Properties

Label 475.2.l.f.176.3
Level $475$
Weight $2$
Character 475.176
Analytic conductor $3.793$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(101,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, 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("475.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 176.3
Character \(\chi\) \(=\) 475.176
Dual form 475.2.l.f.251.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.984236 + 0.358233i) q^{2} +(-0.0922859 + 0.523379i) q^{3} +(-0.691698 + 0.580404i) q^{4} +(-0.0966605 - 0.548189i) q^{6} +(-1.37016 - 2.37320i) q^{7} +(1.52028 - 2.63320i) q^{8} +(2.55367 + 0.929459i) q^{9} +O(q^{10})\) \(q+(-0.984236 + 0.358233i) q^{2} +(-0.0922859 + 0.523379i) q^{3} +(-0.691698 + 0.580404i) q^{4} +(-0.0966605 - 0.548189i) q^{6} +(-1.37016 - 2.37320i) q^{7} +(1.52028 - 2.63320i) q^{8} +(2.55367 + 0.929459i) q^{9} +(-0.416418 + 0.721257i) q^{11} +(-0.239937 - 0.415583i) q^{12} +(-0.106070 - 0.601551i) q^{13} +(2.19872 + 1.84495i) q^{14} +(-0.239424 + 1.35784i) q^{16} +(4.54662 - 1.65483i) q^{17} -2.84638 q^{18} +(4.35537 - 0.175314i) q^{19} +(1.36853 - 0.498103i) q^{21} +(0.151476 - 0.859062i) q^{22} +(-2.87338 + 2.41106i) q^{23} +(1.23786 + 1.03869i) q^{24} +(0.319893 + 0.554071i) q^{26} +(-1.51931 + 2.63152i) q^{27} +(2.32515 + 0.846286i) q^{28} +(3.73543 + 1.35958i) q^{29} +(3.46338 + 5.99875i) q^{31} +(0.805200 + 4.56652i) q^{32} +(-0.339061 - 0.284506i) q^{33} +(-3.88213 + 3.25750i) q^{34} +(-2.30583 + 0.839253i) q^{36} -4.33071 q^{37} +(-4.22391 + 1.73279i) q^{38} +0.324628 q^{39} +(0.923271 - 5.23613i) q^{41} +(-1.16852 + 0.980503i) q^{42} +(8.01164 + 6.72257i) q^{43} +(-0.130585 - 0.740582i) q^{44} +(1.96437 - 3.40239i) q^{46} +(3.19511 + 1.16292i) q^{47} +(-0.688571 - 0.250619i) q^{48} +(-0.254704 + 0.441160i) q^{49} +(0.446517 + 2.53232i) q^{51} +(0.422511 + 0.354529i) q^{52} +(10.4702 - 8.78556i) q^{53} +(0.552662 - 3.13430i) q^{54} -8.33212 q^{56} +(-0.310183 + 2.29569i) q^{57} -4.16359 q^{58} +(-9.41315 + 3.42610i) q^{59} +(6.94990 - 5.83166i) q^{61} +(-5.55774 - 4.66350i) q^{62} +(-1.29316 - 7.33387i) q^{63} +(-3.80717 - 6.59422i) q^{64} +(0.435636 + 0.158558i) q^{66} +(10.2751 + 3.73984i) q^{67} +(-2.18442 + 3.78352i) q^{68} +(-0.996723 - 1.72638i) q^{69} +(-0.519169 - 0.435634i) q^{71} +(6.32974 - 5.31128i) q^{72} +(-1.21787 + 6.90688i) q^{73} +(4.26244 - 1.55140i) q^{74} +(-2.91085 + 2.64914i) q^{76} +2.28224 q^{77} +(-0.319511 + 0.116292i) q^{78} +(0.604220 - 3.42670i) q^{79} +(5.00824 + 4.20241i) q^{81} +(0.967036 + 5.48434i) q^{82} +(-2.48742 - 4.30834i) q^{83} +(-0.657507 + 1.13884i) q^{84} +(-10.2936 - 3.74656i) q^{86} +(-1.05630 + 1.82957i) q^{87} +(1.26614 + 2.19302i) q^{88} +(-1.02256 - 5.79921i) q^{89} +(-1.28227 + 1.07595i) q^{91} +(0.588129 - 3.33544i) q^{92} +(-3.45924 + 1.25906i) q^{93} -3.56134 q^{94} -2.46433 q^{96} +(-11.6886 + 4.25430i) q^{97} +(0.0926508 - 0.525449i) q^{98} +(-1.73377 + 1.45481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984236 + 0.358233i −0.695960 + 0.253309i −0.665685 0.746233i \(-0.731861\pi\)
−0.0302752 + 0.999542i \(0.509638\pi\)
\(3\) −0.0922859 + 0.523379i −0.0532813 + 0.302173i −0.999790 0.0205059i \(-0.993472\pi\)
0.946508 + 0.322679i \(0.104583\pi\)
\(4\) −0.691698 + 0.580404i −0.345849 + 0.290202i
\(5\) 0 0
\(6\) −0.0966605 0.548189i −0.0394615 0.223797i
\(7\) −1.37016 2.37320i −0.517874 0.896983i −0.999784 0.0207632i \(-0.993390\pi\)
0.481911 0.876220i \(-0.339943\pi\)
\(8\) 1.52028 2.63320i 0.537499 0.930976i
\(9\) 2.55367 + 0.929459i 0.851223 + 0.309820i
\(10\) 0 0
\(11\) −0.416418 + 0.721257i −0.125555 + 0.217467i −0.921950 0.387310i \(-0.873404\pi\)
0.796395 + 0.604777i \(0.206738\pi\)
\(12\) −0.239937 0.415583i −0.0692639 0.119969i
\(13\) −0.106070 0.601551i −0.0294185 0.166840i 0.966559 0.256444i \(-0.0825510\pi\)
−0.995977 + 0.0896039i \(0.971440\pi\)
\(14\) 2.19872 + 1.84495i 0.587633 + 0.493083i
\(15\) 0 0
\(16\) −0.239424 + 1.35784i −0.0598561 + 0.339461i
\(17\) 4.54662 1.65483i 1.10272 0.401356i 0.274400 0.961616i \(-0.411521\pi\)
0.828317 + 0.560259i \(0.189299\pi\)
\(18\) −2.84638 −0.670897
\(19\) 4.35537 0.175314i 0.999191 0.0402198i
\(20\) 0 0
\(21\) 1.36853 0.498103i 0.298637 0.108695i
\(22\) 0.151476 0.859062i 0.0322947 0.183153i
\(23\) −2.87338 + 2.41106i −0.599142 + 0.502740i −0.891170 0.453670i \(-0.850114\pi\)
0.292028 + 0.956410i \(0.405670\pi\)
\(24\) 1.23786 + 1.03869i 0.252677 + 0.212021i
\(25\) 0 0
\(26\) 0.319893 + 0.554071i 0.0627362 + 0.108662i
\(27\) −1.51931 + 2.63152i −0.292391 + 0.506436i
\(28\) 2.32515 + 0.846286i 0.439412 + 0.159933i
\(29\) 3.73543 + 1.35958i 0.693651 + 0.252468i 0.664698 0.747112i \(-0.268560\pi\)
0.0289533 + 0.999581i \(0.490783\pi\)
\(30\) 0 0
\(31\) 3.46338 + 5.99875i 0.622042 + 1.07741i 0.989105 + 0.147212i \(0.0470300\pi\)
−0.367063 + 0.930196i \(0.619637\pi\)
\(32\) 0.805200 + 4.56652i 0.142341 + 0.807254i
\(33\) −0.339061 0.284506i −0.0590230 0.0495262i
\(34\) −3.88213 + 3.25750i −0.665780 + 0.558656i
\(35\) 0 0
\(36\) −2.30583 + 0.839253i −0.384305 + 0.139876i
\(37\) −4.33071 −0.711965 −0.355982 0.934493i \(-0.615854\pi\)
−0.355982 + 0.934493i \(0.615854\pi\)
\(38\) −4.22391 + 1.73279i −0.685209 + 0.281095i
\(39\) 0.324628 0.0519821
\(40\) 0 0
\(41\) 0.923271 5.23613i 0.144191 0.817746i −0.823823 0.566848i \(-0.808163\pi\)
0.968013 0.250899i \(-0.0807260\pi\)
\(42\) −1.16852 + 0.980503i −0.180306 + 0.151295i
\(43\) 8.01164 + 6.72257i 1.22176 + 1.02518i 0.998731 + 0.0503713i \(0.0160405\pi\)
0.223034 + 0.974811i \(0.428404\pi\)
\(44\) −0.130585 0.740582i −0.0196864 0.111647i
\(45\) 0 0
\(46\) 1.96437 3.40239i 0.289631 0.501655i
\(47\) 3.19511 + 1.16292i 0.466054 + 0.169630i 0.564364 0.825526i \(-0.309121\pi\)
−0.0983098 + 0.995156i \(0.531344\pi\)
\(48\) −0.688571 0.250619i −0.0993867 0.0361738i
\(49\) −0.254704 + 0.441160i −0.0363862 + 0.0630228i
\(50\) 0 0
\(51\) 0.446517 + 2.53232i 0.0625249 + 0.354596i
\(52\) 0.422511 + 0.354529i 0.0585917 + 0.0491643i
\(53\) 10.4702 8.78556i 1.43820 1.20679i 0.497535 0.867444i \(-0.334239\pi\)
0.940662 0.339346i \(-0.110206\pi\)
\(54\) 0.552662 3.13430i 0.0752077 0.426524i
\(55\) 0 0
\(56\) −8.33212 −1.11343
\(57\) −0.310183 + 2.29569i −0.0410848 + 0.304072i
\(58\) −4.16359 −0.546706
\(59\) −9.41315 + 3.42610i −1.22549 + 0.446041i −0.872050 0.489417i \(-0.837210\pi\)
−0.353437 + 0.935458i \(0.614987\pi\)
\(60\) 0 0
\(61\) 6.94990 5.83166i 0.889844 0.746668i −0.0783350 0.996927i \(-0.524960\pi\)
0.968179 + 0.250260i \(0.0805159\pi\)
\(62\) −5.55774 4.66350i −0.705833 0.592265i
\(63\) −1.29316 7.33387i −0.162923 0.923980i
\(64\) −3.80717 6.59422i −0.475897 0.824277i
\(65\) 0 0
\(66\) 0.435636 + 0.158558i 0.0536231 + 0.0195172i
\(67\) 10.2751 + 3.73984i 1.25531 + 0.456894i 0.882191 0.470891i \(-0.156067\pi\)
0.373115 + 0.927785i \(0.378290\pi\)
\(68\) −2.18442 + 3.78352i −0.264899 + 0.458819i
\(69\) −0.996723 1.72638i −0.119991 0.207831i
\(70\) 0 0
