Properties

Label 729.2.c.d.244.4
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.4
Root \(1.91182i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.d.487.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.789202 + 1.36694i) q^{2} +(-0.245680 + 0.425530i) q^{4} +(-0.839254 + 1.45363i) q^{5} +(-1.38964 - 2.40693i) q^{7} +2.38124 q^{8} +O(q^{10})\) \(q+(0.789202 + 1.36694i) q^{2} +(-0.245680 + 0.425530i) q^{4} +(-0.839254 + 1.45363i) q^{5} +(-1.38964 - 2.40693i) q^{7} +2.38124 q^{8} -2.64936 q^{10} +(2.07561 + 3.59506i) q^{11} +(-3.43802 + 5.95483i) q^{13} +(2.19342 - 3.79911i) q^{14} +(2.37064 + 4.10607i) q^{16} +0.976551 q^{17} +2.68529 q^{19} +(-0.412376 - 0.714256i) q^{20} +(-3.27615 + 5.67446i) q^{22} +(-0.806585 + 1.39705i) q^{23} +(1.09131 + 1.89020i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(4.11394 + 7.12555i) q^{29} +(-0.522035 + 0.904190i) q^{31} +(-1.36059 + 2.35661i) q^{32} +(0.770696 + 1.33489i) q^{34} +4.66505 q^{35} -1.30834 q^{37} +(2.11924 + 3.67062i) q^{38} +(-1.99847 + 3.46145i) q^{40} +(2.42408 - 4.19864i) q^{41} +(-4.92011 - 8.52189i) q^{43} -2.03974 q^{44} -2.54623 q^{46} +(-6.24885 - 10.8233i) q^{47} +(-0.362204 + 0.627356i) q^{49} +(-1.72252 + 2.98350i) q^{50} +(-1.68931 - 2.92596i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(-3.30907 - 5.73148i) q^{56} +(-6.49346 + 11.2470i) q^{58} +(-4.52594 + 7.83915i) q^{59} +(0.642871 + 1.11349i) q^{61} -1.64796 q^{62} +5.18745 q^{64} +(-5.77075 - 9.99523i) q^{65} +(2.32315 - 4.02381i) q^{67} +(-0.239919 + 0.415552i) q^{68} +(3.68166 + 6.37683i) q^{70} +5.62373 q^{71} -4.56144 q^{73} +(-1.03255 - 1.78843i) q^{74} +(-0.659722 + 1.14267i) q^{76} +(5.76871 - 9.99170i) q^{77} +(-2.32840 - 4.03291i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(-2.88220 - 4.99211i) q^{83} +(-0.819574 + 1.41954i) q^{85} +(7.76593 - 13.4510i) q^{86} +(4.94254 + 8.56072i) q^{88} +4.54442 q^{89} +19.1105 q^{91} +(-0.396323 - 0.686452i) q^{92} +(9.86321 - 17.0836i) q^{94} +(-2.25364 + 3.90342i) q^{95} +(-4.28772 - 7.42655i) q^{97} -1.14341 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.789202 + 1.36694i 0.558050 + 0.966571i 0.997659 + 0.0683820i \(0.0217837\pi\)
−0.439609 + 0.898189i \(0.644883\pi\)
\(3\) 0 0
\(4\) −0.245680 + 0.425530i −0.122840 + 0.212765i
\(5\) −0.839254 + 1.45363i −0.375326 + 0.650083i −0.990376 0.138405i \(-0.955802\pi\)
0.615050 + 0.788488i \(0.289136\pi\)
\(6\) 0 0
\(7\) −1.38964 2.40693i −0.525235 0.909734i −0.999568 0.0293881i \(-0.990644\pi\)
0.474333 0.880345i \(-0.342689\pi\)
\(8\) 2.38124 0.841897
\(9\) 0 0
\(10\) −2.64936 −0.837802
\(11\) 2.07561 + 3.59506i 0.625820 + 1.08395i 0.988382 + 0.151993i \(0.0485690\pi\)
−0.362561 + 0.931960i \(0.618098\pi\)
\(12\) 0 0
\(13\) −3.43802 + 5.95483i −0.953536 + 1.65157i −0.215852 + 0.976426i \(0.569253\pi\)
−0.737684 + 0.675147i \(0.764080\pi\)
\(14\) 2.19342 3.79911i 0.586215 1.01535i
\(15\) 0 0
\(16\) 2.37064 + 4.10607i 0.592661 + 1.02652i
\(17\) 0.976551 0.236848 0.118424 0.992963i \(-0.462216\pi\)
0.118424 + 0.992963i \(0.462216\pi\)
\(18\) 0 0
\(19\) 2.68529 0.616048 0.308024 0.951379i \(-0.400332\pi\)
0.308024 + 0.951379i \(0.400332\pi\)
\(20\) −0.412376 0.714256i −0.0922100 0.159712i
\(21\) 0 0
\(22\) −3.27615 + 5.67446i −0.698478 + 1.20980i
\(23\) −0.806585 + 1.39705i −0.168185 + 0.291304i −0.937782 0.347226i \(-0.887124\pi\)
0.769597 + 0.638530i \(0.220457\pi\)
\(24\) 0 0
\(25\) 1.09131 + 1.89020i 0.218261 + 0.378040i
\(26\) −10.8532 −2.12848
\(27\) 0 0
\(28\) 1.36563 0.258079
\(29\) 4.11394 + 7.12555i 0.763939 + 1.32318i 0.940806 + 0.338947i \(0.110071\pi\)
−0.176866 + 0.984235i \(0.556596\pi\)
\(30\) 0 0
\(31\) −0.522035 + 0.904190i −0.0937602 + 0.162397i −0.909090 0.416599i \(-0.863222\pi\)
0.815330 + 0.578996i \(0.196555\pi\)
\(32\) −1.36059 + 2.35661i −0.240520 + 0.416593i
\(33\) 0 0
\(34\) 0.770696 + 1.33489i 0.132173 + 0.228931i
\(35\) 4.66505 0.788537
\(36\) 0 0
\(37\) −1.30834 −0.215091 −0.107545 0.994200i \(-0.534299\pi\)
−0.107545 + 0.994200i \(0.534299\pi\)
\(38\) 2.11924 + 3.67062i 0.343785 + 0.595454i
\(39\) 0 0
\(40\) −1.99847 + 3.46145i −0.315986 + 0.547303i
\(41\) 2.42408 4.19864i 0.378578 0.655717i −0.612277 0.790643i \(-0.709746\pi\)
0.990856 + 0.134926i \(0.0430797\pi\)
\(42\) 0 0
\(43\) −4.92011 8.52189i −0.750310 1.29958i −0.947672 0.319245i \(-0.896571\pi\)
0.197362 0.980331i \(-0.436763\pi\)
\(44\) −2.03974 −0.307503
\(45\) 0 0
\(46\) −2.54623 −0.375422
\(47\) −6.24885 10.8233i −0.911488 1.57874i −0.811963 0.583709i \(-0.801601\pi\)
−0.0995258 0.995035i \(-0.531733\pi\)
\(48\) 0 0
\(49\) −0.362204 + 0.627356i −0.0517434 + 0.0896222i
\(50\) −1.72252 + 2.98350i −0.243601 + 0.421930i
\(51\) 0 0
\(52\) −1.68931 2.92596i −0.234265 0.405758i
\(53\) 7.34280 1.00861 0.504305 0.863525i \(-0.331749\pi\)
0.504305 + 0.863525i \(0.331749\pi\)
\(54\) 0 0
\(55\) −6.96786 −0.939546
\(56\) −3.30907 5.73148i −0.442194 0.765902i
\(57\) 0 0
\(58\) −6.49346 + 11.2470i −0.852633 + 1.47680i
\(59\) −4.52594 + 7.83915i −0.589227 + 1.02057i 0.405107 + 0.914269i \(0.367234\pi\)
−0.994334 + 0.106302i \(0.966099\pi\)
\(60\) 0 0
\(61\) 0.642871 + 1.11349i 0.0823112 + 0.142567i 0.904242 0.427020i \(-0.140437\pi\)
−0.821931 + 0.569587i \(0.807103\pi\)
\(62\) −1.64796 −0.209292
\(63\) 0 0
\(64\) 5.18745 0.648432
\(65\) −5.77075 9.99523i −0.715773 1.23976i
\(66\) 0 0
\(67\) 2.32315 4.02381i 0.283818 0.491587i −0.688504 0.725233i \(-0.741732\pi\)
0.972322 + 0.233646i \(0.0750655\pi\)
\(68\) −0.239919 + 0.415552i −0.0290945 + 0.0503931i
\(69\) 0 0
\(70\) 3.68166 + 6.37683i 0.440043 + 0.762177i
\(71\) 5.62373 0.667414 0.333707 0.942677i \(-0.391700\pi\)
0.333707 + 0.942677i \(0.391700\pi\)
\(72\) 0 0
\(73\) −4.56144 −0.533877 −0.266938 0.963714i \(-0.586012\pi\)
−0.266938 + 0.963714i \(0.586012\pi\)
\(74\) −1.03255 1.78843i −0.120031 0.207900i
\(75\) 0 0
