Properties

Label 441.2.g.e.79.2
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(67,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.e.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.119562 + 0.207087i) q^{2} +(1.71053 - 0.272169i) q^{3} +(0.971410 - 1.68253i) q^{4} +1.18194 q^{5} +(0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(2.85185 - 0.931107i) q^{9} +O(q^{10})\) \(q+(0.119562 + 0.207087i) q^{2} +(1.71053 - 0.272169i) q^{3} +(0.971410 - 1.68253i) q^{4} +1.18194 q^{5} +(0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(2.85185 - 0.931107i) q^{9} +(0.141315 + 0.244765i) q^{10} -3.70370 q^{11} +(1.20370 - 3.14241i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(2.02175 - 0.321688i) q^{15} +(-1.83009 - 3.16982i) q^{16} +(3.47141 + 6.01266i) q^{17} +(0.533792 + 0.479256i) q^{18} +(-0.971410 + 1.68253i) q^{19} +(1.14815 - 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} -5.60301 q^{23} +(1.61273 - 0.256606i) q^{24} -3.60301 q^{25} +(0.119562 - 0.207087i) q^{26} +(4.62476 - 2.36887i) q^{27} +(-0.119562 + 0.207087i) q^{29} +(0.308342 + 0.380217i) q^{30} +(-0.830095 + 1.43777i) q^{31} +(1.38044 - 2.39099i) q^{32} +(-6.33530 + 1.00803i) q^{33} +(-0.830095 + 1.43777i) q^{34} +(1.20370 - 5.70281i) q^{36} +(4.77292 - 8.26693i) q^{37} -0.464574 q^{38} +(-1.09097 - 1.34528i) q^{39} +1.11436 q^{40} +(5.09097 + 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(-3.59781 + 6.23159i) q^{44} +(3.37072 - 1.10052i) q^{45} +(-0.669905 - 1.16031i) q^{46} +(-2.91423 - 5.04759i) q^{47} +(-3.99316 - 4.92398i) q^{48} +(-0.430782 - 0.746136i) q^{50} +(7.57442 + 9.34004i) q^{51} -1.94282 q^{52} +(5.80150 + 10.0485i) q^{53} +(1.04351 + 0.674501i) q^{54} -4.37756 q^{55} +(-1.20370 + 3.14241i) q^{57} -0.0571799 q^{58} +(-1.30150 + 2.25427i) q^{59} +(1.42270 - 3.71415i) q^{60} +(3.80150 + 6.58440i) q^{61} -0.396990 q^{62} -6.66019 q^{64} +(-0.590972 - 1.02359i) q^{65} +(-0.966208 - 1.19143i) q^{66} +(-1.75404 + 3.03809i) q^{67} +13.4887 q^{68} +(-9.58414 + 1.52496i) q^{69} +8.60301 q^{71} +(2.68878 - 0.877867i) q^{72} +(-7.57442 - 13.1193i) q^{73} +2.28263 q^{74} +(-6.16307 + 0.980627i) q^{75} +(1.88727 + 3.26886i) q^{76} +(0.148152 - 0.386770i) q^{78} +(-3.68878 - 6.38915i) q^{79} +(-2.16307 - 3.74654i) q^{80} +(7.26608 - 5.31075i) q^{81} +(-1.21737 + 2.10855i) q^{82} +(3.47141 - 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} -0.532157 q^{86} +(-0.148152 + 0.386770i) q^{87} -3.49192 q^{88} +(-1.37360 + 2.37915i) q^{89} +(0.630912 + 0.566453i) q^{90} +(-5.44282 + 9.42724i) q^{92} +(-1.02859 + 2.68527i) q^{93} +(0.696860 - 1.20700i) q^{94} +(-1.14815 + 1.98866i) q^{95} +(1.71053 - 4.46558i) q^{96} +(-3.58414 + 6.20790i) q^{97} +(-10.5624 + 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} - 11 q^{12} - 3 q^{13} + 11 q^{15} - 3 q^{16} + 12 q^{17} - 23 q^{18} + 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} - 7 q^{27} - q^{29} - 5 q^{30} + 3 q^{31} + 8 q^{32} + 5 q^{33} + 3 q^{34} - 11 q^{36} + 3 q^{37} + 16 q^{38} + 2 q^{39} + 42 q^{40} + 22 q^{41} + 3 q^{43} - 23 q^{44} - 4 q^{45} - 12 q^{46} + 9 q^{47} - 14 q^{48} - 10 q^{50} + 3 q^{51} + 6 q^{52} + 18 q^{53} + 4 q^{54} - 12 q^{55} + 11 q^{57} - 18 q^{58} + 9 q^{59} + 37 q^{60} + 6 q^{61} - 36 q^{62} - 24 q^{64} + 5 q^{65} - 32 q^{66} + 12 q^{68} - 39 q^{69} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 12 q^{74} - 35 q^{75} + 21 q^{76} + 10 q^{78} - 15 q^{79} - 11 q^{80} + 8 q^{81} - 9 q^{82} + 12 q^{83} - 9 q^{85} + 68 q^{86} - 10 q^{87} - 42 q^{88} + 2 q^{89} + 73 q^{90} - 15 q^{92} - 15 q^{93} - 24 q^{94} - 16 q^{95} + 2 q^{96} - 3 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.119562 + 0.207087i 0.0845428 + 0.146433i 0.905196 0.424994i \(-0.139724\pi\)
−0.820653 + 0.571426i \(0.806390\pi\)
\(3\) 1.71053 0.272169i 0.987577 0.157137i
\(4\) 0.971410 1.68253i 0.485705 0.841266i
\(5\) 1.18194 0.528581 0.264291 0.964443i \(-0.414862\pi\)
0.264291 + 0.964443i \(0.414862\pi\)
\(6\) 0.260877 + 0.321688i 0.106502 + 0.131329i
\(7\) 0 0
\(8\) 0.942820 0.333337
\(9\) 2.85185 0.931107i 0.950616 0.310369i
\(10\) 0.141315 + 0.244765i 0.0446878 + 0.0774015i
\(11\) −3.70370 −1.11671 −0.558353 0.829603i \(-0.688567\pi\)
−0.558353 + 0.829603i \(0.688567\pi\)
\(12\) 1.20370 3.14241i 0.347477 0.907137i
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 2.02175 0.321688i 0.522014 0.0830595i
\(16\) −1.83009 3.16982i −0.457524 0.792454i
\(17\) 3.47141 + 6.01266i 0.841941 + 1.45828i 0.888252 + 0.459357i \(0.151920\pi\)
−0.0463112 + 0.998927i \(0.514747\pi\)
\(18\) 0.533792 + 0.479256i 0.125816 + 0.112962i
\(19\) −0.971410 + 1.68253i −0.222857 + 0.385999i −0.955674 0.294426i \(-0.904872\pi\)
0.732818 + 0.680425i \(0.238205\pi\)
\(20\) 1.14815 1.98866i 0.256735 0.444677i
\(21\) 0 0
\(22\) −0.442820 0.766987i −0.0944096 0.163522i
\(23\) −5.60301 −1.16831 −0.584154 0.811643i \(-0.698574\pi\)
−0.584154 + 0.811643i \(0.698574\pi\)
\(24\) 1.61273 0.256606i 0.329196 0.0523795i
\(25\) −3.60301 −0.720602
\(26\) 0.119562 0.207087i 0.0234480 0.0406131i
\(27\) 4.62476 2.36887i 0.890036 0.455890i
\(28\) 0 0
\(29\) −0.119562 + 0.207087i −0.0222020 + 0.0384551i −0.876913 0.480649i \(-0.840401\pi\)
0.854711 + 0.519104i \(0.173734\pi\)
\(30\) 0.308342 + 0.380217i 0.0562952 + 0.0694178i
\(31\) −0.830095 + 1.43777i −0.149089 + 0.258231i −0.930891 0.365297i \(-0.880968\pi\)
0.781802 + 0.623527i \(0.214301\pi\)
\(32\) 1.38044 2.39099i 0.244029 0.422671i
