Properties

Label 726.2.e.m.511.1
Level $726$
Weight $2$
Character 726.511
Analytic conductor $5.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [726,2,Mod(487,726)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(726, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("726.487");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.e (of order \(5\), degree \(4\), 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: \(5.79713918674\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 511.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 726.511
Dual form 726.2.e.m.493.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.23607 + 3.80423i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.61803 + 1.17557i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.23607 + 3.80423i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.61803 + 1.17557i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +4.00000 q^{10} +1.00000 q^{12} +(-1.23607 - 3.80423i) q^{13} +(1.61803 + 1.17557i) q^{14} +(3.23607 - 2.35114i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.618034 - 1.90211i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.23607 - 3.80423i) q^{20} +2.00000 q^{21} -6.00000 q^{23} +(-0.309017 - 0.951057i) q^{24} +(-8.89919 - 6.46564i) q^{25} +(-3.23607 + 2.35114i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.618034 - 1.90211i) q^{28} +(8.09017 - 5.87785i) q^{29} +(-3.23607 - 2.35114i) q^{30} +(-2.47214 - 7.60845i) q^{31} -1.00000 q^{32} -2.00000 q^{34} +(-2.47214 - 7.60845i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(1.61803 - 1.17557i) q^{37} +(-1.23607 + 3.80423i) q^{39} +(-3.23607 + 2.35114i) q^{40} +(1.61803 + 1.17557i) q^{41} +(-0.618034 - 1.90211i) q^{42} -4.00000 q^{43} -4.00000 q^{45} +(1.85410 + 5.70634i) q^{46} +(1.61803 + 1.17557i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(-3.39919 + 10.4616i) q^{50} +(-1.61803 + 1.17557i) q^{51} +(3.23607 + 2.35114i) q^{52} +(1.23607 + 3.80423i) q^{53} -1.00000 q^{54} -2.00000 q^{56} +(-8.09017 - 5.87785i) q^{58} +(-1.23607 + 3.80423i) q^{60} +(2.47214 - 7.60845i) q^{61} +(-6.47214 + 4.70228i) q^{62} +(-1.61803 - 1.17557i) q^{63} +(0.309017 + 0.951057i) q^{64} +16.0000 q^{65} -12.0000 q^{67} +(0.618034 + 1.90211i) q^{68} +(4.85410 + 3.52671i) q^{69} +(-6.47214 + 4.70228i) q^{70} +(0.618034 - 1.90211i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-4.85410 + 3.52671i) q^{73} +(-1.61803 - 1.17557i) q^{74} +(3.39919 + 10.4616i) q^{75} +4.00000 q^{78} +(-3.09017 - 9.51057i) q^{79} +(3.23607 + 2.35114i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.618034 - 1.90211i) q^{82} +(-1.23607 + 3.80423i) q^{83} +(-1.61803 + 1.17557i) q^{84} +(6.47214 + 4.70228i) q^{85} +(1.23607 + 3.80423i) q^{86} -10.0000 q^{87} +10.0000 q^{89} +(1.23607 + 3.80423i) q^{90} +(6.47214 + 4.70228i) q^{91} +(4.85410 - 3.52671i) q^{92} +(-2.47214 + 7.60845i) q^{93} +(0.618034 - 1.90211i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-0.618034 - 1.90211i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 16 q^{10} + 4 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{15} - q^{16} - 2 q^{17} + q^{18} + 4 q^{20} + 8 q^{21} - 24 q^{23} + q^{24} - 11 q^{25} - 4 q^{26} - q^{27} - 2 q^{28} + 10 q^{29} - 4 q^{30} + 8 q^{31} - 4 q^{32} - 8 q^{34} + 8 q^{35} - q^{36} + 2 q^{37} + 4 q^{39} - 4 q^{40} + 2 q^{41} + 2 q^{42} - 16 q^{43} - 16 q^{45} - 6 q^{46} + 2 q^{47} - q^{48} + 3 q^{49} + 11 q^{50} - 2 q^{51} + 4 q^{52} - 4 q^{53} - 4 q^{54} - 8 q^{56} - 10 q^{58} + 4 q^{60} - 8 q^{61} - 8 q^{62} - 2 q^{63} - q^{64} + 64 q^{65} - 48 q^{67} - 2 q^{68} + 6 q^{69} - 8 q^{70} - 2 q^{71} + q^{72} - 6 q^{73} - 2 q^{74} - 11 q^{75} + 16 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 2 q^{82} + 4 q^{83} - 2 q^{84} + 8 q^{85} - 4 q^{86} - 40 q^{87} + 40 q^{89} - 4 q^{90} + 8 q^{91} + 6 q^{92} + 8 q^{93} - 2 q^{94} + q^{96} + 2 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(607\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −1.23607 + 3.80423i −0.552786 + 1.70130i 0.148932 + 0.988847i \(0.452416\pi\)
−0.701719 + 0.712454i \(0.747584\pi\)
\(6\) −0.309017 + 0.951057i −0.126156 + 0.388267i
\(7\) −1.61803 + 1.17557i −0.611559 + 0.444324i −0.849963 0.526842i \(-0.823376\pi\)
0.238404 + 0.971166i \(0.423376\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 4.00000 1.26491
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) −1.23607 3.80423i −0.342824 1.05510i −0.962739 0.270434i \(-0.912833\pi\)
0.619915 0.784669i \(-0.287167\pi\)
\(14\) 1.61803 + 1.17557i 0.432438 + 0.314184i
\(15\) 3.23607 2.35114i 0.835549 0.607062i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 0.618034 1.90211i 0.149895 0.461330i −0.847713 0.530456i \(-0.822021\pi\)
0.997608 + 0.0691254i \(0.0220209\pi\)
\(18\) 0.809017 0.587785i 0.190687 0.138542i
\(19\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(20\) −1.23607 3.80423i −0.276393 0.850651i
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −0.309017 0.951057i −0.0630778 0.194134i
\(25\) −8.89919 6.46564i −1.77984 1.29313i
\(26\) −3.23607 + 2.35114i −0.634645 + 0.461097i
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 0.618034 1.90211i 0.116797 0.359466i
\(29\) 8.09017 5.87785i 1.50231 1.09149i 0.532855 0.846206i \(-0.321119\pi\)
0.969451 0.245284i \(-0.0788811\pi\)
\(30\) −3.23607 2.35114i −0.590822 0.429258i
\(31\) −2.47214 7.60845i −0.444009 1.36652i −0.883567 0.468304i \(-0.844865\pi\)
0.439558 0.898214i \(-0.355135\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −2.47214 7.60845i −0.417867 1.28606i
\(36\) −0.809017 0.587785i −0.134836 0.0979642i
\(37\) 1.61803 1.17557i 0.266003 0.193263i −0.446786 0.894641i \(-0.647432\pi\)
0.712789 + 0.701378i \(0.247432\pi\)
\(38\) 0 0
\(39\) −1.23607 + 3.80423i −0.197929 + 0.609164i
\(40\) −3.23607 + 2.35114i −0.511667 + 0.371748i
\(41\) 1.61803 + 1.17557i 0.252694 + 0.183593i 0.706920 0.707293i \(-0.250084\pi\)
−0.454226 + 0.890887i \(0.650084\pi\)
\(42\) −0.618034 1.90211i −0.0953647 0.293502i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −4.00000 −0.596285
\(46\) 1.85410 + 5.70634i 0.273372 + 0.841354i
\(47\) 1.61803 + 1.17557i 0.236015 + 0.171475i 0.699506 0.714627i \(-0.253403\pi\)
−0.463491 + 0.886101i \(0.653403\pi\)
\(48\) −0.809017 + 0.587785i −0.116772 + 0.0848395i
\(49\) −0.927051 + 2.85317i −0.132436 + 0.407596i
\(50\) −3.39919 + 10.4616i −0.480718 + 1.47950i
\(51\) −1.61803 + 1.17557i −0.226570 + 0.164613i
\(52\) 3.23607 + 2.35114i 0.448762 + 0.326045i
\(53\) 1.23607 + 3.80423i 0.169787 + 0.522551i 0.999357 0.0358519i \(-0.0114145\pi\)
−0.829570 + 0.558403i \(0.811414\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) −8.09017 5.87785i −1.06229 0.771800i
