Properties

Label 729.2.e.p.649.2
Level $729$
Weight $2$
Character 729.649
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 649.2
Root \(-0.483690 - 1.32893i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.p.82.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.425349 - 2.41228i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-1.87642 + 1.57450i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})\) \(q+(0.425349 - 2.41228i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-1.87642 + 1.57450i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(1.87642 + 1.57450i) q^{11} +(-0.173648 - 0.984808i) q^{13} +(0.850699 + 4.82455i) q^{14} +(3.06418 + 2.57115i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(9.20707 - 3.35110i) q^{20} +(4.59627 - 3.85673i) q^{22} +(2.30177 + 0.837775i) q^{23} +(0.173648 - 0.984808i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-0.850699 + 4.82455i) q^{29} +(0.939693 + 0.342020i) q^{31} +(16.9145 - 6.15636i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-1.87642 - 1.57450i) q^{38} +(-2.08378 - 11.8177i) q^{40} +(0.850699 + 4.82455i) q^{41} +(8.42649 + 7.07066i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-9.20707 + 3.35110i) q^{47} +(-2.29813 + 1.92836i) q^{49} +(-2.30177 - 0.837775i) q^{50} +(-0.694593 + 3.93923i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(1.70140 - 9.64911i) q^{56} +(11.2763 + 4.10424i) q^{58} +(-1.87642 + 1.57450i) q^{59} +(-4.69846 + 1.71010i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(1.87642 + 1.57450i) q^{65} +(-1.21554 - 6.89365i) q^{67} +(-5.10419 - 28.9473i) q^{68} +(-9.19253 - 7.71345i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(-18.4141 + 6.70220i) q^{74} +(-3.06418 + 2.57115i) q^{76} +(-4.60353 - 1.67555i) q^{77} +(-1.21554 + 6.89365i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-2.12675 + 12.0614i) q^{83} +(-16.9145 - 6.15636i) q^{85} +(20.6406 - 17.3195i) q^{86} +(-11.2763 + 4.10424i) q^{88} +(1.00000 + 1.73205i) q^{91} +(-7.50567 - 6.29801i) q^{92} +(4.16756 + 23.6354i) q^{94} +(0.425349 + 2.41228i) q^{95} +(-5.36231 - 4.49951i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.425349 2.41228i 0.300767 1.70574i −0.342020 0.939693i \(-0.611111\pi\)
0.642788 0.766044i \(-0.277778\pi\)
\(3\) 0 0
\(4\) −3.75877 1.36808i −1.87939 0.684040i
\(5\) −1.87642 + 1.57450i −0.839160 + 0.704139i −0.957375 0.288849i \(-0.906727\pi\)
0.118215 + 0.992988i \(0.462283\pi\)
\(6\) 0 0
\(7\) −1.87939 + 0.684040i −0.710341 + 0.258543i −0.671820 0.740715i \(-0.734487\pi\)
−0.0385213 + 0.999258i \(0.512265\pi\)
\(8\) −2.44949 + 4.24264i −0.866025 + 1.50000i
\(9\) 0 0
\(10\) 3.00000 + 5.19615i 0.948683 + 1.64317i
\(11\) 1.87642 + 1.57450i 0.565761 + 0.474730i 0.880236 0.474536i \(-0.157384\pi\)
−0.314475 + 0.949266i \(0.601828\pi\)
\(12\) 0 0
\(13\) −0.173648 0.984808i −0.0481613 0.273137i 0.951212 0.308539i \(-0.0998399\pi\)
−0.999373 + 0.0354021i \(0.988729\pi\)
\(14\) 0.850699 + 4.82455i 0.227359 + 1.28942i
\(15\) 0 0
\(16\) 3.06418 + 2.57115i 0.766044 + 0.642788i
\(17\) 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 \(0.130073\pi\)
\(20\) 9.20707 3.35110i 2.05876 0.749329i
\(21\) 0 0
\(22\) 4.59627 3.85673i 0.979927 0.822257i
\(23\) 2.30177 + 0.837775i 0.479952 + 0.174688i 0.570655 0.821190i \(-0.306689\pi\)
−0.0907034 + 0.995878i \(0.528912\pi\)
\(24\) 0 0
\(25\) 0.173648 0.984808i 0.0347296 0.196962i
\(26\) −2.44949 −0.480384
\(27\) 0 0
\(28\) 8.00000 1.51186
\(29\) −0.850699 + 4.82455i −0.157971 + 0.895897i 0.798048 + 0.602593i \(0.205866\pi\)
−0.956019 + 0.293304i \(0.905245\pi\)
\(30\) 0 0
\(31\) 0.939693 + 0.342020i 0.168774 + 0.0614286i 0.425025 0.905182i \(-0.360265\pi\)
−0.256251 + 0.966610i \(0.582487\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 16.9145 6.15636i 2.90081 1.05581i
\(35\) 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 \(-0.395093\pi\)
\(38\) −1.87642 1.57450i −0.304395 0.255418i
\(39\) 0 0
\(40\) −2.08378 11.8177i −0.329474 1.86854i
\(41\) 0.850699 + 4.82455i 0.132857 + 0.753469i 0.976328 + 0.216294i \(0.0693971\pi\)
−0.843471 + 0.537174i \(0.819492\pi\)
\(42\) 0 0
\(43\) 8.42649 + 7.07066i 1.28503 + 1.07827i 0.992530 + 0.122000i \(0.0389307\pi\)
0.292497 + 0.956266i \(0.405514\pi\)
\(44\) −4.89898 8.48528i −0.738549 1.27920i
\(45\) 0 0
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −9.20707 + 3.35110i −1.34299 + 0.488808i −0.910753 0.412952i \(-0.864498\pi\)
−0.432236 + 0.901760i \(0.642275\pi\)
\(48\) 0 0
\(49\) −2.29813 + 1.92836i −0.328305 + 0.275480i
\(50\) −2.30177 0.837775i −0.325519 0.118479i
\(51\) 0 0
\(52\) −0.694593 + 3.93923i −0.0963227 + 0.546273i
\(53\) 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
\(56\) 1.70140 9.64911i 0.227359 1.28942i
\(57\) 0 0
\(58\) 11.2763 + 4.10424i 1.48065 + 0.538913i
\(59\) −1.87642 + 1.57450i −0.244289 + 0.204983i −0.756708 0.653753i \(-0.773194\pi\)
0.512420 + 0.858735i \(0.328749\pi\)
\(60\) 0 0
\(61\) −4.69846 + 1.71010i −0.601577 + 0.218956i −0.624814 0.780774i \(-0.714825\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(62\) 1.22474 2.12132i 0.155543 0.269408i
\(63\) 0 0
\(64\) 4.00000 + 6.92820i 0.500000 + 0.866025i
\(65\) 1.87642 + 1.57450i 0.232741 + 0.195293i
\(66\) 0 0
\(67\) −1.21554 6.89365i −0.148502 0.842194i −0.964489 0.264124i \(-0.914917\pi\)
0.815987 0.578070i \(-0.196194\pi\)
\(68\) −5.10419 28.9473i −0.618974 3.51038i
\(69\) 0 0
\(70\) −9.19253 7.71345i −1.09872 0.921934i
\(71\) −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 \(0.944054\pi\)
