Properties

Label 441.3.n.a.410.1
Level $441$
Weight $3$
Character 441.410
Analytic conductor $12.016$
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] = [441,3,Mod(128,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.128");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 441.n (of order \(6\), degree \(2\), not 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: \(12.0163796583\)
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: no (minimal twist has level 9)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 410.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.410
Dual form 441.3.n.a.128.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{2} -3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{2} -3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +(-3.00000 + 5.19615i) q^{10} -1.73205i q^{11} +(1.50000 + 2.59808i) q^{12} +(-2.00000 + 3.46410i) q^{13} -10.3923i q^{15} +(5.50000 - 9.52628i) q^{16} +(13.5000 + 7.79423i) q^{17} +(13.5000 + 7.79423i) q^{18} +(5.50000 + 9.52628i) q^{19} +(3.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +27.7128i q^{23} +25.9808i q^{24} +13.0000 q^{25} +(-6.00000 + 3.46410i) q^{26} -27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} +(9.00000 - 15.5885i) q^{30} +(16.0000 + 27.7128i) q^{31} +(-13.5000 + 7.79423i) q^{32} +5.19615i q^{33} +(13.5000 + 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 + 29.4449i) q^{37} +19.0526i q^{38} +(6.00000 - 10.3923i) q^{39} +30.0000 q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(-1.50000 + 0.866025i) q^{44} +31.1769i q^{45} +(-24.0000 + 41.5692i) q^{46} +(-42.0000 - 24.2487i) q^{47} +(-16.5000 + 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +(-40.5000 - 23.3827i) q^{51} +4.00000 q^{52} +(-40.5000 - 23.3827i) q^{54} +6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +78.0000 q^{58} +(43.5000 - 25.1147i) q^{59} +(-9.00000 + 5.19615i) q^{60} +(28.0000 - 48.4974i) q^{61} +55.4256i q^{62} -71.0000 q^{64} +(-12.0000 - 6.92820i) q^{65} +(-4.50000 + 7.79423i) q^{66} +(15.5000 + 26.8468i) q^{67} -15.5885i q^{68} -83.1384i q^{69} -31.1769i q^{71} -77.9423i q^{72} +(32.5000 - 56.2917i) q^{73} +58.8897i q^{74} -39.0000 q^{75} +(5.50000 - 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +(-19.0000 + 32.9090i) q^{79} +(33.0000 + 19.0526i) q^{80} +81.0000 q^{81} +(10.5000 + 18.1865i) q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +105.655i q^{86} +(-117.000 + 67.5500i) q^{87} -15.0000 q^{88} +(-108.000 + 62.3538i) q^{89} +(-27.0000 + 46.7654i) q^{90} +(24.0000 - 13.8564i) q^{92} +(-48.0000 - 83.1384i) q^{93} +(-42.0000 - 72.7461i) q^{94} +(-33.0000 + 19.0526i) q^{95} +(40.5000 - 23.3827i) q^{96} +(-57.5000 - 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} - 6 q^{3} - q^{4} - 9 q^{6} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} - 6 q^{3} - q^{4} - 9 q^{6} + 18 q^{9} - 6 q^{10} + 3 q^{12} - 4 q^{13} + 11 q^{16} + 27 q^{17} + 27 q^{18} + 11 q^{19} + 6 q^{20} + 3 q^{22} + 26 q^{25} - 12 q^{26} - 54 q^{27} + 78 q^{29} + 18 q^{30} + 32 q^{31} - 27 q^{32} + 27 q^{34} - 9 q^{36} + 34 q^{37} + 12 q^{39} + 60 q^{40} + 21 q^{41} + 61 q^{43} - 3 q^{44} - 48 q^{46} - 84 q^{47} - 33 q^{48} + 39 q^{50} - 81 q^{51} + 8 q^{52} - 81 q^{54} + 12 q^{55} - 33 q^{57} + 156 q^{58} + 87 q^{59} - 18 q^{60} + 56 q^{61} - 142 q^{64} - 24 q^{65} - 9 q^{66} + 31 q^{67} + 65 q^{73} - 78 q^{75} + 11 q^{76} + 36 q^{78} - 38 q^{79} + 66 q^{80} + 162 q^{81} + 21 q^{82} + 84 q^{83} - 54 q^{85} - 234 q^{87} - 30 q^{88} - 216 q^{89} - 54 q^{90} + 48 q^{92} - 96 q^{93} - 84 q^{94} - 66 q^{95} + 81 q^{96} - 115 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 + 0.866025i 0.750000 + 0.433013i 0.825694 0.564118i \(-0.190784\pi\)
−0.0756939 + 0.997131i \(0.524117\pi\)
\(3\) −3.00000 −1.00000
\(4\) −0.500000 0.866025i −0.125000 0.216506i
\(5\) 3.46410i 0.692820i 0.938083 + 0.346410i \(0.112599\pi\)
−0.938083 + 0.346410i \(0.887401\pi\)
\(6\) −4.50000 2.59808i −0.750000 0.433013i
\(7\) 0 0
\(8\) 8.66025i 1.08253i
\(9\) 9.00000 1.00000
\(10\) −3.00000 + 5.19615i −0.300000 + 0.519615i
\(11\) 1.73205i 0.157459i −0.996896 0.0787296i \(-0.974914\pi\)
0.996896 0.0787296i \(-0.0250864\pi\)
\(12\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(13\) −2.00000 + 3.46410i −0.153846 + 0.266469i −0.932638 0.360813i \(-0.882499\pi\)
0.778792 + 0.627282i \(0.215833\pi\)
\(14\) 0 0
\(15\) 10.3923i 0.692820i
\(16\) 5.50000 9.52628i 0.343750 0.595392i
\(17\) 13.5000 + 7.79423i 0.794118 + 0.458484i 0.841410 0.540397i \(-0.181726\pi\)
−0.0472925 + 0.998881i \(0.515059\pi\)
\(18\) 13.5000 + 7.79423i 0.750000 + 0.433013i
\(19\) 5.50000 + 9.52628i 0.289474 + 0.501383i 0.973684 0.227901i \(-0.0731864\pi\)
−0.684211 + 0.729285i \(0.739853\pi\)
\(20\) 3.00000 1.73205i 0.150000 0.0866025i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.0681818 0.118094i
\(23\) 27.7128i 1.20490i 0.798155 + 0.602452i \(0.205810\pi\)
−0.798155 + 0.602452i \(0.794190\pi\)
\(24\) 25.9808i 1.08253i
\(25\) 13.0000 0.520000
\(26\) −6.00000 + 3.46410i −0.230769 + 0.133235i
\(27\) −27.0000 −1.00000
\(28\) 0 0
\(29\) 39.0000 22.5167i 1.34483 0.776437i 0.357316 0.933984i \(-0.383692\pi\)
0.987511 + 0.157547i \(0.0503586\pi\)
\(30\) 9.00000 15.5885i 0.300000 0.519615i
\(31\) 16.0000 + 27.7128i 0.516129 + 0.893962i 0.999825 + 0.0187254i \(0.00596084\pi\)
−0.483696 + 0.875236i \(0.660706\pi\)
\(32\) −13.5000 + 7.79423i −0.421875 + 0.243570i
\(33\) 5.19615i 0.157459i
\(34\) 13.5000 + 23.3827i 0.397059 + 0.687726i
\(35\) 0 0
\(36\) −4.50000 7.79423i −0.125000 0.216506i
\(37\) 17.0000 + 29.4449i 0.459459 + 0.795807i 0.998932 0.0461958i \(-0.0147098\pi\)
−0.539473 + 0.842003i \(0.681376\pi\)
\(38\) 19.0526i 0.501383i
\(39\) 6.00000 10.3923i 0.153846 0.266469i
\(40\) 30.0000 0.750000
\(41\) 10.5000 + 6.06218i 0.256098 + 0.147858i 0.622553 0.782578i \(-0.286095\pi\)
−0.366456 + 0.930436i \(0.619429\pi\)
\(42\) 0 0
\(43\) 30.5000 + 52.8275i 0.709302 + 1.22855i 0.965116 + 0.261822i \(0.0843232\pi\)
−0.255814 + 0.966726i \(0.582343\pi\)
\(44\) −1.50000 + 0.866025i −0.0340909 + 0.0196824i
\(45\) 31.1769i 0.692820i
\(46\) −24.0000 + 41.5692i −0.521739 + 0.903679i
\(47\) −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
\(49\) 0 0
\(50\) 19.5000 + 11.2583i 0.390000 + 0.225167i
\(51\) −40.5000 23.3827i −0.794118 0.458484i
\(52\) 4.00000 0.0769231
