Properties

Label 729.2.e.o.568.1
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: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 568.1
Root \(0.342020 + 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.o.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.62760 - 0.592396i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.300767 + 1.70574i) q^{5} +(1.53209 - 1.28558i) q^{7} +(0.866025 + 1.50000i) q^{8} +O(q^{10})\) \(q+(-1.62760 - 0.592396i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.300767 + 1.70574i) q^{5} +(1.53209 - 1.28558i) q^{7} +(0.866025 + 1.50000i) q^{8} +(1.50000 - 2.59808i) q^{10} +(-0.601535 - 3.41147i) q^{11} +(0.939693 - 0.342020i) q^{13} +(-3.25519 + 1.18479i) q^{14} +(-0.868241 - 4.92404i) q^{16} +(-2.59808 + 4.50000i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.32683 + 1.11334i) q^{20} +(-1.04189 + 5.90885i) q^{22} +(2.65366 + 2.22668i) q^{23} +(1.87939 + 0.684040i) q^{25} -1.73205 q^{26} +2.00000 q^{28} +(-1.62760 - 0.592396i) q^{29} +(6.12836 + 5.14230i) q^{31} +(-0.902302 + 5.11721i) q^{32} +(6.89440 - 5.78509i) q^{34} +(1.73205 + 3.00000i) q^{35} +(3.50000 - 6.06218i) q^{37} +(0.601535 + 3.41147i) q^{38} +(-2.81908 + 1.02606i) q^{40} +(6.51038 - 2.36959i) q^{41} +(0.347296 + 1.96962i) q^{43} +(1.73205 - 3.00000i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(5.30731 - 4.45336i) q^{47} +(-0.520945 + 2.95442i) q^{49} +(-2.65366 - 2.22668i) q^{50} +(0.939693 + 0.342020i) q^{52} +6.00000 q^{55} +(3.25519 + 1.18479i) q^{56} +(2.29813 + 1.92836i) q^{58} +(2.40614 - 13.6459i) q^{59} +(-5.36231 + 4.49951i) q^{61} +(-6.92820 - 12.0000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(0.300767 + 1.70574i) q^{65} +(9.39693 - 3.42020i) q^{67} +(-4.88279 + 1.77719i) q^{68} +(-1.04189 - 5.90885i) q^{70} +(5.19615 - 9.00000i) q^{71} +(3.50000 + 6.06218i) q^{73} +(-9.28780 + 7.79339i) q^{74} +(0.347296 - 1.96962i) q^{76} +(-5.30731 - 4.45336i) q^{77} +(-1.87939 - 0.684040i) q^{79} +8.66025 q^{80} -12.0000 q^{82} +(13.0208 + 4.73917i) q^{83} +(-6.89440 - 5.78509i) q^{85} +(0.601535 - 3.41147i) q^{86} +(4.59627 - 3.85673i) q^{88} +(2.59808 + 4.50000i) q^{89} +(1.00000 - 1.73205i) q^{91} +(0.601535 + 3.41147i) q^{92} +(-11.2763 + 4.10424i) q^{94} +(3.25519 - 1.18479i) q^{95} +(0.347296 + 1.96962i) q^{97} +(2.59808 - 4.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 18 q^{10} - 12 q^{19} + 24 q^{28} + 42 q^{37} - 36 q^{46} + 72 q^{55} - 6 q^{64} + 42 q^{73} - 144 q^{82} + 12 q^{91}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.62760 0.592396i −1.15088 0.418887i −0.305051 0.952336i \(-0.598674\pi\)
−0.845833 + 0.533449i \(0.820896\pi\)
\(3\) 0 0
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) −0.300767 + 1.70574i −0.134507 + 0.762829i 0.840694 + 0.541510i \(0.182147\pi\)
−0.975202 + 0.221319i \(0.928964\pi\)
\(6\) 0 0
\(7\) 1.53209 1.28558i 0.579075 0.485902i −0.305568 0.952170i \(-0.598846\pi\)
0.884643 + 0.466268i \(0.154402\pi\)
\(8\) 0.866025 + 1.50000i 0.306186 + 0.530330i
\(9\) 0 0
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) −0.601535 3.41147i −0.181370 1.02860i −0.930532 0.366211i \(-0.880655\pi\)
0.749162 0.662387i \(-0.230456\pi\)
\(12\) 0 0
\(13\) 0.939693 0.342020i 0.260624 0.0948593i −0.208404 0.978043i \(-0.566827\pi\)
0.469027 + 0.883184i \(0.344605\pi\)
\(14\) −3.25519 + 1.18479i −0.869986 + 0.316649i
\(15\) 0 0
\(16\) −0.868241 4.92404i −0.217060 1.23101i
\(17\) −2.59808 + 4.50000i −0.630126 + 1.09141i 0.357400 + 0.933952i \(0.383663\pi\)
−0.987526 + 0.157459i \(0.949670\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) −1.32683 + 1.11334i −0.296688 + 0.248951i
\(21\) 0 0
\(22\) −1.04189 + 5.90885i −0.222131 + 1.25977i
\(23\) 2.65366 + 2.22668i 0.553325 + 0.464295i 0.876065 0.482193i \(-0.160159\pi\)
−0.322740 + 0.946488i \(0.604604\pi\)
\(24\) 0 0
\(25\) 1.87939 + 0.684040i 0.375877 + 0.136808i
\(26\) −1.73205 −0.339683
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) −1.62760 0.592396i −0.302237 0.110005i 0.186450 0.982464i \(-0.440302\pi\)
−0.488687 + 0.872459i \(0.662524\pi\)
\(30\) 0 0
\(31\) 6.12836 + 5.14230i 1.10069 + 0.923585i 0.997471 0.0710747i \(-0.0226429\pi\)
0.103214 + 0.994659i \(0.467087\pi\)
\(32\) −0.902302 + 5.11721i −0.159506 + 0.904604i
\(33\) 0 0
\(34\) 6.89440 5.78509i 1.18238 0.992134i
\(35\) 1.73205 + 3.00000i 0.292770 + 0.507093i
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 0.601535 + 3.41147i 0.0975819 + 0.553414i
\(39\) 0 0
\(40\) −2.81908 + 1.02606i −0.445735 + 0.162234i
\(41\) 6.51038 2.36959i 1.01675 0.370067i 0.220729 0.975335i \(-0.429156\pi\)
0.796022 + 0.605268i \(0.206934\pi\)
\(42\) 0 0
\(43\) 0.347296 + 1.96962i 0.0529622 + 0.300364i 0.999770 0.0214354i \(-0.00682361\pi\)
−0.946808 + 0.321799i \(0.895712\pi\)
\(44\) 1.73205 3.00000i 0.261116 0.452267i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 5.30731 4.45336i 0.774151 0.649590i −0.167617 0.985852i \(-0.553607\pi\)
0.941768 + 0.336262i \(0.109163\pi\)
\(48\) 0 0
\(49\) −0.520945 + 2.95442i −0.0744206 + 0.422060i
\(50\) −2.65366 2.22668i −0.375284 0.314900i
\(51\) 0 0
\(52\) 0.939693 + 0.342020i 0.130312 + 0.0474297i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 3.25519 + 1.18479i 0.434993 + 0.158325i
\(57\) 0 0
\(58\) 2.29813 + 1.92836i 0.301760 + 0.253206i
\(59\) 2.40614 13.6459i 0.313253 1.77654i −0.268602 0.963251i \(-0.586562\pi\)
0.581854 0.813293i \(-0.302327\pi\)
\(60\) 0 0
\(61\) −5.36231 + 4.49951i −0.686574 + 0.576104i −0.917919 0.396768i \(-0.870132\pi\)
0.231345 + 0.972872i \(0.425687\pi\)
\(62\) −6.92820 12.0000i −0.879883 1.52400i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0.300767 + 1.70574i 0.0373056 + 0.211571i
\(66\) 0 0
\(67\) 9.39693 3.42020i 1.14802 0.417844i 0.303215 0.952922i \(-0.401940\pi\)
0.844803 + 0.535078i \(0.179718\pi\)
\(68\) −4.88279 + 1.77719i −0.592125 + 0.215516i
\(69\) 0 0
\(70\) −1.04189 5.90885i −0.124530 0.706242i
\(71\) 5.19615 9.00000i 0.616670 1.06810i −0.373419 0.927663i \(-0.621815\pi\)
0.990089 0.140441i \(-0.0448520\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −9.28780 + 7.79339i −1.07968 + 0.905963i
\(75\) 0 0
\(76\) 0.347296 1.96962i 0.0398376 0.225930i
