Properties

Label 91.2.q.a.43.1
Level $91$
Weight $2$
Character 91.43
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
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] = [91,2,Mod(36,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.36");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), 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: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.1
Root \(-1.12906 + 0.851598i\) of defining polynomial
Character \(\chi\) \(=\) 91.43
Dual form 91.2.q.a.36.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.34104 - 1.35160i) q^{2} +(0.172975 - 0.299601i) q^{3} +(2.65363 + 4.59623i) q^{4} +3.25812i q^{5} +(-0.809880 + 0.467584i) q^{6} +(0.866025 - 0.500000i) q^{7} -8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +O(q^{10})\) \(q+(-2.34104 - 1.35160i) q^{2} +(0.172975 - 0.299601i) q^{3} +(2.65363 + 4.59623i) q^{4} +3.25812i q^{5} +(-0.809880 + 0.467584i) q^{6} +(0.866025 - 0.500000i) q^{7} -8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +(4.40367 - 7.62739i) q^{10} +(-1.59871 - 0.923014i) q^{11} +1.83605 q^{12} +(3.60550 - 0.0186461i) q^{13} -2.70320 q^{14} +(0.976136 + 0.563573i) q^{15} +(-6.77628 + 11.7369i) q^{16} +(1.07657 + 1.86467i) q^{17} -7.78607i q^{18} +(-2.07929 + 1.20048i) q^{19} +(-14.9751 + 8.64587i) q^{20} -0.345949i q^{21} +(2.49509 + 4.32162i) q^{22} +(0.906314 - 1.56978i) q^{23} +(-2.67849 - 1.54643i) q^{24} -5.61537 q^{25} +(-8.46582 - 4.82954i) q^{26} +2.03429 q^{27} +(4.59623 + 2.65363i) q^{28} +(1.36703 - 2.36777i) q^{29} +(-1.52345 - 2.63869i) q^{30} +1.74236i q^{31} +(16.2422 - 9.37743i) q^{32} +(-0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(1.62906 + 2.82162i) q^{35} +(-7.64331 + 13.2386i) q^{36} +(-5.14042 - 2.96783i) q^{37} +6.49025 q^{38} +(0.618074 - 1.08344i) q^{39} +29.1283 q^{40} +(3.65577 + 2.11066i) q^{41} +(-0.467584 + 0.809880i) q^{42} +(-4.34111 - 7.51903i) q^{43} -9.79737i q^{44} +(-8.12716 + 4.69222i) q^{45} +(-4.24343 + 2.44994i) q^{46} -5.87774i q^{47} +(2.34425 + 4.06036i) q^{48} +(0.500000 - 0.866025i) q^{49} +(13.1458 + 7.58972i) q^{50} +0.744877 q^{51} +(9.65339 + 16.5222i) q^{52} -9.30628 q^{53} +(-4.76235 - 2.74954i) q^{54} +(3.00729 - 5.20878i) q^{55} +(-4.47010 - 7.74244i) q^{56} +0.830609i q^{57} +(-6.40054 + 3.69535i) q^{58} +(9.31173 - 5.37613i) q^{59} +5.98206i q^{60} +(-5.05504 - 8.75558i) q^{61} +(2.35497 - 4.07893i) q^{62} +(2.49443 + 1.44016i) q^{63} -23.5929 q^{64} +(0.0607514 + 11.7472i) q^{65} +1.72635 q^{66} +(0.716130 + 0.413458i) q^{67} +(-5.71365 + 9.89633i) q^{68} +(-0.313538 - 0.543065i) q^{69} -8.80735i q^{70} +(-2.03884 + 1.17712i) q^{71} +(22.3007 - 12.8753i) q^{72} -3.19482i q^{73} +(8.02261 + 13.8956i) q^{74} +(-0.971316 + 1.68237i) q^{75} +(-11.0353 - 6.37126i) q^{76} -1.84603 q^{77} +(-2.91130 + 1.70098i) q^{78} +0.801911 q^{79} +(-38.2402 - 22.0780i) q^{80} +(-3.96860 + 6.87381i) q^{81} +(-5.70552 - 9.88225i) q^{82} +9.97031i q^{83} +(1.59006 - 0.918023i) q^{84} +(-6.07534 + 3.50760i) q^{85} +23.4698i q^{86} +(-0.472923 - 0.819127i) q^{87} +(-8.25193 + 14.2928i) q^{88} +(13.0886 + 7.55674i) q^{89} +25.3680 q^{90} +(3.11313 - 1.81890i) q^{91} +9.62010 q^{92} +(0.522012 + 0.301384i) q^{93} +(-7.94435 + 13.7600i) q^{94} +(-3.91130 - 6.77458i) q^{95} -6.48823i q^{96} +(7.99489 - 4.61585i) q^{97} +(-2.34104 + 1.35160i) q^{98} -5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34104 1.35160i −1.65536 0.955724i −0.974813 0.223022i \(-0.928408\pi\)
−0.680549 0.732702i \(-0.738259\pi\)
\(3\) 0.172975 0.299601i 0.0998669 0.172975i −0.811763 0.583988i \(-0.801492\pi\)
0.911629 + 0.411013i \(0.134825\pi\)
\(4\) 2.65363 + 4.59623i 1.32682 + 2.29811i
\(5\) 3.25812i 1.45708i 0.685005 + 0.728539i \(0.259800\pi\)
−0.685005 + 0.728539i \(0.740200\pi\)
\(6\) −0.809880 + 0.467584i −0.330632 + 0.190890i
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 8.94020i 3.16084i
\(9\) 1.44016 + 2.49443i 0.480053 + 0.831477i
\(10\) 4.40367 7.62739i 1.39256 2.41199i
\(11\) −1.59871 0.923014i −0.482028 0.278299i 0.239233 0.970962i \(-0.423104\pi\)
−0.721261 + 0.692663i \(0.756437\pi\)
\(12\) 1.83605 0.530021
\(13\) 3.60550 0.0186461i 0.999987 0.00517151i
\(14\) −2.70320 −0.722460
\(15\) 0.976136 + 0.563573i 0.252037 + 0.145514i
\(16\) −6.77628 + 11.7369i −1.69407 + 2.93422i
\(17\) 1.07657 + 1.86467i 0.261107 + 0.452250i 0.966536 0.256530i \(-0.0825793\pi\)
−0.705430 + 0.708780i \(0.749246\pi\)
\(18\) 7.78607i 1.83519i
\(19\) −2.07929 + 1.20048i −0.477021 + 0.275408i −0.719174 0.694830i \(-0.755480\pi\)
0.242153 + 0.970238i \(0.422146\pi\)
\(20\) −14.9751 + 8.64587i −3.34853 + 1.93328i
\(21\) 0.345949i 0.0754923i
\(22\) 2.49509 + 4.32162i 0.531954 + 0.921372i
\(23\) 0.906314 1.56978i 0.188979 0.327322i −0.755931 0.654652i \(-0.772815\pi\)
0.944910 + 0.327329i \(0.106149\pi\)
\(24\) −2.67849 1.54643i −0.546744 0.315663i
\(25\) −5.61537 −1.12307
\(26\) −8.46582 4.82954i −1.66028 0.947151i
\(27\) 2.03429 0.391500
\(28\) 4.59623 + 2.65363i 0.868606 + 0.501490i
\(29\) 1.36703 2.36777i 0.253851 0.439683i −0.710732 0.703463i \(-0.751636\pi\)
0.964583 + 0.263780i \(0.0849693\pi\)
\(30\) −1.52345 2.63869i −0.278142 0.481756i
\(31\) 1.74236i 0.312937i 0.987683 + 0.156468i \(0.0500110\pi\)
−0.987683 + 0.156468i \(0.949989\pi\)
\(32\) 16.2422 9.37743i 2.87124 1.65771i
\(33\) −0.553071 + 0.319316i −0.0962774 + 0.0555858i
\(34\) 5.82036i 0.998183i
\(35\) 1.62906 + 2.82162i 0.275362 + 0.476940i
\(36\) −7.64331 + 13.2386i −1.27389 + 2.20643i
\(37\) −5.14042 2.96783i −0.845081 0.487908i 0.0139073 0.999903i \(-0.495573\pi\)
−0.858988 + 0.511996i \(0.828906\pi\)
\(38\) 6.49025 1.05286
\(39\) 0.618074 1.08344i 0.0989710 0.173489i
\(40\) 29.1283 4.60558
\(41\) 3.65577 + 2.11066i 0.570935 + 0.329629i 0.757523 0.652809i \(-0.226410\pi\)
−0.186588 + 0.982438i \(0.559743\pi\)
\(42\) −0.467584 + 0.809880i −0.0721498 + 0.124967i
\(43\) −4.34111 7.51903i −0.662014 1.14664i −0.980086 0.198575i \(-0.936369\pi\)
0.318072 0.948067i \(-0.396965\pi\)
\(44\) 9.79737i 1.47701i
\(45\) −8.12716 + 4.69222i −1.21153 + 0.699475i
\(46\) −4.24343 + 2.44994i −0.625659 + 0.361224i
\(47\) 5.87774i 0.857357i −0.903457 0.428678i \(-0.858979\pi\)
0.903457 0.428678i \(-0.141021\pi\)
\(48\) 2.34425 + 4.06036i 0.338363 + 0.586062i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 13.1458 + 7.58972i 1.85910 + 1.07335i
\(51\) 0.744877 0.104304
\(52\) 9.65339 + 16.5222i 1.33868 + 2.29122i
\(53\) −9.30628 −1.27832 −0.639158 0.769076i \(-0.720717\pi\)
−0.639158 + 0.769076i \(0.720717\pi\)
\(54\) −4.76235 2.74954i −0.648074 0.374166i
\(55\) 3.00729 5.20878i 0.405503 0.702352i
\(56\) −4.47010 7.74244i −0.597342 1.03463i
\(57\) 0.830609i 0.110017i
\(58\) −6.40054 + 3.69535i −0.840432 + 0.485224i
\(59\) 9.31173 5.37613i 1.21228 0.699912i 0.249028 0.968496i \(-0.419889\pi\)
0.963256 + 0.268584i \(0.0865557\pi\)
\(60\) 5.98206i 0.772281i
\(61\) −5.05504 8.75558i −0.647231 1.12104i −0.983781 0.179371i \(-0.942594\pi\)
0.336550 0.941665i \(-0.390740\pi\)
\(62\) 2.35497 4.07893i 0.299081 0.518024i
\(63\) 2.49443 + 1.44016i 0.314269 + 0.181443i
\(64\) −23.5929 −2.94911
\(65\) 0.0607514 + 11.7472i 0.00753529 + 1.45706i
\(66\) 1.72635 0.212499
\(67\) 0.716130 + 0.413458i 0.0874892 + 0.0505119i 0.543106 0.839664i \(-0.317248\pi\)
