Properties

Label 729.2.e.p.568.2
Level $729$
Weight $2$
Character 729.568
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 568.2
Root \(0.909039 + 1.08335i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.p.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.30177 + 0.837775i) q^{2} +(3.06418 + 2.57115i) q^{4} +(0.425349 - 2.41228i) q^{5} +(1.53209 - 1.28558i) q^{7} +(2.44949 + 4.24264i) q^{8} +O(q^{10})\) \(q+(2.30177 + 0.837775i) q^{2} +(3.06418 + 2.57115i) q^{4} +(0.425349 - 2.41228i) q^{5} +(1.53209 - 1.28558i) q^{7} +(2.44949 + 4.24264i) q^{8} +(3.00000 - 5.19615i) q^{10} +(-0.425349 - 2.41228i) q^{11} +(0.939693 - 0.342020i) q^{13} +(4.60353 - 1.67555i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-3.67423 + 6.36396i) q^{17} +(0.500000 + 0.866025i) q^{19} +(7.50567 - 6.29801i) q^{20} +(1.04189 - 5.90885i) q^{22} +(1.87642 + 1.57450i) q^{23} +(-0.939693 - 0.342020i) q^{25} +2.44949 q^{26} +8.00000 q^{28} +(-4.60353 - 1.67555i) q^{29} +(-0.766044 - 0.642788i) q^{31} +(-13.7888 + 11.5702i) q^{34} +(-2.44949 - 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(0.425349 + 2.41228i) q^{38} +(11.2763 - 4.10424i) q^{40} +(4.60353 - 1.67555i) q^{41} +(1.91013 + 10.8329i) q^{43} +(4.89898 - 8.48528i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-7.50567 + 6.29801i) q^{47} +(-0.520945 + 2.95442i) q^{49} +(-1.87642 - 1.57450i) q^{50} +(3.75877 + 1.36808i) q^{52} -7.34847 q^{53} -6.00000 q^{55} +(9.20707 + 3.35110i) q^{56} +(-9.19253 - 7.71345i) q^{58} +(0.425349 - 2.41228i) q^{59} +(3.83022 - 3.21394i) q^{61} +(-1.22474 - 2.12132i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-0.425349 - 2.41228i) q^{65} +(6.57785 - 2.39414i) q^{67} +(-27.6212 + 10.0533i) q^{68} +(-2.08378 - 11.8177i) q^{70} +(3.67423 - 6.36396i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(-15.0113 + 12.5960i) q^{74} +(-0.694593 + 3.93923i) q^{76} +(-3.75284 - 3.14900i) q^{77} +(6.57785 + 2.39414i) q^{79} +9.79796 q^{80} +12.0000 q^{82} +(-11.5088 - 4.18887i) q^{83} +(13.7888 + 11.5702i) q^{85} +(-4.67884 + 26.5350i) q^{86} +(9.19253 - 7.71345i) q^{88} +(1.00000 - 1.73205i) q^{91} +(1.70140 + 9.64911i) q^{92} +(-22.5526 + 8.20848i) q^{94} +(2.30177 - 0.837775i) q^{95} +(-1.21554 - 6.89365i) q^{97} +(-3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30177 + 0.837775i 1.62760 + 0.592396i 0.984808 0.173648i \(-0.0555556\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(3\) 0 0
\(4\) 3.06418 + 2.57115i 1.53209 + 1.28558i
\(5\) 0.425349 2.41228i 0.190222 1.07880i −0.728838 0.684686i \(-0.759939\pi\)
0.919060 0.394117i \(-0.128950\pi\)
\(6\) 0 0
\(7\) 1.53209 1.28558i 0.579075 0.485902i −0.305568 0.952170i \(-0.598846\pi\)
0.884643 + 0.466268i \(0.154402\pi\)
\(8\) 2.44949 + 4.24264i 0.866025 + 1.50000i
\(9\) 0 0
\(10\) 3.00000 5.19615i 0.948683 1.64317i
\(11\) −0.425349 2.41228i −0.128248 0.727329i −0.979326 0.202290i \(-0.935162\pi\)
0.851078 0.525039i \(-0.175949\pi\)
\(12\) 0 0
\(13\) 0.939693 0.342020i 0.260624 0.0948593i −0.208404 0.978043i \(-0.566827\pi\)
0.469027 + 0.883184i \(0.344605\pi\)
\(14\) 4.60353 1.67555i 1.23035 0.447809i
\(15\) 0 0
\(16\) 0.694593 + 3.93923i 0.173648 + 0.984808i
\(17\) −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 \(0.796740\pi\)
\(20\) 7.50567 6.29801i 1.67832 1.40828i
\(21\) 0 0
\(22\) 1.04189 5.90885i 0.222131 1.25977i
\(23\) 1.87642 + 1.57450i 0.391260 + 0.328306i 0.817104 0.576490i \(-0.195578\pi\)
−0.425844 + 0.904797i \(0.640023\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 2.44949 0.480384
\(27\) 0 0
\(28\) 8.00000 1.51186
\(29\) −4.60353 1.67555i −0.854855 0.311142i −0.122837 0.992427i \(-0.539199\pi\)
−0.732018 + 0.681285i \(0.761421\pi\)
\(30\) 0 0
\(31\) −0.766044 0.642788i −0.137586 0.115448i 0.571398 0.820673i \(-0.306401\pi\)
−0.708983 + 0.705225i \(0.750846\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −13.7888 + 11.5702i −2.36476 + 1.98427i
\(35\) −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 \(0.938240\pi\)
\(38\) 0.425349 + 2.41228i 0.0690008 + 0.391323i
\(39\) 0 0
\(40\) 11.2763 4.10424i 1.78294 0.648938i
\(41\) 4.60353 1.67555i 0.718951 0.261677i 0.0434708 0.999055i \(-0.486158\pi\)
0.675481 + 0.737378i \(0.263936\pi\)
\(42\) 0 0
\(43\) 1.91013 + 10.8329i 0.291292 + 1.65200i 0.681902 + 0.731443i \(0.261153\pi\)
