Properties

Label 105.2.x.a.32.8
Level $105$
Weight $2$
Character 105.32
Analytic conductor $0.838$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(2,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.8
Character \(\chi\) \(=\) 105.32
Dual form 105.2.x.a.23.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.907300 + 0.243110i) q^{2} +(1.12459 + 1.31730i) q^{3} +(-0.967960 - 0.558852i) q^{4} +(2.12501 - 0.695932i) q^{5} +(0.700094 + 1.46859i) q^{6} +(-2.64571 + 0.0144144i) q^{7} +(-2.07075 - 2.07075i) q^{8} +(-0.470578 + 2.96286i) q^{9} +O(q^{10})\) \(q+(0.907300 + 0.243110i) q^{2} +(1.12459 + 1.31730i) q^{3} +(-0.967960 - 0.558852i) q^{4} +(2.12501 - 0.695932i) q^{5} +(0.700094 + 1.46859i) q^{6} +(-2.64571 + 0.0144144i) q^{7} +(-2.07075 - 2.07075i) q^{8} +(-0.470578 + 2.96286i) q^{9} +(2.09721 - 0.114806i) q^{10} +(0.630122 + 0.363801i) q^{11} +(-0.352384 - 1.90358i) q^{12} +(-1.44243 + 1.44243i) q^{13} +(-2.40396 - 0.630122i) q^{14} +(3.30653 + 2.01665i) q^{15} +(-0.257666 - 0.446291i) q^{16} +(-1.90004 - 7.09105i) q^{17} +(-1.14726 + 2.57380i) q^{18} +(0.664374 - 0.383576i) q^{19} +(-2.44585 - 0.513933i) q^{20} +(-2.99434 - 3.46900i) q^{21} +(0.483266 + 0.483266i) q^{22} +(-0.840245 + 3.13584i) q^{23} +(0.399053 - 5.05655i) q^{24} +(4.03136 - 2.95773i) q^{25} +(-1.65938 + 0.958046i) q^{26} +(-4.43220 + 2.71212i) q^{27} +(2.56900 + 1.46461i) q^{28} +4.07354 q^{29} +(2.50975 + 2.63356i) q^{30} +(-0.209930 + 0.363609i) q^{31} +(1.39061 + 5.18983i) q^{32} +(0.229395 + 1.23919i) q^{33} -6.89563i q^{34} +(-5.61214 + 1.87187i) q^{35} +(2.11130 - 2.60495i) q^{36} +(-1.63050 + 6.08510i) q^{37} +(0.696038 - 0.186503i) q^{38} +(-3.52226 - 0.277970i) q^{39} +(-5.84146 - 2.95927i) q^{40} -4.44452i q^{41} +(-1.87342 - 3.87538i) q^{42} +(-5.15881 + 5.15881i) q^{43} +(-0.406622 - 0.704289i) q^{44} +(1.06197 + 6.62361i) q^{45} +(-1.52471 + 2.64087i) q^{46} +(6.79316 + 1.82022i) q^{47} +(0.298131 - 0.841320i) q^{48} +(6.99958 - 0.0762729i) q^{49} +(4.37671 - 1.70348i) q^{50} +(7.20429 - 10.4775i) q^{51} +(2.20232 - 0.590109i) q^{52} +(5.26849 - 1.41169i) q^{53} +(-4.68068 + 1.38320i) q^{54} +(1.59220 + 0.334560i) q^{55} +(5.50845 + 5.44875i) q^{56} +(1.25244 + 0.443814i) q^{57} +(3.69592 + 0.990320i) q^{58} +(0.807790 - 1.39913i) q^{59} +(-2.07358 - 3.79989i) q^{60} +(4.78904 + 8.29486i) q^{61} +(-0.278866 + 0.278866i) q^{62} +(1.20230 - 7.84567i) q^{63} +6.07747i q^{64} +(-2.06135 + 4.06901i) q^{65} +(-0.0931301 + 1.18009i) q^{66} +(-6.90351 + 1.84979i) q^{67} +(-2.12368 + 7.92569i) q^{68} +(-5.07578 + 2.41969i) q^{69} +(-5.54697 + 0.333975i) q^{70} +7.06501i q^{71} +(7.10979 - 5.16089i) q^{72} +(-4.08458 - 15.2439i) q^{73} +(-2.95870 + 5.12462i) q^{74} +(8.42987 + 1.98428i) q^{75} -0.857449 q^{76} +(-1.67236 - 0.953430i) q^{77} +(-3.12817 - 1.10850i) q^{78} +(5.80845 - 3.35351i) q^{79} +(-0.858131 - 0.769055i) q^{80} +(-8.55711 - 2.78851i) q^{81} +(1.08051 - 4.03251i) q^{82} +(1.83008 + 1.83008i) q^{83} +(0.959745 + 5.03124i) q^{84} +(-8.97250 - 13.7463i) q^{85} +(-5.93475 + 3.42643i) q^{86} +(4.58108 + 5.36609i) q^{87} +(-0.551483 - 2.05816i) q^{88} +(-6.94977 - 12.0373i) q^{89} +(-0.646746 + 6.26778i) q^{90} +(3.79546 - 3.83704i) q^{91} +(2.56579 - 2.56579i) q^{92} +(-0.715068 + 0.132371i) q^{93} +(5.72092 + 3.30298i) q^{94} +(1.14486 - 1.27746i) q^{95} +(-5.27271 + 7.66830i) q^{96} +(5.62554 + 5.62554i) q^{97} +(6.36927 + 1.63247i) q^{98} +(-1.37441 + 1.69577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7} - 8 q^{10} - 10 q^{12} - 16 q^{13} + 4 q^{15} - 8 q^{16} + 14 q^{18} - 28 q^{21} - 8 q^{22} + 4 q^{25} + 40 q^{27} - 60 q^{28} + 40 q^{30} - 24 q^{31} - 4 q^{33} + 8 q^{36} + 4 q^{37} - 16 q^{40} + 14 q^{42} + 16 q^{43} + 40 q^{45} - 32 q^{46} + 44 q^{48} + 8 q^{51} + 36 q^{52} - 40 q^{55} - 88 q^{57} + 56 q^{58} - 50 q^{60} - 8 q^{61} + 44 q^{63} + 76 q^{66} + 12 q^{67} + 140 q^{70} - 34 q^{72} + 52 q^{73} + 6 q^{75} + 64 q^{76} - 120 q^{78} + 20 q^{81} + 104 q^{82} - 24 q^{85} - 46 q^{87} - 84 q^{90} + 72 q^{91} - 44 q^{93} + 12 q^{96} - 120 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.907300 + 0.243110i 0.641558 + 0.171905i 0.564909 0.825153i \(-0.308911\pi\)
0.0766491 + 0.997058i \(0.475578\pi\)
\(3\) 1.12459 + 1.31730i 0.649285 + 0.760546i
\(4\) −0.967960 0.558852i −0.483980 0.279426i
\(5\) 2.12501 0.695932i 0.950335 0.311230i
\(6\) 0.700094 + 1.46859i 0.285812 + 0.599550i
\(7\) −2.64571 + 0.0144144i −0.999985 + 0.00544814i
\(8\) −2.07075 2.07075i −0.732120 0.732120i
\(9\) −0.470578 + 2.96286i −0.156859 + 0.987621i
\(10\) 2.09721 0.114806i 0.663197 0.0363049i
\(11\) 0.630122 + 0.363801i 0.189989 + 0.109690i 0.591977 0.805955i \(-0.298347\pi\)
−0.401988 + 0.915645i \(0.631681\pi\)
\(12\) −0.352384 1.90358i −0.101724 0.549516i
\(13\) −1.44243 + 1.44243i −0.400058 + 0.400058i −0.878253 0.478196i \(-0.841291\pi\)
0.478196 + 0.878253i \(0.341291\pi\)
\(14\) −2.40396 0.630122i −0.642485 0.168407i
\(15\) 3.30653 + 2.01665i 0.853742 + 0.520696i
\(16\) −0.257666 0.446291i −0.0644165 0.111573i
\(17\) −1.90004 7.09105i −0.460828 1.71983i −0.670365 0.742031i \(-0.733863\pi\)
0.209538 0.977801i \(-0.432804\pi\)
\(18\) −1.14726 + 2.57380i −0.270411 + 0.606651i
\(19\) 0.664374 0.383576i 0.152418 0.0879985i −0.421851 0.906665i \(-0.638620\pi\)
0.574269 + 0.818667i \(0.305286\pi\)
\(20\) −2.44585 0.513933i −0.546908 0.114919i
\(21\) −2.99434 3.46900i −0.653418 0.756997i
\(22\) 0.483266 + 0.483266i 0.103033 + 0.103033i
\(23\) −0.840245 + 3.13584i −0.175203 + 0.653867i 0.821314 + 0.570477i \(0.193242\pi\)
−0.996517 + 0.0833906i \(0.973425\pi\)
\(24\) 0.399053 5.05655i 0.0814564 1.03216i
\(25\) 4.03136 2.95773i 0.806272 0.591545i
\(26\) −1.65938 + 0.958046i −0.325432 + 0.187888i
\(27\) −4.43220 + 2.71212i −0.852977 + 0.521948i
\(28\) 2.56900 + 1.46461i 0.485495 + 0.276785i
\(29\) 4.07354 0.756437 0.378219 0.925716i \(-0.376537\pi\)
0.378219 + 0.925716i \(0.376537\pi\)
\(30\) 2.50975 + 2.63356i 0.458215 + 0.480819i
\(31\) −0.209930 + 0.363609i −0.0377045 + 0.0653060i −0.884262 0.466991i \(-0.845338\pi\)
0.846557 + 0.532297i \(0.178671\pi\)
\(32\) 1.39061 + 5.18983i 0.245827 + 0.917440i
\(33\) 0.229395 + 1.23919i 0.0399325 + 0.215715i
\(34\) 6.89563i 1.18259i
\(35\) −5.61214 + 1.87187i −0.948625 + 0.316403i
\(36\) 2.11130 2.60495i 0.351884 0.434158i
\(37\) −1.63050 + 6.08510i −0.268052 + 1.00038i 0.692303 + 0.721607i \(0.256596\pi\)
−0.960356 + 0.278778i \(0.910071\pi\)
\(38\) 0.696038 0.186503i 0.112912 0.0302548i
\(39\) −3.52226 0.277970i −0.564013 0.0445108i
\(40\) −5.84146 2.95927i −0.923616 0.467901i
\(41\) 4.44452i 0.694117i −0.937843 0.347058i \(-0.887181\pi\)
0.937843 0.347058i \(-0.112819\pi\)
\(42\) −1.87342 3.87538i −0.289074 0.597983i
\(43\) −5.15881 + 5.15881i −0.786711 + 0.786711i −0.980953 0.194243i \(-0.937775\pi\)
0.194243 + 0.980953i \(0.437775\pi\)
\(44\) −0.406622 0.704289i −0.0613005 0.106176i
\(45\) 1.06197 + 6.62361i 0.158309 + 0.987390i
\(46\) −1.52471 + 2.64087i −0.224806 + 0.389376i
\(47\) 6.79316 + 1.82022i 0.990885 + 0.265507i 0.717622 0.696433i \(-0.245231\pi\)
0.273263 + 0.961939i \(0.411897\pi\)
\(48\) 0.298131 0.841320i 0.0430315 0.121434i
\(49\) 6.99958 0.0762729i 0.999941 0.0108961i
\(50\) 4.37671 1.70348i 0.618960 0.240909i
\(51\) 7.20429 10.4775i 1.00880 1.46714i
\(52\) 2.20232 0.590109i 0.305406 0.0818334i
\(53\) 5.26849 1.41169i 0.723683 0.193910i 0.121869 0.992546i \(-0.461111\pi\)
0.601814 + 0.798636i \(0.294445\pi\)
\(54\) −4.68068 + 1.38320i −0.636960 + 0.188229i
\(55\) 1.59220 + 0.334560i 0.214692 + 0.0451121i
\(56\) 5.50845 + 5.44875i 0.736098 + 0.728120i
\(57\) 1.25244 + 0.443814i 0.165889 + 0.0587846i
\(58\) 3.69592 + 0.990320i 0.485298 + 0.130035i
\(59\) 0.807790 1.39913i 0.105165 0.182152i −0.808640 0.588303i \(-0.799796\pi\)
0.913806 + 0.406152i \(0.133130\pi\)
\(60\) −2.07358 3.79989i −0.267698 0.490564i
\(61\) 4.78904 + 8.29486i 0.613174 + 1.06205i 0.990702 + 0.136050i \(0.0434409\pi\)
−0.377528 + 0.925998i \(0.623226\pi\)
\(62\) −0.278866 + 0.278866i −0.0354160 + 0.0354160i
\(63\) 1.20230 7.84567i 0.151476 0.988461i
\(64\) 6.07747i 0.759683i
