Properties

Label 729.2.e.p.325.1
Level $729$
Weight $2$
Character 729.325
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), 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: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.101559956668416.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 8x^{6} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 325.1
Root \(-1.39273 + 0.245576i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.p.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.87642 + 1.57450i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-2.30177 + 0.837775i) q^{5} +(0.347296 + 1.96962i) q^{7} +(2.44949 + 4.24264i) q^{8} +O(q^{10})\) \(q+(-1.87642 + 1.57450i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-2.30177 + 0.837775i) q^{5} +(0.347296 + 1.96962i) q^{7} +(2.44949 + 4.24264i) q^{8} +(3.00000 - 5.19615i) q^{10} +(2.30177 + 0.837775i) q^{11} +(-0.766044 - 0.642788i) q^{13} +(-3.75284 - 3.14900i) q^{14} +(-3.75877 - 1.36808i) q^{16} +(-3.67423 + 6.36396i) q^{17} +(0.500000 + 0.866025i) q^{19} +(1.70140 + 9.64911i) q^{20} +(-5.63816 + 2.05212i) q^{22} +(0.425349 - 2.41228i) q^{23} +(0.766044 - 0.642788i) q^{25} +2.44949 q^{26} +8.00000 q^{28} +(3.75284 - 3.14900i) q^{29} +(-0.173648 + 0.984808i) q^{31} +(-3.12567 - 17.7265i) q^{34} +(-2.44949 - 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-2.30177 - 0.837775i) q^{38} +(-9.19253 - 7.71345i) q^{40} +(-3.75284 - 3.14900i) q^{41} +(-10.3366 - 3.76222i) q^{43} +(4.89898 - 8.48528i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-1.70140 - 9.64911i) q^{47} +(2.81908 - 1.02606i) q^{49} +(-0.425349 + 2.41228i) q^{50} +(-3.06418 + 2.57115i) q^{52} -7.34847 q^{53} -6.00000 q^{55} +(-7.50567 + 6.29801i) q^{56} +(-2.08378 + 11.8177i) q^{58} +(-2.30177 + 0.837775i) q^{59} +(0.868241 + 4.92404i) q^{61} +(-1.22474 - 2.12132i) q^{62} +(4.00000 - 6.92820i) q^{64} +(2.30177 + 0.837775i) q^{65} +(-5.36231 - 4.49951i) q^{67} +(22.5170 + 18.8940i) q^{68} +(11.2763 + 4.10424i) q^{70} +(3.67423 - 6.36396i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(-3.40280 - 19.2982i) q^{74} +(3.75877 - 1.36808i) q^{76} +(-0.850699 + 4.82455i) q^{77} +(-5.36231 + 4.49951i) q^{79} +9.79796 q^{80} +12.0000 q^{82} +(9.38209 - 7.87251i) q^{83} +(3.12567 - 17.7265i) q^{85} +(25.3194 - 9.21552i) q^{86} +(2.08378 + 11.8177i) q^{88} +(1.00000 - 1.73205i) q^{91} +(-9.20707 - 3.35110i) q^{92} +(18.3851 + 15.4269i) q^{94} +(-1.87642 - 1.57450i) q^{95} +(6.57785 + 2.39414i) q^{97} +(-3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 36 q^{10} + 6 q^{19} + 96 q^{28} - 48 q^{37} + 36 q^{46} - 72 q^{55} + 48 q^{64} - 66 q^{73} + 144 q^{82} + 12 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87642 + 1.57450i −1.32683 + 1.11334i −0.342020 + 0.939693i \(0.611111\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(3\) 0 0
\(4\) 0.694593 3.93923i 0.347296 1.96962i
\(5\) −2.30177 + 0.837775i −1.02938 + 0.374664i −0.800845 0.598871i \(-0.795616\pi\)
−0.228536 + 0.973535i \(0.573394\pi\)
\(6\) 0 0
\(7\) 0.347296 + 1.96962i 0.131266 + 0.744445i 0.977388 + 0.211455i \(0.0678203\pi\)
−0.846122 + 0.532989i \(0.821069\pi\)
\(8\) 2.44949 + 4.24264i 0.866025 + 1.50000i
\(9\) 0 0
\(10\) 3.00000 5.19615i 0.948683 1.64317i
\(11\) 2.30177 + 0.837775i 0.694009 + 0.252599i 0.664851 0.746976i \(-0.268495\pi\)
0.0291582 + 0.999575i \(0.490717\pi\)
\(12\) 0 0
\(13\) −0.766044 0.642788i −0.212463 0.178277i 0.530346 0.847781i \(-0.322062\pi\)
−0.742808 + 0.669504i \(0.766507\pi\)
\(14\) −3.75284 3.14900i −1.00299 0.841607i
\(15\) 0 0
\(16\) −3.75877 1.36808i −0.939693 0.342020i
\(17\) −3.67423 + 6.36396i −0.891133 + 1.54349i −0.0526138 + 0.998615i \(0.516755\pi\)
−0.838519 + 0.544872i \(0.816578\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.70140 + 9.64911i 0.380444 + 2.15761i
\(21\) 0 0
\(22\) −5.63816 + 2.05212i −1.20206 + 0.437514i
\(23\) 0.425349 2.41228i 0.0886915 0.502994i −0.907807 0.419387i \(-0.862245\pi\)
0.996499 0.0836069i \(-0.0266440\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 2.44949 0.480384
\(27\) 0 0
\(28\) 8.00000 1.51186
\(29\) 3.75284 3.14900i 0.696884 0.584755i −0.224001 0.974589i \(-0.571912\pi\)
0.920885 + 0.389834i \(0.127467\pi\)
\(30\) 0 0
\(31\) −0.173648 + 0.984808i −0.0311881 + 0.176877i −0.996423 0.0845082i \(-0.973068\pi\)
0.965235 + 0.261385i \(0.0841792\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −3.12567 17.7265i −0.536048 3.04008i
\(35\) −2.44949 4.24264i −0.414039 0.717137i
\(36\) 0 0
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) −2.30177 0.837775i −0.373396 0.135905i
\(39\) 0 0
\(40\) −9.19253 7.71345i −1.45347 1.21960i
\(41\) −3.75284 3.14900i −0.586095 0.491792i 0.300848 0.953672i \(-0.402730\pi\)
−0.886942 + 0.461881i \(0.847175\pi\)
\(42\) 0 0