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) −40.5000 23.3827i −0.750000 0.433013i
\(55\) 6.00000 0.109091
\(56\) 0 0
\(57\) −16.5000 28.5788i −0.289474 0.501383i
\(58\) 78.0000 1.34483
\(59\) 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 −0.539893 0.841734i \(-0.681535\pi\)
0.998909 + 0.0466940i \(0.0148686\pi\)
\(62\) 55.4256i 0.893962i
\(63\) 0 0
\(64\) −71.0000 −1.10938
\(65\) −12.0000 6.92820i −0.184615 0.106588i
\(66\) −4.50000 + 7.79423i −0.0681818 + 0.118094i
\(67\) 15.5000 + 26.8468i 0.231343 + 0.400698i 0.958204 0.286087i \(-0.0923546\pi\)
−0.726860 + 0.686785i \(0.759021\pi\)
\(68\) 15.5885i 0.229242i
\(69\) 83.1384i 1.20490i
\(70\) 0 0
\(71\) 31.1769i 0.439111i −0.975600 0.219556i \(-0.929539\pi\)
0.975600 0.219556i \(-0.0704608\pi\)
\(72\) 77.9423i 1.08253i
\(73\) 32.5000 56.2917i 0.445205 0.771119i −0.552861 0.833273i \(-0.686464\pi\)
0.998067 + 0.0621550i \(0.0197973\pi\)
\(74\) 58.8897i 0.795807i
\(75\) −39.0000 −0.520000
\(76\) 5.50000 9.52628i 0.0723684 0.125346i
\(77\) 0 0
\(78\) 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 \(0.243980\pi\)
\(80\) 33.0000 + 19.0526i 0.412500 + 0.238157i
\(81\) 81.0000 1.00000
\(82\) 10.5000 + 18.1865i 0.128049 + 0.221787i
\(83\) 42.0000 24.2487i 0.506024 0.292153i −0.225174 0.974319i \(-0.572295\pi\)
0.731198 + 0.682165i \(0.238962\pi\)
\(84\) 0 0
\(85\) −27.0000 + 46.7654i −0.317647 + 0.550181i
\(86\) 105.655i 1.22855i
\(87\) −117.000 + 67.5500i −1.34483 + 0.776437i
\(88\) −15.0000 −0.170455
\(89\) −108.000 + 62.3538i −1.21348 + 0.700605i −0.963516 0.267650i \(-0.913753\pi\)
−0.249967 + 0.968254i \(0.580420\pi\)
\(90\) −27.0000 + 46.7654i −0.300000 + 0.519615i
\(91\) 0 0
\(92\) 24.0000 13.8564i 0.260870 0.150613i
\(93\) −48.0000 83.1384i −0.516129 0.893962i
\(94\) −42.0000 72.7461i −0.446809 0.773895i
\(95\) −33.0000 + 19.0526i −0.347368 + 0.200553i
\(96\) 40.5000 23.3827i 0.421875 0.243570i
\(97\) −57.5000 99.5929i −0.592784 1.02673i −0.993856 0.110685i \(-0.964696\pi\)
0.401072 0.916047i \(-0.368638\pi\)
\(98\) 0 0
\(99\) 15.5885i 0.157459i
\(100\) −6.50000 11.2583i −0.0650000 0.112583i
\(101\) 45.0333i 0.445874i −0.974833 0.222937i \(-0.928436\pi\)
0.974833 0.222937i \(-0.0715645\pi\)
\(102\) −40.5000 70.1481i −0.397059 0.687726i
\(103\) 40.0000 0.388350 0.194175 0.980967i \(-0.437797\pi\)
0.194175 + 0.980967i \(0.437797\pi\)
\(104\) 30.0000 + 17.3205i 0.288462 + 0.166543i
\(105\) 0 0
\(106\) 0 0
\(107\) −121.500 + 70.1481i −1.13551 + 0.655589i −0.945316 0.326156i \(-0.894246\pi\)
−0.190198 + 0.981746i \(0.560913\pi\)
\(108\) 13.5000 + 23.3827i 0.125000 + 0.216506i
\(109\) 26.0000 45.0333i 0.238532 0.413150i −0.721761 0.692142i \(-0.756667\pi\)
0.960293 + 0.278992i \(0.0900004\pi\)
\(110\) 9.00000 + 5.19615i 0.0818182 + 0.0472377i
\(111\) −51.0000 88.3346i −0.459459 0.795807i
\(112\) 0 0
\(113\) −78.0000 45.0333i −0.690265 0.398525i 0.113446 0.993544i \(-0.463811\pi\)
−0.803711 + 0.595019i \(0.797144\pi\)
\(114\) 57.1577i 0.501383i
\(115\) −96.0000 −0.834783
\(116\) −39.0000 22.5167i −0.336207 0.194109i
\(117\) −18.0000 + 31.1769i −0.153846 + 0.266469i
\(118\) 87.0000 0.737288
\(119\) 0 0
\(120\) −90.0000 −0.750000
\(121\) 118.000 0.975207
\(122\) 84.0000 48.4974i 0.688525 0.397520i
\(123\) −31.5000 18.1865i −0.256098 0.147858i
\(124\) 16.0000 27.7128i 0.129032 0.223490i
\(125\) 131.636i 1.05309i
\(126\) 0 0
\(127\) −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
\(131\) 159.349i 1.21640i 0.793783 + 0.608201i \(0.208109\pi\)
−0.793783 + 0.608201i \(0.791891\pi\)
\(132\) 4.50000 2.59808i 0.0340909 0.0196824i
\(133\) 0 0
\(134\) 53.6936i 0.400698i
\(135\) 93.5307i 0.692820i
\(136\) 67.5000 116.913i 0.496324 0.859658i
\(137\) 188.794i 1.37806i −0.724735 0.689028i \(-0.758038\pi\)
0.724735 0.689028i \(-0.241962\pi\)
\(138\) 72.0000 124.708i 0.521739 0.903679i
\(139\) 2.50000 4.33013i 0.0179856 0.0311520i −0.856893 0.515495i \(-0.827608\pi\)
0.874878 + 0.484343i \(0.160941\pi\)
\(140\) 0 0
\(141\) 126.000 + 72.7461i 0.893617 + 0.515930i
\(142\) 27.0000 46.7654i 0.190141 0.329334i
\(143\) 6.00000 + 3.46410i 0.0419580 + 0.0242245i
\(144\) 49.5000 85.7365i 0.343750 0.595392i
\(145\) 78.0000 + 135.100i 0.537931 + 0.931724i
\(146\) 97.5000 56.2917i 0.667808 0.385559i
\(147\) 0 0
\(148\) 17.0000 29.4449i 0.114865 0.198952i
\(149\) 152.420i 1.02296i 0.859296 + 0.511478i \(0.170902\pi\)
−0.859296 + 0.511478i \(0.829098\pi\)
\(150\) −58.5000 33.7750i −0.390000 0.225167i
\(151\) 20.0000 0.132450 0.0662252 0.997805i \(-0.478904\pi\)
0.0662252 + 0.997805i \(0.478904\pi\)
\(152\) 82.5000 47.6314i 0.542763 0.313364i
\(153\) 121.500 + 70.1481i 0.794118 + 0.458484i
\(154\) 0 0
\(155\) −96.0000 + 55.4256i −0.619355 + 0.357585i
\(156\) −12.0000 −0.0769231
\(157\) −20.0000 34.6410i −0.127389 0.220643i 0.795276 0.606248i \(-0.207326\pi\)
−0.922664 + 0.385605i \(0.873993\pi\)
\(158\) −57.0000 + 32.9090i −0.360759 + 0.208285i
\(159\) 0 0
\(160\) −27.0000 46.7654i −0.168750 0.292284i
\(161\) 0 0
\(162\) 121.500 + 70.1481i 0.750000 + 0.433013i
\(163\) 53.0000 + 91.7987i 0.325153 + 0.563182i 0.981543 0.191240i \(-0.0612507\pi\)
−0.656390 + 0.754422i \(0.727917\pi\)
\(164\) 12.1244i 0.0739290i
\(165\) −18.0000 −0.109091
\(166\) 84.0000 0.506024
\(167\) −165.000 95.2628i −0.988024 0.570436i −0.0833409 0.996521i \(-0.526559\pi\)
−0.904683 + 0.426085i \(0.859892\pi\)
\(168\) 0 0
\(169\) 76.5000 + 132.502i 0.452663 + 0.784035i
\(170\) −81.0000 + 46.7654i −0.476471 + 0.275090i
\(171\) 49.5000 + 85.7365i 0.289474 + 0.501383i
\(172\) 30.5000 52.8275i 0.177326 0.307137i
\(173\) 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
\(175\) 0 0
\(176\) −16.5000 9.52628i −0.0937500 0.0541266i
\(177\) −130.500 + 75.3442i −0.737288 + 0.425674i
\(178\) −216.000 −1.21348
\(179\) −54.0000 31.1769i −0.301676 0.174173i 0.341520 0.939875i \(-0.389058\pi\)
−0.643196 + 0.765702i \(0.722392\pi\)
\(180\) 27.0000 15.5885i 0.150000 0.0866025i
\(181\) 232.000 1.28177 0.640884 0.767638i \(-0.278568\pi\)
0.640884 + 0.767638i \(0.278568\pi\)
\(182\) 0 0
\(183\) −84.0000 + 145.492i −0.459016 + 0.795040i
\(184\) 240.000 1.30435
\(185\) −102.000 + 58.8897i −0.551351 + 0.318323i
\(186\) 166.277i 0.893962i
\(187\) 13.5000 23.3827i 0.0721925 0.125041i
\(188\) 48.4974i 0.257965i
\(189\) 0 0
\(190\) −66.0000 −0.347368
\(191\) −201.000 116.047i −1.05236 0.607578i −0.129048 0.991638i \(-0.541192\pi\)
−0.923308 + 0.384060i \(0.874525\pi\)
\(192\) 213.000 1.10938
