Properties

Label 731.2.e.b.307.19
Level $731$
Weight $2$
Character 731.307
Analytic conductor $5.837$
Analytic rank $0$
Dimension $58$
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] = [731,2,Mod(307,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.e (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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.19
Character \(\chi\) \(=\) 731.307
Dual form 731.2.e.b.681.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.34037 q^{2} +(-0.719541 + 1.24628i) q^{3} -0.203418 q^{4} +(2.16961 - 3.75787i) q^{5} +(-0.964449 + 1.67047i) q^{6} +(-1.07792 - 1.86701i) q^{7} -2.95339 q^{8} +(0.464522 + 0.804575i) q^{9} +O(q^{10})\) \(q+1.34037 q^{2} +(-0.719541 + 1.24628i) q^{3} -0.203418 q^{4} +(2.16961 - 3.75787i) q^{5} +(-0.964449 + 1.67047i) q^{6} +(-1.07792 - 1.86701i) q^{7} -2.95339 q^{8} +(0.464522 + 0.804575i) q^{9} +(2.90807 - 5.03692i) q^{10} -4.35461 q^{11} +(0.146367 - 0.253516i) q^{12} +(-2.54109 - 4.40129i) q^{13} +(-1.44480 - 2.50247i) q^{14} +(3.12224 + 5.40788i) q^{15} -3.55179 q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.622629 + 1.07843i) q^{18} +(-0.476959 + 0.826117i) q^{19} +(-0.441337 + 0.764418i) q^{20} +3.10242 q^{21} -5.83677 q^{22} +(0.518993 - 0.898922i) q^{23} +(2.12508 - 3.68075i) q^{24} +(-6.91440 - 11.9761i) q^{25} +(-3.40599 - 5.89934i) q^{26} -5.65422 q^{27} +(0.219267 + 0.379782i) q^{28} +(3.28660 + 5.69256i) q^{29} +(4.18495 + 7.24855i) q^{30} +(-0.897787 + 1.55501i) q^{31} +1.14608 q^{32} +(3.13332 - 5.42706i) q^{33} +(-0.670183 - 1.16079i) q^{34} -9.35462 q^{35} +(-0.0944919 - 0.163665i) q^{36} +(1.28100 - 2.21875i) q^{37} +(-0.639300 + 1.10730i) q^{38} +7.31366 q^{39} +(-6.40769 + 11.0984i) q^{40} +10.9569 q^{41} +4.15838 q^{42} +(4.03207 - 5.17131i) q^{43} +0.885804 q^{44} +4.03132 q^{45} +(0.695641 - 1.20489i) q^{46} +2.71691 q^{47} +(2.55566 - 4.42652i) q^{48} +(1.17619 - 2.03723i) q^{49} +(-9.26783 - 16.0523i) q^{50} +1.43908 q^{51} +(0.516902 + 0.895300i) q^{52} +(5.32875 - 9.22967i) q^{53} -7.57872 q^{54} +(-9.44779 + 16.3640i) q^{55} +(3.18350 + 5.51399i) q^{56} +(-0.686383 - 1.18885i) q^{57} +(4.40525 + 7.63012i) q^{58} -10.9632 q^{59} +(-0.635120 - 1.10006i) q^{60} +(3.94784 + 6.83786i) q^{61} +(-1.20336 + 2.08429i) q^{62} +(1.00143 - 1.73453i) q^{63} +8.63974 q^{64} -22.0526 q^{65} +(4.19979 - 7.27425i) q^{66} +(2.80430 - 4.85718i) q^{67} +(0.101709 + 0.176165i) q^{68} +(0.746873 + 1.29362i) q^{69} -12.5386 q^{70} +(0.806022 + 1.39607i) q^{71} +(-1.37191 - 2.37622i) q^{72} +(-0.802311 - 1.38964i) q^{73} +(1.71700 - 2.97394i) q^{74} +19.9008 q^{75} +(0.0970219 - 0.168047i) q^{76} +(4.69390 + 8.13007i) q^{77} +9.80299 q^{78} +(-1.85195 - 3.20767i) q^{79} +(-7.70598 + 13.3472i) q^{80} +(2.67487 - 4.63302i) q^{81} +14.6863 q^{82} +(4.52149 - 7.83144i) q^{83} -0.631087 q^{84} -4.33922 q^{85} +(5.40445 - 6.93145i) q^{86} -9.45938 q^{87} +12.8608 q^{88} +(-2.13561 + 3.69898i) q^{89} +5.40345 q^{90} +(-5.47815 + 9.48844i) q^{91} +(-0.105572 + 0.182857i) q^{92} +(-1.29199 - 2.23779i) q^{93} +3.64165 q^{94} +(2.06963 + 3.58470i) q^{95} +(-0.824651 + 1.42834i) q^{96} -10.4038 q^{97} +(1.57653 - 2.73063i) q^{98} +(-2.02281 - 3.50361i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34037 0.947782 0.473891 0.880583i \(-0.342849\pi\)
0.473891 + 0.880583i \(0.342849\pi\)
\(3\) −0.719541 + 1.24628i −0.415427 + 0.719541i −0.995473 0.0950428i \(-0.969701\pi\)
0.580046 + 0.814584i \(0.303035\pi\)
\(4\) −0.203418 −0.101709
\(5\) 2.16961 3.75787i 0.970278 1.68057i 0.275567 0.961282i \(-0.411134\pi\)
0.694711 0.719289i \(-0.255532\pi\)
\(6\) −0.964449 + 1.67047i −0.393734 + 0.681968i
\(7\) −1.07792 1.86701i −0.407414 0.705662i 0.587185 0.809453i \(-0.300236\pi\)
−0.994599 + 0.103791i \(0.966903\pi\)
\(8\) −2.95339 −1.04418
\(9\) 0.464522 + 0.804575i 0.154841 + 0.268192i
\(10\) 2.90807 5.03692i 0.919612 1.59282i
\(11\) −4.35461 −1.31296 −0.656481 0.754342i \(-0.727956\pi\)
−0.656481 + 0.754342i \(0.727956\pi\)
\(12\) 0.146367 0.253516i 0.0422526 0.0731837i
\(13\) −2.54109 4.40129i −0.704771 1.22070i −0.966774 0.255631i \(-0.917717\pi\)
0.262004 0.965067i \(-0.415617\pi\)
\(14\) −1.44480 2.50247i −0.386140 0.668813i
\(15\) 3.12224 + 5.40788i 0.806160 + 1.39631i
\(16\) −3.55179 −0.887946
\(17\) −0.500000 0.866025i −0.121268 0.210042i
\(18\) 0.622629 + 1.07843i 0.146755 + 0.254187i
\(19\) −0.476959 + 0.826117i −0.109422 + 0.189524i −0.915536 0.402236i \(-0.868233\pi\)
0.806114 + 0.591760i \(0.201567\pi\)
\(20\) −0.441337 + 0.764418i −0.0986859 + 0.170929i
\(21\) 3.10242 0.677003
\(22\) −5.83677 −1.24440
\(23\) 0.518993 0.898922i 0.108218 0.187438i −0.806831 0.590783i \(-0.798819\pi\)
0.915048 + 0.403345i \(0.132152\pi\)
\(24\) 2.12508 3.68075i 0.433781 0.751330i
\(25\) −6.91440 11.9761i −1.38288 2.39522i
\(26\) −3.40599 5.89934i −0.667969 1.15696i
\(27\) −5.65422 −1.08815
\(28\) 0.219267 + 0.379782i 0.0414376 + 0.0717720i
\(29\) 3.28660 + 5.69256i 0.610307 + 1.05708i 0.991189 + 0.132459i \(0.0422872\pi\)
−0.380882 + 0.924624i \(0.624379\pi\)
\(30\) 4.18495 + 7.24855i 0.764064 + 1.32340i
\(31\) −0.897787 + 1.55501i −0.161247 + 0.279288i −0.935316 0.353813i \(-0.884885\pi\)
0.774069 + 0.633101i \(0.218218\pi\)
\(32\) 1.14608 0.202600
\(33\) 3.13332 5.42706i 0.545440 0.944731i
\(34\) −0.670183 1.16079i −0.114935 0.199074i
\(35\) −9.35462 −1.58122
\(36\) −0.0944919 0.163665i −0.0157487 0.0272775i
\(37\) 1.28100 2.21875i 0.210594 0.364760i −0.741306 0.671167i \(-0.765793\pi\)
0.951901 + 0.306407i \(0.0991267\pi\)
\(38\) −0.639300 + 1.10730i −0.103708 + 0.179628i
\(39\) 7.31366 1.17112
\(40\) −6.40769 + 11.0984i −1.01315 + 1.75482i
\(41\) 10.9569 1.71119 0.855594 0.517648i \(-0.173192\pi\)
0.855594 + 0.517648i \(0.173192\pi\)
\(42\) 4.15838 0.641652
\(43\) 4.03207 5.17131i 0.614884 0.788617i
\(44\) 0.885804 0.133540
\(45\) 4.03132 0.600954
\(46\) 0.695641 1.20489i 0.102567 0.177651i
\(47\) 2.71691 0.396302 0.198151 0.980172i \(-0.436506\pi\)
0.198151 + 0.980172i \(0.436506\pi\)
\(48\) 2.55566 4.42652i 0.368877 0.638914i
\(49\) 1.17619 2.03723i 0.168028 0.291033i
\(50\) −9.26783 16.0523i −1.31067 2.27014i
\(51\) 1.43908 0.201512
\(52\) 0.516902 + 0.895300i 0.0716814 + 0.124156i
\(53\) 5.32875 9.22967i 0.731960 1.26779i −0.224084 0.974570i \(-0.571939\pi\)
0.956044 0.293223i \(-0.0947277\pi\)
\(54\) −7.57872 −1.03133
\(55\) −9.44779 + 16.3640i −1.27394 + 2.20653i
\(56\) 3.18350 + 5.51399i 0.425413 + 0.736838i
\(57\) −0.686383 1.18885i −0.0909136 0.157467i
\(58\) 4.40525 + 7.63012i 0.578438 + 1.00188i
\(59\) −10.9632 −1.42728 −0.713642 0.700511i \(-0.752956\pi\)
−0.713642 + 0.700511i \(0.752956\pi\)
\(60\) −0.635120 1.10006i −0.0819936 0.142017i
\(61\) 3.94784 + 6.83786i 0.505469 + 0.875498i 0.999980 + 0.00632695i \(0.00201395\pi\)
−0.494511 + 0.869172i \(0.664653\pi\)
\(62\) −1.20336 + 2.08429i −0.152827 + 0.264705i
\(63\) 1.00143 1.73453i 0.126168 0.218530i
\(64\) 8.63974 1.07997
\(65\) −22.0526 −2.73529
\(66\) 4.19979 7.27425i 0.516959 0.895399i
\(67\) 2.80430 4.85718i 0.342599 0.593400i −0.642315 0.766441i \(-0.722026\pi\)
