Properties

Label 483.2.d.a.461.2
Level $483$
Weight $2$
Character 483.461
Analytic conductor $3.857$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(461,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.461");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.d (of order \(2\), degree \(1\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 3x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.2
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 483.461
Dual form 483.2.d.a.461.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.618034i q^{2} +(-1.61803 - 0.618034i) q^{3} +1.61803 q^{4} -0.381966 q^{5} +(-0.381966 + 1.00000i) q^{6} +(0.381966 + 2.61803i) q^{7} -2.23607i q^{8} +(2.23607 + 2.00000i) q^{9} +O(q^{10})\) \(q-0.618034i q^{2} +(-1.61803 - 0.618034i) q^{3} +1.61803 q^{4} -0.381966 q^{5} +(-0.381966 + 1.00000i) q^{6} +(0.381966 + 2.61803i) q^{7} -2.23607i q^{8} +(2.23607 + 2.00000i) q^{9} +0.236068i q^{10} +2.23607i q^{11} +(-2.61803 - 1.00000i) q^{12} +0.145898i q^{13} +(1.61803 - 0.236068i) q^{14} +(0.618034 + 0.236068i) q^{15} +1.85410 q^{16} +7.47214 q^{17} +(1.23607 - 1.38197i) q^{18} +3.47214i q^{19} -0.618034 q^{20} +(1.00000 - 4.47214i) q^{21} +1.38197 q^{22} -1.00000i q^{23} +(-1.38197 + 3.61803i) q^{24} -4.85410 q^{25} +0.0901699 q^{26} +(-2.38197 - 4.61803i) q^{27} +(0.618034 + 4.23607i) q^{28} +6.23607i q^{29} +(0.145898 - 0.381966i) q^{30} -9.47214i q^{31} -5.61803i q^{32} +(1.38197 - 3.61803i) q^{33} -4.61803i q^{34} +(-0.145898 - 1.00000i) q^{35} +(3.61803 + 3.23607i) q^{36} +10.2361 q^{37} +2.14590 q^{38} +(0.0901699 - 0.236068i) q^{39} +0.854102i q^{40} +4.23607 q^{41} +(-2.76393 - 0.618034i) q^{42} +5.38197 q^{43} +3.61803i q^{44} +(-0.854102 - 0.763932i) q^{45} -0.618034 q^{46} +8.00000 q^{47} +(-3.00000 - 1.14590i) q^{48} +(-6.70820 + 2.00000i) q^{49} +3.00000i q^{50} +(-12.0902 - 4.61803i) q^{51} +0.236068i q^{52} -6.56231i q^{53} +(-2.85410 + 1.47214i) q^{54} -0.854102i q^{55} +(5.85410 - 0.854102i) q^{56} +(2.14590 - 5.61803i) q^{57} +3.85410 q^{58} -12.5623 q^{59} +(1.00000 + 0.381966i) q^{60} +5.85410i q^{61} -5.85410 q^{62} +(-4.38197 + 6.61803i) q^{63} +0.236068 q^{64} -0.0557281i q^{65} +(-2.23607 - 0.854102i) q^{66} -8.38197 q^{67} +12.0902 q^{68} +(-0.618034 + 1.61803i) q^{69} +(-0.618034 + 0.0901699i) q^{70} +10.3262i q^{71} +(4.47214 - 5.00000i) q^{72} +3.76393i q^{73} -6.32624i q^{74} +(7.85410 + 3.00000i) q^{75} +5.61803i q^{76} +(-5.85410 + 0.854102i) q^{77} +(-0.145898 - 0.0557281i) q^{78} -12.2361 q^{79} -0.708204 q^{80} +(1.00000 + 8.94427i) q^{81} -2.61803i q^{82} -2.70820 q^{83} +(1.61803 - 7.23607i) q^{84} -2.85410 q^{85} -3.32624i q^{86} +(3.85410 - 10.0902i) q^{87} +5.00000 q^{88} +3.09017 q^{89} +(-0.472136 + 0.527864i) q^{90} +(-0.381966 + 0.0557281i) q^{91} -1.61803i q^{92} +(-5.85410 + 15.3262i) q^{93} -4.94427i q^{94} -1.32624i q^{95} +(-3.47214 + 9.09017i) q^{96} -15.9443i q^{97} +(1.23607 + 4.14590i) q^{98} +(-4.47214 + 5.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{12} + 2 q^{14} - 2 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 2 q^{20} + 4 q^{21} + 10 q^{22} - 10 q^{24} - 6 q^{25} - 22 q^{26} - 14 q^{27} - 2 q^{28} + 14 q^{30} + 10 q^{33} - 14 q^{35} + 10 q^{36} + 32 q^{37} + 22 q^{38} - 22 q^{39} + 8 q^{41} - 20 q^{42} + 26 q^{43} + 10 q^{45} + 2 q^{46} + 32 q^{47} - 12 q^{48} - 26 q^{51} + 2 q^{54} + 10 q^{56} + 22 q^{57} + 2 q^{58} - 10 q^{59} + 4 q^{60} - 10 q^{62} - 22 q^{63} - 8 q^{64} - 38 q^{67} + 26 q^{68} + 2 q^{69} + 2 q^{70} + 18 q^{75} - 10 q^{77} - 14 q^{78} - 40 q^{79} + 24 q^{80} + 4 q^{81} + 16 q^{83} + 2 q^{84} + 2 q^{85} + 2 q^{87} + 20 q^{88} - 10 q^{89} + 16 q^{90} - 6 q^{91} - 10 q^{93} + 4 q^{96} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034i 0.437016i −0.975835 0.218508i \(-0.929881\pi\)
0.975835 0.218508i \(-0.0701190\pi\)
\(3\) −1.61803 0.618034i −0.934172 0.356822i
\(4\) 1.61803 0.809017
\(5\) −0.381966 −0.170820 −0.0854102 0.996346i \(-0.527220\pi\)
−0.0854102 + 0.996346i \(0.527220\pi\)
\(6\) −0.381966 + 1.00000i −0.155937 + 0.408248i
\(7\) 0.381966 + 2.61803i 0.144370 + 0.989524i
\(8\) 2.23607i 0.790569i
\(9\) 2.23607 + 2.00000i 0.745356 + 0.666667i
\(10\) 0.236068i 0.0746512i
\(11\) 2.23607i 0.674200i 0.941469 + 0.337100i \(0.109446\pi\)
−0.941469 + 0.337100i \(0.890554\pi\)
\(12\) −2.61803 1.00000i −0.755761 0.288675i
\(13\) 0.145898i 0.0404648i 0.999795 + 0.0202324i \(0.00644062\pi\)
−0.999795 + 0.0202324i \(0.993559\pi\)
\(14\) 1.61803 0.236068i 0.432438 0.0630918i
\(15\) 0.618034 + 0.236068i 0.159576 + 0.0609525i
\(16\) 1.85410 0.463525
\(17\) 7.47214 1.81226 0.906130 0.423000i \(-0.139023\pi\)
0.906130 + 0.423000i \(0.139023\pi\)
\(18\) 1.23607 1.38197i 0.291344 0.325733i
\(19\) 3.47214i 0.796563i 0.917263 + 0.398281i \(0.130393\pi\)
−0.917263 + 0.398281i \(0.869607\pi\)
\(20\) −0.618034 −0.138197
\(21\) 1.00000 4.47214i 0.218218 0.975900i
\(22\) 1.38197 0.294636
\(23\) 1.00000i 0.208514i
\(24\) −1.38197 + 3.61803i −0.282093 + 0.738528i
\(25\) −4.85410 −0.970820
\(26\) 0.0901699 0.0176838
\(27\) −2.38197 4.61803i −0.458410 0.888741i
\(28\) 0.618034 + 4.23607i 0.116797 + 0.800542i
\(29\) 6.23607i 1.15801i 0.815324 + 0.579004i \(0.196559\pi\)
−0.815324 + 0.579004i \(0.803441\pi\)
\(30\) 0.145898 0.381966i 0.0266372 0.0697371i
\(31\) 9.47214i 1.70125i −0.525776 0.850623i \(-0.676225\pi\)
0.525776 0.850623i \(-0.323775\pi\)
\(32\) 5.61803i 0.993137i
\(33\) 1.38197 3.61803i 0.240569 0.629819i
\(34\) 4.61803i 0.791986i
\(35\) −0.145898 1.00000i −0.0246613 0.169031i
\(36\) 3.61803 + 3.23607i 0.603006 + 0.539345i
\(37\) 10.2361 1.68280 0.841400 0.540413i \(-0.181732\pi\)
0.841400 + 0.540413i \(0.181732\pi\)
\(38\) 2.14590 0.348111
\(39\) 0.0901699 0.236068i 0.0144387 0.0378011i
\(40\) 0.854102i 0.135045i
\(41\) 4.23607 0.661563 0.330781 0.943707i \(-0.392688\pi\)
0.330781 + 0.943707i \(0.392688\pi\)
\(42\) −2.76393 0.618034i −0.426484 0.0953647i
\(43\) 5.38197 0.820742 0.410371 0.911919i \(-0.365399\pi\)
0.410371 + 0.911919i \(0.365399\pi\)
\(44\) 3.61803i 0.545439i
\(45\) −0.854102 0.763932i −0.127322 0.113880i
\(46\) −0.618034 −0.0911241
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −3.00000 1.14590i −0.433013 0.165396i
\(49\) −6.70820 + 2.00000i −0.958315 + 0.285714i
\(50\) 3.00000i 0.424264i
\(51\) −12.0902 4.61803i −1.69296 0.646654i
\(52\) 0.236068i 0.0327367i
\(53\) 6.56231i 0.901402i −0.892675 0.450701i \(-0.851174\pi\)
0.892675 0.450701i \(-0.148826\pi\)
\(54\) −2.85410 + 1.47214i −0.388394 + 0.200332i