\(193\) 132.500 + 229.497i 0.686528 + 1.18910i 0.972954 + 0.231000i \(0.0741996\pi\)
−0.286425 + 0.958103i \(0.592467\pi\)
\(194\) 199.186i 1.02673i
\(195\) 36.0000 + 20.7846i 0.184615 + 0.106588i
\(196\) 0 0
\(197\) 124.708i 0.633034i 0.948587 + 0.316517i \(0.102513\pi\)
−0.948587 + 0.316517i \(0.897487\pi\)
\(198\) 13.5000 23.3827i 0.0681818 0.118094i
\(199\) 145.000 251.147i 0.728643 1.26205i −0.228814 0.973470i \(-0.573485\pi\)
0.957457 0.288577i \(-0.0931821\pi\)
\(200\) 112.583i 0.562917i
\(201\) −46.5000 80.5404i −0.231343 0.400698i
\(202\) 39.0000 67.5500i 0.193069 0.334406i
\(203\) 0 0
\(204\) 46.7654i 0.229242i
\(205\) −21.0000 + 36.3731i −0.102439 + 0.177430i
\(206\) 60.0000 + 34.6410i 0.291262 + 0.168160i
\(207\) 249.415i 1.20490i
\(208\) 22.0000 + 38.1051i 0.105769 + 0.183198i
\(209\) 16.5000 9.52628i 0.0789474 0.0455803i
\(210\) 0 0
\(211\) 47.0000 81.4064i 0.222749 0.385812i −0.732893 0.680344i \(-0.761830\pi\)
0.955642 + 0.294532i \(0.0951637\pi\)
\(212\) 0 0
\(213\) 93.5307i 0.439111i
\(214\) −243.000 −1.13551
\(215\) −183.000 + 105.655i −0.851163 + 0.491419i
\(216\) 233.827i 1.08253i
\(217\) 0 0
\(218\) 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
\(222\) 176.669i 0.795807i
\(223\) −26.0000 45.0333i −0.116592 0.201943i 0.801823 0.597562i \(-0.203864\pi\)
−0.918415 + 0.395618i \(0.870530\pi\)
\(224\) 0 0
\(225\) 117.000 0.520000
\(226\) −78.0000 135.100i −0.345133 0.597787i
\(227\) 188.794i 0.831690i 0.909436 + 0.415845i \(0.136514\pi\)
−0.909436 + 0.415845i \(0.863486\pi\)
\(228\) −16.5000 + 28.5788i −0.0723684 + 0.125346i
\(229\) −266.000 −1.16157 −0.580786 0.814056i \(-0.697255\pi\)
−0.580786 + 0.814056i \(0.697255\pi\)
\(230\) −144.000 83.1384i −0.626087 0.361471i
\(231\) 0 0
\(232\) −195.000 337.750i −0.840517 1.45582i
\(233\) 175.500 101.325i 0.753219 0.434871i −0.0736369 0.997285i \(-0.523461\pi\)
0.826856 + 0.562414i \(0.190127\pi\)
\(234\) −54.0000 + 31.1769i −0.230769 + 0.133235i
\(235\) 84.0000 145.492i 0.357447 0.619116i
\(236\) −43.5000 25.1147i −0.184322 0.106418i
\(237\) 57.0000 98.7269i 0.240506 0.416569i
\(238\) 0 0
\(239\) −348.000 200.918i −1.45607 0.840661i −0.457252 0.889337i \(-0.651166\pi\)
−0.998815 + 0.0486764i \(0.984500\pi\)
\(240\) −99.0000 57.1577i −0.412500 0.238157i
\(241\) −119.000 −0.493776 −0.246888 0.969044i \(-0.579408\pi\)
−0.246888 + 0.969044i \(0.579408\pi\)
\(242\) 177.000 + 102.191i 0.731405 + 0.422277i
\(243\) −243.000 −1.00000
\(244\) −56.0000 −0.229508
\(245\) 0 0
\(246\) −31.5000 54.5596i −0.128049 0.221787i
\(247\) −44.0000 −0.178138
\(248\) 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 \(0.717085\pi\)
\(252\) 0 0
\(253\) 48.0000 0.189723
\(254\) −24.0000 13.8564i −0.0944882 0.0545528i
\(255\) 81.0000 140.296i 0.317647 0.550181i
\(256\) 89.5000 + 155.019i 0.349609 + 0.605541i
\(257\) 174.937i 0.680689i 0.940301 + 0.340345i \(0.110544\pi\)
−0.940301 + 0.340345i \(0.889456\pi\)
\(258\) 316.965i 1.22855i
\(259\) 0 0
\(260\) 13.8564i 0.0532939i
\(261\) 351.000 202.650i 1.34483 0.776437i
\(262\) −138.000 + 239.023i −0.526718 + 0.912302i
\(263\) 45.0333i 0.171229i 0.996328 + 0.0856147i \(0.0272854\pi\)
−0.996328 + 0.0856147i \(0.972715\pi\)
\(264\) 45.0000 0.170455
\(265\) 0 0
\(266\) 0 0
\(267\) 324.000 187.061i 1.21348 0.700605i
\(268\) 15.5000 26.8468i 0.0578358 0.100175i
\(269\) −162.000 93.5307i −0.602230 0.347698i 0.167688 0.985840i \(-0.446370\pi\)
−0.769919 + 0.638142i \(0.779703\pi\)
\(270\) 81.0000 140.296i 0.300000 0.519615i
\(271\) −134.000 232.095i −0.494465 0.856438i 0.505515 0.862818i \(-0.331303\pi\)
−0.999980 + 0.00637958i \(0.997969\pi\)
\(272\) 148.500 85.7365i 0.545956 0.315208i
\(273\) 0 0
\(274\) 163.500 283.190i 0.596715 1.03354i
\(275\) 22.5167i 0.0818788i
\(276\) −72.0000 + 41.5692i −0.260870 + 0.150613i
\(277\) 56.0000 0.202166 0.101083 0.994878i \(-0.467769\pi\)
0.101083 + 0.994878i \(0.467769\pi\)
\(278\) 7.50000 4.33013i 0.0269784 0.0155760i
\(279\) 144.000 + 249.415i 0.516129 + 0.893962i
\(280\) 0 0
\(281\) −42.0000 + 24.2487i −0.149466 + 0.0862943i −0.572868 0.819648i \(-0.694169\pi\)
0.423402 + 0.905942i \(0.360836\pi\)
\(282\) 126.000 + 218.238i 0.446809 + 0.773895i
\(283\) 187.000 + 323.894i 0.660777 + 1.14450i 0.980412 + 0.196959i \(0.0631066\pi\)
−0.319634 + 0.947541i \(0.603560\pi\)
\(284\) −27.0000 + 15.5885i −0.0950704 + 0.0548889i
\(285\) 99.0000 57.1577i 0.347368 0.200553i
\(286\) 6.00000 + 10.3923i 0.0209790 + 0.0363367i
\(287\) 0 0
\(288\) −121.500 + 70.1481i −0.421875 + 0.243570i
\(289\) −23.0000 39.8372i −0.0795848 0.137845i
\(290\) 270.200i 0.931724i
\(291\) 172.500 + 298.779i 0.592784 + 1.02673i
\(292\) −65.0000 −0.222603
\(293\) −219.000 126.440i −0.747440 0.431535i 0.0773280 0.997006i \(-0.475361\pi\)
−0.824768 + 0.565471i \(0.808694\pi\)
\(294\) 0 0
\(295\) 87.0000 + 150.688i 0.294915 + 0.510808i
\(296\) 255.000 147.224i 0.861486 0.497379i
\(297\) 46.7654i 0.157459i
\(298\) −132.000 + 228.631i −0.442953 + 0.767217i
\(299\) −96.0000 55.4256i −0.321070 0.185370i
\(300\) 19.5000 + 33.7750i 0.0650000 + 0.112583i
\(301\) 0 0
\(302\) 30.0000 + 17.3205i 0.0993377 + 0.0573527i
\(303\) 135.100i 0.445874i
\(304\) 121.000 0.398026
\(305\) 168.000 + 96.9948i 0.550820 + 0.318016i
\(306\) 121.500 + 210.444i 0.397059 + 0.687726i
\(307\) −533.000 −1.73616 −0.868078 0.496428i \(-0.834645\pi\)
−0.868078 + 0.496428i \(0.834645\pi\)
\(308\) 0 0
\(309\) −120.000 −0.388350
\(310\) −192.000 −0.619355
\(311\) −213.000 + 122.976i −0.684887 + 0.395420i −0.801694 0.597735i \(-0.796068\pi\)
0.116806 + 0.993155i \(0.462734\pi\)
\(312\) −90.0000 51.9615i −0.288462 0.166543i
\(313\) 77.5000 134.234i 0.247604 0.428862i −0.715257 0.698862i \(-0.753690\pi\)
0.962860 + 0.269999i \(0.0870235\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 0 0
\(316\) 38.0000 0.120253
\(317\) 42.0000 + 24.2487i 0.132492 + 0.0764944i 0.564781 0.825241i \(-0.308961\pi\)
−0.432289 + 0.901735i \(0.642294\pi\)
\(318\) 0 0
\(319\) −39.0000 67.5500i −0.122257 0.211755i
\(320\) 245.951i 0.768598i
\(321\) 364.500 210.444i 1.13551 0.655589i
\(322\) 0 0
\(323\) 171.473i 0.530876i
\(324\) −40.5000 70.1481i −0.125000 0.216506i
\(325\) −26.0000 + 45.0333i −0.0800000 + 0.138564i
\(326\) 183.597i 0.563182i
\(327\) −78.0000 + 135.100i −0.238532 + 0.413150i
\(328\) 52.5000 90.9327i 0.160061 0.277234i
\(329\) 0 0
\(330\) −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 \(0.167628\pi\)
