Properties

Label 363.2.e.h.202.1
Level $363$
Weight $2$
Character 363.202
Analytic conductor $2.899$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(124,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.124");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 202.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 363.202
Dual form 363.2.e.h.124.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(2.11803 - 1.53884i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.927051 + 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(2.11803 - 1.53884i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.927051 + 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.61803 q^{10} -1.61803 q^{12} +(-1.42705 - 1.03681i) q^{13} +(-0.572949 + 1.76336i) q^{14} +(-0.809017 - 2.48990i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(-1.30902 + 0.951057i) q^{17} +(-0.190983 - 0.587785i) q^{18} +(1.80902 - 5.56758i) q^{19} +(-3.42705 - 2.48990i) q^{20} +3.00000 q^{21} +3.47214 q^{23} +(-1.80902 - 1.31433i) q^{24} +(0.572949 - 1.76336i) q^{25} +(-0.336881 - 1.03681i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(3.92705 - 2.85317i) q^{28} +(1.38197 + 4.25325i) q^{29} +(0.500000 - 1.53884i) q^{30} +(-2.30902 - 1.67760i) q^{31} -5.61803 q^{32} -1.00000 q^{34} +(6.35410 + 4.61653i) q^{35} +(-0.500000 + 1.53884i) q^{36} +(0.0729490 + 0.224514i) q^{37} +(2.92705 - 2.12663i) q^{38} +(-1.42705 + 1.03681i) q^{39} +(-1.80902 - 5.56758i) q^{40} +(-3.69098 + 11.3597i) q^{41} +(1.50000 + 1.08981i) q^{42} +6.23607 q^{43} -2.61803 q^{45} +(1.73607 + 1.26133i) q^{46} +(0.500000 - 1.53884i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(0.927051 - 0.673542i) q^{50} +(0.500000 + 1.53884i) q^{51} +(-0.881966 + 2.71441i) q^{52} +(7.78115 + 5.65334i) q^{53} -0.618034 q^{54} +6.70820 q^{56} +(-4.73607 - 3.44095i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(3.19098 + 9.82084i) q^{59} +(-3.42705 + 2.48990i) q^{60} +(-6.35410 + 4.61653i) q^{61} +(-0.545085 - 1.67760i) q^{62} +(0.927051 - 2.85317i) q^{63} +(0.190983 + 0.138757i) q^{64} -4.61803 q^{65} -9.56231 q^{67} +(2.11803 + 1.53884i) q^{68} +(1.07295 - 3.30220i) q^{69} +(1.50000 + 4.61653i) q^{70} +(4.50000 - 3.26944i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(-1.00000 - 3.07768i) q^{73} +(-0.0450850 + 0.138757i) q^{74} +(-1.50000 - 1.08981i) q^{75} -9.47214 q^{76} -1.09017 q^{78} +(-7.66312 - 5.56758i) q^{79} +(-1.50000 + 4.61653i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.97214 + 4.33901i) q^{82} +(-0.572949 + 0.416272i) q^{83} +(-1.50000 - 4.61653i) q^{84} +(-1.30902 + 4.02874i) q^{85} +(3.11803 + 2.26538i) q^{86} +4.47214 q^{87} +0.527864 q^{89} +(-1.30902 - 0.951057i) q^{90} +(1.63525 - 5.03280i) q^{91} +(-1.73607 - 5.34307i) q^{92} +(-2.30902 + 1.67760i) q^{93} +(0.809017 - 0.587785i) q^{94} +(-4.73607 - 14.5761i) q^{95} +(-1.73607 + 5.34307i) q^{96} +(11.3541 + 8.24924i) q^{97} -1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} - q^{9} + 2 q^{10} - 2 q^{12} + q^{13} - 9 q^{14} - q^{15} - 6 q^{16} - 3 q^{17} - 3 q^{18} + 5 q^{19} - 7 q^{20} + 12 q^{21} - 4 q^{23} - 5 q^{24} + 9 q^{25} - 17 q^{26} - q^{27} + 9 q^{28} + 10 q^{29} + 2 q^{30} - 7 q^{31} - 18 q^{32} - 4 q^{34} + 12 q^{35} - 2 q^{36} + 7 q^{37} + 5 q^{38} + q^{39} - 5 q^{40} - 17 q^{41} + 6 q^{42} + 16 q^{43} - 6 q^{45} - 2 q^{46} + 2 q^{47} + 9 q^{48} - 2 q^{49} - 3 q^{50} + 2 q^{51} - 8 q^{52} + 11 q^{53} + 2 q^{54} - 10 q^{57} + 10 q^{58} + 15 q^{59} - 7 q^{60} - 12 q^{61} + 9 q^{62} - 3 q^{63} + 3 q^{64} - 14 q^{65} + 2 q^{67} + 4 q^{68} + 11 q^{69} + 6 q^{70} + 18 q^{71} - 5 q^{72} - 4 q^{73} + 11 q^{74} - 6 q^{75} - 20 q^{76} + 18 q^{78} - 15 q^{79} - 6 q^{80} - q^{81} - 6 q^{82} - 9 q^{83} - 6 q^{84} - 3 q^{85} + 8 q^{86} + 20 q^{89} - 3 q^{90} - 27 q^{91} + 2 q^{92} - 7 q^{93} + q^{94} - 10 q^{95} + 2 q^{96} + 32 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.363271i 0.353553 + 0.256872i 0.750358 0.661031i \(-0.229881\pi\)
−0.396805 + 0.917903i \(0.629881\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) −0.500000 1.53884i −0.250000 0.769421i
\(5\) 2.11803 1.53884i 0.947214 0.688191i −0.00293261 0.999996i \(-0.500933\pi\)
0.950146 + 0.311805i \(0.100933\pi\)
\(6\) 0.500000 0.363271i 0.204124 0.148305i
\(7\) 0.927051 + 2.85317i 0.350392 + 1.07840i 0.958633 + 0.284644i \(0.0918755\pi\)
−0.608241 + 0.793752i \(0.708125\pi\)
\(8\) 0.690983 2.12663i 0.244299 0.751876i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 1.61803 0.511667
\(11\) 0 0
\(12\) −1.61803 −0.467086
\(13\) −1.42705 1.03681i −0.395793 0.287560i 0.372032 0.928220i \(-0.378661\pi\)
−0.767825 + 0.640660i \(0.778661\pi\)
\(14\) −0.572949 + 1.76336i −0.153127 + 0.471277i
\(15\) −0.809017 2.48990i −0.208887 0.642889i
\(16\) −1.50000 + 1.08981i −0.375000 + 0.272453i
\(17\) −1.30902 + 0.951057i −0.317483 + 0.230665i −0.735101 0.677958i \(-0.762865\pi\)
0.417618 + 0.908623i \(0.362865\pi\)
\(18\) −0.190983 0.587785i −0.0450151 0.138542i
\(19\) 1.80902 5.56758i 0.415017 1.27729i −0.497219 0.867625i \(-0.665645\pi\)
0.912236 0.409666i \(-0.134355\pi\)
\(20\) −3.42705 2.48990i −0.766312 0.556758i
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) 3.47214 0.723990 0.361995 0.932180i \(-0.382096\pi\)
0.361995 + 0.932180i \(0.382096\pi\)
\(24\) −1.80902 1.31433i −0.369264 0.268286i
\(25\) 0.572949 1.76336i 0.114590 0.352671i
\(26\) −0.336881 1.03681i −0.0660678 0.203336i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 3.92705 2.85317i 0.742143 0.539198i
\(29\) 1.38197 + 4.25325i 0.256625 + 0.789809i 0.993505 + 0.113787i \(0.0362980\pi\)
−0.736881 + 0.676023i \(0.763702\pi\)
\(30\) 0.500000 1.53884i 0.0912871 0.280953i
\(31\) −2.30902 1.67760i −0.414712 0.301306i 0.360795 0.932645i \(-0.382505\pi\)
−0.775507 + 0.631340i \(0.782505\pi\)
\(32\) −5.61803 −0.993137
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 6.35410 + 4.61653i 1.07404 + 0.780335i
\(36\) −0.500000 + 1.53884i −0.0833333 + 0.256474i
\(37\) 0.0729490 + 0.224514i 0.0119927 + 0.0369099i 0.956874 0.290504i \(-0.0938229\pi\)
−0.944881 + 0.327414i \(0.893823\pi\)
\(38\) 2.92705 2.12663i 0.474830 0.344984i
\(39\) −1.42705 + 1.03681i −0.228511 + 0.166023i
\(40\) −1.80902 5.56758i −0.286031 0.880312i
\(41\) −3.69098 + 11.3597i −0.576435 + 1.77408i 0.0548065 + 0.998497i \(0.482546\pi\)
−0.631241 + 0.775587i \(0.717454\pi\)
\(42\) 1.50000 + 1.08981i 0.231455 + 0.168162i
\(43\) 6.23607 0.950991 0.475496 0.879718i \(-0.342269\pi\)
0.475496 + 0.879718i \(0.342269\pi\)
\(44\) 0 0
\(45\) −2.61803 −0.390273
\(46\) 1.73607 + 1.26133i 0.255969 + 0.185973i
\(47\) 0.500000 1.53884i 0.0729325 0.224463i −0.907945 0.419089i \(-0.862349\pi\)
0.980877 + 0.194626i \(0.0623494\pi\)
\(48\) 0.572949 + 1.76336i 0.0826981 + 0.254518i
\(49\) −1.61803 + 1.17557i −0.231148 + 0.167939i
\(50\) 0.927051 0.673542i 0.131105 0.0952532i
\(51\) 0.500000 + 1.53884i 0.0700140 + 0.215481i
\(52\) −0.881966 + 2.71441i −0.122307 + 0.376421i
\(53\) 7.78115 + 5.65334i 1.06882 + 0.776546i 0.975700 0.219109i \(-0.0703150\pi\)
0.0931231 + 0.995655i \(0.470315\pi\)
\(54\) −0.618034 −0.0841038
\(55\) 0 0
\(56\) 6.70820 0.896421
\(57\) −4.73607 3.44095i −0.627308 0.455766i
\(58\) −0.854102 + 2.62866i −0.112149 + 0.345159i
\(59\) 3.19098 + 9.82084i 0.415431 + 1.27856i 0.911865 + 0.410490i \(0.134642\pi\)
−0.496435 + 0.868074i \(0.665358\pi\)