\(33\) −6.33530 + 1.00803i −1.10283 + 0.175476i
\(34\) −0.830095 + 1.43777i −0.142360 + 0.246575i
\(35\) 0 0
\(36\) 1.20370 5.70281i 0.200616 0.950469i
\(37\) 4.77292 8.26693i 0.784662 1.35908i −0.144538 0.989499i \(-0.546170\pi\)
0.929201 0.369576i \(-0.120497\pi\)
\(38\) −0.464574 −0.0753638
\(39\) −1.09097 1.34528i −0.174695 0.215417i
\(40\) 1.11436 0.176196
\(41\) 5.09097 + 8.81782i 0.795076 + 1.37711i 0.922791 + 0.385301i \(0.125903\pi\)
−0.127715 + 0.991811i \(0.540764\pi\)
\(42\) 0 0
\(43\) −1.11273 + 1.92730i −0.169689 + 0.293910i −0.938311 0.345794i \(-0.887610\pi\)
0.768622 + 0.639704i \(0.220943\pi\)
\(44\) −3.59781 + 6.23159i −0.542390 + 0.939447i
\(45\) 3.37072 1.10052i 0.502478 0.164055i
\(46\) −0.669905 1.16031i −0.0987721 0.171078i
\(47\) −2.91423 5.04759i −0.425084 0.736267i 0.571344 0.820711i \(-0.306422\pi\)
−0.996428 + 0.0844432i \(0.973089\pi\)
\(48\) −3.99316 4.92398i −0.576364 0.710716i
\(49\) 0 0
\(50\) −0.430782 0.746136i −0.0609217 0.105520i
\(51\) 7.57442 + 9.34004i 1.06063 + 1.30787i
\(52\) −1.94282 −0.269421
\(53\) 5.80150 + 10.0485i 0.796898 + 1.38027i 0.921627 + 0.388077i \(0.126861\pi\)
−0.124729 + 0.992191i \(0.539806\pi\)
\(54\) 1.04351 + 0.674501i 0.142003 + 0.0917880i
\(55\) −4.37756 −0.590270
\(56\) 0 0
\(57\) −1.20370 + 3.14241i −0.159434 + 0.416223i
\(58\) −0.0571799 −0.00750809
\(59\) −1.30150 + 2.25427i −0.169442 + 0.293481i −0.938224 0.346029i \(-0.887530\pi\)
0.768782 + 0.639511i \(0.220863\pi\)
\(60\) 1.42270 3.71415i 0.183670 0.479495i
\(61\) 3.80150 + 6.58440i 0.486733 + 0.843046i 0.999884 0.0152524i \(-0.00485519\pi\)
−0.513151 + 0.858298i \(0.671522\pi\)
\(62\) −0.396990 −0.0504178
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) −0.590972 1.02359i −0.0733010 0.126961i
\(66\) −0.966208 1.19143i −0.118932 0.146655i
\(67\) −1.75404 + 3.03809i −0.214290 + 0.371161i −0.953053 0.302804i \(-0.902077\pi\)
0.738763 + 0.673966i \(0.235410\pi\)
\(68\) 13.4887 1.63574
\(69\) −9.58414 + 1.52496i −1.15379 + 0.183584i
\(70\) 0 0
\(71\) 8.60301 1.02099 0.510495 0.859881i \(-0.329462\pi\)
0.510495 + 0.859881i \(0.329462\pi\)
\(72\) 2.68878 0.877867i 0.316876 0.103458i
\(73\) −7.57442 13.1193i −0.886519 1.53550i −0.843963 0.536402i \(-0.819783\pi\)
−0.0425559 0.999094i \(-0.513550\pi\)
\(74\) 2.28263 0.265350
\(75\) −6.16307 + 0.980627i −0.711650 + 0.113233i
\(76\) 1.88727 + 3.26886i 0.216485 + 0.374963i
\(77\) 0 0
\(78\) 0.148152 0.386770i 0.0167749 0.0437931i
\(79\) −3.68878 6.38915i −0.415020 0.718836i 0.580410 0.814324i \(-0.302892\pi\)
−0.995431 + 0.0954881i \(0.969559\pi\)
\(80\) −2.16307 3.74654i −0.241838 0.418876i
\(81\) 7.26608 5.31075i 0.807342 0.590084i
\(82\) −1.21737 + 2.10855i −0.134436 + 0.232850i
\(83\) 3.47141 6.01266i 0.381037 0.659975i −0.610174 0.792267i \(-0.708900\pi\)
0.991211 + 0.132292i \(0.0422338\pi\)
\(84\) 0 0
\(85\) 4.10301 + 7.10662i 0.445034 + 0.770821i
\(86\) −0.532157 −0.0573840
\(87\) −0.148152 + 0.386770i −0.0158835 + 0.0414661i
\(88\) −3.49192 −0.372240
\(89\) −1.37360 + 2.37915i −0.145602 + 0.252189i −0.929597 0.368577i \(-0.879845\pi\)
0.783996 + 0.620766i \(0.213178\pi\)
\(90\) 0.630912 + 0.566453i 0.0665039 + 0.0597094i
\(91\) 0 0
\(92\) −5.44282 + 9.42724i −0.567453 + 0.982858i
\(93\) −1.02859 + 2.68527i −0.106660 + 0.278450i
\(94\) 0.696860 1.20700i 0.0718756 0.124492i
\(95\) −1.14815 + 1.98866i −0.117798 + 0.204032i
\(96\) 1.71053 4.46558i 0.174581 0.455766i
\(97\) −3.58414 + 6.20790i −0.363914 + 0.630317i −0.988601 0.150558i \(-0.951893\pi\)
0.624687 + 0.780875i \(0.285226\pi\)
\(98\) 0 0
\(99\) −10.5624 + 3.44854i −1.06156 + 0.346591i
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) −12.7850 −1.27215 −0.636075 0.771627i \(-0.719443\pi\)
−0.636075 + 0.771627i \(0.719443\pi\)
\(102\) −1.02859 + 2.68527i −0.101846 + 0.265882i
\(103\) −4.39699 −0.433248 −0.216624 0.976255i \(-0.569505\pi\)
−0.216624 + 0.976255i \(0.569505\pi\)
\(104\) −0.471410 0.816506i −0.0462256 0.0800650i
\(105\) 0 0
\(106\) −1.38727 + 2.40283i −0.134744 + 0.233384i
\(107\) −6.86389 + 11.8886i −0.663557 + 1.14931i 0.316117 + 0.948720i \(0.397621\pi\)
−0.979674 + 0.200594i \(0.935713\pi\)
\(108\) 0.506837 10.0825i 0.0487704 0.970185i
\(109\) −0.631600 1.09396i −0.0604963 0.104783i 0.834191 0.551476i \(-0.185935\pi\)
−0.894687 + 0.446693i \(0.852602\pi\)
\(110\) −0.523388 0.906535i −0.0499031 0.0864347i
\(111\) 5.91423 15.4399i 0.561354 1.46549i
\(112\) 0 0
\(113\) −6.08126 10.5330i −0.572076 0.990866i −0.996353 0.0853326i \(-0.972805\pi\)
0.424276 0.905533i \(-0.360529\pi\)
\(114\) −0.794668 + 0.126442i −0.0744275 + 0.0118424i
\(115\) −6.62244 −0.617546
\(116\) 0.232287 + 0.402332i 0.0215673 + 0.0373556i
\(117\) −2.23229 2.00422i −0.206375 0.185290i
\(118\) −0.622440 −0.0573003
\(119\) 0 0
\(120\) 1.90615 0.303294i 0.174007 0.0276868i
\(121\) 2.71737 0.247034
\(122\) −0.909028 + 1.57448i −0.0822996 + 0.142547i
\(123\) 11.1082 + 13.6976i 1.00159 + 1.23507i
\(124\) 1.61273 + 2.79332i 0.144827 + 0.250848i
\(125\) −10.1683 −0.909478
\(126\) 0 0
\(127\) 1.33981 0.118889 0.0594445 0.998232i \(-0.481067\pi\)
0.0594445 + 0.998232i \(0.481067\pi\)
\(128\) −3.55718 6.16122i −0.314413 0.544580i
\(129\) −1.37880 + 3.59955i −0.121397 + 0.316923i
\(130\) 0.141315 0.244765i 0.0123942 0.0214673i
\(131\) −4.96690 −0.433960 −0.216980 0.976176i \(-0.569621\pi\)
−0.216980 + 0.976176i \(0.569621\pi\)
\(132\) −4.45813 + 11.6385i −0.388030 + 1.01301i
