Properties

Label 418.2.f.h.191.3
Level $418$
Weight $2$
Character 418.191
Analytic conductor $3.338$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + 7288 x^{12} + 5704 x^{11} + 24392 x^{10} + 10376 x^{9} + 48880 x^{8} + 21224 x^{7} + \cdots + 1936 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 191.3
Root \(0.0978632 - 0.0711018i\) of defining polynomial
Character \(\chi\) \(=\) 418.191
Dual form 418.2.f.h.267.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.0373804 - 0.115045i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.75481 - 1.27494i) q^{5} +(0.0978632 - 0.0711018i) q^{6} +(-1.23224 - 3.79244i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.41521 + 1.75475i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.0373804 - 0.115045i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.75481 - 1.27494i) q^{5} +(0.0978632 - 0.0711018i) q^{6} +(-1.23224 - 3.79244i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.41521 + 1.75475i) q^{9} +2.16907 q^{10} +(3.30226 + 0.308300i) q^{11} +0.120966 q^{12} +(-4.23528 - 3.07711i) q^{13} +(1.23224 - 3.79244i) q^{14} +(-0.0810806 - 0.249540i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.125478 - 0.0911651i) q^{17} +(0.922529 + 2.83925i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.75481 + 1.27494i) q^{20} -0.482362 q^{21} +(2.49037 + 2.19044i) q^{22} +5.81978 q^{23} +(0.0978632 + 0.0711018i) q^{24} +(-0.0912072 + 0.280707i) q^{25} +(-1.61773 - 4.97887i) q^{26} +(0.585747 - 0.425570i) q^{27} +(3.22604 - 2.34385i) q^{28} +(1.66553 + 5.12596i) q^{29} +(0.0810806 - 0.249540i) q^{30} +(-2.64494 - 1.92166i) q^{31} -1.00000 q^{32} +(0.158908 - 0.368385i) q^{33} +0.155099 q^{34} +(-6.99749 - 5.08397i) q^{35} +(-0.922529 + 2.83925i) q^{36} +(2.17820 + 6.70380i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-0.512323 + 0.372225i) q^{39} +(0.670278 + 2.06290i) q^{40} +(-3.28743 + 10.1177i) q^{41} +(-0.390239 - 0.283526i) q^{42} -9.72748 q^{43} +(0.727246 + 3.23591i) q^{44} +6.47546 q^{45} +(4.70830 + 3.42078i) q^{46} +(2.05486 - 6.32420i) q^{47} +(0.0373804 + 0.115045i) q^{48} +(-7.20104 + 5.23186i) q^{49} +(-0.238784 + 0.173486i) q^{50} +(-0.00579768 - 0.0178434i) q^{51} +(1.61773 - 4.97887i) q^{52} +(-4.73271 - 3.43852i) q^{53} +0.724023 q^{54} +(6.18792 - 3.66920i) q^{55} +3.98760 q^{56} +(0.0978632 + 0.0711018i) q^{57} +(-1.66553 + 5.12596i) q^{58} +(-1.34214 - 4.13068i) q^{59} +(0.212272 - 0.154224i) q^{60} +(2.21329 - 1.60805i) q^{61} +(-1.01028 - 3.10932i) q^{62} +(3.67868 - 11.3218i) q^{63} +(-0.809017 - 0.587785i) q^{64} -11.3553 q^{65} +(0.345091 - 0.204626i) q^{66} +5.66850 q^{67} +(0.125478 + 0.0911651i) q^{68} +(0.217546 - 0.669537i) q^{69} +(-2.67280 - 8.22604i) q^{70} +(-2.97495 + 2.16143i) q^{71} +(-2.41521 + 1.75475i) q^{72} +(-1.06087 - 3.26503i) q^{73} +(-2.17820 + 6.70380i) q^{74} +(0.0288846 + 0.0209859i) q^{75} -1.00000 q^{76} +(-2.89997 - 12.9035i) q^{77} -0.633266 q^{78} +(0.416307 + 0.302465i) q^{79} +(-0.670278 + 2.06290i) q^{80} +(2.74052 + 8.43446i) q^{81} +(-8.60661 + 6.25307i) q^{82} +(-11.2169 + 8.14955i) q^{83} +(-0.149058 - 0.458754i) q^{84} +(0.103960 - 0.319955i) q^{85} +(-7.86969 - 5.71767i) q^{86} +0.651975 q^{87} +(-1.31367 + 3.04537i) q^{88} -7.18374 q^{89} +(5.23876 + 3.80618i) q^{90} +(-6.45088 + 19.8538i) q^{91} +(1.79841 + 5.53494i) q^{92} +(-0.319947 + 0.232455i) q^{93} +(5.37969 - 3.90857i) q^{94} +(0.670278 + 2.06290i) q^{95} +(-0.0373804 + 0.115045i) q^{96} +(-9.81172 - 7.12863i) q^{97} -8.90098 q^{98} +(7.43468 + 6.53927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0.0373804 0.115045i 0.0215816 0.0664213i −0.939686 0.342039i \(-0.888882\pi\)
0.961267 + 0.275618i \(0.0888824\pi\)
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 1.75481 1.27494i 0.784775 0.570173i −0.121633 0.992575i \(-0.538813\pi\)
0.906408 + 0.422402i \(0.138813\pi\)
\(6\) 0.0978632 0.0711018i 0.0399525 0.0290272i
\(7\) −1.23224 3.79244i −0.465742 1.43341i −0.858047 0.513571i \(-0.828322\pi\)
0.392305 0.919835i \(-0.371678\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) 2.41521 + 1.75475i 0.805071 + 0.584918i
\(10\) 2.16907 0.685919
\(11\) 3.30226 + 0.308300i 0.995670 + 0.0929558i
\(12\) 0.120966 0.0349197
\(13\) −4.23528 3.07711i −1.17466 0.853438i −0.183097 0.983095i \(-0.558612\pi\)
−0.991559 + 0.129657i \(0.958612\pi\)
\(14\) 1.23224 3.79244i 0.329329 1.01357i
\(15\) −0.0810806 0.249540i −0.0209349 0.0644310i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 0.125478 0.0911651i 0.0304329 0.0221108i −0.572465 0.819929i \(-0.694013\pi\)
0.602898 + 0.797818i \(0.294013\pi\)
\(18\) 0.922529 + 2.83925i 0.217442 + 0.669218i
\(19\) −0.309017 + 0.951057i −0.0708934 + 0.218187i
\(20\) 1.75481 + 1.27494i 0.392388 + 0.285086i
\(21\) −0.482362 −0.105260
\(22\) 2.49037 + 2.19044i 0.530950 + 0.467004i
\(23\) 5.81978 1.21351 0.606754 0.794890i \(-0.292471\pi\)
0.606754 + 0.794890i \(0.292471\pi\)
\(24\) 0.0978632 + 0.0711018i 0.0199762 + 0.0145136i
\(25\) −0.0912072 + 0.280707i −0.0182414 + 0.0561414i
\(26\) −1.61773 4.97887i −0.317264 0.976437i
\(27\) 0.585747 0.425570i 0.112727 0.0819010i
\(28\) 3.22604 2.34385i 0.609664 0.442947i
\(29\) 1.66553 + 5.12596i 0.309280 + 0.951867i 0.978045 + 0.208393i \(0.0668233\pi\)
−0.668765 + 0.743474i \(0.733177\pi\)
\(30\) 0.0810806 0.249540i 0.0148032 0.0455596i
\(31\) −2.64494 1.92166i −0.475046 0.345141i 0.324359 0.945934i \(-0.394852\pi\)
−0.799405 + 0.600793i \(0.794852\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.158908 0.368385i 0.0276624 0.0641276i
\(34\) 0.155099 0.0265993
\(35\) −6.99749 5.08397i −1.18279 0.859349i
\(36\) −0.922529 + 2.83925i −0.153755 + 0.473209i
\(37\) 2.17820 + 6.70380i 0.358093 + 1.10210i 0.954194 + 0.299188i \(0.0967157\pi\)
−0.596101 + 0.802909i \(0.703284\pi\)
\(38\) −0.809017 + 0.587785i −0.131240 + 0.0953514i
\(39\) −0.512323 + 0.372225i −0.0820374 + 0.0596036i
\(40\) 0.670278 + 2.06290i 0.105980 + 0.326174i
\(41\) −3.28743 + 10.1177i −0.513411 + 1.58012i 0.272744 + 0.962087i \(0.412069\pi\)
−0.786155 + 0.618030i \(0.787931\pi\)
\(42\) −0.390239 0.283526i −0.0602153 0.0437489i
\(43\) −9.72748 −1.48343 −0.741713 0.670717i \(-0.765986\pi\)
−0.741713 + 0.670717i \(0.765986\pi\)
\(44\) 0.727246 + 3.23591i 0.109636 + 0.487832i
\(45\) 6.47546 0.965304
\(46\) 4.70830 + 3.42078i 0.694201 + 0.504367i
\(47\) 2.05486 6.32420i 0.299732 0.922480i −0.681859 0.731484i \(-0.738828\pi\)
0.981591 0.190996i \(-0.0611718\pi\)
\(48\) 0.0373804 + 0.115045i 0.00539540 + 0.0166053i
\(49\) −7.20104 + 5.23186i −1.02872 + 0.747409i
\(50\) −0.238784 + 0.173486i −0.0337691 + 0.0245347i
\(51\) −0.00579768 0.0178434i −0.000811837 0.00249858i
\(52\) 1.61773 4.97887i 0.224339 0.690445i
\(53\) −4.73271 3.43852i −0.650088 0.472317i 0.213213 0.977006i \(-0.431607\pi\)
−0.863301 + 0.504689i \(0.831607\pi\)
\(54\) 0.724023 0.0985271
\(55\) 6.18792 3.66920i 0.834378 0.494755i
\(56\) 3.98760 0.532866
\(57\) 0.0978632 + 0.0711018i 0.0129623 + 0.00941766i
\(58\) −1.66553 + 5.12596i −0.218694 + 0.673072i
\(59\) −1.34214 4.13068i −0.174732 0.537769i 0.824889 0.565294i \(-0.191237\pi\)
−0.999621 + 0.0275253i \(0.991237\pi\)
\(60\) 0.212272 0.154224i 0.0274042 0.0199103i
\(61\) 2.21329 1.60805i 0.283382 0.205889i −0.437009 0.899457i \(-0.643962\pi\)
0.720391 + 0.693568i \(0.243962\pi\)
\(62\) −1.01028 3.10932i −0.128306 0.394884i
\(63\) 3.67868 11.3218i 0.463470 1.42641i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −11.3553 −1.40845
\(66\) 0.345091 0.204626i 0.0424777 0.0251877i
\(67\) 5.66850 0.692518 0.346259 0.938139i \(-0.387452\pi\)
0.346259 + 0.938139i \(0.387452\pi\)
