Properties

Label 9.3.d.a.2.1
Level $9$
Weight $3$
Character 9.2
Analytic conductor $0.245$
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] = [9,3,Mod(2,9)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 9.d (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.245232237924\)
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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 9.2
Dual form 9.3.d.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} +(4.50000 - 2.59808i) q^{6} +(-1.00000 + 1.73205i) q^{7} +8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} +(4.50000 - 2.59808i) q^{6} +(-1.00000 + 1.73205i) q^{7} +8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} -6.00000 q^{10} +(-1.50000 - 0.866025i) q^{11} +3.00000 q^{12} +(2.00000 + 3.46410i) q^{13} +(3.00000 - 1.73205i) q^{14} +10.3923i q^{15} +(5.50000 - 9.52628i) q^{16} -15.5885i q^{17} +15.5885i q^{18} +11.0000 q^{19} +(-3.00000 - 1.73205i) q^{20} +(-3.00000 - 5.19615i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-24.0000 + 13.8564i) q^{23} +(-22.5000 - 12.9904i) q^{24} +(-6.50000 + 11.2583i) q^{25} -6.92820i q^{26} +27.0000 q^{27} +2.00000 q^{28} +(39.0000 + 22.5167i) q^{29} +(9.00000 - 15.5885i) q^{30} +(-16.0000 - 27.7128i) q^{31} +(13.5000 - 7.79423i) q^{32} +(4.50000 - 2.59808i) q^{33} +(-13.5000 + 23.3827i) q^{34} +6.92820i q^{35} +(-4.50000 + 7.79423i) q^{36} -34.0000 q^{37} +(-16.5000 - 9.52628i) q^{38} -12.0000 q^{39} +(15.0000 + 25.9808i) q^{40} +(-10.5000 + 6.06218i) q^{41} +10.3923i q^{42} +(30.5000 - 52.8275i) q^{43} +1.73205i q^{44} +(-27.0000 - 15.5885i) q^{45} +48.0000 q^{46} +(-42.0000 - 24.2487i) q^{47} +(16.5000 + 28.5788i) q^{48} +(22.5000 + 38.9711i) q^{49} +(19.5000 - 11.2583i) q^{50} +(40.5000 + 23.3827i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-40.5000 - 23.3827i) q^{54} -6.00000 q^{55} +(-15.0000 - 8.66025i) q^{56} +(-16.5000 + 28.5788i) q^{57} +(-39.0000 - 67.5500i) q^{58} +(43.5000 - 25.1147i) q^{59} +(9.00000 - 5.19615i) q^{60} +(-28.0000 + 48.4974i) q^{61} +55.4256i q^{62} +18.0000 q^{63} -71.0000 q^{64} +(12.0000 + 6.92820i) q^{65} -9.00000 q^{66} +(15.5000 + 26.8468i) q^{67} +(-13.5000 + 7.79423i) q^{68} -83.1384i q^{69} +(6.00000 - 10.3923i) q^{70} +31.1769i q^{71} +(67.5000 - 38.9711i) q^{72} +65.0000 q^{73} +(51.0000 + 29.4449i) q^{74} +(-19.5000 - 33.7750i) q^{75} +(-5.50000 - 9.52628i) q^{76} +(3.00000 - 1.73205i) q^{77} +(18.0000 + 10.3923i) q^{78} +(-19.0000 + 32.9090i) q^{79} -38.1051i q^{80} +(-40.5000 + 70.1481i) q^{81} +21.0000 q^{82} +(-42.0000 - 24.2487i) q^{83} +(-3.00000 + 5.19615i) q^{84} +(-27.0000 - 46.7654i) q^{85} +(-91.5000 + 52.8275i) q^{86} +(-117.000 + 67.5500i) q^{87} +(7.50000 - 12.9904i) q^{88} -124.708i q^{89} +(27.0000 + 46.7654i) q^{90} -8.00000 q^{91} +(24.0000 + 13.8564i) q^{92} +96.0000 q^{93} +(42.0000 + 72.7461i) q^{94} +(33.0000 - 19.0526i) q^{95} +46.7654i q^{96} +(57.5000 - 99.5929i) q^{97} -77.9423i q^{98} +15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9} - 12 q^{10} - 3 q^{11} + 6 q^{12} + 4 q^{13} + 6 q^{14} + 11 q^{16} + 22 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 48 q^{23} - 45 q^{24} - 13 q^{25} + 54 q^{27} + 4 q^{28} + 78 q^{29} + 18 q^{30} - 32 q^{31} + 27 q^{32} + 9 q^{33} - 27 q^{34} - 9 q^{36} - 68 q^{37} - 33 q^{38} - 24 q^{39} + 30 q^{40} - 21 q^{41} + 61 q^{43} - 54 q^{45} + 96 q^{46} - 84 q^{47} + 33 q^{48} + 45 q^{49} + 39 q^{50} + 81 q^{51} + 4 q^{52} - 81 q^{54} - 12 q^{55} - 30 q^{56} - 33 q^{57} - 78 q^{58} + 87 q^{59} + 18 q^{60} - 56 q^{61} + 36 q^{63} - 142 q^{64} + 24 q^{65} - 18 q^{66} + 31 q^{67} - 27 q^{68} + 12 q^{70} + 135 q^{72} + 130 q^{73} + 102 q^{74} - 39 q^{75} - 11 q^{76} + 6 q^{77} + 36 q^{78} - 38 q^{79} - 81 q^{81} + 42 q^{82} - 84 q^{83} - 6 q^{84} - 54 q^{85} - 183 q^{86} - 234 q^{87} + 15 q^{88} + 54 q^{90} - 16 q^{91} + 48 q^{92} + 192 q^{93} + 84 q^{94} + 66 q^{95} + 115 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 0.866025i −0.750000 0.433013i 0.0756939 0.997131i \(-0.475883\pi\)
−0.825694 + 0.564118i \(0.809216\pi\)
\(3\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(4\) −0.500000 0.866025i −0.125000 0.216506i
\(5\) 3.00000 1.73205i 0.600000 0.346410i −0.169042 0.985609i \(-0.554067\pi\)
0.769042 + 0.639199i \(0.220734\pi\)
\(6\) 4.50000 2.59808i 0.750000 0.433013i
\(7\) −1.00000 + 1.73205i −0.142857 + 0.247436i −0.928571 0.371154i \(-0.878962\pi\)
0.785714 + 0.618590i \(0.212296\pi\)
\(8\) 8.66025i 1.08253i
\(9\) −4.50000 7.79423i −0.500000 0.866025i
\(10\) −6.00000 −0.600000
\(11\) −1.50000 0.866025i −0.136364 0.0787296i 0.430266 0.902702i \(-0.358420\pi\)
−0.566630 + 0.823972i \(0.691753\pi\)
\(12\) 3.00000 0.250000
\(13\) 2.00000 + 3.46410i 0.153846 + 0.266469i 0.932638 0.360813i \(-0.117501\pi\)
−0.778792 + 0.627282i \(0.784167\pi\)
\(14\) 3.00000 1.73205i 0.214286 0.123718i
\(15\) 10.3923i 0.692820i
\(16\) 5.50000 9.52628i 0.343750 0.595392i
\(17\) 15.5885i 0.916968i −0.888703 0.458484i \(-0.848393\pi\)
0.888703 0.458484i \(-0.151607\pi\)
\(18\) 15.5885i 0.866025i
\(19\) 11.0000 0.578947 0.289474 0.957186i \(-0.406520\pi\)
0.289474 + 0.957186i \(0.406520\pi\)
\(20\) −3.00000 1.73205i −0.150000 0.0866025i
\(21\) −3.00000 5.19615i −0.142857 0.247436i
\(22\) 1.50000 + 2.59808i 0.0681818 + 0.118094i
\(23\) −24.0000 + 13.8564i −1.04348 + 0.602452i −0.920817 0.389996i \(-0.872476\pi\)
−0.122662 + 0.992449i \(0.539143\pi\)
\(24\) −22.5000 12.9904i −0.937500 0.541266i
\(25\) −6.50000 + 11.2583i −0.260000 + 0.450333i
\(26\) 6.92820i 0.266469i
\(27\) 27.0000 1.00000
\(28\) 2.00000 0.0714286
\(29\) 39.0000 + 22.5167i 1.34483 + 0.776437i 0.987511 0.157547i \(-0.0503586\pi\)
0.357316 + 0.933984i \(0.383692\pi\)
\(30\) 9.00000 15.5885i 0.300000 0.519615i
\(31\) −16.0000 27.7128i −0.516129 0.893962i −0.999825 0.0187254i \(-0.994039\pi\)
0.483696 0.875236i \(-0.339294\pi\)
\(32\) 13.5000 7.79423i 0.421875 0.243570i
\(33\) 4.50000 2.59808i 0.136364 0.0787296i
\(34\) −13.5000 + 23.3827i −0.397059 + 0.687726i
\(35\) 6.92820i 0.197949i
\(36\) −4.50000 + 7.79423i −0.125000 + 0.216506i
\(37\) −34.0000 −0.918919 −0.459459 0.888199i \(-0.651957\pi\)
−0.459459 + 0.888199i \(0.651957\pi\)
\(38\) −16.5000 9.52628i −0.434211 0.250692i
\(39\) −12.0000 −0.307692
\(40\) 15.0000 + 25.9808i 0.375000 + 0.649519i
\(41\) −10.5000 + 6.06218i −0.256098 + 0.147858i −0.622553 0.782578i \(-0.713905\pi\)
0.366456 + 0.930436i \(0.380571\pi\)
\(42\) 10.3923i 0.247436i
\(43\) 30.5000 52.8275i 0.709302 1.22855i −0.255814 0.966726i \(-0.582343\pi\)
0.965116 0.261822i \(-0.0843232\pi\)
\(44\) 1.73205i 0.0393648i
\(45\) −27.0000 15.5885i −0.600000 0.346410i
\(46\) 48.0000 1.04348
\(47\) −42.0000 24.2487i −0.893617 0.515930i −0.0184931 0.999829i \(-0.505887\pi\)
−0.875124 + 0.483899i \(0.839220\pi\)
\(48\) 16.5000 + 28.5788i 0.343750 + 0.595392i
\(49\) 22.5000 + 38.9711i 0.459184 + 0.795329i
\(50\) 19.5000 11.2583i 0.390000 0.225167i
\(51\) 40.5000 + 23.3827i 0.794118 + 0.458484i
\(52\) 2.00000 3.46410i 0.0384615 0.0666173i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −40.5000 23.3827i −0.750000 0.433013i
\(55\) −6.00000 −0.109091
\(56\) −15.0000 8.66025i −0.267857 0.154647i
\(57\) −16.5000 + 28.5788i −0.289474 + 0.501383i
\(58\) −39.0000 67.5500i −0.672414 1.16465i
\(59\) 43.5000 25.1147i 0.737288 0.425674i −0.0837943 0.996483i \(-0.526704\pi\)
