Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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 | 379.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.379 |
Dual form | 462.2.j.c.295.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.427051 | + | 1.31433i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(6\) | −0.309017 | + | 0.951057i | −0.126156 | + | 0.388267i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 1.38197 | 0.437016 | ||||||||
\(11\) | −0.309017 | − | 3.30220i | −0.0931721 | − | 0.995650i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.381966 | − | 1.17557i | −0.105938 | − | 0.326045i | 0.884011 | − | 0.467466i | \(-0.154833\pi\) |
−0.989950 | + | 0.141421i | \(0.954833\pi\) | |||||||
\(14\) | −0.809017 | − | 0.587785i | −0.216219 | − | 0.157092i | ||||
\(15\) | 1.11803 | − | 0.812299i | 0.288675 | − | 0.209735i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 2.35410 | − | 7.24518i | 0.570954 | − | 1.75721i | −0.0786081 | − | 0.996906i | \(-0.525048\pi\) |
0.649562 | − | 0.760309i | \(-0.274952\pi\) | |||||||
\(18\) | 0.809017 | − | 0.587785i | 0.190687 | − | 0.138542i | ||||
\(19\) | −3.30902 | − | 2.40414i | −0.759141 | − | 0.551548i | 0.139506 | − | 0.990221i | \(-0.455449\pi\) |
−0.898647 | + | 0.438673i | \(0.855449\pi\) | |||||||
\(20\) | −0.427051 | − | 1.31433i | −0.0954915 | − | 0.293893i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.04508 | + | 1.31433i | −0.649214 | + | 0.280216i | ||||
\(23\) | −9.32624 | −1.94466 | −0.972328 | − | 0.233622i | \(-0.924942\pi\) | ||||
−0.972328 | + | 0.233622i | \(0.924942\pi\) | |||||||
\(24\) | −0.309017 | − | 0.951057i | −0.0630778 | − | 0.194134i | ||||
\(25\) | 2.50000 | + | 1.81636i | 0.500000 | + | 0.363271i | ||||
\(26\) | −1.00000 | + | 0.726543i | −0.196116 | + | 0.142487i | ||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | −0.309017 | + | 0.951057i | −0.0583987 | + | 0.179733i | ||||
\(29\) | 1.00000 | − | 0.726543i | 0.185695 | − | 0.134916i | −0.491054 | − | 0.871129i | \(-0.663388\pi\) |
0.676749 | + | 0.736214i | \(0.263388\pi\) | |||||||
\(30\) | −1.11803 | − | 0.812299i | −0.204124 | − | 0.148305i | ||||
\(31\) | 0.336881 | + | 1.03681i | 0.0605056 | + | 0.186217i | 0.976741 | − | 0.214424i | \(-0.0687874\pi\) |
−0.916235 | + | 0.400641i | \(0.868787\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.69098 | + | 2.85317i | −0.294362 | + | 0.496673i | ||||
\(34\) | −7.61803 | −1.30648 | ||||||||
\(35\) | 0.427051 | + | 1.31433i | 0.0721848 | + | 0.222162i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | 6.97214 | − | 5.06555i | 1.14621 | − | 0.832772i | 0.158239 | − | 0.987401i | \(-0.449418\pi\) |
0.987973 | + | 0.154629i | \(0.0494182\pi\) | |||||||
\(38\) | −1.26393 | + | 3.88998i | −0.205037 | + | 0.631039i | ||||
\(39\) | −0.381966 | + | 1.17557i | −0.0611635 | + | 0.188242i | ||||
\(40\) | −1.11803 | + | 0.812299i | −0.176777 | + | 0.128436i | ||||
\(41\) | −9.59017 | − | 6.96767i | −1.49773 | − | 1.08817i | −0.971273 | − | 0.237966i | \(-0.923519\pi\) |
−0.526460 | − | 0.850200i | \(-0.676481\pi\) | |||||||
\(42\) | 0.309017 | + | 0.951057i | 0.0476824 | + | 0.146751i | ||||
\(43\) | 5.23607 | 0.798493 | 0.399246 | − | 0.916844i | \(-0.369272\pi\) | ||||
0.399246 | + | 0.916844i | \(0.369272\pi\) | |||||||
\(44\) | 2.19098 | + | 2.48990i | 0.330303 | + | 0.375366i | ||||
\(45\) | −1.38197 | −0.206011 | ||||||||
\(46\) | 2.88197 | + | 8.86978i | 0.424923 | + | 1.30778i | ||||
\(47\) | −8.23607 | − | 5.98385i | −1.20135 | − | 0.872835i | −0.206937 | − | 0.978354i | \(-0.566349\pi\) |
−0.994417 | + | 0.105520i | \(0.966349\pi\) | |||||||
\(48\) | −0.809017 | + | 0.587785i | −0.116772 | + | 0.0848395i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 0.954915 | − | 2.93893i | 0.135045 | − | 0.415627i | ||||
\(51\) | −6.16312 | + | 4.47777i | −0.863009 | + | 0.627013i | ||||
\(52\) | 1.00000 | + | 0.726543i | 0.138675 | + | 0.100753i | ||||
\(53\) | 2.76393 | + | 8.50651i | 0.379655 | + | 1.16846i | 0.940284 | + | 0.340391i | \(0.110560\pi\) |
−0.560629 | + | 0.828067i | \(0.689440\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.47214 | + | 1.00406i | 0.603023 | + | 0.135387i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.26393 | + | 3.88998i | 0.167412 | + | 0.515241i | ||||
\(58\) | −1.00000 | − | 0.726543i | −0.131306 | − | 0.0953997i | ||||
\(59\) | 7.23607 | − | 5.25731i | 0.942056 | − | 0.684444i | −0.00685884 | − | 0.999976i | \(-0.502183\pi\) |
0.948915 | + | 0.315533i | \(0.102183\pi\) | |||||||
\(60\) | −0.427051 | + | 1.31433i | −0.0551320 | + | 0.169679i | ||||
\(61\) | −2.85410 | + | 8.78402i | −0.365430 | + | 1.12468i | 0.584281 | + | 0.811552i | \(0.301377\pi\) |
−0.949711 | + | 0.313127i | \(0.898623\pi\) | |||||||
\(62\) | 0.881966 | − | 0.640786i | 0.112010 | − | 0.0813799i | ||||
\(63\) | 0.809017 | + | 0.587785i | 0.101927 | + | 0.0740540i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 1.70820 | 0.211877 | ||||||||
\(66\) | 3.23607 | + | 0.726543i | 0.398332 | + | 0.0894312i | ||||
\(67\) | −1.23607 | −0.151010 | −0.0755049 | − | 0.997145i | \(-0.524057\pi\) | ||||
−0.0755049 | + | 0.997145i | \(0.524057\pi\) | |||||||
\(68\) | 2.35410 | + | 7.24518i | 0.285477 | + | 0.878607i | ||||
\(69\) | 7.54508 | + | 5.48183i | 0.908321 | + | 0.659934i | ||||
\(70\) | 1.11803 | − | 0.812299i | 0.133631 | − | 0.0970883i | ||||
\(71\) | 0.472136 | − | 1.45309i | 0.0560322 | − | 0.172449i | −0.919124 | − | 0.393969i | \(-0.871102\pi\) |
0.975156 | + | 0.221520i | \(0.0711017\pi\) | |||||||
\(72\) | −0.309017 | + | 0.951057i | −0.0364180 | + | 0.112083i | ||||
\(73\) | 6.47214 | − | 4.70228i | 0.757506 | − | 0.550360i | −0.140638 | − | 0.990061i | \(-0.544915\pi\) |
0.898144 | + | 0.439701i | \(0.144915\pi\) | |||||||
\(74\) | −6.97214 | − | 5.06555i | −0.810494 | − | 0.588859i | ||||
\(75\) | −0.954915 | − | 2.93893i | −0.110264 | − | 0.339358i | ||||
\(76\) | 4.09017 | 0.469175 | ||||||||
\(77\) | −2.19098 | − | 2.48990i | −0.249686 | − | 0.283750i | ||||
\(78\) | 1.23607 | 0.139957 | ||||||||
\(79\) | −2.38197 | − | 7.33094i | −0.267992 | − | 0.824795i | −0.990989 | − | 0.133944i | \(-0.957236\pi\) |
0.722997 | − | 0.690851i | \(-0.242764\pi\) | |||||||
\(80\) | 1.11803 | + | 0.812299i | 0.125000 | + | 0.0908178i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −3.66312 | + | 11.2739i | −0.404524 | + | 1.24500i | ||||
\(83\) | 4.70820 | − | 14.4904i | 0.516793 | − | 1.59052i | −0.263204 | − | 0.964740i | \(-0.584779\pi\) |
0.779997 | − | 0.625784i | \(-0.215221\pi\) | |||||||
\(84\) | 0.809017 | − | 0.587785i | 0.0882710 | − | 0.0641326i | ||||
\(85\) | 8.51722 | + | 6.18812i | 0.923822 | + | 0.671196i | ||||
\(86\) | −1.61803 | − | 4.97980i | −0.174477 | − | 0.536985i | ||||
\(87\) | −1.23607 | −0.132520 | ||||||||
\(88\) | 1.69098 | − | 2.85317i | 0.180259 | − | 0.304149i | ||||
\(89\) | −5.14590 | −0.545464 | −0.272732 | − | 0.962090i | \(-0.587927\pi\) | ||||
−0.272732 | + | 0.962090i | \(0.587927\pi\) | |||||||
\(90\) | 0.427051 | + | 1.31433i | 0.0450151 | + | 0.138542i | ||||
\(91\) | −1.00000 | − | 0.726543i | −0.104828 | − | 0.0761624i | ||||
\(92\) | 7.54508 | − | 5.48183i | 0.786629 | − | 0.571520i | ||||
\(93\) | 0.336881 | − | 1.03681i | 0.0349329 | − | 0.107513i | ||||
\(94\) | −3.14590 | + | 9.68208i | −0.324475 | + | 0.998630i | ||||
\(95\) | 4.57295 | − | 3.32244i | 0.469175 | − | 0.340875i | ||||
\(96\) | 0.809017 | + | 0.587785i | 0.0825700 | + | 0.0599906i | ||||
\(97\) | 3.47214 | + | 10.6861i | 0.352542 | + | 1.08501i | 0.957421 | + | 0.288695i | \(0.0932215\pi\) |
−0.604879 | + | 0.796317i | \(0.706779\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 3.04508 | − | 1.31433i | 0.306043 | − | 0.132095i | ||||
\(100\) | −3.09017 | −0.309017 | ||||||||
\(101\) | 3.66312 | + | 11.2739i | 0.364494 | + | 1.12180i | 0.950297 | + | 0.311344i | \(0.100779\pi\) |
−0.585803 | + | 0.810453i | \(0.699221\pi\) | |||||||
\(102\) | 6.16312 | + | 4.47777i | 0.610240 | + | 0.443365i | ||||
\(103\) | −4.69098 | + | 3.40820i | −0.462216 | + | 0.335820i | −0.794400 | − | 0.607395i | \(-0.792215\pi\) |
0.332184 | + | 0.943215i | \(0.392215\pi\) | |||||||
\(104\) | 0.381966 | − | 1.17557i | 0.0374548 | − | 0.115274i | ||||
\(105\) | 0.427051 | − | 1.31433i | 0.0416759 | − | 0.128265i | ||||
\(106\) | 7.23607 | − | 5.25731i | 0.702829 | − | 0.510635i | ||||
\(107\) | 15.3992 | + | 11.1882i | 1.48870 | + | 1.08160i | 0.974623 | + | 0.223854i | \(0.0718639\pi\) |
0.514073 | + | 0.857746i | \(0.328136\pi\) | |||||||
\(108\) | 0.309017 | + | 0.951057i | 0.0297352 | + | 0.0915155i | ||||
\(109\) | 4.61803 | 0.442327 | 0.221164 | − | 0.975237i | \(-0.429014\pi\) | ||||
0.221164 | + | 0.975237i | \(0.429014\pi\) | |||||||
\(110\) | −0.427051 | − | 4.56352i | −0.0407177 | − | 0.435115i | ||||
\(111\) | −8.61803 | −0.817988 | ||||||||
\(112\) | −0.309017 | − | 0.951057i | −0.0291994 | − | 0.0898664i | ||||
\(113\) | 5.23607 | + | 3.80423i | 0.492568 | + | 0.357871i | 0.806171 | − | 0.591683i | \(-0.201536\pi\) |
−0.313603 | + | 0.949554i | \(0.601536\pi\) | |||||||
\(114\) | 3.30902 | − | 2.40414i | 0.309918 | − | 0.225168i | ||||
\(115\) | 3.98278 | − | 12.2577i | 0.371396 | − | 1.14304i | ||||
\(116\) | −0.381966 | + | 1.17557i | −0.0354647 | + | 0.109149i | ||||
\(117\) | 1.00000 | − | 0.726543i | 0.0924500 | − | 0.0671689i | ||||
\(118\) | −7.23607 | − | 5.25731i | −0.666134 | − | 0.483975i | ||||
\(119\) | −2.35410 | − | 7.24518i | −0.215800 | − | 0.664165i | ||||
\(120\) | 1.38197 | 0.126156 | ||||||||
\(121\) | −10.8090 | + | 2.04087i | −0.982638 | + | 0.185534i | ||||
\(122\) | 9.23607 | 0.836194 | ||||||||
\(123\) | 3.66312 | + | 11.2739i | 0.330292 | + | 1.01654i | ||||
\(124\) | −0.881966 | − | 0.640786i | −0.0792029 | − | 0.0575443i | ||||
\(125\) | −9.04508 | + | 6.57164i | −0.809017 | + | 0.587785i | ||||
