Properties

Label 187.2.g.a.137.1
Level $187$
Weight $2$
Character 187.137
Analytic conductor $1.493$
Analytic rank $1$
Dimension $4$
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] = [187,2,Mod(69,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.69");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.g (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: \(1.49320251780\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 137.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 187.137
Dual form 187.2.g.a.86.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 1.53884i) q^{2} +(-1.80902 - 1.31433i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-1.11803 + 3.44095i) q^{6} +(-3.11803 + 2.26538i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.618034 + 1.90211i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 1.53884i) q^{2} +(-1.80902 - 1.31433i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-1.11803 + 3.44095i) q^{6} +(-3.11803 + 2.26538i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.618034 + 1.90211i) q^{9} +3.61803 q^{10} +(1.23607 + 3.07768i) q^{11} +1.38197 q^{12} +(-1.57295 - 4.84104i) q^{13} +(5.04508 + 3.66547i) q^{14} +(4.04508 - 2.93893i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(2.61803 - 1.90211i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-0.427051 - 1.31433i) q^{20} +8.61803 q^{21} +(4.11803 - 3.44095i) q^{22} -6.23607 q^{23} +(1.54508 + 4.75528i) q^{24} +(-6.66312 + 4.84104i) q^{26} +(-0.690983 + 2.12663i) q^{27} +(0.736068 - 2.26538i) q^{28} +(-3.73607 + 2.71441i) q^{29} +(-6.54508 - 4.75528i) q^{30} +(-2.85410 - 8.78402i) q^{31} +3.38197 q^{32} +(1.80902 - 7.19218i) q^{33} +1.61803 q^{34} +(-2.66312 - 8.19624i) q^{35} +(-1.00000 - 0.726543i) q^{36} +(4.61803 - 3.35520i) q^{37} +(-0.500000 + 1.53884i) q^{38} +(-3.51722 + 10.8249i) q^{39} +(4.04508 - 2.93893i) q^{40} +(-4.23607 - 3.07768i) q^{41} +(-4.30902 - 13.2618i) q^{42} -9.00000 q^{43} +(-1.73607 - 1.08981i) q^{44} -4.47214 q^{45} +(3.11803 + 9.59632i) q^{46} +(1.80902 + 1.31433i) q^{47} +(8.78115 - 6.37988i) q^{48} +(2.42705 - 7.46969i) q^{49} +(1.80902 - 1.31433i) q^{51} +(2.54508 + 1.84911i) q^{52} +(3.11803 + 9.59632i) q^{53} +3.61803 q^{54} +(-7.39919 + 0.502029i) q^{55} +8.61803 q^{56} +(0.690983 + 2.12663i) q^{57} +(6.04508 + 4.39201i) q^{58} +(-3.50000 + 2.54290i) q^{59} +(-0.954915 + 2.93893i) q^{60} +(2.33688 - 7.19218i) q^{61} +(-12.0902 + 8.78402i) q^{62} +(-6.23607 - 4.53077i) q^{63} +(1.30902 + 4.02874i) q^{64} +11.3820 q^{65} +(-11.9721 + 0.812299i) q^{66} -7.14590 q^{67} +(-0.190983 - 0.587785i) q^{68} +(11.2812 + 8.19624i) q^{69} +(-11.2812 + 8.19624i) q^{70} +(0.354102 - 1.08981i) q^{71} +(1.38197 - 4.25325i) q^{72} +(10.7812 - 7.83297i) q^{73} +(-7.47214 - 5.42882i) q^{74} +0.618034 q^{76} +(-10.8262 - 6.79615i) q^{77} +18.4164 q^{78} +(0.309017 + 0.951057i) q^{79} +(-8.78115 - 6.37988i) q^{80} +(8.89919 - 6.46564i) q^{81} +(-2.61803 + 8.05748i) q^{82} +(-0.336881 + 1.03681i) q^{83} +(-4.30902 + 3.13068i) q^{84} +(-1.80902 - 1.31433i) q^{85} +(4.50000 + 13.8496i) q^{86} +10.3262 q^{87} +(1.80902 - 7.19218i) q^{88} +4.09017 q^{89} +(2.23607 + 6.88191i) q^{90} +(15.8713 + 11.5312i) q^{91} +(3.11803 - 2.26538i) q^{92} +(-6.38197 + 19.6417i) q^{93} +(1.11803 - 3.44095i) q^{94} +(1.80902 - 1.31433i) q^{95} +(-6.11803 - 4.44501i) q^{96} +(3.32624 + 10.2371i) q^{97} -12.7082 q^{98} +(-5.09017 + 4.25325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 5 q^{5} - 8 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 5 q^{5} - 8 q^{7} - 5 q^{8} - 2 q^{9} + 10 q^{10} - 4 q^{11} + 10 q^{12} - 13 q^{13} + 9 q^{14} + 5 q^{15} - 6 q^{16} + q^{17} + 6 q^{18} - q^{19} + 5 q^{20} + 30 q^{21} + 12 q^{22} - 16 q^{23} - 5 q^{24} - 11 q^{26} - 5 q^{27} - 6 q^{28} - 6 q^{29} - 15 q^{30} + 2 q^{31} + 18 q^{32} + 5 q^{33} + 2 q^{34} + 5 q^{35} - 4 q^{36} + 14 q^{37} - 2 q^{38} + 15 q^{39} + 5 q^{40} - 8 q^{41} - 15 q^{42} - 36 q^{43} + 2 q^{44} + 8 q^{46} + 5 q^{47} + 15 q^{48} + 3 q^{49} + 5 q^{51} - q^{52} + 8 q^{53} + 10 q^{54} - 5 q^{55} + 30 q^{56} + 5 q^{57} + 13 q^{58} - 14 q^{59} - 15 q^{60} + 25 q^{61} - 26 q^{62} - 16 q^{63} + 3 q^{64} + 50 q^{65} - 30 q^{66} - 42 q^{67} - 3 q^{68} + 25 q^{69} - 25 q^{70} - 12 q^{71} + 10 q^{72} + 23 q^{73} - 12 q^{74} - 2 q^{76} - 12 q^{77} + 20 q^{78} - q^{79} - 15 q^{80} + 11 q^{81} - 6 q^{82} - 17 q^{83} - 15 q^{84} - 5 q^{85} + 18 q^{86} + 10 q^{87} + 5 q^{88} - 6 q^{89} + 21 q^{91} + 8 q^{92} - 30 q^{93} + 5 q^{95} - 20 q^{96} - 18 q^{97} - 24 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 1.53884i −0.353553 1.08813i −0.956844 0.290604i \(-0.906144\pi\)
0.603290 0.797522i \(-0.293856\pi\)
\(3\) −1.80902 1.31433i −1.04444 0.758827i −0.0732898 0.997311i \(-0.523350\pi\)
−0.971147 + 0.238483i \(0.923350\pi\)
\(4\) −0.500000 + 0.363271i −0.250000 + 0.181636i
\(5\) −0.690983 + 2.12663i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(6\) −1.11803 + 3.44095i −0.456435 + 1.40476i
\(7\) −3.11803 + 2.26538i −1.17851 + 0.856235i −0.992002 0.126219i \(-0.959716\pi\)
−0.186504 + 0.982454i \(0.559716\pi\)
\(8\) −1.80902 1.31433i −0.639584 0.464685i
\(9\) 0.618034 + 1.90211i 0.206011 + 0.634038i
\(10\) 3.61803 1.14412
\(11\) 1.23607 + 3.07768i 0.372689 + 0.927957i
\(12\) 1.38197 0.398939
\(13\) −1.57295 4.84104i −0.436258 1.34266i −0.891792 0.452445i \(-0.850552\pi\)
0.455535 0.890218i \(-0.349448\pi\)
\(14\) 5.04508 + 3.66547i 1.34836 + 0.979638i
\(15\) 4.04508 2.93893i 1.04444 0.758827i
\(16\) −1.50000 + 4.61653i −0.375000 + 1.15413i
\(17\) −0.309017 + 0.951057i −0.0749476 + 0.230665i
\(18\) 2.61803 1.90211i 0.617077 0.448332i
\(19\) −0.809017 0.587785i −0.185601 0.134847i 0.491105 0.871100i \(-0.336593\pi\)
−0.676706 + 0.736253i \(0.736593\pi\)
\(20\) −0.427051 1.31433i −0.0954915 0.293893i
\(21\) 8.61803 1.88061
\(22\) 4.11803 3.44095i 0.877968 0.733614i
\(23\) −6.23607 −1.30031 −0.650155 0.759802i \(-0.725296\pi\)
−0.650155 + 0.759802i \(0.725296\pi\)
\(24\) 1.54508 + 4.75528i 0.315389 + 0.970668i
\(25\) 0 0
\(26\) −6.66312 + 4.84104i −1.30675 + 0.949406i
\(27\) −0.690983 + 2.12663i −0.132980 + 0.409270i
\(28\) 0.736068 2.26538i 0.139104 0.428117i
\(29\) −3.73607 + 2.71441i −0.693770 + 0.504054i −0.877897 0.478849i \(-0.841054\pi\)
0.184127 + 0.982902i \(0.441054\pi\)
\(30\) −6.54508 4.75528i −1.19496 0.868192i
\(31\) −2.85410 8.78402i −0.512612 1.57766i −0.787586 0.616205i \(-0.788669\pi\)
0.274974 0.961452i \(-0.411331\pi\)
\(32\) 3.38197 0.597853
\(33\) 1.80902 7.19218i 0.314909 1.25200i
\(34\) 1.61803 0.277491
\(35\) −2.66312 8.19624i −0.450149 1.38542i
\(36\) −1.00000 0.726543i −0.166667 0.121090i
\(37\) 4.61803 3.35520i 0.759200 0.551591i −0.139465 0.990227i \(-0.544538\pi\)
0.898665 + 0.438636i \(0.144538\pi\)
\(38\) −0.500000 + 1.53884i −0.0811107 + 0.249633i
\(39\) −3.51722 + 10.8249i −0.563206 + 1.73337i
\(40\) 4.04508 2.93893i 0.639584 0.464685i
\(41\) −4.23607 3.07768i −0.661563 0.480653i 0.205628 0.978630i \(-0.434076\pi\)
−0.867190 + 0.497977i \(0.834076\pi\)
\(42\) −4.30902 13.2618i −0.664896 2.04634i
\(43\) −9.00000 −1.37249 −0.686244 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) −1.73607 1.08981i −0.261722 0.164296i
\(45\) −4.47214 −0.666667
\(46\) 3.11803 + 9.59632i 0.459729 + 1.41490i
\(47\) 1.80902 + 1.31433i 0.263872 + 0.191714i 0.711852 0.702329i \(-0.247856\pi\)
−0.447980 + 0.894043i \(0.647856\pi\)
\(48\) 8.78115 6.37988i 1.26745 0.920857i
