Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (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: | \(3.33774680449\) |
Analytic rank: | \(1\) |
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 | 267.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.267 |
Dual form | 418.2.f.a.191.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −1.00000 | − | 3.07768i | −0.577350 | − | 1.77690i | −0.628033 | − | 0.778187i | \(-0.716140\pi\) |
0.0506828 | − | 0.998715i | \(-0.483860\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −3.11803 | − | 2.26538i | −1.39443 | − | 1.01311i | −0.995363 | − | 0.0961876i | \(-0.969335\pi\) |
−0.399064 | − | 0.916923i | \(-0.630665\pi\) | |||||||
\(6\) | 2.61803 | + | 1.90211i | 1.06881 | + | 0.776534i | ||||
\(7\) | −1.19098 | + | 3.66547i | −0.450149 | + | 1.38542i | 0.426587 | + | 0.904446i | \(0.359716\pi\) |
−0.876737 | + | 0.480971i | \(0.840284\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | −6.04508 | + | 4.39201i | −2.01503 | + | 1.46400i | ||||
\(10\) | 3.85410 | 1.21877 | ||||||||
\(11\) | −0.309017 | − | 3.30220i | −0.0931721 | − | 0.995650i | ||||
\(12\) | −3.23607 | −0.934172 | ||||||||
\(13\) | 3.23607 | − | 2.35114i | 0.897524 | − | 0.652089i | −0.0403050 | − | 0.999187i | \(-0.512833\pi\) |
0.937829 | + | 0.347098i | \(0.112833\pi\) | |||||||
\(14\) | −1.19098 | − | 3.66547i | −0.318304 | − | 0.979638i | ||||
\(15\) | −3.85410 | + | 11.8617i | −0.995125 | + | 3.06268i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.30902 | − | 0.951057i | −0.317483 | − | 0.230665i | 0.417618 | − | 0.908623i | \(-0.362865\pi\) |
−0.735101 | + | 0.677958i | \(0.762865\pi\) | |||||||
\(18\) | 2.30902 | − | 7.10642i | 0.544241 | − | 1.67500i | ||||
\(19\) | 0.309017 | + | 0.951057i | 0.0708934 | + | 0.218187i | ||||
\(20\) | −3.11803 | + | 2.26538i | −0.697214 | + | 0.506555i | ||||
\(21\) | 12.4721 | 2.72164 | ||||||||
\(22\) | 2.19098 | + | 2.48990i | 0.467119 | + | 0.530848i | ||||
\(23\) | 0.854102 | 0.178093 | 0.0890463 | − | 0.996027i | \(-0.471618\pi\) | ||||
0.0890463 | + | 0.996027i | \(0.471618\pi\) | |||||||
\(24\) | 2.61803 | − | 1.90211i | 0.534404 | − | 0.388267i | ||||
\(25\) | 3.04508 | + | 9.37181i | 0.609017 | + | 1.87436i | ||||
\(26\) | −1.23607 | + | 3.80423i | −0.242413 | + | 0.746070i | ||||
\(27\) | 11.7082 | + | 8.50651i | 2.25324 | + | 1.63708i | ||||
\(28\) | 3.11803 | + | 2.26538i | 0.589253 | + | 0.428117i | ||||
\(29\) | −1.76393 | + | 5.42882i | −0.327554 | + | 1.00811i | 0.642721 | + | 0.766101i | \(0.277806\pi\) |
−0.970275 | + | 0.242007i | \(0.922194\pi\) | |||||||
\(30\) | −3.85410 | − | 11.8617i | −0.703660 | − | 2.16564i | ||||
\(31\) | 2.23607 | − | 1.62460i | 0.401610 | − | 0.291787i | −0.368587 | − | 0.929593i | \(-0.620158\pi\) |
0.770196 | + | 0.637807i | \(0.220158\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −9.85410 | + | 4.25325i | −1.71538 | + | 0.740396i | ||||
\(34\) | 1.61803 | 0.277491 | ||||||||
\(35\) | 12.0172 | − | 8.73102i | 2.03128 | − | 1.47581i | ||||
\(36\) | 2.30902 | + | 7.10642i | 0.384836 | + | 1.18440i | ||||
\(37\) | −1.00000 | + | 3.07768i | −0.164399 | + | 0.505968i | −0.998991 | − | 0.0448998i | \(-0.985703\pi\) |
0.834593 | + | 0.550868i | \(0.185703\pi\) | |||||||
\(38\) | −0.809017 | − | 0.587785i | −0.131240 | − | 0.0953514i | ||||
\(39\) | −10.4721 | − | 7.60845i | −1.67688 | − | 1.21833i | ||||
\(40\) | 1.19098 | − | 3.66547i | 0.188311 | − | 0.579562i | ||||
\(41\) | 0.145898 | + | 0.449028i | 0.0227854 | + | 0.0701264i | 0.961803 | − | 0.273744i | \(-0.0882620\pi\) |
−0.939017 | + | 0.343870i | \(0.888262\pi\) | |||||||
\(42\) | −10.0902 | + | 7.33094i | −1.55695 | + | 1.13119i | ||||
\(43\) | −7.61803 | −1.16174 | −0.580870 | − | 0.813997i | \(-0.697287\pi\) | ||||
−0.580870 | + | 0.813997i | \(0.697287\pi\) | |||||||
\(44\) | −3.23607 | − | 0.726543i | −0.487856 | − | 0.109530i | ||||
\(45\) | 28.7984 | 4.29301 | ||||||||
\(46\) | −0.690983 | + | 0.502029i | −0.101880 | + | 0.0740201i | ||||
\(47\) | −0.263932 | − | 0.812299i | −0.0384984 | − | 0.118486i | 0.929960 | − | 0.367660i | \(-0.119841\pi\) |
−0.968459 | + | 0.249174i | \(0.919841\pi\) | |||||||
\(48\) | −1.00000 | + | 3.07768i | −0.144338 | + | 0.444225i | ||||
\(49\) | −6.35410 | − | 4.61653i | −0.907729 | − | 0.659504i | ||||
\(50\) | −7.97214 | − | 5.79210i | −1.12743 | − | 0.819126i | ||||
\(51\) | −1.61803 | + | 4.97980i | −0.226570 | + | 0.697311i | ||||
\(52\) | −1.23607 | − | 3.80423i | −0.171412 | − | 0.527551i | ||||
\(53\) | −9.09017 | + | 6.60440i | −1.24863 | + | 0.907183i | −0.998142 | − | 0.0609360i | \(-0.980591\pi\) |
−0.250489 | + | 0.968119i | \(0.580591\pi\) | |||||||
\(54\) | −14.4721 | −1.96941 | ||||||||
\(55\) | −6.51722 | + | 10.9964i | −0.878782 | + | 1.48276i | ||||
\(56\) | −3.85410 | −0.515026 | ||||||||
\(57\) | 2.61803 | − | 1.90211i | 0.346767 | − | 0.251941i | ||||
\(58\) | −1.76393 | − | 5.42882i | −0.231616 | − | 0.712840i | ||||
\(59\) | 2.14590 | − | 6.60440i | 0.279372 | − | 0.859819i | −0.708657 | − | 0.705553i | \(-0.750699\pi\) |
0.988029 | − | 0.154266i | \(-0.0493013\pi\) | |||||||
\(60\) | 10.0902 | + | 7.33094i | 1.30264 | + | 0.946420i | ||||
\(61\) | 0.927051 | + | 0.673542i | 0.118697 | + | 0.0862382i | 0.645550 | − | 0.763718i | \(-0.276628\pi\) |
−0.526853 | + | 0.849956i | \(0.676628\pi\) | |||||||
\(62\) | −0.854102 | + | 2.62866i | −0.108471 | + | 0.333840i | ||||
\(63\) | −8.89919 | − | 27.3889i | −1.12119 | − | 3.45067i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −15.4164 | −1.91217 | ||||||||
\(66\) | 5.47214 | − | 9.23305i | 0.673573 | − | 1.13651i | ||||
\(67\) | −9.23607 | −1.12837 | −0.564183 | − | 0.825650i | \(-0.690809\pi\) | ||||
−0.564183 | + | 0.825650i | \(0.690809\pi\) | |||||||
\(68\) | −1.30902 | + | 0.951057i | −0.158742 | + | 0.115333i | ||||
\(69\) | −0.854102 | − | 2.62866i | −0.102822 | − | 0.316453i | ||||
\(70\) | −4.59017 | + | 14.1271i | −0.548630 | + | 1.68851i | ||||
\(71\) | 2.23607 | + | 1.62460i | 0.265372 | + | 0.192804i | 0.712512 | − | 0.701660i | \(-0.247557\pi\) |
−0.447140 | + | 0.894464i | \(0.647557\pi\) | |||||||
\(72\) | −6.04508 | − | 4.39201i | −0.712420 | − | 0.517603i | ||||
\(73\) | −3.38197 | + | 10.4086i | −0.395829 | + | 1.21824i | 0.532485 | + | 0.846440i | \(0.321258\pi\) |
−0.928314 | + | 0.371797i | \(0.878742\pi\) | |||||||
\(74\) | −1.00000 | − | 3.07768i | −0.116248 | − | 0.357773i | ||||
\(75\) | 25.7984 | − | 18.7436i | 2.97894 | − | 2.16433i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 12.4721 | + | 2.80017i | 1.42133 | + | 0.319109i | ||||
\(78\) | 12.9443 | 1.46565 | ||||||||
\(79\) | 7.47214 | − | 5.42882i | 0.840681 | − | 0.610790i | −0.0818798 | − | 0.996642i | \(-0.526092\pi\) |
0.922561 | + | 0.385852i | \(0.126092\pi\) | |||||||
\(80\) | 1.19098 | + | 3.66547i | 0.133156 | + | 0.409812i | ||||
\(81\) | 7.54508 | − | 23.2214i | 0.838343 | − | 2.58015i | ||||
\(82\) | −0.381966 | − | 0.277515i | −0.0421811 | − | 0.0306464i | ||||
\(83\) | −1.73607 | − | 1.26133i | −0.190558 | − | 0.138449i | 0.488416 | − | 0.872611i | \(-0.337575\pi\) |
−0.678974 | + | 0.734162i | \(0.737575\pi\) | |||||||
\(84\) | 3.85410 | − | 11.8617i | 0.420517 | − | 1.29422i | ||||
\(85\) | 1.92705 | + | 5.93085i | 0.209018 | + | 0.643291i | ||||
\(86\) | 6.16312 | − | 4.47777i | 0.664586 | − | 0.482850i | ||||
\(87\) | 18.4721 | 1.98042 | ||||||||
\(88\) | 3.04508 | − | 1.31433i | 0.324607 | − | 0.140108i | ||||
\(89\) | −14.1803 | −1.50311 | −0.751557 | − | 0.659669i | \(-0.770697\pi\) | ||||
−0.751557 | + | 0.659669i | \(0.770697\pi\) | |||||||
\(90\) | −23.2984 | + | 16.9273i | −2.45586 | + | 1.78429i | ||||
\(91\) | 4.76393 | + | 14.6619i | 0.499396 | + | 1.53698i | ||||
\(92\) | 0.263932 | − | 0.812299i | 0.0275168 | − | 0.0846881i | ||||
\(93\) | −7.23607 | − | 5.25731i | −0.750345 | − | 0.545158i | ||||
\(94\) | 0.690983 | + | 0.502029i | 0.0712695 | + | 0.0517803i | ||||
\(95\) | 1.19098 | − | 3.66547i | 0.122192 | − | 0.376069i | ||||
\(96\) | −1.00000 | − | 3.07768i | −0.102062 | − | 0.314115i | ||||
\(97\) | −13.7082 | + | 9.95959i | −1.39186 | + | 1.01124i | −0.396198 | + | 0.918165i | \(0.629671\pi\) |
−0.995659 | + | 0.0930786i | \(0.970329\pi\) | |||||||
\(98\) | 7.85410 | 0.793384 | ||||||||
\(99\) | 16.3713 | + | 18.6049i | 1.64538 | + | 1.86986i | ||||
\(100\) | 9.85410 | 0.985410 | ||||||||
\(101\) | −2.88197 | + | 2.09387i | −0.286766 | + | 0.208348i | −0.721863 | − | 0.692036i | \(-0.756714\pi\) |
0.435097 | + | 0.900384i | \(0.356714\pi\) | |||||||
\(102\) | −1.61803 | − | 4.97980i | −0.160209 | − | 0.493073i | ||||
\(103\) | −2.14590 | + | 6.60440i | −0.211442 | + | 0.650750i | 0.787946 | + | 0.615745i | \(0.211145\pi\) |
−0.999387 | + | 0.0350054i | \(0.988855\pi\) | |||||||
\(104\) | 3.23607 | + | 2.35114i | 0.317323 | + | 0.230548i | ||||
\(105\) | −38.8885 | − | 28.2542i | −3.79513 | − | 2.75733i | ||||
\(106\) | 3.47214 | − | 10.6861i | 0.337244 | − | 1.03793i | ||||
\(107\) | −0.763932 | − | 2.35114i | −0.0738521 | − | 0.227293i | 0.907316 | − | 0.420450i | \(-0.138128\pi\) |
−0.981168 | + | 0.193156i | \(0.938128\pi\) | |||||||
\(108\) | 11.7082 | − | 8.50651i | 1.12662 | − | 0.818539i | ||||
\(109\) | 0.944272 | 0.0904448 | 0.0452224 | − | 0.998977i | \(-0.485600\pi\) | ||||
0.0452224 | + | 0.998977i | \(0.485600\pi\) | |||||||
\(110\) | −1.19098 | − | 12.7270i | −0.113556 | − | 1.21347i | ||||
\(111\) | 10.4721 | 0.993971 | ||||||||
\(112\) | 3.11803 | − | 2.26538i | 0.294627 | − | 0.214059i | ||||
\(113\) | −2.32624 | − | 7.15942i | −0.218834 | − | 0.673502i | −0.998859 | − | 0.0477537i | \(-0.984794\pi\) |
0.780025 | − | 0.625748i | \(-0.215206\pi\) | |||||||
\(114\) | −1.00000 | + | 3.07768i | −0.0936586 | + | 0.288251i | ||||
\(115\) | −2.66312 | − | 1.93487i | −0.248337 | − | 0.180427i | ||||
\(116\) | 4.61803 | + | 3.35520i | 0.428774 | + | 0.311522i | ||||