−0.390610 + 0.920556i \(0.627736\pi\)
\(44\) 4.89898 8.48528i 0.738549 1.27920i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −7.50567 + 6.29801i −1.09481 + 0.918659i −0.997066 0.0765524i \(-0.975609\pi\)
−0.0977492 + 0.995211i \(0.531164\pi\)
\(48\) 0 0
\(49\) −0.520945 + 2.95442i −0.0744206 + 0.422060i
\(50\) −1.87642 1.57450i −0.265366 0.222668i
\(51\) 0 0
\(52\) 3.75877 + 1.36808i 0.521248 + 0.189719i
\(53\) −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
\(56\) 9.20707 + 3.35110i 1.23035 + 0.447809i
\(57\) 0 0
\(58\) −9.19253 7.71345i −1.20704 1.01283i
\(59\) 0.425349 2.41228i 0.0553758 0.314052i −0.944521 0.328452i \(-0.893473\pi\)
0.999896 + 0.0144007i \(0.00458406\pi\)
\(60\) 0 0
\(61\) 3.83022 3.21394i 0.490410 0.411503i −0.363763 0.931491i \(-0.618508\pi\)
0.854173 + 0.519989i \(0.174064\pi\)
\(62\) −1.22474 2.12132i −0.155543 0.269408i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.500000 0.866025i
\(65\) −0.425349 2.41228i −0.0527581 0.299206i
\(66\) 0 0
\(67\) 6.57785 2.39414i 0.803612 0.292491i 0.0926296 0.995701i \(-0.470473\pi\)
0.710982 + 0.703210i \(0.248251\pi\)
\(68\) −27.6212 + 10.0533i −3.34956 + 1.21914i
\(69\) 0 0
\(70\) −2.08378 11.8177i −0.249059 1.41248i
\(71\) 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 \(-0.389279\pi\)
\(74\) −15.0113 + 12.5960i −1.74503 + 1.46426i
\(75\) 0 0
\(76\) −0.694593 + 3.93923i −0.0796752 + 0.451861i
\(77\) −3.75284 3.14900i −0.427675 0.358862i
\(78\) 0 0
\(79\) 6.57785 + 2.39414i 0.740066 + 0.269362i 0.684419 0.729089i \(-0.260056\pi\)
0.0556465 + 0.998451i \(0.482278\pi\)
\(80\) 9.79796 1.09545
\(81\) 0 0
\(82\) 12.0000 1.32518
\(83\) −11.5088 4.18887i −1.26326 0.459789i −0.378398 0.925643i \(-0.623525\pi\)
−0.884861 + 0.465854i \(0.845747\pi\)
\(84\) 0 0
\(85\) 13.7888 + 11.5702i 1.49561 + 1.25496i
\(86\) −4.67884 + 26.5350i −0.504533 + 2.86135i
\(87\) 0 0
\(88\) 9.19253 7.71345i 0.979927 0.822257i
\(89\) 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
\(92\) 1.70140 + 9.64911i 0.177383 + 1.00599i
\(93\) 0 0
\(94\) −22.5526 + 8.20848i −2.32613 + 0.846640i
\(95\) 2.30177 0.837775i 0.236156 0.0859539i
\(96\) 0 0
\(97\) −1.21554 6.89365i −0.123419 0.699945i −0.982234 0.187659i \(-0.939910\pi\)
0.858815 0.512286i \(-0.171201\pi\)
\(98\) −3.67423 + 6.36396i −0.371154 + 0.642857i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 3.75284 3.14900i 0.373421 0.313338i −0.436692 0.899611i \(-0.643850\pi\)
0.810113 + 0.586274i \(0.199406\pi\)
\(102\) 0 0
\(103\) −1.21554 + 6.89365i −0.119770 + 0.679252i 0.864507 + 0.502621i \(0.167631\pi\)
−0.984277 + 0.176631i \(0.943480\pi\)
\(104\) 3.75284 + 3.14900i 0.367996 + 0.308785i
\(105\) 0 0
\(106\) −16.9145 6.15636i −1.64288 0.597959i
\(107\) −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 \(0.515250\pi\)
\(110\) −13.8106 5.02665i −1.31679 0.479272i
\(111\) 0 0
\(112\) 6.12836 + 5.14230i 0.579075 + 0.485902i
\(113\) 1.70140 9.64911i 0.160054 0.907712i −0.793965 0.607964i \(-0.791986\pi\)
0.954019 0.299747i \(-0.0969024\pi\)
\(114\) 0 0
\(115\) 4.59627 3.85673i 0.428604 0.359642i
\(116\) −9.79796 16.9706i −0.909718 1.57568i
\(117\) 0 0
\(118\) 3.00000 5.19615i 0.276172 0.478345i
\(119\) 2.55210 + 14.4737i 0.233950 + 1.32680i
\(120\) 0 0
\(121\) 4.69846 1.71010i 0.427133 0.155464i
\(122\) 11.5088 4.18887i 1.04196 0.379243i
\(123\) 0 0
\(124\) −0.694593 3.93923i −0.0623763 0.353753i
\(125\) 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 \(0.514127\pi\)
\(128\) 15.0113 12.5960i 1.32683 1.11334i
\(129\) 0 0
\(130\) 1.04189 5.90885i 0.0913797 0.518240i
\(131\) −9.38209 7.87251i −0.819717 0.687824i 0.133189 0.991091i \(-0.457478\pi\)
−0.952906 + 0.303266i \(0.901923\pi\)
\(132\) 0 0
\(133\) 1.87939 + 0.684040i 0.162963 + 0.0593138i
\(134\) 17.1464 1.48123
\(135\) 0 0
\(136\) −36.0000 −3.08697
\(137\) 9.20707 + 3.35110i 0.786613 + 0.286304i 0.703927 0.710272i \(-0.251428\pi\)
0.0826857 + 0.996576i \(0.473650\pi\)
\(138\) 0 0
\(139\) −7.66044 6.42788i −0.649750 0.545205i 0.257245 0.966346i \(-0.417185\pi\)
−0.906995 + 0.421141i \(0.861630\pi\)
\(140\) 3.40280 19.2982i 0.287589 1.63100i
\(141\) 0 0
\(142\) 13.7888 11.5702i 1.15713 0.970948i
\(143\) −1.22474 2.12132i −0.102418 0.177394i
\(144\) 0 0
\(145\) −6.00000 + 10.3923i −0.498273 + 0.863034i
