Properties

Label 63.2.g.a.16.1
Level $63$
Weight $2$
Character 63.16
Analytic conductor $0.503$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,2,Mod(4,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.g (of order \(3\), 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: \(0.503057532734\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 63.16
Dual form 63.2.g.a.4.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(-1.50000 + 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +(-2.50000 + 0.866025i) q^{14} +(1.50000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.00000 + 3.46410i) q^{21} +(-2.50000 - 4.33013i) q^{22} +3.00000 q^{23} +(4.50000 + 2.59808i) q^{24} -4.00000 q^{25} +(2.50000 - 4.33013i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} -1.73205i q^{30} +(-2.50000 + 4.33013i) q^{32} +(-7.50000 - 4.33013i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(-0.500000 + 2.59808i) q^{35} +3.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +1.00000 q^{38} -8.66025i q^{39} +3.00000 q^{40} +(2.50000 + 4.33013i) q^{41} +(4.50000 + 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +(2.50000 - 4.33013i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-1.50000 - 2.59808i) q^{46} -1.73205i q^{48} +(-6.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +5.19615i q^{51} +5.00000 q^{52} +(4.50000 + 7.79423i) q^{53} +(-4.50000 + 2.59808i) q^{54} -5.00000 q^{55} +(-1.50000 + 7.79423i) q^{56} +(1.50000 - 0.866025i) q^{57} -1.00000 q^{58} +(1.50000 - 0.866025i) q^{60} +(7.00000 + 12.1244i) q^{61} +(7.50000 - 2.59808i) q^{63} +7.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +8.66025i q^{66} +(-2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-4.50000 - 2.59808i) q^{69} +(2.50000 - 0.866025i) q^{70} -12.0000 q^{71} +(-4.50000 - 7.79423i) q^{72} +(-1.50000 - 2.59808i) q^{73} +3.00000 q^{74} +(6.00000 + 3.46410i) q^{75} +(0.500000 + 0.866025i) q^{76} +(2.50000 - 12.9904i) q^{77} +(-7.50000 + 4.33013i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(2.50000 - 4.33013i) q^{82} +(4.50000 - 7.79423i) q^{83} +(1.50000 + 4.33013i) q^{84} +(1.50000 + 2.59808i) q^{85} -1.00000 q^{86} +(-1.50000 + 0.866025i) q^{87} -15.0000 q^{88} +(6.50000 - 11.2583i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(12.5000 - 4.33013i) q^{91} +(1.50000 - 2.59808i) q^{92} +(0.500000 - 0.866025i) q^{95} +(7.50000 - 4.33013i) q^{96} +(4.50000 - 7.79423i) q^{97} +(1.00000 + 6.92820i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 3 q^{12} + 5 q^{13} - 5 q^{14} + 3 q^{15} + q^{16} - 3 q^{17} + 3 q^{18} - q^{19} - q^{20} - 6 q^{21} - 5 q^{22} + 6 q^{23} + 9 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{28} + q^{29} - 5 q^{32} - 15 q^{33} - 3 q^{34} - q^{35} + 6 q^{36} - 3 q^{37} + 2 q^{38} + 6 q^{40} + 5 q^{41} + 9 q^{42} + q^{43} + 5 q^{44} - 3 q^{45} - 3 q^{46} - 13 q^{49} + 4 q^{50} + 10 q^{52} + 9 q^{53} - 9 q^{54} - 10 q^{55} - 3 q^{56} + 3 q^{57} - 2 q^{58} + 3 q^{60} + 14 q^{61} + 15 q^{63} + 14 q^{64} - 5 q^{65} - 4 q^{67} - 6 q^{68} - 9 q^{69} + 5 q^{70} - 24 q^{71} - 9 q^{72} - 3 q^{73} + 6 q^{74} + 12 q^{75} + q^{76} + 5 q^{77} - 15 q^{78} - 8 q^{79} - q^{80} - 9 q^{81} + 5 q^{82} + 9 q^{83} + 3 q^{84} + 3 q^{85} - 2 q^{86} - 3 q^{87} - 30 q^{88} + 13 q^{89} - 3 q^{90} + 25 q^{91} + 3 q^{92} + q^{95} + 15 q^{96} + 9 q^{97} + 2 q^{98} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) −3.00000 −1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) −1.50000 + 0.866025i −0.433013 + 0.250000i
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 1.50000 + 0.866025i 0.387298 + 0.223607i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) −3.00000 + 3.46410i −0.654654 + 0.755929i
\(22\) −2.50000 4.33013i −0.533002 0.923186i
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 4.50000 + 2.59808i 0.918559 + 0.530330i
\(25\) −4.00000 −0.800000
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 5.19615i 1.00000i
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 1.73205i 0.316228i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) −7.50000 4.33013i −1.30558 0.753778i
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) −0.500000 + 2.59808i −0.0845154 + 0.439155i
\(36\) 3.00000 0.500000
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 1.00000 0.162221
\(39\) 8.66025i 1.38675i
\(40\) 3.00000 0.474342
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 4.50000 + 0.866025i 0.694365 + 0.133631i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 5.19615i 0.727607i
\(52\) 5.00000 0.693375
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) −5.00000 −0.674200
\(56\) −1.50000 + 7.79423i −0.200446 + 1.04155i
\(57\) 1.50000 0.866025i 0.198680 0.114708i
\(58\) −1.00000 −0.131306
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 1.50000 0.866025i 0.193649 0.111803i
\(61\) 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 0 0
\(63\) 7.50000 2.59808i 0.944911 0.327327i
\(64\) 7.00000 0.875000
\(65\) −2.50000 4.33013i −0.310087 0.537086i
\(66\) 8.66025i 1.06600i
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) −3.00000 −0.363803
\(69\) −4.50000 2.59808i −0.541736 0.312772i
\(70\) 2.50000 0.866025i 0.298807 0.103510i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −4.50000 7.79423i −0.530330 0.918559i
\(73\) −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i \(-0.222841\pi\)
−0.940356 + 0.340193i \(0.889507\pi\)
\(74\) 3.00000 0.348743
\(75\) 6.00000 + 3.46410i 0.692820 + 0.400000i
\(76\) 0.500000 + 0.866025i 0.0573539 + 0.0993399i
\(77\) 2.50000 12.9904i 0.284901 1.48039i
\(78\) −7.50000 + 4.33013i −0.849208 + 0.490290i
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 2.50000 4.33013i 0.276079 0.478183i
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 1.50000 + 4.33013i 0.163663 + 0.472456i
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) −1.00000 −0.107833
\(87\) −1.50000 + 0.866025i −0.160817 + 0.0928477i
\(88\) −15.0000 −1.59901
\(89\) 6.50000 11.2583i 0.688999 1.19338i −0.283164 0.959072i \(-0.591384\pi\)
0.972162 0.234309i \(-0.0752827\pi\)
\(90\) −1.50000 + 2.59808i −0.158114 + 0.273861i
\(91\) 12.5000 4.33013i 1.31036 0.453921i
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 7.50000 4.33013i 0.765466 0.441942i
\(97\) 4.50000 7.79423i 0.456906 0.791384i −0.541890 0.840450i \(-0.682291\pi\)