\(43\) −10.3366 3.76222i −1.57632 0.573733i −0.601920 0.798556i \(-0.705597\pi\)
−0.974400 + 0.224823i \(0.927820\pi\)
\(44\) 4.89898 8.48528i 0.738549 1.27920i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −1.70140 9.64911i −0.248174 1.40747i −0.813003 0.582259i \(-0.802169\pi\)
0.564829 0.825208i \(-0.308942\pi\)
\(48\) 0 0
\(49\) 2.81908 1.02606i 0.402725 0.146580i
\(50\) −0.425349 + 2.41228i −0.0601535 + 0.341147i
\(51\) 0 0
\(52\) −3.06418 + 2.57115i −0.424925 + 0.356554i
\(53\) −7.34847 −1.00939 −0.504695 0.863298i \(-0.668395\pi\)
−0.504695 + 0.863298i \(0.668395\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) −7.50567 + 6.29801i −1.00299 + 0.841607i
\(57\) 0 0
\(58\) −2.08378 + 11.8177i −0.273613 + 1.55174i
\(59\) −2.30177 + 0.837775i −0.299665 + 0.109069i −0.487477 0.873136i \(-0.662083\pi\)
0.187812 + 0.982205i \(0.439860\pi\)
\(60\) 0 0
\(61\) 0.868241 + 4.92404i 0.111167 + 0.630459i 0.988577 + 0.150717i \(0.0481583\pi\)
−0.877410 + 0.479741i \(0.840731\pi\)
\(62\) −1.22474 2.12132i −0.155543 0.269408i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.500000 0.866025i
\(65\) 2.30177 + 0.837775i 0.285499 + 0.103913i
\(66\) 0 0
\(67\) −5.36231 4.49951i −0.655111 0.549703i 0.253506 0.967334i \(-0.418416\pi\)
−0.908617 + 0.417631i \(0.862861\pi\)
\(68\) 22.5170 + 18.8940i 2.73059 + 2.29124i
\(69\) 0 0
\(70\) 11.2763 + 4.10424i 1.34778 + 0.490551i
\(71\) 3.67423 6.36396i 0.436051 0.755263i −0.561329 0.827592i \(-0.689710\pi\)
0.997381 + 0.0723293i \(0.0230432\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) −3.40280 19.2982i −0.395567 2.24337i
\(75\) 0 0
\(76\) 3.75877 1.36808i 0.431161 0.156930i
\(77\) −0.850699 + 4.82455i −0.0969461 + 0.549809i
\(78\) 0 0
\(79\) −5.36231 + 4.49951i −0.603307 + 0.506235i −0.892507 0.451034i \(-0.851055\pi\)
0.289200 + 0.957269i \(0.406611\pi\)
\(80\) 9.79796 1.09545
\(81\) 0 0
\(82\) 12.0000 1.32518
\(83\) 9.38209 7.87251i 1.02982 0.864120i 0.0389889 0.999240i \(-0.487586\pi\)
0.990829 + 0.135120i \(0.0431419\pi\)
\(84\) 0 0
\(85\) 3.12567 17.7265i 0.339026 1.92271i
\(86\) 25.3194 9.21552i 2.73027 0.993735i
\(87\) 0 0
\(88\) 2.08378 + 11.8177i 0.222131 + 1.25977i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) 1.00000 1.73205i 0.104828 0.181568i
\(92\) −9.20707 3.35110i −0.959903 0.349376i
\(93\) 0 0
\(94\) 18.3851 + 15.4269i 1.89627 + 1.59116i
\(95\) −1.87642 1.57450i −0.192516 0.161540i
\(96\) 0 0
\(97\) 6.57785 + 2.39414i 0.667879 + 0.243088i 0.653635 0.756810i \(-0.273243\pi\)
0.0142448 + 0.999899i \(0.495466\pi\)
\(98\) −3.67423 + 6.36396i −0.371154 + 0.642857i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 0.850699 + 4.82455i 0.0846477 + 0.480061i 0.997432 + 0.0716191i \(0.0228166\pi\)
−0.912784 + 0.408442i \(0.866072\pi\)
\(102\) 0 0
\(103\) 6.57785 2.39414i 0.648135 0.235902i 0.00302937 0.999995i \(-0.499036\pi\)
0.645105 + 0.764094i \(0.276813\pi\)
\(104\) 0.850699 4.82455i 0.0834179 0.473086i
\(105\) 0 0
\(106\) 13.7888 11.5702i 1.33929 1.12379i
\(107\) −14.6969 −1.42081 −0.710403 0.703795i \(-0.751487\pi\)
−0.710403 + 0.703795i \(0.751487\pi\)
\(108\) 0 0
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 11.2585 9.44701i 1.07346 0.900737i
\(111\) 0 0
\(112\) 1.38919 7.87846i 0.131266 0.744445i
\(113\) −9.20707 + 3.35110i −0.866128 + 0.315245i −0.736598 0.676331i \(-0.763569\pi\)
−0.129530 + 0.991575i \(0.541347\pi\)
\(114\) 0 0
\(115\) 1.04189 + 5.90885i 0.0971567 + 0.551003i
\(116\) −9.79796 16.9706i −0.909718 1.57568i
\(117\) 0 0
\(118\) 3.00000 5.19615i 0.276172 0.478345i
\(119\) −13.8106 5.02665i −1.26602 0.460792i
\(120\) 0 0
\(121\) −3.83022 3.21394i −0.348202 0.292176i
\(122\) −9.38209 7.87251i −0.849415 0.712743i
\(123\) 0 0
\(124\) 3.75877 + 1.36808i 0.337548 + 0.122857i
\(125\) 4.89898 8.48528i 0.438178 0.758947i
\(126\) 0 0
\(127\) 9.50000 + 16.4545i 0.842989 + 1.46010i 0.887357 + 0.461084i \(0.152539\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 3.40280 + 19.2982i 0.300767 + 1.70574i
\(129\) 0 0
\(130\) −5.63816 + 2.05212i −0.494499 + 0.179983i
\(131\) −2.12675 + 12.0614i −0.185815 + 1.05381i 0.739089 + 0.673607i \(0.235256\pi\)
−0.924904 + 0.380200i \(0.875855\pi\)
\(132\) 0 0
\(133\) −1.53209 + 1.28558i −0.132849 + 0.111474i
\(134\) 17.1464 1.48123
\(135\) 0 0
\(136\) −36.0000 −3.08697
\(137\) −7.50567 + 6.29801i −0.641253 + 0.538075i −0.904403 0.426680i \(-0.859683\pi\)
0.263150 + 0.964755i \(0.415239\pi\)
\(138\) 0 0
\(139\) −1.73648 + 9.84808i −0.147286 + 0.835303i 0.818216 + 0.574910i \(0.194963\pi\)
−0.965503 + 0.260393i \(0.916148\pi\)
\(140\) −18.4141 + 6.70220i −1.55628 + 0.566439i
\(141\) 0 0
\(142\) 3.12567 + 17.7265i 0.262300 + 1.48758i
\(143\) −1.22474 2.12132i −0.102418 0.177394i
\(144\) 0 0
\(145\) −6.00000 + 10.3923i −0.498273 + 0.863034i
