Properties

Label 819.2.fy.a.50.9
Level $819$
Weight $2$
Character 819.50
Analytic conductor $6.540$
Analytic rank $0$
Dimension $336$
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] = [819,2,Mod(50,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.50");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fy (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(84\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 50.9
Character \(\chi\) \(=\) 819.50
Dual form 819.2.fy.a.344.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.606137 - 2.26213i) q^{2} +(1.35078 - 1.08415i) q^{3} +(-3.01779 + 1.74232i) q^{4} +(0.760590 + 2.83856i) q^{5} +(-3.27125 - 2.39851i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.45857 + 2.45857i) q^{8} +(0.649233 - 2.92891i) q^{9} +O(q^{10})\) \(q+(-0.606137 - 2.26213i) q^{2} +(1.35078 - 1.08415i) q^{3} +(-3.01779 + 1.74232i) q^{4} +(0.760590 + 2.83856i) q^{5} +(-3.27125 - 2.39851i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.45857 + 2.45857i) q^{8} +(0.649233 - 2.92891i) q^{9} +(5.96018 - 3.44111i) q^{10} +(-0.0575643 + 0.0154243i) q^{11} +(-2.18744 + 5.62525i) q^{12} +(2.96165 - 2.05636i) q^{13} +(2.02817 + 1.17097i) q^{14} +(4.10482 + 3.00968i) q^{15} +(0.586737 - 1.01626i) q^{16} +(2.24538 - 3.88911i) q^{17} +(-7.01910 + 0.306668i) q^{18} +(4.01039 - 1.07458i) q^{19} +(-7.24099 - 7.24099i) q^{20} +(-0.188538 + 1.72176i) q^{21} +(0.0697837 + 0.120869i) q^{22} +7.03141 q^{23} +(5.98646 + 0.655535i) q^{24} +(-3.14879 + 1.81796i) q^{25} +(-6.44693 - 5.45321i) q^{26} +(-2.29841 - 4.66019i) q^{27} +(0.901893 - 3.36591i) q^{28} +(2.95704 + 1.70725i) q^{29} +(4.32023 - 11.1099i) q^{30} +(-5.73172 + 1.53581i) q^{31} +(4.06239 + 1.08851i) q^{32} +(-0.0610346 + 0.0832433i) q^{33} +(-10.1587 - 2.72201i) q^{34} +(-2.54498 - 1.46935i) q^{35} +(3.14386 + 9.97001i) q^{36} +(-10.0125 - 2.68285i) q^{37} +(-4.86168 - 8.42069i) q^{38} +(1.77114 - 5.98858i) q^{39} +(-5.10884 + 8.84876i) q^{40} +(4.55639 - 4.55639i) q^{41} +(4.00913 - 0.617124i) q^{42} -4.18894i q^{43} +(0.146843 - 0.146843i) q^{44} +(8.80768 - 0.384811i) q^{45} +(-4.26200 - 15.9060i) q^{46} +(0.366584 - 1.36811i) q^{47} +(-0.309223 - 2.00886i) q^{48} -1.00000i q^{49} +(6.02106 + 6.02106i) q^{50} +(-1.18336 - 7.68767i) q^{51} +(-5.35480 + 11.3658i) q^{52} -1.16332i q^{53} +(-9.14881 + 8.02401i) q^{54} +(-0.0875656 - 0.151668i) q^{55} -3.47694 q^{56} +(4.25216 - 5.79939i) q^{57} +(2.06965 - 7.72404i) q^{58} +(-0.959905 + 3.58241i) q^{59} +(-17.6313 - 1.93068i) q^{60} -0.463646 q^{61} +(6.94841 + 12.0350i) q^{62} +(1.61197 + 2.53013i) q^{63} -12.1964i q^{64} +(8.08971 + 6.84277i) q^{65} +(0.225303 + 0.0876116i) q^{66} +(4.02924 + 4.02924i) q^{67} +15.6487i q^{68} +(9.49792 - 7.62312i) q^{69} +(-1.78125 + 6.64771i) q^{70} +(1.38821 + 5.18087i) q^{71} +(8.79711 - 5.60474i) q^{72} +(-4.78119 + 4.78119i) q^{73} +24.2759i q^{74} +(-2.28240 + 5.86943i) q^{75} +(-10.2303 + 10.2303i) q^{76} +(0.0297975 - 0.0516108i) q^{77} +(-14.6205 - 0.376655i) q^{78} +(1.84857 + 3.20181i) q^{79} +(3.33097 + 0.892532i) q^{80} +(-8.15699 - 3.80308i) q^{81} +(-13.0689 - 7.54536i) q^{82} +(6.23872 + 1.67166i) q^{83} +(-2.43089 - 5.52441i) q^{84} +(12.7473 + 3.41562i) q^{85} +(-9.47594 + 2.53907i) q^{86} +(5.84523 - 0.899755i) q^{87} +(-0.179448 - 0.103604i) q^{88} +(-0.136146 + 0.508106i) q^{89} +(-6.20915 - 19.6909i) q^{90} +(-0.640134 + 3.54827i) q^{91} +(-21.2194 + 12.2510i) q^{92} +(-6.07726 + 8.28859i) q^{93} -3.31705 q^{94} +(6.10052 + 10.5664i) q^{95} +(6.66752 - 2.93390i) q^{96} +(-6.33386 - 6.33386i) q^{97} +(-2.26213 + 0.606137i) q^{98} +(0.00780375 + 0.178614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.606137 2.26213i −0.428603 1.59957i −0.755926 0.654657i \(-0.772813\pi\)
0.327323 0.944913i \(-0.393854\pi\)
\(3\) 1.35078 1.08415i 0.779875 0.625935i
\(4\) −3.01779 + 1.74232i −1.50890 + 0.871162i
\(5\) 0.760590 + 2.83856i 0.340146 + 1.26944i 0.898181 + 0.439625i \(0.144889\pi\)
−0.558035 + 0.829817i \(0.688445\pi\)
\(6\) −3.27125 2.39851i −1.33548 0.979187i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 2.45857 + 2.45857i 0.869236 + 0.869236i
\(9\) 0.649233 2.92891i 0.216411 0.976302i
\(10\) 5.96018 3.44111i 1.88477 1.08817i
\(11\) −0.0575643 + 0.0154243i −0.0173563 + 0.00465060i −0.267487 0.963562i \(-0.586193\pi\)
0.250130 + 0.968212i \(0.419526\pi\)
\(12\) −2.18744 + 5.62525i −0.631460 + 1.62387i
\(13\) 2.96165 2.05636i 0.821414 0.570333i
\(14\) 2.02817 + 1.17097i 0.542052 + 0.312954i
\(15\) 4.10482 + 3.00968i 1.05986 + 0.777097i
\(16\) 0.586737 1.01626i 0.146684 0.254064i
\(17\) 2.24538 3.88911i 0.544584 0.943247i −0.454049 0.890977i \(-0.650021\pi\)
0.998633 0.0522706i \(-0.0166458\pi\)
\(18\) −7.01910 + 0.306668i −1.65442 + 0.0722823i
\(19\) 4.01039 1.07458i 0.920046 0.246526i 0.232441 0.972611i \(-0.425329\pi\)
0.687605 + 0.726085i \(0.258662\pi\)
\(20\) −7.24099 7.24099i −1.61913 1.61913i
\(21\) −0.188538 + 1.72176i −0.0411423 + 0.375719i
\(22\) 0.0697837 + 0.120869i 0.0148779 + 0.0257693i
\(23\) 7.03141 1.46615 0.733076 0.680147i \(-0.238084\pi\)
0.733076 + 0.680147i \(0.238084\pi\)
\(24\) 5.98646 + 0.655535i 1.22198 + 0.133810i
\(25\) −3.14879 + 1.81796i −0.629759 + 0.363591i
\(26\) −6.44693 5.45321i −1.26435 1.06946i
\(27\) −2.29841 4.66019i −0.442328 0.896853i
\(28\) 0.901893 3.36591i 0.170442 0.636097i
\(29\) 2.95704 + 1.70725i 0.549108 + 0.317028i 0.748762 0.662839i \(-0.230649\pi\)
−0.199654 + 0.979866i \(0.563982\pi\)
\(30\) 4.32023 11.1099i 0.788762 2.02839i
\(31\) −5.73172 + 1.53581i −1.02945 + 0.275839i −0.733734 0.679437i \(-0.762224\pi\)
−0.295713 + 0.955277i \(0.595557\pi\)
\(32\) 4.06239 + 1.08851i 0.718135 + 0.192424i
\(33\) −0.0610346 + 0.0832433i −0.0106248 + 0.0144908i
\(34\) −10.1587 2.72201i −1.74220 0.466821i
\(35\) −2.54498 1.46935i −0.430181 0.248365i
\(36\) 3.14386 + 9.97001i 0.523976 + 1.66167i
\(37\) −10.0125 2.68285i −1.64605 0.441059i −0.687549 0.726138i \(-0.741313\pi\)
−0.958504 + 0.285079i \(0.907980\pi\)
\(38\) −4.86168 8.42069i −0.788669 1.36602i
\(39\) 1.77114 5.98858i 0.283609 0.958940i
\(40\) −5.10884 + 8.84876i −0.807778 + 1.39911i
\(41\) 4.55639 4.55639i 0.711588 0.711588i −0.255279 0.966867i \(-0.582167\pi\)
0.966867 + 0.255279i \(0.0821674\pi\)
\(42\) 4.00913 0.617124i 0.618622 0.0952243i
\(43\) 4.18894i 0.638807i −0.947619 0.319404i \(-0.896517\pi\)
0.947619 0.319404i \(-0.103483\pi\)
\(44\) 0.146843 0.146843i 0.0221374 0.0221374i
\(45\) 8.80768 0.384811i 1.31297 0.0573643i
\(46\) −4.26200 15.9060i −0.628397 2.34521i
\(47\) 0.366584 1.36811i 0.0534718 0.199560i −0.934022 0.357214i \(-0.883727\pi\)
0.987494 + 0.157655i \(0.0503933\pi\)
\(48\) −0.309223 2.00886i −0.0446325 0.289953i
\(49\) 1.00000i 0.142857i
\(50\) 6.02106 + 6.02106i 0.851506 + 0.851506i
\(51\) −1.18336 7.68767i −0.165704 1.07649i
\(52\) −5.35480 + 11.3658i −0.742577 + 1.57616i
\(53\) 1.16332i 0.159794i −0.996803 0.0798970i \(-0.974541\pi\)
0.996803 0.0798970i \(-0.0254591\pi\)
\(54\) −9.14881 + 8.02401i −1.24500 + 1.09193i
\(55\) −0.0875656 0.151668i −0.0118073 0.0204509i
\(56\) −3.47694 −0.464626
\(57\) 4.25216 5.79939i 0.563212 0.768148i
\(58\) 2.06965 7.72404i 0.271758 1.01422i
\(59\) −0.959905 + 3.58241i −0.124969 + 0.466390i −0.999839 0.0179681i \(-0.994280\pi\)
0.874870 + 0.484358i \(0.160947\pi\)
\(60\) −17.6313 1.93068i −2.27620 0.249250i
\(61\) −0.463646 −0.0593638 −0.0296819 0.999559i \(-0.509449\pi\)
−0.0296819 + 0.999559i \(0.509449\pi\)
\(62\) 6.94841 + 12.0350i 0.882449 + 1.52845i
\(63\) 1.61197 + 2.53013i 0.203090 + 0.318766i
\(64\) 12.1964i 1.52455i
\(65\) 8.08971 + 6.84277i 1.00340 + 0.848741i
\(66\) 0.225303 + 0.0876116i 0.0277329 + 0.0107842i