\(68\) 0.125478 + 0.0911651i 0.0152164 + 0.0110554i
\(69\) 0.217546 0.669537i 0.0261894 0.0806028i
\(70\) −2.67280 8.22604i −0.319461 0.983200i
\(71\) −2.97495 + 2.16143i −0.353062 + 0.256514i −0.750152 0.661265i \(-0.770020\pi\)
0.397091 + 0.917779i \(0.370020\pi\)
\(72\) −2.41521 + 1.75475i −0.284636 + 0.206800i
\(73\) −1.06087 3.26503i −0.124166 0.382142i 0.869583 0.493788i \(-0.164388\pi\)
−0.993748 + 0.111645i \(0.964388\pi\)
\(74\) −2.17820 + 6.70380i −0.253210 + 0.779300i
\(75\) 0.0288846 + 0.0209859i 0.00333530 + 0.00242324i
\(76\) −1.00000 −0.114708
\(77\) −2.89997 12.9035i −0.330482 1.47049i
\(78\) −0.633266 −0.0717033
\(79\) 0.416307 + 0.302465i 0.0468382 + 0.0340299i 0.610958 0.791663i \(-0.290784\pi\)
−0.564120 + 0.825693i \(0.690784\pi\)
\(80\) −0.670278 + 2.06290i −0.0749394 + 0.230640i
\(81\) 2.74052 + 8.43446i 0.304503 + 0.937163i
\(82\) −8.60661 + 6.25307i −0.950441 + 0.690536i
\(83\) −11.2169 + 8.14955i −1.23121 + 0.894529i −0.996981 0.0776512i \(-0.975258\pi\)
−0.234233 + 0.972180i \(0.575258\pi\)
\(84\) −0.149058 0.458754i −0.0162636 0.0500542i
\(85\) 0.103960 0.319955i 0.0112760 0.0347040i
\(86\) −7.86969 5.71767i −0.848611 0.616552i
\(87\) 0.651975 0.0698990
\(88\) −1.31367 + 3.04537i −0.140037 + 0.324638i
\(89\) −7.18374 −0.761475 −0.380738 0.924683i \(-0.624330\pi\)
−0.380738 + 0.924683i \(0.624330\pi\)
\(90\) 5.23876 + 3.80618i 0.552213 + 0.401207i
\(91\) −6.45088 + 19.8538i −0.676236 + 2.08124i
\(92\) 1.79841 + 5.53494i 0.187497 + 0.577057i
\(93\) −0.319947 + 0.232455i −0.0331770 + 0.0241045i
\(94\) 5.37969 3.90857i 0.554872 0.403138i
\(95\) 0.670278 + 2.06290i 0.0687691 + 0.211650i
\(96\) −0.0373804 + 0.115045i −0.00381512 + 0.0117417i
\(97\) −9.81172 7.12863i −0.996229 0.723803i −0.0349527 0.999389i \(-0.511128\pi\)
−0.961276 + 0.275586i \(0.911128\pi\)
\(98\) −8.90098 −0.899135
\(99\) 7.43468 + 6.53927i 0.747214 + 0.657222i
\(100\) −0.295153 −0.0295153
\(101\) 2.05733 + 1.49474i 0.204712 + 0.148732i 0.685418 0.728150i \(-0.259620\pi\)
−0.480706 + 0.876882i \(0.659620\pi\)
\(102\) 0.00579768 0.0178434i 0.000574056 0.00176676i
\(103\) −1.05045 3.23294i −0.103504 0.318551i 0.885873 0.463928i \(-0.153560\pi\)
−0.989376 + 0.145377i \(0.953560\pi\)
\(104\) 4.23528 3.07711i 0.415304 0.301736i
\(105\) −0.846455 + 0.614986i −0.0826056 + 0.0600165i
\(106\) −1.80774 5.56364i −0.175583 0.540388i
\(107\) 3.63072 11.1742i 0.350995 1.08025i −0.607300 0.794472i \(-0.707747\pi\)
0.958295 0.285780i \(-0.0922526\pi\)
\(108\) 0.585747 + 0.425570i 0.0563635 + 0.0409505i
\(109\) −6.76320 −0.647797 −0.323898 0.946092i \(-0.604994\pi\)
−0.323898 + 0.946092i \(0.604994\pi\)
\(110\) 7.16283 + 0.668722i 0.682949 + 0.0637601i
\(111\) 0.852660 0.0809309
\(112\) 3.22604 + 2.34385i 0.304832 + 0.221473i
\(113\) −4.13152 + 12.7155i −0.388661 + 1.19618i 0.545128 + 0.838353i \(0.316481\pi\)
−0.933789 + 0.357823i \(0.883519\pi\)
\(114\) 0.0373804 + 0.115045i 0.00350100 + 0.0107750i
\(115\) 10.2126 7.41990i 0.952331 0.691909i
\(116\) −4.36040 + 3.16802i −0.404853 + 0.294143i
\(117\) −4.82953 14.8638i −0.446490 1.37416i
\(118\) 1.34214 4.13068i 0.123554 0.380260i
\(119\) −0.500357 0.363530i −0.0458676 0.0333248i
\(120\) 0.262382 0.0239521
\(121\) 10.8099 + 2.03617i 0.982718 + 0.185107i
\(122\) 2.73577 0.247685
\(123\) 1.04110 + 0.756406i 0.0938731 + 0.0682028i
\(124\) 1.01028 3.10932i 0.0907257 0.279225i
\(125\) 3.54923 + 10.9234i 0.317452 + 0.977018i
\(126\) 9.63091 6.99727i 0.857990 0.623366i
\(127\) 10.6384 7.72926i 0.944006 0.685861i −0.00537549 0.999986i \(-0.501711\pi\)
0.949382 + 0.314125i \(0.101711\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) −0.363617 + 1.11910i −0.0320147 + 0.0985311i
\(130\) −9.18661 6.67446i −0.805719 0.585389i
\(131\) 0.0333999 0.00291816 0.00145908 0.999999i \(-0.499536\pi\)
0.00145908 + 0.999999i \(0.499536\pi\)
\(132\) 0.399460 + 0.0372936i 0.0347685 + 0.00324599i
\(133\) 3.98760 0.345769
\(134\) 4.58592 + 3.33186i 0.396163 + 0.287829i
\(135\) 0.485297 1.49359i 0.0417677 0.128548i
\(136\) 0.0479283 + 0.147508i 0.00410982 + 0.0126487i
\(137\) 1.08909 0.791271i 0.0930474 0.0676029i −0.540289 0.841480i \(-0.681685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(138\) 0.569542 0.413797i 0.0484826 0.0352247i
\(139\) 0.469782 + 1.44584i 0.0398464 + 0.122635i 0.969001 0.247057i \(-0.0794634\pi\)
−0.929155 + 0.369691i \(0.879463\pi\)
\(140\) 2.67280 8.22604i 0.225893 0.695228i
\(141\) −0.650757 0.472802i −0.0548036 0.0398172i
\(142\) −3.67724 −0.308587
\(143\) −13.0374 11.4672i −1.09024 0.958933i
\(144\) −2.98537 −0.248781
\(145\) 9.45800 + 6.87164i 0.785444 + 0.570659i
\(146\) 1.06087 3.26503i 0.0877983 0.270215i
\(147\) 0.332722 + 1.02401i 0.0274425 + 0.0844592i
\(148\) −5.70259 + 4.14317i −0.468750 + 0.340567i
\(149\) 12.5485 9.11700i 1.02801 0.746894i 0.0601016 0.998192i \(-0.480858\pi\)
0.967910 + 0.251298i \(0.0808575\pi\)
\(150\) 0.0110329 + 0.0339559i 0.000900835 + 0.00277249i
\(151\) −5.37898 + 16.5548i −0.437735 + 1.34721i 0.452523 + 0.891753i \(0.350524\pi\)
−0.890258 + 0.455457i \(0.849476\pi\)
\(152\) −0.809017 0.587785i −0.0656199 0.0476757i
\(153\) 0.463029 0.0374336
\(154\) 5.23838 12.1437i 0.422121 0.978570i
\(155\) −7.09139 −0.569595
\(156\) −0.512323 0.372225i −0.0410187 0.0298018i
\(157\) −6.37738 + 19.6275i −0.508970 + 1.56645i 0.285022 + 0.958521i \(0.407999\pi\)
−0.793992 + 0.607928i \(0.792001\pi\)
\(158\) 0.159015 + 0.489398i 0.0126506 + 0.0389344i
\(159\) −0.572495 + 0.415942i −0.0454018 + 0.0329864i
\(160\) −1.75481 + 1.27494i −0.138730 + 0.100793i
\(161\) −7.17135 22.0711i −0.565181 1.73945i
\(162\) −2.74052 + 8.43446i −0.215316 + 0.662674i
\(163\) 12.7142 + 9.23740i 0.995852 + 0.723529i 0.961195 0.275870i \(-0.0889659\pi\)
0.0346576 + 0.999399i \(0.488966\pi\)
\(164\) −10.6384 −0.830716
\(165\) −0.190816 0.849045i −0.0148550 0.0660981i
\(166\) −13.8648 −1.07612
\(167\) 4.41584 + 3.20829i 0.341708 + 0.248265i 0.745382 0.666638i \(-0.232267\pi\)
−0.403674 + 0.914903i \(0.632267\pi\)
\(168\) 0.149058 0.458754i 0.0115001 0.0353936i
\(169\) 4.45177 + 13.7012i 0.342444 + 1.05393i
\(170\) 0.272170 0.197743i 0.0208745 0.0151662i
\(171\) −2.41521 + 1.75475i −0.184696 + 0.134189i
\(172\) −3.00596 9.25138i −0.229202 0.705411i
\(173\) −3.25748 + 10.0255i −0.247661 + 0.762223i 0.747526 + 0.664233i \(0.231242\pi\)
−0.995187 + 0.0979908i \(0.968758\pi\)
\(174\) 0.527458 + 0.383221i 0.0399865 + 0.0290519i
\(175\) 1.17695 0.0889692
\(176\) −2.85280 + 1.69160i −0.215038 + 0.127509i
\(177\) −0.525384 −0.0394903
\(178\) −5.81177 4.22250i −0.435611 0.316490i
\(179\) 2.44757 7.53284i 0.182940 0.563031i −0.816967 0.576685i \(-0.804346\pi\)
0.999907 + 0.0136534i \(0.00434616\pi\)
\(180\) 2.00103 + 6.15853i 0.149148 + 0.459030i
\(181\) 4.65889 3.38488i 0.346293 0.251597i −0.401019 0.916070i \(-0.631344\pi\)
0.747312 + 0.664473i \(0.231344\pi\)
\(182\) −16.8886 + 12.2703i −1.25187 + 0.909535i
\(183\) −0.102264 0.314737i −0.00755959 0.0232660i
\(184\) −1.79841 + 5.53494i −0.132581 + 0.408041i
\(185\) 12.3693 + 8.98682i 0.909408 + 0.660724i
\(186\) −0.395476 −0.0289977
\(187\) 0.442468 0.262367i 0.0323564 0.0191861i
\(188\) 6.64966 0.484976
\(189\) −2.33573 1.69700i −0.169899 0.123439i
\(190\) −0.670278 + 2.06290i −0.0486271 + 0.149659i
\(191\) −5.03467 15.4951i −0.364296 1.12119i −0.950421 0.310967i \(-0.899347\pi\)
0.586125 0.810221i \(-0.300653\pi\)
\(192\) −0.0978632 + 0.0711018i −0.00706267 + 0.00513133i
\(193\) 20.7531 15.0780i 1.49384 1.08534i 0.521089 0.853502i \(-0.325526\pi\)
0.972754 0.231838i \(-0.0744740\pi\)
\(194\) −3.74774 11.5344i −0.269072 0.828119i
