Properties

Label 99.2.e.a.34.1
Level $99$
Weight $2$
Character 99.34
Analytic conductor $0.791$
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] = [99,2,Mod(34,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.e (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: \(0.790518980011\)
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 34.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 99.34
Dual form 99.2.e.a.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(1.50000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +4.00000 q^{17} +(1.50000 + 2.59808i) q^{18} +6.00000 q^{19} +(0.500000 - 0.866025i) q^{20} -6.92820i q^{21} +(-0.500000 - 0.866025i) q^{22} +(2.00000 + 3.46410i) q^{23} +(4.50000 - 2.59808i) q^{24} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +5.19615i q^{27} -4.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(-2.50000 - 4.33013i) q^{32} -1.73205i q^{33} +(-2.00000 + 3.46410i) q^{34} +4.00000 q^{35} +3.00000 q^{36} +3.00000 q^{37} +(-3.00000 + 5.19615i) q^{38} +(-3.00000 - 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{40} +(1.00000 + 1.73205i) q^{41} +(6.00000 + 3.46410i) q^{42} +(-3.00000 + 5.19615i) q^{43} -1.00000 q^{44} -3.00000 q^{45} -4.00000 q^{46} +(3.50000 - 6.06218i) q^{47} +1.73205i q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-6.00000 + 3.46410i) q^{51} +(-1.00000 + 1.73205i) q^{52} -9.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} +1.00000 q^{55} +(6.00000 - 10.3923i) q^{56} +(-9.00000 + 5.19615i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(3.50000 + 6.06218i) q^{59} +1.73205i q^{60} +7.00000 q^{62} +(6.00000 + 10.3923i) q^{63} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(1.50000 + 0.866025i) q^{66} +(-5.50000 - 9.52628i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-6.00000 - 3.46410i) q^{69} +(-2.00000 + 3.46410i) q^{70} +9.00000 q^{71} +(-4.50000 + 7.79423i) q^{72} +4.00000 q^{73} +(-1.50000 + 2.59808i) q^{74} +6.92820i q^{75} +(3.00000 + 5.19615i) q^{76} +(-2.00000 - 3.46410i) q^{77} +(3.00000 - 1.73205i) q^{78} +(-4.00000 + 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -2.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(6.00000 - 3.46410i) q^{84} +(-2.00000 - 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} -10.3923i q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +(1.50000 - 2.59808i) q^{90} -8.00000 q^{91} +(-2.00000 + 3.46410i) q^{92} +(10.5000 + 6.06218i) q^{93} +(3.50000 + 6.06218i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(7.50000 + 4.33013i) q^{96} +(9.50000 - 16.4545i) q^{97} +9.00000 q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 4 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 4 q^{7} - 6 q^{8} + 3 q^{9} + 2 q^{10} - q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{15} + q^{16} + 8 q^{17} + 3 q^{18} + 12 q^{19} + q^{20} - q^{22} + 4 q^{23} + 9 q^{24} + 4 q^{25} - 4 q^{26} - 8 q^{28} - 6 q^{29} - 3 q^{30} - 7 q^{31} - 5 q^{32} - 4 q^{34} + 8 q^{35} + 6 q^{36} + 6 q^{37} - 6 q^{38} - 6 q^{39} + 3 q^{40} + 2 q^{41} + 12 q^{42} - 6 q^{43} - 2 q^{44} - 6 q^{45} - 8 q^{46} + 7 q^{47} - 9 q^{49} + 4 q^{50} - 12 q^{51} - 2 q^{52} - 18 q^{53} - 9 q^{54} + 2 q^{55} + 12 q^{56} - 18 q^{57} - 6 q^{58} + 7 q^{59} + 14 q^{62} + 12 q^{63} + 14 q^{64} + 2 q^{65} + 3 q^{66} - 11 q^{67} + 4 q^{68} - 12 q^{69} - 4 q^{70} + 18 q^{71} - 9 q^{72} + 8 q^{73} - 3 q^{74} + 6 q^{76} - 4 q^{77} + 6 q^{78} - 8 q^{79} - 2 q^{80} - 9 q^{81} - 4 q^{82} + 12 q^{83} + 12 q^{84} - 4 q^{85} - 6 q^{86} + 3 q^{88} + 12 q^{89} + 3 q^{90} - 16 q^{91} - 4 q^{92} + 21 q^{93} + 7 q^{94} - 6 q^{95} + 15 q^{96} + 19 q^{97} + 18 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 1.73205i 0.707107i
\(7\) −2.00000 + 3.46410i −0.755929 + 1.30931i 0.188982 + 0.981981i \(0.439481\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 1.00000 0.316228
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −2.00000 3.46410i −0.534522 0.925820i
\(15\) 1.50000 + 0.866025i 0.387298 + 0.223607i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 6.92820i 1.51186i
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 4.50000 2.59808i 0.918559 0.530330i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −2.00000 −0.392232
\(27\) 5.19615i 1.00000i
\(28\) −4.00000 −0.755929
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) −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 \(-0.383046\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) 1.73205i 0.301511i
\(34\) −2.00000 + 3.46410i −0.342997 + 0.594089i
\(35\) 4.00000 0.676123
\(36\) 3.00000 0.500000
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) −3.00000 + 5.19615i −0.486664 + 0.842927i
\(39\) −3.00000 1.73205i −0.480384 0.277350i
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(42\) 6.00000 + 3.46410i 0.925820 + 0.534522i
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) −1.00000 −0.150756
\(45\) −3.00000 −0.447214
\(46\) −4.00000 −0.589768
\(47\) 3.50000 6.06218i 0.510527 0.884260i −0.489398 0.872060i \(-0.662783\pi\)
0.999926 0.0121990i \(-0.00388317\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) −6.00000 + 3.46410i −0.840168 + 0.485071i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 1.00000 0.134840
\(56\) 6.00000 10.3923i 0.801784 1.38873i
\(57\) −9.00000 + 5.19615i −1.19208 + 0.688247i
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 1.73205i 0.223607i
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 7.00000 0.889001
\(63\) 6.00000 + 10.3923i 0.755929 + 1.30931i
\(64\) 7.00000 0.875000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 1.50000 + 0.866025i 0.184637 + 0.106600i
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) −6.00000 3.46410i −0.722315 0.417029i
\(70\) −2.00000 + 3.46410i −0.239046 + 0.414039i
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) −4.50000 + 7.79423i −0.530330 + 0.918559i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) 6.92820i 0.800000i
\(76\) 3.00000 + 5.19615i 0.344124 + 0.596040i
\(77\) −2.00000 3.46410i −0.227921 0.394771i
\(78\) 3.00000 1.73205i 0.339683 0.196116i
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −1.00000 −0.111803
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −2.00000 −0.220863