0.998796 + 0.0490655i \(0.0156243\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) 7.50000 + 12.9904i 0.753778 + 1.30558i
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −17.0000 −1.69156 −0.845782 0.533529i \(-0.820865\pi\)
−0.845782 + 0.533529i \(0.820865\pi\)
\(102\) 4.50000 2.59808i 0.445566 0.257248i
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −7.50000 12.9904i −0.735436 1.27381i
\(105\) 3.00000 3.46410i 0.292770 0.338062i
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) −8.50000 + 14.7224i −0.821726 + 1.42327i 0.0826699 + 0.996577i \(0.473655\pi\)
−0.904396 + 0.426694i \(0.859678\pi\)
\(108\) −4.50000 2.59808i −0.433013 0.250000i
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) 2.50000 + 4.33013i 0.238366 + 0.412861i
\(111\) 4.50000 2.59808i 0.427121 0.246598i
\(112\) 2.50000 0.866025i 0.236228 0.0818317i
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) −1.50000 0.866025i −0.140488 0.0811107i
\(115\) −3.00000 −0.279751
\(116\) −0.500000 0.866025i −0.0464238 0.0804084i
\(117\) −7.50000 + 12.9904i −0.693375 + 1.20096i
\(118\) 0 0
\(119\) −7.50000 + 2.59808i −0.687524 + 0.238165i
\(120\) −4.50000 2.59808i −0.410792 0.237171i
\(121\) 14.0000 1.27273
\(122\) 7.00000 12.1244i 0.633750 1.09769i
\(123\) 8.66025i 0.780869i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) −6.00000 5.19615i −0.534522 0.462910i
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) −1.50000 + 0.866025i −0.132068 + 0.0762493i
\(130\) −2.50000 + 4.33013i −0.219265 + 0.379777i
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) −7.50000 + 4.33013i −0.652791 + 0.376889i
\(133\) 2.00000 + 1.73205i 0.173422 + 0.150188i
\(134\) 4.00000 0.345547
\(135\) 5.19615i 0.447214i
\(136\) 4.50000 + 7.79423i 0.385872 + 0.668350i
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 5.19615i 0.442326i
\(139\) −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i \(-0.291323\pi\)
−0.991303 + 0.131597i \(0.957989\pi\)
\(140\) 2.00000 + 1.73205i 0.169031 + 0.146385i
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 12.5000 + 21.6506i 1.04530 + 1.81052i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) −0.500000 + 0.866025i −0.0415227 + 0.0719195i
\(146\) −1.50000 + 2.59808i −0.124141 + 0.215018i
\(147\) 7.50000 + 9.52628i 0.618590 + 0.785714i
\(148\) 1.50000 + 2.59808i 0.123299 + 0.213561i
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 6.92820i 0.565685i
\(151\) 5.00000 0.406894 0.203447 0.979086i \(-0.434786\pi\)
0.203447 + 0.979086i \(0.434786\pi\)
\(152\) 1.50000 2.59808i 0.121666 0.210732i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) −12.5000 + 4.33013i −1.00728 + 0.348932i
\(155\) 0 0
\(156\) −7.50000 4.33013i −0.600481 0.346688i
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 15.5885i 1.23625i
\(160\) 2.50000 4.33013i 0.197642 0.342327i
\(161\) 1.50000 7.79423i 0.118217 0.614271i
\(162\) 9.00000 0.707107
\(163\) 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i \(-0.691567\pi\)
0.996942 + 0.0781474i \(0.0249005\pi\)
\(164\) 5.00000 0.390434
\(165\) 7.50000 + 4.33013i 0.583874 + 0.337100i
\(166\) −9.00000 −0.698535
\(167\) 9.50000 + 16.4545i 0.735132 + 1.27329i 0.954665 + 0.297681i \(0.0962132\pi\)
−0.219533 + 0.975605i \(0.570453\pi\)
\(168\) 9.00000 10.3923i 0.694365 0.801784i
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 1.50000 2.59808i 0.115045 0.199263i
\(171\) −3.00000 −0.229416
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) 7.00000 + 12.1244i 0.532200 + 0.921798i 0.999293 + 0.0375896i \(0.0119679\pi\)
−0.467093 + 0.884208i \(0.654699\pi\)
\(174\) 1.50000 + 0.866025i 0.113715 + 0.0656532i
\(175\) −2.00000 + 10.3923i −0.151186 + 0.785584i
\(176\) 2.50000 + 4.33013i 0.188445 + 0.326396i
\(177\) 0 0
\(178\) −13.0000 −0.974391
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) −3.00000 −0.223607
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −10.0000 8.66025i −0.741249 0.641941i
\(183\) 24.2487i 1.79252i
\(184\) −9.00000 −0.663489
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) −7.50000 12.9904i −0.548454 0.949951i
\(188\) 0 0
\(189\) −13.5000 2.59808i −0.981981 0.188982i
\(190\) −1.00000 −0.0725476
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) −10.5000 6.06218i −0.757772 0.437500i
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) −9.00000 −0.646162
\(195\) 8.66025i 0.620174i
\(196\) −5.50000 + 4.33013i −0.392857 + 0.309295i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 7.50000 12.9904i 0.533002 0.923186i
\(199\) −1.50000 2.59808i −0.106332 0.184173i 0.807950 0.589252i \(-0.200577\pi\)
−0.914282 + 0.405079i \(0.867244\pi\)
\(200\) 12.0000 0.848528
\(201\) 6.00000 3.46410i 0.423207 0.244339i
\(202\) 8.50000 + 14.7224i 0.598058 + 1.03587i
\(203\) −2.00000 1.73205i −0.140372 0.121566i
\(204\) 4.50000 + 2.59808i 0.315063 + 0.181902i
\(205\) −2.50000 4.33013i −0.174608 0.302429i
\(206\) 0.500000 + 0.866025i 0.0348367 + 0.0603388i
\(207\) 4.50000 + 7.79423i 0.312772 + 0.541736i
\(208\) −2.50000 + 4.33013i −0.173344 + 0.300240i
\(209\) −2.50000 + 4.33013i −0.172929 + 0.299521i
\(210\) −4.50000 0.866025i −0.310530 0.0597614i
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 9.00000 0.618123
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) 17.0000 1.16210
\(215\) −0.500000 + 0.866025i −0.0340997 + 0.0590624i
\(216\) 15.5885i 1.06066i
\(217\) 0 0
\(218\) 4.50000 7.79423i 0.304778 0.527892i
\(219\) 5.19615i 0.351123i
\(220\) −2.50000 + 4.33013i −0.168550 + 0.291937i
\(221\) 7.50000 12.9904i 0.504505 0.873828i
\(222\) −4.50000 2.59808i −0.302020 0.174371i
\(223\) −9.50000 + 16.4545i −0.636167 + 1.10187i 0.350100 + 0.936713i \(0.386148\pi\)
−0.986267 + 0.165161i \(0.947186\pi\)
\(224\) 10.0000 + 8.66025i 0.668153 + 0.578638i
\(225\) −6.00000 10.3923i −0.400000 0.692820i
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 1.73205i 0.114708i
\(229\) −1.00000 −0.0660819 −0.0330409 0.999454i \(-0.510519\pi\)
−0.0330409 + 0.999454i \(0.510519\pi\)
\(230\) 1.50000 + 2.59808i 0.0989071 + 0.171312i
\(231\) −15.0000 + 17.3205i −0.986928 + 1.13961i
\(232\) −1.50000 + 2.59808i −0.0984798 + 0.170572i
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 15.0000 0.980581
\(235\) 0 0
\(236\) 0 0
\(237\) 13.8564i 0.900070i
\(238\) 6.00000 + 5.19615i 0.388922 + 0.336817i
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) 1.73205i 0.111803i
\(241\) 11.0000 0.708572 0.354286 0.935137i \(-0.384724\pi\)