\(117\) | −9.23607 | + | 28.4257i | −0.853875 | + | 2.62796i | ||||
\(118\) | 2.14590 | + | 6.60440i | 0.197546 | + | 0.607984i | ||||
\(119\) | 5.04508 | − | 3.66547i | 0.462482 | − | 0.336013i | ||||
\(120\) | −12.4721 | −1.13855 | ||||||||
\(121\) | −10.8090 | + | 2.04087i | −0.982638 | + | 0.185534i | ||||
\(122\) | −1.14590 | −0.103745 | ||||||||
\(123\) | 1.23607 | − | 0.898056i | 0.111452 | − | 0.0809750i | ||||
\(124\) | −0.854102 | − | 2.62866i | −0.0767006 | − | 0.236060i | ||||
\(125\) | 5.78115 | − | 17.7926i | 0.517082 | − | 1.59141i | ||||
\(126\) | 23.2984 | + | 16.9273i | 2.07558 | + | 1.50800i | ||||
\(127\) | 1.85410 | + | 1.34708i | 0.164525 | + | 0.119534i | 0.667001 | − | 0.745057i | \(-0.267578\pi\) |
−0.502476 | + | 0.864591i | \(0.667578\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 7.61803 | + | 23.4459i | 0.670730 | + | 2.06430i | ||||
\(130\) | 12.4721 | − | 9.06154i | 1.09388 | − | 0.794749i | ||||
\(131\) | 13.8541 | 1.21044 | 0.605219 | − | 0.796059i | \(-0.293085\pi\) | ||||
0.605219 | + | 0.796059i | \(0.293085\pi\) | |||||||
\(132\) | 1.00000 | + | 10.6861i | 0.0870388 | + | 0.930109i | ||||
\(133\) | −3.85410 | −0.334193 | ||||||||
\(134\) | 7.47214 | − | 5.42882i | 0.645494 | − | 0.468979i | ||||
\(135\) | −17.2361 | − | 53.0472i | −1.48344 | − | 4.56557i | ||||
\(136\) | 0.500000 | − | 1.53884i | 0.0428746 | − | 0.131955i | ||||
\(137\) | 7.73607 | + | 5.62058i | 0.660937 | + | 0.480199i | 0.866979 | − | 0.498344i | \(-0.166058\pi\) |
−0.206042 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(138\) | 2.23607 | + | 1.62460i | 0.190347 | + | 0.138295i | ||||
\(139\) | 4.35410 | − | 13.4005i | 0.369310 | − | 1.13662i | −0.577928 | − | 0.816088i | \(-0.696138\pi\) |
0.947238 | − | 0.320532i | \(-0.103862\pi\) | |||||||
\(140\) | −4.59017 | − | 14.1271i | −0.387940 | − | 1.19396i | ||||
\(141\) | −2.23607 | + | 1.62460i | −0.188311 | + | 0.136816i | ||||
\(142\) | −2.76393 | −0.231944 | ||||||||
\(143\) | −8.76393 | − | 9.95959i | −0.732877 | − | 0.832863i | ||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | 17.7984 | − | 12.9313i | 1.47807 | − | 1.07388i | ||||
\(146\) | −3.38197 | − | 10.4086i | −0.279893 | − | 0.861424i | ||||
\(147\) | −7.85410 | + | 24.1724i | −0.647795 | + | 1.99371i | ||||
\(148\) | 2.61803 | + | 1.90211i | 0.215201 | + | 0.156353i | ||||
\(149\) | 2.85410 | + | 2.07363i | 0.233817 | + | 0.169878i | 0.698524 | − | 0.715586i | \(-0.253840\pi\) |
−0.464707 | + | 0.885464i | \(0.653840\pi\) | |||||||
\(150\) | −9.85410 | + | 30.3278i | −0.804584 | + | 2.47626i | ||||
\(151\) | −3.32624 | − | 10.2371i | −0.270685 | − | 0.833084i | −0.990329 | − | 0.138740i | \(-0.955695\pi\) |
0.719643 | − | 0.694344i | \(-0.244305\pi\) | |||||||
\(152\) | −0.809017 | + | 0.587785i | −0.0656199 | + | 0.0476757i | ||||
\(153\) | 12.0902 | 0.977432 | ||||||||
\(154\) | −11.7361 | + | 5.06555i | −0.945719 | + | 0.408194i | ||||
\(155\) | −10.6525 | −0.855627 | ||||||||
\(156\) | −10.4721 | + | 7.60845i | −0.838442 | + | 0.609164i | ||||
\(157\) | −6.89919 | − | 21.2335i | −0.550615 | − | 1.69462i | −0.707251 | − | 0.706963i | \(-0.750065\pi\) |
0.156636 | − | 0.987656i | \(-0.449935\pi\) | |||||||
\(158\) | −2.85410 | + | 8.78402i | −0.227060 | + | 0.698819i | ||||
\(159\) | 29.4164 | + | 21.3723i | 2.33287 | + | 1.69493i | ||||
\(160\) | −3.11803 | − | 2.26538i | −0.246502 | − | 0.179094i | ||||
\(161\) | −1.01722 | + | 3.13068i | −0.0801682 | + | 0.246732i | ||||
\(162\) | 7.54508 | + | 23.2214i | 0.592798 | + | 1.82444i | ||||
\(163\) | −13.9721 | + | 10.1514i | −1.09438 | + | 0.795115i | −0.980134 | − | 0.198337i | \(-0.936446\pi\) |
−0.114248 | + | 0.993452i | \(0.536446\pi\) | |||||||
\(164\) | 0.472136 | 0.0368676 | ||||||||
\(165\) | 40.3607 | + | 9.06154i | 3.14207 | + | 0.705440i | ||||
\(166\) | 2.14590 | 0.166554 | ||||||||
\(167\) | −5.09017 | + | 3.69822i | −0.393889 | + | 0.286177i | −0.767047 | − | 0.641591i | \(-0.778275\pi\) |
0.373158 | + | 0.927768i | \(0.378275\pi\) | |||||||
\(168\) | 3.85410 | + | 11.8617i | 0.297350 | + | 0.915150i | ||||
\(169\) | 0.927051 | − | 2.85317i | 0.0713116 | − | 0.219475i | ||||
\(170\) | −5.04508 | − | 3.66547i | −0.386940 | − | 0.281129i | ||||
\(171\) | −6.04508 | − | 4.39201i | −0.462279 | − | 0.335865i | ||||
\(172\) | −2.35410 | + | 7.24518i | −0.179499 | + | 0.552440i | ||||
\(173\) | 1.23607 | + | 3.80423i | 0.0939765 | + | 0.289230i | 0.986986 | − | 0.160809i | \(-0.0514102\pi\) |
−0.893009 | + | 0.450039i | \(0.851410\pi\) | |||||||
\(174\) | −14.9443 | + | 10.8576i | −1.13292 | + | 0.823116i | ||||
\(175\) | −37.9787 | −2.87092 | ||||||||
\(176\) | −1.69098 | + | 2.85317i | −0.127463 | + | 0.215066i | ||||
\(177\) | −22.4721 | −1.68911 | ||||||||
\(178\) | 11.4721 | − | 8.33499i | 0.859873 | − | 0.624734i | ||||
\(179\) | −6.52786 | − | 20.0907i | −0.487915 | − | 1.50165i | −0.827713 | − | 0.561151i | \(-0.810359\pi\) |
0.339798 | − | 0.940498i | \(-0.389641\pi\) | |||||||
\(180\) | 8.89919 | − | 27.3889i | 0.663306 | − | 2.04145i | ||||
\(181\) | 4.38197 | + | 3.18368i | 0.325709 | + | 0.236641i | 0.738608 | − | 0.674136i | \(-0.235484\pi\) |
−0.412899 | + | 0.910777i | \(0.635484\pi\) | |||||||
\(182\) | −12.4721 | − | 9.06154i | −0.924496 | − | 0.671686i | ||||
\(183\) | 1.14590 | − | 3.52671i | 0.0847072 | − | 0.260702i | ||||
\(184\) | 0.263932 | + | 0.812299i | 0.0194573 | + | 0.0598835i | ||||
\(185\) | 10.0902 | − | 7.33094i | 0.741844 | − | 0.538981i | ||||
\(186\) | 8.94427 | 0.655826 | ||||||||
\(187\) | −2.73607 | + | 4.61653i | −0.200081 | + | 0.337594i | ||||
\(188\) | −0.854102 | −0.0622918 | ||||||||
\(189\) | −45.1246 | + | 32.7849i | −3.28233 | + | 2.38475i | ||||
\(190\) | 1.19098 | + | 3.66547i | 0.0864030 | + | 0.265921i | ||||
\(191\) | −4.13525 | + | 12.7270i | −0.299217 | + | 0.920894i | 0.682556 | + | 0.730833i | \(0.260868\pi\) |
−0.981772 | + | 0.190060i | \(0.939132\pi\) | |||||||
\(192\) | 2.61803 | + | 1.90211i | 0.188940 | + | 0.137273i | ||||
\(193\) | 14.9443 | + | 10.8576i | 1.07571 | + | 0.781551i | 0.976930 | − | 0.213558i | \(-0.0685054\pi\) |
0.0987819 | + | 0.995109i | \(0.468505\pi\) | |||||||
\(194\) | 5.23607 | − | 16.1150i | 0.375928 | − | 1.15699i | ||||
\(195\) | 15.4164 | + | 47.4468i | 1.10399 | + | 3.39774i | ||||
\(196\) | −6.35410 | + | 4.61653i | −0.453864 | + | 0.329752i | ||||
\(197\) | −10.9443 | −0.779747 | −0.389874 | − | 0.920868i | \(-0.627481\pi\) | ||||
−0.389874 | + | 0.920868i | \(0.627481\pi\) | |||||||
\(198\) | −24.1803 | − | 5.42882i | −1.71842 | − | 0.385810i | ||||
\(199\) | 26.6180 | 1.88690 | 0.943451 | − | 0.331511i | \(-0.107559\pi\) | ||||
0.943451 | + | 0.331511i | \(0.107559\pi\) | |||||||
\(200\) | −7.97214 | + | 5.79210i | −0.563715 | + | 0.409563i | ||||
\(201\) | 9.23607 | + | 28.4257i | 0.651462 | + | 2.00499i | ||||
\(202\) | 1.10081 | − | 3.38795i | 0.0774529 | − | 0.238376i | ||||
\(203\) | −17.7984 | − | 12.9313i | −1.24920 | − | 0.907598i | ||||
\(204\) | 4.23607 | + | 3.07768i | 0.296584 | + | 0.215481i | ||||
\(205\) | 0.562306 | − | 1.73060i | 0.0392731 | − | 0.120870i | ||||
\(206\) | −2.14590 | − | 6.60440i | −0.149512 | − | 0.460150i | ||||
\(207\) | −5.16312 | + | 3.75123i | −0.358862 | + | 0.260728i | ||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 3.04508 | − | 1.31433i | 0.210633 | − | 0.0909140i | ||||
\(210\) | 48.0689 | 3.31707 | ||||||||
\(211\) | −12.0902 | + | 8.78402i | −0.832322 | + | 0.604717i | −0.920215 | − | 0.391413i | \(-0.871986\pi\) |
0.0878936 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(212\) | 3.47214 | + | 10.6861i | 0.238467 | + | 0.733927i | ||||
\(213\) | 2.76393 | − | 8.50651i | 0.189382 | − | 0.582856i | ||||
\(214\) | 2.00000 | + | 1.45309i | 0.136717 | + | 0.0993308i | ||||
\(215\) | 23.7533 | + | 17.2578i | 1.61996 | + | 1.17697i | ||||
\(216\) | −4.47214 | + | 13.7638i | −0.304290 | + | 0.936509i | ||||
\(217\) | 3.29180 | + | 10.1311i | 0.223462 | + | 0.687744i | ||||
\(218\) | −0.763932 | + | 0.555029i | −0.0517400 | + | 0.0375913i | ||||
\(219\) | 35.4164 | 2.39322 | ||||||||
\(220\) | 8.44427 | + | 9.59632i | 0.569313 | + | 0.646984i | ||||
\(221\) | −6.47214 | −0.435363 | ||||||||
\(222\) | −8.47214 | + | 6.15537i | −0.568613 | + | 0.413121i | ||||
\(223\) | −3.29180 | − | 10.1311i | −0.220435 | − | 0.678429i | −0.998723 | − | 0.0505216i | \(-0.983912\pi\) |
0.778288 | − | 0.627907i | \(-0.216088\pi\) | |||||||
\(224\) | −1.19098 | + | 3.66547i | −0.0795759 | + | 0.244909i | ||||
\(225\) | −59.5689 | − | 43.2793i | −3.97126 | − | 2.88529i | ||||
\(226\) | 6.09017 | + | 4.42477i | 0.405112 | + | 0.294331i | ||||
\(227\) | −8.09017 | + | 24.8990i | −0.536963 | + | 1.65260i | 0.202405 | + | 0.979302i | \(0.435124\pi\) |
−0.739368 | + | 0.673302i | \(0.764876\pi\) | |||||||
\(228\) | −1.00000 | − | 3.07768i | −0.0662266 | − | 0.203825i | ||||
\(229\) | 8.78115 | − | 6.37988i | 0.580275 | − | 0.421594i | −0.258548 | − | 0.965998i | \(-0.583244\pi\) |
0.838823 | + | 0.544404i | \(0.183244\pi\) | |||||||
\(230\) | 3.29180 | 0.217055 | ||||||||
\(231\) | −3.85410 | − | 41.1855i | −0.253581 | − | 2.70980i | ||||
\(232\) | −5.70820 | −0.374762 | ||||||||
\(233\) | 0.263932 | − | 0.191758i | 0.0172908 | − | 0.0125625i | −0.579106 | − | 0.815252i | \(-0.696598\pi\) |
0.596397 | + | 0.802690i | \(0.296598\pi\) | |||||||
\(234\) | −9.23607 | − | 28.4257i | −0.603781 | − | 1.85825i | ||||
\(235\) | −1.01722 | + | 3.13068i | −0.0663562 | + | 0.204223i | ||||
\(236\) | −5.61803 | − | 4.08174i | −0.365703 | − | 0.265699i | ||||
\(237\) | −24.1803 | − | 17.5680i | −1.57068 | − | 1.14117i | ||||
\(238\) | −1.92705 | + | 5.93085i | −0.124912 | + | 0.384440i | ||||
\(239\) | −4.73607 | − | 14.5761i | −0.306351 | − | 0.942851i | −0.979170 | − | 0.203044i | \(-0.934917\pi\) |
0.672819 | − | 0.739807i | \(-0.265083\pi\) | |||||||