\(55\) 0.854102i 0.115167i
\(56\) 5.85410 0.854102i 0.782287 0.114134i
\(57\) 2.14590 5.61803i 0.284231 0.744127i
\(58\) 3.85410 0.506068
\(59\) −12.5623 −1.63547 −0.817736 0.575593i \(-0.804771\pi\)
−0.817736 + 0.575593i \(0.804771\pi\)
\(60\) 1.00000 + 0.381966i 0.129099 + 0.0493116i
\(61\) 5.85410i 0.749541i 0.927118 + 0.374770i \(0.122278\pi\)
−0.927118 + 0.374770i \(0.877722\pi\)
\(62\) −5.85410 −0.743472
\(63\) −4.38197 + 6.61803i −0.552076 + 0.833794i
\(64\) 0.236068 0.0295085
\(65\) 0.0557281i 0.00691222i
\(66\) −2.23607 0.854102i −0.275241 0.105133i
\(67\) −8.38197 −1.02402 −0.512010 0.858979i \(-0.671099\pi\)
−0.512010 + 0.858979i \(0.671099\pi\)
\(68\) 12.0902 1.46615
\(69\) −0.618034 + 1.61803i −0.0744025 + 0.194788i
\(70\) −0.618034 + 0.0901699i −0.0738692 + 0.0107774i
\(71\) 10.3262i 1.22550i 0.790277 + 0.612749i \(0.209937\pi\)
−0.790277 + 0.612749i \(0.790063\pi\)
\(72\) 4.47214 5.00000i 0.527046 0.589256i
\(73\) 3.76393i 0.440535i 0.975440 + 0.220267i \(0.0706930\pi\)
−0.975440 + 0.220267i \(0.929307\pi\)
\(74\) 6.32624i 0.735410i
\(75\) 7.85410 + 3.00000i 0.906914 + 0.346410i
\(76\) 5.61803i 0.644433i
\(77\) −5.85410 + 0.854102i −0.667137 + 0.0973340i
\(78\) −0.145898 0.0557281i −0.0165197 0.00630996i
\(79\) −12.2361 −1.37667 −0.688333 0.725395i \(-0.741657\pi\)
−0.688333 + 0.725395i \(0.741657\pi\)
\(80\) −0.708204 −0.0791796
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 2.61803i 0.289113i
\(83\) −2.70820 −0.297264 −0.148632 0.988893i \(-0.547487\pi\)
−0.148632 + 0.988893i \(0.547487\pi\)
\(84\) 1.61803 7.23607i 0.176542 0.789520i
\(85\) −2.85410 −0.309571
\(86\) 3.32624i 0.358677i
\(87\) 3.85410 10.0902i 0.413203 1.08178i
\(88\) 5.00000 0.533002
\(89\) 3.09017 0.327557 0.163779 0.986497i \(-0.447632\pi\)
0.163779 + 0.986497i \(0.447632\pi\)
\(90\) −0.472136 + 0.527864i −0.0497675 + 0.0556418i
\(91\) −0.381966 + 0.0557281i −0.0400409 + 0.00584189i
\(92\) 1.61803i 0.168692i
\(93\) −5.85410 + 15.3262i −0.607042 + 1.58926i
\(94\) 4.94427i 0.509963i
\(95\) 1.32624i 0.136069i
\(96\) −3.47214 + 9.09017i −0.354373 + 0.927762i
\(97\) 15.9443i 1.61890i −0.587192 0.809448i \(-0.699767\pi\)
0.587192 0.809448i \(-0.300233\pi\)
\(98\) 1.23607 + 4.14590i 0.124862 + 0.418799i
\(99\) −4.47214 + 5.00000i −0.449467 + 0.502519i
\(100\) −7.85410 −0.785410
\(101\) −6.09017 −0.605995 −0.302997 0.952991i \(-0.597987\pi\)
−0.302997 + 0.952991i \(0.597987\pi\)
\(102\) −2.85410 + 7.47214i −0.282598 + 0.739852i
\(103\) 12.1803i 1.20016i 0.799938 + 0.600082i \(0.204866\pi\)
−0.799938 + 0.600082i \(0.795134\pi\)
\(104\) 0.326238 0.0319903
\(105\) −0.381966 + 1.70820i −0.0372761 + 0.166704i
\(106\) −4.05573 −0.393927
\(107\) 9.38197i 0.906989i 0.891259 + 0.453494i \(0.149823\pi\)
−0.891259 + 0.453494i \(0.850177\pi\)
\(108\) −3.85410 7.47214i −0.370861 0.719007i
\(109\) −8.09017 −0.774898 −0.387449 0.921891i \(-0.626644\pi\)
−0.387449 + 0.921891i \(0.626644\pi\)
\(110\) −0.527864 −0.0503299
\(111\) −16.5623 6.32624i −1.57202 0.600460i
\(112\) 0.708204 + 4.85410i 0.0669190 + 0.458670i
\(113\) 13.7984i 1.29804i −0.760771 0.649021i \(-0.775179\pi\)
0.760771 0.649021i \(-0.224821\pi\)
\(114\) −3.47214 1.32624i −0.325195 0.124214i
\(115\) 0.381966i 0.0356185i
\(116\) 10.0902i 0.936849i
\(117\) −0.291796 + 0.326238i −0.0269766 + 0.0301607i
\(118\) 7.76393i 0.714728i
\(119\) 2.85410 + 19.5623i 0.261635 + 1.79327i
\(120\) 0.527864 1.38197i 0.0481872 0.126156i
\(121\) 6.00000 0.545455
\(122\) 3.61803 0.327561
\(123\) −6.85410 2.61803i −0.618014 0.236060i
\(124\) 15.3262i 1.37634i
\(125\) 3.76393 0.336656
\(126\) 4.09017 + 2.70820i 0.364381 + 0.241266i
\(127\) −16.7984 −1.49061 −0.745307 0.666721i \(-0.767697\pi\)
−0.745307 + 0.666721i \(0.767697\pi\)
\(128\) 11.3820i 1.00603i
\(129\) −8.70820 3.32624i −0.766715 0.292859i
\(130\) −0.0344419 −0.00302075
\(131\) 5.29180 0.462346 0.231173 0.972913i \(-0.425744\pi\)
0.231173 + 0.972913i \(0.425744\pi\)
\(132\) 2.23607 5.85410i 0.194625 0.509534i
\(133\) −9.09017 + 1.32624i −0.788218 + 0.114999i
\(134\) 5.18034i 0.447513i
\(135\) 0.909830 + 1.76393i 0.0783057 + 0.151815i
\(136\) 16.7082i 1.43272i
\(137\) 9.76393i 0.834189i −0.908863 0.417095i \(-0.863048\pi\)
0.908863 0.417095i \(-0.136952\pi\)
\(138\) 1.00000 + 0.381966i 0.0851257 + 0.0325151i
\(139\) 12.0902i 1.02547i 0.858545 + 0.512737i \(0.171369\pi\)
−0.858545 + 0.512737i \(0.828631\pi\)
\(140\) −0.236068 1.61803i −0.0199514 0.136749i
\(141\) −12.9443 4.94427i −1.09010 0.416383i
\(142\) 6.38197 0.535563
\(143\) −0.326238 −0.0272814
\(144\) 4.14590 + 3.70820i 0.345492 + 0.309017i
\(145\) 2.38197i 0.197812i
\(146\) 2.32624 0.192521
\(147\) 12.0902 + 0.909830i 0.997180 + 0.0750415i
\(148\) 16.5623 1.36141
\(149\) 5.70820i 0.467634i 0.972281 + 0.233817i \(0.0751217\pi\)
−0.972281 + 0.233817i \(0.924878\pi\)
\(150\) 1.85410 4.85410i 0.151387 0.396336i
\(151\) 6.47214 0.526695 0.263347 0.964701i \(-0.415173\pi\)
0.263347 + 0.964701i \(0.415173\pi\)
\(152\) 7.76393 0.629738
\(153\) 16.7082 + 14.9443i 1.35078 + 1.20817i
\(154\) 0.527864 + 3.61803i 0.0425365 + 0.291549i
\(155\) 3.61803i 0.290607i
\(156\) 0.145898 0.381966i 0.0116812 0.0305818i
\(157\) 16.4721i 1.31462i −0.753620 0.657310i \(-0.771694\pi\)
0.753620 0.657310i \(-0.228306\pi\)
\(158\) 7.56231i 0.601625i
\(159\) −4.05573 + 10.6180i −0.321640 + 0.842065i
\(160\) 2.14590i 0.169648i
\(161\) 2.61803 0.381966i 0.206330 0.0301031i
\(162\) 5.52786 0.618034i 0.434310 0.0485573i
\(163\) −7.90983 −0.619546 −0.309773 0.950811i \(-0.600253\pi\)
−0.309773 + 0.950811i \(0.600253\pi\)
\(164\) 6.85410 0.535215
\(165\) −0.527864 + 1.38197i −0.0410942 + 0.107586i
\(166\) 1.67376i 0.129909i
\(167\) −3.18034 −0.246102 −0.123051 0.992400i \(-0.539268\pi\)
−0.123051 + 0.992400i \(0.539268\pi\)
\(168\) −10.0000 2.23607i −0.771517 0.172516i
\(169\) 12.9787 0.998363
\(170\) 1.76393i 0.135287i
\(171\) −6.94427 + 7.76393i −0.531042 + 0.593723i
\(172\) 8.70820 0.663994
\(173\) −5.47214 −0.416039 −0.208019 0.978125i \(-0.566702\pi\)
−0.208019 + 0.978125i \(0.566702\pi\)
\(174\) −6.23607 2.38197i −0.472755 0.180576i
\(175\) −1.85410 12.7082i −0.140157 0.960650i
\(176\) 4.14590i 0.312509i
\(177\) 20.3262 + 7.76393i 1.52781 + 0.583573i
\(178\) 1.90983i 0.143148i
\(179\) 21.3262i 1.59400i −0.603981 0.796999i \(-0.706420\pi\)
0.603981 0.796999i \(-0.293580\pi\)
\(180\) −1.38197 1.23607i −0.103006 0.0921311i
\(181\) 6.70820i 0.498617i −0.968424 0.249308i \(-0.919797\pi\)
0.968424 0.249308i \(-0.0802033\pi\)
\(182\) 0.0344419 + 0.236068i 0.00255300 + 0.0174985i
