Properties

Label 342.2.f.c.7.1
Level $342$
Weight $2$
Character 342.7
Analytic conductor $2.731$
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] = [342,2,Mod(7,342)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(342, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("342.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.f (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: \(2.73088374913\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 342.7
Dual form 342.2.f.c.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.73205i q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} -1.73205i q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.73205i q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} -1.73205i q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} -1.73205i q^{12} +2.00000 q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} -3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-4.50000 - 2.59808i) q^{21} +(-2.50000 + 4.33013i) q^{22} +8.00000 q^{23} -1.73205i q^{24} +(2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +(1.50000 - 2.59808i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +1.00000 q^{32} +(7.50000 + 4.33013i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(-1.50000 - 2.59808i) q^{35} -3.00000 q^{36} +10.0000 q^{37} +(-4.00000 - 1.73205i) q^{38} -3.46410i q^{39} +(0.500000 - 0.866025i) q^{40} +(-3.50000 + 6.06218i) q^{41} +(-4.50000 - 2.59808i) q^{42} -8.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +8.00000 q^{46} +(0.500000 + 0.866025i) q^{47} -1.73205i q^{48} +(-1.00000 - 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 + 2.59808i) q^{51} +2.00000 q^{52} +(-5.50000 + 9.52628i) q^{53} +5.19615i q^{54} +(2.50000 + 4.33013i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-3.00000 + 6.92820i) q^{57} +(2.50000 + 4.33013i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +(-3.50000 - 6.06218i) q^{62} +(-4.50000 + 7.79423i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(7.50000 + 4.33013i) q^{66} +12.0000 q^{67} +(-1.50000 - 2.59808i) q^{68} -13.8564i q^{69} +(-1.50000 - 2.59808i) q^{70} +(0.500000 + 0.866025i) q^{71} -3.00000 q^{72} +(-1.50000 - 2.59808i) q^{73} +10.0000 q^{74} +(6.00000 - 3.46410i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(7.50000 + 12.9904i) q^{77} -3.46410i q^{78} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +(-3.50000 + 6.06218i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} -3.00000 q^{85} -8.00000 q^{86} +(7.50000 - 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-7.50000 + 12.9904i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(3.00000 - 5.19615i) q^{91} +8.00000 q^{92} +(-10.5000 + 6.06218i) q^{93} +(0.500000 + 0.866025i) q^{94} +(-3.50000 + 2.59808i) q^{95} -1.73205i q^{96} -2.00000 q^{97} +(-1.00000 - 1.73205i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{4} + q^{5} + 3 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 2 q^{4} + q^{5} + 3 q^{7} + 2 q^{8} - 6 q^{9} + q^{10} - 5 q^{11} + 4 q^{13} + 3 q^{14} - 3 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} - 5 q^{22} + 16 q^{23} + 4 q^{25} + 4 q^{26} + 3 q^{28} + 5 q^{29} - 3 q^{30} - 7 q^{31} + 2 q^{32} + 15 q^{33} - 3 q^{34} - 3 q^{35} - 6 q^{36} + 20 q^{37} - 8 q^{38} + q^{40} - 7 q^{41} - 9 q^{42} - 16 q^{43} - 5 q^{44} - 3 q^{45} + 16 q^{46} + q^{47} - 2 q^{49} + 4 q^{50} - 9 q^{51} + 4 q^{52} - 11 q^{53} + 5 q^{55} + 3 q^{56} - 6 q^{57} + 5 q^{58} + 3 q^{59} - 3 q^{60} + q^{61} - 7 q^{62} - 9 q^{63} + 2 q^{64} + 2 q^{65} + 15 q^{66} + 24 q^{67} - 3 q^{68} - 3 q^{70} + q^{71} - 6 q^{72} - 3 q^{73} + 20 q^{74} + 12 q^{75} - 8 q^{76} + 15 q^{77} - 8 q^{79} + q^{80} + 18 q^{81} - 7 q^{82} - 9 q^{83} - 9 q^{84} - 6 q^{85} - 16 q^{86} + 15 q^{87} - 5 q^{88} - 15 q^{89} - 3 q^{90} + 6 q^{91} + 16 q^{92} - 21 q^{93} + q^{94} - 7 q^{95} - 4 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.73205i 1.00000i
\(4\) 1.00000 0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i \(-0.641458\pi\)
0.996866 0.0791130i \(-0.0252088\pi\)
\(8\) 1.00000 0.353553
\(9\) −3.00000 −1.00000
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) 1.00000 0.250000
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) −3.00000 −0.707107
\(19\) −4.00000 1.73205i −0.917663 0.397360i
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) −4.50000 2.59808i −0.981981 0.566947i
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 2.00000 0.392232
\(27\) 5.19615i 1.00000i
\(28\) 1.50000 2.59808i 0.283473 0.490990i
\(29\) 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) −1.50000 0.866025i −0.273861 0.158114i
\(31\) −3.50000 6.06218i −0.628619 1.08880i −0.987829 0.155543i \(-0.950287\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) 7.50000 + 4.33013i 1.30558 + 0.753778i
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) −1.50000 2.59808i −0.253546 0.439155i
\(36\) −3.00000 −0.500000
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −4.00000 1.73205i −0.648886 0.280976i
\(39\) 3.46410i 0.554700i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −3.50000 + 6.06218i −0.546608 + 0.946753i 0.451896 + 0.892071i \(0.350748\pi\)
−0.998504 + 0.0546823i \(0.982585\pi\)
\(42\) −4.50000 2.59808i −0.694365 0.400892i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 8.00000 1.17954
\(47\) 0.500000 + 0.866025i 0.0729325 + 0.126323i 0.900185 0.435507i \(-0.143431\pi\)
−0.827253 + 0.561830i \(0.810098\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) −4.50000 + 2.59808i −0.630126 + 0.363803i
\(52\) 2.00000 0.277350
\(53\) −5.50000 + 9.52628i −0.755483 + 1.30854i 0.189651 + 0.981852i \(0.439264\pi\)
−0.945134 + 0.326683i \(0.894069\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 2.50000 + 4.33013i 0.337100 + 0.583874i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) −3.00000 + 6.92820i −0.397360 + 0.917663i
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) −1.50000 0.866025i −0.193649 0.111803i
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −3.50000 6.06218i −0.444500 0.769897i
\(63\) −4.50000 + 7.79423i −0.566947 + 0.981981i
\(64\) 1.00000 0.125000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 7.50000 + 4.33013i 0.923186 + 0.533002i
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 13.8564i 1.66812i
\(70\) −1.50000 2.59808i −0.179284 0.310530i
\(71\) 0.500000 + 0.866025i 0.0593391 + 0.102778i 0.894169 0.447730i \(-0.147767\pi\)
−0.834830 + 0.550508i \(0.814434\pi\)
