Properties

Label 171.2.g.c.121.5
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 121.5
Character \(\chi\) \(=\) 171.121
Dual form 171.2.g.c.106.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.803309 + 1.39137i) q^{2} +(-1.24014 + 1.20915i) q^{3} +(-0.290611 - 0.503353i) q^{4} +3.75880 q^{5} +(-0.686165 - 2.69682i) q^{6} +(2.27973 + 3.94861i) q^{7} -2.27943 q^{8} +(0.0758986 - 2.99904i) q^{9} +O(q^{10})\) \(q+(-0.803309 + 1.39137i) q^{2} +(-1.24014 + 1.20915i) q^{3} +(-0.290611 - 0.503353i) q^{4} +3.75880 q^{5} +(-0.686165 - 2.69682i) q^{6} +(2.27973 + 3.94861i) q^{7} -2.27943 q^{8} +(0.0758986 - 2.99904i) q^{9} +(-3.01948 + 5.22989i) q^{10} +(-1.29616 - 2.24501i) q^{11} +(0.969030 + 0.272836i) q^{12} +(0.268857 + 0.465674i) q^{13} -7.32531 q^{14} +(-4.66144 + 4.54496i) q^{15} +(2.41231 - 4.17825i) q^{16} +(-1.73001 - 2.99646i) q^{17} +(4.11181 + 2.51476i) q^{18} +(-4.01417 + 1.69894i) q^{19} +(-1.09235 - 1.89200i) q^{20} +(-7.60165 - 2.14029i) q^{21} +4.16486 q^{22} +(0.104462 + 0.180933i) q^{23} +(2.82682 - 2.75618i) q^{24} +9.12855 q^{25} -0.863901 q^{26} +(3.53217 + 3.81100i) q^{27} +(1.32503 - 2.29502i) q^{28} -0.853801 q^{29} +(-2.57916 - 10.1368i) q^{30} +(3.83524 - 6.64283i) q^{31} +(1.59623 + 2.76475i) q^{32} +(4.32198 + 1.21688i) q^{33} +5.55892 q^{34} +(8.56903 + 14.8420i) q^{35} +(-1.53163 + 0.833350i) q^{36} +4.41513 q^{37} +(0.860764 - 6.94999i) q^{38} +(-0.896491 - 0.252412i) q^{39} -8.56793 q^{40} +0.939316 q^{41} +(9.08441 - 8.85741i) q^{42} +(-1.99417 + 3.45401i) q^{43} +(-0.753355 + 1.30485i) q^{44} +(0.285287 - 11.2728i) q^{45} -0.335660 q^{46} -3.14090 q^{47} +(2.06053 + 8.09847i) q^{48} +(-6.89432 + 11.9413i) q^{49} +(-7.33305 + 12.7012i) q^{50} +(5.76863 + 1.62419i) q^{51} +(0.156266 - 0.270660i) q^{52} +(5.68786 - 9.85167i) q^{53} +(-8.13995 + 1.85315i) q^{54} +(-4.87199 - 8.43853i) q^{55} +(-5.19649 - 9.00059i) q^{56} +(2.92386 - 6.96068i) q^{57} +(0.685866 - 1.18796i) q^{58} +2.40432 q^{59} +(3.64238 + 1.02553i) q^{60} -7.18979 q^{61} +(6.16176 + 10.6725i) q^{62} +(12.0151 - 6.53730i) q^{63} +4.52018 q^{64} +(1.01058 + 1.75037i) q^{65} +(-5.16501 + 5.03595i) q^{66} +(-0.140263 - 0.242942i) q^{67} +(-1.00552 + 1.74161i) q^{68} +(-0.348323 - 0.0980722i) q^{69} -27.5343 q^{70} +(3.43003 + 5.94099i) q^{71} +(-0.173006 + 6.83611i) q^{72} +(-0.416690 - 0.721728i) q^{73} +(-3.54671 + 6.14309i) q^{74} +(-11.3207 + 11.0378i) q^{75} +(2.02173 + 1.52682i) q^{76} +(5.90977 - 10.2360i) q^{77} +(1.07136 - 1.04459i) q^{78} +(5.91744 - 10.2493i) q^{79} +(9.06739 - 15.7052i) q^{80} +(-8.98848 - 0.455246i) q^{81} +(-0.754561 + 1.30694i) q^{82} +(3.63125 + 6.28951i) q^{83} +(1.13180 + 4.44831i) q^{84} +(-6.50274 - 11.2631i) q^{85} +(-3.20387 - 5.54927i) q^{86} +(1.05883 - 1.03238i) q^{87} +(2.95450 + 5.11735i) q^{88} +(-3.20392 + 5.54936i) q^{89} +(15.4555 + 9.45247i) q^{90} +(-1.22584 + 2.12322i) q^{91} +(0.0607154 - 0.105162i) q^{92} +(3.27596 + 12.8754i) q^{93} +(2.52311 - 4.37015i) q^{94} +(-15.0885 + 6.38597i) q^{95} +(-5.32256 - 1.49860i) q^{96} +(3.18119 - 5.50998i) q^{97} +(-11.0765 - 19.1851i) q^{98} +(-6.83125 + 3.71683i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.803309 + 1.39137i −0.568025 + 0.983849i 0.428736 + 0.903430i \(0.358959\pi\)
−0.996761 + 0.0804188i \(0.974374\pi\)
\(3\) −1.24014 + 1.20915i −0.715996 + 0.698105i
\(4\) −0.290611 0.503353i −0.145306 0.251677i
\(5\) 3.75880 1.68098 0.840492 0.541823i \(-0.182266\pi\)
0.840492 + 0.541823i \(0.182266\pi\)
\(6\) −0.686165 2.69682i −0.280126 1.10097i
\(7\) 2.27973 + 3.94861i 0.861656 + 1.49243i 0.870329 + 0.492470i \(0.163906\pi\)
−0.00867312 + 0.999962i \(0.502761\pi\)
\(8\) −2.27943 −0.805902
\(9\) 0.0758986 2.99904i 0.0252995 0.999680i
\(10\) −3.01948 + 5.22989i −0.954842 + 1.65383i
\(11\) −1.29616 2.24501i −0.390806 0.676896i 0.601750 0.798684i \(-0.294470\pi\)
−0.992556 + 0.121789i \(0.961137\pi\)
\(12\) 0.969030 + 0.272836i 0.279735 + 0.0787608i
\(13\) 0.268857 + 0.465674i 0.0745675 + 0.129155i 0.900898 0.434031i \(-0.142909\pi\)
−0.826331 + 0.563185i \(0.809576\pi\)
\(14\) −7.32531 −1.95777
\(15\) −4.66144 + 4.54496i −1.20358 + 1.17350i
\(16\) 2.41231 4.17825i 0.603078 1.04456i
\(17\) −1.73001 2.99646i −0.419588 0.726748i 0.576310 0.817231i \(-0.304492\pi\)
−0.995898 + 0.0904832i \(0.971159\pi\)
\(18\) 4.11181 + 2.51476i 0.969163 + 0.592734i
\(19\) −4.01417 + 1.69894i −0.920915 + 0.389764i
\(20\) −1.09235 1.89200i −0.244256 0.423065i
\(21\) −7.60165 2.14029i −1.65882 0.467049i
\(22\) 4.16486 0.887951
\(23\) 0.104462 + 0.180933i 0.0217818 + 0.0377271i 0.876711 0.481018i \(-0.159733\pi\)
−0.854929 + 0.518745i \(0.826399\pi\)
\(24\) 2.82682 2.75618i 0.577022 0.562604i
\(25\) 9.12855 1.82571
\(26\) −0.863901 −0.169425
\(27\) 3.53217 + 3.81100i 0.679767 + 0.733428i
\(28\) 1.32503 2.29502i 0.250407 0.433717i
\(29\) −0.853801 −0.158547 −0.0792735 0.996853i \(-0.525260\pi\)
−0.0792735 + 0.996853i \(0.525260\pi\)
\(30\) −2.57916 10.1368i −0.470887 1.85072i
\(31\) 3.83524 6.64283i 0.688829 1.19309i −0.283388 0.959005i \(-0.591458\pi\)
0.972217 0.234082i \(-0.0752084\pi\)
\(32\) 1.59623 + 2.76475i 0.282176 + 0.488744i
\(33\) 4.32198 + 1.21688i 0.752360 + 0.211831i
\(34\) 5.55892 0.953347
\(35\) 8.56903 + 14.8420i 1.44843 + 2.50876i
\(36\) −1.53163 + 0.833350i −0.255272 + 0.138892i
\(37\) 4.41513 0.725843 0.362921 0.931820i \(-0.381779\pi\)
0.362921 + 0.931820i \(0.381779\pi\)
\(38\) 0.860764 6.94999i 0.139634 1.12744i
\(39\) −0.896491 0.252412i −0.143554 0.0404183i
\(40\) −8.56793 −1.35471
\(41\) 0.939316 0.146697 0.0733483 0.997306i \(-0.476632\pi\)
0.0733483 + 0.997306i \(0.476632\pi\)
\(42\) 9.08441 8.85741i 1.40176 1.36673i
\(43\) −1.99417 + 3.45401i −0.304108 + 0.526731i −0.977062 0.212953i \(-0.931692\pi\)
0.672954 + 0.739684i \(0.265025\pi\)
\(44\) −0.753355 + 1.30485i −0.113573 + 0.196713i
\(45\) 0.285287 11.2728i 0.0425281 1.68045i
\(46\) −0.335660 −0.0494904
\(47\) −3.14090 −0.458147 −0.229073 0.973409i \(-0.573570\pi\)
−0.229073 + 0.973409i \(0.573570\pi\)
\(48\) 2.06053 + 8.09847i 0.297412 + 1.16891i
\(49\) −6.89432 + 11.9413i −0.984903 + 1.70590i
\(50\) −7.33305 + 12.7012i −1.03705 + 1.79622i
\(51\) 5.76863 + 1.62419i 0.807770 + 0.227432i
\(52\) 0.156266 0.270660i 0.0216701 0.0375338i
\(53\) 5.68786 9.85167i 0.781288 1.35323i −0.149903 0.988701i \(-0.547896\pi\)
0.931192 0.364530i \(-0.118770\pi\)
\(54\) −8.13995 + 1.85315i −1.10771 + 0.252182i
\(55\) −4.87199 8.43853i −0.656939 1.13785i
\(56\) −5.19649 9.00059i −0.694410 1.20275i
\(57\) 2.92386 6.96068i 0.387275 0.921964i
\(58\) 0.685866 1.18796i 0.0900587 0.155986i
\(59\) 2.40432 0.313016 0.156508 0.987677i \(-0.449976\pi\)
0.156508 + 0.987677i \(0.449976\pi\)
\(60\) 3.64238 + 1.02553i 0.470230 + 0.132396i
\(61\) −7.18979 −0.920558 −0.460279 0.887774i \(-0.652251\pi\)
−0.460279 + 0.887774i \(0.652251\pi\)
\(62\) 6.16176 + 10.6725i 0.782545 + 1.35541i
\(63\) 12.0151 6.53730i 1.51375 0.823623i
\(64\) 4.52018 0.565023
\(65\) 1.01058 + 1.75037i 0.125347 + 0.217107i
\(66\) −5.16501 + 5.03595i −0.635769 + 0.619883i
\(67\) −0.140263 0.242942i −0.0171358 0.0296801i 0.857330 0.514767i \(-0.172121\pi\)
−0.874466 + 0.485087i \(0.838788\pi\)
\(68\) −1.00552 + 1.74161i −0.121937 + 0.211201i
\(69\) −0.348323 0.0980722i −0.0419331 0.0118065i
\(70\) −27.5343 −3.29098
\(71\) 3.43003 + 5.94099i 0.407070 + 0.705066i 0.994560 0.104165i \(-0.0332172\pi\)
