Properties

Label 950.2.l.g.251.1
Level $950$
Weight $2$
Character 950.251
Analytic conductor $7.586$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 24x^{10} + 264x^{8} - 1511x^{6} + 4812x^{4} - 7788x^{2} + 5329 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 251.1
Root \(-1.34865 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 950.251
Dual form 950.2.l.g.651.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{2} +(-0.397366 - 2.25357i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(1.38429 - 2.39766i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.10161 + 0.764925i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{2} +(-0.397366 - 2.25357i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(1.38429 - 2.39766i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.10161 + 0.764925i) q^{9} +(-1.21064 - 2.09689i) q^{11} +(1.14417 - 1.98176i) q^{12} +(0.300428 - 1.70381i) q^{13} +(2.12086 - 1.77961i) q^{14} +(0.173648 + 0.984808i) q^{16} +(3.79213 + 1.38022i) q^{17} -2.23649 q^{18} +(0.0664727 + 4.35839i) q^{19} +(-5.95337 - 2.16685i) q^{21} +(-0.420451 - 2.38450i) q^{22} +(-6.84561 - 5.74414i) q^{23} +(1.75297 - 1.47092i) q^{24} +(0.865049 - 1.49831i) q^{26} +(-0.873583 - 1.51309i) q^{27} +(2.60161 - 0.946910i) q^{28} +(4.18479 - 1.52314i) q^{29} +(0.953372 - 1.65129i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-4.24443 + 3.56150i) q^{33} +(3.09138 + 2.59397i) q^{34} +(-2.10161 - 0.764925i) q^{36} -2.89348 q^{37} +(-1.42819 + 4.11828i) q^{38} -3.95905 q^{39} +(-0.808735 - 4.58656i) q^{41} +(-4.85323 - 4.07235i) q^{42} +(2.28003 - 1.91317i) q^{43} +(0.420451 - 2.38450i) q^{44} +(-4.46815 - 7.73907i) q^{46} +(-9.33064 + 3.39608i) q^{47} +(2.15033 - 0.782658i) q^{48} +(-0.332517 - 0.575937i) q^{49} +(1.60357 - 9.09430i) q^{51} +(1.32533 - 1.11209i) q^{52} +(8.56514 + 7.18700i) q^{53} +(-0.303392 - 1.72062i) q^{54} +2.76858 q^{56} +(9.79554 - 1.88168i) q^{57} +4.45336 q^{58} +(-1.89474 - 0.689630i) q^{59} +(6.66844 + 5.59549i) q^{61} +(1.46065 - 1.22563i) q^{62} +(-1.07521 + 6.09783i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.20657 + 1.89504i) q^{66} +(-12.6795 + 4.61495i) q^{67} +(2.01775 + 3.49485i) q^{68} +(-10.2246 + 17.7096i) q^{69} +(10.2246 - 8.57949i) q^{71} +(-1.71325 - 1.43759i) q^{72} +(-0.991298 - 5.62193i) q^{73} +(-2.71898 - 0.989627i) q^{74} +(-2.75060 + 3.38145i) q^{76} -6.70352 q^{77} +(-3.72029 - 1.35407i) q^{78} +(1.16772 + 6.62249i) q^{79} +(-8.20248 + 6.88270i) q^{81} +(0.808735 - 4.58656i) q^{82} +(8.47670 - 14.6821i) q^{83} +(-3.16772 - 5.48666i) q^{84} +(2.79687 - 1.01798i) q^{86} +(-5.09540 - 8.82549i) q^{87} +(1.21064 - 2.09689i) q^{88} +(0.964193 - 5.46821i) q^{89} +(-3.66929 - 3.07890i) q^{91} +(-1.55177 - 8.80054i) q^{92} +(-4.10014 - 1.49233i) q^{93} -9.92946 q^{94} +2.28834 q^{96} +(7.22610 + 2.63009i) q^{97} +(-0.115482 - 0.654931i) q^{98} +(4.14827 + 3.48081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 + 0.342020i 0.664463 + 0.241845i
\(3\) −0.397366 2.25357i −0.229419 1.30110i −0.854054 0.520184i \(-0.825863\pi\)
0.624635 0.780917i \(-0.285248\pi\)
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) 0 0
\(6\) 0.397366 2.25357i 0.162224 0.920017i
\(7\) 1.38429 2.39766i 0.523212 0.906230i −0.476423 0.879216i \(-0.658067\pi\)
0.999635 0.0270141i \(-0.00859990\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) −2.10161 + 0.764925i −0.700538 + 0.254975i
\(10\) 0 0
\(11\) −1.21064 2.09689i −0.365022 0.632237i 0.623758 0.781618i \(-0.285605\pi\)
−0.988780 + 0.149381i \(0.952272\pi\)
\(12\) 1.14417 1.98176i 0.330293 0.572085i
\(13\) 0.300428 1.70381i 0.0833238 0.472553i −0.914382 0.404853i \(-0.867323\pi\)
0.997706 0.0677001i \(-0.0215661\pi\)
\(14\) 2.12086 1.77961i 0.566822 0.475620i
\(15\) 0 0
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) 3.79213 + 1.38022i 0.919728 + 0.334753i 0.758130 0.652103i \(-0.226113\pi\)
0.161597 + 0.986857i \(0.448335\pi\)
\(18\) −2.23649 −0.527146
\(19\) 0.0664727 + 4.35839i 0.0152499 + 0.999884i
\(20\) 0 0
\(21\) −5.95337 2.16685i −1.29913 0.472846i
\(22\) −0.420451 2.38450i −0.0896406 0.508377i
\(23\) −6.84561 5.74414i −1.42741 1.19774i −0.947225 0.320568i \(-0.896126\pi\)
−0.480182 0.877169i \(-0.659429\pi\)
\(24\) 1.75297 1.47092i 0.357823 0.300249i
\(25\) 0 0
\(26\) 0.865049 1.49831i 0.169650 0.293842i
\(27\) −0.873583 1.51309i −0.168121 0.291194i
\(28\) 2.60161 0.946910i 0.491659 0.178949i
\(29\) 4.18479 1.52314i 0.777096 0.282840i 0.0771351 0.997021i \(-0.475423\pi\)
0.699961 + 0.714181i \(0.253201\pi\)
\(30\) 0 0
\(31\) 0.953372 1.65129i 0.171231 0.296580i −0.767620 0.640906i \(-0.778559\pi\)
0.938850 + 0.344325i \(0.111892\pi\)
\(32\) −0.173648 + 0.984808i −0.0306970 + 0.174091i
\(33\) −4.24443 + 3.56150i −0.738861 + 0.619978i
\(34\) 3.09138 + 2.59397i 0.530167 + 0.444863i
\(35\) 0 0
\(36\) −2.10161 0.764925i −0.350269 0.127487i
\(37\) −2.89348 −0.475685 −0.237842 0.971304i \(-0.576440\pi\)
−0.237842 + 0.971304i \(0.576440\pi\)
\(38\) −1.42819 + 4.11828i −0.231684 + 0.668074i
\(39\) −3.95905 −0.633955
\(40\) 0 0
\(41\) −0.808735 4.58656i −0.126303 0.716301i −0.980525 0.196393i \(-0.937077\pi\)
0.854222 0.519908i \(-0.174034\pi\)
\(42\) −4.85323 4.07235i −0.748870 0.628377i
\(43\) 2.28003 1.91317i 0.347702 0.291756i −0.452165 0.891934i \(-0.649348\pi\)
0.799866 + 0.600178i \(0.204904\pi\)
\(44\) 0.420451 2.38450i 0.0633854 0.359477i
\(45\) 0 0
\(46\) −4.46815 7.73907i −0.658793 1.14106i
\(47\) −9.33064 + 3.39608i −1.36101 + 0.495369i −0.916368 0.400338i \(-0.868893\pi\)
−0.444646 + 0.895706i \(0.646671\pi\)
\(48\) 2.15033 0.782658i 0.310374 0.112967i
\(49\) −0.332517 0.575937i −0.0475025 0.0822767i
\(50\) 0 0
\(51\) 1.60357 9.09430i 0.224545 1.27346i
\(52\) 1.32533 1.11209i 0.183790 0.154218i
\(53\) 8.56514 + 7.18700i 1.17651 + 0.987211i 0.999996 + 0.00291297i \(0.000927229\pi\)
0.176516 + 0.984298i \(0.443517\pi\)
\(54\) −0.303392 1.72062i −0.0412865 0.234147i
\(55\) 0 0
\(56\) 2.76858 0.369967
\(57\) 9.79554 1.88168i 1.29745 0.249234i
\(58\) 4.45336 0.584755
\(59\) −1.89474 0.689630i −0.246674 0.0897821i 0.215724 0.976454i \(-0.430789\pi\)
−0.462399 + 0.886672i \(0.653011\pi\)
\(60\) 0 0
\(61\) 6.66844 + 5.59549i 0.853806 + 0.716429i 0.960624 0.277850i \(-0.0896218\pi\)
−0.106818 + 0.994279i \(0.534066\pi\)
\(62\) 1.46065 1.22563i 0.185503 0.155655i
\(63\) −1.07521 + 6.09783i −0.135464 + 0.768255i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −5.20657 + 1.89504i −0.640884 + 0.233263i
\(67\) −12.6795 + 4.61495i −1.54904 + 0.563805i −0.968193 0.250205i \(-0.919502\pi\)
−0.580850 + 0.814011i \(0.697280\pi\)
\(68\) 2.01775 + 3.49485i 0.244688 + 0.423813i
\(69\) −10.2246 + 17.7096i −1.23090 + 2.13199i
\(70\) 0 0
\(71\) 10.2246 8.57949i 1.21344 1.01820i 0.214300 0.976768i \(-0.431253\pi\)
0.999141 0.0414306i \(-0.0131916\pi\)