\(126\) | 0.309017 | − | 0.951057i | 0.0275294 | − | 0.0847268i | ||||
\(127\) | 3.47214 | − | 10.6861i | 0.308102 | − | 0.948241i | −0.670399 | − | 0.742001i | \(-0.733877\pi\) |
0.978501 | − | 0.206240i | \(-0.0661229\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | −4.23607 | − | 3.07768i | −0.372965 | − | 0.270975i | ||||
\(130\) | −0.527864 | − | 1.62460i | −0.0462967 | − | 0.142487i | ||||
\(131\) | 15.2361 | 1.33118 | 0.665591 | − | 0.746317i | \(-0.268180\pi\) | ||||
0.665591 | + | 0.746317i | \(0.268180\pi\) | |||||||
\(132\) | −0.309017 | − | 3.30220i | −0.0268965 | − | 0.287419i | ||||
\(133\) | −4.09017 | −0.354663 | ||||||||
\(134\) | 0.381966 | + | 1.17557i | 0.0329968 | + | 0.101554i | ||||
\(135\) | 1.11803 | + | 0.812299i | 0.0962250 | + | 0.0699116i | ||||
\(136\) | 6.16312 | − | 4.47777i | 0.528483 | − | 0.383965i | ||||
\(137\) | 2.00000 | − | 6.15537i | 0.170872 | − | 0.525888i | −0.828549 | − | 0.559916i | \(-0.810833\pi\) |
0.999421 | + | 0.0340275i | \(0.0108334\pi\) | |||||||
\(138\) | 2.88197 | − | 8.86978i | 0.245329 | − | 0.755046i | ||||
\(139\) | −13.6353 | + | 9.90659i | −1.15653 | + | 0.840266i | −0.989335 | − | 0.145658i | \(-0.953470\pi\) |
−0.167192 | + | 0.985924i | \(0.553470\pi\) | |||||||
\(140\) | −1.11803 | − | 0.812299i | −0.0944911 | − | 0.0686518i | ||||
\(141\) | 3.14590 | + | 9.68208i | 0.264932 | + | 0.815378i | ||||
\(142\) | −1.52786 | −0.128216 | ||||||||
\(143\) | −3.76393 | + | 1.62460i | −0.314756 | + | 0.135856i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.527864 | + | 1.62460i | 0.0438367 | + | 0.134916i | ||||
\(146\) | −6.47214 | − | 4.70228i | −0.535638 | − | 0.389164i | ||||
\(147\) | −0.809017 | + | 0.587785i | −0.0667266 | + | 0.0484797i | ||||
\(148\) | −2.66312 | + | 8.19624i | −0.218907 | + | 0.673727i | ||||
\(149\) | −6.00000 | + | 18.4661i | −0.491539 | + | 1.51280i | 0.330742 | + | 0.943721i | \(0.392701\pi\) |
−0.822282 | + | 0.569081i | \(0.807299\pi\) | |||||||
\(150\) | −2.50000 | + | 1.81636i | −0.204124 | + | 0.148305i | ||||
\(151\) | 7.23607 | + | 5.25731i | 0.588863 | + | 0.427834i | 0.841908 | − | 0.539620i | \(-0.181432\pi\) |
−0.253046 | + | 0.967454i | \(0.581432\pi\) | |||||||
\(152\) | −1.26393 | − | 3.88998i | −0.102518 | − | 0.315519i | ||||
\(153\) | 7.61803 | 0.615882 | ||||||||
\(154\) | −1.69098 | + | 2.85317i | −0.136263 | + | 0.229915i | ||||
\(155\) | −1.50658 | −0.121011 | ||||||||
\(156\) | −0.381966 | − | 1.17557i | −0.0305818 | − | 0.0941210i | ||||
\(157\) | −3.00000 | − | 2.17963i | −0.239426 | − | 0.173953i | 0.461601 | − | 0.887087i | \(-0.347275\pi\) |
−0.701028 | + | 0.713134i | \(0.747275\pi\) | |||||||
\(158\) | −6.23607 | + | 4.53077i | −0.496115 | + | 0.360449i | ||||
\(159\) | 2.76393 | − | 8.50651i | 0.219194 | − | 0.674610i | ||||
\(160\) | 0.427051 | − | 1.31433i | 0.0337613 | − | 0.103907i | ||||
\(161\) | −7.54508 | + | 5.48183i | −0.594636 | + | 0.432028i | ||||
\(162\) | 0.809017 | + | 0.587785i | 0.0635624 | + | 0.0461808i | ||||
\(163\) | 6.32624 | + | 19.4702i | 0.495509 | + | 1.52502i | 0.816162 | + | 0.577824i | \(0.196098\pi\) |
−0.320652 | + | 0.947197i | \(0.603902\pi\) | |||||||
\(164\) | 11.8541 | 0.925650 | ||||||||
\(165\) | −3.02786 | − | 3.44095i | −0.235719 | − | 0.267878i | ||||
\(166\) | −15.2361 | −1.18255 | ||||||||
\(167\) | 2.32624 | + | 7.15942i | 0.180010 | + | 0.554013i | 0.999827 | − | 0.0186126i | \(-0.00592492\pi\) |
−0.819817 | + | 0.572625i | \(0.805925\pi\) | |||||||
\(168\) | −0.809017 | − | 0.587785i | −0.0624170 | − | 0.0453486i | ||||
\(169\) | 9.28115 | − | 6.74315i | 0.713935 | − | 0.518704i | ||||
\(170\) | 3.25329 | − | 10.0126i | 0.249516 | − | 0.767931i | ||||
\(171\) | 1.26393 | − | 3.88998i | 0.0966553 | − | 0.297474i | ||||
\(172\) | −4.23607 | + | 3.07768i | −0.322997 | + | 0.234671i | ||||
\(173\) | −5.54508 | − | 4.02874i | −0.421585 | − | 0.306299i | 0.356690 | − | 0.934223i | \(-0.383905\pi\) |
−0.778275 | + | 0.627923i | \(0.783905\pi\) | |||||||
\(174\) | 0.381966 | + | 1.17557i | 0.0289568 | + | 0.0891198i | ||||
\(175\) | 3.09017 | 0.233595 | ||||||||
\(176\) | −3.23607 | − | 0.726543i | −0.243928 | − | 0.0547652i | ||||
\(177\) | −8.94427 | −0.672293 | ||||||||
\(178\) | 1.59017 | + | 4.89404i | 0.119188 | + | 0.366824i | ||||
\(179\) | −17.4443 | − | 12.6740i | −1.30385 | − | 0.947300i | −0.303861 | − | 0.952716i | \(-0.598276\pi\) |
−0.999985 | + | 0.00541681i | \(0.998276\pi\) | |||||||
\(180\) | 1.11803 | − | 0.812299i | 0.0833333 | − | 0.0605452i | ||||
\(181\) | 2.47214 | − | 7.60845i | 0.183752 | − | 0.565532i | −0.816172 | − | 0.577809i | \(-0.803908\pi\) |
0.999925 | + | 0.0122769i | \(0.00390796\pi\) | |||||||
\(182\) | −0.381966 | + | 1.17557i | −0.0283132 | + | 0.0871391i | ||||
\(183\) | 7.47214 | − | 5.42882i | 0.552356 | − | 0.401310i | ||||
\(184\) | −7.54508 | − | 5.48183i | −0.556231 | − | 0.404126i | ||||
\(185\) | 3.68034 | + | 11.3269i | 0.270584 | + | 0.832772i | ||||
\(186\) | −1.09017 | −0.0799351 | ||||||||
\(187\) | −24.6525 | − | 5.53483i | −1.80277 | − | 0.404747i | ||||
\(188\) | 10.1803 | 0.742478 | ||||||||
\(189\) | −0.309017 | − | 0.951057i | −0.0224777 | − | 0.0691792i | ||||
\(190\) | −4.57295 | − | 3.32244i | −0.331757 | − | 0.241035i | ||||
\(191\) | −8.97214 | + | 6.51864i | −0.649201 | + | 0.471672i | −0.862999 | − | 0.505206i | \(-0.831417\pi\) |
0.213798 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(192\) | 0.309017 | − | 0.951057i | 0.0223014 | − | 0.0686366i | ||||
\(193\) | −0.572949 | + | 1.76336i | −0.0412418 | + | 0.126929i | −0.969558 | − | 0.244864i | \(-0.921257\pi\) |
0.928316 | + | 0.371793i | \(0.121257\pi\) | |||||||
\(194\) | 9.09017 | − | 6.60440i | 0.652636 | − | 0.474168i | ||||
\(195\) | −1.38197 | − | 1.00406i | −0.0989646 | − | 0.0719020i | ||||
\(196\) | 0.309017 | + | 0.951057i | 0.0220726 | + | 0.0679326i | ||||
\(197\) | 18.7639 | 1.33687 | 0.668437 | − | 0.743768i | \(-0.266963\pi\) | ||||
0.668437 | + | 0.743768i | \(0.266963\pi\) | |||||||
\(198\) | −2.19098 | − | 2.48990i | −0.155706 | − | 0.176949i | ||||
\(199\) | −8.27051 | −0.586281 | −0.293140 | − | 0.956069i | \(-0.594700\pi\) | ||||
−0.293140 | + | 0.956069i | \(0.594700\pi\) | |||||||
\(200\) | 0.954915 | + | 2.93893i | 0.0675227 | + | 0.207813i | ||||
\(201\) | 1.00000 | + | 0.726543i | 0.0705346 | + | 0.0512464i | ||||
\(202\) | 9.59017 | − | 6.96767i | 0.674762 | − | 0.490243i | ||||
\(203\) | 0.381966 | − | 1.17557i | 0.0268088 | − | 0.0825089i | ||||
\(204\) | 2.35410 | − | 7.24518i | 0.164820 | − | 0.507264i | ||||
\(205\) | 13.2533 | − | 9.62908i | 0.925650 | − | 0.672524i | ||||
\(206\) | 4.69098 | + | 3.40820i | 0.326836 | + | 0.237460i | ||||
\(207\) | −2.88197 | − | 8.86978i | −0.200310 | − | 0.616492i | ||||
\(208\) | −1.23607 | −0.0857059 | ||||||||
\(209\) | −6.91641 | + | 11.6699i | −0.478418 | + | 0.807227i | ||||
\(210\) | −1.38197 | −0.0953647 | ||||||||
\(211\) | 0.236068 | + | 0.726543i | 0.0162516 | + | 0.0500173i | 0.958853 | − | 0.283902i | \(-0.0916289\pi\) |
−0.942602 | + | 0.333919i | \(0.891629\pi\) | |||||||
\(212\) | −7.23607 | − | 5.25731i | −0.496975 | − | 0.361074i | ||||
\(213\) | −1.23607 | + | 0.898056i | −0.0846940 | + | 0.0615338i | ||||
\(214\) | 5.88197 | − | 18.1028i | 0.402083 | − | 1.23748i | ||||
\(215\) | −2.23607 | + | 6.88191i | −0.152499 | + | 0.469342i | ||||
\(216\) | 0.809017 | − | 0.587785i | 0.0550466 | − | 0.0399937i | ||||
\(217\) | 0.881966 | + | 0.640786i | 0.0598718 | + | 0.0434994i | ||||
\(218\) | −1.42705 | − | 4.39201i | −0.0966521 | − | 0.297465i | ||||
\(219\) | −8.00000 | −0.540590 | ||||||||
\(220\) | −4.20820 | + | 1.81636i | −0.283717 | + | 0.122459i | ||||
\(221\) | −9.41641 | −0.633416 | ||||||||
\(222\) | 2.66312 | + | 8.19624i | 0.178737 | + | 0.550095i | ||||
\(223\) | −2.54508 | − | 1.84911i | −0.170431 | − | 0.123826i | 0.499300 | − | 0.866429i | \(-0.333591\pi\) |
−0.669731 | + | 0.742604i | \(0.733591\pi\) | |||||||
\(224\) | −0.809017 | + | 0.587785i | −0.0540547 | + | 0.0392731i | ||||
\(225\) | −0.954915 | + | 2.93893i | −0.0636610 | + | 0.195928i | ||||
\(226\) | 2.00000 | − | 6.15537i | 0.133038 | − | 0.409449i | ||||
\(227\) | −10.9443 | + | 7.95148i | −0.726397 | + | 0.527758i | −0.888422 | − | 0.459029i | \(-0.848198\pi\) |
0.162025 | + | 0.986787i | \(0.448198\pi\) | |||||||
\(228\) | −3.30902 | − | 2.40414i | −0.219145 | − | 0.159218i | ||||
\(229\) | −8.90983 | − | 27.4216i | −0.588778 | − | 1.81207i | −0.583537 | − | 0.812087i | \(-0.698332\pi\) |
−0.00524111 | − | 0.999986i | \(-0.501668\pi\) | |||||||
\(230\) | −12.8885 | −0.849845 | ||||||||
\(231\) | 0.309017 | + | 3.30220i | 0.0203318 | + | 0.217269i | ||||
\(232\) | 1.23607 | 0.0811518 | ||||||||
\(233\) | 6.14590 | + | 18.9151i | 0.402631 | + | 1.23917i | 0.922857 | + | 0.385143i | \(0.125848\pi\) |
−0.520226 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(234\) | −1.00000 | − | 0.726543i | −0.0653720 | − | 0.0474956i | ||||
\(235\) | 11.3820 | − | 8.26948i | 0.742478 | − | 0.539442i | ||||
\(236\) | −2.76393 | + | 8.50651i | −0.179917 | + | 0.553727i | ||||
\(237\) | −2.38197 | + | 7.33094i | −0.154725 | + | 0.476196i | ||||
\(238\) | −6.16312 | + | 4.47777i | −0.399496 | + | 0.290251i | ||||
\(239\) | −9.39919 | − | 6.82891i | −0.607983 | − | 0.441725i | 0.240721 | − | 0.970594i | \(-0.422616\pi\) |
−0.848703 | + | 0.528869i | \(0.822616\pi\) | |||||||
\(240\) | −0.427051 | − | 1.31433i | −0.0275660 | − | 0.0848395i | ||||
\(241\) | −6.18034 | −0.398111 | −0.199055 | − | 0.979988i | \(-0.563787\pi\) | ||||
−0.199055 | + | 0.979988i | \(0.563787\pi\) | |||||||
\(242\) | 5.28115 | + | 9.64932i | 0.339485 | + | 0.620282i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.85410 | − | 8.78402i | −0.182715 | − | 0.562339i | ||||
\(245\) | 1.11803 | + | 0.812299i | 0.0714286 | + | 0.0518959i | ||||
