Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,2,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), 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: | \(1.41335211578\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.19298288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} - 2x^{3} + 9x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.1 | ||
Root | \(1.34067 + 1.09664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.2.d.c.176.2 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93543 | −1.36856 | −0.684279 | − | 0.729221i | \(-0.739883\pi\) | ||||
−0.684279 | + | 0.729221i | \(0.739883\pi\) | |||||||
\(3\) | −1.34067 | − | 1.09664i | −0.774033 | − | 0.633145i | ||||
\(4\) | 1.74590 | 0.872949 | ||||||||
\(5\) | − | 3.21911i | − | 1.43963i | −0.694166 | − | 0.719815i | \(-0.744227\pi\) | ||
0.694166 | − | 0.719815i | \(-0.255773\pi\) | |||||||
\(6\) | 2.59477 | + | 2.12247i | 1.05931 | + | 0.866495i | ||||
\(7\) | 0.254102 | 0.0960414 | 0.0480207 | − | 0.998846i | \(-0.484709\pi\) | ||||
0.0480207 | + | 0.998846i | \(0.484709\pi\) | |||||||
\(8\) | 0.491797 | 0.173876 | ||||||||
\(9\) | 0.594767 | + | 2.94045i | 0.198256 | + | 0.980150i | ||||
\(10\) | 6.23037i | 1.97022i | ||||||||
\(11\) | −5.68133 | −1.71299 | −0.856493 | − | 0.516159i | \(-0.827361\pi\) | ||||
−0.856493 | + | 0.516159i | \(0.827361\pi\) | |||||||
\(12\) | −2.34067 | − | 1.91462i | −0.675692 | − | 0.552703i | ||||
\(13\) | − | 2.66179i | − | 0.738249i | −0.929380 | − | 0.369124i | \(-0.879658\pi\) | ||
0.929380 | − | 0.369124i | \(-0.120342\pi\) | |||||||
\(14\) | −0.491797 | −0.131438 | ||||||||
\(15\) | −3.53020 | + | 4.31575i | −0.911494 | + | 1.11432i | ||||
\(16\) | −4.44364 | −1.11091 | ||||||||
\(17\) | 4.03709i | 0.979138i | 0.871965 | + | 0.489569i | \(0.162846\pi\) | ||||
−0.871965 | + | 0.489569i | \(0.837154\pi\) | |||||||
\(18\) | −1.15113 | − | 5.69104i | −0.271324 | − | 1.34139i | ||||
\(19\) | −2.44364 | −0.560608 | −0.280304 | − | 0.959911i | \(-0.590435\pi\) | ||||
−0.280304 | + | 0.959911i | \(0.590435\pi\) | |||||||
\(20\) | − | 5.62024i | − | 1.25672i | ||||||
\(21\) | −0.340665 | − | 0.278658i | −0.0743393 | − | 0.0608081i | ||||
\(22\) | 10.9958 | 2.34432 | ||||||||
\(23\) | −3.25410 | −0.678527 | −0.339264 | − | 0.940691i | \(-0.610178\pi\) | ||||
−0.339264 | + | 0.940691i | \(0.610178\pi\) | |||||||
\(24\) | −0.659335 | − | 0.539323i | −0.134586 | − | 0.110089i | ||||
\(25\) | −5.36266 | −1.07253 | ||||||||
\(26\) | 5.15172i | 1.01034i | ||||||||
\(27\) | 2.42723 | − | 4.59441i | 0.467120 | − | 0.884194i | ||||
\(28\) | 0.443636 | 0.0838393 | ||||||||
\(29\) | 3.56857i | 0.662668i | 0.943514 | + | 0.331334i | \(0.107499\pi\) | ||||
−0.943514 | + | 0.331334i | \(0.892501\pi\) | |||||||
\(30\) | 6.83246 | − | 8.35284i | 1.24743 | − | 1.52501i | ||||
\(31\) | 7.81351i | 1.40335i | 0.712498 | + | 0.701674i | \(0.247564\pi\) | ||||
−0.712498 | + | 0.701674i | \(0.752436\pi\) | |||||||
\(32\) | 7.61676 | 1.34647 | ||||||||
\(33\) | 7.61676 | + | 6.23037i | 1.32591 | + | 1.08457i | ||||
\(34\) | − | 7.81351i | − | 1.34001i | ||||||
\(35\) | − | 0.817981i | − | 0.138264i | ||||||
\(36\) | 1.03840 | + | 5.13373i | 0.173067 | + | 0.855621i | ||||
\(37\) | − | 5.15172i | − | 0.846938i | −0.905911 | − | 0.423469i | \(-0.860812\pi\) | ||
0.905911 | − | 0.423469i | \(-0.139188\pi\) | |||||||
\(38\) | 4.72949 | 0.767225 | ||||||||
\(39\) | −2.91903 | + | 3.56857i | −0.467418 | + | 0.571429i | ||||
\(40\) | − | 1.58315i | − | 0.250317i | ||||||
\(41\) | − | 7.25620i | − | 1.13323i | −0.823983 | − | 0.566614i | \(-0.808253\pi\) | ||
0.823983 | − | 0.566614i | \(-0.191747\pi\) | |||||||
\(42\) | 0.659335 | + | 0.539323i | 0.101738 | + | 0.0832194i | ||||
\(43\) | − | 9.79894i | − | 1.49432i | −0.664642 | − | 0.747162i | \(-0.731416\pi\) | ||
0.664642 | − | 0.747162i | \(-0.268584\pi\) | |||||||
\(44\) | −9.91903 | −1.49535 | ||||||||
\(45\) | 9.46563 | − | 1.91462i | 1.41105 | − | 0.285415i | ||||
\(46\) | 6.29809 | 0.928603 | ||||||||
\(47\) | 5.06457 | 0.738743 | 0.369372 | − | 0.929282i | \(-0.379573\pi\) | ||||
0.369372 | + | 0.929282i | \(0.379573\pi\) | |||||||
\(48\) | 5.95743 | + | 4.87306i | 0.859881 | + | 0.703366i | ||||
\(49\) | −6.93543 | −0.990776 | ||||||||
\(50\) | 10.3791 | 1.46782 | ||||||||
\(51\) | 4.42723 | − | 5.41239i | 0.619936 | − | 0.757886i | ||||
\(52\) | − | 4.64722i | − | 0.644454i | ||||||
\(53\) | 1.16745i | 0.160361i | 0.996780 | + | 0.0801805i | \(0.0255497\pi\) | ||||
−0.996780 | + | 0.0801805i | \(0.974450\pi\) | |||||||
\(54\) | −4.69774 | + | 8.89216i | −0.639281 | + | 1.21007i | ||||
\(55\) | 18.2888i | 2.46606i | ||||||||
\(56\) | 0.124966 | 0.0166993 | ||||||||
\(57\) | 3.27610 | + | 2.67979i | 0.433930 | + | 0.354946i | ||||
\(58\) | − | 6.90673i | − | 0.906899i | ||||||
\(59\) | −7.12497 | + | 2.86964i | −0.927592 | + | 0.373596i | ||||
\(60\) | −6.16337 | + | 7.53486i | −0.795688 | + | 0.972746i | ||||
\(61\) | 0.676366i | 0.0865998i | 0.999062 | + | 0.0432999i | \(0.0137871\pi\) | ||||
−0.999062 | + | 0.0432999i | \(0.986213\pi\) | |||||||
\(62\) | − | 15.1225i | − | 1.92056i | ||||||
\(63\) | 0.151131 | + | 0.747174i | 0.0190408 | + | 0.0941350i | ||||
\(64\) | −5.85446 | −0.731807 | ||||||||
\(65\) | −8.56860 | −1.06280 | ||||||||
\(66\) | −14.7417 | − | 12.0585i | −1.81458 | − | 1.48429i | ||||
\(67\) | 2.66179i | 0.325190i | 0.986693 | + | 0.162595i | \(0.0519864\pi\) | ||||
−0.986693 | + | 0.162595i | \(0.948014\pi\) | |||||||
\(68\) | 7.04835i | 0.854738i | ||||||||
\(69\) | 4.36266 | + | 3.56857i | 0.525203 | + | 0.429606i | ||||
\(70\) | 1.58315i | 0.189222i | ||||||||
\(71\) | − | 16.2372i | − | 1.92700i | −0.267715 | − | 0.963498i | \(-0.586269\pi\) | ||
0.267715 | − | 0.963498i | \(-0.413731\pi\) | |||||||
\(72\) | 0.292504 | + | 1.44610i | 0.0344720 | + | 0.170425i | ||||
\(73\) | − | 13.1371i | − | 1.53758i | −0.639501 | − | 0.768791i | \(-0.720859\pi\) | ||
0.639501 | − | 0.768791i | \(-0.279141\pi\) | |||||||
\(74\) | 9.97081i | 1.15908i | ||||||||
\(75\) | 7.18953 | + | 5.88090i | 0.830176 | + | 0.679068i | ||||
\(76\) | −4.26634 | −0.489383 | ||||||||
\(77\) | −1.44364 | −0.164518 | ||||||||
\(78\) | 5.64958 | − | 6.90673i | 0.639689 | − | 0.782034i | ||||
\(79\) | −11.7253 | −1.31920 | −0.659601 | − | 0.751616i | \(-0.729275\pi\) | ||||
−0.659601 | + | 0.751616i | \(0.729275\pi\) | |||||||
\(80\) | 14.3045i | 1.59930i | ||||||||
\(81\) | −8.29250 | + | 3.49777i | −0.921389 | + | 0.388641i | ||||
\(82\) | 14.0439i | 1.55089i | ||||||||
\(83\) | −9.91903 | −1.08875 | −0.544377 | − | 0.838841i | \(-0.683234\pi\) | ||||
−0.544377 | + | 0.838841i | \(0.683234\pi\) | |||||||
\(84\) | −0.594767 | − | 0.486508i | −0.0648944 | − | 0.0530824i | ||||
\(85\) | 12.9958 | 1.40960 | ||||||||
\(86\) | 18.9652i | 2.04507i | ||||||||
\(87\) | 3.91344 | − | 4.78426i | 0.419564 | − | 0.512927i | ||||
\(88\) | −2.79406 | −0.297848 | ||||||||
\(89\) | 7.95184 | 0.842893 | 0.421447 | − | 0.906853i | \(-0.361522\pi\) | ||||
0.421447 | + | 0.906853i | \(0.361522\pi\) | |||||||
\(90\) | −18.3201 | + | 3.70562i | −1.93111 | + | 0.390606i | ||||
\(91\) | − | 0.676366i | − | 0.0709024i | ||||||
\(92\) | −5.68133 | −0.592320 | ||||||||
\(93\) | 8.56860 | − | 10.4753i | 0.888523 | − | 1.08624i | ||||
\(94\) | −9.80213 | −1.01101 | ||||||||
\(95\) | 7.86633i | 0.807068i | ||||||||
\(96\) | −10.2115 | − | 8.35284i | −1.04221 | − | 0.852508i | ||||
\(97\) | − | 4.47535i | − | 0.454403i | −0.973848 | − | 0.227202i | \(-0.927042\pi\) | ||
0.973848 | − | 0.227202i | \(-0.0729577\pi\) | |||||||
\(98\) | 13.4231 | 1.35593 | ||||||||
\(99\) | −3.37907 | − | 16.7057i | −0.339609 | − | 1.67898i | ||||
\(100\) | −9.36266 | −0.936266 | ||||||||
\(101\) | 4.85446 | 0.483037 | 0.241518 | − | 0.970396i | \(-0.422355\pi\) | ||||
0.241518 | + | 0.970396i | \(0.422355\pi\) | |||||||
\(102\) | −8.56860 | + | 10.4753i | −0.848418 | + | 1.03721i | ||||
\(103\) | 12.4607i | 1.22779i | 0.789387 | + | 0.613896i | \(0.210399\pi\) | ||||
−0.789387 | + | 0.613896i | \(0.789601\pi\) | |||||||
\(104\) | − | 1.30906i | − | 0.128364i | ||||||
\(105\) | −0.897030 | + | 1.09664i | −0.0875411 | + | 0.107021i | ||||
\(106\) | − | 2.25951i | − | 0.219463i | ||||||
\(107\) | − | 9.91799i | − | 0.958808i | −0.877594 | − | 0.479404i | \(-0.840853\pi\) | ||
0.877594 | − | 0.479404i | \(-0.159147\pi\) | |||||||
\(108\) | 4.23769 | − | 8.02136i | 0.407772 | − | 0.771856i | ||||
\(109\) | − | 3.33816i | − | 0.319738i | −0.987138 | − | 0.159869i | \(-0.948893\pi\) | ||