\(60\) −3.42705 + 2.48990i −0.442430 + 0.321444i
\(61\) −6.35410 + 4.61653i −0.813559 + 0.591085i −0.914860 0.403770i \(-0.867699\pi\)
0.101301 + 0.994856i \(0.467699\pi\)
\(62\) −0.545085 1.67760i −0.0692259 0.213055i
\(63\) 0.927051 2.85317i 0.116797 0.359466i
\(64\) 0.190983 + 0.138757i 0.0238729 + 0.0173447i
\(65\) −4.61803 −0.572797
\(66\) 0 0
\(67\) −9.56231 −1.16822 −0.584111 0.811674i \(-0.698557\pi\)
−0.584111 + 0.811674i \(0.698557\pi\)
\(68\) 2.11803 + 1.53884i 0.256849 + 0.186612i
\(69\) 1.07295 3.30220i 0.129168 0.397538i
\(70\) 1.50000 + 4.61653i 0.179284 + 0.551780i
\(71\) 4.50000 3.26944i 0.534052 0.388011i −0.287819 0.957685i \(-0.592930\pi\)
0.821871 + 0.569673i \(0.192930\pi\)
\(72\) −1.80902 + 1.31433i −0.213195 + 0.154895i
\(73\) −1.00000 3.07768i −0.117041 0.360216i 0.875326 0.483533i \(-0.160647\pi\)
−0.992367 + 0.123317i \(0.960647\pi\)
\(74\) −0.0450850 + 0.138757i −0.00524102 + 0.0161302i
\(75\) −1.50000 1.08981i −0.173205 0.125841i
\(76\) −9.47214 −1.08653
\(77\) 0 0
\(78\) −1.09017 −0.123437
\(79\) −7.66312 5.56758i −0.862168 0.626402i 0.0663057 0.997799i \(-0.478879\pi\)
−0.928474 + 0.371397i \(0.878879\pi\)
\(80\) −1.50000 + 4.61653i −0.167705 + 0.516143i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −5.97214 + 4.33901i −0.659512 + 0.479164i
\(83\) −0.572949 + 0.416272i −0.0628893 + 0.0456918i −0.618786 0.785560i \(-0.712375\pi\)
0.555896 + 0.831252i \(0.312375\pi\)
\(84\) −1.50000 4.61653i −0.163663 0.503704i
\(85\) −1.30902 + 4.02874i −0.141983 + 0.436978i
\(86\) 3.11803 + 2.26538i 0.336226 + 0.244283i
\(87\) 4.47214 0.479463
\(88\) 0 0
\(89\) 0.527864 0.0559535 0.0279767 0.999609i \(-0.491094\pi\)
0.0279767 + 0.999609i \(0.491094\pi\)
\(90\) −1.30902 0.951057i −0.137983 0.100250i
\(91\) 1.63525 5.03280i 0.171421 0.527580i
\(92\) −1.73607 5.34307i −0.180998 0.557053i
\(93\) −2.30902 + 1.67760i −0.239434 + 0.173959i
\(94\) 0.809017 0.587785i 0.0834437 0.0606254i
\(95\) −4.73607 14.5761i −0.485910 1.49548i
\(96\) −1.73607 + 5.34307i −0.177187 + 0.545325i
\(97\) 11.3541 + 8.24924i 1.15283 + 0.837583i 0.988855 0.148881i \(-0.0475670\pi\)
0.163979 + 0.986464i \(0.447567\pi\)
\(98\) −1.23607 −0.124862
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) 2.42705 + 1.76336i 0.241501 + 0.175460i 0.701952 0.712225i \(-0.252312\pi\)
−0.460451 + 0.887685i \(0.652312\pi\)
\(102\) −0.309017 + 0.951057i −0.0305972 + 0.0941686i
\(103\) −1.85410 5.70634i −0.182690 0.562262i 0.817211 0.576339i \(-0.195519\pi\)
−0.999901 + 0.0140765i \(0.995519\pi\)
\(104\) −3.19098 + 2.31838i −0.312902 + 0.227336i
\(105\) 6.35410 4.61653i 0.620097 0.450527i
\(106\) 1.83688 + 5.65334i 0.178414 + 0.549101i
\(107\) −1.30902 + 4.02874i −0.126547 + 0.389473i −0.994180 0.107733i \(-0.965641\pi\)
0.867632 + 0.497206i \(0.165641\pi\)
\(108\) 1.30902 + 0.951057i 0.125960 + 0.0915155i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0.236068 0.0224066
\(112\) −4.50000 3.26944i −0.425210 0.308933i
\(113\) 0.218847 0.673542i 0.0205874 0.0633615i −0.940235 0.340526i \(-0.889395\pi\)
0.960822 + 0.277165i \(0.0893948\pi\)
\(114\) −1.11803 3.44095i −0.104713 0.322275i
\(115\) 7.35410 5.34307i 0.685774 0.498244i
\(116\) 5.85410 4.25325i 0.543540 0.394905i
\(117\) 0.545085 + 1.67760i 0.0503931 + 0.155094i
\(118\) −1.97214 + 6.06961i −0.181550 + 0.558753i
\(119\) −3.92705 2.85317i −0.359992 0.261550i
\(120\) −5.85410 −0.534404
\(121\) 0 0
\(122\) −4.85410 −0.439470
\(123\) 9.66312 + 7.02067i 0.871294 + 0.633032i
\(124\) −1.42705 + 4.39201i −0.128153 + 0.394414i
\(125\) 2.54508 + 7.83297i 0.227639 + 0.700602i
\(126\) 1.50000 1.08981i 0.133631 0.0970883i
\(127\) 3.00000 2.17963i 0.266207 0.193411i −0.446672 0.894698i \(-0.647391\pi\)
0.712879 + 0.701287i \(0.247391\pi\)
\(128\) 3.51722 + 10.8249i 0.310881 + 0.956794i
\(129\) 1.92705 5.93085i 0.169667 0.522182i
\(130\) −2.30902 1.67760i −0.202514 0.147135i
\(131\) −7.14590 −0.624340 −0.312170 0.950026i \(-0.601056\pi\)
−0.312170 + 0.950026i \(0.601056\pi\)
\(132\) 0 0
\(133\) 17.5623 1.52285
\(134\) −4.78115 3.47371i −0.413029 0.300083i
\(135\) −0.809017 + 2.48990i −0.0696291 + 0.214296i
\(136\) 1.11803 + 3.44095i 0.0958706 + 0.295059i
\(137\) −6.04508 + 4.39201i −0.516466 + 0.375235i −0.815271 0.579079i \(-0.803412\pi\)
0.298805 + 0.954314i \(0.403412\pi\)
\(138\) 1.73607 1.26133i 0.147784 0.107371i
\(139\) −0.263932 0.812299i −0.0223864 0.0688983i 0.939239 0.343263i \(-0.111532\pi\)
−0.961626 + 0.274365i \(0.911532\pi\)
\(140\) 3.92705 12.0862i 0.331896 1.02147i
\(141\) −1.30902 0.951057i −0.110239 0.0800934i
\(142\) 3.43769 0.288485
\(143\) 0 0
\(144\) 1.85410 0.154508
\(145\) 9.47214 + 6.88191i 0.786618 + 0.571511i
\(146\) 0.618034 1.90211i 0.0511489 0.157420i
\(147\) 0.618034 + 1.90211i 0.0509746 + 0.156884i
\(148\) 0.309017 0.224514i 0.0254010 0.0184549i
\(149\) −12.1353 + 8.81678i −0.994159 + 0.722299i −0.960828 0.277146i \(-0.910612\pi\)
−0.0333309 + 0.999444i \(0.510612\pi\)
\(150\) −0.354102 1.08981i −0.0289123 0.0889829i
\(151\) 0.618034 1.90211i 0.0502949 0.154792i −0.922755 0.385388i \(-0.874068\pi\)
0.973050 + 0.230596i \(0.0740676\pi\)
\(152\) −10.5902 7.69421i −0.858976 0.624083i
\(153\) 1.61803 0.130810
\(154\) 0 0
\(155\) −7.47214 −0.600176
\(156\) 2.30902 + 1.67760i 0.184869 + 0.134315i
\(157\) −1.14590 + 3.52671i −0.0914526 + 0.281462i −0.986313 0.164884i \(-0.947275\pi\)
0.894860 + 0.446346i \(0.147275\pi\)
\(158\) −1.80902 5.56758i −0.143918 0.442933i
\(159\) 7.78115 5.65334i 0.617086 0.448339i
\(160\) −11.8992 + 8.64527i −0.940713 + 0.683468i
\(161\) 3.21885 + 9.90659i 0.253681 + 0.780749i
\(162\) −0.190983 + 0.587785i −0.0150050 + 0.0461808i
\(163\) −14.7812 10.7391i −1.15775 0.841154i −0.168257 0.985743i \(-0.553814\pi\)
−0.989492 + 0.144589i \(0.953814\pi\)
\(164\) 19.3262 1.50913
\(165\) 0 0
\(166\) −0.437694 −0.0339717
\(167\) −8.11803 5.89810i −0.628192 0.456408i 0.227581 0.973759i \(-0.426918\pi\)
−0.855774 + 0.517351i \(0.826918\pi\)
\(168\) 2.07295 6.37988i 0.159931 0.492219i
\(169\) −3.05573 9.40456i −0.235056 0.723428i
\(170\) −2.11803 + 1.53884i −0.162446 + 0.118024i
\(171\) −4.73607 + 3.44095i −0.362176 + 0.263136i
\(172\) −3.11803 9.59632i −0.237748 0.731713i
\(173\) 4.75329 14.6291i 0.361386 1.11223i −0.590828 0.806798i \(-0.701199\pi\)
0.952213 0.305433i \(-0.0988014\pi\)
\(174\) 2.23607 + 1.62460i 0.169516 + 0.123160i
\(175\) 5.56231 0.420471
\(176\) 0 0
\(177\) 10.3262 0.776168
\(178\) 0.263932 + 0.191758i 0.0197825 + 0.0143729i
\(179\) −0.690983 + 2.12663i −0.0516465 + 0.158952i −0.973553 0.228460i \(-0.926631\pi\)
0.921907 + 0.387412i \(0.126631\pi\)
\(180\) 1.30902 + 4.02874i 0.0975684 + 0.300285i
\(181\) 14.1353 10.2699i 1.05067 0.763353i 0.0783264 0.996928i \(-0.475042\pi\)
0.972339 + 0.233575i \(0.0750424\pi\)
\(182\) 2.64590 1.92236i 0.196127 0.142495i
\(183\) 2.42705 + 7.46969i 0.179413 + 0.552176i
\(184\) 2.39919 7.38394i 0.176870 0.544351i
\(185\) 0.500000 + 0.363271i 0.0367607 + 0.0267082i
\(186\) −1.76393 −0.129338
\(187\) 0 0
\(188\) −2.61803 −0.190940
\(189\) −2.42705 1.76336i −0.176542 0.128265i
\(190\) 2.92705 9.00854i 0.212351 0.653548i
\(191\) −2.30902 7.10642i −0.167075 0.514203i 0.832109 0.554613i \(-0.187134\pi\)
−0.999183 + 0.0404100i \(0.987134\pi\)
\(192\) 0.190983 0.138757i 0.0137830 0.0100139i
\(193\) 15.0172 10.9106i 1.08096 0.785366i 0.103113 0.994670i \(-0.467120\pi\)