\(246\) | 9.59017 | − | 6.96767i | 0.611447 | − | 0.444242i | ||||
\(247\) | −1.56231 | + | 4.80828i | −0.0994071 | + | 0.305944i | ||||
\(248\) | −0.336881 | + | 1.03681i | −0.0213920 | + | 0.0658377i | ||||
\(249\) | −12.3262 | + | 8.95554i | −0.781144 | + | 0.567534i | ||||
\(250\) | 9.04508 | + | 6.57164i | 0.572061 | + | 0.415627i | ||||
\(251\) | −2.76393 | − | 8.50651i | −0.174458 | − | 0.536926i | 0.825150 | − | 0.564913i | \(-0.191090\pi\) |
−0.999608 | + | 0.0279870i | \(0.991090\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 2.88197 | + | 30.7971i | 0.181188 | + | 1.93620i | ||||
\(254\) | −11.2361 | −0.705014 | ||||||||
\(255\) | −3.25329 | − | 10.0126i | −0.203729 | − | 0.627013i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 7.39919 | − | 5.37582i | 0.461549 | − | 0.335335i | −0.332590 | − | 0.943072i | \(-0.607922\pi\) |
0.794138 | + | 0.607737i | \(0.207922\pi\) | |||||||
\(258\) | −1.61803 | + | 4.97980i | −0.100734 | + | 0.310029i | ||||
\(259\) | 2.66312 | − | 8.19624i | 0.165478 | − | 0.509289i | ||||
\(260\) | −1.38197 | + | 1.00406i | −0.0857059 | + | 0.0622690i | ||||
\(261\) | 1.00000 | + | 0.726543i | 0.0618984 | + | 0.0449719i | ||||
\(262\) | −4.70820 | − | 14.4904i | −0.290874 | − | 0.895218i | ||||
\(263\) | 7.03444 | 0.433762 | 0.216881 | − | 0.976198i | \(-0.430412\pi\) | ||||
0.216881 | + | 0.976198i | \(0.430412\pi\) | |||||||
\(264\) | −3.04508 | + | 1.31433i | −0.187412 | + | 0.0808913i | ||||
\(265\) | −12.3607 | −0.759311 | ||||||||
\(266\) | 1.26393 | + | 3.88998i | 0.0774966 | + | 0.238510i | ||||
\(267\) | 4.16312 | + | 3.02468i | 0.254779 | + | 0.185108i | ||||
\(268\) | 1.00000 | − | 0.726543i | 0.0610847 | − | 0.0443806i | ||||
\(269\) | 1.85410 | − | 5.70634i | 0.113047 | − | 0.347922i | −0.878488 | − | 0.477764i | \(-0.841447\pi\) |
0.991535 | + | 0.129843i | \(0.0414473\pi\) | |||||||
\(270\) | 0.427051 | − | 1.31433i | 0.0259895 | − | 0.0799874i | ||||
\(271\) | −4.11803 | + | 2.99193i | −0.250153 | + | 0.181747i | −0.705795 | − | 0.708417i | \(-0.749410\pi\) |
0.455642 | + | 0.890163i | \(0.349410\pi\) | |||||||
\(272\) | −6.16312 | − | 4.47777i | −0.373694 | − | 0.271505i | ||||
\(273\) | 0.381966 | + | 1.17557i | 0.0231176 | + | 0.0711488i | ||||
\(274\) | −6.47214 | −0.390996 | ||||||||
\(275\) | 5.22542 | − | 8.81678i | 0.315105 | − | 0.531672i | ||||
\(276\) | −9.32624 | −0.561374 | ||||||||
\(277\) | 0.972136 | + | 2.99193i | 0.0584100 | + | 0.179767i | 0.976005 | − | 0.217750i | \(-0.0698718\pi\) |
−0.917595 | + | 0.397518i | \(0.869872\pi\) | |||||||
\(278\) | 13.6353 | + | 9.90659i | 0.817788 | + | 0.594158i | ||||
\(279\) | −0.881966 | + | 0.640786i | −0.0528019 | + | 0.0383628i | ||||
\(280\) | −0.427051 | + | 1.31433i | −0.0255212 | + | 0.0785461i | ||||
\(281\) | 4.52786 | − | 13.9353i | 0.270110 | − | 0.831312i | −0.720362 | − | 0.693598i | \(-0.756024\pi\) |
0.990472 | − | 0.137714i | \(-0.0439756\pi\) | |||||||
\(282\) | 8.23607 | − | 5.98385i | 0.490451 | − | 0.356333i | ||||
\(283\) | −0.881966 | − | 0.640786i | −0.0524274 | − | 0.0380908i | 0.561263 | − | 0.827638i | \(-0.310316\pi\) |
−0.613690 | + | 0.789547i | \(0.710316\pi\) | |||||||
\(284\) | 0.472136 | + | 1.45309i | 0.0280161 | + | 0.0862247i | ||||
\(285\) | −5.65248 | −0.334824 | ||||||||
\(286\) | 2.70820 | + | 3.07768i | 0.160139 | + | 0.181987i | ||||
\(287\) | −11.8541 | −0.699726 | ||||||||
\(288\) | −0.309017 | − | 0.951057i | −0.0182090 | − | 0.0560415i | ||||
\(289\) | −33.1976 | − | 24.1194i | −1.95280 | − | 1.41879i | ||||
\(290\) | 1.38197 | − | 1.00406i | 0.0811518 | − | 0.0589603i | ||||
\(291\) | 3.47214 | − | 10.6861i | 0.203540 | − | 0.626432i | ||||
\(292\) | −2.47214 | + | 7.60845i | −0.144671 | + | 0.445251i | ||||
\(293\) | −7.11803 | + | 5.17155i | −0.415840 | + | 0.302125i | −0.775962 | − | 0.630780i | \(-0.782735\pi\) |
0.360122 | + | 0.932905i | \(0.382735\pi\) | |||||||
\(294\) | 0.809017 | + | 0.587785i | 0.0471828 | + | 0.0342803i | ||||
\(295\) | 3.81966 | + | 11.7557i | 0.222389 | + | 0.684444i | ||||
\(296\) | 8.61803 | 0.500913 | ||||||||
\(297\) | −3.23607 | − | 0.726543i | −0.187776 | − | 0.0421583i | ||||
\(298\) | 19.4164 | 1.12476 | ||||||||
\(299\) | 3.56231 | + | 10.9637i | 0.206013 | + | 0.634044i | ||||
\(300\) | 2.50000 | + | 1.81636i | 0.144338 | + | 0.104867i | ||||
\(301\) | 4.23607 | − | 3.07768i | 0.244163 | − | 0.177395i | ||||
\(302\) | 2.76393 | − | 8.50651i | 0.159046 | − | 0.489495i | ||||
\(303\) | 3.66312 | − | 11.2739i | 0.210441 | − | 0.647670i | ||||
\(304\) | −3.30902 | + | 2.40414i | −0.189785 | + | 0.137887i | ||||
\(305\) | −10.3262 | − | 7.50245i | −0.591279 | − | 0.429589i | ||||
\(306\) | −2.35410 | − | 7.24518i | −0.134575 | − | 0.414179i | ||||
\(307\) | 15.8541 | 0.904841 | 0.452421 | − | 0.891805i | \(-0.350561\pi\) | ||||
0.452421 | + | 0.891805i | \(0.350561\pi\) | |||||||
\(308\) | 3.23607 | + | 0.726543i | 0.184392 | + | 0.0413986i | ||||
\(309\) | 5.79837 | 0.329858 | ||||||||
\(310\) | 0.465558 | + | 1.43284i | 0.0264419 | + | 0.0813799i | ||||
\(311\) | 10.9443 | + | 7.95148i | 0.620593 | + | 0.450887i | 0.853128 | − | 0.521701i | \(-0.174702\pi\) |
−0.232536 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(312\) | −1.00000 | + | 0.726543i | −0.0566139 | + | 0.0411324i | ||||
\(313\) | 4.41641 | − | 13.5923i | 0.249630 | − | 0.768283i | −0.745210 | − | 0.666830i | \(-0.767651\pi\) |
0.994840 | − | 0.101453i | \(-0.0323491\pi\) | |||||||
\(314\) | −1.14590 | + | 3.52671i | −0.0646668 | + | 0.199024i | ||||
\(315\) | −1.11803 | + | 0.812299i | −0.0629941 | + | 0.0457679i | ||||
\(316\) | 6.23607 | + | 4.53077i | 0.350806 | + | 0.254876i | ||||
\(317\) | 3.70820 | + | 11.4127i | 0.208273 | + | 0.641000i | 0.999563 | + | 0.0295583i | \(0.00941007\pi\) |
−0.791290 | + | 0.611442i | \(0.790590\pi\) | |||||||
\(318\) | −8.94427 | −0.501570 | ||||||||
\(319\) | −2.70820 | − | 3.07768i | −0.151630 | − | 0.172317i | ||||
\(320\) | −1.38197 | −0.0772542 | ||||||||
\(321\) | −5.88197 | − | 18.1028i | −0.328299 | − | 1.01040i | ||||
\(322\) | 7.54508 | + | 5.48183i | 0.420471 | + | 0.305490i | ||||
\(323\) | −25.2082 | + | 18.3148i | −1.40262 | + | 1.01906i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | 1.18034 | − | 3.63271i | 0.0654735 | − | 0.201507i | ||||
\(326\) | 16.5623 | − | 12.0332i | 0.917301 | − | 0.666458i | ||||
\(327\) | −3.73607 | − | 2.71441i | −0.206605 | − | 0.150107i | ||||
\(328\) | −3.66312 | − | 11.2739i | −0.202262 | − | 0.622498i | ||||
\(329\) | −10.1803 | −0.561260 | ||||||||
\(330\) | −2.33688 | + | 3.94298i | −0.128641 | + | 0.217054i | ||||
\(331\) | −0.180340 | −0.00991238 | −0.00495619 | − | 0.999988i | \(-0.501578\pi\) | ||||
−0.00495619 | + | 0.999988i | \(0.501578\pi\) | |||||||
\(332\) | 4.70820 | + | 14.4904i | 0.258396 | + | 0.795262i | ||||
\(333\) | 6.97214 | + | 5.06555i | 0.382071 | + | 0.277591i | ||||
\(334\) | 6.09017 | − | 4.42477i | 0.333239 | − | 0.242113i | ||||
\(335\) | 0.527864 | − | 1.62460i | 0.0288403 | − | 0.0887613i | ||||
\(336\) | −0.309017 | + | 0.951057i | −0.0168583 | + | 0.0518844i | ||||
\(337\) | 6.73607 | − | 4.89404i | 0.366937 | − | 0.266595i | −0.389003 | − | 0.921237i | \(-0.627180\pi\) |
0.755940 | + | 0.654641i | \(0.227180\pi\) | |||||||
\(338\) | −9.28115 | − | 6.74315i | −0.504828 | − | 0.366779i | ||||
\(339\) | −2.00000 | − | 6.15537i | −0.108625 | − | 0.334314i | ||||
\(340\) | −10.5279 | −0.570954 | ||||||||
\(341\) | 3.31966 | − | 1.43284i | 0.179770 | − | 0.0775927i | ||||
\(342\) | −4.09017 | −0.221171 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | 4.23607 | + | 3.07768i | 0.228393 | + | 0.165938i | ||||
\(345\) | −10.4271 | + | 7.57570i | −0.561374 | + | 0.407862i | ||||
\(346\) | −2.11803 | + | 6.51864i | −0.113866 | + | 0.350444i | ||||
\(347\) | 3.33688 | − | 10.2699i | 0.179133 | − | 0.551315i | −0.820665 | − | 0.571410i | \(-0.806397\pi\) |
0.999798 | + | 0.0200946i | \(0.00639673\pi\) | |||||||
\(348\) | 1.00000 | − | 0.726543i | 0.0536056 | − | 0.0389468i | ||||
\(349\) | 7.70820 | + | 5.60034i | 0.412611 | + | 0.299779i | 0.774658 | − | 0.632381i | \(-0.217922\pi\) |
−0.362047 | + | 0.932160i | \(0.617922\pi\) | |||||||
\(350\) | −0.954915 | − | 2.93893i | −0.0510424 | − | 0.157092i | ||||
\(351\) | −1.23607 | −0.0659764 | ||||||||
\(352\) | 0.309017 | + | 3.30220i | 0.0164707 | + | 0.176008i | ||||
\(353\) | 22.9443 | 1.22120 | 0.610600 | − | 0.791939i | \(-0.290928\pi\) | ||||
0.610600 | + | 0.791939i | \(0.290928\pi\) | |||||||
\(354\) | 2.76393 | + | 8.50651i | 0.146901 | + | 0.452116i | ||||
\(355\) | 1.70820 | + | 1.24108i | 0.0906621 | + | 0.0658698i | ||||
\(356\) | 4.16312 | − | 3.02468i | 0.220645 | − | 0.160308i | ||||
\(357\) | −2.35410 | + | 7.24518i | −0.124592 | + | 0.383456i | ||||
\(358\) | −6.66312 | + | 20.5070i | −0.352157 | + | 1.08383i | ||||
\(359\) | 24.4443 | − | 17.7598i | 1.29012 | − | 0.937327i | 0.290312 | − | 0.956932i | \(-0.406241\pi\) |
0.999808 | + | 0.0196056i | \(0.00624107\pi\) | |||||||
\(360\) | −1.11803 | − | 0.812299i | −0.0589256 | − | 0.0428119i | ||||
\(361\) | −0.701626 | − | 2.15938i | −0.0369277 | − | 0.113652i | ||||
\(362\) | −8.00000 | −0.420471 | ||||||||
\(363\) | 9.94427 | + | 4.70228i | 0.521939 | + | 0.246806i | ||||
\(364\) | 1.23607 | 0.0647876 | ||||||||
\(365\) | 3.41641 | + | 10.5146i | 0.178823 | + | 0.550360i | ||||
\(366\) | −7.47214 | − | 5.42882i | −0.390575 | − | 0.283769i | ||||
\(367\) | 15.8262 | − | 11.4984i | 0.826123 | − | 0.600213i | −0.0923369 | − | 0.995728i | \(-0.529434\pi\) |
0.918460 | + | 0.395514i | \(0.129434\pi\) | |||||||
\(368\) | −2.88197 | + | 8.86978i | −0.150233 | + | 0.462369i | ||||
\(369\) | 3.66312 | − | 11.2739i | 0.190694 | − | 0.586897i | ||||
\(370\) | 9.63525 | − | 7.00042i | 0.500913 | − | 0.363935i | ||||
\(371\) | 7.23607 | + | 5.25731i | 0.375678 | + | 0.272946i | ||||