\(183\) 3.61803 9.47214i 0.267453 0.700200i
\(184\) −2.23607 −0.164845
\(185\) −3.90983 −0.287456
\(186\) 9.47214 + 3.61803i 0.694531 + 0.265287i
\(187\) 16.7082i 1.22182i
\(188\) 12.9443 0.944058
\(189\) 11.1803 8.00000i 0.813250 0.581914i
\(190\) −0.819660 −0.0594644
\(191\) 8.29180i 0.599973i −0.953943 0.299987i \(-0.903018\pi\)
0.953943 0.299987i \(-0.0969822\pi\)
\(192\) −0.381966 0.145898i −0.0275660 0.0105293i
\(193\) 2.29180 0.164967 0.0824835 0.996592i \(-0.473715\pi\)
0.0824835 + 0.996592i \(0.473715\pi\)
\(194\) −9.85410 −0.707483
\(195\) −0.0344419 + 0.0901699i −0.00246643 + 0.00645720i
\(196\) −10.8541 + 3.23607i −0.775293 + 0.231148i
\(197\) 14.9098i 1.06228i 0.847284 + 0.531141i \(0.178236\pi\)
−0.847284 + 0.531141i \(0.821764\pi\)
\(198\) 3.09017 + 2.76393i 0.219609 + 0.196424i
\(199\) 12.3820i 0.877734i −0.898552 0.438867i \(-0.855380\pi\)
0.898552 0.438867i \(-0.144620\pi\)
\(200\) 10.8541i 0.767501i
\(201\) 13.5623 + 5.18034i 0.956611 + 0.365393i
\(202\) 3.76393i 0.264829i
\(203\) −16.3262 + 2.38197i −1.14588 + 0.167181i
\(204\) −19.5623 7.47214i −1.36964 0.523154i
\(205\) −1.61803 −0.113008
\(206\) 7.52786 0.524491
\(207\) 2.00000 2.23607i 0.139010 0.155417i
\(208\) 0.270510i 0.0187565i
\(209\) −7.76393 −0.537042
\(210\) 1.05573 + 0.236068i 0.0728522 + 0.0162902i
\(211\) −3.00000 −0.206529 −0.103264 0.994654i \(-0.532929\pi\)
−0.103264 + 0.994654i \(0.532929\pi\)
\(212\) 10.6180i 0.729250i
\(213\) 6.38197 16.7082i 0.437285 1.14483i
\(214\) 5.79837 0.396369
\(215\) −2.05573 −0.140199
\(216\) −10.3262 + 5.32624i −0.702611 + 0.362405i
\(217\) 24.7984 3.61803i 1.68342 0.245608i
\(218\) 5.00000i 0.338643i
\(219\) 2.32624 6.09017i 0.157193 0.411536i
\(220\) 1.38197i 0.0931721i
\(221\) 1.09017i 0.0733328i
\(222\) −3.90983 + 10.2361i −0.262411 + 0.687000i
\(223\) 5.90983i 0.395751i −0.980227 0.197876i \(-0.936596\pi\)
0.980227 0.197876i \(-0.0634043\pi\)
\(224\) 14.7082 2.14590i 0.982733 0.143379i
\(225\) −10.8541 9.70820i −0.723607 0.647214i
\(226\) −8.52786 −0.567265
\(227\) −6.67376 −0.442953 −0.221477 0.975166i \(-0.571088\pi\)
−0.221477 + 0.975166i \(0.571088\pi\)
\(228\) 3.47214 9.09017i 0.229948 0.602011i
\(229\) 22.0902i 1.45976i 0.683576 + 0.729880i \(0.260424\pi\)
−0.683576 + 0.729880i \(0.739576\pi\)
\(230\) 0.236068 0.0155659
\(231\) 10.0000 + 2.23607i 0.657952 + 0.147122i
\(232\) 13.9443 0.915486
\(233\) 29.3262i 1.92123i −0.277890 0.960613i \(-0.589635\pi\)
0.277890 0.960613i \(-0.410365\pi\)
\(234\) 0.201626 + 0.180340i 0.0131807 + 0.0117892i
\(235\) −3.05573 −0.199334
\(236\) −20.3262 −1.32313
\(237\) 19.7984 + 7.56231i 1.28604 + 0.491225i
\(238\) 12.0902 1.76393i 0.783689 0.114339i
\(239\) 21.3262i 1.37948i −0.724057 0.689740i \(-0.757725\pi\)
0.724057 0.689740i \(-0.242275\pi\)
\(240\) 1.14590 + 0.437694i 0.0739674 + 0.0282530i
\(241\) 9.47214i 0.610154i −0.952328 0.305077i \(-0.901318\pi\)
0.952328 0.305077i \(-0.0986822\pi\)
\(242\) 3.70820i 0.238372i
\(243\) 3.90983 15.0902i 0.250816 0.968035i
\(244\) 9.47214i 0.606391i
\(245\) 2.56231 0.763932i 0.163700 0.0488058i
\(246\) −1.61803 + 4.23607i −0.103162 + 0.270082i
\(247\) −0.506578 −0.0322328
\(248\) −21.1803 −1.34495
\(249\) 4.38197 + 1.67376i 0.277696 + 0.106070i
\(250\) 2.32624i 0.147124i
\(251\) −2.47214 −0.156040 −0.0780199 0.996952i \(-0.524860\pi\)
−0.0780199 + 0.996952i \(0.524860\pi\)
\(252\) −7.09017 + 10.7082i −0.446639 + 0.674553i
\(253\) 2.23607 0.140580
\(254\) 10.3820i 0.651422i
\(255\) 4.61803 + 1.76393i 0.289193 + 0.110462i
\(256\) −6.56231 −0.410144
\(257\) −13.0557 −0.814394 −0.407197 0.913340i \(-0.633494\pi\)
−0.407197 + 0.913340i \(0.633494\pi\)
\(258\) −2.05573 + 5.38197i −0.127984 + 0.335067i
\(259\) 3.90983 + 26.7984i 0.242945 + 1.66517i
\(260\) 0.0901699i 0.00559210i
\(261\) −12.4721 + 13.9443i −0.772006 + 0.863129i
\(262\) 3.27051i 0.202053i
\(263\) 0.0557281i 0.00343634i −0.999999 0.00171817i \(-0.999453\pi\)
0.999999 0.00171817i \(-0.000546911\pi\)
\(264\) −8.09017 3.09017i −0.497916 0.190187i
\(265\) 2.50658i 0.153978i
\(266\) 0.819660 + 5.61803i 0.0502566 + 0.344464i
\(267\) −5.00000 1.90983i −0.305995 0.116880i
\(268\) −13.5623 −0.828450
\(269\) 4.14590 0.252780 0.126390 0.991981i \(-0.459661\pi\)
0.126390 + 0.991981i \(0.459661\pi\)
\(270\) 1.09017 0.562306i 0.0663456 0.0342208i
\(271\) 2.23607i 0.135831i −0.997691 0.0679157i \(-0.978365\pi\)
0.997691 0.0679157i \(-0.0216349\pi\)
\(272\) 13.8541 0.840028
\(273\) 0.652476 + 0.145898i 0.0394896 + 0.00883015i
\(274\) −6.03444 −0.364554
\(275\) 10.8541i 0.654527i
\(276\) −1.00000 + 2.61803i −0.0601929 + 0.157587i
\(277\) 13.8541 0.832412 0.416206 0.909270i \(-0.363359\pi\)
0.416206 + 0.909270i \(0.363359\pi\)
\(278\) 7.47214 0.448149
\(279\) 18.9443 21.1803i 1.13416 1.26803i
\(280\) −2.23607 + 0.326238i −0.133631 + 0.0194964i
\(281\) 18.9443i 1.13012i −0.825050 0.565060i \(-0.808853\pi\)
0.825050 0.565060i \(-0.191147\pi\)
\(282\) −3.05573 + 8.00000i −0.181966 + 0.476393i
\(283\) 15.7984i 0.939116i 0.882902 + 0.469558i \(0.155587\pi\)
−0.882902 + 0.469558i \(0.844413\pi\)
\(284\) 16.7082i 0.991449i
\(285\) −0.819660 + 2.14590i −0.0485525 + 0.127112i
\(286\) 0.201626i 0.0119224i
\(287\) 1.61803 + 11.0902i 0.0955095 + 0.654632i
\(288\) 11.2361 12.5623i 0.662092 0.740241i
\(289\) 38.8328 2.28428
\(290\) −1.47214 −0.0864468
\(291\) −9.85410 + 25.7984i −0.577658 + 1.51233i
\(292\) 6.09017i 0.356400i
\(293\) −27.7082 −1.61873 −0.809365 0.587306i \(-0.800189\pi\)
−0.809365 + 0.587306i \(0.800189\pi\)
\(294\) 0.562306 7.47214i 0.0327943 0.435784i
\(295\) 4.79837 0.279372
\(296\) 22.8885i 1.33037i
\(297\) 10.3262 5.32624i 0.599189 0.309060i
\(298\) 3.52786 0.204364
\(299\) 0.145898 0.00843750
\(300\) 12.7082 + 4.85410i 0.733708 + 0.280252i
\(301\) 2.05573 + 14.0902i 0.118490 + 0.812144i
\(302\) 4.00000i 0.230174i
\(303\) 9.85410 + 3.76393i 0.566103 + 0.216232i
\(304\) 6.43769i 0.369227i
\(305\) 2.23607i 0.128037i
\(306\) 9.23607 10.3262i 0.527991 0.590312i
\(307\) 12.5279i 0.715003i −0.933913 0.357501i \(-0.883629\pi\)
0.933913 0.357501i \(-0.116371\pi\)
\(308\) −9.47214 + 1.38197i −0.539725 + 0.0787448i
\(309\) 7.52786 19.7082i 0.428245 1.12116i
\(310\) 2.23607 0.127000
\(311\) −7.67376 −0.435139 −0.217570 0.976045i \(-0.569813\pi\)
−0.217570 + 0.976045i \(0.569813\pi\)
\(312\) −0.527864 0.201626i −0.0298844 0.0114148i
\(313\) 12.1803i 0.688474i 0.938883 + 0.344237i \(0.111862\pi\)
−0.938883 + 0.344237i \(0.888138\pi\)
\(314\) −10.1803 −0.574510
\(315\) 1.67376 2.52786i 0.0943058 0.142429i