\(195\) −0.424465 + 1.30637i −0.0303965 + 0.0935509i
\(196\) −7.20104 5.23186i −0.514360 0.373705i
\(197\) 11.2089 0.798603 0.399302 0.916820i \(-0.369253\pi\)
0.399302 + 0.916820i \(0.369253\pi\)
\(198\) 2.17110 + 9.66038i 0.154293 + 0.686533i
\(199\) 15.4109 1.09245 0.546226 0.837638i \(-0.316064\pi\)
0.546226 + 0.837638i \(0.316064\pi\)
\(200\) −0.238784 0.173486i −0.0168846 0.0122673i
\(201\) 0.211891 0.652133i 0.0149456 0.0459979i
\(202\) 0.785830 + 2.41854i 0.0552908 + 0.170168i
\(203\) 17.3876 12.6328i 1.22037 0.886649i
\(204\) 0.0151785 0.0110278i 0.00106271 0.000772103i
\(205\) 7.13066 + 21.9459i 0.498027 + 1.53277i
\(206\) 1.05045 3.23294i 0.0731881 0.225250i
\(207\) 14.0560 + 10.2123i 0.976960 + 0.709803i
\(208\) 5.23510 0.362989
\(209\) −1.31367 + 3.04537i −0.0908682 + 0.210653i
\(210\) −1.04628 −0.0721999
\(211\) −2.18132 1.58482i −0.150168 0.109104i 0.510164 0.860077i \(-0.329585\pi\)
−0.660332 + 0.750973i \(0.729585\pi\)
\(212\) 1.80774 5.56364i 0.124156 0.382112i
\(213\) 0.137457 + 0.423048i 0.00941838 + 0.0289868i
\(214\) 9.50536 6.90605i 0.649773 0.472088i
\(215\) −17.0699 + 12.4020i −1.16416 + 0.845809i
\(216\) 0.223735 + 0.688587i 0.0152233 + 0.0468524i
\(217\) −4.02859 + 12.3987i −0.273479 + 0.841680i
\(218\) −5.47154 3.97531i −0.370580 0.269242i
\(219\) −0.415281 −0.0280621
\(220\) 5.40179 + 4.75121i 0.364188 + 0.320327i
\(221\) −0.811960 −0.0546184
\(222\) 0.689817 + 0.501181i 0.0462975 + 0.0336371i
\(223\) −7.12392 + 21.9252i −0.477053 + 1.46822i 0.366115 + 0.930570i \(0.380688\pi\)
−0.843168 + 0.537650i \(0.819312\pi\)
\(224\) 1.23224 + 3.79244i 0.0823323 + 0.253393i
\(225\) −0.712857 + 0.517921i −0.0475238 + 0.0345281i
\(226\) −10.8165 + 7.85863i −0.719501 + 0.522748i
\(227\) −4.42509 13.6190i −0.293703 0.903926i −0.983654 0.180069i \(-0.942368\pi\)
0.689951 0.723856i \(-0.257632\pi\)
\(228\) −0.0373804 + 0.115045i −0.00247558 + 0.00761904i
\(229\) −13.3961 9.73286i −0.885242 0.643166i 0.0493914 0.998780i \(-0.484272\pi\)
−0.934633 + 0.355614i \(0.884272\pi\)
\(230\) 12.6235 0.832368
\(231\) −1.59289 0.148712i −0.104804 0.00978454i
\(232\) −5.38975 −0.353855
\(233\) 15.9575 + 11.5938i 1.04541 + 0.759537i 0.971335 0.237715i \(-0.0763985\pi\)
0.0740785 + 0.997252i \(0.476398\pi\)
\(234\) 4.82953 14.8638i 0.315716 0.971675i
\(235\) −4.45712 13.7176i −0.290751 0.894838i
\(236\) 3.51377 2.55290i 0.228727 0.166180i
\(237\) 0.0503588 0.0365878i 0.00327115 0.00237663i
\(238\) −0.191119 0.588204i −0.0123884 0.0381276i
\(239\) 8.14593 25.0706i 0.526916 1.62168i −0.233578 0.972338i \(-0.575044\pi\)
0.760495 0.649344i \(-0.224956\pi\)
\(240\) 0.212272 + 0.154224i 0.0137021 + 0.00995514i
\(241\) 13.0793 0.842514 0.421257 0.906941i \(-0.361589\pi\)
0.421257 + 0.906941i \(0.361589\pi\)
\(242\) 7.54856 + 8.00120i 0.485240 + 0.514337i
\(243\) 3.24485 0.208158
\(244\) 2.21329 + 1.60805i 0.141691 + 0.102945i
\(245\) −5.96613 + 18.3619i −0.381162 + 1.17310i
\(246\) 0.397666 + 1.22389i 0.0253543 + 0.0780324i
\(247\) 4.23528 3.07711i 0.269485 0.195792i
\(248\) 2.64494 1.92166i 0.167954 0.122026i
\(249\) 0.518273 + 1.59508i 0.0328442 + 0.101084i
\(250\) −3.54923 + 10.9234i −0.224473 + 0.690856i
\(251\) −23.2026 16.8577i −1.46453 1.06405i −0.982153 0.188086i \(-0.939772\pi\)
−0.482382 0.875961i \(-0.660228\pi\)
\(252\) 11.9045 0.749910
\(253\) 19.2185 + 1.79424i 1.20825 + 0.112803i
\(254\) 13.1498 0.825092
\(255\) −0.0329232 0.0239201i −0.00206173 0.00149794i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −2.26128 6.95950i −0.141055 0.434121i 0.855428 0.517922i \(-0.173294\pi\)
−0.996483 + 0.0838004i \(0.973294\pi\)
\(258\) −0.951962 + 0.691641i −0.0592665 + 0.0430597i
\(259\) 22.7397 16.5213i 1.41297 1.02659i
\(260\) −3.50897 10.7995i −0.217617 0.669757i
\(261\) −4.97221 + 15.3029i −0.307772 + 0.947224i
\(262\) 0.0270211 + 0.0196320i 0.00166937 + 0.00121287i
\(263\) −19.5212 −1.20373 −0.601865 0.798598i \(-0.705576\pi\)
−0.601865 + 0.798598i \(0.705576\pi\)
\(264\) 0.301249 + 0.264968i 0.0185406 + 0.0163077i
\(265\) −12.6889 −0.779475
\(266\) 3.22604 + 2.34385i 0.197801 + 0.143711i
\(267\) −0.268531 + 0.826454i −0.0164338 + 0.0505782i
\(268\) 1.75166 + 5.39107i 0.107000 + 0.329312i
\(269\) 5.17012 3.75631i 0.315227 0.229026i −0.418909 0.908028i \(-0.637587\pi\)
0.734136 + 0.679002i \(0.237587\pi\)
\(270\) 1.27052 0.923090i 0.0773216 0.0561774i
\(271\) 2.88667 + 8.88426i 0.175353 + 0.539681i 0.999649 0.0264777i \(-0.00842909\pi\)
−0.824297 + 0.566158i \(0.808429\pi\)
\(272\) −0.0479283 + 0.147508i −0.00290608 + 0.00894400i
\(273\) 2.04294 + 1.48428i 0.123644 + 0.0898329i
\(274\) 1.34619 0.0813264
\(275\) −0.387732 + 0.898850i −0.0233811 + 0.0542027i
\(276\) 0.703993 0.0423754
\(277\) −19.9475 14.4927i −1.19853 0.870782i −0.204390 0.978890i \(-0.565521\pi\)
−0.994139 + 0.108107i \(0.965521\pi\)
\(278\) −0.469782 + 1.44584i −0.0281757 + 0.0867158i
\(279\) −3.01605 9.28246i −0.180566 0.555726i
\(280\) 6.99749 5.08397i 0.418180 0.303826i
\(281\) 0.739203 0.537063i 0.0440972 0.0320385i −0.565518 0.824736i \(-0.691324\pi\)
0.609616 + 0.792697i \(0.291324\pi\)
\(282\) −0.248567 0.765010i −0.0148019 0.0455557i
\(283\) −7.64752 + 23.5366i −0.454598 + 1.39911i 0.417009 + 0.908902i \(0.363078\pi\)
−0.871607 + 0.490206i \(0.836922\pi\)
\(284\) −2.97495 2.16143i −0.176531 0.128257i
\(285\) 0.262382 0.0155422
\(286\) −3.80720 16.9403i −0.225125 1.00170i
\(287\) 42.4216 2.50407
\(288\) −2.41521 1.75475i −0.142318 0.103400i
\(289\) −5.24586 + 16.1451i −0.308580 + 0.949711i
\(290\) 3.61264 + 11.1185i 0.212141 + 0.652904i
\(291\) −1.18688 + 0.862319i −0.0695761 + 0.0505500i
\(292\) 2.77740 2.01790i 0.162535 0.118088i
\(293\) 4.40611 + 13.5606i 0.257408 + 0.792219i 0.993346 + 0.115170i \(0.0367414\pi\)
−0.735938 + 0.677049i \(0.763259\pi\)
\(294\) −0.332722 + 1.02401i −0.0194047 + 0.0597217i
\(295\) −7.62159 5.53741i −0.443746 0.322401i
\(296\) −7.04879 −0.409702
\(297\) 2.06549 1.22476i 0.119852 0.0710678i
\(298\) 15.5108 0.898515
\(299\) −24.6484 17.9081i −1.42545 1.03565i
\(300\) −0.0110329 + 0.0339559i −0.000636987 + 0.00196044i
\(301\) 11.9866 + 36.8908i 0.690894 + 2.12635i
\(302\) −14.0824 + 10.2314i −0.810348 + 0.588752i
\(303\) 0.248866 0.180812i 0.0142970 0.0103874i
\(304\) −0.309017 0.951057i −0.0177233 0.0545468i
\(305\) 1.83373 5.64363i 0.104999 0.323154i
\(306\) 0.374598 + 0.272161i 0.0214143 + 0.0155584i
\(307\) 15.6653 0.894068 0.447034 0.894517i \(-0.352480\pi\)
0.447034 + 0.894517i \(0.352480\pi\)
\(308\) 11.3758 6.74544i 0.648199 0.384357i
\(309\) −0.411200 −0.0233924
\(310\) −5.73706 4.16822i −0.325843 0.236739i
\(311\) 4.09870 12.6145i 0.232416 0.715303i −0.765038 0.643985i \(-0.777280\pi\)
0.997454 0.0713172i \(-0.0227203\pi\)
\(312\) −0.195690 0.602272i −0.0110788 0.0340969i
\(313\) 15.5263 11.2805i 0.877599 0.637613i −0.0550159 0.998485i \(-0.517521\pi\)
0.932615 + 0.360872i \(0.117521\pi\)
\(314\) −16.6962 + 12.1305i −0.942220 + 0.684563i
\(315\) −7.97930 24.5578i −0.449583 1.38367i
\(316\) −0.159015 + 0.489398i −0.00894529 + 0.0275308i
\(317\) −19.5748 14.2219i −1.09943 0.798782i −0.118463 0.992958i \(-0.537797\pi\)
−0.980967 + 0.194176i \(0.937797\pi\)
\(318\) −0.707643 −0.0396826
\(319\) 3.91968 + 17.4408i 0.219460 + 0.976495i
\(320\) −2.16907 −0.121254
\(321\) −1.14982 0.835393i −0.0641767 0.0466271i
\(322\) 7.17135 22.0711i 0.399644 1.22998i
\(323\) 0.0479283 + 0.147508i 0.00266680 + 0.00820758i
\(324\) −7.17478 + 5.21279i −0.398599 + 0.289599i
\(325\) 1.25006 0.908219i 0.0693406 0.0503789i
\(326\) 4.85639 + 14.9464i 0.268971 + 0.827806i
\(327\) −0.252811 + 0.778073i −0.0139805 + 0.0430275i
