Properties

Label 418.2.f.g.191.1
Level $418$
Weight $2$
Character 418.191
Analytic conductor $3.338$
Analytic rank $0$
Dimension $16$
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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} - 2960 x^{7} + 5348 x^{6} - 6872 x^{5} + 8232 x^{4} - 6344 x^{3} + 3984 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 191.1
Root \(-0.744204 + 2.29042i\) of defining polynomial
Character \(\chi\) \(=\) 418.191
Dual form 418.2.f.g.267.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.744204 + 2.29042i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.77774 - 2.01814i) q^{5} +(-1.94835 + 1.41556i) q^{6} +(0.326530 + 1.00496i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.26515 - 1.64573i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.744204 + 2.29042i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.77774 - 2.01814i) q^{5} +(-1.94835 + 1.41556i) q^{6} +(0.326530 + 1.00496i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.26515 - 1.64573i) q^{9} +3.43347 q^{10} +(0.637485 + 3.25478i) q^{11} -2.40829 q^{12} +(0.266156 + 0.193374i) q^{13} +(-0.326530 + 1.00496i) q^{14} +(2.55520 + 7.86410i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.82037 - 2.04912i) q^{17} +(-0.865209 - 2.66284i) q^{18} +(0.309017 - 0.951057i) q^{19} +(2.77774 + 2.01814i) q^{20} -2.54478 q^{21} +(-1.39738 + 3.00788i) q^{22} -7.90827 q^{23} +(-1.94835 - 1.41556i) q^{24} +(2.09783 - 6.45646i) q^{25} +(0.101663 + 0.312886i) q^{26} +(-0.389910 + 0.283287i) q^{27} +(-0.854868 + 0.621098i) q^{28} +(-1.91607 - 5.89707i) q^{29} +(-2.55520 + 7.86410i) q^{30} +(-1.78552 - 1.29725i) q^{31} -1.00000 q^{32} +(-7.92925 - 0.962110i) q^{33} +3.48617 q^{34} +(2.93516 + 2.13252i) q^{35} +(0.865209 - 2.66284i) q^{36} +(1.98483 + 6.10867i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-0.640983 + 0.465701i) q^{39} +(1.06100 + 3.26543i) q^{40} +(-1.26074 + 3.88017i) q^{41} +(-2.05877 - 1.49579i) q^{42} +4.47258 q^{43} +(-2.89849 + 1.61207i) q^{44} -9.61330 q^{45} +(-6.39793 - 4.64837i) q^{46} +(3.18543 - 9.80375i) q^{47} +(-0.744204 - 2.29042i) q^{48} +(4.75980 - 3.45820i) q^{49} +(5.49220 - 3.99031i) q^{50} +(2.59442 + 7.98481i) q^{51} +(-0.101663 + 0.312886i) q^{52} +(-0.313656 - 0.227885i) q^{53} -0.481956 q^{54} +(8.33939 + 7.75439i) q^{55} -1.05667 q^{56} +(1.94835 + 1.41556i) q^{57} +(1.91607 - 5.89707i) q^{58} +(-0.235855 - 0.725888i) q^{59} +(-6.68961 + 4.86028i) q^{60} +(2.77448 - 2.01578i) q^{61} +(-0.682007 - 2.09900i) q^{62} +(0.914245 - 2.81376i) q^{63} +(-0.809017 - 0.587785i) q^{64} +1.12957 q^{65} +(-5.84938 - 5.43906i) q^{66} -11.9017 q^{67} +(2.82037 + 2.04912i) q^{68} +(5.88537 - 18.1133i) q^{69} +(1.12113 + 3.45049i) q^{70} +(10.1982 - 7.40946i) q^{71} +(2.26515 - 1.64573i) q^{72} +(-1.34810 - 4.14903i) q^{73} +(-1.98483 + 6.10867i) q^{74} +(13.2268 + 9.60985i) q^{75} +1.00000 q^{76} +(-3.06276 + 1.70343i) q^{77} -0.792298 q^{78} +(12.2517 + 8.90136i) q^{79} +(-1.06100 + 3.26543i) q^{80} +(-2.95430 - 9.09241i) q^{81} +(-3.30067 + 2.39808i) q^{82} +(7.76891 - 5.64444i) q^{83} +(-0.786381 - 2.42023i) q^{84} +(3.69883 - 11.3838i) q^{85} +(3.61839 + 2.62892i) q^{86} +14.9327 q^{87} +(-3.29248 - 0.399499i) q^{88} -6.50467 q^{89} +(-7.77732 - 5.65055i) q^{90} +(-0.107424 + 0.330618i) q^{91} +(-2.44379 - 7.52122i) q^{92} +(4.30005 - 3.12417i) q^{93} +(8.33956 - 6.05905i) q^{94} +(-1.06100 - 3.26543i) q^{95} +(0.744204 - 2.29042i) q^{96} +(3.88851 + 2.82517i) q^{97} +5.88344 q^{98} +(3.91248 - 8.42169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 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
\(3\) −0.744204 + 2.29042i −0.429666 + 1.32238i 0.468789 + 0.883310i \(0.344691\pi\)
−0.898455 + 0.439066i \(0.855309\pi\)
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 2.77774 2.01814i 1.24224 0.902541i 0.244496 0.969650i \(-0.421377\pi\)
0.997746 + 0.0671088i \(0.0213775\pi\)
\(6\) −1.94835 + 1.41556i −0.795411 + 0.577900i
\(7\) 0.326530 + 1.00496i 0.123417 + 0.379838i 0.993609 0.112874i \(-0.0360056\pi\)
−0.870192 + 0.492712i \(0.836006\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) −2.26515 1.64573i −0.755049 0.548575i
\(10\) 3.43347 1.08576
\(11\) 0.637485 + 3.25478i 0.192209 + 0.981354i
\(12\) −2.40829 −0.695214
\(13\) 0.266156 + 0.193374i 0.0738185 + 0.0536323i 0.624082 0.781358i \(-0.285473\pi\)
−0.550264 + 0.834991i \(0.685473\pi\)
\(14\) −0.326530 + 1.00496i −0.0872689 + 0.268586i
\(15\) 2.55520 + 7.86410i 0.659750 + 2.03050i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 2.82037 2.04912i 0.684041 0.496985i −0.190655 0.981657i \(-0.561061\pi\)
0.874696 + 0.484672i \(0.161061\pi\)
\(18\) −0.865209 2.66284i −0.203932 0.627638i
\(19\) 0.309017 0.951057i 0.0708934 0.218187i
\(20\) 2.77774 + 2.01814i 0.621121 + 0.451271i
\(21\) −2.54478 −0.555317
\(22\) −1.39738 + 3.00788i −0.297922 + 0.641282i
\(23\) −7.90827 −1.64899 −0.824495 0.565870i \(-0.808540\pi\)
−0.824495 + 0.565870i \(0.808540\pi\)
\(24\) −1.94835 1.41556i −0.397705 0.288950i
\(25\) 2.09783 6.45646i 0.419566 1.29129i
\(26\) 0.101663 + 0.312886i 0.0199377 + 0.0613619i
\(27\) −0.389910 + 0.283287i −0.0750383 + 0.0545185i
\(28\) −0.854868 + 0.621098i −0.161555 + 0.117376i
\(29\) −1.91607 5.89707i −0.355806 1.09506i −0.955541 0.294859i \(-0.904727\pi\)
0.599735 0.800199i \(-0.295273\pi\)
\(30\) −2.55520 + 7.86410i −0.466514 + 1.43578i
\(31\) −1.78552 1.29725i −0.320688 0.232994i 0.415781 0.909465i \(-0.363508\pi\)
−0.736469 + 0.676471i \(0.763508\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.92925 0.962110i −1.38031 0.167482i
\(34\) 3.48617 0.597874
\(35\) 2.93516 + 2.13252i 0.496133 + 0.360462i
\(36\) 0.865209 2.66284i 0.144202 0.443807i
\(37\) 1.98483 + 6.10867i 0.326303 + 1.00426i 0.970849 + 0.239693i \(0.0770467\pi\)
−0.644545 + 0.764566i \(0.722953\pi\)
\(38\) 0.809017 0.587785i 0.131240 0.0953514i
\(39\) −0.640983 + 0.465701i −0.102639 + 0.0745719i
\(40\) 1.06100 + 3.26543i 0.167759 + 0.516309i
\(41\) −1.26074 + 3.88017i −0.196895 + 0.605980i 0.803054 + 0.595906i \(0.203207\pi\)
−0.999949 + 0.0100745i \(0.996793\pi\)
\(42\) −2.05877 1.49579i −0.317675 0.230805i
\(43\) 4.47258 0.682062 0.341031 0.940052i \(-0.389224\pi\)
0.341031 + 0.940052i \(0.389224\pi\)
\(44\) −2.89849 + 1.61207i −0.436964 + 0.243028i
\(45\) −9.61330 −1.43307
\(46\) −6.39793 4.64837i −0.943323 0.685364i
\(47\) 3.18543 9.80375i 0.464643 1.43002i −0.394789 0.918772i \(-0.629182\pi\)
0.859431 0.511251i \(-0.170818\pi\)
\(48\) −0.744204 2.29042i −0.107417 0.330594i
\(49\) 4.75980 3.45820i 0.679972 0.494028i
\(50\) 5.49220 3.99031i 0.776714 0.564316i
\(51\) 2.59442 + 7.98481i 0.363292 + 1.11810i
\(52\) −0.101663 + 0.312886i −0.0140981 + 0.0433894i
\(53\) −0.313656 0.227885i −0.0430840 0.0313024i 0.566035 0.824381i \(-0.308477\pi\)
−0.609119 + 0.793079i \(0.708477\pi\)
\(54\) −0.481956 −0.0655859
\(55\) 8.33939 + 7.75439i 1.12448 + 1.04560i
\(56\) −1.05667 −0.141204
\(57\) 1.94835 + 1.41556i 0.258065 + 0.187495i
\(58\) 1.91607 5.89707i 0.251593 0.774323i
\(59\) −0.235855 0.725888i −0.0307057 0.0945025i 0.934529 0.355887i \(-0.115821\pi\)
−0.965235 + 0.261384i \(0.915821\pi\)
\(60\) −6.68961 + 4.86028i −0.863624 + 0.627460i
\(61\) 2.77448 2.01578i 0.355236 0.258094i −0.395826 0.918325i \(-0.629542\pi\)
0.751062 + 0.660231i \(0.229542\pi\)
\(62\) −0.682007 2.09900i −0.0866150 0.266573i
\(63\) 0.914245 2.81376i 0.115184 0.354500i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 1.12957 0.140106