\(74\) −18.4141 + 6.70220i −2.14060 + 0.779115i
\(75\) 0 0
\(76\) −3.06418 + 2.57115i −0.351485 + 0.294931i
\(77\) −4.60353 1.67555i −0.524621 0.190947i
\(78\) 0 0
\(79\) −1.21554 + 6.89365i −0.136759 + 0.775597i 0.836860 + 0.547417i \(0.184389\pi\)
−0.973619 + 0.228180i \(0.926722\pi\)
\(80\) −9.79796 −1.09545
\(81\) 0 0
\(82\) 12.0000 1.32518
\(83\) −2.12675 + 12.0614i −0.233441 + 1.32391i 0.612432 + 0.790524i \(0.290191\pi\)
−0.845872 + 0.533385i \(0.820920\pi\)
\(84\) 0 0
\(85\) −16.9145 6.15636i −1.83463 0.667751i
\(86\) 20.6406 17.3195i 2.22573 1.86761i
\(87\) 0 0
\(88\) −11.2763 + 4.10424i −1.20206 + 0.437514i
\(89\) 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
\(92\) −7.50567 6.29801i −0.782520 0.656613i
\(93\) 0 0
\(94\) 4.16756 + 23.6354i 0.429851 + 2.43780i
\(95\) 0.425349 + 2.41228i 0.0436399 + 0.247494i
\(96\) 0 0
\(97\) −5.36231 4.49951i −0.544460 0.456856i 0.328600 0.944469i \(-0.393423\pi\)
−0.873060 + 0.487613i \(0.837868\pi\)
\(98\) 3.67423 + 6.36396i 0.371154 + 0.642857i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 4.60353 1.67555i 0.458069 0.166723i −0.102671 0.994715i \(-0.532739\pi\)
0.560740 + 0.827992i \(0.310517\pi\)
\(102\) 0 0
\(103\) −5.36231 + 4.49951i −0.528364 + 0.443350i −0.867536 0.497374i \(-0.834298\pi\)
0.339172 + 0.940724i \(0.389853\pi\)
\(104\) 4.60353 + 1.67555i 0.451414 + 0.164301i
\(105\) 0 0
\(106\) 3.12567 17.7265i 0.303592 1.72175i
\(107\) 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 \(0.515250\pi\)
\(110\) −2.55210 + 14.4737i −0.243333 + 1.38001i
\(111\) 0 0
\(112\) −7.51754 2.73616i −0.710341 0.258543i
\(113\) −7.50567 + 6.29801i −0.706074 + 0.592467i −0.923495 0.383611i \(-0.874680\pi\)
0.217420 + 0.976078i \(0.430236\pi\)
\(114\) 0 0
\(115\) −5.63816 + 2.05212i −0.525761 + 0.191361i
\(116\) 9.79796 16.9706i 0.909718 1.57568i
\(117\) 0 0
\(118\) 3.00000 + 5.19615i 0.276172 + 0.478345i
\(119\) −11.2585 9.44701i −1.03207 0.866006i
\(120\) 0 0
\(121\) −0.868241 4.92404i −0.0789310 0.447640i
\(122\) 2.12675 + 12.0614i 0.192547 + 1.09199i
\(123\) 0 0
\(124\) −3.06418 2.57115i −0.275171 0.230896i
\(125\) −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 \(-0.152539\pi\)
\(128\) 18.4141 6.70220i 1.62760 0.592396i
\(129\) 0 0
\(130\) 4.59627 3.85673i 0.403119 0.338257i
\(131\) −11.5088 4.18887i −1.00553 0.365984i −0.213816 0.976874i \(-0.568589\pi\)
−0.791715 + 0.610890i \(0.790812\pi\)
\(132\) 0 0
\(133\) −0.347296 + 1.96962i −0.0301144 + 0.170787i
\(134\) −17.1464 −1.48123
\(135\) 0 0
\(136\) −36.0000 −3.08697
\(137\) 1.70140 9.64911i 0.145360 0.824379i −0.821717 0.569896i \(-0.806984\pi\)
0.967077 0.254483i \(-0.0819053\pi\)
\(138\) 0 0
\(139\) 9.39693 + 3.42020i 0.797037 + 0.290098i 0.708258 0.705954i \(-0.249481\pi\)
0.0887789 + 0.996051i \(0.471704\pi\)
\(140\) −15.0113 + 12.5960i −1.26869 + 1.06456i
\(141\) 0 0
\(142\) −16.9145 + 6.15636i −1.41943 + 0.516630i
\(143\) 1.22474 2.12132i 0.102418 0.177394i
\(144\) 0 0
\(145\) −6.00000 10.3923i −0.498273 0.863034i
\(146\) 20.6406 + 17.3195i 1.70823 + 1.43337i
\(147\) 0 0
\(148\) 5.55674 + 31.5138i 0.456761 + 2.59042i
\(149\) 2.12675 + 12.0614i 0.174230 + 0.988107i 0.939029 + 0.343838i \(0.111727\pi\)
−0.764799 + 0.644269i \(0.777162\pi\)
\(150\) 0 0
\(151\) 3.83022 + 3.21394i 0.311699 + 0.261547i 0.785194 0.619250i \(-0.212563\pi\)
−0.473495 + 0.880797i \(0.657008\pi\)
\(152\) 2.44949 + 4.24264i 0.198680 + 0.344124i
\(153\) 0 0
\(154\) −6.00000 + 10.3923i −0.483494 + 0.837436i
\(155\) −2.30177 + 0.837775i −0.184882 + 0.0672917i
\(156\) 0 0
\(157\) 13.0228 10.9274i 1.03933 0.872101i 0.0473976 0.998876i \(-0.484907\pi\)
0.991931 + 0.126775i \(0.0404628\pi\)
\(158\) 16.1124 + 5.86442i 1.28183 + 0.466549i
\(159\) 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 \(0.628089\pi\)
\(164\) 3.40280 19.2982i 0.265714 1.50694i
\(165\) 0 0
\(166\) 28.1908 + 10.2606i 2.18803 + 0.796377i
\(167\) 3.75284 3.14900i 0.290403 0.243677i −0.485933 0.873996i \(-0.661520\pi\)
0.776336 + 0.630319i \(0.217076\pi\)
\(168\) 0 0
\(169\) 11.2763 4.10424i 0.867409 0.315711i
\(170\) −22.0454 + 38.1838i −1.69081 + 2.92856i
\(171\) 0 0
\(172\) −22.0000 38.1051i −1.67748 2.90549i
\(173\) 7.50567 + 6.29801i 0.570646 + 0.478829i 0.881860 0.471511i \(-0.156291\pi\)
−0.311214 + 0.950340i \(0.600736\pi\)
\(174\) 0 0
\(175\) 0.347296 + 1.96962i 0.0262531 + 0.148889i
\(176\) 1.70140 + 9.64911i 0.128248 + 0.727329i
\(177\) 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 \(0.262759\pi\)
\(182\) 4.60353 1.67555i 0.341237 0.124200i
\(183\) 0 0
\(184\) −9.19253 + 7.71345i −0.677683 + 0.568643i
\(185\) 18.4141 + 6.70220i 1.35383 + 0.492755i
\(186\) 0 0
\(187\) −3.12567 + 17.7265i −0.228571 + 1.29629i
\(188\) 39.1918 2.85836
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 1.70140 9.64911i 0.123109 0.698185i −0.859304 0.511465i \(-0.829103\pi\)
0.982413 0.186720i \(-0.0597858\pi\)
\(192\) 0 0
\(193\) −10.3366 3.76222i −0.744046 0.270811i −0.0579479 0.998320i \(-0.518456\pi\)
−0.686098 + 0.727509i \(0.740678\pi\)
\(194\) −13.1349 + 11.0215i −0.943033 + 0.791298i
\(195\) 0 0
\(196\) 11.2763 4.10424i 0.805451 0.293160i
\(197\) −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 \(0.822049\pi\)
\(200\) 3.75284 + 3.14900i 0.265366 + 0.222668i
\(201\) 0 0
\(202\) −2.08378 11.8177i −0.146614 0.831490i
\(203\) −1.70140 9.64911i −0.119415 0.677234i
\(204\) 0 0
\(205\) −9.19253 7.71345i −0.642034 0.538731i
\(206\) 8.57321 + 14.8492i 0.597324 + 1.03460i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) 2.30177 0.837775i 0.159217 0.0579501i