\(372\) | 0.336881 | + | 1.03681i | 0.0174665 | + | 0.0537563i | ||||
\(373\) | 26.5066 | 1.37246 | 0.686229 | − | 0.727385i | \(-0.259265\pi\) | ||||
0.686229 | + | 0.727385i | \(0.259265\pi\) | |||||||
\(374\) | 2.35410 | + | 25.1563i | 0.121728 | + | 1.30080i | ||||
\(375\) | 11.1803 | 0.577350 | ||||||||
\(376\) | −3.14590 | − | 9.68208i | −0.162237 | − | 0.499315i | ||||
\(377\) | −1.23607 | − | 0.898056i | −0.0636607 | − | 0.0462522i | ||||
\(378\) | −0.809017 | + | 0.587785i | −0.0416113 | + | 0.0302324i | ||||
\(379\) | 6.70820 | − | 20.6457i | 0.344577 | − | 1.06050i | −0.617232 | − | 0.786781i | \(-0.711746\pi\) |
0.961810 | − | 0.273719i | \(-0.0882538\pi\) | |||||||
\(380\) | −1.74671 | + | 5.37582i | −0.0896044 | + | 0.275774i | ||||
\(381\) | −9.09017 | + | 6.60440i | −0.465704 | + | 0.338353i | ||||
\(382\) | 8.97214 | + | 6.51864i | 0.459054 | + | 0.333523i | ||||
\(383\) | 1.85410 | + | 5.70634i | 0.0947402 | + | 0.291580i | 0.987186 | − | 0.159575i | \(-0.0510122\pi\) |
−0.892446 | + | 0.451155i | \(0.851012\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 4.20820 | − | 1.81636i | 0.214470 | − | 0.0925701i | ||||
\(386\) | 1.85410 | 0.0943713 | ||||||||
\(387\) | 1.61803 | + | 4.97980i | 0.0822493 | + | 0.253137i | ||||
\(388\) | −9.09017 | − | 6.60440i | −0.461483 | − | 0.335287i | ||||
\(389\) | −21.1803 | + | 15.3884i | −1.07389 | + | 0.780224i | −0.976607 | − | 0.215033i | \(-0.931014\pi\) |
−0.0972792 | + | 0.995257i | \(0.531014\pi\) | |||||||
\(390\) | −0.527864 | + | 1.62460i | −0.0267294 | + | 0.0822647i | ||||
\(391\) | −21.9549 | + | 67.5703i | −1.11031 | + | 3.41718i | ||||
\(392\) | 0.809017 | − | 0.587785i | 0.0408615 | − | 0.0296876i | ||||
\(393\) | −12.3262 | − | 8.95554i | −0.621776 | − | 0.451747i | ||||
\(394\) | −5.79837 | − | 17.8456i | −0.292118 | − | 0.899046i | ||||
\(395\) | 10.6525 | 0.535984 | ||||||||
\(396\) | −1.69098 | + | 2.85317i | −0.0849751 | + | 0.143377i | ||||
\(397\) | 16.0000 | 0.803017 | 0.401508 | − | 0.915855i | \(-0.368486\pi\) | ||||
0.401508 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(398\) | 2.55573 | + | 7.86572i | 0.128107 | + | 0.394273i | ||||
\(399\) | 3.30902 | + | 2.40414i | 0.165658 | + | 0.120358i | ||||
\(400\) | 2.50000 | − | 1.81636i | 0.125000 | − | 0.0908178i | ||||
\(401\) | −3.61803 | + | 11.1352i | −0.180676 | + | 0.556064i | −0.999847 | − | 0.0174857i | \(-0.994434\pi\) |
0.819171 | + | 0.573549i | \(0.194434\pi\) | |||||||
\(402\) | 0.381966 | − | 1.17557i | 0.0190507 | − | 0.0586321i | ||||
\(403\) | 1.09017 | − | 0.792055i | 0.0543052 | − | 0.0394551i | ||||
\(404\) | −9.59017 | − | 6.96767i | −0.477129 | − | 0.346654i | ||||
\(405\) | −0.427051 | − | 1.31433i | −0.0212203 | − | 0.0653095i | ||||
\(406\) | −1.23607 | −0.0613450 | ||||||||
\(407\) | −18.8820 | − | 21.4580i | −0.935944 | − | 1.06363i | ||||
\(408\) | −7.61803 | −0.377149 | ||||||||
\(409\) | −11.0344 | − | 33.9605i | −0.545618 | − | 1.67924i | −0.719516 | − | 0.694476i | \(-0.755636\pi\) |
0.173898 | − | 0.984764i | \(-0.444364\pi\) | |||||||
\(410\) | −13.2533 | − | 9.62908i | −0.654533 | − | 0.475546i | ||||
\(411\) | −5.23607 | + | 3.80423i | −0.258276 | + | 0.187649i | ||||
\(412\) | 1.79180 | − | 5.51458i | 0.0882755 | − | 0.271684i | ||||
\(413\) | 2.76393 | − | 8.50651i | 0.136004 | − | 0.418578i | ||||
\(414\) | −7.54508 | + | 5.48183i | −0.370821 | + | 0.269417i | ||||
\(415\) | 17.0344 | + | 12.3762i | 0.836188 | + | 0.607526i | ||||
\(416\) | 0.381966 | + | 1.17557i | 0.0187274 | + | 0.0576371i | ||||
\(417\) | 16.8541 | 0.825349 | ||||||||
\(418\) | 13.2361 | + | 2.97168i | 0.647397 | + | 0.145350i | ||||
\(419\) | 2.94427 | 0.143837 | 0.0719185 | − | 0.997411i | \(-0.477088\pi\) | ||||
0.0719185 | + | 0.997411i | \(0.477088\pi\) | |||||||
\(420\) | 0.427051 | + | 1.31433i | 0.0208380 | + | 0.0641326i | ||||
\(421\) | 12.3992 | + | 9.00854i | 0.604299 | + | 0.439049i | 0.847402 | − | 0.530951i | \(-0.178165\pi\) |
−0.243103 | + | 0.970000i | \(0.578165\pi\) | |||||||
\(422\) | 0.618034 | − | 0.449028i | 0.0300854 | − | 0.0218583i | ||||
\(423\) | 3.14590 | − | 9.68208i | 0.152959 | − | 0.470759i | ||||
\(424\) | −2.76393 | + | 8.50651i | −0.134228 | + | 0.413113i | ||||
\(425\) | 19.0451 | − | 13.8371i | 0.923822 | − | 0.671196i | ||||
\(426\) | 1.23607 | + | 0.898056i | 0.0598877 | + | 0.0435110i | ||||
\(427\) | 2.85410 | + | 8.78402i | 0.138120 | + | 0.425089i | ||||
\(428\) | −19.0344 | −0.920064 | ||||||||
\(429\) | 4.00000 | + | 0.898056i | 0.193122 | + | 0.0433585i | ||||
\(430\) | 7.23607 | 0.348954 | ||||||||
\(431\) | 2.86475 | + | 8.81678i | 0.137990 | + | 0.424689i | 0.996043 | − | 0.0888716i | \(-0.0283261\pi\) |
−0.858053 | + | 0.513561i | \(0.828326\pi\) | |||||||
\(432\) | −0.809017 | − | 0.587785i | −0.0389238 | − | 0.0282798i | ||||
\(433\) | 2.70820 | − | 1.96763i | 0.130148 | − | 0.0945580i | −0.520807 | − | 0.853675i | \(-0.674369\pi\) |
0.650955 | + | 0.759117i | \(0.274369\pi\) | |||||||
\(434\) | 0.336881 | − | 1.03681i | 0.0161708 | − | 0.0497686i | ||||
\(435\) | 0.527864 | − | 1.62460i | 0.0253091 | − | 0.0778935i | ||||
\(436\) | −3.73607 | + | 2.71441i | −0.178925 | + | 0.129997i | ||||
\(437\) | 30.8607 | + | 22.4216i | 1.47627 | + | 1.07257i | ||||
\(438\) | 2.47214 | + | 7.60845i | 0.118123 | + | 0.363546i | ||||
\(439\) | 22.0344 | 1.05165 | 0.525823 | − | 0.850594i | \(-0.323757\pi\) | ||||
0.525823 | + | 0.850594i | \(0.323757\pi\) | |||||||
\(440\) | 3.02786 | + | 3.44095i | 0.144348 | + | 0.164041i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.90983 | + | 8.95554i | 0.138407 | + | 0.425971i | ||||
\(443\) | 16.1631 | + | 11.7432i | 0.767933 | + | 0.557936i | 0.901333 | − | 0.433126i | \(-0.142590\pi\) |
−0.133400 | + | 0.991062i | \(0.542590\pi\) | |||||||
\(444\) | 6.97214 | − | 5.06555i | 0.330883 | − | 0.240401i | ||||
\(445\) | 2.19756 | − | 6.76340i | 0.104174 | − | 0.320616i | ||||
\(446\) | −0.972136 | + | 2.99193i | −0.0460320 | + | 0.141672i | ||||
\(447\) | 15.7082 | − | 11.4127i | 0.742973 | − | 0.539801i | ||||
\(448\) | 0.809017 | + | 0.587785i | 0.0382225 | + | 0.0277702i | ||||
\(449\) | 3.76393 | + | 11.5842i | 0.177631 | + | 0.546692i | 0.999744 | − | 0.0226327i | \(-0.00720482\pi\) |
−0.822113 | + | 0.569324i | \(0.807205\pi\) | |||||||
\(450\) | 3.09017 | 0.145672 | ||||||||
\(451\) | −20.0451 | + | 33.8218i | −0.943886 | + | 1.59260i | ||||
\(452\) | −6.47214 | −0.304424 | ||||||||
\(453\) | −2.76393 | − | 8.50651i | −0.129861 | − | 0.399671i | ||||
\(454\) | 10.9443 | + | 7.95148i | 0.513640 | + | 0.373181i | ||||
\(455\) | 1.38197 | − | 1.00406i | 0.0647876 | − | 0.0470709i | ||||
\(456\) | −1.26393 | + | 3.88998i | −0.0591890 | + | 0.182165i | ||||
\(457\) | −2.03444 | + | 6.26137i | −0.0951672 | + | 0.292894i | −0.987297 | − | 0.158884i | \(-0.949210\pi\) |
0.892130 | + | 0.451779i | \(0.149210\pi\) | |||||||
\(458\) | −23.3262 | + | 16.9475i | −1.08996 | + | 0.791905i | ||||
\(459\) | −6.16312 | − | 4.47777i | −0.287670 | − | 0.209004i | ||||
\(460\) | 3.98278 | + | 12.2577i | 0.185698 | + | 0.571520i | ||||
\(461\) | 19.8885 | 0.926302 | 0.463151 | − | 0.886279i | \(-0.346719\pi\) | ||||
0.463151 | + | 0.886279i | \(0.346719\pi\) | |||||||
\(462\) | 3.04508 | − | 1.31433i | 0.141670 | − | 0.0611481i | ||||
\(463\) | −37.4164 | −1.73889 | −0.869444 | − | 0.494032i | \(-0.835523\pi\) | ||||
−0.869444 | + | 0.494032i | \(0.835523\pi\) | |||||||
\(464\) | −0.381966 | − | 1.17557i | −0.0177323 | − | 0.0545745i | ||||
\(465\) | 1.21885 | + | 0.885544i | 0.0565227 | + | 0.0410661i | ||||
\(466\) | 16.0902 | − | 11.6902i | 0.745363 | − | 0.541538i | ||||
\(467\) | 2.47214 | − | 7.60845i | 0.114397 | − | 0.352077i | −0.877424 | − | 0.479716i | \(-0.840740\pi\) |
0.991821 | + | 0.127639i | \(0.0407398\pi\) | |||||||
\(468\) | −0.381966 | + | 1.17557i | −0.0176564 | + | 0.0543408i | ||||
\(469\) | −1.00000 | + | 0.726543i | −0.0461757 | + | 0.0335486i | ||||
\(470\) | −11.3820 | − | 8.26948i | −0.525011 | − | 0.381443i | ||||
\(471\) | 1.14590 | + | 3.52671i | 0.0528002 | + | 0.162502i | ||||
\(472\) | 8.94427 | 0.411693 | ||||||||
\(473\) | −1.61803 | − | 17.2905i | −0.0743973 | − | 0.795019i | ||||
\(474\) | 7.70820 | 0.354050 | ||||||||
\(475\) | −3.90576 | − | 12.0207i | −0.179209 | − | 0.551548i | ||||
\(476\) | 6.16312 | + | 4.47777i | 0.282486 | + | 0.205238i | ||||
\(477\) | −7.23607 | + | 5.25731i | −0.331317 | + | 0.240716i | ||||
\(478\) | −3.59017 | + | 11.0494i | −0.164211 | + | 0.505388i | ||||
\(479\) | 1.52786 | − | 4.70228i | 0.0698099 | − | 0.214853i | −0.910065 | − | 0.414466i | \(-0.863968\pi\) |
0.979875 | + | 0.199613i | \(0.0639685\pi\) | |||||||
\(480\) | −1.11803 | + | 0.812299i | −0.0510310 | + | 0.0370762i | ||||
\(481\) | −8.61803 | − | 6.26137i | −0.392949 | − | 0.285494i | ||||
\(482\) | 1.90983 | + | 5.87785i | 0.0869904 | + | 0.267729i | ||||
\(483\) | 9.32624 | 0.424359 | ||||||||
\(484\) | 7.54508 | − | 8.00448i | 0.342958 | − | 0.363840i | ||||
\(485\) | −15.5279 | −0.705084 | ||||||||
\(486\) | −0.309017 | − | 0.951057i | −0.0140173 | − | 0.0431408i | ||||
\(487\) | −26.1803 | − | 19.0211i | −1.18634 | − | 0.861930i | −0.193471 | − | 0.981106i | \(-0.561975\pi\) |
−0.992873 | + | 0.119176i | \(0.961975\pi\) | |||||||
\(488\) | −7.47214 | + | 5.42882i | −0.338248 | + | 0.245751i | ||||
\(489\) | 6.32624 | − | 19.4702i | 0.286082 | − | 0.880471i | ||||
\(490\) | 0.427051 | − | 1.31433i | 0.0192922 | − | 0.0593753i | ||||
\(491\) | 9.07295 | − | 6.59188i | 0.409456 | − | 0.297488i | −0.363925 | − | 0.931428i | \(-0.618564\pi\) |
0.773382 | + | 0.633941i | \(0.218564\pi\) | |||||||
\(492\) | −9.59017 | − | 6.96767i | −0.432358 | − | 0.314127i | ||||
\(493\) | −2.90983 | − | 8.95554i | −0.131052 | − | 0.403337i | ||||
\(494\) | 5.05573 | 0.227468 | ||||||||
\(495\) | 0.427051 | + | 4.56352i | 0.0191945 | + | 0.205115i | ||||
\(496\) | 1.09017 | 0.0489501 | ||||||||