\(76\) −0.659722 + 1.14267i −0.0756753 + 0.131073i
\(77\) 5.76871 9.99170i 0.657405 1.13866i
\(78\) 0 0
\(79\) −2.32840 4.03291i −0.261966 0.453738i 0.704799 0.709407i \(-0.251037\pi\)
−0.966764 + 0.255670i \(0.917704\pi\)
\(80\) −7.95828 −0.889763
\(81\) 0 0
\(82\) 7.65237 0.845063
\(83\) −2.88220 4.99211i −0.316362 0.547955i 0.663364 0.748297i \(-0.269128\pi\)
−0.979726 + 0.200342i \(0.935795\pi\)
\(84\) 0 0
\(85\) −0.819574 + 1.41954i −0.0888953 + 0.153971i
\(86\) 7.76593 13.4510i 0.837422 1.45046i
\(87\) 0 0
\(88\) 4.94254 + 8.56072i 0.526876 + 0.912576i
\(89\) 4.54442 0.481707 0.240854 0.970561i \(-0.422573\pi\)
0.240854 + 0.970561i \(0.422573\pi\)
\(90\) 0 0
\(91\) 19.1105 2.00332
\(92\) −0.396323 0.686452i −0.0413196 0.0715676i
\(93\) 0 0
\(94\) 9.86321 17.0836i 1.01731 1.76204i
\(95\) −2.25364 + 3.90342i −0.231218 + 0.400482i
\(96\) 0 0
\(97\) −4.28772 7.42655i −0.435352 0.754052i 0.561972 0.827156i \(-0.310043\pi\)
−0.997324 + 0.0731042i \(0.976709\pi\)
\(98\) −1.14341 −0.115502
\(99\) 0 0
\(100\) −1.07245 −0.107245
\(101\) 3.90285 + 6.75994i 0.388348 + 0.672639i 0.992228 0.124437i \(-0.0397124\pi\)
−0.603879 + 0.797076i \(0.706379\pi\)
\(102\) 0 0
\(103\) 1.08307 1.87594i 0.106718 0.184842i −0.807721 0.589565i \(-0.799299\pi\)
0.914439 + 0.404724i \(0.132632\pi\)
\(104\) −8.18677 + 14.1799i −0.802779 + 1.39045i
\(105\) 0 0
\(106\) 5.79495 + 10.0371i 0.562855 + 0.974894i
\(107\) 12.5849 1.21663 0.608317 0.793695i \(-0.291845\pi\)
0.608317 + 0.793695i \(0.291845\pi\)
\(108\) 0 0
\(109\) −12.2140 −1.16989 −0.584945 0.811073i \(-0.698884\pi\)
−0.584945 + 0.811073i \(0.698884\pi\)
\(110\) −5.49905 9.52463i −0.524314 0.908138i
\(111\) 0 0
\(112\) 6.58868 11.4119i 0.622572 1.07833i
\(113\) −0.225417 + 0.390433i −0.0212054 + 0.0367288i −0.876433 0.481523i \(-0.840084\pi\)
0.855228 + 0.518252i \(0.173417\pi\)
\(114\) 0 0
\(115\) −1.35386 2.34495i −0.126248 0.218668i
\(116\) −4.04285 −0.375369
\(117\) 0 0
\(118\) −14.2875 −1.31527
\(119\) −1.35706 2.35049i −0.124401 0.215469i
\(120\) 0 0
\(121\) −3.11632 + 5.39763i −0.283302 + 0.490694i
\(122\) −1.01471 + 1.75753i −0.0918675 + 0.159119i
\(123\) 0 0
\(124\) −0.256507 0.444283i −0.0230350 0.0398978i
\(125\) −12.0561 −1.07833
\(126\) 0 0
\(127\) −0.531069 −0.0471247 −0.0235624 0.999722i \(-0.507501\pi\)
−0.0235624 + 0.999722i \(0.507501\pi\)
\(128\) 6.81513 + 11.8041i 0.602378 + 1.04335i
\(129\) 0 0
\(130\) 9.10857 15.7765i 0.798875 1.38369i
\(131\) 5.70802 9.88658i 0.498712 0.863794i −0.501287 0.865281i \(-0.667140\pi\)
0.999999 + 0.00148672i \(0.000473237\pi\)
\(132\) 0 0
\(133\) −3.73159 6.46330i −0.323570 0.560439i
\(134\) 7.33374 0.633539
\(135\) 0 0
\(136\) 2.32541 0.199402
\(137\) 2.11462 + 3.66263i 0.180664 + 0.312920i 0.942107 0.335313i \(-0.108842\pi\)
−0.761443 + 0.648232i \(0.775509\pi\)
\(138\) 0 0
\(139\) 5.57776 9.66097i 0.473100 0.819433i −0.526426 0.850221i \(-0.676468\pi\)
0.999526 + 0.0307879i \(0.00980165\pi\)
\(140\) −1.14611 + 1.98512i −0.0968638 + 0.167773i
\(141\) 0 0
\(142\) 4.43826 + 7.68730i 0.372451 + 0.645104i
\(143\) −28.5440 −2.38697
\(144\) 0 0
\(145\) −13.8106 −1.14690
\(146\) −3.59990 6.23521i −0.297930 0.516030i
\(147\) 0 0
\(148\) 0.321434 0.556740i 0.0264217 0.0457638i
\(149\) −9.73885 + 16.8682i −0.797837 + 1.38189i 0.123184 + 0.992384i \(0.460689\pi\)
−0.921022 + 0.389511i \(0.872644\pi\)
\(150\) 0 0
\(151\) 0.621430 + 1.07635i 0.0505713 + 0.0875920i 0.890203 0.455564i \(-0.150562\pi\)
−0.839632 + 0.543156i \(0.817229\pi\)
\(152\) 6.39433 0.518649
\(153\) 0 0
\(154\) 18.2107 1.46746
\(155\) −0.876239 1.51769i −0.0703812 0.121904i
\(156\) 0 0
\(157\) 1.76657 3.05979i 0.140988 0.244198i −0.786881 0.617105i \(-0.788306\pi\)
0.927869 + 0.372907i \(0.121639\pi\)
\(158\) 3.67516 6.36556i 0.292380 0.506417i
\(159\) 0 0
\(160\) −2.28376 3.95558i −0.180547 0.312716i
\(161\) 4.48345 0.353346
\(162\) 0 0
\(163\) 15.9509 1.24937 0.624685 0.780877i \(-0.285228\pi\)
0.624685 + 0.780877i \(0.285228\pi\)
\(164\) 1.19110 + 2.06304i 0.0930091 + 0.161097i
\(165\) 0 0
\(166\) 4.54927 7.87957i 0.353092 0.611573i
\(167\) 7.24232 12.5441i 0.560428 0.970689i −0.437031 0.899446i \(-0.643970\pi\)
0.997459 0.0712430i \(-0.0226966\pi\)
\(168\) 0 0
\(169\) −17.1400 29.6873i −1.31846 2.28364i
\(170\) −2.58724 −0.198432
\(171\) 0 0
\(172\) 4.83509 0.368672
\(173\) 6.30870 + 10.9270i 0.479641 + 0.830763i 0.999727 0.0233506i \(-0.00743341\pi\)
−0.520086 + 0.854114i \(0.674100\pi\)
\(174\) 0 0
\(175\) 3.03305 5.25339i 0.229277 0.397119i
\(176\) −9.84106 + 17.0452i −0.741798 + 1.28483i
\(177\) 0 0
\(178\) 3.58646 + 6.21194i 0.268817 + 0.465605i
\(179\) −0.295899 −0.0221165 −0.0110582 0.999939i \(-0.503520\pi\)
−0.0110582 + 0.999939i \(0.503520\pi\)
\(180\) 0 0
\(181\) 1.42050 0.105585 0.0527925 0.998606i \(-0.483188\pi\)
0.0527925 + 0.998606i \(0.483188\pi\)
\(182\) 15.0820 + 26.1228i 1.11795 + 1.93635i
\(183\) 0 0
\(184\) −1.92068 + 3.32671i −0.141594 + 0.245248i
\(185\) 1.09803 1.90185i 0.0807290 0.139827i
\(186\) 0 0
\(187\) 2.02694 + 3.51076i 0.148225 + 0.256732i
\(188\) 6.14087 0.447869
\(189\) 0 0
\(190\) −7.11431 −0.516126
\(191\) 10.3120 + 17.8610i 0.746153 + 1.29238i 0.949654 + 0.313301i \(0.101435\pi\)
−0.203501 + 0.979075i \(0.565232\pi\)
\(192\) 0 0
\(193\) 10.4780 18.1484i 0.754221 1.30635i −0.191540 0.981485i \(-0.561348\pi\)
0.945761 0.324864i \(-0.105319\pi\)
\(194\) 6.76776 11.7221i 0.485897 0.841598i
\(195\) 0 0
\(196\) −0.177972 0.308257i −0.0127123 0.0220184i
\(197\) 9.59621 0.683702 0.341851 0.939754i \(-0.388946\pi\)
0.341851 + 0.939754i \(0.388946\pi\)
\(198\) 0 0
\(199\) −10.6917 −0.757912 −0.378956 0.925415i \(-0.623717\pi\)
−0.378956 + 0.925415i \(0.623717\pi\)
\(200\) 2.59867 + 4.50102i 0.183753 + 0.318270i
\(201\) 0 0
\(202\) −6.16028 + 10.6699i −0.433436 + 0.750732i
\(203\) 11.4338 19.8039i 0.802495 1.38996i