−0.587490 + 0.809231i \(0.699884\pi\)
\(72\) −0.173006 + 6.83611i −0.0203889 + 0.805644i
\(73\) −0.416690 0.721728i −0.0487698 0.0844718i 0.840610 0.541641i \(-0.182197\pi\)
−0.889380 + 0.457169i \(0.848863\pi\)
\(74\) −3.54671 + 6.14309i −0.412297 + 0.714120i
\(75\) −11.3207 + 11.0378i −1.30720 + 1.27454i
\(76\) 2.02173 + 1.52682i 0.231908 + 0.175138i
\(77\) 5.90977 10.2360i 0.673481 1.16650i
\(78\) 1.07136 1.04459i 0.121307 0.118276i
\(79\) 5.91744 10.2493i 0.665764 1.15314i −0.313313 0.949650i \(-0.601439\pi\)
0.979077 0.203488i \(-0.0652278\pi\)
\(80\) 9.06739 15.7052i 1.01377 1.75589i
\(81\) −8.98848 0.455246i −0.998720 0.0505829i
\(82\) −0.754561 + 1.30694i −0.0833273 + 0.144327i
\(83\) 3.63125 + 6.28951i 0.398582 + 0.690364i 0.993551 0.113385i \(-0.0361692\pi\)
−0.594970 + 0.803748i \(0.702836\pi\)
\(84\) 1.13180 + 4.44831i 0.123490 + 0.485350i
\(85\) −6.50274 11.2631i −0.705322 1.22165i
\(86\) −3.20387 5.54927i −0.345483 0.598393i
\(87\) 1.05883 1.03238i 0.113519 0.110682i
\(88\) 2.95450 + 5.11735i 0.314951 + 0.545512i
\(89\) −3.20392 + 5.54936i −0.339615 + 0.588231i −0.984360 0.176167i \(-0.943630\pi\)
0.644745 + 0.764398i \(0.276963\pi\)
\(90\) 15.4555 + 9.45247i 1.62915 + 0.996378i
\(91\) −1.22584 + 2.12322i −0.128503 + 0.222574i
\(92\) 0.0607154 0.105162i 0.00633002 0.0109639i
\(93\) 3.27596 + 12.8754i 0.339701 + 1.33512i
\(94\) 2.52311 4.37015i 0.260239 0.450747i
\(95\) −15.0885 + 6.38597i −1.54804 + 0.655187i
\(96\) −5.32256 1.49860i −0.543232 0.152950i
\(97\) 3.18119 5.50998i 0.323001 0.559453i −0.658105 0.752926i \(-0.728642\pi\)
0.981106 + 0.193473i \(0.0619751\pi\)
\(98\) −11.0765 19.1851i −1.11890 1.93799i
\(99\) −6.83125 + 3.71683i −0.686566 + 0.373556i
\(100\) −2.65286 4.59489i −0.265286 0.459489i
\(101\) −2.31014 −0.229868 −0.114934 0.993373i \(-0.536666\pi\)
−0.114934 + 0.993373i \(0.536666\pi\)
\(102\) −6.89384 + 6.72159i −0.682592 + 0.665536i
\(103\) −3.73572 + 6.47046i −0.368092 + 0.637554i −0.989267 0.146118i \(-0.953322\pi\)
0.621175 + 0.783672i \(0.286655\pi\)
\(104\) −0.612842 1.06147i −0.0600941 0.104086i
\(105\) −28.5731 8.04490i −2.78845 0.785102i
\(106\) 9.13823 + 15.8279i 0.887583 + 1.53734i
\(107\) −8.56202 −0.827722 −0.413861 0.910340i \(-0.635820\pi\)
−0.413861 + 0.910340i \(0.635820\pi\)
\(108\) 0.891793 2.88545i 0.0858128 0.277653i
\(109\) 5.16271 + 8.94207i 0.494498 + 0.856495i 0.999980 0.00634184i \(-0.00201868\pi\)
−0.505482 + 0.862837i \(0.668685\pi\)
\(110\) 15.6549 1.49263
\(111\) −5.47538 + 5.33857i −0.519700 + 0.506714i
\(112\) 21.9977 2.07858
\(113\) −7.77287 + 13.4630i −0.731210 + 1.26649i 0.225156 + 0.974323i \(0.427711\pi\)
−0.956366 + 0.292170i \(0.905623\pi\)
\(114\) 7.33613 + 9.65976i 0.687091 + 0.904719i
\(115\) 0.392650 + 0.680090i 0.0366148 + 0.0634187i
\(116\) 0.248124 + 0.429764i 0.0230377 + 0.0399026i
\(117\) 1.41698 0.770969i 0.131000 0.0712761i
\(118\) −1.93141 + 3.34531i −0.177801 + 0.307960i
\(119\) 7.88789 13.6622i 0.723082 1.25241i
\(120\) 10.6254 10.3599i 0.969966 0.945729i
\(121\) 2.13996 3.70651i 0.194541 0.336956i
\(122\) 5.77562 10.0037i 0.522900 0.905690i
\(123\) −1.16488 + 1.13578i −0.105034 + 0.102410i
\(124\) −4.45825 −0.400363
\(125\) 15.5184 1.38801
\(126\) −0.555980 + 21.9689i −0.0495307 + 1.95714i
\(127\) 6.30706 10.9241i 0.559661 0.969361i −0.437864 0.899041i \(-0.644265\pi\)
0.997525 0.0703197i \(-0.0224020\pi\)
\(128\) −6.82357 + 11.8188i −0.603124 + 1.04464i
\(129\) −1.70337 6.69472i −0.149973 0.589437i
\(130\) −3.24723 −0.284801
\(131\) 19.7774 1.72796 0.863980 0.503526i \(-0.167964\pi\)
0.863980 + 0.503526i \(0.167964\pi\)
\(132\) −0.643496 2.52912i −0.0560091 0.220131i
\(133\) −15.8597 11.9773i −1.37521 1.03856i
\(134\) 0.450697 0.0389343
\(135\) 13.2767 + 14.3248i 1.14268 + 1.23288i
\(136\) 3.94344 + 6.83023i 0.338147 + 0.585688i
\(137\) 11.7148 1.00086 0.500430 0.865777i \(-0.333175\pi\)
0.500430 + 0.865777i \(0.333175\pi\)
\(138\) 0.416266 0.405864i 0.0354349 0.0345495i
\(139\) −8.92017 15.4502i −0.756599 1.31047i −0.944575 0.328294i \(-0.893526\pi\)
0.187976 0.982174i \(-0.439807\pi\)
\(140\) 4.98051 8.62650i 0.420930 0.729072i
\(141\) 3.89515 3.79782i 0.328031 0.319834i
\(142\) −11.0215 −0.924904
\(143\) 0.696961 1.20717i 0.0582828 0.100949i
\(144\) −12.3476 7.55174i −1.02897 0.629312i
\(145\) −3.20927 −0.266515
\(146\) 1.33892 0.110810
\(147\) −5.88895 23.1452i −0.485712 1.90898i
\(148\) −1.28309 2.22237i −0.105469 0.182678i
\(149\) −16.1092 −1.31972 −0.659859 0.751389i \(-0.729384\pi\)
−0.659859 + 0.751389i \(0.729384\pi\)
\(150\) −6.26370 24.6181i −0.511429 2.01006i
\(151\) −0.821225 1.42240i −0.0668303 0.115754i 0.830674 0.556759i \(-0.187955\pi\)
−0.897504 + 0.441005i \(0.854622\pi\)
\(152\) 9.15005 3.87262i 0.742167 0.314111i
\(153\) −9.11781 + 4.96093i −0.737131 + 0.401068i
\(154\) 9.49474 + 16.4454i 0.765108 + 1.32521i
\(155\) 14.4159 24.9690i 1.15791 2.00556i
\(156\) 0.133478 + 0.524605i 0.0106868 + 0.0420021i
\(157\) 10.6210 0.847648 0.423824 0.905745i \(-0.360688\pi\)
0.423824 + 0.905745i \(0.360688\pi\)
\(158\) 9.50707 + 16.4667i 0.756342 + 1.31002i
\(159\) 4.85842 + 19.0950i 0.385298 + 1.51433i
\(160\) 5.99991 + 10.3921i 0.474334 + 0.821571i
\(161\) −0.476288 + 0.824956i −0.0375368 + 0.0650156i
\(162\) 7.85394 12.1406i 0.617064 0.953857i
\(163\) −22.0892 −1.73016 −0.865080 0.501634i \(-0.832732\pi\)
−0.865080 + 0.501634i \(0.832732\pi\)
\(164\) −0.272976 0.472808i −0.0213158 0.0369201i
\(165\) 16.2454 + 4.57399i 1.26471 + 0.356085i
\(166\) −11.6681 −0.905618
\(167\) −6.54741 11.3404i −0.506654 0.877550i −0.999970 0.00770038i \(-0.997549\pi\)
0.493316 0.869850i \(-0.335784\pi\)
\(168\) 17.3275 + 4.87864i 1.33684 + 0.376395i
\(169\) 6.35543 11.0079i 0.488879 0.846764i
\(170\) 20.8949 1.60256
\(171\) 4.79052 + 12.1676i 0.366340 + 0.930481i
\(172\) 2.31811 0.176755
\(173\) −6.28949 + 10.8937i −0.478181 + 0.828234i −0.999687 0.0250137i \(-0.992037\pi\)
0.521506 + 0.853248i \(0.325370\pi\)
\(174\) 0.585849 + 2.30255i 0.0444131 + 0.174556i
\(175\) 20.8106 + 36.0450i 1.57313 + 2.72475i
\(176\) −12.5069 −0.942746
\(177\) −2.98170 + 2.90719i −0.224118 + 0.218518i
\(178\) −5.14748 8.91570i −0.385820 0.668260i
\(179\) −23.1728 −1.73202 −0.866008 0.500031i \(-0.833322\pi\)
−0.866008 + 0.500031i \(0.833322\pi\)
\(180\) −5.75710 + 3.13239i −0.429109 + 0.233475i
\(181\) 1.87031 3.23948i 0.139019 0.240789i −0.788106 0.615539i \(-0.788938\pi\)
0.927126 + 0.374751i \(0.122272\pi\)
\(182\) −1.96946 3.41120i −0.145986 0.252855i
\(183\) 8.91635 8.69355i 0.659116 0.642646i
\(184\) −0.238113 0.412425i −0.0175540 0.0304044i
\(185\) 16.5956 1.22013
\(186\) −20.5461 5.78487i −1.50652 0.424168i
\(187\) −4.48472 + 7.76776i −0.327955 + 0.568035i
\(188\) 0.912779 + 1.58098i 0.0665712 + 0.115305i
\(189\) −6.99576 + 22.6352i −0.508867 + 1.64647i
\(190\) 3.23544 26.1236i 0.234723 1.89520i
\(191\) −7.37837 12.7797i −0.533880 0.924707i −0.999217 0.0395734i \(-0.987400\pi\)
0.465337 0.885134i \(-0.345933\pi\)
\(192\) −5.60566 + 5.46559i −0.404554 + 0.394445i
\(193\) −5.67586 −0.408558 −0.204279 0.978913i \(-0.565485\pi\)
−0.204279 + 0.978913i \(0.565485\pi\)
\(194\) 5.11095 + 8.85243i 0.366945 + 0.635568i
\(195\) −3.36973 0.948766i −0.241311 0.0679425i
\(196\) 8.01426 0.572447
\(197\) −12.2959 −0.876046 −0.438023 0.898964i \(-0.644321\pi\)
−0.438023 + 0.898964i \(0.644321\pi\)
\(198\) 0.316107 12.4906i 0.0224647 0.887667i
