Properties

Label 729.2.e.p.406.2
Level $729$
Weight $2$
Character 729.406
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 406.2
Root \(1.39273 + 0.245576i\) of defining polynomial
Character \(\chi\) \(=\) 729.406
Dual form 729.2.e.p.325.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.87642 + 1.57450i) q^{2} +(0.694593 + 3.93923i) q^{4} +(2.30177 + 0.837775i) q^{5} +(0.347296 - 1.96962i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})\) \(q+(1.87642 + 1.57450i) q^{2} +(0.694593 + 3.93923i) q^{4} +(2.30177 + 0.837775i) q^{5} +(0.347296 - 1.96962i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(-2.30177 + 0.837775i) q^{11} +(-0.766044 + 0.642788i) q^{13} +(3.75284 - 3.14900i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-1.70140 + 9.64911i) q^{20} +(-5.63816 - 2.05212i) q^{22} +(-0.425349 - 2.41228i) q^{23} +(0.766044 + 0.642788i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-3.75284 - 3.14900i) q^{29} +(-0.173648 - 0.984808i) q^{31} +(-3.12567 + 17.7265i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.30177 - 0.837775i) q^{38} +(-9.19253 + 7.71345i) q^{40} +(3.75284 - 3.14900i) q^{41} +(-10.3366 + 3.76222i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(1.70140 - 9.64911i) q^{47} +(2.81908 + 1.02606i) q^{49} +(0.425349 + 2.41228i) q^{50} +(-3.06418 - 2.57115i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(7.50567 + 6.29801i) q^{56} +(-2.08378 - 11.8177i) q^{58} +(2.30177 + 0.837775i) q^{59} +(0.868241 - 4.92404i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-2.30177 + 0.837775i) q^{65} +(-5.36231 + 4.49951i) q^{67} +(-22.5170 + 18.8940i) q^{68} +(11.2763 - 4.10424i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(3.40280 - 19.2982i) q^{74} +(3.75877 + 1.36808i) q^{76} +(0.850699 + 4.82455i) q^{77} +(-5.36231 - 4.49951i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-9.38209 - 7.87251i) q^{83} +(3.12567 + 17.7265i) q^{85} +(-25.3194 - 9.21552i) q^{86} +(2.08378 - 11.8177i) q^{88} +(1.00000 + 1.73205i) q^{91} +(9.20707 - 3.35110i) q^{92} +(18.3851 - 15.4269i) q^{94} +(1.87642 - 1.57450i) q^{95} +(6.57785 - 2.39414i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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 0.984808 + 0.173648i \(0.0555556\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(3\) 0 0
\(4\) 0.694593 + 3.93923i 0.347296 + 1.96962i
\(5\) 2.30177 + 0.837775i 1.02938 + 0.374664i 0.800845 0.598871i \(-0.204384\pi\)
0.228536 + 0.973535i \(0.426606\pi\)
\(6\) 0 0
\(7\) 0.347296 1.96962i 0.131266 0.744445i −0.846122 0.532989i \(-0.821069\pi\)
0.977388 0.211455i \(-0.0678203\pi\)
\(8\) −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 \(-0.731505\pi\)
−0.0291582 + 0.999575i \(0.509283\pi\)
\(12\) 0 0
\(13\) −0.766044 + 0.642788i −0.212463 + 0.178277i −0.742808 0.669504i \(-0.766507\pi\)
0.530346 + 0.847781i \(0.322062\pi\)
\(14\) 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 0.838519 + 0.544872i \(0.183422\pi\)
0.0526138 + 0.998615i \(0.483245\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −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 −0.996499 0.0836069i \(-0.973356\pi\)
0.907807 0.419387i \(-0.137755\pi\)
\(24\) 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 \(-0.428088\pi\)
−0.920885 + 0.389834i \(0.872533\pi\)
\(30\) 0 0
\(31\) −0.173648 0.984808i −0.0311881 0.176877i 0.965235 0.261385i \(-0.0841792\pi\)
−0.996423 + 0.0845082i \(0.973068\pi\)
\(32\) 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 −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 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 \(-0.597270\pi\)
0.886942 + 0.461881i \(0.152825\pi\)
\(42\) 0 0