−0.455617 + 0.890176i \(0.650581\pi\)
\(68\) −5.71365 + 9.89633i −0.692881 + 1.20011i
\(69\) −0.313538 0.543065i −0.0377456 0.0653773i
\(70\) 8.80735i 1.05268i
\(71\) −2.03884 + 1.17712i −0.241965 + 0.139699i −0.616080 0.787684i \(-0.711280\pi\)
0.374114 + 0.927383i \(0.377947\pi\)
\(72\) 22.3007 12.8753i 2.62816 1.51737i
\(73\) 3.19482i 0.373925i −0.982367 0.186963i \(-0.940136\pi\)
0.982367 0.186963i \(-0.0598644\pi\)
\(74\) 8.02261 + 13.8956i 0.932610 + 1.61533i
\(75\) −0.971316 + 1.68237i −0.112158 + 0.194263i
\(76\) −11.0353 6.37126i −1.26584 0.730833i
\(77\) −1.84603 −0.210374
\(78\) −2.91130 + 1.70098i −0.329640 + 0.192598i
\(79\) 0.801911 0.0902220 0.0451110 0.998982i \(-0.485636\pi\)
0.0451110 + 0.998982i \(0.485636\pi\)
\(80\) −38.2402 22.0780i −4.27538 2.46839i
\(81\) −3.96860 + 6.87381i −0.440955 + 0.763757i
\(82\) −5.70552 9.88225i −0.630069 1.09131i
\(83\) 9.97031i 1.09438i 0.837007 + 0.547192i \(0.184303\pi\)
−0.837007 + 0.547192i \(0.815697\pi\)
\(84\) 1.59006 0.918023i 0.173490 0.100164i
\(85\) −6.07534 + 3.50760i −0.658963 + 0.380452i
\(86\) 23.4698i 2.53081i
\(87\) −0.472923 0.819127i −0.0507027 0.0878196i
\(88\) −8.25193 + 14.2928i −0.879658 + 1.52361i
\(89\) 13.0886 + 7.55674i 1.38739 + 0.801012i 0.993021 0.117938i \(-0.0376284\pi\)
0.394373 + 0.918950i \(0.370962\pi\)
\(90\) 25.3680 2.67402
\(91\) 3.11313 1.81890i 0.326345 0.190672i
\(92\) 9.62010 1.00296
\(93\) 0.522012 + 0.301384i 0.0541301 + 0.0312520i
\(94\) −7.94435 + 13.7600i −0.819397 + 1.41924i
\(95\) −3.91130 6.77458i −0.401291 0.695057i
\(96\) 6.48823i 0.662202i
\(97\) 7.99489 4.61585i 0.811758 0.468669i −0.0358079 0.999359i \(-0.511400\pi\)
0.847566 + 0.530690i \(0.178067\pi\)
\(98\) −2.34104 + 1.35160i −0.236480 + 0.136532i
\(99\) 5.31715i 0.534394i
\(100\) −14.9011 25.8095i −1.49011 2.58095i
\(101\) 7.41169 12.8374i 0.737491 1.27737i −0.216131 0.976364i \(-0.569344\pi\)
0.953622 0.301007i \(-0.0973228\pi\)
\(102\) −1.74378 1.00677i −0.172660 0.0996855i
\(103\) 4.28286 0.422003 0.211001 0.977486i \(-0.432328\pi\)
0.211001 + 0.977486i \(0.432328\pi\)
\(104\) −0.166700 32.2339i −0.0163463 3.16079i
\(105\) 1.12715 0.109998
\(106\) 21.7863 + 12.5783i 2.11608 + 1.22172i
\(107\) 9.56289 16.5634i 0.924479 1.60124i 0.132082 0.991239i \(-0.457834\pi\)
0.792397 0.610006i \(-0.208833\pi\)
\(108\) 5.39827 + 9.35007i 0.519448 + 0.899711i
\(109\) 4.27153i 0.409139i 0.978852 + 0.204569i \(0.0655794\pi\)
−0.978852 + 0.204569i \(0.934421\pi\)
\(110\) −14.0804 + 8.12930i −1.34251 + 0.775099i
\(111\) −1.77833 + 1.02672i −0.168791 + 0.0974516i
\(112\) 13.5526i 1.28060i
\(113\) −1.37488 2.38137i −0.129338 0.224020i 0.794082 0.607810i \(-0.207952\pi\)
−0.923420 + 0.383790i \(0.874619\pi\)
\(114\) 1.12265 1.94448i 0.105146 0.182118i
\(115\) 5.11454 + 2.95288i 0.476934 + 0.275358i
\(116\) 14.5104 1.34726
\(117\) 5.23901 + 8.96682i 0.484347 + 0.828983i
\(118\) −29.0655 −2.67569
\(119\) 1.86467 + 1.07657i 0.170934 + 0.0986890i
\(120\) 5.03845 8.72685i 0.459945 0.796649i
\(121\) −3.79609 6.57502i −0.345099 0.597729i
\(122\) 27.3295i 2.47430i
\(123\) 1.26471 0.730180i 0.114035 0.0658381i
\(124\) −8.00828 + 4.62358i −0.719165 + 0.415210i
\(125\) 2.00495i 0.179329i
\(126\) −3.89303 6.74293i −0.346819 0.600708i
\(127\) −4.86719 + 8.43022i −0.431893 + 0.748061i −0.997036 0.0769320i \(-0.975488\pi\)
0.565143 + 0.824993i \(0.308821\pi\)
\(128\) 22.7475 + 13.1333i 2.01061 + 1.16083i
\(129\) −3.00361 −0.264453
\(130\) 15.7352 27.5827i 1.38007 2.41916i
\(131\) −18.6615 −1.63046 −0.815230 0.579138i \(-0.803389\pi\)
−0.815230 + 0.579138i \(0.803389\pi\)
\(132\) −2.93530 1.69470i −0.255485 0.147504i
\(133\) −1.20048 + 2.07929i −0.104095 + 0.180297i
\(134\) −1.11766 1.93584i −0.0965509 0.167231i
\(135\) 6.62797i 0.570445i
\(136\) 16.6706 9.62475i 1.42949 0.825315i
\(137\) −7.29328 + 4.21078i −0.623107 + 0.359751i −0.778078 0.628168i \(-0.783805\pi\)
0.154971 + 0.987919i \(0.450472\pi\)
\(138\) 1.69511i 0.144298i
\(139\) 8.81809 + 15.2734i 0.747941 + 1.29547i 0.948808 + 0.315853i \(0.102291\pi\)
−0.200867 + 0.979619i \(0.564376\pi\)
\(140\) −8.64587 + 14.9751i −0.730709 + 1.26563i
\(141\) −1.76098 1.01670i −0.148301 0.0856216i
\(142\) 6.36399 0.534054
\(143\) −5.78135 3.29812i −0.483461 0.275803i
\(144\) −39.0357 −3.25298
\(145\) 7.71448 + 4.45396i 0.640653 + 0.369881i
\(146\) −4.31811 + 7.47919i −0.357370 + 0.618982i
\(147\) −0.172975 0.299601i −0.0142667 0.0247107i
\(148\) 31.5021i 2.58946i
\(149\) −3.48232 + 2.01052i −0.285283 + 0.164708i −0.635813 0.771843i \(-0.719335\pi\)
0.350530 + 0.936552i \(0.386002\pi\)
\(150\) 4.54777 2.62566i 0.371324 0.214384i
\(151\) 18.9010i 1.53814i −0.639165 0.769069i \(-0.720720\pi\)
0.639165 0.769069i \(-0.279280\pi\)
\(152\) 10.7325 + 18.5892i 0.870521 + 1.50779i
\(153\) −3.10086 + 5.37086i −0.250690 + 0.434208i
\(154\) 4.32162 + 2.49509i 0.348246 + 0.201060i
\(155\) −5.67682 −0.455973
\(156\) 6.61987 0.0342352i 0.530014 0.00274101i
\(157\) −11.5735 −0.923670 −0.461835 0.886966i \(-0.652809\pi\)
−0.461835 + 0.886966i \(0.652809\pi\)
\(158\) −1.87730 1.08386i −0.149350 0.0862273i
\(159\) −1.60975 + 2.78817i −0.127661 + 0.221116i
\(160\) 30.5528 + 52.9190i 2.41541 + 4.18362i
\(161\) 1.81263i 0.142855i
\(162\) 18.5813 10.7279i 1.45988 0.842863i
\(163\) −3.81520 + 2.20271i −0.298830 + 0.172529i −0.641917 0.766774i \(-0.721861\pi\)
0.343087 + 0.939304i \(0.388527\pi\)
\(164\) 22.4037i 1.74943i
\(165\) −1.04037 1.80197i −0.0809927 0.140284i
\(166\) 13.4759 23.3409i 1.04593 1.81160i
\(167\) −7.81076 4.50954i −0.604415 0.348959i 0.166362 0.986065i \(-0.446798\pi\)
−0.770776 + 0.637106i \(0.780131\pi\)
\(168\) −3.09285 −0.238619
\(169\) 12.9993 0.134457i 0.999947 0.0103429i
\(170\) 18.9635 1.45443
\(171\) −5.98901 3.45776i −0.457991 0.264421i
\(172\) 23.0395 39.9055i 1.75674 3.04277i
\(173\) 3.04600 + 5.27583i 0.231583 + 0.401114i 0.958274 0.285851i \(-0.0922761\pi\)
−0.726691 + 0.686964i \(0.758943\pi\)
\(174\) 2.55681i 0.193831i
\(175\) −4.86305 + 2.80769i −0.367612 + 0.212241i
\(176\) 21.6666 12.5092i 1.63318 0.942917i
\(177\) 3.71974i 0.279592i
\(178\) −20.4273 35.3812i −1.53109 2.65193i
\(179\) 1.93982 3.35987i 0.144989 0.251128i −0.784380 0.620281i \(-0.787019\pi\)
0.929369 + 0.369152i \(0.120352\pi\)
\(180\) −43.1330 24.9029i −3.21495 1.85615i
\(181\) −6.58392 −0.489379 −0.244690 0.969601i \(-0.578686\pi\)
−0.244690 + 0.969601i \(0.578686\pi\)
\(182\) −9.74638 + 0.0504042i −0.722450 + 0.00373621i
\(183\) −3.49757 −0.258548
\(184\) −14.0342 8.10262i −1.03461 0.597333i
\(185\) 9.66954 16.7481i 0.710919 1.23135i
\(186\) −0.814700 1.41110i −0.0597367 0.103467i
\(187\) 3.97476i 0.290663i
\(188\) 27.0155 15.5974i 1.97030 1.13756i
\(189\) 1.76175 1.01715i 0.128148 0.0739865i
\(190\) 21.1460i 1.53410i
\(191\) 6.87168 + 11.9021i 0.497218 + 0.861206i 0.999995 0.00320983i \(-0.00102172\pi\)
−0.502777 + 0.864416i \(0.667688\pi\)
\(192\) −4.08097 + 7.06845i −0.294519 + 0.510122i
\(193\) 19.7047 + 11.3765i 1.41838 + 0.818899i 0.996156 0.0875946i \(-0.0279180\pi\)
0.422219 + 0.906494i \(0.361251\pi\)
\(194\) −24.9551 −1.79167
\(195\) 3.52997 + 2.01376i 0.252786 + 0.144208i
\(196\) 5.30727 0.379091
\(197\) −12.5809 7.26358i −0.896352 0.517509i −0.0203371 0.999793i \(-0.506474\pi\)