\(66\) −5.84938 5.43906i −0.720009 0.669502i
\(67\) −11.9017 −1.45402 −0.727012 0.686625i \(-0.759091\pi\)
−0.727012 + 0.686625i \(0.759091\pi\)
\(68\) 2.82037 + 2.04912i 0.342020 + 0.248492i
\(69\) 5.88537 18.1133i 0.708515 2.18058i
\(70\) 1.12113 + 3.45049i 0.134001 + 0.412413i
\(71\) 10.1982 7.40946i 1.21031 0.879341i 0.215050 0.976603i \(-0.431009\pi\)
0.995259 + 0.0972622i \(0.0310085\pi\)
\(72\) 2.26515 1.64573i 0.266950 0.193951i
\(73\) −1.34810 4.14903i −0.157783 0.485607i 0.840649 0.541581i \(-0.182174\pi\)
−0.998432 + 0.0559731i \(0.982174\pi\)
\(74\) −1.98483 + 6.10867i −0.230731 + 0.710118i
\(75\) 13.2268 + 9.60985i 1.52730 + 1.10965i
\(76\) 1.00000 0.114708
\(77\) −3.06276 + 1.70343i −0.349034 + 0.194124i
\(78\) −0.792298 −0.0897101
\(79\) 12.2517 + 8.90136i 1.37842 + 1.00148i 0.997026 + 0.0770688i \(0.0245561\pi\)
0.381395 + 0.924412i \(0.375444\pi\)
\(80\) −1.06100 + 3.26543i −0.118624 + 0.365086i
\(81\) −2.95430 9.09241i −0.328256 1.01027i
\(82\) −3.30067 + 2.39808i −0.364498 + 0.264823i
\(83\) 7.76891 5.64444i 0.852748 0.619558i −0.0731543 0.997321i \(-0.523307\pi\)
0.925902 + 0.377763i \(0.123307\pi\)
\(84\) −0.786381 2.42023i −0.0858012 0.264069i
\(85\) 3.69883 11.3838i 0.401195 1.23475i
\(86\) 3.61839 + 2.62892i 0.390181 + 0.283483i
\(87\) 14.9327 1.60096
\(88\) −3.29248 0.399499i −0.350979 0.0425867i
\(89\) −6.50467 −0.689493 −0.344747 0.938696i \(-0.612035\pi\)
−0.344747 + 0.938696i \(0.612035\pi\)
\(90\) −7.77732 5.65055i −0.819802 0.595621i
\(91\) −0.107424 + 0.330618i −0.0112611 + 0.0346582i
\(92\) −2.44379 7.52122i −0.254783 0.784141i
\(93\) 4.30005 3.12417i 0.445894 0.323961i
\(94\) 8.33956 6.05905i 0.860160 0.624943i
\(95\) −1.06100 3.26543i −0.108856 0.335026i
\(96\) 0.744204 2.29042i 0.0759550 0.233765i
\(97\) 3.88851 + 2.82517i 0.394818 + 0.286852i 0.767427 0.641136i \(-0.221537\pi\)
−0.372609 + 0.927988i \(0.621537\pi\)
\(98\) 5.88344 0.594317
\(99\) 3.91248 8.42169i 0.393219 0.846412i
\(100\) 6.78873 0.678873
\(101\) 4.36800 + 3.17354i 0.434632 + 0.315779i 0.783499 0.621394i \(-0.213433\pi\)
−0.348866 + 0.937173i \(0.613433\pi\)
\(102\) −2.59442 + 7.98481i −0.256886 + 0.790614i
\(103\) −3.36832 10.3666i −0.331891 1.02145i −0.968233 0.250048i \(-0.919554\pi\)
0.636343 0.771406i \(-0.280446\pi\)
\(104\) −0.266156 + 0.193374i −0.0260988 + 0.0189619i
\(105\) −7.06873 + 5.13574i −0.689838 + 0.501197i
\(106\) −0.119806 0.368725i −0.0116366 0.0358137i
\(107\) 1.65702 5.09978i 0.160190 0.493014i −0.838460 0.544964i \(-0.816543\pi\)
0.998650 + 0.0519495i \(0.0165435\pi\)
\(108\) −0.389910 0.283287i −0.0375191 0.0272593i
\(109\) −2.66422 −0.255186 −0.127593 0.991827i \(-0.540725\pi\)
−0.127593 + 0.991827i \(0.540725\pi\)
\(110\) 2.18879 + 11.1752i 0.208693 + 1.06551i
\(111\) −15.4685 −1.46821
\(112\) −0.854868 0.621098i −0.0807774 0.0586882i
\(113\) −4.96552 + 15.2823i −0.467117 + 1.43764i 0.389183 + 0.921161i \(0.372757\pi\)
−0.856300 + 0.516479i \(0.827243\pi\)
\(114\) 0.744204 + 2.29042i 0.0697010 + 0.214518i
\(115\) −21.9671 + 15.9600i −2.04844 + 1.48828i
\(116\) 5.01635 3.64459i 0.465756 0.338392i
\(117\) −0.284643 0.876041i −0.0263152 0.0809900i
\(118\) 0.235855 0.725888i 0.0217122 0.0668234i
\(119\) 2.98022 + 2.16525i 0.273196 + 0.198488i
\(120\) −8.26881 −0.754835
\(121\) −10.1872 + 4.14975i −0.926111 + 0.377250i
\(122\) 3.42944 0.310487
\(123\) −7.94898 5.77527i −0.716735 0.520739i
\(124\) 0.682007 2.09900i 0.0612460 0.188496i
\(125\) −1.89784 5.84096i −0.169748 0.522431i
\(126\) 2.39352 1.73900i 0.213232 0.154922i
\(127\) −14.4279 + 10.4825i −1.28027 + 0.930170i −0.999561 0.0296235i \(-0.990569\pi\)
−0.280708 + 0.959793i \(0.590569\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) −3.32851 + 10.2441i −0.293059 + 0.901943i
\(130\) 0.913840 + 0.663944i 0.0801491 + 0.0582317i
\(131\) −1.04772 −0.0915400 −0.0457700 0.998952i \(-0.514574\pi\)
−0.0457700 + 0.998952i \(0.514574\pi\)
\(132\) −1.53525 7.83847i −0.133627 0.682251i
\(133\) 1.05667 0.0916253
\(134\) −9.62867 6.99564i −0.831791 0.604331i
\(135\) −0.511356 + 1.57379i −0.0440105 + 0.135450i
\(136\) 1.07729 + 3.31555i 0.0923766 + 0.284306i
\(137\) −7.79713 + 5.66494i −0.666153 + 0.483989i −0.868735 0.495277i \(-0.835067\pi\)
0.202582 + 0.979265i \(0.435067\pi\)
\(138\) 15.4081 11.1946i 1.31162 0.952950i
\(139\) −1.19610 3.68121i −0.101452 0.312236i 0.887430 0.460943i \(-0.152489\pi\)
−0.988881 + 0.148707i \(0.952489\pi\)
\(140\) −1.12113 + 3.45049i −0.0947530 + 0.291620i
\(141\) 20.0841 + 14.5920i 1.69139 + 1.22887i
\(142\) 12.6057 1.05785
\(143\) −0.459719 + 0.989554i −0.0384437 + 0.0827507i
\(144\) 2.79988 0.233323
\(145\) −17.2235 12.5136i −1.43033 1.03920i
\(146\) 1.34810 4.14903i 0.111570 0.343376i
\(147\) 4.37848 + 13.4756i 0.361131 + 1.11145i
\(148\) −5.19634 + 3.77536i −0.427137 + 0.310333i
\(149\) 11.1463 8.09826i 0.913140 0.663435i −0.0286669 0.999589i \(-0.509126\pi\)
0.941807 + 0.336154i \(0.109126\pi\)
\(150\) 5.05220 + 15.5491i 0.412510 + 1.26958i
\(151\) 5.60789 17.2593i 0.456363 1.40454i −0.413164 0.910657i \(-0.635576\pi\)
0.869527 0.493885i \(-0.164424\pi\)
\(152\) 0.809017 + 0.587785i 0.0656199 + 0.0476757i
\(153\) −9.76085 −0.789118
\(154\) −3.47908 0.422140i −0.280352 0.0340170i
\(155\) −7.57774 −0.608659
\(156\) −0.640983 0.465701i −0.0513197 0.0372859i
\(157\) −5.77683 + 17.7793i −0.461041 + 1.41894i 0.402852 + 0.915265i \(0.368019\pi\)
−0.863894 + 0.503674i \(0.831981\pi\)
\(158\) 4.67972 + 14.4027i 0.372299 + 1.14582i
\(159\) 0.755376 0.548813i 0.0599052 0.0435237i
\(160\) −2.77774 + 2.01814i −0.219599 + 0.159548i
\(161\) −2.58229 7.94748i −0.203513 0.626349i
\(162\) 2.95430 9.09241i 0.232112 0.714367i
\(163\) −18.2254 13.2415i −1.42752 1.03716i −0.990471 0.137718i \(-0.956023\pi\)
−0.437050 0.899437i \(-0.643977\pi\)
\(164\) −4.07985 −0.318583
\(165\) −23.9670 + 13.3299i −1.86583 + 1.03773i
\(166\) 9.60289 0.745329
\(167\) 10.2303 + 7.43277i 0.791647 + 0.575165i 0.908452 0.417990i \(-0.137265\pi\)
−0.116805 + 0.993155i \(0.537265\pi\)
\(168\) 0.786381 2.42023i 0.0606706 0.186725i
\(169\) −3.98378 12.2608i −0.306444 0.943138i
\(170\) 9.68367 7.03560i 0.742704 0.539606i
\(171\) −2.26515 + 1.64573i −0.173220 + 0.125852i
\(172\) 1.38210 + 4.25368i 0.105384 + 0.324340i
\(173\) 4.50828 13.8751i 0.342758 1.05490i −0.620015 0.784590i \(-0.712874\pi\)
0.962773 0.270311i \(-0.0871265\pi\)
\(174\) 12.0808 + 8.77724i 0.915846 + 0.665401i
\(175\) 7.17348 0.542264
\(176\) −2.42885 2.25847i −0.183081 0.170239i
\(177\) 1.83811 0.138161
\(178\) −5.26239 3.82335i −0.394433 0.286572i
\(179\) 1.74130 5.35917i 0.130151 0.400563i −0.864653 0.502369i \(-0.832462\pi\)
0.994804 + 0.101806i \(0.0324620\pi\)
\(180\) −2.97067 9.14279i −0.221421 0.681463i
\(181\) 0.324711 0.235917i 0.0241356 0.0175355i −0.575652 0.817695i \(-0.695252\pi\)
0.599788 + 0.800159i \(0.295252\pi\)
\(182\) −0.281241 + 0.204333i −0.0208469 + 0.0151462i
\(183\) 2.55221 + 7.85488i 0.188664 + 0.580649i
\(184\) 2.44379 7.52122i 0.180159 0.554471i
\(185\) 17.8415 + 12.9626i 1.31173 + 0.953030i
\(186\) 5.31515 0.389726
\(187\) 8.46739 + 7.87342i 0.619197 + 0.575761i
\(188\) 10.3083 0.751808
\(189\) −0.412008 0.299342i −0.0299692 0.0217739i
\(190\) 1.06100 3.26543i 0.0769731 0.236899i
\(191\) −3.45316 10.6277i −0.249862 0.768995i −0.994799 0.101860i \(-0.967521\pi\)
0.744937 0.667135i \(-0.232479\pi\)
\(192\) 1.94835 1.41556i 0.140610 0.102159i
\(193\) −19.3491 + 14.0579i −1.39278 + 1.01191i −0.397222 + 0.917723i \(0.630026\pi\)
