Properties

Label 403.2.g.a.87.15
Level $403$
Weight $2$
Character 403.87
Analytic conductor $3.218$
Analytic rank $0$
Dimension $70$
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] = [403,2,Mod(87,403)]
 
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([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.87");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 87.15
Character \(\chi\) \(=\) 403.87
Dual form 403.2.g.a.315.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.351546 + 0.608895i) q^{2} -3.24498 q^{3} +(0.752831 + 1.30394i) q^{4} +(-1.57412 + 2.72646i) q^{5} +(1.14076 - 1.97585i) q^{6} +(-2.53334 + 4.38787i) q^{7} -2.46480 q^{8} +7.52991 q^{9} +O(q^{10})\) \(q+(-0.351546 + 0.608895i) q^{2} -3.24498 q^{3} +(0.752831 + 1.30394i) q^{4} +(-1.57412 + 2.72646i) q^{5} +(1.14076 - 1.97585i) q^{6} +(-2.53334 + 4.38787i) q^{7} -2.46480 q^{8} +7.52991 q^{9} +(-1.10675 - 1.91695i) q^{10} +(-0.348040 - 0.602824i) q^{11} +(-2.44292 - 4.23127i) q^{12} +(2.77836 + 2.29797i) q^{13} +(-1.78117 - 3.08508i) q^{14} +(5.10800 - 8.84732i) q^{15} +(-0.639172 + 1.10708i) q^{16} +(-0.646924 + 1.12051i) q^{17} +(-2.64711 + 4.58492i) q^{18} +(-0.479613 + 0.830713i) q^{19} -4.74020 q^{20} +(8.22064 - 14.2386i) q^{21} +0.489408 q^{22} +(-0.0533488 + 0.0924029i) q^{23} +7.99824 q^{24} +(-2.45573 - 4.25344i) q^{25} +(-2.37595 + 0.883889i) q^{26} -14.6995 q^{27} -7.62871 q^{28} +(3.67126 - 6.35880i) q^{29} +(3.59139 + 6.22047i) q^{30} +(0.714886 + 5.52168i) q^{31} +(-2.91420 - 5.04754i) q^{32} +(1.12938 + 1.95615i) q^{33} +(-0.454847 - 0.787818i) q^{34} +(-7.97558 - 13.8141i) q^{35} +(5.66875 + 9.81856i) q^{36} +2.34164 q^{37} +(-0.337211 - 0.584067i) q^{38} +(-9.01574 - 7.45689i) q^{39} +(3.87990 - 6.72018i) q^{40} +(5.37005 + 9.30120i) q^{41} +(5.77986 + 10.0110i) q^{42} +(-0.0653367 + 0.113166i) q^{43} +(0.524031 - 0.907649i) q^{44} +(-11.8530 + 20.5300i) q^{45} +(-0.0375091 - 0.0649677i) q^{46} +8.88289 q^{47} +(2.07410 - 3.59245i) q^{48} +(-9.33562 - 16.1698i) q^{49} +3.45320 q^{50} +(2.09926 - 3.63602i) q^{51} +(-0.904786 + 5.35281i) q^{52} +(0.521349 - 0.903004i) q^{53} +(5.16754 - 8.95044i) q^{54} +2.19143 q^{55} +(6.24418 - 10.8152i) q^{56} +(1.55633 - 2.69565i) q^{57} +(2.58123 + 4.47082i) q^{58} +(0.0428005 - 0.0741326i) q^{59} +15.3819 q^{60} +(3.66979 + 6.35626i) q^{61} +(-3.61344 - 1.50583i) q^{62} +(-19.0758 + 33.0403i) q^{63} +1.54121 q^{64} +(-10.6388 + 3.95781i) q^{65} -1.58812 q^{66} +(1.13367 + 1.96357i) q^{67} -1.94810 q^{68} +(0.173116 - 0.299846i) q^{69} +11.2151 q^{70} -3.68268 q^{71} -18.5597 q^{72} +(-0.537142 + 0.930358i) q^{73} +(-0.823194 + 1.42581i) q^{74} +(7.96879 + 13.8023i) q^{75} -1.44427 q^{76} +3.52682 q^{77} +(7.70991 - 2.86821i) q^{78} +(6.58335 + 11.4027i) q^{79} +(-2.01227 - 3.48536i) q^{80} +25.1098 q^{81} -7.55127 q^{82} +(4.79021 - 8.29689i) q^{83} +24.7550 q^{84} +(-2.03668 - 3.52763i) q^{85} +(-0.0459377 - 0.0795664i) q^{86} +(-11.9132 + 20.6342i) q^{87} +(0.857850 + 1.48584i) q^{88} +(-0.0447961 + 0.0775891i) q^{89} +(-8.33375 - 14.4345i) q^{90} +(-17.1218 + 6.36956i) q^{91} -0.160651 q^{92} +(-2.31979 - 17.9177i) q^{93} +(-3.12274 + 5.40875i) q^{94} +(-1.50994 - 2.61529i) q^{95} +(9.45652 + 16.3792i) q^{96} +(4.19399 + 7.26421i) q^{97} +13.1276 q^{98} +(-2.62071 - 4.53921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} - 28 q^{16} + 14 q^{17} - 20 q^{18} - 2 q^{19} - 50 q^{20} - 21 q^{21} - 8 q^{22} + 2 q^{23} - 8 q^{24} - 23 q^{25} + 6 q^{26} - 38 q^{27} + 42 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} - 28 q^{36} + 24 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} - 2 q^{41} + 27 q^{42} - q^{43} + 2 q^{44} - 29 q^{45} + 14 q^{46} + q^{48} - 37 q^{49} - 14 q^{50} - 9 q^{51} - 19 q^{52} - 2 q^{53} + 24 q^{54} - 10 q^{55} - 13 q^{56} - q^{57} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 3 q^{61} - 23 q^{62} - 32 q^{63} - 14 q^{64} + 23 q^{65} - 28 q^{66} - 2 q^{67} - 84 q^{68} + 32 q^{69} - 14 q^{70} - 86 q^{71} + 10 q^{72} + 11 q^{73} - 7 q^{74} + 37 q^{75} + 56 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} + 38 q^{80} + 22 q^{81} + 34 q^{82} + 56 q^{83} + 90 q^{84} - 5 q^{85} + 54 q^{86} - 24 q^{87} + 4 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 19 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} - 24 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.351546 + 0.608895i −0.248580 + 0.430554i −0.963132 0.269029i \(-0.913297\pi\)
0.714552 + 0.699583i \(0.246631\pi\)
\(3\) −3.24498 −1.87349 −0.936746 0.350011i \(-0.886178\pi\)
−0.936746 + 0.350011i \(0.886178\pi\)
\(4\) 0.752831 + 1.30394i 0.376416 + 0.651971i
\(5\) −1.57412 + 2.72646i −0.703969 + 1.21931i 0.263093 + 0.964770i \(0.415257\pi\)
−0.967062 + 0.254540i \(0.918076\pi\)
\(6\) 1.14076 1.97585i 0.465713 0.806639i
\(7\) −2.53334 + 4.38787i −0.957513 + 1.65846i −0.229002 + 0.973426i \(0.573546\pi\)
−0.728511 + 0.685034i \(0.759787\pi\)
\(8\) −2.46480 −0.871439
\(9\) 7.52991 2.50997
\(10\) −1.10675 1.91695i −0.349986 0.606193i
\(11\) −0.348040 0.602824i −0.104938 0.181758i 0.808775 0.588118i \(-0.200131\pi\)
−0.913713 + 0.406360i \(0.866798\pi\)
\(12\) −2.44292 4.23127i −0.705211 1.22146i
\(13\) 2.77836 + 2.29797i 0.770580 + 0.637344i
\(14\) −1.78117 3.08508i −0.476038 0.824521i
\(15\) 5.10800 8.84732i 1.31888 2.28437i
\(16\) −0.639172 + 1.10708i −0.159793 + 0.276770i
\(17\) −0.646924 + 1.12051i −0.156902 + 0.271762i −0.933750 0.357926i \(-0.883484\pi\)
0.776848 + 0.629688i \(0.216817\pi\)
\(18\) −2.64711 + 4.58492i −0.623929 + 1.08068i
\(19\) −0.479613 + 0.830713i −0.110031 + 0.190579i −0.915782 0.401675i \(-0.868428\pi\)
0.805752 + 0.592253i \(0.201762\pi\)
\(20\) −4.74020 −1.05994
\(21\) 8.22064 14.2386i 1.79389 3.10711i
\(22\) 0.489408 0.104342
\(23\) −0.0533488 + 0.0924029i −0.0111240 + 0.0192673i −0.871534 0.490335i \(-0.836874\pi\)
0.860410 + 0.509603i \(0.170208\pi\)
\(24\) 7.99824 1.63263
\(25\) −2.45573 4.25344i −0.491145 0.850689i
\(26\) −2.37595 + 0.883889i −0.465962 + 0.173345i
\(27\) −14.6995 −2.82892
\(28\) −7.62871 −1.44169
\(29\) 3.67126 6.35880i 0.681735 1.18080i −0.292716 0.956199i \(-0.594559\pi\)
0.974451 0.224600i \(-0.0721077\pi\)
\(30\) 3.59139 + 6.22047i 0.655695 + 1.13570i
\(31\) 0.714886 + 5.52168i 0.128397 + 0.991723i
\(32\) −2.91420 5.04754i −0.515162 0.892287i
\(33\) 1.12938 + 1.95615i 0.196601 + 0.340522i
\(34\) −0.454847 0.787818i −0.0780056 0.135110i
\(35\) −7.97558 13.8141i −1.34812 2.33501i
\(36\) 5.66875 + 9.81856i 0.944792 + 1.63643i
\(37\) 2.34164 0.384963 0.192482 0.981301i \(-0.438346\pi\)
0.192482 + 0.981301i \(0.438346\pi\)
\(38\) −0.337211 0.584067i −0.0547029 0.0947482i
\(39\) −9.01574 7.45689i −1.44367 1.19406i
\(40\) 3.87990 6.72018i 0.613466 1.06255i
\(41\) 5.37005 + 9.30120i 0.838661 + 1.45260i 0.891015 + 0.453975i \(0.149994\pi\)
−0.0523538 + 0.998629i \(0.516672\pi\)
\(42\) 5.77986 + 10.0110i 0.891852 + 1.54473i
\(43\) −0.0653367 + 0.113166i −0.00996375 + 0.0172577i −0.870964 0.491346i \(-0.836505\pi\)
0.861001 + 0.508604i \(0.169838\pi\)
\(44\) 0.524031 0.907649i 0.0790007 0.136833i
\(45\) −11.8530 + 20.5300i −1.76694 + 3.06043i
\(46\) −0.0375091 0.0649677i −0.00553042 0.00957896i
\(47\) 8.88289 1.29570 0.647852 0.761767i \(-0.275668\pi\)
0.647852 + 0.761767i \(0.275668\pi\)