\(199\) 0.0159042 0.0275469i 0.00112742 0.00195275i −0.865461 0.500976i \(-0.832974\pi\)
0.866589 + 0.499023i \(0.166308\pi\)
\(200\) −20.8079 −1.47134
\(201\) 0.467699 + 0.131683i 0.0329890 + 0.00928822i
\(202\) 1.85576 3.21427i 0.130571 0.226155i
\(203\) −1.94644 3.37132i −0.136613 0.236621i
\(204\) −0.858887 3.37567i −0.0601341 0.236344i
\(205\) 3.53070 0.246595
\(206\) −6.00188 10.3956i −0.418171 0.724293i
\(207\) 0.550553 0.299552i 0.0382661 0.0208203i
\(208\) 2.59427 0.179880
\(209\) 9.01714 + 6.80977i 0.623729 + 0.471041i
\(210\) 34.1465 33.2932i 2.35633 2.29745i
\(211\) −22.3398 −1.53794 −0.768969 0.639286i \(-0.779230\pi\)
−0.768969 + 0.639286i \(0.779230\pi\)
\(212\) −6.61183 −0.454102
\(213\) −11.4373 3.22023i −0.783670 0.220647i
\(214\) 6.87795 11.9130i 0.470167 0.814353i
\(215\) −7.49569 + 12.9829i −0.511202 + 0.885427i
\(216\) −8.05136 8.68694i −0.547825 0.591071i
\(217\) 34.9732 2.37414
\(218\) −16.5890 −1.12355
\(219\) 1.38943 + 0.391202i 0.0938892 + 0.0264350i
\(220\) −2.83171 + 4.90466i −0.190914 + 0.330672i
\(221\) 0.930249 1.61124i 0.0625753 0.108384i
\(222\) −3.02951 11.9068i −0.203327 0.799133i
\(223\) 3.43392 5.94773i 0.229952 0.398289i −0.727841 0.685746i \(-0.759476\pi\)
0.957794 + 0.287456i \(0.0928096\pi\)
\(224\) −7.27795 + 12.6058i −0.486278 + 0.842258i
\(225\) 0.692844 27.3769i 0.0461896 1.82513i
\(226\) −12.4880 21.6299i −0.830692 1.43880i
\(227\) 4.44987 + 7.70739i 0.295348 + 0.511558i 0.975066 0.221916i \(-0.0712311\pi\)
−0.679718 + 0.733474i \(0.737898\pi\)
\(228\) −4.35339 + 0.551115i −0.288310 + 0.0364985i
\(229\) −4.13454 + 7.16123i −0.273218 + 0.473228i −0.969684 0.244362i \(-0.921421\pi\)
0.696466 + 0.717590i \(0.254755\pi\)
\(230\) −1.26168 −0.0831926
\(231\) 5.04797 + 19.8399i 0.332132 + 1.30537i
\(232\) 1.94618 0.127773
\(233\) 0.668571 + 1.15800i 0.0437995 + 0.0758630i 0.887094 0.461589i \(-0.152720\pi\)
−0.843295 + 0.537452i \(0.819387\pi\)
\(234\) −0.0655689 + 2.59087i −0.00428637 + 0.169371i
\(235\) −11.8060 −0.770138
\(236\) −0.698722 1.21022i −0.0454829 0.0787788i
\(237\) 5.05452 + 19.8657i 0.328327 + 1.29042i
\(238\) 12.6728 + 21.9500i 0.821457 + 1.42281i
\(239\) 3.40198 5.89240i 0.220056 0.381147i −0.734769 0.678317i \(-0.762709\pi\)
0.954825 + 0.297170i \(0.0960428\pi\)
\(240\) 7.74513 + 30.4405i 0.499946 + 1.96493i
\(241\) 7.42157 0.478065 0.239033 0.971012i \(-0.423170\pi\)
0.239033 + 0.971012i \(0.423170\pi\)
\(242\) 3.43809 + 5.95495i 0.221009 + 0.382799i
\(243\) 11.6974 10.3039i 0.750391 0.660994i
\(244\) 2.08943 + 3.61900i 0.133762 + 0.231683i
\(245\) −25.9144 + 44.8850i −1.65561 + 2.86760i
\(246\) −0.644526 2.53317i −0.0410935 0.161509i
\(247\) −1.87039 1.41252i −0.119010 0.0898768i
\(248\) −8.74218 + 15.1419i −0.555129 + 0.961511i
\(249\) −12.1082 3.40914i −0.767329 0.216046i
\(250\) −12.4661 + 21.5919i −0.788423 + 1.36559i
\(251\) −7.83717 + 13.5744i −0.494678 + 0.856807i −0.999981 0.00613456i \(-0.998047\pi\)
0.505303 + 0.862942i \(0.331381\pi\)
\(252\) −6.78228 4.14800i −0.427243 0.261300i
\(253\) 0.270797 0.469035i 0.0170249 0.0294880i
\(254\) 10.1330 + 17.5509i 0.635803 + 1.10124i
\(255\) 21.6831 + 6.10500i 1.35785 + 0.382310i
\(256\) −6.44268 11.1591i −0.402668 0.697441i
\(257\) 3.69675 + 6.40296i 0.230597 + 0.399406i 0.957984 0.286822i \(-0.0925987\pi\)
−0.727387 + 0.686228i \(0.759265\pi\)
\(258\) 10.6832 + 3.00791i 0.665105 + 0.187264i
\(259\) 10.0653 + 17.4336i 0.625427 + 1.08327i
\(260\) 0.587371 1.01736i 0.0364272 0.0630937i
\(261\) −0.0648023 + 2.56058i −0.00401116 + 0.158496i
\(262\) −15.8874 + 27.5177i −0.981525 + 1.70005i
\(263\) −1.41631 + 2.45312i −0.0873335 + 0.151266i −0.906383 0.422457i \(-0.861168\pi\)
0.819050 + 0.573723i \(0.194501\pi\)
\(264\) −9.85166 2.77379i −0.606328 0.170715i
\(265\) 21.3795 37.0304i 1.31333 2.27476i
\(266\) 29.4051 12.4453i 1.80294 0.763068i
\(267\) −2.73671 10.7560i −0.167484 0.658258i
\(268\) −0.0815237 + 0.141203i −0.00497985 + 0.00862536i
\(269\) −5.71883 9.90530i −0.348683 0.603937i 0.637333 0.770589i \(-0.280038\pi\)
−0.986016 + 0.166652i \(0.946704\pi\)
\(270\) −30.5964 + 6.96562i −1.86204 + 0.423914i
\(271\) 13.8181 + 23.9337i 0.839390 + 1.45387i 0.890405 + 0.455168i \(0.150421\pi\)
−0.0510155 + 0.998698i \(0.516246\pi\)
\(272\) −16.6933 −1.01218
\(273\) −1.04708 4.11532i −0.0633722 0.249071i
\(274\) −9.41058 + 16.2996i −0.568514 + 0.984695i
\(275\) −11.8320 20.4937i −0.713499 1.23582i
\(276\) 0.0518615 + 0.203830i 0.00312170 + 0.0122691i
\(277\) −5.19514 8.99825i −0.312146 0.540653i 0.666681 0.745343i \(-0.267714\pi\)
−0.978827 + 0.204691i \(0.934381\pi\)
\(278\) 28.6626 1.71907
\(279\) −19.6310 12.0062i −1.17528 0.718793i
\(280\) −19.5326 33.8314i −1.16729 2.02181i
\(281\) 8.50448 0.507335 0.253667 0.967292i \(-0.418363\pi\)
0.253667 + 0.967292i \(0.418363\pi\)
\(282\) 2.15517 + 8.47043i 0.128339 + 0.504407i
\(283\) −1.36691 −0.0812541 −0.0406270 0.999174i \(-0.512936\pi\)
−0.0406270 + 0.999174i \(0.512936\pi\)
\(284\) 1.99361 3.45304i 0.118299 0.204900i
\(285\) 10.9902 26.1638i 0.651004 1.54981i
\(286\) 1.11975 + 1.93947i 0.0662123 + 0.114683i
\(287\) 2.14139 + 3.70899i 0.126402 + 0.218935i
\(288\) 8.41276 4.57732i 0.495726 0.269721i
\(289\) 2.51415 4.35464i 0.147891 0.256155i
\(290\) 2.57803 4.46528i 0.151387 0.262210i
\(291\) 2.71729 + 10.6797i 0.159290 + 0.626055i
\(292\) −0.242189 + 0.419484i −0.0141731 + 0.0245485i
\(293\) −0.373905 + 0.647623i −0.0218438 + 0.0378345i −0.876741 0.480963i \(-0.840287\pi\)
0.854897 + 0.518798i \(0.173620\pi\)
\(294\) 36.9342 + 10.3990i 2.15405 + 0.606484i
\(295\) 9.03735 0.526175
\(296\) −10.0640 −0.584958
\(297\) 3.97749 12.8694i 0.230797 0.746759i
\(298\) 12.9407 22.4139i 0.749633 1.29840i
\(299\) −0.0561705 + 0.0972901i −0.00324842 + 0.00562643i
\(300\) 8.84584 + 2.49059i 0.510715 + 0.143794i
\(301\) −18.1847 −1.04815
\(302\) 2.63879 0.151845
\(303\) 2.86490 2.79332i 0.164584 0.160472i
\(304\) −2.58485 + 20.8706i −0.148251 + 1.19701i
\(305\) −27.0250 −1.54744
\(306\) 0.421914 16.6714i 0.0241192 0.953042i
\(307\) 5.56496 + 9.63880i 0.317609 + 0.550115i 0.979989 0.199053i \(-0.0637866\pi\)
−0.662379 + 0.749169i \(0.730453\pi\)
\(308\) −6.86978 −0.391442
\(309\) −3.19096 12.5413i −0.181527 0.713452i
\(310\) 23.1608 + 40.1157i 1.31545 + 2.27842i
\(311\) 6.07360 10.5198i 0.344402 0.596522i −0.640843 0.767672i \(-0.721415\pi\)
0.985245 + 0.171150i \(0.0547483\pi\)
\(312\) 2.04349 + 0.575357i 0.115690 + 0.0325732i
\(313\) −26.3132 −1.48731 −0.743656 0.668563i \(-0.766910\pi\)
−0.743656 + 0.668563i \(0.766910\pi\)
\(314\) −8.53194 + 14.7778i −0.481485 + 0.833957i
\(315\) 45.1621 24.5724i 2.54460 1.38450i
\(316\) −6.87870 −0.386957
\(317\) −13.4516 −0.755520 −0.377760 0.925904i \(-0.623306\pi\)
−0.377760 + 0.925904i \(0.623306\pi\)
\(318\) −30.4710 8.57928i −1.70873 0.481102i
\(319\) 1.10666 + 1.91679i 0.0619611 + 0.107320i
\(320\) 16.9904 0.949795
\(321\) 10.6181 10.3528i 0.592645 0.577836i
\(322\) −0.765214 1.32539i −0.0426437 0.0738610i
\(323\) 12.0354 + 9.08913i 0.669665 + 0.505733i
\(324\) 2.38300 + 4.65668i 0.132389 + 0.258704i
\(325\) 2.45427 + 4.25093i 0.136139 + 0.235799i
\(326\) 17.7445 30.7343i 0.982775 1.70222i
\(327\) −17.2148 4.84693i −0.951982 0.268036i
\(328\) −2.14111 −0.118223
\(329\) −7.16039 12.4022i −0.394765 0.683753i
\(330\) −19.4142 + 18.9291i −1.06872 + 1.04201i
\(331\) 2.15691 + 3.73589i 0.118555 + 0.205343i 0.919195 0.393802i \(-0.128841\pi\)
