Properties

Label 729.2.c.a.487.3
Level $729$
Weight $2$
Character 729.487
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 487.3
Root \(1.91182i\) of defining polynomial
Character \(\chi\) \(=\) 729.487
Dual form 729.2.c.a.244.3

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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 0.439609 + 0.898189i \(0.355117\pi\)
−0.997659 + 0.0683820i \(0.978216\pi\)
\(3\) 0 0
\(4\) −0.245680 0.425530i −0.122840 0.212765i
\(5\) 0.839254 + 1.45363i 0.375326 + 0.650083i 0.990376 0.138405i \(-0.0441975\pi\)
−0.615050 + 0.788488i \(0.710864\pi\)
\(6\) 0 0
\(7\) −1.38964 + 2.40693i −0.525235 + 0.909734i 0.474333 + 0.880345i \(0.342689\pi\)
−0.999568 + 0.0293881i \(0.990644\pi\)
\(8\) −2.38124 −0.841897
\(9\) 0 0
\(10\) −2.64936 −0.837802
\(11\) −2.07561 + 3.59506i −0.625820 + 1.08395i 0.362561 + 0.931960i \(0.381902\pi\)
−0.988382 + 0.151993i \(0.951431\pi\)
\(12\) 0 0
\(13\) −3.43802 5.95483i −0.953536 1.65157i −0.737684 0.675147i \(-0.764080\pi\)
−0.215852 0.976426i \(-0.569253\pi\)
\(14\) −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 \(-0.537784\pi\)
−0.118424 + 0.992963i \(0.537784\pi\)
\(18\) 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 \(-0.112876\pi\)
−0.769597 + 0.638530i \(0.779543\pi\)
\(24\) 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 0.176866 + 0.984235i \(0.443404\pi\)
−0.940806 + 0.338947i \(0.889929\pi\)
\(30\) 0 0
\(31\) −0.522035 0.904190i −0.0937602 0.162397i 0.815330 0.578996i \(-0.196555\pi\)
−0.909090 + 0.416599i \(0.863222\pi\)
\(32\) 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 \(-0.290254\pi\)
−0.990856 + 0.134926i \(0.956920\pi\)
\(42\) 0 0
\(43\) −4.92011 + 8.52189i −0.750310 + 1.29958i 0.197362 + 0.980331i \(0.436763\pi\)
−0.947672 + 0.319245i \(0.896571\pi\)
\(44\) 2.03974 0.307503
\(45\) 0 0
\(46\) −2.54623 −0.375422
\(47\) 6.24885 10.8233i 0.911488 1.57874i 0.0995258 0.995035i \(-0.468267\pi\)
0.811963 0.583709i \(-0.198399\pi\)
\(48\) 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 \(-0.668251\pi\)
−0.504305 + 0.863525i \(0.668251\pi\)
\(54\) 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 0.994334 + 0.106302i \(0.0339009\pi\)
−0.405107 + 0.914269i \(0.632766\pi\)
\(60\) 0 0
\(61\) 0.642871 1.11349i 0.0823112 0.142567i −0.821931 0.569587i \(-0.807103\pi\)
0.904242 + 0.427020i \(0.140437\pi\)
\(62\) 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 0.972322 0.233646i \(-0.0750655\pi\)
−0.688504 + 0.725233i \(0.741732\pi\)
\(68\) 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 \(-0.608300\pi\)
−0.333707 + 0.942677i \(0.608300\pi\)
\(72\) 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 −0.966764 0.255670i \(-0.917704\pi\)
0.704799 + 0.709407i \(0.251037\pi\)
\(80\) 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 \(-0.730872\pi\)
0.979726 + 0.200342i \(0.0642052\pi\)
\(84\) 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 \(-0.577427\pi\)
−0.240854 + 0.970561i \(0.577427\pi\)
\(90\) 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 −0.997324 0.0731042i \(-0.976709\pi\)
0.561972 + 0.827156i \(0.310043\pi\)
\(98\) 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 \(-0.960288\pi\)
0.603879 + 0.797076i \(0.293621\pi\)
\(102\) 0 0
\(103\) 1.08307 + 1.87594i 0.106718 + 0.184842i 0.914439 0.404724i \(-0.132632\pi\)
−0.807721 + 0.589565i \(0.799299\pi\)
\(104\) 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 \(-0.708155\pi\)
−0.608317 + 0.793695i \(0.708155\pi\)
\(108\) 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 \(-0.159916\pi\)
−0.855228 + 0.518252i \(0.826583\pi\)
\(114\) 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 \(-0.332860\pi\)
−0.999999 + 0.00148672i \(0.999527\pi\)
\(132\) 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 \(-0.891158\pi\)
0.761443 + 0.648232i \(0.224491\pi\)
\(138\) 0 0