\(72\) −1.71325 1.43759i −0.201909 0.169421i
\(73\) −0.991298 5.62193i −0.116023 0.657997i −0.986239 0.165327i \(-0.947132\pi\)
0.870216 0.492670i \(-0.163979\pi\)
\(74\) −2.71898 0.989627i −0.316075 0.115042i
\(75\) 0 0
\(76\) −2.75060 + 3.38145i −0.315515 + 0.387879i
\(77\) −6.70352 −0.763937
\(78\) −3.72029 1.35407i −0.421240 0.153319i
\(79\) 1.16772 + 6.62249i 0.131379 + 0.745088i 0.977313 + 0.211800i \(0.0679326\pi\)
−0.845934 + 0.533288i \(0.820956\pi\)
\(80\) 0 0
\(81\) −8.20248 + 6.88270i −0.911387 + 0.764744i
\(82\) 0.808735 4.58656i 0.0893098 0.506501i
\(83\) 8.47670 14.6821i 0.930439 1.61157i 0.147866 0.989007i \(-0.452760\pi\)
0.782573 0.622559i \(-0.213907\pi\)
\(84\) −3.16772 5.48666i −0.345627 0.598643i
\(85\) 0 0
\(86\) 2.79687 1.01798i 0.301595 0.109771i
\(87\) −5.09540 8.82549i −0.546284 0.946192i
\(88\) 1.21064 2.09689i 0.129055 0.223530i
\(89\) 0.964193 5.46821i 0.102204 0.579629i −0.890096 0.455773i \(-0.849363\pi\)
0.992300 0.123856i \(-0.0395260\pi\)
\(90\) 0 0
\(91\) −3.66929 3.07890i −0.384646 0.322756i
\(92\) −1.55177 8.80054i −0.161783 0.917520i
\(93\) −4.10014 1.49233i −0.425165 0.154747i
\(94\) −9.92946 −1.02415
\(95\) 0 0
\(96\) 2.28834 0.233553
\(97\) 7.22610 + 2.63009i 0.733699 + 0.267045i 0.681730 0.731604i \(-0.261228\pi\)
0.0519694 + 0.998649i \(0.483450\pi\)
\(98\) −0.115482 0.654931i −0.0116654 0.0661580i
\(99\) 4.14827 + 3.48081i 0.416917 + 0.349835i
\(100\) 0 0
\(101\) −1.82471 + 10.3484i −0.181565 + 1.02971i 0.748724 + 0.662882i \(0.230667\pi\)
−0.930289 + 0.366826i \(0.880444\pi\)
\(102\) 4.61730 7.99740i 0.457181 0.791860i
\(103\) 5.15539 + 8.92940i 0.507976 + 0.879840i 0.999957 + 0.00923425i \(0.00293940\pi\)
−0.491982 + 0.870606i \(0.663727\pi\)
\(104\) 1.62576 0.591728i 0.159419 0.0580237i
\(105\) 0 0
\(106\) 5.59050 + 9.68302i 0.542997 + 0.940498i
\(107\) 3.51686 6.09138i 0.339987 0.588876i −0.644442 0.764653i \(-0.722910\pi\)
0.984430 + 0.175777i \(0.0562438\pi\)
\(108\) 0.303392 1.72062i 0.0291939 0.165567i
\(109\) 4.78492 4.01503i 0.458312 0.384570i −0.384197 0.923251i \(-0.625522\pi\)
0.842510 + 0.538681i \(0.181077\pi\)
\(110\) 0 0
\(111\) 1.14977 + 6.52066i 0.109131 + 0.618914i
\(112\) 2.60161 + 0.946910i 0.245829 + 0.0894746i
\(113\) 7.50521 0.706031 0.353015 0.935618i \(-0.385156\pi\)
0.353015 + 0.935618i \(0.385156\pi\)
\(114\) 9.84837 + 1.58207i 0.922384 + 0.148175i
\(115\) 0 0
\(116\) 4.18479 + 1.52314i 0.388548 + 0.141420i
\(117\) 0.671905 + 3.81056i 0.0621177 + 0.352287i
\(118\) −1.54461 1.29608i −0.142193 0.119314i
\(119\) 8.55872 7.18162i 0.784577 0.658338i
\(120\) 0 0
\(121\) 2.56869 4.44911i 0.233518 0.404464i
\(122\) 4.35252 + 7.53878i 0.394058 + 0.682529i
\(123\) −10.0148 + 3.64509i −0.903003 + 0.328666i
\(124\) 1.79175 0.652145i 0.160904 0.0585644i
\(125\) 0 0
\(126\) −3.09595 + 5.36235i −0.275809 + 0.477716i
\(127\) −2.25870 + 12.8097i −0.200427 + 1.13668i 0.704049 + 0.710152i \(0.251374\pi\)
−0.904476 + 0.426526i \(0.859737\pi\)
\(128\) −0.766044 + 0.642788i −0.0677094 + 0.0568149i
\(129\) −5.21748 4.37799i −0.459374 0.385460i
\(130\) 0 0
\(131\) −4.41978 1.60867i −0.386158 0.140550i 0.141643 0.989918i \(-0.454761\pi\)
−0.527802 + 0.849368i \(0.676984\pi\)
\(132\) −5.54072 −0.482257
\(133\) 10.5420 + 5.87390i 0.914104 + 0.509332i
\(134\) −13.4932 −1.16564
\(135\) 0 0
\(136\) 0.700758 + 3.97420i 0.0600895 + 0.340785i
\(137\) 16.8787 + 14.1629i 1.44204 + 1.21002i 0.938139 + 0.346258i \(0.112548\pi\)
0.503903 + 0.863760i \(0.331897\pi\)
\(138\) −15.6651 + 13.1445i −1.33350 + 1.11894i
\(139\) −2.26902 + 12.8682i −0.192456 + 1.09147i 0.723540 + 0.690282i \(0.242514\pi\)
−0.915996 + 0.401188i \(0.868597\pi\)
\(140\) 0 0
\(141\) 11.3610 + 19.6778i 0.956767 + 1.65717i
\(142\) 12.5424 4.56505i 1.05253 0.383091i
\(143\) −3.93643 + 1.43274i −0.329180 + 0.119812i
\(144\) −1.11825 1.93686i −0.0931871 0.161405i
\(145\) 0 0
\(146\) 0.991298 5.62193i 0.0820404 0.465274i
\(147\) −1.16578 + 0.978209i −0.0961523 + 0.0806813i
\(148\) −2.21653 1.85989i −0.182198 0.152882i
\(149\) 0.359724 + 2.04010i 0.0294697 + 0.167131i 0.995991 0.0894563i \(-0.0285129\pi\)
−0.966521 + 0.256587i \(0.917402\pi\)
\(150\) 0 0
\(151\) −3.55532 −0.289328 −0.144664 0.989481i \(-0.546210\pi\)
−0.144664 + 0.989481i \(0.546210\pi\)
\(152\) −3.74124 + 2.23676i −0.303455 + 0.181425i
\(153\) −9.02537 −0.729658
\(154\) −6.29925 2.29274i −0.507608 0.184754i
\(155\) 0 0
\(156\) −3.03281 2.54483i −0.242819 0.203749i
\(157\) −7.05585 + 5.92056i −0.563118 + 0.472512i −0.879354 0.476168i \(-0.842025\pi\)
0.316236 + 0.948681i \(0.397581\pi\)
\(158\) −1.16772 + 6.62249i −0.0928991 + 0.526857i
\(159\) 12.7929 22.1580i 1.01455 1.75725i
\(160\) 0 0
\(161\) −23.2488 + 8.46188i −1.83226 + 0.666889i
\(162\) −10.0618 + 3.66221i −0.790532 + 0.287730i
\(163\) 10.1545 + 17.5880i 0.795359 + 1.37760i 0.922611 + 0.385731i \(0.126051\pi\)
−0.127253 + 0.991870i \(0.540616\pi\)
\(164\) 2.32866 4.03336i 0.181838 0.314952i
\(165\) 0 0
\(166\) 12.9871 10.8974i 1.00799 0.845805i
\(167\) 8.34647 + 7.00352i 0.645869 + 0.541949i 0.905814 0.423675i \(-0.139260\pi\)
−0.259945 + 0.965623i \(0.583704\pi\)
\(168\) −1.10014 6.23920i −0.0848775 0.481364i
\(169\) 9.40328 + 3.42251i 0.723329 + 0.263270i
\(170\) 0 0
\(171\) −3.47354 9.10881i −0.265628 0.696568i
\(172\) 2.97637 0.226946
\(173\) −15.7089 5.71759i −1.19433 0.434700i −0.333087 0.942896i \(-0.608090\pi\)
−0.861242 + 0.508196i \(0.830313\pi\)
\(174\) −1.76961 10.0360i −0.134154 0.760826i
\(175\) 0 0
\(176\) 1.85481 1.55637i 0.139812 0.117316i
\(177\) −0.801225 + 4.54397i −0.0602238 + 0.341546i
\(178\) 2.77628 4.80866i 0.208091 0.360424i
\(179\) 12.7705 + 22.1191i 0.954510 + 1.65326i 0.735486 + 0.677540i \(0.236954\pi\)
0.219024 + 0.975719i \(0.429713\pi\)
\(180\) 0 0
\(181\) −1.96483 + 0.715139i −0.146044 + 0.0531558i −0.414008 0.910273i \(-0.635872\pi\)
0.267964 + 0.963429i \(0.413649\pi\)
\(182\) −2.39496 4.14819i −0.177526 0.307484i
\(183\) 9.96003 17.2513i 0.736266 1.27525i
\(184\) 1.55177 8.80054i 0.114398 0.648784i
\(185\) 0 0
\(186\) −3.34246 2.80466i −0.245081 0.205648i
\(187\) −1.69673 9.62266i −0.124077 0.703678i
\(188\) −9.33064 3.39608i −0.680507 0.247684i
\(189\) −4.83717 −0.351852
\(190\) 0 0
\(191\) 12.9071 0.933924 0.466962 0.884278i \(-0.345349\pi\)
0.466962 + 0.884278i \(0.345349\pi\)
\(192\) 2.15033 + 0.782658i 0.155187 + 0.0564835i
\(193\) 3.73231 + 21.1670i 0.268657 + 1.52363i 0.758415 + 0.651772i \(0.225974\pi\)
−0.489757 + 0.871859i \(0.662915\pi\)
\(194\) 5.89077 + 4.94294i 0.422933 + 0.354883i
\(195\) 0 0
\(196\) 0.115482 0.654931i 0.00824871 0.0467808i
\(197\) −5.67287 + 9.82570i −0.404175 + 0.700052i −0.994225 0.107315i \(-0.965775\pi\)
0.590050 + 0.807367i \(0.299108\pi\)
\(198\) 2.70759 + 4.68968i 0.192420 + 0.333281i