0.821082 + 0.570810i \(0.193371\pi\)
\(60\) 9.00000 5.19615i 0.150000 0.0866025i
\(61\) −28.0000 + 48.4974i −0.459016 + 0.795040i −0.998909 0.0466940i \(-0.985131\pi\)
0.539893 + 0.841734i \(0.318465\pi\)
\(62\) 55.4256i 0.893962i
\(63\) 18.0000 0.285714
\(64\) −71.0000 −1.10938
\(65\) 12.0000 + 6.92820i 0.184615 + 0.106588i
\(66\) −9.00000 −0.136364
\(67\) 15.5000 + 26.8468i 0.231343 + 0.400698i 0.958204 0.286087i \(-0.0923546\pi\)
−0.726860 + 0.686785i \(0.759021\pi\)
\(68\) −13.5000 + 7.79423i −0.198529 + 0.114621i
\(69\) 83.1384i 1.20490i
\(70\) 6.00000 10.3923i 0.0857143 0.148461i
\(71\) 31.1769i 0.439111i 0.975600 + 0.219556i \(0.0704608\pi\)
−0.975600 + 0.219556i \(0.929539\pi\)
\(72\) 67.5000 38.9711i 0.937500 0.541266i
\(73\) 65.0000 0.890411 0.445205 0.895428i \(-0.353131\pi\)
0.445205 + 0.895428i \(0.353131\pi\)
\(74\) 51.0000 + 29.4449i 0.689189 + 0.397904i
\(75\) −19.5000 33.7750i −0.260000 0.450333i
\(76\) −5.50000 9.52628i −0.0723684 0.125346i
\(77\) 3.00000 1.73205i 0.0389610 0.0224942i
\(78\) 18.0000 + 10.3923i 0.230769 + 0.133235i
\(79\) −19.0000 + 32.9090i −0.240506 + 0.416569i −0.960859 0.277039i \(-0.910647\pi\)
0.720352 + 0.693608i \(0.243980\pi\)
\(80\) 38.1051i 0.476314i
\(81\) −40.5000 + 70.1481i −0.500000 + 0.866025i
\(82\) 21.0000 0.256098
\(83\) −42.0000 24.2487i −0.506024 0.292153i 0.225174 0.974319i \(-0.427705\pi\)
−0.731198 + 0.682165i \(0.761038\pi\)
\(84\) −3.00000 + 5.19615i −0.0357143 + 0.0618590i
\(85\) −27.0000 46.7654i −0.317647 0.550181i
\(86\) −91.5000 + 52.8275i −1.06395 + 0.614274i
\(87\) −117.000 + 67.5500i −1.34483 + 0.776437i
\(88\) 7.50000 12.9904i 0.0852273 0.147618i
\(89\) 124.708i 1.40121i −0.713549 0.700605i \(-0.752914\pi\)
0.713549 0.700605i \(-0.247086\pi\)
\(90\) 27.0000 + 46.7654i 0.300000 + 0.519615i
\(91\) −8.00000 −0.0879121
\(92\) 24.0000 + 13.8564i 0.260870 + 0.150613i
\(93\) 96.0000 1.03226
\(94\) 42.0000 + 72.7461i 0.446809 + 0.773895i
\(95\) 33.0000 19.0526i 0.347368 0.200553i
\(96\) 46.7654i 0.487139i
\(97\) 57.5000 99.5929i 0.592784 1.02673i −0.401072 0.916047i \(-0.631362\pi\)
0.993856 0.110685i \(-0.0353044\pi\)
\(98\) 77.9423i 0.795329i
\(99\) 15.5885i 0.157459i
\(100\) 13.0000 0.130000
\(101\) 39.0000 + 22.5167i 0.386139 + 0.222937i 0.680486 0.732761i \(-0.261769\pi\)
−0.294347 + 0.955699i \(0.595102\pi\)
\(102\) −40.5000 70.1481i −0.397059 0.687726i
\(103\) 20.0000 + 34.6410i 0.194175 + 0.336321i 0.946630 0.322323i \(-0.104464\pi\)
−0.752455 + 0.658644i \(0.771130\pi\)
\(104\) −30.0000 + 17.3205i −0.288462 + 0.166543i
\(105\) −18.0000 10.3923i −0.171429 0.0989743i
\(106\) 0 0
\(107\) 140.296i 1.31118i 0.755118 + 0.655589i \(0.227580\pi\)
−0.755118 + 0.655589i \(0.772420\pi\)
\(108\) −13.5000 23.3827i −0.125000 0.216506i
\(109\) −52.0000 −0.477064 −0.238532 0.971135i \(-0.576666\pi\)
−0.238532 + 0.971135i \(0.576666\pi\)
\(110\) 9.00000 + 5.19615i 0.0818182 + 0.0472377i
\(111\) 51.0000 88.3346i 0.459459 0.795807i
\(112\) 11.0000 + 19.0526i 0.0982143 + 0.170112i
\(113\) −78.0000 + 45.0333i −0.690265 + 0.398525i −0.803711 0.595019i \(-0.797144\pi\)
0.113446 + 0.993544i \(0.463811\pi\)
\(114\) 49.5000 28.5788i 0.434211 0.250692i
\(115\) −48.0000 + 83.1384i −0.417391 + 0.722943i
\(116\) 45.0333i 0.388218i
\(117\) 18.0000 31.1769i 0.153846 0.266469i
\(118\) −87.0000 −0.737288
\(119\) 27.0000 + 15.5885i 0.226891 + 0.130995i
\(120\) −90.0000 −0.750000
\(121\) −59.0000 102.191i −0.487603 0.844554i
\(122\) 84.0000 48.4974i 0.688525 0.397520i
\(123\) 36.3731i 0.295716i
\(124\) −16.0000 + 27.7128i −0.129032 + 0.223490i
\(125\) 131.636i 1.05309i
\(126\) −27.0000 15.5885i −0.214286 0.123718i
\(127\) −16.0000 −0.125984 −0.0629921 0.998014i \(-0.520064\pi\)
−0.0629921 + 0.998014i \(0.520064\pi\)
\(128\) 52.5000 + 30.3109i 0.410156 + 0.236804i
\(129\) 91.5000 + 158.483i 0.709302 + 1.22855i
\(130\) −12.0000 20.7846i −0.0923077 0.159882i
\(131\) 138.000 79.6743i 1.05344 0.608201i 0.129826 0.991537i \(-0.458558\pi\)
0.923609 + 0.383336i \(0.125225\pi\)
\(132\) −4.50000 2.59808i −0.0340909 0.0196824i
\(133\) −11.0000 + 19.0526i −0.0827068 + 0.143252i
\(134\) 53.6936i 0.400698i
\(135\) 81.0000 46.7654i 0.600000 0.346410i
\(136\) 135.000 0.992647
\(137\) −163.500 94.3968i −1.19343 0.689028i −0.234348 0.972153i \(-0.575295\pi\)
−0.959083 + 0.283125i \(0.908629\pi\)
\(138\) −72.0000 + 124.708i −0.521739 + 0.903679i
\(139\) −2.50000 4.33013i −0.0179856 0.0311520i 0.856893 0.515495i \(-0.172392\pi\)
−0.874878 + 0.484343i \(0.839059\pi\)
\(140\) 6.00000 3.46410i 0.0428571 0.0247436i
\(141\) 126.000 72.7461i 0.893617 0.515930i
\(142\) 27.0000 46.7654i 0.190141 0.329334i
\(143\) 6.92820i 0.0484490i
\(144\) −99.0000 −0.687500
\(145\) 156.000 1.07586
\(146\) −97.5000 56.2917i −0.667808 0.385559i
\(147\) −135.000 −0.918367
\(148\) 17.0000 + 29.4449i 0.114865 + 0.198952i
\(149\) −132.000 + 76.2102i −0.885906 + 0.511478i −0.872601 0.488433i \(-0.837569\pi\)
−0.0133049 + 0.999911i \(0.504235\pi\)
\(150\) 67.5500i 0.450333i
\(151\) −10.0000 + 17.3205i −0.0662252 + 0.114705i −0.897237 0.441550i \(-0.854429\pi\)
0.831012 + 0.556255i \(0.187762\pi\)
\(152\) 95.2628i 0.626729i
\(153\) −121.500 + 70.1481i −0.794118 + 0.458484i
\(154\) −6.00000 −0.0389610
\(155\) −96.0000 55.4256i −0.619355 0.357585i
\(156\) 6.00000 + 10.3923i 0.0384615 + 0.0666173i
\(157\) 20.0000 + 34.6410i 0.127389 + 0.220643i 0.922664 0.385605i \(-0.126007\pi\)
−0.795276 + 0.606248i \(0.792674\pi\)
\(158\) 57.0000 32.9090i 0.360759 0.208285i
\(159\) 0 0
\(160\) 27.0000 46.7654i 0.168750 0.292284i
\(161\) 55.4256i 0.344259i
\(162\) 121.500 70.1481i 0.750000 0.433013i
\(163\) −106.000 −0.650307 −0.325153 0.945661i \(-0.605416\pi\)
−0.325153 + 0.945661i \(0.605416\pi\)
\(164\) 10.5000 + 6.06218i 0.0640244 + 0.0369645i
\(165\) 9.00000 15.5885i 0.0545455 0.0944755i
\(166\) 42.0000 + 72.7461i 0.253012 + 0.438230i
\(167\) 165.000 95.2628i 0.988024 0.570436i 0.0833409 0.996521i \(-0.473441\pi\)
0.904683 + 0.426085i \(0.140108\pi\)
\(168\) 45.0000 25.9808i 0.267857 0.154647i
\(169\) 76.5000 132.502i 0.452663 0.784035i
\(170\) 93.5307i 0.550181i
\(171\) −49.5000 85.7365i −0.289474 0.501383i
\(172\) −61.0000 −0.354651
\(173\) 201.000 + 116.047i 1.16185 + 0.670794i 0.951747 0.306885i \(-0.0992867\pi\)
0.210103 + 0.977679i \(0.432620\pi\)
\(174\) 234.000 1.34483
\(175\) −13.0000 22.5167i −0.0742857 0.128667i
\(176\) −16.5000 + 9.52628i −0.0937500 + 0.0541266i
\(177\) 150.688i 0.851347i
\(178\) −108.000 + 187.061i −0.606742 + 1.05091i
\(179\) 62.3538i 0.348345i −0.984715 0.174173i \(-0.944275\pi\)
0.984715 0.174173i \(-0.0557251\pi\)
\(180\) 31.1769i 0.173205i
\(181\) −232.000 −1.28177 −0.640884 0.767638i \(-0.721432\pi\)
−0.640884 + 0.767638i \(0.721432\pi\)
\(182\) 12.0000 + 6.92820i 0.0659341 + 0.0380671i
\(183\) −84.0000 145.492i −0.459016 0.795040i
\(184\) −120.000 207.846i −0.652174 1.12960i
\(185\) −102.000 + 58.8897i −0.551351 + 0.318323i
\(186\) −144.000 83.1384i −0.774194 0.446981i
\(187\) −13.5000 + 23.3827i −0.0721925 + 0.125041i
\(188\) 48.4974i 0.257965i
\(189\) −27.0000 + 46.7654i −0.142857 + 0.247436i
\(190\) −66.0000 −0.347368
\(191\) 201.000 + 116.047i 1.05236 + 0.607578i 0.923308 0.384060i \(-0.125475\pi\)
0.129048 + 0.991638i \(0.458808\pi\)
\(192\) 106.500 184.463i 0.554688 0.960747i
\(193\) 132.500 + 229.497i 0.686528 + 1.18910i 0.972954 + 0.231000i \(0.0741996\pi\)