\(71\) −0.519169 0.435634i −0.0616140 0.0517003i 0.611461 0.791275i \(-0.290582\pi\)
−0.673075 + 0.739575i \(0.735027\pi\)
\(72\) 6.32974 5.31128i 0.745967 0.625940i
\(73\) −1.21787 + 6.90688i −0.142541 + 0.808389i 0.826768 + 0.562543i \(0.190177\pi\)
−0.969309 + 0.245846i \(0.920934\pi\)
\(74\) 4.26244 1.55140i 0.495499 0.180347i
\(75\) 0 0
\(76\) −2.91085 + 2.64914i −0.333897 + 0.303877i
\(77\) 2.28224 0.260086
\(78\) −0.319511 + 0.116292i −0.0361775 + 0.0131675i
\(79\) 0.604220 3.42670i 0.0679801 0.385534i −0.931767 0.363056i \(-0.881733\pi\)
0.999747 0.0224781i \(-0.00715559\pi\)
\(80\) 0 0
\(81\) 5.00824 + 4.20241i 0.556471 + 0.466935i
\(82\) 0.967036 + 5.48434i 0.106791 + 0.605644i
\(83\) −2.48742 4.30834i −0.273030 0.472902i 0.696606 0.717454i \(-0.254693\pi\)
−0.969636 + 0.244552i \(0.921359\pi\)
\(84\) −0.657507 + 1.13884i −0.0717399 + 0.124257i
\(85\) 0 0
\(86\) −10.2936 3.74656i −1.10999 0.404002i
\(87\) −1.05630 + 1.82957i −0.113248 + 0.196151i
\(88\) 1.26614 + 2.19302i 0.134971 + 0.233777i
\(89\) −1.02256 5.79921i −0.108391 0.614716i −0.989812 0.142383i \(-0.954523\pi\)
0.881421 0.472332i \(-0.156588\pi\)
\(90\) 0 0
\(91\) −1.28227 + 1.07595i −0.134418 + 0.112790i
\(92\) 0.588129 3.33544i 0.0613167 0.347744i
\(93\) −3.45924 + 1.25906i −0.358707 + 0.130559i
\(94\) −3.56134 −0.367324
\(95\) 0 0
\(96\) −2.46433 −0.251514
\(97\) −11.6886 + 4.25430i −1.18680 + 0.431959i −0.858598 0.512649i \(-0.828664\pi\)
−0.328200 + 0.944608i \(0.606442\pi\)
\(98\) 0.0926508 0.525449i 0.00935914 0.0530783i
\(99\) −1.73377 + 1.45481i −0.174251 + 0.146214i
\(100\) 0 0
\(101\) −3.08004 17.4678i −0.306475 1.73811i −0.616478 0.787372i \(-0.711441\pi\)
0.310003 0.950736i \(-0.399670\pi\)
\(102\) −1.34664 2.33245i −0.133337 0.230947i
\(103\) −2.60925 + 4.51935i −0.257097 + 0.445305i −0.965463 0.260541i \(-0.916099\pi\)
0.708366 + 0.705845i \(0.249433\pi\)
\(104\) −1.74526 0.635222i −0.171137 0.0622887i
\(105\) 0 0
\(106\) −7.15790 + 12.3979i −0.695237 + 1.20419i
\(107\) −7.59356 13.1524i −0.734097 1.27149i −0.955118 0.296225i \(-0.904272\pi\)
0.221021 0.975269i \(-0.429061\pi\)
\(108\) −0.476440 2.70203i −0.0458455 0.260003i
\(109\) 3.00487 + 2.52138i 0.287814 + 0.241505i 0.775251 0.631654i \(-0.217624\pi\)
−0.487437 + 0.873158i \(0.662068\pi\)
\(110\) 0 0
\(111\) 0.399663 2.26660i 0.0379344 0.215137i
\(112\) 3.55048 1.29227i 0.335489 0.122108i
\(113\) −3.97342 −0.373788 −0.186894 0.982380i \(-0.559842\pi\)
−0.186894 + 0.982380i \(0.559842\pi\)
\(114\) −0.517097 2.37062i −0.0484306 0.222029i
\(115\) 0 0
\(116\) −3.37289 + 1.22763i −0.313165 + 0.113983i
\(117\) 0.288251 1.63475i 0.0266488 0.151133i
\(118\) 8.03742 6.74420i 0.739904 0.620853i
\(119\) −10.1569 8.52262i −0.931078 0.781267i
\(120\) 0 0
\(121\) 5.15319 + 8.92559i 0.468472 + 0.811417i
\(122\) −4.75126 + 8.22942i −0.430158 + 0.745056i
\(123\) 2.65528 + 0.966441i 0.239418 + 0.0871411i
\(124\) −5.87731 2.13917i −0.527798 0.192103i
\(125\) 0 0
\(126\) 3.90001 + 6.75501i 0.347440 + 0.601784i
\(127\) −1.59495 9.04543i −0.141529 0.802652i −0.970089 0.242751i \(-0.921950\pi\)
0.828559 0.559901i \(-0.189161\pi\)
\(128\) −0.994815 0.834749i −0.0879301 0.0737821i
\(129\) −4.25781 + 3.57273i −0.374880 + 0.314561i
\(130\) 0 0
\(131\) 3.51355 1.27883i 0.306980 0.111732i −0.183936 0.982938i \(-0.558884\pi\)
0.490917 + 0.871206i \(0.336662\pi\)
\(132\) 0.399656 0.0347856
\(133\) −6.38363 10.0959i −0.553531 0.875429i
\(134\) −11.4529 −0.989379
\(135\) 0 0
\(136\) 2.55462 14.4880i 0.219057 1.24233i
\(137\) −1.81043 + 1.51913i −0.154675 + 0.129788i −0.716841 0.697237i \(-0.754413\pi\)
0.562166 + 0.827025i \(0.309968\pi\)
\(138\) 1.59946 + 1.34210i 0.136155 + 0.114247i
\(139\) 0.424186 + 2.40568i 0.0359790 + 0.204047i 0.997498 0.0706903i \(-0.0225202\pi\)
−0.961519 + 0.274737i \(0.911409\pi\)
\(140\) 0 0
\(141\) −0.903514 + 1.56493i −0.0760896 + 0.131791i
\(142\) 0.667043 + 0.242784i 0.0559770 + 0.0203740i
\(143\) 0.478042 + 0.173993i 0.0399759 + 0.0145500i
\(144\) −1.87347 + 3.24495i −0.156123 + 0.270412i
\(145\) 0 0
\(146\) −1.27560 7.23428i −0.105569 0.598713i
\(147\) −0.207388 0.174019i −0.0171051 0.0143529i
\(148\) 2.99555 2.51356i 0.246232 0.206613i
\(149\) 2.47773 14.0519i 0.202984 1.15118i −0.697598 0.716490i \(-0.745748\pi\)
0.900581 0.434687i \(-0.143141\pi\)
\(150\) 0 0
\(151\) 2.34319 0.190686 0.0953432 0.995444i \(-0.469605\pi\)
0.0953432 + 0.995444i \(0.469605\pi\)
\(152\) 6.15974 11.7351i 0.499621 0.951841i
\(153\) 13.1487 1.06301
\(154\) −2.24627 + 0.817575i −0.181009 + 0.0658820i
\(155\) 0 0
\(156\) −0.224545 + 0.188415i −0.0179780 + 0.0150853i
\(157\) 12.3906 + 10.3969i 0.988875 + 0.829765i 0.985405 0.170229i \(-0.0544508\pi\)
0.00347076 + 0.999994i \(0.498895\pi\)
\(158\) 0.632862 + 3.58914i 0.0503478 + 0.285536i
\(159\) 3.63193 + 6.29068i 0.288031 + 0.498884i
\(160\) 0 0
\(161\) 9.65891 + 3.51556i 0.761229 + 0.277065i
\(162\) −6.43473 2.34205i −0.505560 0.184009i
\(163\) −8.01289 + 13.8787i −0.627618 + 1.08707i 0.360410 + 0.932794i \(0.382637\pi\)
−0.988028 + 0.154273i \(0.950697\pi\)
\(164\) 2.40044 + 4.15769i 0.187443 + 0.324661i
\(165\) 0 0
\(166\) 3.99160 + 3.34935i 0.309809 + 0.259960i
\(167\) −5.80391 + 4.87006i −0.449120 + 0.376856i −0.839109 0.543963i \(-0.816923\pi\)
0.389989 + 0.920819i \(0.372479\pi\)
\(168\) 0.768937 4.36086i 0.0593248 0.336448i
\(169\) 11.8654 4.31865i 0.912722 0.332204i
\(170\) 0 0
\(171\) 11.2851 + 3.60045i 0.862995 + 0.275333i
\(172\) −9.44344 −0.720056
\(173\) −8.32761 + 3.03100i −0.633136 + 0.230443i −0.638596 0.769542i \(-0.720484\pi\)
0.00545960 + 0.999985i \(0.498262\pi\)
\(174\) 0.384240 2.17914i 0.0291292 0.165200i
\(175\) 0 0
\(176\) −0.879653 0.738116i −0.0663063 0.0556376i
\(177\) −0.924452 5.24283i −0.0694860 0.394075i
\(178\) 3.08391 + 5.34148i 0.231149 + 0.400361i
\(179\) −2.73273 + 4.73323i −0.204254 + 0.353778i −0.949895 0.312570i \(-0.898810\pi\)
0.745641 + 0.666348i \(0.232143\pi\)
\(180\) 0 0
\(181\) −17.6816 6.43559i −1.31427 0.478354i −0.412650 0.910890i \(-0.635397\pi\)
−0.901617 + 0.432536i \(0.857619\pi\)
\(182\) 0.876613 1.51834i 0.0649789 0.112547i
\(183\) 2.41079 + 4.17561i 0.178211 + 0.308670i
\(184\) 1.98044 + 11.2317i 0.146000 + 0.828009i
\(185\) 0 0
\(186\) 2.95368 2.47843i 0.216574 0.181727i
\(187\) −0.699733 + 3.96838i −0.0511695 + 0.290197i
\(188\) −2.88502 + 1.05006i −0.210411 + 0.0765835i
\(189\) 8.32680 0.605686
\(190\) 0 0
\(191\) −17.2606 −1.24893 −0.624465 0.781053i \(-0.714683\pi\)
−0.624465 + 0.781053i \(0.714683\pi\)
\(192\) 3.80262 1.38404i 0.274431 0.0998846i
\(193\) −1.29789 + 7.36067i −0.0934238 + 0.529833i 0.901795 + 0.432164i \(0.142250\pi\)
−0.995219 + 0.0976691i \(0.968861\pi\)
\(194\) 9.98032 8.37448i 0.716545 0.601253i
\(195\) 0 0
\(196\) −0.0798727 0.452980i −0.00570519 0.0323557i
\(197\) 6.10400 + 10.5724i 0.434892 + 0.753255i 0.997287 0.0736138i \(-0.0234532\pi\)
−0.562395 + 0.826869i \(0.690120\pi\)
\(198\) 1.18528 2.05297i 0.0842343 0.145898i
\(199\) 7.29002 + 2.65335i 0.516776 + 0.188091i 0.587224 0.809424i \(-0.300221\pi\)