\(43\) −10.3366 + 3.76222i −1.57632 + 0.573733i −0.974400 0.224823i \(-0.927820\pi\)
−0.601920 + 0.798556i \(0.705597\pi\)
\(44\) −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 −0.564829 0.825208i \(-0.691058\pi\)
0.813003 0.582259i \(-0.197831\pi\)
\(48\) 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 \(-0.331605\pi\)
0.504695 + 0.863298i \(0.331605\pi\)
\(54\) 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 \(-0.337917\pi\)
−0.187812 + 0.982205i \(0.560140\pi\)
\(60\) 0 0
\(61\) 0.868241 4.92404i 0.111167 0.630459i −0.877410 0.479741i \(-0.840731\pi\)
0.988577 0.150717i \(-0.0481583\pi\)
\(62\) 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 −0.908617 0.417631i \(-0.862861\pi\)
0.253506 + 0.967334i \(0.418416\pi\)
\(68\) −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 \(-0.310290\pi\)
−0.997381 + 0.0723293i \(0.976957\pi\)
\(72\) 0 0
\(73\) −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i \(0.389279\pi\)
−0.984594 + 0.174855i \(0.944054\pi\)
\(74\) 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 0.289200 0.957269i \(-0.406611\pi\)
−0.892507 + 0.451034i \(0.851055\pi\)
\(80\) −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 \(-0.512414\pi\)
−0.990829 + 0.135120i \(0.956858\pi\)
\(84\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 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 0.0142448 0.999899i \(-0.495466\pi\)
0.653635 + 0.756810i \(0.273243\pi\)
\(98\) 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 0.912784 + 0.408442i \(0.133928\pi\)
−0.997432 + 0.0716191i \(0.977183\pi\)
\(102\) 0 0
\(103\) 6.57785 + 2.39414i 0.648135 + 0.235902i 0.645105 0.764094i \(-0.276813\pi\)
0.00302937 + 0.999995i \(0.499036\pi\)
\(104\) −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 \(-0.248513\pi\)
0.710403 + 0.703795i \(0.248513\pi\)
\(108\) 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 \(-0.236431\pi\)
0.129530 + 0.991575i \(0.458653\pi\)
\(114\) 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 −0.0443678 0.999015i \(-0.514127\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) −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 0.924904 + 0.380200i \(0.124145\pi\)
−0.739089 + 0.673607i \(0.764744\pi\)
\(132\) 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 \(-0.140317\pi\)
−0.263150 + 0.964755i \(0.584761\pi\)
\(138\) 0 0
\(139\) −1.73648 9.84808i −0.147286 0.835303i −0.965503 0.260393i \(-0.916148\pi\)
0.818216 0.574910i \(-0.194963\pi\)
\(140\) 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 \(-0.554940\pi\)
0.940353 + 0.340201i \(0.110495\pi\)
\(150\) 0 0
\(151\) −4.69846 + 1.71010i −0.382356 + 0.139166i −0.526045 0.850457i \(-0.676326\pi\)
0.143689 + 0.989623i \(0.454103\pi\)
\(152\) 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 −0.386175 0.922426i \(-0.626204\pi\)
−0.888751 + 0.458391i \(0.848426\pi\)
\(158\) −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 \(-0.449591\pi\)
−0.513936 + 0.857829i \(0.671813\pi\)
\(168\) 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 \(-0.732598\pi\)
−0.0325894 + 0.999469i \(0.510375\pi\)
\(174\) 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 0.998326 + 0.0578359i \(0.0184200\pi\)
−0.449076 + 0.893494i \(0.648247\pi\)
\(180\) 0 0
\(181\) −4.00000 + 6.92820i −0.297318 + 0.514969i −0.975521 0.219905i \(-0.929425\pi\)
0.678204 + 0.734874i \(0.262759\pi\)
\(182\) −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 \(-0.162436\pi\)
−0.329502 + 0.944155i \(0.606881\pi\)
\(192\) 0 0
\(193\) 1.91013 + 10.8329i 0.137494 + 0.779768i 0.973090 + 0.230424i \(0.0740113\pi\)
−0.835596 + 0.549344i \(0.814878\pi\)
\(194\) 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 0.476067 + 0.879409i \(0.342062\pi\)
−0.999624 + 0.0274180i \(0.991271\pi\)