\(204\) 0 0
\(205\) 4.06885 + 7.04745i 0.284180 + 0.492215i
\(206\) 3.41906 0.238217
\(207\) 0 0
\(208\) −32.6013 −2.26049
\(209\) 5.57362 + 9.65379i 0.385535 + 0.667766i
\(210\) 0 0
\(211\) 7.52512 13.0339i 0.518051 0.897290i −0.481729 0.876320i \(-0.659991\pi\)
0.999780 0.0209700i \(-0.00667546\pi\)
\(212\) −1.80398 + 3.12458i −0.123898 + 0.214597i
\(213\) 0 0
\(214\) 9.93207 + 17.2028i 0.678942 + 1.17596i
\(215\) 16.5169 1.12644
\(216\) 0 0
\(217\) 2.90176 0.196984
\(218\) −9.63931 16.6958i −0.652857 1.13078i
\(219\) 0 0
\(220\) 1.71186 2.96503i 0.115414 0.199903i
\(221\) −3.35741 + 5.81520i −0.225844 + 0.391172i
\(222\) 0 0
\(223\) 6.14405 + 10.6418i 0.411436 + 0.712629i 0.995047 0.0994049i \(-0.0316939\pi\)
−0.583611 + 0.812034i \(0.698361\pi\)
\(224\) 7.56292 0.505319
\(225\) 0 0
\(226\) −0.711597 −0.0473347
\(227\) 1.87628 + 3.24981i 0.124533 + 0.215698i 0.921550 0.388259i \(-0.126923\pi\)
−0.797017 + 0.603957i \(0.793590\pi\)
\(228\) 0 0
\(229\) 9.30121 16.1102i 0.614641 1.06459i −0.375806 0.926698i \(-0.622634\pi\)
0.990447 0.137892i \(-0.0440326\pi\)
\(230\) 2.13694 3.70128i 0.140905 0.244055i
\(231\) 0 0
\(232\) 9.79629 + 16.9677i 0.643158 + 1.11398i
\(233\) −0.545784 −0.0357555 −0.0178777 0.999840i \(-0.505691\pi\)
−0.0178777 + 0.999840i \(0.505691\pi\)
\(234\) 0 0
\(235\) 20.9775 1.36842
\(236\) −2.22386 3.85185i −0.144761 0.250734i
\(237\) 0 0
\(238\) 2.14198 3.71002i 0.138844 0.240485i
\(239\) −10.0474 + 17.4026i −0.649911 + 1.12568i 0.333233 + 0.942844i \(0.391860\pi\)
−0.983144 + 0.182834i \(0.941473\pi\)
\(240\) 0 0
\(241\) −7.64565 13.2427i −0.492500 0.853034i 0.507463 0.861674i \(-0.330583\pi\)
−0.999963 + 0.00863907i \(0.997250\pi\)
\(242\) −9.83763 −0.632387
\(243\) 0 0
\(244\) −0.631762 −0.0404444
\(245\) −0.607962 1.05302i −0.0388413 0.0672751i
\(246\) 0 0
\(247\) −9.23208 + 15.9904i −0.587423 + 1.01745i
\(248\) −1.24309 + 2.15310i −0.0789364 + 0.136722i
\(249\) 0 0
\(250\) −9.51468 16.4799i −0.601761 1.04228i
\(251\) −12.7563 −0.805171 −0.402586 0.915382i \(-0.631888\pi\)
−0.402586 + 0.915382i \(0.631888\pi\)
\(252\) 0 0
\(253\) −6.69663 −0.421013
\(254\) −0.419121 0.725938i −0.0262980 0.0455494i
\(255\) 0 0
\(256\) −5.56957 + 9.64678i −0.348098 + 0.602924i
\(257\) −6.55235 + 11.3490i −0.408725 + 0.707932i −0.994747 0.102363i \(-0.967360\pi\)
0.586023 + 0.810295i \(0.300693\pi\)
\(258\) 0 0
\(259\) 1.81813 + 3.14909i 0.112973 + 0.195675i
\(260\) 5.67103 0.351702
\(261\) 0 0
\(262\) 18.0191 1.11323
\(263\) −4.75709 8.23952i −0.293335 0.508070i 0.681262 0.732040i \(-0.261432\pi\)
−0.974596 + 0.223970i \(0.928098\pi\)
\(264\) 0 0
\(265\) −6.16247 + 10.6737i −0.378557 + 0.655681i
\(266\) 5.88995 10.2017i 0.361136 0.625506i
\(267\) 0 0
\(268\) 1.14150 + 1.97714i 0.0697284 + 0.120773i
\(269\) −22.1408 −1.34995 −0.674973 0.737842i \(-0.735845\pi\)
−0.674973 + 0.737842i \(0.735845\pi\)
\(270\) 0 0
\(271\) 27.9627 1.69861 0.849307 0.527899i \(-0.177020\pi\)
0.849307 + 0.527899i \(0.177020\pi\)
\(272\) 2.31505 + 4.00979i 0.140371 + 0.243129i
\(273\) 0 0
\(274\) −3.33773 + 5.78111i −0.201639 + 0.349250i
\(275\) −4.53025 + 7.84663i −0.273185 + 0.473170i
\(276\) 0 0
\(277\) 9.44184 + 16.3537i 0.567305 + 0.982601i 0.996831 + 0.0795468i \(0.0253473\pi\)
−0.429526 + 0.903054i \(0.641319\pi\)
\(278\) 17.6079 1.05605
\(279\) 0 0
\(280\) 11.1086 0.663867
\(281\) −10.0009 17.3220i −0.596602 1.03335i −0.993319 0.115404i \(-0.963184\pi\)
0.396717 0.917941i \(-0.370150\pi\)
\(282\) 0 0
\(283\) −8.37252 + 14.5016i −0.497695 + 0.862032i −0.999996 0.00266002i \(-0.999153\pi\)
0.502302 + 0.864692i \(0.332487\pi\)
\(284\) −1.38164 + 2.39307i −0.0819852 + 0.142002i
\(285\) 0 0
\(286\) −22.5270 39.0179i −1.33205 2.30717i
\(287\) −13.4744 −0.795371
\(288\) 0 0
\(289\) −16.0463 −0.943903
\(290\) −10.8993 18.8782i −0.640030 1.10856i
\(291\) 0 0
\(292\) 1.12066 1.94103i 0.0655814 0.113590i
\(293\) 9.78600 16.9499i 0.571704 0.990221i −0.424687 0.905340i \(-0.639616\pi\)
0.996391 0.0848806i \(-0.0270509\pi\)
\(294\) 0 0
\(295\) −7.59682 13.1581i −0.442304 0.766093i
\(296\) −3.11549 −0.181084
\(297\) 0 0
\(298\) −30.7437 −1.78093
\(299\) −5.54611 9.60615i −0.320740 0.555538i
\(300\) 0 0
\(301\) −13.6744 + 23.6847i −0.788178 + 1.36517i
\(302\) −0.980868 + 1.69891i −0.0564426 + 0.0977614i
\(303\) 0 0
\(304\) 6.36586 + 11.0260i 0.365107 + 0.632384i
\(305\) −2.15813 −0.123574
\(306\) 0 0
\(307\) 14.8995 0.850357 0.425179 0.905109i \(-0.360211\pi\)
0.425179 + 0.905109i \(0.360211\pi\)
\(308\) 2.83451 + 4.90952i 0.161511 + 0.279746i
\(309\) 0 0
\(310\) 1.38306 2.39553i 0.0785525 0.136057i
\(311\) 2.29618 3.97710i 0.130204 0.225521i −0.793551 0.608504i \(-0.791770\pi\)
0.923755 + 0.382983i \(0.125103\pi\)
\(312\) 0 0
\(313\) −5.93434 10.2786i −0.335429 0.580980i 0.648138 0.761523i \(-0.275548\pi\)
−0.983567 + 0.180543i \(0.942215\pi\)
\(314\) 5.57672 0.314713
\(315\) 0 0
\(316\) 2.28817 0.128719
\(317\) −7.25867 12.5724i −0.407688 0.706136i 0.586943 0.809629i \(-0.300331\pi\)
−0.994630 + 0.103493i \(0.966998\pi\)
\(318\) 0 0
\(319\) −17.0779 + 29.5797i −0.956177 + 1.65615i
\(320\) −4.35359 + 7.54064i −0.243373 + 0.421535i
\(321\) 0 0
\(322\) 3.53835 + 6.12860i 0.197185 + 0.341534i
\(323\) 2.62232 0.145910
\(324\) 0 0
\(325\) −15.0077 −0.832480
\(326\) 12.5885 + 21.8039i 0.697211 + 1.20760i
\(327\) 0 0
\(328\) 5.77234 9.99798i 0.318724 0.552046i
\(329\) −17.3673 + 30.0811i −0.957491 + 1.65842i
\(330\) 0 0
\(331\) 4.05285 + 7.01974i 0.222765 + 0.385840i 0.955647 0.294516i \(-0.0951585\pi\)
−0.732882 + 0.680356i \(0.761825\pi\)
\(332\) 2.83239 0.155448
\(333\) 0 0
\(334\) 22.8626 1.25099
\(335\) 3.89942 + 6.75400i 0.213048 + 0.369010i
\(336\) 0 0
\(337\) 9.40398 16.2882i 0.512267 0.887273i −0.487631 0.873050i \(-0.662139\pi\)
0.999899 0.0142235i \(-0.00452764\pi\)
\(338\) 27.0538 46.8586i 1.47154 2.54877i
\(339\) 0 0