0.987138 | − | 0.159869i | \(-0.0511071\pi\) | |||||||
\(110\) | − | 35.3968i | − | 3.37495i | ||||||
\(111\) | −5.64958 | + | 6.90673i | −0.536234 | + | 0.655558i | ||||
\(112\) | −1.12914 | −0.106693 | ||||||||
\(113\) | 4.69774 | 0.441926 | 0.220963 | − | 0.975282i | \(-0.429080\pi\) | ||||
0.220963 | + | 0.975282i | \(0.429080\pi\) | |||||||
\(114\) | −6.34067 | − | 5.18654i | −0.593858 | − | 0.485764i | ||||
\(115\) | 10.4753i | 0.976827i | ||||||||
\(116\) | 6.23037i | 0.578475i | ||||||||
\(117\) | 7.82687 | − | 1.58315i | 0.723595 | − | 0.146362i | ||||
\(118\) | 13.7899 | − | 5.55400i | 1.26946 | − | 0.511287i | ||||
\(119\) | 1.02583i | 0.0940378i | ||||||||
\(120\) | −1.73614 | + | 2.12247i | −0.158487 | + | 0.193754i | ||||
\(121\) | 21.2775 | 1.93432 | ||||||||
\(122\) | − | 1.30906i | − | 0.118517i | ||||||
\(123\) | −7.95743 | + | 9.72813i | −0.717497 | + | 0.877156i | ||||
\(124\) | 13.6416i | 1.22505i | ||||||||
\(125\) | 1.16745i | 0.104420i | ||||||||
\(126\) | −0.292504 | − | 1.44610i | −0.0260584 | − | 0.128829i | ||||
\(127\) | 2.62093 | 0.232570 | 0.116285 | − | 0.993216i | \(-0.462901\pi\) | ||||
0.116285 | + | 0.993216i | \(0.462901\pi\) | |||||||
\(128\) | −3.90262 | −0.344946 | ||||||||
\(129\) | −10.7459 | + | 13.1371i | −0.946124 | + | 1.15666i | ||||
\(130\) | 16.5839 | 1.45451 | ||||||||
\(131\) | 16.8873 | 1.47545 | 0.737724 | − | 0.675103i | \(-0.235901\pi\) | ||||
0.737724 | + | 0.675103i | \(0.235901\pi\) | |||||||
\(132\) | 13.2981 | + | 10.8776i | 1.15745 | + | 0.946772i | ||||
\(133\) | −0.620932 | −0.0538416 | ||||||||
\(134\) | − | 5.15172i | − | 0.445041i | ||||||
\(135\) | −14.7899 | − | 7.81351i | −1.27291 | − | 0.672480i | ||||
\(136\) | 1.98543i | 0.170249i | ||||||||
\(137\) | 0.646115i | 0.0552013i | 0.999619 | + | 0.0276007i | \(0.00878668\pi\) | ||||
−0.999619 | + | 0.0276007i | \(0.991213\pi\) | |||||||
\(138\) | −8.44364 | − | 6.90673i | −0.718770 | − | 0.587940i | ||||
\(139\) | −12.5358 | −1.06327 | −0.531636 | − | 0.846973i | \(-0.678422\pi\) | ||||
−0.531636 | + | 0.846973i | \(0.678422\pi\) | |||||||
\(140\) | − | 1.42811i | − | 0.120697i | ||||||
\(141\) | −6.78989 | − | 5.55400i | −0.571812 | − | 0.467731i | ||||
\(142\) | 31.4259i | 2.63720i | ||||||||
\(143\) | 15.1225i | 1.26461i | ||||||||
\(144\) | −2.64293 | − | 13.0663i | −0.220244 | − | 1.08886i | ||||
\(145\) | 11.4876 | 0.953996 | ||||||||
\(146\) | 25.4260i | 2.10427i | ||||||||
\(147\) | 9.29809 | + | 7.60566i | 0.766894 | + | 0.627305i | ||||
\(148\) | − | 8.99438i | − | 0.739334i | ||||||
\(149\) | 6.45481 | 0.528799 | 0.264399 | − | 0.964413i | \(-0.414826\pi\) | ||||
0.264399 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(150\) | −13.9149 | − | 11.3821i | −1.13614 | − | 0.929344i | ||||
\(151\) | − | 13.1371i | − | 1.06908i | −0.845143 | − | 0.534541i | \(-0.820484\pi\) | ||
0.845143 | − | 0.534541i | \(-0.179516\pi\) | |||||||
\(152\) | −1.20177 | −0.0974766 | ||||||||
\(153\) | −11.8709 | + | 2.40113i | −0.959703 | + | 0.194120i | ||||
\(154\) | 2.79406 | 0.225152 | ||||||||
\(155\) | 25.1526 | 2.02030 | ||||||||
\(156\) | −5.09632 | + | 6.23037i | −0.408032 | + | 0.498829i | ||||
\(157\) | − | 11.1517i | − | 0.890000i | −0.895530 | − | 0.445000i | \(-0.853204\pi\) | ||
0.895530 | − | 0.445000i | \(-0.146796\pi\) | |||||||
\(158\) | 22.6936 | 1.80540 | ||||||||
\(159\) | 1.28027 | − | 1.56515i | 0.101532 | − | 0.124125i | ||||
\(160\) | − | 24.5192i | − | 1.93841i | ||||||
\(161\) | −0.826873 | −0.0651667 | ||||||||
\(162\) | 16.0496 | − | 6.76969i | 1.26097 | − | 0.531877i | ||||
\(163\) | 7.66075 | 0.600037 | 0.300018 | − | 0.953933i | \(-0.403007\pi\) | ||||
0.300018 | + | 0.953933i | \(0.403007\pi\) | |||||||
\(164\) | − | 12.6686i | − | 0.989250i | ||||||
\(165\) | 20.0562 | − | 24.5192i | 1.56138 | − | 1.90882i | ||||
\(166\) | 19.1976 | 1.49002 | ||||||||
\(167\) | 12.5798i | 0.973453i | 0.873554 | + | 0.486726i | \(0.161809\pi\) | ||||
−0.873554 | + | 0.486726i | \(0.838191\pi\) | |||||||
\(168\) | −0.167538 | − | 0.137043i | −0.0129258 | − | 0.0105731i | ||||
\(169\) | 5.91486 | 0.454989 | ||||||||
\(170\) | −25.1526 | −1.92911 | ||||||||
\(171\) | −1.45339 | − | 7.18539i | −0.111144 | − | 0.549481i | ||||
\(172\) | − | 17.1080i | − | 1.30447i | ||||||
\(173\) | −23.1854 | −1.76275 | −0.881375 | − | 0.472417i | \(-0.843382\pi\) | ||||
−0.881375 | + | 0.472417i | \(0.843382\pi\) | |||||||
\(174\) | −7.57419 | + | 9.25962i | −0.574198 | + | 0.701970i | ||||
\(175\) | −1.36266 | −0.103008 | ||||||||
\(176\) | 25.2458 | 1.90297 | ||||||||
\(177\) | 12.6992 | + | 3.96628i | 0.954527 | + | 0.298124i | ||||
\(178\) | −15.3902 | −1.15355 | ||||||||
\(179\) | −14.8269 | −1.10821 | −0.554106 | − | 0.832446i | \(-0.686940\pi\) | ||||
−0.554106 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(180\) | 16.5260 | − | 3.34273i | 1.23178 | − | 0.249152i | ||||
\(181\) | −2.76231 | −0.205321 | −0.102660 | − | 0.994716i | \(-0.532735\pi\) | ||||
−0.102660 | + | 0.994716i | \(0.532735\pi\) | |||||||
\(182\) | 1.30906i | 0.0970341i | ||||||||
\(183\) | 0.741729 | − | 0.906781i | 0.0548302 | − | 0.0670312i | ||||
\(184\) | −1.60036 | −0.117980 | ||||||||
\(185\) | −16.5839 | −1.21928 | ||||||||
\(186\) | −16.5839 | + | 20.2742i | −1.21599 | + | 1.48658i | ||||
\(187\) | − | 22.9360i | − | 1.67725i | ||||||
\(188\) | 8.84222 | 0.644885 | ||||||||
\(189\) | 0.616763 | − | 1.16745i | 0.0448629 | − | 0.0849192i | ||||
\(190\) | − | 15.2247i | − | 1.10452i | ||||||
\(191\) | 4.69774 | 0.339916 | 0.169958 | − | 0.985451i | \(-0.445637\pi\) | ||||
0.169958 | + | 0.985451i | \(0.445637\pi\) | |||||||
\(192\) | 7.84887 | + | 6.42023i | 0.566443 | + | 0.463340i | ||||
\(193\) | −13.5686 | −0.976689 | −0.488345 | − | 0.872651i | \(-0.662399\pi\) | ||||
−0.488345 | + | 0.872651i | \(0.662399\pi\) | |||||||
\(194\) | 8.66175i | 0.621877i | ||||||||
\(195\) | 11.4876 | + | 9.39666i | 0.822646 | + | 0.672909i | ||||
\(196\) | −12.1086 | −0.864897 | ||||||||
\(197\) | − | 4.62466i | − | 0.329493i | −0.986336 | − | 0.164747i | \(-0.947319\pi\) | ||
0.986336 | − | 0.164747i | \(-0.0526806\pi\) | |||||||
\(198\) | 6.53996 | + | 32.3327i | 0.464775 | + | 2.29779i | ||||
\(199\) | 10.2541 | 0.726894 | 0.363447 | − | 0.931615i | \(-0.381600\pi\) | ||||
0.363447 | + | 0.931615i | \(0.381600\pi\) | |||||||
\(200\) | −2.63734 | −0.186488 | ||||||||
\(201\) | 2.91903 | − | 3.56857i | 0.205892 | − | 0.251708i | ||||
\(202\) | −9.39547 | −0.661063 | ||||||||
\(203\) | 0.906781i | 0.0636435i | ||||||||
\(204\) | 7.72949 | − | 9.44948i | 0.541173 | − | 0.661596i | ||||
\(205\) | −23.3585 | −1.63143 | ||||||||
\(206\) | − | 24.1169i | − | 1.68030i | ||||||
\(207\) | −1.93543 | − | 9.56853i | −0.134522 | − | 0.665059i | ||||
\(208\) | 11.8280i | 0.820127i | ||||||||
\(209\) | 13.8831 | 0.960314 | ||||||||
\(210\) | 1.73614 | − | 2.12247i | 0.119805 | − | 0.146464i | ||||
\(211\) | 9.12257i | 0.628024i | 0.949419 | + | 0.314012i | \(0.101673\pi\) | ||||
−0.949419 | + | 0.314012i | \(0.898327\pi\) | |||||||
\(212\) | 2.03824i | 0.139987i | ||||||||
\(213\) | −17.8063 | + | 21.7686i | −1.22007 | + | 1.49156i | ||||
\(214\) | 19.1956i | 1.31218i | ||||||||
\(215\) | −31.5439 | −2.15127 | ||||||||
\(216\) | 1.19370 | − | 2.25951i | 0.0812212 | − | 0.153740i | ||||
\(217\) | 1.98543i | 0.134780i | ||||||||
\(218\) | 6.46078i | 0.437579i | ||||||||
\(219\) | −14.4067 | + | 17.6125i | −0.973511 | + | 1.19014i | ||||
\(220\) | 31.9304i | 2.15275i | ||||||||
\(221\) | 10.7459 | 0.722847 | ||||||||
\(222\) | 10.9344 | − | 13.3675i | 0.733867 | − | 0.897169i | ||||
\(223\) | −11.2663 | −0.754450 | −0.377225 | − | 0.926122i | \(-0.623122\pi\) | ||||
−0.377225 | + | 0.926122i | \(0.623122\pi\) | |||||||
\(224\) | 1.93543 | 0.129317 | ||||||||
\(225\) | −3.18953 | − | 15.7686i | −0.212636 | − | 1.05124i | ||||
\(226\) | −9.09215 | −0.604801 | ||||||||
\(227\) | 1.28692 | 0.0854156 | 0.0427078 | − | 0.999088i | \(-0.486402\pi\) | ||||
0.0427078 | + | 0.999088i | \(0.486402\pi\) | |||||||
\(228\) | 5.71973 | + | 4.67863i | 0.378799 | + | 0.309850i | ||||
\(229\) | 26.9506i | 1.78094i | 0.455038 | + | 0.890472i | \(0.349626\pi\) | ||||
−0.455038 | + | 0.890472i | \(0.650374\pi\) | |||||||
\(230\) | − | 20.2742i | − | 1.33684i | ||||||
\(231\) | 1.93543 | + | 1.58315i | 0.127342 | + | 0.104163i | ||||
\(232\) | 1.75501i | 0.115222i | ||||||||
\(233\) | −5.52461 | −0.361929 | −0.180965 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180965 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(234\) | −15.1484 | + | 3.06407i | −0.990281 | + | 0.200305i | ||||
