Properties

Label 403.2.f.b.94.9
Level $403$
Weight $2$
Character 403.94
Analytic conductor $3.218$
Analytic rank $0$
Dimension $34$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(94,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.94");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.f (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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 94.9
Character \(\chi\) \(=\) 403.94
Dual form 403.2.f.b.373.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0205421 + 0.0355799i) q^{2} +(-1.04665 - 1.81285i) q^{3} +(0.999156 - 1.73059i) q^{4} +1.98920 q^{5} +(0.0430008 - 0.0744796i) q^{6} +(1.34392 - 2.32775i) q^{7} +0.164267 q^{8} +(-0.690959 + 1.19678i) q^{9} +O(q^{10})\) \(q+(0.0205421 + 0.0355799i) q^{2} +(-1.04665 - 1.81285i) q^{3} +(0.999156 - 1.73059i) q^{4} +1.98920 q^{5} +(0.0430008 - 0.0744796i) q^{6} +(1.34392 - 2.32775i) q^{7} +0.164267 q^{8} +(-0.690959 + 1.19678i) q^{9} +(0.0408622 + 0.0707754i) q^{10} +(1.80430 + 3.12515i) q^{11} -4.18307 q^{12} +(3.58758 - 0.359560i) q^{13} +0.110428 q^{14} +(-2.08199 - 3.60612i) q^{15} +(-1.99494 - 3.45533i) q^{16} +(-3.50423 + 6.06950i) q^{17} -0.0567750 q^{18} +(0.0170007 - 0.0294461i) q^{19} +(1.98752 - 3.44248i) q^{20} -5.62648 q^{21} +(-0.0741283 + 0.128394i) q^{22} +(-1.38334 - 2.39602i) q^{23} +(-0.171931 - 0.297793i) q^{24} -1.04310 q^{25} +(0.0864894 + 0.120260i) q^{26} -3.38713 q^{27} +(-2.68558 - 4.65156i) q^{28} +(3.00345 + 5.20213i) q^{29} +(0.0855370 - 0.148154i) q^{30} -1.00000 q^{31} +(0.246228 - 0.426479i) q^{32} +(3.77695 - 6.54188i) q^{33} -0.287937 q^{34} +(2.67333 - 4.63034i) q^{35} +(1.38075 + 2.39153i) q^{36} +(0.429975 + 0.744738i) q^{37} +0.00139692 q^{38} +(-4.40677 - 6.12742i) q^{39} +0.326760 q^{40} +(0.0394506 + 0.0683304i) q^{41} +(-0.115580 - 0.200190i) q^{42} +(0.629228 - 1.08985i) q^{43} +7.21112 q^{44} +(-1.37445 + 2.38062i) q^{45} +(0.0568335 - 0.0984384i) q^{46} -6.99256 q^{47} +(-4.17601 + 7.23306i) q^{48} +(-0.112268 - 0.194454i) q^{49} +(-0.0214275 - 0.0371135i) q^{50} +14.6708 q^{51} +(2.96230 - 6.56788i) q^{52} -3.93927 q^{53} +(-0.0695788 - 0.120514i) q^{54} +(3.58911 + 6.21652i) q^{55} +(0.220763 - 0.382373i) q^{56} -0.0711753 q^{57} +(-0.123394 + 0.213725i) q^{58} +(1.76441 - 3.05605i) q^{59} -8.32095 q^{60} +(-2.35604 + 4.08078i) q^{61} +(-0.0205421 - 0.0355799i) q^{62} +(1.85719 + 3.21676i) q^{63} -7.95952 q^{64} +(7.13639 - 0.715235i) q^{65} +0.310346 q^{66} +(4.85878 + 8.41565i) q^{67} +(7.00255 + 12.1288i) q^{68} +(-2.89576 + 5.01560i) q^{69} +0.219663 q^{70} +(-2.26972 + 3.93127i) q^{71} +(-0.113502 + 0.196591i) q^{72} -0.0228577 q^{73} +(-0.0176651 + 0.0305969i) q^{74} +(1.09176 + 1.89099i) q^{75} +(-0.0339727 - 0.0588425i) q^{76} +9.69939 q^{77} +(0.127489 - 0.282663i) q^{78} +12.1483 q^{79} +(-3.96832 - 6.87333i) q^{80} +(5.61803 + 9.73071i) q^{81} +(-0.00162079 + 0.00280730i) q^{82} +5.82781 q^{83} +(-5.62174 + 9.73713i) q^{84} +(-6.97060 + 12.0734i) q^{85} +0.0517026 q^{86} +(6.28714 - 10.8896i) q^{87} +(0.296388 + 0.513359i) q^{88} +(1.19024 + 2.06155i) q^{89} -0.112936 q^{90} +(3.98447 - 8.83419i) q^{91} -5.52870 q^{92} +(1.04665 + 1.81285i) q^{93} +(-0.143642 - 0.248795i) q^{94} +(0.0338177 - 0.0585740i) q^{95} -1.03086 q^{96} +(1.56790 - 2.71568i) q^{97} +(0.00461244 - 0.00798899i) q^{98} -4.98680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0205421 + 0.0355799i 0.0145254 + 0.0251588i 0.873197 0.487368i \(-0.162043\pi\)
−0.858671 + 0.512527i \(0.828710\pi\)
\(3\) −1.04665 1.81285i −0.604285 1.04665i −0.992164 0.124942i \(-0.960126\pi\)
0.387879 0.921710i \(-0.373208\pi\)
\(4\) 0.999156 1.73059i 0.499578 0.865295i
\(5\) 1.98920 0.889595 0.444798 0.895631i \(-0.353276\pi\)
0.444798 + 0.895631i \(0.353276\pi\)
\(6\) 0.0430008 0.0744796i 0.0175550 0.0304062i
\(7\) 1.34392 2.32775i 0.507956 0.879805i −0.492002 0.870594i \(-0.663735\pi\)
0.999958 0.00921113i \(-0.00293203\pi\)
\(8\) 0.164267 0.0580772
\(9\) −0.690959 + 1.19678i −0.230320 + 0.398926i
\(10\) 0.0408622 + 0.0707754i 0.0129218 + 0.0223811i
\(11\) 1.80430 + 3.12515i 0.544018 + 0.942267i 0.998668 + 0.0515967i \(0.0164310\pi\)
−0.454650 + 0.890670i \(0.650236\pi\)
\(12\) −4.18307 −1.20755
\(13\) 3.58758 0.359560i 0.995015 0.0997240i
\(14\) 0.110428 0.0295131
\(15\) −2.08199 3.60612i −0.537569 0.931096i
\(16\) −1.99494 3.45533i −0.498734 0.863833i
\(17\) −3.50423 + 6.06950i −0.849901 + 1.47207i 0.0313957 + 0.999507i \(0.490005\pi\)
−0.881296 + 0.472564i \(0.843329\pi\)
\(18\) −0.0567750 −0.0133820
\(19\) 0.0170007 0.0294461i 0.00390023 0.00675539i −0.864069 0.503374i \(-0.832092\pi\)
0.867969 + 0.496619i \(0.165425\pi\)
\(20\) 1.98752 3.44248i 0.444422 0.769762i
\(21\) −5.62648 −1.22780
\(22\) −0.0741283 + 0.128394i −0.0158042 + 0.0273737i
\(23\) −1.38334 2.39602i −0.288447 0.499605i 0.684992 0.728550i \(-0.259806\pi\)
−0.973439 + 0.228946i \(0.926472\pi\)
\(24\) −0.171931 0.297793i −0.0350952 0.0607866i
\(25\) −1.04310 −0.208620
\(26\) 0.0864894 + 0.120260i 0.0169620 + 0.0235849i
\(27\) −3.38713 −0.651854
\(28\) −2.68558 4.65156i −0.507527 0.879063i
\(29\) 3.00345 + 5.20213i 0.557727 + 0.966012i 0.997686 + 0.0679937i \(0.0216598\pi\)
−0.439959 + 0.898018i \(0.645007\pi\)
\(30\) 0.0855370 0.148154i 0.0156168 0.0270492i
\(31\) −1.00000 −0.179605
\(32\) 0.246228 0.426479i 0.0435273 0.0753915i
\(33\) 3.77695 6.54188i 0.657483 1.13879i
\(34\) −0.287937 −0.0493807
\(35\) 2.67333 4.63034i 0.451875 0.782671i
\(36\) 1.38075 + 2.39153i 0.230125 + 0.398589i
\(37\) 0.429975 + 0.744738i 0.0706874 + 0.122434i 0.899203 0.437532i \(-0.144147\pi\)
−0.828515 + 0.559966i \(0.810814\pi\)
\(38\) 0.00139692 0.000226610
\(39\) −4.40677 6.12742i −0.705649 0.981173i
\(40\) 0.326760 0.0516652
\(41\) 0.0394506 + 0.0683304i 0.00616115 + 0.0106714i 0.869090 0.494655i \(-0.164705\pi\)
−0.862928 + 0.505326i \(0.831372\pi\)
\(42\) −0.115580 0.200190i −0.0178343 0.0308900i
\(43\) 0.629228 1.08985i 0.0959564 0.166201i −0.814051 0.580793i \(-0.802742\pi\)
0.910007 + 0.414592i \(0.136076\pi\)
\(44\) 7.21112 1.08712
\(45\) −1.37445 + 2.38062i −0.204891 + 0.354882i
\(46\) 0.0568335 0.0984384i 0.00837964 0.0145140i
\(47\) −6.99256 −1.01997 −0.509985 0.860183i \(-0.670349\pi\)
−0.509985 + 0.860183i \(0.670349\pi\)
\(48\) −4.17601 + 7.23306i −0.602755 + 1.04400i
\(49\) −0.112268 0.194454i −0.0160383 0.0277792i
\(50\) −0.0214275 0.0371135i −0.00303030 0.00524864i
\(51\) 14.6708 2.05433
\(52\) 2.96230 6.56788i 0.410797 0.910801i
\(53\) −3.93927 −0.541101 −0.270550 0.962706i \(-0.587206\pi\)
−0.270550 + 0.962706i \(0.587206\pi\)
\(54\) −0.0695788 0.120514i −0.00946847 0.0163999i
\(55\) 3.58911 + 6.21652i 0.483956 + 0.838236i
\(56\) 0.220763 0.382373i 0.0295007 0.0510967i
\(57\) −0.0711753 −0.00942739
\(58\) −0.123394 + 0.213725i −0.0162025 + 0.0280635i
\(59\) 1.76441 3.05605i 0.229707 0.397864i −0.728014 0.685562i \(-0.759557\pi\)
0.957721 + 0.287698i \(0.0928900\pi\)
\(60\) −8.32095 −1.07423
\(61\) −2.35604 + 4.08078i −0.301660 + 0.522490i −0.976512 0.215463i \(-0.930874\pi\)
0.674852 + 0.737953i \(0.264207\pi\)
\(62\) −0.0205421 0.0355799i −0.00260885 0.00451865i
\(63\) 1.85719 + 3.21676i 0.233985 + 0.405273i
\(64\) −7.95952 −0.994940
\(65\) 7.13639 0.715235i 0.885161 0.0887140i
\(66\) 0.310346 0.0382009
\(67\) 4.85878 + 8.41565i 0.593594 + 1.02814i 0.993744 + 0.111685i \(0.0356248\pi\)
