Properties

Label 121.2.c.a.3.1
Level $121$
Weight $2$
Character 121.3
Analytic conductor $0.966$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [121,2,Mod(3,121)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("121.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 121.c (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: \(0.966189864457\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 11)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 3.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 121.3
Dual form 121.2.c.a.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61803 + 1.17557i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.618034 - 1.90211i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.61803 + 1.17557i) q^{6} +(0.618034 - 1.90211i) q^{7} +(1.61803 - 1.17557i) q^{9} +O(q^{10})\) \(q+(-1.61803 + 1.17557i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.618034 - 1.90211i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.61803 + 1.17557i) q^{6} +(0.618034 - 1.90211i) q^{7} +(1.61803 - 1.17557i) q^{9} +2.00000 q^{10} -2.00000 q^{12} +(3.23607 - 2.35114i) q^{13} +(1.23607 + 3.80423i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-1.61803 - 1.17557i) q^{17} +(-1.23607 + 3.80423i) q^{18} +(-1.61803 + 1.17557i) q^{20} -2.00000 q^{21} -1.00000 q^{23} +(-1.23607 - 3.80423i) q^{25} +(-2.47214 + 7.60845i) q^{26} +(-4.04508 - 2.93893i) q^{27} +(-3.23607 - 2.35114i) q^{28} +(-0.618034 - 1.90211i) q^{30} +(-5.66312 + 4.11450i) q^{31} -8.00000 q^{32} +4.00000 q^{34} +(-1.61803 + 1.17557i) q^{35} +(-1.23607 - 3.80423i) q^{36} +(0.927051 - 2.85317i) q^{37} +(-3.23607 - 2.35114i) q^{39} +(2.47214 + 7.60845i) q^{41} +(3.23607 - 2.35114i) q^{42} +6.00000 q^{43} -2.00000 q^{45} +(1.61803 - 1.17557i) q^{46} +(2.47214 + 7.60845i) q^{47} +(1.23607 - 3.80423i) q^{48} +(2.42705 + 1.76336i) q^{49} +(6.47214 + 4.70228i) q^{50} +(-0.618034 + 1.90211i) q^{51} +(-2.47214 - 7.60845i) q^{52} +(4.85410 - 3.52671i) q^{53} +10.0000 q^{54} +(1.54508 - 4.75528i) q^{59} +(1.61803 + 1.17557i) q^{60} +(9.70820 + 7.05342i) q^{61} +(4.32624 - 13.3148i) q^{62} +(-1.23607 - 3.80423i) q^{63} +(6.47214 - 4.70228i) q^{64} -4.00000 q^{65} -7.00000 q^{67} +(-3.23607 + 2.35114i) q^{68} +(0.309017 + 0.951057i) q^{69} +(1.23607 - 3.80423i) q^{70} +(2.42705 + 1.76336i) q^{71} +(-1.23607 + 3.80423i) q^{73} +(1.85410 + 5.70634i) q^{74} +(-3.23607 + 2.35114i) q^{75} +8.00000 q^{78} +(-8.09017 + 5.87785i) q^{79} +(-1.23607 - 3.80423i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-12.9443 - 9.40456i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(-1.23607 + 3.80423i) q^{84} +(0.618034 + 1.90211i) q^{85} +(-9.70820 + 7.05342i) q^{86} +15.0000 q^{89} +(3.23607 - 2.35114i) q^{90} +(-2.47214 - 7.60845i) q^{91} +(-0.618034 + 1.90211i) q^{92} +(5.66312 + 4.11450i) q^{93} +(-12.9443 - 9.40456i) q^{94} +(2.47214 + 7.60845i) q^{96} +(5.66312 - 4.11450i) q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9} + 8 q^{10} - 8 q^{12} + 4 q^{13} - 4 q^{14} + q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} - 2 q^{20} - 8 q^{21} - 4 q^{23} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 4 q^{28} + 2 q^{30} - 7 q^{31} - 32 q^{32} + 16 q^{34} - 2 q^{35} + 4 q^{36} - 3 q^{37} - 4 q^{39} - 8 q^{41} + 4 q^{42} + 24 q^{43} - 8 q^{45} + 2 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} + 8 q^{50} + 2 q^{51} + 8 q^{52} + 6 q^{53} + 40 q^{54} - 5 q^{59} + 2 q^{60} + 12 q^{61} - 14 q^{62} + 4 q^{63} + 8 q^{64} - 16 q^{65} - 28 q^{67} - 4 q^{68} - q^{69} - 4 q^{70} + 3 q^{71} + 4 q^{73} - 6 q^{74} - 4 q^{75} + 32 q^{78} - 10 q^{79} + 4 q^{80} - q^{81} - 16 q^{82} - 6 q^{83} + 4 q^{84} - 2 q^{85} - 12 q^{86} + 60 q^{89} + 4 q^{90} + 8 q^{91} + 2 q^{92} + 7 q^{93} - 16 q^{94} - 8 q^{96} + 7 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61803 + 1.17557i −1.14412 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i 0.821362 0.570408i \(-0.193215\pi\)
−0.999773 + 0.0213149i \(0.993215\pi\)
\(4\) 0.618034 1.90211i 0.309017 0.951057i
\(5\) −0.809017 0.587785i −0.361803 0.262866i 0.392000 0.919965i \(-0.371783\pi\)
−0.753804 + 0.657099i \(0.771783\pi\)
\(6\) 1.61803 + 1.17557i 0.660560 + 0.479925i
\(7\) 0.618034 1.90211i 0.233595 0.718931i −0.763710 0.645560i \(-0.776624\pi\)
0.997305 0.0733714i \(-0.0233759\pi\)
\(8\) 0 0
\(9\) 1.61803 1.17557i 0.539345 0.391857i
\(10\) 2.00000 0.632456
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) 3.23607 2.35114i 0.897524 0.652089i −0.0403050 0.999187i \(-0.512833\pi\)
0.937829 + 0.347098i \(0.112833\pi\)
\(14\) 1.23607 + 3.80423i 0.330353 + 1.01672i
\(15\) −0.309017 + 0.951057i −0.0797878 + 0.245562i
\(16\) 3.23607 + 2.35114i 0.809017 + 0.587785i
\(17\) −1.61803 1.17557i −0.392431 0.285118i 0.374020 0.927421i \(-0.377979\pi\)
−0.766451 + 0.642303i \(0.777979\pi\)
\(18\) −1.23607 + 3.80423i −0.291344 + 0.896665i
\(19\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(20\) −1.61803 + 1.17557i −0.361803 + 0.262866i
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0 0
\(25\) −1.23607 3.80423i −0.247214 0.760845i
\(26\) −2.47214 + 7.60845i −0.484826 + 1.49214i
\(27\) −4.04508 2.93893i −0.778477 0.565597i
\(28\) −3.23607 2.35114i −0.611559 0.444324i
\(29\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(30\) −0.618034 1.90211i −0.112837 0.347277i
\(31\) −5.66312 + 4.11450i −1.01713 + 0.738985i −0.965692 0.259691i \(-0.916379\pi\)
−0.0514344 + 0.998676i \(0.516379\pi\)
\(32\) −8.00000 −1.41421
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) −1.61803 + 1.17557i −0.273498 + 0.198708i
\(36\) −1.23607 3.80423i −0.206011 0.634038i
\(37\) 0.927051 2.85317i 0.152406 0.469058i −0.845483 0.534003i \(-0.820687\pi\)
0.997889 + 0.0649448i \(0.0206871\pi\)
\(38\) 0 0
\(39\) −3.23607 2.35114i −0.518186 0.376484i
\(40\) 0 0
\(41\) 2.47214 + 7.60845i 0.386083 + 1.18824i 0.935692 + 0.352819i \(0.114777\pi\)
−0.549609 + 0.835422i \(0.685223\pi\)
\(42\) 3.23607 2.35114i 0.499336 0.362789i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) −2.00000 −0.298142
\(46\) 1.61803 1.17557i 0.238566 0.173328i
\(47\) 2.47214 + 7.60845i 0.360598 + 1.10981i 0.952692 + 0.303938i \(0.0983015\pi\)
−0.592094 + 0.805869i \(0.701699\pi\)
\(48\) 1.23607 3.80423i 0.178411 0.549093i
\(49\) 2.42705 + 1.76336i 0.346722 + 0.251908i
\(50\) 6.47214 + 4.70228i 0.915298 + 0.665003i
\(51\) −0.618034 + 1.90211i −0.0865421 + 0.266349i
\(52\) −2.47214 7.60845i −0.342824 1.05510i
\(53\) 4.85410 3.52671i 0.666762 0.484431i −0.202178 0.979349i \(-0.564802\pi\)
0.868940 + 0.494918i \(0.164802\pi\)
\(54\) 10.0000 1.36083
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.54508 4.75528i 0.201153 0.619085i −0.798697 0.601734i \(-0.794477\pi\)
