Properties

Label 273.2.cg.a.19.4
Level $273$
Weight $2$
Character 273.19
Analytic conductor $2.180$
Analytic rank $0$
Dimension $36$
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] = [273,2,Mod(19,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cg (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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 19.4
Character \(\chi\) \(=\) 273.19
Dual form 273.2.cg.a.115.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.759625 - 0.203541i) q^{2} -1.00000i q^{3} +(-1.19645 - 0.690770i) q^{4} +(2.02645 - 0.542987i) q^{5} +(-0.203541 + 0.759625i) q^{6} +(1.65876 - 2.06120i) q^{7} +(1.88042 + 1.88042i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.759625 - 0.203541i) q^{2} -1.00000i q^{3} +(-1.19645 - 0.690770i) q^{4} +(2.02645 - 0.542987i) q^{5} +(-0.203541 + 0.759625i) q^{6} +(1.65876 - 2.06120i) q^{7} +(1.88042 + 1.88042i) q^{8} -1.00000 q^{9} -1.64986 q^{10} +(-1.72874 - 1.72874i) q^{11} +(-0.690770 + 1.19645i) q^{12} +(-1.96880 + 3.02057i) q^{13} +(-1.67957 + 1.22811i) q^{14} +(-0.542987 - 2.02645i) q^{15} +(0.335869 + 0.581741i) q^{16} +(3.27669 - 5.67540i) q^{17} +(0.759625 + 0.203541i) q^{18} +(-5.66612 - 5.66612i) q^{19} +(-2.79963 - 0.750158i) q^{20} +(-2.06120 - 1.65876i) q^{21} +(0.961326 + 1.66506i) q^{22} +(3.33089 - 1.92309i) q^{23} +(1.88042 - 1.88042i) q^{24} +(-0.518448 + 0.299326i) q^{25} +(2.11036 - 1.89376i) q^{26} +1.00000i q^{27} +(-3.40843 + 1.32030i) q^{28} +(-1.25425 + 2.17242i) q^{29} +1.64986i q^{30} +(-0.122460 + 0.457027i) q^{31} +(-1.51329 - 5.64767i) q^{32} +(-1.72874 + 1.72874i) q^{33} +(-3.64424 + 3.64424i) q^{34} +(2.24219 - 5.07760i) q^{35} +(1.19645 + 0.690770i) q^{36} +(-1.83026 + 6.83063i) q^{37} +(3.15084 + 5.45741i) q^{38} +(3.02057 + 1.96880i) q^{39} +(4.83163 + 2.78954i) q^{40} +(11.0034 - 2.94834i) q^{41} +(1.22811 + 1.67957i) q^{42} +(0.810492 - 0.467938i) q^{43} +(0.874188 + 3.26252i) q^{44} +(-2.02645 + 0.542987i) q^{45} +(-2.92166 + 0.782855i) q^{46} +(1.88596 + 7.03848i) q^{47} +(0.581741 - 0.335869i) q^{48} +(-1.49706 - 6.83804i) q^{49} +(0.454751 - 0.121850i) q^{50} +(-5.67540 - 3.27669i) q^{51} +(4.44209 - 2.25396i) q^{52} +(-1.08341 - 1.87652i) q^{53} +(0.203541 - 0.759625i) q^{54} +(-4.44190 - 2.56453i) q^{55} +(6.99508 - 0.756757i) q^{56} +(-5.66612 + 5.66612i) q^{57} +(1.39493 - 1.39493i) q^{58} +(1.43782 + 5.36602i) q^{59} +(-0.750158 + 2.79963i) q^{60} +9.39241i q^{61} +(0.186047 - 0.322243i) q^{62} +(-1.65876 + 2.06120i) q^{63} +3.25466i q^{64} +(-2.34956 + 7.19007i) q^{65} +(1.66506 - 0.961326i) q^{66} +(8.15467 - 8.15467i) q^{67} +(-7.84080 + 4.52689i) q^{68} +(-1.92309 - 3.33089i) q^{69} +(-2.73672 + 3.40069i) q^{70} +(9.44098 + 2.52970i) q^{71} +(-1.88042 - 1.88042i) q^{72} +(9.79963 + 2.62580i) q^{73} +(2.78062 - 4.81618i) q^{74} +(0.299326 + 0.518448i) q^{75} +(2.86524 + 10.6932i) q^{76} +(-6.43083 + 0.695715i) q^{77} +(-1.89376 - 2.11036i) q^{78} +(1.07540 - 1.86264i) q^{79} +(0.996500 + 0.996500i) q^{80} +1.00000 q^{81} -8.95855 q^{82} +(-1.52436 - 1.52436i) q^{83} +(1.32030 + 3.40843i) q^{84} +(3.55840 - 13.2801i) q^{85} +(-0.710914 + 0.190489i) q^{86} +(2.17242 + 1.25425i) q^{87} -6.50152i q^{88} +(6.08297 + 1.62993i) q^{89} +1.64986 q^{90} +(2.96021 + 9.06847i) q^{91} -5.31366 q^{92} +(0.457027 + 0.122460i) q^{93} -5.73048i q^{94} +(-14.5588 - 8.40550i) q^{95} +(-5.64767 + 1.51329i) q^{96} +(-4.17950 + 15.5981i) q^{97} +(-0.254618 + 5.49906i) q^{98} +(1.72874 + 1.72874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.759625 0.203541i −0.537136 0.143925i −0.0199545 0.999801i \(-0.506352\pi\)
−0.517182 + 0.855876i \(0.673019\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −1.19645 0.690770i −0.598225 0.345385i
\(5\) 2.02645 0.542987i 0.906258 0.242831i 0.224556 0.974461i \(-0.427907\pi\)
0.681702 + 0.731630i \(0.261240\pi\)
\(6\) −0.203541 + 0.759625i −0.0830952 + 0.310116i
\(7\) 1.65876 2.06120i 0.626951 0.779059i
\(8\) 1.88042 + 1.88042i 0.664829 + 0.664829i
\(9\) −1.00000 −0.333333
\(10\) −1.64986 −0.521733
\(11\) −1.72874 1.72874i −0.521235 0.521235i 0.396709 0.917944i \(-0.370152\pi\)
−0.917944 + 0.396709i \(0.870152\pi\)
\(12\) −0.690770 + 1.19645i −0.199408 + 0.345385i
\(13\) −1.96880 + 3.02057i −0.546048 + 0.837754i
\(14\) −1.67957 + 1.22811i −0.448884 + 0.328227i
\(15\) −0.542987 2.02645i −0.140199 0.523228i
\(16\) 0.335869 + 0.581741i 0.0839672 + 0.145435i
\(17\) 3.27669 5.67540i 0.794715 1.37649i −0.128305 0.991735i \(-0.540954\pi\)
0.923020 0.384752i \(-0.125713\pi\)
\(18\) 0.759625 + 0.203541i 0.179045 + 0.0479751i
\(19\) −5.66612 5.66612i −1.29990 1.29990i −0.928457 0.371440i \(-0.878864\pi\)
−0.371440 0.928457i \(-0.621136\pi\)
\(20\) −2.79963 0.750158i −0.626016 0.167740i
\(21\) −2.06120 1.65876i −0.449790 0.361970i
\(22\) 0.961326 + 1.66506i 0.204955 + 0.354993i
\(23\) 3.33089 1.92309i 0.694539 0.400992i −0.110771 0.993846i \(-0.535332\pi\)
0.805310 + 0.592854i \(0.201999\pi\)
\(24\) 1.88042 1.88042i 0.383839 0.383839i
\(25\) −0.518448 + 0.299326i −0.103690 + 0.0598652i
\(26\) 2.11036 1.89376i 0.413876 0.371398i
\(27\) 1.00000i 0.192450i
\(28\) −3.40843 + 1.32030i −0.644133 + 0.249513i
\(29\) −1.25425 + 2.17242i −0.232908 + 0.403408i −0.958663 0.284545i \(-0.908157\pi\)
0.725755 + 0.687954i \(0.241491\pi\)
\(30\) 1.64986i 0.301223i
\(31\) −0.122460 + 0.457027i −0.0219945 + 0.0820844i −0.976051 0.217543i \(-0.930196\pi\)
0.954056 + 0.299628i \(0.0968624\pi\)
\(32\) −1.51329 5.64767i −0.267514 0.998377i
\(33\) −1.72874 + 1.72874i −0.300935 + 0.300935i
\(34\) −3.64424 + 3.64424i −0.624981 + 0.624981i
\(35\) 2.24219 5.07760i 0.378999 0.858271i
\(36\) 1.19645 + 0.690770i 0.199408 + 0.115128i
\(37\) −1.83026 + 6.83063i −0.300893 + 1.12295i 0.635530 + 0.772076i \(0.280782\pi\)
−0.936423 + 0.350872i \(0.885885\pi\)
\(38\) 3.15084 + 5.45741i 0.511134 + 0.885309i
\(39\) 3.02057 + 1.96880i 0.483678 + 0.315261i
\(40\) 4.83163 + 2.78954i 0.763948 + 0.441065i
\(41\) 11.0034 2.94834i 1.71844 0.460454i 0.740970 0.671538i \(-0.234366\pi\)
0.977468 + 0.211084i \(0.0676993\pi\)
\(42\) 1.22811 + 1.67957i 0.189502 + 0.259163i
\(43\) 0.810492 0.467938i 0.123599 0.0713598i −0.436926 0.899497i \(-0.643933\pi\)
0.560525 + 0.828138i \(0.310599\pi\)
\(44\) 0.874188 + 3.26252i 0.131789 + 0.491843i
\(45\) −2.02645 + 0.542987i −0.302086 + 0.0809437i
\(46\) −2.92166 + 0.782855i −0.430775 + 0.115426i
\(47\) 1.88596 + 7.03848i 0.275095 + 1.02667i 0.955778 + 0.294090i \(0.0950165\pi\)
−0.680683 + 0.732578i \(0.738317\pi\)
\(48\) 0.581741 0.335869i 0.0839672 0.0484785i
\(49\) −1.49706 6.83804i −0.213865 0.976863i
\(50\) 0.454751 0.121850i 0.0643115 0.0172322i
\(51\) −5.67540 3.27669i −0.794715 0.458829i
\(52\) 4.44209 2.25396i 0.616007 0.312568i
\(53\) −1.08341 1.87652i −0.148818 0.257760i 0.781973 0.623312i \(-0.214213\pi\)
−0.930791 + 0.365552i \(0.880880\pi\)
\(54\) 0.203541 0.759625i 0.0276984 0.103372i
\(55\) −4.44190 2.56453i −0.598945 0.345801i
\(56\) 6.99508 0.756757i 0.934756 0.101126i
\(57\) −5.66612 + 5.66612i −0.750496 + 0.750496i
\(58\) 1.39493 1.39493i 0.183164 0.183164i
\(59\) 1.43782 + 5.36602i 0.187188 + 0.698596i 0.994152 + 0.107994i \(0.0344428\pi\)
−0.806963 + 0.590601i \(0.798891\pi\)
\(60\) −0.750158 + 2.79963i −0.0968450 + 0.361430i
\(61\) 9.39241i 1.20258i 0.799033 + 0.601288i \(0.205345\pi\)
−0.799033 + 0.601288i \(0.794655\pi\)
\(62\) 0.186047 0.322243i 0.0236280 0.0409249i
\(63\) −1.65876 + 2.06120i −0.208984 + 0.259686i
\(64\) 3.25466i 0.406832i
\(65\) −2.34956 + 7.19007i −0.291427 + 0.891818i
\(66\) 1.66506 0.961326i 0.204955 0.118331i
\(67\) 8.15467 8.15467i 0.996252 0.996252i −0.00374130 0.999993i \(-0.501191\pi\)
0.999993 + 0.00374130i \(0.00119090\pi\)