0.984915 + 0.173041i \(0.0553593\pi\)
\(68\) 0.101709 + 0.176165i 0.0123340 + 0.0213631i
\(69\) 0.746873 + 1.29362i 0.0899130 + 0.155734i
\(70\) −12.5386 −1.49865
\(71\) 0.806022 + 1.39607i 0.0956572 + 0.165683i 0.909883 0.414866i \(-0.136171\pi\)
−0.814225 + 0.580549i \(0.802838\pi\)
\(72\) −1.37191 2.37622i −0.161681 0.280040i
\(73\) −0.802311 1.38964i −0.0939034 0.162646i 0.815247 0.579113i \(-0.196601\pi\)
−0.909150 + 0.416468i \(0.863268\pi\)
\(74\) 1.71700 2.97394i 0.199598 0.345713i
\(75\) 19.9008 2.29794
\(76\) 0.0970219 0.168047i 0.0111292 0.0192763i
\(77\) 4.69390 + 8.13007i 0.534919 + 0.926507i
\(78\) 9.80299 1.10997
\(79\) −1.85195 3.20767i −0.208360 0.360891i 0.742838 0.669471i \(-0.233479\pi\)
−0.951198 + 0.308581i \(0.900146\pi\)
\(80\) −7.70598 + 13.3472i −0.861555 + 1.49226i
\(81\) 2.67487 4.63302i 0.297208 0.514780i
\(82\) 14.6863 1.62183
\(83\) 4.52149 7.83144i 0.496298 0.859613i −0.503693 0.863883i \(-0.668026\pi\)
0.999991 + 0.00426984i \(0.00135914\pi\)
\(84\) −0.631087 −0.0688572
\(85\) −4.33922 −0.470654
\(86\) 5.40445 6.93145i 0.582776 0.747438i
\(87\) −9.45938 −1.01415
\(88\) 12.8608 1.37097
\(89\) −2.13561 + 3.69898i −0.226374 + 0.392091i −0.956731 0.290975i \(-0.906020\pi\)
0.730357 + 0.683066i \(0.239354\pi\)
\(90\) 5.40345 0.569573
\(91\) −5.47815 + 9.48844i −0.574267 + 0.994659i
\(92\) −0.105572 + 0.182857i −0.0110067 + 0.0190641i
\(93\) −1.29199 2.23779i −0.133973 0.232048i
\(94\) 3.64165 0.375608
\(95\) 2.06963 + 3.58470i 0.212339 + 0.367782i
\(96\) −0.824651 + 1.42834i −0.0841656 + 0.145779i
\(97\) −10.4038 −1.05635 −0.528174 0.849136i \(-0.677123\pi\)
−0.528174 + 0.849136i \(0.677123\pi\)
\(98\) 1.57653 2.73063i 0.159254 0.275836i
\(99\) −2.02281 3.50361i −0.203300 0.352126i
\(100\) 1.40651 + 2.43615i 0.140651 + 0.243615i
\(101\) 1.51800 + 2.62926i 0.151047 + 0.261621i 0.931613 0.363453i \(-0.118402\pi\)
−0.780566 + 0.625074i \(0.785069\pi\)
\(102\) 1.92890 0.190989
\(103\) 8.32473 + 14.4189i 0.820260 + 1.42073i 0.905488 + 0.424371i \(0.139505\pi\)
−0.0852282 + 0.996361i \(0.527162\pi\)
\(104\) 7.50481 + 12.9987i 0.735907 + 1.27463i
\(105\) 6.73103 11.6585i 0.656881 1.13775i
\(106\) 7.14248 12.3711i 0.693739 1.20159i
\(107\) −14.3054 −1.38296 −0.691479 0.722396i \(-0.743041\pi\)
−0.691479 + 0.722396i \(0.743041\pi\)
\(108\) 1.15017 0.110675
\(109\) 3.64210 6.30831i 0.348850 0.604226i −0.637195 0.770702i \(-0.719906\pi\)
0.986045 + 0.166476i \(0.0532389\pi\)
\(110\) −12.6635 + 21.9338i −1.20742 + 2.09131i
\(111\) 1.84346 + 3.19296i 0.174973 + 0.303063i
\(112\) 3.82853 + 6.63120i 0.361762 + 0.626590i
\(113\) 0.636898 0.0599144 0.0299572 0.999551i \(-0.490463\pi\)
0.0299572 + 0.999551i \(0.490463\pi\)
\(114\) −0.920004 1.59349i −0.0861663 0.149244i
\(115\) −2.25202 3.90062i −0.210002 0.363734i
\(116\) −0.668553 1.15797i −0.0620736 0.107515i
\(117\) 2.36078 4.08899i 0.218254 0.378027i
\(118\) −14.6947 −1.35275
\(119\) −1.07792 + 1.86701i −0.0988124 + 0.171148i
\(120\) −9.22119 15.9716i −0.841776 1.45800i
\(121\) 7.96259 0.723872
\(122\) 5.29155 + 9.16524i 0.479075 + 0.829782i
\(123\) −7.88397 + 13.6554i −0.710874 + 1.23127i
\(124\) 0.182626 0.316317i 0.0164003 0.0284061i
\(125\) −38.3100 −3.42655
\(126\) 1.34228 2.32490i 0.119580 0.207119i
\(127\) −6.97708 −0.619115 −0.309558 0.950881i \(-0.600181\pi\)
−0.309558 + 0.950881i \(0.600181\pi\)
\(128\) 9.28826 0.820974
\(129\) 3.54367 + 8.74606i 0.312003 + 0.770047i
\(130\) −29.5586 −2.59246
\(131\) 9.74079 0.851057 0.425528 0.904945i \(-0.360088\pi\)
0.425528 + 0.904945i \(0.360088\pi\)
\(132\) −0.637372 + 1.10396i −0.0554761 + 0.0960875i
\(133\) 2.05649 0.178320
\(134\) 3.75879 6.51041i 0.324710 0.562414i
\(135\) −12.2674 + 21.2478i −1.05581 + 1.82872i
\(136\) 1.47669 + 2.55771i 0.126625 + 0.219322i
\(137\) −1.76816 −0.151064 −0.0755321 0.997143i \(-0.524066\pi\)
−0.0755321 + 0.997143i \(0.524066\pi\)
\(138\) 1.00108 + 1.73393i 0.0852179 + 0.147602i
\(139\) −6.70923 + 11.6207i −0.569069 + 0.985657i 0.427589 + 0.903973i \(0.359363\pi\)
−0.996658 + 0.0816836i \(0.973970\pi\)
\(140\) 1.90290 0.160824
\(141\) −1.95493 + 3.38603i −0.164634 + 0.285155i
\(142\) 1.08036 + 1.87125i 0.0906622 + 0.157032i
\(143\) 11.0654 + 19.1659i 0.925338 + 1.60273i
\(144\) −1.64988 2.85768i −0.137490 0.238140i
\(145\) 28.5226 2.36867
\(146\) −1.07539 1.86263i −0.0890000 0.154153i
\(147\) 1.69264 + 2.93174i 0.139607 + 0.241806i
\(148\) −0.260577 + 0.451333i −0.0214193 + 0.0370993i
\(149\) −9.02044 + 15.6239i −0.738983 + 1.27996i 0.213971 + 0.976840i \(0.431360\pi\)
−0.952954 + 0.303116i \(0.901973\pi\)
\(150\) 26.6743 2.17795
\(151\) 19.3015 1.57073 0.785366 0.619032i \(-0.212475\pi\)
0.785366 + 0.619032i \(0.212475\pi\)
\(152\) 1.40864 2.43984i 0.114256 0.197897i
\(153\) 0.464522 0.804575i 0.0375544 0.0650460i
\(154\) 6.29154 + 10.8973i 0.506987 + 0.878127i
\(155\) 3.89569 + 6.74753i 0.312909 + 0.541975i
\(156\) −1.48773 −0.119114
\(157\) −5.91251 10.2408i −0.471870 0.817303i 0.527612 0.849485i \(-0.323087\pi\)
−0.999482 + 0.0321827i \(0.989754\pi\)
\(158\) −2.48229 4.29945i −0.197480 0.342046i
\(159\) 7.66851 + 13.2822i 0.608152 + 1.05335i
\(160\) 2.48654 4.30682i 0.196579 0.340484i
\(161\) −2.23772 −0.176357
\(162\) 3.58531 6.20994i 0.281689 0.487899i
\(163\) 3.57678 + 6.19517i 0.280155 + 0.485243i 0.971423 0.237356i \(-0.0762807\pi\)
−0.691268 + 0.722599i \(0.742947\pi\)
\(164\) −2.22884 −0.174043
\(165\) −13.5961 23.5492i −1.05846 1.83330i
\(166\) 6.06045 10.4970i 0.470382 0.814726i
\(167\) 0.362695 0.628206i 0.0280662 0.0486120i −0.851651 0.524109i \(-0.824398\pi\)
0.879717 + 0.475497i \(0.157732\pi\)
\(168\) −9.16264 −0.706913
\(169\) −6.41424 + 11.1098i −0.493403 + 0.854599i
\(170\) −5.81614 −0.446078
\(171\) −0.886231 −0.0677718
\(172\) −0.820194 + 1.05194i −0.0625392 + 0.0802094i
\(173\) −10.6906 −0.812790 −0.406395 0.913697i \(-0.633214\pi\)
−0.406395 + 0.913697i \(0.633214\pi\)
\(174\) −12.6790 −0.961195
\(175\) −14.9063 + 25.8184i −1.12681 + 1.95169i
\(176\) 15.4666 1.16584
\(177\) 7.88845 13.6632i 0.592932 1.02699i
\(178\) −2.86249 + 4.95799i −0.214553 + 0.371617i
\(179\) −10.9988 19.0505i −0.822090 1.42390i −0.904123 0.427272i \(-0.859475\pi\)
0.0820335 0.996630i \(-0.473859\pi\)
\(180\) −0.820042 −0.0611223
\(181\) −7.97236 13.8085i −0.592580 1.02638i −0.993883 0.110434i \(-0.964776\pi\)
0.401303 0.915945i \(-0.368557\pi\)
\(182\) −7.34273 + 12.7180i −0.544280 + 0.942720i
\(183\) −11.3625 −0.839943
\(184\) −1.53279 + 2.65487i −0.112999 + 0.195719i
\(185\) −5.55852 9.62763i −0.408670 0.707838i
\(186\) −1.73174 2.99946i −0.126977 0.219931i
\(187\) 2.17730 + 3.77120i 0.159220 + 0.275777i
\(188\) −0.552667 −0.0403074
\(189\) 6.09477 + 10.5564i 0.443329 + 0.767869i
\(190\) 2.77406 + 4.80481i 0.201251 + 0.348578i
\(191\) 8.96734 15.5319i 0.648854 1.12385i −0.334543 0.942380i \(-0.608582\pi\)
0.983397 0.181467i \(-0.0580847\pi\)
\(192\) −6.21665 + 10.7675i −0.448648 + 0.777081i
\(193\) 12.4557 0.896584 0.448292 0.893887i \(-0.352033\pi\)
0.448292 + 0.893887i \(0.352033\pi\)