\(198\) 0 0
\(199\) 0.500000 + 0.866025i 0.0354441 + 0.0613909i 0.883203 0.468990i \(-0.155382\pi\)
−0.847759 + 0.530381i \(0.822049\pi\)
\(200\) −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 0.374163 0.927363i \(-0.377930\pi\)
−0.309472 + 0.950909i \(0.600152\pi\)
\(212\) 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 0.916677 + 0.399628i \(0.130861\pi\)
−0.998076 + 0.0620053i \(0.980250\pi\)
\(224\) 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 \(-0.716528\pi\)
0.0178875 + 0.999840i \(0.494306\pi\)
\(228\) 0 0
\(229\) −0.766044 + 0.642788i −0.0506216 + 0.0424766i −0.667747 0.744388i \(-0.732741\pi\)
0.617126 + 0.786864i \(0.288297\pi\)
\(230\) 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 \(-0.0892873\pi\)
−0.720209 + 0.693757i \(0.755954\pi\)
\(234\) 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 \(-0.0807992\pi\)
−0.995469 + 0.0950838i \(0.969688\pi\)
\(240\) 0 0
\(241\) −12.2567 10.2846i −0.789524 0.662489i 0.156103 0.987741i \(-0.450107\pi\)
−0.945628 + 0.325251i \(0.894551\pi\)
\(242\) −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 \(-0.758834\pi\)
0.958372 + 0.285523i \(0.0921673\pi\)
\(252\) 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 \(-0.901829\pi\)
0.133482 + 0.991051i \(0.457384\pi\)
\(258\) 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 0.403962 + 0.914776i \(0.367633\pi\)
−0.692472 + 0.721445i \(0.743478\pi\)
\(264\) 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 \(-0.734593\pi\)
−0.672066 + 0.740491i \(0.734593\pi\)
\(270\) 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 −0.872096 0.489335i \(-0.837240\pi\)
0.986865 0.161550i \(-0.0516493\pi\)
\(278\) 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 \(-0.492074\pi\)
0.661661 + 0.749803i \(0.269852\pi\)
\(282\) 0 0
\(283\) 13.0228 10.9274i 0.774122 0.649566i −0.167639 0.985849i \(-0.553614\pi\)
0.941761 + 0.336283i \(0.109170\pi\)
\(284\) 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 \(-0.00984827\pi\)
−0.949823 + 0.312788i \(0.898737\pi\)
\(294\) 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 0.836077 0.548612i \(-0.184843\pi\)
−0.893150 + 0.449758i \(0.851510\pi\)
\(308\) −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 \(-0.966592\pi\)
−0.0695218 + 0.997580i \(0.522147\pi\)
\(312\) 0 0
\(313\) 15.0351 5.47232i 0.849833 0.309314i 0.119861 0.992791i \(-0.461755\pi\)
0.729972 + 0.683477i \(0.239533\pi\)
\(314\) −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 −0.899014 0.437919i \(-0.855716\pi\)
0.994574 0.104029i \(-0.0331733\pi\)
\(318\) 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 0.933007 + 0.359859i \(0.117175\pi\)
−0.999819 + 0.0190501i \(0.993936\pi\)
\(332\) 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 −0.999986 0.00529739i \(-0.998314\pi\)
−0.168429 + 0.985714i \(0.553869\pi\)
\(338\) −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 −0.856197 0.516650i \(-0.827179\pi\)
0.627857 0.778328i \(-0.283932\pi\)
\(348\) 0 0
\(349\) 15.3209 + 12.8558i 0.820108 + 0.688153i 0.952997 0.302978i \(-0.0979810\pi\)
−0.132889 + 0.991131i \(0.542425\pi\)
\(350\) 4.89898 0.261861
\(351\) 0 0
\(352\) 0 0
\(353\) 1.87642 + 1.57450i 0.0998717 + 0.0838023i 0.691356 0.722514i \(-0.257014\pi\)
−0.591485 + 0.806316i \(0.701458\pi\)
\(354\) 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 0.158740 + 0.987320i \(0.449257\pi\)
−0.934414 + 0.356188i \(0.884076\pi\)
\(360\) 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 −0.461724 0.887024i \(-0.652769\pi\)
0.216466 + 0.976290i \(0.430547\pi\)
\(368\) 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 −0.706785 0.707428i \(-0.749855\pi\)
−0.996155 + 0.0876084i \(0.972078\pi\)