\(240\) | 10.0902 | − | 7.33094i | 0.651318 | − | 0.473210i | ||||
\(241\) | −19.5279 | −1.25790 | −0.628950 | − | 0.777446i | \(-0.716515\pi\) | ||||
−0.628950 | + | 0.777446i | \(0.716515\pi\) | |||||||
\(242\) | 7.54508 | − | 8.00448i | 0.485016 | − | 0.514547i | ||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0.927051 | − | 0.673542i | 0.0593484 | − | 0.0431191i | ||||
\(245\) | 9.35410 | + | 28.7890i | 0.597612 | + | 1.83926i | ||||
\(246\) | −0.472136 | + | 1.45309i | −0.0301023 | + | 0.0926453i | ||||
\(247\) | 3.23607 | + | 2.35114i | 0.205906 | + | 0.149600i | ||||
\(248\) | 2.23607 | + | 1.62460i | 0.141990 | + | 0.103162i | ||||
\(249\) | −2.14590 | + | 6.60440i | −0.135991 | + | 0.418537i | ||||
\(250\) | 5.78115 | + | 17.7926i | 0.365632 | + | 1.12530i | ||||
\(251\) | 10.0172 | − | 7.27794i | 0.632281 | − | 0.459379i | −0.224908 | − | 0.974380i | \(-0.572208\pi\) |
0.857190 | + | 0.515001i | \(0.172208\pi\) | |||||||
\(252\) | −28.7984 | −1.81413 | ||||||||
\(253\) | −0.263932 | − | 2.82041i | −0.0165933 | − | 0.177318i | ||||
\(254\) | −2.29180 | −0.143800 | ||||||||
\(255\) | 16.3262 | − | 11.8617i | 1.02239 | − | 0.742809i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −5.61803 | + | 17.2905i | −0.350443 | + | 1.07855i | 0.608161 | + | 0.793813i | \(0.291907\pi\) |
−0.958605 | + | 0.284740i | \(0.908093\pi\) | |||||||
\(258\) | −19.9443 | − | 14.4904i | −1.24168 | − | 0.902131i | ||||
\(259\) | −10.0902 | − | 7.33094i | −0.626973 | − | 0.455522i | ||||
\(260\) | −4.76393 | + | 14.6619i | −0.295447 | + | 0.909291i | ||||
\(261\) | −13.1803 | − | 40.5649i | −0.815843 | − | 2.51091i | ||||
\(262\) | −11.2082 | + | 8.14324i | −0.692445 | + | 0.503091i | ||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | −7.09017 | − | 8.05748i | −0.436370 | − | 0.495904i | ||||
\(265\) | 43.3050 | 2.66020 | ||||||||
\(266\) | 3.11803 | − | 2.26538i | 0.191179 | − | 0.138900i | ||||
\(267\) | 14.1803 | + | 43.6426i | 0.867823 | + | 2.67088i | ||||
\(268\) | −2.85410 | + | 8.78402i | −0.174342 | + | 0.536570i | ||||
\(269\) | −15.9443 | − | 11.5842i | −0.972139 | − | 0.706301i | −0.0162013 | − | 0.999869i | \(-0.505157\pi\) |
−0.955938 | + | 0.293568i | \(0.905157\pi\) | |||||||
\(270\) | 45.1246 | + | 32.7849i | 2.74620 | + | 1.99523i | ||||
\(271\) | 8.68034 | − | 26.7153i | 0.527293 | − | 1.62284i | −0.232443 | − | 0.972610i | \(-0.574672\pi\) |
0.759736 | − | 0.650231i | \(-0.225328\pi\) | |||||||
\(272\) | 0.500000 | + | 1.53884i | 0.0303170 | + | 0.0933060i | ||||
\(273\) | 40.3607 | − | 29.3238i | 2.44274 | − | 1.77475i | ||||
\(274\) | −9.56231 | −0.577680 | ||||||||
\(275\) | 30.0066 | − | 12.9515i | 1.80946 | − | 0.781006i | ||||
\(276\) | −2.76393 | −0.166369 | ||||||||
\(277\) | 16.5623 | − | 12.0332i | 0.995133 | − | 0.723006i | 0.0340934 | − | 0.999419i | \(-0.489146\pi\) |
0.961039 | + | 0.276413i | \(0.0891456\pi\) | |||||||
\(278\) | 4.35410 | + | 13.4005i | 0.261142 | + | 0.803711i | ||||
\(279\) | −6.38197 | + | 19.6417i | −0.382078 | + | 1.17592i | ||||
\(280\) | 12.0172 | + | 8.73102i | 0.718166 | + | 0.521778i | ||||
\(281\) | 3.23607 | + | 2.35114i | 0.193048 | + | 0.140257i | 0.680111 | − | 0.733110i | \(-0.261932\pi\) |
−0.487063 | + | 0.873367i | \(0.661932\pi\) | |||||||
\(282\) | 0.854102 | − | 2.62866i | 0.0508610 | − | 0.156534i | ||||
\(283\) | −3.04508 | − | 9.37181i | −0.181012 | − | 0.557096i | 0.818845 | − | 0.574014i | \(-0.194615\pi\) |
−0.999857 | + | 0.0169180i | \(0.994615\pi\) | |||||||
\(284\) | 2.23607 | − | 1.62460i | 0.132686 | − | 0.0964022i | ||||
\(285\) | −12.4721 | −0.738786 | ||||||||
\(286\) | 12.9443 | + | 2.90617i | 0.765411 | + | 0.171845i | ||||
\(287\) | −1.81966 | −0.107411 | ||||||||
\(288\) | −6.04508 | + | 4.39201i | −0.356210 | + | 0.258802i | ||||
\(289\) | −4.44427 | − | 13.6781i | −0.261428 | − | 0.804592i | ||||
\(290\) | −6.79837 | + | 20.9232i | −0.399214 | + | 1.22866i | ||||
\(291\) | 44.3607 | + | 32.2299i | 2.60047 | + | 1.88935i | ||||
\(292\) | 8.85410 | + | 6.43288i | 0.518147 | + | 0.376456i | ||||
\(293\) | −7.41641 | + | 22.8254i | −0.433271 | + | 1.33347i | 0.461577 | + | 0.887100i | \(0.347284\pi\) |
−0.894848 | + | 0.446371i | \(0.852716\pi\) | |||||||
\(294\) | −7.85410 | − | 24.1724i | −0.458061 | − | 1.40977i | ||||
\(295\) | −21.6525 | + | 15.7314i | −1.26066 | + | 0.915920i | ||||
\(296\) | −3.23607 | −0.188093 | ||||||||
\(297\) | 24.4721 | − | 41.2915i | 1.42002 | − | 2.39597i | ||||
\(298\) | −3.52786 | −0.204364 | ||||||||
\(299\) | 2.76393 | − | 2.00811i | 0.159842 | − | 0.116132i | ||||
\(300\) | −9.85410 | − | 30.3278i | −0.568927 | − | 1.75098i | ||||
\(301\) | 9.07295 | − | 27.9237i | 0.522956 | − | 1.60949i | ||||
\(302\) | 8.70820 | + | 6.32688i | 0.501101 | + | 0.364071i | ||||
\(303\) | 9.32624 | + | 6.77591i | 0.535778 | + | 0.389266i | ||||
\(304\) | 0.309017 | − | 0.951057i | 0.0177233 | − | 0.0545468i | ||||
\(305\) | −1.36475 | − | 4.20025i | −0.0781451 | − | 0.240506i | ||||
\(306\) | −9.78115 | + | 7.10642i | −0.559151 | + | 0.406247i | ||||
\(307\) | −1.52786 | −0.0871998 | −0.0435999 | − | 0.999049i | \(-0.513883\pi\) | ||||
−0.0435999 | + | 0.999049i | \(0.513883\pi\) | |||||||
\(308\) | 6.51722 | − | 10.9964i | 0.371353 | − | 0.626578i | ||||
\(309\) | 22.4721 | 1.27840 | ||||||||
\(310\) | 8.61803 | − | 6.26137i | 0.489471 | − | 0.355622i | ||||
\(311\) | 1.68034 | + | 5.17155i | 0.0952833 | + | 0.293252i | 0.987327 | − | 0.158696i | \(-0.0507291\pi\) |
−0.892044 | + | 0.451948i | \(0.850729\pi\) | |||||||
\(312\) | 4.00000 | − | 12.3107i | 0.226455 | − | 0.696958i | ||||
\(313\) | 12.5451 | + | 9.11454i | 0.709090 | + | 0.515184i | 0.882880 | − | 0.469599i | \(-0.155601\pi\) |
−0.173790 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(314\) | 18.0623 | + | 13.1230i | 1.01931 | + | 0.740576i | ||||
\(315\) | −34.2984 | + | 105.560i | −1.93249 | + | 5.94761i | ||||
\(316\) | −2.85410 | − | 8.78402i | −0.160556 | − | 0.494140i | ||||
\(317\) | 6.85410 | − | 4.97980i | 0.384965 | − | 0.279693i | −0.378424 | − | 0.925632i | \(-0.623534\pi\) |
0.763389 | + | 0.645939i | \(0.223534\pi\) | |||||||
\(318\) | −36.3607 | −2.03901 | ||||||||
\(319\) | 18.4721 | + | 4.14725i | 1.03424 | + | 0.232202i | ||||
\(320\) | 3.85410 | 0.215451 | ||||||||
\(321\) | −6.47214 | + | 4.70228i | −0.361239 | + | 0.262456i | ||||
\(322\) | −1.01722 | − | 3.13068i | −0.0566875 | − | 0.174466i | ||||
\(323\) | 0.500000 | − | 1.53884i | 0.0278207 | − | 0.0856234i | ||||
\(324\) | −19.7533 | − | 14.3516i | −1.09740 | − | 0.797311i | ||||
\(325\) | 31.8885 | + | 23.1684i | 1.76886 | + | 1.28515i | ||||
\(326\) | 5.33688 | − | 16.4252i | 0.295583 | − | 0.909709i | ||||
\(327\) | −0.944272 | − | 2.90617i | −0.0522184 | − | 0.160712i | ||||
\(328\) | −0.381966 | + | 0.277515i | −0.0210905 | + | 0.0153232i | ||||
\(329\) | 3.29180 | 0.181483 | ||||||||
\(330\) | −37.9787 | + | 16.3925i | −2.09066 | + | 0.902376i | ||||
\(331\) | −10.4721 | −0.575601 | −0.287800 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287800 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(332\) | −1.73607 | + | 1.26133i | −0.0952791 | + | 0.0692243i | ||||
\(333\) | −7.47214 | − | 22.9969i | −0.409471 | − | 1.26022i | ||||
\(334\) | 1.94427 | − | 5.98385i | 0.106386 | − | 0.327422i | ||||
\(335\) | 28.7984 | + | 20.9232i | 1.57342 | + | 1.14316i | ||||
\(336\) | −10.0902 | − | 7.33094i | −0.550464 | − | 0.399935i | ||||
\(337\) | 8.09017 | − | 24.8990i | 0.440700 | − | 1.35633i | −0.446432 | − | 0.894818i | \(-0.647306\pi\) |
0.887132 | − | 0.461516i | \(-0.152694\pi\) | |||||||
\(338\) | 0.927051 | + | 2.85317i | 0.0504249 | + | 0.155192i | ||||
\(339\) | −19.7082 | + | 14.3188i | −1.07040 | + | 0.777693i | ||||
\(340\) | 6.23607 | 0.338198 | ||||||||
\(341\) | −6.05573 | − | 6.88191i | −0.327936 | − | 0.372676i | ||||
\(342\) | 7.47214 | 0.404047 | ||||||||
\(343\) | 2.66312 | − | 1.93487i | 0.143795 | − | 0.104473i | ||||
\(344\) | −2.35410 | − | 7.24518i | −0.126925 | − | 0.390634i | ||||
\(345\) | −3.29180 | + | 10.1311i | −0.177224 | + | 0.545440i | ||||
\(346\) | −3.23607 | − | 2.35114i | −0.173972 | − | 0.126398i | ||||
\(347\) | −3.07295 | − | 2.23263i | −0.164965 | − | 0.119854i | 0.502240 | − | 0.864728i | \(-0.332509\pi\) |
−0.667205 | + | 0.744874i | \(0.732509\pi\) | |||||||
\(348\) | 5.70820 | − | 17.5680i | 0.305992 | − | 0.941746i | ||||
\(349\) | 2.98936 | + | 9.20029i | 0.160017 | + | 0.492480i | 0.998635 | − | 0.0522395i | \(-0.0166359\pi\) |
−0.838618 | + | 0.544720i | \(0.816636\pi\) | |||||||
\(350\) | 30.7254 | − | 22.3233i | 1.64234 | − | 1.19323i | ||||
\(351\) | 57.8885 | 3.08986 | ||||||||
\(352\) | −0.309017 | − | 3.30220i | −0.0164707 | − | 0.176008i | ||||
\(353\) | −33.9230 | −1.80554 | −0.902769 | − | 0.430125i | \(-0.858469\pi\) | ||||
−0.902769 | + | 0.430125i | \(0.858469\pi\) | |||||||
\(354\) | 18.1803 | − | 13.2088i | 0.966274 | − | 0.702039i | ||||
\(355\) | −3.29180 | − | 10.1311i | −0.174710 | − | 0.537703i | ||||
\(356\) | −4.38197 | + | 13.4863i | −0.232244 | + | 0.714773i | ||||
\(357\) | −16.3262 | − | 11.8617i | −0.864076 | − | 0.627788i | ||||
\(358\) | 17.0902 | + | 12.4167i | 0.903244 | + | 0.656245i | ||||
\(359\) | −0.680340 | + | 2.09387i | −0.0359070 | + | 0.110510i | −0.967404 | − | 0.253240i | \(-0.918504\pi\) |
0.931497 | + | 0.363750i | \(0.118504\pi\) | |||||||
\(360\) | 8.89919 | + | 27.3889i | 0.469028 | + | 1.44352i | ||||
\(361\) | −0.809017 | + | 0.587785i | −0.0425798 | + | 0.0309361i | ||||
\(362\) | −5.41641 | −0.284680 | ||||||||
\(363\) | 17.0902 | + | 31.2259i | 0.897001 | + | 1.63893i | ||||
\(364\) | 15.4164 | 0.808039 | ||||||||
\(365\) | 34.1246 | − | 24.7930i | 1.78616 | − | 1.29772i | ||||
\(366\) | 1.14590 | + | 3.52671i | 0.0598970 | + | 0.184344i | ||||
\(367\) | 2.80902 | − | 8.64527i | 0.146629 | − | 0.451279i | −0.850587 | − | 0.525834i | \(-0.823753\pi\) |