\(194\) −13.9449 −1.00119
\(195\) 15.8678 27.4838i 1.13632 1.96816i
\(196\) −0.239259 + 0.414409i −0.0170899 + 0.0296006i
\(197\) −10.1245 17.5361i −0.721338 1.24939i −0.960464 0.278406i \(-0.910194\pi\)
0.239125 0.970989i \(-0.423139\pi\)
\(198\) −2.71130 4.69612i −0.192684 0.333739i
\(199\) 4.75936 0.337382 0.168691 0.985669i \(-0.446046\pi\)
0.168691 + 0.985669i \(0.446046\pi\)
\(200\) 20.4209 + 35.3700i 1.44397 + 2.50104i
\(201\) 4.03561 + 6.98989i 0.284650 + 0.493029i
\(202\) 2.03468 + 3.52417i 0.143160 + 0.247960i
\(203\) 7.08536 12.2722i 0.497295 0.861340i
\(204\) −0.292735 −0.0204955
\(205\) 23.7723 41.1748i 1.66033 2.87577i
\(206\) 11.1582 + 19.3266i 0.777428 + 1.34654i
\(207\) 0.964334 0.0670258
\(208\) 9.02539 + 15.6324i 0.625798 + 1.08391i
\(209\) 2.07697 3.59741i 0.143667 0.248838i
\(210\) 9.02205 15.6266i 0.622580 1.07834i
\(211\) 6.59363 0.453924 0.226962 0.973904i \(-0.427121\pi\)
0.226962 + 0.973904i \(0.427121\pi\)
\(212\) −1.08396 + 1.87748i −0.0744468 + 0.128946i
\(213\) −2.31986 −0.158954
\(214\) −19.1745 −1.31074
\(215\) −10.6851 26.3717i −0.728719 1.79853i
\(216\) 16.6991 1.13623
\(217\) 3.87095 0.262777
\(218\) 4.88175 8.45544i 0.330634 0.572675i
\(219\) 2.30918 0.156040
\(220\) 1.92185 3.32874i 0.129571 0.224423i
\(221\) −2.54109 + 4.40129i −0.170932 + 0.296063i
\(222\) 2.47091 + 4.27974i 0.165837 + 0.287237i
\(223\) −1.90792 −0.127764 −0.0638819 0.997957i \(-0.520348\pi\)
−0.0638819 + 0.997957i \(0.520348\pi\)
\(224\) −1.23538 2.13974i −0.0825421 0.142967i
\(225\) 6.42377 11.1263i 0.428252 0.741754i
\(226\) 0.853677 0.0567858
\(227\) 4.79418 8.30376i 0.318201 0.551140i −0.661912 0.749582i \(-0.730255\pi\)
0.980113 + 0.198442i \(0.0635880\pi\)
\(228\) 0.139622 + 0.241833i 0.00924672 + 0.0160158i
\(229\) 8.75644 + 15.1666i 0.578642 + 1.00224i 0.995635 + 0.0933273i \(0.0297503\pi\)
−0.416994 + 0.908909i \(0.636916\pi\)
\(230\) −3.01854 5.22826i −0.199036 0.344741i
\(231\) −13.5098 −0.888880
\(232\) −9.70661 16.8123i −0.637270 1.10378i
\(233\) 7.32426 + 12.6860i 0.479828 + 0.831087i 0.999732 0.0231376i \(-0.00736558\pi\)
−0.519904 + 0.854225i \(0.674032\pi\)
\(234\) 3.16431 5.48074i 0.206857 0.358287i
\(235\) 5.89462 10.2098i 0.384523 0.666013i
\(236\) 2.23010 0.145167
\(237\) 5.33021 0.346234
\(238\) −1.44480 + 2.50247i −0.0936526 + 0.162211i
\(239\) 2.64507 4.58139i 0.171095 0.296345i −0.767708 0.640800i \(-0.778603\pi\)
0.938803 + 0.344455i \(0.111936\pi\)
\(240\) −11.0895 19.2076i −0.715827 1.23985i
\(241\) −7.63513 13.2244i −0.491822 0.851860i 0.508134 0.861278i \(-0.330336\pi\)
−0.999956 + 0.00941781i \(0.997002\pi\)
\(242\) 10.6728 0.686073
\(243\) −4.63196 8.02279i −0.297140 0.514662i
\(244\) −0.803061 1.39094i −0.0514107 0.0890460i
\(245\) −5.10376 8.83998i −0.326067 0.564765i
\(246\) −10.5674 + 18.3033i −0.673754 + 1.16698i
\(247\) 4.84797 0.308469
\(248\) 2.65151 4.59255i 0.168371 0.291627i
\(249\) 6.50679 + 11.2701i 0.412351 + 0.714213i
\(250\) −51.3495 −3.24763
\(251\) −2.47162 4.28098i −0.156007 0.270213i 0.777418 0.628984i \(-0.216529\pi\)
−0.933425 + 0.358772i \(0.883196\pi\)
\(252\) −0.203709 + 0.352834i −0.0128324 + 0.0222264i
\(253\) −2.26001 + 3.91445i −0.142086 + 0.246099i
\(254\) −9.35184 −0.586787
\(255\) 3.12224 5.40788i 0.195522 0.338655i
\(256\) −4.82981 −0.301863
\(257\) 3.26185 0.203469 0.101734 0.994812i \(-0.467561\pi\)
0.101734 + 0.994812i \(0.467561\pi\)
\(258\) 4.74982 + 11.7229i 0.295711 + 0.729837i
\(259\) −5.52322 −0.343196
\(260\) 4.48590 0.278204
\(261\) −3.05340 + 5.28864i −0.189001 + 0.327359i
\(262\) 13.0562 0.806616
\(263\) 15.4307 26.7268i 0.951500 1.64805i 0.209317 0.977848i \(-0.432876\pi\)
0.742182 0.670198i \(-0.233791\pi\)
\(264\) −9.25390 + 16.0282i −0.569538 + 0.986469i
\(265\) −23.1226 40.0495i −1.42041 2.46022i
\(266\) 2.75644 0.169008
\(267\) −3.07331 5.32313i −0.188084 0.325770i
\(268\) −0.570444 + 0.988037i −0.0348454 + 0.0603540i
\(269\) 9.82089 0.598790 0.299395 0.954129i \(-0.403215\pi\)
0.299395 + 0.954129i \(0.403215\pi\)
\(270\) −16.4429 + 28.4799i −1.00068 + 1.73323i
\(271\) −4.93949 8.55545i −0.300053 0.519707i 0.676095 0.736815i \(-0.263671\pi\)
−0.976148 + 0.217108i \(0.930338\pi\)
\(272\) 1.77589 + 3.07594i 0.107679 + 0.186506i
\(273\) −7.88351 13.6546i −0.477132 0.826417i
\(274\) −2.36998 −0.143176
\(275\) 30.1095 + 52.1511i 1.81567 + 3.14483i
\(276\) −0.151927 0.263146i −0.00914495 0.0158395i
\(277\) −9.40910 + 16.2970i −0.565338 + 0.979194i 0.431680 + 0.902027i \(0.357921\pi\)
−0.997018 + 0.0771673i \(0.975412\pi\)
\(278\) −8.99282 + 15.5760i −0.539354 + 0.934188i
\(279\) −1.66817 −0.0998705
\(280\) 27.6278 1.65108
\(281\) 7.91428 13.7079i 0.472126 0.817747i −0.527365 0.849639i \(-0.676820\pi\)
0.999491 + 0.0318920i \(0.0101532\pi\)
\(282\) −2.62032 + 4.53852i −0.156038 + 0.270265i
\(283\) 2.70722 + 4.68904i 0.160928 + 0.278735i 0.935202 0.354116i \(-0.115218\pi\)
−0.774274 + 0.632850i \(0.781885\pi\)
\(284\) −0.163959 0.283986i −0.00972919 0.0168514i
\(285\) −5.95673 −0.352846
\(286\) 14.8317 + 25.6893i 0.877018 + 1.51904i
\(287\) −11.8107 20.4567i −0.697162 1.20752i
\(288\) 0.532379 + 0.922107i 0.0313707 + 0.0543357i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 38.2307 2.24498
\(291\) 7.48597 12.9661i 0.438836 0.760085i
\(292\) 0.163204 + 0.282678i 0.00955081 + 0.0165425i
\(293\) 28.1036 1.64183 0.820914 0.571052i \(-0.193465\pi\)
0.820914 + 0.571052i \(0.193465\pi\)
\(294\) 2.26876 + 3.92961i 0.132317 + 0.229179i
\(295\) −23.7858 + 41.1982i −1.38486 + 2.39865i
\(296\) −3.78328 + 6.55283i −0.219899 + 0.380875i
\(297\) 24.6219 1.42871
\(298\) −12.0907 + 20.9417i −0.700395 + 1.21312i
\(299\) −5.27522 −0.305074
\(300\) −4.04817 −0.233721
\(301\) −14.0011 1.95365i −0.807009 0.112607i
\(302\) 25.8710 1.48871
\(303\) −4.36906 −0.250996
\(304\) 1.69406 2.93419i 0.0971607 0.168287i
\(305\) 34.2611 1.96178
\(306\) 0.622629 1.07843i 0.0355933 0.0616495i
\(307\) −4.40471 + 7.62919i −0.251390 + 0.435421i −0.963909 0.266233i \(-0.914221\pi\)
0.712519 + 0.701653i \(0.247554\pi\)
\(308\) −0.954822 1.65380i −0.0544060 0.0942340i
\(309\) −23.9599 −1.36303
\(310\) 5.22165 + 9.04417i 0.296570 + 0.513674i
\(311\) −10.1821 + 17.6359i −0.577374 + 1.00004i 0.418405 + 0.908260i \(0.362589\pi\)
−0.995779 + 0.0917805i \(0.970744\pi\)
\(312\) −21.6001 −1.22286
\(313\) 6.34778 10.9947i 0.358798 0.621456i −0.628962 0.777436i \(-0.716520\pi\)
0.987760 + 0.155980i \(0.0498534\pi\)
\(314\) −7.92493 13.7264i −0.447230 0.774625i
\(315\) −4.34542 7.52649i −0.244837 0.424070i
\(316\) 0.376719 + 0.652496i 0.0211921 + 0.0367058i
\(317\) 33.2343 1.86662 0.933311 0.359069i \(-0.116906\pi\)
0.933311 + 0.359069i \(0.116906\pi\)
\(318\) 10.2786 + 17.8031i 0.576396 + 0.998347i
\(319\) −14.3119 24.7889i −0.801310 1.38791i
\(320\) 18.7448 32.4670i 1.04787 1.81496i
\(321\) 10.2933 17.8286i 0.574518 0.995095i
\(322\) −2.99937 −0.167148
\(323\) 0.953918 0.0530774
\(324\) −0.544117 + 0.942438i −0.0302287 + 0.0523577i
\(325\) −35.1402 + 60.8645i −1.94923 + 3.37616i
\(326\) 4.79420 + 8.30380i 0.265526 + 0.459905i