\(67\) 4.02924 + 4.02924i 0.492250 + 0.492250i 0.909015 0.416764i \(-0.136836\pi\)
−0.416764 + 0.909015i \(0.636836\pi\)
\(68\) 15.6487i 1.89768i
\(69\) 9.49792 7.62312i 1.14341 0.917715i
\(70\) −1.78125 + 6.64771i −0.212900 + 0.794554i
\(71\) 1.38821 + 5.18087i 0.164750 + 0.614856i 0.998072 + 0.0620676i \(0.0197694\pi\)
−0.833322 + 0.552788i \(0.813564\pi\)
\(72\) 8.79711 5.60474i 1.03675 0.660525i
\(73\) −4.78119 + 4.78119i −0.559596 + 0.559596i −0.929192 0.369596i \(-0.879496\pi\)
0.369596 + 0.929192i \(0.379496\pi\)
\(74\) 24.2759i 2.82202i
\(75\) −2.28240 + 5.86943i −0.263549 + 0.677744i
\(76\) −10.2303 + 10.2303i −1.17349 + 1.17349i
\(77\) 0.0297975 0.0516108i 0.00339574 0.00588159i
\(78\) −14.6205 0.376655i −1.65545 0.0426478i
\(79\) 1.84857 + 3.20181i 0.207980 + 0.360232i 0.951078 0.308951i \(-0.0999778\pi\)
−0.743098 + 0.669183i \(0.766644\pi\)
\(80\) 3.33097 + 0.892532i 0.372414 + 0.0997881i
\(81\) −8.15699 3.80308i −0.906333 0.422565i
\(82\) −13.0689 7.54536i −1.44322 0.833246i
\(83\) 6.23872 + 1.67166i 0.684789 + 0.183489i 0.584407 0.811460i \(-0.301327\pi\)
0.100381 + 0.994949i \(0.467994\pi\)
\(84\) −2.43089 5.52441i −0.265232 0.602762i
\(85\) 12.7473 + 3.41562i 1.38264 + 0.370476i
\(86\) −9.47594 + 2.53907i −1.02182 + 0.273795i
\(87\) 5.84523 0.899755i 0.626674 0.0964639i
\(88\) −0.179448 0.103604i −0.0191292 0.0110442i
\(89\) −0.136146 + 0.508106i −0.0144315 + 0.0538591i −0.972766 0.231789i \(-0.925542\pi\)
0.958335 + 0.285648i \(0.0922088\pi\)
\(90\) −6.20915 19.6909i −0.654502 2.07560i
\(91\) −0.640134 + 3.54827i −0.0671043 + 0.371960i
\(92\) −21.2194 + 12.2510i −2.21227 + 1.27725i
\(93\) −6.07726 + 8.28859i −0.630183 + 0.859487i
\(94\) −3.31705 −0.342128
\(95\) 6.10052 + 10.5664i 0.625900 + 1.08409i
\(96\) 6.66752 2.93390i 0.680501 0.299439i
\(97\) −6.33386 6.33386i −0.643106 0.643106i 0.308212 0.951318i \(-0.400269\pi\)
−0.951318 + 0.308212i \(0.900269\pi\)
\(98\) −2.26213 + 0.606137i −0.228510 + 0.0612291i
\(99\) 0.00780375 + 0.178614i 0.000784307 + 0.0179514i
\(100\) 6.33494 10.9724i 0.633494 1.09724i
\(101\) −6.25278 + 10.8301i −0.622175 + 1.07764i 0.366905 + 0.930258i \(0.380417\pi\)
−0.989080 + 0.147380i \(0.952916\pi\)
\(102\) −16.6733 + 7.33670i −1.65090 + 0.726442i
\(103\) 0.760188 + 0.438895i 0.0749036 + 0.0432456i 0.536984 0.843592i \(-0.319564\pi\)
−0.462080 + 0.886838i \(0.652897\pi\)
\(104\) 12.3371 + 2.22571i 1.20976 + 0.218249i
\(105\) −5.03071 + 0.774377i −0.490947 + 0.0755714i
\(106\) −2.63158 + 0.705129i −0.255602 + 0.0684882i
\(107\) 16.0149 9.24621i 1.54822 0.893865i 0.549941 0.835204i \(-0.314650\pi\)
0.998278 0.0586611i \(-0.0186831\pi\)
\(108\) 15.0557 + 10.0589i 1.44873 + 0.967919i
\(109\) 10.6476 + 10.6476i 1.01985 + 1.01985i 0.999799 + 0.0200551i \(0.00638417\pi\)
0.0200551 + 0.999799i \(0.493616\pi\)
\(110\) −0.290017 + 0.290017i −0.0276520 + 0.0276520i
\(111\) −16.4334 + 7.23116i −1.55979 + 0.686351i
\(112\) 0.303717 + 1.13349i 0.0286986 + 0.107105i
\(113\) −8.18779 + 4.72723i −0.770243 + 0.444700i −0.832961 0.553331i \(-0.813356\pi\)
0.0627184 + 0.998031i \(0.480023\pi\)
\(114\) −15.6964 6.10372i −1.47010 0.571666i
\(115\) 5.34802 + 19.9591i 0.498705 + 1.86119i
\(116\) −11.8983 −1.10473
\(117\) −4.10010 10.0095i −0.379054 0.925374i
\(118\) 8.68573 0.799586
\(119\) 1.16229 + 4.33774i 0.106547 + 0.397640i
\(120\) 2.69247 + 17.4915i 0.245787 + 1.59675i
\(121\) −9.52320 + 5.49822i −0.865746 + 0.499839i
\(122\) 0.281033 + 1.04883i 0.0254435 + 0.0949565i
\(123\) 1.21488 11.0945i 0.109542 1.00036i
\(124\) 14.6213 14.6213i 1.31303 1.31303i
\(125\) 2.83453 + 2.83453i 0.253528 + 0.253528i
\(126\) 4.74641 5.18010i 0.422844 0.461480i
\(127\) 18.7765 10.8406i 1.66614 0.961948i 0.696456 0.717600i \(-0.254759\pi\)
0.969688 0.244348i \(-0.0785740\pi\)
\(128\) −19.4651 + 5.21566i −1.72049 + 0.461003i
\(129\) −4.54144 5.65835i −0.399852 0.498190i
\(130\) 10.5758 22.4477i 0.927558 1.96879i
\(131\) −7.41050 4.27845i −0.647458 0.373810i 0.140024 0.990148i \(-0.455282\pi\)
−0.787482 + 0.616338i \(0.788615\pi\)
\(132\) 0.0391531 0.357553i 0.00340784 0.0311210i
\(133\) −2.07593 + 3.59561i −0.180006 + 0.311779i
\(134\) 6.67241 11.5570i 0.576408 0.998369i
\(135\) 11.4801 10.0686i 0.988047 0.866571i
\(136\) 15.0821 4.04123i 1.29328 0.346533i
\(137\) 15.2852 + 15.2852i 1.30591 + 1.30591i 0.924343 + 0.381563i \(0.124614\pi\)
0.381563 + 0.924343i \(0.375386\pi\)
\(138\) −23.0015 16.8649i −1.95802 1.43564i
\(139\) −8.22750 14.2504i −0.697847 1.20871i −0.969211 0.246230i \(-0.920808\pi\)
0.271364 0.962477i \(-0.412525\pi\)
\(140\) 10.2403 0.865464
\(141\) −0.988064 2.24546i −0.0832100 0.189101i
\(142\) 10.8784 6.28063i 0.912892 0.527058i
\(143\) −0.138767 + 0.164055i −0.0116043 + 0.0137189i
\(144\) −2.59560 2.37829i −0.216300 0.198190i
\(145\) −2.59703 + 9.69224i −0.215671 + 0.804897i
\(146\) 13.7137 + 7.91763i 1.13496 + 0.655268i
\(147\) −1.08415 1.35078i −0.0894193 0.111411i
\(148\) 34.8902 9.34880i 2.86796 0.768467i
\(149\) −11.2160 3.00533i −0.918853 0.246206i −0.231758 0.972773i \(-0.574448\pi\)
−0.687095 + 0.726568i \(0.741114\pi\)
\(150\) 14.6609 + 1.60541i 1.19706 + 0.131081i
\(151\) −20.2538 5.42698i −1.64823 0.441642i −0.689113 0.724654i \(-0.742000\pi\)
−0.959116 + 0.283012i \(0.908666\pi\)
\(152\) 12.5017 + 7.21789i 1.01403 + 0.585448i
\(153\) −9.93307 9.10144i −0.803041 0.735808i
\(154\) −0.134812 0.0361227i −0.0108634 0.00291085i
\(155\) −8.71897 15.1017i −0.700324 1.21300i
\(156\) 5.08911 + 21.1582i 0.407455 + 1.69401i
\(157\) −11.7809 + 20.4052i −0.940220 + 1.62851i −0.175170 + 0.984538i \(0.556048\pi\)
−0.765050 + 0.643971i \(0.777286\pi\)
\(158\) 6.12244 6.12244i 0.487075 0.487075i
\(159\) −1.26121 1.57139i −0.100021 0.124619i
\(160\) 12.3592i 0.977084i
\(161\) −4.97196 + 4.97196i −0.391845 + 0.391845i
\(162\) −3.65883 + 20.7574i −0.287465 + 1.63085i
\(163\) −5.06180 18.8909i −0.396471 1.47965i −0.819260 0.573422i \(-0.805616\pi\)
0.422789 0.906228i \(-0.361051\pi\)
\(164\) −5.81153 + 21.6889i −0.453804 + 1.69362i
\(165\) −0.282713 0.109936i −0.0220092 0.00855854i
\(166\) 15.1261i 1.17401i
\(167\) 7.23371 + 7.23371i 0.559761 + 0.559761i 0.929239 0.369478i \(-0.120464\pi\)
−0.369478 + 0.929239i \(0.620464\pi\)
\(168\) −4.69660 + 3.76953i −0.362351 + 0.290826i
\(169\) 4.54274 12.1805i 0.349441 0.936958i
\(170\) 30.9064i 2.37041i
\(171\) −0.543671 12.4437i −0.0415756 0.951594i
\(172\) 7.29849 + 12.6414i 0.556505 + 0.963894i
\(173\) 6.96895 0.529839 0.264920 0.964271i \(-0.414655\pi\)
0.264920 + 0.964271i \(0.414655\pi\)
\(174\) −5.57837 12.6773i −0.422895 0.961065i
\(175\) 0.941044 3.51202i 0.0711362 0.265484i
\(176\) −0.0181000 + 0.0675502i −0.00136434 + 0.00509179i
\(177\) 2.58725 + 5.87975i 0.194470 + 0.441949i
\(178\) 1.23193 0.0923367
\(179\) −1.35100 2.34000i −0.100979 0.174900i 0.811110 0.584894i \(-0.198864\pi\)
−0.912088 + 0.409994i \(0.865531\pi\)
\(180\) −25.9093 + 16.5071i −1.93116 + 1.23037i
\(181\) 6.08312i 0.452155i 0.974109 + 0.226077i \(0.0725902\pi\)
−0.974109 + 0.226077i \(0.927410\pi\)
\(182\) 8.41467 0.702669i 0.623737 0.0520853i
\(183\) −0.626285 + 0.502662i −0.0462963 + 0.0371578i
\(184\) 17.2872 + 17.2872i 1.27443 + 1.27443i
\(185\) 30.4618i 2.23959i
\(186\) 22.4336 + 8.72355i 1.64491 + 0.639642i
\(187\) −0.0692668 + 0.258507i −0.00506529 + 0.0189039i
\(188\) 1.27742 + 4.76739i 0.0931652 + 0.347697i
\(189\) 4.92047 + 1.67003i 0.357911 + 0.121477i
\(190\) 20.2049 20.2049i 1.46581 1.46581i
\(191\) 15.7566i 1.14010i 0.821608 + 0.570052i \(0.193077\pi\)
−0.821608 + 0.570052i \(0.806923\pi\)
\(192\) −13.2227 16.4747i −0.954269 1.18896i
\(193\) −13.2250 + 13.2250i −0.951954 + 0.951954i −0.998898 0.0469438i \(-0.985052\pi\)
0.0469438 + 0.998898i \(0.485052\pi\)
\(194\) −10.4888 + 18.1672i −0.753055 + 1.30433i