\(235\) | − | 16.3034i | − | 1.06352i | ||||||
\(236\) | −12.4395 | + | 5.01011i | −0.809740 | + | 0.326130i | ||||
\(237\) | 15.7197 | + | 12.8584i | 1.02111 | + | 0.835246i | ||||
\(238\) | − | 1.98543i | − | 0.128696i | ||||||
\(239\) | − | 14.7428i | − | 0.953633i | −0.879003 | − | 0.476817i | \(-0.841791\pi\) | ||
0.879003 | − | 0.476817i | \(-0.158209\pi\) | |||||||
\(240\) | 15.6869 | − | 19.1776i | 1.01259 | − | 1.23791i | ||||
\(241\) | 0.777652 | 0.0500930 | 0.0250465 | − | 0.999686i | \(-0.492027\pi\) | ||||
0.0250465 | + | 0.999686i | \(0.492027\pi\) | |||||||
\(242\) | −41.1812 | −2.64723 | ||||||||
\(243\) | 14.9533 | + | 4.40455i | 0.959252 | + | 0.282552i | ||||
\(244\) | 1.18087i | 0.0755972i | ||||||||
\(245\) | 22.3259i | 1.42635i | ||||||||
\(246\) | 15.4011 | − | 18.8281i | 0.981936 | − | 1.20044i | ||||
\(247\) | 6.50445i | 0.413868i | ||||||||
\(248\) | 3.84266i | 0.244009i | ||||||||
\(249\) | 13.2981 | + | 10.8776i | 0.842732 | + | 0.689339i | ||||
\(250\) | − | 2.25951i | − | 0.142904i | ||||||
\(251\) | 13.5226i | 0.853536i | 0.904361 | + | 0.426768i | \(0.140348\pi\) | ||||
−0.904361 | + | 0.426768i | \(0.859652\pi\) | |||||||
\(252\) | 0.263860 | + | 1.30449i | 0.0166216 | + | 0.0821751i | ||||
\(253\) | 18.4876 | 1.16231 | ||||||||
\(254\) | −5.07264 | −0.318286 | ||||||||
\(255\) | −17.4231 | − | 14.2517i | −1.09107 | − | 0.892478i | ||||
\(256\) | 19.2622 | 1.20389 | ||||||||
\(257\) | − | 17.1214i | − | 1.06800i | −0.845484 | − | 0.534001i | \(-0.820688\pi\) | ||
0.845484 | − | 0.534001i | \(-0.179312\pi\) | |||||||
\(258\) | 20.7980 | − | 25.4260i | 1.29482 | − | 1.58295i | ||||
\(259\) | − | 1.30906i | − | 0.0813411i | ||||||
\(260\) | −14.9599 | −0.927774 | ||||||||
\(261\) | −10.4932 | + | 2.12247i | −0.649514 | + | 0.131378i | ||||
\(262\) | −32.6842 | −2.01923 | ||||||||
\(263\) | − | 26.3327i | − | 1.62375i | −0.583833 | − | 0.811873i | \(-0.698448\pi\) | ||
0.583833 | − | 0.811873i | \(-0.301552\pi\) | |||||||
\(264\) | 3.74590 | + | 3.06407i | 0.230544 | + | 0.188581i | ||||
\(265\) | 3.75814 | 0.230860 | ||||||||
\(266\) | 1.20177 | 0.0736854 | ||||||||
\(267\) | −10.6608 | − | 8.72029i | −0.652428 | − | 0.533673i | ||||
\(268\) | 4.64722i | 0.283874i | ||||||||
\(269\) | −15.6402 | −0.953599 | −0.476799 | − | 0.879012i | \(-0.658203\pi\) | ||||
−0.476799 | + | 0.879012i | \(0.658203\pi\) | |||||||
\(270\) | 28.6248 | + | 15.1225i | 1.74205 | + | 0.920328i | ||||
\(271\) | 26.2663 | 1.59557 | 0.797783 | − | 0.602944i | \(-0.206006\pi\) | ||||
0.797783 | + | 0.602944i | \(0.206006\pi\) | |||||||
\(272\) | − | 17.9394i | − | 1.08773i | ||||||
\(273\) | −0.741729 | + | 0.906781i | −0.0448915 | + | 0.0548809i | ||||
\(274\) | − | 1.25051i | − | 0.0755462i | ||||||
\(275\) | 30.4671 | 1.83723 | ||||||||
\(276\) | 7.61676 | + | 6.23037i | 0.458475 | + | 0.375024i | ||||
\(277\) | −19.0552 | −1.14491 | −0.572457 | − | 0.819935i | \(-0.694010\pi\) | ||||
−0.572457 | + | 0.819935i | \(0.694010\pi\) | |||||||
\(278\) | 24.2622 | 1.45515 | ||||||||
\(279\) | −22.9753 | + | 4.64722i | −1.37549 | + | 0.278222i | ||||
\(280\) | − | 0.402280i | − | 0.0240408i | ||||||
\(281\) | 13.4338i | 0.801390i | 0.916211 | + | 0.400695i | \(0.131231\pi\) | ||||
−0.916211 | + | 0.400695i | \(0.868769\pi\) | |||||||
\(282\) | 13.1414 | + | 10.7494i | 0.782557 | + | 0.640117i | ||||
\(283\) | − | 18.9652i | − | 1.12736i | −0.825992 | − | 0.563682i | \(-0.809384\pi\) | ||
0.825992 | − | 0.563682i | \(-0.190616\pi\) | |||||||
\(284\) | − | 28.3484i | − | 1.68217i | ||||||
\(285\) | 8.62652 | − | 10.5461i | 0.510991 | − | 0.624698i | ||||
\(286\) | − | 29.2686i | − | 1.73069i | ||||||
\(287\) | − | 1.84381i | − | 0.108837i | ||||||
\(288\) | 4.53020 | + | 22.3967i | 0.266945 | + | 1.31974i | ||||
\(289\) | 0.701906 | 0.0412886 | ||||||||
\(290\) | −22.2335 | −1.30560 | ||||||||
\(291\) | −4.90785 | + | 5.99995i | −0.287703 | + | 0.351723i | ||||
\(292\) | − | 22.9360i | − | 1.34223i | ||||||
\(293\) | 6.40797i | 0.374357i | 0.982326 | + | 0.187179i | \(0.0599343\pi\) | ||||
−0.982326 | + | 0.187179i | \(0.940066\pi\) | |||||||
\(294\) | −17.9958 | − | 14.7202i | −1.04954 | − | 0.858502i | ||||
\(295\) | 9.23769 | + | 22.9360i | 0.537839 | + | 1.33539i | ||||
\(296\) | − | 2.53360i | − | 0.147262i | ||||||
\(297\) | −13.7899 | + | 26.1023i | −0.800171 | + | 1.51461i | ||||
\(298\) | −12.4929 | −0.723692 | ||||||||
\(299\) | 8.66175i | 0.500922i | ||||||||
\(300\) | 12.5522 | + | 10.2675i | 0.724701 | + | 0.592792i | ||||
\(301\) | − | 2.48993i | − | 0.143517i | ||||||
\(302\) | 25.4260i | 1.46310i | ||||||||
\(303\) | −6.50820 | − | 5.32359i | −0.373887 | − | 0.305832i | ||||
\(304\) | 10.8586 | 0.622785 | ||||||||
\(305\) | 2.17730 | 0.124672 | ||||||||
\(306\) | 22.9753 | − | 4.64722i | 1.31341 | − | 0.265664i | ||||
\(307\) | 13.9149 | 0.794163 | 0.397081 | − | 0.917783i | \(-0.370023\pi\) | ||||
0.397081 | + | 0.917783i | \(0.370023\pi\) | |||||||
\(308\) | −2.52044 | −0.143615 | ||||||||
\(309\) | 13.6649 | − | 16.7057i | 0.777370 | − | 0.950353i | ||||
\(310\) | −48.6811 | −2.76490 | ||||||||
\(311\) | − | 1.60571i | − | 0.0910515i | −0.998963 | − | 0.0455258i | \(-0.985504\pi\) | ||
0.998963 | − | 0.0455258i | \(-0.0144963\pi\) | |||||||
\(312\) | −1.43557 | + | 1.75501i | −0.0812730 | + | 0.0993580i | ||||
\(313\) | 26.1023i | 1.47539i | 0.675133 | + | 0.737696i | \(0.264086\pi\) | ||||
−0.675133 | + | 0.737696i | \(0.735914\pi\) | |||||||
\(314\) | 21.5833i | 1.21802i | ||||||||
\(315\) | 2.40523 | − | 0.486508i | 0.135520 | − | 0.0274116i | ||||
\(316\) | −20.4712 | −1.15160 | ||||||||
\(317\) | − | 9.27761i | − | 0.521083i | −0.965463 | − | 0.260541i | \(-0.916099\pi\) | ||
0.965463 | − | 0.260541i | \(-0.0839010\pi\) | |||||||
\(318\) | −2.47787 | + | 3.02925i | −0.138952 | + | 0.169872i | ||||
\(319\) | − | 20.2742i | − | 1.13514i | ||||||
\(320\) | 18.8461i | 1.05353i | ||||||||
\(321\) | −10.8765 | + | 13.2967i | −0.607064 | + | 0.742150i | ||||
\(322\) | 1.60036 | 0.0891844 | ||||||||
\(323\) | − | 9.86518i | − | 0.548913i | ||||||
\(324\) | −14.4779 | + | 6.10674i | −0.804326 | + | 0.339264i | ||||
\(325\) | 14.2743i | 0.791795i | ||||||||
\(326\) | −14.8269 | −0.821185 | ||||||||
\(327\) | −3.66075 | + | 4.47535i | −0.202440 | + | 0.247488i | ||||
\(328\) | − | 3.56857i | − | 0.197042i | ||||||
\(329\) | 1.28692 | 0.0709499 | ||||||||
\(330\) | −38.8175 | + | 47.4552i | −2.13683 | + | 2.61232i | ||||
\(331\) | 25.0932 | 1.37925 | 0.689624 | − | 0.724168i | \(-0.257776\pi\) | ||||
0.689624 | + | 0.724168i | \(0.257776\pi\) | |||||||
\(332\) | −17.3176 | −0.950427 | ||||||||
\(333\) | 15.1484 | − | 3.06407i | 0.830126 | − | 0.167910i | ||||
\(334\) | − | 24.3473i | − | 1.33223i | ||||||
\(335\) | 8.56860 | 0.468153 | ||||||||
\(336\) | 1.51379 | + | 1.23825i | 0.0825842 | + | 0.0675523i | ||||
\(337\) | 20.7787i | 1.13189i | 0.824443 | + | 0.565945i | \(0.191489\pi\) | ||||
−0.824443 | + | 0.565945i | \(0.808511\pi\) | |||||||
\(338\) | −11.4478 | −0.622678 | ||||||||
\(339\) | −6.29809 | − | 5.15172i | −0.342065 | − | 0.279803i | ||||
\(340\) | 22.6894 | 1.23051 | ||||||||
\(341\) | − | 44.3912i | − | 2.40392i | ||||||
\(342\) | 2.81295 | + | 13.9068i | 0.152107 | + | 0.751996i | ||||
\(343\) | −3.54102 | −0.191197 | ||||||||
\(344\) | − | 4.81909i | − | 0.259828i | ||||||
\(345\) | 11.4876 | − | 14.0439i | 0.618473 | − | 0.756097i | ||||
\(346\) | 44.8737 | 2.41243 | ||||||||
\(347\) | 1.75708 | 0.0943248 | 0.0471624 | − | 0.998887i | \(-0.484982\pi\) | ||||
0.0471624 | + | 0.998887i | \(0.484982\pi\) | |||||||
\(348\) | 6.83246 | − | 8.35284i | 0.366258 | − | 0.447759i | ||||
\(349\) | 9.79894i | 0.524525i | 0.964997 | + | 0.262263i | \(0.0844687\pi\) | ||||
−0.964997 | + | 0.262263i | \(0.915531\pi\) | |||||||
\(350\) | 2.63734 | 0.140972 | ||||||||
\(351\) | −12.2294 | − | 6.46078i | −0.652755 | − | 0.344851i | ||||
\(352\) | −43.2733 | −2.30648 | ||||||||
\(353\) | 27.2130 | 1.44840 | 0.724200 | − | 0.689590i | \(-0.242209\pi\) | ||||
0.724200 | + | 0.689590i | \(0.242209\pi\) | |||||||
\(354\) | −24.5784 | − | 7.67647i | −1.30633 | − | 0.408000i | ||||
\(355\) | −52.2692 | −2.77416 | ||||||||
\(356\) | 13.8831 | 0.735803 | ||||||||
\(357\) | 1.12497 | − | 1.37530i | 0.0595395 | − | 0.0727884i | ||||
\(358\) | 28.6964 | 1.51665 | ||||||||
\(359\) | 4.24494i | 0.224039i | 0.993706 | + | 0.112020i | \(0.0357320\pi\) | ||||
−0.993706 | + | 0.112020i | \(0.964268\pi\) | |||||||