−0.876015 + 0.482284i \(0.839807\pi\)
\(198\) −7.18665 + 12.4476i −0.510733 + 0.884615i
\(199\) 11.9202 + 20.6464i 0.845001 + 1.46358i 0.885620 + 0.464410i \(0.153734\pi\)
−0.0406192 + 0.999175i \(0.512933\pi\)
\(200\) 50.2025i 3.54985i
\(201\) 0.247745 0.143035i 0.0174746 0.0100889i
\(202\) −34.7021 + 20.0353i −2.44163 + 1.40968i
\(203\) 2.73406i 0.191894i
\(204\) 1.97663 + 3.42363i 0.138392 + 0.239702i
\(205\) −6.87678 + 11.9109i −0.480295 + 0.831896i
\(206\) −10.0263 5.78871i −0.698568 0.403318i
\(207\) 5.22095 0.362881
\(208\) −24.2131 + 42.4437i −1.67887 + 2.94294i
\(209\) 4.43223 0.306584
\(210\) −2.63869 1.52345i −0.182087 0.105128i
\(211\) −2.15764 + 3.73714i −0.148538 + 0.257275i −0.930687 0.365816i \(-0.880790\pi\)
0.782149 + 0.623091i \(0.214123\pi\)
\(212\) −24.6955 42.7738i −1.69609 2.93772i
\(213\) 0.814450i 0.0558052i
\(214\) −44.7741 + 25.8504i −3.06070 + 1.76709i
\(215\) 24.4979 14.1439i 1.67075 0.964605i
\(216\) 18.1870i 1.23747i
\(217\) 0.871180 + 1.50893i 0.0591395 + 0.102433i
\(218\) 5.77339 9.99981i 0.391024 0.677273i
\(219\) −0.957171 0.552623i −0.0646796 0.0373428i
\(220\) 31.9210 2.15212
\(221\) 3.91635 + 6.70301i 0.263442 + 0.450893i
\(222\) 5.55083 0.372548
\(223\) −20.2604 11.6973i −1.35674 0.783312i −0.367553 0.930003i \(-0.619804\pi\)
−0.989182 + 0.146691i \(0.953138\pi\)
\(224\) 9.37743 16.2422i 0.626556 1.08523i
\(225\) −8.08703 14.0071i −0.539135 0.933810i
\(226\) 7.43315i 0.494446i
\(227\) −23.1427 + 13.3614i −1.53603 + 0.886829i −0.536968 + 0.843602i \(0.680431\pi\)
−0.999065 + 0.0432270i \(0.986236\pi\)
\(228\) −3.81767 + 2.20413i −0.252831 + 0.145972i
\(229\) 3.00670i 0.198688i 0.995053 + 0.0993442i \(0.0316745\pi\)
−0.995053 + 0.0993442i \(0.968326\pi\)
\(230\) −7.98222 13.8256i −0.526332 0.911634i
\(231\) −0.319316 + 0.553071i −0.0210094 + 0.0363894i
\(232\) −21.1683 12.2215i −1.38977 0.802383i
\(233\) 11.7148 0.767462 0.383731 0.923445i \(-0.374639\pi\)
0.383731 + 0.923445i \(0.374639\pi\)
\(234\) −0.145180 28.0727i −0.00949072 1.83517i
\(235\) 19.1504 1.24924
\(236\) 49.4199 + 28.5326i 3.21696 + 1.85731i
\(237\) 0.138710 0.240253i 0.00901019 0.0156061i
\(238\) −2.91018 5.04058i −0.188639 0.326732i
\(239\) 1.42797i 0.0923677i −0.998933 0.0461838i \(-0.985294\pi\)
0.998933 0.0461838i \(-0.0147060\pi\)
\(240\) −13.2292 + 7.63786i −0.853938 + 0.493021i
\(241\) −2.32068 + 1.33984i −0.149488 + 0.0863069i −0.572878 0.819640i \(-0.694173\pi\)
0.423390 + 0.905947i \(0.360840\pi\)
\(242\) 20.5232i 1.31928i
\(243\) 4.42437 + 7.66323i 0.283824 + 0.491597i
\(244\) 26.8284 46.4682i 1.71751 2.97482i
\(245\) 2.82162 + 1.62906i 0.180267 + 0.104077i
\(246\) −3.94764 −0.251692
\(247\) −7.47450 + 4.36710i −0.475591 + 0.277872i
\(248\) 15.5770 0.989143
\(249\) 2.98711 + 1.72461i 0.189301 + 0.109293i
\(250\) −2.70989 + 4.69367i −0.171389 + 0.296854i
\(251\) 5.46696 + 9.46906i 0.345072 + 0.597681i 0.985367 0.170447i \(-0.0545213\pi\)
−0.640295 + 0.768129i \(0.721188\pi\)
\(252\) 15.2866i 0.962967i
\(253\) −2.89786 + 1.67308i −0.182187 + 0.105186i
\(254\) 22.7885 13.1570i 1.42988 0.825541i
\(255\) 2.42690i 0.151978i
\(256\) −11.9089 20.6268i −0.744307 1.28918i
\(257\) 2.07569 3.59520i 0.129478 0.224262i −0.793996 0.607922i \(-0.792003\pi\)
0.923474 + 0.383660i \(0.125337\pi\)
\(258\) 7.03156 + 4.05967i 0.437766 + 0.252744i
\(259\) −5.93565 −0.368823
\(260\) −53.8315 + 31.4519i −3.33849 + 1.95057i
\(261\) 7.87497 0.487448
\(262\) 43.6872 + 25.2228i 2.69900 + 1.55827i
\(263\) −2.02680 + 3.51052i −0.124978 + 0.216468i −0.921724 0.387846i \(-0.873219\pi\)
0.796747 + 0.604314i \(0.206553\pi\)
\(264\) 2.85475 + 4.94457i 0.175698 + 0.304317i
\(265\) 30.3210i 1.86260i
\(266\) 5.62072 3.24513i 0.344629 0.198971i
\(267\) 4.52801 2.61425i 0.277110 0.159989i
\(268\) 4.38866i 0.268080i
\(269\) −2.00011 3.46430i −0.121949 0.211222i 0.798587 0.601879i \(-0.205581\pi\)
−0.920536 + 0.390657i \(0.872248\pi\)
\(270\) 8.95836 15.5163i 0.545188 0.944294i
\(271\) −2.41189 1.39251i −0.146512 0.0845888i 0.424952 0.905216i \(-0.360291\pi\)
−0.571464 + 0.820627i \(0.693624\pi\)
\(272\) −29.1806 −1.76933
\(273\) −0.00645062 1.24732i −0.000390409 0.0754913i
\(274\) 22.7651 1.37529
\(275\) 8.97733 + 5.18306i 0.541353 + 0.312551i
\(276\) 1.66403 2.88219i 0.100163 0.173487i
\(277\) 8.34618 + 14.4560i 0.501474 + 0.868578i 0.999999 + 0.00170243i \(0.000541901\pi\)
−0.498525 + 0.866875i \(0.666125\pi\)
\(278\) 47.6741i 2.85930i
\(279\) −4.34619 + 2.50928i −0.260200 + 0.150226i
\(280\) 25.2258 14.5641i 1.50753 0.870373i
\(281\) 13.3731i 0.797774i −0.917000 0.398887i \(-0.869397\pi\)
0.917000 0.398887i \(-0.130603\pi\)
\(282\) 2.74834 + 4.76026i 0.163661 + 0.283470i
\(283\) −9.44312 + 16.3560i −0.561335 + 0.972261i 0.436045 + 0.899925i \(0.356379\pi\)
−0.997380 + 0.0723362i \(0.976955\pi\)
\(284\) −10.8207 6.24731i −0.642088 0.370710i
\(285\) −2.70623 −0.160303
\(286\) 9.07663 + 15.5351i 0.536712 + 0.918609i
\(287\) 4.22131 0.249176
\(288\) 46.7827 + 27.0100i 2.75669 + 1.59158i
\(289\) 6.18199 10.7075i 0.363647 0.629855i
\(290\) −12.0399 20.8537i −0.707008 1.22457i
\(291\) 3.19370i 0.187218i
\(292\) 14.6841 8.47789i 0.859324 0.496131i
\(293\) −2.95999 + 1.70895i −0.172925 + 0.0998380i −0.583964 0.811779i \(-0.698499\pi\)
0.411040 + 0.911617i \(0.365166\pi\)
\(294\) 0.935168i 0.0545401i
\(295\) 17.5161 + 30.3388i 1.01983 + 1.76639i
\(296\) −26.5329 + 45.9564i −1.54220 + 2.67116i
\(297\) −3.25224 1.87768i −0.188714 0.108954i
\(298\) 10.8697 0.629663
\(299\) 3.23845 5.67675i 0.187284 0.328295i
\(300\) −10.3101 −0.595252
\(301\) −7.51903 4.34111i −0.433390 0.250218i
\(302\) −25.5465 + 44.2479i −1.47004 + 2.54618i
\(303\) −2.56407 4.44110i −0.147302 0.255134i
\(304\) 32.5391i 1.86625i
\(305\) 28.5268 16.4699i 1.63344 0.943066i
\(306\) 14.5185 8.38225i 0.829966 0.479181i
\(307\) 16.3679i 0.934165i 0.884214 + 0.467083i \(0.154695\pi\)
−0.884214 + 0.467083i \(0.845305\pi\)
\(308\) −4.89868 8.48477i −0.279128 0.483464i
\(309\) 0.740826 1.28315i 0.0421441 0.0729958i
\(310\) 13.2896 + 7.67278i 0.754801 + 0.435785i
\(311\) −23.6979 −1.34378 −0.671891 0.740650i \(-0.734518\pi\)
−0.671891 + 0.740650i \(0.734518\pi\)
\(312\) −9.68614 5.52570i −0.548370 0.312831i
\(313\) −5.18025 −0.292805 −0.146403 0.989225i \(-0.546769\pi\)
−0.146403 + 0.989225i \(0.546769\pi\)
\(314\) 27.0941 + 15.6428i 1.52901 + 0.882774i
\(315\) −4.69222 + 8.12716i −0.264377 + 0.457914i
\(316\) 2.12798 + 3.68577i 0.119708 + 0.207341i
\(317\) 6.06537i 0.340665i 0.985387 + 0.170332i \(0.0544842\pi\)
−0.985387 + 0.170332i \(0.945516\pi\)
\(318\) 7.53697 4.35147i 0.422652 0.244018i
\(319\) −4.37096 + 2.52358i −0.244727 + 0.141293i
\(320\) 76.8686i 4.29709i
\(321\) −3.30827 5.73010i −0.184650 0.319823i
\(322\) −2.44994 + 4.24343i −0.136530 + 0.236477i
\(323\) −4.47700 2.58480i −0.249107 0.143822i
\(324\) −42.1248 −2.34027
\(325\) −20.2462 + 0.104705i −1.12306 + 0.00580799i
\(326\) 11.9087 0.659562
\(327\) 1.27975 + 0.738866i 0.0707706 + 0.0408594i
\(328\) 18.8697 32.6833i 1.04190 1.80463i
\(329\) −2.93887 5.09027i −0.162025 0.280636i
\(330\) 5.62465i 0.309627i
\(331\) 14.9605 8.63743i 0.822301 0.474756i −0.0289082 0.999582i \(-0.509203\pi\)
0.851209 + 0.524826i \(0.175870\pi\)
\(332\) −45.8258 + 26.4576i −2.51502 + 1.45205i