\(133\) 0 0
\(134\) −0.838864 −0.0724668
\(135\) 5.46621 2.79987i 0.470456 0.240975i
\(136\) 3.27292 + 5.66886i 0.280650 + 0.486100i
\(137\) −4.33981 −0.370775 −0.185387 0.982665i \(-0.559354\pi\)
−0.185387 + 0.982665i \(0.559354\pi\)
\(138\) −1.46169 1.80242i −0.124428 0.153432i
\(139\) −1.97141 3.41458i −0.167213 0.289621i 0.770226 0.637771i \(-0.220143\pi\)
−0.937439 + 0.348150i \(0.886810\pi\)
\(140\) 0 0
\(141\) −6.35868 7.84092i −0.535498 0.660324i
\(142\) 1.02859 + 1.78157i 0.0863174 + 0.149506i
\(143\) 1.85185 + 3.20750i 0.154859 + 0.268224i
\(144\) −8.17059 7.33582i −0.680883 0.611319i
\(145\) −0.141315 + 0.244765i −0.0117356 + 0.0203266i
\(146\) 1.81122 3.13713i 0.149898 0.259630i
\(147\) 0 0
\(148\) −9.27292 16.0612i −0.762229 1.32022i
\(149\) 11.1111 0.910256 0.455128 0.890426i \(-0.349594\pi\)
0.455128 + 0.890426i \(0.349594\pi\)
\(150\) −0.939941 1.15905i −0.0767459 0.0946356i
\(151\) 13.9234 1.13307 0.566535 0.824038i \(-0.308284\pi\)
0.566535 + 0.824038i \(0.308284\pi\)
\(152\) −0.915865 + 1.58632i −0.0742864 + 0.128668i
\(153\) 15.4984 + 13.9149i 1.25297 + 1.12496i
\(154\) 0 0
\(155\) −0.981125 + 1.69936i −0.0788059 + 0.136496i
\(156\) −3.32326 + 0.528775i −0.266074 + 0.0423359i
\(157\) −0.0285900 + 0.0495193i −0.00228173 + 0.00395207i −0.867164 0.498023i \(-0.834060\pi\)
0.864882 + 0.501975i \(0.167393\pi\)
\(158\) 0.882073 1.52780i 0.0701740 0.121545i
\(159\) 12.6586 + 15.6093i 1.00389 + 1.23790i
\(160\) 1.63160 2.82601i 0.128989 0.223416i
\(161\) 0 0
\(162\) 1.96853 + 0.869747i 0.154662 + 0.0683338i
\(163\) 0.754040 1.30604i 0.0590610 0.102297i −0.834983 0.550276i \(-0.814523\pi\)
0.894044 + 0.447979i \(0.147856\pi\)
\(164\) 19.7817 1.54469
\(165\) −7.48796 + 1.19143i −0.582937 + 0.0927531i
\(166\) 1.66019 0.128856
\(167\) 7.34213 + 12.7169i 0.568151 + 0.984067i 0.996749 + 0.0805714i \(0.0256745\pi\)
−0.428598 + 0.903496i \(0.640992\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −0.981125 + 1.69936i −0.0752489 + 0.130335i
\(171\) −1.20370 + 5.70281i −0.0920490 + 0.436105i
\(172\) 2.16182 + 3.74439i 0.164838 + 0.285507i
\(173\) −0.126398 0.218928i −0.00960987 0.0166448i 0.861180 0.508299i \(-0.169726\pi\)
−0.870790 + 0.491655i \(0.836392\pi\)
\(174\) −0.0978082 + 0.0155626i −0.00741482 + 0.00117980i
\(175\) 0 0
\(176\) 6.77812 + 11.7400i 0.510920 + 0.884939i
\(177\) −1.61273 + 4.21024i −0.121220 + 0.316461i
\(178\) −0.656920 −0.0492383
\(179\) −7.09617 12.2909i −0.530393 0.918667i −0.999371 0.0354578i \(-0.988711\pi\)
0.468978 0.883210i \(-0.344622\pi\)
\(180\) 1.42270 6.74040i 0.106042 0.502400i
\(181\) −1.43147 −0.106400 −0.0532002 0.998584i \(-0.516942\pi\)
−0.0532002 + 0.998584i \(0.516942\pi\)
\(182\) 0 0
\(183\) 8.29467 + 10.2282i 0.613160 + 0.756089i
\(184\) −5.28263 −0.389441
\(185\) 5.64132 9.77104i 0.414758 0.718381i
\(186\) −0.679065 + 0.108048i −0.0497914 + 0.00792248i
\(187\) −12.8571 22.2691i −0.940201 1.62848i
\(188\) −11.3236 −0.825862
\(189\) 0 0
\(190\) −0.549100 −0.0398359
\(191\) −7.53379 13.0489i −0.545126 0.944186i −0.998599 0.0529159i \(-0.983148\pi\)
0.453473 0.891270i \(-0.350185\pi\)
\(192\) −11.3925 + 1.81270i −0.822181 + 0.130820i
\(193\) 3.92395 6.79647i 0.282452 0.489221i −0.689536 0.724251i \(-0.742186\pi\)
0.971988 + 0.235030i \(0.0755190\pi\)
\(194\) −1.71410 −0.123065
\(195\) −1.28947 1.59005i −0.0923406 0.113866i
\(196\) 0 0
\(197\) 6.69002 0.476644 0.238322 0.971186i \(-0.423403\pi\)
0.238322 + 0.971186i \(0.423403\pi\)
\(198\) −1.97700 1.77502i −0.140499 0.126145i
\(199\) 9.96978 + 17.2682i 0.706739 + 1.22411i 0.966060 + 0.258316i \(0.0831677\pi\)
−0.259322 + 0.965791i \(0.583499\pi\)
\(200\) −3.39699 −0.240203
\(201\) −2.17347 + 5.67414i −0.153305 + 0.400223i
\(202\) −1.52859 2.64760i −0.107551 0.186284i
\(203\) 0 0
\(204\) 23.0728 3.67119i 1.61542 0.257035i
\(205\) 6.01724 + 10.4222i 0.420262 + 0.727916i
\(206\) −0.525711 0.910559i −0.0366280 0.0634416i
\(207\) −15.9789 + 5.21700i −1.11061 + 0.362607i
\(208\) −1.83009 + 3.16982i −0.126894 + 0.219787i
\(209\) 3.59781 6.23159i 0.248866 0.431048i
\(210\) 0 0
\(211\) 9.04583 + 15.6678i 0.622741 + 1.07862i 0.988973 + 0.148095i \(0.0473141\pi\)
−0.366233 + 0.930523i \(0.619353\pi\)
\(212\) 22.5426 1.54823
\(213\) 14.7157 2.34147i 1.00831 0.160435i
\(214\) −3.28263 −0.224396
\(215\) −1.31518 + 2.27796i −0.0896944 + 0.155355i
\(216\) 4.36032 2.23342i 0.296682 0.151965i
\(217\) 0 0
\(218\) 0.151030 0.261592i 0.0102291 0.0177172i
\(219\) −16.5270 20.3794i −1.11679 1.37712i
\(220\) −4.25241 + 7.36538i −0.286697 + 0.496574i
\(221\) 3.47141 6.01266i 0.233512 0.404455i
\(222\) 3.90451 0.621261i 0.262054 0.0416963i
\(223\) 11.3285 19.6215i 0.758610 1.31395i −0.184950 0.982748i \(-0.559212\pi\)
0.943560 0.331203i \(-0.107454\pi\)
\(224\) 0 0
\(225\) −10.2752 + 3.35479i −0.685016 + 0.223653i
\(226\) 1.45417 2.51870i 0.0967299 0.167541i
\(227\) −5.28263 −0.350620 −0.175310 0.984513i \(-0.556093\pi\)
−0.175310 + 0.984513i \(0.556093\pi\)
\(228\) 4.11793 + 5.07783i 0.272716 + 0.336287i
\(229\) 19.3365 1.27779 0.638897 0.769292i \(-0.279391\pi\)
0.638897 + 0.769292i \(0.279391\pi\)
\(230\) −0.791790 1.37142i −0.0522091 0.0904288i
\(231\) 0 0
\(232\) −0.112725 + 0.195246i −0.00740077 + 0.0128185i
\(233\) 8.49028 14.7056i 0.556217 0.963396i −0.441591 0.897217i \(-0.645586\pi\)
0.997808 0.0661796i \(-0.0210810\pi\)
\(234\) 0.148152 0.701905i 0.00968497 0.0458850i
\(235\) −3.44445 5.96597i −0.224691 0.389177i