\(360\) | 4.65517 | − | 0.941604i | 0.245349 | − | 0.0496269i | ||||
\(361\) | −13.0286 | −0.685718 | ||||||||
\(362\) | 5.34625 | 0.280993 | ||||||||
\(363\) | −28.5260 | − | 23.3338i | −1.49723 | − | 1.22470i | ||||
\(364\) | − | 1.18087i | − | 0.0618942i | ||||||
\(365\) | −42.2898 | −2.21355 | ||||||||
\(366\) | −1.43557 | + | 1.75501i | −0.0750383 | + | 0.0917360i | ||||
\(367\) | − | 23.6124i | − | 1.23256i | −0.787528 | − | 0.616279i | \(-0.788639\pi\) | ||
0.787528 | − | 0.616279i | \(-0.211361\pi\) | |||||||
\(368\) | 14.4600 | 0.753782 | ||||||||
\(369\) | 21.3365 | − | 4.31575i | 1.11073 | − | 0.224669i | ||||
\(370\) | 32.0971 | 1.66865 | ||||||||
\(371\) | 0.296650i | 0.0154013i | ||||||||
\(372\) | 14.9599 | − | 18.2888i | 0.775635 | − | 0.948231i | ||||
\(373\) | 21.5040 | 1.11344 | 0.556718 | − | 0.830701i | \(-0.312060\pi\) | ||||
0.556718 | + | 0.830701i | \(0.312060\pi\) | |||||||
\(374\) | 44.3912i | 2.29541i | ||||||||
\(375\) | 1.28027 | − | 1.56515i | 0.0661127 | − | 0.0808242i | ||||
\(376\) | 2.49074 | 0.128450 | ||||||||
\(377\) | 9.49881 | 0.489213 | ||||||||
\(378\) | −1.19370 | + | 2.25951i | −0.0613975 | + | 0.116217i | ||||
\(379\) | 14.9588 | 0.768384 | 0.384192 | − | 0.923253i | \(-0.374480\pi\) | ||||
0.384192 | + | 0.923253i | \(0.374480\pi\) | |||||||
\(380\) | 13.7338i | 0.704530i | ||||||||
\(381\) | −3.51379 | − | 2.87422i | −0.180017 | − | 0.147251i | ||||
\(382\) | −9.09215 | −0.465195 | ||||||||
\(383\) | − | 9.38324i | − | 0.479461i | −0.970839 | − | 0.239731i | \(-0.922941\pi\) | ||
0.970839 | − | 0.239731i | \(-0.0770591\pi\) | |||||||
\(384\) | 5.23211 | + | 4.27976i | 0.267000 | + | 0.218401i | ||||
\(385\) | 4.64722i | 0.236844i | ||||||||
\(386\) | 26.2611 | 1.33666 | ||||||||
\(387\) | 28.8133 | − | 5.82809i | 1.46466 | − | 0.296258i | ||||
\(388\) | − | 7.81351i | − | 0.396671i | ||||||
\(389\) | 1.39786i | 0.0708743i | 0.999372 | + | 0.0354372i | \(0.0112824\pi\) | ||||
−0.999372 | + | 0.0354372i | \(0.988718\pi\) | |||||||
\(390\) | −22.2335 | − | 18.1866i | −1.12584 | − | 0.920914i | ||||
\(391\) | − | 13.1371i | − | 0.664372i | ||||||
\(392\) | −3.41082 | −0.172273 | ||||||||
\(393\) | −22.6402 | − | 18.5192i | −1.14205 | − | 0.934172i | ||||
\(394\) | 8.95071i | 0.450930i | ||||||||
\(395\) | 37.7451i | 1.89916i | ||||||||
\(396\) | −5.89951 | − | 29.1664i | −0.296461 | − | 1.46567i | ||||
\(397\) | − | 12.9652i | − | 0.650706i | −0.945593 | − | 0.325353i | \(-0.894517\pi\) | ||
0.945593 | − | 0.325353i | \(-0.105483\pi\) | |||||||
\(398\) | −19.8461 | −0.994796 | ||||||||
\(399\) | 0.832462 | + | 0.680938i | 0.0416752 | + | 0.0340895i | ||||
\(400\) | 23.8297 | 1.19149 | ||||||||
\(401\) | −19.9711 | −0.997308 | −0.498654 | − | 0.866801i | \(-0.666172\pi\) | ||||
−0.498654 | + | 0.866801i | \(0.666172\pi\) | |||||||
\(402\) | −5.64958 | + | 6.90673i | −0.281775 | + | 0.344477i | ||||
\(403\) | 20.7980 | 1.03602 | ||||||||
\(404\) | 8.47539 | 0.421666 | ||||||||
\(405\) | 11.2597 | + | 26.6945i | 0.559499 | + | 1.32646i | ||||
\(406\) | − | 1.75501i | − | 0.0870998i | ||||||
\(407\) | 29.2686i | 1.45079i | ||||||||
\(408\) | 2.17730 | − | 2.66179i | 0.107792 | − | 0.131778i | ||||
\(409\) | − | 11.1080i | − | 0.549255i | −0.961551 | − | 0.274628i | \(-0.911445\pi\) | ||
0.961551 | − | 0.274628i | \(-0.0885546\pi\) | |||||||
\(410\) | 45.2088 | 2.23270 | ||||||||
\(411\) | 0.708555 | − | 0.866224i | 0.0349504 | − | 0.0427277i | ||||
\(412\) | 21.7552i | 1.07180i | ||||||||
\(413\) | −1.81047 | + | 0.729181i | −0.0890872 | + | 0.0358807i | ||||
\(414\) | 3.74590 | + | 18.5192i | 0.184101 | + | 0.910171i | ||||
\(415\) | 31.9304i | 1.56740i | ||||||||
\(416\) | − | 20.2742i | − | 0.994027i | ||||||
\(417\) | 16.8063 | + | 13.7472i | 0.823008 | + | 0.673205i | ||||
\(418\) | −26.8698 | −1.31425 | ||||||||
\(419\) | 7.91202 | 0.386527 | 0.193264 | − | 0.981147i | \(-0.438093\pi\) | ||||
0.193264 | + | 0.981147i | \(0.438093\pi\) | |||||||
\(420\) | −1.56612 | + | 1.91462i | −0.0764190 | + | 0.0934239i | ||||
\(421\) | 29.3968i | 1.43271i | 0.697734 | + | 0.716357i | \(0.254192\pi\) | ||||
−0.697734 | + | 0.716357i | \(0.745808\pi\) | |||||||
\(422\) | − | 17.6561i | − | 0.859487i | ||||||
\(423\) | 3.01224 | + | 14.8921i | 0.146460 | + | 0.724079i | ||||
\(424\) | 0.574146i | 0.0278830i | ||||||||
\(425\) | − | 21.6495i | − | 1.05016i | ||||||
\(426\) | 34.4629 | − | 42.1316i | 1.66973 | − | 2.04128i | ||||
\(427\) | 0.171866i | 0.00831717i | ||||||||
\(428\) | − | 17.3158i | − | 0.836991i | ||||||
\(429\) | 16.5839 | − | 20.2742i | 0.800681 | − | 0.978850i | ||||
\(430\) | 61.0510 | 2.94414 | ||||||||
\(431\) | −23.4988 | −1.13190 | −0.565949 | − | 0.824440i | \(-0.691490\pi\) | ||||
−0.565949 | + | 0.824440i | \(0.691490\pi\) | |||||||
\(432\) | −10.7857 | + | 20.4159i | −0.518928 | + | 0.982259i | ||||
\(433\) | −5.16896 | −0.248404 | −0.124202 | − | 0.992257i | \(-0.539637\pi\) | ||||
−0.124202 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(434\) | − | 3.84266i | − | 0.184454i | ||||||
\(435\) | −15.4011 | − | 12.5978i | −0.738424 | − | 0.604017i | ||||
\(436\) | − | 5.82809i | − | 0.279115i | ||||||
\(437\) | 7.95184 | 0.380388 | ||||||||
\(438\) | 27.8831 | − | 34.0877i | 1.33231 | − | 1.62877i | ||||
\(439\) | −22.6084 | −1.07904 | −0.539521 | − | 0.841972i | \(-0.681395\pi\) | ||||
−0.539521 | + | 0.841972i | \(0.681395\pi\) | |||||||
\(440\) | 8.99438i | 0.428790i | ||||||||
\(441\) | −4.12497 | − | 20.3933i | −0.196427 | − | 0.971109i | ||||
\(442\) | −20.7980 | −0.989258 | ||||||||
\(443\) | 29.1166 | 1.38337 | 0.691686 | − | 0.722198i | \(-0.256868\pi\) | ||||
0.691686 | + | 0.722198i | \(0.256868\pi\) | |||||||
\(444\) | −9.86359 | + | 12.0585i | −0.468105 | + | 0.572269i | ||||
\(445\) | − | 25.5978i | − | 1.21345i | ||||||
\(446\) | 21.8052 | 1.03251 | ||||||||
\(447\) | −8.65375 | − | 7.07860i | −0.409308 | − | 0.334806i | ||||
\(448\) | −1.48763 | −0.0702838 | ||||||||
\(449\) | − | 20.0664i | − | 0.946992i | −0.880796 | − | 0.473496i | \(-0.842992\pi\) | ||
0.880796 | − | 0.473496i | \(-0.157008\pi\) | |||||||
\(450\) | 6.17313 | + | 30.5191i | 0.291004 | + | 1.43869i | ||||
\(451\) | 41.2249i | 1.94120i | ||||||||
\(452\) | 8.20177 | 0.385779 | ||||||||
\(453\) | −14.4067 | + | 17.6125i | −0.676884 | + | 0.827505i | ||||
\(454\) | −2.49074 | −0.116896 | ||||||||
\(455\) | −2.17730 | −0.102073 | ||||||||
\(456\) | 1.61117 | + | 1.31791i | 0.0754501 | + | 0.0617168i | ||||
\(457\) | − | 41.2249i | − | 1.92842i | −0.265144 | − | 0.964209i | \(-0.585419\pi\) | ||
0.265144 | − | 0.964209i | \(-0.414581\pi\) | |||||||
\(458\) | − | 52.1610i | − | 2.43732i | ||||||
\(459\) | 18.5480 | + | 9.79894i | 0.865748 | + | 0.457375i | ||||
\(460\) | 18.2888i | 0.852721i | ||||||||
\(461\) | − | 15.7384i | − | 0.733010i | −0.930416 | − | 0.366505i | \(-0.880554\pi\) | ||
0.930416 | − | 0.366505i | \(-0.119446\pi\) | |||||||
\(462\) | −3.74590 | − | 3.06407i | −0.174275 | − | 0.142554i | ||||
\(463\) | 15.7989i | 0.734237i | 0.930174 | + | 0.367118i | \(0.119656\pi\) | ||||
−0.930174 | + | 0.367118i | \(0.880344\pi\) | |||||||
\(464\) | − | 15.8574i | − | 0.736163i | ||||||
\(465\) | −33.7212 | − | 27.5833i | −1.56378 | − | 1.27914i | ||||
\(466\) | 10.6925 | 0.495321 | ||||||||
\(467\) | 16.2171 | 0.750439 | 0.375219 | − | 0.926936i | \(-0.377567\pi\) | ||||
0.375219 | + | 0.926936i | \(0.377567\pi\) | |||||||
\(468\) | 13.6649 | − | 2.76401i | 0.631661 | − | 0.127767i | ||||
\(469\) | 0.676366i | 0.0312317i | ||||||||
\(470\) | 31.5541i | 1.45548i | ||||||||
\(471\) | −12.2294 | + | 14.9507i | −0.563499 | + | 0.688890i | ||||
\(472\) | −3.50403 | + | 1.41128i | −0.161286 | + | 0.0649595i | ||||
\(473\) | 55.6710i | 2.55976i | ||||||||
\(474\) | −30.4245 | − | 24.8866i | −1.39744 | − | 1.14308i | ||||
\(475\) | 13.1044 | 0.601271 | ||||||||
\(476\) | 1.79100i | 0.0820902i | ||||||||
\(477\) | −3.43282 | + | 0.694358i | −0.157178 | + | 0.0317925i | ||||
\(478\) | 28.5337i | 1.30510i | ||||||||
\(479\) | − | 6.37198i | − | 0.291143i | −0.989348 | − | 0.145572i | \(-0.953498\pi\) | ||
0.989348 | − | 0.145572i | \(-0.0465021\pi\) | |||||||
\(480\) | −26.8887 | + | 32.8720i | −1.22730 | + | 1.50040i | ||||
\(481\) | −13.7128 | −0.625251 | ||||||||
\(482\) | −1.50509 | −0.0685551 | ||||||||
\(483\) | 1.10856 | + | 0.906781i | 0.0504412 | + | 0.0412599i | ||||
\(484\) | 37.1484 | 1.68856 | ||||||||
\(485\) | −14.4067 | −0.654172 | ||||||||
\(486\) | −28.9410 | − | 8.52470i | −1.31279 | − | 0.386688i | ||||