\(72\) −3.00000 −0.353553
\(73\) −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i \(-0.222841\pi\)
−0.940356 + 0.340193i \(0.889507\pi\)
\(74\) 10.0000 1.16248
\(75\) 6.00000 3.46410i 0.692820 0.400000i
\(76\) −4.00000 1.73205i −0.458831 0.198680i
\(77\) 7.50000 + 12.9904i 0.854704 + 1.48039i
\(78\) 3.46410i 0.392232i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 9.00000 1.00000
\(82\) −3.50000 + 6.06218i −0.386510 + 0.669456i
\(83\) −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) −4.50000 2.59808i −0.490990 0.283473i
\(85\) −3.00000 −0.325396
\(86\) −8.00000 −0.862662
\(87\) 7.50000 4.33013i 0.804084 0.464238i
\(88\) −2.50000 + 4.33013i −0.266501 + 0.461593i
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) −1.50000 + 2.59808i −0.158114 + 0.273861i
\(91\) 3.00000 5.19615i 0.314485 0.544705i
\(92\) 8.00000 0.834058
\(93\) −10.5000 + 6.06218i −1.08880 + 0.628619i
\(94\) 0.500000 + 0.866025i 0.0515711 + 0.0893237i
\(95\) −3.50000 + 2.59808i −0.359092 + 0.266557i
\(96\) 1.73205i 0.176777i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −1.00000 1.73205i −0.101015 0.174964i
\(99\) 7.50000 12.9904i 0.753778 1.30558i
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) −5.50000 9.52628i −0.547270 0.947900i −0.998460 0.0554722i \(-0.982334\pi\)
0.451190 0.892428i \(-0.351000\pi\)
\(102\) −4.50000 + 2.59808i −0.445566 + 0.257248i
\(103\) −7.50000 12.9904i −0.738997 1.27998i −0.952947 0.303136i \(-0.901966\pi\)
0.213950 0.976845i \(-0.431367\pi\)
\(104\) 2.00000 0.196116
\(105\) −4.50000 + 2.59808i −0.439155 + 0.253546i
\(106\) −5.50000 + 9.52628i −0.534207 + 0.925274i
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 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
\(111\) 17.3205i 1.64399i
\(112\) 1.50000 2.59808i 0.141737 0.245495i
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) −3.00000 + 6.92820i −0.280976 + 0.648886i
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) 2.50000 + 4.33013i 0.232119 + 0.402042i
\(117\) −6.00000 −0.554700
\(118\) 1.50000 2.59808i 0.138086 0.239172i
\(119\) −9.00000 −0.825029
\(120\) −1.50000 0.866025i −0.136931 0.0790569i
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0.500000 + 0.866025i 0.0452679 + 0.0784063i
\(123\) 10.5000 + 6.06218i 0.946753 + 0.546608i
\(124\) −3.50000 6.06218i −0.314309 0.544400i
\(125\) 9.00000 0.804984
\(126\) −4.50000 + 7.79423i −0.400892 + 0.694365i
\(127\) 7.50000 12.9904i 0.665517 1.15271i −0.313627 0.949546i \(-0.601544\pi\)
0.979145 0.203164i \(-0.0651224\pi\)
\(128\) 1.00000 0.0883883
\(129\) 13.8564i 1.21999i
\(130\) 1.00000 1.73205i 0.0877058 0.151911i
\(131\) 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i \(-0.605885\pi\)
0.981824 0.189794i \(-0.0607819\pi\)
\(132\) 7.50000 + 4.33013i 0.652791 + 0.376889i
\(133\) −10.5000 + 7.79423i −0.910465 + 0.675845i
\(134\) 12.0000 1.03664
\(135\) 4.50000 + 2.59808i 0.387298 + 0.223607i
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) −9.50000 16.4545i −0.811640 1.40580i −0.911716 0.410822i \(-0.865242\pi\)
0.100076 0.994980i \(-0.468091\pi\)
\(138\) 13.8564i 1.17954i
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −1.50000 2.59808i −0.126773 0.219578i
\(141\) 1.50000 0.866025i 0.126323 0.0729325i
\(142\) 0.500000 + 0.866025i 0.0419591 + 0.0726752i
\(143\) −5.00000 + 8.66025i −0.418121 + 0.724207i
\(144\) −3.00000 −0.250000
\(145\) 5.00000 0.415227
\(146\) −1.50000 2.59808i −0.124141 0.215018i
\(147\) −3.00000 + 1.73205i −0.247436 + 0.142857i
\(148\) 10.0000 0.821995
\(149\) −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 6.00000 3.46410i 0.489898 0.282843i
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) −4.00000 1.73205i −0.324443 0.140488i
\(153\) 4.50000 + 7.79423i 0.363803 + 0.630126i
\(154\) 7.50000 + 12.9904i 0.604367 + 1.04679i
\(155\) −7.00000 −0.562254
\(156\) 3.46410i 0.277350i
\(157\) 8.50000 14.7224i 0.678374 1.17498i −0.297097 0.954847i \(-0.596018\pi\)
0.975470 0.220131i \(-0.0706483\pi\)
\(158\) −4.00000 −0.318223
\(159\) 16.5000 + 9.52628i 1.30854 + 0.755483i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 12.0000 20.7846i 0.945732 1.63806i
\(162\) 9.00000 0.707107
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −3.50000 + 6.06218i −0.273304 + 0.473377i
\(165\) 7.50000 4.33013i 0.583874 0.337100i
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −4.50000 2.59808i −0.347183 0.200446i
\(169\) −9.00000 −0.692308
\(170\) −3.00000 −0.230089
\(171\) 12.0000 + 5.19615i 0.917663 + 0.397360i
\(172\) −8.00000 −0.609994
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 7.50000 4.33013i 0.568574 0.328266i
\(175\) 12.0000 0.907115
\(176\) −2.50000 + 4.33013i −0.188445 + 0.326396i
\(177\) −4.50000 2.59808i −0.338241 0.195283i
\(178\) −7.50000 + 12.9904i −0.562149 + 0.973670i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.50000 + 2.59808i −0.111803 + 0.193649i
\(181\) −9.50000 + 16.4545i −0.706129 + 1.22305i 0.260153 + 0.965567i \(0.416227\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 3.00000 5.19615i 0.222375 0.385164i
\(183\) 1.50000 0.866025i 0.110883 0.0640184i
\(184\) 8.00000 0.589768
\(185\) 5.00000 8.66025i 0.367607 0.636715i
\(186\) −10.5000 + 6.06218i −0.769897 + 0.444500i
\(187\) 15.0000 1.09691
\(188\) 0.500000 + 0.866025i 0.0364662 + 0.0631614i
\(189\) 13.5000 + 7.79423i 0.981981 + 0.566947i
\(190\) −3.50000 + 2.59808i −0.253917 + 0.188484i
\(191\) −0.500000 + 0.866025i −0.0361787 + 0.0626634i −0.883548 0.468341i \(-0.844852\pi\)
0.847369 + 0.531004i \(0.178185\pi\)
\(192\) 1.73205i 0.125000i
\(193\) 4.50000 7.79423i 0.323917 0.561041i −0.657376 0.753563i \(-0.728333\pi\)
0.981293 + 0.192522i \(0.0616668\pi\)
\(194\) −2.00000 −0.143592
\(195\) −3.00000 1.73205i −0.214834 0.124035i
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) 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
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 20.7846i 1.46603i
\(202\) −5.50000 9.52628i −0.386979 0.670267i
\(203\) 15.0000 1.05279
\(204\) −4.50000 + 2.59808i −0.315063 + 0.181902i
\(205\) 3.50000 + 6.06218i 0.244451 + 0.423401i
\(206\) −7.50000 12.9904i −0.522550 0.905083i
\(207\) −24.0000 −1.66812
\(208\) 2.00000 0.138675
\(209\) 17.5000 12.9904i 1.21050 0.898563i
\(210\) −4.50000 + 2.59808i −0.310530 + 0.179284i
\(211\) −4.50000 + 7.79423i −0.309793 + 0.536577i −0.978317 0.207114i \(-0.933593\pi\)
0.668524 + 0.743690i \(0.266926\pi\)
\(212\) −5.50000 + 9.52628i −0.377742 + 0.654268i
