Properties

Label 42.2.f.a.17.1
Level $42$
Weight $2$
Character 42.17
Analytic conductor $0.335$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [42,2,Mod(5,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42.f (of order \(6\), degree \(2\), 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: \(0.335371688489\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 42.17
Dual form 42.2.f.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +1.73205i q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +1.73205i q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.50000 - 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(-0.866025 - 1.50000i) q^{12} +3.46410i q^{13} +(1.73205 - 2.00000i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 + 3.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +1.73205 q^{20} +(-0.866025 + 4.50000i) q^{21} +3.00000 q^{22} +(5.19615 - 3.00000i) q^{23} +(1.50000 + 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{25} +(-1.73205 - 3.00000i) q^{26} -5.19615 q^{27} +(-0.500000 + 2.59808i) q^{28} -3.00000i q^{29} +(-2.59808 + 1.50000i) q^{30} +(-1.50000 - 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.50000 + 2.59808i) q^{33} -3.46410i q^{34} +(-3.46410 - 3.00000i) q^{35} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(5.19615 + 3.00000i) q^{39} +(-1.50000 + 0.866025i) q^{40} +6.92820 q^{41} +(-1.50000 - 4.33013i) q^{42} -8.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(2.59808 - 4.50000i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(3.46410 + 6.00000i) q^{47} -1.73205 q^{48} +(5.50000 - 4.33013i) q^{49} +2.00000i q^{50} +(3.00000 + 5.19615i) q^{51} +(3.00000 + 1.73205i) q^{52} +(-7.79423 - 4.50000i) q^{53} +(4.50000 - 2.59808i) q^{54} -5.19615i q^{55} +(-0.866025 - 2.50000i) q^{56} -6.00000i q^{57} +(1.50000 + 2.59808i) q^{58} +(-0.866025 + 1.50000i) q^{59} +(1.50000 - 2.59808i) q^{60} +1.73205 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(-5.19615 + 3.00000i) q^{65} +(2.59808 - 4.50000i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(1.73205 + 3.00000i) q^{68} -10.3923i q^{69} +(4.50000 + 0.866025i) q^{70} +12.0000i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-1.73205 - 1.00000i) q^{74} +(-1.73205 - 3.00000i) q^{75} -3.46410i q^{76} +(7.79423 + 1.50000i) q^{77} -6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(0.866025 - 1.50000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 + 3.46410i) q^{82} -8.66025 q^{83} +(3.46410 + 3.00000i) q^{84} -6.00000 q^{85} +(6.92820 - 4.00000i) q^{86} +(-4.50000 - 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +5.19615i q^{90} +(-3.00000 - 8.66025i) q^{91} -6.00000i q^{92} +(-2.59808 + 1.50000i) q^{93} +(-6.00000 - 3.46410i) q^{94} +(5.19615 + 3.00000i) q^{95} +(1.50000 - 0.866025i) q^{96} +5.19615i q^{97} +(-2.59808 + 6.50000i) q^{98} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 10 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 10 q^{7} - 6 q^{9} - 6 q^{10} + 12 q^{15} - 2 q^{16} + 12 q^{19} + 12 q^{22} + 6 q^{24} + 4 q^{25} - 2 q^{28} - 6 q^{31} - 18 q^{33} - 12 q^{36} + 4 q^{37} - 6 q^{40} - 6 q^{42} - 32 q^{43} - 12 q^{46} + 22 q^{49} + 12 q^{51} + 12 q^{52} + 18 q^{54} + 6 q^{58} + 6 q^{60} + 24 q^{63} - 4 q^{64} - 4 q^{67} + 18 q^{70} + 24 q^{73} - 24 q^{78} + 2 q^{79} - 18 q^{81} - 24 q^{82} - 24 q^{85} - 18 q^{87} + 6 q^{88} - 12 q^{91} - 24 q^{94} + 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.866025 + 1.50000i 0.387298 + 0.670820i 0.992085 0.125567i \(-0.0400750\pi\)
−0.604787 + 0.796387i \(0.706742\pi\)
\(6\) 1.73205i 0.707107i
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −1.50000 0.866025i −0.474342 0.273861i
\(11\) −2.59808 1.50000i −0.783349 0.452267i 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) −0.866025 1.50000i −0.250000 0.433013i
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 1.73205 2.00000i 0.462910 0.534522i
\(15\) 3.00000 0.774597
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.73205 + 3.00000i −0.420084 + 0.727607i −0.995947 0.0899392i \(-0.971333\pi\)
0.575863 + 0.817546i \(0.304666\pi\)
\(18\) 2.59808 + 1.50000i 0.612372 + 0.353553i
\(19\) 3.00000 1.73205i 0.688247 0.397360i −0.114708 0.993399i \(-0.536593\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 1.73205 0.387298
\(21\) −0.866025 + 4.50000i −0.188982 + 0.981981i
\(22\) 3.00000 0.639602
\(23\) 5.19615 3.00000i 1.08347 0.625543i 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) 1.50000 + 0.866025i 0.306186 + 0.176777i
\(25\) 1.00000 1.73205i 0.200000 0.346410i
\(26\) −1.73205 3.00000i −0.339683 0.588348i
\(27\) −5.19615 −1.00000
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) −2.59808 + 1.50000i −0.474342 + 0.273861i
\(31\) −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i \(-0.383046\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 3.46410i 0.594089i
\(35\) −3.46410 3.00000i −0.585540 0.507093i
\(36\) −3.00000 −0.500000
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) −1.73205 + 3.00000i −0.280976 + 0.486664i
\(39\) 5.19615 + 3.00000i 0.832050 + 0.480384i
\(40\) −1.50000 + 0.866025i −0.237171 + 0.136931i
\(41\) 6.92820 1.08200 0.541002 0.841021i \(-0.318045\pi\)
0.541002 + 0.841021i \(0.318045\pi\)
\(42\) −1.50000 4.33013i −0.231455 0.668153i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −2.59808 + 1.50000i −0.391675 + 0.226134i
\(45\) 2.59808 4.50000i 0.387298 0.670820i
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 3.46410 + 6.00000i 0.505291 + 0.875190i 0.999981 + 0.00612051i \(0.00194823\pi\)
−0.494690 + 0.869069i \(0.664718\pi\)
\(48\) −1.73205 −0.250000
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 2.00000i 0.282843i
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 3.00000 + 1.73205i 0.416025 + 0.240192i
\(53\) −7.79423 4.50000i −1.07062 0.618123i −0.142269 0.989828i \(-0.545440\pi\)
−0.928351 + 0.371706i \(0.878773\pi\)
\(54\) 4.50000 2.59808i 0.612372 0.353553i
\(55\) 5.19615i 0.700649i
\(56\) −0.866025 2.50000i −0.115728 0.334077i
\(57\) 6.00000i 0.794719i
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) −0.866025 + 1.50000i −0.112747 + 0.195283i −0.916877 0.399170i \(-0.869298\pi\)
0.804130 + 0.594454i \(0.202632\pi\)
\(60\) 1.50000 2.59808i 0.193649 0.335410i
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 1.73205 0.219971
\(63\) 6.00000 + 5.19615i 0.755929 + 0.654654i
\(64\) −1.00000 −0.125000
\(65\) −5.19615 + 3.00000i −0.644503 + 0.372104i
\(66\) 2.59808 4.50000i 0.319801 0.553912i
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 1.73205 + 3.00000i 0.210042 + 0.363803i
\(69\) 10.3923i 1.25109i
\(70\) 4.50000 + 0.866025i 0.537853 + 0.103510i
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) −1.73205 1.00000i −0.201347 0.116248i
\(75\) −1.73205 3.00000i −0.200000 0.346410i
\(76\) 3.46410i 0.397360i
\(77\) 7.79423 + 1.50000i 0.888235 + 0.170941i
\(78\) −6.00000 −0.679366
