Properties

Label 171.2.g.c.121.4
Level $171$
Weight $2$
Character 171.121
Analytic conductor $1.365$
Analytic rank $0$
Dimension $32$
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] = [171,2,Mod(106,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.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: \(1.36544187456\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.4
Character \(\chi\) \(=\) 171.121
Dual form 171.2.g.c.106.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.888985 + 1.53977i) q^{2} +(1.15573 + 1.29008i) q^{3} +(-0.580589 - 1.00561i) q^{4} -1.27957 q^{5} +(-3.01384 + 0.632688i) q^{6} +(0.657761 + 1.13928i) q^{7} -1.49140 q^{8} +(-0.328599 + 2.98195i) q^{9} +O(q^{10})\) \(q+(-0.888985 + 1.53977i) q^{2} +(1.15573 + 1.29008i) q^{3} +(-0.580589 - 1.00561i) q^{4} -1.27957 q^{5} +(-3.01384 + 0.632688i) q^{6} +(0.657761 + 1.13928i) q^{7} -1.49140 q^{8} +(-0.328599 + 2.98195i) q^{9} +(1.13752 - 1.97024i) q^{10} +(-0.130095 - 0.225331i) q^{11} +(0.626313 - 1.91121i) q^{12} +(0.933961 + 1.61767i) q^{13} -2.33896 q^{14} +(-1.47883 - 1.65075i) q^{15} +(2.48701 - 4.30763i) q^{16} +(-0.0508308 - 0.0880415i) q^{17} +(-4.29939 - 3.15688i) q^{18} +(3.11089 - 3.05326i) q^{19} +(0.742905 + 1.28675i) q^{20} +(-0.709563 + 2.16525i) q^{21} +0.462610 q^{22} +(0.611950 + 1.05993i) q^{23} +(-1.72365 - 1.92402i) q^{24} -3.36270 q^{25} -3.32111 q^{26} +(-4.22672 + 3.02240i) q^{27} +(0.763778 - 1.32290i) q^{28} +6.52642 q^{29} +(3.85642 - 0.809570i) q^{30} +(-0.617667 + 1.06983i) q^{31} +(2.93043 + 5.07566i) q^{32} +(0.140340 - 0.428253i) q^{33} +0.180751 q^{34} +(-0.841652 - 1.45778i) q^{35} +(3.18946 - 1.40084i) q^{36} +8.59418 q^{37} +(1.93577 + 7.50434i) q^{38} +(-1.00751 + 3.07446i) q^{39} +1.90835 q^{40} +8.21490 q^{41} +(-2.70319 - 3.01744i) q^{42} +(-1.53770 + 2.66338i) q^{43} +(-0.151063 + 0.261649i) q^{44} +(0.420466 - 3.81562i) q^{45} -2.17606 q^{46} +1.58093 q^{47} +(8.43148 - 1.77000i) q^{48} +(2.63470 - 4.56344i) q^{49} +(2.98939 - 5.17777i) q^{50} +(0.0548339 - 0.167327i) q^{51} +(1.08449 - 1.87840i) q^{52} +(-2.59998 + 4.50330i) q^{53} +(-0.896298 - 9.19502i) q^{54} +(0.166466 + 0.288327i) q^{55} +(-0.980985 - 1.69912i) q^{56} +(7.53427 + 0.484562i) q^{57} +(-5.80189 + 10.0492i) q^{58} +8.02123 q^{59} +(-0.801412 + 2.44553i) q^{60} -14.1310 q^{61} +(-1.09819 - 1.90213i) q^{62} +(-3.61340 + 1.58705i) q^{63} -0.472395 q^{64} +(-1.19507 - 2.06992i) q^{65} +(0.534649 + 0.596802i) q^{66} +(0.390956 + 0.677156i) q^{67} +(-0.0590236 + 0.102232i) q^{68} +(-0.660144 + 2.01445i) q^{69} +2.99287 q^{70} +(-8.19574 - 14.1954i) q^{71} +(0.490073 - 4.44728i) q^{72} +(-0.397074 - 0.687753i) q^{73} +(-7.64010 + 13.2330i) q^{74} +(-3.88635 - 4.33814i) q^{75} +(-4.87653 - 1.35565i) q^{76} +(0.171143 - 0.296428i) q^{77} +(-3.83829 - 4.28449i) q^{78} +(-5.82382 + 10.0871i) q^{79} +(-3.18231 + 5.51192i) q^{80} +(-8.78405 - 1.95973i) q^{81} +(-7.30292 + 12.6490i) q^{82} +(-3.03265 - 5.25271i) q^{83} +(2.58936 - 0.543579i) q^{84} +(0.0650416 + 0.112655i) q^{85} +(-2.73399 - 4.73542i) q^{86} +(7.54275 + 8.41959i) q^{87} +(0.194023 + 0.336058i) q^{88} +(5.75551 - 9.96883i) q^{89} +(5.50137 + 4.03945i) q^{90} +(-1.22865 + 2.12808i) q^{91} +(0.710583 - 1.23077i) q^{92} +(-2.09402 + 0.439592i) q^{93} +(-1.40542 + 2.43426i) q^{94} +(-3.98060 + 3.90686i) q^{95} +(-3.16122 + 9.64654i) q^{96} +(5.83968 - 10.1146i) q^{97} +(4.68442 + 8.11365i) q^{98} +(0.714674 - 0.313893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} + q^{15} - 11 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 11 q^{21} + 16 q^{22} + 5 q^{23} + 27 q^{24} + 18 q^{25} - 4 q^{26} - 5 q^{27} - 10 q^{28} - 20 q^{29} - 5 q^{30} - 10 q^{31} + 17 q^{32} + 34 q^{33} + 26 q^{34} - 3 q^{35} - 16 q^{36} + 2 q^{37} + 38 q^{38} - 24 q^{40} - 12 q^{41} + 25 q^{42} + 7 q^{43} + 20 q^{44} - 35 q^{45} + 18 q^{47} - 33 q^{48} - 13 q^{49} + q^{50} - 28 q^{51} + 19 q^{52} + 16 q^{53} + 35 q^{54} + 15 q^{55} - 6 q^{56} + 6 q^{57} - 74 q^{59} + 50 q^{60} + 24 q^{61} + 54 q^{62} - 30 q^{63} - 64 q^{64} + 54 q^{65} + 4 q^{66} - 11 q^{67} - 2 q^{68} + 3 q^{69} - 48 q^{70} + 9 q^{71} - 10 q^{73} + 6 q^{74} - 76 q^{75} + 29 q^{76} + 46 q^{77} - 82 q^{78} - 8 q^{79} - 24 q^{80} + 26 q^{81} + 7 q^{82} + 3 q^{83} + 12 q^{84} - 27 q^{85} + 17 q^{86} - 9 q^{87} + 9 q^{88} + 30 q^{89} - 74 q^{90} - q^{91} - 17 q^{92} - 24 q^{93} - 18 q^{94} - 6 q^{95} - 5 q^{96} + 18 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.888985 + 1.53977i −0.628607 + 1.08878i 0.359224 + 0.933251i \(0.383041\pi\)
−0.987831 + 0.155529i \(0.950292\pi\)
\(3\) 1.15573 + 1.29008i 0.667258 + 0.744827i
\(4\) −0.580589 1.00561i −0.290295 0.502805i
\(5\) −1.27957 −0.572242 −0.286121 0.958194i \(-0.592366\pi\)
−0.286121 + 0.958194i \(0.592366\pi\)
\(6\) −3.01384 + 0.632688i −1.23040 + 0.258294i
\(7\) 0.657761 + 1.13928i 0.248610 + 0.430606i 0.963140 0.268999i \(-0.0866928\pi\)
−0.714530 + 0.699605i \(0.753359\pi\)
\(8\) −1.49140 −0.527290
\(9\) −0.328599 + 2.98195i −0.109533 + 0.993983i
\(10\) 1.13752 1.97024i 0.359715 0.623045i
\(11\) −0.130095 0.225331i −0.0392251 0.0679398i 0.845746 0.533585i \(-0.179156\pi\)
−0.884971 + 0.465645i \(0.845822\pi\)
\(12\) 0.626313 1.91121i 0.180801 0.551720i
\(13\) 0.933961 + 1.61767i 0.259034 + 0.448660i 0.965983 0.258604i \(-0.0832625\pi\)
−0.706949 + 0.707264i \(0.749929\pi\)
\(14\) −2.33896 −0.625113
\(15\) −1.47883 1.65075i −0.381833 0.426221i
\(16\) 2.48701 4.30763i 0.621753 1.07691i
\(17\) −0.0508308 0.0880415i −0.0123283 0.0213532i 0.859795 0.510639i \(-0.170591\pi\)
−0.872124 + 0.489285i \(0.837258\pi\)
\(18\) −4.29939 3.15688i −1.01338 0.744083i
\(19\) 3.11089 3.05326i 0.713687 0.700465i
\(20\) 0.742905 + 1.28675i 0.166119 + 0.287726i
\(21\) −0.709563 + 2.16525i −0.154839 + 0.472497i
\(22\) 0.462610 0.0986287
\(23\) 0.611950 + 1.05993i 0.127600 + 0.221010i 0.922746 0.385408i \(-0.125939\pi\)
−0.795146 + 0.606418i \(0.792606\pi\)
\(24\) −1.72365 1.92402i −0.351838 0.392739i
\(25\) −3.36270 −0.672540
\(26\) −3.32111 −0.651323
\(27\) −4.22672 + 3.02240i −0.813432 + 0.581660i
\(28\) 0.763778 1.32290i 0.144340 0.250005i
\(29\) 6.52642 1.21193 0.605963 0.795493i \(-0.292788\pi\)
0.605963 + 0.795493i \(0.292788\pi\)
\(30\) 3.85642 0.809570i 0.704084 0.147806i
\(31\) −0.617667 + 1.06983i −0.110936 + 0.192147i −0.916148 0.400840i \(-0.868718\pi\)
0.805212 + 0.592987i \(0.202052\pi\)
\(32\) 2.93043 + 5.07566i 0.518032 + 0.897258i
\(33\) 0.140340 0.428253i 0.0244301 0.0745493i
\(34\) 0.180751 0.0309986
\(35\) −0.841652 1.45778i −0.142265 0.246411i
\(36\) 3.18946 1.40084i 0.531576 0.233474i
\(37\) 8.59418 1.41287 0.706437 0.707776i \(-0.250301\pi\)
0.706437 + 0.707776i \(0.250301\pi\)
\(38\) 1.93577 + 7.50434i 0.314023 + 1.21737i
\(39\) −1.00751 + 3.07446i −0.161331 + 0.492308i
\(40\) 1.90835 0.301737
\(41\) 8.21490 1.28295 0.641476 0.767143i \(-0.278322\pi\)
0.641476 + 0.767143i \(0.278322\pi\)
\(42\) −2.70319 3.01744i −0.417112 0.465601i
\(43\) −1.53770 + 2.66338i −0.234498 + 0.406162i −0.959127 0.282977i \(-0.908678\pi\)
0.724629 + 0.689139i \(0.242011\pi\)
\(44\) −0.151063 + 0.261649i −0.0227736 + 0.0394451i
\(45\) 0.420466 3.81562i 0.0626794 0.568799i
\(46\) −2.17606 −0.320842
\(47\) 1.58093 0.230602 0.115301 0.993331i \(-0.463217\pi\)
0.115301 + 0.993331i \(0.463217\pi\)
\(48\) 8.43148 1.77000i 1.21698 0.255477i
\(49\) 2.63470 4.56344i 0.376386 0.651919i
\(50\) 2.98939 5.17777i 0.422763 0.732248i
\(51\) 0.0548339 0.167327i 0.00767828 0.0234305i
\(52\) 1.08449 1.87840i 0.150392 0.260487i
\(53\) −2.59998 + 4.50330i −0.357135 + 0.618575i −0.987481 0.157739i \(-0.949580\pi\)