−0.995554 + 0.0941884i \(0.969974\pi\)
\(194\) 1.48528 + 4.57122i 0.106637 + 0.328194i
\(195\) −0.840629 + 2.58719i −0.0601987 + 0.185273i
\(196\) 4.75980 + 3.45820i 0.339986 + 0.247014i
\(197\) 24.8502 1.77050 0.885251 0.465114i \(-0.153987\pi\)
0.885251 + 0.465114i \(0.153987\pi\)
\(198\) 8.11541 4.51359i 0.576737 0.320767i
\(199\) −24.4565 −1.73368 −0.866838 0.498589i \(-0.833852\pi\)
−0.866838 + 0.498589i \(0.833852\pi\)
\(200\) 5.49220 + 3.99031i 0.388357 + 0.282158i
\(201\) 8.85728 27.2599i 0.624745 1.92277i
\(202\) 1.66843 + 5.13489i 0.117390 + 0.361290i
\(203\) 5.30064 3.85114i 0.372032 0.270297i
\(204\) −6.79228 + 4.93488i −0.475555 + 0.345511i
\(205\) 4.32873 + 13.3224i 0.302331 + 0.930480i
\(206\) 3.36832 10.3666i 0.234682 0.722277i
\(207\) 17.9134 + 13.0149i 1.24507 + 0.904595i
\(208\) −0.328987 −0.0228112
\(209\) 3.29248 + 0.399499i 0.227745 + 0.0276339i
\(210\) −8.73744 −0.602940
\(211\) −2.82564 2.05295i −0.194525 0.141331i 0.486259 0.873814i \(-0.338361\pi\)
−0.680785 + 0.732484i \(0.738361\pi\)
\(212\) 0.119806 0.368725i 0.00822831 0.0253241i
\(213\) 9.38122 + 28.8724i 0.642791 + 1.97831i
\(214\) 4.33813 3.15184i 0.296548 0.215455i
\(215\) 12.4236 9.02631i 0.847286 0.615589i
\(216\) −0.148933 0.458367i −0.0101336 0.0311879i
\(217\) 0.720659 2.21796i 0.0489215 0.150565i
\(218\) −2.15540 1.56599i −0.145982 0.106062i
\(219\) 10.5063 0.709950
\(220\) −4.79785 + 10.3275i −0.323471 + 0.696278i
\(221\) 1.14691 0.0771493
\(222\) −12.5143 9.09218i −0.839906 0.610227i
\(223\) −5.48537 + 16.8822i −0.367328 + 1.13052i 0.581183 + 0.813773i \(0.302590\pi\)
−0.948511 + 0.316745i \(0.897410\pi\)
\(224\) −0.326530 1.00496i −0.0218172 0.0671465i
\(225\) −15.3775 + 11.1724i −1.02516 + 0.744826i
\(226\) −12.9999 + 9.44499i −0.864741 + 0.628271i
\(227\) 5.85007 + 18.0047i 0.388283 + 1.19501i 0.934071 + 0.357088i \(0.116231\pi\)
−0.545788 + 0.837924i \(0.683769\pi\)
\(228\) −0.744204 + 2.29042i −0.0492861 + 0.151687i
\(229\) −2.44841 1.77888i −0.161796 0.117552i 0.503941 0.863738i \(-0.331883\pi\)
−0.665737 + 0.746186i \(0.731883\pi\)
\(230\) −27.1528 −1.79041
\(231\) −1.62226 8.28271i −0.106737 0.544962i
\(232\) 6.20055 0.407086
\(233\) −13.4216 9.75133i −0.879276 0.638831i 0.0537841 0.998553i \(-0.482872\pi\)
−0.933060 + 0.359721i \(0.882872\pi\)
\(234\) 0.284643 0.876041i 0.0186077 0.0572686i
\(235\) −10.9371 33.6609i −0.713457 2.19579i
\(236\) 0.617477 0.448623i 0.0401943 0.0292029i
\(237\) −29.5056 + 21.4371i −1.91660 + 1.39249i
\(238\) 1.13834 + 3.50345i 0.0737877 + 0.227095i
\(239\) 4.94944 15.2328i 0.320153 0.985329i −0.653429 0.756988i \(-0.726670\pi\)
0.973581 0.228341i \(-0.0733300\pi\)
\(240\) −6.68961 4.86028i −0.431812 0.313730i
\(241\) −22.3425 −1.43921 −0.719604 0.694384i \(-0.755677\pi\)
−0.719604 + 0.694384i \(0.755677\pi\)
\(242\) −10.6808 2.63068i −0.686588 0.169107i
\(243\) 21.5782 1.38424
\(244\) 2.77448 + 2.01578i 0.177618 + 0.129047i
\(245\) 6.24234 19.2119i 0.398808 1.22741i
\(246\) −3.03624 9.34458i −0.193584 0.595789i
\(247\) 0.266156 0.193374i 0.0169351 0.0123041i
\(248\) 1.78552 1.29725i 0.113380 0.0823757i
\(249\) 7.14651 + 21.9947i 0.452892 + 1.39386i
\(250\) 1.89784 5.84096i 0.120030 0.369415i
\(251\) −3.19923 2.32438i −0.201934 0.146713i 0.482223 0.876049i \(-0.339830\pi\)
−0.684157 + 0.729335i \(0.739830\pi\)
\(252\) 2.95856 0.186372
\(253\) −5.04141 25.7397i −0.316951 1.61824i
\(254\) −17.8339 −1.11900
\(255\) 23.3211 + 16.9438i 1.46042 + 1.06106i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 7.81691 + 24.0580i 0.487605 + 1.50069i 0.828172 + 0.560474i \(0.189381\pi\)
−0.340567 + 0.940220i \(0.610619\pi\)
\(258\) −8.71415 + 6.33120i −0.542519 + 0.394163i
\(259\) −5.49084 + 3.98933i −0.341184 + 0.247885i
\(260\) 0.349056 + 1.07428i 0.0216475 + 0.0666242i
\(261\) −5.36477 + 16.5111i −0.332071 + 1.02201i
\(262\) −0.847626 0.615836i −0.0523665 0.0380465i
\(263\) −14.7586 −0.910056 −0.455028 0.890477i \(-0.650371\pi\)
−0.455028 + 0.890477i \(0.650371\pi\)
\(264\) 3.36529 7.24386i 0.207120 0.445828i
\(265\) −1.33116 −0.0817724
\(266\) 0.854868 + 0.621098i 0.0524153 + 0.0380819i
\(267\) 4.84080 14.8984i 0.296252 0.911770i
\(268\) −3.67783 11.3192i −0.224659 0.691429i
\(269\) −16.1888 + 11.7619i −0.987049 + 0.717133i −0.959273 0.282481i \(-0.908843\pi\)
−0.0277761 + 0.999614i \(0.508843\pi\)
\(270\) −1.33875 + 0.972656i −0.0814735 + 0.0591940i
\(271\) 7.25670 + 22.3338i 0.440813 + 1.35668i 0.887010 + 0.461749i \(0.152778\pi\)
−0.446197 + 0.894935i \(0.647222\pi\)
\(272\) −1.07729 + 3.31555i −0.0653201 + 0.201035i
\(273\) −0.677310 0.492094i −0.0409927 0.0297829i
\(274\) −9.63778 −0.582239
\(275\) 22.3517 + 2.71209i 1.34786 + 0.163545i
\(276\) 19.0454 1.14640
\(277\) 14.6899 + 10.6729i 0.882632 + 0.641270i 0.933947 0.357413i \(-0.116341\pi\)
−0.0513142 + 0.998683i \(0.516341\pi\)
\(278\) 1.19610 3.68121i 0.0717371 0.220784i
\(279\) 1.90954 + 5.87695i 0.114321 + 0.351844i
\(280\) −2.93516 + 2.13252i −0.175410 + 0.127443i
\(281\) −2.22572 + 1.61708i −0.132775 + 0.0964668i −0.652191 0.758055i \(-0.726150\pi\)
0.519415 + 0.854522i \(0.326150\pi\)
\(282\) 7.67145 + 23.6103i 0.456828 + 1.40597i
\(283\) −7.83172 + 24.1036i −0.465548 + 1.43281i 0.392745 + 0.919648i \(0.371526\pi\)
−0.858292 + 0.513161i \(0.828474\pi\)
\(284\) 10.1982 + 7.40946i 0.605154 + 0.439670i
\(285\) 8.26881 0.489802
\(286\) −0.953566 + 0.530350i −0.0563855 + 0.0313602i
\(287\) −4.31107 −0.254475
\(288\) 2.26515 + 1.64573i 0.133475 + 0.0969753i
\(289\) −1.49768 + 4.60939i −0.0880990 + 0.271141i
\(290\) −6.57879 20.2474i −0.386320 1.18897i
\(291\) −9.36467 + 6.80383i −0.548967 + 0.398848i
\(292\) 3.52938 2.56424i 0.206541 0.150061i
\(293\) 0.154794 + 0.476408i 0.00904319 + 0.0278321i 0.955476 0.295068i \(-0.0953423\pi\)
−0.946433 + 0.322900i \(0.895342\pi\)
\(294\) −4.37848 + 13.4756i −0.255358 + 0.785911i
\(295\) −2.12009 1.54034i −0.123436 0.0896818i
\(296\) −6.42303 −0.373331
\(297\) −1.17060 1.08848i −0.0679250 0.0631602i
\(298\) 13.7776 0.798114
\(299\) −2.10484 1.52925i −0.121726 0.0884390i
\(300\) −5.05220 + 15.5491i −0.291689 + 0.897725i
\(301\) 1.46043 + 4.49475i 0.0841779 + 0.259073i
\(302\) 14.6816 10.6668i 0.844833 0.613807i
\(303\) −10.5194 + 7.64281i −0.604325 + 0.439068i
\(304\) 0.309017 + 0.951057i 0.0177233 + 0.0545468i
\(305\) 3.63864 11.1986i 0.208348 0.641230i
\(306\) −7.89670 5.73729i −0.451424 0.327979i
\(307\) 10.6138 0.605762 0.302881 0.953028i \(-0.402052\pi\)
0.302881 + 0.953028i \(0.402052\pi\)
\(308\) −2.56650 2.38647i −0.146240 0.135982i
\(309\) 26.2507 1.49335
\(310\) −6.13052 4.45409i −0.348190 0.252975i
\(311\) −3.12776 + 9.62626i −0.177359 + 0.545855i −0.999733 0.0230917i \(-0.992649\pi\)
0.822374 + 0.568947i \(0.192649\pi\)
\(312\) −0.244834 0.753520i −0.0138610 0.0426597i
\(313\) 7.80229 5.66869i 0.441011 0.320414i −0.345025 0.938593i \(-0.612130\pi\)
0.786037 + 0.618180i \(0.212130\pi\)
\(314\) −15.1239 + 10.9882i −0.853493 + 0.620099i
\(315\) −3.13903 9.66095i −0.176864 0.544333i
\(316\) −4.67972 + 14.4027i −0.263255 + 0.810215i
\(317\) −22.5821 16.4069i −1.26834 0.921502i −0.269203 0.963083i \(-0.586760\pi\)
−0.999135 + 0.0415818i \(0.986760\pi\)
\(318\) 0.933696 0.0523591
\(319\) 17.9722 9.99570i 1.00625 0.559652i
\(320\) −3.43347 −0.191937
\(321\) 10.4475 + 7.59054i 0.583122 + 0.423663i
\(322\) 2.58229 7.94748i 0.143905 0.442896i
\(323\) −1.07729 3.31555i −0.0599418 0.184482i
\(324\) 7.73446 5.61942i 0.429692 0.312190i
\(325\) 1.80686 1.31276i 0.100227 0.0728190i