\(65\) −2.06135 + 4.06901i −0.255679 + 0.504699i
\(66\) −0.0931301 + 1.18009i −0.0114635 + 0.145259i
\(67\) −6.90351 + 1.84979i −0.843397 + 0.225988i −0.654550 0.756019i \(-0.727142\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(68\) −2.12368 + 7.92569i −0.257534 + 0.961131i
\(69\) −5.07578 + 2.41969i −0.611053 + 0.291296i
\(70\) −5.54697 + 0.333975i −0.662989 + 0.0399176i
\(71\) 7.06501i 0.838462i 0.907880 + 0.419231i \(0.137700\pi\)
−0.907880 + 0.419231i \(0.862300\pi\)
\(72\) 7.10979 5.16089i 0.837896 0.608217i
\(73\) −4.08458 15.2439i −0.478064 1.78416i −0.609445 0.792828i \(-0.708608\pi\)
0.131381 0.991332i \(-0.458059\pi\)
\(74\) −2.95870 + 5.12462i −0.343942 + 0.595726i
\(75\) 8.42987 + 1.98428i 0.973397 + 0.229125i
\(76\) −0.857449 −0.0983562
\(77\) −1.67236 0.953430i −0.190584 0.108653i
\(78\) −3.12817 1.10850i −0.354196 0.125513i
\(79\) 5.80845 3.35351i 0.653502 0.377300i −0.136294 0.990668i \(-0.543519\pi\)
0.789797 + 0.613369i \(0.210186\pi\)
\(80\) −0.858131 0.769055i −0.0959420 0.0859830i
\(81\) −8.55711 2.78851i −0.950790 0.309835i
\(82\) 1.08051 4.03251i 0.119322 0.445316i
\(83\) 1.83008 + 1.83008i 0.200877 + 0.200877i 0.800376 0.599499i \(-0.204633\pi\)
−0.599499 + 0.800376i \(0.704633\pi\)
\(84\) 0.959745 + 5.03124i 0.104717 + 0.548953i
\(85\) −8.97250 13.7463i −0.973204 1.49099i
\(86\) −5.93475 + 3.42643i −0.639960 + 0.369481i
\(87\) 4.58108 + 5.36609i 0.491143 + 0.575305i
\(88\) −0.551483 2.05816i −0.0587883 0.219401i
\(89\) −6.94977 12.0373i −0.736674 1.27596i −0.953985 0.299854i \(-0.903062\pi\)
0.217311 0.976102i \(-0.430271\pi\)
\(90\) −0.646746 + 6.26778i −0.0681730 + 0.660682i
\(91\) 3.79546 3.83704i 0.397872 0.402231i
\(92\) 2.56579 2.56579i 0.267502 0.267502i
\(93\) −0.715068 + 0.132371i −0.0741491 + 0.0137262i
\(94\) 5.72092 + 3.30298i 0.590068 + 0.340676i
\(95\) 1.14486 1.27746i 0.117460 0.131065i
\(96\) −5.27271 + 7.66830i −0.538143 + 0.782643i
\(97\) 5.62554 + 5.62554i 0.571187 + 0.571187i 0.932460 0.361273i \(-0.117658\pi\)
−0.361273 + 0.932460i \(0.617658\pi\)
\(98\) 6.36927 + 1.63247i 0.643393 + 0.164904i
\(99\) −1.37441 + 1.69577i −0.138134 + 0.170431i
\(100\) −5.55512 + 0.610029i −0.555512 + 0.0610029i
\(101\) −4.57480 2.64126i −0.455209 0.262815i 0.254818 0.966989i \(-0.417984\pi\)
−0.710028 + 0.704174i \(0.751318\pi\)
\(102\) 9.08364 7.75478i 0.899414 0.767838i
\(103\) −7.01482 1.87961i −0.691190 0.185204i −0.103909 0.994587i \(-0.533135\pi\)
−0.587281 + 0.809383i \(0.699802\pi\)
\(104\) 5.97381 0.585780
\(105\) −8.77719 5.28780i −0.856566 0.516037i
\(106\) 5.12330 0.497619
\(107\) −17.6912 4.74035i −1.71028 0.458267i −0.734783 0.678302i \(-0.762716\pi\)
−0.975492 + 0.220035i \(0.929383\pi\)
\(108\) 5.80586 0.148284i 0.558670 0.0142687i
\(109\) 5.47383 + 3.16032i 0.524298 + 0.302704i 0.738691 0.674044i \(-0.235444\pi\)
−0.214393 + 0.976747i \(0.568777\pi\)
\(110\) 1.36327 + 0.690626i 0.129982 + 0.0658486i
\(111\) −9.84958 + 4.69541i −0.934880 + 0.445668i
\(112\) 0.688143 + 1.17704i 0.0650234 + 0.111220i
\(113\) −7.98925 7.98925i −0.751566 0.751566i 0.223206 0.974771i \(-0.428348\pi\)
−0.974771 + 0.223206i \(0.928348\pi\)
\(114\) 1.02844 + 0.707153i 0.0963223 + 0.0662310i
\(115\) 0.396797 + 7.24845i 0.0370015 + 0.675921i
\(116\) −3.94302 2.27650i −0.366100 0.211368i
\(117\) −3.59494 4.95249i −0.332353 0.457858i
\(118\) 1.07305 1.07305i 0.0987824 0.0987824i
\(119\) 5.12917 + 18.7335i 0.470191 + 1.71730i
\(120\) −2.67102 11.0230i −0.243830 1.00625i
\(121\) −5.23530 9.06780i −0.475936 0.824346i
\(122\) 2.32853 + 8.69020i 0.210815 + 0.786774i
\(123\) 5.85478 4.99828i 0.527908 0.450679i
\(124\) 0.406407 0.234639i 0.0364964 0.0210712i
\(125\) 6.50831 9.09076i 0.582121 0.813102i
\(126\) 2.99821 6.82608i 0.267102 0.608116i
\(127\) −1.07524 1.07524i −0.0954126 0.0954126i 0.657789 0.753202i \(-0.271492\pi\)
−0.753202 + 0.657789i \(0.771492\pi\)
\(128\) 1.30372 4.86556i 0.115234 0.430059i
\(129\) −12.5973 0.994153i −1.10913 0.0875303i
\(130\) −2.85948 + 3.19068i −0.250793 + 0.279841i
\(131\) 9.65210 5.57264i 0.843308 0.486884i −0.0150794 0.999886i \(-0.504800\pi\)
0.858387 + 0.513002i \(0.171467\pi\)
\(132\) 0.470479 1.32768i 0.0409499 0.115560i
\(133\) −1.75221 + 1.02441i −0.151936 + 0.0888275i
\(134\) −6.71326 −0.579937
\(135\) −7.53103 + 8.84780i −0.648168 + 0.761498i
\(136\) −10.7493 + 18.6183i −0.921742 + 1.59650i
\(137\) 2.98501 + 11.1402i 0.255026 + 0.951771i 0.968076 + 0.250657i \(0.0806468\pi\)
−0.713050 + 0.701114i \(0.752687\pi\)
\(138\) −5.19351 + 0.961406i −0.442101 + 0.0818403i
\(139\) 1.33168i 0.112952i 0.998404 + 0.0564760i \(0.0179864\pi\)
−0.998404 + 0.0564760i \(0.982014\pi\)
\(140\) 6.47842 + 1.32446i 0.547526 + 0.111938i
\(141\) 5.24176 + 10.9957i 0.441436 + 0.926003i
\(142\) −1.71758 + 6.41009i −0.144136 + 0.537922i
\(143\) −1.43366 + 0.384149i −0.119889 + 0.0321241i
\(144\) 1.44355 0.553415i 0.120296 0.0461179i
\(145\) 8.65632 2.83490i 0.718868 0.235426i
\(146\) 14.8238i 1.22682i
\(147\) 7.97216 + 9.13480i 0.657533 + 0.753426i
\(148\) 4.97893 4.97893i 0.409265 0.409265i
\(149\) 0.650455 + 1.12662i 0.0532873 + 0.0922963i 0.891439 0.453141i \(-0.149697\pi\)
−0.838151 + 0.545438i \(0.816363\pi\)
\(150\) 7.16602 + 3.84973i 0.585103 + 0.314329i
\(151\) 1.58575 2.74659i 0.129046 0.223515i −0.794261 0.607577i \(-0.792142\pi\)
0.923307 + 0.384062i \(0.125475\pi\)
\(152\) −2.17004 0.581460i −0.176013 0.0471627i
\(153\) 21.9039 2.29267i 1.77083 0.185352i
\(154\) −1.28555 1.27162i −0.103592 0.102470i
\(155\) −0.193056 + 0.918770i −0.0155066 + 0.0737974i
\(156\) 3.25406 + 2.23749i 0.260534 + 0.179142i
\(157\) 4.17033 1.11744i 0.332829 0.0891812i −0.0885346 0.996073i \(-0.528218\pi\)
0.421363 + 0.906892i \(0.361552\pi\)
\(158\) 6.08529 1.63055i 0.484119 0.129719i
\(159\) 7.78454 + 5.35263i 0.617354 + 0.424491i
\(160\) 6.56683 + 10.0607i 0.519153 + 0.795366i
\(161\) 2.17785 8.30864i 0.171638 0.654812i
\(162\) −7.08596 4.61034i −0.556725 0.362223i
\(163\) 9.23320 + 2.47403i 0.723200 + 0.193781i 0.601599 0.798798i \(-0.294530\pi\)
0.121601 + 0.992579i \(0.461197\pi\)
\(164\) −2.48383 + 4.30211i −0.193954 + 0.335939i
\(165\) 1.34986 + 2.47365i 0.105086 + 0.192574i
\(166\) 1.21552 + 2.10534i 0.0943426 + 0.163406i
\(167\) 5.52186 5.52186i 0.427294 0.427294i −0.460411 0.887706i \(-0.652298\pi\)
0.887706 + 0.460411i \(0.152298\pi\)
\(168\) −0.982893 + 13.3839i −0.0758318 + 1.03259i
\(169\) 8.83880i 0.679908i
\(170\) −4.79889 14.6533i −0.368058 1.12386i
\(171\) 0.823845 + 2.14895i 0.0630010 + 0.164334i
\(172\) 7.87652 2.11051i 0.600579 0.160925i
\(173\) 3.46278 12.9233i 0.263271 0.982539i −0.700030 0.714114i \(-0.746830\pi\)
0.963300 0.268426i \(-0.0865034\pi\)
\(174\) 2.85186 + 5.98236i 0.216199 + 0.453522i
\(175\) −10.6232 + 7.88340i −0.803037 + 0.595929i
\(176\) 0.374957i 0.0282634i
\(177\) 2.75152 0.509352i 0.206817 0.0382852i
\(178\) −3.37912 12.6110i −0.253276 0.945238i
\(179\) 6.35437 11.0061i 0.474948 0.822633i −0.524641 0.851324i \(-0.675800\pi\)
0.999588 + 0.0286903i \(0.00913367\pi\)
\(180\) 2.67368 7.00487i 0.199284 0.522112i
\(181\) −9.56008 −0.710595 −0.355298 0.934753i \(-0.615620\pi\)
−0.355298 + 0.934753i \(0.615620\pi\)
\(182\) 4.37644 2.55863i 0.324404 0.189659i
\(183\) −5.54113 + 15.6370i −0.409612 + 1.15592i
\(184\) 8.23346 4.75359i 0.606979 0.350439i
\(185\) 0.769986 + 14.0656i 0.0566105 + 1.03413i
\(186\) −0.680963 0.0537403i −0.0499306 0.00394043i
\(187\) 1.38247 5.15946i 0.101096 0.377297i
\(188\) −5.55827 5.55827i −0.405379 0.405379i
\(189\) 11.6872 7.23939i 0.850121 0.526588i
\(190\) 1.34930 0.880716i 0.0978882 0.0638938i
\(191\) −4.05391 + 2.34053i −0.293331 + 0.169355i −0.639443 0.768839i \(-0.720835\pi\)
0.346112 + 0.938193i \(0.387502\pi\)
\(192\) −8.00587 + 6.83468i −0.577774 + 0.493251i
\(193\) 1.86008 + 6.94190i 0.133891 + 0.499689i 1.00000 0.000166726i \(-5.30705e-5\pi\)
−0.866109 + 0.499856i \(0.833386\pi\)
\(194\) 3.73643 + 6.47168i 0.268260 + 0.464640i
\(195\) −7.67830 + 1.86056i −0.549854 + 0.133238i
\(196\) −6.81794 3.83790i −0.486996 0.274136i
\(197\) −3.81705 + 3.81705i −0.271954 + 0.271954i −0.829886 0.557933i \(-0.811595\pi\)