0.354286 + 0.935137i \(0.384724\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 14.0000 0.896258
\(245\) 6.50000 + 2.59808i 0.415270 + 0.165985i
\(246\) −7.50000 + 4.33013i −0.478183 + 0.276079i
\(247\) −5.00000 −0.318142
\(248\) 0 0
\(249\) −13.5000 + 7.79423i −0.855528 + 0.493939i
\(250\) −4.50000 7.79423i −0.284605 0.492950i
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 1.50000 7.79423i 0.0944911 0.490990i
\(253\) 15.0000 0.943042
\(254\) 6.00000 + 10.3923i 0.376473 + 0.652071i
\(255\) 5.19615i 0.325396i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −29.0000 −1.80897 −0.904485 0.426505i \(-0.859745\pi\)
−0.904485 + 0.426505i \(0.859745\pi\)
\(258\) 1.50000 + 0.866025i 0.0933859 + 0.0539164i
\(259\) 6.00000 + 5.19615i 0.372822 + 0.322873i
\(260\) −5.00000 −0.310087
\(261\) 3.00000 0.185695
\(262\) 0.500000 + 0.866025i 0.0308901 + 0.0535032i
\(263\) 5.00000 0.308313 0.154157 0.988046i \(-0.450734\pi\)
0.154157 + 0.988046i \(0.450734\pi\)
\(264\) 22.5000 + 12.9904i 1.38478 + 0.799503i
\(265\) −4.50000 7.79423i −0.276433 0.478796i
\(266\) 0.500000 2.59808i 0.0306570 0.159298i
\(267\) −19.5000 + 11.2583i −1.19338 + 0.688999i
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −1.50000 2.59808i −0.0914566 0.158408i 0.816668 0.577108i \(-0.195819\pi\)
−0.908124 + 0.418701i \(0.862486\pi\)
\(270\) 4.50000 2.59808i 0.273861 0.158114i
\(271\) −0.500000 + 0.866025i −0.0303728 + 0.0526073i −0.880812 0.473466i \(-0.843003\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 1.50000 2.59808i 0.0909509 0.157532i
\(273\) −22.5000 4.33013i −1.36176 0.262071i
\(274\) 4.50000 + 7.79423i 0.271855 + 0.470867i
\(275\) −20.0000 −1.20605
\(276\) −4.50000 + 2.59808i −0.270868 + 0.156386i
\(277\) 19.0000 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(278\) −4.50000 + 7.79423i −0.269892 + 0.467467i
\(279\) 0 0
\(280\) 1.50000 7.79423i 0.0896421 0.465794i
\(281\) 14.5000 25.1147i 0.864997 1.49822i −0.00205220 0.999998i \(-0.500653\pi\)
0.867050 0.498222i \(-0.166013\pi\)
\(282\) 0 0
\(283\) −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) −1.50000 + 0.866025i −0.0888523 + 0.0512989i
\(286\) 12.5000 21.6506i 0.739140 1.28023i
\(287\) 12.5000 4.33013i 0.737852 0.255599i
\(288\) −15.0000 −0.883883
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 1.00000 0.0587220
\(291\) −13.5000 + 7.79423i −0.791384 + 0.456906i
\(292\) −3.00000 −0.175562
\(293\) 2.50000 + 4.33013i 0.146052 + 0.252969i 0.929765 0.368154i \(-0.120010\pi\)
−0.783713 + 0.621123i \(0.786677\pi\)
\(294\) 4.50000 11.2583i 0.262445 0.656599i
\(295\) 0 0
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) 25.9808i 1.50756i
\(298\) −1.50000 2.59808i −0.0868927 0.150503i
\(299\) 7.50000 + 12.9904i 0.433736 + 0.751253i
\(300\) 6.00000 3.46410i 0.346410 0.200000i
\(301\) −2.00000 1.73205i −0.115278 0.0998337i
\(302\) −2.50000 4.33013i −0.143859 0.249171i
\(303\) 25.5000 + 14.7224i 1.46494 + 0.845782i
\(304\) −1.00000 −0.0573539
\(305\) −7.00000 12.1244i −0.400819 0.694239i
\(306\) −9.00000 −0.514496
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) −10.0000 8.66025i −0.569803 0.493464i
\(309\) 1.50000 + 0.866025i 0.0853320 + 0.0492665i
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 25.9808i 1.47087i
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) −14.0000 −0.790066
\(315\) −7.50000 + 2.59808i −0.422577 + 0.146385i
\(316\) −8.00000 −0.450035
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) −13.5000 + 7.79423i −0.757042 + 0.437079i
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) −7.00000 −0.391312
\(321\) 25.5000 14.7224i 1.42327 0.821726i
\(322\) −7.50000 + 2.59808i −0.417959 + 0.144785i
\(323\) 3.00000 0.166924
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) −11.0000 −0.609234
\(327\) 15.5885i 0.862044i
\(328\) −7.50000 12.9904i −0.414118 0.717274i
\(329\) 0 0
\(330\) 8.66025i 0.476731i
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −4.50000 7.79423i −0.246970 0.427764i
\(333\) −9.00000 −0.493197
\(334\) 9.50000 16.4545i 0.519817 0.900349i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) −4.50000 0.866025i −0.245495 0.0472456i
\(337\) 14.5000 + 25.1147i 0.789865 + 1.36809i 0.926049 + 0.377403i \(0.123183\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 12.0000 0.652714
\(339\) 1.73205i 0.0940721i
\(340\) 3.00000 0.162698
\(341\) 0 0
\(342\) 1.50000 + 2.59808i 0.0811107 + 0.140488i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −1.50000 + 2.59808i −0.0808746 + 0.140079i
\(345\) 4.50000 + 2.59808i 0.242272 + 0.139876i
\(346\) 7.00000 12.1244i 0.376322 0.651809i
\(347\) −2.00000 + 3.46410i −0.107366 + 0.185963i −0.914702 0.404128i \(-0.867575\pi\)
0.807337 + 0.590091i \(0.200908\pi\)
\(348\) 1.73205i 0.0928477i
\(349\) −9.50000 + 16.4545i −0.508523 + 0.880788i 0.491428 + 0.870918i \(0.336475\pi\)
−0.999951 + 0.00987003i \(0.996858\pi\)
\(350\) 10.0000 3.46410i 0.534522 0.185164i
\(351\) 22.5000 12.9904i 1.20096 0.693375i
\(352\) −12.5000 + 21.6506i −0.666252 + 1.15398i
\(353\) 11.0000 0.585471 0.292735 0.956193i \(-0.405434\pi\)
0.292735 + 0.956193i \(0.405434\pi\)
\(354\) 0 0
\(355\) 12.0000 0.636894
\(356\) −6.50000 11.2583i −0.344499 0.596690i
\(357\) 13.5000 + 2.59808i 0.714496 + 0.137505i
\(358\) −9.50000 + 16.4545i −0.502091 + 0.869646i
\(359\) 5.50000 9.52628i 0.290279 0.502778i −0.683597 0.729860i \(-0.739585\pi\)
0.973876 + 0.227082i \(0.0729186\pi\)
\(360\) 4.50000 + 7.79423i 0.237171 + 0.410792i
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 7.00000 + 12.1244i 0.367912 + 0.637242i
\(363\) −21.0000 12.1244i −1.10221 0.636364i
\(364\) 2.50000 12.9904i 0.131036 0.680881i
\(365\) 1.50000 + 2.59808i 0.0785136 + 0.135990i
\(366\) −21.0000 + 12.1244i −1.09769 + 0.633750i
\(367\) −3.00000 −0.156599 −0.0782994 0.996930i \(-0.524949\pi\)
−0.0782994 + 0.996930i \(0.524949\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) −7.50000 + 12.9904i −0.390434 + 0.676252i
\(370\) −3.00000 −0.155963
\(371\) 22.5000 7.79423i 1.16814 0.404656i
\(372\) 0 0
\(373\) −25.0000 −1.29445 −0.647225 0.762299i \(-0.724071\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) −7.50000 + 12.9904i −0.387816 + 0.671717i
\(375\) −13.5000 7.79423i −0.697137 0.402492i
\(376\) 0 0
\(377\) 5.00000 0.257513
\(378\) 4.50000 + 12.9904i 0.231455 + 0.668153i