−0.286425 + 0.958103i \(0.592467\pi\)
\(194\) −172.500 + 99.5929i −0.889175 + 0.513366i
\(195\) −36.0000 + 20.7846i −0.184615 + 0.106588i
\(196\) 22.5000 38.9711i 0.114796 0.198832i
\(197\) 124.708i 0.633034i −0.948587 0.316517i \(-0.897487\pi\)
0.948587 0.316517i \(-0.102513\pi\)
\(198\) 13.5000 23.3827i 0.0681818 0.118094i
\(199\) 290.000 1.45729 0.728643 0.684893i \(-0.240151\pi\)
0.728643 + 0.684893i \(0.240151\pi\)
\(200\) −97.5000 56.2917i −0.487500 0.281458i
\(201\) −93.0000 −0.462687
\(202\) −39.0000 67.5500i −0.193069 0.334406i
\(203\) −78.0000 + 45.0333i −0.384236 + 0.221839i
\(204\) 46.7654i 0.229242i
\(205\) −21.0000 + 36.3731i −0.102439 + 0.177430i
\(206\) 69.2820i 0.336321i
\(207\) 216.000 + 124.708i 1.04348 + 0.602452i
\(208\) 44.0000 0.211538
\(209\) −16.5000 9.52628i −0.0789474 0.0455803i
\(210\) 18.0000 + 31.1769i 0.0857143 + 0.148461i
\(211\) 47.0000 + 81.4064i 0.222749 + 0.385812i 0.955642 0.294532i \(-0.0951637\pi\)
−0.732893 + 0.680344i \(0.761830\pi\)
\(212\) 0 0
\(213\) −81.0000 46.7654i −0.380282 0.219556i
\(214\) 121.500 210.444i 0.567757 0.983384i
\(215\) 211.310i 0.982838i
\(216\) 233.827i 1.08253i
\(217\) 64.0000 0.294931
\(218\) 78.0000 + 45.0333i 0.357798 + 0.206575i
\(219\) −97.5000 + 168.875i −0.445205 + 0.771119i
\(220\) 3.00000 + 5.19615i 0.0136364 + 0.0236189i
\(221\) 54.0000 31.1769i 0.244344 0.141072i
\(222\) −153.000 + 88.3346i −0.689189 + 0.397904i
\(223\) 26.0000 45.0333i 0.116592 0.201943i −0.801823 0.597562i \(-0.796136\pi\)
0.918415 + 0.395618i \(0.129470\pi\)
\(224\) 31.1769i 0.139183i
\(225\) 117.000 0.520000
\(226\) 156.000 0.690265
\(227\) −163.500 94.3968i −0.720264 0.415845i 0.0945856 0.995517i \(-0.469847\pi\)
−0.814850 + 0.579672i \(0.803181\pi\)
\(228\) 33.0000 0.144737
\(229\) −133.000 230.363i −0.580786 1.00595i −0.995386 0.0959473i \(-0.969412\pi\)
0.414600 0.910004i \(-0.363921\pi\)
\(230\) 144.000 83.1384i 0.626087 0.361471i
\(231\) 10.3923i 0.0449883i
\(232\) −195.000 + 337.750i −0.840517 + 1.45582i
\(233\) 202.650i 0.869742i −0.900493 0.434871i \(-0.856794\pi\)
0.900493 0.434871i \(-0.143206\pi\)
\(234\) −54.0000 + 31.1769i −0.230769 + 0.133235i
\(235\) −168.000 −0.714894
\(236\) −43.5000 25.1147i −0.184322 0.106418i
\(237\) −57.0000 98.7269i −0.240506 0.416569i
\(238\) −27.0000 46.7654i −0.113445 0.196493i
\(239\) −348.000 + 200.918i −1.45607 + 0.840661i −0.998815 0.0486764i \(-0.984500\pi\)
−0.457252 + 0.889337i \(0.651166\pi\)
\(240\) 99.0000 + 57.1577i 0.412500 + 0.238157i
\(241\) −59.5000 + 103.057i −0.246888 + 0.427623i −0.962661 0.270711i \(-0.912741\pi\)
0.715773 + 0.698333i \(0.246075\pi\)
\(242\) 204.382i 0.844554i
\(243\) −121.500 210.444i −0.500000 0.866025i
\(244\) 56.0000 0.229508
\(245\) 135.000 + 77.9423i 0.551020 + 0.318132i
\(246\) −31.5000 + 54.5596i −0.128049 + 0.221787i
\(247\) 22.0000 + 38.1051i 0.0890688 + 0.154272i
\(248\) 240.000 138.564i 0.967742 0.558726i
\(249\) 126.000 72.7461i 0.506024 0.292153i
\(250\) 114.000 197.454i 0.456000 0.789815i
\(251\) 389.711i 1.55264i 0.630342 + 0.776318i \(0.282915\pi\)
−0.630342 + 0.776318i \(0.717085\pi\)
\(252\) −9.00000 15.5885i −0.0357143 0.0618590i
\(253\) 48.0000 0.189723
\(254\) 24.0000 + 13.8564i 0.0944882 + 0.0545528i
\(255\) 162.000 0.635294
\(256\) 89.5000 + 155.019i 0.349609 + 0.605541i
\(257\) 151.500 87.4686i 0.589494 0.340345i −0.175403 0.984497i \(-0.556123\pi\)
0.764897 + 0.644152i \(0.222790\pi\)
\(258\) 316.965i 1.22855i
\(259\) 34.0000 58.8897i 0.131274 0.227373i
\(260\) 13.8564i 0.0532939i
\(261\) 405.300i 1.55287i
\(262\) −276.000 −1.05344
\(263\) 39.0000 + 22.5167i 0.148289 + 0.0856147i 0.572309 0.820038i \(-0.306048\pi\)
−0.424020 + 0.905653i \(0.639381\pi\)
\(264\) 22.5000 + 38.9711i 0.0852273 + 0.147618i
\(265\) 0 0
\(266\) 33.0000 19.0526i 0.124060 0.0716262i
\(267\) 324.000 + 187.061i 1.21348 + 0.700605i
\(268\) 15.5000 26.8468i 0.0578358 0.100175i
\(269\) 187.061i 0.695396i 0.937607 + 0.347698i \(0.113037\pi\)
−0.937607 + 0.347698i \(0.886963\pi\)
\(270\) −162.000 −0.600000
\(271\) −268.000 −0.988930 −0.494465 0.869198i \(-0.664636\pi\)
−0.494465 + 0.869198i \(0.664636\pi\)
\(272\) −148.500 85.7365i −0.545956 0.315208i
\(273\) 12.0000 20.7846i 0.0439560 0.0761341i
\(274\) 163.500 + 283.190i 0.596715 + 1.03354i
\(275\) 19.5000 11.2583i 0.0709091 0.0409394i
\(276\) −72.0000 + 41.5692i −0.260870 + 0.150613i
\(277\) −28.0000 + 48.4974i −0.101083 + 0.175081i −0.912131 0.409899i \(-0.865564\pi\)
0.811048 + 0.584979i \(0.198897\pi\)
\(278\) 8.66025i 0.0311520i
\(279\) −144.000 + 249.415i −0.516129 + 0.893962i
\(280\) −60.0000 −0.214286
\(281\) −42.0000 24.2487i −0.149466 0.0862943i 0.423402 0.905942i \(-0.360836\pi\)
−0.572868 + 0.819648i \(0.694169\pi\)
\(282\) −252.000 −0.893617
\(283\) −187.000 323.894i −0.660777 1.14450i −0.980412 0.196959i \(-0.936893\pi\)
0.319634 0.947541i \(-0.396440\pi\)
\(284\) 27.0000 15.5885i 0.0950704 0.0548889i
\(285\) 114.315i 0.401107i
\(286\) −6.00000 + 10.3923i −0.0209790 + 0.0363367i
\(287\) 24.2487i 0.0844903i
\(288\) −121.500 70.1481i −0.421875 0.243570i
\(289\) 46.0000 0.159170
\(290\) −234.000 135.100i −0.806897 0.465862i
\(291\) 172.500 + 298.779i 0.592784 + 1.02673i
\(292\) −32.5000 56.2917i −0.111301 0.192780i
\(293\) 219.000 126.440i 0.747440 0.431535i −0.0773280 0.997006i \(-0.524639\pi\)
0.824768 + 0.565471i \(0.191306\pi\)
\(294\) 202.500 + 116.913i 0.688776 + 0.397665i
\(295\) 87.0000 150.688i 0.294915 0.510808i
\(296\) 294.449i 0.994759i
\(297\) −40.5000 23.3827i −0.136364 0.0787296i
\(298\) 264.000 0.885906
\(299\) −96.0000 55.4256i −0.321070 0.185370i
\(300\) −19.5000 + 33.7750i −0.0650000 + 0.112583i
\(301\) 61.0000 + 105.655i 0.202658 + 0.351014i
\(302\) 30.0000 17.3205i 0.0993377 0.0573527i
\(303\) −117.000 + 67.5500i −0.386139 + 0.222937i
\(304\) 60.5000 104.789i 0.199013 0.344701i
\(305\) 193.990i 0.636032i
\(306\) 243.000 0.794118
\(307\) 533.000 1.73616 0.868078 0.496428i \(-0.165355\pi\)
0.868078 + 0.496428i \(0.165355\pi\)
\(308\) −3.00000 1.73205i −0.00974026 0.00562354i
\(309\) −120.000 −0.388350
\(310\) 96.0000 + 166.277i 0.309677 + 0.536377i
\(311\) −213.000 + 122.976i −0.684887 + 0.395420i −0.801694 0.597735i \(-0.796068\pi\)
0.116806 + 0.993155i \(0.462734\pi\)
\(312\) 103.923i 0.333087i
\(313\) −77.5000 + 134.234i −0.247604 + 0.428862i −0.962860 0.269999i \(-0.912976\pi\)
0.715257 + 0.698862i \(0.246310\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 54.0000 31.1769i 0.171429 0.0989743i
\(316\) 38.0000 0.120253
\(317\) −42.0000 24.2487i −0.132492 0.0764944i 0.432289 0.901735i \(-0.357706\pi\)
−0.564781 + 0.825241i \(0.691039\pi\)
\(318\) 0 0
\(319\) −39.0000 67.5500i −0.122257 0.211755i
\(320\) −213.000 + 122.976i −0.665625 + 0.384299i
\(321\) −364.500 210.444i −1.13551 0.655589i
\(322\) −48.0000 + 83.1384i −0.149068 + 0.258194i
\(323\) 171.473i 0.530876i
\(324\) 81.0000 0.250000
\(325\) −52.0000 −0.160000
\(326\) 159.000 + 91.7987i 0.487730 + 0.281591i
\(327\) 78.0000 135.100i 0.238532 0.413150i
\(328\) −52.5000 90.9327i −0.160061 0.277234i
\(329\) 84.0000 48.4974i 0.255319 0.147409i
\(330\) −27.0000 + 15.5885i −0.0818182 + 0.0472377i
\(331\) −1.00000 + 1.73205i −0.00302115 + 0.00523278i −0.867532 0.497381i \(-0.834295\pi\)
0.864511 + 0.502614i \(0.167628\pi\)
\(332\) 48.4974i 0.146077i
\(333\) 153.000 + 265.004i 0.459459 + 0.795807i
\(334\) −330.000 −0.988024
