Properties

Label 133.2.g.a.102.9
Level $133$
Weight $2$
Character 133.102
Analytic conductor $1.062$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [133,2,Mod(30,133)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(133, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("133.30");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 133.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.06201034688\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 102.9
Character \(\chi\) \(=\) 133.102
Dual form 133.2.g.a.30.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.594925 - 1.03044i) q^{2} +0.177362 q^{3} +(0.292129 + 0.505982i) q^{4} +(-0.0570924 + 0.0988869i) q^{5} +(0.105517 - 0.182761i) q^{6} +(1.73984 - 1.99323i) q^{7} +3.07488 q^{8} -2.96854 q^{9} +O(q^{10})\) \(q+(0.594925 - 1.03044i) q^{2} +0.177362 q^{3} +(0.292129 + 0.505982i) q^{4} +(-0.0570924 + 0.0988869i) q^{5} +(0.105517 - 0.182761i) q^{6} +(1.73984 - 1.99323i) q^{7} +3.07488 q^{8} -2.96854 q^{9} +(0.0679313 + 0.117661i) q^{10} +(0.429633 - 0.744146i) q^{11} +(0.0518125 + 0.0897419i) q^{12} +(-1.47479 + 2.55441i) q^{13} +(-1.01883 - 2.97862i) q^{14} +(-0.0101260 + 0.0175388i) q^{15} +(1.24506 - 2.15651i) q^{16} -3.62977 q^{17} +(-1.76606 + 3.05891i) q^{18} +(-4.18378 + 1.22309i) q^{19} -0.0667134 q^{20} +(0.308580 - 0.353523i) q^{21} +(-0.511199 - 0.885422i) q^{22} -0.959049 q^{23} +0.545366 q^{24} +(2.49348 + 4.31884i) q^{25} +(1.75477 + 3.03936i) q^{26} -1.05859 q^{27} +(1.51680 + 0.298046i) q^{28} +(3.06939 - 5.31634i) q^{29} +(0.0120484 + 0.0208685i) q^{30} +(-2.81101 + 4.86882i) q^{31} +(1.59344 + 2.75992i) q^{32} +(0.0762005 - 0.131983i) q^{33} +(-2.15944 + 3.74026i) q^{34} +(0.0977730 + 0.285845i) q^{35} +(-0.867197 - 1.50203i) q^{36} +(-0.886769 - 1.53593i) q^{37} +(-1.22871 + 5.03879i) q^{38} +(-0.261571 + 0.453054i) q^{39} +(-0.175552 + 0.304065i) q^{40} +(-5.49373 - 9.51542i) q^{41} +(-0.180702 - 0.528293i) q^{42} +(5.56640 + 9.64129i) q^{43} +0.502033 q^{44} +(0.169481 - 0.293550i) q^{45} +(-0.570562 + 0.988243i) q^{46} +1.01342 q^{47} +(0.220827 - 0.382483i) q^{48} +(-0.945939 - 6.93579i) q^{49} +5.93373 q^{50} -0.643782 q^{51} -1.72331 q^{52} +(-3.98798 - 6.90739i) q^{53} +(-0.629782 + 1.09081i) q^{54} +(0.0490575 + 0.0849702i) q^{55} +(5.34978 - 6.12894i) q^{56} +(-0.742043 + 0.216930i) q^{57} +(-3.65211 - 6.32564i) q^{58} +1.28223 q^{59} -0.0118324 q^{60} +9.50799 q^{61} +(3.34468 + 5.79316i) q^{62} +(-5.16478 + 5.91699i) q^{63} +8.77216 q^{64} +(-0.168398 - 0.291674i) q^{65} +(-0.0906671 - 0.157040i) q^{66} +(-3.74950 - 6.49432i) q^{67} +(-1.06036 - 1.83660i) q^{68} -0.170099 q^{69} +(0.352714 + 0.0693072i) q^{70} +(-1.01008 - 1.74951i) q^{71} -9.12791 q^{72} -1.88689 q^{73} -2.11024 q^{74} +(0.442248 + 0.765996i) q^{75} +(-1.84107 - 1.75962i) q^{76} +(-0.735764 - 2.15105i) q^{77} +(0.311230 + 0.539066i) q^{78} +(2.06547 - 3.57749i) q^{79} +(0.142167 + 0.246241i) q^{80} +8.71787 q^{81} -13.0734 q^{82} +14.0092 q^{83} +(0.269022 + 0.0528619i) q^{84} +(0.207232 - 0.358936i) q^{85} +13.2464 q^{86} +(0.544392 - 0.942915i) q^{87} +(1.32107 - 2.28816i) q^{88} +10.2607 q^{89} +(-0.201657 - 0.349280i) q^{90} +(2.52563 + 7.38384i) q^{91} +(-0.280166 - 0.485262i) q^{92} +(-0.498566 + 0.863542i) q^{93} +(0.602909 - 1.04427i) q^{94} +(0.117914 - 0.483551i) q^{95} +(0.282615 + 0.489504i) q^{96} +(-5.41182 - 9.37356i) q^{97} +(-7.70968 - 3.15154i) q^{98} +(-1.27538 + 2.20903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/133\mathbb{Z}\right)^\times\).

\(n\) \(78\) \(115\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.594925 1.03044i 0.420675 0.728631i −0.575330 0.817921i \(-0.695126\pi\)
0.996006 + 0.0892901i \(0.0284598\pi\)
\(3\) 0.177362 0.102400 0.0511999 0.998688i \(-0.483695\pi\)
0.0511999 + 0.998688i \(0.483695\pi\)
\(4\) 0.292129 + 0.505982i 0.146064 + 0.252991i
\(5\) −0.0570924 + 0.0988869i −0.0255325 + 0.0442236i −0.878509 0.477725i \(-0.841461\pi\)
0.852977 + 0.521949i \(0.174795\pi\)
\(6\) 0.105517 0.182761i 0.0430771 0.0746117i
\(7\) 1.73984 1.99323i 0.657596 0.753370i
\(8\) 3.07488 1.08713
\(9\) −2.96854 −0.989514
\(10\) 0.0679313 + 0.117661i 0.0214818 + 0.0372075i
\(11\) 0.429633 0.744146i 0.129539 0.224369i −0.793959 0.607971i \(-0.791984\pi\)
0.923498 + 0.383603i \(0.125317\pi\)
\(12\) 0.0518125 + 0.0897419i 0.0149570 + 0.0259063i
\(13\) −1.47479 + 2.55441i −0.409032 + 0.708465i −0.994782 0.102028i \(-0.967467\pi\)
0.585749 + 0.810492i \(0.300800\pi\)
\(14\) −1.01883 2.97862i −0.272295 0.796070i
\(15\) −0.0101260 + 0.0175388i −0.00261452 + 0.00452849i
\(16\) 1.24506 2.15651i 0.311266 0.539128i
\(17\) −3.62977 −0.880348 −0.440174 0.897913i \(-0.645083\pi\)
−0.440174 + 0.897913i \(0.645083\pi\)
\(18\) −1.76606 + 3.05891i −0.416264 + 0.720991i
\(19\) −4.18378 + 1.22309i −0.959826 + 0.280597i
\(20\) −0.0667134 −0.0149176
\(21\) 0.308580 0.353523i 0.0673378 0.0771450i
\(22\) −0.511199 0.885422i −0.108988 0.188773i
\(23\) −0.959049 −0.199976 −0.0999878 0.994989i \(-0.531880\pi\)
−0.0999878 + 0.994989i \(0.531880\pi\)
\(24\) 0.545366 0.111322
\(25\) 2.49348 + 4.31884i 0.498696 + 0.863767i
\(26\) 1.75477 + 3.03936i 0.344140 + 0.596067i
\(27\) −1.05859 −0.203726
\(28\) 1.51680 + 0.298046i 0.286648 + 0.0563254i
\(29\) 3.06939 5.31634i 0.569971 0.987219i −0.426597 0.904442i \(-0.640288\pi\)
0.996568 0.0827769i \(-0.0263789\pi\)
\(30\) 0.0120484 + 0.0208685i 0.00219973 + 0.00381005i
\(31\) −2.81101 + 4.86882i −0.504873 + 0.874466i 0.495111 + 0.868830i \(0.335127\pi\)
−0.999984 + 0.00563600i \(0.998206\pi\)
\(32\) 1.59344 + 2.75992i 0.281683 + 0.487889i
\(33\) 0.0762005 0.131983i 0.0132648 0.0229753i
\(34\) −2.15944 + 3.74026i −0.370341 + 0.641449i
\(35\) 0.0977730 + 0.285845i 0.0165267 + 0.0483167i
\(36\) −0.867197 1.50203i −0.144533 0.250338i
\(37\) −0.886769 1.53593i −0.145784 0.252505i 0.783881 0.620911i \(-0.213237\pi\)
−0.929665 + 0.368406i \(0.879904\pi\)
\(38\) −1.22871 + 5.03879i −0.199323 + 0.817399i
\(39\) −0.261571 + 0.453054i −0.0418849 + 0.0725467i
\(40\) −0.175552 + 0.304065i −0.0277572 + 0.0480769i
\(41\) −5.49373 9.51542i −0.857976 1.48606i −0.873856 0.486185i \(-0.838388\pi\)
0.0158798 0.999874i \(-0.494945\pi\)
\(42\) −0.180702 0.528293i −0.0278829 0.0815174i
\(43\) 5.56640 + 9.64129i 0.848869 + 1.47028i 0.882219 + 0.470840i \(0.156049\pi\)
−0.0333502 + 0.999444i \(0.510618\pi\)
\(44\) 0.502033 0.0756843
\(45\) 0.169481 0.293550i 0.0252648 0.0437598i
\(46\) −0.570562 + 0.988243i −0.0841248 + 0.145708i
\(47\) 1.01342 0.147823 0.0739113 0.997265i \(-0.476452\pi\)
0.0739113 + 0.997265i \(0.476452\pi\)
\(48\) 0.220827 0.382483i 0.0318736 0.0552067i
\(49\) −0.945939 6.93579i −0.135134 0.990827i
\(50\) 5.93373 0.839157
\(51\) −0.643782 −0.0901475
\(52\) −1.72331 −0.238980
\(53\) −3.98798 6.90739i −0.547792 0.948803i −0.998425 0.0560939i \(-0.982135\pi\)
0.450634 0.892709i \(-0.351198\pi\)
\(54\) −0.629782 + 1.09081i −0.0857025 + 0.148441i
\(55\) 0.0490575 + 0.0849702i 0.00661492 + 0.0114574i
\(56\) 5.34978 6.12894i 0.714895 0.819014i
\(57\) −0.742043 + 0.216930i −0.0982860 + 0.0287331i
\(58\) −3.65211 6.32564i −0.479545 0.830597i
\(59\) 1.28223 0.166933 0.0834664 0.996511i \(-0.473401\pi\)
0.0834664 + 0.996511i \(0.473401\pi\)
\(60\) −0.0118324 −0.00152756
\(61\) 9.50799 1.21737 0.608686 0.793411i \(-0.291697\pi\)
0.608686 + 0.793411i \(0.291697\pi\)
\(62\) 3.34468 + 5.79316i 0.424775 + 0.735732i
\(63\) −5.16478 + 5.91699i −0.650701 + 0.745471i
\(64\) 8.77216 1.09652