\(210\) 0 0
\(211\) −0.766044 + 0.642788i −0.0527367 + 0.0442513i −0.668775 0.743465i \(-0.733181\pi\)
0.616038 + 0.787716i \(0.288737\pi\)
\(212\) −27.6212 10.0533i −1.89703 0.690463i
\(213\) 0 0
\(214\) 6.25133 35.4531i 0.427332 2.42352i
\(215\) −26.9444 −1.83759
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) −0.425349 + 2.41228i −0.0288083 + 0.163380i
\(219\) 0 0
\(220\) 22.5526 + 8.20848i 1.52050 + 0.553416i
\(221\) 5.62925 4.72350i 0.378665 0.317737i
\(222\) 0 0
\(223\) 6.57785 2.39414i 0.440485 0.160324i −0.112251 0.993680i \(-0.535806\pi\)
0.552736 + 0.833356i \(0.313584\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.0000 + 20.7846i 0.798228 + 1.38257i
\(227\) 7.50567 + 6.29801i 0.498169 + 0.418013i 0.856943 0.515411i \(-0.172361\pi\)
−0.358774 + 0.933424i \(0.616805\pi\)
\(228\) 0 0
\(229\) −0.173648 0.984808i −0.0114750 0.0650779i 0.978533 0.206092i \(-0.0660747\pi\)
−0.990008 + 0.141014i \(0.954964\pi\)
\(230\) 2.55210 + 14.4737i 0.168280 + 0.954365i
\(231\) 0 0
\(232\) −18.3851 15.4269i −1.20704 1.01283i
\(233\) 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
\(236\) 9.20707 3.35110i 0.599329 0.218138i
\(237\) 0 0
\(238\) −27.5776 + 23.1404i −1.78759 + 1.49997i
\(239\) 2.30177 + 0.837775i 0.148889 + 0.0541911i 0.415390 0.909644i \(-0.363645\pi\)
−0.266501 + 0.963835i \(0.585867\pi\)
\(240\) 0 0
\(241\) −2.77837 + 15.7569i −0.178971 + 1.01499i 0.754490 + 0.656312i \(0.227884\pi\)
−0.933460 + 0.358681i \(0.883227\pi\)
\(242\) −12.2474 −0.787296
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) 1.27605 7.23683i 0.0815237 0.462344i
\(246\) 0 0
\(247\) −0.939693 0.342020i −0.0597912 0.0217622i
\(248\) −3.75284 + 3.14900i −0.238305 + 0.199962i
\(249\) 0 0
\(250\) −22.5526 + 8.20848i −1.42635 + 0.519150i
\(251\) 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
\(254\) −35.6519 29.9155i −2.23700 1.87707i
\(255\) 0 0
\(256\) −5.55674 31.5138i −0.347296 1.96962i
\(257\) −2.97745 16.8859i −0.185728 1.05332i −0.925017 0.379927i \(-0.875949\pi\)
0.739289 0.673389i \(-0.235162\pi\)
\(258\) 0 0
\(259\) 12.2567 + 10.2846i 0.761595 + 0.639054i
\(260\) −4.89898 8.48528i −0.303822 0.526235i
\(261\) 0 0
\(262\) −15.0000 + 25.9808i −0.926703 + 1.60510i
\(263\) 25.3194 9.21552i 1.56126 0.568254i 0.590238 0.807229i \(-0.299034\pi\)
0.971026 + 0.238976i \(0.0768116\pi\)
\(264\) 0 0
\(265\) −13.7888 + 11.5702i −0.847039 + 0.710750i
\(266\) 4.60353 + 1.67555i 0.282261 + 0.102735i
\(267\) 0 0
\(268\) −4.86215 + 27.5746i −0.297003 + 1.68439i
\(269\) −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 \(0.568196\pi\)
\(272\) −5.10419 + 28.9473i −0.309487 + 1.75519i
\(273\) 0 0
\(274\) −22.5526 8.20848i −1.36245 0.495893i
\(275\) 1.87642 1.57450i 0.113152 0.0949460i
\(276\) 0 0
\(277\) −10.3366 + 3.76222i −0.621067 + 0.226050i −0.633339 0.773875i \(-0.718316\pi\)
0.0122715 + 0.999925i \(0.496094\pi\)
\(278\) 12.2474 21.2132i 0.734553 1.27228i
\(279\) 0 0
\(280\) 12.0000 + 20.7846i 0.717137 + 1.24212i
\(281\) −9.38209 7.87251i −0.559689 0.469634i 0.318517 0.947917i \(-0.396815\pi\)
−0.878206 + 0.478283i \(0.841259\pi\)
\(282\) 0 0
\(283\) 2.95202 + 16.7417i 0.175479 + 0.995193i 0.937589 + 0.347745i \(0.113052\pi\)
−0.762110 + 0.647448i \(0.775836\pi\)
\(284\) 5.10419 + 28.9473i 0.302878 + 1.71771i
\(285\) 0 0
\(286\) −4.59627 3.85673i −0.271783 0.228053i
\(287\) −4.89898 8.48528i −0.289178 0.500870i
\(288\) 0 0
\(289\) −18.5000 + 32.0429i −1.08824 + 1.88488i
\(290\) −27.6212 + 10.0533i −1.62197 + 0.590350i
\(291\) 0 0
\(292\) 33.7060 28.2827i 1.97249 1.65512i
\(293\) −4.60353 1.67555i −0.268941 0.0978867i 0.204029 0.978965i \(-0.434596\pi\)
−0.472971 + 0.881078i \(0.656818\pi\)
\(294\) 0 0
\(295\) 1.04189 5.90885i 0.0606611 0.344026i
\(296\) 39.1918 2.27798
\(297\) 0 0
\(298\) 30.0000 1.73785
\(299\) 0.425349 2.41228i 0.0245986 0.139506i
\(300\) 0 0
\(301\) −20.6732 7.52444i −1.19159 0.433702i
\(302\) 9.38209 7.87251i 0.539879 0.453012i
\(303\) 0 0
\(304\) 3.75877 1.36808i 0.215580 0.0784648i
\(305\) 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 \(0.851510\pi\)
\(308\) 15.0113 + 12.5960i 0.855351 + 0.717724i
\(309\) 0 0
\(310\) 1.04189 + 5.90885i 0.0591753 + 0.335600i
\(311\) −4.25349 24.1228i −0.241194 1.36788i −0.829169 0.558998i \(-0.811186\pi\)
0.587976 0.808879i \(-0.299925\pi\)
\(312\) 0 0
\(313\) −12.2567 10.2846i −0.692790 0.581320i 0.226922 0.973913i \(-0.427134\pi\)
−0.919712 + 0.392593i \(0.871578\pi\)
\(314\) −20.8207 36.0624i −1.17498 2.03512i
\(315\) 0 0
\(316\) 14.0000 24.2487i 0.787562 1.36410i
\(317\) −9.20707 + 3.35110i −0.517121 + 0.188216i −0.587378 0.809312i \(-0.699840\pi\)
0.0702579 + 0.997529i \(0.477618\pi\)
\(318\) 0 0
\(319\) −9.19253 + 7.71345i −0.514683 + 0.431870i
\(320\) −18.4141 6.70220i −1.02938 0.374664i
\(321\) 0 0
\(322\) −2.08378 + 11.8177i −0.116124 + 0.658574i
\(323\) 7.34847 0.408880
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −4.25349 + 24.1228i −0.235579 + 1.33604i
\(327\) 0 0
\(328\) −22.5526 8.20848i −1.24526 0.453238i
\(329\) 15.0113 12.5960i 0.827602 0.694441i
\(330\) 0 0
\(331\) 6.57785 2.39414i 0.361551 0.131594i −0.154856 0.987937i \(-0.549491\pi\)
0.516407 + 0.856343i \(0.327269\pi\)
\(332\) 24.4949 42.4264i 1.34433 2.32845i
\(333\) 0 0
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) 13.1349 + 11.0215i 0.717638 + 0.602170i
\(336\) 0 0
\(337\) −4.86215 27.5746i −0.264858 1.50209i −0.769439 0.638721i \(-0.779464\pi\)
0.504581 0.863365i \(-0.331647\pi\)