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 0.866025 1.50000i 0.0968246 0.167705i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −6.00000 + 3.46410i −0.662589 + 0.382546i
\(83\) −8.66025 −0.950586 −0.475293 0.879827i \(-0.657658\pi\)
−0.475293 + 0.879827i \(0.657658\pi\)
\(84\) 3.46410 + 3.00000i 0.377964 + 0.327327i
\(85\) −6.00000 −0.650791
\(86\) 6.92820 4.00000i 0.747087 0.431331i
\(87\) −4.50000 2.59808i −0.482451 0.278543i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −5.19615 9.00000i −0.550791 0.953998i −0.998218 0.0596775i \(-0.980993\pi\)
0.447427 0.894321i \(-0.352341\pi\)
\(90\) 5.19615i 0.547723i
\(91\) −3.00000 8.66025i −0.314485 0.907841i
\(92\) 6.00000i 0.625543i
\(93\) −2.59808 + 1.50000i −0.269408 + 0.155543i
\(94\) −6.00000 3.46410i −0.618853 0.357295i
\(95\) 5.19615 + 3.00000i 0.533114 + 0.307794i
\(96\) 1.50000 0.866025i 0.153093 0.0883883i
\(97\) 5.19615i 0.527589i 0.964579 + 0.263795i \(0.0849741\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) −2.59808 + 6.50000i −0.262445 + 0.656599i
\(99\) 9.00000i 0.904534i
\(100\) −1.00000 1.73205i −0.100000 0.173205i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −5.19615 3.00000i −0.514496 0.297044i
\(103\) −3.00000 + 1.73205i −0.295599 + 0.170664i −0.640464 0.767988i \(-0.721258\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) −3.46410 −0.339683
\(105\) −7.50000 + 2.59808i −0.731925 + 0.253546i
\(106\) 9.00000 0.874157
\(107\) 2.59808 1.50000i 0.251166 0.145010i −0.369132 0.929377i \(-0.620345\pi\)
0.620298 + 0.784366i \(0.287012\pi\)
\(108\) −2.59808 + 4.50000i −0.250000 + 0.433013i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 2.59808 + 4.50000i 0.247717 + 0.429058i
\(111\) 3.46410 0.328798
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) 12.0000i 1.12887i −0.825479 0.564433i \(-0.809095\pi\)
0.825479 0.564433i \(-0.190905\pi\)
\(114\) 3.00000 + 5.19615i 0.280976 + 0.486664i
\(115\) 9.00000 + 5.19615i 0.839254 + 0.484544i
\(116\) −2.59808 1.50000i −0.241225 0.139272i
\(117\) 9.00000 5.19615i 0.832050 0.480384i
\(118\) 1.73205i 0.159448i
\(119\) 1.73205 9.00000i 0.158777 0.825029i
\(120\) 3.00000i 0.273861i
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 0 0
\(123\) 6.00000 10.3923i 0.541002 0.937043i
\(124\) −1.50000 + 0.866025i −0.134704 + 0.0777714i
\(125\) 12.1244 1.08444
\(126\) −7.79423 1.50000i −0.694365 0.133631i
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −6.92820 + 12.0000i −0.609994 + 1.05654i
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) −2.59808 4.50000i −0.226995 0.393167i 0.729921 0.683531i \(-0.239557\pi\)
−0.956916 + 0.290365i \(0.906223\pi\)
\(132\) 5.19615i 0.452267i
\(133\) −6.00000 + 6.92820i −0.520266 + 0.600751i
\(134\) 2.00000i 0.172774i
\(135\) −4.50000 7.79423i −0.387298 0.670820i
\(136\) −3.00000 1.73205i −0.257248 0.148522i
\(137\) 15.5885 + 9.00000i 1.33181 + 0.768922i 0.985577 0.169226i \(-0.0541268\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(138\) 5.19615 + 9.00000i 0.442326 + 0.766131i
\(139\) 17.3205i 1.46911i 0.678551 + 0.734553i \(0.262608\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −4.33013 + 1.50000i −0.365963 + 0.126773i
\(141\) 12.0000 1.01058
\(142\) −6.00000 10.3923i −0.503509 0.872103i
\(143\) 5.19615 9.00000i 0.434524 0.752618i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 4.50000 2.59808i 0.373705 0.215758i
\(146\) −6.92820 −0.573382
\(147\) −1.73205 12.0000i −0.142857 0.989743i
\(148\) 2.00000 0.164399
\(149\) −15.5885 + 9.00000i −1.27706 + 0.737309i −0.976306 0.216394i \(-0.930570\pi\)
−0.300750 + 0.953703i \(0.597237\pi\)
\(150\) 3.00000 + 1.73205i 0.244949 + 0.141421i
\(151\) −3.50000 + 6.06218i −0.284826 + 0.493333i −0.972567 0.232623i \(-0.925269\pi\)
0.687741 + 0.725956i \(0.258602\pi\)
\(152\) 1.73205 + 3.00000i 0.140488 + 0.243332i
\(153\) 10.3923 0.840168
\(154\) −7.50000 + 2.59808i −0.604367 + 0.209359i
\(155\) 3.00000i 0.240966i
\(156\) 5.19615 3.00000i 0.416025 0.240192i
\(157\) −18.0000 10.3923i −1.43656 0.829396i −0.438948 0.898513i \(-0.644649\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −0.866025 0.500000i −0.0688973 0.0397779i
\(159\) −13.5000 + 7.79423i −1.07062 + 0.618123i
\(160\) 1.73205i 0.136931i
\(161\) −10.3923 + 12.0000i −0.819028 + 0.945732i
\(162\) 9.00000i 0.707107i
\(163\) −7.00000 12.1244i −0.548282 0.949653i −0.998392 0.0566798i \(-0.981949\pi\)
0.450110 0.892973i \(-0.351385\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) −7.79423 4.50000i −0.606780 0.350325i
\(166\) 7.50000 4.33013i 0.582113 0.336083i
\(167\) −17.3205 −1.34030 −0.670151 0.742225i \(-0.733770\pi\)
−0.670151 + 0.742225i \(0.733770\pi\)
\(168\) −4.50000 0.866025i −0.347183 0.0668153i
\(169\) 1.00000 0.0769231
\(170\) 5.19615 3.00000i 0.398527 0.230089i
\(171\) −9.00000 5.19615i −0.688247 0.397360i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 5.19615 0.393919
\(175\) −1.00000 + 5.19615i −0.0755929 + 0.392792i
\(176\) 3.00000i 0.226134i
\(177\) 1.50000 + 2.59808i 0.112747 + 0.195283i
\(178\) 9.00000 + 5.19615i 0.674579 + 0.389468i
\(179\) 10.3923 + 6.00000i 0.776757 + 0.448461i 0.835280 0.549825i \(-0.185306\pi\)
−0.0585225 + 0.998286i \(0.518639\pi\)
\(180\) −2.59808 4.50000i −0.193649 0.335410i
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 6.92820 + 6.00000i 0.513553 + 0.444750i
\(183\) 0 0
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) −1.73205 + 3.00000i −0.127343 + 0.220564i
\(186\) 1.50000 2.59808i 0.109985 0.190500i
\(187\) 9.00000 5.19615i 0.658145 0.379980i
\(188\) 6.92820 0.505291
\(189\) 12.9904 4.50000i 0.944911 0.327327i
\(190\) −6.00000 −0.435286
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −0.866025 + 1.50000i −0.0625000 + 0.108253i
\(193\) 11.5000 19.9186i 0.827788 1.43377i −0.0719816 0.997406i \(-0.522932\pi\)
0.899770 0.436365i \(-0.143734\pi\)
\(194\) −2.59808 4.50000i −0.186531 0.323081i
\(195\) 10.3923i 0.744208i
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) −4.50000 7.79423i −0.319801 0.553912i
\(199\) 9.00000 + 5.19615i 0.637993 + 0.368345i 0.783841 0.620962i \(-0.213258\pi\)
−0.145848 + 0.989307i \(0.546591\pi\)
\(200\) 1.73205 + 1.00000i 0.122474 + 0.0707107i
\(201\) 1.73205 + 3.00000i 0.122169 + 0.211604i
\(202\) 0 0
\(203\) 2.59808 + 7.50000i 0.182349 + 0.526397i
\(204\) 6.00000 0.420084
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 1.73205 3.00000i 0.120678 0.209020i
\(207\) −15.5885 9.00000i −1.08347 0.625543i
\(208\) 3.00000 1.73205i 0.208013 0.120096i
\(209\) −10.3923 −0.718851
\(210\) 5.19615 6.00000i 0.358569 0.414039i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −7.79423 + 4.50000i −0.535310 + 0.309061i
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) −6.92820 12.0000i −0.472500 0.818393i
\(216\) 5.19615i 0.353553i
\(217\) 4.50000 + 0.866025i 0.305480 + 0.0587896i
\(218\) 2.00000i 0.135457i
\(219\) 10.3923 6.00000i 0.702247 0.405442i
\(220\) −4.50000 2.59808i −0.303390 0.175162i
\(221\) −10.3923 6.00000i −0.699062 0.403604i