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −0.500000 0.866025i −0.0256495 0.0444262i
\(381\) 18.0000 + 10.3923i 0.922168 + 0.532414i
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) 27.0000 1.37964 0.689818 0.723983i \(-0.257691\pi\)
0.689818 + 0.723983i \(0.257691\pi\)
\(384\) 5.19615i 0.265165i
\(385\) −2.50000 + 12.9904i −0.127412 + 0.662051i
\(386\) −10.0000 −0.508987
\(387\) 3.00000 0.152499
\(388\) −4.50000 7.79423i −0.228453 0.395692i
\(389\) −9.00000 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(390\) 7.50000 4.33013i 0.379777 0.219265i
\(391\) −4.50000 7.79423i −0.227575 0.394171i
\(392\) 19.5000 + 7.79423i 0.984899 + 0.393668i
\(393\) 1.50000 + 0.866025i 0.0756650 + 0.0436852i
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 15.0000 0.753778
\(397\) −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i \(-0.956176\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(398\) −1.50000 + 2.59808i −0.0751882 + 0.130230i
\(399\) −1.50000 4.33013i −0.0750939 0.216777i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) −6.00000 3.46410i −0.299253 0.172774i
\(403\) 0 0
\(404\) −8.50000 + 14.7224i −0.422891 + 0.732468i
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) −0.500000 + 2.59808i −0.0248146 + 0.128940i
\(407\) −7.50000 + 12.9904i −0.371761 + 0.643909i
\(408\) 15.5885i 0.771744i
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −2.50000 + 4.33013i −0.123466 + 0.213850i
\(411\) 13.5000 + 7.79423i 0.665906 + 0.384461i
\(412\) −0.500000 + 0.866025i −0.0246332 + 0.0426660i
\(413\) 0 0
\(414\) 4.50000 7.79423i 0.221163 0.383065i
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) −25.0000 −1.22573
\(417\) 15.5885i 0.763370i
\(418\) 5.00000 0.244558
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) −1.50000 4.33013i −0.0731925 0.211289i
\(421\) 0.500000 0.866025i 0.0243685 0.0422075i −0.853584 0.520955i \(-0.825576\pi\)
0.877952 + 0.478748i \(0.158909\pi\)
\(422\) −6.50000 + 11.2583i −0.316415 + 0.548047i
\(423\) 0 0
\(424\) −13.5000 23.3827i −0.655618 1.13556i
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 20.7846i 1.00702i
\(427\) 35.0000 12.1244i 1.69377 0.586739i
\(428\) 8.50000 + 14.7224i 0.410863 + 0.711636i
\(429\) 43.3013i 2.09061i
\(430\) 1.00000 0.0482243
\(431\) 4.50000 + 7.79423i 0.216757 + 0.375435i 0.953815 0.300395i \(-0.0971186\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(432\) 4.50000 2.59808i 0.216506 0.125000i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 1.50000 0.866025i 0.0719195 0.0415227i
\(436\) 9.00000 0.431022
\(437\) −1.50000 + 2.59808i −0.0717547 + 0.124283i
\(438\) 4.50000 2.59808i 0.215018 0.124141i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 15.0000 0.715097
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) −15.0000 −0.713477
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 5.19615i 0.246598i
\(445\) −6.50000 + 11.2583i −0.308130 + 0.533696i
\(446\) 19.0000 0.899676
\(447\) −4.50000 2.59808i −0.212843 0.122885i
\(448\) 3.50000 18.1865i 0.165359 0.859233i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −6.00000 + 10.3923i −0.282843 + 0.489898i
\(451\) 12.5000 + 21.6506i 0.588602 + 1.01949i
\(452\) 1.00000 0.0470360
\(453\) −7.50000 4.33013i −0.352381 0.203447i
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) −12.5000 + 4.33013i −0.586009 + 0.202999i
\(456\) −4.50000 + 2.59808i −0.210732 + 0.121666i
\(457\) −11.0000 19.0526i −0.514558 0.891241i −0.999857 0.0168929i \(-0.994623\pi\)
0.485299 0.874348i \(-0.338711\pi\)
\(458\) 0.500000 + 0.866025i 0.0233635 + 0.0404667i
\(459\) −13.5000 + 7.79423i −0.630126 + 0.363803i
\(460\) −1.50000 + 2.59808i −0.0699379 + 0.121136i
\(461\) −9.50000 + 16.4545i −0.442459 + 0.766362i −0.997871 0.0652135i \(-0.979227\pi\)
0.555412 + 0.831575i \(0.312560\pi\)
\(462\) 22.5000 + 4.33013i 1.04679 + 0.201456i
\(463\) −6.50000 11.2583i −0.302081 0.523219i 0.674526 0.738251i \(-0.264348\pi\)
−0.976607 + 0.215032i \(0.931015\pi\)
\(464\) 1.00000 0.0464238
\(465\) 0 0
\(466\) 3.00000 0.138972
\(467\) 13.5000 23.3827i 0.624705 1.08202i −0.363892 0.931441i \(-0.618552\pi\)
0.988598 0.150581i \(-0.0481143\pi\)
\(468\) 7.50000 + 12.9904i 0.346688 + 0.600481i
\(469\) 8.00000 + 6.92820i 0.369406 + 0.319915i
\(470\) 0 0
\(471\) −21.0000 + 12.1244i −0.967629 + 0.558661i
\(472\) 0 0
\(473\) 2.50000 4.33013i 0.114950 0.199099i
\(474\) 12.0000 6.92820i 0.551178 0.318223i
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) −1.50000 + 7.79423i −0.0687524 + 0.357248i
\(477\) −13.5000 + 23.3827i −0.618123 + 1.07062i
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 25.0000 1.14228 0.571140 0.820853i \(-0.306501\pi\)
0.571140 + 0.820853i \(0.306501\pi\)
\(480\) −7.50000 + 4.33013i −0.342327 + 0.197642i
\(481\) −15.0000 −0.683941
\(482\) −5.50000 9.52628i −0.250518 0.433910i
\(483\) −9.00000 + 10.3923i −0.409514 + 0.472866i
\(484\) 7.00000 12.1244i 0.318182 0.551107i
\(485\) −4.50000 + 7.79423i −0.204334 + 0.353918i
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i \(-0.308325\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) −21.0000 36.3731i −0.950625 1.64653i
\(489\) −16.5000 + 9.52628i −0.746156 + 0.430793i
\(490\) −1.00000 6.92820i −0.0451754 0.312984i
\(491\) −6.50000 11.2583i −0.293341 0.508081i 0.681257 0.732045i \(-0.261434\pi\)
−0.974598 + 0.223963i \(0.928100\pi\)
\(492\) −7.50000 4.33013i −0.338126 0.195217i
\(493\) −3.00000 −0.135113
\(494\) 2.50000 + 4.33013i 0.112480 + 0.194822i
\(495\) −7.50000 12.9904i −0.337100 0.583874i
\(496\) 0 0
\(497\) −6.00000 + 31.1769i −0.269137 + 1.39848i
\(498\) 13.5000 + 7.79423i 0.604949 + 0.349268i
\(499\) 31.0000 1.38775 0.693875 0.720095i \(-0.255902\pi\)
0.693875 + 0.720095i \(0.255902\pi\)
\(500\) 4.50000 7.79423i 0.201246 0.348569i
\(501\) 32.9090i 1.47026i
\(502\) 14.0000 + 24.2487i 0.624851 + 1.08227i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −22.5000 + 7.79423i −1.00223 + 0.347183i
\(505\) 17.0000 0.756490
\(506\) −7.50000 12.9904i −0.333416 0.577493i
\(507\) 18.0000 10.3923i 0.799408 0.461538i
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −29.0000 −1.28540 −0.642701 0.766117i \(-0.722186\pi\)
−0.642701 + 0.766117i \(0.722186\pi\)
\(510\) −4.50000 + 2.59808i −0.199263 + 0.115045i
\(511\) −7.50000 + 2.59808i −0.331780 + 0.114932i
\(512\) −11.0000 −0.486136
\(513\) 4.50000 + 2.59808i 0.198680 + 0.114708i
\(514\) 14.5000 + 25.1147i 0.639568 + 1.10776i
