Properties

Label 91.2.bb.a.5.1
Level $91$
Weight $2$
Character 91.5
Analytic conductor $0.727$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(5,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.bb (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 91.5
Dual form 91.2.bb.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.639966 - 2.38839i) q^{2} +(-1.77043 + 1.02216i) q^{3} +(-3.56278 + 2.05697i) q^{4} +(-1.58199 + 0.423894i) q^{5} +(3.57432 + 3.57432i) q^{6} +(-2.54693 - 0.716327i) q^{7} +(3.69606 + 3.69606i) q^{8} +(0.589612 - 1.02124i) q^{9} +O(q^{10})\) \(q+(-0.639966 - 2.38839i) q^{2} +(-1.77043 + 1.02216i) q^{3} +(-3.56278 + 2.05697i) q^{4} +(-1.58199 + 0.423894i) q^{5} +(3.57432 + 3.57432i) q^{6} +(-2.54693 - 0.716327i) q^{7} +(3.69606 + 3.69606i) q^{8} +(0.589612 - 1.02124i) q^{9} +(2.02484 + 3.50713i) q^{10} +(1.48887 - 5.55653i) q^{11} +(4.20510 - 7.28345i) q^{12} +(-3.57432 + 0.473526i) q^{13} +(-0.0809133 + 6.54149i) q^{14} +(2.36752 - 2.36752i) q^{15} +(2.34832 - 4.06741i) q^{16} +(0.991968 + 1.71814i) q^{17} +(-2.81644 - 0.754664i) q^{18} +(-0.918664 + 0.246155i) q^{19} +(4.76435 - 4.76435i) q^{20} +(5.24137 - 1.33516i) q^{21} -14.2240 q^{22} +(-3.06647 - 1.77043i) q^{23} +(-10.3216 - 2.76566i) q^{24} +(-2.00711 + 1.15881i) q^{25} +(3.41841 + 8.23382i) q^{26} -3.72224i q^{27} +(10.5476 - 2.68686i) q^{28} +2.83949 q^{29} +(-7.16968 - 4.13942i) q^{30} +(1.16048 - 4.33096i) q^{31} +(-1.11958 - 0.299990i) q^{32} +(3.04372 + 11.3593i) q^{33} +(3.46875 - 3.46875i) q^{34} +(4.33288 + 0.0535944i) q^{35} +4.85126i q^{36} +(-3.73806 + 1.00161i) q^{37} +(1.17583 + 2.03659i) q^{38} +(5.84406 - 4.49186i) q^{39} +(-7.41388 - 4.28040i) q^{40} +(4.02565 + 4.02565i) q^{41} +(-6.54318 - 11.6639i) q^{42} +5.30948i q^{43} +(6.12512 + 22.8593i) q^{44} +(-0.499866 + 1.86552i) q^{45} +(-2.26603 + 8.45694i) q^{46} +(0.120170 + 0.448482i) q^{47} +9.60143i q^{48} +(5.97375 + 3.64888i) q^{49} +(4.05216 + 4.05216i) q^{50} +(-3.51242 - 2.02789i) q^{51} +(11.7605 - 9.03935i) q^{52} +(-6.31835 - 10.9437i) q^{53} +(-8.89014 + 2.38211i) q^{54} +9.42152i q^{55} +(-6.76604 - 12.0612i) q^{56} +(1.37482 - 1.37482i) q^{57} +(-1.81718 - 6.78181i) q^{58} +(-11.5955 - 3.10701i) q^{59} +(-3.56503 + 13.3049i) q^{60} +(-4.38137 - 2.52958i) q^{61} -11.0867 q^{62} +(-2.23324 + 2.17867i) q^{63} -6.52733i q^{64} +(5.45382 - 2.26425i) q^{65} +(25.1825 - 14.5391i) q^{66} +(5.87066 + 1.57304i) q^{67} +(-7.06833 - 4.08090i) q^{68} +7.23863 q^{69} +(-2.64489 - 10.3829i) q^{70} +(-4.84596 + 4.84596i) q^{71} +(5.95380 - 1.59532i) q^{72} +(-4.24311 - 1.13694i) q^{73} +(4.78447 + 8.28694i) q^{74} +(2.36897 - 4.10317i) q^{75} +(2.76666 - 2.76666i) q^{76} +(-7.77235 + 13.0856i) q^{77} +(-14.4683 - 11.0832i) q^{78} +(-3.08258 + 5.33918i) q^{79} +(-1.99088 + 7.43006i) q^{80} +(5.57355 + 9.65367i) q^{81} +(7.03853 - 12.1911i) q^{82} +(-11.5176 - 11.5176i) q^{83} +(-15.9274 + 15.5382i) q^{84} +(-2.29759 - 2.29759i) q^{85} +(12.6811 - 3.39789i) q^{86} +(-5.02712 + 2.90241i) q^{87} +(26.0402 - 15.0343i) q^{88} +(-0.941005 - 3.51188i) q^{89} +4.77549 q^{90} +(9.44276 + 1.35434i) q^{91} +14.5669 q^{92} +(2.37238 + 8.85384i) q^{93} +(0.994243 - 0.574027i) q^{94} +(1.34898 - 0.778832i) q^{95} +(2.28877 - 0.613273i) q^{96} +(7.09855 + 7.09855i) q^{97} +(4.89192 - 16.6028i) q^{98} +(-4.79669 - 4.79669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9} - 10 q^{11} + 28 q^{14} - 44 q^{15} + 12 q^{16} - 4 q^{18} + 12 q^{19} - 26 q^{21} - 8 q^{22} - 12 q^{24} + 24 q^{26} - 6 q^{28} + 16 q^{29} + 24 q^{31} + 4 q^{32} + 48 q^{33} + 28 q^{35} - 8 q^{37} - 6 q^{39} - 132 q^{40} - 16 q^{42} - 42 q^{44} - 24 q^{45} + 12 q^{46} + 30 q^{47} + 88 q^{50} + 36 q^{52} - 12 q^{53} + 78 q^{54} + 40 q^{57} + 26 q^{58} - 54 q^{59} + 16 q^{60} - 48 q^{61} + 24 q^{63} - 8 q^{65} + 12 q^{66} + 16 q^{67} - 48 q^{68} + 50 q^{70} - 36 q^{71} + 22 q^{72} + 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} + 138 q^{80} + 16 q^{81} - 58 q^{84} - 84 q^{85} + 42 q^{86} - 24 q^{87} - 60 q^{89} + 48 q^{92} + 6 q^{93} - 72 q^{94} - 42 q^{96} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.639966 2.38839i −0.452524 1.68884i −0.695266 0.718753i \(-0.744713\pi\)
0.242741 0.970091i \(-0.421953\pi\)
\(3\) −1.77043 + 1.02216i −1.02216 + 0.590143i −0.914728 0.404070i \(-0.867595\pi\)
−0.107429 + 0.994213i \(0.534262\pi\)
\(4\) −3.56278 + 2.05697i −1.78139 + 1.02849i
\(5\) −1.58199 + 0.423894i −0.707488 + 0.189571i −0.594582 0.804035i \(-0.702683\pi\)
−0.112906 + 0.993606i \(0.536016\pi\)
\(6\) 3.57432 + 3.57432i 1.45921 + 1.45921i
\(7\) −2.54693 0.716327i −0.962651 0.270746i
\(8\) 3.69606 + 3.69606i 1.30676 + 1.30676i
\(9\) 0.589612 1.02124i 0.196537 0.340413i
\(10\) 2.02484 + 3.50713i 0.640311 + 1.10905i
\(11\) 1.48887 5.55653i 0.448911 1.67536i −0.256488 0.966547i \(-0.582565\pi\)
0.705399 0.708811i \(-0.250768\pi\)
\(12\) 4.20510 7.28345i 1.21391 2.10255i
\(13\) −3.57432 + 0.473526i −0.991338 + 0.131333i
\(14\) −0.0809133 + 6.54149i −0.0216250 + 1.74829i
\(15\) 2.36752 2.36752i 0.611291 0.611291i
\(16\) 2.34832 4.06741i 0.587081 1.01685i
\(17\) 0.991968 + 1.71814i 0.240588 + 0.416710i 0.960882 0.276959i \(-0.0893266\pi\)
−0.720294 + 0.693669i \(0.755993\pi\)
\(18\) −2.81644 0.754664i −0.663842 0.177876i
\(19\) −0.918664 + 0.246155i −0.210756 + 0.0564719i −0.362652 0.931925i \(-0.618129\pi\)
0.151896 + 0.988396i \(0.451462\pi\)
\(20\) 4.76435 4.76435i 1.06534 1.06534i
\(21\) 5.24137 1.33516i 1.14376 0.291356i
\(22\) −14.2240 −3.03256
\(23\) −3.06647 1.77043i −0.639404 0.369160i 0.144981 0.989434i \(-0.453688\pi\)
−0.784385 + 0.620274i \(0.787021\pi\)
\(24\) −10.3216 2.76566i −2.10688 0.564537i
\(25\) −2.00711 + 1.15881i −0.401423 + 0.231761i
\(26\) 3.41841 + 8.23382i 0.670405 + 1.61478i
\(27\) 3.72224i 0.716345i
\(28\) 10.5476 2.68686i 1.99331 0.507768i
\(29\) 2.83949 0.527281 0.263640 0.964621i \(-0.415077\pi\)
0.263640 + 0.964621i \(0.415077\pi\)
\(30\) −7.16968 4.13942i −1.30900 0.755751i
\(31\) 1.16048 4.33096i 0.208428 0.777863i −0.779950 0.625842i \(-0.784755\pi\)
0.988377 0.152021i \(-0.0485780\pi\)
\(32\) −1.11958 0.299990i −0.197915 0.0530312i
\(33\) 3.04372 + 11.3593i 0.529843 + 1.97740i
\(34\) 3.46875 3.46875i 0.594886 0.594886i
\(35\) 4.33288 + 0.0535944i 0.732390 + 0.00905911i
\(36\) 4.85126i 0.808544i
\(37\) −3.73806 + 1.00161i −0.614534 + 0.164664i −0.552642 0.833419i \(-0.686380\pi\)
−0.0618923 + 0.998083i \(0.519714\pi\)
\(38\) 1.17583 + 2.03659i 0.190745 + 0.330379i
\(39\) 5.84406 4.49186i 0.935799 0.719274i
\(40\) −7.41388 4.28040i −1.17224 0.676791i
\(41\) 4.02565 + 4.02565i 0.628701 + 0.628701i 0.947741 0.319040i \(-0.103360\pi\)
−0.319040 + 0.947741i \(0.603360\pi\)
\(42\) −6.54318 11.6639i −1.00963 1.79979i
\(43\) 5.30948i 0.809688i 0.914386 + 0.404844i \(0.132674\pi\)
−0.914386 + 0.404844i \(0.867326\pi\)
\(44\) 6.12512 + 22.8593i 0.923397 + 3.44616i
\(45\) −0.499866 + 1.86552i −0.0745156 + 0.278096i
\(46\) −2.26603 + 8.45694i −0.334108 + 1.24691i
\(47\) 0.120170 + 0.448482i 0.0175287 + 0.0654178i 0.974136 0.225962i \(-0.0725524\pi\)
−0.956608 + 0.291380i \(0.905886\pi\)
\(48\) 9.60143i 1.38585i
\(49\) 5.97375 + 3.64888i 0.853393 + 0.521268i
\(50\) 4.05216 + 4.05216i 0.573062 + 0.573062i
\(51\) −3.51242 2.02789i −0.491837 0.283962i
\(52\) 11.7605 9.03935i 1.63089 1.25353i
\(53\) −6.31835 10.9437i −0.867891 1.50323i −0.864147 0.503239i \(-0.832141\pi\)
−0.00374432 0.999993i \(-0.501192\pi\)
\(54\) −8.89014 + 2.38211i −1.20980 + 0.324164i
\(55\) 9.42152i 1.27040i
\(56\) −6.76604 12.0612i −0.904150 1.61175i
\(57\) 1.37482 1.37482i 0.182099 0.182099i
\(58\) −1.81718 6.78181i −0.238607 0.890495i
\(59\) −11.5955 3.10701i −1.50961 0.404499i −0.593304 0.804979i \(-0.702177\pi\)
−0.916305 + 0.400480i \(0.868843\pi\)