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 6.00000 3.46410i 0.654654 0.377964i
\(85\) −2.00000 3.46410i −0.216930 0.375735i
\(86\) −3.00000 5.19615i −0.323498 0.560316i
\(87\) 10.3923i 1.11417i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 1.50000 2.59808i 0.158114 0.273861i
\(91\) −8.00000 −0.838628
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) 10.5000 + 6.06218i 1.08880 + 0.628619i
\(94\) 3.50000 + 6.06218i 0.360997 + 0.625266i
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 7.50000 + 4.33013i 0.765466 + 0.441942i
\(97\) 9.50000 16.4545i 0.964579 1.67070i 0.253837 0.967247i \(-0.418307\pi\)
0.710742 0.703452i \(-0.248359\pi\)
\(98\) 9.00000 0.909137
\(99\) 1.50000 + 2.59808i 0.150756 + 0.261116i
\(100\) 4.00000 0.400000
\(101\) 2.00000 3.46410i 0.199007 0.344691i −0.749199 0.662344i \(-0.769562\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(102\) 6.92820i 0.685994i
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) −6.00000 + 3.46410i −0.585540 + 0.338062i
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) −4.50000 + 2.59808i −0.427121 + 0.246598i
\(112\) 2.00000 + 3.46410i 0.188982 + 0.327327i
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) 10.3923i 0.973329i
\(115\) 2.00000 3.46410i 0.186501 0.323029i
\(116\) −6.00000 −0.557086
\(117\) 6.00000 0.554700
\(118\) −7.00000 −0.644402
\(119\) −8.00000 + 13.8564i −0.733359 + 1.27021i
\(120\) −4.50000 2.59808i −0.410792 0.237171i
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 0 0
\(123\) −3.00000 1.73205i −0.270501 0.156174i
\(124\) 3.50000 6.06218i 0.314309 0.544400i
\(125\) −9.00000 −0.804984
\(126\) −12.0000 −1.06904
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) 10.3923i 0.914991i
\(130\) 1.00000 + 1.73205i 0.0877058 + 0.151911i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 1.50000 0.866025i 0.130558 0.0753778i
\(133\) −12.0000 + 20.7846i −1.04053 + 1.80225i
\(134\) 11.0000 0.950255
\(135\) 4.50000 2.59808i 0.387298 0.223607i
\(136\) −12.0000 −1.02899
\(137\) −2.50000 + 4.33013i −0.213589 + 0.369948i −0.952835 0.303488i \(-0.901849\pi\)
0.739246 + 0.673436i \(0.235182\pi\)
\(138\) 6.00000 3.46410i 0.510754 0.294884i
\(139\) 1.00000 + 1.73205i 0.0848189 + 0.146911i 0.905314 0.424743i \(-0.139635\pi\)
−0.820495 + 0.571654i \(0.806302\pi\)
\(140\) 2.00000 + 3.46410i 0.169031 + 0.292770i
\(141\) 12.1244i 1.02105i
\(142\) −4.50000 + 7.79423i −0.377632 + 0.654077i
\(143\) −2.00000 −0.167248
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) 6.00000 0.498273
\(146\) −2.00000 + 3.46410i −0.165521 + 0.286691i
\(147\) 13.5000 + 7.79423i 1.11346 + 0.642857i
\(148\) 1.50000 + 2.59808i 0.123299 + 0.213561i
\(149\) 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i \(-0.114277\pi\)
−0.772399 + 0.635138i \(0.780943\pi\)
\(150\) −6.00000 3.46410i −0.489898 0.282843i
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) −18.0000 −1.45999
\(153\) 6.00000 10.3923i 0.485071 0.840168i
\(154\) 4.00000 0.322329
\(155\) −3.50000 + 6.06218i −0.281127 + 0.486926i
\(156\) 3.46410i 0.277350i
\(157\) 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i \(-0.0765542\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 13.5000 7.79423i 1.07062 0.618123i
\(160\) −2.50000 + 4.33013i −0.197642 + 0.342327i
\(161\) −16.0000 −1.26098
\(162\) 9.00000 0.707107
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) −1.00000 + 1.73205i −0.0780869 + 0.135250i
\(165\) −1.50000 + 0.866025i −0.116775 + 0.0674200i
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 20.7846i 1.60357i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 4.00000 0.306786
\(171\) 9.00000 15.5885i 0.688247 1.19208i
\(172\) −6.00000 −0.457496
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 9.00000 + 5.19615i 0.682288 + 0.393919i
\(175\) 8.00000 + 13.8564i 0.604743 + 1.04745i
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) −10.5000 6.06218i −0.789228 0.455661i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 4.00000 6.92820i 0.296500 0.513553i
\(183\) 0 0
\(184\) −6.00000 10.3923i −0.442326 0.766131i
\(185\) −1.50000 2.59808i −0.110282 0.191014i
\(186\) −10.5000 + 6.06218i −0.769897 + 0.444500i
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) 7.00000 0.510527
\(189\) −18.0000 10.3923i −1.30931 0.755929i
\(190\) 6.00000 0.435286
\(191\) 6.50000 11.2583i 0.470323 0.814624i −0.529101 0.848559i \(-0.677471\pi\)
0.999424 + 0.0339349i \(0.0108039\pi\)
\(192\) −10.5000 + 6.06218i −0.757772 + 0.437500i
\(193\) −2.00000 3.46410i −0.143963 0.249351i 0.785022 0.619467i \(-0.212651\pi\)
−0.928986 + 0.370116i \(0.879318\pi\)
\(194\) 9.50000 + 16.4545i 0.682060 + 1.18136i
\(195\) 3.46410i 0.248069i
\(196\) 4.50000 7.79423i 0.321429 0.556731i
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) −3.00000 −0.213201
\(199\) −3.00000 −0.212664 −0.106332 0.994331i \(-0.533911\pi\)
−0.106332 + 0.994331i \(0.533911\pi\)
\(200\) −6.00000 + 10.3923i −0.424264 + 0.734847i
\(201\) 16.5000 + 9.52628i 1.16382 + 0.671932i
\(202\) 2.00000 + 3.46410i 0.140720 + 0.243733i
\(203\) −12.0000 20.7846i −0.842235 1.45879i
\(204\) −6.00000 3.46410i −0.420084 0.242536i
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) −13.0000 −0.905753
\(207\) 12.0000 0.834058
\(208\) 2.00000 0.138675
\(209\) −3.00000 + 5.19615i −0.207514 + 0.359425i
\(210\) 6.92820i 0.478091i
\(211\) −3.00000 5.19615i −0.206529 0.357718i 0.744090 0.668079i \(-0.232883\pi\)
−0.950619 + 0.310361i \(0.899550\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) −13.5000 + 7.79423i −0.925005 + 0.534052i
\(214\) 9.00000 15.5885i 0.615227 1.06561i
\(215\) 6.00000 0.409197
\(216\) 15.5885i 1.06066i
\(217\) 28.0000 1.90076
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) −6.00000 + 3.46410i −0.405442 + 0.234082i
\(220\) 0.500000 + 0.866025i 0.0337100 + 0.0583874i
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) 5.19615i 0.348743i
\(223\) −8.00000 + 13.8564i −0.535720 + 0.927894i 0.463409 + 0.886145i \(0.346626\pi\)
−0.999128 + 0.0417488i \(0.986707\pi\)
\(224\) 20.0000 1.33631
\(225\) −6.00000 10.3923i −0.400000 0.692820i
\(226\) −15.0000 −0.997785
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) −9.00000 5.19615i −0.596040 0.344124i