\(49\) 2.42705 7.46969i 0.346722 1.06710i
\(50\) 0 0
\(51\) 1.80902 1.31433i 0.253313 0.184043i
\(52\) 2.54508 + 1.84911i 0.352940 + 0.256426i
\(53\) 3.11803 + 9.59632i 0.428295 + 1.31816i 0.899804 + 0.436295i \(0.143710\pi\)
−0.471509 + 0.881861i \(0.656290\pi\)
\(54\) 3.61803 0.492352
\(55\) −7.39919 + 0.502029i −0.997706 + 0.0676935i
\(56\) 8.61803 1.15163
\(57\) 0.690983 + 2.12663i 0.0915229 + 0.281679i
\(58\) 6.04508 + 4.39201i 0.793759 + 0.576699i
\(59\) −3.50000 + 2.54290i −0.455661 + 0.331057i −0.791827 0.610746i \(-0.790870\pi\)
0.336166 + 0.941803i \(0.390870\pi\)
\(60\) −0.954915 + 2.93893i −0.123279 + 0.379414i
\(61\) 2.33688 7.19218i 0.299207 0.920864i −0.682569 0.730821i \(-0.739137\pi\)
0.981776 0.190043i \(-0.0608627\pi\)
\(62\) −12.0902 + 8.78402i −1.53545 + 1.11557i
\(63\) −6.23607 4.53077i −0.785671 0.570823i
\(64\) 1.30902 + 4.02874i 0.163627 + 0.503593i
\(65\) 11.3820 1.41176
\(66\) −11.9721 + 0.812299i −1.47367 + 0.0999871i
\(67\) −7.14590 −0.873010 −0.436505 0.899702i \(-0.643784\pi\)
−0.436505 + 0.899702i \(0.643784\pi\)
\(68\) −0.190983 0.587785i −0.0231601 0.0712794i
\(69\) 11.2812 + 8.19624i 1.35809 + 0.986711i
\(70\) −11.2812 + 8.19624i −1.34836 + 0.979638i
\(71\) 0.354102 1.08981i 0.0420242 0.129337i −0.927843 0.372970i \(-0.878339\pi\)
0.969867 + 0.243633i \(0.0783393\pi\)
\(72\) 1.38197 4.25325i 0.162866 0.501251i
\(73\) 10.7812 7.83297i 1.26184 0.916779i 0.262992 0.964798i \(-0.415291\pi\)
0.998846 + 0.0480187i \(0.0152907\pi\)
\(74\) −7.47214 5.42882i −0.868618 0.631088i
\(75\) 0 0
\(76\) 0.618034 0.0708934
\(77\) −10.8262 6.79615i −1.23376 0.774494i
\(78\) 18.4164 2.08525
\(79\) 0.309017 + 0.951057i 0.0347671 + 0.107002i 0.966934 0.255027i \(-0.0820842\pi\)
−0.932167 + 0.362029i \(0.882084\pi\)
\(80\) −8.78115 6.37988i −0.981763 0.713292i
\(81\) 8.89919 6.46564i 0.988799 0.718404i
\(82\) −2.61803 + 8.05748i −0.289113 + 0.889800i
\(83\) −0.336881 + 1.03681i −0.0369775 + 0.113805i −0.967841 0.251561i \(-0.919056\pi\)
0.930864 + 0.365366i \(0.119056\pi\)
\(84\) −4.30902 + 3.13068i −0.470152 + 0.341586i
\(85\) −1.80902 1.31433i −0.196215 0.142559i
\(86\) 4.50000 + 13.8496i 0.485247 + 1.49344i
\(87\) 10.3262 1.10709
\(88\) 1.80902 7.19218i 0.192842 0.766689i
\(89\) 4.09017 0.433557 0.216779 0.976221i \(-0.430445\pi\)
0.216779 + 0.976221i \(0.430445\pi\)
\(90\) 2.23607 + 6.88191i 0.235702 + 0.725417i
\(91\) 15.8713 + 11.5312i 1.66377 + 1.20880i
\(92\) 3.11803 2.26538i 0.325078 0.236183i
\(93\) −6.38197 + 19.6417i −0.661779 + 2.03675i
\(94\) 1.11803 3.44095i 0.115316 0.354907i
\(95\) 1.80902 1.31433i 0.185601 0.134847i
\(96\) −6.11803 4.44501i −0.624419 0.453667i
\(97\) 3.32624 + 10.2371i 0.337728 + 1.03942i 0.965362 + 0.260912i \(0.0840234\pi\)
−0.627634 + 0.778508i \(0.715977\pi\)
\(98\) −12.7082 −1.28372
\(99\) −5.09017 + 4.25325i −0.511581 + 0.427468i
\(100\) 0 0
\(101\) −3.51722 10.8249i −0.349977 1.07712i −0.958865 0.283861i \(-0.908384\pi\)
0.608889 0.793256i \(-0.291616\pi\)
\(102\) −2.92705 2.12663i −0.289821 0.210567i
\(103\) 12.1353 8.81678i 1.19572 0.868743i 0.201865 0.979413i \(-0.435300\pi\)
0.993857 + 0.110670i \(0.0352998\pi\)
\(104\) −3.51722 + 10.8249i −0.344892 + 1.06147i
\(105\) −5.95492 + 18.3273i −0.581140 + 1.78857i
\(106\) 13.2082 9.59632i 1.28289 0.932077i
\(107\) 2.42705 + 1.76336i 0.234632 + 0.170470i 0.698888 0.715231i \(-0.253678\pi\)
−0.464256 + 0.885701i \(0.653678\pi\)
\(108\) −0.427051 1.31433i −0.0410930 0.126471i
\(109\) −11.5623 −1.10747 −0.553734 0.832694i \(-0.686798\pi\)
−0.553734 + 0.832694i \(0.686798\pi\)
\(110\) 4.47214 + 11.1352i 0.426401 + 1.06170i
\(111\) −12.7639 −1.21150
\(112\) −5.78115 17.7926i −0.546268 1.68124i
\(113\) 0.0450850 + 0.0327561i 0.00424124 + 0.00308144i 0.589904 0.807473i \(-0.299166\pi\)
−0.585663 + 0.810555i \(0.699166\pi\)
\(114\) 2.92705 2.12663i 0.274143 0.199177i
\(115\) 4.30902 13.2618i 0.401818 1.23667i
\(116\) 0.881966 2.71441i 0.0818885 0.252027i
\(117\) 8.23607 5.98385i 0.761425 0.553207i
\(118\) 5.66312 + 4.11450i 0.521332 + 0.378770i
\(119\) −1.19098 3.66547i −0.109177 0.336013i
\(120\) −11.1803 −1.02062
\(121\) −7.94427 + 7.60845i −0.722207 + 0.691677i
\(122\) −12.2361 −1.10780
\(123\) 3.61803 + 11.1352i 0.326227 + 1.00402i
\(124\) 4.61803 + 3.35520i 0.414712 + 0.301306i
\(125\) −9.04508 + 6.57164i −0.809017 + 0.587785i
\(126\) −3.85410 + 11.8617i −0.343351 + 1.05672i
\(127\) 0.0729490 0.224514i 0.00647318 0.0199224i −0.947768 0.318961i \(-0.896666\pi\)
0.954241 + 0.299039i \(0.0966660\pi\)
\(128\) 11.0172 8.00448i 0.973794 0.707503i
\(129\) 16.2812 + 11.8290i 1.43348 + 1.04148i
\(130\) −5.69098 17.5150i −0.499132 1.53617i
\(131\) 3.70820 0.323987 0.161994 0.986792i \(-0.448208\pi\)
0.161994 + 0.986792i \(0.448208\pi\)
\(132\) 1.70820 + 4.25325i 0.148680 + 0.370198i
\(133\) 3.85410 0.334193
\(134\) 3.57295 + 10.9964i 0.308656 + 0.949945i
\(135\) −4.04508 2.93893i −0.348145 0.252942i
\(136\) 1.80902 1.31433i 0.155122 0.112703i
\(137\) −2.06231 + 6.34712i −0.176195 + 0.542271i −0.999686 0.0250574i \(-0.992023\pi\)
0.823491 + 0.567329i \(0.192023\pi\)
\(138\) 6.97214 21.4580i 0.593508 1.82663i
\(139\) −15.3262 + 11.1352i −1.29995 + 0.944472i −0.999955 0.00946715i \(-0.996986\pi\)
−0.299999 + 0.953939i \(0.596986\pi\)
\(140\) 4.30902 + 3.13068i 0.364178 + 0.264591i
\(141\) −1.54508 4.75528i −0.130120 0.400467i
\(142\) −1.85410 −0.155593
\(143\) 12.9549 10.8249i 1.08334 0.905223i
\(144\) −9.70820 −0.809017
\(145\) −3.19098 9.82084i −0.264997 0.815576i
\(146\) −17.4443 12.6740i −1.44370 1.04891i
\(147\) −14.2082 + 10.3229i −1.17187 + 0.851416i
\(148\) −1.09017 + 3.35520i −0.0896114 + 0.275796i
\(149\) 0.354102 1.08981i 0.0290092 0.0892810i −0.935504 0.353317i \(-0.885054\pi\)
0.964513 + 0.264036i \(0.0850537\pi\)
\(150\) 0 0
\(151\) 3.57295 + 2.59590i 0.290762 + 0.211251i 0.723598 0.690222i \(-0.242487\pi\)
−0.432836 + 0.901473i \(0.642487\pi\)
\(152\) 0.690983 + 2.12663i 0.0560461 + 0.172492i
\(153\) −2.00000 −0.161690
\(154\) −5.04508 + 20.0579i −0.406545 + 1.61632i
\(155\) 20.6525 1.65885
\(156\) −2.17376 6.69015i −0.174040 0.535641i
\(157\) −0.500000 0.363271i −0.0399043 0.0289922i 0.567654 0.823267i \(-0.307851\pi\)
−0.607559 + 0.794275i \(0.707851\pi\)
\(158\) 1.30902 0.951057i 0.104140 0.0756620i
\(159\) 6.97214 21.4580i 0.552926 1.70173i
\(160\) −2.33688 + 7.19218i −0.184747 + 0.568592i
\(161\) 19.4443 14.1271i 1.53242 1.11337i
\(162\) −14.3992 10.4616i −1.13131 0.821943i
\(163\) 0.982779 + 3.02468i 0.0769772 + 0.236911i 0.982139 0.188155i \(-0.0602507\pi\)
−0.905162 + 0.425066i \(0.860251\pi\)
\(164\) 3.23607 0.252694
\(165\) 14.0451 + 8.81678i 1.09341 + 0.686385i
\(166\) 1.76393 0.136908
\(167\) −6.07295 18.6906i −0.469939 1.44632i −0.852663 0.522461i \(-0.825014\pi\)
0.382724 0.923863i \(-0.374986\pi\)
\(168\) −15.5902 11.3269i −1.20281 0.873891i
\(169\) −10.4443 + 7.58821i −0.803406 + 0.583708i
\(170\) −1.11803 + 3.44095i −0.0857493 + 0.263909i
\(171\) 0.618034 1.90211i 0.0472622 0.145458i
\(172\) 4.50000 3.26944i 0.343122 0.249293i
\(173\) −10.2812 7.46969i −0.781662 0.567910i 0.123816 0.992305i \(-0.460487\pi\)
−0.905477 + 0.424395i \(0.860487\pi\)
\(174\) −5.16312 15.8904i −0.391415 1.20465i
\(175\) 0 0
\(176\) −16.0623 + 1.08981i −1.21074 + 0.0821478i
\(177\) 9.67376 0.727124
\(178\) −2.04508 6.29412i −0.153286 0.471765i
\(179\) 12.4443 + 9.04129i 0.930129 + 0.675778i 0.946024 0.324096i \(-0.105060\pi\)
−0.0158957 + 0.999874i \(0.505060\pi\)
\(180\) 2.23607 1.62460i 0.166667 0.121090i