\(338\) −5.10419 28.9473i −0.277632 1.57453i
\(339\) 0 0
\(340\) 55.1552 + 46.2807i 2.99121 + 2.50992i
\(341\) 1.22474 + 2.12132i 0.0663237 + 0.114876i
\(342\) 0 0
\(343\) 10.0000 17.3205i 0.539949 0.935220i
\(344\) −50.6389 + 18.4310i −2.73027 + 0.993735i
\(345\) 0 0
\(346\) 18.3851 15.4269i 0.988387 0.829355i
\(347\) 23.0177 + 8.37775i 1.23565 + 0.449741i 0.875530 0.483164i \(-0.160512\pi\)
0.360123 + 0.932905i \(0.382735\pi\)
\(348\) 0 0
\(349\) 3.47296 19.6962i 0.185903 1.05431i −0.738886 0.673831i \(-0.764648\pi\)
0.924789 0.380480i \(-0.124241\pi\)
\(350\) 4.89898 0.261861
\(351\) 0 0
\(352\) 0 0
\(353\) 0.425349 2.41228i 0.0226391 0.128393i −0.971394 0.237475i \(-0.923680\pi\)
0.994033 + 0.109083i \(0.0347913\pi\)
\(354\) 0 0
\(355\) 16.9145 + 6.15636i 0.897727 + 0.326746i
\(356\) 0 0
\(357\) 0 0
\(358\) 33.8289 12.3127i 1.78791 0.650748i
\(359\) −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
\(362\) 15.0113 + 12.5960i 0.788979 + 0.662032i
\(363\) 0 0
\(364\) −1.38919 7.87846i −0.0728131 0.412944i
\(365\) −4.67884 26.5350i −0.244902 1.38891i
\(366\) 0 0
\(367\) 3.83022 + 3.21394i 0.199936 + 0.167766i 0.737259 0.675610i \(-0.236120\pi\)
−0.537323 + 0.843377i \(0.680564\pi\)
\(368\) 4.89898 + 8.48528i 0.255377 + 0.442326i
\(369\) 0 0
\(370\) 24.0000 41.5692i 1.24770 2.16108i
\(371\) −13.8106 + 5.02665i −0.717011 + 0.260971i
\(372\) 0 0
\(373\) 26.8116 22.4976i 1.38825 1.16488i 0.422206 0.906500i \(-0.361256\pi\)
0.966043 0.258380i \(-0.0831887\pi\)
\(374\) 41.4318 + 15.0799i 2.14239 + 0.779765i
\(375\) 0 0
\(376\) 8.33511 47.2708i 0.429851 2.43780i
\(377\) 4.89898 0.252310
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 1.70140 9.64911i 0.0872799 0.494989i
\(381\) 0 0
\(382\) −22.5526 8.20848i −1.15389 0.419983i
\(383\) 26.2699 22.0430i 1.34233 1.12635i 0.361305 0.932448i \(-0.382331\pi\)
0.981022 0.193898i \(-0.0621132\pi\)
\(384\) 0 0
\(385\) 11.2763 4.10424i 0.574694 0.209172i
\(386\) −13.4722 + 23.3345i −0.685717 + 1.18770i
\(387\) 0 0
\(388\) 14.0000 + 24.2487i 0.710742 + 1.23104i
\(389\) −20.6406 17.3195i −1.04652 0.878134i −0.0537965 0.998552i \(-0.517132\pi\)
−0.992723 + 0.120417i \(0.961577\pi\)
\(390\) 0 0
\(391\) 3.12567 + 17.7265i 0.158072 + 0.896470i
\(392\) −2.55210 14.4737i −0.128900 0.731030i
\(393\) 0 0
\(394\) 27.5776 + 23.1404i 1.38934 + 1.16579i
\(395\) −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 \(0.158678\pi\)
\(398\) 2.30177 0.837775i 0.115377 0.0419939i
\(399\) 0 0
\(400\) 3.06418 2.57115i 0.153209 0.128558i
\(401\) −32.2247 11.7288i −1.60923 0.585711i −0.627940 0.778262i \(-0.716102\pi\)
−0.981287 + 0.192551i \(0.938324\pi\)
\(402\) 0 0
\(403\) 0.173648 0.984808i 0.00865003 0.0490568i
\(404\) −19.5959 −0.974933
\(405\) 0 0
\(406\) −24.0000 −1.19110
\(407\) 3.40280 19.2982i 0.168670 0.956577i
\(408\) 0 0
\(409\) 26.3114 + 9.57656i 1.30101 + 0.473531i 0.897327 0.441366i \(-0.145506\pi\)
0.403688 + 0.914897i \(0.367728\pi\)
\(410\) −22.5170 + 18.8940i −1.11204 + 0.933109i
\(411\) 0 0
\(412\) 26.3114 9.57656i 1.29627 0.471803i
\(413\) 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
\(418\) −1.04189 5.90885i −0.0509605 0.289011i
\(419\) 5.95489 + 33.7719i 0.290916 + 1.64986i 0.683355 + 0.730086i \(0.260520\pi\)
−0.392440 + 0.919778i \(0.628369\pi\)
\(420\) 0 0
\(421\) 1.53209 + 1.28558i 0.0746694 + 0.0626551i 0.679358 0.733807i \(-0.262258\pi\)
−0.604689 + 0.796462i \(0.706703\pi\)
\(422\) 1.22474 + 2.12132i 0.0596196 + 0.103264i
\(423\) 0 0
\(424\) −18.0000 + 31.1769i −0.874157 + 1.51408i
\(425\) 6.90530 2.51332i 0.334956 0.121914i
\(426\) 0 0
\(427\) 7.66044 6.42788i 0.370715 0.311067i
\(428\) −55.2424 20.1066i −2.67024 0.971889i
\(429\) 0 0
\(430\) −11.4608 + 64.9973i −0.552688 + 3.13445i
\(431\) −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 \(0.366058\pi\)
\(434\) −0.850699 + 4.82455i −0.0408349 + 0.231586i
\(435\) 0 0
\(436\) 3.75877 + 1.36808i 0.180012 + 0.0655192i
\(437\) 1.87642 1.57450i 0.0897612 0.0753186i
\(438\) 0 0
\(439\) −13.1557 + 4.78828i −0.627887 + 0.228532i −0.636311 0.771432i \(-0.719541\pi\)
0.00842428 + 0.999965i \(0.497318\pi\)
\(440\) 14.6969 25.4558i 0.700649 1.21356i
\(441\) 0 0
\(442\) −9.00000 15.5885i −0.428086 0.741467i
\(443\) −9.38209 7.87251i −0.445757 0.374034i 0.392102 0.919922i \(-0.371748\pi\)
−0.837858 + 0.545888i \(0.816193\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −2.97745 16.8859i −0.140986 0.799572i
\(447\) 0 0
\(448\) −12.2567 10.2846i −0.579075 0.485902i
\(449\) −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
\(452\) 36.8283 13.4044i 1.73226 0.630490i
\(453\) 0 0
\(454\) 18.3851 15.4269i 0.862854 0.724020i
\(455\) −4.60353 1.67555i −0.215817 0.0785510i
\(456\) 0 0
\(457\) 5.03580 28.5594i 0.235565 1.33595i −0.605857 0.795574i \(-0.707169\pi\)
0.841421 0.540380i \(-0.181719\pi\)
\(458\) −2.44949 −0.114457
\(459\) 0 0
\(460\) 24.0000 1.11901
\(461\) −4.67884 + 26.5350i −0.217915 + 1.23586i 0.657860 + 0.753141i \(0.271462\pi\)
−0.875775 + 0.482719i \(0.839649\pi\)
\(462\) 0 0
\(463\) 17.8542 + 6.49838i 0.829753 + 0.302005i 0.721758 0.692146i \(-0.243335\pi\)
0.107996 + 0.994151i \(0.465557\pi\)
\(464\) −15.0113 + 12.5960i −0.696884 + 0.584755i
\(465\) 0 0
\(466\) 16.9145 6.15636i 0.783548 0.285188i
\(467\) −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
\(470\) −45.0340 37.7880i −2.07727 1.74303i
\(471\) 0 0
\(472\) −2.08378 11.8177i −0.0959137 0.543953i
\(473\) 4.67884 + 26.5350i 0.215133 + 1.22008i
\(474\) 0 0
\(475\) −0.766044 0.642788i −0.0351485 0.0294931i