\(68\) −7.84080 + 4.52689i −0.950837 + 0.548966i
\(69\) −1.92309 3.33089i −0.231513 0.400992i
\(70\) −2.73672 + 3.40069i −0.327101 + 0.406461i
\(71\) 9.44098 + 2.52970i 1.12044 + 0.300221i 0.771061 0.636762i \(-0.219726\pi\)
0.349377 + 0.936982i \(0.386393\pi\)
\(72\) −1.88042 1.88042i −0.221610 0.221610i
\(73\) 9.79963 + 2.62580i 1.14696 + 0.307327i 0.781746 0.623597i \(-0.214329\pi\)
0.365214 + 0.930924i \(0.380996\pi\)
\(74\) 2.78062 4.81618i 0.323241 0.559870i
\(75\) 0.299326 + 0.518448i 0.0345632 + 0.0598652i
\(76\) 2.86524 + 10.6932i 0.328665 + 1.22660i
\(77\) −6.43083 + 0.695715i −0.732862 + 0.0792841i
\(78\) −1.89376 2.11036i −0.214427 0.238951i
\(79\) 1.07540 1.86264i 0.120992 0.209564i −0.799167 0.601109i \(-0.794726\pi\)
0.920159 + 0.391545i \(0.128059\pi\)
\(80\) 0.996500 + 0.996500i 0.111412 + 0.111412i
\(81\) 1.00000 0.111111
\(82\) −8.95855 −0.989306
\(83\) −1.52436 1.52436i −0.167320 0.167320i 0.618480 0.785801i \(-0.287749\pi\)
−0.785801 + 0.618480i \(0.787749\pi\)
\(84\) 1.32030 + 3.40843i 0.144056 + 0.371890i
\(85\) 3.55840 13.2801i 0.385963 1.44043i
\(86\) −0.710914 + 0.190489i −0.0766598 + 0.0205409i
\(87\) 2.17242 + 1.25425i 0.232908 + 0.134469i
\(88\) 6.50152i 0.693065i
\(89\) 6.08297 + 1.62993i 0.644793 + 0.172772i 0.566374 0.824149i \(-0.308346\pi\)
0.0784195 + 0.996920i \(0.475013\pi\)
\(90\) 1.64986 0.173911
\(91\) 2.96021 + 9.06847i 0.310315 + 0.950634i
\(92\) −5.31366 −0.553987
\(93\) 0.457027 + 0.122460i 0.0473915 + 0.0126985i
\(94\) 5.73048i 0.591053i
\(95\) −14.5588 8.40550i −1.49370 0.862386i
\(96\) −5.64767 + 1.51329i −0.576413 + 0.154449i
\(97\) −4.17950 + 15.5981i −0.424363 + 1.58375i 0.340946 + 0.940083i \(0.389253\pi\)
−0.765309 + 0.643663i \(0.777414\pi\)
\(98\) −0.254618 + 5.49906i −0.0257203 + 0.555489i
\(99\) 1.72874 + 1.72874i 0.173745 + 0.173745i
\(100\) 0.827063 0.0827063
\(101\) −3.53983 −0.352226 −0.176113 0.984370i \(-0.556352\pi\)
−0.176113 + 0.984370i \(0.556352\pi\)
\(102\) 3.64424 + 3.64424i 0.360833 + 0.360833i
\(103\) 4.58234 7.93684i 0.451511 0.782041i −0.546969 0.837153i \(-0.684218\pi\)
0.998480 + 0.0551124i \(0.0175517\pi\)
\(104\) −9.38211 + 1.97776i −0.919992 + 0.193935i
\(105\) −5.07760 2.24219i −0.495523 0.218815i
\(106\) 0.441036 + 1.64597i 0.0428372 + 0.159871i
\(107\) 1.00880 + 1.74729i 0.0975240 + 0.168917i 0.910659 0.413158i \(-0.135574\pi\)
−0.813135 + 0.582075i \(0.802241\pi\)
\(108\) 0.690770 1.19645i 0.0664694 0.115128i
\(109\) 5.44016 + 1.45769i 0.521073 + 0.139621i 0.509763 0.860315i \(-0.329733\pi\)
0.0113102 + 0.999936i \(0.496400\pi\)
\(110\) 2.85219 + 2.85219i 0.271946 + 0.271946i
\(111\) 6.83063 + 1.83026i 0.648335 + 0.173721i
\(112\) 1.75621 + 0.272676i 0.165946 + 0.0257655i
\(113\) −6.20648 10.7499i −0.583857 1.01127i −0.995017 0.0997064i \(-0.968210\pi\)
0.411160 0.911563i \(-0.365124\pi\)
\(114\) 5.45741 3.15084i 0.511134 0.295103i
\(115\) 5.70568 5.70568i 0.532058 0.532058i
\(116\) 3.00129 1.73279i 0.278663 0.160886i
\(117\) 1.96880 3.02057i 0.182016 0.279251i
\(118\) 4.36881i 0.402182i
\(119\) −6.26288 16.1680i −0.574117 1.48212i
\(120\) 2.78954 4.83163i 0.254649 0.441065i
\(121\) 5.02291i 0.456628i
\(122\) 1.91174 7.13471i 0.173081 0.645947i
\(123\) −2.94834 11.0034i −0.265843 0.992141i
\(124\) 0.462218 0.462218i 0.0415084 0.0415084i
\(125\) −8.30541 + 8.30541i −0.742859 + 0.742859i
\(126\) 1.67957 1.22811i 0.149628 0.109409i
\(127\) −9.05461 5.22768i −0.803467 0.463882i 0.0412153 0.999150i \(-0.486877\pi\)
−0.844682 + 0.535269i \(0.820210\pi\)
\(128\) −2.36412 + 8.82303i −0.208961 + 0.779853i
\(129\) −0.467938 0.810492i −0.0411996 0.0713598i
\(130\) 3.24826 4.98352i 0.284891 0.437084i
\(131\) 18.0680 + 10.4315i 1.57860 + 0.911408i 0.995055 + 0.0993303i \(0.0316700\pi\)
0.583550 + 0.812077i \(0.301663\pi\)
\(132\) 3.26252 0.874188i 0.283965 0.0760883i
\(133\) −21.0777 + 2.28027i −1.82767 + 0.197725i
\(134\) −7.85430 + 4.53468i −0.678508 + 0.391737i
\(135\) 0.542987 + 2.02645i 0.0467328 + 0.174409i
\(136\) 16.8337 4.51058i 1.44348 0.386779i
\(137\) −10.8897 + 2.91789i −0.930370 + 0.249292i −0.692012 0.721886i \(-0.743276\pi\)
−0.238357 + 0.971178i \(0.576609\pi\)
\(138\) 0.782855 + 2.92166i 0.0666411 + 0.248708i
\(139\) 8.83314 5.09981i 0.749217 0.432561i −0.0761940 0.997093i \(-0.524277\pi\)
0.825411 + 0.564532i \(0.190943\pi\)
\(140\) −6.19012 + 4.52625i −0.523161 + 0.382538i
\(141\) 7.03848 1.88596i 0.592747 0.158826i
\(142\) −6.65671 3.84325i −0.558618 0.322518i
\(143\) 8.62533 1.81822i 0.721286 0.152048i
\(144\) −0.335869 0.581741i −0.0279891 0.0484785i
\(145\) −1.36208 + 5.08335i −0.113115 + 0.422149i
\(146\) −6.90958 3.98925i −0.571841 0.330153i
\(147\) −6.83804 + 1.49706i −0.563992 + 0.123475i
\(148\) 6.90821 6.90821i 0.567852 0.567852i
\(149\) −3.32734 + 3.32734i −0.272586 + 0.272586i −0.830140 0.557554i \(-0.811740\pi\)
0.557554 + 0.830140i \(0.311740\pi\)
\(150\) −0.121850 0.454751i −0.00994903 0.0371303i
\(151\) −0.151113 + 0.563961i −0.0122974 + 0.0458945i −0.971802 0.235799i \(-0.924229\pi\)
0.959505 + 0.281693i \(0.0908961\pi\)
\(152\) 21.3094i 1.72842i
\(153\) −3.27669 + 5.67540i −0.264905 + 0.458829i
\(154\) 5.02663 + 0.780455i 0.405057 + 0.0628909i
\(155\) 0.992638i 0.0797306i
\(156\) −2.25396 4.44209i −0.180461 0.355652i
\(157\) −9.61395 + 5.55061i −0.767276 + 0.442987i −0.831902 0.554922i \(-0.812748\pi\)
0.0646257 + 0.997910i \(0.479415\pi\)
\(158\) −1.19602 + 1.19602i −0.0951504 + 0.0951504i
\(159\) −1.87652 + 1.08341i −0.148818 + 0.0859199i
\(160\) −6.13322 10.6231i −0.484874 0.839826i
\(161\) 1.56127 10.0556i 0.123045 0.792489i
\(162\) −0.759625 0.203541i −0.0596818 0.0159917i
\(163\) −11.6512 11.6512i −0.912591 0.912591i 0.0838846 0.996475i \(-0.473267\pi\)
−0.996475 + 0.0838846i \(0.973267\pi\)
\(164\) −15.2016 4.07326i −1.18705 0.318068i
\(165\) −2.56453 + 4.44190i −0.199648 + 0.345801i
\(166\) 0.847673 + 1.46821i 0.0657922 + 0.113955i
\(167\) −0.00245012 0.00914399i −0.000189596 0.000707583i 0.965831 0.259173i \(-0.0834499\pi\)
−0.966021 + 0.258465i \(0.916783\pi\)
\(168\) −0.756757 6.99508i −0.0583851 0.539682i
\(169\) −5.24763 11.8938i −0.403664 0.914907i
\(170\) −5.40610 + 9.36364i −0.414629 + 0.718159i
\(171\) 5.66612 + 5.66612i 0.433299 + 0.433299i
\(172\) −1.29295 −0.0985865
\(173\) 20.9611 1.59365 0.796823 0.604213i \(-0.206512\pi\)
0.796823 + 0.604213i \(0.206512\pi\)
\(174\) −1.39493 1.39493i −0.105750 0.105750i
\(175\) −0.243009 + 1.56513i −0.0183697 + 0.118313i
\(176\) 0.425051 1.58631i 0.0320394 0.119573i
\(177\) 5.36602 1.43782i 0.403334 0.108073i
\(178\) −4.28902 2.47626i −0.321475 0.185604i
\(179\) 9.64897i 0.721198i −0.932721 0.360599i \(-0.882572\pi\)
0.932721 0.360599i \(-0.117428\pi\)
\(180\) 2.79963 + 0.750158i 0.208672 + 0.0559135i
\(181\) −1.25766 −0.0934813 −0.0467407 0.998907i \(-0.514883\pi\)
−0.0467407 + 0.998907i \(0.514883\pi\)
\(182\) −0.402847 7.49116i −0.0298610 0.555282i
\(183\) 9.39241 0.694307
\(184\) 9.87970 + 2.64726i 0.728341 + 0.195158i
\(185\) 14.8358i 1.09075i
\(186\) −0.322243 0.186047i −0.0236280 0.0136416i
\(187\) −15.4759 + 4.14674i −1.13171 + 0.303240i
\(188\) 2.60552 9.72395i 0.190027 0.709192i
\(189\) 2.06120 + 1.65876i 0.149930 + 0.120657i
\(190\) 9.34833 + 9.34833i 0.678199 + 0.678199i
\(191\) 2.44502 0.176916 0.0884578 0.996080i \(-0.471806\pi\)
0.0884578 + 0.996080i \(0.471806\pi\)
\(192\) 3.25466 0.234885
\(193\) 12.1698 + 12.1698i 0.875999 + 0.875999i 0.993118 0.117119i \(-0.0373660\pi\)
−0.117119 + 0.993118i \(0.537366\pi\)
\(194\) 6.34970 10.9980i 0.455882 0.789610i
\(195\) 7.19007 + 2.34956i 0.514891 + 0.168256i
\(196\) −2.93236 + 9.21550i −0.209454 + 0.658250i
\(197\) 6.05858 + 22.6109i 0.431656 + 1.61096i 0.748944 + 0.662634i \(0.230561\pi\)