−0.400150 + 0.916450i \(0.631042\pi\)
\(68\) 7.00255 + 12.1288i 0.849183 + 1.47083i
\(69\) −2.89576 + 5.01560i −0.348608 + 0.603807i
\(70\) 0.219663 0.0262547
\(71\) −2.26972 + 3.93127i −0.269366 + 0.466556i −0.968698 0.248241i \(-0.920147\pi\)
0.699332 + 0.714797i \(0.253481\pi\)
\(72\) −0.113502 + 0.196591i −0.0133763 + 0.0231685i
\(73\) −0.0228577 −0.00267530 −0.00133765 0.999999i \(-0.500426\pi\)
−0.00133765 + 0.999999i \(0.500426\pi\)
\(74\) −0.0176651 + 0.0305969i −0.00205353 + 0.00355682i
\(75\) 1.09176 + 1.89099i 0.126066 + 0.218353i
\(76\) −0.0339727 0.0588425i −0.00389694 0.00674969i
\(77\) 9.69939 1.10535
\(78\) 0.127489 0.282663i 0.0144353 0.0320052i
\(79\) 12.1483 1.36680 0.683398 0.730046i \(-0.260501\pi\)
0.683398 + 0.730046i \(0.260501\pi\)
\(80\) −3.96832 6.87333i −0.443672 0.768462i
\(81\) 5.61803 + 9.73071i 0.624225 + 1.08119i
\(82\) −0.00162079 + 0.00280730i −0.000178987 + 0.000310014i
\(83\) 5.82781 0.639685 0.319842 0.947471i \(-0.396370\pi\)
0.319842 + 0.947471i \(0.396370\pi\)
\(84\) −5.62174 + 9.73713i −0.613382 + 1.06241i
\(85\) −6.97060 + 12.0734i −0.756068 + 1.30955i
\(86\) 0.0517026 0.00557523
\(87\) 6.28714 10.8896i 0.674052 1.16749i
\(88\) 0.296388 + 0.513359i 0.0315951 + 0.0547243i
\(89\) 1.19024 + 2.06155i 0.126165 + 0.218524i 0.922188 0.386743i \(-0.126400\pi\)
−0.796023 + 0.605267i \(0.793067\pi\)
\(90\) −0.112936 −0.0119046
\(91\) 3.98447 8.83419i 0.417686 0.926075i
\(92\) −5.52870 −0.576407
\(93\) 1.04665 + 1.81285i 0.108533 + 0.187984i
\(94\) −0.143642 0.248795i −0.0148155 0.0256612i
\(95\) 0.0338177 0.0585740i 0.00346962 0.00600957i
\(96\) −1.03086 −0.105212
\(97\) 1.56790 2.71568i 0.159196 0.275735i −0.775383 0.631491i \(-0.782443\pi\)
0.934579 + 0.355756i \(0.115777\pi\)
\(98\) 0.00461244 0.00798899i 0.000465927 0.000807009i
\(99\) −4.98680 −0.501192
\(100\) −1.04222 + 1.80518i −0.104222 + 0.180518i
\(101\) 8.99882 + 15.5864i 0.895416 + 1.55091i 0.833289 + 0.552837i \(0.186455\pi\)
0.0621265 + 0.998068i \(0.480212\pi\)
\(102\) 0.301369 + 0.521987i 0.0298400 + 0.0516844i
\(103\) −6.56844 −0.647208 −0.323604 0.946193i \(-0.604895\pi\)
−0.323604 + 0.946193i \(0.604895\pi\)
\(104\) 0.589322 0.0590639i 0.0577877 0.00579170i
\(105\) −11.1922 −1.09224
\(106\) −0.0809208 0.140159i −0.00785973 0.0136134i
\(107\) −7.96611 13.7977i −0.770113 1.33387i −0.937501 0.347983i \(-0.886867\pi\)
0.167388 0.985891i \(-0.446467\pi\)
\(108\) −3.38428 + 5.86174i −0.325652 + 0.564046i
\(109\) −20.3376 −1.94799 −0.973995 0.226568i \(-0.927249\pi\)
−0.973995 + 0.226568i \(0.927249\pi\)
\(110\) −0.147456 + 0.255401i −0.0140593 + 0.0243515i
\(111\) 0.900068 1.55896i 0.0854306 0.147970i
\(112\) −10.7242 −1.01334
\(113\) 0.264425 0.457998i 0.0248750 0.0430848i −0.853320 0.521388i \(-0.825415\pi\)
0.878195 + 0.478303i \(0.158748\pi\)
\(114\) −0.00146209 0.00253241i −0.000136937 0.000237182i
\(115\) −2.75174 4.76615i −0.256601 0.444446i
\(116\) 12.0037 1.11451
\(117\) −2.04856 + 4.54197i −0.189389 + 0.419905i
\(118\) 0.144979 0.0133464
\(119\) 9.41884 + 16.3139i 0.863424 + 1.49549i
\(120\) −0.342004 0.592368i −0.0312205 0.0540755i
\(121\) −1.01102 + 1.75114i −0.0919112 + 0.159195i
\(122\) −0.193592 −0.0175270
\(123\) 0.0825821 0.143036i 0.00744617 0.0128972i
\(124\) −0.999156 + 1.73059i −0.0897269 + 0.155411i
\(125\) −12.0209 −1.07518
\(126\) −0.0763013 + 0.132158i −0.00679746 + 0.0117735i
\(127\) −5.01410 8.68468i −0.444930 0.770641i 0.553118 0.833103i \(-0.313438\pi\)
−0.998047 + 0.0624622i \(0.980105\pi\)
\(128\) −0.655960 1.13616i −0.0579792 0.100423i
\(129\) −2.63433 −0.231940
\(130\) 0.172044 + 0.239220i 0.0150893 + 0.0209810i
\(131\) 12.3846 1.08205 0.541023 0.841008i \(-0.318037\pi\)
0.541023 + 0.841008i \(0.318037\pi\)
\(132\) −7.54753 13.0727i −0.656929 1.13783i
\(133\) −0.0456953 0.0791466i −0.00396229 0.00686288i
\(134\) −0.199619 + 0.345750i −0.0172444 + 0.0298682i
\(135\) −6.73767 −0.579887
\(136\) −0.575630 + 0.997021i −0.0493599 + 0.0854938i
\(137\) 8.14811 14.1129i 0.696140 1.20575i −0.273655 0.961828i \(-0.588233\pi\)
0.969795 0.243921i \(-0.0784339\pi\)
\(138\) −0.237939 −0.0202547
\(139\) 9.61802 16.6589i 0.815789 1.41299i −0.0929702 0.995669i \(-0.529636\pi\)
0.908760 0.417320i \(-0.137031\pi\)
\(140\) −5.34215 9.25287i −0.451494 0.782010i
\(141\) 7.31878 + 12.6765i 0.616352 + 1.06755i
\(142\) −0.186499 −0.0156506
\(143\) 7.59676 + 10.5629i 0.635273 + 0.883318i
\(144\) 5.51368 0.459474
\(145\) 5.97445 + 10.3481i 0.496151 + 0.859359i
\(146\) −0.000469545 0 0.000813277i −3.88599e−5 0 6.73072e-5i
\(147\) −0.235011 + 0.407052i −0.0193834 + 0.0335730i
\(148\) 1.71845 0.141256
\(149\) 6.43875 11.1522i 0.527483 0.913627i −0.472004 0.881596i \(-0.656469\pi\)
0.999487 0.0320306i \(-0.0101974\pi\)
\(150\) −0.0448542 + 0.0776898i −0.00366233 + 0.00634335i
\(151\) −5.70708 −0.464435 −0.232218 0.972664i \(-0.574598\pi\)
−0.232218 + 0.972664i \(0.574598\pi\)
\(152\) 0.00279266 0.00483703i 0.000226515 0.000392335i
\(153\) −4.84256 8.38756i −0.391498 0.678094i
\(154\) 0.199246 + 0.345104i 0.0160557 + 0.0278092i
\(155\) −1.98920 −0.159776
\(156\) −15.0071 + 1.50407i −1.20153 + 0.120422i
\(157\) 0.897113 0.0715974 0.0357987 0.999359i \(-0.488602\pi\)
0.0357987 + 0.999359i \(0.488602\pi\)
\(158\) 0.249552 + 0.432237i 0.0198533 + 0.0343869i
\(159\) 4.12305 + 7.14132i 0.326979 + 0.566344i
\(160\) 0.489795 0.848349i 0.0387217 0.0670679i
\(161\) −7.43643 −0.586073
\(162\) −0.230812 + 0.399778i −0.0181343 + 0.0314095i
\(163\) 9.57684 16.5876i 0.750116 1.29924i −0.197651 0.980273i \(-0.563331\pi\)
0.947766 0.318966i \(-0.103336\pi\)
\(164\) 0.157669 0.0123119
\(165\) 7.51310 13.0131i 0.584894 1.01307i
\(166\) 0.119715 + 0.207353i 0.00929170 + 0.0160937i
\(167\) −3.80717 6.59421i −0.294607 0.510275i 0.680286 0.732947i \(-0.261856\pi\)
−0.974894 + 0.222672i \(0.928522\pi\)
\(168\) −0.924247 −0.0713072
\(169\) 12.7414 2.57990i 0.980110 0.198454i
\(170\) −0.572762 −0.0439289
\(171\) 0.0234936 + 0.0406921i 0.00179660 + 0.00311180i
\(172\) −1.25739 2.17787i −0.0958754 0.166061i
\(173\) −1.58810 + 2.75068i −0.120741 + 0.209130i −0.920060 0.391777i \(-0.871860\pi\)
0.799319 + 0.600907i \(0.205194\pi\)
\(174\) 0.516603 0.0391636
\(175\) −1.40185 + 2.42808i −0.105970 + 0.183545i
\(176\) 7.19895 12.4689i 0.542641 0.939882i
\(177\) −7.38689 −0.555233
\(178\) −0.0488999 + 0.0846970i −0.00366520 + 0.00634831i
\(179\) 12.8532 + 22.2624i 0.960692 + 1.66397i 0.720768 + 0.693176i \(0.243789\pi\)
0.239924 + 0.970792i \(0.422877\pi\)
\(180\) 2.74659 + 4.75723i 0.204718 + 0.354583i
\(181\) −1.20564 −0.0896148 −0.0448074 0.998996i \(-0.514267\pi\)
−0.0448074 + 0.998996i \(0.514267\pi\)
\(182\) 0.396169 0.0397055i 0.0293660 0.00294317i
\(183\) 9.86381 0.729154
\(184\) −0.227238 0.393588i −0.0167522 0.0290157i
\(185\) 0.855304 + 1.48143i 0.0628832 + 0.108917i
\(186\) −0.0430008 + 0.0744796i −0.00315297 + 0.00546111i
\(187\) −25.2908 −1.84945
\(188\) −6.98666 + 12.1013i −0.509555 + 0.882574i
\(189\) −4.55205 + 7.88439i −0.331113 + 0.573505i
\(190\) 0.00277874 0.000201591
\(191\) 9.96159 17.2540i 0.720795 1.24845i −0.239886 0.970801i \(-0.577110\pi\)
0.960681 0.277653i \(-0.0895566\pi\)
\(192\) 8.33084 + 14.4294i 0.601227 + 1.04136i
\(193\) 12.9336 + 22.4016i 0.930980 + 1.61250i 0.781650 + 0.623717i \(0.214378\pi\)
0.149330 + 0.988787i \(0.452288\pi\)