0.997217 | + | 0.0745544i | \(0.0237535\pi\) | |||||||
\(368\) | −0.690983 | − | 0.502029i | −0.0360200 | − | 0.0261700i | ||||
\(369\) | −2.85410 | − | 2.07363i | −0.148579 | − | 0.107949i | ||||
\(370\) | −3.85410 | + | 11.8617i | −0.200365 | + | 0.616661i | ||||
\(371\) | −13.3820 | − | 41.1855i | −0.694757 | − | 2.13824i | ||||
\(372\) | −7.23607 | + | 5.25731i | −0.375173 | + | 0.272579i | ||||
\(373\) | −18.4721 | −0.956451 | −0.478225 | − | 0.878237i | \(-0.658720\pi\) | ||||
−0.478225 | + | 0.878237i | \(0.658720\pi\) | |||||||
\(374\) | −0.500000 | − | 5.34307i | −0.0258544 | − | 0.276283i | ||||
\(375\) | −60.5410 | −3.12632 | ||||||||
\(376\) | 0.690983 | − | 0.502029i | 0.0356347 | − | 0.0258901i | ||||
\(377\) | 7.05573 | + | 21.7153i | 0.363388 | + | 1.11839i | ||||
\(378\) | 17.2361 | − | 53.0472i | 0.886528 | − | 2.72845i | ||||
\(379\) | −6.38197 | − | 4.63677i | −0.327820 | − | 0.238175i | 0.411685 | − | 0.911326i | \(-0.364940\pi\) |
−0.739505 | + | 0.673151i | \(0.764940\pi\) | |||||||
\(380\) | −3.11803 | − | 2.26538i | −0.159952 | − | 0.116212i | ||||
\(381\) | 2.29180 | − | 7.05342i | 0.117412 | − | 0.361358i | ||||
\(382\) | −4.13525 | − | 12.7270i | −0.211578 | − | 0.651170i | ||||
\(383\) | 15.0902 | − | 10.9637i | 0.771072 | − | 0.560216i | −0.131215 | − | 0.991354i | \(-0.541888\pi\) |
0.902286 | + | 0.431138i | \(0.141888\pi\) | |||||||
\(384\) | −3.23607 | −0.165140 | ||||||||
\(385\) | −32.5451 | − | 36.9852i | −1.65865 | − | 1.88494i | ||||
\(386\) | −18.4721 | −0.940207 | ||||||||
\(387\) | 46.0517 | − | 33.4585i | 2.34094 | − | 1.70079i | ||||
\(388\) | 5.23607 | + | 16.1150i | 0.265821 | + | 0.818113i | ||||
\(389\) | 0.701626 | − | 2.15938i | 0.0355739 | − | 0.109485i | −0.931693 | − | 0.363247i | \(-0.881668\pi\) |
0.967267 | + | 0.253762i | \(0.0816680\pi\) | |||||||
\(390\) | −40.3607 | − | 29.3238i | −2.04374 | − | 1.48487i | ||||
\(391\) | −1.11803 | − | 0.812299i | −0.0565414 | − | 0.0410797i | ||||
\(392\) | 2.42705 | − | 7.46969i | 0.122585 | − | 0.377277i | ||||
\(393\) | −13.8541 | − | 42.6385i | −0.698847 | − | 2.15083i | ||||
\(394\) | 8.85410 | − | 6.43288i | 0.446063 | − | 0.324084i | ||||
\(395\) | −35.5967 | −1.79107 | ||||||||
\(396\) | 22.7533 | − | 9.82084i | 1.14340 | − | 0.493516i | ||||
\(397\) | 16.5623 | 0.831238 | 0.415619 | − | 0.909539i | \(-0.363565\pi\) | ||||
0.415619 | + | 0.909539i | \(0.363565\pi\) | |||||||
\(398\) | −21.5344 | + | 15.6457i | −1.07942 | + | 0.784247i | ||||
\(399\) | 3.85410 | + | 11.8617i | 0.192946 | + | 0.593828i | ||||
\(400\) | 3.04508 | − | 9.37181i | 0.152254 | − | 0.468590i | ||||
\(401\) | 15.5623 | + | 11.3067i | 0.777144 | + | 0.564629i | 0.904121 | − | 0.427277i | \(-0.140527\pi\) |
−0.126976 | + | 0.991906i | \(0.540527\pi\) | |||||||
\(402\) | −24.1803 | − | 17.5680i | −1.20601 | − | 0.876214i | ||||
\(403\) | 3.41641 | − | 10.5146i | 0.170183 | − | 0.523771i | ||||
\(404\) | 1.10081 | + | 3.38795i | 0.0547675 | + | 0.168557i | ||||
\(405\) | −76.1312 | + | 55.3125i | −3.78299 | + | 2.74850i | ||||
\(406\) | 22.0000 | 1.09184 | ||||||||
\(407\) | 10.4721 | + | 2.35114i | 0.519085 | + | 0.116542i | ||||
\(408\) | −5.23607 | −0.259224 | ||||||||
\(409\) | −23.8885 | + | 17.3560i | −1.18121 | + | 0.858201i | −0.992308 | − | 0.123794i | \(-0.960494\pi\) |
−0.188905 | + | 0.981995i | \(0.560494\pi\) | |||||||
\(410\) | 0.562306 | + | 1.73060i | 0.0277703 | + | 0.0854682i | ||||
\(411\) | 9.56231 | − | 29.4298i | 0.471674 | − | 1.45166i | ||||
\(412\) | 5.61803 | + | 4.08174i | 0.276781 | + | 0.201093i | ||||
\(413\) | 21.6525 | + | 15.7314i | 1.06545 | + | 0.774094i | ||||
\(414\) | 1.97214 | − | 6.06961i | 0.0969252 | − | 0.298305i | ||||
\(415\) | 2.55573 | + | 7.86572i | 0.125456 | + | 0.386113i | ||||
\(416\) | 3.23607 | − | 2.35114i | 0.158661 | − | 0.115274i | ||||
\(417\) | −45.5967 | −2.23288 | ||||||||
\(418\) | −1.69098 | + | 2.85317i | −0.0827087 | + | 0.139553i | ||||
\(419\) | −28.7426 | −1.40417 | −0.702085 | − | 0.712093i | \(-0.747747\pi\) | ||||
−0.702085 | + | 0.712093i | \(0.747747\pi\) | |||||||
\(420\) | −38.8885 | + | 28.2542i | −1.89757 | + | 1.37866i | ||||
\(421\) | 7.56231 | + | 23.2744i | 0.368564 | + | 1.13432i | 0.947719 | + | 0.319106i | \(0.103383\pi\) |
−0.579155 | + | 0.815218i | \(0.696617\pi\) | |||||||
\(422\) | 4.61803 | − | 14.2128i | 0.224802 | − | 0.691871i | ||||
\(423\) | 5.16312 | + | 3.75123i | 0.251039 | + | 0.182391i | ||||
\(424\) | −9.09017 | − | 6.60440i | −0.441458 | − | 0.320738i | ||||
\(425\) | 4.92705 | − | 15.1639i | 0.238997 | − | 0.735557i | ||||
\(426\) | 2.76393 | + | 8.50651i | 0.133913 | + | 0.412142i | ||||
\(427\) | −3.57295 | + | 2.59590i | −0.172907 | + | 0.125624i | ||||
\(428\) | −2.47214 | −0.119495 | ||||||||
\(429\) | −21.8885 | + | 36.9322i | −1.05679 | + | 1.78310i | ||||
\(430\) | −29.3607 | −1.41590 | ||||||||
\(431\) | −8.56231 | + | 6.22088i | −0.412432 | + | 0.299649i | −0.774586 | − | 0.632469i | \(-0.782042\pi\) |
0.362154 | + | 0.932118i | \(0.382042\pi\) | |||||||
\(432\) | −4.47214 | − | 13.7638i | −0.215166 | − | 0.662212i | ||||
\(433\) | 3.67376 | − | 11.3067i | 0.176550 | − | 0.543364i | −0.823151 | − | 0.567822i | \(-0.807786\pi\) |
0.999701 | + | 0.0244581i | \(0.00778604\pi\) | |||||||
\(434\) | −8.61803 | − | 6.26137i | −0.413679 | − | 0.300555i | ||||
\(435\) | −57.5967 | − | 41.8465i | −2.76155 | − | 2.00639i | ||||
\(436\) | 0.291796 | − | 0.898056i | 0.0139745 | − | 0.0430091i | ||||
\(437\) | 0.263932 | + | 0.812299i | 0.0126256 | + | 0.0388575i | ||||
\(438\) | −28.6525 | + | 20.8172i | −1.36907 | + | 0.994686i | ||||
\(439\) | 18.3607 | 0.876307 | 0.438154 | − | 0.898900i | \(-0.355633\pi\) | ||||
0.438154 | + | 0.898900i | \(0.355633\pi\) | |||||||
\(440\) | −12.4721 | − | 2.80017i | −0.594586 | − | 0.133493i | ||||
\(441\) | 58.6869 | 2.79462 | ||||||||
\(442\) | 5.23607 | − | 3.80423i | 0.249054 | − | 0.180949i | ||||
\(443\) | −6.57295 | − | 20.2295i | −0.312290 | − | 0.961131i | −0.976856 | − | 0.213900i | \(-0.931383\pi\) |
0.664565 | − | 0.747230i | \(-0.268617\pi\) | |||||||
\(444\) | 3.23607 | − | 9.95959i | 0.153577 | − | 0.472661i | ||||
\(445\) | 44.2148 | + | 32.1239i | 2.09598 | + | 1.52282i | ||||
\(446\) | 8.61803 | + | 6.26137i | 0.408076 | + | 0.296484i | ||||
\(447\) | 3.52786 | − | 10.8576i | 0.166862 | − | 0.513549i | ||||
\(448\) | −1.19098 | − | 3.66547i | −0.0562687 | − | 0.173177i | ||||
\(449\) | −12.7082 | + | 9.23305i | −0.599737 | + | 0.435735i | −0.845786 | − | 0.533523i | \(-0.820868\pi\) |
0.246048 | + | 0.969258i | \(0.420868\pi\) | |||||||
\(450\) | 73.6312 | 3.47101 | ||||||||
\(451\) | 1.43769 | − | 0.620541i | 0.0676984 | − | 0.0292202i | ||||
\(452\) | −7.52786 | −0.354081 | ||||||||
\(453\) | −28.1803 | + | 20.4742i | −1.32403 | + | 0.961963i | ||||
\(454\) | −8.09017 | − | 24.8990i | −0.379690 | − | 1.16857i | ||||
\(455\) | 18.3607 | − | 56.5084i | 0.860762 | − | 2.64915i | ||||
\(456\) | 2.61803 | + | 1.90211i | 0.122601 | + | 0.0890746i | ||||
\(457\) | −8.97214 | − | 6.51864i | −0.419699 | − | 0.304929i | 0.357818 | − | 0.933791i | \(-0.383521\pi\) |
−0.777517 | + | 0.628862i | \(0.783521\pi\) | |||||||
\(458\) | −3.35410 | + | 10.3229i | −0.156727 | + | 0.482356i | ||||
\(459\) | −7.23607 | − | 22.2703i | −0.337751 | − | 1.03949i | ||||
\(460\) | −2.66312 | + | 1.93487i | −0.124169 | + | 0.0902137i | ||||
\(461\) | −30.6869 | −1.42923 | −0.714616 | − | 0.699517i | \(-0.753399\pi\) | ||||
−0.714616 | + | 0.699517i | \(0.753399\pi\) | |||||||
\(462\) | 27.3262 | + | 31.0543i | 1.27133 | + | 1.44478i | ||||
\(463\) | −12.2148 | −0.567669 | −0.283835 | − | 0.958873i | \(-0.591607\pi\) | ||||
−0.283835 | + | 0.958873i | \(0.591607\pi\) | |||||||
\(464\) | 4.61803 | − | 3.35520i | 0.214387 | − | 0.155761i | ||||
\(465\) | 10.6525 | + | 32.7849i | 0.493997 | + | 1.52037i | ||||
\(466\) | −0.100813 | + | 0.310271i | −0.00467007 | + | 0.0143730i | ||||
\(467\) | −7.50000 | − | 5.44907i | −0.347059 | − | 0.252153i | 0.400575 | − | 0.916264i | \(-0.368810\pi\) |
−0.747634 | + | 0.664111i | \(0.768810\pi\) | |||||||
\(468\) | 24.1803 | + | 17.5680i | 1.11774 | + | 0.812083i | ||||
\(469\) | 11.0000 | − | 33.8545i | 0.507933 | − | 1.56326i | ||||
\(470\) | −1.01722 | − | 3.13068i | −0.0469209 | − | 0.144408i | ||||
\(471\) | −58.4508 | + | 42.4670i | −2.69327 | + | 1.95678i | ||||
\(472\) | 6.94427 | 0.319636 | ||||||||
\(473\) | 2.35410 | + | 25.1563i | 0.108242 | + | 1.15669i | ||||
\(474\) | 29.8885 | 1.37283 | ||||||||
\(475\) | −7.97214 | + | 5.79210i | −0.365787 | + | 0.265760i | ||||
\(476\) | −1.92705 | − | 5.93085i | −0.0883262 | − | 0.271840i | ||||
\(477\) | 25.9443 | − | 79.8483i | 1.18791 | − | 3.65600i | ||||
\(478\) | 12.3992 | + | 9.00854i | 0.567126 | + | 0.412041i | ||||
\(479\) | −16.1074 | − | 11.7027i | −0.735965 | − | 0.534710i | 0.155480 | − | 0.987839i | \(-0.450308\pi\) |
−0.891445 | + | 0.453129i | \(0.850308\pi\) | |||||||
\(480\) | −3.85410 | + | 11.8617i | −0.175915 | + | 0.541410i | ||||
\(481\) | 4.00000 | + | 12.3107i | 0.182384 | + | 0.561321i | ||||
\(482\) | 15.7984 | − | 11.4782i | 0.719596 | − | 0.522817i | ||||
\(483\) | 10.6525 | 0.484704 | ||||||||
\(484\) | −1.39919 | + | 10.9106i | −0.0635994 | + | 0.495939i | ||||
\(485\) | 65.3050 | 2.96535 | ||||||||
\(486\) | 28.7984 | − | 20.9232i | 1.30632 | − | 0.949098i | ||||
\(487\) | 6.61803 | + | 20.3682i | 0.299892 | + | 0.922972i | 0.981534 | + | 0.191287i | \(0.0612660\pi\) |
−0.681642 | + | 0.731685i | \(0.738734\pi\) | |||||||
\(488\) | −0.354102 | + | 1.08981i | −0.0160294 | + | 0.0493336i | ||||
\(489\) | 45.2148 | + | 32.8505i | 2.04468 | + | 1.48555i | ||||
\(490\) | −24.4894 | − | 17.7926i | −1.10632 | − | 0.803786i | ||||
\(491\) | −7.33688 | + | 22.5806i | −0.331109 | + | 1.01905i | 0.637498 | + | 0.770452i | \(0.279969\pi\) |
−0.968607 | + | 0.248596i | \(0.920031\pi\) | |||||||