\(222\) −3.00000 + 1.73205i −0.201347 + 0.116248i
\(223\) 25.9808i 1.73980i −0.493228 0.869900i \(-0.664183\pi\)
0.493228 0.869900i \(-0.335817\pi\)
\(224\) −2.59808 0.500000i −0.173591 0.0334077i
\(225\) −6.00000 −0.400000
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) 2.59808 4.50000i 0.172440 0.298675i −0.766832 0.641848i \(-0.778168\pi\)
0.939272 + 0.343172i \(0.111501\pi\)
\(228\) −5.19615 3.00000i −0.344124 0.198680i
\(229\) −12.0000 + 6.92820i −0.792982 + 0.457829i −0.841011 0.541017i \(-0.818039\pi\)
0.0480291 + 0.998846i \(0.484706\pi\)
\(230\) −10.3923 −0.685248
\(231\) 9.00000 10.3923i 0.592157 0.683763i
\(232\) 3.00000 0.196960
\(233\) 15.5885 9.00000i 1.02123 0.589610i 0.106773 0.994283i \(-0.465948\pi\)
0.914461 + 0.404674i \(0.132615\pi\)
\(234\) −5.19615 + 9.00000i −0.339683 + 0.588348i
\(235\) −6.00000 + 10.3923i −0.391397 + 0.677919i
\(236\) 0.866025 + 1.50000i 0.0563735 + 0.0976417i
\(237\) 1.73205 0.112509
\(238\) 3.00000 + 8.66025i 0.194461 + 0.561361i
\(239\) 6.00000i 0.388108i −0.980991 0.194054i \(-0.937836\pi\)
0.980991 0.194054i \(-0.0621637\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) −22.5000 12.9904i −1.44935 0.836784i −0.450910 0.892570i \(-0.648900\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 1.73205 + 1.00000i 0.111340 + 0.0642824i
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 0 0
\(245\) 11.2583 + 4.50000i 0.719268 + 0.287494i
\(246\) 12.0000i 0.765092i
\(247\) 6.00000 + 10.3923i 0.381771 + 0.661247i
\(248\) 0.866025 1.50000i 0.0549927 0.0952501i
\(249\) −7.50000 + 12.9904i −0.475293 + 0.823232i
\(250\) −10.5000 + 6.06218i −0.664078 + 0.383406i
\(251\) 19.0526 1.20259 0.601293 0.799028i \(-0.294652\pi\)
0.601293 + 0.799028i \(0.294652\pi\)
\(252\) 7.50000 2.59808i 0.472456 0.163663i
\(253\) −18.0000 −1.13165
\(254\) −9.52628 + 5.50000i −0.597732 + 0.345101i
\(255\) −5.19615 + 9.00000i −0.325396 + 0.563602i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.19615 + 9.00000i 0.324127 + 0.561405i 0.981335 0.192304i \(-0.0615961\pi\)
−0.657208 + 0.753709i \(0.728263\pi\)
\(258\) 13.8564i 0.862662i
\(259\) −4.00000 3.46410i −0.248548 0.215249i
\(260\) 6.00000i 0.372104i
\(261\) −7.79423 + 4.50000i −0.482451 + 0.278543i
\(262\) 4.50000 + 2.59808i 0.278011 + 0.160510i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −2.59808 4.50000i −0.159901 0.276956i
\(265\) 15.5885i 0.957591i
\(266\) 1.73205 9.00000i 0.106199 0.551825i
\(267\) −18.0000 −1.10158
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 14.7224 25.5000i 0.897643 1.55476i 0.0671428 0.997743i \(-0.478612\pi\)
0.830500 0.557019i \(-0.188055\pi\)
\(270\) 7.79423 + 4.50000i 0.474342 + 0.273861i
\(271\) 4.50000 2.59808i 0.273356 0.157822i −0.357056 0.934083i \(-0.616219\pi\)
0.630412 + 0.776261i \(0.282886\pi\)
\(272\) 3.46410 0.210042
\(273\) −15.5885 3.00000i −0.943456 0.181568i
\(274\) −18.0000 −1.08742
\(275\) −5.19615 + 3.00000i −0.313340 + 0.180907i
\(276\) −9.00000 5.19615i −0.541736 0.312772i
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) −8.66025 15.0000i −0.519408 0.899640i
\(279\) 5.19615i 0.311086i
\(280\) 3.00000 3.46410i 0.179284 0.207020i
\(281\) 30.0000i 1.78965i −0.446417 0.894825i \(-0.647300\pi\)
0.446417 0.894825i \(-0.352700\pi\)
\(282\) −10.3923 + 6.00000i −0.618853 + 0.357295i
\(283\) 24.0000 + 13.8564i 1.42665 + 0.823678i 0.996855 0.0792477i \(-0.0252518\pi\)
0.429797 + 0.902926i \(0.358585\pi\)
\(284\) 10.3923 + 6.00000i 0.616670 + 0.356034i
\(285\) 9.00000 5.19615i 0.533114 0.307794i
\(286\) 10.3923i 0.614510i
\(287\) −17.3205 + 6.00000i −1.02240 + 0.354169i
\(288\) 3.00000i 0.176777i
\(289\) 2.50000 + 4.33013i 0.147059 + 0.254713i
\(290\) −2.59808 + 4.50000i −0.152564 + 0.264249i
\(291\) 7.79423 + 4.50000i 0.456906 + 0.263795i
\(292\) 6.00000 3.46410i 0.351123 0.202721i
\(293\) −19.0526 −1.11306 −0.556531 0.830827i \(-0.687868\pi\)
−0.556531 + 0.830827i \(0.687868\pi\)
\(294\) 7.50000 + 9.52628i 0.437409 + 0.555584i
\(295\) −3.00000 −0.174667
\(296\) −1.73205 + 1.00000i −0.100673 + 0.0581238i
\(297\) 13.5000 + 7.79423i 0.783349 + 0.452267i
\(298\) 9.00000 15.5885i 0.521356 0.903015i
\(299\) 10.3923 + 18.0000i 0.601003 + 1.04097i
\(300\) −3.46410 −0.200000
\(301\) 20.0000 6.92820i 1.15278 0.399335i
\(302\) 7.00000i 0.402805i
\(303\) 0 0
\(304\) −3.00000 1.73205i −0.172062 0.0993399i
\(305\) 0 0
\(306\) −9.00000 + 5.19615i −0.514496 + 0.297044i
\(307\) 24.2487i 1.38395i −0.721923 0.691974i \(-0.756741\pi\)
0.721923 0.691974i \(-0.243259\pi\)
\(308\) 5.19615 6.00000i 0.296078 0.341882i
\(309\) 6.00000i 0.341328i
\(310\) 1.50000 + 2.59808i 0.0851943 + 0.147561i
\(311\) −6.92820 + 12.0000i −0.392862 + 0.680458i −0.992826 0.119570i \(-0.961848\pi\)
0.599963 + 0.800027i \(0.295182\pi\)
\(312\) −3.00000 + 5.19615i −0.169842 + 0.294174i
\(313\) 1.50000 0.866025i 0.0847850 0.0489506i −0.457008 0.889463i \(-0.651079\pi\)
0.541793 + 0.840512i \(0.317746\pi\)
\(314\) 20.7846 1.17294
\(315\) −2.59808 + 13.5000i −0.146385 + 0.760639i
\(316\) 1.00000 0.0562544
\(317\) 12.9904 7.50000i 0.729612 0.421242i −0.0886679 0.996061i \(-0.528261\pi\)
0.818280 + 0.574819i \(0.194928\pi\)
\(318\) 7.79423 13.5000i 0.437079 0.757042i
\(319\) −4.50000 + 7.79423i −0.251952 + 0.436393i
\(320\) −0.866025 1.50000i −0.0484123 0.0838525i
\(321\) 5.19615i 0.290021i
\(322\) 3.00000 15.5885i 0.167183 0.868711i
\(323\) 12.0000i 0.667698i
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 6.00000 + 3.46410i 0.332820 + 0.192154i
\(326\) 12.1244 + 7.00000i 0.671506 + 0.387694i
\(327\) −1.73205 3.00000i −0.0957826 0.165900i
\(328\) 6.92820i 0.382546i
\(329\) −13.8564 12.0000i −0.763928 0.661581i
\(330\) 9.00000 0.495434
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) −4.33013 + 7.50000i −0.237647 + 0.411616i
\(333\) 3.00000 5.19615i 0.164399 0.284747i
\(334\) 15.0000 8.66025i 0.820763 0.473868i
\(335\) −3.46410 −0.189264
\(336\) 4.33013 1.50000i 0.236228 0.0818317i
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) −0.866025 + 0.500000i −0.0471056 + 0.0271964i
\(339\) −18.0000 10.3923i −0.977626 0.564433i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 2.59808 + 4.50000i 0.140694 + 0.243689i
\(342\) 10.3923 0.561951
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 8.00000i 0.431331i
\(345\) 15.5885 9.00000i 0.839254 0.484544i
\(346\) 0 0
\(347\) −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) −4.50000 + 2.59808i −0.241225 + 0.139272i
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) −1.73205 5.00000i −0.0925820 0.267261i
\(351\) 18.0000i 0.960769i
\(352\) −1.50000 2.59808i −0.0799503 0.138478i
\(353\) −17.3205 + 30.0000i −0.921878 + 1.59674i −0.125370 + 0.992110i \(0.540012\pi\)
−0.796507 + 0.604629i \(0.793321\pi\)
\(354\) −2.59808 1.50000i −0.138086 0.0797241i
\(355\) −18.0000 + 10.3923i −0.955341 + 0.551566i
\(356\) −10.3923 −0.550791
\(357\) −12.0000 10.3923i −0.635107 0.550019i
\(358\) −12.0000 −0.634220
\(359\) −5.19615 + 3.00000i −0.274242 + 0.158334i −0.630814 0.775934i \(-0.717279\pi\)