−0.317287 + 0.948329i \(0.602772\pi\)
\(198\) −0.961326 1.66506i −0.0683184 0.118331i
\(199\) −9.32077 + 16.1440i −0.660732 + 1.14442i 0.319692 + 0.947521i \(0.396421\pi\)
−0.980424 + 0.196899i \(0.936913\pi\)
\(200\) −1.53776 0.412042i −0.108736 0.0291357i
\(201\) −8.15467 8.15467i −0.575186 0.575186i
\(202\) 2.68894 + 0.720500i 0.189193 + 0.0506942i
\(203\) 2.39729 + 6.18877i 0.168257 + 0.434366i
\(204\) 4.52689 + 7.84080i 0.316946 + 0.548966i
\(205\) 20.6969 11.9494i 1.44553 0.834580i
\(206\) −5.09633 + 5.09633i −0.355078 + 0.355078i
\(207\) −3.33089 + 1.92309i −0.231513 + 0.133664i
\(208\) −2.41845 0.130822i −0.167689 0.00907085i
\(209\) 19.5905i 1.35510i
\(210\) 3.40069 + 2.73672i 0.234670 + 0.188852i
\(211\) −5.61294 + 9.72190i −0.386411 + 0.669283i −0.991964 0.126522i \(-0.959619\pi\)
0.605553 + 0.795805i \(0.292952\pi\)
\(212\) 2.99355i 0.205598i
\(213\) 2.52970 9.44098i 0.173332 0.646885i
\(214\) −0.410663 1.53261i −0.0280723 0.104767i
\(215\) 1.38834 1.38834i 0.0946840 0.0946840i
\(216\) −1.88042 + 1.88042i −0.127946 + 0.127946i
\(217\) 0.738891 + 1.01051i 0.0501592 + 0.0685979i
\(218\) −3.83579 2.21459i −0.259792 0.149991i
\(219\) 2.62580 9.79963i 0.177435 0.662197i
\(220\) 3.54300 + 6.13666i 0.238869 + 0.413734i
\(221\) 10.6918 + 21.0712i 0.719205 + 1.41740i
\(222\) −4.81618 2.78062i −0.323241 0.186623i
\(223\) −9.81982 + 2.63121i −0.657584 + 0.176199i −0.572155 0.820145i \(-0.693893\pi\)
−0.0854284 + 0.996344i \(0.527226\pi\)
\(224\) −14.1511 6.24893i −0.945513 0.417524i
\(225\) 0.518448 0.299326i 0.0345632 0.0199551i
\(226\) 2.52655 + 9.42920i 0.168063 + 0.627221i
\(227\) −6.35951 + 1.70402i −0.422095 + 0.113100i −0.463613 0.886038i \(-0.653447\pi\)
0.0415179 + 0.999138i \(0.486781\pi\)
\(228\) 10.6932 2.86524i 0.708175 0.189755i
\(229\) 0.321690 + 1.20056i 0.0212578 + 0.0793354i 0.975740 0.218933i \(-0.0702576\pi\)
−0.954482 + 0.298268i \(0.903591\pi\)
\(230\) −5.49552 + 3.17284i −0.362364 + 0.209211i
\(231\) 0.695715 + 6.43083i 0.0457747 + 0.423118i
\(232\) −6.44358 + 1.72655i −0.423042 + 0.113354i
\(233\) −12.6928 7.32822i −0.831536 0.480088i 0.0228423 0.999739i \(-0.492728\pi\)
−0.854378 + 0.519652i \(0.826062\pi\)
\(234\) −2.11036 + 1.89376i −0.137959 + 0.123799i
\(235\) 7.64360 + 13.2391i 0.498614 + 0.863624i
\(236\) 1.98641 7.41337i 0.129304 0.482569i
\(237\) −1.86264 1.07540i −0.120992 0.0698545i
\(238\) 1.46659 + 13.5564i 0.0950647 + 0.878730i
\(239\) −4.85743 + 4.85743i −0.314201 + 0.314201i −0.846535 0.532334i \(-0.821315\pi\)
0.532334 + 0.846535i \(0.321315\pi\)
\(240\) 0.996500 0.996500i 0.0643238 0.0643238i
\(241\) 4.94711 + 18.4629i 0.318671 + 1.18930i 0.920522 + 0.390690i \(0.127763\pi\)
−0.601851 + 0.798608i \(0.705570\pi\)
\(242\) −1.02237 + 3.81553i −0.0657202 + 0.245271i
\(243\) 1.00000i 0.0641500i
\(244\) 6.48800 11.2375i 0.415352 0.719410i
\(245\) −6.74668 13.0441i −0.431030 0.833356i
\(246\) 8.95855i 0.571176i
\(247\) 28.2704 5.95941i 1.79880 0.379188i
\(248\) −1.08968 + 0.629127i −0.0691947 + 0.0399496i
\(249\) −1.52436 + 1.52436i −0.0966025 + 0.0966025i
\(250\) 7.99949 4.61851i 0.505932 0.292100i
\(251\) 1.37023 + 2.37330i 0.0864880 + 0.149802i 0.906024 0.423226i \(-0.139102\pi\)
−0.819536 + 0.573027i \(0.805769\pi\)
\(252\) 3.40843 1.32030i 0.214711 0.0831709i
\(253\) −9.08277 2.43372i −0.571029 0.153007i
\(254\) 5.81406 + 5.81406i 0.364807 + 0.364807i
\(255\) −13.2801 3.55840i −0.831634 0.222836i
\(256\) 6.84635 11.8582i 0.427897 0.741139i
\(257\) −5.48074 9.49291i −0.341879 0.592152i 0.642903 0.765948i \(-0.277730\pi\)
−0.984782 + 0.173796i \(0.944397\pi\)
\(258\) 0.190489 + 0.710914i 0.0118593 + 0.0442596i
\(259\) 11.0433 + 15.1029i 0.686198 + 0.938447i
\(260\) 7.77782 6.97955i 0.482360 0.432853i
\(261\) 1.25425 2.17242i 0.0776360 0.134469i
\(262\) −11.6016 11.6016i −0.716751 0.716751i
\(263\) −22.1190 −1.36392 −0.681958 0.731391i \(-0.738871\pi\)
−0.681958 + 0.731391i \(0.738871\pi\)
\(264\) −6.50152 −0.400141
\(265\) −3.21440 3.21440i −0.197459 0.197459i
\(266\) 16.4753 + 2.55802i 1.01016 + 0.156842i
\(267\) 1.62993 6.08297i 0.0997498 0.372271i
\(268\) −15.3897 + 4.12365i −0.940073 + 0.251892i
\(269\) 7.90566 + 4.56433i 0.482017 + 0.278292i 0.721256 0.692668i \(-0.243565\pi\)
−0.239240 + 0.970960i \(0.576898\pi\)
\(270\) 1.64986i 0.100408i
\(271\) 18.7534 + 5.02495i 1.13919 + 0.305244i 0.778624 0.627491i \(-0.215918\pi\)
0.360562 + 0.932735i \(0.382585\pi\)
\(272\) 4.40216 0.266920
\(273\) 9.06847 2.96021i 0.548849 0.179160i
\(274\) 8.86600 0.535614
\(275\) 1.41372 + 0.378805i 0.0852505 + 0.0228428i
\(276\) 5.31366i 0.319845i
\(277\) −24.3199 14.0411i −1.46124 0.843649i −0.462173 0.886790i \(-0.652930\pi\)
−0.999069 + 0.0431410i \(0.986264\pi\)
\(278\) −7.74789 + 2.07604i −0.464688 + 0.124513i
\(279\) 0.122460 0.457027i 0.00733149 0.0273615i
\(280\) 13.7643 5.33177i 0.822573 0.318634i
\(281\) 3.79779 + 3.79779i 0.226557 + 0.226557i 0.811253 0.584695i \(-0.198786\pi\)
−0.584695 + 0.811253i \(0.698786\pi\)
\(282\) −5.73048 −0.341245
\(283\) 1.38508 0.0823344 0.0411672 0.999152i \(-0.486892\pi\)
0.0411672 + 0.999152i \(0.486892\pi\)
\(284\) −9.54821 9.54821i −0.566582 0.566582i
\(285\) −8.40550 + 14.5588i −0.497899 + 0.862386i
\(286\) −6.92210 0.374439i −0.409312 0.0221410i
\(287\) 12.1748 27.5707i 0.718655 1.62745i
\(288\) 1.51329 + 5.64767i 0.0891715 + 0.332792i
\(289\) −12.9735 22.4707i −0.763144 1.32180i
\(290\) 2.06934 3.58420i 0.121516 0.210471i
\(291\) 15.5981 + 4.17950i 0.914376 + 0.245006i
\(292\) −9.91093 9.91093i −0.579993 0.579993i
\(293\) 17.3288 + 4.64324i 1.01236 + 0.271261i 0.726615 0.687045i \(-0.241092\pi\)
0.285745 + 0.958306i \(0.407759\pi\)
\(294\) 5.49906 + 0.254618i 0.320712 + 0.0148497i
\(295\) 5.82735 + 10.0933i 0.339281 + 0.587653i
\(296\) −16.2861 + 9.40280i −0.946612 + 0.546526i
\(297\) 1.72874 1.72874i 0.100312 0.100312i
\(298\) 3.20478 1.85028i 0.185648 0.107184i
\(299\) −0.749048 + 13.8474i −0.0433186 + 0.800813i
\(300\) 0.827063i 0.0477505i
\(301\) 0.379897 2.44678i 0.0218969 0.141030i
\(302\) 0.229578 0.397641i 0.0132107 0.0228817i
\(303\) 3.53983i 0.203358i
\(304\) 1.39315 5.19929i 0.0799024 0.298200i
\(305\) 5.09995 + 19.0333i 0.292023 + 1.08984i
\(306\) 3.64424 3.64424i 0.208327 0.208327i
\(307\) 5.47242 5.47242i 0.312327 0.312327i −0.533483 0.845811i \(-0.679117\pi\)
0.845811 + 0.533483i \(0.179117\pi\)
\(308\) 8.17475 + 3.60984i 0.465799 + 0.205690i
\(309\) −7.93684 4.58234i −0.451511 0.260680i
\(310\) 0.202042 0.754032i 0.0114752 0.0428262i
\(311\) −3.27357 5.66998i −0.185627 0.321515i 0.758161 0.652068i \(-0.226098\pi\)
−0.943788 + 0.330553i \(0.892765\pi\)
\(312\) 1.97776 + 9.38211i 0.111968 + 0.531158i
\(313\) −14.8538 8.57583i −0.839585 0.484735i 0.0175379 0.999846i \(-0.494417\pi\)
−0.857123 + 0.515111i \(0.827751\pi\)
\(314\) 8.43277 2.25955i 0.475889 0.127514i
\(315\) −2.24219 + 5.07760i −0.126333 + 0.286090i
\(316\) −2.57332 + 1.48570i −0.144760 + 0.0835774i
\(317\) 4.15537 + 15.5081i 0.233389 + 0.871019i 0.978869 + 0.204491i \(0.0655538\pi\)
−0.745480 + 0.666528i \(0.767780\pi\)
\(318\) 1.64597 0.441036i 0.0923014 0.0247321i
\(319\) 5.92382 1.58728i 0.331670 0.0888708i
\(320\) 1.76723 + 6.59541i 0.0987914 + 0.368695i
\(321\) 1.74729 1.00880i 0.0975240 0.0563055i
\(322\) −3.23270 + 7.32067i −0.180151 + 0.407965i
\(323\) −50.7236 + 13.5914i −2.82234 + 0.756243i
\(324\) −1.19645 0.690770i −0.0664694 0.0383761i
\(325\) 0.116588 2.15532i 0.00646715 0.119556i
\(326\) 6.47904 + 11.2220i 0.358841 + 0.621530i
\(327\) 1.45769 5.44016i 0.0806103 0.300842i
\(328\) 26.2351 + 15.1468i 1.44859 + 0.836345i
\(329\) 17.6360 + 7.78780i 0.972306 + 0.429355i
\(330\) 2.85219 2.85219i 0.157008 0.157008i
