Properties

Label 456.2.u.d.11.16
Level $456$
Weight $2$
Character 456.11
Analytic conductor $3.641$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [456,2,Mod(11,456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(456, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("456.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.u (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(68\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.16
Character \(\chi\) \(=\) 456.11
Dual form 456.2.u.d.83.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.07067 - 0.923935i) q^{2} +(0.703983 - 1.58253i) q^{3} +(0.292687 + 1.97847i) q^{4} +(-1.52878 + 2.64792i) q^{5} +(-2.21589 + 1.04394i) q^{6} -2.32537i q^{7} +(1.51460 - 2.38872i) q^{8} +(-2.00882 - 2.22815i) q^{9} +O(q^{10})\) \(q+(-1.07067 - 0.923935i) q^{2} +(0.703983 - 1.58253i) q^{3} +(0.292687 + 1.97847i) q^{4} +(-1.52878 + 2.64792i) q^{5} +(-2.21589 + 1.04394i) q^{6} -2.32537i q^{7} +(1.51460 - 2.38872i) q^{8} +(-2.00882 - 2.22815i) q^{9} +(4.08334 - 1.42257i) q^{10} -1.59767i q^{11} +(3.33704 + 0.929621i) q^{12} +(-3.06692 + 1.77069i) q^{13} +(-2.14849 + 2.48972i) q^{14} +(3.11419 + 4.28344i) q^{15} +(-3.82867 + 1.15814i) q^{16} +(-2.45821 - 1.41925i) q^{17} +(0.0921191 + 4.24164i) q^{18} +(-0.478692 - 4.33253i) q^{19} +(-5.68629 - 2.24963i) q^{20} +(-3.67997 - 1.63702i) q^{21} +(-1.47614 + 1.71058i) q^{22} +(-2.62710 - 4.55027i) q^{23} +(-2.71397 - 4.07853i) q^{24} +(-2.17434 - 3.76606i) q^{25} +(4.91967 + 0.937807i) q^{26} +(-4.94029 + 1.61043i) q^{27} +(4.60067 - 0.680606i) q^{28} +(-3.36504 - 5.82841i) q^{29} +(0.623336 - 7.46348i) q^{30} -0.183320i q^{31} +(5.16931 + 2.29745i) q^{32} +(-2.52836 - 1.12473i) q^{33} +(1.32065 + 3.79079i) q^{34} +(6.15741 + 3.55498i) q^{35} +(3.82037 - 4.62653i) q^{36} +9.54314i q^{37} +(-3.49046 + 5.08101i) q^{38} +(0.643109 + 6.10003i) q^{39} +(4.00965 + 7.66238i) q^{40} +(-7.72651 - 4.46090i) q^{41} +(2.42755 + 5.15278i) q^{42} +(-2.14446 + 3.71432i) q^{43} +(3.16093 - 0.467616i) q^{44} +(8.97102 - 1.91284i) q^{45} +(-1.39139 + 7.29913i) q^{46} +(-1.18924 - 2.05982i) q^{47} +(-0.862519 + 6.87430i) q^{48} +1.59265 q^{49} +(-1.15159 + 6.04117i) q^{50} +(-3.97655 + 2.89107i) q^{51} +(-4.40090 - 5.54955i) q^{52} +(3.76838 + 6.52703i) q^{53} +(6.77738 + 2.84026i) q^{54} +(4.23050 + 2.44248i) q^{55} +(-5.55466 - 3.52202i) q^{56} +(-7.19337 - 2.29248i) q^{57} +(-1.78222 + 9.34941i) q^{58} +(7.63836 + 4.41001i) q^{59} +(-7.56316 + 7.41503i) q^{60} +(10.6923 - 6.17319i) q^{61} +(-0.169376 + 0.196276i) q^{62} +(-5.18128 + 4.67124i) q^{63} +(-3.41195 - 7.23592i) q^{64} -10.8280i q^{65} +(1.66787 + 3.54026i) q^{66} +(-2.73899 - 4.74407i) q^{67} +(2.08845 - 5.27889i) q^{68} +(-9.05039 + 0.954157i) q^{69} +(-3.30801 - 9.49527i) q^{70} +(2.38111 - 4.12421i) q^{71} +(-8.36499 + 1.42373i) q^{72} +(0.471204 - 0.816150i) q^{73} +(8.81724 - 10.2176i) q^{74} +(-7.49061 + 0.789714i) q^{75} +(8.43167 - 2.21515i) q^{76} -3.71517 q^{77} +(4.94748 - 7.12534i) q^{78} +(-13.6753 - 7.89546i) q^{79} +(2.78651 - 11.9086i) q^{80} +(-0.929320 + 8.95189i) q^{81} +(4.15099 + 11.9150i) q^{82} +8.26352i q^{83} +(2.16171 - 7.75985i) q^{84} +(7.51614 - 4.33944i) q^{85} +(5.72781 - 1.99548i) q^{86} +(-11.5926 + 1.22217i) q^{87} +(-3.81637 - 2.41983i) q^{88} +(13.4259 - 7.75144i) q^{89} +(-11.3724 - 6.24061i) q^{90} +(4.11751 + 7.13173i) q^{91} +(8.23365 - 6.52944i) q^{92} +(-0.290109 - 0.129054i) q^{93} +(-0.629853 + 3.30417i) q^{94} +(12.2040 + 5.35595i) q^{95} +(7.27489 - 6.56323i) q^{96} +(0.397803 - 0.689015i) q^{97} +(-1.70521 - 1.47150i) q^{98} +(-3.55984 + 3.20942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07067 0.923935i −0.757081 0.653321i
\(3\) 0.703983 1.58253i 0.406445 0.913675i
\(4\) 0.292687 + 1.97847i 0.146344 + 0.989234i
\(5\) −1.52878 + 2.64792i −0.683691 + 1.18419i 0.290155 + 0.956980i \(0.406293\pi\)
−0.973846 + 0.227208i \(0.927040\pi\)
\(6\) −2.21589 + 1.04394i −0.904635 + 0.426187i
\(7\) 2.32537i 0.878908i −0.898265 0.439454i \(-0.855172\pi\)
0.898265 0.439454i \(-0.144828\pi\)
\(8\) 1.51460 2.38872i 0.535493 0.844539i
\(9\) −2.00882 2.22815i −0.669605 0.742717i
\(10\) 4.08334 1.42257i 1.29126 0.449856i
\(11\) 1.59767i 0.481714i −0.970561 0.240857i \(-0.922571\pi\)
0.970561 0.240857i \(-0.0774285\pi\)
\(12\) 3.33704 + 0.929621i 0.963319 + 0.268359i
\(13\) −3.06692 + 1.77069i −0.850611 + 0.491100i −0.860857 0.508847i \(-0.830072\pi\)
0.0102461 + 0.999948i \(0.496739\pi\)
\(14\) −2.14849 + 2.48972i −0.574209 + 0.665404i
\(15\) 3.11419 + 4.28344i 0.804081 + 1.10598i
\(16\) −3.82867 + 1.15814i −0.957167 + 0.289536i
\(17\) −2.45821 1.41925i −0.596205 0.344219i 0.171342 0.985212i \(-0.445190\pi\)
−0.767547 + 0.640993i \(0.778523\pi\)
\(18\) 0.0921191 + 4.24164i 0.0217127 + 0.999764i
\(19\) −0.478692 4.33253i −0.109820 0.993952i
\(20\) −5.68629 2.24963i −1.27149 0.503032i
\(21\) −3.67997 1.63702i −0.803036 0.357228i
\(22\) −1.47614 + 1.71058i −0.314714 + 0.364697i
\(23\) −2.62710 4.55027i −0.547789 0.948798i −0.998426 0.0560904i \(-0.982136\pi\)
0.450637 0.892707i \(-0.351197\pi\)
\(24\) −2.71397 4.07853i −0.553986 0.832526i
\(25\) −2.17434 3.76606i −0.434867 0.753212i
\(26\) 4.91967 + 0.937807i 0.964828 + 0.183919i
\(27\) −4.94029 + 1.61043i −0.950760 + 0.309928i
\(28\) 4.60067 0.680606i 0.869445 0.128622i
\(29\) −3.36504 5.82841i −0.624872 1.08231i −0.988566 0.150791i \(-0.951818\pi\)
0.363694 0.931518i \(-0.381515\pi\)
\(30\) 0.623336 7.46348i 0.113805 1.36264i
\(31\) 0.183320i 0.0329252i −0.999864 0.0164626i \(-0.994760\pi\)
0.999864 0.0164626i \(-0.00524045\pi\)
\(32\) 5.16931 + 2.29745i 0.913813 + 0.406135i
\(33\) −2.52836 1.12473i −0.440130 0.195790i
\(34\) 1.32065 + 3.79079i 0.226490 + 0.650115i
\(35\) 6.15741 + 3.55498i 1.04079 + 0.600902i
\(36\) 3.82037 4.62653i 0.636729 0.771088i
\(37\) 9.54314i 1.56888i 0.620203 + 0.784441i \(0.287050\pi\)
−0.620203 + 0.784441i \(0.712950\pi\)
\(38\) −3.49046 + 5.08101i −0.566227 + 0.824249i
\(39\) 0.643109 + 6.10003i 0.102980 + 0.976787i
\(40\) 4.00965 + 7.66238i 0.633981 + 1.21153i
\(41\) −7.72651 4.46090i −1.20668 0.696676i −0.244646 0.969612i \(-0.578672\pi\)
−0.962032 + 0.272937i \(0.912005\pi\)
\(42\) 2.42755 + 5.15278i 0.374579 + 0.795091i
\(43\) −2.14446 + 3.71432i −0.327027 + 0.566428i −0.981921 0.189293i \(-0.939380\pi\)
0.654893 + 0.755721i \(0.272714\pi\)
\(44\) 3.16093 0.467616i 0.476528 0.0704958i
\(45\) 8.97102 1.91284i 1.33732 0.285149i
\(46\) −1.39139 + 7.29913i −0.205149 + 1.07620i
\(47\) −1.18924 2.05982i −0.173468 0.300455i 0.766162 0.642647i \(-0.222164\pi\)
−0.939630 + 0.342192i \(0.888831\pi\)
\(48\) −0.862519 + 6.87430i −0.124494 + 0.992220i
\(49\) 1.59265 0.227521
\(50\) −1.15159 + 6.04117i −0.162860 + 0.854351i
\(51\) −3.97655 + 2.89107i −0.556829 + 0.404831i
\(52\) −4.40090 5.54955i −0.610295 0.769584i
\(53\) 3.76838 + 6.52703i 0.517627 + 0.896557i 0.999790 + 0.0204755i \(0.00651801\pi\)
−0.482163 + 0.876082i \(0.660149\pi\)
\(54\) 6.77738 + 2.84026i 0.922285 + 0.386511i
\(55\) 4.23050 + 2.44248i 0.570440 + 0.329344i
\(56\) −5.55466 3.52202i −0.742272 0.470649i
\(57\) −7.19337 2.29248i −0.952785 0.303647i
\(58\) −1.78222 + 9.34941i −0.234017 + 1.22764i
\(59\) 7.63836 + 4.41001i 0.994430 + 0.574134i 0.906596 0.422001i \(-0.138672\pi\)
0.0878345 + 0.996135i \(0.472005\pi\)
\(60\) −7.56316 + 7.41503i −0.976400 + 0.957276i
\(61\) 10.6923 6.17319i 1.36901 0.790395i 0.378204 0.925722i \(-0.376542\pi\)
0.990801 + 0.135327i \(0.0432084\pi\)
\(62\) −0.169376 + 0.196276i −0.0215107 + 0.0249270i
\(63\) −5.18128 + 4.67124i −0.652780 + 0.588521i
\(64\) −3.41195 7.23592i −0.426494 0.904490i
\(65\) 10.8280i 1.34304i
\(66\) 1.66787 + 3.54026i 0.205301 + 0.435776i
\(67\) −2.73899 4.74407i −0.334621 0.579580i 0.648791 0.760966i \(-0.275275\pi\)