\(181\) −5.35410 + 16.4782i −0.397967 + 1.22482i 0.528659 + 0.848834i \(0.322695\pi\)
−0.926627 + 0.375983i \(0.877305\pi\)
\(182\) 9.80902 30.1891i 0.727093 2.23776i
\(183\) −13.6803 + 9.93935i −1.01128 + 0.734738i
\(184\) 11.2812 + 8.19624i 0.831658 + 0.604235i
\(185\) 3.94427 + 12.1392i 0.289989 + 0.892493i
\(186\) 33.4164 2.45021
\(187\) −3.30902 + 0.224514i −0.241979 + 0.0164181i
\(188\) −1.38197 −0.100790
\(189\) −2.66312 8.19624i −0.193713 0.596189i
\(190\) −2.92705 2.12663i −0.212351 0.154282i
\(191\) −4.28115 + 3.11044i −0.309773 + 0.225064i −0.731799 0.681520i \(-0.761319\pi\)
0.422026 + 0.906584i \(0.361319\pi\)
\(192\) 2.92705 9.00854i 0.211242 0.650135i
\(193\) −2.47214 + 7.60845i −0.177948 + 0.547668i −0.999756 0.0220967i \(-0.992966\pi\)
0.821808 + 0.569765i \(0.192966\pi\)
\(194\) 14.0902 10.2371i 1.01162 0.734981i
\(195\) −20.5902 14.9596i −1.47449 1.07128i
\(196\) 1.50000 + 4.61653i 0.107143 + 0.329752i
\(197\) −22.6180 −1.61147 −0.805734 0.592277i \(-0.798229\pi\)
−0.805734 + 0.592277i \(0.798229\pi\)
\(198\) 9.09017 + 5.70634i 0.646010 + 0.405532i
\(199\) −12.2361 −0.867392 −0.433696 0.901059i \(-0.642791\pi\)
−0.433696 + 0.901059i \(0.642791\pi\)
\(200\) 0 0
\(201\) 12.9271 + 9.39205i 0.911804 + 0.662464i
\(202\) −14.8992 + 10.8249i −1.04830 + 0.761637i
\(203\) 5.50000 16.9273i 0.386024 1.18806i
\(204\) −0.427051 + 1.31433i −0.0298995 + 0.0920214i
\(205\) 9.47214 6.88191i 0.661563 0.480653i
\(206\) −19.6353 14.2658i −1.36805 0.993949i
\(207\) −3.85410 11.8617i −0.267879 0.824446i
\(208\) 24.7082 1.71321
\(209\) 0.809017 3.21644i 0.0559609 0.222486i
\(210\) 31.1803 2.15165
\(211\) 5.18034 + 15.9434i 0.356629 + 1.09759i 0.955059 + 0.296417i \(0.0957917\pi\)
−0.598429 + 0.801176i \(0.704208\pi\)
\(212\) −5.04508 3.66547i −0.346498 0.251745i
\(213\) −2.07295 + 1.50609i −0.142036 + 0.103195i
\(214\) 1.50000 4.61653i 0.102538 0.315579i
\(215\) 6.21885 19.1396i 0.424122 1.30531i
\(216\) 4.04508 2.93893i 0.275233 0.199969i
\(217\) 28.7984 + 20.9232i 1.95496 + 1.42036i
\(218\) 5.78115 + 17.7926i 0.391549 + 1.20506i
\(219\) −29.7984 −2.01359
\(220\) 3.51722 2.93893i 0.237131 0.198142i
\(221\) 5.09017 0.342402
\(222\) 6.38197 + 19.6417i 0.428330 + 1.31826i
\(223\) 0.545085 + 0.396027i 0.0365016 + 0.0265200i 0.605886 0.795551i \(-0.292819\pi\)
−0.569385 + 0.822071i \(0.692819\pi\)
\(224\) −10.5451 + 7.66145i −0.704573 + 0.511902i
\(225\) 0 0
\(226\) 0.0278640 0.0857567i 0.00185349 0.00570445i
\(227\) 4.23607 3.07768i 0.281158 0.204273i −0.438265 0.898846i \(-0.644407\pi\)
0.719422 + 0.694573i \(0.244407\pi\)
\(228\) −1.11803 0.812299i −0.0740436 0.0537958i
\(229\) −4.54508 13.9883i −0.300348 0.924375i −0.981372 0.192115i \(-0.938465\pi\)
0.681025 0.732260i \(-0.261535\pi\)
\(230\) −22.5623 −1.48771
\(231\) 10.6525 + 26.5236i 0.700881 + 1.74512i
\(232\) 10.3262 0.677951
\(233\) 5.30902 + 16.3395i 0.347805 + 1.07043i 0.960065 + 0.279778i \(0.0902608\pi\)
−0.612260 + 0.790657i \(0.709739\pi\)
\(234\) −13.3262 9.68208i −0.871163 0.632937i
\(235\) −4.04508 + 2.93893i −0.263872 + 0.191714i
\(236\) 0.826238 2.54290i 0.0537835 0.165529i
\(237\) 0.690983 2.12663i 0.0448842 0.138139i
\(238\) −5.04508 + 3.66547i −0.327024 + 0.237597i
\(239\) −3.85410 2.80017i −0.249301 0.181128i 0.456116 0.889920i \(-0.349240\pi\)
−0.705417 + 0.708793i \(0.749240\pi\)
\(240\) 7.50000 + 23.0826i 0.484123 + 1.48998i
\(241\) −6.29180 −0.405290 −0.202645 0.979252i \(-0.564954\pi\)
−0.202645 + 0.979252i \(0.564954\pi\)
\(242\) 15.6803 + 8.42075i 1.00797 + 0.541306i
\(243\) −17.8885 −1.14755
\(244\) 1.44427 + 4.44501i 0.0924600 + 0.284563i
\(245\) 14.2082 + 10.3229i 0.907729 + 0.659504i
\(246\) 15.3262 11.1352i 0.977165 0.709952i
\(247\) −1.57295 + 4.84104i −0.100084 + 0.308028i
\(248\) −6.38197 + 19.6417i −0.405255 + 1.24725i
\(249\) 1.97214 1.43284i 0.124979 0.0908026i
\(250\) 14.6353 + 10.6331i 0.925615 + 0.672499i
\(251\) −2.78115 8.55951i −0.175545 0.540271i 0.824113 0.566425i \(-0.191674\pi\)
−0.999658 + 0.0261539i \(0.991674\pi\)
\(252\) 4.76393 0.300100
\(253\) −7.70820 19.1926i −0.484611 1.20663i
\(254\) −0.381966 −0.0239667
\(255\) 1.54508 + 4.75528i 0.0967570 + 0.297787i
\(256\) −10.9721 7.97172i −0.685758 0.498233i
\(257\) −8.85410 + 6.43288i −0.552304 + 0.401272i −0.828634 0.559791i \(-0.810882\pi\)
0.276330 + 0.961063i \(0.410882\pi\)
\(258\) 10.0623 30.9686i 0.626452 1.92802i
\(259\) −6.79837 + 20.9232i −0.422430 + 1.30011i
\(260\) −5.69098 + 4.13474i −0.352940 + 0.256426i
\(261\) −7.47214 5.42882i −0.462514 0.336036i
\(262\) −1.85410 5.70634i −0.114547 0.352539i
\(263\) 15.6180 0.963049 0.481525 0.876433i \(-0.340083\pi\)
0.481525 + 0.876433i \(0.340083\pi\)
\(264\) −12.7254 + 10.6331i −0.783196 + 0.654424i
\(265\) −22.5623 −1.38599
\(266\) −1.92705 5.93085i −0.118155 0.363644i
\(267\) −7.39919 5.37582i −0.452823 0.328995i
\(268\) 3.57295 2.59590i 0.218253 0.158570i
\(269\) −5.97214 + 18.3803i −0.364128 + 1.12067i 0.586398 + 0.810023i \(0.300545\pi\)
−0.950526 + 0.310646i \(0.899455\pi\)
\(270\) −2.50000 + 7.69421i −0.152145 + 0.468255i
\(271\) −24.8435 + 18.0498i −1.50913 + 1.09645i −0.542573 + 0.840009i \(0.682550\pi\)
−0.966560 + 0.256440i \(0.917450\pi\)
\(272\) −3.92705 2.85317i −0.238112 0.172999i
\(273\) −13.5557 41.7202i −0.820430 2.52502i
\(274\) 10.7984 0.652354
\(275\) 0 0
\(276\) −8.61803 −0.518745
\(277\) 2.26393 + 6.96767i 0.136026 + 0.418646i 0.995748 0.0921161i \(-0.0293631\pi\)
−0.859722 + 0.510763i \(0.829363\pi\)
\(278\) 24.7984 + 18.0171i 1.48731 + 1.08059i
\(279\) 14.9443 10.8576i 0.894690 0.650030i
\(280\) −5.95492 + 18.3273i −0.355874 + 1.09527i
\(281\) 4.48936 13.8168i 0.267813 0.824242i −0.723220 0.690618i \(-0.757339\pi\)
0.991032 0.133624i \(-0.0426615\pi\)
\(282\) −6.54508 + 4.75528i −0.389754 + 0.283173i
\(283\) 15.2533 + 11.0822i 0.906714 + 0.658766i 0.940182 0.340674i \(-0.110655\pi\)
−0.0334677 + 0.999440i \(0.510655\pi\)
\(284\) 0.218847 + 0.673542i 0.0129862 + 0.0399674i
\(285\) −5.00000 −0.296174
\(286\) −23.1353 14.5231i −1.36802 0.858770i
\(287\) 20.1803 1.19121
\(288\) 2.09017 + 6.43288i 0.123164 + 0.379061i
\(289\) −0.809017 0.587785i −0.0475892 0.0345756i
\(290\) −13.5172 + 9.82084i −0.793759 + 0.576699i
\(291\) 7.43769 22.8909i 0.436005 1.34189i
\(292\) −2.54508 + 7.83297i −0.148940 + 0.458390i
\(293\) −25.6803 + 18.6579i −1.50026 + 1.09000i −0.529984 + 0.848007i \(0.677802\pi\)
−0.970277 + 0.241996i \(0.922198\pi\)
\(294\) 22.9894 + 16.7027i 1.34077 + 0.974124i
\(295\) −2.98936 9.20029i −0.174047 0.535662i
\(296\) −12.7639 −0.741888
\(297\) −7.39919 + 0.502029i −0.429344 + 0.0291307i
\(298\) −1.85410 −0.107405
\(299\) 9.80902 + 30.1891i 0.567270 + 1.74588i
\(300\) 0 0
\(301\) 28.0623 20.3885i 1.61748 1.17517i
\(302\) 2.20820 6.79615i 0.127068 0.391075i
\(303\) −7.86475 + 24.2052i −0.451818 + 1.39055i
\(304\) 3.92705 2.85317i 0.225232 0.163640i
\(305\) 13.6803 + 9.93935i 0.783334 + 0.569125i
\(306\) 1.00000 + 3.07768i 0.0571662 + 0.175939i
\(307\) 4.32624 0.246911 0.123456 0.992350i \(-0.460602\pi\)
0.123456 + 0.992350i \(0.460602\pi\)
\(308\) 7.88197 0.534785i 0.449117 0.0304722i
\(309\) −33.5410 −1.90808
\(310\) −10.3262 31.7809i −0.586491 1.80503i
\(311\) 6.85410 + 4.97980i 0.388660 + 0.282378i 0.764906 0.644141i \(-0.222785\pi\)
−0.376246 + 0.926520i \(0.622785\pi\)
\(312\) 20.5902 14.9596i 1.16569 0.846923i
\(313\) 8.01722 24.6745i 0.453160 1.39468i −0.420122 0.907468i \(-0.638013\pi\)
0.873282 0.487216i \(-0.161987\pi\)
