Properties

Label 21.3.f.b.19.1
Level $21$
Weight $3$
Character 21.19
Analytic conductor $0.572$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,3,Mod(10,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.572208555157\)
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 19.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 21.19
Dual form 21.3.f.b.10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.50000 + 2.59808i) q^{4} +(-4.50000 - 2.59808i) q^{5} +1.73205i q^{6} +(-3.50000 - 6.06218i) q^{7} -7.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.50000 + 2.59808i) q^{4} +(-4.50000 - 2.59808i) q^{5} +1.73205i q^{6} +(-3.50000 - 6.06218i) q^{7} -7.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(4.50000 - 2.59808i) q^{10} +(5.50000 + 9.52628i) q^{11} +(4.50000 + 2.59808i) q^{12} +6.92820i q^{13} +7.00000 q^{14} -9.00000 q^{15} +(-2.50000 + 4.33013i) q^{16} +(21.0000 - 12.1244i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-3.00000 - 1.73205i) q^{19} -15.5885i q^{20} +(-10.5000 - 6.06218i) q^{21} -11.0000 q^{22} +(-14.0000 + 24.2487i) q^{23} +(-10.5000 + 6.06218i) q^{24} +(1.00000 + 1.73205i) q^{25} +(-6.00000 - 3.46410i) q^{26} -5.19615i q^{27} +(10.5000 - 18.1865i) q^{28} +25.0000 q^{29} +(4.50000 - 7.79423i) q^{30} +(-28.5000 + 16.4545i) q^{31} +(-16.5000 - 28.5788i) q^{32} +(16.5000 + 9.52628i) q^{33} +24.2487i q^{34} +36.3731i q^{35} +9.00000 q^{36} +(29.0000 - 50.2295i) q^{37} +(3.00000 - 1.73205i) q^{38} +(6.00000 + 10.3923i) q^{39} +(31.5000 + 18.1865i) q^{40} +3.46410i q^{41} +(10.5000 - 6.06218i) q^{42} +26.0000 q^{43} +(-16.5000 + 28.5788i) q^{44} +(-13.5000 + 7.79423i) q^{45} +(-14.0000 - 24.2487i) q^{46} +(-66.0000 - 38.1051i) q^{47} +8.66025i q^{48} +(-24.5000 + 42.4352i) q^{49} -2.00000 q^{50} +(21.0000 - 36.3731i) q^{51} +(-18.0000 + 10.3923i) q^{52} +(-15.5000 - 26.8468i) q^{53} +(4.50000 + 2.59808i) q^{54} -57.1577i q^{55} +(24.5000 + 42.4352i) q^{56} -6.00000 q^{57} +(-12.5000 + 21.6506i) q^{58} +(-7.50000 + 4.33013i) q^{59} +(-13.5000 - 23.3827i) q^{60} +(12.0000 + 6.92820i) q^{61} -32.9090i q^{62} -21.0000 q^{63} +13.0000 q^{64} +(18.0000 - 31.1769i) q^{65} +(-16.5000 + 9.52628i) q^{66} +(26.0000 + 45.0333i) q^{67} +(63.0000 + 36.3731i) q^{68} +48.4974i q^{69} +(-31.5000 - 18.1865i) q^{70} +64.0000 q^{71} +(-10.5000 + 18.1865i) q^{72} +(6.00000 - 3.46410i) q^{73} +(29.0000 + 50.2295i) q^{74} +(3.00000 + 1.73205i) q^{75} -10.3923i q^{76} +(38.5000 - 66.6840i) q^{77} -12.0000 q^{78} +(-8.50000 + 14.7224i) q^{79} +(22.5000 - 12.9904i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 - 1.73205i) q^{82} +53.6936i q^{83} -36.3731i q^{84} -126.000 q^{85} +(-13.0000 + 22.5167i) q^{86} +(37.5000 - 21.6506i) q^{87} +(-38.5000 - 66.6840i) q^{88} +(-69.0000 - 39.8372i) q^{89} -15.5885i q^{90} +(42.0000 - 24.2487i) q^{91} -84.0000 q^{92} +(-28.5000 + 49.3634i) q^{93} +(66.0000 - 38.1051i) q^{94} +(9.00000 + 15.5885i) q^{95} +(-49.5000 - 28.5788i) q^{96} +91.7987i q^{97} +(-24.5000 - 42.4352i) q^{98} +33.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 3 q^{3} + 3 q^{4} - 9 q^{5} - 7 q^{7} - 14 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 3 q^{3} + 3 q^{4} - 9 q^{5} - 7 q^{7} - 14 q^{8} + 3 q^{9} + 9 q^{10} + 11 q^{11} + 9 q^{12} + 14 q^{14} - 18 q^{15} - 5 q^{16} + 42 q^{17} + 3 q^{18} - 6 q^{19} - 21 q^{21} - 22 q^{22} - 28 q^{23} - 21 q^{24} + 2 q^{25} - 12 q^{26} + 21 q^{28} + 50 q^{29} + 9 q^{30} - 57 q^{31} - 33 q^{32} + 33 q^{33} + 18 q^{36} + 58 q^{37} + 6 q^{38} + 12 q^{39} + 63 q^{40} + 21 q^{42} + 52 q^{43} - 33 q^{44} - 27 q^{45} - 28 q^{46} - 132 q^{47} - 49 q^{49} - 4 q^{50} + 42 q^{51} - 36 q^{52} - 31 q^{53} + 9 q^{54} + 49 q^{56} - 12 q^{57} - 25 q^{58} - 15 q^{59} - 27 q^{60} + 24 q^{61} - 42 q^{63} + 26 q^{64} + 36 q^{65} - 33 q^{66} + 52 q^{67} + 126 q^{68} - 63 q^{70} + 128 q^{71} - 21 q^{72} + 12 q^{73} + 58 q^{74} + 6 q^{75} + 77 q^{77} - 24 q^{78} - 17 q^{79} + 45 q^{80} - 9 q^{81} - 6 q^{82} - 252 q^{85} - 26 q^{86} + 75 q^{87} - 77 q^{88} - 138 q^{89} + 84 q^{91} - 168 q^{92} - 57 q^{93} + 132 q^{94} + 18 q^{95} - 99 q^{96} - 49 q^{98} + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.250000 + 0.433013i −0.963525 0.267617i \(-0.913764\pi\)
0.713525 + 0.700629i \(0.247097\pi\)
\(3\) 1.50000 0.866025i 0.500000 0.288675i
\(4\) 1.50000 + 2.59808i 0.375000 + 0.649519i
\(5\) −4.50000 2.59808i −0.900000 0.519615i −0.0227998 0.999740i \(-0.507258\pi\)
−0.877200 + 0.480125i \(0.840591\pi\)
\(6\) 1.73205i 0.288675i
\(7\) −3.50000 6.06218i −0.500000 0.866025i
\(8\) −7.00000 −0.875000
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 4.50000 2.59808i 0.450000 0.259808i
\(11\) 5.50000 + 9.52628i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 4.50000 + 2.59808i 0.375000 + 0.216506i
\(13\) 6.92820i 0.532939i 0.963843 + 0.266469i \(0.0858571\pi\)
−0.963843 + 0.266469i \(0.914143\pi\)
\(14\) 7.00000 0.500000
\(15\) −9.00000 −0.600000
\(16\) −2.50000 + 4.33013i −0.156250 + 0.270633i
\(17\) 21.0000 12.1244i 1.23529 0.713197i 0.267165 0.963651i \(-0.413913\pi\)
0.968129 + 0.250453i \(0.0805797\pi\)
\(18\) 1.50000 + 2.59808i 0.0833333 + 0.144338i
\(19\) −3.00000 1.73205i −0.157895 0.0911606i 0.418971 0.908000i \(-0.362391\pi\)
−0.576865 + 0.816839i \(0.695724\pi\)
\(20\) 15.5885i 0.779423i
\(21\) −10.5000 6.06218i −0.500000 0.288675i
\(22\) −11.0000 −0.500000
\(23\) −14.0000 + 24.2487i −0.608696 + 1.05429i 0.382760 + 0.923848i \(0.374974\pi\)
−0.991456 + 0.130444i \(0.958360\pi\)
\(24\) −10.5000 + 6.06218i −0.437500 + 0.252591i
\(25\) 1.00000 + 1.73205i 0.0400000 + 0.0692820i
\(26\) −6.00000 3.46410i −0.230769 0.133235i
\(27\) 5.19615i 0.192450i
\(28\) 10.5000 18.1865i 0.375000 0.649519i
\(29\) 25.0000 0.862069 0.431034 0.902335i \(-0.358149\pi\)
0.431034 + 0.902335i \(0.358149\pi\)
\(30\) 4.50000 7.79423i 0.150000 0.259808i
\(31\) −28.5000 + 16.4545i −0.919355 + 0.530790i −0.883429 0.468565i \(-0.844771\pi\)
−0.0359257 + 0.999354i \(0.511438\pi\)
\(32\) −16.5000 28.5788i −0.515625 0.893089i
\(33\) 16.5000 + 9.52628i 0.500000 + 0.288675i
\(34\) 24.2487i 0.713197i
\(35\) 36.3731i 1.03923i
\(36\) 9.00000 0.250000
\(37\) 29.0000 50.2295i 0.783784 1.35755i −0.145939 0.989294i \(-0.546620\pi\)
0.929723 0.368260i \(-0.120046\pi\)
\(38\) 3.00000 1.73205i 0.0789474 0.0455803i
\(39\) 6.00000 + 10.3923i 0.153846 + 0.266469i
\(40\) 31.5000 + 18.1865i 0.787500 + 0.454663i
\(41\) 3.46410i 0.0844903i 0.999107 + 0.0422451i \(0.0134510\pi\)
−0.999107 + 0.0422451i \(0.986549\pi\)
\(42\) 10.5000 6.06218i 0.250000 0.144338i
\(43\) 26.0000 0.604651 0.302326 0.953205i \(-0.402237\pi\)
0.302326 + 0.953205i \(0.402237\pi\)
\(44\) −16.5000 + 28.5788i −0.375000 + 0.649519i
\(45\) −13.5000 + 7.79423i −0.300000 + 0.173205i
\(46\) −14.0000 24.2487i −0.304348 0.527146i
\(47\) −66.0000 38.1051i −1.40426 0.810747i −0.409429 0.912342i \(-0.634272\pi\)
−0.994826 + 0.101595i \(0.967606\pi\)
\(48\) 8.66025i 0.180422i
\(49\) −24.5000 + 42.4352i −0.500000 + 0.866025i
\(50\) −2.00000 −0.0400000
\(51\) 21.0000 36.3731i 0.411765 0.713197i
\(52\) −18.0000 + 10.3923i −0.346154 + 0.199852i
\(53\) −15.5000 26.8468i −0.292453 0.506543i 0.681936 0.731412i \(-0.261138\pi\)
−0.974389 + 0.224868i \(0.927805\pi\)
\(54\) 4.50000 + 2.59808i 0.0833333 + 0.0481125i