0.630346 + 0.776314i \(0.282913\pi\)
\(54\) −0.896298 9.19502i −0.121971 1.25128i
\(55\) 0.166466 + 0.288327i 0.0224462 + 0.0388780i
\(56\) −0.980985 1.69912i −0.131090 0.227054i
\(57\) 7.53427 + 0.484562i 0.997938 + 0.0641818i
\(58\) −5.80189 + 10.0492i −0.761826 + 1.31952i
\(59\) 8.02123 1.04428 0.522138 0.852861i \(-0.325135\pi\)
0.522138 + 0.852861i \(0.325135\pi\)
\(60\) −0.801412 + 2.44553i −0.103462 + 0.315717i
\(61\) −14.1310 −1.80928 −0.904642 0.426171i \(-0.859862\pi\)
−0.904642 + 0.426171i \(0.859862\pi\)
\(62\) −1.09819 1.90213i −0.139471 0.241570i
\(63\) −3.61340 + 1.58705i −0.455246 + 0.199949i
\(64\) −0.472395 −0.0590494
\(65\) −1.19507 2.06992i −0.148230 0.256742i
\(66\) 0.534649 + 0.596802i 0.0658108 + 0.0734613i
\(67\) 0.390956 + 0.677156i 0.0477629 + 0.0827277i 0.888918 0.458065i \(-0.151457\pi\)
−0.841156 + 0.540793i \(0.818124\pi\)
\(68\) −0.0590236 + 0.102232i −0.00715766 + 0.0123974i
\(69\) −0.660144 + 2.01445i −0.0794720 + 0.242511i
\(70\) 2.99287 0.357716
\(71\) −8.19574 14.1954i −0.972656 1.68469i −0.687463 0.726219i \(-0.741276\pi\)
−0.285193 0.958470i \(-0.592058\pi\)
\(72\) 0.490073 4.44728i 0.0577556 0.524117i
\(73\) −0.397074 0.687753i −0.0464740 0.0804954i 0.841853 0.539707i \(-0.181465\pi\)
−0.888327 + 0.459212i \(0.848132\pi\)
\(74\) −7.64010 + 13.2330i −0.888143 + 1.53831i
\(75\) −3.88635 4.33814i −0.448758 0.500925i
\(76\) −4.87653 1.35565i −0.559377 0.155504i
\(77\) 0.171143 0.296428i 0.0195035 0.0337811i
\(78\) −3.83829 4.28449i −0.434601 0.485123i
\(79\) −5.82382 + 10.0871i −0.655230 + 1.13489i 0.326606 + 0.945161i \(0.394095\pi\)
−0.981836 + 0.189732i \(0.939238\pi\)
\(80\) −3.18231 + 5.51192i −0.355793 + 0.616251i
\(81\) −8.78405 1.95973i −0.976005 0.217748i
\(82\) −7.30292 + 12.6490i −0.806473 + 1.39685i
\(83\) −3.03265 5.25271i −0.332877 0.576560i 0.650198 0.759765i \(-0.274686\pi\)
−0.983075 + 0.183205i \(0.941353\pi\)
\(84\) 2.58936 0.543579i 0.282523 0.0593093i
\(85\) 0.0650416 + 0.112655i 0.00705475 + 0.0122192i
\(86\) −2.73399 4.73542i −0.294814 0.510633i
\(87\) 7.54275 + 8.41959i 0.808668 + 0.902675i
\(88\) 0.194023 + 0.336058i 0.0206830 + 0.0358240i
\(89\) 5.75551 9.96883i 0.610082 1.05669i −0.381144 0.924516i \(-0.624470\pi\)
0.991226 0.132178i \(-0.0421970\pi\)
\(90\) 5.50137 + 4.03945i 0.579896 + 0.425795i
\(91\) −1.22865 + 2.12808i −0.128797 + 0.223083i
\(92\) 0.710583 1.23077i 0.0740834 0.128316i
\(93\) −2.09402 + 0.439592i −0.217140 + 0.0455836i
\(94\) −1.40542 + 2.43426i −0.144958 + 0.251075i
\(95\) −3.98060 + 3.90686i −0.408401 + 0.400835i
\(96\) −3.16122 + 9.64654i −0.322640 + 0.984546i
\(97\) 5.83968 10.1146i 0.592930 1.02698i −0.400906 0.916119i \(-0.631304\pi\)
0.993835 0.110865i \(-0.0353622\pi\)
\(98\) 4.68442 + 8.11365i 0.473198 + 0.819603i
\(99\) 0.714674 0.313893i 0.0718275 0.0315474i
\(100\) 1.95235 + 3.38156i 0.195235 + 0.338156i
\(101\) −13.7351 −1.36670 −0.683349 0.730092i \(-0.739477\pi\)
−0.683349 + 0.730092i \(0.739477\pi\)
\(102\) 0.208899 + 0.233183i 0.0206840 + 0.0230886i
\(103\) −3.88901 + 6.73596i −0.383195 + 0.663714i −0.991517 0.129977i \(-0.958510\pi\)
0.608322 + 0.793691i \(0.291843\pi\)
\(104\) −1.39291 2.41259i −0.136586 0.236574i
\(105\) 0.907936 2.77059i 0.0886055 0.270382i
\(106\) −4.62269 8.00673i −0.448995 0.777682i
\(107\) 2.71691 0.262654 0.131327 0.991339i \(-0.458076\pi\)
0.131327 + 0.991339i \(0.458076\pi\)
\(108\) 5.49334 + 2.49566i 0.528596 + 0.240145i
\(109\) −9.03891 15.6558i −0.865770 1.49956i −0.866280 0.499559i \(-0.833496\pi\)
0.000509715 1.00000i \(-0.499838\pi\)
\(110\) −0.591942 −0.0564394
\(111\) 9.93251 + 11.0872i 0.942752 + 1.05235i
\(112\) 6.54344 0.618297
\(113\) 5.83591 10.1081i 0.548997 0.950890i −0.449347 0.893357i \(-0.648343\pi\)
0.998344 0.0575326i \(-0.0183233\pi\)
\(114\) −7.44397 + 11.1703i −0.697191 + 1.04619i
\(115\) −0.783034 1.35625i −0.0730183 0.126471i
\(116\) −3.78917 6.56304i −0.351816 0.609363i
\(117\) −5.13070 + 2.25346i −0.474333 + 0.208332i
\(118\) −7.13075 + 12.3508i −0.656439 + 1.13699i
\(119\) 0.0668690 0.115820i 0.00612987 0.0106172i
\(120\) 2.20553 + 2.46192i 0.201337 + 0.224742i
\(121\) 5.46615 9.46765i 0.496923 0.860696i
\(122\) 12.5622 21.7584i 1.13733 1.96991i
\(123\) 9.49417 + 10.5979i 0.856060 + 0.955577i
\(124\) 1.43444 0.128817
\(125\) 10.7007 0.957097
\(126\) 0.768580 6.97466i 0.0684706 0.621352i
\(127\) 2.39063 4.14069i 0.212134 0.367427i −0.740248 0.672334i \(-0.765292\pi\)
0.952382 + 0.304907i \(0.0986253\pi\)
\(128\) −5.44091 + 9.42393i −0.480913 + 0.832966i
\(129\) −5.21313 + 1.09438i −0.458991 + 0.0963548i
\(130\) 4.24959 0.372714
\(131\) −11.5587 −1.00989 −0.504945 0.863151i \(-0.668487\pi\)
−0.504945 + 0.863151i \(0.668487\pi\)
\(132\) −0.512135 + 0.107511i −0.0445757 + 0.00935766i
\(133\) 5.52472 + 1.53585i 0.479054 + 0.133175i
\(134\) −1.39022 −0.120096
\(135\) 5.40838 3.86737i 0.465480 0.332850i
\(136\) 0.0758090 + 0.131305i 0.00650057 + 0.0112593i
\(137\) 11.8095 1.00895 0.504476 0.863426i \(-0.331686\pi\)
0.504476 + 0.863426i \(0.331686\pi\)
\(138\) −2.51493 2.80728i −0.214085 0.238972i
\(139\) 2.61207 + 4.52424i 0.221553 + 0.383741i 0.955280 0.295704i \(-0.0955542\pi\)
−0.733727 + 0.679445i \(0.762221\pi\)
\(140\) −0.977308 + 1.69275i −0.0825976 + 0.143063i
\(141\) 1.82712 + 2.03952i 0.153871 + 0.171759i
\(142\) 29.1436 2.44568
\(143\) 0.243007 0.420900i 0.0203213 0.0351974i
\(144\) 12.0279 + 8.83162i 1.00233 + 0.735969i
\(145\) −8.35102 −0.693515
\(146\) 1.41197 0.116856
\(147\) 8.93217 1.87511i 0.736713 0.154656i
\(148\) −4.98969 8.64239i −0.410150 0.710400i
\(149\) −13.2345 −1.08422 −0.542108 0.840309i \(-0.682374\pi\)
−0.542108 + 0.840309i \(0.682374\pi\)
\(150\) 10.1346 2.12754i 0.827490 0.173713i
\(151\) 7.38449 + 12.7903i 0.600942 + 1.04086i 0.992679 + 0.120784i \(0.0385409\pi\)
−0.391737 + 0.920077i \(0.628126\pi\)
\(152\) −4.63958 + 4.55363i −0.376320 + 0.369348i
\(153\) 0.279238 0.122644i 0.0225751 0.00991521i
\(154\) 0.304287 + 0.527040i 0.0245201 + 0.0424701i
\(155\) 0.790349 1.36892i 0.0634824 0.109955i
\(156\) 3.67666 0.771832i 0.294368 0.0617960i
\(157\) −0.0780549 −0.00622946 −0.00311473 0.999995i \(-0.500991\pi\)
−0.00311473 + 0.999995i \(0.500991\pi\)
\(158\) −10.3546 17.9346i −0.823765 1.42680i
\(159\) −8.81446 + 1.85040i −0.699032 + 0.146746i
\(160\) −3.74969 6.49466i −0.296439 0.513448i
\(161\) −0.805034 + 1.39436i −0.0634456 + 0.109891i
\(162\) 10.8264 11.7832i 0.850604 0.925777i
\(163\) −19.5891 −1.53434 −0.767170 0.641444i \(-0.778336\pi\)
−0.767170 + 0.641444i \(0.778336\pi\)
\(164\) −4.76948 8.26099i −0.372434 0.645075i
\(165\) −0.179576 + 0.547980i −0.0139799 + 0.0426602i
\(166\) 10.7839 0.836996
\(167\) 11.6324 + 20.1479i 0.900140 + 1.55909i 0.827311 + 0.561744i \(0.189869\pi\)
0.0728285 + 0.997344i \(0.476797\pi\)
\(168\) 1.05824 3.22926i 0.0816451 0.249143i
\(169\) 4.75544 8.23666i 0.365803 0.633589i
\(170\) −0.231284 −0.0177387
\(171\) 8.08242 + 10.2798i 0.618078 + 0.786117i
\(172\) 3.57110 0.272294
\(173\) 2.86145 4.95618i 0.217552 0.376811i −0.736507 0.676430i \(-0.763526\pi\)
0.954059 + 0.299619i \(0.0968595\pi\)
\(174\) −19.6696 + 4.12919i −1.49115 + 0.313033i
\(175\) −2.21185 3.83104i −0.167200 0.289599i
\(176\) −1.29419 −0.0975532
\(177\) 9.27034 + 10.3480i 0.696801 + 0.777804i
\(178\) 10.2331 + 17.7243i 0.767005 + 1.32849i
\(179\) −7.56033 −0.565085 −0.282543 0.959255i \(-0.591178\pi\)
−0.282543 + 0.959255i \(0.591178\pi\)
\(180\) −4.08114 + 1.79248i −0.304190 + 0.133604i
\(181\) −4.37626 + 7.57990i −0.325285 + 0.563410i −0.981570 0.191103i \(-0.938793\pi\)
0.656285 + 0.754513i \(0.272127\pi\)
\(182\) −2.18450 3.78366i −0.161926 0.280463i