\(340\) −0.402706 0.697507i −0.0218398 0.0378276i
\(341\) −4.33416 −0.234708
\(342\) 0 0
\(343\) −17.4416 −0.941760
\(344\) −11.7160 20.2927i −0.631684 1.09411i
\(345\) 0 0
\(346\) −9.95768 + 17.2472i −0.535328 + 0.927215i
\(347\) −8.80881 + 15.2573i −0.472882 + 0.819056i −0.999518 0.0310351i \(-0.990120\pi\)
0.526636 + 0.850091i \(0.323453\pi\)
\(348\) 0 0
\(349\) 8.49465 + 14.7132i 0.454708 + 0.787577i 0.998671 0.0515316i \(-0.0164103\pi\)
−0.543963 + 0.839109i \(0.683077\pi\)
\(350\) 9.57475 0.511792
\(351\) 0 0
\(352\) −11.2962 −0.602090
\(353\) −7.57780 13.1251i −0.403326 0.698580i 0.590799 0.806818i \(-0.298812\pi\)
−0.994125 + 0.108238i \(0.965479\pi\)
\(354\) 0 0
\(355\) −4.71974 + 8.17483i −0.250498 + 0.433875i
\(356\) −1.11647 + 1.93379i −0.0591729 + 0.102491i
\(357\) 0 0
\(358\) −0.233524 0.404475i −0.0123421 0.0213772i
\(359\) −2.45096 −0.129357 −0.0646783 0.997906i \(-0.520602\pi\)
−0.0646783 + 0.997906i \(0.520602\pi\)
\(360\) 0 0
\(361\) −11.7892 −0.620485
\(362\) 1.12106 + 1.94174i 0.0589218 + 0.102055i
\(363\) 0 0
\(364\) −4.69506 + 8.13208i −0.246088 + 0.426237i
\(365\) 3.82821 6.63065i 0.200378 0.347064i
\(366\) 0 0
\(367\) 0.656767 + 1.13755i 0.0342829 + 0.0593798i 0.882658 0.470016i \(-0.155752\pi\)
−0.848375 + 0.529396i \(0.822419\pi\)
\(368\) −7.64850 −0.398706
\(369\) 0 0
\(370\) 3.46628 0.180203
\(371\) −10.2039 17.6736i −0.529758 0.917567i
\(372\) 0 0
\(373\) 4.81309 8.33651i 0.249212 0.431648i −0.714095 0.700048i \(-0.753162\pi\)
0.963307 + 0.268400i \(0.0864950\pi\)
\(374\) −3.19933 + 5.54140i −0.165433 + 0.286539i
\(375\) 0 0
\(376\) −14.8800 25.7730i −0.767379 1.32914i
\(377\) −56.5753 −2.91377
\(378\) 0 0
\(379\) −8.56311 −0.439857 −0.219929 0.975516i \(-0.570582\pi\)
−0.219929 + 0.975516i \(0.570582\pi\)
\(380\) −1.10735 1.91798i −0.0568057 0.0983904i
\(381\) 0 0
\(382\) −16.2766 + 28.1918i −0.832782 + 1.44242i
\(383\) 16.8173 29.1284i 0.859324 1.48839i −0.0132498 0.999912i \(-0.504218\pi\)
0.872574 0.488481i \(-0.162449\pi\)
\(384\) 0 0
\(385\) 9.68282 + 16.7711i 0.493482 + 0.854736i
\(386\) 33.0769 1.68357
\(387\) 0 0
\(388\) 4.21363 0.213915
\(389\) −7.47699 12.9505i −0.379098 0.656618i 0.611833 0.790987i \(-0.290433\pi\)
−0.990931 + 0.134369i \(0.957099\pi\)
\(390\) 0 0
\(391\) −0.787671 + 1.36429i −0.0398343 + 0.0689950i
\(392\) −0.862496 + 1.49389i −0.0435626 + 0.0754527i
\(393\) 0 0
\(394\) 7.57335 + 13.1174i 0.381540 + 0.660846i
\(395\) 7.81648 0.393290
\(396\) 0 0
\(397\) −16.7788 −0.842102 −0.421051 0.907037i \(-0.638339\pi\)
−0.421051 + 0.907037i \(0.638339\pi\)
\(398\) −8.43788 14.6148i −0.422953 0.732576i
\(399\) 0 0
\(400\) −5.17419 + 8.96197i −0.258710 + 0.448098i
\(401\) 6.56315 11.3677i 0.327748 0.567676i −0.654317 0.756221i \(-0.727044\pi\)
0.982065 + 0.188545i \(0.0603770\pi\)
\(402\) 0 0
\(403\) −3.58953 6.21725i −0.178807 0.309704i
\(404\) −3.83541 −0.190819
\(405\) 0 0
\(406\) 36.0943 1.79133
\(407\) −2.71561 4.70358i −0.134608 0.233148i
\(408\) 0 0
\(409\) −12.7253 + 22.0408i −0.629223 + 1.08985i 0.358485 + 0.933536i \(0.383294\pi\)
−0.987708 + 0.156311i \(0.950040\pi\)
\(410\) −6.42228 + 11.1237i −0.317174 + 0.549361i
\(411\) 0 0
\(412\) 0.532179 + 0.921761i 0.0262186 + 0.0454119i
\(413\) 25.1577 1.23793
\(414\) 0 0
\(415\) 9.67558 0.474955
\(416\) −9.35547 16.2041i −0.458689 0.794474i
\(417\) 0 0
\(418\) −8.79742 + 15.2376i −0.430296 + 0.745294i
\(419\) −6.33503 + 10.9726i −0.309486 + 0.536046i −0.978250 0.207429i \(-0.933490\pi\)
0.668764 + 0.743475i \(0.266824\pi\)
\(420\) 0 0
\(421\) 8.83862 + 15.3089i 0.430768 + 0.746112i 0.996940 0.0781752i \(-0.0249094\pi\)
−0.566172 + 0.824287i \(0.691576\pi\)
\(422\) 23.7554 1.15639
\(423\) 0 0
\(424\) 17.4850 0.849146
\(425\) 1.06572 + 1.84587i 0.0516948 + 0.0895381i
\(426\) 0 0
\(427\) 1.78672 3.09469i 0.0864654 0.149762i
\(428\) −3.09187 + 5.35528i −0.149451 + 0.258857i
\(429\) 0 0
\(430\) 13.0352 + 22.5776i 0.628612 + 1.08879i
\(431\) −15.6974 −0.756117 −0.378059 0.925782i \(-0.623408\pi\)
−0.378059 + 0.925782i \(0.623408\pi\)
\(432\) 0 0
\(433\) −12.6258 −0.606759 −0.303380 0.952870i \(-0.598115\pi\)
−0.303380 + 0.952870i \(0.598115\pi\)
\(434\) 2.29008 + 3.96653i 0.109927 + 0.190400i
\(435\) 0 0
\(436\) 3.00073 5.19742i 0.143709 0.248912i
\(437\) −2.16591 + 3.75147i −0.103610 + 0.179457i
\(438\) 0 0
\(439\) −13.4685 23.3281i −0.642814 1.11339i −0.984802 0.173683i \(-0.944433\pi\)
0.341987 0.939705i \(-0.388900\pi\)
\(440\) −16.5922 −0.791001
\(441\) 0 0
\(442\) −10.5987 −0.504128
\(443\) 17.3639 + 30.0752i 0.824986 + 1.42892i 0.901930 + 0.431882i \(0.142150\pi\)
−0.0769438 + 0.997035i \(0.524516\pi\)
\(444\) 0 0
\(445\) −3.81392 + 6.60590i −0.180797 + 0.313150i
\(446\) −9.69780 + 16.7971i −0.459204 + 0.795365i
\(447\) 0 0
\(448\) −7.20870 12.4858i −0.340579 0.589900i
\(449\) 20.7461 0.979070 0.489535 0.871984i \(-0.337166\pi\)
0.489535 + 0.871984i \(0.337166\pi\)
\(450\) 0 0
\(451\) 20.1258 0.947688
\(452\) −0.110761 0.191843i −0.00520974 0.00902354i
\(453\) 0 0
\(454\) −2.96153 + 5.12952i −0.138991 + 0.240740i
\(455\) −16.0385 + 27.7796i −0.751898 + 1.30233i
\(456\) 0 0
\(457\) 3.60387 + 6.24208i 0.168582 + 0.291992i 0.937921 0.346848i \(-0.112748\pi\)
−0.769340 + 0.638840i \(0.779415\pi\)
\(458\) 29.3621 1.37200
\(459\) 0 0
\(460\) 1.33046 0.0620332
\(461\) 11.5634 + 20.0284i 0.538562 + 0.932817i 0.998982 + 0.0451156i \(0.0143656\pi\)
−0.460420 + 0.887701i \(0.652301\pi\)
\(462\) 0 0
\(463\) −2.48792 + 4.30921i −0.115623 + 0.200266i −0.918029 0.396514i \(-0.870220\pi\)
0.802405 + 0.596779i \(0.203553\pi\)
\(464\) −19.5054 + 33.7843i −0.905513 + 1.56840i
\(465\) 0 0
\(466\) −0.430734 0.746053i −0.0199534 0.0345602i
\(467\) 12.4814 0.577569 0.288784 0.957394i \(-0.406749\pi\)
0.288784 + 0.957394i \(0.406749\pi\)
\(468\) 0 0
\(469\) −12.9134 −0.596284
\(470\) 16.5555 + 28.6749i 0.763647 + 1.32268i