−0.800640 + 0.599145i \(0.795507\pi\)
\(332\) 2.11056 3.65560i 0.115832 0.200627i
\(333\) 0.335102 13.2412i 0.0183635 0.725611i
\(334\) 21.0384 1.15117
\(335\) −0.527219 0.913169i −0.0288050 0.0498918i
\(336\) −27.2802 + 26.5985i −1.48826 + 1.45107i
\(337\) −2.91534 −0.158809 −0.0794044 0.996842i \(-0.525302\pi\)
−0.0794044 + 0.996842i \(0.525302\pi\)
\(338\) 10.2108 + 17.6855i 0.555392 + 0.961967i
\(339\) −6.63938 26.0946i −0.360602 1.41726i
\(340\) −3.77954 + 6.54635i −0.204974 + 0.355026i
\(341\) −19.8843 −1.07679
\(342\) −20.7780 3.10896i −1.12354 0.168113i
\(343\) −30.9525 −1.67128
\(344\) 4.54558 7.87318i 0.245082 0.424494i
\(345\) −1.30927 0.368633i −0.0704890 0.0198466i
\(346\) −10.1048 17.5020i −0.543238 0.940916i
\(347\) −14.7943 −0.794199 −0.397099 0.917776i \(-0.629983\pi\)
−0.397099 + 0.917776i \(0.629983\pi\)
\(348\) −0.827359 0.232947i −0.0443511 0.0124873i
\(349\) 0.668641 + 1.15812i 0.0357915 + 0.0619927i 0.883366 0.468683i \(-0.155271\pi\)
−0.847575 + 0.530676i \(0.821938\pi\)
\(350\) −66.8694 −3.57432
\(351\) −0.825036 + 2.66946i −0.0440372 + 0.142485i
\(352\) 4.13793 7.16711i 0.220552 0.382008i
\(353\) 10.3662 + 17.9549i 0.551739 + 0.955641i 0.998149 + 0.0608121i \(0.0193691\pi\)
−0.446410 + 0.894829i \(0.647298\pi\)
\(354\) −1.64976 6.48402i −0.0876838 0.344622i
\(355\) 12.8928 + 22.3310i 0.684279 + 1.18521i
\(356\) 3.72438 0.197392
\(357\) 6.73763 + 26.4808i 0.356593 + 1.40151i
\(358\) 18.6149 32.2420i 0.983829 1.70404i
\(359\) −2.38736 4.13504i −0.126000 0.218239i 0.796123 0.605135i \(-0.206881\pi\)
−0.922123 + 0.386896i \(0.873547\pi\)
\(360\) −0.650294 + 25.6956i −0.0342735 + 1.35428i
\(361\) 13.2272 13.6397i 0.696168 0.717879i
\(362\) 3.00488 + 5.20460i 0.157933 + 0.273548i
\(363\) 1.82789 + 7.18413i 0.0959395 + 0.377069i
\(364\) 1.42497 0.0746888
\(365\) −1.56625 2.71283i −0.0819814 0.141996i
\(366\) 4.93338 + 19.3896i 0.257872 + 1.01351i
\(367\) 21.7614 1.13594 0.567969 0.823050i \(-0.307729\pi\)
0.567969 + 0.823050i \(0.307729\pi\)
\(368\) 1.00798 0.0525444
\(369\) 0.0712928 2.81705i 0.00371135 0.146650i
\(370\) −13.3314 + 23.0906i −0.693065 + 1.20042i
\(371\) 51.8671 2.69281
\(372\) 5.52886 5.39071i 0.286658 0.279495i
\(373\) 11.3702 19.6938i 0.588727 1.01971i −0.405672 0.914019i \(-0.632963\pi\)
0.994399 0.105687i \(-0.0337041\pi\)
\(374\) −7.20523 12.4798i −0.372574 0.645317i
\(375\) −19.2450 + 18.7641i −0.993807 + 0.968974i
\(376\) 7.15946 0.369221
\(377\) −0.229550 0.397593i −0.0118224 0.0204771i
\(378\) −25.8742 27.9168i −1.33083 1.43588i
\(379\) −21.1367 −1.08572 −0.542859 0.839824i \(-0.682658\pi\)
−0.542859 + 0.839824i \(0.682658\pi\)
\(380\) 7.59928 + 5.73899i 0.389835 + 0.294404i
\(381\) 5.38732 + 21.1737i 0.276001 + 1.08476i
\(382\) 23.7084 1.21303
\(383\) −9.57967 −0.489498 −0.244749 0.969586i \(-0.578706\pi\)
−0.244749 + 0.969586i \(0.578706\pi\)
\(384\) −5.82851 22.9077i −0.297435 1.16900i
\(385\) 22.2136 38.4751i 1.13211 1.96087i
\(386\) 4.55947 7.89724i 0.232071 0.401959i
\(387\) 10.2074 + 6.24276i 0.518869 + 0.317337i
\(388\) −3.69795 −0.187735
\(389\) 34.4668 1.74754 0.873768 0.486343i \(-0.161670\pi\)
0.873768 + 0.486343i \(0.161670\pi\)
\(390\) 4.02702 3.92639i 0.203916 0.198821i
\(391\) 0.361439 0.626030i 0.0182787 0.0316597i
\(392\) 15.7152 27.2194i 0.793735 1.37479i
\(393\) −24.5268 + 23.9139i −1.23721 + 1.20630i
\(394\) 9.87741 17.1082i 0.497617 0.861897i
\(395\) 22.2425 38.5251i 1.11914 1.93841i
\(396\) 3.85612 + 2.35838i 0.193777 + 0.118513i
\(397\) 17.8313 + 30.8848i 0.894928 + 1.55006i 0.833893 + 0.551926i \(0.186107\pi\)
0.0610353 + 0.998136i \(0.480560\pi\)
\(398\) 0.0255520 + 0.0442574i 0.00128081 + 0.00221842i
\(399\) 34.1506 4.32327i 1.70967 0.216434i
\(400\) 22.0209 38.1414i 1.10105 1.90707i
\(401\) 1.13355 0.0566066 0.0283033 0.999599i \(-0.490990\pi\)
0.0283033 + 0.999599i \(0.490990\pi\)
\(402\) −0.558928 + 0.544961i −0.0278768 + 0.0271802i
\(403\) 4.12452 0.205457
\(404\) 0.671354 + 1.16282i 0.0334011 + 0.0578524i
\(405\) −33.7859 1.71118i −1.67883 0.0850290i
\(406\) 6.25436 0.310399
\(407\) −5.72270 9.91201i −0.283664 0.491320i
\(408\) −13.1492 3.70223i −0.650983 0.183288i
\(409\) −6.71319 11.6276i −0.331946 0.574947i 0.650947 0.759123i \(-0.274372\pi\)
−0.982893 + 0.184176i \(0.941038\pi\)
\(410\) −2.83624 + 4.91251i −0.140072 + 0.242612i
\(411\) −14.5280 + 14.1649i −0.716612 + 0.698705i
\(412\) 4.34257 0.213943
\(413\) 5.48120 + 9.49371i 0.269712 + 0.467155i
\(414\) −0.0254761 + 1.00666i −0.00125208 + 0.0494745i
\(415\) 13.6491 + 23.6410i 0.670010 + 1.16049i
\(416\) −0.858315 + 1.48665i −0.0420824 + 0.0728888i
\(417\) 29.7439 + 8.37456i 1.45657 + 0.410104i
\(418\) −16.7185 + 7.07585i −0.817727 + 0.346091i
\(419\) 1.95049 3.37834i 0.0952875 0.165043i −0.814441 0.580246i \(-0.802956\pi\)
0.909729 + 0.415203i \(0.136290\pi\)
\(420\) 4.25422 + 16.7203i 0.207585 + 0.815866i
\(421\) −13.6227 + 23.5953i −0.663932 + 1.14996i 0.315642 + 0.948878i \(0.397780\pi\)
−0.979574 + 0.201085i \(0.935553\pi\)
\(422\) 17.9458 31.0830i 0.873588 1.51310i
\(423\) −0.238390 + 9.41967i −0.0115909 + 0.458000i
\(424\) −12.9651 + 22.4562i −0.629642 + 1.09057i
\(425\) −15.7925 27.3533i −0.766047 1.32683i
\(426\) 13.6682 13.3267i 0.662228 0.645680i
\(427\) −16.3908 28.3896i −0.793205 1.37387i
\(428\) 2.48822 + 4.30972i 0.120273 + 0.208318i
\(429\) 0.595326 + 2.33980i 0.0287426 + 0.112966i
\(430\) −12.0427 20.8586i −0.580751 1.00589i
\(431\) 20.2776 35.1217i 0.976735 1.69176i 0.302650 0.953102i \(-0.402129\pi\)
0.674086 0.738653i \(-0.264538\pi\)
\(432\) 24.4440 5.56496i 1.17606 0.267744i
\(433\) −9.37164 + 16.2322i −0.450372 + 0.780068i −0.998409 0.0563866i \(-0.982042\pi\)
0.548037 + 0.836454i \(0.315375\pi\)
\(434\) −28.0943 + 48.6608i −1.34857 + 2.33579i
\(435\) 3.97994 3.88049i 0.190824 0.186055i
\(436\) 3.00068 5.19733i 0.143707 0.248907i
\(437\) −0.726722 0.548822i −0.0347638 0.0262537i
\(438\) −1.66045 + 1.61896i −0.0793395 + 0.0773570i
\(439\) −8.15172 + 14.1192i −0.389060 + 0.673872i −0.992323 0.123670i \(-0.960534\pi\)
0.603263 + 0.797542i \(0.293867\pi\)
\(440\) 11.1054 + 19.2351i 0.529428 + 0.916997i
\(441\) 35.2892 + 21.5827i 1.68044 + 1.02775i
\(442\) 1.49455 + 2.58864i 0.0710887 + 0.123129i
\(443\) −26.4906 −1.25861 −0.629303 0.777160i \(-0.716659\pi\)
−0.629303 + 0.777160i \(0.716659\pi\)
\(444\) 4.27839 + 1.20460i 0.203043 + 0.0571680i
\(445\) −12.0429 + 20.8589i −0.570888 + 0.988807i
\(446\) 5.51700 + 9.55573i 0.261238 + 0.452477i
\(447\) 19.9777 19.4785i 0.944912 0.921301i
\(448\) 10.3048 + 17.8484i 0.486855 + 0.843258i
\(449\) 19.2529 0.908602 0.454301 0.890848i \(-0.349889\pi\)
0.454301 + 0.890848i \(0.349889\pi\)
\(450\) 37.5349 + 22.9561i 1.76941 + 1.08216i
\(451\) −1.21750 2.10877i −0.0573299 0.0992982i
\(452\) 9.03553 0.424995
\(453\) 2.73834 + 0.770994i 0.128658 + 0.0362244i
\(454\) −14.2985 −0.671061
\(455\) −4.60769 + 7.98075i −0.216012 + 0.374143i
\(456\) −6.66475 + 15.8664i −0.312106 + 0.743013i
\(457\) 18.2664 + 31.6384i 0.854467 + 1.47998i 0.877139 + 0.480237i \(0.159449\pi\)
−0.0226720 + 0.999743i \(0.507217\pi\)
\(458\) −6.64263 11.5054i −0.310390 0.537610i
\(459\) 5.30884 17.1771i 0.247795 0.801757i
\(460\) 0.228217 0.395283i 0.0106407 0.0184302i
\(461\) 2.91815 5.05439i 0.135912 0.235406i −0.790034 0.613064i \(-0.789937\pi\)
0.925945 + 0.377657i \(0.123270\pi\)
\(462\) −31.6598 8.91399i −1.47295 0.414716i