\(183\) −16.3315 18.2300i −1.20726 1.34760i
\(184\) −0.912663 1.58078i −0.0672824 0.116536i
\(185\) −10.9969 −0.808505
\(186\) 1.18468 3.61509i 0.0868651 0.265071i
\(187\) −0.0132256 + 0.0229075i −0.000967154 + 0.00167516i
\(188\) −0.917870 1.58980i −0.0669425 0.115948i
\(189\) −6.22351 2.82738i −0.452694 0.205662i
\(190\) −2.47696 9.60234i −0.179697 0.696627i
\(191\) 1.36408 + 2.36265i 0.0987011 + 0.170955i 0.911147 0.412081i \(-0.135198\pi\)
−0.812446 + 0.583036i \(0.801865\pi\)
\(192\) −0.545959 0.609426i −0.0394012 0.0439816i
\(193\) −24.5813 −1.76940 −0.884699 0.466164i \(-0.845636\pi\)
−0.884699 + 0.466164i \(0.845636\pi\)
\(194\) 10.3828 + 17.9835i 0.745440 + 1.29114i
\(195\) 1.28919 3.93399i 0.0923205 0.281719i
\(196\) −6.11871 −0.437051
\(197\) 4.62417 0.329458 0.164729 0.986339i \(-0.447325\pi\)
0.164729 + 0.986339i \(0.447325\pi\)
\(198\) −0.152013 + 1.37948i −0.0108031 + 0.0980352i
\(199\) 3.26083 5.64792i 0.231154 0.400370i −0.726994 0.686644i \(-0.759083\pi\)
0.958148 + 0.286273i \(0.0924165\pi\)
\(200\) 5.01513 0.354623
\(201\) −0.421745 + 1.28697i −0.0297476 + 0.0907758i
\(202\) 12.2103 21.1489i 0.859116 1.48803i
\(203\) 4.29283 + 7.43540i 0.301297 + 0.521862i
\(204\) −0.200102 + 0.0420069i −0.0140099 + 0.00294107i
\(205\) −10.5115 −0.734158
\(206\) −6.91454 11.9763i −0.481759 0.834431i
\(207\) −3.36174 + 1.47651i −0.233657 + 0.102625i
\(208\) 9.29108 0.644220
\(209\) −1.09270 0.303766i −0.0755839 0.0210120i
\(210\) 3.45893 + 3.86103i 0.238689 + 0.266436i
\(211\) 5.21704 0.359156 0.179578 0.983744i \(-0.442527\pi\)
0.179578 + 0.983744i \(0.442527\pi\)
\(212\) 6.03808 0.414697
\(213\) 8.84120 26.9792i 0.605789 1.84858i
\(214\) −2.41530 + 4.18341i −0.165106 + 0.285972i
\(215\) 1.96760 3.40799i 0.134189 0.232423i
\(216\) 6.30372 4.50760i 0.428914 0.306703i
\(217\) −1.62511 −0.110320
\(218\) 32.1418 2.17692
\(219\) 0.428346 1.30711i 0.0289449 0.0883263i
\(220\) 0.193296 0.334799i 0.0130320 0.0225721i
\(221\) 0.0949478 0.164454i 0.00638688 0.0110624i
\(222\) −25.9015 + 5.43744i −1.73839 + 0.364937i
\(223\) −2.46764 + 4.27407i −0.165245 + 0.286213i −0.936742 0.350020i \(-0.886175\pi\)
0.771497 + 0.636233i \(0.219508\pi\)
\(224\) −3.85505 + 6.67714i −0.257576 + 0.446135i
\(225\) 1.10498 10.0274i 0.0736653 0.668493i
\(226\) 10.3761 + 17.9719i 0.690207 + 1.19547i
\(227\) −7.33746 12.7089i −0.487004 0.843516i 0.512884 0.858458i \(-0.328577\pi\)
−0.999888 + 0.0149416i \(0.995244\pi\)
\(228\) −3.88703 7.85787i −0.257425 0.520400i
\(229\) 0.589497 1.02104i 0.0389551 0.0674722i −0.845891 0.533357i \(-0.820930\pi\)
0.884846 + 0.465884i \(0.154264\pi\)
\(230\) 2.78442 0.183599
\(231\) 0.580209 0.121802i 0.0381749 0.00801397i
\(232\) −9.73351 −0.639036
\(233\) 10.8188 + 18.7387i 0.708761 + 1.22761i 0.965317 + 0.261081i \(0.0840790\pi\)
−0.256555 + 0.966530i \(0.582588\pi\)
\(234\) 1.09131 9.90338i 0.0713414 0.647404i
\(235\) −2.02291 −0.131960
\(236\) −4.65704 8.06623i −0.303147 0.525067i
\(237\) −19.7439 + 4.14479i −1.28251 + 0.269233i
\(238\) 0.118891 + 0.205925i 0.00770656 + 0.0133482i
\(239\) −8.89153 + 15.4006i −0.575145 + 0.996180i 0.420881 + 0.907116i \(0.361721\pi\)
−0.996026 + 0.0890644i \(0.971612\pi\)
\(240\) −10.7887 + 2.26484i −0.696406 + 0.146195i
\(241\) −2.65337 −0.170919 −0.0854594 0.996342i \(-0.527236\pi\)
−0.0854594 + 0.996342i \(0.527236\pi\)
\(242\) 9.71865 + 16.8332i 0.624739 + 1.08208i
\(243\) −7.62374 13.5970i −0.489063 0.872249i
\(244\) 8.20429 + 14.2102i 0.525226 + 0.909717i
\(245\) −3.37129 + 5.83924i −0.215384 + 0.373055i
\(246\) −24.7584 + 5.19747i −1.57854 + 0.331379i
\(247\) 7.84460 + 2.18076i 0.499140 + 0.138759i
\(248\) 0.921189 1.59555i 0.0584956 0.101317i
\(249\) 3.27149 9.98305i 0.207322 0.632650i
\(250\) −9.51273 + 16.4765i −0.601638 + 1.04207i
\(251\) 3.23211 5.59818i 0.204009 0.353354i −0.745807 0.666162i \(-0.767936\pi\)
0.949817 + 0.312807i \(0.101269\pi\)
\(252\) 3.69385 + 2.71225i 0.232691 + 0.170856i
\(253\) 0.159223 0.275783i 0.0100103 0.0173383i
\(254\) 4.25047 + 7.36203i 0.266698 + 0.461935i
\(255\) −0.0701639 + 0.214107i −0.00439383 + 0.0134079i
\(256\) −10.1462 17.5737i −0.634136 1.09836i
\(257\) 8.36616 + 14.4906i 0.521867 + 0.903899i 0.999676 + 0.0254362i \(0.00809745\pi\)
−0.477810 + 0.878463i \(0.658569\pi\)
\(258\) 2.94931 8.99990i 0.183616 0.560309i
\(259\) 5.65292 + 9.79114i 0.351255 + 0.608392i
\(260\) −1.38769 + 2.40355i −0.0860608 + 0.149062i
\(261\) −2.14458 + 19.4615i −0.132746 + 1.20463i
\(262\) 10.2755 17.7978i 0.634825 1.09955i
\(263\) −10.4792 + 18.1506i −0.646178 + 1.11921i 0.337851 + 0.941200i \(0.390300\pi\)
−0.984028 + 0.178013i \(0.943033\pi\)
\(264\) −0.209304 + 0.638697i −0.0128818 + 0.0393091i
\(265\) 3.32686 5.76229i 0.204367 0.353974i
\(266\) −7.27624 + 7.14144i −0.446135 + 0.437870i
\(267\) 19.5123 4.09618i 1.19414 0.250682i
\(268\) 0.453970 0.786298i 0.0277306 0.0480308i
\(269\) 8.04348 + 13.9317i 0.490420 + 0.849432i 0.999939 0.0110273i \(-0.00351018\pi\)
−0.509520 + 0.860459i \(0.670177\pi\)
\(270\) 1.14688 + 11.7657i 0.0697967 + 0.716037i
\(271\) 13.0212 + 22.5533i 0.790979 + 1.37002i 0.925362 + 0.379086i \(0.123761\pi\)
−0.134383 + 0.990929i \(0.542905\pi\)
\(272\) −0.505667 −0.0306605
\(273\) −4.16536 + 0.874424i −0.252099 + 0.0529225i
\(274\) −10.4984 + 18.1838i −0.634234 + 1.09853i
\(275\) 0.437470 + 0.757720i 0.0263804 + 0.0456922i
\(276\) 2.40902 0.505720i 0.145006 0.0304408i
\(277\) −7.36125 12.7501i −0.442295 0.766077i 0.555564 0.831473i \(-0.312502\pi\)
−0.997859 + 0.0653962i \(0.979169\pi\)
\(278\) −9.28836 −0.557079
\(279\) −2.98722 2.19340i −0.178840 0.131315i
\(280\) 1.25524 + 2.17414i 0.0750149 + 0.129930i
\(281\) 17.7201 1.05709 0.528545 0.848905i \(-0.322738\pi\)
0.528545 + 0.848905i \(0.322738\pi\)
\(282\) −4.76467 + 1.00023i −0.283732 + 0.0595631i
\(283\) −13.7058 −0.814723 −0.407361 0.913267i \(-0.633551\pi\)
−0.407361 + 0.913267i \(0.633551\pi\)
\(284\) −9.51672 + 16.4834i −0.564713 + 0.978112i
\(285\) −9.64063 0.620032i −0.571062 0.0367275i
\(286\) 0.432059 + 0.748348i 0.0255482 + 0.0442508i
\(287\) 5.40344 + 9.35904i 0.318955 + 0.552447i
\(288\) −16.0983 + 7.07054i −0.948601 + 0.416636i
\(289\) 8.49483 14.7135i 0.499696 0.865499i
\(290\) 7.42393 12.8586i 0.435948 0.755085i
\(291\) 19.7977 4.15608i 1.16056 0.243634i
\(292\) −0.461074 + 0.798604i −0.0269823 + 0.0467347i
\(293\) 14.2271 24.6420i 0.831153 1.43960i −0.0659708 0.997822i \(-0.521014\pi\)
0.897124 0.441778i \(-0.145652\pi\)
\(294\) −5.05334 + 15.4204i −0.294717 + 0.899337i
\(295\) −10.2637 −0.597578
\(296\) −12.8174 −0.744994
\(297\) 1.23091 + 0.559212i 0.0714248 + 0.0324487i
\(298\) 11.7653 20.3781i 0.681546 1.18047i
\(299\) −1.14307 + 1.97986i −0.0661057 + 0.114498i
\(300\) −2.10610 + 6.42683i −0.121596 + 0.371053i
\(301\) −4.04577 −0.233194
\(302\) −26.2588 −1.51103
\(303\) −15.8740 17.7194i −0.911940 1.01795i
\(304\) −5.41548 20.9940i −0.310599 1.20409i
\(305\) 18.0816 1.03535
\(306\) −0.0593947 + 0.538991i −0.00339537 + 0.0308121i
\(307\) −4.96283 8.59587i −0.283244 0.490592i 0.688938 0.724820i \(-0.258077\pi\)
−0.972182 + 0.234228i \(0.924744\pi\)
\(308\) −0.397454 −0.0226471
\(309\) −13.1845 + 2.76780i −0.750042 + 0.157454i
\(310\) 1.40522 + 2.43391i 0.0798110 + 0.138237i
\(311\) −5.07553 + 8.79108i −0.287807 + 0.498496i −0.973286 0.229596i \(-0.926260\pi\)
0.685479 + 0.728092i \(0.259593\pi\)
\(312\) 1.50261 4.58525i 0.0850683 0.259589i
\(313\) 25.9255 1.46540 0.732699 0.680552i \(-0.238260\pi\)
0.732699 + 0.680552i \(0.238260\pi\)
\(314\) 0.0693896 0.120186i 0.00391588 0.00678251i
\(315\) 4.62361 2.03074i 0.260511 0.114419i
\(316\) 13.5250 0.760839