\(497\) | −0.472136 | − | 1.45309i | −0.0211782 | − | 0.0651798i | ||||
\(498\) | 12.3262 | + | 8.95554i | 0.552352 | + | 0.401307i | ||||
\(499\) | −10.7082 | + | 7.77997i | −0.479365 | + | 0.348279i | −0.801080 | − | 0.598558i | \(-0.795741\pi\) |
0.321715 | + | 0.946837i | \(0.395741\pi\) | |||||||
\(500\) | 3.45492 | − | 10.6331i | 0.154508 | − | 0.475528i | ||||
\(501\) | 2.32624 | − | 7.15942i | 0.103929 | − | 0.319859i | ||||
\(502\) | −7.23607 | + | 5.25731i | −0.322962 | + | 0.234645i | ||||
\(503\) | 2.52786 | + | 1.83660i | 0.112712 | + | 0.0818900i | 0.642713 | − | 0.766107i | \(-0.277809\pi\) |
−0.530001 | + | 0.847997i | \(0.677809\pi\) | |||||||
\(504\) | 0.309017 | + | 0.951057i | 0.0137647 | + | 0.0423634i | ||||
\(505\) | −16.3820 | −0.728988 | ||||||||
\(506\) | 28.3992 | − | 12.2577i | 1.26250 | − | 0.544923i | ||||
\(507\) | −11.4721 | −0.509495 | ||||||||
\(508\) | 3.47214 | + | 10.6861i | 0.154051 | + | 0.474121i | ||||
\(509\) | 14.0623 | + | 10.2169i | 0.623301 | + | 0.452855i | 0.854073 | − | 0.520153i | \(-0.174125\pi\) |
−0.230772 | + | 0.973008i | \(0.574125\pi\) | |||||||
\(510\) | −8.51722 | + | 6.18812i | −0.377149 | + | 0.274015i | ||||
\(511\) | 2.47214 | − | 7.60845i | 0.109361 | − | 0.336578i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | −3.30902 | + | 2.40414i | −0.146097 | + | 0.106145i | ||||
\(514\) | −7.39919 | − | 5.37582i | −0.326364 | − | 0.237117i | ||||
\(515\) | −2.47620 | − | 7.62096i | −0.109114 | − | 0.335820i | ||||
\(516\) | 5.23607 | 0.230505 | ||||||||
\(517\) | −17.2148 | + | 29.0462i | −0.757105 | + | 1.27745i | ||||
\(518\) | −8.61803 | −0.378655 | ||||||||
\(519\) | 2.11803 | + | 6.51864i | 0.0929714 | + | 0.286136i | ||||
\(520\) | 1.38197 | + | 1.00406i | 0.0606032 | + | 0.0440308i | ||||
\(521\) | −23.0623 | + | 16.7557i | −1.01038 | + | 0.734083i | −0.964288 | − | 0.264855i | \(-0.914676\pi\) |
−0.0460896 | + | 0.998937i | \(0.514676\pi\) | |||||||
\(522\) | 0.381966 | − | 1.17557i | 0.0167182 | − | 0.0514533i | ||||
\(523\) | −1.26393 | + | 3.88998i | −0.0552679 | + | 0.170097i | −0.974880 | − | 0.222730i | \(-0.928503\pi\) |
0.919612 | + | 0.392827i | \(0.128503\pi\) | |||||||
\(524\) | −12.3262 | + | 8.95554i | −0.538474 | + | 0.391224i | ||||
\(525\) | −2.50000 | − | 1.81636i | −0.109109 | − | 0.0792723i | ||||
\(526\) | −2.17376 | − | 6.69015i | −0.0947805 | − | 0.291704i | ||||
\(527\) | 8.30495 | 0.361769 | ||||||||
\(528\) | 2.19098 | + | 2.48990i | 0.0953503 | + | 0.108359i | ||||
\(529\) | 63.9787 | 2.78168 | ||||||||
\(530\) | 3.81966 | + | 11.7557i | 0.165915 | + | 0.510635i | ||||
\(531\) | 7.23607 | + | 5.25731i | 0.314019 | + | 0.228148i | ||||
\(532\) | 3.30902 | − | 2.40414i | 0.143464 | − | 0.104233i | ||||
\(533\) | −4.52786 | + | 13.9353i | −0.196124 | + | 0.603606i | ||||
\(534\) | 1.59017 | − | 4.89404i | 0.0688134 | − | 0.211786i | ||||
\(535\) | −21.2812 | + | 15.4617i | −0.920064 | + | 0.668466i | ||||
\(536\) | −1.00000 | − | 0.726543i | −0.0431934 | − | 0.0313819i | ||||
\(537\) | 6.66312 | + | 20.5070i | 0.287535 | + | 0.884941i | ||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | −3.23607 | − | 0.726543i | −0.139387 | − | 0.0312944i | ||||
\(540\) | −1.38197 | −0.0594703 | ||||||||
\(541\) | −3.71885 | − | 11.4454i | −0.159886 | − | 0.492078i | 0.838737 | − | 0.544536i | \(-0.183294\pi\) |
−0.998623 | + | 0.0524585i | \(0.983294\pi\) | |||||||
\(542\) | 4.11803 | + | 2.99193i | 0.176885 | + | 0.128514i | ||||
\(543\) | −6.47214 | + | 4.70228i | −0.277746 | + | 0.201794i | ||||
\(544\) | −2.35410 | + | 7.24518i | −0.100931 | + | 0.310635i | ||||
\(545\) | −1.97214 | + | 6.06961i | −0.0844770 | + | 0.259994i | ||||
\(546\) | 1.00000 | − | 0.726543i | 0.0427960 | − | 0.0310931i | ||||
\(547\) | −14.1803 | − | 10.3026i | −0.606308 | − | 0.440508i | 0.241805 | − | 0.970325i | \(-0.422261\pi\) |
−0.848112 | + | 0.529817i | \(0.822261\pi\) | |||||||
\(548\) | 2.00000 | + | 6.15537i | 0.0854358 | + | 0.262944i | ||||
\(549\) | −9.23607 | −0.394186 | ||||||||
\(550\) | −10.0000 | − | 2.24514i | −0.426401 | − | 0.0957331i | ||||
\(551\) | −5.05573 | −0.215381 | ||||||||
\(552\) | 2.88197 | + | 8.86978i | 0.122665 | + | 0.377523i | ||||
\(553\) | −6.23607 | − | 4.53077i | −0.265185 | − | 0.192668i | ||||
\(554\) | 2.54508 | − | 1.84911i | 0.108130 | − | 0.0785613i | ||||
\(555\) | 3.68034 | − | 11.3269i | 0.156222 | − | 0.480801i | ||||
\(556\) | 5.20820 | − | 16.0292i | 0.220877 | − | 0.679790i | ||||
\(557\) | 23.3262 | − | 16.9475i | 0.988364 | − | 0.718089i | 0.0288021 | − | 0.999585i | \(-0.490831\pi\) |
0.959562 | + | 0.281496i | \(0.0908307\pi\) | |||||||
\(558\) | 0.881966 | + | 0.640786i | 0.0373366 | + | 0.0271266i | ||||
\(559\) | −2.00000 | − | 6.15537i | −0.0845910 | − | 0.260344i | ||||
\(560\) | 1.38197 | 0.0583987 | ||||||||
\(561\) | 16.6910 | + | 18.9681i | 0.704694 | + | 0.800835i | ||||
\(562\) | −14.6525 | −0.618077 | ||||||||
\(563\) | 3.85410 | + | 11.8617i | 0.162431 | + | 0.499911i | 0.998838 | − | 0.0481979i | \(-0.0153478\pi\) |
−0.836407 | + | 0.548109i | \(0.815348\pi\) | |||||||
\(564\) | −8.23607 | − | 5.98385i | −0.346801 | − | 0.251966i | ||||
\(565\) | −7.23607 | + | 5.25731i | −0.304424 | + | 0.221177i | ||||
\(566\) | −0.336881 | + | 1.03681i | −0.0141602 | + | 0.0435805i | ||||
\(567\) | −0.309017 | + | 0.951057i | −0.0129775 | + | 0.0399406i | ||||
\(568\) | 1.23607 | − | 0.898056i | 0.0518643 | − | 0.0376816i | ||||
\(569\) | −18.7082 | − | 13.5923i | −0.784289 | − | 0.569819i | 0.121974 | − | 0.992533i | \(-0.461077\pi\) |
−0.906263 | + | 0.422714i | \(0.861077\pi\) | |||||||
\(570\) | 1.74671 | + | 5.37582i | 0.0731617 | + | 0.225168i | ||||
\(571\) | −19.7082 | −0.824763 | −0.412381 | − | 0.911011i | \(-0.635303\pi\) | ||||
−0.412381 | + | 0.911011i | \(0.635303\pi\) | |||||||
\(572\) | 2.09017 | − | 3.52671i | 0.0873944 | − | 0.147459i | ||||
\(573\) | 11.0902 | 0.463298 | ||||||||
\(574\) | 3.66312 | + | 11.2739i | 0.152896 | + | 0.470564i | ||||
\(575\) | −23.3156 | − | 16.9398i | −0.972328 | − | 0.706437i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 0.472136 | − | 1.45309i | 0.0196553 | − | 0.0604927i | −0.940748 | − | 0.339107i | \(-0.889875\pi\) |
0.960403 | + | 0.278614i | \(0.0898751\pi\) | |||||||
\(578\) | −12.6803 | + | 39.0261i | −0.527433 | + | 1.62327i | ||||
\(579\) | 1.50000 | − | 1.08981i | 0.0623379 | − | 0.0452911i | ||||
\(580\) | −1.38197 | − | 1.00406i | −0.0573830 | − | 0.0416912i | ||||
\(581\) | −4.70820 | − | 14.4904i | −0.195329 | − | 0.601162i | ||||
\(582\) | −11.2361 | −0.465750 | ||||||||
\(583\) | 27.2361 | − | 11.7557i | 1.12800 | − | 0.486872i | ||||
\(584\) | 8.00000 | 0.331042 | ||||||||
\(585\) | 0.527864 | + | 1.62460i | 0.0218245 | + | 0.0671689i | ||||
\(586\) | 7.11803 | + | 5.17155i | 0.294043 | + | 0.213635i | ||||
\(587\) | 19.3262 | − | 14.0413i | 0.797679 | − | 0.579548i | −0.112553 | − | 0.993646i | \(-0.535903\pi\) |
0.910232 | + | 0.414098i | \(0.135903\pi\) | |||||||
\(588\) | 0.309017 | − | 0.951057i | 0.0127436 | − | 0.0392209i | ||||
\(589\) | 1.37790 | − | 4.24074i | 0.0567754 | − | 0.174737i | ||||
\(590\) | 10.0000 | − | 7.26543i | 0.411693 | − | 0.299113i | ||||
\(591\) | −15.1803 | − | 11.0292i | −0.624436 | − | 0.453679i | ||||
\(592\) | −2.66312 | − | 8.19624i | −0.109454 | − | 0.336863i | ||||
\(593\) | −13.7426 | −0.564343 | −0.282171 | − | 0.959364i | \(-0.591055\pi\) | ||||
−0.282171 | + | 0.959364i | \(0.591055\pi\) | |||||||
\(594\) | 0.309017 | + | 3.30220i | 0.0126791 | + | 0.135491i | ||||
\(595\) | 10.5279 | 0.431600 | ||||||||
\(596\) | −6.00000 | − | 18.4661i | −0.245770 | − | 0.756401i | ||||
\(597\) | 6.69098 | + | 4.86128i | 0.273844 | + | 0.198959i | ||||
\(598\) | 9.32624 | − | 6.77591i | 0.381378 | − | 0.277088i | ||||
\(599\) | 2.82624 | − | 8.69827i | 0.115477 | − | 0.355402i | −0.876569 | − | 0.481276i | \(-0.840174\pi\) |
0.992046 | + | 0.125874i | \(0.0401736\pi\) | |||||||
\(600\) | 0.954915 | − | 2.93893i | 0.0389842 | − | 0.119981i | ||||
\(601\) | 6.09017 | − | 4.42477i | 0.248423 | − | 0.180490i | −0.456604 | − | 0.889670i | \(-0.650935\pi\) |
0.705028 | + | 0.709180i | \(0.250935\pi\) | |||||||
\(602\) | −4.23607 | − | 3.07768i | −0.172649 | − | 0.125437i | ||||
\(603\) | −0.381966 | − | 1.17557i | −0.0155549 | − | 0.0478729i | ||||
\(604\) | −8.94427 | −0.363937 | ||||||||
\(605\) | 1.93363 | − | 15.0781i | 0.0786132 | − | 0.613014i | ||||
\(606\) | −11.8541 | −0.481540 | ||||||||
\(607\) | 9.38854 | + | 28.8950i | 0.381069 | + | 1.17281i | 0.939292 | + | 0.343119i | \(0.111484\pi\) |
−0.558223 | + | 0.829691i | \(0.688516\pi\) | |||||||
\(608\) | 3.30902 | + | 2.40414i | 0.134198 | + | 0.0975008i | ||||
\(609\) | −1.00000 | + | 0.726543i | −0.0405220 | + | 0.0294410i | ||||
\(610\) | −3.94427 | + | 12.1392i | −0.159699 | + | 0.491503i | ||||
\(611\) | −3.88854 | + | 11.9677i | −0.157314 | + | 0.484162i | ||||
\(612\) | −6.16312 | + | 4.47777i | −0.249129 | + | 0.181003i | ||||
\(613\) | −7.01722 | − | 5.09831i | −0.283423 | − | 0.205919i | 0.436986 | − | 0.899468i | \(-0.356046\pi\) |
−0.720409 | + | 0.693549i | \(0.756046\pi\) | |||||||
\(614\) | −4.89919 | − | 15.0781i | −0.197715 | − | 0.608504i | ||||
\(615\) | −16.3820 | −0.660585 | ||||||||
\(616\) | −0.309017 | − | 3.30220i | −0.0124506 | − | 0.133049i | ||||
\(617\) | −33.4164 | −1.34529 | −0.672647 | − | 0.739964i | \(-0.734843\pi\) | ||||
−0.672647 | + | 0.739964i | \(0.734843\pi\) | |||||||
\(618\) | −1.79180 | − | 5.51458i | −0.0720766 | − | 0.221829i | ||||
\(619\) | 7.88197 | + | 5.72658i | 0.316803 | + | 0.230171i | 0.734810 | − | 0.678273i | \(-0.237271\pi\) |
−0.418007 | + | 0.908444i | \(0.637271\pi\) | |||||||
\(620\) | 1.21885 | − | 0.885544i | 0.0489501 | − | 0.0355643i | ||||
\(621\) | −2.88197 | + | 8.86978i | −0.115649 | + | 0.355932i | ||||