\(492\) | −0.472136 | − | 1.45309i | −0.0212855 | − | 0.0655101i | ||||
\(493\) | 7.47214 | − | 5.42882i | 0.336528 | − | 0.244502i | ||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | −8.89919 | − | 95.0979i | −0.399989 | − | 4.27433i | ||||
\(496\) | −2.76393 | −0.124104 | ||||||||
\(497\) | −8.61803 | + | 6.26137i | −0.386572 | + | 0.280861i | ||||
\(498\) | −2.14590 | − | 6.60440i | −0.0961600 | − | 0.295950i | ||||
\(499\) | −6.19098 | + | 19.0539i | −0.277146 | + | 0.852969i | 0.711497 | + | 0.702689i | \(0.248018\pi\) |
−0.988643 | + | 0.150280i | \(0.951982\pi\) | |||||||
\(500\) | −15.1353 | − | 10.9964i | −0.676869 | − | 0.491774i | ||||
\(501\) | 16.4721 | + | 11.9677i | 0.735921 | + | 0.534678i | ||||
\(502\) | −3.82624 | + | 11.7759i | −0.170773 | + | 0.525586i | ||||
\(503\) | 7.70820 | + | 23.7234i | 0.343692 | + | 1.05777i | 0.962280 | + | 0.272060i | \(0.0877048\pi\) |
−0.618589 | + | 0.785715i | \(0.712295\pi\) | |||||||
\(504\) | 23.2984 | − | 16.9273i | 1.03779 | − | 0.754000i | ||||
\(505\) | 13.7295 | 0.610954 | ||||||||
\(506\) | 1.87132 | + | 2.12663i | 0.0831904 | + | 0.0945401i | ||||
\(507\) | −9.70820 | −0.431156 | ||||||||
\(508\) | 1.85410 | − | 1.34708i | 0.0822625 | − | 0.0597672i | ||||
\(509\) | 7.18034 | + | 22.0988i | 0.318263 | + | 0.979513i | 0.974390 | + | 0.224863i | \(0.0721933\pi\) |
−0.656128 | + | 0.754650i | \(0.727807\pi\) | |||||||
\(510\) | −6.23607 | + | 19.1926i | −0.276138 | + | 0.849865i | ||||
\(511\) | −34.1246 | − | 24.7930i | −1.50958 | − | 1.09678i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −4.47214 | + | 13.7638i | −0.197450 | + | 0.607687i | ||||
\(514\) | −5.61803 | − | 17.2905i | −0.247801 | − | 0.762653i | ||||
\(515\) | 21.6525 | − | 15.7314i | 0.954122 | − | 0.693210i | ||||
\(516\) | 24.6525 | 1.08526 | ||||||||
\(517\) | −2.60081 | + | 1.12257i | −0.114384 | + | 0.0493706i | ||||
\(518\) | 12.4721 | 0.547994 | ||||||||
\(519\) | 10.4721 | − | 7.60845i | 0.459676 | − | 0.333974i | ||||
\(520\) | −4.76393 | − | 14.6619i | −0.208912 | − | 0.642966i | ||||
\(521\) | −7.23607 | + | 22.2703i | −0.317018 | + | 0.975681i | 0.657898 | + | 0.753107i | \(0.271446\pi\) |
−0.974916 | + | 0.222574i | \(0.928554\pi\) | |||||||
\(522\) | 34.5066 | + | 25.0705i | 1.51031 | + | 1.09731i | ||||
\(523\) | 23.7984 | + | 17.2905i | 1.04063 | + | 0.756062i | 0.970408 | − | 0.241469i | \(-0.0776293\pi\) |
0.0702218 | + | 0.997531i | \(0.477629\pi\) | |||||||
\(524\) | 4.28115 | − | 13.1760i | 0.187023 | − | 0.575598i | ||||
\(525\) | 37.9787 | + | 116.886i | 1.65753 | + | 5.10134i | ||||
\(526\) | 12.9443 | − | 9.40456i | 0.564397 | − | 0.410058i | ||||
\(527\) | −4.47214 | −0.194809 | ||||||||
\(528\) | 10.4721 | + | 2.35114i | 0.455741 | + | 0.102320i | ||||
\(529\) | −22.2705 | −0.968283 | ||||||||
\(530\) | −35.0344 | + | 25.4540i | −1.52180 | + | 1.10565i | ||||
\(531\) | 16.0344 | + | 49.3489i | 0.695836 | + | 2.14156i | ||||
\(532\) | −1.19098 | + | 3.66547i | −0.0516357 | + | 0.158918i | ||||
\(533\) | 1.52786 | + | 1.11006i | 0.0661791 | + | 0.0480820i | ||||
\(534\) | −37.1246 | − | 26.9726i | −1.60654 | − | 1.16722i | ||||
\(535\) | −2.94427 | + | 9.06154i | −0.127292 | + | 0.391764i | ||||
\(536\) | −2.85410 | − | 8.78402i | −0.123278 | − | 0.379412i | ||||
\(537\) | −55.3050 | + | 40.1814i | −2.38658 | + | 1.73396i | ||||
\(538\) | 19.7082 | 0.849681 | ||||||||
\(539\) | −13.2812 | + | 22.4091i | −0.572060 | + | 0.965228i | ||||
\(540\) | −55.7771 | −2.40026 | ||||||||
\(541\) | −12.0172 | + | 8.73102i | −0.516661 | + | 0.375376i | −0.815344 | − | 0.578976i | \(-0.803452\pi\) |
0.298684 | + | 0.954352i | \(0.403452\pi\) | |||||||
\(542\) | 8.68034 | + | 26.7153i | 0.372853 | + | 1.14752i | ||||
\(543\) | 5.41641 | − | 16.6700i | 0.232440 | − | 0.715378i | ||||
\(544\) | −1.30902 | − | 0.951057i | −0.0561236 | − | 0.0407762i | ||||
\(545\) | −2.94427 | − | 2.13914i | −0.126119 | − | 0.0916306i | ||||
\(546\) | −15.4164 | + | 47.4468i | −0.659761 | + | 2.03054i | ||||
\(547\) | −13.3820 | − | 41.1855i | −0.572172 | − | 1.76096i | −0.645614 | − | 0.763664i | \(-0.723399\pi\) |
0.0734429 | − | 0.997299i | \(-0.476601\pi\) | |||||||
\(548\) | 7.73607 | − | 5.62058i | 0.330468 | − | 0.240099i | ||||
\(549\) | −8.56231 | −0.365430 | ||||||||
\(550\) | −16.6631 | + | 28.1154i | −0.710518 | + | 1.19885i | ||||
\(551\) | −5.70820 | −0.243178 | ||||||||
\(552\) | 2.23607 | − | 1.62460i | 0.0951734 | − | 0.0691475i | ||||
\(553\) | 11.0000 | + | 33.8545i | 0.467768 | + | 1.43964i | ||||
\(554\) | −6.32624 | + | 19.4702i | −0.268776 | + | 0.827208i | ||||
\(555\) | −32.6525 | − | 23.7234i | −1.38602 | − | 1.00700i | ||||
\(556\) | −11.3992 | − | 8.28199i | −0.483433 | − | 0.351235i | ||||
\(557\) | 8.69756 | − | 26.7683i | 0.368527 | − | 1.13421i | −0.579215 | − | 0.815175i | \(-0.696641\pi\) |
0.947743 | − | 0.319036i | \(-0.103359\pi\) | |||||||
\(558\) | −6.38197 | − | 19.6417i | −0.270170 | − | 0.831498i | ||||
\(559\) | −24.6525 | + | 17.9111i | −1.04269 | + | 0.757558i | ||||
\(560\) | −14.8541 | −0.627700 | ||||||||
\(561\) | 16.9443 | + | 3.80423i | 0.715388 | + | 0.160615i | ||||
\(562\) | −4.00000 | −0.168730 | ||||||||
\(563\) | −26.6525 | + | 19.3642i | −1.12327 | + | 0.816102i | −0.984701 | − | 0.174251i | \(-0.944250\pi\) |
−0.138567 | + | 0.990353i | \(0.544250\pi\) | |||||||
\(564\) | 0.854102 | + | 2.62866i | 0.0359642 | + | 0.110686i | ||||
\(565\) | −8.96556 | + | 27.5932i | −0.377184 | + | 1.16085i | ||||
\(566\) | 7.97214 | + | 5.79210i | 0.335094 | + | 0.243460i | ||||
\(567\) | 76.1312 | + | 55.3125i | 3.19721 | + | 2.32291i | ||||
\(568\) | −0.854102 | + | 2.62866i | −0.0358373 | + | 0.110296i | ||||
\(569\) | 4.38197 | + | 13.4863i | 0.183702 | + | 0.565375i | 0.999924 | − | 0.0123631i | \(-0.00393539\pi\) |
−0.816222 | + | 0.577738i | \(0.803935\pi\) | |||||||
\(570\) | 10.0902 | − | 7.33094i | 0.422631 | − | 0.307059i | ||||
\(571\) | 14.2148 | 0.594870 | 0.297435 | − | 0.954742i | \(-0.403869\pi\) | ||||
0.297435 | + | 0.954742i | \(0.403869\pi\) | |||||||
\(572\) | −12.1803 | + | 5.25731i | −0.509286 | + | 0.219819i | ||||
\(573\) | 43.3050 | 1.80909 | ||||||||
\(574\) | 1.47214 | − | 1.06957i | 0.0614458 | − | 0.0446430i | ||||
\(575\) | 2.60081 | + | 8.00448i | 0.108461 | + | 0.333810i | ||||
\(576\) | 2.30902 | − | 7.10642i | 0.0962090 | − | 0.296101i | ||||
\(577\) | −31.7984 | − | 23.1029i | −1.32378 | − | 0.961785i | −0.999877 | − | 0.0156961i | \(-0.995004\pi\) |
−0.323907 | − | 0.946089i | \(-0.604996\pi\) | |||||||
\(578\) | 11.6353 | + | 8.45351i | 0.483963 | + | 0.351620i | ||||
\(579\) | 18.4721 | − | 56.8514i | 0.767676 | − | 2.36266i | ||||
\(580\) | −6.79837 | − | 20.9232i | −0.282287 | − | 0.868790i | ||||
\(581\) | 6.69098 | − | 4.86128i | 0.277589 | − | 0.201680i | ||||
\(582\) | −54.8328 | −2.27289 | ||||||||
\(583\) | 24.6180 | + | 27.9767i | 1.01957 | + | 1.15868i | ||||
\(584\) | −10.9443 | −0.452877 | ||||||||
\(585\) | 93.1935 | − | 67.7090i | 3.85308 | − | 2.79942i | ||||
\(586\) | −7.41641 | − | 22.8254i | −0.306369 | − | 0.942907i | ||||
\(587\) | 10.3607 | − | 31.8869i | 0.427631 | − | 1.31611i | −0.472821 | − | 0.881158i | \(-0.656764\pi\) |
0.900452 | − | 0.434955i | \(-0.143236\pi\) | |||||||
\(588\) | 20.5623 | + | 14.9394i | 0.847975 | + | 0.616090i | ||||
\(589\) | 2.23607 | + | 1.62460i | 0.0921356 | + | 0.0669404i | ||||
\(590\) | 8.27051 | − | 25.4540i | 0.340492 | − | 1.04793i | ||||
\(591\) | 10.9443 | + | 33.6830i | 0.450187 | + | 1.38553i | ||||
\(592\) | 2.61803 | − | 1.90211i | 0.107601 | − | 0.0781764i | ||||
\(593\) | 10.7426 | 0.441148 | 0.220574 | − | 0.975370i | \(-0.429207\pi\) | ||||
0.220574 | + | 0.975370i | \(0.429207\pi\) | |||||||
\(594\) | 4.47214 | + | 47.7899i | 0.183494 | + | 1.96084i | ||||
\(595\) | −24.0344 | −0.985316 | ||||||||
\(596\) | 2.85410 | − | 2.07363i | 0.116909 | − | 0.0849390i | ||||
\(597\) | −26.6180 | − | 81.9219i | −1.08940 | − | 3.35284i | ||||
\(598\) | −1.05573 | + | 3.24920i | −0.0431719 | + | 0.132870i | ||||
\(599\) | −23.7984 | − | 17.2905i | −0.972375 | − | 0.706472i | −0.0163835 | − | 0.999866i | \(-0.505215\pi\) |
−0.955992 | + | 0.293394i | \(0.905215\pi\) | |||||||
\(600\) | 25.7984 | + | 18.7436i | 1.05321 | + | 0.765205i | ||||
\(601\) | 9.05573 | − | 27.8707i | 0.369391 | − | 1.13687i | −0.577795 | − | 0.816182i | \(-0.696087\pi\) |
0.947186 | − | 0.320686i | \(-0.103913\pi\) | |||||||
\(602\) | 9.07295 | + | 27.9237i | 0.369786 | + | 1.13808i | ||||
\(603\) | 55.8328 | − | 40.5649i | 2.27369 | − | 1.65193i | ||||
\(604\) | −10.7639 | −0.437978 | ||||||||
\(605\) | 38.3262 | + | 18.1231i | 1.55818 | + | 0.736808i | ||||
\(606\) | −11.5279 | −0.468287 | ||||||||
\(607\) | 7.47214 | − | 5.42882i | 0.303285 | − | 0.220349i | −0.425725 | − | 0.904853i | \(-0.639981\pi\) |
0.729010 | + | 0.684503i | \(0.239981\pi\) | |||||||
\(608\) | 0.309017 | + | 0.951057i | 0.0125323 | + | 0.0385704i | ||||
\(609\) | −22.0000 | + | 67.7090i | −0.891485 | + | 2.74371i | ||||
\(610\) | 3.57295 | + | 2.59590i | 0.144664 | + | 0.105105i | ||||
\(611\) | −2.76393 | − | 2.00811i | −0.111817 | − | 0.0812396i | ||||
\(612\) | 3.73607 | − | 11.4984i | 0.151022 | − | 0.464797i | ||||
\(613\) | −0.701626 | − | 2.15938i | −0.0283384 | − | 0.0872167i | 0.935887 | − | 0.352300i | \(-0.114600\pi\) |
−0.964225 | + | 0.265084i | \(0.914600\pi\) | |||||||
\(614\) | 1.23607 | − | 0.898056i | 0.0498836 | − | 0.0362426i | ||||
\(615\) | −5.88854 | −0.237449 | ||||||||
\(616\) | 1.19098 | + | 12.7270i | 0.0479861 | + | 0.512786i | ||||
\(617\) | 2.36068 | 0.0950374 | 0.0475187 | − | 0.998870i | \(-0.484869\pi\) | ||||
0.0475187 | + | 0.998870i | \(0.484869\pi\) | |||||||
\(618\) | −18.1803 | + | 13.2088i | −0.731321 | + | 0.531335i | ||||
\(619\) | 10.5902 | + | 32.5932i | 0.425655 | + | 1.31003i | 0.902366 | + | 0.430971i | \(0.141829\pi\) |