\(487\) | 29.6688 | 1.34442 | 0.672211 | − | 0.740359i | \(-0.265345\pi\) | ||||
0.672211 | + | 0.740359i | \(0.265345\pi\) | |||||||
\(488\) | 0.332635i | 0.0150577i | ||||||||
\(489\) | −10.2705 | − | 8.40108i | −0.464448 | − | 0.379910i | ||||
\(490\) | − | 43.2103i | − | 1.95204i | ||||||
\(491\) | 28.7281i | 1.29648i | 0.761435 | + | 0.648241i | \(0.224495\pi\) | ||||
−0.761435 | + | 0.648241i | \(0.775505\pi\) | |||||||
\(492\) | −13.8929 | + | 16.9843i | −0.626339 | + | 0.765713i | ||||
\(493\) | −14.4067 | −0.648843 | ||||||||
\(494\) | − | 12.5889i | − | 0.566403i | ||||||
\(495\) | −53.7774 | + | 10.8776i | −2.41711 | + | 0.488911i | ||||
\(496\) | − | 34.7204i | − | 1.55899i | ||||||
\(497\) | − | 4.12589i | − | 0.185071i | ||||||
\(498\) | −25.7376 | − | 21.0528i | −1.15333 | − | 0.943400i | ||||
\(499\) | −23.0328 | −1.03109 | −0.515545 | − | 0.856862i | \(-0.672411\pi\) | ||||
−0.515545 | + | 0.856862i | \(0.672411\pi\) | |||||||
\(500\) | 2.03824i | 0.0911530i | ||||||||
\(501\) | 13.7955 | − | 16.8653i | 0.616337 | − | 0.753485i | ||||
\(502\) | − | 26.1720i | − | 1.16811i | ||||||
\(503\) | 22.4517 | 1.00107 | 0.500536 | − | 0.865716i | \(-0.333136\pi\) | ||||
0.500536 | + | 0.865716i | \(0.333136\pi\) | |||||||
\(504\) | 0.0743259 | + | 0.367457i | 0.00331074 | + | 0.0163679i | ||||
\(505\) | − | 15.6270i | − | 0.695394i | ||||||
\(506\) | −35.7816 | −1.59068 | ||||||||
\(507\) | −7.92984 | − | 6.48646i | −0.352177 | − | 0.288074i | ||||
\(508\) | 4.57588 | 0.203022 | ||||||||
\(509\) | −3.16089 | −0.140104 | −0.0700520 | − | 0.997543i | \(-0.522317\pi\) | ||||
−0.0700520 | + | 0.997543i | \(0.522317\pi\) | |||||||
\(510\) | 33.7212 | + | 27.5833i | 1.49320 | + | 1.22141i | ||||
\(511\) | − | 3.33816i | − | 0.147671i | ||||||
\(512\) | −29.4754 | −1.30264 | ||||||||
\(513\) | −5.93126 | + | 11.2271i | −0.261872 | + | 0.495686i | ||||
\(514\) | 33.1373i | 1.46162i | ||||||||
\(515\) | 40.1125 | 1.76757 | ||||||||
\(516\) | −18.7612 | + | 22.9360i | −0.825918 | + | 1.00970i | ||||
\(517\) | −28.7735 | −1.26546 | ||||||||
\(518\) | 2.53360i | 0.111320i | ||||||||
\(519\) | 31.0838 | + | 25.4260i | 1.36443 | + | 1.11608i | ||||
\(520\) | −4.21401 | −0.184797 | ||||||||
\(521\) | 16.5415i | 0.724696i | 0.932043 | + | 0.362348i | \(0.118025\pi\) | ||||
−0.932043 | + | 0.362348i | \(0.881975\pi\) | |||||||
\(522\) | 20.3089 | − | 4.10790i | 0.888897 | − | 0.179798i | ||||
\(523\) | −28.0716 | −1.22748 | −0.613742 | − | 0.789507i | \(-0.710337\pi\) | ||||
−0.613742 | + | 0.789507i | \(0.710337\pi\) | |||||||
\(524\) | 29.4835 | 1.28799 | ||||||||
\(525\) | 1.82687 | + | 1.49435i | 0.0797313 | + | 0.0652187i | ||||
\(526\) | 50.9653i | 2.22219i | ||||||||
\(527\) | −31.5439 | −1.37407 | ||||||||
\(528\) | −33.8461 | − | 27.6855i | −1.47296 | − | 1.20486i | ||||
\(529\) | −12.4108 | −0.539601 | ||||||||
\(530\) | −7.27362 | −0.315946 | ||||||||
\(531\) | −12.6757 | − | 19.2438i | −0.550080 | − | 0.835112i | ||||
\(532\) | −1.08408 | −0.0470010 | ||||||||
\(533\) | −19.3145 | −0.836604 | ||||||||
\(534\) | 20.6332 | + | 16.8775i | 0.892885 | + | 0.730363i | ||||
\(535\) | −31.9271 | −1.38033 | ||||||||
\(536\) | 1.30906i | 0.0565428i | ||||||||
\(537\) | 19.8779 | + | 16.2597i | 0.857794 | + | 0.701659i | ||||
\(538\) | 30.2705 | 1.30505 | ||||||||
\(539\) | 39.4025 | 1.69719 | ||||||||
\(540\) | −25.8216 | − | 13.6416i | −1.11119 | − | 0.587041i | ||||
\(541\) | 12.9652i | 0.557419i | 0.960375 | + | 0.278709i | \(0.0899067\pi\) | ||||
−0.960375 | + | 0.278709i | \(0.910093\pi\) | |||||||
\(542\) | −50.8367 | −2.18362 | ||||||||
\(543\) | 3.70333 | + | 3.02925i | 0.158925 | + | 0.129998i | ||||
\(544\) | 30.7496i | 1.31838i | ||||||||
\(545\) | −10.7459 | −0.460304 | ||||||||
\(546\) | 1.43557 | − | 1.75501i | 0.0614366 | − | 0.0751076i | ||||
\(547\) | 5.30927 | 0.227008 | 0.113504 | − | 0.993538i | \(-0.463793\pi\) | ||||
0.113504 | + | 0.993538i | \(0.463793\pi\) | |||||||
\(548\) | 1.12805i | 0.0481880i | ||||||||
\(549\) | −1.98882 | + | 0.402280i | −0.0848808 | + | 0.0171689i | ||||
\(550\) | −58.9669 | −2.51436 | ||||||||
\(551\) | − | 8.72029i | − | 0.371497i | ||||||
\(552\) | 2.14554 | + | 1.75501i | 0.0913203 | + | 0.0746983i | ||||
\(553\) | −2.97942 | −0.126698 | ||||||||
\(554\) | 36.8800 | 1.56688 | ||||||||
\(555\) | 22.2335 | + | 18.1866i | 0.943761 | + | 0.771978i | ||||
\(556\) | −21.8862 | −0.928182 | ||||||||
\(557\) | 39.0541i | 1.65478i | 0.561630 | + | 0.827389i | \(0.310175\pi\) | ||||
−0.561630 | + | 0.827389i | \(0.689825\pi\) | |||||||
\(558\) | 44.4671 | − | 8.99438i | 1.88244 | − | 0.380762i | ||||
\(559\) | −26.0828 | −1.10318 | ||||||||
\(560\) | 3.63481i | 0.153599i | ||||||||
\(561\) | −25.1526 | + | 30.7496i | −1.06194 | + | 1.29825i | ||||
\(562\) | − | 26.0001i | − | 1.09675i | ||||||
\(563\) | 5.26111 | 0.221729 | 0.110865 | − | 0.993836i | \(-0.464638\pi\) | ||||
0.110865 | + | 0.993836i | \(0.464638\pi\) | |||||||
\(564\) | −11.8545 | − | 9.69672i | −0.499163 | − | 0.408306i | ||||
\(565\) | − | 15.1225i | − | 0.636210i | ||||||
\(566\) | 36.7058i | 1.54286i | ||||||||
\(567\) | −2.10714 | + | 0.888788i | −0.0884915 | + | 0.0373256i | ||||
\(568\) | − | 7.98538i | − | 0.335059i | ||||||
\(569\) | −9.43530 | −0.395548 | −0.197774 | − | 0.980248i | \(-0.563371\pi\) | ||||
−0.197774 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(570\) | −16.6960 | + | 20.4113i | −0.699320 | + | 0.854935i | ||||
\(571\) | − | 24.0732i | − | 1.00743i | −0.863869 | − | 0.503717i | \(-0.831966\pi\) | ||
0.863869 | − | 0.503717i | \(-0.168034\pi\) | |||||||
\(572\) | 26.4024i | 1.10394i | ||||||||
\(573\) | −6.29809 | − | 5.15172i | −0.263107 | − | 0.215216i | ||||
\(574\) | 3.56857i | 0.148949i | ||||||||
\(575\) | 17.4506 | 0.727742 | ||||||||
\(576\) | −3.48204 | − | 17.2147i | −0.145085 | − | 0.717281i | ||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | −1.35849 | −0.0565058 | ||||||||
\(579\) | 18.1910 | + | 14.8799i | 0.755990 | + | 0.618386i | ||||
\(580\) | 20.0562 | 0.832790 | ||||||||
\(581\) | −2.52044 | −0.104566 | ||||||||
\(582\) | 9.49881 | − | 11.6125i | 0.393738 | − | 0.481354i | ||||
\(583\) | − | 6.63265i | − | 0.274696i | ||||||
\(584\) | − | 6.46078i | − | 0.267349i | ||||||
\(585\) | −5.09632 | − | 25.1956i | −0.210707 | − | 1.04171i | ||||
\(586\) | − | 12.4022i | − | 0.512330i | ||||||
\(587\) | 25.2856 | 1.04365 | 0.521824 | − | 0.853053i | \(-0.325252\pi\) | ||||
0.521824 | + | 0.853053i | \(0.325252\pi\) | |||||||
\(588\) | 16.2335 | + | 13.2787i | 0.669459 | + | 0.547605i | ||||
\(589\) | − | 19.0934i | − | 0.786729i | ||||||
\(590\) | −17.8789 | − | 44.3912i | −0.736064 | − | 1.82755i | ||||
\(591\) | −5.07158 | + | 6.20012i | −0.208617 | + | 0.255039i | ||||
\(592\) | 22.8924i | 0.940871i | ||||||||
\(593\) | 40.9056i | 1.67979i | 0.542746 | + | 0.839897i | \(0.317385\pi\) | ||||
−0.542746 | + | 0.839897i | \(0.682615\pi\) | |||||||
\(594\) | 26.6894 | − | 50.5193i | 1.09508 | − | 2.07283i | ||||
\(595\) | 3.30226 | 0.135380 | ||||||||
\(596\) | 11.2694 | 0.461615 | ||||||||
\(597\) | −13.7473 | − | 11.2450i | −0.562640 | − | 0.460229i | ||||
\(598\) | − | 16.7642i | − | 0.685540i | ||||||
\(599\) | − | 5.46520i | − | 0.223302i | −0.993747 | − | 0.111651i | \(-0.964386\pi\) | ||
0.993747 | − | 0.111651i | \(-0.0356139\pi\) | |||||||
\(600\) | 3.53579 | + | 2.89221i | 0.144348 | + | 0.118074i | ||||
\(601\) | 13.6416i | 0.556453i | 0.960516 | + | 0.278226i | \(0.0897465\pi\) | ||||
−0.960516 | + | 0.278226i | \(0.910253\pi\) | |||||||
\(602\) | 4.81909i | 0.196411i | ||||||||
\(603\) | −7.82687 | + | 1.58315i | −0.318735 | + | 0.0644707i | ||||
\(604\) | − | 22.9360i | − | 0.933254i | ||||||
\(605\) | − | 68.4946i | − | 2.78470i | ||||||
\(606\) | 12.5962 | + | 10.3034i | 0.511685 | + | 0.418549i | ||||
\(607\) | 13.7581 | 0.558426 | 0.279213 | − | 0.960229i | \(-0.409927\pi\) | ||||
0.279213 | + | 0.960229i | \(0.409927\pi\) | |||||||
\(608\) | −18.6126 | −0.754840 | ||||||||
\(609\) | 0.994411 | − | 1.21569i | 0.0402956 | − | 0.0492622i | ||||
\(610\) | −4.21401 | −0.170620 | ||||||||
\(611\) | − | 13.4808i | − | 0.545376i | ||||||
\(612\) | −20.7253 | + | 4.19212i | −0.837772 | + | 0.169457i | ||||
\(613\) | 13.8135i | 0.557921i | 0.960303 | + | 0.278960i | \(0.0899898\pi\) | ||||
−0.960303 | + | 0.278960i | \(0.910010\pi\) | |||||||
\(614\) | −26.9313 | −1.08686 | ||||||||
\(615\) | 31.3159 | + | 25.6158i | 1.26278 | + | 1.03293i | ||||
\(616\) | −0.709975 | −0.0286057 | ||||||||
\(617\) | − | 31.3899i | − | 1.26371i | −0.775086 | − | 0.631856i | \(-0.782294\pi\) | ||