\(327\) 5.24129 + 9.07817i 0.289844 + 0.502024i
\(328\) −32.3601 −1.78679
\(329\) −2.92860 5.07248i −0.161459 0.279655i
\(330\) −18.2238 31.5646i −1.00319 1.73757i
\(331\) 1.63717 + 2.83567i 0.0899872 + 0.155862i 0.907505 0.420040i \(-0.137984\pi\)
−0.817518 + 0.575903i \(0.804651\pi\)
\(332\) −0.919751 + 1.59305i −0.0504779 + 0.0874302i
\(333\) 2.38020 0.130434
\(334\) 0.486144 0.842026i 0.0266006 0.0460736i
\(335\) −12.1684 21.0764i −0.664833 1.15153i
\(336\) −11.0191 −0.601143
\(337\) 1.77204 + 3.06927i 0.0965293 + 0.167194i 0.910246 0.414068i \(-0.135893\pi\)
−0.813717 + 0.581262i \(0.802559\pi\)
\(338\) −8.59743 + 14.8912i −0.467639 + 0.809974i
\(339\) −0.458274 + 0.793755i −0.0248901 + 0.0431108i
\(340\) 0.882673 0.0478697
\(341\) 3.90951 6.77146i 0.211712 0.366695i
\(342\) −1.18787 −0.0642329
\(343\) −20.1622 −1.08866
\(344\) −11.9083 + 15.2729i −0.642050 + 0.823459i
\(345\) 6.48169 0.348962
\(346\) −14.3293 −0.770348
\(347\) −10.7373 + 18.5975i −0.576408 + 0.998369i 0.419479 + 0.907765i \(0.362213\pi\)
−0.995887 + 0.0906034i \(0.971120\pi\)
\(348\) 1.92421 0.103148
\(349\) −8.23099 + 14.2565i −0.440595 + 0.763132i −0.997734 0.0672869i \(-0.978566\pi\)
0.557139 + 0.830419i \(0.311899\pi\)
\(350\) −19.9799 + 34.6062i −1.06797 + 1.84978i
\(351\) 14.3678 + 24.8858i 0.766899 + 1.32831i
\(352\) −4.99073 −0.266007
\(353\) −11.9581 20.7121i −0.636466 1.10239i −0.986202 0.165544i \(-0.947062\pi\)
0.349736 0.936848i \(-0.386271\pi\)
\(354\) 10.5734 18.3137i 0.561971 0.973362i
\(355\) 6.99501 0.371256
\(356\) 0.434420 0.752438i 0.0230242 0.0398791i
\(357\) −1.55121 2.68677i −0.0820987 0.142199i
\(358\) −14.7424 25.5347i −0.779162 1.34955i
\(359\) −4.59779 7.96361i −0.242662 0.420303i 0.718809 0.695207i \(-0.244687\pi\)
−0.961472 + 0.274904i \(0.911354\pi\)
\(360\) −11.9060 −0.627504
\(361\) 9.04502 + 15.6664i 0.476054 + 0.824549i
\(362\) −10.6859 18.5085i −0.561637 0.972784i
\(363\) −5.72941 + 9.92363i −0.300716 + 0.520855i
\(364\) 1.11435 1.93012i 0.0584080 0.101166i
\(365\) −6.96280 −0.364450
\(366\) −15.2300 −0.796083
\(367\) −16.8169 + 29.1278i −0.877838 + 1.52046i −0.0241286 + 0.999709i \(0.507681\pi\)
−0.853709 + 0.520750i \(0.825652\pi\)
\(368\) −1.84335 + 3.19278i −0.0960914 + 0.166435i
\(369\) 5.08974 + 8.81569i 0.264961 + 0.458926i
\(370\) −7.45045 12.9046i −0.387330 0.670876i
\(371\) −22.9758 −1.19284
\(372\) 0.262813 + 0.455206i 0.0136262 + 0.0236013i
\(373\) −7.25065 12.5585i −0.375425 0.650254i 0.614966 0.788554i \(-0.289170\pi\)
−0.990390 + 0.138299i \(0.955836\pi\)
\(374\) 2.91838 + 5.05479i 0.150906 + 0.261377i
\(375\) 27.5656 47.7451i 1.42348 2.46555i
\(376\) −8.02408 −0.413810
\(377\) 16.7031 28.9306i 0.860253 1.49000i
\(378\) 8.16922 + 14.1495i 0.420179 + 0.727772i
\(379\) 21.9952 1.12982 0.564910 0.825153i \(-0.308911\pi\)
0.564910 + 0.825153i \(0.308911\pi\)
\(380\) −0.420999 0.729191i −0.0215968 0.0374067i
\(381\) 5.02029 8.69540i 0.257197 0.445479i
\(382\) 12.0195 20.8184i 0.614972 1.06516i
\(383\) 30.7013 1.56877 0.784383 0.620277i \(-0.212980\pi\)
0.784383 + 0.620277i \(0.212980\pi\)
\(384\) −6.68328 + 11.5758i −0.341055 + 0.590724i
\(385\) 40.7357 2.07608
\(386\) 16.6953 0.849766
\(387\) 6.03369 + 0.841914i 0.306710 + 0.0427969i
\(388\) 2.11632 0.107440
\(389\) −36.7768 −1.86466 −0.932328 0.361614i \(-0.882226\pi\)
−0.932328 + 0.361614i \(0.882226\pi\)
\(390\) 21.2686 36.8384i 1.07698 1.86538i
\(391\) −1.03799 −0.0524932
\(392\) −3.47376 + 6.01673i −0.175451 + 0.303891i
\(393\) −7.00890 + 12.1398i −0.353552 + 0.612370i
\(394\) −13.5705 23.5048i −0.683672 1.18415i
\(395\) −16.0720 −0.808670
\(396\) 0.411475 + 0.712696i 0.0206774 + 0.0358143i
\(397\) −3.96148 + 6.86148i −0.198821 + 0.344368i −0.948146 0.317834i \(-0.897045\pi\)
0.749325 + 0.662202i \(0.230378\pi\)
\(398\) 6.37929 0.319765
\(399\) −1.47973 + 2.56296i −0.0740789 + 0.128308i
\(400\) 24.5585 + 42.5365i 1.22792 + 2.12682i
\(401\) 7.18159 + 12.4389i 0.358631 + 0.621168i 0.987732 0.156156i \(-0.0499101\pi\)
−0.629101 + 0.777324i \(0.716577\pi\)
\(402\) 5.40920 + 9.36901i 0.269786 + 0.467284i
\(403\) 9.12541 0.454569
\(404\) −0.308789 0.534838i −0.0153628 0.0266092i
\(405\) −11.6069 20.1037i −0.576749 0.998959i
\(406\) 9.49698 16.4493i 0.471327 0.816363i
\(407\) −5.57823 + 9.66178i −0.276503 + 0.478917i
\(408\) −4.25017 −0.210415
\(409\) 2.01227 0.0995005 0.0497503 0.998762i \(-0.484157\pi\)
0.0497503 + 0.998762i \(0.484157\pi\)
\(410\) 31.8636 55.1893i 1.57363 2.72561i
\(411\) 1.27226 2.20363i 0.0627562 0.108697i
\(412\) −1.69340 2.93305i −0.0834277 0.144501i
\(413\) 11.8174 + 20.4683i 0.581495 + 1.00718i
\(414\) 1.29256 0.0635259
\(415\) −19.6197 33.9823i −0.963094 1.66813i
\(416\) −2.91229 5.04423i −0.142787 0.247314i
\(417\) −9.65513 16.7232i −0.472814 0.818937i
\(418\) 2.78390 4.82185i 0.136165 0.235844i
\(419\) 14.8728 0.726585 0.363292 0.931675i \(-0.381653\pi\)
0.363292 + 0.931675i \(0.381653\pi\)
\(420\) −1.36921 + 2.37154i −0.0668107 + 0.115719i
\(421\) −15.2612 26.4332i −0.743786 1.28827i −0.950760 0.309928i \(-0.899695\pi\)
0.206974 0.978346i \(-0.433638\pi\)
\(422\) 8.83788 0.430221
\(423\) 1.26206 + 2.18596i 0.0613636 + 0.106285i
\(424\) −15.7379 + 27.2588i −0.764298 + 1.32380i
\(425\) −6.91440 + 11.9761i −0.335397 + 0.580925i
\(426\) −3.10947 −0.150654
\(427\) 8.51088 14.7413i 0.411870 0.713381i
\(428\) 2.90998 0.140659
\(429\) −31.8481 −1.53764
\(430\) −14.3220 35.3477i −0.690667 1.70462i
\(431\) 4.91194 0.236600 0.118300 0.992978i \(-0.462256\pi\)
0.118300 + 0.992978i \(0.462256\pi\)
\(432\) 20.0826 0.966223
\(433\) −18.9320 + 32.7911i −0.909813 + 1.57584i −0.0954890 + 0.995430i \(0.530441\pi\)
−0.814324 + 0.580411i \(0.802892\pi\)
\(434\) 5.18850 0.249056
\(435\) −20.5232 + 35.5471i −0.984010 + 1.70435i
\(436\) −0.740868 + 1.28322i −0.0354812 + 0.0614552i
\(437\) 0.495077 + 0.857498i 0.0236827 + 0.0410197i
\(438\) 3.09515 0.147892
\(439\) −14.8055 25.6439i −0.706630 1.22392i −0.966100 0.258167i \(-0.916881\pi\)
0.259470 0.965751i \(-0.416452\pi\)
\(440\) 27.9030 48.3294i 1.33022 2.30401i
\(441\) 2.18547 0.104070
\(442\) −3.40599 + 5.89934i −0.162006 + 0.280603i
\(443\) 15.7188 + 27.2258i 0.746824 + 1.29354i 0.949338 + 0.314258i \(0.101756\pi\)
−0.202513 + 0.979280i \(0.564911\pi\)
\(444\) −0.374992 0.649505i −0.0177963 0.0308242i
\(445\) 9.26686 + 16.0507i 0.439291 + 0.760874i
\(446\) −2.55731 −0.121092
\(447\) −12.9811 22.4840i −0.613987 1.06346i
\(448\) −9.31291 16.1304i −0.439994 0.762091i
\(449\) −8.20779 + 14.2163i −0.387349 + 0.670909i −0.992092 0.125512i \(-0.959943\pi\)
0.604743 + 0.796421i \(0.293276\pi\)
\(450\) 8.61021 14.9133i 0.405889 0.703021i
\(451\) −47.7132 −2.24673
\(452\) −0.129556 −0.00609382
\(453\) −13.8882 + 24.0551i −0.652524 + 1.13021i
\(454\) 6.42596 11.1301i 0.301585 0.522361i
\(455\) 23.7709 + 41.1724i 1.11440 + 1.93019i
\(456\) 2.02715 + 3.51113i 0.0949302 + 0.164424i
\(457\) 33.3958 1.56219 0.781096 0.624412i \(-0.214661\pi\)
0.781096 + 0.624412i \(0.214661\pi\)
\(458\) 11.7368 + 20.3288i 0.548426 + 0.949902i
\(459\) 2.82711 + 4.89669i 0.131958 + 0.228558i