\(515\) 1.00000 0.0440653
\(516\) 1.73205i 0.0762493i
\(517\) 0 0
\(518\) 1.50000 7.79423i 0.0659062 0.342459i
\(519\) 24.2487i 1.06440i
\(520\) 7.50000 + 12.9904i 0.328897 + 0.569666i
\(521\) −1.50000 2.59808i −0.0657162 0.113824i 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) −1.50000 2.59808i −0.0656532 0.113715i
\(523\) −0.500000 + 0.866025i −0.0218635 + 0.0378686i −0.876750 0.480946i \(-0.840293\pi\)
0.854887 + 0.518815i \(0.173627\pi\)
\(524\) −0.500000 + 0.866025i −0.0218426 + 0.0378325i
\(525\) 12.0000 13.8564i 0.523723 0.604743i
\(526\) −2.50000 4.33013i −0.109005 0.188803i
\(527\) 0 0
\(528\) 8.66025i 0.376889i
\(529\) −14.0000 −0.608696
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 0 0
\(532\) 2.50000 0.866025i 0.108389 0.0375470i
\(533\) −12.5000 + 21.6506i −0.541435 + 0.937793i
\(534\) 19.5000 + 11.2583i 0.843848 + 0.487196i
\(535\) 8.50000 14.7224i 0.367487 0.636506i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 32.9090i 1.42013i
\(538\) −1.50000 + 2.59808i −0.0646696 + 0.112011i
\(539\) −32.5000 12.9904i −1.39987 0.559535i
\(540\) 4.50000 + 2.59808i 0.193649 + 0.111803i
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 1.00000 0.0429537
\(543\) 21.0000 + 12.1244i 0.901196 + 0.520306i
\(544\) 15.0000 0.643120
\(545\) −4.50000 7.79423i −0.192759 0.333868i
\(546\) 7.50000 + 21.6506i 0.320970 + 0.926562i
\(547\) 14.5000 25.1147i 0.619975 1.07383i −0.369514 0.929225i \(-0.620476\pi\)
0.989490 0.144604i \(-0.0461907\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) −21.0000 + 36.3731i −0.896258 + 1.55236i
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) 0.500000 + 0.866025i 0.0213007 + 0.0368939i
\(552\) 13.5000 + 7.79423i 0.574598 + 0.331744i
\(553\) −20.0000 + 6.92820i −0.850487 + 0.294617i
\(554\) −9.50000 16.4545i −0.403616 0.699084i
\(555\) −4.50000 + 2.59808i −0.191014 + 0.110282i
\(556\) −9.00000 −0.381685
\(557\) 18.5000 + 32.0429i 0.783870 + 1.35770i 0.929672 + 0.368389i \(0.120091\pi\)
−0.145802 + 0.989314i \(0.546576\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) −2.50000 + 0.866025i −0.105644 + 0.0365963i
\(561\) 25.9808i 1.09691i
\(562\) −29.0000 −1.22329
\(563\) 14.0000 24.2487i 0.590030 1.02196i −0.404198 0.914671i \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 0 0
\(565\) −0.500000 0.866025i −0.0210352 0.0364340i
\(566\) 28.0000 1.17693
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) 36.0000 1.51053
\(569\) 17.0000 + 29.4449i 0.712677 + 1.23439i 0.963849 + 0.266450i \(0.0858508\pi\)
−0.251172 + 0.967943i \(0.580816\pi\)
\(570\) 1.50000 + 0.866025i 0.0628281 + 0.0362738i
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 25.0000 1.04530
\(573\) 13.8564i 0.578860i
\(574\) −10.0000 8.66025i −0.417392 0.361472i
\(575\) −12.0000 −0.500435
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) −8.00000 −0.332756
\(579\) −15.0000 + 8.66025i −0.623379 + 0.359908i
\(580\) 0.500000 + 0.866025i 0.0207614 + 0.0359597i
\(581\) −18.0000 15.5885i −0.746766 0.646718i
\(582\) 13.5000 + 7.79423i 0.559593 + 0.323081i
\(583\) 22.5000 + 38.9711i 0.931855 + 1.61402i
\(584\) 4.50000 + 7.79423i 0.186211 + 0.322527i
\(585\) 7.50000 12.9904i 0.310087 0.537086i
\(586\) 2.50000 4.33013i 0.103274 0.178876i
\(587\) 18.5000 32.0429i 0.763577 1.32255i −0.177419 0.984135i \(-0.556775\pi\)
0.940996 0.338418i \(-0.109892\pi\)
\(588\) 12.0000 1.73205i 0.494872 0.0714286i
\(589\) 0 0
\(590\) 0 0
\(591\) −3.00000 1.73205i −0.123404 0.0712470i
\(592\) −3.00000 −0.123299
\(593\) −7.50000 + 12.9904i −0.307988 + 0.533451i −0.977922 0.208970i \(-0.932989\pi\)
0.669934 + 0.742421i \(0.266322\pi\)
\(594\) −22.5000 + 12.9904i −0.923186 + 0.533002i
\(595\) 7.50000 2.59808i 0.307470 0.106511i
\(596\) 1.50000 2.59808i 0.0614424 0.106421i
\(597\) 5.19615i 0.212664i
\(598\) 7.50000 12.9904i 0.306698 0.531216i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) −18.0000 10.3923i −0.734847 0.424264i
\(601\) 4.50000 7.79423i 0.183559 0.317933i −0.759531 0.650471i \(-0.774572\pi\)
0.943090 + 0.332538i \(0.107905\pi\)
\(602\) −0.500000 + 2.59808i −0.0203785 + 0.105890i
\(603\) −12.0000 −0.488678
\(604\) 2.50000 4.33013i 0.101724 0.176190i
\(605\) −14.0000 −0.569181
\(606\) 29.4449i 1.19612i
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 1.50000 + 4.33013i 0.0607831 + 0.175466i
\(610\) −7.00000 + 12.1244i −0.283422 + 0.490901i
\(611\) 0 0
\(612\) −4.50000 7.79423i −0.181902 0.315063i
\(613\) −9.50000 16.4545i −0.383701 0.664590i 0.607887 0.794024i \(-0.292017\pi\)
−0.991588 + 0.129433i \(0.958684\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) 8.66025i 0.349215i
\(616\) −7.50000 + 38.9711i −0.302184 + 1.57019i
\(617\) −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i \(-0.983769\pi\)
0.455211 0.890384i \(-0.349564\pi\)
\(618\) 1.73205i 0.0696733i
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) 0 0
\(621\) 15.5885i 0.625543i
\(622\) 0 0
\(623\) −26.0000 22.5167i −1.04167 0.902111i
\(624\) 7.50000 4.33013i 0.300240 0.173344i
\(625\) 11.0000 0.440000
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) 7.50000 4.33013i 0.299521 0.172929i
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) 9.00000 0.358854
\(630\) 6.00000 + 5.19615i 0.239046 + 0.207020i
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 12.0000 + 20.7846i 0.477334 + 0.826767i
\(633\) 22.5167i 0.894957i
\(634\) 3.00000 5.19615i 0.119145 0.206366i
\(635\) 12.0000 0.476205
\(636\) −13.5000 7.79423i −0.535310 0.309061i
\(637\) −5.00000 34.6410i −0.198107 1.37253i
\(638\) −5.00000 −0.197952
\(639\) −18.0000 31.1769i −0.712069 1.23334i
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) −25.5000 14.7224i −1.00640 0.581048i
\(643\) 9.50000 + 16.4545i 0.374643 + 0.648901i 0.990274 0.139134i \(-0.0444318\pi\)
−0.615630 + 0.788035i \(0.711098\pi\)
\(644\) −6.00000 5.19615i −0.236433 0.204757i
\(645\) 1.50000 0.866025i 0.0590624 0.0340997i
\(646\) −1.50000 2.59808i −0.0590167 0.102220i
\(647\) −15.5000 26.8468i −0.609368 1.05546i −0.991345 0.131284i \(-0.958090\pi\)
0.381977 0.924172i \(-0.375243\pi\)
\(648\) 13.5000 23.3827i 0.530330 0.918559i
\(649\) 0 0
\(650\) −10.0000 + 17.3205i −0.392232 + 0.679366i
\(651\) 0 0
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) 3.00000 0.117399 0.0586995 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) −13.5000 + 7.79423i −0.527892 + 0.304778i