\(194\) 0.128832 0.00924957
\(195\) −8.76593 12.1886i −0.627742 0.872846i
\(196\) −0.448694 −0.0320496
\(197\) −6.04285 10.4665i −0.430535 0.745708i 0.566384 0.824141i \(-0.308342\pi\)
−0.996919 + 0.0784327i \(0.975008\pi\)
\(198\) −0.102439 0.177430i −0.00728004 0.0126094i
\(199\) −8.57853 + 14.8584i −0.608116 + 1.05329i 0.383435 + 0.923568i \(0.374741\pi\)
−0.991551 + 0.129719i \(0.958592\pi\)
\(200\) −0.171348 −0.0121161
\(201\) 10.1709 17.6165i 0.717399 1.24257i
\(202\) −0.369709 + 0.640354i −0.0260126 + 0.0450552i
\(203\) 16.1457 1.13320
\(204\) 14.6585 25.3892i 1.02630 1.77760i
\(205\) 0.0784750 + 0.135923i 0.00548093 + 0.00949325i
\(206\) −0.134929 0.233705i −0.00940098 0.0162830i
\(207\) 3.82333 0.265740
\(208\) −8.39939 11.6790i −0.582393 0.809791i
\(209\) 0.122698 0.00848718
\(210\) −0.229911 0.398217i −0.0158653 0.0274796i
\(211\) −9.17184 15.8861i −0.631415 1.09364i −0.987263 0.159099i \(-0.949141\pi\)
0.355847 0.934544i \(-0.384192\pi\)
\(212\) −3.93595 + 6.81726i −0.270322 + 0.468211i
\(213\) 9.50242 0.651095
\(214\) 0.327281 0.566867i 0.0223725 0.0387502i
\(215\) 1.25166 2.16793i 0.0853623 0.147852i
\(216\) −0.556395 −0.0378579
\(217\) −1.34392 + 2.32775i −0.0912316 + 0.158018i
\(218\) −0.417777 0.723611i −0.0282954 0.0490091i
\(219\) 0.0239241 + 0.0414377i 0.00161664 + 0.00280010i
\(220\) 14.3443 0.967095
\(221\) −10.3893 + 23.0348i −0.698863 + 1.54949i
\(222\) 0.0739570 0.00496367
\(223\) −3.31293 5.73817i −0.221850 0.384256i 0.733520 0.679668i \(-0.237876\pi\)
−0.955370 + 0.295412i \(0.904543\pi\)
\(224\) −0.661823 1.14631i −0.0442199 0.0765911i
\(225\) 0.720741 1.24836i 0.0480494 0.0832240i
\(226\) 0.0217274 0.00144528
\(227\) 2.19602 3.80362i 0.145755 0.252455i −0.783899 0.620888i \(-0.786772\pi\)
0.929654 + 0.368433i \(0.120106\pi\)
\(228\) −0.0711152 + 0.123175i −0.00470972 + 0.00815747i
\(229\) −16.5022 −1.09049 −0.545247 0.838275i \(-0.683564\pi\)
−0.545247 + 0.838275i \(0.683564\pi\)
\(230\) 0.113053 0.195813i 0.00745448 0.0129115i
\(231\) −10.1519 17.5836i −0.667945 1.15691i
\(232\) 0.493369 + 0.854540i 0.0323913 + 0.0561033i
\(233\) 0.112192 0.00734994 0.00367497 0.999993i \(-0.498830\pi\)
0.00367497 + 0.999993i \(0.498830\pi\)
\(234\) −0.203685 + 0.0204140i −0.0133153 + 0.00133451i
\(235\) −13.9096 −0.907360
\(236\) −3.52584 6.10694i −0.229513 0.397528i
\(237\) −12.7151 22.0232i −0.825934 1.43056i
\(238\) −0.386965 + 0.670243i −0.0250832 + 0.0434454i
\(239\) −0.152681 −0.00987612 −0.00493806 0.999988i \(-0.501572\pi\)
−0.00493806 + 0.999988i \(0.501572\pi\)
\(240\) −8.30690 + 14.3880i −0.536208 + 0.928739i
\(241\) −14.0857 + 24.3971i −0.907339 + 1.57156i −0.0895917 + 0.995979i \(0.528556\pi\)
−0.817747 + 0.575578i \(0.804777\pi\)
\(242\) −0.0830741 −0.00534020
\(243\) 6.67953 11.5693i 0.428492 0.742171i
\(244\) 4.70810 + 8.15467i 0.301405 + 0.522049i
\(245\) −0.223323 0.386807i −0.0142676 0.0247122i
\(246\) 0.00678563 0.000432636
\(247\) 0.0504037 0.111753i 0.00320711 0.00711067i
\(248\) −0.164267 −0.0104310
\(249\) −6.09968 10.5650i −0.386552 0.669527i
\(250\) −0.246934 0.427703i −0.0156175 0.0270503i
\(251\) −13.7048 + 23.7373i −0.865036 + 1.49829i 0.00197471 + 0.999998i \(0.499371\pi\)
−0.867011 + 0.498289i \(0.833962\pi\)
\(252\) 7.42251 0.467574
\(253\) 4.99194 8.64629i 0.313841 0.543588i
\(254\) 0.206000 0.356803i 0.0129256 0.0223878i
\(255\) 29.1832 1.82752
\(256\) −7.93257 + 13.7396i −0.495786 + 0.858726i
\(257\) −6.88259 11.9210i −0.429324 0.743611i 0.567489 0.823381i \(-0.307915\pi\)
−0.996813 + 0.0797697i \(0.974582\pi\)
\(258\) −0.0541146 0.0937292i −0.00336903 0.00583533i
\(259\) 2.31142 0.143624
\(260\) 5.89259 13.0648i 0.365443 0.810244i
\(261\) −8.30105 −0.513822
\(262\) 0.254405 + 0.440643i 0.0157172 + 0.0272230i
\(263\) −10.8283 18.7552i −0.667703 1.15650i −0.978545 0.206034i \(-0.933944\pi\)
0.310842 0.950462i \(-0.399389\pi\)
\(264\) 0.620430 1.07462i 0.0381848 0.0661381i
\(265\) −7.83598 −0.481361
\(266\) 0.00187735 0.00325167i 0.000115108 0.000199373i
\(267\) 2.49153 4.31545i 0.152479 0.264101i
\(268\) 19.4187 1.18619
\(269\) −0.731367 + 1.26676i −0.0445922 + 0.0772360i −0.887460 0.460885i \(-0.847532\pi\)
0.842868 + 0.538121i \(0.180866\pi\)
\(270\) −0.138406 0.239726i −0.00842311 0.0145893i
\(271\) 4.65133 + 8.05635i 0.282548 + 0.489388i 0.972012 0.234932i \(-0.0754869\pi\)
−0.689463 + 0.724321i \(0.742154\pi\)
\(272\) 27.9629 1.69550
\(273\) −20.1855 + 2.02306i −1.22168 + 0.122441i
\(274\) 0.669516 0.0404469
\(275\) −1.88207 3.25985i −0.113493 0.196576i
\(276\) 5.78662 + 10.0227i 0.348314 + 0.603297i
\(277\) 9.97120 17.2706i 0.599111 1.03769i −0.393841 0.919178i \(-0.628854\pi\)
0.992953 0.118513i \(-0.0378126\pi\)
\(278\) 0.790296 0.0473988
\(279\) 0.690959 1.19678i 0.0413667 0.0716491i
\(280\) 0.439140 0.760614i 0.0262437 0.0454554i
\(281\) 3.44422 0.205465 0.102732 0.994709i \(-0.467241\pi\)
0.102732 + 0.994709i \(0.467241\pi\)
\(282\) −0.300686 + 0.520803i −0.0179056 + 0.0310134i
\(283\) 9.99651 + 17.3145i 0.594231 + 1.02924i 0.993655 + 0.112472i \(0.0358768\pi\)
−0.399424 + 0.916766i \(0.630790\pi\)
\(284\) 4.53561 + 7.85590i 0.269139 + 0.466162i
\(285\) −0.141581 −0.00838656
\(286\) −0.219776 + 0.487277i −0.0129956 + 0.0288133i
\(287\) 0.212075 0.0125184
\(288\) 0.340267 + 0.589359i 0.0200504 + 0.0347283i
\(289\) −16.0593 27.8155i −0.944662 1.63620i
\(290\) −0.245455 + 0.425141i −0.0144136 + 0.0249652i
\(291\) −6.56417 −0.384799
\(292\) −0.0228384 + 0.0395574i −0.00133652 + 0.00231492i
\(293\) −4.74966 + 8.22665i −0.277478 + 0.480606i −0.970757 0.240063i \(-0.922832\pi\)
0.693279 + 0.720669i \(0.256165\pi\)
\(294\) −0.0193105 −0.00112621
\(295\) 3.50976 6.07908i 0.204346 0.353938i
\(296\) 0.0706308 + 0.122336i 0.00410533 + 0.00711064i
\(297\) −6.11142 10.5853i −0.354621 0.614221i
\(298\) 0.529061 0.0306477
\(299\) −5.82436 8.09851i −0.336832 0.468349i
\(300\) 4.36337 0.251919
\(301\) −1.69127 2.92937i −0.0974832 0.168846i
\(302\) −0.117235 0.203057i −0.00674613 0.0116846i
\(303\) 18.8373 32.6271i 1.08217 1.87438i
\(304\) −0.135661 −0.00778071
\(305\) −4.68662 + 8.11747i −0.268355 + 0.464805i
\(306\) 0.198953 0.344596i 0.0113734 0.0196992i
\(307\) −25.8098 −1.47304 −0.736522 0.676413i \(-0.763533\pi\)
−0.736522 + 0.676413i \(0.763533\pi\)
\(308\) 9.69121 16.7857i 0.552208 0.956452i
\(309\) 6.87487 + 11.9076i 0.391098 + 0.677401i
\(310\) −0.0408622 0.0707754i −0.00232082 0.00401977i
\(311\) 7.38471 0.418749 0.209374 0.977836i \(-0.432857\pi\)
0.209374 + 0.977836i \(0.432857\pi\)
\(312\) −0.723889 1.00653i −0.0409821 0.0569838i
\(313\) −16.9040 −0.955468 −0.477734 0.878505i \(-0.658542\pi\)
−0.477734 + 0.878505i \(0.658542\pi\)
\(314\) 0.0184286 + 0.0319192i 0.00103998 + 0.00180131i
\(315\) 3.69432 + 6.39876i 0.208152 + 0.360529i
\(316\) 12.1381 21.0238i 0.682821 1.18268i
\(317\) −17.7091 −0.994643 −0.497321 0.867566i \(-0.665683\pi\)
−0.497321 + 0.867566i \(0.665683\pi\)
\(318\) −0.169392 + 0.293395i −0.00949902 + 0.0164528i
\(319\) −10.8383 + 18.7725i −0.606827 + 1.05106i
\(320\) −15.8330 −0.885094
\(321\) −16.6755 + 28.8828i −0.930735 + 1.61208i
\(322\) −0.152760 0.264588i −0.00851297 0.0147449i
\(323\) 0.119149 + 0.206372i 0.00662961 + 0.0114828i
\(324\) 22.4531 1.24740
\(325\) −3.74221 + 0.375058i −0.207581 + 0.0208045i
\(326\) 0.786912 0.0435830
\(327\) 21.2864 + 36.8691i 1.17714 + 2.03887i