−0.0704481 + 0.997515i \(0.522443\pi\)
\(200\) 0 0
\(201\) −2.90560 + 5.03265i −0.204945 + 0.354976i
\(202\) 9.28901 + 16.0890i 0.653573 + 1.13202i
\(203\) −1.89159 10.7277i −0.132764 0.752940i
\(204\) −1.77862 1.49244i −0.124529 0.104492i
\(205\) 0 0
\(206\) 0.949137 5.38282i 0.0661295 0.375039i
\(207\) −9.57865 + 3.48634i −0.665762 + 0.242318i
\(208\) 0.842208 0.0583966
\(209\) −1.68721 + 3.21434i −0.116707 + 0.222341i
\(210\) 0 0
\(211\) −9.45058 + 3.43973i −0.650605 + 0.236801i −0.646175 0.763190i \(-0.723632\pi\)
−0.00442979 + 0.999990i \(0.501410\pi\)
\(212\) −2.14306 + 12.1539i −0.147186 + 0.834734i
\(213\) 0.275914 0.231519i 0.0189053 0.0158634i
\(214\) 12.1855 + 10.2248i 0.832983 + 0.698956i
\(215\) 0 0
\(216\) 4.61954 + 8.00127i 0.314320 + 0.544418i
\(217\) 9.49081 16.4386i 0.644278 1.11592i
\(218\) −3.86074 1.40519i −0.261482 0.0951718i
\(219\) −3.50252 1.27481i −0.236679 0.0861440i
\(220\) 0 0
\(221\) −1.47773 2.55950i −0.0994027 0.172170i
\(222\) 0.418609 + 2.37405i 0.0280952 + 0.159336i
\(223\) −21.6954 18.2046i −1.45283 1.21907i −0.930482 0.366339i \(-0.880611\pi\)
−0.522350 0.852731i \(-0.674944\pi\)
\(224\) 9.73398 8.16778i 0.650379 0.545733i
\(225\) 0 0
\(226\) 3.91079 1.42341i 0.260142 0.0946839i
\(227\) 15.8786 1.05390 0.526949 0.849897i \(-0.323336\pi\)
0.526949 + 0.849897i \(0.323336\pi\)
\(228\) −1.11787 1.76796i −0.0740330 0.117086i
\(229\) 11.3865 0.752438 0.376219 0.926531i \(-0.377224\pi\)
0.376219 + 0.926531i \(0.377224\pi\)
\(230\) 0 0
\(231\) −0.210619 + 1.19448i −0.0138577 + 0.0785909i
\(232\) 9.25894 7.76917i 0.607879 0.510071i
\(233\) 12.1527 + 10.1973i 0.796151 + 0.668050i 0.947260 0.320467i \(-0.103840\pi\)
−0.151109 + 0.988517i \(0.548284\pi\)
\(234\) 0.301914 + 1.71224i 0.0197368 + 0.111933i
\(235\) 0 0
\(236\) 4.52253 7.83325i 0.294392 0.509901i
\(237\) 1.73770 + 0.632473i 0.112876 + 0.0410835i
\(238\) 13.0498 + 4.74975i 0.845895 + 0.307881i
\(239\) −10.4324 + 18.0695i −0.674817 + 1.16882i 0.301705 + 0.953401i \(0.402444\pi\)
−0.976522 + 0.215416i \(0.930889\pi\)
\(240\) 0 0
\(241\) 4.93664 + 27.9971i 0.317997 + 1.80345i 0.554899 + 0.831917i \(0.312757\pi\)
−0.236902 + 0.971533i \(0.576132\pi\)
\(242\) −8.26940 6.93885i −0.531577 0.446046i
\(243\) −9.64478 + 8.09293i −0.618713 + 0.519162i
\(244\) −1.42252 + 8.06750i −0.0910673 + 0.516469i
\(245\) 0 0
\(246\) −2.95963 −0.188699
\(247\) −0.567434 2.60138i −0.0361049 0.165522i
\(248\) 21.0612 1.33739
\(249\) 2.48445 0.904266i 0.157446 0.0573056i
\(250\) 0 0
\(251\) 19.0083 15.9499i 1.19979 1.00675i 0.200157 0.979764i \(-0.435855\pi\)
0.999636 0.0269823i \(-0.00858979\pi\)
\(252\) 5.15108 + 4.32227i 0.324487 + 0.272277i
\(253\) −0.542462 3.07645i −0.0341043 0.193415i
\(254\) 4.81018 + 8.33148i 0.301818 + 0.522763i
\(255\) 0 0
\(256\) 15.5885 + 5.67373i 0.974279 + 0.354608i
\(257\) −5.11403 1.86135i −0.319004 0.116108i 0.177555 0.984111i \(-0.443181\pi\)
−0.496559 + 0.868003i \(0.665403\pi\)
\(258\) 2.91083 5.04170i 0.181220 0.313882i
\(259\) 5.93379 + 10.2776i 0.368708 + 0.638620i
\(260\) 0 0
\(261\) 8.27536 + 6.94385i 0.512232 + 0.429814i
\(262\) −3.00005 + 2.51734i −0.185344 + 0.155522i
\(263\) 3.38955 19.2231i 0.209009 1.18535i −0.681997 0.731355i \(-0.738888\pi\)
0.891006 0.453992i \(-0.150001\pi\)
\(264\) −1.26463 + 0.460287i −0.0778325 + 0.0283287i
\(265\) 0 0
\(266\) 9.89970 + 7.64996i 0.606990 + 0.469049i
\(267\) 3.12956 0.191526
\(268\) −9.27790 + 3.37688i −0.566738 + 0.206276i
\(269\) 3.22722 18.3025i 0.196767 1.11592i −0.713113 0.701049i \(-0.752715\pi\)
0.909880 0.414872i \(-0.136174\pi\)
\(270\) 0 0
\(271\) 1.44946 + 1.21624i 0.0880485 + 0.0738815i 0.685749 0.727838i \(-0.259475\pi\)
−0.597701 + 0.801719i \(0.703919\pi\)
\(272\) 1.15843 + 6.56980i 0.0702403 + 0.398353i
\(273\) −0.444794 0.770406i −0.0269202 0.0466271i
\(274\) 1.23769 2.14374i 0.0747715 0.129508i
\(275\) 0 0
\(276\) 1.69143 + 0.615629i 0.101812 + 0.0370565i
\(277\) −3.38944 + 5.87068i −0.203652 + 0.352735i −0.949702 0.313154i \(-0.898614\pi\)
0.746051 + 0.665889i \(0.231948\pi\)
\(278\) −1.27929 2.21580i −0.0767269 0.132895i
\(279\) 3.26873 + 18.5379i 0.195694 + 1.10984i
\(280\) 0 0
\(281\) −9.41170 + 7.89735i −0.561455 + 0.471116i −0.878798 0.477194i \(-0.841654\pi\)
0.317343 + 0.948311i \(0.397209\pi\)
\(282\) 0.328661 1.86393i 0.0195715 0.110995i
\(283\) 24.1188 8.77851i 1.43371 0.521829i 0.495719 0.868483i \(-0.334905\pi\)
0.937993 + 0.346654i \(0.112682\pi\)
\(284\) 0.611952 0.0363126
\(285\) 0 0
\(286\) −0.532837 −0.0315073
\(287\) −13.6914 + 4.98326i −0.808177 + 0.294152i
\(288\) −2.18818 + 12.4098i −0.128940 + 0.731253i
\(289\) 4.91052 4.12042i 0.288854 0.242377i
\(290\) 0 0
\(291\) −1.14792 6.51018i −0.0672923 0.381634i
\(292\) −3.16638 5.48433i −0.185298 0.320946i
\(293\) −14.0560 + 24.3458i −0.821162 + 1.42229i 0.0836552 + 0.996495i \(0.473341\pi\)
−0.904817 + 0.425800i \(0.859993\pi\)
\(294\) 0.266459 + 0.0969830i 0.0155402 + 0.00565616i
\(295\) 0 0
\(296\) −6.58388 + 11.4036i −0.382680 + 0.662822i
\(297\) −1.26533 2.19162i −0.0734220 0.127171i
\(298\) 2.59518 + 14.7180i 0.150335 + 0.852591i
\(299\) 1.75515 + 1.47275i 0.101503 + 0.0851712i
\(300\) 0 0
\(301\) 4.97669 28.2242i 0.286852 1.62682i
\(302\) −2.30626 + 0.839409i −0.132710 + 0.0483025i
\(303\) 9.42651 0.541539
\(304\) −0.804733 + 5.95588i −0.0461546 + 0.341593i
\(305\) 0 0
\(306\) −12.9414 + 4.71028i −0.739810 + 0.269269i
\(307\) 0.447450 2.53762i 0.0255373 0.144829i −0.969373 0.245593i \(-0.921017\pi\)
0.994910 + 0.100763i \(0.0321285\pi\)
\(308\) −1.57862 + 1.32462i −0.0899504 + 0.0754774i
\(309\) −2.12454 1.78270i −0.120861 0.101414i
\(310\) 0 0
\(311\) −7.31837 12.6758i −0.414987 0.718778i 0.580440 0.814303i \(-0.302880\pi\)
−0.995427 + 0.0955246i \(0.969547\pi\)
\(312\) 0.493525 0.854810i 0.0279403 0.0483941i
\(313\) 1.40398 + 0.511007i 0.0793577 + 0.0288838i 0.381394 0.924413i \(-0.375444\pi\)
−0.302036 + 0.953296i \(0.597666\pi\)
\(314\) −15.9198 5.79432i −0.898405 0.326993i
\(315\) 0 0
\(316\) 1.57093 + 2.72094i 0.0883719 + 0.153065i
\(317\) −0.979782 5.55662i −0.0550301 0.312091i 0.944851 0.327500i \(-0.106206\pi\)
−0.999881 + 0.0154089i \(0.995095\pi\)
\(318\) −5.82820 4.89044i −0.326829 0.274242i
\(319\) −2.53611 + 2.12805i −0.141995 + 0.119148i
\(320\) 0 0
\(321\) 7.58449 2.76053i 0.423325 0.154078i
\(322\) −10.7660 −0.599968
\(323\) 19.5121 8.00451i 1.08568 0.445383i
\(324\) −5.90329 −0.327960
\(325\) 0 0
\(326\) 2.91476 16.5304i 0.161434 0.915536i
\(327\) −1.59694 + 1.34000i −0.0883113 + 0.0741019i
\(328\) −12.3841 10.3915i −0.683800 0.573776i
\(329\) −1.61798 9.17601i −0.0892021 0.505890i
\(330\) 0 0
\(331\) −15.9460 + 27.6193i −0.876472 + 1.51809i −0.0212866 + 0.999773i \(0.506776\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(332\) 4.22113 + 1.53636i 0.231664 + 0.0843189i
\(333\) −11.0592 4.02522i −0.606041 0.220581i
\(334\) 3.96780 6.87244i 0.217109 0.376043i
\(335\) 0 0
\(336\) 0.348687 + 1.97750i 0.0190224 + 0.107882i