\(146\) 25.3194 + 9.21552i 2.09545 + 0.762682i
\(147\) 0 0
\(148\) 24.5134 + 20.5692i 2.01499 + 1.69078i
\(149\) −9.38209 7.87251i −0.768611 0.644941i 0.171742 0.985142i \(-0.445060\pi\)
−0.940353 + 0.340201i \(0.889505\pi\)
\(150\) 0 0
\(151\) −4.69846 1.71010i −0.382356 0.139166i 0.143689 0.989623i \(-0.454103\pi\)
−0.526045 + 0.850457i \(0.676326\pi\)
\(152\) −2.44949 + 4.24264i −0.198680 + 0.344124i
\(153\) 0 0
\(154\) −6.00000 10.3923i −0.483494 0.837436i
\(155\) −0.425349 2.41228i −0.0341649 0.193759i
\(156\) 0 0
\(157\) −15.9748 + 5.81434i −1.27493 + 0.464035i −0.888751 0.458391i \(-0.848426\pi\)
−0.386175 + 0.922426i \(0.626204\pi\)
\(158\) 2.97745 16.8859i 0.236873 1.34337i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.89898 0.386094
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −15.0113 + 12.5960i −1.17219 + 0.983583i
\(165\) 0 0
\(166\) −5.20945 + 29.5442i −0.404331 + 2.29308i
\(167\) 4.60353 1.67555i 0.356232 0.129658i −0.157704 0.987486i \(-0.550409\pi\)
0.513936 + 0.857829i \(0.328187\pi\)
\(168\) 0 0
\(169\) −2.08378 11.8177i −0.160291 0.909053i
\(170\) 22.0454 + 38.1838i 1.69081 + 2.92856i
\(171\) 0 0
\(172\) −22.0000 + 38.1051i −1.67748 + 2.90549i
\(173\) 9.20707 + 3.35110i 0.700001 + 0.254779i 0.667411 0.744689i \(-0.267402\pi\)
0.0325894 + 0.999469i \(0.489625\pi\)
\(174\) 0 0
\(175\) 1.53209 + 1.28558i 0.115815 + 0.0971804i
\(176\) −7.50567 6.29801i −0.565761 0.474730i
\(177\) 0 0
\(178\) 0 0
\(179\) −7.34847 + 12.7279i −0.549250 + 0.951330i 0.449076 + 0.893494i \(0.351753\pi\)
−0.998326 + 0.0578359i \(0.981580\pi\)
\(180\) 0 0
\(181\) −4.00000 6.92820i −0.297318 0.514969i 0.678204 0.734874i \(-0.262759\pi\)
−0.975521 + 0.219905i \(0.929425\pi\)
\(182\) 0.850699 + 4.82455i 0.0630580 + 0.357620i
\(183\) 0 0
\(184\) 11.2763 4.10424i 0.831301 0.302569i
\(185\) 3.40280 19.2982i 0.250178 1.41883i
\(186\) 0 0
\(187\) −13.7888 + 11.5702i −1.00834 + 0.846095i
\(188\) −39.1918 −2.85836
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) −7.50567 + 6.29801i −0.543091 + 0.455708i −0.872594 0.488447i \(-0.837564\pi\)
0.329502 + 0.944155i \(0.393119\pi\)
\(192\) 0 0
\(193\) 1.91013 10.8329i 0.137494 0.779768i −0.835596 0.549344i \(-0.814878\pi\)
0.973090 0.230424i \(-0.0740113\pi\)
\(194\) −16.1124 + 5.86442i −1.15680 + 0.421041i
\(195\) 0 0
\(196\) −2.08378 11.8177i −0.148841 0.844121i
\(197\) 7.34847 + 12.7279i 0.523557 + 0.906827i 0.999624 + 0.0274180i \(0.00872853\pi\)
−0.476067 + 0.879409i \(0.657938\pi\)
\(198\) 0 0
\(199\) 0.500000 0.866025i 0.0354441 0.0613909i −0.847759 0.530381i \(-0.822049\pi\)
0.883203 + 0.468990i \(0.155382\pi\)
\(200\) 4.60353 + 1.67555i 0.325519 + 0.118479i
\(201\) 0 0
\(202\) −9.19253 7.71345i −0.646784 0.542717i
\(203\) 7.50567 + 6.29801i 0.526795 + 0.442033i
\(204\) 0 0
\(205\) 11.2763 + 4.10424i 0.787572 + 0.286653i
\(206\) −8.57321 + 14.8492i −0.597324 + 1.03460i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 0.425349 + 2.41228i 0.0294220 + 0.166861i
\(210\) 0 0
\(211\) 0.939693 0.342020i 0.0646911 0.0235456i −0.309472 0.950909i \(-0.600152\pi\)
0.374163 + 0.927363i \(0.377930\pi\)
\(212\) −5.10419 + 28.9473i −0.350557 + 1.98811i
\(213\) 0 0
\(214\) 27.5776 23.1404i 1.88517 1.58184i
\(215\) 26.9444 1.83759
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 1.87642 1.57450i 0.127087 0.106639i
\(219\) 0 0
\(220\) −4.16756 + 23.6354i −0.280977 + 1.59350i
\(221\) 6.90530 2.51332i 0.464501 0.169065i
\(222\) 0 0
\(223\) −1.21554 6.89365i −0.0813984 0.461633i −0.998076 0.0620053i \(-0.980250\pi\)
0.916677 0.399628i \(-0.130861\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.0000 20.7846i 0.798228 1.38257i
\(227\) 9.20707 + 3.35110i 0.611095 + 0.222420i 0.628982 0.777420i \(-0.283472\pi\)
−0.0178875 + 0.999840i \(0.505694\pi\)
\(228\) 0 0
\(229\) −0.766044 0.642788i −0.0506216 0.0424766i 0.617126 0.786864i \(-0.288297\pi\)
−0.667747 + 0.744388i \(0.732741\pi\)
\(230\) −11.2585 9.44701i −0.742364 0.622917i
\(231\) 0 0
\(232\) 22.5526 + 8.20848i 1.48065 + 0.538913i
\(233\) −3.67423 + 6.36396i −0.240707 + 0.416917i −0.960916 0.276840i \(-0.910713\pi\)
0.720209 + 0.693757i \(0.244046\pi\)
\(234\) 0 0
\(235\) 12.0000 + 20.7846i 0.782794 + 1.35584i
\(236\) 1.70140 + 9.64911i 0.110752 + 0.628103i
\(237\) 0 0
\(238\) 33.8289 12.3127i 2.19280 0.798115i
\(239\) 0.425349 2.41228i 0.0275136 0.156037i −0.967956 0.251121i \(-0.919201\pi\)
0.995469 + 0.0950838i \(0.0303119\pi\)
\(240\) 0 0
\(241\) −12.2567 + 10.2846i −0.789524 + 0.662489i −0.945628 0.325251i \(-0.894551\pi\)
0.156103 + 0.987741i \(0.450107\pi\)
\(242\) 12.2474 0.787296
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) −5.62925 + 4.72350i −0.359640 + 0.301774i
\(246\) 0 0
\(247\) 0.173648 0.984808i 0.0110490 0.0626618i
\(248\) −4.60353 + 1.67555i −0.292325 + 0.106398i