\(59\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(60\) −1.23607 + 3.80423i −0.159576 + 0.491123i
\(61\) 2.47214 7.60845i 0.316525 0.974162i −0.658598 0.752495i \(-0.728850\pi\)
0.975122 0.221667i \(-0.0711499\pi\)
\(62\) −6.47214 + 4.70228i −0.821962 + 0.597190i
\(63\) −1.61803 1.17557i −0.203853 0.148108i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 16.0000 1.98456
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0.618034 + 1.90211i 0.0749476 + 0.230665i
\(69\) 4.85410 + 3.52671i 0.584365 + 0.424566i
\(70\) −6.47214 + 4.70228i −0.773568 + 0.562030i
\(71\) 0.618034 1.90211i 0.0733471 0.225739i −0.907662 0.419703i \(-0.862134\pi\)
0.981009 + 0.193963i \(0.0621343\pi\)
\(72\) −0.309017 + 0.951057i −0.0364180 + 0.112083i
\(73\) −4.85410 + 3.52671i −0.568130 + 0.412770i −0.834425 0.551121i \(-0.814200\pi\)
0.266296 + 0.963891i \(0.414200\pi\)
\(74\) −1.61803 1.17557i −0.188093 0.136657i
\(75\) 3.39919 + 10.4616i 0.392504 + 1.20800i
\(76\) 0 0
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) −3.09017 9.51057i −0.347671 1.07002i −0.960138 0.279526i \(-0.909823\pi\)
0.612467 0.790496i \(-0.290177\pi\)
\(80\) 3.23607 + 2.35114i 0.361803 + 0.262866i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0.618034 1.90211i 0.0682504 0.210053i
\(83\) −1.23607 + 3.80423i −0.135676 + 0.417568i −0.995695 0.0926948i \(-0.970452\pi\)
0.860018 + 0.510263i \(0.170452\pi\)
\(84\) −1.61803 + 1.17557i −0.176542 + 0.128265i
\(85\) 6.47214 + 4.70228i 0.702002 + 0.510034i
\(86\) 1.23607 + 3.80423i 0.133289 + 0.410220i
\(87\) −10.0000 −1.07211
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 1.23607 + 3.80423i 0.130293 + 0.401001i
\(91\) 6.47214 + 4.70228i 0.678464 + 0.492933i
\(92\) 4.85410 3.52671i 0.506075 0.367685i
\(93\) −2.47214 + 7.60845i −0.256349 + 0.788960i
\(94\) 0.618034 1.90211i 0.0637453 0.196188i
\(95\) 0 0
\(96\) 0.809017 + 0.587785i 0.0825700 + 0.0599906i
\(97\) −0.618034 1.90211i −0.0627518 0.193130i 0.914766 0.403985i \(-0.132375\pi\)
−0.977517 + 0.210855i \(0.932375\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 11.0000 1.10000
\(101\) −0.618034 1.90211i −0.0614967 0.189267i 0.915588 0.402117i \(-0.131726\pi\)
−0.977085 + 0.212850i \(0.931726\pi\)
\(102\) 1.61803 + 1.17557i 0.160209 + 0.116399i
\(103\) −3.23607 + 2.35114i −0.318859 + 0.231665i −0.735689 0.677320i \(-0.763141\pi\)
0.416829 + 0.908985i \(0.363141\pi\)
\(104\) 1.23607 3.80423i 0.121206 0.373035i
\(105\) −2.47214 + 7.60845i −0.241256 + 0.742509i
\(106\) 3.23607 2.35114i 0.314315 0.228363i
\(107\) −9.70820 7.05342i −0.938527 0.681880i 0.00953827 0.999955i \(-0.496964\pi\)
−0.948066 + 0.318074i \(0.896964\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) −20.0000 −1.91565 −0.957826 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0.618034 + 1.90211i 0.0583987 + 0.179733i
\(113\) 4.85410 + 3.52671i 0.456636 + 0.331765i 0.792210 0.610249i \(-0.208930\pi\)
−0.335575 + 0.942014i \(0.608930\pi\)
\(114\) 0 0
\(115\) 7.41641 22.8254i 0.691584 2.12848i
\(116\) −3.09017 + 9.51057i −0.286915 + 0.883034i
\(117\) 3.23607 2.35114i 0.299175 0.217363i
\(118\) 0 0
\(119\) 1.23607 + 3.80423i 0.113310 + 0.348733i
\(120\) 4.00000 0.365148
\(121\) 0 0
\(122\) −8.00000 −0.724286
\(123\) −0.618034 1.90211i −0.0557262 0.171508i
\(124\) 6.47214 + 4.70228i 0.581215 + 0.422277i
\(125\) 19.4164 14.1068i 1.73666 1.26175i
\(126\) −0.618034 + 1.90211i −0.0550588 + 0.169454i
\(127\) 6.79837 20.9232i 0.603258 1.85664i 0.0949102 0.995486i \(-0.469744\pi\)
0.508348 0.861152i \(-0.330256\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) 3.23607 + 2.35114i 0.284920 + 0.207006i
\(130\) −4.94427 15.2169i −0.433641 1.33461i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.70820 + 11.4127i 0.320340 + 0.985905i
\(135\) 3.23607 + 2.35114i 0.278516 + 0.202354i
\(136\) 1.61803 1.17557i 0.138745 0.100804i
\(137\) −0.618034 + 1.90211i −0.0528022 + 0.162508i −0.973980 0.226633i \(-0.927228\pi\)
0.921178 + 0.389141i \(0.127228\pi\)
\(138\) 1.85410 5.70634i 0.157832 0.485756i
\(139\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(140\) 6.47214 + 4.70228i 0.546995 + 0.397415i
\(141\) −0.618034 1.90211i −0.0520479 0.160187i
\(142\) −2.00000 −0.167836
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 12.3607 + 38.0423i 1.02650 + 3.15924i
\(146\) 4.85410 + 3.52671i 0.401728 + 0.291873i
\(147\) 2.42705 1.76336i 0.200180 0.145439i
\(148\) −0.618034 + 1.90211i −0.0508021 + 0.156353i
\(149\) 3.09017 9.51057i 0.253157 0.779136i −0.741031 0.671471i \(-0.765663\pi\)
0.994187 0.107665i \(-0.0343373\pi\)
\(150\) 8.89919 6.46564i 0.726616 0.527917i
\(151\) 1.61803 + 1.17557i 0.131674 + 0.0956666i 0.651673 0.758500i \(-0.274068\pi\)
−0.519999 + 0.854167i \(0.674068\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 32.0000 2.57030
\(156\) −1.23607 3.80423i −0.0989646 0.304582i
\(157\) −14.5623 10.5801i −1.16220 0.844387i −0.172144 0.985072i \(-0.555069\pi\)
−0.990054 + 0.140685i \(0.955069\pi\)
\(158\) −8.09017 + 5.87785i −0.643619 + 0.467617i
\(159\) 1.23607 3.80423i 0.0980266 0.301695i
\(160\) 1.23607 3.80423i 0.0977198 0.300750i
\(161\) 9.70820 7.05342i 0.765114 0.555888i
\(162\) 0.809017 + 0.587785i 0.0635624 + 0.0461808i
\(163\) 1.23607 + 3.80423i 0.0968163 + 0.297970i 0.987723 0.156217i \(-0.0499299\pi\)
−0.890906 + 0.454187i \(0.849930\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 3.70820 + 11.4127i 0.286949 + 0.883140i 0.985808 + 0.167879i \(0.0536919\pi\)
−0.698858 + 0.715260i \(0.746308\pi\)
\(168\) 1.61803 + 1.17557i 0.124834 + 0.0906972i
\(169\) −2.42705 + 1.76336i −0.186696 + 0.135643i
\(170\) 2.47214 7.60845i 0.189604 0.583542i
\(171\) 0 0
\(172\) 3.23607 2.35114i 0.246748 0.179273i
\(173\) −4.85410 3.52671i −0.369051 0.268131i 0.387767 0.921758i \(-0.373247\pi\)
−0.756817 + 0.653627i \(0.773247\pi\)
\(174\) 3.09017 + 9.51057i 0.234265 + 0.720994i
\(175\) 22.0000 1.66304
\(176\) 0 0
\(177\) 0 0
\(178\) −3.09017 9.51057i −0.231618 0.712847i
\(179\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(180\) 3.23607 2.35114i 0.241202 0.175244i
\(181\) 0.618034 1.90211i 0.0459381 0.141383i −0.925457 0.378854i \(-0.876318\pi\)
0.971395 + 0.237471i \(0.0763184\pi\)
\(182\) 2.47214 7.60845i 0.183247 0.563976i
\(183\) −6.47214 + 4.70228i −0.478434 + 0.347603i
\(184\) −4.85410 3.52671i −0.357849 0.259993i
\(185\) 2.47214 + 7.60845i 0.181755 + 0.559385i
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −2.00000 −0.145865
\(189\) 0.618034 + 1.90211i 0.0449554 + 0.138358i
\(190\) 0 0
\(191\) −17.7984 + 12.9313i −1.28785 + 0.935674i −0.999760 0.0219304i \(-0.993019\pi\)
−0.288086 + 0.957605i \(0.593019\pi\)
\(192\) 0.309017 0.951057i 0.0223014 0.0686366i
\(193\) −4.32624 + 13.3148i −0.311409 + 0.958420i 0.665798 + 0.746132i \(0.268091\pi\)