\(333\) 17.0966i 0.936886i
\(334\) 12.1902 + 21.1140i 0.667017 + 1.15531i
\(335\) −1.34710 + 2.33324i −0.0735998 + 0.127479i
\(336\) 4.06036 + 2.34425i 0.221511 + 0.127889i
\(337\) −8.35464 −0.455106 −0.227553 0.973766i \(-0.573073\pi\)
−0.227553 + 0.973766i \(0.573073\pi\)
\(338\) −30.6136 17.2551i −1.66516 0.938552i
\(339\) −0.951279 −0.0516664
\(340\) −32.2435 18.6158i −1.74865 1.00958i
\(341\) 1.60822 2.78552i 0.0870901 0.150844i
\(342\) 9.34700 + 16.1895i 0.505428 + 0.875427i
\(343\) 1.00000i 0.0539949i
\(344\) −67.2216 + 38.8104i −3.62435 + 2.09252i
\(345\) 1.76937 1.02155i 0.0952598 0.0549983i
\(346\) 16.4679i 0.885318i
\(347\) −14.4110 24.9606i −0.773623 1.33995i −0.935565 0.353154i \(-0.885109\pi\)
0.161942 0.986800i \(-0.448224\pi\)
\(348\) 2.50993 4.34733i 0.134546 0.233041i
\(349\) −10.1516 5.86103i −0.543403 0.313734i 0.203054 0.979167i \(-0.434913\pi\)
−0.746457 + 0.665434i \(0.768247\pi\)
\(350\) 15.1794 0.811376
\(351\) 7.33464 0.0379317i 0.391494 0.00202464i
\(352\) −34.6220 −1.84536
\(353\) 15.4466 + 8.91811i 0.822141 + 0.474663i 0.851154 0.524916i \(-0.175903\pi\)
−0.0290134 + 0.999579i \(0.509237\pi\)
\(354\) −5.02759 + 8.70804i −0.267213 + 0.462827i
\(355\) −3.83521 6.64278i −0.203552 0.352562i
\(356\) 80.2113i 4.25119i
\(357\) 0.645082 0.372438i 0.0341414 0.0197115i
\(358\) −9.08239 + 5.24372i −0.480019 + 0.277139i
\(359\) 5.68162i 0.299864i 0.988696 + 0.149932i \(0.0479055\pi\)
−0.988696 + 0.149932i \(0.952094\pi\)
\(360\) 41.9494 + 72.6584i 2.21093 + 3.82943i
\(361\) −6.61771 + 11.4622i −0.348300 + 0.603274i
\(362\) 15.4132 + 8.89882i 0.810100 + 0.467712i
\(363\) −2.62651 −0.137856
\(364\) 16.6212 + 9.48199i 0.871188 + 0.496991i
\(365\) 10.4091 0.544838
\(366\) 8.18794 + 4.72731i 0.427991 + 0.247100i
\(367\) 9.81580 17.0015i 0.512381 0.887469i −0.487516 0.873114i \(-0.662097\pi\)
0.999897 0.0143554i \(-0.00456964\pi\)
\(368\) 12.2829 + 21.2746i 0.640289 + 1.10901i
\(369\) 12.1587i 0.632958i
\(370\) −45.2735 + 26.1387i −2.35366 + 1.35888i
\(371\) −8.05947 + 4.65314i −0.418427 + 0.241579i
\(372\) 3.19905i 0.165863i
\(373\) −16.0323 27.7687i −0.830119 1.43781i −0.897943 0.440111i \(-0.854939\pi\)
0.0678240 0.997697i \(-0.478394\pi\)
\(374\) −5.37227 + 9.30505i −0.277794 + 0.481153i
\(375\) −0.600686 0.346806i −0.0310193 0.0179090i
\(376\) −52.5482 −2.70997
\(377\) 4.88468 8.56248i 0.251574 0.440990i
\(378\) −5.49909 −0.282843
\(379\) −16.4745 9.51154i −0.846237 0.488575i 0.0131425 0.999914i \(-0.495816\pi\)
−0.859379 + 0.511339i \(0.829150\pi\)
\(380\) 20.7583 35.9545i 1.06488 1.84443i
\(381\) 1.68380 + 2.91643i 0.0862637 + 0.149413i
\(382\) 37.1510i 1.90081i
\(383\) 0.606070 0.349915i 0.0309687 0.0178798i −0.484436 0.874827i \(-0.660975\pi\)
0.515404 + 0.856947i \(0.327642\pi\)
\(384\) 7.86948 4.54345i 0.401588 0.231857i
\(385\) 6.01459i 0.306532i
\(386\) −30.7529 53.2657i −1.56528 2.71115i
\(387\) 12.5038 21.6572i 0.635604 1.10090i
\(388\) 42.4310 + 24.4976i 2.15411 + 1.24368i
\(389\) 20.0547 1.01681 0.508407 0.861117i \(-0.330235\pi\)
0.508407 + 0.861117i \(0.330235\pi\)
\(390\) −5.54200 9.48539i −0.280630 0.480311i
\(391\) 3.90284 0.197375
\(392\) −7.74244 4.47010i −0.391052 0.225774i
\(393\) −3.22796 + 5.59099i −0.162829 + 0.282028i
\(394\) 19.6349 + 34.0086i 0.989192 + 1.71333i
\(395\) 2.61272i 0.131460i
\(396\) 24.4388 14.1098i 1.22810 0.709043i
\(397\) −19.2953 + 11.1401i −0.968403 + 0.559108i −0.898749 0.438463i \(-0.855523\pi\)
−0.0696541 + 0.997571i \(0.522190\pi\)
\(398\) 64.4453i 3.23035i
\(399\) 0.415304 + 0.719328i 0.0207912 + 0.0360114i
\(400\) 38.0513 65.9069i 1.90257 3.29534i
\(401\) −4.16341 2.40374i −0.207911 0.120037i 0.392429 0.919782i \(-0.371635\pi\)
−0.600340 + 0.799745i \(0.704968\pi\)
\(402\) −0.773306 −0.0385690
\(403\) 0.0324883 + 6.28208i 0.00161836 + 0.312933i
\(404\) 78.6717 3.91406
\(405\) −22.3957 12.9302i −1.11285 0.642506i
\(406\) −3.69535 + 6.40054i −0.183397 + 0.317653i
\(407\) 5.47869 + 9.48937i 0.271568 + 0.470370i
\(408\) 6.65935i 0.329687i
\(409\) 31.8727 18.4017i 1.57601 0.909907i 0.580597 0.814191i \(-0.302819\pi\)
0.995409 0.0957164i \(-0.0305142\pi\)
\(410\) 32.1976 18.5893i 1.59013 0.918060i
\(411\) 2.91343i 0.143709i
\(412\) 11.3651 + 19.6850i 0.559921 + 0.969811i
\(413\) 5.37613 9.31173i 0.264542 0.458200i
\(414\) −12.2224 7.05662i −0.600699 0.346814i
\(415\) −32.4845 −1.59460
\(416\) 58.3864 34.1132i 2.86263 1.67254i
\(417\) 6.10122 0.298778
\(418\) −10.3760 5.99059i −0.507507 0.293009i
\(419\) −14.6334 + 25.3457i −0.714887 + 1.23822i 0.248116 + 0.968730i \(0.420188\pi\)
−0.963003 + 0.269490i \(0.913145\pi\)
\(420\) 2.99103 + 5.18062i 0.145947 + 0.252788i
\(421\) 7.53862i 0.367410i 0.982981 + 0.183705i \(0.0588091\pi\)
−0.982981 + 0.183705i \(0.941191\pi\)
\(422\) 10.1022 5.83251i 0.491768 0.283922i
\(423\) 14.6616 8.46489i 0.712872 0.411577i
\(424\) 83.2000i 4.04055i
\(425\) −6.04534 10.4708i −0.293242 0.507910i
\(426\) 1.10081 1.90666i 0.0533343 0.0923778i
\(427\) −8.75558 5.05504i −0.423712 0.244630i
\(428\) 101.506 4.90646
\(429\) −1.98815 + 1.16161i −0.0959886 + 0.0560829i
\(430\) −76.4674 −3.68759
\(431\) −27.0426 15.6131i −1.30260 0.752055i −0.321748 0.946825i \(-0.604270\pi\)
−0.980849 + 0.194771i \(0.937604\pi\)
\(432\) −13.7849 + 23.8762i −0.663228 + 1.14874i
\(433\) 2.94202 + 5.09573i 0.141384 + 0.244885i 0.928018 0.372535i \(-0.121511\pi\)
−0.786634 + 0.617420i \(0.788178\pi\)
\(434\) 4.70994i 0.226084i
\(435\) 2.66882 1.54084i 0.127960 0.0738777i
\(436\) −19.6329 + 11.3351i −0.940247 + 0.542852i
\(437\) 4.35204i 0.208186i
\(438\) 1.49385 + 2.58742i 0.0713788 + 0.123632i
\(439\) −4.97821 + 8.62251i −0.237597 + 0.411530i −0.960024 0.279917i \(-0.909693\pi\)
0.722427 + 0.691447i \(0.243026\pi\)
\(440\) −46.5676 26.8858i −2.22002 1.28173i
\(441\) 2.88032 0.137158
\(442\) −0.108527 20.9853i −0.00516212 0.998170i
\(443\) −35.8813 −1.70477 −0.852385 0.522915i \(-0.824845\pi\)
−0.852385 + 0.522915i \(0.824845\pi\)
\(444\) −9.43805 5.44906i −0.447910 0.258601i
\(445\) −24.6208 + 42.6444i −1.16714 + 2.02154i
\(446\) 31.6202 + 54.7678i 1.49726 + 2.59333i
\(447\) 1.39108i 0.0657956i
\(448\) −20.4321 + 11.7965i −0.965324 + 0.557330i
\(449\) 3.46001 1.99764i 0.163288 0.0942744i −0.416129 0.909306i \(-0.636614\pi\)
0.579417 + 0.815031i \(0.303280\pi\)
\(450\) 43.7217i 2.06106i
\(451\) −3.89633 6.74864i −0.183471 0.317781i
\(452\) 7.29687 12.6386i 0.343216 0.594467i
\(453\) −5.66274 3.26939i −0.266059 0.153609i
\(454\) 72.2371 3.39026
\(455\) 5.92620 + 10.1430i 0.277825 + 0.475510i
\(456\) 7.42580 0.347745
\(457\) 35.6995 + 20.6111i 1.66995 + 0.964147i 0.967660 + 0.252257i \(0.0811729\pi\)
0.702291 + 0.711890i \(0.252160\pi\)
\(458\) 4.06385 7.03880i 0.189891 0.328901i
\(459\) 2.19006 + 3.79329i 0.102223 + 0.177056i
\(460\) 31.3435i 1.46140i
\(461\) 21.4139 12.3633i 0.997343 0.575816i 0.0898818 0.995952i \(-0.471351\pi\)
0.907461 + 0.420136i \(0.138018\pi\)
\(462\) 1.49506 0.863173i 0.0695565 0.0401585i
\(463\) 24.4057i 1.13423i 0.823639 + 0.567115i \(0.191940\pi\)
−0.823639 + 0.567115i \(0.808060\pi\)
\(464\) 18.5268 + 32.0893i 0.860084 + 1.48971i
\(465\) −0.981946 + 1.70078i −0.0455366 + 0.0788718i
\(466\) −27.4248 15.8337i −1.27043 0.733482i
\(467\) 4.44860 0.205857 0.102928 0.994689i \(-0.467179\pi\)