\(460\) 0.458101 + 0.793455i 0.0213591 + 0.0369950i
\(461\) 14.5174 25.1448i 0.676141 1.17111i −0.299993 0.953941i \(-0.596984\pi\)
0.976134 0.217169i \(-0.0696824\pi\)
\(462\) −18.1081 −0.842465
\(463\) 2.74539 4.75516i 0.127589 0.220991i −0.795153 0.606409i \(-0.792609\pi\)
0.922742 + 0.385418i \(0.125943\pi\)
\(464\) −11.6733 20.2188i −0.541920 0.938633i
\(465\) −11.2124 −0.519964
\(466\) 9.81720 + 17.0039i 0.454773 + 0.787690i
\(467\) 18.7768 32.5224i 0.868887 1.50496i 0.00575141 0.999983i \(-0.498169\pi\)
0.863135 0.504973i \(-0.168497\pi\)
\(468\) −0.480224 + 0.831773i −0.0221984 + 0.0384487i
\(469\) −12.0912 −0.558319
\(470\) 7.90096 13.6849i 0.364444 0.631235i
\(471\) 17.0172 0.784110
\(472\) 32.3785 1.49034
\(473\) −17.5581 + 22.5190i −0.807320 + 1.03543i
\(474\) 7.14443 0.328155
\(475\) 13.1915 0.605269
\(476\) 0.219267 0.379782i 0.0100501 0.0174073i
\(477\) 9.90128 0.453349
\(478\) 3.54536 6.14074i 0.162161 0.280871i
\(479\) −1.37345 + 2.37888i −0.0627545 + 0.108694i −0.895696 0.444667i \(-0.853322\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(480\) 3.57834 + 6.19787i 0.163328 + 0.282893i
\(481\) −13.0205 −0.593683
\(482\) −10.2339 17.7256i −0.466140 0.807378i
\(483\) 1.61013 2.78883i 0.0732636 0.126896i
\(484\) −1.61973 −0.0736242
\(485\) −22.5722 + 39.0962i −1.02495 + 1.77527i
\(486\) −6.20852 10.7535i −0.281624 0.487788i
\(487\) 20.8994 + 36.1988i 0.947043 + 1.64033i 0.751608 + 0.659610i \(0.229278\pi\)
0.195435 + 0.980717i \(0.437388\pi\)
\(488\) −11.6595 20.1949i −0.527801 0.914178i
\(489\) −10.2946 −0.465536
\(490\) −6.84091 11.8488i −0.309041 0.535275i
\(491\) −7.29797 12.6405i −0.329353 0.570456i 0.653031 0.757331i \(-0.273497\pi\)
−0.982384 + 0.186876i \(0.940164\pi\)
\(492\) 1.60374 2.77776i 0.0723022 0.125231i
\(493\) 3.28660 5.69256i 0.148021 0.256380i
\(494\) 6.49806 0.292362
\(495\) −17.5548 −0.789030
\(496\) 3.18875 5.52307i 0.143179 0.247993i
\(497\) 1.73765 3.00969i 0.0779442 0.135003i
\(498\) 8.72148 + 15.1061i 0.390819 + 0.676918i
\(499\) 10.1686 + 17.6124i 0.455207 + 0.788441i 0.998700 0.0509721i \(-0.0162320\pi\)
−0.543493 + 0.839414i \(0.682899\pi\)
\(500\) 7.79294 0.348511
\(501\) 0.521948 + 0.904040i 0.0233189 + 0.0403895i
\(502\) −3.31288 5.73808i −0.147861 0.256103i
\(503\) −6.67890 11.5682i −0.297797 0.515800i 0.677834 0.735215i \(-0.262919\pi\)
−0.975632 + 0.219414i \(0.929585\pi\)
\(504\) −2.95761 + 5.12273i −0.131743 + 0.228185i
\(505\) 13.1739 0.586230
\(506\) −3.02924 + 5.24680i −0.134666 + 0.233249i
\(507\) −9.23061 15.9879i −0.409946 0.710047i
\(508\) 1.41926 0.0629695
\(509\) 2.48732 + 4.30816i 0.110248 + 0.190956i 0.915870 0.401474i \(-0.131502\pi\)
−0.805622 + 0.592430i \(0.798169\pi\)
\(510\) 4.18495 7.24855i 0.185313 0.320971i
\(511\) −1.72965 + 2.99584i −0.0765151 + 0.132528i
\(512\) −25.0502 −1.10707
\(513\) 2.69683 4.67104i 0.119068 0.206232i
\(514\) 4.37208 0.192844
\(515\) 72.2456 3.18352
\(516\) −0.720846 1.77910i −0.0317335 0.0783207i
\(517\) −11.8311 −0.520329
\(518\) −7.40314 −0.325275
\(519\) 7.69232 13.3235i 0.337655 0.584836i
\(520\) 65.1300 2.85614
\(521\) −11.6827 + 20.2350i −0.511829 + 0.886513i 0.488077 + 0.872800i \(0.337698\pi\)
−0.999906 + 0.0137129i \(0.995635\pi\)
\(522\) −4.09267 + 7.08871i −0.179131 + 0.310265i
\(523\) −13.1400 22.7591i −0.574570 0.995184i −0.996088 0.0883645i \(-0.971836\pi\)
0.421518 0.906820i \(-0.361497\pi\)
\(524\) −1.98145 −0.0865600
\(525\) −21.4514 37.1548i −0.936214 1.62157i
\(526\) 20.6828 35.8237i 0.901814 1.56199i
\(527\) 1.79557 0.0782164
\(528\) −11.1289 + 19.2758i −0.484322 + 0.838870i
\(529\) 10.9613 + 18.9855i 0.476578 + 0.825457i
\(530\) −30.9928 53.6810i −1.34624 2.33176i
\(531\) −5.09263 8.82070i −0.221001 0.382786i
\(532\) −0.418326 −0.0181367
\(533\) −27.8425 48.2247i −1.20599 2.08884i
\(534\) −4.11936 7.13495i −0.178262 0.308759i
\(535\) −31.0372 + 53.7580i −1.34185 + 2.32416i
\(536\) −8.28217 + 14.3451i −0.357735 + 0.619616i
\(537\) 31.6564 1.36607
\(538\) 13.1636 0.567523
\(539\) −5.12186 + 8.87133i −0.220614 + 0.382115i
\(540\) 2.49541 4.32218i 0.107385 0.185997i
\(541\) −2.33746 4.04859i −0.100495 0.174063i 0.811394 0.584500i \(-0.198709\pi\)
−0.911889 + 0.410437i \(0.865376\pi\)
\(542\) −6.62073 11.4674i −0.284385 0.492569i
\(543\) 22.9457 0.984696
\(544\) −0.573040 0.992534i −0.0245689 0.0425546i
\(545\) −15.8039 27.3731i −0.676964 1.17254i
\(546\) −10.5668 18.3022i −0.452217 0.783263i
\(547\) −5.12112 + 8.87004i −0.218963 + 0.379256i −0.954491 0.298239i \(-0.903601\pi\)
0.735528 + 0.677494i \(0.236934\pi\)
\(548\) 0.359675 0.0153646
\(549\) −3.66772 + 6.35267i −0.156534 + 0.271125i
\(550\) 40.3577 + 69.9016i 1.72086 + 2.98062i
\(551\) −6.27030 −0.267124
\(552\) −2.20581 3.82057i −0.0938853 0.162614i
\(553\) −3.99249 + 6.91519i −0.169778 + 0.294064i
\(554\) −12.6116 + 21.8440i −0.535817 + 0.928063i
\(555\) 15.9983 0.679091
\(556\) 1.36478 2.36386i 0.0578794 0.100250i
\(557\) −2.99255 −0.126799 −0.0633993 0.997988i \(-0.520194\pi\)
−0.0633993 + 0.997988i \(0.520194\pi\)
\(558\) −2.23595 −0.0946554
\(559\) −33.0063 4.60555i −1.39602 0.194794i
\(560\) 33.2256 1.40404
\(561\) −6.26663 −0.264577
\(562\) 10.6080 18.3737i 0.447473 0.775046i
\(563\) −12.4117 −0.523090 −0.261545 0.965191i \(-0.584232\pi\)
−0.261545 + 0.965191i \(0.584232\pi\)
\(564\) 0.397667 0.688779i 0.0167448 0.0290028i
\(565\) 1.38182 2.39338i 0.0581336 0.100690i
\(566\) 3.62867 + 6.28503i 0.152524 + 0.264180i
\(567\) −11.5332 −0.484347
\(568\) −2.38050 4.12314i −0.0998834 0.173003i
\(569\) 21.7587 37.6872i 0.912172 1.57993i 0.101181 0.994868i \(-0.467738\pi\)
0.810990 0.585060i \(-0.198929\pi\)
\(570\) −7.98420 −0.334421
\(571\) 21.3381 36.9586i 0.892970 1.54667i 0.0566729 0.998393i \(-0.481951\pi\)
0.836297 0.548277i \(-0.184716\pi\)
\(572\) −2.25090 3.89868i −0.0941150 0.163012i
\(573\) 12.9047 + 22.3517i 0.539103 + 0.933754i
\(574\) −15.8306 27.4194i −0.660757 1.14447i
\(575\) −14.3541 −0.598607
\(576\) 4.01335 + 6.95132i 0.167223 + 0.289638i
\(577\) 5.00651 + 8.67152i 0.208424 + 0.361000i 0.951218 0.308519i \(-0.0998334\pi\)
−0.742795 + 0.669519i \(0.766500\pi\)
\(578\) −0.670183 + 1.16079i −0.0278759 + 0.0482826i
\(579\) −8.96241 + 15.5234i −0.372465 + 0.645129i
\(580\) −5.80199 −0.240915
\(581\) −19.4951 −0.808794
\(582\) 10.0339 17.3793i 0.415920 0.720395i
\(583\) −23.2046 + 40.1916i −0.961037 + 1.66456i
\(584\) 2.36954 + 4.10416i 0.0980521 + 0.169831i
\(585\) −10.2439 17.7430i −0.423534 0.733583i
\(586\) 37.6691 1.55610
\(587\) −2.41137 4.17661i −0.0995278 0.172387i 0.811962 0.583711i \(-0.198400\pi\)
−0.911489 + 0.411324i \(0.865067\pi\)
\(588\) −0.344313 0.596368i −0.0141992 0.0245938i
\(589\) −0.856415 1.48335i −0.0352879 0.0611205i
\(590\) −31.8817 + 55.2207i −1.31255 + 2.27340i
\(591\) 29.1399 1.19865
\(592\) −4.54982 + 7.88052i −0.186997 + 0.323888i
\(593\) 12.1810 + 21.0982i 0.500215 + 0.866398i 1.00000 0.000248476i \(7.90923e-5\pi\)
−0.499785 + 0.866150i \(0.666588\pi\)
\(594\) 33.0023 1.35410
\(595\) 4.67731 + 8.10134i 0.191751 + 0.332122i
\(596\) 1.83492 3.17817i 0.0751611 0.130183i