\(55\) 57.1577i 1.03923i
\(56\) 24.5000 + 42.4352i 0.437500 + 0.757772i
\(57\) −6.00000 −0.105263
\(58\) −12.5000 + 21.6506i −0.215517 + 0.373287i
\(59\) −7.50000 + 4.33013i −0.127119 + 0.0733920i −0.562211 0.826994i \(-0.690049\pi\)
0.435092 + 0.900386i \(0.356716\pi\)
\(60\) −13.5000 23.3827i −0.225000 0.389711i
\(61\) 12.0000 + 6.92820i 0.196721 + 0.113577i 0.595125 0.803633i \(-0.297102\pi\)
−0.398404 + 0.917210i \(0.630436\pi\)
\(62\) 32.9090i 0.530790i
\(63\) −21.0000 −0.333333
\(64\) 13.0000 0.203125
\(65\) 18.0000 31.1769i 0.276923 0.479645i
\(66\) −16.5000 + 9.52628i −0.250000 + 0.144338i
\(67\) 26.0000 + 45.0333i 0.388060 + 0.672139i 0.992189 0.124748i \(-0.0398121\pi\)
−0.604129 + 0.796887i \(0.706479\pi\)
\(68\) 63.0000 + 36.3731i 0.926471 + 0.534898i
\(69\) 48.4974i 0.702861i
\(70\) −31.5000 18.1865i −0.450000 0.259808i
\(71\) 64.0000 0.901408 0.450704 0.892673i \(-0.351173\pi\)
0.450704 + 0.892673i \(0.351173\pi\)
\(72\) −10.5000 + 18.1865i −0.145833 + 0.252591i
\(73\) 6.00000 3.46410i 0.0821918 0.0474534i −0.458341 0.888777i \(-0.651556\pi\)
0.540533 + 0.841323i \(0.318223\pi\)
\(74\) 29.0000 + 50.2295i 0.391892 + 0.678777i
\(75\) 3.00000 + 1.73205i 0.0400000 + 0.0230940i
\(76\) 10.3923i 0.136741i
\(77\) 38.5000 66.6840i 0.500000 0.866025i
\(78\) −12.0000 −0.153846
\(79\) −8.50000 + 14.7224i −0.107595 + 0.186360i −0.914795 0.403917i \(-0.867648\pi\)
0.807200 + 0.590277i \(0.200982\pi\)
\(80\) 22.5000 12.9904i 0.281250 0.162380i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −3.00000 1.73205i −0.0365854 0.0211226i
\(83\) 53.6936i 0.646911i 0.946243 + 0.323455i \(0.104845\pi\)
−0.946243 + 0.323455i \(0.895155\pi\)
\(84\) 36.3731i 0.433013i
\(85\) −126.000 −1.48235
\(86\) −13.0000 + 22.5167i −0.151163 + 0.261822i
\(87\) 37.5000 21.6506i 0.431034 0.248858i
\(88\) −38.5000 66.6840i −0.437500 0.757772i
\(89\) −69.0000 39.8372i −0.775281 0.447609i 0.0594743 0.998230i \(-0.481058\pi\)
−0.834755 + 0.550621i \(0.814391\pi\)
\(90\) 15.5885i 0.173205i
\(91\) 42.0000 24.2487i 0.461538 0.266469i
\(92\) −84.0000 −0.913043
\(93\) −28.5000 + 49.3634i −0.306452 + 0.530790i
\(94\) 66.0000 38.1051i 0.702128 0.405374i
\(95\) 9.00000 + 15.5885i 0.0947368 + 0.164089i
\(96\) −49.5000 28.5788i −0.515625 0.297696i
\(97\) 91.7987i 0.946378i 0.880961 + 0.473189i \(0.156897\pi\)
−0.880961 + 0.473189i \(0.843103\pi\)
\(98\) −24.5000 42.4352i −0.250000 0.433013i
\(99\) 33.0000 0.333333
\(100\) −3.00000 + 5.19615i −0.0300000 + 0.0519615i
\(101\) −18.0000 + 10.3923i −0.178218 + 0.102894i −0.586455 0.809982i \(-0.699477\pi\)
0.408237 + 0.912876i \(0.366144\pi\)
\(102\) 21.0000 + 36.3731i 0.205882 + 0.356599i
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 48.4974i 0.466321i
\(105\) 31.5000 + 54.5596i 0.300000 + 0.519615i
\(106\) 31.0000 0.292453
\(107\) −15.5000 + 26.8468i −0.144860 + 0.250905i −0.929321 0.369274i \(-0.879606\pi\)
0.784461 + 0.620178i \(0.212940\pi\)
\(108\) 13.5000 7.79423i 0.125000 0.0721688i
\(109\) 68.0000 + 117.779i 0.623853 + 1.08055i 0.988761 + 0.149502i \(0.0477670\pi\)
−0.364908 + 0.931043i \(0.618900\pi\)
\(110\) 49.5000 + 28.5788i 0.450000 + 0.259808i
\(111\) 100.459i 0.905036i
\(112\) 35.0000 0.312500
\(113\) −74.0000 −0.654867 −0.327434 0.944874i \(-0.606184\pi\)
−0.327434 + 0.944874i \(0.606184\pi\)
\(114\) 3.00000 5.19615i 0.0263158 0.0455803i
\(115\) 126.000 72.7461i 1.09565 0.632575i
\(116\) 37.5000 + 64.9519i 0.323276 + 0.559930i
\(117\) 18.0000 + 10.3923i 0.153846 + 0.0888231i
\(118\) 8.66025i 0.0733920i
\(119\) −147.000 84.8705i −1.23529 0.713197i
\(120\) 63.0000 0.525000
\(121\) 0 0
\(122\) −12.0000 + 6.92820i −0.0983607 + 0.0567886i
\(123\) 3.00000 + 5.19615i 0.0243902 + 0.0422451i
\(124\) −85.5000 49.3634i −0.689516 0.398092i
\(125\) 119.512i 0.956092i
\(126\) 10.5000 18.1865i 0.0833333 0.144338i
\(127\) −1.00000 −0.00787402 −0.00393701 0.999992i \(-0.501253\pi\)
−0.00393701 + 0.999992i \(0.501253\pi\)
\(128\) 59.5000 103.057i 0.464844 0.805133i
\(129\) 39.0000 22.5167i 0.302326 0.174548i
\(130\) 18.0000 + 31.1769i 0.138462 + 0.239822i
\(131\) 157.500 + 90.9327i 1.20229 + 0.694142i 0.961064 0.276326i \(-0.0891171\pi\)
0.241226 + 0.970469i \(0.422450\pi\)
\(132\) 57.1577i 0.433013i
\(133\) 24.2487i 0.182321i
\(134\) −52.0000 −0.388060
\(135\) −13.5000 + 23.3827i −0.100000 + 0.173205i
\(136\) −147.000 + 84.8705i −1.08088 + 0.624048i
\(137\) −44.0000 76.2102i −0.321168 0.556279i 0.659561 0.751651i \(-0.270742\pi\)
−0.980729 + 0.195372i \(0.937409\pi\)
\(138\) −42.0000 24.2487i −0.304348 0.175715i
\(139\) 190.526i 1.37069i −0.728220 0.685344i \(-0.759652\pi\)
0.728220 0.685344i \(-0.240348\pi\)
\(140\) −94.5000 + 54.5596i −0.675000 + 0.389711i
\(141\) −132.000 −0.936170
\(142\) −32.0000 + 55.4256i −0.225352 + 0.390321i
\(143\) −66.0000 + 38.1051i −0.461538 + 0.266469i
\(144\) 7.50000 + 12.9904i 0.0520833 + 0.0902110i
\(145\) −112.500 64.9519i −0.775862 0.447944i
\(146\) 6.92820i 0.0474534i
\(147\) 84.8705i 0.577350i
\(148\) 174.000 1.17568
\(149\) 115.000 199.186i 0.771812 1.33682i −0.164757 0.986334i \(-0.552684\pi\)
0.936569 0.350484i \(-0.113983\pi\)
\(150\) −3.00000 + 1.73205i −0.0200000 + 0.0115470i
\(151\) −113.500 196.588i −0.751656 1.30191i −0.947020 0.321175i \(-0.895922\pi\)
0.195364 0.980731i \(-0.437411\pi\)
\(152\) 21.0000 + 12.1244i 0.138158 + 0.0797655i
\(153\) 72.7461i 0.475465i
\(154\) 38.5000 + 66.6840i 0.250000 + 0.433013i
\(155\) 171.000 1.10323
\(156\) −18.0000 + 31.1769i −0.115385 + 0.199852i
\(157\) −42.0000 + 24.2487i −0.267516 + 0.154450i −0.627758 0.778408i \(-0.716027\pi\)
0.360242 + 0.932859i \(0.382694\pi\)
\(158\) −8.50000 14.7224i −0.0537975 0.0931799i
\(159\) −46.5000 26.8468i −0.292453 0.168848i
\(160\) 171.473i 1.07171i
\(161\) 196.000 1.21739
\(162\) 9.00000 0.0555556
\(163\) −106.000 + 183.597i −0.650307 + 1.12636i 0.332742 + 0.943018i \(0.392026\pi\)
−0.983048 + 0.183346i \(0.941307\pi\)
\(164\) −9.00000 + 5.19615i −0.0548780 + 0.0316839i
\(165\) −49.5000 85.7365i −0.300000 0.519615i
\(166\) −46.5000 26.8468i −0.280120 0.161728i
\(167\) 96.9948i 0.580807i 0.956904 + 0.290404i \(0.0937896\pi\)
−0.956904 + 0.290404i \(0.906210\pi\)
\(168\) 73.5000 + 42.4352i 0.437500 + 0.252591i
\(169\) 121.000 0.715976
\(170\) 63.0000 109.119i 0.370588 0.641878i
\(171\) −9.00000 + 5.19615i −0.0526316 + 0.0303869i
\(172\) 39.0000 + 67.5500i 0.226744 + 0.392732i
\(173\) 186.000 + 107.387i 1.07514 + 0.620735i 0.929582 0.368614i \(-0.120168\pi\)
0.145562 + 0.989349i \(0.453501\pi\)
\(174\) 43.3013i 0.248858i
\(175\) 7.00000 12.1244i 0.0400000 0.0692820i
\(176\) −55.0000 −0.312500
\(177\) −7.50000 + 12.9904i −0.0423729 + 0.0733920i
\(178\) 69.0000 39.8372i 0.387640 0.223804i
\(179\) −23.0000 39.8372i −0.128492 0.222554i 0.794601 0.607132i \(-0.207680\pi\)
−0.923092 + 0.384578i \(0.874347\pi\)
\(180\) −40.5000 23.3827i −0.225000 0.129904i
\(181\) 31.1769i 0.172248i −0.996284 0.0861241i \(-0.972552\pi\)
0.996284 0.0861241i \(-0.0274481\pi\)
\(182\) 48.4974i 0.266469i
\(183\) 24.0000 0.131148
\(184\) 98.0000 169.741i 0.532609 0.922505i
\(185\) −261.000 + 150.688i −1.41081 + 0.814532i
\(186\) −28.5000 49.3634i −0.153226 0.265395i
\(187\) 231.000 + 133.368i 1.23529 + 0.713197i
\(188\) 228.631i 1.21612i