\(622\) | 4.18034 | − | 12.8658i | 0.167616 | − | 0.515870i | ||||
\(623\) | −4.16312 | + | 3.02468i | −0.166792 | + | 0.121181i | ||||
\(624\) | 1.00000 | + | 0.726543i | 0.0400320 | + | 0.0290850i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.2918 | −0.571215 | ||||||||
\(627\) | 12.4549 | − | 5.37582i | 0.497401 | − | 0.214690i | ||||
\(628\) | 3.70820 | 0.147973 | ||||||||
\(629\) | −20.2877 | − | 62.4392i | −0.808925 | − | 2.48961i | ||||
\(630\) | 1.11803 | + | 0.812299i | 0.0445435 | + | 0.0323628i | ||||
\(631\) | 7.94427 | − | 5.77185i | 0.316256 | − | 0.229774i | −0.418320 | − | 0.908300i | \(-0.637381\pi\) |
0.734576 | + | 0.678526i | \(0.237381\pi\) | |||||||
\(632\) | 2.38197 | − | 7.33094i | 0.0947495 | − | 0.291609i | ||||
\(633\) | 0.236068 | − | 0.726543i | 0.00938286 | − | 0.0288775i | ||||
\(634\) | 9.70820 | − | 7.05342i | 0.385562 | − | 0.280127i | ||||
\(635\) | 12.5623 | + | 9.12705i | 0.498520 | + | 0.362196i | ||||
\(636\) | 2.76393 | + | 8.50651i | 0.109597 | + | 0.337305i | ||||
\(637\) | −1.23607 | −0.0489748 | ||||||||
\(638\) | −2.09017 | + | 3.52671i | −0.0827506 | + | 0.139624i | ||||
\(639\) | 1.52786 | 0.0604414 | ||||||||
\(640\) | 0.427051 | + | 1.31433i | 0.0168807 | + | 0.0519534i | ||||
\(641\) | −31.8885 | − | 23.1684i | −1.25952 | − | 0.915096i | −0.260788 | − | 0.965396i | \(-0.583982\pi\) |
−0.998734 | + | 0.0503001i | \(0.983982\pi\) | |||||||
\(642\) | −15.3992 | + | 11.1882i | −0.607757 | + | 0.441562i | ||||
\(643\) | −2.15248 | + | 6.62464i | −0.0848854 | + | 0.261250i | −0.984486 | − | 0.175463i | \(-0.943858\pi\) |
0.899601 | + | 0.436714i | \(0.143858\pi\) | |||||||
\(644\) | 2.88197 | − | 8.86978i | 0.113565 | − | 0.349518i | ||||
\(645\) | 5.85410 | − | 4.25325i | 0.230505 | − | 0.167472i | ||||
\(646\) | 25.2082 | + | 18.3148i | 0.991804 | + | 0.720587i | ||||
\(647\) | −0.381966 | − | 1.17557i | −0.0150166 | − | 0.0462164i | 0.943267 | − | 0.332034i | \(-0.107735\pi\) |
−0.958284 | + | 0.285818i | \(0.907735\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −19.5967 | − | 22.2703i | −0.769240 | − | 0.874187i | ||||
\(650\) | −3.81966 | −0.149819 | ||||||||
\(651\) | −0.336881 | − | 1.03681i | −0.0132034 | − | 0.0406359i | ||||
\(652\) | −16.5623 | − | 12.0332i | −0.648630 | − | 0.471257i | ||||
\(653\) | 22.0902 | − | 16.0494i | 0.864455 | − | 0.628063i | −0.0646382 | − | 0.997909i | \(-0.520589\pi\) |
0.929093 | + | 0.369845i | \(0.120589\pi\) | |||||||
\(654\) | −1.42705 | + | 4.39201i | −0.0558021 | + | 0.171741i | ||||
\(655\) | −6.50658 | + | 20.0252i | −0.254233 | + | 0.782449i | ||||
\(656\) | −9.59017 | + | 6.96767i | −0.374433 | + | 0.272042i | ||||
\(657\) | 6.47214 | + | 4.70228i | 0.252502 | + | 0.183453i | ||||
\(658\) | 3.14590 | + | 9.68208i | 0.122640 | + | 0.377447i | ||||
\(659\) | −31.1591 | −1.21378 | −0.606892 | − | 0.794784i | \(-0.707584\pi\) | ||||
−0.606892 | + | 0.794784i | \(0.707584\pi\) | |||||||
\(660\) | 4.47214 | + | 1.00406i | 0.174078 | + | 0.0390829i | ||||
\(661\) | 15.8885 | 0.617993 | 0.308996 | − | 0.951063i | \(-0.400007\pi\) | ||||
0.308996 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(662\) | 0.0557281 | + | 0.171513i | 0.00216593 | + | 0.00666606i | ||||
\(663\) | 7.61803 | + | 5.53483i | 0.295860 | + | 0.214955i | ||||
\(664\) | 12.3262 | − | 8.95554i | 0.478351 | − | 0.347542i | ||||
\(665\) | 1.74671 | − | 5.37582i | 0.0677346 | − | 0.208466i | ||||
\(666\) | 2.66312 | − | 8.19624i | 0.103194 | − | 0.317598i | ||||
\(667\) | −9.32624 | + | 6.77591i | −0.361113 | + | 0.262364i | ||||
\(668\) | −6.09017 | − | 4.42477i | −0.235636 | − | 0.171199i | ||||
\(669\) | 0.972136 | + | 2.99193i | 0.0375849 | + | 0.115675i | ||||
\(670\) | −1.70820 | −0.0659937 | ||||||||
\(671\) | 29.8885 | + | 6.71040i | 1.15383 | + | 0.259052i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −8.43769 | − | 25.9686i | −0.325249 | − | 1.00101i | −0.971328 | − | 0.237743i | \(-0.923592\pi\) |
0.646079 | − | 0.763271i | \(-0.276408\pi\) | |||||||
\(674\) | −6.73607 | − | 4.89404i | −0.259464 | − | 0.188511i | ||||
\(675\) | 2.50000 | − | 1.81636i | 0.0962250 | − | 0.0699116i | ||||
\(676\) | −3.54508 | + | 10.9106i | −0.136349 | + | 0.419640i | ||||
\(677\) | 4.14590 | − | 12.7598i | 0.159340 | − | 0.490397i | −0.839235 | − | 0.543769i | \(-0.816997\pi\) |
0.998575 | + | 0.0533715i | \(0.0169968\pi\) | |||||||
\(678\) | −5.23607 | + | 3.80423i | −0.201090 | + | 0.146100i | ||||
\(679\) | 9.09017 | + | 6.60440i | 0.348849 | + | 0.253453i | ||||
\(680\) | 3.25329 | + | 10.0126i | 0.124758 | + | 0.383965i | ||||
\(681\) | 13.5279 | 0.518389 | ||||||||
\(682\) | −2.38854 | − | 2.71441i | −0.0914621 | − | 0.103940i | ||||
\(683\) | 18.4377 | 0.705499 | 0.352749 | − | 0.935718i | \(-0.385247\pi\) | ||||
0.352749 | + | 0.935718i | \(0.385247\pi\) | |||||||
\(684\) | 1.26393 | + | 3.88998i | 0.0483276 | + | 0.148737i | ||||
\(685\) | 7.23607 | + | 5.25731i | 0.276476 | + | 0.200872i | ||||
\(686\) | −0.809017 | + | 0.587785i | −0.0308884 | + | 0.0224417i | ||||
\(687\) | −8.90983 | + | 27.4216i | −0.339931 | + | 1.04620i | ||||
\(688\) | 1.61803 | − | 4.97980i | 0.0616870 | − | 0.189853i | ||||
\(689\) | 8.94427 | − | 6.49839i | 0.340750 | − | 0.247569i | ||||
\(690\) | 10.4271 | + | 7.57570i | 0.396951 | + | 0.288402i | ||||
\(691\) | −7.50000 | − | 23.0826i | −0.285313 | − | 0.878104i | −0.986305 | − | 0.164934i | \(-0.947259\pi\) |
0.700991 | − | 0.713170i | \(-0.252741\pi\) | |||||||
\(692\) | 6.85410 | 0.260554 | ||||||||
\(693\) | 1.69098 | − | 2.85317i | 0.0642351 | − | 0.108383i | ||||
\(694\) | −10.7984 | −0.409901 | ||||||||
\(695\) | −7.19756 | − | 22.1518i | −0.273019 | − | 0.840266i | ||||
\(696\) | −1.00000 | − | 0.726543i | −0.0379049 | − | 0.0275395i | ||||
\(697\) | −73.0582 | + | 53.0799i | −2.76728 | + | 2.01055i | ||||
\(698\) | 2.94427 | − | 9.06154i | 0.111442 | − | 0.342984i | ||||
\(699\) | 6.14590 | − | 18.9151i | 0.232459 | − | 0.715436i | ||||
\(700\) | −2.50000 | + | 1.81636i | −0.0944911 | + | 0.0686518i | ||||
\(701\) | −24.0902 | − | 17.5025i | −0.909873 | − | 0.661062i | 0.0311096 | − | 0.999516i | \(-0.490096\pi\) |
−0.940983 | + | 0.338454i | \(0.890096\pi\) | |||||||
\(702\) | 0.381966 | + | 1.17557i | 0.0144164 | + | 0.0443690i | ||||
\(703\) | −35.2492 | −1.32945 | ||||||||
\(704\) | 3.04508 | − | 1.31433i | 0.114766 | − | 0.0495356i | ||||
\(705\) | −14.0689 | −0.529865 | ||||||||
\(706\) | −7.09017 | − | 21.8213i | −0.266842 | − | 0.821255i | ||||
\(707\) | 9.59017 | + | 6.96767i | 0.360675 | + | 0.262046i | ||||
\(708\) | 7.23607 | − | 5.25731i | 0.271948 | − | 0.197582i | ||||
\(709\) | −4.10081 | + | 12.6210i | −0.154009 | + | 0.473992i | −0.998059 | − | 0.0622729i | \(-0.980165\pi\) |
0.844050 | + | 0.536265i | \(0.180165\pi\) | |||||||
\(710\) | 0.652476 | − | 2.00811i | 0.0244870 | − | 0.0753632i | ||||
\(711\) | 6.23607 | − | 4.53077i | 0.233871 | − | 0.169917i | ||||
\(712\) | −4.16312 | − | 3.02468i | −0.156019 | − | 0.113355i | ||||
\(713\) | −3.14183 | − | 9.66957i | −0.117663 | − | 0.362128i | ||||
\(714\) | 7.61803 | 0.285098 | ||||||||
\(715\) | −0.527864 | − | 5.64083i | −0.0197410 | − | 0.210955i | ||||
\(716\) | 21.5623 | 0.805821 | ||||||||
\(717\) | 3.59017 | + | 11.0494i | 0.134077 | + | 0.412648i | ||||
\(718\) | −24.4443 | − | 17.7598i | −0.912252 | − | 0.662790i | ||||
\(719\) | 1.90983 | − | 1.38757i | 0.0712246 | − | 0.0517477i | −0.551603 | − | 0.834107i | \(-0.685984\pi\) |
0.622828 | + | 0.782359i | \(0.285984\pi\) | |||||||
\(720\) | −0.427051 | + | 1.31433i | −0.0159153 | + | 0.0489821i | ||||
\(721\) | −1.79180 | + | 5.51458i | −0.0667300 | + | 0.205374i | ||||
\(722\) | −1.83688 | + | 1.33457i | −0.0683616 | + | 0.0496676i | ||||
\(723\) | 5.00000 | + | 3.63271i | 0.185952 | + | 0.135102i | ||||
\(724\) | 2.47214 | + | 7.60845i | 0.0918762 | + | 0.282766i | ||||
\(725\) | 3.81966 | 0.141859 | ||||||||
\(726\) | 1.39919 | − | 10.9106i | 0.0519287 | − | 0.404932i | ||||
\(727\) | 23.5066 | 0.871811 | 0.435905 | − | 0.899993i | \(-0.356428\pi\) | ||||
0.435905 | + | 0.899993i | \(0.356428\pi\) | |||||||
\(728\) | −0.381966 | − | 1.17557i | −0.0141566 | − | 0.0435695i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 8.94427 | − | 6.49839i | 0.331042 | − | 0.240516i | ||||
\(731\) | 12.3262 | − | 37.9363i | 0.455902 | − | 1.40312i | ||||
\(732\) | −2.85410 | + | 8.78402i | −0.105491 | + | 0.324667i | ||||
\(733\) | 1.52786 | − | 1.11006i | 0.0564329 | − | 0.0410009i | −0.559211 | − | 0.829025i | \(-0.688896\pi\) |
0.615644 | + | 0.788024i | \(0.288896\pi\) | |||||||
\(734\) | −15.8262 | − | 11.4984i | −0.584157 | − | 0.424415i | ||||
\(735\) | −0.427051 | − | 1.31433i | −0.0157520 | − | 0.0484797i | ||||
\(736\) | 9.32624 | 0.343770 | ||||||||
\(737\) | 0.381966 | + | 4.08174i | 0.0140699 | + | 0.150353i | ||||
\(738\) | −11.8541 | −0.436356 | ||||||||
\(739\) | 0.236068 | + | 0.726543i | 0.00868390 | + | 0.0267263i | 0.955305 | − | 0.295623i | \(-0.0955273\pi\) |
−0.946621 | + | 0.322350i | \(0.895527\pi\) | |||||||
\(740\) | −9.63525 | − | 7.00042i | −0.354199 | − | 0.257341i | ||||
\(741\) | 4.09017 | − | 2.97168i | 0.150256 | − | 0.109167i | ||||
\(742\) | 2.76393 | − | 8.50651i | 0.101467 | − | 0.312284i | ||||
\(743\) | 11.6287 | − | 35.7894i | 0.426615 | − | 1.31299i | −0.474825 | − | 0.880080i | \(-0.657489\pi\) |
0.901440 | − | 0.432905i | \(-0.142511\pi\) | |||||||
\(744\) | 0.881966 | − | 0.640786i | 0.0323344 | − | 0.0234923i | ||||
\(745\) | −21.7082 | − | 15.7719i | −0.795327 | − | 0.577839i | ||||
\(746\) | −8.19098 | − | 25.2093i | −0.299893 | − | 0.922976i | ||||
\(747\) | 15.2361 | 0.557459 | ||||||||
\(748\) | 23.1976 | − | 10.0126i | 0.848187 | − | 0.366097i | ||||
\(749\) | 19.0344 | 0.695503 | ||||||||
\(750\) | −3.45492 | − | 10.6331i | −0.126156 | − | 0.388267i | ||||