0.356572 + 0.934268i \(0.383946\pi\)
\(360\) 4.50000 + 2.59808i 0.237171 + 0.136931i
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) −3.46410 6.00000i −0.182069 0.315353i
\(363\) −3.46410 −0.181818
\(364\) −9.00000 1.73205i −0.471728 0.0907841i
\(365\) 12.0000i 0.628109i
\(366\) 0 0
\(367\) −19.5000 11.2583i −1.01789 0.587680i −0.104399 0.994535i \(-0.533292\pi\)
−0.913493 + 0.406855i \(0.866625\pi\)
\(368\) −5.19615 3.00000i −0.270868 0.156386i
\(369\) −10.3923 18.0000i −0.541002 0.937043i
\(370\) 3.46410i 0.180090i
\(371\) 23.3827 + 4.50000i 1.21397 + 0.233628i
\(372\) 3.00000i 0.155543i
\(373\) −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) −5.19615 + 9.00000i −0.268687 + 0.465379i
\(375\) 10.5000 18.1865i 0.542218 0.939149i
\(376\) −6.00000 + 3.46410i −0.309426 + 0.178647i
\(377\) 10.3923 0.535231
\(378\) −9.00000 + 10.3923i −0.462910 + 0.534522i
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 5.19615 3.00000i 0.266557 0.153897i
\(381\) 9.52628 16.5000i 0.488046 0.845321i
\(382\) 0 0
\(383\) 1.73205 + 3.00000i 0.0885037 + 0.153293i 0.906879 0.421392i \(-0.138458\pi\)
−0.818375 + 0.574684i \(0.805125\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 4.50000 + 12.9904i 0.229341 + 0.662051i
\(386\) 23.0000i 1.17067i
\(387\) 12.0000 + 20.7846i 0.609994 + 1.05654i
\(388\) 4.50000 + 2.59808i 0.228453 + 0.131897i
\(389\) −15.5885 9.00000i −0.790366 0.456318i 0.0497253 0.998763i \(-0.484165\pi\)
−0.840091 + 0.542445i \(0.817499\pi\)
\(390\) −5.19615 9.00000i −0.263117 0.455733i
\(391\) 20.7846i 1.05112i
\(392\) 4.33013 + 5.50000i 0.218704 + 0.277792i
\(393\) −9.00000 −0.453990
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) −0.866025 + 1.50000i −0.0435745 + 0.0754732i
\(396\) 7.79423 + 4.50000i 0.391675 + 0.226134i
\(397\) −24.0000 + 13.8564i −1.20453 + 0.695433i −0.961558 0.274601i \(-0.911454\pi\)
−0.242967 + 0.970034i \(0.578121\pi\)
\(398\) −10.3923 −0.520919
\(399\) 5.19615 + 15.0000i 0.260133 + 0.750939i
\(400\) −2.00000 −0.100000
\(401\) 10.3923 6.00000i 0.518967 0.299626i −0.217545 0.976050i \(-0.569805\pi\)
0.736512 + 0.676425i \(0.236472\pi\)
\(402\) −3.00000 1.73205i −0.149626 0.0863868i
\(403\) 3.00000 5.19615i 0.149441 0.258839i
\(404\) 0 0
\(405\) −15.5885 −0.774597
\(406\) −6.00000 5.19615i −0.297775 0.257881i
\(407\) 6.00000i 0.297409i
\(408\) −5.19615 + 3.00000i −0.257248 + 0.148522i
\(409\) 7.50000 + 4.33013i 0.370851 + 0.214111i 0.673830 0.738886i \(-0.264648\pi\)
−0.302979 + 0.952997i \(0.597981\pi\)
\(410\) −10.3923 6.00000i −0.513239 0.296319i
\(411\) 27.0000 15.5885i 1.33181 0.768922i
\(412\) 3.46410i 0.170664i
\(413\) 0.866025 4.50000i 0.0426143 0.221431i
\(414\) 18.0000 0.884652
\(415\) −7.50000 12.9904i −0.368161 0.637673i
\(416\) −1.73205 + 3.00000i −0.0849208 + 0.147087i
\(417\) 25.9808 + 15.0000i 1.27228 + 0.734553i
\(418\) 9.00000 5.19615i 0.440204 0.254152i
\(419\) 24.2487 1.18463 0.592314 0.805708i \(-0.298215\pi\)
0.592314 + 0.805708i \(0.298215\pi\)
\(420\) −1.50000 + 7.79423i −0.0731925 + 0.380319i
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) −3.46410 + 2.00000i −0.168630 + 0.0973585i
\(423\) 10.3923 18.0000i 0.505291 0.875190i
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) 3.46410 + 6.00000i 0.168034 + 0.291043i
\(426\) −20.7846 −1.00702
\(427\) 0 0
\(428\) 3.00000i 0.145010i
\(429\) −9.00000 15.5885i −0.434524 0.752618i
\(430\) 12.0000 + 6.92820i 0.578691 + 0.334108i
\(431\) −20.7846 12.0000i −1.00116 0.578020i −0.0925683 0.995706i \(-0.529508\pi\)
−0.908591 + 0.417687i \(0.862841\pi\)
\(432\) 2.59808 + 4.50000i 0.125000 + 0.216506i
\(433\) 34.6410i 1.66474i 0.554220 + 0.832370i \(0.313017\pi\)
−0.554220 + 0.832370i \(0.686983\pi\)
\(434\) −4.33013 + 1.50000i −0.207853 + 0.0720023i
\(435\) 9.00000i 0.431517i
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 10.3923 18.0000i 0.497131 0.861057i
\(438\) −6.00000 + 10.3923i −0.286691 + 0.496564i
\(439\) 31.5000 18.1865i 1.50341 0.867996i 0.503421 0.864041i \(-0.332075\pi\)
0.999992 0.00395451i \(-0.00125876\pi\)
\(440\) 5.19615 0.247717
\(441\) −19.5000 7.79423i −0.928571 0.371154i
\(442\) 12.0000 0.570782
\(443\) −7.79423 + 4.50000i −0.370315 + 0.213801i −0.673596 0.739100i \(-0.735251\pi\)
0.303281 + 0.952901i \(0.401918\pi\)
\(444\) 1.73205 3.00000i 0.0821995 0.142374i
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 12.9904 + 22.5000i 0.615112 + 1.06541i
\(447\) 31.1769i 1.47462i
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) 30.0000i 1.41579i 0.706319 + 0.707894i \(0.250354\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(450\) 5.19615 3.00000i 0.244949 0.141421i
\(451\) −18.0000 10.3923i −0.847587 0.489355i
\(452\) −10.3923 6.00000i −0.488813 0.282216i
\(453\) 6.06218 + 10.5000i 0.284826 + 0.493333i
\(454\) 5.19615i 0.243868i
\(455\) 10.3923 12.0000i 0.487199 0.562569i
\(456\) 6.00000 0.280976
\(457\) 2.50000 + 4.33013i 0.116945 + 0.202555i 0.918556 0.395292i \(-0.129357\pi\)
−0.801611 + 0.597847i \(0.796023\pi\)
\(458\) 6.92820 12.0000i 0.323734 0.560723i
\(459\) 9.00000 15.5885i 0.420084 0.727607i
\(460\) 9.00000 5.19615i 0.419627 0.242272i
\(461\) −13.8564 −0.645357 −0.322679 0.946509i \(-0.604583\pi\)
−0.322679 + 0.946509i \(0.604583\pi\)
\(462\) −2.59808 + 13.5000i −0.120873 + 0.628077i
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) −2.59808 + 1.50000i −0.120613 + 0.0696358i
\(465\) −4.50000 2.59808i −0.208683 0.120483i
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) −15.5885 27.0000i −0.721348 1.24941i −0.960460 0.278419i \(-0.910190\pi\)
0.239112 0.970992i \(-0.423144\pi\)
\(468\) 10.3923i 0.480384i
\(469\) 1.00000 5.19615i 0.0461757 0.239936i
\(470\) 12.0000i 0.553519i
\(471\) −31.1769 + 18.0000i −1.43656 + 0.829396i
\(472\) −1.50000 0.866025i −0.0690431 0.0398621i
\(473\) 20.7846 + 12.0000i 0.955677 + 0.551761i
\(474\) −1.50000 + 0.866025i −0.0688973 + 0.0397779i
\(475\) 6.92820i 0.317888i
\(476\) −6.92820 6.00000i −0.317554 0.275010i
\(477\) 27.0000i 1.23625i
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) −3.46410 + 6.00000i −0.158279 + 0.274147i −0.934248 0.356624i \(-0.883928\pi\)
0.775969 + 0.630771i \(0.217261\pi\)
\(480\) 2.59808 + 1.50000i 0.118585 + 0.0684653i
\(481\) −6.00000 + 3.46410i −0.273576 + 0.157949i
\(482\) 25.9808 1.18339
\(483\) 9.00000 + 25.9808i 0.409514 + 1.18217i
\(484\) −2.00000 −0.0909091
\(485\) −7.79423 + 4.50000i −0.353918 + 0.204334i
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) −0.500000 + 0.866025i −0.0226572 + 0.0392434i −0.877132 0.480250i \(-0.840546\pi\)
0.854475 + 0.519493i \(0.173879\pi\)
\(488\) 0 0
\(489\) −24.2487 −1.09656
\(490\) −12.0000 + 1.73205i −0.542105 + 0.0782461i
\(491\) 33.0000i 1.48927i −0.667472 0.744635i \(-0.732624\pi\)
0.667472 0.744635i \(-0.267376\pi\)
\(492\) −6.00000 10.3923i −0.270501 0.468521i
\(493\) 9.00000 + 5.19615i 0.405340 + 0.234023i
\(494\) −10.3923 6.00000i −0.467572 0.269953i