0.557933 + 0.829886i \(0.311595\pi\)
\(198\) −1.65926 + 1.20444i −0.117919 + 0.0855956i
\(199\) −10.1820 5.87860i −0.721785 0.416723i 0.0936244 0.995608i \(-0.470155\pi\)
−0.815409 + 0.578885i \(0.803488\pi\)
\(200\) −14.4726 2.22322i −1.02337 0.157205i
\(201\) −10.2004 7.01375i −0.719479 0.494712i
\(202\) −3.50860 3.50860i −0.246864 0.246864i
\(203\) −10.7774 + 0.0587177i −0.756426 + 0.00412118i
\(204\) −12.8288 + 6.11565i −0.898197 + 0.428181i
\(205\) −3.09308 9.44466i −0.216030 0.659643i
\(206\) −5.90759 3.41075i −0.411601 0.237638i
\(207\) −8.89566 3.96519i −0.618291 0.275599i
\(208\) 1.01541 + 0.272077i 0.0704058 + 0.0188652i
\(209\) 0.558182 0.0386103
\(210\) −6.67803 6.93145i −0.460828 0.478316i
\(211\) 25.4378 1.75121 0.875606 0.483025i \(-0.160462\pi\)
0.875606 + 0.483025i \(0.160462\pi\)
\(212\) −5.88861 1.57785i −0.404432 0.108367i
\(213\) −9.30676 + 7.94527i −0.637689 + 0.544401i
\(214\) −14.8988 8.60184i −1.01846 0.588010i
\(215\) −7.37235 + 14.5527i −0.502790 + 0.992486i
\(216\) 14.7941 + 3.56184i 1.00661 + 0.242353i
\(217\) 0.550172 0.965030i 0.0373481 0.0655105i
\(218\) 4.19810 + 4.19810i 0.284331 + 0.284331i
\(219\) 15.4873 22.5238i 1.04654 1.52202i
\(220\) −1.35421 1.21364i −0.0913011 0.0818238i
\(221\) 12.9690 + 7.48766i 0.872389 + 0.503674i
\(222\) −10.0780 + 1.86561i −0.676393 + 0.125212i
\(223\) −7.63840 + 7.63840i −0.511505 + 0.511505i −0.914987 0.403482i \(-0.867800\pi\)
0.403482 + 0.914987i \(0.367800\pi\)
\(224\) −3.75396 13.7107i −0.250822 0.916087i
\(225\) 6.86627 + 13.3362i 0.457752 + 0.889080i
\(226\) −5.30638 9.19092i −0.352975 0.611371i
\(227\) −0.209579 0.782158i −0.0139102 0.0519137i 0.958622 0.284682i \(-0.0918881\pi\)
−0.972532 + 0.232769i \(0.925221\pi\)
\(228\) −0.964282 1.12952i −0.0638611 0.0748044i
\(229\) −14.0174 + 8.09297i −0.926299 + 0.534799i −0.885639 0.464374i \(-0.846279\pi\)
−0.0406596 + 0.999173i \(0.512946\pi\)
\(230\) −1.40216 + 6.67298i −0.0924556 + 0.440004i
\(231\) −0.624775 3.27523i −0.0411072 0.215495i
\(232\) −8.43527 8.43527i −0.553803 0.553803i
\(233\) −3.42317 + 12.7754i −0.224259 + 0.836946i 0.758441 + 0.651742i \(0.225961\pi\)
−0.982700 + 0.185204i \(0.940705\pi\)
\(234\) −2.05769 5.36736i −0.134515 0.350876i
\(235\) 15.7023 0.859581i 1.02431 0.0560729i
\(236\) −1.56382 + 0.902869i −0.101796 + 0.0587718i
\(237\) 10.9497 + 3.88016i 0.711263 + 0.252043i
\(238\) 0.0993966 + 18.2439i 0.00644292 + 1.18257i
\(239\) 0.0827799 0.00535459 0.00267729 0.999996i \(-0.499148\pi\)
0.00267729 + 0.999996i \(0.499148\pi\)
\(240\) 0.0480302 1.99529i 0.00310034 0.128796i
\(241\) −7.25921 + 12.5733i −0.467607 + 0.809919i −0.999315 0.0370088i \(-0.988217\pi\)
0.531708 + 0.846928i \(0.321550\pi\)
\(242\) −2.54551 9.49997i −0.163632 0.610681i
\(243\) −5.94996 14.4083i −0.381690 0.924290i
\(244\) 10.7055i 0.685347i
\(245\) 14.8211 5.03331i 0.946887 0.321567i
\(246\) 6.52718 3.11158i 0.416158 0.198387i
\(247\) −0.405030 + 1.51159i −0.0257714 + 0.0961803i
\(248\) 1.18765 0.318231i 0.0754160 0.0202077i
\(249\) −0.352674 + 4.46886i −0.0223498 + 0.283203i
\(250\) 8.11505 6.66581i 0.513241 0.421583i
\(251\) 16.4075i 1.03563i 0.855493 + 0.517815i \(0.173254\pi\)
−0.855493 + 0.517815i \(0.826746\pi\)
\(252\) −5.54835 + 6.92238i −0.349513 + 0.436069i
\(253\) −1.67028 + 1.67028i −0.105009 + 0.105009i
\(254\) −0.714167 1.23697i −0.0448108 0.0776146i
\(255\) 8.01760 27.2785i 0.502082 1.70824i
\(256\) 8.44320 14.6241i 0.527700 0.914004i
\(257\) 1.33133 + 0.356728i 0.0830459 + 0.0222521i 0.300103 0.953907i \(-0.402979\pi\)
−0.217057 + 0.976159i \(0.569646\pi\)
\(258\) −11.1878 3.96452i −0.696523 0.246820i
\(259\) 4.22612 16.1229i 0.262598 1.00183i
\(260\) 4.26927 2.78665i 0.264769 0.172821i
\(261\) −1.91692 + 12.0693i −0.118654 + 0.747073i
\(262\) 10.1121 2.70953i 0.624729 0.167396i
\(263\) −19.1314 + 5.12625i −1.17969 + 0.316098i −0.794805 0.606865i \(-0.792427\pi\)
−0.384888 + 0.922963i \(0.625760\pi\)
\(264\) 2.09103 3.04107i 0.128694 0.187165i
\(265\) 10.2132 6.66637i 0.627390 0.409512i
\(266\) −1.83883 + 0.503466i −0.112746 + 0.0308695i
\(267\) 8.04118 22.6921i 0.492112 1.38873i
\(268\) 7.71607 + 2.06752i 0.471334 + 0.126294i
\(269\) 0.835235 1.44667i 0.0509252 0.0882050i −0.839439 0.543454i \(-0.817116\pi\)
0.890364 + 0.455249i \(0.150450\pi\)
\(270\) −8.98390 + 6.19675i −0.546742 + 0.377122i
\(271\) −0.646739 1.12018i −0.0392866 0.0680464i 0.845714 0.533637i \(-0.179175\pi\)
−0.885000 + 0.465591i \(0.845842\pi\)
\(272\) −2.67509 + 2.67509i −0.162201 + 0.162201i
\(273\) 9.32290 + 0.684657i 0.564247 + 0.0414373i
\(274\) 10.8332i 0.654457i
\(275\) 3.61627 0.397116i 0.218069 0.0239470i
\(276\) 6.26540 + 0.494453i 0.377133 + 0.0297626i
\(277\) −11.3088 + 3.03017i −0.679477 + 0.182065i −0.582020 0.813174i \(-0.697738\pi\)
−0.0974572 + 0.995240i \(0.531071\pi\)
\(278\) −0.323746 + 1.20824i −0.0194170 + 0.0724653i
\(279\) −0.978534 0.793099i −0.0585833 0.0474816i
\(280\) 15.4975 + 7.74516i 0.926152 + 0.462862i
\(281\) 14.3020i 0.853186i 0.904444 + 0.426593i \(0.140286\pi\)
−0.904444 + 0.426593i \(0.859714\pi\)
\(282\) 2.08269 + 11.2507i 0.124023 + 0.669970i
\(283\) 2.70377 + 10.0906i 0.160722 + 0.599823i 0.998547 + 0.0538844i \(0.0171603\pi\)
−0.837825 + 0.545939i \(0.816173\pi\)
\(284\) 3.94829 6.83864i 0.234288 0.405799i
\(285\) 2.97031 + 0.0715005i 0.175946 + 0.00423533i
\(286\) −1.39415 −0.0824380
\(287\) 0.0640652 + 11.7589i 0.00378165 + 0.694107i
\(288\) −16.0311 + 1.67797i −0.944644 + 0.0988753i
\(289\) −31.9504 + 18.4466i −1.87943 + 1.08509i
\(290\) 8.54308 0.467668i 0.501667 0.0274624i
\(291\) −1.08410 + 13.7370i −0.0635509 + 0.805277i
\(292\) −4.56535 + 17.0381i −0.267167 + 0.997081i
\(293\) 9.37059 + 9.37059i 0.547436 + 0.547436i 0.925698 0.378262i \(-0.123478\pi\)
−0.378262 + 0.925698i \(0.623478\pi\)
\(294\) 5.01238 + 10.2261i 0.292328 + 0.596400i
\(295\) 0.742863 3.53534i 0.0432511 0.205836i
\(296\) 15.9771 9.22436i 0.928648 0.536155i
\(297\) −3.77950 + 0.0965300i −0.219309 + 0.00560124i
\(298\) 0.316265 + 1.18032i 0.0183207 + 0.0683738i
\(299\) −3.31123 5.73521i −0.191493 0.331676i
\(300\) −7.05085 6.63175i −0.407081 0.382884i
\(301\) 13.5744 13.7231i 0.782413 0.790985i
\(302\) 2.10647 2.10647i 0.121214 0.121214i
\(303\) −1.66545 8.99674i −0.0956774 0.516849i
\(304\) −0.342373 0.197669i −0.0196364 0.0113371i
\(305\) 15.9494 + 14.2938i 0.913262 + 0.818463i
\(306\) 20.4308 + 3.24493i 1.16795 + 0.185500i
\(307\) −16.7040 16.7040i −0.953350 0.953350i 0.0456091 0.998959i \(-0.485477\pi\)
−0.998959 + 0.0456091i \(0.985477\pi\)
\(308\) 1.08596 + 1.85749i 0.0618781 + 0.105840i
\(309\) −5.41280 11.3544i −0.307923 0.645932i
\(310\) −0.398522 + 0.786666i −0.0226346 + 0.0446796i
\(311\) −13.5200 7.80578i −0.766649 0.442625i 0.0650288 0.997883i \(-0.479286\pi\)
−0.831678 + 0.555258i \(0.812619\pi\)
\(312\) 6.71811 + 7.86932i 0.380338 + 0.445512i
\(313\) 15.8163 + 4.23797i 0.893991 + 0.239544i 0.676434 0.736504i \(-0.263525\pi\)
0.217557 + 0.976048i \(0.430191\pi\)
\(314\) 4.05540 0.228860
\(315\) −2.90513 17.5089i −0.163686 0.986513i
\(316\) −7.49647 −0.421709
\(317\) 23.2486 + 6.22945i 1.30577 + 0.349881i 0.843630 0.536924i \(-0.180414\pi\)
0.462143 + 0.886805i \(0.347081\pi\)
\(318\) 5.76163 + 6.74894i 0.323096 + 0.378462i
\(319\) 2.56683 + 1.48196i 0.143715 + 0.0829737i
\(320\) 4.22950 + 12.9147i 0.236436 + 0.721953i
\(321\) −13.6510 28.6357i −0.761922 1.59829i
\(322\) 3.99588 7.00897i 0.222681 0.390595i
\(323\) −3.98230 3.98230i −0.221581 0.221581i
\(324\) 6.72457 + 7.48133i 0.373587 + 0.415629i
\(325\) −1.54864 + 10.0813i −0.0859029 + 0.559207i
\(326\) 7.77582 + 4.48937i 0.430663 + 0.248643i
\(327\) 1.99274 + 10.7648i 0.110199 + 0.595293i
\(328\) −9.20347 + 9.20347i −0.508177 + 0.508177i
\(329\) −17.9990 4.71787i −0.992317 0.260104i
\(330\) 0.623356 + 2.57251i 0.0343146 + 0.141612i
\(331\) −4.82052 8.34938i −0.264960 0.458923i 0.702594 0.711591i \(-0.252025\pi\)
−0.967553 + 0.252668i \(0.918692\pi\)
\(332\) −0.748700 2.79418i −0.0410902 0.153351i
\(333\) −17.2621 7.69446i −0.945955 0.421654i
\(334\) 6.35241 3.66756i 0.347588 0.200680i
\(335\) −13.3827 + 8.73519i −0.731176 + 0.477255i