\(655\) 1.00000 0.0390732
\(656\) −2.50000 + 4.33013i −0.0976086 + 0.169063i
\(657\) 4.50000 7.79423i 0.175562 0.304082i
\(658\) 0 0
\(659\) −13.5000 + 23.3827i −0.525885 + 0.910860i 0.473660 + 0.880708i \(0.342933\pi\)
−0.999545 + 0.0301523i \(0.990401\pi\)
\(660\) 7.50000 4.33013i 0.291937 0.168550i
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) −22.5000 + 12.9904i −0.873828 + 0.504505i
\(664\) −13.5000 + 23.3827i −0.523902 + 0.907424i
\(665\) −2.00000 1.73205i −0.0775567 0.0671660i
\(666\) 4.50000 + 7.79423i 0.174371 + 0.302020i
\(667\) 1.50000 2.59808i 0.0580802 0.100598i
\(668\) 19.0000 0.735132
\(669\) 28.5000 16.4545i 1.10187 0.636167i
\(670\) −4.00000 −0.154533
\(671\) 35.0000 + 60.6218i 1.35116 + 2.34028i
\(672\) −7.50000 21.6506i −0.289319 0.835191i
\(673\) 14.5000 25.1147i 0.558934 0.968102i −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) 14.5000 25.1147i 0.558519 0.967384i
\(675\) 20.7846i 0.800000i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −21.0000 36.3731i −0.807096 1.39793i −0.914867 0.403755i \(-0.867705\pi\)
0.107772 0.994176i \(-0.465628\pi\)
\(678\) −1.50000 + 0.866025i −0.0576072 + 0.0332595i
\(679\) −18.0000 15.5885i −0.690777 0.598230i
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 4.50000 + 2.59808i 0.172440 + 0.0995585i
\(682\) 0 0
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) −1.50000 + 2.59808i −0.0573539 + 0.0993399i
\(685\) 9.00000 0.343872
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 1.50000 + 0.866025i 0.0572286 + 0.0330409i
\(688\) 1.00000 0.0381246
\(689\) −22.5000 + 38.9711i −0.857182 + 1.48468i
\(690\) 5.19615i 0.197814i
\(691\) 14.0000 + 24.2487i 0.532585 + 0.922464i 0.999276 + 0.0380440i \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 14.0000 0.532200
\(693\) 37.5000 12.9904i 1.42451 0.493464i
\(694\) 4.00000 0.151838
\(695\) 4.50000 + 7.79423i 0.170695 + 0.295652i
\(696\) 4.50000 2.59808i 0.170572 0.0984798i
\(697\) 7.50000 12.9904i 0.284083 0.492046i
\(698\) 19.0000 0.719161
\(699\) 4.50000 2.59808i 0.170206 0.0982683i
\(700\) 8.00000 + 6.92820i 0.302372 + 0.261861i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −22.5000 12.9904i −0.849208 0.490290i
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) 35.0000 1.31911
\(705\) 0 0
\(706\) −5.50000 9.52628i −0.206995 0.358526i
\(707\) −8.50000 + 44.1673i −0.319675 + 1.66108i
\(708\) 0 0
\(709\) 3.00000 + 5.19615i 0.112667 + 0.195146i 0.916845 0.399244i \(-0.130727\pi\)
−0.804178 + 0.594389i \(0.797394\pi\)
\(710\) −6.00000 10.3923i −0.225176 0.390016i
\(711\) 12.0000 20.7846i 0.450035 0.779484i
\(712\) −19.5000 + 33.7750i −0.730793 + 1.26577i
\(713\) 0 0
\(714\) −4.50000 12.9904i −0.168408 0.486153i
\(715\) −12.5000 21.6506i −0.467473 0.809688i
\(716\) −19.0000 −0.710063
\(717\) 25.9808i 0.970269i
\(718\) −11.0000 −0.410516
\(719\) 13.5000 23.3827i 0.503465 0.872027i −0.496527 0.868021i \(-0.665392\pi\)
0.999992 0.00400572i \(-0.00127506\pi\)
\(720\) 1.50000 2.59808i 0.0559017 0.0968246i
\(721\) −0.500000 + 2.59808i −0.0186210 + 0.0967574i
\(722\) 9.00000 15.5885i 0.334945 0.580142i
\(723\) −16.5000 9.52628i −0.613642 0.354286i
\(724\) −7.00000 + 12.1244i −0.260153 + 0.450598i
\(725\) −2.00000 + 3.46410i −0.0742781 + 0.128654i
\(726\) 24.2487i 0.899954i
\(727\) −23.5000 + 40.7032i −0.871567 + 1.50960i −0.0111912 + 0.999937i \(0.503562\pi\)
−0.860376 + 0.509661i \(0.829771\pi\)
\(728\) −37.5000 + 12.9904i −1.38984 + 0.481456i
\(729\) −27.0000 −1.00000
\(730\) 1.50000 2.59808i 0.0555175 0.0961591i
\(731\) −3.00000 −0.110959
\(732\) −21.0000 12.1244i −0.776182 0.448129i
\(733\) 27.0000 0.997268 0.498634 0.866813i \(-0.333835\pi\)
0.498634 + 0.866813i \(0.333835\pi\)
\(734\) 1.50000 + 2.59808i 0.0553660 + 0.0958967i
\(735\) −7.50000 9.52628i −0.276642 0.351382i
\(736\) −7.50000 + 12.9904i −0.276454 + 0.478832i
\(737\) −10.0000 + 17.3205i −0.368355 + 0.638009i
\(738\) 15.0000 0.552158
\(739\) 4.50000 + 7.79423i 0.165535 + 0.286715i 0.936845 0.349744i \(-0.113732\pi\)
−0.771310 + 0.636460i \(0.780398\pi\)
\(740\) −1.50000 2.59808i −0.0551411 0.0955072i
\(741\) 7.50000 + 4.33013i 0.275519 + 0.159071i
\(742\) −18.0000 15.5885i −0.660801 0.572270i
\(743\) 7.50000 + 12.9904i 0.275148 + 0.476571i 0.970173 0.242415i \(-0.0779397\pi\)
−0.695024 + 0.718986i \(0.744606\pi\)
\(744\) 0 0
\(745\) −3.00000 −0.109911
\(746\) 12.5000 + 21.6506i 0.457658 + 0.792686i
\(747\) 27.0000 0.987878
\(748\) −15.0000 −0.548454
\(749\) 34.0000 + 29.4449i 1.24233 + 1.07589i
\(750\) 15.5885i 0.569210i
\(751\) 31.0000 1.13121 0.565603 0.824678i \(-0.308643\pi\)
0.565603 + 0.824678i \(0.308643\pi\)
\(752\) 0 0
\(753\) 42.0000 + 24.2487i 1.53057 + 0.883672i
\(754\) −2.50000 4.33013i −0.0910446 0.157694i
\(755\) −5.00000 −0.181969
\(756\) −9.00000 + 10.3923i −0.327327 + 0.377964i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 6.00000 + 10.3923i 0.217930 + 0.377466i
\(759\) −22.5000 12.9904i −0.816698 0.471521i
\(760\) −1.50000 + 2.59808i −0.0544107 + 0.0942421i
\(761\) 27.0000 0.978749 0.489375 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) 20.7846i 0.752947i
\(763\) 22.5000 7.79423i 0.814555 0.282170i
\(764\) −8.00000 −0.289430
\(765\) −4.50000 + 7.79423i −0.162698 + 0.281801i
\(766\) −13.5000 23.3827i −0.487775 0.844851i
\(767\) 0 0
\(768\) −25.5000 + 14.7224i −0.920152 + 0.531250i
\(769\) −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i \(-0.302780\pi\)
−0.995397 + 0.0958377i \(0.969447\pi\)
\(770\) 12.5000 4.33013i 0.450469 0.156047i
\(771\) 43.5000 + 25.1147i 1.56661 + 0.904485i
\(772\) −5.00000 8.66025i −0.179954 0.311689i
\(773\) −15.5000 26.8468i −0.557496 0.965612i −0.997705 0.0677162i \(-0.978429\pi\)
0.440208 0.897896i \(-0.354905\pi\)
\(774\) −1.50000 2.59808i −0.0539164 0.0933859i
\(775\) 0 0
\(776\) −13.5000 + 23.3827i −0.484622 + 0.839390i
\(777\) −4.50000 12.9904i −0.161437 0.466027i
\(778\) 4.50000 + 7.79423i 0.161333 + 0.279437i
\(779\) −5.00000 −0.179144
\(780\) 7.50000 + 4.33013i 0.268543 + 0.155043i
\(781\) −60.0000 −2.14697
\(782\) −4.50000 + 7.79423i −0.160920 + 0.278721i
\(783\) −4.50000 2.59808i −0.160817 0.0928477i
\(784\) −1.00000 6.92820i −0.0357143 0.247436i
\(785\) −7.00000 + 12.1244i −0.249841 + 0.432737i
\(786\) 1.73205i 0.0617802i
\(787\) −14.0000 + 24.2487i −0.499046 + 0.864373i −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) 1.00000 1.73205i 0.0356235 0.0617018i