−0.977207 + 0.212287i \(0.931909\pi\)
\(194\) −1.61803 + 1.17557i −0.116168 + 0.0844010i
\(195\) −12.9443 9.40456i −0.926959 0.673475i
\(196\) −0.927051 2.85317i −0.0662179 0.203798i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −3.39919 10.4616i −0.240359 0.739748i
\(201\) 9.70820 + 7.05342i 0.684764 + 0.497510i
\(202\) −1.61803 + 1.17557i −0.113844 + 0.0827129i
\(203\) −6.18034 + 19.0211i −0.433775 + 1.33502i
\(204\) 0.618034 1.90211i 0.0432710 0.133175i
\(205\) −6.47214 + 4.70228i −0.452034 + 0.328422i
\(206\) 3.23607 + 2.35114i 0.225468 + 0.163812i
\(207\) −1.85410 5.70634i −0.128869 0.396618i
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 8.00000 0.552052
\(211\) −3.70820 11.4127i −0.255283 0.785681i −0.993774 0.111417i \(-0.964461\pi\)
0.738490 0.674264i \(-0.235539\pi\)
\(212\) −3.23607 2.35114i −0.222254 0.161477i
\(213\) −1.61803 + 1.17557i −0.110866 + 0.0805488i
\(214\) −3.70820 + 11.4127i −0.253488 + 0.780155i
\(215\) 4.94427 15.2169i 0.337197 1.03778i
\(216\) 0.809017 0.587785i 0.0550466 0.0399937i
\(217\) 12.9443 + 9.40456i 0.878714 + 0.638423i
\(218\) 6.18034 + 19.0211i 0.418585 + 1.28827i
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0.618034 + 1.90211i 0.0414797 + 0.127661i
\(223\) 12.9443 + 9.40456i 0.866813 + 0.629776i 0.929730 0.368243i \(-0.120040\pi\)
−0.0629172 + 0.998019i \(0.520040\pi\)
\(224\) 1.61803 1.17557i 0.108109 0.0785461i
\(225\) 3.39919 10.4616i 0.226612 0.697441i
\(226\) 1.85410 5.70634i 0.123333 0.379580i
\(227\) −9.70820 + 7.05342i −0.644356 + 0.468152i −0.861344 0.508022i \(-0.830377\pi\)
0.216988 + 0.976174i \(0.430377\pi\)
\(228\) 0 0
\(229\) 3.09017 + 9.51057i 0.204204 + 0.628476i 0.999745 + 0.0225760i \(0.00718678\pi\)
−0.795541 + 0.605900i \(0.792813\pi\)
\(230\) −24.0000 −1.58251
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) 1.85410 + 5.70634i 0.121466 + 0.373835i 0.993241 0.116073i \(-0.0370306\pi\)
−0.871774 + 0.489907i \(0.837031\pi\)
\(234\) −3.23607 2.35114i −0.211548 0.153699i
\(235\) −6.47214 + 4.70228i −0.422196 + 0.306743i
\(236\) 0 0
\(237\) −3.09017 + 9.51057i −0.200728 + 0.617778i
\(238\) 3.23607 2.35114i 0.209763 0.152402i
\(239\) −16.1803 11.7557i −1.04662 0.760413i −0.0750525 0.997180i \(-0.523912\pi\)
−0.971567 + 0.236766i \(0.923912\pi\)
\(240\) −1.23607 3.80423i −0.0797878 0.245562i
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 2.47214 + 7.60845i 0.158262 + 0.487081i
\(245\) −9.70820 7.05342i −0.620234 0.450627i
\(246\) −1.61803 + 1.17557i −0.103162 + 0.0749516i
\(247\) 0 0
\(248\) 2.47214 7.60845i 0.156981 0.483137i
\(249\) 3.23607 2.35114i 0.205077 0.148998i
\(250\) −19.4164 14.1068i −1.22800 0.892195i
\(251\) −2.47214 7.60845i −0.156040 0.480241i 0.842225 0.539126i \(-0.181245\pi\)
−0.998265 + 0.0588851i \(0.981245\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) −22.0000 −1.38040
\(255\) −2.47214 7.60845i −0.154811 0.476460i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −14.5623 + 10.5801i −0.908372 + 0.659971i −0.940603 0.339510i \(-0.889739\pi\)
0.0322308 + 0.999480i \(0.489739\pi\)
\(258\) 1.23607 3.80423i 0.0769542 0.236841i
\(259\) −1.23607 + 3.80423i −0.0768055 + 0.236383i
\(260\) −12.9443 + 9.40456i −0.802770 + 0.583246i
\(261\) 8.09017 + 5.87785i 0.500769 + 0.363830i
\(262\) 3.70820 + 11.4127i 0.229094 + 0.705078i
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) −16.0000 −0.982872
\(266\) 0 0
\(267\) −8.09017 5.87785i −0.495110 0.359719i
\(268\) 9.70820 7.05342i 0.593023 0.430856i
\(269\) −6.18034 + 19.0211i −0.376822 + 1.15974i 0.565419 + 0.824804i \(0.308714\pi\)
−0.942241 + 0.334935i \(0.891286\pi\)
\(270\) 1.23607 3.80423i 0.0752247 0.231518i
\(271\) 17.7984 12.9313i 1.08117 0.785519i 0.103287 0.994652i \(-0.467064\pi\)
0.977887 + 0.209133i \(0.0670640\pi\)
\(272\) −1.61803 1.17557i −0.0981077 0.0712794i
\(273\) −2.47214 7.60845i −0.149620 0.460484i
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) −2.47214 7.60845i −0.148536 0.457148i 0.848913 0.528533i \(-0.177258\pi\)
−0.997449 + 0.0713858i \(0.977258\pi\)
\(278\) 0 0
\(279\) 6.47214 4.70228i 0.387477 0.281518i
\(280\) 2.47214 7.60845i 0.147738 0.454692i
\(281\) −6.79837 + 20.9232i −0.405557 + 1.24818i 0.514872 + 0.857267i \(0.327839\pi\)
−0.920429 + 0.390909i \(0.872161\pi\)
\(282\) −1.61803 + 1.17557i −0.0963525 + 0.0700042i
\(283\) 3.23607 + 2.35114i 0.192364 + 0.139761i 0.679799 0.733399i \(-0.262067\pi\)
−0.487434 + 0.873160i \(0.662067\pi\)
\(284\) 0.618034 + 1.90211i 0.0366736 + 0.112870i
\(285\) 0 0
\(286\) 0 0
\(287\) −4.00000 −0.236113
\(288\) −0.309017 0.951057i −0.0182090 0.0560415i
\(289\) 10.5172 + 7.64121i 0.618660 + 0.449483i
\(290\) 32.3607 23.5114i 1.90028 1.38064i
\(291\) −0.618034 + 1.90211i −0.0362298 + 0.111504i
\(292\) 1.85410 5.70634i 0.108503 0.333938i
\(293\) 11.3262 8.22899i 0.661686 0.480743i −0.205546 0.978647i \(-0.565897\pi\)
0.867232 + 0.497905i \(0.165897\pi\)
\(294\) −2.42705 1.76336i −0.141548 0.102841i
\(295\) 0 0
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 7.41641 + 22.8254i 0.428902 + 1.32002i
\(300\) −8.89919 6.46564i −0.513795 0.373294i
\(301\) 6.47214 4.70228i 0.373048 0.271035i
\(302\) 0.618034 1.90211i 0.0355639 0.109454i
\(303\) −0.618034 + 1.90211i −0.0355051 + 0.109274i
\(304\) 0 0
\(305\) 25.8885 + 18.8091i 1.48237 + 1.07701i
\(306\) −0.618034 1.90211i −0.0353307 0.108737i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) −9.88854 30.4338i −0.561632 1.72852i
\(311\) −1.61803 1.17557i −0.0917503 0.0666605i 0.540964 0.841046i \(-0.318059\pi\)
−0.632715 + 0.774385i \(0.718059\pi\)
\(312\) −3.23607 + 2.35114i −0.183206 + 0.133107i
\(313\) −1.85410 + 5.70634i −0.104800 + 0.322541i −0.989683 0.143271i \(-0.954238\pi\)
0.884883 + 0.465813i \(0.154238\pi\)
\(314\) −5.56231 + 17.1190i −0.313899 + 0.966082i
\(315\) 6.47214 4.70228i 0.364664 0.264944i
\(316\) 8.09017 + 5.87785i 0.455108 + 0.330655i
\(317\) −9.88854 30.4338i −0.555396 1.70933i −0.694895 0.719111i \(-0.744549\pi\)
0.139499 0.990222i \(-0.455451\pi\)
\(318\) −4.00000 −0.224309
\(319\) 0 0
\(320\) −4.00000 −0.223607
\(321\) 3.70820 + 11.4127i 0.206972 + 0.636994i
\(322\) −9.70820 7.05342i −0.541017 0.393072i
\(323\) 0 0
\(324\) 0.309017 0.951057i 0.0171676 0.0528365i
\(325\) −13.5967 + 41.8465i −0.754212 + 2.32123i
\(326\) 3.23607 2.35114i 0.179229 0.130218i
\(327\) 16.1803 + 11.7557i 0.894775 + 0.650092i
\(328\) 0.618034 + 1.90211i 0.0341252 + 0.105027i
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −1.23607 3.80423i −0.0678380 0.208784i
\(333\) 1.61803 + 1.17557i 0.0886677 + 0.0644209i
\(334\) 9.70820 7.05342i 0.531209 0.385946i
\(335\) 14.8328 45.6507i 0.810403 2.49416i
\(336\) 0.618034 1.90211i 0.0337165 0.103769i