0.102928 + 0.994689i \(0.467179\pi\)
\(468\) −27.3111 + 47.8744i −1.26246 + 2.21299i
\(469\) 0.826916 0.0381834
\(470\) −44.8318 25.8837i −2.06794 1.19392i
\(471\) −2.00193 + 3.46744i −0.0922441 + 0.159771i
\(472\) −48.0637 83.2487i −2.21231 3.83183i
\(473\) 16.0276i 0.736951i
\(474\) −0.649451 + 0.374961i −0.0298303 + 0.0172225i
\(475\) 11.6760 6.74113i 0.535730 0.309304i
\(476\) 11.4273i 0.523769i
\(477\) −13.4025 23.2139i −0.613660 1.06289i
\(478\) −1.93004 + 3.34293i −0.0882780 + 0.152902i
\(479\) −27.4328 15.8383i −1.25343 0.723671i −0.281645 0.959519i \(-0.590880\pi\)
−0.971790 + 0.235848i \(0.924213\pi\)
\(480\) 21.1394 0.964879
\(481\) −18.5892 10.6047i −0.847593 0.483531i
\(482\) 7.24372 0.329942
\(483\) −0.543065 0.313538i −0.0247103 0.0142665i
\(484\) 20.1469 34.8954i 0.915767 1.58616i
\(485\) 15.0390 + 26.0483i 0.682887 + 1.18279i
\(486\) 23.9199i 1.08503i
\(487\) 23.3096 13.4578i 1.05626 0.609832i 0.131864 0.991268i \(-0.457904\pi\)
0.924395 + 0.381436i \(0.124570\pi\)
\(488\) −78.2766 + 45.1930i −3.54341 + 2.04579i
\(489\) 1.52405i 0.0689200i
\(490\) −4.40367 7.62739i −0.198938 0.344570i
\(491\) 4.86358 8.42396i 0.219490 0.380168i −0.735162 0.677891i \(-0.762894\pi\)
0.954652 + 0.297723i \(0.0962273\pi\)
\(492\) 6.71215 + 3.87526i 0.302607 + 0.174710i
\(493\) 5.88682 0.265129
\(494\) 23.4006 0.121018i 1.05284 0.00544487i
\(495\) 17.3239 0.778653
\(496\) −20.4498 11.8067i −0.918225 0.530137i
\(497\) −1.17712 + 2.03884i −0.0528012 + 0.0914543i
\(498\) −4.66196 8.07475i −0.208907 0.361838i
\(499\) 7.87525i 0.352545i −0.984341 0.176272i \(-0.943596\pi\)
0.984341 0.176272i \(-0.0564039\pi\)
\(500\) 9.21523 5.32042i 0.412118 0.237936i
\(501\) −2.70213 + 1.56007i −0.120722 + 0.0696989i
\(502\) 29.5565i 1.31917i
\(503\) 4.87603 + 8.44553i 0.217411 + 0.376568i 0.954016 0.299756i \(-0.0969053\pi\)
−0.736604 + 0.676324i \(0.763572\pi\)
\(504\) 12.8753 22.3007i 0.573512 0.993352i
\(505\) 41.8259 + 24.1482i 1.86123 + 1.07458i
\(506\) 9.04533 0.402114
\(507\) 2.20827 3.91786i 0.0980725 0.173998i
\(508\) −51.6630 −2.29217
\(509\) −19.9407 11.5128i −0.883857 0.510295i −0.0119288 0.999929i \(-0.503797\pi\)
−0.871928 + 0.489634i \(0.837130\pi\)
\(510\) 3.28019 5.68146i 0.145249 0.251579i
\(511\) −1.59741 2.76680i −0.0706653 0.122396i
\(512\) 11.8512i 0.523752i
\(513\) −4.22988 + 2.44212i −0.186754 + 0.107822i
\(514\) −9.71853 + 5.61100i −0.428666 + 0.247490i
\(515\) 13.9541i 0.614891i
\(516\) −7.97048 13.8053i −0.350881 0.607744i
\(517\) −5.42524 + 9.39679i −0.238602 + 0.413270i
\(518\) 13.8956 + 8.02261i 0.610537 + 0.352493i
\(519\) 2.10752 0.0925100
\(520\) 105.022 0.543130i 4.60552 0.0238178i
\(521\) 0.486481 0.0213131 0.0106566 0.999943i \(-0.496608\pi\)
0.0106566 + 0.999943i \(0.496608\pi\)
\(522\) −18.4356 10.6438i −0.806904 0.465866i
\(523\) 17.3135 29.9878i 0.757065 1.31128i −0.187275 0.982307i \(-0.559966\pi\)
0.944341 0.328968i \(-0.106701\pi\)
\(524\) −49.5207 85.7724i −2.16332 3.74698i
\(525\) 1.94263i 0.0847834i
\(526\) 9.48962 5.47883i 0.413767 0.238888i
\(527\) −3.24893 + 1.87577i −0.141526 + 0.0817099i
\(528\) 8.65510i 0.376665i
\(529\) 9.85719 + 17.0732i 0.428574 + 0.742311i
\(530\) −40.9818 + 70.9826i −1.78014 + 3.08329i
\(531\) 26.8208 + 15.4850i 1.16392 + 0.671990i
\(532\) −12.7425 −0.552458
\(533\) 13.2202 + 7.54182i 0.572632 + 0.326672i
\(534\) −14.1336 −0.611622
\(535\) 53.9656 + 31.1571i 2.33314 + 1.34704i
\(536\) 3.69639 6.40234i 0.159660 0.276539i
\(537\) −0.671080 1.16234i −0.0289592 0.0501589i
\(538\) 10.8134i 0.466198i
\(539\) −1.59871 + 0.923014i −0.0688612 + 0.0397570i
\(540\) −30.4637 + 17.5882i −1.31095 + 0.756876i
\(541\) 22.5384i 0.969002i −0.874791 0.484501i \(-0.839001\pi\)
0.874791 0.484501i \(-0.160999\pi\)
\(542\) 3.76422 + 6.51982i 0.161687 + 0.280050i
\(543\) −1.13885 + 1.97255i −0.0488728 + 0.0846502i
\(544\) 34.9717 + 20.1909i 1.49940 + 0.865678i
\(545\) −13.9172 −0.596146
\(546\) −1.67078 + 2.92874i −0.0715026 + 0.125339i
\(547\) 39.3716 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(548\) −38.7074 22.3477i −1.65350 0.954648i
\(549\) 14.5601 25.2189i 0.621411 1.07631i
\(550\) −14.0108 24.2675i −0.597424 1.03477i
\(551\) 6.56436i 0.279651i
\(552\) −4.85510 + 2.80310i −0.206647 + 0.119308i
\(553\) 0.694475 0.400955i 0.0295321 0.0170504i
\(554\) 45.1227i 1.91708i
\(555\) −3.34517 5.79401i −0.141995 0.245942i
\(556\) −46.8000 + 81.0600i −1.98476 + 3.43771i
\(557\) 0.629579 + 0.363487i 0.0266761 + 0.0154015i 0.513279 0.858222i \(-0.328431\pi\)
−0.486603 + 0.873623i \(0.661764\pi\)
\(558\) 13.5661 0.574300
\(559\) −15.7921 27.0289i −0.667935 1.14320i
\(560\) −44.1559 −1.86593
\(561\) −1.19084 0.687532i −0.0502773 0.0290276i
\(562\) −18.0751 + 31.3070i −0.762452 + 1.32061i
\(563\) 20.8038 + 36.0333i 0.876777 + 1.51862i 0.854857 + 0.518863i \(0.173645\pi\)
0.0219200 + 0.999760i \(0.493022\pi\)
\(564\) 10.7918i 0.454417i
\(565\) 7.75879 4.47954i 0.326415 0.188456i
\(566\) 44.2134 25.5266i 1.85843 1.07296i
\(567\) 7.93720i 0.333331i
\(568\) 10.5237 + 18.2276i 0.441565 + 0.764813i
\(569\) −12.6944 + 21.9873i −0.532177 + 0.921757i 0.467118 + 0.884195i \(0.345292\pi\)
−0.999294 + 0.0375618i \(0.988041\pi\)
\(570\) 6.33537 + 3.65773i 0.265360 + 0.153205i
\(571\) −16.9992 −0.711393 −0.355697 0.934602i \(-0.615756\pi\)
−0.355697 + 0.934602i \(0.615756\pi\)
\(572\) −0.182683 35.3244i −0.00763836 1.47699i
\(573\) 4.75451 0.198622
\(574\) −9.88225 5.70552i −0.412477 0.238144i
\(575\) −5.08929 + 8.81490i −0.212238 + 0.367607i
\(576\) −33.9776 58.8508i −1.41573 2.45212i
\(577\) 15.9759i 0.665084i 0.943088 + 0.332542i \(0.107906\pi\)
−0.943088 + 0.332542i \(0.892094\pi\)
\(578\) −28.9445 + 16.7111i −1.20393 + 0.695092i
\(579\) 6.81682 3.93570i 0.283298 0.163562i
\(580\) 47.2767i 1.96306i
\(581\) 4.98516 + 8.63454i 0.206819 + 0.358221i
\(582\) −4.31660 + 7.47657i −0.178929 + 0.309914i
\(583\) 14.8780 + 8.58982i 0.616184 + 0.355754i
\(584\) −28.5623 −1.18192
\(585\) −29.2150 + 17.0693i −1.20789 + 0.705731i
\(586\) 9.23926 0.381670
\(587\) −13.8404 7.99075i −0.571254 0.329814i 0.186396 0.982475i \(-0.440319\pi\)
−0.757650 + 0.652661i \(0.773653\pi\)
\(588\) 0.918023 1.59006i 0.0378586 0.0655730i
\(589\) −2.09166 3.62287i −0.0861855 0.149278i
\(590\) 94.6989i 3.89869i
\(591\) −4.35235 + 2.51283i −0.179032 + 0.103364i
\(592\) 69.6660 40.2217i 2.86325 1.65310i
\(593\) 29.0532i 1.19307i 0.802586 + 0.596536i \(0.203457\pi\)
−0.802586 + 0.596536i \(0.796543\pi\)
\(594\) 5.07574 + 8.79143i 0.208260 + 0.360717i
\(595\) −3.50760 + 6.07534i −0.143797 + 0.249065i
\(596\) −18.4816 10.6704i −0.757037 0.437075i
\(597\) 8.24757 0.337551
\(598\) −15.2540 + 8.91240i −0.623783 + 0.364455i
\(599\) 3.45554 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(600\) 15.0407 + 8.68376i 0.614035 + 0.354513i
\(601\) −7.76518 + 13.4497i −0.316748 + 0.548624i −0.979808 0.199943i \(-0.935924\pi\)
0.663059 + 0.748567i \(0.269258\pi\)
\(602\) 11.7349 + 20.3254i 0.478278 + 0.828402i
\(603\) 2.38178i 0.0969936i
\(604\) 86.8732 50.1563i 3.53482 2.04083i
\(605\) 21.4222 12.3681i 0.870938 0.502836i
\(606\) 13.8624i 0.563120i
\(607\) −7.73922 13.4047i −0.314125 0.544081i 0.665126 0.746731i \(-0.268378\pi\)
−0.979251 + 0.202650i \(0.935044\pi\)
\(608\) −22.5148 + 38.9967i −0.913095 + 1.58153i