\(60\) −3.56503 + 13.3049i −0.460243 + 1.71765i
\(61\) −4.38137 2.52958i −0.560977 0.323880i 0.192561 0.981285i \(-0.438321\pi\)
−0.753537 + 0.657405i \(0.771654\pi\)
\(62\) −11.0867 −1.40801
\(63\) −2.23324 + 2.17867i −0.281362 + 0.274487i
\(64\) 6.52733i 0.815916i
\(65\) 5.45382 2.26425i 0.676464 0.280845i
\(66\) 25.1825 14.5391i 3.09976 1.78965i
\(67\) 5.87066 + 1.57304i 0.717215 + 0.192177i 0.598929 0.800802i \(-0.295593\pi\)
0.118286 + 0.992980i \(0.462260\pi\)
\(68\) −7.06833 4.08090i −0.857160 0.494882i
\(69\) 7.23863 0.871429
\(70\) −2.64489 10.3829i −0.316125 1.24099i
\(71\) −4.84596 + 4.84596i −0.575110 + 0.575110i −0.933552 0.358442i \(-0.883308\pi\)
0.358442 + 0.933552i \(0.383308\pi\)
\(72\) 5.95380 1.59532i 0.701663 0.188010i
\(73\) −4.24311 1.13694i −0.496619 0.133069i 0.00181149 0.999998i \(-0.499423\pi\)
−0.498430 + 0.866930i \(0.666090\pi\)
\(74\) 4.78447 + 8.28694i 0.556183 + 0.963338i
\(75\) 2.36897 4.10317i 0.273545 0.473794i
\(76\) 2.76666 2.76666i 0.317358 0.317358i
\(77\) −7.77235 + 13.0856i −0.885741 + 1.49124i
\(78\) −14.4683 11.0832i −1.63821 1.25493i
\(79\) −3.08258 + 5.33918i −0.346817 + 0.600704i −0.985682 0.168614i \(-0.946071\pi\)
0.638865 + 0.769319i \(0.279404\pi\)
\(80\) −1.99088 + 7.43006i −0.222587 + 0.830706i
\(81\) 5.57355 + 9.65367i 0.619284 + 1.07263i
\(82\) 7.03853 12.1911i 0.777276 1.34628i
\(83\) −11.5176 11.5176i −1.26422 1.26422i −0.949027 0.315194i \(-0.897930\pi\)
−0.315194 0.949027i \(-0.602070\pi\)
\(84\) −15.9274 + 15.5382i −1.73783 + 1.69536i
\(85\) −2.29759 2.29759i −0.249209 0.249209i
\(86\) 12.6811 3.39789i 1.36744 0.366403i
\(87\) −5.02712 + 2.90241i −0.538964 + 0.311171i
\(88\) 26.0402 15.0343i 2.77590 1.60267i
\(89\) −0.941005 3.51188i −0.0997463 0.372258i 0.897950 0.440098i \(-0.145056\pi\)
−0.997696 + 0.0678393i \(0.978389\pi\)
\(90\) 4.77549 0.503381
\(91\) 9.44276 + 1.35434i 0.989870 + 0.141974i
\(92\) 14.5669 1.51870
\(93\) 2.37238 + 8.85384i 0.246004 + 0.918101i
\(94\) 0.994243 0.574027i 0.102548 0.0592063i
\(95\) 1.34898 0.778832i 0.138402 0.0799065i
\(96\) 2.28877 0.613273i 0.233596 0.0625919i
\(97\) 7.09855 + 7.09855i 0.720749 + 0.720749i 0.968758 0.248009i \(-0.0797763\pi\)
−0.248009 + 0.968758i \(0.579776\pi\)
\(98\) 4.89192 16.6028i 0.494159 1.67713i
\(99\) −4.79669 4.79669i −0.482086 0.482086i
\(100\) 4.76727 8.25715i 0.476727 0.825715i
\(101\) −2.12979 3.68890i −0.211922 0.367059i 0.740394 0.672173i \(-0.234639\pi\)
−0.952316 + 0.305114i \(0.901306\pi\)
\(102\) −2.59557 + 9.68679i −0.257000 + 0.959135i
\(103\) −2.08562 + 3.61240i −0.205502 + 0.355940i −0.950293 0.311358i \(-0.899216\pi\)
0.744790 + 0.667298i \(0.232549\pi\)
\(104\) −14.9611 11.4607i −1.46706 1.12382i
\(105\) −7.72583 + 4.33400i −0.753964 + 0.422955i
\(106\) −22.0942 + 22.0942i −2.14598 + 2.14598i
\(107\) 1.91482 3.31657i 0.185113 0.320625i −0.758502 0.651671i \(-0.774068\pi\)
0.943615 + 0.331046i \(0.107402\pi\)
\(108\) 7.65654 + 13.2615i 0.736751 + 1.27609i
\(109\) 1.38124 + 0.370102i 0.132299 + 0.0354494i 0.324361 0.945933i \(-0.394851\pi\)
−0.192062 + 0.981383i \(0.561517\pi\)
\(110\) 22.5022 6.02945i 2.14550 0.574886i
\(111\) 5.59417 5.59417i 0.530975 0.530975i
\(112\) −8.89462 + 8.67727i −0.840463 + 0.819925i
\(113\) 15.2149 1.43129 0.715647 0.698462i \(-0.246132\pi\)
0.715647 + 0.698462i \(0.246132\pi\)
\(114\) −4.16344 2.40376i −0.389942 0.225133i
\(115\) 5.60161 + 1.50095i 0.522353 + 0.139964i
\(116\) −10.1165 + 5.84076i −0.939292 + 0.542301i
\(117\) −1.62388 + 3.92943i −0.150128 + 0.363276i
\(118\) 29.6830i 2.73254i
\(119\) −1.29573 5.08656i −0.118779 0.466284i
\(120\) 17.5010 1.59761
\(121\) −19.1321 11.0459i −1.73928 1.00417i
\(122\) −3.23769 + 12.0832i −0.293127 + 1.09397i
\(123\) −11.2420 3.01228i −1.01366 0.271608i
\(124\) 4.77414 + 17.8173i 0.428730 + 1.60004i
\(125\) 8.47452 8.47452i 0.757984 0.757984i
\(126\) 6.63271 + 3.93957i 0.590889 + 0.350965i
\(127\) 6.12999i 0.543949i −0.962304 0.271974i \(-0.912323\pi\)
0.962304 0.271974i \(-0.0876766\pi\)
\(128\) −17.8289 + 4.77725i −1.57587 + 0.422253i
\(129\) −5.42712 9.40005i −0.477832 0.827629i
\(130\) −8.89816 11.5768i −0.780420 1.01535i
\(131\) 1.30691 + 0.754542i 0.114185 + 0.0659247i 0.556005 0.831179i \(-0.312334\pi\)
−0.441820 + 0.897104i \(0.645667\pi\)
\(132\) −34.2099 34.2099i −2.97759 2.97759i
\(133\) 2.51611 + 0.0311223i 0.218174 + 0.00269865i
\(134\) 15.0281i 1.29823i
\(135\) 1.57783 + 5.88855i 0.135798 + 0.506806i
\(136\) −2.68397 + 10.0167i −0.230149 + 0.858927i
\(137\) 1.76458 6.58552i 0.150759 0.562639i −0.848673 0.528918i \(-0.822598\pi\)
0.999431 0.0337203i \(-0.0107356\pi\)
\(138\) −4.63248 17.2886i −0.394343 1.47171i
\(139\) 6.26924i 0.531750i −0.964007 0.265875i \(-0.914339\pi\)
0.964007 0.265875i \(-0.0856609\pi\)
\(140\) −15.5473 + 8.72166i −1.31399 + 0.737115i
\(141\) −0.671172 0.671172i −0.0565229 0.0565229i
\(142\) 14.6753 + 8.47278i 1.23152 + 0.711020i
\(143\) −2.69053 + 20.5659i −0.224994 + 1.71980i
\(144\) −2.76920 4.79640i −0.230767 0.399700i
\(145\) −4.49206 + 1.20364i −0.373045 + 0.0999571i
\(146\) 10.8618i 0.898929i
\(147\) −14.3058 0.353959i −1.17992 0.0291940i
\(148\) 11.2576 11.2576i 0.925370 0.925370i
\(149\) −0.700828 2.61553i −0.0574141 0.214272i 0.931259 0.364358i \(-0.118712\pi\)
−0.988673 + 0.150086i \(0.952045\pi\)
\(150\) −11.3160 3.03212i −0.923949 0.247571i
\(151\) −0.0731992 + 0.273183i −0.00595686 + 0.0222313i −0.968840 0.247686i \(-0.920330\pi\)
0.962883 + 0.269918i \(0.0869965\pi\)
\(152\) −4.30525 2.48563i −0.349202 0.201612i
\(153\) 2.33951 0.189138
\(154\) 36.2275 + 10.1890i 2.91930 + 0.821054i
\(155\) 7.34346i 0.589841i
\(156\) −11.5815 + 28.0246i −0.927260 + 2.24376i
\(157\) −0.885412 + 0.511193i −0.0706636 + 0.0407976i −0.534916 0.844906i \(-0.679657\pi\)
0.464252 + 0.885703i \(0.346323\pi\)
\(158\) 14.7248 + 3.94549i 1.17144 + 0.313886i
\(159\) 22.3724 + 12.9167i 1.77424 + 1.02436i
\(160\) 1.89832 0.150076
\(161\) 6.54190 + 6.70576i 0.515574 + 0.528488i
\(162\) 19.4898 19.4898i 1.53126 1.53126i
\(163\) 16.3776 4.38836i 1.28279 0.343723i 0.447874 0.894097i \(-0.352181\pi\)
0.834918 + 0.550374i \(0.185515\pi\)
\(164\) −22.6232 6.06186i −1.76657 0.473352i
\(165\) −9.63028 16.6801i −0.749716 1.29855i
\(166\) −20.1376 + 34.8794i −1.56298 + 2.70716i
\(167\) 0.350041 0.350041i 0.0270870 0.0270870i −0.693434 0.720521i \(-0.743903\pi\)
0.720521 + 0.693434i \(0.243903\pi\)
\(168\) 24.3073 + 14.4376i 1.87535 + 1.11388i
\(169\) 12.5515 3.38507i 0.965504 0.260390i
\(170\) −4.01716 + 6.95792i −0.308102 + 0.533648i
\(171\) −0.290273 + 1.08331i −0.0221977 + 0.0828429i
\(172\) −10.9214 18.9165i −0.832753 1.44237i
\(173\) 1.98781 3.44298i 0.151130 0.261765i −0.780513 0.625139i \(-0.785042\pi\)
0.931643 + 0.363374i \(0.118375\pi\)
\(174\) 10.1493 + 10.1493i 0.769413 + 0.769413i
\(175\) 5.94207 1.51366i 0.449178 0.114422i
\(176\) −19.1044 19.1044i −1.44005 1.44005i
\(177\) 23.7049 6.35171i 1.78177 0.477424i
\(178\) −7.78551 + 4.49497i −0.583549 + 0.336912i
\(179\) −5.57272 + 3.21741i −0.416524 + 0.240481i −0.693589 0.720371i \(-0.743972\pi\)
0.277065 + 0.960851i \(0.410638\pi\)
\(180\) −2.05642 7.67466i −0.153276 0.572036i
\(181\) −10.7701 −0.800535 −0.400268 0.916398i \(-0.631083\pi\)
−0.400268 + 0.916398i \(0.631083\pi\)
\(182\) −2.80836 23.4197i −0.208169 1.73598i
\(183\) 10.3425 0.764542
\(184\) −4.79026 17.8775i −0.353142 1.31795i
\(185\) 5.48901 3.16908i 0.403560 0.232996i
\(186\) 19.6282 11.3323i 1.43921 0.830926i
\(187\) 11.0238 2.95382i 0.806141 0.216005i
\(188\) −1.35066 1.35066i −0.0985067 0.0985067i
\(189\) −2.66634 + 9.48030i −0.193948 + 0.689590i
\(190\) −2.72345 2.72345i −0.197580 0.197580i
\(191\) −1.02334 + 1.77247i −0.0740461 + 0.128252i −0.900671 0.434502i \(-0.856925\pi\)