\(335\) 93.0000 + 53.6936i 0.277612 + 0.160279i
\(336\) −66.0000 −0.196429
\(337\) −38.5000 66.6840i −0.114243 0.197875i 0.803234 0.595664i \(-0.203111\pi\)
−0.917477 + 0.397789i \(0.869778\pi\)
\(338\) −229.500 + 132.502i −0.678994 + 0.392017i
\(339\) 270.200i 0.797050i
\(340\) −27.0000 + 46.7654i −0.0794118 + 0.137545i
\(341\) 55.4256i 0.162538i
\(342\) 171.473i 0.501383i
\(343\) −188.000 −0.548105
\(344\) 457.500 + 264.138i 1.32994 + 0.767842i
\(345\) −144.000 249.415i −0.417391 0.722943i
\(346\) −201.000 348.142i −0.580925 1.00619i
\(347\) 97.5000 56.2917i 0.280980 0.162224i −0.352887 0.935666i \(-0.614800\pi\)
0.633867 + 0.773442i \(0.281467\pi\)
\(348\) 117.000 + 67.5500i 0.336207 + 0.194109i
\(349\) −208.000 + 360.267i −0.595989 + 1.03228i 0.397418 + 0.917638i \(0.369906\pi\)
−0.993407 + 0.114645i \(0.963427\pi\)
\(350\) 45.0333i 0.128667i
\(351\) 54.0000 + 93.5307i 0.153846 + 0.266469i
\(352\) −27.0000 −0.0767045
\(353\) −1.50000 0.866025i −0.00424929 0.00245333i 0.497874 0.867249i \(-0.334114\pi\)
−0.502123 + 0.864796i \(0.667448\pi\)
\(354\) 130.500 226.033i 0.368644 0.638510i
\(355\) 54.0000 + 93.5307i 0.152113 + 0.263467i
\(356\) −108.000 + 62.3538i −0.303371 + 0.175151i
\(357\) −81.0000 + 46.7654i −0.226891 + 0.130995i
\(358\) −54.0000 + 93.5307i −0.150838 + 0.261259i
\(359\) 592.361i 1.65003i −0.565110 0.825016i \(-0.691166\pi\)
0.565110 0.825016i \(-0.308834\pi\)
\(360\) 135.000 233.827i 0.375000 0.649519i
\(361\) −240.000 −0.664820
\(362\) 348.000 + 200.918i 0.961326 + 0.555022i
\(363\) 354.000 0.975207
\(364\) 4.00000 + 6.92820i 0.0109890 + 0.0190335i
\(365\) 195.000 112.583i 0.534247 0.308447i
\(366\) 290.985i 0.795040i
\(367\) 179.000 310.037i 0.487738 0.844788i −0.512162 0.858889i \(-0.671155\pi\)
0.999901 + 0.0141011i \(0.00448865\pi\)
\(368\) 304.841i 0.828372i
\(369\) 94.5000 + 54.5596i 0.256098 + 0.147858i
\(370\) 204.000 0.551351
\(371\) 0 0
\(372\) −48.0000 83.1384i −0.129032 0.223490i
\(373\) 290.000 + 502.295i 0.777480 + 1.34663i 0.933390 + 0.358863i \(0.116836\pi\)
−0.155910 + 0.987771i \(0.549831\pi\)
\(374\) 40.5000 23.3827i 0.108289 0.0625206i
\(375\) −342.000 197.454i −0.912000 0.526543i
\(376\) 210.000 363.731i 0.558511 0.967369i
\(377\) 180.133i 0.477807i
\(378\) 81.0000 46.7654i 0.214286 0.123718i
\(379\) 83.0000 0.218997 0.109499 0.993987i \(-0.465075\pi\)
0.109499 + 0.993987i \(0.465075\pi\)
\(380\) −33.0000 19.0526i −0.0868421 0.0501383i
\(381\) 24.0000 41.5692i 0.0629921 0.109106i
\(382\) −201.000 348.142i −0.526178 0.911367i
\(383\) −483.000 + 278.860i −1.26110 + 0.728094i −0.973287 0.229593i \(-0.926260\pi\)
−0.287810 + 0.957688i \(0.592927\pi\)
\(384\) −157.500 + 90.9327i −0.410156 + 0.236804i
\(385\) 6.00000 10.3923i 0.0155844 0.0269930i
\(386\) 458.993i 1.18910i
\(387\) −549.000 −1.41860
\(388\) −115.000 −0.296392
\(389\) −447.000 258.076i −1.14910 0.663433i −0.200432 0.979708i \(-0.564235\pi\)
−0.948668 + 0.316274i \(0.897568\pi\)
\(390\) 72.0000 0.184615
\(391\) 216.000 + 374.123i 0.552430 + 0.956836i
\(392\) −337.500 + 194.856i −0.860969 + 0.497081i
\(393\) 478.046i 1.21640i
\(394\) −108.000 + 187.061i −0.274112 + 0.474775i
\(395\) 131.636i 0.333255i
\(396\) 13.5000 7.79423i 0.0340909 0.0196824i
\(397\) 362.000 0.911839 0.455919 0.890021i \(-0.349311\pi\)
0.455919 + 0.890021i \(0.349311\pi\)
\(398\) −435.000 251.147i −1.09296 0.631024i
\(399\) −33.0000 57.1577i −0.0827068 0.143252i
\(400\) 71.5000 + 123.842i 0.178750 + 0.309604i
\(401\) 340.500 196.588i 0.849127 0.490244i −0.0112291 0.999937i \(-0.503574\pi\)
0.860356 + 0.509693i \(0.170241\pi\)
\(402\) 139.500 + 80.5404i 0.347015 + 0.200349i
\(403\) 64.0000 110.851i 0.158809 0.275065i
\(404\) 45.0333i 0.111469i
\(405\) 280.592i 0.692820i
\(406\) 156.000 0.384236
\(407\) 51.0000 + 29.4449i 0.125307 + 0.0723461i
\(408\) −202.500 + 350.740i −0.496324 + 0.859658i
\(409\) −110.500 191.392i −0.270171 0.467950i 0.698734 0.715381i \(-0.253747\pi\)
−0.968905 + 0.247431i \(0.920414\pi\)
\(410\) 63.0000 36.3731i 0.153659 0.0887148i
\(411\) 490.500 283.190i 1.19343 0.689028i
\(412\) 20.0000 34.6410i 0.0485437 0.0840801i
\(413\) 100.459i 0.243242i
\(414\) −216.000 374.123i −0.521739 0.903679i
\(415\) −168.000 −0.404819
\(416\) 54.0000 + 31.1769i 0.129808 + 0.0749445i
\(417\) 15.0000 0.0359712
\(418\) 16.5000 + 28.5788i 0.0394737 + 0.0683704i
\(419\) 678.000 391.443i 1.61814 0.934233i 0.630737 0.775997i \(-0.282753\pi\)
0.987401 0.158236i \(-0.0505807\pi\)
\(420\) 20.7846i 0.0494872i
\(421\) 341.000 590.629i 0.809976 1.40292i −0.102903 0.994691i \(-0.532813\pi\)
0.912880 0.408229i \(-0.133853\pi\)
\(422\) 162.813i 0.385812i
\(423\) 436.477i 1.03186i
\(424\) 0 0
\(425\) 175.500 + 101.325i 0.412941 + 0.238412i
\(426\) 81.0000 + 140.296i 0.190141 + 0.329334i
\(427\) −56.0000 96.9948i −0.131148 0.227154i
\(428\) 121.500 70.1481i 0.283879 0.163897i
\(429\) 18.0000 + 10.3923i 0.0419580 + 0.0242245i
\(430\) −183.000 + 316.965i −0.425581 + 0.737129i
\(431\) 280.592i 0.651026i 0.945538 + 0.325513i \(0.105537\pi\)
−0.945538 + 0.325513i \(0.894463\pi\)
\(432\) 148.500 257.210i 0.343750 0.595392i
\(433\) −295.000 −0.681293 −0.340647 0.940191i \(-0.610646\pi\)
−0.340647 + 0.940191i \(0.610646\pi\)
\(434\) −96.0000 55.4256i −0.221198 0.127709i
\(435\) −234.000 + 405.300i −0.537931 + 0.931724i
\(436\) 26.0000 + 45.0333i 0.0596330 + 0.103287i
\(437\) −264.000 + 152.420i −0.604119 + 0.348788i
\(438\) 292.500 168.875i 0.667808 0.385559i
\(439\) −406.000 + 703.213i −0.924829 + 1.60185i −0.132993 + 0.991117i \(0.542459\pi\)
−0.791836 + 0.610734i \(0.790874\pi\)
\(440\) 51.9615i 0.118094i
\(441\) 202.500 350.740i 0.459184 0.795329i
\(442\) −108.000 −0.244344
\(443\) 79.5000 + 45.8993i 0.179458 + 0.103610i 0.587038 0.809559i \(-0.300294\pi\)
−0.407580 + 0.913170i \(0.633627\pi\)
\(444\) −102.000 −0.229730
\(445\) −216.000 374.123i −0.485393 0.840726i
\(446\) −78.0000 + 45.0333i −0.174888 + 0.100972i
\(447\) 457.261i 1.02296i
\(448\) 71.0000 122.976i 0.158482 0.274499i
\(449\) 639.127i 1.42344i 0.702461 + 0.711722i \(0.252085\pi\)
−0.702461 + 0.711722i \(0.747915\pi\)
\(450\) −175.500 101.325i −0.390000 0.225167i
\(451\) 21.0000 0.0465632
\(452\) 78.0000 + 45.0333i 0.172566 + 0.0996312i
\(453\) −30.0000 51.9615i −0.0662252 0.114705i
\(454\) 163.500 + 283.190i 0.360132 + 0.623767i
\(455\) −24.0000 + 13.8564i −0.0527473 + 0.0304536i
\(456\) −247.500 142.894i −0.542763 0.313364i
\(457\) −32.5000 + 56.2917i −0.0711160 + 0.123176i −0.899391 0.437146i \(-0.855989\pi\)
0.828275 + 0.560322i \(0.189323\pi\)
\(458\) 460.726i 1.00595i
\(459\) 420.888i 0.916968i
\(460\) 96.0000 0.208696
\(461\) −690.000 398.372i −1.49675 0.864147i −0.496753 0.867892i \(-0.665475\pi\)
−0.999993 + 0.00374501i \(0.998808\pi\)
\(462\) 9.00000 15.5885i 0.0194805 0.0337412i
\(463\) −367.000 635.663i −0.792657 1.37292i −0.924317 0.381627i \(-0.875364\pi\)
0.131660 0.991295i \(-0.457969\pi\)
\(464\) 429.000 247.683i 0.924569 0.533800i
\(465\) 288.000 166.277i 0.619355 0.357585i
\(466\) −175.500 + 303.975i −0.376609 + 0.652307i
\(467\) 202.650i 0.433940i 0.976178 + 0.216970i \(0.0696174\pi\)
−0.976178 + 0.216970i \(0.930383\pi\)
\(468\) −36.0000 −0.0769231
\(469\) −62.0000 −0.132196
\(470\) 252.000 + 145.492i 0.536170 + 0.309558i
\(471\) −120.000 −0.254777
\(472\) 217.500 + 376.721i 0.460805 + 0.798138i
\(473\) −91.5000 + 52.8275i −0.193446 + 0.111686i