\(476\) 29.3939 + 50.9117i 1.34727 + 2.33353i
\(477\) 0 0
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) 25.3194 9.21552i 1.15687 0.421068i 0.308895 0.951096i \(-0.400041\pi\)
0.847980 + 0.530028i \(0.177819\pi\)
\(480\) 0 0
\(481\) −6.12836 + 5.14230i −0.279429 + 0.234469i
\(482\) 36.8283 + 13.4044i 1.67748 + 0.610554i
\(483\) 0 0
\(484\) −3.47296 + 19.6962i −0.157862 + 0.895280i
\(485\) 17.1464 0.778579
\(486\) 0 0
\(487\) 35.0000 1.58600 0.793001 0.609221i \(-0.208518\pi\)
0.793001 + 0.609221i \(0.208518\pi\)
\(488\) 4.25349 24.1228i 0.192547 1.09199i
\(489\) 0 0
\(490\) −16.9145 6.15636i −0.764118 0.278116i
\(491\) −30.0227 + 25.1920i −1.35490 + 1.13690i −0.377385 + 0.926056i \(0.623177\pi\)
−0.977520 + 0.210844i \(0.932379\pi\)
\(492\) 0 0
\(493\) −33.8289 + 12.3127i −1.52358 + 0.554537i
\(494\) −1.22474 + 2.12132i −0.0551039 + 0.0954427i
\(495\) 0 0
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) 11.2585 + 9.44701i 0.505013 + 0.423756i
\(498\) 0 0
\(499\) 0.347296 + 1.96962i 0.0155471 + 0.0881721i 0.991594 0.129388i \(-0.0413013\pi\)
−0.976047 + 0.217560i \(0.930190\pi\)
\(500\) 6.80559 + 38.5964i 0.304355 + 1.72608i
\(501\) 0 0
\(502\) −13.7888 11.5702i −0.615424 0.516402i
\(503\) 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
\(506\) 13.8106 5.02665i 0.613956 0.223462i
\(507\) 0 0
\(508\) −58.2194 + 48.8519i −2.58307 + 2.16745i
\(509\) 9.20707 + 3.35110i 0.408096 + 0.148535i 0.537908 0.843004i \(-0.319215\pi\)
−0.129811 + 0.991539i \(0.541437\pi\)
\(510\) 0 0
\(511\) 3.82026 21.6658i 0.168998 0.958437i
\(512\) −39.1918 −1.73205
\(513\) 0 0
\(514\) −42.0000 −1.85254
\(515\) 2.97745 16.8859i 0.131202 0.744083i
\(516\) 0 0
\(517\) −22.5526 8.20848i −0.991863 0.361009i
\(518\) 30.0227 25.1920i 1.31912 1.10687i
\(519\) 0 0
\(520\) −11.2763 + 4.10424i −0.494499 + 0.179983i
\(521\) −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 \(0.649260\pi\)
\(524\) 37.5284 + 31.4900i 1.63943 + 1.37565i
\(525\) 0 0
\(526\) −11.4608 64.9973i −0.499714 2.83402i
\(527\) 1.27605 + 7.23683i 0.0555855 + 0.315241i
\(528\) 0 0
\(529\) −13.0228 10.9274i −0.566207 0.475104i
\(530\) 22.0454 + 38.1838i 0.957591 + 1.65860i
\(531\) 0 0
\(532\) 4.00000 6.92820i 0.173422 0.300376i
\(533\) 4.60353 1.67555i 0.199401 0.0725761i
\(534\) 0 0
\(535\) −27.5776 + 23.1404i −1.19228 + 1.00044i
\(536\) 32.2247 + 11.7288i 1.39190 + 0.506609i
\(537\) 0 0
\(538\) −9.37700 + 53.1796i −0.404271 + 2.29274i
\(539\) −7.34847 −0.316521
\(540\) 0 0
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) −2.97745 + 16.8859i −0.127892 + 0.725313i
\(543\) 0 0
\(544\) 0 0
\(545\) 1.87642 1.57450i 0.0803769 0.0674442i
\(546\) 0 0
\(547\) 12.2160 4.44626i 0.522319 0.190108i −0.0673867 0.997727i \(-0.521466\pi\)
0.589705 + 0.807619i \(0.299244\pi\)
\(548\) −19.5959 + 33.9411i −0.837096 + 1.44989i
\(549\) 0 0
\(550\) −3.00000 5.19615i −0.127920 0.221565i
\(551\) 3.75284 + 3.14900i 0.159876 + 0.134152i
\(552\) 0 0
\(553\) −2.43107 13.7873i −0.103380 0.586296i
\(554\) 4.67884 + 26.5350i 0.198785 + 1.12737i
\(555\) 0 0
\(556\) −30.6418 25.7115i −1.29950 1.09041i
\(557\) −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
\(560\) 18.4141 6.70220i 0.778139 0.283220i
\(561\) 0 0
\(562\) −22.9813 + 19.2836i −0.969409 + 0.813431i
\(563\) −11.5088 4.18887i −0.485040 0.176540i 0.0879135 0.996128i \(-0.471980\pi\)
−0.572953 + 0.819588i \(0.694202\pi\)
\(564\) 0 0
\(565\) 4.16756 23.6354i 0.175330 0.994348i
\(566\) 41.6413 1.75032
\(567\) 0 0
\(568\) 36.0000 1.51053
\(569\) −2.12675 + 12.0614i −0.0891579 + 0.505639i 0.907224 + 0.420648i \(0.138197\pi\)
−0.996382 + 0.0849912i \(0.972914\pi\)
\(570\) 0 0
\(571\) 9.39693 + 3.42020i 0.393249 + 0.143131i 0.531074 0.847326i \(-0.321789\pi\)
−0.137824 + 0.990457i \(0.544011\pi\)
\(572\) −7.50567 + 6.29801i −0.313828 + 0.263333i
\(573\) 0 0
\(574\) −22.5526 + 8.20848i −0.941328 + 0.342615i
\(575\) 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 \(0.659123\pi\)
\(578\) 69.4275 + 58.2566i 2.88780 + 2.42315i
\(579\) 0 0
\(580\) 8.33511 + 47.2708i 0.346097 + 1.96281i
\(581\) −4.25349 24.1228i −0.176465 1.00078i
\(582\) 0 0
\(583\) 13.7888 + 11.5702i 0.571074 + 0.479188i
\(584\) −26.9444 46.6690i −1.11497 1.93118i
\(585\) 0 0
\(586\) −6.00000 + 10.3923i −0.247858 + 0.429302i
\(587\) −2.30177 + 0.837775i −0.0950041 + 0.0345787i −0.389085 0.921202i \(-0.627209\pi\)
0.294081 + 0.955781i \(0.404987\pi\)
\(588\) 0 0
\(589\) 0.766044 0.642788i 0.0315643 0.0264856i
\(590\) −13.8106 5.02665i −0.568574 0.206944i
\(591\) 0 0
\(592\) 5.55674 31.5138i 0.228381 1.29521i
\(593\) 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
\(596\) 8.50699 48.2455i 0.348460 1.97621i
\(597\) 0 0
\(598\) −5.63816 2.05212i −0.230561 0.0839175i
\(599\) −30.0227 + 25.1920i −1.22669 + 1.02932i −0.228247 + 0.973603i \(0.573299\pi\)
−0.998447 + 0.0557151i \(0.982256\pi\)
\(600\) 0 0
\(601\) 6.57785 2.39414i 0.268316 0.0976590i −0.204359 0.978896i \(-0.565511\pi\)
0.472675 + 0.881237i \(0.343289\pi\)
\(602\) −26.9444 + 46.6690i −1.09817 + 1.90209i
\(603\) 0 0
\(604\) −10.0000 17.3205i −0.406894 0.704761i
\(605\) 9.38209 + 7.87251i 0.381436 + 0.320063i
\(606\) 0 0
\(607\) 7.64052 + 43.3315i 0.310119 + 1.75877i 0.598372 + 0.801219i \(0.295815\pi\)
−0.288253 + 0.957554i \(0.593074\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −22.9813 19.2836i −0.930487 0.780771i
\(611\) 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 \(0.237972\pi\)
\(614\) −4.60353 + 1.67555i −0.185784 + 0.0676197i