\(146\) −4.67884 26.5350i −0.387224 2.19606i
\(147\) 0 0
\(148\) −30.0702 + 10.9446i −2.47175 + 0.899644i
\(149\) 11.5088 4.18887i 0.942841 0.343166i 0.175554 0.984470i \(-0.443828\pi\)
0.767287 + 0.641304i \(0.221606\pi\)
\(150\) 0 0
\(151\) 0.868241 + 4.92404i 0.0706564 + 0.400713i 0.999540 + 0.0303398i \(0.00965894\pi\)
−0.928883 + 0.370373i \(0.879230\pi\)
\(152\) −2.44949 + 4.24264i −0.198680 + 0.344124i
\(153\) 0 0
\(154\) −6.00000 10.3923i −0.483494 0.837436i
\(155\) −1.87642 + 1.57450i −0.150718 + 0.126467i
\(156\) 0 0
\(157\) 2.95202 16.7417i 0.235597 1.33614i −0.605757 0.795650i \(-0.707129\pi\)
0.841353 0.540486i \(-0.181759\pi\)
\(158\) 13.1349 + 11.0215i 1.04496 + 0.876824i
\(159\) 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 \(0.628089\pi\)
\(164\) 18.4141 + 6.70220i 1.43790 + 0.523354i
\(165\) 0 0
\(166\) −22.9813 19.2836i −1.78370 1.49670i
\(167\) −0.850699 + 4.82455i −0.0658291 + 0.373335i 0.934040 + 0.357168i \(0.116258\pi\)
−0.999869 + 0.0161673i \(0.994854\pi\)
\(168\) 0 0
\(169\) −9.19253 + 7.71345i −0.707118 + 0.593342i
\(170\) 22.0454 + 38.1838i 1.69081 + 2.92856i
\(171\) 0 0
\(172\) −22.0000 + 38.1051i −1.67748 + 2.90549i
\(173\) −1.70140 9.64911i −0.129355 0.733608i −0.978626 0.205650i \(-0.934069\pi\)
0.849271 0.527958i \(-0.177042\pi\)
\(174\) 0 0
\(175\) −1.87939 + 0.684040i −0.142068 + 0.0517086i
\(176\) 9.20707 3.35110i 0.694009 0.252599i
\(177\) 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 \(0.929425\pi\)
\(182\) 3.75284 3.14900i 0.278179 0.233420i
\(183\) 0 0
\(184\) −2.08378 + 11.8177i −0.153618 + 0.871212i
\(185\) 15.0113 + 12.5960i 1.10366 + 0.926077i
\(186\) 0 0
\(187\) 16.9145 + 6.15636i 1.23691 + 0.450198i
\(188\) −39.1918 −2.85836
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 9.20707 + 3.35110i 0.666200 + 0.242477i 0.652911 0.757435i \(-0.273548\pi\)
0.0132892 + 0.999912i \(0.495770\pi\)
\(192\) 0 0
\(193\) 8.42649 + 7.07066i 0.606552 + 0.508958i 0.893544 0.448975i \(-0.148211\pi\)
−0.286992 + 0.957933i \(0.592655\pi\)
\(194\) 2.97745 16.8859i 0.213768 1.21234i
\(195\) 0 0
\(196\) −9.19253 + 7.71345i −0.656610 + 0.550961i
\(197\) 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 \(0.155382\pi\)
\(200\) −0.850699 4.82455i −0.0601535 0.341147i
\(201\) 0 0
\(202\) 11.2763 4.10424i 0.793399 0.288773i
\(203\) −9.20707 + 3.35110i −0.646210 + 0.235201i
\(204\) 0 0
\(205\) −2.08378 11.8177i −0.145537 0.825383i
\(206\) −8.57321 + 14.8492i −0.597324 + 1.03460i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 1.87642 1.57450i 0.129795 0.108911i
\(210\) 0 0
\(211\) −0.173648 + 0.984808i −0.0119544 + 0.0677970i −0.990201 0.139647i \(-0.955403\pi\)
0.978247 + 0.207444i \(0.0665144\pi\)
\(212\) −22.5170 18.8940i −1.54648 1.29765i
\(213\) 0 0
\(214\) −33.8289 12.3127i −2.31250 0.841681i
\(215\) 26.9444 1.83759
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) −2.30177 0.837775i −0.155895 0.0567413i
\(219\) 0 0
\(220\) −18.3851 15.4269i −1.23952 1.04008i
\(221\) −1.27605 + 7.23683i −0.0858363 + 0.486802i
\(222\) 0 0
\(223\) −5.36231 + 4.49951i −0.359087 + 0.301310i −0.804427 0.594052i \(-0.797527\pi\)
0.445340 + 0.895362i \(0.353083\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.0000 20.7846i 0.798228 1.38257i
\(227\) −1.70140 9.64911i −0.112926 0.640434i −0.987756 0.156005i \(-0.950139\pi\)
0.874831 0.484429i \(-0.160973\pi\)
\(228\) 0 0
\(229\) 0.939693 0.342020i 0.0620966 0.0226013i −0.310785 0.950480i \(-0.600592\pi\)
0.372882 + 0.927879i \(0.378370\pi\)
\(230\) 13.8106 5.02665i 0.910644 0.331447i
\(231\) 0 0
\(232\) −4.16756 23.6354i −0.273613 1.55174i
\(233\) −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
\(236\) 7.50567 6.29801i 0.488578 0.409965i
\(237\) 0 0
\(238\) −6.25133 + 35.4531i −0.405214 + 2.29808i
\(239\) 1.87642 + 1.57450i 0.121375 + 0.101846i 0.701455 0.712714i \(-0.252534\pi\)
−0.580080 + 0.814560i \(0.696979\pi\)
\(240\) 0 0
\(241\) 15.0351 + 5.47232i 0.968495 + 0.352503i 0.777357 0.629060i \(-0.216560\pi\)
0.191138 + 0.981563i \(0.438782\pi\)
\(242\) 12.2474 0.787296
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) 6.90530 + 2.51332i 0.441164 + 0.160570i
\(246\) 0 0
\(247\) 0.766044 + 0.642788i 0.0487422 + 0.0408996i
\(248\) 0.850699 4.82455i 0.0540194 0.306359i
\(249\) 0 0