\(314\) −0.309017 + 0.951057i −0.0174388 + 0.0536712i
\(315\) 13.9443 10.1311i 0.785671 0.570823i
\(316\) −0.500000 0.363271i −0.0281272 0.0204356i
\(317\) −5.05573 15.5599i −0.283958 0.873933i −0.986709 0.162497i \(-0.948045\pi\)
0.702751 0.711436i \(-0.251955\pi\)
\(318\) −36.5066 −2.04719
\(319\) −12.9721 8.14324i −0.726300 0.455934i
\(320\) −9.47214 −0.529508
\(321\) −2.07295 6.37988i −0.115701 0.356090i
\(322\) −31.4615 22.8581i −1.75328 1.27383i
\(323\) 0.809017 0.587785i 0.0450149 0.0327052i
\(324\) −2.10081 + 6.46564i −0.116712 + 0.359202i
\(325\) 0 0
\(326\) 4.16312 3.02468i 0.230574 0.167522i
\(327\) 20.9164 + 15.1967i 1.15668 + 0.840377i
\(328\) 3.61803 + 11.1352i 0.199773 + 0.614837i
\(329\) −8.61803 −0.475128
\(330\) 6.54508 26.0216i 0.360295 1.43244i
\(331\) −3.00000 −0.164895 −0.0824475 0.996595i \(-0.526274\pi\)
−0.0824475 + 0.996595i \(0.526274\pi\)
\(332\) −0.208204 0.640786i −0.0114267 0.0351677i
\(333\) 9.23607 + 6.71040i 0.506133 + 0.367727i
\(334\) −25.7254 + 18.6906i −1.40763 + 1.02270i
\(335\) 4.93769 15.1967i 0.269775 0.830282i
\(336\) −12.9271 + 39.7854i −0.705228 + 2.17047i
\(337\) −13.0623 + 9.49032i −0.711549 + 0.516971i −0.883673 0.468105i \(-0.844937\pi\)
0.172124 + 0.985075i \(0.444937\pi\)
\(338\) 16.8992 + 12.2780i 0.919195 + 0.667834i
\(339\) −0.0385072 0.118513i −0.00209142 0.00643674i
\(340\) 1.38197 0.0749476
\(341\) 23.5066 19.6417i 1.27295 1.06366i
\(342\) −3.23607 −0.174987
\(343\) 1.01722 + 3.13068i 0.0549248 + 0.169041i
\(344\) 16.2812 + 11.8290i 0.877821 + 0.637774i
\(345\) −25.2254 + 18.3273i −1.35809 + 0.986711i
\(346\) −6.35410 + 19.5559i −0.341599 + 1.05133i
\(347\) −3.21885 + 9.90659i −0.172797 + 0.531814i −0.999526 0.0307863i \(-0.990199\pi\)
0.826729 + 0.562600i \(0.190199\pi\)
\(348\) −5.16312 + 3.75123i −0.276772 + 0.201087i
\(349\) 7.61803 + 5.53483i 0.407784 + 0.296272i 0.772704 0.634766i \(-0.218904\pi\)
−0.364920 + 0.931039i \(0.618904\pi\)
\(350\) 0 0
\(351\) 11.3820 0.607524
\(352\) 4.18034 + 10.4086i 0.222813 + 0.554781i
\(353\) 4.41641 0.235062 0.117531 0.993069i \(-0.462502\pi\)
0.117531 + 0.993069i \(0.462502\pi\)
\(354\) −4.83688 14.8864i −0.257077 0.791203i
\(355\) 2.07295 + 1.50609i 0.110021 + 0.0799347i
\(356\) −2.04508 + 1.48584i −0.108389 + 0.0787494i
\(357\) −2.66312 + 8.19624i −0.140947 + 0.433791i
\(358\) 7.69098 23.6704i 0.406481 1.25102i
\(359\) 23.3435 16.9600i 1.23202 0.895115i 0.234981 0.972000i \(-0.424497\pi\)
0.997040 + 0.0768847i \(0.0244973\pi\)
\(360\) 8.09017 + 5.87785i 0.426389 + 0.309790i
\(361\) −5.56231 17.1190i −0.292753 0.901001i
\(362\) 28.0344 1.47346
\(363\) 24.3713 3.32244i 1.27916 0.174383i
\(364\) −12.1246 −0.635502
\(365\) 9.20820 + 28.3399i 0.481979 + 1.48338i
\(366\) 22.1353 + 16.0822i 1.15703 + 0.840630i
\(367\) 17.5623 12.7598i 0.916745 0.666054i −0.0259668 0.999663i \(-0.508266\pi\)
0.942712 + 0.333609i \(0.108266\pi\)
\(368\) 9.35410 28.7890i 0.487616 1.50073i
\(369\) 3.23607 9.95959i 0.168463 0.518476i
\(370\) 16.7082 12.1392i 0.868618 0.631088i
\(371\) −31.4615 22.8581i −1.63340 1.18673i
\(372\) −3.94427 12.1392i −0.204501 0.629389i
\(373\) 6.43769 0.333331 0.166666 0.986013i \(-0.446700\pi\)
0.166666 + 0.986013i \(0.446700\pi\)
\(374\) 2.00000 + 4.97980i 0.103418 + 0.257499i
\(375\) 25.0000 1.29099
\(376\) −1.54508 4.75528i −0.0796817 0.245235i
\(377\) 19.0172 + 13.8168i 0.979437 + 0.711602i
\(378\) −11.2812 + 8.19624i −0.580240 + 0.421569i
\(379\) 9.18034 28.2542i 0.471562 1.45132i −0.378976 0.925407i \(-0.623724\pi\)
0.850538 0.525913i \(-0.176276\pi\)
\(380\) −0.427051 + 1.31433i −0.0219073 + 0.0674236i
\(381\) −0.427051 + 0.310271i −0.0218785 + 0.0158956i
\(382\) 6.92705 + 5.03280i 0.354419 + 0.257500i
\(383\) 0.937694 + 2.88593i 0.0479139 + 0.147464i 0.972151 0.234355i \(-0.0752978\pi\)
−0.924237 + 0.381819i \(0.875298\pi\)
\(384\) −30.4508 −1.55394
\(385\) 21.9336 18.3273i 1.11784 0.934048i
\(386\) 12.9443 0.658846
\(387\) −5.56231 17.1190i −0.282748 0.870209i
\(388\) −5.38197 3.91023i −0.273228 0.198512i
\(389\) 9.66312 7.02067i 0.489940 0.355962i −0.315221 0.949018i \(-0.602079\pi\)
0.805161 + 0.593056i \(0.202079\pi\)
\(390\) −12.7254 + 39.1648i −0.644377 + 1.98319i
\(391\) 1.92705 5.93085i 0.0974552 0.299936i
\(392\) −14.2082 + 10.3229i −0.717623 + 0.521383i
\(393\) −6.70820 4.87380i −0.338384 0.245850i
\(394\) 11.3090 + 34.8056i 0.569740 + 1.75348i
\(395\) −2.23607 −0.112509
\(396\) 1.00000 3.97574i 0.0502519 0.199788i
\(397\) −20.4164 −1.02467 −0.512335 0.858786i \(-0.671219\pi\)
−0.512335 + 0.858786i \(0.671219\pi\)
\(398\) 6.11803 + 18.8294i 0.306669 + 0.943831i
\(399\) −6.97214 5.06555i −0.349043 0.253595i
\(400\) 0 0
\(401\) 7.41641 22.8254i 0.370358 1.13984i −0.576200 0.817309i \(-0.695465\pi\)
0.946558 0.322535i \(-0.104535\pi\)
\(402\) 7.98936 24.5887i 0.398473 1.22637i
\(403\) −38.0344 + 27.6336i −1.89463 + 1.37653i
\(404\) 5.69098 + 4.13474i 0.283137 + 0.205711i
\(405\) 7.60081 + 23.3929i 0.377687 + 1.16240i
\(406\) −28.7984 −1.42924
\(407\) 16.0344 + 10.0656i 0.794798 + 0.498933i
\(408\) −5.00000 −0.247537
\(409\) 0.173762 + 0.534785i 0.00859198 + 0.0264434i 0.955261 0.295765i \(-0.0955747\pi\)
−0.946669 + 0.322209i \(0.895575\pi\)
\(410\) −15.3262 11.1352i −0.756909 0.549927i
\(411\) 12.0729 8.77151i 0.595515 0.432667i
\(412\) −2.86475 + 8.81678i −0.141136 + 0.434372i
\(413\) 5.15248 15.8577i 0.253537 0.780306i
\(414\) −16.3262 + 11.8617i −0.802391 + 0.582971i
\(415\) −1.97214 1.43284i −0.0968083 0.0703354i
\(416\) −5.31966 16.3722i −0.260818 0.802715i
\(417\) 42.3607 2.07441
\(418\) −5.35410 + 0.363271i −0.261878 + 0.0177682i
\(419\) −33.5410 −1.63859 −0.819293 0.573375i \(-0.805634\pi\)
−0.819293 + 0.573375i \(0.805634\pi\)
\(420\) −3.68034 11.3269i −0.179582 0.552697i
\(421\) −18.7082 13.5923i −0.911782 0.662448i 0.0296829 0.999559i \(-0.490550\pi\)
−0.941465 + 0.337111i \(0.890550\pi\)
\(422\) 21.9443 15.9434i 1.06823 0.776115i
\(423\) −1.38197 + 4.25325i −0.0671935 + 0.206800i
\(424\) 6.97214 21.4580i 0.338597 1.04209i
\(425\) 0 0
\(426\) 3.35410 + 2.43690i 0.162507 + 0.118068i
\(427\) 9.00658 + 27.7194i 0.435859 + 1.34144i
\(428\) −1.85410 −0.0896214
\(429\) −37.6631 + 2.55541i −1.81839 + 0.123376i
\(430\) −32.5623 −1.57029
\(431\) −10.5279 32.4014i −0.507109 1.56072i −0.797195 0.603722i \(-0.793684\pi\)
0.290086 0.957001i \(-0.406316\pi\)
\(432\) −8.78115 6.37988i −0.422483 0.306952i
\(433\) 5.23607 3.80423i 0.251629 0.182819i −0.454819 0.890584i \(-0.650296\pi\)
0.706449 + 0.707764i \(0.250296\pi\)
\(434\) 17.7984 54.7778i 0.854349 2.62942i
\(435\) −7.13525 + 21.9601i −0.342109 + 1.05290i
\(436\) 5.78115 4.20025i 0.276867 0.201156i
\(437\) 5.04508 + 3.66547i 0.241339 + 0.175343i
\(438\) 14.8992 + 45.8550i 0.711911 + 2.19104i
\(439\) 35.1246 1.67641 0.838203 0.545358i \(-0.183606\pi\)
0.838203 + 0.545358i \(0.183606\pi\)
\(440\) 14.0451 + 8.81678i 0.669573 + 0.420323i
\(441\) 15.7082 0.748010
\(442\) −2.54508 7.83297i −0.121057 0.372576i
\(443\) −19.0172 13.8168i −0.903535 0.656457i 0.0358362 0.999358i \(-0.488591\pi\)
−0.939372 + 0.342901i \(0.888591\pi\)
\(444\) 6.38197 4.63677i 0.302875 0.220051i
\(445\) −2.82624 + 8.69827i −0.133977 + 0.412337i
\(446\) 0.336881 1.03681i 0.0159518 0.0490945i
\(447\) −2.07295 + 1.50609i −0.0980471 + 0.0712354i
\(448\) −13.2082 9.59632i −0.624029 0.453384i
\(449\) 0.854102 + 2.62866i 0.0403076 + 0.124054i 0.969185 0.246332i \(-0.0792254\pi\)
−0.928878 + 0.370386i \(0.879225\pi\)
\(450\) 0 0