\(495\) −13.5000 + 7.79423i −0.606780 + 0.350325i
\(496\) 1.73205i 0.0777714i
\(497\) −10.3923 30.0000i −0.466159 1.34568i
\(498\) 15.0000i 0.672166i
\(499\) −11.0000 19.0526i −0.492428 0.852910i 0.507534 0.861632i \(-0.330557\pi\)
−0.999962 + 0.00872186i \(0.997224\pi\)
\(500\) 6.06218 10.5000i 0.271109 0.469574i
\(501\) −15.0000 + 25.9808i −0.670151 + 1.16073i
\(502\) −16.5000 + 9.52628i −0.736431 + 0.425179i
\(503\) 38.1051 1.69902 0.849512 0.527570i \(-0.176897\pi\)
0.849512 + 0.527570i \(0.176897\pi\)
\(504\) −5.19615 + 6.00000i −0.231455 + 0.267261i
\(505\) 0 0
\(506\) 15.5885 9.00000i 0.692991 0.400099i
\(507\) 0.866025 1.50000i 0.0384615 0.0666173i
\(508\) 5.50000 9.52628i 0.244023 0.422660i
\(509\) 9.52628 + 16.5000i 0.422245 + 0.731350i 0.996159 0.0875661i \(-0.0279089\pi\)
−0.573914 + 0.818916i \(0.694576\pi\)
\(510\) 10.3923i 0.460179i
\(511\) −18.0000 3.46410i −0.796273 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) −15.5885 + 9.00000i −0.688247 + 0.397360i
\(514\) −9.00000 5.19615i −0.396973 0.229192i
\(515\) −5.19615 3.00000i −0.228970 0.132196i
\(516\) 6.92820 + 12.0000i 0.304997 + 0.528271i
\(517\) 20.7846i 0.914106i
\(518\) 5.19615 + 1.00000i 0.228306 + 0.0439375i
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) −13.8564 + 24.0000i −0.607060 + 1.05146i 0.384662 + 0.923057i \(0.374318\pi\)
−0.991722 + 0.128402i \(0.959015\pi\)
\(522\) 4.50000 7.79423i 0.196960 0.341144i
\(523\) −33.0000 + 19.0526i −1.44299 + 0.833110i −0.998048 0.0624496i \(-0.980109\pi\)
−0.444941 + 0.895560i \(0.646775\pi\)
\(524\) −5.19615 −0.226995
\(525\) 6.92820 + 6.00000i 0.302372 + 0.261861i
\(526\) 0 0
\(527\) 5.19615 3.00000i 0.226348 0.130682i
\(528\) 4.50000 + 2.59808i 0.195837 + 0.113067i
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 7.79423 + 13.5000i 0.338560 + 0.586403i
\(531\) 5.19615 0.225494
\(532\) 3.00000 + 8.66025i 0.130066 + 0.375470i
\(533\) 24.0000i 1.03956i
\(534\) 15.5885 9.00000i 0.674579 0.389468i
\(535\) 4.50000 + 2.59808i 0.194552 + 0.112325i
\(536\) −1.73205 1.00000i −0.0748132 0.0431934i
\(537\) 18.0000 10.3923i 0.776757 0.448461i
\(538\) 29.4449i 1.26946i
\(539\) −20.7846 + 3.00000i −0.895257 + 0.129219i
\(540\) −9.00000 −0.387298
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) −2.59808 + 4.50000i −0.111597 + 0.193292i
\(543\) 10.3923 + 6.00000i 0.445976 + 0.257485i
\(544\) −3.00000 + 1.73205i −0.128624 + 0.0742611i
\(545\) 3.46410 0.148386
\(546\) 15.0000 5.19615i 0.641941 0.222375i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 15.5885 9.00000i 0.665906 0.384461i
\(549\) 0 0
\(550\) 3.00000 5.19615i 0.127920 0.221565i
\(551\) −5.19615 9.00000i −0.221364 0.383413i
\(552\) 10.3923 0.442326
\(553\) −2.00000 1.73205i −0.0850487 0.0736543i
\(554\) 8.00000i 0.339887i
\(555\) 3.00000 + 5.19615i 0.127343 + 0.220564i
\(556\) 15.0000 + 8.66025i 0.636142 + 0.367277i
\(557\) −2.59808 1.50000i −0.110084 0.0635570i 0.443947 0.896053i \(-0.353578\pi\)
−0.554031 + 0.832496i \(0.686911\pi\)
\(558\) −2.59808 4.50000i −0.109985 0.190500i
\(559\) 27.7128i 1.17213i
\(560\) −0.866025 + 4.50000i −0.0365963 + 0.190160i
\(561\) 18.0000i 0.759961i
\(562\) 15.0000 + 25.9808i 0.632737 + 1.09593i
\(563\) −12.9904 + 22.5000i −0.547479 + 0.948262i 0.450967 + 0.892541i \(0.351079\pi\)
−0.998446 + 0.0557214i \(0.982254\pi\)
\(564\) 6.00000 10.3923i 0.252646 0.437595i
\(565\) 18.0000 10.3923i 0.757266 0.437208i
\(566\) −27.7128 −1.16486
\(567\) 4.50000 23.3827i 0.188982 0.981981i
\(568\) −12.0000 −0.503509
\(569\) 5.19615 3.00000i 0.217834 0.125767i −0.387113 0.922032i \(-0.626528\pi\)
0.604947 + 0.796266i \(0.293194\pi\)
\(570\) −5.19615 + 9.00000i −0.217643 + 0.376969i
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −5.19615 9.00000i −0.217262 0.376309i
\(573\) 0 0
\(574\) 12.0000 13.8564i 0.500870 0.578355i
\(575\) 12.0000i 0.500435i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −1.50000 0.866025i −0.0624458 0.0360531i 0.468452 0.883489i \(-0.344812\pi\)
−0.530898 + 0.847436i \(0.678145\pi\)
\(578\) −4.33013 2.50000i −0.180110 0.103986i
\(579\) −19.9186 34.5000i −0.827788 1.43377i
\(580\) 5.19615i 0.215758i
\(581\) 21.6506 7.50000i 0.898220 0.311152i
\(582\) −9.00000 −0.373062
\(583\) 13.5000 + 23.3827i 0.559113 + 0.968412i
\(584\) −3.46410 + 6.00000i −0.143346 + 0.248282i
\(585\) 15.5885 + 9.00000i 0.644503 + 0.372104i
\(586\) 16.5000 9.52628i 0.681609 0.393527i
\(587\) −15.5885 −0.643404 −0.321702 0.946841i \(-0.604255\pi\)
−0.321702 + 0.946841i \(0.604255\pi\)
\(588\) −11.2583 4.50000i −0.464286 0.185577i
\(589\) −6.00000 −0.247226
\(590\) 2.59808 1.50000i 0.106961 0.0617540i
\(591\) 27.0000 + 15.5885i 1.11063 + 0.641223i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −19.0526 33.0000i −0.782395 1.35515i −0.930543 0.366182i \(-0.880665\pi\)
0.148148 0.988965i \(-0.452669\pi\)
\(594\) −15.5885 −0.639602
\(595\) 15.0000 5.19615i 0.614940 0.213021i
\(596\) 18.0000i 0.737309i
\(597\) 15.5885 9.00000i 0.637993 0.368345i
\(598\) −18.0000 10.3923i −0.736075 0.424973i
\(599\) 25.9808 + 15.0000i 1.06155 + 0.612883i 0.925859 0.377869i \(-0.123343\pi\)
0.135686 + 0.990752i \(0.456676\pi\)
\(600\) 3.00000 1.73205i 0.122474 0.0707107i
\(601\) 29.4449i 1.20108i −0.799594 0.600541i \(-0.794952\pi\)
0.799594 0.600541i \(-0.205048\pi\)
\(602\) −13.8564 + 16.0000i −0.564745 + 0.652111i
\(603\) 6.00000 0.244339
\(604\) 3.50000 + 6.06218i 0.142413 + 0.246667i
\(605\) 1.73205 3.00000i 0.0704179 0.121967i
\(606\) 0 0
\(607\) 19.5000 11.2583i 0.791481 0.456962i −0.0490029 0.998799i \(-0.515604\pi\)
0.840484 + 0.541837i \(0.182271\pi\)
\(608\) 3.46410 0.140488
\(609\) 13.5000 + 2.59808i 0.547048 + 0.105279i
\(610\) 0 0
\(611\) −20.7846 + 12.0000i −0.840855 + 0.485468i
\(612\) 5.19615 9.00000i 0.210042 0.363803i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 12.1244 + 21.0000i 0.489299 + 0.847491i
\(615\) 20.7846 0.838116
\(616\) −1.50000 + 7.79423i −0.0604367 + 0.314038i
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) −3.00000 5.19615i −0.120678 0.209020i
\(619\) 6.00000 + 3.46410i 0.241160 + 0.139234i 0.615710 0.787973i \(-0.288869\pi\)
−0.374550 + 0.927207i \(0.622203\pi\)
\(620\) −2.59808 1.50000i −0.104341 0.0602414i
\(621\) −27.0000 + 15.5885i −1.08347 + 0.625543i
\(622\) 13.8564i 0.555591i
\(623\) 20.7846 + 18.0000i 0.832718 + 0.721155i
\(624\) 6.00000i 0.240192i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) −0.866025 + 1.50000i −0.0346133 + 0.0599521i
\(627\) −9.00000 + 15.5885i −0.359425 + 0.622543i
\(628\) −18.0000 + 10.3923i −0.718278 + 0.414698i
\(629\) −6.92820 −0.276246
\(630\) −4.50000 12.9904i −0.179284 0.517549i
\(631\) −31.0000 −1.23409 −0.617045 0.786928i \(-0.711670\pi\)
−0.617045 + 0.786928i \(0.711670\pi\)
\(632\) −0.866025 + 0.500000i −0.0344486 + 0.0198889i
\(633\) 3.46410 6.00000i 0.137686 0.238479i
\(634\) −7.50000 + 12.9904i −0.297863 + 0.515914i
\(635\) 9.52628 + 16.5000i 0.378039 + 0.654783i
\(636\) 15.5885i 0.618123i