0.999849 0.0173510i \(-0.00552328\pi\)
\(60\) 1.61803 + 1.17557i 0.208887 + 0.151765i
\(61\) 9.70820 + 7.05342i 1.24301 + 0.903098i 0.997795 0.0663709i \(-0.0211421\pi\)
0.245213 + 0.969469i \(0.421142\pi\)
\(62\) 4.32624 13.3148i 0.549433 1.69098i
\(63\) −1.23607 3.80423i −0.155730 0.479287i
\(64\) 6.47214 4.70228i 0.809017 0.587785i
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) −3.23607 + 2.35114i −0.392431 + 0.285118i
\(69\) 0.309017 + 0.951057i 0.0372013 + 0.114494i
\(70\) 1.23607 3.80423i 0.147738 0.454692i
\(71\) 2.42705 + 1.76336i 0.288038 + 0.209272i 0.722416 0.691459i \(-0.243032\pi\)
−0.434378 + 0.900731i \(0.643032\pi\)
\(72\) 0 0
\(73\) −1.23607 + 3.80423i −0.144671 + 0.445251i −0.996969 0.0778060i \(-0.975209\pi\)
0.852298 + 0.523057i \(0.175209\pi\)
\(74\) 1.85410 + 5.70634i 0.215535 + 0.663348i
\(75\) −3.23607 + 2.35114i −0.373669 + 0.271486i
\(76\) 0 0
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) −8.09017 + 5.87785i −0.910215 + 0.661310i −0.941069 0.338214i \(-0.890177\pi\)
0.0308541 + 0.999524i \(0.490177\pi\)
\(80\) −1.23607 3.80423i −0.138197 0.425325i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −12.9443 9.40456i −1.42946 1.03856i
\(83\) −4.85410 3.52671i −0.532807 0.387107i 0.288600 0.957450i \(-0.406810\pi\)
−0.821407 + 0.570343i \(0.806810\pi\)
\(84\) −1.23607 + 3.80423i −0.134866 + 0.415075i
\(85\) 0.618034 + 1.90211i 0.0670352 + 0.206313i
\(86\) −9.70820 + 7.05342i −1.04686 + 0.760590i
\(87\) 0 0
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 3.23607 2.35114i 0.341112 0.247832i
\(91\) −2.47214 7.60845i −0.259150 0.797582i
\(92\) −0.618034 + 1.90211i −0.0644345 + 0.198309i
\(93\) 5.66312 + 4.11450i 0.587238 + 0.426653i
\(94\) −12.9443 9.40456i −1.33510 0.970007i
\(95\) 0 0
\(96\) 2.47214 + 7.60845i 0.252311 + 0.776534i
\(97\) 5.66312 4.11450i 0.575003 0.417764i −0.261916 0.965091i \(-0.584354\pi\)
0.836919 + 0.547327i \(0.184354\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) −8.00000 −0.800000
\(101\) 1.61803 1.17557i 0.161000 0.116974i −0.504368 0.863489i \(-0.668274\pi\)
0.665368 + 0.746515i \(0.268274\pi\)
\(102\) −1.23607 3.80423i −0.122389 0.376675i
\(103\) −4.94427 + 15.2169i −0.487174 + 1.49937i 0.341634 + 0.939833i \(0.389020\pi\)
−0.828808 + 0.559533i \(0.810980\pi\)
\(104\) 0 0
\(105\) 1.61803 + 1.17557i 0.157904 + 0.114724i
\(106\) −3.70820 + 11.4127i −0.360173 + 1.10850i
\(107\) −5.56231 17.1190i −0.537728 1.65496i −0.737679 0.675152i \(-0.764078\pi\)
0.199950 0.979806i \(-0.435922\pi\)
\(108\) −8.09017 + 5.87785i −0.778477 + 0.565597i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 6.47214 4.70228i 0.611559 0.444324i
\(113\) 2.78115 + 8.55951i 0.261629 + 0.805211i 0.992451 + 0.122643i \(0.0391369\pi\)
−0.730822 + 0.682568i \(0.760863\pi\)
\(114\) 0 0
\(115\) 0.809017 + 0.587785i 0.0754412 + 0.0548113i
\(116\) 0 0
\(117\) 2.47214 7.60845i 0.228549 0.703402i
\(118\) 3.09017 + 9.51057i 0.284473 + 0.875518i
\(119\) −3.23607 + 2.35114i −0.296650 + 0.215529i
\(120\) 0 0
\(121\) 0 0
\(122\) −24.0000 −2.17286
\(123\) 6.47214 4.70228i 0.583573 0.423990i
\(124\) 4.32624 + 13.3148i 0.388508 + 1.19570i
\(125\) −2.78115 + 8.55951i −0.248754 + 0.765586i
\(126\) 6.47214 + 4.70228i 0.576584 + 0.418913i
\(127\) 6.47214 + 4.70228i 0.574309 + 0.417260i 0.836668 0.547710i \(-0.184500\pi\)
−0.262359 + 0.964970i \(0.584500\pi\)
\(128\) 0 0
\(129\) −1.85410 5.70634i −0.163245 0.502415i
\(130\) 6.47214 4.70228i 0.567644 0.412417i
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 11.3262 8.22899i 0.978438 0.710877i
\(135\) 1.54508 + 4.75528i 0.132980 + 0.409270i
\(136\) 0 0
\(137\) 5.66312 + 4.11450i 0.483833 + 0.351525i 0.802808 0.596238i \(-0.203339\pi\)
−0.318975 + 0.947763i \(0.603339\pi\)
\(138\) −1.61803 1.17557i −0.137736 0.100071i
\(139\) −3.09017 + 9.51057i −0.262105 + 0.806676i 0.730241 + 0.683189i \(0.239408\pi\)
−0.992346 + 0.123486i \(0.960592\pi\)
\(140\) 1.23607 + 3.80423i 0.104467 + 0.321516i
\(141\) 6.47214 4.70228i 0.545052 0.396004i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 8.00000 0.666667
\(145\) 0 0
\(146\) −2.47214 7.60845i −0.204595 0.629680i
\(147\) 0.927051 2.85317i 0.0764619 0.235325i
\(148\) −4.85410 3.52671i −0.399005 0.289894i
\(149\) −8.09017 5.87785i −0.662773 0.481532i 0.204826 0.978798i \(-0.434337\pi\)
−0.867598 + 0.497266i \(0.834337\pi\)
\(150\) 2.47214 7.60845i 0.201849 0.621228i
\(151\) −0.618034 1.90211i −0.0502949 0.154792i 0.922755 0.385388i \(-0.125932\pi\)
−0.973050 + 0.230596i \(0.925932\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) 7.00000 0.562254
\(156\) −6.47214 + 4.70228i −0.518186 + 0.376484i
\(157\) −2.16312 6.65740i −0.172636 0.531318i 0.826882 0.562376i \(-0.190112\pi\)
−0.999518 + 0.0310576i \(0.990112\pi\)
\(158\) 6.18034 19.0211i 0.491681 1.51324i
\(159\) −4.85410 3.52671i −0.384955 0.279686i
\(160\) 6.47214 + 4.70228i 0.511667 + 0.371748i
\(161\) −0.618034 + 1.90211i −0.0487079 + 0.149908i
\(162\) 0.618034 + 1.90211i 0.0485573 + 0.149444i
\(163\) −3.23607 + 2.35114i −0.253468 + 0.184156i −0.707263 0.706951i \(-0.750070\pi\)
0.453794 + 0.891107i \(0.350070\pi\)
\(164\) 16.0000 1.24939
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −9.70820 + 7.05342i −0.751243 + 0.545810i −0.896212 0.443626i \(-0.853692\pi\)
0.144969 + 0.989436i \(0.453692\pi\)
\(168\) 0 0
\(169\) 0.927051 2.85317i 0.0713116 0.219475i
\(170\) −3.23607 2.35114i −0.248195 0.180324i
\(171\) 0 0
\(172\) 3.70820 11.4127i 0.282748 0.870209i
\(173\) 1.85410 + 5.70634i 0.140965 + 0.433845i 0.996470 0.0839492i \(-0.0267533\pi\)
−0.855505 + 0.517794i \(0.826753\pi\)
\(174\) 0 0
\(175\) −8.00000 −0.604743
\(176\) 0 0
\(177\) −5.00000 −0.375823
\(178\) −24.2705 + 17.6336i −1.81915 + 1.32169i
\(179\) −4.63525 14.2658i −0.346455 1.06628i −0.960800 0.277242i \(-0.910580\pi\)
0.614345 0.789038i \(-0.289420\pi\)
\(180\) −1.23607 + 3.80423i −0.0921311 + 0.283550i
\(181\) −5.66312 4.11450i −0.420936 0.305828i 0.357078 0.934075i \(-0.383773\pi\)
−0.778014 + 0.628246i \(0.783773\pi\)
\(182\) 12.9443 + 9.40456i 0.959493 + 0.697113i
\(183\) 3.70820 11.4127i 0.274118 0.843649i
\(184\) 0 0
\(185\) −2.42705 + 1.76336i −0.178440 + 0.129644i
\(186\) −14.0000 −1.02653
\(187\) 0 0
\(188\) 16.0000 1.16692
\(189\) −8.09017 + 5.87785i −0.588473 + 0.427551i
\(190\) 0 0
\(191\) 5.25329 16.1680i 0.380115 1.16987i −0.559848 0.828595i \(-0.689140\pi\)
0.939963 0.341277i \(-0.110860\pi\)
\(192\) −6.47214 4.70228i −0.467086 0.339358i
\(193\) 3.23607 + 2.35114i 0.232937 + 0.169239i 0.698131 0.715970i \(-0.254015\pi\)
−0.465194 + 0.885209i \(0.654015\pi\)
\(194\) −4.32624 + 13.3148i −0.310606 + 0.955946i
\(195\) 1.23607 + 3.80423i 0.0885167 + 0.272426i