\(199\) 12.7763 4.65019i 0.905688 0.329643i 0.153158 0.988202i \(-0.451056\pi\)
0.752530 + 0.658558i \(0.228833\pi\)
\(200\) 0 0
\(201\) 15.4385 + 26.7403i 1.08895 + 1.88611i
\(202\) −5.25404 + 9.10027i −0.369673 + 0.640292i
\(203\) 2.14099 12.1422i 0.150268 0.852214i
\(204\) 7.07411 5.93589i 0.495287 0.415595i
\(205\) 0 0
\(206\) 1.79045 + 10.1541i 0.124746 + 0.707472i
\(207\) 18.7807 + 6.83560i 1.30535 + 0.475107i
\(208\) 1.73010 0.119961
\(209\) 9.05861 5.41584i 0.626597 0.374621i
\(210\) 0 0
\(211\) −4.18459 1.52307i −0.288079 0.104852i 0.193939 0.981014i \(-0.437874\pi\)
−0.482018 + 0.876161i \(0.660096\pi\)
\(212\) 1.94156 + 11.0111i 0.133347 + 0.756247i
\(213\) −23.3974 19.6328i −1.60317 1.34522i
\(214\) 5.38814 4.52119i 0.368326 0.309062i
\(215\) 0 0
\(216\) 0.873583 1.51309i 0.0594398 0.102953i
\(217\) −2.63949 4.57173i −0.179180 0.310349i
\(218\) 5.86958 2.13635i 0.397538 0.144692i
\(219\) −12.2755 + 4.46792i −0.829503 + 0.301914i
\(220\) 0 0
\(221\) 3.49091 6.04643i 0.234824 0.406727i
\(222\) −1.14977 + 6.52066i −0.0771674 + 0.437638i
\(223\) 15.1924 12.7480i 1.01736 0.853667i 0.0280676 0.999606i \(-0.491065\pi\)
0.989294 + 0.145939i \(0.0466202\pi\)
\(224\) 2.12086 + 1.77961i 0.141706 + 0.118905i
\(225\) 0 0
\(226\) 7.05259 + 2.56693i 0.469131 + 0.170750i
\(227\) 12.8345 0.851857 0.425928 0.904757i \(-0.359948\pi\)
0.425928 + 0.904757i \(0.359948\pi\)
\(228\) 8.71334 + 4.85500i 0.577055 + 0.321531i
\(229\) −11.4892 −0.759230 −0.379615 0.925145i \(-0.623944\pi\)
−0.379615 + 0.925145i \(0.623944\pi\)
\(230\) 0 0
\(231\) 2.66375 + 15.1069i 0.175262 + 0.993959i
\(232\) 3.41147 + 2.86257i 0.223974 + 0.187937i
\(233\) 2.09048 1.75412i 0.136952 0.114916i −0.571738 0.820436i \(-0.693731\pi\)
0.708690 + 0.705520i \(0.249286\pi\)
\(234\) −0.671905 + 3.81056i −0.0439238 + 0.249104i
\(235\) 0 0
\(236\) −1.00817 1.74620i −0.0656264 0.113668i
\(237\) 14.4602 5.26310i 0.939294 0.341875i
\(238\) 10.4988 3.82126i 0.680538 0.247696i
\(239\) −12.5128 21.6728i −0.809386 1.40190i −0.913290 0.407310i \(-0.866467\pi\)
0.103904 0.994587i \(-0.466867\pi\)
\(240\) 0 0
\(241\) 4.37954 24.8376i 0.282111 1.59993i −0.433316 0.901242i \(-0.642656\pi\)
0.715426 0.698688i \(-0.246232\pi\)
\(242\) 3.93547 3.30225i 0.252981 0.212277i
\(243\) 14.7548 + 12.3808i 0.946523 + 0.794227i
\(244\) 1.51161 + 8.57278i 0.0967711 + 0.548816i
\(245\) 0 0
\(246\) −10.6575 −0.679499
\(247\) 7.44586 + 1.19613i 0.473769 + 0.0761077i
\(248\) 1.90674 0.121078
\(249\) −36.4555 13.2687i −2.31027 0.840870i
\(250\) 0 0
\(251\) −2.55784 2.14629i −0.161450 0.135472i 0.558484 0.829515i \(-0.311383\pi\)
−0.719933 + 0.694043i \(0.755828\pi\)
\(252\) −4.74327 + 3.98008i −0.298798 + 0.250721i
\(253\) −3.75728 + 21.3086i −0.236218 + 1.33966i
\(254\) −6.50366 + 11.2647i −0.408076 + 0.706808i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −8.91294 + 3.24404i −0.555974 + 0.202358i −0.604699 0.796454i \(-0.706706\pi\)
0.0487248 + 0.998812i \(0.484484\pi\)
\(258\) −3.40547 5.89845i −0.212015 0.367221i
\(259\) −4.00541 + 6.93758i −0.248884 + 0.431080i
\(260\) 0 0
\(261\) −7.62973 + 6.40210i −0.472268 + 0.396280i
\(262\) −3.60304 3.02331i −0.222597 0.186781i
\(263\) −4.91064 27.8496i −0.302803 1.71728i −0.633671 0.773603i \(-0.718453\pi\)
0.330868 0.943677i \(-0.392659\pi\)
\(264\) −5.20657 1.89504i −0.320442 0.116631i
\(265\) 0 0
\(266\) 7.89721 + 9.12522i 0.484209 + 0.559503i
\(267\) −12.7061 −0.777603
\(268\) −12.6795 4.61495i −0.774521 0.281903i
\(269\) −0.907359 5.14589i −0.0553227 0.313750i 0.944571 0.328306i \(-0.106478\pi\)
−0.999894 + 0.0145556i \(0.995367\pi\)
\(270\) 0 0
\(271\) 0.277215 0.232611i 0.0168396 0.0141301i −0.634329 0.773063i \(-0.718724\pi\)
0.651169 + 0.758933i \(0.274279\pi\)
\(272\) −0.700758 + 3.97420i −0.0424897 + 0.240971i
\(273\) −5.48047 + 9.49245i −0.331693 + 0.574509i
\(274\) 11.0168 + 19.0816i 0.665548 + 1.15276i
\(275\) 0 0
\(276\) −19.2160 + 6.99407i −1.15667 + 0.420993i
\(277\) −6.53530 11.3195i −0.392668 0.680121i 0.600132 0.799901i \(-0.295115\pi\)
−0.992801 + 0.119779i \(0.961781\pi\)
\(278\) −6.53338 + 11.3161i −0.391846 + 0.678697i
\(279\) −0.740508 + 4.19963i −0.0443331 + 0.251425i
\(280\) 0 0
\(281\) 7.77732 + 6.52595i 0.463956 + 0.389305i 0.844584 0.535423i \(-0.179848\pi\)
−0.380628 + 0.924728i \(0.624292\pi\)
\(282\) 3.94563 + 22.3768i 0.234959 + 1.33252i
\(283\) −9.64467 3.51037i −0.573316 0.208670i 0.0390595 0.999237i \(-0.487564\pi\)
−0.612376 + 0.790567i \(0.709786\pi\)
\(284\) 13.3473 0.792018
\(285\) 0 0
\(286\) −4.18906 −0.247704
\(287\) −12.1165 4.41006i −0.715217 0.260318i
\(288\) −0.388363 2.20251i −0.0228845 0.129784i
\(289\) −0.547493 0.459401i −0.0322054 0.0270236i
\(290\) 0 0
\(291\) 3.05568 17.3296i 0.179127 1.01588i
\(292\) 2.85433 4.94384i 0.167037 0.289316i
\(293\) −3.57090 6.18499i −0.208614 0.361331i 0.742664 0.669664i \(-0.233562\pi\)
−0.951278 + 0.308334i \(0.900229\pi\)
\(294\) −1.43005 + 0.520494i −0.0834020 + 0.0303558i
\(295\) 0 0
\(296\) −1.44674 2.50582i −0.0840900 0.145648i
\(297\) −2.11519 + 3.66362i −0.122736 + 0.212585i
\(298\) −0.359724 + 2.04010i −0.0208383 + 0.118180i
\(299\) −11.8436 + 9.93793i −0.684931 + 0.574725i
\(300\) 0 0
\(301\) −1.43092 8.11513i −0.0824766 0.467748i
\(302\) −3.34091 1.21599i −0.192248 0.0699725i
\(303\) 24.0460 1.38141
\(304\) −4.28064 + 0.822290i −0.245511 + 0.0471615i
\(305\) 0 0
\(306\) −8.48107 3.08686i −0.484831 0.176464i
\(307\) 1.87916 + 10.6573i 0.107250 + 0.608242i 0.990298 + 0.138960i \(0.0443761\pi\)
−0.883048 + 0.469282i \(0.844513\pi\)
\(308\) −5.13519 4.30894i −0.292605 0.245524i
\(309\) 18.0745 15.1663i 1.02822 0.862780i
\(310\) 0 0
\(311\) −13.1789 + 22.8265i −0.747307 + 1.29437i 0.201802 + 0.979426i \(0.435320\pi\)
−0.949109 + 0.314947i \(0.898013\pi\)
\(312\) −1.97952 3.42864i −0.112068 0.194108i
\(313\) −28.3558 + 10.3207i −1.60276 + 0.583358i −0.979990 0.199046i \(-0.936216\pi\)
−0.622772 + 0.782403i \(0.713994\pi\)
\(314\) −8.65528 + 3.15027i −0.488446 + 0.177780i
\(315\) 0 0
\(316\) −3.36233 + 5.82372i −0.189146 + 0.327610i
\(317\) 2.07593 11.7732i 0.116596 0.661248i −0.869352 0.494194i \(-0.835463\pi\)
0.985948 0.167054i \(-0.0534255\pi\)
\(318\) 19.5999 16.4463i 1.09911 0.922262i
\(319\) −8.26015 6.93109i −0.462479 0.388066i
\(320\) 0 0
\(321\) −15.1248 5.50499i −0.844186 0.307259i
\(322\) −24.7409 −1.37875
\(323\) −5.76348 + 16.6194i −0.320689 + 0.924726i
\(324\) −10.7076 −0.594866
\(325\) 0 0
\(326\) 3.52661 + 20.0004i 0.195321 + 1.10772i
\(327\) −10.9495 9.18774i −0.605510 0.508083i
\(328\) 3.56771 2.99367i 0.196994 0.165298i
\(329\) −4.77368 + 27.0729i −0.263181 + 1.49258i
\(330\) 0 0
\(331\) 14.4811 + 25.0820i 0.795954 + 1.37863i 0.922232 + 0.386638i \(0.126364\pi\)
−0.126277 + 0.991995i \(0.540303\pi\)
\(332\) 15.9310 5.79840i 0.874326 0.318229i
\(333\) 6.08097 2.21329i 0.333235 0.121288i