\(463\) 6.34039 10.9819i 0.294663 0.510371i −0.680243 0.732986i \(-0.738126\pi\)
0.974906 + 0.222615i \(0.0714593\pi\)
\(464\) −2.05964 + 3.56739i −0.0956162 + 0.165612i
\(465\) 12.3137 + 48.3961i 0.571033 + 2.24432i
\(466\) −2.14828 −0.0995170
\(467\) −24.0640 −1.11355 −0.556774 0.830664i \(-0.687961\pi\)
−0.556774 + 0.830664i \(0.687961\pi\)
\(468\) −0.799860 0.489189i −0.0369735 0.0226128i
\(469\) 0.639521 1.10768i 0.0295303 0.0511481i
\(470\) 9.48386 16.4265i 0.437458 0.757699i
\(471\) −13.1715 + 12.8424i −0.606912 + 0.591747i
\(472\) −5.48049 −0.252260
\(473\) 10.3390 0.475390
\(474\) −31.7009 8.92556i −1.45607 0.409965i
\(475\) −36.6436 + 15.5089i −1.68132 + 0.711596i
\(476\) −9.16923 −0.420271
\(477\) −29.1138 17.8059i −1.33303 0.815274i
\(478\) 5.46568 + 9.46683i 0.249994 + 0.433003i
\(479\) 5.01131 0.228973 0.114486 0.993425i \(-0.463478\pi\)
0.114486 + 0.993425i \(0.463478\pi\)
\(480\) −20.0064 5.63292i −0.913164 0.257106i
\(481\) 1.18704 + 2.05601i 0.0541243 + 0.0937460i
\(482\) −5.96182 + 10.3262i −0.271553 + 0.470344i
\(483\) −0.406833 1.59897i −0.0185115 0.0727555i
\(484\) −2.48758 −0.113072
\(485\) 11.9574 20.7109i 0.542959 0.940433i
\(486\) 4.93987 + 24.5527i 0.224077 + 1.11373i
\(487\) −31.5079 −1.42776 −0.713880 0.700268i \(-0.753064\pi\)
−0.713880 + 0.700268i \(0.753064\pi\)
\(488\) 16.3887 0.741879
\(489\) 27.3937 26.7092i 1.23879 1.20783i
\(490\) −41.6345 72.1130i −1.88085 3.25773i
\(491\) 30.6070 1.38127 0.690636 0.723202i \(-0.257331\pi\)
0.690636 + 0.723202i \(0.257331\pi\)
\(492\) 0.910225 + 0.256279i 0.0410361 + 0.0115539i
\(493\) 1.47708 + 2.55838i 0.0665244 + 0.115224i
\(494\) 3.46785 1.46772i 0.156026 0.0660357i
\(495\) −25.6773 + 13.9708i −1.15411 + 0.627942i
\(496\) −18.5036 32.0492i −0.830836 1.43905i
\(497\) −15.6391 + 27.0877i −0.701509 + 1.21505i
\(498\) 14.4701 14.1085i 0.648418 0.632216i
\(499\) −10.9239 −0.489021 −0.244511 0.969647i \(-0.578627\pi\)
−0.244511 + 0.969647i \(0.578627\pi\)
\(500\) −4.50982 7.81123i −0.201685 0.349329i
\(501\) 21.8320 + 6.14693i 0.975384 + 0.274625i
\(502\) −12.5913 21.8088i −0.561979 0.973376i
\(503\) −15.0754 + 26.1113i −0.672178 + 1.16425i 0.305108 + 0.952318i \(0.401307\pi\)
−0.977285 + 0.211928i \(0.932026\pi\)
\(504\) −27.3875 + 14.9014i −1.21994 + 0.663759i
\(505\) −8.68336 −0.386405
\(506\) 0.435068 + 0.753560i 0.0193411 + 0.0334998i
\(507\) 5.42864 + 21.3361i 0.241094 + 0.947568i
\(508\) −7.33160 −0.325287
\(509\) −1.38957 2.40680i −0.0615916 0.106680i 0.833585 0.552391i \(-0.186284\pi\)
−0.895177 + 0.445711i \(0.852951\pi\)
\(510\) −25.9126 + 25.2651i −1.14743 + 1.11876i
\(511\) 1.89988 3.29069i 0.0840457 0.145571i
\(512\) −6.59240 −0.291346
\(513\) −20.6534 9.29709i −0.911871 0.410476i
\(514\) −11.8785 −0.523940
\(515\) −14.0418 + 24.3212i −0.618757 + 1.07172i
\(516\) −2.87479 + 2.80295i −0.126555 + 0.123393i
\(517\) 4.07109 + 7.05134i 0.179046 + 0.310118i
\(518\) −32.3422 −1.42103
\(519\) −5.37231 21.1147i −0.235818 0.926832i
\(520\) −2.30355 3.98986i −0.101017 0.174967i
\(521\) 13.4298 0.588371 0.294186 0.955748i \(-0.404952\pi\)
0.294186 + 0.955748i \(0.404952\pi\)
\(522\) −3.51067 2.14711i −0.153658 0.0939762i
\(523\) 5.62130 9.73637i 0.245802 0.425742i −0.716555 0.697531i \(-0.754282\pi\)
0.962357 + 0.271789i \(0.0876153\pi\)
\(524\) −5.74753 9.95502i −0.251082 0.434887i
\(525\) −69.3921 19.5377i −3.02852 0.852696i
\(526\) −2.27547 3.94123i −0.0992153 0.171846i
\(527\) −26.5400 −1.15610
\(528\) 15.5104 15.1228i 0.675002 0.658136i
\(529\) 11.4782 19.8808i 0.499051 0.864382i
\(530\) 34.3487 + 59.4938i 1.49201 + 2.58424i
\(531\) 0.182485 7.21065i 0.00791916 0.312916i
\(532\) −1.41980 + 11.4637i −0.0615560 + 0.497016i
\(533\) 0.252542 + 0.437415i 0.0109388 + 0.0189465i
\(534\) 17.1640 + 4.83263i 0.742761 + 0.209128i
\(535\) −32.1829 −1.39139
\(536\) 0.319719 + 0.553770i 0.0138098 + 0.0239192i
\(537\) 28.7375 28.0194i 1.24012 1.20913i
\(538\) 18.3760 0.792244
\(539\) 35.7445 1.53962
\(540\) 3.35207 10.8458i 0.144250 0.466730i
\(541\) 9.55755 16.5542i 0.410911 0.711719i −0.584078 0.811697i \(-0.698544\pi\)
0.994990 + 0.0999781i \(0.0318773\pi\)
\(542\) −44.4008 −1.90718
\(543\) 1.59757 + 6.27890i 0.0685584 + 0.269454i
\(544\) 5.52298 9.56608i 0.236796 0.410142i
\(545\) 19.4056 + 33.6114i 0.831243 + 1.43976i
\(546\) 6.56707 + 1.84900i 0.281045 + 0.0791297i
\(547\) −41.0410 −1.75479 −0.877393 0.479772i \(-0.840719\pi\)
−0.877393 + 0.479772i \(0.840719\pi\)
\(548\) −3.40444 5.89667i −0.145431 0.251893i
\(549\) −0.545695 + 21.5625i −0.0232897 + 0.920263i
\(550\) 38.0191 1.62114
\(551\) 3.42731 1.45056i 0.146008 0.0617959i
\(552\) 0.793979 + 0.223549i 0.0337940 + 0.00951488i
\(553\) 53.9607 2.29464
\(554\) 16.6932 0.709227
\(555\) −20.5809 + 20.0666i −0.873608 + 0.851779i
\(556\) −5.18460 + 8.97999i −0.219876 + 0.380836i
\(557\) −19.9467 + 34.5487i −0.845169 + 1.46388i 0.0403059 + 0.999187i \(0.487167\pi\)
−0.885475 + 0.464688i \(0.846167\pi\)
\(558\) 32.4749 17.6694i 1.37477 0.748003i
\(559\) −2.14459 −0.0907064
\(560\) 82.6848 3.49407
\(561\) −3.83073 15.0558i −0.161733 0.635658i
\(562\) −6.83172 + 11.8329i −0.288179 + 0.499140i
\(563\) 4.46506 7.73371i 0.188180 0.325937i −0.756464 0.654036i \(-0.773075\pi\)
0.944643 + 0.328099i \(0.106408\pi\)
\(564\) −3.04362 0.856948i −0.128160 0.0360840i
\(565\) −29.2166 + 50.6047i −1.22915 + 2.12896i
\(566\) 1.09805 1.90187i 0.0461544 0.0799417i
\(567\) −18.6937 36.5298i −0.785062 1.53411i
\(568\) −7.81854 13.5421i −0.328058 0.568214i
\(569\) −2.87302 4.97622i −0.120443 0.208614i 0.799499 0.600667i \(-0.205098\pi\)
−0.919943 + 0.392053i \(0.871765\pi\)
\(570\) 27.5750 + 36.3091i 1.15499 + 1.52082i
\(571\) −6.75539 + 11.7007i −0.282704 + 0.489658i −0.972050 0.234774i \(-0.924565\pi\)
0.689346 + 0.724433i \(0.257898\pi\)
\(572\) −0.810179 −0.0338753
\(573\) 24.6028 + 6.92706i 1.02780 + 0.289382i
\(574\) −6.88078 −0.287198
\(575\) 0.953584 + 1.65166i 0.0397672 + 0.0688788i
\(576\) 0.343075 13.5562i 0.0142948 0.564842i
\(577\) −10.9961 −0.457774 −0.228887 0.973453i \(-0.573509\pi\)
−0.228887 + 0.973453i \(0.573509\pi\)
\(578\) 4.03928 + 6.99625i 0.168012 + 0.291005i
\(579\) 7.03887 6.86299i 0.292525 0.285216i
\(580\) 0.932648 + 1.61539i 0.0387261 + 0.0670756i
\(581\) −16.5565 + 28.6768i −0.686881 + 1.18971i
\(582\) −17.0422 4.79834i −0.706424 0.198897i
\(583\) −29.4895 −1.22133
\(584\) 0.949817 + 1.64513i 0.0393037 + 0.0680760i
\(585\) 5.32614 2.89791i 0.220209 0.119814i
\(586\) −0.600723 1.04048i −0.0248156 0.0429820i
\(587\) 14.2331 24.6525i 0.587464 1.01752i −0.407100 0.913384i \(-0.633460\pi\)
0.994563 0.104133i \(-0.0332068\pi\)
\(588\) −9.93882 + 9.69047i −0.409870 + 0.399628i
\(589\) −4.10954 + 33.1813i −0.169331 + 1.36721i
\(590\) −7.25979 + 12.5743i −0.298881 + 0.517677i
\(591\) 15.2486 14.8676i 0.627245 0.611572i
\(592\) 10.6507 18.4475i 0.437740 0.758188i
\(593\) −2.56192 + 4.43738i −0.105206 + 0.182222i −0.913822 0.406114i \(-0.866883\pi\)
0.808617 + 0.588336i \(0.200217\pi\)
\(594\) 14.7110 + 15.8723i 0.603600 + 0.651248i
\(595\) 29.6490 51.3535i 1.21549 2.10529i
\(596\) 4.68152 + 8.10862i 0.191762 + 0.332142i
\(597\) 0.0135850 + 0.0533928i 0.000555996 + 0.00218522i
\(598\) −0.0902445 0.156308i −0.00369037 0.00639191i
\(599\) −13.5015 23.3853i −0.551656 0.955497i −0.998155 0.0607125i \(-0.980663\pi\)
0.446499 0.894784i \(-0.352671\pi\)
\(600\) 25.8048 25.1600i 1.05348 1.02715i