0.977851 + 0.209304i \(0.0671198\pi\)
\(194\) 2.68034 + 8.24924i 0.192437 + 0.592261i
\(195\) −1.42705 + 4.39201i −0.102193 + 0.314518i
\(196\) 2.61803 + 1.90211i 0.187002 + 0.135865i
\(197\) 24.3820 1.73714 0.868572 0.495564i \(-0.165039\pi\)
0.868572 + 0.495564i \(0.165039\pi\)
\(198\) 0 0
\(199\) −16.7082 −1.18441 −0.592207 0.805786i \(-0.701743\pi\)
−0.592207 + 0.805786i \(0.701743\pi\)
\(200\) −3.35410 2.43690i −0.237171 0.172315i
\(201\) −2.95492 + 9.09429i −0.208424 + 0.641462i
\(202\) 0.572949 + 1.76336i 0.0403126 + 0.124069i
\(203\) −10.8541 + 7.88597i −0.761809 + 0.553486i
\(204\) 2.11803 1.53884i 0.148292 0.107740i
\(205\) 9.66312 + 29.7400i 0.674902 + 2.07713i
\(206\) 1.14590 3.52671i 0.0798385 0.245718i
\(207\) −2.80902 2.04087i −0.195240 0.141850i
\(208\) 3.27051 0.226769
\(209\) 0 0
\(210\) 4.85410 0.334965
\(211\) 18.0172 + 13.0903i 1.24036 + 0.901172i 0.997622 0.0689209i \(-0.0219556\pi\)
0.242735 + 0.970093i \(0.421956\pi\)
\(212\) 4.80902 14.8006i 0.330285 1.01651i
\(213\) −1.71885 5.29007i −0.117773 0.362469i
\(214\) −2.11803 + 1.53884i −0.144786 + 0.105193i
\(215\) 13.2082 9.59632i 0.900792 0.654464i
\(216\) 0.690983 + 2.12663i 0.0470154 + 0.144699i
\(217\) 2.64590 8.14324i 0.179615 0.552799i
\(218\) 0 0
\(219\) −3.23607 −0.218673
\(220\) 0 0
\(221\) 2.85410 0.191988
\(222\) 0.118034 + 0.0857567i 0.00792192 + 0.00575561i
\(223\) 0.218847 0.673542i 0.0146551 0.0451037i −0.943462 0.331482i \(-0.892451\pi\)
0.958117 + 0.286378i \(0.0924514\pi\)
\(224\) −5.20820 16.0292i −0.347988 1.07100i
\(225\) −1.50000 + 1.08981i −0.100000 + 0.0726543i
\(226\) 0.354102 0.257270i 0.0235545 0.0171134i
\(227\) −7.69098 23.6704i −0.510468 1.57106i −0.791379 0.611326i \(-0.790636\pi\)
0.280910 0.959734i \(-0.409364\pi\)
\(228\) −2.92705 + 9.00854i −0.193849 + 0.596605i
\(229\) −8.09017 5.87785i −0.534613 0.388419i 0.287467 0.957790i \(-0.407187\pi\)
−0.822081 + 0.569371i \(0.807187\pi\)
\(230\) 5.61803 0.370442
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) −19.6803 14.2986i −1.28930 0.936733i −0.289511 0.957175i \(-0.593493\pi\)
−0.999791 + 0.0204420i \(0.993493\pi\)
\(234\) −0.336881 + 1.03681i −0.0220226 + 0.0677786i
\(235\) −1.30902 4.02874i −0.0853909 0.262806i
\(236\) 13.5172 9.82084i 0.879896 0.639282i
\(237\) −7.66312 + 5.56758i −0.497773 + 0.361653i
\(238\) −0.927051 2.85317i −0.0600918 0.184944i
\(239\) 0.791796 2.43690i 0.0512170 0.157630i −0.922177 0.386769i \(-0.873591\pi\)
0.973394 + 0.229139i \(0.0735911\pi\)
\(240\) 3.92705 + 2.85317i 0.253490 + 0.184171i
\(241\) −23.1246 −1.48959 −0.744794 0.667295i \(-0.767452\pi\)
−0.744794 + 0.667295i \(0.767452\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 10.2812 + 7.46969i 0.658183 + 0.478198i
\(245\) −1.61803 + 4.97980i −0.103372 + 0.318148i
\(246\) 2.28115 + 7.02067i 0.145441 + 0.447621i
\(247\) −8.35410 + 6.06961i −0.531559 + 0.386200i
\(248\) −5.16312 + 3.75123i −0.327858 + 0.238203i
\(249\) 0.218847 + 0.673542i 0.0138689 + 0.0426840i
\(250\) −1.57295 + 4.84104i −0.0994820 + 0.306174i
\(251\) 6.30902 + 4.58377i 0.398222 + 0.289325i 0.768816 0.639470i \(-0.220846\pi\)
−0.370595 + 0.928795i \(0.620846\pi\)
\(252\) −4.85410 −0.305780
\(253\) 0 0
\(254\) 2.29180 0.143800
\(255\) 3.42705 + 2.48990i 0.214610 + 0.155923i
\(256\) −2.02786 + 6.24112i −0.126742 + 0.390070i
\(257\) −3.60739 11.1024i −0.225023 0.692549i −0.998289 0.0584679i \(-0.981378\pi\)
0.773266 0.634081i \(-0.218622\pi\)
\(258\) 3.11803 2.26538i 0.194120 0.141037i
\(259\) −0.572949 + 0.416272i −0.0356013 + 0.0258659i
\(260\) 2.30902 + 7.10642i 0.143199 + 0.440722i
\(261\) 1.38197 4.25325i 0.0855415 0.263270i
\(262\) −3.57295 2.59590i −0.220738 0.160375i
\(263\) −16.3262 −1.00672 −0.503359 0.864077i \(-0.667903\pi\)
−0.503359 + 0.864077i \(0.667903\pi\)
\(264\) 0 0
\(265\) 25.1803 1.54682
\(266\) 8.78115 + 6.37988i 0.538407 + 0.391176i
\(267\) 0.163119 0.502029i 0.00998272 0.0307236i
\(268\) 4.78115 + 14.7149i 0.292055 + 0.898854i
\(269\) −12.5623 + 9.12705i −0.765937 + 0.556486i −0.900726 0.434388i \(-0.856965\pi\)
0.134788 + 0.990874i \(0.456965\pi\)
\(270\) −1.30902 + 0.951057i −0.0796642 + 0.0578795i
\(271\) −8.42705 25.9358i −0.511907 1.57549i −0.788840 0.614598i \(-0.789318\pi\)
0.276933 0.960889i \(-0.410682\pi\)
\(272\) 0.927051 2.85317i 0.0562107 0.172999i
\(273\) −4.28115 3.11044i −0.259107 0.188252i
\(274\) −4.61803 −0.278986
\(275\) 0 0
\(276\) −5.61803 −0.338166
\(277\) −24.7254 17.9641i −1.48561 1.07936i −0.975696 0.219129i \(-0.929678\pi\)
−0.509911 0.860227i \(-0.670322\pi\)
\(278\) 0.163119 0.502029i 0.00978323 0.0301097i
\(279\) 0.881966 + 2.71441i 0.0528019 + 0.162508i
\(280\) 14.2082 10.3229i 0.849103 0.616909i
\(281\) 0.618034 0.449028i 0.0368688 0.0267868i −0.569198 0.822200i \(-0.692746\pi\)
0.606067 + 0.795414i \(0.292746\pi\)
\(282\) −0.309017 0.951057i −0.0184017 0.0566346i
\(283\) 0.0557281 0.171513i 0.00331269 0.0101954i −0.949387 0.314110i \(-0.898294\pi\)
0.952699 + 0.303915i \(0.0982938\pi\)
\(284\) −7.28115 5.29007i −0.432057 0.313908i
\(285\) −15.3262 −0.907848
\(286\) 0 0
\(287\) −35.8328 −2.11514
\(288\) 4.54508 + 3.30220i 0.267822 + 0.194584i
\(289\) −4.44427 + 13.6781i −0.261428 + 0.804592i
\(290\) 2.23607 + 6.88191i 0.131306 + 0.404120i
\(291\) 11.3541 8.24924i 0.665589 0.483579i
\(292\) −4.23607 + 3.07768i −0.247897 + 0.180108i
\(293\) 0.0172209 + 0.0530006i 0.00100606 + 0.00309633i 0.951558 0.307468i \(-0.0994818\pi\)
−0.950552 + 0.310565i \(0.899482\pi\)
\(294\) −0.381966 + 1.17557i −0.0222767 + 0.0685607i
\(295\) 21.8713 + 15.8904i 1.27340 + 0.925178i
\(296\) 0.527864 0.0306815
\(297\) 0 0
\(298\) −9.27051 −0.537026
\(299\) −4.95492 3.59996i −0.286550 0.208191i
\(300\) −0.927051 + 2.85317i −0.0535233 + 0.164728i
\(301\) 5.78115 + 17.7926i 0.333220 + 1.02555i
\(302\) 1.00000 0.726543i 0.0575435 0.0418078i
\(303\) 2.42705 1.76336i 0.139430 0.101302i
\(304\) 3.35410 + 10.3229i 0.192371 + 0.592057i
\(305\) −6.35410 + 19.5559i −0.363835 + 1.11977i
\(306\) 0.809017 + 0.587785i 0.0462484 + 0.0336014i
\(307\) 0.562306 0.0320925 0.0160462 0.999871i \(-0.494892\pi\)
0.0160462 + 0.999871i \(0.494892\pi\)
\(308\) 0 0
\(309\) −6.00000 −0.341328
\(310\) −3.73607 2.71441i −0.212194 0.154168i
\(311\) 0.781153 2.40414i 0.0442951 0.136326i −0.926463 0.376385i \(-0.877167\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(312\) 1.21885 + 3.75123i 0.0690036 + 0.212371i
\(313\) −20.8992 + 15.1841i −1.18129 + 0.858259i −0.992317 0.123723i \(-0.960517\pi\)
−0.188975 + 0.981982i \(0.560517\pi\)
\(314\) −1.85410 + 1.34708i −0.104633 + 0.0760203i
\(315\) −2.42705 7.46969i −0.136749 0.420870i
\(316\) −4.73607 + 14.5761i −0.266425 + 0.819971i
\(317\) 15.6631 + 11.3799i 0.879728 + 0.639160i 0.933180 0.359410i \(-0.117022\pi\)
−0.0534512 + 0.998570i \(0.517022\pi\)
\(318\) 5.94427 0.333338
\(319\) 0 0
\(320\) 0.618034 0.0345492
\(321\) 3.42705 + 2.48990i 0.191279 + 0.138973i
\(322\) −1.98936 + 6.12261i −0.110863 + 0.341200i
\(323\) 2.92705 + 9.00854i 0.162865 + 0.501248i
\(324\) 1.30902 0.951057i 0.0727232 0.0528365i
\(325\) −2.64590 + 1.92236i −0.146768 + 0.106633i
\(326\) −3.48936 10.7391i −0.193258 0.594786i
\(327\) 0 0
\(328\) 21.6074 + 15.6987i 1.19307 + 0.866815i
\(329\) 4.85410 0.267615
\(330\) 0 0
\(331\) 26.5967 1.46189 0.730945 0.682437i \(-0.239080\pi\)
0.730945 + 0.682437i \(0.239080\pi\)