\(250\) 18.3851 15.4269i 1.16277 0.975683i
\(251\) −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
\(254\) 8.08164 + 45.8333i 0.507087 + 2.87583i
\(255\) 0 0
\(256\) 30.0702 10.9446i 1.87939 0.684040i
\(257\) −16.1124 + 5.86442i −1.00506 + 0.365813i −0.791535 0.611124i \(-0.790718\pi\)
−0.213528 + 0.976937i \(0.568495\pi\)
\(258\) 0 0
\(259\) 2.77837 + 15.7569i 0.172640 + 0.979088i
\(260\) 4.89898 8.48528i 0.303822 0.526235i
\(261\) 0 0
\(262\) −15.0000 25.9808i −0.926703 1.60510i
\(263\) 20.6406 17.3195i 1.27275 1.06797i 0.278554 0.960421i \(-0.410145\pi\)
0.994200 0.107547i \(-0.0342995\pi\)
\(264\) 0 0
\(265\) −3.12567 + 17.7265i −0.192008 + 1.08893i
\(266\) 3.75284 + 3.14900i 0.230101 + 0.193078i
\(267\) 0 0
\(268\) 26.3114 + 9.57656i 1.60722 + 0.584982i
\(269\) 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 \(0.568196\pi\)
\(272\) −27.6212 10.0533i −1.67478 0.609571i
\(273\) 0 0
\(274\) 18.3851 + 15.4269i 1.11068 + 0.931973i
\(275\) −0.425349 + 2.41228i −0.0256495 + 0.145466i
\(276\) 0 0
\(277\) 8.42649 7.07066i 0.506299 0.424835i −0.353526 0.935425i \(-0.615017\pi\)
0.859824 + 0.510590i \(0.170573\pi\)
\(278\) −12.2474 21.2132i −0.734553 1.27228i
\(279\) 0 0
\(280\) 12.0000 20.7846i 0.717137 1.24212i
\(281\) 2.12675 + 12.0614i 0.126871 + 0.719522i 0.980179 + 0.198114i \(0.0634817\pi\)
−0.853308 + 0.521407i \(0.825407\pi\)
\(282\) 0 0
\(283\) −15.9748 + 5.81434i −0.949602 + 0.345627i −0.769951 0.638104i \(-0.779719\pi\)
−0.179651 + 0.983730i \(0.557497\pi\)
\(284\) 27.6212 10.0533i 1.63902 0.596553i
\(285\) 0 0
\(286\) −1.04189 5.90885i −0.0616082 0.349397i
\(287\) 4.89898 8.48528i 0.289178 0.500870i
\(288\) 0 0
\(289\) −18.5000 32.0429i −1.08824 1.88488i
\(290\) −22.5170 + 18.8940i −1.32224 + 1.10950i
\(291\) 0 0
\(292\) 7.64052 43.3315i 0.447128 2.53579i
\(293\) −3.75284 3.14900i −0.219243 0.183967i 0.526551 0.850144i \(-0.323485\pi\)
−0.745794 + 0.666177i \(0.767930\pi\)
\(294\) 0 0
\(295\) −5.63816 2.05212i −0.328266 0.119479i
\(296\) −39.1918 −2.27798
\(297\) 0 0
\(298\) 30.0000 1.73785
\(299\) 2.30177 + 0.837775i 0.133115 + 0.0484498i
\(300\) 0 0
\(301\) 16.8530 + 14.1413i 0.971389 + 0.815093i
\(302\) −2.12675 + 12.0614i −0.122381 + 0.694055i
\(303\) 0 0
\(304\) −3.06418 + 2.57115i −0.175743 + 0.147466i
\(305\) −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 \(0.184843\pi\)
\(308\) −3.40280 19.2982i −0.193892 1.09962i
\(309\) 0 0
\(310\) −5.63816 + 2.05212i −0.320226 + 0.116553i
\(311\) −23.0177 + 8.37775i −1.30521 + 0.475059i −0.898691 0.438583i \(-0.855481\pi\)
−0.406522 + 0.913641i \(0.633258\pi\)
\(312\) 0 0
\(313\) −2.77837 15.7569i −0.157043 0.890634i −0.956894 0.290436i \(-0.906200\pi\)
0.799852 0.600198i \(-0.204911\pi\)
\(314\) 20.8207 36.0624i 1.17498 2.03512i
\(315\) 0 0
\(316\) 14.0000 + 24.2487i 0.787562 + 1.36410i
\(317\) −7.50567 + 6.29801i −0.421561 + 0.353731i −0.828756 0.559610i \(-0.810951\pi\)
0.407196 + 0.913341i \(0.366507\pi\)
\(318\) 0 0
\(319\) −2.08378 + 11.8177i −0.116669 + 0.661664i
\(320\) −15.0113 12.5960i −0.839160 0.704139i
\(321\) 0 0
\(322\) 11.2763 + 4.10424i 0.628404 + 0.228720i
\(323\) −7.34847 −0.408880
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −23.0177 8.37775i −1.27483 0.464001i
\(327\) 0 0
\(328\) 18.3851 + 15.4269i 1.01515 + 0.851808i
\(329\) −3.40280 + 19.2982i −0.187602 + 1.06394i
\(330\) 0 0
\(331\) −5.36231 + 4.49951i −0.294739 + 0.247316i −0.778151 0.628078i \(-0.783842\pi\)
0.483411 + 0.875393i \(0.339398\pi\)
\(332\) −24.4949 42.4264i −1.34433 2.32845i
\(333\) 0 0
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) −2.97745 16.8859i −0.162675 0.922577i
\(336\) 0 0
\(337\) 26.3114 9.57656i 1.43327 0.521669i 0.495405 0.868662i \(-0.335020\pi\)
0.937868 + 0.346993i \(0.112797\pi\)
\(338\) −27.6212 + 10.0533i −1.50240 + 0.546827i
\(339\) 0 0
\(340\) 12.5027 + 70.9062i 0.678052 + 3.84543i
\(341\) −1.22474 + 2.12132i −0.0663237 + 0.114876i
\(342\) 0 0
\(343\) 10.0000 + 17.3205i 0.539949 + 0.935220i
\(344\) −41.2812 + 34.6390i −2.22573 + 1.86761i
\(345\) 0 0
\(346\) 4.16756 23.6354i 0.224049 1.27065i
\(347\) 18.7642 + 15.7450i 1.00731 + 0.845237i 0.987981 0.154576i \(-0.0494013\pi\)
0.0193331 + 0.999813i \(0.493846\pi\)
\(348\) 0 0
\(349\) −18.7939 6.84040i −1.00601 0.366158i −0.214112 0.976809i \(-0.568686\pi\)