\(789\) −7.50000 4.33013i −0.267007 0.154157i
\(790\) 4.00000 6.92820i 0.142314 0.246494i
\(791\) 2.50000 0.866025i 0.0888898 0.0307923i
\(792\) −22.5000 38.9711i −0.799503 1.38478i
\(793\) −35.0000 + 60.6218i −1.24289 + 2.15274i
\(794\) 15.0000 0.532330
\(795\) 15.5885i 0.552866i
\(796\) −3.00000 −0.106332
\(797\) −11.5000 19.9186i −0.407351 0.705552i 0.587241 0.809412i \(-0.300214\pi\)
−0.994592 + 0.103860i \(0.966881\pi\)
\(798\) −3.00000 + 3.46410i −0.106199 + 0.122628i
\(799\) 0 0
\(800\) 10.0000 17.3205i 0.353553 0.612372i
\(801\) 39.0000 1.37800
\(802\) −1.50000 2.59808i −0.0529668 0.0917413i
\(803\) −7.50000 12.9904i −0.264669 0.458421i
\(804\) 6.92820i 0.244339i
\(805\) −1.50000 + 7.79423i −0.0528681 + 0.274710i
\(806\) 0 0
\(807\) 5.19615i 0.182913i
\(808\) 51.0000 1.79417
\(809\) 4.50000 + 7.79423i 0.158212 + 0.274030i 0.934224 0.356687i \(-0.116094\pi\)
−0.776012 + 0.630718i \(0.782761\pi\)
\(810\) −9.00000 −0.316228
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) −2.50000 + 0.866025i −0.0877328 + 0.0303915i
\(813\) 1.50000 0.866025i 0.0526073 0.0303728i
\(814\) 15.0000 0.525750
\(815\) −5.50000 + 9.52628i −0.192657 + 0.333691i
\(816\) −4.50000 + 2.59808i −0.157532 + 0.0909509i
\(817\) 0.500000 + 0.866025i 0.0174928 + 0.0302984i
\(818\) 14.0000 0.489499
\(819\) 30.0000 + 25.9808i 1.04828 + 0.907841i
\(820\) −5.00000 −0.174608
\(821\) −11.0000 19.0526i −0.383903 0.664939i 0.607714 0.794156i \(-0.292087\pi\)
−0.991616 + 0.129217i \(0.958754\pi\)
\(822\) 15.5885i 0.543710i
\(823\) 12.0000 20.7846i 0.418294 0.724506i −0.577474 0.816409i \(-0.695962\pi\)
0.995768 + 0.0919029i \(0.0292950\pi\)
\(824\) 3.00000 0.104510
\(825\) 30.0000 + 17.3205i 1.04447 + 0.603023i
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 9.00000 0.312772
\(829\) 12.5000 + 21.6506i 0.434143 + 0.751958i 0.997225 0.0744432i \(-0.0237179\pi\)
−0.563082 + 0.826401i \(0.690385\pi\)
\(830\) 9.00000 0.312395
\(831\) −28.5000 16.4545i −0.988654 0.570800i
\(832\) 17.5000 + 30.3109i 0.606703 + 1.05084i
\(833\) 3.00000 + 20.7846i 0.103944 + 0.720144i
\(834\) 13.5000 7.79423i 0.467467 0.269892i
\(835\) −9.50000 16.4545i −0.328761 0.569431i
\(836\) 2.50000 + 4.33013i 0.0864643 + 0.149761i
\(837\) 0 0
\(838\) −4.50000 + 7.79423i −0.155450 + 0.269247i
\(839\) 18.5000 32.0429i 0.638691 1.10625i −0.347029 0.937854i \(-0.612810\pi\)
0.985720 0.168391i \(-0.0538571\pi\)
\(840\) −9.00000 + 10.3923i −0.310530 + 0.358569i
\(841\) 14.0000 + 24.2487i 0.482759 + 0.836162i
\(842\) −1.00000 −0.0344623
\(843\) −43.5000 + 25.1147i −1.49822 + 0.864997i
\(844\) −13.0000 −0.447478
\(845\) 6.00000 10.3923i 0.206406 0.357506i
\(846\) 0 0
\(847\) 7.00000 36.3731i 0.240523 1.24979i
\(848\) −4.50000 + 7.79423i −0.154531 + 0.267655i
\(849\) 42.0000 24.2487i 1.44144 0.832214i
\(850\) 6.00000 10.3923i 0.205798 0.356453i
\(851\) −4.50000 + 7.79423i −0.154258 + 0.267183i
\(852\) 18.0000 10.3923i 0.616670 0.356034i
\(853\) 18.5000 32.0429i 0.633428 1.09713i −0.353418 0.935466i \(-0.614981\pi\)
0.986846 0.161664i \(-0.0516860\pi\)
\(854\) −28.0000 24.2487i −0.958140 0.829774i
\(855\) 3.00000 0.102598
\(856\) 25.5000 44.1673i 0.871572 1.50961i
\(857\) 11.0000 0.375753 0.187876 0.982193i \(-0.439840\pi\)
0.187876 + 0.982193i \(0.439840\pi\)
\(858\) −37.5000 + 21.6506i −1.28023 + 0.739140i
\(859\) −1.00000 −0.0341196 −0.0170598 0.999854i \(-0.505431\pi\)
−0.0170598 + 0.999854i \(0.505431\pi\)
\(860\) 0.500000 + 0.866025i 0.0170499 + 0.0295312i
\(861\) −22.5000 4.33013i −0.766798 0.147570i
\(862\) 4.50000 7.79423i 0.153271 0.265472i
\(863\) 19.5000 33.7750i 0.663788 1.14971i −0.315825 0.948818i \(-0.602281\pi\)
0.979612 0.200897i \(-0.0643855\pi\)
\(864\) 22.5000 + 12.9904i 0.765466 + 0.441942i
\(865\) −7.00000 12.1244i −0.238007 0.412240i
\(866\) 7.00000 + 12.1244i 0.237870 + 0.412002i
\(867\) −12.0000 + 6.92820i −0.407541 + 0.235294i
\(868\) 0 0
\(869\) −20.0000 34.6410i −0.678454 1.17512i
\(870\) −1.50000 0.866025i −0.0508548 0.0293610i
\(871\) −20.0000 −0.677674
\(872\) −13.5000 23.3827i −0.457168 0.791838i
\(873\) 27.0000 0.913812
\(874\) 3.00000 0.101477
\(875\) 4.50000 23.3827i 0.152128 0.790479i
\(876\) 4.50000 + 2.59808i 0.152041 + 0.0877809i
\(877\) −53.0000 −1.78968 −0.894841 0.446384i \(-0.852711\pi\)
−0.894841 + 0.446384i \(0.852711\pi\)
\(878\) 0 0
\(879\) 8.66025i 0.292103i
\(880\) −2.50000 4.33013i −0.0842750 0.145969i
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) −16.5000 + 12.9904i −0.555584 + 0.437409i
\(883\) 44.0000 1.48072 0.740359 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) −7.50000 12.9904i −0.252252 0.436914i
\(885\) 0 0
\(886\) −18.0000 + 31.1769i −0.604722 + 1.04741i
\(887\) −29.0000 −0.973725 −0.486862 0.873479i \(-0.661859\pi\)
−0.486862 + 0.873479i \(0.661859\pi\)
\(888\) −13.5000 + 7.79423i −0.453030 + 0.261557i
\(889\) −6.00000 + 31.1769i −0.201234 + 1.04564i
\(890\) 13.0000 0.435761
\(891\) −22.5000 + 38.9711i −0.753778 + 1.30558i
\(892\) 9.50000 + 16.4545i 0.318084 + 0.550937i
\(893\) 0 0
\(894\) 5.19615i 0.173785i
\(895\) 9.50000 + 16.4545i 0.317550 + 0.550013i
\(896\) 7.50000 2.59808i 0.250557 0.0867956i
\(897\) 25.9808i 0.867472i
\(898\) −15.0000 25.9808i −0.500556 0.866989i
\(899\) 0 0
\(900\) −12.0000 −0.400000
\(901\) 13.5000 23.3827i 0.449750 0.778990i
\(902\) 12.5000 21.6506i 0.416204 0.720887i
\(903\) 1.50000 + 4.33013i 0.0499169 + 0.144098i
\(904\) −1.50000 2.59808i −0.0498893 0.0864107i
\(905\) 14.0000 0.465376
\(906\) 8.66025i 0.287718i
\(907\) 5.00000 0.166022 0.0830111 0.996549i \(-0.473546\pi\)
0.0830111 + 0.996549i \(0.473546\pi\)
\(908\) −1.50000 + 2.59808i −0.0497792 + 0.0862202i
\(909\) −25.5000 44.1673i −0.845782 1.46494i
\(910\) 10.0000 + 8.66025i 0.331497 + 0.287085i
\(911\) −13.5000 + 23.3827i −0.447275 + 0.774703i −0.998208 0.0598468i \(-0.980939\pi\)
0.550933 + 0.834550i \(0.314272\pi\)
\(912\) 1.50000 + 0.866025i 0.0496700 + 0.0286770i
\(913\) 22.5000 38.9711i 0.744641 1.28976i
\(914\) −11.0000 + 19.0526i −0.363848 + 0.630203i
\(915\) 24.2487i 0.801638i
\(916\) −0.500000 + 0.866025i −0.0165205 + 0.0286143i
\(917\) −0.500000 + 2.59808i −0.0165115 + 0.0857960i
\(918\) 13.5000 + 7.79423i 0.445566 + 0.257248i
\(919\) −8.50000 + 14.7224i −0.280389 + 0.485648i −0.971481 0.237119i \(-0.923797\pi\)
0.691091 + 0.722767i \(0.257130\pi\)
\(920\) 9.00000 0.296721
\(921\) −42.0000 24.2487i −1.38395 0.799022i