\(332\) −42.0000 24.2487i −0.126506 0.0730383i
\(333\) 153.000 + 265.004i 0.459459 + 0.795807i
\(334\) −165.000 285.788i −0.494012 0.855654i
\(335\) −93.0000 + 53.6936i −0.277612 + 0.160279i
\(336\) 0 0
\(337\) −38.5000 + 66.6840i −0.114243 + 0.197875i −0.917477 0.397789i \(-0.869778\pi\)
0.803234 + 0.595664i \(0.203111\pi\)
\(338\) 265.004i 0.784035i
\(339\) 234.000 + 135.100i 0.690265 + 0.398525i
\(340\) 54.0000 0.158824
\(341\) 48.0000 27.7128i 0.140762 0.0812692i
\(342\) 171.473i 0.501383i
\(343\) 0 0
\(344\) 457.500 264.138i 1.32994 0.767842i
\(345\) 288.000 0.834783
\(346\) 201.000 + 348.142i 0.580925 + 1.00619i
\(347\) −97.5000 + 56.2917i −0.280980 + 0.162224i −0.633867 0.773442i \(-0.718533\pi\)
0.352887 + 0.935666i \(0.385200\pi\)
\(348\) 117.000 + 67.5500i 0.336207 + 0.194109i
\(349\) 208.000 + 360.267i 0.595989 + 1.03228i 0.993407 + 0.114645i \(0.0365730\pi\)
−0.397418 + 0.917638i \(0.630094\pi\)
\(350\) 0 0
\(351\) 54.0000 93.5307i 0.153846 0.266469i
\(352\) 13.5000 + 23.3827i 0.0383523 + 0.0664281i
\(353\) 1.73205i 0.00490666i 0.999997 + 0.00245333i \(0.000780920\pi\)
−0.999997 + 0.00245333i \(0.999219\pi\)
\(354\) −261.000 −0.737288
\(355\) 108.000 0.304225
\(356\) 108.000 + 62.3538i 0.303371 + 0.175151i
\(357\) 0 0
\(358\) −54.0000 93.5307i −0.150838 0.261259i
\(359\) 513.000 296.181i 1.42897 0.825016i 0.431930 0.901907i \(-0.357833\pi\)
0.997039 + 0.0768913i \(0.0244995\pi\)
\(360\) 270.000 0.750000
\(361\) 120.000 207.846i 0.332410 0.575751i
\(362\) 348.000 + 200.918i 0.961326 + 0.555022i
\(363\) −354.000 −0.975207
\(364\) 0 0
\(365\) 195.000 + 112.583i 0.534247 + 0.308447i
\(366\) −252.000 + 145.492i −0.688525 + 0.397520i
\(367\) 358.000 0.975477 0.487738 0.872990i \(-0.337822\pi\)
0.487738 + 0.872990i \(0.337822\pi\)
\(368\) 264.000 + 152.420i 0.717391 + 0.414186i
\(369\) 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
\(373\) −580.000 −1.55496 −0.777480 0.628908i \(-0.783502\pi\)
−0.777480 + 0.628908i \(0.783502\pi\)
\(374\) 40.5000 23.3827i 0.108289 0.0625206i
\(375\) 394.908i 1.05309i
\(376\) −210.000 + 363.731i −0.558511 + 0.967369i
\(377\) 180.133i 0.477807i
\(378\) 0 0
\(379\) 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
\(381\) 48.0000 0.125984
\(382\) −201.000 348.142i −0.526178 0.911367i
\(383\) 557.720i 1.45619i −0.685477 0.728094i \(-0.740406\pi\)
0.685477 0.728094i \(-0.259594\pi\)
\(384\) 157.500 + 90.9327i 0.410156 + 0.236804i
\(385\) 0 0
\(386\) 458.993i 1.18910i
\(387\) 274.500 + 475.448i 0.709302 + 1.22855i
\(388\) −57.5000 + 99.5929i −0.148196 + 0.256683i
\(389\) 516.151i 1.32687i −0.748235 0.663433i \(-0.769099\pi\)
0.748235 0.663433i \(-0.230901\pi\)
\(390\) 36.0000 + 62.3538i 0.0923077 + 0.159882i
\(391\) −216.000 + 374.123i −0.552430 + 0.956836i
\(392\) 0 0
\(393\) 478.046i 1.21640i
\(394\) −108.000 + 187.061i −0.274112 + 0.474775i
\(395\) −114.000 65.8179i −0.288608 0.166628i
\(396\) −13.5000 + 7.79423i −0.0340909 + 0.0196824i
\(397\) 181.000 + 313.501i 0.455919 + 0.789676i 0.998741 0.0501728i \(-0.0159772\pi\)
−0.542821 + 0.839848i \(0.682644\pi\)
\(398\) 435.000 251.147i 1.09296 0.631024i
\(399\) 0 0
\(400\) 71.5000 123.842i 0.178750 0.309604i
\(401\) 393.176i 0.980488i −0.871585 0.490244i \(-0.836908\pi\)
0.871585 0.490244i \(-0.163092\pi\)
\(402\) 161.081i 0.400698i
\(403\) −128.000 −0.317618
\(404\) −39.0000 + 22.5167i −0.0965347 + 0.0557343i
\(405\) 280.592i 0.692820i
\(406\) 0 0
\(407\) 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 0.968905 0.247431i \(-0.0795864\pi\)
−0.698734 + 0.715381i \(0.746253\pi\)
\(410\) −63.0000 + 36.3731i −0.153659 + 0.0887148i
\(411\) 566.381i 1.37806i
\(412\) −20.0000 34.6410i −0.0485437 0.0840801i
\(413\) 0 0
\(414\) −216.000 + 374.123i −0.521739 + 0.903679i
\(415\) 84.0000 + 145.492i 0.202410 + 0.350584i
\(416\) 62.3538i 0.149889i
\(417\) −7.50000 + 12.9904i −0.0179856 + 0.0311520i
\(418\) 33.0000 0.0789474
\(419\) −678.000 391.443i −1.61814 0.934233i −0.987401 0.158236i \(-0.949419\pi\)
−0.630737 0.775997i \(-0.717247\pi\)
\(420\) 0 0
\(421\) 341.000 + 590.629i 0.809976 + 1.40292i 0.912880 + 0.408229i \(0.133853\pi\)
−0.102903 + 0.994691i \(0.532813\pi\)
\(422\) 141.000 81.4064i 0.334123 0.192906i
\(423\) −378.000 218.238i −0.893617 0.515930i
\(424\) 0 0
\(425\) 175.500 + 101.325i 0.412941 + 0.238412i
\(426\) −81.0000 + 140.296i −0.190141 + 0.329334i
\(427\) 0 0
\(428\) 121.500 + 70.1481i 0.283879 + 0.163897i
\(429\) −18.0000 10.3923i −0.0419580 0.0242245i
\(430\) −366.000 −0.851163
\(431\) 243.000 + 140.296i 0.563805 + 0.325513i 0.754671 0.656103i \(-0.227796\pi\)
−0.190866 + 0.981616i \(0.561130\pi\)
\(432\) −148.500 + 257.210i −0.343750 + 0.595392i
\(433\) 295.000 0.681293 0.340647 0.940191i \(-0.389354\pi\)
0.340647 + 0.940191i \(0.389354\pi\)
\(434\) 0 0
\(435\) −234.000 405.300i −0.537931 0.931724i
\(436\) −52.0000 −0.119266
\(437\) −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 \(-0.457541\pi\)
0.791836 0.610734i \(-0.209126\pi\)
\(440\) 51.9615i 0.118094i
\(441\) 0 0
\(442\) −108.000 −0.244344
\(443\) −79.5000 45.8993i −0.179458 0.103610i 0.407580 0.913170i \(-0.366373\pi\)
−0.587038 + 0.809559i \(0.699706\pi\)
\(444\) −51.0000 + 88.3346i −0.114865 + 0.198952i
\(445\) −216.000 374.123i −0.485393 0.840726i
\(446\) 90.0666i 0.201943i
\(447\) 457.261i 1.02296i
\(448\) 0 0
\(449\) 639.127i 1.42344i −0.702461 0.711722i \(-0.747915\pi\)
0.702461 0.711722i \(-0.252085\pi\)
\(450\) 175.500 + 101.325i 0.390000 + 0.225167i
\(451\) 10.5000 18.1865i 0.0232816 0.0403249i
\(452\) 90.0666i 0.199262i
\(453\) −60.0000 −0.132450
\(454\) −163.500 + 283.190i −0.360132 + 0.623767i
\(455\) 0 0
\(456\) −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 \(0.189323\pi\)
\(458\) −399.000 230.363i −0.871179 0.502975i
\(459\) −364.500 210.444i −0.794118 0.458484i
\(460\) 48.0000 + 83.1384i 0.104348 + 0.180736i
\(461\) 690.000 398.372i 1.49675 0.864147i 0.496753 0.867892i \(-0.334525\pi\)
0.999993 + 0.00374501i \(0.00119208\pi\)
\(462\) 0 0
\(463\) −367.000 + 635.663i −0.792657 + 1.37292i 0.131660 + 0.991295i \(0.457969\pi\)
−0.924317 + 0.381627i \(0.875364\pi\)
\(464\) 495.367i 1.06760i
\(465\) 288.000 166.277i 0.619355 0.357585i
\(466\) 351.000 0.753219
\(467\) 175.500 101.325i 0.375803 0.216970i −0.300188 0.953880i \(-0.597049\pi\)
0.675991 + 0.736910i \(0.263716\pi\)
\(468\) 36.0000 0.0769231
\(469\) 0 0
\(470\) 252.000 145.492i 0.536170 0.309558i