\(189\) −31.5000 + 18.1865i −0.166667 + 0.0962250i
\(190\) −18.0000 −0.0947368
\(191\) −104.000 + 180.133i −0.544503 + 0.943106i 0.454135 + 0.890933i \(0.349948\pi\)
−0.998638 + 0.0521735i \(0.983385\pi\)
\(192\) 19.5000 11.2583i 0.101562 0.0586371i
\(193\) −119.500 206.980i −0.619171 1.07244i −0.989637 0.143590i \(-0.954135\pi\)
0.370466 0.928846i \(-0.379198\pi\)
\(194\) −79.5000 45.8993i −0.409794 0.236595i
\(195\) 62.3538i 0.319763i
\(196\) −147.000 −0.750000
\(197\) −26.0000 −0.131980 −0.0659898 0.997820i \(-0.521020\pi\)
−0.0659898 + 0.997820i \(0.521020\pi\)
\(198\) −16.5000 + 28.5788i −0.0833333 + 0.144338i
\(199\) −210.000 + 121.244i −1.05528 + 0.609264i −0.924122 0.382098i \(-0.875202\pi\)
−0.131155 + 0.991362i \(0.541868\pi\)
\(200\) −7.00000 12.1244i −0.0350000 0.0606218i
\(201\) 78.0000 + 45.0333i 0.388060 + 0.224046i
\(202\) 20.7846i 0.102894i
\(203\) −87.5000 151.554i −0.431034 0.746574i
\(204\) 126.000 0.617647
\(205\) 9.00000 15.5885i 0.0439024 0.0760413i
\(206\) 0 0
\(207\) 42.0000 + 72.7461i 0.202899 + 0.351431i
\(208\) −30.0000 17.3205i −0.144231 0.0832717i
\(209\) 38.1051i 0.182321i
\(210\) −63.0000 −0.300000
\(211\) −52.0000 −0.246445 −0.123223 0.992379i \(-0.539323\pi\)
−0.123223 + 0.992379i \(0.539323\pi\)
\(212\) 46.5000 80.5404i 0.219340 0.379907i
\(213\) 96.0000 55.4256i 0.450704 0.260214i
\(214\) −15.5000 26.8468i −0.0724299 0.125452i
\(215\) −117.000 67.5500i −0.544186 0.314186i
\(216\) 36.3731i 0.168394i
\(217\) 199.500 + 115.181i 0.919355 + 0.530790i
\(218\) −136.000 −0.623853
\(219\) 6.00000 10.3923i 0.0273973 0.0474534i
\(220\) 148.500 85.7365i 0.675000 0.389711i
\(221\) 84.0000 + 145.492i 0.380090 + 0.658336i
\(222\) 87.0000 + 50.2295i 0.391892 + 0.226259i
\(223\) 22.5167i 0.100972i −0.998725 0.0504858i \(-0.983923\pi\)
0.998725 0.0504858i \(-0.0160770\pi\)
\(224\) −115.500 + 200.052i −0.515625 + 0.893089i
\(225\) 6.00000 0.0266667
\(226\) 37.0000 64.0859i 0.163717 0.283566i
\(227\) 58.5000 33.7750i 0.257709 0.148789i −0.365580 0.930780i \(-0.619129\pi\)
0.623289 + 0.781991i \(0.285796\pi\)
\(228\) −9.00000 15.5885i −0.0394737 0.0683704i
\(229\) −27.0000 15.5885i −0.117904 0.0680719i 0.439888 0.898053i \(-0.355018\pi\)
−0.557792 + 0.829981i \(0.688351\pi\)
\(230\) 145.492i 0.632575i
\(231\) 133.368i 0.577350i
\(232\) −175.000 −0.754310
\(233\) −131.000 + 226.899i −0.562232 + 0.973814i 0.435070 + 0.900397i \(0.356724\pi\)
−0.997301 + 0.0734171i \(0.976610\pi\)
\(234\) −18.0000 + 10.3923i −0.0769231 + 0.0444116i
\(235\) 198.000 + 342.946i 0.842553 + 1.45934i
\(236\) −22.5000 12.9904i −0.0953390 0.0550440i
\(237\) 29.4449i 0.124240i
\(238\) 147.000 84.8705i 0.617647 0.356599i
\(239\) 160.000 0.669456 0.334728 0.942315i \(-0.391356\pi\)
0.334728 + 0.942315i \(0.391356\pi\)
\(240\) 22.5000 38.9711i 0.0937500 0.162380i
\(241\) 409.500 236.425i 1.69917 0.981016i 0.752622 0.658452i \(-0.228789\pi\)
0.946548 0.322564i \(-0.104545\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 41.5692i 0.170366i
\(245\) 220.500 127.306i 0.900000 0.519615i
\(246\) −6.00000 −0.0243902
\(247\) 12.0000 20.7846i 0.0485830 0.0841482i
\(248\) 199.500 115.181i 0.804435 0.464441i
\(249\) 46.5000 + 80.5404i 0.186747 + 0.323455i
\(250\) −103.500 59.7558i −0.414000 0.239023i
\(251\) 67.5500i 0.269123i −0.990905 0.134562i \(-0.957037\pi\)
0.990905 0.134562i \(-0.0429626\pi\)
\(252\) −31.5000 54.5596i −0.125000 0.216506i
\(253\) −308.000 −1.21739
\(254\) 0.500000 0.866025i 0.00196850 0.00340955i
\(255\) −189.000 + 109.119i −0.741176 + 0.427918i
\(256\) 85.5000 + 148.090i 0.333984 + 0.578478i
\(257\) −351.000 202.650i −1.36576 0.788521i −0.375376 0.926873i \(-0.622486\pi\)
−0.990383 + 0.138352i \(0.955820\pi\)
\(258\) 45.0333i 0.174548i
\(259\) −406.000 −1.56757
\(260\) 108.000 0.415385
\(261\) 37.5000 64.9519i 0.143678 0.248858i
\(262\) −157.500 + 90.9327i −0.601145 + 0.347071i
\(263\) −53.0000 91.7987i −0.201521 0.349044i 0.747498 0.664264i \(-0.231255\pi\)
−0.949019 + 0.315220i \(0.897922\pi\)
\(264\) −115.500 66.6840i −0.437500 0.252591i
\(265\) 161.081i 0.607852i
\(266\) −21.0000 12.1244i −0.0789474 0.0455803i
\(267\) −138.000 −0.516854
\(268\) −78.0000 + 135.100i −0.291045 + 0.504104i
\(269\) 376.500 217.372i 1.39963 0.808076i 0.405275 0.914195i \(-0.367176\pi\)
0.994353 + 0.106119i \(0.0338425\pi\)
\(270\) −13.5000 23.3827i −0.0500000 0.0866025i
\(271\) 109.500 + 63.2199i 0.404059 + 0.233284i 0.688234 0.725489i \(-0.258386\pi\)
−0.284175 + 0.958772i \(0.591720\pi\)
\(272\) 121.244i 0.445748i
\(273\) 42.0000 72.7461i 0.153846 0.266469i
\(274\) 88.0000 0.321168
\(275\) −11.0000 + 19.0526i −0.0400000 + 0.0692820i
\(276\) −126.000 + 72.7461i −0.456522 + 0.263573i
\(277\) −118.000 204.382i −0.425993 0.737841i 0.570520 0.821284i \(-0.306742\pi\)
−0.996513 + 0.0834427i \(0.973408\pi\)
\(278\) 165.000 + 95.2628i 0.593525 + 0.342672i
\(279\) 98.7269i 0.353860i
\(280\) 254.611i 0.909327i
\(281\) −116.000 −0.412811 −0.206406 0.978466i \(-0.566177\pi\)
−0.206406 + 0.978466i \(0.566177\pi\)
\(282\) 66.0000 114.315i 0.234043 0.405374i
\(283\) −321.000 + 185.329i −1.13428 + 0.654874i −0.945007 0.327051i \(-0.893945\pi\)
−0.189269 + 0.981925i \(0.560612\pi\)
\(284\) 96.0000 + 166.277i 0.338028 + 0.585482i
\(285\) 27.0000 + 15.5885i 0.0947368 + 0.0546963i
\(286\) 76.2102i 0.266469i
\(287\) 21.0000 12.1244i 0.0731707 0.0422451i
\(288\) −99.0000 −0.343750
\(289\) 149.500 258.942i 0.517301 0.895992i
\(290\) 112.500 64.9519i 0.387931 0.223972i
\(291\) 79.5000 + 137.698i 0.273196 + 0.473189i
\(292\) 18.0000 + 10.3923i 0.0616438 + 0.0355901i
\(293\) 19.0526i 0.0650258i 0.999471 + 0.0325129i \(0.0103510\pi\)
−0.999471 + 0.0325129i \(0.989649\pi\)
\(294\) −73.5000 42.4352i −0.250000 0.144338i
\(295\) 45.0000 0.152542
\(296\) −203.000 + 351.606i −0.685811 + 1.18786i
\(297\) 49.5000 28.5788i 0.166667 0.0962250i
\(298\) 115.000 + 199.186i 0.385906 + 0.668409i
\(299\) −168.000 96.9948i −0.561873 0.324397i
\(300\) 10.3923i 0.0346410i
\(301\) −91.0000 157.617i −0.302326 0.523643i
\(302\) 227.000 0.751656
\(303\) −18.0000 + 31.1769i −0.0594059 + 0.102894i
\(304\) 15.0000 8.66025i 0.0493421 0.0284877i
\(305\) −36.0000 62.3538i −0.118033 0.204439i
\(306\) 63.0000 + 36.3731i 0.205882 + 0.118866i
\(307\) 457.261i 1.48945i −0.667371 0.744725i \(-0.732580\pi\)
0.667371 0.744725i \(-0.267420\pi\)
\(308\) 231.000 0.750000
\(309\) 0 0
\(310\) −85.5000 + 148.090i −0.275806 + 0.477711i
\(311\) 285.000 164.545i 0.916399 0.529083i 0.0339143 0.999425i \(-0.489203\pi\)
0.882484 + 0.470342i \(0.155869\pi\)
\(312\) −42.0000 72.7461i −0.134615 0.233161i
\(313\) 475.500 + 274.530i 1.51917 + 0.877093i 0.999745 + 0.0225763i \(0.00718687\pi\)
0.519424 + 0.854517i \(0.326146\pi\)
\(314\) 48.4974i 0.154450i
\(315\) 94.5000 + 54.5596i 0.300000 + 0.173205i
\(316\) −51.0000 −0.161392
\(317\) −93.5000 + 161.947i −0.294953 + 0.510873i −0.974974 0.222319i \(-0.928637\pi\)
0.680021 + 0.733192i \(0.261971\pi\)
\(318\) 46.5000 26.8468i 0.146226 0.0844239i
\(319\) 137.500 + 238.157i 0.431034 + 0.746574i
\(320\) −58.5000 33.7750i −0.182812 0.105547i
\(321\) 53.6936i 0.167270i
\(322\) −98.0000 + 169.741i −0.304348 + 0.527146i
\(323\) −84.0000 −0.260062
\(324\) 13.5000 23.3827i 0.0416667 0.0721688i
\(325\) −12.0000 + 6.92820i −0.0369231 + 0.0213175i