−0.983412 + 0.181386i \(0.941942\pi\)
\(68\) 2.08845 5.27889i 0.253262 0.640160i
\(69\) −9.05039 + 0.954157i −1.08954 + 0.114867i
\(70\) −3.30801 9.49527i −0.395382 1.13490i
\(71\) 2.38111 4.12421i 0.282586 0.489453i −0.689435 0.724348i \(-0.742141\pi\)
0.972021 + 0.234894i \(0.0754744\pi\)
\(72\) −8.36499 + 1.42373i −0.985823 + 0.167788i
\(73\) 0.471204 0.816150i 0.0551503 0.0955231i −0.837132 0.547001i \(-0.815770\pi\)
0.892283 + 0.451477i \(0.149103\pi\)
\(74\) 8.81724 10.2176i 1.02498 1.18777i
\(75\) −7.49061 + 0.789714i −0.864941 + 0.0911883i
\(76\) 8.43167 2.21515i 0.967179 0.254096i
\(77\) −3.71517 −0.423382
\(78\) 4.94748 7.12534i 0.560191 0.806786i
\(79\) −13.6753 7.89546i −1.53860 0.888309i −0.998921 0.0464355i \(-0.985214\pi\)
−0.539675 0.841873i \(-0.681453\pi\)
\(80\) 2.78651 11.9086i 0.311542 1.33142i
\(81\) −0.929320 + 8.95189i −0.103258 + 0.994655i
\(82\) 4.15099 + 11.9150i 0.458400 + 1.31579i
\(83\) 8.26352i 0.907039i 0.891246 + 0.453519i \(0.149832\pi\)
−0.891246 + 0.453519i \(0.850168\pi\)
\(84\) 2.16171 7.75985i 0.235862 0.846669i
\(85\) 7.51614 4.33944i 0.815240 0.470679i
\(86\) 5.72781 1.99548i 0.617646 0.215178i
\(87\) −11.5926 + 1.22217i −1.24286 + 0.131031i
\(88\) −3.81637 2.41983i −0.406827 0.257955i
\(89\) 13.4259 7.75144i 1.42314 0.821651i 0.426576 0.904452i \(-0.359720\pi\)
0.996566 + 0.0828003i \(0.0263864\pi\)
\(90\) −11.3724 6.24061i −1.19875 0.657818i
\(91\) 4.11751 + 7.13173i 0.431632 + 0.747609i
\(92\) 8.23365 6.52944i 0.858417 0.680741i
\(93\) −0.290109 0.129054i −0.0300829 0.0133823i
\(94\) −0.629853 + 3.30417i −0.0649644 + 0.340799i
\(95\) 12.2040 + 5.35595i 1.25211 + 0.549509i
\(96\) 7.27489 6.56323i 0.742490 0.669857i
\(97\) 0.397803 0.689015i 0.0403907 0.0699588i −0.845123 0.534571i \(-0.820473\pi\)
0.885514 + 0.464613i \(0.153806\pi\)
\(98\) −1.70521 1.47150i −0.172252 0.148644i
\(99\) −3.55984 + 3.20942i −0.357778 + 0.322558i
\(100\) 6.81463 5.40413i 0.681463 0.540413i
\(101\) −1.74326 3.01942i −0.173461 0.300443i 0.766167 0.642642i \(-0.222162\pi\)
−0.939628 + 0.342199i \(0.888828\pi\)
\(102\) 6.92876 + 0.578677i 0.686049 + 0.0572976i
\(103\) 2.74073i 0.270052i 0.990842 + 0.135026i \(0.0431119\pi\)
−0.990842 + 0.135026i \(0.956888\pi\)
\(104\) −0.415496 + 10.0079i −0.0407427 + 0.981355i
\(105\) 9.96058 7.24165i 0.972053 0.706713i
\(106\) 1.99584 10.4701i 0.193854 1.01694i
\(107\) 3.91415i 0.378395i 0.981939 + 0.189198i \(0.0605886\pi\)
−0.981939 + 0.189198i \(0.939411\pi\)
\(108\) −4.63215 9.30286i −0.445729 0.895168i
\(109\) −16.6876 9.63461i −1.59838 0.922828i −0.991799 0.127810i \(-0.959205\pi\)
−0.606586 0.795018i \(-0.707461\pi\)
\(110\) −2.27279 6.52381i −0.216702 0.622021i
\(111\) 15.1023 + 6.71821i 1.43345 + 0.637664i
\(112\) 2.69311 + 8.90308i 0.254475 + 0.841262i
\(113\) 4.55402i 0.428406i −0.976789 0.214203i \(-0.931285\pi\)
0.976789 0.214203i \(-0.0687154\pi\)
\(114\) 5.58364 + 9.10071i 0.522956 + 0.852360i
\(115\) 16.0650 1.49807
\(116\) 10.5464 8.36352i 0.979211 0.776533i
\(117\) 10.1062 + 3.27658i 0.934322 + 0.302920i
\(118\) −4.10363 11.7790i −0.377770 1.08435i
\(119\) −3.30029 + 5.71626i −0.302537 + 0.524009i
\(120\) 14.9487 0.951213i 1.36462 0.0868335i
\(121\) 8.44746 0.767951
\(122\) −17.1516 3.26950i −1.55283 0.296006i
\(123\) −12.4989 + 9.08705i −1.12698 + 0.819352i
\(124\) 0.362692 0.0536553i 0.0325707 0.00481839i
\(125\) −1.99147 −0.178122
\(126\) 9.86339 0.214211i 0.878701 0.0190834i
\(127\) 4.59173 2.65104i 0.407450 0.235241i −0.282243 0.959343i \(-0.591079\pi\)
0.689693 + 0.724101i \(0.257745\pi\)
\(128\) −3.03244 + 10.8997i −0.268032 + 0.963410i
\(129\) 4.36836 + 6.00850i 0.384613 + 0.529019i
\(130\) −10.0043 + 11.5932i −0.877439 + 1.01679i
\(131\) 16.7656 + 9.67963i 1.46482 + 0.845714i 0.999228 0.0392864i \(-0.0125085\pi\)
0.465591 + 0.885000i \(0.345842\pi\)
\(132\) 1.48522 5.33147i 0.129272 0.464045i
\(133\) −10.0748 + 1.11314i −0.873592 + 0.0965213i
\(134\) −1.45065 + 7.61000i −0.125317 + 0.657404i
\(135\) 3.28832 15.5435i 0.283013 1.33777i
\(136\) −7.11341 + 3.72238i −0.609970 + 0.319191i
\(137\) 1.99877 1.15399i 0.170766 0.0985918i −0.412181 0.911102i \(-0.635233\pi\)
0.582947 + 0.812510i \(0.301900\pi\)
\(138\) 10.5716 + 7.34038i 0.899914 + 0.624855i
\(139\) −6.93403 12.0101i −0.588136 1.01868i −0.994476 0.104960i \(-0.966528\pi\)
0.406340 0.913722i \(-0.366805\pi\)
\(140\) −5.23122 + 13.2227i −0.442119 + 1.11752i
\(141\) −4.09693 + 0.431927i −0.345024 + 0.0363748i
\(142\) −6.35990 + 2.21569i −0.533711 + 0.185937i
\(143\) 2.82897 + 4.89991i 0.236570 + 0.409751i
\(144\) 10.2716 + 6.20436i 0.855967 + 0.517030i
\(145\) 20.5776 1.70888
\(146\) −1.25858 + 0.438468i −0.104160 + 0.0362879i
\(147\) 1.12120 2.52042i 0.0924748 0.207880i
\(148\) −18.8808 + 2.79315i −1.55199 + 0.229596i
\(149\) 10.6301 18.4119i 0.870853 1.50836i 0.00973639 0.999953i \(-0.496901\pi\)
0.861116 0.508408i \(-0.169766\pi\)
\(150\) 8.74965 + 6.07531i 0.714406 + 0.496047i
\(151\) 8.42696i 0.685776i −0.939376 0.342888i \(-0.888595\pi\)
0.939376 0.342888i \(-0.111405\pi\)
\(152\) −11.0742 5.41861i −0.898239 0.439507i
\(153\) 1.77579 + 8.32829i 0.143564 + 0.673302i
\(154\) 3.97773 + 3.43257i 0.320535 + 0.276605i
\(155\) 0.485417 + 0.280256i 0.0389896 + 0.0225107i
\(156\) −11.8805 + 3.05777i −0.951201 + 0.244818i
\(157\) 1.93574 + 1.11760i 0.154489 + 0.0891944i 0.575252 0.817976i \(-0.304904\pi\)
−0.420763 + 0.907171i \(0.638237\pi\)
\(158\) 7.34694 + 21.0886i 0.584491 + 1.67772i
\(159\) 12.9821 1.36867i 1.02955 0.108542i
\(160\) −13.9862 + 10.1756i −1.10571 + 0.804455i
\(161\) −10.5811 + 6.10899i −0.833906 + 0.481456i
\(162\) 9.26597 8.72593i 0.728003 0.685574i
\(163\) 12.3222 0.965147 0.482574 0.875855i \(-0.339702\pi\)
0.482574 + 0.875855i \(0.339702\pi\)
\(164\) 6.56430 16.5923i 0.512586 1.29564i
\(165\) 6.84350 4.97544i 0.532766 0.387337i
\(166\) 7.63495 8.84753i 0.592587 0.686702i
\(167\) −2.66564 4.61702i −0.206273 0.357276i 0.744264 0.667885i \(-0.232800\pi\)
−0.950538 + 0.310609i \(0.899467\pi\)
\(168\) −9.48409 + 6.31098i −0.731713 + 0.486903i
\(169\) −0.229331 + 0.397212i −0.0176408 + 0.0305548i
\(170\) −12.0567 2.29829i −0.924707 0.176271i
\(171\) −8.69194 + 9.76986i −0.664689 + 0.747120i
\(172\) −7.97631 3.15562i −0.608188 0.240613i
\(173\) −12.2325 + 21.1872i −0.930017 + 1.61084i −0.146729 + 0.989177i \(0.546875\pi\)
−0.783287 + 0.621660i \(0.786459\pi\)
\(174\) 13.5411 + 9.40225i 1.02655 + 0.712783i
\(175\) −8.75749 + 5.05614i −0.662004 + 0.382208i
\(176\) 1.85033 + 6.11693i 0.139474 + 0.461081i
\(177\) 12.3563 8.98338i 0.928753 0.675232i
\(178\) −21.5366 4.10539i −1.61424 0.307712i
\(179\) 5.59775i 0.418396i 0.977873 + 0.209198i \(0.0670853\pi\)
−0.977873 + 0.209198i \(0.932915\pi\)
\(180\) 6.41019 + 17.1890i 0.477787 + 1.28119i
\(181\) −12.1054 + 6.98903i −0.899784 + 0.519491i −0.877130 0.480253i \(-0.840545\pi\)
−0.0226541 + 0.999743i \(0.507212\pi\)
\(182\) 2.18075 11.4401i 0.161648 0.847994i
\(183\) −2.24209 21.2667i −0.165740 1.57208i
\(184\) −14.8483 0.616455i −1.09463 0.0454457i
\(185\) −25.2695 14.5894i −1.85785 1.07263i
\(186\) 0.191375 + 0.406217i 0.0140323 + 0.0297853i
\(187\) −2.26749 + 3.92740i −0.165815 + 0.287200i
\(188\) 3.72721 2.95575i 0.271834 0.215570i
\(189\) 3.74486 + 11.4880i 0.272398 + 0.835630i
\(190\) −8.11800 17.0102i −0.588942 1.23405i
\(191\) 7.36427 0.532860 0.266430 0.963854i \(-0.414156\pi\)
0.266430 + 0.963854i \(0.414156\pi\)
\(192\) −13.8530 + 0.305555i −0.999757 + 0.0220515i
\(193\) 1.90362 3.29716i 0.137025 0.237335i −0.789344 0.613951i \(-0.789579\pi\)
0.926369 + 0.376616i \(0.122912\pi\)
\(194\) −1.06252 + 0.370166i −0.0762846 + 0.0265764i
\(195\) −17.1356 7.62271i −1.22711 0.545873i
\(196\) 0.466147 + 3.15100i 0.0332962 + 0.225072i