\(316\) −19.7984 −1.11375
\(317\) 1.61803i 0.0908778i 0.998967 + 0.0454389i \(0.0144686\pi\)
−0.998967 + 0.0454389i \(0.985531\pi\)
\(318\) 6.56231 + 2.50658i 0.367996 + 0.140562i
\(319\) −13.9443 −0.780729
\(320\) −0.0901699 −0.00504065
\(321\) 5.79837 15.1803i 0.323634 0.847284i
\(322\) −0.236068 1.61803i −0.0131556 0.0901695i
\(323\) 25.9443i 1.44358i
\(324\) 1.61803 + 14.4721i 0.0898908 + 0.804008i
\(325\) 0.708204i 0.0392841i
\(326\) 4.88854i 0.270751i
\(327\) 13.0902 + 5.00000i 0.723888 + 0.276501i
\(328\) 9.47214i 0.523011i
\(329\) 3.05573 + 20.9443i 0.168468 + 1.15470i
\(330\) 0.854102 + 0.326238i 0.0470168 + 0.0179588i
\(331\) −22.0689 −1.21302 −0.606508 0.795078i \(-0.707430\pi\)
−0.606508 + 0.795078i \(0.707430\pi\)
\(332\) −4.38197 −0.240492
\(333\) 22.8885 + 20.4721i 1.25428 + 1.12187i
\(334\) 1.96556i 0.107551i
\(335\) 3.20163 0.174924
\(336\) 1.85410 8.29180i 0.101150 0.452355i
\(337\) 23.4508 1.27745 0.638725 0.769435i \(-0.279462\pi\)
0.638725 + 0.769435i \(0.279462\pi\)
\(338\) 8.02129i 0.436300i
\(339\) −8.52786 + 22.3262i −0.463170 + 1.21259i
\(340\) −4.61803 −0.250448
\(341\) 21.1803 1.14698
\(342\) 4.79837 + 4.29180i 0.259466 + 0.232074i
\(343\) −7.79837 16.7984i −0.421073 0.907027i
\(344\) 12.0344i 0.648854i
\(345\) 0.236068 0.618034i 0.0127095 0.0332738i
\(346\) 3.38197i 0.181816i
\(347\) 0.819660i 0.0440017i −0.999758 0.0220008i \(-0.992996\pi\)
0.999758 0.0220008i \(-0.00700365\pi\)
\(348\) 6.23607 16.3262i 0.334288 0.875178i
\(349\) 25.1459i 1.34603i −0.739629 0.673015i \(-0.764999\pi\)
0.739629 0.673015i \(-0.235001\pi\)
\(350\) −7.85410 + 1.14590i −0.419819 + 0.0612508i
\(351\) 0.673762 0.347524i 0.0359628 0.0185495i
\(352\) 12.5623 0.669573
\(353\) −35.4721 −1.88799 −0.943996 0.329958i \(-0.892965\pi\)
−0.943996 + 0.329958i \(0.892965\pi\)
\(354\) 4.79837 12.5623i 0.255031 0.667679i
\(355\) 3.94427i 0.209340i
\(356\) 5.00000 0.264999
\(357\) 7.47214 33.4164i 0.395467 1.76858i
\(358\) −13.1803 −0.696603
\(359\) 14.0902i 0.743651i −0.928303 0.371825i \(-0.878732\pi\)
0.928303 0.371825i \(-0.121268\pi\)
\(360\) −1.70820 + 1.90983i −0.0900303 + 0.100657i
\(361\) 6.94427 0.365488
\(362\) −4.14590 −0.217904
\(363\) −9.70820 3.70820i −0.509549 0.194630i
\(364\) −0.618034 + 0.0901699i −0.0323938 + 0.00472619i
\(365\) 1.43769i 0.0752523i
\(366\) −5.85410 2.23607i −0.305999 0.116881i
\(367\) 11.2705i 0.588316i −0.955757 0.294158i \(-0.904961\pi\)
0.955757 0.294158i \(-0.0950392\pi\)
\(368\) 1.85410i 0.0966517i
\(369\) 9.47214 + 8.47214i 0.493100 + 0.441042i
\(370\) 2.41641i 0.125623i
\(371\) 17.1803 2.50658i 0.891959 0.130135i
\(372\) −9.47214 + 24.7984i −0.491107 + 1.28574i
\(373\) −1.00000 −0.0517780 −0.0258890 0.999665i \(-0.508242\pi\)
−0.0258890 + 0.999665i \(0.508242\pi\)
\(374\) 10.3262 0.533957
\(375\) −6.09017 2.32624i −0.314495 0.120126i
\(376\) 17.8885i 0.922531i
\(377\) −0.909830 −0.0468586
\(378\) −4.94427 6.90983i −0.254306 0.355403i
\(379\) 15.5279 0.797613 0.398806 0.917035i \(-0.369425\pi\)
0.398806 + 0.917035i \(0.369425\pi\)
\(380\) 2.14590i 0.110082i
\(381\) 27.1803 + 10.3820i 1.39249 + 0.531884i
\(382\) −5.12461 −0.262198
\(383\) −3.76393 −0.192328 −0.0961640 0.995366i \(-0.530657\pi\)
−0.0961640 + 0.995366i \(0.530657\pi\)
\(384\) −7.03444 + 18.4164i −0.358975 + 0.939808i
\(385\) 2.23607 0.326238i 0.113961 0.0166266i
\(386\) 1.41641i 0.0720933i
\(387\) 12.0344 + 10.7639i 0.611745 + 0.547161i
\(388\) 25.7984i 1.30971i
\(389\) 19.2918i 0.978133i −0.872247 0.489066i \(-0.837338\pi\)
0.872247 0.489066i \(-0.162662\pi\)
\(390\) 0.0557281 + 0.0212862i 0.00282190 + 0.00107787i
\(391\) 7.47214i 0.377882i
\(392\) 4.47214 + 15.0000i 0.225877 + 0.757614i
\(393\) −8.56231 3.27051i −0.431911 0.164975i
\(394\) 9.21478 0.464234
\(395\) 4.67376 0.235162
\(396\) −7.23607 + 8.09017i −0.363626 + 0.406546i
\(397\) 10.7639i 0.540226i 0.962829 + 0.270113i \(0.0870611\pi\)
−0.962829 + 0.270113i \(0.912939\pi\)
\(398\) −7.65248 −0.383584
\(399\) 15.5279 + 3.47214i 0.777366 + 0.173824i
\(400\) −9.00000 −0.450000
\(401\) 18.4164i 0.919672i 0.888004 + 0.459836i \(0.152092\pi\)
−0.888004 + 0.459836i \(0.847908\pi\)
\(402\) 3.20163 8.38197i 0.159683 0.418054i
\(403\) 1.38197 0.0688406
\(404\) −9.85410 −0.490260
\(405\) −0.381966 3.41641i −0.0189800 0.169763i
\(406\) 1.47214 + 10.0902i 0.0730609 + 0.500767i
\(407\) 22.8885i 1.13454i
\(408\) −10.3262 + 27.0344i −0.511225 + 1.33840i
\(409\) 24.5279i 1.21282i 0.795150 + 0.606412i \(0.207392\pi\)
−0.795150 + 0.606412i \(0.792608\pi\)
\(410\) 1.00000i 0.0493865i
\(411\) −6.03444 + 15.7984i −0.297657 + 0.779276i
\(412\) 19.7082i 0.970954i
\(413\) −4.79837 32.8885i −0.236113 1.61834i
\(414\) −1.38197 1.23607i −0.0679199 0.0607494i
\(415\) 1.03444 0.0507788
\(416\) 0.819660 0.0401871
\(417\) 7.47214 19.5623i 0.365912 0.957970i
\(418\) 4.79837i 0.234696i
\(419\) −0.201626 −0.00985008 −0.00492504 0.999988i \(-0.501568\pi\)
−0.00492504 + 0.999988i \(0.501568\pi\)
\(420\) −0.618034 + 2.76393i −0.0301570 + 0.134866i
\(421\) −20.6869 −1.00822 −0.504109 0.863640i \(-0.668179\pi\)
−0.504109 + 0.863640i \(0.668179\pi\)
\(422\) 1.85410i 0.0902563i
\(423\) 17.8885 + 16.0000i 0.869771 + 0.777947i
\(424\) −14.6738 −0.712621
\(425\) −36.2705 −1.75938
\(426\) −10.3262 3.94427i −0.500308 0.191101i
\(427\) −15.3262 + 2.23607i −0.741689 + 0.108211i
\(428\) 15.1803i 0.733769i
\(429\) 0.527864 + 0.201626i 0.0254855 + 0.00973460i
\(430\) 1.27051i 0.0612694i
\(431\) 33.0902i 1.59390i 0.604047 + 0.796949i \(0.293554\pi\)
−0.604047 + 0.796949i \(0.706446\pi\)
\(432\) −4.41641 8.56231i −0.212485 0.411954i
\(433\) 10.4721i 0.503259i 0.967824 + 0.251629i \(0.0809664\pi\)
−0.967824 + 0.251629i \(0.919034\pi\)
\(434\) −2.23607 15.3262i −0.107335 0.735683i
\(435\) −1.47214 + 3.85410i −0.0705835 + 0.184790i
\(436\) −13.0902 −0.626905
\(437\) 3.47214 0.166095
\(438\) −3.76393 1.43769i −0.179848 0.0686957i
\(439\) 16.5279i 0.788832i −0.918932 0.394416i \(-0.870947\pi\)
0.918932 0.394416i \(-0.129053\pi\)
\(440\) −1.90983 −0.0910476
\(441\) −19.0000 8.94427i −0.904762 0.425918i
\(442\) 0.673762 0.0320476
\(443\) 0.180340i 0.00856821i −0.999991 0.00428410i \(-0.998636\pi\)
0.999991 0.00428410i \(-0.00136368\pi\)
\(444\) −26.7984 10.2361i −1.27179 0.485782i
\(445\) −1.18034 −0.0559535
\(446\) −3.65248 −0.172950
\(447\) 3.52786 9.23607i 0.166862 0.436851i
\(448\) 0.0901699 + 0.618034i 0.00426013 + 0.0291994i
\(449\) 22.0902i 1.04250i 0.853404 + 0.521250i \(0.174534\pi\)
−0.853404 + 0.521250i \(0.825466\pi\)