\(326\) −106.000 183.597i −0.325153 0.563182i
\(327\) 204.000 + 117.779i 0.623853 + 0.360182i
\(328\) 24.2487i 0.0739290i
\(329\) 533.472i 1.62149i
\(330\) 99.0000 0.300000
\(331\) 8.00000 13.8564i 0.0241692 0.0418623i −0.853688 0.520785i \(-0.825639\pi\)
0.877857 + 0.478923i \(0.158973\pi\)
\(332\) −139.500 + 80.5404i −0.420181 + 0.242591i
\(333\) −87.0000 150.688i −0.261261 0.452518i
\(334\) −84.0000 48.4974i −0.251497 0.145202i
\(335\) 270.200i 0.806567i
\(336\) 52.5000 30.3109i 0.156250 0.0902110i
\(337\) 83.0000 0.246291 0.123145 0.992389i \(-0.460702\pi\)
0.123145 + 0.992389i \(0.460702\pi\)
\(338\) −60.5000 + 104.789i −0.178994 + 0.310027i
\(339\) −111.000 + 64.0859i −0.327434 + 0.189044i
\(340\) −189.000 327.358i −0.555882 0.962816i
\(341\) −313.500 180.999i −0.919355 0.530790i
\(342\) 10.3923i 0.0303869i
\(343\) 343.000 1.00000
\(344\) −182.000 −0.529070
\(345\) 126.000 218.238i 0.365217 0.632575i
\(346\) −186.000 + 107.387i −0.537572 + 0.310367i
\(347\) −179.000 310.037i −0.515850 0.893479i −0.999831 0.0183999i \(-0.994143\pi\)
0.483981 0.875079i \(-0.339191\pi\)
\(348\) 112.500 + 64.9519i 0.323276 + 0.186643i
\(349\) 678.964i 1.94546i 0.231950 + 0.972728i \(0.425489\pi\)
−0.231950 + 0.972728i \(0.574511\pi\)
\(350\) 7.00000 + 12.1244i 0.0200000 + 0.0346410i
\(351\) 36.0000 0.102564
\(352\) 181.500 314.367i 0.515625 0.893089i
\(353\) −558.000 + 322.161i −1.58074 + 0.912639i −0.585985 + 0.810322i \(0.699292\pi\)
−0.994752 + 0.102317i \(0.967375\pi\)
\(354\) −7.50000 12.9904i −0.0211864 0.0366960i
\(355\) −288.000 166.277i −0.811268 0.468386i
\(356\) 239.023i 0.671413i
\(357\) −294.000 −0.823529
\(358\) 46.0000 0.128492
\(359\) 142.000 245.951i 0.395543 0.685101i −0.597627 0.801774i \(-0.703890\pi\)
0.993170 + 0.116673i \(0.0372230\pi\)
\(360\) 94.5000 54.5596i 0.262500 0.151554i
\(361\) −174.500 302.243i −0.483380 0.837238i
\(362\) 27.0000 + 15.5885i 0.0745856 + 0.0430620i
\(363\) 0 0
\(364\) 126.000 + 72.7461i 0.346154 + 0.199852i
\(365\) −36.0000 −0.0986301
\(366\) −12.0000 + 20.7846i −0.0327869 + 0.0567886i
\(367\) 238.500 137.698i 0.649864 0.375199i −0.138540 0.990357i \(-0.544241\pi\)
0.788404 + 0.615158i \(0.210908\pi\)
\(368\) −70.0000 121.244i −0.190217 0.329466i
\(369\) 9.00000 + 5.19615i 0.0243902 + 0.0140817i
\(370\) 301.377i 0.814532i
\(371\) −108.500 + 187.928i −0.292453 + 0.506543i
\(372\) −171.000 −0.459677
\(373\) −25.0000 + 43.3013i −0.0670241 + 0.116089i −0.897590 0.440831i \(-0.854684\pi\)
0.830566 + 0.556920i \(0.188017\pi\)
\(374\) −231.000 + 133.368i −0.617647 + 0.356599i
\(375\) 103.500 + 179.267i 0.276000 + 0.478046i
\(376\) 462.000 + 266.736i 1.22872 + 0.709404i
\(377\) 173.205i 0.459430i
\(378\) 36.3731i 0.0962250i
\(379\) 458.000 1.20844 0.604222 0.796816i \(-0.293484\pi\)
0.604222 + 0.796816i \(0.293484\pi\)
\(380\) −27.0000 + 46.7654i −0.0710526 + 0.123067i
\(381\) −1.50000 + 0.866025i −0.00393701 + 0.00227303i
\(382\) −104.000 180.133i −0.272251 0.471553i
\(383\) 351.000 + 202.650i 0.916449 + 0.529112i 0.882501 0.470311i \(-0.155858\pi\)
0.0339486 + 0.999424i \(0.489192\pi\)
\(384\) 206.114i 0.536755i
\(385\) −346.500 + 200.052i −0.900000 + 0.519615i
\(386\) 239.000 0.619171
\(387\) 39.0000 67.5500i 0.100775 0.174548i
\(388\) −238.500 + 137.698i −0.614691 + 0.354892i
\(389\) 349.000 + 604.486i 0.897172 + 1.55395i 0.831093 + 0.556134i \(0.187716\pi\)
0.0660793 + 0.997814i \(0.478951\pi\)
\(390\) 54.0000 + 31.1769i 0.138462 + 0.0799408i
\(391\) 678.964i 1.73648i
\(392\) 171.500 297.047i 0.437500 0.757772i
\(393\) 315.000 0.801527
\(394\) 13.0000 22.5167i 0.0329949 0.0571489i
\(395\) 76.5000 44.1673i 0.193671 0.111816i
\(396\) 49.5000 + 85.7365i 0.125000 + 0.216506i
\(397\) −498.000 287.520i −1.25441 0.724233i −0.282426 0.959289i \(-0.591139\pi\)
−0.971982 + 0.235056i \(0.924473\pi\)
\(398\) 242.487i 0.609264i
\(399\) 21.0000 + 36.3731i 0.0526316 + 0.0911606i
\(400\) −10.0000 −0.0250000
\(401\) 142.000 245.951i 0.354115 0.613345i −0.632851 0.774273i \(-0.718116\pi\)
0.986966 + 0.160929i \(0.0514489\pi\)
\(402\) −78.0000 + 45.0333i −0.194030 + 0.112023i
\(403\) −114.000 197.454i −0.282878 0.489960i
\(404\) −54.0000 31.1769i −0.133663 0.0771706i
\(405\) 46.7654i 0.115470i
\(406\) 175.000 0.431034
\(407\) 638.000 1.56757
\(408\) −147.000 + 254.611i −0.360294 + 0.624048i
\(409\) −181.500 + 104.789i −0.443765 + 0.256208i −0.705193 0.709015i \(-0.749140\pi\)
0.261428 + 0.965223i \(0.415807\pi\)
\(410\) 9.00000 + 15.5885i 0.0219512 + 0.0380206i
\(411\) −132.000 76.2102i −0.321168 0.185426i
\(412\) 0 0
\(413\) 52.5000 + 30.3109i 0.127119 + 0.0733920i
\(414\) −84.0000 −0.202899
\(415\) 139.500 241.621i 0.336145 0.582219i
\(416\) 198.000 114.315i 0.475962 0.274797i
\(417\) −165.000 285.788i −0.395683 0.685344i
\(418\) 33.0000 + 19.0526i 0.0789474 + 0.0455803i
\(419\) 131.636i 0.314167i −0.987585 0.157083i \(-0.949791\pi\)
0.987585 0.157083i \(-0.0502091\pi\)
\(420\) −94.5000 + 163.679i −0.225000 + 0.389711i
\(421\) −28.0000 −0.0665083 −0.0332542 0.999447i \(-0.510587\pi\)
−0.0332542 + 0.999447i \(0.510587\pi\)
\(422\) 26.0000 45.0333i 0.0616114 0.106714i
\(423\) −198.000 + 114.315i −0.468085 + 0.270249i
\(424\) 108.500 + 187.928i 0.255896 + 0.443225i
\(425\) 42.0000 + 24.2487i 0.0988235 + 0.0570558i
\(426\) 110.851i 0.260214i
\(427\) 96.9948i 0.227154i
\(428\) −93.0000 −0.217290
\(429\) −66.0000 + 114.315i −0.153846 + 0.266469i
\(430\) 117.000 67.5500i 0.272093 0.157093i
\(431\) −59.0000 102.191i −0.136891 0.237102i 0.789427 0.613844i \(-0.210378\pi\)
−0.926318 + 0.376742i \(0.877044\pi\)
\(432\) 22.5000 + 12.9904i 0.0520833 + 0.0300703i
\(433\) 561.184i 1.29604i −0.761624 0.648019i \(-0.775598\pi\)
0.761624 0.648019i \(-0.224402\pi\)
\(434\) −199.500 + 115.181i −0.459677 + 0.265395i
\(435\) −225.000 −0.517241
\(436\) −204.000 + 353.338i −0.467890 + 0.810409i
\(437\) 84.0000 48.4974i 0.192220 0.110978i
\(438\) 6.00000 + 10.3923i 0.0136986 + 0.0237267i
\(439\) −640.500 369.793i −1.45900 0.842353i −0.460036 0.887900i \(-0.652163\pi\)
−0.998962 + 0.0455478i \(0.985497\pi\)
\(440\) 400.104i 0.909327i
\(441\) 73.5000 + 127.306i 0.166667 + 0.288675i
\(442\) −168.000 −0.380090
\(443\) 77.5000 134.234i 0.174944 0.303011i −0.765198 0.643795i \(-0.777359\pi\)
0.940142 + 0.340784i \(0.110692\pi\)
\(444\) 261.000 150.688i 0.587838 0.339388i
\(445\) 207.000 + 358.535i 0.465169 + 0.805696i
\(446\) 19.5000 + 11.2583i 0.0437220 + 0.0252429i
\(447\) 398.372i 0.891212i
\(448\) −45.5000 78.8083i −0.101562 0.175911i
\(449\) −368.000 −0.819599 −0.409800 0.912176i \(-0.634401\pi\)
−0.409800 + 0.912176i \(0.634401\pi\)
\(450\) −3.00000 + 5.19615i −0.00666667 + 0.0115470i
\(451\) −33.0000 + 19.0526i −0.0731707 + 0.0422451i
\(452\) −111.000 192.258i −0.245575 0.425349i
\(453\) −340.500 196.588i −0.751656 0.433969i
\(454\) 67.5500i 0.148789i
\(455\) −252.000 −0.553846
\(456\) 42.0000 0.0921053
\(457\) −170.500 + 295.315i −0.373085 + 0.646203i −0.990038 0.140797i \(-0.955033\pi\)
0.616953 + 0.787000i \(0.288367\pi\)
\(458\) 27.0000 15.5885i 0.0589520 0.0340359i
\(459\) −63.0000 109.119i −0.137255 0.237732i
\(460\) 378.000 + 218.238i 0.821739 + 0.474431i
\(461\) 55.4256i 0.120229i −0.998191 0.0601146i \(-0.980853\pi\)
0.998191 0.0601146i \(-0.0191466\pi\)
\(462\) 115.500 + 66.6840i 0.250000 + 0.144338i