\(195\) 18.3460 + 0.472632i 1.31379 + 0.0338459i
\(196\) 1.74232 + 3.01779i 0.124452 + 0.215557i
\(197\) 10.1898 + 2.73034i 0.725992 + 0.194529i 0.602844 0.797859i \(-0.294034\pi\)
0.123148 + 0.992388i \(0.460701\pi\)
\(198\) 0.399320 0.125918i 0.0283784 0.00894860i
\(199\) −2.84426 1.64213i −0.201624 0.116408i 0.395789 0.918342i \(-0.370471\pi\)
−0.597413 + 0.801934i \(0.703805\pi\)
\(200\) −12.2111 3.27196i −0.863456 0.231362i
\(201\) 9.81094 + 1.07433i 0.692010 + 0.0757771i
\(202\) 28.2892 + 7.58008i 1.99042 + 0.533332i
\(203\) −3.29815 + 0.883736i −0.231485 + 0.0620261i
\(204\) 16.9656 + 21.1380i 1.18783 + 1.47996i
\(205\) 16.3991 + 9.46803i 1.14536 + 0.661276i
\(206\) 0.532061 1.98568i 0.0370704 0.138349i
\(207\) 4.56502 20.5944i 0.317291 1.43141i
\(208\) −0.352087 4.21634i −0.0244128 0.292351i
\(209\) −0.214280 + 0.123715i −0.0148221 + 0.00855754i
\(210\) 4.80104 + 10.9108i 0.331303 + 0.752914i
\(211\) −17.5502 −1.20820 −0.604101 0.796908i \(-0.706468\pi\)
−0.604101 + 0.796908i \(0.706468\pi\)
\(212\) 2.02688 + 3.51065i 0.139206 + 0.241113i
\(213\) 7.49201 + 5.49320i 0.513344 + 0.376388i
\(214\) −30.6234 30.6234i −2.09337 2.09337i
\(215\) 11.8906 3.18606i 0.810929 0.217288i
\(216\) 5.80660 17.1082i 0.395089 1.16406i
\(217\) 2.96696 5.13892i 0.201410 0.348852i
\(218\) 17.6324 30.5402i 1.19421 2.06844i
\(219\) −1.27482 + 11.6419i −0.0861444 + 0.786686i
\(220\) 0.528510 + 0.305135i 0.0356321 + 0.0205722i
\(221\) −1.34740 16.1355i −0.0906358 1.08539i
\(222\) 26.3187 + 32.7915i 1.76640 + 2.20082i
\(223\) 14.2210 3.81050i 0.952307 0.255170i 0.250966 0.967996i \(-0.419252\pi\)
0.701341 + 0.712826i \(0.252585\pi\)
\(224\) −3.64224 + 2.10285i −0.243357 + 0.140502i
\(225\) 3.28033 + 10.4028i 0.218689 + 0.693520i
\(226\) 15.6565 + 15.6565i 1.04146 + 1.04146i
\(227\) −6.71545 + 6.71545i −0.445720 + 0.445720i −0.893929 0.448209i \(-0.852062\pi\)
0.448209 + 0.893929i \(0.352062\pi\)
\(228\) −2.72772 + 24.9100i −0.180647 + 1.64970i
\(229\) 5.96986 + 22.2798i 0.394499 + 1.47229i 0.822631 + 0.568576i \(0.192505\pi\)
−0.428132 + 0.903716i \(0.640828\pi\)
\(230\) 41.9085 24.1959i 2.76336 1.59543i
\(231\) −0.0157039 0.102020i −0.00103324 0.00671242i
\(232\) 3.07270 + 11.4675i 0.201733 + 0.752876i
\(233\) −3.40298 −0.222937 −0.111468 0.993768i \(-0.535555\pi\)
−0.111468 + 0.993768i \(0.535555\pi\)
\(234\) −20.1575 + 15.3421i −1.31774 + 1.00294i
\(235\) 4.16229 0.271518
\(236\) −3.34493 12.4834i −0.217736 0.812603i
\(237\) 5.96826 + 2.32083i 0.387680 + 0.150754i
\(238\) 9.10803 5.25852i 0.590386 0.340859i
\(239\) −0.830833 3.10071i −0.0537421 0.200568i 0.933835 0.357705i \(-0.116441\pi\)
−0.987577 + 0.157136i \(0.949774\pi\)
\(240\) 5.46706 2.40566i 0.352897 0.155285i
\(241\) −12.2596 + 12.2596i −0.789710 + 0.789710i −0.981447 0.191736i \(-0.938588\pi\)
0.191736 + 0.981447i \(0.438588\pi\)
\(242\) 18.2101 + 18.2101i 1.17059 + 1.17059i
\(243\) −15.1415 + 3.70627i −0.971325 + 0.237757i
\(244\) 1.39919 0.807821i 0.0895738 0.0517154i
\(245\) 2.83856 0.760590i 0.181349 0.0485923i
\(246\) −25.8336 + 3.97657i −1.64709 + 0.253537i
\(247\) 9.66763 11.4293i 0.615137 0.727232i
\(248\) −17.8677 10.3159i −1.13460 0.655063i
\(249\) 10.2395 4.50567i 0.648902 0.285535i
\(250\) 4.69397 8.13020i 0.296873 0.514199i
\(251\) 10.7864 18.6825i 0.680829 1.17923i −0.293899 0.955836i \(-0.594953\pi\)
0.974728 0.223394i \(-0.0717137\pi\)
\(252\) −9.27290 4.82682i −0.584138 0.304061i
\(253\) −0.404758 + 0.108455i −0.0254469 + 0.00681849i
\(254\) −35.9040 35.9040i −2.25282 2.25282i
\(255\) 20.9219 9.20621i 1.31018 0.576515i
\(256\) 11.4006 + 19.7465i 0.712539 + 1.23415i
\(257\) 1.52613 0.0951972 0.0475986 0.998867i \(-0.484843\pi\)
0.0475986 + 0.998867i \(0.484843\pi\)
\(258\) −10.0472 + 13.7031i −0.625512 + 0.853117i
\(259\) 8.97701 5.18288i 0.557804 0.322048i
\(260\) −36.3354 6.55517i −2.25343 0.406534i
\(261\) 6.92017 7.55249i 0.428348 0.467487i
\(262\) −5.18665 + 19.3569i −0.320432 + 1.19587i
\(263\) −26.3237 15.1980i −1.62319 0.937148i −0.986060 0.166391i \(-0.946789\pi\)
−0.637128 0.770758i \(-0.719878\pi\)
\(264\) −0.354718 + 0.0546016i −0.0218314 + 0.00336050i
\(265\) 3.30215 0.884807i 0.202849 0.0543533i
\(266\) 9.39205 + 2.51659i 0.575864 + 0.154302i
\(267\) 0.366959 + 0.833944i 0.0224575 + 0.0510365i
\(268\) −19.1797 5.13918i −1.17158 0.313925i
\(269\) −14.4571 8.34679i −0.881463 0.508913i −0.0103225 0.999947i \(-0.503286\pi\)
−0.871141 + 0.491034i \(0.836619\pi\)
\(270\) −29.7351 19.8665i −1.80962 1.20903i
\(271\) −8.31725 2.22860i −0.505237 0.135378i −0.00280742 0.999996i \(-0.500894\pi\)
−0.502429 + 0.864618i \(0.667560\pi\)
\(272\) −2.63489 4.56377i −0.159764 0.276719i
\(273\) 2.98218 + 5.48695i 0.180490 + 0.332085i
\(274\) 25.3123 43.8422i 1.52917 2.64860i
\(275\) 0.153217 0.153217i 0.00923936 0.00923936i
\(276\) −15.3808 + 39.5534i −0.925816 + 2.38084i
\(277\) 20.5242i 1.23318i 0.787284 + 0.616591i \(0.211487\pi\)
−0.787284 + 0.616591i \(0.788513\pi\)
\(278\) −27.2494 + 27.2494i −1.63431 + 1.63431i
\(279\) 0.777025 + 17.7848i 0.0465193 + 1.06475i
\(280\) −2.64453 9.86951i −0.158041 0.589816i
\(281\) −0.311023 + 1.16075i −0.0185541 + 0.0692447i −0.974582 0.224030i \(-0.928079\pi\)
0.956028 + 0.293275i \(0.0947452\pi\)
\(282\) −4.48062 + 3.59618i −0.266817 + 0.214150i
\(283\) 4.18999i 0.249069i 0.992215 + 0.124534i \(0.0397437\pi\)
−0.992215 + 0.124534i \(0.960256\pi\)
\(284\) −13.2161 13.2161i −0.784230 0.784230i
\(285\) 19.6961 + 7.65904i 1.16669 + 0.453683i
\(286\) 0.455225 + 0.214471i 0.0269180 + 0.0126819i
\(287\) 6.44370i 0.380360i
\(288\) 5.82559 11.1917i 0.343276 0.659475i
\(289\) −1.58345 2.74261i −0.0931438 0.161330i
\(290\) 23.4993 1.37993
\(291\) −15.4225 1.68881i −0.904085 0.0989999i
\(292\) 6.09826 22.7590i 0.356874 1.33187i
\(293\) −5.42807 + 20.2578i −0.317111 + 1.18347i 0.604897 + 0.796304i \(0.293214\pi\)
−0.922008 + 0.387171i \(0.873452\pi\)
\(294\) −2.39851 + 3.27125i −0.139884 + 0.190783i
\(295\) −10.8990 −0.634563
\(296\) −18.0206 31.2125i −1.04742 1.81419i
\(297\) 0.204186 + 0.232809i 0.0118481 + 0.0135090i
\(298\) 27.1938i 1.57529i
\(299\) 20.8246 14.4591i 1.20432 0.836194i
\(300\) −3.33865 21.6894i −0.192757 1.25224i
\(301\) 2.96203 + 2.96203i 0.170728 + 0.170728i
\(302\) 49.1062i 2.82575i
\(303\) 3.29535 + 21.4081i 0.189313 + 1.22986i
\(304\) 1.26099 4.70608i 0.0723228 0.269912i
\(305\) −0.352644 1.31609i −0.0201923 0.0753589i
\(306\) −14.5679 + 27.9866i −0.832790 + 1.59989i
\(307\) −23.4759 + 23.4759i −1.33984 + 1.33984i −0.443627 + 0.896211i \(0.646309\pi\)
−0.896211 + 0.443627i \(0.853691\pi\)
\(308\) 0.207667i 0.0118330i
\(309\) 1.50268 0.231307i 0.0854844 0.0131586i
\(310\) −28.8772 + 28.8772i −1.64011 + 1.64011i
\(311\) 7.02464 12.1670i 0.398331 0.689929i −0.595189 0.803585i \(-0.702923\pi\)
0.993520 + 0.113657i \(0.0362563\pi\)
\(312\) 19.0778 10.3689i 1.08007 0.587022i
\(313\) −2.48795 4.30926i −0.140627 0.243574i 0.787106 0.616818i \(-0.211579\pi\)
−0.927733 + 0.373245i \(0.878245\pi\)
\(314\) 53.3000 + 14.2817i 3.00790 + 0.805963i
\(315\) −5.95586 + 6.50007i −0.335575 + 0.366237i
\(316\) −11.1572 6.44161i −0.627641 0.362369i
\(317\) −13.4702 3.60934i −0.756564 0.202721i −0.140136 0.990132i \(-0.544754\pi\)
−0.616428 + 0.787412i \(0.711421\pi\)
\(318\) −2.79023 + 3.80551i −0.156468 + 0.213402i
\(319\) −0.196553 0.0526662i −0.0110049 0.00294874i
\(320\) 34.6202 9.27645i 1.93533 0.518569i
\(321\) 11.6084 29.8522i 0.647917 1.66619i
\(322\) 14.2609 + 8.23355i 0.794730 + 0.458838i
\(323\) 4.82568 18.0097i 0.268508 1.00208i
\(324\) 31.2423 2.73520i 1.73568 0.151956i
\(325\) −5.58724 + 11.8592i −0.309925 + 0.657831i
\(326\) −39.6656 + 22.9009i −2.19687 + 1.26837i
\(327\) 25.9262 + 2.83899i 1.43372 + 0.156997i