\(474\) 197.454i 0.416569i
\(475\) −71.5000 + 123.842i −0.150526 + 0.260719i
\(476\) 31.1769i 0.0654977i
\(477\) 0 0
\(478\) 696.000 1.45607
\(479\) 525.000 + 303.109i 1.09603 + 0.632795i 0.935176 0.354183i \(-0.115241\pi\)
0.160857 + 0.986978i \(0.448574\pi\)
\(480\) 81.0000 + 140.296i 0.168750 + 0.292284i
\(481\) −68.0000 117.779i −0.141372 0.244864i
\(482\) 178.500 103.057i 0.370332 0.213811i
\(483\) 144.000 + 83.1384i 0.298137 + 0.172129i
\(484\) −59.0000 + 102.191i −0.121901 + 0.211138i
\(485\) 398.372i 0.821385i
\(486\) 420.888i 0.866025i
\(487\) −106.000 −0.217659 −0.108830 0.994060i \(-0.534710\pi\)
−0.108830 + 0.994060i \(0.534710\pi\)
\(488\) −420.000 242.487i −0.860656 0.496900i
\(489\) 159.000 275.396i 0.325153 0.563182i
\(490\) −135.000 233.827i −0.275510 0.477198i
\(491\) −199.500 + 115.181i −0.406314 + 0.234585i −0.689205 0.724567i \(-0.742040\pi\)
0.282891 + 0.959152i \(0.408707\pi\)
\(492\) −31.5000 + 18.1865i −0.0640244 + 0.0369645i
\(493\) 351.000 607.950i 0.711968 1.23316i
\(494\) 76.2102i 0.154272i
\(495\) 27.0000 + 46.7654i 0.0545455 + 0.0944755i
\(496\) −352.000 −0.709677
\(497\) −54.0000 31.1769i −0.108652 0.0627302i
\(498\) −252.000 −0.506024
\(499\) 393.500 + 681.562i 0.788577 + 1.36586i 0.926839 + 0.375460i \(0.122515\pi\)
−0.138261 + 0.990396i \(0.544151\pi\)
\(500\) 114.000 65.8179i 0.228000 0.131636i
\(501\) 571.577i 1.14087i
\(502\) 337.500 584.567i 0.672311 1.16448i
\(503\) 623.538i 1.23964i −0.784745 0.619819i \(-0.787206\pi\)
0.784745 0.619819i \(-0.212794\pi\)
\(504\) 155.885i 0.309295i
\(505\) 156.000 0.308911
\(506\) −72.0000 41.5692i −0.142292 0.0821526i
\(507\) 229.500 + 397.506i 0.452663 + 0.784035i
\(508\) 8.00000 + 13.8564i 0.0157480 + 0.0272764i
\(509\) −186.000 + 107.387i −0.365422 + 0.210977i −0.671457 0.741044i \(-0.734331\pi\)
0.306034 + 0.952020i \(0.400998\pi\)
\(510\) −243.000 140.296i −0.476471 0.275090i
\(511\) −65.0000 + 112.583i −0.127202 + 0.220320i
\(512\) 552.524i 1.07915i
\(513\) 297.000 0.578947
\(514\) −303.000 −0.589494
\(515\) 120.000 + 69.2820i 0.233010 + 0.134528i
\(516\) 91.5000 158.483i 0.177326 0.307137i
\(517\) 42.0000 + 72.7461i 0.0812379 + 0.140708i
\(518\) −102.000 + 58.8897i −0.196911 + 0.113687i
\(519\) −603.000 + 348.142i −1.16185 + 0.670794i
\(520\) −60.0000 + 103.923i −0.115385 + 0.199852i
\(521\) 202.650i 0.388963i 0.980906 + 0.194482i \(0.0623025\pi\)
−0.980906 + 0.194482i \(0.937698\pi\)
\(522\) −351.000 + 607.950i −0.672414 + 1.16465i
\(523\) −250.000 −0.478011 −0.239006 0.971018i \(-0.576821\pi\)
−0.239006 + 0.971018i \(0.576821\pi\)
\(524\) −138.000 79.6743i −0.263359 0.152050i
\(525\) 78.0000 0.148571
\(526\) −39.0000 67.5500i −0.0741445 0.128422i
\(527\) −432.000 + 249.415i −0.819734 + 0.473274i
\(528\) 57.1577i 0.108253i
\(529\) 119.500 206.980i 0.225898 0.391267i
\(530\) 0 0
\(531\) −391.500 226.033i −0.737288 0.425674i
\(532\) 22.0000 0.0413534
\(533\) −42.0000 24.2487i −0.0787992 0.0454948i
\(534\) −324.000 561.184i −0.606742 1.05091i
\(535\) 243.000 + 420.888i 0.454206 + 0.786707i
\(536\) −232.500 + 134.234i −0.433769 + 0.250436i
\(537\) 162.000 + 93.5307i 0.301676 + 0.174173i
\(538\) 162.000 280.592i 0.301115 0.521547i
\(539\) 77.9423i 0.144605i
\(540\) −81.0000 46.7654i −0.150000 0.0866025i
\(541\) 650.000 1.20148 0.600739 0.799445i \(-0.294873\pi\)
0.600739 + 0.799445i \(0.294873\pi\)
\(542\) 402.000 + 232.095i 0.741697 + 0.428219i
\(543\) 348.000 602.754i 0.640884 1.11004i
\(544\) −121.500 210.444i −0.223346 0.386846i
\(545\) −156.000 + 90.0666i −0.286239 + 0.165260i
\(546\) −36.0000 + 20.7846i −0.0659341 + 0.0380671i
\(547\) −311.500 + 539.534i −0.569470 + 0.986351i 0.427149 + 0.904181i \(0.359518\pi\)
−0.996618 + 0.0821692i \(0.973815\pi\)
\(548\) 188.794i 0.344514i
\(549\) 504.000 0.918033
\(550\) −39.0000 −0.0709091
\(551\) 429.000 + 247.683i 0.778584 + 0.449516i
\(552\) 720.000 1.30435
\(553\) −38.0000 65.8179i −0.0687161 0.119020i
\(554\) 84.0000 48.4974i 0.151625 0.0875405i
\(555\) 353.338i 0.636646i
\(556\) −2.50000 + 4.33013i −0.00449640 + 0.00778800i
\(557\) 530.008i 0.951540i −0.879570 0.475770i \(-0.842170\pi\)
0.879570 0.475770i \(-0.157830\pi\)
\(558\) 432.000 249.415i 0.774194 0.446981i
\(559\) 244.000 0.436494
\(560\) 66.0000 + 38.1051i 0.117857 + 0.0680449i
\(561\) −40.5000 70.1481i −0.0721925 0.125041i
\(562\) 42.0000 + 72.7461i 0.0747331 + 0.129442i
\(563\) 97.5000 56.2917i 0.173179 0.0999852i −0.410905 0.911678i \(-0.634787\pi\)
0.584084 + 0.811693i \(0.301454\pi\)
\(564\) −126.000 72.7461i −0.223404 0.128983i
\(565\) −156.000 + 270.200i −0.276106 + 0.478230i
\(566\) 647.787i 1.14450i
\(567\) −81.0000 140.296i −0.142857 0.247436i
\(568\) −270.000 −0.475352
\(569\) 565.500 + 326.492i 0.993849 + 0.573799i 0.906423 0.422372i \(-0.138802\pi\)
0.0874263 + 0.996171i \(0.472136\pi\)
\(570\) 99.0000 171.473i 0.173684 0.300830i
\(571\) −272.500 471.984i −0.477233 0.826592i 0.522427 0.852684i \(-0.325027\pi\)
−0.999660 + 0.0260926i \(0.991694\pi\)
\(572\) −6.00000 + 3.46410i −0.0104895 + 0.00605612i
\(573\) −603.000 + 348.142i −1.05236 + 0.607578i
\(574\) −21.0000 + 36.3731i −0.0365854 + 0.0633677i
\(575\) 360.267i 0.626551i
\(576\) 319.500 + 553.390i 0.554688 + 0.960747i
\(577\) −871.000 −1.50953 −0.754766 0.655994i \(-0.772250\pi\)
−0.754766 + 0.655994i \(0.772250\pi\)
\(578\) −69.0000 39.8372i −0.119377 0.0689224i
\(579\) −795.000 −1.37306
\(580\) −78.0000 135.100i −0.134483 0.232931i
\(581\) 84.0000 48.4974i 0.144578 0.0834723i
\(582\) 597.558i 1.02673i
\(583\) 0 0
\(584\) 562.917i 0.963898i
\(585\) 124.708i 0.213175i
\(586\) −438.000 −0.747440
\(587\) −1.50000 0.866025i −0.00255537 0.00147534i 0.498722 0.866762i \(-0.333803\pi\)
−0.501277 + 0.865287i \(0.667136\pi\)
\(588\) 67.5000 + 116.913i 0.114796 + 0.198832i
\(589\) −176.000 304.841i −0.298812 0.517557i
\(590\) −261.000 + 150.688i −0.442373 + 0.255404i
\(591\) 324.000 + 187.061i 0.548223 + 0.316517i
\(592\) −187.000 + 323.894i −0.315878 + 0.547117i
\(593\) 187.061i 0.315449i −0.987483 0.157725i \(-0.949584\pi\)
0.987483 0.157725i \(-0.0504159\pi\)
\(594\) 40.5000 + 70.1481i 0.0681818 + 0.118094i
\(595\) 108.000 0.181513
\(596\) 132.000 + 76.2102i 0.221477 + 0.127870i
\(597\) −435.000 + 753.442i −0.728643 + 1.26205i
\(598\) 96.0000 + 166.277i 0.160535 + 0.278055i
\(599\) 489.000 282.324i 0.816361 0.471326i −0.0327992 0.999462i \(-0.510442\pi\)
0.849160 + 0.528136i \(0.177109\pi\)
\(600\) 292.500 168.875i 0.487500 0.281458i
\(601\) −230.500 + 399.238i −0.383527 + 0.664289i −0.991564 0.129620i \(-0.958624\pi\)
0.608036 + 0.793909i \(0.291958\pi\)
\(602\) 211.310i 0.351014i
\(603\) 139.500 241.621i 0.231343 0.400698i
\(604\) 20.0000 0.0331126
\(605\) −354.000 204.382i −0.585124 0.337821i
\(606\) 234.000 0.386139
\(607\) 56.0000 + 96.9948i 0.0922570 + 0.159794i 0.908461 0.417971i \(-0.137259\pi\)
−0.816204 + 0.577765i \(0.803925\pi\)
\(608\) 148.500 85.7365i 0.244243 0.141014i
\(609\) 270.200i 0.443678i
\(610\) 168.000 290.985i 0.275410 0.477024i
\(611\) 193.990i 0.317495i
\(612\) 121.500 + 70.1481i 0.198529 + 0.114621i
\(613\) 902.000 1.47145 0.735726 0.677279i \(-0.236841\pi\)
0.735726 + 0.677279i \(0.236841\pi\)
\(614\) −799.500 461.592i −1.30212 0.751778i
\(615\) −63.0000 109.119i −0.102439 0.177430i
\(616\) 15.0000 + 25.9808i 0.0243506 + 0.0421766i
\(617\) −307.500 + 177.535i −0.498379 + 0.287739i −0.728044 0.685530i \(-0.759570\pi\)
