i | ||||
\(901\) | 58.8328 | 1.96001 | ||||||||
\(902\) | −11.5902 | + | 19.5559i | −0.385910 | + | 0.651141i | ||||
\(903\) | −14.5623 | − | 10.5801i | −0.484603 | − | 0.352085i | ||||
\(904\) | −27.2361 | −0.905858 | ||||||||
\(905\) | 22.6631 | − | 16.4657i | 0.753348 | − | 0.547339i | ||||
\(906\) | −0.746711 | − | 2.29814i | −0.0248078 | − | 0.0763506i | ||||
\(907\) | −39.6074 | − | 28.7765i | −1.31514 | − | 0.955506i | −0.999979 | − | 0.00646883i | \(-0.997941\pi\) |
−0.315163 | − | 0.949038i | \(-0.602059\pi\) | |||||||
\(908\) | −21.3262 | −0.707736 | ||||||||
\(909\) | 11.4721 | 0.380507 | ||||||||
\(910\) | −5.12461 | −0.169879 | ||||||||
\(911\) | −1.22949 | − | 3.78398i | −0.0407348 | − | 0.125369i | 0.928621 | − | 0.371030i | \(-0.120995\pi\) |
−0.969356 | + | 0.245661i | \(0.920995\pi\) | |||||||
\(912\) | 2.07295 | + | 6.37988i | 0.0686422 | + | 0.211259i | ||||
\(913\) | −2.35410 | − | 25.1563i | −0.0779094 | − | 0.832550i | ||||
\(914\) | 1.60081 | − | 4.92680i | 0.0529502 | − | 0.162964i | ||||
\(915\) | 8.51722 | + | 6.18812i | 0.281571 | + | 0.204573i | ||||
\(916\) | −32.7254 | + | 23.7764i | −1.08128 | + | 0.785595i | ||||
\(917\) | −14.7812 | − | 45.4917i | −0.488117 | − | 1.50227i | ||||
\(918\) | −2.61803 | − | 1.90211i | −0.0864080 | − | 0.0627791i | ||||
\(919\) | 6.70820 | 0.221283 | 0.110642 | − | 0.993860i | \(-0.464709\pi\) | ||||
0.110642 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(920\) | −7.50000 | + | 23.0826i | −0.247268 | + | 0.761012i | ||||
\(921\) | −0.517221 | + | 1.59184i | −0.0170430 | + | 0.0524530i | ||||
\(922\) | 6.15905 | 0.202838 | ||||||||
\(923\) | 4.43769 | − | 13.6578i | 0.146068 | − | 0.449553i | ||||
\(924\) | −1.50000 | − | 16.0292i | −0.0493464 | − | 0.527322i | ||||
\(925\) | −3.31559 | + | 10.2044i | −0.109016 | + | 0.335517i | ||||
\(926\) | 13.7082 | − | 9.95959i | 0.450480 | − | 0.327293i | ||||
\(927\) | −6.23607 | −0.204819 | ||||||||
\(928\) | 46.9336 | − | 34.0993i | 1.54067 | − | 1.11936i | ||||
\(929\) | 7.09675 | + | 21.8415i | 0.232837 | + | 0.716598i | 0.997401 | + | 0.0720503i | \(0.0229542\pi\) |
−0.764564 | + | 0.644548i | \(0.777046\pi\) | |||||||
\(930\) | −2.46149 | − | 7.57570i | −0.0807155 | − | 0.248417i | ||||
\(931\) | −2.23607 | − | 6.88191i | −0.0732842 | − | 0.225545i | ||||
\(932\) | 1.14590 | + | 3.52671i | 0.0375351 | + | 0.115521i | ||||
\(933\) | −2.59017 | + | 7.97172i | −0.0847984 | + | 0.260983i | ||||
\(934\) | −3.63932 | − | 11.2007i | −0.119082 | − | 0.366497i | ||||
\(935\) | −25.6525 | − | 29.1522i | −0.838926 | − | 0.953380i | ||||
\(936\) | 0.854102 | − | 2.62866i | 0.0279172 | − | 0.0859203i | ||||
\(937\) | −12.5729 | − | 9.13478i | −0.410740 | − | 0.298420i | 0.363161 | − | 0.931726i | \(-0.381697\pi\) |