\(751\) | 13.3262 | + | 9.68208i | 0.486281 | + | 0.353304i | 0.803752 | − | 0.594964i | \(-0.202834\pi\) |
−0.317471 | + | 0.948268i | \(0.602834\pi\) | |||||||
\(752\) | −8.23607 | + | 5.98385i | −0.300338 | + | 0.218209i | ||||
\(753\) | −2.76393 | + | 8.50651i | −0.100723 | + | 0.309994i | ||||
\(754\) | −0.472136 | + | 1.45309i | −0.0171942 | + | 0.0529182i | ||||
\(755\) | −10.0000 | + | 7.26543i | −0.363937 | + | 0.264416i | ||||
\(756\) | 0.809017 | + | 0.587785i | 0.0294237 | + | 0.0213775i | ||||
\(757\) | −2.02786 | − | 6.24112i | −0.0737040 | − | 0.226838i | 0.907417 | − | 0.420230i | \(-0.138051\pi\) |
−0.981121 | + | 0.193393i | \(0.938051\pi\) | |||||||
\(758\) | −21.7082 | −0.788477 | ||||||||
\(759\) | 15.7705 | − | 26.6093i | 0.572433 | − | 0.965858i | ||||
\(760\) | 5.65248 | 0.205037 | ||||||||
\(761\) | 7.67376 | + | 23.6174i | 0.278174 | + | 0.856130i | 0.988362 | + | 0.152119i | \(0.0486097\pi\) |
−0.710189 | + | 0.704012i | \(0.751390\pi\) | |||||||
\(762\) | 9.09017 | + | 6.60440i | 0.329302 | + | 0.239252i | ||||
\(763\) | 3.73607 | − | 2.71441i | 0.135255 | − | 0.0982683i | ||||
\(764\) | 3.42705 | − | 10.5474i | 0.123986 | − | 0.381591i | ||||
\(765\) | −3.25329 | + | 10.0126i | −0.117623 | + | 0.362006i | ||||
\(766\) | 4.85410 | − | 3.52671i | 0.175386 | − | 0.127425i | ||||
\(767\) | −8.94427 | − | 6.49839i | −0.322959 | − | 0.234643i | ||||
\(768\) | 0.309017 | + | 0.951057i | 0.0111507 | + | 0.0343183i | ||||
\(769\) | 10.4721 | 0.377635 | 0.188817 | − | 0.982012i | \(-0.439535\pi\) | ||||
0.188817 | + | 0.982012i | \(0.439535\pi\) | |||||||
\(770\) | −3.02786 | − | 3.44095i | −0.109117 | − | 0.124003i | ||||
\(771\) | −9.14590 | −0.329381 | ||||||||
\(772\) | −0.572949 | − | 1.76336i | −0.0206209 | − | 0.0634646i | ||||
\(773\) | 32.5623 | + | 23.6579i | 1.17118 | + | 0.850916i | 0.991150 | − | 0.132745i | \(-0.0423791\pi\) |
0.180034 | + | 0.983660i | \(0.442379\pi\) | |||||||
\(774\) | 4.23607 | − | 3.07768i | 0.152262 | − | 0.110625i | ||||
\(775\) | −1.04102 | + | 3.20393i | −0.0373945 | + | 0.115089i | ||||
\(776\) | −3.47214 | + | 10.6861i | −0.124642 | + | 0.383610i | ||||
\(777\) | −6.97214 | + | 5.06555i | −0.250124 | + | 0.181726i | ||||
\(778\) | 21.1803 | + | 15.3884i | 0.759352 | + | 0.551702i | ||||
\(779\) | 14.9828 | + | 46.1123i | 0.536814 | + | 1.65214i | ||||
\(780\) | 1.70820 | 0.0611635 | ||||||||
\(781\) | −4.94427 | − | 1.11006i | −0.176920 | − | 0.0397210i | ||||
\(782\) | 71.0476 | 2.54066 | ||||||||
\(783\) | −0.381966 | − | 1.17557i | −0.0136504 | − | 0.0420115i | ||||
\(784\) | −0.809017 | − | 0.587785i | −0.0288935 | − | 0.0209923i | ||||
\(785\) | 4.14590 | − | 3.01217i | 0.147973 | − | 0.107509i | ||||
\(786\) | −4.70820 | + | 14.4904i | −0.167936 | + | 0.516854i | ||||
\(787\) | −4.60739 | + | 14.1801i | −0.164236 | + | 0.505466i | −0.998979 | − | 0.0451735i | \(-0.985616\pi\) |
0.834743 | + | 0.550639i | \(0.185616\pi\) | |||||||
\(788\) | −15.1803 | + | 11.0292i | −0.540777 | + | 0.392898i | ||||
\(789\) | −5.69098 | − | 4.13474i | −0.202604 | − | 0.147201i | ||||
\(790\) | −3.29180 | − | 10.1311i | −0.117117 | − | 0.360449i | ||||
\(791\) | 6.47214 | 0.230123 | ||||||||
\(792\) | 3.23607 | + | 0.726543i | 0.114989 | + | 0.0258166i | ||||
\(793\) | 11.4164 | 0.405409 | ||||||||
\(794\) | −4.94427 | − | 15.2169i | −0.175466 | − | 0.540028i | ||||
\(795\) | 10.0000 | + | 7.26543i | 0.354663 | + | 0.257678i | ||||
\(796\) | 6.69098 | − | 4.86128i | 0.237156 | − | 0.172304i | ||||
\(797\) | 1.07953 | − | 3.32244i | 0.0382388 | − | 0.117687i | −0.930115 | − | 0.367268i | \(-0.880293\pi\) |
0.968354 | + | 0.249581i | \(0.0802930\pi\) | |||||||
\(798\) | 1.26393 | − | 3.88998i | 0.0447427 | − | 0.137704i | ||||
\(799\) | −62.7426 | + | 45.5852i | −2.21968 | + | 1.61269i | ||||
\(800\) | −2.50000 | − | 1.81636i | −0.0883883 | − | 0.0642179i | ||||
\(801\) | −1.59017 | − | 4.89404i | −0.0561859 | − | 0.172922i | ||||
\(802\) | 11.7082 | 0.413431 | ||||||||
\(803\) | −17.5279 | − | 19.9192i | −0.618545 | − | 0.702933i | ||||
\(804\) | −1.23607 | −0.0435928 | ||||||||
\(805\) | −3.98278 | − | 12.2577i | −0.140375 | − | 0.432028i | ||||
\(806\) | −1.09017 | − | 0.792055i | −0.0383996 | − | 0.0278989i | ||||
\(807\) | −4.85410 | + | 3.52671i | −0.170872 | + | 0.124146i | ||||
\(808\) | −3.66312 | + | 11.2739i | −0.128868 | + | 0.396615i | ||||
\(809\) | 7.14590 | − | 21.9928i | 0.251236 | − | 0.773226i | −0.743312 | − | 0.668945i | \(-0.766746\pi\) |
0.994548 | − | 0.104281i | \(-0.0332540\pi\) | |||||||
\(810\) | −1.11803 | + | 0.812299i | −0.0392837 | + | 0.0285413i | ||||
\(811\) | 11.4164 | + | 8.29451i | 0.400884 | + | 0.291259i | 0.769901 | − | 0.638163i | \(-0.220306\pi\) |
−0.369017 | + | 0.929423i | \(0.620306\pi\) | |||||||
\(812\) | 0.381966 | + | 1.17557i | 0.0134044 | + | 0.0412544i | ||||
\(813\) | 5.09017 | 0.178520 | ||||||||
\(814\) | −14.5729 | + | 24.5887i | −0.510782 | + | 0.861834i | ||||
\(815\) | −28.2918 | −0.991018 | ||||||||
\(816\) | 2.35410 | + | 7.24518i | 0.0824101 | + | 0.253632i | ||||
\(817\) | −17.3262 | − | 12.5882i | −0.606168 | − | 0.440407i | ||||
\(818\) | −28.8885 | + | 20.9888i | −1.01006 | + | 0.733855i | ||||
\(819\) | 0.381966 | − | 1.17557i | 0.0133470 | − | 0.0410778i | ||||
\(820\) | −5.06231 | + | 15.5802i | −0.176783 | + | 0.544083i | ||||
\(821\) | 15.9443 | − | 11.5842i | 0.556459 | − | 0.404291i | −0.273702 | − | 0.961814i | \(-0.588248\pi\) |
0.830161 | + | 0.557523i | \(0.188248\pi\) | |||||||
\(822\) | 5.23607 | + | 3.80423i | 0.182629 | + | 0.132688i | ||||
\(823\) | 14.5836 | + | 44.8837i | 0.508352 | + | 1.56455i | 0.795061 | + | 0.606529i | \(0.207439\pi\) |
−0.286709 | + | 0.958018i | \(0.592561\pi\) | |||||||
\(824\) | −5.79837 | −0.201996 | ||||||||
\(825\) | −9.40983 | + | 4.06150i | −0.327608 | + | 0.141403i | ||||
\(826\) | −8.94427 | −0.311211 | ||||||||
\(827\) | −14.7016 | − | 45.2470i | −0.511226 | − | 1.57339i | −0.790046 | − | 0.613047i | \(-0.789943\pi\) |
0.278820 | − | 0.960343i | \(-0.410057\pi\) | |||||||
\(828\) | 7.54508 | + | 5.48183i | 0.262210 | + | 0.190507i | ||||
\(829\) | 2.61803 | − | 1.90211i | 0.0909281 | − | 0.0660631i | −0.541392 | − | 0.840770i | \(-0.682103\pi\) |
0.632320 | + | 0.774707i | \(0.282103\pi\) | |||||||
\(830\) | 6.50658 | − | 20.0252i | 0.225847 | − | 0.695084i | ||||
\(831\) | 0.972136 | − | 2.99193i | 0.0337230 | − | 0.103789i | ||||
\(832\) | 1.00000 | − | 0.726543i | 0.0346688 | − | 0.0251883i | ||||
\(833\) | −6.16312 | − | 4.47777i | −0.213539 | − | 0.155145i | ||||
\(834\) | −5.20820 | − | 16.0292i | −0.180345 | − | 0.555046i | ||||
\(835\) | −10.4033 | −0.360019 | ||||||||
\(836\) | −1.26393 | − | 13.5065i | −0.0437140 | − | 0.467134i | ||||
\(837\) | 1.09017 | 0.0376818 | ||||||||
\(838\) | −0.909830 | − | 2.80017i | −0.0314296 | − | 0.0967302i | ||||
\(839\) | 25.8885 | + | 18.8091i | 0.893772 | + | 0.649363i | 0.936859 | − | 0.349708i | \(-0.113719\pi\) |
−0.0430869 | + | 0.999071i | \(0.513719\pi\) | |||||||
\(840\) | 1.11803 | − | 0.812299i | 0.0385758 | − | 0.0280270i | ||||
\(841\) | −8.48936 | + | 26.1276i | −0.292736 | + | 0.900950i | ||||
\(842\) | 4.73607 | − | 14.5761i | 0.163216 | − | 0.502326i | ||||
\(843\) | −11.8541 | + | 8.61251i | −0.408277 | + | 0.296631i | ||||
\(844\) | −0.618034 | − | 0.449028i | −0.0212736 | − | 0.0154562i | ||||
\(845\) | 4.89919 | + | 15.0781i | 0.168537 | + | 0.518704i | ||||
\(846\) | −10.1803 | −0.350007 | ||||||||
\(847\) | −7.54508 | + | 8.00448i | −0.259252 | + | 0.275037i | ||||
\(848\) | 8.94427 | 0.307148 | ||||||||
\(849\) | 0.336881 | + | 1.03681i | 0.0115617 | + | 0.0355833i | ||||
\(850\) | −19.0451 | − | 13.8371i | −0.653241 | − | 0.474607i | ||||
\(851\) | −65.0238 | + | 47.2426i | −2.22899 | + | 1.61945i | ||||
\(852\) | 0.472136 | − | 1.45309i | 0.0161751 | − | 0.0497819i | ||||
\(853\) | 6.81966 | − | 20.9888i | 0.233501 | − | 0.718641i | −0.763816 | − | 0.645434i | \(-0.776677\pi\) |
0.997317 | − | 0.0732073i | \(-0.0233235\pi\) | |||||||
\(854\) | 7.47214 | − | 5.42882i | 0.255691 | − | 0.185771i | ||||
\(855\) | 4.57295 | + | 3.32244i | 0.156392 | + | 0.113625i | ||||
\(856\) | 5.88197 | + | 18.1028i | 0.201041 | + | 0.618742i | ||||
\(857\) | −7.30495 | −0.249532 | −0.124766 | − | 0.992186i | \(-0.539818\pi\) | ||||
−0.124766 | + | 0.992186i | \(0.539818\pi\) | |||||||
\(858\) | −0.381966 | − | 4.08174i | −0.0130401 | − | 0.139348i | ||||
\(859\) | 25.5279 | 0.870999 | 0.435500 | − | 0.900189i | \(-0.356572\pi\) | ||||
0.435500 | + | 0.900189i | \(0.356572\pi\) | |||||||
\(860\) | −2.23607 | − | 6.88191i | −0.0762493 | − | 0.234671i | ||||
\(861\) | 9.59017 | + | 6.96767i | 0.326832 | + | 0.237457i | ||||
\(862\) | 7.50000 | − | 5.44907i | 0.255451 | − | 0.185596i | ||||
\(863\) | −3.42705 | + | 10.5474i | −0.116658 | + | 0.359037i | −0.992289 | − | 0.123944i | \(-0.960446\pi\) |
0.875631 | + | 0.482981i | \(0.160446\pi\) | |||||||
\(864\) | −0.309017 | + | 0.951057i | −0.0105130 | + | 0.0323556i | ||||
\(865\) | 7.66312 | − | 5.56758i | 0.260554 | − | 0.189303i | ||||
\(866\) | −2.70820 | − | 1.96763i | −0.0920285 | − | 0.0668626i | ||||
\(867\) | 12.6803 | + | 39.0261i | 0.430647 | + | 1.32539i | ||||
\(868\) | −1.09017 | −0.0370028 | ||||||||
\(869\) | −23.4721 | + | 10.1311i | −0.796238 | + | 0.343674i | ||||
\(870\) | −1.70820 | −0.0579135 | ||||||||
\(871\) | 0.472136 | + | 1.45309i | 0.0159977 | + | 0.0492359i | ||||
\(872\) | 3.73607 | + | 2.71441i | 0.126519 | + | 0.0919216i | ||||
\(873\) | −9.09017 | + | 6.60440i | −0.307656 | + | 0.223525i | ||||
\(874\) | 11.7877 | − | 36.2789i | 0.398726 | − | 1.22715i | ||||
\(875\) | −3.45492 | + | 10.6331i | −0.116797 | + | 0.359466i | ||||
\(876\) | 6.47214 | − | 4.70228i | 0.218673 | − | 0.158875i | ||||
\(877\) | −31.7984 | − | 23.1029i | −1.07375 | − | 0.780129i | −0.0971714 | − | 0.995268i | \(-0.530979\pi\) |
−0.976583 | + | 0.215139i | \(0.930979\pi\) | |||||||