\(328\) 0.00648044 + 0.0112245i 0.000357823 + 0.000619767i
\(329\) −9.39748 + 16.2769i −0.518100 + 0.897375i
\(330\) 0.617339 0.0339834
\(331\) −9.33397 + 16.1669i −0.513042 + 0.888614i 0.486844 + 0.873489i \(0.338148\pi\)
−0.999886 + 0.0151253i \(0.995185\pi\)
\(332\) 5.82289 10.0855i 0.319572 0.553516i
\(333\) −1.18838 −0.0651228
\(334\) 0.156414 0.270917i 0.00855861 0.0148239i
\(335\) 9.66506 + 16.7404i 0.528058 + 0.914624i
\(336\) 11.2245 + 19.4414i 0.612346 + 1.06061i
\(337\) −1.90926 −0.104004 −0.0520021 0.998647i \(-0.516560\pi\)
−0.0520021 + 0.998647i \(0.516560\pi\)
\(338\) 0.353528 + 0.400343i 0.0192294 + 0.0217758i
\(339\) −1.10704 −0.0601264
\(340\) 13.9294 + 24.1265i 0.755429 + 1.30844i
\(341\) −1.80430 3.12515i −0.0977085 0.169236i
\(342\) −0.000965214 0.00167180i −5.21928e−5 9.04006e-5i
\(343\) 18.2114 0.983325
\(344\) 0.103362 0.179027i 0.00557288 0.00965251i
\(345\) −5.76022 + 9.97700i −0.310120 + 0.537144i
\(346\) −0.130492 −0.00701529
\(347\) −13.4274 + 23.2569i −0.720821 + 1.24850i 0.239850 + 0.970810i \(0.422902\pi\)
−0.960671 + 0.277688i \(0.910432\pi\)
\(348\) −12.5637 21.7609i −0.673483 1.16651i
\(349\) −2.15875 3.73906i −0.115555 0.200147i 0.802446 0.596724i \(-0.203531\pi\)
−0.918002 + 0.396577i \(0.870198\pi\)
\(350\) −0.115188 −0.00615704
\(351\) −12.1516 + 1.21788i −0.648605 + 0.0650055i
\(352\) 1.77708 0.0947185
\(353\) 16.1893 + 28.0407i 0.861668 + 1.49245i 0.870318 + 0.492491i \(0.163913\pi\)
−0.00864939 + 0.999963i \(0.502753\pi\)
\(354\) −0.151742 0.262825i −0.00806500 0.0139690i
\(355\) −4.51491 + 7.82006i −0.239627 + 0.415046i
\(356\) 4.75693 0.252117
\(357\) 19.7165 34.1500i 1.04351 1.80741i
\(358\) −0.528062 + 0.914631i −0.0279090 + 0.0483397i
\(359\) −16.4956 −0.870604 −0.435302 0.900284i \(-0.643358\pi\)
−0.435302 + 0.900284i \(0.643358\pi\)
\(360\) −0.225778 + 0.391058i −0.0118995 + 0.0206106i
\(361\) 9.49942 + 16.4535i 0.499970 + 0.865973i
\(362\) −0.0247664 0.0428967i −0.00130169 0.00225460i
\(363\) 4.23276 0.222162
\(364\) −11.3072 15.7222i −0.592661 0.824068i
\(365\) −0.0454685 −0.00237993
\(366\) 0.202623 + 0.350953i 0.0105913 + 0.0183446i
\(367\) −1.70630 2.95539i −0.0890680 0.154270i 0.818049 0.575148i \(-0.195055\pi\)
−0.907117 + 0.420878i \(0.861722\pi\)
\(368\) −5.51936 + 9.55982i −0.287717 + 0.498340i
\(369\) −0.109035 −0.00567614
\(370\) −0.0351394 + 0.0608633i −0.00182681 + 0.00316413i
\(371\) −5.29409 + 9.16963i −0.274855 + 0.476063i
\(372\) 4.18307 0.216882
\(373\) 14.2657 24.7089i 0.738649 1.27938i −0.214455 0.976734i \(-0.568798\pi\)
0.953104 0.302643i \(-0.0978691\pi\)
\(374\) −0.519525 0.899844i −0.0268640 0.0465298i
\(375\) 12.5817 + 21.7922i 0.649716 + 1.12534i
\(376\) −1.14865 −0.0592371
\(377\) 12.6456 + 17.5831i 0.651282 + 0.905578i
\(378\) −0.374035 −0.0192383
\(379\) −14.3408 24.8389i −0.736636 1.27589i −0.954002 0.299800i \(-0.903080\pi\)
0.217366 0.976090i \(-0.430253\pi\)
\(380\) −0.0675783 0.117049i −0.00346670 0.00600449i
\(381\) −10.4960 + 18.1797i −0.537728 + 0.931373i
\(382\) 0.818527 0.0418795
\(383\) −17.1762 + 29.7500i −0.877661 + 1.52015i −0.0237595 + 0.999718i \(0.507564\pi\)
−0.853901 + 0.520435i \(0.825770\pi\)
\(384\) −1.37312 + 2.37832i −0.0700719 + 0.121368i
\(385\) 19.2940 0.983313
\(386\) −0.531366 + 0.920352i −0.0270458 + 0.0468447i
\(387\) 0.869542 + 1.50609i 0.0442013 + 0.0765589i
\(388\) −3.13315 5.42677i −0.159062 0.275503i
\(389\) −6.09669 −0.309114 −0.154557 0.987984i \(-0.549395\pi\)
−0.154557 + 0.987984i \(0.549395\pi\)
\(390\) 0.253600 0.562271i 0.0128415 0.0284717i
\(391\) 19.3902 0.980605
\(392\) −0.0184420 0.0319425i −0.000931461 0.00161334i
\(393\) −12.9624 22.4515i −0.653864 1.13253i
\(394\) 0.248265 0.430008i 0.0125074 0.0216635i
\(395\) 24.1654 1.21589
\(396\) −4.98259 + 8.63010i −0.250385 + 0.433679i
\(397\) 3.60147 6.23793i 0.180753 0.313073i −0.761384 0.648301i \(-0.775480\pi\)
0.942137 + 0.335228i \(0.108813\pi\)
\(398\) −0.704883 −0.0353326
\(399\) −0.0956542 + 0.165678i −0.00478870 + 0.00829427i
\(400\) 2.08092 + 3.60427i 0.104046 + 0.180213i
\(401\) −7.03467 12.1844i −0.351295 0.608460i 0.635182 0.772363i \(-0.280925\pi\)
−0.986477 + 0.163902i \(0.947592\pi\)
\(402\) 0.835725 0.0416822
\(403\) −3.58758 + 0.359560i −0.178710 + 0.0179110i
\(404\) 35.9649 1.78932
\(405\) 11.1754 + 19.3563i 0.555308 + 0.961821i
\(406\) 0.331665 + 0.574461i 0.0164603 + 0.0285100i
\(407\) −1.55161 + 2.68747i −0.0769105 + 0.133213i
\(408\) 2.40994 0.119310
\(409\) 6.99004 12.1071i 0.345635 0.598658i −0.639834 0.768513i \(-0.720997\pi\)
0.985469 + 0.169856i \(0.0543302\pi\)
\(410\) −0.00322408 + 0.00558427i −0.000159226 + 0.000275787i
\(411\) −34.1129 −1.68267
\(412\) −6.56290 + 11.3673i −0.323331 + 0.560025i
\(413\) −4.74247 8.21420i −0.233362 0.404194i
\(414\) 0.0785392 + 0.136034i 0.00385999 + 0.00668570i
\(415\) 11.5926 0.569061
\(416\) 0.730016 1.61856i 0.0357920 0.0793564i
\(417\) −40.2668 −1.97188
\(418\) 0.00252047 + 0.00436557i 0.000123280 + 0.000213527i
\(419\) −15.0909 26.1382i −0.737239 1.27694i −0.953734 0.300652i \(-0.902796\pi\)
0.216494 0.976284i \(-0.430538\pi\)
\(420\) −11.1827 + 19.3691i −0.545661 + 0.945113i
\(421\) 37.8526 1.84482 0.922412 0.386207i \(-0.126215\pi\)
0.922412 + 0.386207i \(0.126215\pi\)
\(422\) 0.376817 0.652666i 0.0183432 0.0317713i
\(423\) 4.83158 8.36853i 0.234919 0.406892i
\(424\) −0.647094 −0.0314256
\(425\) 3.65527 6.33111i 0.177307 0.307104i
\(426\) 0.195199 + 0.338095i 0.00945744 + 0.0163808i
\(427\) 6.33268 + 10.9685i 0.306460 + 0.530804i
\(428\) −31.8375 −1.53893
\(429\) 11.1979 24.8275i 0.540641 1.19868i
\(430\) 0.102847 0.00495970
\(431\) 15.0132 + 26.0037i 0.723163 + 1.25255i 0.959726 + 0.280938i \(0.0906457\pi\)
−0.236563 + 0.971616i \(0.576021\pi\)
\(432\) 6.75712 + 11.7037i 0.325102 + 0.563094i
\(433\) 9.29335 16.0966i 0.446610 0.773551i −0.551553 0.834140i \(-0.685965\pi\)
0.998163 + 0.0605888i \(0.0192978\pi\)
\(434\) −0.110428 −0.00530072
\(435\) 12.5063 21.6616i 0.599633 1.03860i
\(436\) −20.3205 + 35.1961i −0.973173 + 1.68559i
\(437\) −0.0940712 −0.00450003
\(438\) −0.000982901 0.00170243i −4.69648e−5 8.13455e-5i
\(439\) 15.5556 + 26.9432i 0.742430 + 1.28593i 0.951386 + 0.308002i \(0.0996604\pi\)
−0.208955 + 0.977925i \(0.567006\pi\)
\(440\) 0.589574 + 1.02117i 0.0281068 + 0.0486824i
\(441\) 0.310291 0.0147758
\(442\) −1.03300 + 0.103531i −0.0491346 + 0.00492444i
\(443\) 14.2242 0.675811 0.337906 0.941180i \(-0.390282\pi\)
0.337906 + 0.941180i \(0.390282\pi\)
\(444\) −1.79862 3.11529i −0.0853585 0.147845i
\(445\) 2.36761 + 4.10083i 0.112236 + 0.194398i
\(446\) 0.136109 0.235748i 0.00644495 0.0111630i
\(447\) −26.9565 −1.27500
\(448\) −10.6970 + 18.5277i −0.505386 + 0.875353i
\(449\) −3.43382 + 5.94755i −0.162052 + 0.280682i −0.935604 0.353050i \(-0.885145\pi\)
0.773553 + 0.633732i \(0.218478\pi\)
\(450\) 0.0592221 0.00279176
\(451\) −0.142362 + 0.246578i −0.00670355 + 0.0116109i
\(452\) −0.528404 0.915223i −0.0248540 0.0430485i
\(453\) 5.97332 + 10.3461i 0.280651 + 0.486102i
\(454\) 0.180443 0.00846862
\(455\) 7.92589 17.5729i 0.371571 0.823832i
\(456\) −0.0116918 −0.000547517
\(457\) 8.69170 + 15.0545i 0.406581 + 0.704218i 0.994504 0.104698i \(-0.0333877\pi\)
−0.587923 + 0.808917i \(0.700054\pi\)
\(458\) −0.338989 0.587146i −0.0158399 0.0274355i
\(459\) 11.8693 20.5582i 0.554012 0.959576i
\(460\) −10.9977 −0.512769