\(615\) 0 0
\(616\) 18.3851 15.4269i 0.740755 0.621568i
\(617\) 23.0177 + 8.37775i 0.926657 + 0.337275i 0.760884 0.648888i \(-0.224766\pi\)
0.165773 + 0.986164i \(0.446988\pi\)
\(618\) 0 0
\(619\) −8.50876 + 48.2556i −0.341996 + 1.93956i 0.000400419 1.00000i \(0.499873\pi\)
−0.342396 + 0.939556i \(0.611239\pi\)
\(620\) 9.79796 0.393496
\(621\) 0 0
\(622\) −60.0000 −2.40578
\(623\) 0 0
\(624\) 0 0
\(625\) 27.2511 + 9.91858i 1.09004 + 0.396743i
\(626\) −30.0227 + 25.1920i −1.19995 + 1.00688i
\(627\) 0 0
\(628\) −63.8991 + 23.2574i −2.54985 + 0.928070i
\(629\) 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 \(-0.506336\pi\)
\(632\) −26.2699 22.0430i −1.04496 0.876824i
\(633\) 0 0
\(634\) 4.16756 + 23.6354i 0.165515 + 0.938681i
\(635\) 8.08164 + 45.8333i 0.320710 + 1.81884i
\(636\) 0 0
\(637\) 2.29813 + 1.92836i 0.0910554 + 0.0764045i
\(638\) 14.6969 + 25.4558i 0.581857 + 1.00781i
\(639\) 0 0
\(640\) −24.0000 + 41.5692i −0.948683 + 1.64317i
\(641\) −16.1124 + 5.86442i −0.636400 + 0.231631i −0.640015 0.768363i \(-0.721072\pi\)
0.00361428 + 0.999993i \(0.498850\pi\)
\(642\) 0 0
\(643\) 29.1097 24.4259i 1.14797 0.963265i 0.148304 0.988942i \(-0.452619\pi\)
0.999670 + 0.0256772i \(0.00817422\pi\)
\(644\) 18.4141 + 6.70220i 0.725619 + 0.264104i
\(645\) 0 0
\(646\) 3.12567 17.7265i 0.122978 0.697441i
\(647\) 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
\(650\) −0.425349 + 2.41228i −0.0166836 + 0.0946173i
\(651\) 0 0
\(652\) 37.5877 + 13.6808i 1.47205 + 0.535782i
\(653\) −7.50567 + 6.29801i −0.293720 + 0.246460i −0.777725 0.628605i \(-0.783626\pi\)
0.484005 + 0.875065i \(0.339182\pi\)
\(654\) 0 0
\(655\) 28.1908 10.2606i 1.10150 0.400915i
\(656\) −9.79796 + 16.9706i −0.382546 + 0.662589i
\(657\) 0 0
\(658\) −24.0000 41.5692i −0.935617 1.62054i
\(659\) −15.0113 12.5960i −0.584759 0.490671i 0.301747 0.953388i \(-0.402430\pi\)
−0.886506 + 0.462717i \(0.846875\pi\)
\(660\) 0 0
\(661\) 1.91013 + 10.8329i 0.0742954 + 0.421350i 0.999157 + 0.0410470i \(0.0130693\pi\)
−0.924862 + 0.380303i \(0.875820\pi\)
\(662\) −2.97745 16.8859i −0.115722 0.656291i
\(663\) 0 0
\(664\) −45.9627 38.5673i −1.78370 1.49670i
\(665\) −2.44949 4.24264i −0.0949871 0.164523i
\(666\) 0 0
\(667\) −6.00000 + 10.3923i −0.232321 + 0.402392i
\(668\) −18.4141 + 6.70220i −0.712464 + 0.259316i
\(669\) 0 0
\(670\) 32.1739 26.9971i 1.24298 1.04299i
\(671\) −11.5088 4.18887i −0.444294 0.161710i
\(672\) 0 0
\(673\) 5.03580 28.5594i 0.194116 1.10088i −0.719557 0.694434i \(-0.755655\pi\)
0.913672 0.406451i \(-0.133234\pi\)
\(674\) −68.5857 −2.64182
\(675\) 0 0
\(676\) −48.0000 −1.84615
\(677\) 8.08164 45.8333i 0.310603 1.76152i −0.285281 0.958444i \(-0.592087\pi\)
0.595883 0.803071i \(-0.296802\pi\)
\(678\) 0 0
\(679\) 13.1557 + 4.78828i 0.504869 + 0.183757i
\(680\) 67.5510 56.6821i 2.59046 2.17366i
\(681\) 0 0
\(682\) 5.63816 2.05212i 0.215896 0.0785798i
\(683\) 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
\(686\) −37.5284 31.4900i −1.43284 1.20230i
\(687\) 0 0
\(688\) 7.64052 + 43.3315i 0.291292 + 1.65200i
\(689\) −1.27605 7.23683i −0.0486136 0.275701i
\(690\) 0 0
\(691\) 36.0041 + 30.2110i 1.36966 + 1.14928i 0.972865 + 0.231374i \(0.0743221\pi\)
0.396795 + 0.917907i \(0.370122\pi\)
\(692\) −19.5959 33.9411i −0.744925 1.29025i
\(693\) 0 0
\(694\) 30.0000 51.9615i 1.13878 1.97243i
\(695\) −23.0177 + 8.37775i −0.873110 + 0.317786i
\(696\) 0 0
\(697\) −27.5776 + 23.1404i −1.04458 + 0.876503i
\(698\) −46.0353 16.7555i −1.74246 0.634205i
\(699\) 0 0
\(700\) 1.38919 7.87846i 0.0525063 0.297778i
\(701\) −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
\(704\) −3.40280 + 19.2982i −0.128248 + 0.727329i
\(705\) 0 0
\(706\) −5.63816 2.05212i −0.212195 0.0772326i
\(707\) −7.50567 + 6.29801i −0.282280 + 0.236861i
\(708\) 0 0
\(709\) 6.57785 2.39414i 0.247036 0.0899139i −0.215534 0.976496i \(-0.569149\pi\)
0.462571 + 0.886582i \(0.346927\pi\)
\(710\) 22.0454 38.1838i 0.827349 1.43301i
\(711\) 0 0
\(712\) 0 0
\(713\) 1.87642 + 1.57450i 0.0702724 + 0.0589656i
\(714\) 0 0
\(715\) 1.04189 + 5.90885i 0.0389644 + 0.220978i
\(716\) −10.2084 57.8946i −0.381505 2.16362i
\(717\) 0 0
\(718\) 55.1552 + 46.2807i 2.05837 + 1.72718i
\(719\) 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
\(722\) 41.4318 15.0799i 1.54193 0.561218i
\(723\) 0 0
\(724\) 24.5134 20.5692i 0.911034 0.764448i
\(725\) 4.60353 + 1.67555i 0.170971 + 0.0622284i
\(726\) 0 0
\(727\) 2.43107 13.7873i 0.0901636 0.511343i −0.905959 0.423366i \(-0.860849\pi\)
0.996122 0.0879774i \(-0.0280403\pi\)
\(728\) −9.79796 −0.363137
\(729\) 0 0
\(730\) −66.0000 −2.44277
\(731\) −14.0365 + 79.6051i −0.519160 + 2.94430i
\(732\) 0 0
\(733\) −15.9748 5.81434i −0.590042 0.214758i 0.0297060 0.999559i \(-0.490543\pi\)
−0.619748 + 0.784801i \(0.712765\pi\)
\(734\) 9.38209 7.87251i 0.346299 0.290580i
\(735\) 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 \(0.827478\pi\)
\(740\) −60.0454 50.3841i −2.20731 1.85215i
\(741\) 0 0
\(742\) 6.25133 + 35.4531i 0.229494 + 1.30152i
\(743\) −5.52954 31.3596i −0.202859 1.15047i −0.900773 0.434290i \(-0.856999\pi\)
0.697914 0.716182i \(-0.254112\pi\)
\(744\) 0 0
\(745\) −22.9813 19.2836i −0.841971 0.706497i
\(746\) −42.8661 74.2462i −1.56944 2.71835i
\(747\) 0 0
\(748\) 36.0000 62.3538i 1.31629 2.27988i
\(749\) −27.6212 + 10.0533i −1.00926 + 0.367340i
\(750\) 0 0
\(751\) 19.9172 16.7125i 0.726787 0.609847i −0.202466 0.979289i \(-0.564896\pi\)
0.929254 + 0.369442i \(0.120451\pi\)
\(752\) −36.8283 13.4044i −1.34299 0.488808i