−0.791900 + 0.610651i \(0.790908\pi\)
\(350\) −4.89898 −0.261861
\(351\) 0 0
\(352\) 0 0
\(353\) 2.30177 + 0.837775i 0.122511 + 0.0445903i 0.402548 0.915399i \(-0.368125\pi\)
−0.280037 + 0.959989i \(0.590347\pi\)
\(354\) 0 0
\(355\) −13.7888 11.5702i −0.731834 0.614081i
\(356\) 0 0
\(357\) 0 0
\(358\) −27.5776 + 23.1404i −1.45752 + 1.22301i
\(359\) 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
\(362\) −3.40280 19.2982i −0.178847 1.01429i
\(363\) 0 0
\(364\) 7.51754 2.73616i 0.394026 0.143414i
\(365\) −25.3194 + 9.21552i −1.32528 + 0.482363i
\(366\) 0 0
\(367\) 0.868241 + 4.92404i 0.0453218 + 0.257033i 0.999047 0.0436469i \(-0.0138976\pi\)
−0.953725 + 0.300680i \(0.902787\pi\)
\(368\) −4.89898 + 8.48528i −0.255377 + 0.442326i
\(369\) 0 0
\(370\) 24.0000 + 41.5692i 1.24770 + 2.16108i
\(371\) −11.2585 + 9.44701i −0.584513 + 0.490464i
\(372\) 0 0
\(373\) 6.07769 34.4683i 0.314691 1.78470i −0.259258 0.965808i \(-0.583478\pi\)
0.573949 0.818891i \(-0.305411\pi\)
\(374\) 33.7755 + 28.3410i 1.74649 + 1.46548i
\(375\) 0 0
\(376\) −45.1052 16.4170i −2.32613 0.846640i
\(377\) −4.89898 −0.252310
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 9.20707 + 3.35110i 0.472313 + 0.171908i
\(381\) 0 0
\(382\) 18.3851 + 15.4269i 0.940662 + 0.789309i
\(383\) −5.95489 + 33.7719i −0.304281 + 1.72566i 0.322590 + 0.946539i \(0.395446\pi\)
−0.626871 + 0.779123i \(0.715665\pi\)
\(384\) 0 0
\(385\) −9.19253 + 7.71345i −0.468495 + 0.393114i
\(386\) 13.4722 + 23.3345i 0.685717 + 1.18770i
\(387\) 0 0
\(388\) 14.0000 24.2487i 0.710742 1.23104i
\(389\) 4.67884 + 26.5350i 0.237227 + 1.34538i 0.837873 + 0.545865i \(0.183799\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(390\) 0 0
\(391\) −16.9145 + 6.15636i −0.855401 + 0.311341i
\(392\) −13.8106 + 5.02665i −0.697541 + 0.253884i
\(393\) 0 0
\(394\) 6.25133 + 35.4531i 0.314938 + 1.78610i
\(395\) 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 \(0.825345\pi\)
\(398\) 1.87642 1.57450i 0.0940563 0.0789226i
\(399\) 0 0
\(400\) 0.694593 3.93923i 0.0347296 0.196962i
\(401\) −26.2699 22.0430i −1.31185 1.10078i −0.987964 0.154681i \(-0.950565\pi\)
−0.323889 0.946095i \(-0.604991\pi\)
\(402\) 0 0
\(403\) −0.939693 0.342020i −0.0468094 0.0170372i
\(404\) 19.5959 0.974933
\(405\) 0 0
\(406\) −24.0000 −1.19110
\(407\) 18.4141 + 6.70220i 0.912755 + 0.332216i
\(408\) 0 0
\(409\) −21.4492 17.9981i −1.06060 0.889946i −0.0664291 0.997791i \(-0.521161\pi\)
−0.994168 + 0.107845i \(0.965605\pi\)
\(410\) 5.10419 28.9473i 0.252078 1.42961i
\(411\) 0 0
\(412\) −21.4492 + 17.9981i −1.05673 + 0.886700i
\(413\) −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
\(418\) 5.63816 2.05212i 0.275771 0.100373i
\(419\) 32.2247 11.7288i 1.57428 0.572992i 0.600331 0.799752i \(-0.295035\pi\)
0.973951 + 0.226760i \(0.0728133\pi\)
\(420\) 0 0
\(421\) 0.347296 + 1.96962i 0.0169262 + 0.0959932i 0.992101 0.125445i \(-0.0400359\pi\)
−0.975174 + 0.221438i \(0.928925\pi\)
\(422\) −1.22474 + 2.12132i −0.0596196 + 0.103264i
\(423\) 0 0
\(424\) −18.0000 31.1769i −0.874157 1.51408i
\(425\) 5.62925 4.72350i 0.273059 0.229124i
\(426\) 0 0
\(427\) 1.73648 9.84808i 0.0840342 0.476582i
\(428\) −45.0340 37.7880i −2.17680 1.82655i
\(429\) 0 0
\(430\) 62.0197 + 22.5733i 2.99086 + 1.08858i
\(431\) 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 \(0.366058\pi\)
\(434\) −4.60353 1.67555i −0.220977 0.0804290i
\(435\) 0 0
\(436\) −3.06418 2.57115i −0.146748 0.123136i
\(437\) −0.425349 + 2.41228i −0.0203472 + 0.115395i
\(438\) 0 0
\(439\) 10.7246 8.99903i 0.511858 0.429500i −0.349924 0.936778i \(-0.613793\pi\)
0.861783 + 0.507278i \(0.169348\pi\)
\(440\) −14.6969 25.4558i −0.700649 1.21356i
\(441\) 0 0
\(442\) −9.00000 + 15.5885i −0.428086 + 0.741467i
\(443\) 2.12675 + 12.0614i 0.101045 + 0.573054i 0.992727 + 0.120391i \(0.0384148\pi\)
−0.891682 + 0.452663i \(0.850474\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −16.1124 + 5.86442i −0.762943 + 0.277689i
\(447\) 0 0
\(448\) −2.77837 15.7569i −0.131266 0.744445i
\(449\) 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
\(452\) 30.0227 25.1920i 1.41215 1.18493i
\(453\) 0 0
\(454\) 4.16756 23.6354i 0.195593 1.10926i
\(455\) −3.75284 3.14900i −0.175936 0.147628i
\(456\) 0 0
\(457\) −27.2511 9.91858i −1.27475 0.463972i −0.386059 0.922474i \(-0.626164\pi\)