\(197\) 1.07852 0.0768414 0.0384207 0.999262i \(-0.487767\pi\)
0.0384207 + 0.999262i \(0.487767\pi\)
\(198\) 6.77672 0.147176i 0.481601 0.0104593i
\(199\) 11.6223 6.71017i 0.823886 0.475671i −0.0278684 0.999612i \(-0.508872\pi\)
0.851755 + 0.523941i \(0.175539\pi\)
\(200\) −12.2893 0.510213i −0.868986 0.0360775i
\(201\) −9.43584 + 0.994794i −0.665553 + 0.0701673i
\(202\) −0.923281 + 4.84347i −0.0649618 + 0.340786i
\(203\) −13.5532 + 7.82496i −0.951250 + 0.549205i
\(204\) −6.88378 7.02130i −0.481961 0.491589i
\(205\) 23.6243 13.6395i 1.64999 0.952622i
\(206\) 2.53226 2.93443i 0.176431 0.204452i
\(207\) −4.86134 + 14.9942i −0.337886 + 1.04217i
\(208\) 9.69151 10.3313i 0.671986 0.716348i
\(209\) −6.92194 + 0.764790i −0.478801 + 0.0529017i
\(210\) −17.3554 1.44949i −1.19763 0.100024i
\(211\) −4.40018 + 7.62134i −0.302921 + 0.524675i −0.976796 0.214170i \(-0.931295\pi\)
0.673875 + 0.738845i \(0.264629\pi\)
\(212\) −11.8106 + 9.36601i −0.811153 + 0.643260i
\(213\) −4.85043 6.67156i −0.332346 0.457128i
\(214\) 3.61642 4.19078i 0.247213 0.286476i
\(215\) −6.55682 11.3567i −0.447171 0.774524i
\(216\) −3.63571 + 14.2401i −0.247379 + 0.968919i
\(217\) −0.426287 −0.0289382
\(218\) 8.96526 + 25.7338i 0.607204 + 1.74291i
\(219\) −0.959863 1.32025i −0.0648615 0.0892143i
\(220\) −3.59415 + 9.08479i −0.242318 + 0.612496i
\(221\) 10.0522 0.676184
\(222\) −9.96248 21.1466i −0.668638 1.41927i
\(223\) 21.1334 + 12.2014i 1.41520 + 0.817064i 0.995872 0.0907716i \(-0.0289333\pi\)
0.419325 + 0.907836i \(0.362267\pi\)
\(224\) 5.34242 12.0206i 0.356955 0.803157i
\(225\) −4.02352 + 12.4101i −0.268234 + 0.827338i
\(226\) −4.20762 + 4.87587i −0.279887 + 0.324338i
\(227\) 27.0923i 1.79818i −0.437762 0.899091i \(-0.644229\pi\)
0.437762 0.899091i \(-0.355771\pi\)
\(228\) 2.43020 14.9028i 0.160944 0.986964i
\(229\) 2.47490i 0.163546i 0.996651 + 0.0817731i \(0.0260583\pi\)
−0.996651 + 0.0817731i \(0.973942\pi\)
\(230\) −17.2004 14.8431i −1.13416 0.978722i
\(231\) −2.61541 + 5.87937i −0.172082 + 0.386834i
\(232\) −19.0191 0.789613i −1.24867 0.0518406i
\(233\) −0.255230 0.147357i −0.0167206 0.00965367i 0.491616 0.870812i \(-0.336406\pi\)
−0.508337 + 0.861158i \(0.669740\pi\)
\(234\) −7.79314 12.8457i −0.509454 0.839747i
\(235\) 7.27232 0.474394
\(236\) −6.48941 + 16.4030i −0.422425 + 1.06774i
\(237\) −22.1220 + 16.0834i −1.43698 + 1.04473i
\(238\) 8.81499 3.07100i 0.571391 0.199064i
\(239\) −16.2187 −1.04910 −0.524549 0.851380i \(-0.675766\pi\)
−0.524549 + 0.851380i \(0.675766\pi\)
\(240\) −16.8840 12.7932i −1.08986 0.825796i
\(241\) 13.5618 + 23.4897i 0.873592 + 1.51311i 0.858255 + 0.513223i \(0.171549\pi\)
0.0153367 + 0.999882i \(0.495118\pi\)
\(242\) −9.04448 7.80491i −0.581401 0.501719i
\(243\) 13.5124 + 7.77266i 0.866823 + 0.498616i
\(244\) 15.3429 + 19.3475i 0.982231 + 1.23860i
\(245\) −2.43481 + 4.21721i −0.155554 + 0.269428i
\(246\) 21.7780 + 1.81886i 1.38852 + 0.115966i
\(247\) 9.13968 + 12.4399i 0.581544 + 0.791534i
\(248\) −0.437899 0.277657i −0.0278066 0.0176312i
\(249\) 13.0773 + 5.81738i 0.828739 + 0.368661i
\(250\) 2.13222 + 1.83999i 0.134853 + 0.116371i
\(251\) 10.4624 6.04048i 0.660382 0.381272i −0.132040 0.991244i \(-0.542153\pi\)
0.792423 + 0.609973i \(0.208820\pi\)
\(252\) −10.7584 8.88378i −0.677715 0.559626i
\(253\) −7.26982 + 4.19723i −0.457049 + 0.263878i
\(254\) −7.36563 1.40406i −0.462161 0.0880988i
\(255\) −1.57608 14.9494i −0.0986977 0.936169i
\(256\) 13.3174 8.86830i 0.832338 0.554269i
\(257\) −8.21495 + 4.74290i −0.512434 + 0.295854i −0.733834 0.679329i \(-0.762271\pi\)
0.221399 + 0.975183i \(0.428938\pi\)
\(258\) 0.874370 10.4692i 0.0544359 0.651785i
\(259\) 22.1913 1.37890
\(260\) 21.4228 3.16921i 1.32858 0.196546i
\(261\) −6.22685 + 19.2060i −0.385433 + 1.18882i
\(262\) −9.00716 25.8541i −0.556464 1.59727i
\(263\) −5.60343 + 9.70543i −0.345522 + 0.598462i −0.985449 0.169974i \(-0.945632\pi\)
0.639926 + 0.768436i \(0.278965\pi\)
\(264\) −6.51612 + 4.33601i −0.401040 + 0.266863i
\(265\) −23.0441 −1.41559
\(266\) 11.8152 + 8.11661i 0.724439 + 0.497661i
\(267\) −2.81531 26.7038i −0.172294 1.63425i
\(268\) 8.58432 6.80753i 0.524371 0.415836i
\(269\) −8.91499 + 15.4412i −0.543557 + 0.941468i 0.455140 + 0.890420i \(0.349589\pi\)
−0.998696 + 0.0510476i \(0.983744\pi\)
\(270\) −17.8819 + 13.6039i −1.08826 + 0.827905i
\(271\) −4.43875 2.56272i −0.269635 0.155674i 0.359087 0.933304i \(-0.383088\pi\)
−0.628722 + 0.777630i \(0.716422\pi\)
\(272\) 11.0554 + 2.58688i 0.670331 + 0.156852i
\(273\) 14.1848 1.49547i 0.858506 0.0905099i
\(274\) −3.20624 0.611185i −0.193696 0.0369230i
\(275\) −6.01691 + 3.47386i −0.362833 + 0.209482i
\(276\) −4.53670 17.6266i −0.273077 1.06100i
\(277\) 25.4042i 1.52639i −0.646169 0.763195i \(-0.723630\pi\)
0.646169 0.763195i \(-0.276370\pi\)
\(278\) −3.67246 + 19.2655i −0.220259 + 1.15547i
\(279\) −0.408464 + 0.368256i −0.0244541 + 0.0220469i
\(280\) 17.8179 9.32393i 1.06482 0.557211i
\(281\) −18.2678 + 10.5469i −1.08977 + 0.629177i −0.933515 0.358540i \(-0.883275\pi\)
−0.156253 + 0.987717i \(0.549941\pi\)
\(282\) 4.78555 + 3.32284i 0.284975 + 0.197872i
\(283\) −9.35633 + 16.2056i −0.556176 + 0.963326i 0.441635 + 0.897195i \(0.354399\pi\)
−0.997811 + 0.0661307i \(0.978935\pi\)
\(284\) 8.85653 + 3.50385i 0.525539 + 0.207915i
\(285\) 17.0674 15.5428i 1.01099 0.920675i
\(286\) 1.49830 7.85999i 0.0885964 0.464771i
\(287\) −10.3733 + 17.9670i −0.612314 + 1.06056i
\(288\) −5.26512 16.1331i −0.310250 0.950655i
\(289\) −4.47145 7.74479i −0.263027 0.455576i
\(290\) −22.0319 19.0124i −1.29376 1.11645i
\(291\) −0.810341 1.11459i −0.0475030 0.0653384i
\(292\) 1.75264 + 0.693386i 0.102566 + 0.0405773i
\(293\) 23.9713 1.40042 0.700209 0.713938i \(-0.253090\pi\)
0.700209 + 0.713938i \(0.253090\pi\)
\(294\) −3.52914 + 1.66263i −0.205823 + 0.0969666i
\(295\) −23.3547 + 13.4839i −1.35977 + 0.785061i
\(296\) 22.7959 + 14.4541i 1.32498 + 0.840126i
\(297\) 2.57293 + 7.89294i 0.149297 + 0.457995i
\(298\) −28.3928 + 9.89160i −1.64475 + 0.573005i
\(299\) 16.1142 + 9.30355i 0.931910 + 0.538038i
\(300\) −3.75483 14.5888i −0.216785 0.842284i
\(301\) 8.63717 + 4.98667i 0.497838 + 0.287427i
\(302\) −7.78597 + 9.02253i −0.448032 + 0.519188i
\(303\) −6.00555 + 0.633148i −0.345010 + 0.0363734i
\(304\) 6.85045 + 16.0334i 0.392900 + 0.919581i
\(305\) 37.7498i 2.16155i
\(306\) 5.79350 10.5576i 0.331193 0.603538i
\(307\) 7.90289 13.6882i 0.451042 0.781227i −0.547409 0.836865i \(-0.684386\pi\)
0.998451 + 0.0556379i \(0.0177192\pi\)
\(308\) −1.08738 7.35034i −0.0619593 0.418824i
\(309\) 4.33730 + 1.92943i 0.246740 + 0.109761i
\(310\) −0.260785 0.748556i −0.0148116 0.0425151i
\(311\) 3.58329 0.203189 0.101595 0.994826i \(-0.467606\pi\)
0.101595 + 0.994826i \(0.467606\pi\)
\(312\) 15.5453 + 7.70293i 0.880081 + 0.436092i
\(313\) 2.16886 + 3.75658i 0.122591 + 0.212335i 0.920789 0.390061i \(-0.127546\pi\)
−0.798197 + 0.602396i \(0.794213\pi\)
\(314\) −1.03996 2.98509i −0.0586883 0.168458i
\(315\) −4.44806 20.8609i −0.250620 1.17538i
\(316\) 11.6183 29.3671i 0.653582 1.65203i
\(317\) −8.57067 14.8448i −0.481377 0.833769i 0.518395 0.855141i \(-0.326530\pi\)
−0.999772 + 0.0213725i \(0.993196\pi\)
\(318\) −15.1642 10.5292i −0.850365 0.590451i
\(319\) −9.31186 + 5.37620i −0.521364 + 0.301010i
\(320\) 24.3763 + 2.02754i 1.36268 + 0.113343i
\(321\) 6.19427 + 2.75549i 0.345730 + 0.153797i
\(322\) 16.9732 + 3.23549i 0.945879 + 0.180307i
\(323\) −4.97222 + 11.3297i −0.276662 + 0.630400i
\(324\) −17.9830 + 0.781472i −0.999057 + 0.0434151i
\(325\) 13.3370 + 7.70014i 0.739806 + 0.427127i
\(326\) −13.1930 11.3849i −0.730695 0.630551i
\(327\) −26.9949 + 19.6261i −1.49282 + 1.08533i
\(328\) −22.3584 + 11.7000i −1.23454 + 0.646022i
\(329\) −4.78984 + 2.76541i −0.264072 + 0.152462i