\(461\) 3.00746 5.20907i 0.140071 0.242611i −0.787452 0.616376i \(-0.788600\pi\)
0.927523 + 0.373765i \(0.121933\pi\)
\(462\) 0.417082 0.722407i 0.0194044 0.0336094i
\(463\) 21.3532 0.992369 0.496184 0.868217i \(-0.334734\pi\)
0.496184 + 0.868217i \(0.334734\pi\)
\(464\) 11.9834 20.7559i 0.556315 0.963567i
\(465\) 2.08199 + 3.60612i 0.0965502 + 0.167230i
\(466\) 0.00230466 + 0.00399178i 0.000106761 + 0.000184916i
\(467\) 6.16489 0.285277 0.142639 0.989775i \(-0.454441\pi\)
0.142639 + 0.989775i \(0.454441\pi\)
\(468\) 5.81346 + 8.08335i 0.268727 + 0.373653i
\(469\) 26.1193 1.20608
\(470\) −0.285731 0.494901i −0.0131798 0.0228281i
\(471\) −0.938965 1.62633i −0.0432652 0.0749376i
\(472\) 0.289835 0.502009i 0.0133407 0.0231068i
\(473\) 4.54127 0.208808
\(474\) 0.522389 0.904803i 0.0239941 0.0415590i
\(475\) −0.0177335 + 0.0307153i −0.000813667 + 0.00140931i
\(476\) 37.6436 1.72539
\(477\) 2.72188 4.71443i 0.124626 0.215859i
\(478\) −0.00313639 0.00543238i −0.000143455 0.000248471i
\(479\) −11.0367 19.1161i −0.504280 0.873438i −0.999988 0.00494881i \(-0.998425\pi\)
0.495708 0.868489i \(-0.334909\pi\)
\(480\) −2.05058 −0.0935957
\(481\) 1.81035 + 2.51720i 0.0825447 + 0.114775i
\(482\) −1.15740 −0.0527180
\(483\) 7.78336 + 13.4812i 0.354155 + 0.613414i
\(484\) 2.02034 + 3.49933i 0.0918337 + 0.159061i
\(485\) 3.11886 5.40202i 0.141620 0.245293i
\(486\) 0.548846 0.0248962
\(487\) 2.68945 4.65827i 0.121871 0.211086i −0.798635 0.601816i \(-0.794444\pi\)
0.920505 + 0.390730i \(0.127777\pi\)
\(488\) −0.387020 + 0.670338i −0.0175196 + 0.0303448i
\(489\) −40.0944 −1.81313
\(490\) 0.00917505 0.0158917i 0.000414486 0.000717912i
\(491\) −4.79971 8.31335i −0.216608 0.375176i 0.737161 0.675717i \(-0.236166\pi\)
−0.953769 + 0.300541i \(0.902833\pi\)
\(492\) −0.165025 0.285831i −0.00743989 0.0128863i
\(493\) −42.0992 −1.89605
\(494\) 0.00501156 0.000502276i 0.000225481 2.25985e-5i
\(495\) −9.91972 −0.445858
\(496\) 1.99494 + 3.45533i 0.0895753 + 0.155149i
\(497\) 6.10066 + 10.5667i 0.273652 + 0.473979i
\(498\) 0.250600 0.434052i 0.0112297 0.0194504i
\(499\) −39.3295 −1.76063 −0.880315 0.474389i \(-0.842669\pi\)
−0.880315 + 0.474389i \(0.842669\pi\)
\(500\) −12.0108 + 20.8033i −0.537138 + 0.930350i
\(501\) −7.96956 + 13.8037i −0.356054 + 0.616703i
\(502\) −1.12610 −0.0502601
\(503\) −6.59642 + 11.4253i −0.294120 + 0.509431i −0.974780 0.223169i \(-0.928360\pi\)
0.680660 + 0.732600i \(0.261693\pi\)
\(504\) 0.305076 + 0.528408i 0.0135892 + 0.0235372i
\(505\) 17.9004 + 31.0044i 0.796558 + 1.37968i
\(506\) 0.410179 0.0182347
\(507\) −18.0128 20.3981i −0.799978 0.905911i
\(508\) −20.0395 −0.889109
\(509\) −13.4832 23.3536i −0.597633 1.03513i −0.993169 0.116681i \(-0.962775\pi\)
0.395536 0.918450i \(-0.370559\pi\)
\(510\) 0.599483 + 1.03833i 0.0265455 + 0.0459782i
\(511\) −0.0307191 + 0.0532070i −0.00135893 + 0.00235374i
\(512\) −3.27565 −0.144765
\(513\) −0.0575837 + 0.0997378i −0.00254238 + 0.00440353i
\(514\) 0.282765 0.489764i 0.0124722 0.0216026i
\(515\) −13.0659 −0.575753
\(516\) −2.63211 + 4.55894i −0.115872 + 0.200696i
\(517\) −12.6167 21.8528i −0.554882 0.961084i
\(518\) 0.0474813 + 0.0822400i 0.00208621 + 0.00361342i
\(519\) 6.64877 0.291849
\(520\) 1.17228 0.117490i 0.0514077 0.00515227i
\(521\) 2.93885 0.128753 0.0643767 0.997926i \(-0.479494\pi\)
0.0643767 + 0.997926i \(0.479494\pi\)
\(522\) −0.170521 0.295351i −0.00746350 0.0129272i
\(523\) −8.15907 14.1319i −0.356771 0.617946i 0.630648 0.776069i \(-0.282789\pi\)
−0.987419 + 0.158123i \(0.949456\pi\)
\(524\) 12.3741 21.4326i 0.540567 0.936289i
\(525\) 5.86900 0.256144
\(526\) 0.444872 0.770542i 0.0193974 0.0335972i
\(527\) 3.50423 6.06950i 0.152647 0.264392i
\(528\) −30.1392 −1.31164
\(529\) 7.67273 13.2896i 0.333597 0.577807i
\(530\) −0.160967 0.278804i −0.00699197 0.0121105i
\(531\) 2.43827 + 4.22321i 0.105812 + 0.183272i
\(532\) −0.182627 −0.00791789
\(533\) 0.166101 + 0.230956i 0.00719463 + 0.0100038i
\(534\) 0.204724 0.00885929
\(535\) −15.8461 27.4463i −0.685089 1.18661i
\(536\) 0.798138 + 1.38242i 0.0344743 + 0.0597113i
\(537\) 26.9056 46.6019i 1.16106 2.01102i
\(538\) −0.0600952 −0.00259089
\(539\) 0.405132 0.701709i 0.0174503 0.0302247i
\(540\) −6.73199 + 11.6601i −0.289699 + 0.501773i
\(541\) 46.1372 1.98359 0.991797 0.127824i \(-0.0407992\pi\)
0.991797 + 0.127824i \(0.0407992\pi\)
\(542\) −0.191096 + 0.330988i −0.00820828 + 0.0142172i
\(543\) 1.26189 + 2.18566i 0.0541529 + 0.0937955i
\(544\) 1.72568 + 2.98896i 0.0739878 + 0.128151i
\(545\) −40.4555 −1.73292
\(546\) −0.486631 0.676639i −0.0208259 0.0289575i
\(547\) −20.6177 −0.881549 −0.440774 0.897618i \(-0.645296\pi\)
−0.440774 + 0.897618i \(0.645296\pi\)
\(548\) −16.2825 28.2020i −0.695552 1.20473i
\(549\) −3.25585 5.63930i −0.138956 0.240680i
\(550\) 0.0773234 0.133928i 0.00329708 0.00571071i
\(551\) 0.204243 0.00870105
\(552\) −0.475678 + 0.823898i −0.0202462 + 0.0350674i
\(553\) 16.3265 28.2783i 0.694272 1.20251i
\(554\) 0.819316 0.0348094
\(555\) 1.79041 3.10108i 0.0759987 0.131634i
\(556\) −19.2198 33.2897i −0.815101 1.41180i
\(557\) −22.3926 38.7852i −0.948807 1.64338i −0.747944 0.663762i \(-0.768959\pi\)
−0.200862 0.979619i \(-0.564374\pi\)
\(558\) 0.0567750 0.00240348
\(559\) 1.86554 4.13618i 0.0789038 0.174942i
\(560\) −21.3325 −0.901463
\(561\) 26.4706 + 45.8485i 1.11759 + 1.93572i
\(562\) 0.0707513 + 0.122545i 0.00298447 + 0.00516925i
\(563\) −17.1000 + 29.6181i −0.720679 + 1.24825i 0.240049 + 0.970761i \(0.422836\pi\)
−0.960728 + 0.277492i \(0.910497\pi\)
\(564\) 29.2504 1.23166
\(565\) 0.525994 0.911048i 0.0221287 0.0383281i
\(566\) −0.410698 + 0.711350i −0.0172629 + 0.0299003i
\(567\) 30.2008 1.26832
\(568\) −0.372840 + 0.645779i −0.0156440 + 0.0270963i
\(569\) 23.1112 + 40.0297i 0.968870 + 1.67813i 0.698836 + 0.715282i \(0.253702\pi\)
0.270034 + 0.962851i \(0.412965\pi\)
\(570\) −0.00290838 0.00503746i −0.000121819 0.000210996i
\(571\) 8.09392 0.338720 0.169360 0.985554i \(-0.445830\pi\)
0.169360 + 0.985554i \(0.445830\pi\)
\(572\) 25.8705 2.59283i 1.08170 0.108412i
\(573\) −41.7053 −1.74226
\(574\) 0.00435645 + 0.00754560i 0.000181835 + 0.000314947i
\(575\) 1.44297 + 2.49929i 0.0601759 + 0.104228i
\(576\) 5.49970 9.52577i 0.229154 0.396907i
\(577\) 16.6135 0.691628 0.345814 0.938303i \(-0.387603\pi\)
0.345814 + 0.938303i \(0.387603\pi\)
\(578\) 0.659781 1.14277i 0.0274433 0.0475331i
\(579\) 27.0739 46.8934i 1.12515 1.94882i
\(580\) 23.8776 0.991465
\(581\) 7.83213 13.5657i 0.324932 0.562798i
\(582\) −0.134842 0.233553i −0.00558937 0.00968107i
\(583\) −7.10764 12.3108i −0.294369 0.509861i
\(584\) −0.00375478 −0.000155374
\(585\) −4.07498 + 9.03487i −0.168480 + 0.373546i
\(586\) −0.390271 −0.0161220
\(587\) −21.6739 37.5404i −0.894579 1.54946i −0.834325 0.551273i \(-0.814142\pi\)
−0.0602542 0.998183i \(-0.519191\pi\)
\(588\) 0.469626 + 0.813416i 0.0193671 + 0.0335447i
\(589\) −0.0170007 + 0.0294461i −0.000700502 + 0.00121330i
\(590\) 0.288391 0.0118729
\(591\) −12.6495 + 21.9096i −0.520331 + 0.901240i
\(592\) 1.71555 2.97141i 0.0705085 0.122124i
\(593\) −26.2397 −1.07754 −0.538768 0.842454i \(-0.681110\pi\)
−0.538768 + 0.842454i \(0.681110\pi\)
\(594\) 0.251083 0.434888i 0.0103020 0.0178437i
\(595\) 18.7359 + 32.4516i 0.768098 + 1.33038i
\(596\) −12.8666 22.2857i −0.527038 0.912856i
\(597\) 35.9149 1.46990
\(598\) 0.168500 0.373591i 0.00689048 0.0152773i