\(139\) 5.57776 + 9.66097i 0.473100 + 0.819433i 0.999526 0.0307879i \(-0.00980165\pi\)
−0.526426 + 0.850221i \(0.676468\pi\)
\(140\) 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 0.921022 + 0.389511i \(0.127356\pi\)
−0.123184 + 0.992384i \(0.539311\pi\)
\(150\) 0 0
\(151\) 0.621430 1.07635i 0.0505713 0.0875920i −0.839632 0.543156i \(-0.817229\pi\)
0.890203 + 0.455564i \(0.150562\pi\)
\(152\) −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 0.927869 0.372907i \(-0.121639\pi\)
−0.786881 + 0.617105i \(0.788306\pi\)
\(158\) −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 −0.997459 0.0712430i \(-0.977303\pi\)
0.437031 0.899446i \(-0.356030\pi\)
\(168\) 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 \(-0.992567\pi\)
0.520086 + 0.854114i \(0.325900\pi\)
\(174\) 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 \(-0.496480\pi\)
0.0110582 + 0.999939i \(0.496480\pi\)
\(180\) 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 0.203501 + 0.979075i \(0.434768\pi\)
−0.949654 + 0.313301i \(0.898565\pi\)
\(192\) 0 0
\(193\) 10.4780 + 18.1484i 0.754221 + 1.30635i 0.945761 + 0.324864i \(0.105319\pi\)
−0.191540 + 0.981485i \(0.561348\pi\)
\(194\) −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 \(-0.611054\pi\)
−0.341851 + 0.939754i \(0.611054\pi\)
\(198\) 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 0.999780 + 0.0209700i \(0.00667546\pi\)
−0.481729 + 0.876320i \(0.659991\pi\)
\(212\) 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 −0.583611 0.812034i \(-0.698361\pi\)
0.995047 + 0.0994049i \(0.0316939\pi\)
\(224\) −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 \(-0.873077\pi\)
0.797017 + 0.603957i \(0.206410\pi\)
\(228\) 0 0
\(229\) 9.30121 + 16.1102i 0.614641 + 1.06459i 0.990447 + 0.137892i \(0.0440326\pi\)
−0.375806 + 0.926698i \(0.622634\pi\)
\(230\) −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 \(-0.494309\pi\)
0.0178777 + 0.999840i \(0.494309\pi\)
\(234\) 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 0.983144 + 0.182834i \(0.0585270\pi\)
−0.333233 + 0.942844i \(0.608140\pi\)
\(240\) 0 0
\(241\) −7.64565 + 13.2427i −0.492500 + 0.853034i −0.999963 0.00863907i \(-0.997250\pi\)
0.507463 + 0.861674i \(0.330583\pi\)
\(242\) 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 \(-0.368112\pi\)
0.402586 + 0.915382i \(0.368112\pi\)
\(252\) 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 \(-0.0326403\pi\)
−0.586023 + 0.810295i \(0.699307\pi\)
\(258\) 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 \(-0.738568\pi\)
0.974596 + 0.223970i \(0.0719017\pi\)
\(264\) 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 \(-0.264155\pi\)
0.674973 + 0.737842i \(0.264155\pi\)
\(270\) 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 −0.429526 0.903054i \(-0.641319\pi\)
0.996831 0.0795468i \(-0.0253473\pi\)
\(278\) −17.6079 −1.05605
\(279\) 0 0
\(280\) 11.1086 0.663867
\(281\) 10.0009 17.3220i 0.596602 1.03335i −0.396717 0.917941i \(-0.629850\pi\)
0.993319 0.115404i \(-0.0368162\pi\)
\(282\) 0 0
\(283\) −8.37252 14.5016i −0.497695 0.862032i 0.502302 0.864692i \(-0.332487\pi\)
−0.999996 + 0.00266002i \(0.999153\pi\)
\(284\) 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 −0.996391 0.0848806i \(-0.972949\pi\)
0.424687 0.905340i \(-0.360384\pi\)
\(294\) 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 \(-0.208230\pi\)
−0.923755 + 0.382983i \(0.874897\pi\)
\(312\) 0 0
\(313\) −5.93434 + 10.2786i −0.335429 + 0.580980i −0.983567 0.180543i \(-0.942215\pi\)
0.648138 + 0.761523i \(0.275548\pi\)
\(314\) −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 \(-0.699669\pi\)
0.994630 + 0.103493i \(0.0330019\pi\)
\(318\) 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 −0.732882 0.680356i \(-0.761825\pi\)
0.955647 + 0.294516i \(0.0951585\pi\)
\(332\) −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 0.999899 + 0.0142235i \(0.00452764\pi\)