\(471\) 0 0
\(472\) −10.7774 + 18.6669i −0.496068 + 0.859216i
\(473\) 20.4245 35.3762i 0.939119 1.62660i
\(474\) 0 0
\(475\) 2.93047 + 5.07573i 0.134459 + 0.232890i
\(476\) 1.33361 0.0611257
\(477\) 0 0
\(478\) −31.7176 −1.45073
\(479\) 14.2356 + 24.6568i 0.650443 + 1.12660i 0.983016 + 0.183522i \(0.0587499\pi\)
−0.332573 + 0.943078i \(0.607917\pi\)
\(480\) 0 0
\(481\) 4.49812 7.79097i 0.205097 0.355238i
\(482\) 12.0679 20.9023i 0.549679 0.952072i
\(483\) 0 0
\(484\) −1.53124 2.65218i −0.0696016 0.120554i
\(485\) 14.3939 0.653595
\(486\) 0 0
\(487\) 29.6841 1.34511 0.672557 0.740045i \(-0.265196\pi\)
0.672557 + 0.740045i \(0.265196\pi\)
\(488\) 1.53083 + 2.65148i 0.0692975 + 0.120027i
\(489\) 0 0
\(490\) 0.959610 1.66209i 0.0433508 0.0750857i
\(491\) 6.20248 10.7430i 0.279914 0.484825i −0.691449 0.722425i \(-0.743027\pi\)
0.971363 + 0.237600i \(0.0763608\pi\)
\(492\) 0 0
\(493\) 4.01747 + 6.95846i 0.180938 + 0.313394i
\(494\) −29.1439 −1.31125
\(495\) 0 0
\(496\) −4.95023 −0.222272
\(497\) −7.81497 13.5359i −0.350549 0.607169i
\(498\) 0 0
\(499\) 1.13991 1.97438i 0.0510294 0.0883856i −0.839382 0.543541i \(-0.817083\pi\)
0.890412 + 0.455156i \(0.150416\pi\)
\(500\) 2.96193 5.13022i 0.132462 0.229430i
\(501\) 0 0
\(502\) −10.0673 17.4371i −0.449326 0.778256i
\(503\) −41.2812 −1.84064 −0.920320 0.391167i \(-0.872071\pi\)
−0.920320 + 0.391167i \(0.872071\pi\)
\(504\) 0 0
\(505\) −13.1019 −0.583028
\(506\) −5.28499 9.15387i −0.234947 0.406939i
\(507\) 0 0
\(508\) 0.130473 0.225986i 0.00578880 0.0100265i
\(509\) 8.21208 14.2237i 0.363994 0.630456i −0.624620 0.780929i \(-0.714746\pi\)
0.988614 + 0.150473i \(0.0480796\pi\)
\(510\) 0 0
\(511\) 6.33877 + 10.9791i 0.280411 + 0.485685i
\(512\) 9.67844 0.427731
\(513\) 0 0
\(514\) −20.6845 −0.912355
\(515\) 1.81795 + 3.14878i 0.0801083 + 0.138752i
\(516\) 0 0
\(517\) 25.9404 44.9300i 1.14086 1.97602i
\(518\) −2.86974 + 4.97054i −0.126089 + 0.218393i
\(519\) 0 0
\(520\) −13.7416 23.8011i −0.602607 1.04375i
\(521\) 9.29672 0.407297 0.203648 0.979044i \(-0.434720\pi\)
0.203648 + 0.979044i \(0.434720\pi\)
\(522\) 0 0
\(523\) −22.7471 −0.994662 −0.497331 0.867561i \(-0.665686\pi\)
−0.497331 + 0.867561i \(0.665686\pi\)
\(524\) 2.80469 + 4.85787i 0.122524 + 0.212217i
\(525\) 0 0
\(526\) 7.50861 13.0053i 0.327391 0.567058i
\(527\) −0.509794 + 0.882988i −0.0222070 + 0.0384636i
\(528\) 0 0
\(529\) 10.1988 + 17.6649i 0.443428 + 0.768040i
\(530\) −19.4537 −0.845016
\(531\) 0 0
\(532\) 3.66710 0.158989
\(533\) 16.6681 + 28.8700i 0.721976 + 1.25050i
\(534\) 0 0
\(535\) −10.5620 + 18.2939i −0.456634 + 0.790913i
\(536\) 5.53199 9.58168i 0.238945 0.413866i
\(537\) 0 0
\(538\) −17.4735 30.2651i −0.753338 1.30482i
\(539\) −3.00718 −0.129528
\(540\) 0 0
\(541\) 2.38959 0.102737 0.0513683 0.998680i \(-0.483642\pi\)
0.0513683 + 0.998680i \(0.483642\pi\)
\(542\) 22.0682 + 38.2233i 0.947912 + 1.64183i
\(543\) 0 0
\(544\) −1.32868 + 2.30135i −0.0569669 + 0.0986695i
\(545\) 10.2506 17.7546i 0.439089 0.760525i
\(546\) 0 0
\(547\) −14.8334 25.6922i −0.634230 1.09852i −0.986678 0.162687i \(-0.947984\pi\)
0.352448 0.935832i \(-0.385349\pi\)
\(548\) −2.07808 −0.0887712
\(549\) 0 0
\(550\) −14.3011 −0.609803
\(551\) 11.0471 + 19.1342i 0.470623 + 0.815143i
\(552\) 0 0
\(553\) −6.47128 + 11.2086i −0.275187 + 0.476638i
\(554\) −14.9030 + 25.8128i −0.633169 + 1.09668i
\(555\) 0 0
\(556\) 2.74069 + 4.74701i 0.116231 + 0.201318i
\(557\) −8.41413 −0.356518 −0.178259 0.983984i \(-0.557046\pi\)
−0.178259 + 0.983984i \(0.557046\pi\)
\(558\) 0 0
\(559\) 67.6619 2.86179
\(560\) 11.0592 + 19.1550i 0.467335 + 0.809447i
\(561\) 0 0
\(562\) 15.7854 27.3411i 0.665868 1.15332i
\(563\) −13.6133 + 23.5788i −0.573730 + 0.993730i 0.422448 + 0.906387i \(0.361171\pi\)
−0.996178 + 0.0873428i \(0.972162\pi\)
\(564\) 0 0
\(565\) −0.378363 0.655345i −0.0159179 0.0275706i
\(566\) −26.4304 −1.11095
\(567\) 0 0
\(568\) 13.3915 0.561894
\(569\) −10.9747 19.0087i −0.460082 0.796885i 0.538883 0.842381i \(-0.318846\pi\)
−0.998965 + 0.0454960i \(0.985513\pi\)
\(570\) 0 0
\(571\) 22.4267 38.8442i 0.938530 1.62558i 0.170314 0.985390i \(-0.445522\pi\)
0.768216 0.640191i \(-0.221145\pi\)
\(572\) 7.01269 12.1463i 0.293215 0.507863i
\(573\) 0 0
\(574\) −10.6340 18.4187i −0.443857 0.768782i
\(575\) −3.52092 −0.146833
\(576\) 0 0
\(577\) 12.0191 0.500361 0.250181 0.968199i \(-0.419510\pi\)
0.250181 + 0.968199i \(0.419510\pi\)
\(578\) −12.6638 21.9344i −0.526745 0.912349i
\(579\) 0 0
\(580\) 3.39298 5.87681i 0.140886 0.244021i
\(581\) −8.01043 + 13.8745i −0.332329 + 0.575610i
\(582\) 0 0
\(583\) 15.2408 + 26.3978i 0.631209 + 1.09329i
\(584\) −10.8619 −0.449469
\(585\) 0 0
\(586\) 30.8925 1.27616
\(587\) −8.51493 14.7483i −0.351449 0.608727i 0.635055 0.772467i \(-0.280978\pi\)
−0.986504 + 0.163740i \(0.947644\pi\)
\(588\) 0 0
\(589\) −1.40181 + 2.42801i −0.0577607 + 0.100045i
\(590\) 11.9909 20.7688i 0.493656 0.855037i
\(591\) 0 0
\(592\) −3.10162 5.37216i −0.127476 0.220794i
\(593\) 14.9284 0.613037 0.306519 0.951865i \(-0.400836\pi\)
0.306519 + 0.951865i \(0.400836\pi\)
\(594\) 0 0
\(595\) 4.55566 0.186764
\(596\) −4.78528 8.28835i −0.196013 0.339504i
\(597\) 0 0
\(598\) 8.75401 15.1624i 0.357978 0.620036i
\(599\) 6.76740 11.7215i 0.276508 0.478927i −0.694006 0.719969i \(-0.744156\pi\)
0.970515 + 0.241042i \(0.0774893\pi\)
\(600\) 0 0
\(601\) 22.6586 + 39.2459i 0.924265 + 1.60087i 0.792739 + 0.609561i \(0.208654\pi\)
0.131525 + 0.991313i \(0.458013\pi\)
\(602\) −43.1674 −1.75937
\(603\) 0 0
\(604\) −0.610691 −0.0248487
\(605\) −5.23077 9.05996i −0.212661 0.368340i
\(606\) 0 0
\(607\) −12.2184 + 21.1629i −0.495929 + 0.858975i −0.999989 0.00469404i \(-0.998506\pi\)
0.504060 + 0.863669i \(0.331839\pi\)
\(608\) −3.65357 + 6.32817i −0.148172 + 0.256641i
\(609\) 0 0
\(610\) −1.70320 2.95003i −0.0689605 0.119443i
\(611\) 85.9348 3.47655