\(374\) −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 \(-0.728780\pi\)
−0.988176 + 0.153324i \(0.951002\pi\)
\(384\) 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 \(-0.371757\pi\)
0.891670 + 0.452687i \(0.149534\pi\)
\(390\) 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 −0.853206 0.521575i \(-0.825345\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) −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 0.657398 + 0.753544i \(0.271657\pi\)
−0.360024 + 0.932943i \(0.617232\pi\)
\(402\) 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 −0.830898 0.556425i \(-0.812173\pi\)
0.590480 0.807052i \(-0.298938\pi\)
\(410\) 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 0.290596 0.956846i \(-0.406147\pi\)
0.992771 0.120026i \(-0.0382978\pi\)
\(420\) 0 0
\(421\) −1.87939 + 0.684040i −0.0915956 + 0.0333381i −0.387412 0.921907i \(-0.626631\pi\)
0.295816 + 0.955245i \(0.404409\pi\)
\(422\) 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 \(-0.556633\pi\)
−0.176982 + 0.984214i \(0.556633\pi\)
\(432\) 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 −0.870207 0.492687i \(-0.836015\pi\)
0.986236 0.165346i \(-0.0528740\pi\)
\(440\) 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 \(-0.517141\pi\)
0.600625 + 0.799531i \(0.294919\pi\)
\(444\) 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 −0.999724 0.0234766i \(-0.992526\pi\)
0.479531 0.877525i \(-0.340807\pi\)
\(450\) 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 0.991915 0.126900i \(-0.0405028\pi\)
0.0472719 + 0.998882i \(0.484947\pi\)
\(458\) −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 \(-0.493684\pi\)
−0.981169 + 0.193153i \(0.938129\pi\)
\(462\) 0 0
\(463\) −3.29932 18.7113i −0.153332 0.869590i −0.960295 0.278987i \(-0.910001\pi\)
0.806963 0.590603i \(-0.201110\pi\)
\(464\) 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 \(-0.943776\pi\)
0.644394 + 0.764693i \(0.277110\pi\)
\(468\) 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 0.669226 + 0.743059i \(0.266626\pi\)
−0.883008 + 0.469358i \(0.844485\pi\)
\(480\) 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 \(-0.0434899\pi\)
0.671356 + 0.741135i \(0.265712\pi\)
\(492\) 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 −0.607850 0.794052i \(-0.707968\pi\)
0.676436 + 0.736501i \(0.263524\pi\)
\(500\) 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 \(-0.0604093\pi\)
−0.654393 + 0.756154i \(0.727076\pi\)
\(504\) 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 −0.999017 0.0443397i \(-0.985882\pi\)
0.923603 0.383349i \(-0.125229\pi\)
\(510\) 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 \(-0.993755\pi\)
0.516894 + 0.856049i \(0.327088\pi\)
\(522\) 0 0
\(523\) 12.5000 + 21.6506i 0.546587 + 0.946716i 0.998505 + 0.0546569i \(0.0174065\pi\)
−0.451918 + 0.892059i \(0.649260\pi\)
\(524\) −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 0.897750 + 0.440505i \(0.145201\pi\)
−0.994271 + 0.106891i \(0.965911\pi\)
\(548\) −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 \(-0.216424\pi\)
−0.933307 + 0.359079i \(0.883091\pi\)
\(558\) 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 0.996261 + 0.0863979i \(0.0275356\pi\)
−0.906629 + 0.421929i \(0.861353\pi\)
\(564\) 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 \(-0.360420\pi\)
−0.817904 + 0.575355i \(0.804864\pi\)
\(570\) 0 0
\(571\) −1.73648 9.84808i −0.0726695 0.412129i −0.999342 0.0362604i \(-0.988455\pi\)
0.926673 0.375869i \(-0.122656\pi\)
\(572\) 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 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) −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 \(-0.928347\pi\)
0.992327 + 0.123644i \(0.0394579\pi\)