\(317\) −24.3048 −1.36509 −0.682546 0.730843i \(-0.739127\pi\)
−0.682546 + 0.730843i \(0.739127\pi\)
\(318\) 4.98674 15.2172i 0.279643 0.853338i
\(319\) −0.849054 1.47060i −0.0475379 0.0823381i
\(320\) 0.604463 0.0337905
\(321\) 3.14000 + 3.50503i 0.175258 + 0.195632i
\(322\) −1.43133 2.47913i −0.0797647 0.138157i
\(323\) −0.426942 0.118688i −0.0237557 0.00660397i
\(324\) 3.12919 + 9.97112i 0.173844 + 0.553951i
\(325\) −3.14063 5.43973i −0.174211 0.301742i
\(326\) 17.4145 30.1627i 0.964498 1.67056i
\(327\) 9.75076 29.7547i 0.539218 1.64544i
\(328\) −12.2517 −0.676487
\(329\) 1.03987 + 1.80111i 0.0573301 + 0.0992986i
\(330\) −0.684122 0.763651i −0.0376597 0.0420376i
\(331\) −4.85091 8.40202i −0.266630 0.461817i 0.701359 0.712808i \(-0.252577\pi\)
−0.967989 + 0.250991i \(0.919244\pi\)
\(332\) −3.52145 + 6.09933i −0.193265 + 0.334744i
\(333\) −2.82404 + 25.6274i −0.154756 + 1.40437i
\(334\) −41.3640 −2.26334
\(335\) −0.500256 0.866469i −0.0273319 0.0473402i
\(336\) 7.56241 + 8.44154i 0.412563 + 0.460524i
\(337\) 33.7366 1.83775 0.918876 0.394546i \(-0.129098\pi\)
0.918876 + 0.394546i \(0.129098\pi\)
\(338\) 8.45502 + 14.6445i 0.459893 + 0.796557i
\(339\) 19.7849 4.15340i 1.07457 0.225582i
\(340\) 0.0755249 0.130813i 0.00409591 0.00709432i
\(341\) 0.321421 0.0174059
\(342\) −23.0137 + 3.30645i −1.24444 + 0.178792i
\(343\) 16.1407 0.871514
\(344\) 2.29333 3.97217i 0.123648 0.214165i
\(345\) 0.844701 2.57763i 0.0454772 0.138775i
\(346\) 5.08757 + 8.81193i 0.273510 + 0.473732i
\(347\) −29.2979 −1.57279 −0.786396 0.617723i \(-0.788055\pi\)
−0.786396 + 0.617723i \(0.788055\pi\)
\(348\) 4.08758 12.4734i 0.219118 0.668644i
\(349\) −1.69824 2.94144i −0.0909049 0.157452i 0.816987 0.576656i \(-0.195643\pi\)
−0.907892 + 0.419204i \(0.862309\pi\)
\(350\) 7.86521 0.420413
\(351\) −8.83681 4.01462i −0.471674 0.214285i
\(352\) 0.762468 1.32063i 0.0406397 0.0703900i
\(353\) −3.31809 5.74710i −0.176604 0.305887i 0.764111 0.645085i \(-0.223178\pi\)
−0.940715 + 0.339197i \(0.889845\pi\)
\(354\) −24.1747 + 5.07494i −1.28487 + 0.269730i
\(355\) 10.4870 + 18.1641i 0.556594 + 0.964049i
\(356\) −13.3663 −0.708414
\(357\) 0.226700 0.0475905i 0.0119982 0.00251875i
\(358\) 6.72102 11.6411i 0.355217 0.615254i
\(359\) −18.5021 32.0466i −0.976505 1.69136i −0.674876 0.737931i \(-0.735803\pi\)
−0.301629 0.953425i \(-0.597530\pi\)
\(360\) −0.627083 + 5.69061i −0.0330502 + 0.299922i
\(361\) 0.355254 18.9967i 0.0186976 0.999825i
\(362\) −7.78086 13.4768i −0.408953 0.708327i
\(363\) 18.5314 3.89024i 0.972645 0.204185i
\(364\) 2.85335 0.149556
\(365\) 0.508085 + 0.880029i 0.0265944 + 0.0460628i
\(366\) 42.5885 8.94050i 2.22614 0.467327i
\(367\) 14.7101 0.767859 0.383929 0.923363i \(-0.374571\pi\)
0.383929 + 0.923363i \(0.374571\pi\)
\(368\) 6.08771 0.317344
\(369\) −2.69941 + 24.4964i −0.140526 + 1.27523i
\(370\) 9.77605 16.9326i 0.508233 0.880285i
\(371\) −6.84066 −0.355149
\(372\) 1.65782 + 1.85054i 0.0859541 + 0.0959462i
\(373\) −0.728793 + 1.26231i −0.0377355 + 0.0653598i −0.884276 0.466964i \(-0.845348\pi\)
0.846541 + 0.532324i \(0.178681\pi\)
\(374\) −0.0235148 0.0407288i −0.00121592 0.00210604i
\(375\) 12.3670 + 13.8047i 0.638631 + 0.712871i
\(376\) −2.35780 −0.121594
\(377\) 6.09542 + 10.5576i 0.313930 + 0.543743i
\(378\) 9.88612 7.06926i 0.508487 0.363604i
\(379\) 30.8963 1.58704 0.793519 0.608546i \(-0.208247\pi\)
0.793519 + 0.608546i \(0.208247\pi\)
\(380\) 6.23987 + 1.73465i 0.320099 + 0.0889859i
\(381\) 8.10473 1.70141i 0.415218 0.0871656i
\(382\) −4.85058 −0.248177
\(383\) 18.4547 0.942990 0.471495 0.881869i \(-0.343715\pi\)
0.471495 + 0.881869i \(0.343715\pi\)
\(384\) −18.4458 + 3.87228i −0.941308 + 0.197606i
\(385\) −0.218989 + 0.379300i −0.0111607 + 0.0193309i
\(386\) 21.8524 37.8494i 1.11226 1.92648i
\(387\) −7.43679 5.46054i −0.378033 0.277575i
\(388\) −13.5618 −0.688497
\(389\) −0.838973 −0.0425376 −0.0212688 0.999774i \(-0.506771\pi\)
−0.0212688 + 0.999774i \(0.506771\pi\)
\(390\) 4.91136 + 5.48230i 0.248696 + 0.277607i
\(391\) 0.0622118 0.107754i 0.00314618 0.00544935i
\(392\) −3.92939 + 6.80591i −0.198464 + 0.343750i
\(393\) −13.3587 14.9117i −0.673858 0.752193i
\(394\) −4.11081 + 7.12014i −0.207100 + 0.358707i
\(395\) 7.45199 12.9072i 0.374950 0.649433i
\(396\) −0.730586 0.536441i −0.0367133 0.0269572i
\(397\) 10.4063 + 18.0243i 0.522279 + 0.904613i 0.999664 + 0.0259191i \(0.00825123\pi\)
−0.477385 + 0.878694i \(0.658415\pi\)
\(398\) 5.79766 + 10.0418i 0.290610 + 0.503352i
\(399\) 4.40370 + 8.90234i 0.220461 + 0.445674i
\(400\) −8.36307 + 14.4853i −0.418153 + 0.724263i
\(401\) −34.0303 −1.69939 −0.849697 0.527271i \(-0.823215\pi\)
−0.849697 + 0.527271i \(0.823215\pi\)
\(402\) −1.60671 1.79349i −0.0801353 0.0894510i
\(403\) −2.30751 −0.114945
\(404\) 7.97447 + 13.8122i 0.396745 + 0.687182i
\(405\) 11.2398 + 2.50762i 0.558511 + 0.124604i
\(406\) −15.2650 −0.757591
\(407\) −1.11806 1.93653i −0.0554201 0.0959904i
\(408\) −0.0817793 + 0.249552i −0.00404868 + 0.0123547i
\(409\) 15.7351 + 27.2540i 0.778051 + 1.34762i 0.933064 + 0.359711i \(0.117125\pi\)
−0.155013 + 0.987912i \(0.549542\pi\)
\(410\) 9.34461 16.1853i 0.461497 0.799337i
\(411\) 13.6485 + 15.2351i 0.673231 + 0.751494i
\(412\) 9.03166 0.444958
\(413\) 5.27605 + 9.13839i 0.259618 + 0.449671i
\(414\) 0.715051 6.48890i 0.0351428 0.318912i
\(415\) 3.88050 + 6.72122i 0.190486 + 0.329932i
\(416\) −5.47381 + 9.48092i −0.268376 + 0.464841i
\(417\) −2.81778 + 8.59854i −0.137987 + 0.421072i
\(418\) 1.43913 1.41247i 0.0703900 0.0690859i
\(419\) 9.72553 16.8451i 0.475123 0.822938i −0.524471 0.851428i \(-0.675737\pi\)
0.999594 + 0.0284908i \(0.00907012\pi\)
\(420\) −3.31327 + 0.695547i −0.161671 + 0.0339392i
\(421\) 9.96050 17.2521i 0.485445 0.840815i −0.514415 0.857541i \(-0.671991\pi\)
0.999860 + 0.0167261i \(0.00532433\pi\)
\(422\) −4.63787 + 8.03303i −0.225768 + 0.391042i
\(423\) −0.519492 + 4.71425i −0.0252586 + 0.229215i
\(424\) 3.87761 6.71622i 0.188313 0.326168i
\(425\) 0.170928 + 0.296057i 0.00829125 + 0.0143609i
\(426\) 33.6820 + 37.5975i 1.63190 + 1.82160i
\(427\) −9.29480 16.0991i −0.449807 0.779088i
\(428\) −1.57741 2.73215i −0.0762470 0.132064i
\(429\) 0.823843 0.172947i 0.0397755 0.00834997i
\(430\) 3.49834 + 6.05930i 0.168705 + 0.292205i
\(431\) 1.45784 2.52505i 0.0702215 0.121627i −0.828777 0.559579i \(-0.810963\pi\)
0.898998 + 0.437952i \(0.144296\pi\)
\(432\) 2.50747 + 25.7239i 0.120641 + 1.23764i
\(433\) −16.0100 + 27.7302i −0.769393 + 1.33263i 0.168500 + 0.985702i \(0.446108\pi\)
−0.937893 + 0.346926i \(0.887226\pi\)
\(434\) 1.44470 2.50229i 0.0693478 0.120114i
\(435\) −9.65149 10.7735i −0.462753 0.516548i
\(436\) −10.4958 + 18.1792i −0.502657 + 0.870627i
\(437\) 5.13994 + 1.42888i 0.245877 + 0.0683526i
\(438\) 1.63185 + 1.82155i 0.0779729 + 0.0870372i
\(439\) −5.64478 + 9.77704i −0.269411 + 0.466633i −0.968710 0.248196i \(-0.920162\pi\)
0.699299 + 0.714829i \(0.253496\pi\)
\(440\) −0.248267 0.430011i −0.0118357 0.0205000i
\(441\) 12.7422 + 9.35608i 0.606770 + 0.445528i
\(442\) 0.168814 + 0.292395i 0.00802968 + 0.0139078i
\(443\) −38.4359 −1.82614 −0.913071 0.407800i \(-0.866296\pi\)
−0.913071 + 0.407800i \(0.866296\pi\)
\(444\) 5.38265 16.4253i 0.255449 0.779511i
\(445\) −7.36458 + 12.7558i −0.349115 + 0.604684i
\(446\) −4.38738 7.59917i −0.207749 0.359831i
\(447\) −15.2955 17.0736i −0.723452 0.807553i
\(448\) −0.310723 0.538188i −0.0146803 0.0254270i
\(449\) −0.523696 −0.0247147 −0.0123574 0.999924i \(-0.503934\pi\)
−0.0123574 + 0.999924i \(0.503934\pi\)
\(450\) 14.4575 + 10.6156i 0.681535 + 0.500425i
\(451\) −1.06872 1.85107i −0.0503239 0.0871635i
\(452\) −13.5531 −0.637483