\(48\) 2.07410 3.59245i 0.299371 0.518526i
\(49\) −9.33562 16.1698i −1.33366 2.30997i
\(50\) 3.45320 0.488356
\(51\) 2.09926 3.63602i 0.293955 0.509145i
\(52\) −0.904786 + 5.35281i −0.125471 + 0.742302i
\(53\) 0.521349 0.903004i 0.0716128 0.124037i −0.827995 0.560735i \(-0.810519\pi\)
0.899608 + 0.436698i \(0.143852\pi\)
\(54\) 5.16754 8.95044i 0.703213 1.21800i
\(55\) 2.19143 0.295493
\(56\) 6.24418 10.8152i 0.834414 1.44525i
\(57\) 1.55633 2.69565i 0.206141 0.357048i
\(58\) 2.58123 + 4.47082i 0.338932 + 0.587047i
\(59\) 0.0428005 0.0741326i 0.00557215 0.00965124i −0.863226 0.504818i \(-0.831560\pi\)
0.868798 + 0.495167i \(0.164893\pi\)
\(60\) 15.3819 1.98579
\(61\) 3.66979 + 6.35626i 0.469868 + 0.813836i 0.999406 0.0344505i \(-0.0109681\pi\)
−0.529538 + 0.848286i \(0.677635\pi\)
\(62\) −3.61344 1.50583i −0.458907 0.191241i
\(63\) −19.0758 + 33.0403i −2.40333 + 4.16269i
\(64\) 1.54121 0.192651
\(65\) −10.6388 + 3.95781i −1.31958 + 0.490906i
\(66\) −1.58812 −0.195484
\(67\) 1.13367 + 1.96357i 0.138500 + 0.239889i 0.926929 0.375237i \(-0.122439\pi\)
−0.788429 + 0.615126i \(0.789105\pi\)
\(68\) −1.94810 −0.236242
\(69\) 0.173116 0.299846i 0.0208407 0.0360972i
\(70\) 11.2151 1.34046
\(71\) −3.68268 −0.437054 −0.218527 0.975831i \(-0.570125\pi\)
−0.218527 + 0.975831i \(0.570125\pi\)
\(72\) −18.5597 −2.18729
\(73\) −0.537142 + 0.930358i −0.0628678 + 0.108890i −0.895746 0.444566i \(-0.853358\pi\)
0.832878 + 0.553456i \(0.186691\pi\)
\(74\) −0.823194 + 1.42581i −0.0956943 + 0.165747i
\(75\) 7.96879 + 13.8023i 0.920157 + 1.59376i
\(76\) −1.44427 −0.165669
\(77\) 3.52682 0.401918
\(78\) 7.70991 2.86821i 0.872975 0.324760i
\(79\) 6.58335 + 11.4027i 0.740685 + 1.28290i 0.952184 + 0.305525i \(0.0988321\pi\)
−0.211499 + 0.977378i \(0.567835\pi\)
\(80\) −2.01227 3.48536i −0.224979 0.389675i
\(81\) 25.1098 2.78998
\(82\) −7.55127 −0.833898
\(83\) 4.79021 8.29689i 0.525794 0.910702i −0.473754 0.880657i \(-0.657101\pi\)
0.999549 0.0300454i \(-0.00956518\pi\)
\(84\) 24.7550 2.70099
\(85\) −2.03668 3.52763i −0.220909 0.382625i
\(86\) −0.0459377 0.0795664i −0.00495359 0.00857986i
\(87\) −11.9132 + 20.6342i −1.27722 + 2.21222i
\(88\) 0.857850 + 1.48584i 0.0914472 + 0.158391i
\(89\) −0.0447961 + 0.0775891i −0.00474838 + 0.00822443i −0.868390 0.495882i \(-0.834845\pi\)
0.863641 + 0.504107i \(0.168178\pi\)
\(90\) −8.33375 14.4345i −0.878454 1.52153i
\(91\) −17.1218 + 6.36956i −1.79485 + 0.667712i
\(92\) −0.160651 −0.0167490
\(93\) −2.31979 17.9177i −0.240551 1.85798i
\(94\) −3.12274 + 5.40875i −0.322086 + 0.557870i
\(95\) −1.50994 2.61529i −0.154916 0.268323i
\(96\) 9.45652 + 16.3792i 0.965152 + 1.67169i
\(97\) 4.19399 + 7.26421i 0.425836 + 0.737569i 0.996498 0.0836159i \(-0.0266469\pi\)
−0.570663 + 0.821185i \(0.693314\pi\)
\(98\) 13.1276 1.32609
\(99\) −2.62071 4.53921i −0.263392 0.456207i
\(100\) 3.69750 6.40425i 0.369750 0.640425i
\(101\) −2.79393 + 4.83923i −0.278006 + 0.481521i −0.970889 0.239529i \(-0.923007\pi\)
0.692883 + 0.721050i \(0.256340\pi\)
\(102\) 1.47597 + 2.55645i 0.146143 + 0.253127i
\(103\) −2.15262 + 3.72845i −0.212104 + 0.367376i −0.952373 0.304936i \(-0.901365\pi\)
0.740269 + 0.672311i \(0.234698\pi\)
\(104\) −6.84812 5.66405i −0.671513 0.555406i
\(105\) 25.8806 + 44.8265i 2.52569 + 4.37462i
\(106\) 0.366556 + 0.634894i 0.0356031 + 0.0616664i
\(107\) −1.70260 −0.164596 −0.0822981 0.996608i \(-0.526226\pi\)
−0.0822981 + 0.996608i \(0.526226\pi\)
\(108\) −11.0662 19.1673i −1.06485 1.84437i
\(109\) −9.55259 −0.914972 −0.457486 0.889217i \(-0.651250\pi\)
−0.457486 + 0.889217i \(0.651250\pi\)
\(110\) −0.770389 + 1.33435i −0.0734537 + 0.127226i
\(111\) −7.59858 −0.721225
\(112\) −3.23848 5.60921i −0.306008 0.530021i
\(113\) −1.85421 −0.174430 −0.0872149 0.996190i \(-0.527797\pi\)
−0.0872149 + 0.996190i \(0.527797\pi\)
\(114\) 1.09425 + 1.89529i 0.102485 + 0.177510i
\(115\) −0.167955 0.290907i −0.0156619 0.0271272i
\(116\) 11.0553 1.02646
\(117\) 20.9208 + 17.3035i 1.93413 + 1.59971i
\(118\) 0.0300926 + 0.0521220i 0.00277025 + 0.00479822i
\(119\) −3.27776 5.67724i −0.300471 0.520432i
\(120\) −12.5902 + 21.8069i −1.14932 + 1.99069i
\(121\) 5.25774 9.10667i 0.477976 0.827879i
\(122\) −5.16039 −0.467200
\(123\) −17.4257 30.1822i −1.57122 2.72144i
\(124\) −6.66176 + 5.08906i −0.598244 + 0.457011i
\(125\) −0.278765 −0.0249335
\(126\) −13.4120 23.2303i −1.19484 2.06952i
\(127\) −4.71961 −0.418798 −0.209399 0.977830i \(-0.567151\pi\)
−0.209399 + 0.977830i \(0.567151\pi\)
\(128\) 5.28659 9.15664i 0.467273 0.809341i
\(129\) 0.212016 0.367223i 0.0186670 0.0323322i
\(130\) 1.33014 7.86928i 0.116661 0.690182i
\(131\) −6.46743 11.2019i −0.565062 0.978716i −0.997044 0.0768340i \(-0.975519\pi\)
0.431982 0.901882i \(-0.357814\pi\)
\(132\) −1.70047 + 2.94530i −0.148007 + 0.256356i
\(133\) −2.43004 4.20896i −0.210711 0.364963i
\(134\) −1.59415 −0.137713
\(135\) 23.1388 40.0775i 1.99147 3.44933i
\(136\) 1.59454 2.76182i 0.136731 0.236824i
\(137\) −16.1109 −1.37645 −0.688224 0.725498i \(-0.741609\pi\)
−0.688224 + 0.725498i \(0.741609\pi\)
\(138\) 0.121716 + 0.210819i 0.0103612 + 0.0179461i
\(139\) −8.07781 13.9912i −0.685151 1.18672i −0.973389 0.229158i \(-0.926403\pi\)
0.288238 0.957559i \(-0.406931\pi\)
\(140\) 12.0085 20.7994i 1.01491 1.75787i
\(141\) −28.8248 −2.42749
\(142\) 1.29463 2.24237i 0.108643 0.188175i
\(143\) 0.418290 2.47465i 0.0349792 0.206941i
\(144\) −4.81291 + 8.33620i −0.401076 + 0.694683i
\(145\) 11.5580 + 20.0191i 0.959841 + 1.66249i
\(146\) −0.377660 0.654127i −0.0312554 0.0541359i
\(147\) 30.2939 + 52.4706i 2.49860 + 4.32770i
\(148\) 1.76286 + 3.05336i 0.144906 + 0.250985i
\(149\) 5.46698 9.46910i 0.447873 0.775738i −0.550375 0.834918i \(-0.685515\pi\)
0.998247 + 0.0591794i \(0.0188484\pi\)
\(150\) −11.2056 −0.914932
\(151\) 3.87728 0.315528 0.157764 0.987477i \(-0.449571\pi\)
0.157764 + 0.987477i \(0.449571\pi\)
\(152\) 1.18215 2.04754i 0.0958850 0.166078i
\(153\) −4.87128 + 8.43730i −0.393820 + 0.682116i
\(154\) −1.23984 + 2.14746i −0.0999090 + 0.173047i
\(155\) −16.1800 6.74269i −1.29961 0.541586i
\(156\) 2.93601 17.3698i 0.235069 1.39070i
\(157\) 6.26211 0.499771 0.249885 0.968275i \(-0.419607\pi\)
0.249885 + 0.968275i \(0.419607\pi\)
\(158\) −9.25739 −0.736479
\(159\) −1.69177 + 2.93023i −0.134166 + 0.232382i
\(160\) 18.3492 1.45063
\(161\) −0.270302 0.468176i −0.0213027 0.0368974i
\(162\) −8.82725 + 15.2892i −0.693534 + 1.20124i
\(163\) −0.143956 0.249340i −0.0112755 0.0195298i 0.860333 0.509733i \(-0.170256\pi\)
−0.871608 + 0.490203i \(0.836923\pi\)
\(164\) −8.08548 + 14.0045i −0.631370 + 1.09356i
\(165\) −7.11116 −0.553603
\(166\) 3.36796 + 5.83348i 0.261404 + 0.452766i
\(167\) −4.03843 −0.312503 −0.156252 0.987717i \(-0.549941\pi\)
−0.156252 + 0.987717i \(0.549941\pi\)
\(168\) −20.2623 + 35.0952i −1.56327 + 2.70766i
\(169\) 2.43862 + 12.7692i 0.187586 + 0.982248i
\(170\) 2.86394 0.219654
\(171\) −3.61144 + 6.25520i −0.276174 + 0.478347i
\(172\) −0.196750 −0.0150020
\(173\) 9.55708 0.726612 0.363306 0.931670i \(-0.381648\pi\)
0.363306 + 0.931670i \(0.381648\pi\)
\(174\) −8.37604 14.5077i −0.634986 1.09983i
\(175\) 24.8848 1.88111
\(176\) 0.889831 0.0670735
\(177\) −0.138887 + 0.240559i −0.0104394 + 0.0180815i
\(178\) −0.0314958 0.0545523i −0.00236071 0.00408886i
\(179\) −7.56308 −0.565291 −0.282645 0.959224i \(-0.591212\pi\)