\(249\) 0 0
\(250\) 4.16756 + 23.6354i 0.263579 + 1.49483i
\(251\) −3.67423 6.36396i −0.231916 0.401690i 0.726456 0.687213i \(-0.241166\pi\)
−0.958372 + 0.285523i \(0.907833\pi\)
\(252\) 0 0
\(253\) 3.00000 5.19615i 0.188608 0.326679i
\(254\) −43.7336 15.9177i −2.74409 0.998767i
\(255\) 0 0
\(256\) −24.5134 20.5692i −1.53209 1.28558i
\(257\) 13.1349 + 11.0215i 0.819334 + 0.687503i 0.952816 0.303548i \(-0.0981714\pi\)
−0.133482 + 0.991051i \(0.542616\pi\)
\(258\) 0 0
\(259\) −15.0351 5.47232i −0.934235 0.340034i
\(260\) 4.89898 8.48528i 0.303822 0.526235i
\(261\) 0 0
\(262\) −15.0000 25.9808i −0.926703 1.60510i
\(263\) 4.67884 + 26.5350i 0.288510 + 1.63622i 0.692472 + 0.721445i \(0.256522\pi\)
−0.403962 + 0.914776i \(0.632367\pi\)
\(264\) 0 0
\(265\) 16.9145 6.15636i 1.03905 0.378182i
\(266\) 0.850699 4.82455i 0.0521597 0.295812i
\(267\) 0 0
\(268\) −21.4492 + 17.9981i −1.31022 + 1.09941i
\(269\) 22.0454 1.34413 0.672066 0.740491i \(-0.265407\pi\)
0.672066 + 0.740491i \(0.265407\pi\)
\(270\) 0 0
\(271\) −7.00000 −0.425220 −0.212610 0.977137i \(-0.568196\pi\)
−0.212610 + 0.977137i \(0.568196\pi\)
\(272\) 22.5170 18.8940i 1.36529 1.14562i
\(273\) 0 0
\(274\) 4.16756 23.6354i 0.251771 1.42787i
\(275\) 2.30177 0.837775i 0.138802 0.0505197i
\(276\) 0 0
\(277\) 1.91013 + 10.8329i 0.114769 + 0.650885i 0.986865 + 0.161550i \(0.0516493\pi\)
−0.872096 + 0.489335i \(0.837240\pi\)
\(278\) −12.2474 21.2132i −0.734553 1.27228i
\(279\) 0 0
\(280\) 12.0000 20.7846i 0.717137 1.24212i
\(281\) −11.5088 4.18887i −0.686560 0.249887i −0.0248982 0.999690i \(-0.507926\pi\)
−0.661661 + 0.749803i \(0.730148\pi\)
\(282\) 0 0
\(283\) 13.0228 + 10.9274i 0.774122 + 0.649566i 0.941761 0.336283i \(-0.109170\pi\)
−0.167639 + 0.985849i \(0.553614\pi\)
\(284\) −22.5170 18.8940i −1.33614 1.12115i
\(285\) 0 0
\(286\) 5.63816 + 2.05212i 0.333391 + 0.121344i
\(287\) 4.89898 8.48528i 0.289178 0.500870i
\(288\) 0 0
\(289\) −18.5000 32.0429i −1.08824 1.88488i
\(290\) −5.10419 28.9473i −0.299729 1.69985i
\(291\) 0 0
\(292\) −41.3465 + 15.0489i −2.41962 + 0.880669i
\(293\) −0.850699 + 4.82455i −0.0496984 + 0.281853i −0.999521 0.0309343i \(-0.990152\pi\)
0.949823 + 0.312788i \(0.101263\pi\)
\(294\) 0 0
\(295\) 4.59627 3.85673i 0.267605 0.224547i
\(296\) −39.1918 −2.27798
\(297\) 0 0
\(298\) 30.0000 1.73785
\(299\) −1.87642 + 1.57450i −0.108516 + 0.0910558i
\(300\) 0 0
\(301\) 3.82026 21.6658i 0.220196 1.24879i
\(302\) 11.5088 4.18887i 0.662259 0.241043i
\(303\) 0 0
\(304\) −0.694593 3.93923i −0.0398376 0.225930i
\(305\) −6.12372 10.6066i −0.350643 0.607332i
\(306\) 0 0
\(307\) −1.00000 + 1.73205i −0.0570730 + 0.0988534i −0.893150 0.449758i \(-0.851510\pi\)
0.836077 + 0.548612i \(0.184843\pi\)
\(308\) 18.4141 + 6.70220i 1.04924 + 0.381893i
\(309\) 0 0
\(310\) 4.59627 + 3.85673i 0.261050 + 0.219047i
\(311\) 18.7642 + 15.7450i 1.06402 + 0.892818i 0.994497 0.104762i \(-0.0334082\pi\)
0.0695218 + 0.997580i \(0.477853\pi\)
\(312\) 0 0
\(313\) 15.0351 + 5.47232i 0.849833 + 0.309314i 0.729972 0.683477i \(-0.239533\pi\)
0.119861 + 0.992791i \(0.461755\pi\)
\(314\) 20.8207 36.0624i 1.17498 2.03512i
\(315\) 0 0
\(316\) 14.0000 + 24.2487i 0.787562 + 1.36410i
\(317\) −1.70140 9.64911i −0.0955600 0.541948i −0.994574 0.104029i \(-0.966827\pi\)
0.899014 0.437919i \(-0.144284\pi\)
\(318\) 0 0
\(319\) 11.2763 4.10424i 0.631352 0.229793i
\(320\) −3.40280 + 19.2982i −0.190222 + 1.07880i
\(321\) 0 0
\(322\) −9.19253 + 7.71345i −0.512280 + 0.429854i
\(323\) −7.34847 −0.408880
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 18.7642 15.7450i 1.03925 0.872036i
\(327\) 0 0
\(328\) 4.16756 23.6354i 0.230115 1.30505i
\(329\) 18.4141 6.70220i 1.01520 0.369504i
\(330\) 0 0
\(331\) −1.21554 6.89365i −0.0668120 0.378910i −0.999819 0.0190501i \(-0.993936\pi\)
0.933007 0.359859i \(-0.117175\pi\)
\(332\) −24.4949 42.4264i −1.34433 2.32845i
\(333\) 0 0
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) 16.1124 + 5.86442i 0.880313 + 0.320408i
\(336\) 0 0
\(337\) −21.4492 17.9981i −1.16841 0.980416i −0.168429 0.985714i \(-0.553869\pi\)
−0.999986 + 0.00529739i \(0.998314\pi\)
\(338\) 22.5170 + 18.8940i 1.22476 + 1.02770i
\(339\) 0 0
\(340\) −67.6579 24.6255i −3.66926 1.33550i
\(341\) −1.22474 + 2.12132i −0.0663237 + 0.114876i
\(342\) 0 0
\(343\) 10.0000 + 17.3205i 0.539949 + 0.935220i
\(344\) −9.35769 53.0701i −0.504533 2.86135i
\(345\) 0 0
\(346\) −22.5526 + 8.20848i −1.21244 + 0.441291i
\(347\) 4.25349 24.1228i 0.228340 1.29498i −0.627857 0.778328i \(-0.716068\pi\)
0.856197 0.516650i \(-0.172821\pi\)
\(348\) 0 0
\(349\) 15.3209 12.8558i 0.820108 0.688153i −0.132889 0.991131i \(-0.542425\pi\)
0.952997 + 0.302978i \(0.0979810\pi\)
\(350\) −4.89898 −0.261861
\(351\) 0 0
\(352\) 0 0
\(353\) −1.87642 + 1.57450i −0.0998717 + 0.0838023i −0.691356 0.722514i \(-0.742986\pi\)