\(334\) 5.44777 + 9.43582i 0.298089 + 0.516305i
\(335\) 0 0
\(336\) 1.10014 6.23920i 0.0600175 0.340376i
\(337\) 3.41545 2.86591i 0.186052 0.156116i −0.545005 0.838433i \(-0.683472\pi\)
0.731056 + 0.682317i \(0.239028\pi\)
\(338\) 7.66562 + 6.43222i 0.416955 + 0.349867i
\(339\) −2.98231 16.9135i −0.161977 0.918617i
\(340\) 0 0
\(341\) −4.61677 −0.250012
\(342\) −0.148666 9.74750i −0.00803892 0.527085i
\(343\) 17.5389 0.947009
\(344\) 2.79687 + 1.01798i 0.150797 + 0.0548857i
\(345\) 0 0
\(346\) −12.8061 10.7456i −0.688458 0.577684i
\(347\) −19.7859 + 16.6023i −1.06216 + 0.891260i −0.994320 0.106436i \(-0.966056\pi\)
−0.0678428 + 0.997696i \(0.521612\pi\)
\(348\) 1.76961 10.0360i 0.0948613 0.537985i
\(349\) 10.9499 18.9659i 0.586137 1.01522i −0.408595 0.912716i \(-0.633981\pi\)
0.994733 0.102504i \(-0.0326854\pi\)
\(350\) 0 0
\(351\) −2.84047 + 1.03385i −0.151613 + 0.0551827i
\(352\) 2.27526 0.828128i 0.121272 0.0441394i
\(353\) −6.36930 11.0320i −0.339004 0.587172i 0.645242 0.763978i \(-0.276757\pi\)
−0.984246 + 0.176807i \(0.943423\pi\)
\(354\) −2.30704 + 3.99590i −0.122618 + 0.212380i
\(355\) 0 0
\(356\) 4.25351 3.56912i 0.225436 0.189163i
\(357\) −19.5852 16.4340i −1.03656 0.869778i
\(358\) 4.43514 + 25.1529i 0.234404 + 1.32937i
\(359\) −23.3776 8.50877i −1.23382 0.449075i −0.358919 0.933369i \(-0.616855\pi\)
−0.874906 + 0.484293i \(0.839077\pi\)
\(360\) 0 0
\(361\) −18.9912 + 0.579428i −0.999535 + 0.0304962i
\(362\) −2.09093 −0.109897
\(363\) −11.0471 4.02081i −0.579822 0.211038i
\(364\) −0.831760 4.71714i −0.0435961 0.247246i
\(365\) 0 0
\(366\) 15.2596 12.8044i 0.797635 0.669295i
\(367\) 1.92492 10.9168i 0.100480 0.569851i −0.892450 0.451147i \(-0.851015\pi\)
0.992930 0.118704i \(-0.0378739\pi\)
\(368\) 4.46815 7.73907i 0.232919 0.403427i
\(369\) 5.20803 + 9.02056i 0.271119 + 0.469592i
\(370\) 0 0
\(371\) 29.0886 10.5874i 1.51021 0.549670i
\(372\) −2.18164 3.77871i −0.113113 0.195917i
\(373\) −16.7466 + 29.0060i −0.867108 + 1.50188i −0.00216955 + 0.999998i \(0.500691\pi\)
−0.864939 + 0.501878i \(0.832643\pi\)
\(374\) 1.69673 9.62266i 0.0877360 0.497576i
\(375\) 0 0
\(376\) −7.60641 6.38254i −0.392271 0.329154i
\(377\) −1.33792 7.58770i −0.0689062 0.390786i
\(378\) −4.54545 1.65441i −0.233793 0.0850937i
\(379\) 13.5486 0.695946 0.347973 0.937504i \(-0.386870\pi\)
0.347973 + 0.937504i \(0.386870\pi\)
\(380\) 0 0
\(381\) 29.7651 1.52491
\(382\) 12.1287 + 4.41448i 0.620558 + 0.225865i
\(383\) −6.66222 37.7833i −0.340423 1.93064i −0.365164 0.930943i \(-0.618987\pi\)
0.0247406 0.999694i \(-0.492124\pi\)
\(384\) 1.75297 + 1.47092i 0.0894558 + 0.0750623i
\(385\) 0 0
\(386\) −3.73231 + 21.1670i −0.189969 + 1.07737i
\(387\) −3.32831 + 5.76481i −0.169188 + 0.293042i
\(388\) 3.84493 + 6.65961i 0.195197 + 0.338090i
\(389\) −12.5980 + 4.58528i −0.638742 + 0.232483i −0.641032 0.767514i \(-0.721493\pi\)
0.00228971 + 0.999997i \(0.499271\pi\)
\(390\) 0 0
\(391\) −18.0312 31.2310i −0.911879 1.57942i
\(392\) 0.332517 0.575937i 0.0167947 0.0290892i
\(393\) −1.86898 + 10.5995i −0.0942778 + 0.534676i
\(394\) −8.69134 + 7.29290i −0.437863 + 0.367411i
\(395\) 0 0
\(396\) 0.940336 + 5.33291i 0.0472537 + 0.267989i
\(397\) −28.3472 10.3175i −1.42270 0.517822i −0.487872 0.872915i \(-0.662227\pi\)
−0.934831 + 0.355094i \(0.884449\pi\)
\(398\) 13.5963 0.681519
\(399\) 9.04825 26.0912i 0.452979 1.30619i
\(400\) 0 0
\(401\) −9.60460 3.49579i −0.479631 0.174571i 0.0908794 0.995862i \(-0.471032\pi\)
−0.570510 + 0.821291i \(0.693254\pi\)
\(402\) 5.36174 + 30.4079i 0.267419 + 1.51661i
\(403\) −2.52707 2.12046i −0.125882 0.105628i
\(404\) −8.04966 + 6.75447i −0.400485 + 0.336047i
\(405\) 0 0
\(406\) 6.16475 10.6777i 0.305951 0.529923i
\(407\) 3.50296 + 6.06731i 0.173635 + 0.300745i
\(408\) 8.67768 3.15842i 0.429609 0.156365i
\(409\) 23.6095 8.59314i 1.16741 0.424904i 0.315673 0.948868i \(-0.397770\pi\)
0.851740 + 0.523964i \(0.175548\pi\)
\(410\) 0 0
\(411\) 25.2101 43.6652i 1.24352 2.15384i
\(412\) −1.79045 + 10.1541i −0.0882091 + 0.500258i
\(413\) −4.27637 + 3.58830i −0.210426 + 0.176569i
\(414\) 15.3101 + 12.8467i 0.752452 + 0.631382i
\(415\) 0 0
\(416\) 1.62576 + 0.591728i 0.0797094 + 0.0290119i
\(417\) 29.9012 1.46427
\(418\) 10.3646 1.99100i 0.506951 0.0973828i
\(419\) −4.75112 −0.232107 −0.116054 0.993243i \(-0.537024\pi\)
−0.116054 + 0.993243i \(0.537024\pi\)
\(420\) 0 0
\(421\) 2.00373 + 11.3637i 0.0976559 + 0.553834i 0.993901 + 0.110275i \(0.0351732\pi\)
−0.896245 + 0.443559i \(0.853716\pi\)
\(422\) −3.41131 2.86243i −0.166060 0.139341i
\(423\) 17.0117 14.2745i 0.827136 0.694049i
\(424\) −1.94156 + 11.0111i −0.0942904 + 0.534748i
\(425\) 0 0
\(426\) −15.2716 26.4512i −0.739911 1.28156i
\(427\) 22.6471 8.24288i 1.09597 0.398901i
\(428\) 6.60953 2.40567i 0.319484 0.116283i
\(429\) 4.79299 + 8.30170i 0.231408 + 0.400810i
\(430\) 0 0
\(431\) 1.50718 8.54765i 0.0725984 0.411726i −0.926752 0.375675i \(-0.877411\pi\)
0.999350 0.0360511i \(-0.0114779\pi\)
\(432\) 1.33841 1.12306i 0.0643942 0.0540331i
\(433\) −0.999529 0.838704i −0.0480343 0.0403056i 0.618454 0.785821i \(-0.287759\pi\)
−0.666489 + 0.745515i \(0.732204\pi\)
\(434\) −0.916684 5.19878i −0.0440023 0.249549i
\(435\) 0 0
\(436\) 6.24627 0.299142
\(437\) 24.5802 30.2177i 1.17583 1.44551i
\(438\) −13.0633 −0.624190
\(439\) 21.7294 + 7.90886i 1.03709 + 0.377469i 0.803776 0.594932i \(-0.202821\pi\)
0.233313 + 0.972402i \(0.425043\pi\)
\(440\) 0 0
\(441\) 1.13937 + 0.956046i 0.0542558 + 0.0455260i
\(442\) 5.34838 4.48783i 0.254397 0.213464i
\(443\) −5.53159 + 31.3712i −0.262814 + 1.49049i 0.512375 + 0.858762i \(0.328766\pi\)
−0.775189 + 0.631730i \(0.782345\pi\)
\(444\) −3.31063 + 5.73417i −0.157115 + 0.272132i
\(445\) 0 0
\(446\) 18.6363 6.78306i 0.882454 0.321187i
\(447\) 4.45456 1.62133i 0.210694 0.0766862i
\(448\) 1.38429 + 2.39766i 0.0654016 + 0.113279i
\(449\) 16.7627 29.0338i 0.791080 1.37019i −0.134218 0.990952i \(-0.542852\pi\)
0.925298 0.379240i \(-0.123814\pi\)
\(450\) 0 0
\(451\) −8.63844 + 7.24852i −0.406768 + 0.341319i
\(452\) 5.74932 + 4.82426i 0.270425 + 0.226914i
\(453\) 1.41276 + 8.01218i 0.0663774 + 0.376445i
\(454\) 12.0605 + 4.38966i 0.566027 + 0.206017i
\(455\) 0 0
\(456\) 6.52735 + 7.54235i 0.305671 + 0.353203i
\(457\) −2.81534 −0.131696 −0.0658479 0.997830i \(-0.520975\pi\)
−0.0658479 + 0.997830i \(0.520975\pi\)
\(458\) −10.7963 3.92955i −0.504480 0.183616i
\(459\) −1.22434 6.94358i −0.0571474 0.324099i
\(460\) 0 0
\(461\) −6.64940 + 5.57951i −0.309693 + 0.259864i −0.784365 0.620299i \(-0.787011\pi\)
0.474672 + 0.880163i \(0.342567\pi\)
\(462\) −2.66375 + 15.1069i −0.123929 + 0.702835i
\(463\) −9.47085 + 16.4040i −0.440148 + 0.762358i −0.997700 0.0677837i \(-0.978407\pi\)
0.557552 + 0.830142i \(0.311741\pi\)
\(464\) 2.22668 + 3.85673i 0.103371 + 0.179044i
\(465\) 0 0
\(466\) 2.56436 0.933350i 0.118792 0.0432366i