0.229665 + 0.973270i \(0.426237\pi\)
\(618\) 180.000 + 103.923i 0.291262 + 0.168160i
\(619\) 399.500 691.954i 0.645396 1.11786i −0.338814 0.940853i \(-0.610026\pi\)
0.984210 0.177005i \(-0.0566409\pi\)
\(620\) 110.851i 0.178792i
\(621\) −648.000 + 374.123i −1.04348 + 0.602452i
\(622\) 426.000 0.684887
\(623\) 216.000 + 124.708i 0.346709 + 0.200173i
\(624\) −66.0000 + 114.315i −0.105769 + 0.183198i
\(625\) 65.5000 + 113.449i 0.104800 + 0.181519i
\(626\) 232.500 134.234i 0.371406 0.214431i
\(627\) 49.5000 28.5788i 0.0789474 0.0455803i
\(628\) 20.0000 34.6410i 0.0318471 0.0551609i
\(629\) 530.008i 0.842619i
\(630\) −108.000 −0.171429
\(631\) 830.000 1.31537 0.657686 0.753292i \(-0.271535\pi\)
0.657686 + 0.753292i \(0.271535\pi\)
\(632\) −285.000 164.545i −0.450949 0.260356i
\(633\) −282.000 −0.445498
\(634\) 42.0000 + 72.7461i 0.0662461 + 0.114742i
\(635\) −48.0000 + 27.7128i −0.0755906 + 0.0436422i
\(636\) 0 0
\(637\) −90.0000 + 155.885i −0.141287 + 0.244717i
\(638\) 135.100i 0.211755i
\(639\) 243.000 140.296i 0.380282 0.219556i
\(640\) 210.000 0.328125
\(641\) −325.500 187.928i −0.507800 0.293179i 0.224129 0.974560i \(-0.428046\pi\)
−0.731929 + 0.681381i \(0.761380\pi\)
\(642\) 364.500 + 631.333i 0.567757 + 0.983384i
\(643\) 6.50000 + 11.2583i 0.0101089 + 0.0175091i 0.871036 0.491220i \(-0.163449\pi\)
−0.860927 + 0.508729i \(0.830116\pi\)
\(644\) −48.0000 + 27.7128i −0.0745342 + 0.0430323i
\(645\) 549.000 + 316.965i 0.851163 + 0.491419i
\(646\) −148.500 + 257.210i −0.229876 + 0.398157i
\(647\) 467.654i 0.722803i −0.932410 0.361402i \(-0.882298\pi\)
0.932410 0.361402i \(-0.117702\pi\)
\(648\) −607.500 350.740i −0.937500 0.541266i
\(649\) −87.0000 −0.134052
\(650\) 78.0000 + 45.0333i 0.120000 + 0.0692820i
\(651\) −96.0000 + 166.277i −0.147465 + 0.255418i
\(652\) 53.0000 + 91.7987i 0.0812883 + 0.140796i
\(653\) 327.000 188.794i 0.500766 0.289117i −0.228264 0.973599i \(-0.573305\pi\)
0.729030 + 0.684482i \(0.239972\pi\)
\(654\) −234.000 + 135.100i −0.357798 + 0.206575i
\(655\) 276.000 478.046i 0.421374 0.729841i
\(656\) 133.368i 0.203305i
\(657\) −292.500 506.625i −0.445205 0.771119i
\(658\) −168.000 −0.255319
\(659\) −852.000 491.902i −1.29287 0.746438i −0.313706 0.949520i \(-0.601571\pi\)
−0.979162 + 0.203082i \(0.934904\pi\)
\(660\) −18.0000 −0.0272727
\(661\) 191.000 + 330.822i 0.288956 + 0.500487i 0.973561 0.228428i \(-0.0733585\pi\)
−0.684605 + 0.728915i \(0.740025\pi\)
\(662\) 3.00000 1.73205i 0.00453172 0.00261639i
\(663\) 187.061i 0.282144i
\(664\) 210.000 363.731i 0.316265 0.547787i
\(665\) 76.2102i 0.114602i
\(666\) 530.008i 0.795807i
\(667\) −1248.00 −1.87106
\(668\) −165.000 95.2628i −0.247006 0.142609i
\(669\) 78.0000 + 135.100i 0.116592 + 0.201943i
\(670\) −93.0000 161.081i −0.138806 0.240419i
\(671\) 84.0000 48.4974i 0.125186 0.0722763i
\(672\) −81.0000 46.7654i −0.120536 0.0695913i
\(673\) −289.000 + 500.563i −0.429421 + 0.743778i −0.996822 0.0796633i \(-0.974615\pi\)
0.567401 + 0.823441i \(0.307949\pi\)
\(674\) 133.368i 0.197875i
\(675\) −175.500 + 303.975i −0.260000 + 0.450333i
\(676\) −153.000 −0.226331
\(677\) 606.000 + 349.874i 0.895126 + 0.516801i 0.875616 0.483009i \(-0.160456\pi\)
0.0195100 + 0.999810i \(0.493789\pi\)
\(678\) −234.000 + 405.300i −0.345133 + 0.597787i
\(679\) 115.000 + 199.186i 0.169367 + 0.293352i
\(680\) 405.000 233.827i 0.595588 0.343863i
\(681\) 490.500 283.190i 0.720264 0.415845i
\(682\) 48.0000 83.1384i 0.0703812 0.121904i
\(683\) 1044.43i 1.52918i 0.644520 + 0.764588i \(0.277057\pi\)
−0.644520 + 0.764588i \(0.722943\pi\)
\(684\) −49.5000 + 85.7365i −0.0723684 + 0.125346i
\(685\) −654.000 −0.954745
\(686\) 282.000 + 162.813i 0.411079 + 0.237336i
\(687\) 798.000 1.16157
\(688\) −335.500 581.103i −0.487645 0.844627i
\(689\) 0 0
\(690\) 498.831i 0.722943i
\(691\) −91.0000 + 157.617i −0.131693 + 0.228099i −0.924329 0.381596i \(-0.875375\pi\)
0.792636 + 0.609695i \(0.208708\pi\)
\(692\) 232.095i 0.335397i
\(693\) −27.0000 15.5885i −0.0389610 0.0224942i
\(694\) −195.000 −0.280980
\(695\) −15.0000 8.66025i −0.0215827 0.0124608i
\(696\) −585.000 1013.25i −0.840517 1.45582i
\(697\) 94.5000 + 163.679i 0.135581 + 0.234833i
\(698\) 624.000 360.267i 0.893983 0.516141i
\(699\) 526.500 + 303.975i 0.753219 + 0.434871i
\(700\) −13.0000 + 22.5167i −0.0185714 + 0.0321667i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 187.061i 0.266469i
\(703\) −374.000 −0.532006
\(704\) 106.500 + 61.4878i 0.151278 + 0.0873406i
\(705\) 252.000 436.477i 0.357447 0.619116i
\(706\) 1.50000 + 2.59808i 0.00212465 + 0.00367999i
\(707\) −78.0000 + 45.0333i −0.110325 + 0.0636964i
\(708\) 130.500 75.3442i 0.184322 0.106418i
\(709\) 350.000 606.218i 0.493653 0.855032i −0.506320 0.862346i \(-0.668995\pi\)
0.999973 + 0.00731341i \(0.00232795\pi\)
\(710\) 187.061i 0.263467i
\(711\) 342.000 0.481013
\(712\) 1080.00 1.51685
\(713\) 768.000 + 443.405i 1.07714 + 0.621886i
\(714\) 162.000 0.226891
\(715\) −12.0000 20.7846i −0.0167832 0.0290694i
\(716\) −54.0000 + 31.1769i −0.0754190 + 0.0435432i
\(717\) 1205.51i 1.68132i
\(718\) −513.000 + 888.542i −0.714485 + 1.23752i
\(719\) 592.361i 0.823868i 0.911214 + 0.411934i \(0.135147\pi\)
−0.911214 + 0.411934i \(0.864853\pi\)
\(720\) −297.000 + 171.473i −0.412500 + 0.238157i
\(721\) −80.0000 −0.110957
\(722\) 360.000 + 207.846i 0.498615 + 0.287875i
\(723\) −178.500 309.171i −0.246888 0.427623i
\(724\) 116.000 + 200.918i 0.160221 + 0.277511i
\(725\) −507.000 + 292.717i −0.699310 + 0.403747i
\(726\) −531.000 306.573i −0.731405 0.422277i
\(727\) 332.000 575.041i 0.456671 0.790978i −0.542111 0.840307i \(-0.682375\pi\)
0.998783 + 0.0493289i \(0.0157082\pi\)
\(728\) 69.2820i 0.0951676i
\(729\) 729.000 1.00000
\(730\) −390.000 −0.534247
\(731\) −823.500 475.448i −1.12654 0.650408i
\(732\) −84.0000 + 145.492i −0.114754 + 0.198760i
\(733\) 335.000 + 580.237i 0.457026 + 0.791592i 0.998802 0.0489306i \(-0.0155813\pi\)
−0.541776 + 0.840523i \(0.682248\pi\)
\(734\) −537.000 + 310.037i −0.731608 + 0.422394i
\(735\) −405.000 + 233.827i −0.551020 + 0.318132i
\(736\) −216.000 + 374.123i −0.293478 + 0.508319i
\(737\) 53.6936i 0.0728542i
\(738\) −94.5000 163.679i −0.128049 0.221787i
\(739\) 317.000 0.428958 0.214479 0.976729i \(-0.431195\pi\)
0.214479 + 0.976729i \(0.431195\pi\)
\(740\) 102.000 + 58.8897i 0.137838 + 0.0795807i
\(741\) −132.000 −0.178138
\(742\) 0 0
\(743\) −537.000 + 310.037i −0.722746 + 0.417277i −0.815762 0.578387i \(-0.803682\pi\)
0.0930168 + 0.995665i \(0.470349\pi\)
\(744\) 831.384i 1.11745i
\(745\) −264.000 + 457.261i −0.354362 + 0.613774i
\(746\) 1004.59i 1.34663i
\(747\) 436.477i 0.584306i
\(748\) 27.0000 0.0360963
\(749\) −243.000 140.296i −0.324433 0.187311i
\(750\) 342.000 + 592.361i 0.456000 + 0.789815i
\(751\) −655.000 1134.49i −0.872170 1.51064i −0.859747 0.510721i \(-0.829379\pi\)
−0.0124237 0.999923i \(-0.503955\pi\)
\(752\) −462.000 + 266.736i −0.614362 + 0.354702i
\(753\) −1012.50 584.567i −1.34462 0.776318i
\(754\) 156.000 270.200i 0.206897 0.358355i
\(755\) 69.2820i 0.0917643i
\(756\) 54.0000 0.0714286
\(757\) 218.000 0.287979 0.143989 0.989579i \(-0.454007\pi\)
0.143989 + 0.989579i \(0.454007\pi\)
\(758\) −124.500 71.8801i −0.164248 0.0948286i
\(759\) −72.0000 + 124.708i −0.0948617 + 0.164305i
\(760\) 165.000 + 285.788i 0.217105 + 0.376037i
\(761\) 570.000 329.090i 0.749014 0.432444i −0.0763232 0.997083i \(-0.524318\pi\)