\(326\) −6.96147 21.4252i −0.385560 1.18663i
\(327\) 1.98272 6.10219i 0.109645 0.337452i
\(328\) −3.30067 2.39808i −0.182249 0.132412i
\(329\) 10.8925 0.600522
\(330\) −27.2249 3.30338i −1.49868 0.181845i
\(331\) 1.00668 0.0553319 0.0276659 0.999617i \(-0.491193\pi\)
0.0276659 + 0.999617i \(0.491193\pi\)
\(332\) 7.76891 + 5.64444i 0.426374 + 0.309779i
\(333\) 5.55727 17.1035i 0.304536 0.937267i
\(334\) 3.90764 + 12.0265i 0.213816 + 0.658059i
\(335\) −33.0598 + 24.0193i −1.80625 + 1.31232i
\(336\) 2.05877 1.49579i 0.112315 0.0816018i
\(337\) 2.79242 + 8.59418i 0.152113 + 0.468155i 0.997857 0.0654337i \(-0.0208431\pi\)
−0.845744 + 0.533589i \(0.820843\pi\)
\(338\) 3.98378 12.2608i 0.216689 0.666900i
\(339\) −31.3076 22.7463i −1.70040 1.23541i
\(340\) 11.9697 0.649147
\(341\) 3.08404 6.63845i 0.167010 0.359492i
\(342\) −2.79988 −0.151400
\(343\) 11.0136 + 8.00187i 0.594680 + 0.432061i
\(344\) −1.38210 + 4.25368i −0.0745180 + 0.229343i
\(345\) −20.2072 62.1915i −1.08792 3.34828i
\(346\) 11.8028 8.57525i 0.634524 0.461009i
\(347\) 23.1396 16.8119i 1.24220 0.902511i 0.244457 0.969660i \(-0.421390\pi\)
0.997743 + 0.0671488i \(0.0213902\pi\)
\(348\) 4.61447 + 14.2019i 0.247361 + 0.761300i
\(349\) 2.03829 6.27322i 0.109107 0.335798i −0.881565 0.472062i \(-0.843510\pi\)
0.990672 + 0.136265i \(0.0435097\pi\)
\(350\) 5.80346 + 4.21646i 0.310208 + 0.225379i
\(351\) −0.158557 −0.00846317
\(352\) −0.637485 3.25478i −0.0339781 0.173481i
\(353\) −10.2956 −0.547980 −0.273990 0.961732i \(-0.588344\pi\)
−0.273990 + 0.961732i \(0.588344\pi\)
\(354\) 1.48707 + 1.08042i 0.0790366 + 0.0574235i
\(355\) 13.3747 41.1630i 0.709855 2.18471i
\(356\) −2.01005 6.18631i −0.106533 0.327874i
\(357\) −7.17723 + 5.21457i −0.379859 + 0.275984i
\(358\) 4.55878 3.31215i 0.240939 0.175053i
\(359\) 6.23315 + 19.1837i 0.328973 + 1.01248i 0.969615 + 0.244636i \(0.0786684\pi\)
−0.640642 + 0.767840i \(0.721332\pi\)
\(360\) 2.97067 9.14279i 0.156568 0.481867i
\(361\) −0.809017 0.587785i −0.0425798 0.0309361i
\(362\) 0.401365 0.0210953
\(363\) −1.92332 26.4213i −0.100948 1.38676i
\(364\) −0.347632 −0.0182209
\(365\) −12.1180 8.80425i −0.634286 0.460836i
\(366\) −2.55221 + 7.85488i −0.133406 + 0.410581i
\(367\) 9.84135 + 30.2886i 0.513714 + 1.58105i 0.785609 + 0.618723i \(0.212350\pi\)
−0.271895 + 0.962327i \(0.587650\pi\)
\(368\) 6.39793 4.64837i 0.333515 0.242313i
\(369\) 9.24146 6.71432i 0.481091 0.349533i
\(370\) 6.81485 + 20.9739i 0.354287 + 1.09038i
\(371\) 0.126596 0.389622i 0.00657253 0.0202282i
\(372\) 4.30005 + 3.12417i 0.222947 + 0.161981i
\(373\) 24.0754 1.24658 0.623290 0.781991i \(-0.285796\pi\)
0.623290 + 0.781991i \(0.285796\pi\)
\(374\) 2.22238 + 11.3467i 0.114917 + 0.586726i
\(375\) 14.7906 0.763786
\(376\) 8.33956 + 6.05905i 0.430080 + 0.312472i
\(377\) 0.630364 1.94006i 0.0324654 0.0999182i
\(378\) −0.157373 0.484345i −0.00809440 0.0249120i
\(379\) 3.49284 2.53770i 0.179415 0.130353i −0.494453 0.869204i \(-0.664632\pi\)
0.673868 + 0.738852i \(0.264632\pi\)
\(380\) 2.77774 2.01814i 0.142495 0.103529i
\(381\) −13.2720 40.8471i −0.679946 2.09266i
\(382\) 3.45316 10.6277i 0.176679 0.543761i
\(383\) 6.92535 + 5.03156i 0.353869 + 0.257101i 0.750490 0.660882i \(-0.229817\pi\)
−0.396621 + 0.917982i \(0.629817\pi\)
\(384\) 2.40829 0.122898
\(385\) −5.06977 + 10.9128i −0.258379 + 0.556166i
\(386\) −23.9168 −1.21733
\(387\) −10.1311 7.36064i −0.514990 0.374162i
\(388\) −1.48528 + 4.57122i −0.0754036 + 0.232068i
\(389\) 3.28968 + 10.1246i 0.166793 + 0.513337i 0.999164 0.0408822i \(-0.0130168\pi\)
−0.832371 + 0.554219i \(0.813017\pi\)
\(390\) −2.20080 + 1.59897i −0.111442 + 0.0809671i
\(391\) −22.3043 + 16.2050i −1.12798 + 0.819523i
\(392\) 1.81808 + 5.59548i 0.0918270 + 0.282615i
\(393\) 0.779719 2.39973i 0.0393316 0.121050i
\(394\) 20.1042 + 14.6066i 1.01284 + 0.735868i
\(395\) 51.9961 2.61621
\(396\) 9.21853 + 1.11855i 0.463248 + 0.0562091i
\(397\) −19.1392 −0.960569 −0.480285 0.877113i \(-0.659467\pi\)
−0.480285 + 0.877113i \(0.659467\pi\)
\(398\) −19.7857 14.3752i −0.991769 0.720563i
\(399\) −0.786381 + 2.42023i −0.0393683 + 0.121163i
\(400\) 2.09783 + 6.45646i 0.104892 + 0.322823i
\(401\) 4.13138 3.00163i 0.206311 0.149894i −0.479832 0.877360i \(-0.659302\pi\)
0.686143 + 0.727466i \(0.259302\pi\)
\(402\) 23.1887 16.8476i 1.15655 0.840280i
\(403\) −0.224372 0.690545i −0.0111767 0.0343985i
\(404\) −1.66843 + 5.13489i −0.0830074 + 0.255471i
\(405\) −26.5561 19.2941i −1.31958 0.958732i
\(406\) 6.55196 0.325168
\(407\) −18.6171 + 10.3544i −0.922815 + 0.513247i
\(408\) −8.39573 −0.415650
\(409\) 15.6587 + 11.3767i 0.774271 + 0.562541i 0.903254 0.429106i \(-0.141171\pi\)
−0.128983 + 0.991647i \(0.541171\pi\)
\(410\) −4.32873 + 13.3224i −0.213781 + 0.657949i
\(411\) −7.17247 22.0746i −0.353792 1.08886i
\(412\) 8.81838 6.40693i 0.434450 0.315647i
\(413\) 0.652472 0.474049i 0.0321061 0.0233264i
\(414\) 6.84231 + 21.0585i 0.336281 + 1.03497i
\(415\) 10.1887 31.3575i 0.500143 1.53928i
\(416\) −0.266156 0.193374i −0.0130494 0.00948094i
\(417\) 9.32166 0.456483
\(418\) 2.42885 + 2.25847i 0.118799 + 0.110465i
\(419\) −9.86427 −0.481901 −0.240951 0.970537i \(-0.577459\pi\)
−0.240951 + 0.970537i \(0.577459\pi\)
\(420\) −7.06873 5.13574i −0.344919 0.250598i
\(421\) 7.53847 23.2010i 0.367403 1.13075i −0.581060 0.813860i \(-0.697362\pi\)
0.948463 0.316888i \(-0.102638\pi\)
\(422\) −1.07930 3.32174i −0.0525394 0.161700i
\(423\) −23.3497 + 16.9646i −1.13530 + 0.824846i
\(424\) 0.313656 0.227885i 0.0152325 0.0110671i
\(425\) −7.31341 22.5083i −0.354752 1.09182i
\(426\) −9.38122 + 28.8724i −0.454522 + 1.39887i
\(427\) 2.93172 + 2.13002i 0.141876 + 0.103079i
\(428\) 5.36222 0.259193
\(429\) −1.92437 1.78938i −0.0929096 0.0863921i
\(430\) 15.3565 0.740555
\(431\) −12.8013 9.30069i −0.616617 0.447998i 0.235121 0.971966i \(-0.424451\pi\)
−0.851738 + 0.523968i \(0.824451\pi\)
\(432\) 0.148933 0.458367i 0.00716552 0.0220532i
\(433\) 3.08362 + 9.49041i 0.148189 + 0.456080i 0.997407 0.0719624i \(-0.0229261\pi\)
−0.849218 + 0.528043i \(0.822926\pi\)
\(434\) 1.88671 1.37078i 0.0905650 0.0657993i
\(435\) 41.4792 30.1364i 1.98878 1.44493i
\(436\) −0.823290 2.53383i −0.0394284 0.121348i
\(437\) −2.44379 + 7.52122i −0.116902 + 0.359789i
\(438\) 8.49978 + 6.17545i 0.406135 + 0.295074i
\(439\) −26.9775 −1.28757 −0.643783 0.765208i \(-0.722636\pi\)
−0.643783 + 0.765208i \(0.722636\pi\)
\(440\) −9.95188 + 5.53499i −0.474437 + 0.263870i
\(441\) −16.4729 −0.784424
\(442\) 0.927867 + 0.674135i 0.0441341 + 0.0320653i
\(443\) −6.29218 + 19.3653i −0.298951 + 0.920075i 0.682915 + 0.730498i \(0.260712\pi\)
−0.981866 + 0.189578i \(0.939288\pi\)
\(444\) −4.78004 14.7115i −0.226851 0.698175i
\(445\) −18.0683 + 13.1274i −0.856518 + 0.622296i
\(446\) −14.3609 + 10.4338i −0.680008 + 0.494055i
\(447\) 10.2533 + 31.5565i 0.484966 + 1.49257i
\(448\) 0.326530 1.00496i 0.0154271 0.0474798i
\(449\) −7.46859 5.42625i −0.352465 0.256081i 0.397438 0.917629i \(-0.369900\pi\)
−0.749902 + 0.661549i \(0.769900\pi\)
\(450\) −19.0076 −0.896027
\(451\) −13.4328 1.62989i −0.632526 0.0767487i
\(452\) −16.0688 −0.755812
\(453\) 35.3577 + 25.6889i 1.66125 + 1.20697i
\(454\) −5.85007 + 18.0047i −0.274557 + 0.845001i
\(455\) 0.368838 + 1.13517i 0.0172914 + 0.0532175i
\(456\) −1.94835 + 1.41556i −0.0912399 + 0.0662896i
\(457\) −15.5083 + 11.2675i −0.725450 + 0.527070i −0.888121 0.459610i \(-0.847989\pi\)
0.162671 + 0.986680i \(0.447989\pi\)
\(458\) −0.935211 2.87828i −0.0436995 0.134493i
\(459\) −0.519204 + 1.59795i −0.0242344 + 0.0745858i