\(236\) 2.52859 + 4.37965i 0.164597 + 0.285091i
\(237\) −8.04871 9.92489i −0.522820 0.644691i
\(238\) 0 0
\(239\) −8.44282 14.6234i −0.546121 0.945909i −0.998535 0.0541011i \(-0.982771\pi\)
0.452415 0.891808i \(-0.350563\pi\)
\(240\) −4.71969 5.81987i −0.304655 0.375671i
\(241\) 27.1456 1.74860 0.874300 0.485386i \(-0.161321\pi\)
0.874300 + 0.485386i \(0.161321\pi\)
\(242\) 0.324893 + 0.562732i 0.0208849 + 0.0361738i
\(243\) 10.9834 11.0618i 0.704589 0.709616i
\(244\) 14.7713 0.945634
\(245\) 0 0
\(246\) −1.50847 + 3.93807i −0.0961766 + 0.251082i
\(247\) 1.94282 0.123619
\(248\) −0.782630 + 1.35556i −0.0496971 + 0.0860778i
\(249\) 4.30150 11.2297i 0.272597 0.711651i
\(250\) −1.21574 2.10571i −0.0768898 0.133177i
\(251\) −19.0780 −1.20419 −0.602096 0.798424i \(-0.705668\pi\)
−0.602096 + 0.798424i \(0.705668\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) 0.160190 + 0.277457i 0.0100512 + 0.0174092i
\(255\) 8.95254 + 11.0394i 0.560630 + 0.691314i
\(256\) −5.80959 + 10.0625i −0.363099 + 0.628906i
\(257\) −14.8421 −0.925827 −0.462913 0.886404i \(-0.653196\pi\)
−0.462913 + 0.886404i \(0.653196\pi\)
\(258\) −0.910272 + 0.144836i −0.0566711 + 0.00901712i
\(259\) 0 0
\(260\) −2.29630 −0.142411
\(261\) −0.148152 + 0.701905i −0.00917035 + 0.0434468i
\(262\) −0.593850 1.02858i −0.0366882 0.0635458i
\(263\) −7.74145 −0.477358 −0.238679 0.971099i \(-0.576714\pi\)
−0.238679 + 0.971099i \(0.576714\pi\)
\(264\) −5.97304 + 0.950391i −0.367615 + 0.0584925i
\(265\) 6.85705 + 11.8768i 0.421225 + 0.729584i
\(266\) 0 0
\(267\) −1.70206 + 4.44346i −0.104165 + 0.271936i
\(268\) 3.40778 + 5.90246i 0.208164 + 0.360550i
\(269\) 0.755675 + 1.30887i 0.0460743 + 0.0798031i 0.888143 0.459567i \(-0.151996\pi\)
−0.842069 + 0.539371i \(0.818662\pi\)
\(270\) 1.23337 + 0.797222i 0.0750603 + 0.0485174i
\(271\) 10.9903 19.0357i 0.667612 1.15634i −0.310958 0.950424i \(-0.600650\pi\)
0.978570 0.205915i \(-0.0660169\pi\)
\(272\) 12.7060 22.0075i 0.770416 1.33440i
\(273\) 0 0
\(274\) −0.518875 0.898718i −0.0313464 0.0542935i
\(275\) 13.3445 0.804701
\(276\) −6.74433 + 17.6070i −0.405961 + 1.05982i
\(277\) −10.8285 −0.650619 −0.325310 0.945608i \(-0.605469\pi\)
−0.325310 + 0.945608i \(0.605469\pi\)
\(278\) 0.471410 0.816506i 0.0282733 0.0489708i
\(279\) −1.02859 + 4.87320i −0.0615801 + 0.291751i
\(280\) 0 0
\(281\) 8.43831 14.6156i 0.503387 0.871892i −0.496605 0.867977i \(-0.665420\pi\)
0.999992 0.00391559i \(-0.00124638\pi\)
\(282\) 0.863496 2.25427i 0.0514204 0.134240i
\(283\) 7.65856 13.2650i 0.455254 0.788523i −0.543449 0.839442i \(-0.682882\pi\)
0.998703 + 0.0509194i \(0.0162152\pi\)
\(284\) 8.35705 14.4748i 0.495900 0.858923i
\(285\) −1.42270 + 3.71415i −0.0842736 + 0.220008i
\(286\) −0.442820 + 0.766987i −0.0261845 + 0.0453529i
\(287\) 0 0
\(288\) 1.71053 8.10408i 0.100794 0.477537i
\(289\) −15.6014 + 27.0224i −0.917728 + 1.58955i
\(290\) −0.0675835 −0.00396864
\(291\) −4.44119 + 11.5943i −0.260347 + 0.679671i
\(292\) −29.4315 −1.72235
\(293\) 4.68482 + 8.11435i 0.273690 + 0.474045i 0.969804 0.243886i \(-0.0784224\pi\)
−0.696114 + 0.717932i \(0.745089\pi\)
\(294\) 0 0
\(295\) −1.53831 + 2.66442i −0.0895636 + 0.155129i
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) −17.1287 + 8.77359i −0.993909 + 0.509095i
\(298\) 1.32846 + 2.30096i 0.0769556 + 0.133291i
\(299\) 2.80150 + 4.85235i 0.162015 + 0.280619i
\(300\) −4.33693 + 11.3221i −0.250393 + 0.653684i
\(301\) 0 0
\(302\) 1.66470 + 2.88335i 0.0957929 + 0.165918i
\(303\) −21.8691 + 3.47966i −1.25635 + 0.199901i
\(304\) 7.11109 0.407849
\(305\) 4.49316 + 7.78239i 0.257278 + 0.445618i
\(306\) −1.02859 + 4.87320i −0.0588006 + 0.278582i
\(307\) 2.71410 0.154902 0.0774509 0.996996i \(-0.475322\pi\)
0.0774509 + 0.996996i \(0.475322\pi\)
\(308\) 0 0
\(309\) −7.52120 + 1.19672i −0.427866 + 0.0680792i
\(310\) −0.469220 −0.0266499
\(311\) 6.99028 12.1075i 0.396383 0.686555i −0.596894 0.802320i \(-0.703599\pi\)
0.993277 + 0.115765i \(0.0369320\pi\)
\(312\) −1.02859 1.26836i −0.0582324 0.0718066i
\(313\) 9.52696 + 16.5012i 0.538495 + 0.932701i 0.998985 + 0.0450364i \(0.0143404\pi\)
−0.460490 + 0.887665i \(0.652326\pi\)
\(314\) −0.0136731 −0.000771615
\(315\) 0 0
\(316\) −14.3333 −0.806309
\(317\) 2.00972 + 3.48093i 0.112877 + 0.195508i 0.916929 0.399050i \(-0.130660\pi\)
−0.804052 + 0.594559i \(0.797327\pi\)
\(318\) −1.71900 + 4.48769i −0.0963970 + 0.251657i
\(319\) 0.442820 0.766987i 0.0247932 0.0429430i
\(320\) −7.87197 −0.440056
\(321\) −8.50520 + 22.2040i −0.474714 + 1.23931i
\(322\) 0 0
\(323\) −13.4887 −0.750529
\(324\) −1.87717 17.3843i −0.104287 0.965796i
\(325\) 1.80150 + 3.12030i 0.0999295 + 0.173083i
\(326\) 0.360617 0.0199727
\(327\) −1.37812 1.69936i −0.0762099 0.0939747i
\(328\) 4.79987 + 8.31362i 0.265028 + 0.459043i
\(329\) 0 0
\(330\) −1.14200 1.40821i −0.0628652 0.0775193i
\(331\) 6.18878 + 10.7193i 0.340166 + 0.589185i 0.984463 0.175590i \(-0.0561834\pi\)
−0.644297 + 0.764775i \(0.722850\pi\)
\(332\) −6.74433 11.6815i −0.370143 0.641106i
\(333\) 5.91423 28.0201i 0.324098 1.53549i
\(334\) −1.75567 + 3.04092i −0.0960663 + 0.166392i
\(335\) −2.07318 + 3.59085i −0.113270 + 0.196189i
\(336\) 0 0
\(337\) −6.12997 10.6174i −0.333920 0.578367i 0.649356 0.760484i \(-0.275038\pi\)
−0.983277 + 0.182117i \(0.941705\pi\)
\(338\) 2.86948 0.156079
\(339\) −13.2690 16.3620i −0.720671 0.888662i
\(340\) 15.9428 0.864621
\(341\) 3.07442 5.32505i 0.166489 0.288368i
\(342\) −1.32489 + 0.432568i −0.0716420 + 0.0233906i