−0.476711 | + | 0.879060i | \(0.658171\pi\) | |||||||
\(620\) | −3.29180 | + | 10.1311i | −0.132202 | + | 0.406875i | ||||
\(621\) | 10.0000 | + | 7.26543i | 0.401286 | + | 0.291551i | ||||
\(622\) | −4.39919 | − | 3.19620i | −0.176391 | − | 0.128156i | ||||
\(623\) | 16.8885 | − | 51.9776i | 0.676625 | − | 2.08244i | ||||
\(624\) | 4.00000 | + | 12.3107i | 0.160128 | + | 0.492824i | ||||
\(625\) | −18.4721 | + | 13.4208i | −0.738885 | + | 0.536832i | ||||
\(626\) | −15.5066 | −0.619767 | ||||||||
\(627\) | −7.09017 | − | 8.05748i | −0.283154 | − | 0.321785i | ||||
\(628\) | −22.3262 | −0.890914 | ||||||||
\(629\) | 4.23607 | − | 3.07768i | 0.168903 | − | 0.122715i | ||||
\(630\) | −34.2984 | − | 105.560i | −1.36648 | − | 4.20559i | ||||
\(631\) | −4.18034 | + | 12.8658i | −0.166417 | + | 0.512178i | −0.999138 | − | 0.0415146i | \(-0.986782\pi\) |
0.832721 | + | 0.553693i | \(0.186782\pi\) | |||||||
\(632\) | 7.47214 | + | 5.42882i | 0.297226 | + | 0.215947i | ||||
\(633\) | 39.1246 | + | 28.4257i | 1.55506 | + | 1.12982i | ||||
\(634\) | −2.61803 | + | 8.05748i | −0.103975 | + | 0.320003i | ||||
\(635\) | −2.72949 | − | 8.40051i | −0.108317 | − | 0.333364i | ||||
\(636\) | 29.4164 | − | 21.3723i | 1.16644 | − | 0.847466i | ||||
\(637\) | −31.4164 | −1.24476 | ||||||||
\(638\) | −17.3820 | + | 7.50245i | −0.688159 | + | 0.297025i | ||||
\(639\) | −20.6525 | −0.816999 | ||||||||
\(640\) | −3.11803 | + | 2.26538i | −0.123251 | + | 0.0895472i | ||||
\(641\) | 0.652476 | + | 2.00811i | 0.0257712 | + | 0.0793157i | 0.963115 | − | 0.269090i | \(-0.0867230\pi\) |
−0.937344 | + | 0.348406i | \(0.886723\pi\) | |||||||
\(642\) | 2.47214 | − | 7.60845i | 0.0975674 | − | 0.300282i | ||||
\(643\) | −23.7254 | − | 17.2375i | −0.935639 | − | 0.679782i | 0.0117276 | − | 0.999931i | \(-0.496267\pi\) |
−0.947367 | + | 0.320149i | \(0.896267\pi\) | |||||||
\(644\) | 2.66312 | + | 1.93487i | 0.104942 | + | 0.0762445i | ||||
\(645\) | 29.3607 | − | 90.3629i | 1.15608 | − | 3.55803i | ||||
\(646\) | 0.500000 | + | 1.53884i | 0.0196722 | + | 0.0605449i | ||||
\(647\) | 26.9443 | − | 19.5762i | 1.05929 | − | 0.769618i | 0.0853320 | − | 0.996353i | \(-0.472805\pi\) |
0.973957 | + | 0.226734i | \(0.0728049\pi\) | |||||||
\(648\) | 24.4164 | 0.959167 | ||||||||
\(649\) | −22.4721 | − | 5.04531i | −0.882108 | − | 0.198046i | ||||
\(650\) | −39.4164 | −1.54604 | ||||||||
\(651\) | 27.8885 | − | 20.2622i | 1.09304 | − | 0.794139i | ||||
\(652\) | 5.33688 | + | 16.4252i | 0.209008 | + | 0.643262i | ||||
\(653\) | 8.53444 | − | 26.2663i | 0.333979 | − | 1.02788i | −0.633245 | − | 0.773952i | \(-0.718277\pi\) |
0.967223 | − | 0.253928i | \(-0.0817228\pi\) | |||||||
\(654\) | 2.47214 | + | 1.79611i | 0.0966682 | + | 0.0702335i | ||||
\(655\) | −43.1976 | − | 31.3849i | −1.68787 | − | 1.22631i | ||||
\(656\) | 0.145898 | − | 0.449028i | 0.00569636 | − | 0.0175316i | ||||
\(657\) | −25.2705 | − | 77.7746i | −0.985896 | − | 3.03428i | ||||
\(658\) | −2.66312 | + | 1.93487i | −0.103819 | + | 0.0754291i | ||||
\(659\) | 29.4164 | 1.14590 | 0.572950 | − | 0.819590i | \(-0.305799\pi\) | ||||
0.572950 | + | 0.819590i | \(0.305799\pi\) | |||||||
\(660\) | 21.0902 | − | 35.5851i | 0.820934 | − | 1.38515i | ||||
\(661\) | −19.4164 | −0.755211 | −0.377605 | − | 0.925967i | \(-0.623252\pi\) | ||||
−0.377605 | + | 0.925967i | \(0.623252\pi\) | |||||||
\(662\) | 8.47214 | − | 6.15537i | 0.329279 | − | 0.239235i | ||||
\(663\) | 6.47214 | + | 19.9192i | 0.251357 | + | 0.773597i | ||||
\(664\) | 0.663119 | − | 2.04087i | 0.0257340 | − | 0.0792011i | ||||
\(665\) | 12.0172 | + | 8.73102i | 0.466008 | + | 0.338575i | ||||
\(666\) | 19.5623 | + | 14.2128i | 0.758024 | + | 0.550737i | ||||
\(667\) | −1.50658 | + | 4.63677i | −0.0583349 | + | 0.179536i | ||||
\(668\) | 1.94427 | + | 5.98385i | 0.0752261 | + | 0.231522i | ||||
\(669\) | −27.8885 | + | 20.2622i | −1.07823 | + | 0.783382i | ||||
\(670\) | −35.5967 | −1.37522 | ||||||||
\(671\) | 1.93769 | − | 3.26944i | 0.0748039 | − | 0.126215i | ||||
\(672\) | 12.4721 | 0.481123 | ||||||||
\(673\) | 19.9443 | − | 14.4904i | 0.768795 | − | 0.558562i | −0.132800 | − | 0.991143i | \(-0.542397\pi\) |
0.901595 | + | 0.432580i | \(0.142397\pi\) | |||||||
\(674\) | 8.09017 | + | 24.8990i | 0.311622 | + | 0.959073i | ||||
\(675\) | −44.0689 | + | 135.630i | −1.69621 | + | 5.22040i | ||||
\(676\) | −2.42705 | − | 1.76336i | −0.0933481 | − | 0.0678214i | ||||
\(677\) | 14.0902 | + | 10.2371i | 0.541529 | + | 0.393444i | 0.824653 | − | 0.565639i | \(-0.191371\pi\) |
−0.283123 | + | 0.959083i | \(0.591371\pi\) | |||||||
\(678\) | 7.52786 | − | 23.1684i | 0.289106 | − | 0.889776i | ||||
\(679\) | −20.1803 | − | 62.1087i | −0.774450 | − | 2.38351i | ||||
\(680\) | −5.04508 | + | 3.66547i | −0.193470 | + | 0.140564i | ||||
\(681\) | 84.7214 | 3.24653 | ||||||||
\(682\) | 8.94427 | + | 2.00811i | 0.342494 | + | 0.0768947i | ||||
\(683\) | −9.70820 | −0.371474 | −0.185737 | − | 0.982599i | \(-0.559467\pi\) | ||||
−0.185737 | + | 0.982599i | \(0.559467\pi\) | |||||||
\(684\) | −6.04508 | + | 4.39201i | −0.231140 | + | 0.167933i | ||||
\(685\) | −11.3885 | − | 35.0503i | −0.435134 | − | 1.33920i | ||||
\(686\) | −1.01722 | + | 3.13068i | −0.0388377 | + | 0.119530i | ||||
\(687\) | −28.4164 | − | 20.6457i | −1.08415 | − | 0.787684i | ||||
\(688\) | 6.16312 | + | 4.47777i | 0.234967 | + | 0.170713i | ||||
\(689\) | −13.8885 | + | 42.7445i | −0.529111 | + | 1.62844i | ||||
\(690\) | −3.29180 | − | 10.1311i | −0.125317 | − | 0.385685i | ||||
\(691\) | −11.5000 | + | 8.35524i | −0.437481 | + | 0.317848i | −0.784633 | − | 0.619960i | \(-0.787149\pi\) |
0.347152 | + | 0.937809i | \(0.387149\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | −87.6935 | + | 37.8505i | −3.33120 | + | 1.43782i | ||||
\(694\) | 3.79837 | 0.144184 | ||||||||
\(695\) | −43.9336 | + | 31.9196i | −1.66650 | + | 1.21078i | ||||
\(696\) | 5.70820 | + | 17.5680i | 0.216369 | + | 0.665915i | ||||
\(697\) | 0.236068 | − | 0.726543i | 0.00894171 | − | 0.0275198i | ||||
\(698\) | −7.82624 | − | 5.68609i | −0.296227 | − | 0.215222i | ||||
\(699\) | −0.854102 | − | 0.620541i | −0.0323051 | − | 0.0234710i | ||||
\(700\) | −11.7361 | + | 36.1199i | −0.443582 | + | 1.36520i | ||||
\(701\) | 13.0066 | + | 40.0301i | 0.491252 | + | 1.51192i | 0.822718 | + | 0.568450i | \(0.192457\pi\) |
−0.331466 | + | 0.943467i | \(0.607543\pi\) | |||||||
\(702\) | −46.8328 | + | 34.0260i | −1.76759 | + | 1.28423i | ||||
\(703\) | −3.23607 | −0.122051 | ||||||||
\(704\) | 2.19098 | + | 2.48990i | 0.0825758 | + | 0.0938416i | ||||
\(705\) | 10.6525 | 0.401195 | ||||||||
\(706\) | 27.4443 | − | 19.9394i | 1.03288 | − | 0.750430i | ||||
\(707\) | −4.24265 | − | 13.0575i | −0.159561 | − | 0.491079i | ||||
\(708\) | −6.94427 | + | 21.3723i | −0.260982 | + | 0.803219i | ||||
\(709\) | −37.2426 | − | 27.0584i | −1.39868 | − | 1.01620i | −0.994849 | − | 0.101363i | \(-0.967680\pi\) |
−0.403827 | − | 0.914835i | \(-0.632320\pi\) | |||||||
\(710\) | 8.61803 | + | 6.26137i | 0.323429 | + | 0.234985i | ||||
\(711\) | −21.3262 | + | 65.6354i | −0.799796 | + | 2.46152i | ||||
\(712\) | −4.38197 | − | 13.4863i | −0.164221 | − | 0.505421i | ||||
\(713\) | 1.90983 | − | 1.38757i | 0.0715237 | − | 0.0519650i | ||||
\(714\) | 20.1803 | 0.755230 | ||||||||
\(715\) | 4.76393 | + | 50.9080i | 0.178161 | + | 1.90385i | ||||
\(716\) | −21.1246 | −0.789464 | ||||||||
\(717\) | −40.1246 | + | 29.1522i | −1.49848 | + | 1.08871i | ||||
\(718\) | −0.680340 | − | 2.09387i | −0.0253901 | − | 0.0781426i | ||||
\(719\) | −2.69756 | + | 8.30224i | −0.100602 | + | 0.309621i | −0.988673 | − | 0.150085i | \(-0.952045\pi\) |
0.888071 | + | 0.459706i | \(0.152045\pi\) | |||||||
\(720\) | −23.2984 | − | 16.9273i | −0.868279 | − | 0.630842i | ||||
\(721\) | −21.6525 | − | 15.7314i | −0.806380 | − | 0.585870i | ||||
\(722\) | 0.309017 | − | 0.951057i | 0.0115004 | − | 0.0353947i | ||||
\(723\) | 19.5279 | + | 60.1006i | 0.726249 | + | 2.23516i | ||||
\(724\) | 4.38197 | − | 3.18368i | 0.162854 | − | 0.118321i | ||||
\(725\) | −56.2492 | −2.08904 | ||||||||
\(726\) | −32.1803 | − | 15.2169i | −1.19432 | − | 0.564752i | ||||
\(727\) | 34.1591 | 1.26689 | 0.633445 | − | 0.773788i | \(-0.281640\pi\) | ||||
0.633445 | + | 0.773788i | \(0.281640\pi\) | |||||||
\(728\) | −12.4721 | + | 9.06154i | −0.462248 | + | 0.335843i | ||||
\(729\) | 12.9615 | + | 39.8914i | 0.480055 | + | 1.47746i | ||||
\(730\) | −13.0344 | + | 40.1159i | −0.482426 | + | 1.48476i | ||||
\(731\) | 9.97214 | + | 7.24518i | 0.368833 | + | 0.267973i | ||||
\(732\) | −3.00000 | − | 2.17963i | −0.110883 | − | 0.0805614i | ||||
\(733\) | 6.42705 | − | 19.7804i | 0.237389 | − | 0.730607i | −0.759407 | − | 0.650616i | \(-0.774511\pi\) |
0.996796 | − | 0.0799910i | \(-0.0254892\pi\) | |||||||
\(734\) | 2.80902 | + | 8.64527i | 0.103683 | + | 0.319103i | ||||
\(735\) | 79.2492 | − | 57.5779i | 2.92315 | − | 2.12379i | ||||
\(736\) | 0.854102 | 0.0314826 | ||||||||
\(737\) | 2.85410 | + | 30.4993i | 0.105132 | + | 1.12346i | ||||
\(738\) | 3.52786 | 0.129862 | ||||||||
\(739\) | 37.3885 | − | 27.1644i | 1.37536 | − | 0.999257i | 0.378063 | − | 0.925780i | \(-0.376590\pi\) |
0.997297 | − | 0.0734775i | \(-0.0234097\pi\) | |||||||
\(740\) | −3.85410 | − | 11.8617i | −0.141680 | − | 0.436045i | ||||
\(741\) | 4.00000 | − | 12.3107i | 0.146944 | − | 0.452246i | ||||
\(742\) | 35.0344 | + | 25.4540i | 1.28615 | + | 0.934446i | ||||
\(743\) | −2.76393 | − | 2.00811i | −0.101399 | − | 0.0736706i | 0.535931 | − | 0.844262i | \(-0.319961\pi\) |
−0.637329 | + | 0.770592i | \(0.719961\pi\) | |||||||
\(744\) | 2.76393 | − | 8.50651i | 0.101331 | − | 0.311864i | ||||
\(745\) | −4.20163 | − | 12.9313i | −0.153936 | − | 0.473765i | ||||
\(746\) | 14.9443 | − | 10.8576i | 0.547149 | − | 0.397527i | ||||
\(747\) | 16.0344 | 0.586670 | ||||||||
\(748\) | 3.54508 | + | 4.02874i | 0.129621 | + | 0.147305i | ||||