\(229\) 3.00000 + 5.19615i 0.198246 + 0.343371i 0.947960 0.318390i \(-0.103142\pi\)
−0.749714 + 0.661762i \(0.769809\pi\)
\(230\) 2.00000 + 3.46410i 0.131876 + 0.228416i
\(231\) 6.00000 + 3.46410i 0.394771 + 0.227921i
\(232\) 9.00000 15.5885i 0.590879 1.02343i
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) −7.00000 −0.456630
\(236\) −3.50000 + 6.06218i −0.227831 + 0.394614i
\(237\) 13.8564i 0.900070i
\(238\) −8.00000 13.8564i −0.518563 0.898177i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 1.50000 0.866025i 0.0968246 0.0559017i
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 1.00000 0.0642824
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 0 0
\(245\) −4.50000 + 7.79423i −0.287494 + 0.497955i
\(246\) 3.00000 1.73205i 0.191273 0.110432i
\(247\) 6.00000 + 10.3923i 0.381771 + 0.661247i
\(248\) 10.5000 + 18.1865i 0.666751 + 1.15485i
\(249\) 20.7846i 1.31717i
\(250\) 4.50000 7.79423i 0.284605 0.492950i
\(251\) 28.0000 1.76734 0.883672 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) −6.00000 + 10.3923i −0.377964 + 0.654654i
\(253\) −4.00000 −0.251478
\(254\) −1.00000 + 1.73205i −0.0627456 + 0.108679i
\(255\) 6.00000 + 3.46410i 0.375735 + 0.216930i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −11.0000 19.0526i −0.686161 1.18847i −0.973070 0.230508i \(-0.925961\pi\)
0.286909 0.957958i \(-0.407372\pi\)
\(258\) 9.00000 + 5.19615i 0.560316 + 0.323498i
\(259\) −6.00000 + 10.3923i −0.372822 + 0.645746i
\(260\) 2.00000 0.124035
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) −6.00000 −0.370681
\(263\) 8.00000 13.8564i 0.493301 0.854423i −0.506669 0.862141i \(-0.669123\pi\)
0.999970 + 0.00771799i \(0.00245674\pi\)
\(264\) 5.19615i 0.319801i
\(265\) 4.50000 + 7.79423i 0.276433 + 0.478796i
\(266\) −12.0000 20.7846i −0.735767 1.27439i
\(267\) −9.00000 + 5.19615i −0.550791 + 0.317999i
\(268\) 5.50000 9.52628i 0.335966 0.581910i
\(269\) −17.0000 −1.03651 −0.518254 0.855227i \(-0.673418\pi\)
−0.518254 + 0.855227i \(0.673418\pi\)
\(270\) 5.19615i 0.316228i
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) 2.00000 3.46410i 0.121268 0.210042i
\(273\) 12.0000 6.92820i 0.726273 0.419314i
\(274\) −2.50000 4.33013i −0.151031 0.261593i
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 6.92820i 0.417029i
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) −2.00000 −0.119952
\(279\) −21.0000 −1.25724
\(280\) −12.0000 −0.717137
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) −10.5000 6.06218i −0.625266 0.360997i
\(283\) −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i \(-0.853740\pi\)
0.0640654 0.997946i \(-0.479593\pi\)
\(284\) 4.50000 + 7.79423i 0.267026 + 0.462502i
\(285\) 9.00000 + 5.19615i 0.533114 + 0.307794i
\(286\) 1.00000 1.73205i 0.0591312 0.102418i
\(287\) −8.00000 −0.472225
\(288\) −15.0000 −0.883883
\(289\) −1.00000 −0.0588235
\(290\) −3.00000 + 5.19615i −0.176166 + 0.305129i
\(291\) 32.9090i 1.92916i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) −6.00000 10.3923i −0.350524 0.607125i 0.635818 0.771839i \(-0.280663\pi\)
−0.986341 + 0.164714i \(0.947330\pi\)
\(294\) −13.5000 + 7.79423i −0.787336 + 0.454569i
\(295\) 3.50000 6.06218i 0.203778 0.352954i
\(296\) −9.00000 −0.523114
\(297\) −4.50000 2.59808i −0.261116 0.150756i
\(298\) −4.00000 −0.231714
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) −6.00000 + 3.46410i −0.346410 + 0.200000i
\(301\) −12.0000 20.7846i −0.691669 1.19800i
\(302\) 8.00000 + 13.8564i 0.460348 + 0.797347i
\(303\) 6.92820i 0.398015i
\(304\) 3.00000 5.19615i 0.172062 0.298020i
\(305\) 0 0
\(306\) 6.00000 + 10.3923i 0.342997 + 0.594089i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) −19.5000 11.2583i −1.10932 0.640464i
\(310\) −3.50000 6.06218i −0.198787 0.344309i
\(311\) 10.5000 + 18.1865i 0.595400 + 1.03126i 0.993490 + 0.113917i \(0.0363399\pi\)
−0.398090 + 0.917346i \(0.630327\pi\)
\(312\) 9.00000 + 5.19615i 0.509525 + 0.294174i
\(313\) −7.00000 + 12.1244i −0.395663 + 0.685309i −0.993186 0.116543i \(-0.962819\pi\)
0.597522 + 0.801852i \(0.296152\pi\)
\(314\) −7.00000 −0.395033
\(315\) 6.00000 10.3923i 0.338062 0.585540i
\(316\) −8.00000 −0.450035
\(317\) −11.0000 + 19.0526i −0.617822 + 1.07010i 0.372061 + 0.928208i \(0.378651\pi\)
−0.989882 + 0.141890i \(0.954682\pi\)
\(318\) 15.5885i 0.874157i
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) −3.50000 6.06218i −0.195656 0.338886i
\(321\) 27.0000 15.5885i 1.50699 0.870063i
\(322\) 8.00000 13.8564i 0.445823 0.772187i
\(323\) 24.0000 1.33540
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 8.00000 0.443760
\(326\) 5.50000 9.52628i 0.304617 0.527612i
\(327\) 3.00000 1.73205i 0.165900 0.0957826i
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) 14.0000 + 24.2487i 0.771845 + 1.33687i
\(330\) 1.73205i 0.0953463i
\(331\) −0.500000 + 0.866025i −0.0274825 + 0.0476011i −0.879440 0.476011i \(-0.842082\pi\)
0.851957 + 0.523612i \(0.175416\pi\)
\(332\) 12.0000 0.658586
\(333\) 4.50000 7.79423i 0.246598 0.427121i
\(334\) 12.0000 0.656611
\(335\) −5.50000 + 9.52628i −0.300497 + 0.520476i
\(336\) −6.00000 3.46410i −0.327327 0.188982i
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) −22.5000 12.9904i −1.22203 0.705541i
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) 7.00000 0.379071
\(342\) 9.00000 + 15.5885i 0.486664 + 0.842927i
\(343\) 8.00000 0.431959
\(344\) 9.00000 15.5885i 0.485247 0.840473i
\(345\) 6.92820i 0.373002i
\(346\) 0 0
\(347\) −2.00000 3.46410i −0.107366 0.185963i 0.807337 0.590091i \(-0.200908\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(348\) 9.00000 5.19615i 0.482451 0.278543i
\(349\) −15.0000 + 25.9808i −0.802932 + 1.39072i 0.114747 + 0.993395i \(0.463394\pi\)
−0.917679 + 0.397324i \(0.869939\pi\)
\(350\) −16.0000 −0.855236
\(351\) −9.00000 + 5.19615i −0.480384 + 0.277350i
\(352\) 5.00000 0.266501
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 10.5000 6.06218i 0.558069 0.322201i
\(355\) −4.50000 7.79423i −0.238835 0.413675i
\(356\) 3.00000 + 5.19615i 0.159000 + 0.275396i
\(357\) 27.7128i 1.46672i
\(358\) 4.50000 7.79423i 0.237832 0.411938i
\(359\) −32.0000 −1.68890 −0.844448 0.535638i \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) 9.00000 0.474342