\(331\) −4.03496 + 4.03496i −0.221781 + 0.221781i −0.809248 0.587467i \(-0.800125\pi\)
0.587467 + 0.809248i \(0.300125\pi\)
\(332\) 0.770838 + 2.87681i 0.0423052 + 0.157885i
\(333\) 1.83026 6.83063i 0.100298 0.374316i
\(334\) 0.00744470i 0.000407356i
\(335\) 12.0972 20.9529i 0.660940 1.14478i
\(336\) 0.272676 1.75621i 0.0148757 0.0958090i
\(337\) 6.54996i 0.356799i −0.983958 0.178399i \(-0.942908\pi\)
0.983958 0.178399i \(-0.0570919\pi\)
\(338\) 1.56535 + 10.1029i 0.0851441 + 0.549527i
\(339\) −10.7499 + 6.20648i −0.583857 + 0.337090i
\(340\) −13.4310 + 13.4310i −0.728397 + 0.728397i
\(341\) 1.00178 0.578379i 0.0542496 0.0313210i
\(342\) −3.15084 5.45741i −0.170378 0.295103i
\(343\) −16.5778 8.25691i −0.895117 0.445831i
\(344\) 2.40399 + 0.644146i 0.129614 + 0.0347300i
\(345\) −5.70568 5.70568i −0.307184 0.307184i
\(346\) −15.9226 4.26645i −0.856005 0.229366i
\(347\) 11.4025 19.7498i 0.612120 1.06022i −0.378763 0.925494i \(-0.623650\pi\)
0.990883 0.134729i \(-0.0430163\pi\)
\(348\) −1.73279 3.00129i −0.0928875 0.160886i
\(349\) 0.529316 + 1.97543i 0.0283336 + 0.105743i 0.978645 0.205560i \(-0.0659015\pi\)
−0.950311 + 0.311302i \(0.899235\pi\)
\(350\) 0.503164 1.13945i 0.0268953 0.0609062i
\(351\) −3.02057 1.96880i −0.161226 0.105087i
\(352\) −7.14728 + 12.3795i −0.380951 + 0.659827i
\(353\) −18.2898 18.2898i −0.973469 0.973469i 0.0261885 0.999657i \(-0.491663\pi\)
−0.999657 + 0.0261885i \(0.991663\pi\)
\(354\) −4.36881 −0.232200
\(355\) 20.5053 1.08831
\(356\) −6.15206 6.15206i −0.326058 0.326058i
\(357\) −16.1680 + 6.26288i −0.855702 + 0.331467i
\(358\) −1.96396 + 7.32960i −0.103798 + 0.387381i
\(359\) 14.5374 3.89528i 0.767255 0.205585i 0.146096 0.989270i \(-0.453329\pi\)
0.621158 + 0.783685i \(0.286662\pi\)
\(360\) −4.83163 2.78954i −0.254649 0.147022i
\(361\) 45.2098i 2.37946i
\(362\) 0.955352 + 0.255986i 0.0502122 + 0.0134543i
\(363\) −5.02291 −0.263634
\(364\) 2.72249 12.8948i 0.142697 0.675871i
\(365\) 21.2843 1.11407
\(366\) −7.13471 1.91174i −0.372937 0.0999283i
\(367\) 15.2972i 0.798506i −0.916841 0.399253i \(-0.869270\pi\)
0.916841 0.399253i \(-0.130730\pi\)
\(368\) 2.23748 + 1.29181i 0.116637 + 0.0673403i
\(369\) −11.0034 + 2.94834i −0.572813 + 0.153485i
\(370\) 3.01968 11.2696i 0.156986 0.585879i
\(371\) −5.66499 0.879569i −0.294111 0.0456650i
\(372\) −0.462218 0.462218i −0.0239649 0.0239649i
\(373\) −20.4419 −1.05844 −0.529221 0.848484i \(-0.677516\pi\)
−0.529221 + 0.848484i \(0.677516\pi\)
\(374\) 12.5999 0.651524
\(375\) 8.30541 + 8.30541i 0.428890 + 0.428890i
\(376\) −9.68892 + 16.7817i −0.499668 + 0.865450i
\(377\) −4.09257 8.06561i −0.210778 0.415400i
\(378\) −1.22811 1.67957i −0.0631672 0.0863878i
\(379\) −1.64237 6.12940i −0.0843628 0.314846i 0.910830 0.412782i \(-0.135443\pi\)
−0.995193 + 0.0979355i \(0.968776\pi\)
\(380\) 11.6125 + 20.1135i 0.595711 + 1.03180i
\(381\) −5.22768 + 9.05461i −0.267822 + 0.463882i
\(382\) −1.85730 0.497662i −0.0950277 0.0254626i
\(383\) −4.42655 4.42655i −0.226186 0.226186i 0.584911 0.811097i \(-0.301129\pi\)
−0.811097 + 0.584911i \(0.801129\pi\)
\(384\) 8.82303 + 2.36412i 0.450248 + 0.120644i
\(385\) −12.6540 + 4.90169i −0.644909 + 0.249813i
\(386\) −6.76741 11.7215i −0.344452 0.596609i
\(387\) −0.810492 + 0.467938i −0.0411996 + 0.0237866i
\(388\) 15.7753 15.7753i 0.800867 0.800867i
\(389\) −4.72095 + 2.72564i −0.239362 + 0.138196i −0.614883 0.788618i \(-0.710797\pi\)
0.375522 + 0.926814i \(0.377464\pi\)
\(390\) −4.98352 3.24826i −0.252351 0.164482i
\(391\) 25.2055i 1.27470i
\(392\) 10.0433 15.6735i 0.507263 0.791631i
\(393\) 10.4315 18.0680i 0.526201 0.911408i
\(394\) 18.4090i 0.927433i
\(395\) 1.16785 4.35848i 0.0587610 0.219299i
\(396\) −0.874188 3.26252i −0.0439296 0.163948i
\(397\) −6.77902 + 6.77902i −0.340229 + 0.340229i −0.856453 0.516224i \(-0.827337\pi\)
0.516224 + 0.856453i \(0.327337\pi\)
\(398\) 10.3663 10.3663i 0.519614 0.519614i
\(399\) 2.28027 + 21.0777i 0.114156 + 1.05520i
\(400\) −0.348261 0.201069i −0.0174130 0.0100534i
\(401\) 9.70794 36.2305i 0.484791 1.80927i −0.0962083 0.995361i \(-0.530671\pi\)
0.580999 0.813904i \(-0.302662\pi\)
\(402\) 4.53468 + 7.85430i 0.226169 + 0.391737i
\(403\) −1.13938 1.26969i −0.0567565 0.0632480i
\(404\) 4.23523 + 2.44521i 0.210710 + 0.121654i
\(405\) 2.02645 0.542987i 0.100695 0.0269812i
\(406\) −0.561378 5.18909i −0.0278607 0.257530i
\(407\) 14.9724 8.64434i 0.742156 0.428484i
\(408\) −4.51058 16.8337i −0.223307 0.833393i
\(409\) −29.6891 + 7.95517i −1.46803 + 0.393358i −0.902256 0.431202i \(-0.858090\pi\)
−0.565775 + 0.824559i \(0.691423\pi\)
\(410\) −18.1541 + 4.86437i −0.896566 + 0.240234i
\(411\) 2.91789 + 10.8897i 0.143929 + 0.537149i
\(412\) −10.9651 + 6.33069i −0.540210 + 0.311891i
\(413\) 13.4454 + 5.93728i 0.661605 + 0.292155i
\(414\) 2.92166 0.782855i 0.143592 0.0384752i
\(415\) −3.91676 2.26134i −0.192266 0.111005i
\(416\) 20.0385 + 6.54817i 0.982470 + 0.321050i
\(417\) −5.09981 8.83314i −0.249739 0.432561i
\(418\) 3.98747 14.8814i 0.195034 0.727875i
\(419\) −20.2493 11.6909i −0.989241 0.571138i −0.0841936 0.996449i \(-0.526831\pi\)
−0.905047 + 0.425311i \(0.860165\pi\)
\(420\) 4.52625 + 6.19012i 0.220859 + 0.302047i
\(421\) 14.1492 14.1492i 0.689589 0.689589i −0.272552 0.962141i \(-0.587868\pi\)
0.962141 + 0.272552i \(0.0878676\pi\)
\(422\) 6.24254 6.24254i 0.303882 0.303882i
\(423\) −1.88596 7.03848i −0.0916983 0.342223i
\(424\) 1.49138 5.56591i 0.0724279 0.270305i
\(425\) 3.92320i 0.190303i
\(426\) −3.84325 + 6.65671i −0.186206 + 0.322518i
\(427\) 19.3596 + 15.5797i 0.936877 + 0.753956i
\(428\) 2.78739i 0.134733i
\(429\) −1.81822 8.62533i −0.0877847 0.416435i
\(430\) −1.33720 + 0.772034i −0.0644856 + 0.0372308i
\(431\) 9.32545 9.32545i 0.449191 0.449191i −0.445894 0.895086i \(-0.647114\pi\)
0.895086 + 0.445894i \(0.147114\pi\)
\(432\) −0.581741 + 0.335869i −0.0279891 + 0.0161595i
\(433\) 5.53868 + 9.59327i 0.266172 + 0.461023i 0.967870 0.251451i \(-0.0809078\pi\)
−0.701698 + 0.712474i \(0.747574\pi\)
\(434\) −0.355600 0.918003i −0.0170693 0.0440656i
\(435\) 5.08335 + 1.36208i 0.243728 + 0.0653067i
\(436\) −5.50195 5.50195i −0.263496 0.263496i
\(437\) −29.7697 7.97676i −1.42408 0.381580i
\(438\) −3.98925 + 6.90958i −0.190614 + 0.330153i
\(439\) 6.61652 + 11.4601i 0.315789 + 0.546963i 0.979605 0.200933i \(-0.0643974\pi\)
−0.663816 + 0.747896i \(0.731064\pi\)
\(440\) −3.53024 13.1750i −0.168298 0.628095i
\(441\) 1.49706 + 6.83804i 0.0712885 + 0.325621i
\(442\) −3.83287 18.1824i −0.182311 0.864850i
\(443\) 2.45582 4.25360i 0.116679 0.202095i −0.801770 0.597632i \(-0.796108\pi\)
0.918450 + 0.395537i \(0.129442\pi\)
\(444\) −6.90821 6.90821i −0.327849 0.327849i
\(445\) 13.2119 0.626303
\(446\) 7.99494 0.378571
\(447\) 3.32734 + 3.32734i 0.157378 + 0.157378i
\(448\) 6.70849 + 5.39868i 0.316946 + 0.255064i
\(449\) 0.246197 0.918821i 0.0116188 0.0433618i −0.959873 0.280435i \(-0.909521\pi\)
0.971492 + 0.237073i \(0.0761880\pi\)
\(450\) −0.454751 + 0.121850i −0.0214372 + 0.00574407i
\(451\) −24.1189 13.9251i −1.13572 0.655705i
\(452\) 17.1490i 0.806622i
\(453\) 0.563961 + 0.151113i 0.0264972 + 0.00709990i
\(454\) 5.17768 0.243001
\(455\) 10.9228 + 16.7695i 0.512068 + 0.786165i
\(456\) −21.3094 −0.997903
\(457\) 18.5842 + 4.97961i 0.869331 + 0.232937i 0.665798 0.746132i \(-0.268091\pi\)
0.203533 + 0.979068i \(0.434758\pi\)
\(458\) 0.977454i 0.0456734i
\(459\) 5.67540 + 3.27669i 0.264905 + 0.152943i
\(460\) −10.7679 + 2.88524i −0.502055 + 0.134525i
\(461\) −1.66867 + 6.22758i −0.0777179 + 0.290047i −0.993836 0.110862i \(-0.964639\pi\)
0.916118 + 0.400909i \(0.131306\pi\)
\(462\) 0.780455 5.02663i 0.0363101 0.233860i
\(463\) 7.67988 + 7.67988i 0.356914 + 0.356914i 0.862674 0.505760i \(-0.168788\pi\)