−0.487631 + 0.873050i \(0.662139\pi\)
\(338\) −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 \(-0.00988038\pi\)
−0.526636 + 0.850091i \(0.676547\pi\)
\(348\) 0 0
\(349\) 8.49465 14.7132i 0.454708 0.787577i −0.543963 0.839109i \(-0.683077\pi\)
0.998671 + 0.0515316i \(0.0164103\pi\)
\(350\) −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 \(-0.701188\pi\)
0.994125 + 0.108238i \(0.0345209\pi\)
\(354\) 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 \(-0.479398\pi\)
0.0646783 + 0.997906i \(0.479398\pi\)
\(360\) 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 −0.848375 0.529396i \(-0.822419\pi\)
0.882658 + 0.470016i \(0.155752\pi\)
\(368\) 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 0.963307 0.268400i \(-0.0864950\pi\)
−0.714095 + 0.700048i \(0.753162\pi\)
\(374\) 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 −0.872574 0.488481i \(-0.837551\pi\)
0.0132498 0.999912i \(-0.495782\pi\)
\(384\) 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 \(-0.709567\pi\)
0.990931 + 0.134369i \(0.0429008\pi\)
\(390\) 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 \(-0.272956\pi\)
−0.982065 + 0.188545i \(0.939623\pi\)
\(402\) 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 −0.987708 0.156311i \(-0.950040\pi\)
0.358485 0.933536i \(-0.383294\pi\)
\(410\) 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 \(-0.0665096\pi\)
−0.668764 + 0.743475i \(0.733176\pi\)
\(420\) 0 0
\(421\) 8.83862 15.3089i 0.430768 0.746112i −0.566172 0.824287i \(-0.691576\pi\)
0.996940 + 0.0781752i \(0.0249094\pi\)
\(422\) −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 \(-0.376592\pi\)
0.378059 + 0.925782i \(0.376592\pi\)
\(432\) 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 0.341987 + 0.939705i \(0.388900\pi\)
−0.984802 + 0.173683i \(0.944433\pi\)
\(440\) 16.5922 0.791001
\(441\) 0 0
\(442\) −10.5987 −0.504128
\(443\) −17.3639 + 30.0752i −0.824986 + 1.42892i 0.0769438 + 0.997035i \(0.475484\pi\)
−0.901930 + 0.431882i \(0.857850\pi\)
\(444\) 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 \(-0.662834\pi\)
−0.489535 + 0.871984i \(0.662834\pi\)
\(450\) 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 −0.769340 0.638840i \(-0.779415\pi\)
0.937921 + 0.346848i \(0.112748\pi\)
\(458\) −29.3621 −1.37200
\(459\) 0 0
\(460\) 1.33046 0.0620332
\(461\) −11.5634 + 20.0284i −0.538562 + 0.932817i 0.460420 + 0.887701i \(0.347699\pi\)
−0.998982 + 0.0451156i \(0.985634\pi\)
\(462\) 0 0
\(463\) −2.48792 4.30921i −0.115623 0.200266i 0.802405 0.596779i \(-0.203553\pi\)
−0.918029 + 0.396514i \(0.870220\pi\)
\(464\) 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 \(-0.593251\pi\)
−0.288784 + 0.957394i \(0.593251\pi\)
\(468\) 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 0.332573 + 0.943078i \(0.392083\pi\)
−0.983016 + 0.183522i \(0.941250\pi\)
\(480\) 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 \(-0.256973\pi\)
−0.971363 + 0.237600i \(0.923639\pi\)
\(492\) 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 0.890412 0.455156i \(-0.150416\pi\)
−0.839382 + 0.543541i \(0.817083\pi\)
\(500\) −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 \(-0.127929\pi\)
0.920320 + 0.391167i \(0.127929\pi\)
\(504\) 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 \(-0.285254\pi\)
−0.988614 + 0.150473i \(0.951920\pi\)
\(510\) 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 \(-0.565280\pi\)
−0.203648 + 0.979044i \(0.565280\pi\)
\(522\) 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 0.352448 + 0.935832i \(0.385349\pi\)
−0.986678 + 0.162687i \(0.947984\pi\)
\(548\) 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 \(-0.442954\pi\)
0.178259 + 0.983984i \(0.442954\pi\)
\(558\) 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 0.996178 + 0.0873428i \(0.0278376\pi\)