\(330\) −11.9241 0.995882i −0.656402 0.0548215i
\(331\) −1.25012 −0.0687131 −0.0343565 0.999410i \(-0.510938\pi\)
−0.0343565 + 0.999410i \(0.510938\pi\)
\(332\) −16.3491 + 2.41862i −0.897273 + 0.132739i
\(333\) 21.2636 19.1704i 1.16524 1.05053i
\(334\) −1.41180 + 7.40620i −0.0772501 + 0.405249i
\(335\) 16.7492 0.915109
\(336\) 15.9853 + 2.00568i 0.872070 + 0.109419i
\(337\) −7.44553 + 12.8960i −0.405584 + 0.702491i −0.994389 0.105783i \(-0.966265\pi\)
0.588806 + 0.808275i \(0.299598\pi\)
\(338\) 0.612537 0.213398i 0.0333176 0.0116073i
\(339\) −7.20688 3.20595i −0.391424 0.174123i
\(340\) 10.7853 + 13.6003i 0.584916 + 0.737582i
\(341\) −0.292884 −0.0158605
\(342\) 18.3330 2.42955i 0.991333 0.131375i
\(343\) 19.9811i 1.07888i
\(344\) 5.62445 + 10.7482i 0.303250 + 0.579506i
\(345\) 11.3095 25.4234i 0.608884 1.36875i
\(346\) 32.6726 11.3826i 1.75649 0.611934i
\(347\) −27.9737 16.1506i −1.50171 0.867012i −0.999998 0.00197608i \(-0.999371\pi\)
−0.501710 0.865036i \(-0.667296\pi\)
\(348\) −5.81103 22.5778i −0.311504 1.21030i
\(349\) 1.43421i 0.0767717i −0.999263 0.0383858i \(-0.987778\pi\)
0.999263 0.0383858i \(-0.0122216\pi\)
\(350\) 14.0480 + 2.67788i 0.750896 + 0.143139i
\(351\) 12.2999 13.6868i 0.656521 0.730547i
\(352\) 3.67055 8.25882i 0.195641 0.440197i
\(353\) 14.1746i 0.754435i 0.926125 + 0.377218i \(0.123119\pi\)
−0.926125 + 0.377218i \(0.876881\pi\)
\(354\) −21.5296 1.79811i −1.14428 0.0955685i
\(355\) 7.28040 + 12.6100i 0.386403 + 0.669270i
\(356\) 19.2656 + 24.2940i 1.02107 + 1.28758i
\(357\) 6.72282 + 9.24696i 0.355810 + 0.489401i
\(358\) 5.17196 5.99337i 0.273347 0.316759i
\(359\) 13.3696 23.1568i 0.705620 1.22217i −0.260847 0.965380i \(-0.584002\pi\)
0.966467 0.256790i \(-0.0826647\pi\)
\(360\) 9.01830 24.3264i 0.475306 1.28211i
\(361\) −18.5417 + 4.14790i −0.975879 + 0.218311i
\(362\) 19.4183 + 3.70159i 1.02060 + 0.194551i
\(363\) 5.94687 13.3684i 0.312130 0.701658i
\(364\) −12.9048 + 10.2337i −0.676393 + 0.536393i
\(365\) 1.44074 + 2.49543i 0.0754115 + 0.130617i
\(366\) −17.2485 + 24.8412i −0.901593 + 1.29847i
\(367\) 13.2170 7.63085i 0.689922 0.398327i −0.113661 0.993520i \(-0.536258\pi\)
0.803583 + 0.595193i \(0.202924\pi\)
\(368\) 15.3282 + 14.3789i 0.799036 + 0.749553i
\(369\) 5.58156 + 26.1770i 0.290565 + 1.36272i
\(370\) 13.5758 + 38.9678i 0.705772 + 2.02584i
\(371\) 15.1778 8.76289i 0.787991 0.454947i
\(372\) 0.170418 0.611745i 0.00883576 0.0317175i
\(373\) 18.5885i 0.962474i −0.876591 0.481237i \(-0.840188\pi\)
0.876591 0.481237i \(-0.159812\pi\)
\(374\) 6.05641 2.10996i 0.313169 0.109103i
\(375\) −1.40196 + 3.15157i −0.0723970 + 0.162746i
\(376\) −6.72154 0.279057i −0.346637 0.0143912i
\(377\) 20.6406 + 11.9169i 1.06305 + 0.613749i
\(378\) 6.60466 15.7599i 0.339707 0.810603i
\(379\) −38.1107 −1.95762 −0.978809 0.204776i \(-0.934353\pi\)
−0.978809 + 0.204776i \(0.934353\pi\)
\(380\) −7.02461 + 25.7129i −0.360355 + 1.31904i
\(381\) −0.962850 9.13284i −0.0493283 0.467890i
\(382\) −7.88473 6.80411i −0.403418 0.348128i
\(383\) 11.0245 19.0951i 0.563328 0.975713i −0.433875 0.900973i \(-0.642854\pi\)
0.997203 0.0747397i \(-0.0238126\pi\)
\(384\) 15.1144 + 12.4722i 0.771304 + 0.636467i
\(385\) 5.67967 9.83748i 0.289463 0.501364i
\(386\) −5.08452 + 1.77137i −0.258795 + 0.0901603i
\(387\) 12.5839 2.68319i 0.639675 0.136394i
\(388\) 1.47962 + 0.585374i 0.0751166 + 0.0297179i
\(389\) 2.51778 + 4.36092i 0.127657 + 0.221108i 0.922768 0.385355i \(-0.125921\pi\)
−0.795112 + 0.606463i \(0.792588\pi\)
\(390\) 11.3038 + 23.9936i 0.572388 + 1.21496i
\(391\) 14.9141i 0.754237i
\(392\) 2.41223 3.80439i 0.121836 0.192151i
\(393\) 27.1210 19.7178i 1.36808 0.994633i
\(394\) −1.15474 0.996484i −0.0581752 0.0502021i
\(395\) 41.8132 24.1409i 2.10385 1.21466i
\(396\) −7.39164 6.10368i −0.371444 0.306721i
\(397\) −10.1916 5.88414i −0.511503 0.295316i 0.221948 0.975058i \(-0.428758\pi\)
−0.733451 + 0.679742i \(0.762092\pi\)
\(398\) −18.6435 3.55390i −0.934515 0.178141i
\(399\) −5.33088 + 16.7272i −0.266878 + 0.837410i
\(400\) 12.6865 + 11.9008i 0.634323 + 0.595040i
\(401\) −14.4846 8.36267i −0.723325 0.417612i 0.0926501 0.995699i \(-0.470466\pi\)
−0.815975 + 0.578087i \(0.803800\pi\)
\(402\) 11.0218 + 7.65301i 0.549719 + 0.381697i
\(403\) 0.324602 + 0.562227i 0.0161696 + 0.0280065i
\(404\) 5.46359 4.33273i 0.271824 0.215561i
\(405\) −22.2832 16.1462i −1.10726 0.802313i
\(406\) 21.7409 + 4.14432i 1.07898 + 0.205679i
\(407\) 15.2467 0.755753
\(408\) 0.883064 + 13.8777i 0.0437182 + 0.687048i
\(409\) −16.3774 28.3664i −0.809808 1.40263i −0.912996 0.407968i \(-0.866238\pi\)
0.103188 0.994662i \(-0.467096\pi\)
\(410\) −37.8959 7.22386i −1.87154 0.356761i
\(411\) −0.419125 3.97550i −0.0206739 0.196097i
\(412\) −5.42245 + 0.802177i −0.267145 + 0.0395204i
\(413\) 10.2549 17.7620i 0.504611 0.874012i
\(414\) 19.0586 11.5624i 0.936680 0.568260i
\(415\) −21.8812 12.6331i −1.07410 0.620134i
\(416\) −19.9219 + 2.10714i −0.976752 + 0.103311i
\(417\) −23.8878 + 2.51842i −1.16979 + 0.123328i
\(418\) 8.11776 + 5.57658i 0.397053 + 0.272760i
\(419\) 14.9989i 0.732744i −0.930468 0.366372i \(-0.880600\pi\)
0.930468 0.366372i \(-0.119400\pi\)
\(420\) 17.2427 + 17.5872i 0.841358 + 0.858165i
\(421\) −2.84671 1.64355i −0.138740 0.0801015i 0.429023 0.903293i \(-0.358858\pi\)
−0.567763 + 0.823192i \(0.692191\pi\)
\(422\) 11.7528 4.09449i 0.572117 0.199317i
\(423\) −2.20063 + 6.78759i −0.106998 + 0.330024i
\(424\) 21.2989 + 0.884259i 1.03436 + 0.0429434i
\(425\) 12.3437i 0.598758i
\(426\) −0.970861 + 11.6246i −0.0470384 + 0.563211i
\(427\) −14.3550 24.8635i −0.694685 1.20323i
\(428\) −7.74402 + 1.14562i −0.374321 + 0.0553757i
\(429\) 9.74582 1.02747i 0.470532 0.0496069i
\(430\) −3.47268 + 18.2175i −0.167467 + 0.878524i
\(431\) −12.2387 21.1980i −0.589516 1.02107i −0.994296 0.106657i \(-0.965985\pi\)
0.404780 0.914414i \(-0.367348\pi\)
\(432\) 17.0496 11.8874i 0.820301 0.571932i
\(433\) 1.72415 + 2.98631i 0.0828571 + 0.143513i 0.904476 0.426524i \(-0.140262\pi\)
−0.821619 + 0.570037i \(0.806929\pi\)
\(434\) 0.456414 + 0.393861i 0.0219086 + 0.0189059i
\(435\) 14.4863 32.5647i 0.694564 1.56136i
\(436\) 14.1775 35.8359i 0.678979 1.71623i
\(437\) −18.4566 + 13.5602i −0.882901 + 0.648672i
\(438\) −0.192126 + 2.30041i −0.00918014 + 0.109918i
\(439\) 20.4331 + 11.7971i 0.975220 + 0.563044i 0.900824 0.434185i \(-0.142964\pi\)
0.0743965 + 0.997229i \(0.476297\pi\)
\(440\) 12.2419 6.40608i 0.583611 0.305398i
\(441\) −3.19933 3.54866i −0.152349 0.168984i
\(442\) −10.7626 9.28758i −0.511926 0.441765i
\(443\) −8.81900 + 5.09165i −0.419003 + 0.241912i −0.694651 0.719347i \(-0.744441\pi\)
0.275648 + 0.961259i \(0.411108\pi\)
\(444\) −8.87150 + 31.8458i −0.421023 + 1.51133i
\(445\) 47.4010i 2.24702i
\(446\) −11.3537 32.5896i −0.537614 1.54316i
\(447\) −21.6540 29.7842i −1.02420 1.40874i
\(448\) −16.8262 + 7.93405i −0.794964 + 0.374849i
\(449\) 3.19906i 0.150973i −0.997147 0.0754865i \(-0.975949\pi\)
0.997147 0.0754865i \(-0.0240510\pi\)
\(450\) 15.7740 9.56968i 0.743593 0.451119i
\(451\) −7.12703 + 12.3444i −0.335599 + 0.581274i
\(452\) 9.00998 1.33290i 0.423794 0.0626944i
\(453\) −13.3359 5.93244i −0.626577 0.278730i
\(454\) −25.0316 + 29.0071i −1.17479 + 1.36137i
\(455\) −25.1790 −1.18041
\(456\) −16.3712 + 13.7107i −0.766652 + 0.642063i
\(457\) 4.69972 0.219844 0.109922 0.993940i \(-0.464940\pi\)
0.109922 + 0.993940i \(0.464940\pi\)
\(458\) 2.28665 2.64981i 0.106848 0.123818i
\(459\) 14.4299 + 3.05272i 0.673531 + 0.142489i
\(460\) 4.70203 + 31.7842i 0.219233 + 1.48194i
\(461\) −10.6853 + 18.5075i −0.497664 + 0.861979i −0.999996 0.00269571i \(-0.999142\pi\)
0.502333 + 0.864674i \(0.332475\pi\)
\(462\) 8.23241 3.87842i 0.383007 0.180440i
\(463\) 6.48809i 0.301527i 0.988570 + 0.150764i \(0.0481732\pi\)