\(213\) 1.50000 0.866025i 0.102778 0.0593391i
\(214\) −4.00000 −0.273434
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 5.19615i 0.353553i
\(217\) −21.0000 −1.42557
\(218\) 4.50000 + 7.79423i 0.304778 + 0.527892i
\(219\) −4.50000 + 2.59808i −0.304082 + 0.175562i
\(220\) 2.50000 + 4.33013i 0.168550 + 0.291937i
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 17.3205i 1.16248i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) −6.00000 10.3923i −0.400000 0.692820i
\(226\) 0.500000 + 0.866025i 0.0332595 + 0.0576072i
\(227\) 5.50000 9.52628i 0.365048 0.632281i −0.623736 0.781635i \(-0.714386\pi\)
0.988784 + 0.149354i \(0.0477193\pi\)
\(228\) −3.00000 + 6.92820i −0.198680 + 0.458831i
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) 4.00000 6.92820i 0.263752 0.456832i
\(231\) 22.5000 12.9904i 1.48039 0.854704i
\(232\) 2.50000 + 4.33013i 0.164133 + 0.284287i
\(233\) −7.50000 12.9904i −0.491341 0.851028i 0.508609 0.860998i \(-0.330160\pi\)
−0.999950 + 0.00996947i \(0.996827\pi\)
\(234\) −6.00000 −0.392232
\(235\) 1.00000 0.0652328
\(236\) 1.50000 2.59808i 0.0976417 0.169120i
\(237\) 6.92820i 0.450035i
\(238\) −9.00000 −0.583383
\(239\) −13.5000 23.3827i −0.873242 1.51250i −0.858623 0.512607i \(-0.828680\pi\)
−0.0146191 0.999893i \(-0.504654\pi\)
\(240\) −1.50000 0.866025i −0.0968246 0.0559017i
\(241\) 8.50000 + 14.7224i 0.547533 + 0.948355i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 15.5885i 1.00000i
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) −2.00000 −0.127775
\(246\) 10.5000 + 6.06218i 0.669456 + 0.386510i
\(247\) −8.00000 3.46410i −0.509028 0.220416i
\(248\) −3.50000 6.06218i −0.222250 0.384949i
\(249\) 13.5000 + 7.79423i 0.855528 + 0.493939i
\(250\) 9.00000 0.569210
\(251\) −2.50000 + 4.33013i −0.157799 + 0.273315i −0.934075 0.357078i \(-0.883773\pi\)
0.776276 + 0.630393i \(0.217106\pi\)
\(252\) −4.50000 + 7.79423i −0.283473 + 0.490990i
\(253\) −20.0000 + 34.6410i −1.25739 + 2.17786i
\(254\) 7.50000 12.9904i 0.470592 0.815089i
\(255\) 5.19615i 0.325396i
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 13.8564i 0.862662i
\(259\) 15.0000 25.9808i 0.932055 1.61437i
\(260\) 1.00000 1.73205i 0.0620174 0.107417i
\(261\) −7.50000 12.9904i −0.464238 0.804084i
\(262\) 7.50000 12.9904i 0.463352 0.802548i
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 7.50000 + 4.33013i 0.461593 + 0.266501i
\(265\) 5.50000 + 9.52628i 0.337862 + 0.585195i
\(266\) −10.5000 + 7.79423i −0.643796 + 0.477895i
\(267\) 22.5000 + 12.9904i 1.37698 + 0.794998i
\(268\) 12.0000 0.733017
\(269\) −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
\(271\) −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i \(-0.234863\pi\)
−0.952531 + 0.304443i \(0.901530\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) −9.00000 5.19615i −0.544705 0.314485i
\(274\) −9.50000 16.4545i −0.573916 0.994052i
\(275\) −20.0000 −1.20605
\(276\) 13.8564i 0.834058i
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) −12.0000 −0.719712
\(279\) 10.5000 + 18.1865i 0.628619 + 1.08880i
\(280\) −1.50000 2.59808i −0.0896421 0.155265i
\(281\) 2.50000 + 4.33013i 0.149137 + 0.258314i 0.930909 0.365251i \(-0.119017\pi\)
−0.781771 + 0.623565i \(0.785684\pi\)
\(282\) 1.50000 0.866025i 0.0893237 0.0515711i
\(283\) 1.50000 2.59808i 0.0891657 0.154440i −0.817993 0.575228i \(-0.804913\pi\)
0.907159 + 0.420789i \(0.138247\pi\)
\(284\) 0.500000 + 0.866025i 0.0296695 + 0.0513892i
\(285\) 4.50000 + 6.06218i 0.266557 + 0.359092i
\(286\) −5.00000 + 8.66025i −0.295656 + 0.512092i
\(287\) 10.5000 + 18.1865i 0.619795 + 1.07352i
\(288\) −3.00000 −0.176777
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 5.00000 0.293610
\(291\) 3.46410i 0.203069i
\(292\) −1.50000 2.59808i −0.0877809 0.152041i
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) −3.00000 + 1.73205i −0.174964 + 0.101015i
\(295\) −1.50000 2.59808i −0.0873334 0.151266i
\(296\) 10.0000 0.581238
\(297\) −22.5000 12.9904i −1.30558 0.753778i
\(298\) −1.50000 + 2.59808i −0.0868927 + 0.150503i
\(299\) 16.0000 0.925304
\(300\) 6.00000 3.46410i 0.346410 0.200000i
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) −2.50000 + 4.33013i −0.143859 + 0.249171i
\(303\) −16.5000 + 9.52628i −0.947900 + 0.547270i
\(304\) −4.00000 1.73205i −0.229416 0.0993399i
\(305\) 1.00000 0.0572598
\(306\) 4.50000 + 7.79423i 0.257248 + 0.445566i
\(307\) 16.5000 + 28.5788i 0.941705 + 1.63108i 0.762218 + 0.647320i \(0.224110\pi\)
0.179486 + 0.983760i \(0.442556\pi\)
\(308\) 7.50000 + 12.9904i 0.427352 + 0.740196i
\(309\) −22.5000 + 12.9904i −1.27998 + 0.738997i
\(310\) −7.00000 −0.397573
\(311\) −3.50000 6.06218i −0.198467 0.343755i 0.749565 0.661931i \(-0.230263\pi\)
−0.948031 + 0.318177i \(0.896930\pi\)
\(312\) 3.46410i 0.196116i
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 8.50000 14.7224i 0.479683 0.830835i
\(315\) 4.50000 + 7.79423i 0.253546 + 0.439155i
\(316\) −4.00000 −0.225018
\(317\) −1.50000 2.59808i −0.0842484 0.145922i 0.820822 0.571184i \(-0.193516\pi\)
−0.905071 + 0.425261i \(0.860182\pi\)
\(318\) 16.5000 + 9.52628i 0.925274 + 0.534207i
\(319\) −25.0000 −1.39973
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 6.92820i 0.386695i
\(322\) 12.0000 20.7846i 0.668734 1.15828i
\(323\) 1.50000 + 12.9904i 0.0834622 + 0.722804i
\(324\) 9.00000 0.500000
\(325\) 4.00000 + 6.92820i 0.221880 + 0.384308i
\(326\) −4.00000 −0.221540
\(327\) 13.5000 7.79423i 0.746552 0.431022i
\(328\) −3.50000 + 6.06218i −0.193255 + 0.334728i
\(329\) 3.00000 0.165395
\(330\) 7.50000 4.33013i 0.412861 0.238366i
\(331\) −14.5000 + 25.1147i −0.796992 + 1.38043i 0.124574 + 0.992210i \(0.460243\pi\)
−0.921567 + 0.388221i \(0.873090\pi\)
\(332\) −4.50000 + 7.79423i −0.246970 + 0.427764i
\(333\) −30.0000 −1.64399
\(334\) −12.0000 −0.656611
\(335\) 6.00000 10.3923i 0.327815 0.567792i
\(336\) −4.50000 2.59808i −0.245495 0.141737i
\(337\) 2.50000 4.33013i 0.136184 0.235877i −0.789865 0.613280i \(-0.789850\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) −9.00000 −0.489535
\(339\) 1.50000 0.866025i 0.0814688 0.0470360i
\(340\) −3.00000 −0.162698
\(341\) 35.0000 1.89536
\(342\) 12.0000 + 5.19615i 0.648886 + 0.280976i
\(343\) 15.0000 0.809924
\(344\) −8.00000 −0.431331
\(345\) −12.0000 6.92820i −0.646058 0.373002i
\(346\) −6.00000 −0.322562
\(347\) 11.5000 19.9186i 0.617352 1.06929i −0.372615 0.927986i \(-0.621539\pi\)
0.989967 0.141299i \(-0.0451280\pi\)
\(348\) 7.50000 4.33013i 0.402042 0.232119i