\(599\) 24.4417 0.998661 0.499330 0.866412i \(-0.333579\pi\)
0.499330 + 0.866412i \(0.333579\pi\)
\(600\) 0.179341 + 0.310628i 0.00732157 + 0.0126813i
\(601\) 21.8006 + 37.7598i 0.889265 + 1.54025i 0.840746 + 0.541430i \(0.182117\pi\)
0.0485197 + 0.998822i \(0.484550\pi\)
\(602\) 0.0694844 0.120351i 0.00283197 0.00490512i
\(603\) −13.4289 −0.546866
\(604\) −5.70226 + 9.87660i −0.232022 + 0.401873i
\(605\) −2.01112 + 3.48337i −0.0817638 + 0.141619i
\(606\) 1.54783 0.0628761
\(607\) −1.88667 + 3.26781i −0.0765776 + 0.132636i −0.901771 0.432214i \(-0.857733\pi\)
0.825194 + 0.564850i \(0.191066\pi\)
\(608\) −0.00837208 0.0145009i −0.000339533 0.000588088i
\(609\) −16.8989 29.2697i −0.684777 1.18607i
\(610\) −0.385092 −0.0155919
\(611\) −25.0864 + 2.51425i −1.01489 + 0.101715i
\(612\) −19.3539 −0.782335
\(613\) −21.7807 37.7253i −0.879714 1.52371i −0.851655 0.524103i \(-0.824401\pi\)
−0.0280589 0.999606i \(-0.508933\pi\)
\(614\) −0.530187 0.918312i −0.0213966 0.0370600i
\(615\) 0.164272 0.284527i 0.00662408 0.0114732i
\(616\) 1.59329 0.0641956
\(617\) 4.98840 8.64017i 0.200825 0.347840i −0.747969 0.663733i \(-0.768971\pi\)
0.948795 + 0.315894i \(0.102304\pi\)
\(618\) −0.282448 + 0.489215i −0.0113617 + 0.0196791i
\(619\) 14.5672 0.585506 0.292753 0.956188i \(-0.405429\pi\)
0.292753 + 0.956188i \(0.405429\pi\)
\(620\) −1.98752 + 3.44248i −0.0798206 + 0.138253i
\(621\) 4.68557 + 8.11564i 0.188025 + 0.325669i
\(622\) 0.151697 + 0.262748i 0.00608251 + 0.0105352i
\(623\) 6.39835 0.256345
\(624\) −12.3810 + 27.4507i −0.495638 + 1.09891i
\(625\) −18.6964 −0.747857
\(626\) −0.347242 0.601441i −0.0138786 0.0240384i
\(627\) −0.128422 0.222433i −0.00512867 0.00888312i
\(628\) 0.896356 1.55253i 0.0357685 0.0619528i
\(629\) −6.02692 −0.240309
\(630\) −0.151778 + 0.262887i −0.00604699 + 0.0104737i
\(631\) 22.4972 38.9663i 0.895600 1.55122i 0.0625391 0.998043i \(-0.480080\pi\)
0.833061 0.553182i \(-0.186586\pi\)
\(632\) 1.99558 0.0793797
\(633\) −19.1994 + 33.2544i −0.763109 + 1.32174i
\(634\) −0.363782 0.630089i −0.0144476 0.0250240i
\(635\) −9.97403 17.2755i −0.395807 0.685558i
\(636\) 16.4783 0.653406
\(637\) −0.472689 0.657252i −0.0187286 0.0260413i
\(638\) −0.890563 −0.0352577
\(639\) −3.13657 5.43269i −0.124081 0.214914i
\(640\) −1.30483 2.26004i −0.0515781 0.0893358i
\(641\) −13.8003 + 23.9029i −0.545080 + 0.944106i 0.453522 + 0.891245i \(0.350167\pi\)
−0.998602 + 0.0528613i \(0.983166\pi\)
\(642\) −1.37020 −0.0540773
\(643\) −19.1219 + 33.1200i −0.754092 + 1.30613i 0.191732 + 0.981447i \(0.438590\pi\)
−0.945824 + 0.324679i \(0.894744\pi\)
\(644\) −7.43016 + 12.8694i −0.292789 + 0.507126i
\(645\) −5.24020 −0.206333
\(646\) −0.00489513 + 0.00847861i −0.000192596 + 0.000333586i
\(647\) 6.30460 + 10.9199i 0.247860 + 0.429305i 0.962932 0.269745i \(-0.0869395\pi\)
−0.715072 + 0.699051i \(0.753606\pi\)
\(648\) 0.922858 + 1.59844i 0.0362533 + 0.0627925i
\(649\) 12.7341 0.499858
\(650\) −0.0902173 0.125443i −0.00353861 0.00492028i
\(651\) 5.62648 0.220519
\(652\) −19.1375 33.1471i −0.749483 1.29814i
\(653\) 16.5492 + 28.6641i 0.647621 + 1.12171i 0.983690 + 0.179875i \(0.0575692\pi\)
−0.336069 + 0.941837i \(0.609097\pi\)
\(654\) −0.874534 + 1.51474i −0.0341970 + 0.0592309i
\(655\) 24.6354 0.962584
\(656\) 0.157403 0.272630i 0.00614555 0.0106444i
\(657\) 0.0157938 0.0273556i 0.000616174 0.00106724i
\(658\) −0.772175 −0.0301025
\(659\) −3.38838 + 5.86884i −0.131992 + 0.228618i −0.924445 0.381317i \(-0.875471\pi\)
0.792452 + 0.609934i \(0.208804\pi\)
\(660\) −15.0135 26.0042i −0.584400 1.01221i
\(661\) −17.4740 30.2659i −0.679661 1.17721i −0.975083 0.221841i \(-0.928793\pi\)
0.295422 0.955367i \(-0.404540\pi\)
\(662\) −0.766957 −0.0298086
\(663\) 52.6328 5.27505i 2.04409 0.204866i
\(664\) 0.957318 0.0371511
\(665\) −0.0908969 0.157438i −0.00352483 0.00610519i
\(666\) −0.0244118 0.0422825i −0.000945938 0.00163841i
\(667\) 8.30961 14.3927i 0.321749 0.557286i
\(668\) −15.2158 −0.588718
\(669\) −6.93497 + 12.0117i −0.268121 + 0.464400i
\(670\) −0.397081 + 0.687764i −0.0153406 + 0.0265706i
\(671\) −17.0040 −0.656434
\(672\) −1.38540 + 2.39958i −0.0534428 + 0.0925657i
\(673\) 6.42548 + 11.1293i 0.247684 + 0.429001i 0.962883 0.269920i \(-0.0869972\pi\)
−0.715199 + 0.698921i \(0.753664\pi\)
\(674\) −0.0392203 0.0679315i −0.00151071 0.00261662i
\(675\) 3.53313 0.135990
\(676\) 8.26593 24.6279i 0.317921 0.947227i
\(677\) 5.23104 0.201045 0.100523 0.994935i \(-0.467949\pi\)
0.100523 + 0.994935i \(0.467949\pi\)
\(678\) −0.0227410 0.0393886i −0.000873363 0.00151271i
\(679\) −4.21427 7.29934i −0.161729 0.280123i
\(680\) −1.14504 + 1.98327i −0.0439103 + 0.0760549i
\(681\) −9.19387 −0.352310
\(682\) 0.0741283 0.128394i 0.00283852 0.00491646i
\(683\) 12.4003 21.4780i 0.474485 0.821832i −0.525088 0.851048i \(-0.675968\pi\)
0.999573 + 0.0292159i \(0.00930102\pi\)
\(684\) 0.0938950 0.00359017
\(685\) 16.2082 28.0734i 0.619282 1.07263i
\(686\) 0.374101 + 0.647961i 0.0142832 + 0.0247393i
\(687\) 17.2720 + 29.9160i 0.658969 + 1.14137i
\(688\) −5.02108 −0.191427
\(689\) −14.1324 + 1.41640i −0.538403 + 0.0539607i
\(690\) −0.473308 −0.0180185
\(691\) −6.67222 11.5566i −0.253823 0.439635i 0.710752 0.703443i \(-0.248355\pi\)
−0.964575 + 0.263808i \(0.915022\pi\)
\(692\) 3.17353 + 5.49671i 0.120639 + 0.208954i
\(693\) −6.70189 + 11.6080i −0.254584 + 0.440952i
\(694\) −1.10331 −0.0418810
\(695\) 19.1321 33.1378i 0.725722 1.25699i
\(696\) 1.03277 1.78881i 0.0391471 0.0678047i
\(697\) −0.552976 −0.0209455
\(698\) 0.0886904 0.153616i 0.00335698 0.00581446i
\(699\) −0.117426 0.203388i −0.00444146 0.00769283i
\(700\) 2.80134 + 4.85206i 0.105881 + 0.183390i
\(701\) −14.1263 −0.533544 −0.266772 0.963760i \(-0.585957\pi\)
−0.266772 + 0.963760i \(0.585957\pi\)
\(702\) −0.292951 0.407336i −0.0110567 0.0153739i
\(703\) 0.0292395 0.00110279
\(704\) −14.3614 24.8747i −0.541265 0.937499i
\(705\) 14.5585 + 25.2160i 0.548304 + 0.949690i
\(706\) −0.665123 + 1.15203i −0.0250322 + 0.0433571i
\(707\) 48.3749 1.81933
\(708\) −7.38066 + 12.7837i −0.277382 + 0.480440i
\(709\) −6.63696 + 11.4956i −0.249256 + 0.431724i −0.963320 0.268357i \(-0.913519\pi\)
0.714063 + 0.700081i \(0.246853\pi\)
\(710\) −0.370983 −0.0139227
\(711\) −8.39401 + 14.5389i −0.314800 + 0.545250i
\(712\) 0.195517 + 0.338645i 0.00732731 + 0.0126913i
\(713\) 1.38334 + 2.39602i 0.0518066 + 0.0897316i
\(714\) 1.62007 0.0606296
\(715\) 15.1114 + 21.0118i 0.565136 + 0.785796i
\(716\) 51.3694 1.91976
\(717\) 0.159804 + 0.276788i 0.00596799 + 0.0103369i
\(718\) −0.338854 0.586912i −0.0126459 0.0219034i
\(719\) −11.2548 + 19.4939i −0.419734 + 0.727000i −0.995912 0.0903235i \(-0.971210\pi\)
0.576179 + 0.817324i \(0.304543\pi\)
\(720\) 10.9678 0.408745
\(721\) −8.82749 + 15.2897i −0.328753 + 0.569417i
\(722\) −0.390276 + 0.675977i −0.0145246 + 0.0251573i
\(723\) 58.9712 2.19316
\(724\) −1.20463 + 2.08647i −0.0447696 + 0.0775432i
\(725\) −3.13291 5.42636i −0.116353 0.201530i
\(726\) 0.0869496 + 0.150601i 0.00322700 + 0.00558933i
\(727\) 19.7975 0.734248 0.367124 0.930172i \(-0.380342\pi\)
0.367124 + 0.930172i \(0.380342\pi\)
\(728\) 0.654518 1.45117i 0.0242581 0.0537839i
\(729\) 5.74359 0.212725
\(730\) −0.000934018 0.00161777i −3.45695e−5 5.98762e-5i
\(731\) 4.40992 + 7.63820i 0.163107 + 0.282509i
\(732\) 9.85548 17.0702i 0.364269 0.630933i