\(463\) −178.000 −0.384449 −0.192225 0.981351i \(-0.561570\pi\)
−0.192225 + 0.981351i \(0.561570\pi\)
\(464\) −62.5000 + 108.253i −0.134698 + 0.233304i
\(465\) 256.500 148.090i 0.551613 0.318474i
\(466\) −131.000 226.899i −0.281116 0.486907i
\(467\) 570.000 + 329.090i 1.22056 + 0.704689i 0.965037 0.262115i \(-0.0844200\pi\)
0.255520 + 0.966804i \(0.417753\pi\)
\(468\) 62.3538i 0.133235i
\(469\) 182.000 315.233i 0.388060 0.672139i
\(470\) −396.000 −0.842553
\(471\) −42.0000 + 72.7461i −0.0891720 + 0.154450i
\(472\) 52.5000 30.3109i 0.111229 0.0642180i
\(473\) 143.000 + 247.683i 0.302326 + 0.523643i
\(474\) −25.5000 14.7224i −0.0537975 0.0310600i
\(475\) 6.92820i 0.0145857i
\(476\) 509.223i 1.06980i
\(477\) −93.0000 −0.194969
\(478\) −80.0000 + 138.564i −0.167364 + 0.289883i
\(479\) 441.000 254.611i 0.920668 0.531548i 0.0368199 0.999322i \(-0.488277\pi\)
0.883848 + 0.467774i \(0.154944\pi\)
\(480\) 148.500 + 257.210i 0.309375 + 0.535853i
\(481\) 348.000 + 200.918i 0.723493 + 0.417709i
\(482\) 472.850i 0.981016i
\(483\) 294.000 169.741i 0.608696 0.351431i
\(484\) 0 0
\(485\) 238.500 413.094i 0.491753 0.851740i
\(486\) 13.5000 7.79423i 0.0277778 0.0160375i
\(487\) 420.500 + 728.327i 0.863450 + 1.49554i 0.868578 + 0.495552i \(0.165034\pi\)
−0.00512864 + 0.999987i \(0.501633\pi\)
\(488\) −84.0000 48.4974i −0.172131 0.0993800i
\(489\) 367.195i 0.750910i
\(490\) 254.611i 0.519615i
\(491\) −959.000 −1.95316 −0.976578 0.215162i \(-0.930972\pi\)
−0.976578 + 0.215162i \(0.930972\pi\)
\(492\) −9.00000 + 15.5885i −0.0182927 + 0.0316839i
\(493\) 525.000 303.109i 1.06491 0.614825i
\(494\) 12.0000 + 20.7846i 0.0242915 + 0.0420741i
\(495\) −148.500 85.7365i −0.300000 0.173205i
\(496\) 164.545i 0.331744i
\(497\) −224.000 387.979i −0.450704 0.780643i
\(498\) −93.0000 −0.186747
\(499\) 59.0000 102.191i 0.118236 0.204792i −0.800832 0.598889i \(-0.795609\pi\)
0.919069 + 0.394097i \(0.128943\pi\)
\(500\) −310.500 + 179.267i −0.621000 + 0.358535i
\(501\) 84.0000 + 145.492i 0.167665 + 0.290404i
\(502\) 58.5000 + 33.7750i 0.116534 + 0.0672809i
\(503\) 363.731i 0.723123i 0.932348 + 0.361561i \(0.117756\pi\)
−0.932348 + 0.361561i \(0.882244\pi\)
\(504\) 147.000 0.291667
\(505\) 108.000 0.213861
\(506\) 154.000 266.736i 0.304348 0.527146i
\(507\) 181.500 104.789i 0.357988 0.206685i
\(508\) −1.50000 2.59808i −0.00295276 0.00511432i
\(509\) 382.500 + 220.836i 0.751473 + 0.433863i 0.826226 0.563339i \(-0.190483\pi\)
−0.0747526 + 0.997202i \(0.523817\pi\)
\(510\) 218.238i 0.427918i
\(511\) −42.0000 24.2487i −0.0821918 0.0474534i
\(512\) 305.000 0.595703
\(513\) −9.00000 + 15.5885i −0.0175439 + 0.0303869i
\(514\) 351.000 202.650i 0.682879 0.394261i
\(515\) 0 0
\(516\) 117.000 + 67.5500i 0.226744 + 0.130911i
\(517\) 838.313i 1.62149i
\(518\) 203.000 351.606i 0.391892 0.678777i
\(519\) 372.000 0.716763
\(520\) −126.000 + 218.238i −0.242308 + 0.419689i
\(521\) −843.000 + 486.706i −1.61804 + 0.934177i −0.630616 + 0.776095i \(0.717198\pi\)
−0.987426 + 0.158082i \(0.949469\pi\)
\(522\) 37.5000 + 64.9519i 0.0718391 + 0.124429i
\(523\) −408.000 235.559i −0.780115 0.450399i 0.0563562 0.998411i \(-0.482052\pi\)
−0.836471 + 0.548011i \(0.815385\pi\)
\(524\) 545.596i 1.04121i
\(525\) 24.2487i 0.0461880i
\(526\) 106.000 0.201521
\(527\) −399.000 + 691.088i −0.757116 + 1.31136i
\(528\) −82.5000 + 47.6314i −0.156250 + 0.0902110i
\(529\) −127.500 220.836i −0.241021 0.417460i
\(530\) −139.500 80.5404i −0.263208 0.151963i
\(531\) 25.9808i 0.0489280i
\(532\) −63.0000 + 36.3731i −0.118421 + 0.0683704i
\(533\) −24.0000 −0.0450281
\(534\) 69.0000 119.512i 0.129213 0.223804i
\(535\) 139.500 80.5404i 0.260748 0.150543i
\(536\) −182.000 315.233i −0.339552 0.588122i
\(537\) −69.0000 39.8372i −0.128492 0.0741847i
\(538\) 434.745i 0.808076i
\(539\) −539.000 −1.00000
\(540\) −81.0000 −0.150000
\(541\) −403.000 + 698.016i −0.744917 + 1.29023i 0.205317 + 0.978696i \(0.434178\pi\)
−0.950234 + 0.311538i \(0.899156\pi\)
\(542\) −109.500 + 63.2199i −0.202030 + 0.116642i
\(543\) −27.0000 46.7654i −0.0497238 0.0861241i
\(544\) −693.000 400.104i −1.27390 0.735485i
\(545\) 706.677i 1.29665i
\(546\) 42.0000 + 72.7461i 0.0769231 + 0.133235i
\(547\) −154.000 −0.281536 −0.140768 0.990043i \(-0.544957\pi\)
−0.140768 + 0.990043i \(0.544957\pi\)
\(548\) 132.000 228.631i 0.240876 0.417209i
\(549\) 36.0000 20.7846i 0.0655738 0.0378590i
\(550\) −11.0000 19.0526i −0.0200000 0.0346410i
\(551\) −75.0000 43.3013i −0.136116 0.0785867i
\(552\) 339.482i 0.615004i
\(553\) 119.000 0.215190
\(554\) 236.000 0.425993
\(555\) −261.000 + 452.065i −0.470270 + 0.814532i
\(556\) 495.000 285.788i 0.890288 0.514008i
\(557\) 425.500 + 736.988i 0.763914 + 1.32314i 0.940819 + 0.338910i \(0.110058\pi\)
−0.176905 + 0.984228i \(0.556609\pi\)
\(558\) −85.5000 49.3634i −0.153226 0.0884650i
\(559\) 180.133i 0.322242i
\(560\) −157.500 90.9327i −0.281250 0.162380i
\(561\) 462.000 0.823529
\(562\) 58.0000 100.459i 0.103203 0.178753i
\(563\) 370.500 213.908i 0.658082 0.379944i −0.133464 0.991054i \(-0.542610\pi\)
0.791546 + 0.611110i \(0.209277\pi\)
\(564\) −198.000 342.946i −0.351064 0.608060i
\(565\) 333.000 + 192.258i 0.589381 + 0.340279i
\(566\) 370.659i 0.654874i
\(567\) −31.5000 + 54.5596i −0.0555556 + 0.0962250i
\(568\) −448.000 −0.788732
\(569\) 409.000 708.409i 0.718805 1.24501i −0.242669 0.970109i \(-0.578023\pi\)
0.961474 0.274897i \(-0.0886439\pi\)
\(570\) −27.0000 + 15.5885i −0.0473684 + 0.0273482i
\(571\) −142.000 245.951i −0.248687 0.430738i 0.714475 0.699661i \(-0.246666\pi\)
−0.963162 + 0.268923i \(0.913332\pi\)
\(572\) −198.000 114.315i −0.346154 0.199852i
\(573\) 360.267i 0.628737i
\(574\) 24.2487i 0.0422451i
\(575\) −56.0000 −0.0973913
\(576\) 19.5000 33.7750i 0.0338542 0.0586371i
\(577\) −655.500 + 378.453i −1.13605 + 0.655898i −0.945449 0.325770i \(-0.894377\pi\)
−0.190599 + 0.981668i \(0.561043\pi\)
\(578\) 149.500 + 258.942i 0.258651 + 0.447996i
\(579\) −358.500 206.980i −0.619171 0.357479i
\(580\) 389.711i 0.671916i
\(581\) 325.500 187.928i 0.560241 0.323455i
\(582\) −159.000 −0.273196
\(583\) 170.500 295.315i 0.292453 0.506543i
\(584\) −42.0000 + 24.2487i −0.0719178 + 0.0415218i
\(585\) −54.0000 93.5307i −0.0923077 0.159882i
\(586\) −16.5000 9.52628i −0.0281570 0.0162564i
\(587\) 947.432i 1.61402i 0.590535 + 0.807012i \(0.298917\pi\)
−0.590535 + 0.807012i \(0.701083\pi\)
\(588\) −220.500 + 127.306i −0.375000 + 0.216506i
\(589\) 114.000 0.193548
\(590\) −22.5000 + 38.9711i −0.0381356 + 0.0660528i
\(591\) −39.0000 + 22.5167i −0.0659898 + 0.0380993i
\(592\) 145.000 + 251.147i 0.244932 + 0.424235i
\(593\) 354.000 + 204.382i 0.596965 + 0.344658i 0.767847 0.640634i \(-0.221328\pi\)
−0.170882 + 0.985292i \(0.554662\pi\)
\(594\) 57.1577i 0.0962250i
\(595\) 441.000 + 763.834i 0.741176 + 1.28376i
\(596\) 690.000 1.15772
\(597\) −210.000 + 363.731i −0.351759 + 0.609264i
\(598\) 168.000 96.9948i 0.280936 0.162199i
\(599\) −278.000 481.510i −0.464107 0.803857i 0.535054 0.844818i \(-0.320291\pi\)
−0.999161 + 0.0409613i \(0.986958\pi\)
\(600\) −21.0000 12.1244i −0.0350000 0.0202073i
\(601\) 580.237i 0.965453i 0.875771 + 0.482726i \(0.160353\pi\)
−0.875771 + 0.482726i \(0.839647\pi\)
\(602\) 182.000 0.302326
\(603\) 156.000 0.258706
\(604\) 340.500 589.763i 0.563742 0.976429i