\(328\) 22.4044 1.23708
\(329\) 0.708187 + 1.22662i 0.0390436 + 0.0676255i
\(330\) −0.0773279 + 0.706172i −0.00425676 + 0.0388735i
\(331\) 21.4346 + 21.4346i 1.17815 + 1.17815i 0.980215 + 0.197938i \(0.0634244\pi\)
0.197938 + 0.980215i \(0.436576\pi\)
\(332\) −21.7398 + 5.82515i −1.19312 + 0.319697i
\(333\) −14.3583 + 27.5840i −0.786830 + 1.51160i
\(334\) 11.9790 20.7482i 0.655461 1.13529i
\(335\) −8.37264 + 14.5018i −0.457446 + 0.792320i
\(336\) 1.63913 + 1.20182i 0.0894218 + 0.0655648i
\(337\) −18.2537 10.5388i −0.994345 0.574085i −0.0877748 0.996140i \(-0.527976\pi\)
−0.906570 + 0.422055i \(0.861309\pi\)
\(338\) −30.3073 2.89326i −1.64850 0.157372i
\(339\) −5.93491 + 15.2623i −0.322340 + 0.828932i
\(340\) −44.4198 + 11.9022i −2.40900 + 0.645490i
\(341\) 0.306254 0.176816i 0.0165846 0.00957510i
\(342\) −27.8198 + 8.77244i −1.50432 + 0.474359i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 10.2988 10.2988i 0.555274 0.555274i
\(345\) 28.8627 + 21.1623i 1.55391 + 1.13934i
\(346\) −4.22413 15.7647i −0.227091 0.847515i
\(347\) −11.4319 + 6.60020i −0.613695 + 0.354317i −0.774410 0.632684i \(-0.781953\pi\)
0.160715 + 0.987001i \(0.448620\pi\)
\(348\) −16.0720 + 12.8996i −0.861551 + 0.691489i
\(349\) 1.99059 + 7.42899i 0.106554 + 0.397665i 0.998517 0.0544439i \(-0.0173386\pi\)
−0.891963 + 0.452109i \(0.850672\pi\)
\(350\) −8.51506 −0.455149
\(351\) −16.3901 9.07548i −0.874839 0.484413i
\(352\) −0.250638 −0.0133591
\(353\) −3.65637 13.6457i −0.194609 0.726290i −0.992368 0.123313i \(-0.960648\pi\)
0.797759 0.602976i \(-0.206019\pi\)
\(354\) 11.7325 9.41664i 0.623577 0.500489i
\(355\) −13.6503 + 7.88102i −0.724485 + 0.418281i
\(356\) −0.474422 1.77057i −0.0251443 0.0938400i
\(357\) 6.27277 + 4.59924i 0.331990 + 0.243418i
\(358\) −4.47451 + 4.47451i −0.236485 + 0.236485i
\(359\) 3.67540 + 3.67540i 0.193980 + 0.193980i 0.797414 0.603433i \(-0.206201\pi\)
−0.603433 + 0.797414i \(0.706201\pi\)
\(360\) 22.6004 + 20.7082i 1.19114 + 1.09142i
\(361\) −1.52601 + 0.881040i −0.0803161 + 0.0463705i
\(362\) 13.7608 3.68720i 0.723253 0.193795i
\(363\) −6.90288 + 17.7515i −0.362307 + 0.931712i
\(364\) −4.25045 11.8233i −0.222784 0.619708i
\(365\) −17.2082 9.93517i −0.900719 0.520030i
\(366\) 1.51670 + 1.11206i 0.0792793 + 0.0581282i
\(367\) 14.2831 24.7390i 0.745570 1.29136i −0.204358 0.978896i \(-0.565511\pi\)
0.949928 0.312469i \(-0.101156\pi\)
\(368\) 4.12559 7.14573i 0.215061 0.372497i
\(369\) −10.3871 16.3034i −0.540730 0.848721i
\(370\) −68.9086 + 18.4640i −3.58239 + 0.959897i
\(371\) 0.822590 + 0.822590i 0.0427067 + 0.0427067i
\(372\) 3.89850 35.6018i 0.202128 1.84587i
\(373\) −1.88754 3.26931i −0.0977329 0.169278i 0.813013 0.582246i \(-0.197826\pi\)
−0.910746 + 0.412967i \(0.864492\pi\)
\(374\) 0.626763 0.0324091
\(375\) 6.90189 + 0.755778i 0.356412 + 0.0390282i
\(376\) 4.26487 2.46233i 0.219944 0.126985i
\(377\) 12.2684 1.02448i 0.631856 0.0527633i
\(378\) 0.795356 12.1430i 0.0409087 0.624569i
\(379\) 7.92355 29.5711i 0.407005 1.51897i −0.393321 0.919401i \(-0.628674\pi\)
0.800327 0.599564i \(-0.204659\pi\)
\(380\) −36.8202 21.2581i −1.88884 1.09052i
\(381\) 13.6101 34.9999i 0.697267 1.79310i
\(382\) 35.6434 9.55063i 1.82368 0.488653i
\(383\) −34.5699 9.26298i −1.76644 0.473316i −0.778433 0.627728i \(-0.783985\pi\)
−0.988007 + 0.154412i \(0.950652\pi\)
\(384\) −20.6386 + 28.1483i −1.05321 + 1.43644i
\(385\) 0.169164 + 0.0453273i 0.00862139 + 0.00231009i
\(386\) 37.9328 + 21.9005i 1.93073 + 1.11471i
\(387\) −12.2690 2.71960i −0.623669 0.138245i
\(388\) 30.1499 + 8.07864i 1.53063 + 0.410131i
\(389\) −8.29832 14.3731i −0.420742 0.728746i 0.575270 0.817963i \(-0.304897\pi\)
−0.996012 + 0.0892172i \(0.971563\pi\)
\(390\) −10.0511 41.7877i −0.508955 2.11600i
\(391\) 15.7882 27.3459i 0.798443 1.38294i
\(392\) 2.45857 2.45857i 0.124177 0.124177i
\(393\) −14.6485 + 2.25484i −0.738917 + 0.113741i
\(394\) 24.7056i 1.24465i
\(395\) −7.68253 + 7.68253i −0.386550 + 0.386550i
\(396\) −0.334754 0.525425i −0.0168220 0.0264036i
\(397\) 7.53244 + 28.1114i 0.378042 + 1.41087i 0.848849 + 0.528636i \(0.177296\pi\)
−0.470807 + 0.882236i \(0.656037\pi\)
\(398\) −1.99072 + 7.42946i −0.0997856 + 0.372405i
\(399\) 1.09406 + 7.10752i 0.0547714 + 0.355821i
\(400\) 4.26665i 0.213332i
\(401\) 16.0754 + 16.0754i 0.802768 + 0.802768i 0.983527 0.180760i \(-0.0578556\pi\)
−0.180760 + 0.983527i \(0.557856\pi\)
\(402\) −3.51650 22.8448i −0.175387 1.13940i
\(403\) −13.8172 + 16.3350i −0.688282 + 0.813705i
\(404\) 43.5775i 2.16806i
\(405\) 4.59115 26.0467i 0.228136 1.29427i
\(406\) 3.99826 + 6.92518i 0.198430 + 0.343691i
\(407\) 0.617747 0.0306206
\(408\) 15.9913 21.8101i 0.791688 1.07976i
\(409\) −0.557013 + 2.07880i −0.0275425 + 0.102790i −0.978329 0.207057i \(-0.933611\pi\)
0.950786 + 0.309847i \(0.100278\pi\)
\(410\) 11.4778 42.8359i 0.566850 2.11551i
\(411\) 37.2186 + 4.07554i 1.83586 + 0.201032i
\(412\) −3.05879 −0.150696
\(413\) −1.85439 3.21190i −0.0912487 0.158047i
\(414\) −49.3542 + 2.15631i −2.42563 + 0.105977i
\(415\) 18.9804i 0.931713i
\(416\) 14.2697 5.12995i 0.699632 0.251516i
\(417\) −26.5632 10.3294i −1.30081 0.505834i
\(418\) 0.409743 + 0.409743i 0.0200412 + 0.0200412i
\(419\) 20.1997i 0.986821i −0.869797 0.493410i \(-0.835750\pi\)
0.869797 0.493410i \(-0.164250\pi\)
\(420\) 13.8324 11.1020i 0.674954 0.541724i
\(421\) 0.461762 1.72332i 0.0225049 0.0839894i −0.953760 0.300569i \(-0.902823\pi\)
0.976265 + 0.216580i \(0.0694901\pi\)
\(422\) 10.6378 + 39.7008i 0.517840 + 1.93260i
\(423\) −3.76907 1.96191i −0.183259 0.0953915i
\(424\) 2.86010 2.86010i 0.138899 0.138899i
\(425\) 16.3280i 0.792024i
\(426\) 7.88517 20.2776i 0.382038 0.982451i
\(427\) 0.327847 0.327847i 0.0158656 0.0158656i
\(428\) −32.2198 + 55.8063i −1.55740 + 2.69750i
\(429\) −0.00958470 + 0.372047i −0.000462754 + 0.0179626i
\(430\) −14.4146 24.9668i −0.695134 1.20401i
\(431\) −11.5032 3.08228i −0.554090 0.148468i −0.0291003 0.999576i \(-0.509264\pi\)
−0.524990 + 0.851108i \(0.675931\pi\)
\(432\) −6.08451 0.398530i −0.292741 0.0191743i
\(433\) 11.4331 + 6.60091i 0.549440 + 0.317219i 0.748896 0.662687i \(-0.230584\pi\)
−0.199456 + 0.979907i \(0.563917\pi\)
\(434\) −13.4233 3.59676i −0.644339 0.172650i
\(435\) 6.99983 + 15.9077i 0.335616 + 0.762715i
\(436\) −50.6838 13.5807i −2.42731 0.650396i
\(437\) 28.1987 7.55581i 1.34893 0.361444i
\(438\) 27.1082 4.17276i 1.29528 0.199382i
\(439\) 22.1743 + 12.8024i 1.05832 + 0.611023i 0.924968 0.380045i \(-0.124091\pi\)
0.133356 + 0.991068i \(0.457425\pi\)
\(440\) 0.157601 0.588173i 0.00751331 0.0280401i
\(441\) −2.92891 0.649233i −0.139472 0.0309158i
\(442\) −35.6839 + 12.8283i −1.69731 + 0.610180i
\(443\) 5.38321 3.10800i 0.255764 0.147665i −0.366637 0.930364i \(-0.619491\pi\)
0.622401 + 0.782699i \(0.286157\pi\)
\(444\) 36.9936 50.4545i 1.75564 2.39446i
\(445\) −1.54584 −0.0732798
\(446\) −17.2397 29.8601i −0.816324 1.41391i
\(447\) −18.4087 + 8.10033i −0.870700 + 0.383132i
\(448\) 8.62415 + 8.62415i 0.407453 + 0.407453i
\(449\) −13.1728 + 3.52965i −0.621665 + 0.166575i −0.555885 0.831259i \(-0.687620\pi\)
−0.0657804 + 0.997834i \(0.520954\pi\)
\(450\) 21.5442 13.7261i 1.01560 0.647053i
\(451\) −0.192006 + 0.332564i −0.00904122 + 0.0156598i
\(452\) 16.4727 28.5316i 0.774811 1.34201i
\(453\) −33.2421 + 14.6275i −1.56185 + 0.687259i
\(454\) 19.2617 + 11.1208i 0.903997 + 0.521923i
\(455\) −10.5589 + 0.881720i −0.495007 + 0.0413357i
\(456\) 24.7124 3.80398i 1.15727 0.178138i
\(457\) −14.6416 + 3.92321i −0.684905 + 0.183520i −0.584460 0.811423i \(-0.698694\pi\)
−0.100446 + 0.994943i \(0.532027\pi\)
\(458\) 46.7814 27.0092i 2.18595 1.26206i
\(459\) −23.2848 1.52513i −1.08684 0.0711870i
\(460\) −50.9144 50.9144i −2.37390 2.37390i