−0.773901 | + | 0.633306i | \(0.781697\pi\) | |||||||
\(938\) | −4.50000 | + | 3.26944i | −0.146930 | + | 0.106751i | ||||
\(939\) | 9.00000 | + | 6.53888i | 0.293704 | + | 0.213388i | ||||
\(940\) | 3.19098 | + | 2.31838i | 0.104078 | + | 0.0756174i | ||||
\(941\) | −5.56231 | + | 17.1190i | −0.181326 | + | 0.558064i | −0.999866 | − | 0.0163859i | \(-0.994784\pi\) |
0.818540 | + | 0.574450i | \(0.194784\pi\) | |||||||
\(942\) | 1.06231 | + | 3.26944i | 0.0346118 | + | 0.106524i | ||||
\(943\) | 16.6353 | + | 51.1981i | 0.541718 | + | 1.66724i | ||||
\(944\) | −8.29180 | + | 25.5195i | −0.269875 | + | 0.830590i | ||||
\(945\) | 5.42705 | + | 3.94298i | 0.176542 | + | 0.128265i | ||||
\(946\) | −11.2918 | + | 4.87380i | −0.367128 | + | 0.158461i | ||||
\(947\) | −9.70820 | − | 7.05342i | −0.315474 | − | 0.229205i | 0.418768 | − | 0.908093i | \(-0.362462\pi\) |
−0.734242 | + | 0.678888i | \(0.762462\pi\) | |||||||
\(948\) | −2.50000 | − | 7.69421i | −0.0811962 | − | 0.249896i | ||||
\(949\) | 4.41641 | + | 13.5923i | 0.143363 | + | 0.441225i | ||||
\(950\) | 9.04508 | + | 6.57164i | 0.293461 | + | 0.213212i | ||||
\(951\) | 13.8541 | + | 10.0656i | 0.449250 | + | 0.326399i | ||||
\(952\) | 28.4164 | − | 20.6457i | 0.920981 | − | 0.669132i | ||||
\(953\) | −29.6525 | + | 21.5438i | −0.960538 | + | 0.697872i | −0.953276 | − | 0.302102i | \(-0.902312\pi\) |
−0.00726230 | + | 0.999974i | \(0.502312\pi\) | |||||||
\(954\) | −2.14590 | + | 6.60440i | −0.0694760 | + | 0.213825i | ||||
\(955\) | 1.11803 | − | 0.812299i | 0.0361787 | − | 0.0262854i | ||||
\(956\) | 13.7812 | − | 10.0126i | 0.445714 | − | 0.323830i | ||||
\(957\) | −31.4443 | + | 13.5721i | −1.01645 | + | 0.438722i | ||||
\(958\) | −6.54508 | + | 4.75528i | −0.211462 | + | 0.153636i | ||||
\(959\) | 34.0623 | + | 24.7477i | 1.09993 | + | 0.799145i | ||||
\(960\) | 0.427051 | − | 0.310271i | 0.0137830 | − | 0.0100139i | ||||
\(961\) | −1.79837 | − | 1.30660i | −0.0580121 | − | 0.0421482i | ||||
\(962\) | 0.506578 | − | 1.55909i | 0.0163327 | − | 0.0502670i | ||||
\(963\) | −2.40983 | + | 7.41669i | −0.0776557 | + | 0.239000i | ||||
\(964\) | −0.736068 | − | 0.534785i | −0.0237072 | − | 0.0172243i | ||||
\(965\) | −21.0557 | −0.677808 | ||||||||
\(966\) | 7.28115 | + | 5.29007i | 0.234267 | + | 0.170205i | ||||
\(967\) | −1.51722 | + | 1.10233i | −0.0487905 | + | 0.0354484i | −0.611913 | − | 0.790925i | \(-0.709600\pi\) |
0.563123 | + | 0.826373i | \(0.309600\pi\) | |||||||
\(968\) | −22.2361 | − | 10.5146i | −0.714694 | − | 0.337953i | ||||
\(969\) | 15.3262 | − | 11.1352i | 0.492350 | − | 0.357713i | ||||
\(970\) | 12.8262 | + | 9.31881i | 0.411826 | + | 0.299209i | ||||
\(971\) | 7.69098 | − | 23.6704i | 0.246815 | − | 0.759620i | −0.748517 | − | 0.663115i | \(-0.769234\pi\) |