\(605\) 0 0
\(606\) −18.0000 31.1769i −0.0297030 0.0514471i
\(607\) 571.500 + 329.956i 0.941516 + 0.543584i 0.890435 0.455110i \(-0.150400\pi\)
0.0510805 + 0.998695i \(0.483733\pi\)
\(608\) 114.315i 0.188019i
\(609\) −262.500 151.554i −0.431034 0.248858i
\(610\) 72.0000 0.118033
\(611\) 264.000 457.261i 0.432079 0.748382i
\(612\) 189.000 109.119i 0.308824 0.178299i
\(613\) −160.000 277.128i −0.261011 0.452085i 0.705500 0.708710i \(-0.250723\pi\)
−0.966511 + 0.256625i \(0.917389\pi\)
\(614\) 396.000 + 228.631i 0.644951 + 0.372363i
\(615\) 31.1769i 0.0506942i
\(616\) −269.500 + 466.788i −0.437500 + 0.757772i
\(617\) 652.000 1.05673 0.528363 0.849019i \(-0.322806\pi\)
0.528363 + 0.849019i \(0.322806\pi\)
\(618\) 0 0
\(619\) −558.000 + 322.161i −0.901454 + 0.520455i −0.877672 0.479262i \(-0.840904\pi\)
−0.0237823 + 0.999717i \(0.507571\pi\)
\(620\) 256.500 + 444.271i 0.413710 + 0.716566i
\(621\) 126.000 + 72.7461i 0.202899 + 0.117144i
\(622\) 329.090i 0.529083i
\(623\) 557.720i 0.895217i
\(624\) −60.0000 −0.0961538
\(625\) 335.500 581.103i 0.536800 0.929765i
\(626\) −475.500 + 274.530i −0.759585 + 0.438546i
\(627\) −33.0000 57.1577i −0.0526316 0.0911606i
\(628\) −126.000 72.7461i −0.200637 0.115838i
\(629\) 1406.43i 2.23597i
\(630\) −94.5000 + 54.5596i −0.150000 + 0.0866025i
\(631\) −97.0000 −0.153724 −0.0768621 0.997042i \(-0.524490\pi\)
−0.0768621 + 0.997042i \(0.524490\pi\)
\(632\) 59.5000 103.057i 0.0941456 0.163065i
\(633\) −78.0000 + 45.0333i −0.123223 + 0.0711427i
\(634\) −93.5000 161.947i −0.147476 0.255437i
\(635\) 4.50000 + 2.59808i 0.00708661 + 0.00409146i
\(636\) 161.081i 0.253272i
\(637\) −294.000 169.741i −0.461538 0.266469i
\(638\) −275.000 −0.431034
\(639\) 96.0000 166.277i 0.150235 0.260214i
\(640\) −535.500 + 309.171i −0.836719 + 0.483080i
\(641\) −350.000 606.218i −0.546022 0.945738i −0.998542 0.0539833i \(-0.982808\pi\)
0.452520 0.891754i \(-0.350525\pi\)
\(642\) −46.5000 26.8468i −0.0724299 0.0418174i
\(643\) 325.626i 0.506416i −0.967412 0.253208i \(-0.918514\pi\)
0.967412 0.253208i \(-0.0814857\pi\)
\(644\) 294.000 + 509.223i 0.456522 + 0.790719i
\(645\) −234.000 −0.362791
\(646\) 42.0000 72.7461i 0.0650155 0.112610i
\(647\) −312.000 + 180.133i −0.482226 + 0.278413i −0.721344 0.692577i \(-0.756475\pi\)
0.239118 + 0.970991i \(0.423142\pi\)
\(648\) 31.5000 + 54.5596i 0.0486111 + 0.0841969i
\(649\) −82.5000 47.6314i −0.127119 0.0733920i
\(650\) 13.8564i 0.0213175i
\(651\) 399.000 0.612903
\(652\) −636.000 −0.975460
\(653\) −186.500 + 323.027i −0.285605 + 0.494682i −0.972756 0.231833i \(-0.925528\pi\)
0.687151 + 0.726515i \(0.258861\pi\)
\(654\) −204.000 + 117.779i −0.311927 + 0.180091i
\(655\) −472.500 818.394i −0.721374 1.24946i
\(656\) −15.0000 8.66025i −0.0228659 0.0132016i
\(657\) 20.7846i 0.0316356i
\(658\) −462.000 266.736i −0.702128 0.405374i
\(659\) −818.000 −1.24127 −0.620637 0.784098i \(-0.713126\pi\)
−0.620637 + 0.784098i \(0.713126\pi\)
\(660\) 148.500 257.210i 0.225000 0.389711i
\(661\) 327.000 188.794i 0.494705 0.285618i −0.231819 0.972759i \(-0.574468\pi\)
0.726524 + 0.687141i \(0.241134\pi\)
\(662\) 8.00000 + 13.8564i 0.0120846 + 0.0209311i
\(663\) 252.000 + 145.492i 0.380090 + 0.219445i
\(664\) 375.855i 0.566047i
\(665\) 63.0000 109.119i 0.0947368 0.164089i
\(666\) 174.000 0.261261
\(667\) −350.000 + 606.218i −0.524738 + 0.908872i
\(668\) −252.000 + 145.492i −0.377246 + 0.217803i
\(669\) −19.5000 33.7750i −0.0291480 0.0504858i
\(670\) 234.000 + 135.100i 0.349254 + 0.201642i
\(671\) 152.420i 0.227154i
\(672\) 400.104i 0.595392i
\(673\) 1205.00 1.79049 0.895245 0.445574i \(-0.147000\pi\)
0.895245 + 0.445574i \(0.147000\pi\)
\(674\) −41.5000 + 71.8801i −0.0615727 + 0.106647i
\(675\) 9.00000 5.19615i 0.0133333 0.00769800i
\(676\) 181.500 + 314.367i 0.268491 + 0.465040i
\(677\) −466.500 269.334i −0.689069 0.397834i 0.114194 0.993458i \(-0.463571\pi\)
−0.803263 + 0.595624i \(0.796905\pi\)
\(678\) 128.172i 0.189044i
\(679\) 556.500 321.295i 0.819588 0.473189i
\(680\) 882.000 1.29706
\(681\) 58.5000 101.325i 0.0859031 0.148789i
\(682\) 313.500 180.999i 0.459677 0.265395i
\(683\) −474.500 821.858i −0.694729 1.20331i −0.970272 0.242017i \(-0.922191\pi\)
0.275543 0.961289i \(-0.411142\pi\)
\(684\) −27.0000 15.5885i −0.0394737 0.0227901i
\(685\) 457.261i 0.667535i
\(686\) −171.500 + 297.047i −0.250000 + 0.433013i
\(687\) −54.0000 −0.0786026
\(688\) −65.0000 + 112.583i −0.0944767 + 0.163639i
\(689\) 186.000 107.387i 0.269956 0.155859i
\(690\) 126.000 + 218.238i 0.182609 + 0.316288i
\(691\) −267.000 154.153i −0.386397 0.223086i 0.294201 0.955744i \(-0.404946\pi\)
−0.680598 + 0.732657i \(0.738280\pi\)
\(692\) 644.323i 0.931102i
\(693\) −115.500 200.052i −0.166667 0.288675i
\(694\) 358.000 0.515850
\(695\) −495.000 + 857.365i −0.712230 + 1.23362i
\(696\) −262.500 + 151.554i −0.377155 + 0.217751i
\(697\) 42.0000 + 72.7461i 0.0602582 + 0.104370i
\(698\) −588.000 339.482i −0.842407 0.486364i
\(699\) 453.797i 0.649209i
\(700\) 42.0000 0.0600000
\(701\) −413.000 −0.589158 −0.294579 0.955627i \(-0.595179\pi\)
−0.294579 + 0.955627i \(0.595179\pi\)
\(702\) −18.0000 + 31.1769i −0.0256410 + 0.0444116i
\(703\) −174.000 + 100.459i −0.247511 + 0.142900i
\(704\) 71.5000 + 123.842i 0.101562 + 0.175911i
\(705\) 594.000 + 342.946i 0.842553 + 0.486448i
\(706\) 644.323i 0.912639i
\(707\) 126.000 + 72.7461i 0.178218 + 0.102894i
\(708\) −45.0000 −0.0635593
\(709\) −445.000 + 770.763i −0.627645 + 1.08711i 0.360379 + 0.932806i \(0.382648\pi\)
−0.988023 + 0.154306i \(0.950686\pi\)
\(710\) 288.000 166.277i 0.405634 0.234193i
\(711\) 25.5000 + 44.1673i 0.0358650 + 0.0621200i
\(712\) 483.000 + 278.860i 0.678371 + 0.391658i
\(713\) 921.451i 1.29236i
\(714\) 147.000 254.611i 0.205882 0.356599i
\(715\) 396.000 0.553846
\(716\) 69.0000 119.512i 0.0963687 0.166916i
\(717\) 240.000 138.564i 0.334728 0.193255i
\(718\) 142.000 + 245.951i 0.197772 + 0.342550i
\(719\) 579.000 + 334.286i 0.805285 + 0.464932i 0.845316 0.534267i \(-0.179412\pi\)
−0.0400307 + 0.999198i \(0.512746\pi\)
\(720\) 77.9423i 0.108253i
\(721\) 0 0
\(722\) 349.000 0.483380
\(723\) 409.500 709.275i 0.566390 0.981016i
\(724\) 81.0000 46.7654i 0.111878 0.0645931i
\(725\) 25.0000 + 43.3013i 0.0344828 + 0.0597259i
\(726\) 0 0
\(727\) 417.424i 0.574174i −0.957905 0.287087i \(-0.907313\pi\)
0.957905 0.287087i \(-0.0926868\pi\)
\(728\) −294.000 + 169.741i −0.403846 + 0.233161i
\(729\) −27.0000 −0.0370370
\(730\) 18.0000 31.1769i 0.0246575 0.0427081i
\(731\) 546.000 315.233i 0.746922 0.431236i
\(732\) 36.0000 + 62.3538i 0.0491803 + 0.0851828i
\(733\) 171.000 + 98.7269i 0.233288 + 0.134689i 0.612088 0.790790i \(-0.290330\pi\)
−0.378800 + 0.925479i \(0.623663\pi\)
\(734\) 275.396i 0.375199i
\(735\) 220.500 381.917i 0.300000 0.519615i
\(736\) 924.000 1.25543
\(737\) −286.000 + 495.367i −0.388060 + 0.672139i
\(738\) −9.00000 + 5.19615i −0.0121951 + 0.00704086i
\(739\) 155.000 + 268.468i 0.209743 + 0.363285i 0.951633 0.307236i \(-0.0994040\pi\)
−0.741891 + 0.670521i \(0.766071\pi\)
\(740\) −783.000 452.065i −1.05811 0.610899i
\(741\) 41.5692i 0.0560988i
\(742\) −108.500 187.928i −0.146226 0.253272i
\(743\) −812.000 −1.09287 −0.546433 0.837503i \(-0.684015\pi\)
−0.546433 + 0.837503i \(0.684015\pi\)