\(343\) 0 0
\(344\) −1.04910 + 1.81709i −0.0565637 + 0.0979711i
\(345\) −11.3279 + 1.80242i −0.609874 + 0.0970391i
\(346\) 0.0302247 0.0523508i 0.00162489 0.00281440i
\(347\) −3.32489 + 5.75888i −0.178490 + 0.309153i −0.941363 0.337394i \(-0.890454\pi\)
0.762874 + 0.646547i \(0.223788\pi\)
\(348\) 0.506837 + 0.624982i 0.0271693 + 0.0335025i
\(349\) −5.71737 + 9.90278i −0.306044 + 0.530083i −0.977493 0.210967i \(-0.932339\pi\)
0.671449 + 0.741050i \(0.265672\pi\)
\(350\) 0 0
\(351\) −4.36389 2.82073i −0.232927 0.150559i
\(352\) −5.11273 + 8.85550i −0.272509 + 0.472000i
\(353\) −22.1956 −1.18135 −0.590677 0.806908i \(-0.701139\pi\)
−0.590677 + 0.806908i \(0.701139\pi\)
\(354\) −1.06470 + 0.169409i −0.0565884 + 0.00900397i
\(355\) 10.1683 0.539676
\(356\) 2.66866 + 4.62226i 0.141439 + 0.244979i
\(357\) 0 0
\(358\) 1.69686 2.93905i 0.0896819 0.155334i
\(359\) 3.77812 6.54389i 0.199401 0.345373i −0.748933 0.662646i \(-0.769434\pi\)
0.948334 + 0.317272i \(0.102767\pi\)
\(360\) 3.17799 1.03759i 0.167495 0.0546857i
\(361\) 7.61273 + 13.1856i 0.400670 + 0.693980i
\(362\) −0.171149 0.296439i −0.00899539 0.0155805i
\(363\) 4.64815 0.739583i 0.243965 0.0388180i
\(364\) 0 0
\(365\) −8.95254 15.5062i −0.468597 0.811634i
\(366\) −1.12640 + 2.94062i −0.0588778 + 0.153708i
\(367\) −18.5231 −0.966900 −0.483450 0.875372i \(-0.660616\pi\)
−0.483450 + 0.875372i \(0.660616\pi\)
\(368\) 10.2540 + 17.7605i 0.534529 + 0.925831i
\(369\) 22.7290 + 20.4068i 1.18323 + 1.06234i
\(370\) 2.69794 0.140259
\(371\) 0 0
\(372\) 3.51887 + 4.33914i 0.182445 + 0.224974i
\(373\) 15.6602 0.810854 0.405427 0.914127i \(-0.367123\pi\)
0.405427 + 0.914127i \(0.367123\pi\)
\(374\) 3.07442 5.32505i 0.158974 0.275352i
\(375\) −17.3932 + 2.76748i −0.898179 + 0.142912i
\(376\) −2.74759 4.75897i −0.141696 0.245425i
\(377\) 0.239123 0.0123155
\(378\) 0 0
\(379\) 4.03775 0.207405 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(380\) 2.23065 + 3.86360i 0.114430 + 0.198199i
\(381\) 2.29179 0.364654i 0.117412 0.0186818i
\(382\) 1.80150 3.12030i 0.0921730 0.159648i
\(383\) 0.225450 0.0115200 0.00575998 0.999983i \(-0.498167\pi\)
0.00575998 + 0.999983i \(0.498167\pi\)
\(384\) −7.76157 9.57081i −0.396081 0.488408i
\(385\) 0 0
\(386\) 1.87661 0.0955171
\(387\) −1.37880 + 6.53242i −0.0700885 + 0.332062i
\(388\) 6.96333 + 12.0608i 0.353510 + 0.612296i
\(389\) 25.2632 1.28090 0.640448 0.768002i \(-0.278749\pi\)
0.640448 + 0.768002i \(0.278749\pi\)
\(390\) 0.175107 0.457140i 0.00886688 0.0231482i
\(391\) −19.4503 33.6890i −0.983646 1.70373i
\(392\) 0 0
\(393\) −8.49604 + 1.35183i −0.428569 + 0.0681910i
\(394\) 0.799870 + 1.38542i 0.0402969 + 0.0697962i
\(395\) −4.35993 7.55162i −0.219372 0.379963i
\(396\) −4.45813 + 21.1215i −0.224029 + 1.06139i
\(397\) 10.1505 17.5811i 0.509438 0.882372i −0.490503 0.871440i \(-0.663187\pi\)
0.999940 0.0109322i \(-0.00347991\pi\)
\(398\) −2.38401 + 4.12922i −0.119499 + 0.206979i
\(399\) 0 0
\(400\) 6.59385 + 11.4209i 0.329693 + 0.571044i
\(401\) −15.2255 −0.760323 −0.380161 0.924920i \(-0.624132\pi\)
−0.380161 + 0.924920i \(0.624132\pi\)
\(402\) −1.43490 + 0.228312i −0.0715665 + 0.0113872i
\(403\) 1.66019 0.0826999
\(404\) −12.4194 + 21.5111i −0.617890 + 1.07022i
\(405\) 8.58809 6.27701i 0.426746 0.311907i
\(406\) 0 0
\(407\) −17.6774 + 30.6182i −0.876238 + 1.51769i
\(408\) 7.14132 + 8.80598i 0.353548 + 0.435961i
\(409\) −0.828460 + 1.43494i −0.0409647 + 0.0709530i −0.885781 0.464104i \(-0.846376\pi\)
0.844816 + 0.535057i \(0.179710\pi\)
\(410\) −1.43886 + 2.49218i −0.0710603 + 0.123080i
\(411\) −7.42339 + 1.18116i −0.366169 + 0.0582624i
\(412\) −4.27128 + 7.39807i −0.210431 + 0.364477i
\(413\) 0 0
\(414\) −2.99084 2.68527i −0.146992 0.131974i
\(415\) 4.10301 7.10662i 0.201409 0.348850i
\(416\) −2.76088 −0.135363
\(417\) −4.30150 5.30420i −0.210646 0.259748i
\(418\) 1.72064 0.0841592
\(419\) −16.6871 28.9030i −0.815220 1.41200i −0.909170 0.416426i \(-0.863282\pi\)
0.0939492 0.995577i \(-0.470051\pi\)
\(420\) 0 0
\(421\) −9.12025 + 15.7967i −0.444494 + 0.769886i −0.998017 0.0629481i \(-0.979950\pi\)
0.553523 + 0.832834i \(0.313283\pi\)
\(422\) −2.16307 + 3.74654i −0.105297 + 0.182379i
\(423\) −13.0108 11.6815i −0.632606 0.567975i
\(424\) 5.46978 + 9.47393i 0.265636 + 0.460095i
\(425\) −12.5075 21.6637i −0.606704 1.05084i
\(426\) 2.24433 + 2.76748i 0.108738 + 0.134085i
\(427\) 0 0
\(428\) 13.3353 + 23.0974i 0.644586 + 1.11646i
\(429\) 4.04063 + 4.98251i 0.195083 + 0.240558i
\(430\) −0.628979 −0.0303321
\(431\) −14.6413 25.3595i −0.705247 1.22152i −0.966602 0.256281i \(-0.917503\pi\)
0.261355 0.965243i \(-0.415831\pi\)
\(432\) −15.9727 10.3244i −0.768485 0.496733i
\(433\) −12.2449 −0.588451 −0.294226 0.955736i \(-0.595062\pi\)
−0.294226 + 0.955736i \(0.595062\pi\)
\(434\) 0 0
\(435\) −0.175107 + 0.457140i −0.00839573 + 0.0219182i
\(436\) −2.45417 −0.117533
\(437\) 5.44282 9.42724i 0.260365 0.450966i
\(438\) 2.24433 5.85911i 0.107238 0.279959i
\(439\) 2.41586 + 4.18440i 0.115303 + 0.199711i 0.917901 0.396810i \(-0.129883\pi\)
−0.802598 + 0.596520i \(0.796549\pi\)
\(440\) −4.12725 −0.196759
\(441\) 0 0
\(442\) 1.66019 0.0789672
\(443\) −0.622440 1.07810i −0.0295730 0.0512220i 0.850860 0.525392i \(-0.176081\pi\)
−0.880433 + 0.474170i \(0.842748\pi\)
\(444\) −20.2330 24.9494i −0.960215 1.18404i
\(445\) −1.62352 + 2.81202i −0.0769622 + 0.133302i
\(446\) 5.41780 0.256540
\(447\) 19.0059 3.02409i 0.898948 0.143035i