\(451\) 4.23607 16.8415i 0.199469 0.793035i
\(452\) −0.0344419 −0.00162001
\(453\) −3.05166 9.39205i −0.143380 0.441277i
\(454\) −6.85410 4.97980i −0.321679 0.233713i
\(455\) −35.4894 + 25.7845i −1.66377 + 1.20880i
\(456\) 1.54508 4.75528i 0.0723552 0.222687i
\(457\) 0.0450850 0.138757i 0.00210899 0.00649079i −0.949996 0.312261i \(-0.898914\pi\)
0.952105 + 0.305770i \(0.0989138\pi\)
\(458\) −19.2533 + 13.9883i −0.899647 + 0.653632i
\(459\) −1.80902 1.31433i −0.0844377 0.0613476i
\(460\) 2.66312 + 8.19624i 0.124169 + 0.382152i
\(461\) 5.09017 0.237073 0.118536 0.992950i \(-0.462180\pi\)
0.118536 + 0.992950i \(0.462180\pi\)
\(462\) 35.4894 29.6543i 1.65111 1.37964i
\(463\) −24.7984 −1.15248 −0.576239 0.817281i \(-0.695480\pi\)
−0.576239 + 0.817281i \(0.695480\pi\)
\(464\) −6.92705 21.3193i −0.321580 0.989722i
\(465\) −37.3607 27.1441i −1.73256 1.25878i
\(466\) 22.4894 16.3395i 1.04180 0.756912i
\(467\) −11.1246 + 34.2380i −0.514786 + 1.58435i 0.268886 + 0.963172i \(0.413345\pi\)
−0.783672 + 0.621175i \(0.786655\pi\)
\(468\) −1.94427 + 5.98385i −0.0898740 + 0.276604i
\(469\) 22.2812 16.1882i 1.02885 0.747502i
\(470\) 6.54508 + 4.75528i 0.301902 + 0.219345i
\(471\) 0.427051 + 1.31433i 0.0196775 + 0.0605610i
\(472\) 9.67376 0.445271
\(473\) −11.1246 27.6992i −0.511510 1.27361i
\(474\) −3.61803 −0.166182
\(475\) 0 0
\(476\) 1.92705 + 1.40008i 0.0883262 + 0.0641728i
\(477\) −16.3262 + 11.8617i −0.747527 + 0.543110i
\(478\) −2.38197 + 7.33094i −0.108949 + 0.335309i
\(479\) 2.07295 6.37988i 0.0947155 0.291504i −0.892464 0.451119i \(-0.851025\pi\)
0.987179 + 0.159614i \(0.0510251\pi\)
\(480\) 13.6803 9.93935i 0.624419 0.453667i
\(481\) −23.5066 17.0785i −1.07181 0.778714i
\(482\) 3.14590 + 9.68208i 0.143292 + 0.441007i
\(483\) −53.7426 −2.44538
\(484\) 1.20820 6.69015i 0.0549184 0.304098i
\(485\) −24.0689 −1.09291
\(486\) 8.94427 + 27.5276i 0.405720 + 1.24868i
\(487\) −6.07295 4.41226i −0.275192 0.199938i 0.441626 0.897199i \(-0.354402\pi\)
−0.716817 + 0.697261i \(0.754402\pi\)
\(488\) −13.6803 + 9.93935i −0.619280 + 0.449933i
\(489\) 2.19756 6.76340i 0.0993771 0.305851i
\(490\) 8.78115 27.0256i 0.396692 1.22089i
\(491\) −8.23607 + 5.98385i −0.371689 + 0.270048i −0.757911 0.652358i \(-0.773780\pi\)
0.386222 + 0.922406i \(0.373780\pi\)
\(492\) −5.85410 4.25325i −0.263923 0.191752i
\(493\) −1.42705 4.39201i −0.0642711 0.197806i
\(494\) 8.23607 0.370558
\(495\) −5.52786 13.7638i −0.248459 0.618638i
\(496\) 44.8328 2.01305
\(497\) 1.36475 + 4.20025i 0.0612172 + 0.188407i
\(498\) −3.19098 2.31838i −0.142991 0.103889i
\(499\) 22.7705 16.5437i 1.01935 0.740600i 0.0531989 0.998584i \(-0.483058\pi\)
0.966149 + 0.257984i \(0.0830583\pi\)
\(500\) 2.13525 6.57164i 0.0954915 0.293893i
\(501\) −13.5795 + 41.7935i −0.606689 + 1.86720i
\(502\) −11.7812 + 8.55951i −0.525819 + 0.382030i
\(503\) −16.2082 11.7759i −0.722688 0.525064i 0.164554 0.986368i \(-0.447382\pi\)
−0.887242 + 0.461304i \(0.847382\pi\)
\(504\) 5.32624 + 16.3925i 0.237249 + 0.730179i
\(505\) 25.4508 1.13255
\(506\) −25.6803 + 21.4580i −1.14163 + 0.953926i
\(507\) 28.8673 1.28204
\(508\) 0.0450850 + 0.138757i 0.00200032 + 0.00615636i
\(509\) −24.2705 17.6336i −1.07577 0.781594i −0.0988307 0.995104i \(-0.531510\pi\)
−0.976941 + 0.213511i \(0.931510\pi\)
\(510\) 6.54508 4.75528i 0.289821 0.210567i
\(511\) −15.8713 + 48.8469i −0.702106 + 2.16086i
\(512\) 1.63525 5.03280i 0.0722687 0.222420i
\(513\) 1.80902 1.31433i 0.0798701 0.0580290i
\(514\) 14.3262 + 10.4086i 0.631903 + 0.459105i
\(515\) 10.3647 + 31.8994i 0.456725 + 1.40566i
\(516\) −12.4377 −0.547539
\(517\) −1.80902 + 7.19218i −0.0795605 + 0.316312i
\(518\) 35.5967 1.56403
\(519\) 8.78115 + 27.0256i 0.385450 + 1.18629i
\(520\) −20.5902 14.9596i −0.902939 0.656023i
\(521\) −10.6353 + 7.72696i −0.465939 + 0.338524i −0.795857 0.605485i \(-0.792979\pi\)
0.329918 + 0.944010i \(0.392979\pi\)
\(522\) −4.61803 + 14.2128i −0.202126 + 0.622079i
\(523\) 0.746711 2.29814i 0.0326514 0.100491i −0.933403 0.358831i \(-0.883176\pi\)
0.966054 + 0.258340i \(0.0831755\pi\)
\(524\) −1.85410 + 1.34708i −0.0809968 + 0.0588476i
\(525\) 0 0
\(526\) −7.80902 24.0337i −0.340489 1.04792i
\(527\) 9.23607 0.402329
\(528\) 30.4894 + 19.1396i 1.32688 + 0.832946i
\(529\) 15.8885 0.690806
\(530\) 11.2812 + 34.7198i 0.490022 + 1.50813i
\(531\) −7.00000 5.08580i −0.303774 0.220705i
\(532\) −1.92705 + 1.40008i −0.0835483 + 0.0607014i
\(533\) −8.23607 + 25.3480i −0.356744 + 1.09794i
\(534\) −4.57295 + 14.0741i −0.197891 + 0.609045i
\(535\) −5.42705 + 3.94298i −0.234632 + 0.170470i
\(536\) 12.9271 + 9.39205i 0.558364 + 0.405675i
\(537\) −10.6287 32.7117i −0.458661 1.41161i
\(538\) 31.2705 1.34817
\(539\) 25.9894 1.76336i 1.11944 0.0759531i
\(540\) 3.09017 0.132980
\(541\) 11.1180 + 34.2178i 0.478002 + 1.47114i 0.841866 + 0.539686i \(0.181457\pi\)
−0.363865 + 0.931452i \(0.618543\pi\)
\(542\) 40.1976 + 29.2052i 1.72663 + 1.25447i
\(543\) 31.3435 22.7724i 1.34508 0.977255i
\(544\) −1.04508 + 3.21644i −0.0448076 + 0.137904i
\(545\) 7.98936 24.5887i 0.342226 1.05326i
\(546\) −57.4230 + 41.7202i −2.45748 + 1.78546i
\(547\) −0.590170 0.428784i −0.0252338 0.0183335i 0.575097 0.818085i \(-0.304964\pi\)
−0.600331 + 0.799752i \(0.704964\pi\)
\(548\) −1.27458 3.92274i −0.0544472 0.167571i
\(549\) 15.1246 0.645503
\(550\) 0 0
\(551\) 4.61803 0.196735
\(552\) −9.63525 29.6543i −0.410104 1.26217i
\(553\) −3.11803 2.26538i −0.132592 0.0963339i
\(554\) 9.59017 6.96767i 0.407447 0.296028i
\(555\) 8.81966 27.1441i 0.374374 1.15220i
\(556\) 3.61803 11.1352i 0.153439 0.472236i
\(557\) −25.2533 + 18.3476i −1.07002 + 0.777412i −0.975915 0.218150i \(-0.929998\pi\)
−0.0941010 + 0.995563i \(0.529998\pi\)
\(558\) −24.1803 17.5680i −1.02364 0.743715i
\(559\) 14.1565 + 43.5694i 0.598758 + 1.84279i
\(560\) 41.8328 1.76776
\(561\) 6.28115 + 3.94298i 0.265190 + 0.166473i
\(562\) −23.5066 −0.991565
\(563\) −1.30902 4.02874i −0.0551685 0.169791i 0.919676 0.392679i \(-0.128452\pi\)
−0.974844 + 0.222888i \(0.928452\pi\)
\(564\) 2.50000 + 1.81636i 0.105269 + 0.0764824i
\(565\) −0.100813 + 0.0732450i −0.00424124 + 0.00308144i
\(566\) 9.42705 29.0135i 0.396249 1.21953i
\(567\) −13.1008 + 40.3202i −0.550182 + 1.69329i
\(568\) −2.07295 + 1.50609i −0.0869790 + 0.0631939i
\(569\) 14.1353 + 10.2699i 0.592581 + 0.430535i 0.843238 0.537541i \(-0.180647\pi\)
−0.250657 + 0.968076i \(0.580647\pi\)
\(570\) 2.50000 + 7.69421i 0.104713 + 0.322275i
\(571\) 7.56231 0.316473 0.158236 0.987401i \(-0.449419\pi\)
0.158236 + 0.987401i \(0.449419\pi\)
\(572\) −2.54508 + 10.1186i −0.106415 + 0.423080i
\(573\) 11.8328 0.494323
\(574\) −10.0902 31.0543i −0.421156 1.29618i
\(575\) 0 0
\(576\) −6.85410 + 4.97980i −0.285588 + 0.207492i
\(577\) −11.1976 + 34.4625i −0.466161 + 1.43469i 0.391357 + 0.920239i \(0.372006\pi\)
−0.857517 + 0.514456i \(0.827994\pi\)
\(578\) −0.500000 + 1.53884i −0.0207973 + 0.0640074i
\(579\) 14.4721 10.5146i 0.601441 0.436973i
\(580\) 5.16312 + 3.75123i 0.214387 + 0.155761i
\(581\) −1.29837 3.99598i −0.0538656 0.165781i
\(582\) −38.9443 −1.61429
\(583\) −25.6803 + 21.4580i −1.06357 + 0.888701i
\(584\) −29.7984 −1.23307
\(585\) 7.03444 + 21.6498i 0.290838 + 0.895108i
\(586\) 41.5517 + 30.1891i 1.71648 + 1.24710i
\(587\) −11.7812 + 8.55951i −0.486260 + 0.353289i −0.803744 0.594975i \(-0.797162\pi\)
0.317484 + 0.948264i \(0.397162\pi\)
\(588\) 3.35410 10.3229i 0.138321 0.425708i
\(589\) −2.85410 + 8.78402i −0.117601 + 0.361939i