\(328\) −8.60661 6.25307i −0.475221 0.345268i
\(329\) −26.5162 −1.46189
\(330\) 0.344683 0.799051i 0.0189742 0.0439863i
\(331\) 13.9663 0.767656 0.383828 0.923405i \(-0.374606\pi\)
0.383828 + 0.923405i \(0.374606\pi\)
\(332\) −11.2169 8.14955i −0.615607 0.447265i
\(333\) −6.50271 + 20.0133i −0.356346 + 1.09672i
\(334\) 1.68670 + 5.19113i 0.0922921 + 0.284046i
\(335\) 9.94716 7.22703i 0.543471 0.394855i
\(336\) 0.390239 0.283526i 0.0212893 0.0154676i
\(337\) −10.5470 32.4604i −0.574533 1.76823i −0.637763 0.770233i \(-0.720140\pi\)
0.0632291 0.997999i \(-0.479860\pi\)
\(338\) −4.45177 + 13.7012i −0.242145 + 0.745244i
\(339\) 1.30842 + 0.950623i 0.0710636 + 0.0516307i
\(340\) 0.336421 0.0182450
\(341\) −8.14186 7.16128i −0.440906 0.387805i
\(342\) −2.98537 −0.161430
\(343\) 6.13263 + 4.45561i 0.331131 + 0.240581i
\(344\) 3.00596 9.25138i 0.162070 0.498801i
\(345\) −0.471871 1.45227i −0.0254047 0.0781876i
\(346\) −8.52819 + 6.19609i −0.458478 + 0.333104i
\(347\) −12.3287 + 8.95730i −0.661837 + 0.480853i −0.867283 0.497816i \(-0.834136\pi\)
0.205446 + 0.978669i \(0.434136\pi\)
\(348\) 0.201471 + 0.620065i 0.0108000 + 0.0332390i
\(349\) 10.5382 32.4333i 0.564099 1.73612i −0.106516 0.994311i \(-0.533969\pi\)
0.670614 0.741806i \(-0.266031\pi\)
\(350\) 0.952174 + 0.691795i 0.0508959 + 0.0369780i
\(351\) −3.79033 −0.202313
\(352\) −3.30226 0.308300i −0.176011 0.0164324i
\(353\) 28.6062 1.52255 0.761277 0.648427i \(-0.224573\pi\)
0.761277 + 0.648427i \(0.224573\pi\)
\(354\) −0.425045 0.308813i −0.0225909 0.0164132i
\(355\) −2.46477 + 7.58579i −0.130817 + 0.402612i
\(356\) −2.21990 6.83214i −0.117654 0.362103i
\(357\) −0.0605259 + 0.0439746i −0.00320337 + 0.00232738i
\(358\) 6.40782 4.65555i 0.338664 0.246054i
\(359\) 2.18724 + 6.73162i 0.115438 + 0.355281i 0.992038 0.125938i \(-0.0401940\pi\)
−0.876600 + 0.481219i \(0.840194\pi\)
\(360\) −2.00103 + 6.15853i −0.105463 + 0.324583i
\(361\) −0.809017 0.587785i −0.0425798 0.0309361i
\(362\) 5.75871 0.302671
\(363\) 0.638330 1.16751i 0.0335036 0.0612785i
\(364\) −20.8755 −1.09417
\(365\) −6.02436 4.37695i −0.315329 0.229100i
\(366\) 0.102264 0.314737i 0.00534544 0.0164516i
\(367\) −9.43568 29.0400i −0.492538 1.51588i −0.820758 0.571276i \(-0.806449\pi\)
0.328219 0.944602i \(-0.393551\pi\)
\(368\) −4.70830 + 3.42078i −0.245437 + 0.178321i
\(369\) −25.6939 + 18.6677i −1.33757 + 0.971802i
\(370\) 4.72465 + 14.5410i 0.245623 + 0.755949i
\(371\) −7.20853 + 22.1856i −0.374248 + 1.15182i
\(372\) −0.319947 0.232455i −0.0165885 0.0120522i
\(373\) −33.0808 −1.71286 −0.856430 0.516264i \(-0.827322\pi\)
−0.856430 + 0.516264i \(0.827322\pi\)
\(374\) 0.512179 + 0.0478171i 0.0264842 + 0.00247256i
\(375\) 1.38935 0.0717459
\(376\) 5.37969 + 3.90857i 0.277436 + 0.201569i
\(377\) 8.71919 26.8349i 0.449061 1.38207i
\(378\) −0.892168 2.74581i −0.0458882 0.141229i
\(379\) −7.32077 + 5.31885i −0.376043 + 0.273211i −0.759712 0.650259i \(-0.774660\pi\)
0.383669 + 0.923471i \(0.374660\pi\)
\(380\) −1.75481 + 1.27494i −0.0900199 + 0.0654033i
\(381\) −0.491545 1.51282i −0.0251826 0.0775041i
\(382\) 5.03467 15.4951i 0.257596 0.792800i
\(383\) 20.1604 + 14.6474i 1.03015 + 0.748445i 0.968338 0.249643i \(-0.0803131\pi\)
0.0618087 + 0.998088i \(0.480313\pi\)
\(384\) −0.120966 −0.00617300
\(385\) −21.5402 18.9460i −1.09779 0.965575i
\(386\) 25.6523 1.30567
\(387\) −23.4939 17.0693i −1.19426 0.867683i
\(388\) 3.74774 11.5344i 0.190263 0.585569i
\(389\) −8.64121 26.5949i −0.438127 1.34842i −0.889848 0.456257i \(-0.849190\pi\)
0.451721 0.892159i \(-0.350810\pi\)
\(390\) −1.11126 + 0.807380i −0.0562710 + 0.0408833i
\(391\) 0.730254 0.530561i 0.0369306 0.0268316i
\(392\) −2.75055 8.46533i −0.138924 0.427564i
\(393\) 0.00124850 0.00384250i 6.29786e−5 0.000193828i
\(394\) 9.06821 + 6.58844i 0.456850 + 0.331921i
\(395\) 1.11617 0.0561604
\(396\) −3.92178 + 9.09155i −0.197077 + 0.456868i
\(397\) −7.15719 −0.359209 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(398\) 12.4677 + 9.05831i 0.624949 + 0.454052i
\(399\) 0.149058 0.458754i 0.00746224 0.0229664i
\(400\) −0.0912072 0.280707i −0.00456036 0.0140354i
\(401\) −16.3447 + 11.8751i −0.816216 + 0.593016i −0.915626 0.402031i \(-0.868305\pi\)
0.0994098 + 0.995047i \(0.468305\pi\)
\(402\) 0.554738 0.403041i 0.0276678 0.0201018i
\(403\) 5.28891 + 16.2776i 0.263459 + 0.810844i
\(404\) −0.785830 + 2.41854i −0.0390965 + 0.120327i
\(405\) 15.5626 + 11.3069i 0.773311 + 0.561843i
\(406\) 21.4922 1.06664
\(407\) 5.12620 + 22.8092i 0.254096 + 1.13061i
\(408\) 0.0187617 0.000928841
\(409\) 29.8258 + 21.6697i 1.47479 + 1.07150i 0.979189 + 0.202951i \(0.0650531\pi\)
0.495604 + 0.868549i \(0.334947\pi\)
\(410\) −7.13066 + 21.9459i −0.352158 + 1.08383i
\(411\) −0.0503212 0.154873i −0.00248216 0.00763930i
\(412\) 2.75010 1.99807i 0.135488 0.0984377i
\(413\) −14.0115 + 10.1800i −0.689461 + 0.500923i
\(414\) 5.36892 + 16.5238i 0.263868 + 0.812102i
\(415\) −9.29330 + 28.6018i −0.456190 + 1.40401i
\(416\) 4.23528 + 3.07711i 0.207652 + 0.150868i
\(417\) 0.183898 0.00900550
\(418\) −2.85280 + 1.69160i −0.139535 + 0.0827390i
\(419\) −4.93748 −0.241212 −0.120606 0.992700i \(-0.538484\pi\)
−0.120606 + 0.992700i \(0.538484\pi\)
\(420\) −0.846455 0.614986i −0.0413028 0.0300082i
\(421\) −2.02715 + 6.23893i −0.0987972 + 0.304067i −0.988225 0.153010i \(-0.951103\pi\)
0.889427 + 0.457076i \(0.151103\pi\)
\(422\) −0.833190 2.56430i −0.0405591 0.124828i
\(423\) 16.0603 11.6685i 0.780881 0.567343i
\(424\) 4.73271 3.43852i 0.229841 0.166989i
\(425\) 0.0141462 + 0.0435375i 0.000686191 + 0.00211188i
\(426\) −0.137457 + 0.423048i −0.00665980 + 0.0204968i
\(427\) −8.82570 6.41225i −0.427106 0.310310i
\(428\) 11.7493 0.567922
\(429\) −1.80658 + 1.07124i −0.0872227 + 0.0517197i
\(430\) −21.0995 −1.01751
\(431\) −7.37198 5.35605i −0.355096 0.257992i 0.395908 0.918290i \(-0.370430\pi\)
−0.751004 + 0.660298i \(0.770430\pi\)
\(432\) −0.223735 + 0.688587i −0.0107645 + 0.0331297i
\(433\) −9.23470 28.4215i −0.443791 1.36585i −0.883804 0.467858i \(-0.845026\pi\)
0.440012 0.897992i \(-0.354974\pi\)
\(434\) −10.5470 + 7.66284i −0.506272 + 0.367828i
\(435\) 1.14409 0.831232i 0.0548550 0.0398545i
\(436\) −2.08994 6.43218i −0.100090 0.308046i
\(437\) −1.79841 + 5.53494i −0.0860297 + 0.264772i
\(438\) −0.335969 0.244096i −0.0160532 0.0116634i
\(439\) −40.6715 −1.94114 −0.970572 0.240812i \(-0.922586\pi\)
−0.970572 + 0.240812i \(0.922586\pi\)
\(440\) 1.57744 + 7.01890i 0.0752017 + 0.334613i
\(441\) −26.5727 −1.26537
\(442\) −0.656890 0.477258i −0.0312451 0.0227009i
\(443\) −12.1875 + 37.5092i −0.579045 + 1.78212i 0.0429289 + 0.999078i \(0.486331\pi\)
−0.621974 + 0.783038i \(0.713669\pi\)
\(444\) 0.263487 + 0.810928i 0.0125045 + 0.0384849i
\(445\) −12.6061 + 9.15888i −0.597587 + 0.434172i
\(446\) −18.6507 + 13.5505i −0.883135 + 0.641635i
\(447\) −0.579799 1.78444i −0.0274235 0.0844010i
\(448\) −1.23224 + 3.79244i −0.0582177 + 0.179176i
\(449\) 7.10876 + 5.16482i 0.335483 + 0.243743i 0.742754 0.669565i \(-0.233519\pi\)
−0.407271 + 0.913308i \(0.633519\pi\)
\(450\) −0.881140 −0.0415373
\(451\) −13.9753 + 32.3977i −0.658069 + 1.52555i
\(452\) −13.3699 −0.628867
\(453\) 1.70348 + 1.23765i 0.0800364 + 0.0581499i
\(454\) 4.42509 13.6190i 0.207680 0.639172i
\(455\) 13.9924 + 43.0641i 0.655973 + 2.01888i
\(456\) −0.0978632 + 0.0711018i −0.00458286 + 0.00332964i
\(457\) 10.9188 7.93301i 0.510762 0.371090i −0.302351 0.953197i \(-0.597771\pi\)
0.813113 + 0.582106i \(0.197771\pi\)
\(458\) −5.11687 15.7481i −0.239096 0.735861i
\(459\) 0.0347012 0.106799i 0.00161971 0.00498497i
\(460\) 10.2126 + 7.41990i 0.476166 + 0.345955i