\(601\) 20.4168 + 35.3630i 0.832819 + 1.44249i 0.895794 + 0.444470i \(0.146608\pi\)
−0.0629745 + 0.998015i \(0.520059\pi\)
\(602\) 14.6079 25.3017i 0.595374 1.03122i
\(603\) −0.739238 + 0.402214i −0.0301041 + 0.0163794i
\(604\) −0.477314 + 0.826732i −0.0194216 + 0.0336393i
\(605\) 8.04366 13.9320i 0.327021 0.566417i
\(606\) 1.58514 + 6.23005i 0.0643920 + 0.253078i
\(607\) −0.992746 + 1.71949i −0.0402943 + 0.0697918i −0.885469 0.464698i \(-0.846163\pi\)
0.845175 + 0.534490i \(0.179496\pi\)
\(608\) −11.1047 8.38630i −0.450355 0.340109i
\(609\) 6.49030 + 1.82738i 0.263000 + 0.0740492i
\(610\) 21.7094 37.6018i 0.878988 1.52245i
\(611\) −0.844451 1.46263i −0.0341628 0.0591718i
\(612\) 5.14684 + 3.14777i 0.208049 + 0.127241i
\(613\) −14.2449 24.6729i −0.575346 0.996528i −0.996004 0.0893089i \(-0.971534\pi\)
0.420658 0.907219i \(-0.361799\pi\)
\(614\) −17.8815 −0.721640
\(615\) −4.37856 + 4.26915i −0.176561 + 0.172149i
\(616\) −13.4709 + 23.3323i −0.542759 + 0.940087i
\(617\) −14.7097 25.4779i −0.592189 1.02570i −0.993937 0.109951i \(-0.964931\pi\)
0.401748 0.915750i \(-0.368403\pi\)
\(618\) 20.0130 + 5.63477i 0.805041 + 0.226664i
\(619\) −14.3363 24.8312i −0.576224 0.998049i −0.995907 0.0903786i \(-0.971192\pi\)
0.419684 0.907670i \(-0.362141\pi\)
\(620\) −16.7577 −0.673004
\(621\) −0.320560 + 1.03719i −0.0128636 + 0.0416210i
\(622\) 9.75796 + 16.9013i 0.391258 + 0.677679i
\(623\) −29.2163 −1.17053
\(624\) −3.21726 + 3.13687i −0.128793 + 0.125575i
\(625\) 12.6877 0.507508
\(626\) 21.1377 36.6115i 0.844831 1.46329i
\(627\) −19.4166 + 2.45803i −0.775423 + 0.0981643i
\(628\) −3.08658 5.34611i −0.123168 0.213333i
\(629\) −7.63820 13.2298i −0.304555 0.527505i
\(630\) −2.08982 + 82.5766i −0.0832603 + 3.28993i
\(631\) 9.49043 16.4379i 0.377808 0.654383i −0.612935 0.790133i \(-0.710011\pi\)
0.990743 + 0.135750i \(0.0433446\pi\)
\(632\) −13.4884 + 23.3626i −0.536541 + 0.929316i
\(633\) 27.7046 27.0123i 1.10116 1.07364i
\(634\) 10.8058 18.7162i 0.429154 0.743317i
\(635\) 23.7070 41.0616i 0.940782 1.62948i
\(636\) 8.19959 7.99471i 0.325135 0.317011i
\(637\) −7.41434 −0.293767
\(638\) −3.55596 −0.140782
\(639\) 18.0776 9.83589i 0.715139 0.389102i
\(640\) −25.6484 + 44.4243i −1.01384 + 1.75603i
\(641\) 2.73944 4.74484i 0.108201 0.187410i −0.806840 0.590770i \(-0.798824\pi\)
0.915042 + 0.403359i \(0.132158\pi\)
\(642\) 5.87496 + 23.0902i 0.231866 + 0.911299i
\(643\) 22.3400 0.881004 0.440502 0.897752i \(-0.354801\pi\)
0.440502 + 0.897752i \(0.354801\pi\)
\(644\) 0.553659 0.0218172
\(645\) −6.40262 25.1641i −0.252103 0.990834i
\(646\) −22.3145 + 9.44428i −0.877951 + 0.371580i
\(647\) 4.90902 0.192994 0.0964968 0.995333i \(-0.469236\pi\)
0.0964968 + 0.995333i \(0.469236\pi\)
\(648\) 20.4886 + 1.03770i 0.804870 + 0.0407648i
\(649\) −3.11638 5.39772i −0.122328 0.211879i
\(650\) −7.88616 −0.309321
\(651\) −43.3717 + 42.2880i −1.69987 + 1.65740i
\(652\) 6.41937 + 11.1187i 0.251402 + 0.435441i
\(653\) −19.2926 + 33.4157i −0.754977 + 1.30766i 0.190409 + 0.981705i \(0.439019\pi\)
−0.945386 + 0.325953i \(0.894315\pi\)
\(654\) 20.5727 20.0586i 0.804456 0.784355i
\(655\) 74.3392 2.90467
\(656\) 2.26592 3.92470i 0.0884695 0.153234i
\(657\) −2.19612 + 1.19489i −0.0856787 + 0.0466171i
\(658\) 23.0080 0.896946
\(659\) −20.4933 −0.798304 −0.399152 0.916885i \(-0.630696\pi\)
−0.399152 + 0.916885i \(0.630696\pi\)
\(660\) −2.41877 9.50644i −0.0941505 0.370038i
\(661\) 23.2088 + 40.1988i 0.902718 + 1.56355i 0.823951 + 0.566660i \(0.191765\pi\)
0.0787667 + 0.996893i \(0.474902\pi\)
\(662\) −6.93068 −0.269368
\(663\) 0.794594 + 3.12297i 0.0308595 + 0.121286i
\(664\) −8.27720 14.3365i −0.321218 0.556365i
\(665\) −59.6133 45.0201i −2.31170 1.74581i
\(666\) 18.1542 + 11.1030i 0.703460 + 0.430232i
\(667\) −0.0891895 0.154481i −0.00345343 0.00598152i
\(668\) −3.80550 + 6.59132i −0.147239 + 0.255026i
\(669\) 2.93317 + 11.5282i 0.113403 + 0.445704i
\(670\) 1.69408 0.0654479
\(671\) 9.31909 + 16.1411i 0.359760 + 0.623122i
\(672\) −6.21663 24.4331i −0.239812 0.942527i
\(673\) 12.7950 + 22.1615i 0.493209 + 0.854263i 0.999969 0.00782366i \(-0.00249037\pi\)
−0.506760 + 0.862087i \(0.669157\pi\)
\(674\) 2.34192 4.05632i 0.0902074 0.156244i
\(675\) 32.2436 + 34.7890i 1.24106 + 1.33903i
\(676\) −7.38784 −0.284148
\(677\) 15.8898 + 27.5220i 0.610695 + 1.05775i 0.991123 + 0.132944i \(0.0424432\pi\)
−0.380428 + 0.924810i \(0.624223\pi\)
\(678\) 41.6408 + 11.7242i 1.59920 + 0.450265i
\(679\) 29.0090 1.11326
\(680\) 14.8226 + 25.6735i 0.568420 + 0.984532i
\(681\) −14.8379 4.17769i −0.568589 0.160089i
\(682\) 15.9732 27.6664i 0.611646 1.05940i
\(683\) 46.5132 1.77978 0.889890 0.456176i \(-0.150781\pi\)
0.889890 + 0.456176i \(0.150781\pi\)
\(684\) 4.73243 5.94737i 0.180949 0.227403i
\(685\) 44.0334 1.68243
\(686\) 24.8644 43.0665i 0.949329 1.64429i
\(687\) −3.53161 13.8802i −0.134739 0.529564i
\(688\) 9.62113 + 16.6643i 0.366802 + 0.635320i
\(689\) 6.11689 0.233035
\(690\) 1.56466 1.52556i 0.0595655 0.0580771i
\(691\) −8.31573 14.4033i −0.316345 0.547926i 0.663377 0.748285i \(-0.269122\pi\)
−0.979723 + 0.200359i \(0.935789\pi\)
\(692\) 7.31118 0.277929
\(693\) −30.2497 18.5005i −1.14909 0.702777i
\(694\) 11.8844 20.5844i 0.451125 0.781371i
\(695\) −33.5291 58.0741i −1.27183 2.20288i
\(696\) −2.41354 + 2.35323i −0.0914851 + 0.0891991i
\(697\) −1.62502 2.81462i −0.0615521 0.106611i
\(698\) −2.14850 −0.0813220
\(699\) −2.22932 0.627677i −0.0843206 0.0237409i
\(700\) 12.0956 20.9502i 0.457170 0.791842i
\(701\) 18.3672 + 31.8130i 0.693721 + 1.20156i 0.970610 + 0.240658i \(0.0773632\pi\)
−0.276889 + 0.960902i \(0.589303\pi\)
\(702\) −3.05145 3.29233i −0.115169 0.124261i
\(703\) −17.7231 + 7.50105i −0.668439 + 0.282907i
\(704\) −5.85887 10.1479i −0.220814 0.382462i
\(705\) 14.6411 14.2752i 0.551415 0.537637i
\(706\) −33.3092 −1.25361
\(707\) −5.26650 9.12185i −0.198067 0.343062i
\(708\) 2.32986 + 0.655984i 0.0875614 + 0.0246534i
\(709\) −39.7998 −1.49471 −0.747356 0.664424i \(-0.768677\pi\)
−0.747356 + 0.664424i \(0.768677\pi\)
\(710\) −41.4276 −1.55475
\(711\) −30.2890 18.5246i −1.13593 0.694725i
\(712\) 7.30313 12.6494i 0.273696 0.474056i
\(713\) 1.60254 0.0600157
\(714\) −42.2570 11.8977i −1.58143 0.445260i
\(715\) 2.61974 4.53752i 0.0979726 0.169693i
\(716\) 6.73427 + 11.6641i 0.251671 + 0.435908i
\(717\) 2.90588 + 11.4209i 0.108522 + 0.426522i
\(718\) 7.67116 0.286285
\(719\) 11.0069 + 19.0645i 0.410487 + 0.710985i 0.994943 0.100441i \(-0.0320253\pi\)
−0.584456 + 0.811425i \(0.698692\pi\)
\(720\) −46.4123 28.3855i −1.72968 1.05786i
\(721\) −34.0657 −1.26867
\(722\) 8.35236 + 29.3608i 0.310843 + 1.09270i
\(723\) −9.20379 + 8.97381i −0.342293 + 0.333740i
\(724\) −2.17414 −0.0808011
\(725\) −7.79397 −0.289461
\(726\) −11.4642 3.22780i −0.425475 0.119795i
\(727\) 8.41740 14.5794i 0.312184 0.540719i −0.666651 0.745370i \(-0.732273\pi\)
0.978835 + 0.204652i \(0.0656061\pi\)
\(728\) 2.79423 4.83974i 0.103561 0.179373i
\(729\) −2.04751 + 26.9223i −0.0758338 + 0.997120i
\(730\) 5.03274 0.186270
\(731\) 13.7997 0.510401
\(732\) −6.96712 1.96163i −0.257512 0.0725039i
\(733\) 11.6819 20.2337i 0.431481 0.747347i −0.565520 0.824735i \(-0.691324\pi\)
0.997001 + 0.0773873i \(0.0246578\pi\)
\(734\) −17.4812 + 30.2783i −0.645242 + 1.11759i
\(735\) −22.1354 86.9981i −0.816475 3.20897i
\(736\) −0.333490 + 0.577621i −0.0122926 + 0.0212914i
\(737\) −0.363605 + 0.629782i −0.0133935 + 0.0231983i
\(738\) 3.86229 + 2.36215i 0.142173 + 0.0869521i