\(337\) −11.7495 9.85896i −0.640033 0.537052i 0.263995 0.964524i \(-0.414960\pi\)
−0.904029 + 0.427472i \(0.859404\pi\)
\(338\) −10.1313 + 8.50114i −0.551068 + 0.462401i
\(339\) 0.366691 2.07961i 0.0199159 0.112949i
\(340\) 0 0
\(341\) −5.76886 −0.312401
\(342\) −12.3970 + 0.499010i −0.670355 + 0.0269834i
\(343\) −17.7864 −0.960373
\(344\) 29.8818 10.8761i 1.61112 0.586399i
\(345\) 0 0
\(346\) 7.11053 5.96644i 0.382264 0.320758i
\(347\) 0.0633501 + 0.0531571i 0.00340081 + 0.00285362i 0.644486 0.764616i \(-0.277071\pi\)
−0.641086 + 0.767469i \(0.721516\pi\)
\(348\) −0.331247 1.87860i −0.0177567 0.100703i
\(349\) 2.32166 + 4.02124i 0.124276 + 0.215252i 0.921450 0.388498i \(-0.127006\pi\)
−0.797174 + 0.603750i \(0.793673\pi\)
\(350\) 0 0
\(351\) 1.74415 + 0.634817i 0.0930956 + 0.0338840i
\(352\) −3.62893 1.32082i −0.193423 0.0704001i
\(353\) 1.99701 3.45892i 0.106290 0.184100i −0.807974 0.589218i \(-0.799436\pi\)
0.914265 + 0.405118i \(0.132769\pi\)
\(354\) 2.78803 + 4.82901i 0.148182 + 0.256659i
\(355\) 0 0
\(356\) 4.07319 + 3.41781i 0.215878 + 0.181144i
\(357\) 5.39790 4.52937i 0.285687 0.239720i
\(358\) 0.994055 5.63757i 0.0525374 0.297955i
\(359\) −28.3973 + 10.3358i −1.49875 + 0.545502i −0.955738 0.294220i \(-0.904940\pi\)
−0.543017 + 0.839722i \(0.682718\pi\)
\(360\) 0 0
\(361\) 18.9385 1.52712i 0.996765 0.0803746i
\(362\) 19.7084 1.03585
\(363\) −5.14704 + 1.87337i −0.270149 + 0.0983263i
\(364\) 0.262456 1.48846i 0.0137564 0.0780167i
\(365\) 0 0
\(366\) −3.86863 3.24617i −0.202217 0.169680i
\(367\) −3.14996 17.8643i −0.164427 0.932511i −0.949653 0.313302i \(-0.898565\pi\)
0.785227 0.619208i \(-0.212546\pi\)
\(368\) −2.58588 4.47887i −0.134798 0.233477i
\(369\) 7.22450 12.5132i 0.376092 0.651411i
\(370\) 0 0
\(371\) −35.1958 12.8102i −1.82727 0.665074i
\(372\) 1.66199 2.87865i 0.0861701 0.149251i
\(373\) −12.6075 21.8369i −0.652794 1.13067i −0.982442 0.186568i \(-0.940264\pi\)
0.329648 0.944104i \(-0.393070\pi\)
\(374\) −0.732902 4.15649i −0.0378975 0.214927i
\(375\) 0 0
\(376\) 7.91966 6.64538i 0.408425 0.342710i
\(377\) 0.421644 2.39126i 0.0217158 0.123156i
\(378\) −8.19554 + 2.98293i −0.421533 + 0.153426i
\(379\) −27.5634 −1.41584 −0.707918 0.706294i \(-0.750366\pi\)
−0.707918 + 0.706294i \(0.750366\pi\)
\(380\) 0 0
\(381\) 4.88138 0.250081
\(382\) 16.9885 6.18330i 0.869206 0.316365i
\(383\) −3.18187 + 18.0453i −0.162586 + 0.922072i 0.788932 + 0.614480i \(0.210634\pi\)
−0.951518 + 0.307592i \(0.900477\pi\)
\(384\) 0.528698 0.443630i 0.0269800 0.0226389i
\(385\) 0 0
\(386\) −1.35941 7.70959i −0.0691921 0.392408i
\(387\) 14.2107 + 24.6137i 0.722372 + 1.25119i
\(388\) 5.61577 9.72680i 0.285098 0.493803i
\(389\) 6.75172 + 2.45743i 0.342326 + 0.124596i 0.507461 0.861674i \(-0.330584\pi\)
−0.165136 + 0.986271i \(0.552806\pi\)
\(390\) 0 0
\(391\) −9.07429 + 15.7171i −0.458906 + 0.794849i
\(392\) 0.774441 + 1.34137i 0.0391152 + 0.0677495i
\(393\) 0.345061 + 1.95694i 0.0174060 + 0.0987144i
\(394\) −9.79517 8.21913i −0.493474 0.414074i
\(395\) 0 0
\(396\) 0.354871 2.01257i 0.0178330 0.101136i
\(397\) −11.0172 + 4.00993i −0.552937 + 0.201252i −0.603351 0.797476i \(-0.706168\pi\)
0.0504142 + 0.998728i \(0.483946\pi\)
\(398\) −8.12562 −0.407301
\(399\) 5.87312 2.40935i 0.294024 0.120618i
\(400\) 0 0
\(401\) −36.8475 + 13.4114i −1.84008 + 0.669734i −0.850455 + 0.526048i \(0.823673\pi\)
−0.989623 + 0.143686i \(0.954105\pi\)
\(402\) 1.05694 5.99420i 0.0527154 0.298964i
\(403\) 3.24120 2.71969i 0.161456 0.135477i
\(404\) 12.2688 + 10.2948i 0.610396 + 0.512183i
\(405\) 0 0
\(406\) 5.70480 + 9.88101i 0.283125 + 0.490386i
\(407\) 1.80339 3.12355i 0.0893905 0.154829i
\(408\) 7.34694 + 2.67407i 0.363728 + 0.132386i
\(409\) −8.34099 3.03587i −0.412436 0.150114i 0.127465 0.991843i \(-0.459316\pi\)
−0.539901 + 0.841729i \(0.681538\pi\)
\(410\) 0 0
\(411\) −0.628004 1.08773i −0.0309772 0.0536540i
\(412\) −0.818235 4.64044i −0.0403115 0.228618i
\(413\) 21.0284 + 17.6449i 1.03474 + 0.868249i
\(414\) 8.17873 6.86277i 0.401963 0.337287i
\(415\) 0 0
\(416\) 2.66159 0.968738i 0.130495 0.0474963i
\(417\) −1.29823 −0.0635745
\(418\) 0.509128 3.76809i 0.0249022 0.184303i
\(419\) −7.80196 −0.381151 −0.190575 0.981673i \(-0.561035\pi\)
−0.190575 + 0.981673i \(0.561035\pi\)
\(420\) 0 0
\(421\) 6.00077 34.0320i 0.292459 1.65862i −0.384893 0.922961i \(-0.625762\pi\)
0.677352 0.735659i \(-0.263127\pi\)
\(422\) 8.06938 6.77101i 0.392811 0.329608i
\(423\) 7.07836 + 5.93945i 0.344161 + 0.288786i
\(424\) −7.21648 40.9267i −0.350463 1.98758i
\(425\) 0 0
\(426\) −0.188627 + 0.326711i −0.00913899 + 0.0158292i
\(427\) −23.3622 8.50314i −1.13058 0.411496i
\(428\) 12.8862 + 4.69018i 0.622877 + 0.226709i
\(429\) −0.135181 + 0.234140i −0.00652660 + 0.0113044i
\(430\) 0 0
\(431\) 0.493077 + 2.79638i 0.0237507 + 0.134697i 0.994377 0.105893i \(-0.0337702\pi\)
−0.970627 + 0.240590i \(0.922659\pi\)
\(432\) −3.20943 2.69303i −0.154414 0.129568i
\(433\) 16.7402 14.0467i 0.804481 0.675040i −0.144803 0.989461i \(-0.546255\pi\)
0.949284 + 0.314421i \(0.101810\pi\)
\(434\) −3.45237 + 19.5794i −0.165719 + 0.939839i
\(435\) 0 0
\(436\) −3.54188 −0.169625
\(437\) −12.0920 + 11.0048i −0.578437 + 0.526430i
\(438\) 3.90399 0.186540
\(439\) −30.6114 + 11.1416i −1.46100 + 0.531761i −0.945641 0.325212i \(-0.894564\pi\)
−0.515361 + 0.856973i \(0.672342\pi\)
\(440\) 0 0
\(441\) −1.06047 + 0.889839i −0.0504985 + 0.0423733i
\(442\) 2.37133 + 1.98978i 0.112793 + 0.0946442i
\(443\) −1.34781 7.64381i −0.0640364 0.363169i −0.999940 0.0109135i \(-0.996526\pi\)
0.935904 0.352255i \(-0.114585\pi\)
\(444\) 1.03910 + 1.79977i 0.0493134 + 0.0854134i
\(445\) 0 0
\(446\) 27.8749 + 10.1456i 1.31991 + 0.480409i
\(447\) 7.12581 + 2.59358i 0.337039 + 0.122672i
\(448\) −10.4329 + 18.0703i −0.492909 + 0.853743i
\(449\) −11.4911 19.9031i −0.542296 0.939285i −0.998772 0.0495489i \(-0.984222\pi\)
0.456475 0.889736i \(-0.349112\pi\)
\(450\) 0 0
\(451\) 3.39213 + 2.84633i 0.159729 + 0.134029i
\(452\) 2.74841 2.30619i 0.129274 0.108474i
\(453\) −0.216244 + 1.22638i −0.0101600 + 0.0576203i
\(454\) −15.6283 + 5.68822i −0.733470 + 0.266961i
\(455\) 0 0
\(456\) 5.57344 + 4.30686i 0.261000 + 0.201687i
\(457\) −3.38866 −0.158515 −0.0792573 0.996854i \(-0.525255\pi\)
−0.0792573 + 0.996854i \(0.525255\pi\)
\(458\) −11.2070 + 4.07900i −0.523667 + 0.190599i
\(459\) −2.55299 + 14.4787i −0.119163 + 0.675808i
\(460\) 0 0
\(461\) −8.31382 6.97612i −0.387213 0.324910i 0.428313 0.903630i \(-0.359108\pi\)
−0.815526 + 0.578720i \(0.803552\pi\)
\(462\) −0.220603 1.25110i −0.0102634 0.0582064i
\(463\) 3.65586 + 6.33213i 0.169902 + 0.294279i 0.938385 0.345591i \(-0.112322\pi\)
−0.768483 + 0.639870i \(0.778988\pi\)
\(464\) −2.74045 + 4.74660i −0.127222 + 0.220355i
\(465\) 0 0
\(466\) −15.6142 5.68309i −0.723313 0.263264i
\(467\) −5.42091 + 9.38929i −0.250850 + 0.434484i −0.963760 0.266771i \(-0.914043\pi\)
0.712910 + 0.701255i \(0.247377\pi\)
\(468\) 0.749433 + 1.29806i 0.0346425 + 0.0600026i
