Properties

Label 483.2.i.g.415.4
Level $483$
Weight $2$
Character 483.415
Analytic conductor $3.857$
Analytic rank $0$
Dimension $16$
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] = [483,2,Mod(277,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} - 158 x^{7} + 8993 x^{6} + 265 x^{5} + 15176 x^{4} + 383 x^{3} + 12649 x^{2} + \cdots + 6400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.4
Root \(0.595971 + 1.03225i\) of defining polynomial
Character \(\chi\) \(=\) 483.415
Dual form 483.2.i.g.277.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.595971 + 1.03225i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.289637 + 0.501666i) q^{4} +(1.89410 - 3.28068i) q^{5} +1.19194 q^{6} +(2.62328 - 0.344130i) q^{7} -3.07435 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.595971 + 1.03225i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.289637 + 0.501666i) q^{4} +(1.89410 - 3.28068i) q^{5} +1.19194 q^{6} +(2.62328 - 0.344130i) q^{7} -3.07435 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.25766 + 3.91038i) q^{10} +(0.745201 + 1.29073i) q^{11} +(0.289637 - 0.501666i) q^{12} -0.460711 q^{13} +(-1.20817 + 2.91297i) q^{14} -3.78820 q^{15} +(1.25295 - 2.17017i) q^{16} +(-3.02964 - 5.24749i) q^{17} +(-0.595971 - 1.03225i) q^{18} +(2.95317 - 5.11504i) q^{19} +2.19441 q^{20} +(-1.60966 - 2.09976i) q^{21} -1.77647 q^{22} +(0.500000 - 0.866025i) q^{23} +(1.53717 + 2.66246i) q^{24} +(-4.67524 - 8.09776i) q^{25} +(0.274571 - 0.475570i) q^{26} +1.00000 q^{27} +(0.932436 + 1.21633i) q^{28} +2.10833 q^{29} +(2.25766 - 3.91038i) q^{30} +(4.03574 + 6.99011i) q^{31} +(-1.58090 - 2.73821i) q^{32} +(0.745201 - 1.29073i) q^{33} +7.22231 q^{34} +(3.83977 - 9.25795i) q^{35} -0.579274 q^{36} +(-5.65171 + 9.78904i) q^{37} +(3.52001 + 6.09683i) q^{38} +(0.230356 + 0.398988i) q^{39} +(-5.82312 + 10.0859i) q^{40} +5.23193 q^{41} +(3.12679 - 0.410183i) q^{42} +4.64064 q^{43} +(-0.431675 + 0.747683i) q^{44} +(1.89410 + 3.28068i) q^{45} +(0.595971 + 1.03225i) q^{46} +(2.30279 - 3.98854i) q^{47} -2.50589 q^{48} +(6.76315 - 1.80550i) q^{49} +11.1452 q^{50} +(-3.02964 + 5.24749i) q^{51} +(-0.133439 - 0.231123i) q^{52} +(2.66141 + 4.60970i) q^{53} +(-0.595971 + 1.03225i) q^{54} +5.64594 q^{55} +(-8.06485 + 1.05797i) q^{56} -5.90634 q^{57} +(-1.25650 + 2.17632i) q^{58} +(-6.14546 - 10.6443i) q^{59} +(-1.09720 - 1.90041i) q^{60} +(-0.205912 + 0.356650i) q^{61} -9.62074 q^{62} +(-1.01361 + 2.44389i) q^{63} +8.78048 q^{64} +(-0.872634 + 1.51145i) q^{65} +(0.888236 + 1.53847i) q^{66} +(-7.56042 - 13.0950i) q^{67} +(1.75499 - 3.03973i) q^{68} -1.00000 q^{69} +(7.26814 + 9.48108i) q^{70} +6.85490 q^{71} +(1.53717 - 2.66246i) q^{72} +(6.07119 + 10.5156i) q^{73} +(-6.73651 - 11.6680i) q^{74} +(-4.67524 + 8.09776i) q^{75} +3.42139 q^{76} +(2.39904 + 3.12948i) q^{77} -0.549141 q^{78} +(-3.23685 + 5.60638i) q^{79} +(-4.74642 - 8.22104i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.11808 + 5.40067i) q^{82} -4.68019 q^{83} +(0.587159 - 1.41568i) q^{84} -22.9538 q^{85} +(-2.76569 + 4.79031i) q^{86} +(-1.05416 - 1.82586i) q^{87} +(-2.29100 - 3.96814i) q^{88} +(-8.14048 + 14.0997i) q^{89} -4.51532 q^{90} +(-1.20857 + 0.158545i) q^{91} +0.579274 q^{92} +(4.03574 - 6.99011i) q^{93} +(2.74479 + 4.75412i) q^{94} +(-11.1872 - 19.3768i) q^{95} +(-1.58090 + 2.73821i) q^{96} -6.78248 q^{97} +(-2.16691 + 8.05730i) q^{98} -1.49040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.595971 + 1.03225i −0.421415 + 0.729913i −0.996078 0.0884776i \(-0.971800\pi\)
0.574663 + 0.818390i \(0.305133\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.289637 + 0.501666i 0.144818 + 0.250833i
\(5\) 1.89410 3.28068i 0.847068 1.46717i −0.0367448 0.999325i \(-0.511699\pi\)
0.883813 0.467840i \(-0.154968\pi\)
\(6\) 1.19194 0.486608
\(7\) 2.62328 0.344130i 0.991505 0.130069i
\(8\) −3.07435 −1.08695
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 2.25766 + 3.91038i 0.713935 + 1.23657i
\(11\) 0.745201 + 1.29073i 0.224686 + 0.389168i 0.956225 0.292631i \(-0.0945309\pi\)
−0.731539 + 0.681800i \(0.761198\pi\)
\(12\) 0.289637 0.501666i 0.0836110 0.144818i
\(13\) −0.460711 −0.127778 −0.0638892 0.997957i \(-0.520350\pi\)
−0.0638892 + 0.997957i \(0.520350\pi\)
\(14\) −1.20817 + 2.91297i −0.322896 + 0.778525i
\(15\) −3.78820 −0.978110
\(16\) 1.25295 2.17017i 0.313237 0.542542i
\(17\) −3.02964 5.24749i −0.734796 1.27270i −0.954813 0.297207i \(-0.903945\pi\)
0.220017 0.975496i \(-0.429389\pi\)
\(18\) −0.595971 1.03225i −0.140472 0.243304i
\(19\) 2.95317 5.11504i 0.677504 1.17347i −0.298227 0.954495i \(-0.596395\pi\)
0.975730 0.218976i \(-0.0702715\pi\)
\(20\) 2.19441 0.490684
\(21\) −1.60966 2.09976i −0.351257 0.458205i
\(22\) −1.77647 −0.378745
\(23\) 0.500000 0.866025i 0.104257 0.180579i
\(24\) 1.53717 + 2.66246i 0.313774 + 0.543473i
\(25\) −4.67524 8.09776i −0.935049 1.61955i
\(26\) 0.274571 0.475570i 0.0538477 0.0932670i
\(27\) 1.00000 0.192450
\(28\) 0.932436 + 1.21633i 0.176214 + 0.229866i
\(29\) 2.10833 0.391506 0.195753 0.980653i \(-0.437285\pi\)
0.195753 + 0.980653i \(0.437285\pi\)
\(30\) 2.25766 3.91038i 0.412190 0.713935i
\(31\) 4.03574 + 6.99011i 0.724841 + 1.25546i 0.959040 + 0.283272i \(0.0914200\pi\)
−0.234199 + 0.972189i \(0.575247\pi\)
\(32\) −1.58090 2.73821i −0.279467 0.484051i
\(33\) 0.745201 1.29073i 0.129723 0.224686i
\(34\) 7.22231 1.23862
\(35\) 3.83977 9.25795i 0.649040 1.56488i
\(36\) −0.579274 −0.0965456
\(37\) −5.65171 + 9.78904i −0.929135 + 1.60931i −0.144362 + 0.989525i \(0.546113\pi\)
−0.784773 + 0.619784i \(0.787220\pi\)
\(38\) 3.52001 + 6.09683i 0.571021 + 0.989037i
\(39\) 0.230356 + 0.398988i 0.0368864 + 0.0638892i
\(40\) −5.82312 + 10.0859i −0.920717 + 1.59473i
\(41\) 5.23193 0.817090 0.408545 0.912738i \(-0.366036\pi\)
0.408545 + 0.912738i \(0.366036\pi\)
\(42\) 3.12679 0.410183i 0.482475 0.0632926i
\(43\) 4.64064 0.707691 0.353845 0.935304i \(-0.384874\pi\)
0.353845 + 0.935304i \(0.384874\pi\)
\(44\) −0.431675 + 0.747683i −0.0650775 + 0.112718i
\(45\) 1.89410 + 3.28068i 0.282356 + 0.489055i
\(46\) 0.595971 + 1.03225i 0.0878711 + 0.152197i