\(361\) 17.0000 0.894737
\(362\) −3.50000 + 6.06218i −0.183956 + 0.318621i
\(363\) 1.50000 + 0.866025i 0.0787296 + 0.0454545i
\(364\) −4.00000 6.92820i −0.209657 0.363137i
\(365\) −2.00000 3.46410i −0.104685 0.181319i
\(366\) 0 0
\(367\) 5.50000 9.52628i 0.287098 0.497268i −0.686018 0.727585i \(-0.740643\pi\)
0.973116 + 0.230317i \(0.0739762\pi\)
\(368\) 4.00000 0.208514
\(369\) 6.00000 0.312348
\(370\) 3.00000 0.155963
\(371\) 18.0000 31.1769i 0.934513 1.61862i
\(372\) 12.1244i 0.628619i
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) −2.00000 3.46410i −0.103418 0.179124i
\(375\) 13.5000 7.79423i 0.697137 0.402492i
\(376\) −10.5000 + 18.1865i −0.541496 + 0.937899i
\(377\) −12.0000 −0.618031
\(378\) 18.0000 10.3923i 0.925820 0.534522i
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 3.00000 5.19615i 0.153897 0.266557i
\(381\) −3.00000 + 1.73205i −0.153695 + 0.0887357i
\(382\) 6.50000 + 11.2583i 0.332569 + 0.576026i
\(383\) −14.5000 25.1147i −0.740915 1.28330i −0.952079 0.305852i \(-0.901059\pi\)
0.211164 0.977451i \(-0.432275\pi\)
\(384\) 5.19615i 0.265165i
\(385\) −2.00000 + 3.46410i −0.101929 + 0.176547i
\(386\) 4.00000 0.203595
\(387\) 9.00000 + 15.5885i 0.457496 + 0.792406i
\(388\) 19.0000 0.964579
\(389\) −16.5000 + 28.5788i −0.836583 + 1.44900i 0.0561516 + 0.998422i \(0.482117\pi\)
−0.892735 + 0.450582i \(0.851216\pi\)
\(390\) −3.00000 1.73205i −0.151911 0.0877058i
\(391\) 8.00000 + 13.8564i 0.404577 + 0.700749i
\(392\) 13.5000 + 23.3827i 0.681853 + 1.18100i
\(393\) −9.00000 5.19615i −0.453990 0.262111i
\(394\) −8.00000 + 13.8564i −0.403034 + 0.698076i
\(395\) 8.00000 0.402524
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) 1.50000 2.59808i 0.0751882 0.130230i
\(399\) 41.5692i 2.08106i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −8.50000 14.7224i −0.424470 0.735203i 0.571901 0.820323i \(-0.306206\pi\)
−0.996371 + 0.0851195i \(0.972873\pi\)
\(402\) −16.5000 + 9.52628i −0.822945 + 0.475128i
\(403\) 7.00000 12.1244i 0.348695 0.603957i
\(404\) 4.00000 0.199007
\(405\) −4.50000 + 7.79423i −0.223607 + 0.387298i
\(406\) 24.0000 1.19110
\(407\) −1.50000 + 2.59808i −0.0743522 + 0.128782i
\(408\) 18.0000 10.3923i 0.891133 0.514496i
\(409\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(410\) 1.00000 + 1.73205i 0.0493865 + 0.0855399i
\(411\) 8.66025i 0.427179i
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) −28.0000 −1.37779
\(414\) −6.00000 + 10.3923i −0.294884 + 0.510754i
\(415\) −12.0000 −0.589057
\(416\) 5.00000 8.66025i 0.245145 0.424604i
\(417\) −3.00000 1.73205i −0.146911 0.0848189i
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −2.50000 4.33013i −0.122133 0.211541i 0.798476 0.602027i \(-0.205640\pi\)
−0.920609 + 0.390487i \(0.872307\pi\)
\(420\) −6.00000 3.46410i −0.292770 0.169031i
\(421\) −6.50000 + 11.2583i −0.316791 + 0.548697i −0.979817 0.199899i \(-0.935939\pi\)
0.663026 + 0.748596i \(0.269272\pi\)
\(422\) 6.00000 0.292075
\(423\) −10.5000 18.1865i −0.510527 0.884260i
\(424\) 27.0000 1.31124
\(425\) 8.00000 13.8564i 0.388057 0.672134i
\(426\) 15.5885i 0.755263i
\(427\) 0 0
\(428\) −9.00000 15.5885i −0.435031 0.753497i
\(429\) 3.00000 1.73205i 0.144841 0.0836242i
\(430\) −3.00000 + 5.19615i −0.144673 + 0.250581i
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) −14.0000 + 24.2487i −0.672022 + 1.16398i
\(435\) −9.00000 + 5.19615i −0.431517 + 0.249136i
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) 6.92820i 0.331042i
\(439\) 7.00000 12.1244i 0.334092 0.578664i −0.649218 0.760602i \(-0.724904\pi\)
0.983310 + 0.181938i \(0.0582371\pi\)
\(440\) −3.00000 −0.143019
\(441\) −27.0000 −1.28571
\(442\) −8.00000 −0.380521
\(443\) −0.500000 + 0.866025i −0.0237557 + 0.0411461i −0.877659 0.479286i \(-0.840896\pi\)
0.853903 + 0.520432i \(0.174229\pi\)
\(444\) −4.50000 2.59808i −0.213561 0.123299i
\(445\) −3.00000 5.19615i −0.142214 0.246321i
\(446\) −8.00000 13.8564i −0.378811 0.656120i
\(447\) −6.00000 3.46410i −0.283790 0.163846i
\(448\) −14.0000 + 24.2487i −0.661438 + 1.14564i
\(449\) 23.0000 1.08544 0.542719 0.839915i \(-0.317395\pi\)
0.542719 + 0.839915i \(0.317395\pi\)
\(450\) 12.0000 0.565685
\(451\) −2.00000 −0.0941763
\(452\) −7.50000 + 12.9904i −0.352770 + 0.611016i
\(453\) 27.7128i 1.30206i
\(454\) 9.00000 + 15.5885i 0.422391 + 0.731603i
\(455\) 4.00000 + 6.92820i 0.187523 + 0.324799i
\(456\) 27.0000 15.5885i 1.26439 0.729996i
\(457\) 3.00000 5.19615i 0.140334 0.243066i −0.787288 0.616585i \(-0.788516\pi\)
0.927622 + 0.373519i \(0.121849\pi\)
\(458\) −6.00000 −0.280362
\(459\) 20.7846i 0.970143i
\(460\) 4.00000 0.186501
\(461\) 6.00000 10.3923i 0.279448 0.484018i −0.691800 0.722089i \(-0.743182\pi\)
0.971248 + 0.238071i \(0.0765153\pi\)
\(462\) −6.00000 + 3.46410i −0.279145 + 0.161165i
\(463\) 4.00000 + 6.92820i 0.185896 + 0.321981i 0.943878 0.330294i \(-0.107148\pi\)
−0.757982 + 0.652275i \(0.773815\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 12.1244i 0.562254i
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 3.00000 + 5.19615i 0.138675 + 0.240192i
\(469\) 44.0000 2.03173
\(470\) 3.50000 6.06218i 0.161443 0.279627i
\(471\) −10.5000 6.06218i −0.483814 0.279330i
\(472\) −10.5000 18.1865i −0.483302 0.837103i
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 12.0000 + 6.92820i 0.551178 + 0.318223i
\(475\) 12.0000 20.7846i 0.550598 0.953663i
\(476\) −16.0000 −0.733359
\(477\) −13.5000 + 23.3827i −0.618123 + 1.07062i
\(478\) 6.00000 0.274434
\(479\) 2.00000 3.46410i 0.0913823 0.158279i −0.816711 0.577047i \(-0.804205\pi\)
0.908093 + 0.418769i \(0.137538\pi\)
\(480\) 8.66025i 0.395285i
\(481\) 3.00000 + 5.19615i 0.136788 + 0.236924i
\(482\) −5.00000 8.66025i −0.227744 0.394464i
\(483\) 24.0000 13.8564i 1.09204 0.630488i
\(484\) 0.500000 0.866025i 0.0227273 0.0393648i
\(485\) −19.0000 −0.862746
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) −37.0000 −1.67663 −0.838315 0.545186i \(-0.816459\pi\)
−0.838315 + 0.545186i \(0.816459\pi\)
\(488\) 0 0
\(489\) 16.5000 9.52628i 0.746156 0.430793i
\(490\) −4.50000 7.79423i −0.203289 0.352107i
\(491\) 4.00000 + 6.92820i 0.180517 + 0.312665i 0.942057 0.335453i \(-0.108889\pi\)
−0.761539 + 0.648119i \(0.775556\pi\)