\(453\) −7.96605 + 24.3087i −0.374278 + 1.14212i
\(454\) 26.0916 1.22454
\(455\) 1.57214 2.72303i 0.0737030 0.127657i
\(456\) −11.2366 0.722676i −0.526202 0.0338424i
\(457\) −10.7106 18.5513i −0.501022 0.867795i −0.999999 0.00118016i \(-0.999624\pi\)
0.498978 0.866615i \(-0.333709\pi\)
\(458\) 1.04811 + 1.81538i 0.0489749 + 0.0848270i
\(459\) 0.480943 + 0.218496i 0.0224485 + 0.0101985i
\(460\) −0.909242 + 1.57485i −0.0423936 + 0.0734279i
\(461\) 0.504860 0.874443i 0.0235137 0.0407269i −0.854029 0.520225i \(-0.825848\pi\)
0.877543 + 0.479498i \(0.159181\pi\)
\(462\) −0.328250 + 1.00167i −0.0152716 + 0.0466017i
\(463\) 5.44085 9.42382i 0.252858 0.437962i −0.711454 0.702733i \(-0.751963\pi\)
0.964311 + 0.264771i \(0.0852963\pi\)
\(464\) 16.2313 28.1134i 0.753518 1.30513i
\(465\) 2.67945 0.562489i 0.124256 0.0260848i
\(466\) −38.4709 −1.78213
\(467\) −0.227947 −0.0105481 −0.00527407 0.999986i \(-0.501679\pi\)
−0.00527407 + 0.999986i \(0.501679\pi\)
\(468\) 5.24493 + 3.85115i 0.242447 + 0.178019i
\(469\) −0.514311 + 0.890813i −0.0237487 + 0.0411339i
\(470\) 1.79834 3.11481i 0.0829511 0.143676i
\(471\) −0.0902100 0.100697i −0.00415666 0.00463986i
\(472\) −11.9629 −0.550635
\(473\) 0.800190 0.0367928
\(474\) 11.1700 34.0857i 0.513057 1.56561i
\(475\) −10.4610 + 10.2672i −0.479983 + 0.471090i
\(476\) −0.155294 −0.00711787
\(477\) −12.5742 9.23279i −0.575735 0.422740i
\(478\) −15.8089 27.3818i −0.723081 1.25241i
\(479\) −13.6303 −0.622786 −0.311393 0.950281i \(-0.600796\pi\)
−0.311393 + 0.950281i \(0.600796\pi\)
\(480\) 4.04500 12.3434i 0.184628 0.563398i
\(481\) 8.02662 + 13.9025i 0.365983 + 0.633900i
\(482\) 2.35881 4.08558i 0.107441 0.186093i
\(483\) −2.72923 + 0.572940i −0.124184 + 0.0260697i
\(484\) −12.6944 −0.577016
\(485\) −7.47229 + 12.9424i −0.339299 + 0.587683i
\(486\) 27.7136 + 0.348760i 1.25712 + 0.0158201i
\(487\) −18.8745 −0.855286 −0.427643 0.903948i \(-0.640656\pi\)
−0.427643 + 0.903948i \(0.640656\pi\)
\(488\) 21.0749 0.954017
\(489\) −22.6397 25.2715i −1.02380 1.14282i
\(490\) −5.99405 10.3820i −0.270783 0.469011i
\(491\) −0.829442 −0.0374322 −0.0187161 0.999825i \(-0.505958\pi\)
−0.0187161 + 0.999825i \(0.505958\pi\)
\(492\) 5.14510 15.7004i 0.231959 0.707830i
\(493\) −0.331743 0.574596i −0.0149410 0.0258785i
\(494\) −10.3316 + 10.1402i −0.464841 + 0.456229i
\(495\) −0.914477 + 0.401648i −0.0411027 + 0.0180527i
\(496\) 3.07229 + 5.32136i 0.137950 + 0.238936i
\(497\) 10.7817 18.6744i 0.483625 0.837663i
\(498\) 12.4633 + 13.9121i 0.558492 + 0.623417i
\(499\) 1.50254 0.0672629 0.0336314 0.999434i \(-0.489293\pi\)
0.0336314 + 0.999434i \(0.489293\pi\)
\(500\) −6.21269 10.7607i −0.277840 0.481233i
\(501\) −12.5485 + 38.2920i −0.560624 + 1.71076i
\(502\) 5.74660 + 9.95340i 0.256483 + 0.444242i
\(503\) −4.60299 + 7.97262i −0.205237 + 0.355481i −0.950208 0.311615i \(-0.899130\pi\)
0.744971 + 0.667097i \(0.232463\pi\)
\(504\) 5.38903 2.36692i 0.240046 0.105431i
\(505\) 17.5751 0.782081
\(506\) 0.283094 + 0.490333i 0.0125851 + 0.0217980i
\(507\) 16.1219 3.38443i 0.715999 0.150308i
\(508\) −5.55190 −0.246326
\(509\) −1.22085 2.11458i −0.0541133 0.0937271i 0.837700 0.546131i \(-0.183900\pi\)
−0.891813 + 0.452404i \(0.850567\pi\)
\(510\) −0.267301 0.298374i −0.0118363 0.0132122i
\(511\) 0.522360 0.904754i 0.0231078 0.0400240i
\(512\) 14.3155 0.632664
\(513\) −3.92069 + 22.3076i −0.173103 + 0.984904i
\(514\) −29.7496 −1.31220
\(515\) 4.97626 8.61914i 0.219280 0.379805i
\(516\) 4.12721 + 4.60699i 0.181690 + 0.202812i
\(517\) −0.205671 0.356232i −0.00904538 0.0156671i
\(518\) −20.1014 −0.883206
\(519\) 9.70090 2.03649i 0.425822 0.0893918i
\(520\) 1.78233 + 3.08708i 0.0781602 + 0.135377i
\(521\) 4.12120 0.180553 0.0902764 0.995917i \(-0.471225\pi\)
0.0902764 + 0.995917i \(0.471225\pi\)
\(522\) −28.0596 20.6031i −1.22814 0.901773i
\(523\) −15.9501 + 27.6263i −0.697448 + 1.20802i 0.271900 + 0.962325i \(0.412348\pi\)
−0.969348 + 0.245690i \(0.920985\pi\)
\(524\) 6.71087 + 11.6236i 0.293166 + 0.507778i
\(525\) 2.38605 7.28109i 0.104136 0.317773i
\(526\) −18.6318 32.2712i −0.812384 1.40709i
\(527\) 0.125586 0.00547061
\(528\) −1.49573 1.66960i −0.0650932 0.0726602i
\(529\) 10.7510 18.6213i 0.467436 0.809623i
\(530\) 5.91505 + 10.2452i 0.256934 + 0.445022i
\(531\) −2.63577 + 23.9189i −0.114383 + 1.03799i
\(532\) −1.66313 6.44741i −0.0721059 0.279531i
\(533\) 7.67239 + 13.2890i 0.332328 + 0.575609i
\(534\) −11.0390 + 33.6859i −0.477705 + 1.45773i
\(535\) −3.47648 −0.150301
\(536\) −0.583072 1.00991i −0.0251849 0.0436215i
\(537\) −8.73766 9.75341i −0.377058 0.420891i
\(538\) −28.6021 −1.23313
\(539\) −1.37104 −0.0590550
\(540\) −7.02911 3.19337i −0.302485 0.137421i
\(541\) −7.44884 + 12.9018i −0.320251 + 0.554690i −0.980540 0.196321i \(-0.937100\pi\)
0.660289 + 0.751012i \(0.270434\pi\)
\(542\) −46.3024 −1.98886
\(543\) −14.8364 + 3.11457i −0.636691 + 0.133659i
\(544\) 0.297912 0.515999i 0.0127729 0.0221233i
\(545\) 11.5659 + 20.0328i 0.495430 + 0.858110i
\(546\) 2.35653 7.19104i 0.100850 0.307748i
\(547\) −7.85484 −0.335849 −0.167924 0.985800i \(-0.553706\pi\)
−0.167924 + 0.985800i \(0.553706\pi\)
\(548\) −6.85645 11.8757i −0.292893 0.507306i
\(549\) 4.64342 42.1378i 0.198177 1.79840i
\(550\) −1.55562 −0.0663317
\(551\) 20.3030 19.9268i 0.864936 0.848912i
\(552\) 0.984539 3.00435i 0.0419048 0.127874i
\(553\) −15.3227 −0.651588
\(554\) 26.1762 1.11212
\(555\) −12.7093 14.1868i −0.539482 0.602196i
\(556\) 3.03308 5.25344i 0.128631 0.222796i
\(557\) −12.9954 + 22.5087i −0.550632 + 0.953722i 0.447597 + 0.894235i \(0.352280\pi\)
−0.998229 + 0.0594871i \(0.981053\pi\)
\(558\) 6.03291 2.64972i 0.255394 0.112172i
\(559\) −5.74462 −0.242972
\(560\) −8.37279 −0.353815
\(561\) −0.0448376 + 0.00941265i −0.00189305 + 0.000397402i
\(562\) −15.7529 + 27.2848i −0.664494 + 1.15094i
\(563\) 0.182015 0.315259i 0.00767101 0.0132866i −0.862164 0.506629i \(-0.830892\pi\)
0.869835 + 0.493342i \(0.164225\pi\)
\(564\) 0.990156 3.02149i 0.0416931 0.127228i
\(565\) −7.46747 + 12.9340i −0.314159 + 0.544139i
\(566\) 12.1842 21.1037i 0.512141 0.887054i
\(567\) −3.54513 11.2965i −0.148881 0.474408i
\(568\) 12.2231 + 21.1711i 0.512871 + 0.888319i
\(569\) −6.09470 10.5563i −0.255503 0.442544i 0.709529 0.704676i \(-0.248908\pi\)
−0.965032 + 0.262132i \(0.915574\pi\)
\(570\) 9.52508 14.2931i 0.398962 0.598673i
\(571\) −0.379660 + 0.657591i −0.0158883 + 0.0275193i −0.873860 0.486177i \(-0.838391\pi\)
0.857972 + 0.513697i \(0.171724\pi\)
\(572\) −0.564349 −0.0235966
\(573\) −1.47150 + 4.49034i −0.0614730 + 0.187587i
\(574\) −19.2143 −0.801990
\(575\) −2.05780 3.56422i −0.0858163 0.148638i
\(576\) 0.155229 1.40866i 0.00646786 0.0586941i
\(577\) −10.8385 −0.451212 −0.225606 0.974219i \(-0.572436\pi\)
−0.225606 + 0.974219i \(0.572436\pi\)
\(578\) 15.1036 + 26.1601i 0.628225 + 1.08812i
\(579\) −28.4092 31.7117i −1.18064 1.31789i
\(580\) 4.84851 + 8.39787i 0.201324 + 0.348703i
\(581\) 3.98952 6.91006i 0.165513 0.286678i
\(582\) −11.2005 + 34.1786i −0.464274 + 1.41675i
\(583\) 1.35298 0.0560345
\(584\) 0.592197 + 1.02571i 0.0245053 + 0.0424444i
\(585\) 6.56510 2.88346i 0.271433 0.119216i
\(586\) 25.2953 + 43.8127i 1.04494 + 1.80989i
\(587\) 6.63595 11.4938i 0.273895 0.474400i −0.695961 0.718080i \(-0.745021\pi\)
0.969856 + 0.243680i \(0.0783546\pi\)
\(588\) −7.07155 7.89361i −0.291626 0.325527i
\(589\) 1.34497 + 5.21402i 0.0554187 + 0.214840i
\(590\) 9.12431 15.8038i 0.375642 0.650631i
\(591\) 5.34426 + 5.96553i 0.219834 + 0.245389i
\(592\) 21.3738 37.0205i 0.878458 1.52153i
\(593\) −0.533785 + 0.924543i −0.0219199 + 0.0379664i −0.876777 0.480897i \(-0.840311\pi\)
0.854857 + 0.518863i \(0.173645\pi\)