\(65\) −0.168398 0.291674i −0.0208872 0.0361777i
\(66\) −0.0906671 0.157040i −0.0111604 0.0193303i
\(67\) −3.74950 6.49432i −0.458074 0.793408i 0.540785 0.841161i \(-0.318127\pi\)
−0.998859 + 0.0477533i \(0.984794\pi\)
\(68\) −1.06036 1.83660i −0.128588 0.222720i
\(69\) −0.170099 −0.0204775
\(70\) 0.352714 + 0.0693072i 0.0421574 + 0.00828380i
\(71\) −1.01008 1.74951i −0.119874 0.207629i 0.799843 0.600209i \(-0.204916\pi\)
−0.919718 + 0.392580i \(0.871583\pi\)
\(72\) −9.12791 −1.07573
\(73\) −1.88689 −0.220844 −0.110422 0.993885i \(-0.535220\pi\)
−0.110422 + 0.993885i \(0.535220\pi\)
\(74\) −2.11024 −0.245311
\(75\) 0.442248 + 0.765996i 0.0510664 + 0.0884496i
\(76\) −1.84107 1.75962i −0.211185 0.201842i
\(77\) −0.735764 2.15105i −0.0838481 0.245135i
\(78\) 0.311230 + 0.539066i 0.0352398 + 0.0610372i
\(79\) 2.06547 3.57749i 0.232383 0.402499i −0.726126 0.687562i \(-0.758681\pi\)
0.958509 + 0.285062i \(0.0920144\pi\)
\(80\) 0.142167 + 0.246241i 0.0158948 + 0.0275306i
\(81\) 8.71787 0.968653
\(82\) −13.0734 −1.44372
\(83\) 14.0092 1.53771 0.768855 0.639423i \(-0.220827\pi\)
0.768855 + 0.639423i \(0.220827\pi\)
\(84\) 0.269022 + 0.0528619i 0.0293527 + 0.00576771i
\(85\) 0.207232 0.358936i 0.0224775 0.0389321i
\(86\) 13.2464 1.42839
\(87\) 0.544392 0.942915i 0.0583650 0.101091i
\(88\) 1.32107 2.28816i 0.140826 0.243919i
\(89\) 10.2607 1.08763 0.543817 0.839204i \(-0.316979\pi\)
0.543817 + 0.839204i \(0.316979\pi\)
\(90\) −0.201657 0.349280i −0.0212565 0.0368174i
\(91\) 2.52563 + 7.38384i 0.264758 + 0.774037i
\(92\) −0.280166 0.485262i −0.0292093 0.0505920i
\(93\) −0.498566 + 0.863542i −0.0516989 + 0.0895452i
\(94\) 0.602909 1.04427i 0.0621853 0.107708i
\(95\) 0.117914 0.483551i 0.0120977 0.0496112i
\(96\) 0.282615 + 0.489504i 0.0288443 + 0.0499598i
\(97\) −5.41182 9.37356i −0.549488 0.951740i −0.998310 0.0581193i \(-0.981490\pi\)
0.448822 0.893621i \(-0.351844\pi\)
\(98\) −7.70968 3.15154i −0.778795 0.318354i
\(99\) −1.27538 + 2.20903i −0.128181 + 0.222016i
\(100\) −1.45684 + 2.52331i −0.145684 + 0.252331i
\(101\) 5.64751 + 9.78177i 0.561948 + 0.973323i 0.997326 + 0.0730752i \(0.0232813\pi\)
−0.435378 + 0.900248i \(0.643385\pi\)
\(102\) −0.383002 + 0.663378i −0.0379228 + 0.0656843i
\(103\) 5.86343 + 10.1558i 0.577741 + 1.00068i 0.995738 + 0.0922282i \(0.0293989\pi\)
−0.417997 + 0.908448i \(0.637268\pi\)
\(104\) −4.53479 + 7.85449i −0.444673 + 0.770196i
\(105\) 0.0173412 + 0.0506980i 0.00169233 + 0.00494762i
\(106\) −9.49020 −0.921770
\(107\) 2.79121 + 4.83452i 0.269837 + 0.467371i 0.968820 0.247768i \(-0.0796969\pi\)
−0.698983 + 0.715139i \(0.746364\pi\)
\(108\) −0.309245 0.535628i −0.0297571 0.0515409i
\(109\) −8.68473 −0.831846 −0.415923 0.909400i \(-0.636541\pi\)
−0.415923 + 0.909400i \(0.636541\pi\)
\(110\) 0.116742 0.0111309
\(111\) −0.157279 0.272415i −0.0149282 0.0258565i
\(112\) −2.13222 6.23368i −0.201476 0.589027i
\(113\) −13.3461 −1.25550 −0.627749 0.778415i \(-0.716024\pi\)
−0.627749 + 0.778415i \(0.716024\pi\)
\(114\) −0.217926 + 0.893688i −0.0204107 + 0.0837016i
\(115\) 0.0547544 0.0948374i 0.00510587 0.00884363i
\(116\) 3.58663 0.333010
\(117\) 4.37797 7.58286i 0.404743 0.701036i
\(118\) 0.762833 1.32127i 0.0702245 0.121632i
\(119\) −6.31520 + 7.23496i −0.578913 + 0.663228i
\(120\) −0.0311362 + 0.0539295i −0.00284234 + 0.00492307i
\(121\) 5.13083 + 8.88686i 0.466439 + 0.807896i
\(122\) 5.65654 9.79741i 0.512119 0.887016i
\(123\) −0.974378 1.68767i −0.0878567 0.152172i
\(124\) −3.28471 −0.294976
\(125\) −1.14036 −0.101997
\(126\) 3.02445 + 8.84216i 0.269439 + 0.787722i
\(127\) −5.72401 + 9.91428i −0.507924 + 0.879750i 0.492034 + 0.870576i \(0.336254\pi\)
−0.999958 + 0.00917386i \(0.997080\pi\)
\(128\) 2.03190 3.51935i 0.179596 0.311069i
\(129\) 0.987267 + 1.71000i 0.0869240 + 0.150557i
\(130\) −0.400737 −0.0351470
\(131\) 3.67384 6.36328i 0.320985 0.555962i −0.659706 0.751523i \(-0.729319\pi\)
0.980692 + 0.195561i \(0.0626527\pi\)
\(132\) 0.0890415 0.00775007
\(133\) −4.84119 + 10.4672i −0.419784 + 0.907624i
\(134\) −8.92268 −0.770802
\(135\) 0.0604375 0.104681i 0.00520163 0.00900949i
\(136\) −11.1611 −0.957055
\(137\) −5.08162 8.80163i −0.434152 0.751974i 0.563074 0.826407i \(-0.309619\pi\)
−0.997226 + 0.0744330i \(0.976285\pi\)
\(138\) −0.101196 + 0.175276i −0.00861437 + 0.0149205i
\(139\) 3.37357 5.84319i 0.286142 0.495613i −0.686743 0.726900i \(-0.740960\pi\)
0.972886 + 0.231287i \(0.0742937\pi\)
\(140\) −0.116070 + 0.132975i −0.00980973 + 0.0112384i
\(141\) 0.179742 0.0151370
\(142\) −2.40369 −0.201713
\(143\) 1.26723 + 2.19491i 0.105971 + 0.183548i
\(144\) −3.69602 + 6.40170i −0.308002 + 0.533475i
\(145\) 0.350477 + 0.607044i 0.0291055 + 0.0504123i
\(146\) −1.12256 + 1.94433i −0.0929036 + 0.160914i
\(147\) −0.167773 1.23014i −0.0138377 0.101461i
\(148\) 0.518102 0.897378i 0.0425877 0.0737640i
\(149\) −1.17694 + 2.03852i −0.0964186 + 0.167002i −0.910200 0.414170i \(-0.864072\pi\)
0.813781 + 0.581171i \(0.197405\pi\)
\(150\) 1.05242 0.0859295
\(151\) −2.05996 + 3.56796i −0.167637 + 0.290357i −0.937589 0.347746i \(-0.886947\pi\)
0.769951 + 0.638103i \(0.220280\pi\)
\(152\) −12.8646 + 3.76086i −1.04346 + 0.305046i
\(153\) 10.7751 0.871116
\(154\) −2.65425 0.521553i −0.213886 0.0420279i
\(155\) −0.320975 0.555945i −0.0257813 0.0446546i
\(156\) −0.305650 −0.0244716
\(157\) −4.85746 −0.387667 −0.193834 0.981034i \(-0.562092\pi\)
−0.193834 + 0.981034i \(0.562092\pi\)
\(158\) −2.45759 4.25668i −0.195516 0.338643i
\(159\) −0.707316 1.22511i −0.0560938 0.0971573i
\(160\) −0.363893 −0.0287683
\(161\) −1.66859 + 1.91161i −0.131503 + 0.150656i
\(162\) 5.18648 8.98325i 0.407488 0.705791i
\(163\) −2.90722 5.03545i −0.227711 0.394407i 0.729418 0.684068i \(-0.239791\pi\)
−0.957129 + 0.289661i \(0.906457\pi\)
\(164\) 3.20976 5.55946i 0.250640 0.434121i
\(165\) 0.00870093 + 0.0150705i 0.000677367 + 0.00117323i
\(166\) 8.33442 14.4356i 0.646877 1.12042i
\(167\) −11.8892 + 20.5927i −0.920014 + 1.59351i −0.120625 + 0.992698i \(0.538490\pi\)
−0.799390 + 0.600813i \(0.794844\pi\)
\(168\) 0.948847 1.08704i 0.0732052 0.0838670i
\(169\) 2.15001 + 3.72392i 0.165385 + 0.286456i
\(170\) −0.246575 0.427080i −0.0189114 0.0327556i
\(171\) 12.4197 3.63081i 0.949761 0.277655i
\(172\) −3.25222 + 5.63300i −0.247979 + 0.429512i
\(173\) 0.396238 0.686304i 0.0301254 0.0521787i −0.850570 0.525862i \(-0.823743\pi\)
0.880695 + 0.473684i \(0.157076\pi\)
\(174\) −0.647745 1.12193i −0.0491054 0.0850530i
\(175\) 12.9467 + 2.54398i 0.978677 + 0.192307i
\(176\) −1.06984 1.85302i −0.0806423 0.139677i
\(177\) 0.227419 0.0170939
\(178\) 6.10435 10.5731i 0.457541 0.792484i
\(179\) 5.74256 9.94641i 0.429219 0.743430i −0.567585 0.823315i \(-0.692122\pi\)
0.996804 + 0.0798853i \(0.0254554\pi\)
\(180\) 0.198041 0.0147611
\(181\) 10.8465 18.7867i 0.806217 1.39641i −0.109250 0.994014i \(-0.534845\pi\)
0.915467 0.402394i \(-0.131822\pi\)
\(182\) 9.11116 + 1.79032i 0.675364 + 0.132707i
\(183\) 1.68635 0.124659
\(184\) −2.94896 −0.217400
\(185\) 0.202511 0.0148889
\(186\) 0.593219 + 1.02749i 0.0434969 + 0.0753389i
\(187\) −1.55947 + 2.70108i −0.114040 + 0.197522i
\(188\) 0.296049 + 0.512773i 0.0215916 + 0.0373978i
\(189\) −1.84178 + 2.11002i −0.133969 + 0.153481i
\(190\) −0.428120 0.409180i −0.0310591 0.0296850i
\(191\) 9.24598 + 16.0145i 0.669015 + 1.15877i 0.978180 + 0.207760i \(0.0666174\pi\)
−0.309164 + 0.951009i \(0.600049\pi\)
\(192\) 1.55585 0.112284
\(193\) 15.6194 1.12431 0.562156 0.827031i \(-0.309972\pi\)