\(744\) 199.500 345.544i 0.268145 0.464441i
\(745\) −1035.00 + 597.558i −1.38926 + 0.802091i
\(746\) −25.0000 43.3013i −0.0335121 0.0580446i
\(747\) 139.500 + 80.5404i 0.186747 + 0.107818i
\(748\) 800.207i 1.06980i
\(749\) 217.000 0.289720
\(750\) −207.000 −0.276000
\(751\) 537.500 930.977i 0.715712 1.23965i −0.246972 0.969023i \(-0.579435\pi\)
0.962684 0.270628i \(-0.0872312\pi\)
\(752\) 330.000 190.526i 0.438830 0.253358i
\(753\) −58.5000 101.325i −0.0776892 0.134562i
\(754\) −150.000 86.6025i −0.198939 0.114857i
\(755\) 1179.53i 1.56229i
\(756\) −94.5000 54.5596i −0.125000 0.0721688i
\(757\) −484.000 −0.639366 −0.319683 0.947525i \(-0.603576\pi\)
−0.319683 + 0.947525i \(0.603576\pi\)
\(758\) −229.000 + 396.640i −0.302111 + 0.523271i
\(759\) −462.000 + 266.736i −0.608696 + 0.351431i
\(760\) −63.0000 109.119i −0.0828947 0.143578i
\(761\) 144.000 + 83.1384i 0.189225 + 0.109249i 0.591620 0.806217i \(-0.298489\pi\)
−0.402395 + 0.915466i \(0.631822\pi\)
\(762\) 1.73205i 0.00227303i
\(763\) 476.000 824.456i 0.623853 1.08055i
\(764\) −624.000 −0.816754
\(765\) −189.000 + 327.358i −0.247059 + 0.427918i
\(766\) −351.000 + 202.650i −0.458225 + 0.264556i
\(767\) −30.0000 51.9615i −0.0391134 0.0677464i
\(768\) 256.500 + 148.090i 0.333984 + 0.192826i
\(769\) 594.093i 0.772553i 0.922383 + 0.386277i \(0.126239\pi\)
−0.922383 + 0.386277i \(0.873761\pi\)
\(770\) 400.104i 0.519615i
\(771\) −702.000 −0.910506
\(772\) 358.500 620.940i 0.464378 0.804327i
\(773\) 894.000 516.151i 1.15653 0.667725i 0.206062 0.978539i \(-0.433935\pi\)
0.950471 + 0.310814i \(0.100602\pi\)
\(774\) 39.0000 + 67.5500i 0.0503876 + 0.0872739i
\(775\) −57.0000 32.9090i −0.0735484 0.0424632i
\(776\) 642.591i 0.828081i
\(777\) −609.000 + 351.606i −0.783784 + 0.452518i
\(778\) −698.000 −0.897172
\(779\) 6.00000 10.3923i 0.00770218 0.0133406i
\(780\) 162.000 93.5307i 0.207692 0.119911i
\(781\) 352.000 + 609.682i 0.450704 + 0.780643i
\(782\) −588.000 339.482i −0.751918 0.434120i
\(783\) 129.904i 0.165905i
\(784\) −122.500 212.176i −0.156250 0.270633i
\(785\) 252.000 0.321019
\(786\) −157.500 + 272.798i −0.200382 + 0.347071i
\(787\) 354.000 204.382i 0.449809 0.259698i −0.257940 0.966161i \(-0.583044\pi\)
0.707750 + 0.706463i \(0.249710\pi\)
\(788\) −39.0000 67.5500i −0.0494924 0.0857233i
\(789\) −159.000 91.7987i −0.201521 0.116348i
\(790\) 88.3346i 0.111816i
\(791\) 259.000 + 448.601i 0.327434 + 0.567132i
\(792\) −231.000 −0.291667
\(793\) −48.0000 + 83.1384i −0.0605296 + 0.104840i
\(794\) 498.000 287.520i 0.627204 0.362116i
\(795\) 139.500 + 241.621i 0.175472 + 0.303926i
\(796\) −630.000 363.731i −0.791457 0.456948i
\(797\) 625.270i 0.784530i −0.919852 0.392265i \(-0.871692\pi\)
0.919852 0.392265i \(-0.128308\pi\)
\(798\) −42.0000 −0.0526316
\(799\) −1848.00 −2.31289
\(800\) 33.0000 57.1577i 0.0412500 0.0714471i
\(801\) −207.000 + 119.512i −0.258427 + 0.149203i
\(802\) 142.000 + 245.951i 0.177057 + 0.306672i
\(803\) 66.0000 + 38.1051i 0.0821918 + 0.0474534i
\(804\) 270.200i 0.336070i
\(805\) −882.000 509.223i −1.09565 0.632575i
\(806\) 228.000 0.282878
\(807\) 376.500 652.117i 0.466543 0.808076i
\(808\) 126.000 72.7461i 0.155941 0.0900323i
\(809\) 376.000 + 651.251i 0.464771 + 0.805008i 0.999191 0.0402116i \(-0.0128032\pi\)
−0.534420 + 0.845219i \(0.679470\pi\)
\(810\) −40.5000 23.3827i −0.0500000 0.0288675i
\(811\) 270.200i 0.333169i 0.986027 + 0.166584i \(0.0532738\pi\)
−0.986027 + 0.166584i \(0.946726\pi\)
\(812\) 262.500 454.663i 0.323276 0.559930i
\(813\) 219.000 0.269373
\(814\) −319.000 + 552.524i −0.391892 + 0.678777i
\(815\) 954.000 550.792i 1.17055 0.675819i
\(816\) 105.000 + 181.865i 0.128676 + 0.222874i
\(817\) −78.0000 45.0333i −0.0954712 0.0551203i
\(818\) 209.578i 0.256208i
\(819\) 145.492i 0.177646i
\(820\) 54.0000 0.0658537
\(821\) −441.500 + 764.700i −0.537759 + 0.931426i 0.461265 + 0.887262i \(0.347396\pi\)
−0.999024 + 0.0441635i \(0.985938\pi\)
\(822\) 132.000 76.2102i 0.160584 0.0927132i
\(823\) 245.000 + 424.352i 0.297691 + 0.515617i 0.975607 0.219523i \(-0.0704500\pi\)
−0.677916 + 0.735139i \(0.737117\pi\)
\(824\) 0 0
\(825\) 38.1051i 0.0461880i
\(826\) −52.5000 + 30.3109i −0.0635593 + 0.0366960i
\(827\) 1279.00 1.54655 0.773277 0.634068i \(-0.218616\pi\)
0.773277 + 0.634068i \(0.218616\pi\)
\(828\) −126.000 + 218.238i −0.152174 + 0.263573i
\(829\) 1311.00 756.906i 1.58142 0.913035i 0.586771 0.809753i \(-0.300399\pi\)
0.994652 0.103283i \(-0.0329346\pi\)
\(830\) 139.500 + 241.621i 0.168072 + 0.291110i
\(831\) −354.000 204.382i −0.425993 0.245947i
\(832\) 90.0666i 0.108253i
\(833\) 1188.19i 1.42639i
\(834\) 330.000 0.395683
\(835\) 252.000 436.477i 0.301796 0.522727i
\(836\) 99.0000 57.1577i 0.118421 0.0683704i
\(837\) 85.5000 + 148.090i 0.102151 + 0.176930i
\(838\) 114.000 + 65.8179i 0.136038 + 0.0785417i
\(839\) 523.079i 0.623456i −0.950171 0.311728i \(-0.899092\pi\)
0.950171 0.311728i \(-0.100908\pi\)
\(840\) −220.500 381.917i −0.262500 0.454663i
\(841\) −216.000 −0.256837
\(842\) 14.0000 24.2487i 0.0166271 0.0287989i
\(843\) −174.000 + 100.459i −0.206406 + 0.119168i
\(844\) −78.0000 135.100i −0.0924171 0.160071i
\(845\) −544.500 314.367i −0.644379 0.372032i
\(846\) 228.631i 0.270249i
\(847\) 0 0
\(848\) 155.000 0.182783
\(849\) −321.000 + 555.988i −0.378092 + 0.654874i
\(850\) −42.0000 + 24.2487i −0.0494118 + 0.0285279i
\(851\) 812.000 + 1406.43i 0.954172 + 1.65267i
\(852\) 288.000 + 166.277i 0.338028 + 0.195161i
\(853\) 387.979i 0.454841i 0.973797 + 0.227421i \(0.0730292\pi\)
−0.973797 + 0.227421i \(0.926971\pi\)
\(854\) 84.0000 + 48.4974i 0.0983607 + 0.0567886i
\(855\) 54.0000 0.0631579
\(856\) 108.500 187.928i 0.126752 0.219541i
\(857\) −720.000 + 415.692i −0.840140 + 0.485055i −0.857312 0.514797i \(-0.827867\pi\)
0.0171718 + 0.999853i \(0.494534\pi\)
\(858\) −66.0000 114.315i −0.0769231 0.133235i
\(859\) 981.000 + 566.381i 1.14203 + 0.659349i 0.946931 0.321436i \(-0.104165\pi\)
0.195094 + 0.980785i \(0.437499\pi\)
\(860\) 405.300i 0.471279i
\(861\) 21.0000 36.3731i 0.0243902 0.0422451i
\(862\) 118.000 0.136891
\(863\) −11.0000 + 19.0526i −0.0127462 + 0.0220771i −0.872328 0.488921i \(-0.837391\pi\)
0.859582 + 0.510998i \(0.170724\pi\)
\(864\) −148.500 + 85.7365i −0.171875 + 0.0992321i
\(865\) −558.000 966.484i −0.645087 1.11732i
\(866\) 486.000 + 280.592i 0.561201 + 0.324010i
\(867\) 517.883i 0.597328i
\(868\) 691.088i 0.796185i
\(869\) −187.000 −0.215190
\(870\) 112.500 194.856i 0.129310 0.223972i
\(871\) −312.000 + 180.133i −0.358209 + 0.206812i
\(872\) −476.000 824.456i −0.545872 0.945477i
\(873\) 238.500 + 137.698i 0.273196 + 0.157730i
\(874\) 96.9948i 0.110978i
\(875\) 724.500 418.290i 0.828000 0.478046i
\(876\) 36.0000 0.0410959
\(877\) 20.0000 34.6410i 0.0228050 0.0394994i −0.854398 0.519620i \(-0.826074\pi\)
0.877203 + 0.480120i \(0.159407\pi\)
\(878\) 640.500 369.793i 0.729499 0.421176i
\(879\) 16.5000 + 28.5788i 0.0187713 + 0.0325129i
\(880\) 247.500 + 142.894i 0.281250 + 0.162380i
\(881\) 20.7846i 0.0235921i 0.999930 + 0.0117960i \(0.00375488\pi\)
−0.999930 + 0.0117960i \(0.996245\pi\)
\(882\) −147.000 −0.166667
\(883\) 386.000 0.437146 0.218573 0.975821i \(-0.429860\pi\)
0.218573 + 0.975821i \(0.429860\pi\)
\(884\) −252.000 + 436.477i −0.285068 + 0.493752i
\(885\) 67.5000 38.9711i 0.0762712 0.0440352i