\(612\) 0 0
\(613\) −25.1996 −1.01780 −0.508901 0.860825i \(-0.669948\pi\)
−0.508901 + 0.860825i \(0.669948\pi\)
\(614\) 11.7587 + 20.3666i 0.474542 + 0.821931i
\(615\) 0 0
\(616\) 13.7367 23.7927i 0.553467 0.958634i
\(617\) 2.02093 3.50034i 0.0813594 0.140919i −0.822475 0.568802i \(-0.807407\pi\)
0.903834 + 0.427883i \(0.140741\pi\)
\(618\) 0 0
\(619\) 22.3850 + 38.7719i 0.899729 + 1.55838i 0.827841 + 0.560964i \(0.189569\pi\)
0.0718884 + 0.997413i \(0.477097\pi\)
\(620\) 0.861097 0.0345825
\(621\) 0 0
\(622\) 7.24860 0.290642
\(623\) −6.31511 10.9381i −0.253010 0.438225i
\(624\) 0 0
\(625\) 4.66157 8.07408i 0.186463 0.322963i
\(626\) 9.36679 16.2238i 0.374372 0.648432i
\(627\) 0 0
\(628\) 0.868022 + 1.50346i 0.0346378 + 0.0599945i
\(629\) −1.27767 −0.0509439
\(630\) 0 0
\(631\) 31.4116 1.25048 0.625238 0.780434i \(-0.285002\pi\)
0.625238 + 0.780434i \(0.285002\pi\)
\(632\) −5.54449 9.60334i −0.220548 0.382000i
\(633\) 0 0
\(634\) 11.4571 19.8443i 0.455020 0.788118i
\(635\) 0.445701 0.771978i 0.0176871 0.0306350i
\(636\) 0 0
\(637\) −2.49053 4.31373i −0.0986784 0.170916i
\(638\) −53.9116 −2.13438
\(639\) 0 0
\(640\) −22.8785 −0.904351
\(641\) 24.3203 + 42.1240i 0.960594 + 1.66380i 0.721013 + 0.692922i \(0.243677\pi\)
0.239581 + 0.970876i \(0.422990\pi\)
\(642\) 0 0
\(643\) 14.0162 24.2767i 0.552744 0.957381i −0.445331 0.895366i \(-0.646914\pi\)
0.998075 0.0620150i \(-0.0197527\pi\)
\(644\) −1.10149 + 1.90784i −0.0434050 + 0.0751796i
\(645\) 0 0
\(646\) 2.06954 + 3.58455i 0.0814251 + 0.141032i
\(647\) 37.5519 1.47632 0.738159 0.674627i \(-0.235696\pi\)
0.738159 + 0.674627i \(0.235696\pi\)
\(648\) 0 0
\(649\) −37.5763 −1.47500
\(650\) −11.8441 20.5147i −0.464565 0.804651i
\(651\) 0 0
\(652\) −3.91881 + 6.78758i −0.153472 + 0.265822i
\(653\) −2.55611 + 4.42731i −0.100028 + 0.173254i −0.911696 0.410865i \(-0.865227\pi\)
0.811668 + 0.584119i \(0.198560\pi\)
\(654\) 0 0
\(655\) 9.58095 + 16.5947i 0.374359 + 0.648408i
\(656\) 22.9866 0.897474
\(657\) 0 0
\(658\) −54.8253 −2.13731
\(659\) 17.5030 + 30.3160i 0.681818 + 1.18094i 0.974425 + 0.224711i \(0.0721439\pi\)
−0.292607 + 0.956233i \(0.594523\pi\)
\(660\) 0 0
\(661\) −0.666731 + 1.15481i −0.0259328 + 0.0449170i −0.878701 0.477373i \(-0.841589\pi\)
0.852768 + 0.522290i \(0.174922\pi\)
\(662\) −6.39704 + 11.0800i −0.248628 + 0.430636i
\(663\) 0 0
\(664\) −6.86321 11.8874i −0.266344 0.461322i
\(665\) 12.5270 0.485776
\(666\) 0 0
\(667\) −13.2730 −0.513931
\(668\) 3.55859 + 6.16365i 0.137686 + 0.238479i
\(669\) 0 0
\(670\) −6.15487 + 10.6605i −0.237783 + 0.411853i
\(671\) −2.66870 + 4.62232i −0.103024 + 0.178443i
\(672\) 0 0
\(673\) 1.78976 + 3.09996i 0.0689904 + 0.119495i 0.898457 0.439061i \(-0.144689\pi\)
−0.829467 + 0.558556i \(0.811356\pi\)
\(674\) 29.6866 1.14348
\(675\) 0 0
\(676\) 16.8438 0.647839
\(677\) −18.4694 31.9900i −0.709839 1.22948i −0.964917 0.262556i \(-0.915435\pi\)
0.255078 0.966920i \(-0.417899\pi\)
\(678\) 0 0
\(679\) −11.9168 + 20.6405i −0.457324 + 0.792109i
\(680\) −1.95161 + 3.38028i −0.0748407 + 0.129628i
\(681\) 0 0
\(682\) −3.42053 5.92453i −0.130979 0.226862i
\(683\) −38.0166 −1.45466 −0.727332 0.686286i \(-0.759240\pi\)
−0.727332 + 0.686286i \(0.759240\pi\)
\(684\) 0 0
\(685\) −7.09881 −0.271232
\(686\) −13.7650 23.8416i −0.525549 0.910278i
\(687\) 0 0
\(688\) 23.3277 40.4047i 0.889359 1.54041i
\(689\) −25.2447 + 43.7251i −0.961746 + 1.66579i
\(690\) 0 0
\(691\) −0.275232 0.476716i −0.0104703 0.0181351i 0.860743 0.509040i \(-0.170000\pi\)
−0.871213 + 0.490905i \(0.836666\pi\)
\(692\) −6.19968 −0.235677
\(693\) 0 0
\(694\) −27.8077 −1.05557
\(695\) 9.36232 + 16.2160i 0.355133 + 0.615108i
\(696\) 0 0
\(697\) 2.36724 4.10019i 0.0896657 0.155306i
\(698\) −13.4080 + 23.2233i −0.507500 + 0.879015i
\(699\) 0 0
\(700\) 1.49032 + 2.58131i 0.0563287 + 0.0975642i
\(701\) −19.0242 −0.718534 −0.359267 0.933235i \(-0.616973\pi\)
−0.359267 + 0.933235i \(0.616973\pi\)
\(702\) 0 0
\(703\) −3.51328 −0.132506
\(704\) 10.7671 + 18.6492i 0.405802 + 0.702869i
\(705\) 0 0
\(706\) 11.9608 20.7168i 0.450152 0.779686i
\(707\) 10.8471 18.7878i 0.407948 0.706587i
\(708\) 0 0
\(709\) −6.07839 10.5281i −0.228279 0.395390i 0.729019 0.684493i \(-0.239976\pi\)
−0.957298 + 0.289103i \(0.906643\pi\)
\(710\) −14.8993 −0.559161
\(711\) 0 0
\(712\) 10.8214 0.405548
\(713\) −0.842130 1.45861i −0.0315380 0.0546255i
\(714\) 0 0
\(715\) 23.9557 41.4924i 0.895891 1.55173i
\(716\) 0.0726963 0.125914i 0.00271679 0.00470562i
\(717\) 0 0
\(718\) −1.93430 3.35031i −0.0721875 0.125032i
\(719\) −9.77667 −0.364608 −0.182304 0.983242i \(-0.558356\pi\)
−0.182304 + 0.983242i \(0.558356\pi\)
\(720\) 0 0
\(721\) −6.02033 −0.224209
\(722\) −9.30408 16.1151i −0.346262 0.599743i
\(723\) 0 0
\(724\) −0.348989 + 0.604466i −0.0129701 + 0.0224648i
\(725\) −8.97913 + 15.5523i −0.333477 + 0.577598i
\(726\) 0 0
\(727\) −2.16746 3.75416i −0.0803868 0.139234i 0.823029 0.567999i \(-0.192282\pi\)
−0.903416 + 0.428765i \(0.858949\pi\)
\(728\) 45.5067 1.68659
\(729\) 0 0
\(730\) 12.0849 0.447283
\(731\) −4.80474 8.32206i −0.177710 0.307803i
\(732\) 0 0
\(733\) −14.5968 + 25.2824i −0.539146 + 0.933829i 0.459804 + 0.888020i \(0.347920\pi\)
−0.998950 + 0.0458082i \(0.985414\pi\)
\(734\) −1.03664 + 1.79552i −0.0382632 + 0.0662738i
\(735\) 0 0
\(736\) −2.19486 3.80161i −0.0809036 0.140129i
\(737\) 19.2878 0.710476
\(738\) 0 0
\(739\) 41.5553 1.52864 0.764319 0.644838i \(-0.223075\pi\)
0.764319 + 0.644838i \(0.223075\pi\)
\(740\) 0.539529 + 0.934492i 0.0198335 + 0.0343526i
\(741\) 0 0
\(742\) 16.1058 27.8961i 0.591263 1.02410i
\(743\) 10.6887 18.5133i 0.392130 0.679188i −0.600601 0.799549i \(-0.705072\pi\)
0.992730 + 0.120361i \(0.0384051\pi\)
\(744\) 0 0
\(745\) −16.3467 28.3134i −0.598898 1.03732i
\(746\) 15.1940 0.556291
\(747\) 0 0
\(748\) −1.99191 −0.0728316
\(749\) −17.4886 30.2911i −0.639018 1.10681i