0.562156 + 0.827031i \(0.309972\pi\)
\(194\) −12.8785 −0.924624
\(195\) −0.0298674 0.0517318i −0.00213885 0.00370459i
\(196\) 3.23305 2.50477i 0.230932 0.178912i
\(197\) −7.44363 −0.530336 −0.265168 0.964202i \(-0.585427\pi\)
−0.265168 + 0.964202i \(0.585427\pi\)
\(198\) 1.51752 + 2.62841i 0.107845 + 0.186793i
\(199\) −5.59170 9.68510i −0.396385 0.686559i 0.596892 0.802322i \(-0.296402\pi\)
−0.993277 + 0.115763i \(0.963069\pi\)
\(200\) 7.66715 + 13.2799i 0.542149 + 0.939030i
\(201\) −0.665018 1.15184i −0.0469067 0.0812448i
\(202\) 13.4394 0.945591
\(203\) −5.25645 15.3676i −0.368931 1.07859i
\(204\) −0.188067 0.325742i −0.0131673 0.0228065i
\(205\) 1.25460 0.0876251
\(206\) 13.9532 0.972165
\(207\) 2.84698 0.197879
\(208\) 3.67241 + 6.36079i 0.254636 + 0.441042i
\(209\) −0.887331 + 3.63883i −0.0613780 + 0.251703i
\(210\) 0.0625580 + 0.0122925i 0.00431691 + 0.000848260i
\(211\) −0.271262 0.469839i −0.0186744 0.0323451i 0.856537 0.516085i \(-0.172611\pi\)
−0.875212 + 0.483740i \(0.839278\pi\)
\(212\) 2.33001 4.03570i 0.160026 0.277173i
\(213\) −0.179150 0.310296i −0.0122751 0.0212611i
\(214\) 6.64225 0.454055
\(215\) −1.27120 −0.0866949
\(216\) −3.25504 −0.221477
\(217\) 4.81398 + 14.0739i 0.326794 + 0.955402i
\(218\) −5.16676 + 8.94909i −0.349937 + 0.606109i
\(219\) −0.334663 −0.0226144
\(220\) −0.0286623 + 0.0496445i −0.00193241 + 0.00334703i
\(221\) 5.35313 9.27189i 0.360091 0.623695i
\(222\) −0.374276 −0.0251198
\(223\) 0.382864 + 0.663140i 0.0256385 + 0.0444072i 0.878560 0.477632i \(-0.158505\pi\)
−0.852921 + 0.522039i \(0.825171\pi\)
\(224\) 8.27348 + 1.62571i 0.552795 + 0.108623i
\(225\) −7.40200 12.8206i −0.493467 0.854710i
\(226\) −7.93995 + 13.7524i −0.528157 + 0.914796i
\(227\) 5.75298 9.96445i 0.381839 0.661364i −0.609486 0.792796i \(-0.708624\pi\)
0.991325 + 0.131432i \(0.0419577\pi\)
\(228\) −0.326535 0.312089i −0.0216253 0.0206686i
\(229\) −11.3569 19.6707i −0.750483 1.29987i −0.947589 0.319492i \(-0.896488\pi\)
0.197106 0.980382i \(-0.436846\pi\)
\(230\) −0.0651495 0.112842i −0.00429583 0.00744060i
\(231\) −0.130496 0.381514i −0.00858604 0.0251018i
\(232\) 9.43799 16.3471i 0.619635 1.07324i
\(233\) −1.24143 + 2.15022i −0.0813289 + 0.140866i −0.903821 0.427911i \(-0.859250\pi\)
0.822492 + 0.568777i \(0.192583\pi\)
\(234\) −5.20912 9.02247i −0.340531 0.589817i
\(235\) −0.0578586 + 0.100214i −0.00377428 + 0.00653724i
\(236\) 0.374578 + 0.648788i 0.0243829 + 0.0422325i
\(237\) 0.366335 0.634510i 0.0237960 0.0412159i
\(238\) 3.69813 + 10.8117i 0.239714 + 0.700818i
\(239\) −22.6283 −1.46371 −0.731853 0.681463i \(-0.761344\pi\)
−0.731853 + 0.681463i \(0.761344\pi\)
\(240\) 0.0252150 + 0.0436737i 0.00162762 + 0.00281913i
\(241\) −10.5295 18.2376i −0.678262 1.17478i −0.975504 0.219982i \(-0.929400\pi\)
0.297242 0.954802i \(-0.403933\pi\)
\(242\) 12.2098 0.784878
\(243\) 4.72199 0.302916
\(244\) 2.77756 + 4.81087i 0.177815 + 0.307985i
\(245\) 0.739865 + 0.302440i 0.0472682 + 0.0193222i
\(246\) −2.31873 −0.147837
\(247\) 3.04591 12.4909i 0.193807 0.794776i
\(248\) −8.64353 + 14.9710i −0.548864 + 0.950661i
\(249\) 2.48470 0.157461
\(250\) −0.678428 + 1.17507i −0.0429075 + 0.0743180i
\(251\) −6.00759 + 10.4055i −0.379196 + 0.656787i −0.990945 0.134265i \(-0.957133\pi\)
0.611750 + 0.791052i \(0.290466\pi\)
\(252\) −4.50267 0.884762i −0.283642 0.0557347i
\(253\) −0.412039 + 0.713673i −0.0259047 + 0.0448682i
\(254\) 6.81071 + 11.7965i 0.427342 + 0.740178i
\(255\) 0.0367550 0.0636616i 0.00230169 0.00398664i
\(256\) 6.35451 + 11.0063i 0.397157 + 0.687896i
\(257\) −25.5551 −1.59408 −0.797041 0.603925i \(-0.793603\pi\)
−0.797041 + 0.603925i \(0.793603\pi\)
\(258\) 2.34940 0.146267
\(259\) −4.60429 0.904729i −0.286097 0.0562171i
\(260\) 0.0983880 0.170413i 0.00610176 0.0105686i
\(261\) −9.11161 + 15.7818i −0.563994 + 0.976867i
\(262\) −4.37132 7.57135i −0.270061 0.467759i
\(263\) −29.4409 −1.81540 −0.907701 0.419617i \(-0.862164\pi\)
−0.907701 + 0.419617i \(0.862164\pi\)
\(264\) 0.234307 0.405832i 0.0144206 0.0249772i
\(265\) 0.910734 0.0559459
\(266\) 7.90571 + 11.2158i 0.484730 + 0.687683i
\(267\) 1.81986 0.111374
\(268\) 2.19067 3.79436i 0.133817 0.231777i
\(269\) 8.66452 0.528285 0.264143 0.964484i \(-0.414911\pi\)
0.264143 + 0.964484i \(0.414911\pi\)
\(270\) −0.0719115 0.124554i −0.00437640 0.00758014i
\(271\) −4.39911 + 7.61949i −0.267227 + 0.462851i −0.968145 0.250391i \(-0.919441\pi\)
0.700918 + 0.713242i \(0.252774\pi\)
\(272\) −4.51929 + 7.82764i −0.274022 + 0.474620i
\(273\) 0.447951 + 1.30961i 0.0271112 + 0.0792612i
\(274\) −12.0927 −0.730548
\(275\) 4.28513 0.258403
\(276\) −0.0496908 0.0860669i −0.00299103 0.00518062i
\(277\) −11.6029 + 20.0967i −0.697148 + 1.20750i 0.272303 + 0.962211i \(0.412215\pi\)
−0.969451 + 0.245284i \(0.921119\pi\)
\(278\) −4.01404 6.95252i −0.240746 0.416984i
\(279\) 8.34461 14.4533i 0.499579 0.865296i
\(280\) 0.300640 + 0.878939i 0.0179667 + 0.0525267i
\(281\) −0.0951519 + 0.164808i −0.00567629 + 0.00983162i −0.868850 0.495076i \(-0.835140\pi\)
0.863173 + 0.504908i \(0.168473\pi\)
\(282\) 0.106933 0.185213i 0.00636777 0.0110293i
\(283\) 23.5838 1.40191 0.700956 0.713204i \(-0.252757\pi\)
0.700956 + 0.713204i \(0.252757\pi\)
\(284\) 0.590147 1.02216i 0.0350188 0.0606543i
\(285\) 0.0209135 0.0857634i 0.00123881 0.00508019i
\(286\) 3.01564 0.178318
\(287\) −28.5246 5.60500i −1.68375 0.330853i
\(288\) −4.73020 8.19294i −0.278729 0.482774i
\(289\) −3.82480 −0.224988
\(290\) 0.834030 0.0489759
\(291\) −0.959851 1.66251i −0.0562675 0.0974581i
\(292\) −0.551216 0.954734i −0.0322575 0.0558716i
\(293\) −26.5936 −1.55362 −0.776808 0.629737i \(-0.783163\pi\)
−0.776808 + 0.629737i \(0.783163\pi\)
\(294\) −1.36740 0.558963i −0.0797485 0.0325994i
\(295\) −0.0732058 + 0.126796i −0.00426221 + 0.00738236i
\(296\) −2.72671 4.72279i −0.158487 0.274507i
\(297\) −0.454806 + 0.787747i −0.0263905 + 0.0457097i
\(298\) 1.40038 + 2.42553i 0.0811218 + 0.140507i
\(299\) 1.41439 2.44980i 0.0817965 0.141676i
\(300\) −0.258387 + 0.447540i −0.0149180 + 0.0258387i
\(301\) 28.9020 + 5.67915i 1.66588 + 0.327341i
\(302\) 2.45105 + 4.24534i 0.141042 + 0.244292i
\(303\) 1.00165 + 1.73491i 0.0575434 + 0.0996681i
\(304\) −2.57146 + 10.5452i −0.147483 + 0.604809i
\(305\) −0.542833 + 0.940215i −0.0310826 + 0.0538366i
\(306\) 6.41038 11.1031i 0.366457 0.634723i
\(307\) 9.48346 + 16.4258i 0.541250 + 0.937472i 0.998833 + 0.0483048i \(0.0153819\pi\)
−0.457583 + 0.889167i \(0.651285\pi\)
\(308\) 0.873456 1.00067i 0.0497697 0.0570184i
\(309\) 1.03995 + 1.80124i 0.0591606 + 0.102469i
\(310\) −0.763824 −0.0433823
\(311\) −14.9039 + 25.8143i −0.845124 + 1.46380i 0.0403901 + 0.999184i \(0.487140\pi\)
−0.885514 + 0.464613i \(0.846193\pi\)
\(312\) −0.804298 + 1.39309i −0.0455344 + 0.0788679i
\(313\) 16.7240 0.945299 0.472649 0.881251i \(-0.343298\pi\)
0.472649 + 0.881251i \(0.343298\pi\)
\(314\) −2.88982 + 5.00532i −0.163082 + 0.282466i
\(315\) −0.290243 0.848544i −0.0163534 0.0478100i
\(316\) 2.41353 0.135772
\(317\) 9.17717 0.515441 0.257721 0.966219i \(-0.417029\pi\)
0.257721 + 0.966219i \(0.417029\pi\)
\(318\) −1.68320 −0.0943891
\(319\) −2.63742 4.56815i −0.147667 0.255767i
\(320\) −0.500824 + 0.867452i −0.0279969 + 0.0484920i
\(321\) 0.495055 + 0.857460i 0.0276313 + 0.0478587i
\(322\) 0.977111 + 2.85664i 0.0544523 + 0.159194i
\(323\) 15.1862 4.43954i 0.844980 0.247023i
\(324\) 2.54674 + 4.41109i 0.141486 + 0.245061i
\(325\) −14.7094 −0.815931
\(326\) −6.91830 −0.383169
\(327\) −1.54034 −0.0851809