−0.888693 + 0.458502i \(0.848386\pi\)
\(458\) 2.44949 0.114457
\(459\) 0 0
\(460\) 24.0000 1.11901
\(461\) −25.3194 9.21552i −1.17924 0.429210i −0.323309 0.946293i \(-0.604795\pi\)
−0.855935 + 0.517084i \(0.827018\pi\)
\(462\) 0 0
\(463\) −14.5548 12.2130i −0.676421 0.567585i 0.238537 0.971133i \(-0.423332\pi\)
−0.914958 + 0.403549i \(0.867777\pi\)
\(464\) 3.40280 19.2982i 0.157971 0.895897i
\(465\) 0 0
\(466\) −13.7888 + 11.5702i −0.638754 + 0.535978i
\(467\) 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
\(470\) 10.2084 + 57.8946i 0.470878 + 2.67048i
\(471\) 0 0
\(472\) 11.2763 4.10424i 0.519034 0.188913i
\(473\) 25.3194 9.21552i 1.16419 0.423730i
\(474\) 0 0
\(475\) −0.173648 0.984808i −0.00796752 0.0451861i
\(476\) −29.3939 + 50.9117i −1.34727 + 2.33353i
\(477\) 0 0
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 20.6406 17.3195i 0.943093 0.791349i −0.0350279 0.999386i \(-0.511152\pi\)
0.978121 + 0.208037i \(0.0667076\pi\)
\(480\) 0 0
\(481\) −1.38919 + 7.87846i −0.0633414 + 0.359227i
\(482\) 30.0227 + 25.1920i 1.36750 + 1.14747i
\(483\) 0 0
\(484\) 18.7939 + 6.84040i 0.854266 + 0.310927i
\(485\) −17.1464 −0.778579
\(486\) 0 0
\(487\) 35.0000 1.58600 0.793001 0.609221i \(-0.208518\pi\)
0.793001 + 0.609221i \(0.208518\pi\)
\(488\) 23.0177 + 8.37775i 1.04196 + 0.379243i
\(489\) 0 0
\(490\) 13.7888 + 11.5702i 0.622914 + 0.522687i
\(491\) 6.80559 38.5964i 0.307132 1.74183i −0.306164 0.951979i \(-0.599046\pi\)
0.613296 0.789853i \(-0.289843\pi\)
\(492\) 0 0
\(493\) 27.5776 23.1404i 1.24203 1.04219i
\(494\) 1.22474 + 2.12132i 0.0551039 + 0.0954427i
\(495\) 0 0
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) −2.55210 14.4737i −0.114477 0.649232i
\(498\) 0 0
\(499\) −1.87939 + 0.684040i −0.0841328 + 0.0306218i −0.383744 0.923440i \(-0.625365\pi\)
0.299611 + 0.954061i \(0.403143\pi\)
\(500\) 36.8283 13.4044i 1.64701 0.599463i
\(501\) 0 0
\(502\) −3.12567 17.7265i −0.139505 0.791174i
\(503\) −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
\(506\) 11.2585 9.44701i 0.500502 0.419971i
\(507\) 0 0
\(508\) −13.1973 + 74.8454i −0.585534 + 3.32073i
\(509\) 7.50567 + 6.29801i 0.332683 + 0.279154i 0.793792 0.608189i \(-0.208104\pi\)
−0.461109 + 0.887344i \(0.652548\pi\)
\(510\) 0 0
\(511\) −20.6732 7.52444i −0.914530 0.332862i
\(512\) 39.1918 1.73205
\(513\) 0 0
\(514\) −42.0000 −1.85254
\(515\) 16.1124 + 5.86442i 0.709996 + 0.258417i
\(516\) 0 0
\(517\) 18.3851 + 15.4269i 0.808574 + 0.678474i
\(518\) −6.80559 + 38.5964i −0.299020 + 1.69583i
\(519\) 0 0
\(520\) 9.19253 7.71345i 0.403119 0.338257i
\(521\) 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 \(-0.0174065\pi\)
\(524\) −8.50699 48.2455i −0.371630 2.10762i
\(525\) 0 0
\(526\) 62.0197 22.5733i 2.70419 0.984244i
\(527\) 6.90530 2.51332i 0.300800 0.109482i
\(528\) 0 0
\(529\) −2.95202 16.7417i −0.128349 0.727901i
\(530\) −22.0454 + 38.1838i −0.957591 + 1.65860i
\(531\) 0 0
\(532\) 4.00000 + 6.92820i 0.173422 + 0.300376i
\(533\) 3.75284 3.14900i 0.162553 0.136398i
\(534\) 0 0
\(535\) −6.25133 + 35.4531i −0.270269 + 1.53277i
\(536\) 26.2699 + 22.0430i 1.13468 + 0.952114i
\(537\) 0 0
\(538\) 50.7434 + 18.4691i 2.18770 + 0.796259i
\(539\) 7.34847 0.316521
\(540\) 0 0
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) −16.1124 5.86442i −0.692086 0.251899i
\(543\) 0 0
\(544\) 0 0
\(545\) −0.425349 + 2.41228i −0.0182200 + 0.103331i
\(546\) 0 0
\(547\) −9.95858 + 8.35624i −0.425798 + 0.357287i −0.830364 0.557222i \(-0.811867\pi\)
0.404565 + 0.914509i \(0.367423\pi\)
\(548\) 19.5959 + 33.9411i 0.837096 + 1.44989i
\(549\) 0 0
\(550\) −3.00000 + 5.19615i −0.127920 + 0.221565i
\(551\) −0.850699 4.82455i −0.0362410 0.205533i
\(552\) 0 0
\(553\) 13.1557 4.78828i 0.559437 0.203618i
\(554\) 25.3194 9.21552i 1.07572 0.391530i
\(555\) 0 0
\(556\) −6.94593 39.3923i −0.294573 1.67061i
\(557\) 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
\(560\) 15.0113 12.5960i 0.634345 0.532279i
\(561\) 0 0
\(562\) −5.20945 + 29.5442i −0.219747 + 1.24625i
\(563\) −9.38209 7.87251i −0.395408 0.331787i 0.423308 0.905986i \(-0.360869\pi\)
−0.818715 + 0.574199i \(0.805313\pi\)
\(564\) 0 0
\(565\) −22.5526 8.20848i −0.948796 0.345333i
\(566\) −41.6413 −1.75032
\(567\) 0 0
\(568\) 36.0000 1.51053
\(569\) −11.5088 4.18887i −0.482476 0.175607i 0.0893199 0.996003i \(-0.471531\pi\)