\(597\) −3.42456 + 5.93151i −0.140158 + 0.242760i
\(598\) −7.07073 −0.289144
\(599\) 1.63080 2.82463i 0.0666328 0.115411i −0.830784 0.556594i \(-0.812108\pi\)
0.897417 + 0.441183i \(0.145441\pi\)
\(600\) −58.7747 −2.39947
\(601\) 0.984057 0.0401405 0.0200703 0.999799i \(-0.493611\pi\)
0.0200703 + 0.999799i \(0.493611\pi\)
\(602\) −18.7666 2.61861i −0.764869 0.106726i
\(603\) 5.21063 0.212193
\(604\) −3.92626 −0.159757
\(605\) 17.2757 29.9224i 0.702357 1.21652i
\(606\) −5.85614 −0.237890
\(607\) −13.9823 + 24.2180i −0.567523 + 0.982979i 0.429287 + 0.903168i \(0.358765\pi\)
−0.996810 + 0.0798106i \(0.974568\pi\)
\(608\) −0.546633 + 0.946796i −0.0221689 + 0.0383976i
\(609\) 10.1964 + 17.6607i 0.413180 + 0.715648i
\(610\) 45.9224 1.85934
\(611\) −6.90390 11.9579i −0.279302 0.483765i
\(612\) −0.0944919 + 0.163665i −0.00381961 + 0.00661576i
\(613\) −35.8340 −1.44732 −0.723662 0.690155i \(-0.757542\pi\)
−0.723662 + 0.690155i \(0.757542\pi\)
\(614\) −5.90393 + 10.2259i −0.238263 + 0.412684i
\(615\) 34.2103 + 59.2539i 1.37949 + 2.38935i
\(616\) −13.8629 24.0112i −0.558552 0.967441i
\(617\) −11.4184 19.7772i −0.459686 0.796200i 0.539258 0.842141i \(-0.318705\pi\)
−0.998944 + 0.0459405i \(0.985372\pi\)
\(618\) −32.1151 −1.29186
\(619\) 0.770758 + 1.33499i 0.0309794 + 0.0536578i 0.881099 0.472931i \(-0.156804\pi\)
−0.850120 + 0.526589i \(0.823471\pi\)
\(620\) −0.792452 1.37257i −0.0318257 0.0551237i
\(621\) −2.93450 + 5.08270i −0.117757 + 0.203962i
\(622\) −13.6477 + 23.6386i −0.547225 + 0.947821i
\(623\) 9.20801 0.368911
\(624\) −25.9766 −1.03989
\(625\) −48.5458 + 84.0837i −1.94183 + 3.36335i
\(626\) 8.50835 14.7369i 0.340062 0.589005i
\(627\) 2.98893 + 5.17697i 0.119366 + 0.206748i
\(628\) 1.20271 + 2.08315i 0.0479934 + 0.0831269i
\(629\) −2.56199 −0.102153
\(630\) −5.82446 10.0883i −0.232052 0.401926i
\(631\) 10.2304 + 17.7195i 0.407265 + 0.705404i 0.994582 0.103953i \(-0.0331492\pi\)
−0.587317 + 0.809357i \(0.699816\pi\)
\(632\) 5.46952 + 9.47348i 0.217566 + 0.376835i
\(633\) −4.74438 + 8.21751i −0.188572 + 0.326617i
\(634\) 44.5461 1.76915
\(635\) −15.1375 + 26.2190i −0.600714 + 1.04047i
\(636\) −1.55991 2.70184i −0.0618545 0.107135i
\(637\) −11.9553 −0.473684
\(638\) −19.1831 33.2262i −0.759468 1.31544i
\(639\) −0.748829 + 1.29701i −0.0296232 + 0.0513089i
\(640\) 20.1519 34.9041i 0.796573 1.37970i
\(641\) 0.150539 0.00594595 0.00297298 0.999996i \(-0.499054\pi\)
0.00297298 + 0.999996i \(0.499054\pi\)
\(642\) 13.7969 23.8969i 0.544518 0.943133i
\(643\) 16.2152 0.639464 0.319732 0.947508i \(-0.396407\pi\)
0.319732 + 0.947508i \(0.396407\pi\)
\(644\) 0.455192 0.0179371
\(645\) 40.5549 + 5.65886i 1.59685 + 0.222817i
\(646\) 1.27860 0.0503058
\(647\) 37.4429 1.47203 0.736017 0.676964i \(-0.236705\pi\)
0.736017 + 0.676964i \(0.236705\pi\)
\(648\) −7.89994 + 13.6831i −0.310339 + 0.537523i
\(649\) 47.7403 1.87397
\(650\) −47.1007 + 81.5808i −1.84744 + 3.19986i
\(651\) −2.78531 + 4.82430i −0.109165 + 0.189079i
\(652\) −0.727581 1.26021i −0.0284943 0.0493535i
\(653\) 32.9918 1.29107 0.645534 0.763731i \(-0.276635\pi\)
0.645534 + 0.763731i \(0.276635\pi\)
\(654\) 7.02524 + 12.1681i 0.274709 + 0.475809i
\(655\) 21.1337 36.6046i 0.825762 1.43026i
\(656\) −38.9167 −1.51944
\(657\) 0.745382 1.29104i 0.0290801 0.0503682i
\(658\) −3.92539 6.79898i −0.153028 0.265052i
\(659\) −5.46477 9.46526i −0.212877 0.368714i 0.739737 0.672897i \(-0.234950\pi\)
−0.952614 + 0.304182i \(0.901617\pi\)
\(660\) 2.76570 + 4.79032i 0.107655 + 0.186463i
\(661\) −22.2747 −0.866384 −0.433192 0.901302i \(-0.642613\pi\)
−0.433192 + 0.901302i \(0.642613\pi\)
\(662\) 2.19441 + 3.80084i 0.0852883 + 0.147724i
\(663\) −3.65683 6.33382i −0.142020 0.245985i
\(664\) −13.3537 + 23.1293i −0.518224 + 0.897591i
\(665\) 4.46177 7.72801i 0.173020 0.299679i
\(666\) 3.19034 0.123623
\(667\) 6.82290 0.264184
\(668\) −0.0737786 + 0.127788i −0.00285458 + 0.00494427i
\(669\) 1.37283 2.37780i 0.0530765 0.0919312i
\(670\) −16.3102 28.2501i −0.630117 1.09140i
\(671\) −17.1913 29.7762i −0.663662 1.14950i
\(672\) 3.55562 0.137161
\(673\) −22.9705 39.7861i −0.885448 1.53364i −0.845200 0.534451i \(-0.820518\pi\)
−0.0402482 0.999190i \(-0.512815\pi\)
\(674\) 2.37519 + 4.11394i 0.0914888 + 0.158463i
\(675\) 39.0955 + 67.7154i 1.50479 + 2.60637i
\(676\) 1.30477 2.25993i 0.0501835 0.0869203i
\(677\) −50.1762 −1.92843 −0.964214 0.265124i \(-0.914587\pi\)
−0.964214 + 0.265124i \(0.914587\pi\)
\(678\) −0.614256 + 1.06392i −0.0235903 + 0.0408597i
\(679\) 11.2144 + 19.4240i 0.430371 + 0.745424i
\(680\) 12.8154 0.491448
\(681\) 6.89922 + 11.9498i 0.264379 + 0.457917i
\(682\) 5.24017 9.07624i 0.200657 0.347547i
\(683\) −17.0189 + 29.4777i −0.651212 + 1.12793i 0.331618 + 0.943414i \(0.392406\pi\)
−0.982829 + 0.184518i \(0.940928\pi\)
\(684\) 0.180275 0.00689299
\(685\) −3.83622 + 6.64452i −0.146574 + 0.253874i
\(686\) −27.0247 −1.03181
\(687\) −25.2025 −0.961534
\(688\) −14.3210 + 18.3674i −0.545984 + 0.700250i
\(689\) −54.1633 −2.06346
\(690\) 8.68784 0.330740
\(691\) 9.56776 16.5719i 0.363975 0.630423i −0.624636 0.780916i \(-0.714753\pi\)
0.988611 + 0.150493i \(0.0480860\pi\)
\(692\) 2.17466 0.0826680
\(693\) −4.36083 + 7.55319i −0.165654 + 0.286922i
\(694\) −14.3919 + 24.9275i −0.546310 + 0.946236i
\(695\) 29.1128 + 50.4248i 1.10431 + 1.91272i
\(696\) 27.9372 1.05896
\(697\) −5.47847 9.48900i −0.207512 0.359421i
\(698\) −11.0325 + 19.1089i −0.417588 + 0.723283i
\(699\) −21.0804 −0.797335
\(700\) 3.03220 5.25193i 0.114606 0.198504i
\(701\) 0.660487 + 1.14400i 0.0249463 + 0.0432082i 0.878229 0.478240i \(-0.158725\pi\)
−0.853283 + 0.521448i \(0.825392\pi\)
\(702\) 19.2582 + 33.3561i 0.726853 + 1.25895i
\(703\) 1.22196 + 2.11650i 0.0460873 + 0.0798255i
\(704\) −37.6227 −1.41796
\(705\) 8.48285 + 14.6927i 0.319482 + 0.553360i
\(706\) −16.0283 27.7618i −0.603232 1.04483i
\(707\) 3.27256 5.66824i 0.123077 0.213176i
\(708\) −1.60465 + 2.77934i −0.0603065 + 0.104454i
\(709\) 1.62908 0.0611814 0.0305907 0.999532i \(-0.490261\pi\)
0.0305907 + 0.999532i \(0.490261\pi\)
\(710\) 9.37587 0.351870
\(711\) 1.72054 2.98006i 0.0645253 0.111761i
\(712\) 6.30727 10.9245i 0.236375 0.409414i
\(713\) 0.931890 + 1.61408i 0.0348996 + 0.0604478i
\(714\) −2.07919 3.60126i −0.0778117 0.134774i
\(715\) 96.0306 3.59134
\(716\) 2.23735 + 3.87521i 0.0836138 + 0.144823i
\(717\) 3.80647 + 6.59299i 0.142155 + 0.246220i
\(718\) −6.16273 10.6742i −0.229991 0.398356i
\(719\) −3.49095 + 6.04651i −0.130191 + 0.225497i −0.923750 0.382996i \(-0.874892\pi\)
0.793559 + 0.608493i \(0.208226\pi\)
\(720\) −14.3184 −0.533615
\(721\) 17.9467 31.0846i 0.668371 1.15765i
\(722\) 12.1236 + 20.9988i 0.451195 + 0.781493i
\(723\) 21.9751 0.817264
\(724\) 1.62172 + 2.80890i 0.0602707 + 0.104392i
\(725\) 45.4498 78.7213i 1.68796 2.92364i
\(726\) −7.67951 + 13.3013i −0.285013 + 0.493657i
\(727\) −14.2138 −0.527161 −0.263581 0.964637i \(-0.584903\pi\)
−0.263581 + 0.964637i \(0.584903\pi\)
\(728\) 16.1791 28.0230i 0.599638 1.03860i
\(729\) 29.3808 1.08818
\(730\) −9.33271 −0.345419