\(336\) −0.776641 + 2.23019i −0.0423692 + 0.121667i
\(337\) −1.92766 1.92766i −0.105006 0.105006i 0.652652 0.757658i \(-0.273656\pi\)
−0.757658 + 0.652652i \(0.773656\pi\)
\(338\) −2.14880 + 8.01945i −0.116880 + 0.436200i
\(339\) 1.53961 19.5089i 0.0836200 1.05958i
\(340\) 1.00289 + 18.3201i 0.0543892 + 0.993549i
\(341\) −0.264562 + 0.152745i −0.0143269 + 0.00827162i
\(342\) 0.225042 + 2.15003i 0.0121689 + 0.116260i
\(343\) −18.5178 + 0.302691i −0.999866 + 0.0163438i
\(344\) 21.3652 1.15193
\(345\) −9.10217 + 8.67426i −0.490044 + 0.467007i
\(346\) 6.28357 10.8835i 0.337807 0.585099i
\(347\) −7.09301 26.4715i −0.380773 1.42106i −0.844724 0.535202i \(-0.820235\pi\)
0.463951 0.885861i \(-0.346431\pi\)
\(348\) −1.43545 7.75430i −0.0769482 0.415674i
\(349\) 4.09834i 0.219379i 0.993966 + 0.109690i \(0.0349857\pi\)
−0.993966 + 0.109690i \(0.965014\pi\)
\(350\) −11.5550 + 4.57001i −0.617638 + 0.244277i
\(351\) 2.48108 10.3052i 0.132430 0.550049i
\(352\) −1.01181 + 3.77613i −0.0539297 + 0.201268i
\(353\) 28.5015 7.63696i 1.51698 0.406474i 0.598236 0.801320i \(-0.295869\pi\)
0.918747 + 0.394846i \(0.129202\pi\)
\(354\) 2.62028 + 0.206788i 0.139266 + 0.0109906i
\(355\) 4.91676 + 15.0132i 0.260955 + 0.796820i
\(356\) 15.5356i 0.823383i
\(357\) −18.9095 + 27.8242i −1.00079 + 1.47262i
\(358\) 8.44101 8.44101i 0.446121 0.446121i
\(359\) 14.3554 + 24.8643i 0.757650 + 1.31229i 0.944046 + 0.329814i \(0.106986\pi\)
−0.186396 + 0.982475i \(0.559681\pi\)
\(360\) 11.5168 15.9149i 0.606987 0.838788i
\(361\) −9.20574 + 15.9448i −0.484513 + 0.839200i
\(362\) −8.67386 2.32415i −0.455888 0.122155i
\(363\) 6.05746 17.0941i 0.317934 0.897206i
\(364\) −5.81819 + 1.59300i −0.304956 + 0.0834960i
\(365\) −19.2885 29.5508i −1.00961 1.54676i
\(366\) −8.82898 + 12.8403i −0.461498 + 0.671175i
\(367\) 29.6717 7.95050i 1.54885 0.415013i 0.619737 0.784810i \(-0.287239\pi\)
0.929113 + 0.369797i \(0.120573\pi\)
\(368\) 1.61600 0.433005i 0.0842397 0.0225720i
\(369\) 13.1685 + 2.09149i 0.685524 + 0.108879i
\(370\) −2.72089 + 12.9489i −0.141453 + 0.673184i
\(371\) −13.9186 + 3.81086i −0.722616 + 0.197850i
\(372\) 0.766133 + 0.271487i 0.0397222 + 0.0140760i
\(373\) 23.4885 + 6.29374i 1.21619 + 0.325877i 0.809188 0.587550i \(-0.199907\pi\)
0.407003 + 0.913427i \(0.366574\pi\)
\(374\) 2.50864 4.34509i 0.129719 0.224679i
\(375\) 19.2945 1.64999i 0.996363 0.0852050i
\(376\) −10.2977 17.8361i −0.531064 0.919829i
\(377\) −5.87579 + 5.87579i −0.302618 + 0.302618i
\(378\) 12.3638 3.72701i 0.635925 0.191697i
\(379\) 8.45766i 0.434441i −0.976123 0.217220i \(-0.930301\pi\)
0.976123 0.217220i \(-0.0696990\pi\)
\(380\) −1.82209 + 0.596726i −0.0934713 + 0.0306114i
\(381\) 0.207210 2.62564i 0.0106157 0.134516i
\(382\) −4.24712 + 1.13801i −0.217302 + 0.0582258i
\(383\) −2.64013 + 9.85308i −0.134904 + 0.503469i 0.865094 + 0.501610i \(0.167259\pi\)
−0.999998 + 0.00185953i \(0.999408\pi\)
\(384\) 7.87559 3.75438i 0.401899 0.191590i
\(385\) −4.21732 0.862199i −0.214934 0.0439417i
\(386\) 6.75059i 0.343596i
\(387\) −12.8572 17.7125i −0.653569 0.900375i
\(388\) −2.30145 8.58914i −0.116839 0.436048i
\(389\) −8.33093 + 14.4296i −0.422395 + 0.731609i −0.996173 0.0874014i \(-0.972144\pi\)
0.573778 + 0.819011i \(0.305477\pi\)
\(390\) −7.41885 0.178585i −0.375668 0.00904298i
\(391\) 23.8329 1.20528
\(392\) −14.6523 14.3364i −0.740054 0.724099i
\(393\) 18.1956 + 6.44779i 0.917844 + 0.325248i
\(394\) −4.39118 + 2.53525i −0.221224 + 0.127724i
\(395\) 10.0092 11.1685i 0.503619 0.561951i
\(396\) 2.27806 0.873341i 0.114477 0.0438871i
\(397\) 2.47392 9.23281i 0.124163 0.463381i −0.875646 0.482954i \(-0.839564\pi\)
0.999808 + 0.0195726i \(0.00623055\pi\)
\(398\) −7.80901 7.80901i −0.391430 0.391430i
\(399\) −3.31999 1.15615i −0.166207 0.0578800i
\(400\) −2.35875 1.03705i −0.117937 0.0518526i
\(401\) 17.1970 9.92869i 0.858777 0.495815i −0.00482553 0.999988i \(-0.501536\pi\)
0.863603 + 0.504173i \(0.168203\pi\)
\(402\) −7.54969 8.84340i −0.376544 0.441068i
\(403\) −0.221671 0.827288i −0.0110422 0.0412101i
\(404\) 2.95215 + 5.11327i 0.146875 + 0.254394i
\(405\) −20.1246 + 0.0295385i −0.999999 + 0.00146778i
\(406\) −9.79262 2.56683i −0.486000 0.127389i
\(407\) −3.24118 + 3.24118i −0.160659 + 0.160659i
\(408\) −36.6145 + 6.77795i −1.81269 + 0.335558i
\(409\) 22.7311 + 13.1238i 1.12398 + 0.648930i 0.942414 0.334448i \(-0.108550\pi\)
0.181566 + 0.983379i \(0.441883\pi\)
\(410\) −0.510259 9.32110i −0.0251999 0.460336i
\(411\) −11.3181 + 16.4604i −0.558281 + 0.811929i
\(412\) 5.73963 + 5.73963i 0.282771 + 0.282771i
\(413\) −2.11701 + 3.71335i −0.104171 + 0.182722i
\(414\) −7.10705 5.76024i −0.349293 0.283100i
\(415\) 5.16255 + 2.61533i 0.253420 + 0.128382i
\(416\) −9.49181 5.48010i −0.465374 0.268684i
\(417\) −1.75423 + 1.49760i −0.0859052 + 0.0733380i
\(418\) 0.506439 + 0.135700i 0.0247707 + 0.00663730i
\(419\) −23.9293 −1.16902 −0.584511 0.811386i \(-0.698714\pi\)
−0.584511 + 0.811386i \(0.698714\pi\)
\(420\) 5.54087 + 10.0235i 0.270367 + 0.489098i
\(421\) −9.89428 −0.482218 −0.241109 0.970498i \(-0.577511\pi\)
−0.241109 + 0.970498i \(0.577511\pi\)
\(422\) 23.0798 + 6.18420i 1.12350 + 0.301042i
\(423\) −8.58978 + 19.2707i −0.417649 + 0.936971i
\(424\) −13.8330 7.98647i −0.671788 0.387857i
\(425\) −28.6331 22.9668i −1.38891 1.11405i
\(426\) −10.3756 + 4.94617i −0.502700 + 0.239643i
\(427\) −12.7900 21.8768i −0.618951 1.05869i
\(428\) 14.4752 + 14.4752i 0.699687 + 0.699687i
\(429\) −2.11833 1.45656i −0.102274 0.0703233i
\(430\) −10.2269 + 11.4114i −0.493183 + 0.550306i
\(431\) −27.8066 16.0542i −1.33940 0.773302i −0.352680 0.935744i \(-0.614729\pi\)
−0.986718 + 0.162443i \(0.948063\pi\)
\(432\) 2.35242 + 1.27923i 0.113181 + 0.0615468i
\(433\) 13.5310 13.5310i 0.650257 0.650257i −0.302798 0.953055i \(-0.597921\pi\)
0.953055 + 0.302798i \(0.0979208\pi\)
\(434\) 0.733780 0.741819i 0.0352226 0.0356085i
\(435\) 13.4693 + 8.21489i 0.645802 + 0.393874i
\(436\) −3.53230 6.11812i −0.169166 0.293005i
\(437\) 0.644596 + 2.40567i 0.0308352 + 0.115079i
\(438\) 19.5274 16.6707i 0.933056 0.796558i
\(439\) −29.4491 + 17.0025i −1.40553 + 0.811483i −0.994953 0.100343i \(-0.968006\pi\)
−0.410577 + 0.911826i \(0.634673\pi\)
\(440\) −2.60425 3.98983i −0.124153 0.190208i
\(441\) −3.06786 + 20.7747i −0.146089 + 0.989272i
\(442\) 9.94645 + 9.94645i 0.473104 + 0.473104i
\(443\) 6.89265 25.7237i 0.327480 1.22217i −0.584316 0.811526i \(-0.698637\pi\)
0.911796 0.410644i \(-0.134696\pi\)
\(444\) 12.1580 + 0.959488i 0.576995 + 0.0455353i
\(445\) −23.1455 20.7430i −1.09720 0.983310i
\(446\) −8.78730 + 5.07335i −0.416091 + 0.240230i
\(447\) −0.752604 + 2.12384i −0.0355969 + 0.100454i
\(448\) −0.0876032 16.0792i −0.00413886 0.759672i
\(449\) −13.5069 −0.637430 −0.318715 0.947851i \(-0.603251\pi\)
−0.318715 + 0.947851i \(0.603251\pi\)
\(450\) 2.98760 + 13.7692i 0.140837 + 0.649086i
\(451\) 1.61692 2.80059i 0.0761378 0.131875i
\(452\) 3.26847 + 12.1981i 0.153736 + 0.573750i
\(453\) 5.40142 0.999893i 0.253781 0.0469791i
\(454\) 0.760603i 0.0356969i
\(455\) 5.39508 10.7951i 0.252925 0.506084i
\(456\) −1.67445 3.51251i −0.0784135 0.164488i
\(457\) 3.39846 12.6832i 0.158973 0.593297i −0.839759 0.542959i \(-0.817304\pi\)
0.998732 0.0503372i \(-0.0160296\pi\)
\(458\) −14.6855 + 3.93497i −0.686209 + 0.183869i
\(459\) 27.6532 + 26.2758i 1.29074 + 1.22645i
\(460\) 3.66672 7.23796i 0.170962 0.337471i
\(461\) 4.02367i 0.187401i 0.995600 + 0.0937006i \(0.0298696\pi\)
−0.995600 + 0.0937006i \(0.970130\pi\)
\(462\) 0.229385 3.12351i 0.0106720 0.145319i
\(463\) −12.2088 + 12.2088i −0.567392 + 0.567392i −0.931397 0.364005i \(-0.881409\pi\)
0.364005 + 0.931397i \(0.381409\pi\)
\(464\) −1.04961 1.81798i −0.0487270 0.0843977i
\(465\) −1.42741 + 0.778929i −0.0661945 + 0.0361220i
\(466\) −6.21168 + 10.7589i −0.287750 + 0.498398i
\(467\) 29.1344 + 7.80654i 1.34818 + 0.361244i 0.859462 0.511199i \(-0.170798\pi\)
0.488717 + 0.872442i \(0.337465\pi\)
\(468\) 0.712051 + 6.80285i 0.0329146 + 0.314462i
\(469\) 18.2380 4.99352i 0.842154 0.230579i
\(470\) 14.4557 + 3.03750i 0.666791 + 0.140109i
\(471\) 6.16193 + 4.23693i 0.283927 + 0.195227i