\(47\) 2.30279 3.98854i 0.335896 0.581789i −0.647760 0.761844i \(-0.724294\pi\)
0.983657 + 0.180055i \(0.0576276\pi\)
\(48\) −2.50589 −0.361695
\(49\) 6.76315 1.80550i 0.966164 0.257928i
\(50\) 11.1452 1.57618
\(51\) −3.02964 + 5.24749i −0.424234 + 0.734796i
\(52\) −0.133439 0.231123i −0.0185047 0.0320510i
\(53\) 2.66141 + 4.60970i 0.365573 + 0.633191i 0.988868 0.148796i \(-0.0475397\pi\)
−0.623295 + 0.781987i \(0.714206\pi\)
\(54\) −0.595971 + 1.03225i −0.0811014 + 0.140472i
\(55\) 5.64594 0.761299
\(56\) −8.06485 + 1.05797i −1.07771 + 0.141378i
\(57\) −5.90634 −0.782314
\(58\) −1.25650 + 2.17632i −0.164987 + 0.285765i
\(59\) −6.14546 10.6443i −0.800071 1.38576i −0.919569 0.392929i \(-0.871462\pi\)
0.119498 0.992834i \(-0.461872\pi\)
\(60\) −1.09720 1.90041i −0.141648 0.245342i
\(61\) −0.205912 + 0.356650i −0.0263643 + 0.0456644i −0.878907 0.476994i \(-0.841726\pi\)
0.852542 + 0.522658i \(0.175060\pi\)
\(62\) −9.62074 −1.22184
\(63\) −1.01361 + 2.44389i −0.127703 + 0.307901i
\(64\) 8.78048 1.09756
\(65\) −0.872634 + 1.51145i −0.108237 + 0.187472i
\(66\) 0.888236 + 1.53847i 0.109334 + 0.189373i
\(67\) −7.56042 13.0950i −0.923652 1.59981i −0.793715 0.608290i \(-0.791856\pi\)
−0.129937 0.991522i \(-0.541478\pi\)
\(68\) 1.75499 3.03973i 0.212824 0.368622i
\(69\) −1.00000 −0.120386
\(70\) 7.26814 + 9.48108i 0.868709 + 1.13321i
\(71\) 6.85490 0.813527 0.406764 0.913533i \(-0.366657\pi\)
0.406764 + 0.913533i \(0.366657\pi\)
\(72\) 1.53717 2.66246i 0.181158 0.313774i
\(73\) 6.07119 + 10.5156i 0.710579 + 1.23076i 0.964640 + 0.263571i \(0.0849003\pi\)
−0.254061 + 0.967188i \(0.581766\pi\)
\(74\) −6.73651 11.6680i −0.783103 1.35637i
\(75\) −4.67524 + 8.09776i −0.539851 + 0.935049i
\(76\) 3.42139 0.392460
\(77\) 2.39904 + 3.12948i 0.273396 + 0.356638i
\(78\) −0.549141 −0.0621780
\(79\) −3.23685 + 5.60638i −0.364174 + 0.630767i −0.988643 0.150282i \(-0.951982\pi\)
0.624470 + 0.781049i \(0.285315\pi\)
\(80\) −4.74642 8.22104i −0.530666 0.919140i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.11808 + 5.40067i −0.344334 + 0.596404i
\(83\) −4.68019 −0.513717 −0.256859 0.966449i \(-0.582687\pi\)
−0.256859 + 0.966449i \(0.582687\pi\)
\(84\) 0.587159 1.41568i 0.0640643 0.154463i
\(85\) −22.9538 −2.48969
\(86\) −2.76569 + 4.79031i −0.298232 + 0.516552i
\(87\) −1.05416 1.82586i −0.113018 0.195753i
\(88\) −2.29100 3.96814i −0.244222 0.423005i
\(89\) −8.14048 + 14.0997i −0.862889 + 1.49457i 0.00623959 + 0.999981i \(0.498014\pi\)
−0.869128 + 0.494587i \(0.835319\pi\)
\(90\) −4.51532 −0.475957
\(91\) −1.20857 + 0.158545i −0.126693 + 0.0166200i
\(92\) 0.579274 0.0603935
\(93\) 4.03574 6.99011i 0.418487 0.724841i
\(94\) 2.74479 + 4.75412i 0.283103 + 0.490350i
\(95\) −11.1872 19.3768i −1.14778 1.98802i
\(96\) −1.58090 + 2.73821i −0.161350 + 0.279467i
\(97\) −6.78248 −0.688656 −0.344328 0.938849i \(-0.611893\pi\)
−0.344328 + 0.938849i \(0.611893\pi\)
\(98\) −2.16691 + 8.05730i −0.218891 + 0.813910i
\(99\) −1.49040 −0.149791
\(100\) 2.70825 4.69082i 0.270825 0.469082i
\(101\) 1.21872 + 2.11089i 0.121267 + 0.210041i 0.920268 0.391289i \(-0.127971\pi\)
−0.799000 + 0.601330i \(0.794638\pi\)
\(102\) −3.61116 6.25470i −0.357558 0.619308i
\(103\) −2.90373 + 5.02940i −0.286113 + 0.495562i −0.972878 0.231317i \(-0.925697\pi\)
0.686766 + 0.726879i \(0.259030\pi\)
\(104\) 1.41639 0.138888
\(105\) −9.93750 + 1.30364i −0.969801 + 0.127222i
\(106\) −6.34450 −0.616232
\(107\) −6.12909 + 10.6159i −0.592521 + 1.02628i 0.401371 + 0.915916i \(0.368534\pi\)
−0.993892 + 0.110361i \(0.964799\pi\)
\(108\) 0.289637 + 0.501666i 0.0278703 + 0.0482728i
\(109\) 4.49419 + 7.78417i 0.430465 + 0.745588i 0.996913 0.0785096i \(-0.0250161\pi\)
−0.566448 + 0.824097i \(0.691683\pi\)
\(110\) −3.36482 + 5.82804i −0.320823 + 0.555682i
\(111\) 11.3034 1.07287
\(112\) 2.54001 6.12413i 0.240008 0.578675i
\(113\) 6.08150 0.572099 0.286050 0.958215i \(-0.407658\pi\)
0.286050 + 0.958215i \(0.407658\pi\)
\(114\) 3.52001 6.09683i 0.329679 0.571021i
\(115\) −1.89410 3.28068i −0.176626 0.305925i
\(116\) 0.610649 + 1.05768i 0.0566973 + 0.0982027i
\(117\) 0.230356 0.398988i 0.0212964 0.0368864i
\(118\) 14.6501 1.34865
\(119\) −9.75340 12.7230i −0.894093 1.16632i
\(120\) 11.6462 1.06315
\(121\) 4.38935 7.60258i 0.399032 0.691144i
\(122\) −0.245435 0.425106i −0.0222207 0.0384873i
\(123\) −2.61596 4.53098i −0.235874 0.408545i
\(124\) −2.33780 + 4.04919i −0.209941 + 0.363628i
\(125\) −16.4805 −1.47406
\(126\) −1.91863 2.50279i −0.170925 0.222966i
\(127\) 2.84429 0.252390 0.126195 0.992005i \(-0.459724\pi\)
0.126195 + 0.992005i \(0.459724\pi\)
\(128\) −2.07110 + 3.58726i −0.183061 + 0.317072i
\(129\) −2.32032 4.01891i −0.204293 0.353845i
\(130\) −1.04013 1.80156i −0.0912254 0.158007i
\(131\) −4.96443 + 8.59865i −0.433745 + 0.751268i −0.997192 0.0748841i \(-0.976141\pi\)
0.563448 + 0.826152i \(0.309475\pi\)
\(132\) 0.863350 0.0751450
\(133\) 5.98674 14.4344i 0.519116 1.25162i
\(134\) 18.0232 1.55696
\(135\) 1.89410 3.28068i 0.163018 0.282356i
\(136\) 9.31416 + 16.1326i 0.798682 + 1.38336i
\(137\) 6.02046 + 10.4278i 0.514363 + 0.890903i 0.999861 + 0.0166652i \(0.00530494\pi\)
−0.485498 + 0.874238i \(0.661362\pi\)
\(138\) 0.595971 1.03225i 0.0507324 0.0878711i
\(139\) −1.51537 −0.128532 −0.0642659 0.997933i \(-0.520471\pi\)
−0.0642659 + 0.997933i \(0.520471\pi\)
\(140\) 5.75654 0.755162i 0.486516 0.0638228i
\(141\) −4.60558 −0.387859
\(142\) −4.08532 + 7.07599i −0.342833 + 0.593804i
\(143\) −0.343322 0.594652i −0.0287101 0.0497273i
\(144\) 1.25295 + 2.17017i 0.104412 + 0.180847i
\(145\) 3.99338 6.91674i 0.331633 0.574404i
\(146\) −14.4730 −1.19780
\(147\) −4.94518 4.95431i −0.407872 0.408625i
\(148\) −6.54777 −0.538223
\(149\) −9.12604 + 15.8068i −0.747635 + 1.29494i 0.201319 + 0.979526i \(0.435477\pi\)
−0.948954 + 0.315415i \(0.897856\pi\)
\(150\) −5.57262 9.65206i −0.455003 0.788088i
\(151\) 1.46583 + 2.53889i 0.119287 + 0.206612i 0.919485 0.393124i \(-0.128606\pi\)
−0.800198 + 0.599736i \(0.795272\pi\)
\(152\) −9.07906 + 15.7254i −0.736409 + 1.27550i
\(153\) 6.05928 0.489864
\(154\) −4.66018 + 0.611338i −0.375528 + 0.0492630i
\(155\) 30.5764 2.45596