\(460\) −21.9671 15.9600i −1.02422 0.744141i
\(461\) 34.2672 1.59598 0.797991 0.602669i \(-0.205896\pi\)
0.797991 + 0.602669i \(0.205896\pi\)
\(462\) 3.55602 7.65440i 0.165441 0.356115i
\(463\) −1.71478 −0.0796927 −0.0398463 0.999206i \(-0.512687\pi\)
−0.0398463 + 0.999206i \(0.512687\pi\)
\(464\) 5.01635 + 3.64459i 0.232878 + 0.169196i
\(465\) 5.63938 17.3562i 0.261520 0.804876i
\(466\) −5.12658 15.7780i −0.237484 0.730901i
\(467\) 25.2744 18.3630i 1.16956 0.849736i 0.178605 0.983921i \(-0.442842\pi\)
0.990956 + 0.134185i \(0.0428415\pi\)
\(468\) 0.745205 0.541423i 0.0344471 0.0250273i
\(469\) −3.88626 11.9607i −0.179451 0.552293i
\(470\) 10.9371 33.6609i 0.504490 1.55266i
\(471\) −36.4229 26.4628i −1.67828 1.21934i
\(472\) 0.763244 0.0351311
\(473\) 2.85120 + 14.5573i 0.131098 + 0.669344i
\(474\) −36.4709 −1.67517
\(475\) −5.49220 3.99031i −0.251999 0.183088i
\(476\) −1.13834 + 3.50345i −0.0521758 + 0.160581i
\(477\) 0.335442 + 1.03238i 0.0153588 + 0.0472696i
\(478\) 12.9578 9.41440i 0.592676 0.430605i
\(479\) 33.8867 24.6201i 1.54832 1.12492i 0.603486 0.797373i \(-0.293778\pi\)
0.944835 0.327548i \(-0.106222\pi\)
\(480\) −2.55520 7.86410i −0.116628 0.358946i
\(481\) −0.652983 + 2.00967i −0.0297735 + 0.0916333i
\(482\) −18.0755 13.1326i −0.823316 0.598174i
\(483\) 20.1248 0.915712
\(484\) −7.09468 8.40628i −0.322485 0.382104i
\(485\) 16.5028 0.749356
\(486\) 17.4571 + 12.6833i 0.791871 + 0.575328i
\(487\) −5.75022 + 17.6973i −0.260567 + 0.801943i 0.732114 + 0.681182i \(0.238534\pi\)
−0.992682 + 0.120762i \(0.961466\pi\)
\(488\) 1.05976 + 3.26160i 0.0479729 + 0.147646i
\(489\) 43.8921 31.8894i 1.98487 1.44209i
\(490\) 16.3426 11.8736i 0.738286 0.536396i
\(491\) −1.42767 4.39391i −0.0644298 0.198294i 0.913659 0.406480i \(-0.133244\pi\)
−0.978089 + 0.208186i \(0.933244\pi\)
\(492\) 3.03624 9.34458i 0.136884 0.421286i
\(493\) −17.4878 12.7057i −0.787613 0.572234i
\(494\) 0.328987 0.0148018
\(495\) −6.12834 31.2892i −0.275448 1.40634i
\(496\) 2.20702 0.0990982
\(497\) 10.7762 + 7.82938i 0.483380 + 0.351196i
\(498\) −7.14651 + 21.9947i −0.320243 + 0.985606i
\(499\) 3.30931 + 10.1850i 0.148145 + 0.455943i 0.997402 0.0720364i \(-0.0229498\pi\)
−0.849257 + 0.527979i \(0.822950\pi\)
\(500\) 4.96862 3.60991i 0.222203 0.161440i
\(501\) −24.6376 + 17.9003i −1.10073 + 0.799726i
\(502\) −1.22200 3.76092i −0.0545404 0.167858i
\(503\) −6.74982 + 20.7738i −0.300959 + 0.926258i 0.680195 + 0.733031i \(0.261895\pi\)
−0.981154 + 0.193227i \(0.938105\pi\)
\(504\) 2.39352 + 1.73900i 0.106616 + 0.0774611i
\(505\) 18.5378 0.824922
\(506\) 11.0508 23.7871i 0.491270 1.05747i
\(507\) 31.0472 1.37885
\(508\) −14.4279 10.4825i −0.640134 0.465085i
\(509\) 11.6423 35.8314i 0.516037 1.58820i −0.265352 0.964152i \(-0.585488\pi\)
0.781388 0.624045i \(-0.214512\pi\)
\(510\) 8.90787 + 27.4156i 0.394447 + 1.21398i
\(511\) 3.72940 2.70957i 0.164979 0.119864i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 0.148933 + 0.458367i 0.00657553 + 0.0202374i
\(514\) −7.81691 + 24.0580i −0.344789 + 1.06115i
\(515\) −30.2777 21.9980i −1.33419 0.969348i
\(516\) −10.7713 −0.474179
\(517\) 33.9397 + 4.11814i 1.49267 + 0.181116i
\(518\) −6.78705 −0.298206
\(519\) 28.4247 + 20.6517i 1.24770 + 0.906510i
\(520\) −0.349056 + 1.07428i −0.0153071 + 0.0471105i
\(521\) 1.18872 + 3.65850i 0.0520786 + 0.160282i 0.973713 0.227777i \(-0.0731458\pi\)
−0.921635 + 0.388059i \(0.873146\pi\)
\(522\) −14.0452 + 10.2044i −0.614740 + 0.446634i
\(523\) −26.4220 + 19.1967i −1.15535 + 0.839414i −0.989184 0.146682i \(-0.953140\pi\)
−0.166171 + 0.986097i \(0.553140\pi\)
\(524\) −0.323764 0.996444i −0.0141437 0.0435299i
\(525\) −5.33853 + 16.4303i −0.232992 + 0.717077i
\(526\) −11.9400 8.67490i −0.520608 0.378244i
\(527\) −7.69406 −0.335158
\(528\) 6.98041 3.88233i 0.303783 0.168957i
\(529\) 39.5408 1.71917
\(530\) −1.07693 0.782435i −0.0467788 0.0339868i
\(531\) −0.660365 + 2.03240i −0.0286574 + 0.0881985i
\(532\) 0.326530 + 1.00496i 0.0141569 + 0.0435704i
\(533\) −1.08588 + 0.788937i −0.0470346 + 0.0341726i
\(534\) 12.6734 9.20774i 0.548430 0.398458i
\(535\) −5.68932 17.5099i −0.245971 0.757021i
\(536\) 3.67783 11.3192i 0.158858 0.488914i
\(537\) 10.9789 + 7.97663i 0.473774 + 0.344217i
\(538\) −20.0105 −0.862712
\(539\) 14.2900 + 13.2876i 0.615513 + 0.572336i
\(540\) −1.65478 −0.0712105
\(541\) −26.8602 19.5151i −1.15481 0.839020i −0.165699 0.986176i \(-0.552988\pi\)
−0.989113 + 0.147156i \(0.952988\pi\)
\(542\) −7.25670 + 22.3338i −0.311702 + 0.959321i
\(543\) 0.298698 + 0.919297i 0.0128183 + 0.0394508i
\(544\) −2.82037 + 2.04912i −0.120922 + 0.0878553i
\(545\) −7.40051 + 5.37678i −0.317003 + 0.230316i
\(546\) −0.258709 0.796225i −0.0110717 0.0340753i
\(547\) 11.5142 35.4372i 0.492313 1.51518i −0.328790 0.944403i \(-0.606641\pi\)
0.821103 0.570781i \(-0.193359\pi\)
\(548\) −7.79713 5.66494i −0.333077 0.241994i
\(549\) −9.60202 −0.409804
\(550\) 16.4888 + 15.3321i 0.703085 + 0.653765i
\(551\) −6.20055 −0.264152
\(552\) 15.4081 + 11.1946i 0.655812 + 0.476475i
\(553\) −4.94494 + 15.2190i −0.210280 + 0.647176i
\(554\) 5.61105 + 17.2690i 0.238391 + 0.733692i
\(555\) −42.9676 + 31.2178i −1.82387 + 1.32512i
\(556\) 3.13142 2.27511i 0.132802 0.0964862i
\(557\) 1.69335 + 5.21159i 0.0717495 + 0.220822i 0.980501 0.196516i \(-0.0629629\pi\)
−0.908751 + 0.417339i \(0.862963\pi\)
\(558\) −1.90954 + 5.87695i −0.0808371 + 0.248791i
\(559\) 1.19041 + 0.864880i 0.0503488 + 0.0365805i
\(560\) −3.62806 −0.153314
\(561\) −24.3349 + 13.5345i −1.02742 + 0.571426i
\(562\) −2.75114 −0.116050
\(563\) −32.5043 23.6158i −1.36989 0.995287i −0.997745 0.0671142i \(-0.978621\pi\)
−0.372150 0.928173i \(-0.621379\pi\)
\(564\) −7.67145 + 23.6103i −0.323026 + 0.994173i
\(565\) 17.0490 + 52.4714i 0.717256 + 2.20749i
\(566\) −20.5037 + 14.8968i −0.861836 + 0.626160i
\(567\) 8.17281 5.93789i 0.343226 0.249368i
\(568\) 3.89538 + 11.9888i 0.163447 + 0.503037i
\(569\) −10.3170 + 31.7524i −0.432511 + 1.33113i 0.463106 + 0.886303i \(0.346735\pi\)
−0.895616 + 0.444828i \(0.853265\pi\)
\(570\) 6.68961 + 4.86028i 0.280197 + 0.203575i
\(571\) −30.1103 −1.26008 −0.630038 0.776564i \(-0.716961\pi\)
−0.630038 + 0.776564i \(0.716961\pi\)
\(572\) −1.08318 0.131430i −0.0452902 0.00549536i
\(573\) 26.9118 1.12426
\(574\) −3.48773 2.53399i −0.145575 0.105767i
\(575\) −16.5902 + 51.0595i −0.691861 + 2.12933i
\(576\) 0.865209 + 2.66284i 0.0360504 + 0.110952i
\(577\) 9.24959 6.72022i 0.385066 0.279767i −0.378365 0.925657i \(-0.623514\pi\)
0.763430 + 0.645890i \(0.223514\pi\)
\(578\) −3.92098 + 2.84876i −0.163091 + 0.118493i
\(579\) −17.7989 54.7795i −0.739699 2.27656i
\(580\) 6.57879 20.2474i 0.273169 0.840728i
\(581\) 8.20920 + 5.96434i 0.340575 + 0.247442i
\(582\) −11.5754 −0.479814
\(583\) 0.541764 1.16616i 0.0224376 0.0482972i
\(584\) 4.36255 0.180524
\(585\) −2.55864 1.85896i −0.105787 0.0768586i
\(586\) −0.154794 + 0.476408i −0.00639450 + 0.0196802i
\(587\) −1.13763 3.50125i −0.0469548 0.144512i 0.924830 0.380380i \(-0.124207\pi\)
−0.971785 + 0.235868i \(0.924207\pi\)
\(588\) −11.4630 + 8.32836i −0.472726 + 0.343456i
\(589\) −1.78552 + 1.29725i −0.0735710 + 0.0534524i
\(590\) −0.809802 2.49231i −0.0333390 0.102607i
\(591\) −18.4936 + 56.9174i −0.760725 + 2.34127i
\(592\) −5.19634 3.77536i −0.213568 0.155167i
\(593\) −9.81520 −0.403062 −0.201531 0.979482i \(-0.564592\pi\)
−0.201531 + 0.979482i \(0.564592\pi\)
\(594\) −0.307240 1.56866i −0.0126062 0.0643630i
\(595\) 12.6480 0.518519
\(596\) 11.1463 + 8.09826i 0.456570 + 0.331718i