\(878\) | −6.80902 | − | 20.9560i | −0.229793 | − | 0.707231i | ||||
\(879\) | 8.79837 | 0.296762 | ||||||||
\(880\) | 2.33688 | − | 3.94298i | 0.0787762 | − | 0.132918i | ||||
\(881\) | −23.2148 | −0.782126 | −0.391063 | − | 0.920364i | \(-0.627893\pi\) | ||||
−0.391063 | + | 0.920364i | \(0.627893\pi\) | |||||||
\(882\) | −0.309017 | − | 0.951057i | −0.0104051 | − | 0.0320237i | ||||
\(883\) | −1.61803 | − | 1.17557i | −0.0544512 | − | 0.0395611i | 0.560227 | − | 0.828339i | \(-0.310714\pi\) |
−0.614678 | + | 0.788778i | \(0.710714\pi\) | |||||||
\(884\) | 7.61803 | − | 5.53483i | 0.256222 | − | 0.186156i | ||||
\(885\) | 3.81966 | − | 11.7557i | 0.128396 | − | 0.395164i | ||||
\(886\) | 6.17376 | − | 19.0009i | 0.207412 | − | 0.638347i | ||||
\(887\) | −6.00000 | + | 4.35926i | −0.201460 | + | 0.146369i | −0.683942 | − | 0.729537i | \(-0.739736\pi\) |
0.482481 | + | 0.875906i | \(0.339736\pi\) | |||||||
\(888\) | −6.97214 | − | 5.06555i | −0.233970 | − | 0.169989i | ||||
\(889\) | −3.47214 | − | 10.6861i | −0.116452 | − | 0.358401i | ||||
\(890\) | −7.11146 | −0.238377 | ||||||||
\(891\) | 2.19098 | + | 2.48990i | 0.0734007 | + | 0.0834147i | ||||
\(892\) | 3.14590 | 0.105332 | ||||||||
\(893\) | 12.8673 | + | 39.6013i | 0.430586 | + | 1.32521i | ||||
\(894\) | −15.7082 | − | 11.4127i | −0.525361 | − | 0.381697i | ||||
\(895\) | 24.1074 | − | 17.5150i | 0.805821 | − | 0.585463i | ||||
\(896\) | 0.309017 | − | 0.951057i | 0.0103235 | − | 0.0317726i | ||||
\(897\) | 3.56231 | − | 10.9637i | 0.118942 | − | 0.366066i | ||||
\(898\) | 9.85410 | − | 7.15942i | 0.328836 | − | 0.238913i | ||||
\(899\) | 1.09017 | + | 0.792055i | 0.0363592 | + | 0.0264165i | ||||
\(900\) | −0.954915 | − | 2.93893i | −0.0318305 | − | 0.0979642i | ||||
\(901\) | 68.1378 | 2.27000 | ||||||||
\(902\) | 38.3607 | + | 8.61251i | 1.27727 | + | 0.286765i | ||||
\(903\) | −5.23607 | −0.174245 | ||||||||
\(904\) | 2.00000 | + | 6.15537i | 0.0665190 | + | 0.204724i | ||||
\(905\) | 8.94427 | + | 6.49839i | 0.297318 | + | 0.216014i | ||||
\(906\) | −7.23607 | + | 5.25731i | −0.240402 | + | 0.174662i | ||||
\(907\) | −13.6180 | + | 41.9120i | −0.452179 | + | 1.39167i | 0.422236 | + | 0.906486i | \(0.361246\pi\) |
−0.874415 | + | 0.485179i | \(0.838754\pi\) | |||||||
\(908\) | 4.18034 | − | 12.8658i | 0.138729 | − | 0.426965i | ||||
\(909\) | −9.59017 | + | 6.96767i | −0.318086 | + | 0.231103i | ||||
\(910\) | −1.38197 | − | 1.00406i | −0.0458117 | − | 0.0332842i | ||||
\(911\) | 17.5967 | + | 54.1572i | 0.583006 | + | 1.79431i | 0.607133 | + | 0.794600i | \(0.292319\pi\) |
−0.0241272 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(912\) | 4.09017 | 0.135439 | ||||||||
\(913\) | −49.3050 | − | 11.0697i | −1.63176 | − | 0.366352i | ||||
\(914\) | 6.58359 | 0.217766 | ||||||||
\(915\) | 3.94427 | + | 12.1392i | 0.130394 | + | 0.401310i | ||||
\(916\) | 23.3262 | + | 16.9475i | 0.770721 | + | 0.559961i | ||||
\(917\) | 12.3262 | − | 8.95554i | 0.407048 | − | 0.295738i | ||||
\(918\) | −2.35410 | + | 7.24518i | −0.0776969 | + | 0.239127i | ||||
\(919\) | −12.6738 | + | 39.0058i | −0.418069 | + | 1.28668i | 0.491408 | + | 0.870929i | \(0.336482\pi\) |
−0.909477 | + | 0.415754i | \(0.863518\pi\) | |||||||
\(920\) | 10.4271 | − | 7.57570i | 0.343770 | − | 0.249763i | ||||
\(921\) | −12.8262 | − | 9.31881i | −0.422639 | − | 0.307065i | ||||
\(922\) | −6.14590 | − | 18.9151i | −0.202404 | − | 0.622937i | ||||
\(923\) | −1.88854 | −0.0621622 | ||||||||
\(924\) | −2.19098 | − | 2.48990i | −0.0720780 | − | 0.0819116i | ||||
\(925\) | 26.6312 | 0.875628 | ||||||||
\(926\) | 11.5623 | + | 35.5851i | 0.379961 | + | 1.16940i | ||||
\(927\) | −4.69098 | − | 3.40820i | −0.154072 | − | 0.111940i | ||||
\(928\) | −1.00000 | + | 0.726543i | −0.0328266 | + | 0.0238499i | ||||
\(929\) | −15.1869 | + | 46.7405i | −0.498267 | + | 1.53351i | 0.313537 | + | 0.949576i | \(0.398486\pi\) |
−0.811803 | + | 0.583931i | \(0.801514\pi\) | |||||||
\(930\) | 0.465558 | − | 1.43284i | 0.0152663 | − | 0.0469847i | ||||
\(931\) | −3.30902 | + | 2.40414i | −0.108449 | + | 0.0787926i | ||||
\(932\) | −16.0902 | − | 11.6902i | −0.527051 | − | 0.382925i | ||||
\(933\) | −4.18034 | − | 12.8658i | −0.136858 | − | 0.421206i | ||||
\(934\) | −8.00000 | −0.261768 | ||||||||
\(935\) | 17.8024 | − | 30.0378i | 0.582202 | − | 0.982340i | ||||
\(936\) | 1.23607 | 0.0404021 | ||||||||
\(937\) | −5.81966 | − | 17.9111i | −0.190120 | − | 0.585129i | 0.809879 | − | 0.586597i | \(-0.199533\pi\) |
−0.999999 | + | 0.00146787i | \(0.999533\pi\) | |||||||
\(938\) | 1.00000 | + | 0.726543i | 0.0326512 | + | 0.0237225i | ||||
\(939\) | −11.5623 | + | 8.40051i | −0.377322 | + | 0.274140i | ||||
\(940\) | −4.34752 | + | 13.3803i | −0.141801 | + | 0.436417i | ||||
\(941\) | 0.354102 | − | 1.08981i | 0.0115434 | − | 0.0355269i | −0.945119 | − | 0.326727i | \(-0.894054\pi\) |
0.956662 | + | 0.291200i | \(0.0940544\pi\) | |||||||
\(942\) | 3.00000 | − | 2.17963i | 0.0977453 | − | 0.0710161i | ||||
\(943\) | 89.4402 | + | 64.9821i | 2.91257 | + | 2.11611i | ||||
\(944\) | −2.76393 | − | 8.50651i | −0.0899583 | − | 0.276863i | ||||
\(945\) | 1.38197 | 0.0449554 | ||||||||
\(946\) | −15.9443 | + | 6.88191i | −0.518393 | + | 0.223750i | ||||
\(947\) | 3.38197 | 0.109899 | 0.0549496 | − | 0.998489i | \(-0.482500\pi\) | ||||
0.0549496 | + | 0.998489i | \(0.482500\pi\) | |||||||
\(948\) | −2.38197 | − | 7.33094i | −0.0773627 | − | 0.238098i | ||||
\(949\) | −8.00000 | − | 5.81234i | −0.259691 | − | 0.188677i | ||||
\(950\) | −10.2254 | + | 7.42921i | −0.331757 | + | 0.241035i | ||||
\(951\) | 3.70820 | − | 11.4127i | 0.120247 | − | 0.370081i | ||||
\(952\) | 2.35410 | − | 7.24518i | 0.0762969 | − | 0.234818i | ||||
\(953\) | −1.47214 | + | 1.06957i | −0.0476872 | + | 0.0346468i | −0.611373 | − | 0.791342i | \(-0.709383\pi\) |
0.563686 | + | 0.825989i | \(0.309383\pi\) | |||||||
\(954\) | 7.23607 | + | 5.25731i | 0.234276 | + | 0.170212i | ||||
\(955\) | −4.73607 | − | 14.5761i | −0.153256 | − | 0.471672i | ||||
\(956\) | 11.6180 | 0.375754 | ||||||||
\(957\) | 0.381966 | + | 4.08174i | 0.0123472 | + | 0.131944i | ||||
\(958\) | −4.94427 | −0.159742 | ||||||||
\(959\) | −2.00000 | − | 6.15537i | −0.0645834 | − | 0.198767i | ||||
\(960\) | 1.11803 | + | 0.812299i | 0.0360844 | + | 0.0262168i | ||||
\(961\) | 24.1180 | − | 17.5228i | 0.778001 | − | 0.565251i | ||||
\(962\) | −3.29180 | + | 10.1311i | −0.106132 | + | 0.326640i | ||||
\(963\) | −5.88197 | + | 18.1028i | −0.189544 | + | 0.583356i | ||||
\(964\) | 5.00000 | − | 3.63271i | 0.161039 | − | 0.117002i | ||||
\(965\) | −2.07295 | − | 1.50609i | −0.0667306 | − | 0.0484826i | ||||
\(966\) | −2.88197 | − | 8.86978i | −0.0927257 | − | 0.285380i | ||||
\(967\) | 20.1803 | 0.648956 | 0.324478 | − | 0.945893i | \(-0.394811\pi\) | ||||
0.324478 | + | 0.945893i | \(0.394811\pi\) | |||||||
\(968\) | −9.94427 | − | 4.70228i | −0.319621 | − | 0.151137i | ||||
\(969\) | 31.1591 | 1.00097 | ||||||||
\(970\) | 4.79837 | + | 14.7679i | 0.154067 | + | 0.474168i | ||||
\(971\) | −32.5623 | − | 23.6579i | −1.04497 | − | 0.759218i | −0.0737238 | − | 0.997279i | \(-0.523488\pi\) |
−0.971250 | + | 0.238061i | \(0.923488\pi\) | |||||||
\(972\) | −0.809017 | + | 0.587785i | −0.0259492 | + | 0.0188532i | ||||
\(973\) | −5.20820 | + | 16.0292i | −0.166967 | + | 0.513873i | ||||
\(974\) | −10.0000 | + | 30.7768i | −0.320421 | + | 0.986153i | ||||
\(975\) | −3.09017 | + | 2.24514i | −0.0989646 | + | 0.0719020i | ||||
\(976\) | 7.47214 | + | 5.42882i | 0.239177 | + | 0.173772i | ||||
\(977\) | −15.1459 | − | 46.6143i | −0.484560 | − | 1.49132i | −0.832617 | − | 0.553849i | \(-0.813158\pi\) |
0.348057 | − | 0.937474i | \(-0.386842\pi\) | |||||||
\(978\) | −20.4721 | −0.654627 | ||||||||
\(979\) | 1.59017 | + | 16.9928i | 0.0508221 | + | 0.543091i | ||||
\(980\) | −1.38197 | −0.0441453 | ||||||||
\(981\) | 1.42705 | + | 4.39201i | 0.0455622 | + | 0.140226i | ||||
\(982\) | −9.07295 | − | 6.59188i | −0.289529 | − | 0.210355i | ||||
\(983\) | −12.5623 | + | 9.12705i | −0.400675 | + | 0.291108i | −0.769816 | − | 0.638266i | \(-0.779652\pi\) |
0.369141 | + | 0.929374i | \(0.379652\pi\) | |||||||
\(984\) | −3.66312 | + | 11.2739i | −0.116776 | + | 0.359399i | ||||
\(985\) | −8.01316 | + | 24.6620i | −0.255320 | + | 0.785795i | ||||
\(986\) | −7.61803 | + | 5.53483i | −0.242608 | + | 0.176265i | ||||
\(987\) | 8.23607 | + | 5.98385i | 0.262157 | + | 0.190468i | ||||
\(988\) | −1.56231 | − | 4.80828i | −0.0497036 | − | 0.152972i | ||||
\(989\) | −48.8328 | −1.55279 | ||||||||
\(990\) | 4.20820 | − | 1.81636i | 0.133746 | − | 0.0577276i | ||||
\(991\) | 4.29180 | 0.136333 | 0.0681667 | − | 0.997674i | \(-0.478285\pi\) | ||||
0.0681667 | + | 0.997674i | \(0.478285\pi\) | |||||||
\(992\) | −0.336881 | − | 1.03681i | −0.0106960 | − | 0.0329189i | ||||
\(993\) | 0.145898 | + | 0.106001i | 0.00462993 | + | 0.00336384i | ||||
\(994\) | −1.23607 | + | 0.898056i | −0.0392057 | + | 0.0284846i | ||||
\(995\) | 3.53193 | − | 10.8702i | 0.111970 | − | 0.344607i | ||||
\(996\) | 4.70820 | − | 14.4904i | 0.149185 | − | 0.459145i | ||||
\(997\) | −21.3262 | + | 15.4944i | −0.675409 | + | 0.490713i | −0.871831 | − | 0.489806i | \(-0.837068\pi\) |
0.196423 | + | 0.980519i | \(0.437068\pi\) | |||||||
\(998\) | 10.7082 | + | 7.77997i | 0.338962 | + | 0.246271i | ||||
\(999\) | −2.66312 | − | 8.19624i | −0.0842574 | − | 0.259317i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 462.2.j.c.379.1 | yes | 4 | |
11.3 | even | 5 | 5082.2.a.bh.1.2 | 2 | |||
11.8 | odd | 10 | 5082.2.a.br.1.2 | 2 | |||
11.9 | even | 5 | inner | 462.2.j.c.295.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.c.295.1 | ✓ | 4 | 11.9 | even | 5 | inner | |
462.2.j.c.379.1 | yes | 4 | 1.1 | even | 1 | trivial | |
5082.2.a.bh.1.2 | 2 | 11.3 | even | 5 | |||
5082.2.a.br.1.2 | 2 | 11.8 | odd | 10 |