\(461\) −5.63968 + 5.63968i −0.262666 + 0.262666i −0.826136 0.563470i \(-0.809466\pi\)
0.563470 + 0.826136i \(0.309466\pi\)
\(462\) −0.221264 + 0.0973624i −0.0102941 + 0.00452971i
\(463\) −8.46256 31.5827i −0.393289 1.46777i −0.824675 0.565606i \(-0.808642\pi\)
0.431387 0.902167i \(-0.358024\pi\)
\(464\) 3.47001 2.00341i 0.161091 0.0930059i
\(465\) −28.1500 10.9464i −1.30542 0.507629i
\(466\) 2.06267 + 7.69799i 0.0955514 + 0.356603i
\(467\) −15.3536 −0.710479 −0.355240 0.934775i \(-0.615601\pi\)
−0.355240 + 0.934775i \(0.615601\pi\)
\(468\) 29.8130 + 23.0628i 1.37810 + 1.06608i
\(469\) −5.69821 −0.263119
\(470\) −2.52291 9.41564i −0.116373 0.434311i
\(471\) 6.20880 + 40.3353i 0.286086 + 1.85855i
\(472\) −11.1676 + 6.44762i −0.514031 + 0.296776i
\(473\) 0.0646115 + 0.241133i 0.00297084 + 0.0110873i
\(474\) 1.63244 14.9077i 0.0749805 0.684735i
\(475\) −10.6743 + 10.6743i −0.489772 + 0.489772i
\(476\) −11.0653 11.0653i −0.507177 0.507177i
\(477\) −3.40725 0.755264i −0.156007 0.0345811i
\(478\) −6.51063 + 3.75891i −0.297789 + 0.171929i
\(479\) 11.4406 3.06551i 0.522736 0.140067i 0.0122039 0.999926i \(-0.496115\pi\)
0.510532 + 0.859859i \(0.329449\pi\)
\(480\) 13.3993 + 16.6947i 0.611591 + 0.762003i
\(481\) −35.1706 + 12.6438i −1.60364 + 0.576506i
\(482\) 35.1638 + 20.3019i 1.60167 + 0.924724i
\(483\) −1.32569 + 12.1064i −0.0603208 + 0.550860i
\(484\) 19.1594 33.1850i 0.870881 1.50841i
\(485\) 13.1616 22.7965i 0.597636 1.03514i
\(486\) 17.5619 + 32.0055i 0.796623 + 1.45180i
\(487\) −9.20606 + 2.46676i −0.417166 + 0.111779i −0.461296 0.887246i \(-0.652615\pi\)
0.0441295 + 0.999026i \(0.485949\pi\)
\(488\) −1.13991 1.13991i −0.0516011 0.0516011i
\(489\) −27.3180 20.0298i −1.23536 0.905777i
\(490\) −3.44111 5.96018i −0.155453 0.269253i
\(491\) −16.4744 −0.743478 −0.371739 0.928337i \(-0.621238\pi\)
−0.371739 + 0.928337i \(0.621238\pi\)
\(492\) 15.6640 + 35.5976i 0.706186 + 1.60487i
\(493\) 13.2793 7.66683i 0.598071 0.345296i
\(494\) −31.7146 14.9417i −1.42691 0.672260i
\(495\) −0.501072 + 0.158004i −0.0225215 + 0.00710174i
\(496\) −1.80223 + 6.72602i −0.0809226 + 0.302007i
\(497\) −4.64504 2.68181i −0.208358 0.120296i
\(498\) −16.3990 20.4321i −0.734855 0.915582i
\(499\) 4.12047 1.10408i 0.184458 0.0494253i −0.165408 0.986225i \(-0.552894\pi\)
0.349865 + 0.936800i \(0.386227\pi\)
\(500\) −13.4927 3.61536i −0.603412 0.161684i
\(501\) 17.6136 + 1.92874i 0.786918 + 0.0861698i
\(502\) −48.8004 13.0760i −2.17807 0.583611i
\(503\) 29.1559 + 16.8332i 1.30000 + 0.750553i 0.980403 0.197001i \(-0.0631203\pi\)
0.319594 + 0.947555i \(0.396454\pi\)
\(504\) −2.25735 + 10.1836i −0.100550 + 0.453616i
\(505\) −35.4978 9.51160i −1.57963 0.423260i
\(506\) 0.490678 + 0.849879i 0.0218133 + 0.0377817i
\(507\) −7.06920 21.3782i −0.313954 0.949438i
\(508\) −37.7757 + 65.4294i −1.67603 + 2.90296i
\(509\) −30.2174 + 30.2174i −1.33936 + 1.33936i −0.442686 + 0.896677i \(0.645974\pi\)
−0.896677 + 0.442686i \(0.854026\pi\)
\(510\) −33.5072 41.7478i −1.48372 1.84862i
\(511\) 6.76162i 0.299117i
\(512\) 9.25990 9.25990i 0.409234 0.409234i
\(513\) −14.2252 16.2193i −0.628059 0.716101i
\(514\) −0.925042 3.45230i −0.0408018 0.152275i
\(515\) −0.667638 + 2.49166i −0.0294196 + 0.109796i
\(516\) 23.5638 + 9.16307i 1.03734 + 0.403382i
\(517\) 0.0844087i 0.00371229i
\(518\) −17.1656 17.1656i −0.754215 0.754215i
\(519\) 9.41354 7.55539i 0.413208 0.331645i
\(520\) 3.06569 + 36.7126i 0.134439 + 1.60995i
\(521\) 11.9258i 0.522478i −0.965274 0.261239i \(-0.915869\pi\)
0.965274 0.261239i \(-0.0841310\pi\)
\(522\) −21.2793 11.0765i −0.931370 0.484805i
\(523\) 5.91296 + 10.2415i 0.258556 + 0.447831i 0.965855 0.259083i \(-0.0834202\pi\)
−0.707300 + 0.706914i \(0.750087\pi\)
\(524\) 29.8178 1.30260
\(525\) −2.53642 5.76422i −0.110698 0.251571i
\(526\) −18.4241 + 68.7598i −0.803330 + 2.99807i
\(527\) −6.89694 + 25.7397i −0.300436 + 1.12124i
\(528\) 0.0487854 + 0.110869i 0.00212311 + 0.00482495i
\(529\) 26.4408 1.14960
\(530\) −4.00310 6.93358i −0.173884 0.301175i
\(531\) 9.86935 + 5.13729i 0.428293 + 0.222939i
\(532\) 14.4678i 0.627257i
\(533\) 4.12483 22.8640i 0.178666 0.990350i
\(534\) 1.66407 1.33559i 0.0720111 0.0577968i
\(535\) 38.4267 + 38.4267i 1.66133 + 1.66133i
\(536\) 19.8124i 0.855763i
\(537\) −4.36183 1.69615i −0.188227 0.0731942i
\(538\) −10.1186 + 37.7631i −0.436244 + 1.62808i
\(539\) 0.0154243 + 0.0575643i 0.000664372 + 0.00247947i
\(540\) −17.1016 + 50.3871i −0.735937 + 2.16832i
\(541\) 20.9915 20.9915i 0.902495 0.902495i −0.0931566 0.995651i \(-0.529696\pi\)
0.995651 + 0.0931566i \(0.0296957\pi\)
\(542\) 20.1656i 0.866185i
\(543\) 6.59502 + 8.21698i 0.283020 + 0.352624i
\(544\) 13.3549 13.3549i 0.572588 0.572588i
\(545\) −22.1254 + 38.3223i −0.947746 + 1.64154i
\(546\) 10.6046 10.0719i 0.453835 0.431039i
\(547\) 4.78257 + 8.28365i 0.204488 + 0.354183i 0.949969 0.312343i \(-0.101114\pi\)
−0.745482 + 0.666526i \(0.767780\pi\)
\(548\) −72.7595 19.4959i −3.10813 0.832822i
\(549\) −0.301014 + 1.35798i −0.0128470 + 0.0579570i
\(550\) −0.439469 0.253727i −0.0187390 0.0108190i
\(551\) 13.6934 + 3.66914i 0.583360 + 0.156311i
\(552\) 42.0933 + 4.60934i 1.79161 + 0.196186i
\(553\) −3.57116 0.956889i −0.151861 0.0406910i
\(554\) 46.4286 12.4405i 1.97256 0.528546i
\(555\) −33.0252 41.1472i −1.40184 1.74660i
\(556\) 49.6578 + 28.6699i 2.10596 + 1.21588i
\(557\) 6.44177 24.0410i 0.272947 1.01865i −0.684258 0.729240i \(-0.739874\pi\)
0.957205 0.289411i \(-0.0934595\pi\)
\(558\) 39.7605 12.5377i 1.68320 0.530765i
\(559\) −8.61398 12.4062i −0.364333 0.524725i
\(560\) −2.98647 + 1.72424i −0.126201 + 0.0728624i
\(561\) 0.186696 + 0.424283i 0.00788233 + 0.0179132i
\(562\) 2.81430 0.118714
\(563\) 21.0766 + 36.5057i 0.888272 + 1.53853i 0.841917 + 0.539607i \(0.181427\pi\)
0.0463546 + 0.998925i \(0.485240\pi\)
\(564\) 6.89408 + 5.05479i 0.290293 + 0.212845i
\(565\) −19.6461 19.6461i −0.826516 0.826516i
\(566\) 9.47831 2.53970i 0.398403 0.106752i
\(567\) 8.45705 3.07868i 0.355163 0.129292i
\(568\) −9.32452 + 16.1505i −0.391248 + 0.677661i
\(569\) 6.89976 11.9507i 0.289253 0.501001i −0.684379 0.729127i \(-0.739926\pi\)
0.973632 + 0.228126i \(0.0732598\pi\)
\(570\) 5.38727 49.1975i 0.225648 2.06066i
\(571\) −3.88212 2.24134i −0.162462 0.0937972i 0.416565 0.909106i \(-0.363234\pi\)
−0.579026 + 0.815309i \(0.696567\pi\)
\(572\) 0.132935 0.736860i 0.00555829 0.0308097i
\(573\) 17.0825 + 21.2837i 0.713631 + 0.889139i
\(574\) 14.5765 3.90577i 0.608412 0.163024i
\(575\) −22.1405 + 12.7828i −0.923321 + 0.533080i
\(576\) −35.7221 7.91830i −1.48842 0.329929i
\(577\) 10.8344 + 10.8344i 0.451044 + 0.451044i 0.895701 0.444657i \(-0.146674\pi\)
−0.444657 + 0.895701i \(0.646674\pi\)
\(578\) −5.24436 + 5.24436i −0.218137 + 0.218137i
\(579\) −3.52620 + 32.2019i −0.146544 + 1.33827i
\(580\) −9.04973 33.7740i −0.375769 1.40239i
\(581\) −5.59349 + 3.22940i −0.232057 + 0.133978i
\(582\) 5.52785 + 35.9115i 0.229137 + 1.48858i
\(583\) 0.0179434 + 0.0669656i 0.000743138 + 0.00277343i
\(584\) −23.5098 −0.972842
\(585\) 25.2939 19.2515i 1.04578 0.795950i
\(586\) 49.1160 2.02896
\(587\) 6.20259 + 23.1484i 0.256008 + 0.955436i 0.967527 + 0.252769i \(0.0813411\pi\)
−0.711518 + 0.702667i \(0.751992\pi\)
\(588\) 5.62525 + 2.18744i 0.231981 + 0.0902086i
\(589\) −21.3361 + 12.3184i −0.879137 + 0.507570i
\(590\) 6.60627 + 24.6549i 0.271976 + 1.01503i
\(591\) 16.7243 7.35916i 0.687946 0.302715i
\(592\) −8.60120 + 8.60120i −0.353507 + 0.353507i
\(593\) −7.17944 7.17944i −0.294824 0.294824i 0.544158 0.838983i \(-0.316849\pi\)
−0.838983 + 0.544158i \(0.816849\pi\)
\(594\) 0.402880 0.603011i 0.0165304 0.0247418i
\(595\) −11.4289 + 6.59848i −0.468539 + 0.270511i
\(596\) 39.0839 10.4725i 1.60094 0.428970i