\(450\) −6.00000 + 6.70820i −0.282843 + 0.316228i
\(451\) 9.47214i 0.446025i
\(452\) 22.3262i 1.05014i
\(453\) −10.4721 4.00000i −0.492024 0.187936i
\(454\) 4.12461i 0.193578i
\(455\) 0.145898 0.0212862i 0.00683981 0.000997914i
\(456\) −12.5623 4.79837i −0.588284 0.224704i
\(457\) −4.56231 −0.213416 −0.106708 0.994290i \(-0.534031\pi\)
−0.106708 + 0.994290i \(0.534031\pi\)
\(458\) 13.6525 0.637938
\(459\) −17.7984 34.5066i −0.830757 1.61063i
\(460\) 0.618034i 0.0288160i
\(461\) −35.6869 −1.66211 −0.831053 0.556194i \(-0.812261\pi\)
−0.831053 + 0.556194i \(0.812261\pi\)
\(462\) 1.38197 6.18034i 0.0642949 0.287535i
\(463\) −25.4721 −1.18379 −0.591895 0.806015i \(-0.701620\pi\)
−0.591895 + 0.806015i \(0.701620\pi\)
\(464\) 11.5623i 0.536767i
\(465\) 2.23607 5.85410i 0.103695 0.271477i
\(466\) −18.1246 −0.839606
\(467\) 19.8328 0.917753 0.458877 0.888500i \(-0.348252\pi\)
0.458877 + 0.888500i \(0.348252\pi\)
\(468\) −0.472136 + 0.527864i −0.0218245 + 0.0244005i
\(469\) −3.20163 21.9443i −0.147837 1.01329i
\(470\) 1.88854i 0.0871120i
\(471\) −10.1803 + 26.6525i −0.469085 + 1.22808i
\(472\) 28.0902i 1.29295i
\(473\) 12.0344i 0.553344i
\(474\) 4.67376 12.2361i 0.214673 0.562021i
\(475\) 16.8541i 0.773319i
\(476\) 4.61803 + 31.6525i 0.211667 + 1.45079i
\(477\) 13.1246 14.6738i 0.600935 0.671865i
\(478\) −13.1803 −0.602855
\(479\) −5.65248 −0.258268 −0.129134 0.991627i \(-0.541220\pi\)
−0.129134 + 0.991627i \(0.541220\pi\)
\(480\) 1.32624 3.47214i 0.0605342 0.158481i
\(481\) 1.49342i 0.0680942i
\(482\) −5.85410 −0.266647
\(483\) −4.47214 1.00000i −0.203489 0.0455016i
\(484\) 9.70820 0.441282
\(485\) 6.09017i 0.276540i
\(486\) −9.32624 2.41641i −0.423047 0.109610i
\(487\) 1.29180 0.0585369 0.0292684 0.999572i \(-0.490682\pi\)
0.0292684 + 0.999572i \(0.490682\pi\)
\(488\) 13.0902 0.592564
\(489\) 12.7984 + 4.88854i 0.578762 + 0.221068i
\(490\) −0.472136 1.58359i −0.0213289 0.0715394i
\(491\) 33.0902i 1.49334i 0.665196 + 0.746669i \(0.268348\pi\)
−0.665196 + 0.746669i \(0.731652\pi\)
\(492\) −11.0902 4.23607i −0.499983 0.190977i
\(493\) 46.5967i 2.09861i
\(494\) 0.313082i 0.0140862i
\(495\) 1.70820 1.90983i 0.0767781 0.0858405i
\(496\) 17.5623i 0.788571i
\(497\) −27.0344 + 3.94427i −1.21266 + 0.176925i
\(498\) 1.03444 2.70820i 0.0463544 0.121358i
\(499\) 2.56231 0.114705 0.0573523 0.998354i \(-0.481734\pi\)
0.0573523 + 0.998354i \(0.481734\pi\)
\(500\) 6.09017 0.272361
\(501\) 5.14590 + 1.96556i 0.229902 + 0.0878147i
\(502\) 1.52786i 0.0681919i
\(503\) 42.7426 1.90580 0.952900 0.303284i \(-0.0980831\pi\)
0.952900 + 0.303284i \(0.0980831\pi\)
\(504\) 14.7984 + 9.79837i 0.659172 + 0.436454i
\(505\) 2.32624 0.103516
\(506\) 1.38197i 0.0614359i
\(507\) −21.0000 8.02129i −0.932643 0.356238i
\(508\) −27.1803 −1.20593
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 1.09017 2.85410i 0.0482735 0.126382i
\(511\) −9.85410 + 1.43769i −0.435920 + 0.0635998i
\(512\) 18.7082i 0.826794i
\(513\) 16.0344 8.27051i 0.707938 0.365152i
\(514\) 8.06888i 0.355903i
\(515\) 4.65248i 0.205013i
\(516\) −14.0902 5.38197i −0.620285 0.236928i
\(517\) 17.8885i 0.786737i
\(518\) 16.5623 2.41641i 0.727706 0.106171i
\(519\) 8.85410 + 3.38197i 0.388652 + 0.148452i
\(520\) −0.124612 −0.00546459
\(521\) 27.5279 1.20602 0.603009 0.797735i \(-0.293968\pi\)
0.603009 + 0.797735i \(0.293968\pi\)
\(522\) 8.61803 + 7.70820i 0.377201 + 0.337379i
\(523\) 23.5967i 1.03181i −0.856645 0.515907i \(-0.827455\pi\)
0.856645 0.515907i \(-0.172545\pi\)
\(524\) 8.56231 0.374046
\(525\) −4.85410 + 21.7082i −0.211850 + 0.947424i
\(526\) −0.0344419 −0.00150174
\(527\) 70.7771i 3.08310i
\(528\) 2.56231 6.70820i 0.111510 0.291937i
\(529\) −1.00000 −0.0434783
\(530\) 1.54915 0.0672908
\(531\) −28.0902 25.1246i −1.21901 1.09032i
\(532\) −14.7082 + 2.14590i −0.637682 + 0.0930365i
\(533\) 0.618034i 0.0267700i
\(534\) −1.18034 + 3.09017i −0.0510783 + 0.133725i
\(535\) 3.58359i 0.154932i
\(536\) 18.7426i 0.809559i
\(537\) −13.1803 + 34.5066i −0.568774 + 1.48907i
\(538\) 2.56231i 0.110469i
\(539\) −4.47214 15.0000i −0.192629 0.646096i
\(540\) 1.47214 + 2.85410i 0.0633506 + 0.122821i
\(541\) −20.7639 −0.892711 −0.446356 0.894856i \(-0.647278\pi\)
−0.446356 + 0.894856i \(0.647278\pi\)
\(542\) −1.38197 −0.0593605
\(543\) −4.14590 + 10.8541i −0.177918 + 0.465794i
\(544\) 41.9787i 1.79982i
\(545\) 3.09017 0.132368
\(546\) 0.0901699 0.403252i 0.00385892 0.0172576i
\(547\) 31.2148 1.33465 0.667324 0.744768i \(-0.267440\pi\)
0.667324 + 0.744768i \(0.267440\pi\)
\(548\) 15.7984i 0.674873i
\(549\) −11.7082 + 13.0902i −0.499694 + 0.558675i
\(550\) −6.70820 −0.286039
\(551\) −21.6525 −0.922426
\(552\) 3.61803 + 1.38197i 0.153994 + 0.0588204i
\(553\) −4.67376 32.0344i −0.198749 1.36224i
\(554\) 8.56231i 0.363778i
\(555\) 6.32624 + 2.41641i 0.268534 + 0.102571i
\(556\) 19.5623i 0.829627i
\(557\) 26.0689i 1.10457i −0.833654 0.552287i \(-0.813755\pi\)
0.833654 0.552287i \(-0.186245\pi\)
\(558\) −13.0902 11.7082i −0.554151 0.495648i
\(559\) 0.785218i 0.0332112i
\(560\) −0.270510 1.85410i −0.0114311 0.0783501i
\(561\) 10.3262 27.0344i 0.435974 1.14140i
\(562\) −11.7082 −0.493881
\(563\) 18.1459 0.764758 0.382379 0.924005i \(-0.375105\pi\)
0.382379 + 0.924005i \(0.375105\pi\)
\(564\) −20.9443 8.00000i −0.881913 0.336861i
\(565\) 5.27051i 0.221732i
\(566\) 9.76393 0.410409
\(567\) −23.0344 + 6.03444i −0.967356 + 0.253423i
\(568\) 23.0902 0.968842
\(569\) 13.5967i 0.570005i 0.958527 + 0.285003i \(0.0919945\pi\)
−0.958527 + 0.285003i \(0.908006\pi\)
\(570\) 1.32624 + 0.506578i 0.0555500 + 0.0212182i
\(571\) 10.4164 0.435913 0.217957 0.975958i \(-0.430061\pi\)
0.217957 + 0.975958i \(0.430061\pi\)
\(572\) −0.527864 −0.0220711
\(573\) −5.12461 + 13.4164i −0.214084 + 0.560478i
\(574\) 6.85410 1.00000i 0.286085 0.0417392i
\(575\) 4.85410i 0.202430i
\(576\) 0.527864 + 0.472136i 0.0219943 + 0.0196723i
\(577\) 29.3050i 1.21998i 0.792409 + 0.609991i \(0.208827\pi\)
−0.792409 + 0.609991i \(0.791173\pi\)
\(578\) 24.0000i 0.998268i
\(579\) −3.70820 1.41641i −0.154108 0.0588639i
\(580\) 3.85410i 0.160033i
\(581\) −1.03444 7.09017i −0.0429159 0.294150i
\(582\) 15.9443 + 6.09017i 0.660911 + 0.252446i
\(583\) 14.6738 0.607725
\(584\) 8.41641 0.348273
\(585\) 0.111456 0.124612i 0.00460815 0.00515206i
\(586\) 17.1246i 0.707411i
\(587\) −2.32624 −0.0960141 −0.0480071 0.998847i \(-0.515287\pi\)
−0.0480071 + 0.998847i \(0.515287\pi\)
\(588\) 19.5623 + 1.47214i 0.806736 + 0.0607099i
\(589\) 32.8885 1.35515
\(590\) 2.96556i 0.122090i
\(591\) 9.21478 24.1246i 0.379045 0.992354i