\(590\) −12.6631 + 9.20029i −0.521332 + 0.378770i
\(591\) 40.9164 + 29.7275i 1.68308 + 1.22283i
\(592\) 8.56231 + 26.3521i 0.351909 + 1.08306i
\(593\) 35.3050 1.44980 0.724900 0.688854i \(-0.241886\pi\)
0.724900 + 0.688854i \(0.241886\pi\)
\(594\) 4.47214 + 11.1352i 0.183494 + 0.456881i
\(595\) 8.61803 0.353305
\(596\) 0.218847 + 0.673542i 0.00896432 + 0.0275894i
\(597\) 22.1353 + 16.0822i 0.905936 + 0.658201i
\(598\) 41.5517 30.1891i 1.69917 1.23452i
\(599\) 6.65248 20.4742i 0.271813 0.836554i −0.718232 0.695803i \(-0.755048\pi\)
0.990045 0.140750i \(-0.0449515\pi\)
\(600\) 0 0
\(601\) 18.8262 13.6781i 0.767938 0.557940i −0.133397 0.991063i \(-0.542588\pi\)
0.901335 + 0.433123i \(0.142588\pi\)
\(602\) −45.4058 32.9892i −1.85060 1.34454i
\(603\) −4.41641 13.5923i −0.179850 0.553521i
\(604\) −2.72949 −0.111061
\(605\) −10.6910 22.1518i −0.434650 0.900599i
\(606\) 41.1803 1.67284
\(607\) −1.80244 5.54734i −0.0731587 0.225159i 0.907790 0.419424i \(-0.137768\pi\)
−0.980949 + 0.194265i \(0.937768\pi\)
\(608\) −2.73607 1.98787i −0.110962 0.0806188i
\(609\) −32.1976 + 23.3929i −1.30471 + 0.947928i
\(610\) 8.45492 26.0216i 0.342330 1.05358i
\(611\) 3.51722 10.8249i 0.142292 0.437928i
\(612\) 1.00000 0.726543i 0.0404226 0.0293687i
\(613\) 3.32624 + 2.41665i 0.134345 + 0.0976077i 0.652928 0.757420i \(-0.273540\pi\)
−0.518583 + 0.855027i \(0.673540\pi\)
\(614\) −2.16312 6.65740i −0.0872964 0.268671i
\(615\) −26.1803 −1.05569
\(616\) 10.6525 + 26.5236i 0.429200 + 1.06867i
\(617\) 27.0132 1.08751 0.543754 0.839244i \(-0.317002\pi\)
0.543754 + 0.839244i \(0.317002\pi\)
\(618\) 16.7705 + 51.6143i 0.674609 + 2.07623i
\(619\) −21.5623 15.6659i −0.866662 0.629667i 0.0630270 0.998012i \(-0.479925\pi\)
−0.929689 + 0.368345i \(0.879925\pi\)
\(620\) −10.3262 + 7.50245i −0.414712 + 0.301306i
\(621\) 4.30902 13.2618i 0.172915 0.532177i
\(622\) 4.23607 13.0373i 0.169851 0.522747i
\(623\) −12.7533 + 9.26581i −0.510950 + 0.371227i
\(624\) −44.6976 32.4747i −1.78933 1.30003i
\(625\) −7.72542 23.7764i −0.309017 0.951057i
\(626\) −41.9787 −1.67781
\(627\) −5.69098 + 4.75528i −0.227276 + 0.189908i
\(628\) 0.381966 0.0152421
\(629\) 1.76393 + 5.42882i 0.0703326 + 0.216461i
\(630\) −22.5623 16.3925i −0.898904 0.653092i
\(631\) −14.3262 + 10.4086i −0.570319 + 0.414361i −0.835221 0.549915i \(-0.814660\pi\)
0.264902 + 0.964275i \(0.414660\pi\)
\(632\) 0.690983 2.12663i 0.0274858 0.0845927i
\(633\) 11.5836 35.6506i 0.460406 1.41699i
\(634\) −21.4164 + 15.5599i −0.850554 + 0.617964i
\(635\) 0.427051 + 0.310271i 0.0169470 + 0.0123127i
\(636\) 4.30902 + 13.2618i 0.170864 + 0.525864i
\(637\) −39.9787 −1.58401
\(638\) −6.04508 + 24.0337i −0.239327 + 0.951503i
\(639\) 2.29180 0.0906621
\(640\) 9.40983 + 28.9605i 0.371956 + 1.14476i
\(641\) −28.2254 20.5070i −1.11484 0.809977i −0.131419 0.991327i \(-0.541953\pi\)
−0.983419 + 0.181350i \(0.941953\pi\)
\(642\) −8.78115 + 6.37988i −0.346564 + 0.251794i
\(643\) 14.1287 43.4836i 0.557181 1.71483i −0.132933 0.991125i \(-0.542440\pi\)
0.690114 0.723701i \(-0.257560\pi\)
\(644\) −4.59017 + 14.1271i −0.180878 + 0.556685i
\(645\) −36.4058 + 26.4503i −1.43348 + 1.04148i
\(646\) −1.30902 0.951057i −0.0515026 0.0374188i
\(647\) −9.23607 28.4257i −0.363107 1.11753i −0.951158 0.308705i \(-0.900104\pi\)
0.588050 0.808824i \(-0.299896\pi\)
\(648\) −24.5967 −0.966252
\(649\) −12.1525 7.62870i −0.477026 0.299453i
\(650\) 0 0
\(651\) −24.5967 75.7010i −0.964023 2.96696i
\(652\) −1.59017 1.15533i −0.0622759 0.0452461i
\(653\) 28.9615 21.0418i 1.13335 0.823428i 0.147172 0.989111i \(-0.452983\pi\)
0.986179 + 0.165683i \(0.0529830\pi\)
\(654\) 12.9271 39.7854i 0.505488 1.55573i
\(655\) −2.56231 + 7.88597i −0.100118 + 0.308130i
\(656\) 20.5623 14.9394i 0.802823 0.583285i
\(657\) 21.5623 + 15.6659i 0.841226 + 0.611186i
\(658\) 4.30902 + 13.2618i 0.167983 + 0.516998i
\(659\) 26.1246 1.01767 0.508835 0.860864i \(-0.330076\pi\)
0.508835 + 0.860864i \(0.330076\pi\)
\(660\) −10.2254 + 0.693786i −0.398024 + 0.0270056i
\(661\) −9.83282 −0.382452 −0.191226 0.981546i \(-0.561246\pi\)
−0.191226 + 0.981546i \(0.561246\pi\)
\(662\) 1.50000 + 4.61653i 0.0582992 + 0.179426i
\(663\) −9.20820 6.69015i −0.357617 0.259824i
\(664\) 1.97214 1.43284i 0.0765337 0.0556050i
\(665\) −2.66312 + 8.19624i −0.103271 + 0.317836i
\(666\) 5.70820 17.5680i 0.221188 0.680748i
\(667\) 23.2984 16.9273i 0.902117 0.655426i
\(668\) 9.82624 + 7.13918i 0.380189 + 0.276223i
\(669\) −0.465558 1.43284i −0.0179995 0.0553968i
\(670\) −25.8541 −0.998831
\(671\) 25.0238 1.69784i 0.966033 0.0655445i
\(672\) 29.1459 1.12433
\(673\) 2.64590 + 8.14324i 0.101992 + 0.313899i 0.989013 0.147831i \(-0.0472291\pi\)
−0.887021 + 0.461729i \(0.847229\pi\)
\(674\) 21.1353 + 15.3557i 0.814100 + 0.591478i
\(675\) 0 0
\(676\) 2.46556 7.58821i 0.0948292 0.291854i
\(677\) −13.9377 + 42.8958i −0.535669 + 1.64862i 0.206530 + 0.978440i \(0.433783\pi\)
−0.742199 + 0.670180i \(0.766217\pi\)
\(678\) −0.163119 + 0.118513i −0.00626455 + 0.00455146i
\(679\) −33.5623 24.3844i −1.28800 0.935789i
\(680\) 1.54508 + 4.75528i 0.0592513 + 0.182357i
\(681\) −11.7082 −0.448659
\(682\) −41.9787 26.3521i −1.60745 1.00907i
\(683\) 25.8541 0.989280 0.494640 0.869098i \(-0.335300\pi\)
0.494640 + 0.869098i \(0.335300\pi\)
\(684\) 0.381966 + 1.17557i 0.0146048 + 0.0449491i
\(685\) −12.0729 8.77151i −0.461284 0.335142i
\(686\) 4.30902 3.13068i 0.164519 0.119530i
\(687\) −10.1631 + 31.2789i −0.387747 + 1.19336i
\(688\) 13.5000 41.5487i 0.514683 1.58403i
\(689\) 41.5517 30.1891i 1.58299 1.15011i
\(690\) 40.8156 + 29.6543i 1.55382 + 1.12892i
\(691\) 14.5902 + 44.9039i 0.555036 + 1.70823i 0.695848 + 0.718189i \(0.255029\pi\)
−0.140811 + 0.990036i \(0.544971\pi\)
\(692\) 7.85410 0.298568
\(693\) 6.23607 24.7930i 0.236889 0.941807i
\(694\) 16.8541 0.639773
\(695\) −13.0902 40.2874i −0.496538 1.52819i
\(696\) −18.6803 13.5721i −0.708076 0.514448i
\(697\) 4.23607 3.07768i 0.160453 0.116576i
\(698\) 4.70820 14.4904i 0.178208 0.548468i
\(699\) 11.8713 36.5362i 0.449015 1.38193i
\(700\) 0 0
\(701\) −9.04508 6.57164i −0.341628 0.248207i 0.403720 0.914882i \(-0.367717\pi\)
−0.745348 + 0.666675i \(0.767717\pi\)
\(702\) −5.69098 17.5150i −0.214792 0.661063i
\(703\) −5.70820 −0.215289
\(704\) −10.7812 + 9.00854i −0.406330 + 0.339522i
\(705\) 11.1803 0.421076
\(706\) −2.20820 6.79615i −0.0831069 0.255777i
\(707\) 35.4894 + 25.7845i 1.33471 + 0.969727i
\(708\) −4.83688 + 3.51420i −0.181781 + 0.132072i
\(709\) −1.63525 + 5.03280i −0.0614133 + 0.189011i −0.977056 0.212982i \(-0.931682\pi\)
0.915643 + 0.401993i \(0.131682\pi\)
\(710\) 1.28115 3.94298i 0.0480808 0.147978i
\(711\) −1.61803 + 1.17557i −0.0606810 + 0.0440873i
\(712\) −7.39919 5.37582i −0.277296 0.201468i
\(713\) 17.7984 + 54.7778i 0.666554 + 2.05144i
\(714\) 13.9443 0.521851
\(715\) 14.0689 + 35.0301i 0.526146 + 1.31005i
\(716\) −9.50658 −0.355277
\(717\) 3.29180 + 10.1311i 0.122934 + 0.378353i
\(718\) −37.7705 27.4419i −1.40958 1.02412i
\(719\) −42.3607 + 30.7768i −1.57979 + 1.14778i −0.662848 + 0.748754i \(0.730653\pi\)
−0.916939 + 0.399029i \(0.869347\pi\)
\(720\) 6.70820 20.6457i 0.250000 0.769421i
\(721\) −17.8647 + 54.9820i −0.665318 + 2.04764i
\(722\) −23.5623 + 17.1190i −0.876898 + 0.637104i
\(723\) 11.3820 + 8.26948i 0.423300 + 0.307545i
\(724\) −3.30902 10.1841i −0.122979 0.378489i
\(725\) 0 0
\(726\) −17.2984 35.8424i −0.642003 1.33024i
\(727\) 24.0000 0.890111 0.445055 0.895503i \(-0.353184\pi\)
0.445055 + 0.895503i \(0.353184\pi\)