−0.505760 + 0.862674i \(0.668788\pi\)
\(464\) −1.68505 −0.0782265
\(465\) 0.992638 0.0460325
\(466\) 8.15021 + 8.15021i 0.377551 + 0.377551i
\(467\) 10.7238 18.5741i 0.496236 0.859507i −0.503754 0.863847i \(-0.668048\pi\)
0.999991 + 0.00434034i \(0.00138158\pi\)
\(468\) −4.44209 + 2.25396i −0.205336 + 0.104189i
\(469\) −3.28177 30.3350i −0.151538 1.40074i
\(470\) −3.11157 11.6125i −0.143526 0.535647i
\(471\) 5.55061 + 9.61395i 0.255759 + 0.442987i
\(472\) −7.38666 + 12.7941i −0.339999 + 0.588895i
\(473\) −2.21007 0.592187i −0.101619 0.0272288i
\(474\) 1.19602 + 1.19602i 0.0549351 + 0.0549351i
\(475\) 4.63361 + 1.24157i 0.212604 + 0.0569672i
\(476\) −3.67517 + 23.6704i −0.168451 + 1.08493i
\(477\) 1.08341 + 1.87652i 0.0496059 + 0.0859199i
\(478\) 4.67851 2.70114i 0.213990 0.123547i
\(479\) −12.8006 + 12.8006i −0.584876 + 0.584876i −0.936239 0.351363i \(-0.885718\pi\)
0.351363 + 0.936239i \(0.385718\pi\)
\(480\) −10.6231 + 6.13322i −0.484874 + 0.279942i
\(481\) −17.0289 18.9766i −0.776453 0.865258i
\(482\) 15.0318i 0.684680i
\(483\) −10.0556 1.56127i −0.457544 0.0710401i
\(484\) −3.46968 + 6.00966i −0.157713 + 0.273166i
\(485\) 33.8782i 1.53833i
\(486\) −0.203541 + 0.759625i −0.00923280 + 0.0344573i
\(487\) 1.86380 + 6.95580i 0.0844569 + 0.315197i 0.995211 0.0977522i \(-0.0311653\pi\)
−0.910754 + 0.412949i \(0.864499\pi\)
\(488\) −17.6617 + 17.6617i −0.799507 + 0.799507i
\(489\) −11.6512 + 11.6512i −0.526885 + 0.526885i
\(490\) 2.46994 + 11.2818i 0.111581 + 0.509662i
\(491\) −24.3966 14.0854i −1.10101 0.635666i −0.164520 0.986374i \(-0.552608\pi\)
−0.936485 + 0.350708i \(0.885941\pi\)
\(492\) −4.07326 + 15.2016i −0.183637 + 0.685342i
\(493\) 8.21957 + 14.2367i 0.370191 + 0.641190i
\(494\) −22.6879 1.22726i −1.02077 0.0552170i
\(495\) 4.44190 + 2.56453i 0.199648 + 0.115267i
\(496\) −0.307002 + 0.0822609i −0.0137848 + 0.00369362i
\(497\) 20.8745 15.2636i 0.936349 0.684664i
\(498\) 1.46821 0.847673i 0.0657922 0.0379852i
\(499\) 5.44491 + 20.3207i 0.243748 + 0.909678i 0.974009 + 0.226510i \(0.0727317\pi\)
−0.730261 + 0.683168i \(0.760602\pi\)
\(500\) 15.6741 4.19987i 0.700969 0.187824i
\(501\) −0.00914399 + 0.00245012i −0.000408523 + 0.000109463i
\(502\) −0.557794 2.08172i −0.0248956 0.0929116i
\(503\) 18.9822 10.9594i 0.846374 0.488655i −0.0130514 0.999915i \(-0.504155\pi\)
0.859426 + 0.511260i \(0.170821\pi\)
\(504\) −6.99508 + 0.756757i −0.311585 + 0.0337086i
\(505\) −7.17330 + 1.92208i −0.319208 + 0.0855314i
\(506\) 6.40414 + 3.69743i 0.284699 + 0.164371i
\(507\) −11.8938 + 5.24763i −0.528222 + 0.233055i
\(508\) 7.22226 + 12.5093i 0.320436 + 0.555011i
\(509\) 0.779515 2.90919i 0.0345514 0.128948i −0.946496 0.322716i \(-0.895404\pi\)
0.981047 + 0.193768i \(0.0620709\pi\)
\(510\) 9.36364 + 5.40610i 0.414629 + 0.239386i
\(511\) 21.6675 15.8434i 0.958513 0.700870i
\(512\) 5.30352 5.30352i 0.234385 0.234385i
\(513\) 5.66612 5.66612i 0.250165 0.250165i
\(514\) 2.23111 + 8.32661i 0.0984100 + 0.367271i
\(515\) 4.97630 18.5718i 0.219282 0.818371i
\(516\) 1.29295i 0.0569189i
\(517\) 8.90738 15.4280i 0.391746 0.678525i
\(518\) −5.31472 13.7203i −0.233515 0.602835i
\(519\) 20.9611i 0.920092i
\(520\) −17.9385 + 9.10219i −0.786656 + 0.399157i
\(521\) 20.7786 11.9965i 0.910328 0.525578i 0.0297912 0.999556i \(-0.490516\pi\)
0.880537 + 0.473978i \(0.157182\pi\)
\(522\) −1.39493 + 1.39493i −0.0610546 + 0.0610546i
\(523\) 8.29910 4.79149i 0.362894 0.209517i −0.307455 0.951563i \(-0.599477\pi\)
0.670350 + 0.742045i \(0.266144\pi\)
\(524\) −14.4116 24.9616i −0.629573 1.09045i
\(525\) 1.56513 + 0.243009i 0.0683080 + 0.0106058i
\(526\) 16.8021 + 4.50212i 0.732608 + 0.196302i
\(527\) 2.19255 + 2.19255i 0.0955088 + 0.0955088i
\(528\) −1.58631 0.425051i −0.0690353 0.0184980i
\(529\) −4.10344 + 7.10737i −0.178411 + 0.309016i
\(530\) 1.78748 + 3.09600i 0.0776431 + 0.134482i
\(531\) −1.43782 5.36602i −0.0623961 0.232865i
\(532\) 26.7935 + 11.8316i 1.16165 + 0.512966i
\(533\) −12.7578 + 39.0411i −0.552602 + 1.69106i
\(534\) −2.47626 + 4.28902i −0.107158 + 0.185604i
\(535\) 2.99303 + 2.99303i 0.129400 + 0.129400i
\(536\) 30.6684 1.32467
\(537\) −9.64897 −0.416384
\(538\) −5.07631 5.07631i −0.218855 0.218855i
\(539\) −9.23318 + 14.4092i −0.397701 + 0.620650i
\(540\) 0.750158 2.79963i 0.0322817 0.120477i
\(541\) 20.9526 5.61424i 0.900823 0.241375i 0.221454 0.975171i \(-0.428920\pi\)
0.679370 + 0.733796i \(0.262253\pi\)
\(542\) −13.2227 7.63415i −0.567965 0.327915i
\(543\) 1.25766i 0.0539715i
\(544\) −37.0114 9.91718i −1.58685 0.425195i
\(545\) 11.8157 0.506131
\(546\) −7.49116 + 0.402847i −0.320592 + 0.0172403i
\(547\) −24.6132 −1.05238 −0.526191 0.850366i \(-0.676380\pi\)
−0.526191 + 0.850366i \(0.676380\pi\)
\(548\) 15.0446 + 4.03118i 0.642672 + 0.172203i
\(549\) 9.39241i 0.400858i
\(550\) −0.996795 0.575500i −0.0425035 0.0245394i
\(551\) 19.4159 5.20248i 0.827146 0.221633i
\(552\) 2.64726 9.87970i 0.112675 0.420508i
\(553\) −2.05545 5.30627i −0.0874066 0.225646i
\(554\) 15.6161 + 15.6161i 0.663464 + 0.663464i
\(555\) 14.8358 0.629743
\(556\) −14.0912 −0.597600
\(557\) 0.362938 + 0.362938i 0.0153782 + 0.0153782i 0.714754 0.699376i \(-0.246539\pi\)
−0.699376 + 0.714754i \(0.746539\pi\)
\(558\) −0.186047 + 0.322243i −0.00787601 + 0.0136416i
\(559\) −0.182263 + 3.36942i −0.00770889 + 0.142511i
\(560\) 3.70693 0.401032i 0.156646 0.0169467i
\(561\) 4.14674 + 15.4759i 0.175076 + 0.653391i
\(562\) −2.11189 3.65791i −0.0890848 0.154299i
\(563\) −21.6004 + 37.4130i −0.910349 + 1.57677i −0.0967769 + 0.995306i \(0.530853\pi\)
−0.813572 + 0.581464i \(0.802480\pi\)
\(564\) −9.72395 2.60552i −0.409452 0.109712i
\(565\) −18.4142 18.4142i −0.774692 0.774692i
\(566\) −1.05214 0.281920i −0.0442248 0.0118500i
\(567\) 1.65876 2.06120i 0.0696612 0.0865621i
\(568\) 12.9961 + 22.5099i 0.545305 + 0.944496i
\(569\) 26.6085 15.3624i 1.11549 0.644027i 0.175242 0.984525i \(-0.443929\pi\)
0.940245 + 0.340499i \(0.110596\pi\)
\(570\) 9.34833 9.34833i 0.391558 0.391558i
\(571\) −18.1885 + 10.5012i −0.761167 + 0.439460i −0.829715 0.558188i \(-0.811497\pi\)
0.0685475 + 0.997648i \(0.478164\pi\)
\(572\) −11.5757 3.78271i −0.484006 0.158163i
\(573\) 2.44502i 0.102142i
\(574\) −14.8600 + 18.4653i −0.620246 + 0.770728i
\(575\) −1.15126 + 1.99405i −0.0480110 + 0.0831574i
\(576\) 3.25466i 0.135611i
\(577\) −2.29545 + 8.56673i −0.0955608 + 0.356638i −0.997104 0.0760516i \(-0.975769\pi\)
0.901543 + 0.432689i \(0.142435\pi\)
\(578\) 5.28126 + 19.7099i 0.219671 + 0.819825i
\(579\) 12.1698 12.1698i 0.505758 0.505758i
\(580\) 5.14109 5.14109i 0.213472 0.213472i
\(581\) −5.67055 + 0.613465i −0.235254 + 0.0254508i
\(582\) −10.9980 6.34970i −0.455882 0.263203i
\(583\) −1.37108 + 5.11695i −0.0567844 + 0.211922i
\(584\) 13.4898 + 23.3650i 0.558212 + 0.966852i
\(585\) 2.34956 7.19007i 0.0971424 0.297273i
\(586\) −12.2183 7.05424i −0.504734 0.291408i
\(587\) −30.5954 + 8.19801i −1.26281 + 0.338368i −0.827271 0.561803i \(-0.810108\pi\)
−0.435536 + 0.900171i \(0.643441\pi\)
\(588\) 9.21550 + 2.93236i 0.380041 + 0.120929i
\(589\) 3.28344 1.89570i 0.135292 0.0781108i
\(590\) −2.37221 8.85320i −0.0976622 0.364480i
\(591\) 22.6109 6.05858i 0.930090 0.249217i
\(592\) −4.58839 + 1.22945i −0.188582 + 0.0505303i
\(593\) −1.47098 5.48978i −0.0604060 0.225438i 0.929123 0.369770i \(-0.120563\pi\)
−0.989529 + 0.144332i \(0.953897\pi\)
\(594\) −1.66506 + 0.961326i −0.0683184 + 0.0394437i
\(595\) −21.4704 29.3631i −0.880202 1.20377i
\(596\) 6.27941 1.68256i 0.257215 0.0689205i
\(597\) 16.1440 + 9.32077i 0.660732 + 0.381474i
\(598\) 3.38750 10.3663i 0.138525 0.423911i
\(599\) 5.44521 + 9.43138i 0.222485 + 0.385356i 0.955562 0.294790i \(-0.0952498\pi\)
−0.733077 + 0.680146i \(0.761916\pi\)