\(886\) 77.5000 + 134.234i 0.0874718 + 0.151506i
\(887\) −1494.00 862.561i −1.68433 0.972448i −0.958725 0.284336i \(-0.908227\pi\)
−0.725604 0.688112i \(-0.758440\pi\)
\(888\) 703.213i 0.791906i
\(889\) 3.50000 + 6.06218i 0.00393701 + 0.00681910i
\(890\) −414.000 −0.465169
\(891\) 49.5000 85.7365i 0.0555556 0.0962250i
\(892\) 58.5000 33.7750i 0.0655830 0.0378643i
\(893\) 132.000 + 228.631i 0.147816 + 0.256025i
\(894\) 345.000 + 199.186i 0.385906 + 0.222803i
\(895\) 239.023i 0.267065i
\(896\) −833.000 −0.929688
\(897\) −336.000 −0.374582
\(898\) 184.000 318.697i 0.204900 0.354897i
\(899\) −712.500 + 411.362i −0.792547 + 0.457577i
\(900\) 9.00000 + 15.5885i 0.0100000 + 0.0173205i
\(901\) −651.000 375.855i −0.722531 0.417153i
\(902\) 38.1051i 0.0422451i
\(903\) −273.000 157.617i −0.302326 0.174548i
\(904\) 518.000 0.573009
\(905\) −81.0000 + 140.296i −0.0895028 + 0.155023i
\(906\) 340.500 196.588i 0.375828 0.216984i
\(907\) 296.000 + 512.687i 0.326351 + 0.565256i 0.981785 0.189996i \(-0.0608477\pi\)
−0.655434 + 0.755252i \(0.727514\pi\)
\(908\) 175.500 + 101.325i 0.193282 + 0.111591i
\(909\) 62.3538i 0.0685961i
\(910\) 126.000 218.238i 0.138462 0.239822i
\(911\) −416.000 −0.456641 −0.228321 0.973586i \(-0.573323\pi\)
−0.228321 + 0.973586i \(0.573323\pi\)
\(912\) 15.0000 25.9808i 0.0164474 0.0284877i
\(913\) −511.500 + 295.315i −0.560241 + 0.323455i
\(914\) −170.500 295.315i −0.186543 0.323101i
\(915\) −108.000 62.3538i −0.118033 0.0681463i
\(916\) 93.5307i 0.102108i
\(917\) 1273.06i 1.38828i
\(918\) 126.000 0.137255
\(919\) −25.0000 + 43.3013i −0.0272035 + 0.0471178i −0.879307 0.476256i \(-0.841994\pi\)
0.852103 + 0.523374i \(0.175327\pi\)
\(920\) −882.000 + 509.223i −0.958696 + 0.553503i
\(921\) −396.000 685.892i −0.429967 0.744725i
\(922\) 48.0000 + 27.7128i 0.0520607 + 0.0300573i
\(923\) 443.405i 0.480395i
\(924\) 346.500 200.052i 0.375000 0.216506i
\(925\) 116.000 0.125405
\(926\) 89.0000 154.153i 0.0961123 0.166471i
\(927\) 0 0
\(928\) −412.500 714.471i −0.444504 0.769904i
\(929\) 357.000 + 206.114i 0.384284 + 0.221867i 0.679681 0.733508i \(-0.262118\pi\)
−0.295396 + 0.955375i \(0.595452\pi\)
\(930\) 296.181i 0.318474i
\(931\) 147.000 84.8705i 0.157895 0.0911606i
\(932\) −786.000 −0.843348
\(933\) 285.000 493.634i 0.305466 0.529083i
\(934\) −570.000 + 329.090i −0.610278 + 0.352344i
\(935\) −693.000 1200.31i −0.741176 1.28376i
\(936\) −126.000 72.7461i −0.134615 0.0777202i
\(937\) 1605.61i 1.71357i −0.515677 0.856783i \(-0.672460\pi\)
0.515677 0.856783i \(-0.327540\pi\)
\(938\) 182.000 + 315.233i 0.194030 + 0.336070i
\(939\) 951.000 1.01278
\(940\) −594.000 + 1028.84i −0.631915 + 1.09451i
\(941\) −1150.50 + 664.241i −1.22264 + 0.705889i −0.965479 0.260481i \(-0.916119\pi\)
−0.257156 + 0.966370i \(0.582786\pi\)
\(942\) −42.0000 72.7461i −0.0445860 0.0772252i
\(943\) −84.0000 48.4974i −0.0890774 0.0514289i
\(944\) 43.3013i 0.0458700i
\(945\) 189.000 0.200000
\(946\) −286.000 −0.302326
\(947\) 685.000 1186.45i 0.723337 1.25286i −0.236318 0.971676i \(-0.575941\pi\)
0.959655 0.281180i \(-0.0907259\pi\)
\(948\) −76.5000 + 44.1673i −0.0806962 + 0.0465900i
\(949\) 24.0000 + 41.5692i 0.0252898 + 0.0438032i
\(950\) 6.00000 + 3.46410i 0.00631579 + 0.00364642i
\(951\) 323.894i 0.340582i
\(952\) 1029.00 + 594.093i 1.08088 + 0.624048i
\(953\) 1150.00 1.20672 0.603358 0.797471i \(-0.293829\pi\)
0.603358 + 0.797471i \(0.293829\pi\)
\(954\) 46.5000 80.5404i 0.0487421 0.0844239i
\(955\) 936.000 540.400i 0.980105 0.565864i
\(956\) 240.000 + 415.692i 0.251046 + 0.434824i
\(957\) 412.500 + 238.157i 0.431034 + 0.248858i
\(958\) 509.223i 0.531548i
\(959\) −308.000 + 533.472i −0.321168 + 0.556279i
\(960\) −117.000 −0.121875
\(961\) 61.0000 105.655i 0.0634755 0.109943i
\(962\) −348.000 + 200.918i −0.361746 + 0.208854i
\(963\) 46.5000 + 80.5404i 0.0482866 + 0.0836349i
\(964\) 1228.50 + 709.275i 1.27438 + 0.735762i
\(965\) 1241.88i 1.28692i
\(966\) 339.482i 0.351431i
\(967\) 5.00000 0.00517063 0.00258532 0.999997i \(-0.499177\pi\)
0.00258532 + 0.999997i \(0.499177\pi\)
\(968\) 0 0
\(969\) −126.000 + 72.7461i −0.130031 + 0.0750734i
\(970\) 238.500 + 413.094i 0.245876 + 0.425870i
\(971\) 385.500 + 222.569i 0.397013 + 0.229216i 0.685195 0.728360i \(-0.259717\pi\)
−0.288181 + 0.957576i \(0.593051\pi\)
\(972\) 46.7654i 0.0481125i
\(973\) −1155.00 + 666.840i −1.18705 + 0.685344i
\(974\) −841.000 −0.863450
\(975\) −12.0000 + 20.7846i −0.0123077 + 0.0213175i
\(976\) −60.0000 + 34.6410i −0.0614754 + 0.0354928i
\(977\) −479.000 829.652i −0.490276 0.849184i 0.509661 0.860375i \(-0.329771\pi\)
−0.999937 + 0.0111917i \(0.996437\pi\)
\(978\) −318.000 183.597i −0.325153 0.187727i
\(979\) 876.418i 0.895217i
\(980\) 661.500 + 381.917i 0.675000 + 0.389711i
\(981\) 408.000 0.415902
\(982\) 479.500 830.518i 0.488289 0.845742i
\(983\) 243.000 140.296i 0.247202 0.142722i −0.371280 0.928521i \(-0.621081\pi\)
0.618483 + 0.785798i \(0.287748\pi\)
\(984\) −21.0000 36.3731i −0.0213415 0.0369645i
\(985\) 117.000 + 67.5500i 0.118782 + 0.0685787i
\(986\) 606.218i 0.614825i
\(987\) 462.000 + 800.207i 0.468085 + 0.810747i
\(988\) 72.0000 0.0728745
\(989\) −364.000 + 630.466i −0.368049 + 0.637479i
\(990\) 148.500 85.7365i 0.150000 0.0866025i
\(991\) −461.500 799.341i −0.465691 0.806601i 0.533541 0.845774i \(-0.320861\pi\)
−0.999232 + 0.0391732i \(0.987528\pi\)
\(992\) 940.500 + 542.998i 0.948085 + 0.547377i
\(993\) 27.7128i 0.0279082i
\(994\) 448.000 0.450704
\(995\) 1260.00 1.26633
\(996\) −139.500 + 241.621i −0.140060 + 0.242591i
\(997\) 18.0000 10.3923i 0.0180542 0.0104236i −0.490946 0.871190i \(-0.663349\pi\)
0.509000 + 0.860767i \(0.330015\pi\)
\(998\) 59.0000 + 102.191i 0.0591182 + 0.102396i
\(999\) −261.000 150.688i −0.261261 0.150839i
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 21.3.f.b.19.1 yes 2
3.2 odd 2 63.3.m.c.19.1 2
4.3 odd 2 336.3.bh.a.145.1 2
5.2 odd 4 525.3.s.c.124.1 4
5.3 odd 4 525.3.s.c.124.2 4
5.4 even 2 525.3.o.g.376.1 2
7.2 even 3 147.3.d.b.97.2 2
7.3 odd 6 inner 21.3.f.b.10.1 2
7.4 even 3 147.3.f.c.31.1 2
7.5 odd 6 147.3.d.b.97.1 2
7.6 odd 2 147.3.f.c.19.1 2
12.11 even 2 1008.3.cg.g.145.1 2
21.2 odd 6 441.3.d.b.244.1 2
21.5 even 6 441.3.d.b.244.2 2
21.11 odd 6 441.3.m.e.325.1 2
21.17 even 6 63.3.m.c.10.1 2
21.20 even 2 441.3.m.e.19.1 2
28.3 even 6 336.3.bh.a.241.1 2
28.19 even 6 2352.3.f.d.97.2 2
28.23 odd 6 2352.3.f.d.97.1 2
35.3 even 12 525.3.s.c.199.1 4
35.17 even 12 525.3.s.c.199.2 4
35.24 odd 6 525.3.o.g.451.1 2
84.59 odd 6 1008.3.cg.g.577.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.f.b.10.1 2 7.3 odd 6 inner
21.3.f.b.19.1 yes 2 1.1 even 1 trivial
63.3.m.c.10.1 2 21.17 even 6
63.3.m.c.19.1 2 3.2 odd 2
147.3.d.b.97.1 2 7.5 odd 6
147.3.d.b.97.2 2 7.2 even 3
147.3.f.c.19.1 2 7.6 odd 2
147.3.f.c.31.1 2 7.4 even 3
336.3.bh.a.145.1 2 4.3 odd 2
336.3.bh.a.241.1 2 28.3 even 6
441.3.d.b.244.1 2 21.2 odd 6
441.3.d.b.244.2 2 21.5 even 6
441.3.m.e.19.1 2 21.20 even 2
441.3.m.e.325.1 2 21.11 odd 6
525.3.o.g.376.1 2 5.4 even 2
525.3.o.g.451.1 2 35.24 odd 6
525.3.s.c.124.1 4 5.2 odd 4
525.3.s.c.124.2 4 5.3 odd 4
525.3.s.c.199.1 4 35.3 even 12
525.3.s.c.199.2 4 35.17 even 12
1008.3.cg.g.145.1 2 12.11 even 2
1008.3.cg.g.577.1 2 84.59 odd 6
2352.3.f.d.97.1 2 28.23 odd 6
2352.3.f.d.97.2 2 28.19 even 6