\(332\) 0.927051 + 0.673542i 0.0508785 + 0.0369654i
\(333\) 0.0729490 0.224514i 0.00399758 0.0123033i
\(334\) −1.91641 5.89810i −0.104861 0.322730i
\(335\) −20.2533 + 14.7149i −1.10656 + 0.803960i
\(336\) −4.50000 + 3.26944i −0.245495 + 0.178363i
\(337\) −0.0901699 0.277515i −0.00491187 0.0151172i 0.948571 0.316566i \(-0.102530\pi\)
−0.953482 + 0.301449i \(0.902530\pi\)
\(338\) 1.88854 5.81234i 0.102723 0.316150i
\(339\) −0.572949 0.416272i −0.0311183 0.0226088i
\(340\) 6.85410 0.371716
\(341\) 0 0
\(342\) −3.61803 −0.195641
\(343\) 12.1353 + 8.81678i 0.655242 + 0.476061i
\(344\) 4.30902 13.2618i 0.232327 0.715028i
\(345\) −2.80902 8.64527i −0.151232 0.465445i
\(346\) 7.69098 5.58783i 0.413470 0.300403i
\(347\) 16.9443 12.3107i 0.909616 0.660875i −0.0313016 0.999510i \(-0.509965\pi\)
0.940918 + 0.338635i \(0.109965\pi\)
\(348\) −2.23607 6.88191i −0.119866 0.368909i
\(349\) −3.12868 + 9.62908i −0.167474 + 0.515433i −0.999210 0.0397388i \(-0.987347\pi\)
0.831736 + 0.555172i \(0.187347\pi\)
\(350\) 2.78115 + 2.02063i 0.148659 + 0.108007i
\(351\) 1.76393 0.0941517
\(352\) 0 0
\(353\) −10.4721 −0.557376 −0.278688 0.960382i \(-0.589899\pi\)
−0.278688 + 0.960382i \(0.589899\pi\)
\(354\) 5.16312 + 3.75123i 0.274417 + 0.199375i
\(355\) 4.50000 13.8496i 0.238835 0.735059i
\(356\) −0.263932 0.812299i −0.0139884 0.0430518i
\(357\) −3.92705 + 2.85317i −0.207842 + 0.151006i
\(358\) −1.11803 + 0.812299i −0.0590899 + 0.0429313i
\(359\) −3.94427 12.1392i −0.208171 0.640684i −0.999568 0.0293817i \(-0.990646\pi\)
0.791398 0.611302i \(-0.209354\pi\)
\(360\) −1.80902 + 5.56758i −0.0953436 + 0.293437i
\(361\) −12.3541 8.97578i −0.650216 0.472409i
\(362\) 10.7984 0.567550
\(363\) 0 0
\(364\) −8.56231 −0.448787
\(365\) −6.85410 4.97980i −0.358760 0.260654i
\(366\) −1.50000 + 4.61653i −0.0784063 + 0.241310i
\(367\) 1.71885 + 5.29007i 0.0897231 + 0.276139i 0.985843 0.167674i \(-0.0536255\pi\)
−0.896119 + 0.443813i \(0.853625\pi\)
\(368\) −5.20820 + 3.78398i −0.271496 + 0.197254i
\(369\) 9.66312 7.02067i 0.503042 0.365481i
\(370\) 0.118034 + 0.363271i 0.00613629 + 0.0188856i
\(371\) −8.91641 + 27.4419i −0.462917 + 1.42471i
\(372\) 3.73607 + 2.71441i 0.193706 + 0.140736i
\(373\) −4.41641 −0.228673 −0.114336 0.993442i \(-0.536474\pi\)
−0.114336 + 0.993442i \(0.536474\pi\)
\(374\) 0 0
\(375\) 8.23607 0.425309
\(376\) −2.92705 2.12663i −0.150951 0.109672i
\(377\) 2.43769 7.50245i 0.125548 0.386396i
\(378\) −0.572949 1.76336i −0.0294693 0.0906972i
\(379\) −1.28115 + 0.930812i −0.0658084 + 0.0478126i −0.620203 0.784441i \(-0.712950\pi\)
0.554395 + 0.832254i \(0.312950\pi\)
\(380\) −20.0623 + 14.5761i −1.02917 + 0.747739i
\(381\) −1.14590 3.52671i −0.0587061 0.180679i
\(382\) 1.42705 4.39201i 0.0730143 0.224715i
\(383\) −21.7533 15.8047i −1.11154 0.807582i −0.128635 0.991692i \(-0.541060\pi\)
−0.982906 + 0.184110i \(0.941060\pi\)
\(384\) 11.3820 0.580834
\(385\) 0 0
\(386\) 11.4721 0.583916
\(387\) −5.04508 3.66547i −0.256456 0.186326i
\(388\) 7.01722 21.5968i 0.356245 1.09641i
\(389\) 7.50000 + 23.0826i 0.380265 + 1.17034i 0.939857 + 0.341567i \(0.110958\pi\)
−0.559592 + 0.828768i \(0.689042\pi\)
\(390\) −2.30902 + 1.67760i −0.116922 + 0.0849485i
\(391\) −4.54508 + 3.30220i −0.229855 + 0.166999i
\(392\) 1.38197 + 4.25325i 0.0697998 + 0.214822i
\(393\) −2.20820 + 6.79615i −0.111389 + 0.342821i
\(394\) 12.1910 + 8.85727i 0.614173 + 0.446223i
\(395\) −24.7984 −1.24774
\(396\) 0 0
\(397\) −38.7082 −1.94271 −0.971355 0.237635i \(-0.923628\pi\)
−0.971355 + 0.237635i \(0.923628\pi\)
\(398\) −8.35410 6.06961i −0.418753 0.304242i
\(399\) 5.42705 16.7027i 0.271692 0.836183i
\(400\) 1.06231 + 3.26944i 0.0531153 + 0.163472i
\(401\) 21.1074 15.3354i 1.05405 0.765814i 0.0810739 0.996708i \(-0.474165\pi\)
0.972979 + 0.230894i \(0.0741650\pi\)
\(402\) −4.78115 + 3.47371i −0.238462 + 0.173253i
\(403\) 1.55573 + 4.78804i 0.0774963 + 0.238509i
\(404\) 1.50000 4.61653i 0.0746278 0.229681i
\(405\) 2.11803 + 1.53884i 0.105246 + 0.0764657i
\(406\) −8.29180 −0.411515
\(407\) 0 0
\(408\) 3.61803 0.179119
\(409\) 8.94427 + 6.49839i 0.442266 + 0.321325i 0.786535 0.617546i \(-0.211873\pi\)
−0.344269 + 0.938871i \(0.611873\pi\)
\(410\) −5.97214 + 18.3803i −0.294943 + 0.907741i
\(411\) 2.30902 + 7.10642i 0.113895 + 0.350534i
\(412\) −7.85410 + 5.70634i −0.386944 + 0.281131i
\(413\) −25.0623 + 18.2088i −1.23324 + 0.895998i
\(414\) −0.663119 2.04087i −0.0325905 0.100303i
\(415\) −0.572949 + 1.76336i −0.0281250 + 0.0865597i
\(416\) 8.01722 + 5.82485i 0.393077 + 0.285587i
\(417\) −0.854102 −0.0418256
\(418\) 0 0
\(419\) 16.5066 0.806399 0.403200 0.915112i \(-0.367898\pi\)
0.403200 + 0.915112i \(0.367898\pi\)
\(420\) −10.2812 7.46969i −0.501669 0.364484i
\(421\) −11.5172 + 35.4464i −0.561315 + 1.72755i 0.117339 + 0.993092i \(0.462564\pi\)
−0.678654 + 0.734458i \(0.737436\pi\)
\(422\) 4.25329 + 13.0903i 0.207047 + 0.637225i
\(423\) −1.30902 + 0.951057i −0.0636466 + 0.0462420i
\(424\) 17.3992 12.6412i 0.844979 0.613913i
\(425\) 0.927051 + 2.85317i 0.0449686 + 0.138399i
\(426\) 1.06231 3.26944i 0.0514689 0.158405i
\(427\) −19.0623 13.8496i −0.922490 0.670228i
\(428\) 6.85410 0.331306
\(429\) 0 0
\(430\) 10.0902 0.486591
\(431\) 31.9615 + 23.2214i 1.53953 + 1.11853i 0.950629 + 0.310330i \(0.100440\pi\)
0.588902 + 0.808204i \(0.299560\pi\)
\(432\) 0.572949 1.76336i 0.0275660 0.0848395i
\(433\) −1.85410 5.70634i −0.0891025 0.274229i 0.896569 0.442903i \(-0.146051\pi\)
−0.985672 + 0.168674i \(0.946051\pi\)
\(434\) 4.28115 3.11044i 0.205502 0.149306i
\(435\) 9.47214 6.88191i 0.454154 0.329962i
\(436\) 0 0
\(437\) 6.28115 19.3314i 0.300468 0.924746i
\(438\) −1.61803 1.17557i −0.0773127 0.0561709i
\(439\) 3.29180 0.157109 0.0785544 0.996910i \(-0.474970\pi\)
0.0785544 + 0.996910i \(0.474970\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 1.42705 + 1.03681i 0.0678779 + 0.0493162i
\(443\) −12.7082 + 39.1118i −0.603785 + 1.85826i −0.0988488 + 0.995102i \(0.531516\pi\)
−0.504936 + 0.863157i \(0.668484\pi\)
\(444\) −0.118034 0.363271i −0.00560165 0.0172401i
\(445\) 1.11803 0.812299i 0.0529999 0.0385067i
\(446\) 0.354102 0.257270i 0.0167672 0.0121821i
\(447\) 4.63525 + 14.2658i 0.219240 + 0.674751i
\(448\) −0.218847 + 0.673542i −0.0103396 + 0.0318219i
\(449\) 19.7984 + 14.3844i 0.934343 + 0.678840i 0.947052 0.321079i \(-0.104046\pi\)
−0.0127093 + 0.999919i \(0.504046\pi\)
\(450\) −1.14590 −0.0540182
\(451\) 0 0
\(452\) −1.14590 −0.0538985
\(453\) −1.61803 1.17557i −0.0760219 0.0552331i
\(454\) 4.75329 14.6291i 0.223083 0.686579i
\(455\) −4.28115 13.1760i −0.200704 0.617702i
\(456\) −10.5902 + 7.69421i −0.495930 + 0.360314i
\(457\) −6.63525 + 4.82079i −0.310384 + 0.225507i −0.732061 0.681239i \(-0.761442\pi\)
0.421677 + 0.906746i \(0.361442\pi\)
\(458\) −1.90983 5.87785i −0.0892405 0.274654i
\(459\) 0.500000 1.53884i 0.0233380 0.0718270i
\(460\) −11.8992 8.64527i −0.554802 0.403088i
\(461\) −21.0902 −0.982267 −0.491134 0.871084i \(-0.663417\pi\)
−0.491134 + 0.871084i \(0.663417\pi\)
\(462\) 0 0
\(463\) −15.7984 −0.734213 −0.367106 0.930179i \(-0.619651\pi\)
−0.367106 + 0.930179i \(0.619651\pi\)
\(464\) −6.70820 4.87380i −0.311421 0.226260i
\(465\) −2.30902 + 7.10642i −0.107078 + 0.329553i
\(466\) −4.64590 14.2986i −0.215217 0.662370i
\(467\) 7.89919 5.73910i 0.365531 0.265574i −0.389824 0.920889i \(-0.627464\pi\)
0.755355 + 0.655316i \(0.227464\pi\)