\(492\) 3.46410i 0.156174i
\(493\) −12.0000 + 20.7846i −0.540453 + 0.936092i
\(494\) −12.0000 −0.539906
\(495\) 1.50000 2.59808i 0.0674200 0.116775i
\(496\) −7.00000 −0.314309
\(497\) −18.0000 + 31.1769i −0.807410 + 1.39848i
\(498\) −18.0000 10.3923i −0.806599 0.465690i
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) −4.50000 7.79423i −0.201246 0.348569i
\(501\) 18.0000 + 10.3923i 0.804181 + 0.464294i
\(502\) −14.0000 + 24.2487i −0.624851 + 1.08227i
\(503\) −14.0000 −0.624229 −0.312115 0.950044i \(-0.601037\pi\)
−0.312115 + 0.950044i \(0.601037\pi\)
\(504\) −18.0000 31.1769i −0.801784 1.38873i
\(505\) −4.00000 −0.177998
\(506\) 2.00000 3.46410i 0.0889108 0.153998i
\(507\) 15.5885i 0.692308i
\(508\) 1.00000 + 1.73205i 0.0443678 + 0.0768473i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) −6.00000 + 3.46410i −0.265684 + 0.153393i
\(511\) −8.00000 + 13.8564i −0.353899 + 0.612971i
\(512\) −11.0000 −0.486136
\(513\) 31.1769i 1.37649i
\(514\) 22.0000 0.970378
\(515\) 6.50000 11.2583i 0.286424 0.496101i
\(516\) 9.00000 5.19615i 0.396203 0.228748i
\(517\) 3.50000 + 6.06218i 0.153930 + 0.266614i
\(518\) −6.00000 10.3923i −0.263625 0.456612i
\(519\) 0 0
\(520\) −3.00000 + 5.19615i −0.131559 + 0.227866i
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) −18.0000 −0.787839
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −3.00000 + 5.19615i −0.131056 + 0.226995i
\(525\) −24.0000 13.8564i −1.04745 0.604743i
\(526\) 8.00000 + 13.8564i 0.348817 + 0.604168i
\(527\) −14.0000 24.2487i −0.609850 1.05629i
\(528\) −1.50000 0.866025i −0.0652791 0.0376889i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −9.00000 −0.390935
\(531\) 21.0000 0.911322
\(532\) −24.0000 −1.04053
\(533\) −2.00000 + 3.46410i −0.0866296 + 0.150047i
\(534\) 10.3923i 0.449719i
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) 16.5000 + 28.5788i 0.712691 + 1.23442i
\(537\) 13.5000 7.79423i 0.582568 0.336346i
\(538\) 8.50000 14.7224i 0.366461 0.634729i
\(539\) 9.00000 0.387657
\(540\) 4.50000 + 2.59808i 0.193649 + 0.111803i
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 11.0000 19.0526i 0.472490 0.818377i
\(543\) −10.5000 + 6.06218i −0.450598 + 0.260153i
\(544\) −10.0000 17.3205i −0.428746 0.742611i
\(545\) 1.00000 + 1.73205i 0.0428353 + 0.0741929i
\(546\) 13.8564i 0.592999i
\(547\) 11.0000 19.0526i 0.470326 0.814629i −0.529098 0.848561i \(-0.677470\pi\)
0.999424 + 0.0339321i \(0.0108030\pi\)
\(548\) −5.00000 −0.213589
\(549\) 0 0
\(550\) −4.00000 −0.170561
\(551\) −18.0000 + 31.1769i −0.766826 + 1.32818i
\(552\) 18.0000 + 10.3923i 0.766131 + 0.442326i
\(553\) −16.0000 27.7128i −0.680389 1.17847i
\(554\) 1.00000 + 1.73205i 0.0424859 + 0.0735878i
\(555\) 4.50000 + 2.59808i 0.191014 + 0.110282i
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 40.0000 1.69485 0.847427 0.530912i \(-0.178150\pi\)
0.847427 + 0.530912i \(0.178150\pi\)
\(558\) 10.5000 18.1865i 0.444500 0.769897i
\(559\) −12.0000 −0.507546
\(560\) 2.00000 3.46410i 0.0845154 0.146385i
\(561\) 6.92820i 0.292509i
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) 7.00000 + 12.1244i 0.295015 + 0.510981i 0.974988 0.222256i \(-0.0713421\pi\)
−0.679974 + 0.733237i \(0.738009\pi\)
\(564\) −10.5000 + 6.06218i −0.442130 + 0.255264i
\(565\) 7.50000 12.9904i 0.315527 0.546509i
\(566\) 28.0000 1.17693
\(567\) 36.0000 1.51186
\(568\) −27.0000 −1.13289
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) −9.00000 + 5.19615i −0.376969 + 0.217643i
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −1.00000 1.73205i −0.0418121 0.0724207i
\(573\) 22.5167i 0.940647i
\(574\) 4.00000 6.92820i 0.166957 0.289178i
\(575\) 16.0000 0.667246
\(576\) 10.5000 18.1865i 0.437500 0.757772i
\(577\) −3.00000 −0.124892 −0.0624458 0.998048i \(-0.519890\pi\)
−0.0624458 + 0.998048i \(0.519890\pi\)
\(578\) 0.500000 0.866025i 0.0207973 0.0360219i
\(579\) 6.00000 + 3.46410i 0.249351 + 0.143963i
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) 24.0000 + 41.5692i 0.995688 + 1.72458i
\(582\) −28.5000 16.4545i −1.18136 0.682060i
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) −12.0000 −0.496564
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) 12.0000 0.495715
\(587\) 2.50000 4.33013i 0.103186 0.178723i −0.809810 0.586693i \(-0.800430\pi\)
0.912996 + 0.407969i \(0.133763\pi\)
\(588\) 15.5885i 0.642857i
\(589\) −21.0000 36.3731i −0.865290 1.49873i
\(590\) 3.50000 + 6.06218i 0.144093 + 0.249576i
\(591\) −24.0000 + 13.8564i −0.987228 + 0.569976i
\(592\) 1.50000 2.59808i 0.0616496 0.106780i
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 4.50000 2.59808i 0.184637 0.106600i
\(595\) 16.0000 0.655936
\(596\) −2.00000 + 3.46410i −0.0819232 + 0.141895i
\(597\) 4.50000 2.59808i 0.184173 0.106332i
\(598\) −4.00000 6.92820i −0.163572 0.283315i
\(599\) −2.00000 3.46410i −0.0817178 0.141539i 0.822270 0.569097i \(-0.192707\pi\)
−0.903988 + 0.427558i \(0.859374\pi\)
\(600\) 20.7846i 0.848528i
\(601\) −1.00000 + 1.73205i −0.0407909 + 0.0706518i −0.885700 0.464258i \(-0.846321\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(602\) 24.0000 0.978167
\(603\) −33.0000 −1.34386
\(604\) 16.0000 0.651031
\(605\) −0.500000 + 0.866025i −0.0203279 + 0.0352089i
\(606\) −6.00000 3.46410i −0.243733 0.140720i
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) −15.0000 25.9808i −0.608330 1.05366i
\(609\) 36.0000 + 20.7846i 1.45879 + 0.842235i
\(610\) 0 0
\(611\) 14.0000 0.566379
\(612\) 12.0000 0.485071
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) 3.46410i 0.139686i
\(616\) 6.00000 + 10.3923i 0.241747 + 0.418718i
\(617\) 7.50000 + 12.9904i 0.301939 + 0.522973i 0.976575 0.215177i \(-0.0690329\pi\)
−0.674636 + 0.738150i \(0.735700\pi\)
\(618\) 19.5000 11.2583i 0.784405 0.452876i
\(619\) 12.5000 21.6506i 0.502417 0.870212i −0.497579 0.867419i \(-0.665777\pi\)
0.999996 0.00279365i \(-0.000889247\pi\)
\(620\) −7.00000 −0.281127
\(621\) −18.0000 + 10.3923i −0.722315 + 0.417029i
\(622\) −21.0000 −0.842023
\(623\) −12.0000 + 20.7846i −0.480770 + 0.832718i
\(624\) −3.00000 + 1.73205i −0.120096 + 0.0693375i
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) −7.00000 12.1244i −0.279776 0.484587i
\(627\) 10.3923i 0.415029i
\(628\) −3.50000 + 6.06218i −0.139665 + 0.241907i