−0.282645 + 0.959224i \(0.591212\pi\)
\(180\) −35.6932 −2.66042
\(181\) 6.95906 12.0534i 0.517263 0.895925i −0.482536 0.875876i \(-0.660284\pi\)
0.999799 0.0200493i \(-0.00638231\pi\)
\(182\) 2.14069 12.6646i 0.158678 0.938759i
\(183\) −11.9084 20.6259i −0.880294 1.52471i
\(184\) 0.131494 0.227755i 0.00969389 0.0167903i
\(185\) −3.68603 + 6.38439i −0.271002 + 0.469390i
\(186\) 11.7255 + 4.88640i 0.859758 + 0.358288i
\(187\) 0.900623 0.0658601
\(188\) 6.68732 + 11.5828i 0.487723 + 0.844761i
\(189\) 37.2388 64.4994i 2.70872 4.69164i
\(190\) 2.12325 0.154037
\(191\) 13.2529 0.958947 0.479474 0.877556i \(-0.340828\pi\)
0.479474 + 0.877556i \(0.340828\pi\)
\(192\) −5.00119 −0.360930
\(193\) 12.8753 0.926787 0.463394 0.886153i \(-0.346632\pi\)
0.463394 + 0.886153i \(0.346632\pi\)
\(194\) −5.89752 −0.423417
\(195\) 34.5228 12.8430i 2.47223 0.919708i
\(196\) 14.0563 24.3462i 1.00402 1.73902i
\(197\) 5.19363 + 8.99564i 0.370031 + 0.640912i 0.989570 0.144053i \(-0.0460137\pi\)
−0.619539 + 0.784966i \(0.712680\pi\)
\(198\) 3.68520 0.261896
\(199\) −8.60982 −0.610334 −0.305167 0.952299i \(-0.598712\pi\)
−0.305167 + 0.952299i \(0.598712\pi\)
\(200\) 6.05288 + 10.4839i 0.428003 + 0.741323i
\(201\) −3.67874 6.37176i −0.259478 0.449429i
\(202\) −1.96439 3.40242i −0.138214 0.239393i
\(203\) 18.6011 + 32.2180i 1.30554 + 2.26126i
\(204\) 6.32154 0.442597
\(205\) −33.8125 −2.36157
\(206\) −1.51349 2.62144i −0.105450 0.182645i
\(207\) −0.401712 + 0.695786i −0.0279209 + 0.0483604i
\(208\) −4.31989 + 1.60707i −0.299531 + 0.111430i
\(209\) 0.667698 0.0461856
\(210\) −36.3929 −2.51135
\(211\) 20.5389 1.41395 0.706977 0.707237i \(-0.250058\pi\)
0.706977 + 0.707237i \(0.250058\pi\)
\(212\) 1.56995 0.107825
\(213\) 11.9502 0.818817
\(214\) 0.598540 1.03670i 0.0409154 0.0708675i
\(215\) −0.205696 0.356276i −0.0140283 0.0242978i
\(216\) 36.2313 2.46523
\(217\) −26.0395 10.8515i −1.76767 0.736645i
\(218\) 3.35817 5.81652i 0.227444 0.393945i
\(219\) 1.74302 3.01899i 0.117782 0.204005i
\(220\) 1.64978 + 2.85750i 0.111228 + 0.192653i
\(221\) −4.37228 + 1.62656i −0.294112 + 0.109414i
\(222\) 2.67125 4.62674i 0.179282 0.310526i
\(223\) 18.0402 1.20806 0.604031 0.796961i \(-0.293560\pi\)
0.604031 + 0.796961i \(0.293560\pi\)
\(224\) 29.5306 1.97310
\(225\) −18.4914 32.0280i −1.23276 2.13520i
\(226\) 0.651841 1.12902i 0.0433598 0.0751014i
\(227\) −21.3706 −1.41841 −0.709207 0.705000i \(-0.750947\pi\)
−0.709207 + 0.705000i \(0.750947\pi\)
\(228\) 4.68663 0.310380
\(229\) −12.5388 21.7178i −0.828586 1.43515i −0.899148 0.437645i \(-0.855813\pi\)
0.0705621 0.997507i \(-0.477521\pi\)
\(230\) 0.236176 0.0155730
\(231\) −11.4445 −0.752990
\(232\) −9.04892 + 15.6732i −0.594090 + 1.02899i
\(233\) −16.7542 −1.09761 −0.548803 0.835951i \(-0.684916\pi\)
−0.548803 + 0.835951i \(0.684916\pi\)
\(234\) −17.8907 + 6.65561i −1.16955 + 0.435091i
\(235\) −13.9828 + 24.2189i −0.912135 + 1.57986i
\(236\) 0.128886 0.00838977
\(237\) −21.3629 37.0015i −1.38767 2.40351i
\(238\) 4.60913 0.298765
\(239\) 1.70582 2.95456i 0.110340 0.191115i −0.805567 0.592504i \(-0.798139\pi\)
0.915907 + 0.401390i \(0.131473\pi\)
\(240\) 6.52978 + 11.3099i 0.421496 + 0.730052i
\(241\) −14.1082 + 24.4362i −0.908791 + 1.57407i −0.0930447 + 0.995662i \(0.529660\pi\)
−0.815746 + 0.578410i \(0.803673\pi\)
\(242\) 3.69667 + 6.40282i 0.237631 + 0.411589i
\(243\) −37.3825 −2.39809
\(244\) −5.52546 + 9.57038i −0.353731 + 0.612681i
\(245\) 58.7817 3.75542
\(246\) 24.5037 1.56230
\(247\) −3.24150 + 1.20589i −0.206252 + 0.0767288i
\(248\) −1.76205 13.6098i −0.111890 0.864226i
\(249\) −15.5442 + 26.9233i −0.985071 + 1.70619i
\(250\) 0.0979985 0.169738i 0.00619797 0.0107352i
\(251\) −10.7452 + 18.6112i −0.678231 + 1.17473i 0.297282 + 0.954790i \(0.403920\pi\)
−0.975513 + 0.219941i \(0.929414\pi\)
\(252\) −57.4435 −3.61860
\(253\) 0.0742702 0.00466933
\(254\) 1.65916 2.87375i 0.104105 0.180315i
\(255\) 6.60898 + 11.4471i 0.413870 + 0.716844i
\(256\) 5.25816 + 9.10741i 0.328635 + 0.569213i
\(257\) 6.91930 + 11.9846i 0.431614 + 0.747577i 0.997012 0.0772405i \(-0.0246109\pi\)
−0.565398 + 0.824818i \(0.691278\pi\)
\(258\) 0.149067 + 0.258191i 0.00928050 + 0.0160743i
\(259\) −5.93217 + 10.2748i −0.368607 + 0.638446i
\(260\) −13.1700 10.8929i −0.816768 0.675546i
\(261\) 27.6442 47.8812i 1.71113 2.96377i
\(262\) 9.09439 0.561853
\(263\) 5.24819 9.09014i 0.323617 0.560522i −0.657614 0.753355i \(-0.728434\pi\)
0.981232 + 0.192833i \(0.0617676\pi\)
\(264\) −2.78371 4.82153i −0.171325 0.296744i
\(265\) 1.64134 + 2.84288i 0.100826 + 0.174637i
\(266\) 3.41709 0.209515
\(267\) 0.145363 0.251775i 0.00889605 0.0154084i
\(268\) −1.70692 + 2.95648i −0.104267 + 0.180596i
\(269\) 7.04900 0.429785 0.214892 0.976638i \(-0.431060\pi\)
0.214892 + 0.976638i \(0.431060\pi\)
\(270\) 16.2687 + 28.1782i 0.990080 + 1.71487i
\(271\) 0.0515000 0.0892005i 0.00312840 0.00541855i −0.864457 0.502707i \(-0.832338\pi\)
0.867585 + 0.497288i \(0.165671\pi\)
\(272\) −0.826992 1.43239i −0.0501437 0.0868515i
\(273\) 55.5598 20.6691i 3.36263 1.25095i
\(274\) 5.66372 9.80985i 0.342158 0.592635i
\(275\) −1.70938 + 2.96074i −0.103080 + 0.178539i
\(276\) 0.521309 0.0313791
\(277\) −3.87075 6.70434i −0.232571 0.402825i 0.725993 0.687702i \(-0.241380\pi\)
−0.958564 + 0.284877i \(0.908047\pi\)
\(278\) 11.3589 0.681261
\(279\) 5.38303 + 41.5777i 0.322274 + 2.48919i
\(280\) 19.6582 + 34.0490i 1.17480 + 2.03482i
\(281\) −28.6031 −1.70632 −0.853160 0.521649i \(-0.825317\pi\)
−0.853160 + 0.521649i \(0.825317\pi\)
\(282\) 10.1332 17.5513i 0.603426 1.04516i
\(283\) −2.68044 + 4.64266i −0.159336 + 0.275977i −0.934629 0.355624i \(-0.884269\pi\)
0.775294 + 0.631601i \(0.217602\pi\)
\(284\) −2.77244 4.80201i −0.164514 0.284947i
\(285\) 4.89972 + 8.48657i 0.290235 + 0.502701i
\(286\) 1.35976 + 1.12465i 0.0804040 + 0.0665018i
\(287\) −54.4166 −3.21211
\(288\) −21.9436 38.0075i −1.29304 2.23961i
\(289\) 7.66298 + 13.2727i 0.450763 + 0.780745i
\(290\) −16.2527 −0.954391
\(291\) −13.6094 23.5722i −0.797799 1.38183i
\(292\) −1.61751 −0.0946576
\(293\) 8.86195 15.3493i 0.517721 0.896718i −0.482068 0.876134i \(-0.660114\pi\)
0.999788 0.0205843i \(-0.00655266\pi\)
\(294\) −42.5988 −2.48441
\(295\) 0.134746 + 0.233388i 0.00784524 + 0.0135884i
\(296\) −5.77168 −0.335472
\(297\) 5.11601 + 8.86119i 0.296861 + 0.514178i
\(298\) 3.84379 + 6.65764i 0.222665 + 0.385667i
\(299\) −0.360562 + 0.134135i −0.0208518 + 0.00775721i
\(300\) −11.9983 + 20.7817i −0.692723 + 1.19983i
\(301\) −0.331040 0.573378i −0.0190808 0.0330490i
\(302\) −1.36304 + 2.36085i −0.0784341 + 0.135852i
\(303\) 9.06625 15.7032i 0.520842 0.902125i
\(304\) −0.613110 1.06194i −0.0351643 0.0609063i
\(305\) −23.1068 −1.32309
\(306\) −3.42495 5.93220i −0.195792 0.339121i
\(307\) −1.34436 2.32849i −0.0767265 0.132894i 0.825109 0.564973i \(-0.191113\pi\)
−0.901836 + 0.432079i \(0.857780\pi\)
\(308\) 2.65510 + 4.59877i 0.151288 + 0.262039i
\(309\) 6.98523 12.0988i 0.397376 0.688275i
\(310\) 9.79359 7.48153i 0.556238 0.424923i
\(311\) 1.56118 0.0885265 0.0442633 0.999020i \(-0.485906\pi\)
0.0442633 + 0.999020i \(0.485906\pi\)
\(312\) 22.2220 + 18.3797i 1.25807 + 1.04055i
\(313\) −9.82704 17.0209i −0.555457 0.962080i −0.997868 0.0652677i \(-0.979210\pi\)
0.442410 0.896813i \(-0.354123\pi\)
\(314\) −2.20142 + 3.81297i −0.124233 + 0.215178i