\(597\) 18.2006 56.0158i 0.744902 2.29257i
\(598\) −0.803976 2.47438i −0.0328770 0.101185i
\(599\) 3.11410 2.26252i 0.127239 0.0924443i −0.522346 0.852734i \(-0.674943\pi\)
0.649584 + 0.760290i \(0.274943\pi\)
\(600\) −13.2268 + 9.60985i −0.539983 + 0.392320i
\(601\) 6.14577 + 18.9148i 0.250691 + 0.771549i 0.994648 + 0.103321i \(0.0329469\pi\)
−0.743957 + 0.668228i \(0.767053\pi\)
\(602\) −1.46043 + 4.49475i −0.0595228 + 0.183192i
\(603\) 26.9591 + 19.5869i 1.09786 + 0.797641i
\(604\) 18.1475 0.738411
\(605\) −19.9226 + 32.0862i −0.809970 + 1.30449i
\(606\) −13.0027 −0.528200
\(607\) −6.07452 4.41340i −0.246557 0.179134i 0.457642 0.889136i \(-0.348694\pi\)
−0.704200 + 0.710002i \(0.748694\pi\)
\(608\) −0.309017 + 0.951057i −0.0125323 + 0.0385704i
\(609\) 4.87599 + 15.0068i 0.197585 + 0.608104i
\(610\) 9.52610 6.92111i 0.385700 0.280228i
\(611\) 2.74361 1.99335i 0.110995 0.0806423i
\(612\) −3.01627 9.28312i −0.121925 0.375248i
\(613\) 0.214923 0.661466i 0.00868067 0.0267164i −0.946622 0.322345i \(-0.895529\pi\)
0.955303 + 0.295628i \(0.0955290\pi\)
\(614\) 8.58675 + 6.23864i 0.346533 + 0.251771i
\(615\) −33.7355 −1.36035
\(616\) −0.673614 3.43925i −0.0271407 0.138571i
\(617\) −0.548806 −0.0220941 −0.0110471 0.999939i \(-0.503516\pi\)
−0.0110471 + 0.999939i \(0.503516\pi\)
\(618\) 21.2372 + 15.4298i 0.854287 + 0.620676i
\(619\) −12.7916 + 39.3685i −0.514138 + 1.58236i 0.270706 + 0.962662i \(0.412743\pi\)
−0.784844 + 0.619693i \(0.787257\pi\)
\(620\) −2.34165 7.20686i −0.0940430 0.289435i
\(621\) 3.08352 2.24031i 0.123737 0.0899004i
\(622\) −8.18859 + 5.94936i −0.328332 + 0.238547i
\(623\) −2.12397 6.53691i −0.0850951 0.261896i
\(624\) 0.244834 0.753520i 0.00980119 0.0301649i
\(625\) 10.4014 + 7.55704i 0.416055 + 0.302282i
\(626\) 9.64416 0.385458
\(627\) −3.36529 + 7.24386i −0.134397 + 0.289292i
\(628\) −18.6942 −0.745980
\(629\) 18.1153 + 13.1616i 0.722306 + 0.524786i
\(630\) 3.13903 9.66095i 0.125062 0.384902i
\(631\) −2.19126 6.74401i −0.0872328 0.268475i 0.897919 0.440161i \(-0.145079\pi\)
−0.985152 + 0.171686i \(0.945079\pi\)
\(632\) −12.2517 + 8.90136i −0.487345 + 0.354077i
\(633\) 6.80497 4.94410i 0.270473 0.196510i
\(634\) −8.62560 26.5469i −0.342566 1.05431i
\(635\) −18.9217 + 58.2352i −0.750887 + 2.31099i
\(636\) 0.755376 + 0.548813i 0.0299526 + 0.0217618i
\(637\) 1.93558 0.0766903
\(638\) 20.4151 + 2.47711i 0.808243 + 0.0980697i
\(639\) −35.2945 −1.39623
\(640\) −2.77774 2.01814i −0.109800 0.0797741i
\(641\) 6.94537 21.3756i 0.274326 0.844287i −0.715071 0.699051i \(-0.753606\pi\)
0.989397 0.145236i \(-0.0463941\pi\)
\(642\) 3.99058 + 12.2818i 0.157496 + 0.484722i
\(643\) −3.13820 + 2.28004i −0.123759 + 0.0899158i −0.647943 0.761689i \(-0.724370\pi\)
0.524184 + 0.851605i \(0.324370\pi\)
\(644\) 6.76053 4.91181i 0.266402 0.193552i
\(645\) 11.4283 + 35.1728i 0.449991 + 1.38493i
\(646\) 1.07729 3.31555i 0.0423853 0.130448i
\(647\) −8.28292 6.01790i −0.325635 0.236588i 0.412941 0.910758i \(-0.364502\pi\)
−0.738576 + 0.674170i \(0.764502\pi\)
\(648\) 9.56032 0.375565
\(649\) 2.21225 1.23040i 0.0868385 0.0482974i
\(650\) 2.23341 0.0876014
\(651\) 4.54375 + 3.30123i 0.178084 + 0.129385i
\(652\) 6.96147 21.4252i 0.272632 0.839076i
\(653\) −4.52089 13.9139i −0.176916 0.544491i 0.822800 0.568331i \(-0.192411\pi\)
−0.999716 + 0.0238399i \(0.992411\pi\)
\(654\) 5.19084 3.77136i 0.202978 0.147472i
\(655\) −2.91030 + 2.11446i −0.113715 + 0.0826187i
\(656\) −1.26074 3.88017i −0.0492237 0.151495i
\(657\) −3.77452 + 11.6168i −0.147258 + 0.453214i
\(658\) 8.81220 + 6.40244i 0.343535 + 0.249593i
\(659\) 23.4146 0.912102 0.456051 0.889954i \(-0.349263\pi\)
0.456051 + 0.889954i \(0.349263\pi\)
\(660\) −20.0837 18.6749i −0.781757 0.726918i
\(661\) 5.06352 0.196948 0.0984740 0.995140i \(-0.468604\pi\)
0.0984740 + 0.995140i \(0.468604\pi\)
\(662\) 0.814417 + 0.591709i 0.0316532 + 0.0229974i
\(663\) −0.853532 + 2.62690i −0.0331484 + 0.102020i
\(664\) 2.96746 + 9.13290i 0.115160 + 0.354425i
\(665\) 2.93516 2.13252i 0.113821 0.0826956i
\(666\) 14.5491 10.5706i 0.563767 0.409601i
\(667\) 15.1528 + 46.6356i 0.586720 + 1.80574i
\(668\) −3.90764 + 12.0265i −0.151191 + 0.465318i
\(669\) −34.5852 25.1276i −1.33714 0.971491i
\(670\) −40.8641 −1.57872
\(671\) 8.32961 + 7.74530i 0.321561 + 0.299004i
\(672\) 2.54478 0.0981671
\(673\) −10.9078 7.92501i −0.420466 0.305486i 0.357359 0.933967i \(-0.383677\pi\)
−0.777825 + 0.628481i \(0.783677\pi\)
\(674\) −2.79242 + 8.59418i −0.107560 + 0.331035i
\(675\) 1.01106 + 3.11173i 0.0389158 + 0.119771i
\(676\) 10.4297 7.57759i 0.401141 0.291446i
\(677\) 21.2023 15.4044i 0.814871 0.592039i −0.100368 0.994950i \(-0.532002\pi\)
0.915239 + 0.402912i \(0.132002\pi\)
\(678\) −11.9584 36.8043i −0.459261 1.41346i
\(679\) −1.56946 + 4.83029i −0.0602302 + 0.185369i
\(680\) 9.68367 + 7.03560i 0.371352 + 0.269803i
\(681\) −45.5920 −1.74709
\(682\) 6.39703 3.55787i 0.244955 0.136238i
\(683\) −24.1621 −0.924536 −0.462268 0.886740i \(-0.652964\pi\)
−0.462268 + 0.886740i \(0.652964\pi\)
\(684\) −2.26515 1.64573i −0.0866101 0.0629259i
\(685\) −10.2257 + 31.4714i −0.390704 + 1.20246i
\(686\) 4.20683 + 12.9473i 0.160618 + 0.494330i
\(687\) 5.89650 4.28406i 0.224966 0.163447i
\(688\) −3.61839 + 2.62892i −0.137950 + 0.100226i
\(689\) −0.0394147 0.121306i −0.00150158 0.00462138i
\(690\) 20.2072 62.1915i 0.769276 2.36759i
\(691\) 27.5510 + 20.0169i 1.04809 + 0.761480i 0.971848 0.235609i \(-0.0757085\pi\)
0.0762400 + 0.997089i \(0.475708\pi\)
\(692\) 14.5891 0.554594
\(693\) 9.74098 + 1.18194i 0.370029 + 0.0448982i
\(694\) 28.6021 1.08572
\(695\) −10.7516 7.81153i −0.407833 0.296308i
\(696\) −4.61447 + 14.2019i −0.174911 + 0.538321i
\(697\) 4.39517 + 13.5269i 0.166479 + 0.512369i
\(698\) 5.33632 3.87706i 0.201983 0.146749i
\(699\) 32.3231 23.4841i 1.22257 0.888249i
\(700\) 2.21673 + 6.82238i 0.0837844 + 0.257862i
\(701\) −6.51256 + 20.0436i −0.245976 + 0.757036i 0.749499 + 0.662006i \(0.230295\pi\)
−0.995474 + 0.0950300i \(0.969705\pi\)
\(702\) −0.128276 0.0931977i −0.00484145 0.00351752i
\(703\) 6.42303 0.242249
\(704\) 1.39738 3.00788i 0.0526656 0.113364i
\(705\) 85.2371 3.21021
\(706\) −8.32933 6.05161i −0.313478 0.227755i
\(707\) −1.76299 + 5.42591i −0.0663039 + 0.204062i
\(708\) 0.568009 + 1.74815i 0.0213471 + 0.0656995i
\(709\) 8.50727 6.18089i 0.319497 0.232128i −0.416464 0.909152i \(-0.636731\pi\)
0.735961 + 0.677024i \(0.236731\pi\)
\(710\) 35.0154 25.4402i 1.31410 0.954752i
\(711\) −13.1026 40.3258i −0.491387 1.51234i
\(712\) 2.01005 6.18631i 0.0753299 0.231842i
\(713\) 14.1204 + 10.2590i 0.528812 + 0.384204i
\(714\) −8.87155 −0.332009
\(715\) 0.720083 + 3.67650i 0.0269296 + 0.137493i
\(716\) 5.63497 0.210589
\(717\) 31.2062 + 22.6726i 1.16542 + 0.846725i
\(718\) −6.23315 + 19.1837i −0.232619 + 0.715928i
\(719\) 13.2455 + 40.7654i 0.493973 + 1.52029i 0.818552 + 0.574433i \(0.194777\pi\)
−0.324579 + 0.945859i \(0.605223\pi\)
\(720\) 7.77732 5.65055i 0.289844 0.210584i
\(721\) 9.31816 6.77004i 0.347026 0.252129i
\(722\) −0.309017 0.951057i −0.0115004 0.0353947i
\(723\) 16.6274 51.1738i 0.618379 1.90318i
\(724\) 0.324711 + 0.235917i 0.0120678 + 0.00876777i
\(725\) −42.0938 −1.56333
\(726\) 13.9741 22.5058i 0.518626 0.835268i
\(727\) −17.8183 −0.660843 −0.330422 0.943833i \(-0.607191\pi\)
−0.330422 + 0.943833i \(0.607191\pi\)
\(728\) −0.281241 0.204333i −0.0104235 0.00757309i
\(729\) −7.19566 + 22.1460i −0.266506 + 0.820221i
\(730\) −4.62867 14.2456i −0.171315 0.527253i