\(592\) 18.9787 0.780020
\(593\) 9.12461 0.374703 0.187351 0.982293i \(-0.440010\pi\)
0.187351 + 0.982293i \(0.440010\pi\)
\(594\) −3.29180 6.38197i −0.135064 0.261855i
\(595\) −1.09017 7.47214i −0.0446926 0.306328i
\(596\) 9.23607i 0.378324i
\(597\) −7.65248 + 20.0344i −0.313195 + 0.819955i
\(598\) 0.0901699i 0.00368732i
\(599\) 9.85410i 0.402628i 0.979527 + 0.201314i \(0.0645211\pi\)
−0.979527 + 0.201314i \(0.935479\pi\)
\(600\) 6.70820 17.5623i 0.273861 0.716978i
\(601\) 25.3262i 1.03308i 0.856263 + 0.516539i \(0.172780\pi\)
−0.856263 + 0.516539i \(0.827220\pi\)
\(602\) 8.70820 1.27051i 0.354920 0.0517821i
\(603\) −18.7426 16.7639i −0.763260 0.682680i
\(604\) 10.4721 0.426105
\(605\) −2.29180 −0.0931748
\(606\) 2.32624 6.09017i 0.0944970 0.247396i
\(607\) 14.4377i 0.586008i −0.956111 0.293004i \(-0.905345\pi\)
0.956111 0.293004i \(-0.0946549\pi\)
\(608\) 19.5066 0.791096
\(609\) 27.8885 + 6.23607i 1.13010 + 0.252698i
\(610\) −1.38197 −0.0559542
\(611\) 1.16718i 0.0472192i
\(612\) 27.0344 + 24.1803i 1.09280 + 0.977432i
\(613\) 3.47214 0.140238 0.0701191 0.997539i \(-0.477662\pi\)
0.0701191 + 0.997539i \(0.477662\pi\)
\(614\) −7.74265 −0.312468
\(615\) 2.61803 + 1.00000i 0.105569 + 0.0403239i
\(616\) 1.90983 + 13.0902i 0.0769492 + 0.527418i
\(617\) 21.0902i 0.849058i 0.905414 + 0.424529i \(0.139560\pi\)
−0.905414 + 0.424529i \(0.860440\pi\)
\(618\) −12.1803 4.65248i −0.489965 0.187150i
\(619\) 6.97871i 0.280498i −0.990116 0.140249i \(-0.955210\pi\)
0.990116 0.140249i \(-0.0447903\pi\)
\(620\) 5.85410i 0.235106i
\(621\) −4.61803 + 2.38197i −0.185315 + 0.0955850i
\(622\) 4.74265i 0.190163i
\(623\) 1.18034 + 8.09017i 0.0472893 + 0.324126i
\(624\) 0.167184 0.437694i 0.00669273 0.0175218i
\(625\) 22.8328 0.913313
\(626\) 7.52786 0.300874
\(627\) 12.5623 + 4.79837i 0.501690 + 0.191629i
\(628\) 26.6525i 1.06355i
\(629\) 76.4853 3.04967
\(630\) −1.56231 1.03444i −0.0622438 0.0412131i
\(631\) −29.1803 −1.16165 −0.580825 0.814028i \(-0.697270\pi\)
−0.580825 + 0.814028i \(0.697270\pi\)
\(632\) 27.3607i 1.08835i
\(633\) 4.85410 + 1.85410i 0.192933 + 0.0736939i
\(634\) 1.00000 0.0397151
\(635\) 6.41641 0.254627
\(636\) −6.56231 + 17.1803i −0.260212 + 0.681245i
\(637\) −0.291796 0.978714i −0.0115614 0.0387781i
\(638\) 8.61803i 0.341191i
\(639\) −20.6525 + 23.0902i −0.816999 + 0.913433i
\(640\) 4.34752i 0.171851i
\(641\) 27.5623i 1.08865i −0.838876 0.544323i \(-0.816787\pi\)
0.838876 0.544323i \(-0.183213\pi\)
\(642\) −9.38197 3.58359i −0.370277 0.141433i
\(643\) 18.7984i 0.741335i −0.928766 0.370668i \(-0.879129\pi\)
0.928766 0.370668i \(-0.120871\pi\)
\(644\) 4.23607 0.618034i 0.166924 0.0243540i
\(645\) 3.32624 + 1.27051i 0.130970 + 0.0500263i
\(646\) 16.0344 0.630867
\(647\) −4.96556 −0.195216 −0.0976081 0.995225i \(-0.531119\pi\)
−0.0976081 + 0.995225i \(0.531119\pi\)
\(648\) 20.0000 2.23607i 0.785674 0.0878410i
\(649\) 28.0902i 1.10264i
\(650\) −0.437694 −0.0171678
\(651\) −42.3607 9.47214i −1.66025 0.371242i
\(652\) −12.7984 −0.501223
\(653\) 35.5066i 1.38948i −0.719261 0.694740i \(-0.755519\pi\)
0.719261 0.694740i \(-0.244481\pi\)
\(654\) 3.09017 8.09017i 0.120835 0.316351i
\(655\) −2.02129 −0.0789782
\(656\) 7.85410 0.306651
\(657\) −7.52786 + 8.41641i −0.293690 + 0.328355i
\(658\) 12.9443 1.88854i 0.504620 0.0736231i
\(659\) 22.4164i 0.873219i 0.899651 + 0.436610i \(0.143821\pi\)
−0.899651 + 0.436610i \(0.856179\pi\)
\(660\) −0.854102 + 2.23607i −0.0332459 + 0.0870388i
\(661\) 33.9443i 1.32028i −0.751143 0.660140i \(-0.770497\pi\)
0.751143 0.660140i \(-0.229503\pi\)
\(662\) 13.6393i 0.530107i
\(663\) 0.673762 1.76393i 0.0261668 0.0685054i
\(664\) 6.05573i 0.235008i
\(665\) 3.47214 0.506578i 0.134644 0.0196442i
\(666\) 12.6525 14.1459i 0.490273 0.548142i
\(667\) 6.23607 0.241462
\(668\) −5.14590 −0.199101
\(669\) −3.65248 + 9.56231i −0.141213 + 0.369700i
\(670\) 1.97871i 0.0764444i
\(671\) −13.0902 −0.505340
\(672\) −25.1246 5.61803i −0.969203 0.216720i
\(673\) 1.76393 0.0679946 0.0339973 0.999422i \(-0.489176\pi\)
0.0339973 + 0.999422i \(0.489176\pi\)
\(674\) 14.4934i 0.558266i
\(675\) 11.5623 + 22.4164i 0.445033 + 0.862808i
\(676\) 21.0000 0.807692
\(677\) 24.5066 0.941864 0.470932 0.882169i \(-0.343918\pi\)
0.470932 + 0.882169i \(0.343918\pi\)
\(678\) 13.7984 + 5.27051i 0.529923 + 0.202413i
\(679\) 41.7426 6.09017i 1.60194 0.233719i
\(680\) 6.38197i 0.244737i
\(681\) 10.7984 + 4.12461i 0.413795 + 0.158055i
\(682\) 13.0902i 0.501249i
\(683\) 20.5967i 0.788113i 0.919086 + 0.394056i \(0.128929\pi\)
−0.919086 + 0.394056i \(0.871071\pi\)
\(684\) −11.2361 + 12.5623i −0.429622 + 0.480332i
\(685\) 3.72949i 0.142496i
\(686\) −10.3820 + 4.81966i −0.396385 + 0.184015i
\(687\) 13.6525 35.7426i 0.520874 1.36367i
\(688\) 9.97871 0.380435
\(689\) 0.957428 0.0364751
\(690\) −0.381966 0.145898i −0.0145412 0.00555424i
\(691\) 3.09017i 0.117556i −0.998271 0.0587778i \(-0.981280\pi\)
0.998271 0.0587778i \(-0.0187203\pi\)
\(692\) −8.85410 −0.336582
\(693\) −14.7984 9.79837i −0.562144 0.372209i
\(694\) −0.506578 −0.0192294
\(695\) 4.61803i 0.175172i
\(696\) −22.5623 8.61803i −0.855222 0.326666i
\(697\) 31.6525 1.19892
\(698\) −15.5410 −0.588236
\(699\) −18.1246 + 47.4508i −0.685536 + 1.79476i
\(700\) −3.00000 20.5623i −0.113389 0.777182i
\(701\) 46.6312i 1.76124i 0.473827 + 0.880618i \(0.342872\pi\)
−0.473827 + 0.880618i \(0.657128\pi\)
\(702\) −0.214782 0.416408i −0.00810641 0.0157163i
\(703\) 35.5410i 1.34045i
\(704\) 0.527864i 0.0198946i
\(705\) 4.94427 + 1.88854i 0.186212 + 0.0711267i
\(706\) 21.9230i 0.825082i
\(707\) −2.32624 15.9443i −0.0874872 0.599646i
\(708\) 32.8885 + 12.5623i 1.23603 + 0.472120i
\(709\) 12.4377 0.467107 0.233554 0.972344i \(-0.424965\pi\)
0.233554 + 0.972344i \(0.424965\pi\)
\(710\) −2.43769 −0.0914850
\(711\) −27.3607 24.4721i −1.02611 0.917777i
\(712\) 6.90983i 0.258957i
\(713\) −9.47214 −0.354734
\(714\) −20.6525 4.61803i −0.772899 0.172826i
\(715\) 0.124612 0.00466022
\(716\) 34.5066i 1.28957i
\(717\) −13.1803 + 34.5066i −0.492229 + 1.28867i
\(718\) −8.70820 −0.324987
\(719\) 22.2361 0.829265 0.414633 0.909989i \(-0.363910\pi\)
0.414633 + 0.909989i \(0.363910\pi\)
\(720\) −1.58359 1.41641i −0.0590170 0.0527864i
\(721\) −31.8885 + 4.65248i −1.18759 + 0.173267i
\(722\) 4.29180i 0.159724i
\(723\) −5.85410 + 15.3262i −0.217716 + 0.569989i
\(724\) 10.8541i 0.403390i
\(725\) 30.2705i 1.12422i
\(726\) −2.29180 + 6.00000i −0.0850565 + 0.222681i
\(727\) 11.4721i 0.425478i −0.977109 0.212739i \(-0.931762\pi\)
0.977109 0.212739i \(-0.0682384\pi\)