\(77\) −5.30731 4.45336i −0.604824 0.507508i
\(78\) 0 0
\(79\) −1.87939 0.684040i −0.211447 0.0769605i 0.234125 0.972207i \(-0.424778\pi\)
−0.445572 + 0.895246i \(0.647000\pi\)
\(80\) 8.66025 0.968246
\(81\) 0 0
\(82\) −12.0000 −1.32518
\(83\) 13.0208 + 4.73917i 1.42921 + 0.520192i 0.936706 0.350116i \(-0.113858\pi\)
0.492508 + 0.870308i \(0.336080\pi\)
\(84\) 0 0
\(85\) −6.89440 5.78509i −0.747803 0.627481i
\(86\) 0.601535 3.41147i 0.0648652 0.367869i
\(87\) 0 0
\(88\) 4.59627 3.85673i 0.489964 0.411128i
\(89\) 2.59808 + 4.50000i 0.275396 + 0.476999i 0.970235 0.242166i \(-0.0778579\pi\)
−0.694839 + 0.719165i \(0.744525\pi\)
\(90\) 0 0
\(91\) 1.00000 1.73205i 0.104828 0.181568i
\(92\) 0.601535 + 3.41147i 0.0627144 + 0.355671i
\(93\) 0 0
\(94\) −11.2763 + 4.10424i −1.16306 + 0.423320i
\(95\) 3.25519 1.18479i 0.333976 0.121557i
\(96\) 0 0
\(97\) 0.347296 + 1.96962i 0.0352626 + 0.199984i 0.997350 0.0727587i \(-0.0231803\pi\)
−0.962087 + 0.272743i \(0.912069\pi\)
\(98\) 2.59808 4.50000i 0.262445 0.454569i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 5.30731 4.45336i 0.528097 0.443126i −0.339347 0.940661i \(-0.610206\pi\)
0.867444 + 0.497535i \(0.165761\pi\)
\(102\) 0 0
\(103\) 1.38919 7.87846i 0.136881 0.776288i −0.836651 0.547736i \(-0.815490\pi\)
0.973532 0.228552i \(-0.0733991\pi\)
\(104\) 1.32683 + 1.11334i 0.130106 + 0.109172i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) −9.76557 3.55438i −0.931111 0.338897i
\(111\) 0 0
\(112\) −7.66044 6.42788i −0.723844 0.607377i
\(113\) −0.300767 + 1.70574i −0.0282938 + 0.160462i −0.995681 0.0928398i \(-0.970406\pi\)
0.967387 + 0.253302i \(0.0815167\pi\)
\(114\) 0 0
\(115\) −4.59627 + 3.85673i −0.428604 + 0.359642i
\(116\) −0.866025 1.50000i −0.0804084 0.139272i
\(117\) 0 0
\(118\) −12.0000 + 20.7846i −1.10469 + 1.91338i
\(119\) 1.80460 + 10.2344i 0.165428 + 0.938188i
\(120\) 0 0
\(121\) −0.939693 + 0.342020i −0.0854266 + 0.0310927i
\(122\) 11.3932 4.14677i 1.03149 0.375431i
\(123\) 0 0
\(124\) 1.38919 + 7.87846i 0.124753 + 0.707507i
\(125\) −6.06218 + 10.5000i −0.542218 + 0.939149i
\(126\) 0 0
\(127\) −1.00000 1.73205i −0.0887357 0.153695i 0.818241 0.574875i \(-0.194949\pi\)
−0.906977 + 0.421180i \(0.861616\pi\)
\(128\) 9.28780 7.79339i 0.820933 0.688844i
\(129\) 0 0
\(130\) 0.520945 2.95442i 0.0456899 0.259120i
\(131\) 2.65366 + 2.22668i 0.231851 + 0.194546i 0.751310 0.659949i \(-0.229422\pi\)
−0.519459 + 0.854495i \(0.673867\pi\)
\(132\) 0 0
\(133\) −3.75877 1.36808i −0.325927 0.118628i
\(134\) −17.3205 −1.49626
\(135\) 0 0
\(136\) −9.00000 −0.771744
\(137\) −1.62760 0.592396i −0.139055 0.0506118i 0.271555 0.962423i \(-0.412462\pi\)
−0.410610 + 0.911811i \(0.634684\pi\)
\(138\) 0 0
\(139\) 6.12836 + 5.14230i 0.519800 + 0.436164i 0.864562 0.502526i \(-0.167596\pi\)
−0.344762 + 0.938690i \(0.612040\pi\)
\(140\) −0.601535 + 3.41147i −0.0508390 + 0.288322i
\(141\) 0 0
\(142\) −13.7888 + 11.5702i −1.15713 + 0.970948i
\(143\) −1.73205 3.00000i −0.144841 0.250873i
\(144\) 0 0
\(145\) 1.50000 2.59808i 0.124568 0.215758i
\(146\) −2.10537 11.9402i −0.174242 0.988175i
\(147\) 0 0
\(148\) 6.57785 2.39414i 0.540696 0.196797i
\(149\) −8.13798 + 2.96198i −0.666689 + 0.242655i −0.653122 0.757253i \(-0.726541\pi\)
−0.0135674 + 0.999908i \(0.504319\pi\)
\(150\) 0 0
\(151\) 3.47296 + 19.6962i 0.282626 + 1.60285i 0.713645 + 0.700508i \(0.247043\pi\)
−0.431019 + 0.902343i \(0.641846\pi\)
\(152\) 1.73205 3.00000i 0.140488 0.243332i
\(153\) 0 0
\(154\) 6.00000 + 10.3923i 0.483494 + 0.837436i
\(155\) −10.6146 + 8.90673i −0.852587 + 0.715405i
\(156\) 0 0
\(157\) 2.95202 16.7417i 0.235597 1.33614i −0.605757 0.795650i \(-0.707129\pi\)
0.841353 0.540486i \(-0.181759\pi\)
\(158\) 2.65366 + 2.22668i 0.211114 + 0.177145i
\(159\) 0 0
\(160\) −8.45723 3.07818i −0.668603 0.243352i
\(161\) 6.92820 0.546019
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 6.51038 + 2.36959i 0.508375 + 0.185034i
\(165\) 0 0
\(166\) −18.3851 15.4269i −1.42696 1.19736i
\(167\) −3.00767 + 17.0574i −0.232741 + 1.31994i 0.614579 + 0.788856i \(0.289326\pi\)
−0.847320 + 0.531083i \(0.821785\pi\)
\(168\) 0 0
\(169\) −9.19253 + 7.71345i −0.707118 + 0.593342i
\(170\) 7.79423 + 13.5000i 0.597790 + 1.03540i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −3.30844 18.7631i −0.251536 1.42653i −0.804810 0.593533i \(-0.797733\pi\)
0.553273 0.833000i \(-0.313378\pi\)
\(174\) 0 0
\(175\) 3.75877 1.36808i 0.284136 0.103417i
\(176\) −16.2760 + 5.92396i −1.22685 + 0.446535i
\(177\) 0 0
\(178\) −1.56283 8.86327i −0.117139 0.664330i
\(179\) −10.3923 + 18.0000i −0.776757 + 1.34538i 0.157044 + 0.987592i \(0.449804\pi\)
−0.933801 + 0.357792i \(0.883530\pi\)
\(180\) 0 0
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) −2.65366 + 2.22668i −0.196702 + 0.165053i
\(183\) 0 0
\(184\) −1.04189 + 5.90885i −0.0768091 + 0.435606i
\(185\) 9.28780 + 7.79339i 0.682852 + 0.572981i
\(186\) 0 0
\(187\) 16.9145 + 6.15636i 1.23691 + 0.450198i
\(188\) 6.92820 0.505291
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −16.2760 5.92396i −1.17769 0.428643i −0.322302 0.946637i \(-0.604457\pi\)
−0.855384 + 0.517994i \(0.826679\pi\)
\(192\) 0 0
\(193\) −0.766044 0.642788i −0.0551411 0.0462689i 0.614801 0.788683i \(-0.289236\pi\)
−0.669942 + 0.742414i \(0.733681\pi\)
\(194\) 0.601535 3.41147i 0.0431877 0.244930i
\(195\) 0 0
\(196\) −2.29813 + 1.92836i −0.164152 + 0.137740i
\(197\) 2.59808 + 4.50000i 0.185105 + 0.320612i 0.943612 0.331053i \(-0.107404\pi\)
−0.758507 + 0.651665i \(0.774071\pi\)
\(198\) 0 0
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) 0.601535 + 3.41147i 0.0425349 + 0.241228i
\(201\) 0 0
\(202\) −11.2763 + 4.10424i −0.793399 + 0.288773i
\(203\) −3.25519 + 1.18479i −0.228470 + 0.0831561i
\(204\) 0 0
\(205\) 2.08378 + 11.8177i 0.145537 + 0.825383i
\(206\) −6.92820 + 12.0000i −0.482711 + 0.836080i
\(207\) 0 0
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) −5.30731 + 4.45336i −0.367114 + 0.308046i
\(210\) 0 0
\(211\) −1.73648 + 9.84808i −0.119544 + 0.677970i 0.864855 + 0.502022i \(0.167410\pi\)
−0.984399 + 0.175948i \(0.943701\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.46410 −0.236250
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) −17.9035 6.51636i −1.21258 0.441344i