\(337\) −17.7984 + 12.9313i −0.969539 + 0.704411i −0.955347 0.295488i \(-0.904518\pi\)
−0.0141927 + 0.999899i \(0.504518\pi\)
\(338\) 2.42705 + 1.76336i 0.132014 + 0.0959139i
\(339\) −1.85410 5.70634i −0.100701 0.309926i
\(340\) −8.00000 −0.433861
\(341\) 0 0
\(342\) 0 0
\(343\) −6.18034 19.0211i −0.333707 1.02704i
\(344\) −3.23607 2.35114i −0.174477 0.126765i
\(345\) −19.4164 + 14.1068i −1.04534 + 0.759487i
\(346\) −1.85410 + 5.70634i −0.0996771 + 0.306775i
\(347\) 3.70820 11.4127i 0.199067 0.612665i −0.800838 0.598881i \(-0.795612\pi\)
0.999905 0.0137839i \(-0.00438768\pi\)
\(348\) 8.09017 5.87785i 0.433679 0.315086i
\(349\) −16.1803 11.7557i −0.866114 0.629268i 0.0634276 0.997986i \(-0.479797\pi\)
−0.929541 + 0.368718i \(0.879797\pi\)
\(350\) −6.79837 20.9232i −0.363388 1.11839i
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 6.47214 + 4.70228i 0.343505 + 0.249571i
\(356\) −8.09017 + 5.87785i −0.428778 + 0.311526i
\(357\) 1.23607 3.80423i 0.0654197 0.201341i
\(358\) 0 0
\(359\) −16.1803 + 11.7557i −0.853966 + 0.620442i −0.926237 0.376943i \(-0.876975\pi\)
0.0722709 + 0.997385i \(0.476975\pi\)
\(360\) −3.23607 2.35114i −0.170556 0.123916i
\(361\) −5.87132 18.0701i −0.309017 0.951057i
\(362\) −2.00000 −0.105118
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) −7.41641 22.8254i −0.388193 1.19473i
\(366\) 6.47214 + 4.70228i 0.338304 + 0.245792i
\(367\) −6.47214 + 4.70228i −0.337843 + 0.245457i −0.743751 0.668457i \(-0.766955\pi\)
0.405908 + 0.913914i \(0.366955\pi\)
\(368\) −1.85410 + 5.70634i −0.0966517 + 0.297463i
\(369\) −0.618034 + 1.90211i −0.0321736 + 0.0990200i
\(370\) 6.47214 4.70228i 0.336470 0.244460i
\(371\) −6.47214 4.70228i −0.336017 0.244130i
\(372\) −2.47214 7.60845i −0.128174 0.394480i
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) −24.0000 −1.23935
\(376\) 0.618034 + 1.90211i 0.0318727 + 0.0980940i
\(377\) −32.3607 23.5114i −1.66666 1.21090i
\(378\) 1.61803 1.17557i 0.0832227 0.0604648i
\(379\) −6.18034 + 19.0211i −0.317463 + 0.977050i 0.657266 + 0.753659i \(0.271713\pi\)
−0.974729 + 0.223391i \(0.928287\pi\)
\(380\) 0 0
\(381\) −17.7984 + 12.9313i −0.911838 + 0.662489i
\(382\) 17.7984 + 12.9313i 0.910644 + 0.661622i
\(383\) −1.85410 5.70634i −0.0947402 0.291580i 0.892446 0.451155i \(-0.148988\pi\)
−0.987186 + 0.159575i \(0.948988\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) −1.23607 3.80423i −0.0628329 0.193380i
\(388\) 1.61803 + 1.17557i 0.0821432 + 0.0596806i
\(389\) 16.1803 11.7557i 0.820376 0.596038i −0.0964443 0.995338i \(-0.530747\pi\)
0.916820 + 0.399300i \(0.130747\pi\)
\(390\) −4.94427 + 15.2169i −0.250363 + 0.770538i
\(391\) −3.70820 + 11.4127i −0.187532 + 0.577164i
\(392\) −2.42705 + 1.76336i −0.122585 + 0.0890629i
\(393\) 9.70820 + 7.05342i 0.489714 + 0.355798i
\(394\) 5.56231 + 17.1190i 0.280225 + 0.862444i
\(395\) 40.0000 2.01262
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) −6.18034 19.0211i −0.309792 0.953443i
\(399\) 0 0
\(400\) −8.89919 + 6.46564i −0.444959 + 0.323282i
\(401\) −5.56231 + 17.1190i −0.277768 + 0.854883i 0.710705 + 0.703490i \(0.248376\pi\)
−0.988474 + 0.151393i \(0.951624\pi\)
\(402\) 3.70820 11.4127i 0.184948 0.569213i
\(403\) −25.8885 + 18.8091i −1.28960 + 0.936949i
\(404\) 1.61803 + 1.17557i 0.0805002 + 0.0584868i
\(405\) −1.23607 3.80423i −0.0614207 0.189034i
\(406\) 20.0000 0.992583
\(407\) 0 0
\(408\) −2.00000 −0.0990148
\(409\) 3.09017 + 9.51057i 0.152799 + 0.470267i 0.997931 0.0642902i \(-0.0204783\pi\)
−0.845132 + 0.534557i \(0.820478\pi\)
\(410\) 6.47214 + 4.70228i 0.319636 + 0.232229i
\(411\) 1.61803 1.17557i 0.0798117 0.0579866i
\(412\) 1.23607 3.80423i 0.0608967 0.187421i
\(413\) 0 0
\(414\) −4.85410 + 3.52671i −0.238566 + 0.173328i
\(415\) −12.9443 9.40456i −0.635409 0.461652i
\(416\) 1.23607 + 3.80423i 0.0606032 + 0.186518i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −2.47214 7.60845i −0.120628 0.371254i
\(421\) 14.5623 + 10.5801i 0.709723 + 0.515644i 0.883084 0.469214i \(-0.155463\pi\)
−0.173361 + 0.984858i \(0.555463\pi\)
\(422\) −9.70820 + 7.05342i −0.472588 + 0.343355i
\(423\) −0.618034 + 1.90211i −0.0300498 + 0.0924839i
\(424\) −1.23607 + 3.80423i −0.0600288 + 0.184750i
\(425\) −17.7984 + 12.9313i −0.863348 + 0.627259i
\(426\) 1.61803 + 1.17557i 0.0783940 + 0.0569566i
\(427\) 4.94427 + 15.2169i 0.239270 + 0.736398i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −16.0000 −0.771589
\(431\) −9.88854 30.4338i −0.476314 1.46594i −0.844177 0.536065i \(-0.819910\pi\)
0.367862 0.929880i \(-0.380090\pi\)
\(432\) −0.809017 0.587785i −0.0389238 0.0282798i
\(433\) 4.85410 3.52671i 0.233273 0.169483i −0.465008 0.885307i \(-0.653949\pi\)
0.698281 + 0.715824i \(0.253949\pi\)
\(434\) 4.94427 15.2169i 0.237333 0.730435i
\(435\) 12.3607 38.0423i 0.592649 1.82399i
\(436\) 16.1803 11.7557i 0.774898 0.562996i
\(437\) 0 0
\(438\) −1.85410 5.70634i −0.0885924 0.272659i
\(439\) −10.0000 −0.477274 −0.238637 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 2.47214 + 7.60845i 0.117588 + 0.361897i
\(443\) −19.4164 14.1068i −0.922501 0.670236i 0.0216440 0.999766i \(-0.493110\pi\)
−0.944145 + 0.329529i \(0.893110\pi\)
\(444\) 1.61803 1.17557i 0.0767885 0.0557901i
\(445\) −12.3607 + 38.0423i −0.585952 + 1.80338i
\(446\) 4.94427 15.2169i 0.234118 0.720541i
\(447\) −8.09017 + 5.87785i −0.382652 + 0.278013i
\(448\) −1.61803 1.17557i −0.0764449 0.0555405i
\(449\) 9.27051 + 28.5317i 0.437502 + 1.34649i 0.890500 + 0.454982i \(0.150354\pi\)
−0.452998 + 0.891512i \(0.649646\pi\)
\(450\) −11.0000 −0.518545
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) −0.618034 1.90211i −0.0290378 0.0893691i
\(454\) 9.70820 + 7.05342i 0.455629 + 0.331034i
\(455\) −25.8885 + 18.8091i −1.21367 + 0.881786i
\(456\) 0 0
\(457\) 0.618034 1.90211i 0.0289104 0.0889771i −0.935560 0.353167i \(-0.885105\pi\)
0.964471 + 0.264190i \(0.0851047\pi\)
\(458\) 8.09017 5.87785i 0.378029 0.274654i
\(459\) −1.61803 1.17557i −0.0755234 0.0548709i
\(460\) 7.41641 + 22.8254i 0.345792 + 1.06424i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −3.09017 9.51057i −0.143458 0.441517i
\(465\) −25.8885 18.8091i −1.20055 0.872252i
\(466\) 4.85410 3.52671i 0.224862 0.163372i
\(467\) 8.65248 26.6296i 0.400389 1.23227i −0.524296 0.851536i \(-0.675671\pi\)
0.924685 0.380734i \(-0.124329\pi\)
\(468\) −1.23607 + 3.80423i −0.0571373 + 0.175850i
\(469\) 19.4164 14.1068i 0.896566 0.651394i
\(470\) 6.47214 + 4.70228i 0.298537 + 0.216900i
\(471\) 5.56231 + 17.1190i 0.256298 + 0.788803i
\(472\) 0 0
\(473\) 0 0
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) −3.23607 2.35114i −0.148325 0.107764i
\(477\) −3.23607 + 2.35114i −0.148169 + 0.107651i
\(478\) −6.18034 + 19.0211i −0.282682 + 0.870006i