\(471\) 60.0000 + 103.923i 0.127389 + 0.220643i
\(472\) −217.500 376.721i −0.460805 0.798138i
\(473\) 91.5000 52.8275i 0.193446 0.111686i
\(474\) 171.000 98.7269i 0.360759 0.208285i
\(475\) 71.5000 + 123.842i 0.150526 + 0.260719i
\(476\) 0 0
\(477\) 0 0
\(478\) −348.000 602.754i −0.728033 1.26099i
\(479\) 606.218i 1.26559i −0.774319 0.632795i \(-0.781908\pi\)
0.774319 0.632795i \(-0.218092\pi\)
\(480\) 81.0000 + 140.296i 0.168750 + 0.292284i
\(481\) −136.000 −0.282744
\(482\) −178.500 103.057i −0.370332 0.213811i
\(483\) 0 0
\(484\) −59.0000 102.191i −0.121901 0.211138i
\(485\) 345.000 199.186i 0.711340 0.410692i
\(486\) −364.500 210.444i −0.750000 0.433013i
\(487\) 53.0000 91.7987i 0.108830 0.188498i −0.806467 0.591279i \(-0.798623\pi\)
0.915296 + 0.402781i \(0.131956\pi\)
\(488\) −420.000 242.487i −0.860656 0.496900i
\(489\) −159.000 275.396i −0.325153 0.563182i
\(490\) 0 0
\(491\) −199.500 115.181i −0.406314 0.234585i 0.282891 0.959152i \(-0.408707\pi\)
−0.689205 + 0.724567i \(0.742040\pi\)
\(492\) 36.3731i 0.0739290i
\(493\) 702.000 1.42394
\(494\) −66.0000 38.1051i −0.133603 0.0771359i
\(495\) 54.0000 0.109091
\(496\) 352.000 0.709677
\(497\) 0 0
\(498\) −252.000 −0.506024
\(499\) −787.000 −1.57715 −0.788577 0.614936i \(-0.789182\pi\)
−0.788577 + 0.614936i \(0.789182\pi\)
\(500\) 114.000 65.8179i 0.228000 0.131636i
\(501\) 495.000 + 285.788i 0.988024 + 0.570436i
\(502\) −337.500 + 584.567i −0.672311 + 1.16448i
\(503\) 623.538i 1.23964i −0.784745 0.619819i \(-0.787206\pi\)
0.784745 0.619819i \(-0.212794\pi\)
\(504\) 0 0
\(505\) 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
\(509\) 214.774i 0.421953i −0.977491 0.210977i \(-0.932336\pi\)
0.977491 0.210977i \(-0.0676644\pi\)
\(510\) 243.000 140.296i 0.476471 0.275090i
\(511\) 0 0
\(512\) 552.524i 1.07915i
\(513\) −148.500 257.210i −0.289474 0.501383i
\(514\) −151.500 + 262.406i −0.294747 + 0.510517i
\(515\) 138.564i 0.269056i
\(516\) −91.5000 + 158.483i −0.177326 + 0.307137i
\(517\) −42.0000 + 72.7461i −0.0812379 + 0.140708i
\(518\) 0 0
\(519\) −603.000 348.142i −1.16185 0.670794i
\(520\) −60.0000 + 103.923i −0.115385 + 0.199852i
\(521\) −175.500 101.325i −0.336852 0.194482i 0.322027 0.946730i \(-0.395636\pi\)
−0.658879 + 0.752249i \(0.728969\pi\)
\(522\) 702.000 1.34483
\(523\) −125.000 216.506i −0.239006 0.413970i 0.721424 0.692494i \(-0.243488\pi\)
−0.960429 + 0.278524i \(0.910155\pi\)
\(524\) 138.000 79.6743i 0.263359 0.152050i
\(525\) 0 0
\(526\) −39.0000 + 67.5500i −0.0741445 + 0.128422i
\(527\) 498.831i 0.946548i
\(528\) 49.5000 + 28.5788i 0.0937500 + 0.0541266i
\(529\) −239.000 −0.451796
\(530\) 0 0
\(531\) 391.500 226.033i 0.737288 0.425674i
\(532\) 0 0
\(533\) −42.0000 + 24.2487i −0.0787992 + 0.0454948i
\(534\) 648.000 1.21348
\(535\) −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
\(539\) 0 0
\(540\) −81.0000 + 46.7654i −0.150000 + 0.0866025i
\(541\) −325.000 562.917i −0.600739 1.04051i −0.992709 0.120533i \(-0.961540\pi\)
0.391970 0.919978i \(-0.371794\pi\)
\(542\) 464.190i 0.856438i
\(543\) −696.000 −1.28177
\(544\) −243.000 −0.446691
\(545\) 156.000 + 90.0666i 0.286239 + 0.165260i
\(546\) 0 0
\(547\) −311.500 539.534i −0.569470 0.986351i −0.996618 0.0821692i \(-0.973815\pi\)
0.427149 0.904181i \(-0.359518\pi\)
\(548\) −163.500 + 94.3968i −0.298358 + 0.172257i
\(549\) 252.000 436.477i 0.459016 0.795040i
\(550\) 19.5000 33.7750i 0.0354545 0.0614091i
\(551\) 429.000 + 247.683i 0.778584 + 0.449516i
\(552\) −720.000 −1.30435
\(553\) 0 0
\(554\) 84.0000 + 48.4974i 0.151625 + 0.0875405i
\(555\) 306.000 176.669i 0.551351 0.318323i
\(556\) −5.00000 −0.00899281
\(557\) −459.000 265.004i −0.824057 0.475770i 0.0277562 0.999615i \(-0.491164\pi\)
−0.851814 + 0.523845i \(0.824497\pi\)
\(558\) 498.831i 0.893962i
\(559\) −244.000 −0.436494
\(560\) 0 0
\(561\) −40.5000 + 70.1481i −0.0721925 + 0.125041i
\(562\) −84.0000 −0.149466
\(563\) 97.5000 56.2917i 0.173179 0.0999852i −0.410905 0.911678i \(-0.634787\pi\)
0.584084 + 0.811693i \(0.301454\pi\)
\(564\) 145.492i 0.257965i
\(565\) 156.000 270.200i 0.276106 0.478230i
\(566\) 647.787i 1.14450i
\(567\) 0 0
\(568\) −270.000 −0.475352
\(569\) −565.500 326.492i −0.993849 0.573799i −0.0874263 0.996171i \(-0.527864\pi\)
−0.906423 + 0.422372i \(0.861198\pi\)
\(570\) 198.000 0.347368
\(571\) −272.500 471.984i −0.477233 0.826592i 0.522427 0.852684i \(-0.325027\pi\)
−0.999660 + 0.0260926i \(0.991694\pi\)
\(572\) 6.92820i 0.0121122i
\(573\) 603.000 + 348.142i 1.05236 + 0.607578i
\(574\) 0 0
\(575\) 360.267i 0.626551i
\(576\) −639.000 −1.10938
\(577\) −435.500 + 754.308i −0.754766 + 1.30729i 0.190725 + 0.981644i \(0.438916\pi\)
−0.945491 + 0.325650i \(0.894417\pi\)
\(578\) 79.6743i 0.137845i
\(579\) −397.500 688.490i −0.686528 1.18910i
\(580\) 78.0000 135.100i 0.134483 0.232931i
\(581\) 0 0
\(582\) 597.558i 1.02673i
\(583\) 0 0
\(584\) −487.500 281.458i −0.834760 0.481949i
\(585\) −108.000 62.3538i −0.184615 0.106588i
\(586\) −219.000 379.319i −0.373720 0.647302i
\(587\) 1.50000 0.866025i 0.00255537 0.00147534i −0.498722 0.866762i \(-0.666197\pi\)
0.501277 + 0.865287i \(0.332864\pi\)
\(588\) 0 0
\(589\) −176.000 + 304.841i −0.298812 + 0.517557i
\(590\) 301.377i 0.510808i
\(591\) 374.123i 0.633034i
\(592\) 374.000 0.631757
\(593\) −162.000 + 93.5307i −0.273187 + 0.157725i −0.630335 0.776323i \(-0.717083\pi\)
0.357148 + 0.934048i \(0.383749\pi\)
\(594\) −40.5000 + 70.1481i −0.0681818 + 0.118094i
\(595\) 0 0
\(596\) 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 −0.849160 0.528136i \(-0.822891\pi\)
0.0327992 + 0.999462i \(0.489558\pi\)
\(600\) 337.750i 0.562917i
\(601\) 230.500 + 399.238i 0.383527 + 0.664289i 0.991564 0.129620i \(-0.0413758\pi\)
−0.608036 + 0.793909i \(0.708042\pi\)
\(602\) 0 0
\(603\) 139.500 + 241.621i 0.231343 + 0.400698i
\(604\) −10.0000 17.3205i −0.0165563 0.0286763i
\(605\) 408.764i 0.675643i
\(606\) −117.000 + 202.650i −0.193069 + 0.334406i
\(607\) 112.000 0.184514 0.0922570 0.995735i \(-0.470592\pi\)
0.0922570 + 0.995735i \(0.470592\pi\)
\(608\) −148.500 85.7365i −0.244243 0.141014i
\(609\) 0 0
\(610\) 168.000 + 290.985i 0.275410 + 0.477024i
\(611\) 168.000 96.9948i 0.274959 0.158748i
\(612\) 140.296i 0.229242i
\(613\) −451.000 + 781.155i −0.735726 + 1.27431i 0.218678 + 0.975797i \(0.429826\pi\)
−0.954404 + 0.298518i \(0.903508\pi\)
\(614\) −799.500 461.592i −1.30212 0.751778i
\(615\) 63.0000 109.119i 0.102439 0.177430i