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 12.0000 0.641427
\(351\) 10.3923i 0.554700i
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) −1.50000 + 2.59808i −0.0798369 + 0.138282i −0.903179 0.429263i \(-0.858773\pi\)
0.823343 + 0.567545i \(0.192107\pi\)
\(354\) −4.50000 2.59808i −0.239172 0.138086i
\(355\) 1.00000 0.0530745
\(356\) −7.50000 + 12.9904i −0.397499 + 0.688489i
\(357\) 15.5885i 0.825029i
\(358\) 12.0000 0.634220
\(359\) −7.50000 12.9904i −0.395835 0.685606i 0.597372 0.801964i \(-0.296211\pi\)
−0.993207 + 0.116358i \(0.962878\pi\)
\(360\) −1.50000 + 2.59808i −0.0790569 + 0.136931i
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) −9.50000 + 16.4545i −0.499309 + 0.864828i
\(363\) −21.0000 + 12.1244i −1.10221 + 0.636364i
\(364\) 3.00000 5.19615i 0.157243 0.272352i
\(365\) −3.00000 −0.157027
\(366\) 1.50000 0.866025i 0.0784063 0.0452679i
\(367\) 8.50000 + 14.7224i 0.443696 + 0.768505i 0.997960 0.0638362i \(-0.0203335\pi\)
−0.554264 + 0.832341i \(0.687000\pi\)
\(368\) 8.00000 0.417029
\(369\) 10.5000 18.1865i 0.546608 0.946753i
\(370\) 5.00000 8.66025i 0.259938 0.450225i
\(371\) 16.5000 + 28.5788i 0.856637 + 1.48374i
\(372\) −10.5000 + 6.06218i −0.544400 + 0.314309i
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 15.0000 0.775632
\(375\) 15.5885i 0.804984i
\(376\) 0.500000 + 0.866025i 0.0257855 + 0.0446619i
\(377\) 5.00000 + 8.66025i 0.257513 + 0.446026i
\(378\) 13.5000 + 7.79423i 0.694365 + 0.400892i
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −3.50000 + 2.59808i −0.179546 + 0.133278i
\(381\) −22.5000 12.9904i −1.15271 0.665517i
\(382\) −0.500000 + 0.866025i −0.0255822 + 0.0443097i
\(383\) −6.50000 + 11.2583i −0.332134 + 0.575274i −0.982930 0.183979i \(-0.941102\pi\)
0.650796 + 0.759253i \(0.274435\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 15.0000 0.764471
\(386\) 4.50000 7.79423i 0.229044 0.396716i
\(387\) 24.0000 1.21999
\(388\) −2.00000 −0.101535
\(389\) 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) −3.00000 1.73205i −0.151911 0.0877058i
\(391\) −12.0000 20.7846i −0.606866 1.05112i
\(392\) −1.00000 1.73205i −0.0505076 0.0874818i
\(393\) −22.5000 12.9904i −1.13497 0.655278i
\(394\) 2.00000 0.100759
\(395\) −2.00000 + 3.46410i −0.100631 + 0.174298i
\(396\) 7.50000 12.9904i 0.376889 0.652791i
\(397\) −17.5000 30.3109i −0.878300 1.52126i −0.853206 0.521575i \(-0.825345\pi\)
−0.0250943 0.999685i \(-0.507989\pi\)
\(398\) 3.50000 6.06218i 0.175439 0.303870i
\(399\) 13.5000 + 18.1865i 0.675845 + 0.910465i
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −15.5000 + 26.8468i −0.774033 + 1.34066i 0.161303 + 0.986905i \(0.448430\pi\)
−0.935336 + 0.353760i \(0.884903\pi\)
\(402\) 20.7846i 1.03664i
\(403\) −7.00000 12.1244i −0.348695 0.603957i
\(404\) −5.50000 9.52628i −0.273635 0.473950i
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) 15.0000 0.744438
\(407\) −25.0000 + 43.3013i −1.23920 + 2.14636i
\(408\) −4.50000 + 2.59808i −0.222783 + 0.128624i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 3.50000 + 6.06218i 0.172853 + 0.299390i
\(411\) −28.5000 + 16.4545i −1.40580 + 0.811640i
\(412\) −7.50000 12.9904i −0.369498 0.639990i
\(413\) −4.50000 7.79423i −0.221431 0.383529i
\(414\) −24.0000 −1.17954
\(415\) 4.50000 + 7.79423i 0.220896 + 0.382604i
\(416\) 2.00000 0.0980581
\(417\) 20.7846i 1.01783i
\(418\) 17.5000 12.9904i 0.855953 0.635380i
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) −4.50000 + 2.59808i −0.219578 + 0.126773i
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) −4.50000 + 7.79423i −0.219057 + 0.379417i
\(423\) −1.50000 2.59808i −0.0729325 0.126323i
\(424\) −5.50000 + 9.52628i −0.267104 + 0.462637i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 1.50000 0.866025i 0.0726752 0.0419591i
\(427\) 3.00000 0.145180
\(428\) −4.00000 −0.193347
\(429\) 15.0000 + 8.66025i 0.724207 + 0.418121i
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i \(-0.810315\pi\)
0.899888 + 0.436121i \(0.143648\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 18.5000 32.0429i 0.889053 1.53989i 0.0480569 0.998845i \(-0.484697\pi\)
0.840996 0.541041i \(-0.181970\pi\)
\(434\) −21.0000 −1.00803
\(435\) 8.66025i 0.415227i
\(436\) 4.50000 + 7.79423i 0.215511 + 0.373276i
\(437\) −32.0000 13.8564i −1.53077 0.662842i
\(438\) −4.50000 + 2.59808i −0.215018 + 0.124141i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 2.50000 + 4.33013i 0.119183 + 0.206431i
\(441\) 3.00000 + 5.19615i 0.142857 + 0.247436i
\(442\) −3.00000 5.19615i −0.142695 0.247156i
\(443\) −15.5000 26.8468i −0.736427 1.27553i −0.954094 0.299506i \(-0.903178\pi\)
0.217667 0.976023i \(-0.430155\pi\)
\(444\) 17.3205i 0.821995i
\(445\) 7.50000 + 12.9904i 0.355534 + 0.615803i
\(446\) −16.0000 −0.757622
\(447\) 4.50000 + 2.59808i 0.212843 + 0.122885i
\(448\) 1.50000 2.59808i 0.0708683 0.122748i
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) −6.00000 10.3923i −0.282843 0.489898i
\(451\) −17.5000 30.3109i −0.824043 1.42728i
\(452\) 0.500000 + 0.866025i 0.0235180 + 0.0407344i
\(453\) 7.50000 + 4.33013i 0.352381 + 0.203447i
\(454\) 5.50000 9.52628i 0.258128 0.447090i
\(455\) −3.00000 5.19615i −0.140642 0.243599i
\(456\) −3.00000 + 6.92820i −0.140488 + 0.324443i
\(457\) 6.50000 11.2583i 0.304057 0.526642i −0.672994 0.739648i \(-0.734992\pi\)
0.977051 + 0.213006i \(0.0683253\pi\)
\(458\) 6.50000 + 11.2583i 0.303725 + 0.526067i
\(459\) 13.5000 7.79423i 0.630126 0.363803i
\(460\) 4.00000 6.92820i 0.186501 0.323029i
\(461\) 26.0000 1.21094 0.605470 0.795868i \(-0.292985\pi\)
0.605470 + 0.795868i \(0.292985\pi\)
\(462\) 22.5000 12.9904i 1.04679 0.604367i
\(463\) 14.5000 + 25.1147i 0.673872 + 1.16718i 0.976797 + 0.214166i \(0.0687035\pi\)
−0.302925 + 0.953014i \(0.597963\pi\)
\(464\) 2.50000 + 4.33013i 0.116060 + 0.201021i
\(465\) 12.1244i 0.562254i
\(466\) −7.50000 12.9904i −0.347431 0.601768i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) −6.00000 −0.277350
\(469\) 18.0000 31.1769i 0.831163 1.43962i
\(470\) 1.00000 0.0461266
\(471\) −25.5000 14.7224i −1.17498 0.678374i
\(472\) 1.50000 2.59808i 0.0690431 0.119586i
\(473\) 20.0000 34.6410i 0.919601 1.59280i
\(474\) 6.92820i 0.318223i
\(475\) −2.00000 17.3205i −0.0917663 0.794719i
\(476\) −9.00000 −0.412514
\(477\) 16.5000 28.5788i 0.755483 1.30854i
\(478\) −13.5000 23.3827i −0.617476 1.06950i
\(479\) 8.50000 + 14.7224i 0.388375 + 0.672685i 0.992231 0.124408i \(-0.0397032\pi\)
−0.603856 + 0.797093i \(0.706370\pi\)