\(609\) −0.819127 0.472923i −0.0331927 0.0191638i
\(610\) −89.0429 −3.60524
\(611\) −0.109597 21.1922i −0.00443383 0.857345i
\(612\) −32.9142 −1.33048
\(613\) −6.17669 3.56611i −0.249474 0.144034i 0.370049 0.929012i \(-0.379341\pi\)
−0.619523 + 0.784978i \(0.712674\pi\)
\(614\) 22.1228 38.3178i 0.892804 1.54638i
\(615\) 2.37902 + 4.12058i 0.0959312 + 0.166158i
\(616\) 16.5039i 0.664959i
\(617\) −4.30142 + 2.48342i −0.173168 + 0.0999789i −0.584079 0.811697i \(-0.698544\pi\)
0.410911 + 0.911676i \(0.365211\pi\)
\(618\) −3.46860 + 2.00260i −0.139528 + 0.0805563i
\(619\) 42.3570i 1.70247i 0.524784 + 0.851235i \(0.324146\pi\)
−0.524784 + 0.851235i \(0.675854\pi\)
\(620\) −15.0642 26.0920i −0.604993 1.04788i
\(621\) 1.84371 3.19339i 0.0739854 0.128146i
\(622\) 55.4776 + 32.0300i 2.22445 + 1.28429i
\(623\) 15.1135 0.605508
\(624\) 8.52791 + 14.5959i 0.341390 + 0.584305i
\(625\) −21.5445 −0.861779
\(626\) 12.1272 + 7.00162i 0.484699 + 0.279841i
\(627\) 0.766663 1.32790i 0.0306176 0.0530312i
\(628\) −30.7120 53.1947i −1.22554 2.12270i
\(629\) 12.7803i 0.509583i
\(630\) 21.9693 12.6840i 0.875278 0.505342i
\(631\) −5.42803 + 3.13387i −0.216086 + 0.124758i −0.604137 0.796881i \(-0.706482\pi\)
0.388050 + 0.921638i \(0.373149\pi\)
\(632\) 7.16924i 0.285177i
\(633\) 0.746432 + 1.29286i 0.0296680 + 0.0513865i
\(634\) 8.19794 14.1992i 0.325582 0.563924i
\(635\) −27.4667 15.8579i −1.08998 0.629302i
\(636\) −17.0868 −0.677534
\(637\) 1.78660 3.13178i 0.0707878 0.124086i
\(638\) 13.6434 0.540149
\(639\) −5.87250 3.39049i −0.232313 0.134126i
\(640\) −42.7898 + 74.1142i −1.69142 + 2.92962i
\(641\) −15.7818 27.3350i −0.623345 1.07967i −0.988858 0.148860i \(-0.952440\pi\)
0.365513 0.930806i \(-0.380894\pi\)
\(642\) 17.8858i 0.705897i
\(643\) 15.8053 9.12520i 0.623300 0.359863i −0.154852 0.987938i \(-0.549490\pi\)
0.778153 + 0.628075i \(0.216157\pi\)
\(644\) 8.33125 4.81005i 0.328297 0.189543i
\(645\) 9.78613i 0.385329i
\(646\) 6.98721 + 12.1022i 0.274908 + 0.476155i
\(647\) 11.5137 19.9423i 0.452649 0.784011i −0.545901 0.837850i \(-0.683812\pi\)
0.998550 + 0.0538387i \(0.0171457\pi\)
\(648\) 61.4532 + 35.4800i 2.41411 + 1.39379i
\(649\) −19.8490 −0.779140
\(650\) 47.5387 + 27.1197i 1.86462 + 1.06372i
\(651\) 0.602768 0.0236243
\(652\) −20.2483 11.6904i −0.792985 0.457830i
\(653\) −14.4062 + 24.9523i −0.563759 + 0.976459i 0.433405 + 0.901199i \(0.357312\pi\)
−0.997164 + 0.0752597i \(0.976021\pi\)
\(654\) −1.99730 3.45943i −0.0781006 0.135274i
\(655\) 60.8014i 2.37571i
\(656\) −49.5450 + 28.6048i −1.93441 + 1.11683i
\(657\) 7.96926 4.60105i 0.310910 0.179504i
\(658\) 15.8887i 0.619406i
\(659\) 15.6114 + 27.0397i 0.608134 + 1.05332i 0.991548 + 0.129742i \(0.0414149\pi\)
−0.383414 + 0.923577i \(0.625252\pi\)
\(660\) 5.52153 9.56356i 0.214925 0.372261i
\(661\) −23.0000 13.2791i −0.894598 0.516496i −0.0191541 0.999817i \(-0.506097\pi\)
−0.875444 + 0.483320i \(0.839431\pi\)
\(662\) −46.6973 −1.81494
\(663\) 2.68566 0.0138891i 0.104302 0.000539407i
\(664\) 89.1366 3.45917
\(665\) −6.77458 3.91130i −0.262707 0.151674i
\(666\) −23.1077 + 40.0237i −0.895405 + 1.55089i
\(667\) −2.47792 4.29188i −0.0959454 0.166182i
\(668\) 47.8667i 1.85202i
\(669\) −7.00906 + 4.04668i −0.270986 + 0.156454i
\(670\) 6.30721 3.64147i 0.243669 0.140682i
\(671\) 18.6635i 0.720495i
\(672\) −3.24411 5.61897i −0.125144 0.216756i
\(673\) −9.86930 + 17.0941i −0.380434 + 0.658930i −0.991124 0.132939i \(-0.957559\pi\)
0.610691 + 0.791869i \(0.290892\pi\)
\(674\) 19.5585 + 11.2921i 0.753366 + 0.434956i
\(675\) −11.4233 −0.439683
\(676\) 35.1134 + 59.3910i 1.35052 + 2.28427i
\(677\) −13.1440 −0.505163 −0.252582 0.967576i \(-0.581280\pi\)
−0.252582 + 0.967576i \(0.581280\pi\)
\(678\) 2.22698 + 1.28575i 0.0855266 + 0.0493788i
\(679\) 4.61585 7.99489i 0.177140 0.306816i
\(680\) 31.3586 + 54.3147i 1.20255 + 2.08287i
\(681\) 9.24475i 0.354260i
\(682\) −7.52981 + 4.34734i −0.288331 + 0.166468i
\(683\) −5.85654 + 3.38128i −0.224094 + 0.129381i −0.607845 0.794056i \(-0.707966\pi\)
0.383750 + 0.923437i \(0.374632\pi\)
\(684\) 36.7025i 1.40336i
\(685\) −13.7192 23.7624i −0.524185 0.907915i
\(686\) −1.35160 + 2.34104i −0.0516043 + 0.0893812i
\(687\) 0.900810 + 0.520083i 0.0343681 + 0.0198424i
\(688\) 117.666 4.48599
\(689\) −33.5538 + 0.173526i −1.27830 + 0.00661082i
\(690\) −5.52288 −0.210253
\(691\) 7.94223 + 4.58545i 0.302137 + 0.174439i 0.643402 0.765528i \(-0.277522\pi\)
−0.341266 + 0.939967i \(0.610856\pi\)
\(692\) −16.1659 + 28.0002i −0.614537 + 1.06441i
\(693\) −2.65857 4.60479i −0.100991 0.174921i
\(694\) 77.9115i 2.95748i
\(695\) −49.7626 + 28.7304i −1.88760 + 1.08981i
\(696\) −7.32316 + 4.22803i −0.277584 + 0.160263i
\(697\) 9.08908i 0.344273i
\(698\) 15.8435 + 27.4418i 0.599686 + 1.03869i
\(699\) 2.02636 3.50976i 0.0766440 0.132751i
\(700\) −25.8095 14.9011i −0.975509 0.563210i
\(701\) 47.4700 1.79292 0.896459 0.443127i \(-0.146131\pi\)
0.896459 + 0.443127i \(0.146131\pi\)
\(702\) −17.2219 9.82469i −0.650000 0.370809i
\(703\) 14.2512 0.537495
\(704\) 37.7181 + 21.7766i 1.42156 + 0.820736i
\(705\) 3.31253 5.73748i 0.124757 0.216086i
\(706\) −24.1074 41.7552i −0.907294 1.57148i
\(707\) 14.8234i 0.557491i
\(708\) 17.0968 9.87082i 0.642535 0.370968i
\(709\) 30.2866 17.4860i 1.13744 0.656699i 0.191642 0.981465i \(-0.438619\pi\)
0.945795 + 0.324766i \(0.105285\pi\)
\(710\) 20.7347i 0.778158i
\(711\) 1.15488 + 2.00031i 0.0433114 + 0.0750175i
\(712\) 67.5587 117.015i 2.53187 4.38533i
\(713\) 2.73512 + 1.57912i 0.102431 + 0.0591387i
\(714\) −2.01355 −0.0753552
\(715\) 10.7457 18.8364i 0.401866 0.704440i
\(716\) 20.5903 0.769496
\(717\) −0.427821 0.247002i −0.0159773 0.00922448i
\(718\) 7.67926 13.3009i 0.286588 0.496384i
\(719\) −4.18051 7.24085i −0.155907 0.270038i 0.777482 0.628905i \(-0.216497\pi\)
−0.933389 + 0.358867i \(0.883163\pi\)
\(720\) 127.183i 4.73984i
\(721\) 3.70907 2.14143i 0.138133 0.0797511i
\(722\) 30.9846 17.8890i 1.15313 0.665758i
\(723\) 0.927035i 0.0344768i
\(724\) −17.4713 30.2612i −0.649317 1.12465i
\(725\) −7.67639 + 13.2959i −0.285094 + 0.493797i
\(726\) 6.14875 + 3.54998i 0.228202 + 0.131752i
\(727\) −27.4014 −1.01626 −0.508131 0.861280i \(-0.669663\pi\)
−0.508131 + 0.861280i \(0.669663\pi\)
\(728\) −16.2613 27.8320i −0.602685 1.03152i
\(729\) −20.7504 −0.768532
\(730\) −24.3681 14.0689i −0.901905 0.520715i
\(731\) 9.34703 16.1895i 0.345712 0.598791i
\(732\) −9.28127 16.0756i −0.343046 0.594173i
\(733\) 12.1569i 0.449026i 0.974471 + 0.224513i \(0.0720792\pi\)
−0.974471 + 0.224513i \(0.927921\pi\)
\(734\) −45.9583 + 26.5340i −1.69635 + 0.979389i
\(735\) 0.976136 0.563573i 0.0360053 0.0207877i
\(736\) 33.9956i 1.25309i
\(737\) −0.763255 1.32200i −0.0281148 0.0486963i
\(738\) 16.4337 28.4640i 0.604934 1.04778i
\(739\) −41.9537 24.2220i −1.54329 0.891019i −0.998628 0.0523634i \(-0.983325\pi\)
−0.544662 0.838656i \(-0.683342\pi\)
\(740\) 102.638 3.77304
\(741\) 0.0154876 + 2.99476i 0.000568953 + 0.110015i
\(742\) 25.1567 0.923531
\(743\) −14.7143 8.49532i −0.539816 0.311663i 0.205188 0.978722i \(-0.434219\pi\)
−0.745004 + 0.667060i \(0.767553\pi\)
\(744\) 2.69443 4.66689i 0.0987826 0.171097i
\(745\) −6.55052 11.3458i −0.239993 0.415679i
\(746\) 86.6767i 3.17346i
\(747\) −24.8702 + 14.3588i −0.909955 + 0.525363i