\(196\) 4.85410 3.52671i 0.346722 0.251908i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 2.16312 + 6.65740i 0.152575 + 0.469576i
\(202\) −1.23607 + 3.80423i −0.0869694 + 0.267664i
\(203\) 0 0
\(204\) 3.23607 + 2.35114i 0.226570 + 0.164613i
\(205\) 2.47214 7.60845i 0.172661 0.531397i
\(206\) −9.88854 30.4338i −0.688967 2.12042i
\(207\) −1.61803 + 1.17557i −0.112461 + 0.0817078i
\(208\) 16.0000 1.10940
\(209\) 0 0
\(210\) −4.00000 −0.276026
\(211\) 9.70820 7.05342i 0.668340 0.485578i −0.201129 0.979565i \(-0.564461\pi\)
0.869469 + 0.493987i \(0.164461\pi\)
\(212\) −3.70820 11.4127i −0.254680 0.783826i
\(213\) 0.927051 2.85317i 0.0635205 0.195496i
\(214\) 29.1246 + 21.1603i 1.99092 + 1.44649i
\(215\) −4.85410 3.52671i −0.331047 0.240520i
\(216\) 0 0
\(217\) 4.32624 + 13.3148i 0.293684 + 0.903867i
\(218\) 16.1803 11.7557i 1.09587 0.796197i
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 4.85410 3.52671i 0.325786 0.236697i
\(223\) 5.87132 + 18.0701i 0.393173 + 1.21006i 0.930375 + 0.366608i \(0.119481\pi\)
−0.537203 + 0.843453i \(0.680519\pi\)
\(224\) −4.94427 + 15.2169i −0.330353 + 1.01672i
\(225\) −6.47214 4.70228i −0.431476 0.313485i
\(226\) −14.5623 10.5801i −0.968670 0.703780i
\(227\) −5.56231 + 17.1190i −0.369183 + 1.13623i 0.578137 + 0.815940i \(0.303780\pi\)
−0.947320 + 0.320289i \(0.896220\pi\)
\(228\) 0 0
\(229\) −12.1353 + 8.81678i −0.801920 + 0.582629i −0.911477 0.411351i \(-0.865057\pi\)
0.109557 + 0.993981i \(0.465057\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0 0
\(232\) 0 0
\(233\) 19.4164 14.1068i 1.27201 0.924170i 0.272730 0.962090i \(-0.412073\pi\)
0.999281 + 0.0379203i \(0.0120733\pi\)
\(234\) 4.94427 + 15.2169i 0.323217 + 0.994760i
\(235\) 2.47214 7.60845i 0.161264 0.496321i
\(236\) −8.09017 5.87785i −0.526625 0.382616i
\(237\) 8.09017 + 5.87785i 0.525513 + 0.381808i
\(238\) 2.47214 7.60845i 0.160245 0.493183i
\(239\) 9.27051 + 28.5317i 0.599659 + 1.84556i 0.530012 + 0.847990i \(0.322188\pi\)
0.0696477 + 0.997572i \(0.477812\pi\)
\(240\) −3.23607 + 2.35114i −0.208887 + 0.151765i
\(241\) 8.00000 0.515325 0.257663 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 19.4164 14.1068i 1.24301 0.903098i
\(245\) −0.927051 2.85317i −0.0592271 0.182282i
\(246\) −4.94427 + 15.2169i −0.315235 + 0.970194i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.85410 + 5.70634i −0.117499 + 0.361625i
\(250\) −5.56231 17.1190i −0.351791 1.08270i
\(251\) 18.6074 13.5191i 1.17449 0.853316i 0.182949 0.983122i \(-0.441436\pi\)
0.991539 + 0.129807i \(0.0414357\pi\)
\(252\) −8.00000 −0.503953
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) 1.61803 1.17557i 0.101325 0.0736171i
\(256\) 4.94427 + 15.2169i 0.309017 + 0.951057i
\(257\) −0.618034 + 1.90211i −0.0385519 + 0.118651i −0.968480 0.249090i \(-0.919869\pi\)
0.929928 + 0.367740i \(0.119869\pi\)
\(258\) 9.70820 + 7.05342i 0.604406 + 0.439127i
\(259\) −4.85410 3.52671i −0.301619 0.219139i
\(260\) −2.47214 + 7.60845i −0.153315 + 0.471856i
\(261\) 0 0
\(262\) −29.1246 + 21.1603i −1.79932 + 1.30729i
\(263\) −14.0000 −0.863277 −0.431638 0.902047i \(-0.642064\pi\)
−0.431638 + 0.902047i \(0.642064\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) −4.63525 14.2658i −0.283673 0.873056i
\(268\) −4.32624 + 13.3148i −0.264267 + 0.813330i
\(269\) −8.09017 5.87785i −0.493266 0.358379i 0.313173 0.949696i \(-0.398608\pi\)
−0.806439 + 0.591317i \(0.798608\pi\)
\(270\) −8.09017 5.87785i −0.492352 0.357715i
\(271\) 8.65248 26.6296i 0.525600 1.61763i −0.237525 0.971381i \(-0.576336\pi\)
0.763125 0.646250i \(-0.223664\pi\)
\(272\) −2.47214 7.60845i −0.149895 0.461330i
\(273\) −6.47214 + 4.70228i −0.391711 + 0.284595i
\(274\) −14.0000 −0.845771
\(275\) 0 0
\(276\) 2.00000 0.120386
\(277\) −1.61803 + 1.17557i −0.0972182 + 0.0706332i −0.635332 0.772239i \(-0.719137\pi\)
0.538114 + 0.842872i \(0.319137\pi\)
\(278\) −6.18034 19.0211i −0.370672 1.14081i
\(279\) −4.32624 + 13.3148i −0.259005 + 0.797136i
\(280\) 0 0
\(281\) −14.5623 10.5801i −0.868714 0.631158i 0.0615273 0.998105i \(-0.480403\pi\)
−0.930242 + 0.366947i \(0.880403\pi\)
\(282\) −4.94427 + 15.2169i −0.294427 + 0.906153i
\(283\) −1.23607 3.80423i −0.0734766 0.226138i 0.907573 0.419894i \(-0.137933\pi\)
−0.981050 + 0.193756i \(0.937933\pi\)
\(284\) 4.85410 3.52671i 0.288038 0.209272i
\(285\) 0 0
\(286\) 0 0
\(287\) 16.0000 0.944450
\(288\) −12.9443 + 9.40456i −0.762749 + 0.554169i
\(289\) −4.01722 12.3637i −0.236307 0.727279i
\(290\) 0 0
\(291\) −5.66312 4.11450i −0.331978 0.241196i
\(292\) 6.47214 + 4.70228i 0.378753 + 0.275180i
\(293\) −7.41641 + 22.8254i −0.433271 + 1.33347i 0.461577 + 0.887100i \(0.347284\pi\)
−0.894848 + 0.446371i \(0.852716\pi\)
\(294\) 1.85410 + 5.70634i 0.108133 + 0.332800i
\(295\) −4.04508 + 2.93893i −0.235514 + 0.171111i
\(296\) 0 0
\(297\) 0 0
\(298\) 20.0000 1.15857
\(299\) −3.23607 + 2.35114i −0.187147 + 0.135970i
\(300\) 2.47214 + 7.60845i 0.142729 + 0.439274i
\(301\) 3.70820 11.4127i 0.213737 0.657816i
\(302\) 3.23607 + 2.35114i 0.186215 + 0.135293i
\(303\) −1.61803 1.17557i −0.0929536 0.0675348i
\(304\) 0 0
\(305\) −3.70820 11.4127i −0.212331 0.653488i
\(306\) 6.47214 4.70228i 0.369987 0.268812i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −11.3262 + 8.22899i −0.643287 + 0.467375i
\(311\) 3.70820 + 11.4127i 0.210273 + 0.647154i 0.999456 + 0.0329949i \(0.0105045\pi\)
−0.789183 + 0.614159i \(0.789495\pi\)
\(312\) 0 0
\(313\) 0.809017 + 0.587785i 0.0457283 + 0.0332236i 0.610415 0.792082i \(-0.291003\pi\)
−0.564686 + 0.825306i \(0.691003\pi\)
\(314\) 11.3262 + 8.22899i 0.639177 + 0.464389i
\(315\) −1.23607 + 3.80423i −0.0696445 + 0.214344i
\(316\) 6.18034 + 19.0211i 0.347671 + 1.07002i
\(317\) −10.5172 + 7.64121i −0.590706 + 0.429173i −0.842568 0.538590i \(-0.818957\pi\)
0.251862 + 0.967763i \(0.418957\pi\)
\(318\) 12.0000 0.672927
\(319\) 0 0
\(320\) −8.00000 −0.447214
\(321\) −14.5623 + 10.5801i −0.812789 + 0.590526i
\(322\) −1.23607 3.80423i −0.0688834 0.212001i
\(323\) 0 0
\(324\) −1.61803 1.17557i −0.0898908 0.0653095i
\(325\) −12.9443 9.40456i −0.718019 0.521671i
\(326\) 2.47214 7.60845i 0.136919 0.421393i
\(327\) 3.09017 + 9.51057i 0.170887 + 0.525935i
\(328\) 0 0
\(329\) 16.0000 0.882109
\(330\) 0 0
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) −9.70820 + 7.05342i −0.532807 + 0.387107i
\(333\) −1.85410 5.70634i −0.101604 0.312705i
\(334\) 7.41641 22.8254i 0.405808 1.24895i
\(335\) 5.66312 + 4.11450i 0.309409 + 0.224799i
\(336\) −6.47214 4.70228i −0.353084 0.256531i
\(337\) 6.79837 20.9232i 0.370331 1.13976i −0.576244 0.817278i \(-0.695482\pi\)
0.946575 0.322484i \(-0.104518\pi\)
\(338\) 1.85410 + 5.70634i 0.100850 + 0.310384i
\(339\) 7.28115 5.29007i 0.395458 0.287317i
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 0 0