\(731\) −6.49452 0.906216i −0.240208 0.0335176i
\(732\) 2.31134 0.0854296
\(733\) −3.40208 −0.125659 −0.0628294 0.998024i \(-0.520012\pi\)
−0.0628294 + 0.998024i \(0.520012\pi\)
\(734\) −22.5409 + 39.0419i −0.831999 + 1.44106i
\(735\) 14.6895 0.541829
\(736\) 0.594807 1.03024i 0.0219249 0.0379750i
\(737\) −12.2116 + 21.1511i −0.449820 + 0.779112i
\(738\) 6.82212 + 11.8163i 0.251126 + 0.434962i
\(739\) −6.88779 −0.253371 −0.126686 0.991943i \(-0.540434\pi\)
−0.126686 + 0.991943i \(0.540434\pi\)
\(740\) 1.13070 + 1.95843i 0.0415654 + 0.0719934i
\(741\) −3.48832 + 6.04194i −0.128146 + 0.221956i
\(742\) −30.7960 −1.13056
\(743\) 14.3559 24.8651i 0.526666 0.912213i −0.472851 0.881142i \(-0.656775\pi\)
0.999517 0.0310703i \(-0.00989158\pi\)
\(744\) 3.81574 + 6.60906i 0.139892 + 0.242300i
\(745\) 39.1416 + 67.7953i 1.43404 + 2.48383i
\(746\) −9.71853 16.8330i −0.355821 0.616300i
\(747\) 8.40131 0.307388
\(748\) −0.442902 0.767129i −0.0161941 0.0280490i
\(749\) 15.4201 + 26.7083i 0.563436 + 0.975901i
\(750\) 36.9481 63.9959i 1.34915 2.33680i
\(751\) 7.09430 12.2877i 0.258875 0.448384i −0.707066 0.707148i \(-0.749982\pi\)
0.965941 + 0.258763i \(0.0833149\pi\)
\(752\) −9.64987 −0.351895
\(753\) 7.11373 0.259239
\(754\) 22.3883 38.7776i 0.815332 1.41220i
\(755\) 41.8766 72.5324i 1.52405 2.63973i
\(756\) −1.23978 2.14737i −0.0450905 0.0780990i
\(757\) 24.8520 + 43.0449i 0.903260 + 1.56449i 0.823236 + 0.567700i \(0.192167\pi\)
0.0800247 + 0.996793i \(0.474500\pi\)
\(758\) 29.4817 1.07082
\(759\) −3.25234 5.63322i −0.118052 0.204473i
\(760\) −6.11241 10.5870i −0.221720 0.384031i
\(761\) 5.88447 + 10.1922i 0.213312 + 0.369467i 0.952749 0.303759i \(-0.0982417\pi\)
−0.739437 + 0.673225i \(0.764908\pi\)
\(762\) 6.72903 11.6550i 0.243767 0.422217i
\(763\) −15.7035 −0.568506
\(764\) −1.82412 + 3.15946i −0.0659942 + 0.114305i
\(765\) −2.01566 3.49123i −0.0728763 0.126226i
\(766\) 41.1510 1.48685
\(767\) 27.8584 + 48.2521i 1.00591 + 1.74228i
\(768\) 3.47525 6.01930i 0.125402 0.217203i
\(769\) −21.9294 + 37.9828i −0.790793 + 1.36969i 0.134683 + 0.990889i \(0.456998\pi\)
−0.925476 + 0.378805i \(0.876335\pi\)
\(770\) 54.6007 1.96767
\(771\) −2.34704 + 4.06518i −0.0845264 + 0.146404i
\(772\) −2.53372 −0.0911905
\(773\) 50.2312 1.80669 0.903345 0.428914i \(-0.141104\pi\)
0.903345 + 0.428914i \(0.141104\pi\)
\(774\) 8.08735 + 1.12847i 0.290694 + 0.0405622i
\(775\) 24.8306 0.891942
\(776\) 30.7265 1.10302
\(777\) 3.97419 6.88349i 0.142573 0.246944i
\(778\) −49.2943 −1.76729
\(779\) −5.22601 + 9.05172i −0.187241 + 0.324312i
\(780\) −3.22779 + 5.59069i −0.115573 + 0.200179i
\(781\) −3.50991 6.07934i −0.125594 0.217536i
\(782\) −1.39128 −0.0497521
\(783\) −18.5832 32.1870i −0.664108 1.15027i
\(784\) −4.17759 + 7.23580i −0.149200 + 0.258421i
\(785\) −51.3113 −1.83138
\(786\) −9.39449 + 16.2717i −0.335090 + 0.580393i
\(787\) −4.37166 7.57194i −0.155833 0.269911i 0.777529 0.628847i \(-0.216473\pi\)
−0.933362 + 0.358936i \(0.883139\pi\)
\(788\) 2.05950 + 3.56715i 0.0733665 + 0.127074i
\(789\) 22.2061 + 38.4621i 0.790558 + 1.36929i
\(790\) −21.5424 −0.766443
\(791\) −0.686523 1.18909i −0.0244099 0.0422793i
\(792\) 5.97414 + 10.3475i 0.212282 + 0.367683i
\(793\) 20.0636 34.7512i 0.712480 1.23405i
\(794\) −5.30983 + 9.19690i −0.188439 + 0.326386i
\(795\) 66.5506 2.36031
\(796\) −0.968139 −0.0343148
\(797\) −6.83607 + 11.8404i −0.242146 + 0.419409i −0.961325 0.275415i \(-0.911185\pi\)
0.719179 + 0.694825i \(0.244518\pi\)
\(798\) −1.98337 + 3.43531i −0.0702107 + 0.121609i
\(799\) −1.35845 2.35291i −0.0480586 0.0832400i
\(800\) −7.92445 13.7256i −0.280172 0.485272i
\(801\) −3.96814 −0.140207
\(802\) 9.62596 + 16.6727i 0.339905 + 0.588732i
\(803\) 3.49375 + 6.05135i 0.123292 + 0.213548i
\(804\) −0.820915 1.42187i −0.0289514 0.0501454i
\(805\) −4.85498 + 8.40907i −0.171116 + 0.296381i
\(806\) 12.2314 0.430833
\(807\) −7.06653 + 12.2396i −0.248754 + 0.430854i
\(808\) −4.48325 7.76522i −0.157720 0.273179i
\(809\) −49.3139 −1.73378 −0.866892 0.498496i \(-0.833886\pi\)
−0.866892 + 0.498496i \(0.833886\pi\)
\(810\) −15.5574 26.9463i −0.546633 0.946796i
\(811\) 4.12218 7.13982i 0.144749 0.250713i −0.784530 0.620091i \(-0.787096\pi\)
0.929279 + 0.369378i \(0.120429\pi\)
\(812\) −1.44129 + 2.49638i −0.0505793 + 0.0876059i
\(813\) 14.2167 0.498600
\(814\) −7.47687 + 12.9503i −0.262064 + 0.453909i
\(815\) 31.0409 1.08731
\(816\) −5.11131 −0.178932
\(817\) 2.34898 + 5.79746i 0.0821803 + 0.202827i
\(818\) 2.69718 0.0943048
\(819\) −10.1789 −0.355679
\(820\) −4.83570 + 8.37568i −0.168870 + 0.292492i
\(821\) −42.7785 −1.49298 −0.746490 0.665396i \(-0.768263\pi\)
−0.746490 + 0.665396i \(0.768263\pi\)
\(822\) 1.70530 2.95367i 0.0594792 0.103021i
\(823\) −10.6286 + 18.4093i −0.370490 + 0.641708i −0.989641 0.143564i \(-0.954144\pi\)
0.619151 + 0.785272i \(0.287477\pi\)
\(824\) −24.5862 42.5845i −0.856499 1.48350i
\(825\) −86.6600 −3.01711
\(826\) 15.8396 + 27.4350i 0.551131 + 0.954587i
\(827\) 0.450476 0.780247i 0.0156646 0.0271319i −0.858087 0.513505i \(-0.828347\pi\)
0.873751 + 0.486373i \(0.161680\pi\)
\(828\) −0.196163 −0.00681712
\(829\) −3.79302 + 6.56970i −0.131737 + 0.228175i −0.924346 0.381555i \(-0.875389\pi\)
0.792609 + 0.609730i \(0.208722\pi\)
\(830\) −26.2976 45.5488i −0.912803 1.58102i
\(831\) −13.5405 23.4528i −0.469713 0.813568i
\(832\) −21.9543 38.0260i −0.761129 1.31831i
\(833\) −2.35239 −0.0815055
\(834\) −12.9414 22.4152i −0.448124 0.776174i
\(835\) −1.57381 2.72592i −0.0544640 0.0943344i
\(836\) −0.422492 + 0.731778i −0.0146122 + 0.0253091i
\(837\) 5.07628 8.79237i 0.175462 0.303909i
\(838\) 19.9350 0.688644
\(839\) 46.1269 1.59248 0.796239 0.604983i \(-0.206820\pi\)
0.796239 + 0.604983i \(0.206820\pi\)
\(840\) −19.8793 + 34.4320i −0.685902 + 1.18802i
\(841\) −7.10352 + 12.3037i −0.244949 + 0.424264i
\(842\) −20.4556 35.4302i −0.704947 1.22100i
\(843\) 11.3893 + 19.7268i 0.392268 + 0.679429i
\(844\) −1.34126 −0.0461681
\(845\) 27.8328 + 48.2078i 0.957476 + 1.65840i
\(846\) 1.69163 + 2.92998i 0.0581593 + 0.100735i
\(847\) −8.58300 14.8662i −0.294915 0.510808i
\(848\) −18.9266 + 32.7818i −0.649942 + 1.12573i
\(849\) −7.79182 −0.267415
\(850\) −9.26783 + 16.0523i −0.317884 + 0.550591i
\(851\) −1.32966 2.30303i −0.0455800 0.0789469i
\(852\) 0.471901 0.0161671
\(853\) −2.15658 3.73530i −0.0738399 0.127894i 0.826741 0.562582i \(-0.190192\pi\)
−0.900581 + 0.434688i \(0.856859\pi\)
\(854\) 11.4077 19.7587i 0.390363 0.676129i
\(855\) −1.92277 + 3.33034i −0.0657575 + 0.113895i
\(856\) 42.2495 1.44406
\(857\) 2.37205 4.10852i 0.0810278 0.140344i −0.822664 0.568528i \(-0.807513\pi\)
0.903692 + 0.428184i \(0.140846\pi\)
\(858\) −42.6881 −1.45735
\(859\) −31.5897 −1.07783 −0.538913 0.842361i \(-0.681165\pi\)
−0.538913 + 0.842361i \(0.681165\pi\)
\(860\) 2.17354 + 5.36447i 0.0741172 + 0.182927i
\(861\) 33.9930 1.15848
\(862\) 6.58380 0.224245
\(863\) −5.58640 + 9.67593i −0.190163 + 0.329372i −0.945304 0.326190i \(-0.894235\pi\)
0.755141 + 0.655562i \(0.227568\pi\)
\(864\) −6.48018 −0.220460
\(865\) −23.1944 + 40.1739i −0.788633 + 1.36595i