\(629\) 12.0000 0.478471
\(630\) 6.00000 + 10.3923i 0.239046 + 0.414039i
\(631\) 37.0000 1.47295 0.736473 0.676467i \(-0.236490\pi\)
0.736473 + 0.676467i \(0.236490\pi\)
\(632\) 12.0000 20.7846i 0.477334 0.826767i
\(633\) 9.00000 + 5.19615i 0.357718 + 0.206529i
\(634\) −11.0000 19.0526i −0.436866 0.756674i
\(635\) −1.00000 1.73205i −0.0396838 0.0687343i
\(636\) 13.5000 + 7.79423i 0.535310 + 0.309061i
\(637\) 9.00000 15.5885i 0.356593 0.617637i
\(638\) 6.00000 0.237542
\(639\) 13.5000 23.3827i 0.534052 0.925005i
\(640\) −3.00000 −0.118585
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 31.1769i 1.23045i
\(643\) 8.00000 + 13.8564i 0.315489 + 0.546443i 0.979541 0.201243i \(-0.0644981\pi\)
−0.664052 + 0.747686i \(0.731165\pi\)
\(644\) −8.00000 13.8564i −0.315244 0.546019i
\(645\) −9.00000 + 5.19615i −0.354375 + 0.204598i
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 13.5000 + 23.3827i 0.530330 + 0.918559i
\(649\) −7.00000 −0.274774
\(650\) −4.00000 + 6.92820i −0.156893 + 0.271746i
\(651\) −42.0000 + 24.2487i −1.64611 + 0.950382i
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) −15.5000 26.8468i −0.606562 1.05060i −0.991803 0.127780i \(-0.959215\pi\)
0.385241 0.922816i \(-0.374118\pi\)
\(654\) 3.46410i 0.135457i
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) 2.00000 0.0780869
\(657\) 6.00000 10.3923i 0.234082 0.405442i
\(658\) −28.0000 −1.09155
\(659\) −17.0000 + 29.4449i −0.662226 + 1.14701i 0.317803 + 0.948157i \(0.397055\pi\)
−0.980029 + 0.198852i \(0.936279\pi\)
\(660\) −1.50000 0.866025i −0.0583874 0.0337100i
\(661\) −24.5000 42.4352i −0.952940 1.65054i −0.739014 0.673690i \(-0.764708\pi\)
−0.213925 0.976850i \(-0.568625\pi\)
\(662\) −0.500000 0.866025i −0.0194331 0.0336590i
\(663\) −12.0000 6.92820i −0.466041 0.269069i
\(664\) −18.0000 + 31.1769i −0.698535 + 1.20990i
\(665\) 24.0000 0.930680
\(666\) 4.50000 + 7.79423i 0.174371 + 0.302020i
\(667\) −24.0000 −0.929284
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 27.7128i 1.07144i
\(670\) −5.50000 9.52628i −0.212484 0.368032i
\(671\) 0 0
\(672\) −30.0000 + 17.3205i −1.15728 + 0.668153i
\(673\) 11.0000 19.0526i 0.424019 0.734422i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856156i \(0.0272857\pi\)
\(674\) −22.0000 −0.847408
\(675\) 18.0000 + 10.3923i 0.692820 + 0.400000i
\(676\) 9.00000 0.346154
\(677\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 22.5000 12.9904i 0.864107 0.498893i
\(679\) 38.0000 + 65.8179i 1.45831 + 2.52586i
\(680\) 6.00000 + 10.3923i 0.230089 + 0.398527i
\(681\) 31.1769i 1.19470i
\(682\) −3.50000 + 6.06218i −0.134022 + 0.232133i
\(683\) 5.00000 0.191320 0.0956598 0.995414i \(-0.469504\pi\)
0.0956598 + 0.995414i \(0.469504\pi\)
\(684\) 18.0000 0.688247
\(685\) 5.00000 0.191040
\(686\) −4.00000 + 6.92820i −0.152721 + 0.264520i
\(687\) −9.00000 5.19615i −0.343371 0.198246i
\(688\) 3.00000 + 5.19615i 0.114374 + 0.198101i
\(689\) −9.00000 15.5885i −0.342873 0.593873i
\(690\) −6.00000 3.46410i −0.228416 0.131876i
\(691\) −17.5000 + 30.3109i −0.665731 + 1.15308i 0.313355 + 0.949636i \(0.398547\pi\)
−0.979086 + 0.203445i \(0.934786\pi\)
\(692\) 0 0
\(693\) −12.0000 −0.455842
\(694\) 4.00000 0.151838
\(695\) 1.00000 1.73205i 0.0379322 0.0657004i
\(696\) 31.1769i 1.18176i
\(697\) 4.00000 + 6.92820i 0.151511 + 0.262424i
\(698\) −15.0000 25.9808i −0.567758 0.983386i
\(699\) −36.0000 + 20.7846i −1.36165 + 0.786146i
\(700\) −8.00000 + 13.8564i −0.302372 + 0.523723i
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 10.3923i 0.392232i
\(703\) 18.0000 0.678883
\(704\) −3.50000 + 6.06218i −0.131911 + 0.228477i
\(705\) 10.5000 6.06218i 0.395453 0.228315i
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) 8.00000 + 13.8564i 0.300871 + 0.521124i
\(708\) 12.1244i 0.455661i
\(709\) 6.50000 11.2583i 0.244113 0.422815i −0.717769 0.696281i \(-0.754837\pi\)
0.961882 + 0.273466i \(0.0881700\pi\)
\(710\) 9.00000 0.337764
\(711\) 12.0000 + 20.7846i 0.450035 + 0.779484i
\(712\) −18.0000 −0.674579
\(713\) 14.0000 24.2487i 0.524304 0.908121i
\(714\) 24.0000 + 13.8564i 0.898177 + 0.518563i
\(715\) 1.00000 + 1.73205i 0.0373979 + 0.0647750i
\(716\) −4.50000 7.79423i −0.168173 0.291284i
\(717\) 9.00000 + 5.19615i 0.336111 + 0.194054i
\(718\) 16.0000 27.7128i 0.597115 1.03423i
\(719\) −15.0000 −0.559406 −0.279703 0.960087i \(-0.590236\pi\)
−0.279703 + 0.960087i \(0.590236\pi\)
\(720\) −1.50000 + 2.59808i −0.0559017 + 0.0968246i
\(721\) −52.0000 −1.93658
\(722\) −8.50000 + 14.7224i −0.316337 + 0.547912i
\(723\) 17.3205i 0.644157i
\(724\) 3.50000 + 6.06218i 0.130076 + 0.225299i
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) −1.50000 + 0.866025i −0.0556702 + 0.0321412i
\(727\) 16.5000 28.5788i 0.611951 1.05993i −0.378960 0.925413i \(-0.623718\pi\)
0.990911 0.134517i \(-0.0429484\pi\)
\(728\) 24.0000 0.889499
\(729\) −27.0000 −1.00000
\(730\) 4.00000 0.148047
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 0 0
\(733\) 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) 5.50000 + 9.52628i 0.203009 + 0.351621i
\(735\) 15.5885i 0.574989i
\(736\) 10.0000 17.3205i 0.368605 0.638442i
\(737\) 11.0000 0.405190
\(738\) −3.00000 + 5.19615i −0.110432 + 0.191273i
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 1.50000 2.59808i 0.0551411 0.0955072i
\(741\) −18.0000 10.3923i −0.661247 0.381771i
\(742\) 18.0000 + 31.1769i 0.660801 + 1.14454i
\(743\) 25.0000 + 43.3013i 0.917161 + 1.58857i 0.803706 + 0.595026i \(0.202858\pi\)
0.113455 + 0.993543i \(0.463808\pi\)
\(744\) −31.5000 18.1865i −1.15485 0.666751i
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) 10.0000 0.366126
\(747\) −18.0000 31.1769i −0.658586 1.14070i
\(748\) −4.00000 −0.146254
\(749\) 36.0000 62.3538i 1.31541 2.27836i
\(750\) 15.5885i 0.569210i
\(751\) 5.50000 + 9.52628i 0.200698 + 0.347619i 0.948753 0.316017i \(-0.102346\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(752\) −3.50000 6.06218i −0.127632 0.221065i
\(753\) −42.0000 + 24.2487i −1.53057 + 0.883672i
\(754\) 6.00000 10.3923i 0.218507 0.378465i
\(755\) −16.0000 −0.582300
\(756\) 20.7846i 0.755929i
\(757\) −19.0000 −0.690567 −0.345283 0.938498i \(-0.612217\pi\)
−0.345283 + 0.938498i \(0.612217\pi\)
\(758\) −8.00000 + 13.8564i −0.290573 + 0.503287i