\(461\) −13.3209 −0.620418 −0.310209 0.950668i \(-0.600399\pi\)
−0.310209 + 0.950668i \(0.600399\pi\)
\(462\) −1.20126 1.05659i −0.0558878 0.0491569i
\(463\) 8.27643 0.384638 0.192319 0.981332i \(-0.438399\pi\)
0.192319 + 0.981332i \(0.438399\pi\)
\(464\) −4.36040 3.16802i −0.202427 0.147072i
\(465\) −0.265079 + 0.815830i −0.0122928 + 0.0378332i
\(466\) 6.09524 + 18.7592i 0.282356 + 0.869004i
\(467\) −14.8511 + 10.7899i −0.687226 + 0.499299i −0.875747 0.482770i \(-0.839631\pi\)
0.188521 + 0.982069i \(0.439631\pi\)
\(468\) 12.6439 9.18631i 0.584463 0.424637i
\(469\) −6.98494 21.4974i −0.322535 0.992660i
\(470\) 4.45712 13.7176i 0.205592 0.632746i
\(471\) 2.01966 + 1.46737i 0.0930612 + 0.0676129i
\(472\) 4.34325 0.199915
\(473\) −32.1227 2.99898i −1.47700 0.137893i
\(474\) 0.0622469 0.00285909
\(475\) −0.238784 0.173486i −0.0109561 0.00796011i
\(476\) 0.191119 0.588204i 0.00875993 0.0269603i
\(477\) −5.39675 16.6095i −0.247100 0.760497i
\(478\) 21.3263 15.4945i 0.975443 0.708701i
\(479\) 15.8552 11.5195i 0.724444 0.526340i −0.163357 0.986567i \(-0.552232\pi\)
0.887801 + 0.460227i \(0.152232\pi\)
\(480\) 0.0810806 + 0.249540i 0.00370080 + 0.0113899i
\(481\) 11.4031 35.0950i 0.519935 1.60020i
\(482\) 10.5814 + 7.68784i 0.481969 + 0.350171i
\(483\) −2.80724 −0.127734
\(484\) 1.40393 + 10.9100i 0.0638149 + 0.495911i
\(485\) −26.3063 −1.19451
\(486\) 2.62514 + 1.90728i 0.119079 + 0.0865159i
\(487\) 12.1253 37.3178i 0.549449 1.69103i −0.160721 0.987000i \(-0.551382\pi\)
0.710170 0.704030i \(-0.248618\pi\)
\(488\) 0.845400 + 2.60187i 0.0382694 + 0.117781i
\(489\) 1.53798 1.11741i 0.0695498 0.0505309i
\(490\) −15.6195 + 11.3483i −0.705619 + 0.512662i
\(491\) −5.75554 17.7137i −0.259744 0.799410i −0.992858 0.119304i \(-0.961934\pi\)
0.733114 0.680106i \(-0.238066\pi\)
\(492\) −0.397666 + 1.22389i −0.0179282 + 0.0551772i
\(493\) 0.676296 + 0.491358i 0.0304588 + 0.0221296i
\(494\) 5.23510 0.235538
\(495\) 21.3837 + 1.99638i 0.961125 + 0.0897307i
\(496\) 3.26933 0.146797
\(497\) 11.8629 + 8.61891i 0.532125 + 0.386611i
\(498\) −0.518273 + 1.59508i −0.0232244 + 0.0714773i
\(499\) −3.14563 9.68125i −0.140818 0.433392i 0.855632 0.517585i \(-0.173169\pi\)
−0.996449 + 0.0841926i \(0.973169\pi\)
\(500\) −9.29199 + 6.75103i −0.415551 + 0.301915i
\(501\) 0.534164 0.388093i 0.0238647 0.0173387i
\(502\) −8.86260 27.2763i −0.395557 1.21740i
\(503\) 7.59558 23.3768i 0.338670 1.04232i −0.626215 0.779650i \(-0.715397\pi\)
0.964886 0.262670i \(-0.0846030\pi\)
\(504\) 9.63091 + 6.99727i 0.428995 + 0.311683i
\(505\) 5.51593 0.245456
\(506\) 14.4934 + 12.7479i 0.644312 + 0.566713i
\(507\) 1.74266 0.0773942
\(508\) 10.6384 + 7.72926i 0.472003 + 0.342930i
\(509\) −2.14934 + 6.61500i −0.0952680 + 0.293205i −0.987323 0.158721i \(-0.949263\pi\)
0.892055 + 0.451926i \(0.149263\pi\)
\(510\) −0.0125755 0.0387035i −0.000556854 0.00171382i
\(511\) −11.0752 + 8.04657i −0.489936 + 0.355959i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 0.223735 + 0.688587i 0.00987816 + 0.0304019i
\(514\) 2.26128 6.95950i 0.0997407 0.306970i
\(515\) −5.96516 4.33394i −0.262856 0.190976i
\(516\) −1.17669 −0.0518009
\(517\) 8.73543 20.2507i 0.384184 0.890624i
\(518\) 28.1078 1.23498
\(519\) 1.03162 + 0.749513i 0.0452829 + 0.0329000i
\(520\) 3.50897 10.7995i 0.153879 0.473590i
\(521\) −3.98526 12.2654i −0.174597 0.537355i 0.825018 0.565107i \(-0.191165\pi\)
−0.999615 + 0.0277519i \(0.991165\pi\)
\(522\) −13.0174 + 9.45770i −0.569756 + 0.413952i
\(523\) −19.4428 + 14.1261i −0.850176 + 0.617689i −0.925195 0.379493i \(-0.876098\pi\)
0.0750183 + 0.997182i \(0.476098\pi\)
\(524\) 0.0103211 + 0.0317652i 0.000450881 + 0.00138767i
\(525\) 0.0439949 0.135403i 0.00192010 0.00590945i
\(526\) −15.7930 11.4743i −0.688608 0.500303i
\(527\) −0.507071 −0.0220884
\(528\) 0.0879716 + 0.391434i 0.00382847 + 0.0170350i
\(529\) 10.8698 0.472602
\(530\) −10.2656 7.45837i −0.445908 0.323971i
\(531\) 4.00678 12.3316i 0.173879 0.535146i
\(532\) 1.23224 + 3.79244i 0.0534243 + 0.164423i
\(533\) 45.0565 32.7354i 1.95161 1.41793i
\(534\) −0.703024 + 0.510777i −0.0304228 + 0.0221035i
\(535\) −7.87528 24.2376i −0.340478 1.04788i
\(536\) −1.75166 + 5.39107i −0.0756604 + 0.232859i
\(537\) −0.775125 0.563161i −0.0334491 0.0243022i
\(538\) 6.39061 0.275519
\(539\) −25.3927 + 15.0569i −1.09374 + 0.648547i
\(540\) 1.57045 0.0675816
\(541\) 9.92043 + 7.20761i 0.426513 + 0.309880i 0.780253 0.625464i \(-0.215090\pi\)
−0.353740 + 0.935344i \(0.615090\pi\)
\(542\) −2.88667 + 8.88426i −0.123993 + 0.381612i
\(543\) −0.215263 0.662511i −0.00923782 0.0284311i
\(544\) −0.125478 + 0.0911651i −0.00537983 + 0.00390867i
\(545\) −11.8681 + 8.62271i −0.508375 + 0.369356i
\(546\) 0.780334 + 2.40162i 0.0333952 + 0.102780i
\(547\) 2.19117 6.74373i 0.0936877 0.288341i −0.893222 0.449616i \(-0.851561\pi\)
0.986909 + 0.161275i \(0.0515607\pi\)
\(548\) 1.08909 + 0.791271i 0.0465237 + 0.0338014i
\(549\) 8.16728 0.348571
\(550\) −0.842013 + 0.499281i −0.0359035 + 0.0212894i
\(551\) −5.38975 −0.229611
\(552\) 0.569542 + 0.413797i 0.0242413 + 0.0176124i
\(553\) 0.634089 1.95152i 0.0269642 0.0829873i
\(554\) −7.61927 23.4497i −0.323712 0.996282i
\(555\) 1.49626 1.08709i 0.0635126 0.0461446i
\(556\) −1.22991 + 0.893579i −0.0521596 + 0.0378962i
\(557\) 12.5264 + 38.5522i 0.530760 + 1.63351i 0.752637 + 0.658435i \(0.228781\pi\)
−0.221878 + 0.975075i \(0.571219\pi\)
\(558\) 3.01605 9.28246i 0.127680 0.392958i
\(559\) 41.1986 + 29.9325i 1.74252 + 1.26601i
\(560\) 8.64937 0.365503
\(561\) −0.0136443 0.0607111i −0.000576065 0.00256322i
\(562\) 0.913705 0.0385423
\(563\) −33.0758 24.0310i −1.39398 1.01279i −0.995415 0.0956454i \(-0.969509\pi\)
−0.398565 0.917140i \(-0.630491\pi\)
\(564\) 0.248567 0.765010i 0.0104666 0.0322128i
\(565\) 8.96155 + 27.5808i 0.377015 + 1.16033i
\(566\) −20.0215 + 14.5464i −0.841565 + 0.611433i
\(567\) 28.6102 20.7865i 1.20151 0.872952i
\(568\) −1.13633 3.49726i −0.0476793 0.146742i
\(569\) 5.75518 17.7126i 0.241270 0.742551i −0.754958 0.655773i \(-0.772343\pi\)
0.996228 0.0867782i \(-0.0276572\pi\)
\(570\) 0.212272 + 0.154224i 0.00889108 + 0.00645975i
\(571\) −7.25678 −0.303687 −0.151843 0.988405i \(-0.548521\pi\)
−0.151843 + 0.988405i \(0.548521\pi\)
\(572\) 6.87717 15.9428i 0.287549 0.666602i
\(573\) −1.97084 −0.0823328
\(574\) 34.3198 + 24.9348i 1.43248 + 1.04076i
\(575\) −0.530806 + 1.63365i −0.0221361 + 0.0681280i
\(576\) −0.922529 2.83925i −0.0384387 0.118302i
\(577\) 11.5090 8.36174i 0.479124 0.348104i −0.321862 0.946786i \(-0.604309\pi\)
0.800986 + 0.598683i \(0.204309\pi\)
\(578\) −13.7338 + 9.97821i −0.571252 + 0.415039i
\(579\) −0.958893 2.95117i −0.0398502 0.122646i
\(580\) −3.61264 + 11.1185i −0.150007 + 0.461673i
\(581\) 44.7285 + 32.4972i 1.85565 + 1.34821i
\(582\) −1.46706 −0.0608118
\(583\) −14.5686 12.8140i −0.603369 0.530701i
\(584\) 3.43305 0.142061
\(585\) −27.4254 19.9257i −1.13390 0.823827i
\(586\) −4.40611 + 13.5606i −0.182015 + 0.560184i
\(587\) −6.53528 20.1135i −0.269740 0.830173i −0.990563 0.137055i \(-0.956236\pi\)
0.720824 0.693118i \(-0.243764\pi\)
\(588\) −0.871078 + 0.632875i −0.0359226 + 0.0260993i
\(589\) 2.64494 1.92166i 0.108983 0.0791808i
\(590\) −2.91119 8.95972i −0.119852 0.368866i
\(591\) 0.418994 1.28953i 0.0172351 0.0530442i
\(592\) −5.70259 4.14317i −0.234375 0.170283i
\(593\) 4.97843 0.204440 0.102220 0.994762i \(-0.467405\pi\)
0.102220 + 0.994762i \(0.467405\pi\)
\(594\) 2.39092 + 0.223216i 0.0981005 + 0.00915866i
\(595\) −1.34151 −0.0549966
\(596\) 12.5485 + 9.11700i 0.514006 + 0.373447i
\(597\) 0.576066 1.77295i 0.0235768 0.0725620i
\(598\) −9.41486 28.9759i −0.385002 1.18491i