\(219\) 0 0
\(220\) 4.59627 + 3.85673i 0.309880 + 0.260020i
\(221\) −0.902302 + 5.11721i −0.0606954 + 0.344221i
\(222\) 0 0
\(223\) 1.53209 1.28558i 0.102596 0.0860885i −0.590047 0.807369i \(-0.700891\pi\)
0.692643 + 0.721281i \(0.256446\pi\)
\(224\) 5.19615 + 9.00000i 0.347183 + 0.601338i
\(225\) 0 0
\(226\) 1.50000 2.59808i 0.0997785 0.172821i
\(227\) −0.601535 3.41147i −0.0399253 0.226427i 0.958316 0.285711i \(-0.0922296\pi\)
−0.998241 + 0.0592832i \(0.981119\pi\)
\(228\) 0 0
\(229\) 0.939693 0.342020i 0.0620966 0.0226013i −0.310785 0.950480i \(-0.600592\pi\)
0.372882 + 0.927879i \(0.378370\pi\)
\(230\) 9.76557 3.55438i 0.643923 0.234369i
\(231\) 0 0
\(232\) −0.520945 2.95442i −0.0342017 0.193967i
\(233\) 12.9904 22.5000i 0.851028 1.47402i −0.0292532 0.999572i \(-0.509313\pi\)
0.880281 0.474452i \(-0.157354\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 10.6146 8.90673i 0.690953 0.579779i
\(237\) 0 0
\(238\) 3.12567 17.7265i 0.202607 1.14904i
\(239\) −21.2292 17.8135i −1.37321 1.15226i −0.971651 0.236422i \(-0.924025\pi\)
−0.401555 0.915835i \(-0.631530\pi\)
\(240\) 0 0
\(241\) −27.2511 9.91858i −1.75540 0.638912i −0.755528 0.655116i \(-0.772620\pi\)
−0.999869 + 0.0162041i \(0.994842\pi\)
\(242\) 1.73205 0.111340
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) −4.88279 1.77719i −0.311950 0.113540i
\(246\) 0 0
\(247\) −1.53209 1.28558i −0.0974845 0.0817992i
\(248\) −2.40614 + 13.6459i −0.152790 + 0.866515i
\(249\) 0 0
\(250\) 16.0869 13.4985i 1.01743 0.853723i
\(251\) −5.19615 9.00000i −0.327978 0.568075i 0.654132 0.756380i \(-0.273034\pi\)
−0.982111 + 0.188305i \(0.939701\pi\)
\(252\) 0 0
\(253\) 6.00000 10.3923i 0.377217 0.653359i
\(254\) 0.601535 + 3.41147i 0.0377437 + 0.214055i
\(255\) 0 0
\(256\) −17.8542 + 6.49838i −1.11588 + 0.406149i
\(257\) −8.13798 + 2.96198i −0.507633 + 0.184763i −0.583124 0.812383i \(-0.698170\pi\)
0.0754909 + 0.997146i \(0.475948\pi\)
\(258\) 0 0
\(259\) −2.43107 13.7873i −0.151060 0.856702i
\(260\) −0.866025 + 1.50000i −0.0537086 + 0.0930261i
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) 5.30731 4.45336i 0.327263 0.274606i −0.464321 0.885667i \(-0.653701\pi\)
0.791583 + 0.611061i \(0.209257\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 5.30731 + 4.45336i 0.325412 + 0.273053i
\(267\) 0 0
\(268\) 9.39693 + 3.42020i 0.574009 + 0.208922i
\(269\) −15.5885 −0.950445 −0.475223 0.879866i \(-0.657632\pi\)
−0.475223 + 0.879866i \(0.657632\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 24.4139 + 8.88594i 1.48031 + 0.538789i
\(273\) 0 0
\(274\) 2.29813 + 1.92836i 0.138835 + 0.116497i
\(275\) 1.20307 6.82295i 0.0725478 0.411439i
\(276\) 0 0
\(277\) 1.53209 1.28558i 0.0920543 0.0772427i −0.595599 0.803282i \(-0.703085\pi\)
0.687653 + 0.726039i \(0.258641\pi\)
\(278\) −6.92820 12.0000i −0.415526 0.719712i
\(279\) 0 0
\(280\) −3.00000 + 5.19615i −0.179284 + 0.310530i
\(281\) 2.10537 + 11.9402i 0.125596 + 0.712290i 0.980952 + 0.194250i \(0.0622272\pi\)
−0.855356 + 0.518040i \(0.826662\pi\)
\(282\) 0 0
\(283\) 26.3114 9.57656i 1.56405 0.569268i 0.592390 0.805651i \(-0.298184\pi\)
0.971660 + 0.236384i \(0.0759622\pi\)
\(284\) 9.76557 3.55438i 0.579480 0.210914i
\(285\) 0 0
\(286\) 1.04189 + 5.90885i 0.0616082 + 0.349397i
\(287\) 6.92820 12.0000i 0.408959 0.708338i
\(288\) 0 0
\(289\) −5.00000 8.66025i −0.294118 0.509427i
\(290\) −3.98048 + 3.34002i −0.233742 + 0.196133i
\(291\) 0 0
\(292\) −1.21554 + 6.89365i −0.0711339 + 0.403421i
\(293\) 14.5951 + 12.2467i 0.852655 + 0.715463i 0.960373 0.278719i \(-0.0899098\pi\)
−0.107717 + 0.994182i \(0.534354\pi\)
\(294\) 0 0
\(295\) 22.5526 + 8.20848i 1.31306 + 0.477916i
\(296\) 12.1244 0.704714
\(297\) 0 0
\(298\) 15.0000 0.868927
\(299\) 3.25519 + 1.18479i 0.188253 + 0.0685183i
\(300\) 0 0
\(301\) 3.06418 + 2.57115i 0.176616 + 0.148199i
\(302\) 6.01535 34.1147i 0.346144 1.96308i
\(303\) 0 0
\(304\) −7.66044 + 6.42788i −0.439357 + 0.368664i
\(305\) −6.06218 10.5000i −0.347119 0.601228i
\(306\) 0 0
\(307\) 8.00000 13.8564i 0.456584 0.790827i −0.542194 0.840254i \(-0.682406\pi\)
0.998778 + 0.0494267i \(0.0157394\pi\)
\(308\) −1.20307 6.82295i −0.0685513 0.388774i
\(309\) 0 0
\(310\) 22.5526 8.20848i 1.28090 0.466211i
\(311\) 6.51038 2.36959i 0.369170 0.134367i −0.150772 0.988569i \(-0.548176\pi\)
0.519942 + 0.854202i \(0.325954\pi\)
\(312\) 0 0
\(313\) −4.34120 24.6202i −0.245379 1.39162i −0.819610 0.572922i \(-0.805810\pi\)
0.574231 0.818694i \(-0.305301\pi\)
\(314\) −14.7224 + 25.5000i −0.830835 + 1.43905i
\(315\) 0 0
\(316\) −1.00000 1.73205i −0.0562544 0.0974355i
\(317\) −6.63414 + 5.56670i −0.372610 + 0.312657i −0.809793 0.586715i \(-0.800421\pi\)
0.437183 + 0.899373i \(0.355976\pi\)
\(318\) 0 0
\(319\) −1.04189 + 5.90885i −0.0583346 + 0.330832i
\(320\) −1.32683 1.11334i −0.0741719 0.0622376i
\(321\) 0 0
\(322\) −11.2763 4.10424i −0.628404 0.228720i
\(323\) 10.3923 0.578243
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 26.0415 + 9.47834i 1.44231 + 0.524957i
\(327\) 0 0
\(328\) 9.19253 + 7.71345i 0.507573 + 0.425904i
\(329\) 2.40614 13.6459i 0.132655 0.752323i
\(330\) 0 0
\(331\) 1.53209 1.28558i 0.0842112 0.0706616i −0.599710 0.800217i \(-0.704718\pi\)
0.683922 + 0.729556i \(0.260273\pi\)
\(332\) 6.92820 + 12.0000i 0.380235 + 0.658586i
\(333\) 0 0
\(334\) 15.0000 25.9808i 0.820763 1.42160i
\(335\) 3.00767 + 17.0574i 0.164327 + 0.931944i
\(336\) 0 0
\(337\) −24.4320 + 8.89252i −1.33090 + 0.484407i −0.906934 0.421273i \(-0.861583\pi\)
−0.423962 + 0.905680i \(0.639361\pi\)
\(338\) 19.5311 7.10876i 1.06235 0.386665i
\(339\) 0 0
\(340\) −1.56283 8.86327i −0.0847566 0.480678i
\(341\) 13.8564 24.0000i 0.750366 1.29967i
\(342\) 0 0
\(343\) 10.0000 + 17.3205i 0.539949 + 0.935220i
\(344\) −2.65366 + 2.22668i −0.143076 + 0.120055i
\(345\) 0 0
\(346\) −5.73039 + 32.4987i −0.308068 + 1.74714i
\(347\) 2.65366 + 2.22668i 0.142456 + 0.119535i 0.711231 0.702959i \(-0.248138\pi\)
−0.568775 + 0.822493i \(0.692583\pi\)
\(348\) 0 0
\(349\) −1.87939 0.684040i −0.100601 0.0366158i 0.291229 0.956653i \(-0.405936\pi\)
−0.391830 + 0.920037i \(0.628158\pi\)
\(350\) −6.92820 −0.370328
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) 13.0208 + 4.73917i 0.693025 + 0.252241i 0.664430 0.747350i \(-0.268674\pi\)