\(156\) −0.133439 + 0.231123i −0.0106837 + 0.0185047i
\(157\) −8.39877 14.5471i −0.670295 1.16098i −0.977820 0.209445i \(-0.932834\pi\)
0.307526 0.951540i \(-0.400499\pi\)
\(158\) −3.85813 6.68248i −0.306937 0.531630i
\(159\) 2.66141 4.60970i 0.211064 0.365573i
\(160\) −11.9776 −0.946911
\(161\) 1.01361 2.44389i 0.0798838 0.192605i
\(162\) 1.19194 0.0936478
\(163\) 1.82489 3.16081i 0.142937 0.247574i −0.785665 0.618653i \(-0.787679\pi\)
0.928601 + 0.371079i \(0.121012\pi\)
\(164\) 1.51536 + 2.62468i 0.118330 + 0.204953i
\(165\) −2.82297 4.88953i −0.219768 0.380649i
\(166\) 2.78926 4.83113i 0.216488 0.374969i
\(167\) −15.2399 −1.17930 −0.589649 0.807660i \(-0.700734\pi\)
−0.589649 + 0.807660i \(0.700734\pi\)
\(168\) 4.94866 + 6.45538i 0.381797 + 0.498044i
\(169\) −12.7877 −0.983673
\(170\) 13.6798 23.6941i 1.04919 1.81725i
\(171\) 2.95317 + 5.11504i 0.225835 + 0.391157i
\(172\) 1.34410 + 2.32805i 0.102487 + 0.177512i
\(173\) −1.09316 + 1.89341i −0.0831113 + 0.143953i −0.904585 0.426294i \(-0.859819\pi\)
0.821474 + 0.570247i \(0.193152\pi\)
\(174\) 2.51300 0.190510
\(175\) −15.0511 19.6338i −1.13776 1.48417i
\(176\) 3.73479 0.281520
\(177\) −6.14546 + 10.6443i −0.461921 + 0.800071i
\(178\) −9.70298 16.8060i −0.727269 1.25967i
\(179\) 0.930522 + 1.61171i 0.0695505 + 0.120465i 0.898704 0.438557i \(-0.144510\pi\)
−0.829153 + 0.559022i \(0.811177\pi\)
\(180\) −1.09720 + 1.90041i −0.0817807 + 0.141648i
\(181\) −14.4867 −1.07679 −0.538394 0.842693i \(-0.680969\pi\)
−0.538394 + 0.842693i \(0.680969\pi\)
\(182\) 0.556616 1.34204i 0.0412592 0.0994786i
\(183\) 0.411824 0.0304429
\(184\) −1.53717 + 2.66246i −0.113322 + 0.196279i
\(185\) 21.4098 + 37.0829i 1.57408 + 2.72639i
\(186\) 4.81037 + 8.33181i 0.352714 + 0.610918i
\(187\) 4.51538 7.82087i 0.330197 0.571918i
\(188\) 2.66789 0.194576
\(189\) 2.62328 0.344130i 0.190815 0.0250318i
\(190\) 26.6690 1.93477
\(191\) −9.92673 + 17.1936i −0.718273 + 1.24409i 0.243411 + 0.969923i \(0.421734\pi\)
−0.961684 + 0.274162i \(0.911600\pi\)
\(192\) −4.39024 7.60412i −0.316838 0.548780i
\(193\) −0.779443 1.35003i −0.0561055 0.0971776i 0.836609 0.547801i \(-0.184535\pi\)
−0.892714 + 0.450624i \(0.851202\pi\)
\(194\) 4.04216 7.00123i 0.290210 0.502659i
\(195\) 1.74527 0.124981
\(196\) 2.86461 + 2.86990i 0.204615 + 0.204993i
\(197\) −2.48101 −0.176764 −0.0883822 0.996087i \(-0.528170\pi\)
−0.0883822 + 0.996087i \(0.528170\pi\)
\(198\) 0.888236 1.53847i 0.0631242 0.109334i
\(199\) 2.64623 + 4.58340i 0.187586 + 0.324909i 0.944445 0.328670i \(-0.106600\pi\)
−0.756859 + 0.653578i \(0.773267\pi\)
\(200\) 14.3733 + 24.8953i 1.01635 + 1.76036i
\(201\) −7.56042 + 13.0950i −0.533271 + 0.923652i
\(202\) −2.90529 −0.204415
\(203\) 5.53072 0.725538i 0.388180 0.0509228i
\(204\) −3.50998 −0.245748
\(205\) 9.90980 17.1643i 0.692131 1.19881i
\(206\) −3.46108 5.99476i −0.241145 0.417675i
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) −0.577247 + 0.999821i −0.0400249 + 0.0693251i
\(209\) 8.80282 0.608904
\(210\) 4.57678 11.0349i 0.315828 0.761483i
\(211\) 27.0118 1.85957 0.929784 0.368105i \(-0.119993\pi\)
0.929784 + 0.368105i \(0.119993\pi\)
\(212\) −1.54169 + 2.67028i −0.105883 + 0.183395i
\(213\) −3.42745 5.93652i −0.234845 0.406764i
\(214\) −7.30551 12.6535i −0.499395 0.864977i
\(215\) 8.78984 15.2245i 0.599462 1.03830i
\(216\) −3.07435 −0.209183
\(217\) 12.9924 + 16.9482i 0.881980 + 1.15052i
\(218\) −10.7136 −0.725619
\(219\) 6.07119 10.5156i 0.410253 0.710579i
\(220\) 1.63527 + 2.83238i 0.110250 + 0.190959i
\(221\) 1.39579 + 2.41758i 0.0938909 + 0.162624i
\(222\) −6.73651 + 11.6680i −0.452125 + 0.783103i
\(223\) −4.93735 −0.330630 −0.165315 0.986241i \(-0.552864\pi\)
−0.165315 + 0.986241i \(0.552864\pi\)
\(224\) −5.08945 6.63904i −0.340053 0.443589i
\(225\) 9.35049 0.623366
\(226\) −3.62440 + 6.27764i −0.241091 + 0.417582i
\(227\) −5.72866 9.92233i −0.380224 0.658568i 0.610870 0.791731i \(-0.290820\pi\)
−0.991094 + 0.133163i \(0.957487\pi\)
\(228\) −1.71069 2.96301i −0.113293 0.196230i
\(229\) 4.85646 8.41164i 0.320924 0.555857i −0.659755 0.751481i \(-0.729340\pi\)
0.980679 + 0.195624i \(0.0626732\pi\)
\(230\) 4.51532 0.297731
\(231\) 1.51069 3.64237i 0.0993961 0.239651i
\(232\) −6.48172 −0.425546
\(233\) −4.46345 + 7.73092i −0.292410 + 0.506470i −0.974379 0.224912i \(-0.927791\pi\)
0.681969 + 0.731381i \(0.261124\pi\)
\(234\) 0.274571 + 0.475570i 0.0179492 + 0.0310890i
\(235\) −8.72343 15.1094i −0.569054 0.985630i
\(236\) 3.55991 6.16594i 0.231730 0.401368i
\(237\) 6.47369 0.420511
\(238\) 18.9461 2.48541i 1.22809 0.161105i
\(239\) 14.7250 0.952480 0.476240 0.879315i \(-0.341999\pi\)
0.476240 + 0.879315i \(0.341999\pi\)
\(240\) −4.74642 + 8.22104i −0.306380 + 0.530666i
\(241\) 12.2335 + 21.1890i 0.788027 + 1.36490i 0.927174 + 0.374631i \(0.122231\pi\)
−0.139147 + 0.990272i \(0.544436\pi\)
\(242\) 5.23185 + 9.06184i 0.336316 + 0.582517i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −0.238559 −0.0152722
\(245\) 6.88684 25.6075i 0.439984 1.63600i
\(246\) 6.23615 0.397603
\(247\) −1.36056 + 2.35656i −0.0865703 + 0.149944i
\(248\) −12.4073 21.4900i −0.787862 1.36462i
\(249\) 2.34009 + 4.05316i 0.148297 + 0.256859i
\(250\) 9.82193 17.0121i 0.621193 1.07594i
\(251\) −2.61433 −0.165015 −0.0825076 0.996590i \(-0.526293\pi\)
−0.0825076 + 0.996590i \(0.526293\pi\)
\(252\) −1.51959 + 0.199346i −0.0957255 + 0.0125576i
\(253\) 1.49040 0.0937007
\(254\) −1.69511 + 2.93602i −0.106361 + 0.184222i
\(255\) 11.4769 + 19.8786i 0.718711 + 1.24484i
\(256\) 6.31185 + 10.9324i 0.394490 + 0.683277i
\(257\) 0.509978 0.883308i 0.0318116 0.0550993i −0.849681 0.527297i \(-0.823206\pi\)
0.881493 + 0.472197i \(0.156539\pi\)
\(258\) 5.53137 0.344368
\(259\) −11.4573 + 27.6243i −0.711921 + 1.71649i
\(260\) −1.01099 −0.0626988
\(261\) −1.05416 + 1.82586i −0.0652510 + 0.113018i
\(262\) −5.91732 10.2491i −0.365573 0.633191i
\(263\) −4.46901 7.74054i −0.275571 0.477302i 0.694708 0.719292i \(-0.255533\pi\)
−0.970279 + 0.241989i \(0.922200\pi\)
\(264\) −2.29100 + 3.96814i −0.141002 + 0.244222i
\(265\) 20.1639 1.23866
\(266\) 11.3321 + 14.7823i 0.694813 + 0.906363i
\(267\) 16.2810 0.996378