\(616\) 0 0
\(617\) −307.500 177.535i −0.498379 0.287739i 0.229665 0.973270i \(-0.426237\pi\)
−0.728044 + 0.685530i \(0.759570\pi\)
\(618\) −180.000 103.923i −0.291262 0.168160i
\(619\) 799.000 1.29079 0.645396 0.763848i \(-0.276692\pi\)
0.645396 + 0.763848i \(0.276692\pi\)
\(620\) 96.0000 + 55.4256i 0.154839 + 0.0893962i
\(621\) 748.246i 1.20490i
\(622\) −426.000 −0.684887
\(623\) 0 0
\(624\) −66.0000 114.315i −0.105769 0.183198i
\(625\) −131.000 −0.209600
\(626\) 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
\(630\) 0 0
\(631\) 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
\(633\) −141.000 + 244.219i −0.222749 + 0.385812i
\(634\) 42.0000 + 72.7461i 0.0662461 + 0.114742i
\(635\) 55.4256i 0.0872845i
\(636\) 0 0
\(637\) 0 0
\(638\) 135.100i 0.211755i
\(639\) 280.592i 0.439111i
\(640\) 105.000 181.865i 0.164062 0.284165i
\(641\) 375.855i 0.586357i −0.956058 0.293179i \(-0.905287\pi\)
0.956058 0.293179i \(-0.0947131\pi\)
\(642\) 729.000 1.13551
\(643\) −6.50000 + 11.2583i −0.0101089 + 0.0175091i −0.871036 0.491220i \(-0.836551\pi\)
0.860927 + 0.508729i \(0.169884\pi\)
\(644\) 0 0
\(645\) 549.000 316.965i 0.851163 0.491419i
\(646\) −148.500 + 257.210i −0.229876 + 0.398157i
\(647\) 405.000 + 233.827i 0.625966 + 0.361402i 0.779188 0.626790i \(-0.215632\pi\)
−0.153222 + 0.988192i \(0.548965\pi\)
\(648\) 701.481i 1.08253i
\(649\) −43.5000 75.3442i −0.0670262 0.116093i
\(650\) −78.0000 + 45.0333i −0.120000 + 0.0692820i
\(651\) 0 0
\(652\) 53.0000 91.7987i 0.0812883 0.140796i
\(653\) 377.587i 0.578234i −0.957294 0.289117i \(-0.906638\pi\)
0.957294 0.289117i \(-0.0933617\pi\)
\(654\) −234.000 + 135.100i −0.357798 + 0.206575i
\(655\) −552.000 −0.842748
\(656\) 115.500 66.6840i 0.176067 0.101652i
\(657\) 292.500 506.625i 0.445205 0.771119i
\(658\) 0 0
\(659\) −852.000 + 491.902i −1.29287 + 0.746438i −0.979162 0.203082i \(-0.934904\pi\)
−0.313706 + 0.949520i \(0.601571\pi\)
\(660\) 9.00000 + 15.5885i 0.0136364 + 0.0236189i
\(661\) −191.000 330.822i −0.288956 0.500487i 0.684605 0.728915i \(-0.259975\pi\)
−0.973561 + 0.228428i \(0.926642\pi\)
\(662\) −3.00000 + 1.73205i −0.00453172 + 0.00261639i
\(663\) 162.000 93.5307i 0.244344 0.141072i
\(664\) −210.000 363.731i −0.316265 0.547787i
\(665\) 0 0
\(666\) 530.008i 0.795807i
\(667\) 624.000 + 1080.80i 0.935532 + 1.62039i
\(668\) 190.526i 0.285218i
\(669\) 78.0000 + 135.100i 0.116592 + 0.201943i
\(670\) −186.000 −0.277612
\(671\) −84.0000 48.4974i −0.125186 0.0722763i
\(672\) 0 0
\(673\) −289.000 500.563i −0.429421 0.743778i 0.567401 0.823441i \(-0.307949\pi\)
−0.996822 + 0.0796633i \(0.974615\pi\)
\(674\) −115.500 + 66.6840i −0.171365 + 0.0989376i
\(675\) −351.000 −0.520000
\(676\) 76.5000 132.502i 0.113166 0.196009i
\(677\) 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
\(679\) 0 0
\(680\) 405.000 + 233.827i 0.595588 + 0.343863i
\(681\) 566.381i 0.831690i
\(682\) 96.0000 0.140762
\(683\) 904.500 + 522.213i 1.32430 + 0.764588i 0.984412 0.175877i \(-0.0562760\pi\)
0.339892 + 0.940464i \(0.389609\pi\)
\(684\) 49.5000 85.7365i 0.0723684 0.125346i
\(685\) 654.000 0.954745
\(686\) 0 0
\(687\) 798.000 1.16157
\(688\) 671.000 0.975291
\(689\) 0 0
\(690\) 432.000 + 249.415i 0.626087 + 0.361471i
\(691\) 91.0000 157.617i 0.131693 0.228099i −0.792636 0.609695i \(-0.791292\pi\)
0.924329 + 0.381596i \(0.124625\pi\)
\(692\) 232.095i 0.335397i
\(693\) 0 0
\(694\) −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
\(698\) 720.533i 1.03228i
\(699\) −526.500 + 303.975i −0.753219 + 0.434871i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 162.000 93.5307i 0.230769 0.133235i
\(703\) −187.000 + 323.894i −0.266003 + 0.460730i
\(704\) 122.976i 0.174681i
\(705\) −252.000 + 436.477i −0.357447 + 0.619116i
\(706\) −1.50000 + 2.59808i −0.00212465 + 0.00367999i
\(707\) 0 0
\(708\) 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 \(0.00232795\pi\)
\(710\) 162.000 + 93.5307i 0.228169 + 0.131733i
\(711\) −171.000 + 296.181i −0.240506 + 0.416569i
\(712\) 540.000 + 935.307i 0.758427 + 1.31363i
\(713\) −768.000 + 443.405i −1.07714 + 0.621886i
\(714\) 0 0
\(715\) −12.0000 + 20.7846i −0.0167832 + 0.0290694i
\(716\) 62.3538i 0.0870864i
\(717\) 1044.00 + 602.754i 1.45607 + 0.840661i
\(718\) 1026.00 1.42897
\(719\) 513.000 296.181i 0.713491 0.411934i −0.0988613 0.995101i \(-0.531520\pi\)
0.812352 + 0.583167i \(0.198187\pi\)
\(720\) 297.000 + 171.473i 0.412500 + 0.238157i
\(721\) 0 0
\(722\) 360.000 207.846i 0.498615 0.287875i
\(723\) 357.000 0.493776
\(724\) −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 \(-0.317625\pi\)
−0.998783 + 0.0493289i \(0.984292\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 195.000 + 337.750i 0.267123 + 0.462671i
\(731\) 950.896i 1.30082i
\(732\) 168.000 0.229508
\(733\) 670.000 0.914052 0.457026 0.889453i \(-0.348915\pi\)
0.457026 + 0.889453i \(0.348915\pi\)
\(734\) 537.000 + 310.037i 0.731608 + 0.422394i
\(735\) 0 0
\(736\) −216.000 374.123i −0.293478 0.508319i
\(737\) 46.5000 26.8468i 0.0630936 0.0364271i
\(738\) 94.5000 + 163.679i 0.128049 + 0.221787i
\(739\) −158.500 + 274.530i −0.214479 + 0.371489i −0.953111 0.302620i \(-0.902139\pi\)
0.738632 + 0.674109i \(0.235472\pi\)
\(740\) 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 0.0930168 0.995665i \(-0.470349\pi\)
−0.815762 + 0.578387i \(0.803682\pi\)
\(744\) −720.000 + 415.692i −0.967742 + 0.558726i
\(745\) −528.000 −0.708725
\(746\) −870.000 502.295i −1.16622 0.673317i
\(747\) 378.000 218.238i 0.506024 0.292153i
\(748\) −27.0000 −0.0360963
\(749\) 0 0
\(750\) 342.000 592.361i 0.456000 0.789815i
\(751\) 1310.00 1.74434 0.872170 0.489202i \(-0.162712\pi\)
0.872170 + 0.489202i \(0.162712\pi\)
\(752\) −462.000 + 266.736i −0.614362 + 0.354702i
\(753\) 1169.13i 1.55264i
\(754\) −156.000 + 270.200i −0.206897 + 0.358355i
\(755\) 69.2820i 0.0917643i
\(756\) 0 0
\(757\) 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
\(759\) −144.000 −0.189723
\(760\) 165.000 + 285.788i 0.217105 + 0.376037i
\(761\) 658.179i 0.864887i 0.901661 + 0.432444i \(0.142349\pi\)
−0.901661 + 0.432444i \(0.857651\pi\)
\(762\) 72.0000 + 41.5692i 0.0944882 + 0.0545528i
\(763\) 0 0
\(764\) 232.095i 0.303789i
\(765\) −243.000 + 420.888i −0.317647 + 0.550181i
\(766\) 483.000 836.581i 0.630548 1.09214i
\(767\) 200.918i 0.261953i
\(768\) −268.500 465.056i −0.349609 0.605541i
\(769\) 511.000 885.078i 0.664499 1.15095i −0.314921 0.949118i \(-0.601978\pi\)