\(480\) −1.50000 0.866025i −0.0684653 0.0395285i
\(481\) 20.0000 0.911922
\(482\) 8.50000 + 14.7224i 0.387164 + 0.670588i
\(483\) −36.0000 20.7846i −1.63806 0.945732i
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 15.5885i 0.707107i
\(487\) 40.0000 1.81257 0.906287 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) 0.500000 + 0.866025i 0.0226339 + 0.0392031i
\(489\) 6.92820i 0.313304i
\(490\) −2.00000 −0.0903508
\(491\) 9.50000 16.4545i 0.428729 0.742580i −0.568032 0.823007i \(-0.692295\pi\)
0.996761 + 0.0804264i \(0.0256282\pi\)
\(492\) 10.5000 + 6.06218i 0.473377 + 0.273304i
\(493\) 7.50000 12.9904i 0.337783 0.585057i
\(494\) −8.00000 3.46410i −0.359937 0.155857i
\(495\) −7.50000 12.9904i −0.337100 0.583874i
\(496\) −3.50000 6.06218i −0.157155 0.272200i
\(497\) 3.00000 0.134568
\(498\) 13.5000 + 7.79423i 0.604949 + 0.349268i
\(499\) 5.50000 9.52628i 0.246214 0.426455i −0.716258 0.697835i \(-0.754147\pi\)
0.962472 + 0.271380i \(0.0874801\pi\)
\(500\) 9.00000 0.402492
\(501\) 20.7846i 0.928588i
\(502\) −2.50000 + 4.33013i −0.111580 + 0.193263i
\(503\) −16.5000 + 28.5788i −0.735699 + 1.27427i 0.218718 + 0.975788i \(0.429813\pi\)
−0.954416 + 0.298479i \(0.903521\pi\)
\(504\) −4.50000 + 7.79423i −0.200446 + 0.347183i
\(505\) −11.0000 −0.489494
\(506\) −20.0000 + 34.6410i −0.889108 + 1.53998i
\(507\) 15.5885i 0.692308i
\(508\) 7.50000 12.9904i 0.332759 0.576355i
\(509\) 42.0000 1.86162 0.930809 0.365507i \(-0.119104\pi\)
0.930809 + 0.365507i \(0.119104\pi\)
\(510\) 5.19615i 0.230089i
\(511\) −9.00000 −0.398137
\(512\) 1.00000 0.0441942
\(513\) 9.00000 20.7846i 0.397360 0.917663i
\(514\) 14.0000 0.617514
\(515\) −15.0000 −0.660979
\(516\) 13.8564i 0.609994i
\(517\) −5.00000 −0.219900
\(518\) 15.0000 25.9808i 0.659062 1.14153i
\(519\) 10.3923i 0.456172i
\(520\) 1.00000 1.73205i 0.0438529 0.0759555i
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) −7.50000 12.9904i −0.328266 0.568574i
\(523\) −14.5000 + 25.1147i −0.634041 + 1.09819i 0.352677 + 0.935745i \(0.385272\pi\)
−0.986718 + 0.162446i \(0.948062\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 20.7846i 0.907115i
\(526\) −24.0000 −1.04645
\(527\) −10.5000 + 18.1865i −0.457387 + 0.792218i
\(528\) 7.50000 + 4.33013i 0.326396 + 0.188445i
\(529\) 41.0000 1.78261
\(530\) 5.50000 + 9.52628i 0.238905 + 0.413795i
\(531\) −4.50000 + 7.79423i −0.195283 + 0.338241i
\(532\) −10.5000 + 7.79423i −0.455233 + 0.337923i
\(533\) −7.00000 + 12.1244i −0.303204 + 0.525164i
\(534\) 22.5000 + 12.9904i 0.973670 + 0.562149i
\(535\) −2.00000 + 3.46410i −0.0864675 + 0.149766i
\(536\) 12.0000 0.518321
\(537\) 20.7846i 0.896922i
\(538\) −1.50000 2.59808i −0.0646696 0.112011i
\(539\) 10.0000 0.430730
\(540\) 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 \(-0.0139332\pi\)
\(542\) −3.50000 6.06218i −0.150338 0.260393i
\(543\) 28.5000 + 16.4545i 1.22305 + 0.706129i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 9.00000 0.385518
\(546\) −9.00000 5.19615i −0.385164 0.222375i
\(547\) 2.50000 + 4.33013i 0.106892 + 0.185143i 0.914510 0.404564i \(-0.132577\pi\)
−0.807617 + 0.589707i \(0.799243\pi\)
\(548\) −9.50000 16.4545i −0.405820 0.702901i
\(549\) −1.50000 2.59808i −0.0640184 0.110883i
\(550\) −20.0000 −0.852803
\(551\) −2.50000 21.6506i −0.106504 0.922348i
\(552\) 13.8564i 0.589768i
\(553\) −6.00000 + 10.3923i −0.255146 + 0.441926i
\(554\) −9.50000 + 16.4545i −0.403616 + 0.699084i
\(555\) −15.0000 8.66025i −0.636715 0.367607i
\(556\) −12.0000 −0.508913
\(557\) 8.50000 14.7224i 0.360157 0.623809i −0.627830 0.778351i \(-0.716057\pi\)
0.987986 + 0.154541i \(0.0493899\pi\)
\(558\) 10.5000 + 18.1865i 0.444500 + 0.769897i
\(559\) −16.0000 −0.676728
\(560\) −1.50000 2.59808i −0.0633866 0.109789i
\(561\) 25.9808i 1.09691i
\(562\) 2.50000 + 4.33013i 0.105456 + 0.182655i
\(563\) 10.5000 + 18.1865i 0.442522 + 0.766471i 0.997876 0.0651433i \(-0.0207504\pi\)
−0.555354 + 0.831614i \(0.687417\pi\)
\(564\) 1.50000 0.866025i 0.0631614 0.0364662i
\(565\) 1.00000 0.0420703
\(566\) 1.50000 2.59808i 0.0630497 0.109205i
\(567\) 13.5000 23.3827i 0.566947 0.981981i
\(568\) 0.500000 + 0.866025i 0.0209795 + 0.0363376i
\(569\) 20.5000 35.5070i 0.859405 1.48853i −0.0130929 0.999914i \(-0.504168\pi\)
0.872498 0.488618i \(-0.162499\pi\)
\(570\) 4.50000 + 6.06218i 0.188484 + 0.253917i
\(571\) −5.50000 9.52628i −0.230168 0.398662i 0.727690 0.685907i \(-0.240594\pi\)
−0.957857 + 0.287244i \(0.907261\pi\)
\(572\) −5.00000 + 8.66025i −0.209061 + 0.362103i
\(573\) 1.50000 + 0.866025i 0.0626634 + 0.0361787i
\(574\) 10.5000 + 18.1865i 0.438262 + 0.759091i
\(575\) 16.0000 + 27.7128i 0.667246 + 1.15570i
\(576\) −3.00000 −0.125000
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) −13.5000 7.79423i −0.561041 0.323917i
\(580\) 5.00000 0.207614
\(581\) 13.5000 + 23.3827i 0.560074 + 0.970077i
\(582\) 3.46410i 0.143592i
\(583\) −27.5000 47.6314i −1.13893 1.97269i
\(584\) −1.50000 2.59808i −0.0620704 0.107509i
\(585\) −3.00000 + 5.19615i −0.124035 + 0.214834i
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −3.00000 + 1.73205i −0.123718 + 0.0714286i
\(589\) 3.50000 + 30.3109i 0.144215 + 1.24894i
\(590\) −1.50000 2.59808i −0.0617540 0.106961i
\(591\) 3.46410i 0.142494i
\(592\) 10.0000 0.410997
\(593\) 20.5000 35.5070i 0.841834 1.45810i −0.0465084 0.998918i \(-0.514809\pi\)
0.888342 0.459182i \(-0.151857\pi\)
\(594\) −22.5000 12.9904i −0.923186 0.533002i
\(595\) −4.50000 + 7.79423i −0.184482 + 0.319532i
\(596\) −1.50000 + 2.59808i −0.0614424 + 0.106421i
\(597\) −10.5000 6.06218i −0.429736 0.248108i
\(598\) 16.0000 0.654289
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 6.00000 3.46410i 0.244949 0.141421i
\(601\) 2.50000 4.33013i 0.101977 0.176630i −0.810522 0.585708i \(-0.800816\pi\)
0.912499 + 0.409079i \(0.134150\pi\)
\(602\) −12.0000 + 20.7846i −0.489083 + 0.847117i
\(603\) −36.0000 −1.46603
\(604\) −2.50000 + 4.33013i −0.101724 + 0.176190i
\(605\) −14.0000 −0.569181
\(606\) −16.5000 + 9.52628i −0.670267 + 0.386979i
\(607\) 6.50000 + 11.2583i 0.263827 + 0.456962i 0.967256 0.253804i \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) −4.00000 1.73205i −0.162221 0.0702439i
\(609\) 25.9808i 1.05279i
\(610\) 1.00000 0.0404888
\(611\) 1.00000 + 1.73205i 0.0404557 + 0.0700713i
\(612\) 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 \(0.958684\pi\)
\(614\) 16.5000 + 28.5788i 0.665886 + 1.15335i
\(615\) 10.5000 6.06218i 0.423401 0.244451i