0.0285953 + 0.999591i \(0.490897\pi\)
\(354\) 0 0
\(355\) 13.7888 + 11.5702i 0.731834 + 0.614081i
\(356\) −0.902302 + 5.11721i −0.0478219 + 0.271212i
\(357\) 0 0
\(358\) 27.5776 23.1404i 1.45752 1.22301i
\(359\) −5.19615 9.00000i −0.274242 0.475002i 0.695701 0.718331i \(-0.255094\pi\)
−0.969944 + 0.243329i \(0.921760\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0.601535 + 3.41147i 0.0316160 + 0.179303i
\(363\) 0 0
\(364\) 1.87939 0.684040i 0.0985066 0.0358535i
\(365\) −11.3932 + 4.14677i −0.596346 + 0.217052i
\(366\) 0 0
\(367\) 3.47296 + 19.6962i 0.181287 + 1.02813i 0.930633 + 0.365953i \(0.119257\pi\)
−0.749346 + 0.662178i \(0.769632\pi\)
\(368\) 8.66025 15.0000i 0.451447 0.781929i
\(369\) 0 0
\(370\) −10.5000 18.1865i −0.545869 0.945473i
\(371\) 0 0
\(372\) 0 0
\(373\) −1.73648 + 9.84808i −0.0899116 + 0.509914i 0.906277 + 0.422685i \(0.138912\pi\)
−0.996188 + 0.0872291i \(0.972199\pi\)
\(374\) −23.8829 20.0401i −1.23496 1.03625i
\(375\) 0 0
\(376\) 11.2763 + 4.10424i 0.581531 + 0.211660i
\(377\) −1.73205 −0.0892052
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 3.25519 + 1.18479i 0.166988 + 0.0607786i
\(381\) 0 0
\(382\) 22.9813 + 19.2836i 1.17583 + 0.986636i
\(383\) −3.00767 + 17.0574i −0.153685 + 0.871591i 0.806293 + 0.591516i \(0.201470\pi\)
−0.959978 + 0.280075i \(0.909641\pi\)
\(384\) 0 0
\(385\) 9.19253 7.71345i 0.468495 0.393114i
\(386\) 0.866025 + 1.50000i 0.0440795 + 0.0763480i
\(387\) 0 0
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) 4.81228 + 27.2918i 0.243992 + 1.38375i 0.822821 + 0.568300i \(0.192399\pi\)
−0.578829 + 0.815449i \(0.696490\pi\)
\(390\) 0 0
\(391\) −16.9145 + 6.15636i −0.855401 + 0.311341i
\(392\) −4.88279 + 1.77719i −0.246618 + 0.0897616i
\(393\) 0 0
\(394\) −1.56283 8.86327i −0.0787344 0.446525i
\(395\) 1.73205 3.00000i 0.0871489 0.150946i
\(396\) 0 0
\(397\) −14.5000 25.1147i −0.727734 1.26047i −0.957839 0.287307i \(-0.907240\pi\)
0.230105 0.973166i \(-0.426093\pi\)
\(398\) 26.5366 22.2668i 1.33016 1.11613i
\(399\) 0 0
\(400\) 1.73648 9.84808i 0.0868241 0.492404i
\(401\) −9.28780 7.79339i −0.463810 0.389183i 0.380720 0.924690i \(-0.375676\pi\)
−0.844531 + 0.535507i \(0.820121\pi\)
\(402\) 0 0
\(403\) 7.51754 + 2.73616i 0.374475 + 0.136298i
\(404\) 6.92820 0.344691
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) −22.7863 8.29355i −1.12948 0.411096i
\(408\) 0 0
\(409\) −14.5548 12.2130i −0.719691 0.603892i 0.207609 0.978212i \(-0.433432\pi\)
−0.927300 + 0.374320i \(0.877876\pi\)
\(410\) 3.60921 20.4688i 0.178246 1.01088i
\(411\) 0 0
\(412\) 6.12836 5.14230i 0.301922 0.253343i
\(413\) −13.8564 24.0000i −0.681829 1.18096i
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 0.902302 + 5.11721i 0.0442390 + 0.250892i
\(417\) 0 0
\(418\) 11.2763 4.10424i 0.551542 0.200745i
\(419\) 6.51038 2.36959i 0.318053 0.115762i −0.178060 0.984020i \(-0.556982\pi\)
0.496113 + 0.868258i \(0.334760\pi\)
\(420\) 0 0
\(421\) −4.34120 24.6202i −0.211577 1.19991i −0.886748 0.462253i \(-0.847041\pi\)
0.675171 0.737662i \(-0.264070\pi\)
\(422\) 8.66025 15.0000i 0.421575 0.730189i
\(423\) 0 0
\(424\) 0 0
\(425\) −7.96097 + 6.68004i −0.386164 + 0.324030i
\(426\) 0 0
\(427\) −2.43107 + 13.7873i −0.117648 + 0.667215i
\(428\) 0 0
\(429\) 0 0
\(430\) 5.63816 + 2.05212i 0.271896 + 0.0989621i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) −26.0415 9.47834i −1.25003 0.454975i
\(435\) 0 0
\(436\) 8.42649 + 7.07066i 0.403556 + 0.338623i
\(437\) 1.20307 6.82295i 0.0575506 0.326386i
\(438\) 0 0
\(439\) 15.3209 12.8558i 0.731226 0.613572i −0.199239 0.979951i \(-0.563847\pi\)
0.930466 + 0.366379i \(0.119403\pi\)
\(440\) 5.19615 + 9.00000i 0.247717 + 0.429058i
\(441\) 0 0
\(442\) 4.50000 7.79423i 0.214043 0.370734i
\(443\) −6.01535 34.1147i −0.285798 1.62084i −0.702422 0.711761i \(-0.747898\pi\)
0.416624 0.909079i \(-0.363213\pi\)
\(444\) 0 0
\(445\) −8.45723 + 3.07818i −0.400911 + 0.145920i
\(446\) −3.25519 + 1.18479i −0.154138 + 0.0561016i
\(447\) 0 0
\(448\) 0.347296 + 1.96962i 0.0164082 + 0.0930556i
\(449\) −10.3923 + 18.0000i −0.490443 + 0.849473i −0.999939 0.0110003i \(-0.996498\pi\)
0.509496 + 0.860473i \(0.329832\pi\)
\(450\) 0 0
\(451\) −12.0000 20.7846i −0.565058 0.978709i
\(452\) −1.32683 + 1.11334i −0.0624087 + 0.0523671i
\(453\) 0 0
\(454\) −1.04189 + 5.90885i −0.0488983 + 0.277316i
\(455\) 2.65366 + 2.22668i 0.124405 + 0.104388i
\(456\) 0 0
\(457\) −27.2511 9.91858i −1.27475 0.463972i −0.386059 0.922474i \(-0.626164\pi\)
−0.888693 + 0.458502i \(0.848386\pi\)
\(458\) −1.73205 −0.0809334
\(459\) 0 0
\(460\) −6.00000 −0.279751
\(461\) 13.0208 + 4.73917i 0.606437 + 0.220725i 0.626944 0.779065i \(-0.284306\pi\)
−0.0205063 + 0.999790i \(0.506528\pi\)
\(462\) 0 0
\(463\) 6.12836 + 5.14230i 0.284809 + 0.238983i 0.773988 0.633200i \(-0.218259\pi\)
−0.489179 + 0.872183i \(0.662704\pi\)
\(464\) −1.50384 + 8.52869i −0.0698139 + 0.395934i
\(465\) 0 0
\(466\) −34.4720 + 28.9254i −1.59688 + 1.33995i
\(467\) 10.3923 + 18.0000i 0.480899 + 0.832941i 0.999760 0.0219178i \(-0.00697721\pi\)
−0.518861 + 0.854858i \(0.673644\pi\)
\(468\) 0 0
\(469\) 10.0000 17.3205i 0.461757 0.799787i
\(470\) −3.60921 20.4688i −0.166480 0.944157i
\(471\) 0 0
\(472\) 22.5526 8.20848i 1.03807 0.377826i
\(473\) 6.51038 2.36959i 0.299348 0.108954i
\(474\) 0 0
\(475\) −0.694593 3.93923i −0.0318701 0.180744i
\(476\) −5.19615 + 9.00000i −0.238165 + 0.412514i
\(477\) 0 0
\(478\) 24.0000 + 41.5692i 1.09773 + 1.90133i
\(479\) −18.5756 + 15.5868i −0.848740 + 0.712178i −0.959512 0.281668i \(-0.909112\pi\)
0.110771 + 0.993846i \(0.464668\pi\)
\(480\) 0 0
\(481\) 1.21554 6.89365i 0.0554237 0.314324i
\(482\) 38.4780 + 32.2869i 1.75263 + 1.47063i
\(483\) 0 0
\(484\) −0.939693 0.342020i −0.0427133 0.0155464i
\(485\) −3.46410 −0.157297
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −11.3932 4.14677i −0.515744 0.187716i
\(489\) 0 0
\(490\) 6.89440 + 5.78509i 0.311457 + 0.261344i
\(491\) −3.00767 + 17.0574i −0.135734 + 0.769788i 0.838611 + 0.544731i \(0.183368\pi\)
−0.974345 + 0.225058i \(0.927743\pi\)
\(492\) 0 0
\(493\) 6.89440 5.78509i 0.310508 0.260547i
\(494\) 1.73205 + 3.00000i 0.0779287 + 0.134976i
\(495\) 0 0