\(728\) −13.5557 41.7202i −0.502409 1.54626i
\(729\) 5.66312 + 4.11450i 0.209745 + 0.152389i
\(730\) 39.0066 28.3399i 1.44370 1.04891i
\(731\) 2.78115 8.55951i 0.102865 0.316585i
\(732\) 3.22949 9.93935i 0.119365 0.367369i
\(733\) −8.57295 + 6.22861i −0.316649 + 0.230059i −0.734744 0.678344i \(-0.762698\pi\)
0.418095 + 0.908403i \(0.362698\pi\)
\(734\) −28.4164 20.6457i −1.04887 0.762048i
\(735\) −12.1353 37.3485i −0.447616 1.37762i
\(736\) −21.0902 −0.777394
\(737\) −8.83282 21.9928i −0.325361 0.810116i
\(738\) −16.9443 −0.623727
\(739\) −0.281153 0.865300i −0.0103424 0.0318306i 0.945752 0.324889i \(-0.105327\pi\)
−0.956095 + 0.293058i \(0.905327\pi\)
\(740\) −6.38197 4.63677i −0.234606 0.170451i
\(741\) 9.20820 6.69015i 0.338272 0.245769i
\(742\) −19.4443 + 59.8433i −0.713822 + 2.19692i
\(743\) −11.7148 + 36.0544i −0.429774 + 1.32271i 0.468575 + 0.883424i \(0.344768\pi\)
−0.898348 + 0.439284i \(0.855232\pi\)
\(744\) 37.3607 27.1441i 1.36971 0.995152i
\(745\) 2.07295 + 1.50609i 0.0759470 + 0.0551787i
\(746\) −3.21885 9.90659i −0.117850 0.362706i
\(747\) −2.18034 −0.0797745
\(748\) 1.57295 1.31433i 0.0575127 0.0480566i
\(749\) −11.5623 −0.422477
\(750\) −12.5000 38.4710i −0.456435 1.40476i
\(751\) 34.0795 + 24.7602i 1.24358 + 0.903513i 0.997831 0.0658203i \(-0.0209664\pi\)
0.245748 + 0.969334i \(0.420966\pi\)
\(752\) −8.78115 + 6.37988i −0.320216 + 0.232650i
\(753\) −6.21885 + 19.1396i −0.226627 + 0.697487i
\(754\) 11.7533 36.1729i 0.428030 1.31734i
\(755\) −7.98936 + 5.80461i −0.290762 + 0.211251i
\(756\) 4.30902 + 3.13068i 0.156717 + 0.113862i
\(757\) 12.3262 + 37.9363i 0.448005 + 1.37882i 0.879155 + 0.476537i \(0.158108\pi\)
−0.431150 + 0.902280i \(0.641892\pi\)
\(758\) −48.0689 −1.74594
\(759\) −11.2812 + 44.8509i −0.409480 + 1.62799i
\(760\) −5.00000 −0.181369
\(761\) 5.51064 + 16.9600i 0.199761 + 0.614800i 0.999888 + 0.0149698i \(0.00476523\pi\)
−0.800127 + 0.599830i \(0.795235\pi\)
\(762\) 0.690983 + 0.502029i 0.0250317 + 0.0181866i
\(763\) 36.0517 26.1931i 1.30516 0.948253i
\(764\) 1.01064 3.11044i 0.0365638 0.112532i
\(765\) 1.38197 4.25325i 0.0499651 0.153777i
\(766\) 3.97214 2.88593i 0.143519 0.104273i
\(767\) 17.8156 + 12.9438i 0.643284 + 0.467373i
\(768\) 9.37132 + 28.8420i 0.338158 + 1.04074i
\(769\) −31.8541 −1.14869 −0.574344 0.818614i \(-0.694743\pi\)
−0.574344 + 0.818614i \(0.694743\pi\)
\(770\) −39.1697 24.5887i −1.41158 0.886116i
\(771\) 24.4721 0.881342
\(772\) −1.52786 4.70228i −0.0549890 0.169239i
\(773\) −40.1697 29.1850i −1.44480 1.04971i −0.987011 0.160652i \(-0.948640\pi\)
−0.457792 0.889059i \(-0.651360\pi\)
\(774\) −23.5623 + 17.1190i −0.846930 + 0.615330i
\(775\) 0 0
\(776\) 7.43769 22.8909i 0.266998 0.821734i
\(777\) 39.7984 28.9152i 1.42776 1.03733i
\(778\) −15.6353 11.3597i −0.560551 0.407264i
\(779\) 1.61803 + 4.97980i 0.0579721 + 0.178420i
\(780\) 15.7295 0.563206
\(781\) 3.79180 0.257270i 0.135681 0.00920585i
\(782\) −10.0902 −0.360824
\(783\) −3.19098 9.82084i −0.114036 0.350968i
\(784\) 30.8435 + 22.4091i 1.10155 + 0.800324i
\(785\) 1.11803 0.812299i 0.0399043 0.0289922i
\(786\) −4.14590 + 12.7598i −0.147879 + 0.455126i
\(787\) 10.3885 31.9727i 0.370312 1.13970i −0.576276 0.817255i \(-0.695495\pi\)
0.946588 0.322447i \(-0.104505\pi\)
\(788\) 11.3090 8.21648i 0.402867 0.292700i
\(789\) −28.2533 20.5272i −1.00584 0.730788i
\(790\) 1.11803 + 3.44095i 0.0397779 + 0.122424i
\(791\) −0.214782 −0.00763676
\(792\) 14.7984 1.00406i 0.525837 0.0356776i
\(793\) −38.4934 −1.36694
\(794\) 10.2082 + 31.4176i 0.362276 + 1.11497i
\(795\) 40.8156 + 29.6543i 1.44758 + 1.05173i
\(796\) 6.11803 4.44501i 0.216848 0.157549i
\(797\) 4.06231 12.5025i 0.143894 0.442861i −0.852973 0.521955i \(-0.825203\pi\)
0.996867 + 0.0790942i \(0.0252028\pi\)
\(798\) −4.30902 + 13.2618i −0.152538 + 0.469462i
\(799\) −1.80902 + 1.31433i −0.0639984 + 0.0464976i
\(800\) 0 0
\(801\) 2.52786 + 7.77997i 0.0893177 + 0.274892i
\(802\) −38.8328 −1.37123
\(803\) 37.4336 + 23.4989i 1.32100 + 0.829258i
\(804\) −9.87539 −0.348278
\(805\) 16.6074 + 51.1123i 0.585334 + 1.80147i
\(806\) 61.5410 + 44.7122i 2.16769 + 1.57492i
\(807\) 34.9615 25.4010i 1.23070 0.894158i
\(808\) −7.86475 + 24.2052i −0.276681 + 0.851536i
\(809\) −5.91641 + 18.2088i −0.208010 + 0.640188i 0.791567 + 0.611083i \(0.209266\pi\)
−0.999576 + 0.0291054i \(0.990734\pi\)
\(810\) 32.1976 23.3929i 1.13131 0.821943i
\(811\) −2.88197 2.09387i −0.101200 0.0735258i 0.536035 0.844196i \(-0.319922\pi\)
−0.637234 + 0.770670i \(0.719922\pi\)
\(812\) 3.39919 + 10.4616i 0.119288 + 0.367131i
\(813\) 68.6656 2.40821
\(814\) 7.47214 29.7073i 0.261898 1.04124i
\(815\) −7.11146 −0.249103
\(816\) 3.35410 + 10.3229i 0.117417 + 0.361373i
\(817\) 7.28115 + 5.29007i 0.254735 + 0.185076i
\(818\) 0.736068 0.534785i 0.0257360 0.0186983i
\(819\) −12.1246 + 37.3157i −0.423668 + 1.30392i
\(820\) −2.23607 + 6.88191i −0.0780869 + 0.240327i
\(821\) −5.00000 + 3.63271i −0.174501 + 0.126783i −0.671608 0.740907i \(-0.734396\pi\)
0.497106 + 0.867690i \(0.334396\pi\)
\(822\) −19.5344 14.1926i −0.681342 0.495024i
\(823\) −6.18034 19.0211i −0.215433 0.663035i −0.999123 0.0418821i \(-0.986665\pi\)
0.783689 0.621153i \(-0.213335\pi\)
\(824\) −33.5410 −1.16846
\(825\) 0 0
\(826\) −26.9787 −0.938710
\(827\) 0.375388 + 1.15533i 0.0130535 + 0.0401746i 0.957371 0.288861i \(-0.0932765\pi\)
−0.944318 + 0.329035i \(0.893276\pi\)
\(828\) 6.23607 + 4.53077i 0.216718 + 0.157455i
\(829\) 21.9443 15.9434i 0.762156 0.553739i −0.137415 0.990514i \(-0.543879\pi\)
0.899571 + 0.436775i \(0.143879\pi\)
\(830\) −1.21885 + 3.75123i −0.0423068 + 0.130207i
\(831\) 5.06231 15.5802i 0.175609 0.540470i
\(832\) 17.4443 12.6740i 0.604771 0.439392i
\(833\) 6.35410 + 4.61653i 0.220157 + 0.159953i
\(834\) −21.1803 65.1864i −0.733415 2.25722i
\(835\) 43.9443 1.52075
\(836\) 0.763932 + 1.90211i 0.0264211 + 0.0657860i
\(837\) 20.6525 0.713854
\(838\) 16.7705 + 51.6143i 0.579328 + 1.78299i
\(839\) −6.85410 4.97980i −0.236630 0.171922i 0.463151 0.886280i \(-0.346719\pi\)
−0.699781 + 0.714358i \(0.746719\pi\)
\(840\) 34.8607 25.3278i 1.20281 0.873891i
\(841\) −2.37132 + 7.29818i −0.0817698 + 0.251661i
\(842\) −11.5623 + 35.5851i −0.398463 + 1.22634i
\(843\) −26.2812 + 19.0944i −0.905171 + 0.657645i
\(844\) −8.38197 6.08985i −0.288519 0.209621i
\(845\) −8.92047 27.4544i −0.306874 0.944460i
\(846\) 7.23607 0.248781
\(847\) 7.53444 41.7202i 0.258886 1.43352i
\(848\) −48.9787 −1.68194
\(849\) −13.0279 40.0956i −0.447115 1.37608i
\(850\) 0 0
\(851\) −28.7984 + 20.9232i −0.987196 + 0.717240i
\(852\) 0.489357 1.50609i 0.0167651 0.0515976i
\(853\) −3.13525 + 9.64932i −0.107349 + 0.330387i −0.990275 0.139127i \(-0.955571\pi\)
0.882926 + 0.469513i \(0.155571\pi\)
\(854\) 38.1525 27.7194i 1.30555 0.948538i
\(855\) 3.61803 + 2.62866i 0.123734 + 0.0898981i
\(856\) −2.07295 6.37988i −0.0708519 0.218060i
\(857\) −40.3394 −1.37797 −0.688984 0.724777i \(-0.741943\pi\)
−0.688984 + 0.724777i \(0.741943\pi\)
\(858\) 22.7639 + 56.6799i 0.777148 + 1.93502i
\(859\) 26.4164 0.901316 0.450658 0.892697i \(-0.351189\pi\)
0.450658 + 0.892697i \(0.351189\pi\)
\(860\) 3.84346 + 11.8290i 0.131061 + 0.403364i
\(861\) −36.5066 26.5236i −1.24414 0.903921i
\(862\) −44.5967 + 32.4014i −1.51897 + 1.10360i
\(863\) 8.23607 25.3480i 0.280359 0.862856i −0.707392 0.706821i \(-0.750129\pi\)
0.987751 0.156035i \(-0.0498714\pi\)
\(864\) −2.33688 + 7.19218i −0.0795023 + 0.244683i
\(865\) 22.9894 16.7027i 0.781662 0.567910i
\(866\) −8.47214 6.15537i −0.287895 0.209168i