\(616\) 7.50000 + 12.9904i 0.302184 + 0.523397i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −22.5000 + 12.9904i −0.905083 + 0.522550i
\(619\) 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957138\pi\)
\(620\) −7.00000 −0.281127
\(621\) 41.5692i 1.66812i
\(622\) −3.50000 6.06218i −0.140337 0.243071i
\(623\) 22.5000 + 38.9711i 0.901443 + 1.56135i
\(624\) 3.46410i 0.138675i
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) −22.5000 30.3109i −0.898563 1.21050i
\(628\) 8.50000 14.7224i 0.339187 0.587489i
\(629\) −15.0000 25.9808i −0.598089 1.03592i
\(630\) 4.50000 + 7.79423i 0.179284 + 0.310530i
\(631\) 21.5000 37.2391i 0.855901 1.48246i −0.0199047 0.999802i \(-0.506336\pi\)
0.875806 0.482663i \(-0.160330\pi\)
\(632\) −4.00000 −0.159111
\(633\) 13.5000 + 7.79423i 0.536577 + 0.309793i
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) −7.50000 12.9904i −0.297628 0.515508i
\(636\) 16.5000 + 9.52628i 0.654268 + 0.377742i
\(637\) −2.00000 3.46410i −0.0792429 0.137253i
\(638\) −25.0000 −0.989759
\(639\) −1.50000 2.59808i −0.0593391 0.102778i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 6.92820i 0.273434i
\(643\) −24.5000 + 42.4352i −0.966186 + 1.67348i −0.259791 + 0.965665i \(0.583654\pi\)
−0.706395 + 0.707818i \(0.749680\pi\)
\(644\) 12.0000 20.7846i 0.472866 0.819028i
\(645\) 12.0000 + 6.92820i 0.472500 + 0.272798i
\(646\) 1.50000 + 12.9904i 0.0590167 + 0.511100i
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 9.00000 0.353553
\(649\) 7.50000 + 12.9904i 0.294401 + 0.509917i
\(650\) 4.00000 + 6.92820i 0.156893 + 0.271746i
\(651\) 36.3731i 1.42557i
\(652\) −4.00000 −0.156652
\(653\) −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) 13.5000 7.79423i 0.527892 0.304778i
\(655\) −7.50000 12.9904i −0.293049 0.507576i
\(656\) −3.50000 + 6.06218i −0.136652 + 0.236688i
\(657\) 4.50000 + 7.79423i 0.175562 + 0.304082i
\(658\) 3.00000 0.116952
\(659\) −11.5000 19.9186i −0.447976 0.775918i 0.550278 0.834982i \(-0.314522\pi\)
−0.998254 + 0.0590638i \(0.981188\pi\)
\(660\) 7.50000 4.33013i 0.291937 0.168550i
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) −14.5000 + 25.1147i −0.563559 + 0.976112i
\(663\) −9.00000 + 5.19615i −0.349531 + 0.201802i
\(664\) −4.50000 + 7.79423i −0.174634 + 0.302475i
\(665\) 1.50000 + 12.9904i 0.0581675 + 0.503745i
\(666\) −30.0000 −1.16248
\(667\) 20.0000 + 34.6410i 0.774403 + 1.34131i
\(668\) −12.0000 −0.464294
\(669\) 27.7128i 1.07144i
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) −5.00000 −0.193023
\(672\) −4.50000 2.59808i −0.173591 0.100223i
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) 2.50000 4.33013i 0.0962964 0.166790i
\(675\) −18.0000 + 10.3923i −0.692820 + 0.400000i
\(676\) −9.00000 −0.346154
\(677\) −3.50000 + 6.06218i −0.134516 + 0.232988i −0.925412 0.378962i \(-0.876281\pi\)
0.790897 + 0.611950i \(0.209615\pi\)
\(678\) 1.50000 0.866025i 0.0576072 0.0332595i
\(679\) −3.00000 + 5.19615i −0.115129 + 0.199410i
\(680\) −3.00000 −0.115045
\(681\) −16.5000 9.52628i −0.632281 0.365048i
\(682\) 35.0000 1.34022
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) 12.0000 + 5.19615i 0.458831 + 0.198680i
\(685\) −19.0000 −0.725953
\(686\) 15.0000 0.572703
\(687\) 19.5000 11.2583i 0.743971 0.429532i
\(688\) −8.00000 −0.304997
\(689\) −11.0000 + 19.0526i −0.419067 + 0.725845i
\(690\) −12.0000 6.92820i −0.456832 0.263752i
\(691\) −10.5000 + 18.1865i −0.399439 + 0.691848i −0.993657 0.112456i \(-0.964128\pi\)
0.594218 + 0.804304i \(0.297462\pi\)
\(692\) −6.00000 −0.228086
\(693\) −22.5000 38.9711i −0.854704 1.48039i
\(694\) 11.5000 19.9186i 0.436534 0.756099i
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 7.50000 4.33013i 0.284287 0.164133i
\(697\) 21.0000 0.795432
\(698\) 2.50000 4.33013i 0.0946264 0.163898i
\(699\) −22.5000 + 12.9904i −0.851028 + 0.491341i
\(700\) 12.0000 0.453557
\(701\) 0.500000 + 0.866025i 0.0188847 + 0.0327093i 0.875313 0.483556i \(-0.160655\pi\)
−0.856429 + 0.516265i \(0.827322\pi\)
\(702\) 10.3923i 0.392232i
\(703\) −40.0000 17.3205i −1.50863 0.653255i
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 1.73205i 0.0652328i
\(706\) −1.50000 + 2.59808i −0.0564532 + 0.0977799i
\(707\) −33.0000 −1.24109
\(708\) −4.50000 2.59808i −0.169120 0.0976417i
\(709\) −1.50000 2.59808i −0.0563337 0.0975728i 0.836483 0.547992i \(-0.184608\pi\)
−0.892817 + 0.450420i \(0.851274\pi\)
\(710\) 1.00000 0.0375293
\(711\) 12.0000 0.450035
\(712\) −7.50000 + 12.9904i −0.281074 + 0.486835i
\(713\) −28.0000 48.4974i −1.04861 1.81624i
\(714\) 15.5885i 0.583383i
\(715\) 5.00000 + 8.66025i 0.186989 + 0.323875i
\(716\) 12.0000 0.448461
\(717\) −40.5000 + 23.3827i −1.51250 + 0.873242i
\(718\) −7.50000 12.9904i −0.279898 0.484797i
\(719\) −3.50000 6.06218i −0.130528 0.226081i 0.793352 0.608763i \(-0.208334\pi\)
−0.923880 + 0.382682i \(0.875001\pi\)
\(720\) −1.50000 + 2.59808i −0.0559017 + 0.0968246i
\(721\) −45.0000 −1.67589
\(722\) 13.0000 + 13.8564i 0.483810 + 0.515682i
\(723\) 25.5000 14.7224i 0.948355 0.547533i
\(724\) −9.50000 + 16.4545i −0.353065 + 0.611526i
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) −21.0000 + 12.1244i −0.779383 + 0.449977i
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 3.00000 5.19615i 0.111187 0.192582i
\(729\) −27.0000 −1.00000
\(730\) −3.00000 −0.111035
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 1.50000 0.866025i 0.0554416 0.0320092i
\(733\) −7.50000 12.9904i −0.277019 0.479811i 0.693624 0.720338i \(-0.256013\pi\)
−0.970642 + 0.240527i \(0.922680\pi\)
\(734\) 8.50000 + 14.7224i 0.313741 + 0.543415i
\(735\) 3.46410i 0.127775i
\(736\) 8.00000 0.294884
\(737\) −30.0000 + 51.9615i −1.10506 + 1.91403i
\(738\) 10.5000 18.1865i 0.386510 0.669456i
\(739\) 18.5000 + 32.0429i 0.680534 + 1.17872i 0.974818 + 0.223001i \(0.0715853\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 5.00000 8.66025i 0.183804 0.318357i
\(741\) −6.00000 + 13.8564i −0.220416 + 0.509028i
\(742\) 16.5000 + 28.5788i 0.605734 + 1.04916i
\(743\) 9.50000 16.4545i 0.348521 0.603656i −0.637466 0.770479i \(-0.720017\pi\)
0.985987 + 0.166822i \(0.0533506\pi\)
\(744\) −10.5000 + 6.06218i −0.384949 + 0.222250i
\(745\) 1.50000 + 2.59808i 0.0549557 + 0.0951861i
\(746\) 12.5000 + 21.6506i 0.457658 + 0.792686i
\(747\) 13.5000 23.3827i 0.493939 0.855528i
\(748\) 15.0000 0.548454
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 15.5885i 0.569210i
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 0.500000 + 0.866025i 0.0182331 + 0.0315807i