\(448\) 0 0
\(449\) 8.82846 0.416641 0.208320 0.978061i \(-0.433200\pi\)
0.208320 + 0.978061i \(0.433200\pi\)
\(450\) −1.92326 1.72676i −0.0906632 0.0814004i
\(451\) −18.8554 32.6585i −0.887867 1.53783i
\(452\) −23.6296 −1.11144
\(453\) 23.8164 3.78951i 1.11899 0.178047i
\(454\) −0.631600 1.09396i −0.0296425 0.0513422i
\(455\) 0 0
\(456\) −1.13487 + 2.96273i −0.0531451 + 0.138743i
\(457\) 5.25404 + 9.10026i 0.245774 + 0.425692i 0.962349 0.271817i \(-0.0876247\pi\)
−0.716575 + 0.697510i \(0.754291\pi\)
\(458\) 2.31191 + 4.00434i 0.108028 + 0.187111i
\(459\) 30.2977 + 19.5838i 1.41417 + 0.914093i
\(460\) −6.43310 + 11.1425i −0.299945 + 0.519520i
\(461\) −11.2758 + 19.5302i −0.525166 + 0.909614i 0.474404 + 0.880307i \(0.342663\pi\)
−0.999570 + 0.0293073i \(0.990670\pi\)
\(462\) 0 0
\(463\) −5.19850 9.00406i −0.241595 0.418454i 0.719574 0.694416i \(-0.244337\pi\)
−0.961169 + 0.275962i \(0.911004\pi\)
\(464\) 0.875237 0.0406318
\(465\) −1.21574 + 3.17384i −0.0563784 + 0.147183i
\(466\) 4.06045 0.188097
\(467\) −6.65856 + 11.5330i −0.308121 + 0.533682i −0.977951 0.208833i \(-0.933034\pi\)
0.669830 + 0.742514i \(0.266367\pi\)
\(468\) −5.54063 + 1.80897i −0.256116 + 0.0836198i
\(469\) 0 0
\(470\) 0.823649 1.42660i 0.0379921 0.0658043i
\(471\) −0.0354265 + 0.0924857i −0.00163237 + 0.00426152i
\(472\) −1.22708 + 2.12537i −0.0564812 + 0.0978282i
\(473\) 4.12120 7.13812i 0.189493 0.328211i
\(474\) 1.09300 2.85342i 0.0502030 0.131062i
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 0 0
\(477\) 25.9012 + 23.2550i 1.18594 + 1.06477i
\(478\) 2.01887 3.49679i 0.0923412 0.159940i
\(479\) 14.5354 0.664141 0.332070 0.943255i \(-0.392253\pi\)
0.332070 + 0.943255i \(0.392253\pi\)
\(480\) 2.02175 5.27806i 0.0922800 0.240909i
\(481\) −9.54583 −0.435252
\(482\) 3.24557 + 5.62149i 0.147832 + 0.256052i
\(483\) 0 0
\(484\) 2.63968 4.57206i 0.119985 0.207821i
\(485\) −4.23624 + 7.33739i −0.192358 + 0.333174i
\(486\) 3.60396 + 0.951958i 0.163479 + 0.0431817i
\(487\) −6.52696 11.3050i −0.295765 0.512279i 0.679398 0.733770i \(-0.262241\pi\)
−0.975162 + 0.221491i \(0.928908\pi\)
\(488\) 3.58414 + 6.20790i 0.162246 + 0.281019i
\(489\) 0.934349 2.43924i 0.0422527 0.110306i
\(490\) 0 0
\(491\) −9.67223 16.7528i −0.436502 0.756043i 0.560915 0.827873i \(-0.310449\pi\)
−0.997417 + 0.0718303i \(0.977116\pi\)
\(492\) 33.8372 5.38396i 1.52550 0.242727i
\(493\) −1.66019 −0.0747712
\(494\) 0.232287 + 0.402332i 0.0104511 + 0.0181018i
\(495\) −12.4841 + 4.07598i −0.561120 + 0.183202i
\(496\) 6.07661 0.272848
\(497\) 0 0
\(498\) 2.83981 0.451852i 0.127255 0.0202480i
\(499\) −36.2222 −1.62153 −0.810764 0.585374i \(-0.800948\pi\)
−0.810764 + 0.585374i \(0.800948\pi\)
\(500\) −9.87756 + 17.1084i −0.441738 + 0.765112i
\(501\) 16.0201 + 19.7545i 0.715726 + 0.882564i
\(502\) −2.28100 3.95080i −0.101806 0.176333i
\(503\) 15.6764 0.698974 0.349487 0.936941i \(-0.386356\pi\)
0.349487 + 0.936941i \(0.386356\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) 2.48113 + 4.29743i 0.110299 + 0.191044i
\(507\) 7.43474 19.4094i 0.330188 0.862002i
\(508\) 1.30150 2.25427i 0.0577449 0.100017i
\(509\) 34.3034 1.52047 0.760237 0.649646i \(-0.225083\pi\)
0.760237 + 0.649646i \(0.225083\pi\)
\(510\) −1.21574 + 3.17384i −0.0538337 + 0.140540i
\(511\) 0 0
\(512\) −17.0071 −0.751616
\(513\) −0.506837 + 10.0825i −0.0223774 + 0.445151i
\(514\) −1.77455 3.07361i −0.0782720 0.135571i
\(515\) −5.19699 −0.229007
\(516\) 4.71698 + 5.81652i 0.207653 + 0.256058i
\(517\) 10.7934 + 18.6948i 0.474694 + 0.822195i
\(518\) 0 0
\(519\) −0.275794 0.340082i −0.0121060 0.0149279i
\(520\) −0.557180 0.965064i −0.0244340 0.0423209i
\(521\) 5.12244 + 8.87233i 0.224418 + 0.388704i 0.956145 0.292895i \(-0.0946185\pi\)
−0.731727 + 0.681598i \(0.761285\pi\)
\(522\) −0.163069 + 0.0532407i −0.00713732 + 0.00233028i
\(523\) −15.3015 + 26.5030i −0.669088 + 1.15889i 0.309071 + 0.951039i \(0.399982\pi\)
−0.978159 + 0.207856i \(0.933352\pi\)
\(524\) −4.82489 + 8.35696i −0.210776 + 0.365075i
\(525\) 0 0
\(526\) −0.925580 1.60315i −0.0403572 0.0699007i
\(527\) −11.5264 −0.502098
\(528\) 14.7895 + 18.2369i 0.643629 + 0.793661i
\(529\) 8.39372 0.364944
\(530\) −1.63968 + 2.84001i −0.0712232 + 0.123362i
\(531\) −1.61273 + 7.64068i −0.0699863 + 0.331577i
\(532\) 0 0
\(533\) 5.09097 8.81782i 0.220514 0.381942i
\(534\) −1.12368 + 0.178793i −0.0486266 + 0.00773714i
\(535\) −8.11273 + 14.0517i −0.350744 + 0.607506i
\(536\) −1.65374 + 2.86437i −0.0714309 + 0.123722i
\(537\) −15.4834 19.0927i −0.668160 0.823911i
\(538\) −0.180699 + 0.312981i −0.00779051 + 0.0134936i
\(539\) 0 0
\(540\) 0.599052 11.9169i 0.0257791 0.512821i
\(541\) 13.0458 22.5960i 0.560884 0.971480i −0.436536 0.899687i \(-0.643795\pi\)
0.997420 0.0717926i \(-0.0228720\pi\)
\(542\) 5.25607 0.225767
\(543\) −2.44858 + 0.389601i −0.105079 + 0.0167194i
\(544\) 19.1683 0.821833
\(545\) −0.746515 1.29300i −0.0319772 0.0553861i
\(546\) 0 0
\(547\) 5.46169 9.45993i 0.233525 0.404478i −0.725318 0.688414i \(-0.758307\pi\)
0.958843 + 0.283937i \(0.0916405\pi\)
\(548\) −4.21574 + 7.30187i −0.180087 + 0.311920i
\(549\) 16.9721 + 15.2381i 0.724352 + 0.650346i
\(550\) 1.59549 + 2.76346i 0.0680317 + 0.117834i
\(551\) −0.232287 0.402332i −0.00989575 0.0171399i
\(552\) −9.03611 + 1.43777i −0.384603 + 0.0611954i
\(553\) 0 0
\(554\) −1.29467 2.24243i −0.0550052 0.0952718i
\(555\) 6.99028 18.2491i 0.296721 0.774631i
\(556\) −7.66019 −0.324864