\(268\) 4.37955 7.58561i 0.267524 0.463365i
\(269\) 6.84056 + 11.8482i 0.417076 + 0.722397i 0.995644 0.0932372i \(-0.0297215\pi\)
−0.578568 + 0.815634i \(0.696388\pi\)
\(270\) 2.25766 + 3.91038i 0.137397 + 0.237978i
\(271\) 1.98691 3.44144i 0.120696 0.209052i −0.799346 0.600871i \(-0.794821\pi\)
0.920043 + 0.391819i \(0.128154\pi\)
\(272\) −15.1839 −0.920660
\(273\) 0.741590 + 0.967382i 0.0448831 + 0.0585486i
\(274\) −14.3521 −0.867042
\(275\) 6.96799 12.0689i 0.420186 0.727783i
\(276\) −0.289637 0.501666i −0.0174341 0.0301967i
\(277\) 5.00728 + 8.67286i 0.300858 + 0.521101i 0.976331 0.216284i \(-0.0693936\pi\)
−0.675472 + 0.737385i \(0.736060\pi\)
\(278\) 0.903115 1.56424i 0.0541652 0.0938169i
\(279\) −8.07148 −0.483227
\(280\) −11.8048 + 28.4621i −0.705471 + 1.70094i
\(281\) −21.3379 −1.27291 −0.636456 0.771313i \(-0.719600\pi\)
−0.636456 + 0.771313i \(0.719600\pi\)
\(282\) 2.74479 4.75412i 0.163450 0.283103i
\(283\) −7.24152 12.5427i −0.430463 0.745585i 0.566450 0.824096i \(-0.308317\pi\)
−0.996913 + 0.0785118i \(0.974983\pi\)
\(284\) 1.98543 + 3.43887i 0.117814 + 0.204059i
\(285\) −11.1872 + 19.3768i −0.662673 + 1.14778i
\(286\) 0.818441 0.0483954
\(287\) 13.7248 1.80046i 0.810149 0.106278i
\(288\) 3.16181 0.186311
\(289\) −9.85743 + 17.0736i −0.579849 + 1.00433i
\(290\) 4.75988 + 8.24436i 0.279510 + 0.484125i
\(291\) 3.39124 + 5.87380i 0.198798 + 0.344328i
\(292\) −3.51688 + 6.09142i −0.205810 + 0.356473i
\(293\) 33.1986 1.93948 0.969741 0.244134i \(-0.0785038\pi\)
0.969741 + 0.244134i \(0.0785038\pi\)
\(294\) 8.06128 2.15205i 0.470144 0.125510i
\(295\) −46.5605 −2.71086
\(296\) 17.3753 30.0949i 1.00992 1.74923i
\(297\) 0.745201 + 1.29073i 0.0432409 + 0.0748955i
\(298\) −10.8777 18.8408i −0.630129 1.09142i
\(299\) −0.230356 + 0.398988i −0.0133218 + 0.0230741i
\(300\) −5.41649 −0.312721
\(301\) 12.1737 1.59698i 0.701679 0.0920486i
\(302\) −3.49436 −0.201078
\(303\) 1.21872 2.11089i 0.0700137 0.121267i
\(304\) −7.40033 12.8178i −0.424438 0.735148i
\(305\) 0.780037 + 1.35106i 0.0446648 + 0.0773616i
\(306\) −3.61116 + 6.25470i −0.206436 + 0.357558i
\(307\) 31.4823 1.79679 0.898396 0.439187i \(-0.144733\pi\)
0.898396 + 0.439187i \(0.144733\pi\)
\(308\) −0.875103 + 2.10993i −0.0498636 + 0.120225i
\(309\) 5.80746 0.330375
\(310\) −18.2227 + 31.5626i −1.03498 + 1.79263i
\(311\) 9.10379 + 15.7682i 0.516229 + 0.894135i 0.999822 + 0.0188419i \(0.00599793\pi\)
−0.483594 + 0.875293i \(0.660669\pi\)
\(312\) −0.708193 1.22663i −0.0400935 0.0694440i
\(313\) −10.7276 + 18.5807i −0.606359 + 1.05025i 0.385476 + 0.922718i \(0.374037\pi\)
−0.991835 + 0.127527i \(0.959296\pi\)
\(314\) 20.0217 1.12989
\(315\) 6.09773 + 7.95431i 0.343568 + 0.448175i
\(316\) −3.75004 −0.210956
\(317\) 1.40432 2.43236i 0.0788747 0.136615i −0.823890 0.566750i \(-0.808201\pi\)
0.902765 + 0.430135i \(0.141534\pi\)
\(318\) 3.17225 + 5.49450i 0.177891 + 0.308116i
\(319\) 1.57113 + 2.72127i 0.0879662 + 0.152362i
\(320\) 16.6311 28.8060i 0.929708 1.61030i
\(321\) 12.2582 0.684184
\(322\) 1.91863 + 2.50279i 0.106921 + 0.139475i
\(323\) −35.7882 −1.99131
\(324\) 0.289637 0.501666i 0.0160909 0.0278703i
\(325\) 2.15394 + 3.73073i 0.119479 + 0.206944i
\(326\) 2.17517 + 3.76750i 0.120471 + 0.208663i
\(327\) 4.49419 7.78417i 0.248529 0.430465i
\(328\) −16.0848 −0.888132
\(329\) 4.66827 11.2555i 0.257370 0.620536i
\(330\) 6.72964 0.370454
\(331\) 13.5491 23.4678i 0.744727 1.28991i −0.205595 0.978637i \(-0.565913\pi\)
0.950322 0.311268i \(-0.100754\pi\)
\(332\) −1.35556 2.34789i −0.0743957 0.128857i
\(333\) −5.65171 9.78904i −0.309712 0.536436i
\(334\) 9.08253 15.7314i 0.496974 0.860784i
\(335\) −57.2808 −3.12959
\(336\) −6.57365 + 0.862354i −0.358622 + 0.0470452i
\(337\) 8.21670 0.447592 0.223796 0.974636i \(-0.428155\pi\)
0.223796 + 0.974636i \(0.428155\pi\)
\(338\) 7.62113 13.2002i 0.414535 0.717995i
\(339\) −3.04075 5.26673i −0.165151 0.286050i
\(340\) −6.64826 11.5151i −0.360553 0.624496i
\(341\) −6.01488 + 10.4181i −0.325724 + 0.564170i
\(342\) −7.04002 −0.380680
\(343\) 17.1203 7.06372i 0.924408 0.381405i
\(344\) −14.2669 −0.769221
\(345\) −1.89410 + 3.28068i −0.101975 + 0.176626i
\(346\) −1.30298 2.25683i −0.0700487 0.121328i
\(347\) −1.30625 2.26249i −0.0701230 0.121457i 0.828832 0.559497i \(-0.189006\pi\)
−0.898955 + 0.438041i \(0.855673\pi\)
\(348\) 0.610649 1.05768i 0.0327342 0.0566973i
\(349\) −16.3975 −0.877740 −0.438870 0.898551i \(-0.644621\pi\)
−0.438870 + 0.898551i \(0.644621\pi\)
\(350\) 29.2370 3.83541i 1.56279 0.205011i
\(351\) −0.460711 −0.0245910
\(352\) 2.35618 4.08103i 0.125585 0.217520i
\(353\) −14.5072 25.1273i −0.772142 1.33739i −0.936387 0.350969i \(-0.885852\pi\)
0.164245 0.986420i \(-0.447481\pi\)
\(354\) −7.32503 12.6873i −0.389321 0.674324i
\(355\) 12.9839 22.4887i 0.689113 1.19358i
\(356\) −9.43113 −0.499849
\(357\) −6.14176 + 14.8082i −0.325056 + 0.783733i
\(358\) −2.21826 −0.117239
\(359\) 15.0803 26.1199i 0.795910 1.37856i −0.126349 0.991986i \(-0.540326\pi\)
0.922259 0.386571i \(-0.126341\pi\)
\(360\) −5.82312 10.0859i −0.306906 0.531576i
\(361\) −7.94243 13.7567i −0.418022 0.724036i
\(362\) 8.63365 14.9539i 0.453775 0.785961i
\(363\) −8.77870 −0.460762
\(364\) −0.429584 0.560379i −0.0225163 0.0293719i
\(365\) 45.9978 2.40764
\(366\) −0.245435 + 0.425106i −0.0128291 + 0.0222207i
\(367\) −4.35916 7.55029i −0.227546 0.394122i 0.729534 0.683945i \(-0.239737\pi\)
−0.957080 + 0.289823i \(0.906404\pi\)
\(368\) −1.25295 2.17017i −0.0653144 0.113128i
\(369\) −2.61596 + 4.53098i −0.136182 + 0.235874i
\(370\) −51.0385 −2.65337
\(371\) 8.56795 + 11.1766i 0.444826 + 0.580262i
\(372\) 4.67560 0.242419
\(373\) 5.45347 9.44568i 0.282370 0.489079i −0.689598 0.724192i \(-0.742213\pi\)
0.971968 + 0.235113i \(0.0755461\pi\)
\(374\) 5.38207 + 9.32202i 0.278300 + 0.482030i
\(375\) 8.24027 + 14.2726i 0.425526 + 0.737032i
\(376\) −7.07956 + 12.2622i −0.365101 + 0.632373i
\(377\) −0.971330 −0.0500260
\(378\) −1.20817 + 2.91297i −0.0621414 + 0.149827i
\(379\) −11.5747 −0.594551 −0.297275 0.954792i \(-0.596078\pi\)
−0.297275 + 0.954792i \(0.596078\pi\)
\(380\) 6.48046 11.2245i 0.332440 0.575804i