\(599\) 28.2903 20.5541i 1.15591 0.839818i 0.166655 0.986015i \(-0.446704\pi\)
0.989255 + 0.146198i \(0.0467035\pi\)
\(600\) −0.0288846 + 0.0209859i −0.00117921 + 0.000856745i
\(601\) 5.38629 + 16.5773i 0.219711 + 0.676202i 0.998785 + 0.0492703i \(0.0156896\pi\)
−0.779074 + 0.626932i \(0.784310\pi\)
\(602\) −11.9866 + 36.8908i −0.488536 + 1.50356i
\(603\) 13.6906 + 9.94684i 0.557526 + 0.405066i
\(604\) −17.4067 −0.708270
\(605\) 21.5653 10.2089i 0.876756 0.415052i
\(606\) 0.307615 0.0124960
\(607\) 24.5383 + 17.8281i 0.995977 + 0.723620i 0.961222 0.275776i \(-0.0889349\pi\)
0.0347550 + 0.999396i \(0.488935\pi\)
\(608\) 0.309017 0.951057i 0.0125323 0.0385704i
\(609\) −0.803387 2.47257i −0.0325549 0.100194i
\(610\) 4.80076 3.48796i 0.194377 0.141223i
\(611\) −28.1632 + 20.4618i −1.13936 + 0.827794i
\(612\) 0.143084 + 0.440366i 0.00578382 + 0.0178008i
\(613\) −7.13642 + 21.9636i −0.288237 + 0.887103i 0.697172 + 0.716903i \(0.254441\pi\)
−0.985410 + 0.170199i \(0.945559\pi\)
\(614\) 12.6735 + 9.20786i 0.511462 + 0.371599i
\(615\) 2.79132 0.112557
\(616\) 13.1681 + 1.22938i 0.530559 + 0.0495330i
\(617\) 10.8162 0.435445 0.217722 0.976011i \(-0.430137\pi\)
0.217722 + 0.976011i \(0.430137\pi\)
\(618\) −0.332668 0.241697i −0.0133819 0.00972249i
\(619\) −0.549042 + 1.68978i −0.0220678 + 0.0679179i −0.961484 0.274861i \(-0.911368\pi\)
0.939416 + 0.342779i \(0.111368\pi\)
\(620\) −2.19136 6.74432i −0.0880072 0.270858i
\(621\) 3.40892 2.47672i 0.136795 0.0993875i
\(622\) 10.7305 7.79619i 0.430255 0.312599i
\(623\) 8.85207 + 27.2439i 0.354651 + 1.09150i
\(624\) 0.195690 0.602272i 0.00783387 0.0241102i
\(625\) 18.9610 + 13.7760i 0.758441 + 0.551040i
\(626\) 19.1916 0.767050
\(627\) 0.301249 + 0.264968i 0.0120307 + 0.0105818i
\(628\) −20.6376 −0.823531
\(629\) 0.884468 + 0.642604i 0.0352660 + 0.0256223i
\(630\) 7.97930 24.5578i 0.317903 0.978405i
\(631\) 8.36332 + 25.7396i 0.332938 + 1.02468i 0.967729 + 0.251995i \(0.0810865\pi\)
−0.634790 + 0.772684i \(0.718914\pi\)
\(632\) −0.416307 + 0.302465i −0.0165598 + 0.0120314i
\(633\) −0.263865 + 0.191709i −0.0104877 + 0.00761974i
\(634\) −7.47690 23.0115i −0.296946 0.913905i
\(635\) 8.81402 27.1268i 0.349774 1.07649i
\(636\) −0.572495 0.415942i −0.0227009 0.0164932i
\(637\) 46.5975 1.84626
\(638\) −7.08034 + 16.4138i −0.280313 + 0.649829i
\(639\) −10.9779 −0.434279
\(640\) −1.75481 1.27494i −0.0693650 0.0503966i
\(641\) −0.191186 + 0.588409i −0.00755138 + 0.0232408i −0.954761 0.297374i \(-0.903889\pi\)
0.947210 + 0.320614i \(0.103889\pi\)
\(642\) −0.439192 1.35169i −0.0173335 0.0533471i
\(643\) −9.80040 + 7.12040i −0.386490 + 0.280801i −0.764016 0.645198i \(-0.776775\pi\)
0.377526 + 0.925999i \(0.376775\pi\)
\(644\) 18.7748 13.6407i 0.739832 0.537519i
\(645\) 0.788709 + 2.42740i 0.0310554 + 0.0955787i
\(646\) −0.0479283 + 0.147508i −0.00188572 + 0.00580363i
\(647\) 31.2641 + 22.7147i 1.22912 + 0.893006i 0.996824 0.0796402i \(-0.0253771\pi\)
0.232293 + 0.972646i \(0.425377\pi\)
\(648\) −8.86852 −0.348388
\(649\) −3.15861 14.0544i −0.123986 0.551683i
\(650\) 1.54515 0.0606059
\(651\) 1.27582 + 0.926939i 0.0500034 + 0.0363296i
\(652\) −4.85639 + 14.9464i −0.190191 + 0.585347i
\(653\) −7.36665 22.6722i −0.288279 0.887233i −0.985396 0.170276i \(-0.945534\pi\)
0.697117 0.716957i \(-0.254466\pi\)
\(654\) −0.661868 + 0.480875i −0.0258811 + 0.0188037i
\(655\) 0.0586106 0.0425831i 0.00229010 0.00166386i
\(656\) −3.28743 10.1177i −0.128353 0.395029i
\(657\) 3.16709 9.74730i 0.123560 0.380278i
\(658\) −21.4521 15.5858i −0.836288 0.607599i
\(659\) 36.4845 1.42124 0.710618 0.703578i \(-0.248415\pi\)
0.710618 + 0.703578i \(0.248415\pi\)
\(660\) 0.748524 0.443846i 0.0291363 0.0172767i
\(661\) 30.3365 1.17995 0.589976 0.807421i \(-0.299137\pi\)
0.589976 + 0.807421i \(0.299137\pi\)
\(662\) 11.2990 + 8.20917i 0.439147 + 0.319059i
\(663\) −0.0303514 + 0.0934120i −0.00117875 + 0.00362782i
\(664\) −4.28447 13.1862i −0.166270 0.511726i
\(665\) 6.99749 5.08397i 0.271351 0.197148i
\(666\) −17.0243 + 12.3689i −0.659679 + 0.479285i
\(667\) 9.69299 + 29.8320i 0.375314 + 1.15510i
\(668\) −1.68670 + 5.19113i −0.0652603 + 0.200851i
\(669\) 2.25609 + 1.63914i 0.0872254 + 0.0633730i
\(670\) 12.2954 0.475011
\(671\) 7.80461 4.62784i 0.301294 0.178656i
\(672\) 0.482362 0.0186075
\(673\) 6.16978 + 4.48261i 0.237828 + 0.172792i 0.700315 0.713834i \(-0.253043\pi\)
−0.462487 + 0.886626i \(0.653043\pi\)
\(674\) 10.5470 32.4604i 0.406256 1.25033i
\(675\) 0.0660361 + 0.203238i 0.00254173 + 0.00782265i
\(676\) −11.6549 + 8.46778i −0.448265 + 0.325684i
\(677\) 21.8062 15.8431i 0.838080 0.608901i −0.0837535 0.996487i \(-0.526691\pi\)
0.921834 + 0.387586i \(0.126691\pi\)
\(678\) 0.499772 + 1.53814i 0.0191936 + 0.0590719i
\(679\) −14.9445 + 45.9945i −0.573518 + 1.76511i
\(680\) 0.272170 + 0.197743i 0.0104372 + 0.00758310i
\(681\) −1.73221 −0.0663785
\(682\) −2.37761 10.5793i −0.0910433 0.405101i
\(683\) −46.1845 −1.76720 −0.883600 0.468242i \(-0.844888\pi\)
−0.883600 + 0.468242i \(0.844888\pi\)
\(684\) −2.41521 1.75475i −0.0923480 0.0670947i
\(685\) 0.902323 2.77706i 0.0344760 0.106106i
\(686\) 2.34246 + 7.20934i 0.0894354 + 0.275254i
\(687\) −1.62047 + 1.17734i −0.0618248 + 0.0449184i
\(688\) 7.86969 5.71767i 0.300029 0.217984i
\(689\) 9.46367 + 29.1262i 0.360537 + 1.10962i
\(690\) 0.471871 1.45227i 0.0179638 0.0552870i
\(691\) 4.54652 + 3.30324i 0.172958 + 0.125661i 0.670896 0.741551i \(-0.265909\pi\)
−0.497939 + 0.867212i \(0.665909\pi\)
\(692\) −10.5414 −0.400725
\(693\) 15.6385 36.2535i 0.594057 1.37716i
\(694\) −15.2391 −0.578467
\(695\) 2.66775 + 1.93823i 0.101193 + 0.0735213i
\(696\) −0.201471 + 0.620065i −0.00763675 + 0.0235035i
\(697\) 0.509879 + 1.56925i 0.0193130 + 0.0594394i
\(698\) 27.5895 20.0449i 1.04428 0.758711i
\(699\) 1.93031 1.40245i 0.0730111 0.0530457i
\(700\) 0.363698 + 1.11935i 0.0137465 + 0.0423074i
\(701\) 8.85554 27.2545i 0.334469 1.02939i −0.632514 0.774549i \(-0.717977\pi\)
0.966983 0.254841i \(-0.0820230\pi\)
\(702\) −3.06644 2.22790i −0.115735 0.0840867i
\(703\) −7.04879 −0.265850
\(704\) −2.49037 2.19044i −0.0938595 0.0825554i
\(705\) −1.74475 −0.0657112
\(706\) 23.1429 + 16.8143i 0.870994 + 0.632814i
\(707\) 3.13358 9.64416i 0.117850 0.362706i
\(708\) −0.162353 0.499670i −0.00610158 0.0187787i
\(709\) 5.04815 3.66769i 0.189587 0.137743i −0.488943 0.872316i \(-0.662617\pi\)
0.678530 + 0.734573i \(0.262617\pi\)
\(710\) −6.45286 + 4.68828i −0.242172 + 0.175948i
\(711\) 0.474718 + 1.46103i 0.0178033 + 0.0547930i
\(712\) 2.21990 6.83214i 0.0831942 0.256045i
\(713\) −15.3930 11.1837i −0.576472 0.418832i
\(714\) −0.0748141 −0.00279985
\(715\) −37.4981 3.50082i −1.40235 0.130923i
\(716\) 7.92050 0.296003
\(717\) −2.57975 1.87430i −0.0963425 0.0699969i
\(718\) −2.18724 + 6.73162i −0.0816269 + 0.251222i
\(719\) 5.81747 + 17.9043i 0.216955 + 0.667718i 0.999009 + 0.0445080i \(0.0141720\pi\)
−0.782054 + 0.623210i \(0.785828\pi\)
\(720\) −5.23876 + 3.80618i −0.195237 + 0.141848i
\(721\) −10.9663 + 7.96750i −0.408407 + 0.296725i
\(722\) −0.309017 0.951057i −0.0115004 0.0353947i
\(723\) 0.488911 1.50471i 0.0181828 0.0559608i
\(724\) 4.65889 + 3.38488i 0.173146 + 0.125798i
\(725\) −1.59080 −0.0590809
\(726\) 1.20267 0.569337i 0.0446352 0.0211301i
\(727\) −16.7788 −0.622290 −0.311145 0.950362i \(-0.600712\pi\)
−0.311145 + 0.950362i \(0.600712\pi\)
\(728\) −16.8886 12.2703i −0.625934 0.454768i
\(729\) −8.10028 + 24.9301i −0.300010 + 0.923337i
\(730\) −2.30110 7.08206i −0.0851675 0.262119i
\(731\) −1.22058 + 0.886807i −0.0451449 + 0.0327997i
\(732\) 0.267731 0.194518i 0.00989563 0.00718960i