0.591485 + 0.806316i \(0.298542\pi\)
\(354\) 0 0
\(355\) −3.12567 + 17.7265i −0.165893 + 0.940827i
\(356\) 0 0
\(357\) 0 0
\(358\) −6.25133 35.4531i −0.330393 1.87375i
\(359\) 14.6969 + 25.4558i 0.775675 + 1.34351i 0.934414 + 0.356188i \(0.115924\pi\)
−0.158740 + 0.987320i \(0.550743\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 18.4141 + 6.70220i 0.967826 + 0.352260i
\(363\) 0 0
\(364\) −6.12836 5.14230i −0.321213 0.269530i
\(365\) 20.6406 + 17.3195i 1.08038 + 0.906545i
\(366\) 0 0
\(367\) −4.69846 1.71010i −0.245258 0.0892665i 0.216466 0.976290i \(-0.430547\pi\)
−0.461724 + 0.887024i \(0.652769\pi\)
\(368\) −4.89898 + 8.48528i −0.255377 + 0.442326i
\(369\) 0 0
\(370\) 24.0000 + 41.5692i 1.24770 + 2.16108i
\(371\) −2.55210 14.4737i −0.132498 0.751435i
\(372\) 0 0
\(373\) −32.8892 + 11.9707i −1.70294 + 0.619820i −0.996155 0.0876084i \(-0.972078\pi\)
−0.706785 + 0.707428i \(0.749855\pi\)
\(374\) 7.65629 43.4210i 0.395897 2.24525i
\(375\) 0 0
\(376\) 36.7701 30.8538i 1.89627 1.59116i
\(377\) −4.89898 −0.252310
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) −7.50567 + 6.29801i −0.385033 + 0.323081i
\(381\) 0 0
\(382\) 4.16756 23.6354i 0.213231 1.20929i
\(383\) 32.2247 11.7288i 1.64661 0.599316i 0.658432 0.752641i \(-0.271220\pi\)
0.988176 + 0.153324i \(0.0489980\pi\)
\(384\) 0 0
\(385\) −2.08378 11.8177i −0.106199 0.602285i
\(386\) 13.4722 + 23.3345i 0.685717 + 1.18770i
\(387\) 0 0
\(388\) 14.0000 24.2487i 0.710742 1.23104i
\(389\) −25.3194 9.21552i −1.28375 0.467246i −0.392077 0.919932i \(-0.628243\pi\)
−0.891670 + 0.452687i \(0.850466\pi\)
\(390\) 0 0
\(391\) 13.7888 + 11.5702i 0.697330 + 0.585129i
\(392\) 11.2585 + 9.44701i 0.568641 + 0.477146i
\(393\) 0 0
\(394\) −33.8289 12.3127i −1.70428 0.620306i
\(395\) 8.57321 14.8492i 0.431365 0.747146i
\(396\) 0 0
\(397\) 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i \(-0.158678\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 0.425349 + 2.41228i 0.0213208 + 0.120916i
\(399\) 0 0
\(400\) −3.75877 + 1.36808i −0.187939 + 0.0684040i
\(401\) −5.95489 + 33.7719i −0.297373 + 1.68649i 0.360024 + 0.932943i \(0.382768\pi\)
−0.657398 + 0.753544i \(0.728343\pi\)
\(402\) 0 0
\(403\) 0.766044 0.642788i 0.0381594 0.0320195i
\(404\) 19.5959 0.974933
\(405\) 0 0
\(406\) −24.0000 −1.19110
\(407\) −15.0113 + 12.5960i −0.744085 + 0.624361i
\(408\) 0 0
\(409\) −4.86215 + 27.5746i −0.240418 + 1.36348i 0.590480 + 0.807052i \(0.298938\pi\)
−0.830898 + 0.556425i \(0.812173\pi\)
\(410\) −27.6212 + 10.0533i −1.36411 + 0.496497i
\(411\) 0 0
\(412\) −4.86215 27.5746i −0.239541 1.35850i
\(413\) −2.44949 4.24264i −0.120532 0.208767i
\(414\) 0 0
\(415\) −15.0000 + 25.9808i −0.736321 + 1.27535i
\(416\) 0 0
\(417\) 0 0
\(418\) −4.59627 3.85673i −0.224811 0.188639i
\(419\) −26.2699 22.0430i −1.28337 1.07687i −0.992771 0.120026i \(-0.961702\pi\)
−0.290596 0.956846i \(-0.593853\pi\)
\(420\) 0 0
\(421\) −1.87939 0.684040i −0.0915956 0.0333381i 0.295816 0.955245i \(-0.404409\pi\)
−0.387412 + 0.921907i \(0.626631\pi\)
\(422\) −1.22474 + 2.12132i −0.0596196 + 0.103264i
\(423\) 0 0
\(424\) −18.0000 31.1769i −0.874157 1.51408i
\(425\) 1.27605 + 7.23683i 0.0618974 + 0.351038i
\(426\) 0 0
\(427\) −9.39693 + 3.42020i −0.454749 + 0.165515i
\(428\) −10.2084 + 57.8946i −0.493441 + 2.79844i
\(429\) 0 0
\(430\) −50.5589 + 42.4240i −2.43817 + 2.04587i
\(431\) 7.34847 0.353963 0.176982 0.984214i \(-0.443367\pi\)
0.176982 + 0.984214i \(0.443367\pi\)
\(432\) 0 0
\(433\) 17.0000 0.816968 0.408484 0.912766i \(-0.366058\pi\)
0.408484 + 0.912766i \(0.366058\pi\)
\(434\) 3.75284 3.14900i 0.180142 0.151157i
\(435\) 0 0
\(436\) −0.694593 + 3.93923i −0.0332650 + 0.188655i
\(437\) 2.30177 0.837775i 0.110108 0.0400762i
\(438\) 0 0
\(439\) 2.43107 + 13.7873i 0.116029 + 0.658032i 0.986236 + 0.165346i \(0.0528740\pi\)
−0.870207 + 0.492687i \(0.836015\pi\)
\(440\) −14.6969 25.4558i −0.700649 1.21356i
\(441\) 0 0
\(442\) −9.00000 + 15.5885i −0.428086 + 0.741467i
\(443\) −11.5088 4.18887i −0.546801 0.199019i 0.0538234 0.998550i \(-0.482859\pi\)
−0.600625 + 0.799531i \(0.705081\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 13.1349 + 11.0215i 0.621957 + 0.521884i
\(447\) 0 0
\(448\) 15.0351 + 5.47232i 0.710341 + 0.258543i
\(449\) 11.0227 19.0919i 0.520194 0.901002i −0.479531 0.877525i \(-0.659193\pi\)
0.999724 0.0234766i \(-0.00747353\pi\)
\(450\) 0 0
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 6.80559 + 38.5964i 0.320108 + 1.81542i
\(453\) 0 0
\(454\) −22.5526 + 8.20848i −1.05845 + 0.385243i
\(455\) −0.850699 + 4.82455i −0.0398814 + 0.226179i
\(456\) 0 0
\(457\) 22.2153 18.6408i 1.03919 0.871982i 0.0472719 0.998882i \(-0.484947\pi\)
0.991915 + 0.126900i \(0.0405028\pi\)
\(458\) 2.44949 0.114457
\(459\) 0 0