−0.571795 + 0.820396i \(0.693753\pi\)
\(570\) 0 0
\(571\) −7.66044 6.42788i −0.320580 0.268998i 0.468269 0.883586i \(-0.344878\pi\)
−0.788848 + 0.614588i \(0.789322\pi\)
\(572\) 1.70140 9.64911i 0.0711390 0.403449i
\(573\) 0 0
\(574\) 18.3851 15.4269i 0.767378 0.643906i
\(575\) −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 \(-0.00754370\pi\)
\(578\) −15.7379 89.2542i −0.654612 3.71249i
\(579\) 0 0
\(580\) −45.1052 + 16.4170i −1.87289 + 0.681677i
\(581\) −23.0177 + 8.37775i −0.954934 + 0.347568i
\(582\) 0 0
\(583\) 3.12567 + 17.7265i 0.129452 + 0.734158i
\(584\) 26.9444 46.6690i 1.11497 1.93118i
\(585\) 0 0
\(586\) −6.00000 10.3923i −0.247858 0.429302i
\(587\) −1.87642 + 1.57450i −0.0774481 + 0.0649866i −0.680690 0.732572i \(-0.738320\pi\)
0.603242 + 0.797558i \(0.293875\pi\)
\(588\) 0 0
\(589\) 0.173648 0.984808i 0.00715505 0.0405783i
\(590\) −11.2585 9.44701i −0.463505 0.388927i
\(591\) 0 0
\(592\) −30.0702 10.9446i −1.23588 0.449822i
\(593\) −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
\(596\) 46.0353 + 16.7555i 1.88568 + 0.686332i
\(597\) 0 0
\(598\) 4.59627 + 3.85673i 0.187955 + 0.157713i
\(599\) 6.80559 38.5964i 0.278069 1.57701i −0.450973 0.892538i \(-0.648923\pi\)
0.729042 0.684469i \(-0.239966\pi\)
\(600\) 0 0
\(601\) −5.36231 + 4.49951i −0.218733 + 0.183539i −0.745570 0.666428i \(-0.767822\pi\)
0.526836 + 0.849967i \(0.323378\pi\)
\(602\) 26.9444 + 46.6690i 1.09817 + 1.90209i
\(603\) 0 0
\(604\) −10.0000 + 17.3205i −0.406894 + 0.704761i
\(605\) −2.12675 12.0614i −0.0864646 0.490365i
\(606\) 0 0
\(607\) −41.3465 + 15.0489i −1.67820 + 0.610815i −0.993062 0.117596i \(-0.962481\pi\)
−0.685140 + 0.728411i \(0.740259\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −5.20945 29.5442i −0.210924 1.19621i
\(611\) −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 \(0.904638\pi\)
\(614\) −3.75284 + 3.14900i −0.151452 + 0.127083i
\(615\) 0 0
\(616\) 4.16756 23.6354i 0.167916 0.952297i
\(617\) 18.7642 + 15.7450i 0.755417 + 0.633870i 0.936930 0.349518i \(-0.113655\pi\)
−0.181512 + 0.983389i \(0.558099\pi\)
\(618\) 0 0
\(619\) 46.0449 + 16.7590i 1.85070 + 0.673601i 0.984877 + 0.173254i \(0.0554281\pi\)
0.865825 + 0.500347i \(0.166794\pi\)
\(620\) −9.79796 −0.393496
\(621\) 0 0
\(622\) −60.0000 −2.40578
\(623\) 0 0
\(624\) 0 0
\(625\) −22.2153 18.6408i −0.888612 0.745634i
\(626\) 6.80559 38.5964i 0.272006 1.54262i
\(627\) 0 0
\(628\) 52.0910 43.7096i 2.07866 1.74420i
\(629\) −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 \(0.826997\pi\)
\(632\) 5.95489 + 33.7719i 0.236873 + 1.34337i
\(633\) 0 0
\(634\) −22.5526 + 8.20848i −0.895679 + 0.326001i
\(635\) 43.7336 15.9177i 1.73551 0.631676i
\(636\) 0 0
\(637\) 0.520945 + 2.95442i 0.0206406 + 0.117059i
\(638\) −14.6969 + 25.4558i −0.581857 + 1.00781i
\(639\) 0 0
\(640\) −24.0000 41.5692i −0.948683 1.64317i
\(641\) −13.1349 + 11.0215i −0.518798 + 0.435324i −0.864213 0.503127i \(-0.832183\pi\)
0.345414 + 0.938450i \(0.387738\pi\)
\(642\) 0 0
\(643\) 6.59863 37.4227i 0.260225 1.47581i −0.522072 0.852901i \(-0.674841\pi\)
0.782297 0.622906i \(-0.214048\pi\)
\(644\) 15.0113 + 12.5960i 0.591530 + 0.496352i
\(645\) 0 0
\(646\) −16.9145 6.15636i −0.665491 0.242219i
\(647\) −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
\(650\) −2.30177 0.837775i −0.0902827 0.0328602i
\(651\) 0 0
\(652\) −30.6418 25.7115i −1.20002 1.00694i
\(653\) 1.70140 9.64911i 0.0665808 0.377599i −0.933250 0.359227i \(-0.883041\pi\)
0.999831 0.0183721i \(-0.00584836\pi\)
\(654\) 0 0
\(655\) −22.9813 + 19.2836i −0.897955 + 0.753474i
\(656\) 9.79796 + 16.9706i 0.382546 + 0.662589i
\(657\) 0 0
\(658\) −24.0000 + 41.5692i −0.935617 + 1.62054i
\(659\) 3.40280 + 19.2982i 0.132554 + 0.751752i 0.976532 + 0.215373i \(0.0690968\pi\)
−0.843978 + 0.536378i \(0.819792\pi\)
\(660\) 0 0
\(661\) −10.3366 + 3.76222i −0.402048 + 0.146333i −0.535126 0.844772i \(-0.679736\pi\)
0.133078 + 0.991106i \(0.457514\pi\)
\(662\) −16.1124 + 5.86442i −0.626225 + 0.227927i
\(663\) 0 0
\(664\) −10.4189 59.0885i −0.404331 2.29308i
\(665\) 2.44949 4.24264i 0.0949871 0.164523i
\(666\) 0 0
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) −15.0113 + 12.5960i −0.580806 + 0.487354i
\(669\) 0 0
\(670\) 7.29322 41.3619i 0.281762 1.59795i