−0.988570 + 0.150764i \(0.951827\pi\)
\(464\) 19.6338 + 18.4179i 0.911474 + 0.855028i
\(465\) 0.785239 0.570893i 0.0364146 0.0264745i
\(466\) 0.137120 + 0.393587i 0.00635194 + 0.0182326i
\(467\) 15.3004i 0.708018i −0.935242 0.354009i \(-0.884818\pi\)
0.935242 0.354009i \(-0.115182\pi\)
\(468\) −3.52464 + 20.9539i −0.162927 + 0.968593i
\(469\) −11.0317 + 6.36917i −0.509397 + 0.294101i
\(470\) −7.78628 6.71915i −0.359155 0.309931i
\(471\) 3.13137 2.27660i 0.144286 0.104900i
\(472\) 22.1034 11.5665i 1.01739 0.532390i
\(473\) 5.93424 + 3.42613i 0.272856 + 0.157534i
\(474\) 38.5455 + 3.21925i 1.77045 + 0.147865i
\(475\) −15.2758 + 11.2232i −0.700900 + 0.514955i
\(476\) −12.2754 4.85643i −0.562642 0.222594i
\(477\) 6.97323 21.5081i 0.319282 0.984790i
\(478\) 17.3649 + 14.9850i 0.794252 + 0.685398i
\(479\) 4.82921 + 8.36444i 0.220652 + 0.382181i 0.955006 0.296586i \(-0.0958480\pi\)
−0.734354 + 0.678767i \(0.762515\pi\)
\(480\) 6.25723 + 29.2971i 0.285602 + 1.33722i
\(481\) −16.8979 29.2681i −0.770479 1.33451i
\(482\) 7.18271 37.6801i 0.327164 1.71628i
\(483\) 2.21877 + 21.0455i 0.100957 + 0.957604i
\(484\) 2.47246 + 16.7130i 0.112385 + 0.759683i
\(485\) 1.21631 + 2.10670i 0.0552296 + 0.0956605i
\(486\) −7.28598 20.8066i −0.330499 0.943806i
\(487\) 2.53353i 0.114805i 0.998351 + 0.0574027i \(0.0182819\pi\)
−0.998351 + 0.0574027i \(0.981718\pi\)
\(488\) 1.44855 34.8908i 0.0655728 1.57943i
\(489\) 8.67460 19.5002i 0.392279 0.881831i
\(490\) 6.50332 2.26565i 0.293790 0.102352i
\(491\) 17.6869 + 10.2115i 0.798197 + 0.460839i 0.842840 0.538164i \(-0.180882\pi\)
−0.0446433 + 0.999003i \(0.514215\pi\)
\(492\) −21.6367 22.0689i −0.975457 0.994943i
\(493\) 19.1033i 0.860370i
\(494\) 1.70807 21.7636i 0.0768497 0.979190i
\(495\) −3.05608 14.3327i −0.137360 0.644206i
\(496\) 0.212311 + 0.701871i 0.00953303 + 0.0315149i
\(497\) −9.59032 5.53697i −0.430184 0.248367i
\(498\) −8.62663 18.3111i −0.386568 0.820539i
\(499\) 10.9759 19.0109i 0.491350 0.851043i −0.508601 0.861003i \(-0.669837\pi\)
0.999950 + 0.00995967i \(0.00317032\pi\)
\(500\) −0.582877 3.94006i −0.0260671 0.176205i
\(501\) −9.18314 + 0.968153i −0.410273 + 0.0432539i
\(502\) −16.7829 3.19921i −0.749056 0.142788i
\(503\) 13.1844 + 22.8360i 0.587863 + 1.01821i 0.994512 + 0.104624i \(0.0333640\pi\)
−0.406649 + 0.913585i \(0.633303\pi\)
\(504\) 3.31070 + 19.4517i 0.147470 + 0.866448i
\(505\) 10.6603 0.474375
\(506\) 11.6616 + 2.22297i 0.518420 + 0.0988232i
\(507\) 0.467156 + 0.642554i 0.0207471 + 0.0285368i
\(508\) 6.58893 + 8.30866i 0.292336 + 0.368637i
\(509\) −14.2206 24.6308i −0.630316 1.09174i −0.987487 0.157700i \(-0.949592\pi\)
0.357171 0.934039i \(-0.383741\pi\)
\(510\) −12.1248 + 17.4622i −0.536897 + 0.773237i
\(511\) −1.89785 1.09572i −0.0839560 0.0484720i
\(512\) −22.4523 2.80936i −0.992263 0.124158i
\(513\) 9.34214 + 20.6331i 0.412466 + 0.910973i
\(514\) 13.1777 + 2.51198i 0.581242 + 0.110799i
\(515\) −7.25726 4.18998i −0.319793 0.184633i
\(516\) −10.6091 + 10.4013i −0.467037 + 0.457890i
\(517\) −3.29090 + 1.90000i −0.144734 + 0.0835619i
\(518\) −23.7597 20.5034i −1.04394 0.900866i
\(519\) 24.9180 + 34.2737i 1.09378 + 1.50445i
\(520\) −25.8650 16.4001i −1.13425 0.719191i
\(521\) 15.3912i 0.674299i 0.941451 + 0.337150i \(0.109463\pi\)
−0.941451 + 0.337150i \(0.890537\pi\)
\(522\) 24.4121 14.8102i 1.06849 0.648224i
\(523\) −20.4745 35.4629i −0.895289 1.55069i −0.833446 0.552601i \(-0.813635\pi\)
−0.0618431 0.998086i \(-0.519698\pi\)
\(524\) −14.2438 + 36.0033i −0.622242 + 1.57281i
\(525\) 1.83638 + 17.4185i 0.0801461 + 0.760203i
\(526\) 14.9666 5.21414i 0.652576 0.227347i
\(527\) −0.260177 + 0.450639i −0.0113335 + 0.0196302i
\(528\) 10.9828 + 1.37802i 0.477967 + 0.0599705i
\(529\) −2.30333 + 3.98948i −0.100145 + 0.173456i
\(530\) 24.6728 + 21.2913i 1.07172 + 0.924834i
\(531\) −5.51789 25.8783i −0.239456 1.12302i
\(532\) −5.15106 19.6068i −0.223327 0.850061i
\(533\) 31.5955 1.36855
\(534\) −21.6583 + 31.1922i −0.937247 + 1.34982i
\(535\) −10.3644 5.98387i −0.448091 0.258705i
\(536\) −15.4807 0.642709i −0.668665 0.0277608i
\(537\) 8.85862 + 3.94072i 0.382278 + 0.170055i
\(538\) 23.8117 8.29564i 1.02660 0.357650i
\(539\) 2.54452i 0.109600i
\(540\) 31.7148 + 1.95644i 1.36479 + 0.0841916i
\(541\) −15.2088 + 8.78078i −0.653876 + 0.377515i −0.789940 0.613185i \(-0.789888\pi\)
0.136064 + 0.990700i \(0.456555\pi\)
\(542\) 2.38468 + 6.84496i 0.102431 + 0.294016i
\(543\) 2.53840 + 24.0773i 0.108933 + 1.03325i
\(544\) −9.44661 12.9842i −0.405020 0.556691i
\(545\) 51.0234 29.4584i 2.18560 1.26186i
\(546\) −16.5691 11.5047i −0.709091 0.492357i
\(547\) 10.2145 + 17.6921i 0.436742 + 0.756459i 0.997436 0.0715637i \(-0.0227989\pi\)
−0.560694 + 0.828023i \(0.689466\pi\)
\(548\) 2.86814 + 3.61673i 0.122521 + 0.154499i
\(549\) −35.2336 11.4232i −1.50373 0.487531i
\(550\) 9.65177 + 1.83986i 0.411553 + 0.0784518i
\(551\) −23.6410 + 17.3692i −1.00714 + 0.739951i
\(552\) −11.4285 + 23.0640i −0.486431 + 0.981669i
\(553\) −18.3599 + 31.8003i −0.780742 + 1.35228i
\(554\) −23.4718 + 27.1996i −0.997222 + 1.15560i
\(555\) −40.8774 + 29.7192i −1.73515 + 1.26151i
\(556\) 21.7321 17.2339i 0.921645 0.730882i
\(557\) 8.79774 + 15.2381i 0.372772 + 0.645660i 0.989991 0.141131i \(-0.0450740\pi\)
−0.617219 + 0.786792i \(0.711741\pi\)
\(558\) 0.777577 0.0168873i 0.0329174 0.000714894i
\(559\) 15.1887i 0.642413i
\(560\) −27.6919 6.47968i −1.17019 0.273817i
\(561\) 4.61897 + 6.35320i 0.195013 + 0.268232i
\(562\) 29.3036 + 5.58596i 1.23610 + 0.235629i
\(563\) 24.9734i 1.05250i 0.850329 + 0.526251i \(0.176403\pi\)
−0.850329 + 0.526251i \(0.823597\pi\)
\(564\) −2.05367 7.97922i −0.0864752 0.335986i
\(565\) 12.0587 + 6.96209i 0.507313 + 0.292897i
\(566\) 24.9906 8.70632i 1.05043 0.365954i
\(567\) 20.8165 + 2.16102i 0.874210 + 0.0907541i
\(568\) −6.24513 11.9343i −0.262040 0.500754i
\(569\) 10.9401i 0.458634i 0.973352 + 0.229317i \(0.0736492\pi\)
−0.973352 + 0.229317i \(0.926351\pi\)
\(570\) −32.6342 + 0.872087i −1.36689 + 0.0365277i
\(571\) −31.6820 −1.32585 −0.662925 0.748685i \(-0.730685\pi\)
−0.662925 + 0.748685i \(0.730685\pi\)
\(572\) −8.86632 + 7.03116i −0.370719 + 0.293988i
\(573\) 5.18432 11.6542i 0.216578 0.486861i
\(574\) 27.7067 9.65259i 1.15646 0.402891i
\(575\) −11.4244 + 19.7877i −0.476431 + 0.825202i
\(576\) −9.26875 + 22.1380i −0.386198 + 0.922416i
\(577\) −14.1170 −0.587700 −0.293850 0.955851i \(-0.594937\pi\)
−0.293850 + 0.955851i \(0.594937\pi\)
\(578\) −2.36821 + 12.4235i −0.0985046 + 0.516749i
\(579\) −3.87775 5.33368i −0.161154 0.221660i
\(580\) 6.02280 + 40.7121i 0.250083 + 1.69048i
\(581\) 19.2157 0.797203
\(582\) −0.162198 + 1.94207i −0.00672331 + 0.0805012i
\(583\) 10.4280 6.02062i 0.431884 0.249349i
\(584\) −1.23586 2.36172i −0.0511404 0.0977286i
\(585\) −24.1264 + 21.7514i −0.997502 + 0.899309i
\(586\) −25.6654 22.1479i −1.06023 0.914922i
\(587\) −39.9934 23.0902i −1.65070 0.953035i −0.976783 0.214232i \(-0.931275\pi\)
−0.673922 0.738803i \(-0.735391\pi\)
\(588\) 5.31472 + 1.48056i 0.219175 + 0.0610572i
\(589\) −0.794239 + 0.0877538i −0.0327261 + 0.00361583i
\(590\) 37.4636 + 7.14144i 1.54235 + 0.294009i
\(591\) 0.759261 1.70679i 0.0312318 0.0702081i
\(592\) −11.0523 36.5375i −0.454248 1.50168i
\(593\) 32.3512 18.6779i 1.32850 0.767011i 0.343435 0.939177i \(-0.388410\pi\)
0.985068 + 0.172165i \(0.0550763\pi\)
\(594\) 4.53779 10.8280i 0.186188 0.444278i
\(595\) −10.0908 17.4778i −0.413683 0.716521i
\(596\) 39.5386 + 15.6424i 1.61957 + 0.640738i
\(597\) −2.43712 23.1166i −0.0997445 0.946099i
\(598\) −8.65721 24.8496i −0.354020 1.01617i
\(599\) 18.3176 + 31.7269i 0.748435 + 1.29633i 0.948573 + 0.316560i \(0.102528\pi\)
−0.200137 + 0.979768i \(0.564139\pi\)
\(600\) −9.45890 + 19.0891i −0.386158 + 0.779308i