\(468\) 2.30902 1.67760i 0.106734 0.0775470i
\(469\) −8.86475 27.2829i −0.409336 1.25981i
\(470\) 0.809017 2.48990i 0.0373172 0.114850i
\(471\) 3.00000 + 2.17963i 0.138233 + 0.100432i
\(472\) 23.0902 1.06281
\(473\) 0 0
\(474\) −5.85410 −0.268888
\(475\) −8.78115 6.37988i −0.402907 0.292729i
\(476\) −2.42705 + 7.46969i −0.111244 + 0.342373i
\(477\) −2.97214 9.14729i −0.136085 0.418826i
\(478\) 1.28115 0.930812i 0.0585986 0.0425744i
\(479\) 22.7254 16.5110i 1.03835 0.754406i 0.0683882 0.997659i \(-0.478214\pi\)
0.969963 + 0.243253i \(0.0782144\pi\)
\(480\) 4.54508 + 13.9883i 0.207454 + 0.638477i
\(481\) 0.128677 0.396027i 0.00586717 0.0180573i
\(482\) −11.5623 8.40051i −0.526649 0.382633i
\(483\) 10.4164 0.473963
\(484\) 0 0
\(485\) 36.7426 1.66840
\(486\) 0.500000 + 0.363271i 0.0226805 + 0.0164783i
\(487\) 5.19756 15.9964i 0.235524 0.724868i −0.761528 0.648133i \(-0.775550\pi\)
0.997051 0.0767356i \(-0.0244497\pi\)
\(488\) 5.42705 + 16.7027i 0.245671 + 0.756098i
\(489\) −14.7812 + 10.7391i −0.668427 + 0.485641i
\(490\) −2.61803 + 1.90211i −0.118271 + 0.0859287i
\(491\) 7.79180 + 23.9807i 0.351639 + 1.08223i 0.957933 + 0.286992i \(0.0926555\pi\)
−0.606294 + 0.795241i \(0.707345\pi\)
\(492\) 5.97214 18.3803i 0.269245 0.828650i
\(493\) −5.85410 4.25325i −0.263655 0.191557i
\(494\) −6.38197 −0.287138
\(495\) 0 0
\(496\) 5.29180 0.237609
\(497\) 13.5000 + 9.80832i 0.605558 + 0.439963i
\(498\) −0.135255 + 0.416272i −0.00606092 + 0.0186536i
\(499\) −5.42705 16.7027i −0.242948 0.747718i −0.995967 0.0897188i \(-0.971403\pi\)
0.753019 0.657999i \(-0.228597\pi\)
\(500\) 10.7812 7.83297i 0.482148 0.350301i
\(501\) −8.11803 + 5.89810i −0.362687 + 0.263508i
\(502\) 1.48936 + 4.58377i 0.0664733 + 0.204584i
\(503\) 8.67376 26.6951i 0.386744 1.19028i −0.548463 0.836175i \(-0.684787\pi\)
0.935207 0.354101i \(-0.115213\pi\)
\(504\) −5.42705 3.94298i −0.241740 0.175634i
\(505\) 7.85410 0.349503
\(506\) 0 0
\(507\) −9.88854 −0.439166
\(508\) −4.85410 3.52671i −0.215366 0.156473i
\(509\) 7.29837 22.4621i 0.323495 0.995614i −0.648621 0.761112i \(-0.724654\pi\)
0.972115 0.234503i \(-0.0753462\pi\)
\(510\) 0.809017 + 2.48990i 0.0358239 + 0.110255i
\(511\) 7.85410 5.70634i 0.347445 0.252434i
\(512\) 15.1353 10.9964i 0.668890 0.485977i
\(513\) 1.80902 + 5.56758i 0.0798701 + 0.245815i
\(514\) 2.22949 6.86167i 0.0983386 0.302655i
\(515\) −12.7082 9.23305i −0.559990 0.406857i
\(516\) −10.0902 −0.444195
\(517\) 0 0
\(518\) −0.437694 −0.0192312
\(519\) −12.4443 9.04129i −0.546243 0.396869i
\(520\) −3.19098 + 9.82084i −0.139934 + 0.430672i
\(521\) −4.58359 14.1068i −0.200811 0.618032i −0.999859 0.0167657i \(-0.994663\pi\)
0.799049 0.601266i \(-0.205337\pi\)
\(522\) 2.23607 1.62460i 0.0978700 0.0711067i
\(523\) 9.69098 7.04091i 0.423757 0.307878i −0.355391 0.934718i \(-0.615652\pi\)
0.779148 + 0.626840i \(0.215652\pi\)
\(524\) 3.57295 + 10.9964i 0.156085 + 0.480380i
\(525\) 1.71885 5.29007i 0.0750166 0.230877i
\(526\) −8.16312 5.93085i −0.355929 0.258597i
\(527\) 4.61803 0.201165
\(528\) 0 0
\(529\) −10.9443 −0.475838
\(530\) 12.5902 + 9.14729i 0.546882 + 0.397333i
\(531\) 3.19098 9.82084i 0.138477 0.426188i
\(532\) −8.78115 27.0256i −0.380711 1.17171i
\(533\) 17.0451 12.3840i 0.738305 0.536410i
\(534\) 0.263932 0.191758i 0.0114215 0.00829817i
\(535\) 3.42705 + 10.5474i 0.148164 + 0.456003i
\(536\) −6.60739 + 20.3355i −0.285396 + 0.878358i
\(537\) 1.80902 + 1.31433i 0.0780648 + 0.0567174i
\(538\) −9.59675 −0.413745
\(539\) 0 0
\(540\) 4.23607 0.182291
\(541\) −15.8262 11.4984i −0.680423 0.494356i 0.193075 0.981184i \(-0.438154\pi\)
−0.873498 + 0.486828i \(0.838154\pi\)
\(542\) 5.20820 16.0292i 0.223712 0.688513i
\(543\) −5.39919 16.6170i −0.231701 0.713103i
\(544\) 7.35410 5.34307i 0.315305 0.229082i
\(545\) 0 0
\(546\) −1.01064 3.11044i −0.0432515 0.133115i
\(547\) 6.68034 20.5600i 0.285631 0.879081i −0.700578 0.713576i \(-0.747075\pi\)
0.986209 0.165505i \(-0.0529255\pi\)
\(548\) 9.78115 + 7.10642i 0.417830 + 0.303571i
\(549\) 7.85410 0.335205
\(550\) 0 0
\(551\) 26.1803 1.11532
\(552\) −6.28115 4.56352i −0.267344 0.194237i
\(553\) 8.78115 27.0256i 0.373413 1.14925i
\(554\) −5.83688 17.9641i −0.247985 0.763220i
\(555\) 0.500000 0.363271i 0.0212238 0.0154200i
\(556\) −1.11803 + 0.812299i −0.0474152 + 0.0344492i
\(557\) 4.60739 + 14.1801i 0.195221 + 0.600830i 0.999974 + 0.00721928i \(0.00229799\pi\)
−0.804753 + 0.593610i \(0.797702\pi\)
\(558\) −0.545085 + 1.67760i −0.0230753 + 0.0710184i
\(559\) −8.89919 6.46564i −0.376396 0.273467i
\(560\) −14.5623 −0.615370
\(561\) 0 0
\(562\) 0.472136 0.0199159
\(563\) 7.19098 + 5.22455i 0.303064 + 0.220189i 0.728915 0.684605i \(-0.240025\pi\)
−0.425851 + 0.904793i \(0.640025\pi\)
\(564\) −0.809017 + 2.48990i −0.0340658 + 0.104844i
\(565\) −0.572949 1.76336i −0.0241041 0.0741849i
\(566\) 0.0901699 0.0655123i 0.00379013 0.00275369i
\(567\) −2.42705 + 1.76336i −0.101927 + 0.0740540i
\(568\) −3.84346 11.8290i −0.161268 0.496332i
\(569\) −7.43769 + 22.8909i −0.311804 + 0.959635i 0.665246 + 0.746625i \(0.268327\pi\)
−0.977050 + 0.213010i \(0.931673\pi\)
\(570\) −7.66312 5.56758i −0.320973 0.233200i
\(571\) 34.6869 1.45160 0.725801 0.687905i \(-0.241469\pi\)
0.725801 + 0.687905i \(0.241469\pi\)
\(572\) 0 0
\(573\) −7.47214 −0.312153
\(574\) −17.9164 13.0170i −0.747816 0.543320i
\(575\) 1.98936 6.12261i 0.0829619 0.255331i
\(576\) −0.0729490 0.224514i −0.00303954 0.00935475i
\(577\) −8.70820 + 6.32688i −0.362527 + 0.263391i −0.754105 0.656753i \(-0.771929\pi\)
0.391578 + 0.920145i \(0.371929\pi\)
\(578\) −7.19098 + 5.22455i −0.299105 + 0.217313i
\(579\) −5.73607 17.6538i −0.238383 0.733667i
\(580\) 5.85410 18.0171i 0.243078 0.748118i
\(581\) −1.71885 1.24882i −0.0713098 0.0518096i
\(582\) 8.67376 0.359539
\(583\) 0 0
\(584\) −7.23607 −0.299431
\(585\) 3.73607 + 2.71441i 0.154467 + 0.112227i
\(586\) −0.0106431 + 0.0327561i −0.000439663 + 0.00135314i
\(587\) −11.8369 36.4302i −0.488560 1.50363i −0.826757 0.562559i \(-0.809817\pi\)
0.338197 0.941075i \(-0.390183\pi\)
\(588\) 2.61803 1.90211i 0.107966 0.0784418i
\(589\) −13.5172 + 9.82084i −0.556967 + 0.404660i
\(590\) 5.16312 + 15.8904i 0.212562 + 0.654199i
\(591\) 7.53444 23.1886i 0.309926 0.953853i
\(592\) −0.354102 0.257270i −0.0145535 0.0105737i
\(593\) 22.2148 0.912252 0.456126 0.889915i \(-0.349237\pi\)
0.456126 + 0.889915i \(0.349237\pi\)
\(594\) 0 0
\(595\) −12.7082 −0.520986
\(596\) 19.6353 + 14.2658i 0.804291 + 0.584352i
\(597\) −5.16312 + 15.8904i −0.211312 + 0.650353i
\(598\) −1.16970 3.59996i −0.0478325 0.147213i
\(599\) 6.70820 4.87380i 0.274090 0.199138i −0.442246 0.896894i \(-0.645818\pi\)
0.716335 + 0.697756i \(0.245818\pi\)
\(600\) −3.35410 + 2.43690i −0.136931 + 0.0994859i
\(601\) 10.4549 + 32.1769i 0.426465 + 1.31252i 0.901585 + 0.432603i \(0.142405\pi\)
−0.475120 + 0.879921i \(0.657595\pi\)
\(602\) −3.57295 + 10.9964i −0.145623 + 0.448180i
\(603\) 7.73607 + 5.62058i 0.315037 + 0.228888i
\(604\) −3.23607 −0.131674
\(605\) 0 0
\(606\) 1.85410 0.0753177
\(607\) −10.7812 7.83297i −0.437593 0.317930i 0.347084 0.937834i \(-0.387172\pi\)
−0.784678 + 0.619904i \(0.787172\pi\)
\(608\) −10.1631 + 31.2789i −0.412169 + 1.26853i
\(609\) 4.14590 + 12.7598i 0.168000 + 0.517052i
\(610\) −10.2812 + 7.46969i −0.416272 + 0.302439i
\(611\) −2.30902 + 1.67760i −0.0934128 + 0.0678684i
\(612\) −0.809017 2.48990i −0.0327026 0.100648i