0.775086 | − | 0.631856i | \(-0.217706\pi\) | |||||||
\(618\) | −26.4475 | + | 32.3327i | −1.06388 | + | 1.30061i | ||||
\(619\) | 26.4835 | 1.06446 | 0.532230 | − | 0.846600i | \(-0.321354\pi\) | ||||
0.532230 | + | 0.846600i | \(0.321354\pi\) | |||||||
\(620\) | 43.9138 | 1.76362 | ||||||||
\(621\) | −7.89845 | + | 14.9507i | −0.316954 | + | 0.599949i | ||||
\(622\) | 3.10774i | 0.124609i | ||||||||
\(623\) | 2.02058 | 0.0809527 | ||||||||
\(624\) | 12.9711 | − | 15.8574i | 0.519259 | − | 0.634806i | ||||
\(625\) | −23.0552 | −0.922207 | ||||||||
\(626\) | − | 50.5193i | − | 2.01916i | ||||||
\(627\) | −18.6126 | − | 15.2247i | −0.743315 | − | 0.608018i | ||||
\(628\) | − | 19.4697i | − | 0.776925i | ||||||
\(629\) | 20.7980 | 0.829269 | ||||||||
\(630\) | −4.65517 | + | 0.941604i | −0.185466 | + | 0.0375144i | ||||
\(631\) | −18.4723 | −0.735370 | −0.367685 | − | 0.929950i | \(-0.619850\pi\) | ||||
−0.367685 | + | 0.929950i | \(0.619850\pi\) | |||||||
\(632\) | −5.76647 | −0.229378 | ||||||||
\(633\) | 10.0042 | − | 12.2303i | 0.397630 | − | 0.486112i | ||||
\(634\) | 17.9562i | 0.713131i | ||||||||
\(635\) | − | 8.43707i | − | 0.334815i | ||||||
\(636\) | 2.23522 | − | 2.73260i | 0.0886321 | − | 0.108355i | ||||
\(637\) | 18.4607i | 0.731439i | ||||||||
\(638\) | 39.2394i | 1.55350i | ||||||||
\(639\) | 47.7446 | − | 9.65733i | 1.88875 | − | 0.382038i | ||||
\(640\) | 12.5630i | 0.496594i | ||||||||
\(641\) | 33.8439i | 1.33675i | 0.743823 | + | 0.668376i | \(0.233010\pi\) | ||||
−0.743823 | + | 0.668376i | \(0.766990\pi\) | |||||||
\(642\) | 21.0506 | − | 25.7349i | 0.830803 | − | 1.01567i | ||||
\(643\) | 10.2405 | 0.403847 | 0.201924 | − | 0.979401i | \(-0.435281\pi\) | ||||
0.201924 | + | 0.979401i | \(0.435281\pi\) | |||||||
\(644\) | −1.44364 | −0.0568872 | ||||||||
\(645\) | 42.2898 | + | 34.5922i | 1.66516 | + | 1.36207i | ||||
\(646\) | 19.0934i | 0.751219i | ||||||||
\(647\) | − | 14.7865i | − | 0.581317i | −0.956827 | − | 0.290658i | \(-0.906126\pi\) | ||
0.956827 | − | 0.290658i | \(-0.0938743\pi\) | |||||||
\(648\) | −4.07823 | + | 1.72019i | −0.160208 | + | 0.0675754i | ||||
\(649\) | 40.4793 | − | 16.3034i | 1.58895 | − | 0.639964i | ||||
\(650\) | − | 27.6269i | − | 1.08362i | ||||||
\(651\) | 2.17730 | − | 2.66179i | 0.0853350 | − | 0.104324i | ||||
\(652\) | 13.3749 | 0.523801 | ||||||||
\(653\) | − | 18.7348i | − | 0.733148i | −0.930389 | − | 0.366574i | \(-0.880531\pi\) | ||
0.930389 | − | 0.366574i | \(-0.119469\pi\) | |||||||
\(654\) | 7.08514 | − | 8.66175i | 0.277051 | − | 0.338701i | ||||
\(655\) | − | 54.3620i | − | 2.12410i | ||||||
\(656\) | 32.2439i | 1.25891i | ||||||||
\(657\) | 38.6290 | − | 7.81351i | 1.50706 | − | 0.304834i | ||||
\(658\) | −2.49074 | −0.0970990 | ||||||||
\(659\) | −25.8091 | −1.00538 | −0.502691 | − | 0.864466i | \(-0.667657\pi\) | ||||
−0.502691 | + | 0.864466i | \(0.667657\pi\) | |||||||
\(660\) | 35.0161 | − | 42.8080i | 1.36300 | − | 1.66630i | ||||
\(661\) | 37.9547 | 1.47627 | 0.738133 | − | 0.674655i | \(-0.235708\pi\) | ||||
0.738133 | + | 0.674655i | \(0.235708\pi\) | |||||||
\(662\) | −48.5662 | −1.88758 | ||||||||
\(663\) | −14.4067 | − | 11.7844i | −0.559508 | − | 0.457667i | ||||
\(664\) | −4.87814 | −0.189309 | ||||||||
\(665\) | 1.99885i | 0.0775120i | ||||||||
\(666\) | −29.3187 | + | 5.93031i | −1.13608 | + | 0.229795i | ||||
\(667\) | − | 11.6125i | − | 0.449638i | ||||||
\(668\) | 21.9630i | 0.849775i | ||||||||
\(669\) | 15.1044 | + | 12.3551i | 0.583969 | + | 0.477676i | ||||
\(670\) | −16.5839 | −0.640694 | ||||||||
\(671\) | − | 3.84266i | − | 0.148344i | ||||||
\(672\) | −2.59477 | − | 2.12247i | −0.100095 | − | 0.0818761i | ||||
\(673\) | − | 15.1662i | − | 0.584614i | −0.956325 | − | 0.292307i | \(-0.905577\pi\) | ||
0.956325 | − | 0.292307i | \(-0.0944229\pi\) | |||||||
\(674\) | − | 40.2159i | − | 1.54906i | ||||||
\(675\) | −13.0164 | + | 24.6382i | −0.501002 | + | 0.948326i | ||||
\(676\) | 10.3267 | 0.397182 | ||||||||
\(677\) | 36.7552i | 1.41262i | 0.707903 | + | 0.706309i | \(0.249641\pi\) | ||||
−0.707903 | + | 0.706309i | \(0.750359\pi\) | |||||||
\(678\) | 12.1895 | + | 9.97081i | 0.468136 | + | 0.382927i | ||||
\(679\) | − | 1.13720i | − | 0.0436415i | ||||||
\(680\) | 6.39131 | 0.245095 | ||||||||
\(681\) | −1.72532 | − | 1.41128i | −0.0661145 | − | 0.0540804i | ||||
\(682\) | 85.9161i | 3.28990i | ||||||||
\(683\) | 16.4806 | 0.630613 | 0.315307 | − | 0.948990i | \(-0.397893\pi\) | ||||
0.315307 | + | 0.948990i | \(0.397893\pi\) | |||||||
\(684\) | −2.53748 | − | 12.5450i | −0.0970229 | − | 0.479669i | ||||
\(685\) | 2.07992 | 0.0794695 | ||||||||
\(686\) | 6.85340 | 0.261664 | ||||||||
\(687\) | 29.5550 | − | 36.1317i | 1.12759 | − | 1.37851i | ||||
\(688\) | 43.5429i | 1.66006i | ||||||||
\(689\) | 3.10750 | 0.118386 | ||||||||
\(690\) | −22.2335 | + | 27.1810i | −0.846416 | + | 1.03476i | ||||
\(691\) | − | 16.0879i | − | 0.612011i | −0.952030 | − | 0.306005i | \(-0.901007\pi\) | ||
0.952030 | − | 0.306005i | \(-0.0989926\pi\) | |||||||
\(692\) | −40.4793 | −1.53879 | ||||||||
\(693\) | −0.858627 | − | 4.24494i | −0.0326165 | − | 0.161252i | ||||
\(694\) | −3.40070 | −0.129089 | ||||||||
\(695\) | 40.3541i | 1.53072i | ||||||||
\(696\) | 1.92461 | − | 2.35288i | 0.0729523 | − | 0.0891859i | ||||
\(697\) | 29.2939 | 1.10959 | ||||||||
\(698\) | − | 18.9652i | − | 0.717843i | ||||||
\(699\) | 7.40665 | + | 6.05850i | 0.280145 | + | 0.229154i | ||||
\(700\) | −2.37907 | −0.0899203 | ||||||||
\(701\) | −26.3861 | −0.996588 | −0.498294 | − | 0.867008i | \(-0.666040\pi\) | ||||
−0.498294 | + | 0.867008i | \(0.666040\pi\) | |||||||
\(702\) | 23.6691 | + | 12.5044i | 0.893332 | + | 0.471948i | ||||
\(703\) | 12.5889i | 0.474800i | ||||||||
\(704\) | 33.2611 | 1.25358 | ||||||||
\(705\) | −17.8789 | + | 21.8574i | −0.673360 | + | 0.823197i | ||||
\(706\) | −52.6688 | −1.98222 | ||||||||
\(707\) | 1.23353 | 0.0463915 | ||||||||
\(708\) | 22.1714 | + | 6.92473i | 0.833254 | + | 0.260247i | ||||
\(709\) | 32.8901 | 1.23521 | 0.617607 | − | 0.786487i | \(-0.288102\pi\) | ||||
0.617607 | + | 0.786487i | \(0.288102\pi\) | |||||||
\(710\) | 101.163 | 3.79660 | ||||||||
\(711\) | −6.97384 | − | 34.4777i | −0.261539 | − | 1.29302i | ||||
\(712\) | 3.91069 | 0.146559 | ||||||||
\(713\) | − | 25.4260i | − | 0.952210i | ||||||
\(714\) | −2.17730 | + | 2.66179i | −0.0814833 | + | 0.0996151i | ||||
\(715\) | 48.6811 | 1.82057 | ||||||||
\(716\) | −25.8862 | −0.967413 | ||||||||
\(717\) | −16.1675 | + | 19.7652i | −0.603788 | + | 0.738144i | ||||
\(718\) | − | 8.21579i | − | 0.306611i | ||||||
\(719\) | 33.0510 | 1.23259 | 0.616297 | − | 0.787514i | \(-0.288632\pi\) | ||||
0.616297 | + | 0.787514i | \(0.288632\pi\) | |||||||
\(720\) | −42.0618 | + | 8.50787i | −1.56755 | + | 0.317070i | ||||
\(721\) | 3.16629i | 0.117919i | ||||||||
\(722\) | 25.2161 | 0.938445 | ||||||||
\(723\) | −1.04257 | − | 0.852804i | −0.0387737 | − | 0.0317161i | ||||
\(724\) | −4.82270 | −0.179234 | ||||||||
\(725\) | − | 19.1371i | − | 0.710732i | ||||||
\(726\) | 55.2102 | + | 45.1609i | 2.04904 | + | 1.67608i | ||||
\(727\) | −47.6043 | −1.76554 | −0.882772 | − | 0.469802i | \(-0.844325\pi\) | ||||
−0.882772 | + | 0.469802i | \(0.844325\pi\) | |||||||
\(728\) | − | 0.332635i | − | 0.0123283i | ||||||
\(729\) | −15.2171 | − | 22.3033i | −0.563597 | − | 0.826050i | ||||
\(730\) | 81.8490 | 3.02937 | ||||||||
\(731\) | 39.5592 | 1.46315 | ||||||||
\(732\) | 1.29498 | − | 1.58315i | 0.0478640 | − | 0.0585148i | ||||
\(733\) | −44.3900 | −1.63958 | −0.819791 | − | 0.572663i | \(-0.805910\pi\) | ||||
−0.819791 | + | 0.572663i | \(0.805910\pi\) | |||||||
\(734\) | 45.7002i | 1.68683i | ||||||||
\(735\) | 24.4835 | − | 29.9316i | 0.903086 | − | 1.10404i | ||||
\(736\) | −24.7857 | −0.913614 | ||||||||
\(737\) | − | 15.1225i | − | 0.557045i | ||||||
\(738\) | −41.2953 | + | 8.35284i | −1.52010 | + | 0.307472i | ||||
\(739\) | − | 27.4551i | − | 1.00995i | −0.863134 | − | 0.504975i | \(-0.831502\pi\) | ||
0.863134 | − | 0.504975i | \(-0.168498\pi\) | |||||||
\(740\) | −28.9539 | −1.06437 | ||||||||
\(741\) | 7.13304 | − | 8.72029i | 0.262039 | − | 0.320348i | ||||
\(742\) | − | 0.574146i | − | 0.0210776i | ||||||
\(743\) | − | 5.49545i | − | 0.201609i | −0.994906 | − | 0.100804i | \(-0.967858\pi\) | ||
0.994906 | − | 0.100804i | \(-0.0321416\pi\) | |||||||
\(744\) | 4.21401 | − | 5.15172i | 0.154493 | − | 0.188871i | ||||
\(745\) | − | 20.7787i | − | 0.761274i | ||||||