\(601\) −13.2257 −0.539486 −0.269743 0.962932i \(-0.586939\pi\)
−0.269743 + 0.962932i \(0.586939\pi\)
\(602\) −4.64023 13.3193i −0.189122 0.542853i
\(603\) −5.06838 + 15.6328i −0.206400 + 0.636618i
\(604\) 16.6725 2.46646i 0.678393 0.100359i
\(605\) −12.9143 + 22.3682i −0.525042 + 0.909399i
\(606\) 7.01498 + 4.87085i 0.284964 + 0.197865i
\(607\) 9.47858i 0.384724i −0.981324 0.192362i \(-0.938385\pi\)
0.981324 0.192362i \(-0.0616147\pi\)
\(608\) 7.47926 23.4960i 0.303324 0.952887i
\(609\) 2.84201 + 26.9571i 0.115164 + 1.09236i
\(610\) 34.8783 40.4177i 1.41218 1.63647i
\(611\) 7.29458 + 4.21153i 0.295107 + 0.170380i
\(612\) −15.9575 + 5.95093i −0.645044 + 0.240552i
\(613\) 30.5235 + 17.6228i 1.23283 + 0.711776i 0.967619 0.252414i \(-0.0812244\pi\)
0.265213 + 0.964190i \(0.414558\pi\)
\(614\) −21.1084 + 7.35385i −0.851867 + 0.296777i
\(615\) −4.95382 46.9881i −0.199757 1.89474i
\(616\) −5.62700 + 8.87449i −0.226718 + 0.357563i
\(617\) 10.6872 6.17026i 0.430250 0.248405i −0.269203 0.963083i \(-0.586760\pi\)
0.699453 + 0.714678i \(0.253427\pi\)
\(618\) −2.86117 6.07317i −0.115093 0.244299i
\(619\) 20.9632 0.842580 0.421290 0.906926i \(-0.361577\pi\)
0.421290 + 0.906926i \(0.361577\pi\)
\(620\) −0.412401 + 1.04241i −0.0165624 + 0.0418641i
\(621\) 20.3066 + 18.2489i 0.814875 + 0.732304i
\(622\) −3.83653 3.31072i −0.153831 0.132748i
\(623\) −18.0250 31.2202i −0.722156 1.25081i
\(624\) −9.52697 22.6102i −0.381384 0.905132i
\(625\) 13.9162 24.1036i 0.556648 0.964143i
\(626\) 1.14869 6.02596i 0.0459110 0.240846i
\(627\) −3.66262 + 11.4926i −0.146271 + 0.458970i
\(628\) −1.64457 + 4.15692i −0.0656256 + 0.165879i
\(629\) 13.5441 23.4591i 0.540039 0.935375i
\(630\) −14.5117 + 26.4450i −0.578161 + 1.05359i
\(631\) 22.1698 12.7998i 0.882567 0.509550i 0.0110630 0.999939i \(-0.496478\pi\)
0.871504 + 0.490389i \(0.163145\pi\)
\(632\) −39.5728 + 20.7080i −1.57412 + 0.823722i
\(633\) 8.96336 + 12.3287i 0.356262 + 0.490023i
\(634\) −4.53927 + 23.8127i −0.180277 + 0.945724i
\(635\) 16.2114i 0.643330i
\(636\) 6.50756 + 25.2841i 0.258042 + 1.00258i
\(637\) −4.88452 + 2.82008i −0.193532 + 0.111736i
\(638\) 14.9372 + 2.84739i 0.591371 + 0.112729i
\(639\) −13.9726 + 2.97929i −0.552747 + 0.117859i
\(640\) −24.2258 24.6930i −0.957607 0.976075i
\(641\) −30.1634 17.4149i −1.19138 0.687846i −0.232763 0.972533i \(-0.574777\pi\)
−0.958620 + 0.284688i \(0.908110\pi\)
\(642\) −4.08614 8.67334i −0.161267 0.342309i
\(643\) −2.52436 + 4.37233i −0.0995512 + 0.172428i −0.911499 0.411302i \(-0.865074\pi\)
0.811948 + 0.583730i \(0.198407\pi\)
\(644\) −15.1834 19.1463i −0.598309 0.754470i
\(645\) −22.5883 + 2.38142i −0.889414 + 0.0937684i
\(646\) 15.7915 7.53639i 0.621309 0.296515i
\(647\) −10.5740 −0.415707 −0.207854 0.978160i \(-0.566648\pi\)
−0.207854 + 0.978160i \(0.566648\pi\)
\(648\) 19.9760 + 15.7785i 0.784731 + 0.619836i
\(649\) 7.04572 12.2035i 0.276569 0.479031i
\(650\) −7.16519 20.5669i −0.281042 0.806700i
\(651\) −0.300099 + 0.674612i −0.0117618 + 0.0264401i
\(652\) 3.60654 + 24.3790i 0.141243 + 0.954756i
\(653\) −33.1756 −1.29826 −0.649131 0.760677i \(-0.724867\pi\)
−0.649131 + 0.760677i \(0.724867\pi\)
\(654\) 47.0360 + 3.92836i 1.83925 + 0.153611i
\(655\) −51.2619 + 29.5961i −2.00297 + 1.15641i
\(656\) 34.7486 + 8.13091i 1.35671 + 0.317459i
\(657\) −2.76507 + 0.589580i −0.107876 + 0.0230017i
\(658\) 7.68342 + 1.46464i 0.299531 + 0.0570977i
\(659\) −38.4896 + 22.2220i −1.49934 + 0.865646i −1.00000 0.000758275i \(-0.999759\pi\)
−0.499343 + 0.866404i \(0.666425\pi\)
\(660\) 11.8467 + 12.0834i 0.461134 + 0.470346i
\(661\) −15.9383 + 9.20198i −0.619928 + 0.357916i −0.776841 0.629697i \(-0.783179\pi\)
0.156913 + 0.987612i \(0.449846\pi\)
\(662\) 1.33848 + 1.15503i 0.0520214 + 0.0448917i
\(663\) 7.07658 15.9079i 0.274832 0.617813i
\(664\) 19.7392 + 12.5160i 0.766030 + 0.485713i
\(665\) 12.4546 28.3789i 0.482968 1.10049i
\(666\) −40.4786 + 0.879105i −1.56851 + 0.0340646i
\(667\) −17.6806 + 30.6237i −0.684595 + 1.18575i
\(668\) 8.35443 6.62522i 0.323242 0.256337i
\(669\) 34.1866 24.8547i 1.32173 0.960939i
\(670\) −17.9330 15.4752i −0.692812 0.597860i
\(671\) −9.86269 17.0827i −0.380745 0.659469i
\(672\) −15.2619 16.9168i −0.588742 0.652581i
\(673\) −4.94153 −0.190482 −0.0952409 0.995454i \(-0.530362\pi\)
−0.0952409 + 0.995454i \(0.530362\pi\)
\(674\) 19.8868 6.92826i 0.766012 0.266867i
\(675\) 16.8069 + 15.1038i 0.646896 + 0.581347i
\(676\) −0.852994 0.337464i −0.0328074 0.0129794i
\(677\) −7.66717 −0.294673 −0.147337 0.989086i \(-0.547070\pi\)
−0.147337 + 0.989086i \(0.547070\pi\)
\(678\) 4.75413 + 10.0912i 0.182581 + 0.387551i
\(679\) −1.60221 0.925039i −0.0614874 0.0354997i
\(680\) 1.01826 24.5265i 0.0390485 0.940547i
\(681\) −42.8745 19.0726i −1.64295 0.730862i
\(682\) 0.313583 + 0.270606i 0.0120077 + 0.0103620i
\(683\) 34.5515i 1.32208i −0.750352 0.661038i \(-0.770116\pi\)
0.750352 0.661038i \(-0.229884\pi\)
\(684\) −21.8734 14.3372i −0.836349 0.548197i
\(685\) 7.05677i 0.269625i
\(686\) −18.4612 + 21.3932i −0.704853 + 0.816798i
\(687\) 3.91661 + 1.74229i 0.149428 + 0.0664725i
\(688\) 3.90872 16.7045i 0.149019 0.636852i
\(689\) −23.1147 13.3453i −0.880599 0.508414i
\(690\) −35.5984 + 16.7710i −1.35521 + 0.638460i
\(691\) 31.8602 1.21202 0.606009 0.795457i \(-0.292769\pi\)
0.606009 + 0.795457i \(0.292769\pi\)
\(692\) −45.4986 18.0003i −1.72960 0.684269i
\(693\) 7.46308 + 8.27795i 0.283499 + 0.314453i
\(694\) 15.0286 + 43.1380i 0.570478 + 1.63750i
\(695\) 42.4024 1.60841
\(696\) −14.6387 + 29.5425i −0.554880 + 1.11981i
\(697\) 12.6623 + 21.9317i 0.479618 + 0.830723i
\(698\) −1.32512 + 1.53558i −0.0501565 + 0.0581224i
\(699\) −0.412874 + 0.300172i −0.0156163 + 0.0113536i
\(700\) −12.5666 15.8465i −0.474973 0.598943i
\(701\) 21.2208 36.7555i 0.801498 1.38823i −0.117132 0.993116i \(-0.537370\pi\)
0.918630 0.395119i \(-0.129296\pi\)
\(702\) −25.8149 + 3.28977i −0.974321 + 0.124164i
\(703\) 41.3460 4.56823i 1.55939 0.172294i
\(704\) −11.5606 + 5.45116i −0.435706 + 0.205448i
\(705\) 5.11959 11.5087i 0.192815 0.433442i
\(706\) 13.0964 15.1763i 0.492888 0.571169i
\(707\) −7.02127 + 4.05373i −0.264062 + 0.152456i
\(708\) 21.3898 + 21.8171i 0.803880 + 0.819938i
\(709\) −1.86140 + 1.07468i −0.0699064 + 0.0403605i −0.534546 0.845140i \(-0.679517\pi\)
0.464639 + 0.885500i \(0.346184\pi\)
\(710\) 3.85591 20.2278i 0.144710 0.759137i
\(711\) 9.87895 + 46.3313i 0.370490 + 1.73756i
\(712\) 1.81889 43.8111i 0.0681659 1.64189i
\(713\) −0.834155 + 0.481600i −0.0312394 + 0.0180360i
\(714\) 1.34564 16.1119i 0.0503593 0.602974i
\(715\) −17.2995 −0.646964
\(716\) −11.0750 + 1.63839i −0.413891 + 0.0612295i
\(717\) −11.4177 + 25.6665i −0.426400 + 0.958535i
\(718\) −35.7099 + 12.4408i −1.33268 + 0.464285i
\(719\) 12.8246 22.2128i 0.478276 0.828399i −0.521413 0.853304i \(-0.674595\pi\)
0.999690 + 0.0249052i \(0.00792840\pi\)
\(720\) −32.1317 + 17.7133i −1.19748 + 0.660138i
\(721\) 6.37322 0.237351
\(722\) 23.6845 + 12.6903i 0.881447 + 0.472284i
\(723\) 46.7205 4.92561i 1.73755 0.183185i
\(724\) −17.3707 21.9045i −0.645575 0.814073i
\(725\) −14.6334 + 25.3459i −0.543473 + 0.941322i
\(726\) −18.7187 + 8.81866i −0.694716 + 0.327291i
\(727\) −16.0360 9.25836i −0.594741 0.343374i 0.172229 0.985057i \(-0.444903\pi\)
−0.766970 + 0.641683i \(0.778236\pi\)
\(728\) 23.2721 + 0.966182i 0.862521 + 0.0358091i
\(729\) 21.8130 15.9120i 0.807889 0.589335i
\(730\) 0.763055 4.00294i 0.0282419 0.148155i
\(731\) 10.5431 6.08706i 0.389950 0.225138i
\(732\) 41.4192 10.6604i 1.53090 0.394019i
\(733\) 40.6193i 1.50031i −0.661262 0.750155i \(-0.729979\pi\)
0.661262 0.750155i \(-0.270021\pi\)
\(734\) −21.2015 4.04151i −0.782562 0.149175i
\(735\) 4.95981 + 6.82201i 0.182945 + 0.251633i
\(736\) −3.12628 29.5574i −0.115236 1.08950i
\(737\) −7.57943 + 4.37599i −0.279192 + 0.161192i