\(753\) 7.50000 + 4.33013i 0.273315 + 0.157799i
\(754\) 5.00000 + 8.66025i 0.182089 + 0.315388i
\(755\) 2.50000 + 4.33013i 0.0909843 + 0.157589i
\(756\) 13.5000 + 7.79423i 0.490990 + 0.283473i
\(757\) 14.5000 + 25.1147i 0.527011 + 0.912811i 0.999505 + 0.0314762i \(0.0100208\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −12.0000 −0.435860
\(759\) 60.0000 + 34.6410i 2.17786 + 1.25739i
\(760\) −3.50000 + 2.59808i −0.126958 + 0.0942421i
\(761\) −7.50000 12.9904i −0.271875 0.470901i 0.697467 0.716617i \(-0.254310\pi\)
−0.969342 + 0.245716i \(0.920977\pi\)
\(762\) −22.5000 12.9904i −0.815089 0.470592i
\(763\) 27.0000 0.977466
\(764\) −0.500000 + 0.866025i −0.0180894 + 0.0313317i
\(765\) 9.00000 0.325396
\(766\) −6.50000 + 11.2583i −0.234855 + 0.406780i
\(767\) 3.00000 5.19615i 0.108324 0.187622i
\(768\) 1.73205i 0.0625000i
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 15.0000 0.540562
\(771\) 24.2487i 0.873296i
\(772\) 4.50000 7.79423i 0.161959 0.280520i
\(773\) 10.5000 18.1865i 0.377659 0.654124i −0.613062 0.790034i \(-0.710063\pi\)
0.990721 + 0.135910i \(0.0433959\pi\)
\(774\) 24.0000 0.862662
\(775\) 14.0000 24.2487i 0.502895 0.871039i
\(776\) −2.00000 −0.0717958
\(777\) −45.0000 25.9808i −1.61437 0.932055i
\(778\) 4.50000 + 7.79423i 0.161333 + 0.279437i
\(779\) 24.5000 18.1865i 0.877804 0.651600i
\(780\) −3.00000 1.73205i −0.107417 0.0620174i
\(781\) −5.00000 −0.178914
\(782\) −12.0000 20.7846i −0.429119 0.743256i
\(783\) −22.5000 + 12.9904i −0.804084 + 0.464238i
\(784\) −1.00000 1.73205i −0.0357143 0.0618590i
\(785\) −8.50000 14.7224i −0.303378 0.525466i
\(786\) −22.5000 12.9904i −0.802548 0.463352i
\(787\) −3.50000 6.06218i −0.124762 0.216093i 0.796878 0.604140i \(-0.206483\pi\)
−0.921640 + 0.388047i \(0.873150\pi\)
\(788\) 2.00000 0.0712470
\(789\) 41.5692i 1.47990i
\(790\) −2.00000 + 3.46410i −0.0711568 + 0.123247i
\(791\) 3.00000 0.106668
\(792\) 7.50000 12.9904i 0.266501 0.461593i
\(793\) 1.00000 + 1.73205i 0.0355110 + 0.0615069i
\(794\) −17.5000 30.3109i −0.621052 1.07569i
\(795\) 16.5000 9.52628i 0.585195 0.337862i
\(796\) 3.50000 6.06218i 0.124054 0.214868i
\(797\) 4.50000 + 7.79423i 0.159398 + 0.276086i 0.934652 0.355564i \(-0.115711\pi\)
−0.775254 + 0.631650i \(0.782378\pi\)
\(798\) 13.5000 + 18.1865i 0.477895 + 0.643796i
\(799\) 1.50000 2.59808i 0.0530662 0.0919133i
\(800\) 2.00000 + 3.46410i 0.0707107 + 0.122474i
\(801\) 22.5000 38.9711i 0.794998 1.37698i
\(802\) −15.5000 + 26.8468i −0.547324 + 0.947993i
\(803\) 15.0000 0.529339
\(804\) 20.7846i 0.733017i
\(805\) −12.0000 20.7846i −0.422944 0.732561i
\(806\) −7.00000 12.1244i −0.246564 0.427062i
\(807\) −4.50000 + 2.59808i −0.158408 + 0.0914566i
\(808\) −5.50000 9.52628i −0.193489 0.335133i
\(809\) 54.0000 1.89854 0.949269 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 4.50000 7.79423i 0.158114 0.273861i
\(811\) −16.5000 + 28.5788i −0.579393 + 1.00354i 0.416156 + 0.909293i \(0.363377\pi\)
−0.995549 + 0.0942453i \(0.969956\pi\)
\(812\) 15.0000 0.526397
\(813\) −10.5000 + 6.06218i −0.368251 + 0.212610i
\(814\) −25.0000 + 43.3013i −0.876250 + 1.51771i
\(815\) −2.00000 + 3.46410i −0.0700569 + 0.121342i
\(816\) −4.50000 + 2.59808i −0.157532 + 0.0909509i
\(817\) 32.0000 + 13.8564i 1.11954 + 0.484774i
\(818\) 10.0000 0.349642
\(819\) −9.00000 + 15.5885i −0.314485 + 0.544705i
\(820\) 3.50000 + 6.06218i 0.122225 + 0.211700i
\(821\) −1.50000 2.59808i −0.0523504 0.0906735i 0.838663 0.544651i \(-0.183338\pi\)
−0.891013 + 0.453978i \(0.850005\pi\)
\(822\) −28.5000 + 16.4545i −0.994052 + 0.573916i
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) −7.50000 12.9904i −0.261275 0.452541i
\(825\) 34.6410i 1.20605i
\(826\) −4.50000 7.79423i −0.156575 0.271196i
\(827\) −20.5000 + 35.5070i −0.712855 + 1.23470i 0.250926 + 0.968006i \(0.419265\pi\)
−0.963781 + 0.266695i \(0.914068\pi\)
\(828\) −24.0000 −0.834058
\(829\) 18.0000 0.625166 0.312583 0.949890i \(-0.398806\pi\)
0.312583 + 0.949890i \(0.398806\pi\)
\(830\) 4.50000 + 7.79423i 0.156197 + 0.270542i
\(831\) 28.5000 + 16.4545i 0.988654 + 0.570800i
\(832\) 2.00000 0.0693375
\(833\) −3.00000 + 5.19615i −0.103944 + 0.180036i
\(834\) 20.7846i 0.719712i
\(835\) −6.00000 + 10.3923i −0.207639 + 0.359641i
\(836\) 17.5000 12.9904i 0.605250 0.449282i
\(837\) 31.5000 18.1865i 1.08880 0.628619i
\(838\) 4.50000 + 7.79423i 0.155450 + 0.269247i
\(839\) −16.0000 −0.552381 −0.276191 0.961103i \(-0.589072\pi\)
−0.276191 + 0.961103i \(0.589072\pi\)
\(840\) −4.50000 + 2.59808i −0.155265 + 0.0896421i
\(841\) 2.00000 3.46410i 0.0689655 0.119452i
\(842\) −22.0000 −0.758170
\(843\) 7.50000 4.33013i 0.258314 0.149137i
\(844\) −4.50000 + 7.79423i −0.154896 + 0.268288i
\(845\) −4.50000 + 7.79423i −0.154805 + 0.268130i
\(846\) −1.50000 2.59808i −0.0515711 0.0893237i
\(847\) −42.0000 −1.44314
\(848\) −5.50000 + 9.52628i −0.188871 + 0.327134i
\(849\) −4.50000 2.59808i −0.154440 0.0891657i
\(850\) 6.00000 10.3923i 0.205798 0.356453i
\(851\) 80.0000 2.74236
\(852\) 1.50000 0.866025i 0.0513892 0.0296695i
\(853\) −30.0000 −1.02718 −0.513590 0.858036i \(-0.671685\pi\)
−0.513590 + 0.858036i \(0.671685\pi\)
\(854\) 3.00000 0.102658
\(855\) 10.5000 7.79423i 0.359092 0.266557i
\(856\) −4.00000 −0.136717
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 15.0000 + 8.66025i 0.512092 + 0.295656i
\(859\) 28.0000 0.955348 0.477674 0.878537i \(-0.341480\pi\)
0.477674 + 0.878537i \(0.341480\pi\)
\(860\) −4.00000 + 6.92820i −0.136399 + 0.236250i
\(861\) 31.5000 18.1865i 1.07352 0.619795i
\(862\) 1.50000 2.59808i 0.0510902 0.0884908i
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 5.19615i 0.176777i
\(865\) −3.00000 + 5.19615i −0.102003 + 0.176674i
\(866\) 18.5000 32.0429i 0.628656 1.08886i
\(867\) −12.0000 6.92820i −0.407541 0.235294i
\(868\) −21.0000 −0.712786
\(869\) 10.0000 17.3205i 0.339227 0.587558i
\(870\) 8.66025i 0.293610i
\(871\) 24.0000 0.813209
\(872\) 4.50000 + 7.79423i 0.152389 + 0.263946i
\(873\) 6.00000 0.203069
\(874\) −32.0000 13.8564i −1.08242 0.468700i
\(875\) 13.5000 23.3827i 0.456383 0.790479i
\(876\) −4.50000 + 2.59808i −0.152041 + 0.0877809i
\(877\) 26.5000 45.8993i 0.894841 1.54991i 0.0608407 0.998147i \(-0.480622\pi\)
0.834001 0.551763i \(-0.186045\pi\)
\(878\) 8.00000 0.269987
\(879\) 13.5000 7.79423i 0.455344 0.262893i
\(880\) 2.50000 + 4.33013i 0.0842750 + 0.145969i
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 3.00000 + 5.19615i 0.101015 + 0.174964i
\(883\) −6.50000 + 11.2583i −0.218742 + 0.378873i −0.954424 0.298455i \(-0.903529\pi\)