\(613\) 10.7082 32.9565i 0.432500 1.33110i −0.463126 0.886292i \(-0.653272\pi\)
0.895627 0.444807i \(-0.146728\pi\)
\(614\) 0.281153 + 0.204270i 0.0113464 + 0.00824365i
\(615\) 31.2705 1.26095
\(616\) 0 0
\(617\) 19.5836 0.788406 0.394203 0.919023i \(-0.371021\pi\)
0.394203 + 0.919023i \(0.371021\pi\)
\(618\) −3.00000 2.17963i −0.120678 0.0876775i
\(619\) −2.72542 + 8.38800i −0.109544 + 0.337142i −0.990770 0.135553i \(-0.956719\pi\)
0.881226 + 0.472695i \(0.156719\pi\)
\(620\) 3.73607 + 11.4984i 0.150044 + 0.461788i
\(621\) −2.80902 + 2.04087i −0.112722 + 0.0818973i
\(622\) 1.26393 0.918300i 0.0506791 0.0368205i
\(623\) 0.489357 + 1.50609i 0.0196057 + 0.0603400i
\(624\) 1.01064 3.11044i 0.0404581 0.124517i
\(625\) 24.9443 + 18.1231i 0.997771 + 0.724923i
\(626\) −15.9656 −0.638112
\(627\) 0 0
\(628\) 6.00000 0.239426
\(629\) −0.309017 0.224514i −0.0123213 0.00895196i
\(630\) 1.50000 4.61653i 0.0597614 0.183927i
\(631\) 14.2984 + 44.0059i 0.569209 + 1.75185i 0.655101 + 0.755542i \(0.272626\pi\)
−0.0858915 + 0.996304i \(0.527374\pi\)
\(632\) −17.1353 + 12.4495i −0.681604 + 0.495214i
\(633\) 18.0172 13.0903i 0.716120 0.520292i
\(634\) 3.69756 + 11.3799i 0.146849 + 0.451954i
\(635\) 3.00000 9.23305i 0.119051 0.366402i
\(636\) −12.5902 9.14729i −0.499233 0.362714i
\(637\) 3.52786 0.139779
\(638\) 0 0
\(639\) −5.56231 −0.220041
\(640\) 24.1074 + 17.5150i 0.952928 + 0.692343i
\(641\) 11.0451 33.9933i 0.436255 1.34265i −0.455541 0.890215i \(-0.650554\pi\)
0.891795 0.452439i \(-0.149446\pi\)
\(642\) 0.809017 + 2.48990i 0.0319294 + 0.0982684i
\(643\) 31.1976 22.6664i 1.23031 0.893874i 0.233398 0.972381i \(-0.425015\pi\)
0.996914 + 0.0785075i \(0.0250154\pi\)
\(644\) 13.6353 9.90659i 0.537304 0.390374i
\(645\) −5.04508 15.5272i −0.198650 0.611382i
\(646\) −1.80902 + 5.56758i −0.0711748 + 0.219054i
\(647\) −22.4894 16.3395i −0.884148 0.642371i 0.0501977 0.998739i \(-0.484015\pi\)
−0.934346 + 0.356368i \(0.884015\pi\)
\(648\) 2.23607 0.0878410
\(649\) 0 0
\(650\) −2.02129 −0.0792814
\(651\) −6.92705 5.03280i −0.271493 0.197251i
\(652\) −9.13525 + 28.1154i −0.357764 + 1.10108i
\(653\) 15.7705 + 48.5366i 0.617148 + 1.89939i 0.359488 + 0.933150i \(0.382951\pi\)
0.257660 + 0.966236i \(0.417049\pi\)
\(654\) 0 0
\(655\) −15.1353 + 10.9964i −0.591383 + 0.429665i
\(656\) −6.84346 21.0620i −0.267192 0.822333i
\(657\) −1.00000 + 3.07768i −0.0390137 + 0.120072i
\(658\) 2.42705 + 1.76336i 0.0946163 + 0.0687428i
\(659\) −10.6525 −0.414962 −0.207481 0.978239i \(-0.566526\pi\)
−0.207481 + 0.978239i \(0.566526\pi\)
\(660\) 0 0
\(661\) −9.90983 −0.385448 −0.192724 0.981253i \(-0.561732\pi\)
−0.192724 + 0.981253i \(0.561732\pi\)
\(662\) 13.2984 + 9.66183i 0.516856 + 0.375518i
\(663\) 0.881966 2.71441i 0.0342527 0.105419i
\(664\) 0.489357 + 1.50609i 0.0189907 + 0.0584475i
\(665\) 37.1976 27.0256i 1.44246 1.04801i
\(666\) 0.118034 0.0857567i 0.00457372 0.00332301i
\(667\) 4.79837 + 14.7679i 0.185794 + 0.571814i
\(668\) −5.01722 + 15.4414i −0.194122 + 0.597446i
\(669\) −0.572949 0.416272i −0.0221515 0.0160940i
\(670\) −15.4721 −0.597741
\(671\) 0 0
\(672\) −16.8541 −0.650161
\(673\) −10.0451 7.29818i −0.387210 0.281324i 0.377102 0.926172i \(-0.376921\pi\)
−0.764311 + 0.644848i \(0.776921\pi\)
\(674\) 0.0557281 0.171513i 0.00214657 0.00660645i
\(675\) 0.572949 + 1.76336i 0.0220528 + 0.0678716i
\(676\) −12.9443 + 9.40456i −0.497857 + 0.361714i
\(677\) −10.9443 + 7.95148i −0.420623 + 0.305600i −0.777888 0.628403i \(-0.783709\pi\)
0.357266 + 0.934003i \(0.383709\pi\)
\(678\) −0.135255 0.416272i −0.00519443 0.0159868i
\(679\) −13.0106 + 40.0426i −0.499303 + 1.53670i
\(680\) 7.66312 + 5.56758i 0.293867 + 0.213507i
\(681\) −24.8885 −0.953731
\(682\) 0 0
\(683\) −3.11146 −0.119057 −0.0595283 0.998227i \(-0.518960\pi\)
−0.0595283 + 0.998227i \(0.518960\pi\)
\(684\) 7.66312 + 5.56758i 0.293007 + 0.212882i
\(685\) −6.04508 + 18.6049i −0.230971 + 0.710855i
\(686\) 2.86475 + 8.81678i 0.109376 + 0.336626i
\(687\) −8.09017 + 5.87785i −0.308659 + 0.224254i
\(688\) −9.35410 + 6.79615i −0.356622 + 0.259101i
\(689\) −5.24265 16.1352i −0.199729 0.614702i
\(690\) 1.73607 5.34307i 0.0660910 0.203407i
\(691\) 21.2705 + 15.4539i 0.809168 + 0.587895i 0.913589 0.406638i \(-0.133299\pi\)
−0.104421 + 0.994533i \(0.533299\pi\)
\(692\) −24.8885 −0.946120
\(693\) 0 0
\(694\) 12.9443 0.491358
\(695\) −1.80902 1.31433i −0.0686199 0.0498553i
\(696\) 3.09017 9.51057i 0.117133 0.360497i
\(697\) −5.97214 18.3803i −0.226211 0.696205i
\(698\) −5.06231 + 3.67798i −0.191611 + 0.139214i
\(699\) −19.6803 + 14.2986i −0.744379 + 0.540823i
\(700\) −2.78115 8.55951i −0.105118 0.323519i
\(701\) −3.30244 + 10.1639i −0.124731 + 0.383884i −0.993852 0.110716i \(-0.964685\pi\)
0.869121 + 0.494600i \(0.164685\pi\)
\(702\) 0.881966 + 0.640786i 0.0332877 + 0.0241849i
\(703\) 1.38197 0.0521218
\(704\) 0 0
\(705\) −4.23607 −0.159540
\(706\) −5.23607 3.80423i −0.197062 0.143174i
\(707\) −2.78115 + 8.55951i −0.104596 + 0.321913i
\(708\) −5.16312 15.8904i −0.194042 0.597200i
\(709\) −39.4336 + 28.6502i −1.48096 + 1.07598i −0.503716 + 0.863870i \(0.668034\pi\)
−0.977245 + 0.212112i \(0.931966\pi\)
\(710\) 7.28115 5.29007i 0.273257 0.198533i
\(711\) 2.92705 + 9.00854i 0.109773 + 0.337847i
\(712\) 0.364745 1.12257i 0.0136694 0.0420701i
\(713\) −8.01722 5.82485i −0.300247 0.218142i
\(714\) −3.00000 −0.112272
\(715\) 0 0
\(716\) 3.61803 0.135212
\(717\) −2.07295 1.50609i −0.0774157 0.0562458i
\(718\) 2.43769 7.50245i 0.0909739 0.279989i
\(719\) −0.489357 1.50609i −0.0182499 0.0561675i 0.941517 0.336966i \(-0.109401\pi\)
−0.959767 + 0.280798i \(0.909401\pi\)
\(720\) 3.92705 2.85317i 0.146353 0.106331i
\(721\) 14.5623 10.5801i 0.542329 0.394025i
\(722\) −2.91641 8.97578i −0.108537 0.334044i
\(723\) −7.14590 + 21.9928i −0.265759 + 0.817922i
\(724\) −22.8713 16.6170i −0.850006 0.617566i
\(725\) 8.29180 0.307950
\(726\) 0 0
\(727\) 38.8541 1.44102 0.720509 0.693445i \(-0.243908\pi\)
0.720509 + 0.693445i \(0.243908\pi\)
\(728\) −9.57295 6.95515i −0.354797 0.257775i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −1.61803 4.97980i −0.0598861 0.184311i
\(731\) −8.16312 + 5.93085i −0.301924 + 0.219361i
\(732\) 10.2812 7.46969i 0.380002 0.276088i
\(733\) −11.6525 35.8626i −0.430394 1.32462i −0.897734 0.440539i \(-0.854787\pi\)
0.467340 0.884078i \(-0.345213\pi\)
\(734\) −1.06231 + 3.26944i −0.0392104 + 0.120677i
\(735\) 4.23607 + 3.07768i 0.156250 + 0.113522i
\(736\) −19.5066 −0.719022
\(737\) 0 0
\(738\) 7.38197 0.271734
\(739\) 20.2254 + 14.6946i 0.744004 + 0.540551i 0.893963 0.448142i \(-0.147914\pi\)
−0.149958 + 0.988692i \(0.547914\pi\)
\(740\) 0.309017 0.951057i 0.0113597 0.0349615i
\(741\) 3.19098 + 9.82084i 0.117224 + 0.360777i
\(742\) −14.4271 + 10.4819i −0.529634 + 0.384801i
\(743\) −28.4615 + 20.6785i −1.04415 + 0.758620i −0.971092 0.238708i \(-0.923276\pi\)
−0.0730594 + 0.997328i \(0.523276\pi\)
\(744\) 1.97214 + 6.06961i 0.0723020 + 0.222523i
\(745\) −12.1353 + 37.3485i −0.444601 + 1.36834i
\(746\) −2.20820 1.60435i −0.0808481 0.0587396i
\(747\) 0.708204 0.0259118
\(748\) 0 0
\(749\) −12.7082 −0.464348
\(750\) 4.11803 + 2.99193i 0.150369 + 0.109250i
\(751\) 3.68441 11.3394i 0.134446 0.413782i −0.861058 0.508508i \(-0.830197\pi\)
0.995503 + 0.0947257i \(0.0301974\pi\)
\(752\) 0.927051 + 2.85317i 0.0338061 + 0.104044i
\(753\) 6.30902 4.58377i 0.229913 0.167042i