\(460\) 24.0000 1.11901
\(461\) 20.6406 17.3195i 0.961328 0.806650i −0.0198402 0.999803i \(-0.506316\pi\)
0.981169 + 0.193153i \(0.0618713\pi\)
\(462\) 0 0
\(463\) −3.29932 + 18.7113i −0.153332 + 0.869590i 0.806963 + 0.590603i \(0.201110\pi\)
−0.960295 + 0.278987i \(0.910001\pi\)
\(464\) −18.4141 + 6.70220i −0.854855 + 0.311142i
\(465\) 0 0
\(466\) −3.12567 17.7265i −0.144794 0.821166i
\(467\) 7.34847 + 12.7279i 0.340047 + 0.588978i 0.984441 0.175715i \(-0.0562238\pi\)
−0.644394 + 0.764693i \(0.722890\pi\)
\(468\) 0 0
\(469\) 7.00000 12.1244i 0.323230 0.559851i
\(470\) −55.2424 20.1066i −2.54814 0.927448i
\(471\) 0 0
\(472\) −9.19253 7.71345i −0.423121 0.355040i
\(473\) −20.6406 17.3195i −0.949056 0.796352i
\(474\) 0 0
\(475\) 0.939693 + 0.342020i 0.0431161 + 0.0156930i
\(476\) −29.3939 + 50.9117i −1.34727 + 2.33353i
\(477\) 0 0
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 4.67884 + 26.5350i 0.213782 + 1.21242i 0.883008 + 0.469358i \(0.155515\pi\)
−0.669226 + 0.743059i \(0.733374\pi\)
\(480\) 0 0
\(481\) 7.51754 2.73616i 0.342770 0.124758i
\(482\) 6.80559 38.5964i 0.309986 1.75802i
\(483\) 0 0
\(484\) −15.3209 + 12.8558i −0.696404 + 0.584352i
\(485\) −17.1464 −0.778579
\(486\) 0 0
\(487\) 35.0000 1.58600 0.793001 0.609221i \(-0.208518\pi\)
0.793001 + 0.609221i \(0.208518\pi\)
\(488\) −18.7642 + 15.7450i −0.849415 + 0.712743i
\(489\) 0 0
\(490\) 3.12567 17.7265i 0.141203 0.800803i
\(491\) −36.8283 + 13.4044i −1.66204 + 0.604932i −0.990681 0.136203i \(-0.956510\pi\)
−0.671356 + 0.741135i \(0.734288\pi\)
\(492\) 0 0
\(493\) 6.25133 + 35.4531i 0.281546 + 1.59673i
\(494\) 1.22474 + 2.12132i 0.0551039 + 0.0954427i
\(495\) 0 0
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) 13.8106 + 5.02665i 0.619490 + 0.225476i
\(498\) 0 0
\(499\) 1.53209 + 1.28558i 0.0685857 + 0.0575503i 0.676436 0.736501i \(-0.263524\pi\)
−0.607850 + 0.794052i \(0.707968\pi\)
\(500\) −30.0227 25.1920i −1.34266 1.12662i
\(501\) 0 0
\(502\) 16.9145 + 6.15636i 0.754930 + 0.274772i
\(503\) −7.34847 + 12.7279i −0.327652 + 0.567510i −0.982045 0.188644i \(-0.939591\pi\)
0.654393 + 0.756154i \(0.272924\pi\)
\(504\) 0 0
\(505\) −6.00000 10.3923i −0.266996 0.462451i
\(506\) 2.55210 + 14.4737i 0.113455 + 0.643433i
\(507\) 0 0
\(508\) 71.4166 25.9935i 3.16860 1.15328i
\(509\) 1.70140 9.64911i 0.0754131 0.427689i −0.923603 0.383349i \(-0.874771\pi\)
0.999017 0.0443397i \(-0.0141184\pi\)
\(510\) 0 0
\(511\) 16.8530 14.1413i 0.745532 0.625575i
\(512\) 39.1918 1.73205
\(513\) 0 0
\(514\) −42.0000 −1.85254
\(515\) −13.1349 + 11.0215i −0.578794 + 0.485666i
\(516\) 0 0
\(517\) 4.16756 23.6354i 0.183289 1.03948i
\(518\) 36.8283 13.4044i 1.61814 0.588955i
\(519\) 0 0
\(520\) 2.08378 + 11.8177i 0.0913797 + 0.518240i
\(521\) 11.0227 + 19.0919i 0.482913 + 0.836431i 0.999808 0.0196188i \(-0.00624525\pi\)
−0.516894 + 0.856049i \(0.672912\pi\)
\(522\) 0 0
\(523\) 12.5000 21.6506i 0.546587 0.946716i −0.451918 0.892059i \(-0.649260\pi\)
0.998505 0.0546569i \(-0.0174065\pi\)
\(524\) 46.0353 + 16.7555i 2.01106 + 0.731967i
\(525\) 0 0
\(526\) −50.5589 42.4240i −2.20447 1.84977i
\(527\) −5.62925 4.72350i −0.245214 0.205759i
\(528\) 0 0
\(529\) 15.9748 + 5.81434i 0.694555 + 0.252797i
\(530\) −22.0454 + 38.1838i −0.957591 + 1.65860i
\(531\) 0 0
\(532\) 4.00000 + 6.92820i 0.173422 + 0.300376i
\(533\) 0.850699 + 4.82455i 0.0368479 + 0.208975i
\(534\) 0 0
\(535\) 33.8289 12.3127i 1.46255 0.532326i
\(536\) 5.95489 33.7719i 0.257212 1.45872i
\(537\) 0 0
\(538\) −41.3664 + 34.7105i −1.78343 + 1.49648i
\(539\) 7.34847 0.316521
\(540\) 0 0
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) 13.1349 11.0215i 0.564193 0.473414i
\(543\) 0 0
\(544\) 0 0
\(545\) 2.30177 0.837775i 0.0985969 0.0358863i
\(546\) 0 0
\(547\) −2.25743 12.8025i −0.0965206 0.547395i −0.994271 0.106891i \(-0.965911\pi\)
0.897750 0.440505i \(-0.145201\pi\)
\(548\) 19.5959 + 33.9411i 0.837096 + 1.44989i
\(549\) 0 0
\(550\) −3.00000 + 5.19615i −0.127920 + 0.221565i
\(551\) 4.60353 + 1.67555i 0.196117 + 0.0713808i
\(552\) 0 0
\(553\) −10.7246 8.99903i −0.456057 0.382678i
\(554\) −20.6406 17.3195i −0.876935 0.735836i
\(555\) 0 0
\(556\) 37.5877 + 13.6808i 1.59407 + 0.580195i
\(557\) 3.67423 6.36396i 0.155682 0.269650i −0.777625 0.628728i \(-0.783576\pi\)
0.933307 + 0.359079i \(0.116909\pi\)
\(558\) 0 0
\(559\) 5.50000 + 9.52628i 0.232625 + 0.402919i
\(560\) 3.40280 + 19.2982i 0.143794 + 0.815498i
\(561\) 0 0
\(562\) 28.1908 10.2606i 1.18916 0.432817i
\(563\) −2.12675 + 12.0614i −0.0896317 + 0.508327i 0.906629 + 0.421929i \(0.138647\pi\)
−0.996261 + 0.0863979i \(0.972464\pi\)
\(564\) 0 0
\(565\) 18.3851 15.4269i 0.773466 0.649015i
\(566\) −41.6413 −1.75032
\(567\) 0 0
\(568\) 36.0000 1.51053
\(569\) 9.38209 7.87251i 0.393318 0.330033i −0.424586 0.905387i \(-0.639580\pi\)