\(749\) | 9.52786 | 0.348141 | ||||||||
\(750\) | 48.9787 | − | 35.5851i | 1.78845 | − | 1.29938i | ||||
\(751\) | −11.7082 | − | 36.0341i | −0.427238 | − | 1.31490i | −0.900835 | − | 0.434163i | \(-0.857044\pi\) |
0.473596 | − | 0.880742i | \(-0.342956\pi\) | |||||||
\(752\) | −0.263932 | + | 0.812299i | −0.00962461 | + | 0.0296215i | ||||
\(753\) | −32.4164 | − | 23.5519i | −1.18132 | − | 0.858279i | ||||
\(754\) | −18.4721 | − | 13.4208i | −0.672716 | − | 0.488756i | ||||
\(755\) | −12.8197 | + | 39.4549i | −0.466555 | + | 1.43591i | ||||
\(756\) | 17.2361 | + | 53.0472i | 0.626870 | + | 1.92931i | ||||
\(757\) | −24.5623 | + | 17.8456i | −0.892732 | + | 0.648608i | −0.936589 | − | 0.350430i | \(-0.886035\pi\) |
0.0438568 | + | 0.999038i | \(0.486035\pi\) | |||||||
\(758\) | 7.88854 | 0.286525 | ||||||||
\(759\) | −8.41641 | + | 3.63271i | −0.305496 | + | 0.131859i | ||||
\(760\) | 3.85410 | 0.139803 | ||||||||
\(761\) | 25.5066 | − | 18.5316i | 0.924613 | − | 0.671770i | −0.0200551 | − | 0.999799i | \(-0.506384\pi\) |
0.944668 | + | 0.328028i | \(0.106384\pi\) | |||||||
\(762\) | 2.29180 | + | 7.05342i | 0.0830230 | + | 0.255519i | ||||
\(763\) | −1.12461 | + | 3.46120i | −0.0407137 | + | 0.125304i | ||||
\(764\) | 10.8262 | + | 7.86572i | 0.391680 | + | 0.284572i | ||||
\(765\) | −37.6976 | − | 27.3889i | −1.36296 | − | 0.990247i | ||||
\(766\) | −5.76393 | + | 17.7396i | −0.208259 | + | 0.640956i | ||||
\(767\) | −8.58359 | − | 26.4176i | −0.309936 | − | 0.953884i | ||||
\(768\) | 2.61803 | − | 1.90211i | 0.0944702 | − | 0.0686366i | ||||
\(769\) | −13.2705 | −0.478547 | −0.239273 | − | 0.970952i | \(-0.576909\pi\) | ||||
−0.239273 | + | 0.970952i | \(0.576909\pi\) | |||||||
\(770\) | 48.0689 | + | 10.7921i | 1.73228 | + | 0.388922i | ||||
\(771\) | 58.8328 | 2.11881 | ||||||||
\(772\) | 14.9443 | − | 10.8576i | 0.537856 | − | 0.390775i | ||||
\(773\) | 4.43769 | + | 13.6578i | 0.159613 | + | 0.491238i | 0.998599 | − | 0.0529150i | \(-0.0168512\pi\) |
−0.838986 | + | 0.544153i | \(0.816851\pi\) | |||||||
\(774\) | −17.5902 | + | 54.1370i | −0.632266 | + | 1.94591i | ||||
\(775\) | 22.0344 | + | 16.0090i | 0.791501 | + | 0.575059i | ||||
\(776\) | −13.7082 | − | 9.95959i | −0.492096 | − | 0.357529i | ||||
\(777\) | −12.4721 | + | 38.3853i | −0.447435 | + | 1.37706i | ||||
\(778\) | 0.701626 | + | 2.15938i | 0.0251545 | + | 0.0774176i | ||||
\(779\) | −0.381966 | + | 0.277515i | −0.0136854 | + | 0.00994299i | ||||
\(780\) | 49.8885 | 1.78630 | ||||||||
\(781\) | 4.67376 | − | 7.88597i | 0.167240 | − | 0.282182i | ||||
\(782\) | 1.38197 | 0.0494190 | ||||||||
\(783\) | −66.8328 | + | 48.5569i | −2.38841 | + | 1.73528i | ||||
\(784\) | 2.42705 | + | 7.46969i | 0.0866804 | + | 0.266775i | ||||
\(785\) | −26.5902 | + | 81.8361i | −0.949044 | + | 2.92086i | ||||
\(786\) | 36.2705 | + | 26.3521i | 1.29373 | + | 0.939947i | ||||
\(787\) | −14.0902 | − | 10.2371i | −0.502260 | − | 0.364913i | 0.307619 | − | 0.951509i | \(-0.400468\pi\) |
−0.809880 | + | 0.586596i | \(0.800468\pi\) | |||||||
\(788\) | −3.38197 | + | 10.4086i | −0.120478 | + | 0.370792i | ||||
\(789\) | 16.0000 | + | 49.2429i | 0.569615 | + | 1.75309i | ||||
\(790\) | 28.7984 | − | 20.9232i | 1.02460 | − | 0.744416i | ||||
\(791\) | 29.0132 | 1.03159 | ||||||||
\(792\) | −12.6353 | + | 21.3193i | −0.448974 | + | 0.757547i | ||||
\(793\) | 4.58359 | 0.162768 | ||||||||
\(794\) | −13.3992 | + | 9.73508i | −0.475519 | + | 0.345485i | ||||
\(795\) | −43.3050 | − | 133.279i | −1.53587 | − | 4.72692i | ||||
\(796\) | 8.22542 | − | 25.3153i | 0.291542 | − | 0.897275i | ||||
\(797\) | −27.5066 | − | 19.9847i | −0.974333 | − | 0.707894i | −0.0178980 | − | 0.999840i | \(-0.505697\pi\) |
−0.956435 | + | 0.291945i | \(0.905697\pi\) | |||||||
\(798\) | −10.0902 | − | 7.33094i | −0.357188 | − | 0.259512i | ||||
\(799\) | −0.427051 | + | 1.31433i | −0.0151080 | + | 0.0464976i | ||||
\(800\) | 3.04508 | + | 9.37181i | 0.107660 | + | 0.331343i | ||||
\(801\) | 85.7214 | − | 62.2802i | 3.02882 | − | 2.20056i | ||||
\(802\) | −19.2361 | −0.679249 | ||||||||
\(803\) | 35.4164 | + | 7.95148i | 1.24982 | + | 0.280602i | ||||
\(804\) | 29.8885 | 1.05409 | ||||||||
\(805\) | 10.2639 | − | 7.45718i | 0.361756 | − | 0.262831i | ||||
\(806\) | 3.41641 | + | 10.5146i | 0.120338 | + | 0.370362i | ||||
\(807\) | −19.7082 | + | 60.6556i | −0.693762 | + | 2.13518i | ||||
\(808\) | −2.88197 | − | 2.09387i | −0.101387 | − | 0.0736621i | ||||
\(809\) | −28.3885 | − | 20.6255i | −0.998088 | − | 0.725153i | −0.0364107 | − | 0.999337i | \(-0.511592\pi\) |
−0.961677 | + | 0.274183i | \(0.911592\pi\) | |||||||
\(810\) | 29.0795 | − | 89.4976i | 1.02175 | − | 3.14462i | ||||
\(811\) | −3.94427 | − | 12.1392i | −0.138502 | − | 0.426266i | 0.857616 | − | 0.514290i | \(-0.171945\pi\) |
−0.996118 | + | 0.0880246i | \(0.971945\pi\) | |||||||
\(812\) | −17.7984 | + | 12.9313i | −0.624600 | + | 0.453799i | ||||
\(813\) | −90.9017 | −3.18806 | ||||||||
\(814\) | −9.85410 | + | 4.25325i | −0.345386 | + | 0.149076i | ||||
\(815\) | 66.5623 | 2.33158 | ||||||||
\(816\) | 4.23607 | − | 3.07768i | 0.148292 | − | 0.107740i | ||||
\(817\) | −2.35410 | − | 7.24518i | −0.0823596 | − | 0.253477i | ||||
\(818\) | 9.12461 | − | 28.0827i | 0.319035 | − | 0.981887i | ||||
\(819\) | −93.1935 | − | 67.7090i | −3.25644 | − | 2.36595i | ||||
\(820\) | −1.47214 | − | 1.06957i | −0.0514092 | − | 0.0373510i | ||||
\(821\) | 14.7148 | − | 45.2874i | 0.513549 | − | 1.58054i | −0.272356 | − | 0.962196i | \(-0.587803\pi\) |
0.785906 | − | 0.618346i | \(-0.212197\pi\) | |||||||
\(822\) | 9.56231 | + | 29.4298i | 0.333524 | + | 1.02648i | ||||
\(823\) | 1.40983 | − | 1.02430i | 0.0491436 | − | 0.0357049i | −0.562942 | − | 0.826496i | \(-0.690331\pi\) |
0.612086 | + | 0.790791i | \(0.290331\pi\) | |||||||
\(824\) | −6.94427 | −0.241915 | ||||||||
\(825\) | −69.8673 | − | 79.3992i | −2.43247 | − | 2.76433i | ||||
\(826\) | −26.7639 | −0.931236 | ||||||||
\(827\) | 9.76393 | − | 7.09391i | 0.339525 | − | 0.246679i | −0.404936 | − | 0.914345i | \(-0.632706\pi\) |
0.744461 | + | 0.667665i | \(0.232706\pi\) | |||||||
\(828\) | 1.97214 | + | 6.06961i | 0.0685365 | + | 0.210934i | ||||
\(829\) | 13.0902 | − | 40.2874i | 0.454640 | − | 1.39924i | −0.416916 | − | 0.908945i | \(-0.636889\pi\) |
0.871557 | − | 0.490294i | \(-0.163111\pi\) | |||||||
\(830\) | −6.69098 | − | 4.86128i | −0.232247 | − | 0.168738i | ||||
\(831\) | −53.5967 | − | 38.9403i | −1.85925 | − | 1.35082i | ||||
\(832\) | −1.23607 | + | 3.80423i | −0.0428529 | + | 0.131888i | ||||
\(833\) | 3.92705 | + | 12.0862i | 0.136064 | + | 0.418763i | ||||
\(834\) | 36.8885 | − | 26.8011i | 1.27735 | − | 0.928046i | ||||
\(835\) | 24.2492 | 0.839179 | ||||||||
\(836\) | −0.309017 | − | 3.30220i | −0.0106876 | − | 0.114209i | ||||
\(837\) | 40.0000 | 1.38260 | ||||||||
\(838\) | 23.2533 | − | 16.8945i | 0.803272 | − | 0.583611i | ||||
\(839\) | 7.11146 | + | 21.8868i | 0.245515 | + | 0.755617i | 0.995551 | + | 0.0942204i | \(0.0300358\pi\) |
−0.750037 | + | 0.661396i | \(0.769964\pi\) | |||||||
\(840\) | 14.8541 | − | 45.7162i | 0.512515 | − | 1.57736i | ||||
\(841\) | −2.89919 | − | 2.10638i | −0.0999720 | − | 0.0726339i | ||||
\(842\) | −19.7984 | − | 14.3844i | −0.682297 | − | 0.495718i | ||||
\(843\) | 4.00000 | − | 12.3107i | 0.137767 | − | 0.424004i | ||||
\(844\) | 4.61803 | + | 14.2128i | 0.158959 | + | 0.489226i | ||||
\(845\) | −9.35410 | + | 6.79615i | −0.321791 | + | 0.233795i | ||||
\(846\) | −6.38197 | −0.219417 | ||||||||
\(847\) | 5.39261 | − | 42.0508i | 0.185292 | − | 1.44488i | ||||
\(848\) | 11.2361 | 0.385848 | ||||||||
\(849\) | −25.7984 | + | 18.7436i | −0.885398 | + | 0.643279i | ||||
\(850\) | 4.92705 | + | 15.1639i | 0.168996 | + | 0.520118i | ||||
\(851\) | −0.854102 | + | 2.62866i | −0.0292782 | + | 0.0901092i | ||||
\(852\) | −7.23607 | − | 5.25731i | −0.247904 | − | 0.180113i | ||||
\(853\) | −5.54508 | − | 4.02874i | −0.189860 | − | 0.137941i | 0.488795 | − | 0.872399i | \(-0.337437\pi\) |
−0.678655 | + | 0.734457i | \(0.737437\pi\) | |||||||
\(854\) | 1.36475 | − | 4.20025i | 0.0467006 | − | 0.143730i | ||||
\(855\) | 8.89919 | + | 27.3889i | 0.304346 | + | 0.936680i | ||||
\(856\) | 2.00000 | − | 1.45309i | 0.0683586 | − | 0.0496654i | ||||
\(857\) | 26.8328 | 0.916592 | 0.458296 | − | 0.888800i | \(-0.348460\pi\) | ||||
0.458296 | + | 0.888800i | \(0.348460\pi\) | |||||||
\(858\) | −4.00000 | − | 42.7445i | −0.136558 | − | 1.45927i | ||||
\(859\) | 7.03444 | 0.240012 | 0.120006 | − | 0.992773i | \(-0.461709\pi\) | ||||
0.120006 | + | 0.992773i | \(0.461709\pi\) | |||||||
\(860\) | 23.7533 | − | 17.2578i | 0.809980 | − | 0.588485i | ||||
\(861\) | 1.81966 | + | 5.60034i | 0.0620139 | + | 0.190859i | ||||
\(862\) | 3.27051 | − | 10.0656i | 0.111394 | − | 0.342836i | ||||
\(863\) | 15.1803 | + | 11.0292i | 0.516745 | + | 0.375437i | 0.815376 | − | 0.578931i | \(-0.196530\pi\) |
−0.298631 | + | 0.954369i | \(0.596530\pi\) | |||||||
\(864\) | 11.7082 | + | 8.50651i | 0.398321 | + | 0.289397i | ||||
\(865\) | 4.76393 | − | 14.6619i | 0.161979 | − | 0.498519i | ||||
\(866\) | 3.67376 | + | 11.3067i | 0.124840 | + | 0.384217i | ||||
\(867\) | −37.6525 | + | 27.3561i | −1.27875 | + | 0.929063i | ||||
\(868\) | 10.6525 | 0.361569 | ||||||||
\(869\) | −20.2361 | − | 22.9969i | −0.686462 | − | 0.780115i | ||||
\(870\) | 71.1935 | 2.41369 | ||||||||
\(871\) | −29.8885 | + | 21.7153i | −1.01273 | + | 0.735795i | ||||
\(872\) | 0.291796 | + | 0.898056i | 0.00988146 | + | 0.0304120i | ||||
\(873\) | 39.1246 | − | 120.413i | 1.32417 | − | 4.07537i | ||||
\(874\) | −0.690983 | − | 0.502029i | −0.0233728 | − | 0.0169814i | ||||
\(875\) | 58.3328 | + | 42.3813i | 1.97201 | + | 1.43275i | ||||
\(876\) | 10.9443 | − | 33.6830i | 0.369773 | − | 1.13804i | ||||
\(877\) | 10.0902 | + | 31.0543i | 0.340721 | + | 1.04863i | 0.963835 | + | 0.266500i | \(0.0858672\pi\) |