\(733\) 1.77745 + 5.47041i 0.0656514 + 0.202054i 0.978501 0.206241i \(-0.0661232\pi\)
−0.912850 + 0.408296i \(0.866123\pi\)
\(734\) 9.43568 29.0400i 0.348277 1.07189i
\(735\) 1.88943 + 1.37275i 0.0696925 + 0.0506346i
\(736\) −5.81978 −0.214520
\(737\) 18.7189 + 1.74760i 0.689520 + 0.0643736i
\(738\) −31.7594 −1.16908
\(739\) −32.4602 23.5837i −1.19407 0.867541i −0.200380 0.979718i \(-0.564218\pi\)
−0.993688 + 0.112177i \(0.964218\pi\)
\(740\) −4.72465 + 14.5410i −0.173682 + 0.534537i
\(741\) −0.195690 0.602272i −0.00718885 0.0221250i
\(742\) −18.8722 + 13.7114i −0.692820 + 0.503363i
\(743\) 2.12568 1.54440i 0.0779837 0.0566585i −0.548110 0.836406i \(-0.684653\pi\)
0.626094 + 0.779748i \(0.284653\pi\)
\(744\) −0.122209 0.376120i −0.00448040 0.0137892i
\(745\) 10.3965 31.9972i 0.380899 1.17229i
\(746\) −26.7629 19.4444i −0.979861 0.711911i
\(747\) −41.3916 −1.51444
\(748\) 0.386255 + 0.339736i 0.0141229 + 0.0124220i
\(749\) −46.8514 −1.71191
\(750\) 1.12401 + 0.816642i 0.0410431 + 0.0298195i
\(751\) 9.46795 29.1393i 0.345490 1.06331i −0.615831 0.787879i \(-0.711179\pi\)
0.961321 0.275431i \(-0.0888206\pi\)
\(752\) 2.05486 + 6.32420i 0.0749330 + 0.230620i
\(753\) −2.80671 + 2.03920i −0.102282 + 0.0743125i
\(754\) 22.8271 16.5849i 0.831315 0.603986i
\(755\) 11.6674 + 35.9084i 0.424619 + 1.30684i
\(756\) 0.892168 2.74581i 0.0324478 0.0998642i
\(757\) −31.8917 23.1706i −1.15912 0.842151i −0.169455 0.985538i \(-0.554201\pi\)
−0.989667 + 0.143386i \(0.954201\pi\)
\(758\) −9.04897 −0.328673
\(759\) 0.924811 2.14392i 0.0335685 0.0778193i
\(760\) −2.16907 −0.0786803
\(761\) 9.07229 + 6.59140i 0.328870 + 0.238938i 0.739951 0.672661i \(-0.234849\pi\)
−0.411081 + 0.911599i \(0.634849\pi\)
\(762\) 0.491545 1.51282i 0.0178068 0.0548037i
\(763\) 8.33386 + 25.6490i 0.301706 + 0.928556i
\(764\) 13.1809 9.57652i 0.476870 0.346466i
\(765\) 0.812528 0.590336i 0.0293770 0.0213436i
\(766\) 7.70058 + 23.6999i 0.278233 + 0.856313i
\(767\) −7.02623 + 21.6245i −0.253702 + 0.780816i
\(768\) −0.0978632 0.0711018i −0.00353133 0.00256566i
\(769\) 25.6746 0.925850 0.462925 0.886398i \(-0.346800\pi\)
0.462925 + 0.886398i \(0.346800\pi\)
\(770\) −6.29022 27.9886i −0.226684 1.00864i
\(771\) −0.885183 −0.0318791
\(772\) 20.7531 + 15.0780i 0.746922 + 0.542670i
\(773\) 10.9146 33.5916i 0.392570 1.20820i −0.538269 0.842773i \(-0.680921\pi\)
0.930838 0.365431i \(-0.119079\pi\)
\(774\) −8.97388 27.6188i −0.322560 0.992736i
\(775\) 0.780663 0.567185i 0.0280422 0.0203739i
\(776\) 9.81172 7.12863i 0.352220 0.255903i
\(777\) −1.05068 3.23366i −0.0376929 0.116007i
\(778\) 8.64121 26.5949i 0.309802 0.953474i
\(779\) −8.60661 6.25307i −0.308364 0.224040i
\(780\) −1.37360 −0.0491826
\(781\) −10.4904 + 6.22043i −0.375377 + 0.222584i
\(782\) 0.902644 0.0322785
\(783\) 3.15703 + 2.29372i 0.112823 + 0.0819708i
\(784\) 2.75055 8.46533i 0.0982340 0.302333i
\(785\) 13.8329 + 42.5734i 0.493719 + 1.51951i
\(786\) 0.00326862 0.00237479i 0.000116588 8.47060e-5i
\(787\) 8.67585 6.30337i 0.309261 0.224691i −0.422319 0.906447i \(-0.638784\pi\)
0.731579 + 0.681757i \(0.238784\pi\)
\(788\) 3.46375 + 10.6603i 0.123391 + 0.379758i
\(789\) −0.729711 + 2.24582i −0.0259784 + 0.0799533i
\(790\) 0.902997 + 0.656066i 0.0321272 + 0.0233418i
\(791\) 53.3138 1.89562
\(792\) −8.51666 + 5.05006i −0.302626 + 0.179446i
\(793\) −14.3220 −0.508590
\(794\) −5.79029 4.20689i −0.205490 0.149297i
\(795\) −0.474318 + 1.45980i −0.0168223 + 0.0517738i
\(796\) 4.76224 + 14.6567i 0.168793 + 0.519491i
\(797\) −19.4278 + 14.1151i −0.688167 + 0.499982i −0.876057 0.482208i \(-0.839835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(798\) 0.390239 0.283526i 0.0138143 0.0100367i
\(799\) −0.318707 0.980880i −0.0112750 0.0347010i
\(800\) 0.0912072 0.280707i 0.00322466 0.00992449i
\(801\) −17.3503 12.6057i −0.613041 0.445401i
\(802\) −20.2032 −0.713399
\(803\) −2.49667 11.1090i −0.0881056 0.392030i
\(804\) 0.685694 0.0241826
\(805\) −40.7239 29.5876i −1.43533 1.04283i
\(806\) −5.28891 + 16.2776i −0.186294 + 0.573353i
\(807\) −0.238884 0.735209i −0.00840911 0.0258806i
\(808\) −2.05733 + 1.49474i −0.0723766 + 0.0525847i
\(809\) −18.1983 + 13.2218i −0.639817 + 0.464854i −0.859787 0.510652i \(-0.829404\pi\)
0.219970 + 0.975507i \(0.429404\pi\)
\(810\) 5.94438 + 18.2949i 0.208864 + 0.642818i
\(811\) −12.7737 + 39.3136i −0.448547 + 1.38049i 0.430000 + 0.902829i \(0.358514\pi\)
−0.878547 + 0.477657i \(0.841486\pi\)
\(812\) 17.3876 + 12.6328i 0.610184 + 0.443324i
\(813\) 1.13000 0.0396307
\(814\) −9.25975 + 21.4662i −0.324554 + 0.752389i
\(815\) 34.0882 1.19406
\(816\) 0.0151785 + 0.0110278i 0.000531354 + 0.000386051i
\(817\) 3.00596 9.25138i 0.105165 0.323665i
\(818\) 11.3925 + 35.0624i 0.398328 + 1.22593i
\(819\) −50.4188 + 36.6314i −1.76177 + 1.28000i
\(820\) −18.6683 + 13.5633i −0.651926 + 0.473652i
\(821\) −8.78037 27.0232i −0.306437 0.943117i −0.979137 0.203201i \(-0.934865\pi\)
0.672700 0.739915i \(-0.265135\pi\)
\(822\) 0.0503212 0.154873i 0.00175515 0.00540180i
\(823\) −12.3064 8.94116i −0.428976 0.311669i 0.352263 0.935901i \(-0.385412\pi\)
−0.781239 + 0.624232i \(0.785412\pi\)
\(824\) 3.39932 0.118421
\(825\) 0.0889146 + 0.0782060i 0.00309561 + 0.00272278i
\(826\) −17.3192 −0.602611
\(827\) 39.3941 + 28.6215i 1.36987 + 0.995267i 0.997747 + 0.0670819i \(0.0213689\pi\)
0.372120 + 0.928185i \(0.378631\pi\)
\(828\) −5.36892 + 16.5238i −0.186583 + 0.574243i
\(829\) 2.70468 + 8.32415i 0.0939374 + 0.289110i 0.986975 0.160872i \(-0.0514306\pi\)
−0.893038 + 0.449982i \(0.851431\pi\)
\(830\) −24.3302 + 17.6769i −0.844513 + 0.613574i
\(831\) −2.41296 + 1.75312i −0.0837046 + 0.0608150i
\(832\) 1.61773 + 4.97887i 0.0560848 + 0.172611i
\(833\) −0.426609 + 1.31297i −0.0147811 + 0.0454916i
\(834\) 0.148776 + 0.108092i 0.00515170 + 0.00374293i
\(835\) 11.8394 0.409718
\(836\) −3.30226 0.308300i −0.114211 0.0106628i
\(837\) −2.36707 −0.0818179
\(838\) −3.99450 2.90218i −0.137988 0.100254i
\(839\) 0.408727 1.25793i 0.0141108 0.0434287i −0.943753 0.330651i \(-0.892732\pi\)
0.957864 + 0.287222i \(0.0927318\pi\)
\(840\) −0.323317 0.995068i −0.0111555 0.0343331i
\(841\) −0.0400120 + 0.0290704i −0.00137972 + 0.00100243i
\(842\) −5.30715 + 3.85587i −0.182896 + 0.132882i
\(843\) −0.0341547 0.105117i −0.00117635 0.00362043i
\(844\) 0.833190 2.56430i 0.0286796 0.0882667i
\(845\) 25.2802 + 18.3672i 0.869667 + 0.631850i
\(846\) 19.8517 0.682515
\(847\) −5.59831 43.5049i −0.192360 1.49485i
\(848\) 5.84996 0.200888
\(849\) 2.42191 + 1.75962i 0.0831196 + 0.0603899i
\(850\) −0.0141462 + 0.0435375i −0.000485210 + 0.00149332i
\(851\) 12.6766 + 39.0146i 0.434549 + 1.33740i
\(852\) −0.359866 + 0.261458i −0.0123288 + 0.00895741i
\(853\) 24.3801 17.7132i 0.834759 0.606488i −0.0861424 0.996283i \(-0.527454\pi\)
0.920902 + 0.389795i \(0.127454\pi\)
\(854\) −3.37112 10.3752i −0.115357 0.355033i
\(855\) −2.00103 + 6.15853i −0.0684337 + 0.210617i
\(856\) 9.50536 + 6.90605i 0.324886 + 0.236044i
\(857\) 43.4283 1.48348 0.741741 0.670687i \(-0.234001\pi\)
0.741741 + 0.670687i \(0.234001\pi\)
\(858\) −2.09121 0.195236i −0.0713928 0.00666524i
\(859\) −45.4700 −1.55142 −0.775709 0.631091i \(-0.782607\pi\)
−0.775709 + 0.631091i \(0.782607\pi\)
\(860\) −17.0699 12.4020i −0.582078 0.422905i
\(861\) 1.58573 4.88039i 0.0540417 0.166323i
\(862\) −2.81584 8.66628i −0.0959080 0.295175i
\(863\) −11.3784 + 8.26686i −0.387324 + 0.281407i −0.764358 0.644792i \(-0.776944\pi\)
0.377034 + 0.926199i \(0.376944\pi\)
\(864\) −0.585747 + 0.425570i −0.0199275 + 0.0144782i
\(865\) 7.06568 + 21.7459i 0.240240 + 0.739384i
\(866\) 9.23470 28.4215i 0.313808 0.965802i
\(867\) 1.66132 + 1.20702i 0.0564214 + 0.0409925i