\(328\) −16.8925 29.2588i −0.932735 1.61554i
\(329\) 1.76319 2.01998i 0.0972075 0.111365i
\(330\) 0.0207056 0.00113981
\(331\) −8.41959 14.5832i −0.462783 0.801563i 0.536316 0.844017i \(-0.319816\pi\)
−0.999098 + 0.0424544i \(0.986482\pi\)
\(332\) 4.09250 + 7.08841i 0.224605 + 0.389027i
\(333\) 2.63241 + 4.55947i 0.144255 + 0.249857i
\(334\) 14.1464 + 24.5022i 0.774055 + 1.34070i
\(335\) 0.856271 0.0467831
\(336\) −0.378175 1.10562i −0.0206311 0.0603163i
\(337\) 6.35605 + 11.0090i 0.346236 + 0.599699i 0.985578 0.169224i \(-0.0541263\pi\)
−0.639341 + 0.768923i \(0.720793\pi\)
\(338\) 5.11637 0.278294
\(339\) −2.36709 −0.128563
\(340\) 0.242154 0.0131326
\(341\) 2.41541 + 4.18361i 0.130802 + 0.226555i
\(342\) 3.64748 14.9579i 0.197233 0.808828i
\(343\) −15.4704 10.1817i −0.835324 0.549758i
\(344\) 17.1160 + 29.6458i 0.922834 + 1.59839i
\(345\) 0.00971134 0.0168205i 0.000522841 0.000905587i
\(346\) −0.471463 0.816598i −0.0253460 0.0439006i
\(347\) −4.62457 −0.248260 −0.124130 0.992266i \(-0.539614\pi\)
−0.124130 + 0.992266i \(0.539614\pi\)
\(348\) 0.636131 0.0341002
\(349\) 7.10208 0.380166 0.190083 0.981768i \(-0.439124\pi\)
0.190083 + 0.981768i \(0.439124\pi\)
\(350\) 10.3237 11.8273i 0.551826 0.632196i
\(351\) 1.56120 2.70407i 0.0833305 0.144333i
\(352\) 2.73838 0.145956
\(353\) 7.60757 13.1767i 0.404910 0.701325i −0.589401 0.807841i \(-0.700636\pi\)
0.994311 + 0.106516i \(0.0339696\pi\)
\(354\) 0.135297 0.234342i 0.00719098 0.0124551i
\(355\) 0.230671 0.0122428
\(356\) 2.99745 + 5.19174i 0.158865 + 0.275162i
\(357\) −1.12007 + 1.28321i −0.0592806 + 0.0679144i
\(358\) −6.83279 11.8347i −0.361124 0.625485i
\(359\) 12.7615 22.1035i 0.673525 1.16658i −0.303372 0.952872i \(-0.598113\pi\)
0.976898 0.213708i \(-0.0685541\pi\)
\(360\) 0.521134 0.902630i 0.0274662 0.0475728i
\(361\) 16.0081 10.2343i 0.842531 0.538648i
\(362\) −12.9057 22.3534i −0.678311 1.17487i
\(363\) 0.910013 + 1.57619i 0.0477633 + 0.0827285i
\(364\) −2.99828 + 3.43496i −0.157153 + 0.180041i
\(365\) 0.107727 0.186589i 0.00563870 0.00976651i
\(366\) 1.00325 1.73769i 0.0524409 0.0908303i
\(367\) 1.94322 + 3.36575i 0.101435 + 0.175691i 0.912276 0.409576i \(-0.134323\pi\)
−0.810841 + 0.585267i \(0.800990\pi\)
\(368\) −1.19408 + 2.06820i −0.0622456 + 0.107812i
\(369\) 16.3084 + 28.2469i 0.848980 + 1.47048i
\(370\) 0.120479 0.208675i 0.00626339 0.0108485i
\(371\) −20.7065 4.06876i −1.07503 0.211239i
\(372\) −0.582583 −0.0302055
\(373\) −6.24975 10.8249i −0.323600 0.560492i 0.657628 0.753343i \(-0.271560\pi\)
−0.981228 + 0.192851i \(0.938227\pi\)
\(374\) 1.85553 + 3.21388i 0.0959473 + 0.166186i
\(375\) −0.202256 −0.0104445
\(376\) 3.11614 0.160703
\(377\) 9.05338 + 15.6809i 0.466273 + 0.807609i
\(378\) 1.07853 + 3.15314i 0.0554735 + 0.162180i
\(379\) 9.69449 0.497972 0.248986 0.968507i \(-0.419903\pi\)
0.248986 + 0.968507i \(0.419903\pi\)
\(380\) 0.279114 0.0815967i 0.0143183 0.00418582i
\(381\) −1.01522 + 1.75841i −0.0520113 + 0.0900863i
\(382\) 22.0026 1.12575
\(383\) 0.642289 1.11248i 0.0328194 0.0568449i −0.849149 0.528153i \(-0.822885\pi\)
0.881969 + 0.471308i \(0.156218\pi\)
\(384\) 0.360381 0.624198i 0.0183906 0.0318535i
\(385\) 0.254717 + 0.0500512i 0.0129816 + 0.00255084i
\(386\) 9.29239 16.0949i 0.472970 0.819209i
\(387\) −16.5241 28.6206i −0.839968 1.45487i
\(388\) 3.16190 5.47657i 0.160521 0.278031i
\(389\) −14.8987 25.8054i −0.755396 1.30838i −0.945177 0.326557i \(-0.894111\pi\)
0.189782 0.981826i \(-0.439222\pi\)
\(390\) −0.0710754 −0.00359904
\(391\) 3.48112 0.176048
\(392\) −2.90865 21.3267i −0.146909 1.07716i
\(393\) 0.651599 1.12860i 0.0328688 0.0569305i
\(394\) −4.42840 + 7.67021i −0.223099 + 0.386420i
\(395\) 0.235845 + 0.408495i 0.0118666 + 0.0205536i
\(396\) −1.49031 −0.0748907
\(397\) −11.2031 + 19.4043i −0.562268 + 0.973876i 0.435031 + 0.900416i \(0.356738\pi\)
−0.997298 + 0.0734604i \(0.976596\pi\)
\(398\) −13.3066 −0.666997
\(399\) −0.858642 + 1.85649i −0.0429859 + 0.0929406i
\(400\) 12.4182 0.620908
\(401\) −12.6531 + 21.9159i −0.631868 + 1.09443i 0.355301 + 0.934752i \(0.384378\pi\)
−0.987170 + 0.159676i \(0.948955\pi\)
\(402\) −1.58254 −0.0789300
\(403\) −8.29129 14.3609i −0.413019 0.715369i
\(404\) −3.29960 + 5.71508i −0.164161 + 0.284336i
\(405\) −0.497724 + 0.862084i −0.0247321 + 0.0428373i
\(406\) −18.9625 3.72608i −0.941095 0.184922i
\(407\) −1.52394 −0.0755389
\(408\) −1.97955 −0.0980024
\(409\) 9.08706 + 15.7392i 0.449326 + 0.778256i 0.998342 0.0575562i \(-0.0183308\pi\)
−0.549016 + 0.835812i \(0.684997\pi\)
\(410\) 0.746393 1.29279i 0.0368617 0.0638464i
\(411\) −0.901285 1.56107i −0.0444571 0.0770020i
\(412\) −3.42576 + 5.93358i −0.168775 + 0.292327i
\(413\) 2.23088 2.55579i 0.109774 0.125762i
\(414\) 1.69374 2.93364i 0.0832427 0.144181i
\(415\) −0.799819 + 1.38533i −0.0392616 + 0.0680030i
\(416\) −9.39994 −0.460870
\(417\) 0.598342 1.03636i 0.0293009 0.0507507i
\(418\) 3.22170 + 3.07917i 0.157578 + 0.150607i
\(419\) 30.9918 1.51405 0.757023 0.653388i \(-0.226653\pi\)
0.757023 + 0.653388i \(0.226653\pi\)
\(420\) −0.0205864 + 0.0235847i −0.00100452 + 0.00115082i
\(421\) 19.9882 + 34.6206i 0.974167 + 1.68731i 0.682657 + 0.730739i \(0.260824\pi\)
0.291510 + 0.956568i \(0.405842\pi\)
\(422\) −0.645522 −0.0314235
\(423\) −3.00838 −0.146272
\(424\) −12.2626 21.2394i −0.595523 1.03148i
\(425\) −9.05075 15.6764i −0.439026 0.760415i
\(426\) −0.426322 −0.0206554
\(427\) 16.5423 18.9516i 0.800540 0.917133i
\(428\) −1.63079 + 2.82461i −0.0788272 + 0.136533i
\(429\) 0.224759 + 0.389294i 0.0108515 + 0.0187953i
\(430\) −0.756266 + 1.30989i −0.0364704 + 0.0631686i
\(431\) 6.84363 + 11.8535i 0.329646 + 0.570964i 0.982442 0.186570i \(-0.0597372\pi\)
−0.652795 + 0.757534i \(0.726404\pi\)
\(432\) −1.31801 + 2.28287i −0.0634129 + 0.109834i
\(433\) 0.272024 0.471159i 0.0130726 0.0226424i −0.859415 0.511278i \(-0.829172\pi\)
0.872488 + 0.488636i \(0.162505\pi\)
\(434\) 17.3663 + 3.41243i 0.833610 + 0.163802i
\(435\) 0.0621613 + 0.107666i 0.00298040 + 0.00516221i
\(436\) −2.53706 4.39432i −0.121503 0.210450i
\(437\) 4.01245 1.17301i 0.191942 0.0561125i
\(438\) −0.199099 + 0.344850i −0.00951332 + 0.0164776i
\(439\) 18.0862 31.3262i 0.863207 1.49512i −0.00560994 0.999984i \(-0.501786\pi\)
0.868817 0.495134i \(-0.164881\pi\)
\(440\) 0.150846 + 0.261273i 0.00719130 + 0.0124557i
\(441\) 2.80806 + 20.5892i 0.133717 + 0.980438i
\(442\) −6.36942 11.0322i −0.302962 0.524746i
\(443\) 28.3388 1.34642 0.673210 0.739452i \(-0.264915\pi\)
0.673210 + 0.739452i \(0.264915\pi\)
\(444\) 0.0918914 0.159161i 0.00436097 0.00755343i
\(445\) −0.585809 + 1.01465i −0.0277700 + 0.0480990i
\(446\) 0.911102 0.0431419
\(447\) −0.208744 + 0.361555i −0.00987325 + 0.0171010i
\(448\) 15.2621 17.4849i 0.721068 0.826086i
\(449\) −18.3226 −0.864699 −0.432350 0.901706i \(-0.642315\pi\)
−0.432350 + 0.901706i \(0.642315\pi\)
\(450\) −17.6145 −0.830358
\(451\) −9.44115 −0.444566
\(452\) −3.89879 6.75291i −0.183384 0.317630i
\(453\) −0.365359 + 0.632820i −0.0171661 + 0.0297325i
\(454\) −6.84518 11.8562i −0.321260 0.556439i
\(455\) −0.874359 0.171809i −0.0409906 0.00805453i
\(456\) −2.28169 + 0.667034i −0.106850 + 0.0312367i
\(457\) 8.23493 + 14.2633i 0.385214 + 0.667210i 0.991799 0.127809i \(-0.0407943\pi\)
−0.606585 + 0.795019i \(0.707461\pi\)
\(458\) −27.0259 −1.26284
\(459\) 3.84244 0.179350
\(460\) 0.0639814 0.00298315
\(461\) −9.03040 15.6411i −0.420587 0.728479i 0.575410 0.817865i \(-0.304843\pi\)
−0.995997 + 0.0893866i \(0.971509\pi\)
\(462\) −0.470763 0.0925035i −0.0219019 0.00430365i