\(496\) 20.0000 34.6410i 0.898027 1.55543i
\(497\) −3.60921 20.4688i −0.161895 0.918153i
\(498\) 0 0
\(499\) 9.39693 3.42020i 0.420664 0.153109i −0.123010 0.992405i \(-0.539255\pi\)
0.543675 + 0.839296i \(0.317033\pi\)
\(500\) −11.3932 + 4.14677i −0.509518 + 0.185449i
\(501\) 0 0
\(502\) 3.12567 + 17.7265i 0.139505 + 0.791174i
\(503\) −10.3923 + 18.0000i −0.463370 + 0.802580i −0.999126 0.0417923i \(-0.986693\pi\)
0.535756 + 0.844373i \(0.320027\pi\)
\(504\) 0 0
\(505\) 6.00000 + 10.3923i 0.266996 + 0.462451i
\(506\) −15.9219 + 13.3601i −0.707816 + 0.593928i
\(507\) 0 0
\(508\) 0.347296 1.96962i 0.0154088 0.0873876i
\(509\) −21.2292 17.8135i −0.940970 0.789567i 0.0367840 0.999323i \(-0.488289\pi\)
−0.977754 + 0.209756i \(0.932733\pi\)
\(510\) 0 0
\(511\) 13.1557 + 4.78828i 0.581974 + 0.211821i
\(512\) 8.66025 0.382733
\(513\) 0 0
\(514\) 15.0000 0.661622
\(515\) 13.0208 + 4.73917i 0.573763 + 0.208833i
\(516\) 0 0
\(517\) −18.3851 15.4269i −0.808574 0.678474i
\(518\) −4.21074 + 23.8803i −0.185009 + 1.04924i
\(519\) 0 0
\(520\) −2.29813 + 1.92836i −0.100780 + 0.0845643i
\(521\) 10.3923 + 18.0000i 0.455295 + 0.788594i 0.998705 0.0508731i \(-0.0162004\pi\)
−0.543410 + 0.839467i \(0.682867\pi\)
\(522\) 0 0
\(523\) −19.0000 + 32.9090i −0.830812 + 1.43901i 0.0665832 + 0.997781i \(0.478790\pi\)
−0.897395 + 0.441228i \(0.854543\pi\)
\(524\) 0.601535 + 3.41147i 0.0262782 + 0.149031i
\(525\) 0 0
\(526\) −11.2763 + 4.10424i −0.491671 + 0.178953i
\(527\) −39.0623 + 14.2175i −1.70158 + 0.619324i
\(528\) 0 0
\(529\) −1.91013 10.8329i −0.0830491 0.470995i
\(530\) 0 0
\(531\) 0 0
\(532\) −2.00000 3.46410i −0.0867110 0.150188i
\(533\) 5.30731 4.45336i 0.229885 0.192897i
\(534\) 0 0
\(535\) 0 0
\(536\) 13.2683 + 11.1334i 0.573102 + 0.480890i
\(537\) 0 0
\(538\) 25.3717 + 9.23454i 1.09385 + 0.398129i
\(539\) 10.3923 0.447628
\(540\) 0 0
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) −3.25519 1.18479i −0.139822 0.0508912i
\(543\) 0 0
\(544\) −20.6832 17.3553i −0.886785 0.744101i
\(545\) −3.30844 + 18.7631i −0.141718 + 0.803723i
\(546\) 0 0
\(547\) 15.3209 12.8558i 0.655074 0.549672i −0.253532 0.967327i \(-0.581592\pi\)
0.908606 + 0.417655i \(0.137148\pi\)
\(548\) −0.866025 1.50000i −0.0369948 0.0640768i
\(549\) 0 0
\(550\) −6.00000 + 10.3923i −0.255841 + 0.443129i
\(551\) 0.601535 + 3.41147i 0.0256262 + 0.145334i
\(552\) 0 0
\(553\) −3.75877 + 1.36808i −0.159839 + 0.0581767i
\(554\) −3.25519 + 1.18479i −0.138300 + 0.0503370i
\(555\) 0 0
\(556\) 1.38919 + 7.87846i 0.0589146 + 0.334121i
\(557\) −18.1865 + 31.5000i −0.770588 + 1.33470i 0.166653 + 0.986016i \(0.446704\pi\)
−0.937241 + 0.348682i \(0.886629\pi\)
\(558\) 0 0
\(559\) 1.00000 + 1.73205i 0.0422955 + 0.0732579i
\(560\) 13.2683 11.1334i 0.560687 0.470472i
\(561\) 0 0
\(562\) 3.64661 20.6810i 0.153823 0.872374i
\(563\) 26.5366 + 22.2668i 1.11838 + 0.938434i 0.998522 0.0543563i \(-0.0173107\pi\)
0.119861 + 0.992791i \(0.461755\pi\)
\(564\) 0 0
\(565\) −2.81908 1.02606i −0.118599 0.0431667i
\(566\) −48.4974 −2.03850
\(567\) 0 0
\(568\) 18.0000 0.755263
\(569\) −30.9243 11.2555i −1.29641 0.471856i −0.400587 0.916259i \(-0.631194\pi\)
−0.895827 + 0.444402i \(0.853416\pi\)
\(570\) 0 0
\(571\) 6.12836 + 5.14230i 0.256464 + 0.215199i 0.761950 0.647636i \(-0.224242\pi\)
−0.505486 + 0.862835i \(0.668687\pi\)
\(572\) 0.601535 3.41147i 0.0251514 0.142641i
\(573\) 0 0
\(574\) −18.3851 + 15.4269i −0.767378 + 0.643906i
\(575\) 3.46410 + 6.00000i 0.144463 + 0.250217i
\(576\) 0 0
\(577\) −5.50000 + 9.52628i −0.228968 + 0.396584i −0.957503 0.288425i \(-0.906868\pi\)
0.728535 + 0.685009i \(0.240202\pi\)
\(578\) 3.00767 + 17.0574i 0.125103 + 0.709493i
\(579\) 0 0
\(580\) 2.81908 1.02606i 0.117056 0.0426048i
\(581\) 26.0415 9.47834i 1.08038 0.393228i
\(582\) 0 0
\(583\) 0 0
\(584\) −6.06218 + 10.5000i −0.250855 + 0.434493i
\(585\) 0 0
\(586\) −16.5000 28.5788i −0.681609 1.18058i
\(587\) 29.1902 24.4935i 1.20481 1.01095i 0.205330 0.978693i \(-0.434173\pi\)
0.999479 0.0322620i \(-0.0102711\pi\)
\(588\) 0 0
\(589\) 2.77837 15.7569i 0.114481 0.649253i
\(590\) −31.8439 26.7202i −1.31099 1.10005i
\(591\) 0 0
\(592\) −32.8892 11.9707i −1.35174 0.491993i
\(593\) 15.5885 0.640141 0.320071 0.947394i \(-0.396293\pi\)
0.320071 + 0.947394i \(0.396293\pi\)
\(594\) 0 0
\(595\) −18.0000 −0.737928
\(596\) −8.13798 2.96198i −0.333345 0.121327i
\(597\) 0 0
\(598\) −4.59627 3.85673i −0.187955 0.157713i
\(599\) 2.40614 13.6459i 0.0983122 0.557556i −0.895370 0.445323i \(-0.853089\pi\)
0.993682 0.112233i \(-0.0358002\pi\)
\(600\) 0 0
\(601\) −19.1511 + 16.0697i −0.781190 + 0.655496i −0.943548 0.331236i \(-0.892535\pi\)
0.162358 + 0.986732i \(0.448090\pi\)
\(602\) −3.46410 6.00000i −0.141186 0.244542i
\(603\) 0 0
\(604\) −10.0000 + 17.3205i −0.406894 + 0.704761i
\(605\) −0.300767 1.70574i −0.0122279 0.0693481i
\(606\) 0 0
\(607\) −24.4320 + 8.89252i −0.991665 + 0.360936i −0.786365 0.617763i \(-0.788039\pi\)
−0.205300 + 0.978699i \(0.565817\pi\)
\(608\) 9.76557 3.55438i 0.396046 0.144149i
\(609\) 0 0
\(610\) 3.64661 + 20.6810i 0.147647 + 0.837348i
\(611\) 3.46410 6.00000i 0.140143 0.242734i
\(612\) 0 0
\(613\) 17.0000 + 29.4449i 0.686624 + 1.18927i 0.972924 + 0.231127i \(0.0742412\pi\)
−0.286300 + 0.958140i \(0.592425\pi\)
\(614\) −21.2292 + 17.8135i −0.856743 + 0.718892i
\(615\) 0 0
\(616\) 2.08378 11.8177i 0.0839578 0.476148i
\(617\) −9.28780 7.79339i −0.373913 0.313750i 0.436394 0.899755i \(-0.356255\pi\)
−0.810307 + 0.586006i \(0.800700\pi\)
\(618\) 0 0
\(619\) −18.7939 6.84040i −0.755389 0.274939i −0.0645172 0.997917i \(-0.520551\pi\)
−0.690871 + 0.722978i \(0.742773\pi\)
\(620\) −13.8564 −0.556487
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 9.76557 + 3.55438i 0.391249 + 0.142403i
\(624\) 0 0
\(625\) −8.42649 7.07066i −0.337060 0.282827i
\(626\) −7.51919 + 42.6434i −0.300527 + 1.70437i
\(627\) 0 0
\(628\) 13.0228 10.9274i 0.519665 0.436050i
\(629\) 18.1865 + 31.5000i 0.725145 + 1.25599i
\(630\) 0 0
\(631\) −10.0000 + 17.3205i −0.398094 + 0.689519i −0.993491 0.113913i \(-0.963661\pi\)
0.595397 + 0.803432i \(0.296995\pi\)
\(632\) −0.601535 3.41147i −0.0239278 0.135701i
\(633\) 0 0
\(634\) 14.0954 5.13030i 0.559799 0.203750i
\(635\) 3.25519 1.18479i 0.129178 0.0470171i