−0.623114 | + | 0.782131i | \(0.714133\pi\) | |||||||
\(878\) | −14.8541 | + | 10.7921i | −0.501302 | + | 0.364217i | ||||
\(879\) | 77.6656 | 2.61960 | ||||||||
\(880\) | 11.7361 | − | 5.06555i | 0.395623 | − | 0.170760i | ||||
\(881\) | 5.41641 | 0.182483 | 0.0912417 | − | 0.995829i | \(-0.470916\pi\) | ||||
0.0912417 | + | 0.995829i | \(0.470916\pi\) | |||||||
\(882\) | −47.4787 | + | 34.4953i | −1.59869 | + | 1.16152i | ||||
\(883\) | 8.66312 | + | 26.6623i | 0.291537 | + | 0.897259i | 0.984363 | + | 0.176154i | \(0.0563656\pi\) |
−0.692825 | + | 0.721105i | \(0.743634\pi\) | |||||||
\(884\) | −2.00000 | + | 6.15537i | −0.0672673 | + | 0.207027i | ||||
\(885\) | 70.0689 | + | 50.9080i | 2.35534 | + | 1.71125i | ||||
\(886\) | 17.2082 | + | 12.5025i | 0.578121 | + | 0.420029i | ||||
\(887\) | −10.9098 | + | 33.5770i | −0.366316 | + | 1.12741i | 0.582836 | + | 0.812589i | \(0.301943\pi\) |
−0.949153 | + | 0.314816i | \(0.898057\pi\) | |||||||
\(888\) | 3.23607 | + | 9.95959i | 0.108595 | + | 0.334222i | ||||
\(889\) | −7.14590 | + | 5.19180i | −0.239666 | + | 0.174127i | ||||
\(890\) | −54.6525 | −1.83196 | ||||||||
\(891\) | −79.0132 | − | 17.7396i | −2.64704 | − | 0.594298i | ||||
\(892\) | −10.6525 | −0.356671 | ||||||||
\(893\) | 0.690983 | − | 0.502029i | 0.0231229 | − | 0.0167997i | ||||
\(894\) | 3.52786 | + | 10.8576i | 0.117989 | + | 0.363134i | ||||
\(895\) | −25.1591 | + | 77.4316i | −0.840974 | + | 2.58825i | ||||
\(896\) | 3.11803 | + | 2.26538i | 0.104166 | + | 0.0756812i | ||||
\(897\) | −8.94427 | − | 6.49839i | −0.298641 | − | 0.216975i | ||||
\(898\) | 4.85410 | − | 14.9394i | 0.161983 | − | 0.498534i | ||||
\(899\) | 4.87539 | + | 15.0049i | 0.162603 | + | 0.500442i | ||||
\(900\) | −59.5689 | + | 43.2793i | −1.98563 | + | 1.44264i | ||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | −0.798374 | + | 1.34708i | −0.0265829 | + | 0.0448530i | ||||
\(903\) | −95.0132 | −3.16184 | ||||||||
\(904\) | 6.09017 | − | 4.42477i | 0.202556 | − | 0.147166i | ||||
\(905\) | −6.45085 | − | 19.8537i | −0.214434 | − | 0.659958i | ||||
\(906\) | 10.7639 | − | 33.1280i | 0.357608 | − | 1.10060i | ||||
\(907\) | −14.0344 | − | 10.1966i | −0.466006 | − | 0.338573i | 0.329877 | − | 0.944024i | \(-0.392993\pi\) |
−0.795883 | + | 0.605451i | \(0.792993\pi\) | |||||||
\(908\) | 21.1803 | + | 15.3884i | 0.702894 | + | 0.510683i | ||||
\(909\) | 8.22542 | − | 25.3153i | 0.272820 | − | 0.839654i | ||||
\(910\) | 18.3607 | + | 56.5084i | 0.608651 | + | 1.87323i | ||||
\(911\) | −19.0902 | + | 13.8698i | −0.632486 | + | 0.459528i | −0.857260 | − | 0.514883i | \(-0.827835\pi\) |
0.224775 | + | 0.974411i | \(0.427835\pi\) | |||||||
\(912\) | −3.23607 | −0.107157 | ||||||||
\(913\) | −3.62868 | + | 6.12261i | −0.120092 | + | 0.202629i | ||||
\(914\) | 11.0902 | 0.366830 | ||||||||
\(915\) | −11.5623 | + | 8.40051i | −0.382238 | + | 0.277712i | ||||
\(916\) | −3.35410 | − | 10.3229i | −0.110823 | − | 0.341077i | ||||
\(917\) | −16.5000 | + | 50.7818i | −0.544878 | + | 1.67696i | ||||
\(918\) | 18.9443 | + | 13.7638i | 0.625254 | + | 0.454274i | ||||
\(919\) | −32.0623 | − | 23.2946i | −1.05764 | − | 0.768419i | −0.0839880 | − | 0.996467i | \(-0.526766\pi\) |
−0.973650 | + | 0.228048i | \(0.926766\pi\) | |||||||
\(920\) | 1.01722 | − | 3.13068i | 0.0335368 | − | 0.103216i | ||||
\(921\) | 1.52786 | + | 4.70228i | 0.0503448 | + | 0.154945i | ||||
\(922\) | 24.8262 | − | 18.0373i | 0.817609 | − | 0.594027i | ||||
\(923\) | 11.0557 | 0.363904 | ||||||||
\(924\) | −40.3607 | − | 9.06154i | −1.32777 | − | 0.298103i | ||||
\(925\) | −31.8885 | −1.04849 | ||||||||
\(926\) | 9.88197 | − | 7.17967i | 0.324742 | − | 0.235939i | ||||
\(927\) | −16.0344 | − | 49.3489i | −0.526640 | − | 1.62083i | ||||
\(928\) | −1.76393 | + | 5.42882i | −0.0579039 | + | 0.178210i | ||||
\(929\) | 40.1418 | + | 29.1647i | 1.31701 | + | 0.956864i | 0.999964 | + | 0.00845439i | \(0.00269115\pi\) |
0.317047 | + | 0.948410i | \(0.397309\pi\) | |||||||
\(930\) | −27.8885 | − | 20.2622i | −0.914501 | − | 0.664424i | ||||
\(931\) | 2.42705 | − | 7.46969i | 0.0795434 | − | 0.244809i | ||||
\(932\) | −0.100813 | − | 0.310271i | −0.00330224 | − | 0.0101633i | ||||
\(933\) | 14.2361 | − | 10.3431i | 0.466068 | − | 0.338618i | ||||
\(934\) | 9.27051 | 0.303340 | ||||||||
\(935\) | 18.9894 | − | 8.19624i | 0.621018 | − | 0.268046i | ||||
\(936\) | −29.8885 | −0.976938 | ||||||||
\(937\) | 6.87132 | − | 4.99231i | 0.224476 | − | 0.163092i | −0.469863 | − | 0.882739i | \(-0.655697\pi\) |
0.694339 | + | 0.719648i | \(0.255697\pi\) | |||||||
\(938\) | 11.0000 | + | 33.8545i | 0.359163 | + | 1.10539i | ||||
\(939\) | 15.5066 | − | 47.7243i | 0.506038 | − | 1.55742i | ||||
\(940\) | 2.66312 | + | 1.93487i | 0.0868614 | + | 0.0631085i | ||||
\(941\) | −16.7984 | − | 12.2047i | −0.547611 | − | 0.397863i | 0.279293 | − | 0.960206i | \(-0.409900\pi\) |
−0.826904 | + | 0.562343i | \(0.809900\pi\) | |||||||
\(942\) | 22.3262 | − | 68.7131i | 0.727428 | − | 2.23879i | ||||
\(943\) | 0.124612 | + | 0.383516i | 0.00405792 | + | 0.0124890i | ||||
\(944\) | −5.61803 | + | 4.08174i | −0.182851 | + | 0.132849i | ||||
\(945\) | 214.971 | 6.99299 | ||||||||
\(946\) | −16.6910 | − | 18.9681i | −0.542671 | − | 0.616707i | ||||
\(947\) | −1.49342 | −0.0485297 | −0.0242649 | − | 0.999706i | \(-0.507724\pi\) | ||||
−0.0242649 | + | 0.999706i | \(0.507724\pi\) | |||||||
\(948\) | −24.1803 | + | 17.5680i | −0.785341 | + | 0.570584i | ||||
\(949\) | 13.5279 | + | 41.6345i | 0.439133 | + | 1.35151i | ||||
\(950\) | 3.04508 | − | 9.37181i | 0.0987956 | − | 0.304062i | ||||
\(951\) | −22.1803 | − | 16.1150i | −0.719247 | − | 0.522563i | ||||
\(952\) | 5.04508 | + | 3.66547i | 0.163512 | + | 0.118799i | ||||
\(953\) | 7.11146 | − | 21.8868i | 0.230363 | − | 0.708983i | −0.767340 | − | 0.641240i | \(-0.778420\pi\) |
0.997703 | − | 0.0677431i | \(-0.0215798\pi\) | |||||||
\(954\) | 25.9443 | + | 79.8483i | 0.839977 | + | 2.58518i | ||||
\(955\) | 41.7254 | − | 30.3153i | 1.35020 | − | 0.980980i | ||||
\(956\) | −15.3262 | −0.495686 | ||||||||
\(957\) | −5.70820 | − | 60.9986i | −0.184520 | − | 1.97181i | ||||
\(958\) | 19.9098 | 0.643257 | ||||||||
\(959\) | −29.8156 | + | 21.6623i | −0.962796 | + | 0.699512i | ||||
\(960\) | −3.85410 | − | 11.8617i | −0.124391 | − | 0.382835i | ||||
\(961\) | −7.21885 | + | 22.2173i | −0.232866 | + | 0.716688i | ||||
\(962\) | −10.4721 | − | 7.60845i | −0.337635 | − | 0.245306i | ||||
\(963\) | 14.9443 | + | 10.8576i | 0.481572 | + | 0.349883i | ||||
\(964\) | −6.03444 | + | 18.5721i | −0.194356 | + | 0.598167i | ||||
\(965\) | −22.0000 | − | 67.7090i | −0.708205 | − | 2.17963i | ||||
\(966\) | −8.61803 | + | 6.26137i | −0.277281 | + | 0.201456i | ||||
\(967\) | −48.8541 | −1.57104 | −0.785521 | − | 0.618835i | \(-0.787605\pi\) | ||||
−0.785521 | + | 0.618835i | \(0.787605\pi\) | |||||||
\(968\) | −5.28115 | − | 9.64932i | −0.169743 | − | 0.310141i | ||||
\(969\) | −5.23607 | −0.168207 | ||||||||
\(970\) | −52.8328 | + | 38.3853i | −1.69636 | + | 1.23248i | ||||
\(971\) | −10.1803 | − | 31.3319i | −0.326703 | − | 1.00549i | −0.970666 | − | 0.240431i | \(-0.922711\pi\) |
0.643964 | − | 0.765056i | \(-0.277289\pi\) | |||||||
\(972\) | −11.0000 | + | 33.8545i | −0.352825 | + | 1.08588i | ||||
\(973\) | 43.9336 | + | 31.9196i | 1.40845 | + | 1.02330i | ||||
\(974\) | −17.3262 | − | 12.5882i | −0.555168 | − | 0.403354i | ||||
\(975\) | 39.4164 | − | 121.311i | 1.26234 | − | 3.88507i | ||||
\(976\) | −0.354102 | − | 1.08981i | −0.0113345 | − | 0.0348841i | ||||
\(977\) | −5.52786 | + | 4.01623i | −0.176852 | + | 0.128491i | −0.672690 | − | 0.739925i | \(-0.734861\pi\) |
0.495838 | + | 0.868415i | \(0.334861\pi\) | |||||||
\(978\) | −55.8885 | −1.78712 | ||||||||
\(979\) | 4.38197 | + | 46.8263i | 0.140048 | + | 1.49657i | ||||
\(980\) | 30.2705 | 0.966956 | ||||||||
\(981\) | −5.70820 | + | 4.14725i | −0.182249 | + | 0.132412i | ||||
\(982\) | −7.33688 | − | 22.5806i | −0.234129 | − | 0.720576i | ||||
\(983\) | 0.180340 | − | 0.555029i | 0.00575195 | − | 0.0177027i | −0.948139 | − | 0.317855i | \(-0.897037\pi\) |
0.953891 | + | 0.300152i | \(0.0970375\pi\) | |||||||
\(984\) | 1.23607 | + | 0.898056i | 0.0394044 | + | 0.0286290i | ||||
\(985\) | 34.1246 | + | 24.7930i | 1.08730 | + | 0.789970i | ||||
\(986\) | −2.85410 | + | 8.78402i | −0.0908931 | + | 0.279740i | ||||
\(987\) | −3.29180 | − | 10.1311i | −0.104779 | − | 0.322477i | ||||
\(988\) | 3.23607 | − | 2.35114i | 0.102953 | − | 0.0747998i | ||||
\(989\) | −6.50658 | −0.206897 | ||||||||
\(990\) | 63.0967 | + | 71.7050i | 2.00535 | + | 2.27894i | ||||
\(991\) | 12.9443 | 0.411188 | 0.205594 | − | 0.978637i | \(-0.434087\pi\) | ||||
0.205594 | + | 0.978637i | \(0.434087\pi\) | |||||||
\(992\) | 2.23607 | − | 1.62460i | 0.0709952 | − | 0.0515811i | ||||
\(993\) | 10.4721 | + | 32.2299i | 0.332323 | + | 1.02279i | ||||
\(994\) | 3.29180 | − | 10.1311i | 0.104409 | − | 0.321339i | ||||
\(995\) | −82.9959 | − | 60.3001i | −2.63115 | − | 1.91164i | ||||
\(996\) | 5.61803 | + | 4.08174i | 0.178014 | + | 0.129335i | ||||
\(997\) | 12.3369 | − | 37.9690i | 0.390713 | − | 1.20249i | −0.541537 | − | 0.840677i | \(-0.682158\pi\) |
0.932250 | − | 0.361814i | \(-0.117842\pi\) | |||||||
\(998\) | −6.19098 | − | 19.0539i | −0.195972 | − | 0.603140i | ||||
\(999\) | −37.8885 | + | 27.5276i | −1.19874 | + | 0.870936i |
(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 | 418.2.f.a.267.1 | yes | 4 | |
11.2 | odd | 10 | 4598.2.a.v.1.1 | 2 | |||
11.4 | even | 5 | inner | 418.2.f.a.191.1 | ✓ | 4 | |
11.9 | even | 5 | 4598.2.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.a.191.1 | ✓ | 4 | 11.4 | even | 5 | inner | |
418.2.f.a.267.1 | yes | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.v.1.1 | 2 | 11.2 | odd | 10 | |||
4598.2.a.be.1.1 | 2 | 11.9 | even | 5 |