\(381\) −1.42214 2.46322i −0.0728586 0.126195i
\(382\) −11.8321 20.4938i −0.605382 1.04855i
\(383\) −12.1224 + 20.9967i −0.619428 + 1.07288i 0.370163 + 0.928967i \(0.379302\pi\)
−0.989590 + 0.143913i \(0.954031\pi\)
\(384\) 4.14221 0.211381
\(385\) 14.8109 1.94294i 0.754832 0.0990214i
\(386\) 1.85810 0.0945748
\(387\) −2.32032 + 4.01891i −0.117948 + 0.204293i
\(388\) −1.96446 3.40254i −0.0997301 0.172738i
\(389\) −2.90240 5.02710i −0.147157 0.254884i 0.783018 0.621999i \(-0.213679\pi\)
−0.930176 + 0.367115i \(0.880346\pi\)
\(390\) −1.04013 + 1.80156i −0.0526690 + 0.0912254i
\(391\) −6.05928 −0.306431
\(392\) −20.7923 + 5.55072i −1.05017 + 0.280354i
\(393\) 9.92887 0.500845
\(394\) 1.47861 2.56103i 0.0744912 0.129023i
\(395\) 12.2618 + 21.2381i 0.616960 + 1.06861i
\(396\) −0.431675 0.747683i −0.0216925 0.0375725i
\(397\) 6.60091 11.4331i 0.331290 0.573812i −0.651475 0.758670i \(-0.725849\pi\)
0.982765 + 0.184859i \(0.0591827\pi\)
\(398\) −6.30830 −0.316207
\(399\) −15.4940 + 2.03255i −0.775668 + 0.101755i
\(400\) −23.4313 −1.17157
\(401\) −11.7994 + 20.4372i −0.589236 + 1.02059i 0.405097 + 0.914274i \(0.367238\pi\)
−0.994333 + 0.106313i \(0.966095\pi\)
\(402\) −9.01158 15.6085i −0.449457 0.778482i
\(403\) −1.85931 3.22042i −0.0926189 0.160421i
\(404\) −0.705973 + 1.22278i −0.0351235 + 0.0608356i
\(405\) −3.78820 −0.188237
\(406\) −2.54721 + 6.14150i −0.126416 + 0.304797i
\(407\) −16.8466 −0.835056
\(408\) 9.31416 16.1326i 0.461120 0.798682i
\(409\) −4.32065 7.48358i −0.213642 0.370039i 0.739209 0.673476i \(-0.235199\pi\)
−0.952852 + 0.303436i \(0.901866\pi\)
\(410\) 11.8119 + 20.4588i 0.583349 + 1.01039i
\(411\) 6.02046 10.4278i 0.296968 0.514363i
\(412\) −3.36411 −0.165738
\(413\) −19.7842 25.8080i −0.973519 1.26993i
\(414\) −1.19194 −0.0585808
\(415\) −8.86475 + 15.3542i −0.435154 + 0.753708i
\(416\) 0.728341 + 1.26152i 0.0357098 + 0.0618513i
\(417\) 0.757684 + 1.31235i 0.0371039 + 0.0642659i
\(418\) −5.24622 + 9.08673i −0.256601 + 0.444446i
\(419\) 30.0603 1.46854 0.734270 0.678858i \(-0.237525\pi\)
0.734270 + 0.678858i \(0.237525\pi\)
\(420\) −3.53226 4.60773i −0.172356 0.224834i
\(421\) −24.7510 −1.20629 −0.603144 0.797632i \(-0.706085\pi\)
−0.603144 + 0.797632i \(0.706085\pi\)
\(422\) −16.0982 + 27.8830i −0.783650 + 1.35732i
\(423\) 2.30279 + 3.98854i 0.111965 + 0.193930i
\(424\) −8.18210 14.1718i −0.397358 0.688244i
\(425\) −28.3286 + 49.0666i −1.37414 + 2.38008i
\(426\) 8.17065 0.395869
\(427\) −0.417430 + 1.00645i −0.0202008 + 0.0487056i
\(428\) −7.10084 −0.343232
\(429\) −0.343322 + 0.594652i −0.0165758 + 0.0287101i
\(430\) 10.4770 + 18.1467i 0.505245 + 0.875110i
\(431\) 7.82692 + 13.5566i 0.377010 + 0.653000i 0.990626 0.136605i \(-0.0436191\pi\)
−0.613616 + 0.789605i \(0.710286\pi\)
\(432\) 1.25295 2.17017i 0.0602824 0.104412i
\(433\) −0.941683 −0.0452544 −0.0226272 0.999744i \(-0.507203\pi\)
−0.0226272 + 0.999744i \(0.507203\pi\)
\(434\) −25.2379 + 3.31079i −1.21146 + 0.158923i
\(435\) −7.98677 −0.382936
\(436\) −2.60337 + 4.50916i −0.124679 + 0.215950i
\(437\) −2.95317 5.11504i −0.141269 0.244686i
\(438\) 7.23651 + 12.5340i 0.345774 + 0.598898i
\(439\) 9.42204 16.3194i 0.449689 0.778885i −0.548676 0.836035i \(-0.684868\pi\)
0.998366 + 0.0571502i \(0.0182014\pi\)
\(440\) −17.3576 −0.827490
\(441\) −1.81797 + 6.75981i −0.0865699 + 0.321896i
\(442\) −3.32740 −0.158268
\(443\) 1.26840 2.19693i 0.0602634 0.104379i −0.834320 0.551281i \(-0.814139\pi\)
0.894583 + 0.446902i \(0.147473\pi\)
\(444\) 3.27389 + 5.67054i 0.155372 + 0.269112i
\(445\) 30.8378 + 53.4126i 1.46185 + 2.53200i
\(446\) 2.94252 5.09659i 0.139332 0.241331i
\(447\) 18.2521 0.863294
\(448\) 23.0336 3.02163i 1.08824 0.142759i
\(449\) −34.2788 −1.61772 −0.808859 0.588003i \(-0.799914\pi\)
−0.808859 + 0.588003i \(0.799914\pi\)
\(450\) −5.57262 + 9.65206i −0.262696 + 0.455003i
\(451\) 3.89884 + 6.75298i 0.183589 + 0.317985i
\(452\) 1.76143 + 3.05088i 0.0828505 + 0.143501i
\(453\) 1.46583 2.53889i 0.0688706 0.119287i
\(454\) 13.6565 0.640929
\(455\) −1.76903 + 4.26524i −0.0829332 + 0.199958i
\(456\) 18.1581 0.850332
\(457\) 7.54327 13.0653i 0.352859 0.611170i −0.633890 0.773423i \(-0.718543\pi\)
0.986749 + 0.162253i \(0.0518762\pi\)
\(458\) 5.78862 + 10.0262i 0.270485 + 0.468493i
\(459\) −3.02964 5.24749i −0.141411 0.244932i
\(460\) 1.09720 1.90041i 0.0511574 0.0886072i
\(461\) 15.6065 0.726865 0.363433 0.931621i \(-0.381605\pi\)
0.363433 + 0.931621i \(0.381605\pi\)
\(462\) 2.85952 + 3.73016i 0.133037 + 0.173543i
\(463\) 6.25815 0.290841 0.145420 0.989370i \(-0.453547\pi\)
0.145420 + 0.989370i \(0.453547\pi\)
\(464\) 2.64162 4.57542i 0.122634 0.212409i
\(465\) −15.2882 26.4800i −0.708974 1.22798i
\(466\) −5.32018 9.21481i −0.246452 0.426868i
\(467\) −4.38154 + 7.58905i −0.202753 + 0.351179i −0.949415 0.314025i \(-0.898322\pi\)
0.746661 + 0.665205i \(0.231656\pi\)
\(468\) 0.266878 0.0123364
\(469\) −24.3395 31.7501i −1.12389 1.46608i
\(470\) 20.7956 0.959232
\(471\) −8.39877 + 14.5471i −0.386995 + 0.670295i
\(472\) 18.8933 + 32.7241i 0.869633 + 1.50625i
\(473\) 3.45821 + 5.98979i 0.159009 + 0.275411i
\(474\) −3.85813 + 6.68248i −0.177210 + 0.306937i
\(475\) −55.2272 −2.53400
\(476\) 3.55776 8.57800i 0.163070 0.393172i
\(477\) −5.32282 −0.243715
\(478\) −8.77567 + 15.1999i −0.401390 + 0.695227i
\(479\) 7.88811 + 13.6626i 0.360417 + 0.624260i 0.988029 0.154266i \(-0.0493012\pi\)
−0.627613 + 0.778526i \(0.715968\pi\)
\(480\) 5.98879 + 10.3729i 0.273350 + 0.473455i
\(481\) 2.60380 4.50992i 0.118723 0.205635i
\(482\) −29.1632 −1.32835
\(483\) −2.62328 + 0.344130i −0.119363 + 0.0156585i
\(484\) 5.08527 0.231149
\(485\) −12.8467 + 22.2511i −0.583339 + 1.01037i
\(486\) −0.595971 1.03225i −0.0270338 0.0468239i
\(487\) −20.2877 35.1393i −0.919323 1.59231i −0.800446 0.599405i \(-0.795404\pi\)
−0.118877 0.992909i \(-0.537929\pi\)
\(488\) 0.633045 1.09647i 0.0286566 0.0496347i
\(489\) −3.64979 −0.165049
\(490\) 22.3291 + 22.3703i 1.00872 + 1.01059i
\(491\) 9.38984 0.423757 0.211879 0.977296i \(-0.432042\pi\)
0.211879 + 0.977296i \(0.432042\pi\)
\(492\) 1.51536 2.62468i 0.0683177 0.118330i