\(594\) −1.95532 + 1.39819i −0.0802277 + 0.0573684i
\(595\) −0.0855636 + 0.148201i −0.00350777 + 0.00607563i
\(596\) 7.68383 + 13.3088i 0.314742 + 0.545149i
\(597\) 11.0549 2.32072i 0.452446 0.0949808i
\(598\) −2.03235 3.52014i −0.0831091 0.143949i
\(599\) −6.67115 11.5548i −0.272576 0.472115i 0.696945 0.717125i \(-0.254542\pi\)
−0.969521 + 0.245010i \(0.921209\pi\)
\(600\) 5.79611 + 6.46990i 0.236625 + 0.264133i
\(601\) 22.5595 + 39.0742i 0.920220 + 1.59387i 0.799074 + 0.601233i \(0.205324\pi\)
0.121147 + 0.992635i \(0.461343\pi\)
\(602\) 3.59663 6.22955i 0.146588 0.253897i
\(603\) −2.14771 + 0.943298i −0.0874616 + 0.0384141i
\(604\) 8.57471 14.8518i 0.348900 0.604313i
\(605\) −6.99433 + 12.1145i −0.284360 + 0.492526i
\(606\) 41.3955 8.69006i 1.68158 0.353010i
\(607\) 12.5161 21.6785i 0.508012 0.879903i −0.491944 0.870627i \(-0.663714\pi\)
0.999957 0.00927687i \(-0.00295296\pi\)
\(608\) 24.6135 + 6.84244i 0.998210 + 0.277498i
\(609\) −4.63091 + 14.1314i −0.187654 + 0.572631i
\(610\) −16.0743 + 27.8414i −0.650827 + 1.12727i
\(611\) 1.47652 + 2.55742i 0.0597338 + 0.103462i
\(612\) −0.285455 0.209599i −0.0115388 0.00847252i
\(613\) 10.4697 + 18.1341i 0.422869 + 0.732430i 0.996219 0.0868805i \(-0.0276898\pi\)
−0.573350 + 0.819310i \(0.694357\pi\)
\(614\) 17.6475 0.712196
\(615\) −12.1485 13.5607i −0.489873 0.546821i
\(616\) −0.255242 + 0.442092i −0.0102840 + 0.0178124i
\(617\) 9.25883 + 16.0368i 0.372746 + 0.645616i 0.989987 0.141159i \(-0.0450828\pi\)
−0.617241 + 0.786774i \(0.711750\pi\)
\(618\) 7.45909 22.7616i 0.300049 0.915607i
\(619\) 13.2353 + 22.9241i 0.531970 + 0.921398i 0.999303 + 0.0373175i \(0.0118813\pi\)
−0.467334 + 0.884081i \(0.654785\pi\)
\(620\) −1.83547 −0.0737144
\(621\) −5.79006 2.63046i −0.232347 0.105557i
\(622\) −9.02415 15.6303i −0.361835 0.626717i
\(623\) 15.1430 0.606691
\(624\) 10.7379 + 11.9862i 0.429861 + 0.479832i
\(625\) 3.12123 0.124849
\(626\) −23.0474 + 39.9193i −0.921160 + 1.59550i
\(627\) −0.870983 1.76074i −0.0347837 0.0703173i
\(628\) 0.0453178 + 0.0784927i 0.00180838 + 0.00313220i
\(629\) −0.436849 0.756644i −0.0174183 0.0301694i
\(630\) −0.983453 + 8.92457i −0.0391817 + 0.355563i
\(631\) 7.09305 12.2855i 0.282370 0.489079i −0.689598 0.724192i \(-0.742213\pi\)
0.971968 + 0.235113i \(0.0755462\pi\)
\(632\) 8.68564 15.0440i 0.345496 0.598417i
\(633\) 6.02947 + 6.73039i 0.239650 + 0.267509i
\(634\) 21.6066 37.4237i 0.858107 1.48628i
\(635\) −3.05898 + 5.29831i −0.121392 + 0.210257i
\(636\) 6.97836 + 7.78959i 0.276710 + 0.308877i
\(637\) 9.84282 0.389987
\(638\) 3.01919 0.119531
\(639\) 45.0232 19.7747i 1.78109 0.782274i
\(640\) 6.96203 12.0586i 0.275198 0.476658i
\(641\) 8.29318 14.3642i 0.327561 0.567352i −0.654466 0.756091i \(-0.727107\pi\)
0.982027 + 0.188739i \(0.0604400\pi\)
\(642\) −8.18834 + 1.71896i −0.323168 + 0.0678419i
\(643\) −22.0545 −0.869745 −0.434872 0.900492i \(-0.643207\pi\)
−0.434872 + 0.900492i \(0.643207\pi\)
\(644\) 1.86958 0.0736716
\(645\) 6.67058 1.40034i 0.262654 0.0551382i
\(646\) 0.562297 0.551880i 0.0221233 0.0217134i
\(647\) −20.3310 −0.799292 −0.399646 0.916669i \(-0.630867\pi\)
−0.399646 + 0.916669i \(0.630867\pi\)
\(648\) 13.1005 + 2.92274i 0.514637 + 0.114816i
\(649\) −1.04352 1.80743i −0.0409618 0.0709479i
\(650\) 11.1679 0.438040
\(651\) −1.87818 2.09652i −0.0736117 0.0821690i
\(652\) 11.3732 + 19.6990i 0.445411 + 0.771474i
\(653\) 10.5732 18.3133i 0.413761 0.716655i −0.581537 0.813520i \(-0.697548\pi\)
0.995297 + 0.0968655i \(0.0308817\pi\)
\(654\) 37.1471 + 41.4654i 1.45257 + 1.62143i
\(655\) 14.7902 0.577901
\(656\) 20.4305 35.3867i 0.797679 1.38162i
\(657\) 2.18132 0.958060i 0.0851015 0.0373775i
\(658\) −3.69773 −0.144152
\(659\) −31.4873 −1.22657 −0.613286 0.789861i \(-0.710153\pi\)
−0.613286 + 0.789861i \(0.710153\pi\)
\(660\) 0.655314 0.137568i 0.0255081 0.00535484i
\(661\) −1.49130 2.58300i −0.0580047 0.100467i 0.835565 0.549392i \(-0.185140\pi\)
−0.893570 + 0.448925i \(0.851807\pi\)
\(662\) 17.2495 0.670423
\(663\) 0.321893 0.0675741i 0.0125013 0.00262436i
\(664\) 4.52290 + 7.83389i 0.175523 + 0.304014i
\(665\) −7.06927 1.96522i −0.274135 0.0762082i
\(666\) −36.9497 27.1307i −1.43177 1.05130i
\(667\) 3.99385 + 6.91754i 0.154642 + 0.267848i
\(668\) 13.5073 23.3953i 0.522611 0.905190i
\(669\) −8.36579 + 1.75621i −0.323440 + 0.0678990i
\(670\) 1.77888 0.0687241
\(671\) 1.83837 + 3.18414i 0.0709693 + 0.122922i
\(672\) −13.0694 + 2.74363i −0.504163 + 0.105838i
\(673\) −22.7026 39.3221i −0.875122 1.51576i −0.856633 0.515927i \(-0.827448\pi\)
−0.0184895 0.999829i \(-0.505886\pi\)
\(674\) −29.9914 + 51.9466i −1.15522 + 2.00091i
\(675\) 14.2132 10.1634i 0.547065 0.391190i
\(676\) −11.0438 −0.424762
\(677\) 17.5918 + 30.4700i 0.676109 + 1.17106i 0.976143 + 0.217127i \(0.0696686\pi\)
−0.300034 + 0.953928i \(0.596998\pi\)
\(678\) −11.1932 + 34.1565i −0.429874 + 1.31177i
\(679\) 15.3645 0.589634
\(680\) −0.0970030 0.168014i −0.00371990 0.00644305i
\(681\) 7.91532 24.1538i 0.303316 0.925577i
\(682\) −0.285739 + 0.494914i −0.0109415 + 0.0189512i
\(683\) 13.9565 0.534031 0.267015 0.963692i \(-0.413963\pi\)
0.267015 + 0.963692i \(0.413963\pi\)
\(684\) 5.64491 14.0961i 0.215839 0.538978i
\(685\) −15.1111 −0.577364
\(686\) −14.3488 + 24.8529i −0.547840 + 0.948887i
\(687\) 1.99852 0.419543i 0.0762481 0.0160066i
\(688\) 7.64858 + 13.2477i 0.291599 + 0.505065i
\(689\) −9.71311 −0.370040
\(690\) 3.21803 + 3.59212i 0.122508 + 0.136750i
\(691\) 5.37036 + 9.30173i 0.204298 + 0.353854i 0.949909 0.312527i \(-0.101176\pi\)
−0.745611 + 0.666382i \(0.767842\pi\)
\(692\) −6.64531 −0.252617
\(693\) 0.827695 + 0.607745i 0.0314415 + 0.0230863i
\(694\) 26.0454 45.1119i 0.988668 1.71242i
\(695\) −3.34233 5.78908i −0.126782 0.219592i
\(696\) −11.2493 12.5570i −0.426402 0.475971i
\(697\) −0.417570 0.723252i −0.0158166 0.0273951i
\(698\) 6.03885 0.228574
\(699\) −11.6708 + 35.6138i −0.441430 + 1.34704i
\(700\) −2.56835 + 4.44852i −0.0970747 + 0.168138i
\(701\) −13.3387 23.1033i −0.503795 0.872599i −0.999990 0.00438802i \(-0.998603\pi\)
0.496195 0.868211i \(-0.334730\pi\)
\(702\) 14.0374 10.0377i 0.529807 0.378849i
\(703\) 26.7355 26.2402i 1.00835 0.989669i
\(704\) 0.0614562 + 0.106445i 0.00231622 + 0.00401181i
\(705\) −2.33793 2.60971i −0.0880515 0.0982874i
\(706\) 11.7989 0.444059
\(707\) −9.03444 15.6481i −0.339775 0.588508i
\(708\) 5.02380 15.3303i 0.188806 0.576147i
\(709\) 23.1688 0.870123 0.435061 0.900401i \(-0.356727\pi\)
0.435061 + 0.900401i \(0.356727\pi\)
\(710\) −37.2913 −1.39952
\(711\) −28.1657 20.6810i −1.05629 0.775596i
\(712\) −8.58376 + 14.8675i −0.321690 + 0.557184i
\(713\) −1.51193 −0.0566221
\(714\) −0.128254 + 0.391372i −0.00479980 + 0.0146467i
\(715\) −0.310945 + 0.538572i −0.0116287 + 0.0201414i
\(716\) 4.38944 + 7.60274i 0.164041 + 0.284128i
\(717\) −30.1441 + 6.32807i −1.12575 + 0.236326i
\(718\) 65.7925 2.45535
\(719\) −7.72298 13.3766i −0.288019 0.498863i 0.685318 0.728244i \(-0.259663\pi\)
−0.973337 + 0.229381i \(0.926330\pi\)
\(720\) −15.3906 11.3007i −0.573572 0.421152i
\(721\) −10.2322 −0.381065
\(722\) 28.9347 + 17.4348i 1.07684 + 0.648855i
\(723\) −3.06657 3.42305i −0.114047 0.127305i
\(724\) 10.1632 0.377714
\(725\) −21.9464 −0.815068
\(726\) −10.4840 + 31.9924i −0.389099 + 1.18735i
\(727\) 18.5288 32.0927i 0.687193 1.19025i −0.285549 0.958364i \(-0.592176\pi\)
0.972742 0.231890i \(-0.0744909\pi\)
\(728\) 1.83240 3.17381i 0.0679134 0.117629i
\(729\) 8.73025 25.5496i 0.323343 0.946282i
\(730\) −1.80672 −0.0668697
\(731\) 0.312651 0.0115638
\(732\) −8.85041 + 27.0073i −0.327121 + 0.998218i
\(733\) 18.8660 32.6769i 0.696832 1.20695i −0.272727 0.962091i \(-0.587926\pi\)