\(739\) 26.2097 + 45.3966i 0.964141 + 1.66994i 0.711906 + 0.702275i \(0.247832\pi\)
0.252235 + 0.967666i \(0.418834\pi\)
\(740\) −4.82286 8.35343i −0.177292 0.307078i
\(741\) 4.02751 0.509860i 0.147954 0.0187302i
\(742\) −41.6653 + 72.1665i −1.52958 + 2.64932i
\(743\) 13.1393 0.482033 0.241016 0.970521i \(-0.422519\pi\)
0.241016 + 0.970521i \(0.422519\pi\)
\(744\) −7.46733 29.3487i −0.273766 1.07598i
\(745\) −60.5513 −2.21843
\(746\) 18.2676 + 31.6404i 0.668824 + 1.15844i
\(747\) 19.1381 10.4129i 0.700227 0.380988i
\(748\) 5.21324 0.190615
\(749\) −19.5191 33.8080i −0.713212 1.23532i
\(750\) −10.6482 41.8503i −0.388817 1.52816i
\(751\) 24.1989 + 41.9138i 0.883032 + 1.52946i 0.847953 + 0.530071i \(0.177835\pi\)
0.0350783 + 0.999385i \(0.488832\pi\)
\(752\) −7.57682 + 13.1234i −0.276298 + 0.478563i
\(753\) −6.69430 26.3105i −0.243954 0.958807i
\(754\) 0.737600 0.0268618
\(755\) −3.08682 5.34652i −0.112341 0.194580i
\(756\) 13.4265 3.05671i 0.488319 0.111171i
\(757\) −8.62645 14.9414i −0.313533 0.543056i 0.665591 0.746317i \(-0.268179\pi\)
−0.979125 + 0.203261i \(0.934846\pi\)
\(758\) 16.9793 29.4090i 0.616715 1.06818i
\(759\) 0.231308 + 0.909105i 0.00839595 + 0.0329984i
\(760\) 34.3932 14.5564i 1.24757 0.528016i
\(761\) 14.8377 25.6997i 0.537867 0.931612i −0.461152 0.887321i \(-0.652564\pi\)
0.999019 0.0442911i \(-0.0141029\pi\)
\(762\) −33.7882 9.51324i −1.22402 0.344628i
\(763\) −23.5391 + 40.7710i −0.852174 + 1.47601i
\(764\) −4.28847 + 7.42785i −0.155151 + 0.268730i
\(765\) −34.2720 + 18.6471i −1.23911 + 0.674189i
\(766\) 7.69544 13.3289i 0.278048 0.481592i
\(767\) 0.646418 + 1.11963i 0.0233408 + 0.0404275i
\(768\) 21.4828 + 6.04861i 0.775195 + 0.218260i
\(769\) 4.88919 + 8.46833i 0.176309 + 0.305376i 0.940613 0.339479i \(-0.110251\pi\)
−0.764305 + 0.644855i \(0.776918\pi\)
\(770\) 35.6888 + 61.8148i 1.28614 + 2.22765i
\(771\) −12.3267 3.47064i −0.443934 0.124992i
\(772\) 1.64947 + 2.85696i 0.0593657 + 0.102824i
\(773\) 10.7481 18.6163i 0.386583 0.669581i −0.605405 0.795918i \(-0.706989\pi\)
0.991987 + 0.126337i \(0.0403220\pi\)
\(774\) −16.8857 + 9.18736i −0.606942 + 0.330233i
\(775\) 35.0102 60.6394i 1.25760 2.17823i
\(776\) −7.25131 + 12.5596i −0.260307 + 0.450865i
\(777\) −33.5623 9.44964i −1.20404 0.339004i
\(778\) −27.6875 + 47.9561i −0.992645 + 1.71931i
\(779\) −3.77058 + 1.59584i −0.135095 + 0.0571770i
\(780\) 0.501716 + 1.97189i 0.0179643 + 0.0706048i
\(781\) 8.89172 15.4009i 0.318171 0.551088i
\(782\) 0.580694 + 1.00579i 0.0207656 + 0.0359670i
\(783\) −3.01577 3.25384i −0.107775 0.116283i
\(784\) 33.2625 + 57.6124i 1.18795 + 2.05758i
\(785\) 39.9222 1.42488
\(786\) −13.5706 53.3361i −0.484046 1.90244i
\(787\) 10.9841 19.0250i 0.391541 0.678169i −0.601112 0.799165i \(-0.705275\pi\)
0.992653 + 0.120996i \(0.0386088\pi\)
\(788\) 3.57332 + 6.18918i 0.127294 + 0.220480i
\(789\) −1.20978 4.75476i −0.0430692 0.169274i
\(790\) 35.7352 + 61.8951i 1.27140 + 2.20213i
\(791\) −70.8801 −2.52021
\(792\) 15.5714 8.47228i 0.553305 0.301049i
\(793\) −1.93302 3.34810i −0.0686437 0.118894i
\(794\) −57.2963 −2.03337
\(795\) 18.2618 + 71.7741i 0.647680 + 2.54556i
\(796\) −0.0184878 −0.000655282
\(797\) −16.8742 + 29.2269i −0.597713 + 1.03527i 0.395444 + 0.918490i \(0.370591\pi\)
−0.993158 + 0.116780i \(0.962743\pi\)
\(798\) −21.4182 + 50.9891i −0.758196 + 1.80499i
\(799\) 5.43377 + 9.41157i 0.192233 + 0.332957i
\(800\) 14.5713 + 25.2382i 0.515172 + 0.892305i
\(801\) 16.3996 + 10.0299i 0.579450 + 0.354388i
\(802\) −0.910589 + 1.57719i −0.0321540 + 0.0556924i
\(803\) −1.08019 + 1.87094i −0.0381191 + 0.0660242i
\(804\) −0.0696354 0.273687i −0.00245585 0.00965218i
\(805\) −1.79027 + 3.10084i −0.0630988 + 0.109290i
\(806\) −3.31327 + 5.73875i −0.116705 + 0.202139i
\(807\) 19.0692 + 5.36903i 0.671267 + 0.188999i
\(808\) 5.26582 0.185251
\(809\) −11.4422 −0.402288 −0.201144 0.979562i \(-0.564466\pi\)
−0.201144 + 0.979562i \(0.564466\pi\)
\(810\) 29.5214 45.6341i 1.03728 1.60342i
\(811\) 18.0483 31.2606i 0.633762 1.09771i −0.353014 0.935618i \(-0.614843\pi\)
0.986776 0.162090i \(-0.0518235\pi\)
\(812\) −1.13131 + 1.95949i −0.0397012 + 0.0687646i
\(813\) −46.0758 12.9729i −1.61595 0.454980i
\(814\) 18.3884 0.644513
\(815\) −83.0288 −2.90837
\(816\) 20.7020 20.1847i 0.724715 0.706606i
\(817\) 2.13680 17.2530i 0.0747572 0.603605i
\(818\) 21.5711 0.754215
\(819\) 6.27458 + 3.83750i 0.219252 + 0.134093i
\(820\) −1.02606 1.77719i −0.0358316 0.0620621i
\(821\) −29.8000 −1.04003 −0.520014 0.854158i \(-0.674073\pi\)
−0.520014 + 0.854158i \(0.674073\pi\)
\(822\) −8.03827 31.5926i −0.280367 1.10192i
\(823\) 1.97734 + 3.42485i 0.0689256 + 0.119383i 0.898429 0.439120i \(-0.144710\pi\)
−0.829503 + 0.558502i \(0.811376\pi\)
\(824\) 8.51534 14.7490i 0.296646 0.513806i
\(825\) 39.4534 + 11.1083i 1.37359 + 0.386742i
\(826\) −17.6124 −0.612813
\(827\) −22.5669 + 39.0870i −0.784728 + 1.35919i 0.144433 + 0.989515i \(0.453864\pi\)
−0.929161 + 0.369675i \(0.879469\pi\)
\(828\) −0.310777 0.190070i −0.0108003 0.00660538i
\(829\) −37.7440 −1.31090 −0.655452 0.755237i \(-0.727522\pi\)
−0.655452 + 0.755237i \(0.727522\pi\)
\(830\) −43.8579 −1.52233
\(831\) 17.3230 + 4.87738i 0.600927 + 0.169194i
\(832\) 1.21528 + 2.10493i 0.0421323 + 0.0729754i
\(833\) 47.7089 1.65302
\(834\) −35.5457 + 34.6575i −1.23085 + 1.20009i
\(835\) −24.6104 42.6264i −0.851678 1.47515i
\(836\) 0.807237 6.51780i 0.0279189 0.225423i
\(837\) 38.8626 8.84750i 1.34329 0.305814i
\(838\) 3.13369 + 5.42771i 0.108251 + 0.187497i
\(839\) 10.4100 18.0306i 0.359392 0.622486i −0.628467 0.777836i \(-0.716317\pi\)
0.987859 + 0.155350i \(0.0496506\pi\)
\(840\) 65.1304 + 18.3378i 2.24721 + 0.632715i
\(841\) −28.2710 −0.974863
\(842\) −21.8865 37.9086i −0.754260 1.30642i
\(843\) −10.5467 + 10.2832i −0.363249 + 0.354173i
\(844\) 6.49221 + 11.2448i 0.223471 + 0.387063i
\(845\) 23.8888 41.3766i 0.821799 1.42340i
\(846\) −12.9148 7.89860i −0.444019 0.271559i
\(847\) 19.5141 0.670511
\(848\) −27.4418 47.5306i −0.942356 1.63221i
\(849\) 1.69516 1.65280i 0.0581776 0.0567239i
\(850\) 50.7449 1.74054
\(851\) 0.461212 + 0.798842i 0.0158101 + 0.0273840i
\(852\) 1.70289 + 6.69283i 0.0583400 + 0.229293i
\(853\) 14.2391 24.6629i 0.487539 0.844442i −0.512358 0.858772i \(-0.671228\pi\)
0.999897 + 0.0143294i \(0.00456135\pi\)
\(854\) 52.6674 1.80224
\(855\) 18.0066 + 45.7356i 0.615813 + 1.56412i
\(856\) 19.5166 0.667062
\(857\) −2.78592 + 4.82535i −0.0951651 + 0.164831i −0.909677 0.415315i \(-0.863671\pi\)
0.814512 + 0.580146i \(0.197005\pi\)
\(858\) −3.73376 1.05126i −0.127468 0.0358894i
\(859\) 3.07779 + 5.33088i 0.105013 + 0.181887i 0.913743 0.406292i \(-0.133178\pi\)
−0.808731 + 0.588179i \(0.799845\pi\)
\(860\) 8.71332 0.297122
\(861\) −7.14035 2.01041i −0.243343 0.0685144i
\(862\) 32.5783 + 56.4272i 1.10962 + 1.92192i
\(863\) 26.1393 0.889794 0.444897 0.895582i \(-0.353240\pi\)
0.444897 + 0.895582i \(0.353240\pi\)
\(864\) −4.89832 + 15.8488i −0.166644 + 0.539188i
\(865\) −23.6409 + 40.9473i −0.803815 + 1.39225i
\(866\) −15.0566 26.0789i −0.511646 0.886196i
\(867\) 2.14752 + 8.44036i 0.0729337 + 0.286650i
\(868\) −10.1636 17.6039i −0.344975 0.597514i
\(869\) −30.6797 −1.04074
\(870\) 2.20209 + 8.65482i 0.0746577 + 0.293426i
\(871\) 0.0754211 0.130633i 0.00255555 0.00442634i
\(872\) −11.7681 20.3829i −0.398517 0.690251i
\(873\) −16.2832 9.95871i −0.551103 0.337051i
\(874\) 1.34740 0.570267i 0.0455764 0.0192896i