\(588\) 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 \(-0.451788\pi\)
0.150883 + 0.988552i \(0.451788\pi\)
\(594\) 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 \(-0.0933673\pi\)
0.547474 + 0.836823i \(0.315589\pi\)
\(600\) 0 0
\(601\) −1.21554 + 6.89365i −0.0495828 + 0.281198i −0.999511 0.0312703i \(-0.990045\pi\)
0.949928 + 0.312468i \(0.101156\pi\)
\(602\) −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 0.394690 0.918814i \(-0.370852\pi\)
0.973393 0.229143i \(-0.0735924\pi\)
\(608\) 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 −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) 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 −0.942396 0.334500i \(-0.891432\pi\)
0.771156 0.636646i \(-0.219679\pi\)
\(618\) 0 0
\(619\) −37.5362 31.4966i −1.50871 1.26595i −0.866226 0.499653i \(-0.833461\pi\)
−0.642481 0.766302i \(-0.722095\pi\)
\(620\) 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 −0.855901 0.517139i \(-0.826997\pi\)
−0.0199047 0.999802i \(-0.506336\pi\)
\(632\) 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 −0.867827 0.496867i \(-0.834484\pi\)
0.985429 0.170088i \(-0.0544051\pi\)
\(642\) 0 0
\(643\) −35.7083 12.9968i −1.40820 0.512542i −0.477598 0.878578i \(-0.658492\pi\)
−0.930601 + 0.366036i \(0.880715\pi\)
\(644\) −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 \(-0.243110\pi\)
0.722245 + 0.691637i \(0.243110\pi\)
\(648\) 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 \(-0.327485\pi\)
−0.155526 + 0.987832i \(0.549707\pi\)
\(654\) 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 \(-0.486459\pi\)
0.674785 + 0.738015i \(0.264236\pi\)
\(660\) 0 0
\(661\) 8.42649 7.07066i 0.327752 0.275017i −0.464031 0.885819i \(-0.653597\pi\)
0.791783 + 0.610802i \(0.209153\pi\)
\(662\) −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 0.961176 0.275938i \(-0.0889883\pi\)
−0.104839 + 0.994489i \(0.533433\pi\)
\(674\) −68.5857 −2.64182
\(675\) 0 0
\(676\) −48.0000 −1.84615
\(677\) 35.6519 + 29.9155i 1.37022 + 1.14975i 0.972677 + 0.232162i \(0.0745798\pi\)
0.397538 + 0.917586i \(0.369865\pi\)
\(678\) 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 \(-0.694742\pi\)
0.996113 + 0.0880857i \(0.0280749\pi\)
\(684\) 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 −0.993329 0.115319i \(-0.963211\pi\)
−0.686808 + 0.726839i \(0.740989\pi\)
\(692\) −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 \(-0.589522\pi\)
−0.277548 + 0.960712i \(0.589522\pi\)
\(702\) 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 −0.999088 0.0426932i \(-0.986406\pi\)
0.953438 + 0.301590i \(0.0975173\pi\)
\(710\) 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 0.973396 + 0.229128i \(0.0735876\pi\)
−0.288267 + 0.957550i \(0.593079\pi\)
\(720\) 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 0.819625 0.572901i \(-0.194182\pi\)
−0.421871 + 0.906656i \(0.638626\pi\)
\(728\) −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 0.989532 + 0.144317i \(0.0460984\pi\)
−0.880496 + 0.474053i \(0.842790\pi\)
\(734\) −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 0.875075 0.483987i \(-0.160812\pi\)
−0.856683 + 0.515844i \(0.827478\pi\)
\(740\) 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 \(-0.920779\pi\)
0.0742802 + 0.997237i \(0.476334\pi\)
\(744\) 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 −0.144680 0.989478i \(-0.546215\pi\)
−0.746856 + 0.664986i \(0.768438\pi\)
\(752\) 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 \(-0.374752\pi\)
−0.299963 + 0.953951i \(0.596974\pi\)
\(762\) 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 −0.989890 0.141839i \(-0.954698\pi\)
−0.0322082 + 0.999481i \(0.510254\pi\)