\(343\) 16.1803 11.7557i 0.873656 0.634748i
\(344\) 0 0
\(345\) 0.309017 0.951057i 0.0166369 0.0512032i
\(346\) −9.70820 7.05342i −0.521916 0.379194i
\(347\) 22.6525 + 16.4580i 1.21605 + 0.883511i 0.995766 0.0919250i \(-0.0293020\pi\)
0.220283 + 0.975436i \(0.429302\pi\)
\(348\) 0 0
\(349\) −9.27051 28.5317i −0.496239 1.52727i −0.815017 0.579437i \(-0.803272\pi\)
0.318778 0.947829i \(-0.396728\pi\)
\(350\) 12.9443 9.40456i 0.691900 0.502695i
\(351\) −20.0000 −1.06752
\(352\) 0 0
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 8.09017 5.87785i 0.429988 0.312404i
\(355\) −0.927051 2.85317i −0.0492028 0.151431i
\(356\) 9.27051 28.5317i 0.491336 1.51218i
\(357\) 3.23607 + 2.35114i 0.171271 + 0.124436i
\(358\) 24.2705 + 17.6336i 1.28274 + 0.931962i
\(359\) 6.18034 19.0211i 0.326186 1.00390i −0.644717 0.764422i \(-0.723025\pi\)
0.970902 0.239475i \(-0.0769754\pi\)
\(360\) 0 0
\(361\) 15.3713 11.1679i 0.809017 0.587785i
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) −16.0000 −0.838628
\(365\) 3.23607 2.35114i 0.169384 0.123064i
\(366\) 7.41641 + 22.8254i 0.387662 + 1.19310i
\(367\) −5.25329 + 16.1680i −0.274219 + 0.843961i 0.715205 + 0.698914i \(0.246333\pi\)
−0.989425 + 0.145046i \(0.953667\pi\)
\(368\) −3.23607 2.35114i −0.168692 0.122562i
\(369\) 12.9443 + 9.40456i 0.673852 + 0.489582i
\(370\) 1.85410 5.70634i 0.0963902 0.296658i
\(371\) −3.70820 11.4127i −0.192520 0.592517i
\(372\) 11.3262 8.22899i 0.587238 0.426653i
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) 9.00000 0.464758
\(376\) 0 0
\(377\) 0 0
\(378\) 6.18034 19.0211i 0.317882 0.978341i
\(379\) 4.04508 + 2.93893i 0.207782 + 0.150963i 0.686810 0.726837i \(-0.259011\pi\)
−0.479028 + 0.877800i \(0.659011\pi\)
\(380\) 0 0
\(381\) 2.47214 7.60845i 0.126651 0.389793i
\(382\) 10.5066 + 32.3359i 0.537563 + 1.65445i
\(383\) 0.809017 0.587785i 0.0413388 0.0300344i −0.566924 0.823770i \(-0.691867\pi\)
0.608263 + 0.793736i \(0.291867\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8.00000 −0.407189
\(387\) 9.70820 7.05342i 0.493496 0.358546i
\(388\) −4.32624 13.3148i −0.219631 0.675956i
\(389\) −4.63525 + 14.2658i −0.235017 + 0.723307i 0.762102 + 0.647456i \(0.224167\pi\)
−0.997119 + 0.0758507i \(0.975833\pi\)
\(390\) −6.47214 4.70228i −0.327729 0.238109i
\(391\) 1.61803 + 1.17557i 0.0818275 + 0.0594512i
\(392\) 0 0
\(393\) −5.56231 17.1190i −0.280581 0.863540i
\(394\) −3.23607 + 2.35114i −0.163031 + 0.118449i
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.94427 15.2169i 0.247214 0.760845i
\(401\) −1.61803 1.17557i −0.0808008 0.0587052i 0.546652 0.837360i \(-0.315902\pi\)
−0.627452 + 0.778655i \(0.715902\pi\)
\(402\) −11.3262 8.22899i −0.564901 0.410425i
\(403\) −8.65248 + 26.6296i −0.431011 + 1.32651i
\(404\) −1.23607 3.80423i −0.0614967 0.189267i
\(405\) −0.809017 + 0.587785i −0.0402004 + 0.0292073i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −24.2705 + 17.6336i −1.20010 + 0.871923i −0.994295 0.106670i \(-0.965981\pi\)
−0.205805 + 0.978593i \(0.565981\pi\)
\(410\) 4.94427 + 15.2169i 0.244180 + 0.751509i
\(411\) 2.16312 6.65740i 0.106699 0.328385i
\(412\) 25.8885 + 18.8091i 1.27544 + 0.926659i
\(413\) −8.09017 5.87785i −0.398091 0.289230i
\(414\) 1.23607 3.80423i 0.0607494 0.186968i
\(415\) 1.85410 + 5.70634i 0.0910143 + 0.280113i
\(416\) −25.8885 + 18.8091i −1.26929 + 0.922193i
\(417\) 10.0000 0.489702
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 3.23607 2.35114i 0.157904 0.114724i
\(421\) 6.79837 + 20.9232i 0.331332 + 1.01974i 0.968501 + 0.249012i \(0.0801057\pi\)
−0.637168 + 0.770725i \(0.719894\pi\)
\(422\) −7.41641 + 22.8254i −0.361025 + 1.11112i
\(423\) 12.9443 + 9.40456i 0.629372 + 0.457266i
\(424\) 0 0
\(425\) −2.47214 + 7.60845i −0.119916 + 0.369064i
\(426\) 1.85410 + 5.70634i 0.0898315 + 0.276473i
\(427\) 19.4164 14.1068i 0.939626 0.682678i
\(428\) −36.0000 −1.74013
\(429\) 0 0
\(430\) 12.0000 0.578691
\(431\) −14.5623 + 10.5801i −0.701442 + 0.509627i −0.880401 0.474229i \(-0.842727\pi\)
0.178960 + 0.983856i \(0.442727\pi\)
\(432\) −6.18034 19.0211i −0.297352 0.915155i
\(433\) −3.39919 + 10.4616i −0.163354 + 0.502753i −0.998911 0.0466507i \(-0.985145\pi\)
0.835557 + 0.549404i \(0.185145\pi\)
\(434\) −22.6525 16.4580i −1.08735 0.790009i
\(435\) 0 0
\(436\) −6.18034 + 19.0211i −0.295985 + 0.910947i
\(437\) 0 0
\(438\) −6.47214 + 4.70228i −0.309251 + 0.224684i
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 12.9443 9.40456i 0.615696 0.447329i
\(443\) −3.39919 10.4616i −0.161500 0.497047i 0.837261 0.546803i \(-0.184155\pi\)
−0.998761 + 0.0497566i \(0.984155\pi\)
\(444\) −1.85410 + 5.70634i −0.0879918 + 0.270811i
\(445\) −12.1353 8.81678i −0.575266 0.417955i
\(446\) −30.7426 22.3358i −1.45571 1.05763i
\(447\) −3.09017 + 9.51057i −0.146160 + 0.449834i
\(448\) −4.94427 15.2169i −0.233595 0.718931i
\(449\) −28.3156 + 20.5725i −1.33630 + 0.970876i −0.336724 + 0.941603i \(0.609319\pi\)
−0.999571 + 0.0292722i \(0.990681\pi\)
\(450\) 16.0000 0.754247
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) −1.61803 + 1.17557i −0.0760219 + 0.0552331i
\(454\) −11.1246 34.2380i −0.522104 1.60687i
\(455\) −2.47214 + 7.60845i −0.115896 + 0.356690i
\(456\) 0 0
\(457\) −9.70820 7.05342i −0.454131 0.329945i 0.337094 0.941471i \(-0.390556\pi\)
−0.791224 + 0.611526i \(0.790556\pi\)
\(458\) 9.27051 28.5317i 0.433182 1.33320i
\(459\) 3.09017 + 9.51057i 0.144237 + 0.443915i
\(460\) 1.61803 1.17557i 0.0754412 0.0548113i
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) −11.0000 −0.511213 −0.255607 0.966781i \(-0.582275\pi\)
−0.255607 + 0.966781i \(0.582275\pi\)
\(464\) 0 0
\(465\) −2.16312 6.65740i −0.100312 0.308729i
\(466\) −14.8328 + 45.6507i −0.687117 + 2.11473i
\(467\) 21.8435 + 15.8702i 1.01079 + 0.734385i 0.964376 0.264537i \(-0.0852190\pi\)
0.0464191 + 0.998922i \(0.485219\pi\)
\(468\) −12.9443 9.40456i −0.598349 0.434726i
\(469\) −4.32624 + 13.3148i −0.199767 + 0.614820i
\(470\) 4.94427 + 15.2169i 0.228062 + 0.701903i
\(471\) −5.66312 + 4.11450i −0.260943 + 0.189586i
\(472\) 0 0
\(473\) 0 0
\(474\) −20.0000 −0.918630
\(475\) 0 0
\(476\) 2.47214 + 7.60845i 0.113310 + 0.348733i
\(477\) 3.70820 11.4127i 0.169787 0.522551i
\(478\) −48.5410 35.2671i −2.22021 1.61308i
\(479\) 16.1803 + 11.7557i 0.739299 + 0.537132i 0.892491 0.451064i \(-0.148956\pi\)
−0.153193 + 0.988196i \(0.548956\pi\)
\(480\) 2.47214 7.60845i 0.112837 0.347277i
\(481\) −3.70820 11.4127i −0.169080 0.520373i
\(482\) −12.9443 + 9.40456i −0.589595 + 0.428366i
\(483\) 2.00000 0.0910032
\(484\) 0 0
\(485\) −7.00000 −0.317854
\(486\) 25.8885 18.8091i 1.17433 0.853199i
\(487\) 7.10739 + 21.8743i 0.322067 + 0.991219i 0.972747 + 0.231868i \(0.0744836\pi\)
−0.650681 + 0.759351i \(0.725516\pi\)
\(488\) 0 0
\(489\) 3.23607 + 2.35114i 0.146340 + 0.106322i