\(733\) −44.0398 −1.62665 −0.813323 0.581813i \(-0.802344\pi\)
−0.813323 + 0.581813i \(0.802344\pi\)
\(734\) 0.0701018 0.121420i 0.00258750 0.00448169i
\(735\) −0.467483 + 0.809705i −0.0172434 + 0.0298664i
\(736\) −1.36247 −0.0502213
\(737\) −17.5334 + 30.3688i −0.645852 + 1.11865i
\(738\) −0.00223981 0.00387946i −8.24484e−5 0.000142805i
\(739\) −16.4368 28.4693i −0.604636 1.04726i −0.992109 0.125379i \(-0.959985\pi\)
0.387473 0.921881i \(-0.373348\pi\)
\(740\) 3.41833 0.125660
\(741\) −0.255347 + 0.0255918i −0.00938040 + 0.000940137i
\(742\) −0.435006 −0.0159696
\(743\) 3.31391 + 5.73986i 0.121576 + 0.210575i 0.920389 0.391003i \(-0.127872\pi\)
−0.798814 + 0.601579i \(0.794539\pi\)
\(744\) 0.171931 + 0.297793i 0.00630328 + 0.0109176i
\(745\) 12.8079 22.1840i 0.469246 0.812758i
\(746\) 1.17219 0.0429168
\(747\) −4.02678 + 6.97458i −0.147332 + 0.255187i
\(748\) −25.2694 + 43.7679i −0.923942 + 1.60031i
\(749\) −42.8234 −1.56473
\(750\) −0.516909 + 0.895312i −0.0188748 + 0.0326922i
\(751\) −9.92026 17.1824i −0.361996 0.626995i 0.626294 0.779587i \(-0.284571\pi\)
−0.988289 + 0.152593i \(0.951238\pi\)
\(752\) 13.9497 + 24.1616i 0.508694 + 0.881084i
\(753\) 57.3764 2.09091
\(754\) −0.365840 + 0.811124i −0.0133231 + 0.0295394i
\(755\) −11.3525 −0.413159
\(756\) 9.09643 + 15.7555i 0.330834 + 0.573021i
\(757\) 15.2756 + 26.4580i 0.555200 + 0.961634i 0.997888 + 0.0649585i \(0.0206915\pi\)
−0.442688 + 0.896676i \(0.645975\pi\)
\(758\) 0.589178 1.02049i 0.0213999 0.0370657i
\(759\) −20.8993 −0.758596
\(760\) 0.00555514 0.00962179i 0.000201506 0.000349019i
\(761\) 21.2874 36.8709i 0.771669 1.33657i −0.164978 0.986297i \(-0.552755\pi\)
0.936648 0.350273i \(-0.113911\pi\)
\(762\) −0.862442 −0.0312430
\(763\) −27.3322 + 47.3408i −0.989493 + 1.71385i
\(764\) −19.9064 34.4788i −0.720187 1.24740i
\(765\) −9.63280 16.6845i −0.348275 0.603229i
\(766\) −1.41134 −0.0509936
\(767\) 5.23113 11.5982i 0.188885 0.418788i
\(768\) 33.2105 1.19838
\(769\) 13.4929 + 23.3703i 0.486565 + 0.842756i 0.999881 0.0154443i \(-0.00491628\pi\)
−0.513316 + 0.858200i \(0.671583\pi\)
\(770\) 0.396339 + 0.686479i 0.0142831 + 0.0247390i
\(771\) −14.4073 + 24.9543i −0.518868 + 0.898705i
\(772\) 51.6907 1.86039
\(773\) 3.78686 6.55903i 0.136204 0.235912i −0.789853 0.613296i \(-0.789843\pi\)
0.926057 + 0.377384i \(0.123176\pi\)
\(774\) −0.0357244 + 0.0618765i −0.00128409 + 0.00222410i
\(775\) 1.04310 0.0374693
\(776\) 0.257554 0.446097i 0.00924566 0.0160140i
\(777\) −2.41925 4.19026i −0.0867900 0.150325i
\(778\) −0.125239 0.216920i −0.00449002 0.00777695i
\(779\) 0.00268275 9.61196e−5
\(780\) −29.8521 + 2.99188i −1.06888 + 0.107127i
\(781\) −16.3810 −0.586160
\(782\) 0.398315 + 0.689902i 0.0142437 + 0.0246708i
\(783\) −10.1731 17.6203i −0.363557 0.629699i
\(784\) −0.447936 + 0.775848i −0.0159977 + 0.0277089i
\(785\) 1.78453 0.0636927
\(786\) 0.532547 0.922399i 0.0189953 0.0329009i
\(787\) −1.47164 + 2.54895i −0.0524583 + 0.0908604i −0.891062 0.453881i \(-0.850039\pi\)
0.838604 + 0.544742i \(0.183372\pi\)
\(788\) −24.1510 −0.860343
\(789\) −22.6670 + 39.2603i −0.806965 + 1.39770i
\(790\) 0.496408 + 0.859804i 0.0176614 + 0.0305905i
\(791\) −0.710736 1.23103i −0.0252708 0.0437704i
\(792\) −0.819168 −0.0291079
\(793\) −6.98519 + 15.4873i −0.248051 + 0.549968i
\(794\) 0.295927 0.0105020
\(795\) 8.20154 + 14.2055i 0.290879 + 0.503817i
\(796\) 17.1426 + 29.6918i 0.607602 + 1.05240i
\(797\) −3.67337 + 6.36247i −0.130118 + 0.225370i −0.923722 0.383064i \(-0.874869\pi\)
0.793604 + 0.608434i \(0.208202\pi\)
\(798\) −0.00785974 −0.000278232
\(799\) 24.5035 42.4414i 0.866873 1.50147i
\(800\) −0.256841 + 0.444861i −0.00908069 + 0.0157282i
\(801\) −3.28962 −0.116233
\(802\) 0.289013 0.500586i 0.0102054 0.0176763i
\(803\) −0.0412423 0.0714338i −0.00145541 0.00252084i
\(804\) −20.3246 35.2033i −0.716794 1.24152i
\(805\) −14.7925 −0.521368
\(806\) −0.0864894 0.120260i −0.00304646 0.00423596i
\(807\) 3.06194 0.107786
\(808\) 1.47821 + 2.56034i 0.0520033 + 0.0900723i
\(809\) −4.20373 7.28107i −0.147795 0.255989i 0.782617 0.622503i \(-0.213884\pi\)
−0.930412 + 0.366515i \(0.880551\pi\)
\(810\) −0.459130 + 0.795237i −0.0161322 + 0.0279418i
\(811\) −15.7063 −0.551524 −0.275762 0.961226i \(-0.588930\pi\)
−0.275762 + 0.961226i \(0.588930\pi\)
\(812\) 16.1320 27.9415i 0.566123 0.980554i
\(813\) 9.73665 16.8644i 0.341479 0.591460i
\(814\) −0.127493 −0.00446863
\(815\) 19.0502 32.9959i 0.667299 1.15580i
\(816\) −29.2674 50.6926i −1.02456 1.77460i
\(817\) −0.0213946 0.0370566i −0.000748503 0.00129645i
\(818\) 0.574360 0.0200820
\(819\) 7.81945 + 10.8726i 0.273234 + 0.379919i
\(820\) 0.313635 0.0109526
\(821\) −24.7471 42.8633i −0.863680 1.49594i −0.868352 0.495949i \(-0.834820\pi\)
0.00467124 0.999989i \(-0.498513\pi\)
\(822\) −0.700750 1.21373i −0.0244415 0.0423339i
\(823\) −19.3056 + 33.4383i −0.672952 + 1.16559i 0.304112 + 0.952636i \(0.401640\pi\)
−0.977063 + 0.212950i \(0.931693\pi\)
\(824\) −1.07898 −0.0375880
\(825\) −3.93975 + 6.82385i −0.137164 + 0.237576i
\(826\) 0.194840 0.337473i 0.00677936 0.0117422i
\(827\) −7.87477 −0.273833 −0.136916 0.990583i \(-0.543719\pi\)
−0.136916 + 0.990583i \(0.543719\pi\)
\(828\) 3.82011 6.61662i 0.132758 0.229943i
\(829\) 11.4000 + 19.7454i 0.395939 + 0.685786i 0.993221 0.116246i \(-0.0370859\pi\)
−0.597282 + 0.802031i \(0.703753\pi\)
\(830\) 0.238137 + 0.412465i 0.00826586 + 0.0143169i
\(831\) −41.7455 −1.44813
\(832\) −28.5554 + 2.86192i −0.989980 + 0.0992194i
\(833\) 1.57365 0.0545239
\(834\) −0.827165 1.43269i −0.0286424 0.0496100i
\(835\) −7.57320 13.1172i −0.262081 0.453938i
\(836\) 0.122594 0.212339i 0.00424001 0.00734391i
\(837\) 3.38713 0.117077
\(838\) 0.619997 1.07387i 0.0214175 0.0370961i
\(839\) −8.91233 + 15.4366i −0.307688 + 0.532931i −0.977856 0.209278i \(-0.932889\pi\)
0.670168 + 0.742209i \(0.266222\pi\)
\(840\) −1.83851 −0.0634346
\(841\) −3.54146 + 6.13398i −0.122119 + 0.211517i
\(842\) 0.777572 + 1.34679i 0.0267969 + 0.0464136i
\(843\) −3.60489 6.24386i −0.124159 0.215050i
\(844\) −36.6564 −1.26176
\(845\) 25.3452 5.13192i 0.871901 0.176544i
\(846\) 0.397002 0.0136492
\(847\) 2.71748 + 4.70681i 0.0933737 + 0.161728i
\(848\) 7.85860 + 13.6115i 0.269866 + 0.467421i
\(849\) 20.9257 36.2444i 0.718169 1.24391i
\(850\) 0.300347 0.0103018
\(851\) 1.18960 2.06046i 0.0407791 0.0706315i
\(852\) 9.49440 16.4448i 0.325273 0.563389i
\(853\) 10.3020 0.352733 0.176367 0.984325i \(-0.443566\pi\)
0.176367 + 0.984325i \(0.443566\pi\)
\(854\) −0.260173 + 0.450632i −0.00890293 + 0.0154203i
\(855\) 0.0467333 + 0.0809445i 0.00159825 + 0.00276824i
\(856\) −1.30857 2.26651i −0.0447260 0.0774678i
\(857\) −23.0595 −0.787696 −0.393848 0.919176i \(-0.628856\pi\)
−0.393848 + 0.919176i \(0.628856\pi\)
\(858\) 1.11339 0.111588i 0.0380105 0.00380955i
\(859\) 44.7548 1.52701 0.763507 0.645799i \(-0.223476\pi\)
0.763507 + 0.645799i \(0.223476\pi\)
\(860\) −2.50120 4.33221i −0.0852903 0.147727i
\(861\) −0.221968 0.384460i −0.00756466 0.0131024i
\(862\) −0.616807 + 1.06834i −0.0210085 + 0.0363878i
\(863\) −19.6422 −0.668630 −0.334315 0.942461i \(-0.608505\pi\)
−0.334315 + 0.942461i \(0.608505\pi\)
\(864\) −0.834006 + 1.44454i −0.0283735 + 0.0491443i
\(865\) −3.15905 + 5.47163i −0.107411 + 0.186041i
\(866\) 0.763619 0.0259488
\(867\) −33.6169 + 58.2262i −1.14169 + 1.97746i
\(868\) 2.68558 + 4.65156i 0.0911546 + 0.157884i