\(315\) −60.0554 104.019i −3.38374 5.86080i
\(316\) −9.91230 + 17.1686i −0.557611 + 0.965810i
\(317\) 6.99545 + 12.1165i 0.392904 + 0.680529i 0.992831 0.119525i \(-0.0381372\pi\)
−0.599927 + 0.800054i \(0.704804\pi\)
\(318\) −1.18947 2.06022i −0.0667021 0.115531i
\(319\) −5.11098 −0.286160
\(320\) −2.42605 + 4.20204i −0.135620 + 0.234901i
\(321\) 5.52489 0.308370
\(322\) 0.380093 0.0211818
\(323\) −0.620546 1.07482i −0.0345281 0.0598044i
\(324\) 18.9034 + 32.7417i 1.05019 + 1.81899i
\(325\) 2.95140 17.4608i 0.163714 0.968552i
\(326\) 0.202429 0.0112115
\(327\) 30.9980 1.71419
\(328\) −13.2361 22.9256i −0.730842 1.26585i
\(329\) −22.5034 + 38.9770i −1.24065 + 2.14887i
\(330\) 2.49990 4.32995i 0.137615 0.238356i
\(331\) 24.2327 1.33195 0.665975 0.745974i \(-0.268016\pi\)
0.665975 + 0.745974i \(0.268016\pi\)
\(332\) 14.4249 0.791669
\(333\) 17.6323 0.966246
\(334\) 1.41969 2.45898i 0.0776821 0.134549i
\(335\) −7.13814 −0.389998
\(336\) 10.5088 + 18.2018i 0.573303 + 0.992989i
\(337\) 34.6356 1.88672 0.943359 0.331773i \(-0.107647\pi\)
0.943359 + 0.331773i \(0.107647\pi\)
\(338\) −8.63241 3.00410i −0.469541 0.163402i
\(339\) 6.01689 0.326793
\(340\) 3.06655 5.31141i 0.166307 0.288052i
\(341\) 3.07979 2.35272i 0.166780 0.127407i
\(342\) −2.53917 4.39797i −0.137303 0.237815i
\(343\) 59.1345 3.19296
\(344\) 0.161042 0.278933i 0.00868280 0.0150390i
\(345\) 0.545012 + 0.943988i 0.0293425 + 0.0508226i
\(346\) −3.35975 + 5.81926i −0.180621 + 0.312845i
\(347\) 6.13438 10.6251i 0.329311 0.570383i −0.653064 0.757302i \(-0.726517\pi\)
0.982375 + 0.186919i \(0.0598502\pi\)
\(348\) −35.8744 −1.92307
\(349\) −15.2206 + 26.3629i −0.814740 + 1.41117i 0.0947745 + 0.995499i \(0.469787\pi\)
−0.909514 + 0.415672i \(0.863546\pi\)
\(350\) −8.74813 + 15.1522i −0.467607 + 0.809920i
\(351\) −40.8405 33.7790i −2.17990 1.80299i
\(352\) −2.02852 + 3.51349i −0.108120 + 0.187270i
\(353\) 6.41247 0.341301 0.170651 0.985332i \(-0.445413\pi\)
0.170651 + 0.985332i \(0.445413\pi\)
\(354\) −0.0976501 0.169135i −0.00519004 0.00898942i
\(355\) 5.79700 10.0407i 0.307673 0.532905i
\(356\) −0.134896 −0.00714945
\(357\) 10.6363 + 18.4225i 0.562931 + 0.975025i
\(358\) 2.65877 4.60512i 0.140520 0.243388i
\(359\) 6.48885 11.2390i 0.342468 0.593172i −0.642422 0.766351i \(-0.722070\pi\)
0.984890 + 0.173179i \(0.0554038\pi\)
\(360\) 29.2153 50.6024i 1.53978 2.66698i
\(361\) 9.03994 + 15.6576i 0.475787 + 0.824086i
\(362\) 4.89285 + 8.47467i 0.257163 + 0.445419i
\(363\) −17.0613 + 29.5510i −0.895484 + 1.55102i
\(364\) −21.1953 17.5306i −1.11094 0.918852i
\(365\) −1.69106 2.92900i −0.0885139 0.153311i
\(366\) 16.7454 0.875295
\(367\) −6.21277 10.7608i −0.324304 0.561711i 0.657067 0.753832i \(-0.271797\pi\)
−0.981371 + 0.192121i \(0.938463\pi\)
\(368\) −0.0681982 0.118123i −0.00355508 0.00615757i
\(369\) 40.4360 + 70.0372i 2.10501 + 3.64599i
\(370\) −2.59162 4.48881i −0.134732 0.233362i
\(371\) 2.64151 + 4.57523i 0.137140 + 0.237534i
\(372\) 21.6173 16.5139i 1.12080 0.856207i
\(373\) −10.8988 18.8773i −0.564319 0.977430i −0.997113 0.0759364i \(-0.975805\pi\)
0.432793 0.901493i \(-0.357528\pi\)
\(374\) −0.316610 + 0.548385i −0.0163715 + 0.0283563i
\(375\) 0.904586 0.0467126
\(376\) −21.8946 −1.12913
\(377\) 24.8125 9.23062i 1.27791 0.475401i
\(378\) 26.1823 + 45.3490i 1.34667 + 2.33250i
\(379\) 20.2131 1.03828 0.519138 0.854691i \(-0.326253\pi\)
0.519138 + 0.854691i \(0.326253\pi\)
\(380\) 2.27346 3.93774i 0.116626 0.202002i
\(381\) 15.3151 0.784614
\(382\) −4.65901 + 8.06963i −0.238375 + 0.412878i
\(383\) 21.6200 1.10473 0.552366 0.833602i \(-0.313725\pi\)
0.552366 + 0.833602i \(0.313725\pi\)
\(384\) −17.1549 + 29.7131i −0.875432 + 1.51629i
\(385\) −5.55165 + 9.61573i −0.282938 + 0.490063i
\(386\) −4.52627 + 7.83973i −0.230381 + 0.399032i
\(387\) −0.491979 + 0.852133i −0.0250087 + 0.0433164i
\(388\) −6.31474 + 10.9374i −0.320582 + 0.555265i
\(389\) 4.59022 + 7.95050i 0.232733 + 0.403106i 0.958612 0.284717i \(-0.0918997\pi\)
−0.725878 + 0.687823i \(0.758566\pi\)
\(390\) −4.31629 + 25.5357i −0.218564 + 1.29305i
\(391\) −0.0690253 0.119555i −0.00349076 0.00604617i
\(392\) 23.0105 + 39.8553i 1.16220 + 2.01300i
\(393\) 20.9867 + 36.3500i 1.05864 + 1.83362i
\(394\) −7.30320 −0.367930
\(395\) −41.4520 −2.08568
\(396\) 3.94591 6.83451i 0.198289 0.343447i
\(397\) 1.04103 1.80311i 0.0522476 0.0904955i −0.838719 0.544565i \(-0.816695\pi\)
0.890966 + 0.454069i \(0.150028\pi\)
\(398\) 3.02675 5.24248i 0.151717 0.262782i
\(399\) 7.88545 + 13.6580i 0.394766 + 0.683755i
\(400\) 6.27853 0.313926
\(401\) −3.86201 + 6.68919i −0.192859 + 0.334042i −0.946197 0.323592i \(-0.895109\pi\)
0.753337 + 0.657634i \(0.228443\pi\)
\(402\) 5.17298 0.258005
\(403\) −10.7025 + 16.9840i −0.533128 + 0.846035i
\(404\) −8.41343 −0.418584
\(405\) −39.5259 + 68.4609i −1.96406 + 3.40185i
\(406\) −26.1565 −1.29813
\(407\) −0.814985 1.41160i −0.0403973 0.0699702i
\(408\) −5.17425 + 8.96207i −0.256164 + 0.443688i
\(409\) 3.01195 5.21684i 0.148931 0.257956i −0.781902 0.623402i \(-0.785750\pi\)
0.930833 + 0.365446i \(0.119083\pi\)
\(410\) 11.8866 20.5882i 0.587039 1.01678i
\(411\) 52.2796 2.57876
\(412\) −6.48225 −0.319358
\(413\) 0.216856 + 0.375606i 0.0106708 + 0.0184824i
\(414\) −0.282440 0.489201i −0.0138812 0.0240429i
\(415\) 15.0808 + 26.1207i 0.740286 + 1.28221i
\(416\) 3.50241 20.7207i 0.171720 1.01591i
\(417\) 26.2124 + 45.4011i 1.28363 + 2.22330i
\(418\) −0.234726 + 0.406558i −0.0114808 + 0.0198854i
\(419\) −0.146218 + 0.253256i −0.00714320 + 0.0123724i −0.869575 0.493801i \(-0.835607\pi\)
0.862432 + 0.506173i \(0.168940\pi\)
\(420\) −38.9675 + 67.4936i −1.90142 + 3.29335i
\(421\) −12.2268 + 21.1775i −0.595899 + 1.03213i 0.397520 + 0.917593i \(0.369871\pi\)
−0.993419 + 0.114534i \(0.963462\pi\)
\(422\) −7.22035 + 12.5060i −0.351481 + 0.608783i
\(423\) 66.8874 3.25218
\(424\) −1.28502 + 2.22572i −0.0624062 + 0.108091i
\(425\) 6.35468 0.308247
\(426\) −4.20106 + 7.27644i −0.203542 + 0.352545i
\(427\) −37.1873 −1.79962
\(428\) −1.28177 2.22009i −0.0619566 0.107312i
\(429\) −1.35734 + 8.03020i −0.0655332 + 0.387702i
\(430\) 0.289246 0.0139487
\(431\) −19.0391 −0.917079 −0.458539 0.888674i \(-0.651627\pi\)
−0.458539 + 0.888674i \(0.651627\pi\)
\(432\) 9.39549 16.2735i 0.452041 0.782958i
\(433\) −5.60518 9.70845i −0.269368 0.466558i 0.699331 0.714798i \(-0.253481\pi\)
−0.968699 + 0.248240i \(0.920148\pi\)
\(434\) 15.7615 12.0405i 0.756575 0.577964i
\(435\) −37.5056 64.9615i −1.79825 3.11467i
\(436\) −7.19149 12.4560i −0.344410 0.596535i
\(437\) −0.0511736 0.0886352i −0.00244796 0.00424000i
\(438\) 1.22550 + 2.12263i 0.0585567 + 0.101423i
\(439\) 5.49864 + 9.52393i 0.262436 + 0.454552i 0.966889 0.255199i \(-0.0821409\pi\)
−0.704453 + 0.709751i \(0.748808\pi\)
\(440\) −5.40145 −0.257504
\(441\) −70.2964 121.757i −3.34745 5.79795i
\(442\) 0.546655 3.23407i 0.0260017 0.153829i
\(443\) 4.03510 6.98900i 0.191713 0.332057i −0.754105 0.656754i \(-0.771929\pi\)
0.945818 + 0.324697i \(0.105262\pi\)
\(444\) −5.72045 9.90811i −0.271481 0.470218i
\(445\) −0.141029 0.244270i −0.00668542 0.0115795i
\(446\) −6.34196 + 10.9846i −0.300301 + 0.520136i
\(447\) −17.7403 + 30.7270i −0.839086 + 1.45334i
\(448\) −3.90440 + 6.76262i −0.184466 + 0.319504i
\(449\) 18.6990 + 32.3875i 0.882458 + 1.52846i 0.848599 + 0.529036i \(0.177446\pi\)