\(597\) −5.62230 + 0.865440i −0.230106 + 0.0354201i
\(598\) −45.3310 38.3438i −1.85372 1.56799i
\(599\) 9.55142 + 5.51452i 0.390261 + 0.225317i 0.682273 0.731097i \(-0.260992\pi\)
−0.292012 + 0.956415i \(0.594325\pi\)
\(600\) −20.0419 + 8.81898i −0.818205 + 0.360033i
\(601\) −17.4744 + 30.2666i −0.712797 + 1.23460i 0.251006 + 0.967985i \(0.419239\pi\)
−0.963803 + 0.266615i \(0.914095\pi\)
\(602\) 4.90511 8.49589i 0.199917 0.346267i
\(603\) 14.4172 9.18536i 0.587113 0.374057i
\(604\) 70.5773 18.9111i 2.87175 0.769483i
\(605\) −22.8503 22.8503i −0.928996 0.928996i
\(606\) 46.4306 20.4308i 1.88611 0.829943i
\(607\) 1.84595 + 3.19728i 0.0749249 + 0.129774i 0.901054 0.433708i \(-0.142795\pi\)
−0.826129 + 0.563481i \(0.809462\pi\)
\(608\) 17.4614 0.708155
\(609\) −3.49698 + 4.76942i −0.141705 + 0.193267i
\(610\) −2.76341 + 1.59546i −0.111887 + 0.0645981i
\(611\) −1.72764 4.80570i −0.0698928 0.194418i
\(612\) 45.8336 + 10.1596i 1.85271 + 0.410679i
\(613\) 7.66100 28.5912i 0.309425 1.15479i −0.619644 0.784883i \(-0.712723\pi\)
0.929069 0.369907i \(-0.120610\pi\)
\(614\) 67.3351 + 38.8760i 2.71742 + 1.56891i
\(615\) 32.4164 4.98985i 1.30716 0.201210i
\(616\) 0.200148 0.0536295i 0.00806419 0.00216079i
\(617\) −9.53728 2.55551i −0.383956 0.102881i 0.0616775 0.998096i \(-0.480355\pi\)
−0.445634 + 0.895215i \(0.647022\pi\)
\(618\) −1.43408 3.25905i −0.0576870 0.131098i
\(619\) 14.4942 + 3.88372i 0.582573 + 0.156100i 0.538057 0.842909i \(-0.319159\pi\)
0.0445163 + 0.999009i \(0.485825\pi\)
\(620\) 52.6241 + 30.3825i 2.11343 + 1.22019i
\(621\) −16.1610 32.7677i −0.648520 1.31492i
\(622\) −31.7813 8.51578i −1.27432 0.341452i
\(623\) −0.263015 0.455555i −0.0105375 0.0182514i
\(624\) −5.04675 5.31365i −0.202032 0.212716i
\(625\) −14.9799 + 25.9459i −0.599194 + 1.03783i
\(626\) −8.24007 + 8.24007i −0.329340 + 0.329340i
\(627\) −0.155321 + 0.399424i −0.00620292 + 0.0159515i
\(628\) 82.1047i 3.27634i
\(629\) −32.9159 + 32.9159i −1.31244 + 1.31244i
\(630\) 18.3141 + 9.53303i 0.729651 + 0.379805i
\(631\) −10.8008 40.3092i −0.429974 1.60469i −0.752815 0.658232i \(-0.771304\pi\)
0.322841 0.946453i \(-0.395362\pi\)
\(632\) −3.32705 + 12.4167i −0.132343 + 0.493910i
\(633\) −23.7065 + 19.0270i −0.942247 + 0.756256i
\(634\) 32.6592i 1.29706i
\(635\) 45.0529 + 45.0529i 1.78787 + 1.78787i
\(636\) 6.54395 + 2.54469i 0.259484 + 0.100904i
\(637\) −2.05636 2.96165i −0.0814761 0.117345i
\(638\) 0.476552i 0.0188669i
\(639\) 16.0755 0.702348i 0.635939 0.0277845i
\(640\) −29.6099 51.2858i −1.17043 2.02725i
\(641\) 11.0525 0.436548 0.218274 0.975888i \(-0.429957\pi\)
0.218274 + 0.975888i \(0.429957\pi\)
\(642\) −74.5659 8.16518i −2.94288 0.322254i
\(643\) 5.88168 21.9507i 0.231951 0.865652i −0.747549 0.664207i \(-0.768769\pi\)
0.979500 0.201445i \(-0.0645639\pi\)
\(644\) 6.34158 23.6671i 0.249893 0.932615i
\(645\) 12.6074 17.1948i 0.496415 0.677046i
\(646\) −43.6653 −1.71799
\(647\) 10.5518 + 18.2762i 0.414833 + 0.718512i 0.995411 0.0956927i \(-0.0305066\pi\)
−0.580578 + 0.814205i \(0.697173\pi\)
\(648\) −10.7044 29.4047i −0.420508 1.15513i
\(649\) 0.221025i 0.00867599i
\(650\) 30.2138 + 5.45078i 1.18508 + 0.213797i
\(651\) −1.56365 10.1582i −0.0612842 0.398131i
\(652\) 48.1895 + 48.1895i 1.88725 + 1.88725i
\(653\) 40.2185i 1.57387i 0.617035 + 0.786936i \(0.288334\pi\)
−0.617035 + 0.786936i \(0.711666\pi\)
\(654\) −9.29263 60.3693i −0.363371 2.36063i
\(655\) 6.50829 24.2893i 0.254300 0.949060i
\(656\) −1.95706 7.30386i −0.0764105 0.285168i
\(657\) 10.8996 + 17.1078i 0.425232 + 0.667437i
\(658\) 2.34551 2.34551i 0.0914375 0.0914375i
\(659\) 24.6844i 0.961568i 0.876839 + 0.480784i \(0.159648\pi\)
−0.876839 + 0.480784i \(0.840352\pi\)
\(660\) 1.04472 0.160813i 0.0406655 0.00625963i
\(661\) 22.9248 22.9248i 0.891671 0.891671i −0.103009 0.994680i \(-0.532847\pi\)
0.994680 + 0.103009i \(0.0328472\pi\)
\(662\) 35.4956 61.4802i 1.37958 2.38950i
\(663\) −19.3134 20.3348i −0.750069 0.789737i
\(664\) 11.2284 + 19.4482i 0.435748 + 0.754738i
\(665\) −11.7853 3.15786i −0.457014 0.122457i
\(666\) 71.1018 + 15.7607i 2.75514 + 0.610715i
\(667\) 20.7922 + 12.0044i 0.805075 + 0.464810i
\(668\) −34.4333 9.22637i −1.33226 0.356979i
\(669\) 15.0783 20.5648i 0.582961 0.795083i
\(670\) 37.8801 + 10.1499i 1.46343 + 0.392126i
\(671\) 0.0266894 0.00715142i 0.00103033 0.000276077i
\(672\) −2.64007 + 6.78923i −0.101843 + 0.261900i
\(673\) 23.9809 + 13.8454i 0.924396 + 0.533700i 0.885035 0.465525i \(-0.154134\pi\)
0.0393610 + 0.999225i \(0.487468\pi\)
\(674\) −12.7759 + 47.6804i −0.492110 + 1.83658i
\(675\) 15.7092 + 10.4956i 0.604648 + 0.403974i
\(676\) 7.51325 + 44.6730i 0.288971 + 1.71819i
\(677\) 6.25797 3.61304i 0.240513 0.138860i −0.374899 0.927066i \(-0.622323\pi\)
0.615413 + 0.788205i \(0.288989\pi\)
\(678\) 38.1226 + 4.17454i 1.46409 + 0.160322i
\(679\) 8.95743 0.343755
\(680\) 22.9425 + 39.7376i 0.879806 + 1.52387i
\(681\) −1.79056 + 16.3517i −0.0686143 + 0.626598i
\(682\) −0.585612 0.585612i −0.0224242 0.0224242i
\(683\) −8.02988 + 2.15160i −0.307255 + 0.0823287i −0.409152 0.912466i \(-0.634175\pi\)
0.101897 + 0.994795i \(0.467509\pi\)
\(684\) 23.3216 + 36.6053i 0.891725 + 1.39964i
\(685\) −31.7623 + 55.0138i −1.21357 + 2.10197i
\(686\) 1.17097 2.02817i 0.0447077 0.0774360i
\(687\) 32.2187 + 23.6230i 1.22922 + 0.901273i
\(688\) −4.25704 2.45781i −0.162298 0.0937029i
\(689\) −2.39220 3.44534i −0.0911357 0.131257i
\(690\) 30.3773 78.1185i 1.15644 2.97392i
\(691\) 18.2478 4.88949i 0.694180 0.186005i 0.105558 0.994413i \(-0.466337\pi\)
0.588622 + 0.808408i \(0.299670\pi\)
\(692\) −21.0308 + 12.1422i −0.799473 + 0.461576i
\(693\) −0.131818 0.120781i −0.00500734 0.00458811i
\(694\) 21.8598 + 21.8598i 0.829787 + 0.829787i
\(695\) 34.1930 34.1930i 1.29701 1.29701i
\(696\) 16.5830 + 12.1588i 0.628578 + 0.460878i
\(697\) −7.48947 27.9511i −0.283684 1.05872i
\(698\) 15.5988 9.00597i 0.590423 0.340881i
\(699\) −4.59669 + 3.68935i −0.173863 + 0.139544i
\(700\) 3.27921 + 12.2382i 0.123942 + 0.462559i
\(701\) 42.0641 1.58874 0.794370 0.607434i \(-0.207801\pi\)
0.794370 + 0.607434i \(0.207801\pi\)
\(702\) −10.5953 + 42.5776i −0.399894 + 1.60699i
\(703\) −43.0371 −1.62318
\(704\) 0.188121 + 0.702077i 0.00709008 + 0.0264605i
\(705\) 5.62235 4.51255i 0.211750 0.169952i
\(706\) −28.6522 + 16.5424i −1.07834 + 0.622580i
\(707\) −3.23668 12.0794i −0.121728 0.454294i
\(708\) −18.0522 13.2360i −0.678444 0.497440i
\(709\) 35.3794 35.3794i 1.32870 1.32870i 0.422201 0.906502i \(-0.361258\pi\)
0.906502 0.422201i \(-0.138742\pi\)
\(710\) 26.1019 + 26.1019i 0.979587 + 0.979587i
\(711\) 10.5780 3.33556i 0.396705 0.125093i
\(712\) −1.58394 + 0.914488i −0.0593606 + 0.0342719i
\(713\) −40.3021 + 10.7989i −1.50932 + 0.404422i
\(714\) 6.60194 16.9776i 0.247072 0.635371i
\(715\) −0.571224 0.269121i −0.0213625 0.0100646i
\(716\) 8.15408 + 4.70776i 0.304732 + 0.175937i
\(717\) −4.48392 3.28764i −0.167455 0.122779i
\(718\) 6.08645 10.5420i 0.227144 0.393426i
\(719\) −6.33043 + 10.9646i −0.236085 + 0.408912i −0.959588 0.281410i \(-0.909198\pi\)
0.723502 + 0.690322i \(0.242531\pi\)
\(720\) 4.77672 9.17665i 0.178018 0.341994i
\(721\) −0.847880 + 0.227189i −0.0315767 + 0.00846095i
\(722\) 2.91800 + 2.91800i 0.108597 + 0.108597i
\(723\) −3.26881 + 29.8513i −0.121568 + 1.11018i
\(724\) −10.5988 18.3576i −0.393900 0.682255i
\(725\) −12.4148 −0.461074
\(726\) 44.3404 + 4.85540i 1.64562 + 0.180201i
\(727\) 8.55735 4.94059i 0.317374 0.183236i −0.332847 0.942981i \(-0.608009\pi\)
0.650222 + 0.759745i \(0.274676\pi\)
\(728\) −10.2975 + 7.14986i −0.381650 + 0.264991i
\(729\) −16.4347 + 21.4220i −0.608691 + 0.793407i
\(730\) −12.0441 + 44.9493i −0.445774 + 1.66365i
\(731\) −16.2912 9.40575i −0.602553 0.347884i