\(467\) 2.47059 + 4.27919i 0.114325 + 0.198017i 0.917510 0.397713i \(-0.130196\pi\)
−0.803184 + 0.595730i \(0.796863\pi\)
\(468\) −1.93467 + 3.35095i −0.0894303 + 0.154898i
\(469\) −6.48698 + 36.7895i −0.299541 + 1.69878i
\(470\) 0 0
\(471\) 16.1462 + 13.5482i 0.743976 + 0.624270i
\(472\) −0.350134 1.98571i −0.0161162 0.0913997i
\(473\) −6.77202 2.46481i −0.311378 0.113332i
\(474\) 15.3883 0.706807
\(475\) 0 0
\(476\) 11.1726 0.512096
\(477\) −23.4981 8.55262i −1.07591 0.391598i
\(478\) −4.34565 24.6454i −0.198765 1.12725i
\(479\) −19.4138 16.2901i −0.887038 0.744313i 0.0805757 0.996748i \(-0.474324\pi\)
−0.967614 + 0.252435i \(0.918769\pi\)
\(480\) 0 0
\(481\) −0.869282 + 4.92995i −0.0396359 + 0.224786i
\(482\) 12.6104 21.8418i 0.574387 0.994867i
\(483\) 28.3077 + 49.0304i 1.28805 + 2.23096i
\(484\) 4.82756 1.75709i 0.219435 0.0798677i
\(485\) 0 0
\(486\) 9.63053 + 16.6806i 0.436850 + 0.756646i
\(487\) 9.98344 17.2918i 0.452393 0.783567i −0.546141 0.837693i \(-0.683904\pi\)
0.998534 + 0.0541258i \(0.0172372\pi\)
\(488\) −1.51161 + 8.57278i −0.0684275 + 0.388072i
\(489\) 35.6009 29.8727i 1.60993 1.35089i
\(490\) 0 0
\(491\) −2.43814 13.8274i −0.110032 0.624020i −0.989091 0.147308i \(-0.952939\pi\)
0.879059 0.476713i \(-0.158172\pi\)
\(492\) −10.0148 3.64509i −0.451502 0.164333i
\(493\) 17.9716 0.809399
\(494\) 6.58772 + 3.67063i 0.296395 + 0.165149i
\(495\) 0 0
\(496\) 1.79175 + 0.652145i 0.0804521 + 0.0292822i
\(497\) −6.41684 36.3917i −0.287835 1.63239i
\(498\) −29.7188 24.9370i −1.33173 1.11745i
\(499\) −14.2758 + 11.9788i −0.639072 + 0.536245i −0.903733 0.428097i \(-0.859184\pi\)
0.264661 + 0.964341i \(0.414740\pi\)
\(500\) 0 0
\(501\) 12.4663 21.5923i 0.556955 0.964674i
\(502\) −1.66951 2.89168i −0.0745140 0.129062i
\(503\) −7.72785 + 2.81271i −0.344568 + 0.125412i −0.508507 0.861058i \(-0.669802\pi\)
0.163939 + 0.986470i \(0.447580\pi\)
\(504\) −5.81849 + 2.11776i −0.259176 + 0.0943323i
\(505\) 0 0
\(506\) −10.8187 + 18.7385i −0.480948 + 0.833027i
\(507\) 3.97634 22.5510i 0.176596 1.00152i
\(508\) −9.96418 + 8.36094i −0.442089 + 0.370957i
\(509\) 20.2854 + 17.0215i 0.899136 + 0.754465i 0.970021 0.243020i \(-0.0781379\pi\)
−0.0708852 + 0.997484i \(0.522582\pi\)
\(510\) 0 0
\(511\) −14.8517 5.40558i −0.657001 0.239129i
\(512\) −1.00000 −0.0441942
\(513\) 6.53657 3.90800i 0.288597 0.172542i
\(514\) −9.48495 −0.418363
\(515\) 0 0
\(516\) −1.18271 6.70747i −0.0520658 0.295280i
\(517\) 18.4173 + 15.4539i 0.809991 + 0.679663i
\(518\) −6.13665 + 5.14926i −0.269629 + 0.226245i
\(519\) −6.64281 + 37.6732i −0.291587 + 1.65367i
\(520\) 0 0
\(521\) −14.7837 25.6061i −0.647686 1.12183i −0.983674 0.179959i \(-0.942404\pi\)
0.335988 0.941866i \(-0.390930\pi\)
\(522\) −9.35925 + 3.40649i −0.409643 + 0.149098i
\(523\) −2.30677 + 0.839597i −0.100868 + 0.0367130i −0.391961 0.919982i \(-0.628203\pi\)
0.291093 + 0.956695i \(0.405981\pi\)
\(524\) −2.35172 4.07330i −0.102735 0.177943i
\(525\) 0 0
\(526\) 4.91064 27.8496i 0.214114 1.21430i
\(527\) 5.89447 4.94604i 0.256767 0.215453i
\(528\) −4.24443 3.56150i −0.184715 0.154995i
\(529\) 9.87320 + 55.9937i 0.429270 + 2.43451i
\(530\) 0 0
\(531\) 4.50953 0.195697
\(532\) 4.29994 + 11.2759i 0.186426 + 0.488873i
\(533\) −8.05761 −0.349014
\(534\) −11.9399 4.34576i −0.516689 0.188059i
\(535\) 0 0
\(536\) −10.3364 8.67326i −0.446464 0.374628i
\(537\) 44.7725 37.5686i 1.93207 1.62120i
\(538\) 0.907359 5.14589i 0.0391190 0.221855i
\(539\) −0.805118 + 1.39451i −0.0346789 + 0.0600656i
\(540\) 0 0
\(541\) −35.2607 + 12.8338i −1.51597 + 0.551769i −0.960139 0.279523i \(-0.909824\pi\)
−0.555835 + 0.831293i \(0.687601\pi\)
\(542\) 0.340055 0.123770i 0.0146066 0.00531637i
\(543\) 2.39237 + 4.14371i 0.102667 + 0.177824i
\(544\) −2.01775 + 3.49485i −0.0865104 + 0.149840i
\(545\) 0 0
\(546\) −8.39657 + 7.04556i −0.359340 + 0.301522i
\(547\) −2.92850 2.45730i −0.125213 0.105067i 0.578031 0.816015i \(-0.303821\pi\)
−0.703244 + 0.710949i \(0.748266\pi\)
\(548\) 3.82609 + 21.6988i 0.163442 + 0.926927i
\(549\) −18.2946 6.65870i −0.780795 0.284186i
\(550\) 0 0
\(551\) 6.91662 + 18.1377i 0.294658 + 0.772693i
\(552\) −20.4493 −0.870379
\(553\) 17.4949 + 6.36764i 0.743961 + 0.270780i
\(554\) −2.26969 12.8720i −0.0964298 0.546880i
\(555\) 0 0
\(556\) −10.0097 + 8.39915i −0.424507 + 0.356203i
\(557\) 0.412140 2.33736i 0.0174629 0.0990373i −0.974831 0.222947i \(-0.928432\pi\)
0.992293 + 0.123910i \(0.0395434\pi\)
\(558\) −2.13221 + 3.69309i −0.0902636 + 0.156341i
\(559\) −2.57470 4.45952i −0.108898 0.188618i
\(560\) 0 0
\(561\) −21.0111 + 7.64743i −0.887091 + 0.322875i
\(562\) 5.07629 + 8.79238i 0.214130 + 0.370884i
\(563\) 9.18301 15.9054i 0.387018 0.670335i −0.605029 0.796203i \(-0.706838\pi\)
0.992047 + 0.125869i \(0.0401718\pi\)
\(564\) −3.94563 + 22.3768i −0.166141 + 0.942232i
\(565\) 0 0
\(566\) −7.86241 6.59734i −0.330482 0.277307i
\(567\) 5.14776 + 29.1944i 0.216186 + 1.22605i
\(568\) 12.5424 + 4.56505i 0.526267 + 0.191545i
\(569\) 3.09691 0.129829 0.0649146 0.997891i \(-0.479322\pi\)
0.0649146 + 0.997891i \(0.479322\pi\)
\(570\) 0 0
\(571\) −21.1742 −0.886113 −0.443056 0.896494i \(-0.646106\pi\)
−0.443056 + 0.896494i \(0.646106\pi\)
\(572\) −3.93643 1.43274i −0.164590 0.0599059i
\(573\) −5.12883 29.0870i −0.214260 1.21513i
\(574\) −9.87750 8.28820i −0.412279 0.345943i
\(575\) 0 0
\(576\) 0.388363 2.20251i 0.0161818 0.0917714i
\(577\) −9.06063 + 15.6935i −0.377199 + 0.653328i −0.990654 0.136402i \(-0.956446\pi\)
0.613455 + 0.789730i \(0.289779\pi\)
\(578\) −0.357350 0.618949i −0.0148638 0.0257449i
\(579\) 46.2182 16.8220i 1.92076 0.699100i
\(580\) 0 0
\(581\) −23.4684 40.6485i −0.973634 1.68638i
\(582\) 8.79849 15.2394i 0.364709 0.631695i
\(583\) 4.70106 26.6611i 0.194698 1.10419i
\(584\) 4.37308 3.66945i 0.180960 0.151843i
\(585\) 0 0
\(586\) −1.24016 7.03331i −0.0512306 0.290543i
\(587\) 7.20361 + 2.62190i 0.297325 + 0.108217i 0.486375 0.873750i \(-0.338319\pi\)
−0.189051 + 0.981967i \(0.560541\pi\)
\(588\) −1.52182 −0.0627589
\(589\) 7.26034 + 4.04540i 0.299157 + 0.166688i
\(590\) 0 0
\(591\) 24.3971 + 8.87983i 1.00356 + 0.365267i
\(592\) −0.502447 2.84952i −0.0206504 0.117114i
\(593\) 0.970306 + 0.814183i 0.0398457 + 0.0334345i 0.662493 0.749068i \(-0.269498\pi\)
−0.622647 + 0.782503i \(0.713943\pi\)
\(594\) −3.24066 + 2.71924i −0.132966 + 0.111572i
\(595\) 0 0
\(596\) −1.03578 + 1.79403i −0.0424274 + 0.0734864i
\(597\) −15.5564 26.9445i −0.636682 1.10277i
\(598\) −14.5283 + 5.28786i −0.594106 + 0.216237i
\(599\) −6.46096 + 2.35160i −0.263987 + 0.0960836i −0.470623 0.882334i \(-0.655971\pi\)
0.206636 + 0.978418i \(0.433749\pi\)
\(600\) 0 0
\(601\) 10.4282 18.0622i 0.425376 0.736772i −0.571080 0.820895i \(-0.693475\pi\)
0.996455 + 0.0841223i \(0.0268086\pi\)
\(602\) 1.43092 8.11513i 0.0583198 0.330748i