0.826625 + 0.562753i \(0.190258\pi\)
\(192\) 6.67196 + 11.5562i 0.481507 + 0.833995i
\(193\) −0.744802 + 2.77964i −0.0536120 + 0.200083i −0.987537 0.157386i \(-0.949693\pi\)
0.933925 + 0.357469i \(0.116360\pi\)
\(194\) 12.4112 21.4969i 0.891076 1.54339i
\(195\) −7.34119 + 9.58336i −0.525714 + 0.686278i
\(196\) −28.7888 0.712301i −2.05634 0.0508786i
\(197\) −4.42190 + 4.42190i −0.315047 + 0.315047i −0.846861 0.531814i \(-0.821511\pi\)
0.531814 + 0.846861i \(0.321511\pi\)
\(198\) −8.38663 + 14.5261i −0.596012 + 1.03232i
\(199\) 10.4063 + 18.0243i 0.737687 + 1.27771i 0.953535 + 0.301284i \(0.0974151\pi\)
−0.215848 + 0.976427i \(0.569252\pi\)
\(200\) −11.7014 3.13539i −0.827417 0.221706i
\(201\) −12.0015 + 3.21578i −0.846518 + 0.226824i
\(202\) −7.44753 + 7.44753i −0.524006 + 0.524006i
\(203\) −7.23200 2.03401i −0.507587 0.142759i
\(204\) 16.6853 1.16820
\(205\) −8.07500 4.66210i −0.563982 0.325615i
\(206\) 9.96252 + 2.66945i 0.694122 + 0.185989i
\(207\) −3.61606 + 2.08773i −0.251334 + 0.145108i
\(208\) −6.46763 + 15.6502i −0.448450 + 1.08515i
\(209\) 5.47108i 0.378443i
\(210\) 15.2955 + 15.6787i 1.05549 + 1.08193i
\(211\) −15.4637 −1.06456 −0.532281 0.846568i \(-0.678665\pi\)
−0.532281 + 0.846568i \(0.678665\pi\)
\(212\) 45.0217 + 25.9933i 3.09211 + 1.78523i
\(213\) 3.62610 13.5328i 0.248456 0.927250i
\(214\) −9.14666 2.45084i −0.625253 0.167536i
\(215\) −2.25065 8.39955i −0.153493 0.572845i
\(216\) 13.7576 13.7576i 0.936088 0.936088i
\(217\) −6.05804 + 10.1994i −0.411247 + 0.692379i
\(218\) 3.53579i 0.239474i
\(219\) 8.67426 2.32426i 0.586152 0.157059i
\(220\) −19.3798 33.5668i −1.30659 2.26307i
\(221\) −4.35920 5.67146i −0.293231 0.381503i
\(222\) −16.9411 9.78096i −1.13701 0.656455i
\(223\) −16.7037 16.7037i −1.11856 1.11856i −0.991953 0.126611i \(-0.959590\pi\)
−0.126611 0.991953i \(-0.540410\pi\)
\(224\) 2.63660 + 1.56604i 0.176165 + 0.104635i
\(225\) 2.73299i 0.182199i
\(226\) −9.73700 36.3390i −0.647696 2.41723i
\(227\) 5.55282 20.7234i 0.368553 1.37546i −0.493986 0.869470i \(-0.664461\pi\)
0.862539 0.505990i \(-0.168873\pi\)
\(228\) −2.07022 + 7.72615i −0.137103 + 0.511677i
\(229\) −0.261946 0.977595i −0.0173099 0.0646013i 0.956731 0.290975i \(-0.0939796\pi\)
−0.974041 + 0.226374i \(0.927313\pi\)
\(230\) 14.3394i 0.945509i
\(231\) 0.384829 31.1117i 0.0253199 2.04700i
\(232\) 10.4949 + 10.4949i 0.689027 + 0.689027i
\(233\) −1.88448 1.08800i −0.123456 0.0712775i 0.437000 0.899461i \(-0.356041\pi\)
−0.560456 + 0.828184i \(0.689374\pi\)
\(234\) 10.4242 + 1.36375i 0.681453 + 0.0891512i
\(235\) −0.380217 0.658556i −0.0248026 0.0429594i
\(236\) 47.7034 12.7821i 3.10522 0.832042i
\(237\) 12.6035i 0.818686i
\(238\) −11.3194 + 6.34992i −0.733731 + 0.411604i
\(239\) −8.20062 + 8.20062i −0.530454 + 0.530454i −0.920708 0.390253i \(-0.872387\pi\)
0.390253 + 0.920708i \(0.372387\pi\)
\(240\) −4.06998 15.1894i −0.262716 0.980470i
\(241\) −6.21307 1.66479i −0.400219 0.107238i 0.0530945 0.998589i \(-0.483092\pi\)
−0.453314 + 0.891351i \(0.649758\pi\)
\(242\) −14.1380 + 52.7638i −0.908826 + 3.39178i
\(243\) −10.0645 5.81074i −0.645638 0.372759i
\(244\) 20.8131 1.33242
\(245\) −10.9972 3.24026i −0.702583 0.207012i
\(246\) 28.7780i 1.83482i
\(247\) 3.16704 1.31485i 0.201514 0.0836619i
\(248\) 20.2967 11.7183i 1.28884 0.744112i
\(249\) 32.1639 + 8.61829i 2.03830 + 0.546162i
\(250\) −25.6638 14.8170i −1.62312 0.937111i
\(251\) 1.99071 0.125652 0.0628261 0.998024i \(-0.479989\pi\)
0.0628261 + 0.998024i \(0.479989\pi\)
\(252\) 3.47509 12.3559i 0.218910 0.778346i
\(253\) −14.4030 + 14.4030i −0.905511 + 0.905511i
\(254\) −14.6408 + 3.92299i −0.918645 + 0.246150i
\(255\) 6.41623 + 1.71922i 0.401800 + 0.107662i
\(256\) 16.2925 + 28.2194i 1.01828 + 1.76371i
\(257\) 1.05283 1.82355i 0.0656735 0.113750i −0.831319 0.555796i \(-0.812414\pi\)
0.896993 + 0.442046i \(0.145747\pi\)
\(258\) −18.9778 + 18.9778i −1.18151 + 1.18151i
\(259\) 10.2381 + 0.126637i 0.636164 + 0.00786887i
\(260\) −14.7733 + 19.2854i −0.916200 + 1.19603i
\(261\) 1.67420 2.89980i 0.103630 0.179493i
\(262\) 0.965763 3.60428i 0.0596650 0.222673i
\(263\) 10.1364 + 17.5568i 0.625040 + 1.08260i 0.988533 + 0.151004i \(0.0482507\pi\)
−0.363493 + 0.931597i \(0.618416\pi\)
\(264\) −30.7349 + 53.2345i −1.89160 + 3.27636i
\(265\) 14.6345 + 14.6345i 0.898992 + 0.898992i
\(266\) −1.53589 6.02935i −0.0941715 0.369683i
\(267\) 5.25567 + 5.25567i 0.321642 + 0.321642i
\(268\) −24.1515 + 6.47139i −1.47529 + 0.395303i
\(269\) 1.14303 0.659927i 0.0696916 0.0402365i −0.464749 0.885442i \(-0.653856\pi\)
0.534441 + 0.845206i \(0.320522\pi\)
\(270\) 13.0544 7.53695i 0.794464 0.458684i
\(271\) −7.12464 26.5895i −0.432791 1.61520i −0.746298 0.665611i \(-0.768171\pi\)
0.313508 0.949586i \(-0.398496\pi\)
\(272\) 9.31784 0.564977
\(273\) −18.1021 + 7.25422i −1.09559 + 0.439046i
\(274\) −16.8580 −1.01843
\(275\) 3.45062 + 12.8779i 0.208081 + 0.776567i
\(276\) −25.7896 + 14.8897i −1.55235 + 0.896252i
\(277\) −14.5623 + 8.40757i −0.874966 + 0.505162i −0.868995 0.494820i \(-0.835234\pi\)
−0.00597071 + 0.999982i \(0.501901\pi\)
\(278\) −14.9734 + 4.01210i −0.898043 + 0.240630i
\(279\) −3.73871 3.73871i −0.223831 0.223831i
\(280\) 15.8165 + 16.2127i 0.945216 + 0.968892i
\(281\) −14.9251 14.9251i −0.890356 0.890356i 0.104200 0.994556i \(-0.466772\pi\)
−0.994556 + 0.104200i \(0.966772\pi\)
\(282\) −1.17349 + 2.03255i −0.0698804 + 0.121036i
\(283\) 15.5423 + 26.9201i 0.923895 + 1.60023i 0.793328 + 0.608794i \(0.208346\pi\)
0.130567 + 0.991440i \(0.458320\pi\)
\(284\) 7.29709 27.2331i 0.433003 1.61599i
\(285\) −1.59218 + 2.75773i −0.0943125 + 0.163354i
\(286\) 50.8411 6.73543i 3.00629 0.398274i
\(287\) −7.36939 13.1368i −0.435001 0.775438i
\(288\) −0.966477 + 0.966477i −0.0569502 + 0.0569502i
\(289\) 6.53200 11.3138i 0.384235 0.665515i
\(290\) 5.74953 + 9.95847i 0.337624 + 0.584782i
\(291\) −19.8233 5.31164i −1.16206 0.311374i
\(292\) 17.4559 4.67730i 1.02153 0.273718i
\(293\) −10.7578 + 10.7578i −0.628478 + 0.628478i −0.947685 0.319207i \(-0.896583\pi\)
0.319207 + 0.947685i \(0.396583\pi\)
\(294\) 8.30985 + 34.3944i 0.484641 + 2.00592i
\(295\) 19.6611 1.14471
\(296\) −17.5181 10.1141i −1.01822 0.587870i
\(297\) −20.6827 5.54193i −1.20013 0.321575i
\(298\) −5.79838 + 3.34769i −0.335891 + 0.193927i
\(299\) 11.7989 + 4.87603i 0.682348 + 0.281988i
\(300\) 19.4916i 1.12535i
\(301\) 3.80332 13.5229i 0.219220 0.779447i
\(302\) 0.699311 0.0402408
\(303\) 7.54128 + 4.35396i 0.433235 + 0.250128i
\(304\) −1.15610 + 4.31464i −0.0663072 + 0.247462i
\(305\) 8.00356 + 2.14455i 0.458283 + 0.122796i
\(306\) −1.49720 5.58764i −0.0855895 0.319424i
\(307\) −18.9532 + 18.9532i −1.08172 + 1.08172i −0.0853681 + 0.996349i \(0.527207\pi\)
−0.996349 + 0.0853681i \(0.972793\pi\)
\(308\) 0.774422 62.6087i 0.0441268 3.56746i
\(309\) 8.52732i 0.485102i
\(310\) 17.5390 4.69957i 0.996149 0.266917i
\(311\) −5.62362 9.74040i −0.318886 0.552328i 0.661370 0.750060i \(-0.269976\pi\)
−0.980256 + 0.197733i \(0.936642\pi\)
\(312\) 38.2022 + 4.99781i 2.16277 + 0.282945i
\(313\) 25.3774 + 14.6516i 1.43441 + 0.828159i 0.997453 0.0713218i \(-0.0227217\pi\)
0.436960 + 0.899481i \(0.356055\pi\)
\(314\) 1.78756 + 1.78756i 0.100878 + 0.100878i
\(315\) 2.60945 4.39330i 0.147026 0.247535i
\(316\) 25.3631i 1.42679i
\(317\) 3.93824 + 14.6977i 0.221194 + 0.825507i 0.983894 + 0.178754i \(0.0572067\pi\)
−0.762700 + 0.646752i \(0.776127\pi\)
\(318\) 16.5325 61.7001i 0.927096 3.45997i
\(319\) 4.22763 15.7777i 0.236702 0.883384i
\(320\) 2.76689 + 10.3262i 0.154674 + 0.577251i
\(321\) 7.82900i 0.436972i
\(322\) 11.8294 19.9160i 0.659224 1.10988i
\(323\) −1.33421 1.33421i −0.0742377 0.0742377i
\(324\) −39.7147 22.9293i −2.20637 1.27385i
\(325\) 6.62534 5.09237i 0.367508 0.282474i
\(326\) −20.9622 36.3076i −1.16099 2.01089i