\(732\) 1.01420 2.60812i 0.0374859 0.0963989i
\(733\) −28.7720 + 7.70942i −1.06272 + 0.284754i −0.747497 0.664265i \(-0.768745\pi\)
−0.315219 + 0.949019i \(0.602078\pi\)
\(734\) −64.6204 17.3150i −2.38518 0.639107i
\(735\) 3.00968 4.10482i 0.111014 0.151409i
\(736\) 28.5643 + 7.65379i 1.05289 + 0.282122i
\(737\) −0.294089 0.169792i −0.0108329 0.00625438i
\(738\) −30.5844 + 33.3790i −1.12583 + 1.22870i
\(739\) −2.86248 0.767000i −0.105298 0.0282146i 0.205785 0.978597i \(-0.434025\pi\)
−0.311083 + 0.950383i \(0.600692\pi\)
\(740\) 53.0743 + 91.9273i 1.95105 + 3.37931i
\(741\) 0.667746 25.9197i 0.0245303 0.952185i
\(742\) 1.36221 2.35941i 0.0500081 0.0866166i
\(743\) −13.9265 + 13.9265i −0.510912 + 0.510912i −0.914806 0.403894i \(-0.867657\pi\)
0.403894 + 0.914806i \(0.367657\pi\)
\(744\) −35.3195 + 5.43672i −1.29487 + 0.199320i
\(745\) 34.1232i 1.25018i
\(746\) −6.25151 + 6.25151i −0.228884 + 0.228884i
\(747\) 8.94652 17.1873i 0.327336 0.628852i
\(748\) −0.241370 0.900807i −0.00882538 0.0329368i
\(749\) −4.78619 + 17.8623i −0.174884 + 0.652674i
\(750\) −2.47382 16.0711i −0.0903312 0.586834i
\(751\) 13.5978i 0.496190i −0.968736 0.248095i \(-0.920196\pi\)
0.968736 0.248095i \(-0.0798045\pi\)
\(752\) −1.17527 1.17527i −0.0428575 0.0428575i
\(753\) −5.68464 36.9301i −0.207160 1.34581i
\(754\) −9.75385 27.1318i −0.355214 0.988083i
\(755\) 61.6193i 2.24255i
\(756\) −17.7587 + 3.53324i −0.645877 + 0.128503i
\(757\) 23.5506 + 40.7908i 0.855959 + 1.48257i 0.875752 + 0.482761i \(0.160366\pi\)
−0.0197926 + 0.999804i \(0.506301\pi\)
\(758\) −71.6965 −2.60413
\(759\) −0.429160 + 0.585318i −0.0155775 + 0.0212457i
\(760\) −10.9797 + 40.9768i −0.398276 + 1.48638i
\(761\) 13.4332 50.1333i 0.486953 1.81733i −0.0841495 0.996453i \(-0.526817\pi\)
0.571102 0.820879i \(-0.306516\pi\)
\(762\) −87.4239 9.57317i −3.16703 0.346799i
\(763\) −15.0580 −0.545135
\(764\) −27.4530 47.5500i −0.993216 1.72030i
\(765\) 18.2800 35.1181i 0.660914 1.26970i
\(766\) 83.8164i 3.02841i
\(767\) 4.52384 + 12.5838i 0.163346 + 0.454373i
\(768\) 36.8079 + 14.3132i 1.32819 + 0.516483i
\(769\) 5.42708 + 5.42708i 0.195706 + 0.195706i 0.798156 0.602451i \(-0.205809\pi\)
−0.602451 + 0.798156i \(0.705809\pi\)
\(770\) 0.410146i 0.0147806i
\(771\) 2.06147 1.65455i 0.0742419 0.0595873i
\(772\) 16.8680 62.9524i 0.607094 2.26571i
\(773\) 7.95119 + 29.6743i 0.285985 + 1.06731i 0.948117 + 0.317922i \(0.102985\pi\)
−0.662132 + 0.749387i \(0.730348\pi\)
\(774\) 1.28461 + 29.4026i 0.0461745 + 1.05685i
\(775\) 15.2560 15.2560i 0.548010 0.548010i
\(776\) 31.1445i 1.11802i
\(777\) 6.50697 16.7334i 0.233436 0.600307i
\(778\) −27.4840 + 27.4840i −0.985349 + 0.985349i
\(779\) 13.3767 23.1691i 0.479269 0.830118i
\(780\) −56.1880 + 30.5384i −2.01185 + 1.09345i
\(781\) −0.159823 0.276821i −0.00571890 0.00990543i
\(782\) −71.4299 19.1396i −2.55433 0.684430i
\(783\) 1.15961 17.7043i 0.0414412 0.632700i
\(784\) −1.01626 0.586737i −0.0362949 0.0209549i
\(785\) −66.8817 17.9209i −2.38711 0.639624i
\(786\) 13.9797 + 31.7700i 0.498640 + 1.13320i
\(787\) −28.1443 7.54124i −1.00324 0.268816i −0.280435 0.959873i \(-0.590479\pi\)
−0.722801 + 0.691057i \(0.757146\pi\)
\(788\) −35.5078 + 9.51429i −1.26491 + 0.338932i
\(789\) −52.0345 + 8.00967i −1.85248 + 0.285152i
\(790\) 22.0356 + 12.7222i 0.783991 + 0.452637i
\(791\) 2.44699 9.13230i 0.0870050 0.324707i
\(792\) −0.419950 + 0.458322i −0.0149223 + 0.0162858i
\(793\) −1.37316 + 0.953424i −0.0487622 + 0.0338571i
\(794\) 59.0261 34.0787i 2.09476 1.20941i
\(795\) 3.50122 4.77521i 0.124175 0.169359i
\(796\) 11.4445 0.405640
\(797\) 6.01205 + 10.4132i 0.212958 + 0.368854i 0.952639 0.304104i \(-0.0983570\pi\)
−0.739681 + 0.672958i \(0.765024\pi\)
\(798\) 15.4150 6.78303i 0.545685 0.240117i
\(799\) −4.49761 4.49761i −0.159114 0.159114i
\(800\) −14.7705 + 3.95774i −0.522216 + 0.139927i
\(801\) 1.39980 + 0.728639i 0.0494596 + 0.0257452i
\(802\) 26.6208 46.1086i 0.940014 1.62815i
\(803\) 0.201479 0.348972i 0.00711005 0.0123150i
\(804\) −31.4792 + 13.8517i −1.11019 + 0.488513i
\(805\) −17.8948 10.3316i −0.630710 0.364140i
\(806\) 45.3271 + 21.3550i 1.59658 + 0.752198i
\(807\) −28.5776 + 4.39894i −1.00598 + 0.154850i
\(808\) −41.9995 + 11.2537i −1.47754 + 0.395905i
\(809\) 31.6319 18.2627i 1.11212 0.642081i 0.172740 0.984967i \(-0.444738\pi\)
0.939377 + 0.342886i \(0.111404\pi\)
\(810\) −61.7040 + 5.40206i −2.16806 + 0.189809i
\(811\) 37.4115 + 37.4115i 1.31370 + 1.31370i 0.918670 + 0.395025i \(0.129264\pi\)
0.395025 + 0.918670i \(0.370736\pi\)
\(812\) 8.41337 8.41337i 0.295251 0.295251i
\(813\) −13.6509 + 6.00680i −0.478759 + 0.210668i
\(814\) −0.374439 1.39743i −0.0131241 0.0489797i
\(815\) 49.7730 28.7364i 1.74347 1.00659i
\(816\) −8.50698 3.30804i −0.297804 0.115805i
\(817\) −4.50135 16.7993i −0.157482 0.587732i
\(818\) 5.04015 0.176225
\(819\) 9.97696 + 4.17855i 0.348623 + 0.146010i
\(820\) −65.9855 −2.30431
\(821\) −7.11985 26.5716i −0.248484 0.927357i −0.971600 0.236629i \(-0.923957\pi\)
0.723116 0.690727i \(-0.242709\pi\)
\(822\) −13.3401 86.6637i −0.465290 3.02274i
\(823\) −34.2057 + 19.7487i −1.19234 + 0.688396i −0.958836 0.283960i \(-0.908352\pi\)
−0.233501 + 0.972356i \(0.575018\pi\)
\(824\) 0.789922 + 2.94803i 0.0275183 + 0.102700i
\(825\) 0.0408527 0.373074i 0.00142231 0.0129888i
\(826\) −6.14174 + 6.14174i −0.213698 + 0.213698i
\(827\) −5.54555 5.54555i −0.192838 0.192838i 0.604083 0.796921i \(-0.293539\pi\)
−0.796921 + 0.604083i \(0.793539\pi\)
\(828\) 22.1057 + 70.1033i 0.768228 + 2.43626i
\(829\) −17.5415 + 10.1276i −0.609241 + 0.351746i −0.772669 0.634810i \(-0.781078\pi\)
0.163427 + 0.986555i \(0.447745\pi\)
\(830\) 42.9363 11.5047i 1.49034 0.399335i
\(831\) 22.2514 + 27.7238i 0.771892 + 0.961728i
\(832\) −25.0802 36.1215i −0.869500 1.25229i
\(833\) −3.88911 2.24538i −0.134750 0.0777977i
\(834\) −7.26558 + 66.3505i −0.251586 + 2.29753i
\(835\) −15.0314 + 26.0352i −0.520184 + 0.900985i
\(836\) 0.431103 0.746692i 0.0149100 0.0258249i
\(837\) 20.3310 + 23.1810i 0.702741 + 0.801251i
\(838\) −45.6944 + 12.2438i −1.57849 + 0.422955i
\(839\) −39.2982 39.2982i −1.35672 1.35672i −0.877925 0.478799i \(-0.841072\pi\)
−0.478799 0.877925i \(-0.658928\pi\)
\(840\) −14.2722 10.4645i −0.492439 0.361060i
\(841\) −8.67062 15.0180i −0.298987 0.517861i
\(842\) −4.17827 −0.143993
\(843\) 0.838307 + 1.90512i 0.0288728 + 0.0656159i
\(844\) 52.9627 30.5780i 1.82305 1.05254i
\(845\) 38.0301 + 3.63050i 1.30828 + 0.124893i
\(846\) −2.15354 + 9.71533i −0.0740401 + 0.334020i
\(847\) 2.84609 10.6218i 0.0977928 0.364968i
\(848\) −1.18223 0.682561i −0.0405980 0.0234392i
\(849\) 4.54258 + 5.65977i 0.155901 + 0.194243i
\(850\) 36.9361 9.89700i 1.26690 0.339464i
\(851\) −70.4024 18.8643i −2.41336 0.646658i
\(852\) −32.1803 3.52383i −1.10248 0.120725i
\(853\) 8.84616 + 2.37032i 0.302887 + 0.0811582i 0.407061 0.913401i \(-0.366553\pi\)
−0.104175 + 0.994559i \(0.533220\pi\)
\(854\) −0.940354 0.542914i −0.0321782 0.0185781i
\(855\) 34.9087 11.0078i 1.19385 0.376459i
\(856\) 62.1062 + 16.6413i 2.12275 + 0.568788i
\(857\) −1.16875 2.02433i −0.0399237 0.0691498i 0.845373 0.534176i \(-0.179378\pi\)
−0.885297 + 0.465026i \(0.846045\pi\)
\(858\) 0.847429 0.203829i 0.0289308 0.00695862i
\(859\) 12.0011 20.7866i 0.409474 0.709230i −0.585357 0.810776i \(-0.699046\pi\)
0.994831 + 0.101546i \(0.0323789\pi\)
\(860\) −30.3321 + 30.3321i −1.03432 + 1.03432i
\(861\) 6.98595 + 8.70405i 0.238081 + 0.296633i
\(862\) 27.8901i 0.949940i
\(863\) 34.7306 34.7306i 1.18224 1.18224i 0.203081 0.979162i \(-0.434905\pi\)
0.979162 0.203081i \(-0.0650954\pi\)
\(864\) −4.26434 21.4333i −0.145076 0.729177i
\(865\) 5.30051 + 19.7818i 0.180223 + 0.672600i
\(866\) 8.00211 29.8643i 0.271923 1.01483i
\(867\) −5.11229 1.98798i −0.173623 0.0675152i