\(469\) −5.20325 29.5091i −0.240264 1.36260i
\(470\) 0 0
\(471\) −6.58501 + 5.52548i −0.303421 + 0.254601i
\(472\) −5.28898 + 29.9953i −0.243445 + 1.38065i
\(473\) −8.18489 + 2.97906i −0.376342 + 0.136977i
\(474\) −1.93688 −0.0889640
\(475\) 0 0
\(476\) 11.9720 0.548738
\(477\) 34.9033 12.7038i 1.59811 0.581666i
\(478\) 3.79489 21.5219i 0.173574 0.984388i
\(479\) 2.64084 2.21593i 0.120663 0.101249i −0.580459 0.814289i \(-0.697127\pi\)
0.701123 + 0.713041i \(0.252683\pi\)
\(480\) 0 0
\(481\) 0.459357 + 2.60515i 0.0209449 + 0.118784i
\(482\) −14.8883 25.7873i −0.678143 1.17458i
\(483\) −2.73135 + 4.73084i −0.124281 + 0.215261i
\(484\) −8.74490 3.18288i −0.397495 0.144677i
\(485\) 0 0
\(486\) 6.59359 11.4204i 0.299091 0.518042i
\(487\) 13.4986 + 23.3802i 0.611680 + 1.05946i 0.990957 + 0.134177i \(0.0428391\pi\)
−0.379278 + 0.925283i \(0.623828\pi\)
\(488\) −4.79014 27.1662i −0.216839 1.22976i
\(489\) −6.52436 5.47459i −0.295042 0.247570i
\(490\) 0 0
\(491\) 0.0423665 0.240272i 0.00191197 0.0108433i −0.983837 0.179067i \(-0.942692\pi\)
0.985749 + 0.168224i \(0.0538032\pi\)
\(492\) −2.39758 + 0.872646i −0.108091 + 0.0393419i
\(493\) 19.2334 0.866231
\(494\) 1.49039 + 2.35710i 0.0670558 + 0.106051i
\(495\) 0 0
\(496\) −8.97458 + 3.26648i −0.402971 + 0.146669i
\(497\) −0.322498 + 1.82898i −0.0144660 + 0.0820409i
\(498\) −2.12135 + 1.78002i −0.0950600 + 0.0797648i
\(499\) −2.48864 2.08821i −0.111407 0.0934813i 0.585383 0.810757i \(-0.300944\pi\)
−0.696789 + 0.717276i \(0.745389\pi\)
\(500\) 0 0
\(501\) −2.01327 3.48708i −0.0899462 0.155791i
\(502\) −12.9949 + 22.5078i −0.579991 + 1.00457i
\(503\) 6.69573 + 2.43705i 0.298548 + 0.108663i 0.486951 0.873429i \(-0.338109\pi\)
−0.188403 + 0.982092i \(0.560331\pi\)
\(504\) −21.2775 7.74437i −0.947774 0.344962i
\(505\) 0 0
\(506\) 1.63600 + 2.83363i 0.0727289 + 0.125970i
\(507\) 1.16528 + 6.60865i 0.0517520 + 0.293500i
\(508\) 6.35323 + 5.33099i 0.281879 + 0.236524i
\(509\) 1.32543 1.11216i 0.0587485 0.0492958i −0.612941 0.790129i \(-0.710014\pi\)
0.671689 + 0.740833i \(0.265569\pi\)
\(510\) 0 0
\(511\) 18.0600 6.57332i 0.798929 0.290787i
\(512\) −14.7780 −0.653100
\(513\) −6.15580 + 11.7276i −0.271785 + 0.517786i
\(514\) 5.70021 0.251426
\(515\) 0 0
\(516\) 0.871496 4.94250i 0.0383655 0.217581i
\(517\) −2.16927 + 1.82023i −0.0954042 + 0.0800537i
\(518\) −9.52203 7.98993i −0.418374 0.351058i
\(519\) −0.817842 4.63821i −0.0358993 0.203595i
\(520\) 0 0
\(521\) −6.40164 + 11.0880i −0.280461 + 0.485773i −0.971498 0.237046i \(-0.923821\pi\)
0.691037 + 0.722819i \(0.257154\pi\)
\(522\) −10.6324 3.86989i −0.465369 0.169380i
\(523\) 8.19075 + 2.98119i 0.358157 + 0.130358i 0.514830 0.857292i \(-0.327855\pi\)
−0.156674 + 0.987650i \(0.550077\pi\)
\(524\) −1.68808 + 2.92384i −0.0737441 + 0.127729i
\(525\) 0 0
\(526\) 3.55023 + 20.1343i 0.154797 + 0.877898i
\(527\) 25.6736 + 21.5427i 1.11836 + 0.938416i
\(528\) 0.467494 0.392274i 0.0203451 0.0170715i
\(529\) −1.55076 + 8.79481i −0.0674244 + 0.382383i
\(530\) 0 0
\(531\) −27.2225 −1.18136
\(532\) 10.2753 + 3.27826i 0.445489 + 0.142131i
\(533\) −3.24773 −0.140675
\(534\) −3.08022 + 1.12111i −0.133294 + 0.0485151i
\(535\) 0 0
\(536\) 25.4688 21.3708i 1.10008 0.923080i
\(537\) −2.22508 1.86706i −0.0960193 0.0805697i
\(538\) 3.38020 + 19.1701i 0.145731 + 0.826480i
\(539\) −0.212126 0.367414i −0.00913693 0.0158256i
\(540\) 0 0
\(541\) −10.3511 3.76748i −0.445027 0.161977i 0.109780 0.993956i \(-0.464985\pi\)
−0.554806 + 0.831979i \(0.687208\pi\)
\(542\) −1.86231 0.677825i −0.0799931 0.0291151i
\(543\) 5.00002 8.66029i 0.214571 0.371649i
\(544\) 11.2178 + 19.4297i 0.480958 + 0.833043i
\(545\) 0 0
\(546\) 0.713767 + 0.598922i 0.0305464 + 0.0256315i
\(547\) 14.0921 11.8246i 0.602533 0.505585i −0.289726 0.957110i \(-0.593564\pi\)
0.892259 + 0.451525i \(0.149120\pi\)
\(548\) 0.370562 2.10156i 0.0158296 0.0897741i
\(549\) 23.1680 8.43248i 0.988788 0.359889i
\(550\) 0 0
\(551\) 16.5075 + 5.26662i 0.703244 + 0.224366i
\(552\) −6.06118 −0.257981
\(553\) −8.96012 + 3.26122i −0.381023 + 0.138681i
\(554\) 1.23294 6.99234i 0.0523825 0.297076i
\(555\) 0 0
\(556\) −1.68967 1.41780i −0.0716581 0.0601283i
\(557\) −0.0350939 0.199028i −0.00148698 0.00843307i 0.984055 0.177863i \(-0.0569184\pi\)
−0.985542 + 0.169430i \(0.945807\pi\)
\(558\) −9.85809 17.0747i −0.417326 0.722830i
\(559\) 3.19418 5.53248i 0.135099 0.233999i
\(560\) 0 0
\(561\) −2.01239 0.732451i −0.0849633 0.0309241i
\(562\) 6.43424 11.1444i 0.271412 0.470100i
\(563\) −3.38187 5.85758i −0.142529 0.246867i 0.785919 0.618329i \(-0.212190\pi\)
−0.928448 + 0.371462i \(0.878857\pi\)
\(564\) −0.283333 1.60686i −0.0119305 0.0676611i
\(565\) 0 0
\(566\) −20.5938 + 17.2803i −0.865623 + 0.726344i
\(567\) 3.11103 17.6435i 0.130651 0.740958i
\(568\) −1.93639 + 0.704789i −0.0812492 + 0.0295723i
\(569\) 7.15701 0.300038 0.150019 0.988683i \(-0.452067\pi\)
0.150019 + 0.988683i \(0.452067\pi\)
\(570\) 0 0
\(571\) −18.3153 −0.766471 −0.383236 0.923651i \(-0.625190\pi\)
−0.383236 + 0.923651i \(0.625190\pi\)
\(572\) −0.431647 + 0.157107i −0.0180481 + 0.00656896i
\(573\) 1.59291 9.03382i 0.0665446 0.377393i
\(574\) 11.6904 9.80941i 0.487948 0.409437i
\(575\) 0 0
\(576\) −3.59320 20.3781i −0.149717 0.849086i
\(577\) −10.7897 18.6883i −0.449182 0.778006i 0.549151 0.835723i \(-0.314951\pi\)
−0.998333 + 0.0577173i \(0.981618\pi\)
\(578\) −3.35704 + 5.81457i −0.139635 + 0.241854i
\(579\) −3.73265 1.35857i −0.155124 0.0564603i
\(580\) 0 0
\(581\) −6.81636 + 11.8063i −0.282790 + 0.489807i
\(582\) 3.46199 + 5.99634i 0.143504 + 0.248556i
\(583\) 1.97666 + 11.2102i 0.0818648 + 0.464278i
\(584\) 16.3357 + 13.7073i 0.675975 + 0.567210i
\(585\) 0 0
\(586\) 5.11301 28.9973i 0.211216 1.19787i
\(587\) 27.1976 9.89913i 1.12257 0.408581i 0.286978 0.957937i \(-0.407349\pi\)
0.835588 + 0.549356i \(0.185127\pi\)
\(588\) 0.244452 0.0100810
\(589\) 16.1360 + 25.5196i 0.664872 + 1.05152i
\(590\) 0 0
\(591\) −6.09671 + 2.21902i −0.250785 + 0.0912783i
\(592\) 1.03688 5.88043i 0.0426154 0.241684i
\(593\) −13.6533 + 11.4565i −0.560674 + 0.470461i −0.878536 0.477676i \(-0.841479\pi\)
0.317863 + 0.948137i \(0.397035\pi\)
\(594\) 2.03050 + 1.70379i 0.0833123 + 0.0699073i
\(595\) 0 0
\(596\) 6.44194 + 11.1578i 0.263872 + 0.457040i
\(597\) −2.06147 + 3.57058i −0.0843706 + 0.146134i
\(598\) −2.25507 0.820779i −0.0922167 0.0335642i
\(599\) 8.03512 + 2.92455i 0.328306 + 0.119494i 0.500914 0.865497i \(-0.332997\pi\)
−0.172608 + 0.984991i \(0.555219\pi\)
\(600\) 0 0
\(601\) 2.09514 + 3.62889i 0.0854627 + 0.148026i 0.905588 0.424158i \(-0.139430\pi\)
−0.820126 + 0.572184i \(0.806096\pi\)
\(602\) 5.21260 + 29.5621i 0.212450 + 1.20486i
\(603\) 22.7632 + 19.1006i 0.926991 + 0.777838i
\(604\) −1.62078 + 1.36000i −0.0659487 + 0.0553375i
\(605\) 0 0
\(606\) −9.27791 + 3.37688i −0.376889 + 0.137177i
\(607\) −7.59458 −0.308254 −0.154127 0.988051i \(-0.549257\pi\)
−0.154127 + 0.988051i \(0.549257\pi\)
\(608\) 4.30752 + 19.7477i 0.174693 + 0.800876i
\(609\) 5.78925 0.234592