\(479\) −12.3607 + 38.0423i −0.564774 + 1.73820i 0.103848 + 0.994593i \(0.466884\pi\)
−0.668622 + 0.743602i \(0.733116\pi\)
\(480\) −3.23607 + 2.35114i −0.147706 + 0.107314i
\(481\) −6.47214 4.70228i −0.295104 0.214406i
\(482\) −5.56231 17.1190i −0.253356 0.779750i
\(483\) −12.0000 −0.546019
\(484\) 0 0
\(485\) 8.00000 0.363261
\(486\) −0.309017 0.951057i −0.0140173 0.0431408i
\(487\) −22.6525 16.4580i −1.02648 0.745783i −0.0588802 0.998265i \(-0.518753\pi\)
−0.967601 + 0.252482i \(0.918753\pi\)
\(488\) 6.47214 4.70228i 0.292980 0.212862i
\(489\) 1.23607 3.80423i 0.0558969 0.172033i
\(490\) −3.70820 + 11.4127i −0.167520 + 0.515572i
\(491\) 9.70820 7.05342i 0.438125 0.318317i −0.346764 0.937952i \(-0.612720\pi\)
0.784890 + 0.619636i \(0.212720\pi\)
\(492\) 1.61803 + 1.17557i 0.0729466 + 0.0529988i
\(493\) −6.18034 19.0211i −0.278349 0.856669i
\(494\) 0 0
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 1.23607 + 3.80423i 0.0554452 + 0.170643i
\(498\) −3.23607 2.35114i −0.145012 0.105357i
\(499\) 16.1803 11.7557i 0.724331 0.526258i −0.163434 0.986554i \(-0.552257\pi\)
0.887765 + 0.460297i \(0.152257\pi\)
\(500\) −7.41641 + 22.8254i −0.331672 + 1.02078i
\(501\) 3.70820 11.4127i 0.165670 0.509881i
\(502\) −6.47214 + 4.70228i −0.288866 + 0.209873i
\(503\) 3.23607 + 2.35114i 0.144289 + 0.104832i 0.657588 0.753378i \(-0.271577\pi\)
−0.513299 + 0.858210i \(0.671577\pi\)
\(504\) −0.618034 1.90211i −0.0275294 0.0847268i
\(505\) 8.00000 0.355995
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 6.79837 + 20.9232i 0.301629 + 0.928319i
\(509\) 16.1803 + 11.7557i 0.717181 + 0.521062i 0.885482 0.464673i \(-0.153828\pi\)
−0.168301 + 0.985736i \(0.553828\pi\)
\(510\) −6.47214 + 4.70228i −0.286591 + 0.208221i
\(511\) 3.70820 11.4127i 0.164041 0.504867i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) 0 0
\(514\) 14.5623 + 10.5801i 0.642316 + 0.466670i
\(515\) −4.94427 15.2169i −0.217871 0.670537i
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 4.00000 0.175750
\(519\) 1.85410 + 5.70634i 0.0813860 + 0.250480i
\(520\) 12.9443 + 9.40456i 0.567644 + 0.412417i
\(521\) 14.5623 10.5801i 0.637986 0.463524i −0.221172 0.975235i \(-0.570988\pi\)
0.859158 + 0.511711i \(0.170988\pi\)
\(522\) 3.09017 9.51057i 0.135253 0.416266i
\(523\) −13.5967 + 41.8465i −0.594544 + 1.82982i −0.0375627 + 0.999294i \(0.511959\pi\)
−0.556982 + 0.830525i \(0.688041\pi\)
\(524\) 9.70820 7.05342i 0.424105 0.308130i
\(525\) −17.7984 12.9313i −0.776785 0.564367i
\(526\) −4.94427 15.2169i −0.215580 0.663489i
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 4.94427 + 15.2169i 0.214765 + 0.660980i
\(531\) 0 0
\(532\) 0 0
\(533\) 2.47214 7.60845i 0.107080 0.329559i
\(534\) −3.09017 + 9.51057i −0.133725 + 0.411562i
\(535\) 38.8328 28.2137i 1.67889 1.21978i
\(536\) −9.70820 7.05342i −0.419331 0.304661i
\(537\) 0 0
\(538\) 20.0000 0.862261
\(539\) 0 0
\(540\) −4.00000 −0.172133
\(541\) −3.70820 11.4127i −0.159428 0.490669i 0.839154 0.543893i \(-0.183050\pi\)
−0.998583 + 0.0532238i \(0.983050\pi\)
\(542\) −17.7984 12.9313i −0.764506 0.555446i
\(543\) −1.61803 + 1.17557i −0.0694365 + 0.0504486i
\(544\) −0.618034 + 1.90211i −0.0264980 + 0.0815524i
\(545\) 24.7214 76.0845i 1.05895 3.25910i
\(546\) −6.47214 + 4.70228i −0.276982 + 0.201239i
\(547\) −25.8885 18.8091i −1.10691 0.804220i −0.124739 0.992190i \(-0.539809\pi\)
−0.982175 + 0.187969i \(0.939809\pi\)
\(548\) −0.618034 1.90211i −0.0264011 0.0812542i
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) 0 0
\(552\) 1.85410 + 5.70634i 0.0789158 + 0.242878i
\(553\) 16.1803 + 11.7557i 0.688058 + 0.499903i
\(554\) −6.47214 + 4.70228i −0.274975 + 0.199781i
\(555\) 2.47214 7.60845i 0.104936 0.322961i
\(556\) 0 0
\(557\) 30.7426 22.3358i 1.30261 0.946400i 0.302630 0.953108i \(-0.402135\pi\)
0.999978 + 0.00670815i \(0.00213529\pi\)
\(558\) −6.47214 4.70228i −0.273987 0.199063i
\(559\) 4.94427 + 15.2169i 0.209120 + 0.643606i
\(560\) −8.00000 −0.338062
\(561\) 0 0
\(562\) 22.0000 0.928014
\(563\) 11.1246 + 34.2380i 0.468846 + 1.44296i 0.854080 + 0.520142i \(0.174121\pi\)
−0.385233 + 0.922819i \(0.625879\pi\)
\(564\) 1.61803 + 1.17557i 0.0681315 + 0.0495004i
\(565\) −19.4164 + 14.1068i −0.816854 + 0.593479i
\(566\) 1.23607 3.80423i 0.0519558 0.159904i
\(567\) 0.618034 1.90211i 0.0259550 0.0798812i
\(568\) 1.61803 1.17557i 0.0678912 0.0493258i
\(569\) −8.09017 5.87785i −0.339158 0.246412i 0.405149 0.914251i \(-0.367220\pi\)
−0.744306 + 0.667838i \(0.767220\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 0 0
\(573\) 22.0000 0.919063
\(574\) 1.23607 + 3.80423i 0.0515925 + 0.158785i
\(575\) 53.3951 + 38.7938i 2.22673 + 1.61781i
\(576\) −0.809017 + 0.587785i −0.0337090 + 0.0244911i
\(577\) −0.618034 + 1.90211i −0.0257291 + 0.0791860i −0.963097 0.269156i \(-0.913255\pi\)
0.937367 + 0.348342i \(0.113255\pi\)
\(578\) 4.01722 12.3637i 0.167094 0.514264i
\(579\) 11.3262 8.22899i 0.470702 0.341985i
\(580\) −32.3607 23.5114i −1.34370 0.976258i
\(581\) −2.47214 7.60845i −0.102561 0.315652i
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) 4.94427 + 15.2169i 0.204420 + 0.629142i
\(586\) −11.3262 8.22899i −0.467883 0.339937i
\(587\) −6.47214 + 4.70228i −0.267134 + 0.194084i −0.713286 0.700873i \(-0.752794\pi\)
0.446152 + 0.894957i \(0.352794\pi\)
\(588\) −0.927051 + 2.85317i −0.0382309 + 0.117663i
\(589\) 0 0
\(590\) 0 0
\(591\) 14.5623 + 10.5801i 0.599013 + 0.435209i
\(592\) −0.618034 1.90211i −0.0254010 0.0781764i
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 3.09017 + 9.51057i 0.126578 + 0.389568i
\(597\) −16.1803 11.7557i −0.662217 0.481129i
\(598\) 19.4164 14.1068i 0.793996 0.576872i
\(599\) −9.27051 + 28.5317i −0.378783 + 1.16577i 0.562108 + 0.827064i \(0.309990\pi\)
−0.940891 + 0.338710i \(0.890010\pi\)
\(600\) −3.39919 + 10.4616i −0.138771 + 0.427094i
\(601\) 33.9787 24.6870i 1.38602 1.00700i 0.389732 0.920928i \(-0.372568\pi\)
0.996289 0.0860746i \(-0.0274323\pi\)
\(602\) −6.47214 4.70228i −0.263785 0.191651i
\(603\) −3.70820 11.4127i −0.151010 0.464760i
\(604\) −2.00000 −0.0813788
\(605\) 0 0
\(606\) 2.00000 0.0812444
\(607\) 6.79837 + 20.9232i 0.275937 + 0.849248i 0.988970 + 0.148117i \(0.0473213\pi\)
−0.713032 + 0.701131i \(0.752679\pi\)
\(608\) 0 0
\(609\) 16.1803 11.7557i 0.655660 0.476365i
\(610\) 9.88854 30.4338i 0.400375 1.23223i
\(611\) 2.47214 7.60845i 0.100012 0.307805i
\(612\) −1.61803 + 1.17557i −0.0654051 + 0.0475196i
\(613\) −12.9443 9.40456i −0.522814 0.379847i 0.294849 0.955544i \(-0.404731\pi\)
−0.817663 + 0.575697i \(0.804731\pi\)
\(614\) 2.47214 + 7.60845i 0.0997673 + 0.307052i
\(615\) 8.00000 0.322591
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) −1.23607 3.80423i −0.0497219 0.153028i