\(490\) 4.85410 + 3.52671i 0.219286 + 0.159321i
\(491\) 2.47214 7.60845i 0.111566 0.343365i −0.879649 0.475623i \(-0.842223\pi\)
0.991215 + 0.132258i \(0.0422228\pi\)
\(492\) −4.94427 15.2169i −0.222905 0.686031i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −28.0000 −1.25724
\(497\) 4.85410 3.52671i 0.217736 0.158195i
\(498\) −3.70820 11.4127i −0.166169 0.511414i
\(499\) 6.18034 19.0211i 0.276670 0.851503i −0.712103 0.702075i \(-0.752257\pi\)
0.988773 0.149427i \(-0.0477430\pi\)
\(500\) 14.5623 + 10.5801i 0.651246 + 0.473158i
\(501\) 9.70820 + 7.05342i 0.433731 + 0.315124i
\(502\) −14.2148 + 43.7486i −0.634437 + 1.95260i
\(503\) 8.03444 + 24.7275i 0.358238 + 1.10254i 0.954108 + 0.299462i \(0.0968073\pi\)
−0.595870 + 0.803081i \(0.703193\pi\)
\(504\) 0 0
\(505\) −2.00000 −0.0889988
\(506\) 0 0
\(507\) −3.00000 −0.133235
\(508\) 12.9443 9.40456i 0.574309 0.417260i
\(509\) 4.63525 + 14.2658i 0.205454 + 0.632323i 0.999694 + 0.0247189i \(0.00786908\pi\)
−0.794240 + 0.607604i \(0.792131\pi\)
\(510\) −1.23607 + 3.80423i −0.0547340 + 0.168454i
\(511\) 6.47214 + 4.70228i 0.286310 + 0.208017i
\(512\) −25.8885 18.8091i −1.14412 0.831254i
\(513\) 0 0
\(514\) −1.23607 3.80423i −0.0545206 0.167797i
\(515\) 12.9443 9.40456i 0.570393 0.414415i
\(516\) −12.0000 −0.528271
\(517\) 0 0
\(518\) 12.0000 0.527250
\(519\) 4.85410 3.52671i 0.213071 0.154805i
\(520\) 0 0
\(521\) −0.927051 + 2.85317i −0.0406148 + 0.125000i −0.969308 0.245849i \(-0.920933\pi\)
0.928693 + 0.370849i \(0.120933\pi\)
\(522\) 0 0
\(523\) −12.9443 9.40456i −0.566013 0.411233i 0.267641 0.963519i \(-0.413756\pi\)
−0.833655 + 0.552286i \(0.813756\pi\)
\(524\) 11.1246 34.2380i 0.485981 1.49570i
\(525\) 2.47214 + 7.60845i 0.107893 + 0.332060i
\(526\) 22.6525 16.4580i 0.987695 0.717602i
\(527\) 14.0000 0.609850
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 9.70820 7.05342i 0.421697 0.306381i
\(531\) −3.09017 9.51057i −0.134102 0.412723i
\(532\) 0 0
\(533\) 25.8885 + 18.8091i 1.12136 + 0.814714i
\(534\) 24.2705 + 17.6336i 1.05029 + 0.763079i
\(535\) −5.56231 + 17.1190i −0.240479 + 0.740120i
\(536\) 0 0
\(537\) −12.1353 + 8.81678i −0.523675 + 0.380472i
\(538\) 20.0000 0.862261
\(539\) 0 0
\(540\) 10.0000 0.430331
\(541\) −6.47214 + 4.70228i −0.278259 + 0.202167i −0.718158 0.695880i \(-0.755014\pi\)
0.439899 + 0.898047i \(0.355014\pi\)
\(542\) 17.3050 + 53.2592i 0.743311 + 2.28768i
\(543\) −2.16312 + 6.65740i −0.0928283 + 0.285696i
\(544\) 12.9443 + 9.40456i 0.554981 + 0.403217i
\(545\) 8.09017 + 5.87785i 0.346545 + 0.251780i
\(546\) 4.94427 15.2169i 0.211595 0.651223i
\(547\) −2.47214 7.60845i −0.105701 0.325314i 0.884193 0.467121i \(-0.154709\pi\)
−0.989894 + 0.141807i \(0.954709\pi\)
\(548\) 11.3262 8.22899i 0.483833 0.351525i
\(549\) 24.0000 1.02430
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 6.18034 + 19.0211i 0.262815 + 0.808861i
\(554\) 1.23607 3.80423i 0.0525155 0.161626i
\(555\) 2.42705 + 1.76336i 0.103023 + 0.0748503i
\(556\) 16.1803 + 11.7557i 0.686199 + 0.498553i
\(557\) 0.618034 1.90211i 0.0261869 0.0805951i −0.937109 0.349037i \(-0.886509\pi\)
0.963296 + 0.268442i \(0.0865087\pi\)
\(558\) −8.65248 26.6296i −0.366289 1.12732i
\(559\) 19.4164 14.1068i 0.821227 0.596656i
\(560\) −8.00000 −0.338062
\(561\) 0 0
\(562\) 36.0000 1.51857
\(563\) 3.23607 2.35114i 0.136384 0.0990888i −0.517501 0.855682i \(-0.673138\pi\)
0.653885 + 0.756594i \(0.273138\pi\)
\(564\) −4.94427 15.2169i −0.208191 0.640747i
\(565\) 2.78115 8.55951i 0.117004 0.360101i
\(566\) 6.47214 + 4.70228i 0.272044 + 0.197652i
\(567\) −1.61803 1.17557i −0.0679510 0.0493693i
\(568\) 0 0
\(569\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) −17.0000 −0.710185
\(574\) −25.8885 + 18.8091i −1.08057 + 0.785078i
\(575\) 1.23607 + 3.80423i 0.0515476 + 0.158647i
\(576\) 4.94427 15.2169i 0.206011 0.634038i
\(577\) −26.6976 19.3969i −1.11143 0.807504i −0.128545 0.991704i \(-0.541031\pi\)
−0.982889 + 0.184200i \(0.941031\pi\)
\(578\) 21.0344 + 15.2824i 0.874917 + 0.635665i
\(579\) 1.23607 3.80423i 0.0513692 0.158098i
\(580\) 0 0
\(581\) −9.70820 + 7.05342i −0.402764 + 0.292625i
\(582\) 14.0000 0.580319
\(583\) 0 0
\(584\) 0 0
\(585\) −6.47214 + 4.70228i −0.267590 + 0.194415i
\(586\) −14.8328 45.6507i −0.612738 1.88581i
\(587\) 8.65248 26.6296i 0.357126 1.09912i −0.597641 0.801764i \(-0.703895\pi\)
0.954767 0.297356i \(-0.0961050\pi\)
\(588\) −4.85410 3.52671i −0.200180 0.145439i
\(589\) 0 0
\(590\) 3.09017 9.51057i 0.127220 0.391544i
\(591\) −0.618034 1.90211i −0.0254225 0.0782425i
\(592\) 9.70820 7.05342i 0.399005 0.289894i
\(593\) −44.0000 −1.80686 −0.903432 0.428732i \(-0.858960\pi\)
−0.903432 + 0.428732i \(0.858960\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) −16.1803 + 11.7557i −0.662773 + 0.481532i
\(597\) 0 0
\(598\) 2.47214 7.60845i 0.101093 0.311133i
\(599\) −32.3607 23.5114i −1.32222 0.960650i −0.999902 0.0140193i \(-0.995537\pi\)
−0.322320 0.946631i \(-0.604463\pi\)
\(600\) 0 0
\(601\) −0.618034 + 1.90211i −0.0252101 + 0.0775888i −0.962870 0.269965i \(-0.912988\pi\)
0.937660 + 0.347554i \(0.112988\pi\)
\(602\) 7.41641 + 22.8254i 0.302270 + 0.930292i
\(603\) −11.3262 + 8.22899i −0.461240 + 0.335111i
\(604\) −4.00000 −0.162758
\(605\) 0 0
\(606\) 4.00000 0.162489
\(607\) −17.7984 + 12.9313i −0.722414 + 0.524864i −0.887154 0.461473i \(-0.847321\pi\)
0.164741 + 0.986337i \(0.447321\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 19.4164 + 14.1068i 0.786147 + 0.571170i
\(611\) 25.8885 + 18.8091i 1.04734 + 0.760936i
\(612\) −2.47214 + 7.60845i −0.0999302 + 0.307553i
\(613\) 4.94427 + 15.2169i 0.199697 + 0.614605i 0.999890 + 0.0148615i \(0.00473072\pi\)
−0.800192 + 0.599744i \(0.795269\pi\)
\(614\) 12.9443 9.40456i 0.522388 0.379537i
\(615\) −8.00000 −0.322591
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −25.8885 + 18.8091i −1.04139 + 0.756614i
\(619\) −7.72542 23.7764i −0.310511 0.955655i −0.977563 0.210643i \(-0.932444\pi\)
0.667052 0.745011i \(-0.267556\pi\)
\(620\) 4.32624 13.3148i 0.173746 0.534735i
\(621\) 4.04508 + 2.93893i 0.162324 + 0.117935i
\(622\) −19.4164 14.1068i −0.778527 0.565633i
\(623\) 9.27051 28.5317i 0.371415 1.14310i
\(624\) −4.94427 15.2169i −0.197929 0.609164i
\(625\) −8.89919 + 6.46564i −0.355967 + 0.258626i
\(626\) −2.00000 −0.0799361
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −4.85410 + 3.52671i −0.193546 + 0.140619i
\(630\) −2.47214 7.60845i −0.0984923 0.303128i
\(631\) 2.16312 6.65740i 0.0861124 0.265027i −0.898723 0.438516i \(-0.855504\pi\)
0.984836 + 0.173489i \(0.0555042\pi\)
\(632\) 0 0
\(633\) −9.70820 7.05342i −0.385866 0.280348i
\(634\) 8.03444 24.7275i 0.319088 0.982053i
\(635\) −2.47214 7.60845i −0.0981037 0.301932i