\(327\) −2.82369 + 0.756606i −0.156151 + 0.0418404i
\(328\) 29.7581i 1.64312i
\(329\) 0.0151936 1.22834i 0.000837650 0.0677203i
\(330\) −33.6755 + 33.6755i −1.85378 + 1.85378i
\(331\) 6.65652 + 24.8425i 0.365876 + 1.36547i 0.866230 + 0.499646i \(0.166536\pi\)
−0.500354 + 0.865821i \(0.666797\pi\)
\(332\) 64.7261 + 17.3433i 3.55231 + 0.951837i
\(333\) −1.18113 + 4.40802i −0.0647253 + 0.241558i
\(334\) −1.06005 0.612019i −0.0580032 0.0334882i
\(335\) −9.95413 −0.543852
\(336\) 6.87776 24.4542i 0.375213 1.33409i
\(337\) 3.72672i 0.203008i −0.994835 0.101504i \(-0.967635\pi\)
0.994835 0.101504i \(-0.0323654\pi\)
\(338\) −16.1174 27.8116i −0.876672 1.51275i
\(339\) −26.9369 + 15.5520i −1.46301 + 0.844669i
\(340\) 12.9119 + 3.45973i 0.700246 + 0.187630i
\(341\) −22.3373 12.8965i −1.20963 0.698382i
\(342\) 2.77313 0.149954
\(343\) −12.6010 13.5726i −0.680388 0.732852i
\(344\) −19.6242 + 19.6242i −1.05806 + 1.05806i
\(345\) −11.4515 + 3.06841i −0.616526 + 0.165198i
\(346\) −9.49530 2.54426i −0.510470 0.136780i
\(347\) 6.77145 + 11.7285i 0.363511 + 0.629619i 0.988536 0.150986i \(-0.0482447\pi\)
−0.625025 + 0.780604i \(0.714911\pi\)
\(348\) 11.9404 20.6813i 0.640070 1.10863i
\(349\) 21.5796 21.5796i 1.15513 1.15513i 0.169620 0.985509i \(-0.445746\pi\)
0.985509 0.169620i \(-0.0542541\pi\)
\(350\) −7.41792 13.2233i −0.396505 0.706814i
\(351\) 1.76258 + 13.3045i 0.0940794 + 0.710140i
\(352\) −3.33380 + 5.77432i −0.177692 + 0.307772i
\(353\) −0.717375 + 2.67728i −0.0381820 + 0.142497i −0.982386 0.186865i \(-0.940167\pi\)
0.944204 + 0.329363i \(0.106834\pi\)
\(354\) −30.3407 52.5516i −1.61259 2.79309i
\(355\) 5.61210 9.72045i 0.297860 0.515908i
\(356\) 10.5764 + 10.5764i 0.560550 + 0.560550i
\(357\) 7.49326 + 7.68095i 0.396585 + 0.406519i
\(358\) 11.2508 + 11.2508i 0.594621 + 0.594621i
\(359\) −8.80969 + 2.36055i −0.464958 + 0.124585i −0.483690 0.875239i \(-0.660704\pi\)
0.0187320 + 0.999825i \(0.494037\pi\)
\(360\) −8.74263 + 5.04756i −0.460777 + 0.266030i
\(361\) −15.6711 + 9.04773i −0.824796 + 0.476196i
\(362\) 6.89250 + 25.7232i 0.362262 + 1.35198i
\(363\) 45.1626 2.37042
\(364\) −36.4283 + 14.5983i −1.90936 + 0.765157i
\(365\) 7.19451 0.376578
\(366\) −6.61887 24.7020i −0.345974 1.29119i
\(367\) 10.4995 6.06190i 0.548071 0.316429i −0.200273 0.979740i \(-0.564183\pi\)
0.748343 + 0.663311i \(0.230850\pi\)
\(368\) −14.4021 + 8.31508i −0.750763 + 0.433453i
\(369\) 6.48473 1.73758i 0.337581 0.0904547i
\(370\) −11.0818 11.0818i −0.576114 0.576114i
\(371\) 8.25315 + 32.3989i 0.428482 + 1.68207i
\(372\) −26.6644 26.6644i −1.38248 1.38248i
\(373\) −13.8527 + 23.9936i −0.717266 + 1.24234i 0.244813 + 0.969570i \(0.421273\pi\)
−0.962079 + 0.272771i \(0.912060\pi\)
\(374\) −14.1097 24.4388i −0.729597 1.26370i
\(375\) −6.34124 + 23.6658i −0.327460 + 1.22210i
\(376\) −1.21346 + 2.10177i −0.0625794 + 0.108391i
\(377\) −10.1493 + 1.34457i −0.522714 + 0.0692491i
\(378\) 24.3490 + 0.301179i 1.25238 + 0.0154910i
\(379\) 1.97532 1.97532i 0.101466 0.101466i −0.654552 0.756017i \(-0.727143\pi\)
0.756017 + 0.654552i \(0.227143\pi\)
\(380\) −3.20407 + 5.54961i −0.164365 + 0.284689i
\(381\) 6.26582 + 10.8527i 0.321008 + 0.556001i
\(382\) 4.88825 + 1.30980i 0.250105 + 0.0670153i
\(383\) −17.5608 + 4.70541i −0.897317 + 0.240435i −0.677864 0.735188i \(-0.737094\pi\)
−0.219453 + 0.975623i \(0.570427\pi\)
\(384\) 26.6818 26.6818i 1.36160 1.36160i
\(385\) 6.74889 23.9960i 0.343955 1.22295i
\(386\) 7.11550 0.362169
\(387\) 5.42224 + 3.13053i 0.275628 + 0.159134i
\(388\) −39.8921 10.6891i −2.02521 0.542654i
\(389\) 4.76738 2.75245i 0.241716 0.139555i −0.374249 0.927328i \(-0.622100\pi\)
0.615965 + 0.787773i \(0.288766\pi\)
\(390\) 27.5869 + 11.4006i 1.39692 + 0.577291i
\(391\) 7.02483i 0.355261i
\(392\) 8.59288 + 35.5658i 0.434006 + 1.79635i
\(393\) −3.08505 −0.155620
\(394\) 13.3911 + 7.73133i 0.674632 + 0.389499i
\(395\) 2.61337 9.75322i 0.131493 0.490738i
\(396\) 26.9562 + 7.22290i 1.35460 + 0.362964i
\(397\) −6.45307 24.0832i −0.323870 1.20870i −0.915443 0.402449i \(-0.868159\pi\)
0.591572 0.806252i \(-0.298507\pi\)
\(398\) 36.3893 36.3893i 1.82403 1.82403i
\(399\) −4.48640 + 2.51676i −0.224601 + 0.125995i
\(400\) 10.8850i 0.544251i
\(401\) 7.90338 2.11770i 0.394676 0.105753i −0.0560222 0.998430i \(-0.517842\pi\)
0.450698 + 0.892676i \(0.351175\pi\)
\(402\) 15.3611 + 26.6061i 0.766140 + 1.32699i
\(403\) −2.09709 + 16.0298i −0.104464 + 0.798499i
\(404\) 15.1759 + 8.76183i 0.755031 + 0.435917i
\(405\) −12.9094 12.9094i −0.641476 0.641476i
\(406\) −0.229753 + 18.5745i −0.0114024 + 0.921837i
\(407\) 22.2620i 1.10348i
\(408\) −5.48688 20.4773i −0.271641 1.01378i
\(409\) 1.16168 4.33547i 0.0574416 0.214375i −0.931239 0.364408i \(-0.881271\pi\)
0.988681 + 0.150033i \(0.0479380\pi\)
\(410\) −5.96718 + 22.2698i −0.294698 + 1.09983i
\(411\) 3.60737 + 13.4629i 0.177938 + 0.664075i
\(412\) 17.1602i 0.845424i
\(413\) 27.3074 + 16.2195i 1.34371 + 0.798112i
\(414\) 7.30047 + 7.30047i 0.358799 + 0.358799i
\(415\) 23.1030 + 13.3385i 1.13408 + 0.654762i
\(416\) 4.14378 + 0.542110i 0.203165 + 0.0265791i
\(417\) 6.40815 + 11.0992i 0.313809 + 0.543533i
\(418\) 13.0671 3.50131i 0.639131 0.171255i
\(419\) 35.1474i 1.71706i 0.512760 + 0.858532i \(0.328623\pi\)
−0.512760 + 0.858532i \(0.671377\pi\)
\(420\) 18.6105 31.3329i 0.908101 1.52889i
\(421\) 24.7123 24.7123i 1.20440 1.20440i 0.231589 0.972814i \(-0.425607\pi\)
0.972814 0.231589i \(-0.0743926\pi\)
\(422\) 9.89621 + 36.9332i 0.481740 + 1.79788i
\(423\) 0.528861 + 0.141708i 0.0257141 + 0.00689007i
\(424\) 17.0956 63.8016i 0.830235 3.09848i
\(425\) −3.98198 2.29900i −0.193155 0.111518i
\(426\) −34.6421 −1.67841
\(427\) 9.34705 + 9.58117i 0.452335 + 0.463665i
\(428\) 15.7549i 0.761543i
\(429\) −16.2582 39.1605i −0.784951 1.89069i
\(430\) −18.6210 + 10.7509i −0.897986 + 0.518452i
\(431\) −34.5526 9.25833i −1.66434 0.445958i −0.700763 0.713395i \(-0.747157\pi\)
−0.963575 + 0.267437i \(0.913823\pi\)
\(432\) −15.1399 8.74102i −0.728418 0.420552i
\(433\) 3.82925 0.184022 0.0920110 0.995758i \(-0.470670\pi\)
0.0920110 + 0.995758i \(0.470670\pi\)
\(434\) 28.2370 + 7.94168i 1.35542 + 0.381213i
\(435\) 6.72255 6.72255i 0.322322 0.322322i
\(436\) −5.68235 + 1.52258i −0.272135 + 0.0729184i
\(437\) 3.25286 + 0.871601i 0.155605 + 0.0416943i
\(438\) −11.1025 19.2300i −0.530496 0.918847i
\(439\) −2.14941 + 3.72288i −0.102586 + 0.177684i −0.912749 0.408520i \(-0.866045\pi\)
0.810164 + 0.586204i \(0.199378\pi\)
\(440\) −34.8225 + 34.8225i −1.66010 + 1.66010i
\(441\) 7.24857 3.94920i 0.345170 0.188057i
\(442\) −10.7559 + 14.0410i −0.511606 + 0.667861i
\(443\) 7.37495 12.7738i 0.350395 0.606901i −0.635924 0.771752i \(-0.719381\pi\)
0.986319 + 0.164851i \(0.0527142\pi\)
\(444\) −8.42375 + 31.4379i −0.399774 + 1.49198i
\(445\) 2.97732 + 5.15688i 0.141139 + 0.244459i
\(446\) −29.2051 + 50.5847i −1.38290 + 2.39526i
\(447\) 3.91425 + 3.91425i 0.185137 + 0.185137i
\(448\) −4.67570 + 16.6247i −0.220906 + 0.785442i
\(449\) −13.9834 13.9834i −0.659915 0.659915i 0.295445 0.955360i \(-0.404532\pi\)
−0.955360 + 0.295445i \(0.904532\pi\)
\(450\) 6.52743 1.74902i 0.307706 0.0824496i
\(451\) 28.3624 16.3750i 1.33553 0.771069i
\(452\) −54.2072 + 31.2966i −2.54969 + 1.47207i
\(453\) −0.149642 0.558472i −0.00703080 0.0262393i
\(454\) −53.0491 −2.48972
\(455\) −15.5125 + 1.86017i −0.727236 + 0.0872060i
\(456\) 10.1628 0.475919
\(457\) −7.91853 29.5523i −0.370413 1.38240i −0.859932 0.510408i \(-0.829494\pi\)
0.489519 0.871992i \(-0.337172\pi\)
\(458\) −2.16724 + 1.25126i −0.101268 + 0.0584673i
\(459\) 6.39532 3.69234i 0.298508 0.172344i
\(460\) −23.0447 + 6.17481i −1.07447 + 0.287902i
\(461\) 4.39870 + 4.39870i 0.204868 + 0.204868i 0.802082 0.597214i \(-0.203726\pi\)
−0.597214 + 0.802082i \(0.703726\pi\)