\(610\) 0 0
\(611\) 0.360654 2.04537i 0.0145905 0.0827469i
\(612\) −9.09491 + 7.63153i −0.367640 + 0.308486i
\(613\) −13.7466 11.5348i −0.555220 0.465885i 0.321484 0.946915i \(-0.395818\pi\)
−0.876704 + 0.481030i \(0.840263\pi\)
\(614\) 0.468661 + 2.65791i 0.0189136 + 0.107264i
\(615\) 0 0
\(616\) 3.46964 6.00960i 0.139796 0.242134i
\(617\) 38.1365 + 13.8805i 1.53532 + 0.558809i 0.964916 0.262558i \(-0.0845662\pi\)
0.570400 + 0.821367i \(0.306788\pi\)
\(618\) 2.72967 + 0.993517i 0.109803 + 0.0399651i
\(619\) 12.7804 22.1363i 0.513688 0.889733i −0.486186 0.873855i \(-0.661612\pi\)
0.999874 0.0158781i \(-0.00505438\pi\)
\(620\) 0 0
\(621\) −1.97918 11.2245i −0.0794218 0.450423i
\(622\) 11.7439 + 9.85430i 0.470887 + 0.395121i
\(623\) −12.3616 + 10.3726i −0.495257 + 0.415570i
\(624\) −0.0777239 + 0.440794i −0.00311145 + 0.0176459i
\(625\) 0 0
\(626\) −1.56491 −0.0625463
\(627\) −1.52662 1.17969i −0.0609672 0.0471122i
\(628\) −14.6049 −0.582801
\(629\) −19.6901 + 7.16661i −0.785096 + 0.285751i
\(630\) 0 0
\(631\) 3.55051 2.97923i 0.141344 0.118601i −0.569375 0.822078i \(-0.692815\pi\)
0.710718 + 0.703477i \(0.248370\pi\)
\(632\) −8.10461 6.80057i −0.322384 0.270512i
\(633\) −0.928128 5.26367i −0.0368898 0.209212i
\(634\) 2.95490 + 5.11804i 0.117354 + 0.203263i
\(635\) 0 0
\(636\) −6.16333 2.24327i −0.244392 0.0889514i
\(637\) 0.292397 + 0.106424i 0.0115852 + 0.00421666i
\(638\) 1.73379 3.00302i 0.0686415 0.118891i
\(639\) −0.920880 1.59501i −0.0364295 0.0630977i
\(640\) 0 0
\(641\) 17.7783 + 14.9178i 0.702201 + 0.589217i 0.922399 0.386239i \(-0.126226\pi\)
−0.220198 + 0.975455i \(0.570670\pi\)
\(642\) −6.47602 + 5.43402i −0.255588 + 0.214464i
\(643\) −2.64733 + 15.0138i −0.104401 + 0.592086i 0.887057 + 0.461659i \(0.152746\pi\)
−0.991458 + 0.130426i \(0.958365\pi\)
\(644\) −8.72149 + 3.17436i −0.343675 + 0.125087i
\(645\) 0 0
\(646\) −16.3370 + 14.8682i −0.642773 + 0.584982i
\(647\) −17.6749 −0.694872 −0.347436 0.937704i \(-0.612948\pi\)
−0.347436 + 0.937704i \(0.612948\pi\)
\(648\) 18.6797 6.79885i 0.733808 0.267084i
\(649\) 1.44870 8.21599i 0.0568664 0.322506i
\(650\) 0 0
\(651\) 7.72773 + 6.48434i 0.302874 + 0.254141i
\(652\) −2.51277 14.2506i −0.0984075 0.558097i
\(653\) −3.43228 5.94488i −0.134315 0.232641i 0.791020 0.611790i \(-0.209550\pi\)
−0.925336 + 0.379149i \(0.876217\pi\)
\(654\) 1.09174 1.89095i 0.0426905 0.0739420i
\(655\) 0 0
\(656\) 6.88879 + 2.50731i 0.268962 + 0.0978941i
\(657\) −9.52969 + 16.5059i −0.371789 + 0.643957i
\(658\) 4.87962 + 8.45175i 0.190227 + 0.329484i
\(659\) 4.75738 + 26.9804i 0.185321 + 1.05101i 0.925542 + 0.378645i \(0.123610\pi\)
−0.740221 + 0.672364i \(0.765279\pi\)
\(660\) 0 0
\(661\) 21.8707 18.3517i 0.850673 0.713800i −0.109265 0.994013i \(-0.534850\pi\)
0.959938 + 0.280213i \(0.0904051\pi\)
\(662\) 5.80051 32.8963i 0.225443 1.27855i
\(663\) 1.47596 0.537206i 0.0573216 0.0208633i
\(664\) −15.1263 −0.587014
\(665\) 0 0
\(666\) 12.3268 0.477655
\(667\) −14.0113 + 5.09971i −0.542521 + 0.197462i
\(668\) 1.18795 6.73722i 0.0459633 0.260671i
\(669\) 11.5301 9.67489i 0.445779 0.374053i
\(670\) 0 0
\(671\) 1.31206 + 7.44107i 0.0506516 + 0.287259i
\(672\) 3.37654 + 5.84833i 0.130253 + 0.225604i
\(673\) 22.5844 39.1173i 0.870565 1.50786i 0.00915115 0.999958i \(-0.497087\pi\)
0.861414 0.507904i \(-0.169580\pi\)
\(674\) 15.0960 + 5.49451i 0.581478 + 0.211641i
\(675\) 0 0
\(676\) −5.70071 + 9.87392i −0.219258 + 0.379766i
\(677\) −23.4814 40.6710i −0.902463 1.56311i −0.824287 0.566172i \(-0.808424\pi\)
−0.0781759 0.996940i \(-0.524910\pi\)
\(678\) 0.384073 + 2.17819i 0.0147502 + 0.0836527i
\(679\) 26.1116 + 21.9102i 1.00207 + 0.840838i
\(680\) 0 0
\(681\) −1.46537 + 8.31051i −0.0561530 + 0.318459i
\(682\) 5.67792 2.06659i 0.217419 0.0791339i
\(683\) −19.4215 −0.743142 −0.371571 0.928405i \(-0.621181\pi\)
−0.371571 + 0.928405i \(0.621181\pi\)
\(684\) −9.89561 + 4.05951i −0.378368 + 0.155219i
\(685\) 0 0
\(686\) 17.5060 6.37166i 0.668382 0.243271i
\(687\) −1.05081 + 5.95943i −0.0400909 + 0.227367i
\(688\) −11.0464 + 9.26901i −0.421139 + 0.353378i
\(689\) −6.39554 5.36650i −0.243651 0.204447i
\(690\) 0 0
\(691\) 8.93344 + 15.4732i 0.339844 + 0.588627i 0.984403 0.175927i \(-0.0562923\pi\)
−0.644559 + 0.764555i \(0.722959\pi\)
\(692\) 4.00099 6.92991i 0.152095 0.263436i
\(693\) 5.82809 + 2.12125i 0.221391 + 0.0805797i
\(694\) −0.0813941 0.0296250i −0.00308968 0.00112455i
\(695\) 0 0
\(696\) 3.21175 + 5.56292i 0.121741 + 0.210862i
\(697\) −4.46716 25.3346i −0.169206 0.959615i
\(698\) −3.72561 3.12615i −0.141016 0.118327i
\(699\) −6.45860 + 5.41941i −0.244287 + 0.204981i
\(700\) 0 0
\(701\) −4.04522 + 1.47234i −0.152786 + 0.0556096i −0.417281 0.908777i \(-0.637017\pi\)
0.264495 + 0.964387i \(0.414795\pi\)
\(702\) −1.94406 −0.0733739
\(703\) −18.8619 + 0.759235i −0.711389 + 0.0286351i
\(704\) 6.34150 0.239004
\(705\) 0 0
\(706\) −0.726431 + 4.11979i −0.0273396 + 0.155050i
\(707\) −37.2343 + 31.2432i −1.40034 + 1.17502i
\(708\) 3.68240 + 3.08990i 0.138393 + 0.116125i
\(709\) 6.10059 + 34.5982i 0.229112 + 1.29936i 0.854665 + 0.519179i \(0.173762\pi\)
−0.625553 + 0.780182i \(0.715127\pi\)
\(710\) 0 0
\(711\) 4.72796 8.18907i 0.177312 0.307114i
\(712\) −16.8251 6.12382i −0.630545 0.229500i
\(713\) −24.4150 8.88632i −0.914347 0.332795i
\(714\) −3.69024 + 6.39168i −0.138104 + 0.239203i
\(715\) 0 0
\(716\) −0.856958 4.86005i −0.0320260 0.181629i
\(717\) −8.49442 7.12767i −0.317230 0.266188i
\(718\) 24.2471 20.3457i 0.904893 0.759295i
\(719\) 5.10577 28.9563i 0.190413 1.07989i −0.728388 0.685165i \(-0.759730\pi\)
0.918801 0.394722i \(-0.129159\pi\)
\(720\) 0 0
\(721\) 14.3004 0.532574
\(722\) −18.0929 + 8.28745i −0.673349 + 0.308427i
\(723\) −15.1087 −0.561898
\(724\) 15.9656 5.81100i 0.593357 0.215964i
\(725\) 0 0
\(726\) 4.39480 3.68767i 0.163106 0.136862i
\(727\) −17.2796 14.4993i −0.640864 0.537749i 0.263419 0.964681i \(-0.415150\pi\)
−0.904283 + 0.426933i \(0.859594\pi\)
\(728\) 0.883786 + 5.01220i 0.0327553 + 0.185765i
\(729\) 6.46109 + 11.1909i 0.239300 + 0.414479i
\(730\) 0 0
\(731\) 47.5506 + 17.3070i 1.75872 + 0.640123i
\(732\) −4.09108 1.48903i −0.151211 0.0550362i
\(733\) 18.9501 32.8225i 0.699938 1.21233i −0.268550 0.963266i \(-0.586544\pi\)
0.968488 0.249062i \(-0.0801223\pi\)
\(734\) 9.49990 + 16.4543i 0.350648 + 0.607340i
\(735\) 0 0
\(736\) −13.3238 11.1800i −0.491121 0.412099i
\(737\) −6.97613 + 5.85367i −0.256969 + 0.215623i
\(738\) −2.62798 + 14.9040i −0.0967372 + 0.548624i
\(739\) 24.4523 8.89989i 0.899491 0.327388i 0.149442 0.988770i \(-0.452252\pi\)
0.750049 + 0.661383i \(0.230030\pi\)
\(740\) 0 0
\(741\) 1.41388 0.0569119i 0.0519401 0.00209071i
\(742\) 39.2300 1.44018
\(743\) 47.3487 17.2335i 1.73706 0.632237i 0.737964 0.674841i \(-0.235788\pi\)
0.999092 + 0.0426041i \(0.0135654\pi\)
\(744\) −1.94365 + 11.0230i −0.0712577 + 0.404123i
\(745\) 0 0
\(746\) 20.2315 + 16.9762i 0.740728 + 0.621544i
\(747\) −2.34763 13.3140i −0.0858951 0.487135i
\(748\) −1.81926 3.15105i −0.0665187 0.115214i