\(557\) 6.97210 + 12.0760i 0.295417 + 0.511678i 0.975082 0.221845i \(-0.0712080\pi\)
−0.679665 + 0.733523i \(0.737875\pi\)
\(558\) −1.13216 + 0.369640i −0.0479280 + 0.0156481i
\(559\) 2.22545 0.0941265
\(560\) 0 0
\(561\) −28.0534 34.5927i −1.18441 1.46050i
\(562\) 4.03559 0.170231
\(563\) −15.1287 + 26.2037i −0.637600 + 1.10435i 0.348358 + 0.937361i \(0.386739\pi\)
−0.985958 + 0.166993i \(0.946594\pi\)
\(564\) −19.3695 + 3.08194i −0.815602 + 0.129773i
\(565\) −7.18770 12.4495i −0.302389 0.523753i
\(566\) 3.66268 0.153954
\(567\) 0 0
\(568\) 8.11109 0.340334
\(569\) 10.5676 + 18.3036i 0.443016 + 0.767326i 0.997912 0.0645936i \(-0.0205751\pi\)
−0.554896 + 0.831920i \(0.687242\pi\)
\(570\) −0.939253 + 0.149448i −0.0393410 + 0.00625968i
\(571\) 16.3932 28.3938i 0.686033 1.18824i −0.287078 0.957907i \(-0.592684\pi\)
0.973111 0.230336i \(-0.0739826\pi\)
\(572\) 7.19562 0.300864
\(573\) −16.4383 20.2701i −0.686720 0.846797i
\(574\) 0 0
\(575\) 20.1877 0.841885
\(576\) −18.9939 + 6.20135i −0.791410 + 0.258390i
\(577\) 8.68715 + 15.0466i 0.361651 + 0.626397i 0.988233 0.152958i \(-0.0488800\pi\)
−0.626582 + 0.779355i \(0.715547\pi\)
\(578\) −7.46130 −0.310349
\(579\) 4.86225 12.6936i 0.202068 0.527527i
\(580\) 0.274550 + 0.475534i 0.0114001 + 0.0197455i
\(581\) 0 0
\(582\) −2.93203 + 0.466524i −0.121536 + 0.0193381i
\(583\) −21.4870 37.2166i −0.889901 1.54135i
\(584\) −7.14132 12.3691i −0.295510 0.511838i
\(585\) −2.63844 2.36887i −0.109086 0.0979409i
\(586\) −1.12025 + 1.94033i −0.0462771 + 0.0801543i
\(587\) −8.48796 + 14.7016i −0.350336 + 0.606799i −0.986308 0.164913i \(-0.947266\pi\)
0.635973 + 0.771712i \(0.280599\pi\)
\(588\) 0 0
\(589\) −1.61273 2.79332i −0.0664512 0.115097i
\(590\) −0.735689 −0.0302878
\(591\) 11.4435 1.82082i 0.470723 0.0748983i
\(592\) −34.9396 −1.43601
\(593\) 6.53667 11.3218i 0.268429 0.464932i −0.700027 0.714116i \(-0.746829\pi\)
0.968456 + 0.249184i \(0.0801622\pi\)
\(594\) −3.86483 2.49815i −0.158576 0.102500i
\(595\) 0 0
\(596\) 10.7934 18.6948i 0.442116 0.765767i
\(597\) 21.7535 + 26.8243i 0.890311 + 1.09785i
\(598\) −0.669905 + 1.16031i −0.0273945 + 0.0474486i
\(599\) −14.6030 + 25.2932i −0.596663 + 1.03345i 0.396647 + 0.917971i \(0.370174\pi\)
−0.993310 + 0.115479i \(0.963160\pi\)
\(600\) −5.81066 + 0.924554i −0.237219 + 0.0377448i
\(601\) −3.89536 + 6.74695i −0.158895 + 0.275214i −0.934470 0.356041i \(-0.884126\pi\)
0.775576 + 0.631255i \(0.217460\pi\)
\(602\) 0 0
\(603\) −2.17347 + 10.2974i −0.0885106 + 0.419341i
\(604\) 13.5253 23.4265i 0.550337 0.953212i
\(605\) 3.21178 0.130577
\(606\) −3.33530 4.11277i −0.135487 0.167070i
\(607\) −19.6408 −0.797194 −0.398597 0.917126i \(-0.630503\pi\)
−0.398597 + 0.917126i \(0.630503\pi\)
\(608\) 2.68194 + 4.64526i 0.108767 + 0.188390i
\(609\) 0 0
\(610\) −1.07442 + 1.86095i −0.0435020 + 0.0753477i
\(611\) −2.91423 + 5.04759i −0.117897 + 0.204204i
\(612\) 38.4676 12.5594i 1.55496 0.507683i
\(613\) −11.7826 20.4081i −0.475896 0.824276i 0.523723 0.851889i \(-0.324543\pi\)
−0.999619 + 0.0276128i \(0.991209\pi\)
\(614\) 0.324502 + 0.562054i 0.0130958 + 0.0226827i
\(615\) 13.1293 + 16.1898i 0.529424 + 0.652834i
\(616\) 0 0
\(617\) 5.33009 + 9.23200i 0.214582 + 0.371666i 0.953143 0.302520i \(-0.0978279\pi\)
−0.738562 + 0.674186i \(0.764495\pi\)
\(618\) −1.14707 1.41446i −0.0461420 0.0568979i
\(619\) −18.0150 −0.724086 −0.362043 0.932161i \(-0.617921\pi\)
−0.362043 + 0.932161i \(0.617921\pi\)
\(620\) 1.90615 + 3.30155i 0.0765528 + 0.132593i
\(621\) −25.9126 + 13.2728i −1.03984 + 0.532620i
\(622\) 3.34308 0.134045
\(623\) 0 0
\(624\) −2.26771 + 5.92017i −0.0907812 + 0.236997i
\(625\) 5.99673 0.239869
\(626\) −2.27812 + 3.94581i −0.0910519 + 0.157706i
\(627\) 4.45813 11.6385i 0.178040 0.464799i
\(628\) 0.0555452 + 0.0962071i 0.00221649 + 0.00383908i
\(629\) 66.2750 2.64256
\(630\) 0 0
\(631\) 12.4703 0.496436 0.248218 0.968704i \(-0.420155\pi\)
0.248218 + 0.968704i \(0.420155\pi\)
\(632\) −3.47786 6.02382i −0.138342 0.239615i
\(633\) 19.7375 + 24.3384i 0.784495 + 0.967363i
\(634\) −0.480570 + 0.832371i −0.0190859 + 0.0330577i
\(635\) 1.58358 0.0628424
\(636\) 38.5598 6.13538i 1.52900 0.243284i
\(637\) 0 0
\(638\) 0.211777 0.00838434
\(639\) 24.5345 8.01033i 0.970569 0.316884i
\(640\) −4.20439 7.28221i −0.166193 0.287855i
\(641\) 19.1456 0.756205 0.378102 0.925764i \(-0.376577\pi\)
0.378102 + 0.925764i \(0.376577\pi\)
\(642\) −5.61505 + 0.893429i −0.221608 + 0.0352608i
\(643\) −3.24433 5.61934i −0.127944 0.221605i 0.794936 0.606693i \(-0.207504\pi\)
−0.922880 + 0.385088i \(0.874171\pi\)
\(644\) 0 0
\(645\) −1.62967 + 4.25447i −0.0641681 + 0.167520i
\(646\) −1.61273 2.79332i −0.0634518 0.109902i
\(647\) 24.0494 + 41.6548i 0.945479 + 1.63762i 0.754789 + 0.655968i \(0.227739\pi\)
0.190691 + 0.981650i \(0.438927\pi\)
\(648\) 6.85060 5.00708i 0.269117 0.196697i
\(649\) 4.82038 8.34914i 0.189216 0.327733i
\(650\) −0.430782 + 0.746136i −0.0168967 + 0.0292659i
\(651\) 0 0
\(652\) −1.46496 2.53739i −0.0573724 0.0993720i
\(653\) −43.2405 −1.69213 −0.846066 0.533079i \(-0.821035\pi\)
−0.846066 + 0.533079i \(0.821035\pi\)
\(654\) 0.187145 0.488568i 0.00731795 0.0191045i
\(655\) −5.87059 −0.229383
\(656\) 18.6339 32.2749i 0.727532 1.26012i
\(657\) −33.8166 30.3616i −1.31931 1.18452i
\(658\) 0 0
\(659\) 1.25404 2.17206i 0.0488505 0.0846115i −0.840566 0.541709i \(-0.817778\pi\)
0.889417 + 0.457097i \(0.151111\pi\)
\(660\) −5.26925 + 13.7561i −0.205105 + 0.535456i