\(922\) 19.0000 0.625732
\(923\) −30.0000 51.9615i −0.987462 1.71033i
\(924\) 7.50000 + 21.6506i 0.246732 + 0.712254i
\(925\) 6.00000 10.3923i 0.197279 0.341697i
\(926\) −6.50000 + 11.2583i −0.213603 + 0.369972i
\(927\) −1.50000 2.59808i −0.0492665 0.0853320i
\(928\) 2.50000 + 4.33013i 0.0820665 + 0.142143i
\(929\) 7.00000 + 12.1244i 0.229663 + 0.397787i 0.957708 0.287742i \(-0.0929044\pi\)
−0.728046 + 0.685529i \(0.759571\pi\)
\(930\) 0 0
\(931\) 5.50000 4.33013i 0.180255 0.141914i
\(932\) 1.50000 + 2.59808i 0.0491341 + 0.0851028i
\(933\) 0 0
\(934\) −27.0000 −0.883467
\(935\) 7.50000 + 12.9904i 0.245276 + 0.424831i
\(936\) 22.5000 38.9711i 0.735436 1.27381i
\(937\) 42.0000 1.37208 0.686040 0.727564i \(-0.259347\pi\)
0.686040 + 0.727564i \(0.259347\pi\)
\(938\) 2.00000 10.3923i 0.0653023 0.339321i
\(939\) 24.2487i 0.791327i
\(940\) 0 0
\(941\) 7.00000 12.1244i 0.228193 0.395243i −0.729079 0.684429i \(-0.760051\pi\)
0.957273 + 0.289187i \(0.0933848\pi\)
\(942\) 21.0000 + 12.1244i 0.684217 + 0.395033i
\(943\) 7.50000 + 12.9904i 0.244234 + 0.423025i
\(944\) 0 0
\(945\) 13.5000 + 2.59808i 0.439155 + 0.0845154i
\(946\) −5.00000 −0.162564
\(947\) 10.0000 + 17.3205i 0.324956 + 0.562841i 0.981504 0.191444i \(-0.0613171\pi\)
−0.656547 + 0.754285i \(0.727984\pi\)
\(948\) 12.0000 + 6.92820i 0.389742 + 0.225018i
\(949\) 7.50000 12.9904i 0.243460 0.421686i
\(950\) −4.00000 −0.129777
\(951\) 10.3923i 0.336994i
\(952\) 22.5000 7.79423i 0.729229 0.252612i
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 27.0000 0.874157
\(955\) 4.00000 + 6.92820i 0.129437 + 0.224191i
\(956\) 15.0000 0.485135
\(957\) −7.50000 + 4.33013i −0.242441 + 0.139973i
\(958\) −12.5000 21.6506i −0.403857 0.699500i
\(959\) −4.50000 + 23.3827i −0.145313 + 0.755066i
\(960\) 10.5000 + 6.06218i 0.338886 + 0.195656i
\(961\) 15.5000 + 26.8468i 0.500000 + 0.866025i
\(962\) 7.50000 + 12.9904i 0.241810 + 0.418827i
\(963\) −51.0000 −1.64345
\(964\) 5.50000 9.52628i 0.177143 0.306821i
\(965\) −5.00000 + 8.66025i −0.160956 + 0.278783i
\(966\) 13.5000 + 2.59808i 0.434355 + 0.0835917i
\(967\) −6.50000 11.2583i −0.209026 0.362043i 0.742382 0.669977i \(-0.233696\pi\)
−0.951408 + 0.307933i \(0.900363\pi\)
\(968\) −42.0000 −1.34993
\(969\) −4.50000 2.59808i −0.144561 0.0834622i
\(970\) 9.00000 0.288973
\(971\) −28.5000 + 49.3634i −0.914609 + 1.58415i −0.107135 + 0.994244i \(0.534168\pi\)
−0.807473 + 0.589904i \(0.799166\pi\)
\(972\) 15.5885i 0.500000i
\(973\) −22.5000 + 7.79423i −0.721317 + 0.249871i
\(974\) −9.50000 + 16.4545i −0.304400 + 0.527236i
\(975\) 34.6410i 1.10940i
\(976\) −7.00000 + 12.1244i −0.224065 + 0.388091i
\(977\) −9.00000 + 15.5885i −0.287936 + 0.498719i −0.973317 0.229465i \(-0.926302\pi\)
0.685381 + 0.728184i \(0.259636\pi\)
\(978\) 16.5000 + 9.52628i 0.527612 + 0.304617i
\(979\) 32.5000 56.2917i 1.03870 1.79909i
\(980\) 5.50000 4.33013i 0.175691 0.138321i
\(981\) −13.5000 + 23.3827i −0.431022 + 0.746552i
\(982\) −6.50000 + 11.2583i −0.207423 + 0.359268i
\(983\) −3.00000 −0.0956851 −0.0478426 0.998855i \(-0.515235\pi\)
−0.0478426 + 0.998855i \(0.515235\pi\)
\(984\) 25.9808i 0.828236i
\(985\) −2.00000 −0.0637253
\(986\) 1.50000 + 2.59808i 0.0477697 + 0.0827396i
\(987\) 0 0
\(988\) −2.50000 + 4.33013i −0.0795356 + 0.137760i
\(989\) 1.50000 2.59808i 0.0476972 0.0826140i
\(990\) −7.50000 + 12.9904i −0.238366 + 0.412861i
\(991\) 18.5000 + 32.0429i 0.587672 + 1.01788i 0.994537 + 0.104389i \(0.0332887\pi\)
−0.406865 + 0.913488i \(0.633378\pi\)
\(992\) 0 0
\(993\) 13.8564i 0.439720i
\(994\) 30.0000 10.3923i 0.951542 0.329624i
\(995\) 1.50000 + 2.59808i 0.0475532 + 0.0823646i
\(996\) 15.5885i 0.493939i
\(997\) −17.0000 −0.538395 −0.269198 0.963085i \(-0.586759\pi\)
−0.269198 + 0.963085i \(0.586759\pi\)
\(998\) −15.5000 26.8468i −0.490644 0.849820i
\(999\) 13.5000 + 7.79423i 0.427121 + 0.246598i
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 63.2.g.a.16.1 yes 2
3.2 odd 2 189.2.g.a.100.1 2
4.3 odd 2 1008.2.t.d.961.1 2
7.2 even 3 441.2.f.b.295.1 2
7.3 odd 6 441.2.h.a.214.1 2
7.4 even 3 63.2.h.a.25.1 yes 2
7.5 odd 6 441.2.f.a.295.1 2
7.6 odd 2 441.2.g.a.79.1 2
9.2 odd 6 567.2.e.b.163.1 2
9.4 even 3 63.2.h.a.58.1 yes 2
9.5 odd 6 189.2.h.a.37.1 2
9.7 even 3 567.2.e.a.163.1 2
12.11 even 2 3024.2.t.d.289.1 2
21.2 odd 6 1323.2.f.a.883.1 2
21.5 even 6 1323.2.f.b.883.1 2
21.11 odd 6 189.2.h.a.46.1 2
21.17 even 6 1323.2.h.a.802.1 2
21.20 even 2 1323.2.g.a.667.1 2
28.11 odd 6 1008.2.q.c.529.1 2
36.23 even 6 3024.2.q.b.2305.1 2
36.31 odd 6 1008.2.q.c.625.1 2
63.2 odd 6 3969.2.a.c.1.1 1
63.4 even 3 inner 63.2.g.a.4.1 2
63.5 even 6 1323.2.f.b.442.1 2
63.11 odd 6 567.2.e.b.487.1 2
63.13 odd 6 441.2.h.a.373.1 2
63.16 even 3 3969.2.a.d.1.1 1
63.23 odd 6 1323.2.f.a.442.1 2
63.25 even 3 567.2.e.a.487.1 2
63.31 odd 6 441.2.g.a.67.1 2
63.32 odd 6 189.2.g.a.172.1 2
63.40 odd 6 441.2.f.a.148.1 2
63.41 even 6 1323.2.h.a.226.1 2
63.47 even 6 3969.2.a.a.1.1 1
63.58 even 3 441.2.f.b.148.1 2
63.59 even 6 1323.2.g.a.361.1 2
63.61 odd 6 3969.2.a.f.1.1 1
84.11 even 6 3024.2.q.b.2881.1 2
252.67 odd 6 1008.2.t.d.193.1 2
252.95 even 6 3024.2.t.d.1873.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.a.4.1 2 63.4 even 3 inner
63.2.g.a.16.1 yes 2 1.1 even 1 trivial
63.2.h.a.25.1 yes 2 7.4 even 3
63.2.h.a.58.1 yes 2 9.4 even 3
189.2.g.a.100.1 2 3.2 odd 2
189.2.g.a.172.1 2 63.32 odd 6
189.2.h.a.37.1 2 9.5 odd 6
189.2.h.a.46.1 2 21.11 odd 6
441.2.f.a.148.1 2 63.40 odd 6
441.2.f.a.295.1 2 7.5 odd 6
441.2.f.b.148.1 2 63.58 even 3
441.2.f.b.295.1 2 7.2 even 3
441.2.g.a.67.1 2 63.31 odd 6
441.2.g.a.79.1 2 7.6 odd 2
441.2.h.a.214.1 2 7.3 odd 6
441.2.h.a.373.1 2 63.13 odd 6
567.2.e.a.163.1 2 9.7 even 3
567.2.e.a.487.1 2 63.25 even 3
567.2.e.b.163.1 2 9.2 odd 6
567.2.e.b.487.1 2 63.11 odd 6
1008.2.q.c.529.1 2 28.11 odd 6
1008.2.q.c.625.1 2 36.31 odd 6
1008.2.t.d.193.1 2 252.67 odd 6
1008.2.t.d.961.1 2 4.3 odd 2
1323.2.f.a.442.1 2 63.23 odd 6
1323.2.f.a.883.1 2 21.2 odd 6
1323.2.f.b.442.1 2 63.5 even 6
1323.2.f.b.883.1 2 21.5 even 6
1323.2.g.a.361.1 2 63.59 even 6
1323.2.g.a.667.1 2 21.20 even 2
1323.2.h.a.226.1 2 63.41 even 6
1323.2.h.a.802.1 2 21.17 even 6
3024.2.q.b.2305.1 2 36.23 even 6
3024.2.q.b.2881.1 2 84.11 even 6
3024.2.t.d.289.1 2 12.11 even 2
3024.2.t.d.1873.1 2 252.95 even 6
3969.2.a.a.1.1 1 63.47 even 6
3969.2.a.c.1.1 1 63.2 odd 6
3969.2.a.d.1.1 1 63.16 even 3
3969.2.a.f.1.1 1 63.61 odd 6