\(749\) −20.8089 + 36.0420i −0.760339 + 1.31695i
\(750\) 0 0
\(751\) −25.5462 9.29806i −0.932195 0.339291i −0.169116 0.985596i \(-0.554091\pi\)
−0.763079 + 0.646305i \(0.776313\pi\)
\(752\) −2.34405 + 4.06002i −0.0854789 + 0.148054i
\(753\) 6.59363 + 11.4205i 0.240285 + 0.416186i
\(754\) 0.441631 + 2.50461i 0.0160832 + 0.0912126i
\(755\) 0 0
\(756\) −5.75963 + 4.83291i −0.209476 + 0.175771i
\(757\) −5.71273 + 32.3985i −0.207633 + 1.17754i 0.685610 + 0.727969i \(0.259536\pi\)
−0.893243 + 0.449575i \(0.851576\pi\)
\(758\) 27.1289 9.87411i 0.985366 0.358644i
\(759\) 1.66021 0.0602619
\(760\) 0 0
\(761\) 3.47213 0.125865 0.0629323 0.998018i \(-0.479955\pi\)
0.0629323 + 0.998018i \(0.479955\pi\)
\(762\) −4.80443 + 1.74867i −0.174046 + 0.0633476i
\(763\) 1.86657 10.5858i 0.0675743 0.383233i
\(764\) 11.9391 10.0181i 0.431941 0.362442i
\(765\) 0 0
\(766\) −3.33270 18.9007i −0.120415 0.682910i
\(767\) 3.05943 + 5.29909i 0.110470 + 0.191339i
\(768\) −4.40811 + 7.63507i −0.159064 + 0.275507i
\(769\) 29.7634 + 10.8330i 1.07330 + 0.390648i 0.817408 0.576059i \(-0.195410\pi\)
0.255887 + 0.966707i \(0.417632\pi\)
\(770\) 0 0
\(771\) 1.44615 2.50480i 0.0520817 0.0902081i
\(772\) −3.37442 5.84466i −0.121448 0.210354i
\(773\) 6.08960 + 34.5358i 0.219028 + 1.24217i 0.873779 + 0.486323i \(0.161662\pi\)
−0.654752 + 0.755844i \(0.727227\pi\)
\(774\) −22.8042 19.1350i −0.819679 0.687792i
\(775\) 0 0
\(776\) −6.56750 + 37.2461i −0.235759 + 1.33706i
\(777\) −5.92670 + 2.15714i −0.212619 + 0.0773870i
\(778\) −7.52562 −0.269807
\(779\) 3.10322 22.9672i 0.111184 0.822884i
\(780\) 0 0
\(781\) 0.530395 0.193048i 0.0189790 0.00690780i
\(782\) 3.30085 18.7201i 0.118038 0.669428i
\(783\) −9.25302 + 7.76421i −0.330676 + 0.277470i
\(784\) −0.538043 0.451472i −0.0192158 0.0161240i
\(785\) 0 0
\(786\) −1.04066 1.80248i −0.0371191 0.0642922i
\(787\) 21.0914 36.5314i 0.751829 1.30221i −0.195107 0.980782i \(-0.562505\pi\)
0.946936 0.321424i \(-0.104161\pi\)
\(788\) −10.3584 3.77015i −0.369003 0.134306i
\(789\) 9.74816 + 3.54804i 0.347044 + 0.126314i
\(790\) 0 0
\(791\) 5.44425 + 9.42971i 0.193575 + 0.335282i
\(792\) 1.19498 + 6.77708i 0.0424618 + 0.240813i
\(793\) −4.24522 3.56216i −0.150752 0.126496i
\(794\) 9.40703 7.89343i 0.333843 0.280127i
\(795\) 0 0
\(796\) −6.58251 + 2.39584i −0.233311 + 0.0849182i
\(797\) 20.4194 0.723291 0.361646 0.932316i \(-0.382215\pi\)
0.361646 + 0.932316i \(0.382215\pi\)
\(798\) −4.91743 + 4.47531i −0.174075 + 0.158424i
\(799\) 16.4514 0.582008
\(800\) 0 0
\(801\) 2.77886 15.7597i 0.0981862 0.556842i
\(802\) 31.4623 26.4000i 1.11097 0.932216i
\(803\) −4.47449 3.75454i −0.157901 0.132495i
\(804\) −0.911169 5.16750i −0.0321345 0.182244i
\(805\) 0 0
\(806\) −2.21582 + 3.83792i −0.0780491 + 0.135185i
\(807\) 9.28131 + 3.37812i 0.326717 + 0.118915i
\(808\) −50.6786 18.4455i −1.78287 0.648910i
\(809\) −14.2768 + 24.7282i −0.501946 + 0.869396i 0.498051 + 0.867148i \(0.334049\pi\)
−0.999997 + 0.00224865i \(0.999284\pi\)
\(810\) 0 0
\(811\) −0.279849 1.58710i −0.00982681 0.0557306i 0.979500 0.201444i \(-0.0645634\pi\)
−0.989327 + 0.145713i \(0.953452\pi\)
\(812\) 7.53483 + 6.32248i 0.264421 + 0.221875i
\(813\) −0.770321 + 0.646376i −0.0270163 + 0.0226694i
\(814\) −0.655998 + 3.72035i −0.0229927 + 0.130398i
\(815\) 0 0
\(816\) −3.54540 −0.124114
\(817\) 36.0723 + 27.8747i 1.26201 + 0.975213i
\(818\) 9.29706 0.325064
\(819\) −4.27453 + 1.55580i −0.149364 + 0.0543642i
\(820\) 0 0
\(821\) −6.16578 + 5.17371i −0.215187 + 0.180564i −0.744010 0.668169i \(-0.767078\pi\)
0.528822 + 0.848733i \(0.322634\pi\)
\(822\) 1.00777 + 0.845617i 0.0351499 + 0.0294943i
\(823\) 6.48442 + 36.7750i 0.226033 + 1.28189i 0.860701 + 0.509110i \(0.170025\pi\)
−0.634669 + 0.772784i \(0.718863\pi\)
\(824\) 7.93356 + 13.7413i 0.276379 + 0.478702i
\(825\) 0 0
\(826\) −27.0179 9.83370i −0.940072 0.342158i
\(827\) −10.2711 3.73836i −0.357160 0.129996i 0.157207 0.987566i \(-0.449751\pi\)
−0.514367 + 0.857570i \(0.671973\pi\)
\(828\) 4.60205 7.97098i 0.159932 0.277011i
\(829\) −16.8187 29.1309i −0.584139 1.01176i −0.994982 0.100052i \(-0.968099\pi\)
0.410843 0.911706i \(-0.365234\pi\)
\(830\) 0 0
\(831\) −2.75979 2.31574i −0.0957361 0.0803322i
\(832\) −3.56293 + 2.98966i −0.123523 + 0.103648i
\(833\) −0.427995 + 2.42728i −0.0148291 + 0.0841002i
\(834\) 1.27776 0.465068i 0.0442454 0.0161040i
\(835\) 0 0
\(836\) −0.698579 3.20262i −0.0241609 0.110765i
\(837\) −21.0478 −0.727517
\(838\) 7.67897 2.79492i 0.265266 0.0965488i
\(839\) 2.40910 13.6627i 0.0831714 0.471689i −0.914565 0.404439i \(-0.867467\pi\)
0.997736 0.0672492i \(-0.0214222\pi\)
\(840\) 0 0
\(841\) −10.1104 8.48360i −0.348633 0.292538i
\(842\) 6.28522 + 35.6452i 0.216603 + 1.22842i
\(843\) −3.26474 5.65470i −0.112444 0.194758i
\(844\) 4.54052 7.86440i 0.156291 0.270704i
\(845\) 0 0
\(846\) −9.09448 3.31012i −0.312675 0.113804i
\(847\) 14.1214 24.4591i 0.485219 0.840423i
\(848\) 9.42259 + 16.3204i 0.323573 + 0.560445i
\(849\) 2.36867 + 13.4334i 0.0812925 + 0.461033i
\(850\) 0 0
\(851\) 12.4438 10.4416i 0.426568 0.357933i
\(852\) −0.0564745 + 0.320283i −0.00193478 + 0.0109727i
\(853\) −27.7657 + 10.1059i −0.950680 + 0.346019i −0.770375 0.637591i \(-0.779931\pi\)
−0.180305 + 0.983611i \(0.557709\pi\)
\(854\) 26.0400 0.891071
\(855\) 0 0
\(856\) −46.1773 −1.57831
\(857\) 4.02741 1.46586i 0.137574 0.0500727i −0.272316 0.962208i \(-0.587790\pi\)
0.409889 + 0.912135i \(0.365567\pi\)
\(858\) 0.0491733 0.278876i 0.00167875 0.00952066i
\(859\) −26.7935 + 22.4824i −0.914181 + 0.767089i −0.972910 0.231185i \(-0.925740\pi\)
0.0587290 + 0.998274i \(0.481295\pi\)
\(860\) 0 0
\(861\) −1.34461 7.62567i −0.0458243 0.259882i
\(862\) −1.48706 2.57566i −0.0506494 0.0877273i
\(863\) 10.0153 17.3470i 0.340924 0.590498i −0.643681 0.765294i \(-0.722593\pi\)
0.984605 + 0.174797i \(0.0559268\pi\)
\(864\) −13.2402 4.81904i −0.450441 0.163947i
\(865\) 0 0
\(866\) −11.4443 + 19.8221i −0.388893 + 0.673583i
\(867\) 1.70337 + 2.95032i 0.0578494 + 0.100198i
\(868\) 2.97623 + 16.8790i 0.101020 + 0.572911i
\(869\) 2.21992 + 1.86274i 0.0753058 + 0.0631891i
\(870\) 0 0
\(871\) 1.15983 6.57770i 0.0392992 0.222877i
\(872\) 11.2075 4.07921i 0.379535 0.138139i
\(873\) −33.8030 −1.14406
\(874\) 7.95907 15.1630i 0.269220 0.512898i
\(875\) 0 0
\(876\) 3.16260 1.15109i 0.106854 0.0388917i
\(877\) −7.91697 + 44.8994i −0.267337 + 1.51614i 0.494959 + 0.868916i \(0.335183\pi\)
−0.762297 + 0.647228i \(0.775928\pi\)
\(878\) 26.1376 21.9320i 0.882100 0.740170i
\(879\) −11.4449 9.60340i −0.386027 0.323915i
\(880\) 0 0
\(881\) 8.63649 + 14.9588i 0.290971 + 0.503976i 0.974040 0.226378i \(-0.0726885\pi\)
−0.683069 + 0.730354i \(0.739355\pi\)
\(882\) 0.724983 1.25571i 0.0244114 0.0422819i
\(883\) −33.0707 12.0368i −1.11292 0.405069i −0.280856 0.959750i \(-0.590618\pi\)
−0.832063 + 0.554680i \(0.812840\pi\)
\(884\) 2.50768 + 0.912722i 0.0843425 + 0.0306982i
\(885\) 0 0
\(886\) 4.06483 + 7.04049i 0.136561 + 0.236530i