0.0338591 + 0.999427i \(0.489220\pi\)
\(450\) 26.0023 1.22576
\(451\) 3.73799 6.47439i 0.176015 0.304867i
\(452\) −1.39591 2.41779i −0.0656581 0.113723i
\(453\) −12.5817 −0.591139
\(454\) 7.51273 13.0124i 0.352590 0.610704i
\(455\) 9.58540 56.7083i 0.449371 2.65853i
\(456\) −3.83605 + 6.64424i −0.179640 + 0.311145i
\(457\) 19.9401 34.5372i 0.932757 1.61558i 0.154172 0.988044i \(-0.450729\pi\)
0.778586 0.627538i \(-0.215938\pi\)
\(458\) 17.6318 0.823881
\(459\) 9.50944 16.4708i 0.443863 0.768793i
\(460\) 0.252884 0.438008i 0.0117908 0.0204222i
\(461\) −15.0884 26.1339i −0.702739 1.21718i −0.967501 0.252865i \(-0.918627\pi\)
0.264763 0.964314i \(-0.414706\pi\)
\(462\) 4.02325 6.96848i 0.187179 0.324203i
\(463\) 17.1859 0.798695 0.399347 0.916800i \(-0.369237\pi\)
0.399347 + 0.916800i \(0.369237\pi\)
\(464\) 4.69313 + 8.12874i 0.217873 + 0.377367i
\(465\) 52.5037 + 21.8799i 2.43480 + 1.01466i
\(466\) 5.88988 10.2016i 0.272843 0.472579i
\(467\) −15.7431 −0.728504 −0.364252 0.931300i \(-0.618675\pi\)
−0.364252 + 0.931300i \(0.618675\pi\)
\(468\) −6.81296 + 40.3062i −0.314929 + 1.86315i
\(469\) −11.4879 −0.530461
\(470\) −9.83116 17.0281i −0.453478 0.785447i
\(471\) −20.3204 −0.936316
\(472\) −0.105495 + 0.182722i −0.00485578 + 0.00841047i
\(473\) 0.0909592 0.00418231
\(474\) 30.0401 1.37979
\(475\) 4.71119 0.216164
\(476\) 4.93520 8.54801i 0.226204 0.391797i
\(477\) 3.92571 6.79954i 0.179746 0.311329i
\(478\) 1.19934 + 2.07733i 0.0548567 + 0.0950146i
\(479\) 17.9862 0.821811 0.410906 0.911678i \(-0.365213\pi\)
0.410906 + 0.911678i \(0.365213\pi\)
\(480\) −59.5429 −2.71775
\(481\) 6.50593 + 5.38103i 0.296645 + 0.245354i
\(482\) −9.91937 17.1809i −0.451815 0.782567i
\(483\) 0.877124 + 1.51922i 0.0399105 + 0.0691270i
\(484\) 15.8328 0.719670
\(485\) −26.4074 −1.19910
\(486\) 13.1416 22.7620i 0.596117 1.03250i
\(487\) −14.7501 −0.668389 −0.334194 0.942504i \(-0.608464\pi\)
−0.334194 + 0.942504i \(0.608464\pi\)
\(488\) −9.04530 15.6669i −0.409461 0.709208i
\(489\) 0.467135 + 0.809102i 0.0211246 + 0.0365889i
\(490\) −20.6644 + 35.7919i −0.933525 + 1.61691i
\(491\) 15.8445 + 27.4435i 0.715052 + 1.23851i 0.962939 + 0.269718i \(0.0869304\pi\)
−0.247887 + 0.968789i \(0.579736\pi\)
\(492\) 26.2372 45.4442i 1.18287 2.04878i
\(493\) 4.75005 + 8.22732i 0.213931 + 0.370540i
\(494\) 0.405276 2.39766i 0.0182342 0.107876i
\(495\) 16.5013 0.741678
\(496\) −6.56987 2.73787i −0.294996 0.122934i
\(497\) 9.32949 16.1592i 0.418485 0.724837i
\(498\) −10.9290 18.9295i −0.489739 0.848252i
\(499\) −0.266771 0.462061i −0.0119423 0.0206847i 0.859992 0.510307i \(-0.170468\pi\)
−0.871935 + 0.489622i \(0.837135\pi\)
\(500\) −0.209863 0.363493i −0.00938534 0.0162559i
\(501\) 13.1046 0.585472
\(502\) −7.55486 13.0854i −0.337190 0.584030i
\(503\) −14.2583 + 24.6961i −0.635745 + 1.10114i 0.350612 + 0.936521i \(0.385974\pi\)
−0.986357 + 0.164622i \(0.947360\pi\)
\(504\) 47.0181 81.4377i 2.09435 3.62753i
\(505\) −8.79598 15.2351i −0.391416 0.677952i
\(506\) −0.0261094 + 0.0452228i −0.00116070 + 0.00201040i
\(507\) −7.91329 41.4359i −0.351441 1.84023i
\(508\) −3.55307 6.15410i −0.157642 0.273044i
\(509\) −0.345521 0.598459i −0.0153149 0.0265262i 0.858266 0.513204i \(-0.171542\pi\)
−0.873581 + 0.486678i \(0.838208\pi\)
\(510\) −9.29343 −0.411520
\(511\) −2.72153 4.71383i −0.120393 0.208527i
\(512\) 13.7524 0.607777
\(513\) 7.05005 12.2110i 0.311267 0.539131i
\(514\) −9.72980 −0.429163
\(515\) −6.77699 11.7381i −0.298630 0.517242i
\(516\) 0.638450 0.0281062
\(517\) −3.09161 5.35482i −0.135969 0.235505i
\(518\) −4.17086 7.22414i −0.183257 0.317410i
\(519\) −31.0126 −1.36130
\(520\) 26.2226 9.75521i 1.14994 0.427794i
\(521\) −15.4391 26.7413i −0.676400 1.17156i −0.976058 0.217512i \(-0.930206\pi\)
0.299658 0.954047i \(-0.403127\pi\)
\(522\) 19.4364 + 33.6649i 0.850709 + 1.47347i
\(523\) −0.339900 + 0.588724i −0.0148628 + 0.0257431i −0.873361 0.487073i \(-0.838064\pi\)
0.858498 + 0.512816i \(0.171398\pi\)
\(524\) 9.73777 16.8663i 0.425396 0.736808i
\(525\) −80.7506 −3.52425
\(526\) 3.68996 + 6.39120i 0.160890 + 0.278669i
\(527\) −6.64955 2.77107i −0.289659 0.120710i
\(528\) −2.88748 −0.125662
\(529\) 11.4943 + 19.9087i 0.499753 + 0.865597i
\(530\) −2.30802 −0.100254
\(531\) 0.322284 0.558212i 0.0139859 0.0242243i
\(532\) 3.65882 6.33727i 0.158630 0.274756i
\(533\) −6.45396 + 38.1824i −0.279552 + 1.65386i
\(534\) 0.102203 + 0.177021i 0.00442276 + 0.00766045i
\(535\) 2.68010 4.64206i 0.115871 0.200694i
\(536\) −2.79427 4.83982i −0.120694 0.209048i
\(537\) 24.5420 1.05907
\(538\) −2.47804 + 4.29210i −0.106836 + 0.185046i
\(539\) −6.49835 + 11.2555i −0.279904 + 0.484807i
\(540\) 69.6784 2.99848
\(541\) −2.13486 3.69769i −0.0917848 0.158976i 0.816477 0.577377i \(-0.195924\pi\)
−0.908262 + 0.418401i \(0.862591\pi\)
\(542\) 0.0362092 + 0.0627161i 0.00155532 + 0.00269389i
\(543\) −22.5820 + 39.1132i −0.969087 + 1.67851i
\(544\) 7.54106 0.323320
\(545\) 15.0370 26.0448i 0.644112 1.11564i
\(546\) −6.94650 + 41.0962i −0.297283 + 1.75876i
\(547\) 16.2298 28.1108i 0.693936 1.20193i −0.276602 0.960985i \(-0.589208\pi\)
0.970538 0.240948i \(-0.0774583\pi\)
\(548\) −12.1288 21.0077i −0.518116 0.897404i
\(549\) 27.6332 + 47.8621i 1.17935 + 2.04270i
\(550\) −1.20185 2.08167i −0.0512472 0.0887628i
\(551\) 3.52156 + 6.09952i 0.150024 + 0.259848i
\(552\) −0.426697 + 0.739060i −0.0181614 + 0.0314565i
\(553\) −66.7115 −2.83686
\(554\) 5.44298 0.231250
\(555\) 11.9611 20.7172i 0.507721 0.879398i
\(556\) 12.1625 21.0660i 0.515803 0.893397i
\(557\) 0.626683 1.08545i 0.0265534 0.0459918i −0.852443 0.522820i \(-0.824880\pi\)
0.878997 + 0.476828i \(0.158213\pi\)
\(558\) −27.2089 11.3388i −1.15184 0.480009i
\(559\) −0.441583 + 0.164276i −0.0186770 + 0.00694812i
\(560\) 20.3911 0.861680
\(561\) −2.92250 −0.123388
\(562\) 10.0553 17.4163i 0.424158 0.734663i
\(563\) −15.3460 −0.646757 −0.323378 0.946270i \(-0.604819\pi\)
−0.323378 + 0.946270i \(0.604819\pi\)
\(564\) −21.7002 37.5859i −0.913745 1.58265i
\(565\) 2.91876 5.05544i 0.122793 0.212684i
\(566\) −1.88459 3.26421i −0.0792154 0.137205i
\(567\) −63.6117 + 110.179i −2.67144 + 4.62707i
\(568\) 9.07708 0.380866
\(569\) 4.52705 + 7.84108i 0.189784 + 0.328715i 0.945178 0.326555i \(-0.105888\pi\)
−0.755394 + 0.655271i \(0.772555\pi\)
\(570\) −6.88991 −0.288586
\(571\) 5.05545 8.75629i 0.211564 0.366439i −0.740640 0.671902i \(-0.765478\pi\)
0.952204 + 0.305462i \(0.0988110\pi\)
\(572\) 3.54170 1.31757i 0.148086 0.0550903i
\(573\) −43.0055 −1.79658
\(574\) 19.1299 33.1340i 0.798468 1.38299i
\(575\) 0.524041 0.0218540
\(576\) 11.6051 0.483548
\(577\) −17.8614 30.9368i −0.743579 1.28792i −0.950856 0.309635i \(-0.899793\pi\)
0.207276 0.978282i \(-0.433540\pi\)
\(578\) −10.7755 −0.448204
\(579\) −41.7803 −1.73633
\(580\) −17.4025 + 30.1420i −0.722598 + 1.25158i
\(581\) 24.2705 + 42.0377i 1.00691 + 1.74402i
\(582\) 19.1374 0.793269
\(583\) −0.725803 −0.0300597
\(584\) 1.32395 2.29315i 0.0547854 0.0948911i
\(585\) −80.1094 + 29.8019i −3.31212 + 1.23216i
\(586\) 6.23076 + 10.7920i 0.257390 + 0.445813i
\(587\) −13.3553 + 23.1321i −0.551234 + 0.954765i 0.446952 + 0.894558i \(0.352509\pi\)
−0.998186 + 0.0602070i \(0.980824\pi\)
\(588\) −45.6124 + 79.0031i −1.88103 + 3.25803i
\(589\) −4.92980 2.05440i −0.203129 0.0846501i