\(866\) −25.3758 + 43.9521i −0.862304 + 1.49355i
\(867\) −0.719541 1.24628i −0.0244369 0.0423259i
\(868\) −0.787421 −0.0267268
\(869\) 8.06450 + 13.9681i 0.273569 + 0.473836i
\(870\) −27.5085 + 47.6462i −0.932627 + 1.61536i
\(871\) −28.5038 −0.965816
\(872\) −10.7565 + 18.6309i −0.364262 + 0.630921i
\(873\) −4.83280 8.37065i −0.163565 0.283304i
\(874\) 0.663584 + 1.14936i 0.0224461 + 0.0388777i
\(875\) 41.2950 + 71.5250i 1.39603 + 2.41799i
\(876\) −0.469729 −0.0158707
\(877\) 0.507116 + 0.878350i 0.0171241 + 0.0296598i 0.874460 0.485097i \(-0.161216\pi\)
−0.857336 + 0.514757i \(0.827882\pi\)
\(878\) −19.8448 34.3723i −0.669731 1.16001i
\(879\) −20.2217 + 35.0250i −0.682060 + 1.18136i
\(880\) 33.5565 58.1216i 1.13119 1.95928i
\(881\) 27.4802 0.925830 0.462915 0.886403i \(-0.346803\pi\)
0.462915 + 0.886403i \(0.346803\pi\)
\(882\) 2.92933 0.0986358
\(883\) 24.9022 43.1319i 0.838026 1.45150i −0.0535166 0.998567i \(-0.517043\pi\)
0.891543 0.452937i \(-0.149624\pi\)
\(884\) 0.516902 0.895300i 0.0173853 0.0301122i
\(885\) −34.2297 59.2876i −1.15062 1.99293i
\(886\) 21.0690 + 36.4926i 0.707827 + 1.22599i
\(887\) −28.0717 −0.942555 −0.471278 0.881985i \(-0.656207\pi\)
−0.471278 + 0.881985i \(0.656207\pi\)
\(888\) −5.44445 9.43006i −0.182704 0.316452i
\(889\) 7.52070 + 13.0262i 0.252236 + 0.436886i
\(890\) 12.4210 + 21.5138i 0.416352 + 0.721143i
\(891\) −11.6480 + 20.1750i −0.390223 + 0.675887i
\(892\) 0.388105 0.0129947
\(893\) −1.29585 + 2.24448i −0.0433641 + 0.0751088i
\(894\) −17.3995 30.1368i −0.581926 1.00793i
\(895\) −95.4524 −3.19062
\(896\) −10.0120 17.3412i −0.334476 0.579330i
\(897\) 3.79574 6.57441i 0.126736 0.219513i
\(898\) −11.0014 + 19.0551i −0.367123 + 0.635875i
\(899\) −11.8027 −0.393641
\(900\) −1.30671 + 2.26329i −0.0435570 + 0.0754429i
\(901\) −10.6575 −0.355053
\(902\) −63.9532 −2.12941
\(903\) 12.5092 16.0436i 0.416279 0.533896i
\(904\) −1.88101 −0.0625614
\(905\) −69.1875 −2.29987
\(906\) −18.6153 + 32.2426i −0.618451 + 1.07119i
\(907\) 55.2863 1.83575 0.917875 0.396869i \(-0.129903\pi\)
0.917875 + 0.396869i \(0.129903\pi\)
\(908\) −0.975221 + 1.68913i −0.0323638 + 0.0560558i
\(909\) −1.41029 + 2.44269i −0.0467764 + 0.0810191i
\(910\) 31.8617 + 55.1861i 1.05621 + 1.82940i
\(911\) 25.2169 0.835473 0.417737 0.908568i \(-0.362823\pi\)
0.417737 + 0.908568i \(0.362823\pi\)
\(912\) 2.43788 + 4.22254i 0.0807264 + 0.139822i
\(913\) −19.6893 + 34.1029i −0.651620 + 1.12864i
\(914\) 44.7627 1.48062
\(915\) −24.6522 + 42.6989i −0.814978 + 1.41158i
\(916\) −1.78121 3.08515i −0.0588530 0.101936i
\(917\) −10.4997 18.1861i −0.346732 0.600558i
\(918\) 3.78936 + 6.56336i 0.125068 + 0.216623i
\(919\) 44.5266 1.46880 0.734398 0.678719i \(-0.237465\pi\)
0.734398 + 0.678719i \(0.237465\pi\)
\(920\) 6.65109 + 11.5200i 0.219280 + 0.379804i
\(921\) −6.33874 10.9790i −0.208869 0.361771i
\(922\) 19.4586 33.7033i 0.640835 1.10996i
\(923\) 4.09634 7.09507i 0.134833 0.233537i
\(924\) 2.74813 0.0904070
\(925\) −35.4293 −1.16491
\(926\) 3.67983 6.37365i 0.120927 0.209451i
\(927\) −7.73404 + 13.3957i −0.254019 + 0.439974i
\(928\) 3.76671 + 6.52413i 0.123648 + 0.214165i
\(929\) 9.56255 + 16.5628i 0.313737 + 0.543409i 0.979168 0.203051i \(-0.0650856\pi\)
−0.665431 + 0.746459i \(0.731752\pi\)
\(930\) −15.0288 −0.492813
\(931\) 1.12199 + 1.94335i 0.0367718 + 0.0636907i
\(932\) −1.48988 2.58056i −0.0488028 0.0845289i
\(933\) −14.6529 25.3795i −0.479714 0.830888i
\(934\) 25.1678 43.5919i 0.823515 1.42637i
\(935\) 18.8956 0.617951
\(936\) −6.97230 + 12.0764i −0.227897 + 0.394728i
\(937\) −7.32103 12.6804i −0.239168 0.414250i 0.721308 0.692614i \(-0.243541\pi\)
−0.960476 + 0.278364i \(0.910208\pi\)
\(938\) −16.2066 −0.529165
\(939\) 9.13498 + 15.8222i 0.298109 + 0.516339i
\(940\) −1.19907 + 2.07685i −0.0391094 + 0.0677394i
\(941\) 2.61589 4.53085i 0.0852754 0.147701i −0.820233 0.572029i \(-0.806156\pi\)
0.905509 + 0.424328i \(0.139490\pi\)
\(942\) 22.8093 0.743166
\(943\) 5.68658 9.84944i 0.185180 0.320742i
\(944\) 38.9389 1.26735
\(945\) 52.8930 1.72061
\(946\) −23.5342 + 30.1837i −0.765164 + 0.981358i
\(947\) 24.3089 0.789932 0.394966 0.918696i \(-0.370756\pi\)
0.394966 + 0.918696i \(0.370756\pi\)
\(948\) −1.08426 −0.0352151
\(949\) −4.07748 + 7.06241i −0.132361 + 0.229256i
\(950\) 17.6815 0.573663
\(951\) −23.9134 + 41.4193i −0.775446 + 1.34311i
\(952\) 3.18350 5.51399i 0.103178 0.178709i
\(953\) −7.43248 12.8734i −0.240762 0.417011i 0.720170 0.693798i \(-0.244064\pi\)
−0.960931 + 0.276787i \(0.910731\pi\)
\(954\) 13.2713 0.429676
\(955\) −38.9112 67.3962i −1.25914 2.18089i
\(956\) −0.538053 + 0.931936i −0.0174019 + 0.0301410i
\(957\) 41.1919 1.33154
\(958\) −1.84093 + 3.18858i −0.0594776 + 0.103018i
\(959\) 1.90593 + 3.30116i 0.0615456 + 0.106600i
\(960\) 26.9754 + 46.7227i 0.870626 + 1.50797i
\(961\) 13.8880 + 24.0546i 0.447999 + 0.775956i
\(962\) −17.4522 −0.562682
\(963\) −6.64518 11.5098i −0.214138 0.370898i
\(964\) 1.55312 + 2.69008i 0.0500226 + 0.0866417i
\(965\) 27.0241 46.8071i 0.869935 1.50677i
\(966\) 2.15817 3.73806i 0.0694379 0.120270i
\(967\) 30.2322 0.972203 0.486102 0.873902i \(-0.338419\pi\)
0.486102 + 0.873902i \(0.338419\pi\)
\(968\) −23.5166 −0.755852
\(969\) −0.686383 + 1.18885i −0.0220498 + 0.0381914i
\(970\) −30.2550 + 52.4032i −0.971430 + 1.68257i
\(971\) −15.5599 26.9505i −0.499341 0.864884i 0.500659 0.865645i \(-0.333091\pi\)
−1.00000 0.000760789i \(0.999758\pi\)
\(972\) 0.942223 + 1.63198i 0.0302218 + 0.0523457i
\(973\) 28.9279 0.927387
\(974\) 28.0129 + 48.5197i 0.897590 + 1.55467i
\(975\) −50.5696 87.5890i −1.61952 2.80509i
\(976\) −14.0219 24.2866i −0.448830 0.777396i
\(977\) 17.0953 29.6100i 0.546928 0.947308i −0.451554 0.892244i \(-0.649130\pi\)
0.998483 0.0550642i \(-0.0175363\pi\)
\(978\) −13.7985 −0.441227
\(979\) 9.29972 16.1076i 0.297220 0.514801i
\(980\) 1.03820 + 1.79821i 0.0331640 + 0.0574416i
\(981\) 6.76734 0.216065
\(982\) −9.78195 16.9428i −0.312155 0.540668i
\(983\) 6.09940 10.5645i 0.194541 0.336954i −0.752209 0.658924i \(-0.771012\pi\)
0.946750 + 0.321970i \(0.104345\pi\)
\(984\) 23.2844 40.3298i 0.742280 1.28567i
\(985\) −87.8645 −2.79959
\(986\) 4.40525 7.63012i 0.140292 0.242993i
\(987\) 8.42898 0.268297
\(988\) −0.986164 −0.0313740
\(989\) −2.55599 6.30839i −0.0812758 0.200595i
\(990\) −23.5299 −0.747828
\(991\) −15.2905 −0.485718 −0.242859 0.970062i \(-0.578085\pi\)
−0.242859 + 0.970062i \(0.578085\pi\)
\(992\) −1.02894 + 1.78217i −0.0326687 + 0.0565839i
\(993\) −4.71206 −0.149533
\(994\) 2.32908 4.03409i 0.0738741 0.127954i
\(995\) 10.3260 17.8851i 0.327355 0.566995i
\(996\) −1.32360 2.29254i −0.0419398 0.0726418i
\(997\) 52.0231 1.64759 0.823794 0.566889i \(-0.191853\pi\)
0.823794 + 0.566889i \(0.191853\pi\)
\(998\) 13.6296 + 23.6071i 0.431437 + 0.747271i
\(999\) −7.24303 + 12.5453i −0.229159 + 0.396915i
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 731.2.e.b.307.19 58
43.36 even 3 inner 731.2.e.b.681.19 yes 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.e.b.307.19 58 1.1 even 1 trivial
731.2.e.b.681.19 yes 58 43.36 even 3 inner