\(759\) 6.00000 3.46410i 0.217786 0.125739i
\(760\) 9.00000 + 15.5885i 0.326464 + 0.565453i
\(761\) −18.0000 31.1769i −0.652499 1.13016i −0.982514 0.186187i \(-0.940387\pi\)
0.330015 0.943976i \(-0.392946\pi\)
\(762\) 3.46410i 0.125491i
\(763\) 4.00000 6.92820i 0.144810 0.250818i
\(764\) 13.0000 0.470323
\(765\) −12.0000 −0.433861
\(766\) 29.0000 1.04781
\(767\) −7.00000 + 12.1244i −0.252755 + 0.437785i
\(768\) −25.5000 14.7224i −0.920152 0.531250i
\(769\) 8.00000 + 13.8564i 0.288487 + 0.499675i 0.973449 0.228904i \(-0.0735143\pi\)
−0.684962 + 0.728579i \(0.740181\pi\)
\(770\) −2.00000 3.46410i −0.0720750 0.124838i
\(771\) 33.0000 + 19.0526i 1.18847 + 0.686161i
\(772\) 2.00000 3.46410i 0.0719816 0.124676i
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) −18.0000 −0.646997
\(775\) −28.0000 −1.00579
\(776\) −28.5000 + 49.3634i −1.02309 + 1.77204i
\(777\) 20.7846i 0.745644i
\(778\) −16.5000 28.5788i −0.591554 1.02460i
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) −3.00000 + 1.73205i −0.107417 + 0.0620174i
\(781\) −4.50000 + 7.79423i −0.161023 + 0.278899i
\(782\) −16.0000 −0.572159
\(783\) −27.0000 15.5885i −0.964901 0.557086i
\(784\) −9.00000 −0.321429
\(785\) 3.50000 6.06218i 0.124920 0.216368i
\(786\) 9.00000 5.19615i 0.321019 0.185341i
\(787\) 7.00000 + 12.1244i 0.249523 + 0.432187i 0.963394 0.268091i \(-0.0863928\pi\)
−0.713871 + 0.700278i \(0.753059\pi\)
\(788\) 8.00000 + 13.8564i 0.284988 + 0.493614i
\(789\) 27.7128i 0.986602i
\(790\) −4.00000 + 6.92820i −0.142314 + 0.246494i
\(791\) −60.0000 −2.13335
\(792\) −4.50000 7.79423i −0.159901 0.276956i
\(793\) 0 0
\(794\) −6.50000 + 11.2583i −0.230676 + 0.399543i
\(795\) −13.5000 7.79423i −0.478796 0.276433i
\(796\) −1.50000 2.59808i −0.0531661 0.0920864i
\(797\) −2.50000 4.33013i −0.0885545 0.153381i 0.818346 0.574726i \(-0.194891\pi\)
−0.906900 + 0.421345i \(0.861558\pi\)
\(798\) 36.0000 + 20.7846i 1.27439 + 0.735767i
\(799\) 14.0000 24.2487i 0.495284 0.857858i
\(800\) −20.0000 −0.707107
\(801\) 9.00000 15.5885i 0.317999 0.550791i
\(802\) 17.0000 0.600291
\(803\) −2.00000 + 3.46410i −0.0705785 + 0.122245i
\(804\) 19.0526i 0.671932i
\(805\) 8.00000 + 13.8564i 0.281963 + 0.488374i
\(806\) 7.00000 + 12.1244i 0.246564 + 0.427062i
\(807\) 25.5000 14.7224i 0.897643 0.518254i
\(808\) −6.00000 + 10.3923i −0.211079 + 0.365600i
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) −4.50000 7.79423i −0.158114 0.273861i
\(811\) −14.0000 −0.491606 −0.245803 0.969320i \(-0.579052\pi\)
−0.245803 + 0.969320i \(0.579052\pi\)
\(812\) 12.0000 20.7846i 0.421117 0.729397i
\(813\) 33.0000 19.0526i 1.15736 0.668202i
\(814\) −1.50000 2.59808i −0.0525750 0.0910625i
\(815\) 5.50000 + 9.52628i 0.192657 + 0.333691i
\(816\) 6.92820i 0.242536i
\(817\) −18.0000 + 31.1769i −0.629740 + 1.09074i
\(818\) 0 0
\(819\) −12.0000 + 20.7846i −0.419314 + 0.726273i
\(820\) 2.00000 0.0698430
\(821\) 10.0000 17.3205i 0.349002 0.604490i −0.637070 0.770806i \(-0.719854\pi\)
0.986073 + 0.166316i \(0.0531872\pi\)
\(822\) 7.50000 + 4.33013i 0.261593 + 0.151031i
\(823\) 12.0000 + 20.7846i 0.418294 + 0.724506i 0.995768 0.0919029i \(-0.0292950\pi\)
−0.577474 + 0.816409i \(0.695962\pi\)
\(824\) −19.5000 33.7750i −0.679315 1.17661i
\(825\) −6.00000 3.46410i −0.208893 0.120605i
\(826\) 14.0000 24.2487i 0.487122 0.843721i
\(827\) −40.0000 −1.39094 −0.695468 0.718557i \(-0.744803\pi\)
−0.695468 + 0.718557i \(0.744803\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) 25.0000 0.868286 0.434143 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(830\) 6.00000 10.3923i 0.208263 0.360722i
\(831\) 3.46410i 0.120168i
\(832\) 7.00000 + 12.1244i 0.242681 + 0.420336i
\(833\) −18.0000 31.1769i −0.623663 1.08022i
\(834\) 3.00000 1.73205i 0.103882 0.0599760i
\(835\) −6.00000 + 10.3923i −0.207639 + 0.359641i
\(836\) −6.00000 −0.207514
\(837\) 31.5000 18.1865i 1.08880 0.628619i
\(838\) 5.00000 0.172722
\(839\) −8.00000 + 13.8564i −0.276191 + 0.478376i −0.970435 0.241363i \(-0.922405\pi\)
0.694244 + 0.719740i \(0.255739\pi\)
\(840\) 18.0000 10.3923i 0.621059 0.358569i
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) −6.50000 11.2583i −0.224005 0.387988i
\(843\) 10.3923i 0.357930i
\(844\) 3.00000 5.19615i 0.103264 0.178859i
\(845\) −9.00000 −0.309609
\(846\) 21.0000 0.721995
\(847\) 4.00000 0.137442
\(848\) −4.50000 + 7.79423i −0.154531 + 0.267655i
\(849\) 42.0000 + 24.2487i 1.44144 + 0.832214i
\(850\) 8.00000 + 13.8564i 0.274398 + 0.475271i
\(851\) 6.00000 + 10.3923i 0.205677 + 0.356244i
\(852\) −13.5000 7.79423i −0.462502 0.267026i
\(853\) −1.00000 + 1.73205i −0.0342393 + 0.0593043i −0.882637 0.470055i \(-0.844234\pi\)
0.848398 + 0.529359i \(0.177568\pi\)
\(854\) 0 0
\(855\) −18.0000 −0.615587
\(856\) 54.0000 1.84568
\(857\) −19.0000 + 32.9090i −0.649028 + 1.12415i 0.334328 + 0.942457i \(0.391491\pi\)
−0.983355 + 0.181692i \(0.941843\pi\)
\(858\) 3.46410i 0.118262i
\(859\) −7.50000 12.9904i −0.255897 0.443226i 0.709242 0.704965i \(-0.249037\pi\)
−0.965139 + 0.261739i \(0.915704\pi\)
\(860\) 3.00000 + 5.19615i 0.102299 + 0.177187i
\(861\) 12.0000 6.92820i 0.408959 0.236113i
\(862\) 15.0000 25.9808i 0.510902 0.884908i
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 22.5000 12.9904i 0.765466 0.441942i
\(865\) 0 0
\(866\) 7.00000 12.1244i 0.237870 0.412002i
\(867\) 1.50000 0.866025i 0.0509427 0.0294118i
\(868\) 14.0000 + 24.2487i 0.475191 + 0.823055i
\(869\) −4.00000 6.92820i −0.135691 0.235023i
\(870\) 10.3923i 0.352332i
\(871\) 11.0000 19.0526i 0.372721 0.645571i
\(872\) 6.00000 0.203186
\(873\) −28.5000 49.3634i −0.964579 1.67070i
\(874\) −24.0000 −0.811812
\(875\) 18.0000 31.1769i 0.608511 1.05397i
\(876\) −6.00000 3.46410i −0.202721 0.117041i
\(877\) 9.00000 + 15.5885i 0.303908 + 0.526385i 0.977018 0.213158i \(-0.0683750\pi\)
−0.673109 + 0.739543i \(0.735042\pi\)
\(878\) 7.00000 + 12.1244i 0.236239 + 0.409177i
\(879\) 18.0000 + 10.3923i 0.607125 + 0.350524i
\(880\) 0.500000 0.866025i 0.0168550 0.0291937i
\(881\) −7.00000 −0.235836 −0.117918 0.993023i \(-0.537622\pi\)
−0.117918 + 0.993023i \(0.537622\pi\)
\(882\) 13.5000 23.3827i 0.454569 0.787336i
\(883\) −5.00000 −0.168263 −0.0841317 0.996455i \(-0.526812\pi\)
−0.0841317 + 0.996455i \(0.526812\pi\)