\(462\) −74.5531 + 18.9913i −3.46852 + 0.883556i
\(463\) 6.67812 + 6.67812i 0.310358 + 0.310358i 0.845048 0.534690i \(-0.179572\pi\)
−0.534690 + 0.845048i \(0.679572\pi\)
\(464\) 6.66805 11.5494i 0.309556 0.536167i
\(465\) −7.50617 13.0011i −0.348090 0.602910i
\(466\) −1.39257 + 5.19714i −0.0645096 + 0.240753i
\(467\) 19.0523 32.9996i 0.881636 1.52704i 0.0321149 0.999484i \(-0.489776\pi\)
0.849521 0.527554i \(-0.176891\pi\)
\(468\) −2.29720 17.3400i −0.106188 0.801541i
\(469\) −13.8254 8.21173i −0.638396 0.379183i
\(470\) −1.32956 + 1.32956i −0.0613280 + 0.0613280i
\(471\) 1.04504 1.81006i 0.0481529 0.0834032i
\(472\) −31.3741 54.3415i −1.44411 2.50127i
\(473\) 29.5023 + 7.90512i 1.35652 + 0.363478i
\(474\) −30.1021 + 8.06582i −1.38263 + 0.370475i
\(475\) 1.55862 1.55862i 0.0715142 0.0715142i
\(476\) 15.0793 + 15.4570i 0.691159 + 0.708471i
\(477\) −14.9015 −0.682293
\(478\) 24.8344 + 14.3381i 1.13590 + 0.655811i
\(479\) 11.2140 + 3.00477i 0.512379 + 0.137291i 0.505739 0.862686i \(-0.331220\pi\)
0.00663970 + 0.999978i \(0.497887\pi\)
\(480\) −3.36085 + 1.94039i −0.153401 + 0.0885661i
\(481\) 12.8868 5.35015i 0.587585 0.243946i
\(482\) 15.9046i 0.724436i
\(483\) −18.4363 5.18523i −0.838881 0.235936i
\(484\) 90.8845 4.13111
\(485\) −14.2389 8.22082i −0.646554 0.373288i
\(486\) −7.43735 + 27.7566i −0.337365 + 1.25906i
\(487\) −32.1240 8.60759i −1.45568 0.390047i −0.557681 0.830055i \(-0.688309\pi\)
−0.897994 + 0.440008i \(0.854976\pi\)
\(488\) −6.84431 25.5433i −0.309827 1.15629i
\(489\) −24.5098 + 24.5098i −1.10837 + 1.10837i
\(490\) −0.701175 + 28.3391i −0.0316758 + 1.28023i
\(491\) 2.41523i 0.108998i 0.998514 + 0.0544989i \(0.0173561\pi\)
−0.998514 + 0.0544989i \(0.982644\pi\)
\(492\) 46.2489 12.3924i 2.08506 0.558690i
\(493\) 2.81669 + 4.87864i 0.126857 + 0.219723i
\(494\) −5.16717 6.72266i −0.232482 0.302467i
\(495\) 9.62162 + 5.55504i 0.432460 + 0.249681i
\(496\) −14.8906 14.8906i −0.668609 0.668609i
\(497\) 15.8136 8.87106i 0.709339 0.397921i
\(498\) 82.3352i 3.68953i
\(499\) −0.127329 0.475197i −0.00570002 0.0212727i 0.963017 0.269440i \(-0.0868385\pi\)
−0.968717 + 0.248167i \(0.920172\pi\)
\(500\) −12.7610 + 47.6247i −0.570689 + 2.12984i
\(501\) −0.261926 + 0.977520i −0.0117020 + 0.0436724i
\(502\) −1.27398 4.75457i −0.0568607 0.212207i
\(503\) 15.5328i 0.692575i −0.938128 0.346288i \(-0.887442\pi\)
0.938128 0.346288i \(-0.112558\pi\)
\(504\) −16.3067 0.201702i −0.726359 0.00898452i
\(505\) 4.93301 + 4.93301i 0.219516 + 0.219516i
\(506\) 43.6174 + 25.1825i 1.93903 + 1.11950i
\(507\) −18.7615 + 18.8227i −0.833229 + 0.835945i
\(508\) 12.6092 + 21.8398i 0.559444 + 0.968985i
\(509\) −33.6436 + 9.01478i −1.49123 + 0.399573i −0.910151 0.414276i \(-0.864035\pi\)
−0.581076 + 0.813849i \(0.697368\pi\)
\(510\) 16.4247i 0.727297i
\(511\) 9.99251 + 5.93517i 0.442043 + 0.262556i
\(512\) 30.8689 30.8689i 1.36422 1.36422i
\(513\) 0.916249 + 3.41949i 0.0404534 + 0.150974i
\(514\) −5.02911 1.34755i −0.221825 0.0594377i
\(515\) 1.76816 6.59886i 0.0779145 0.290781i
\(516\) 38.6713 + 22.3269i 1.70241 + 0.982886i
\(517\) 2.67092 0.117467
\(518\) −6.24957 24.5335i −0.274590 1.07794i
\(519\) 8.12741i 0.356754i
\(520\) 28.5265 + 11.7889i 1.25097 + 0.516976i
\(521\) 4.95243 2.85928i 0.216970 0.125268i −0.387577 0.921837i \(-0.626688\pi\)
0.604546 + 0.796570i \(0.293354\pi\)
\(522\) −7.99727 2.14286i −0.350031 0.0937906i
\(523\) −23.2231 13.4079i −1.01548 0.586286i −0.102686 0.994714i \(-0.532744\pi\)
−0.912791 + 0.408428i \(0.866077\pi\)
\(524\) −6.20829 −0.271210
\(525\) −8.97282 + 8.75356i −0.391606 + 0.382037i
\(526\) 35.4455 35.4455i 1.54550 1.54550i
\(527\) 8.59234 2.30231i 0.374288 0.100290i
\(528\) 53.3507 + 14.2953i 2.32179 + 0.622122i
\(529\) −5.23116 9.06064i −0.227442 0.393941i
\(530\) 25.5873 44.3185i 1.11144 1.92507i
\(531\) −10.0099 + 10.0099i −0.434391 + 0.434391i
\(532\) −9.02835 + 5.06468i −0.391429 + 0.219582i
\(533\) −16.2952 12.4827i −0.705825 0.540687i
\(534\) 9.18913 15.9160i 0.397652 0.688754i
\(535\) −1.62336 + 6.05846i −0.0701840 + 0.261930i
\(536\) 15.8843 + 27.5123i 0.686096 + 1.18835i
\(537\) 6.57740 11.3924i 0.283836 0.491618i
\(538\) −2.30766 2.30766i −0.0994903 0.0994903i
\(539\) 29.1692 27.7607i 1.25641 1.19574i
\(540\) −17.7341 17.7341i −0.763152 0.763152i
\(541\) −19.2806 + 5.16622i −0.828938 + 0.222113i −0.648250 0.761427i \(-0.724499\pi\)
−0.180688 + 0.983541i \(0.557832\pi\)
\(542\) −58.9465 + 34.0328i −2.53197 + 1.46183i
\(543\) 19.0677 11.0087i 0.818273 0.472430i
\(544\) −0.595160 2.22117i −0.0255173 0.0952317i
\(545\) −2.34200 −0.100320
\(546\) 28.9106 + 38.5923i 1.23726 + 1.65160i
\(547\) −11.1973 −0.478763 −0.239382 0.970926i \(-0.576945\pi\)
−0.239382 + 0.970926i \(0.576945\pi\)
\(548\) 7.25940 + 27.0924i 0.310106 + 1.15733i
\(549\) −5.16662 + 2.98295i −0.220506 + 0.127309i
\(550\) 28.5491 16.4828i 1.21734 0.702831i
\(551\) −2.60854 + 0.698957i −0.111128 + 0.0297765i
\(552\) 26.7544 + 26.7544i 1.13874 + 1.13874i
\(553\) 11.6757 11.3904i 0.496502 0.484369i
\(554\) 29.3999 + 29.3999i 1.24908 + 1.24908i
\(555\) −6.47861 + 11.2213i −0.275001 + 0.476317i
\(556\) 12.8957 + 22.3359i 0.546898 + 0.947255i
\(557\) 8.01858 29.9257i 0.339758 1.26799i −0.558860 0.829262i \(-0.688761\pi\)
0.898618 0.438732i \(-0.144572\pi\)
\(558\) −6.53683 + 11.3221i −0.276726 + 0.479304i
\(559\) −2.51418 18.9778i −0.106338 0.802675i
\(560\) 10.3930 17.4978i 0.439184 0.739415i
\(561\) −16.4976 + 16.4976i −0.696529 + 0.696529i
\(562\) −26.0953 + 45.1984i −1.10077 + 1.90658i
\(563\) −17.8356 30.8922i −0.751682 1.30195i −0.947007 0.321213i \(-0.895910\pi\)
0.195325 0.980739i \(-0.437424\pi\)
\(564\) 3.77182 + 1.01066i 0.158822 + 0.0425563i
\(565\) −24.0698 + 6.44949i −1.01262 + 0.271332i
\(566\) 54.3490 54.3490i 2.28446 2.28446i
\(567\) −7.28028 28.5798i −0.305743 1.20024i
\(568\) −35.8220 −1.50306
\(569\) 13.6314 + 7.87011i 0.571459 + 0.329932i 0.757732 0.652566i \(-0.226307\pi\)
−0.186273 + 0.982498i \(0.559641\pi\)
\(570\) 7.60547 + 2.03788i 0.318558 + 0.0853574i
\(571\) −4.87728 + 2.81590i −0.204108 + 0.117842i −0.598570 0.801070i \(-0.704264\pi\)
0.394462 + 0.918912i \(0.370931\pi\)
\(572\) −32.7176 78.8060i −1.36799 3.29504i
\(573\) 4.18405i 0.174791i
\(574\) −26.6595 + 26.0080i −1.11275 + 1.08555i
\(575\) 8.20634 0.342228
\(576\) −6.66596 3.84859i −0.277748 0.160358i
\(577\) −9.91860 + 37.0167i −0.412917 + 1.54103i 0.376055 + 0.926597i \(0.377280\pi\)
−0.788972 + 0.614429i \(0.789386\pi\)
\(578\) −31.2019 8.36052i −1.29783 0.347752i
\(579\) −1.52261 5.68246i −0.0632775 0.236155i
\(580\) 13.5283 13.5283i 0.561734 0.561734i
\(581\) 21.0842 + 37.5850i 0.874721 + 1.55929i
\(582\) 50.7450i 2.10345i
\(583\) −70.2162 + 18.8144i −2.90806 + 0.779212i
\(584\) −11.4806 19.8850i −0.475071 0.822847i
\(585\) 0.903306 6.90468i 0.0373471 0.285474i
\(586\) 32.5784 + 18.8092i 1.34580 + 0.776999i
\(587\) 18.6594 + 18.6594i 0.770156 + 0.770156i 0.978134 0.207977i \(-0.0666880\pi\)
−0.207977 + 0.978134i \(0.566688\pi\)
\(588\) 51.6966 28.1656i 2.13193 1.16153i
\(589\) 4.26435i 0.175710i
\(590\) −12.5824 46.9582i −0.518010 1.93324i
\(591\) 3.30878 12.3485i 0.136105 0.507951i
\(592\) −4.70421 + 17.5564i −0.193342 + 0.721562i
\(593\) 11.8139 + 44.0900i 0.485138 + 1.81056i 0.579440 + 0.815015i \(0.303271\pi\)
−0.0943021 + 0.995544i \(0.530062\pi\)
\(594\) 52.9450i 2.17236i
\(595\) 4.20599 + 7.49765i 0.172429 + 0.307374i
\(596\) 7.87696 + 7.87696i 0.322653 + 0.322653i
\(597\) −36.8474 21.2739i −1.50806 0.870681i
\(598\) 4.09494 31.3008i 0.167454 1.27999i
\(599\) −2.34380 4.05958i −0.0957650 0.165870i 0.814163 0.580637i \(-0.197196\pi\)
−0.909928 + 0.414767i \(0.863863\pi\)
\(600\) 23.9214 6.40973i 0.976588 0.261676i
\(601\) 34.8781i 1.42271i −0.702835 0.711353i \(-0.748083\pi\)