\(603\) 23.1172 19.3977i 0.941407 0.789934i
\(604\) −2.72354 2.28532i −0.110819 0.0929883i
\(605\) 0 0
\(606\) 22.5959 + 8.22423i 0.917895 + 0.334087i
\(607\) −8.73323 −0.354471 −0.177235 0.984168i \(-0.556715\pi\)
−0.177235 + 0.984168i \(0.556715\pi\)
\(608\) −4.30372 0.691364i −0.174539 0.0280385i
\(609\) −28.2140 −1.14329
\(610\) 0 0
\(611\) 2.98309 + 16.9180i 0.120683 + 0.684427i
\(612\) −6.91383 5.80140i −0.279475 0.234508i
\(613\) 16.6001 13.9291i 0.670470 0.562591i −0.242734 0.970093i \(-0.578044\pi\)
0.913205 + 0.407501i \(0.133600\pi\)
\(614\) −1.87916 + 10.6573i −0.0758369 + 0.430092i
\(615\) 0 0
\(616\) −3.35176 5.80542i −0.135046 0.233907i
\(617\) −11.1916 + 4.07342i −0.450559 + 0.163990i −0.557325 0.830294i \(-0.688172\pi\)
0.106767 + 0.994284i \(0.465950\pi\)
\(618\) 22.1716 8.06981i 0.891874 0.324615i
\(619\) −4.19167 7.26019i −0.168478 0.291812i 0.769407 0.638759i \(-0.220552\pi\)
−0.937885 + 0.346947i \(0.887218\pi\)
\(620\) 0 0
\(621\) −2.71121 + 15.3760i −0.108797 + 0.617018i
\(622\) −20.1912 + 16.9425i −0.809595 + 0.679331i
\(623\) −11.7762 9.88139i −0.471803 0.395890i
\(624\) −0.687481 3.89890i −0.0275213 0.156081i
\(625\) 0 0
\(626\) −30.1756 −1.20606
\(627\) −15.8046 18.2622i −0.631174 0.729321i
\(628\) −9.21076 −0.367549
\(629\) −10.9725 3.99365i −0.437500 0.159237i
\(630\) 0 0
\(631\) 34.4895 + 28.9401i 1.37301 + 1.15209i 0.971720 + 0.236135i \(0.0758807\pi\)
0.401285 + 0.915953i \(0.368564\pi\)
\(632\) −5.15138 + 4.32252i −0.204911 + 0.171941i
\(633\) −1.76953 + 10.0355i −0.0703324 + 0.398875i
\(634\) 5.97740 10.3532i 0.237393 0.411177i
\(635\) 0 0
\(636\) 24.0429 8.75089i 0.953362 0.346995i
\(637\) −1.08119 + 0.393520i −0.0428382 + 0.0155918i
\(638\) −5.39143 9.33823i −0.213449 0.369704i
\(639\) −14.9256 + 25.8519i −0.590447 + 1.02268i
\(640\) 0 0
\(641\) −0.336944 + 0.282730i −0.0133085 + 0.0111672i −0.649418 0.760432i \(-0.724987\pi\)
0.636109 + 0.771599i \(0.280543\pi\)
\(642\) −12.3299 10.3460i −0.486622 0.408324i
\(643\) −0.950798 5.39224i −0.0374958 0.212649i 0.960303 0.278958i \(-0.0899890\pi\)
−0.997799 + 0.0663085i \(0.978878\pi\)
\(644\) −23.2488 8.46188i −0.916132 0.333445i
\(645\) 0 0
\(646\) −11.1001 + 13.6459i −0.436726 + 0.536889i
\(647\) −20.1149 −0.790797 −0.395398 0.918510i \(-0.629393\pi\)
−0.395398 + 0.918510i \(0.629393\pi\)
\(648\) −10.0618 3.66221i −0.395266 0.143865i
\(649\) 0.847774 + 4.80797i 0.0332780 + 0.188729i
\(650\) 0 0
\(651\) −9.25388 + 7.76493i −0.362688 + 0.304331i
\(652\) −3.52661 + 20.0004i −0.138113 + 0.783275i
\(653\) 13.0225 22.5556i 0.509610 0.882671i −0.490328 0.871538i \(-0.663123\pi\)
0.999938 0.0111325i \(-0.00354367\pi\)
\(654\) −7.14679 12.3786i −0.279462 0.484042i
\(655\) 0 0
\(656\) 4.37645 1.59290i 0.170872 0.0621922i
\(657\) 6.38368 + 11.0569i 0.249051 + 0.431369i
\(658\) −13.7453 + 23.8075i −0.535846 + 0.928112i
\(659\) −0.984194 + 5.58164i −0.0383387 + 0.217430i −0.997958 0.0638720i \(-0.979655\pi\)
0.959619 + 0.281302i \(0.0907662\pi\)
\(660\) 0 0
\(661\) −10.2769 8.62333i −0.399724 0.335409i 0.420663 0.907217i \(-0.361798\pi\)
−0.820387 + 0.571809i \(0.806242\pi\)
\(662\) 5.02924 + 28.5222i 0.195467 + 1.10855i
\(663\) −15.0132 5.46437i −0.583066 0.212219i
\(664\) 16.9534 0.657919
\(665\) 0 0
\(666\) 6.47124 0.250755
\(667\) −37.3966 13.6112i −1.44800 0.527029i
\(668\) 1.89199 + 10.7300i 0.0732033 + 0.415157i
\(669\) −34.7654 29.1717i −1.34411 1.12784i
\(670\) 0 0
\(671\) 3.66004 20.7571i 0.141294 0.801320i
\(672\) 3.16772 5.48666i 0.122198 0.211652i
\(673\) 15.3125 + 26.5220i 0.590252 + 1.02235i 0.994198 + 0.107564i \(0.0343050\pi\)
−0.403946 + 0.914783i \(0.632362\pi\)
\(674\) 4.18967 1.52492i 0.161380 0.0587376i
\(675\) 0 0
\(676\) 5.00338 + 8.66611i 0.192438 + 0.333312i
\(677\) −6.67895 + 11.5683i −0.256693 + 0.444605i −0.965354 0.260944i \(-0.915966\pi\)
0.708661 + 0.705549i \(0.249300\pi\)
\(678\) 2.98231 16.9135i 0.114535 0.649561i
\(679\) 16.3091 13.6849i 0.625885 0.525179i
\(680\) 0 0
\(681\) −5.10000 28.9235i −0.195432 1.10835i
\(682\) −4.33834 1.57903i −0.166124 0.0604641i
\(683\) −9.75308 −0.373191 −0.186596 0.982437i \(-0.559745\pi\)
−0.186596 + 0.982437i \(0.559745\pi\)
\(684\) 3.19414 9.21050i 0.122131 0.352172i
\(685\) 0 0
\(686\) 16.4811 + 5.99864i 0.629253 + 0.229029i
\(687\) 4.56543 + 25.8918i 0.174182 + 0.987835i
\(688\) 2.28003 + 1.91317i 0.0869254 + 0.0729391i
\(689\) 14.8185 12.4342i 0.564541 0.473706i
\(690\) 0 0
\(691\) −1.80854 + 3.13248i −0.0688001 + 0.119165i −0.898373 0.439233i \(-0.855250\pi\)
0.829573 + 0.558398i \(0.188584\pi\)
\(692\) −8.35856 14.4774i −0.317745 0.550350i
\(693\) 14.0882 5.12769i 0.535167 0.194785i
\(694\) −24.2710 + 8.83392i −0.921314 + 0.335331i
\(695\) 0 0
\(696\) 5.09540 8.82549i 0.193141 0.334529i
\(697\) 3.26365 18.5091i 0.123620 0.701082i
\(698\) 16.7763 14.0770i 0.634992 0.532822i
\(699\) −4.78373 4.01403i −0.180937 0.151825i
\(700\) 0 0
\(701\) −16.7716 6.10435i −0.633453 0.230558i 0.00528040 0.999986i \(-0.498319\pi\)
−0.638734 + 0.769428i \(0.720541\pi\)
\(702\) −3.02277 −0.114087
\(703\) −0.192337 12.6109i −0.00725414 0.475629i
\(704\) 2.42128 0.0912556
\(705\) 0 0
\(706\) −2.21203 12.5451i −0.0832510 0.472140i
\(707\) 22.2861 + 18.7003i 0.838156 + 0.703296i
\(708\) −3.53458 + 2.96587i −0.132838 + 0.111464i
\(709\) −6.05271 + 34.3266i −0.227314 + 1.28916i 0.630897 + 0.775867i \(0.282687\pi\)
−0.858211 + 0.513297i \(0.828424\pi\)
\(710\) 0 0
\(711\) −7.51981 13.0247i −0.282015 0.488464i
\(712\) 5.21770 1.89909i 0.195542 0.0711714i
\(713\) −16.0117 + 5.82777i −0.599641 + 0.218252i
\(714\) −12.7834 22.1414i −0.478405 0.828622i
\(715\) 0 0
\(716\) −4.43514 + 25.1529i −0.165749 + 0.940009i
\(717\) −43.8691 + 36.8105i −1.63832 + 1.37472i
\(718\) −19.0576 15.9912i −0.711224 0.596788i
\(719\) −3.64425 20.6676i −0.135908 0.770771i −0.974223 0.225586i \(-0.927570\pi\)
0.838316 0.545185i \(-0.183541\pi\)
\(720\) 0 0
\(721\) 28.5462 1.06312
\(722\) −18.0440 5.95088i −0.671529 0.221469i
\(723\) −57.7136 −2.14639
\(724\) −1.96483 0.715139i −0.0730222 0.0265779i
\(725\) 0 0
\(726\) −9.00568 7.55666i −0.334232 0.280454i
\(727\) 6.43176 5.39689i 0.238541 0.200159i −0.515678 0.856782i \(-0.672460\pi\)
0.754219 + 0.656623i \(0.228016\pi\)
\(728\) 0.831760 4.71714i 0.0308271 0.174829i
\(729\) 5.97654 10.3517i 0.221353 0.383395i
\(730\) 0 0
\(731\) 11.2868 4.10806i 0.417457 0.151942i
\(732\) 18.7187 6.81306i 0.691864 0.251818i
\(733\) 4.33942 + 7.51610i 0.160280 + 0.277614i 0.934969 0.354729i \(-0.115427\pi\)
−0.774689 + 0.632343i \(0.782094\pi\)
\(734\) 5.54259 9.60005i 0.204581 0.354344i
\(735\) 0 0
\(736\) 6.84561 5.74414i 0.252332 0.211732i
\(737\) 25.0273 + 21.0004i 0.921894 + 0.773561i
\(738\) 1.80873 + 10.2578i 0.0665802 + 0.377595i
\(739\) −9.63552 3.50704i −0.354448 0.129009i 0.158658 0.987334i \(-0.449283\pi\)