\(636\) 0 0
\(637\) 0.520945 + 2.95442i 0.0206406 + 0.117059i
\(638\) 5.19615 9.00000i 0.205718 0.356313i
\(639\) 0 0
\(640\) 10.5000 + 18.1865i 0.415049 + 0.718886i
\(641\) 17.2488 14.4734i 0.681285 0.571666i −0.235096 0.971972i \(-0.575541\pi\)
0.916382 + 0.400306i \(0.131096\pi\)
\(642\) 0 0
\(643\) 1.38919 7.87846i 0.0547841 0.310696i −0.945086 0.326822i \(-0.894022\pi\)
0.999870 + 0.0161260i \(0.00513328\pi\)
\(644\) 5.30731 + 4.45336i 0.209137 + 0.175487i
\(645\) 0 0
\(646\) −16.9145 6.15636i −0.665491 0.242219i
\(647\) −31.1769 −1.22569 −0.612845 0.790203i \(-0.709975\pi\)
−0.612845 + 0.790203i \(0.709975\pi\)
\(648\) 0 0
\(649\) −48.0000 −1.88416
\(650\) −3.25519 1.18479i −0.127679 0.0464714i
\(651\) 0 0
\(652\) −12.2567 10.2846i −0.480010 0.402776i
\(653\) 2.40614 13.6459i 0.0941595 0.534005i −0.900842 0.434147i \(-0.857050\pi\)
0.995002 0.0998584i \(-0.0318390\pi\)
\(654\) 0 0
\(655\) −4.59627 + 3.85673i −0.179591 + 0.150695i
\(656\) −17.3205 30.0000i −0.676252 1.17130i
\(657\) 0 0
\(658\) −12.0000 + 20.7846i −0.467809 + 0.810268i
\(659\) −0.601535 3.41147i −0.0234325 0.132892i 0.970847 0.239699i \(-0.0770486\pi\)
−0.994280 + 0.106806i \(0.965937\pi\)
\(660\) 0 0
\(661\) −15.9748 + 5.81434i −0.621347 + 0.226152i −0.633461 0.773775i \(-0.718366\pi\)
0.0121139 + 0.999927i \(0.496144\pi\)
\(662\) −3.25519 + 1.18479i −0.126517 + 0.0460483i
\(663\) 0 0
\(664\) 4.16756 + 23.6354i 0.161733 + 0.917231i
\(665\) 3.46410 6.00000i 0.134332 0.232670i
\(666\) 0 0
\(667\) −3.00000 5.19615i −0.116160 0.201196i
\(668\) −13.2683 + 11.1334i −0.513365 + 0.430764i
\(669\) 0 0
\(670\) 5.20945 29.5442i 0.201258 1.14139i
\(671\) 18.5756 + 15.5868i 0.717103 + 0.601721i
\(672\) 0 0
\(673\) 23.4923 + 8.55050i 0.905562 + 0.329598i 0.752479 0.658616i \(-0.228858\pi\)
0.153083 + 0.988213i \(0.451080\pi\)
\(674\) 45.0333 1.73462
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 13.0208 + 4.73917i 0.500429 + 0.182141i 0.579887 0.814697i \(-0.303097\pi\)
−0.0794582 + 0.996838i \(0.525319\pi\)
\(678\) 0 0
\(679\) 3.06418 + 2.57115i 0.117592 + 0.0986717i
\(680\) 2.70691 15.3516i 0.103805 0.588708i
\(681\) 0 0
\(682\) −36.7701 + 30.8538i −1.40800 + 1.18145i
\(683\) 10.3923 + 18.0000i 0.397650 + 0.688751i 0.993436 0.114393i \(-0.0364923\pi\)
−0.595785 + 0.803144i \(0.703159\pi\)
\(684\) 0 0
\(685\) 1.50000 2.59808i 0.0573121 0.0992674i
\(686\) −6.01535 34.1147i −0.229667 1.30251i
\(687\) 0 0
\(688\) 9.39693 3.42020i 0.358254 0.130394i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.347296 + 1.96962i 0.0132118 + 0.0749277i 0.990701 0.136059i \(-0.0434436\pi\)
−0.977489 + 0.210986i \(0.932332\pi\)
\(692\) 9.52628 16.5000i 0.362135 0.627236i
\(693\) 0 0
\(694\) −3.00000 5.19615i −0.113878 0.197243i
\(695\) −10.6146 + 8.90673i −0.402636 + 0.337851i
\(696\) 0 0
\(697\) −6.25133 + 35.4531i −0.236786 + 1.34288i
\(698\) 2.65366 + 2.22668i 0.100442 + 0.0842811i
\(699\) 0 0
\(700\) 3.75877 + 1.36808i 0.142068 + 0.0517086i
\(701\) 46.7654 1.76630 0.883152 0.469087i \(-0.155417\pi\)
0.883152 + 0.469087i \(0.155417\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) 3.25519 + 1.18479i 0.122685 + 0.0446535i
\(705\) 0 0
\(706\) −18.3851 15.4269i −0.691931 0.580599i
\(707\) 2.40614 13.6459i 0.0904922 0.513207i
\(708\) 0 0
\(709\) −19.1511 + 16.0697i −0.719235 + 0.603510i −0.927174 0.374632i \(-0.877769\pi\)
0.207939 + 0.978142i \(0.433325\pi\)
\(710\) −15.5885 27.0000i −0.585024 1.01329i
\(711\) 0 0
\(712\) −4.50000 + 7.79423i −0.168645 + 0.292101i
\(713\) 4.81228 + 27.2918i 0.180221 + 1.02209i
\(714\) 0 0
\(715\) 5.63816 2.05212i 0.210855 0.0767450i
\(716\) −19.5311 + 7.10876i −0.729913 + 0.265667i
\(717\) 0 0
\(718\) 3.12567 + 17.7265i 0.116649 + 0.661549i
\(719\) 5.19615 9.00000i 0.193784 0.335643i −0.752717 0.658344i \(-0.771257\pi\)
0.946501 + 0.322700i \(0.104591\pi\)
\(720\) 0 0
\(721\) −8.00000 13.8564i −0.297936 0.516040i
\(722\) −19.9024 + 16.7001i −0.740691 + 0.621514i
\(723\) 0 0
\(724\) 0.347296 1.96962i 0.0129072 0.0732002i
\(725\) −2.65366 2.22668i −0.0985543 0.0826969i
\(726\) 0 0
\(727\) 31.9495 + 11.6287i 1.18494 + 0.431284i 0.857945 0.513741i \(-0.171741\pi\)
0.326998 + 0.945025i \(0.393963\pi\)
\(728\) 3.46410 0.128388
\(729\) 0 0
\(730\) 21.0000 0.777245
\(731\) −9.76557 3.55438i −0.361193 0.131463i
\(732\) 0 0
\(733\) −35.2380 29.5682i −1.30155 1.09213i −0.989876 0.141937i \(-0.954667\pi\)
−0.311671 0.950190i \(-0.600889\pi\)
\(734\) 6.01535 34.1147i 0.222031 1.25920i
\(735\) 0 0
\(736\) −13.7888 + 11.5702i −0.508262 + 0.426482i
\(737\) −17.3205 30.0000i −0.638009 1.10506i
\(738\) 0 0
\(739\) −10.0000 + 17.3205i −0.367856 + 0.637145i −0.989230 0.146369i \(-0.953241\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(740\) 2.10537 + 11.9402i 0.0773950 + 0.438929i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.51038 2.36959i 0.238843 0.0869316i −0.219826 0.975539i \(-0.570549\pi\)
0.458668 + 0.888608i \(0.348327\pi\)
\(744\) 0 0
\(745\) −2.60472 14.7721i −0.0954297 0.541208i
\(746\) 8.66025 15.0000i 0.317074 0.549189i
\(747\) 0 0
\(748\) 9.00000 + 15.5885i 0.329073 + 0.569970i
\(749\) 0 0
\(750\) 0 0
\(751\) −1.73648 + 9.84808i −0.0633651 + 0.359361i 0.936595 + 0.350414i \(0.113959\pi\)
−0.999960 + 0.00894729i \(0.997152\pi\)
\(752\) −26.5366 22.2668i −0.967689 0.811987i
\(753\) 0 0
\(754\) 2.81908 + 1.02606i 0.102665 + 0.0373669i
\(755\) −34.6410 −1.26072
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 26.0415 + 9.47834i 0.945871 + 0.344269i
\(759\) 0 0
\(760\) 4.59627 + 3.85673i 0.166724 + 0.139898i
\(761\) 5.11305 28.9975i 0.185348 1.05116i −0.740160 0.672431i \(-0.765250\pi\)
0.925508 0.378729i \(-0.123639\pi\)
\(762\) 0 0
\(763\) 16.8530 14.1413i 0.610119 0.511950i
\(764\) −8.66025 15.0000i −0.313317 0.542681i
\(765\) 0 0
\(766\) 15.0000 25.9808i 0.541972 0.938723i
\(767\) −2.40614 13.6459i −0.0868807 0.492725i
\(768\) 0 0
\(769\) 0.939693 0.342020i 0.0338862 0.0123336i −0.325021 0.945707i \(-0.605372\pi\)
0.358908 + 0.933373i \(0.383149\pi\)
\(770\) −19.5311 + 7.10876i −0.703854 + 0.256182i
\(771\) 0 0
\(772\) −0.173648 0.984808i −0.00624973 0.0354440i
\(773\) 12.9904 22.5000i 0.467232 0.809269i −0.532068 0.846702i \(-0.678585\pi\)
0.999299 + 0.0374331i \(0.0119181\pi\)