\(600\) −0.412042 + 1.53776i −0.0168215 + 0.0627788i
\(601\) 1.42936 + 0.825243i 0.0583049 + 0.0336624i 0.528869 0.848703i \(-0.322616\pi\)
−0.470564 + 0.882366i \(0.655950\pi\)
\(602\) −0.786598 + 1.78131i −0.0320593 + 0.0726007i
\(603\) −8.15467 + 8.15467i −0.332084 + 0.332084i
\(604\) 0.570367 0.570367i 0.0232079 0.0232079i
\(605\) −2.72737 10.1787i −0.110883 0.413823i
\(606\) 0.720500 2.68894i 0.0292683 0.109231i
\(607\) 26.1975i 1.06332i 0.846957 + 0.531662i \(0.178432\pi\)
−0.846957 + 0.531662i \(0.821568\pi\)
\(608\) −23.4259 + 40.5749i −0.950046 + 1.64553i
\(609\) 6.18877 2.39729i 0.250781 0.0971433i
\(610\) 15.4962i 0.627423i
\(611\) −24.9733 8.16074i −1.01031 0.330148i
\(612\) 7.84080 4.52689i 0.316946 0.182989i
\(613\) −16.6089 + 16.6089i −0.670827 + 0.670827i −0.957907 0.287079i \(-0.907316\pi\)
0.287079 + 0.957907i \(0.407316\pi\)
\(614\) −5.27084 + 3.04312i −0.212714 + 0.122810i
\(615\) −11.9494 20.6969i −0.481845 0.834580i
\(616\) −13.4009 10.7844i −0.539938 0.434517i
\(617\) −7.41451 1.98671i −0.298497 0.0799820i 0.106462 0.994317i \(-0.466048\pi\)
−0.404959 + 0.914335i \(0.632714\pi\)
\(618\) 5.09633 + 5.09633i 0.205005 + 0.205005i
\(619\) −27.5031 7.36942i −1.10544 0.296202i −0.340463 0.940258i \(-0.610584\pi\)
−0.764978 + 0.644056i \(0.777250\pi\)
\(620\) 0.685685 1.18764i 0.0275378 0.0476968i
\(621\) 1.92309 + 3.33089i 0.0771710 + 0.133664i
\(622\) 1.33261 + 4.97337i 0.0534328 + 0.199414i
\(623\) 13.4498 9.83454i 0.538853 0.394012i
\(624\) −0.130822 + 2.41845i −0.00523706 + 0.0968154i
\(625\) −10.8242 + 18.7480i −0.432967 + 0.749921i
\(626\) 9.53777 + 9.53777i 0.381206 + 0.381206i
\(627\) 19.5905 0.782370
\(628\) 15.3368 0.612005
\(629\) 32.7694 + 32.7694i 1.30660 + 1.30660i
\(630\) 2.73672 3.40069i 0.109034 0.135487i
\(631\) −2.62809 + 9.80818i −0.104623 + 0.390458i −0.998302 0.0582487i \(-0.981448\pi\)
0.893679 + 0.448706i \(0.148115\pi\)
\(632\) 5.52475 1.48035i 0.219763 0.0588852i
\(633\) 9.72190 + 5.61294i 0.386411 + 0.223094i
\(634\) 12.6261i 0.501446i
\(635\) −21.1873 5.67712i −0.840793 0.225290i
\(636\) 2.99355 0.118702
\(637\) 23.6022 + 8.94080i 0.935152 + 0.354247i
\(638\) −4.82296 −0.190943
\(639\) −9.44098 2.52970i −0.373479 0.100074i
\(640\) 19.1631i 0.757490i
\(641\) −20.0662 11.5852i −0.792569 0.457590i 0.0482973 0.998833i \(-0.484621\pi\)
−0.840866 + 0.541243i \(0.817954\pi\)
\(642\) −1.53261 + 0.410663i −0.0604875 + 0.0162076i
\(643\) −6.46488 + 24.1273i −0.254950 + 0.951486i 0.713168 + 0.700993i \(0.247259\pi\)
−0.968118 + 0.250493i \(0.919407\pi\)
\(644\) −8.81406 + 10.9525i −0.347323 + 0.431589i
\(645\) −1.38834 1.38834i −0.0546658 0.0546658i
\(646\) 41.2973 1.62482
\(647\) 4.58441 0.180232 0.0901160 0.995931i \(-0.471276\pi\)
0.0901160 + 0.995931i \(0.471276\pi\)
\(648\) 1.88042 + 1.88042i 0.0738699 + 0.0738699i
\(649\) 6.79083 11.7621i 0.266564 0.461702i
\(650\) −0.527259 + 1.61350i −0.0206808 + 0.0632869i
\(651\) 1.01051 0.738891i 0.0396050 0.0289594i
\(652\) 5.89176 + 21.9883i 0.230739 + 0.861130i
\(653\) 12.7283 + 22.0460i 0.498096 + 0.862728i 0.999998 0.00219688i \(-0.000699289\pi\)
−0.501901 + 0.864925i \(0.667366\pi\)
\(654\) −2.21459 + 3.83579i −0.0865974 + 0.149991i
\(655\) 42.2780 + 11.3284i 1.65194 + 0.442636i
\(656\) 5.41086 + 5.41086i 0.211259 + 0.211259i
\(657\) −9.79963 2.62580i −0.382320 0.102442i
\(658\) −11.8116 9.50546i −0.460465 0.370561i
\(659\) −6.21741 10.7689i −0.242196 0.419496i 0.719144 0.694861i \(-0.244534\pi\)
−0.961339 + 0.275366i \(0.911201\pi\)
\(660\) 6.13666 3.54300i 0.238869 0.137911i
\(661\) 26.6523 26.6523i 1.03665 1.03665i 0.0373506 0.999302i \(-0.488108\pi\)
0.999302 0.0373506i \(-0.0118918\pi\)
\(662\) 3.88634 2.24378i 0.151047 0.0872069i
\(663\) 21.0712 10.6918i 0.818338 0.415233i
\(664\) 5.73288i 0.222479i
\(665\) −41.4748 + 16.0658i −1.60832 + 0.623004i
\(666\) −2.78062 + 4.81618i −0.107747 + 0.186623i
\(667\) 9.64813i 0.373577i
\(668\) −0.00338495 + 0.0126328i −0.000130968 + 0.000488778i
\(669\) 2.63121 + 9.81982i 0.101729 + 0.379656i
\(670\) −13.4541 + 13.4541i −0.519777 + 0.519777i
\(671\) 16.2371 16.2371i 0.626825 0.626825i
\(672\) −6.24893 + 14.1511i −0.241058 + 0.545892i
\(673\) 21.1591 + 12.2162i 0.815624 + 0.470901i 0.848905 0.528545i \(-0.177262\pi\)
−0.0332811 + 0.999446i \(0.510596\pi\)
\(674\) −1.33318 + 4.97551i −0.0513524 + 0.191650i
\(675\) −0.299326 0.518448i −0.0115211 0.0199551i
\(676\) −1.93736 + 17.8552i −0.0745140 + 0.686740i
\(677\) −3.00229 1.73338i −0.115388 0.0666190i 0.441195 0.897411i \(-0.354555\pi\)
−0.556583 + 0.830792i \(0.687888\pi\)
\(678\) 9.42920 2.52655i 0.362126 0.0970314i
\(679\) 25.2180 + 34.4882i 0.967776 + 1.32353i
\(680\) 31.6635 18.2810i 1.21424 0.701043i
\(681\) 1.70402 + 6.35951i 0.0652984 + 0.243697i
\(682\) −0.878703 + 0.235448i −0.0336473 + 0.00901576i
\(683\) −36.7999 + 9.86051i −1.40811 + 0.377302i −0.881250 0.472650i \(-0.843297\pi\)
−0.526860 + 0.849952i \(0.676631\pi\)
\(684\) −2.86524 10.6932i −0.109555 0.408865i
\(685\) −20.4831 + 11.8259i −0.782619 + 0.451845i
\(686\) 10.9123 + 9.64642i 0.416633 + 0.368302i
\(687\) 1.20056 0.321690i 0.0458043 0.0122732i
\(688\) 0.544437 + 0.314331i 0.0207565 + 0.0119838i
\(689\) 7.80117 + 0.421990i 0.297201 + 0.0160765i
\(690\) 3.17284 + 5.49552i 0.120788 + 0.209211i
\(691\) −5.81255 + 21.6927i −0.221120 + 0.825230i 0.762802 + 0.646632i \(0.223823\pi\)
−0.983922 + 0.178598i \(0.942844\pi\)
\(692\) −25.0789 14.4793i −0.953359 0.550422i
\(693\) 6.43083 0.695715i 0.244287 0.0264280i
\(694\) −12.6815 + 12.6815i −0.481384 + 0.481384i
\(695\) 15.1308 15.1308i 0.573944 0.573944i
\(696\) 1.72655 + 6.44358i 0.0654448 + 0.244243i
\(697\) 19.3217 72.1094i 0.731860 2.73134i
\(698\) 1.60833i 0.0608761i
\(699\) −7.32822 + 12.6928i −0.277179 + 0.480088i
\(700\) 1.37189 1.70474i 0.0518528 0.0644330i
\(701\) 43.0296i 1.62520i −0.582819 0.812602i \(-0.698050\pi\)
0.582819 0.812602i \(-0.301950\pi\)
\(702\) 1.89376 + 2.11036i 0.0714755 + 0.0796504i
\(703\) 49.0736 28.3327i 1.85085 1.06859i
\(704\) 5.62646 5.62646i 0.212055 0.212055i
\(705\) 13.2391 7.64360i 0.498614 0.287875i
\(706\) 10.1707 + 17.6161i 0.382778 + 0.662992i
\(707\) −5.87171 + 7.29628i −0.220829 + 0.274405i
\(708\) −7.41337 1.98641i −0.278611 0.0746537i
\(709\) −14.0137 14.0137i −0.526295 0.526295i 0.393171 0.919466i \(-0.371378\pi\)
−0.919466 + 0.393171i \(0.871378\pi\)
\(710\) −15.5763 4.17367i −0.584570 0.156635i
\(711\) −1.07540 + 1.86264i −0.0403305 + 0.0698545i
\(712\) 8.37359 + 14.5035i 0.313814 + 0.543541i
\(713\) 0.471003 + 1.75781i 0.0176392 + 0.0658304i
\(714\) 13.5564 1.46659i 0.507335 0.0548856i
\(715\) 16.4916 8.36798i 0.616749 0.312945i
\(716\) −6.66522 + 11.5445i −0.249091 + 0.431438i
\(717\) 4.85743 + 4.85743i 0.181404 + 0.181404i
\(718\) −11.8358 −0.441709
\(719\) 46.5796 1.73713 0.868563 0.495579i \(-0.165044\pi\)
0.868563 + 0.495579i \(0.165044\pi\)
\(720\) −0.996500 0.996500i −0.0371374 0.0371374i
\(721\) −8.75841 22.6104i −0.326180 0.842055i
\(722\) 9.20205 34.3425i 0.342465 1.27810i
\(723\) 18.4629 4.94711i 0.686641 0.183985i
\(724\) 1.50473 + 0.868756i 0.0559229 + 0.0322871i
\(725\) 1.50172i 0.0557723i
\(726\) 3.81553 + 1.02237i 0.141607 + 0.0379436i
\(727\) −38.0896 −1.41266 −0.706332 0.707880i \(-0.749652\pi\)
−0.706332 + 0.707880i \(0.749652\pi\)
\(728\) −11.4861 + 22.6190i −0.425703 + 0.838316i
\(729\) −1.00000 −0.0370370
\(730\) −16.1681 4.33222i −0.598407 0.160343i
\(731\) 6.13315i 0.226843i
\(732\) −11.2375 6.48800i −0.415352 0.239803i
\(733\) 30.4740 8.16549i 1.12558 0.301599i 0.352443 0.935833i \(-0.385351\pi\)
0.773141 + 0.634234i \(0.218684\pi\)
\(734\) −3.11360 + 11.6201i −0.114925 + 0.428906i
\(735\) −13.0441 + 6.74668i −0.481139 + 0.248855i