0.702835 0.711353i \(-0.251917\pi\)
\(602\) −34.7319 0.429607i −1.41557 0.0175095i
\(603\) 5.06786 5.06786i 0.206379 0.206379i
\(604\) −0.301137 1.12386i −0.0122531 0.0457292i
\(605\) 34.9491 + 9.36458i 1.42088 + 0.380724i
\(606\) 5.57277 20.7979i 0.226378 0.844855i
\(607\) 25.8405 + 14.9190i 1.04884 + 0.605545i 0.922323 0.386420i \(-0.126288\pi\)
0.126512 + 0.991965i \(0.459622\pi\)
\(608\) 1.10236 0.0447066
\(609\) 14.8828 3.79119i 0.603082 0.153627i
\(610\) 20.4880i 0.829536i
\(611\) −0.641896 1.54612i −0.0259683 0.0625491i
\(612\) −8.33515 + 4.81230i −0.336928 + 0.194526i
\(613\) 41.1194 + 11.0179i 1.66080 + 0.445009i 0.962607 0.270903i \(-0.0873223\pi\)
0.698190 + 0.715912i \(0.253989\pi\)
\(614\) 57.3970 + 33.1382i 2.31636 + 1.33735i
\(615\) 19.0616 0.768639
\(616\) −77.0923 + 19.6382i −3.10614 + 0.791244i
\(617\) 13.3408 13.3408i 0.537079 0.537079i −0.385591 0.922670i \(-0.626002\pi\)
0.922670 + 0.385591i \(0.126002\pi\)
\(618\) −20.3665 + 5.45720i −0.819262 + 0.219521i
\(619\) 2.78249 + 0.745565i 0.111838 + 0.0299668i 0.314304 0.949322i \(-0.398229\pi\)
−0.202466 + 0.979289i \(0.564896\pi\)
\(620\) −15.1053 26.1631i −0.606643 1.05074i
\(621\) −6.58996 + 11.4141i −0.264446 + 0.458034i
\(622\) −19.6649 + 19.6649i −0.788491 + 0.788491i
\(623\) −0.118975 + 9.61859i −0.00476662 + 0.385361i
\(624\) −4.54653 34.3186i −0.182007 1.37384i
\(625\) −4.02029 + 6.96335i −0.160812 + 0.278534i
\(626\) 18.7531 69.9875i 0.749524 2.79726i
\(627\) −5.59231 9.68617i −0.223335 0.386828i
\(628\) 2.10302 3.64254i 0.0839196 0.145353i
\(629\) −5.42895 5.42895i −0.216466 0.216466i
\(630\) −12.1629 3.42081i −0.484580 0.136288i
\(631\) −25.3632 25.3632i −1.00969 1.00969i −0.999953 0.00973923i \(-0.996900\pi\)
−0.00973923 0.999953i \(-0.503100\pi\)
\(632\) −31.1273 + 8.34054i −1.23818 + 0.331769i
\(633\) 27.3773 15.8063i 1.08815 0.628244i
\(634\) 32.5835 18.8121i 1.29406 0.747124i
\(635\) 2.59846 + 9.69760i 0.103117 + 0.384838i
\(636\) −106.277 −4.21416
\(637\) −23.0799 10.2135i −0.914461 0.404675i
\(638\) −40.3889 −1.59901
\(639\) 2.09165 + 7.80613i 0.0827442 + 0.308806i
\(640\) 26.1802 15.1151i 1.03486 0.597478i
\(641\) 2.83626 1.63751i 0.112025 0.0646779i −0.442940 0.896551i \(-0.646065\pi\)
0.554966 + 0.831873i \(0.312731\pi\)
\(642\) 18.6987 5.01029i 0.737977 0.197740i
\(643\) −30.3555 30.3555i −1.19710 1.19710i −0.975030 0.222072i \(-0.928718\pi\)
−0.222072 0.975030i \(-0.571282\pi\)
\(644\) −37.1009 10.4347i −1.46198 0.411183i
\(645\) 12.5703 + 12.5703i 0.494955 + 0.494955i
\(646\) −2.33277 + 4.04047i −0.0917815 + 0.158970i
\(647\) −16.6342 28.8112i −0.653956 1.13269i −0.982154 0.188077i \(-0.939775\pi\)
0.328198 0.944609i \(-0.393559\pi\)
\(648\) −15.0804 + 56.2808i −0.592413 + 2.21092i
\(649\) −34.5284 + 59.8050i −1.35536 + 2.34755i
\(650\) −16.4025 12.5649i −0.643361 0.492837i
\(651\) 0.299949 24.2496i 0.0117559 0.950415i
\(652\) −49.3230 + 49.3230i −1.93164 + 1.93164i
\(653\) 15.4772 26.8072i 0.605668 1.04905i −0.386278 0.922382i \(-0.626239\pi\)
0.991946 0.126665i \(-0.0404272\pi\)
\(654\) 3.61413 + 6.25986i 0.141324 + 0.244780i
\(655\) −2.38736 0.639691i −0.0932819 0.0249948i
\(656\) 25.8275 6.92047i 1.00840 0.270199i
\(657\) −3.66288 + 3.66288i −0.142902 + 0.142902i
\(658\) −2.94346 + 0.749805i −0.114748 + 0.0292304i
\(659\) −43.2836 −1.68609 −0.843045 0.537843i \(-0.819239\pi\)
−0.843045 + 0.537843i \(0.819239\pi\)
\(660\) 68.6211 + 39.6184i 2.67107 + 1.54214i
\(661\) 40.0343 + 10.7272i 1.55715 + 0.417238i 0.931761 0.363072i \(-0.118272\pi\)
0.625393 + 0.780310i \(0.284939\pi\)
\(662\) 55.0735 31.7967i 2.14049 1.23581i
\(663\) 13.5148 + 5.58513i 0.524870 + 0.216908i
\(664\) 85.1395i 3.30406i
\(665\) −3.99365 + 1.01733i −0.154867 + 0.0394502i
\(666\) 11.2839 0.437243
\(667\) −8.70723 5.02712i −0.337145 0.194651i
\(668\) −0.527095 + 1.96714i −0.0203939 + 0.0761111i
\(669\) 46.6466 + 12.4989i 1.80346 + 0.483236i
\(670\) 6.37031 + 23.7743i 0.246106 + 0.918482i
\(671\) −20.5790 + 20.5790i −0.794443 + 0.794443i
\(672\) −6.26864 0.0775384i −0.241818 0.00299111i
\(673\) 12.5591i 0.484116i −0.970262 0.242058i \(-0.922178\pi\)
0.970262 0.242058i \(-0.0778224\pi\)
\(674\) −8.90085 + 2.38498i −0.342848 + 0.0918659i
\(675\) 4.31336 + 7.47095i 0.166021 + 0.287557i
\(676\) −37.7554 + 37.8784i −1.45213 + 1.45686i
\(677\) 7.26874 + 4.19661i 0.279361 + 0.161289i 0.633134 0.774042i \(-0.281768\pi\)
−0.353773 + 0.935331i \(0.615102\pi\)
\(678\) 54.3828 + 54.3828i 2.08856 + 2.08856i
\(679\) −12.9947 23.1644i −0.498689 0.888969i
\(680\) 16.9841i 0.651310i
\(681\) 11.3517 + 42.3651i 0.434998 + 1.62344i
\(682\) −16.5066 + 61.6034i −0.632070 + 2.35892i
\(683\) 2.72266 10.1611i 0.104180 0.388804i −0.894071 0.447925i \(-0.852163\pi\)
0.998251 + 0.0591213i \(0.0188299\pi\)
\(684\) −1.19416 4.45668i −0.0456600 0.170406i
\(685\) 11.1662i 0.426640i
\(686\) −24.3524 + 38.7820i −0.929780 + 1.48070i
\(687\) 1.46301 + 1.46301i 0.0558174 + 0.0558174i
\(688\) 21.5959 + 12.4684i 0.823334 + 0.475352i
\(689\) 27.7659 + 36.1244i 1.05780 + 1.37623i
\(690\) 14.6571 + 25.3868i 0.557986 + 0.966460i
\(691\) 33.9813 9.10526i 1.29271 0.346380i 0.454021 0.890991i \(-0.349989\pi\)
0.838689 + 0.544611i \(0.183323\pi\)
\(692\) 16.3555i 0.621741i
\(693\) 8.78086 + 15.6529i 0.333557 + 0.594603i
\(694\) 23.6787 23.6787i 0.898830 0.898830i
\(695\) 2.65749 + 9.91789i 0.100804 + 0.376207i
\(696\) −29.3080 7.85306i −1.11092 0.297670i
\(697\) −2.92331 + 10.9099i −0.110728 + 0.413244i
\(698\) −65.3506 37.7302i −2.47356 1.42811i
\(699\) 4.44844 0.168256
\(700\) −18.0567 + 17.6155i −0.682481 + 0.665803i
\(701\) 0.321018i 0.0121247i −0.999982 0.00606234i \(-0.998070\pi\)
0.999982 0.00606234i \(-0.00192972\pi\)
\(702\) 30.6482 12.7241i 1.15674 0.480241i
\(703\) 3.18748 1.84029i 0.120218 0.0694078i
\(704\) −36.2693 9.71834i −1.36695 0.366274i
\(705\) 1.34630 + 0.777284i 0.0507044 + 0.0292742i
\(706\) 6.85348 0.257934
\(707\) 2.78197 + 10.9210i 0.104627 + 0.410727i
\(708\) −71.3901 + 71.3901i −2.68300 + 2.68300i
\(709\) −24.2000 + 6.48436i −0.908849 + 0.243525i −0.682813 0.730593i \(-0.739243\pi\)
−0.226036 + 0.974119i \(0.572577\pi\)
\(710\) −26.8077 7.18311i −1.00608 0.269577i
\(711\) 3.63505 + 6.29609i 0.136325 + 0.236122i
\(712\) 9.50210 16.4581i 0.356106 0.616794i
\(713\) −11.2262 + 11.2262i −0.420425 + 0.420425i
\(714\) 13.5497 22.8123i 0.507083 0.853731i
\(715\) −4.46134 33.6755i −0.166844 1.25939i
\(716\) 13.2362 22.9258i 0.494662 0.856779i
\(717\) 6.13629 22.9009i 0.229164 0.855252i
\(718\) 11.2758 + 19.5303i 0.420809 + 0.728863i
\(719\) 15.5251 26.8903i 0.578990 1.00284i −0.416606 0.909087i \(-0.636781\pi\)
0.995596 0.0937521i \(-0.0298861\pi\)
\(720\) 6.41402 + 6.41402i 0.239036 + 0.239036i
\(721\) 7.89959 7.70655i 0.294196 0.287007i
\(722\) 31.6385 + 31.6385i 1.17746 + 1.17746i
\(723\) 12.7015 3.40335i 0.472373 0.126572i
\(724\) 38.3715 22.1538i 1.42607 0.823339i
\(725\) −5.69918 + 3.29043i −0.211662 + 0.122203i
\(726\) −28.9025 107.866i −1.07267 4.00327i
\(727\) 40.0423 1.48509 0.742543 0.669798i \(-0.233619\pi\)
0.742543 + 0.669798i \(0.233619\pi\)
\(728\) 29.8953 + 39.9068i 1.10799 + 1.47904i
\(729\) −9.68335 −0.358642
\(730\) −4.60424 17.1833i −0.170411 0.635982i
\(731\) −9.12242 + 5.26683i −0.337405 + 0.194801i
\(732\) −36.8482 + 21.2743i −1.36195 + 0.786321i
\(733\) −13.2722 + 3.55628i −0.490221 + 0.131354i −0.495458 0.868632i \(-0.665000\pi\)
0.00523707 + 0.999986i \(0.498333\pi\)
\(734\) −21.1975 21.1975i −0.782414 0.782414i
\(735\) 22.7818 5.50419i 0.840318 0.203025i
\(736\) 2.90204 + 2.90204i 0.106971 + 0.106971i
\(737\) 17.4813 30.2785i 0.643931 1.11532i
\(738\) −8.30001 14.3760i −0.305528 0.529189i
\(739\) −8.67355 + 32.3701i −0.319062 + 1.19075i 0.601087 + 0.799184i \(0.294735\pi\)
−0.920148 + 0.391570i \(0.871932\pi\)