\(728\) 0.124612 + 0.854102i 0.00461842 + 0.0316551i
\(729\) −15.6525 + 22.0000i −0.579721 + 0.814815i
\(730\) −0.888544 −0.0328865
\(731\) 40.2148 1.48740
\(732\) 5.85410 15.3262i 0.216374 0.566474i
\(733\) 6.36068i 0.234937i −0.993077 0.117469i \(-0.962522\pi\)
0.993077 0.117469i \(-0.0374779\pi\)
\(734\) −6.96556 −0.257103
\(735\) −4.61803 0.347524i −0.170339 0.0128186i
\(736\) −5.61803 −0.207083
\(737\) 18.7426i 0.690394i
\(738\) 5.23607 5.85410i 0.192742 0.215492i
\(739\) −1.58359 −0.0582534 −0.0291267 0.999576i \(-0.509273\pi\)
−0.0291267 + 0.999576i \(0.509273\pi\)
\(740\) −6.32624 −0.232557
\(741\) 0.819660 + 0.313082i 0.0301110 + 0.0115014i
\(742\) −1.54915 10.6180i −0.0568711 0.389800i
\(743\) 5.14590i 0.188785i 0.995535 + 0.0943923i \(0.0300908\pi\)
−0.995535 + 0.0943923i \(0.969909\pi\)
\(744\) 34.2705 + 13.0902i 1.25642 + 0.479909i
\(745\) 2.18034i 0.0798815i
\(746\) 0.618034i 0.0226278i
\(747\) −6.05573 5.41641i −0.221568 0.198176i
\(748\) 27.0344i 0.988477i
\(749\) −24.5623 + 3.58359i −0.897487 + 0.130942i
\(750\) −1.43769 + 3.76393i −0.0524972 + 0.137439i
\(751\) 14.9656 0.546101 0.273050 0.962000i \(-0.411967\pi\)
0.273050 + 0.962000i \(0.411967\pi\)
\(752\) 14.8328 0.540897
\(753\) 4.00000 + 1.52786i 0.145768 + 0.0556785i
\(754\) 0.562306i 0.0204780i
\(755\) −2.47214 −0.0899702
\(756\) 18.0902 12.9443i 0.657933 0.470779i
\(757\) −17.0000 −0.617876 −0.308938 0.951082i \(-0.599973\pi\)
−0.308938 + 0.951082i \(0.599973\pi\)
\(758\) 9.59675i 0.348570i
\(759\) −3.61803 1.38197i −0.131326 0.0501622i
\(760\) −2.96556 −0.107572
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 6.41641 16.7984i 0.232442 0.608541i
\(763\) −3.09017 21.1803i −0.111872 0.766780i
\(764\) 13.4164i 0.485389i
\(765\) −6.38197 5.70820i −0.230740 0.206381i
\(766\) 2.32624i 0.0840504i
\(767\) 1.83282i 0.0661791i
\(768\) 10.6180 + 4.05573i 0.383145 + 0.146348i
\(769\) 0.180340i 0.00650322i 0.999995 + 0.00325161i \(0.00103502\pi\)
−0.999995 + 0.00325161i \(0.998965\pi\)
\(770\) −0.201626 1.38197i −0.00726610 0.0498026i
\(771\) 21.1246 + 8.06888i 0.760784 + 0.290594i
\(772\) 3.70820 0.133461
\(773\) −12.7082 −0.457082 −0.228541 0.973534i \(-0.573396\pi\)
−0.228541 + 0.973534i \(0.573396\pi\)
\(774\) 6.65248 7.43769i 0.239118 0.267342i
\(775\) 45.9787i 1.65160i
\(776\) −35.6525 −1.27985
\(777\) 10.2361 45.7771i 0.367217 1.64224i
\(778\) −11.9230 −0.427460
\(779\) 14.7082i 0.526976i
\(780\) −0.0557281 + 0.145898i −0.00199539 + 0.00522399i
\(781\) −23.0902 −0.826231
\(782\) −4.61803 −0.165141
\(783\) 28.7984 14.8541i 1.02917 0.530842i
\(784\) −12.4377 + 3.70820i −0.444203 + 0.132436i
\(785\) 6.29180i 0.224564i
\(786\) −2.02129 + 5.29180i −0.0720969 + 0.188752i
\(787\) 19.5066i 0.695334i 0.937618 + 0.347667i \(0.113026\pi\)
−0.937618 + 0.347667i \(0.886974\pi\)
\(788\) 24.1246i 0.859404i
\(789\) −0.0344419 + 0.0901699i −0.00122616 + 0.00321014i
\(790\) 2.88854i 0.102770i
\(791\) 36.1246 5.27051i 1.28444 0.187398i
\(792\) 11.1803 + 10.0000i 0.397276 + 0.355335i
\(793\) −0.854102 −0.0303301
\(794\) 6.65248 0.236088
\(795\) 1.54915 4.05573i 0.0549427 0.143842i
\(796\) 20.0344i 0.710102i
\(797\) −40.5410 −1.43604 −0.718018 0.696024i \(-0.754951\pi\)
−0.718018 + 0.696024i \(0.754951\pi\)
\(798\) 2.14590 9.59675i 0.0759640 0.339721i
\(799\) 59.7771 2.11476
\(800\) 27.2705i 0.964158i
\(801\) 6.90983 + 6.18034i 0.244147 + 0.218372i
\(802\) 11.3820 0.401911
\(803\) −8.41641 −0.297009
\(804\) 21.9443 + 8.38197i 0.773915 + 0.295609i
\(805\) −1.00000 + 0.145898i −0.0352454 + 0.00514223i
\(806\) 0.854102i 0.0300845i
\(807\) −6.70820 2.56231i −0.236140 0.0901974i
\(808\) 13.6180i 0.479081i
\(809\) 6.03444i 0.212160i 0.994358 + 0.106080i \(0.0338299\pi\)
−0.994358 + 0.106080i \(0.966170\pi\)
\(810\) −2.11146 + 0.236068i −0.0741890 + 0.00829458i
\(811\) 9.06888i 0.318452i −0.987242 0.159226i \(-0.949100\pi\)
0.987242 0.159226i \(-0.0508998\pi\)
\(812\) −26.4164 + 3.85410i −0.927034 + 0.135252i
\(813\) −1.38197 + 3.61803i −0.0484677 + 0.126890i
\(814\) 14.1459 0.495813
\(815\) 3.02129 0.105831
\(816\) −22.4164 8.56231i −0.784731 0.299741i
\(817\) 18.6869i 0.653772i
\(818\) 15.1591 0.530024
\(819\) −0.965558 0.639320i −0.0337393 0.0223397i
\(820\) −2.61803 −0.0914257
\(821\) 3.81966i 0.133307i 0.997776 + 0.0666535i \(0.0212322\pi\)
−0.997776 + 0.0666535i \(0.978768\pi\)
\(822\) 9.76393 + 3.72949i 0.340556 + 0.130081i
\(823\) −8.56231 −0.298463 −0.149232 0.988802i \(-0.547680\pi\)
−0.149232 + 0.988802i \(0.547680\pi\)
\(824\) 27.2361 0.948813
\(825\) −6.70820 + 17.5623i −0.233550 + 0.611441i
\(826\) −20.3262 + 2.96556i −0.707240 + 0.103185i
\(827\) 25.2148i 0.876804i −0.898779 0.438402i \(-0.855545\pi\)
0.898779 0.438402i \(-0.144455\pi\)
\(828\) 3.23607 3.61803i 0.112461 0.125735i
\(829\) 1.00000i 0.0347314i −0.999849 0.0173657i \(-0.994472\pi\)
0.999849 0.0173657i \(-0.00552796\pi\)
\(830\) 0.639320i 0.0221911i
\(831\) −22.4164 8.56231i −0.777617 0.297023i
\(832\) 0.0344419i 0.00119406i
\(833\) −50.1246 + 14.9443i −1.73671 + 0.517788i
\(834\) −12.0902 4.61803i −0.418648 0.159909i
\(835\) 1.21478 0.0420393
\(836\) −12.5623 −0.434476
\(837\) −43.7426 + 22.5623i −1.51197 + 0.779867i
\(838\) 0.124612i 0.00430464i
\(839\) 4.14590 0.143132 0.0715661 0.997436i \(-0.477200\pi\)
0.0715661 + 0.997436i \(0.477200\pi\)
\(840\) 3.81966 + 0.854102i 0.131791 + 0.0294693i
\(841\) −9.88854 −0.340984
\(842\) 12.7852i 0.440608i
\(843\) −11.7082 + 30.6525i −0.403252 + 1.05573i
\(844\) −4.85410 −0.167085
\(845\) −4.95743 −0.170541
\(846\) 9.88854 11.0557i 0.339975 0.380104i
\(847\) 2.29180 + 15.7082i 0.0787470 + 0.539740i
\(848\) 12.1672i 0.417823i
\(849\) 9.76393 25.5623i 0.335097 0.877296i
\(850\) 22.4164i 0.768876i
\(851\) 10.2361i 0.350888i
\(852\) 10.3262 27.0344i 0.353771 0.926185i
\(853\) 36.6525i 1.25496i 0.778634 + 0.627478i \(0.215913\pi\)
−0.778634 + 0.627478i \(0.784087\pi\)
\(854\) 1.38197 + 9.47214i 0.0472899 + 0.324130i
\(855\) 2.65248 2.96556i 0.0907128 0.101420i
\(856\) 20.9787 0.717038
\(857\) −17.5279 −0.598740 −0.299370 0.954137i \(-0.596777\pi\)
−0.299370 + 0.954137i \(0.596777\pi\)
\(858\) 0.124612 0.326238i 0.00425418 0.0111376i
\(859\) 29.5279i 1.00748i 0.863856 + 0.503739i \(0.168043\pi\)
−0.863856 + 0.503739i \(0.831957\pi\)
\(860\) −3.32624 −0.113424
\(861\) 4.23607 18.9443i 0.144365 0.645619i
\(862\) 20.4508 0.696559
\(863\) 28.3607i 0.965409i 0.875783 + 0.482704i \(0.160345\pi\)
−0.875783 + 0.482704i \(0.839655\pi\)
\(864\) −25.9443 + 13.3820i −0.882642 + 0.455264i
\(865\) 2.09017 0.0710679