0.979421 0.201829i \(-0.0646885\pi\)
\(770\) 0 0
\(771\) 524.811i 0.680689i
\(772\) 132.500 229.497i 0.171632 0.297276i
\(773\) 1026.00 + 592.361i 1.32730 + 0.766315i 0.984881 0.173234i \(-0.0554216\pi\)
0.342416 + 0.939549i \(0.388755\pi\)
\(774\) 950.896i 1.22855i
\(775\) 208.000 + 360.267i 0.268387 + 0.464860i
\(776\) −862.500 + 497.965i −1.11147 + 0.641707i
\(777\) 0 0
\(778\) 447.000 774.227i 0.574550 0.995150i
\(779\) 133.368i 0.171204i
\(780\) 41.5692i 0.0532939i
\(781\) −54.0000 −0.0691421
\(782\) −648.000 + 374.123i −0.828645 + 0.478418i
\(783\) −1053.00 + 607.950i −1.34483 + 0.776437i
\(784\) 0 0
\(785\) 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 0.821771 0.569819i \(-0.192987\pi\)
−0.904363 + 0.426765i \(0.859653\pi\)
\(788\) 108.000 62.3538i 0.137056 0.0791292i
\(789\) 135.100i 0.171229i
\(790\) −114.000 197.454i −0.144304 0.249942i
\(791\) 0 0
\(792\) −135.000 −0.170455
\(793\) 112.000 + 193.990i 0.141236 + 0.244628i
\(794\) 627.002i 0.789676i
\(795\) 0 0
\(796\) −290.000 −0.364322
\(797\) −273.000 157.617i −0.342535 0.197762i 0.318858 0.947803i \(-0.396701\pi\)
−0.661392 + 0.750040i \(0.730034\pi\)
\(798\) 0 0
\(799\) −378.000 654.715i −0.473091 0.819418i
\(800\) −175.500 + 101.325i −0.219375 + 0.126656i
\(801\) −972.000 + 561.184i −1.21348 + 0.700605i
\(802\) 340.500 589.763i 0.424564 0.735366i
\(803\) −97.5000 56.2917i −0.121420 0.0701017i
\(804\) −46.5000 + 80.5404i −0.0578358 + 0.100175i
\(805\) 0 0
\(806\) −192.000 110.851i −0.238213 0.137533i
\(807\) 486.000 + 280.592i 0.602230 + 0.347698i
\(808\) −390.000 −0.482673
\(809\) 121.500 + 70.1481i 0.150185 + 0.0867096i 0.573210 0.819409i \(-0.305698\pi\)
−0.423024 + 0.906118i \(0.639031\pi\)
\(810\) −243.000 + 420.888i −0.300000 + 0.519615i
\(811\) −299.000 −0.368681 −0.184340 0.982862i \(-0.559015\pi\)
−0.184340 + 0.982862i \(0.559015\pi\)
\(812\) 0 0
\(813\) 402.000 + 696.284i 0.494465 + 0.856438i
\(814\) 102.000 0.125307
\(815\) −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
\(819\) 0 0
\(820\) 42.0000 0.0512195
\(821\) −525.000 303.109i −0.639464 0.369195i 0.144944 0.989440i \(-0.453700\pi\)
−0.784408 + 0.620245i \(0.787033\pi\)
\(822\) −490.500 + 849.571i −0.596715 + 1.03354i
\(823\) 407.000 + 704.945i 0.494532 + 0.856555i 0.999980 0.00630221i \(-0.00200607\pi\)
−0.505448 + 0.862857i \(0.668673\pi\)
\(824\) 346.410i 0.420401i
\(825\) 67.5500i 0.0818788i
\(826\) 0 0
\(827\) 1434.14i 1.73415i −0.498182 0.867073i \(-0.665999\pi\)
0.498182 0.867073i \(-0.334001\pi\)
\(828\) 216.000 124.708i 0.260870 0.150613i
\(829\) −359.000 + 621.806i −0.433052 + 0.750068i −0.997134 0.0756506i \(-0.975897\pi\)
0.564083 + 0.825718i \(0.309230\pi\)
\(830\) 290.985i 0.350584i
\(831\) −168.000 −0.202166
\(832\) 142.000 245.951i 0.170673 0.295614i
\(833\) 0 0
\(834\) −22.5000 + 12.9904i −0.0269784 + 0.0155760i
\(835\) 330.000 571.577i 0.395210 0.684523i
\(836\) −16.5000 9.52628i −0.0197368 0.0113951i
\(837\) −432.000 748.246i −0.516129 0.893962i
\(838\) −678.000 1174.33i −0.809069 1.40135i
\(839\) 690.000 398.372i 0.822408 0.474817i −0.0288384 0.999584i \(-0.509181\pi\)
0.851246 + 0.524767i \(0.175847\pi\)
\(840\) 0 0
\(841\) 593.500 1027.97i 0.705707 1.22232i
\(842\) 1181.26i 1.40292i
\(843\) 126.000 72.7461i 0.149466 0.0862943i
\(844\) −94.0000 −0.111374
\(845\) −459.000 + 265.004i −0.543195 + 0.313614i
\(846\) −378.000 654.715i −0.446809 0.773895i
\(847\) 0 0
\(848\) 0 0
\(849\) −561.000 971.681i −0.660777 1.14450i
\(850\) 175.500 + 303.975i 0.206471 + 0.357618i
\(851\) −816.000 + 471.118i −0.958872 + 0.553605i
\(852\) 81.0000 46.7654i 0.0950704 0.0548889i
\(853\) 712.000 + 1233.22i 0.834701 + 1.44574i 0.894274 + 0.447521i \(0.147693\pi\)
−0.0595725 + 0.998224i \(0.518974\pi\)
\(854\) 0 0
\(855\) −297.000 + 171.473i −0.347368 + 0.200553i
\(856\) 607.500 + 1052.22i 0.709696 + 1.22923i
\(857\) 699.749i 0.816509i −0.912868 0.408255i \(-0.866138\pi\)
0.912868 0.408255i \(-0.133862\pi\)
\(858\) −18.0000 31.1769i −0.0209790 0.0363367i
\(859\) −311.000 −0.362049 −0.181024 0.983479i \(-0.557941\pi\)
−0.181024 + 0.983479i \(0.557941\pi\)
\(860\) 183.000 + 105.655i 0.212791 + 0.122855i
\(861\) 0 0
\(862\) 243.000 + 420.888i 0.281903 + 0.488270i
\(863\) −891.000 + 514.419i −1.03244 + 0.596082i −0.917684 0.397311i \(-0.869944\pi\)
−0.114761 + 0.993393i \(0.536610\pi\)
\(864\) 364.500 210.444i 0.421875 0.243570i
\(865\) −402.000 + 696.284i −0.464740 + 0.804953i
\(866\) 442.500 + 255.477i 0.510970 + 0.295009i
\(867\) 69.0000 + 119.512i 0.0795848 + 0.137845i
\(868\) 0 0
\(869\) 57.0000 + 32.9090i 0.0655926 + 0.0378699i
\(870\) 810.600i 0.931724i
\(871\) −124.000 −0.142365
\(872\) −390.000 225.167i −0.447248 0.258219i
\(873\) −517.500 896.336i −0.592784 1.02673i
\(874\) −528.000 −0.604119
\(875\) 0 0
\(876\) 195.000 0.222603
\(877\) 104.000 0.118586 0.0592930 0.998241i \(-0.481115\pi\)
0.0592930 + 0.998241i \(0.481115\pi\)
\(878\) 1218.00 703.213i 1.38724 0.800926i
\(879\) 657.000 + 379.319i 0.747440 + 0.431535i
\(880\) 33.0000 57.1577i 0.0375000 0.0649519i
\(881\) 62.3538i 0.0707762i −0.999374 0.0353881i \(-0.988733\pi\)
0.999374 0.0353881i \(-0.0112667\pi\)
\(882\) 0 0
\(883\) 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
\(887\) 1188.19i 1.33956i 0.742561 + 0.669778i \(0.233611\pi\)
−0.742561 + 0.669778i \(0.766389\pi\)
\(888\) −765.000 + 441.673i −0.861486 + 0.497379i
\(889\) 0 0
\(890\) 748.246i 0.840726i
\(891\) 140.296i 0.157459i
\(892\) −26.0000 + 45.0333i −0.0291480 + 0.0504858i
\(893\) 533.472i 0.597393i
\(894\) 396.000 685.892i 0.442953 0.767217i
\(895\) 108.000 187.061i 0.120670 0.209007i
\(896\) 0 0
\(897\) 288.000 + 166.277i 0.321070 + 0.185370i
\(898\) 553.500 958.690i 0.616370 1.06758i
\(899\) 1248.00 + 720.533i 1.38821 + 0.801483i
\(900\) −58.5000 101.325i −0.0650000 0.112583i
\(901\) 0 0
\(902\) 31.5000 18.1865i 0.0349224 0.0201625i
\(903\) 0 0
\(904\) −390.000 + 675.500i −0.431416 + 0.747234i
\(905\) 803.672i 0.888035i
\(906\) −90.0000 51.9615i −0.0993377 0.0573527i
\(907\) 695.000 0.766262 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(908\) 163.500 94.3968i 0.180066 0.103961i
\(909\) 405.300i 0.445874i
\(910\) 0 0
\(911\) −1500.00 + 866.025i −1.64654 + 0.950632i −0.668110 + 0.744062i \(0.732897\pi\)
−0.978432 + 0.206569i \(0.933770\pi\)
\(912\) −363.000 −0.398026
\(913\) −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
\(917\) 0 0