\(472\) −4.56998 + 1.22452i −0.210350 + 0.0563632i
\(473\) −5.12746 + 1.37390i −0.235761 + 0.0631719i
\(474\) 8.99140 + 6.18247i 0.412989 + 0.283970i
\(475\) 1.54381 3.51137i 0.0708351 0.161113i
\(476\) 5.50441 20.9997i 0.252294 0.962520i
\(477\) 1.70340 + 16.2741i 0.0779935 + 0.745141i
\(478\) 0.0751063 + 0.0201247i 0.00343528 + 0.000920481i
\(479\) 6.48360 11.2299i 0.296243 0.513108i −0.679030 0.734110i \(-0.737599\pi\)
0.975273 + 0.221002i \(0.0709328\pi\)
\(480\) −5.86795 + 19.9647i −0.267834 + 0.911259i
\(481\) −6.42545 11.1292i −0.292975 0.507448i
\(482\) −9.64299 + 9.64299i −0.439226 + 0.439226i
\(483\) 13.3942 6.47496i 0.609457 0.294621i
\(484\) 11.7030i 0.531955i
\(485\) 15.8693 + 8.03935i 0.720590 + 0.365048i
\(486\) −1.89560 14.5191i −0.0859862 0.658601i
\(487\) 28.1934 7.55441i 1.27757 0.342323i 0.444641 0.895709i \(-0.353331\pi\)
0.832925 + 0.553386i \(0.186665\pi\)
\(488\) 7.25967 27.0935i 0.328630 1.22646i
\(489\) 7.12455 + 14.9452i 0.322183 + 0.675846i
\(490\) 14.6709 0.963557i 0.662762 0.0435291i
\(491\) 17.3154i 0.781432i −0.920511 0.390716i \(-0.872227\pi\)
0.920511 0.390716i \(-0.127773\pi\)
\(492\) −8.46048 + 1.56618i −0.381428 + 0.0706087i
\(493\) −7.73989 28.8857i −0.348587 1.30094i
\(494\) −0.734968 + 1.27300i −0.0330678 + 0.0572750i
\(495\) −1.74051 + 4.56003i −0.0782300 + 0.204958i
\(496\) 0.216367 0.00971516
\(497\) −0.101838 18.6920i −0.00456806 0.838450i
\(498\) −1.40641 + 3.96886i −0.0630227 + 0.177849i
\(499\) −14.5814 + 8.41859i −0.652754 + 0.376868i −0.789511 0.613737i \(-0.789666\pi\)
0.136756 + 0.990605i \(0.456332\pi\)
\(500\) −11.3802 + 5.16230i −0.508937 + 0.230865i
\(501\) 13.4838 + 1.06412i 0.602413 + 0.0475412i
\(502\) −3.98883 + 14.8865i −0.178030 + 0.664417i
\(503\) −2.89757 2.89757i −0.129196 0.129196i 0.639552 0.768748i \(-0.279120\pi\)
−0.768748 + 0.639552i \(0.779120\pi\)
\(504\) −18.7361 + 13.7567i −0.834570 + 0.612773i
\(505\) −11.5596 2.42897i −0.514397 0.108088i
\(506\) −1.92151 + 1.10938i −0.0854213 + 0.0493180i
\(507\) −11.6434 + 9.94006i −0.517101 + 0.441454i
\(508\) 0.439891 + 1.64170i 0.0195170 + 0.0728385i
\(509\) 1.72948 + 2.99555i 0.0766579 + 0.132775i 0.901806 0.432141i \(-0.142242\pi\)
−0.825148 + 0.564916i \(0.808908\pi\)
\(510\) 13.9060 22.8006i 0.615770 1.00963i
\(511\) 11.0264 + 40.2720i 0.487778 + 1.78153i
\(512\) 4.09210 4.09210i 0.180847 0.180847i
\(513\) −1.90433 + 3.50195i −0.0840782 + 0.154615i
\(514\) 1.12119 + 0.647319i 0.0494536 + 0.0285520i
\(515\) −16.2147 + 0.887628i −0.714503 + 0.0391136i
\(516\) 11.6381 + 8.00231i 0.512337 + 0.352282i
\(517\) 3.61832 + 3.61832i 0.159134 + 0.159134i
\(518\) 7.75401 13.6009i 0.340692 0.597591i
\(519\) 20.9181 9.97191i 0.918204 0.437718i
\(520\) 12.6944 4.15736i 0.556687 0.182312i
\(521\) 31.2875 + 18.0638i 1.37073 + 0.791392i 0.991020 0.133714i \(-0.0426903\pi\)
0.379710 + 0.925105i \(0.376024\pi\)
\(522\) −4.67340 + 10.4845i −0.204549 + 0.458894i
\(523\) −4.71576 1.26359i −0.206206 0.0552527i 0.154237 0.988034i \(-0.450708\pi\)
−0.360443 + 0.932781i \(0.617375\pi\)
\(524\) −12.4571 −0.544192
\(525\) −22.3316 5.12833i −0.974631 0.223818i
\(526\) −18.6042 −0.811181
\(527\) 2.97724 + 0.797749i 0.129691 + 0.0347505i
\(528\) 0.493932 0.421674i 0.0214956 0.0183510i
\(529\) 10.7911 + 6.23025i 0.469179 + 0.270881i
\(530\) 10.8871 3.56547i 0.472905 0.154874i
\(531\) 3.76531 + 3.05177i 0.163401 + 0.132436i
\(532\) 2.26856 0.0123596i 0.0983547 0.000535858i
\(533\) 6.41090 + 6.41090i 0.277687 + 0.277687i
\(534\) 12.8124 18.6336i 0.554449 0.806356i
\(535\) −40.8930 + 2.23858i −1.76796 + 0.0967822i
\(536\) 18.1259 + 10.4650i 0.782918 + 0.452018i
\(537\) 21.6444 4.00675i 0.934026 0.172904i
\(538\) 1.10951 1.10951i 0.0478343 0.0478343i
\(539\) 4.43834 + 2.49839i 0.191173 + 0.107613i
\(540\) 12.2343 4.35559i 0.526482 0.187435i
\(541\) 16.1283 + 27.9350i 0.693408 + 1.20102i 0.970714 + 0.240237i \(0.0772251\pi\)
−0.277306 + 0.960782i \(0.589442\pi\)
\(542\) −0.314458 1.17357i −0.0135071 0.0504093i
\(543\) −10.7512 12.5935i −0.461378 0.540440i
\(544\) 34.1591 19.7218i 1.46456 0.845564i
\(545\) 13.8313 + 2.90630i 0.592469 + 0.124492i
\(546\) 8.29222 + 2.88768i 0.354874 + 0.123581i
\(547\) 21.2554 + 21.2554i 0.908817 + 0.908817i 0.996177 0.0873598i \(-0.0278430\pi\)
−0.0873598 + 0.996177i \(0.527843\pi\)
\(548\) 3.33635 12.4514i 0.142522 0.531899i
\(549\) −26.8302 + 10.2859i −1.14508 + 0.438991i
\(550\) 3.37759 + 0.518849i 0.144021 + 0.0221238i
\(551\) 2.70635 1.56251i 0.115294 0.0665653i
\(552\) 15.5212 + 5.50011i 0.660627 + 0.234100i
\(553\) −15.3192 + 8.95616i −0.651437 + 0.380854i
\(554\) −10.9971 −0.467222
\(555\) −17.6628 + 16.8324i −0.749744 + 0.714497i
\(556\) 0.744214 1.28902i 0.0315617 0.0546665i
\(557\) 1.97731 + 7.37940i 0.0837811 + 0.312675i 0.995081 0.0990688i \(-0.0315864\pi\)
−0.911299 + 0.411744i \(0.864920\pi\)
\(558\) −0.695014 0.957470i −0.0294223 0.0405330i
\(559\) 14.8824i 0.629459i
\(560\) 2.28145 + 2.02233i 0.0964090 + 0.0854590i
\(561\) 8.35130 3.98116i 0.352592 0.168085i
\(562\) −3.47696 + 12.9762i −0.146667 + 0.547368i
\(563\) 6.32147 1.69383i 0.266418 0.0713866i −0.123137 0.992390i \(-0.539295\pi\)
0.389555 + 0.921003i \(0.372629\pi\)
\(564\) 1.07113 13.5727i 0.0451029 0.571515i
\(565\) −22.5372 11.4173i −0.948149 0.480329i
\(566\) 9.81251i 0.412450i
\(567\) 22.6799 + 7.25426i 0.952464 + 0.304650i
\(568\) 14.6298 14.6298i 0.613855 0.613855i
\(569\) −10.0777 17.4551i −0.422481 0.731758i 0.573701 0.819065i \(-0.305507\pi\)
−0.996181 + 0.0873070i \(0.972174\pi\)
\(570\) 2.67758 + 0.786986i 0.112151 + 0.0329632i
\(571\) 8.94741 15.4974i 0.374438 0.648545i −0.615805 0.787898i \(-0.711169\pi\)
0.990243 + 0.139354i \(0.0445025\pi\)
\(572\) 1.60241 + 0.429364i 0.0670001 + 0.0179526i
\(573\) −7.64219 2.70809i −0.319257 0.113132i
\(574\) −2.80059 + 10.6844i −0.116894 + 0.445960i
\(575\) 5.88762 + 15.1269i 0.245531 + 0.630835i
\(576\) −18.0067 2.85992i −0.750279 0.119163i
\(577\) −13.7842 + 3.69346i −0.573844 + 0.153761i −0.534059 0.845447i \(-0.679334\pi\)
−0.0397848 + 0.999208i \(0.512667\pi\)
\(578\) −33.4731 + 8.96910i −1.39230 + 0.373066i
\(579\) −7.05276 + 10.2571i −0.293103 + 0.426271i
\(580\) −9.96326 2.09353i −0.413702 0.0869290i
\(581\) −4.86824 4.81548i −0.201969 0.199780i
\(582\) −4.32321 + 12.2000i −0.179203 + 0.505707i
\(583\) 3.83337 + 1.02715i 0.158762 + 0.0425401i
\(584\) −23.1081 + 40.0243i −0.956219 + 1.65622i
\(585\) −11.0859 8.02227i −0.458345 0.331680i
\(586\) 6.22385 + 10.7800i 0.257105 + 0.445319i
\(587\) 3.21441 3.21441i 0.132673 0.132673i −0.637652 0.770325i \(-0.720094\pi\)
0.770325 + 0.637652i \(0.220094\pi\)
\(588\) −2.61173 13.2974i −0.107706 0.548375i
\(589\) 0.322096i 0.0132717i
\(590\) 1.53348 3.02702i 0.0631323 0.124620i
\(591\) −9.32085 0.735583i −0.383409 0.0302579i
\(592\) 3.13585 0.840248i 0.128883 0.0345340i
\(593\) −10.2065 + 38.0911i −0.419130 + 1.56421i 0.357287 + 0.933995i \(0.383702\pi\)
−0.776417 + 0.630219i \(0.782965\pi\)
\(594\) −3.45261 0.831254i −0.141662 0.0341068i
\(595\) 23.9368 + 36.2393i 0.981313 + 1.48567i
\(596\) 1.45403i 0.0595594i
\(597\) −3.70675 20.0239i −0.151707 0.819522i
\(598\) −1.60999 6.00855i −0.0658373 0.245708i
\(599\) 22.6620 39.2518i 0.925945 1.60378i 0.135911 0.990721i \(-0.456604\pi\)
0.790034 0.613063i \(-0.210063\pi\)
\(600\) −13.3472 21.5651i −0.544896 0.880390i
\(601\) −10.2265 −0.417148 −0.208574 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(602\) 15.6522 9.15089i 0.637938 0.372962i
\(603\) −2.23204 21.3246i −0.0908955 0.868405i
\(604\) −3.06988 + 1.77239i −0.124912 + 0.0721177i
\(605\) −17.4356 15.6258i −0.708860 0.635278i
\(606\) 0.676141 8.56763i 0.0274664 0.348036i
\(607\) 9.10857 33.9936i 0.369705 1.37976i −0.491223 0.871034i \(-0.663450\pi\)
0.860929 0.508725i \(-0.169883\pi\)
\(608\) 2.91458 + 2.91458i 0.118202 + 0.118202i
\(609\) −12.1976 14.1311i −0.494270 0.572621i
\(610\) 10.9959 + 16.8463i 0.445213 + 0.682086i
\(611\) −12.4242 + 7.17311i −0.502629 + 0.290193i
\(612\) −22.4834 10.0218i −0.908837 0.405109i
\(613\) −1.33856 4.99557i −0.0540639 0.201769i 0.933611 0.358288i \(-0.116639\pi\)