\(671\) −9.38209 7.87251i −0.362192 0.303915i
\(672\) 0 0
\(673\) −27.2511 9.91858i −1.05045 0.382333i −0.241619 0.970371i \(-0.577678\pi\)
−0.808833 + 0.588038i \(0.799901\pi\)
\(674\) 68.5857 2.64182
\(675\) 0 0
\(676\) −48.0000 −1.84615
\(677\) 43.7336 + 15.9177i 1.68082 + 0.611768i 0.993422 0.114515i \(-0.0365313\pi\)
0.687397 + 0.726282i \(0.258753\pi\)
\(678\) 0 0
\(679\) −10.7246 8.99903i −0.411573 0.345351i
\(680\) −15.3126 + 86.8420i −0.587211 + 3.33024i
\(681\) 0 0
\(682\) −4.59627 + 3.85673i −0.176000 + 0.147682i
\(683\) −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
\(686\) 8.50699 + 48.2455i 0.324798 + 1.84202i
\(687\) 0 0
\(688\) −41.3465 + 15.0489i −1.57632 + 0.573733i
\(689\) −6.90530 + 2.51332i −0.263071 + 0.0957500i
\(690\) 0 0
\(691\) 8.16146 + 46.2860i 0.310477 + 1.76080i 0.596533 + 0.802588i \(0.296544\pi\)
−0.286057 + 0.958213i \(0.592345\pi\)
\(692\) 19.5959 33.9411i 0.744925 1.29025i
\(693\) 0 0
\(694\) 30.0000 + 51.9615i 1.13878 + 1.97243i
\(695\) −18.7642 + 15.7450i −0.711766 + 0.597243i
\(696\) 0 0
\(697\) −6.25133 + 35.4531i −0.236786 + 1.34288i
\(698\) −37.5284 31.4900i −1.42047 1.19192i
\(699\) 0 0
\(700\) −7.51754 2.73616i −0.284136 0.103417i
\(701\) 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
\(704\) −18.4141 6.70220i −0.694009 0.252599i
\(705\) 0 0
\(706\) 4.59627 + 3.85673i 0.172983 + 0.145150i
\(707\) 1.70140 9.64911i 0.0639876 0.362892i
\(708\) 0 0
\(709\) −5.36231 + 4.49951i −0.201386 + 0.168983i −0.737903 0.674906i \(-0.764184\pi\)
0.536518 + 0.843889i \(0.319740\pi\)
\(710\) −22.0454 38.1838i −0.827349 1.43301i
\(711\) 0 0
\(712\) 0 0
\(713\) −0.425349 2.41228i −0.0159295 0.0903405i
\(714\) 0 0
\(715\) −5.63816 + 2.05212i −0.210855 + 0.0767450i
\(716\) −55.2424 + 20.1066i −2.06451 + 0.751419i
\(717\) 0 0
\(718\) 12.5027 + 70.9062i 0.466595 + 2.64619i
\(719\) −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
\(722\) 33.7755 28.3410i 1.25699 1.05474i
\(723\) 0 0
\(724\) 5.55674 31.5138i 0.206515 1.17120i
\(725\) 3.75284 + 3.14900i 0.139377 + 0.116951i
\(726\) 0 0
\(727\) −13.1557 4.78828i −0.487918 0.177588i 0.0863341 0.996266i \(-0.472485\pi\)
−0.574252 + 0.818679i \(0.694707\pi\)
\(728\) 9.79796 0.363137
\(729\) 0 0
\(730\) −66.0000 −2.44277
\(731\) −75.9583 27.6466i −2.80942 1.02255i
\(732\) 0 0
\(733\) 13.0228 + 10.9274i 0.481006 + 0.403612i 0.850790 0.525506i \(-0.176124\pi\)
−0.369784 + 0.929118i \(0.620568\pi\)
\(734\) −2.12675 + 12.0614i −0.0784997 + 0.445194i
\(735\) 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 \(0.160812\pi\)
\(740\) 13.6112 + 77.1928i 0.500357 + 2.83767i
\(741\) 0 0
\(742\) −33.8289 + 12.3127i −1.24190 + 0.452014i
\(743\) −29.9230 + 10.8911i −1.09777 + 0.399555i −0.826493 0.562947i \(-0.809667\pi\)
−0.271275 + 0.962502i \(0.587445\pi\)
\(744\) 0 0
\(745\) −5.20945 29.5442i −0.190859 1.08242i
\(746\) 42.8661 74.2462i 1.56944 2.71835i
\(747\) 0 0
\(748\) 36.0000 + 62.3538i 1.31629 + 2.27988i
\(749\) −22.5170 + 18.8940i −0.822754 + 0.690372i
\(750\) 0 0
\(751\) 4.51485 25.6050i 0.164749 0.934340i −0.784573 0.620036i \(-0.787118\pi\)
0.949323 0.314304i \(-0.101771\pi\)
\(752\) −30.0227 25.1920i −1.09481 0.918659i
\(753\) 0 0
\(754\) −11.2763 4.10424i −0.410659 0.149468i
\(755\) 12.2474 0.445730
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 18.4141 + 6.70220i 0.668832 + 0.243435i
\(759\) 0 0
\(760\) 9.19253 + 7.71345i 0.333448 + 0.279796i
\(761\) 0.425349 2.41228i 0.0154189 0.0874450i −0.976127 0.217199i \(-0.930308\pi\)
0.991546 + 0.129754i \(0.0414189\pi\)
\(762\) 0 0
\(763\) −1.53209 + 1.28558i −0.0554653 + 0.0465409i
\(764\) 19.5959 + 33.9411i 0.708955 + 1.22795i
\(765\) 0 0
\(766\) −42.0000 + 72.7461i −1.51752 + 2.62842i
\(767\) −0.425349 2.41228i −0.0153585 0.0871023i
\(768\) 0 0
\(769\) 34.7686 12.6547i 1.25379 0.456342i 0.372109 0.928189i \(-0.378635\pi\)
0.881680 + 0.471847i \(0.156413\pi\)
\(770\) −27.6212 + 10.0533i −0.995399 + 0.362296i
\(771\) 0 0
\(772\) 7.64052 + 43.3315i 0.274988 + 1.55954i
\(773\) −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
\(776\) 26.2699 22.0430i 0.943033 0.791298i
\(777\) 0 0
\(778\) −11.4608 + 64.9973i −0.410889 + 2.33027i
\(779\) 3.75284 + 3.14900i 0.134459 + 0.112825i
\(780\) 0 0
\(781\) −16.9145 6.15636i −0.605247 0.220292i
\(782\) −44.0908 −1.57668