\(918\) −364.500 631.333i −0.397059 0.687726i
\(919\) −28.0000 48.4974i −0.0304679 0.0527720i 0.850389 0.526154i \(-0.176366\pi\)
−0.880857 + 0.473382i \(0.843033\pi\)
\(920\) 831.384i 0.903679i
\(921\) 1599.00 1.73616
\(922\) 1380.00 1.49675
\(923\) 108.000 + 62.3538i 0.117010 + 0.0675556i
\(924\) 0 0
\(925\) 221.000 + 382.783i 0.238919 + 0.413820i
\(926\) −1101.00 + 635.663i −1.18898 + 0.686461i
\(927\) 360.000 0.388350
\(928\) −351.000 + 607.950i −0.378233 + 0.655118i
\(929\) −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
\(931\) 0 0
\(932\) −175.500 101.325i −0.188305 0.108718i
\(933\) 639.000 368.927i 0.684887 0.395420i
\(934\) 351.000 0.375803
\(935\) 81.0000 + 46.7654i 0.0866310 + 0.0500164i
\(936\) 270.000 + 155.885i 0.288462 + 0.166543i
\(937\) −470.000 −0.501601 −0.250800 0.968039i \(-0.580694\pi\)
−0.250800 + 0.968039i \(0.580694\pi\)
\(938\) 0 0
\(939\) −232.500 + 402.702i −0.247604 + 0.428862i
\(940\) −168.000 −0.178723
\(941\) −348.000 + 200.918i −0.369819 + 0.213515i −0.673380 0.739297i \(-0.735158\pi\)
0.303560 + 0.952812i \(0.401825\pi\)
\(942\) 207.846i 0.220643i
\(943\) −168.000 + 290.985i −0.178155 + 0.308573i
\(944\) 552.524i 0.585301i
\(945\) 0 0
\(946\) 183.000 0.193446
\(947\) 1.50000 + 0.866025i 0.00158395 + 0.000914494i 0.500792 0.865568i \(-0.333042\pi\)
−0.499208 + 0.866482i \(0.666376\pi\)
\(948\) −114.000 −0.120253
\(949\) 130.000 + 225.167i 0.136986 + 0.237267i
\(950\) 247.683i 0.260719i
\(951\) −126.000 72.7461i −0.132492 0.0764944i
\(952\) 0 0
\(953\) 826.188i 0.866934i 0.901169 + 0.433467i \(0.142710\pi\)
−0.901169 + 0.433467i \(0.857290\pi\)
\(954\) 0 0
\(955\) 402.000 696.284i 0.420942 0.729094i
\(956\) 401.836i 0.420330i
\(957\) 117.000 + 202.650i 0.122257 + 0.211755i
\(958\) 525.000 909.327i 0.548017 0.949193i
\(959\) 0 0
\(960\) 737.854i 0.768598i
\(961\) −31.5000 + 54.5596i −0.0327784 + 0.0567738i
\(962\) −204.000 117.779i −0.212058 0.122432i
\(963\) −1093.50 + 631.333i −1.13551 + 0.655589i
\(964\) 59.5000 + 103.057i 0.0617220 + 0.106906i
\(965\) −795.000 + 458.993i −0.823834 + 0.475641i
\(966\) 0 0
\(967\) −601.000 + 1040.96i −0.621510 + 1.07649i 0.367695 + 0.929946i \(0.380147\pi\)
−0.989205 + 0.146540i \(0.953186\pi\)
\(968\) 1021.91i 1.05569i
\(969\) 514.419i 0.530876i
\(970\) 690.000 0.711340
\(971\) 162.000 93.5307i 0.166838 0.0963241i −0.414256 0.910160i \(-0.635958\pi\)
0.581094 + 0.813836i \(0.302625\pi\)
\(972\) 121.500 + 210.444i 0.125000 + 0.216506i
\(973\) 0 0
\(974\) 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 −0.303453 0.952847i \(-0.598139\pi\)
0.673463 + 0.739221i \(0.264806\pi\)
\(978\) 550.792i 0.563182i
\(979\) 108.000 + 187.061i 0.110317 + 0.191074i
\(980\) 0 0
\(981\) 234.000 405.300i 0.238532 0.413150i
\(982\) −199.500 345.544i −0.203157 0.351878i
\(983\) 1167.40i 1.18759i −0.804616 0.593796i \(-0.797629\pi\)
0.804616 0.593796i \(-0.202371\pi\)
\(984\) −157.500 + 272.798i −0.160061 + 0.277234i
\(985\) −432.000 −0.438579
\(986\) 1053.00 + 607.950i 1.06795 + 0.616582i
\(987\) 0 0
\(988\) 22.0000 + 38.1051i 0.0222672 + 0.0385679i
\(989\) −1464.00 + 845.241i −1.48028 + 0.854642i
\(990\) 81.0000 + 46.7654i 0.0818182 + 0.0472377i
\(991\) 710.000 1229.76i 0.716448 1.24092i −0.245950 0.969282i \(-0.579100\pi\)
0.962398 0.271642i \(-0.0875666\pi\)
\(992\) −432.000 249.415i −0.435484 0.251427i
\(993\) 3.00000 5.19615i 0.00302115 0.00523278i
\(994\) 0 0
\(995\) 870.000 + 502.295i 0.874372 + 0.504819i
\(996\) 126.000 + 72.7461i 0.126506 + 0.0730383i
\(997\) −524.000 −0.525577 −0.262788 0.964853i \(-0.584642\pi\)
−0.262788 + 0.964853i \(0.584642\pi\)
\(998\) −1180.50 681.562i −1.18287 0.682928i
\(999\) −459.000 795.011i −0.459459 0.795807i
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 441.3.n.a.410.1 2
7.2 even 3 441.3.j.b.275.1 2
7.3 odd 6 9.3.d.a.5.1 yes 2
7.4 even 3 441.3.r.a.50.1 2
7.5 odd 6 441.3.j.a.275.1 2
7.6 odd 2 441.3.n.b.410.1 2
9.2 odd 6 441.3.j.b.263.1 2
21.17 even 6 27.3.d.a.17.1 2
28.3 even 6 144.3.q.a.113.1 2
35.3 even 12 225.3.i.a.149.2 4
35.17 even 12 225.3.i.a.149.1 4
35.24 odd 6 225.3.j.a.176.1 2
56.3 even 6 576.3.q.a.257.1 2
56.45 odd 6 576.3.q.b.257.1 2
63.2 odd 6 inner 441.3.n.a.128.1 2
63.11 odd 6 441.3.r.a.344.1 2
63.20 even 6 441.3.j.a.263.1 2
63.31 odd 6 81.3.b.a.80.1 2
63.38 even 6 9.3.d.a.2.1 2
63.47 even 6 441.3.n.b.128.1 2
63.52 odd 6 27.3.d.a.8.1 2
63.59 even 6 81.3.b.a.80.2 2
84.59 odd 6 432.3.q.a.17.1 2
105.17 odd 12 675.3.i.a.449.2 4
105.38 odd 12 675.3.i.a.449.1 4
105.59 even 6 675.3.j.a.476.1 2
168.59 odd 6 1728.3.q.b.449.1 2
168.101 even 6 1728.3.q.a.449.1 2
252.31 even 6 1296.3.e.a.161.1 2
252.59 odd 6 1296.3.e.a.161.2 2
252.115 even 6 432.3.q.a.305.1 2
252.227 odd 6 144.3.q.a.65.1 2
315.38 odd 12 225.3.i.a.74.1 4
315.52 even 12 675.3.i.a.224.1 4
315.164 even 6 225.3.j.a.101.1 2
315.178 even 12 675.3.i.a.224.2 4
315.227 odd 12 225.3.i.a.74.2 4
315.304 odd 6 675.3.j.a.251.1 2
504.101 even 6 576.3.q.b.65.1 2
504.115 even 6 1728.3.q.b.1601.1 2
504.227 odd 6 576.3.q.a.65.1 2
504.493 odd 6 1728.3.q.a.1601.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.3.d.a.2.1 2 63.38 even 6
9.3.d.a.5.1 yes 2 7.3 odd 6
27.3.d.a.8.1 2 63.52 odd 6
27.3.d.a.17.1 2 21.17 even 6
81.3.b.a.80.1 2 63.31 odd 6
81.3.b.a.80.2 2 63.59 even 6
144.3.q.a.65.1 2 252.227 odd 6
144.3.q.a.113.1 2 28.3 even 6
225.3.i.a.74.1 4 315.38 odd 12
225.3.i.a.74.2 4 315.227 odd 12
225.3.i.a.149.1 4 35.17 even 12
225.3.i.a.149.2 4 35.3 even 12
225.3.j.a.101.1 2 315.164 even 6
225.3.j.a.176.1 2 35.24 odd 6
432.3.q.a.17.1 2 84.59 odd 6
432.3.q.a.305.1 2 252.115 even 6
441.3.j.a.263.1 2 63.20 even 6
441.3.j.a.275.1 2 7.5 odd 6
441.3.j.b.263.1 2 9.2 odd 6
441.3.j.b.275.1 2 7.2 even 3
441.3.n.a.128.1 2 63.2 odd 6 inner
441.3.n.a.410.1 2 1.1 even 1 trivial
441.3.n.b.128.1 2 63.47 even 6
441.3.n.b.410.1 2 7.6 odd 2
441.3.r.a.50.1 2 7.4 even 3
441.3.r.a.344.1 2 63.11 odd 6
576.3.q.a.65.1 2 504.227 odd 6
576.3.q.a.257.1 2 56.3 even 6
576.3.q.b.65.1 2 504.101 even 6
576.3.q.b.257.1 2 56.45 odd 6
675.3.i.a.224.1 4 315.52 even 12
675.3.i.a.224.2 4 315.178 even 12
675.3.i.a.449.1 4 105.38 odd 12
675.3.i.a.449.2 4 105.17 odd 12
675.3.j.a.251.1 2 315.304 odd 6
675.3.j.a.476.1 2 105.59 even 6
1296.3.e.a.161.1 2 252.31 even 6
1296.3.e.a.161.2 2 252.59 odd 6
1728.3.q.a.449.1 2 168.101 even 6
1728.3.q.a.1601.1 2 504.493 odd 6
1728.3.q.b.449.1 2 168.59 odd 6
1728.3.q.b.1601.1 2 504.115 even 6