−0.987675 + 0.156519i \(0.949973\pi\)
\(614\) −11.0947 19.2165i −0.447744 0.775515i
\(615\) 8.96302 14.6959i 0.361424 0.592597i
\(616\) 1.48873 + 5.43736i 0.0599828 + 0.219077i
\(617\) −21.2024 + 21.2024i −0.853575 + 0.853575i −0.990572 0.136996i \(-0.956255\pi\)
0.136996 + 0.990572i \(0.456255\pi\)
\(618\) −2.15065 11.6178i −0.0865117 0.467336i
\(619\) 12.7897 + 7.38415i 0.514063 + 0.296794i 0.734502 0.678606i \(-0.237416\pi\)
−0.220439 + 0.975401i \(0.570749\pi\)
\(620\) 0.700327 0.781442i 0.0281258 0.0313835i
\(621\) −4.78065 16.1775i −0.191841 0.649181i
\(622\) −10.3690 10.3690i −0.415761 0.415761i
\(623\) 18.5606 + 31.7472i 0.743614 + 1.27192i
\(624\) 0.783512 + 1.64358i 0.0313656 + 0.0657957i
\(625\) 7.50370 23.8473i 0.300148 0.953893i
\(626\) 13.3199 + 7.69022i 0.532368 + 0.307363i
\(627\) 0.627728 + 0.735295i 0.0250690 + 0.0293649i
\(628\) −4.66119 1.24896i −0.186002 0.0498391i
\(629\) 46.2478 1.84402
\(630\) 1.62076 16.5921i 0.0645725 0.661044i
\(631\) −34.8644 −1.38793 −0.693965 0.720009i \(-0.744138\pi\)
−0.693965 + 0.720009i \(0.744138\pi\)
\(632\) −18.9721 5.08356i −0.754670 0.202213i
\(633\) 28.6072 + 33.5094i 1.13704 + 1.33188i
\(634\) 19.5791 + 11.3040i 0.777583 + 0.448938i
\(635\) −3.03321 1.53661i −0.120369 0.0609786i
\(636\) −4.54379 9.53153i −0.180173 0.377950i
\(637\) −9.98638 + 10.2064i −0.395675 + 0.404393i
\(638\) 1.96860 + 1.96860i 0.0779377 + 0.0779377i
\(639\) −20.9327 3.32464i −0.828083 0.131521i
\(640\) −0.615670 11.2467i −0.0243365 0.444564i
\(641\) −31.5849 18.2355i −1.24753 0.720260i −0.276912 0.960895i \(-0.589311\pi\)
−0.970616 + 0.240635i \(0.922644\pi\)
\(642\) −5.42389 29.2998i −0.214064 1.15637i
\(643\) −23.1512 + 23.1512i −0.912995 + 0.912995i −0.996507 0.0835116i \(-0.973386\pi\)
0.0835116 + 0.996507i \(0.473386\pi\)
\(644\) −6.75136 + 6.82533i −0.266041 + 0.268956i
\(645\) −27.4612 + 6.65426i −1.08128 + 0.262011i
\(646\) −2.64500 4.58128i −0.104066 0.180248i
\(647\) 2.76815 + 10.3309i 0.108827 + 0.406148i 0.998751 0.0499604i \(-0.0159095\pi\)
−0.889924 + 0.456109i \(0.849243\pi\)
\(648\) 11.9453 + 23.4939i 0.469256 + 0.922929i
\(649\) 1.01801 0.587749i 0.0399605 0.0230712i
\(650\) −3.85594 + 8.77024i −0.151242 + 0.343997i
\(651\) 1.88996 0.360523i 0.0740733 0.0141300i
\(652\) −7.55475 7.55475i −0.295867 0.295867i
\(653\) 0.194929 0.727486i 0.00762817 0.0284687i −0.962007 0.273025i \(-0.911976\pi\)
0.969635 + 0.244557i \(0.0786424\pi\)
\(654\) −0.809015 + 10.2513i −0.0316350 + 0.400859i
\(655\) 16.6327 18.5591i 0.649892 0.725166i
\(656\) −1.98355 + 1.14520i −0.0774445 + 0.0447126i
\(657\) 47.0876 4.92864i 1.83706 0.192284i
\(658\) −15.1835 8.65626i −0.591916 0.337456i
\(659\) 7.95212 0.309771 0.154885 0.987932i \(-0.450499\pi\)
0.154885 + 0.987932i \(0.450499\pi\)
\(660\) 0.0757963 3.14877i 0.00295037 0.122566i
\(661\) 11.3090 19.5878i 0.439870 0.761877i −0.557809 0.829969i \(-0.688358\pi\)
0.997679 + 0.0680919i \(0.0216911\pi\)
\(662\) −2.34383 8.74731i −0.0910957 0.339974i
\(663\) 4.72134 + 25.5047i 0.183362 + 0.990520i
\(664\) 7.57926i 0.294132i
\(665\) −3.01056 + 3.39630i −0.116744 + 0.131703i
\(666\) −13.7913 11.1778i −0.534401 0.433130i
\(667\) −3.42277 + 12.7740i −0.132530 + 0.494610i
\(668\) −8.43084 + 2.25904i −0.326199 + 0.0874048i
\(669\) −18.6522 1.47199i −0.721135 0.0569106i
\(670\) −14.2658 + 4.67197i −0.551134 + 0.180494i
\(671\) 6.96903i 0.269037i
\(672\) 13.8395 20.3641i 0.533871 0.785563i
\(673\) 19.5657 19.5657i 0.754203 0.754203i −0.221058 0.975261i \(-0.570951\pi\)
0.975261 + 0.221058i \(0.0709509\pi\)
\(674\) −1.28033 2.21760i −0.0493165 0.0854187i
\(675\) −9.84606 + 24.0428i −0.378975 + 0.925407i
\(676\) 4.93958 8.55560i 0.189984 0.329062i
\(677\) −41.5349 11.1292i −1.59632 0.427731i −0.652388 0.757885i \(-0.726233\pi\)
−0.943927 + 0.330154i \(0.892899\pi\)
\(678\) 6.13971 17.3262i 0.235794 0.665408i
\(679\) −14.9647 14.8025i −0.574291 0.568067i
\(680\) −9.88528 + 47.0448i −0.379083 + 1.80409i
\(681\) 0.794649 1.15569i 0.0304510 0.0442861i
\(682\) −0.277171 + 0.0742679i −0.0106134 + 0.00284386i
\(683\) 40.7282 10.9131i 1.55842 0.417578i 0.626258 0.779616i \(-0.284586\pi\)
0.932163 + 0.362039i \(0.117919\pi\)
\(684\) 0.403496 2.54050i 0.0154281 0.0971386i
\(685\) 14.0960 + 21.5957i 0.538580 + 0.825129i
\(686\) −16.8748 4.22723i −0.644282 0.161397i
\(687\) −26.4248 9.36392i −1.00817 0.357256i
\(688\) 3.63158 + 0.973078i 0.138453 + 0.0370982i
\(689\) −5.56316 + 9.63568i −0.211940 + 0.367090i
\(690\) −10.3672 + 5.65733i −0.394673 + 0.215371i
\(691\) 3.78240 + 6.55130i 0.143889 + 0.249223i 0.928958 0.370185i \(-0.120706\pi\)
−0.785069 + 0.619409i \(0.787372\pi\)
\(692\) −10.5740 + 10.5740i −0.401965 + 0.401965i
\(693\) 3.61186 4.50633i 0.137203 0.171181i
\(694\) 25.7420i 0.977151i
\(695\) 0.926762 + 2.82985i 0.0351541 + 0.107342i
\(696\) 1.62556 20.5981i 0.0616167 0.780768i
\(697\) −31.5163 + 8.44476i −1.19376 + 0.319868i
\(698\) −0.996350 + 3.71843i −0.0377124 + 0.140745i
\(699\) −20.6788 + 9.85782i −0.782143 + 0.372857i
\(700\) 14.6885 1.69403i 0.555172 0.0640285i
\(701\) 39.5039i 1.49204i −0.665923 0.746020i \(-0.731962\pi\)
0.665923 0.746020i \(-0.268038\pi\)
\(702\) 4.75638 8.74671i 0.179518 0.330123i
\(703\) 1.25084 + 4.66820i 0.0471764 + 0.176065i
\(704\) −2.21099 + 3.82954i −0.0833298 + 0.144331i
\(705\) 18.7911 + 19.7180i 0.707712 + 0.742624i
\(706\) 27.7161 1.04311
\(707\) 12.1417 + 6.92207i 0.456634 + 0.260331i
\(708\) −2.94801 1.04466i −0.110793 0.0392607i
\(709\) 17.8431 10.3017i 0.670112 0.386889i −0.126007 0.992029i \(-0.540216\pi\)
0.796119 + 0.605140i \(0.206883\pi\)
\(710\) 0.811108 + 14.8168i 0.0304403 + 0.556066i
\(711\) 7.20267 + 18.7877i 0.270121 + 0.704595i
\(712\) −10.5351 + 39.3175i −0.394819 + 1.47349i
\(713\) −0.963825 0.963825i −0.0360955 0.0360955i
\(714\) −23.9209 + 20.6479i −0.895218 + 0.772727i
\(715\) −2.77921 + 1.81405i −0.103937 + 0.0678417i
\(716\) −12.3015 + 7.10230i −0.459730 + 0.265425i
\(717\) 0.0930938 + 0.109046i 0.00347665 + 0.00407241i
\(718\) 6.97990 + 26.0494i 0.260488 + 0.972153i
\(719\) 3.53101 + 6.11588i 0.131684 + 0.228084i 0.924326 0.381604i \(-0.124628\pi\)
−0.792642 + 0.609688i \(0.791295\pi\)
\(720\) 2.68242 2.18063i 0.0999680 0.0812671i
\(721\) 18.5863 + 4.87180i 0.692189 + 0.181435i
\(722\) −12.2287 + 12.2287i −0.455106 + 0.455106i
\(723\) −24.7265 + 4.57730i −0.919590 + 0.170231i
\(724\) 9.25377 + 5.34267i 0.343914 + 0.198559i
\(725\) 16.4219 12.0484i 0.609894 0.447467i
\(726\) 9.65169 14.0368i 0.358208 0.520955i
\(727\) −8.73967 8.73967i −0.324136 0.324136i 0.526215 0.850351i \(-0.323611\pi\)
−0.850351 + 0.526215i \(0.823611\pi\)
\(728\) −15.8050 + 0.0861090i −0.585771 + 0.00319141i
\(729\) 12.2888 24.0413i 0.455140 0.890420i
\(730\) −10.3163 31.5007i −0.381825 1.16589i
\(731\) 46.3833 + 26.7794i 1.71555 + 0.990472i
\(732\) 14.1023 12.0393i 0.521237 0.444985i
\(733\) 38.7958 + 10.3953i 1.43296 + 0.383959i 0.890061 0.455841i \(-0.150662\pi\)
0.542895 + 0.839801i \(0.317328\pi\)
\(734\) 28.8540 1.06502
\(735\) 23.2981 + 13.8635i 0.859365 + 0.511363i
\(736\) −17.4429 −0.642954
\(737\) −5.02300 1.34591i −0.185025 0.0495772i
\(738\) 11.4393 + 5.09901i 0.421087 + 0.187697i
\(739\) −19.1703 11.0680i −0.705192 0.407143i 0.104086 0.994568i \(-0.466808\pi\)
−0.809278 + 0.587426i \(0.800141\pi\)
\(740\) 7.11529 14.0453i 0.261563 0.516315i
\(741\) −2.44672 + 1.16638i −0.0898825 + 0.0428481i
\(742\) −13.5548 + 0.0738495i −0.497612 + 0.00271110i
\(743\) −24.6420 24.6420i −0.904028 0.904028i 0.0917535 0.995782i \(-0.470753\pi\)
−0.995782 + 0.0917535i \(0.970753\pi\)
\(744\) 1.75483 + 1.20662i 0.0643353 + 0.0442368i
\(745\) 2.16628 + 1.94141i 0.0793662 + 0.0711278i
\(746\) 19.7811 + 11.4206i 0.724237 + 0.418139i
\(747\) −6.28347 + 4.56108i −0.229900 + 0.166881i
\(748\) −4.22155 + 4.22155i −0.154355 + 0.154355i
\(749\) 46.8742 + 12.2866i 1.71275 + 0.448942i
\(750\) 17.9070 + 3.19366i 0.653872 + 0.116616i
\(751\) −8.99819 15.5853i −0.328349 0.568717i 0.653836 0.756637i \(-0.273159\pi\)
−0.982184 + 0.187920i \(0.939825\pi\)
\(752\) −0.938019 3.50073i −0.0342060 0.127659i
\(753\) −21.6136 + 18.4517i −0.787644 + 0.672419i