\(866\) 6.47214 0.219932
\(867\) −62.8328 24.0000i −2.13391 0.815083i
\(868\) 40.1246 5.85410i 1.36192 0.198701i
\(869\) 27.3607i 0.928147i
\(870\) 2.38197 + 0.909830i 0.0807562 + 0.0308461i
\(871\) 1.22291i 0.0414368i
\(872\) 18.0902i 0.612610i
\(873\) 31.8885 35.6525i 1.07926 1.20665i
\(874\) 2.14590i 0.0725861i
\(875\) 1.43769 + 9.85410i 0.0486029 + 0.333129i
\(876\) 3.76393 9.85410i 0.127171 0.332939i
\(877\) −3.70820 −0.125217 −0.0626086 0.998038i \(-0.519942\pi\)
−0.0626086 + 0.998038i \(0.519942\pi\)
\(878\) −10.2148 −0.344732
\(879\) 44.8328 + 17.1246i 1.51217 + 0.577599i
\(880\) 1.58359i 0.0533829i
\(881\) 9.88854 0.333154 0.166577 0.986028i \(-0.446729\pi\)
0.166577 + 0.986028i \(0.446729\pi\)
\(882\) −5.52786 + 11.7426i −0.186133 + 0.395395i
\(883\) −13.1591 −0.442837 −0.221419 0.975179i \(-0.571069\pi\)
−0.221419 + 0.975179i \(0.571069\pi\)
\(884\) 1.76393i 0.0593275i
\(885\) −7.76393 2.96556i −0.260982 0.0996861i
\(886\) −0.111456 −0.00374444
\(887\) 31.0902 1.04391 0.521953 0.852974i \(-0.325204\pi\)
0.521953 + 0.852974i \(0.325204\pi\)
\(888\) −14.1459 + 37.0344i −0.474705 + 1.24279i
\(889\) −6.41641 43.9787i −0.215199 1.47500i
\(890\) 0.729490i 0.0244526i
\(891\) −20.0000 + 2.23607i −0.670025 + 0.0749111i
\(892\) 9.56231i 0.320170i
\(893\) 27.7771i 0.929525i
\(894\) −5.70820 2.18034i −0.190911 0.0729215i
\(895\) 8.14590i 0.272287i
\(896\) 29.7984 4.34752i 0.995494 0.145241i
\(897\) −0.236068 0.0901699i −0.00788208 0.00301069i
\(898\) 13.6525 0.455589
\(899\) 59.0689 1.97006
\(900\) −17.5623 15.7082i −0.585410 0.523607i
\(901\) 49.0344i 1.63357i
\(902\) 5.85410 0.194920
\(903\) 5.38197 24.0689i 0.179101 0.800962i
\(904\) −30.8541 −1.02619
\(905\) 2.56231i 0.0851739i
\(906\) −2.47214 + 6.47214i −0.0821312 + 0.215022i
\(907\) 25.0344 0.831255 0.415627 0.909535i \(-0.363562\pi\)
0.415627 + 0.909535i \(0.363562\pi\)
\(908\) −10.7984 −0.358357
\(909\) −13.6180 12.1803i −0.451682 0.403996i
\(910\) −0.0131556 0.0901699i −0.000436104 0.00298910i
\(911\) 25.1246i 0.832416i −0.909270 0.416208i \(-0.863359\pi\)
0.909270 0.416208i \(-0.136641\pi\)
\(912\) 3.97871 10.4164i 0.131748 0.344922i
\(913\) 6.05573i 0.200415i
\(914\) 2.81966i 0.0932661i
\(915\) −1.38197 + 3.61803i −0.0456864 + 0.119609i
\(916\) 35.7426i 1.18097i
\(917\) 2.02129 + 13.8541i 0.0667488 + 0.457503i
\(918\) −21.3262 + 11.0000i −0.703871 + 0.363054i
\(919\) −45.6525 −1.50594 −0.752968 0.658057i \(-0.771379\pi\)
−0.752968 + 0.658057i \(0.771379\pi\)
\(920\) 0.854102 0.0281589
\(921\) −7.74265 + 20.2705i −0.255129 + 0.667936i
\(922\) 22.0557i 0.726367i
\(923\) −1.50658 −0.0495896
\(924\) 16.1803 + 3.61803i 0.532294 + 0.119025i
\(925\) −49.6869 −1.63370
\(926\) 15.7426i 0.517335i
\(927\) −24.3607 + 27.2361i −0.800110 + 0.894550i
\(928\) 35.0344 1.15006
\(929\) 39.3951 1.29251 0.646256 0.763121i \(-0.276334\pi\)
0.646256 + 0.763121i \(0.276334\pi\)
\(930\) −3.61803 1.38197i −0.118640 0.0453165i
\(931\) −6.94427 23.2918i −0.227589 0.763358i
\(932\) 47.4508i 1.55430i
\(933\) 12.4164 + 4.74265i 0.406495 + 0.155267i
\(934\) 12.2574i 0.401073i
\(935\) 6.38197i 0.208713i
\(936\) 0.729490 + 0.652476i 0.0238441 + 0.0213268i
\(937\) 25.2918i 0.826247i −0.910675 0.413123i \(-0.864438\pi\)
0.910675 0.413123i \(-0.135562\pi\)
\(938\) −13.5623 + 1.97871i −0.442825 + 0.0646073i
\(939\) 7.52786 19.7082i 0.245663 0.643153i
\(940\) −4.94427 −0.161264
\(941\) 17.5279 0.571392 0.285696 0.958320i \(-0.407775\pi\)
0.285696 + 0.958320i \(0.407775\pi\)
\(942\) 16.4721 + 6.29180i 0.536691 + 0.204998i
\(943\) 4.23607i 0.137945i
\(944\) −23.2918 −0.758083
\(945\) −4.27051 + 3.05573i −0.138920 + 0.0994028i
\(946\) 7.43769 0.241820
\(947\) 48.8328i 1.58685i −0.608666 0.793427i \(-0.708295\pi\)
0.608666 0.793427i \(-0.291705\pi\)
\(948\) 32.0344 + 12.2361i 1.04043 + 0.397409i
\(949\) −0.549150 −0.0178262
\(950\) −10.4164 −0.337953
\(951\) 1.00000 2.61803i 0.0324272 0.0848956i
\(952\) 43.7426 6.38197i 1.41771 0.206841i
\(953\) 26.0344i 0.843338i −0.906750 0.421669i \(-0.861444\pi\)
0.906750 0.421669i \(-0.138556\pi\)
\(954\) −9.06888 8.11146i −0.293616 0.262618i
\(955\) 3.16718i 0.102488i
\(956\) 34.5066i 1.11602i
\(957\) 22.5623 + 8.61803i 0.729336 + 0.278581i
\(958\) 3.49342i 0.112867i
\(959\) 25.5623 3.72949i 0.825450 0.120432i
\(960\) 0.145898 + 0.0557281i 0.00470884 + 0.00179862i
\(961\) −58.7214 −1.89424
\(962\) 0.922986 0.0297583
\(963\) −18.7639 + 20.9787i −0.604659 + 0.676030i
\(964\) 15.3262i 0.493625i
\(965\) −0.875388 −0.0281797
\(966\) −0.618034 + 2.76393i −0.0198849 + 0.0889281i
\(967\) −19.8885 −0.639572 −0.319786 0.947490i \(-0.603611\pi\)
−0.319786 + 0.947490i \(0.603611\pi\)
\(968\) 13.4164i 0.431220i
\(969\) 16.0344 41.9787i 0.515100 1.34855i
\(970\) 3.76393 0.120853
\(971\) 35.7426 1.14704 0.573518 0.819193i \(-0.305578\pi\)
0.573518 + 0.819193i \(0.305578\pi\)
\(972\) 6.32624 24.4164i 0.202914 0.783157i
\(973\) −31.6525 + 4.61803i −1.01473 + 0.148047i
\(974\) 0.798374i 0.0255815i
\(975\) −0.437694 + 1.14590i −0.0140174 + 0.0366981i
\(976\) 10.8541i 0.347431i
\(977\) 38.9787i 1.24704i 0.781808 + 0.623520i \(0.214298\pi\)
−0.781808 + 0.623520i \(0.785702\pi\)
\(978\) 3.02129 7.90983i 0.0966101 0.252928i
\(979\) 6.90983i 0.220839i
\(980\) 4.14590 1.23607i 0.132436 0.0394847i
\(981\) −18.0902 16.1803i −0.577575 0.516598i
\(982\) 20.4508 0.652613
\(983\) 25.1803 0.803128 0.401564 0.915831i \(-0.368467\pi\)
0.401564 + 0.915831i \(0.368467\pi\)
\(984\) −5.85410 + 15.3262i −0.186622 + 0.488583i
\(985\) 5.69505i 0.181459i
\(986\) 28.7984 0.917127
\(987\) 8.00000 35.7771i 0.254643 1.13880i
\(988\) −0.819660 −0.0260769
\(989\) 5.38197i 0.171137i
\(990\) −1.18034 1.05573i −0.0375137 0.0335532i
\(991\) 26.7984 0.851278 0.425639 0.904893i \(-0.360049\pi\)
0.425639 + 0.904893i \(0.360049\pi\)
\(992\) −53.2148 −1.68957
\(993\) 35.7082 + 13.6393i 1.13317 + 0.432831i
\(994\) 2.43769 + 16.7082i 0.0773190 + 0.529952i
\(995\) 4.72949i 0.149935i
\(996\) 7.09017 + 2.70820i 0.224661 + 0.0858127i
\(997\) 35.9443i 1.13837i −0.822211 0.569183i \(-0.807259\pi\)
0.822211 0.569183i \(-0.192741\pi\)
\(998\) 1.58359i 0.0501277i
\(999\) −24.3820 47.2705i −0.771411 1.49557i
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 483.2.d.a.461.2 4
3.2 odd 2 483.2.d.b.461.3 yes 4
7.6 odd 2 483.2.d.b.461.2 yes 4
21.20 even 2 inner 483.2.d.a.461.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.d.a.461.2 4 1.1 even 1 trivial
483.2.d.a.461.3 yes 4 21.20 even 2 inner
483.2.d.b.461.2 yes 4 7.6 odd 2
483.2.d.b.461.3 yes 4 3.2 odd 2