\(493\) −6.38747 11.0634i −0.287677 0.498271i
\(494\) −1.62171 2.80888i −0.0729641 0.126377i
\(495\) −2.82297 + 4.88953i −0.126883 + 0.219768i
\(496\) 20.2263 0.908187
\(497\) 17.9823 2.35898i 0.806616 0.105815i
\(498\) −5.57851 −0.249979
\(499\) −9.53902 + 16.5221i −0.427025 + 0.739629i −0.996607 0.0823054i \(-0.973772\pi\)
0.569582 + 0.821934i \(0.307105\pi\)
\(500\) −4.77337 8.26773i −0.213472 0.369744i
\(501\) 7.61994 + 13.1981i 0.340434 + 0.589649i
\(502\) 1.55807 2.69865i 0.0695399 0.120447i
\(503\) 30.4559 1.35796 0.678982 0.734155i \(-0.262422\pi\)
0.678982 + 0.734155i \(0.262422\pi\)
\(504\) 3.11619 7.51336i 0.138806 0.334671i
\(505\) 9.23353 0.410887
\(506\) −0.888236 + 1.53847i −0.0394869 + 0.0683933i
\(507\) 6.39387 + 11.0745i 0.283962 + 0.491836i
\(508\) 0.823810 + 1.42688i 0.0365507 + 0.0633076i
\(509\) 11.1695 19.3462i 0.495082 0.857506i −0.504902 0.863176i \(-0.668472\pi\)
0.999984 + 0.00567004i \(0.00180484\pi\)
\(510\) −27.3596 −1.21150
\(511\) 19.5451 + 25.4961i 0.864626 + 1.12788i
\(512\) −23.3311 −1.03110
\(513\) 2.95317 5.11504i 0.130386 0.225835i
\(514\) 0.607865 + 1.05285i 0.0268118 + 0.0464393i
\(515\) 10.9999 + 19.0524i 0.484714 + 0.839549i
\(516\) 1.34410 2.32805i 0.0591707 0.102487i
\(517\) 6.86416 0.301885
\(518\) −21.6870 28.2901i −0.952873 1.24299i
\(519\) 2.18632 0.0959687
\(520\) 2.68278 4.64671i 0.117648 0.203772i
\(521\) 7.92935 + 13.7340i 0.347391 + 0.601699i 0.985785 0.168010i \(-0.0537342\pi\)
−0.638394 + 0.769710i \(0.720401\pi\)
\(522\) −1.25650 2.17632i −0.0549956 0.0952551i
\(523\) 9.36555 16.2216i 0.409527 0.709321i −0.585310 0.810810i \(-0.699027\pi\)
0.994837 + 0.101489i \(0.0323605\pi\)
\(524\) −5.75153 −0.251257
\(525\) −9.47777 + 22.8516i −0.413644 + 0.997324i
\(526\) 10.6536 0.464519
\(527\) 24.4537 42.3550i 1.06522 1.84501i
\(528\) −1.86739 3.23442i −0.0812679 0.140760i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −12.0171 + 20.8143i −0.521991 + 0.904114i
\(531\) 12.2909 0.533381
\(532\) 8.97524 1.17740i 0.389126 0.0510469i
\(533\) −2.41041 −0.104406
\(534\) −9.70298 + 16.8060i −0.419889 + 0.727269i
\(535\) 23.2182 + 40.2151i 1.00381 + 1.73865i
\(536\) 23.2433 + 40.2586i 1.00396 + 1.73891i
\(537\) 0.930522 1.61171i 0.0401550 0.0695505i
\(538\) −16.3071 −0.703049
\(539\) 7.37030 + 7.38391i 0.317461 + 0.318048i
\(540\) 2.19441 0.0944323
\(541\) 10.1229 17.5333i 0.435217 0.753817i −0.562097 0.827071i \(-0.690005\pi\)
0.997313 + 0.0732543i \(0.0233385\pi\)
\(542\) 2.36829 + 4.10199i 0.101727 + 0.176196i
\(543\) 7.24335 + 12.5458i 0.310842 + 0.538394i
\(544\) −9.57914 + 16.5916i −0.410702 + 0.711357i
\(545\) 34.0498 1.45853
\(546\) −1.44055 + 0.188976i −0.0616498 + 0.00808743i
\(547\) −11.9031 −0.508940 −0.254470 0.967081i \(-0.581901\pi\)
−0.254470 + 0.967081i \(0.581901\pi\)
\(548\) −3.48750 + 6.04052i −0.148979 + 0.258038i
\(549\) −0.205912 0.356650i −0.00878811 0.0152215i
\(550\) 8.30544 + 14.3854i 0.354145 + 0.613398i
\(551\) 6.22624 10.7842i 0.265247 0.459421i
\(552\) 3.07435 0.130853
\(553\) −6.56181 + 15.8210i −0.279037 + 0.672776i
\(554\) −11.9368 −0.507145
\(555\) 21.4098 37.0829i 0.908796 1.57408i
\(556\) −0.438906 0.760208i −0.0186138 0.0322400i
\(557\) −7.78105 13.4772i −0.329694 0.571046i 0.652757 0.757567i \(-0.273612\pi\)
−0.982451 + 0.186521i \(0.940279\pi\)
\(558\) 4.81037 8.33181i 0.203639 0.352714i
\(559\) −2.13799 −0.0904275
\(560\) −15.2803 19.9327i −0.645709 0.842309i
\(561\) −9.03076 −0.381279
\(562\) 12.7168 22.0261i 0.536424 0.929114i
\(563\) −10.0431 17.3951i −0.423264 0.733115i 0.572992 0.819561i \(-0.305782\pi\)
−0.996257 + 0.0864456i \(0.972449\pi\)
\(564\) −1.33394 2.31046i −0.0561692 0.0972879i
\(565\) 11.5190 19.9514i 0.484607 0.839364i
\(566\) 17.2629 0.725615
\(567\) −1.60966 2.09976i −0.0675995 0.0881816i
\(568\) −21.0743 −0.884259
\(569\) −7.55265 + 13.0816i −0.316623 + 0.548408i −0.979781 0.200072i \(-0.935882\pi\)
0.663158 + 0.748480i \(0.269216\pi\)
\(570\) −13.3345 23.0960i −0.558521 0.967387i
\(571\) −12.1016 20.9605i −0.506435 0.877170i −0.999972 0.00744602i \(-0.997630\pi\)
0.493538 0.869724i \(-0.335703\pi\)
\(572\) 0.198878 0.344466i 0.00831549 0.0144029i
\(573\) 19.8535 0.829390
\(574\) −6.32104 + 15.2405i −0.263835 + 0.636125i
\(575\) −9.35049 −0.389942
\(576\) −4.39024 + 7.60412i −0.182927 + 0.316838i
\(577\) −1.17864 2.04146i −0.0490673 0.0849871i 0.840449 0.541891i \(-0.182292\pi\)
−0.889516 + 0.456904i \(0.848958\pi\)
\(578\) −11.7495 20.3507i −0.488714 0.846478i
\(579\) −0.779443 + 1.35003i −0.0323925 + 0.0561055i
\(580\) 4.62653 0.192106
\(581\) −12.2774 + 1.61059i −0.509353 + 0.0668187i
\(582\) −8.08432 −0.335106
\(583\) −3.96657 + 6.87030i −0.164279 + 0.284539i
\(584\) −18.6649 32.3286i −0.772361 1.33777i
\(585\) −0.872634 1.51145i −0.0360790 0.0624906i
\(586\) −19.7854 + 34.2693i −0.817328 + 1.41565i
\(587\) −3.74241 −0.154466 −0.0772329 0.997013i \(-0.524608\pi\)
−0.0772329 + 0.997013i \(0.524608\pi\)
\(588\) 1.05310 3.91578i 0.0434292 0.161484i
\(589\) 47.6729 1.96433
\(590\) 27.7487 48.0622i 1.14240 1.97869i
\(591\) 1.24050 + 2.14862i 0.0510275 + 0.0883822i
\(592\) 14.1626 + 24.5303i 0.582078 + 1.00819i
\(593\) −2.26864 + 3.92941i −0.0931621 + 0.161361i −0.908840 0.417145i \(-0.863031\pi\)
0.815678 + 0.578506i \(0.196364\pi\)
\(594\) −1.77647 −0.0728895
\(595\) −60.2141 + 7.89909i −2.46854 + 0.323831i
\(596\) −10.5730 −0.433085
\(597\) 2.64623 4.58340i 0.108303 0.187586i
\(598\) −0.274571 0.475570i −0.0112280 0.0194475i
\(599\) −17.6106 30.5025i −0.719551 1.24630i −0.961178 0.275930i \(-0.911014\pi\)
0.241626 0.970369i \(-0.422319\pi\)
\(600\) 14.3733 24.8953i 0.586788 1.01635i
\(601\) 29.5802 1.20660 0.603302 0.797513i \(-0.293852\pi\)
0.603302 + 0.797513i \(0.293852\pi\)
\(602\) −5.60667 + 13.5181i −0.228511 + 0.550955i
\(603\) 15.1208 0.615768
\(604\) −0.849115 + 1.47071i −0.0345500 + 0.0598424i
\(605\) −16.6278 28.8001i −0.676015 1.17089i
\(606\) 1.45264 + 2.51605i 0.0590097 + 0.102208i
\(607\) −10.8420 + 18.7789i −0.440062 + 0.762210i −0.997694 0.0678785i \(-0.978377\pi\)
0.557631 + 0.830089i \(0.311710\pi\)
\(608\) −18.6747 −0.757360