\(463\) 4.32242 0.200880 0.100440 0.994943i \(-0.467975\pi\)
0.100440 + 0.994943i \(0.467975\pi\)
\(464\) −7.64316 13.2383i −0.354825 0.614575i
\(465\) −0.0569287 0.0986034i −0.00264000 0.00457262i
\(466\) 1.47712 + 2.55844i 0.0684262 + 0.118518i
\(467\) 18.6575 + 32.3157i 0.863366 + 1.49539i 0.868660 + 0.495408i \(0.164982\pi\)
−0.00529373 + 0.999986i \(0.501685\pi\)
\(468\) 5.11573 0.236474
\(469\) −19.4682 3.82544i −0.898958 0.176642i
\(470\) 0.0688430 + 0.119240i 0.00317549 + 0.00550011i
\(471\) −0.861527 −0.0396971
\(472\) 3.94272 0.181478
\(473\) 9.56604 0.439847
\(474\) −0.435883 0.754972i −0.0200208 0.0346770i
\(475\) −15.7145 15.0193i −0.721032 0.689133i
\(476\) −5.50561 1.08184i −0.252349 0.0495859i
\(477\) 11.8385 + 20.5049i 0.542048 + 0.938854i
\(478\) −13.4622 + 23.3171i −0.615745 + 1.06650i
\(479\) 17.8369 + 30.8944i 0.814988 + 1.41160i 0.909336 + 0.416062i \(0.136590\pi\)
−0.0943480 + 0.995539i \(0.530077\pi\)
\(480\) −0.0645407 −0.00294587
\(481\) 5.23118 0.238521
\(482\) −25.0569 −1.14131
\(483\) −0.295944 + 0.339046i −0.0134659 + 0.0154271i
\(484\) −2.99773 + 5.19222i −0.136260 + 0.236010i
\(485\) 1.23590 0.0561191
\(486\) 2.80923 4.86573i 0.127429 0.220714i
\(487\) −20.1877 + 34.9662i −0.914794 + 1.58447i −0.107592 + 0.994195i \(0.534314\pi\)
−0.807202 + 0.590275i \(0.799019\pi\)
\(488\) 29.2359 1.32345
\(489\) −0.515629 0.893096i −0.0233176 0.0403872i
\(490\) 0.751810 0.582457i 0.0339633 0.0263127i
\(491\) −12.3300 21.3563i −0.556447 0.963794i −0.997789 0.0664556i \(-0.978831\pi\)
0.441342 0.897339i \(-0.354502\pi\)
\(492\) 0.569288 0.986036i 0.0256655 0.0444539i
\(493\) −11.1412 + 19.2971i −0.501773 + 0.869095i
\(494\) −11.0590 10.5698i −0.497569 0.475556i
\(495\) −0.145629 0.252238i −0.00654556 0.0113372i
\(496\) 6.99978 + 12.1240i 0.314299 + 0.544383i
\(497\) −5.24455 1.03054i −0.235250 0.0462259i
\(498\) 1.47821 2.56033i 0.0662401 0.114731i
\(499\) 19.4722 33.7268i 0.871696 1.50982i 0.0114541 0.999934i \(-0.496354\pi\)
0.860242 0.509887i \(-0.170313\pi\)
\(500\) −0.333132 0.577001i −0.0148981 0.0258043i
\(501\) −2.10869 + 3.65236i −0.0942093 + 0.163175i
\(502\) 7.14813 + 12.3809i 0.319037 + 0.552588i
\(503\) −6.02290 + 10.4320i −0.268548 + 0.465139i −0.968487 0.249064i \(-0.919877\pi\)
0.699939 + 0.714203i \(0.253210\pi\)
\(504\) −15.8811 + 18.1940i −0.707399 + 0.810426i
\(505\) −1.28972 −0.0573917
\(506\) 0.490265 + 0.849163i 0.0217949 + 0.0377499i
\(507\) 0.381329 + 0.660482i 0.0169354 + 0.0293330i
\(508\) −6.68860 −0.296759
\(509\) 39.8346 1.76564 0.882819 0.469713i \(-0.155643\pi\)
0.882819 + 0.469713i \(0.155643\pi\)
\(510\) −0.0437330 0.0757477i −0.00193653 0.00335416i
\(511\) −3.28288 + 3.76101i −0.145226 + 0.166377i
\(512\) 23.2494 1.02749
\(513\) 4.42892 1.29476i 0.195541 0.0571649i
\(514\) −15.2034 + 26.3330i −0.670591 + 1.16150i
\(515\) −1.33903 −0.0590046
\(516\) −0.576819 + 0.999079i −0.0253930 + 0.0439820i
\(517\) 0.435399 0.754133i 0.0191488 0.0331667i
\(518\) −3.67148 + 4.20620i −0.161315 + 0.184810i
\(519\) 0.0702774 0.121724i 0.00308484 0.00534309i
\(520\) −0.517804 0.896863i −0.0227072 0.0393300i
\(521\) 7.70499 13.3454i 0.337562 0.584674i −0.646412 0.762989i \(-0.723731\pi\)
0.983973 + 0.178315i \(0.0570645\pi\)
\(522\) 10.8414 + 18.7779i 0.474517 + 0.821888i
\(523\) −29.2537 −1.27918 −0.639589 0.768717i \(-0.720895\pi\)
−0.639589 + 0.768717i \(0.720895\pi\)
\(524\) 4.29294 0.187538
\(525\) 2.29625 + 0.451206i 0.100216 + 0.0196922i
\(526\) −17.5151 + 30.3371i −0.763695 + 1.32276i
\(527\) 10.2033 17.6727i 0.444464 0.769834i
\(528\) −0.189749 0.328655i −0.00825776 0.0143029i
\(529\) −22.0802 −0.960010
\(530\) 0.541818 0.938456i 0.0235351 0.0407639i
\(531\) −3.80637 −0.165182
\(532\) −6.71048 + 0.608225i −0.290936 + 0.0263699i
\(533\) 32.4083 1.40376
\(534\) 1.08268 1.87526i 0.0468521 0.0811502i
\(535\) −0.637428 −0.0275584
\(536\) −11.5292 19.9692i −0.497988 0.862540i
\(537\) 1.01851 1.76411i 0.0439520 0.0761271i
\(538\) 5.15474 8.92827i 0.222237 0.384925i
\(539\) −5.56765 2.27593i −0.239816 0.0980312i
\(540\) 0.0706222 0.00303909
\(541\) −23.5576 −1.01282 −0.506411 0.862292i \(-0.669028\pi\)
−0.506411 + 0.862292i \(0.669028\pi\)
\(542\) 5.23428 + 9.06604i 0.224832 + 0.389420i
\(543\) 1.92376 3.33205i 0.0825565 0.142992i
\(544\) −5.78381 10.0179i −0.247979 0.429512i
\(545\) 0.495832 0.858806i 0.0212391 0.0367872i
\(546\) 1.61597 + 0.317534i 0.0691572 + 0.0135892i
\(547\) 12.4410 21.5485i 0.531940 0.921347i −0.467365 0.884064i \(-0.654797\pi\)
0.999305 0.0372821i \(-0.0118700\pi\)
\(548\) 2.96898 5.14242i 0.126828 0.219673i
\(549\) −28.2249 −1.20461
\(550\) 2.54933 4.41557i 0.108704 0.188280i
\(551\) −6.33928 + 25.9965i −0.270062 + 1.10749i
\(552\) −0.523033 −0.0222617
\(553\) −3.53720 10.3412i −0.150417 0.439753i
\(554\) 13.8057 + 23.9121i 0.586546 + 1.01593i
\(555\) 0.0359177 0.00152462
\(556\) 3.94207 0.167181
\(557\) 19.5163 + 33.8033i 0.826934 + 1.43229i 0.900432 + 0.434997i \(0.143250\pi\)
−0.0734978 + 0.997295i \(0.523416\pi\)
\(558\) −9.92884 17.1972i −0.420321 0.728018i
\(559\) −32.8370 −1.38886
\(560\) 0.738163 + 0.145047i 0.0311931 + 0.00612934i
\(561\) −0.276590 + 0.479068i −0.0116776 + 0.0202263i
\(562\) 0.113216 + 0.196097i 0.00477575 + 0.00827184i
\(563\) −13.0032 + 22.5222i −0.548020 + 0.949199i 0.450390 + 0.892832i \(0.351285\pi\)
−0.998410 + 0.0563667i \(0.982048\pi\)
\(564\) 0.0525078 + 0.0909463i 0.00221098 + 0.00382953i
\(565\) 0.761963 1.31976i 0.0320560 0.0555226i
\(566\) 14.0306 24.3017i 0.589750 1.02148i
\(567\) 15.1677 17.3767i 0.636982 0.729754i
\(568\) −3.10587 5.37953i −0.130319 0.225720i
\(569\) −1.79425 3.10773i −0.0752188 0.130283i 0.825963 0.563725i \(-0.190632\pi\)
−0.901181 + 0.433442i \(0.857299\pi\)
\(570\) −0.0759321 0.0725728i −0.00318045 0.00303974i
\(571\) −0.297305 + 0.514948i −0.0124418 + 0.0215499i −0.872179 0.489186i \(-0.837294\pi\)
0.859737 + 0.510736i \(0.170627\pi\)
\(572\) −0.740392 + 1.28240i −0.0309573 + 0.0536197i
\(573\) 1.63988 + 2.84036i 0.0685071 + 0.118658i
\(574\) −22.7456 + 26.0583i −0.949384 + 1.08765i
\(575\) −2.39137 4.14198i −0.0997271 0.172732i
\(576\) −26.0405 −1.08502
\(577\) −2.68994 + 4.65912i −0.111984 + 0.193962i −0.916570 0.399874i \(-0.869054\pi\)
0.804586 + 0.593836i \(0.202387\pi\)
\(578\) −2.27547 + 3.94123i −0.0946470 + 0.163933i
\(579\) 2.77029 0.115129
\(580\) −0.204769 + 0.354671i −0.00850258 + 0.0147269i
\(581\) 24.3737 27.9236i 1.01119 1.15847i
\(582\) −2.28416 −0.0946813
\(583\) −6.85348 −0.283842
\(584\) −5.80196 −0.240087
\(585\) 0.499897 + 0.865847i 0.0206682 + 0.0357984i
\(586\) −15.8212 + 27.4031i −0.653568 + 1.13201i
\(587\) 2.65579 + 4.59996i 0.109616 + 0.189861i 0.915615 0.402057i \(-0.131705\pi\)
−0.805999 + 0.591917i \(0.798371\pi\)
\(588\) 0.573420 0.444251i 0.0236474 0.0183206i
\(589\) 5.80565 23.8082i 0.239218 0.981000i
\(590\) 0.0871039 + 0.150868i 0.00358601 + 0.00621115i
\(591\) −1.32021 −0.0543064
\(592\) −4.41633 −0.181510
\(593\) −38.5157 −1.58165 −0.790826 0.612041i \(-0.790349\pi\)
−0.790826 + 0.612041i \(0.790349\pi\)
\(594\) 0.541151 + 0.937300i 0.0222037 + 0.0384579i
\(595\) −0.354893 1.03755i −0.0145492 0.0425355i
\(596\) −1.37527 −0.0563333
\(597\) −0.991753 1.71777i −0.0405897 0.0703035i
\(598\) −1.68291 2.91489i −0.0688195 0.119199i
\(599\) −8.46385 14.6598i −0.345824 0.598984i 0.639679 0.768642i \(-0.279067\pi\)
−0.985503 + 0.169658i \(0.945734\pi\)
\(600\) 1.35986 + 2.35535i 0.0555160 + 0.0961566i