0.825338 + 0.564639i \(0.190985\pi\)
\(762\) −72.0000 + 41.5692i −0.0944882 + 0.0545528i
\(763\) 52.0000 90.0666i 0.0681520 0.118043i
\(764\) 232.095i 0.303789i
\(765\) −243.000 + 420.888i −0.317647 + 0.550181i
\(766\) 966.000 1.26110
\(767\) 174.000 + 100.459i 0.226858 + 0.130976i
\(768\) −537.000 −0.699219
\(769\) −511.000 885.078i −0.664499 1.15095i −0.979421 0.201829i \(-0.935312\pi\)
0.314921 0.949118i \(-0.398022\pi\)
\(770\) −18.0000 + 10.3923i −0.0233766 + 0.0134965i
\(771\) 524.811i 0.680689i
\(772\) 132.500 229.497i 0.171632 0.297276i
\(773\) 1184.72i 1.53263i −0.642465 0.766315i \(-0.722088\pi\)
0.642465 0.766315i \(-0.277912\pi\)
\(774\) 823.500 + 475.448i 1.06395 + 0.614274i
\(775\) 416.000 0.536774
\(776\) 862.500 + 497.965i 1.11147 + 0.641707i
\(777\) 102.000 + 176.669i 0.131274 + 0.227373i
\(778\) 447.000 + 774.227i 0.574550 + 0.995150i
\(779\) −115.500 + 66.6840i −0.148267 + 0.0856020i
\(780\) 36.0000 + 20.7846i 0.0461538 + 0.0266469i
\(781\) 27.0000 46.7654i 0.0345711 0.0598788i
\(782\) 748.246i 0.956836i
\(783\) 1053.00 + 607.950i 1.34483 + 0.776437i
\(784\) 495.000 0.631378
\(785\) 120.000 + 69.2820i 0.152866 + 0.0882574i
\(786\) 414.000 717.069i 0.526718 0.912302i
\(787\) 65.0000 + 112.583i 0.0825921 + 0.143054i 0.904363 0.426765i \(-0.140347\pi\)
−0.821771 + 0.569819i \(0.807013\pi\)
\(788\) −108.000 + 62.3538i −0.137056 + 0.0791292i
\(789\) −117.000 + 67.5500i −0.148289 + 0.0856147i
\(790\) 114.000 197.454i 0.144304 0.249942i
\(791\) 180.133i 0.227729i
\(792\) −135.000 −0.170455
\(793\) −224.000 −0.282472
\(794\) −543.000 313.501i −0.683879 0.394838i
\(795\) 0 0
\(796\) −145.000 251.147i −0.182161 0.315512i
\(797\) 273.000 157.617i 0.342535 0.197762i −0.318858 0.947803i \(-0.603299\pi\)
0.661392 + 0.750040i \(0.269966\pi\)
\(798\) 114.315i 0.143252i
\(799\) −378.000 + 654.715i −0.473091 + 0.819418i
\(800\) 202.650i 0.253312i
\(801\) −972.000 + 561.184i −1.21348 + 0.700605i
\(802\) −681.000 −0.849127
\(803\) −97.5000 56.2917i −0.121420 0.0701017i
\(804\) 46.5000 + 80.5404i 0.0578358 + 0.100175i
\(805\) −96.0000 166.277i −0.119255 0.206555i
\(806\) −192.000 + 110.851i −0.238213 + 0.137533i
\(807\) −486.000 280.592i −0.602230 0.347698i
\(808\) −195.000 + 337.750i −0.241337 + 0.418007i
\(809\) 140.296i 0.173419i 0.996234 + 0.0867096i \(0.0276352\pi\)
−0.996234 + 0.0867096i \(0.972365\pi\)
\(810\) 243.000 420.888i 0.300000 0.519615i
\(811\) 299.000 0.368681 0.184340 0.982862i \(-0.440985\pi\)
0.184340 + 0.982862i \(0.440985\pi\)
\(812\) 78.0000 + 45.0333i 0.0960591 + 0.0554598i
\(813\) 402.000 696.284i 0.494465 0.856438i
\(814\) −51.0000 88.3346i −0.0626536 0.108519i
\(815\) −318.000 + 183.597i −0.390184 + 0.225273i
\(816\) 445.500 257.210i 0.545956 0.315208i
\(817\) 335.500 581.103i 0.410649 0.711264i
\(818\) 382.783i 0.467950i
\(819\) 36.0000 + 62.3538i 0.0439560 + 0.0761341i
\(820\) 42.0000 0.0512195
\(821\) 525.000 + 303.109i 0.639464 + 0.369195i 0.784408 0.620245i \(-0.212967\pi\)
−0.144944 + 0.989440i \(0.546300\pi\)
\(822\) −981.000 −1.19343
\(823\) 407.000 + 704.945i 0.494532 + 0.856555i 0.999980 0.00630221i \(-0.00200607\pi\)
−0.505448 + 0.862857i \(0.668673\pi\)
\(824\) −300.000 + 173.205i −0.364078 + 0.210200i
\(825\) 67.5500i 0.0818788i
\(826\) 87.0000 150.688i 0.105327 0.182432i
\(827\) 1434.14i 1.73415i 0.498182 + 0.867073i \(0.334001\pi\)
−0.498182 + 0.867073i \(0.665999\pi\)
\(828\) 249.415i 0.301226i
\(829\) −718.000 −0.866104 −0.433052 0.901369i \(-0.642563\pi\)
−0.433052 + 0.901369i \(0.642563\pi\)
\(830\) 252.000 + 145.492i 0.303614 + 0.175292i
\(831\) −84.0000 145.492i −0.101083 0.175081i
\(832\) −142.000 245.951i −0.170673 0.295614i
\(833\) 607.500 350.740i 0.729292 0.421057i
\(834\) −22.5000 12.9904i −0.0269784 0.0155760i
\(835\) 330.000 571.577i 0.395210 0.684523i
\(836\) 19.0526i 0.0227901i
\(837\) −432.000 748.246i −0.516129 0.893962i
\(838\) −1356.00 −1.61814
\(839\) −690.000 398.372i −0.822408 0.474817i 0.0288384 0.999584i \(-0.490819\pi\)
−0.851246 + 0.524767i \(0.824153\pi\)
\(840\) 90.0000 155.885i 0.107143 0.185577i
\(841\) 593.500 + 1027.97i 0.705707 + 1.22232i
\(842\) −1023.00 + 590.629i −1.21496 + 0.701460i
\(843\) 126.000 72.7461i 0.149466 0.0862943i
\(844\) 47.0000 81.4064i 0.0556872 0.0964531i
\(845\) 530.008i 0.627228i
\(846\) 378.000 654.715i 0.446809 0.773895i
\(847\) 236.000 0.278630
\(848\) 0 0
\(849\) 1122.00 1.32155
\(850\) −175.500 303.975i −0.206471 0.357618i
\(851\) 816.000 471.118i 0.958872 0.553605i
\(852\) 93.5307i 0.109778i
\(853\) −712.000 + 1233.22i −0.834701 + 1.44574i 0.0595725 + 0.998224i \(0.481026\pi\)
−0.894274 + 0.447521i \(0.852307\pi\)
\(854\) 193.990i 0.227154i
\(855\) −297.000 171.473i −0.347368 0.200553i
\(856\) −1215.00 −1.41939
\(857\) 606.000 + 349.874i 0.707118 + 0.408255i 0.809993 0.586440i \(-0.199471\pi\)
−0.102875 + 0.994694i \(0.532804\pi\)
\(858\) −18.0000 31.1769i −0.0209790 0.0363367i
\(859\) −155.500 269.334i −0.181024 0.313544i 0.761205 0.648511i \(-0.224608\pi\)
−0.942230 + 0.334968i \(0.891275\pi\)
\(860\) −183.000 + 105.655i −0.212791 + 0.122855i
\(861\) 63.0000 + 36.3731i 0.0731707 + 0.0422451i
\(862\) 243.000 420.888i 0.281903 0.488270i
\(863\) 1028.84i 1.19216i 0.802923 + 0.596082i \(0.203277\pi\)
−0.802923 + 0.596082i \(0.796723\pi\)
\(864\) 364.500 210.444i 0.421875 0.243570i
\(865\) 804.000 0.929480
\(866\) 442.500 + 255.477i 0.510970 + 0.295009i
\(867\) −69.0000 + 119.512i −0.0795848 + 0.137845i
\(868\) −32.0000 55.4256i −0.0368664 0.0638544i
\(869\) 57.0000 32.9090i 0.0655926 0.0378699i
\(870\) 702.000 405.300i 0.806897 0.465862i
\(871\) −62.0000 + 107.387i −0.0711825 + 0.123292i
\(872\) 450.333i 0.516437i
\(873\) −1035.00 −1.18557
\(874\) 528.000 0.604119
\(875\) −228.000 131.636i −0.260571 0.150441i
\(876\) 195.000 0.222603
\(877\) −52.0000 90.0666i −0.0592930 0.102699i 0.834855 0.550470i \(-0.185551\pi\)
−0.894148 + 0.447771i \(0.852218\pi\)
\(878\) 1218.00 703.213i 1.38724 0.800926i
\(879\) 758.638i 0.863070i
\(880\) −33.0000 + 57.1577i −0.0375000 + 0.0649519i
\(881\) 62.3538i 0.0707762i −0.999374 0.0353881i \(-0.988733\pi\)
0.999374 0.0353881i \(-0.0112667\pi\)
\(882\) −607.500 + 350.740i −0.688776 + 0.397665i
\(883\) 119.000 0.134768 0.0673839 0.997727i \(-0.478535\pi\)
0.0673839 + 0.997727i \(0.478535\pi\)
\(884\) −54.0000 31.1769i −0.0610860 0.0352680i
\(885\) 261.000 + 452.065i 0.294915 + 0.510808i
\(886\) −79.5000 137.698i −0.0897291 0.155415i
\(887\) 1029.00 594.093i 1.16009 0.669778i 0.208765 0.977966i \(-0.433056\pi\)
0.951326 + 0.308188i \(0.0997224\pi\)
\(888\) 765.000 + 441.673i 0.861486 + 0.497379i
\(889\) 16.0000 27.7128i 0.0179978 0.0311730i
\(890\) 748.246i 0.840726i
\(891\) 121.500 70.1481i 0.136364 0.0787296i
\(892\) −52.0000 −0.0582960
\(893\) −462.000 266.736i −0.517357 0.298696i
\(894\) −396.000 + 685.892i −0.442953 + 0.767217i
\(895\) −108.000 187.061i −0.120670 0.209007i
\(896\) −105.000 + 60.6218i −0.117188 + 0.0676582i
\(897\) 288.000 166.277i 0.321070 0.185370i
\(898\) 553.500 958.690i 0.616370 1.06758i
\(899\) 1441.07i 1.60297i
\(900\) −58.5000 101.325i −0.0650000 0.112583i
\(901\) 0 0
\(902\) −31.5000 18.1865i −0.0349224 0.0201625i
\(903\) −366.000 −0.405316
\(904\) −390.000 675.500i −0.431416 0.747234i
\(905\) −696.000 + 401.836i −0.769061 + 0.444017i
\(906\) 103.923i 0.114705i