\(590\) −0.189478 −0.00780069
\(591\) −16.8532 29.1907i −0.693250 1.20074i
\(592\) −1.49671 + 2.59238i −0.0615144 + 0.106546i
\(593\) 25.7939 1.05923 0.529615 0.848238i \(-0.322337\pi\)
0.529615 + 0.848238i \(0.322337\pi\)
\(594\) −7.19405 −0.295175
\(595\) 20.6384 0.846091
\(596\) 16.4629 0.674345
\(597\) 27.9387 1.14346
\(598\) 0.0450801 0.266699i 0.00184346 0.0109061i
\(599\) 10.8558 18.8028i 0.443556 0.768262i −0.554394 0.832254i \(-0.687050\pi\)
0.997950 + 0.0639920i \(0.0203832\pi\)
\(600\) −19.6415 34.0200i −0.801860 1.38886i
\(601\) −11.7433 −0.479020 −0.239510 0.970894i \(-0.576987\pi\)
−0.239510 + 0.970894i \(0.576987\pi\)
\(602\) 0.465503 0.0189725
\(603\) 8.53643 + 14.7855i 0.347630 + 0.602113i
\(604\) 2.91893 + 5.05574i 0.118770 + 0.205715i
\(605\) 16.5526 + 28.6700i 0.672961 + 1.16560i
\(606\) 6.37440 + 11.0408i 0.258942 + 0.448501i
\(607\) 23.5508 0.955896 0.477948 0.878388i \(-0.341381\pi\)
0.477948 + 0.878388i \(0.341381\pi\)
\(608\) 5.59074 0.226735
\(609\) −60.3602 104.547i −2.44592 4.23645i
\(610\) 8.12309 14.0696i 0.328894 0.569662i
\(611\) 24.6799 + 20.4127i 0.998443 + 0.825808i
\(612\) −14.6690 −0.592959
\(613\) −20.8995 −0.844122 −0.422061 0.906567i \(-0.638693\pi\)
−0.422061 + 0.906567i \(0.638693\pi\)
\(614\) 1.89041 0.0762908
\(615\) 109.721 4.42437
\(616\) −8.69291 −0.350247
\(617\) −10.7771 + 18.6664i −0.433869 + 0.751482i −0.997203 0.0747469i \(-0.976185\pi\)
0.563334 + 0.826229i \(0.309518\pi\)
\(618\) 4.91125 + 8.50654i 0.197560 + 0.342183i
\(619\) −28.0171 −1.12610 −0.563051 0.826422i \(-0.690373\pi\)
−0.563051 + 0.826422i \(0.690373\pi\)
\(620\) −3.38870 26.1738i −0.136094 1.05117i
\(621\) 0.784200 1.35827i 0.0314689 0.0545057i
\(622\) −0.548827 + 0.950596i −0.0220059 + 0.0381154i
\(623\) −0.226968 0.393119i −0.00909326 0.0157500i
\(624\) 14.0180 5.21490i 0.561168 0.208763i
\(625\) 12.7174 22.0273i 0.508698 0.881090i
\(626\) 13.8186 0.552303
\(627\) −2.16667 −0.0865284
\(628\) 4.71431 + 8.16542i 0.188121 + 0.325836i
\(629\) −1.51486 + 2.62382i −0.0604016 + 0.104619i
\(630\) 84.4488 3.36452
\(631\) 27.3706 1.08961 0.544803 0.838564i \(-0.316604\pi\)
0.544803 + 0.838564i \(0.316604\pi\)
\(632\) −16.2266 28.1054i −0.645461 1.11797i
\(633\) −66.6483 −2.64903
\(634\) −9.83688 −0.390673
\(635\) 7.42925 12.8678i 0.294821 0.510645i
\(636\) −5.09447 −0.202009
\(637\) 11.2200 66.3786i 0.444551 2.63001i
\(638\) 1.79674 3.11205i 0.0711338 0.123207i
\(639\) −27.7303 −1.09699
\(640\) 16.6435 + 28.8274i 0.657892 + 1.13950i
\(641\) −34.1374 −1.34835 −0.674173 0.738573i \(-0.735500\pi\)
−0.674173 + 0.738573i \(0.735500\pi\)
\(642\) −1.94225 + 3.36408i −0.0766546 + 0.132770i
\(643\) −1.21221 2.09961i −0.0478050 0.0828006i 0.841133 0.540829i \(-0.181889\pi\)
−0.888938 + 0.458028i \(0.848556\pi\)
\(644\) 0.406983 0.704915i 0.0160374 0.0277775i
\(645\) 0.667480 + 1.15611i 0.0262820 + 0.0455217i
\(646\) 0.872601 0.0343320
\(647\) −2.37725 + 4.11752i −0.0934593 + 0.161876i −0.908965 0.416873i \(-0.863126\pi\)
0.815505 + 0.578750i \(0.196459\pi\)
\(648\) −61.8907 −2.43130
\(649\) −0.0595852 −0.00233892
\(650\) 9.59425 + 7.93537i 0.376318 + 0.311251i
\(651\) 84.4976 + 35.2128i 3.31172 + 1.38010i
\(652\) 0.216750 0.375421i 0.00848857 0.0147026i
\(653\) 5.61578 9.72682i 0.219763 0.380640i −0.734973 0.678097i \(-0.762805\pi\)
0.954735 + 0.297457i \(0.0961384\pi\)
\(654\) −10.8972 + 18.8745i −0.426115 + 0.738052i
\(655\) 40.7221 1.59115
\(656\) −13.7295 −0.536049
\(657\) −4.04463 + 7.00551i −0.157796 + 0.273311i
\(658\) −15.8219 27.4044i −0.616803 1.06833i
\(659\) 16.1670 + 28.0021i 0.629778 + 1.09081i 0.987596 + 0.157016i \(0.0501873\pi\)
−0.357819 + 0.933791i \(0.616479\pi\)
\(660\) −5.35351 9.27254i −0.208385 0.360933i
\(661\) −1.82616 3.16301i −0.0710296 0.123027i 0.828323 0.560251i \(-0.189295\pi\)
−0.899353 + 0.437224i \(0.855962\pi\)
\(662\) −8.51890 + 14.7552i −0.331097 + 0.573476i
\(663\) 14.1880 5.27815i 0.551016 0.204986i
\(664\) −11.8069 + 20.4502i −0.458198 + 0.793622i
\(665\) 15.3007 0.593338
\(666\) −6.19857 + 10.7362i −0.240190 + 0.416021i
\(667\) 0.391715 + 0.678470i 0.0151672 + 0.0262704i
\(668\) −3.04026 5.26588i −0.117631 0.203743i
\(669\) −58.5402 −2.26330
\(670\) 2.50938 4.34638i 0.0969459 0.167915i
\(671\) 2.55447 4.42447i 0.0986142 0.170805i
\(672\) −95.8263 −3.69658
\(673\) −14.1942 24.5851i −0.547146 0.947685i −0.998468 0.0553236i \(-0.982381\pi\)
0.451323 0.892361i \(-0.350952\pi\)
\(674\) −12.1760 + 21.0894i −0.469001 + 0.812334i
\(675\) 36.0979 + 62.5234i 1.38941 + 2.40653i
\(676\) −14.8145 + 12.7929i −0.569787 + 0.492034i
\(677\) −22.8075 + 39.5037i −0.876563 + 1.51825i −0.0214749 + 0.999769i \(0.506836\pi\)
−0.855088 + 0.518482i \(0.826497\pi\)
\(678\) −2.11521 + 3.66366i −0.0812342 + 0.140702i
\(679\) −42.4992 −1.63097
\(680\) 5.02000 + 8.69490i 0.192508 + 0.333434i
\(681\) 69.3471 2.65739
\(682\) 0.349871 + 2.70236i 0.0133973 + 0.103479i
\(683\) 7.61262 + 13.1854i 0.291289 + 0.504527i 0.974115 0.226054i \(-0.0725826\pi\)
−0.682826 + 0.730581i \(0.739249\pi\)
\(684\) −10.8752 −0.415824
\(685\) 25.3606 43.9258i 0.968977 1.67832i
\(686\) −20.7885 + 36.0067i −0.793707 + 1.37474i
\(687\) 40.6881 + 70.4739i 1.55235 + 2.68875i
\(688\) −0.0835228 0.144666i −0.00318428 0.00551533i
\(689\) 3.52358 1.31083i 0.134238 0.0499385i
\(690\) −0.766387 −0.0291758
\(691\) −15.4058 26.6836i −0.586064 1.01509i −0.994742 0.102414i \(-0.967343\pi\)
0.408678 0.912679i \(-0.365990\pi\)
\(692\) 7.19487 + 12.4619i 0.273508 + 0.473730i
\(693\) 26.5566 1.00880
\(694\) 4.31303 + 7.47039i 0.163720 + 0.283572i
\(695\) 50.8619 1.92930
\(696\) 29.3636 50.8592i 1.11302 1.92781i
\(697\) −13.8961 −0.526351
\(698\) −10.7015 18.5355i −0.405057 0.701579i
\(699\) 54.3672 2.05636
\(700\) 18.7340 + 32.4483i 0.708080 + 1.22643i
\(701\) 3.56472 + 6.17427i 0.134638 + 0.233199i 0.925459 0.378848i \(-0.123680\pi\)
−0.790821 + 0.612047i \(0.790346\pi\)
\(702\) 34.9252 12.9927i 1.31817 0.490378i
\(703\) −1.12308 + 1.94523i −0.0423578 + 0.0733658i
\(704\) −0.536402 0.929076i −0.0202164 0.0350159i
\(705\) 45.3738 78.5898i 1.70888 2.95986i
\(706\) −2.25427 + 3.90452i −0.0848408 + 0.146948i
\(707\) −14.1559 24.5188i −0.532389 0.922125i
\(708\) −0.418233 −0.0157182
\(709\) −16.6833 28.8964i −0.626556 1.08523i −0.988238 0.152925i \(-0.951131\pi\)
0.361682 0.932302i \(-0.382203\pi\)
\(710\) 4.07582 + 7.05953i 0.152963 + 0.264939i
\(711\) 49.5720 + 85.8613i 1.85910 + 3.22005i
\(712\) 0.110414 0.191242i 0.00413792 0.00716709i
\(713\) −0.548358 0.228518i −0.0205362 0.00855805i
\(714\) −14.9565 −0.559734
\(715\) 6.08860 + 5.03586i 0.227701 + 0.188330i
\(716\) −5.69372 9.86181i −0.212784 0.368553i
\(717\) −5.53534 + 9.58749i −0.206721 + 0.358051i
\(718\) 4.56225 + 7.90205i 0.170262 + 0.294902i
\(719\) 9.47992 16.4197i 0.353542 0.612352i −0.633326 0.773885i \(-0.718311\pi\)
0.986867 + 0.161533i \(0.0516440\pi\)
\(720\) −15.1522 26.2444i −0.564690 0.978072i
\(721\) −10.9067 18.8909i −0.406185 0.703533i
\(722\) −12.7118 −0.473085
\(723\) 45.7809 79.2949i 1.70261 2.94901i
\(724\) 20.9560 0.778823
\(725\) −36.0624 −1.33932
\(726\) −11.9956 20.7770i −0.445199 0.771108i
\(727\) −13.4607 23.3146i −0.499229 0.864691i 0.500770 0.865580i \(-0.333050\pi\)
−1.00000 0.000889681i \(0.999717\pi\)
\(728\) 42.2018 15.6997i 1.56410 0.581870i