\(636\) −9.70820 + 7.05342i −0.384955 + 0.279686i
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −10.1976 31.3849i −0.402779 1.23963i −0.922735 0.385434i \(-0.874052\pi\)
0.519956 0.854193i \(-0.325948\pi\)
\(642\) 11.1246 34.2380i 0.439053 1.35127i
\(643\) −23.4615 17.0458i −0.925231 0.672220i 0.0195896 0.999808i \(-0.493764\pi\)
−0.944821 + 0.327588i \(0.893764\pi\)
\(644\) 3.23607 + 2.35114i 0.127519 + 0.0926479i
\(645\) −1.85410 + 5.70634i −0.0730052 + 0.224687i
\(646\) 0 0
\(647\) 5.66312 4.11450i 0.222640 0.161758i −0.470874 0.882200i \(-0.656061\pi\)
0.693514 + 0.720443i \(0.256061\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 32.0000 1.25514
\(651\) 11.3262 8.22899i 0.443910 0.322520i
\(652\) 2.47214 + 7.60845i 0.0968163 + 0.297970i
\(653\) −12.6697 + 38.9933i −0.495804 + 1.52593i 0.319897 + 0.947452i \(0.396352\pi\)
−0.815701 + 0.578474i \(0.803648\pi\)
\(654\) −16.1803 11.7557i −0.632701 0.459684i
\(655\) −14.5623 10.5801i −0.568996 0.413400i
\(656\) −9.88854 + 30.4338i −0.386083 + 1.18824i
\(657\) 2.47214 + 7.60845i 0.0964472 + 0.296834i
\(658\) −25.8885 + 18.8091i −1.00924 + 0.733256i
\(659\) −10.0000 −0.389545 −0.194772 0.980848i \(-0.562397\pi\)
−0.194772 + 0.980848i \(0.562397\pi\)
\(660\) 0 0
\(661\) 37.0000 1.43913 0.719567 0.694423i \(-0.244340\pi\)
0.719567 + 0.694423i \(0.244340\pi\)
\(662\) −11.3262 + 8.22899i −0.440207 + 0.319829i
\(663\) 2.47214 + 7.60845i 0.0960098 + 0.295488i
\(664\) 0 0
\(665\) 0 0
\(666\) 9.70820 + 7.05342i 0.376185 + 0.273315i
\(667\) 0 0
\(668\) 7.41641 + 22.8254i 0.286949 + 0.883140i
\(669\) 15.3713 11.1679i 0.594290 0.431777i
\(670\) −14.0000 −0.540867
\(671\) 0 0
\(672\) 16.0000 0.617213
\(673\) 11.3262 8.22899i 0.436594 0.317204i −0.347686 0.937611i \(-0.613032\pi\)
0.784280 + 0.620407i \(0.213032\pi\)
\(674\) 13.5967 + 41.8465i 0.523727 + 1.61187i
\(675\) −6.18034 + 19.0211i −0.237881 + 0.732124i
\(676\) −4.85410 3.52671i −0.186696 0.135643i
\(677\) −33.9787 24.6870i −1.30591 0.948798i −0.305913 0.952059i \(-0.598962\pi\)
−0.999995 + 0.00326161i \(0.998962\pi\)
\(678\) −5.56231 + 17.1190i −0.213619 + 0.657452i
\(679\) −4.32624 13.3148i −0.166026 0.510975i
\(680\) 0 0
\(681\) 18.0000 0.689761
\(682\) 0 0
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) 0 0
\(685\) −2.16312 6.65740i −0.0826485 0.254366i
\(686\) −12.3607 + 38.0423i −0.471933 + 1.45246i
\(687\) 12.1353 + 8.81678i 0.462989 + 0.336381i
\(688\) 19.4164 + 14.1068i 0.740244 + 0.537818i
\(689\) 7.41641 22.8254i 0.282543 0.869577i
\(690\) 0.618034 + 1.90211i 0.0235282 + 0.0724122i
\(691\) −13.7533 + 9.99235i −0.523200 + 0.380127i −0.817808 0.575491i \(-0.804811\pi\)
0.294608 + 0.955618i \(0.404811\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −56.0000 −2.12573
\(695\) 8.09017 5.87785i 0.306878 0.222960i
\(696\) 0 0
\(697\) 4.94427 15.2169i 0.187278 0.576381i
\(698\) 48.5410 + 35.2671i 1.83730 + 1.33488i
\(699\) −19.4164 14.1068i −0.734396 0.533570i
\(700\) −4.94427 + 15.2169i −0.186876 + 0.575145i
\(701\) −0.618034 1.90211i −0.0233428 0.0718418i 0.938707 0.344717i \(-0.112025\pi\)
−0.962049 + 0.272876i \(0.912025\pi\)
\(702\) 32.3607 23.5114i 1.22138 0.887381i
\(703\) 0 0
\(704\) 0 0
\(705\) −8.00000 −0.301297
\(706\) 33.9787 24.6870i 1.27881 0.929107i
\(707\) −1.23607 3.80423i −0.0464871 0.143073i
\(708\) −3.09017 + 9.51057i −0.116136 + 0.357429i
\(709\) 20.2254 + 14.6946i 0.759582 + 0.551868i 0.898782 0.438396i \(-0.144453\pi\)
−0.139200 + 0.990264i \(0.544453\pi\)
\(710\) 4.85410 + 3.52671i 0.182171 + 0.132355i
\(711\) −6.18034 + 19.0211i −0.231781 + 0.713348i
\(712\) 0 0
\(713\) 5.66312 4.11450i 0.212085 0.154089i
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) −30.0000 −1.12115
\(717\) 24.2705 17.6336i 0.906399 0.658537i
\(718\) 12.3607 + 38.0423i 0.461296 + 1.41972i
\(719\) 4.63525 14.2658i 0.172866 0.532026i −0.826664 0.562696i \(-0.809764\pi\)
0.999530 + 0.0306699i \(0.00976407\pi\)
\(720\) −6.47214 4.70228i −0.241202 0.175244i
\(721\) 25.8885 + 18.8091i 0.964140 + 0.700489i
\(722\) −11.7426 + 36.1401i −0.437016 + 1.34500i
\(723\) −2.47214 7.60845i −0.0919397 0.282961i
\(724\) −11.3262 + 8.22899i −0.420936 + 0.305828i
\(725\) 0 0
\(726\) 0 0
\(727\) 3.00000 0.111264 0.0556319 0.998451i \(-0.482283\pi\)
0.0556319 + 0.998451i \(0.482283\pi\)
\(728\) 0 0
\(729\) 4.01722 + 12.3637i 0.148786 + 0.457916i
\(730\) −2.47214 + 7.60845i −0.0914979 + 0.281601i
\(731\) −9.70820 7.05342i −0.359071 0.260880i
\(732\) −19.4164 14.1068i −0.717651 0.521404i
\(733\) 11.1246 34.2380i 0.410897 1.26461i −0.504973 0.863135i \(-0.668498\pi\)
0.915870 0.401475i \(-0.131502\pi\)
\(734\) −10.5066 32.3359i −0.387805 1.19354i
\(735\) −2.42705 + 1.76336i −0.0895231 + 0.0650424i
\(736\) 8.00000 0.294884
\(737\) 0 0
\(738\) −32.0000 −1.17794
\(739\) 40.4508 29.3893i 1.48801 1.08110i 0.513144 0.858302i \(-0.328481\pi\)
0.974864 0.222799i \(-0.0715194\pi\)
\(740\) 1.85410 + 5.70634i 0.0681581 + 0.209769i
\(741\) 0 0
\(742\) 19.4164 + 14.1068i 0.712799 + 0.517879i
\(743\) 3.23607 + 2.35114i 0.118720 + 0.0862550i 0.645561 0.763709i \(-0.276624\pi\)
−0.526841 + 0.849964i \(0.676624\pi\)
\(744\) 0 0
\(745\) 3.09017 + 9.51057i 0.113215 + 0.348440i
\(746\) −42.0689 + 30.5648i −1.54025 + 1.11906i
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) −36.0000 −1.31541
\(750\) −14.5623 + 10.5801i −0.531740 + 0.386332i
\(751\) −7.10739 21.8743i −0.259352 0.798205i −0.992941 0.118611i \(-0.962156\pi\)
0.733588 0.679594i \(-0.237844\pi\)
\(752\) −9.88854 + 30.4338i −0.360598 + 1.10981i
\(753\) −18.6074 13.5191i −0.678091 0.492662i
\(754\) 0 0
\(755\) −0.618034 + 1.90211i −0.0224926 + 0.0692250i
\(756\) 6.18034 + 19.0211i 0.224777 + 0.691792i
\(757\) 17.7984 12.9313i 0.646893 0.469995i −0.215318 0.976544i \(-0.569079\pi\)
0.862211 + 0.506549i \(0.169079\pi\)
\(758\) −10.0000 −0.363216
\(759\) 0 0
\(760\) 0 0
\(761\) 9.70820 7.05342i 0.351922 0.255686i −0.397753 0.917493i \(-0.630210\pi\)
0.749675 + 0.661806i \(0.230210\pi\)
\(762\) 4.94427 + 15.2169i 0.179112 + 0.551250i
\(763\) −6.18034 + 19.0211i −0.223743 + 0.688611i
\(764\) −27.5066 19.9847i −0.995153 0.723021i
\(765\) 3.23607 + 2.35114i 0.117000 + 0.0850057i
\(766\) −0.618034 + 1.90211i −0.0223305 + 0.0687261i
\(767\) −6.18034 19.0211i −0.223159 0.686813i
\(768\) 12.9443 9.40456i 0.467086 0.339358i
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) 6.47214 4.70228i 0.232937 0.169239i
\(773\) −1.85410 5.70634i −0.0666874 0.205243i 0.912160 0.409834i \(-0.134413\pi\)
−0.978847 + 0.204591i \(0.934413\pi\)
\(774\) −7.41641 + 22.8254i −0.266577 + 0.820440i
\(775\) 22.6525 + 16.4580i 0.813701 + 0.591188i
\(776\) 0 0
\(777\) −1.85410 + 5.70634i −0.0665155 + 0.204714i
\(778\) −9.27051 28.5317i −0.332364 1.02291i
\(779\) 0 0