\(770\) −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 0.924153 + 0.382023i \(0.124773\pi\)
−0.131235 + 0.991351i \(0.541894\pi\)
\(774\) 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
\(783\) 0 0
\(784\) −12.0000 −0.428571
\(785\) −31.8991 26.7665i −1.13853 0.955338i
\(786\) 0 0
\(787\) −4.34120 24.6202i −0.154747 0.877615i −0.959017 0.283350i \(-0.908554\pi\)
0.804269 0.594265i \(-0.202557\pi\)
\(788\) −55.2424 20.1066i −1.96793 0.716268i
\(789\) 0 0
\(790\) 7.29322 41.3619i 0.259481 1.47159i
\(791\) 9.79796 16.9706i 0.348375 0.603404i
\(792\) 0 0
\(793\) 2.50000 + 4.33013i 0.0887776 + 0.153767i
\(794\) 2.30177 0.837775i 0.0816867 0.0297315i
\(795\) 0 0
\(796\) −3.06418 + 2.57115i −0.108607 + 0.0911320i
\(797\) 31.8991 26.7665i 1.12992 0.948119i 0.130861 0.991401i \(-0.458226\pi\)
0.999063 + 0.0432816i \(0.0137813\pi\)
\(798\) 0 0
\(799\) 67.6579 24.6255i 2.39356 0.871186i
\(800\) 0 0
\(801\) 0 0
\(802\) −42.0000 + 72.7461i −1.48307 + 2.56876i
\(803\) 4.67884 26.5350i 0.165113 0.936401i
\(804\) 0 0
\(805\) −11.2763 4.10424i −0.397438 0.144656i
\(806\) 0.425349 + 2.41228i 0.0149823 + 0.0849688i
\(807\) 0 0
\(808\) −18.3851 15.4269i −0.646784 0.542717i
\(809\) 22.0454 0.775075 0.387538 0.921854i \(-0.373326\pi\)
0.387538 + 0.921854i \(0.373326\pi\)
\(810\) 0 0
\(811\) 35.0000 1.22902 0.614508 0.788911i \(-0.289355\pi\)
0.614508 + 0.788911i \(0.289355\pi\)
\(812\) −30.0227 25.1920i −1.05359 0.884067i
\(813\) 0 0
\(814\) 8.33511 + 47.2708i 0.292146 + 1.65684i
\(815\) −23.0177 8.37775i −0.806274 0.293460i
\(816\) 0 0
\(817\) −1.91013 + 10.8329i −0.0668270 + 0.378995i
\(818\) 34.2929 59.3970i 1.19902 2.07677i
\(819\) 0 0
\(820\) 24.0000 + 41.5692i 0.838116 + 1.45166i
\(821\) −36.8283 + 13.4044i −1.28532 + 0.467817i −0.892187 0.451667i \(-0.850830\pi\)
−0.393129 + 0.919483i \(0.628607\pi\)
\(822\) 0 0
\(823\) 26.8116 22.4976i 0.934592 0.784216i −0.0420440 0.999116i \(-0.513387\pi\)
0.976636 + 0.214900i \(0.0689425\pi\)
\(824\) −26.2699 + 22.0430i −0.915154 + 0.767905i
\(825\) 0 0
\(826\) 11.2763 4.10424i 0.392353 0.142805i
\(827\) 11.0227 + 19.0919i 0.383297 + 0.663890i 0.991531 0.129868i \(-0.0414553\pi\)
−0.608234 + 0.793757i \(0.708122\pi\)
\(828\) 0 0
\(829\) 18.5000 32.0429i 0.642532 1.11290i −0.342334 0.939578i \(-0.611217\pi\)
0.984866 0.173319i \(-0.0554492\pi\)
\(830\) 12.7605 72.3683i 0.442923 2.51194i
\(831\) 0 0
\(832\) −7.51754 2.73616i −0.260624 0.0948593i
\(833\) 3.82814 + 21.7105i 0.132637 + 0.752224i
\(834\) 0 0
\(835\) −9.19253 7.71345i −0.318121 0.266935i
\(836\) −9.79796 −0.338869
\(837\) 0 0
\(838\) 84.0000 2.90173
\(839\) −3.75284 3.14900i −0.129562 0.108716i 0.575704 0.817658i \(-0.304728\pi\)
−0.705266 + 0.708943i \(0.749173\pi\)
\(840\) 0 0
\(841\) −0.868241 4.92404i −0.0299393 0.169794i
\(842\) −4.60353 1.67555i −0.158648 0.0577433i
\(843\) 0 0
\(844\) −0.694593 + 3.93923i −0.0239089 + 0.135594i
\(845\) −14.6969 + 25.4558i −0.505590 + 0.875708i
\(846\) 0 0
\(847\) 5.00000 + 8.66025i 0.171802 + 0.297570i
\(848\) −27.6212 + 10.0533i −0.948516 + 0.345232i
\(849\) 0 0
\(850\) −13.7888 + 11.5702i −0.472952 + 0.396854i
\(851\) −15.0113 + 12.5960i −0.514582 + 0.431786i
\(852\) 0 0
\(853\) 12.2160 4.44626i 0.418268 0.152237i −0.124308 0.992244i \(-0.539671\pi\)
0.542576 + 0.840007i \(0.317449\pi\)
\(854\) −12.2474 21.2132i −0.419099 0.725901i
\(855\) 0 0
\(856\) −36.0000 + 62.3538i −1.23045 + 2.13121i
\(857\) 4.25349 24.1228i 0.145297 0.824018i −0.821832 0.569730i \(-0.807048\pi\)
0.967129 0.254288i \(-0.0818411\pi\)
\(858\) 0 0
\(859\) −24.4320 8.89252i −0.833609 0.303409i −0.110270 0.993902i \(-0.535172\pi\)
−0.723339 + 0.690493i \(0.757394\pi\)
\(860\) −18.7154 106.140i −0.638189 3.61935i
\(861\) 0 0
\(862\) −13.7888 11.5702i −0.469648 0.394082i