\(774\) 0 0
\(775\) 8.00000 + 13.8564i 0.287368 + 0.497737i
\(776\) −2.65366 + 2.22668i −0.0952607 + 0.0799332i
\(777\) 0 0
\(778\) 8.33511 47.2708i 0.298828 1.69474i
\(779\) −10.6146 8.90673i −0.380308 0.319117i
\(780\) 0 0
\(781\) −33.8289 12.3127i −1.21049 0.440584i
\(782\) 31.1769 1.11488
\(783\) 0 0
\(784\) 15.0000 0.535714
\(785\) 27.6691 + 10.0707i 0.987553 + 0.359440i
\(786\) 0 0
\(787\) 19.9172 + 16.7125i 0.709970 + 0.595735i 0.924591 0.380962i \(-0.124407\pi\)
−0.214621 + 0.976697i \(0.568852\pi\)
\(788\) −0.902302 + 5.11721i −0.0321432 + 0.182293i
\(789\) 0 0
\(790\) −4.59627 + 3.85673i −0.163528 + 0.137216i
\(791\) 1.73205 + 3.00000i 0.0615846 + 0.106668i
\(792\) 0 0
\(793\) −3.50000 + 6.06218i −0.124289 + 0.215274i
\(794\) 8.72226 + 49.4664i 0.309541 + 1.75550i
\(795\) 0 0
\(796\) −18.7939 + 6.84040i −0.666130 + 0.242452i
\(797\) 50.4555 18.3643i 1.78722 0.650496i 0.787823 0.615902i \(-0.211208\pi\)
0.999401 0.0345940i \(-0.0110138\pi\)
\(798\) 0 0
\(799\) 6.25133 + 35.4531i 0.221156 + 1.25424i
\(800\) −5.19615 + 9.00000i −0.183712 + 0.318198i
\(801\) 0 0
\(802\) 10.5000 + 18.1865i 0.370768 + 0.642189i
\(803\) 18.5756 15.5868i 0.655518 0.550045i
\(804\) 0 0
\(805\) −2.08378 + 11.8177i −0.0734435 + 0.416519i
\(806\) −10.6146 8.90673i −0.373884 0.313726i
\(807\) 0 0
\(808\) 11.2763 + 4.10424i 0.396699 + 0.144387i
\(809\) −46.7654 −1.64418 −0.822091 0.569355i \(-0.807193\pi\)
−0.822091 + 0.569355i \(0.807193\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) −3.25519 1.18479i −0.114235 0.0415781i
\(813\) 0 0
\(814\) 32.1739 + 26.9971i 1.12769 + 0.946247i
\(815\) 4.81228 27.2918i 0.168567 0.955990i
\(816\) 0 0
\(817\) 3.06418 2.57115i 0.107202 0.0899532i
\(818\) 16.4545 + 28.5000i 0.575317 + 0.996479i
\(819\) 0 0
\(820\) −6.00000 + 10.3923i −0.209529 + 0.362915i
\(821\) 2.10537 + 11.9402i 0.0734780 + 0.416714i 0.999253 + 0.0386400i \(0.0123026\pi\)
−0.925775 + 0.378074i \(0.876586\pi\)
\(822\) 0 0
\(823\) 26.3114 9.57656i 0.917158 0.333818i 0.160050 0.987109i \(-0.448834\pi\)
0.757107 + 0.653291i \(0.226612\pi\)
\(824\) 13.0208 4.73917i 0.453600 0.165097i
\(825\) 0 0
\(826\) 8.33511 + 47.2708i 0.290016 + 1.64476i
\(827\) 5.19615 9.00000i 0.180688 0.312961i −0.761427 0.648251i \(-0.775501\pi\)
0.942115 + 0.335290i \(0.108834\pi\)
\(828\) 0 0
\(829\) −1.00000 1.73205i −0.0347314 0.0601566i 0.848137 0.529777i \(-0.177724\pi\)
−0.882869 + 0.469620i \(0.844391\pi\)
\(830\) 31.8439 26.7202i 1.10532 0.927471i
\(831\) 0 0
\(832\) −0.173648 + 0.984808i −0.00602017 + 0.0341421i
\(833\) −11.9415 10.0201i −0.413747 0.347175i
\(834\) 0 0
\(835\) −28.1908 10.2606i −0.975582 0.355083i
\(836\) −6.92820 −0.239617
\(837\) 0 0
\(838\) −12.0000 −0.414533
\(839\) 42.3175 + 15.4023i 1.46096 + 0.531747i 0.945630 0.325244i \(-0.105447\pi\)
0.515332 + 0.856991i \(0.327669\pi\)
\(840\) 0 0
\(841\) −19.9172 16.7125i −0.686798 0.576292i
\(842\) −7.51919 + 42.6434i −0.259128 + 1.46959i
\(843\) 0 0
\(844\) −7.66044 + 6.42788i −0.263683 + 0.221257i
\(845\) −10.3923 18.0000i −0.357506 0.619219i
\(846\) 0 0
\(847\) −1.00000 + 1.73205i −0.0343604 + 0.0595140i
\(848\) 0 0
\(849\) 0 0
\(850\) 16.9145 6.15636i 0.580161 0.211161i
\(851\) 22.7863 8.29355i 0.781106 0.284299i
\(852\) 0 0
\(853\) −5.90404 33.4835i −0.202150 1.14645i −0.901861 0.432026i \(-0.857799\pi\)
0.699711 0.714426i \(-0.253312\pi\)
\(854\) 12.1244 21.0000i 0.414887 0.718605i
\(855\) 0 0
\(856\) 0 0
\(857\) 17.2488 14.4734i 0.589207 0.494403i −0.298749 0.954332i \(-0.596569\pi\)
0.887956 + 0.459929i \(0.152125\pi\)
\(858\) 0 0
\(859\) 7.64052 43.3315i 0.260691 1.47845i −0.520339 0.853960i \(-0.674194\pi\)
0.781030 0.624493i \(-0.214694\pi\)
\(860\) −2.65366 2.22668i −0.0904889 0.0759292i
\(861\) 0 0
\(862\) 0 0
\(863\) 31.1769 1.06127 0.530637 0.847599i \(-0.321953\pi\)
0.530637 + 0.847599i \(0.321953\pi\)
\(864\) 0 0
\(865\) 33.0000 1.12203
\(866\) −17.9035 6.51636i −0.608387 0.221435i
\(867\) 0 0
\(868\) 12.2567 + 10.2846i 0.416020 + 0.349082i
\(869\) −1.20307 + 6.82295i −0.0408113 + 0.231453i
\(870\) 0 0
\(871\) 7.66044 6.42788i 0.259564 0.217800i
\(872\) 9.52628 + 16.5000i 0.322601 + 0.558761i
\(873\) 0 0
\(874\) −6.00000 + 10.3923i −0.202953 + 0.351525i
\(875\) 4.21074 + 23.8803i 0.142349 + 0.807302i
\(876\) 0 0
\(877\) −49.8037 + 18.1271i −1.68175 + 0.612108i −0.993548 0.113410i \(-0.963823\pi\)
−0.688203 + 0.725518i \(0.741600\pi\)
\(878\) −32.5519 + 11.8479i −1.09857 + 0.399848i
\(879\) 0 0
\(880\) −5.20945 29.5442i −0.175610 0.995936i
\(881\) −10.3923 + 18.0000i −0.350126 + 0.606435i −0.986271 0.165134i \(-0.947194\pi\)
0.636146 + 0.771569i \(0.280528\pi\)
\(882\) 0 0
\(883\) −28.0000 48.4974i −0.942275 1.63207i −0.761117 0.648614i \(-0.775349\pi\)
−0.181158 0.983454i \(-0.557984\pi\)
\(884\) −3.98048 + 3.34002i −0.133878 + 0.112337i
\(885\) 0 0
\(886\) −10.4189 + 59.0885i −0.350029 + 1.98512i
\(887\) 2.65366 + 2.22668i 0.0891010 + 0.0747647i 0.686250 0.727366i \(-0.259256\pi\)
−0.597149 + 0.802130i \(0.703700\pi\)
\(888\) 0 0
\(889\) −3.75877 1.36808i −0.126065 0.0458839i
\(890\) 15.5885 0.522526
\(891\) 0 0
\(892\) 2.00000 0.0669650
\(893\) −13.0208 4.73917i −0.435723 0.158590i
\(894\) 0 0
\(895\) −27.5776 23.1404i −0.921818 0.773497i
\(896\) 4.21074 23.8803i 0.140671 0.797785i
\(897\) 0 0
\(898\) 27.5776 23.1404i 0.920276 0.772204i
\(899\) −6.92820 12.0000i −0.231069 0.400222i
\(900\) 0 0
\(901\) 0 0
\(902\) 7.21842 + 40.9377i 0.240347 + 1.36308i
\(903\) 0 0
\(904\) −2.81908 + 1.02606i −0.0937611 + 0.0341263i
\(905\) 3.25519 1.18479i 0.108206 0.0393838i
\(906\) 0 0
\(907\) −9.02971 51.2100i −0.299826 1.70040i −0.646910 0.762566i \(-0.723939\pi\)
0.347084 0.937834i \(-0.387172\pi\)
\(908\) 1.73205 3.00000i 0.0574801 0.0995585i
\(909\) 0 0
\(910\) −3.00000 5.19615i −0.0994490 0.172251i
\(911\) −18.5756 + 15.5868i −0.615437 + 0.516413i −0.896365 0.443316i \(-0.853802\pi\)
0.280929 + 0.959729i \(0.409358\pi\)
\(912\) 0 0
\(913\) 8.33511 47.2708i 0.275852 1.56443i
\(914\) 38.4780 + 32.2869i 1.27274 + 1.06796i
\(915\) 0 0
\(916\) 0.939693 + 0.342020i 0.0310483 + 0.0113007i
\(917\) 6.92820 0.228789
\(918\) 0 0
\(919\) 2.00000 0.0659739 0.0329870 0.999456i \(-0.489498\pi\)
0.0329870 + 0.999456i \(0.489498\pi\)