\(780\) 8.00000 0.286446
\(781\) 0 0
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) 3.70820 + 11.4127i 0.132436 + 0.407596i
\(785\) −2.16312 + 6.65740i −0.0772050 + 0.237613i
\(786\) 29.1246 + 21.1603i 1.03884 + 0.754762i
\(787\) −25.8885 18.8091i −0.922827 0.670473i 0.0213991 0.999771i \(-0.493188\pi\)
−0.944226 + 0.329298i \(0.893188\pi\)
\(788\) 1.23607 3.80423i 0.0440331 0.135520i
\(789\) 4.32624 + 13.3148i 0.154018 + 0.474019i
\(790\) −16.1803 + 11.7557i −0.575671 + 0.418249i
\(791\) 18.0000 0.640006
\(792\) 0 0
\(793\) 48.0000 1.70453
\(794\) 3.23607 2.35114i 0.114844 0.0834389i
\(795\) 1.85410 + 5.70634i 0.0657582 + 0.202383i
\(796\) 0 0
\(797\) −42.8779 31.1526i −1.51881 1.10348i −0.962072 0.272796i \(-0.912051\pi\)
−0.556741 0.830686i \(-0.687949\pi\)
\(798\) 0 0
\(799\) 4.94427 15.2169i 0.174916 0.538335i
\(800\) 9.88854 + 30.4338i 0.349613 + 1.07600i
\(801\) 24.2705 17.6336i 0.857556 0.623051i
\(802\) 4.00000 0.141245
\(803\) 0 0
\(804\) 14.0000 0.493742
\(805\) 1.61803 1.17557i 0.0570282 0.0414334i
\(806\) −17.3050 53.2592i −0.609541 1.87597i
\(807\) −3.09017 + 9.51057i −0.108779 + 0.334788i
\(808\) 0 0
\(809\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(810\) 0.618034 1.90211i 0.0217155 0.0668334i
\(811\) 11.7426 + 36.1401i 0.412340 + 1.26905i 0.914609 + 0.404340i \(0.132499\pi\)
−0.502268 + 0.864712i \(0.667501\pi\)
\(812\) 0 0
\(813\) −28.0000 −0.982003
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) −6.47214 + 4.70228i −0.226570 + 0.164613i
\(817\) 0 0
\(818\) 18.5410 57.0634i 0.648272 1.99517i
\(819\) −12.9443 9.40456i −0.452309 0.328622i
\(820\) −12.9443 9.40456i −0.452034 0.328422i
\(821\) −6.79837 + 20.9232i −0.237265 + 0.730226i 0.759548 + 0.650451i \(0.225420\pi\)
−0.996813 + 0.0797750i \(0.974580\pi\)
\(822\) 4.32624 + 13.3148i 0.150895 + 0.464407i
\(823\) −31.5517 + 22.9236i −1.09982 + 0.799067i −0.981031 0.193852i \(-0.937902\pi\)
−0.118791 + 0.992919i \(0.537902\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 20.0000 0.695889
\(827\) −42.0689 + 30.5648i −1.46288 + 1.06284i −0.480277 + 0.877117i \(0.659464\pi\)
−0.982601 + 0.185726i \(0.940536\pi\)
\(828\) 1.23607 + 3.80423i 0.0429563 + 0.132206i
\(829\) 7.72542 23.7764i 0.268315 0.825789i −0.722596 0.691271i \(-0.757051\pi\)
0.990911 0.134518i \(-0.0429487\pi\)
\(830\) −9.70820 7.05342i −0.336977 0.244828i
\(831\) 1.61803 + 1.17557i 0.0561290 + 0.0407801i
\(832\) 9.88854 30.4338i 0.342824 1.05510i
\(833\) −1.85410 5.70634i −0.0642408 0.197713i
\(834\) −16.1803 + 11.7557i −0.560279 + 0.407067i
\(835\) 12.0000 0.415277
\(836\) 0 0
\(837\) 35.0000 1.20978
\(838\) −32.3607 + 23.5114i −1.11788 + 0.812188i
\(839\) −1.54508 4.75528i −0.0533423 0.164171i 0.920836 0.389949i \(-0.127507\pi\)
−0.974179 + 0.225779i \(0.927507\pi\)
\(840\) 0 0
\(841\) 23.4615 + 17.0458i 0.809017 + 0.587785i
\(842\) −35.5967 25.8626i −1.22674 0.891282i
\(843\) −5.56231 + 17.1190i −0.191576 + 0.589610i
\(844\) −7.41641 22.8254i −0.255283 0.785681i
\(845\) −2.42705 + 1.76336i −0.0834931 + 0.0606613i
\(846\) −32.0000 −1.10018
\(847\) 0 0
\(848\) 24.0000 0.824163
\(849\) −3.23607 + 2.35114i −0.111062 + 0.0806910i
\(850\) −4.94427 15.2169i −0.169587 0.521936i
\(851\) −0.927051 + 2.85317i −0.0317789 + 0.0978054i
\(852\) −4.85410 3.52671i −0.166299 0.120823i
\(853\) 11.3262 + 8.22899i 0.387803 + 0.281755i 0.764555 0.644559i \(-0.222959\pi\)
−0.376752 + 0.926314i \(0.622959\pi\)
\(854\) −14.8328 + 45.6507i −0.507569 + 1.56214i
\(855\) 0 0
\(856\) 0 0
\(857\) −8.00000 −0.273275 −0.136637 0.990621i \(-0.543630\pi\)
−0.136637 + 0.990621i \(0.543630\pi\)
\(858\) 0 0
\(859\) −15.0000 −0.511793 −0.255897 0.966704i \(-0.582371\pi\)
−0.255897 + 0.966704i \(0.582371\pi\)
\(860\) −9.70820 + 7.05342i −0.331047 + 0.240520i
\(861\) −4.94427 15.2169i −0.168500 0.518591i
\(862\) 11.1246 34.2380i 0.378906 1.16615i
\(863\) −19.4164 14.1068i −0.660942 0.480203i 0.206039 0.978544i \(-0.433943\pi\)
−0.866981 + 0.498341i \(0.833943\pi\)
\(864\) 32.3607 + 23.5114i 1.10093 + 0.799874i
\(865\) 1.85410 5.70634i 0.0630414 0.194021i
\(866\) −6.79837 20.9232i −0.231018 0.711001i
\(867\) −10.5172 + 7.64121i −0.357184 + 0.259509i
\(868\) 28.0000 0.950382
\(869\) 0 0
\(870\) 0 0
\(871\) −22.6525 + 16.4580i −0.767550 + 0.557658i
\(872\) 0 0
\(873\) 4.32624 13.3148i 0.146421 0.450637i
\(874\) 0 0
\(875\) 14.5623 + 10.5801i 0.492296 + 0.357674i
\(876\) 2.47214 7.60845i 0.0835257 0.257066i
\(877\) 3.70820 + 11.4127i 0.125217 + 0.385379i 0.993941 0.109919i \(-0.0350591\pi\)
−0.868723 + 0.495297i \(0.835059\pi\)
\(878\) 64.7214 47.0228i 2.18424 1.58694i
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) −43.0000 −1.44871 −0.724353 0.689429i \(-0.757862\pi\)
−0.724353 + 0.689429i \(0.757862\pi\)
\(882\) −9.70820 + 7.05342i −0.326892 + 0.237501i
\(883\) 1.23607 + 3.80423i 0.0415970 + 0.128022i 0.969698 0.244305i \(-0.0785598\pi\)
−0.928101 + 0.372327i \(0.878560\pi\)
\(884\) −4.94427 + 15.2169i −0.166294 + 0.511800i
\(885\) 4.04508 + 2.93893i 0.135974 + 0.0987909i
\(886\) 17.7984 + 12.9313i 0.597948 + 0.434435i
\(887\) 6.79837 20.9232i 0.228267 0.702534i −0.769676 0.638434i \(-0.779582\pi\)
0.997944 0.0640996i \(-0.0204175\pi\)
\(888\) 0 0
\(889\) 12.9443 9.40456i 0.434137 0.315419i
\(890\) 30.0000 1.00560
\(891\) 0 0
\(892\) 38.0000 1.27233
\(893\) 0 0
\(894\) −6.18034 19.0211i −0.206701 0.636162i
\(895\) −4.63525 + 14.2658i −0.154939 + 0.476855i
\(896\) 0 0
\(897\) 3.23607 + 2.35114i 0.108049 + 0.0785023i
\(898\) 21.6312 66.5740i 0.721842 2.22160i
\(899\) 0 0
\(900\) −12.9443 + 9.40456i −0.431476 + 0.313485i
\(901\) −12.0000 −0.399778
\(902\) 0 0
\(903\) −12.0000 −0.399335
\(904\) 0 0
\(905\) 2.16312 + 6.65740i 0.0719045 + 0.221299i
\(906\) 1.23607 3.80423i 0.0410656 0.126387i
\(907\) 9.70820 + 7.05342i 0.322356 + 0.234205i 0.737180 0.675696i \(-0.236157\pi\)
−0.414824 + 0.909902i \(0.636157\pi\)
\(908\) 29.1246 + 21.1603i 0.966534 + 0.702228i
\(909\) 1.23607 3.80423i 0.0409978 0.126178i
\(910\) −4.94427 15.2169i −0.163901 0.504435i
\(911\) −9.70820 + 7.05342i −0.321647 + 0.233690i −0.736878 0.676026i \(-0.763701\pi\)
0.415231 + 0.909716i \(0.363701\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 24.0000 0.793849
\(915\) −9.70820 + 7.05342i −0.320943 + 0.233179i
\(916\) 9.27051 + 28.5317i 0.306306 + 0.942714i
\(917\) 11.1246 34.2380i 0.367367 1.13064i
\(918\) −16.1803 11.7557i −0.534031 0.387996i
\(919\) 8.09017 + 5.87785i 0.266870 + 0.193892i 0.713170 0.700991i \(-0.247259\pi\)
−0.446300 + 0.894883i \(0.647259\pi\)
\(920\) 0 0
\(921\) 2.47214 + 7.60845i 0.0814596 + 0.250707i
\(922\) 19.4164 14.1068i 0.639445 0.464584i
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) −12.0000 −0.394558
\(926\) 17.7984 12.9313i 0.584891 0.424948i