\(750\) 0 0
\(751\) 19.9838 34.6130i 0.729220 1.26305i −0.227994 0.973663i \(-0.573217\pi\)
0.957213 0.289383i \(-0.0934500\pi\)
\(752\) 29.6276 51.3165i 1.08041 1.87132i
\(753\) 0 0
\(754\) −44.6493 77.3349i −1.62603 2.81637i
\(755\) −2.08615 −0.0759228
\(756\) 0 0
\(757\) 6.68348 0.242915 0.121458 0.992597i \(-0.461243\pi\)
0.121458 + 0.992597i \(0.461243\pi\)
\(758\) −6.75803 11.7052i −0.245463 0.425154i
\(759\) 0 0
\(760\) −5.36646 + 9.29499i −0.194662 + 0.337165i
\(761\) 21.0125 36.3947i 0.761703 1.31931i −0.180269 0.983617i \(-0.557697\pi\)
0.941972 0.335691i \(-0.108970\pi\)
\(762\) 0 0
\(763\) 16.9731 + 29.3982i 0.614467 + 1.06429i
\(764\) −10.1338 −0.366630
\(765\) 0 0
\(766\) 53.0890 1.91818
\(767\) −31.1206 53.9024i −1.12370 1.94630i
\(768\) 0 0
\(769\) −1.20662 + 2.08992i −0.0435117 + 0.0753644i −0.886961 0.461844i \(-0.847188\pi\)
0.843449 + 0.537209i \(0.180521\pi\)
\(770\) −15.2834 + 26.4716i −0.550776 + 0.953971i
\(771\) 0 0
\(772\) 5.14845 + 8.91738i 0.185297 + 0.320944i
\(773\) −1.39780 −0.0502754 −0.0251377 0.999684i \(-0.508002\pi\)
−0.0251377 + 0.999684i \(0.508002\pi\)
\(774\) 0 0
\(775\) −2.27880 −0.0818569
\(776\) −10.2101 17.6844i −0.366522 0.634834i
\(777\) 0 0
\(778\) 11.8017 20.4412i 0.423112 0.732851i
\(779\) 6.50937 11.2746i 0.233222 0.403953i
\(780\) 0 0
\(781\) 11.6727 + 20.2177i 0.417682 + 0.723446i
\(782\) −2.48653 −0.0889181
\(783\) 0 0
\(784\) −3.43462 −0.122665
\(785\) 2.96520 + 5.13588i 0.105833 + 0.183307i
\(786\) 0 0
\(787\) 19.8258 34.3392i 0.706712 1.22406i −0.259358 0.965781i \(-0.583511\pi\)
0.966070 0.258280i \(-0.0831558\pi\)
\(788\) −2.35760 + 4.08348i −0.0839859 + 0.145468i
\(789\) 0 0
\(790\) 6.16878 + 10.6846i 0.219475 + 0.380142i
\(791\) 1.25299 0.0445513
\(792\) 0 0
\(793\) −8.84082 −0.313947
\(794\) −13.2418 22.9355i −0.469935 0.813952i
\(795\) 0 0
\(796\) 2.62673 4.54963i 0.0931019 0.161257i
\(797\) −1.64693 + 2.85257i −0.0583374 + 0.101043i −0.893719 0.448627i \(-0.851913\pi\)
0.835382 + 0.549670i \(0.185247\pi\)
\(798\) 0 0
\(799\) −6.10232 10.5695i −0.215885 0.373923i
\(800\) −5.93927 −0.209985
\(801\) 0 0
\(802\) 20.7186 0.731599
\(803\) −9.46778 16.3987i −0.334111 0.578697i
\(804\) 0 0
\(805\) −3.76276 + 6.51728i −0.132620 + 0.229704i
\(806\) 5.66573 9.81334i 0.199567 0.345660i
\(807\) 0 0
\(808\) 9.29364 + 16.0971i 0.326949 + 0.566293i
\(809\) 6.54436 0.230087 0.115044 0.993360i \(-0.463299\pi\)
0.115044 + 0.993360i \(0.463299\pi\)
\(810\) 0 0
\(811\) −44.7516 −1.57144 −0.785721 0.618581i \(-0.787708\pi\)
−0.785721 + 0.618581i \(0.787708\pi\)
\(812\) 5.61811 + 9.73085i 0.197157 + 0.341486i
\(813\) 0 0
\(814\) 4.28634 7.42415i 0.150236 0.260216i
\(815\) −13.3868 + 23.1867i −0.468920 + 0.812194i
\(816\) 0 0
\(817\) −13.2119 22.8837i −0.462227 0.800600i
\(818\) −40.1712 −1.40455
\(819\) 0 0
\(820\) −3.99853 −0.139635
\(821\) −24.8420 43.0276i −0.866991 1.50167i −0.865057 0.501674i \(-0.832718\pi\)
−0.00193455 0.999998i \(-0.500616\pi\)
\(822\) 0 0
\(823\) −5.31031 + 9.19772i −0.185106 + 0.320612i −0.943612 0.331053i \(-0.892596\pi\)
0.758506 + 0.651666i \(0.225929\pi\)
\(824\) 2.57906 4.46707i 0.0898459 0.155618i
\(825\) 0 0
\(826\) 19.8545 + 34.3890i 0.690827 + 1.19655i
\(827\) 16.4008 0.570311 0.285156 0.958481i \(-0.407955\pi\)
0.285156 + 0.958481i \(0.407955\pi\)
\(828\) 0 0
\(829\) −2.95645 −0.102682 −0.0513409 0.998681i \(-0.516350\pi\)
−0.0513409 + 0.998681i \(0.516350\pi\)
\(830\) 7.63598 + 13.2259i 0.265049 + 0.459078i
\(831\) 0 0
\(832\) −17.8346 + 30.8904i −0.618303 + 1.07093i
\(833\) −0.353711 + 0.612645i −0.0122553 + 0.0212269i
\(834\) 0 0
\(835\) 12.1563 + 21.0553i 0.420686 + 0.728649i
\(836\) −5.47730 −0.189436
\(837\) 0 0
\(838\) −19.9985 −0.690835
\(839\) −16.2232 28.0994i −0.560088 0.970100i −0.997488 0.0708334i \(-0.977434\pi\)
0.437401 0.899267i \(-0.355899\pi\)
\(840\) 0 0
\(841\) −19.3490 + 33.5134i −0.667206 + 1.15563i
\(842\) −13.9509 + 24.1637i −0.480780 + 0.832736i
\(843\) 0 0
\(844\) 3.69754 + 6.40433i 0.127275 + 0.220446i
\(845\) 57.5392 1.97941
\(846\) 0 0
\(847\) 17.3223 0.595201
\(848\) 17.4071 + 30.1501i 0.597764 + 1.03536i
\(849\) 0 0
\(850\) −1.68213 + 2.91354i −0.0576966 + 0.0999335i
\(851\) 1.05529 1.82782i 0.0361749 0.0626568i
\(852\) 0 0
\(853\) −14.1665 24.5372i −0.485053 0.840137i 0.514799 0.857311i \(-0.327867\pi\)
−0.999853 + 0.0171737i \(0.994533\pi\)
\(854\) 5.64033 0.193008
\(855\) 0 0
\(856\) 29.9678 1.02428
\(857\) 7.00173 + 12.1274i 0.239175 + 0.414262i 0.960478 0.278357i \(-0.0897899\pi\)
−0.721303 + 0.692620i \(0.756457\pi\)
\(858\) 0 0
\(859\) 1.07989 1.87042i 0.0368452 0.0638178i −0.847015 0.531569i \(-0.821602\pi\)
0.883860 + 0.467752i \(0.154936\pi\)
\(860\) −4.05787 + 7.02844i −0.138372 + 0.239668i
\(861\) 0 0
\(862\) −12.3884 21.4574i −0.421951 0.730841i
\(863\) 14.9487 0.508859 0.254430 0.967091i \(-0.418112\pi\)
0.254430 + 0.967091i \(0.418112\pi\)
\(864\) 0 0
\(865\) −21.1784 −0.720087
\(866\) −9.96434 17.2588i −0.338602 0.586476i
\(867\) 0 0
\(868\) −0.712905 + 1.23479i −0.0241976 + 0.0419114i
\(869\) 9.66571 16.7415i 0.327887 0.567916i
\(870\) 0 0
\(871\) 15.9741 + 27.6679i 0.541261 + 0.937492i
\(872\) −29.0845 −0.984926
\(873\) 0 0
\(874\) −6.83737 −0.231278
\(875\) 16.7536 + 29.0181i 0.566375 + 0.980991i
\(876\) 0 0
\(877\) 0.943539 1.63426i 0.0318611 0.0551850i −0.849655 0.527339i \(-0.823190\pi\)
0.881516 + 0.472154i \(0.156523\pi\)
\(878\) 21.2587 36.8211i 0.717445 1.24265i
\(879\) 0 0
\(880\) −16.5183 28.6105i −0.556832 0.964461i
\(881\) −46.8258 −1.57760 −0.788800 0.614649i \(-0.789297\pi\)
−0.788800 + 0.614649i \(0.789297\pi\)
\(882\) 0 0
\(883\) −30.0635 −1.01172 −0.505858 0.862617i \(-0.668824\pi\)
−0.505858 + 0.862617i \(0.668824\pi\)
\(884\) −1.64969 2.85735i −0.0554852 0.0961032i
\(885\) 0 0
\(886\) −27.4073 + 47.4709i −0.920767 + 1.59482i