\(601\) −33.3487 −1.36032 −0.680160 0.733064i \(-0.738090\pi\)
−0.680160 + 0.733064i \(0.738090\pi\)
\(602\) 23.0465 26.4031i 0.939306 1.07611i
\(603\) 11.1305 + 19.2787i 0.453271 + 0.785088i
\(604\) −2.40710 −0.0979435
\(605\) −1.17173 −0.0476374
\(606\) 2.38363 0.0968284
\(607\) −3.32915 5.76625i −0.135126 0.234045i 0.790520 0.612437i \(-0.209811\pi\)
−0.925646 + 0.378392i \(0.876477\pi\)
\(608\) −10.0422 9.59798i −0.407267 0.389249i
\(609\) −0.932294 2.72562i −0.0377784 0.110448i
\(610\) 0.645890 + 1.11871i 0.0261513 + 0.0452954i
\(611\) −1.49458 + 2.58869i −0.0604642 + 0.104727i
\(612\) 3.14772 + 5.45202i 0.127239 + 0.220385i
\(613\) 28.2774 1.14211 0.571057 0.820911i \(-0.306534\pi\)
0.571057 + 0.820911i \(0.306534\pi\)
\(614\) 22.5678 0.910761
\(615\) 0.222518 0.00897280
\(616\) −2.26239 6.61422i −0.0911541 0.266495i
\(617\) 15.2369 26.3911i 0.613415 1.06247i −0.377245 0.926113i \(-0.623129\pi\)
0.990660 0.136353i \(-0.0435380\pi\)
\(618\) 2.47476 0.0995496
\(619\) 17.5379 30.3766i 0.704909 1.22094i −0.261815 0.965118i \(-0.584321\pi\)
0.966724 0.255821i \(-0.0823457\pi\)
\(620\) 0.187532 0.324815i 0.00753147 0.0130449i
\(621\) 1.01524 0.0407402
\(622\) 17.7334 + 30.7152i 0.711045 + 1.23157i
\(623\) 17.8520 20.4520i 0.715224 0.819391i
\(624\) 0.651344 + 1.12816i 0.0260746 + 0.0451626i
\(625\) −12.4023 + 21.4814i −0.496092 + 0.859256i
\(626\) 9.94955 17.2331i 0.397664 0.688774i
\(627\) −0.157379 + 0.645389i −0.00628510 + 0.0257744i
\(628\) −1.41900 2.45779i −0.0566244 0.0980764i
\(629\) 3.21876 + 5.57506i 0.128340 + 0.222292i
\(630\) −1.04705 0.205741i −0.0417153 0.00819694i
\(631\) 14.0430 24.3233i 0.559044 0.968293i −0.438532 0.898716i \(-0.644501\pi\)
0.997577 0.0695778i \(-0.0221652\pi\)
\(632\) 6.35106 11.0004i 0.252631 0.437571i
\(633\) −0.0481115 0.0833315i −0.00191226 0.00331213i
\(634\) 5.45973 9.45652i 0.216833 0.375567i
\(635\) −0.653595 1.13206i −0.0259371 0.0449244i
\(636\) 0.413255 0.715778i 0.0163866 0.0283825i
\(637\) 19.1119 + 7.81250i 0.757240 + 0.309543i
\(638\) −6.27627 −0.248480
\(639\) 2.99846 + 5.19349i 0.118617 + 0.205451i
\(640\) 0.232012 + 0.401856i 0.00917106 + 0.0158847i
\(641\) 20.9010 0.825539 0.412770 0.910836i \(-0.364561\pi\)
0.412770 + 0.910836i \(0.364561\pi\)
\(642\) 1.17808 0.0464951
\(643\) 17.7357 + 30.7191i 0.699427 + 1.21144i 0.968665 + 0.248370i \(0.0798949\pi\)
−0.269238 + 0.963074i \(0.586772\pi\)
\(644\) −1.45468 0.285841i −0.0573225 0.0112637i
\(645\) −0.225462 −0.00887755
\(646\) 4.45994 18.2896i 0.175474 0.719595i
\(647\) 8.85659 15.3401i 0.348189 0.603080i −0.637739 0.770252i \(-0.720130\pi\)
0.985928 + 0.167172i \(0.0534636\pi\)
\(648\) 26.8064 1.05305
\(649\) 0.550890 0.954170i 0.0216243 0.0374545i
\(650\) −8.75099 + 15.1572i −0.343242 + 0.594513i
\(651\) 0.853815 + 2.49618i 0.0334637 + 0.0978330i
\(652\) 1.69856 2.94200i 0.0665209 0.115218i
\(653\) 7.88881 + 13.6638i 0.308713 + 0.534706i 0.978081 0.208224i \(-0.0667685\pi\)
−0.669368 + 0.742931i \(0.733435\pi\)
\(654\) −0.916386 + 1.58723i −0.0358335 + 0.0620655i
\(655\) 0.419497 + 0.726590i 0.0163911 + 0.0283902i
\(656\) −27.3602 −1.06823
\(657\) 5.60132 0.218528
\(658\) −1.03251 3.01859i −0.0402513 0.117677i
\(659\) −7.51139 + 13.0101i −0.292602 + 0.506802i −0.974424 0.224716i \(-0.927854\pi\)
0.681822 + 0.731518i \(0.261188\pi\)
\(660\) −0.00508359 + 0.00880504i −0.000197878 + 0.000342736i
\(661\) −7.82830 13.5590i −0.304485 0.527384i 0.672661 0.739951i \(-0.265151\pi\)
−0.977147 + 0.212566i \(0.931818\pi\)
\(662\) −20.0361 −0.778725
\(663\) 0.949441 1.64448i 0.0368732 0.0638663i
\(664\) 43.0766 1.67170
\(665\) −0.758677 1.07633i −0.0294202 0.0417383i
\(666\) 6.26434 0.242738
\(667\) −2.94369 + 5.09863i −0.113980 + 0.197420i
\(668\) −13.8927 −0.537526
\(669\) 0.0679055 + 0.117616i 0.00262538 + 0.00454729i
\(670\) 0.509417 0.882336i 0.0196805 0.0340876i
\(671\) 4.08495 7.07533i 0.157698 0.273140i
\(672\) 1.46740 + 0.288339i 0.0566062 + 0.0111229i
\(673\) −23.6359 −0.911099 −0.455549 0.890211i \(-0.650557\pi\)
−0.455549 + 0.890211i \(0.650557\pi\)
\(674\) 15.1255 0.582612
\(675\) −2.63958 4.57188i −0.101597 0.175972i
\(676\) −1.25616 + 2.17573i −0.0483138 + 0.0836820i
\(677\) −6.84401 11.8542i −0.263037 0.455593i 0.704011 0.710189i \(-0.251391\pi\)
−0.967047 + 0.254596i \(0.918057\pi\)
\(678\) −1.40824 + 2.43915i −0.0540833 + 0.0936749i
\(679\) −28.0994 5.52144i −1.07835 0.211893i
\(680\) 0.637213 1.10369i 0.0244360 0.0423244i
\(681\) 1.02036 1.76731i 0.0391002 0.0677236i
\(682\) 5.74795 0.220100
\(683\) −6.54467 + 11.3357i −0.250425 + 0.433749i −0.963643 0.267194i \(-0.913904\pi\)
0.713218 + 0.700942i \(0.247237\pi\)
\(684\) 5.46529 + 5.22350i 0.208971 + 0.199726i
\(685\) 1.16049 0.0443399
\(686\) −19.6953 + 9.88401i −0.751971 + 0.377373i
\(687\) −2.01427 3.48882i −0.0768493 0.133107i
\(688\) 27.7221 1.05690
\(689\) 23.5257 0.896258
\(690\) −0.0115550 0.0200139i −0.000439892 0.000761916i
\(691\) −20.6714 35.8039i −0.786377 1.36204i −0.928173 0.372149i \(-0.878621\pi\)
0.141796 0.989896i \(-0.454712\pi\)
\(692\) 0.463010 0.0176010
\(693\) 2.18415 + 6.38549i 0.0829689 + 0.242565i
\(694\) −2.75127 + 4.76534i −0.104437 + 0.180890i
\(695\) 0.385210 + 0.667203i 0.0146118 + 0.0253085i
\(696\) 1.67394 2.89935i 0.0634505 0.109899i
\(697\) 19.9409 + 34.5387i 0.755317 + 1.30825i
\(698\) 4.22521 7.31827i 0.159926 0.277001i
\(699\) −0.220183 + 0.381368i −0.00832807 + 0.0144246i
\(700\) 2.49489 + 7.29396i 0.0942980 + 0.275686i
\(701\) −1.46981 2.54579i −0.0555141 0.0961532i 0.836933 0.547306i \(-0.184346\pi\)
−0.892447 + 0.451152i \(0.851013\pi\)
\(702\) −1.85759 3.21744i −0.0701102 0.121434i
\(703\) 5.58863 + 5.34139i 0.210779 + 0.201454i
\(704\) 3.76881 6.52777i 0.142042 0.246025i
\(705\) −0.0102619 + 0.0177741i −0.000386485 + 0.000669412i
\(706\) −9.05186 15.6783i −0.340671 0.590060i
\(707\) 29.3231 + 5.76189i 1.10281 + 0.216698i
\(708\) 0.0664358 + 0.115070i 0.00249681 + 0.00432460i
\(709\) −14.7990 −0.555790 −0.277895 0.960612i \(-0.589637\pi\)
−0.277895 + 0.960612i \(0.589637\pi\)
\(710\) 0.137232 0.237693i 0.00515023 0.00892046i
\(711\) −6.13142 + 10.6199i −0.229946 + 0.398279i
\(712\) 31.5504 1.18240
\(713\) 2.69590 4.66944i 0.100962 0.174872i
\(714\) 0.655906 + 1.91758i 0.0245467 + 0.0717637i
\(715\) −0.289398 −0.0108229
\(716\) 6.71028 0.250775
\(717\) −4.01340 −0.149883
\(718\) −15.1842 26.2999i −0.566671 0.981503i
\(719\) −11.9227 + 20.6507i −0.444640 + 0.770140i −0.998027 0.0627848i \(-0.980002\pi\)
0.553387 + 0.832924i \(0.313335\pi\)
\(720\) −0.422030 0.730977i −0.0157281 0.0272419i
\(721\) 30.4442 + 5.98219i 1.13380 + 0.222788i
\(722\) −1.02225 22.5840i −0.0380440 0.840490i
\(723\) −1.86752 3.23464i −0.0694539 0.120298i
\(724\) 12.6743 0.471038
\(725\) 30.6138 1.13697
\(726\) 2.16556 0.0803714
\(727\) 4.40551 + 7.63057i 0.163391 + 0.283002i 0.936083 0.351780i \(-0.114423\pi\)
−0.772691 + 0.634782i \(0.781090\pi\)
\(728\) 7.76601 + 22.7044i 0.287828 + 0.841481i
\(729\) −25.3161 −0.937634
\(730\) −0.128179 0.222013i −0.00474412 0.00821706i
\(731\) −20.2047 34.9956i −0.747299 1.29436i
\(732\) 0.492633 + 0.853265i 0.0182082 + 0.0315376i
\(733\) 11.3925 + 19.7324i 0.420792 + 0.728834i 0.996017 0.0891616i \(-0.0284188\pi\)
−0.575225 + 0.817995i \(0.695085\pi\)
\(734\) 4.62428 0.170685
\(735\) 0.131224 + 0.0536413i 0.00484026 + 0.00197859i
\(736\) −1.52819 2.64690i −0.0563297 0.0975660i
\(737\) −6.44363 −0.237354
\(738\) 38.8090 1.42858
\(739\) −0.441823 −0.0162527 −0.00812636 0.999967i \(-0.502587\pi\)