\(637\) 15.0000 + 19.0526i 0.594322 + 0.754890i
\(638\) 9.00000i 0.356313i
\(639\) 31.1769 18.0000i 1.23334 0.712069i
\(640\) 1.50000 + 0.866025i 0.0592927 + 0.0342327i
\(641\) 20.7846 + 12.0000i 0.820943 + 0.473972i 0.850741 0.525584i \(-0.176153\pi\)
−0.0297987 + 0.999556i \(0.509487\pi\)
\(642\) 2.59808 + 4.50000i 0.102538 + 0.177601i
\(643\) 17.3205i 0.683054i −0.939872 0.341527i \(-0.889056\pi\)
0.939872 0.341527i \(-0.110944\pi\)
\(644\) 5.19615 + 15.0000i 0.204757 + 0.591083i
\(645\) −24.0000 −0.944999
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) −7.79423 4.50000i −0.306186 0.176777i
\(649\) 4.50000 2.59808i 0.176640 0.101983i
\(650\) −6.92820 −0.271746
\(651\) 5.19615 6.00000i 0.203653 0.235159i
\(652\) −14.0000 −0.548282
\(653\) 2.59808 1.50000i 0.101671 0.0586995i −0.448303 0.893882i \(-0.647971\pi\)
0.549973 + 0.835182i \(0.314638\pi\)
\(654\) 3.00000 + 1.73205i 0.117309 + 0.0677285i
\(655\) 4.50000 7.79423i 0.175830 0.304546i
\(656\) −3.46410 6.00000i −0.135250 0.234261i
\(657\) 20.7846i 0.810885i
\(658\) 18.0000 + 3.46410i 0.701713 + 0.135045i
\(659\) 12.0000i 0.467454i −0.972302 0.233727i \(-0.924908\pi\)
0.972302 0.233727i \(-0.0750921\pi\)
\(660\) −7.79423 + 4.50000i −0.303390 + 0.175162i
\(661\) −6.00000 3.46410i −0.233373 0.134738i 0.378754 0.925497i \(-0.376353\pi\)
−0.612127 + 0.790759i \(0.709686\pi\)
\(662\) −6.92820 4.00000i −0.269272 0.155464i
\(663\) −18.0000 + 10.3923i −0.699062 + 0.403604i
\(664\) 8.66025i 0.336083i
\(665\) −15.5885 3.00000i −0.604494 0.116335i
\(666\) 6.00000i 0.232495i
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) −8.66025 + 15.0000i −0.335075 + 0.580367i
\(669\) −38.9711 22.5000i −1.50671 0.869900i
\(670\) 3.00000 1.73205i 0.115900 0.0669150i
\(671\) 0 0
\(672\) −3.00000 + 3.46410i −0.115728 + 0.133631i
\(673\) −41.0000 −1.58043 −0.790217 0.612827i \(-0.790032\pi\)
−0.790217 + 0.612827i \(0.790032\pi\)
\(674\) −11.2583 + 6.50000i −0.433655 + 0.250371i
\(675\) −5.19615 + 9.00000i −0.200000 + 0.346410i
\(676\) 0.500000 0.866025i 0.0192308 0.0333087i
\(677\) −2.59808 4.50000i −0.0998522 0.172949i 0.811771 0.583976i \(-0.198504\pi\)
−0.911623 + 0.411027i \(0.865170\pi\)
\(678\) 20.7846 0.798228
\(679\) −4.50000 12.9904i −0.172694 0.498525i
\(680\) 6.00000i 0.230089i
\(681\) −4.50000 7.79423i −0.172440 0.298675i
\(682\) −4.50000 2.59808i −0.172314 0.0994855i
\(683\) −18.1865 10.5000i −0.695888 0.401771i 0.109926 0.993940i \(-0.464939\pi\)
−0.805814 + 0.592168i \(0.798272\pi\)
\(684\) −9.00000 + 5.19615i −0.344124 + 0.198680i
\(685\) 31.1769i 1.19121i
\(686\) 0.866025 18.5000i 0.0330650 0.706333i
\(687\) 24.0000i 0.915657i
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) 15.5885 27.0000i 0.593873 1.02862i
\(690\) −9.00000 + 15.5885i −0.342624 + 0.593442i
\(691\) −6.00000 + 3.46410i −0.228251 + 0.131781i −0.609765 0.792582i \(-0.708736\pi\)
0.381514 + 0.924363i \(0.375403\pi\)
\(692\) 0 0
\(693\) −7.79423 22.5000i −0.296078 0.854704i
\(694\) 12.0000 0.455514
\(695\) −25.9808 + 15.0000i −0.985506 + 0.568982i
\(696\) 2.59808 4.50000i 0.0984798 0.170572i
\(697\) −12.0000 + 20.7846i −0.454532 + 0.787273i
\(698\) −5.19615 9.00000i −0.196677 0.340655i
\(699\) 31.1769i 1.17922i
\(700\) 4.00000 + 3.46410i 0.151186 + 0.130931i
\(701\) 3.00000i 0.113308i 0.998394 + 0.0566542i \(0.0180433\pi\)
−0.998394 + 0.0566542i \(0.981957\pi\)
\(702\) 9.00000 + 15.5885i 0.339683 + 0.588348i
\(703\) 6.00000 + 3.46410i 0.226294 + 0.130651i
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 10.3923 + 18.0000i 0.391397 + 0.677919i
\(706\) 34.6410i 1.30373i
\(707\) 0 0
\(708\) 3.00000 0.112747
\(709\) 19.0000 + 32.9090i 0.713560 + 1.23592i 0.963512 + 0.267664i \(0.0862517\pi\)
−0.249952 + 0.968258i \(0.580415\pi\)
\(710\) 10.3923 18.0000i 0.390016 0.675528i
\(711\) 1.50000 2.59808i 0.0562544 0.0974355i
\(712\) 9.00000 5.19615i 0.337289 0.194734i
\(713\) −10.3923 −0.389195
\(714\) 15.5885 + 3.00000i 0.583383 + 0.112272i
\(715\) 18.0000 0.673162
\(716\) 10.3923 6.00000i 0.388379 0.224231i
\(717\) −9.00000 5.19615i −0.336111 0.194054i
\(718\) 3.00000 5.19615i 0.111959 0.193919i
\(719\) 22.5167 + 39.0000i 0.839730 + 1.45445i 0.890121 + 0.455725i \(0.150620\pi\)
−0.0503909 + 0.998730i \(0.516047\pi\)
\(720\) −5.19615 −0.193649
\(721\) 6.00000 6.92820i 0.223452 0.258020i
\(722\) 7.00000i 0.260513i
\(723\) −38.9711 + 22.5000i −1.44935 + 0.836784i
\(724\) 6.00000 + 3.46410i 0.222988 + 0.128742i
\(725\) −5.19615 3.00000i −0.192980 0.111417i
\(726\) 3.00000 1.73205i 0.111340 0.0642824i
\(727\) 29.4449i 1.09205i 0.837769 + 0.546025i \(0.183860\pi\)
−0.837769 + 0.546025i \(0.816140\pi\)
\(728\) 8.66025 3.00000i 0.320970 0.111187i
\(729\) 27.0000 1.00000
\(730\) −6.00000 10.3923i −0.222070 0.384636i
\(731\) 13.8564 24.0000i 0.512498 0.887672i
\(732\) 0 0
\(733\) 30.0000 17.3205i 1.10808 0.639748i 0.169745 0.985488i \(-0.445706\pi\)
0.938330 + 0.345740i \(0.112372\pi\)
\(734\) 22.5167 0.831105
\(735\) 16.5000 12.9904i 0.608612 0.479157i
\(736\) 6.00000 0.221163
\(737\) 5.19615 3.00000i 0.191403 0.110506i
\(738\) 18.0000 + 10.3923i 0.662589 + 0.382546i
\(739\) 5.00000 8.66025i 0.183928 0.318573i −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) 1.73205 + 3.00000i 0.0636715 + 0.110282i
\(741\) 20.7846 0.763542
\(742\) −22.5000 + 7.79423i −0.826001 + 0.286135i
\(743\) 18.0000i 0.660356i 0.943919 + 0.330178i \(0.107109\pi\)
−0.943919 + 0.330178i \(0.892891\pi\)
\(744\) −1.50000 2.59808i −0.0549927 0.0952501i
\(745\) −27.0000 15.5885i −0.989203 0.571117i
\(746\) 27.7128 + 16.0000i 1.01464 + 0.585802i
\(747\) 12.9904 + 22.5000i 0.475293 + 0.823232i
\(748\) 10.3923i 0.379980i
\(749\) −5.19615 + 6.00000i −0.189863 + 0.219235i
\(750\) 21.0000i 0.766812i
\(751\) 5.50000 + 9.52628i 0.200698 + 0.347619i 0.948753 0.316017i \(-0.102346\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(752\) 3.46410 6.00000i 0.126323 0.218797i
\(753\) 16.5000 28.5788i 0.601293 1.04147i
\(754\) −9.00000 + 5.19615i −0.327761 + 0.189233i
\(755\) −12.1244 −0.441250
\(756\) 2.59808 13.5000i 0.0944911 0.490990i
\(757\) 4.00000 0.145382 0.0726912 0.997354i \(-0.476841\pi\)
0.0726912 + 0.997354i \(0.476841\pi\)
\(758\) −13.8564 + 8.00000i −0.503287 + 0.290573i
\(759\) −15.5885 + 27.0000i −0.565825 + 0.980038i
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) −8.66025 15.0000i −0.313934 0.543750i 0.665276 0.746597i \(-0.268314\pi\)
−0.979210 + 0.202848i \(0.934980\pi\)
\(762\) 19.0526i 0.690201i
\(763\) −1.00000 + 5.19615i −0.0362024 + 0.188113i
\(764\) 0 0
\(765\) 9.00000 + 15.5885i 0.325396 + 0.563602i
\(766\) −3.00000 1.73205i −0.108394 0.0625815i
\(767\) −5.19615 3.00000i −0.187622 0.108324i
\(768\) 0.866025 + 1.50000i 0.0312500 + 0.0541266i
\(769\) 19.0526i 0.687053i 0.939143 + 0.343526i \(0.111621\pi\)
−0.939143 + 0.343526i \(0.888379\pi\)
\(770\) −10.3923 9.00000i −0.374513 0.324337i
\(771\) 18.0000 0.648254
\(772\) −11.5000 19.9186i −0.413894 0.716886i
\(773\) 13.8564 24.0000i 0.498380 0.863220i −0.501618 0.865089i \(-0.667262\pi\)