\(863\) −7.34847 −0.250145 −0.125072 0.992148i \(-0.539916\pi\)
−0.125072 + 0.992148i \(0.539916\pi\)
\(864\) 0 0
\(865\) −24.0000 −0.816024
\(866\) 31.8991 + 26.7665i 1.08398 + 0.909564i
\(867\) 0 0
\(868\) −1.38919 7.87846i −0.0471520 0.267412i
\(869\) 16.1124 + 5.86442i 0.546575 + 0.198937i
\(870\) 0 0
\(871\) 1.21554 6.89365i 0.0411869 0.233583i
\(872\) 2.44949 4.24264i 0.0829502 0.143674i
\(873\) 0 0
\(874\) −3.00000 5.19615i −0.101477 0.175762i
\(875\) −18.4141 + 6.70220i −0.622512 + 0.226576i
\(876\) 0 0
\(877\) 6.12836 5.14230i 0.206940 0.173643i −0.533427 0.845846i \(-0.679096\pi\)
0.740367 + 0.672203i \(0.234652\pi\)
\(878\) 26.2699 22.0430i 0.886565 0.743916i
\(879\) 0 0
\(880\) 22.5526 8.20848i 0.760249 0.276708i
\(881\) −18.3712 31.8198i −0.618941 1.07204i −0.989679 0.143299i \(-0.954229\pi\)
0.370739 0.928737i \(-0.379104\pi\)
\(882\) 0 0
\(883\) −8.50000 + 14.7224i −0.286048 + 0.495449i −0.972863 0.231383i \(-0.925675\pi\)
0.686815 + 0.726832i \(0.259008\pi\)
\(884\) 5.10419 28.9473i 0.171673 0.973604i
\(885\) 0 0
\(886\) 28.1908 + 10.2606i 0.947088 + 0.344712i
\(887\) −2.97745 16.8859i −0.0999729 0.566974i −0.993110 0.117189i \(-0.962612\pi\)
0.893137 0.449785i \(-0.148499\pi\)
\(888\) 0 0
\(889\) −29.1097 24.4259i −0.976308 0.819219i
\(890\) 0 0
\(891\) 0 0
\(892\) −28.0000 −0.937509
\(893\) −7.50567 6.29801i −0.251168 0.210755i
\(894\) 0 0
\(895\) 6.25133 + 35.4531i 0.208959 + 1.18507i
\(896\) 36.8283 + 13.4044i 1.23035 + 0.447809i
\(897\) 0 0
\(898\) 9.37700 53.1796i 0.312915 1.77463i
\(899\) −2.44949 + 4.24264i −0.0816951 + 0.141500i
\(900\) 0 0
\(901\) 27.0000 + 46.7654i 0.899500 + 1.55798i
\(902\) −27.6212 + 10.0533i −0.919686 + 0.334738i
\(903\) 0 0
\(904\) −36.7701 + 30.8538i −1.22296 + 1.02618i
\(905\) −15.0113 + 12.5960i −0.498994 + 0.418706i
\(906\) 0 0
\(907\) 6.57785 2.39414i 0.218414 0.0794961i −0.230496 0.973073i \(-0.574035\pi\)
0.448910 + 0.893577i \(0.351813\pi\)
\(908\) −19.5959 33.9411i −0.650313 1.12638i
\(909\) 0 0
\(910\) −6.00000 + 10.3923i −0.198898 + 0.344502i
\(911\) −2.12675 + 12.0614i −0.0704623 + 0.399611i 0.929095 + 0.369842i \(0.120588\pi\)
−0.999557 + 0.0297691i \(0.990523\pi\)
\(912\) 0 0
\(913\) 28.1908 + 10.2606i 0.932979 + 0.339576i
\(914\) 12.3351 + 69.9560i 0.408010 + 2.31394i
\(915\) 0 0
\(916\) −3.06418 2.57115i −0.101243 0.0849532i
\(917\) 24.4949 0.808893
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 22.5170 + 18.8940i 0.742364 + 0.622917i
\(921\) 0 0
\(922\) −11.4608 64.9973i −0.377441 2.14057i
\(923\) 6.90530 + 2.51332i 0.227291 + 0.0827271i
\(924\) 0 0
\(925\) 1.38919 7.87846i 0.0456761 0.259042i
\(926\) 23.2702 40.3051i 0.764705 1.32451i
\(927\) 0 0
\(928\) 0 0
\(929\) 25.3194 9.21552i 0.830704 0.302352i 0.108556 0.994090i \(-0.465377\pi\)
0.722148 + 0.691739i \(0.243155\pi\)
\(930\) 0 0
\(931\) 2.29813 1.92836i 0.0753183 0.0631995i
\(932\) −22.5170 + 18.8940i −0.737569 + 0.618894i
\(933\) 0 0
\(934\) −33.8289 + 12.3127i −1.10692 + 0.402885i
\(935\) −22.0454 38.1838i −0.720962 1.24874i
\(936\) 0 0
\(937\) −4.00000 + 6.92820i −0.130674 + 0.226335i −0.923937 0.382545i \(-0.875048\pi\)
0.793262 + 0.608880i \(0.208381\pi\)
\(938\) −5.95489 + 33.7719i −0.194434 + 1.10269i
\(939\) 0 0
\(940\) 90.2105 + 32.8339i 2.94234 + 1.07092i
\(941\) −1.70140 9.64911i −0.0554640 0.314552i 0.944436 0.328695i \(-0.106609\pi\)
−0.999900 + 0.0141435i \(0.995498\pi\)
\(942\) 0 0
\(943\) −9.19253 7.71345i −0.299350 0.251185i
\(944\) −9.79796 −0.318896
\(945\) 0 0
\(946\) 66.0000 2.14585
\(947\) 18.7642 + 15.7450i 0.609754 + 0.511644i 0.894564 0.446940i \(-0.147486\pi\)
−0.284810 + 0.958584i \(0.591931\pi\)
\(948\) 0 0
\(949\) −1.91013 10.8329i −0.0620054 0.351650i
\(950\) 2.30177 + 0.837775i 0.0746792 + 0.0271810i