\(746\) | −41.6196 | −1.52380 | ||||||||
\(747\) | −5.89951 | − | 29.1664i | −0.215852 | − | 1.06714i | ||||
\(748\) | − | 40.0440i | − | 1.46415i | ||||||
\(749\) | − | 2.52018i | − | 0.0920853i | ||||||
\(750\) | −2.47787 | + | 3.02925i | −0.0904790 | + | 0.110613i | ||||
\(751\) | 2.61812i | 0.0955366i | 0.998858 | + | 0.0477683i | \(0.0152109\pi\) | ||||
−0.998858 | + | 0.0477683i | \(0.984789\pi\) | |||||||
\(752\) | −22.5051 | −0.820676 | ||||||||
\(753\) | 14.8294 | − | 18.1292i | 0.540412 | − | 0.660665i | ||||
\(754\) | −18.3843 | −0.669517 | ||||||||
\(755\) | −42.2898 | −1.53908 | ||||||||
\(756\) | 1.07681 | − | 2.03824i | 0.0391630 | − | 0.0741302i | ||||
\(757\) | −1.36372 | −0.0495653 | −0.0247826 | − | 0.999693i | \(-0.507889\pi\) | ||||
−0.0247826 | + | 0.999693i | \(0.507889\pi\) | |||||||
\(758\) | −28.9518 | −1.05158 | ||||||||
\(759\) | −24.7857 | − | 20.2742i | −0.899665 | − | 0.735909i | ||||
\(760\) | 3.86863i | 0.140330i | ||||||||
\(761\) | − | 9.13600i | − | 0.331180i | −0.986195 | − | 0.165590i | \(-0.947047\pi\) | ||
0.986195 | − | 0.165590i | \(-0.0529528\pi\) | |||||||
\(762\) | 6.80071 | + | 5.56285i | 0.246364 | + | 0.201521i | ||||
\(763\) | − | 0.848232i | − | 0.0307081i | ||||||
\(764\) | 8.20177 | 0.296730 | ||||||||
\(765\) | 7.72949 | + | 38.2136i | 0.279460 | + | 1.38162i | ||||
\(766\) | 18.1606i | 0.656170i | ||||||||
\(767\) | 7.63840 | + | 18.9652i | 0.275807 | + | 0.684793i | ||||
\(768\) | −25.8241 | − | 21.1236i | −0.931848 | − | 0.762234i | ||||
\(769\) | − | 30.0732i | − | 1.08447i | −0.840228 | − | 0.542233i | \(-0.817579\pi\) | ||
0.840228 | − | 0.542233i | \(-0.182421\pi\) | |||||||
\(770\) | − | 8.99438i | − | 0.324135i | ||||||
\(771\) | −18.7760 | + | 22.9540i | −0.676200 | + | 0.826669i | ||||
\(772\) | −23.6894 | −0.852600 | ||||||||
\(773\) | −5.41783 | −0.194866 | −0.0974329 | − | 0.995242i | \(-0.531063\pi\) | ||||
−0.0974329 | + | 0.995242i | \(0.531063\pi\) | |||||||
\(774\) | −55.7662 | + | 11.2799i | −2.00447 | + | 0.405446i | ||||
\(775\) | − | 41.9012i | − | 1.50514i | ||||||
\(776\) | − | 2.20096i | − | 0.0790100i | ||||||
\(777\) | −1.43557 | + | 1.75501i | −0.0515007 | + | 0.0629607i | ||||
\(778\) | − | 2.70546i | − | 0.0969956i | ||||||
\(779\) | 17.7315i | 0.635297i | ||||||||
\(780\) | 20.0562 | + | 16.4056i | 0.718128 | + | 0.587415i | ||||
\(781\) | 92.2487i | 3.30092i | ||||||||
\(782\) | 25.4260i | 0.909231i | ||||||||
\(783\) | 16.3955 | + | 8.66175i | 0.585926 | + | 0.309546i | ||||
\(784\) | 30.8185 | 1.10066 | ||||||||
\(785\) | −35.8984 | −1.28127 | ||||||||
\(786\) | 43.8185 | + | 35.8427i | 1.56296 | + | 1.27847i | ||||
\(787\) | −3.55530 | −0.126733 | −0.0633665 | − | 0.997990i | \(-0.520184\pi\) | ||||
−0.0633665 | + | 0.997990i | \(0.520184\pi\) | |||||||
\(788\) | − | 8.07418i | − | 0.287631i | ||||||
\(789\) | −28.8775 | + | 35.3034i | −1.02807 | + | 1.25683i | ||||
\(790\) | − | 73.0531i | − | 2.59911i | ||||||
\(791\) | 1.19370 | 0.0424432 | ||||||||
\(792\) | −1.66181 | − | 8.21579i | −0.0590500 | − | 0.291936i | ||||
\(793\) | 1.80035 | 0.0639322 | ||||||||
\(794\) | 25.0933i | 0.890529i | ||||||||
\(795\) | −5.03840 | − | 4.12132i | −0.178694 | − | 0.146168i | ||||
\(796\) | 17.9026 | 0.634542 | ||||||||
\(797\) | −28.1864 | −0.998414 | −0.499207 | − | 0.866483i | \(-0.666375\pi\) | ||||
−0.499207 | + | 0.866483i | \(0.666375\pi\) | |||||||
\(798\) | −1.61117 | − | 1.31791i | −0.0570349 | − | 0.0466535i | ||||
\(799\) | 20.4461i | 0.723332i | ||||||||
\(800\) | −40.8461 | −1.44413 | ||||||||
\(801\) | 4.72949 | + | 23.3820i | 0.167108 | + | 0.826162i | ||||
\(802\) | 38.6527 | 1.36487 | ||||||||
\(803\) | 74.6362i | 2.63385i | ||||||||
\(804\) | 5.09632 | − | 6.23037i | 0.179733 | − | 0.219728i | ||||
\(805\) | 2.66179i | 0.0938159i | ||||||||
\(806\) | −40.2530 | −1.41785 | ||||||||
\(807\) | 20.9682 | + | 17.1516i | 0.738117 | + | 0.603766i | ||||
\(808\) | 2.38741 | 0.0839887 | ||||||||
\(809\) | 29.4301 | 1.03471 | 0.517353 | − | 0.855772i | \(-0.326917\pi\) | ||||
0.517353 | + | 0.855772i | \(0.326917\pi\) | |||||||
\(810\) | −21.7924 | − | 51.6653i | −0.765706 | − | 1.81534i | ||||
\(811\) | 0.460829i | 0.0161819i | 0.999967 | + | 0.00809095i | \(0.00257546\pi\) | ||||
−0.999967 | + | 0.00809095i | \(0.997425\pi\) | |||||||
\(812\) | 1.58315i | 0.0555576i | ||||||||
\(813\) | −35.2144 | − | 28.8047i | −1.23502 | − | 1.01022i | ||||
\(814\) | − | 56.6475i | − | 1.98549i | ||||||
\(815\) | − | 24.6608i | − | 0.863830i | ||||||
\(816\) | −19.6730 | + | 24.0507i | −0.688692 | + | 0.841942i | ||||
\(817\) | 23.9450i | 0.837731i | ||||||||
\(818\) | 21.4988i | 0.751687i | ||||||||
\(819\) | 1.98882 | − | 0.402280i | 0.0694951 | − | 0.0140568i | ||||
\(820\) | −40.7816 | −1.42415 | ||||||||
\(821\) | −16.9271 | −0.590760 | −0.295380 | − | 0.955380i | \(-0.595446\pi\) | ||||
−0.295380 | + | 0.955380i | \(0.595446\pi\) | |||||||
\(822\) | −1.37136 | + | 1.67652i | −0.0478317 | + | 0.0584753i | ||||
\(823\) | 2.31806i | 0.0808026i | 0.999184 | + | 0.0404013i | \(0.0128636\pi\) | ||||
−0.999184 | + | 0.0404013i | \(0.987136\pi\) | |||||||
\(824\) | 6.12815i | 0.213484i | ||||||||
\(825\) | −40.8461 | − | 33.4113i | −1.42208 | − | 1.16323i | ||||
\(826\) | 3.50403 | − | 1.41128i | 0.121921 | − | 0.0491047i | ||||
\(827\) | − | 43.8641i | − | 1.52530i | −0.646809 | − | 0.762652i | \(-0.723897\pi\) | ||
0.646809 | − | 0.762652i | \(-0.276103\pi\) | |||||||
\(828\) | −3.37907 | − | 16.7057i | −0.117431 | − | 0.580562i | ||||
\(829\) | −24.1906 | −0.840174 | −0.420087 | − | 0.907484i | \(-0.638000\pi\) | ||||
−0.420087 | + | 0.907484i | \(0.638000\pi\) | |||||||
\(830\) | − | 61.7992i | − | 2.14508i | ||||||
\(831\) | 25.5466 | + | 20.8966i | 0.886202 | + | 0.724896i | ||||
\(832\) | 15.5834i | 0.540256i | ||||||||
\(833\) | − | 27.9990i | − | 0.970107i | ||||||
\(834\) | −32.5275 | − | 26.6068i | −1.12633 | − | 0.921319i | ||||
\(835\) | 40.4957 | 1.40141 | ||||||||
\(836\) | 24.2385 | 0.838306 | ||||||||
\(837\) | 35.8984 | + | 18.9652i | 1.24083 | + | 0.655533i | ||||
\(838\) | −15.3132 | −0.528985 | ||||||||
\(839\) | −23.2388 | −0.802291 | −0.401145 | − | 0.916014i | \(-0.631388\pi\) | ||||
−0.401145 | + | 0.916014i | \(0.631388\pi\) | |||||||
\(840\) | −0.441156 | + | 0.539323i | −0.0152213 | + | 0.0186084i | ||||
\(841\) | 16.2653 | 0.560872 | ||||||||
\(842\) | − | 56.8956i | − | 1.96075i | ||||||
\(843\) | 14.7320 | − | 18.0102i | 0.507396 | − | 0.620303i | ||||
\(844\) | 15.9271i | 0.548233i | ||||||||
\(845\) | − | 19.0406i | − | 0.655015i | ||||||
\(846\) | −5.82998 | − | 28.8227i | −0.200439 | − | 0.990944i | ||||
\(847\) | 5.40665 | 0.185775 | ||||||||
\(848\) | − | 5.18771i | − | 0.178147i | ||||||
\(849\) | −20.7980 | + | 25.4260i | −0.713784 | + | 0.872617i | ||||
\(850\) | 41.9012i | 1.43720i | ||||||||
\(851\) | 16.7642i | 0.574670i | ||||||||
\(852\) | −31.0880 | + | 38.0058i | −1.06506 | + | 1.30206i | ||||
\(853\) | 24.3369 | 0.833278 | 0.416639 | − | 0.909072i | \(-0.363208\pi\) | ||||
0.416639 | + | 0.909072i | \(0.363208\pi\) | |||||||
\(854\) | − | 0.332635i | − | 0.0113825i | ||||||
\(855\) | −23.1306 | + | 4.67863i | −0.791048 | + | 0.160006i | ||||
\(856\) | − | 4.87763i | − | 0.166714i | ||||||
\(857\) | 34.8513 | 1.19050 | 0.595250 | − | 0.803541i | \(-0.297053\pi\) | ||||
0.595250 | + | 0.803541i | \(0.297053\pi\) | |||||||
\(858\) | −32.0971 | + | 39.2394i | −1.09578 | + | 1.33961i | ||||
\(859\) | − | 17.7843i | − | 0.606793i | −0.952864 | − | 0.303397i | \(-0.901879\pi\) | ||
0.952864 | − | 0.303397i | \(-0.0981207\pi\) | |||||||
\(860\) | −55.0724 | −1.87795 | ||||||||
\(861\) | −2.02200 | + | 2.47194i | −0.0689094 | + | 0.0842433i | ||||
\(862\) | 45.4803 | 1.54907 | ||||||||
\(863\) | 8.35849 | 0.284526 | 0.142263 | − | 0.989829i | \(-0.454562\pi\) | ||||
0.142263 | + | 0.989829i | \(0.454562\pi\) | |||||||
\(864\) | 18.4876 | − | 34.9945i | 0.628962 | − | 1.19054i | ||||
\(865\) | 74.6362i | 2.53771i | ||||||||
\(866\) | 10.0042 | 0.339956 | ||||||||
\(867\) | −0.941022 | − | 0.769738i | −0.0319588 | − | 0.0261417i | ||||
\(868\) | 3.46635i | 0.117656i | ||||||||
\(869\) | 66.6154 | 2.25977 | ||||||||
\(870\) | 29.8077 | + | 24.3821i | 1.01058 | + | 0.826632i | ||||
\(871\) | 7.08514 | 0.240071 | ||||||||
\(872\) | − | 1.64170i | − | 0.0555948i | ||||||
\(873\) | 13.1596 | − | 2.66179i | 0.445384 | − | 0.0900881i | ||||
\(874\) | −15.3902 | −0.520583 | ||||||||
\(875\) | 0.296650i | 0.0100286i | ||||||||
\(876\) | −25.1526 | + | 30.7496i | −0.849826 | + | 1.03893i | ||||