0.995333 | − | 0.0965043i | \(-0.0307661\pi\) | |||||||
\(972\) | −1.30902 | + | 0.951057i | −0.0419867 | + | 0.0305052i | ||||
\(973\) | 9.57295 | − | 6.95515i | 0.306895 | − | 0.222972i | ||||
\(974\) | 1.76393 | + | 1.28157i | 0.0565200 | + | 0.0410642i | ||||
\(975\) | 1.90983 | + | 5.87785i | 0.0611635 | + | 0.188242i | ||||
\(976\) | −2.69756 | − | 8.30224i | −0.0863468 | − | 0.265748i | ||||
\(977\) | 13.6459 | + | 41.9978i | 0.436571 | + | 1.34363i | 0.891468 | + | 0.453083i | \(0.149676\pi\) |
−0.454897 | + | 0.890544i | \(0.650324\pi\) | |||||||
\(978\) | 6.78115 | + | 4.92680i | 0.216837 | + | 0.157542i | ||||
\(979\) | 7.23607 | + | 1.62460i | 0.231266 | + | 0.0519224i | ||||
\(980\) | −5.85410 | + | 4.25325i | −0.187002 | + | 0.135865i | ||||
\(981\) | −0.527864 | + | 1.62460i | −0.0168534 | + | 0.0518694i | ||||
\(982\) | 3.33282 | + | 10.2574i | 0.106354 | + | 0.327325i | ||||
\(983\) | −15.5451 | − | 47.8429i | −0.495811 | − | 1.52595i | −0.815689 | − | 0.578491i | \(-0.803642\pi\) |
0.319877 | − | 0.947459i | \(-0.396358\pi\) | |||||||
\(984\) | −7.66312 | + | 23.5847i | −0.244291 | + | 0.751851i | ||||
\(985\) | −21.8328 | −0.695651 | ||||||||
\(986\) | −27.0344 | − | 19.6417i | −0.860952 | − | 0.625518i | ||||
\(987\) | 2.64590 | − | 1.92236i | 0.0842199 | − | 0.0611893i | ||||
\(988\) | 5.85410 | + | 4.25325i | 0.186244 | + | 0.135314i | ||||
\(989\) | −9.00000 | + | 27.6992i | −0.286183 | + | 0.880782i | ||||
\(990\) | 4.20820 | − | 1.81636i | 0.133746 | − | 0.0577276i | ||||
\(991\) | 6.79837 | + | 20.9232i | 0.215957 | + | 0.664649i | 0.999084 | + | 0.0427866i | \(0.0136236\pi\) |
−0.783127 | + | 0.621862i | \(0.786376\pi\) | |||||||
\(992\) | −10.0066 | + | 30.7971i | −0.317709 | + | 0.977808i | ||||
\(993\) | 2.08359 | + | 6.41264i | 0.0661208 | + | 0.203499i | ||||
\(994\) | 6.65654 | + | 20.4867i | 0.211133 | + | 0.649800i | ||||
\(995\) | 26.7705 | − | 19.4499i | 0.848682 | − | 0.616604i | ||||
\(996\) | −3.80902 | − | 11.7229i | −0.120693 | − | 0.371456i | ||||
\(997\) | 33.0795 | − | 24.0337i | 1.04764 | − | 0.761154i | 0.0758770 | − | 0.997117i | \(-0.475824\pi\) |
0.971762 | + | 0.235963i | \(0.0758244\pi\) | |||||||
\(998\) | 15.5279 | 0.491526 | ||||||||
\(999\) | −1.73607 | + | 1.26133i | −0.0549268 | + | 0.0399066i |
(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 | 825.2.o.b.421.1 | yes | 4 | |
11.4 | even | 5 | 825.2.m.a.796.1 | yes | 4 | ||
25.6 | even | 5 | 825.2.m.a.256.1 | ✓ | 4 | ||
275.81 | even | 5 | inner | 825.2.o.b.631.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.m.a.256.1 | ✓ | 4 | 25.6 | even | 5 | ||
825.2.m.a.796.1 | yes | 4 | 11.4 | even | 5 | ||
825.2.o.b.421.1 | yes | 4 | 1.1 | even | 1 | trivial | |
825.2.o.b.631.1 | yes | 4 | 275.81 | even | 5 | inner |