\(619\) 16.1803 + 11.7557i 0.650343 + 0.472502i 0.863388 0.504541i \(-0.168338\pi\)
−0.213045 + 0.977042i \(0.568338\pi\)
\(620\) −25.8885 + 18.8091i −1.03971 + 0.755393i
\(621\) −1.85410 + 5.70634i −0.0744025 + 0.228988i
\(622\) −0.618034 + 1.90211i −0.0247809 + 0.0762678i
\(623\) −16.1803 + 11.7557i −0.648252 + 0.470982i
\(624\) 3.23607 + 2.35114i 0.129546 + 0.0941210i
\(625\) 12.6697 + 38.9933i 0.506788 + 1.55973i
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) −1.23607 3.80423i −0.0492853 0.151684i
\(630\) −6.47214 4.70228i −0.257856 0.187343i
\(631\) 38.8328 28.2137i 1.54591 1.12317i 0.599421 0.800434i \(-0.295398\pi\)
0.946489 0.322735i \(-0.104602\pi\)
\(632\) 3.09017 9.51057i 0.122920 0.378310i
\(633\) −3.70820 + 11.4127i −0.147388 + 0.453613i
\(634\) −25.8885 + 18.8091i −1.02817 + 0.747006i
\(635\) 71.1935 + 51.7251i 2.82523 + 2.05265i
\(636\) 1.23607 + 3.80423i 0.0490133 + 0.150847i
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 1.23607 + 3.80423i 0.0488599 + 0.150375i
\(641\) 14.5623 + 10.5801i 0.575177 + 0.417890i 0.836982 0.547230i \(-0.184318\pi\)
−0.261805 + 0.965121i \(0.584318\pi\)
\(642\) 9.70820 7.05342i 0.383152 0.278376i
\(643\) 13.5967 41.8465i 0.536203 1.65026i −0.204831 0.978797i \(-0.565665\pi\)
0.741034 0.671467i \(-0.234335\pi\)
\(644\) −3.70820 + 11.4127i −0.146124 + 0.449723i
\(645\) −12.9443 + 9.40456i −0.509680 + 0.370304i
\(646\) 0 0
\(647\) −6.79837 20.9232i −0.267272 0.822578i −0.991161 0.132662i \(-0.957648\pi\)
0.723890 0.689916i \(-0.242352\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 44.0000 1.72582
\(651\) −4.94427 15.2169i −0.193781 0.596397i
\(652\) −3.23607 2.35114i −0.126734 0.0920778i
\(653\) −19.4164 + 14.1068i −0.759823 + 0.552044i −0.898856 0.438244i \(-0.855601\pi\)
0.139033 + 0.990288i \(0.455601\pi\)
\(654\) 6.18034 19.0211i 0.241670 0.743785i
\(655\) 14.8328 45.6507i 0.579566 1.78372i
\(656\) 1.61803 1.17557i 0.0631736 0.0458983i
\(657\) −4.85410 3.52671i −0.189377 0.137590i
\(658\) 1.23607 + 3.80423i 0.0481869 + 0.148304i
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 42.0000 1.63361 0.816805 0.576913i \(-0.195743\pi\)
0.816805 + 0.576913i \(0.195743\pi\)
\(662\) 8.65248 + 26.6296i 0.336288 + 1.03499i
\(663\) 6.47214 + 4.70228i 0.251357 + 0.182622i
\(664\) −3.23607 + 2.35114i −0.125584 + 0.0912420i
\(665\) 0 0
\(666\) 0.618034 1.90211i 0.0239483 0.0737054i
\(667\) −48.5410 + 35.2671i −1.87952 + 1.36555i
\(668\) −9.70820 7.05342i −0.375622 0.272905i
\(669\) −4.94427 15.2169i −0.191157 0.588320i
\(670\) −48.0000 −1.85440
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) −4.32624 13.3148i −0.166764 0.513247i 0.832398 0.554179i \(-0.186968\pi\)
−0.999162 + 0.0409312i \(0.986968\pi\)
\(674\) 17.7984 + 12.9313i 0.685568 + 0.498094i
\(675\) −8.89919 + 6.46564i −0.342530 + 0.248863i
\(676\) 0.927051 2.85317i 0.0356558 0.109737i
\(677\) 6.79837 20.9232i 0.261283 0.804146i −0.731244 0.682116i \(-0.761060\pi\)
0.992526 0.122029i \(-0.0389402\pi\)
\(678\) −4.85410 + 3.52671i −0.186421 + 0.135443i
\(679\) 3.23607 + 2.35114i 0.124189 + 0.0902285i
\(680\) 2.47214 + 7.60845i 0.0948021 + 0.291771i
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) 0 0
\(685\) −6.47214 4.70228i −0.247288 0.179665i
\(686\) −16.1803 + 11.7557i −0.617768 + 0.448835i
\(687\) 3.09017 9.51057i 0.117897 0.362851i
\(688\) −1.23607 + 3.80423i −0.0471246 + 0.145035i
\(689\) 12.9443 9.40456i 0.493137 0.358285i
\(690\) 19.4164 + 14.1068i 0.739170 + 0.537038i
\(691\) 16.0689 + 49.4549i 0.611289 + 1.88135i 0.445769 + 0.895148i \(0.352930\pi\)
0.165520 + 0.986206i \(0.447070\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) −8.09017 5.87785i −0.306657 0.222799i
\(697\) 3.23607 2.35114i 0.122575 0.0890558i
\(698\) −6.18034 + 19.0211i −0.233929 + 0.719960i
\(699\) 1.85410 5.70634i 0.0701286 0.215834i
\(700\) −17.7984 + 12.9313i −0.672715 + 0.488756i
\(701\) −14.5623 10.5801i −0.550011 0.399606i 0.277779 0.960645i \(-0.410402\pi\)
−0.827789 + 0.561039i \(0.810402\pi\)
\(702\) 1.23607 + 3.80423i 0.0466524 + 0.143581i
\(703\) 0 0
\(704\) 0 0
\(705\) 8.00000 0.301297
\(706\) 1.85410 + 5.70634i 0.0697800 + 0.214761i
\(707\) 3.23607 + 2.35114i 0.121705 + 0.0884238i
\(708\) 0 0
\(709\) 3.09017 9.51057i 0.116054 0.357177i −0.876112 0.482108i \(-0.839871\pi\)
0.992165 + 0.124932i \(0.0398711\pi\)
\(710\) 2.47214 7.60845i 0.0927776 0.285540i
\(711\) 8.09017 5.87785i 0.303405 0.220437i
\(712\) 8.09017 + 5.87785i 0.303192 + 0.220282i
\(713\) 14.8328 + 45.6507i 0.555493 + 1.70963i
\(714\) −4.00000 −0.149696
\(715\) 0 0
\(716\) 0 0
\(717\) 6.18034 + 19.0211i 0.230809 + 0.710357i
\(718\) 16.1803 + 11.7557i 0.603845 + 0.438719i
\(719\) −8.09017 + 5.87785i −0.301712 + 0.219207i −0.728332 0.685224i \(-0.759704\pi\)
0.426620 + 0.904431i \(0.359704\pi\)
\(720\) −1.23607 + 3.80423i −0.0460655 + 0.141775i
\(721\) 2.47214 7.60845i 0.0920672 0.283354i
\(722\) −15.3713 + 11.1679i −0.572061 + 0.415627i
\(723\) −14.5623 10.5801i −0.541578 0.393479i
\(724\) 0.618034 + 1.90211i 0.0229691 + 0.0706915i
\(725\) −110.000 −4.08530
\(726\) 0 0
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 2.47214 + 7.60845i 0.0916235 + 0.281988i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) −19.4164 + 14.1068i −0.718633 + 0.522118i
\(731\) −2.47214 + 7.60845i −0.0914353 + 0.281409i
\(732\) 2.47214 7.60845i 0.0913728 0.281216i
\(733\) 3.23607 2.35114i 0.119527 0.0868414i −0.526416 0.850227i \(-0.676464\pi\)
0.645943 + 0.763386i \(0.276464\pi\)
\(734\) 6.47214 + 4.70228i 0.238891 + 0.173564i
\(735\) 3.70820 + 11.4127i 0.136779 + 0.420963i
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 2.00000 0.0736210
\(739\) −6.18034 19.0211i −0.227347 0.699704i −0.998045 0.0625022i \(-0.980092\pi\)
0.770697 0.637201i \(-0.219908\pi\)
\(740\) −6.47214 4.70228i −0.237920 0.172859i
\(741\) 0 0
\(742\) −2.47214 + 7.60845i −0.0907550 + 0.279315i
\(743\) −13.5967 + 41.8465i −0.498816 + 1.53520i 0.312107 + 0.950047i \(0.398965\pi\)
−0.810924 + 0.585152i \(0.801035\pi\)
\(744\) −6.47214 + 4.70228i −0.237280 + 0.172394i
\(745\) 32.3607 + 23.5114i 1.18560 + 0.861391i
\(746\) 1.23607 + 3.80423i 0.0452557 + 0.139283i
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 24.0000 0.876941
\(750\) 7.41641 + 22.8254i 0.270809 + 0.833464i
\(751\) 6.47214 + 4.70228i 0.236172 + 0.171589i 0.699576 0.714558i \(-0.253372\pi\)
−0.463404 + 0.886147i \(0.653372\pi\)
\(752\) 1.61803 1.17557i 0.0590036 0.0428686i
\(753\) −2.47214 + 7.60845i −0.0900896 + 0.277267i
\(754\) −12.3607 + 38.0423i −0.450149 + 1.38542i
\(755\) −6.47214 + 4.70228i −0.235545 + 0.171134i
\(756\) −1.61803 1.17557i −0.0588473 0.0427551i
\(757\) −12.9787 39.9444i −0.471719 1.45180i −0.850331 0.526248i \(-0.823599\pi\)