0.999998 + 0.00186926i \(0.000595004\pi\)
\(774\) −20.7846 12.0000i −0.747087 0.431331i
\(775\) −3.00000 + 1.73205i −0.107763 + 0.0622171i
\(776\) −5.19615 −0.186531
\(777\) −8.66025 + 3.00000i −0.310685 + 0.107624i
\(778\) 18.0000 0.645331
\(779\) 20.7846 12.0000i 0.744686 0.429945i
\(780\) 9.00000 + 5.19615i 0.322252 + 0.186052i
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) −10.3923 18.0000i −0.371628 0.643679i
\(783\) 15.5885i 0.557086i
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\) 36.0000i 1.28490i
\(786\) 7.79423 4.50000i 0.278011 0.160510i
\(787\) 36.0000 + 20.7846i 1.28326 + 0.740891i 0.977443 0.211199i \(-0.0677367\pi\)
0.305818 + 0.952090i \(0.401070\pi\)
\(788\) 15.5885 + 9.00000i 0.555316 + 0.320612i
\(789\) 0 0
\(790\) 1.73205i 0.0616236i
\(791\) 10.3923 + 30.0000i 0.369508 + 1.06668i
\(792\) −9.00000 −0.319801
\(793\) 0 0
\(794\) 13.8564 24.0000i 0.491745 0.851728i
\(795\) −23.3827 13.5000i −0.829298 0.478796i
\(796\) 9.00000 5.19615i 0.318997 0.184173i
\(797\) −25.9808 −0.920286 −0.460143 0.887845i \(-0.652202\pi\)
−0.460143 + 0.887845i \(0.652202\pi\)
\(798\) −12.0000 10.3923i −0.424795 0.367884i
\(799\) −24.0000 −0.849059
\(800\) 1.73205 1.00000i 0.0612372 0.0353553i
\(801\) −15.5885 + 27.0000i −0.550791 + 0.953998i
\(802\) −6.00000 + 10.3923i −0.211867 + 0.366965i
\(803\) −10.3923 18.0000i −0.366736 0.635206i
\(804\) 3.46410 0.122169
\(805\) −27.0000 5.19615i −0.951625 0.183140i
\(806\) 6.00000i 0.211341i
\(807\) −25.5000 44.1673i −0.897643 1.55476i
\(808\) 0 0
\(809\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 13.5000 7.79423i 0.474342 0.273861i
\(811\) 31.1769i 1.09477i 0.836881 + 0.547385i \(0.184377\pi\)
−0.836881 + 0.547385i \(0.815623\pi\)
\(812\) 7.79423 + 1.50000i 0.273524 + 0.0526397i
\(813\) 9.00000i 0.315644i
\(814\) 3.00000 + 5.19615i 0.105150 + 0.182125i
\(815\) 12.1244 21.0000i 0.424698 0.735598i
\(816\) 3.00000 5.19615i 0.105021 0.181902i
\(817\) −24.0000 + 13.8564i −0.839654 + 0.484774i
\(818\) −8.66025 −0.302799
\(819\) −18.0000 + 20.7846i −0.628971 + 0.726273i
\(820\) 12.0000 0.419058
\(821\) −2.59808 + 1.50000i −0.0906735 + 0.0523504i −0.544651 0.838663i \(-0.683338\pi\)
0.453978 + 0.891013i \(0.350005\pi\)
\(822\) −15.5885 + 27.0000i −0.543710 + 0.941733i
\(823\) −4.00000 + 6.92820i −0.139431 + 0.241502i −0.927281 0.374365i \(-0.877861\pi\)
0.787850 + 0.615867i \(0.211194\pi\)
\(824\) −1.73205 3.00000i −0.0603388 0.104510i
\(825\) 10.3923i 0.361814i
\(826\) 1.50000 + 4.33013i 0.0521917 + 0.150664i
\(827\) 9.00000i 0.312961i 0.987681 + 0.156480i \(0.0500148\pi\)
−0.987681 + 0.156480i \(0.949985\pi\)
\(828\) −15.5885 + 9.00000i −0.541736 + 0.312772i
\(829\) −15.0000 8.66025i −0.520972 0.300783i 0.216361 0.976314i \(-0.430581\pi\)
−0.737332 + 0.675530i \(0.763915\pi\)
\(830\) 12.9904 + 7.50000i 0.450903 + 0.260329i
\(831\) 6.92820 + 12.0000i 0.240337 + 0.416275i
\(832\) 3.46410i 0.120096i
\(833\) 3.46410 + 24.0000i 0.120024 + 0.831551i
\(834\) −30.0000 −1.03882
\(835\) −15.0000 25.9808i −0.519096 0.899101i
\(836\) −5.19615 + 9.00000i −0.179713 + 0.311272i
\(837\) 7.79423 + 4.50000i 0.269408 + 0.155543i
\(838\) −21.0000 + 12.1244i −0.725433 + 0.418829i
\(839\) 3.46410 0.119594 0.0597970 0.998211i \(-0.480955\pi\)
0.0597970 + 0.998211i \(0.480955\pi\)
\(840\) −2.59808 7.50000i −0.0896421 0.258775i
\(841\) 20.0000 0.689655
\(842\) −27.7128 + 16.0000i −0.955047 + 0.551396i
\(843\) −45.0000 25.9808i −1.54988 0.894825i
\(844\) 2.00000 3.46410i 0.0688428 0.119239i
\(845\) 0.866025 + 1.50000i 0.0297922 + 0.0516016i
\(846\) 20.7846i 0.714590i
\(847\) 4.00000 + 3.46410i 0.137442 + 0.119028i
\(848\) 9.00000i 0.309061i
\(849\) 41.5692 24.0000i 1.42665 0.823678i
\(850\) −6.00000 3.46410i −0.205798 0.118818i
\(851\) 10.3923 + 6.00000i 0.356244 + 0.205677i
\(852\) 18.0000 10.3923i 0.616670 0.356034i
\(853\) 24.2487i 0.830260i −0.909762 0.415130i \(-0.863736\pi\)
0.909762 0.415130i \(-0.136264\pi\)
\(854\) 0 0
\(855\) 18.0000i 0.615587i
\(856\) 1.50000 + 2.59808i 0.0512689 + 0.0888004i
\(857\) −6.92820 + 12.0000i −0.236663 + 0.409912i −0.959755 0.280840i \(-0.909387\pi\)
0.723092 + 0.690752i \(0.242720\pi\)
\(858\) 15.5885 + 9.00000i 0.532181 + 0.307255i
\(859\) −18.0000 + 10.3923i −0.614152 + 0.354581i −0.774589 0.632465i \(-0.782043\pi\)
0.160437 + 0.987046i \(0.448710\pi\)
\(860\) −13.8564 −0.472500
\(861\) −6.00000 + 31.1769i −0.204479 + 1.06251i
\(862\) 24.0000 0.817443
\(863\) 46.7654 27.0000i 1.59191 0.919091i 0.598933 0.800799i \(-0.295592\pi\)
0.992979 0.118291i \(-0.0377417\pi\)
\(864\) −4.50000 2.59808i −0.153093 0.0883883i
\(865\) 0 0
\(866\) −17.3205 30.0000i −0.588575 1.01944i
\(867\) 8.66025 0.294118
\(868\) 3.00000 3.46410i 0.101827 0.117579i
\(869\) 3.00000i 0.101768i
\(870\) 4.50000 + 7.79423i 0.152564 + 0.264249i
\(871\) −6.00000 3.46410i −0.203302 0.117377i
\(872\) 1.73205 + 1.00000i 0.0586546 + 0.0338643i
\(873\) 13.5000 7.79423i 0.456906 0.263795i
\(874\) 20.7846i 0.703050i
\(875\) −30.3109 + 10.5000i −1.02470 + 0.354965i
\(876\) 12.0000i 0.405442i
\(877\) −22.0000 38.1051i −0.742887 1.28672i −0.951175 0.308651i \(-0.900123\pi\)
0.208288 0.978068i \(-0.433211\pi\)
\(878\) −18.1865 + 31.5000i −0.613766 + 1.06307i
\(879\) −16.5000 + 28.5788i −0.556531 + 0.963940i
\(880\) −4.50000 + 2.59808i −0.151695 + 0.0875811i
\(881\) 10.3923 0.350126 0.175063 0.984557i \(-0.443987\pi\)
0.175063 + 0.984557i \(0.443987\pi\)
\(882\) 20.7846 3.00000i 0.699854 0.101015i
\(883\) 52.0000 1.74994 0.874970 0.484178i \(-0.160881\pi\)
0.874970 + 0.484178i \(0.160881\pi\)
\(884\) −10.3923 + 6.00000i −0.349531 + 0.201802i
\(885\) −2.59808 + 4.50000i −0.0873334 + 0.151266i
\(886\) 4.50000 7.79423i 0.151180 0.261852i
\(887\) −12.1244 21.0000i −0.407096 0.705111i 0.587467 0.809248i \(-0.300125\pi\)
−0.994563 + 0.104137i \(0.966792\pi\)
\(888\) 3.46410i 0.116248i
\(889\) −27.5000 + 9.52628i −0.922320 + 0.319501i
\(890\) 18.0000i 0.603361i
\(891\) 23.3827 13.5000i 0.783349 0.452267i
\(892\) −22.5000 12.9904i −0.753356 0.434950i
\(893\) 20.7846 + 12.0000i 0.695530 + 0.401565i
\(894\) −15.5885 27.0000i −0.521356 0.903015i
\(895\) 20.7846i 0.694753i
\(896\) −1.73205 + 2.00000i −0.0578638 + 0.0668153i
\(897\) 36.0000 1.20201
\(898\) −15.0000 25.9808i −0.500556 0.866989i
\(899\) −2.59808 + 4.50000i −0.0866507 + 0.150083i
\(900\) −3.00000 + 5.19615i −0.100000 + 0.173205i
\(901\) 27.0000 15.5885i 0.899500 0.519327i
\(902\) 20.7846 0.692052
\(903\) 6.92820 36.0000i 0.230556 1.19800i
\(904\) 12.0000 0.399114
\(905\) −10.3923 + 6.00000i −0.345452 + 0.199447i
\(906\) −10.5000 6.06218i −0.348839 0.201402i
\(907\) 13.0000 22.5167i 0.431658 0.747653i −0.565358 0.824845i \(-0.691262\pi\)
0.997016 + 0.0771920i \(0.0245954\pi\)
\(908\) −2.59808 4.50000i −0.0862202 0.149338i
\(909\) 0 0
\(910\) −3.00000 + 15.5885i −0.0994490 + 0.516752i
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −5.19615 + 3.00000i −0.172062 + 0.0993399i