0.735681 + 0.677328i \(0.236862\pi\)
\(884\) −3.00000 5.19615i −0.100901 0.174766i
\(885\) −4.50000 + 2.59808i −0.151266 + 0.0873334i
\(886\) −15.5000 26.8468i −0.520733 0.901935i
\(887\) −56.0000 −1.88030 −0.940148 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 17.3205i 0.581238i
\(889\) −22.5000 38.9711i −0.754626 1.30705i
\(890\) 7.50000 + 12.9904i 0.251401 + 0.435439i
\(891\) −22.5000 + 38.9711i −0.753778 + 1.30558i
\(892\) −16.0000 −0.535720
\(893\) −0.500000 4.33013i −0.0167319 0.144902i
\(894\) 4.50000 + 2.59808i 0.150503 + 0.0868927i
\(895\) 6.00000 10.3923i 0.200558 0.347376i
\(896\) 1.50000 2.59808i 0.0501115 0.0867956i
\(897\) 27.7128i 0.925304i
\(898\) −26.0000 −0.867631
\(899\) 17.5000 30.3109i 0.583658 1.01092i
\(900\) −6.00000 10.3923i −0.200000 0.346410i
\(901\) 33.0000 1.09939
\(902\) −17.5000 30.3109i −0.582686 1.00924i
\(903\) 36.0000 + 20.7846i 1.19800 + 0.691669i
\(904\) 0.500000 + 0.866025i 0.0166298 + 0.0288036i
\(905\) 9.50000 + 16.4545i 0.315791 + 0.546966i
\(906\) 7.50000 + 4.33013i 0.249171 + 0.143859i
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 5.50000 9.52628i 0.182524 0.316141i
\(909\) 16.5000 + 28.5788i 0.547270 + 0.947900i
\(910\) −3.00000 5.19615i −0.0994490 0.172251i
\(911\) 7.50000 12.9904i 0.248486 0.430391i −0.714620 0.699513i \(-0.753400\pi\)
0.963106 + 0.269122i \(0.0867336\pi\)
\(912\) −3.00000 + 6.92820i −0.0993399 + 0.229416i
\(913\) −22.5000 38.9711i −0.744641 1.28976i
\(914\) 6.50000 11.2583i 0.215001 0.372392i
\(915\) 1.73205i 0.0572598i
\(916\) 6.50000 + 11.2583i 0.214766 + 0.371986i
\(917\) −22.5000 38.9711i −0.743015 1.28694i
\(918\) 13.5000 7.79423i 0.445566 0.257248i
\(919\) −4.00000 −0.131948 −0.0659739 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) 4.00000 6.92820i 0.131876 0.228416i
\(921\) 49.5000 28.5788i 1.63108 0.941705i
\(922\) 26.0000 0.856264
\(923\) 1.00000 + 1.73205i 0.0329154 + 0.0570111i
\(924\) 22.5000 12.9904i 0.740196 0.427352i
\(925\) 20.0000 + 34.6410i 0.657596 + 1.13899i
\(926\) 14.5000 + 25.1147i 0.476500 + 0.825321i
\(927\) 22.5000 + 38.9711i 0.738997 + 1.27998i
\(928\) 2.50000 + 4.33013i 0.0820665 + 0.142143i
\(929\) 50.0000 1.64045 0.820223 0.572043i \(-0.193849\pi\)
0.820223 + 0.572043i \(0.193849\pi\)
\(930\) 12.1244i 0.397573i
\(931\) 1.00000 + 8.66025i 0.0327737 + 0.283828i
\(932\) −7.50000 12.9904i −0.245671 0.425514i
\(933\) −10.5000 + 6.06218i −0.343755 + 0.198467i
\(934\) −8.00000 −0.261768
\(935\) 7.50000 12.9904i 0.245276 0.424831i
\(936\) −6.00000 −0.196116
\(937\) −23.5000 + 40.7032i −0.767712 + 1.32972i 0.171089 + 0.985255i \(0.445271\pi\)
−0.938801 + 0.344460i \(0.888062\pi\)
\(938\) 18.0000 31.1769i 0.587721 1.01796i
\(939\) 1.50000 0.866025i 0.0489506 0.0282617i
\(940\) 1.00000 0.0326164
\(941\) 10.0000 0.325991 0.162995 0.986627i \(-0.447884\pi\)
0.162995 + 0.986627i \(0.447884\pi\)
\(942\) −25.5000 14.7224i −0.830835 0.479683i
\(943\) −28.0000 + 48.4974i −0.911805 + 1.57929i
\(944\) 1.50000 2.59808i 0.0488208 0.0845602i
\(945\) 13.5000 7.79423i 0.439155 0.253546i
\(946\) 20.0000 34.6410i 0.650256 1.12628i
\(947\) −60.0000 −1.94974 −0.974869 0.222779i \(-0.928487\pi\)
−0.974869 + 0.222779i \(0.928487\pi\)
\(948\) 6.92820i 0.225018i
\(949\) −3.00000 5.19615i −0.0973841 0.168674i
\(950\) −2.00000 17.3205i −0.0648886 0.561951i
\(951\) −4.50000 + 2.59808i −0.145922 + 0.0842484i
\(952\) −9.00000 −0.291692
\(953\) 0.500000 + 0.866025i 0.0161966 + 0.0280533i 0.874010 0.485908i \(-0.161511\pi\)
−0.857814 + 0.513961i \(0.828178\pi\)
\(954\) 16.5000 28.5788i 0.534207 0.925274i
\(955\) 0.500000 + 0.866025i 0.0161796 + 0.0280239i
\(956\) −13.5000 23.3827i −0.436621 0.756250i
\(957\) 43.3013i 1.39973i
\(958\) 8.50000 + 14.7224i 0.274623 + 0.475660i
\(959\) −57.0000 −1.84063
\(960\) −1.50000 0.866025i −0.0484123 0.0279508i
\(961\) −9.00000 + 15.5885i −0.290323 + 0.502853i
\(962\) 20.0000 0.644826
\(963\) 12.0000 0.386695
\(964\) 8.50000 + 14.7224i 0.273767 + 0.474178i
\(965\) −4.50000 7.79423i −0.144860 0.250905i
\(966\) −36.0000 20.7846i −1.15828 0.668734i
\(967\) −4.50000 + 7.79423i −0.144710 + 0.250645i −0.929265 0.369414i \(-0.879558\pi\)
0.784555 + 0.620060i \(0.212892\pi\)
\(968\) −7.00000 12.1244i −0.224989 0.389692i
\(969\) 22.5000 2.59808i 0.722804 0.0834622i
\(970\) −1.00000 + 1.73205i −0.0321081 + 0.0556128i
\(971\) −17.5000 30.3109i −0.561602 0.972723i −0.997357 0.0726575i \(-0.976852\pi\)
0.435755 0.900065i \(-0.356481\pi\)
\(972\) 15.5885i 0.500000i
\(973\) −18.0000 + 31.1769i −0.577054 + 0.999486i
\(974\) 40.0000 1.28168
\(975\) 12.0000 6.92820i 0.384308 0.221880i
\(976\) 0.500000 + 0.866025i 0.0160046 + 0.0277208i
\(977\) −5.50000 9.52628i −0.175961 0.304773i 0.764533 0.644585i \(-0.222970\pi\)
−0.940493 + 0.339812i \(0.889636\pi\)
\(978\) 6.92820i 0.221540i
\(979\) −37.5000 64.9519i −1.19851 2.07587i
\(980\) −2.00000 −0.0638877
\(981\) −13.5000 23.3827i −0.431022 0.746552i
\(982\) 9.50000 16.4545i 0.303157 0.525084i
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 10.5000 + 6.06218i 0.334728 + 0.193255i
\(985\) 1.00000 1.73205i 0.0318626 0.0551877i
\(986\) 7.50000 12.9904i 0.238849 0.413698i
\(987\) 5.19615i 0.165395i
\(988\) −8.00000 3.46410i −0.254514 0.110208i
\(989\) −64.0000 −2.03508
\(990\) −7.50000 12.9904i −0.238366 0.412861i
\(991\) −9.50000 16.4545i −0.301777 0.522694i 0.674761 0.738036i \(-0.264247\pi\)
−0.976539 + 0.215342i \(0.930913\pi\)
\(992\) −3.50000 6.06218i −0.111125 0.192474i
\(993\) 43.5000 + 25.1147i 1.38043 + 0.796992i
\(994\) 3.00000 0.0951542
\(995\) −3.50000 6.06218i −0.110957 0.192184i
\(996\) 13.5000 + 7.79423i 0.427764 + 0.246970i
\(997\) 8.50000 + 14.7224i 0.269198 + 0.466264i 0.968655 0.248410i \(-0.0799082\pi\)
−0.699457 + 0.714675i \(0.746575\pi\)
\(998\) 5.50000 9.52628i 0.174099 0.301549i
\(999\) 51.9615i 1.64399i
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 342.2.f.c.7.1 2
3.2 odd 2 1026.2.f.a.235.1 2
9.4 even 3 342.2.h.a.121.1 yes 2
9.5 odd 6 1026.2.h.d.577.1 2
19.11 even 3 342.2.h.a.277.1 yes 2
57.11 odd 6 1026.2.h.d.505.1 2
171.49 even 3 inner 342.2.f.c.49.1 yes 2
171.68 odd 6 1026.2.f.a.847.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
342.2.f.c.7.1 2 1.1 even 1 trivial
342.2.f.c.49.1 yes 2 171.49 even 3 inner
342.2.h.a.121.1 yes 2 9.4 even 3
342.2.h.a.277.1 yes 2 19.11 even 3
1026.2.f.a.235.1 2 3.2 odd 2
1026.2.f.a.847.1 2 171.68 odd 6
1026.2.h.d.505.1 2 57.11 odd 6
1026.2.h.d.577.1 2 9.5 odd 6