\(869\) 21.9193 + 37.9653i 0.743561 + 1.28789i
\(870\) 1.02763 0.0348398
\(871\) 20.4572 + 28.4448i 0.693165 + 0.963814i
\(872\) −3.34081 −0.113134
\(873\) 2.16671 + 3.75285i 0.0733319 + 0.127015i
\(874\) −0.00193242 0.00334705i −6.53650e−5 0.000113215i
\(875\) −16.1552 + 27.9816i −0.546145 + 0.945952i
\(876\) 0.0956156 0.00323055
\(877\) −4.84953 + 8.39963i −0.163757 + 0.283635i −0.936213 0.351433i \(-0.885695\pi\)
0.772456 + 0.635068i \(0.219028\pi\)
\(878\) −0.639091 + 1.10694i −0.0215683 + 0.0373573i
\(879\) 19.8849 0.670703
\(880\) 14.3201 24.8032i 0.482731 0.836114i
\(881\) −13.8842 24.0481i −0.467769 0.810200i 0.531553 0.847025i \(-0.321609\pi\)
−0.999322 + 0.0368255i \(0.988275\pi\)
\(882\) 0.00637402 + 0.0110401i 0.000214624 + 0.000371740i
\(883\) 32.9099 1.10751 0.553754 0.832681i \(-0.313195\pi\)
0.553754 + 0.832681i \(0.313195\pi\)
\(884\) 29.4832 + 40.9951i 0.991627 + 1.37881i
\(885\) −14.6940 −0.493932
\(886\) 0.292194 + 0.506095i 0.00981646 + 0.0170026i
\(887\) 12.1524 + 21.0486i 0.408038 + 0.706743i 0.994670 0.103111i \(-0.0328797\pi\)
−0.586632 + 0.809854i \(0.699546\pi\)
\(888\) 0.147852 0.256087i 0.00496158 0.00859370i
\(889\) −26.9543 −0.904019
\(890\) −0.0972714 + 0.168479i −0.00326054 + 0.00564743i
\(891\) −20.2733 + 35.1143i −0.679180 + 1.17637i
\(892\) −13.2405 −0.443326
\(893\) −0.118878 + 0.205904i −0.00397812 + 0.00689030i
\(894\) −0.553743 0.959110i −0.0185199 0.0320774i
\(895\) 25.5675 + 44.2842i 0.854627 + 1.48026i
\(896\) −3.52625 −0.117804
\(897\) −8.58534 + 19.0350i −0.286656 + 0.635561i
\(898\) −0.282151 −0.00941550
\(899\) −3.00345 5.20213i −0.100171 0.173501i
\(900\) −1.44027 2.49461i −0.0480089 0.0831538i
\(901\) 13.8041 23.9094i 0.459882 0.796539i
\(902\) −0.0116976 −0.000389488
\(903\) −3.54034 + 6.13205i −0.117815 + 0.204062i
\(904\) 0.0434364 0.0752341i 0.00144467 0.00250225i
\(905\) −2.39826 −0.0797209
\(906\) −0.245409 + 0.425061i −0.00815316 + 0.0141217i
\(907\) 17.4338 + 30.1963i 0.578881 + 1.00265i 0.995608 + 0.0936195i \(0.0298437\pi\)
−0.416727 + 0.909032i \(0.636823\pi\)
\(908\) −4.38833 7.60082i −0.145632 0.252242i
\(909\) −24.8713 −0.824928
\(910\) 0.788058 0.0789820i 0.0261239 0.00261823i
\(911\) −47.0964 −1.56037 −0.780186 0.625547i \(-0.784876\pi\)
−0.780186 + 0.625547i \(0.784876\pi\)
\(912\) 0.141990 + 0.245934i 0.00470177 + 0.00814370i
\(913\) 10.5151 + 18.2127i 0.348000 + 0.602754i
\(914\) −0.357091 + 0.618500i −0.0118115 + 0.0204582i
\(915\) 19.6210 0.648652
\(916\) −16.4882 + 28.5585i −0.544787 + 0.943599i
\(917\) 16.6440 28.8282i 0.549632 0.951990i
\(918\) 0.975280 0.0321890
\(919\) 15.7620 27.3005i 0.519939 0.900561i −0.479792 0.877382i \(-0.659288\pi\)
0.999731 0.0231788i \(-0.00737869\pi\)
\(920\) −0.452021 0.782923i −0.0149027 0.0258122i
\(921\) 27.0139 + 46.7894i 0.890138 + 1.54176i
\(922\) 0.247118 0.00813840
\(923\) −6.72927 + 14.9198i −0.221496 + 0.491092i
\(924\) −40.5733 −1.33476
\(925\) −0.448508 0.776838i −0.0147468 0.0255423i
\(926\) 0.438640 + 0.759746i 0.0144146 + 0.0249668i
\(927\) 4.53853 7.86096i 0.149065 0.258188i
\(928\) 2.95813 0.0971054
\(929\) 0.834419 1.44526i 0.0273764 0.0474173i −0.852013 0.523521i \(-0.824618\pi\)
0.879389 + 0.476104i \(0.157951\pi\)
\(930\) −0.0855370 + 0.148154i −0.00280487 + 0.00485817i
\(931\) −0.00763455 −0.000250212
\(932\) 0.112097 0.194158i 0.00367187 0.00635986i
\(933\) −7.72922 13.3874i −0.253043 0.438284i
\(934\) 0.126640 + 0.219346i 0.00414378 + 0.00717723i
\(935\) −50.3083 −1.64526
\(936\) −0.336511 + 0.746097i −0.0109992 + 0.0243869i
\(937\) 40.6727 1.32872 0.664359 0.747414i \(-0.268705\pi\)
0.664359 + 0.747414i \(0.268705\pi\)
\(938\) 0.536545 + 0.929323i 0.0175188 + 0.0303435i
\(939\) 17.6925 + 30.6444i 0.577374 + 1.00004i
\(940\) −13.8978 + 24.0718i −0.453297 + 0.785134i
\(941\) −3.23019 −0.105301 −0.0526505 0.998613i \(-0.516767\pi\)
−0.0526505 + 0.998613i \(0.516767\pi\)
\(942\) 0.0385766 0.0668166i 0.00125689 0.00217700i
\(943\) 0.109147 0.189049i 0.00355433 0.00615628i
\(944\) −14.0796 −0.458250
\(945\) −9.05493 + 15.6836i −0.294557 + 0.510187i
\(946\) 0.0932872 + 0.161578i 0.00303303 + 0.00525336i
\(947\) 6.87960 + 11.9158i 0.223557 + 0.387212i 0.955886 0.293739i \(-0.0948997\pi\)
−0.732328 + 0.680952i \(0.761566\pi\)
\(948\) −50.8174 −1.65047
\(949\) −0.0820039 + 0.00821873i −0.00266196 + 0.000266791i
\(950\) −0.00145713 −4.72755e−5
\(951\) 18.5353 + 32.1040i 0.601047 + 1.04104i
\(952\) 1.54721 + 2.67984i 0.0501453 + 0.0868542i
\(953\) 6.22403 10.7803i 0.201616 0.349210i −0.747433 0.664337i \(-0.768714\pi\)
0.949049 + 0.315128i \(0.102047\pi\)
\(954\) 0.223652 0.00724100
\(955\) 19.8156 34.3215i 0.641216 1.11062i
\(956\) −0.152552 + 0.264228i −0.00493389 + 0.00854575i
\(957\) 45.3756 1.46679
\(958\) 0.453433 0.785370i 0.0146498 0.0253741i
\(959\) −21.9009 37.9334i −0.707216 1.22493i
\(960\) 16.5717 + 28.7030i 0.534848 + 0.926385i
\(961\) 1.00000 0.0322581
\(962\) −0.0523737 + 0.116121i −0.00168859 + 0.00374388i
\(963\) 22.0170 0.709489
\(964\) 28.1476 + 48.7531i 0.906573 + 1.57023i
\(965\) 25.7274 + 44.5612i 0.828195 + 1.43448i
\(966\) −0.319773 + 0.553862i −0.0102885 + 0.0178202i
\(967\) −39.6282 −1.27436 −0.637179 0.770716i \(-0.719899\pi\)
−0.637179 + 0.770716i \(0.719899\pi\)
\(968\) −0.166078 + 0.287656i −0.00533795 + 0.00924560i
\(969\) 0.249414 0.431999i 0.00801235 0.0138778i
\(970\) 0.256271 0.00822837
\(971\) −11.0548 + 19.1475i −0.354766 + 0.614472i −0.987078 0.160242i \(-0.948773\pi\)
0.632312 + 0.774714i \(0.282106\pi\)
\(972\) −13.3478 23.1191i −0.428131 0.741544i
\(973\) −25.8518 44.7766i −0.828770 1.43547i
\(974\) 0.220988 0.00708091
\(975\) 4.59672 + 6.39153i 0.147213 + 0.204693i
\(976\) 18.8006 0.601793
\(977\) −4.75228 8.23119i −0.152039 0.263339i 0.779938 0.625857i \(-0.215251\pi\)
−0.931977 + 0.362518i \(0.881917\pi\)
\(978\) −0.823623 1.42656i −0.0263366 0.0456163i
\(979\) −4.29510 + 7.43933i −0.137272 + 0.237762i
\(980\) −0.892539 −0.0285111
\(981\) 14.0525 24.3396i 0.448661 0.777103i
\(982\) 0.197192 0.341547i 0.00629266 0.0108992i
\(983\) 34.7301 1.10772 0.553860 0.832610i \(-0.313154\pi\)
0.553860 + 0.832610i \(0.313154\pi\)
\(984\) 0.0135655 0.0234962i 0.000432453 0.000749031i
\(985\) −12.0204 20.8199i −0.383002 0.663379i
\(986\) −0.864804 1.49788i −0.0275410 0.0477024i
\(987\) 39.3435 1.25232
\(988\) −0.143037 0.198887i −0.00455062 0.00632743i
\(989\) −3.48175 −0.110713
\(990\) −0.203772 0.352943i −0.00647629 0.0112173i
\(991\) −1.30857 2.26652i −0.0415682 0.0719983i 0.844493 0.535567i \(-0.179902\pi\)
−0.886061 + 0.463569i \(0.846569\pi\)
\(992\) −0.246228 + 0.426479i −0.00781773 + 0.0135407i
\(993\) 39.0777 1.24009
\(994\) −0.250641 + 0.434122i −0.00794984 + 0.0137695i
\(995\) −17.0644 + 29.5563i −0.540977 + 0.936999i
\(996\) −24.3781 −0.772451
\(997\) 17.7348 30.7176i 0.561667 0.972836i −0.435684 0.900100i \(-0.643493\pi\)
0.997351 0.0727364i \(-0.0231732\pi\)
\(998\) −0.807910 1.39934i −0.0255739 0.0442954i
\(999\) −1.45638 2.52253i −0.0460779 0.0798093i
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 403.2.f.b.94.9 34
13.3 even 3 5239.2.a.m.1.9 17
13.9 even 3 inner 403.2.f.b.373.9 yes 34
13.10 even 6 5239.2.a.n.1.9 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.f.b.94.9 34 1.1 even 1 trivial
403.2.f.b.373.9 yes 34 13.9 even 3 inner
5239.2.a.m.1.9 17 13.3 even 3
5239.2.a.n.1.9 17 13.10 even 6