\(738\) 18.2098 33.1840i 0.670311 1.22152i
\(739\) 18.5402 32.1126i 0.682012 1.18128i −0.292353 0.956310i \(-0.594438\pi\)
0.974366 0.224970i \(-0.0722283\pi\)
\(740\) 21.4685 54.2650i 0.789198 1.99482i
\(741\) 26.1208 5.70633i 0.959570 0.209627i
\(742\) −24.3468 4.64108i −0.893799 0.170379i
\(743\) 16.1173 27.9160i 0.591286 1.02414i −0.402774 0.915300i \(-0.631954\pi\)
0.994060 0.108838i \(-0.0347129\pi\)
\(744\) −0.747674 + 0.497524i −0.0274111 + 0.0182401i
\(745\) 32.5022 + 56.2955i 1.19079 + 2.06251i
\(746\) −17.1745 + 19.9022i −0.628804 + 0.728671i
\(747\) 18.4124 16.5999i 0.673673 0.607358i
\(748\) −8.43391 3.33665i −0.308374 0.122000i
\(749\) 9.10185 0.332574
\(750\) 4.41289 2.07898i 0.161136 0.0759136i
\(751\) 7.66856 4.42745i 0.279830 0.161560i −0.353517 0.935428i \(-0.615014\pi\)
0.633346 + 0.773868i \(0.281681\pi\)
\(752\) 6.93875 + 6.50905i 0.253030 + 0.237361i
\(753\) −2.19389 20.8095i −0.0799497 0.758341i
\(754\) −11.0890 31.8297i −0.403836 1.15917i
\(755\) 22.3140 + 12.8830i 0.812088 + 0.468859i
\(756\) −21.6326 + 10.7715i −0.786770 + 0.391755i
\(757\) −2.31803 1.33832i −0.0842502 0.0486419i 0.457283 0.889321i \(-0.348823\pi\)
−0.541533 + 0.840679i \(0.682156\pi\)
\(758\) 40.8042 + 35.2119i 1.48208 + 1.27895i
\(759\) 1.52442 + 14.4595i 0.0553331 + 0.524846i
\(760\) 31.2781 21.0399i 1.13458 0.763196i
\(761\) 16.9101i 0.612990i 0.951872 + 0.306495i \(0.0991563\pi\)
−0.951872 + 0.306495i \(0.900844\pi\)
\(762\) −7.40726 + 10.6679i −0.268337 + 0.386458i
\(763\) −22.4040 + 38.8049i −0.811081 + 1.40483i
\(764\) 2.15543 + 14.5700i 0.0779806 + 0.527123i
\(765\) −24.7675 8.02995i −0.895470 0.290324i
\(766\) −29.4463 + 10.2586i −1.06394 + 0.370660i
\(767\) −31.2350 −1.12783
\(768\) −4.65913 27.3184i −0.168122 0.985766i
\(769\) −20.3542 35.2545i −0.733992 1.27131i −0.955164 0.296077i \(-0.904322\pi\)
0.221172 0.975235i \(-0.429012\pi\)
\(770\) −15.1703 + 5.28509i −0.546699 + 0.190461i
\(771\) 1.72261 + 16.3393i 0.0620383 + 0.588447i
\(772\) 7.08049 + 2.80121i 0.254833 + 0.100818i
\(773\) −20.1211 34.8508i −0.723707 1.25350i −0.959504 0.281695i \(-0.909103\pi\)
0.235797 0.971802i \(-0.424230\pi\)
\(774\) −15.9523 8.75388i −0.573395 0.314652i
\(775\) −0.690394 + 0.398599i −0.0247997 + 0.0143181i
\(776\) −1.04335 1.99382i −0.0374540 0.0715741i
\(777\) 15.6223 35.1185i 0.560448 1.25987i
\(778\) 1.33349 6.99539i 0.0478079 0.250797i
\(779\) −15.6284 + 35.6108i −0.559945 + 1.27589i
\(780\) 10.0659 36.1333i 0.360417 1.29378i
\(781\) −6.58911 3.80422i −0.235777 0.136126i
\(782\) 13.7796 15.9681i 0.492759 0.571018i
\(783\) 26.0105 + 23.3749i 0.929541 + 0.835351i
\(784\) −6.09772 + 1.84451i −0.217776 + 0.0658755i
\(785\) −5.91865 + 3.41714i −0.211246 + 0.121963i
\(786\) −47.2558 3.94672i −1.68556 0.140775i
\(787\) 20.7098 0.738226 0.369113 0.929385i \(-0.379662\pi\)
0.369113 + 0.929385i \(0.379662\pi\)
\(788\) 0.315669 + 2.13382i 0.0112452 + 0.0760142i
\(789\) 11.4144 + 15.7001i 0.406364 + 0.558937i
\(790\) −67.0729 12.7857i −2.38635 0.454894i
\(791\) −10.5898 −0.376529
\(792\) 2.27464 + 13.3645i 0.0808259 + 0.474885i
\(793\) −21.8616 + 37.8653i −0.776327 + 1.34464i
\(794\) 5.47535 + 15.7164i 0.194313 + 0.557754i
\(795\) −16.2227 + 36.4681i −0.575359 + 1.29339i
\(796\) 16.6776 + 21.0305i 0.591120 + 0.745405i
\(797\) −14.3681 −0.508943 −0.254472 0.967080i \(-0.581902\pi\)
−0.254472 + 0.967080i \(0.581902\pi\)
\(798\) 21.1625 12.9840i 0.749145 0.459630i
\(799\) 6.75129i 0.238844i
\(800\) −2.58749 24.4634i −0.0914814 0.864910i
\(801\) −44.2415 14.3437i −1.56320 0.506810i
\(802\) 7.78169 + 22.3365i 0.274781 + 0.788730i
\(803\) −1.30393 0.752827i −0.0460148 0.0265667i
\(804\) −4.72992 18.3773i −0.166811 0.648119i
\(805\) 37.3572i 1.31667i
\(806\) 0.171919 0.901874i 0.00605557 0.0317671i
\(807\) 18.1602 + 24.9786i 0.639270 + 0.879289i
\(808\) −9.85289 0.409060i −0.346623 0.0143907i
\(809\) 9.93099i 0.349155i 0.984643 + 0.174578i \(0.0558560\pi\)
−0.984643 + 0.174578i \(0.944144\pi\)
\(810\) 8.93997 + 37.8756i 0.314119 + 1.33081i
\(811\) 4.58665 + 7.94432i 0.161059 + 0.278963i 0.935249 0.353991i \(-0.115176\pi\)
−0.774190 + 0.632954i \(0.781842\pi\)
\(812\) −19.4483 24.5244i −0.682501 0.860636i
\(813\) −7.18039 + 5.22036i −0.251827 + 0.183086i
\(814\) −16.3243 14.0870i −0.572166 0.493749i
\(815\) −18.8379 + 32.6282i −0.659863 + 1.14292i
\(816\) 11.8766 15.6744i 0.415765 0.548713i
\(817\) 17.1189 + 7.51294i 0.598916 + 0.262844i
\(818\) −8.67392 + 45.5028i −0.303276 + 1.59097i
\(819\) 7.61927 23.5008i 0.266239 0.821183i
\(820\) 33.8998 + 42.7477i 1.18383 + 1.49282i
\(821\) −4.15246 7.19227i −0.144922 0.251012i 0.784422 0.620228i \(-0.212960\pi\)
−0.929344 + 0.369216i \(0.879626\pi\)
\(822\) −3.22436 + 4.64371i −0.112462 + 0.161968i
\(823\) −31.1529 + 17.9861i −1.08592 + 0.626956i −0.932487 0.361203i \(-0.882366\pi\)
−0.153433 + 0.988159i \(0.549033\pi\)
\(824\) 6.54684 + 4.15112i 0.228070 + 0.144611i
\(825\) 1.26170 + 11.9675i 0.0439267 + 0.416655i
\(826\) −27.3906 + 9.54247i −0.953042 + 0.332025i
\(827\) 4.31370 2.49051i 0.150002 0.0866036i −0.423120 0.906073i \(-0.639065\pi\)
0.573122 + 0.819470i \(0.305732\pi\)
\(828\) −31.0885 5.22938i −1.08040 0.181733i
\(829\) 11.6441i 0.404418i −0.979342 0.202209i \(-0.935188\pi\)
0.979342 0.202209i \(-0.0648120\pi\)
\(830\) 11.7554 + 33.7427i 0.408037 + 1.17123i
\(831\) −40.2029 17.8841i −1.39462 0.620393i
\(832\) 23.2767 + 16.1505i 0.806976 + 0.559918i
\(833\) −3.91507 2.26037i −0.135649 0.0783170i
\(834\) 27.9029 + 19.3744i 0.966198 + 0.670879i
\(835\) 16.3007 0.564109
\(836\) −3.53908 13.4710i −0.122401 0.465904i
\(837\) 0.295224 + 0.905654i 0.0102044 + 0.0313040i
\(838\) −13.8580 + 16.0589i −0.478717 + 0.554747i
\(839\) −0.220419 + 0.381777i −0.00760972 + 0.0131804i −0.869805 0.493395i \(-0.835756\pi\)
0.862195 + 0.506576i \(0.169089\pi\)
\(840\) −2.21192 34.7613i −0.0763187 1.19938i
\(841\) −8.14695 + 14.1109i −0.280929 + 0.486584i
\(842\) 1.52936 + 4.38987i 0.0527054 + 0.151285i
\(843\) 3.83062 + 36.3343i 0.131934 + 1.25142i
\(844\) −16.3665 6.47495i −0.563356 0.222877i
\(845\) −0.701192 1.21450i −0.0241217 0.0417801i
\(846\) 8.62745 5.23406i 0.296618 0.179951i
\(847\) 19.6435i 0.674958i
\(848\) −21.9871 20.6255i −0.755041 0.708283i
\(849\) 19.0593 + 26.2152i 0.654112 + 0.899703i
\(850\) 11.4048 13.2161i 0.391181 0.453308i
\(851\) 43.4239 25.0708i 1.48855 0.859416i
\(852\) 11.7798 11.5491i 0.403570 0.395665i
\(853\) 32.4333 + 18.7254i 1.11049 + 0.641144i 0.938957 0.344033i \(-0.111793\pi\)
0.171537 + 0.985178i \(0.445127\pi\)
\(854\) −7.60279 + 39.8838i −0.260162 + 1.36479i
\(855\) −12.5818 37.9516i −0.430288 1.29792i
\(856\) 9.34980 + 5.92838i 0.319570 + 0.202628i
\(857\) −20.4848 11.8269i −0.699748 0.404000i 0.107505 0.994204i \(-0.465714\pi\)
−0.807254 + 0.590205i \(0.799047\pi\)
\(858\) −11.3839 7.90441i −0.388640 0.269852i
\(859\) 5.35973 + 9.28333i 0.182872 + 0.316743i 0.942857 0.333197i \(-0.108127\pi\)
−0.759986 + 0.649940i \(0.774794\pi\)
\(860\) 20.5499 16.2964i 0.700744 0.555704i
\(861\) 21.1308 + 29.0645i 0.720134 + 0.990515i
\(862\) −6.48195 + 34.0039i −0.220776 + 1.15818i
\(863\) −20.1327 −0.685324 −0.342662 0.939459i \(-0.611329\pi\)
−0.342662 + 0.939459i \(0.611329\pi\)
\(864\) −29.2378 3.02524i −0.994690 0.102921i
\(865\) −37.4015 64.7813i −1.27169 2.20263i
\(866\) 0.913157 4.79036i 0.0310303 0.162783i
\(867\) −15.4042 + 1.62402i −0.523154 + 0.0551547i
\(868\) −0.124769 0.843394i −0.00423492 0.0286267i
\(869\) −12.6143 + 21.8486i −0.427911 + 0.741164i
\(870\) −45.5978 + 21.4818i −1.54591 + 0.728302i
\(871\) 16.8005 + 9.69979i 0.569264 + 0.328665i
\(872\) −48.2895 + 25.2694i −1.63529 + 0.855731i
\(873\) −2.33434 + 0.497738i −0.0790055 + 0.0168459i
\(874\) 32.2898 + 2.53420i 1.09222 + 0.0857205i