\(927\) 9.88854 + 30.4338i 0.324782 + 0.999577i
\(928\) 0 0
\(929\) 24.2705 + 17.6336i 0.796290 + 0.578538i 0.909823 0.414996i \(-0.136217\pi\)
−0.113534 + 0.993534i \(0.536217\pi\)
\(930\) 11.3262 + 8.22899i 0.371402 + 0.269839i
\(931\) 0 0
\(932\) −14.8328 45.6507i −0.485865 1.49534i
\(933\) 9.70820 7.05342i 0.317832 0.230919i
\(934\) −54.0000 −1.76693
\(935\) 0 0
\(936\) 0 0
\(937\) 6.47214 4.70228i 0.211435 0.153617i −0.477027 0.878888i \(-0.658286\pi\)
0.688463 + 0.725272i \(0.258286\pi\)
\(938\) −8.65248 26.6296i −0.282513 0.869487i
\(939\) 0.309017 0.951057i 0.0100844 0.0310366i
\(940\) −12.9443 9.40456i −0.422196 0.306743i
\(941\) 33.9787 + 24.6870i 1.10767 + 0.804773i 0.982296 0.187336i \(-0.0599854\pi\)
0.125379 + 0.992109i \(0.459985\pi\)
\(942\) 4.32624 13.3148i 0.140956 0.433819i
\(943\) −2.47214 7.60845i −0.0805038 0.247765i
\(944\) 16.1803 11.7557i 0.526625 0.382616i
\(945\) 10.0000 0.325300
\(946\) 0 0
\(947\) −27.0000 −0.877382 −0.438691 0.898638i \(-0.644558\pi\)
−0.438691 + 0.898638i \(0.644558\pi\)
\(948\) 16.1803 11.7557i 0.525513 0.381808i
\(949\) 4.94427 + 15.2169i 0.160498 + 0.493962i
\(950\) 0 0
\(951\) 10.5172 + 7.64121i 0.341044 + 0.247783i
\(952\) 0 0
\(953\) −10.5066 + 32.3359i −0.340341 + 1.04746i 0.623689 + 0.781672i \(0.285633\pi\)
−0.964031 + 0.265791i \(0.914367\pi\)
\(954\) 7.41641 + 22.8254i 0.240115 + 0.738998i
\(955\) −13.7533 + 9.99235i −0.445046 + 0.323345i
\(956\) 60.0000 1.94054
\(957\) 0 0
\(958\) −40.0000 −1.29234
\(959\) 11.3262 8.22899i 0.365743 0.265728i
\(960\) 2.47214 + 7.60845i 0.0797878 + 0.245562i
\(961\) 5.56231 17.1190i 0.179429 0.552226i
\(962\) 19.4164 + 14.1068i 0.626010 + 0.454823i
\(963\) −29.1246 21.1603i −0.938527 0.681880i
\(964\) 4.94427 15.2169i 0.159244 0.490103i
\(965\) −1.23607 3.80423i −0.0397904 0.122462i
\(966\) −3.23607 + 2.35114i −0.104119 + 0.0756467i
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 11.3262 8.22899i 0.363664 0.264217i
\(971\) 14.5238 + 44.6997i 0.466091 + 1.43448i 0.857605 + 0.514308i \(0.171951\pi\)
−0.391514 + 0.920172i \(0.628049\pi\)
\(972\) −9.88854 + 30.4338i −0.317175 + 0.976165i
\(973\) 16.1803 + 11.7557i 0.518718 + 0.376871i
\(974\) −37.2148 27.0381i −1.19244 0.866357i
\(975\) −4.94427 + 15.2169i −0.158343 + 0.487331i
\(976\) 14.8328 + 45.6507i 0.474787 + 1.46124i
\(977\) 21.8435 15.8702i 0.698834 0.507733i −0.180718 0.983535i \(-0.557842\pi\)
0.879552 + 0.475802i \(0.157842\pi\)
\(978\) −8.00000 −0.255812
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) −16.1803 + 11.7557i −0.516598 + 0.375331i
\(982\) 4.94427 + 15.2169i 0.157778 + 0.485591i
\(983\) 12.0517 37.0912i 0.384388 1.18303i −0.552535 0.833490i \(-0.686339\pi\)
0.936923 0.349536i \(-0.113661\pi\)
\(984\) 0 0
\(985\) −1.61803 1.17557i −0.0515548 0.0374568i
\(986\) 0 0
\(987\) −4.94427 15.2169i −0.157378 0.484359i
\(988\) 0 0
\(989\) −6.00000 −0.190789
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 45.3050 32.9160i 1.43843 1.04508i
\(993\) −2.16312 6.65740i −0.0686445 0.211266i
\(994\) −3.70820 + 11.4127i −0.117617 + 0.361988i
\(995\) 0 0
\(996\) 9.70820 + 7.05342i 0.307616 + 0.223496i
\(997\) −11.7426 + 36.1401i −0.371893 + 1.14457i 0.573657 + 0.819095i \(0.305524\pi\)
−0.945551 + 0.325475i \(0.894476\pi\)
\(998\) 12.3607 + 38.0423i 0.391270 + 1.20421i
\(999\) −12.1353 + 8.81678i −0.383942 + 0.278951i
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 121.2.c.a.3.1 4
11.2 odd 10 11.2.a.a.1.1 1
11.3 even 5 inner 121.2.c.a.27.1 4
11.4 even 5 inner 121.2.c.a.81.1 4
11.5 even 5 inner 121.2.c.a.9.1 4
11.6 odd 10 121.2.c.e.9.1 4
11.7 odd 10 121.2.c.e.81.1 4
11.8 odd 10 121.2.c.e.27.1 4
11.9 even 5 121.2.a.d.1.1 1
11.10 odd 2 121.2.c.e.3.1 4
33.2 even 10 99.2.a.d.1.1 1
33.20 odd 10 1089.2.a.b.1.1 1
44.31 odd 10 1936.2.a.i.1.1 1
44.35 even 10 176.2.a.b.1.1 1
55.2 even 20 275.2.b.a.199.1 2
55.9 even 10 3025.2.a.a.1.1 1
55.13 even 20 275.2.b.a.199.2 2
55.24 odd 10 275.2.a.b.1.1 1
77.2 odd 30 539.2.e.h.67.1 2
77.13 even 10 539.2.a.a.1.1 1
77.20 odd 10 5929.2.a.h.1.1 1
77.24 even 30 539.2.e.g.177.1 2
77.46 odd 30 539.2.e.h.177.1 2
77.68 even 30 539.2.e.g.67.1 2
88.13 odd 10 704.2.a.h.1.1 1
88.35 even 10 704.2.a.c.1.1 1
88.53 even 10 7744.2.a.x.1.1 1
88.75 odd 10 7744.2.a.k.1.1 1
99.2 even 30 891.2.e.b.595.1 2
99.13 odd 30 891.2.e.k.298.1 2
99.68 even 30 891.2.e.b.298.1 2
99.79 odd 30 891.2.e.k.595.1 2
132.35 odd 10 1584.2.a.g.1.1 1
143.90 odd 10 1859.2.a.b.1.1 1
165.2 odd 20 2475.2.c.a.199.2 2
165.68 odd 20 2475.2.c.a.199.1 2
165.134 even 10 2475.2.a.a.1.1 1
176.13 odd 20 2816.2.c.j.1409.1 2
176.35 even 20 2816.2.c.f.1409.2 2
176.101 odd 20 2816.2.c.j.1409.2 2
176.123 even 20 2816.2.c.f.1409.1 2
187.101 odd 10 3179.2.a.a.1.1 1
209.189 even 10 3971.2.a.b.1.1 1
220.79 even 10 4400.2.a.i.1.1 1
220.123 odd 20 4400.2.b.h.4049.2 2
220.167 odd 20 4400.2.b.h.4049.1 2
231.167 odd 10 4851.2.a.t.1.1 1
253.68 even 10 5819.2.a.a.1.1 1
264.35 odd 10 6336.2.a.bu.1.1 1
264.101 even 10 6336.2.a.br.1.1 1
308.167 odd 10 8624.2.a.j.1.1 1
319.57 odd 10 9251.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.2.a.a.1.1 1 11.2 odd 10
99.2.a.d.1.1 1 33.2 even 10
121.2.a.d.1.1 1 11.9 even 5
121.2.c.a.3.1 4 1.1 even 1 trivial
121.2.c.a.9.1 4 11.5 even 5 inner
121.2.c.a.27.1 4 11.3 even 5 inner
121.2.c.a.81.1 4 11.4 even 5 inner
121.2.c.e.3.1 4 11.10 odd 2
121.2.c.e.9.1 4 11.6 odd 10
121.2.c.e.27.1 4 11.8 odd 10
121.2.c.e.81.1 4 11.7 odd 10
176.2.a.b.1.1 1 44.35 even 10
275.2.a.b.1.1 1 55.24 odd 10
275.2.b.a.199.1 2 55.2 even 20
275.2.b.a.199.2 2 55.13 even 20
539.2.a.a.1.1 1 77.13 even 10
539.2.e.g.67.1 2 77.68 even 30
539.2.e.g.177.1 2 77.24 even 30
539.2.e.h.67.1 2 77.2 odd 30
539.2.e.h.177.1 2 77.46 odd 30
704.2.a.c.1.1 1 88.35 even 10
704.2.a.h.1.1 1 88.13 odd 10
891.2.e.b.298.1 2 99.68 even 30
891.2.e.b.595.1 2 99.2 even 30
891.2.e.k.298.1 2 99.13 odd 30
891.2.e.k.595.1 2 99.79 odd 30
1089.2.a.b.1.1 1 33.20 odd 10
1584.2.a.g.1.1 1 132.35 odd 10
1859.2.a.b.1.1 1 143.90 odd 10
1936.2.a.i.1.1 1 44.31 odd 10
2475.2.a.a.1.1 1 165.134 even 10
2475.2.c.a.199.1 2 165.68 odd 20
2475.2.c.a.199.2 2 165.2 odd 20
2816.2.c.f.1409.1 2 176.123 even 20
2816.2.c.f.1409.2 2 176.35 even 20
2816.2.c.j.1409.1 2 176.13 odd 20
2816.2.c.j.1409.2 2 176.101 odd 20
3025.2.a.a.1.1 1 55.9 even 10
3179.2.a.a.1.1 1 187.101 odd 10
3971.2.a.b.1.1 1 209.189 even 10
4400.2.a.i.1.1 1 220.79 even 10
4400.2.b.h.4049.1 2 220.167 odd 20
4400.2.b.h.4049.2 2 220.123 odd 20
4851.2.a.t.1.1 1 231.167 odd 10
5819.2.a.a.1.1 1 253.68 even 10
5929.2.a.h.1.1 1 77.20 odd 10
6336.2.a.br.1.1 1 264.101 even 10
6336.2.a.bu.1.1 1 264.35 odd 10
7744.2.a.k.1.1 1 88.75 odd 10
7744.2.a.x.1.1 1 88.53 even 10
8624.2.a.j.1.1 1 308.167 odd 10
9251.2.a.d.1.1 1 319.57 odd 10