\(868\) −13.0368 −0.442498
\(869\) 1.28151 + 1.12717i 0.0434721 + 0.0382365i
\(870\) 1.41418 0.0479450
\(871\) −24.0077 17.4426i −0.813471 0.591021i
\(872\) 2.08994 6.43218i 0.0707744 0.217821i
\(873\) −11.1884 34.4343i −0.378670 1.16543i
\(874\) −4.70830 + 3.42078i −0.159261 + 0.115710i
\(875\) 37.0528 26.9204i 1.25261 0.910076i
\(876\) −0.128329 0.394956i −0.00433583 0.0133443i
\(877\) −8.28736 + 25.5059i −0.279844 + 0.861272i 0.708053 + 0.706160i \(0.249574\pi\)
−0.987897 + 0.155112i \(0.950426\pi\)
\(878\) −32.9039 23.9061i −1.11045 0.806792i
\(879\) 1.72478 0.0581755
\(880\) −2.84943 + 6.60561i −0.0960542 + 0.222675i
\(881\) −3.51062 −0.118276 −0.0591379 0.998250i \(-0.518835\pi\)
−0.0591379 + 0.998250i \(0.518835\pi\)
\(882\) −21.4978 15.6190i −0.723867 0.525920i
\(883\) −1.49087 + 4.58843i −0.0501718 + 0.154413i −0.973003 0.230791i \(-0.925869\pi\)
0.922832 + 0.385204i \(0.125869\pi\)
\(884\) −0.250910 0.772220i −0.00843900 0.0259726i
\(885\) −0.921950 + 0.669836i −0.0309910 + 0.0225163i
\(886\) −31.9072 + 23.1820i −1.07194 + 0.778813i
\(887\) 15.9686 + 49.1463i 0.536174 + 1.65017i 0.741100 + 0.671395i \(0.234305\pi\)
−0.204926 + 0.978777i \(0.565695\pi\)
\(888\) −0.263487 + 0.810928i −0.00884203 + 0.0272130i
\(889\) −42.4218 30.8212i −1.42278 1.03371i
\(890\) −15.5820 −0.522310
\(891\) 6.44959 + 28.6977i 0.216069 + 0.961410i
\(892\) −23.0535 −0.771888
\(893\) 5.37969 + 3.90857i 0.180024 + 0.130795i
\(894\) 0.579799 1.78444i 0.0193914 0.0596805i
\(895\) −5.30894 16.3392i −0.177458 0.546160i
\(896\) −3.22604 + 2.34385i −0.107774 + 0.0783027i
\(897\) −2.98161 + 2.16627i −0.0995530 + 0.0723295i
\(898\) 2.71530 + 8.35685i 0.0906109 + 0.278872i
\(899\) 5.44516 16.7585i 0.181606 0.558926i
\(900\) −0.712857 0.517921i −0.0237619 0.0172640i
\(901\) −0.907324 −0.0302274
\(902\) −30.3491 + 17.9959i −1.01052 + 0.599197i
\(903\) 4.69217 0.156146
\(904\) −10.8165 7.85863i −0.359750 0.261374i
\(905\) 3.85994 11.8797i 0.128309 0.394894i
\(906\) 0.650671 + 2.00256i 0.0216171 + 0.0665306i
\(907\) −9.95017 + 7.22922i −0.330390 + 0.240042i −0.740596 0.671950i \(-0.765457\pi\)
0.410206 + 0.911993i \(0.365457\pi\)
\(908\) 11.5850 8.41701i 0.384463 0.279328i
\(909\) 2.34599 + 7.22022i 0.0778116 + 0.239479i
\(910\) −13.9924 + 43.0641i −0.463843 + 1.42756i
\(911\) −0.773700 0.562126i −0.0256338 0.0186241i 0.574895 0.818227i \(-0.305043\pi\)
−0.600528 + 0.799603i \(0.705043\pi\)
\(912\) −0.120966 −0.00400557
\(913\) −39.5536 + 23.4538i −1.30903 + 0.776208i
\(914\) 13.4964 0.446422
\(915\) −0.580727 0.421923i −0.0191982 0.0139483i
\(916\) 5.11687 15.7481i 0.169066 0.520332i
\(917\) −0.0411566 0.126667i −0.00135911 0.00418291i
\(918\) 0.0908490 0.0660057i 0.00299846 0.00217851i
\(919\) −6.38076 + 4.63589i −0.210482 + 0.152924i −0.688032 0.725681i \(-0.741525\pi\)
0.477550 + 0.878605i \(0.341525\pi\)
\(920\) 3.90087 + 12.0056i 0.128608 + 0.395815i
\(921\) 0.585577 1.80222i 0.0192954 0.0593852i
\(922\) −10.7769 7.82985i −0.354917 0.257862i
\(923\) 19.2507 0.633645
\(924\) −0.350796 1.56088i −0.0115403 0.0513492i
\(925\) −2.08047 −0.0684054
\(926\) 6.69577 + 4.86476i 0.220037 + 0.159866i
\(927\) 3.13597 9.65152i 0.102999 0.316997i
\(928\) −1.66553 5.12596i −0.0546736 0.168268i
\(929\) 14.9297 10.8471i 0.489828 0.355881i −0.315290 0.948995i \(-0.602102\pi\)
0.805118 + 0.593115i \(0.202102\pi\)
\(930\) −0.693986 + 0.504211i −0.0227567 + 0.0165337i
\(931\) −2.75055 8.46533i −0.0901457 0.277440i
\(932\) −6.09524 + 18.7592i −0.199656 + 0.614479i
\(933\) −1.29802 0.943070i −0.0424954 0.0308747i
\(934\) −18.3570 −0.600658
\(935\) 0.441945 1.02453i 0.0144531 0.0335056i
\(936\) 15.6287 0.510840
\(937\) 11.1469 + 8.09870i 0.364153 + 0.264573i 0.754782 0.655975i \(-0.227742\pi\)
−0.390629 + 0.920548i \(0.627742\pi\)
\(938\) 6.98494 21.4974i 0.228066 0.701916i
\(939\) −0.717389 2.20790i −0.0234111 0.0720520i
\(940\) 11.6689 8.47795i 0.380597 0.276520i
\(941\) 4.20286 3.05356i 0.137009 0.0995431i −0.517170 0.855883i \(-0.673014\pi\)
0.654179 + 0.756340i \(0.273014\pi\)
\(942\) 0.771443 + 2.37426i 0.0251350 + 0.0773575i
\(943\) −19.1321 + 58.8827i −0.623028 + 1.91748i
\(944\) 3.51377 + 2.55290i 0.114363 + 0.0830899i
\(945\) −6.26235 −0.203714
\(946\) −24.2251 21.3075i −0.787625 0.692766i
\(947\) 24.6482 0.800960 0.400480 0.916305i \(-0.368843\pi\)
0.400480 + 0.916305i \(0.368843\pi\)
\(948\) 0.0503588 + 0.0365878i 0.00163558 + 0.00118832i
\(949\) −5.55376 + 17.0927i −0.180283 + 0.554853i
\(950\) −0.0912072 0.280707i −0.00295915 0.00910734i
\(951\) −2.36787 + 1.72036i −0.0767836 + 0.0557865i
\(952\) 0.500357 0.363530i 0.0162166 0.0117821i
\(953\) −6.64577 20.4536i −0.215277 0.662556i −0.999134 0.0416137i \(-0.986750\pi\)
0.783856 0.620942i \(-0.213250\pi\)
\(954\) 5.39675 16.6095i 0.174726 0.537753i
\(955\) −28.5903 20.7721i −0.925161 0.672169i
\(956\) 26.3608 0.852569
\(957\) 2.15299 + 0.201003i 0.0695964 + 0.00649752i
\(958\) 19.5982 0.633188
\(959\) −4.34286 3.15528i −0.140238 0.101889i
\(960\) −0.0810806 + 0.249540i −0.00261686 + 0.00805388i
\(961\) −6.27659 19.3174i −0.202471 0.623141i
\(962\) 29.8536 21.6899i 0.962519 0.699311i
\(963\) 28.3770 20.6171i 0.914435 0.664376i
\(964\) 4.04173 + 12.4392i 0.130176 + 0.400639i
\(965\) 17.1942 52.9182i 0.553500 1.70350i
\(966\) −2.27111 1.65006i −0.0730717 0.0530897i
\(967\) −4.57648 −0.147170 −0.0735848 0.997289i \(-0.523444\pi\)
−0.0735848 + 0.997289i \(0.523444\pi\)
\(968\) −5.27696 + 9.65162i −0.169608 + 0.310215i
\(969\) 0.0187617 0.000602712
\(970\) −21.2823 15.4625i −0.683332 0.496470i
\(971\) −4.79336 + 14.7524i −0.153826 + 0.473428i −0.998040 0.0625783i \(-0.980068\pi\)
0.844214 + 0.536006i \(0.180068\pi\)
\(972\) 1.00272 + 3.08604i 0.0321621 + 0.0989848i
\(973\) 4.90438 3.56324i 0.157227 0.114232i
\(974\) 31.7444 23.0637i 1.01716 0.739007i
\(975\) −0.0577585 0.177762i −0.00184975 0.00569295i
\(976\) −0.845400 + 2.60187i −0.0270606 + 0.0832839i
\(977\) 26.4004 + 19.1810i 0.844624 + 0.613655i 0.923658 0.383217i \(-0.125184\pi\)
−0.0790345 + 0.996872i \(0.525184\pi\)
\(978\) 1.90105 0.0607888
\(979\) −23.7226 2.21474i −0.758178 0.0707835i
\(980\) −19.3068 −0.616733
\(981\) −16.3346 11.8678i −0.521523 0.378908i
\(982\) 5.75554 17.7137i 0.183667 0.565268i
\(983\) −9.77997 30.0996i −0.311932 0.960029i −0.976999 0.213245i \(-0.931597\pi\)
0.665066 0.746784i \(-0.268403\pi\)
\(984\) −1.04110 + 0.756406i −0.0331892 + 0.0241133i
\(985\) 19.6696 14.2908i 0.626724 0.455342i
\(986\) 0.258322 + 0.795033i 0.00822665 + 0.0253190i
\(987\) −0.991186 + 3.05056i −0.0315498 + 0.0971003i
\(988\) 4.23528 + 3.07711i 0.134742 + 0.0978960i
\(989\) −56.6118 −1.80015
\(990\) 16.1263 + 14.1841i 0.512528 + 0.450801i
\(991\) −22.2935 −0.708177 −0.354089 0.935212i \(-0.615209\pi\)
−0.354089 + 0.935212i \(0.615209\pi\)
\(992\) 2.64494 + 1.92166i 0.0839771 + 0.0610129i
\(993\) 0.522065 1.60675i 0.0165672 0.0509887i
\(994\) 4.53123 + 13.9457i 0.143722 + 0.442331i
\(995\) 27.0433 19.6481i 0.857329 0.622886i
\(996\) −1.35686 + 0.985814i −0.0429937 + 0.0312367i
\(997\) −6.56018 20.1902i −0.207763 0.639429i −0.999589 0.0286814i \(-0.990869\pi\)
0.791826 0.610747i \(-0.209131\pi\)
\(998\) 3.14563 9.68125i 0.0995732 0.306455i
\(999\) 4.12881 + 2.99975i 0.130630 + 0.0949080i
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 418.2.f.h.191.3 20
11.3 even 5 inner 418.2.f.h.267.3 yes 20
11.5 even 5 4598.2.a.cc.1.5 10
11.6 odd 10 4598.2.a.cd.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.h.191.3 20 1.1 even 1 trivial
418.2.f.h.267.3 yes 20 11.3 even 5 inner
4598.2.a.cc.1.5 10 11.5 even 5
4598.2.a.cd.1.5 10 11.6 odd 10