\(877\) | 16.1731 | 0.546128 | 0.273064 | − | 0.961996i | \(-0.411963\pi\) | ||||
0.273064 | + | 0.961996i | \(0.411963\pi\) | |||||||
\(878\) | 43.7571 | 1.47673 | ||||||||
\(879\) | 7.02722 | − | 8.59094i | 0.237022 | − | 0.289765i | ||||
\(880\) | − | 81.2689i | − | 2.73957i | ||||||
\(881\) | −22.0552 | −0.743058 | −0.371529 | − | 0.928421i | \(-0.621166\pi\) | ||||
−0.371529 | + | 0.928421i | \(0.621166\pi\) | |||||||
\(882\) | 7.98359 | + | 39.4699i | 0.268822 | + | 1.32902i | ||||
\(883\) | −6.68133 | −0.224845 | −0.112422 | − | 0.993661i | \(-0.535861\pi\) | ||||
−0.112422 | + | 0.993661i | \(0.535861\pi\) | |||||||
\(884\) | 18.7612 | 0.631009 | ||||||||
\(885\) | 12.7679 | − | 40.8800i | 0.429188 | − | 1.37417i | ||||
\(886\) | −56.3533 | −1.89322 | ||||||||
\(887\) | −1.07681 | −0.0361556 | −0.0180778 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180778 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(888\) | −2.77844 | + | 3.39671i | −0.0932384 | + | 0.113986i | ||||
\(889\) | 0.665983 | 0.0223364 | ||||||||
\(890\) | 49.5429i | 1.66068i | ||||||||
\(891\) | 47.1125 | − | 19.8720i | 1.57833 | − | 0.665736i | ||||
\(892\) | −19.6699 | −0.658596 | ||||||||
\(893\) | −12.3760 | −0.414146 | ||||||||
\(894\) | 16.7487 | + | 13.7001i | 0.560162 | + | 0.458202i | ||||
\(895\) | 47.7293i | 1.59542i | ||||||||
\(896\) | −0.991662 | −0.0331291 | ||||||||
\(897\) | 9.49881 | − | 11.6125i | 0.317156 | − | 0.387730i | ||||
\(898\) | 38.8372i | 1.29601i | ||||||||
\(899\) | −27.8831 | −0.929954 | ||||||||
\(900\) | −5.56860 | − | 27.5304i | −0.185620 | − | 0.917682i | ||||
\(901\) | −4.71308 | −0.157016 | ||||||||
\(902\) | − | 79.7879i | − | 2.65665i | ||||||
\(903\) | −2.73055 | + | 3.33816i | −0.0908670 | + | 0.111087i | ||||
\(904\) | 2.31033 | 0.0768405 | ||||||||
\(905\) | 8.89216i | 0.295585i | ||||||||
\(906\) | 27.8831 | − | 34.0877i | 0.926354 | − | 1.13249i | ||||
\(907\) | −2.36266 | −0.0784509 | −0.0392254 | − | 0.999230i | \(-0.512489\pi\) | ||||
−0.0392254 | + | 0.999230i | \(0.512489\pi\) | |||||||
\(908\) | 2.24682 | 0.0745634 | ||||||||
\(909\) | 2.88727 | + | 14.2743i | 0.0957647 | + | 0.473449i | ||||
\(910\) | 4.21401 | 0.139693 | ||||||||
\(911\) | − | 21.0092i | − | 0.696065i | −0.937483 | − | 0.348032i | \(-0.886850\pi\) | ||
0.937483 | − | 0.348032i | \(-0.113150\pi\) | |||||||
\(912\) | −14.5578 | − | 11.9080i | −0.482056 | − | 0.394313i | ||||
\(913\) | 56.3533 | 1.86502 | ||||||||
\(914\) | 79.7879i | 2.63915i | ||||||||
\(915\) | −2.91903 | − | 2.38771i | −0.0965000 | − | 0.0789352i | ||||
\(916\) | 47.0529i | 1.55467i | ||||||||
\(917\) | 4.29108 | 0.141704 | ||||||||
\(918\) | −35.8984 | − | 18.9652i | −1.18483 | − | 0.625944i | ||||
\(919\) | 39.0787i | 1.28909i | 0.764568 | + | 0.644543i | \(0.222952\pi\) | ||||
−0.764568 | + | 0.644543i | \(0.777048\pi\) | |||||||
\(920\) | 5.15172i | 0.169847i | ||||||||
\(921\) | −18.6552 | − | 15.2596i | −0.614709 | − | 0.502820i | ||||
\(922\) | 30.4606i | 1.00317i | ||||||||
\(923\) | −43.2200 | −1.42260 | ||||||||
\(924\) | 3.37907 | + | 2.76401i | 0.111163 | + | 0.0909294i | ||||
\(925\) | 27.6269i | 0.908368i | ||||||||
\(926\) | − | 30.5777i | − | 1.00485i | ||||||
\(927\) | −36.6402 | + | 7.41123i | −1.20342 | + | 0.243417i | ||||
\(928\) | 27.1810i | 0.892259i | ||||||||
\(929\) | 38.7222 | 1.27043 | 0.635217 | − | 0.772333i | \(-0.280911\pi\) | ||||
0.635217 | + | 0.772333i | \(0.280911\pi\) | |||||||
\(930\) | 65.2650 | + | 53.3855i | 2.14012 | + | 1.75058i | ||||
\(931\) | 16.9477 | 0.555437 | ||||||||
\(932\) | −9.64541 | −0.315946 | ||||||||
\(933\) | −1.76088 | + | 2.15272i | −0.0576488 | + | 0.0704769i | ||||
\(934\) | −31.3871 | −1.02702 | ||||||||
\(935\) | −73.8336 | −2.41462 | ||||||||
\(936\) | 3.84923 | − | 0.778586i | 0.125816 | − | 0.0254489i | ||||
\(937\) | 6.63265i | 0.216679i | 0.994114 | + | 0.108340i | \(0.0345534\pi\) | ||||
−0.994114 | + | 0.108340i | \(0.965447\pi\) | |||||||
\(938\) | − | 1.30906i | − | 0.0427424i | ||||||
\(939\) | 28.6248 | − | 34.9945i | 0.934136 | − | 1.14200i | ||||
\(940\) | − | 28.4641i | − | 0.928396i | ||||||
\(941\) | −35.6485 | −1.16211 | −0.581054 | − | 0.813865i | \(-0.697360\pi\) | ||||
−0.581054 | + | 0.813865i | \(0.697360\pi\) | |||||||
\(942\) | 23.6691 | − | 28.9360i | 0.771181 | − | 0.942786i | ||||
\(943\) | 23.6124i | 0.768926i | ||||||||
\(944\) | 31.6608 | − | 12.7517i | 1.03047 | − | 0.415031i | ||||
\(945\) | −3.75814 | − | 1.98543i | −0.122252 | − | 0.0645859i | ||||
\(946\) | − | 107.748i | − | 3.50317i | ||||||
\(947\) | − | 25.3237i | − | 0.822911i | −0.911430 | − | 0.411456i | \(-0.865021\pi\) | ||
0.911430 | − | 0.411456i | \(-0.134979\pi\) | |||||||
\(948\) | 27.4451 | + | 22.4495i | 0.891374 | + | 0.729127i | ||||
\(949\) | −34.9682 | −1.13512 | ||||||||
\(950\) | −25.3627 | −0.822873 | ||||||||
\(951\) | −10.1742 | + | 12.4382i | −0.329921 | + | 0.403335i | ||||
\(952\) | 0.504500i | 0.0163510i | ||||||||
\(953\) | − | 22.6585i | − | 0.733982i | −0.930224 | − | 0.366991i | \(-0.880388\pi\) | ||
0.930224 | − | 0.366991i | \(-0.119612\pi\) | |||||||
\(954\) | 6.64399 | − | 1.34388i | 0.215107 | − | 0.0435098i | ||||
\(955\) | − | 15.1225i | − | 0.489354i | ||||||
\(956\) | − | 25.7394i | − | 0.832473i | ||||||
\(957\) | −22.2335 | + | 27.1810i | −0.718708 | + | 0.878636i | ||||
\(958\) | 12.3325i | 0.398446i | ||||||||
\(959\) | 0.164179i | 0.00530162i | ||||||||
\(960\) | 20.6674 | − | 25.2664i | 0.667038 | − | 0.815468i | ||||
\(961\) | −30.0510 | −0.969387 | ||||||||
\(962\) | 26.5402 | 0.855691 | ||||||||
\(963\) | 29.1634 | − | 5.89889i | 0.939776 | − | 0.190089i | ||||
\(964\) | 1.35770 | 0.0437286 | ||||||||
\(965\) | 43.6788i | 1.40607i | ||||||||
\(966\) | −2.14554 | − | 1.75501i | −0.0690317 | − | 0.0564666i | ||||
\(967\) | 26.5632i | 0.854214i | 0.904201 | + | 0.427107i | \(0.140467\pi\) | ||||
−0.904201 | + | 0.427107i | \(0.859533\pi\) | |||||||
\(968\) | 10.4642 | 0.336332 | ||||||||
\(969\) | −10.8185 | + | 13.2259i | −0.347541 | + | 0.424877i | ||||
\(970\) | 27.8831 | 0.895272 | ||||||||
\(971\) | − | 49.5295i | − | 1.58948i | −0.606953 | − | 0.794738i | \(-0.707608\pi\) | ||
0.606953 | − | 0.794738i | \(-0.292392\pi\) | |||||||
\(972\) | 26.1069 | + | 7.68989i | 0.837378 | + | 0.246653i | ||||
\(973\) | −3.18537 | −0.102118 | ||||||||
\(974\) | −57.4220 | −1.83992 | ||||||||
\(975\) | 15.6537 | − | 19.1371i | 0.501321 | − | 0.612876i | ||||
\(976\) | − | 3.00552i | − | 0.0962045i | ||||||
\(977\) | −37.1320 | −1.18796 | −0.593979 | − | 0.804481i | \(-0.702444\pi\) | ||||
−0.593979 | + | 0.804481i | \(0.702444\pi\) | |||||||
\(978\) | 19.8779 | + | 16.2597i | 0.635624 | + | 0.519929i | ||||
\(979\) | −45.1770 | −1.44386 | ||||||||
\(980\) | 38.9788i | 1.24513i | ||||||||
\(981\) | 9.81569 | − | 1.98543i | 0.313391 | − | 0.0633898i | ||||
\(982\) | − | 55.6014i | − | 1.77431i | ||||||
\(983\) | 6.24470 | 0.199175 | 0.0995876 | − | 0.995029i | \(-0.468248\pi\) | ||||
0.0995876 | + | 0.995029i | \(0.468248\pi\) | |||||||
\(984\) | −3.91344 | + | 4.78426i | −0.124756 | + | 0.152517i | ||||
\(985\) | −14.8873 | −0.474348 | ||||||||
\(986\) | 27.8831 | 0.887979 | ||||||||
\(987\) | −1.72532 | − | 1.41128i | −0.0549176 | − | 0.0449216i | ||||
\(988\) | 11.3561i | 0.361286i | ||||||||
\(989\) | 31.8868i | 1.01394i | ||||||||
\(990\) | 104.082 | − | 21.0528i | 3.30796 | − | 0.669103i | ||||
\(991\) | − | 16.2597i | − | 0.516507i | −0.966077 | − | 0.258254i | \(-0.916853\pi\) | ||
0.966077 | − | 0.258254i | \(-0.0831470\pi\) | |||||||
\(992\) | 59.5137i | 1.88956i | ||||||||
\(993\) | −33.6416 | − | 27.5182i | −1.06758 | − | 0.873263i | ||||
\(994\) | 7.98538i | 0.253281i | ||||||||
\(995\) | − | 33.0091i | − | 1.04646i | ||||||
\(996\) | 23.2171 | + | 18.9912i | 0.735663 | + | 0.601758i | ||||
\(997\) | −42.4957 | −1.34585 | −0.672926 | − | 0.739710i | \(-0.734963\pi\) | ||||
−0.672926 | + | 0.739710i | \(0.734963\pi\) | |||||||
\(998\) | 44.5785 | 1.41111 | ||||||||
\(999\) | −23.6691 | − | 12.5044i | −0.748857 | − | 0.395622i |
(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 | 177.2.d.c.176.1 | yes | 6 | |
3.2 | odd | 2 | 177.2.d.a.176.6 | yes | 6 | ||
59.58 | odd | 2 | 177.2.d.a.176.5 | ✓ | 6 | ||
177.176 | even | 2 | inner | 177.2.d.c.176.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.2.d.a.176.5 | ✓ | 6 | 59.58 | odd | 2 | ||
177.2.d.a.176.6 | yes | 6 | 3.2 | odd | 2 | ||
177.2.d.c.176.1 | yes | 6 | 1.1 | even | 1 | trivial | |
177.2.d.c.176.2 | yes | 6 | 177.176 | even | 2 | inner |