0.378612 0.925555i \(-0.376401\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) −6.79837 20.9232i −0.246441 0.758467i −0.995396 0.0958464i \(-0.969444\pi\)
0.748955 0.662621i \(-0.230556\pi\)
\(762\) 17.7984 + 12.9313i 0.644767 + 0.468451i
\(763\) 32.3607 23.5114i 1.17154 0.851170i
\(764\) 6.79837 20.9232i 0.245957 0.756976i
\(765\) −2.47214 + 7.60845i −0.0893803 + 0.275084i
\(766\) −4.85410 + 3.52671i −0.175386 + 0.127425i
\(767\) 0 0
\(768\) 0.309017 + 0.951057i 0.0111507 + 0.0343183i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −4.32624 13.3148i −0.155705 0.479210i
\(773\) −3.23607 2.35114i −0.116393 0.0845647i 0.528066 0.849203i \(-0.322917\pi\)
−0.644459 + 0.764639i \(0.722917\pi\)
\(774\) −3.23607 + 2.35114i −0.116318 + 0.0845100i
\(775\) −27.1935 + 83.6930i −0.976819 + 3.00634i
\(776\) 0.618034 1.90211i 0.0221861 0.0682819i
\(777\) 3.23607 2.35114i 0.116093 0.0843467i
\(778\) −16.1803 11.7557i −0.580093 0.421462i
\(779\) 0 0
\(780\) 16.0000 0.572892
\(781\) 0 0
\(782\) 12.0000 0.429119
\(783\) −3.09017 9.51057i −0.110434 0.339880i
\(784\) 2.42705 + 1.76336i 0.0866804 + 0.0629770i
\(785\) 58.2492 42.3205i 2.07900 1.51048i
\(786\) 3.70820 11.4127i 0.132267 0.407077i
\(787\) 16.0689 49.4549i 0.572794 1.76288i −0.0707776 0.997492i \(-0.522548\pi\)
0.643571 0.765386i \(-0.277452\pi\)
\(788\) 14.5623 10.5801i 0.518761 0.376902i
\(789\) −12.9443 9.40456i −0.460828 0.334811i
\(790\) −12.3607 38.0423i −0.439773 1.35348i
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) −5.56231 17.1190i −0.197399 0.607531i
\(795\) 12.9443 + 9.40456i 0.459086 + 0.333546i
\(796\) −16.1803 + 11.7557i −0.573497 + 0.416670i
\(797\) 8.65248 26.6296i 0.306486 0.943268i −0.672632 0.739977i \(-0.734836\pi\)
0.979118 0.203291i \(-0.0651637\pi\)
\(798\) 0 0
\(799\) 3.23607 2.35114i 0.114484 0.0831774i
\(800\) 8.89919 + 6.46564i 0.314634 + 0.228595i
\(801\) 3.09017 + 9.51057i 0.109186 + 0.336039i
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) −12.0000 −0.423207
\(805\) 14.8328 + 45.6507i 0.522788 + 1.60898i
\(806\) 25.8885 + 18.8091i 0.911885 + 0.662523i
\(807\) 16.1803 11.7557i 0.569575 0.413820i
\(808\) 0.618034 1.90211i 0.0217424 0.0669161i
\(809\) −3.09017 + 9.51057i −0.108645 + 0.334374i −0.990569 0.137018i \(-0.956248\pi\)
0.881924 + 0.471392i \(0.156248\pi\)
\(810\) −3.23607 + 2.35114i −0.113704 + 0.0826107i
\(811\) 9.70820 + 7.05342i 0.340901 + 0.247679i 0.745042 0.667018i \(-0.232429\pi\)
−0.404141 + 0.914697i \(0.632429\pi\)
\(812\) −6.18034 19.0211i −0.216887 0.667511i
\(813\) −22.0000 −0.771574
\(814\) 0 0
\(815\) −16.0000 −0.560456
\(816\) 0.618034 + 1.90211i 0.0216355 + 0.0665873i
\(817\) 0 0
\(818\) 8.09017 5.87785i 0.282866 0.205514i
\(819\) −2.47214 + 7.60845i −0.0863834 + 0.265861i
\(820\) 2.47214 7.60845i 0.0863307 0.265699i
\(821\) −30.7426 + 22.3358i −1.07293 + 0.779526i −0.976436 0.215808i \(-0.930762\pi\)
−0.0964899 + 0.995334i \(0.530762\pi\)
\(822\) −1.61803 1.17557i −0.0564354 0.0410027i
\(823\) 7.41641 + 22.8254i 0.258520 + 0.795642i 0.993116 + 0.117137i \(0.0373717\pi\)
−0.734596 + 0.678505i \(0.762628\pi\)
\(824\) −4.00000 −0.139347
\(825\) 0 0
\(826\) 0 0
\(827\) 3.70820 + 11.4127i 0.128947 + 0.396858i 0.994600 0.103787i \(-0.0330962\pi\)
−0.865653 + 0.500645i \(0.833096\pi\)
\(828\) 4.85410 + 3.52671i 0.168692 + 0.122562i
\(829\) −24.2705 + 17.6336i −0.842950 + 0.612439i −0.923193 0.384337i \(-0.874430\pi\)
0.0802434 + 0.996775i \(0.474430\pi\)
\(830\) −4.94427 + 15.2169i −0.171618 + 0.528186i
\(831\) −2.47214 + 7.60845i −0.0857574 + 0.263934i
\(832\) 3.23607 2.35114i 0.112190 0.0815111i
\(833\) 4.85410 + 3.52671i 0.168185 + 0.122193i
\(834\) 0 0
\(835\) −48.0000 −1.66111
\(836\) 0 0
\(837\) −8.00000 −0.276520
\(838\) 0 0
\(839\) −24.2705 17.6336i −0.837911 0.608778i 0.0838753 0.996476i \(-0.473270\pi\)
−0.921786 + 0.387698i \(0.873270\pi\)
\(840\) −6.47214 + 4.70228i −0.223310 + 0.162244i
\(841\) 21.9402 67.5250i 0.756559 2.32845i
\(842\) 5.56231 17.1190i 0.191690 0.589960i
\(843\) 17.7984 12.9313i 0.613009 0.445377i
\(844\) 9.70820 + 7.05342i 0.334170 + 0.242789i
\(845\) −3.70820 11.4127i −0.127566 0.392608i
\(846\) 2.00000 0.0687614
\(847\) 0 0
\(848\) 4.00000 0.137361
\(849\) −1.23607 3.80423i −0.0424217 0.130561i
\(850\) 17.7984 + 12.9313i 0.610479 + 0.443539i
\(851\) −9.70820 + 7.05342i −0.332793 + 0.241788i
\(852\) 0.618034 1.90211i 0.0211735 0.0651653i
\(853\) −7.41641 + 22.8254i −0.253933 + 0.781525i 0.740105 + 0.672491i \(0.234776\pi\)
−0.994038 + 0.109034i \(0.965224\pi\)
\(854\) 12.9443 9.40456i 0.442944 0.321818i
\(855\) 0 0
\(856\) −3.70820 11.4127i −0.126744 0.390077i
\(857\) 22.0000 0.751506 0.375753 0.926720i \(-0.377384\pi\)
0.375753 + 0.926720i \(0.377384\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 4.94427 + 15.2169i 0.168598 + 0.518892i
\(861\) 3.23607 + 2.35114i 0.110285 + 0.0801267i
\(862\) −25.8885 + 18.8091i −0.881767 + 0.640641i
\(863\) 16.6869 51.3571i 0.568029 1.74821i −0.0907454 0.995874i \(-0.528925\pi\)
0.658775 0.752340i \(-0.271075\pi\)
\(864\) −0.309017 + 0.951057i −0.0105130 + 0.0323556i
\(865\) 19.4164 14.1068i 0.660178 0.479647i
\(866\) −4.85410 3.52671i −0.164949 0.119843i
\(867\) −4.01722 12.3637i −0.136432 0.419894i
\(868\) −16.0000 −0.543075
\(869\) 0 0
\(870\) −40.0000 −1.35613
\(871\) 14.8328 + 45.6507i 0.502591 + 1.54682i
\(872\) −16.1803 11.7557i −0.547935 0.398098i
\(873\) 1.61803 1.17557i 0.0547622 0.0397870i
\(874\) 0 0
\(875\) −14.8328 + 45.6507i −0.501441 + 1.54328i
\(876\) −4.85410 + 3.52671i −0.164005 + 0.119157i
\(877\) 22.6525 + 16.4580i 0.764920 + 0.555747i 0.900415 0.435031i \(-0.143263\pi\)
−0.135496 + 0.990778i \(0.543263\pi\)
\(878\) 3.09017 + 9.51057i 0.104288 + 0.320966i
\(879\) −14.0000 −0.472208
\(880\) 0 0
\(881\) −38.0000 −1.28025 −0.640126 0.768270i \(-0.721118\pi\)
−0.640126 + 0.768270i \(0.721118\pi\)
\(882\) 0.927051 + 2.85317i 0.0312154 + 0.0960712i
\(883\) −35.5967 25.8626i −1.19793 0.870344i −0.203847 0.979003i \(-0.565344\pi\)
−0.994079 + 0.108659i \(0.965344\pi\)
\(884\) 6.47214 4.70228i 0.217681 0.158155i
\(885\) 0 0
\(886\) −7.41641 + 22.8254i −0.249159 + 0.766833i
\(887\) −9.70820 + 7.05342i −0.325970 + 0.236831i −0.738718 0.674014i \(-0.764569\pi\)
0.412749 + 0.910845i \(0.364569\pi\)
\(888\) −1.61803 1.17557i −0.0542977 0.0394496i
\(889\) 13.5967 + 41.8465i 0.456020 + 1.40349i
\(890\) 40.0000 1.34080
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) 8.09017 + 5.87785i 0.270576 + 0.196585i
\(895\) 0 0
\(896\) −0.618034 + 1.90211i −0.0206471 + 0.0635451i
\(897\) 7.41641 22.8254i 0.247627 0.762116i
\(898\) 24.2705 17.6336i 0.809917 0.588439i
\(899\) −64.7214 47.0228i −2.15858 1.56830i
\(900\) 3.39919 + 10.4616i 0.113306 + 0.348721i
\(901\) 8.00000 0.266519
\(902\) 0 0