\(661\) 21.1677 36.6636i 0.823329 1.42605i −0.0798613 0.996806i \(-0.525448\pi\)
0.903190 0.429241i \(-0.141219\pi\)
\(662\) −1.47988 + 2.56323i −0.0575172 + 0.0996227i
\(663\) 4.30150 11.2297i 0.167057 0.436124i
\(664\) 3.27292 5.66886i 0.127014 0.219994i
\(665\) 0 0
\(666\) 6.50972 2.12537i 0.252246 0.0823566i
\(667\) 0.669905 1.16031i 0.0259388 0.0449274i
\(668\) 28.5289 1.10382
\(669\) 14.0374 36.6464i 0.542716 1.41683i
\(670\) −0.991489 −0.0383046
\(671\) −14.0796 24.3866i −0.543538 0.941435i
\(672\) 0 0
\(673\) −6.70765 + 11.6180i −0.258561 + 0.447841i −0.965857 0.259077i \(-0.916582\pi\)
0.707296 + 0.706918i \(0.249915\pi\)
\(674\) 1.46582 2.53887i 0.0564612 0.0977936i
\(675\) −16.6631 + 8.53508i −0.641362 + 0.328515i
\(676\) −11.6569 20.1904i −0.448343 0.776553i
\(677\) −0.981125 1.69936i −0.0377077 0.0653117i 0.846556 0.532300i \(-0.178672\pi\)
−0.884263 + 0.466989i \(0.845339\pi\)
\(678\) 1.80190 4.70409i 0.0692014 0.180660i
\(679\) 0 0
\(680\) 3.86840 + 6.70027i 0.148346 + 0.256943i
\(681\) −9.03611 + 1.43777i −0.346265 + 0.0550953i
\(682\) 1.47033 0.0563019
\(683\) −13.5836 23.5275i −0.519761 0.900253i −0.999736 0.0229706i \(-0.992688\pi\)
0.479975 0.877282i \(-0.340646\pi\)
\(684\) 8.42588 + 7.56503i 0.322171 + 0.289256i
\(685\) −5.12941 −0.195985
\(686\) 0 0
\(687\) 33.0758 5.26280i 1.26192 0.200788i
\(688\) 8.14557 0.310547
\(689\) 5.80150 10.0485i 0.221020 0.382817i
\(690\) −1.72764 2.13036i −0.0657702 0.0811014i
\(691\) 25.1586 + 43.5759i 0.957077 + 1.65771i 0.729543 + 0.683935i \(0.239733\pi\)
0.227534 + 0.973770i \(0.426934\pi\)
\(692\) −0.491138 −0.0186703
\(693\) 0 0
\(694\) −1.59012 −0.0603601
\(695\) −2.33009 4.03584i −0.0883855 0.153088i
\(696\) −0.139680 + 0.364654i −0.00529457 + 0.0138222i
\(697\) −35.3457 + 61.2205i −1.33881 + 2.31889i
\(698\) −2.73431 −0.103495
\(699\) 10.5205 27.4652i 0.397922 1.03883i
\(700\) 0 0
\(701\) 45.1672 1.70594 0.852970 0.521960i \(-0.174799\pi\)
0.852970 + 0.521960i \(0.174799\pi\)
\(702\) 0.0623817 1.24095i 0.00235445 0.0468368i
\(703\) 9.27292 + 16.0612i 0.349735 + 0.605758i
\(704\) 24.6673 0.929685
\(705\) −7.51561 9.26752i −0.283054 0.349035i
\(706\) −2.65374 4.59642i −0.0998750 0.172989i
\(707\) 0 0
\(708\) 5.51724 + 6.80333i 0.207351 + 0.255685i
\(709\) −19.8090 34.3102i −0.743944 1.28855i −0.950687 0.310153i \(-0.899620\pi\)
0.206743 0.978395i \(-0.433714\pi\)
\(710\) 1.21574 + 2.10571i 0.0456257 + 0.0790261i
\(711\) −16.4688 14.7862i −0.617629 0.554528i
\(712\) −1.29506 + 2.24311i −0.0485344 + 0.0840640i
\(713\) 4.65103 8.05582i 0.174182 0.301693i
\(714\) 0 0
\(715\) 2.18878 + 3.79108i 0.0818557 + 0.141778i
\(716\) −27.5732 −1.03046
\(717\) −18.4218 22.7159i −0.687973 0.848342i
\(718\) 1.80687 0.0674318
\(719\) 11.0189 19.0853i 0.410935 0.711760i −0.584058 0.811712i \(-0.698536\pi\)
0.994992 + 0.0999525i \(0.0318691\pi\)
\(720\) −9.65718 8.67053i −0.359902 0.323132i
\(721\) 0 0
\(722\) −1.82038 + 3.15299i −0.0677475 + 0.117342i
\(723\) 46.4334 7.38817i 1.72688 0.274769i
\(724\) −1.39054 + 2.40849i −0.0516792 + 0.0895110i
\(725\) 0.430782 0.746136i 0.0159988 0.0277108i
\(726\) 0.708899 + 0.874145i 0.0263097 + 0.0324426i
\(727\) −14.0555 + 24.3449i −0.521291 + 0.902903i 0.478402 + 0.878141i \(0.341216\pi\)
−0.999693 + 0.0247621i \(0.992117\pi\)
\(728\) 0 0
\(729\) 15.7769 21.9110i 0.584329 0.811517i
\(730\) 2.14076 3.70790i 0.0792331 0.137236i
\(731\) −15.4509 −0.571472
\(732\) 25.2668 4.02028i 0.933887 0.148594i
\(733\) 11.8695 0.438409 0.219205 0.975679i \(-0.429654\pi\)
0.219205 + 0.975679i \(0.429654\pi\)
\(734\) −2.21466 3.83590i −0.0817444 0.141586i
\(735\) 0 0
\(736\) −7.73461 + 13.3967i −0.285102 + 0.493810i
\(737\) 6.49643 11.2522i 0.239299 0.414478i
\(738\) −1.50847 + 7.14676i −0.0555276 + 0.263076i
\(739\) 6.09222 + 10.5520i 0.224106 + 0.388163i 0.956051 0.293201i \(-0.0947206\pi\)
−0.731945 + 0.681364i \(0.761387\pi\)
\(740\) −10.9601 18.9834i −0.402900 0.697843i
\(741\) 3.32326 0.528775i 0.122083 0.0194250i
\(742\) 0 0
\(743\) 22.2427 + 38.5255i 0.816005 + 1.41336i 0.908604 + 0.417659i \(0.137149\pi\)
−0.0925987 + 0.995704i \(0.529517\pi\)
\(744\) −0.969775 + 2.53173i −0.0355537 + 0.0928177i
\(745\) 13.1327 0.481144
\(746\) 1.87236 + 3.24302i 0.0685519 + 0.118735i
\(747\) 4.30150 20.3794i 0.157384 0.745645i
\(748\) −49.9579 −1.82664
\(749\) 0 0
\(750\) −2.65267 3.27101i −0.0968616 0.119440i
\(751\) 42.8058 1.56200 0.781002 0.624528i \(-0.214709\pi\)
0.781002 + 0.624528i \(0.214709\pi\)
\(752\) −10.6666 + 18.4752i −0.388972 + 0.673720i
\(753\) −32.6335 + 5.19243i −1.18923 + 0.189223i
\(754\) 0.0285900 + 0.0495193i 0.00104119 + 0.00180339i
\(755\) 16.4567 0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) 0.482760 + 0.836165i 0.0175346 + 0.0303709i
\(759\) 35.4967 5.64800i 1.28845 0.205010i
\(760\) −1.08250 + 1.87495i −0.0392664 + 0.0680114i
\(761\) −14.3365 −0.519699 −0.259850 0.965649i \(-0.583673\pi\)
−0.259850 + 0.965649i \(0.583673\pi\)
\(762\) 0.349525 + 0.431001i 0.0126620 + 0.0156135i
\(763\) 0 0
\(764\) −29.2736 −1.05908
\(765\) 18.3182 + 16.4467i 0.662296 + 0.594630i
\(766\) 0.0269552 + 0.0466878i 0.000973931 + 0.00168690i
\(767\) 2.60301 0.0939892
\(768\) −7.19879 + 18.7934i −0.259764 + 0.678149i
\(769\) 15.6105 + 27.0382i 0.562930 + 0.975024i 0.997239 + 0.0742597i \(0.0236594\pi\)
−0.434309 + 0.900764i \(0.643007\pi\)
\(770\) 0 0
\(771\) −25.3880 + 4.03956i −0.914325 + 0.145481i
\(772\) −7.62352 13.2043i −0.274376 0.475234i