−0.422448 + 0.906387i \(0.638829\pi\)
\(564\) 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 \(-0.681154\pi\)
0.998965 + 0.0454960i \(0.0144868\pi\)
\(570\) 0 0
\(571\) 22.4267 + 38.8442i 0.938530 + 1.62558i 0.768216 + 0.640191i \(0.221145\pi\)
0.170314 + 0.985390i \(0.445522\pi\)
\(572\) −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 \(-0.719022\pi\)
0.986504 + 0.163740i \(0.0523558\pi\)
\(588\) 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 \(-0.599164\pi\)
−0.306519 + 0.951865i \(0.599164\pi\)
\(594\) 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 \(-0.255844\pi\)
−0.970515 + 0.241042i \(0.922511\pi\)
\(600\) 0 0
\(601\) 22.6586 39.2459i 0.924265 1.60087i 0.131525 0.991313i \(-0.458013\pi\)
0.792739 0.609561i \(-0.208654\pi\)
\(602\) 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 0.504060 0.863669i \(-0.331839\pi\)
−0.999989 + 0.00469404i \(0.998506\pi\)
\(608\) 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 \(-0.192593\pi\)
−0.903834 + 0.427883i \(0.859259\pi\)
\(618\) 0 0
\(619\) 22.3850 38.7719i 0.899729 1.55838i 0.0718884 0.997413i \(-0.477097\pi\)
0.827841 0.560964i \(-0.189569\pi\)
\(620\) −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 −0.239581 + 0.970876i \(0.577010\pi\)
−0.721013 + 0.692922i \(0.756323\pi\)
\(642\) 0 0
\(643\) 14.0162 + 24.2767i 0.552744 + 0.957381i 0.998075 + 0.0620150i \(0.0197527\pi\)
−0.445331 + 0.895366i \(0.646914\pi\)
\(644\) 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 \(-0.764304\pi\)
−0.738159 + 0.674627i \(0.764304\pi\)
\(648\) 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 \(-0.134773\pi\)
−0.811668 + 0.584119i \(0.801440\pi\)
\(654\) 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 0.292607 + 0.956233i \(0.405477\pi\)
−0.974425 + 0.224711i \(0.927856\pi\)
\(660\) 0 0
\(661\) −0.666731 1.15481i −0.0259328 0.0449170i 0.852768 0.522290i \(-0.174922\pi\)
−0.878701 + 0.477373i \(0.841589\pi\)
\(662\) 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 −0.829467 0.558556i \(-0.811356\pi\)
0.898457 + 0.439061i \(0.144689\pi\)
\(674\) −29.6866 −1.14348
\(675\) 0 0
\(676\) 16.8438 0.647839
\(677\) 18.4694 31.9900i 0.709839 1.22948i −0.255078 0.966920i \(-0.582101\pi\)
0.964917 0.262556i \(-0.0845654\pi\)
\(678\) 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 \(-0.240760\pi\)
0.727332 + 0.686286i \(0.240760\pi\)
\(684\) 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 −0.871213 0.490905i \(-0.836666\pi\)
0.860743 + 0.509040i \(0.170000\pi\)
\(692\) 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 \(-0.383027\pi\)
0.359267 + 0.933235i \(0.383027\pi\)
\(702\) 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 −0.957298 0.289103i \(-0.906643\pi\)
0.729019 + 0.684493i \(0.239976\pi\)
\(710\) 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 \(-0.441644\pi\)
0.182304 + 0.983242i \(0.441644\pi\)
\(720\) 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 −0.903416 0.428765i \(-0.858949\pi\)
0.823029 + 0.567999i \(0.192282\pi\)
\(728\) −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 −0.998950 0.0458082i \(-0.985414\pi\)
0.459804 0.888020i \(-0.347920\pi\)
\(734\) 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 \(-0.294928\pi\)
−0.992730 + 0.120361i \(0.961595\pi\)
\(744\) 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 0.957213 + 0.289383i \(0.0934500\pi\)
−0.227994 + 0.973663i \(0.573217\pi\)
\(752\) −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 −0.941972 0.335691i \(-0.891030\pi\)
0.180269 0.983617i \(-0.442303\pi\)
\(762\) 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 0.843449 0.537209i \(-0.180521\pi\)
−0.886961 + 0.461844i \(0.847188\pi\)
\(770\) 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 \(-0.491998\pi\)
0.0251377 + 0.999684i \(0.491998\pi\)
\(774\) 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