\(907\) −347.500 + 601.888i −0.383131 + 0.663603i −0.991508 0.130046i \(-0.958488\pi\)
0.608377 + 0.793648i \(0.291821\pi\)
\(908\) 188.794i 0.207922i
\(909\) 405.300i 0.445874i
\(910\) 48.0000 0.0527473
\(911\) −1500.00 866.025i −1.64654 0.950632i −0.978432 0.206569i \(-0.933770\pi\)
−0.668110 0.744062i \(-0.732897\pi\)
\(912\) 181.500 + 314.367i 0.199013 + 0.344701i
\(913\) 42.0000 + 72.7461i 0.0460022 + 0.0796781i
\(914\) 97.5000 56.2917i 0.106674 0.0615882i
\(915\) −504.000 290.985i −0.550820 0.318016i
\(916\) −133.000 + 230.363i −0.145197 + 0.251488i
\(917\) 318.697i 0.347543i
\(918\) −364.500 + 631.333i −0.397059 + 0.687726i
\(919\) 56.0000 0.0609358 0.0304679 0.999536i \(-0.490300\pi\)
0.0304679 + 0.999536i \(0.490300\pi\)
\(920\) −720.000 415.692i −0.782609 0.451839i
\(921\) −799.500 + 1384.77i −0.868078 + 1.50356i
\(922\) 690.000 + 1195.12i 0.748373 + 1.29622i
\(923\) −108.000 + 62.3538i −0.117010 + 0.0675556i
\(924\) 9.00000 5.19615i 0.00974026 0.00562354i
\(925\) 221.000 382.783i 0.238919 0.413820i
\(926\) 1271.33i 1.37292i
\(927\) 180.000 311.769i 0.194175 0.336321i
\(928\) 702.000 0.756466
\(929\) −690.000 398.372i −0.742734 0.428818i 0.0803285 0.996768i \(-0.474403\pi\)
−0.823063 + 0.567951i \(0.807736\pi\)
\(930\) −576.000 −0.619355
\(931\) 247.500 + 428.683i 0.265843 + 0.460454i
\(932\) −175.500 + 101.325i −0.188305 + 0.108718i
\(933\) 737.854i 0.790840i
\(934\) 175.500 303.975i 0.187901 0.325455i
\(935\) 93.5307i 0.100033i
\(936\) 270.000 + 155.885i 0.288462 + 0.166543i
\(937\) 470.000 0.501601 0.250800 0.968039i \(-0.419306\pi\)
0.250800 + 0.968039i \(0.419306\pi\)
\(938\) 93.0000 + 53.6936i 0.0991471 + 0.0572426i
\(939\) −232.500 402.702i −0.247604 0.428862i
\(940\) 84.0000 + 145.492i 0.0893617 + 0.154779i
\(941\) −348.000 + 200.918i −0.369819 + 0.213515i −0.673380 0.739297i \(-0.735158\pi\)
0.303560 + 0.952812i \(0.401825\pi\)
\(942\) 180.000 + 103.923i 0.191083 + 0.110322i
\(943\) 168.000 290.985i 0.178155 0.308573i
\(944\) 552.524i 0.585301i
\(945\) 187.061i 0.197949i
\(946\) 183.000 0.193446
\(947\) −1.50000 0.866025i −0.00158395 0.000914494i 0.499208 0.866482i \(-0.333624\pi\)
−0.500792 + 0.865568i \(0.666958\pi\)
\(948\) −57.0000 + 98.7269i −0.0601266 + 0.104142i
\(949\) 130.000 + 225.167i 0.136986 + 0.237267i
\(950\) 214.500 123.842i 0.225789 0.130360i
\(951\) 126.000 72.7461i 0.132492 0.0764944i
\(952\) −135.000 + 233.827i −0.141807 + 0.245616i
\(953\) 826.188i 0.866934i −0.901169 0.433467i \(-0.857290\pi\)
0.901169 0.433467i \(-0.142710\pi\)
\(954\) 0 0
\(955\) 804.000 0.841885
\(956\) 348.000 + 200.918i 0.364017 + 0.210165i
\(957\) 234.000 0.244514
\(958\) −525.000 909.327i −0.548017 0.949193i
\(959\) 327.000 188.794i 0.340980 0.196865i
\(960\) 737.854i 0.768598i
\(961\) −31.5000 + 54.5596i −0.0327784 + 0.0567738i
\(962\) 235.559i 0.244864i
\(963\) 1093.50 631.333i 1.13551 0.655589i
\(964\) 119.000 0.123444
\(965\) 795.000 + 458.993i 0.823834 + 0.475641i
\(966\) −144.000 249.415i −0.149068 0.258194i
\(967\) −601.000 1040.96i −0.621510 1.07649i −0.989205 0.146540i \(-0.953186\pi\)
0.367695 0.929946i \(-0.380147\pi\)
\(968\) 885.000 510.955i 0.914256 0.527846i
\(969\) 445.500 + 257.210i 0.459752 + 0.265438i
\(970\) −345.000 + 597.558i −0.355670 + 0.616039i
\(971\) 187.061i 0.192648i 0.995350 + 0.0963241i \(0.0307085\pi\)
−0.995350 + 0.0963241i \(0.969291\pi\)
\(972\) −121.500 + 210.444i −0.125000 + 0.216506i
\(973\) 10.0000 0.0102775
\(974\) 159.000 + 91.7987i 0.163244 + 0.0942492i
\(975\) 78.0000 135.100i 0.0800000 0.138564i
\(976\) 308.000 + 533.472i 0.315574 + 0.546590i
\(977\) −361.500 + 208.712i −0.370010 + 0.213626i −0.673463 0.739221i \(-0.735194\pi\)
0.303453 + 0.952847i \(0.401861\pi\)
\(978\) −477.000 + 275.396i −0.487730 + 0.281591i
\(979\) −108.000 + 187.061i −0.110317 + 0.191074i
\(980\) 155.885i 0.159066i
\(981\) 234.000 + 405.300i 0.238532 + 0.413150i
\(982\) 399.000 0.406314
\(983\) 1011.00 + 583.701i 1.02848 + 0.593796i 0.916550 0.399920i \(-0.130962\pi\)
0.111934 + 0.993716i \(0.464295\pi\)
\(984\) 315.000 0.320122
\(985\) −216.000 374.123i −0.219289 0.379820i
\(986\) −1053.00 + 607.950i −1.06795 + 0.616582i
\(987\) 290.985i 0.294817i
\(988\) 22.0000 38.1051i 0.0222672 0.0385679i
\(989\) 1690.48i 1.70928i
\(990\) 93.5307i 0.0944755i
\(991\) −1420.00 −1.43290 −0.716448 0.697640i \(-0.754233\pi\)
−0.716448 + 0.697640i \(0.754233\pi\)
\(992\) −432.000 249.415i −0.435484 0.251427i
\(993\) −3.00000 5.19615i −0.00302115 0.00523278i
\(994\) 54.0000 + 93.5307i 0.0543260 + 0.0940953i
\(995\) 870.000 502.295i 0.874372 0.504819i
\(996\) −126.000 72.7461i −0.126506 0.0730383i
\(997\) −262.000 + 453.797i −0.262788 + 0.455163i −0.966982 0.254845i \(-0.917975\pi\)
0.704193 + 0.710008i \(0.251309\pi\)
\(998\) 1363.12i 1.36586i
\(999\) −918.000 −0.918919
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 9.3.d.a.2.1 2
3.2 odd 2 27.3.d.a.8.1 2
4.3 odd 2 144.3.q.a.65.1 2
5.2 odd 4 225.3.i.a.74.2 4
5.3 odd 4 225.3.i.a.74.1 4
5.4 even 2 225.3.j.a.101.1 2
7.2 even 3 441.3.j.a.263.1 2
7.3 odd 6 441.3.n.a.128.1 2
7.4 even 3 441.3.n.b.128.1 2
7.5 odd 6 441.3.j.b.263.1 2
7.6 odd 2 441.3.r.a.344.1 2
8.3 odd 2 576.3.q.a.65.1 2
8.5 even 2 576.3.q.b.65.1 2
9.2 odd 6 81.3.b.a.80.1 2
9.4 even 3 27.3.d.a.17.1 2
9.5 odd 6 inner 9.3.d.a.5.1 yes 2
9.7 even 3 81.3.b.a.80.2 2
12.11 even 2 432.3.q.a.305.1 2
15.2 even 4 675.3.i.a.224.1 4
15.8 even 4 675.3.i.a.224.2 4
15.14 odd 2 675.3.j.a.251.1 2
24.5 odd 2 1728.3.q.a.1601.1 2
24.11 even 2 1728.3.q.b.1601.1 2
36.7 odd 6 1296.3.e.a.161.2 2
36.11 even 6 1296.3.e.a.161.1 2
36.23 even 6 144.3.q.a.113.1 2
36.31 odd 6 432.3.q.a.17.1 2
45.4 even 6 675.3.j.a.476.1 2
45.13 odd 12 675.3.i.a.449.1 4
45.14 odd 6 225.3.j.a.176.1 2
45.22 odd 12 675.3.i.a.449.2 4
45.23 even 12 225.3.i.a.149.2 4
45.32 even 12 225.3.i.a.149.1 4
63.5 even 6 441.3.n.a.410.1 2
63.23 odd 6 441.3.n.b.410.1 2
63.32 odd 6 441.3.j.a.275.1 2
63.41 even 6 441.3.r.a.50.1 2
63.59 even 6 441.3.j.b.275.1 2
72.5 odd 6 576.3.q.b.257.1 2
72.13 even 6 1728.3.q.a.449.1 2
72.59 even 6 576.3.q.a.257.1 2
72.67 odd 6 1728.3.q.b.449.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.3.d.a.2.1 2 1.1 even 1 trivial
9.3.d.a.5.1 yes 2 9.5 odd 6 inner
27.3.d.a.8.1 2 3.2 odd 2
27.3.d.a.17.1 2 9.4 even 3
81.3.b.a.80.1 2 9.2 odd 6
81.3.b.a.80.2 2 9.7 even 3
144.3.q.a.65.1 2 4.3 odd 2
144.3.q.a.113.1 2 36.23 even 6
225.3.i.a.74.1 4 5.3 odd 4
225.3.i.a.74.2 4 5.2 odd 4
225.3.i.a.149.1 4 45.32 even 12
225.3.i.a.149.2 4 45.23 even 12
225.3.j.a.101.1 2 5.4 even 2
225.3.j.a.176.1 2 45.14 odd 6
432.3.q.a.17.1 2 36.31 odd 6
432.3.q.a.305.1 2 12.11 even 2
441.3.j.a.263.1 2 7.2 even 3
441.3.j.a.275.1 2 63.32 odd 6
441.3.j.b.263.1 2 7.5 odd 6
441.3.j.b.275.1 2 63.59 even 6
441.3.n.a.128.1 2 7.3 odd 6
441.3.n.a.410.1 2 63.5 even 6
441.3.n.b.128.1 2 7.4 even 3
441.3.n.b.410.1 2 63.23 odd 6
441.3.r.a.50.1 2 63.41 even 6
441.3.r.a.344.1 2 7.6 odd 2
576.3.q.a.65.1 2 8.3 odd 2
576.3.q.a.257.1 2 72.59 even 6
576.3.q.b.65.1 2 8.5 even 2
576.3.q.b.257.1 2 72.5 odd 6
675.3.i.a.224.1 4 15.2 even 4
675.3.i.a.224.2 4 15.8 even 4
675.3.i.a.449.1 4 45.13 odd 12
675.3.i.a.449.2 4 45.22 odd 12
675.3.j.a.251.1 2 15.14 odd 2
675.3.j.a.476.1 2 45.4 even 6
1296.3.e.a.161.1 2 36.11 even 6
1296.3.e.a.161.2 2 36.7 odd 6
1728.3.q.a.449.1 2 72.13 even 6
1728.3.q.a.1601.1 2 24.5 odd 2
1728.3.q.b.449.1 2 72.67 odd 6
1728.3.q.b.1601.1 2 24.11 even 2