\(887\) −0.548919 3.11307i −0.0184309 0.104527i 0.974205 0.225667i \(-0.0724561\pi\)
−0.992635 + 0.121140i \(0.961345\pi\)
\(888\) −5.36082 4.49826i −0.179897 0.150952i
\(889\) −19.2812 + 16.1789i −0.646671 + 0.542622i
\(890\) 0 0
\(891\) −5.11654 + 1.86227i −0.171410 + 0.0623883i
\(892\) 25.5727 0.856237
\(893\) 14.1198 + 4.50482i 0.472500 + 0.150748i
\(894\) −7.94259 −0.265640
\(895\) 0 0
\(896\) −0.617962 + 3.50464i −0.0206447 + 0.117082i
\(897\) −0.932781 + 0.782696i −0.0311447 + 0.0261335i
\(898\) 18.4399 + 15.4729i 0.615346 + 0.516337i
\(899\) 4.78140 + 27.1167i 0.159469 + 0.904391i
\(900\) 0 0
\(901\) 33.0655 57.2711i 1.10157 1.90798i
\(902\) −4.35830 1.58629i −0.145116 0.0528178i
\(903\) 14.3127 + 5.20939i 0.476297 + 0.173358i
\(904\) −6.04071 + 10.4628i −0.200911 + 0.347988i
\(905\) 0 0
\(906\) −0.226494 1.28451i −0.00752476 0.0426751i
\(907\) 12.2041 + 10.2405i 0.405230 + 0.340029i 0.822511 0.568749i \(-0.192572\pi\)
−0.417281 + 0.908778i \(0.637017\pi\)
\(908\) −10.9832 + 9.21597i −0.364489 + 0.305843i
\(909\) 8.37018 47.4697i 0.277621 1.57447i
\(910\) 0 0
\(911\) 0.0577380 0.00191294 0.000956472 1.00000i \(-0.499696\pi\)
0.000956472 1.00000i \(0.499696\pi\)
\(912\) −3.04292 0.970824i −0.100761 0.0321472i
\(913\) 4.14323 0.137121
\(914\) 3.33524 1.21393i 0.110320 0.0401532i
\(915\) 0 0
\(916\) −7.87599 + 6.60874i −0.260230 + 0.218359i
\(917\) −7.84905 6.58614i −0.259199 0.217493i
\(918\) −2.67400 15.1650i −0.0882553 0.500521i
\(919\) −25.0245 43.3436i −0.825481 1.42977i −0.901551 0.432672i \(-0.857571\pi\)
0.0760708 0.997102i \(-0.475762\pi\)
\(920\) 0 0
\(921\) 1.28684 + 0.468372i 0.0424029 + 0.0154334i
\(922\) 10.6818 + 3.88787i 0.351788 + 0.128040i
\(923\) −0.206988 + 0.358514i −0.00681310 + 0.0118006i
\(924\) −0.547595 0.948463i −0.0180146 0.0312021i
\(925\) 0 0
\(926\) −5.86660 4.92267i −0.192789 0.161769i
\(927\) −10.8637 + 9.11573i −0.356811 + 0.299400i
\(928\) −3.20080 + 18.1526i −0.105071 + 0.595889i
\(929\) 15.9606 5.80920i 0.523652 0.190594i −0.0666498 0.997776i \(-0.521231\pi\)
0.590302 + 0.807183i \(0.299009\pi\)
\(930\) 0 0
\(931\) −1.03199 + 1.96607i −0.0338220 + 0.0644353i
\(932\) −14.3246 −0.469218
\(933\) 7.30963 2.66049i 0.239306 0.0871004i
\(934\) 1.97190 11.1832i 0.0645227 0.365926i
\(935\) 0 0
\(936\) −3.86640 3.24430i −0.126377 0.106043i
\(937\) 5.85065 + 33.1807i 0.191132 + 1.08397i 0.917820 + 0.396997i \(0.129948\pi\)
−0.726687 + 0.686968i \(0.758941\pi\)
\(938\) 15.6923 + 27.1799i 0.512373 + 0.887456i
\(939\) −0.397018 + 0.687655i −0.0129562 + 0.0224408i
\(940\) 0 0
\(941\) 25.5345 + 9.29380i 0.832401 + 0.302969i 0.722844 0.691011i \(-0.242834\pi\)
0.109557 + 0.993980i \(0.465057\pi\)
\(942\) 4.50180 7.79734i 0.146676 0.254051i
\(943\) 9.97169 + 17.2715i 0.324723 + 0.562436i
\(944\) −2.39838 13.6019i −0.0780605 0.442703i
\(945\) 0 0
\(946\) 6.98867 5.86419i 0.227221 0.190661i
\(947\) 5.78183 32.7904i 0.187884 1.06554i −0.734309 0.678815i \(-0.762494\pi\)
0.922193 0.386729i \(-0.126395\pi\)
\(948\) −1.56906 + 0.571090i −0.0509606 + 0.0185481i
\(949\) 4.28402 0.139065
\(950\) 0 0
\(951\) 2.99864 0.0972376
\(952\) −37.8830 + 13.7883i −1.22780 + 0.446881i
\(953\) 5.28039 29.9466i 0.171049 0.970065i −0.771558 0.636159i \(-0.780522\pi\)
0.942606 0.333906i \(-0.108367\pi\)
\(954\) −29.8022 + 25.0070i −0.964882 + 0.809632i
\(955\) 0 0
\(956\) −3.27151 18.5536i −0.105808 0.600068i
\(957\) −0.879728 1.52373i −0.0284376 0.0492553i
\(958\) −1.80540 + 3.12704i −0.0583297 + 0.101030i
\(959\) 6.08578 + 2.21504i 0.196520 + 0.0715274i
\(960\) 0 0
\(961\) −8.49003 + 14.7052i −0.273872 + 0.474360i
\(962\) −1.38536 2.39952i −0.0446660 0.0773637i
\(963\) −7.16679 40.6449i −0.230946 1.30976i
\(964\) −19.6643 16.5003i −0.633344 0.531438i
\(965\) 0 0
\(966\) 0.993554 5.63472i 0.0319671 0.181294i
\(967\) −55.3648 + 20.1511i −1.78041 + 0.648017i −0.780677 + 0.624934i \(0.785126\pi\)
−0.999734 + 0.0230823i \(0.992652\pi\)
\(968\) 31.3371 1.00721
\(969\) 2.38870 + 10.9509i 0.0767361 + 0.351795i
\(970\) 0 0
\(971\) 38.4033 13.9777i 1.23242 0.448564i 0.357995 0.933724i \(-0.383461\pi\)
0.874426 + 0.485159i \(0.161238\pi\)
\(972\) 1.97411 11.1957i 0.0633196 0.359103i
\(973\) 5.12794 4.30285i 0.164394 0.137943i
\(974\) −21.6614 18.1761i −0.694075 0.582398i
\(975\) 0 0
\(976\) 6.25450 + 10.8331i 0.200202 + 0.346760i
\(977\) −17.9716 + 31.1276i −0.574961 + 0.995862i 0.421085 + 0.907021i \(0.361649\pi\)
−0.996046 + 0.0888405i \(0.971684\pi\)
\(978\) 8.38270 + 3.05105i 0.268049 + 0.0975619i
\(979\) 4.60853 + 1.67737i 0.147289 + 0.0536089i
\(980\) 0 0
\(981\) 5.32991 + 9.23167i 0.170171 + 0.294745i
\(982\) 0.0443747 + 0.251662i 0.00141606 + 0.00803085i
\(983\) 7.71144 + 6.47067i 0.245957 + 0.206382i 0.757429 0.652918i \(-0.226455\pi\)
−0.511472 + 0.859300i \(0.670900\pi\)
\(984\) 6.58159 5.52261i 0.209813 0.176054i
\(985\) 0 0
\(986\) −18.9303 + 6.89005i −0.602862 + 0.219424i
\(987\) 4.95185 0.157619
\(988\) 1.90235 + 1.47003i 0.0605217 + 0.0467680i
\(989\) −39.2290 −1.24741
\(990\) 0 0
\(991\) −3.13089 + 17.7562i −0.0994561 + 0.564043i 0.893834 + 0.448397i \(0.148005\pi\)
−0.993290 + 0.115646i \(0.963106\pi\)
\(992\) −24.6047 + 20.6458i −0.781200 + 0.655504i
\(993\) −12.9838 10.8947i −0.412028 0.345732i
\(994\) −0.337786 1.91568i −0.0107139 0.0607616i
\(995\) 0 0
\(996\) −1.19365 + 2.06746i −0.0378223 + 0.0655101i
\(997\) 17.5954 + 6.40419i 0.557251 + 0.202823i 0.605265 0.796024i \(-0.293067\pi\)
−0.0480143 + 0.998847i \(0.515289\pi\)
\(998\) 3.19747 + 1.16378i 0.101214 + 0.0368390i
\(999\) 6.57968 11.3963i 0.208172 0.360564i
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 475.2.l.f.176.3 48
5.2 odd 4 95.2.p.a.24.3 yes 48
5.3 odd 4 95.2.p.a.24.6 yes 48
5.4 even 2 inner 475.2.l.f.176.6 48
15.2 even 4 855.2.da.b.784.6 48
15.8 even 4 855.2.da.b.784.3 48
19.2 odd 18 9025.2.a.ct.1.9 24
19.4 even 9 inner 475.2.l.f.251.3 48
19.17 even 9 9025.2.a.cu.1.16 24
95.2 even 36 1805.2.b.l.1084.9 24
95.4 even 18 inner 475.2.l.f.251.6 48
95.17 odd 36 1805.2.b.k.1084.16 24
95.23 odd 36 95.2.p.a.4.3 48
95.42 odd 36 95.2.p.a.4.6 yes 48
95.59 odd 18 9025.2.a.ct.1.16 24
95.74 even 18 9025.2.a.cu.1.9 24
95.78 even 36 1805.2.b.l.1084.16 24
95.93 odd 36 1805.2.b.k.1084.9 24
285.23 even 36 855.2.da.b.289.6 48
285.137 even 36 855.2.da.b.289.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.4.3 48 95.23 odd 36
95.2.p.a.4.6 yes 48 95.42 odd 36
95.2.p.a.24.3 yes 48 5.2 odd 4
95.2.p.a.24.6 yes 48 5.3 odd 4
475.2.l.f.176.3 48 1.1 even 1 trivial
475.2.l.f.176.6 48 5.4 even 2 inner
475.2.l.f.251.3 48 19.4 even 9 inner
475.2.l.f.251.6 48 95.4 even 18 inner
855.2.da.b.289.3 48 285.137 even 36
855.2.da.b.289.6 48 285.23 even 36
855.2.da.b.784.3 48 15.8 even 4
855.2.da.b.784.6 48 15.2 even 4
1805.2.b.k.1084.9 24 95.93 odd 36
1805.2.b.k.1084.16 24 95.17 odd 36
1805.2.b.l.1084.9 24 95.2 even 36
1805.2.b.l.1084.16 24 95.78 even 36
9025.2.a.ct.1.9 24 19.2 odd 18
9025.2.a.ct.1.16 24 95.59 odd 18
9025.2.a.cu.1.9 24 95.74 even 18
9025.2.a.cu.1.16 24 19.17 even 9