\(731\) 12.6143 9.16485i 0.466558 0.338974i
\(732\) −6.68176 + 4.85458i −0.246965 + 0.179431i
\(733\) 14.3337 + 44.1145i 0.529426 + 1.62941i 0.755393 + 0.655272i \(0.227446\pi\)
−0.225967 + 0.974135i \(0.572554\pi\)
\(734\) −9.84135 + 30.2886i −0.363251 + 1.11797i
\(735\) 39.3579 + 28.5952i 1.45174 + 1.05475i
\(736\) 7.90827 0.291503
\(737\) −7.58716 38.7374i −0.279476 1.42691i
\(738\) 11.4231 0.420489
\(739\) −36.3539 26.4127i −1.33730 0.971605i −0.999539 0.0303734i \(-0.990330\pi\)
−0.337761 0.941232i \(-0.609670\pi\)
\(740\) −6.81485 + 20.9739i −0.250519 + 0.771017i
\(741\) 0.244834 + 0.753520i 0.00899418 + 0.0276813i
\(742\) 0.331432 0.240800i 0.0121673 0.00884004i
\(743\) −38.8009 + 28.1905i −1.42347 + 1.03421i −0.432281 + 0.901739i \(0.642291\pi\)
−0.991187 + 0.132472i \(0.957709\pi\)
\(744\) 1.64247 + 5.05501i 0.0602160 + 0.185326i
\(745\) 14.6180 44.9897i 0.535563 1.64829i
\(746\) 19.4774 + 14.1512i 0.713120 + 0.518112i
\(747\) −26.8869 −0.983741
\(748\) −4.87150 + 10.4860i −0.178120 + 0.383406i
\(749\) 5.66612 0.207036
\(750\) 11.9659 + 8.69372i 0.436932 + 0.317450i
\(751\) 14.2888 43.9765i 0.521407 1.60473i −0.249906 0.968270i \(-0.580400\pi\)
0.771313 0.636456i \(-0.219600\pi\)
\(752\) 3.18543 + 9.80375i 0.116161 + 0.357506i
\(753\) 7.70468 5.59778i 0.280774 0.203994i
\(754\) 1.65031 1.19902i 0.0601009 0.0436659i
\(755\) −19.2545 59.2593i −0.700744 2.15667i
\(756\) 0.157373 0.484345i 0.00572361 0.0176155i
\(757\) −11.6191 8.44181i −0.422305 0.306823i 0.356259 0.934387i \(-0.384052\pi\)
−0.778565 + 0.627564i \(0.784052\pi\)
\(758\) 4.31739 0.156815
\(759\) 62.7067 + 7.60863i 2.27611 + 0.276176i
\(760\) 3.43347 0.124545
\(761\) −3.14574 2.28551i −0.114033 0.0828497i 0.529307 0.848430i \(-0.322452\pi\)
−0.643340 + 0.765580i \(0.722452\pi\)
\(762\) 13.2720 40.8471i 0.480795 1.47973i
\(763\) −0.869949 2.67743i −0.0314943 0.0969294i
\(764\) 9.04048 6.56829i 0.327073 0.237632i
\(765\) −27.1131 + 19.6988i −0.980275 + 0.712212i
\(766\) 2.64525 + 8.14124i 0.0955767 + 0.294155i
\(767\) 0.0775934 0.238808i 0.00280173 0.00862285i
\(768\) 1.94835 + 1.41556i 0.0703050 + 0.0510796i
\(769\) −38.5275 −1.38934 −0.694669 0.719329i \(-0.744449\pi\)
−0.694669 + 0.719329i \(0.744449\pi\)
\(770\) −10.5159 + 5.84868i −0.378967 + 0.210772i
\(771\) −60.9203 −2.19399
\(772\) −19.3491 14.0579i −0.696388 0.505956i
\(773\) 11.7057 36.0264i 0.421024 1.29578i −0.485726 0.874111i \(-0.661445\pi\)
0.906750 0.421668i \(-0.138555\pi\)
\(774\) −3.86972 11.9098i −0.139094 0.428088i
\(775\) −12.1214 + 8.80671i −0.435413 + 0.316346i
\(776\) −3.88851 + 2.82517i −0.139589 + 0.101418i
\(777\) −5.05095 15.5452i −0.181202 0.557682i
\(778\) −3.28968 + 10.1246i −0.117941 + 0.362984i
\(779\) 3.30067 + 2.39808i 0.118259 + 0.0859200i
\(780\) −2.72033 −0.0974035
\(781\) 30.6174 + 28.4696i 1.09558 + 1.01872i
\(782\) −27.5696 −0.985887
\(783\) 2.41766 + 1.75653i 0.0864000 + 0.0627733i
\(784\) −1.81808 + 5.59548i −0.0649315 + 0.199839i
\(785\) 19.8346 + 61.0446i 0.707927 + 2.17877i
\(786\) 2.04133 1.48311i 0.0728119 0.0529009i
\(787\) 38.1058 27.6854i 1.35832 0.986880i 0.359774 0.933040i \(-0.382854\pi\)
0.998550 0.0538401i \(-0.0171461\pi\)
\(788\) 7.67913 + 23.6339i 0.273558 + 0.841924i
\(789\) 10.9834 33.8035i 0.391020 1.20344i
\(790\) 42.0658 + 30.5626i 1.49663 + 1.08737i
\(791\) −16.9795 −0.603720
\(792\) 6.80048 + 6.32344i 0.241645 + 0.224694i
\(793\) 1.12824 0.0400651
\(794\) −15.4839 11.2497i −0.549504 0.399238i
\(795\) 0.990653 3.04892i 0.0351348 0.108134i
\(796\) −7.55748 23.2595i −0.267868 0.824412i
\(797\) 1.92672 1.39984i 0.0682479 0.0495850i −0.553138 0.833090i \(-0.686570\pi\)
0.621386 + 0.783505i \(0.286570\pi\)
\(798\) −2.05877 + 1.49579i −0.0728797 + 0.0529502i
\(799\) −11.1050 34.1775i −0.392865 1.20911i
\(800\) −2.09783 + 6.45646i −0.0741696 + 0.228270i
\(801\) 14.7340 + 10.7049i 0.520602 + 0.378239i
\(802\) 5.10667 0.180323
\(803\) 12.6448 7.03273i 0.446225 0.248180i
\(804\) 28.6628 1.01086
\(805\) −23.2121 16.8646i −0.818118 0.594398i
\(806\) 0.224372 0.690545i 0.00790315 0.0243234i
\(807\) −14.8919 45.8324i −0.524218 1.61338i
\(808\) −4.36800 + 3.17354i −0.153666 + 0.111645i
\(809\) 2.99939 2.17918i 0.105453 0.0766159i −0.533809 0.845605i \(-0.679240\pi\)
0.639262 + 0.768989i \(0.279240\pi\)
\(810\) −10.1435 31.2185i −0.356407 1.09691i
\(811\) 11.6487 35.8511i 0.409042 1.25890i −0.508430 0.861103i \(-0.669774\pi\)
0.917472 0.397800i \(-0.130226\pi\)
\(812\) 5.30064 + 3.85114i 0.186016 + 0.135149i
\(813\) −56.5544 −1.98345
\(814\) −21.1477 2.56599i −0.741226 0.0899380i
\(815\) −77.3486 −2.70940
\(816\) −6.79228 4.93488i −0.237778 0.172755i
\(817\) 1.38210 4.25368i 0.0483537 0.148817i
\(818\) 5.98107 + 18.4079i 0.209123 + 0.643616i
\(819\) 0.787439 0.572108i 0.0275153 0.0199911i
\(820\) −11.3328 + 8.23373i −0.395757 + 0.287534i
\(821\) 7.82745 + 24.0904i 0.273180 + 0.840761i 0.989695 + 0.143190i \(0.0457359\pi\)
−0.716515 + 0.697571i \(0.754264\pi\)
\(822\) 7.17247 22.0746i 0.250169 0.769940i
\(823\) −4.54680 3.30344i −0.158491 0.115151i 0.505713 0.862702i \(-0.331229\pi\)
−0.664204 + 0.747551i \(0.731229\pi\)
\(824\) 10.9001 0.379724
\(825\) −22.8461 + 49.1766i −0.795398 + 1.71211i
\(826\) 0.806500 0.0280617
\(827\) −3.03197 2.20285i −0.105432 0.0766008i 0.533820 0.845598i \(-0.320756\pi\)
−0.639252 + 0.768997i \(0.720756\pi\)
\(828\) −6.84231 + 21.0585i −0.237787 + 0.731833i
\(829\) 9.83014 + 30.2541i 0.341415 + 1.05077i 0.963475 + 0.267798i \(0.0862959\pi\)
−0.622060 + 0.782969i \(0.713704\pi\)
\(830\) 26.6743 19.3800i 0.925879 0.672690i
\(831\) −35.3777 + 25.7034i −1.22724 + 0.891640i
\(832\) −0.101663 0.312886i −0.00352452 0.0108474i
\(833\) 6.33815 19.5068i 0.219604 0.675871i
\(834\) 7.54138 + 5.47913i 0.261137 + 0.189727i
\(835\) 43.4176 1.50253
\(836\) 0.637485 + 3.25478i 0.0220479 + 0.112569i
\(837\) 1.06369 0.0367664
\(838\) −7.98036 5.79807i −0.275677 0.200291i
\(839\) −14.6207 + 44.9978i −0.504761 + 1.55350i 0.296410 + 0.955061i \(0.404211\pi\)
−0.801171 + 0.598435i \(0.795789\pi\)
\(840\) −2.70002 8.30980i −0.0931594 0.286715i
\(841\) −7.64259 + 5.55267i −0.263538 + 0.191471i
\(842\) 19.7360 14.3390i 0.680146 0.494155i
\(843\) −2.04741 6.30127i −0.0705165 0.217027i
\(844\) 1.07930 3.32174i 0.0371510 0.114339i
\(845\) −35.8099 26.0174i −1.23190 0.895027i
\(846\) −28.8619 −0.992292
\(847\) −7.49676 8.88270i −0.257592 0.305213i
\(848\) 0.387700 0.0133137
\(849\) −49.3790 35.8759i −1.69468 1.23126i
\(850\) 7.31341 22.5083i 0.250848 0.772030i
\(851\) −15.6966 48.3090i −0.538071 1.65601i
\(852\) −24.5604 + 17.8441i −0.841424 + 0.611330i
\(853\) 10.5580 7.67083i 0.361499 0.262644i −0.392178 0.919889i \(-0.628278\pi\)
0.753677 + 0.657245i \(0.228278\pi\)
\(854\) 1.11982 + 3.44645i 0.0383194 + 0.117935i
\(855\) −2.97067 + 9.14279i −0.101595 + 0.312677i
\(856\) 4.33813 + 3.15184i 0.148274 + 0.107728i
\(857\) 11.1935 0.382363 0.191181 0.981555i \(-0.438768\pi\)
0.191181 + 0.981555i \(0.438768\pi\)
\(858\) −0.505078 2.57876i −0.0172431 0.0880373i
\(859\) −17.1818 −0.586237 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(860\) 12.4236 + 9.02631i 0.423643 + 0.307795i
\(861\) 3.20832 9.87418i 0.109339 0.336511i
\(862\) −4.88966 15.0488i −0.166542 0.512565i
\(863\) 1.83060 1.33001i 0.0623143 0.0452740i −0.556192 0.831054i \(-0.687738\pi\)
0.618506 + 0.785780i \(0.287738\pi\)
\(864\) 0.389910 0.283287i 0.0132650 0.00963760i
\(865\) −15.4790 47.6396i −0.526303 1.61980i
\(866\) −3.08362 + 9.49041i −0.104786 + 0.322497i