\(748\) 18.2689 10.5475i 0.667977 0.385657i
\(749\) 19.1258i 0.698841i
\(750\) 0.937485 + 1.62377i 0.0342321 + 0.0592917i
\(751\) 21.5162 37.2671i 0.785136 1.35990i −0.143781 0.989610i \(-0.545926\pi\)
0.928918 0.370287i \(-0.120741\pi\)
\(752\) 68.9863 + 39.8292i 2.51567 + 1.45242i
\(753\) 3.78258 0.137845
\(754\) −23.0083 + 13.4430i −0.837911 + 0.489563i
\(755\) 61.5817 2.24119
\(756\) 9.35007 + 5.39827i 0.340059 + 0.196333i
\(757\) −14.5892 + 25.2693i −0.530255 + 0.918428i 0.469122 + 0.883133i \(0.344570\pi\)
−0.999377 + 0.0352949i \(0.988763\pi\)
\(758\) 25.7116 + 44.5337i 0.933886 + 1.61754i
\(759\) 1.15760i 0.0420183i
\(760\) −60.5661 + 34.9678i −2.19696 + 1.26842i
\(761\) −25.4829 + 14.7126i −0.923754 + 0.533330i −0.884831 0.465912i \(-0.845726\pi\)
−0.0389234 + 0.999242i \(0.512393\pi\)
\(762\) 9.10328i 0.329777i
\(763\) 2.13577 + 3.69925i 0.0773199 + 0.133922i
\(764\) −36.4699 + 63.1677i −1.31943 + 2.28533i
\(765\) −17.4989 10.1030i −0.632675 0.365275i
\(766\) −1.89178 −0.0683526
\(767\) 33.4732 19.5573i 1.20865 0.706172i
\(768\) −8.23976 −0.297327
\(769\) 14.8839 + 8.59322i 0.536727 + 0.309879i 0.743751 0.668456i \(-0.233045\pi\)
−0.207024 + 0.978336i \(0.566378\pi\)
\(770\) −8.12930 + 14.0804i −0.292960 + 0.507421i
\(771\) −0.718083 1.24376i −0.0258611 0.0447928i
\(772\) 120.756i 4.34612i
\(773\) 19.0180 10.9801i 0.684031 0.394926i −0.117341 0.993092i \(-0.537437\pi\)
0.801372 + 0.598166i \(0.204104\pi\)
\(774\) −58.5437 + 33.8002i −2.10431 + 1.21492i
\(775\) 9.78399i 0.351451i
\(776\) −41.2666 71.4759i −1.48139 2.56584i
\(777\) −1.02672 + 1.77833i −0.0368333 + 0.0637971i
\(778\) −46.9488 27.1059i −1.68320 0.971794i
\(779\) −10.1352 −0.363131
\(780\) 0.111542 + 21.5683i 0.00399386 + 0.772271i
\(781\) 4.34600 0.155512
\(782\) −9.13669 5.27507i −0.326727 0.188636i
\(783\) 2.78094 4.81673i 0.0993827 0.172136i
\(784\) 6.77628 + 11.7369i 0.242010 + 0.419174i
\(785\) 37.7081i 1.34586i
\(786\) 15.1135 8.72581i 0.539082 0.311239i
\(787\) −2.02275 + 1.16784i −0.0721033 + 0.0416289i −0.535618 0.844460i \(-0.679921\pi\)
0.463515 + 0.886089i \(0.346588\pi\)
\(788\) 77.0996i 2.74656i
\(789\) 0.701169 + 1.21446i 0.0249623 + 0.0432359i
\(790\) 3.53135 6.11648i 0.125640 0.217615i
\(791\) −2.38137 1.37488i −0.0846716 0.0488852i
\(792\) −47.5364 −1.68913
\(793\) −18.3892 31.4740i −0.653020 1.11767i
\(794\) 60.2280 2.13741
\(795\) −9.08420 5.24476i −0.322183 0.186013i
\(796\) −63.2637 + 109.576i −2.24232 + 3.88382i
\(797\) 13.9020 + 24.0790i 0.492434 + 0.852921i 0.999962 0.00871411i \(-0.00277382\pi\)
−0.507528 + 0.861635i \(0.669440\pi\)
\(798\) 2.24530i 0.0794827i
\(799\) 10.9601 6.32780i 0.387739 0.223861i
\(800\) −91.2059 + 52.6577i −3.22461 + 1.86173i
\(801\) 43.5316i 1.53811i
\(802\) 6.49779 + 11.2545i 0.229445 + 0.397410i
\(803\) −2.94886 + 5.10758i −0.104063 + 0.180243i
\(804\) 1.31485 + 0.759127i 0.0463711 + 0.0267724i
\(805\) 5.90576 0.208151
\(806\) 8.41479 14.7505i 0.296398 0.519564i
\(807\) −1.38387 −0.0487147
\(808\) −114.769 66.2620i −4.03756 2.33109i
\(809\) −7.51017 + 13.0080i −0.264043 + 0.457337i −0.967313 0.253587i \(-0.918390\pi\)
0.703269 + 0.710924i \(0.251723\pi\)
\(810\) 34.9528 + 60.5401i 1.22812 + 2.12716i
\(811\) 43.6933i 1.53428i −0.641481 0.767139i \(-0.721680\pi\)
0.641481 0.767139i \(-0.278320\pi\)
\(812\) 12.5664 7.25520i 0.440993 0.254608i
\(813\) −0.834393 + 0.481737i −0.0292634 + 0.0168953i
\(814\) 29.6199i 1.03818i
\(815\) −7.17670 12.4304i −0.251389 0.435418i
\(816\) −5.04750 + 8.74252i −0.176698 + 0.306049i
\(817\) 18.0529 + 10.4228i 0.631590 + 0.364648i
\(818\) −99.4870 −3.47848
\(819\) 9.02053 + 5.14599i 0.315203 + 0.179815i
\(820\) −72.9939 −2.54906
\(821\) 15.6492 + 9.03506i 0.546160 + 0.315326i 0.747572 0.664181i \(-0.231220\pi\)
−0.201412 + 0.979507i \(0.564553\pi\)
\(822\) 3.93779 6.82045i 0.137346 0.237890i
\(823\) 2.22775 + 3.85857i 0.0776544 + 0.134501i 0.902238 0.431239i \(-0.141924\pi\)
−0.824583 + 0.565741i \(0.808590\pi\)
\(824\) 38.2896i 1.33388i
\(825\) 3.10570 1.79308i 0.108127 0.0624269i
\(826\) −25.1714 + 14.5327i −0.875826 + 0.505658i
\(827\) 11.8352i 0.411549i −0.978599 0.205774i \(-0.934029\pi\)
0.978599 0.205774i \(-0.0659713\pi\)
\(828\) 13.8545 + 23.9967i 0.481477 + 0.833942i
\(829\) −1.76947 + 3.06482i −0.0614563 + 0.106445i −0.895117 0.445832i \(-0.852908\pi\)
0.833660 + 0.552278i \(0.186241\pi\)
\(830\) 76.0474 + 43.9060i 2.63964 + 1.52400i
\(831\) 5.77471 0.200323
\(832\) −85.0643 + 0.439917i −2.94907 + 0.0152514i
\(833\) 2.15314 0.0746019
\(834\) −14.2832 8.24640i −0.494586 0.285550i
\(835\) 14.6927 25.4484i 0.508460 0.880679i
\(836\) 11.7615 + 20.3715i 0.406781 + 0.704565i
\(837\) 3.54447i 0.122515i
\(838\) 68.5145 39.5569i 2.36679 1.36647i
\(839\) −28.9991 + 16.7426i −1.00116 + 0.578020i −0.908591 0.417686i \(-0.862841\pi\)
−0.0925687 + 0.995706i \(0.529508\pi\)
\(840\) 10.0769i 0.347686i
\(841\) 10.7625 + 18.6411i 0.371119 + 0.642797i
\(842\) 10.1892 17.6482i 0.351143 0.608197i
\(843\) −4.00660 2.31321i −0.137995 0.0796713i
\(844\) −22.9023 −0.788330
\(845\) 0.438079 + 42.3533i 0.0150704 + 1.45700i
\(846\) −45.7645 −1.57342
\(847\) −6.57502 3.79609i −0.225920 0.130435i
\(848\) 63.0620 109.227i 2.16556 3.75086i
\(849\) 3.26684 + 5.65833i 0.112118 + 0.194193i
\(850\) 32.6835i 1.12103i
\(851\) −9.31768 + 5.37956i −0.319406 + 0.184409i
\(852\) −3.74340 + 2.16125i −0.128247 + 0.0740433i
\(853\) 22.0871i 0.756248i −0.925755 0.378124i \(-0.876569\pi\)
0.925755 0.378124i \(-0.123431\pi\)
\(854\) 13.6648 + 23.6680i 0.467598 + 0.809904i
\(855\) 11.2658 19.5129i 0.385282 0.667329i
\(856\) −148.080 85.4941i −5.06127 2.92213i
\(857\) 6.89363 0.235482 0.117741 0.993044i \(-0.462435\pi\)
0.117741 + 0.993044i \(0.462435\pi\)
\(858\) 6.22435 0.0321897i 0.212496 0.00109894i
\(859\) −37.4834 −1.27892 −0.639459 0.768825i \(-0.720842\pi\)
−0.639459 + 0.768825i \(0.720842\pi\)
\(860\) 130.017 + 75.0654i 4.43355 + 2.55971i
\(861\) 0.730180 1.26471i 0.0248845 0.0431012i
\(862\) 42.2052 + 73.1015i 1.43751 + 2.48985i
\(863\) 17.5248i 0.596552i 0.954480 + 0.298276i \(0.0964115\pi\)
−0.954480 + 0.298276i \(0.903588\pi\)
\(864\) 33.0413 19.0764i 1.12409 0.648993i
\(865\) −17.1893 + 9.92425i −0.584454 + 0.337435i
\(866\) 15.9057i 0.540498i
\(867\) −2.13866 3.70426i −0.0726326 0.125803i
\(868\) −4.62358 + 8.00828i −0.156935 + 0.271819i
\(869\) −1.28202 0.740175i −0.0434896 0.0251087i
\(870\) −8.33040 −0.282427
\(871\) 2.58972 + 1.47737i 0.0877493 + 0.0500588i
\(872\) 38.1883 1.29322
\(873\) 23.0278 + 13.2951i 0.779374 + 0.449972i
\(874\) 5.88221 10.1883i 0.198969 0.344624i
\(875\) −1.00248 1.73634i −0.0338899 0.0586990i
\(876\) 5.86584i 0.198188i
\(877\) −40.4859 + 23.3745i −1.36711 + 0.789302i −0.990558 0.137093i \(-0.956224\pi\)
−0.376553 + 0.926395i \(0.622891\pi\)
\(878\) 23.3083 13.4571i 0.786618 0.454154i
\(879\) 1.18242i 0.0398821i
\(880\) 40.7565 + 70.5924i 1.37390 + 2.37967i
\(881\) −1.45937 + 2.52771i −0.0491675 + 0.0851606i −0.889562 0.456815i \(-0.848990\pi\)
0.840394 + 0.541976i \(0.182323\pi\)
\(882\) −6.74293 3.89303i −0.227046 0.131085i
\(883\) 28.5505 0.960801 0.480400 0.877049i \(-0.340491\pi\)
0.480400 + 0.877049i \(0.340491\pi\)
\(884\) −20.4160 + 35.7878i −0.686666 + 1.20367i
\(885\) 12.1194 0.407388