−0.00812636 + 0.999967i \(0.502587\pi\)
\(740\) 0.0591593 + 0.102467i 0.00217474 + 0.00376676i
\(741\) 0.540228 2.21541i 0.0198458 0.0813849i
\(742\) −16.5114 + 18.9162i −0.606152 + 0.694434i
\(743\) 18.2847 + 31.6700i 0.670801 + 1.16186i 0.977677 + 0.210112i \(0.0673828\pi\)
−0.306876 + 0.951749i \(0.599284\pi\)
\(744\) −1.53303 + 2.65529i −0.0562036 + 0.0973476i
\(745\) −0.134388 0.232768i −0.00492361 0.00852794i
\(746\) −14.8725 −0.544522
\(747\) −41.5869 −1.52159
\(748\) −1.82226 −0.0666285
\(749\) 14.4926 + 2.84775i 0.529547 + 0.104054i
\(750\) −0.120327 + 0.208413i −0.00439373 + 0.00761016i
\(751\) −8.38453 −0.305956 −0.152978 0.988230i \(-0.548886\pi\)
−0.152978 + 0.988230i \(0.548886\pi\)
\(752\) 1.26177 2.18545i 0.0460121 0.0796953i
\(753\) −1.06552 + 1.84553i −0.0388296 + 0.0672549i
\(754\) 21.5443 0.784598
\(755\) −0.235216 0.407407i −0.00856040 0.0148271i
\(756\) −1.60567 0.315509i −0.0583976 0.0114749i
\(757\) −14.4729 25.0679i −0.526028 0.911107i −0.999540 0.0303197i \(-0.990347\pi\)
0.473512 0.880787i \(-0.342986\pi\)
\(758\) 5.76749 9.98959i 0.209485 0.362838i
\(759\) −0.0730800 + 0.126578i −0.00265264 + 0.00459450i
\(760\) 0.362572 1.48686i 0.0131519 0.0539341i
\(761\) −21.3640 37.0036i −0.774445 1.34138i −0.935106 0.354369i \(-0.884696\pi\)
0.160661 0.987010i \(-0.448638\pi\)
\(762\) 1.20796 + 2.09225i 0.0437598 + 0.0757941i
\(763\) −15.1100 + 17.3107i −0.547019 + 0.626688i
\(764\) −5.40204 + 9.35660i −0.195439 + 0.338510i
\(765\) −0.615177 + 1.06552i −0.0222418 + 0.0385239i
\(766\) −0.764227 1.32368i −0.0276126 0.0478265i
\(767\) −1.89102 + 3.27535i −0.0682809 + 0.118266i
\(768\) 1.12705 + 1.95210i 0.0406688 + 0.0704405i
\(769\) 6.53771 11.3236i 0.235756 0.408341i −0.723736 0.690077i \(-0.757577\pi\)
0.959492 + 0.281736i \(0.0909101\pi\)
\(770\) 0.203112 0.232694i 0.00731966 0.00838572i
\(771\) −4.53250 −0.163234
\(772\) 4.56289 + 7.90316i 0.164222 + 0.284441i
\(773\) −6.11348 10.5889i −0.219887 0.380855i 0.734886 0.678190i \(-0.237235\pi\)
−0.954773 + 0.297335i \(0.903902\pi\)
\(774\) −39.3224 −1.41341
\(775\) −28.0368 −1.00711
\(776\) −16.6407 28.8225i −0.597366 1.03467i
\(777\) −0.816625 0.160464i −0.0292963 0.00575663i
\(778\) −35.4545 −1.27111
\(779\) 34.6228 + 33.0911i 1.24049 + 1.18561i
\(780\) 0.0174503 0.0302247i 0.000624820 0.00108222i
\(781\) −1.73585 −0.0621138
\(782\) 2.07101 3.58709i 0.0740591 0.128274i
\(783\) −3.24923 + 5.62783i −0.116118 + 0.201122i
\(784\) −16.1349 6.59557i −0.576246 0.235556i
\(785\) 0.277324 0.480339i 0.00989811 0.0171440i
\(786\) −0.775305 1.34287i −0.0276542 0.0478985i
\(787\) 13.7375 23.7941i 0.489690 0.848168i −0.510240 0.860032i \(-0.670443\pi\)
0.999930 + 0.0118645i \(0.00377668\pi\)
\(788\) −2.17450 3.76634i −0.0774633 0.134170i
\(789\) −5.22169 −0.185897
\(790\) 0.561240 0.0199680
\(791\) −23.2201 + 26.6019i −0.825612 + 0.945856i
\(792\) −3.92165 + 6.79250i −0.139350 + 0.241361i
\(793\) −14.0223 + 24.2873i −0.497945 + 0.862466i
\(794\) 13.3300 + 23.0882i 0.473064 + 0.819371i
\(795\) 0.161529 0.00572885
\(796\) 3.26699 5.65860i 0.115795 0.200564i
\(797\) −32.4053 −1.14785 −0.573927 0.818907i \(-0.694581\pi\)
−0.573927 + 0.818907i \(0.694581\pi\)
\(798\) 1.40217 + 1.98925i 0.0496363 + 0.0704186i
\(799\) −3.67848 −0.130135
\(800\) −7.94643 + 13.7636i −0.280949 + 0.486617i
\(801\) −30.4594 −1.07623
\(802\) 15.0553 + 26.0766i 0.531623 + 0.920797i
\(803\) −0.810671 + 1.40412i −0.0286080 + 0.0495505i
\(804\) 0.388542 0.672974i 0.0137028 0.0237340i
\(805\) −0.0937691 0.274140i −0.00330493 0.00966215i
\(806\) −19.7308 −0.694987
\(807\) 1.53675 0.0540963
\(808\) 17.3654 + 30.0778i 0.610913 + 1.05813i
\(809\) −5.25814 + 9.10737i −0.184866 + 0.320198i −0.943532 0.331283i \(-0.892519\pi\)
0.758665 + 0.651481i \(0.225852\pi\)
\(810\) 0.592217 + 1.02575i 0.0208084 + 0.0360412i
\(811\) −9.05864 + 15.6900i −0.318092 + 0.550951i −0.980090 0.198554i \(-0.936375\pi\)
0.661998 + 0.749506i \(0.269709\pi\)
\(812\) 6.24015 7.14898i 0.218986 0.250880i
\(813\) −0.780234 + 1.35141i −0.0273640 + 0.0473959i
\(814\) −0.906630 + 1.57033i −0.0317774 + 0.0550400i
\(815\) 0.663920 0.0232561
\(816\) −0.801549 + 1.38832i −0.0280598 + 0.0486010i
\(817\) −35.0808 33.5288i −1.22732 1.17303i
\(818\) 21.6245 0.756082
\(819\) −7.49745 21.9192i −0.261982 0.765920i
\(820\) 0.366505 + 0.634805i 0.0127989 + 0.0221684i
\(821\) −45.5597 −1.59004 −0.795022 0.606580i \(-0.792541\pi\)
−0.795022 + 0.606580i \(0.792541\pi\)
\(822\) −2.14479 −0.0748081
\(823\) −1.88815 3.27038i −0.0658169 0.113998i 0.831239 0.555915i \(-0.187632\pi\)
−0.897056 + 0.441917i \(0.854299\pi\)
\(824\) 18.0293 + 31.2277i 0.628082 + 1.08787i
\(825\) 0.760018 0.0264604
\(826\) −1.30638 3.81929i −0.0454549 0.132890i
\(827\) 9.20739 15.9477i 0.320172 0.554555i −0.660351 0.750957i \(-0.729593\pi\)
0.980523 + 0.196402i \(0.0629258\pi\)
\(828\) 0.831685 + 1.44052i 0.0289030 + 0.0500616i
\(829\) 4.83519 8.37479i 0.167933 0.290868i −0.769760 0.638333i \(-0.779624\pi\)
0.937693 + 0.347465i \(0.112957\pi\)
\(830\) 0.951664 + 1.64833i 0.0330327 + 0.0572144i
\(831\) −2.05790 + 3.56439i −0.0713879 + 0.123647i
\(832\) −12.9371 + 22.4077i −0.448512 + 0.776846i
\(833\) 3.43354 + 25.1753i 0.118965 + 0.872272i
\(834\) −0.711937 1.23311i −0.0246524 0.0426991i
\(835\) −1.35757 2.35137i −0.0469805 0.0813726i
\(836\) −2.10040 + 0.614034i −0.0726438 + 0.0212368i
\(837\) 2.97571 5.15409i 0.102856 0.178151i
\(838\) 18.4378 31.9351i 0.636922 1.10318i
\(839\) 7.85029 + 13.5971i 0.271022 + 0.469424i 0.969124 0.246575i \(-0.0793050\pi\)
−0.698102 + 0.715999i \(0.745972\pi\)
\(840\) 0.0533221 + 0.155890i 0.00183979 + 0.00537873i
\(841\) −4.34228 7.52105i −0.149734 0.259346i
\(842\) 47.5660 1.63923
\(843\) −0.0168763 + 0.0292306i −0.000581251 + 0.00100676i
\(844\) 0.158487 0.274507i 0.00545534 0.00944893i
\(845\) −0.490996 −0.0168908
\(846\) −1.78976 + 3.09996i −0.0615332 + 0.106579i
\(847\) 26.6404 + 5.23475i 0.915374 + 0.179868i
\(848\) −19.8612 −0.682035
\(849\) 4.18287 0.143556
\(850\) −21.5381 −0.738750
\(851\) 0.850455 + 1.47303i 0.0291532 + 0.0504948i
\(852\) 0.104670 0.181293i 0.00358592 0.00621099i
\(853\) 2.20330 + 3.81623i 0.0754397 + 0.130665i 0.901277 0.433243i \(-0.142631\pi\)
−0.825838 + 0.563908i \(0.809297\pi\)
\(854\) −9.68705 28.3207i −0.331484 0.969113i
\(855\) −0.350033 + 1.43544i −0.0119709 + 0.0490910i
\(856\) 8.58264 + 14.8656i 0.293349 + 0.508095i
\(857\) −35.1050 −1.19916 −0.599582 0.800313i \(-0.704667\pi\)
−0.599582 + 0.800313i \(0.704667\pi\)
\(858\) 0.534859 0.0182598
\(859\) 21.8081 0.744082 0.372041 0.928216i \(-0.378658\pi\)
0.372041 + 0.928216i \(0.378658\pi\)
\(860\) −0.371353 0.643203i −0.0126630 0.0219330i
\(861\) −5.05918 0.994113i −0.172416 0.0338793i
\(862\) 16.2858 0.554696
\(863\) −13.4958 23.3754i −0.459402 0.795707i 0.539528 0.841968i \(-0.318603\pi\)
−0.998929 + 0.0462609i \(0.985269\pi\)
\(864\) −1.68680 2.92163i −0.0573862 0.0993958i
\(865\) 0.0452443 + 0.0783654i 0.00153835 + 0.00266450i
\(866\) −0.323667 0.560608i −0.0109987 0.0190502i
\(867\) −0.678373 −0.0230388
\(868\) −5.71487 + 6.54719i −0.193975 + 0.222226i
\(869\) −1.77479 3.07402i −0.0602055 0.104279i
\(870\) 0.147925 0.00501513
\(871\) 22.1188 0.749468
\(872\) −26.7045 −0.904328
\(873\) 16.0652 + 27.8258i 0.543726 + 0.941761i
\(874\) 1.17839 4.83244i 0.0398598 0.163460i
\(875\) −1.98404 + 2.27300i −0.0670727 + 0.0768414i
\(876\) −0.0977646 0.169333i −0.00330316 0.00572124i