\(884\) −4.00000 + 6.92820i −0.134535 + 0.233021i
\(885\) 12.1244i 0.407556i
\(886\) −0.500000 0.866025i −0.0167978 0.0290947i
\(887\) −4.00000 6.92820i −0.134307 0.232626i 0.791026 0.611783i \(-0.209547\pi\)
−0.925332 + 0.379157i \(0.876214\pi\)
\(888\) 13.5000 7.79423i 0.453030 0.261557i
\(889\) −4.00000 + 6.92820i −0.134156 + 0.232364i
\(890\) 6.00000 0.201120
\(891\) 9.00000 0.301511
\(892\) −16.0000 −0.535720
\(893\) 21.0000 36.3731i 0.702738 1.21718i
\(894\) 6.00000 3.46410i 0.200670 0.115857i
\(895\) 4.50000 + 7.79423i 0.150418 + 0.260532i
\(896\) 6.00000 + 10.3923i 0.200446 + 0.347183i
\(897\) 13.8564i 0.462652i
\(898\) −11.5000 + 19.9186i −0.383760 + 0.664692i
\(899\) 42.0000 1.40078
\(900\) 6.00000 10.3923i 0.200000 0.346410i
\(901\) −36.0000 −1.19933
\(902\) 1.00000 1.73205i 0.0332964 0.0576710i
\(903\) 36.0000 + 20.7846i 1.19800 + 0.691669i
\(904\) −22.5000 38.9711i −0.748339 1.29616i
\(905\) −3.50000 6.06218i −0.116344 0.201514i
\(906\) −24.0000 13.8564i −0.797347 0.460348i
\(907\) −6.00000 + 10.3923i −0.199227 + 0.345071i −0.948278 0.317441i \(-0.897176\pi\)
0.749051 + 0.662512i \(0.230510\pi\)
\(908\) 18.0000 0.597351
\(909\) −6.00000 10.3923i −0.199007 0.344691i
\(910\) −8.00000 −0.265197
\(911\) −13.5000 + 23.3827i −0.447275 + 0.774703i −0.998208 0.0598468i \(-0.980939\pi\)
0.550933 + 0.834550i \(0.314272\pi\)
\(912\) 10.3923i 0.344124i
\(913\) 6.00000 + 10.3923i 0.198571 + 0.343935i
\(914\) 3.00000 + 5.19615i 0.0992312 + 0.171873i
\(915\) 0 0
\(916\) −3.00000 + 5.19615i −0.0991228 + 0.171686i
\(917\) −24.0000 −0.792550
\(918\) −18.0000 10.3923i −0.594089 0.342997i
\(919\) 52.0000 1.71532 0.857661 0.514216i \(-0.171917\pi\)
0.857661 + 0.514216i \(0.171917\pi\)
\(920\) −6.00000 + 10.3923i −0.197814 + 0.342624i
\(921\) 42.0000 24.2487i 1.38395 0.799022i
\(922\) 6.00000 + 10.3923i 0.197599 + 0.342252i
\(923\) 9.00000 + 15.5885i 0.296239 + 0.513100i
\(924\) 6.92820i 0.227921i
\(925\) 6.00000 10.3923i 0.197279 0.341697i
\(926\) −8.00000 −0.262896
\(927\) 39.0000 1.28093
\(928\) 30.0000 0.984798
\(929\) −10.5000 + 18.1865i −0.344494 + 0.596681i −0.985262 0.171054i \(-0.945283\pi\)
0.640768 + 0.767735i \(0.278616\pi\)
\(930\) 10.5000 + 6.06218i 0.344309 + 0.198787i
\(931\) −27.0000 46.7654i −0.884889 1.53267i
\(932\) 12.0000 + 20.7846i 0.393073 + 0.680823i
\(933\) −31.5000 18.1865i −1.03126 0.595400i
\(934\) −13.5000 + 23.3827i −0.441733 + 0.765105i
\(935\) 4.00000 0.130814
\(936\) −18.0000 −0.588348
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) −22.0000 + 38.1051i −0.718325 + 1.24418i
\(939\) 24.2487i 0.791327i
\(940\) −3.50000 6.06218i −0.114157 0.197726i
\(941\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(942\) 10.5000 6.06218i 0.342108 0.197516i
\(943\) −4.00000 + 6.92820i −0.130258 + 0.225613i
\(944\) 7.00000 0.227831
\(945\) 20.7846i 0.676123i
\(946\) 6.00000 0.195077
\(947\) −7.50000 + 12.9904i −0.243717 + 0.422131i −0.961770 0.273858i \(-0.911700\pi\)
0.718053 + 0.695988i \(0.245034\pi\)
\(948\) 12.0000 6.92820i 0.389742 0.225018i
\(949\) 4.00000 + 6.92820i 0.129845 + 0.224899i
\(950\) 12.0000 + 20.7846i 0.389331 + 0.674342i
\(951\) 38.1051i 1.23564i
\(952\) 24.0000 41.5692i 0.777844 1.34727i
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) −13.5000 23.3827i −0.437079 0.757042i
\(955\) −13.0000 −0.420670
\(956\) 3.00000 5.19615i 0.0970269 0.168056i
\(957\) 9.00000 + 5.19615i 0.290929 + 0.167968i
\(958\) 2.00000 + 3.46410i 0.0646171 + 0.111920i
\(959\) −10.0000 17.3205i −0.322917 0.559308i
\(960\) 10.5000 + 6.06218i 0.338886 + 0.195656i
\(961\) −9.00000 + 15.5885i −0.290323 + 0.502853i
\(962\) −6.00000 −0.193448
\(963\) −27.0000 + 46.7654i −0.870063 + 1.50699i
\(964\) −10.0000 −0.322078
\(965\) −2.00000 + 3.46410i −0.0643823 + 0.111513i
\(966\) 27.7128i 0.891645i
\(967\) 25.0000 + 43.3013i 0.803946 + 1.39247i 0.917000 + 0.398886i \(0.130603\pi\)
−0.113055 + 0.993589i \(0.536064\pi\)
\(968\) 1.50000 + 2.59808i 0.0482118 + 0.0835053i
\(969\) −36.0000 + 20.7846i −1.15649 + 0.667698i
\(970\) 9.50000 16.4545i 0.305027 0.528322i
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) 15.5885i 0.500000i
\(973\) −8.00000 −0.256468
\(974\) 18.5000 32.0429i 0.592778 1.02672i
\(975\) −12.0000 + 6.92820i −0.384308 + 0.221880i
\(976\) 0 0
\(977\) −9.00000 15.5885i −0.287936 0.498719i 0.685381 0.728184i \(-0.259636\pi\)
−0.973317 + 0.229465i \(0.926302\pi\)
\(978\) 19.0526i 0.609234i
\(979\) −3.00000 + 5.19615i −0.0958804 + 0.166070i
\(980\) −9.00000 −0.287494
\(981\) −3.00000 + 5.19615i −0.0957826 + 0.165900i
\(982\) −8.00000 −0.255290
\(983\) −1.50000 + 2.59808i −0.0478426 + 0.0828658i −0.888955 0.457995i \(-0.848568\pi\)
0.841112 + 0.540860i \(0.181901\pi\)
\(984\) 9.00000 + 5.19615i 0.286910 + 0.165647i
\(985\) −8.00000 13.8564i −0.254901 0.441502i
\(986\) −12.0000 20.7846i −0.382158 0.661917i
\(987\) −42.0000 24.2487i −1.33687 0.771845i
\(988\) −6.00000 + 10.3923i −0.190885 + 0.330623i
\(989\) −24.0000 −0.763156
\(990\) 1.50000 + 2.59808i 0.0476731 + 0.0825723i
\(991\) −44.0000 −1.39771 −0.698853 0.715265i \(-0.746306\pi\)
−0.698853 + 0.715265i \(0.746306\pi\)
\(992\) −17.5000 + 30.3109i −0.555626 + 0.962372i
\(993\) 1.73205i 0.0549650i
\(994\) −18.0000 31.1769i −0.570925 0.988872i
\(995\) 1.50000 + 2.59808i 0.0475532 + 0.0823646i
\(996\) −18.0000 + 10.3923i −0.570352 + 0.329293i
\(997\) 2.00000 3.46410i 0.0633406 0.109709i −0.832616 0.553851i \(-0.813158\pi\)
0.895957 + 0.444141i \(0.146491\pi\)
\(998\) −25.0000 −0.791361
\(999\) 15.5885i 0.493197i
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 99.2.e.a.34.1 2
3.2 odd 2 297.2.e.c.100.1 2
9.2 odd 6 891.2.a.c.1.1 1
9.4 even 3 inner 99.2.e.a.67.1 yes 2
9.5 odd 6 297.2.e.c.199.1 2
9.7 even 3 891.2.a.g.1.1 1
11.10 odd 2 1089.2.e.c.727.1 2
99.43 odd 6 9801.2.a.c.1.1 1
99.65 even 6 9801.2.a.i.1.1 1
99.76 odd 6 1089.2.e.c.364.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.e.a.34.1 2 1.1 even 1 trivial
99.2.e.a.67.1 yes 2 9.4 even 3 inner
297.2.e.c.100.1 2 3.2 odd 2
297.2.e.c.199.1 2 9.5 odd 6
891.2.a.c.1.1 1 9.2 odd 6
891.2.a.g.1.1 1 9.7 even 3
1089.2.e.c.364.1 2 99.76 odd 6
1089.2.e.c.727.1 2 11.10 odd 2
9801.2.a.c.1.1 1 99.43 odd 6
9801.2.a.i.1.1 1 99.65 even 6