0.969559 0.244857i \(-0.0787409\pi\)
\(734\) −13.0770 + 22.6501i −0.482682 + 0.836029i
\(735\) −11.4294 + 2.39934i −0.421578 + 0.0885008i
\(736\) −3.58656 + 6.21210i −0.132202 + 0.228981i
\(737\) 0.101723 0.176189i 0.00374700 0.00649000i
\(738\) −35.3191 25.9334i −1.30011 0.954622i
\(739\) 2.29341 + 3.97230i 0.0843643 + 0.146123i 0.905120 0.425156i \(-0.139781\pi\)
−0.820756 + 0.571279i \(0.806447\pi\)
\(740\) 6.38466 + 11.0586i 0.234705 + 0.406521i
\(741\) 6.25285 + 12.6405i 0.229704 + 0.464360i
\(742\) 6.08125 10.5330i 0.223250 0.386680i
\(743\) −5.67781 −0.208299 −0.104149 0.994562i \(-0.533212\pi\)
−0.104149 + 0.994562i \(0.533212\pi\)
\(744\) 3.12302 0.655608i 0.114495 0.0240357i
\(745\) 16.9345 0.620434
\(746\) −1.29577 2.24434i −0.0474416 0.0821713i
\(747\) 16.6598 7.31718i 0.609552 0.267722i
\(748\) 0.0307146 0.00112304
\(749\) 1.78708 + 3.09531i 0.0652985 + 0.113100i
\(750\) −32.2501 + 6.77019i −1.17761 + 0.247212i
\(751\) −24.9720 43.2529i −0.911243 1.57832i −0.812311 0.583225i \(-0.801791\pi\)
−0.0989320 0.995094i \(-0.531543\pi\)
\(752\) 3.93179 6.81005i 0.143377 0.248337i
\(753\) 10.9575 2.30029i 0.399314 0.0838271i
\(754\) −21.6750 −0.789355
\(755\) −9.44898 16.3661i −0.343884 0.595624i
\(756\) 0.770061 + 7.89997i 0.0280069 + 0.287319i
\(757\) −10.2071 17.6792i −0.370984 0.642563i 0.618733 0.785601i \(-0.287646\pi\)
−0.989717 + 0.143038i \(0.954313\pi\)
\(758\) −27.4664 + 47.5731i −0.997623 + 1.72793i
\(759\) 0.539799 0.113319i 0.0195935 0.00411321i
\(760\) 5.93667 5.82669i 0.215346 0.211356i
\(761\) 5.85476 10.1407i 0.212235 0.367601i −0.740179 0.672410i \(-0.765259\pi\)
0.952414 + 0.304809i \(0.0985925\pi\)
\(762\) −4.58521 + 13.9919i −0.166105 + 0.506874i
\(763\) 11.8909 20.5956i 0.430479 0.745611i
\(764\) 1.58394 2.74346i 0.0573048 0.0992548i
\(765\) −0.357305 + 0.156932i −0.0129184 + 0.00567390i
\(766\) −16.4059 + 28.4159i −0.592770 + 1.02671i
\(767\) 7.49151 + 12.9757i 0.270503 + 0.468525i
\(768\) 10.9452 33.3997i 0.394952 1.20521i
\(769\) −22.3655 38.7381i −0.806520 1.39693i −0.915260 0.402863i \(-0.868015\pi\)
0.108741 0.994070i \(-0.465318\pi\)
\(770\) −0.389356 0.674385i −0.0140314 0.0243031i
\(771\) −9.02503 + 27.5402i −0.325029 + 0.991834i
\(772\) 14.2716 + 24.7191i 0.513646 + 0.889662i
\(773\) −1.53754 + 2.66310i −0.0553014 + 0.0957849i −0.892351 0.451342i \(-0.850945\pi\)
0.837049 + 0.547127i \(0.184279\pi\)
\(774\) 15.0192 6.59658i 0.539853 0.237109i
\(775\) 2.07703 3.59752i 0.0746091 0.129227i
\(776\) −8.70930 + 15.0850i −0.312646 + 0.541518i
\(777\) −6.09811 + 18.6086i −0.218768 + 0.667579i
\(778\) 0.745834 1.29182i 0.0267395 0.0463141i
\(779\) 25.5556 25.0822i 0.915626 0.898663i
\(780\) −4.70455 + 0.987614i −0.168450 + 0.0353622i
\(781\) −2.13245 + 3.69351i −0.0763050 + 0.132164i
\(782\) 0.110611 + 0.191583i 0.00395543 + 0.00685101i
\(783\) −27.5853 + 19.7254i −0.985819 + 0.704929i
\(784\) −13.1051 22.6986i −0.468038 0.810665i
\(785\) 0.0998768 0.00356475
\(786\) 34.8362 7.31307i 1.24257 0.260849i
\(787\) −20.1946 + 34.9780i −0.719859 + 1.24683i 0.241197 + 0.970476i \(0.422460\pi\)
−0.961055 + 0.276356i \(0.910873\pi\)
\(788\) −2.68474 4.65011i −0.0956399 0.165653i
\(789\) −35.5268 + 7.45804i −1.26479 + 0.265513i
\(790\) 13.2494 + 22.9486i 0.471393 + 0.816476i
\(791\) 15.3545 0.545945
\(792\) −1.06587 + 0.468140i −0.0378739 + 0.0166346i
\(793\) −13.1978 22.8592i −0.468666 0.811754i
\(794\) −37.0043 −1.31323
\(795\) 11.2787 2.36772i 0.400015 0.0839742i
\(796\) −7.57281 −0.268411
\(797\) −22.3467 + 38.7056i −0.791561 + 1.37102i 0.133440 + 0.991057i \(0.457398\pi\)
−0.925000 + 0.379966i \(0.875936\pi\)
\(798\) −17.6223 1.13337i −0.623824 0.0401209i
\(799\) −0.0803598 0.139187i −0.00284292 0.00492409i
\(800\) −9.85415 17.0679i −0.348397 0.603441i
\(801\) 27.8353 + 20.4384i 0.983512 + 0.722154i
\(802\) 30.2525 52.3988i 1.06825 1.85027i
\(803\) −0.103315 + 0.178946i −0.00364589 + 0.00631487i
\(804\) 1.53905 0.323089i 0.0542781 0.0113945i
\(805\) 1.03010 1.78418i 0.0363062 0.0628842i
\(806\) 2.05134 3.55302i 0.0722554 0.125150i
\(807\) −8.67694 + 26.4779i −0.305443 + 0.932068i
\(808\) 20.4846 0.720645
\(809\) 27.4216 0.964091 0.482046 0.876146i \(-0.339894\pi\)
0.482046 + 0.876146i \(0.339894\pi\)
\(810\) −13.8532 + 15.0775i −0.486751 + 0.529768i
\(811\) −11.3213 + 19.6090i −0.397543 + 0.688565i −0.993422 0.114509i \(-0.963470\pi\)
0.595879 + 0.803074i \(0.296804\pi\)
\(812\) 4.98474 8.63382i 0.174930 0.302988i
\(813\) −14.0466 + 42.8637i −0.492637 + 1.50330i
\(814\) 3.97575 0.139350
\(815\) 25.0657 0.878013
\(816\) −0.584412 0.652349i −0.0204585 0.0228368i
\(817\) 3.34836 + 12.9805i 0.117144 + 0.454130i
\(818\) −55.9531 −1.95635
\(819\) −5.94209 4.36304i −0.207633 0.152457i
\(820\) 6.10289 + 10.5705i 0.213122 + 0.369138i
\(821\) 4.76813 0.166409 0.0832044 0.996533i \(-0.473485\pi\)
0.0832044 + 0.996533i \(0.473485\pi\)
\(822\) −35.5919 + 7.47171i −1.24141 + 0.260606i
\(823\) −11.3428 19.6464i −0.395386 0.684829i 0.597764 0.801672i \(-0.296056\pi\)
−0.993150 + 0.116843i \(0.962723\pi\)
\(824\) 5.80007 10.0460i 0.202055 0.349969i
\(825\) −0.471922 + 1.44009i −0.0164302 + 0.0501373i
\(826\) −18.7613 −0.652790
\(827\) 18.3589 31.7985i 0.638400 1.10574i −0.347384 0.937723i \(-0.612930\pi\)
0.985784 0.168018i \(-0.0537367\pi\)
\(828\) 3.43659 + 2.52335i 0.119430 + 0.0876925i
\(829\) −4.14173 −0.143848 −0.0719242 0.997410i \(-0.522914\pi\)
−0.0719242 + 0.997410i \(0.522914\pi\)
\(830\) −13.7988 −0.478964
\(831\) 7.94099 24.2322i 0.275470 0.840604i
\(832\) −0.441199 0.764178i −0.0152958 0.0264931i
\(833\) −0.535695 −0.0185607
\(834\) −10.7348 11.9827i −0.371715 0.414927i
\(835\) −14.8844 25.7806i −0.515098 0.892175i
\(836\) 0.328941 + 1.27520i 0.0113767 + 0.0441036i
\(837\) −0.622749 6.38871i −0.0215253 0.220826i
\(838\) 17.2917 + 29.9501i 0.597332 + 1.03461i
\(839\) −25.9853 + 45.0079i −0.897112 + 1.55384i −0.0659441 + 0.997823i \(0.521006\pi\)
−0.831168 + 0.556021i \(0.812327\pi\)
\(840\) −1.35410 + 4.13206i −0.0467207 + 0.142570i
\(841\) 13.5942 0.468766
\(842\) 17.7095 + 30.6737i 0.610308 + 1.05709i
\(843\) 20.4795 + 22.8602i 0.705352 + 0.787348i
\(844\) −3.02896 5.24631i −0.104261 0.180585i
\(845\) −6.08492 + 10.5394i −0.209328 + 0.362566i
\(846\) −6.79703 4.99079i −0.233687 0.171587i
\(847\) 14.3817 0.494161
\(848\) 12.9324 + 22.3995i 0.444099 + 0.769202i
\(849\) −15.8401 17.6815i −0.543630 0.606827i
\(850\) −0.607811 −0.0208478
\(851\) 5.25921 + 9.10922i 0.180283 + 0.312260i
\(852\) −32.2636 + 6.77302i −1.10533 + 0.232040i
\(853\) −11.8152 + 20.4645i −0.404544 + 0.700690i −0.994268 0.106914i \(-0.965903\pi\)
0.589725 + 0.807604i \(0.299236\pi\)
\(854\) 33.0518 1.13101
\(855\) −10.3420 13.1537i −0.353690 0.449849i
\(856\) −4.05200 −0.138495
\(857\) −22.2493 + 38.5369i −0.760021 + 1.31640i 0.182818 + 0.983147i \(0.441478\pi\)
−0.942839 + 0.333249i \(0.891855\pi\)
\(858\) −0.466086 + 1.42227i −0.0159119 + 0.0485556i
\(859\) 21.3956 + 37.0582i 0.730008 + 1.26441i 0.956879 + 0.290486i \(0.0938169\pi\)
−0.226872 + 0.973925i \(0.572850\pi\)
\(860\) −4.56948 −0.155818
\(861\) −5.82899 + 17.7873i −0.198651 + 0.606191i
\(862\) 2.59199 + 4.48946i 0.0882836 + 0.152912i
\(863\) −36.9884 −1.25910 −0.629550 0.776960i \(-0.716761\pi\)
−0.629550 + 0.776960i \(0.716761\pi\)
\(864\) −27.7267 12.5964i −0.943283 0.428539i
\(865\) −3.66143 + 6.34178i −0.124492 + 0.215627i
\(866\) −28.4653 49.3034i −0.967292 1.67540i
\(867\) 28.7992 6.04575i 0.978073 0.205324i
\(868\) 0.943521 + 1.63423i 0.0320252 + 0.0554693i
\(869\) 3.03059 0.102806
\(870\) 25.1687 5.28359i 0.853297 0.179131i
\(871\) −0.730275 + 1.26487i −0.0247444 + 0.0428586i