\(754\) −6.75957 + 3.90264i −0.246169 + 0.142126i
\(755\) 1.45829 6.94012i 0.0530726 0.252577i
\(756\) −15.3585 + 0.476006i −0.558584 + 0.0173122i
\(757\) 22.1895 + 22.1895i 0.806492 + 0.806492i 0.984101 0.177609i \(-0.0568362\pi\)
−0.177609 + 0.984101i \(0.556836\pi\)
\(758\) 2.05614 7.67364i 0.0746825 0.278719i
\(759\) −4.07865 0.321879i −0.148046 0.0116835i
\(760\) −5.01602 + 0.274589i −0.181950 + 0.00996037i
\(761\) −19.5072 + 11.2625i −0.707135 + 0.408265i −0.809999 0.586431i \(-0.800533\pi\)
0.102864 + 0.994695i \(0.467199\pi\)
\(762\) 0.826322 2.33187i 0.0299345 0.0844746i
\(763\) −14.5277 8.28239i −0.525939 0.299843i
\(764\) 5.23203 0.189288
\(765\) 44.9506 20.1156i 1.62519 0.727281i
\(766\) −4.79077 + 8.29786i −0.173098 + 0.299814i
\(767\) 0.852970 + 3.18333i 0.0307990 + 0.114943i
\(768\) 28.7595 5.32386i 1.03777 0.192108i
\(769\) 26.8027i 0.966531i 0.875474 + 0.483265i \(0.160549\pi\)
−0.875474 + 0.483265i \(0.839451\pi\)
\(770\) −3.61677 1.80755i −0.130339 0.0651395i
\(771\) 1.02728 + 2.15494i 0.0369967 + 0.0776082i
\(772\) 2.07901 7.75899i 0.0748253 0.279252i
\(773\) −23.2480 + 6.22929i −0.836174 + 0.224052i −0.651405 0.758730i \(-0.725820\pi\)
−0.184768 + 0.982782i \(0.559153\pi\)
\(774\) −7.35928 19.1962i −0.264524 0.689995i
\(775\) 0.229154 + 2.08675i 0.00823145 + 0.0749583i
\(776\) 23.2981i 0.836355i
\(777\) 25.9915 12.5647i 0.932439 0.450755i
\(778\) −11.0666 + 11.0666i −0.396758 + 0.396758i
\(779\) −1.70481 2.95282i −0.0610812 0.105796i
\(780\) 8.47206 + 2.49008i 0.303348 + 0.0891592i
\(781\) −2.57026 + 4.45182i −0.0919711 + 0.159299i
\(782\) 21.6236 + 5.79402i 0.773258 + 0.207194i
\(783\) −18.0547 + 11.0479i −0.645224 + 0.394821i
\(784\) −1.83759 3.10420i −0.0656284 0.110864i
\(785\) 8.08435 5.27683i 0.288543 0.188338i
\(786\) 14.9413 + 10.2736i 0.532939 + 0.366447i
\(787\) −25.6646 + 6.87680i −0.914844 + 0.245132i −0.685380 0.728186i \(-0.740364\pi\)
−0.229464 + 0.973317i \(0.573697\pi\)
\(788\) 5.82792 1.56159i 0.207611 0.0556292i
\(789\) −28.2679 19.4369i −1.00636 0.691973i
\(790\) 11.7966 7.69988i 0.419703 0.273949i
\(791\) 21.2524 + 21.0221i 0.755649 + 0.747460i
\(792\) 6.35757 0.665444i 0.225906 0.0236455i
\(793\) −18.8726 5.05690i −0.670186 0.179576i
\(794\) 4.48918 7.77549i 0.159315 0.275942i
\(795\) 20.2673 + 5.95690i 0.718807 + 0.211269i
\(796\) 6.57053 + 11.3805i 0.232886 + 0.403371i
\(797\) 19.6457 19.6457i 0.695888 0.695888i −0.267633 0.963521i \(-0.586241\pi\)
0.963521 + 0.267633i \(0.0862415\pi\)
\(798\) −2.73115 1.85610i −0.0966817 0.0657052i
\(799\) 51.6292i 1.82651i
\(800\) 20.9561 + 16.8090i 0.740911 + 0.594288i
\(801\) 38.9354 14.9267i 1.37572 0.527409i
\(802\) 18.0166 4.82754i 0.636189 0.170466i
\(803\) 2.97195 11.0915i 0.104878 0.391410i
\(804\) 5.95390 + 12.4895i 0.209978 + 0.440472i
\(805\) −1.15429 19.1716i −0.0406835 0.675710i
\(806\) 0.804489i 0.0283369i
\(807\) 2.84500 0.526657i 0.100149 0.0185392i
\(808\) 4.00387 + 14.9426i 0.140855 + 0.525680i
\(809\) −19.2730 + 33.3818i −0.677603 + 1.17364i 0.298098 + 0.954535i \(0.403648\pi\)
−0.975701 + 0.219107i \(0.929686\pi\)
\(810\) −18.2662 4.86570i −0.641810 0.170963i
\(811\) 26.0551 0.914919 0.457460 0.889230i \(-0.348759\pi\)
0.457460 + 0.889230i \(0.348759\pi\)
\(812\) 10.4649 + 5.96614i 0.367246 + 0.209370i
\(813\) 0.748305 2.11170i 0.0262442 0.0740607i
\(814\) −3.72869 + 2.15276i −0.130690 + 0.0754542i
\(815\) 21.3424 1.16833i 0.747593 0.0409250i
\(816\) −6.53230 0.515517i −0.228676 0.0180467i
\(817\) −1.44858 + 5.40617i −0.0506794 + 0.189138i
\(818\) 17.4334 + 17.4334i 0.609544 + 0.609544i
\(819\) 9.58257 + 13.0510i 0.334842 + 0.456040i
\(820\) −2.28419 + 10.8706i −0.0797672 + 0.379618i
\(821\) −11.8022 + 6.81400i −0.411899 + 0.237810i −0.691605 0.722276i \(-0.743096\pi\)
0.279706 + 0.960086i \(0.409763\pi\)
\(822\) −14.2706 + 12.1829i −0.497744 + 0.424929i
\(823\) 8.18923 + 30.5626i 0.285459 + 1.06535i 0.948504 + 0.316766i \(0.102597\pi\)
−0.663045 + 0.748580i \(0.730736\pi\)
\(824\) 10.6337 + 18.4181i 0.370443 + 0.641625i
\(825\) 4.58996 + 4.31713i 0.159802 + 0.150303i
\(826\) −2.82352 + 2.85445i −0.0982428 + 0.0993191i
\(827\) 0.690034 0.690034i 0.0239948 0.0239948i −0.695008 0.719002i \(-0.744599\pi\)
0.719002 + 0.695008i \(0.244599\pi\)
\(828\) 6.39469 + 8.80949i 0.222231 + 0.306151i
\(829\) 12.2802 + 7.08996i 0.426508 + 0.246244i 0.697858 0.716236i \(-0.254137\pi\)
−0.271350 + 0.962481i \(0.587470\pi\)
\(830\) 4.04817 + 3.62796i 0.140514 + 0.125928i
\(831\) −16.7094 11.4894i −0.579643 0.398561i
\(832\) −8.76631 8.76631i −0.303917 0.303917i
\(833\) −13.8404 49.4895i −0.479540 1.71471i
\(834\) −1.95570 + 0.932305i −0.0677203 + 0.0322831i
\(835\) 7.89119 15.5769i 0.273086 0.539060i
\(836\) −0.540298 0.311941i −0.0186866 0.0107887i
\(837\) −0.0557022 2.18094i −0.00192535 0.0753843i
\(838\) −21.7110 5.81746i −0.749996 0.200961i
\(839\) −57.1107 −1.97168 −0.985840 0.167690i \(-0.946369\pi\)
−0.985840 + 0.167690i \(0.946369\pi\)
\(840\) 7.22564 + 29.1251i 0.249308 + 1.00491i
\(841\) −12.4063 −0.427803
\(842\) −8.97709 2.40540i −0.309371 0.0828957i
\(843\) −18.8401 + 16.0839i −0.648887 + 0.553960i
\(844\) −24.6228 14.2160i −0.847552 0.489334i
\(845\) 6.15120 + 18.7826i 0.211608 + 0.646140i
\(846\) −12.4784 + 15.3960i −0.429017 + 0.529326i
\(847\) 13.9818 + 23.9153i 0.480420 + 0.821740i
\(848\) −1.98753 1.98753i −0.0682522 0.0682522i
\(849\) −10.2517 + 14.9095i −0.351839 + 0.511692i
\(850\) −20.3954 27.7988i −0.699556 0.953490i
\(851\) −17.7119 10.2260i −0.607155 0.350541i
\(852\) 13.4488 2.48960i 0.460748 0.0852922i
\(853\) −27.4480 + 27.4480i −0.939802 + 0.939802i −0.998288 0.0584858i \(-0.981373\pi\)
0.0584858 + 0.998288i \(0.481373\pi\)
\(854\) −6.28589 22.9582i −0.215099 0.785613i
\(855\) 3.24620 + 3.99321i 0.111018 + 0.136565i
\(856\) 26.8180 + 46.4501i 0.916620 + 1.58763i
\(857\) −4.45470 16.6252i −0.152170 0.567905i −0.999331 0.0365692i \(-0.988357\pi\)
0.847162 0.531335i \(-0.178310\pi\)
\(858\) −1.56786 1.83652i −0.0535257 0.0626978i
\(859\) 14.8376 8.56649i 0.506252 0.292285i −0.225040 0.974350i \(-0.572251\pi\)
0.731292 + 0.682065i \(0.238918\pi\)
\(860\) 15.2689 9.96638i 0.520667 0.339851i
\(861\) −15.4180 + 13.3084i −0.525444 + 0.453549i
\(862\) −21.3260 21.3260i −0.726367 0.726367i
\(863\) 3.92508 14.6486i 0.133611 0.498644i −0.866388 0.499371i \(-0.833565\pi\)
1.00000 0.000726566i \(0.000231273\pi\)
\(864\) −20.2389 19.2308i −0.688542 0.654246i
\(865\) −1.63526 29.8720i −0.0556006 1.01568i
\(866\) 15.5662 8.98713i 0.528960 0.305395i
\(867\) −60.2309 21.3435i −2.04555 0.724862i
\(868\) −1.07185 + 0.626645i −0.0363811 + 0.0212697i
\(869\) 4.88005 0.165544
\(870\) 10.2236 + 10.7279i 0.346611 + 0.363710i
\(871\) 7.28962 12.6260i 0.246999 0.427816i
\(872\) −4.79070 17.8791i −0.162234 0.605464i
\(873\) −19.3150 + 14.0205i −0.653712 + 0.474520i
\(874\) 2.33937i 0.0791304i
\(875\) −17.0881 + 24.1453i −0.577683 + 0.816261i
\(876\) −27.5786 + 13.1470i −0.931793 + 0.444197i
\(877\) −1.59460 + 5.95111i −0.0538456 + 0.200955i −0.987609 0.156938i \(-0.949838\pi\)
0.933763 + 0.357892i \(0.116505\pi\)
\(878\) −30.8527 + 8.26695i −1.04123 + 0.278996i
\(879\) −1.80581 + 22.8820i −0.0609083 + 0.771792i
\(880\) −0.260944 0.796788i −0.00879643 0.0268597i
\(881\) 22.1697i 0.746915i −0.927647 0.373457i \(-0.878172\pi\)
0.927647 0.373457i \(-0.121828\pi\)
\(882\) −7.83402 + 18.1031i −0.263785 + 0.609562i
\(883\) 18.3373 18.3373i 0.617098 0.617098i −0.327688 0.944786i \(-0.606269\pi\)
0.944786 + 0.327688i \(0.106269\pi\)
\(884\) −8.36898 14.4955i −0.281479 0.487536i
\(885\) 5.49254 2.99725i 0.184630 0.100751i
\(886\) 12.5074 21.6635i 0.420194 0.727798i
\(887\) −8.79908 2.35771i −0.295444 0.0791641i 0.108052 0.994145i \(-0.465539\pi\)
−0.403497 + 0.914981i \(0.632205\pi\)
\(888\) 30.1190 + 10.6730i 1.01073 + 0.358162i
\(889\) 2.86029 + 2.82929i 0.0959310 + 0.0948913i
\(890\) −15.9571 24.4470i −0.534883 0.819465i
\(891\) −4.37756 4.87019i −0.146654 0.163158i
\(892\) 11.6624 3.12493i 0.390486 0.104630i
\(893\) 5.21139 1.39639i 0.174393 0.0467284i
\(894\) −1.19916 + 1.74399i −0.0401061 + 0.0583278i
\(895\) 5.84363 27.8103i 0.195331 0.929595i