\(736\) −15.9016 15.9016i −0.586140 0.586140i
\(737\) −28.1946 −1.03856
\(738\) 8.95855 0.329769
\(739\) −20.9621 20.9621i −0.771103 0.771103i 0.207197 0.978299i \(-0.433566\pi\)
−0.978299 + 0.207197i \(0.933566\pi\)
\(740\) 10.2481 17.7502i 0.376728 0.652512i
\(741\) −5.95941 28.2704i −0.218924 1.03854i
\(742\) 4.12424 + 1.82120i 0.151405 + 0.0668583i
\(743\) 6.49849 + 24.2527i 0.238406 + 0.889745i 0.976584 + 0.215138i \(0.0690201\pi\)
−0.738177 + 0.674607i \(0.764313\pi\)
\(744\) 0.629127 + 1.08968i 0.0230649 + 0.0399496i
\(745\) −4.93599 + 8.54939i −0.180841 + 0.313225i
\(746\) 15.5282 + 4.16077i 0.568528 + 0.152337i
\(747\) 1.52436 + 1.52436i 0.0557735 + 0.0557735i
\(748\) 21.3805 + 5.72890i 0.781750 + 0.209469i
\(749\) 5.27485 + 0.818995i 0.192739 + 0.0299254i
\(750\) −4.61851 7.99949i −0.168644 0.292100i
\(751\) −26.9618 + 15.5664i −0.983849 + 0.568025i −0.903430 0.428736i \(-0.858959\pi\)
−0.0804190 + 0.996761i \(0.525626\pi\)
\(752\) −3.46114 + 3.46114i −0.126215 + 0.126215i
\(753\) 2.37330 1.37023i 0.0864880 0.0499338i
\(754\) 1.46714 + 6.95984i 0.0534300 + 0.253462i
\(755\) 1.22489i 0.0445784i
\(756\) −1.32030 3.40843i −0.0480188 0.123963i
\(757\) 1.51455 2.62328i 0.0550472 0.0953446i −0.837189 0.546914i \(-0.815802\pi\)
0.892236 + 0.451570i \(0.149136\pi\)
\(758\) 4.99034i 0.181257i
\(759\) −2.43372 + 9.08277i −0.0883385 + 0.329684i
\(760\) −11.5707 43.1825i −0.419714 1.56639i
\(761\) −20.7427 + 20.7427i −0.751923 + 0.751923i −0.974838 0.222915i \(-0.928443\pi\)
0.222915 + 0.974838i \(0.428443\pi\)
\(762\) 5.81406 5.81406i 0.210621 0.210621i
\(763\) 12.0285 8.79530i 0.435460 0.318411i
\(764\) −2.92535 1.68895i −0.105835 0.0611040i
\(765\) −3.55840 + 13.2801i −0.128654 + 0.480144i
\(766\) 2.46154 + 4.26351i 0.0889389 + 0.154047i
\(767\) −19.0392 6.22160i −0.687465 0.224649i
\(768\) −11.8582 6.84635i −0.427897 0.247046i
\(769\) 30.9694 8.29823i 1.11679 0.299242i 0.347203 0.937790i \(-0.387131\pi\)
0.769582 + 0.638548i \(0.220465\pi\)
\(770\) 10.6100 1.14784i 0.382358 0.0413651i
\(771\) −9.49291 + 5.48074i −0.341879 + 0.197384i
\(772\) −6.15399 22.9670i −0.221487 0.826601i
\(773\) −43.0528 + 11.5360i −1.54850 + 0.414920i −0.929001 0.370076i \(-0.879332\pi\)
−0.619501 + 0.784996i \(0.712665\pi\)
\(774\) 0.710914 0.190489i 0.0255533 0.00684698i
\(775\) −0.0733109 0.273600i −0.00263341 0.00982801i
\(776\) −37.1902 + 21.4718i −1.33505 + 0.770791i
\(777\) 15.1029 11.0433i 0.541813 0.396176i
\(778\) 4.14094 1.10956i 0.148460 0.0397797i
\(779\) −79.0521 45.6408i −2.83234 1.63525i
\(780\) −6.97955 7.77782i −0.249908 0.278491i
\(781\) −11.9478 20.6942i −0.427526 0.740497i
\(782\) −5.13036 + 19.1467i −0.183461 + 0.684686i
\(783\) −2.17242 1.25425i −0.0776360 0.0448232i
\(784\) 3.47516 3.16758i 0.124113 0.113128i
\(785\) −16.4683 + 16.4683i −0.587779 + 0.587779i
\(786\) −11.6016 + 11.6016i −0.413816 + 0.413816i
\(787\) −4.77097 17.8055i −0.170067 0.634698i −0.997339 0.0728975i \(-0.976775\pi\)
0.827273 0.561801i \(-0.189891\pi\)
\(788\) 8.37018 31.2379i 0.298175 1.11281i
\(789\) 22.1190i 0.787457i
\(790\) −1.77426 + 3.07311i −0.0631253 + 0.109336i
\(791\) −32.4528 5.03875i −1.15389 0.179157i
\(792\) 6.50152i 0.231022i
\(793\) −28.3704 18.4918i −1.00746 0.656664i
\(794\) 6.52932 3.76971i 0.231717 0.133782i
\(795\) −3.21440 + 3.21440i −0.114003 + 0.114003i
\(796\) 22.3037 12.8770i 0.790532 0.456414i
\(797\) 6.45241 + 11.1759i 0.228556 + 0.395871i 0.957380 0.288830i \(-0.0932662\pi\)
−0.728824 + 0.684701i \(0.759933\pi\)
\(798\) 2.55802 16.4753i 0.0905529 0.583218i
\(799\) 46.1259 + 12.3594i 1.63182 + 0.437244i
\(800\) 2.47506 + 2.47506i 0.0875065 + 0.0875065i
\(801\) −6.08297 1.62993i −0.214931 0.0575906i
\(802\) −14.7488 + 25.5456i −0.520798 + 0.902048i
\(803\) −12.4017 21.4804i −0.437646 0.758025i
\(804\) 4.12365 + 15.3897i 0.145430 + 0.542751i
\(805\) −2.29620 21.2249i −0.0809303 0.748078i
\(806\) 0.607067 + 1.19640i 0.0213830 + 0.0421415i
\(807\) 4.56433 7.90566i 0.160672 0.278292i
\(808\) −6.65637 6.65637i −0.234170 0.234170i
\(809\) 38.1452 1.34112 0.670558 0.741857i \(-0.266055\pi\)
0.670558 + 0.741857i \(0.266055\pi\)
\(810\) −1.64986 −0.0579703
\(811\) 10.6932 + 10.6932i 0.375490 + 0.375490i 0.869472 0.493982i \(-0.164459\pi\)
−0.493982 + 0.869472i \(0.664459\pi\)
\(812\) 1.40677 9.06053i 0.0493681 0.317962i
\(813\) 5.02495 18.7534i 0.176233 0.657709i
\(814\) −13.1329 + 3.51895i −0.460308 + 0.123339i
\(815\) −29.9370 17.2841i −1.04865 0.605437i
\(816\) 4.40216i 0.154106i
\(817\) −7.24373 1.94095i −0.253426 0.0679053i
\(818\) 24.1718 0.845146
\(819\) −2.96021 9.06847i −0.103438 0.316878i
\(820\) −33.0171 −1.15301
\(821\) 23.6589 + 6.33938i 0.825701 + 0.221246i 0.646837 0.762628i \(-0.276091\pi\)
0.178864 + 0.983874i \(0.442758\pi\)
\(822\) 8.86600i 0.309237i
\(823\) −11.7119 6.76187i −0.408251 0.235704i 0.281787 0.959477i \(-0.409073\pi\)
−0.690038 + 0.723773i \(0.742406\pi\)
\(824\) 23.5413 6.30788i 0.820101 0.219746i
\(825\) 0.378805 1.41372i 0.0131883 0.0492194i
\(826\) −9.00498 7.24680i −0.313323 0.252148i
\(827\) 24.6131 + 24.6131i 0.855881 + 0.855881i 0.990850 0.134969i \(-0.0430935\pi\)
−0.134969 + 0.990850i \(0.543094\pi\)
\(828\) 5.31366 0.184662
\(829\) 19.7093 0.684531 0.342266 0.939603i \(-0.388806\pi\)
0.342266 + 0.939603i \(0.388806\pi\)
\(830\) 2.51499 + 2.51499i 0.0872966 + 0.0872966i
\(831\) −14.0411 + 24.3199i −0.487081 + 0.843649i
\(832\) −9.83090 6.40778i −0.340825 0.222150i
\(833\) −43.7140 13.9098i −1.51460 0.481945i
\(834\) 2.07604 + 7.74789i 0.0718874 + 0.268288i
\(835\) −0.00993013 0.0171995i −0.000343646 0.000595213i
\(836\) 13.5325 23.4391i 0.468033 0.810657i
\(837\) −0.457027 0.122460i −0.0157972 0.00423284i
\(838\) 13.0023 + 13.0023i 0.449156 + 0.449156i
\(839\) −22.4087 6.00440i −0.773635 0.207295i −0.149658 0.988738i \(-0.547817\pi\)
−0.623977 + 0.781443i \(0.714484\pi\)
\(840\) −5.33177 13.7643i −0.183963 0.474913i
\(841\) 11.3537 + 19.6652i 0.391508 + 0.678111i
\(842\) −13.6280 + 7.86814i −0.469652 + 0.271154i
\(843\) 3.79779 3.79779i 0.130803 0.130803i
\(844\) 13.4312 7.75451i 0.462321 0.266921i
\(845\) −17.0922 21.2528i −0.587991 0.731120i
\(846\) 5.73048i 0.197018i
\(847\) −10.3532 8.33178i −0.355740 0.286283i
\(848\) 0.727766 1.26053i 0.0249916 0.0432867i
\(849\) 1.38508i 0.0475358i
\(850\) 0.798532 2.98016i 0.0273894 0.102219i
\(851\) 7.03952 + 26.2718i 0.241312 + 0.900587i
\(852\) −9.54821 + 9.54821i −0.327116 + 0.327116i
\(853\) 25.2631 25.2631i 0.864993 0.864993i −0.126920 0.991913i \(-0.540509\pi\)
0.991913 + 0.126920i \(0.0405091\pi\)
\(854\) −11.5349 15.7752i −0.394717 0.539817i
\(855\) 14.5588 + 8.40550i 0.497899 + 0.287462i
\(856\) −1.38867 + 5.18260i −0.0474639 + 0.177138i
\(857\) 3.17108 + 5.49248i 0.108322 + 0.187619i 0.915091 0.403248i \(-0.132119\pi\)
−0.806769 + 0.590868i \(0.798786\pi\)
\(858\) −0.374439 + 6.92210i −0.0127831 + 0.236316i
\(859\) 12.1601 + 7.02065i 0.414898 + 0.239541i 0.692892 0.721041i \(-0.256336\pi\)
−0.277994 + 0.960583i \(0.589670\pi\)
\(860\) −2.62010 + 0.702054i −0.0893448 + 0.0239399i
\(861\) −27.5707 12.1748i −0.939607 0.414916i
\(862\) −8.98196 + 5.18573i −0.305927 + 0.176627i
\(863\) −8.99722 33.5781i −0.306269 1.14301i −0.931848 0.362850i \(-0.881804\pi\)
0.625579 0.780161i \(-0.284863\pi\)
\(864\) 5.64767 1.51329i 0.192138 0.0514832i
\(865\) 42.4768 11.3816i 1.44425 0.386987i
\(866\) −2.25470 8.41464i −0.0766177 0.285941i
\(867\) −22.4707 + 12.9735i −0.763144 + 0.440602i
\(868\) −0.186015 1.71943i −0.00631376 0.0583612i
\(869\) −5.07911 + 1.36094i −0.172297 + 0.0461668i
\(870\) −3.58420 2.06934i −0.121516 0.0701572i
\(871\) 8.57677 + 40.6867i 0.290613 + 1.37861i
\(872\) 7.48873 + 12.9709i 0.253600 + 0.439249i