\(920\) −9.76557 3.55438i −0.321961 0.117184i
\(921\) 0 0
\(922\) −18.3851 15.4269i −0.605480 0.508058i
\(923\) 1.80460 10.2344i 0.0593993 0.336870i
\(924\) 0 0
\(925\) 10.7246 8.99903i 0.352623 0.295886i
\(926\) −6.92820 12.0000i −0.227675 0.394344i
\(927\) 0 0
\(928\) 4.50000 7.79423i 0.147720 0.255858i
\(929\) −8.72226 49.4664i −0.286168 1.62294i −0.701084 0.713079i \(-0.747300\pi\)
0.414916 0.909860i \(-0.363811\pi\)
\(930\) 0 0
\(931\) 5.63816 2.05212i 0.184783 0.0672555i
\(932\) 24.4139 8.88594i 0.799705 0.291069i
\(933\) 0 0
\(934\) −6.25133 35.4531i −0.204550 1.16006i
\(935\) −15.5885 + 27.0000i −0.509797 + 0.882994i
\(936\) 0 0
\(937\) 12.5000 + 21.6506i 0.408357 + 0.707295i 0.994706 0.102763i \(-0.0327685\pi\)
−0.586349 + 0.810059i \(0.699435\pi\)
\(938\) −26.5366 + 22.2668i −0.866449 + 0.727037i
\(939\) 0 0
\(940\) −2.08378 + 11.8177i −0.0679653 + 0.385451i
\(941\) 38.4780 + 32.2869i 1.25435 + 1.05252i 0.996260 + 0.0864006i \(0.0275365\pi\)
0.258087 + 0.966122i \(0.416908\pi\)
\(942\) 0 0
\(943\) 22.5526 + 8.20848i 0.734414 + 0.267305i
\(944\) −69.2820 −2.25494
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) −16.2760 5.92396i −0.528897 0.192503i 0.0637485 0.997966i \(-0.479694\pi\)
−0.592646 + 0.805463i \(0.701917\pi\)
\(948\) 0 0
\(949\) 5.36231 + 4.49951i 0.174068 + 0.146060i
\(950\) −1.20307 + 6.82295i −0.0390327 + 0.221366i
\(951\) 0 0
\(952\) −13.7888 + 11.5702i −0.446898 + 0.374992i
\(953\) 2.59808 + 4.50000i 0.0841599 + 0.145769i 0.905033 0.425341i \(-0.139846\pi\)
−0.820873 + 0.571111i \(0.806513\pi\)
\(954\) 0 0
\(955\) 15.0000 25.9808i 0.485389 0.840718i
\(956\) −4.81228 27.2918i −0.155640 0.882680i
\(957\) 0 0
\(958\) 39.4671 14.3648i 1.27512 0.464107i
\(959\) −3.25519 + 1.18479i −0.105116 + 0.0382589i
\(960\) 0 0
\(961\) 5.73039 + 32.4987i 0.184851 + 1.04834i
\(962\) −6.06218 + 10.5000i −0.195452 + 0.338534i
\(963\) 0 0
\(964\) −14.5000 25.1147i −0.467014 0.808891i
\(965\) 1.32683 1.11334i 0.0427121 0.0358397i
\(966\) 0 0
\(967\) −7.98782 + 45.3012i −0.256871 + 1.45679i 0.534354 + 0.845261i \(0.320555\pi\)
−0.791224 + 0.611526i \(0.790556\pi\)
\(968\) −1.32683 1.11334i −0.0426459 0.0357841i
\(969\) 0 0
\(970\) 5.63816 + 2.05212i 0.181030 + 0.0658896i
\(971\) 31.1769 1.00051 0.500257 0.865877i \(-0.333239\pi\)
0.500257 + 0.865877i \(0.333239\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 26.0415 + 9.47834i 0.834424 + 0.303706i
\(975\) 0 0
\(976\) 26.8116 + 22.4976i 0.858217 + 0.720130i
\(977\) −8.42149 + 47.7606i −0.269427 + 1.52800i 0.486697 + 0.873571i \(0.338201\pi\)
−0.756125 + 0.654428i \(0.772910\pi\)
\(978\) 0 0
\(979\) 13.7888 11.5702i 0.440692 0.369784i
\(980\) −2.59808 4.50000i −0.0829925 0.143747i
\(981\) 0 0
\(982\) 15.0000 25.9808i 0.478669 0.829079i
\(983\) −6.01535 34.1147i −0.191860 1.08809i −0.916820 0.399301i \(-0.869253\pi\)
0.724960 0.688791i \(-0.241858\pi\)
\(984\) 0 0
\(985\) −8.45723 + 3.07818i −0.269470 + 0.0980790i
\(986\) −14.6484 + 5.33157i −0.466499 + 0.169792i
\(987\) 0 0
\(988\) −0.347296 1.96962i −0.0110490 0.0626618i
\(989\) −3.46410 + 6.00000i −0.110152 + 0.190789i
\(990\) 0 0
\(991\) 17.0000 + 29.4449i 0.540023 + 0.935347i 0.998902 + 0.0468483i \(0.0149177\pi\)
−0.458879 + 0.888499i \(0.651749\pi\)
\(992\) −31.8439 + 26.7202i −1.01104 + 0.848367i
\(993\) 0 0
\(994\) −6.25133 + 35.4531i −0.198280 + 1.12450i
\(995\) −26.5366 22.2668i −0.841265 0.705906i
\(996\) 0 0
\(997\) 6.57785 + 2.39414i 0.208323 + 0.0758232i 0.444074 0.895990i \(-0.353533\pi\)
−0.235751 + 0.971813i \(0.575755\pi\)
\(998\) −17.3205 −0.548271
\(999\) 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.o.568.1 12
3.2 odd 2 inner 729.2.e.o.568.2 12
9.2 odd 6 inner 729.2.e.o.82.1 12
9.4 even 3 inner 729.2.e.o.325.2 12
9.5 odd 6 inner 729.2.e.o.325.1 12
9.7 even 3 inner 729.2.e.o.82.2 12
27.2 odd 18 inner 729.2.e.o.406.1 12
27.4 even 9 81.2.c.b.28.1 4
27.5 odd 18 81.2.c.b.55.2 4
27.7 even 9 inner 729.2.e.o.163.1 12
27.11 odd 18 inner 729.2.e.o.649.1 12
27.13 even 9 81.2.a.a.1.2 yes 2
27.14 odd 18 81.2.a.a.1.1 2
27.16 even 9 inner 729.2.e.o.649.2 12
27.20 odd 18 inner 729.2.e.o.163.2 12
27.22 even 9 81.2.c.b.55.1 4
27.23 odd 18 81.2.c.b.28.2 4
27.25 even 9 inner 729.2.e.o.406.2 12
108.23 even 18 1296.2.i.s.433.1 4
108.31 odd 18 1296.2.i.s.433.2 4
108.59 even 18 1296.2.i.s.865.1 4
108.67 odd 18 1296.2.a.o.1.1 2
108.95 even 18 1296.2.a.o.1.2 2
108.103 odd 18 1296.2.i.s.865.2 4
135.13 odd 36 2025.2.b.k.649.1 4
135.14 odd 18 2025.2.a.j.1.2 2
135.67 odd 36 2025.2.b.k.649.4 4
135.68 even 36 2025.2.b.k.649.3 4
135.94 even 18 2025.2.a.j.1.1 2
135.122 even 36 2025.2.b.k.649.2 4
189.13 odd 18 3969.2.a.i.1.2 2
189.41 even 18 3969.2.a.i.1.1 2
216.13 even 18 5184.2.a.br.1.2 2
216.67 odd 18 5184.2.a.bq.1.2 2
216.149 odd 18 5184.2.a.br.1.1 2
216.203 even 18 5184.2.a.bq.1.1 2
297.175 odd 18 9801.2.a.v.1.1 2
297.230 even 18 9801.2.a.v.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.a.a.1.1 2 27.14 odd 18
81.2.a.a.1.2 yes 2 27.13 even 9
81.2.c.b.28.1 4 27.4 even 9
81.2.c.b.28.2 4 27.23 odd 18
81.2.c.b.55.1 4 27.22 even 9
81.2.c.b.55.2 4 27.5 odd 18
729.2.e.o.82.1 12 9.2 odd 6 inner
729.2.e.o.82.2 12 9.7 even 3 inner
729.2.e.o.163.1 12 27.7 even 9 inner
729.2.e.o.163.2 12 27.20 odd 18 inner
729.2.e.o.325.1 12 9.5 odd 6 inner
729.2.e.o.325.2 12 9.4 even 3 inner
729.2.e.o.406.1 12 27.2 odd 18 inner
729.2.e.o.406.2 12 27.25 even 9 inner
729.2.e.o.568.1 12 1.1 even 1 trivial
729.2.e.o.568.2 12 3.2 odd 2 inner
729.2.e.o.649.1 12 27.11 odd 18 inner
729.2.e.o.649.2 12 27.16 even 9 inner
1296.2.a.o.1.1 2 108.67 odd 18
1296.2.a.o.1.2 2 108.95 even 18
1296.2.i.s.433.1 4 108.23 even 18
1296.2.i.s.433.2 4 108.31 odd 18
1296.2.i.s.865.1 4 108.59 even 18
1296.2.i.s.865.2 4 108.103 odd 18
2025.2.a.j.1.1 2 135.94 even 18
2025.2.a.j.1.2 2 135.14 odd 18
2025.2.b.k.649.1 4 135.13 odd 36
2025.2.b.k.649.2 4 135.122 even 36
2025.2.b.k.649.3 4 135.68 even 36
2025.2.b.k.649.4 4 135.67 odd 36
3969.2.a.i.1.1 2 189.41 even 18
3969.2.a.i.1.2 2 189.13 odd 18
5184.2.a.bq.1.1 2 216.203 even 18
5184.2.a.bq.1.2 2 216.67 odd 18
5184.2.a.br.1.1 2 216.149 odd 18
5184.2.a.br.1.2 2 216.13 even 18
9801.2.a.v.1.1 2 297.175 odd 18
9801.2.a.v.1.2 2 297.230 even 18