0.817904 + 0.575355i \(0.195136\pi\)
\(570\) 0 0
\(571\) −1.73648 + 9.84808i −0.0726695 + 0.412129i 0.926673 + 0.375869i \(0.122656\pi\)
−0.999342 + 0.0362604i \(0.988455\pi\)
\(572\) −9.20707 + 3.35110i −0.384967 + 0.140117i
\(573\) 0 0
\(574\) 4.16756 + 23.6354i 0.173950 + 0.986522i
\(575\) −1.22474 2.12132i −0.0510754 0.0884652i
\(576\) 0 0
\(577\) 12.5000 21.6506i 0.520382 0.901328i −0.479337 0.877631i \(-0.659123\pi\)
0.999719 0.0236970i \(-0.00754370\pi\)
\(578\) 85.1654 + 30.9977i 3.54241 + 1.28933i
\(579\) 0 0
\(580\) 36.7701 + 30.8538i 1.52680 + 1.28113i
\(581\) 18.7642 + 15.7450i 0.778469 + 0.653213i
\(582\) 0 0
\(583\) −16.9145 6.15636i −0.700526 0.254970i
\(584\) 26.9444 46.6690i 1.11497 1.93118i
\(585\) 0 0
\(586\) −6.00000 10.3923i −0.247858 0.429302i
\(587\) −0.425349 2.41228i −0.0175560 0.0995653i 0.974771 0.223209i \(-0.0716532\pi\)
−0.992327 + 0.123644i \(0.960542\pi\)
\(588\) 0 0
\(589\) −0.939693 + 0.342020i −0.0387194 + 0.0140927i
\(590\) −2.55210 + 14.4737i −0.105068 + 0.595871i
\(591\) 0 0
\(592\) 24.5134 20.5692i 1.00750 0.845389i
\(593\) −7.34847 −0.301765 −0.150883 0.988552i \(-0.548212\pi\)
−0.150883 + 0.988552i \(0.548212\pi\)
\(594\) 0 0
\(595\) 36.0000 1.47586
\(596\) −37.5284 + 31.4900i −1.53722 + 1.28988i
\(597\) 0 0
\(598\) 1.04189 5.90885i 0.0426060 0.241631i
\(599\) −36.8283 + 13.4044i −1.50476 + 0.547689i −0.957289 0.289134i \(-0.906633\pi\)
−0.547474 + 0.836823i \(0.684411\pi\)
\(600\) 0 0
\(601\) −1.21554 6.89365i −0.0495828 0.281198i 0.949928 0.312468i \(-0.101156\pi\)
−0.999511 + 0.0312703i \(0.990045\pi\)
\(602\) 26.9444 + 46.6690i 1.09817 + 1.90209i
\(603\) 0 0
\(604\) −10.0000 + 17.3205i −0.406894 + 0.704761i
\(605\) 11.5088 + 4.18887i 0.467901 + 0.170302i
\(606\) 0 0
\(607\) 33.7060 + 28.2827i 1.36808 + 1.14796i 0.973393 + 0.229143i \(0.0735924\pi\)
0.394690 + 0.918814i \(0.370852\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 28.1908 + 10.2606i 1.14141 + 0.415440i
\(611\) −4.89898 + 8.48528i −0.198191 + 0.343278i
\(612\) 0 0
\(613\) −5.50000 9.52628i −0.222143 0.384763i 0.733316 0.679888i \(-0.237972\pi\)
−0.955458 + 0.295126i \(0.904638\pi\)
\(614\) −0.850699 4.82455i −0.0343314 0.194703i
\(615\) 0 0
\(616\) −22.5526 + 8.20848i −0.908671 + 0.330729i
\(617\) 4.25349 24.1228i 0.171239 0.971146i −0.771156 0.636646i \(-0.780321\pi\)
0.942396 0.334500i \(-0.108568\pi\)
\(618\) 0 0
\(619\) −37.5362 + 31.4966i −1.50871 + 1.26595i −0.642481 + 0.766302i \(0.722095\pi\)
−0.866226 + 0.499653i \(0.833461\pi\)
\(620\) −9.79796 −0.393496
\(621\) 0 0
\(622\) −60.0000 −2.40578
\(623\) 0 0
\(624\) 0 0
\(625\) −5.03580 + 28.5594i −0.201432 + 1.14238i
\(626\) −36.8283 + 13.4044i −1.47195 + 0.535747i
\(627\) 0 0
\(628\) 11.8081 + 66.9669i 0.471194 + 2.67227i
\(629\) −29.3939 50.9117i −1.17201 2.02998i
\(630\) 0 0
\(631\) −22.0000 + 38.1051i −0.875806 + 1.51694i −0.0199047 + 0.999802i \(0.506336\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) −32.2247 11.7288i −1.28183 0.466549i
\(633\) 0 0
\(634\) 18.3851 + 15.4269i 0.730164 + 0.612681i
\(635\) −35.6519 29.9155i −1.41480 1.18716i
\(636\) 0 0
\(637\) −2.81908 1.02606i −0.111696 0.0406540i
\(638\) −14.6969 + 25.4558i −0.581857 + 1.00781i
\(639\) 0 0
\(640\) −24.0000 41.5692i −0.948683 1.64317i
\(641\) −2.97745 16.8859i −0.117602 0.666954i −0.985429 0.170088i \(-0.945595\pi\)
0.867827 0.496867i \(-0.165516\pi\)
\(642\) 0 0
\(643\) −35.7083 + 12.9968i −1.40820 + 0.512542i −0.930601 0.366036i \(-0.880715\pi\)
−0.477598 + 0.878578i \(0.658492\pi\)
\(644\) 3.40280 19.2982i 0.134089 0.760456i
\(645\) 0 0
\(646\) 13.7888 11.5702i 0.542513 0.455223i
\(647\) −36.7423 −1.44449 −0.722245 0.691637i \(-0.756890\pi\)
−0.722245 + 0.691637i \(0.756890\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) 1.87642 1.57450i 0.0735992 0.0617570i
\(651\) 0 0
\(652\) −6.94593 + 39.3923i −0.272023 + 1.54272i
\(653\) −9.20707 + 3.35110i −0.360300 + 0.131139i −0.515826 0.856693i \(-0.672515\pi\)
0.155526 + 0.987832i \(0.450293\pi\)
\(654\) 0 0
\(655\) −5.20945 29.5442i −0.203550 1.15439i
\(656\) 9.79796 + 16.9706i 0.382546 + 0.662589i
\(657\) 0 0
\(658\) −24.0000 + 41.5692i −0.935617 + 1.62054i
\(659\) −18.4141 6.70220i −0.717313 0.261081i −0.0425284 0.999095i \(-0.513541\pi\)
−0.674785 + 0.738015i \(0.735764\pi\)
\(660\) 0 0
\(661\) 8.42649 + 7.07066i 0.327752 + 0.275017i 0.791783 0.610802i \(-0.209153\pi\)
−0.464031 + 0.885819i \(0.653597\pi\)
\(662\) 13.1349 + 11.0215i 0.510503 + 0.428363i
\(663\) 0 0
\(664\) 56.3816 + 20.5212i 2.18803 + 0.796377i
\(665\) 2.44949 4.24264i 0.0949871 0.164523i
\(666\) 0 0
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) −3.40280 19.2982i −0.131658 0.746670i
\(669\) 0 0
\(670\) −39.4671 + 14.3648i −1.52475 + 0.554962i
\(671\) −2.12675 + 12.0614i −0.0821022 + 0.465625i