\(903\) −8.00000 −0.266223
\(904\) 1.85410 + 5.70634i 0.0616665 + 0.189790i
\(905\) 6.47214 + 4.70228i 0.215141 + 0.156309i
\(906\) −1.61803 + 1.17557i −0.0537556 + 0.0390557i
\(907\) −3.70820 + 11.4127i −0.123129 + 0.378952i −0.993556 0.113346i \(-0.963843\pi\)
0.870427 + 0.492298i \(0.163843\pi\)
\(908\) 3.70820 11.4127i 0.123061 0.378743i
\(909\) 1.61803 1.17557i 0.0536668 0.0389912i
\(910\) 25.8885 + 18.8091i 0.858197 + 0.623517i
\(911\) 0.618034 + 1.90211i 0.0204764 + 0.0630198i 0.960773 0.277337i \(-0.0894520\pi\)
−0.940296 + 0.340357i \(0.889452\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −2.00000 −0.0661541
\(915\) −9.88854 30.4338i −0.326905 1.00611i
\(916\) −8.09017 5.87785i −0.267307 0.194210i
\(917\) 19.4164 14.1068i 0.641186 0.465849i
\(918\) −0.618034 + 1.90211i −0.0203982 + 0.0627791i
\(919\) 3.09017 9.51057i 0.101935 0.313725i −0.887064 0.461647i \(-0.847259\pi\)
0.988999 + 0.147923i \(0.0472586\pi\)
\(920\) 19.4164 14.1068i 0.640140 0.465089i
\(921\) 6.47214 + 4.70228i 0.213264 + 0.154945i
\(922\) −5.56231 17.1190i −0.183185 0.563785i
\(923\) −8.00000 −0.263323
\(924\) 0 0
\(925\) −22.0000 −0.723356
\(926\) −1.23607 3.80423i −0.0406197 0.125015i
\(927\) −3.23607 2.35114i −0.106286 0.0772216i
\(928\) −8.09017 + 5.87785i −0.265573 + 0.192950i
\(929\) 9.27051 28.5317i 0.304156 0.936095i −0.675835 0.737053i \(-0.736217\pi\)
0.979991 0.199042i \(-0.0637830\pi\)
\(930\) −9.88854 + 30.4338i −0.324258 + 0.997964i
\(931\) 0 0
\(932\) −4.85410 3.52671i −0.159001 0.115521i
\(933\) 0.618034 + 1.90211i 0.0202335 + 0.0622724i
\(934\) −28.0000 −0.916188
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) −17.9230 55.1613i −0.585518 1.80204i −0.597178 0.802108i \(-0.703712\pi\)
0.0116601 0.999932i \(-0.496288\pi\)
\(938\) −19.4164 14.1068i −0.633968 0.460605i
\(939\) 4.85410 3.52671i 0.158408 0.115090i
\(940\) 2.47214 7.60845i 0.0806322 0.248160i
\(941\) −12.9787 + 39.9444i −0.423094 + 1.30215i 0.481714 + 0.876329i \(0.340015\pi\)
−0.904808 + 0.425821i \(0.859985\pi\)
\(942\) 14.5623 10.5801i 0.474466 0.344719i
\(943\) −9.70820 7.05342i −0.316143 0.229691i
\(944\) 0 0
\(945\) −8.00000 −0.260240
\(946\) 0 0
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) −3.09017 9.51057i −0.100364 0.308889i
\(949\) 19.4164 + 14.1068i 0.630283 + 0.457928i
\(950\) 0 0
\(951\) −9.88854 + 30.4338i −0.320658 + 0.986884i
\(952\) −1.23607 + 3.80423i −0.0400612 + 0.123296i
\(953\) −4.85410 + 3.52671i −0.157240 + 0.114241i −0.663623 0.748067i \(-0.730982\pi\)
0.506383 + 0.862309i \(0.330982\pi\)
\(954\) 3.23607 + 2.35114i 0.104772 + 0.0761210i
\(955\) −27.1935 83.6930i −0.879961 2.70824i
\(956\) 20.0000 0.646846
\(957\) 0 0
\(958\) 40.0000 1.29234
\(959\) −1.23607 3.80423i −0.0399147 0.122845i
\(960\) 3.23607 + 2.35114i 0.104444 + 0.0758827i
\(961\) −26.6976 + 19.3969i −0.861212 + 0.625707i
\(962\) −2.47214 + 7.60845i −0.0797049 + 0.245306i
\(963\) 3.70820 11.4127i 0.119495 0.367768i
\(964\) −14.5623 + 10.5801i −0.469020 + 0.340763i
\(965\) −45.3050 32.9160i −1.45842 1.05960i
\(966\) 3.70820 + 11.4127i 0.119310 + 0.367197i
\(967\) 22.0000 0.707472 0.353736 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −2.47214 7.60845i −0.0793755 0.244293i
\(971\) −25.8885 18.8091i −0.830803 0.603614i 0.0889835 0.996033i \(-0.471638\pi\)
−0.919786 + 0.392419i \(0.871638\pi\)
\(972\) −0.809017 + 0.587785i −0.0259492 + 0.0188532i
\(973\) 0 0
\(974\) −8.65248 + 26.6296i −0.277243 + 0.853267i
\(975\) 35.5967 25.8626i 1.14001 0.828265i
\(976\) −6.47214 4.70228i −0.207168 0.150516i
\(977\) 11.7426 + 36.1401i 0.375681 + 1.15623i 0.943018 + 0.332741i \(0.107973\pi\)
−0.567338 + 0.823485i \(0.692027\pi\)
\(978\) −4.00000 −0.127906
\(979\) 0 0
\(980\) 12.0000 0.383326
\(981\) −6.18034 19.0211i −0.197323 0.607298i
\(982\) −9.70820 7.05342i −0.309801 0.225084i
\(983\) 37.2148 27.0381i 1.18697 0.862382i 0.194027 0.980996i \(-0.437845\pi\)
0.992940 + 0.118614i \(0.0378451\pi\)
\(984\) 0.618034 1.90211i 0.0197022 0.0606371i
\(985\) 22.2492 68.4761i 0.708919 2.18183i
\(986\) −16.1803 + 11.7557i −0.515287 + 0.374378i
\(987\) 3.23607 + 2.35114i 0.103005 + 0.0748376i
\(988\) 0 0
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 2.47214 + 7.60845i 0.0784904 + 0.241569i
\(993\) 22.6525 + 16.4580i 0.718855 + 0.522278i
\(994\) 3.23607 2.35114i 0.102642 0.0745737i
\(995\) −24.7214 + 76.0845i −0.783720 + 2.41204i
\(996\) −1.23607 + 3.80423i −0.0391663 + 0.120542i
\(997\) −42.0689 + 30.5648i −1.33233 + 0.967998i −0.332646 + 0.943052i \(0.607941\pi\)
−0.999689 + 0.0249463i \(0.992059\pi\)
\(998\) −16.1803 11.7557i −0.512180 0.372120i
\(999\) −0.618034 1.90211i −0.0195537 0.0601802i
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 726.2.e.m.511.1 4
11.2 odd 10 726.2.e.e.493.1 4
11.3 even 5 726.2.a.d.1.1 1
11.4 even 5 inner 726.2.e.m.487.1 4
11.5 even 5 inner 726.2.e.m.565.1 4
11.6 odd 10 726.2.e.e.565.1 4
11.7 odd 10 726.2.e.e.487.1 4
11.8 odd 10 66.2.a.c.1.1 1
11.9 even 5 inner 726.2.e.m.493.1 4
11.10 odd 2 726.2.e.e.511.1 4
33.8 even 10 198.2.a.c.1.1 1
33.14 odd 10 2178.2.a.m.1.1 1
44.3 odd 10 5808.2.a.b.1.1 1
44.19 even 10 528.2.a.a.1.1 1
55.8 even 20 1650.2.c.m.199.1 2
55.19 odd 10 1650.2.a.c.1.1 1
55.52 even 20 1650.2.c.m.199.2 2
77.41 even 10 3234.2.a.s.1.1 1
88.19 even 10 2112.2.a.bd.1.1 1
88.85 odd 10 2112.2.a.n.1.1 1
99.41 even 30 1782.2.e.n.1189.1 2
99.52 odd 30 1782.2.e.l.595.1 2
99.74 even 30 1782.2.e.n.595.1 2
99.85 odd 30 1782.2.e.l.1189.1 2
132.107 odd 10 1584.2.a.s.1.1 1
165.8 odd 20 4950.2.c.d.199.2 2
165.74 even 10 4950.2.a.bo.1.1 1
165.107 odd 20 4950.2.c.d.199.1 2
231.41 odd 10 9702.2.a.a.1.1 1
264.107 odd 10 6336.2.a.d.1.1 1
264.173 even 10 6336.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
66.2.a.c.1.1 1 11.8 odd 10
198.2.a.c.1.1 1 33.8 even 10
528.2.a.a.1.1 1 44.19 even 10
726.2.a.d.1.1 1 11.3 even 5
726.2.e.e.487.1 4 11.7 odd 10
726.2.e.e.493.1 4 11.2 odd 10
726.2.e.e.511.1 4 11.10 odd 2
726.2.e.e.565.1 4 11.6 odd 10
726.2.e.m.487.1 4 11.4 even 5 inner
726.2.e.m.493.1 4 11.9 even 5 inner
726.2.e.m.511.1 4 1.1 even 1 trivial
726.2.e.m.565.1 4 11.5 even 5 inner
1584.2.a.s.1.1 1 132.107 odd 10
1650.2.a.c.1.1 1 55.19 odd 10
1650.2.c.m.199.1 2 55.8 even 20
1650.2.c.m.199.2 2 55.52 even 20
1782.2.e.l.595.1 2 99.52 odd 30
1782.2.e.l.1189.1 2 99.85 odd 30
1782.2.e.n.595.1 2 99.74 even 30
1782.2.e.n.1189.1 2 99.41 even 30
2112.2.a.n.1.1 1 88.85 odd 10
2112.2.a.bd.1.1 1 88.19 even 10
2178.2.a.m.1.1 1 33.14 odd 10
3234.2.a.s.1.1 1 77.41 even 10
4950.2.a.bo.1.1 1 165.74 even 10
4950.2.c.d.199.1 2 165.107 odd 20
4950.2.c.d.199.2 2 165.8 odd 20
5808.2.a.b.1.1 1 44.3 odd 10
6336.2.a.c.1.1 1 264.173 even 10
6336.2.a.d.1.1 1 264.107 odd 10
9702.2.a.a.1.1 1 231.41 odd 10