\(867\) 0.690983 + 2.12663i 0.0234670 + 0.0722240i
\(868\) −22.0000 −0.746729
\(869\) −2.54508 + 2.12663i −0.0863361 + 0.0721409i
\(870\) 37.3607 1.26665
\(871\) 11.2401 + 34.5936i 0.380857 + 1.17216i
\(872\) 20.9164 + 15.1967i 0.708319 + 0.514624i
\(873\) −17.4164 + 12.6538i −0.589456 + 0.428265i
\(874\) 3.11803 9.59632i 0.105469 0.324600i
\(875\) 13.3156 40.9812i 0.450149 1.38542i
\(876\) 14.8992 10.8249i 0.503397 0.365739i
\(877\) −14.8992 10.8249i −0.503110 0.365531i 0.307094 0.951679i \(-0.400643\pi\)
−0.810204 + 0.586149i \(0.800643\pi\)
\(878\) −17.5623 54.0512i −0.592699 1.82414i
\(879\) 70.9787 2.39405
\(880\) 8.78115 34.9116i 0.296013 1.17687i
\(881\) −41.2148 −1.38856 −0.694281 0.719704i \(-0.744277\pi\)
−0.694281 + 0.719704i \(0.744277\pi\)
\(882\) −7.85410 24.1724i −0.264461 0.813928i
\(883\) 37.3885 + 27.1644i 1.25822 + 0.914154i 0.998669 0.0515744i \(-0.0164239\pi\)
0.259556 + 0.965728i \(0.416424\pi\)
\(884\) −2.54508 + 1.84911i −0.0856005 + 0.0621924i
\(885\) −6.68441 + 20.5725i −0.224694 + 0.691536i
\(886\) −11.7533 + 36.1729i −0.394859 + 1.21525i
\(887\) 20.8262 15.1311i 0.699277 0.508054i −0.180420 0.983590i \(-0.557746\pi\)
0.879697 + 0.475535i \(0.157746\pi\)
\(888\) 23.0902 + 16.7760i 0.774855 + 0.562965i
\(889\) 0.281153 + 0.865300i 0.00942957 + 0.0290212i
\(890\) 14.7984 0.496043
\(891\) 30.8992 + 19.3969i 1.03516 + 0.649821i
\(892\) −0.416408 −0.0139424
\(893\) −0.690983 2.12663i −0.0231229 0.0711649i
\(894\) 3.35410 + 2.43690i 0.112178 + 0.0815021i
\(895\) −27.8262 + 20.2169i −0.930129 + 0.675778i
\(896\) −16.2188 + 49.9165i −0.541834 + 1.66759i
\(897\) 21.9336 67.5048i 0.732343 2.25392i
\(898\) 3.61803 2.62866i 0.120735 0.0877194i
\(899\) 34.5066 + 25.0705i 1.15086 + 0.836148i
\(900\) 0 0
\(901\) −10.0902 −0.336152
\(902\) −28.0344 + 1.90211i −0.933445 + 0.0633334i
\(903\) −77.5623 −2.58111
\(904\) −0.0385072 0.118513i −0.00128073 0.00394168i
\(905\) −31.3435 22.7724i −1.04189 0.756979i
\(906\) −12.9271 + 9.39205i −0.429473 + 0.312030i
\(907\) −6.83688 + 21.0418i −0.227015 + 0.698680i 0.771066 + 0.636755i \(0.219724\pi\)
−0.998081 + 0.0619247i \(0.980276\pi\)
\(908\) −1.00000 + 3.07768i −0.0331862 + 0.102137i
\(909\) 18.4164 13.3803i 0.610834 0.443797i
\(910\) 57.4230 + 41.7202i 1.90355 + 1.38301i
\(911\) −16.9894 52.2879i −0.562883 1.73237i −0.674160 0.738585i \(-0.735494\pi\)
0.111278 0.993789i \(-0.464506\pi\)
\(912\) −10.8541 −0.359415
\(913\) −3.60739 + 0.244758i −0.119387 + 0.00810032i
\(914\) −0.236068 −0.00780843
\(915\) −11.6844 35.9609i −0.386275 1.18883i
\(916\) 7.35410 + 5.34307i 0.242986 + 0.176540i
\(917\) −11.5623 + 8.40051i −0.381821 + 0.277409i
\(918\) −1.11803 + 3.44095i −0.0369006 + 0.113568i
\(919\) −15.3090 + 47.1163i −0.504998 + 1.55422i 0.295776 + 0.955257i \(0.404422\pi\)
−0.800774 + 0.598966i \(0.795578\pi\)
\(920\) −25.2254 + 18.3273i −0.831658 + 0.604235i
\(921\) −7.82624 5.68609i −0.257883 0.187363i
\(922\) −2.54508 7.83297i −0.0838179 0.257965i
\(923\) −5.83282 −0.191989
\(924\) −14.9615 9.39205i −0.492197 0.308976i
\(925\) 0 0
\(926\) 12.3992 + 38.1608i 0.407463 + 1.25404i
\(927\) 24.2705 + 17.6336i 0.797148 + 0.579162i
\(928\) −12.6353 + 9.18005i −0.414773 + 0.301350i
\(929\) −1.99342 + 6.13512i −0.0654021 + 0.201287i −0.978417 0.206638i \(-0.933748\pi\)
0.913015 + 0.407925i \(0.133748\pi\)
\(930\) −23.0902 + 71.0642i −0.757157 + 2.33029i
\(931\) −6.35410 + 4.61653i −0.208247 + 0.151301i
\(932\) −8.59017 6.24112i −0.281380 0.204435i
\(933\) −5.85410 18.0171i −0.191655 0.589852i
\(934\) 58.2492 1.90597
\(935\) 1.80902 7.19218i 0.0591612 0.235209i
\(936\) −22.7639 −0.744062
\(937\) −7.37539 22.6991i −0.240943 0.741548i −0.996277 0.0862074i \(-0.972525\pi\)
0.755334 0.655340i \(-0.227475\pi\)
\(938\) −36.0517 26.1931i −1.17713 0.855234i
\(939\) −46.9336 + 34.0993i −1.53162 + 1.11279i
\(940\) 0.954915 2.93893i 0.0311459 0.0958572i
\(941\) −0.236068 + 0.726543i −0.00769560 + 0.0236846i −0.954831 0.297151i \(-0.903964\pi\)
0.947135 + 0.320835i \(0.103964\pi\)
\(942\) 1.80902 1.31433i 0.0589410 0.0428231i
\(943\) 26.4164 + 19.1926i 0.860237 + 0.624998i
\(944\) −6.48936 19.9722i −0.211211 0.650039i
\(945\) 19.2705 0.626870
\(946\) −37.0623 + 30.9686i −1.20500 + 1.00688i
\(947\) −42.4853 −1.38059 −0.690293 0.723530i \(-0.742518\pi\)
−0.690293 + 0.723530i \(0.742518\pi\)
\(948\) 0.427051 + 1.31433i 0.0138700 + 0.0426874i
\(949\) −54.8779 39.8711i −1.78141 1.29427i
\(950\) 0 0
\(951\) −11.3050 + 34.7931i −0.366588 + 1.12824i
\(952\) −2.66312 + 8.19624i −0.0863122 + 0.265642i
\(953\) −30.3992 + 22.0863i −0.984726 + 0.715446i −0.958760 0.284217i \(-0.908266\pi\)
−0.0259664 + 0.999663i \(0.508266\pi\)
\(954\) 26.4164 + 19.1926i 0.855263 + 0.621385i
\(955\) −3.65654 11.2537i −0.118323 0.364160i
\(956\) 2.94427 0.0952246
\(957\) 12.7639 + 31.7809i 0.412599 + 1.02733i
\(958\) −10.8541 −0.350680
\(959\) −7.94834 24.4625i −0.256665 0.789934i
\(960\) 17.1353 + 12.4495i 0.553038 + 0.401806i
\(961\) −43.9336 + 31.9196i −1.41721 + 1.02967i
\(962\) −14.5279 + 44.7122i −0.468397 + 1.44158i
\(963\) −1.85410 + 5.70634i −0.0597476 + 0.183884i
\(964\) 3.14590 2.28563i 0.101323 0.0736151i
\(965\) −14.4721 10.5146i −0.465875 0.338478i
\(966\) 26.8713 + 82.7014i 0.864571 + 2.66087i
\(967\) −57.4508 −1.84749 −0.923747 0.383002i \(-0.874890\pi\)
−0.923747 + 0.383002i \(0.874890\pi\)
\(968\) 24.3713 3.32244i 0.783324 0.106787i
\(969\) −2.23607 −0.0718329
\(970\) 12.0344 + 37.0382i 0.386403 + 1.18923i
\(971\) 2.00000 + 1.45309i 0.0641831 + 0.0466317i 0.619414 0.785064i \(-0.287370\pi\)
−0.555231 + 0.831696i \(0.687370\pi\)
\(972\) 8.94427 6.49839i 0.286888 0.208436i
\(973\) 22.5623 69.4396i 0.723314 2.22613i
\(974\) −3.75329 + 11.5514i −0.120263 + 0.370132i
\(975\) 0 0
\(976\) 29.6976 + 21.5765i 0.950596 + 0.690648i
\(977\) −7.47214 22.9969i −0.239055 0.735735i −0.996558 0.0829031i \(-0.973581\pi\)
0.757503 0.652832i \(-0.226419\pi\)
\(978\) −11.5066 −0.367940
\(979\) 5.05573 + 12.5882i 0.161582 + 0.402322i
\(980\) −10.8541 −0.346722
\(981\) −7.14590 21.9928i −0.228151 0.702176i
\(982\) 13.3262 + 9.68208i 0.425257 + 0.308968i
\(983\) −11.5623 + 8.40051i −0.368780 + 0.267935i −0.756705 0.653757i \(-0.773192\pi\)
0.387925 + 0.921691i \(0.373192\pi\)
\(984\) 8.09017 24.8990i 0.257905 0.793751i
\(985\) 15.6287 48.1001i 0.497971 1.53260i
\(986\) −6.04508 + 4.39201i −0.192515 + 0.139870i
\(987\) 15.5902 + 11.3269i 0.496241 + 0.360540i
\(988\) −0.972136 2.99193i −0.0309278 0.0951859i
\(989\) 56.1246 1.78466
\(990\) −18.4164 + 15.3884i −0.585312 + 0.489076i
\(991\) −23.2148 −0.737442 −0.368721 0.929540i \(-0.620204\pi\)
−0.368721 + 0.929540i \(0.620204\pi\)
\(992\) −9.65248 29.7073i −0.306466 0.943207i
\(993\) 5.42705 + 3.94298i 0.172222 + 0.125127i
\(994\) 5.78115 4.20025i 0.183367 0.133224i
\(995\) 8.45492 26.0216i 0.268039 0.824939i
\(996\) −0.465558 + 1.43284i −0.0147518 + 0.0454013i
\(997\) 32.0066 23.2541i 1.01366 0.736466i 0.0486852 0.998814i \(-0.484497\pi\)
0.964973 + 0.262348i \(0.0844969\pi\)
\(998\) −36.8435 26.7683i −1.16626 0.847337i
\(999\) 3.94427 + 12.1392i 0.124791 + 0.384068i
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 187.2.g.a.137.1 yes 4
11.3 even 5 2057.2.a.g.1.1 2
11.8 odd 10 2057.2.a.l.1.2 2
11.9 even 5 inner 187.2.g.a.86.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.g.a.86.1 4 11.9 even 5 inner
187.2.g.a.137.1 yes 4 1.1 even 1 trivial
2057.2.a.g.1.1 2 11.3 even 5
2057.2.a.l.1.2 2 11.8 odd 10