\(754\) 3.94427 2.86568i 0.143642 0.104362i
\(755\) −1.61803 4.97980i −0.0588863 0.181233i
\(756\) −1.50000 + 4.61653i −0.0545545 + 0.167901i
\(757\) −1.57295 1.14281i −0.0571698 0.0415363i 0.558833 0.829280i \(-0.311249\pi\)
−0.616003 + 0.787744i \(0.711249\pi\)
\(758\) −0.978714 −0.0355485
\(759\) 0 0
\(760\) −34.2705 −1.24312
\(761\) 24.9894 + 18.1558i 0.905863 + 0.658148i 0.939965 0.341270i \(-0.110857\pi\)
−0.0341018 + 0.999418i \(0.510857\pi\)
\(762\) 0.708204 2.17963i 0.0256555 0.0789596i
\(763\) 0 0
\(764\) −9.78115 + 7.10642i −0.353870 + 0.257101i
\(765\) 3.42705 2.48990i 0.123905 0.0900225i
\(766\) −5.13525 15.8047i −0.185544 0.571047i
\(767\) 5.62868 17.3233i 0.203240 0.625508i
\(768\) 5.30902 + 3.85723i 0.191573 + 0.139186i
\(769\) 12.6869 0.457502 0.228751 0.973485i \(-0.426536\pi\)
0.228751 + 0.973485i \(0.426536\pi\)
\(770\) 0 0
\(771\) −11.6738 −0.420420
\(772\) −24.2984 17.6538i −0.874518 0.635374i
\(773\) −9.65654 + 29.7198i −0.347322 + 1.06895i 0.613008 + 0.790077i \(0.289960\pi\)
−0.960329 + 0.278869i \(0.910040\pi\)
\(774\) −1.19098 3.66547i −0.0428090 0.131753i
\(775\) −4.28115 + 3.11044i −0.153784 + 0.111730i
\(776\) 25.3885 18.4459i 0.911396 0.662168i
\(777\) 0.218847 + 0.673542i 0.00785109 + 0.0241632i
\(778\) −4.63525 + 14.2658i −0.166182 + 0.511455i
\(779\) 56.5689 + 41.0997i 2.02679 + 1.47255i
\(780\) 7.47214 0.267545
\(781\) 0 0
\(782\) −3.47214 −0.124163
\(783\) −3.61803 2.62866i −0.129298 0.0939405i
\(784\) 1.14590 3.52671i 0.0409249 0.125954i
\(785\) 3.00000 + 9.23305i 0.107075 + 0.329542i
\(786\) −3.57295 + 2.59590i −0.127443 + 0.0925927i
\(787\) 8.32624 6.04937i 0.296798 0.215637i −0.429413 0.903108i \(-0.641279\pi\)
0.726211 + 0.687472i \(0.241279\pi\)
\(788\) −12.1910 37.5200i −0.434286 1.33659i
\(789\) −5.04508 + 15.5272i −0.179610 + 0.552782i
\(790\) −12.3992 9.00854i −0.441143 0.320509i
\(791\) 2.12461 0.0755425
\(792\) 0 0
\(793\) 13.8541 0.491974
\(794\) −19.3541 14.0616i −0.686851 0.499027i
\(795\) 7.78115 23.9479i 0.275969 0.849345i
\(796\) 8.35410 + 25.7113i 0.296103 + 0.911312i
\(797\) −8.70820 + 6.32688i −0.308460 + 0.224110i −0.731236 0.682125i \(-0.761056\pi\)
0.422775 + 0.906235i \(0.361056\pi\)
\(798\) 8.78115 6.37988i 0.310849 0.225845i
\(799\) 0.809017 + 2.48990i 0.0286210 + 0.0880863i
\(800\) −3.21885 + 9.90659i −0.113803 + 0.350251i
\(801\) −0.427051 0.310271i −0.0150891 0.0109629i
\(802\) 16.1246 0.569380
\(803\) 0 0
\(804\) 15.4721 0.545660
\(805\) 22.0623 + 16.0292i 0.777594 + 0.564955i
\(806\) −0.961493 + 2.95917i −0.0338671 + 0.104232i
\(807\) 4.79837 + 14.7679i 0.168911 + 0.519854i
\(808\) 5.42705 3.94298i 0.190923 0.138714i
\(809\) −7.82624 + 5.68609i −0.275156 + 0.199912i −0.716802 0.697277i \(-0.754395\pi\)
0.441646 + 0.897189i \(0.354395\pi\)
\(810\) 0.500000 + 1.53884i 0.0175682 + 0.0540694i
\(811\) 1.00658 3.09793i 0.0353457 0.108783i −0.931827 0.362903i \(-0.881786\pi\)
0.967173 + 0.254120i \(0.0817857\pi\)
\(812\) 17.5623 + 12.7598i 0.616316 + 0.447780i
\(813\) −27.2705 −0.956419
\(814\) 0 0
\(815\) −47.8328 −1.67551
\(816\) −2.42705 1.76336i −0.0849638 0.0617298i
\(817\) 11.2812 34.7198i 0.394678 1.21469i
\(818\) 2.11146 + 6.49839i 0.0738253 + 0.227211i
\(819\) −4.28115 + 3.11044i −0.149596 + 0.108688i
\(820\) 40.9336 29.7400i 1.42946 1.03857i
\(821\) 12.4894 + 38.4383i 0.435882 + 1.34151i 0.892181 + 0.451679i \(0.149175\pi\)
−0.456299 + 0.889827i \(0.650825\pi\)
\(822\) −1.42705 + 4.39201i −0.0497741 + 0.153189i
\(823\) 28.6976 + 20.8500i 1.00033 + 0.726785i 0.962160 0.272486i \(-0.0878458\pi\)
0.0381743 + 0.999271i \(0.487846\pi\)
\(824\) −13.4164 −0.467383
\(825\) 0 0
\(826\) −19.1459 −0.666171
\(827\) −42.9787 31.2259i −1.49452 1.08583i −0.972502 0.232893i \(-0.925181\pi\)
−0.522014 0.852937i \(-0.674819\pi\)
\(828\) −1.73607 + 5.34307i −0.0603325 + 0.185684i
\(829\) 5.46556 + 16.8213i 0.189827 + 0.584226i 0.999998 0.00196663i \(-0.000625998\pi\)
−0.810171 + 0.586193i \(0.800626\pi\)
\(830\) −0.927051 + 0.673542i −0.0321784 + 0.0233790i
\(831\) −24.7254 + 17.9641i −0.857715 + 0.623167i
\(832\) −0.128677 0.396027i −0.00446108 0.0137298i
\(833\) 1.00000 3.07768i 0.0346479 0.106635i
\(834\) −0.427051 0.310271i −0.0147876 0.0107438i
\(835\) −26.2705 −0.909128
\(836\) 0 0
\(837\) 2.85410 0.0986522
\(838\) 8.25329 + 5.99637i 0.285105 + 0.207141i
\(839\) −11.3435 + 34.9116i −0.391620 + 1.20528i 0.539943 + 0.841701i \(0.318446\pi\)
−0.931563 + 0.363580i \(0.881554\pi\)
\(840\) −5.42705 16.7027i −0.187251 0.576299i
\(841\) 7.28115 5.29007i 0.251074 0.182416i
\(842\) −18.6353 + 13.5393i −0.642213 + 0.466595i
\(843\) −0.236068 0.726543i −0.00813061 0.0250235i
\(844\) 11.1353 34.2708i 0.383291 1.17965i
\(845\) −20.9443 15.2169i −0.720505 0.523477i
\(846\) −1.00000 −0.0343807
\(847\) 0 0
\(848\) −17.8328 −0.612381
\(849\) −0.145898 0.106001i −0.00500721 0.00363795i
\(850\) −0.572949 + 1.76336i −0.0196520 + 0.0604826i
\(851\) 0.253289 + 0.779543i 0.00868263 + 0.0267224i
\(852\) −7.28115 + 5.29007i −0.249448 + 0.181235i
\(853\) 8.04508 5.84510i 0.275458 0.200132i −0.441476 0.897273i \(-0.645545\pi\)
0.716934 + 0.697141i \(0.245545\pi\)
\(854\) −4.50000 13.8496i −0.153987 0.473923i
\(855\) −4.73607 + 14.5761i −0.161970 + 0.498493i
\(856\) 7.66312 + 5.56758i 0.261920 + 0.190296i
\(857\) 47.7214 1.63013 0.815065 0.579369i \(-0.196701\pi\)
0.815065 + 0.579369i \(0.196701\pi\)
\(858\) 0 0
\(859\) 7.11146 0.242640 0.121320 0.992613i \(-0.461287\pi\)
0.121320 + 0.992613i \(0.461287\pi\)
\(860\) −21.3713 15.5272i −0.728756 0.529472i
\(861\) −11.0729 + 34.0790i −0.377365 + 1.16141i
\(862\) 7.54508 + 23.2214i 0.256987 + 0.790923i
\(863\) −9.61803 + 6.98791i −0.327402 + 0.237871i −0.739327 0.673346i \(-0.764856\pi\)
0.411926 + 0.911217i \(0.364856\pi\)
\(864\) 4.54508 3.30220i 0.154627 0.112343i
\(865\) −12.4443 38.2995i −0.423118 1.30222i
\(866\) 1.14590 3.52671i 0.0389392 0.119843i
\(867\) 11.6353 + 8.45351i 0.395154 + 0.287096i
\(868\) −13.8541 −0.470239
\(869\) 0 0
\(870\) 7.23607 0.245326
\(871\) 13.6459 + 9.91433i 0.462374 + 0.335934i
\(872\) 0 0
\(873\) −4.33688 13.3475i −0.146781 0.451746i
\(874\) 10.1631 7.38394i 0.343773 0.249765i
\(875\) −19.9894 + 14.5231i −0.675764 + 0.490971i
\(876\) 1.61803 + 4.97980i 0.0546683 + 0.168252i
\(877\) 1.98278 6.10237i 0.0669537 0.206062i −0.911982 0.410229i \(-0.865449\pi\)
0.978936 + 0.204167i \(0.0654486\pi\)
\(878\) 1.64590 + 1.19581i 0.0555464 + 0.0403568i
\(879\) 0.0557281 0.00187966
\(880\) 0 0
\(881\) 13.9098 0.468634 0.234317 0.972160i \(-0.424715\pi\)
0.234317 + 0.972160i \(0.424715\pi\)
\(882\) 1.00000 + 0.726543i 0.0336718 + 0.0244640i
\(883\) 3.27051 10.0656i 0.110061 0.338734i −0.880824 0.473445i \(-0.843010\pi\)
0.990885 + 0.134710i \(0.0430104\pi\)
\(884\) −1.42705 4.39201i −0.0479969 0.147719i
\(885\) 21.8713 15.8904i 0.735196 0.534152i
\(886\) −20.5623 + 14.9394i −0.690804 + 0.501899i
\(887\) 0.927051 + 2.85317i 0.0311273 + 0.0958001i 0.965413 0.260725i \(-0.0839615\pi\)
−0.934286 + 0.356525i \(0.883962\pi\)
\(888\) 0.163119 0.502029i 0.00547391 0.0168470i
\(889\) 9.00000 + 6.53888i 0.301850 + 0.219307i
\(890\) 0.854102 0.0286296
\(891\) 0 0
\(892\) −1.14590 −0.0383675
\(893\) −7.66312 5.56758i −0.256436 0.186312i
\(894\) −2.86475 + 8.81678i −0.0958114 + 0.294877i
\(895\) 1.80902 + 5.56758i 0.0604688 + 0.186104i
\(896\) −27.6246 + 20.0705i −0.922874 + 0.670507i