\(867\) −9.44288 6.86065i −0.320697 0.233000i
\(868\) 2.33210 0.0791567
\(869\) −21.1617 + 45.5510i −0.717863 + 1.54521i
\(870\) 51.2711 1.73825
\(871\) −3.16771 2.30148i −0.107334 0.0779826i
\(872\) 0.823290 2.53383i 0.0278801 0.0858061i
\(873\) −4.15859 12.7988i −0.140747 0.433175i
\(874\) −6.39793 + 4.64837i −0.216413 + 0.157233i
\(875\) 5.25021 3.81450i 0.177489 0.128954i
\(876\) 3.24663 + 9.99209i 0.109693 + 0.337601i
\(877\) −2.21835 + 6.82736i −0.0749082 + 0.230544i −0.981499 0.191467i \(-0.938676\pi\)
0.906591 + 0.422011i \(0.138676\pi\)
\(878\) −21.8253 15.8570i −0.736567 0.535147i
\(879\) −1.20638 −0.0406900
\(880\) −11.3046 1.37167i −0.381079 0.0462389i
\(881\) 35.0751 1.18171 0.590854 0.806778i \(-0.298791\pi\)
0.590854 + 0.806778i \(0.298791\pi\)
\(882\) −13.3269 9.68253i −0.448739 0.326028i
\(883\) −9.02356 + 27.7717i −0.303667 + 0.934591i 0.676504 + 0.736439i \(0.263494\pi\)
−0.980171 + 0.198152i \(0.936506\pi\)
\(884\) 0.354414 + 1.09077i 0.0119202 + 0.0366867i
\(885\) 5.10580 3.70958i 0.171630 0.124696i
\(886\) −16.4731 + 11.9684i −0.553426 + 0.402088i
\(887\) 11.8163 + 36.3668i 0.396752 + 1.22108i 0.927588 + 0.373604i \(0.121878\pi\)
−0.530836 + 0.847474i \(0.678122\pi\)
\(888\) 4.78004 14.7115i 0.160408 0.493684i
\(889\) −15.2456 11.0766i −0.511321 0.371496i
\(890\) −22.3336 −0.748624
\(891\) 27.7105 15.4119i 0.928336 0.516318i
\(892\) −17.7510 −0.594349
\(893\) −8.33956 6.05905i −0.279073 0.202758i
\(894\) −10.2533 + 31.5565i −0.342922 + 1.05541i
\(895\) −5.97871 18.4006i −0.199846 0.615063i
\(896\) 0.854868 0.621098i 0.0285591 0.0207494i
\(897\) 5.06907 3.68289i 0.169251 0.122968i
\(898\) −2.85275 8.77986i −0.0951974 0.292988i
\(899\) −4.22882 + 13.0150i −0.141039 + 0.434073i
\(900\) −15.3775 11.1724i −0.512582 0.372413i
\(901\) −1.35159 −0.0450280
\(902\) −9.90934 9.21422i −0.329945 0.306800i
\(903\) −11.3817 −0.378761
\(904\) −12.9999 9.44499i −0.432371 0.314136i
\(905\) 0.425849 1.31063i 0.0141557 0.0435668i
\(906\) 13.5054 + 41.5654i 0.448688 + 1.38092i
\(907\) 18.4491 13.4041i 0.612592 0.445074i −0.237734 0.971330i \(-0.576405\pi\)
0.850326 + 0.526256i \(0.176405\pi\)
\(908\) −15.3157 + 11.1275i −0.508269 + 0.369279i
\(909\) −4.67139 14.3771i −0.154940 0.476857i
\(910\) −0.368838 + 1.13517i −0.0122269 + 0.0376305i
\(911\) 11.4175 + 8.29528i 0.378278 + 0.274835i 0.760635 0.649180i \(-0.224888\pi\)
−0.382357 + 0.924015i \(0.624888\pi\)
\(912\) −2.40829 −0.0797466
\(913\) 23.3240 + 21.6879i 0.771911 + 0.717763i
\(914\) −19.1694 −0.634066
\(915\) 22.9416 + 16.6681i 0.758427 + 0.551029i
\(916\) 0.935211 2.87828i 0.0309002 0.0951012i
\(917\) −0.342113 1.05292i −0.0112976 0.0347704i
\(918\) −1.35929 + 0.987586i −0.0448634 + 0.0325952i
\(919\) −23.2763 + 16.9112i −0.767813 + 0.557849i −0.901297 0.433202i \(-0.857384\pi\)
0.133484 + 0.991051i \(0.457384\pi\)
\(920\) −8.39069 25.8239i −0.276633 0.851388i
\(921\) −7.89883 + 24.3101i −0.260275 + 0.801045i
\(922\) 27.7227 + 20.1417i 0.913000 + 0.663333i
\(923\) 4.14712 0.136504
\(924\) 7.37602 4.10236i 0.242653 0.134958i
\(925\) 43.6042 1.43370
\(926\) −1.38729 1.00792i −0.0455891 0.0331224i
\(927\) −9.43089 + 29.0253i −0.309751 + 0.953315i
\(928\) 1.91607 + 5.89707i 0.0628982 + 0.193581i
\(929\) −20.8634 + 15.1581i −0.684506 + 0.497323i −0.874849 0.484395i \(-0.839040\pi\)
0.190344 + 0.981718i \(0.439040\pi\)
\(930\) 14.7641 10.7267i 0.484134 0.351744i
\(931\) −1.81808 5.59548i −0.0595853 0.183385i
\(932\) 5.12658 15.7780i 0.167927 0.516825i
\(933\) −19.7205 14.3278i −0.645621 0.469071i
\(934\) 31.2409 1.02223
\(935\) 39.4099 + 4.78187i 1.28884 + 0.156384i
\(936\) 0.921124 0.0301079
\(937\) −40.3494 29.3156i −1.31816 0.957698i −0.999953 0.00967549i \(-0.996920\pi\)
−0.318204 0.948022i \(-0.603080\pi\)
\(938\) 3.88626 11.9607i 0.126891 0.390530i
\(939\) 7.17722 + 22.0892i 0.234220 + 0.720854i
\(940\) 28.6337 20.8036i 0.933927 0.678538i
\(941\) 11.1746 8.11881i 0.364281 0.264665i −0.390555 0.920580i \(-0.627717\pi\)
0.754835 + 0.655914i \(0.227717\pi\)
\(942\) −13.9123 42.8177i −0.453287 1.39507i
\(943\) 9.97030 30.6854i 0.324678 0.999255i
\(944\) 0.617477 + 0.448623i 0.0200972 + 0.0146014i
\(945\) −1.74857 −0.0568808
\(946\) −6.24988 + 13.4530i −0.203201 + 0.437394i
\(947\) 40.7217 1.32328 0.661638 0.749823i \(-0.269862\pi\)
0.661638 + 0.749823i \(0.269862\pi\)
\(948\) −29.5056 21.4371i −0.958298 0.696244i
\(949\) 0.443509 1.36498i 0.0143969 0.0443091i
\(950\) −2.09783 6.45646i −0.0680627 0.209475i
\(951\) 54.3844 39.5126i 1.76353 1.28128i
\(952\) −2.98022 + 2.16525i −0.0965893 + 0.0701763i
\(953\) −4.12190 12.6859i −0.133522 0.410937i 0.861836 0.507188i \(-0.169315\pi\)
−0.995357 + 0.0962508i \(0.969315\pi\)
\(954\) −0.335442 + 1.03238i −0.0108603 + 0.0334247i
\(955\) −31.0402 22.5520i −1.00444 0.729767i
\(956\) 16.0167 0.518018
\(957\) 9.51940 + 48.6028i 0.307718 + 1.57111i
\(958\) 41.8862 1.35328
\(959\) −8.23902 5.98600i −0.266052 0.193298i
\(960\) 2.55520 7.86410i 0.0824688 0.253813i
\(961\) −8.07432 24.8502i −0.260462 0.801620i
\(962\) −1.70953 + 1.24205i −0.0551175 + 0.0400452i
\(963\) −12.1462 + 8.82475i −0.391407 + 0.284374i
\(964\) −6.90422 21.2490i −0.222370 0.684384i
\(965\) −25.3757 + 78.0984i −0.816873 + 2.51408i
\(966\) 16.2813 + 11.8291i 0.523843 + 0.380594i
\(967\) 20.4739 0.658395 0.329197 0.944261i \(-0.393222\pi\)
0.329197 + 0.944261i \(0.393222\pi\)
\(968\) −0.798624 10.9710i −0.0256687 0.352620i
\(969\) 8.39573 0.269710
\(970\) 13.3511 + 9.70013i 0.428677 + 0.311452i
\(971\) 10.0151 30.8233i 0.321399 0.989166i −0.651640 0.758528i \(-0.725919\pi\)
0.973040 0.230638i \(-0.0740812\pi\)
\(972\) 6.66803 + 20.5221i 0.213877 + 0.658246i
\(973\) 3.30889 2.40405i 0.106078 0.0770703i
\(974\) −15.0543 + 10.9376i −0.482370 + 0.350462i
\(975\) 1.66211 + 5.11544i 0.0532301 + 0.163825i
\(976\) −1.05976 + 3.26160i −0.0339220 + 0.104401i
\(977\) −25.1349 18.2616i −0.804136 0.584239i 0.107989 0.994152i \(-0.465559\pi\)
−0.912125 + 0.409913i \(0.865559\pi\)
\(978\) 54.2536 1.73484
\(979\) −4.14663 21.1713i −0.132527 0.676637i
\(980\) 20.2006 0.645285
\(981\) 6.03486 + 4.38458i 0.192678 + 0.139989i
\(982\) 1.42767 4.39391i 0.0455587 0.140215i
\(983\) −5.88037 18.0979i −0.187555 0.577234i 0.812428 0.583061i \(-0.198145\pi\)
−0.999983 + 0.00582712i \(0.998145\pi\)
\(984\) 7.94898 5.77527i 0.253404 0.184109i
\(985\) 69.0272 50.1512i 2.19939 1.59795i
\(986\) −6.67976 20.5582i −0.212727 0.654706i
\(987\) −8.10622 + 24.9484i −0.258024 + 0.794116i
\(988\) 0.266156 + 0.193374i 0.00846756 + 0.00615204i
\(989\) −35.3704 −1.12471
\(990\) 13.4334 28.9156i 0.426941 0.918999i
\(991\) 20.3068 0.645065 0.322533 0.946558i \(-0.395466\pi\)
0.322533 + 0.946558i \(0.395466\pi\)
\(992\) 1.78552 + 1.29725i 0.0566902 + 0.0411879i
\(993\) −0.749171 + 2.30571i −0.0237742 + 0.0731696i
\(994\) 4.11615 + 12.6682i 0.130556 + 0.401811i
\(995\) −67.9338 + 49.3568i −2.15365 + 1.56472i
\(996\) −18.7098 + 13.5935i −0.592843 + 0.430725i
\(997\) −5.16849 15.9070i −0.163688 0.503779i 0.835250 0.549871i \(-0.185323\pi\)
−0.998937 + 0.0460924i \(0.985323\pi\)
\(998\) −3.30931 + 10.1850i −0.104754 + 0.322400i
\(999\) −2.50441 1.81956i −0.0792360 0.0575683i
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.g.191.1 16
11.3 even 5 inner 418.2.f.g.267.1 yes 16
11.5 even 5 4598.2.a.bw.1.1 8
11.6 odd 10 4598.2.a.bz.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.g.191.1 16 1.1 even 1 trivial
418.2.f.g.267.1 yes 16 11.3 even 5 inner
4598.2.a.bw.1.1 8 11.5 even 5
4598.2.a.bz.1.1 8 11.6 odd 10