\(875\) 35.3777 + 61.2760i 1.19598 + 2.07151i
\(876\) −0.206872 0.813063i −0.00698954 0.0274709i
\(877\) 0.794874 0.0268410 0.0134205 0.999910i \(-0.495728\pi\)
0.0134205 + 0.999910i \(0.495728\pi\)
\(878\) −13.0967 22.6842i −0.441992 0.765553i
\(879\) −0.319380 1.25525i −0.0107724 0.0423386i
\(880\) −47.0110 −1.58474
\(881\) 36.2565 1.22151 0.610756 0.791819i \(-0.290866\pi\)
0.610756 + 0.791819i \(0.290866\pi\)
\(882\) −58.3777 + 31.7629i −1.96568 + 1.06951i
\(883\) −27.3417 + 47.3571i −0.920120 + 1.59369i −0.120893 + 0.992666i \(0.538576\pi\)
−0.799227 + 0.601029i \(0.794758\pi\)
\(884\) −1.08136 −0.0363701
\(885\) −11.2076 + 10.9275i −0.376739 + 0.367325i
\(886\) 21.2801 36.8583i 0.714920 1.23828i
\(887\) 25.1527 + 43.5658i 0.844545 + 1.46280i 0.886015 + 0.463656i \(0.153463\pi\)
−0.0414702 + 0.999140i \(0.513204\pi\)
\(888\) 12.4808 12.1689i 0.418827 0.408362i
\(889\) 57.5135 1.92894
\(890\) −19.3483 33.5123i −0.648558 1.12333i
\(891\) 10.6284 + 20.7693i 0.356066 + 0.695797i
\(892\) −3.99174 −0.133653
\(893\) 12.6081 5.33620i 0.421914 0.178569i
\(894\) 11.0536 + 43.4437i 0.369687 + 1.45297i
\(895\) −87.1018 −2.91149
\(896\) −62.2235 −2.07874
\(897\) −0.0479793 0.188572i −0.00160198 0.00629624i
\(898\) −15.4661 + 26.7880i −0.516109 + 0.893927i
\(899\) −3.27453 + 5.67166i −0.109212 + 0.189160i
\(900\) −13.9816 + 7.60728i −0.466053 + 0.253576i
\(901\) −39.3602 −1.31128
\(902\) 3.91212 0.130259
\(903\) 22.5516 21.9881i 0.750469 0.731717i
\(904\) 17.7177 30.6880i 0.589284 1.02067i
\(905\) 7.03013 12.1765i 0.233689 0.404762i
\(906\) −3.27247 + 3.19070i −0.108721 + 0.106004i
\(907\) 6.06193 10.4996i 0.201283 0.348633i −0.747659 0.664083i \(-0.768822\pi\)
0.948942 + 0.315450i \(0.102156\pi\)
\(908\) 2.58636 4.47971i 0.0858314 0.148664i
\(909\) −0.175337 + 6.92822i −0.00581555 + 0.229794i
\(910\) −7.40280 12.8220i −0.245400 0.425046i
\(911\) 10.4969 + 18.1811i 0.347777 + 0.602367i 0.985854 0.167605i \(-0.0536034\pi\)
−0.638077 + 0.769972i \(0.720270\pi\)
\(912\) −22.0302 29.0080i −0.729492 0.960549i
\(913\) 9.41334 16.3044i 0.311536 0.539596i
\(914\) −58.6943 −1.94144
\(915\) 33.5147 32.6773i 1.10796 1.08028i
\(916\) 4.80617 0.158800
\(917\) 45.0871 + 78.0932i 1.48891 + 2.57886i
\(918\) 19.6351 + 21.1851i 0.648054 + 0.699212i
\(919\) −5.58553 −0.184250 −0.0921248 0.995747i \(-0.529366\pi\)
−0.0921248 + 0.995747i \(0.529366\pi\)
\(920\) −0.895020 1.55022i −0.0295079 0.0511093i
\(921\) −18.5561 5.22458i −0.611445 0.172156i
\(922\) 4.68836 + 8.12048i 0.154403 + 0.267434i
\(923\) −1.84438 + 3.19455i −0.0607084 + 0.105150i
\(924\) 8.51949 8.30661i 0.280271 0.273267i
\(925\) 40.3037 1.32518
\(926\) 10.1866 + 17.6437i 0.334752 + 0.579808i
\(927\) 19.1216 + 11.6947i 0.628037 + 0.384104i
\(928\) −1.36286 2.36055i −0.0447382 0.0774889i
\(929\) −10.8938 + 18.8685i −0.357413 + 0.619057i −0.987528 0.157445i \(-0.949674\pi\)
0.630115 + 0.776502i \(0.283008\pi\)
\(930\) −77.2287 21.7442i −2.53243 0.713019i
\(931\) 7.38742 59.6476i 0.242113 1.95487i
\(932\) 0.388588 0.673054i 0.0127286 0.0220466i
\(933\) 5.18791 + 20.3899i 0.169844 + 0.667536i
\(934\) 19.3308 33.4819i 0.632523 1.09556i
\(935\) −16.8571 + 29.1974i −0.551288 + 0.954858i
\(936\) −3.22991 + 1.75737i −0.105573 + 0.0574415i
\(937\) −23.1526 + 40.1014i −0.756362 + 1.31006i 0.188333 + 0.982105i \(0.439692\pi\)
−0.944694 + 0.327952i \(0.893642\pi\)
\(938\) 1.02747 + 1.77962i 0.0335480 + 0.0581068i
\(939\) 32.6321 31.8167i 1.06491 1.03830i
\(940\) 3.43095 + 5.94258i 0.111905 + 0.193826i
\(941\) −13.1076 22.7030i −0.427295 0.740097i 0.569336 0.822105i \(-0.307200\pi\)
−0.996632 + 0.0820075i \(0.973867\pi\)
\(942\) −7.28776 28.6429i −0.237448 0.933237i
\(943\) 0.0981225 + 0.169953i 0.00319531 + 0.00553444i
\(944\) 5.79997 10.0458i 0.188773 0.326965i
\(945\) −26.2956 + 85.0812i −0.855397 + 2.76769i
\(946\) −8.30544 + 14.3855i −0.270033 + 0.467711i
\(947\) 17.9942 31.1669i 0.584733 1.01279i −0.410175 0.912007i \(-0.634532\pi\)
0.994909 0.100781i \(-0.0321342\pi\)
\(948\) 8.53056 8.31740i 0.277060 0.270137i
\(949\) 0.224060 0.388083i 0.00727329 0.0125977i
\(950\) 7.85753 63.4433i 0.254932 2.05837i
\(951\) 16.6819 16.2651i 0.540949 0.527432i
\(952\) −17.9799 + 31.1421i −0.582733 + 1.00932i
\(953\) −6.73210 11.6603i −0.218074 0.377716i 0.736145 0.676824i \(-0.236644\pi\)
−0.954219 + 0.299108i \(0.903311\pi\)
\(954\) 48.1620 26.2046i 1.55930 0.848405i
\(955\) −27.7338 48.0363i −0.897444 1.55442i
\(956\) −3.95461 −0.127901
\(957\) −3.69011 1.03897i −0.119284 0.0335851i
\(958\) −4.02563 + 6.97260i −0.130062 + 0.225274i
\(959\) 26.7065 + 46.2570i 0.862397 + 1.49372i
\(960\) −21.0705 + 20.5440i −0.680049 + 0.663056i
\(961\) −13.9181 24.1069i −0.448971 0.777641i
\(962\) −3.81423 −0.122976
\(963\) −0.649845 + 25.6778i −0.0209410 + 0.827457i
\(964\) −2.15679 3.73567i −0.0694655 0.120318i
\(965\) −21.3344 −0.686779
\(966\) 2.55157 + 0.718409i 0.0820954 + 0.0231144i
\(967\) 12.6766 0.407653 0.203826 0.979007i \(-0.434662\pi\)
0.203826 + 0.979007i \(0.434662\pi\)
\(968\) −4.87789 + 8.44875i −0.156781 + 0.271553i
\(969\) −25.9157 + 3.28078i −0.832532 + 0.105394i
\(970\) 19.2110 + 33.2745i 0.616829 + 1.06838i
\(971\) 5.76415 + 9.98379i 0.184980 + 0.320395i 0.943570 0.331174i \(-0.107445\pi\)
−0.758590 + 0.651569i \(0.774111\pi\)
\(972\) −8.58589 2.89352i −0.275393 0.0928098i
\(973\) 40.6711 70.4445i 1.30386 2.25835i
\(974\) 25.3106 43.8392i 0.811004 1.40470i
\(975\) −8.18367 2.30416i −0.262087 0.0737921i
\(976\) −17.3440 + 30.0407i −0.555168 + 0.961580i
\(977\) −19.0964 + 33.0759i −0.610947 + 1.05819i 0.380134 + 0.924932i \(0.375878\pi\)
−0.991081 + 0.133260i \(0.957455\pi\)
\(978\) 15.1568 + 59.5706i 0.484662 + 1.90486i
\(979\) 16.6111 0.530895
\(980\) 30.1240 0.962276
\(981\) 27.2095 14.8045i 0.868732 0.472671i
\(982\) −24.5868 + 42.5857i −0.784598 + 1.35896i
\(983\) 7.91585 13.7107i 0.252476 0.437302i −0.711731 0.702453i \(-0.752088\pi\)
0.964207 + 0.265150i \(0.0854216\pi\)
\(984\) 2.65528 2.58893i 0.0846471 0.0825320i
\(985\) −46.2178 −1.47262
\(986\) −4.74621 −0.151150
\(987\) 23.8760 + 6.72242i 0.759981 + 0.213977i
\(988\) −0.167442 + 1.35196i −0.00532704 + 0.0430117i
\(989\) −0.833258 −0.0264961
\(990\) 1.18818 46.9495i 0.0377629 1.49215i
\(991\) −10.1647 17.6058i −0.322893 0.559267i 0.658191 0.752851i \(-0.271322\pi\)
−0.981084 + 0.193584i \(0.937989\pi\)
\(992\) 24.4877 0.777485
\(993\) −7.19213 2.02498i −0.228235 0.0642610i
\(994\) −25.1260 43.5196i −0.796950 1.38036i
\(995\) 0.0597808 0.103543i 0.00189518 0.00328255i
\(996\) 1.80279 + 7.08546i 0.0571235 + 0.224511i
\(997\) 36.2674 1.14860 0.574300 0.818645i \(-0.305274\pi\)
0.574300 + 0.818645i \(0.305274\pi\)
\(998\) 8.77527 15.1992i 0.277776 0.481123i
\(999\) 15.5950 + 16.8261i 0.493404 + 0.532354i
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.121.5 yes 32
3.2 odd 2 513.2.g.c.64.12 32
9.2 odd 6 513.2.h.c.235.5 32
9.7 even 3 171.2.h.c.7.12 yes 32
19.11 even 3 171.2.h.c.49.12 yes 32
57.11 odd 6 513.2.h.c.334.5 32
171.11 odd 6 513.2.g.c.505.12 32
171.106 even 3 inner 171.2.g.c.106.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.g.c.106.5 32 171.106 even 3 inner
171.2.g.c.121.5 yes 32 1.1 even 1 trivial
171.2.h.c.7.12 yes 32 9.7 even 3
171.2.h.c.49.12 yes 32 19.11 even 3
513.2.g.c.64.12 32 3.2 odd 2
513.2.g.c.505.12 32 171.11 odd 6
513.2.h.c.235.5 32 9.2 odd 6
513.2.h.c.334.5 32 57.11 odd 6