\(897\) −4.95492 + 3.59996i −0.165440 + 0.120199i
\(898\) 4.67376 + 14.3844i 0.155965 + 0.480012i
\(899\) 3.94427 12.1392i 0.131549 0.404866i
\(900\) 2.42705 + 1.76336i 0.0809017 + 0.0587785i
\(901\) −15.5623 −0.518456
\(902\) 0 0
\(903\) 18.7082 0.622570
\(904\) −1.28115 0.930812i −0.0426105 0.0309584i
\(905\) 14.1353 43.5038i 0.469872 1.44612i
\(906\) −0.381966 1.17557i −0.0126900 0.0390557i
\(907\) 34.7705 25.2623i 1.15454 0.838819i 0.165458 0.986217i \(-0.447090\pi\)
0.989077 + 0.147397i \(0.0470896\pi\)
\(908\) −32.5795 + 23.6704i −1.08119 + 0.785530i
\(909\) −0.927051 2.85317i −0.0307483 0.0946337i
\(910\) 2.64590 8.14324i 0.0877107 0.269946i
\(911\) −14.6074 10.6129i −0.483964 0.351621i 0.318894 0.947790i \(-0.396689\pi\)
−0.802859 + 0.596170i \(0.796689\pi\)
\(912\) 10.8541 0.359415
\(913\) 0 0
\(914\) −5.06888 −0.167664
\(915\) 16.6353 + 12.0862i 0.549945 + 0.399558i
\(916\) −5.00000 + 15.3884i −0.165205 + 0.508448i
\(917\) −6.62461 20.3885i −0.218764 0.673286i
\(918\) 0.809017 0.587785i 0.0267015 0.0193998i
\(919\) −37.9894 + 27.6009i −1.25315 + 0.910469i −0.998400 0.0565371i \(-0.981994\pi\)
−0.254753 + 0.967006i \(0.581994\pi\)
\(920\) −6.28115 19.3314i −0.207083 0.637337i
\(921\) 0.173762 0.534785i 0.00572566 0.0176218i
\(922\) −10.5451 7.66145i −0.347284 0.252317i
\(923\) −9.81153 −0.322950
\(924\) 0 0
\(925\) 0.437694 0.0143913
\(926\) −7.89919 5.73910i −0.259583 0.188598i
\(927\) −1.85410 + 5.70634i −0.0608967 + 0.187421i
\(928\) −7.76393 23.8949i −0.254864 0.784389i
\(929\) 26.6074 19.3314i 0.872960 0.634243i −0.0584195 0.998292i \(-0.518606\pi\)
0.931380 + 0.364049i \(0.118606\pi\)
\(930\) −3.73607 + 2.71441i −0.122510 + 0.0890091i
\(931\) 3.61803 + 11.1352i 0.118576 + 0.364940i
\(932\) −12.1631 + 37.4342i −0.398416 + 1.22620i
\(933\) −2.04508 1.48584i −0.0669531 0.0486443i
\(934\) 6.03444 0.197453
\(935\) 0 0
\(936\) 3.94427 0.128923
\(937\) 13.4271 + 9.75532i 0.438643 + 0.318693i 0.785095 0.619375i \(-0.212614\pi\)
−0.346453 + 0.938067i \(0.612614\pi\)
\(938\) 5.47871 16.8617i 0.178886 0.550556i
\(939\) 7.98278 + 24.5685i 0.260508 + 0.801762i
\(940\) −5.54508 + 4.02874i −0.180861 + 0.131403i
\(941\) 36.1074 26.2336i 1.17707 0.855189i 0.185229 0.982695i \(-0.440697\pi\)
0.991838 + 0.127506i \(0.0406972\pi\)
\(942\) 0.708204 + 2.17963i 0.0230745 + 0.0710161i
\(943\) −12.8156 + 39.4423i −0.417333 + 1.28442i
\(944\) −15.4894 11.2537i −0.504136 0.366276i
\(945\) −7.85410 −0.255494
\(946\) 0 0
\(947\) 18.3262 0.595523 0.297761 0.954640i \(-0.403760\pi\)
0.297761 + 0.954640i \(0.403760\pi\)
\(948\) 12.3992 + 9.00854i 0.402707 + 0.292584i
\(949\) −1.76393 + 5.42882i −0.0572597 + 0.176227i
\(950\) −2.07295 6.37988i −0.0672553 0.206991i
\(951\) 15.6631 11.3799i 0.507911 0.369019i
\(952\) −8.78115 + 6.37988i −0.284599 + 0.206773i
\(953\) 11.6869 + 35.9686i 0.378576 + 1.16514i 0.941034 + 0.338312i \(0.109856\pi\)
−0.562458 + 0.826826i \(0.690144\pi\)
\(954\) 1.83688 5.65334i 0.0594712 0.183034i
\(955\) −15.8262 11.4984i −0.512125 0.372081i
\(956\) −4.14590 −0.134088
\(957\) 0 0
\(958\) 17.3607 0.560898
\(959\) −18.1353 13.1760i −0.585618 0.425476i
\(960\) 0.190983 0.587785i 0.00616395 0.0189707i
\(961\) −7.06231 21.7355i −0.227816 0.701147i
\(962\) 0.208204 0.151269i 0.00671276 0.00487711i
\(963\) 3.42705 2.48990i 0.110435 0.0802359i
\(964\) 11.5623 + 35.5851i 0.372397 + 1.14612i
\(965\) 15.0172 46.2183i 0.483421 1.48782i
\(966\) 5.20820 + 3.78398i 0.167571 + 0.121748i
\(967\) −34.6869 −1.11546 −0.557728 0.830024i \(-0.688327\pi\)
−0.557728 + 0.830024i \(0.688327\pi\)
\(968\) 0 0
\(969\) 9.47214 0.304289
\(970\) 18.3713 + 13.3475i 0.589868 + 0.428564i
\(971\) 11.6738 35.9281i 0.374629 1.15299i −0.569100 0.822268i \(-0.692708\pi\)
0.943729 0.330721i \(-0.107292\pi\)
\(972\) −0.500000 1.53884i −0.0160375 0.0493584i
\(973\) 2.07295 1.50609i 0.0664557 0.0482829i
\(974\) 8.40983 6.11010i 0.269468 0.195780i
\(975\) 1.01064 + 3.11044i 0.0323665 + 0.0996138i
\(976\) 4.50000 13.8496i 0.144041 0.443314i
\(977\) 3.75329 + 2.72692i 0.120078 + 0.0872420i 0.646204 0.763165i \(-0.276356\pi\)
−0.526125 + 0.850407i \(0.676356\pi\)
\(978\) −11.2918 −0.361072
\(979\) 0 0
\(980\) 8.47214 0.270632
\(981\) 0 0
\(982\) −4.81559 + 14.8209i −0.153672 + 0.472953i
\(983\) −8.43769 25.9686i −0.269121 0.828268i −0.990715 0.135952i \(-0.956591\pi\)
0.721595 0.692316i \(-0.243409\pi\)
\(984\) 21.6074 15.6987i 0.688818 0.500456i
\(985\) 51.6418 37.5200i 1.64545 1.19549i
\(986\) −1.38197 4.25325i −0.0440108 0.135451i
\(987\) 1.50000 4.61653i 0.0477455 0.146946i
\(988\) 13.5172 + 9.82084i 0.430040 + 0.312442i
\(989\) 21.6525 0.688509
\(990\) 0 0
\(991\) 21.2705 0.675680 0.337840 0.941204i \(-0.390304\pi\)
0.337840 + 0.941204i \(0.390304\pi\)
\(992\) 12.9721 + 9.42481i 0.411866 + 0.299238i
\(993\) 8.21885 25.2950i 0.260817 0.802713i
\(994\) 3.18692 + 9.80832i 0.101083 + 0.311101i
\(995\) −35.3885 + 25.7113i −1.12189 + 0.815102i
\(996\) 0.927051 0.673542i 0.0293747 0.0213420i
\(997\) −4.01064 12.3435i −0.127018 0.390922i 0.867245 0.497882i \(-0.165889\pi\)
−0.994263 + 0.106959i \(0.965889\pi\)
\(998\) 3.35410 10.3229i 0.106172 0.326765i
\(999\) −0.190983 0.138757i −0.00604243 0.00439009i
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 363.2.e.h.202.1 4
11.2 odd 10 363.2.e.j.148.1 4
11.3 even 5 inner 363.2.e.h.124.1 4
11.4 even 5 33.2.e.a.31.1 yes 4
11.5 even 5 363.2.a.h.1.1 2
11.6 odd 10 363.2.a.e.1.2 2
11.7 odd 10 363.2.e.j.130.1 4
11.8 odd 10 363.2.e.c.124.1 4
11.9 even 5 33.2.e.a.16.1 4
11.10 odd 2 363.2.e.c.202.1 4
33.5 odd 10 1089.2.a.m.1.2 2
33.17 even 10 1089.2.a.s.1.1 2
33.20 odd 10 99.2.f.b.82.1 4
33.26 odd 10 99.2.f.b.64.1 4
44.15 odd 10 528.2.y.f.97.1 4
44.27 odd 10 5808.2.a.bl.1.1 2
44.31 odd 10 528.2.y.f.49.1 4
44.39 even 10 5808.2.a.bm.1.1 2
55.4 even 10 825.2.n.f.526.1 4
55.9 even 10 825.2.n.f.676.1 4
55.37 odd 20 825.2.bx.b.724.1 8
55.39 odd 10 9075.2.a.bv.1.1 2
55.42 odd 20 825.2.bx.b.49.2 8
55.48 odd 20 825.2.bx.b.724.2 8
55.49 even 10 9075.2.a.x.1.2 2
55.53 odd 20 825.2.bx.b.49.1 8
99.4 even 15 891.2.n.d.460.1 8
99.20 odd 30 891.2.n.a.676.1 8
99.31 even 15 891.2.n.d.379.1 8
99.59 odd 30 891.2.n.a.460.1 8
99.70 even 15 891.2.n.d.757.1 8
99.86 odd 30 891.2.n.a.379.1 8
99.92 odd 30 891.2.n.a.757.1 8
99.97 even 15 891.2.n.d.676.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 11.9 even 5
33.2.e.a.31.1 yes 4 11.4 even 5
99.2.f.b.64.1 4 33.26 odd 10
99.2.f.b.82.1 4 33.20 odd 10
363.2.a.e.1.2 2 11.6 odd 10
363.2.a.h.1.1 2 11.5 even 5
363.2.e.c.124.1 4 11.8 odd 10
363.2.e.c.202.1 4 11.10 odd 2
363.2.e.h.124.1 4 11.3 even 5 inner
363.2.e.h.202.1 4 1.1 even 1 trivial
363.2.e.j.130.1 4 11.7 odd 10
363.2.e.j.148.1 4 11.2 odd 10
528.2.y.f.49.1 4 44.31 odd 10
528.2.y.f.97.1 4 44.15 odd 10
825.2.n.f.526.1 4 55.4 even 10
825.2.n.f.676.1 4 55.9 even 10
825.2.bx.b.49.1 8 55.53 odd 20
825.2.bx.b.49.2 8 55.42 odd 20
825.2.bx.b.724.1 8 55.37 odd 20
825.2.bx.b.724.2 8 55.48 odd 20
891.2.n.a.379.1 8 99.86 odd 30
891.2.n.a.460.1 8 99.59 odd 30
891.2.n.a.676.1 8 99.20 odd 30
891.2.n.a.757.1 8 99.92 odd 30
891.2.n.d.379.1 8 99.31 even 15
891.2.n.d.460.1 8 99.4 even 15
891.2.n.d.676.1 8 99.97 even 15
891.2.n.d.757.1 8 99.70 even 15
1089.2.a.m.1.2 2 33.5 odd 10
1089.2.a.s.1.1 2 33.17 even 10
5808.2.a.bl.1.1 2 44.27 odd 10
5808.2.a.bm.1.1 2 44.39 even 10
9075.2.a.x.1.2 2 55.49 even 10
9075.2.a.bv.1.1 2 55.39 odd 10