\(753\) 0 0
\(754\) 2.08378 11.8177i 0.0758867 0.430375i
\(755\) −12.2474 −0.445730
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 3.40280 19.2982i 0.123595 0.700943i
\(759\) 0 0
\(760\) −11.2763 4.10424i −0.409035 0.148876i
\(761\) −1.87642 + 1.57450i −0.0680201 + 0.0570756i −0.676164 0.736751i \(-0.736359\pi\)
0.608144 + 0.793827i \(0.291914\pi\)
\(762\) 0 0
\(763\) 1.87939 0.684040i 0.0680383 0.0247639i
\(764\) −19.5959 + 33.9411i −0.708955 + 1.22795i
\(765\) 0 0
\(766\) −42.0000 72.7461i −1.51752 2.62842i
\(767\) 1.87642 + 1.57450i 0.0677535 + 0.0568520i
\(768\) 0 0
\(769\) −6.42498 36.4379i −0.231691 1.31398i −0.849472 0.527634i \(-0.823079\pi\)
0.617781 0.786350i \(-0.288032\pi\)
\(770\) −5.10419 28.9473i −0.183942 1.04319i
\(771\) 0 0
\(772\) 33.7060 + 28.2827i 1.21310 + 1.01792i
\(773\) 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
\(776\) 32.2247 11.7288i 1.15680 0.421041i
\(777\) 0 0
\(778\) −50.5589 + 42.4240i −1.81263 + 1.52097i
\(779\) 4.60353 + 1.67555i 0.164939 + 0.0600328i
\(780\) 0 0
\(781\) 3.12567 17.7265i 0.111845 0.634305i
\(782\) 44.0908 1.57668
\(783\) 0 0
\(784\) −12.0000 −0.428571
\(785\) −7.23094 + 41.0087i −0.258083 + 1.46366i
\(786\) 0 0
\(787\) 23.4923 + 8.55050i 0.837411 + 0.304793i 0.724897 0.688858i \(-0.241887\pi\)
0.112514 + 0.993650i \(0.464110\pi\)
\(788\) 45.0340 37.7880i 1.60427 1.34614i
\(789\) 0 0
\(790\) −39.4671 + 14.3648i −1.40418 + 0.511078i
\(791\) 9.79796 16.9706i 0.348375 0.603404i
\(792\) 0 0
\(793\) 2.50000 + 4.33013i 0.0887776 + 0.153767i
\(794\) −1.87642 1.57450i −0.0665916 0.0558770i
\(795\) 0 0
\(796\) −0.694593 3.93923i −0.0246192 0.139622i
\(797\) 7.23094 + 41.0087i 0.256133 + 1.45260i 0.793147 + 0.609030i \(0.208441\pi\)
−0.537014 + 0.843573i \(0.680448\pi\)
\(798\) 0 0
\(799\) −55.1552 46.2807i −1.95125 1.63729i
\(800\) 0 0
\(801\) 0 0
\(802\) −42.0000 + 72.7461i −1.48307 + 2.56876i
\(803\) −25.3194 + 9.21552i −0.893504 + 0.325209i
\(804\) 0 0
\(805\) 9.19253 7.71345i 0.323994 0.271863i
\(806\) −2.30177 0.837775i −0.0810763 0.0295094i
\(807\) 0 0
\(808\) −4.16756 + 23.6354i −0.146614 + 0.831490i
\(809\) 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 \(0.289355\pi\)
\(812\) −6.80559 + 38.5964i −0.238829 + 1.35447i
\(813\) 0 0
\(814\) −45.1052 16.4170i −1.58094 0.575414i
\(815\) 18.7642 15.7450i 0.657281 0.551524i
\(816\) 0 0
\(817\) 10.3366 3.76222i 0.361633 0.131623i
\(818\) 34.2929 59.3970i 1.19902 2.07677i
\(819\) 0 0
\(820\) 24.0000 + 41.5692i 0.838116 + 1.45166i
\(821\) 30.0227 + 25.1920i 1.04780 + 0.879208i 0.992860 0.119282i \(-0.0380592\pi\)
0.0549386 + 0.998490i \(0.482504\pi\)
\(822\) 0 0
\(823\) 6.07769 + 34.4683i 0.211855 + 1.20149i 0.886282 + 0.463147i \(0.153280\pi\)
−0.674427 + 0.738342i \(0.735609\pi\)
\(824\) −5.95489 33.7719i −0.207448 1.17650i
\(825\) 0 0
\(826\) −9.19253 7.71345i −0.319849 0.268385i
\(827\) 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 \(-0.0554492\pi\)
\(830\) −69.0530 + 25.1332i −2.39687 + 0.872388i
\(831\) 0 0
\(832\) 6.12836 5.14230i 0.212463 0.178277i
\(833\) −20.7159 7.53997i −0.717764 0.261245i
\(834\) 0 0
\(835\) −2.08378 + 11.8177i −0.0721121 + 0.408968i
\(836\) −9.79796 −0.338869
\(837\) 0 0
\(838\) 84.0000 2.90173
\(839\) −0.850699 + 4.82455i −0.0293694 + 0.166562i −0.995965 0.0897451i \(-0.971395\pi\)
0.966595 + 0.256307i \(0.0825059\pi\)
\(840\) 0 0
\(841\) 4.69846 + 1.71010i 0.162016 + 0.0589690i
\(842\) 3.75284 3.14900i 0.129331 0.108522i
\(843\) 0 0
\(844\) 3.75877 1.36808i 0.129382 0.0470913i
\(845\) −14.6969 + 25.4558i −0.505590 + 0.875708i
\(846\) 0 0
\(847\) 5.00000 + 8.66025i 0.171802 + 0.297570i
\(848\) 22.5170 + 18.8940i 0.773238 + 0.648823i
\(849\) 0 0
\(850\) −3.12567 17.7265i −0.107210 0.608015i
\(851\) −3.40280 19.2982i −0.116646 0.661534i
\(852\) 0 0
\(853\) −9.95858 8.35624i −0.340975 0.286112i 0.456179 0.889888i \(-0.349218\pi\)
−0.797154 + 0.603776i \(0.793662\pi\)
\(854\) −12.2474 21.2132i −0.419099 0.725901i
\(855\) 0 0
\(856\) −36.0000 + 62.3538i −1.23045 + 2.13121i
\(857\) −23.0177 + 8.37775i −0.786269 + 0.286178i −0.703784 0.710414i \(-0.748508\pi\)
−0.0824847 + 0.996592i \(0.526286\pi\)
\(858\) 0 0
\(859\) 19.9172 16.7125i 0.679565 0.570222i −0.236315 0.971677i \(-0.575940\pi\)
0.915879 + 0.401454i \(0.131495\pi\)
\(860\) 101.278 + 36.8621i 3.45354 + 1.25699i
\(861\) 0 0
\(862\) −3.12567 + 17.7265i −0.106461 + 0.603768i
\(863\) −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
\(866\) 7.23094 41.0087i 0.245717 1.39353i
\(867\) 0 0
\(868\) 7.51754 + 2.73616i 0.255162 + 0.0928714i
\(869\) −13.1349 + 11.0215i −0.445572 + 0.373879i
\(870\) 0 0
\(871\) −6.57785 + 2.39414i −0.222882 + 0.0811224i
\(872\) 2.44949 4.24264i 0.0829502 0.143674i
\(873\) 0 0
\(874\) −3.00000 5.19615i −0.101477 0.175762i
\(875\) 15.0113 + 12.5960i 0.507476 + 0.425823i
\(876\) 0 0
\(877\) 1.38919 + 7.87846i 0.0469095 + 0.266037i 0.999238 0.0390385i \(-0.0124295\pi\)
−0.952328 + 0.305075i \(0.901318\pi\)
\(878\) 5.95489 + 33.7719i 0.200968 + 1.13975i
\(879\) 0 0
\(880\) −18.3851 15.4269i −0.619760 0.520041i
\(881\) −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 \(0.259008\pi\)
\(884\) −27.6212 + 10.0533i −0.929002 + 0.338129i
\(885\) 0 0
\(886\) −22.9813 + 19.2836i −0.772073 + 0.647846i
\(887\) 16.1124 + 5.86442i 0.541001 + 0.196908i 0.598044 0.801464i \(-0.295945\pi\)
−0.0570430 + 0.998372i \(0.518167\pi\)
\(888\) 0 0
\(889\) −6.59863 + 37.4227i −0.221311 + 1.25512i
\(890\) 0 0
\(891\) 0 0
\(892\) −28.0000 −0.937509
\(893\) −1.70140 + 9.64911i −0.0569351 + 0.322895i