\(672\) 0 0
\(673\) 22.2153 18.6408i 0.856336 0.718552i −0.104839 0.994489i \(-0.533433\pi\)
0.961176 + 0.275938i \(0.0889883\pi\)
\(674\) 68.5857 2.64182
\(675\) 0 0
\(676\) −48.0000 −1.84615
\(677\) −35.6519 + 29.9155i −1.37022 + 1.14975i −0.397538 + 0.917586i \(0.630135\pi\)
−0.972677 + 0.232162i \(0.925420\pi\)
\(678\) 0 0
\(679\) −2.43107 + 13.7873i −0.0932961 + 0.529108i
\(680\) 82.8636 30.1599i 3.17768 1.15658i
\(681\) 0 0
\(682\) −1.04189 5.90885i −0.0398960 0.226261i
\(683\) −11.0227 19.0919i −0.421772 0.730531i 0.574341 0.818616i \(-0.305258\pi\)
−0.996113 + 0.0880857i \(0.971925\pi\)
\(684\) 0 0
\(685\) 12.0000 20.7846i 0.458496 0.794139i
\(686\) −46.0353 16.7555i −1.75764 0.639728i
\(687\) 0 0
\(688\) 33.7060 + 28.2827i 1.28503 + 1.07827i
\(689\) 5.62925 + 4.72350i 0.214457 + 0.179951i
\(690\) 0 0
\(691\) −44.1656 16.0749i −1.68014 0.611520i −0.686808 0.726839i \(-0.740989\pi\)
−0.993329 + 0.115319i \(0.963211\pi\)
\(692\) 19.5959 33.9411i 0.744925 1.29025i
\(693\) 0 0
\(694\) 30.0000 + 51.9615i 1.13878 + 1.97243i
\(695\) −4.25349 24.1228i −0.161344 0.915029i
\(696\) 0 0
\(697\) 33.8289 12.3127i 1.28136 0.466378i
\(698\) −8.50699 + 48.2455i −0.321994 + 1.82612i
\(699\) 0 0
\(700\) 6.12836 5.14230i 0.231630 0.194361i
\(701\) 14.6969 0.555096 0.277548 0.960712i \(-0.410478\pi\)
0.277548 + 0.960712i \(0.410478\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) 15.0113 12.5960i 0.565761 0.474730i
\(705\) 0 0
\(706\) 1.04189 5.90885i 0.0392120 0.222382i
\(707\) −9.20707 + 3.35110i −0.346267 + 0.126031i
\(708\) 0 0
\(709\) −1.21554 6.89365i −0.0456505 0.258897i 0.953438 0.301590i \(-0.0975173\pi\)
−0.999088 + 0.0426932i \(0.986406\pi\)
\(710\) −22.0454 38.1838i −0.827349 1.43301i
\(711\) 0 0
\(712\) 0 0
\(713\) 2.30177 + 0.837775i 0.0862019 + 0.0313749i
\(714\) 0 0
\(715\) 4.59627 + 3.85673i 0.171891 + 0.144233i
\(716\) 45.0340 + 37.7880i 1.68300 + 1.41221i
\(717\) 0 0
\(718\) −67.6579 24.6255i −2.52497 0.919014i
\(719\) −18.3712 + 31.8198i −0.685129 + 1.18668i 0.288267 + 0.957550i \(0.406921\pi\)
−0.973396 + 0.229128i \(0.926412\pi\)
\(720\) 0 0
\(721\) 7.00000 + 12.1244i 0.260694 + 0.451535i
\(722\) 7.65629 + 43.4210i 0.284938 + 1.61596i
\(723\) 0 0
\(724\) −30.0702 + 10.9446i −1.11755 + 0.406755i
\(725\) 0.850699 4.82455i 0.0315942 0.179179i
\(726\) 0 0
\(727\) 10.7246 8.99903i 0.397754 0.333755i −0.421871 0.906656i \(-0.638626\pi\)
0.819625 + 0.572901i \(0.194182\pi\)
\(728\) 9.79796 0.363137
\(729\) 0 0
\(730\) −66.0000 −2.44277
\(731\) 61.9218 51.9586i 2.29026 1.92176i
\(732\) 0 0
\(733\) 2.95202 16.7417i 0.109035 0.618370i −0.880496 0.474053i \(-0.842790\pi\)
0.989532 0.144317i \(-0.0460984\pi\)
\(734\) 11.5088 4.18887i 0.424799 0.154614i
\(735\) 0 0
\(736\) 0 0
\(737\) −8.57321 14.8492i −0.315798 0.546979i
\(738\) 0 0
\(739\) 0.500000 0.866025i 0.0183928 0.0318573i −0.856683 0.515844i \(-0.827478\pi\)
0.875075 + 0.483987i \(0.160812\pi\)
\(740\) −73.6566 26.8088i −2.70767 0.985511i
\(741\) 0 0
\(742\) 27.5776 + 23.1404i 1.01241 + 0.849509i
\(743\) 24.3934 + 20.4685i 0.894908 + 0.750917i 0.969189 0.246320i \(-0.0792215\pi\)
−0.0742802 + 0.997237i \(0.523666\pi\)
\(744\) 0 0
\(745\) 28.1908 + 10.2606i 1.03283 + 0.375919i
\(746\) 42.8661 74.2462i 1.56944 2.71835i
\(747\) 0 0
\(748\) 36.0000 + 62.3538i 1.31629 + 2.27988i
\(749\) −5.10419 28.9473i −0.186503 1.05771i
\(750\) 0 0
\(751\) −24.4320 + 8.89252i −0.891537 + 0.324493i −0.746856 0.664986i \(-0.768438\pi\)
−0.144680 + 0.989478i \(0.546215\pi\)
\(752\) −6.80559 + 38.5964i −0.248174 + 1.40747i
\(753\) 0 0
\(754\) 9.19253 7.71345i 0.334772 0.280907i
\(755\) 12.2474 0.445730
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) −15.0113 + 12.5960i −0.545237 + 0.457508i
\(759\) 0 0
\(760\) 2.08378 11.8177i 0.0755866 0.428673i
\(761\) −2.30177 + 0.837775i −0.0834390 + 0.0303693i −0.383402 0.923581i \(-0.625248\pi\)
0.299963 + 0.953951i \(0.403026\pi\)
\(762\) 0 0
\(763\) −0.347296 1.96962i −0.0125730 0.0713049i
\(764\) 19.5959 + 33.9411i 0.708955 + 1.22795i
\(765\) 0 0
\(766\) −42.0000 + 72.7461i −1.51752 + 2.62842i
\(767\) 2.30177 + 0.837775i 0.0831120 + 0.0302503i
\(768\) 0 0
\(769\) −28.3436 23.7831i −1.02210 0.857642i −0.0322082 0.999481i \(-0.510254\pi\)
−0.989890 + 0.141839i \(0.954698\pi\)
\(770\) 22.5170 + 18.8940i 0.811457 + 0.680893i
\(771\) 0 0
\(772\) −41.3465 15.0489i −1.48809 0.541621i
\(773\) −22.0454 + 38.1838i −0.792918 + 1.37337i 0.131235 + 0.991351i \(0.458106\pi\)
−0.924153 + 0.382023i \(0.875227\pi\)
\(774\) 0 0
\(775\) 0.500000 + 0.866025i 0.0179605 + 0.0311086i
\(776\) 5.95489 + 33.7719i 0.213768 + 1.21234i
\(777\) 0 0
\(778\) 62.0197 22.5733i 2.22351 0.809293i
\(779\) 0.850699 4.82455i 0.0304794 0.172858i
\(780\) 0 0
\(781\) 13.7888 11.5702i 0.493402 0.414013i
\(782\) −44.0908 −1.57668