\(887\) −14.9569 + 25.9062i −0.502205 + 0.869844i 0.497792 + 0.867296i \(0.334144\pi\)
−0.999997 + 0.00254744i \(0.999189\pi\)
\(888\) 0 0
\(889\) 0.737995 + 1.27824i 0.0247516 + 0.0428709i
\(890\) −12.0398 −0.403576
\(891\) 0 0
\(892\) −6.03788 −0.202163
\(893\) −16.7800 29.0638i −0.561520 0.972582i
\(894\) 0 0
\(895\) 0.248334 0.430127i 0.00830089 0.0143776i
\(896\) 18.9412 32.8070i 0.632780 1.09601i
\(897\) 0 0
\(898\) 16.3729 + 28.3587i 0.546370 + 0.946341i
\(899\) −8.59047 −0.286508
\(900\) 0 0
\(901\) 7.17062 0.238888
\(902\) 15.8833 + 27.5108i 0.528858 + 0.916008i
\(903\) 0 0
\(904\) −0.536772 + 0.929716i −0.0178528 + 0.0309219i
\(905\) −1.19216 + 2.06488i −0.0396288 + 0.0686391i
\(906\) 0 0
\(907\) −13.3826 23.1794i −0.444363 0.769659i 0.553645 0.832753i \(-0.313236\pi\)
−0.998008 + 0.0630942i \(0.979903\pi\)
\(908\) −1.84386 −0.0611905
\(909\) 0 0
\(910\) −50.6306 −1.67839
\(911\) 0.220569 + 0.382036i 0.00730776 + 0.0126574i 0.869656 0.493658i \(-0.164341\pi\)
−0.862348 + 0.506315i \(0.831007\pi\)
\(912\) 0 0
\(913\) 11.9646 20.7234i 0.395972 0.685843i
\(914\) −5.68836 + 9.85253i −0.188154 + 0.325893i
\(915\) 0 0
\(916\) 4.57024 + 7.91589i 0.151005 + 0.261548i
\(917\) −31.7284 −1.04776
\(918\) 0 0
\(919\) 49.0749 1.61883 0.809416 0.587236i \(-0.199784\pi\)
0.809416 + 0.587236i \(0.199784\pi\)
\(920\) −3.22387 5.58390i −0.106288 0.184096i
\(921\) 0 0
\(922\) −18.2517 + 31.6130i −0.601089 + 1.04112i
\(923\) −19.3345 + 33.4884i −0.636404 + 1.10228i
\(924\) 0 0
\(925\) −1.42780 2.47303i −0.0469459 0.0813127i
\(926\) −7.85389 −0.258095
\(927\) 0 0
\(928\) −22.3895 −0.734972
\(929\) 16.2156 + 28.0863i 0.532017 + 0.921481i 0.999301 + 0.0373737i \(0.0118992\pi\)
−0.467284 + 0.884107i \(0.654767\pi\)
\(930\) 0 0
\(931\) −0.972622 + 1.68463i −0.0318764 + 0.0552116i
\(932\) 0.134088 0.232247i 0.00439220 0.00760752i
\(933\) 0 0
\(934\) 9.85032 + 17.0613i 0.322312 + 0.558261i
\(935\) −6.80447 −0.222530
\(936\) 0 0
\(937\) 48.6157 1.58821 0.794103 0.607783i \(-0.207941\pi\)
0.794103 + 0.607783i \(0.207941\pi\)
\(938\) −10.1913 17.6518i −0.332757 0.576351i
\(939\) 0 0
\(940\) −5.15375 + 8.92655i −0.168097 + 0.291152i
\(941\) −0.355217 + 0.615254i −0.0115797 + 0.0200567i −0.871757 0.489938i \(-0.837019\pi\)
0.860177 + 0.509995i \(0.170353\pi\)
\(942\) 0 0
\(943\) 3.91046 + 6.77312i 0.127342 + 0.220563i
\(944\) −42.9175 −1.39685
\(945\) 0 0
\(946\) 64.4762 2.09630
\(947\) 13.0539 + 22.6100i 0.424194 + 0.734725i 0.996345 0.0854232i \(-0.0272242\pi\)
−0.572151 + 0.820148i \(0.693891\pi\)
\(948\) 0 0
\(949\) 15.6823 27.1626i 0.509070 0.881736i
\(950\) −4.62547 + 8.01155i −0.150070 + 0.259929i
\(951\) 0 0
\(952\) −3.23148 5.59709i −0.104733 0.181403i
\(953\) 51.0054 1.65223 0.826114 0.563503i \(-0.190547\pi\)
0.826114 + 0.563503i \(0.190547\pi\)
\(954\) 0 0
\(955\) −34.6177 −1.12020
\(956\) −4.93688 8.55092i −0.159670 0.276557i
\(957\) 0 0
\(958\) −22.4696 + 38.9185i −0.725959 + 1.25740i
\(959\) 5.87713 10.1795i 0.189782 0.328713i
\(960\) 0 0
\(961\) 14.9550 + 25.9028i 0.482418 + 0.835573i
\(962\) 14.1997 0.457817
\(963\) 0 0
\(964\) 7.51353 0.241995
\(965\) 17.5874 + 30.4622i 0.566157 + 0.980613i
\(966\) 0 0
\(967\) −5.00241 + 8.66443i −0.160867 + 0.278629i −0.935180 0.354173i \(-0.884762\pi\)
0.774313 + 0.632803i \(0.218096\pi\)
\(968\) −7.42072 + 12.8531i −0.238511 + 0.413113i
\(969\) 0 0
\(970\) 11.3597 + 19.6756i 0.364739 + 0.631746i
\(971\) −44.6269 −1.43215 −0.716073 0.698025i \(-0.754062\pi\)
−0.716073 + 0.698025i \(0.754062\pi\)
\(972\) 0 0
\(973\) −31.0044 −0.993954
\(974\) 23.4267 + 40.5763i 0.750641 + 1.30015i
\(975\) 0 0
\(976\) −3.04803 + 5.27935i −0.0975652 + 0.168988i
\(977\) −19.5428 + 33.8492i −0.625230 + 1.08293i 0.363266 + 0.931685i \(0.381662\pi\)
−0.988496 + 0.151245i \(0.951672\pi\)
\(978\) 0 0
\(979\) 9.43245 + 16.3375i 0.301462 + 0.522148i
\(980\) 0.597456 0.0190850
\(981\) 0 0
\(982\) 19.5800 0.624824
\(983\) 3.39729 + 5.88428i 0.108357 + 0.187680i 0.915105 0.403216i \(-0.132108\pi\)
−0.806748 + 0.590896i \(0.798774\pi\)
\(984\) 0 0
\(985\) −8.05365 + 13.9493i −0.256611 + 0.444463i
\(986\) −6.34119 + 10.9833i −0.201945 + 0.349779i
\(987\) 0 0
\(988\) −4.53628 7.85706i −0.144318 0.249966i
\(989\) 15.8740 0.504763
\(990\) 0 0
\(991\) 17.2046 0.546522 0.273261 0.961940i \(-0.411898\pi\)
0.273261 + 0.961940i \(0.411898\pi\)
\(992\) −1.42055 2.46046i −0.0451025 0.0781197i
\(993\) 0 0
\(994\) 12.3352 21.3652i 0.391248 0.677662i
\(995\) 8.97302 15.5417i 0.284464 0.492706i
\(996\) 0 0
\(997\) −3.66684 6.35116i −0.116130 0.201143i 0.802101 0.597189i \(-0.203716\pi\)
−0.918231 + 0.396045i \(0.870382\pi\)
\(998\) 3.59848 0.113908
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 729.2.c.d.244.4 12
3.2 odd 2 729.2.c.a.244.3 12
9.2 odd 6 729.2.c.a.487.3 12
9.4 even 3 729.2.a.b.1.3 6
9.5 odd 6 729.2.a.e.1.4 yes 6
9.7 even 3 inner 729.2.c.d.487.4 12
27.2 odd 18 729.2.e.k.82.2 12
27.4 even 9 729.2.e.t.649.1 12
27.5 odd 18 729.2.e.u.163.1 12
27.7 even 9 729.2.e.j.568.2 12
27.11 odd 18 729.2.e.l.325.2 12
27.13 even 9 729.2.e.s.406.1 12
27.14 odd 18 729.2.e.l.406.2 12
27.16 even 9 729.2.e.s.325.1 12
27.20 odd 18 729.2.e.u.568.1 12
27.22 even 9 729.2.e.j.163.2 12
27.23 odd 18 729.2.e.k.649.2 12
27.25 even 9 729.2.e.t.82.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.3 6 9.4 even 3
729.2.a.e.1.4 yes 6 9.5 odd 6
729.2.c.a.244.3 12 3.2 odd 2
729.2.c.a.487.3 12 9.2 odd 6
729.2.c.d.244.4 12 1.1 even 1 trivial
729.2.c.d.487.4 12 9.7 even 3 inner
729.2.e.j.163.2 12 27.22 even 9
729.2.e.j.568.2 12 27.7 even 9
729.2.e.k.82.2 12 27.2 odd 18
729.2.e.k.649.2 12 27.23 odd 18
729.2.e.l.325.2 12 27.11 odd 18
729.2.e.l.406.2 12 27.14 odd 18
729.2.e.s.325.1 12 27.16 even 9
729.2.e.s.406.1 12 27.13 even 9
729.2.e.t.82.1 12 27.25 even 9
729.2.e.t.649.1 12 27.4 even 9
729.2.e.u.163.1 12 27.5 odd 18
729.2.e.u.568.1 12 27.20 odd 18