−0.513107 + 0.858325i \(0.671505\pi\)
\(740\) 0 0
\(741\) −0.263169 17.2551i −0.00966774 0.633881i
\(742\) 30.9555 1.13641
\(743\) 32.3326 + 11.7681i 1.18617 + 0.431730i 0.858377 0.513020i \(-0.171473\pi\)
0.327792 + 0.944750i \(0.393695\pi\)
\(744\) −0.757675 4.29699i −0.0277777 0.157535i
\(745\) 0 0
\(746\) −25.6573 + 21.5291i −0.939382 + 0.788235i
\(747\) −6.58407 + 37.3401i −0.240898 + 1.36620i
\(748\) 4.88555 8.46202i 0.178633 0.309402i
\(749\) −9.73670 16.8645i −0.355771 0.616214i
\(750\) 0 0
\(751\) −3.94631 + 1.43634i −0.144003 + 0.0524127i −0.413016 0.910724i \(-0.635525\pi\)
0.269013 + 0.963136i \(0.413302\pi\)
\(752\) −4.96473 8.59917i −0.181045 0.313579i
\(753\) −3.82041 + 6.61715i −0.139224 + 0.241142i
\(754\) 1.33792 7.58770i 0.0487240 0.276328i
\(755\) 0 0
\(756\) −3.70549 3.10927i −0.134767 0.113083i
\(757\) 2.48755 + 14.1076i 0.0904115 + 0.512749i 0.996057 + 0.0887138i \(0.0282757\pi\)
−0.905646 + 0.424035i \(0.860613\pi\)
\(758\) 12.7315 + 4.63390i 0.462431 + 0.168311i
\(759\) 49.5135 1.79723
\(760\) 0 0
\(761\) 15.6963 0.568992 0.284496 0.958677i \(-0.408174\pi\)
0.284496 + 0.958677i \(0.408174\pi\)
\(762\) 27.9701 + 10.1803i 1.01325 + 0.368792i
\(763\) −3.00295 17.0306i −0.108714 0.616548i
\(764\) 9.88740 + 8.29651i 0.357713 + 0.300157i
\(765\) 0 0
\(766\) 6.66222 37.7833i 0.240716 1.36517i
\(767\) −1.74423 + 3.02110i −0.0629807 + 0.109086i
\(768\) 1.14417 + 1.98176i 0.0412866 + 0.0715106i
\(769\) 17.9278 6.52518i 0.646492 0.235304i 0.00209836 0.999998i \(-0.499332\pi\)
0.644394 + 0.764694i \(0.277110\pi\)
\(770\) 0 0
\(771\) 10.8524 + 18.7969i 0.390839 + 0.676953i
\(772\) −10.7467 + 18.6139i −0.386784 + 0.669929i
\(773\) −7.99526 + 45.3434i −0.287570 + 1.63089i 0.408390 + 0.912807i \(0.366090\pi\)
−0.695960 + 0.718081i \(0.745021\pi\)
\(774\) −5.09927 + 4.27880i −0.183289 + 0.153798i
\(775\) 0 0
\(776\) 1.33533 + 7.57303i 0.0479355 + 0.271856i
\(777\) 17.2259 + 6.26973i 0.617977 + 0.224925i
\(778\) −13.4065 −0.480645
\(779\) 19.9363 3.82966i 0.714291 0.137212i
\(780\) 0 0
\(781\) −30.3687 11.0533i −1.08668 0.395518i
\(782\) −6.26219 35.5146i −0.223935 1.27000i
\(783\) −5.96041 5.00138i −0.213008 0.178735i
\(784\) 0.509446 0.427476i 0.0181945 0.0152670i
\(785\) 0 0
\(786\) −5.38153 + 9.32108i −0.191953 + 0.332472i
\(787\) 26.4652 + 45.8391i 0.943383 + 1.63399i 0.758956 + 0.651141i \(0.225710\pi\)
0.184427 + 0.982846i \(0.440957\pi\)
\(788\) −10.6615 + 3.88047i −0.379800 + 0.138236i
\(789\) −60.8098 + 22.1330i −2.16489 + 0.787954i
\(790\) 0 0
\(791\) 10.3894 17.9949i 0.369404 0.639827i
\(792\) −0.940336 + 5.33291i −0.0334134 + 0.189497i
\(793\) 11.5371 9.68074i 0.409693 0.343773i
\(794\) −23.1088 19.3906i −0.820101 0.688146i
\(795\) 0 0
\(796\) 12.7763 + 4.65019i 0.452844 + 0.164822i
\(797\) −40.6890 −1.44128 −0.720639 0.693311i \(-0.756151\pi\)
−0.720639 + 0.693311i \(0.756151\pi\)
\(798\) 17.4263 21.4230i 0.616883 0.758366i
\(799\) −40.0704 −1.41759
\(800\) 0 0
\(801\) 2.15641 + 12.2296i 0.0761929 + 0.432112i
\(802\) −7.82974 6.56993i −0.276478 0.231992i
\(803\) −10.5885 + 8.88479i −0.373659 + 0.313537i
\(804\) −5.36174 + 30.4079i −0.189094 + 1.07240i
\(805\) 0 0
\(806\) −1.64943 2.85689i −0.0580986 0.100630i
\(807\) −11.2361 + 4.08960i −0.395529 + 0.143961i
\(808\) −9.87437 + 3.59398i −0.347379 + 0.126436i
\(809\) 2.30197 + 3.98714i 0.0809331 + 0.140180i 0.903651 0.428270i \(-0.140877\pi\)
−0.822718 + 0.568450i \(0.807543\pi\)
\(810\) 0 0
\(811\) −5.75399 + 32.6325i −0.202050 + 1.14588i 0.699965 + 0.714177i \(0.253199\pi\)
−0.902015 + 0.431705i \(0.857912\pi\)
\(812\) 9.44494 7.92524i 0.331452 0.278122i
\(813\) −0.634362 0.532293i −0.0222481 0.0186683i
\(814\) 1.21657 + 6.89949i 0.0426406 + 0.241827i
\(815\) 0 0
\(816\) 9.23460 0.323276
\(817\) 8.48992 + 9.81010i 0.297025 + 0.343212i
\(818\) 25.1247 0.878464
\(819\) 10.0665 + 3.66392i 0.351754 + 0.128028i
\(820\) 0 0
\(821\) 16.3258 + 13.6990i 0.569774 + 0.478098i 0.881571 0.472051i \(-0.156486\pi\)
−0.311797 + 0.950149i \(0.600931\pi\)
\(822\) 38.6241 32.4095i 1.34717 1.13041i
\(823\) −8.31895 + 47.1791i −0.289980 + 1.64456i 0.396952 + 0.917839i \(0.370068\pi\)
−0.686933 + 0.726721i \(0.741043\pi\)
\(824\) −5.15539 + 8.92940i −0.179597 + 0.311070i
\(825\) 0 0
\(826\) −5.24574 + 1.90929i −0.182523 + 0.0664329i
\(827\) −13.5484 + 4.93122i −0.471125 + 0.171475i −0.566662 0.823950i \(-0.691765\pi\)
0.0955370 + 0.995426i \(0.469543\pi\)
\(828\) 9.99298 + 17.3084i 0.347280 + 0.601507i
\(829\) 3.14956 5.45520i 0.109389 0.189467i −0.806134 0.591733i \(-0.798444\pi\)
0.915523 + 0.402266i \(0.131777\pi\)
\(830\) 0 0
\(831\) −22.9124 + 19.2258i −0.794821 + 0.666934i
\(832\) 1.32533 + 1.11209i 0.0459476 + 0.0385546i
\(833\) −0.466028 2.64298i −0.0161469 0.0915737i
\(834\) 28.0979 + 10.2268i 0.972951 + 0.354125i
\(835\) 0 0
\(836\) 10.4205 + 1.67399i 0.360402 + 0.0578961i
\(837\) −3.33140 −0.115150
\(838\) −4.46459 1.62498i −0.154227 0.0561339i
\(839\) −2.58965 14.6867i −0.0894048 0.507040i −0.996319 0.0857242i \(-0.972680\pi\)
0.906914 0.421316i \(-0.138432\pi\)
\(840\) 0 0
\(841\) −7.02276 + 5.89279i −0.242164 + 0.203200i
\(842\) −2.00373 + 11.3637i −0.0690532 + 0.391620i
\(843\) 11.6163 20.1199i 0.400085 0.692968i
\(844\) −2.22657 3.85654i −0.0766418 0.132747i
\(845\) 0 0
\(846\) 20.8679 7.59529i 0.717453 0.261132i
\(847\) −7.11163 12.3177i −0.244359 0.423241i
\(848\) −5.59050 + 9.68302i −0.191978 + 0.332516i
\(849\) −4.07842 + 23.1299i −0.139971 + 0.793815i
\(850\) 0 0
\(851\) 19.8076 + 16.6206i 0.678996 + 0.569745i
\(852\) −5.30377 30.0792i −0.181704 1.03050i
\(853\) −53.8776 19.6098i −1.84473 0.671428i −0.987741 0.156100i \(-0.950108\pi\)
−0.856993 0.515328i \(-0.827670\pi\)
\(854\) 24.1006 0.824705
\(855\) 0 0
\(856\) 7.03372 0.240407
\(857\) 21.4404 + 7.80367i 0.732390 + 0.266568i 0.681176 0.732120i \(-0.261469\pi\)
0.0512138 + 0.998688i \(0.483691\pi\)
\(858\) 1.66459 + 9.44034i 0.0568281 + 0.322288i
\(859\) −18.2941 15.3506i −0.624188 0.523756i 0.274929 0.961465i \(-0.411346\pi\)
−0.899117 + 0.437709i \(0.855790\pi\)
\(860\) 0 0
\(861\) −5.12370 + 29.0579i −0.174615 + 0.990291i
\(862\) 4.33976 7.51668i 0.147813 0.256019i
\(863\) 0.991588 + 1.71748i 0.0337540 + 0.0584637i 0.882409 0.470483i \(-0.155920\pi\)
−0.848655 + 0.528947i \(0.822587\pi\)
\(864\) 1.64180 0.597566i 0.0558552 0.0203296i
\(865\) 0 0
\(866\) −0.652396 1.12998i −0.0221693 0.0383984i
\(867\) −0.817739 + 1.41636i −0.0277719 + 0.0481023i
\(868\) 0.916684 5.19878i 0.0311143 0.176458i
\(869\) 12.4730 10.4661i 0.423116 0.355036i
\(870\) 0 0
\(871\) 4.05374 + 22.9899i 0.137356 + 0.778983i
\(872\) 5.86958 + 2.13635i 0.198769 + 0.0723460i
\(873\) −17.1983 −0.582074
\(874\) 33.4329 19.9884i 1.13088 0.676117i
\(875\) 0 0
\(876\) −12.2755 4.46792i −0.414751 0.150957i
\(877\) 1.55252 + 8.80479i 0.0524250 + 0.297317i 0.999735 0.0230000i \(-0.00732178\pi\)