\(886\) 83.9993 + 48.4970i 2.82201 + 1.62929i
\(887\) −0.211457 + 0.366254i −0.00710004 + 0.0122976i −0.869554 0.493839i \(-0.835593\pi\)
0.862454 + 0.506136i \(0.168927\pi\)
\(888\) 9.17905 + 15.8986i 0.308029 + 0.533521i
\(889\) 9.73438i 0.326480i
\(890\) 115.276 66.5548i 3.86407 2.23092i
\(891\) 12.6892 7.32614i 0.425106 0.245435i
\(892\) 124.162i 4.15725i
\(893\) 7.05610 + 12.2215i 0.236123 + 0.408978i
\(894\) 1.88018 3.25656i 0.0628825 0.108916i
\(895\) 10.9469 + 6.32018i 0.365914 + 0.211260i
\(896\) 26.2666 0.877504
\(897\) −1.14059 1.95217i −0.0380832 0.0651812i
\(898\) −10.8000 −0.360401
\(899\) 4.12550 + 2.38186i 0.137593 + 0.0794394i
\(900\) 42.9200 74.3397i 1.43067 2.47799i
\(901\) −10.0189 17.3532i −0.333777 0.578118i
\(902\) 21.0651i 0.701391i
\(903\) −2.60120 + 1.50181i −0.0865626 + 0.0499769i
\(904\) −21.2899 + 12.2917i −0.708091 + 0.408816i
\(905\) 21.4512i 0.713063i
\(906\) 8.83779 + 15.3075i 0.293616 + 0.508558i
\(907\) −11.2142 + 19.4236i −0.372361 + 0.644949i −0.989928 0.141570i \(-0.954785\pi\)
0.617567 + 0.786518i \(0.288118\pi\)
\(908\) −122.824 70.9127i −4.07607 2.35332i
\(909\) 42.6961 1.41614
\(910\) −0.164223 31.7549i −0.00544394 1.05267i
\(911\) −32.5788 −1.07938 −0.539692 0.841863i \(-0.681459\pi\)
−0.539692 + 0.841863i \(0.681459\pi\)
\(912\) −9.74874 5.62844i −0.322813 0.186376i
\(913\) 9.20274 15.9396i 0.304566 0.527524i
\(914\) −55.7159 96.5027i −1.84292 3.19203i
\(915\) 11.3955i 0.376724i
\(916\) −13.8195 + 7.97869i −0.456609 + 0.263623i
\(917\) −16.1613 + 9.33073i −0.533693 + 0.308128i
\(918\) 11.8403i 0.390788i
\(919\) 4.93957 + 8.55558i 0.162941 + 0.282223i 0.935922 0.352207i \(-0.114569\pi\)
−0.772981 + 0.634429i \(0.781235\pi\)
\(920\) 26.3993 45.7250i 0.870361 1.50751i
\(921\) 4.90383 + 2.83123i 0.161587 + 0.0932922i
\(922\) −66.8408 −2.20129
\(923\) −7.32908 + 4.28214i −0.241240 + 0.140948i
\(924\) −3.38939 −0.111503
\(925\) 28.8654 + 16.6654i 0.949088 + 0.547956i
\(926\) 32.9867 57.1346i 1.08401 1.87756i
\(927\) 6.16800 + 10.6833i 0.202584 + 0.350886i
\(928\) 51.2769i 1.68325i
\(929\) 25.9060 14.9568i 0.849947 0.490717i −0.0106859 0.999943i \(-0.503401\pi\)
0.860633 + 0.509226i \(0.170068\pi\)
\(930\) 4.59754 2.65439i 0.150759 0.0870409i
\(931\) 2.40096i 0.0786881i
\(932\) 31.0868 + 53.8439i 1.01828 + 1.76371i
\(933\) −4.09913 + 7.09990i −0.134199 + 0.232440i
\(934\) −10.4143 6.01273i −0.340768 0.196742i
\(935\) 12.9502 0.423518
\(936\) 80.1651 46.8378i 2.62028 1.53094i
\(937\) −31.8296 −1.03983 −0.519914 0.854219i \(-0.674036\pi\)
−0.519914 + 0.854219i \(0.674036\pi\)
\(938\) −1.93584 1.11766i −0.0632074 0.0364928i
\(939\) −0.896052 + 1.55201i −0.0292416 + 0.0506479i
\(940\) 50.8182 + 88.0197i 1.65751 + 2.87089i
\(941\) 42.0885i 1.37205i 0.727580 + 0.686023i \(0.240645\pi\)
−0.727580 + 0.686023i \(0.759355\pi\)
\(942\) 9.37318 5.41161i 0.305395 0.176320i
\(943\) 6.62654 3.82584i 0.215790 0.124586i
\(944\) 145.721i 4.74280i
\(945\) 3.31399 + 5.73999i 0.107804 + 0.186722i
\(946\) 21.6629 37.5213i 0.704322 1.21992i
\(947\) 52.2540 + 30.1689i 1.69803 + 0.980357i 0.947630 + 0.319369i \(0.103471\pi\)
0.750397 + 0.660988i \(0.229862\pi\)
\(948\) 1.47234 0.0478195
\(949\) −0.0595711 11.5189i −0.00193376 0.373920i
\(950\) −36.4452 −1.18244
\(951\) 1.81719 + 1.04915i 0.0589264 + 0.0340212i
\(952\) 9.62475 16.6706i 0.311940 0.540296i
\(953\) −8.68770 15.0475i −0.281422 0.487438i 0.690313 0.723511i \(-0.257473\pi\)
−0.971735 + 0.236073i \(0.924139\pi\)
\(954\) 72.4593i 2.34596i
\(955\) −38.7785 + 22.3888i −1.25484 + 0.724484i
\(956\) 6.56328 3.78931i 0.212272 0.122555i
\(957\) 1.74606i 0.0564421i
\(958\) 42.8140 + 74.1561i 1.38326 + 2.39588i
\(959\) −4.21078 + 7.29328i −0.135973 + 0.235512i
\(960\) −23.0299 13.2963i −0.743287 0.429137i
\(961\) 27.9642 0.902070
\(962\) 29.1847 + 49.9510i 0.940951 + 1.61048i
\(963\) 55.0883 1.77520
\(964\) −12.3165 7.11091i −0.396686 0.229027i
\(965\) −37.0661 + 64.2003i −1.19320 + 2.06668i
\(966\) 0.847556 + 1.46801i 0.0272697 + 0.0472324i
\(967\) 18.8630i 0.606594i −0.952896 0.303297i \(-0.901913\pi\)
0.952896 0.303297i \(-0.0980874\pi\)
\(968\) −58.7820 + 33.9378i −1.88932 + 1.09080i
\(969\) −1.54881 + 0.894208i −0.0497551 + 0.0287261i
\(970\) 81.3068i 2.61061i
\(971\) 0.782231 + 1.35486i 0.0251030 + 0.0434797i 0.878304 0.478103i \(-0.158675\pi\)
−0.853201 + 0.521582i \(0.825342\pi\)
\(972\) −23.4813 + 40.6708i −0.753164 + 1.30452i
\(973\) 15.2734 + 8.81809i 0.489642 + 0.282695i
\(974\) −72.7582 −2.33132
\(975\) −3.47071 + 6.08390i −0.111152 + 0.194841i
\(976\) 137.017 4.38582
\(977\) −24.1409 13.9378i −0.772336 0.445909i 0.0613710 0.998115i \(-0.480453\pi\)
−0.833707 + 0.552206i \(0.813786\pi\)
\(978\) 2.05990 3.56786i 0.0658685 0.114088i
\(979\) −13.9499 24.1620i −0.445842 0.772221i
\(980\) 17.2917i 0.552364i
\(981\) −10.6550 + 6.15169i −0.340189 + 0.196408i
\(982\) −22.7716 + 13.1472i −0.726672 + 0.419544i
\(983\) 33.4239i 1.06606i −0.846097 0.533029i \(-0.821054\pi\)
0.846097 0.533029i \(-0.178946\pi\)
\(984\) −6.52795 11.3067i −0.208104 0.360446i
\(985\) 23.6657 40.9901i 0.754051 1.30605i
\(986\) −13.7813 7.95661i −0.438885 0.253390i
\(987\) −2.03340 −0.0647238
\(988\) −39.9068 22.7658i −1.26960 0.724277i
\(989\) −15.7376 −0.500428
\(990\) −40.5559 23.4150i −1.28895 0.744177i
\(991\) 9.45548 16.3774i 0.300363 0.520244i −0.675855 0.737035i \(-0.736225\pi\)
0.976218 + 0.216790i \(0.0695588\pi\)
\(992\) 16.3388 + 28.2997i 0.518759 + 0.898517i
\(993\) 5.97622i 0.189650i
\(994\) 5.51138 3.18199i 0.174810 0.100927i
\(995\) −67.2685 + 38.8375i −2.13256 + 1.23123i
\(996\) 18.3059i 0.580046i
\(997\) −21.7888 37.7393i −0.690057 1.19521i −0.971819 0.235730i \(-0.924252\pi\)
0.281762 0.959484i \(-0.409081\pi\)
\(998\) −10.6442 + 18.4363i −0.336936 + 0.583589i
\(999\) −10.4571 6.03742i −0.330849 0.191016i
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 91.2.q.a.43.1 yes 12
3.2 odd 2 819.2.ct.a.316.6 12
4.3 odd 2 1456.2.cc.c.225.4 12
7.2 even 3 637.2.k.h.459.6 12
7.3 odd 6 637.2.u.i.30.6 12
7.4 even 3 637.2.u.h.30.6 12
7.5 odd 6 637.2.k.g.459.6 12
7.6 odd 2 637.2.q.h.589.1 12
13.4 even 6 1183.2.c.i.337.1 12
13.6 odd 12 1183.2.a.p.1.6 6
13.7 odd 12 1183.2.a.m.1.1 6
13.9 even 3 1183.2.c.i.337.12 12
13.10 even 6 inner 91.2.q.a.36.1 12
39.23 odd 6 819.2.ct.a.127.6 12
52.23 odd 6 1456.2.cc.c.673.4 12
91.6 even 12 8281.2.a.ch.1.6 6
91.10 odd 6 637.2.k.g.569.1 12
91.20 even 12 8281.2.a.by.1.1 6
91.23 even 6 637.2.u.h.361.6 12
91.62 odd 6 637.2.q.h.491.1 12
91.75 odd 6 637.2.u.i.361.6 12
91.88 even 6 637.2.k.h.569.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.1 12 13.10 even 6 inner
91.2.q.a.43.1 yes 12 1.1 even 1 trivial
637.2.k.g.459.6 12 7.5 odd 6
637.2.k.g.569.1 12 91.10 odd 6
637.2.k.h.459.6 12 7.2 even 3
637.2.k.h.569.1 12 91.88 even 6
637.2.q.h.491.1 12 91.62 odd 6
637.2.q.h.589.1 12 7.6 odd 2
637.2.u.h.30.6 12 7.4 even 3
637.2.u.h.361.6 12 91.23 even 6
637.2.u.i.30.6 12 7.3 odd 6
637.2.u.i.361.6 12 91.75 odd 6
819.2.ct.a.127.6 12 39.23 odd 6
819.2.ct.a.316.6 12 3.2 odd 2
1183.2.a.m.1.1 6 13.7 odd 12
1183.2.a.p.1.6 6 13.6 odd 12
1183.2.c.i.337.1 12 13.4 even 6
1183.2.c.i.337.12 12 13.9 even 3
1456.2.cc.c.225.4 12 4.3 odd 2
1456.2.cc.c.673.4 12 52.23 odd 6
8281.2.a.by.1.1 6 91.20 even 12
8281.2.a.ch.1.6 6 91.6 even 12