\(729\) 45.9760 1.70281
\(730\) 2.37793 0.0880113
\(731\) −0.0845357 0.146420i −0.00312667 0.00541555i
\(732\) 17.9300 31.0557i 0.662713 1.14785i
\(733\) −1.30574 + 2.26161i −0.0482287 + 0.0835345i −0.889132 0.457651i \(-0.848691\pi\)
0.840903 + 0.541185i \(0.182024\pi\)
\(734\) 8.73629 0.322462
\(735\) −190.746 −7.03575
\(736\) 0.621876 0.0229227
\(737\) 0.789125 1.36680i 0.0290678 0.0503469i
\(738\) −56.8604 −2.09306
\(739\) 13.2612 + 22.9691i 0.487823 + 0.844934i 0.999902 0.0140045i \(-0.00445791\pi\)
−0.512079 + 0.858938i \(0.671125\pi\)
\(740\) −11.0998 −0.408038
\(741\) 10.5186 3.91308i 0.386410 0.143751i
\(742\) −3.71445 −0.136362
\(743\) 14.1900 24.5779i 0.520582 0.901674i −0.479132 0.877743i \(-0.659048\pi\)
0.999714 0.0239310i \(-0.00761822\pi\)
\(744\) 5.71783 + 44.1637i 0.209626 + 1.61912i
\(745\) 17.2114 + 29.8110i 0.630577 + 1.09219i
\(746\) 15.3257 0.561115
\(747\) 36.0699 62.4749i 1.31973 2.28584i
\(748\) 0.678017 + 1.17436i 0.0247908 + 0.0429388i
\(749\) 4.31326 7.47078i 0.157603 0.272976i
\(750\) −0.318003 + 0.550798i −0.0116118 + 0.0201123i
\(751\) −36.5681 −1.33439 −0.667194 0.744884i \(-0.732505\pi\)
−0.667194 + 0.744884i \(0.732505\pi\)
\(752\) −5.67770 + 9.83406i −0.207044 + 0.358611i
\(753\) 34.8680 60.3931i 1.27066 2.20085i
\(754\) −3.10224 + 18.3532i −0.112977 + 0.668383i
\(755\) −6.10331 + 10.5712i −0.222122 + 0.384727i
\(756\) 112.138 4.07842
\(757\) 17.4917 + 30.2965i 0.635747 + 1.10115i 0.986356 + 0.164625i \(0.0526413\pi\)
−0.350609 + 0.936522i \(0.614025\pi\)
\(758\) −7.10581 + 12.3076i −0.258095 + 0.447033i
\(759\) −0.241006 −0.00874795
\(760\) 3.72170 + 6.44617i 0.135000 + 0.233827i
\(761\) −26.1786 + 45.3427i −0.948975 + 1.64367i −0.201385 + 0.979512i \(0.564544\pi\)
−0.747590 + 0.664161i \(0.768789\pi\)
\(762\) −5.38394 + 9.32526i −0.195040 + 0.337819i
\(763\) 24.2000 41.9156i 0.876097 1.51745i
\(764\) 9.97721 + 17.2810i 0.360963 + 0.625206i
\(765\) −15.3360 26.5627i −0.554474 0.960377i
\(766\) −7.60043 + 13.1643i −0.274615 + 0.475647i
\(767\) 0.289270 0.107613i 0.0104449 0.00388568i
\(768\) −17.0626 29.5534i −0.615695 1.06642i
\(769\) −13.7061 −0.494255 −0.247128 0.968983i \(-0.579487\pi\)
−0.247128 + 0.968983i \(0.579487\pi\)
\(770\) −3.90331 6.76074i −0.140666 0.243640i
\(771\) −22.4530 38.8897i −0.808625 1.40058i
\(772\) 9.69296 + 16.7887i 0.348857 + 0.604238i
\(773\) 18.1591 + 31.4525i 0.653138 + 1.13127i 0.982357 + 0.187014i \(0.0598810\pi\)
−0.329220 + 0.944253i \(0.606786\pi\)
\(774\) −0.345906 0.599128i −0.0124333 0.0215352i
\(775\) 21.7306 16.6005i 0.780586 0.596306i
\(776\) −10.3374 17.9048i −0.371090 0.642746i
\(777\) 19.2498 33.3416i 0.690582 1.19612i
\(778\) −6.45469 −0.231412
\(779\) −10.3022 −0.369114
\(780\) 42.7364 + 35.3471i 1.53021 + 1.26563i
\(781\) 1.28172 + 2.22001i 0.0458636 + 0.0794382i
\(782\) 0.0970622 0.00347094
\(783\) −53.9655 + 93.4711i −1.92857 + 3.34038i
\(784\) 23.8683 0.852439
\(785\) −9.85733 + 17.0734i −0.351823 + 0.609375i
\(786\) −29.5111 −1.05263
\(787\) −2.33952 + 4.05216i −0.0833947 + 0.144444i −0.904706 0.426036i \(-0.859910\pi\)
0.821311 + 0.570480i \(0.193243\pi\)
\(788\) −7.81986 + 13.5444i −0.278571 + 0.482499i
\(789\) −17.0303 + 29.4973i −0.606294 + 1.05013i
\(790\) 14.5723 25.2399i 0.518458 0.897996i
\(791\) 4.69735 8.13606i 0.167019 0.289285i
\(792\) 6.45954 + 11.1882i 0.229530 + 0.397557i
\(793\) −4.41051 + 26.0931i −0.156622 + 0.926593i
\(794\) 0.731937 + 1.26775i 0.0259755 + 0.0449908i
\(795\) −5.32611 9.22509i −0.188898 0.327180i
\(796\) −6.48174 11.2267i −0.229739 0.397920i
\(797\) −39.3312 −1.39318 −0.696592 0.717468i \(-0.745301\pi\)
−0.696592 + 0.717468i \(0.745301\pi\)
\(798\) −11.0884 −0.392524
\(799\) −5.74656 + 9.95333i −0.203299 + 0.352123i
\(800\) −14.3129 + 24.7908i −0.506039 + 0.876485i
\(801\) −0.337311 + 0.584239i −0.0119183 + 0.0206431i
\(802\) −2.71534 4.70311i −0.0958821 0.166073i
\(803\) 0.747789 0.0263889
\(804\) 5.53893 9.59372i 0.195343 0.338344i
\(805\) 1.70195 0.0599859
\(806\) −6.57909 12.4873i −0.231738 0.439848i
\(807\) −22.8739 −0.805198
\(808\) 6.88648 11.9277i 0.242265 0.419616i
\(809\) −44.4152 −1.56155 −0.780777 0.624810i \(-0.785177\pi\)
−0.780777 + 0.624810i \(0.785177\pi\)
\(810\) −27.7903 48.1343i −0.976453 1.69127i
\(811\) −12.1811 + 21.0983i −0.427736 + 0.740860i −0.996672 0.0815219i \(-0.974022\pi\)
0.568936 + 0.822382i \(0.307355\pi\)
\(812\) −28.0069 + 48.5095i −0.982851 + 1.70235i
\(813\) −0.167116 + 0.289454i −0.00586103 + 0.0101516i
\(814\) 1.14602 0.0401679
\(815\) 0.906419 0.0317505
\(816\) 2.68357 + 4.64808i 0.0939438 + 0.162716i
\(817\) −0.0626726 0.108552i −0.00219264 0.00379776i
\(818\) 2.11767 + 3.66792i 0.0740427 + 0.128246i
\(819\) −128.925 + 47.9622i −4.50502 + 1.67594i
\(820\) −25.4551 44.0895i −0.888930 1.53967i
\(821\) 9.95642 17.2450i 0.347481 0.601856i −0.638320 0.769771i \(-0.720370\pi\)
0.985801 + 0.167916i \(0.0537036\pi\)
\(822\) −18.3787 + 31.8328i −0.641030 + 1.11030i
\(823\) −14.6126 + 25.3098i −0.509364 + 0.882245i 0.490577 + 0.871398i \(0.336786\pi\)
−0.999941 + 0.0108471i \(0.996547\pi\)
\(824\) 5.30579 9.18990i 0.184836 0.320145i
\(825\) 5.54692 9.60755i 0.193119 0.334492i
\(826\) −0.304940 −0.0106102
\(827\) −6.75502 + 11.7000i −0.234895 + 0.406850i −0.959242 0.282585i \(-0.908808\pi\)
0.724347 + 0.689435i \(0.242141\pi\)
\(828\) −1.20969 −0.0420395
\(829\) 14.5004 25.1154i 0.503620 0.872295i −0.496371 0.868110i \(-0.665335\pi\)
0.999991 0.00418494i \(-0.00133211\pi\)
\(830\) −21.2063 −0.736082
\(831\) 12.5605 + 21.7555i 0.435719 + 0.754688i
\(832\) 4.28203 + 3.54165i 0.148453 + 0.122785i
\(833\) 24.1578 0.837017
\(834\) −36.8594 −1.27634
\(835\) 6.35699 11.0106i 0.219993 0.381038i
\(836\) 0.502664 + 0.870640i 0.0173850 + 0.0301117i
\(837\) −10.5085 81.1658i −0.363225 2.80550i
\(838\) −0.102804 0.178062i −0.00355132 0.00615106i
\(839\) 17.4176 + 30.1682i 0.601324 + 1.04152i 0.992621 + 0.121259i \(0.0386930\pi\)
−0.391297 + 0.920264i \(0.627974\pi\)
\(840\) −63.7906 110.488i −2.20098 3.81221i
\(841\) −12.4562 21.5748i −0.429526 0.743960i
\(842\) −8.59658 14.8897i −0.296258 0.513133i
\(843\) 92.8167 3.19678
\(844\) 15.4623 + 26.7815i 0.532234 + 0.921857i
\(845\) −38.6535 13.4515i −1.32972 0.462746i
\(846\) −23.5140 + 40.7274i −0.808427 + 1.40024i
\(847\) 26.6393 + 46.1406i 0.915336 + 1.58541i
\(848\) 0.666464 + 1.15435i 0.0228865 + 0.0396405i
\(849\) 8.69798 15.0653i 0.298514 0.517041i
\(850\) −2.23396 + 3.86933i −0.0766242 + 0.132717i
\(851\) −0.124924 + 0.216374i −0.00428233 + 0.00741722i
\(852\) 8.99652 + 15.5824i 0.308216 + 0.533845i
\(853\) −23.6132 −0.808501 −0.404251 0.914648i \(-0.632468\pi\)
−0.404251 + 0.914648i \(0.632468\pi\)
\(854\) 13.0730 22.6432i 0.447350 0.774833i
\(855\) −11.3697 19.6929i −0.388836 0.673483i
\(856\) 4.19656 0.143436
\(857\) −18.3797 + 31.8345i −0.627837 + 1.08745i 0.360148 + 0.932895i \(0.382726\pi\)
−0.987985 + 0.154551i \(0.950607\pi\)
\(858\) −4.41238 3.64946i −0.150636 0.124591i
\(859\) 11.0527 19.1438i 0.377112 0.653177i −0.613529 0.789672i \(-0.710251\pi\)
0.990641 + 0.136495i \(0.0435839\pi\)
\(860\) 0.309709 0.536431i 0.0105610 0.0182922i
\(861\) 176.581 6.01787
\(862\) 6.69310 11.5928i 0.227968 0.394852i
\(863\) 1.94339 3.36605i 0.0661537 0.114582i −0.831051 0.556196i \(-0.812261\pi\)
0.897205 + 0.441614i \(0.145594\pi\)