\(951\) 0 0
\(952\) −12.5027 + 70.9062i −0.405214 + 2.29808i
\(953\) −14.6969 + 25.4558i −0.476081 + 0.824596i −0.999624 0.0274030i \(-0.991276\pi\)
0.523544 + 0.851999i \(0.324610\pi\)
\(954\) 0 0
\(955\) 12.0000 + 20.7846i 0.388311 + 0.672574i
\(956\) 9.20707 3.35110i 0.297778 0.108382i
\(957\) 0 0
\(958\) −50.5589 + 42.4240i −1.63348 + 1.37066i
\(959\) 15.0113 12.5960i 0.484742 0.406746i
\(960\) 0 0
\(961\) 28.1908 10.2606i 0.909380 0.330987i
\(962\) 9.79796 + 16.9706i 0.315899 + 0.547153i
\(963\) 0 0
\(964\) 32.0000 55.4256i 1.03065 1.78514i
\(965\) −4.67884 + 26.5350i −0.150617 + 0.854193i
\(966\) 0 0
\(967\) 6.57785 + 2.39414i 0.211529 + 0.0769904i 0.445612 0.895226i \(-0.352986\pi\)
−0.234082 + 0.972217i \(0.575208\pi\)
\(968\) −4.25349 24.1228i −0.136712 0.775335i
\(969\) 0 0
\(970\) 32.1739 + 26.9971i 1.03304 + 0.866824i
\(971\) 29.3939 0.943294 0.471647 0.881787i \(-0.343660\pi\)
0.471647 + 0.881787i \(0.343660\pi\)
\(972\) 0 0
\(973\) −20.0000 −0.641171
\(974\) 65.6746 + 55.1076i 2.10435 + 1.76576i
\(975\) 0 0
\(976\) 3.47296 + 19.6962i 0.111167 + 0.630459i
\(977\) 23.0177 + 8.37775i 0.736401 + 0.268028i 0.682872 0.730538i \(-0.260731\pi\)
0.0535290 + 0.998566i \(0.482953\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −14.6969 + 25.4558i −0.469476 + 0.813157i
\(981\) 0 0
\(982\) 48.0000 + 83.1384i 1.53174 + 2.65305i
\(983\) 4.60353 1.67555i 0.146830 0.0534417i −0.267560 0.963541i \(-0.586217\pi\)
0.414390 + 0.910100i \(0.363995\pi\)
\(984\) 0 0
\(985\) −27.5776 + 23.1404i −0.878695 + 0.737313i
\(986\) 67.5510 56.6821i 2.15126 1.80512i
\(987\) 0 0
\(988\) −3.75877 + 1.36808i −0.119582 + 0.0435244i
\(989\) 13.4722 + 23.3345i 0.428391 + 0.741995i
\(990\) 0 0
\(991\) 3.50000 6.06218i 0.111181 0.192571i −0.805066 0.593186i \(-0.797870\pi\)
0.916247 + 0.400614i \(0.131203\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −33.8289 12.3127i −1.07299 0.390536i
\(995\) 0.425349 + 2.41228i 0.0134845 + 0.0764743i
\(996\) 0 0
\(997\) 38.3022 + 32.1394i 1.21304 + 1.01786i 0.999159 + 0.0410055i \(0.0130561\pi\)
0.213885 + 0.976859i \(0.431388\pi\)
\(998\) 4.89898 0.155074
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.e.p.406.2 12
3.2 odd 2 inner 729.2.e.p.406.1 12
9.2 odd 6 inner 729.2.e.p.649.1 12
9.4 even 3 inner 729.2.e.p.163.1 12
9.5 odd 6 inner 729.2.e.p.163.2 12
9.7 even 3 inner 729.2.e.p.649.2 12
27.2 odd 18 243.2.c.c.82.2 4
27.4 even 9 inner 729.2.e.p.82.2 12
27.5 odd 18 inner 729.2.e.p.325.1 12
27.7 even 9 243.2.a.d.1.2 yes 2
27.11 odd 18 243.2.c.c.163.2 4
27.13 even 9 inner 729.2.e.p.568.1 12
27.14 odd 18 inner 729.2.e.p.568.2 12
27.16 even 9 243.2.c.c.163.1 4
27.20 odd 18 243.2.a.d.1.1 2
27.22 even 9 inner 729.2.e.p.325.2 12
27.23 odd 18 inner 729.2.e.p.82.1 12
27.25 even 9 243.2.c.c.82.1 4
108.7 odd 18 3888.2.a.z.1.1 2
108.47 even 18 3888.2.a.z.1.2 2
135.34 even 18 6075.2.a.bn.1.1 2
135.74 odd 18 6075.2.a.bn.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.d.1.1 2 27.20 odd 18
243.2.a.d.1.2 yes 2 27.7 even 9
243.2.c.c.82.1 4 27.25 even 9
243.2.c.c.82.2 4 27.2 odd 18
243.2.c.c.163.1 4 27.16 even 9
243.2.c.c.163.2 4 27.11 odd 18
729.2.e.p.82.1 12 27.23 odd 18 inner
729.2.e.p.82.2 12 27.4 even 9 inner
729.2.e.p.163.1 12 9.4 even 3 inner
729.2.e.p.163.2 12 9.5 odd 6 inner
729.2.e.p.325.1 12 27.5 odd 18 inner
729.2.e.p.325.2 12 27.22 even 9 inner
729.2.e.p.406.1 12 3.2 odd 2 inner
729.2.e.p.406.2 12 1.1 even 1 trivial
729.2.e.p.568.1 12 27.13 even 9 inner
729.2.e.p.568.2 12 27.14 odd 18 inner
729.2.e.p.649.1 12 9.2 odd 6 inner
729.2.e.p.649.2 12 9.7 even 3 inner
3888.2.a.z.1.1 2 108.7 odd 18
3888.2.a.z.1.2 2 108.47 even 18
6075.2.a.bn.1.1 2 135.34 even 18
6075.2.a.bn.1.2 2 135.74 odd 18