\(609\) −3.39369 4.42697i −0.137519 0.179390i
\(610\) −1.85952 −0.0752896
\(611\) −1.06092 + 1.83757i −0.0429202 + 0.0743400i
\(612\) 1.75499 + 3.03973i 0.0709413 + 0.122874i
\(613\) 12.4937 + 21.6398i 0.504617 + 0.874023i 0.999986 + 0.00533991i \(0.00169975\pi\)
−0.495368 + 0.868683i \(0.664967\pi\)
\(614\) −18.7626 + 32.4977i −0.757195 + 1.31150i
\(615\) −19.8196 −0.799204
\(616\) −7.37549 9.62111i −0.297167 0.387646i
\(617\) −15.3643 −0.618542 −0.309271 0.950974i \(-0.600085\pi\)
−0.309271 + 0.950974i \(0.600085\pi\)
\(618\) −3.46108 + 5.99476i −0.139225 + 0.241145i
\(619\) −11.8444 20.5151i −0.476067 0.824572i 0.523557 0.851991i \(-0.324605\pi\)
−0.999624 + 0.0274185i \(0.991271\pi\)
\(620\) 8.85606 + 15.3392i 0.355668 + 0.616035i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) −21.7024 −0.870187
\(623\) −16.5026 + 39.7888i −0.661162 + 1.59411i
\(624\) 1.15449 0.0462167
\(625\) −7.83961 + 13.5786i −0.313584 + 0.543144i
\(626\) −12.7867 22.1472i −0.511058 0.885179i
\(627\) −4.40141 7.62346i −0.175775 0.304452i
\(628\) 4.86519 8.42675i 0.194142 0.336264i
\(629\) 68.4905 2.73090
\(630\) −11.8449 + 1.55386i −0.471913 + 0.0619072i
\(631\) 12.2965 0.489515 0.244758 0.969584i \(-0.421292\pi\)
0.244758 + 0.969584i \(0.421292\pi\)
\(632\) 9.95118 17.2360i 0.395837 0.685609i
\(633\) −13.5059 23.3929i −0.536811 0.929784i
\(634\) 1.67387 + 2.89923i 0.0664780 + 0.115143i
\(635\) 5.38737 9.33119i 0.213791 0.370297i
\(636\) 3.08337 0.122264
\(637\) −3.11586 + 0.831813i −0.123455 + 0.0329576i
\(638\) −3.74538 −0.148281
\(639\) −3.42745 + 5.93652i −0.135588 + 0.234845i
\(640\) 7.84577 + 13.5893i 0.310131 + 0.537163i
\(641\) −1.55282 2.68956i −0.0613326 0.106231i 0.833729 0.552174i \(-0.186202\pi\)
−0.895061 + 0.445943i \(0.852868\pi\)
\(642\) −7.30551 + 12.6535i −0.288326 + 0.499395i
\(643\) 44.2523 1.74514 0.872570 0.488489i \(-0.162452\pi\)
0.872570 + 0.488489i \(0.162452\pi\)
\(644\) 1.51959 0.199346i 0.0598804 0.00785532i
\(645\) −17.5797 −0.692199
\(646\) 21.3287 36.9424i 0.839167 1.45348i
\(647\) −14.2931 24.7564i −0.561919 0.973273i −0.997329 0.0730404i \(-0.976730\pi\)
0.435410 0.900232i \(-0.356604\pi\)
\(648\) 1.53717 + 2.66246i 0.0603858 + 0.104591i
\(649\) 9.15920 15.8642i 0.359530 0.622725i
\(650\) −5.13474 −0.201401
\(651\) 8.18136 19.7258i 0.320653 0.773115i
\(652\) 2.11423 0.0827995
\(653\) −4.85971 + 8.41727i −0.190175 + 0.329393i −0.945308 0.326179i \(-0.894239\pi\)
0.755133 + 0.655572i \(0.227572\pi\)
\(654\) 5.35681 + 9.27828i 0.209468 + 0.362809i
\(655\) 18.8063 + 32.5734i 0.734822 + 1.27275i
\(656\) 6.55533 11.3542i 0.255943 0.443306i
\(657\) −12.1424 −0.473719
\(658\) 8.83637 + 11.5268i 0.344478 + 0.449361i
\(659\) 29.8923 1.16444 0.582220 0.813031i \(-0.302184\pi\)
0.582220 + 0.813031i \(0.302184\pi\)
\(660\) 1.63527 2.83238i 0.0636529 0.110250i
\(661\) −21.5812 37.3797i −0.839411 1.45390i −0.890388 0.455202i \(-0.849567\pi\)
0.0509778 0.998700i \(-0.483766\pi\)
\(662\) 16.1498 + 27.9722i 0.627679 + 1.08717i
\(663\) 1.39579 2.41758i 0.0542080 0.0938909i
\(664\) 14.3885 0.558383
\(665\) −36.0153 46.9809i −1.39661 1.82184i
\(666\) 13.4730 0.522069
\(667\) 1.05416 1.82586i 0.0408174 0.0706977i
\(668\) −4.41403 7.64533i −0.170784 0.295807i
\(669\) 2.46868 + 4.27587i 0.0954446 + 0.165315i
\(670\) 34.1377 59.1282i 1.31885 2.28432i
\(671\) −0.613783 −0.0236948
\(672\) −3.20485 + 7.72711i −0.123630 + 0.298080i
\(673\) 2.93645 0.113192 0.0565959 0.998397i \(-0.481975\pi\)
0.0565959 + 0.998397i \(0.481975\pi\)
\(674\) −4.89692 + 8.48171i −0.188622 + 0.326703i
\(675\) −4.67524 8.09776i −0.179950 0.311683i
\(676\) −3.70380 6.41518i −0.142454 0.246738i
\(677\) −19.2810 + 33.3956i −0.741028 + 1.28350i 0.211000 + 0.977486i \(0.432328\pi\)
−0.952028 + 0.306012i \(0.901005\pi\)
\(678\) 7.24879 0.278388
\(679\) −17.7923 + 2.33405i −0.682806 + 0.0895728i
\(680\) 70.5679 2.70615
\(681\) −5.72866 + 9.92233i −0.219523 + 0.380224i
\(682\) −7.16938 12.4177i −0.274530 0.475500i
\(683\) 7.12801 + 12.3461i 0.272746 + 0.472409i 0.969564 0.244839i \(-0.0787350\pi\)
−0.696818 + 0.717248i \(0.745402\pi\)
\(684\) −1.71069 + 2.96301i −0.0654100 + 0.113293i
\(685\) 45.6135 1.74280
\(686\) −2.91165 + 21.8822i −0.111167 + 0.835467i
\(687\) −9.71293 −0.370571
\(688\) 5.81447 10.0710i 0.221675 0.383952i
\(689\) −1.22614 2.12374i −0.0467123 0.0809081i
\(690\) −2.25766 3.91038i −0.0859477 0.148866i
\(691\) −0.731849 + 1.26760i −0.0278408 + 0.0482217i −0.879610 0.475695i \(-0.842196\pi\)
0.851769 + 0.523917i \(0.175530\pi\)
\(692\) −1.26648 −0.0481442
\(693\) −3.90973 + 0.512892i −0.148518 + 0.0194832i
\(694\) 3.11394 0.118204
\(695\) −2.87026 + 4.97144i −0.108875 + 0.188577i
\(696\) 3.24086 + 5.61334i 0.122845 + 0.212773i
\(697\) −15.8509 27.4545i −0.600394 1.03991i
\(698\) 9.77246 16.9264i 0.369893 0.640674i
\(699\) 8.92690 0.337646
\(700\) 5.49023 13.2373i 0.207511 0.500323i
\(701\) −26.8881 −1.01555 −0.507775 0.861490i \(-0.669532\pi\)
−0.507775 + 0.861490i \(0.669532\pi\)
\(702\) 0.274571 0.475570i 0.0103630 0.0179492i
\(703\) 33.3809 + 57.8174i 1.25898 + 2.18062i
\(704\) 6.54322 + 11.3332i 0.246607 + 0.427136i
\(705\) −8.72343 + 15.1094i −0.328543 + 0.569054i
\(706\) 34.5835 1.30157
\(707\) 3.92346 + 5.11804i 0.147557 + 0.192484i
\(708\) −7.11981 −0.267579
\(709\) −1.83576 + 3.17963i −0.0689435 + 0.119414i −0.898437 0.439103i \(-0.855296\pi\)
0.829493 + 0.558517i \(0.188629\pi\)
\(710\) 15.4760 + 26.8053i 0.580805 + 1.00598i
\(711\) −3.23685 5.60638i −0.121391 0.210256i
\(712\) 25.0266 43.3474i 0.937913 1.62451i
\(713\) 8.07148 0.302279
\(714\) −11.6255 15.1651i −0.435073 0.567540i
\(715\) −2.60115 −0.0972775
\(716\) −0.539027 + 0.933622i −0.0201444 + 0.0348911i
\(717\) −7.36249 12.7522i −0.274957 0.476240i
\(718\) 17.9749 + 31.1334i 0.670817 + 1.16189i
\(719\) 9.29585 16.1009i 0.346677 0.600462i −0.638980 0.769223i \(-0.720643\pi\)
0.985657 + 0.168761i \(0.0539767\pi\)
\(720\) 9.49284 0.353777
\(721\) −5.88651 + 14.1928i −0.219225 + 0.528566i
\(722\) 18.9338 0.704644
\(723\) 12.2335 21.1890i 0.454968 0.788027i
\(724\) −4.19588 7.26748i −0.155939 0.270094i
\(725\) −9.85694 17.0727i −0.366078 0.634065i