\(894\) 0 0
\(895\) −33.8289 12.3127i −1.13078 0.411569i
\(896\) −30.0227 + 25.1920i −1.00299 + 0.841607i
\(897\) 0 0
\(898\) −50.7434 + 18.4691i −1.69333 + 0.616321i
\(899\) −2.44949 + 4.24264i −0.0816951 + 0.141500i
\(900\) 0 0
\(901\) 27.0000 + 46.7654i 0.899500 + 1.55798i
\(902\) 22.5170 + 18.8940i 0.749735 + 0.629102i
\(903\) 0 0
\(904\) −8.33511 47.2708i −0.277222 1.57220i
\(905\) −3.40280 19.2982i −0.113113 0.641494i
\(906\) 0 0
\(907\) −5.36231 4.49951i −0.178053 0.149404i 0.549406 0.835556i \(-0.314854\pi\)
−0.727458 + 0.686152i \(0.759299\pi\)
\(908\) −19.5959 33.9411i −0.650313 1.12638i
\(909\) 0 0
\(910\) −6.00000 + 10.3923i −0.198898 + 0.344502i
\(911\) 11.5088 4.18887i 0.381305 0.138784i −0.144254 0.989541i \(-0.546078\pi\)
0.525559 + 0.850757i \(0.323856\pi\)
\(912\) 0 0
\(913\) −22.9813 + 19.2836i −0.760571 + 0.638195i
\(914\) −66.7513 24.2955i −2.20794 0.803623i
\(915\) 0 0
\(916\) −0.694593 + 3.93923i −0.0229500 + 0.130156i
\(917\) 24.4949 0.808893
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 5.10419 28.9473i 0.168280 0.954365i
\(921\) 0 0
\(922\) 62.0197 + 22.5733i 2.04251 + 0.743413i
\(923\) −5.62925 + 4.72350i −0.185289 + 0.155476i
\(924\) 0 0
\(925\) −7.51754 + 2.73616i −0.247175 + 0.0899644i
\(926\) 23.2702 40.3051i 0.764705 1.32451i
\(927\) 0 0
\(928\) 0 0
\(929\) −20.6406 17.3195i −0.677196 0.568235i 0.237989 0.971268i \(-0.423512\pi\)
−0.915186 + 0.403033i \(0.867956\pi\)
\(930\) 0 0
\(931\) 0.520945 + 2.95442i 0.0170733 + 0.0968273i
\(932\) −5.10419 28.9473i −0.167193 0.948201i
\(933\) 0 0
\(934\) 27.5776 + 23.1404i 0.902367 + 0.757176i
\(935\) −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 \(0.208381\pi\)
\(938\) 32.2247 11.7288i 1.05218 0.382960i
\(939\) 0 0
\(940\) −73.5403 + 61.7076i −2.39862 + 2.01268i
\(941\) 9.20707 + 3.35110i 0.300142 + 0.109243i 0.487701 0.873011i \(-0.337836\pi\)
−0.187559 + 0.982253i \(0.560058\pi\)
\(942\) 0 0
\(943\) −2.08378 + 11.8177i −0.0678572 + 0.384837i
\(944\) −9.79796 −0.318896
\(945\) 0 0
\(946\) 66.0000 2.14585
\(947\) 4.25349 24.1228i 0.138220 0.783885i −0.834343 0.551245i \(-0.814153\pi\)
0.972563 0.232639i \(-0.0747361\pi\)
\(948\) 0 0
\(949\) 10.3366 + 3.76222i 0.335541 + 0.122127i
\(950\) −1.87642 + 1.57450i −0.0608790 + 0.0510836i
\(951\) 0 0
\(952\) 67.6579 24.6255i 2.19280 0.798115i
\(953\) −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
\(956\) −7.50567 6.29801i −0.242751 0.203692i
\(957\) 0 0
\(958\) −11.4608 64.9973i −0.370281 2.09997i
\(959\) 3.40280 + 19.2982i 0.109882 + 0.623172i
\(960\) 0 0
\(961\) −22.9813 19.2836i −0.741333 0.622053i
\(962\) 9.79796 + 16.9706i 0.315899 + 0.547153i
\(963\) 0 0
\(964\) 32.0000 55.4256i 1.03065 1.78514i
\(965\) 25.3194 9.21552i 0.815062 0.296658i
\(966\) 0 0
\(967\) −5.36231 + 4.49951i −0.172440 + 0.144695i −0.724923 0.688830i \(-0.758125\pi\)
0.552483 + 0.833524i \(0.313680\pi\)
\(968\) 23.0177 + 8.37775i 0.739816 + 0.269271i
\(969\) 0 0
\(970\) 7.29322 41.3619i 0.234171 1.32805i
\(971\) 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
\(974\) 14.8872 84.4297i 0.477018 2.70530i
\(975\) 0 0
\(976\) −18.7939 6.84040i −0.601577 0.218956i
\(977\) −18.7642 + 15.7450i −0.600319 + 0.503728i −0.891548 0.452926i \(-0.850380\pi\)
0.291229 + 0.956653i \(0.405936\pi\)
\(978\) 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
\(983\) −3.75284 3.14900i −0.119697 0.100438i 0.580974 0.813922i \(-0.302672\pi\)
−0.700671 + 0.713484i \(0.747116\pi\)
\(984\) 0 0
\(985\) −6.25133 35.4531i −0.199184 1.12963i
\(986\) 15.3126 + 86.8420i 0.487652 + 2.76561i
\(987\) 0 0
\(988\) 3.06418 + 2.57115i 0.0974845 + 0.0817992i
\(989\) 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
\(994\) 27.5776 23.1404i 0.874708 0.733967i
\(995\) −2.30177 0.837775i −0.0729709 0.0265592i
\(996\) 0 0
\(997\) 8.68241 49.2404i 0.274975 1.55946i −0.464068 0.885800i \(-0.653611\pi\)
0.739042 0.673659i \(-0.235278\pi\)
\(998\) 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.649.2 12
3.2 odd 2 inner 729.2.e.p.649.1 12
9.2 odd 6 inner 729.2.e.p.163.2 12
9.4 even 3 inner 729.2.e.p.406.2 12
9.5 odd 6 inner 729.2.e.p.406.1 12
9.7 even 3 inner 729.2.e.p.163.1 12
27.2 odd 18 243.2.c.c.163.2 4
27.4 even 9 inner 729.2.e.p.325.2 12
27.5 odd 18 inner 729.2.e.p.568.2 12
27.7 even 9 243.2.c.c.82.1 4
27.11 odd 18 243.2.a.d.1.1 2
27.13 even 9 inner 729.2.e.p.82.2 12
27.14 odd 18 inner 729.2.e.p.82.1 12
27.16 even 9 243.2.a.d.1.2 yes 2
27.20 odd 18 243.2.c.c.82.2 4
27.22 even 9 inner 729.2.e.p.568.1 12
27.23 odd 18 inner 729.2.e.p.325.1 12
27.25 even 9 243.2.c.c.163.1 4
108.11 even 18 3888.2.a.z.1.2 2
108.43 odd 18 3888.2.a.z.1.1 2
135.119 odd 18 6075.2.a.bn.1.2 2
135.124 even 18 6075.2.a.bn.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.d.1.1 2 27.11 odd 18
243.2.a.d.1.2 yes 2 27.16 even 9
243.2.c.c.82.1 4 27.7 even 9
243.2.c.c.82.2 4 27.20 odd 18
243.2.c.c.163.1 4 27.25 even 9
243.2.c.c.163.2 4 27.2 odd 18
729.2.e.p.82.1 12 27.14 odd 18 inner
729.2.e.p.82.2 12 27.13 even 9 inner
729.2.e.p.163.1 12 9.7 even 3 inner
729.2.e.p.163.2 12 9.2 odd 6 inner
729.2.e.p.325.1 12 27.23 odd 18 inner
729.2.e.p.325.2 12 27.4 even 9 inner
729.2.e.p.406.1 12 9.5 odd 6 inner
729.2.e.p.406.2 12 9.4 even 3 inner
729.2.e.p.568.1 12 27.22 even 9 inner
729.2.e.p.568.2 12 27.5 odd 18 inner
729.2.e.p.649.1 12 3.2 odd 2 inner
729.2.e.p.649.2 12 1.1 even 1 trivial
3888.2.a.z.1.1 2 108.43 odd 18
3888.2.a.z.1.2 2 108.11 even 18
6075.2.a.bn.1.1 2 135.124 even 18
6075.2.a.bn.1.2 2 135.119 odd 18