\(896\) −3.37914 + 12.8917i −0.112889 + 0.430681i
\(897\) 3.83123 10.8117i 0.127921 0.360991i
\(898\) −12.2548 3.28367i −0.408949 0.109577i
\(899\) −0.855156 + 1.48117i −0.0285211 + 0.0493999i
\(900\) 0.806685 16.7461i 0.0268895 0.558204i
\(901\) −20.0207 34.6769i −0.666986 1.15525i
\(902\) 2.14788 2.14788i 0.0715167 0.0715167i
\(903\) 33.3431 + 2.44866i 1.10959 + 0.0814863i
\(904\) 33.0875i 1.10047i
\(905\) −20.3153 + 6.65316i −0.675303 + 0.221159i
\(906\) 5.14379 + 0.405938i 0.170891 + 0.0134864i
\(907\) −41.1437 + 11.0244i −1.36615 + 0.366060i −0.866072 0.499919i \(-0.833363\pi\)
−0.500081 + 0.865979i \(0.666696\pi\)
\(908\) −0.234247 + 0.874221i −0.00777376 + 0.0290121i
\(909\) 9.97849 12.3116i 0.330966 0.408349i
\(910\) 7.51937 8.48284i 0.249265 0.281203i
\(911\) 18.4223i 0.610358i 0.952295 + 0.305179i \(0.0987163\pi\)
−0.952295 + 0.305179i \(0.901284\pi\)
\(912\) −0.124640 0.673307i −0.00412725 0.0222954i
\(913\) 0.487388 + 1.81896i 0.0161302 + 0.0601987i
\(914\) 6.16685 10.6813i 0.203981 0.353306i
\(915\) −0.892701 + 37.0850i −0.0295118 + 1.22599i
\(916\) 18.0911 0.597746
\(917\) −25.4564 + 14.8827i −0.840643 + 0.491471i
\(918\) 18.7018 + 30.5628i 0.617251 + 1.00872i
\(919\) 10.2581 5.92250i 0.338382 0.195365i −0.321174 0.947020i \(-0.604077\pi\)
0.659556 + 0.751655i \(0.270744\pi\)
\(920\) 14.1880 15.8314i 0.467766 0.521945i
\(921\) 3.21903 40.7896i 0.106071 1.34406i
\(922\) −0.978197 + 3.65068i −0.0322152 + 0.120229i
\(923\) −10.1908 10.1908i −0.335433 0.335433i
\(924\) −1.22561 + 3.51945i −0.0403197 + 0.115781i
\(925\) 11.4250 + 29.3538i 0.375650 + 0.965147i
\(926\) −14.0451 + 8.10897i −0.461552 + 0.266477i
\(927\) 8.87005 19.8994i 0.291331 0.653583i
\(928\) 5.66470 + 21.1410i 0.185953 + 0.693986i
\(929\) −7.93709 13.7474i −0.260407 0.451039i 0.705943 0.708269i \(-0.250524\pi\)
−0.966350 + 0.257230i \(0.917190\pi\)
\(930\) −1.48445 + 0.359705i −0.0486772 + 0.0117952i
\(931\) 4.62108 2.73555i 0.151450 0.0896540i
\(932\) 10.4531 10.4531i 0.342401 0.342401i
\(933\) −4.92193 26.5883i −0.161137 0.870461i
\(934\) 24.5358 + 14.1658i 0.802836 + 0.463518i
\(935\) −0.652859 11.9260i −0.0213508 0.390023i
\(936\) −2.81114 + 17.6996i −0.0918850 + 0.578529i
\(937\) −12.9594 12.9594i −0.423365 0.423365i 0.462996 0.886360i \(-0.346774\pi\)
−0.886360 + 0.462996i \(0.846774\pi\)
\(938\) 17.7613 0.0967677i 0.579928 0.00315958i
\(939\) 12.2042 + 25.6009i 0.398270 + 0.835453i
\(940\) −15.6796 7.94322i −0.511412 0.259079i
\(941\) −40.5338 23.4022i −1.32136 0.762890i −0.337418 0.941355i \(-0.609554\pi\)
−0.983946 + 0.178464i \(0.942887\pi\)
\(942\) 4.56068 + 5.34220i 0.148595 + 0.174058i
\(943\) 13.9373 + 3.73448i 0.453860 + 0.121612i
\(944\) −0.832560 −0.0270975
\(945\) 19.7974 23.5173i 0.644009 0.765018i
\(946\) −4.98615 −0.162114
\(947\) −5.52955 1.48164i −0.179686 0.0481468i 0.167854 0.985812i \(-0.446316\pi\)
−0.347540 + 0.937665i \(0.612983\pi\)
\(948\) −8.43048 9.87512i −0.273809 0.320729i
\(949\) 27.8799 + 16.0965i 0.905020 + 0.522514i
\(950\) 2.25435 2.81055i 0.0731409 0.0911863i
\(951\) 17.9392 + 37.6311i 0.581718 + 1.22027i
\(952\) 28.1711 49.4135i 0.913030 1.60150i
\(953\) 2.51927 + 2.51927i 0.0816072 + 0.0816072i 0.746732 0.665125i \(-0.231622\pi\)
−0.665125 + 0.746732i \(0.731622\pi\)
\(954\) −2.41091 + 15.1796i −0.0780561 + 0.491459i
\(955\) −6.98577 + 7.79489i −0.226054 + 0.252237i
\(956\) −0.0801276 0.0462617i −0.00259151 0.00149621i
\(957\) 0.934448 + 5.04789i 0.0302064 + 0.163175i
\(958\) 8.61268 8.61268i 0.278263 0.278263i
\(959\) −8.05805 29.4307i −0.260208 0.950368i
\(960\) −12.2561 + 20.0953i −0.395564 + 0.648574i
\(961\) 15.4119 + 26.6941i 0.497157 + 0.861101i
\(962\) −3.12419 11.6596i −0.100728 0.375921i
\(963\) 22.3701 50.1860i 0.720866 1.61722i
\(964\) 14.0532 8.11364i 0.452625 0.261323i
\(965\) 8.78377 + 13.4571i 0.282760 + 0.433201i
\(966\) 13.7267 2.61846i 0.441649 0.0842477i
\(967\) 37.0826 + 37.0826i 1.19250 + 1.19250i 0.976364 + 0.216132i \(0.0693443\pi\)
0.216132 + 0.976364i \(0.430656\pi\)
\(968\) −7.93615 + 29.6181i −0.255077 + 0.951962i
\(969\) 0.767428 9.72436i 0.0246533 0.312391i
\(970\) 12.4438 + 11.1521i 0.399547 + 0.358073i
\(971\) 28.9850 16.7345i 0.930174 0.537036i 0.0433076 0.999062i \(-0.486210\pi\)
0.886867 + 0.462025i \(0.152877\pi\)
\(972\) −2.29276 + 17.2718i −0.0735404 + 0.553992i
\(973\) −0.0191955 3.52326i −0.000615379 0.112950i
\(974\) 27.4165 0.878480
\(975\) −15.0217 + 9.29729i −0.481078 + 0.297752i
\(976\) 2.46795 4.27461i 0.0789971 0.136827i
\(977\) 8.21340 + 30.6528i 0.262770 + 0.980671i 0.963601 + 0.267344i \(0.0861459\pi\)
−0.700831 + 0.713327i \(0.747187\pi\)
\(978\) 2.83077 + 15.2918i 0.0905182 + 0.488979i
\(979\) 10.1133i 0.323223i
\(980\) −17.1591 3.41077i −0.548128 0.108953i
\(981\) −11.9394 + 14.7310i −0.381197 + 0.470326i
\(982\) 4.20955 15.7102i 0.134332 0.501334i
\(983\) −18.3689 + 4.92194i −0.585877 + 0.156985i −0.539568 0.841942i \(-0.681413\pi\)
−0.0463090 + 0.998927i \(0.514746\pi\)
\(984\) −22.4739 1.77360i −0.716443 0.0565403i
\(985\) −5.45488 + 10.7677i −0.173807 + 0.343087i
\(986\) 28.0896i 0.894556i
\(987\) −14.0267 29.0158i −0.446475 0.923584i
\(988\) 1.23681 1.23681i 0.0393481 0.0393481i
\(989\) −11.8425 20.5118i −0.376570 0.652239i
\(990\) −2.68775 + 3.71418i −0.0854224 + 0.118044i
\(991\) −26.0658 + 45.1472i −0.828007 + 1.43415i 0.0715929 + 0.997434i \(0.477192\pi\)
−0.899600 + 0.436716i \(0.856142\pi\)
\(992\) −2.17900 0.583860i −0.0691832 0.0185376i
\(993\) 5.57754 15.7397i 0.176998 0.499486i
\(994\) 4.45182 16.9840i 0.141203 0.538700i
\(995\) −25.7280 5.40610i −0.815634 0.171385i
\(996\) 2.83881 4.12859i 0.0899510 0.130819i
\(997\) −16.3803 + 4.38908i −0.518768 + 0.139003i −0.508697 0.860946i \(-0.669872\pi\)
−0.0100712 + 0.999949i \(0.503206\pi\)
\(998\) −15.2764 + 4.09329i −0.483565 + 0.129571i
\(999\) −9.27686 31.3925i −0.293507 0.993215i
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 105.2.x.a.32.8 yes 48
3.2 odd 2 inner 105.2.x.a.32.5 yes 48
5.2 odd 4 525.2.bf.f.368.5 48
5.3 odd 4 inner 105.2.x.a.53.8 yes 48
5.4 even 2 525.2.bf.f.32.5 48
7.2 even 3 inner 105.2.x.a.2.5 48
7.3 odd 6 735.2.j.e.197.5 24
7.4 even 3 735.2.j.g.197.5 24
7.5 odd 6 735.2.y.i.422.5 48
7.6 odd 2 735.2.y.i.557.8 48
15.2 even 4 525.2.bf.f.368.8 48
15.8 even 4 inner 105.2.x.a.53.5 yes 48
15.14 odd 2 525.2.bf.f.32.8 48
21.2 odd 6 inner 105.2.x.a.2.8 yes 48
21.5 even 6 735.2.y.i.422.8 48
21.11 odd 6 735.2.j.g.197.8 24
21.17 even 6 735.2.j.e.197.8 24
21.20 even 2 735.2.y.i.557.5 48
35.2 odd 12 525.2.bf.f.443.8 48
35.3 even 12 735.2.j.e.638.8 24
35.9 even 6 525.2.bf.f.107.8 48
35.13 even 4 735.2.y.i.263.8 48
35.18 odd 12 735.2.j.g.638.8 24
35.23 odd 12 inner 105.2.x.a.23.5 yes 48
35.33 even 12 735.2.y.i.128.5 48
105.2 even 12 525.2.bf.f.443.5 48
105.23 even 12 inner 105.2.x.a.23.8 yes 48
105.38 odd 12 735.2.j.e.638.5 24
105.44 odd 6 525.2.bf.f.107.5 48
105.53 even 12 735.2.j.g.638.5 24
105.68 odd 12 735.2.y.i.128.8 48
105.83 odd 4 735.2.y.i.263.5 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.5 48 7.2 even 3 inner
105.2.x.a.2.8 yes 48 21.2 odd 6 inner
105.2.x.a.23.5 yes 48 35.23 odd 12 inner
105.2.x.a.23.8 yes 48 105.23 even 12 inner
105.2.x.a.32.5 yes 48 3.2 odd 2 inner
105.2.x.a.32.8 yes 48 1.1 even 1 trivial
105.2.x.a.53.5 yes 48 15.8 even 4 inner
105.2.x.a.53.8 yes 48 5.3 odd 4 inner
525.2.bf.f.32.5 48 5.4 even 2
525.2.bf.f.32.8 48 15.14 odd 2
525.2.bf.f.107.5 48 105.44 odd 6
525.2.bf.f.107.8 48 35.9 even 6
525.2.bf.f.368.5 48 5.2 odd 4
525.2.bf.f.368.8 48 15.2 even 4
525.2.bf.f.443.5 48 105.2 even 12
525.2.bf.f.443.8 48 35.2 odd 12
735.2.j.e.197.5 24 7.3 odd 6
735.2.j.e.197.8 24 21.17 even 6
735.2.j.e.638.5 24 105.38 odd 12
735.2.j.e.638.8 24 35.3 even 12
735.2.j.g.197.5 24 7.4 even 3
735.2.j.g.197.8 24 21.11 odd 6
735.2.j.g.638.5 24 105.53 even 12
735.2.j.g.638.8 24 35.18 odd 12
735.2.y.i.128.5 48 35.33 even 12
735.2.y.i.128.8 48 105.68 odd 12
735.2.y.i.263.5 48 105.83 odd 4
735.2.y.i.263.8 48 35.13 even 4
735.2.y.i.422.5 48 7.5 odd 6
735.2.y.i.422.8 48 21.5 even 6
735.2.y.i.557.5 48 21.20 even 2
735.2.y.i.557.8 48 7.6 odd 2