\(864\) 42.8372 + 74.1962i 1.45735 + 2.52420i
\(865\) −15.0440 + 26.0570i −0.511512 + 0.885965i
\(866\) 7.88190 0.267838
\(867\) −24.8662 43.0696i −0.844501 1.46272i
\(868\) −5.45366 42.1233i −0.185109 1.42976i
\(869\) 4.58254 7.93720i 0.155452 0.269251i
\(870\) 52.7397 1.78804
\(871\) −1.36249 + 8.06066i −0.0461663 + 0.273125i
\(872\) 23.5452 0.797342
\(873\) 31.5804 + 54.6988i 1.06883 + 1.85128i
\(874\) 0.0719594 0.00243406
\(875\) 0.706205 1.22318i 0.0238741 0.0413512i
\(876\) 5.24879 0.177340
\(877\) −55.0667 −1.85947 −0.929736 0.368228i \(-0.879965\pi\)
−0.929736 + 0.368228i \(0.879965\pi\)
\(878\) −7.73209 −0.260946
\(879\) −28.7569 + 49.8084i −0.969945 + 1.67999i
\(880\) −1.40070 + 2.42609i −0.0472177 + 0.0817834i
\(881\) 14.8061 + 25.6449i 0.498830 + 0.864000i 0.999999 0.00135007i \(-0.000429739\pi\)
−0.501169 + 0.865350i \(0.667096\pi\)
\(882\) 98.8496 3.32844
\(883\) 35.1274 1.18213 0.591065 0.806624i \(-0.298708\pi\)
0.591065 + 0.806624i \(0.298708\pi\)
\(884\) −5.41253 4.47668i −0.182043 0.150567i
\(885\) −0.437250 0.757339i −0.0146980 0.0254577i
\(886\) 2.83704 + 4.91390i 0.0953124 + 0.165086i
\(887\) −55.0133 −1.84716 −0.923582 0.383400i \(-0.874753\pi\)
−0.923582 + 0.383400i \(0.874753\pi\)
\(888\) 18.7290 0.628504
\(889\) 11.9564 20.7091i 0.401004 0.694560i
\(890\) 0.198313 0.00664746
\(891\) −8.73923 15.1368i −0.292775 0.507101i
\(892\) 13.5812 + 23.5234i 0.454734 + 0.787622i
\(893\) −4.26035 + 7.37914i −0.142567 + 0.246933i
\(894\) −12.4730 21.6039i −0.417161 0.722543i
\(895\) 11.9052 20.6204i 0.397947 0.689265i
\(896\) 26.7855 + 46.3938i 0.894840 + 1.54991i
\(897\) 1.17002 0.435265i 0.0390658 0.0145331i
\(898\) −26.2942 −0.877447
\(899\) 37.7358 + 15.7257i 1.25856 + 0.524481i
\(900\) 27.8418 48.2234i 0.928060 1.60745i
\(901\) 0.674547 + 1.16835i 0.0224724 + 0.0389234i
\(902\) 2.62815 + 4.55208i 0.0875077 + 0.151568i
\(903\) 1.07422 + 1.86060i 0.0357478 + 0.0619170i
\(904\) 4.57027 0.152005
\(905\) 21.9088 + 37.9472i 0.728274 + 1.26141i
\(906\) 4.42304 7.66093i 0.146946 0.254517i
\(907\) −18.8061 + 32.5730i −0.624445 + 1.08157i 0.364203 + 0.931320i \(0.381341\pi\)
−0.988648 + 0.150251i \(0.951992\pi\)
\(908\) −16.0884 27.8660i −0.533913 0.924765i
\(909\) −21.0380 + 36.4389i −0.697787 + 1.20860i
\(910\) 31.1597 + 25.7721i 1.03293 + 0.854336i
\(911\) −16.4257 28.4502i −0.544209 0.942597i −0.998656 0.0518237i \(-0.983497\pi\)
0.454447 0.890774i \(-0.349837\pi\)
\(912\) 1.98953 + 3.44597i 0.0658799 + 0.114107i
\(913\) −6.66875 −0.220703
\(914\) 14.0197 + 24.2828i 0.463730 + 0.803204i
\(915\) 74.9811 2.47880
\(916\) 18.8792 32.6997i 0.623785 1.08043i
\(917\) 65.5368 2.16422
\(918\) 6.68601 + 11.5805i 0.220671 + 0.382214i
\(919\) −40.6474 −1.34083 −0.670416 0.741985i \(-0.733885\pi\)
−0.670416 + 0.741985i \(0.733885\pi\)
\(920\) 0.413976 + 0.717028i 0.0136484 + 0.0236397i
\(921\) 4.36241 + 7.55592i 0.143746 + 0.248976i
\(922\) 21.2171 0.698748
\(923\) −10.2318 8.46272i −0.336785 0.278554i
\(924\) −8.61575 14.9229i −0.283437 0.490928i
\(925\) −5.75043 9.96004i −0.189073 0.327484i
\(926\) −6.04162 + 10.4644i −0.198540 + 0.343881i
\(927\) −16.2091 + 28.0749i −0.532376 + 0.922102i
\(928\) −42.7951 −1.40482
\(929\) −3.43047 5.94174i −0.112550 0.194942i 0.804248 0.594294i \(-0.202568\pi\)
−0.916798 + 0.399352i \(0.869235\pi\)
\(930\) −31.7800 + 24.2774i −1.04211 + 0.796089i
\(931\) 17.9099 0.586974
\(932\) −12.6131 21.8466i −0.413156 0.715608i
\(933\) −5.06601 −0.165854
\(934\) 5.53442 9.58590i 0.181092 0.313660i
\(935\) −1.41769 + 2.45551i −0.0463635 + 0.0803039i
\(936\) −51.5657 42.6498i −1.68548 1.39405i
\(937\) −0.765487 1.32586i −0.0250074 0.0433141i 0.853251 0.521501i \(-0.174628\pi\)
−0.878258 + 0.478187i \(0.841294\pi\)
\(938\) 4.03851 6.99491i 0.131862 0.228392i
\(939\) 31.8886 + 55.2326i 1.04064 + 1.80245i
\(940\) −42.1067 −1.37337
\(941\) 8.75241 15.1596i 0.285321 0.494190i −0.687366 0.726311i \(-0.741233\pi\)
0.972687 + 0.232121i \(0.0745666\pi\)
\(942\) 7.14356 12.3730i 0.232750 0.403134i
\(943\) −1.14594 −0.0373171
\(944\) 0.0547137 + 0.0947669i 0.00178078 + 0.00308440i
\(945\) 117.237 + 203.060i 3.81371 + 6.60555i
\(946\) −0.0319763 + 0.0553846i −0.00103964 + 0.00180071i
\(947\) 30.5337 0.992211 0.496106 0.868262i \(-0.334763\pi\)
0.496106 + 0.868262i \(0.334763\pi\)
\(948\) 32.1652 55.7118i 1.04468 1.80944i
\(949\) −3.63032 + 1.35053i −0.117845 + 0.0438402i
\(950\) −1.65620 + 2.86862i −0.0537342 + 0.0930703i
\(951\) −22.7001 39.3178i −0.736102 1.27497i
\(952\) 8.07902 + 13.9933i 0.261843 + 0.453525i
\(953\) 5.40468 + 9.36117i 0.175075 + 0.303238i 0.940187 0.340658i \(-0.110650\pi\)
−0.765112 + 0.643897i \(0.777317\pi\)
\(954\) 2.76014 + 4.78070i 0.0893627 + 0.154781i
\(955\) −20.8617 + 36.1336i −0.675069 + 1.16925i
\(956\) 5.13676 0.166135
\(957\) 16.5850 0.536118
\(958\) −6.32298 + 10.9517i −0.204286 + 0.353834i
\(959\) 40.8144 70.6926i 1.31797 2.28278i
\(960\) 7.87249 13.6355i 0.254083 0.440085i
\(961\) −29.9779 + 7.89474i −0.967028 + 0.254669i
\(962\) −5.56362 + 2.06975i −0.179378 + 0.0667315i
\(963\) −12.8204 −0.413131
\(964\) −42.4845 −1.36833
\(965\) −20.2674 + 35.1041i −0.652430 + 1.13004i
\(966\) −1.23340 −0.0396839
\(967\) −1.94762 3.37338i −0.0626313 0.108481i 0.833010 0.553259i \(-0.186616\pi\)
−0.895641 + 0.444778i \(0.853283\pi\)
\(968\) −12.9593 + 22.4461i −0.416527 + 0.721446i
\(969\) 2.01366 + 3.48776i 0.0646881 + 0.112043i
\(970\) 9.28343 16.0794i 0.298073 0.516277i
\(971\) 32.9719 1.05812 0.529059 0.848585i \(-0.322545\pi\)
0.529059 + 0.848585i \(0.322545\pi\)
\(972\) −28.1427 48.7445i −0.902677 1.56348i
\(973\) 81.8554 2.62416
\(974\) 5.18532 8.98124i 0.166148 0.287777i
\(975\) −9.57725 + 56.6600i −0.306717 + 1.81457i
\(976\) −9.38250 −0.300327
\(977\) 21.1583 36.6472i 0.676913 1.17245i −0.298993 0.954255i \(-0.596651\pi\)
0.975906 0.218193i \(-0.0700161\pi\)
\(978\) −0.656878 −0.0210046
\(979\) 0.0623634 0.00199314
\(980\) 44.2527 + 76.6479i 1.41360 + 2.44843i
\(981\) −71.9301 −2.29655
\(982\) −22.2803 −0.710992
\(983\) 24.6411 42.6796i 0.785929 1.36127i −0.142514 0.989793i \(-0.545519\pi\)
0.928443 0.371476i \(-0.121148\pi\)
\(984\) 42.9509 + 74.3932i 1.36923 + 2.37157i
\(985\) −32.7017 −1.04196
\(986\) −6.67944 −0.212717
\(987\) 73.0231 126.480i 2.32435 4.02589i
\(988\) −4.01271 3.31889i −0.127661 0.105588i
\(989\) −0.00697127 0.0120746i −0.000221674 0.000383950i
\(990\) −5.80096 + 10.0476i −0.184367 + 0.319332i
\(991\) 28.5787 49.4998i 0.907833 1.57241i 0.0907640 0.995872i \(-0.471069\pi\)
0.817069 0.576540i \(-0.195598\pi\)
\(992\) 25.7876 19.6997i 0.818756 0.625465i
\(993\) −78.6347 −2.49540
\(994\) 6.55949 + 11.3614i 0.208054 + 0.360361i
\(995\) 13.5529 23.4743i 0.429656 0.744187i
\(996\) −46.8085 −1.48318
\(997\) −6.10206 −0.193254 −0.0966271 0.995321i \(-0.530805\pi\)
−0.0966271 + 0.995321i \(0.530805\pi\)
\(998\) 0.375128 0.0118745
\(999\) −34.4209 −1.08903
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.g.a.87.15 yes 70
13.3 even 3 403.2.e.a.211.15 yes 70
31.5 even 3 403.2.e.a.191.15 70
403.315 even 3 inner 403.2.g.a.315.15 yes 70
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.e.a.191.15 70 31.5 even 3
403.2.e.a.211.15 yes 70 13.3 even 3
403.2.g.a.87.15 yes 70 1.1 even 1 trivial
403.2.g.a.315.15 yes 70 403.315 even 3 inner