\(740\) −13.0374 + 22.5815i −0.479265 + 0.830112i
\(741\) −4.26304 + 5.56506i −0.156607 + 0.204438i
\(742\) 72.0993 40.4459i 2.64685 1.48482i
\(743\) 16.7361 16.7361i 0.613988 0.613988i −0.329994 0.943983i \(-0.607047\pi\)
0.943983 + 0.329994i \(0.107047\pi\)
\(744\) −23.9559 + 41.4928i −0.878265 + 1.52120i
\(745\) 2.21741 + 3.84066i 0.0812396 + 0.140711i
\(746\) 66.1712 + 17.7305i 2.42270 + 0.649161i
\(747\) −18.5531 + 4.97130i −0.678824 + 0.181890i
\(748\) −33.1995 + 33.1995i −1.21389 + 1.21389i
\(749\) −7.25267 + 7.07544i −0.265007 + 0.258531i
\(750\) 60.5813 2.21212
\(751\) 9.94812 + 5.74355i 0.363012 + 0.209585i 0.670401 0.741999i \(-0.266122\pi\)
−0.307389 + 0.951584i \(0.599455\pi\)
\(752\) 2.10636 + 0.564398i 0.0768111 + 0.0205815i
\(753\) −3.52440 + 2.03482i −0.128436 + 0.0741528i
\(754\) 9.70655 + 23.3799i 0.353492 + 0.851445i
\(755\) 0.463202i 0.0168576i
\(756\) −10.0011 39.2608i −0.363737 1.42790i
\(757\) −17.1190 −0.622200 −0.311100 0.950377i \(-0.600697\pi\)
−0.311100 + 0.950377i \(0.600697\pi\)
\(758\) −5.98198 3.45370i −0.217275 0.125444i
\(759\) 10.7774 40.2217i 0.391194 1.45996i
\(760\) 7.86451 + 2.10729i 0.285276 + 0.0764394i
\(761\) 8.84550 + 33.0119i 0.320649 + 1.19668i 0.918614 + 0.395156i \(0.129310\pi\)
−0.597965 + 0.801522i \(0.704024\pi\)
\(762\) 21.9106 21.9106i 0.793736 0.793736i
\(763\) −3.25282 1.93205i −0.117760 0.0699448i
\(764\) 8.41991i 0.304622i
\(765\) −3.70108 + 0.991702i −0.133813 + 0.0358550i
\(766\) 22.4767 + 38.9307i 0.812115 + 1.40663i
\(767\) 42.9174 + 5.61467i 1.54966 + 0.202734i
\(768\) −57.6894 33.3070i −2.08169 1.20186i
\(769\) −5.13005 5.13005i −0.184994 0.184994i 0.608534 0.793528i \(-0.291758\pi\)
−0.793528 + 0.608534i \(0.791758\pi\)
\(770\) −61.6307 0.762326i −2.22102 0.0274723i
\(771\) 4.30462i 0.155027i
\(772\) −3.06407 11.4353i −0.110278 0.411565i
\(773\) −5.60986 + 20.9363i −0.201773 + 0.753026i 0.788636 + 0.614860i \(0.210787\pi\)
−0.990409 + 0.138166i \(0.955879\pi\)
\(774\) 4.00687 14.9538i 0.144024 0.537505i
\(775\) 2.68954 + 10.0375i 0.0966110 + 0.360557i
\(776\) 52.4734i 1.88368i
\(777\) −18.2553 + 10.2407i −0.654903 + 0.367384i
\(778\) −9.62487 9.62487i −0.345068 0.345068i
\(779\) −4.68916 2.70729i −0.168007 0.0969987i
\(780\) 6.44235 49.2440i 0.230673 1.76322i
\(781\) 19.7118 + 34.1418i 0.705342 + 1.22169i
\(782\) −16.7780 + 4.49566i −0.599981 + 0.160764i
\(783\) 10.5693i 0.377715i
\(784\) 28.8698 15.7290i 1.03106 0.561750i
\(785\) 1.18402 1.18402i 0.0422596 0.0422596i
\(786\) 1.97432 + 7.36828i 0.0704218 + 0.262818i
\(787\) −12.9263 3.46358i −0.460771 0.123463i 0.0209637 0.999780i \(-0.493327\pi\)
−0.481735 + 0.876317i \(0.659993\pi\)
\(788\) 6.65853 24.8500i 0.237200 0.885243i
\(789\) −35.8917 20.7221i −1.27778 0.737726i
\(790\) −24.9669 −0.888283
\(791\) −38.7513 10.8988i −1.37784 0.387518i
\(792\) 35.4577i 1.25994i
\(793\) 16.8582 + 6.96685i 0.598654 + 0.247400i
\(794\) −53.3902 + 30.8249i −1.89475 + 1.09393i
\(795\) −40.8682 10.9506i −1.44945 0.388378i
\(796\) −74.1511 42.8111i −2.62821 1.51740i
\(797\) 53.9645 1.91152 0.955760 0.294149i \(-0.0950363\pi\)
0.955760 + 0.294149i \(0.0950363\pi\)
\(798\) 8.88213 + 9.10461i 0.314424 + 0.322300i
\(799\) −0.651349 + 0.651349i −0.0230431 + 0.0230431i
\(800\) 2.59475 0.695260i 0.0917381 0.0245812i
\(801\) −4.14129 1.10966i −0.146325 0.0392078i
\(802\) −10.1158 17.5211i −0.357201 0.618690i
\(803\) −12.6349 + 21.8843i −0.445875 + 0.772279i
\(804\) 36.1438 36.1438i 1.27469 1.27469i
\(805\) −13.1918 7.83540i −0.464949 0.276161i
\(806\) 39.6273 5.24983i 1.39581 0.184917i
\(807\) −1.34910 + 2.33671i −0.0474905 + 0.0822560i
\(808\) 5.76258 21.5062i 0.202727 0.756587i
\(809\) −12.7091 22.0129i −0.446829 0.773931i 0.551348 0.834275i \(-0.314114\pi\)
−0.998178 + 0.0603439i \(0.980780\pi\)
\(810\) −22.5711 + 39.0943i −0.793069 + 1.37364i
\(811\) 15.9565 + 15.9565i 0.560310 + 0.560310i 0.929395 0.369085i \(-0.120329\pi\)
−0.369085 + 0.929395i \(0.620329\pi\)
\(812\) 29.9499 7.62931i 1.05104 0.267736i
\(813\) 39.7923 + 39.7923i 1.39558 + 1.39558i
\(814\) 53.1701 14.2469i 1.86361 0.499353i
\(815\) −24.0490 + 13.8847i −0.842401 + 0.486360i
\(816\) −16.4966 + 9.52430i −0.577496 + 0.333417i
\(817\) −1.30696 4.87763i −0.0457246 0.170647i
\(818\) −11.0982 −0.388040
\(819\) 6.95068 8.84478i 0.242876 0.309062i
\(820\) 38.3593 1.33956
\(821\) 10.1652 + 37.9371i 0.354768 + 1.32401i 0.880776 + 0.473533i \(0.157021\pi\)
−0.526008 + 0.850480i \(0.676312\pi\)
\(822\) 29.8459 17.2316i 1.04100 0.601020i
\(823\) −26.2415 + 15.1505i −0.914722 + 0.528115i −0.881947 0.471348i \(-0.843768\pi\)
−0.0327745 + 0.999463i \(0.510434\pi\)
\(824\) −21.0602 + 5.64307i −0.733667 + 0.196586i
\(825\) −19.2723 19.2723i −0.670977 0.670977i
\(826\) 21.2627 75.6006i 0.739825 2.63048i
\(827\) −7.62275 7.62275i −0.265069 0.265069i 0.562041 0.827110i \(-0.310016\pi\)
−0.827110 + 0.562041i \(0.810016\pi\)
\(828\) 8.58882 14.8763i 0.298482 0.516986i
\(829\) −17.3492 30.0497i −0.602563 1.04367i −0.992431 0.122800i \(-0.960813\pi\)
0.389868 0.920871i \(-0.372521\pi\)
\(830\) 17.0724 63.7151i 0.592592 2.21158i
\(831\) 17.1877 29.7700i 0.596235 1.03271i
\(832\) 3.09086 + 23.3308i 0.107156 + 0.808849i
\(833\) −0.343505 + 13.8833i −0.0119017 + 0.481028i
\(834\) 22.4083 22.4083i 0.775936 0.775936i
\(835\) −0.405382 + 0.702142i −0.0140288 + 0.0242986i
\(836\) −11.2539 19.4923i −0.389223 0.674154i
\(837\) −16.1209 4.31957i −0.557218 0.149306i
\(838\) 83.9456 22.4932i 2.89985 0.777013i
\(839\) −5.64491 + 5.64491i −0.194884 + 0.194884i −0.797803 0.602919i \(-0.794004\pi\)
0.602919 + 0.797803i \(0.294004\pi\)
\(840\) −44.5739 12.5364i −1.53794 0.432548i
\(841\) −20.9373 −0.721975
\(842\) −74.8375 43.2074i −2.57907 1.48903i
\(843\) 41.6796 + 11.1680i 1.43552 + 0.384647i
\(844\) 55.0936 31.8083i 1.89640 1.09489i
\(845\) −18.4215 + 10.6757i −0.633720 + 0.367254i
\(846\) 1.35381i 0.0465450i
\(847\) 40.8157 + 41.8380i 1.40244 + 1.43757i
\(848\) −59.3501 −2.03809
\(849\) −55.0332 31.7734i −1.88873 1.09046i
\(850\) −2.94256 + 10.9818i −0.100929 + 0.376672i
\(851\) 13.2360 + 3.54656i 0.453723 + 0.121575i
\(852\) 14.9176 + 55.6731i 0.511067 + 1.90733i
\(853\) 5.56139 5.56139i 0.190418 0.190418i −0.605458 0.795877i \(-0.707010\pi\)
0.795877 + 0.605458i \(0.207010\pi\)
\(854\) 16.9017 28.4560i 0.578366 0.973744i
\(855\) 1.83684i 0.0628185i
\(856\) 19.3355 5.18094i 0.660875 0.177081i
\(857\) −15.3579 26.6007i −0.524617 0.908663i −0.999589 0.0286624i \(-0.990875\pi\)
0.474972 0.880001i \(-0.342458\pi\)
\(858\) −83.1258 + 63.8922i −2.83787 + 2.18124i
\(859\) −8.40141 4.85056i −0.286652 0.165499i 0.349779 0.936832i \(-0.386257\pi\)
−0.636431 + 0.771333i \(0.719590\pi\)
\(860\) 25.2962 + 25.2962i 0.862594 + 0.862594i
\(861\) 26.4748 + 15.7250i 0.902259 + 0.535907i
\(862\) 88.4499i 3.01261i
\(863\) −1.10156 4.11106i −0.0374974 0.139942i 0.944639 0.328110i \(-0.106412\pi\)
−0.982137 + 0.188168i \(0.939745\pi\)
\(864\) −1.11663 + 4.16733i −0.0379886 + 0.141775i
\(865\) −1.68524 + 6.28939i −0.0572998 + 0.213846i
\(866\) −2.45059 9.14573i −0.0832745 0.310784i
\(867\) 26.7069i 0.907015i
\(868\) 0.603612 48.7994i 0.0204879 1.65636i
\(869\) 25.0778 + 25.0778i 0.850705 + 0.850705i
\(870\) −20.3583 11.7538i −0.690210 0.398493i
\(871\) −21.7285 2.84263i −0.736242 0.0963189i
\(872\) 3.73723 + 6.47307i 0.126559 + 0.219206i
\(873\) 11.4347 3.06392i 0.387006 0.103698i
\(874\) 8.32688i 0.281661i
\(875\) −27.6546 + 15.5135i −0.934895 + 0.524453i
\(876\) −26.1235 + 26.1235i −0.882633 + 0.882633i
\(877\) −4.61225 17.2131i −0.155745 0.581246i −0.999040 0.0437969i \(-0.986055\pi\)
0.843296 0.537449i \(-0.180612\pi\)
\(878\) 10.2672 + 2.75110i 0.346502 + 0.0928450i
\(879\) 8.04976 30.0421i 0.271512 1.01330i
\(880\) 38.3212 + 22.1248i 1.29181 + 0.745826i