\(868\) 20.6776i 0.701843i
\(869\) −0.155797 0.155797i −0.00528506 0.00528506i
\(870\) 31.7424 25.4768i 1.07617 0.863744i
\(871\) 20.2188 + 3.64762i 0.685087 + 0.123595i
\(872\) 52.3557i 1.77299i
\(873\) −22.6634 + 14.4391i −0.767041 + 0.488691i
\(874\) −34.1845 59.2093i −1.15631 2.00279i
\(875\) −4.00863 −0.135516
\(876\) −16.4368 37.3539i −0.555348 1.26207i
\(877\) 12.7147 47.4517i 0.429343 1.60233i −0.324908 0.945746i \(-0.605333\pi\)
0.754252 0.656586i \(-0.228000\pi\)
\(878\) 15.5200 57.9213i 0.523773 1.95475i
\(879\) 14.6304 + 33.2488i 0.493471 + 1.12145i
\(880\) −0.205512 −0.00692781
\(881\) −29.1855 50.5508i −0.983284 1.70310i −0.649326 0.760510i \(-0.724949\pi\)
−0.333959 0.942588i \(-0.608385\pi\)
\(882\) 0.306668 + 7.01910i 0.0103260 + 0.236345i
\(883\) 3.90213i 0.131317i 0.997842 + 0.0656586i \(0.0209148\pi\)
−0.997842 + 0.0656586i \(0.979085\pi\)
\(884\) 32.1794 + 46.3460i 1.08231 + 1.55878i
\(885\) −14.7222 + 11.8161i −0.494880 + 0.397195i
\(886\) −10.2937 10.2937i −0.345822 0.345822i
\(887\) 4.70762i 0.158067i 0.996872 + 0.0790333i \(0.0251833\pi\)
−0.996872 + 0.0790333i \(0.974817\pi\)
\(888\) −58.1810 22.6244i −1.95243 0.759224i
\(889\) −5.61151 + 20.9424i −0.188204 + 0.702387i
\(890\) 0.936990 + 3.49689i 0.0314080 + 0.117216i
\(891\) 0.528212 + 0.0931059i 0.0176958 + 0.00311916i
\(892\) −36.2768 + 36.2768i −1.21464 + 1.21464i
\(893\) 5.88058i 0.196786i
\(894\) 29.4822 + 36.7329i 0.986032 + 1.22853i
\(895\) 5.61468 5.61468i 0.187678 0.187678i
\(896\) 10.0759 17.4519i 0.336611 0.583028i
\(897\) 12.4536 42.1082i 0.415814 1.40595i
\(898\) 15.9691 + 27.6593i 0.532895 + 0.923002i
\(899\) −19.5709 5.24401i −0.652726 0.174897i
\(900\) −28.0244 25.6781i −0.934147 0.855937i
\(901\) −4.52427 2.61209i −0.150725 0.0870213i
\(902\) 0.868687 + 0.232764i 0.0289241 + 0.00775019i
\(903\) 7.21234 + 0.789773i 0.240012 + 0.0262820i
\(904\) −31.7525 8.50805i −1.05607 0.282974i
\(905\) −17.2673 + 4.62676i −0.573985 + 0.153799i
\(906\) 53.2386 + 66.3319i 1.76873 + 2.20373i
\(907\) −5.93193 3.42480i −0.196966 0.113719i 0.398273 0.917267i \(-0.369610\pi\)
−0.595240 + 0.803548i \(0.702943\pi\)
\(908\) 8.56535 31.9663i 0.284251 1.06084i
\(909\) 27.6609 + 25.3451i 0.917455 + 0.840643i
\(910\) 8.39468 + 23.3511i 0.278281 + 0.774081i
\(911\) 22.1286 12.7759i 0.733153 0.423286i −0.0864218 0.996259i \(-0.527543\pi\)
0.819574 + 0.572973i \(0.194210\pi\)
\(912\) −3.39878 7.72400i −0.112545 0.255767i
\(913\) −0.384912 −0.0127387
\(914\) 17.7496 + 30.7433i 0.587106 + 1.01690i
\(915\) −1.90318 1.39543i −0.0629172 0.0461314i
\(916\) −56.8345 56.8345i −1.87786 1.87786i
\(917\) 8.26533 2.21469i 0.272945 0.0731355i
\(918\) 10.6637 + 53.5977i 0.351955 + 1.76899i
\(919\) −7.59755 + 13.1593i −0.250620 + 0.434087i −0.963697 0.266999i \(-0.913968\pi\)
0.713077 + 0.701086i \(0.247301\pi\)
\(920\) −35.9223 + 62.2193i −1.18432 + 2.05131i
\(921\) −6.25943 + 57.1622i −0.206255 + 1.88356i
\(922\) 16.1761 + 9.33929i 0.532732 + 0.307573i
\(923\) 14.7651 + 12.4892i 0.486000 + 0.411089i
\(924\) 0.225143 + 0.280514i 0.00740666 + 0.00922823i
\(925\) 36.4048 9.75463i 1.19698 0.320730i
\(926\) −66.3148 + 38.2869i −2.17924 + 1.25819i
\(927\) 1.77902 1.94158i 0.0584307 0.0637697i
\(928\) 10.1543 + 10.1543i 0.333330 + 0.333330i
\(929\) −33.2707 + 33.2707i −1.09158 + 1.09158i −0.0962146 + 0.995361i \(0.530674\pi\)
−0.995361 + 0.0962146i \(0.969326\pi\)
\(930\) −7.69959 + 70.3140i −0.252479 + 2.30569i
\(931\) −1.07458 4.01039i −0.0352179 0.131435i
\(932\) 10.2695 5.92909i 0.336388 0.194214i
\(933\) −3.70213 24.0508i −0.121202 0.787388i
\(934\) 9.30637 + 34.7319i 0.304514 + 1.13646i
\(935\) −0.786472 −0.0257204
\(936\) 14.5286 34.6893i 0.474881 1.13386i
\(937\) 22.6682 0.740538 0.370269 0.928925i \(-0.379266\pi\)
0.370269 + 0.928925i \(0.379266\pi\)
\(938\) 3.45389 + 12.8901i 0.112774 + 0.420877i
\(939\) −8.03257 3.12356i −0.262133 0.101933i
\(940\) −12.5609 + 7.25205i −0.409692 + 0.236536i
\(941\) −7.49378 27.9672i −0.244290 0.911703i −0.973739 0.227668i \(-0.926890\pi\)
0.729449 0.684035i \(-0.239777\pi\)
\(942\) 87.4803 38.4938i 2.85026 1.25420i
\(943\) 32.0378 32.0378i 1.04330 1.04330i
\(944\) 3.07744 + 3.07744i 0.100162 + 0.100162i
\(945\) −0.998025 + 15.2372i −0.0324658 + 0.495668i
\(946\) 0.506313 0.292320i 0.0164616 0.00950413i
\(947\) 20.6598 5.53577i 0.671353 0.179888i 0.0929887 0.995667i \(-0.470358\pi\)
0.578364 + 0.815779i \(0.303691\pi\)
\(948\) −22.0546 + 3.39486i −0.716301 + 0.110260i
\(949\) −4.32834 + 23.9921i −0.140504 + 0.778816i
\(950\) 30.6169 + 17.6767i 0.993343 + 0.573507i
\(951\) −22.1084 + 9.72833i −0.716915 + 0.315463i
\(952\) −7.80705 + 13.5222i −0.253028 + 0.438258i
\(953\) 14.3156 24.7953i 0.463727 0.803199i −0.535416 0.844588i \(-0.679845\pi\)
0.999143 + 0.0413898i \(0.0131786\pi\)
\(954\) 0.356752 + 8.16544i 0.0115503 + 0.264366i
\(955\) −44.7259 + 11.9843i −1.44730 + 0.387802i
\(956\) 7.90973 + 7.90973i 0.255819 + 0.255819i
\(957\) −0.322599 + 0.141952i −0.0104281 + 0.00458867i
\(958\) −13.8692 24.0221i −0.448092 0.776119i
\(959\) −21.6166 −0.698036
\(960\) 36.7073 50.0640i 1.18472 1.61581i
\(961\) 3.64709 2.10565i 0.117648 0.0679241i
\(962\) 49.9201 + 71.8967i 1.60949 + 2.31804i
\(963\) −16.6839 52.9091i −0.537631 1.70497i
\(964\) 15.6367 58.3571i 0.503626 1.87956i
\(965\) −47.5986 27.4811i −1.53225 0.884647i
\(966\) 28.1898 4.33926i 0.906993 0.139613i
\(967\) 25.3569 6.79437i 0.815424 0.218492i 0.173079 0.984908i \(-0.444628\pi\)
0.642345 + 0.766416i \(0.277962\pi\)
\(968\) −36.9312 9.89570i −1.18702 0.318060i
\(969\) −13.0068 29.5589i −0.417837 0.949569i
\(970\) −59.5464 15.9554i −1.91192 0.512297i
\(971\) −33.8475 19.5418i −1.08622 0.627127i −0.153650 0.988125i \(-0.549103\pi\)
−0.932567 + 0.360998i \(0.882436\pi\)
\(972\) 39.2362 37.5661i 1.25850 1.20493i
\(973\) 15.8943 + 4.25887i 0.509548 + 0.136533i
\(974\) 11.1603 + 19.3301i 0.357598 + 0.619377i
\(975\) 5.31003 + 22.0766i 0.170057 + 0.707019i
\(976\) −0.272038 + 0.471184i −0.00870772 + 0.0150822i
\(977\) 2.12778 2.12778i 0.0680736 0.0680736i −0.672250 0.740324i \(-0.734672\pi\)
0.740324 + 0.672250i \(0.234672\pi\)
\(978\) −28.7515 + 73.9377i −0.919373 + 2.36427i
\(979\) 0.0313487i 0.00100191i
\(980\) −7.24099 + 7.24099i −0.231305 + 0.231305i
\(981\) 38.0986 24.2730i 1.21639 0.774978i
\(982\) 9.98572 + 37.2672i 0.318657 + 1.18924i
\(983\) −7.41689 + 27.6802i −0.236562 + 0.882862i 0.740876 + 0.671641i \(0.234410\pi\)
−0.977438 + 0.211220i \(0.932256\pi\)
\(984\) 30.2635 24.2898i 0.964765 0.774329i
\(985\) 31.0010i 0.987773i
\(986\) −25.3925 25.3925i −0.808661 0.808661i
\(987\) 2.28644 + 0.889110i 0.0727783 + 0.0283007i
\(988\) −9.26131 + 51.3355i −0.294641 + 1.63320i
\(989\) 29.4542i 0.936588i
\(990\) 0.661144 + 1.03772i 0.0210125 + 0.0329809i
\(991\) 4.39628 + 7.61458i 0.139652 + 0.241885i 0.927365 0.374158i \(-0.122068\pi\)
−0.787713 + 0.616043i \(0.788735\pi\)
\(992\) −24.9562 −0.792360
\(993\) 52.1919 + 5.71516i 1.65626 + 0.181365i
\(994\) −3.25109 + 12.1332i −0.103118 + 0.384843i
\(995\) 2.49798 9.32259i 0.0791913 0.295546i
\(996\) −23.0504 + 31.4377i −0.730379 + 0.996142i
\(997\) −39.8882 −1.26327 −0.631636 0.775265i \(-0.717616\pi\)
−0.631636 + 0.775265i \(0.717616\pi\)
\(998\) −4.99514 8.65183i −0.158118 0.273869i
\(999\) 10.5103 + 52.8266i 0.332531 + 1.67136i
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 819.2.fy.a.50.9 yes 336
9.2 odd 6 819.2.ew.a.596.76 336
13.6 odd 12 819.2.ew.a.617.76 yes 336
117.110 even 12 inner 819.2.fy.a.344.9 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.ew.a.596.76 336 9.2 odd 6
819.2.ew.a.617.76 yes 336 13.6 odd 12
819.2.fy.a.50.9 yes 336 1.1 even 1 trivial
819.2.fy.a.344.9 yes 336 117.110 even 12 inner