\(873\) 4.17950 15.5981i 0.141454 0.527915i
\(874\) 20.9902 + 12.1187i 0.710004 + 0.409921i
\(875\) 3.34243 + 30.8957i 0.112995 + 1.04447i
\(876\) −9.91093 + 9.91093i −0.334859 + 0.334859i
\(877\) 19.7076 19.7076i 0.665480 0.665480i −0.291186 0.956666i \(-0.594050\pi\)
0.956666 + 0.291186i \(0.0940500\pi\)
\(878\) −2.69346 10.0521i −0.0909000 0.339244i
\(879\) 4.64324 17.3288i 0.156613 0.584486i
\(880\) 3.44538i 0.116144i
\(881\) −4.46832 + 7.73936i −0.150542 + 0.260746i −0.931427 0.363929i \(-0.881435\pi\)
0.780885 + 0.624675i \(0.214768\pi\)
\(882\) 0.254618 5.49906i 0.00857345 0.185163i
\(883\) 17.8140i 0.599488i −0.954020 0.299744i \(-0.903099\pi\)
0.954020 0.299744i \(-0.0969012\pi\)
\(884\) 1.76323 32.5962i 0.0593039 1.09633i
\(885\) 10.0933 5.82735i 0.339281 0.195884i
\(886\) −2.73128 + 2.73128i −0.0917592 + 0.0917592i
\(887\) −37.5260 + 21.6656i −1.26000 + 0.727461i −0.973074 0.230492i \(-0.925966\pi\)
−0.286925 + 0.957953i \(0.592633\pi\)
\(888\) 9.40280 + 16.2861i 0.315537 + 0.546526i
\(889\) −25.7947 + 9.99188i −0.865125 + 0.335117i
\(890\) −10.0361 2.68916i −0.336410 0.0901407i
\(891\) −1.72874 1.72874i −0.0579150 0.0579150i
\(892\) 13.5665 + 3.63513i 0.454239 + 0.121713i
\(893\) 29.1948 50.5669i 0.976968 1.69216i
\(894\) −1.85028 3.20478i −0.0618826 0.107184i
\(895\) −5.23926 19.5532i −0.175129 0.653591i
\(896\) 14.2645 + 19.5082i 0.476543 + 0.651722i
\(897\) 13.8474 + 0.749048i 0.462350 + 0.0250100i
\(898\) −0.374035 + 0.647848i −0.0124817 + 0.0216190i
\(899\) −0.839259 0.839259i −0.0279909 0.0279909i
\(900\) −0.827063 −0.0275688
\(901\) −14.2000 −0.473071
\(902\) 15.4870 + 15.4870i 0.515661 + 0.515661i
\(903\) −2.44678 0.379897i −0.0814236 0.0126422i
\(904\) 8.54362 31.8852i 0.284157 1.06049i
\(905\) −2.54860 + 0.682894i −0.0847182 + 0.0227002i
\(906\) −0.397641 0.229578i −0.0132107 0.00762723i
\(907\) 35.5242i 1.17956i 0.807563 + 0.589781i \(0.200786\pi\)
−0.807563 + 0.589781i \(0.799214\pi\)
\(908\) 8.78592 + 2.35418i 0.291571 + 0.0781262i
\(909\) 3.53983 0.117409
\(910\) −4.88395 14.9617i −0.161901 0.495977i
\(911\) −56.1740 −1.86113 −0.930564 0.366130i \(-0.880682\pi\)
−0.930564 + 0.366130i \(0.880682\pi\)
\(912\) −5.19929 1.39315i −0.172166 0.0461316i
\(913\) 5.27045i 0.174427i
\(914\) −13.1034 7.56528i −0.433424 0.250237i
\(915\) 19.0333 5.09995i 0.629221 0.168599i
\(916\) 0.444427 1.65863i 0.0146843 0.0548025i
\(917\) 51.4718 19.9382i 1.69975 0.658418i
\(918\) −3.64424 3.64424i −0.120278 0.120278i
\(919\) −42.4656 −1.40081 −0.700405 0.713746i \(-0.746997\pi\)
−0.700405 + 0.713746i \(0.746997\pi\)
\(920\) 21.4582 0.707455
\(921\) −5.47242 5.47242i −0.180322 0.180322i
\(922\) 2.53513 4.39098i 0.0834902 0.144609i
\(923\) −26.2286 + 23.5366i −0.863324 + 0.774717i
\(924\) 3.60984 8.17475i 0.118755 0.268929i
\(925\) −1.09569 4.08917i −0.0360261 0.134451i
\(926\) −4.27066 7.39700i −0.140343 0.243080i
\(927\) −4.58234 + 7.93684i −0.150504 + 0.260680i
\(928\) 14.1672 + 3.79608i 0.465060 + 0.124612i
\(929\) 20.4024 + 20.4024i 0.669380 + 0.669380i 0.957573 0.288192i \(-0.0930542\pi\)
−0.288192 + 0.957573i \(0.593054\pi\)
\(930\) −0.754032 0.202042i −0.0247257 0.00662523i
\(931\) −30.2627 + 47.2277i −0.991818 + 1.54782i
\(932\) 10.1242 + 17.5357i 0.331630 + 0.574400i
\(933\) −5.66998 + 3.27357i −0.185627 + 0.107172i
\(934\) −11.9266 + 11.9266i −0.390251 + 0.390251i
\(935\) −29.1095 + 16.8064i −0.951982 + 0.549627i
\(936\) 9.38211 1.97776i 0.306664 0.0646449i
\(937\) 15.4230i 0.503847i 0.967747 + 0.251923i \(0.0810631\pi\)
−0.967747 + 0.251923i \(0.918937\pi\)
\(938\) −3.68150 + 23.7112i −0.120205 + 0.774198i
\(939\) −8.57583 + 14.8538i −0.279862 + 0.484735i
\(940\) 21.1199i 0.688855i
\(941\) 8.53393 31.8491i 0.278198 1.03825i −0.675470 0.737388i \(-0.736059\pi\)
0.953668 0.300862i \(-0.0972743\pi\)
\(942\) −2.25955 8.43277i −0.0736203 0.274755i
\(943\) 30.9811 30.9811i 1.00888 1.00888i
\(944\) −2.63872 + 2.63872i −0.0858829 + 0.0858829i
\(945\) 5.07760 + 2.24219i 0.165174 + 0.0729384i
\(946\) 1.55829 + 0.899681i 0.0506645 + 0.0292511i
\(947\) −6.40405 + 23.9002i −0.208104 + 0.776654i 0.780377 + 0.625309i \(0.215027\pi\)
−0.988481 + 0.151345i \(0.951640\pi\)
\(948\) 1.48570 + 2.57332i 0.0482534 + 0.0835774i
\(949\) −27.2249 + 24.4307i −0.883759 + 0.793055i
\(950\) −3.26709 1.88626i −0.105998 0.0611983i
\(951\) 15.5081 4.15537i 0.502883 0.134747i
\(952\) 18.6258 42.1795i 0.603667 1.36705i
\(953\) 38.7397 22.3663i 1.25490 0.724517i 0.282822 0.959172i \(-0.408729\pi\)
0.972079 + 0.234655i \(0.0753962\pi\)
\(954\) −0.441036 1.64597i −0.0142791 0.0532902i
\(955\) 4.95472 1.32761i 0.160331 0.0429606i
\(956\) 9.16704 2.45630i 0.296483 0.0794425i
\(957\) −1.58728 5.92382i −0.0513096 0.191490i
\(958\) 12.3291 7.11824i 0.398337 0.229980i
\(959\) −12.0490 + 27.2859i −0.389083 + 0.881106i
\(960\) 6.59541 1.76723i 0.212866 0.0570373i
\(961\) 26.6529 + 15.3881i 0.859771 + 0.496389i
\(962\) 9.07309 + 17.8812i 0.292528 + 0.576512i
\(963\) −1.00880 1.74729i −0.0325080 0.0563055i
\(964\) 6.83464 25.5072i 0.220129 0.821532i
\(965\) 31.2695 + 18.0534i 1.00660 + 0.581161i
\(966\) 7.32067 + 3.23270i 0.235539 + 0.104010i
\(967\) −7.27104 + 7.27104i −0.233821 + 0.233821i −0.814285 0.580465i \(-0.802871\pi\)
0.580465 + 0.814285i \(0.302871\pi\)
\(968\) 9.44518 9.44518i 0.303580 0.303580i
\(969\) 13.5914 + 50.7236i 0.436617 + 1.62948i
\(970\) 6.89560 25.7347i 0.221404 0.826293i
\(971\) 21.8367i 0.700773i 0.936605 + 0.350387i \(0.113950\pi\)
−0.936605 + 0.350387i \(0.886050\pi\)
\(972\) −0.690770 + 1.19645i −0.0221565 + 0.0383761i
\(973\) 4.14030 26.6662i 0.132732 0.854878i
\(974\) 5.66316i 0.181459i
\(975\) −2.15532 0.116588i −0.0690255 0.00373381i
\(976\) −5.46396 + 3.15462i −0.174897 + 0.100977i
\(977\) 2.67081 2.67081i 0.0854467 0.0854467i −0.663092 0.748538i \(-0.730756\pi\)
0.748538 + 0.663092i \(0.230756\pi\)
\(978\) 11.2220 6.47904i 0.358841 0.207177i
\(979\) −7.69815 13.3336i −0.246034 0.426143i
\(980\) −0.938407 + 20.2670i −0.0299763 + 0.647406i
\(981\) −5.44016 1.45769i −0.173691 0.0465404i
\(982\) 15.6653 + 15.6653i 0.499901 + 0.499901i
\(983\) 45.7327 + 12.2540i 1.45865 + 0.390843i 0.899022 0.437903i \(-0.144279\pi\)
0.559625 + 0.828746i \(0.310945\pi\)
\(984\) 15.1468 26.2351i 0.482864 0.836345i
\(985\) 24.5549 + 42.5303i 0.782383 + 1.35513i
\(986\) −3.34604 12.4876i −0.106560 0.397686i
\(987\) 7.78780 17.6360i 0.247888 0.561361i
\(988\) −37.9406 12.3982i −1.20705 0.394439i
\(989\) 1.79977 3.11730i 0.0572294 0.0991243i
\(990\) −2.85219 2.85219i −0.0906485 0.0906485i
\(991\) −10.4973 −0.333459 −0.166729 0.986003i \(-0.553321\pi\)
−0.166729 + 0.986003i \(0.553321\pi\)
\(992\) 2.76646 0.0878351
\(993\) 4.03496 + 4.03496i 0.128046 + 0.128046i
\(994\) −18.9635 + 7.34576i −0.601487 + 0.232993i
\(995\) −10.1221 + 37.7762i −0.320892 + 1.19759i
\(996\) 2.87681 0.770838i 0.0911551 0.0244249i
\(997\) 32.1168 + 18.5426i 1.01715 + 0.587251i 0.913277 0.407339i \(-0.133543\pi\)
0.103872 + 0.994591i \(0.466877\pi\)
\(998\) 16.5444i 0.523702i
\(999\) −6.83063 1.83026i −0.216112 0.0579069i
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 273.2.cg.a.19.4 yes 36
3.2 odd 2 819.2.gh.c.19.6 36
7.3 odd 6 273.2.bt.a.136.6 36
13.11 odd 12 273.2.bt.a.271.6 yes 36
21.17 even 6 819.2.et.c.136.4 36
39.11 even 12 819.2.et.c.271.4 36
91.24 even 12 inner 273.2.cg.a.115.4 yes 36
273.206 odd 12 819.2.gh.c.388.6 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.a.136.6 36 7.3 odd 6
273.2.bt.a.271.6 yes 36 13.11 odd 12
273.2.cg.a.19.4 yes 36 1.1 even 1 trivial
273.2.cg.a.115.4 yes 36 91.24 even 12 inner
819.2.et.c.136.4 36 21.17 even 6
819.2.et.c.271.4 36 39.11 even 12
819.2.gh.c.19.6 36 3.2 odd 2
819.2.gh.c.388.6 36 273.206 odd 12