\(913\) 22.5000 + 12.9904i 0.744641 + 0.429919i
\(914\) −4.33013 2.50000i −0.143228 0.0826927i
\(915\) 0 0
\(916\) 13.8564i 0.457829i
\(917\) 10.3923 + 9.00000i 0.343184 + 0.297206i
\(918\) 18.0000i 0.594089i
\(919\) 10.0000 + 17.3205i 0.329870 + 0.571351i 0.982486 0.186338i \(-0.0596619\pi\)
−0.652616 + 0.757689i \(0.726329\pi\)
\(920\) −5.19615 + 9.00000i −0.171312 + 0.296721i
\(921\) −36.3731 21.0000i −1.19853 0.691974i
\(922\) 12.0000 6.92820i 0.395199 0.228168i
\(923\) −41.5692 −1.36827
\(924\) −4.50000 12.9904i −0.148039 0.427352i
\(925\) 4.00000 0.131519
\(926\) 3.46410 2.00000i 0.113837 0.0657241i
\(927\) 9.00000 + 5.19615i 0.295599 + 0.170664i
\(928\) 1.50000 2.59808i 0.0492399 0.0852860i
\(929\) 24.2487 + 42.0000i 0.795574 + 1.37798i 0.922474 + 0.386060i \(0.126164\pi\)
−0.126899 + 0.991916i \(0.540503\pi\)
\(930\) 5.19615 0.170389
\(931\) 9.00000 22.5167i 0.294963 0.737954i
\(932\) 18.0000i 0.589610i
\(933\) 12.0000 + 20.7846i 0.392862 + 0.680458i
\(934\) 27.0000 + 15.5885i 0.883467 + 0.510070i
\(935\) 15.5885 + 9.00000i 0.509797 + 0.294331i
\(936\) 5.19615 + 9.00000i 0.169842 + 0.294174i
\(937\) 22.5167i 0.735587i 0.929907 + 0.367794i \(0.119887\pi\)
−0.929907 + 0.367794i \(0.880113\pi\)
\(938\) 1.73205 + 5.00000i 0.0565535 + 0.163256i
\(939\) 3.00000i 0.0979013i
\(940\) 6.00000 + 10.3923i 0.195698 + 0.338960i
\(941\) −16.4545 + 28.5000i −0.536401 + 0.929073i 0.462693 + 0.886518i \(0.346883\pi\)
−0.999094 + 0.0425550i \(0.986450\pi\)
\(942\) 18.0000 31.1769i 0.586472 1.01580i
\(943\) 36.0000 20.7846i 1.17232 0.676840i
\(944\) 1.73205 0.0563735
\(945\) 18.0000 + 15.5885i 0.585540 + 0.507093i
\(946\) −24.0000 −0.780307
\(947\) 10.3923 6.00000i 0.337705 0.194974i −0.321552 0.946892i \(-0.604204\pi\)
0.659256 + 0.751918i \(0.270871\pi\)
\(948\) 0.866025 1.50000i 0.0281272 0.0487177i
\(949\) −12.0000 + 20.7846i −0.389536 + 0.674697i
\(950\) 3.46410 + 6.00000i 0.112390 + 0.194666i
\(951\) 25.9808i 0.842484i
\(952\) 9.00000 + 1.73205i 0.291692 + 0.0561361i
\(953\) 24.0000i 0.777436i −0.921357 0.388718i \(-0.872918\pi\)
0.921357 0.388718i \(-0.127082\pi\)
\(954\) −13.5000 23.3827i −0.437079 0.757042i
\(955\) 0 0
\(956\) −5.19615 3.00000i −0.168056 0.0970269i
\(957\) 7.79423 + 13.5000i 0.251952 + 0.436393i
\(958\) 6.92820i 0.223840i
\(959\) −46.7654 9.00000i −1.51013 0.290625i
\(960\) −3.00000 −0.0968246
\(961\) −14.0000 24.2487i −0.451613 0.782216i
\(962\) 3.46410 6.00000i 0.111687 0.193448i
\(963\) −7.79423 4.50000i −0.251166 0.145010i
\(964\) −22.5000 + 12.9904i −0.724676 + 0.418392i
\(965\) 39.8372 1.28240
\(966\) −20.7846 18.0000i −0.668734 0.579141i
\(967\) −7.00000 −0.225105 −0.112552 0.993646i \(-0.535903\pi\)
−0.112552 + 0.993646i \(0.535903\pi\)
\(968\) 1.73205 1.00000i 0.0556702 0.0321412i
\(969\) 18.0000 + 10.3923i 0.578243 + 0.333849i
\(970\) 4.50000 7.79423i 0.144486 0.250258i
\(971\) 4.33013 + 7.50000i 0.138960 + 0.240686i 0.927103 0.374806i \(-0.122291\pi\)
−0.788143 + 0.615492i \(0.788957\pi\)
\(972\) 15.5885 0.500000
\(973\) −15.0000 43.3013i −0.480878 1.38817i
\(974\) 1.00000i 0.0320421i
\(975\) 10.3923 6.00000i 0.332820 0.192154i
\(976\) 0 0
\(977\) −20.7846 12.0000i −0.664959 0.383914i 0.129205 0.991618i \(-0.458757\pi\)
−0.794164 + 0.607704i \(0.792091\pi\)
\(978\) 21.0000 12.1244i 0.671506 0.387694i
\(979\) 31.1769i 0.996419i
\(980\) 9.52628 7.50000i 0.304306 0.239579i
\(981\) −6.00000 −0.191565
\(982\) 16.5000 + 28.5788i 0.526536 + 0.911987i
\(983\) 6.92820 12.0000i 0.220975 0.382741i −0.734129 0.679010i \(-0.762409\pi\)
0.955104 + 0.296269i \(0.0957426\pi\)
\(984\) 10.3923 + 6.00000i 0.331295 + 0.191273i
\(985\) −27.0000 + 15.5885i −0.860292 + 0.496690i
\(986\) −10.3923 −0.330958
\(987\) −30.0000 + 10.3923i −0.954911 + 0.330791i
\(988\) 12.0000 0.381771
\(989\) −41.5692 + 24.0000i −1.32182 + 0.763156i
\(990\) 7.79423 13.5000i 0.247717 0.429058i
\(991\) 23.5000 40.7032i 0.746502 1.29298i −0.202988 0.979181i \(-0.565065\pi\)
0.949490 0.313798i \(-0.101602\pi\)
\(992\) −0.866025 1.50000i −0.0274963 0.0476250i
\(993\) 13.8564 0.439720
\(994\) 24.0000 + 20.7846i 0.761234 + 0.659248i
\(995\) 18.0000i 0.570638i
\(996\) 7.50000 + 12.9904i 0.237647 + 0.411616i
\(997\) 15.0000 + 8.66025i 0.475055 + 0.274273i 0.718353 0.695678i \(-0.244896\pi\)
−0.243299 + 0.969951i \(0.578229\pi\)
\(998\) 19.0526 + 11.0000i 0.603098 + 0.348199i
\(999\) −5.19615 9.00000i −0.164399 0.284747i
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 42.2.f.a.17.1 yes 4
3.2 odd 2 inner 42.2.f.a.17.2 yes 4
4.3 odd 2 336.2.bc.e.17.1 4
5.2 odd 4 1050.2.u.a.899.1 4
5.3 odd 4 1050.2.u.d.899.2 4
5.4 even 2 1050.2.s.b.101.2 4
7.2 even 3 294.2.f.a.215.2 4
7.3 odd 6 294.2.d.a.293.2 4
7.4 even 3 294.2.d.a.293.1 4
7.5 odd 6 inner 42.2.f.a.5.2 yes 4
7.6 odd 2 294.2.f.a.227.1 4
9.2 odd 6 1134.2.t.d.1025.1 4
9.4 even 3 1134.2.l.c.269.1 4
9.5 odd 6 1134.2.l.c.269.2 4
9.7 even 3 1134.2.t.d.1025.2 4
12.11 even 2 336.2.bc.e.17.2 4
15.2 even 4 1050.2.u.d.899.1 4
15.8 even 4 1050.2.u.a.899.2 4
15.14 odd 2 1050.2.s.b.101.1 4
21.2 odd 6 294.2.f.a.215.1 4
21.5 even 6 inner 42.2.f.a.5.1 4
21.11 odd 6 294.2.d.a.293.4 4
21.17 even 6 294.2.d.a.293.3 4
21.20 even 2 294.2.f.a.227.2 4
28.3 even 6 2352.2.k.e.881.1 4
28.11 odd 6 2352.2.k.e.881.3 4
28.19 even 6 336.2.bc.e.257.2 4
35.12 even 12 1050.2.u.a.299.2 4
35.19 odd 6 1050.2.s.b.551.1 4
35.33 even 12 1050.2.u.d.299.1 4
63.5 even 6 1134.2.t.d.593.2 4
63.40 odd 6 1134.2.t.d.593.1 4
63.47 even 6 1134.2.l.c.215.2 4
63.61 odd 6 1134.2.l.c.215.1 4
84.11 even 6 2352.2.k.e.881.2 4
84.47 odd 6 336.2.bc.e.257.1 4
84.59 odd 6 2352.2.k.e.881.4 4
105.47 odd 12 1050.2.u.d.299.2 4
105.68 odd 12 1050.2.u.a.299.1 4
105.89 even 6 1050.2.s.b.551.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.f.a.5.1 4 21.5 even 6 inner
42.2.f.a.5.2 yes 4 7.5 odd 6 inner
42.2.f.a.17.1 yes 4 1.1 even 1 trivial
42.2.f.a.17.2 yes 4 3.2 odd 2 inner
294.2.d.a.293.1 4 7.4 even 3
294.2.d.a.293.2 4 7.3 odd 6
294.2.d.a.293.3 4 21.17 even 6
294.2.d.a.293.4 4 21.11 odd 6
294.2.f.a.215.1 4 21.2 odd 6
294.2.f.a.215.2 4 7.2 even 3
294.2.f.a.227.1 4 7.6 odd 2
294.2.f.a.227.2 4 21.20 even 2
336.2.bc.e.17.1 4 4.3 odd 2
336.2.bc.e.17.2 4 12.11 even 2
336.2.bc.e.257.1 4 84.47 odd 6
336.2.bc.e.257.2 4 28.19 even 6
1050.2.s.b.101.1 4 15.14 odd 2
1050.2.s.b.101.2 4 5.4 even 2
1050.2.s.b.551.1 4 35.19 odd 6
1050.2.s.b.551.2 4 105.89 even 6
1050.2.u.a.299.1 4 105.68 odd 12
1050.2.u.a.299.2 4 35.12 even 12
1050.2.u.a.899.1 4 5.2 odd 4
1050.2.u.a.899.2 4 15.8 even 4
1050.2.u.d.299.1 4 35.33 even 12
1050.2.u.d.299.2 4 105.47 odd 12
1050.2.u.d.899.1 4 15.2 even 4
1050.2.u.d.899.2 4 5.3 odd 4
1134.2.l.c.215.1 4 63.61 odd 6
1134.2.l.c.215.2 4 63.47 even 6
1134.2.l.c.269.1 4 9.4 even 3
1134.2.l.c.269.2 4 9.5 odd 6
1134.2.t.d.593.1 4 63.40 odd 6
1134.2.t.d.593.2 4 63.5 even 6
1134.2.t.d.1025.1 4 9.2 odd 6
1134.2.t.d.1025.2 4 9.7 even 3
2352.2.k.e.881.1 4 28.3 even 6
2352.2.k.e.881.2 4 84.11 even 6
2352.2.k.e.881.3 4 28.11 odd 6
2352.2.k.e.881.4 4 84.59 odd 6