\(881\) 38.7999 1.30720 0.653600 0.756840i \(-0.273258\pi\)
0.653600 + 0.756840i \(0.273258\pi\)
\(882\) −14.0711 14.7850i −0.473797 0.497838i
\(883\) 42.2858i 1.42303i −0.702671 0.711514i \(-0.748010\pi\)
0.702671 0.711514i \(-0.251990\pi\)
\(884\) 27.1969 + 11.2394i 0.914730 + 0.378022i
\(885\) −34.8085 + 20.0967i −1.17008 + 0.675544i
\(886\) −35.2285 9.43944i −1.18352 0.317124i
\(887\) 21.4815 + 12.4023i 0.721278 + 0.416430i 0.815223 0.579147i \(-0.196614\pi\)
−0.0939448 + 0.995577i \(0.529948\pi\)
\(888\) 41.3528 1.38771
\(889\) −4.39108 + 15.6127i −0.147272 + 0.523633i
\(890\) 10.4112 10.4112i 0.348985 0.348985i
\(891\) 61.9393 16.5966i 2.07504 0.556006i
\(892\) 93.8707 + 25.1526i 3.14302 + 0.842171i
\(893\) −0.220793 0.382424i −0.00738854 0.0127973i
\(894\) 6.84374 11.8537i 0.228889 0.396447i
\(895\) 7.45216 7.45216i 0.249098 0.249098i
\(896\) 48.8312 + 0.604005i 1.63134 + 0.0201784i
\(897\) −25.8732 + 3.42768i −0.863881 + 0.114447i
\(898\) −24.4488 + 42.3465i −0.815866 + 1.41312i
\(899\) 3.29517 12.2977i 0.109900 0.410152i
\(900\) −5.62168 9.73704i −0.187389 0.324568i
\(901\) 12.5352 21.7116i 0.417608 0.723318i
\(902\) −57.2608 57.2608i −1.90658 1.90658i
\(903\) 7.08902 + 27.8289i 0.235908 + 0.926088i
\(904\) 56.2351 + 56.2351i 1.87035 + 1.87035i
\(905\) 17.0382 4.56538i 0.566370 0.151758i
\(906\) −1.23808 + 0.714806i −0.0411325 + 0.0237479i
\(907\) −31.7341 + 18.3217i −1.05371 + 0.608361i −0.923686 0.383150i \(-0.874839\pi\)
−0.130026 + 0.991511i \(0.541506\pi\)
\(908\) 22.8440 + 85.2549i 0.758104 + 2.82928i
\(909\) −5.02300 −0.166602
\(910\) 14.3703 + 35.8593i 0.476369 + 1.18873i
\(911\) −22.0142 −0.729363 −0.364682 0.931132i \(-0.618822\pi\)
−0.364682 + 0.931132i \(0.618822\pi\)
\(912\) −2.36344 8.82049i −0.0782614 0.292076i
\(913\) −81.1462 + 46.8498i −2.68555 + 1.55050i
\(914\) −65.5148 + 37.8250i −2.16704 + 1.25114i
\(915\) −16.3618 + 4.38413i −0.540905 + 0.144935i
\(916\) 2.94414 + 2.94414i 0.0972772 + 0.0972772i
\(917\) −2.78810 2.85794i −0.0920713 0.0943776i
\(918\) −12.9115 12.9115i −0.426144 0.426144i
\(919\) −16.8832 + 29.2425i −0.556924 + 0.964621i 0.440827 + 0.897592i \(0.354685\pi\)
−0.997751 + 0.0670286i \(0.978648\pi\)
\(920\) 15.1563 + 26.2515i 0.499688 + 0.865486i
\(921\) 14.1822 52.9285i 0.467318 1.74405i
\(922\) 7.69077 13.3208i 0.253282 0.438697i
\(923\) 15.0263 19.6157i 0.494598 0.645659i
\(924\) 62.6249 + 111.636i 2.06021 + 3.67255i
\(925\) 6.34205 6.34205i 0.208525 0.208525i
\(926\) 11.6762 20.2237i 0.383702 0.664592i
\(927\) 2.45941 + 4.25983i 0.0807777 + 0.139911i
\(928\) −3.17903 0.851818i −0.104357 0.0279623i
\(929\) 22.4304 6.01022i 0.735919 0.197189i 0.128655 0.991689i \(-0.458934\pi\)
0.607264 + 0.794500i \(0.292267\pi\)
\(930\) −26.2479 + 26.2479i −0.860702 + 0.860702i
\(931\) −6.38606 1.88162i −0.209295 0.0616676i
\(932\) 8.95197 0.293231
\(933\) 19.9125 + 11.4965i 0.651904 + 0.376377i
\(934\) −91.0086 24.3857i −2.97789 0.797924i
\(935\) −16.1875 + 9.34584i −0.529387 + 0.305642i
\(936\) −20.5254 + 8.52146i −0.670893 + 0.278533i
\(937\) 7.15492i 0.233741i 0.993147 + 0.116870i \(0.0372862\pi\)
−0.993147 + 0.116870i \(0.962714\pi\)
\(938\) −10.7650 + 38.2755i −0.351490 + 1.24974i
\(939\) −59.9051 −1.95493
\(940\) 2.70926 + 1.56419i 0.0883663 + 0.0510183i
\(941\) −1.24527 + 4.64742i −0.0405947 + 0.151502i −0.983248 0.182271i \(-0.941655\pi\)
0.942654 + 0.333773i \(0.108322\pi\)
\(942\) −4.99191 1.33758i −0.162645 0.0435807i
\(943\) −5.21742 19.4717i −0.169903 0.634085i
\(944\) −39.8676 + 39.8676i −1.29758 + 1.29758i
\(945\) 0.199491 16.1280i 0.00648945 0.524644i
\(946\) 75.5219i 2.45543i
\(947\) −18.1875 + 4.87333i −0.591015 + 0.158362i −0.541917 0.840432i \(-0.682301\pi\)
−0.0490979 + 0.998794i \(0.515635\pi\)
\(948\) 25.9251 + 44.9035i 0.842007 + 1.45840i
\(949\) 15.7046 + 2.05456i 0.509794 + 0.0666938i
\(950\) −4.72004 2.72512i −0.153138 0.0884145i
\(951\) −21.9958 21.9958i −0.713262 0.713262i
\(952\) 14.0111 23.5893i 0.454104 0.764535i
\(953\) 4.93813i 0.159962i −0.996796 0.0799809i \(-0.974514\pi\)
0.996796 0.0799809i \(-0.0254859\pi\)
\(954\) 9.53645 + 35.5905i 0.308754 + 1.15229i
\(955\) 0.867572 3.23782i 0.0280740 0.104774i
\(956\) 12.3486 46.0855i 0.399381 1.49051i
\(957\) 8.64262 + 32.2547i 0.279376 + 1.04265i
\(958\) 28.7062i 0.927456i
\(959\) −9.21166 + 15.5089i −0.297460 + 0.500807i
\(960\) −15.4536 15.4536i −0.498762 0.498762i
\(961\) 9.43630 + 5.44805i 0.304397 + 0.175744i
\(962\) −21.0253 27.3546i −0.677883 0.881949i
\(963\) −2.25800 3.91098i −0.0727632 0.126030i
\(964\) 25.5602 6.84884i 0.823239 0.220586i
\(965\) 4.71308i 0.151720i
\(966\) −0.585701 + 47.3514i −0.0188446 + 1.52351i
\(967\) −10.3931 + 10.3931i −0.334219 + 0.334219i −0.854186 0.519967i \(-0.825944\pi\)
0.519967 + 0.854186i \(0.325944\pi\)
\(968\) −29.8870 111.540i −0.960603 3.58502i
\(969\) 3.72591 + 0.998354i 0.119693 + 0.0320718i
\(970\) −10.5221 + 39.2690i −0.337844 + 1.26085i
\(971\) −5.09889 2.94384i −0.163631 0.0944724i 0.415948 0.909388i \(-0.363450\pi\)
−0.579579 + 0.814916i \(0.696783\pi\)
\(972\) 47.8101 1.53351
\(973\) −4.49083 + 15.9674i −0.143969 + 0.511890i
\(974\) 82.2330i 2.63491i
\(975\) −6.52449 + 15.7878i −0.208951 + 0.505615i
\(976\) −20.5777 + 11.8806i −0.658677 + 0.380287i
\(977\) −11.9143 3.19243i −0.381172 0.102135i 0.0631450 0.998004i \(-0.479887\pi\)
−0.444317 + 0.895870i \(0.646554\pi\)
\(978\) 74.2242 + 42.8534i 2.37343 + 1.37030i
\(979\) −20.9149 −0.668443
\(980\) 45.8456 11.0765i 1.46448 0.353827i
\(981\) 1.19236 1.19236i 0.0380691 0.0380691i
\(982\) 5.76850 1.54567i 0.184080 0.0493242i
\(983\) −4.80462 1.28739i −0.153243 0.0410615i 0.181382 0.983413i \(-0.441943\pi\)
−0.334625 + 0.942351i \(0.608610\pi\)
\(984\) −30.4175 52.6846i −0.969674 1.67952i
\(985\) 5.12099 8.86982i 0.163168 0.282616i
\(986\) 9.84950 9.84950i 0.313672 0.313672i
\(987\) 1.22865 + 2.19021i 0.0391085 + 0.0697152i
\(988\) −8.57886 + 11.1990i −0.272930 + 0.356289i
\(989\) 9.40005 16.2814i 0.298904 0.517717i
\(990\) 7.11008 26.5352i 0.225973 0.843343i
\(991\) 7.59737 + 13.1590i 0.241338 + 0.418010i 0.961096 0.276215i \(-0.0890803\pi\)
−0.719757 + 0.694226i \(0.755747\pi\)
\(992\) −2.59848 + 4.50071i −0.0825019 + 0.142898i
\(993\) −37.1778 37.1778i −1.17980 1.17980i
\(994\) −31.3077 32.0919i −0.993020 1.01789i
\(995\) −24.1032 24.1032i −0.764122 0.764122i
\(996\) −132.321 + 35.4552i −4.19274 + 1.12344i
\(997\) 51.7874 29.8995i 1.64012 0.946926i 0.659337 0.751847i \(-0.270837\pi\)
0.980788 0.195079i \(-0.0624963\pi\)
\(998\) −1.05347 + 0.608220i −0.0333470 + 0.0192529i
\(999\) 3.72824 + 13.9140i 0.117956 + 0.440219i
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 91.2.bb.a.5.1 32
3.2 odd 2 819.2.fn.e.460.8 32
7.2 even 3 637.2.i.a.538.1 32
7.3 odd 6 inner 91.2.bb.a.31.8 yes 32
7.4 even 3 637.2.bc.b.31.8 32
7.5 odd 6 637.2.i.a.538.2 32
7.6 odd 2 637.2.bc.b.460.1 32
13.8 odd 4 inner 91.2.bb.a.47.8 yes 32
21.17 even 6 819.2.fn.e.577.1 32
39.8 even 4 819.2.fn.e.775.1 32
91.34 even 4 637.2.bc.b.411.8 32
91.47 even 12 637.2.i.a.489.2 32
91.60 odd 12 637.2.bc.b.619.1 32
91.73 even 12 inner 91.2.bb.a.73.1 yes 32
91.86 odd 12 637.2.i.a.489.1 32
273.164 odd 12 819.2.fn.e.73.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bb.a.5.1 32 1.1 even 1 trivial
91.2.bb.a.31.8 yes 32 7.3 odd 6 inner
91.2.bb.a.47.8 yes 32 13.8 odd 4 inner
91.2.bb.a.73.1 yes 32 91.73 even 12 inner
637.2.i.a.489.1 32 91.86 odd 12
637.2.i.a.489.2 32 91.47 even 12
637.2.i.a.538.1 32 7.2 even 3
637.2.i.a.538.2 32 7.5 odd 6
637.2.bc.b.31.8 32 7.4 even 3
637.2.bc.b.411.8 32 91.34 even 4
637.2.bc.b.460.1 32 7.6 odd 2
637.2.bc.b.619.1 32 91.60 odd 12
819.2.fn.e.73.8 32 273.164 odd 12
819.2.fn.e.460.8 32 3.2 odd 2
819.2.fn.e.577.1 32 21.17 even 6
819.2.fn.e.775.1 32 39.8 even 4