\(877\) −1.86693 + 3.23362i −0.0630419 + 0.109192i −0.895824 0.444410i \(-0.853413\pi\)
0.832782 + 0.553601i \(0.186747\pi\)
\(878\) −21.5198 37.2735i −0.726260 1.25792i
\(879\) −4.71669 −0.159090
\(880\) 0.244319 0.00823599
\(881\) 29.5676 0.996156 0.498078 0.867132i \(-0.334039\pi\)
0.498078 + 0.867132i \(0.334039\pi\)
\(882\) 22.8865 + 9.35548i 0.770629 + 0.315016i
\(883\) −19.7110 + 34.1405i −0.663328 + 1.14892i 0.316407 + 0.948623i \(0.397523\pi\)
−0.979736 + 0.200295i \(0.935810\pi\)
\(884\) 6.25522 0.210386
\(885\) −0.0129839 + 0.0224888i −0.000436450 + 0.000755953i
\(886\) 16.8595 29.2015i 0.566405 0.981043i
\(887\) 11.9097 0.399887 0.199943 0.979807i \(-0.435924\pi\)
0.199943 + 0.979807i \(0.435924\pi\)
\(888\) −0.483613 0.837643i −0.0162290 0.0281095i
\(889\) 9.80260 + 28.6585i 0.328769 + 0.961175i
\(890\) 0.697024 + 1.20728i 0.0233643 + 0.0404682i
\(891\) 3.74549 6.48737i 0.125479 0.217335i
\(892\) −0.223692 + 0.387445i −0.00748975 + 0.0129726i
\(893\) −4.23993 + 1.23951i −0.141884 + 0.0414785i
\(894\) 0.248374 + 0.430196i 0.00830686 + 0.0143879i
\(895\) 0.655713 + 1.13573i 0.0219181 + 0.0379632i
\(896\) −3.47970 10.1731i −0.116249 0.339860i
\(897\) 0.250859 0.434501i 0.00837595 0.0145076i
\(898\) −10.9006 + 18.8804i −0.363758 + 0.630047i
\(899\) 17.2562 + 29.8886i 0.575526 + 0.996840i
\(900\) 4.32468 7.49057i 0.144156 0.249686i
\(901\) 14.4754 + 25.0722i 0.482247 + 0.835276i
\(902\) −5.61677 + 9.72854i −0.187018 + 0.323925i
\(903\) 5.12610 + 1.00726i 0.170586 + 0.0335196i
\(904\) −41.0377 −1.36490
\(905\) 1.23851 + 2.14516i 0.0411694 + 0.0713075i
\(906\) 0.434722 + 0.752961i 0.0144427 + 0.0250154i
\(907\) 26.4040 0.876732 0.438366 0.898797i \(-0.355557\pi\)
0.438366 + 0.898797i \(0.355557\pi\)
\(908\) 6.72245 0.223092
\(909\) −16.7649 29.0376i −0.556056 0.963117i
\(910\) −0.697217 + 0.798761i −0.0231125 + 0.0264787i
\(911\) −40.5642 −1.34395 −0.671975 0.740574i \(-0.734554\pi\)
−0.671975 + 0.740574i \(0.734554\pi\)
\(912\) −0.456078 + 1.87032i −0.0151023 + 0.0619324i
\(913\) 6.01882 10.4249i 0.199194 0.345014i
\(914\) 19.5967 0.648200
\(915\) −0.0962779 + 0.166758i −0.00318285 + 0.00551286i
\(916\) 6.63534 11.4927i 0.219238 0.379731i
\(917\) −6.29160 18.3939i −0.207767 0.607420i
\(918\) 2.28596 3.95940i 0.0754480 0.130680i
\(919\) 10.6711 + 18.4828i 0.352006 + 0.609693i 0.986601 0.163152i \(-0.0521662\pi\)
−0.634595 + 0.772845i \(0.718833\pi\)
\(920\) 0.168363 0.291613i 0.00555077 0.00961421i
\(921\) 1.68200 + 2.91331i 0.0554239 + 0.0959970i
\(922\) −21.4896 −0.707723
\(923\) 5.95861 0.196130
\(924\) 0.154918 0.177480i 0.00509642 0.00583867i
\(925\) 4.42228 7.65962i 0.145404 0.251847i
\(926\) 2.57151 4.45399i 0.0845052 0.146367i
\(927\) −17.4058 30.1478i −0.571683 0.990184i
\(928\) 19.5635 0.642205
\(929\) 16.6990 28.9235i 0.547876 0.948950i −0.450543 0.892755i \(-0.648770\pi\)
0.998420 0.0561953i \(-0.0178969\pi\)
\(930\) −0.135473 −0.00444234
\(931\) 12.4407 + 27.8609i 0.407728 + 0.913103i
\(932\) −1.45063 −0.0475171
\(933\) −2.64339 + 4.57848i −0.0865406 + 0.149893i
\(934\) 44.3993 1.45279
\(935\) −0.178067 0.308422i −0.00582343 0.0100865i
\(936\) 13.4617 23.3164i 0.440010 0.762120i
\(937\) 17.8073 30.8432i 0.581741 1.00760i −0.413533 0.910489i \(-0.635705\pi\)
0.995273 0.0971149i \(-0.0309614\pi\)
\(938\) −15.5240 + 17.7850i −0.506876 + 0.580699i
\(939\) 2.96621 0.0967985
\(940\) −0.0676086 −0.00220515
\(941\) 7.06111 + 12.2302i 0.230186 + 0.398693i 0.957863 0.287227i \(-0.0927334\pi\)
−0.727677 + 0.685920i \(0.759400\pi\)
\(942\) −0.512544 + 0.887752i −0.0166996 + 0.0289245i
\(943\) 5.26876 + 9.12575i 0.171574 + 0.297175i
\(944\) 1.59646 2.76516i 0.0519605 0.0899982i
\(945\) −0.103502 0.302593i −0.00336691 0.00984336i
\(946\) 5.69108 9.85723i 0.185033 0.320486i
\(947\) 4.38492 7.59490i 0.142491 0.246801i −0.785943 0.618299i \(-0.787822\pi\)
0.928434 + 0.371497i \(0.121156\pi\)
\(948\) 0.428068 0.0139030
\(949\) 2.78276 4.81989i 0.0903323 0.156460i
\(950\) −24.8255 + 7.25751i −0.805444 + 0.235465i
\(951\) 1.62768 0.0527811
\(952\) −19.4185 + 22.2466i −0.629356 + 0.721017i
\(953\) −9.93545 17.2087i −0.321841 0.557445i 0.659027 0.752119i \(-0.270968\pi\)
−0.980868 + 0.194675i \(0.937635\pi\)
\(954\) 28.1721 0.912104
\(955\) −2.11150 −0.0683265
\(956\) −6.61039 11.4495i −0.213795 0.370305i
\(957\) −0.467778 0.810215i −0.0151211 0.0261905i
\(958\) 42.4464 1.37138
\(959\) −26.3849 5.18454i −0.852012 0.167418i
\(960\) −0.0888270 + 0.153853i −0.00286688 + 0.00496558i
\(961\) −0.303597 0.525845i −0.00979344 0.0169627i
\(962\) 3.11216 5.39041i 0.100340 0.173794i
\(963\) −8.28584 14.3515i −0.267007 0.462470i
\(964\) 6.15192 10.6554i 0.198140 0.343188i
\(965\) −0.891751 + 1.54456i −0.0287065 + 0.0497211i
\(966\) 0.173302 + 0.506659i 0.00557590 + 0.0163015i
\(967\) −1.17266 2.03111i −0.0377103 0.0653162i 0.846554 0.532302i \(-0.178673\pi\)
−0.884265 + 0.466986i \(0.845340\pi\)
\(968\) 15.7767 + 27.3260i 0.507082 + 0.878291i
\(969\) 2.69344 0.787405i 0.0865259 0.0252951i
\(970\) 0.735265 1.27352i 0.0236079 0.0408901i
\(971\) 9.46204 16.3887i 0.303651 0.525939i −0.673309 0.739361i \(-0.735128\pi\)
0.976960 + 0.213422i \(0.0684609\pi\)
\(972\) 1.37943 + 2.38924i 0.0442453 + 0.0766350i
\(973\) −5.77737 16.8905i −0.185214 0.541484i
\(974\) 24.0204 + 41.6045i 0.769663 + 1.33309i
\(975\) −2.60889 −0.0835513
\(976\) 11.8380 20.5041i 0.378927 0.656320i
\(977\) 9.89232 17.1340i 0.316483 0.548165i −0.663268 0.748382i \(-0.730831\pi\)
0.979752 + 0.200216i \(0.0641646\pi\)
\(978\) −1.22704 −0.0392365
\(979\) 4.40834 7.63547i 0.140891 0.244031i
\(980\) 0.0631068 + 0.462710i 0.00201587 + 0.0147807i
\(981\) 25.7810 0.823123
\(982\) −29.3418 −0.936334
\(983\) 40.3570 1.28719 0.643594 0.765367i \(-0.277442\pi\)
0.643594 + 0.765367i \(0.277442\pi\)
\(984\) −2.99609 5.18938i −0.0955119 0.165432i
\(985\) 0.424974 0.736077i 0.0135408 0.0234534i
\(986\) 13.2563 + 22.9606i 0.422167 + 0.731214i
\(987\) 0.312722 0.358267i 0.00995404 0.0114038i
\(988\) 7.20996 2.10777i 0.229379 0.0670572i
\(989\) −5.33845 9.24647i −0.169753 0.294021i
\(990\) −0.346554 −0.0110142
\(991\) 3.76412 0.119571 0.0597856 0.998211i \(-0.480958\pi\)
0.0597856 + 0.998211i \(0.480958\pi\)
\(992\) −17.9167 −0.568857
\(993\) −1.49331 2.58650i −0.0473889 0.0820799i
\(994\) −4.18202 + 4.79110i −0.132646 + 0.151964i
\(995\) 1.27697 0.0404828
\(996\) 0.725852 + 1.25721i 0.0229995 + 0.0398363i
\(997\) 15.7182 + 27.2247i 0.497799 + 0.862213i 0.999997 0.00253949i \(-0.000808345\pi\)
−0.502198 + 0.864753i \(0.667475\pi\)
\(998\) −23.1690 40.1299i −0.733402 1.27029i
\(999\) 0.938726 + 1.62592i 0.0297000 + 0.0514418i
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 133.2.g.a.102.9 yes 24
7.2 even 3 133.2.h.a.121.4 yes 24
7.3 odd 6 931.2.e.e.197.9 24
7.4 even 3 931.2.e.f.197.9 24
7.5 odd 6 931.2.h.h.520.4 24
7.6 odd 2 931.2.g.h.900.9 24
19.11 even 3 133.2.h.a.11.4 yes 24
133.11 even 3 931.2.e.f.638.9 24
133.30 even 3 inner 133.2.g.a.30.9 24
133.68 odd 6 931.2.g.h.30.9 24
133.87 odd 6 931.2.e.e.638.9 24
133.125 odd 6 931.2.h.h.410.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
133.2.g.a.30.9 24 133.30 even 3 inner
133.2.g.a.102.9 yes 24 1.1 even 1 trivial
133.2.h.a.11.4 yes 24 19.11 even 3
133.2.h.a.121.4 yes 24 7.2 even 3
931.2.e.e.197.9 24 7.3 odd 6
931.2.e.e.638.9 24 133.87 odd 6
931.2.e.f.197.9 24 7.4 even 3
931.2.e.f.638.9 24 133.11 even 3
931.2.g.h.30.9 24 133.68 odd 6
931.2.g.h.900.9 24 7.6 odd 2
931.2.h.h.410.4 24 133.125 odd 6
931.2.h.h.520.4 24 7.5 odd 6