−0.947311 + 0.320317i \(0.896211\pi\)
\(878\) 17.7140 + 14.8638i 0.597818 + 0.501629i
\(879\) −12.5194 + 10.5050i −0.422268 + 0.354325i
\(880\) 0 0
\(881\) −17.8638 + 30.9409i −0.601845 + 1.04243i 0.390696 + 0.920520i \(0.372234\pi\)
−0.992542 + 0.121907i \(0.961099\pi\)
\(882\) 0.743672 + 1.28808i 0.0250407 + 0.0433718i
\(883\) 44.9250 16.3514i 1.51185 0.550268i 0.552751 0.833346i \(-0.313578\pi\)
0.959097 + 0.283079i \(0.0913558\pi\)
\(884\) 6.56076 2.38792i 0.220662 0.0803145i
\(885\) 0 0
\(886\) −15.9276 + 27.5874i −0.535098 + 0.926816i
\(887\) 2.55270 14.4771i 0.0857112 0.486093i −0.911490 0.411323i \(-0.865067\pi\)
0.997201 0.0747695i \(-0.0238221\pi\)
\(888\) −5.07217 + 4.25606i −0.170211 + 0.142824i
\(889\) 27.5866 + 23.1479i 0.925226 + 0.776357i
\(890\) 0 0
\(891\) 24.3626 + 8.86724i 0.816176 + 0.297064i
\(892\) 19.8323 0.664035
\(893\) −15.4217 40.4409i −0.516066 1.35330i
\(894\) 4.74045 0.158544
\(895\) 0 0
\(896\) 0.480759 + 2.72652i 0.0160610 + 0.0910866i
\(897\) 27.1021 + 22.7413i 0.904912 + 0.759311i
\(898\) 25.6819 21.5497i 0.857017 0.719123i
\(899\) 1.47452 8.36242i 0.0491780 0.278902i
\(900\) 0 0
\(901\) 22.5605 + 39.0759i 0.751598 + 1.30181i
\(902\) −10.5966 + 3.85685i −0.352829 + 0.128419i
\(903\) −17.7194 + 6.44935i −0.589666 + 0.214621i
\(904\) 3.75261 + 6.49970i 0.124810 + 0.216177i
\(905\) 0 0
\(906\) −1.41276 + 8.01218i −0.0469359 + 0.266187i
\(907\) 37.1329 31.1582i 1.23298 1.03459i 0.234936 0.972011i \(-0.424512\pi\)
0.998040 0.0625793i \(-0.0199326\pi\)
\(908\) 9.83181 + 8.24987i 0.326280 + 0.273782i
\(909\) −4.08095 23.1442i −0.135356 0.767644i
\(910\) 0 0
\(911\) −1.23529 −0.0409271 −0.0204635 0.999791i \(-0.506514\pi\)
−0.0204635 + 0.999791i \(0.506514\pi\)
\(912\) 3.55407 + 9.31997i 0.117687 + 0.308615i
\(913\) −41.0490 −1.35852
\(914\) −2.64555 0.962902i −0.0875070 0.0318500i
\(915\) 0 0
\(916\) −8.80126 7.38514i −0.290802 0.244012i
\(917\) −9.97531 + 8.37028i −0.329414 + 0.276411i
\(918\) 1.22434 6.94358i 0.0404093 0.229172i
\(919\) 2.15131 3.72618i 0.0709652 0.122915i −0.828359 0.560197i \(-0.810725\pi\)
0.899325 + 0.437282i \(0.144059\pi\)
\(920\) 0 0
\(921\) 23.2702 8.46966i 0.766780 0.279085i
\(922\) −8.15670 + 2.96880i −0.268627 + 0.0977721i
\(923\) −11.5461 19.9984i −0.380044 0.658255i
\(924\) −7.66996 + 13.2848i −0.252323 + 0.437036i
\(925\) 0 0
\(926\) −14.5102 + 12.1755i −0.476834 + 0.400111i
\(927\) −17.6650 14.8227i −0.580193 0.486840i
\(928\) 0.773318 + 4.38571i 0.0253854 + 0.143968i
\(929\) −32.8280 11.9484i −1.07705 0.392015i −0.258242 0.966080i \(-0.583143\pi\)
−0.818810 + 0.574065i \(0.805366\pi\)
\(930\) 0 0
\(931\) 2.48805 1.48752i 0.0815427 0.0487516i
\(932\) 2.72893 0.0893892
\(933\) 56.6781 + 20.6291i 1.85556 + 0.675368i
\(934\) 0.858028 + 4.86612i 0.0280755 + 0.159224i
\(935\) 0 0
\(936\) −2.96409 + 2.48717i −0.0968844 + 0.0812956i
\(937\) −0.441335 + 2.50293i −0.0144178 + 0.0817673i −0.991168 0.132615i \(-0.957663\pi\)
0.976750 + 0.214382i \(0.0687738\pi\)
\(938\) −18.6785 + 32.3521i −0.609875 + 1.05633i
\(939\) 34.5260 + 59.8007i 1.12671 + 1.95152i
\(940\) 0 0
\(941\) −19.8302 + 7.21759i −0.646445 + 0.235287i −0.644373 0.764711i \(-0.722882\pi\)
−0.00207156 + 0.999998i \(0.500659\pi\)
\(942\) 10.5387 + 18.2535i 0.343368 + 0.594731i
\(943\) −20.8096 + 36.0433i −0.677654 + 1.17373i
\(944\) 0.350134 1.98571i 0.0113959 0.0646293i
\(945\) 0 0
\(946\) −5.52060 4.63234i −0.179490 0.150610i
\(947\) 6.77033 + 38.3965i 0.220006 + 1.24772i 0.872005 + 0.489497i \(0.162820\pi\)
−0.651999 + 0.758220i \(0.726069\pi\)
\(948\) 14.4602 + 5.26310i 0.469647 + 0.170938i
\(949\) −9.87653 −0.320606
\(950\) 0 0
\(951\) −27.3566 −0.887099
\(952\) 10.4988 + 3.82126i 0.340269 + 0.123848i
\(953\) −3.79192 21.5051i −0.122832 0.696618i −0.982572 0.185884i \(-0.940485\pi\)
0.859739 0.510733i \(-0.170626\pi\)
\(954\) −19.1558 16.0737i −0.620194 0.520404i
\(955\) 0 0
\(956\) 4.34565 24.6454i 0.140548 0.797090i
\(957\) −12.3374 + 21.3690i −0.398812 + 0.690762i
\(958\) −12.6714 21.9476i −0.409396 0.709094i
\(959\) 57.3228 20.8638i 1.85105 0.673727i
\(960\) 0 0
\(961\) 13.6822 + 23.6982i 0.441360 + 0.764458i
\(962\) −2.50300 + 4.33532i −0.0806999 + 0.139776i
\(963\) −2.73163 + 15.4919i −0.0880256 + 0.499218i
\(964\) 19.3202 16.2116i 0.622262 0.522140i
\(965\) 0 0
\(966\) 9.83117 + 55.7554i 0.316313 + 1.79390i
\(967\) 9.35186 + 3.40380i 0.300736 + 0.109459i 0.487981 0.872854i \(-0.337734\pi\)
−0.187245 + 0.982313i \(0.559956\pi\)
\(968\) 5.13739 0.165122
\(969\) 39.7431 + 6.38447i 1.27673 + 0.205099i
\(970\) 0 0
\(971\) 17.9288 + 6.52554i 0.575362 + 0.209415i 0.613279 0.789866i \(-0.289850\pi\)
−0.0379172 + 0.999281i \(0.512072\pi\)
\(972\) 3.34465 + 18.9684i 0.107280 + 0.608413i
\(973\) 27.7127 + 23.2537i 0.888429 + 0.745480i
\(974\) 15.2955 12.8345i 0.490100 0.411243i
\(975\) 0 0
\(976\) −4.35252 + 7.53878i −0.139321 + 0.241310i
\(977\) −5.51304 9.54886i −0.176378 0.305495i 0.764260 0.644909i \(-0.223105\pi\)
−0.940637 + 0.339414i \(0.889771\pi\)
\(978\) 43.6710 15.8949i 1.39644 0.508264i
\(979\) −12.6335 + 4.59823i −0.403770 + 0.146960i
\(980\) 0 0
\(981\) −6.98487 + 12.0981i −0.223010 + 0.386264i
\(982\) 2.43814 13.8274i 0.0778041 0.441249i
\(983\) 3.85443 3.23425i 0.122937 0.103157i −0.579246 0.815153i \(-0.696653\pi\)
0.702184 + 0.711996i \(0.252209\pi\)
\(984\) −8.16413 6.85052i −0.260263 0.218387i
\(985\) 0 0
\(986\) 16.8878 + 6.14664i 0.537816 + 0.195749i
\(987\) 62.9076 2.00237
\(988\) 4.93500 + 5.70239i 0.157003 + 0.181417i
\(989\) −26.5977 −0.845759
\(990\) 0 0
\(991\) −8.36382 47.4336i −0.265686 1.50678i −0.767076 0.641556i \(-0.778289\pi\)
0.501390 0.865221i \(-0.332822\pi\)
\(992\) 1.46065 + 1.22563i 0.0463757 + 0.0389139i
\(993\) 50.7699 42.6010i 1.61113 1.35190i
\(994\) 6.41684 36.3917i 0.203530 1.15428i
\(995\) 0 0
\(996\) −19.3976 33.5975i −0.614635 1.06458i
\(997\) 28.7745 10.4731i 0.911298 0.331685i 0.156527 0.987674i \(-0.449970\pi\)
0.754771 + 0.655988i \(0.227748\pi\)
\(998\) −17.5118 + 6.37379i −0.554327 + 0.201759i
\(999\) 2.52769 + 4.37809i 0.0799727 + 0.138517i
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 950.2.l.g.251.1 12
5.2 odd 4 950.2.u.f.99.1 24
5.3 odd 4 950.2.u.f.99.4 24
5.4 even 2 190.2.k.c.61.2 12
19.5 even 9 inner 950.2.l.g.651.1 12
95.9 even 18 3610.2.a.bf.1.5 6
95.24 even 18 190.2.k.c.81.2 yes 12
95.29 odd 18 3610.2.a.bd.1.2 6
95.43 odd 36 950.2.u.f.499.1 24
95.62 odd 36 950.2.u.f.499.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.c.61.2 12 5.4 even 2
190.2.k.c.81.2 yes 12 95.24 even 18
950.2.l.g.251.1 12 1.1 even 1 trivial
950.2.l.g.651.1 12 19.5 even 9 inner
950.2.u.f.99.1 24 5.2 odd 4
950.2.u.f.99.4 24 5.3 odd 4
950.2.u.f.499.1 24 95.43 odd 36
950.2.u.f.499.4 24 95.62 odd 36
3610.2.a.bd.1.2 6 95.29 odd 18
3610.2.a.bf.1.5 6 95.9 even 18