\(875\) 4.63091i 0.156553i
\(876\) 2.33114 2.28548i 0.0787618 0.0772192i
\(877\) 12.9517 + 7.47768i 0.437349 + 0.252503i 0.702472 0.711711i \(-0.252079\pi\)
−0.265124 + 0.964214i \(0.585413\pi\)
\(878\) −10.9775 31.5097i −0.370473 1.06340i
\(879\) 16.8754 37.9353i 0.569193 1.27953i
\(880\) −19.0259 4.45192i −0.641364 0.150074i
\(881\) 28.6212i 0.964273i 0.876096 + 0.482137i \(0.160139\pi\)
−0.876096 + 0.482137i \(0.839861\pi\)
\(882\) 0.146713 + 6.75544i 0.00494009 + 0.227467i
\(883\) 3.60236 + 6.23947i 0.121229 + 0.209975i 0.920253 0.391325i \(-0.127983\pi\)
−0.799024 + 0.601300i \(0.794650\pi\)
\(884\) 2.94215 + 19.8880i 0.0989552 + 0.668904i
\(885\) 4.89731 + 46.4521i 0.164621 + 1.56147i
\(886\) 14.1466 + 2.69668i 0.475265 + 0.0905969i
\(887\) 19.7030 + 34.1266i 0.661563 + 1.14586i 0.980205 + 0.197985i \(0.0634397\pi\)
−0.318643 + 0.947875i \(0.603227\pi\)
\(888\) 38.9219 25.8998i 1.30613 0.869139i
\(889\) −6.16464 10.6775i −0.206755 0.358111i
\(890\) 43.7955 50.7510i 1.46803 1.70118i
\(891\) 14.3021 + 1.48474i 0.479139 + 0.0497408i
\(892\) −17.9546 + 45.3829i −0.601163 + 1.51953i
\(893\) −8.35495 + 6.13842i −0.279588 + 0.205414i
\(894\) −4.33426 + 51.8960i −0.144959 + 1.73566i
\(895\) −14.8224 8.55773i −0.495459 0.286053i
\(896\) 25.3459 + 7.05154i 0.846749 + 0.235575i
\(897\) 26.0673 18.9517i 0.870362 0.632780i
\(898\) −2.95572 + 3.42515i −0.0986338 + 0.114299i
\(899\) −1.06846 + 0.616878i −0.0356353 + 0.0205740i
\(900\) −25.7306 4.32813i −0.857685 0.144271i
\(901\) 21.3931i 0.712709i
\(902\) 19.0361 6.63189i 0.633834 0.220818i
\(903\) 13.9720 10.1581i 0.464959 0.338039i
\(904\) −10.8783 6.89753i −0.361806 0.229409i
\(905\) 42.7388i 1.42068i
\(906\) 8.79725 + 18.6733i 0.292269 + 0.620377i
\(907\) −16.5252 + 28.6226i −0.548712 + 0.950397i 0.449651 + 0.893204i \(0.351548\pi\)
−0.998363 + 0.0571924i \(0.981785\pi\)
\(908\) 53.6013 7.92958i 1.77882 0.263152i
\(909\) −3.22583 + 9.94970i −0.106994 + 0.330011i
\(910\) 26.9586 + 23.2638i 0.893668 + 0.771188i
\(911\) 29.3759 0.973268 0.486634 0.873606i \(-0.338225\pi\)
0.486634 + 0.873606i \(0.338225\pi\)
\(912\) 30.1960 + 0.446214i 0.999891 + 0.0147756i
\(913\) 13.2023 0.436934
\(914\) −5.03187 4.34224i −0.166439 0.143628i
\(915\) 59.7402 + 26.5752i 1.97495 + 0.878549i
\(916\) −4.89651 + 0.724372i −0.161785 + 0.0239339i
\(917\) 22.5087 38.9863i 0.743304 1.28744i
\(918\) −12.6292 16.6008i −0.416826 0.547907i
\(919\) 36.1256i 1.19167i 0.803105 + 0.595837i \(0.203180\pi\)
−0.803105 + 0.595837i \(0.796820\pi\)
\(920\) 24.3322 38.3749i 0.802208 1.26518i
\(921\) −16.0985 22.1428i −0.530464 0.729631i
\(922\) 28.5402 9.94295i 0.939920 0.327454i
\(923\) 16.8648i 0.555113i
\(924\) −12.3976 3.45370i −0.407852 0.113618i
\(925\) 35.9400 20.7500i 1.18170 0.682256i
\(926\) 5.99458 6.94663i 0.196994 0.228281i
\(927\) 6.10677 5.50563i 0.200573 0.180829i
\(928\) −4.00443 37.8599i −0.131452 1.24281i
\(929\) 43.1616 + 24.9194i 1.41609 + 0.817578i 0.995952 0.0898840i \(-0.0286496\pi\)
0.420134 + 0.907462i \(0.361983\pi\)
\(930\) −1.36820 0.114270i −0.0448651 0.00374705i
\(931\) −0.762388 6.90020i −0.0249863 0.226145i
\(932\) 0.216838 0.548093i 0.00710278 0.0179534i
\(933\) 2.52257 5.67066i 0.0825853 0.185649i
\(934\) −14.1366 + 16.3818i −0.462563 + 0.536027i
\(935\) −6.93298 12.0083i −0.226733 0.392713i
\(936\) 23.1338 19.1782i 0.756151 0.626860i
\(937\) 21.1994 + 36.7184i 0.692554 + 1.19954i 0.970998 + 0.239086i \(0.0768478\pi\)
−0.278445 + 0.960452i \(0.589819\pi\)
\(938\) 17.6961 + 3.37329i 0.577797 + 0.110142i
\(939\) 7.47175 0.787726i 0.243831 0.0257065i
\(940\) 2.12851 + 14.3880i 0.0694244 + 0.469286i
\(941\) −0.0527703 0.0914008i −0.00172026 0.00297958i 0.865164 0.501489i \(-0.167214\pi\)
−0.866884 + 0.498509i \(0.833881\pi\)
\(942\) −5.45612 0.455685i −0.177770 0.0148470i
\(943\) 46.8770i 1.52652i
\(944\) −34.3522 8.03815i −1.11807 0.261619i
\(945\) −36.1445 7.64655i −1.17578 0.248742i
\(946\) −3.18811 9.15112i −0.103654 0.297529i
\(947\) 5.50116 + 3.17609i 0.178764 + 0.103209i 0.586712 0.809796i \(-0.300422\pi\)
−0.407948 + 0.913005i \(0.633756\pi\)
\(948\) −38.2953 39.0603i −1.24377 1.26862i
\(949\) 3.33742i 0.108337i
\(950\) 26.7248 + 2.09744i 0.867068 + 0.0680501i
\(951\) −29.5260 + 3.11285i −0.957447 + 0.100941i
\(952\) 8.65592 + 16.5413i 0.280540 + 0.536107i
\(953\) 14.1079 + 8.14519i 0.456999 + 0.263849i 0.710782 0.703413i \(-0.248341\pi\)
−0.253782 + 0.967261i \(0.581675\pi\)
\(954\) −27.3382 + 16.5854i −0.885107 + 0.536972i
\(955\) −11.2583 + 19.5000i −0.364312 + 0.631006i
\(956\) −4.74699 32.0881i −0.153529 1.03780i
\(957\) 1.95262 + 18.5211i 0.0631194 + 0.598701i
\(958\) 2.55769 13.4175i 0.0826352 0.433499i
\(959\) −2.68345 4.64787i −0.0866531 0.150088i
\(960\) 20.3692 37.1489i 0.657412 1.19898i
\(961\) 30.9664 0.998916
\(962\) −8.94962 + 46.9491i −0.288547 + 1.51370i
\(963\) 8.72132 7.86280i 0.281040 0.253375i
\(964\) −42.5043 + 33.7067i −1.36897 + 1.08562i
\(965\) 5.82043 + 10.0813i 0.187366 + 0.324528i
\(966\) 17.0691 24.5829i 0.549190 0.790942i
\(967\) −6.64559 3.83683i −0.213708 0.123384i 0.389326 0.921100i \(-0.372708\pi\)
−0.603033 + 0.797716i \(0.706041\pi\)
\(968\) 12.7946 20.1786i 0.411233 0.648565i
\(969\) 14.4292 + 15.8446i 0.463533 + 0.509002i
\(970\) 0.644190 3.37938i 0.0206837 0.108505i
\(971\) 20.8819 + 12.0561i 0.670131 + 0.386900i 0.796126 0.605131i \(-0.206879\pi\)
−0.125995 + 0.992031i \(0.540212\pi\)
\(972\) −11.4230 + 29.0089i −0.366394 + 0.930460i
\(973\) −27.9279 + 16.1242i −0.895328 + 0.516918i
\(974\) 2.34082 2.71259i 0.0750048 0.0869170i
\(975\) 21.5748 15.6855i 0.690946 0.502339i
\(976\) −33.7877 + 36.0183i −1.08152 + 1.15292i
\(977\) 39.5123i 1.26411i −0.774923 0.632056i \(-0.782211\pi\)
0.774923 0.632056i \(-0.217789\pi\)
\(978\) −27.3046 + 12.8636i −0.873106 + 0.411333i
\(979\) −12.3842 21.4501i −0.395801 0.685548i
\(980\) −9.05625 3.58287i −0.289291 0.114450i
\(981\) 12.0550 + 56.5367i 0.384887 + 1.80508i
\(982\) −9.50209 27.2747i −0.303224 0.870371i
\(983\) −8.91779 + 15.4461i −0.284433 + 0.492653i −0.972472 0.233021i \(-0.925139\pi\)
0.688038 + 0.725674i \(0.258472\pi\)
\(984\) 2.77559 + 43.6195i 0.0884827 + 1.39054i
\(985\) −1.64882 + 2.85584i −0.0525358 + 0.0909947i
\(986\) 17.6502 20.4534i 0.562098 0.651370i
\(987\) 1.00439 + 9.52688i 0.0319701 + 0.303244i
\(988\) −21.9369 + 21.7236i −0.697907 + 0.691119i
\(989\) 22.5349 0.716567
\(990\) −9.97041 + 18.1693i −0.316880 + 0.577457i
\(991\) 20.0109 + 11.5533i 0.635668 + 0.367003i 0.782944 0.622092i \(-0.213717\pi\)
−0.147276 + 0.989095i \(0.547050\pi\)
\(992\) 0.421168 0.947636i 0.0133721 0.0300875i
\(993\) −0.880067 + 1.97836i −0.0279281 + 0.0627814i
\(994\) 5.15230 + 14.7891i 0.163421 + 0.469083i
\(995\) 41.0335i 1.30085i
\(996\) −7.68194 + 27.5756i −0.243412 + 0.873768i
\(997\) 9.14736 5.28123i 0.289700 0.167258i −0.348107 0.937455i \(-0.613175\pi\)
0.637806 + 0.770197i \(0.279842\pi\)
\(998\) −29.3164 + 10.2134i −0.927996 + 0.323299i
\(999\) −15.3686 47.1459i −0.486241 1.49163i
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 456.2.u.d.11.16 yes 136
3.2 odd 2 inner 456.2.u.d.11.53 yes 136
8.3 odd 2 inner 456.2.u.d.11.7 136
19.7 even 3 inner 456.2.u.d.83.62 yes 136
24.11 even 2 inner 456.2.u.d.11.62 yes 136
57.26 odd 6 inner 456.2.u.d.83.7 yes 136
152.83 odd 6 inner 456.2.u.d.83.53 yes 136
456.83 even 6 inner 456.2.u.d.83.16 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.u.d.11.7 136 8.3 odd 2 inner
456.2.u.d.11.16 yes 136 1.1 even 1 trivial
456.2.u.d.11.53 yes 136 3.2 odd 2 inner
456.2.u.d.11.62 yes 136 24.11 even 2 inner
456.2.u.d.83.7 yes 136 57.26 odd 6 inner
456.2.u.d.83.16 yes 136 456.83 even 6 inner
456.2.u.d.83.53 yes 136 152.83 odd 6 inner
456.2.u.d.83.62 yes 136 19.7 even 3 inner