\(872\) 13.4806 + 23.3491i 0.456512 + 0.790702i
\(873\) 28.2424 + 20.7373i 0.955860 + 0.701851i
\(874\) −6.76947 + 6.64406i −0.228981 + 0.224739i
\(875\) 7.03848 + 12.1910i 0.237944 + 0.412131i
\(876\) −1.56314 + 0.328145i −0.0528134 + 0.0110870i
\(877\) −20.8501 −0.704058 −0.352029 0.935989i \(-0.614508\pi\)
−0.352029 + 0.935989i \(0.614508\pi\)
\(878\) −10.0362 17.3833i −0.338707 0.586658i
\(879\) 48.2326 10.1254i 1.62685 0.341520i
\(880\) 1.65601 0.0558240
\(881\) −14.9759 −0.504550 −0.252275 0.967656i \(-0.581179\pi\)
−0.252275 + 0.967656i \(0.581179\pi\)
\(882\) −25.7338 + 11.3026i −0.866502 + 0.380577i
\(883\) −12.7234 + 22.0375i −0.428176 + 0.741622i −0.996711 0.0810366i \(-0.974177\pi\)
0.568535 + 0.822659i \(0.307510\pi\)
\(884\) −0.220503 −0.00741631
\(885\) −11.8621 13.2410i −0.398739 0.445092i
\(886\) 34.1689 59.1823i 1.14793 1.98827i
\(887\) 18.1281 + 31.3988i 0.608681 + 1.05427i 0.991458 + 0.130426i \(0.0416346\pi\)
−0.382777 + 0.923841i \(0.625032\pi\)
\(888\) −14.8133 16.5354i −0.497103 0.554891i
\(889\) 6.28986 0.210955
\(890\) −13.0940 22.6795i −0.438912 0.760218i
\(891\) 0.701171 + 2.23427i 0.0234901 + 0.0748508i
\(892\) 5.73073 0.191879
\(893\) 4.91809 4.82698i 0.164578 0.161529i
\(894\) 39.8868 8.37334i 1.33401 0.280046i
\(895\) 9.67398 0.323365
\(896\) −14.3153 −0.478240
\(897\) −3.87526 + 0.813523i −0.129391 + 0.0271627i
\(898\) 0.465558 0.806370i 0.0155359 0.0269089i
\(899\) −4.03116 + 6.98217i −0.134447 + 0.232868i
\(900\) −10.7252 + 4.71062i −0.357506 + 0.157021i
\(901\) 0.528636 0.0176114
\(902\) 3.80029 0.126536
\(903\) −4.67580 5.21936i −0.155601 0.173689i
\(904\) −8.70368 + 15.0752i −0.289480 + 0.501394i
\(905\) 5.59973 9.69903i 0.186141 0.322407i
\(906\) −30.3480 33.8759i −1.00824 1.12545i
\(907\) −17.2593 + 29.8940i −0.573087 + 0.992615i 0.423160 + 0.906055i \(0.360921\pi\)
−0.996247 + 0.0865602i \(0.972413\pi\)
\(908\) −8.52010 + 14.7572i −0.282749 + 0.489736i
\(909\) 4.51336 40.9575i 0.149699 1.35847i
\(910\) 2.79522 + 4.84146i 0.0926606 + 0.160493i
\(911\) 12.7760 + 22.1287i 0.423289 + 0.733158i 0.996259 0.0864183i \(-0.0275422\pi\)
−0.572970 + 0.819576i \(0.694209\pi\)
\(912\) 20.8251 31.2497i 0.689589 1.03478i
\(913\) −0.789065 + 1.36670i −0.0261142 + 0.0452312i
\(914\) 38.0863 1.25978
\(915\) 20.8973 + 23.3266i 0.690844 + 0.771155i
\(916\) −1.36902 −0.0452338
\(917\) −7.60288 13.1686i −0.251069 0.434865i
\(918\) −0.763984 + 0.546301i −0.0252152 + 0.0180306i
\(919\) 35.7063 1.17784 0.588920 0.808191i \(-0.299553\pi\)
0.588920 + 0.808191i \(0.299553\pi\)
\(920\) 1.16782 + 2.02272i 0.0385018 + 0.0666870i
\(921\) 5.35367 16.3369i 0.176410 0.538319i
\(922\) 0.897626 + 1.55473i 0.0295618 + 0.0512025i
\(923\) 15.3090 26.5160i 0.503902 0.872784i
\(924\) −0.459348 0.512747i −0.0151114 0.0168681i
\(925\) −28.8996 −0.950214
\(926\) 9.67366 + 16.7553i 0.317896 + 0.550612i
\(927\) −18.8084 13.8103i −0.617748 0.453588i
\(928\) 19.1252 + 33.1259i 0.627817 + 1.08741i
\(929\) 25.8611 44.7927i 0.848475 1.46960i −0.0340937 0.999419i \(-0.510854\pi\)
0.882569 0.470183i \(-0.155812\pi\)
\(930\) −1.51588 + 4.62577i −0.0497078 + 0.151685i
\(931\) −5.73708 22.2408i −0.188025 0.728911i
\(932\) 12.5625 21.7589i 0.411499 0.712737i
\(933\) −17.2071 + 3.61224i −0.563335 + 0.118260i
\(934\) 0.202642 0.350986i 0.00663064 0.0114846i
\(935\) 0.0169231 0.0293117i 0.000553446 0.000958597i
\(936\) 7.65193 3.36081i 0.250111 0.109851i
\(937\) −15.7019 + 27.1965i −0.512959 + 0.888470i 0.486929 + 0.873442i \(0.338117\pi\)
−0.999887 + 0.0150285i \(0.995216\pi\)
\(938\) −0.914430 1.58384i −0.0298572 0.0517142i
\(939\) 29.9628 + 33.4460i 0.977799 + 1.09147i
\(940\) 1.17448 + 2.03426i 0.0383073 + 0.0663502i
\(941\) 4.39317 + 7.60920i 0.143213 + 0.248053i 0.928705 0.370819i \(-0.120923\pi\)
−0.785492 + 0.618872i \(0.787590\pi\)
\(942\) 0.235245 0.0493844i 0.00766470 0.00160903i
\(943\) 5.02711 + 8.70721i 0.163705 + 0.283546i
\(944\) 19.9489 34.5525i 0.649281 1.12459i
\(945\) 7.96343 + 3.61783i 0.259050 + 0.117688i
\(946\) −0.711357 + 1.23211i −0.0231282 + 0.0400592i
\(947\) −9.14726 + 15.8435i −0.297246 + 0.514845i −0.975505 0.219978i \(-0.929402\pi\)
0.678259 + 0.734823i \(0.262735\pi\)
\(948\) 15.6312 + 17.4483i 0.507676 + 0.566693i
\(949\) 0.741703 1.28467i 0.0240767 0.0417021i
\(950\) −6.50941 25.2348i −0.211193 0.818726i
\(951\) −28.0896 31.3550i −0.910869 1.01676i
\(952\) −0.0997284 + 0.172735i −0.00323222 + 0.00559836i
\(953\) 1.15491 + 2.00037i 0.0374113 + 0.0647983i 0.884125 0.467251i \(-0.154756\pi\)
−0.846713 + 0.532049i \(0.821422\pi\)
\(954\) 25.3947 11.1536i 0.822183 0.361111i
\(955\) −1.74543 3.02318i −0.0564809 0.0978278i
\(956\) 20.6493 0.667846
\(957\) 0.915921 2.79496i 0.0296075 0.0903482i
\(958\) 12.1172 20.9876i 0.391488 0.678077i
\(959\) 7.76781 + 13.4542i 0.250836 + 0.434460i
\(960\) 0.698593 + 0.779804i 0.0225470 + 0.0251681i
\(961\) 14.7370 + 25.5252i 0.475386 + 0.823393i
\(962\) −28.5422 −0.920237
\(963\) −0.892775 + 8.10170i −0.0287693 + 0.261074i
\(964\) 1.54052 + 2.66826i 0.0496168 + 0.0859388i
\(965\) 31.4535 1.01252
\(966\) 1.54405 4.71172i 0.0496790 0.151597i
\(967\) −44.0535 −1.41667 −0.708333 0.705878i \(-0.750553\pi\)
−0.708333 + 0.705878i \(0.750553\pi\)
\(968\) −8.15222 + 14.1201i −0.262022 + 0.453836i
\(969\) −0.340311 0.687959i −0.0109324 0.0221004i
\(970\) −13.2855 23.0112i −0.426572 0.738844i
\(971\) 6.62462 + 11.4742i 0.212594 + 0.368224i 0.952526 0.304458i \(-0.0984755\pi\)
−0.739932 + 0.672682i \(0.765142\pi\)
\(972\) −9.24703 + 15.5608i −0.296599 + 0.499112i
\(973\) −3.43623 + 5.95173i −0.110161 + 0.190804i
\(974\) 16.7792 29.0624i 0.537639 0.931218i
\(975\) 3.38797 10.3385i 0.108502 0.331096i
\(976\) −35.1439 + 60.8710i −1.12493 + 1.94843i
\(977\) −3.80938 + 6.59803i −0.121873 + 0.211090i −0.920506 0.390728i \(-0.872223\pi\)
0.798633 + 0.601818i \(0.205557\pi\)
\(978\) 59.0386 12.3938i 1.88785 0.396311i
\(979\) −2.99505 −0.0957221
\(980\) 7.82933 0.250099
\(981\) 49.6551 21.8091i 1.58537 0.696310i
\(982\) 0.737362 1.27715i 0.0235302 0.0407554i
\(983\) 22.5126 38.9930i 0.718042 1.24368i −0.243733 0.969842i \(-0.578372\pi\)
0.961775 0.273842i \(-0.0882946\pi\)
\(984\) −14.1596 15.8056i −0.451392 0.503866i
\(985\) −5.91695 −0.188530
\(986\) 1.17966 0.0375680
\(987\) −1.12177 + 3.42311i −0.0357063 + 0.108959i
\(988\) −2.36149 9.15473i −0.0751291 0.291251i
\(989\) −3.76400 −0.119688
\(990\) 0.194512 1.76514i 0.00618198 0.0560998i
\(991\) −9.93366 17.2056i −0.315553 0.546554i 0.664002 0.747731i \(-0.268857\pi\)
−0.979555 + 0.201177i \(0.935523\pi\)
\(992\) −7.24013 −0.229874
\(993\) 5.23294 15.9685i 0.166062 0.506744i
\(994\) 19.1695 + 33.2026i 0.608020 + 1.05312i
\(995\) −4.17246 + 7.22692i −0.132276 + 0.229109i
\(996\) −11.9384 + 2.50621i −0.378284 + 0.0794122i
\(997\) −37.2092 −1.17843 −0.589214 0.807977i \(-0.700563\pi\)
−0.589214 + 0.807977i \(0.700563\pi\)
\(998\) −1.33573 + 2.31356i −0.0422819 + 0.0732345i
\(999\) −36.3252 + 25.9750i −1.14928 + 0.821813i
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 171.2.g.c.121.4 yes 32
3.2 odd 2 513.2.g.c.64.13 32
9.2 odd 6 513.2.h.c.235.4 32
9.7 even 3 171.2.h.c.7.13 yes 32
19.11 even 3 171.2.h.c.49.13 yes 32
57.11 odd 6 513.2.h.c.334.4 32
171.11 odd 6 513.2.g.c.505.13 32
171.106 even 3 inner 171.2.g.c.106.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.g.c.106.4 32 171.106 even 3 inner
171.2.g.c.121.4 yes 32 1.1 even 1 trivial
171.2.h.c.7.13 yes 32 9.7 even 3
171.2.h.c.49.13 yes 32 19.11 even 3
513.2.g.c.64.13 32 3.2 odd 2
513.2.g.c.505.13 32 171.11 odd 6
513.2.h.c.235.4 32 9.2 odd 6
513.2.h.c.334.4 32 57.11 odd 6