\(726\) 5.23185 9.06184i 0.194172 0.336316i
\(727\) 16.8322 0.624273 0.312136 0.950037i \(-0.398955\pi\)
0.312136 + 0.950037i \(0.398955\pi\)
\(728\) 3.71557 0.487421i 0.137708 0.0180650i
\(729\) 1.00000 0.0370370
\(730\) −27.4134 + 47.4814i −1.01461 + 1.75736i
\(731\) −14.0595 24.3517i −0.520008 0.900680i
\(732\) 0.119279 + 0.206598i 0.00440869 + 0.00763608i
\(733\) −9.42942 + 16.3322i −0.348284 + 0.603245i −0.985945 0.167072i \(-0.946569\pi\)
0.637661 + 0.770317i \(0.279902\pi\)
\(734\) 10.3917 0.383566
\(735\) −25.6202 + 6.83959i −0.945015 + 0.252282i
\(736\) −3.16181 −0.116546
\(737\) 11.2681 19.5168i 0.415064 0.718912i
\(738\) −3.11808 5.40067i −0.114778 0.198801i
\(739\) −22.3548 38.7196i −0.822333 1.42432i −0.903940 0.427659i \(-0.859339\pi\)
0.0816069 0.996665i \(-0.473995\pi\)
\(740\) −12.4021 + 21.4811i −0.455912 + 0.789663i
\(741\) 2.72112 0.0999628
\(742\) −16.6434 + 2.18333i −0.610997 + 0.0801527i
\(743\) 49.0083 1.79794 0.898970 0.438011i \(-0.144317\pi\)
0.898970 + 0.438011i \(0.144317\pi\)
\(744\) −12.4073 + 21.4900i −0.454872 + 0.787862i
\(745\) 34.5713 + 59.8793i 1.26659 + 2.19381i
\(746\) 6.50022 + 11.2587i 0.237990 + 0.412211i
\(747\) 2.34009 4.05316i 0.0856196 0.148297i
\(748\) 5.23128 0.191275
\(749\) −12.4250 + 29.9576i −0.454001 + 1.09463i
\(750\) −19.6439 −0.717292
\(751\) −5.85462 + 10.1405i −0.213638 + 0.370032i −0.952850 0.303440i \(-0.901865\pi\)
0.739212 + 0.673472i \(0.235198\pi\)
\(752\) −5.77054 9.99487i −0.210430 0.364475i
\(753\) 1.30717 + 2.26408i 0.0476358 + 0.0825076i
\(754\) 0.578884 1.00266i 0.0210817 0.0365146i
\(755\) 11.1057 0.404178
\(756\) 0.932436 + 1.21633i 0.0339124 + 0.0442377i
\(757\) −24.2422 −0.881096 −0.440548 0.897729i \(-0.645216\pi\)
−0.440548 + 0.897729i \(0.645216\pi\)
\(758\) 6.89817 11.9480i 0.250553 0.433970i
\(759\) −0.745201 1.29073i −0.0270491 0.0468504i
\(760\) 34.3933 + 59.5710i 1.24758 + 2.16087i
\(761\) −15.3628 + 26.6091i −0.556900 + 0.964579i 0.440853 + 0.897579i \(0.354676\pi\)
−0.997753 + 0.0669997i \(0.978657\pi\)
\(762\) 3.39022 0.122815
\(763\) 14.4683 + 18.8734i 0.523786 + 0.683264i
\(764\) −11.5006 −0.416077
\(765\) 11.4769 19.8786i 0.414948 0.718711i
\(766\) −14.4492 25.0268i −0.522072 0.904256i
\(767\) 2.83128 + 4.90393i 0.102232 + 0.177071i
\(768\) 6.31185 10.9324i 0.227759 0.394490i
\(769\) −39.0901 −1.40963 −0.704813 0.709393i \(-0.748969\pi\)
−0.704813 + 0.709393i \(0.748969\pi\)
\(770\) −6.82125 + 16.4465i −0.245821 + 0.592690i
\(771\) −1.01996 −0.0367328
\(772\) 0.451511 0.782039i 0.0162502 0.0281462i
\(773\) −0.437496 0.757766i −0.0157356 0.0272549i 0.858050 0.513566i \(-0.171676\pi\)
−0.873786 + 0.486311i \(0.838342\pi\)
\(774\) −2.76569 4.79031i −0.0994105 0.172184i
\(775\) 37.7362 65.3610i 1.35552 2.34783i
\(776\) 20.8517 0.748532
\(777\) 29.6520 3.88984i 1.06376 0.139547i
\(778\) 6.91898 0.248057
\(779\) 15.4508 26.7615i 0.553581 0.958831i
\(780\) 0.505494 + 0.875542i 0.0180996 + 0.0313494i
\(781\) 5.10828 + 8.84780i 0.182789 + 0.316599i
\(782\) 3.61116 6.25470i 0.129135 0.223668i
\(783\) 2.10833 0.0753454
\(784\) 4.55564 16.9394i 0.162701 0.604977i
\(785\) −63.6325 −2.27114
\(786\) −5.91732 + 10.2491i −0.211064 + 0.365573i
\(787\) −6.16206 10.6730i −0.219654 0.380452i 0.735048 0.678015i \(-0.237159\pi\)
−0.954702 + 0.297563i \(0.903826\pi\)
\(788\) −0.718591 1.24464i −0.0255988 0.0443384i
\(789\) −4.46901 + 7.74054i −0.159101 + 0.275571i
\(790\) −29.2308 −1.03998
\(791\) 15.9534 2.09283i 0.567239 0.0744123i
\(792\) 4.58201 0.162815
\(793\) 0.0948660 0.164313i 0.00336879 0.00583492i
\(794\) 7.86791 + 13.6276i 0.279222 + 0.483626i
\(795\) −10.0820 17.4625i −0.357571 0.619330i
\(796\) −1.53289 + 2.65504i −0.0543319 + 0.0941056i
\(797\) −33.6866 −1.19324 −0.596621 0.802524i \(-0.703490\pi\)
−0.596621 + 0.802524i \(0.703490\pi\)
\(798\) 7.13585 17.2050i 0.252606 0.609051i
\(799\) −27.9065 −0.987260
\(800\) −14.7822 + 25.6036i −0.522631 + 0.905223i
\(801\) −8.14048 14.0997i −0.287630 0.498189i
\(802\) −14.0643 24.3600i −0.496626 0.860181i
\(803\) −9.04851 + 15.6725i −0.319315 + 0.553070i
\(804\) −8.75911 −0.308910
\(805\) −6.09773 7.95431i −0.214917 0.280353i
\(806\) 4.43238 0.156124
\(807\) 6.84056 11.8482i 0.240799 0.417076i
\(808\) −3.74677 6.48959i −0.131811 0.228303i
\(809\) 2.94113 + 5.09419i 0.103405 + 0.179102i 0.913085 0.407769i \(-0.133693\pi\)
−0.809681 + 0.586871i \(0.800360\pi\)
\(810\) 2.25766 3.91038i 0.0793261 0.137397i
\(811\) 13.3036 0.467152 0.233576 0.972339i \(-0.424957\pi\)
0.233576 + 0.972339i \(0.424957\pi\)
\(812\) 1.96588 + 2.56443i 0.0689888 + 0.0899939i
\(813\) −3.97383 −0.139368
\(814\) 10.0401 17.3900i 0.351905 0.609518i
\(815\) −6.91307 11.9738i −0.242154 0.419424i
\(816\) 7.59196 + 13.1497i 0.265772 + 0.460330i
\(817\) 13.7046 23.7371i 0.479463 0.830454i
\(818\) 10.2999 0.360128
\(819\) 0.466983 1.12593i 0.0163177 0.0393431i
\(820\) 11.4810 0.400933
\(821\) −19.5406 + 33.8454i −0.681973 + 1.18121i 0.292405 + 0.956295i \(0.405545\pi\)
−0.974378 + 0.224917i \(0.927789\pi\)
\(822\) 7.17605 + 12.4293i 0.250293 + 0.433521i
\(823\) 9.50351 + 16.4606i 0.331272 + 0.573779i 0.982761 0.184878i \(-0.0591890\pi\)
−0.651490 + 0.758657i \(0.725856\pi\)
\(824\) 8.92706 15.4621i 0.310989 0.538649i
\(825\) −13.9360 −0.485189
\(826\) 38.4312 5.04153i 1.33719 0.175417i
\(827\) 35.8180 1.24551 0.622757 0.782415i \(-0.286012\pi\)
0.622757 + 0.782415i \(0.286012\pi\)
\(828\) −0.289637 + 0.501666i −0.0100656 + 0.0174341i
\(829\) 13.5527 + 23.4740i 0.470706 + 0.815287i 0.999439 0.0335018i \(-0.0106659\pi\)
−0.528733 + 0.848788i \(0.677333\pi\)
\(830\) −10.5663 18.3013i −0.366761 0.635248i
\(831\) 5.00728 8.67286i 0.173700 0.300858i
\(832\) −4.04527 −0.140244
\(833\) −29.9642 30.0196i −1.03820 1.04012i
\(834\) −1.80623 −0.0625446
\(835\) −28.8659 + 49.9972i −0.998945 + 1.73022i
\(836\) 2.54962 + 4.41607i 0.0881805 + 0.152733i
\(837\) 4.03574 + 6.99011i 0.139496 + 0.241614i
\(838\) −17.9150 + 31.0298i −0.618865 + 1.07191i
\(839\) 25.7997 0.890704 0.445352 0.895356i \(-0.353079\pi\)
0.445352 + 0.895356i \(0.353079\pi\)
\(840\) 30.5513 4.00782i 1.05412 0.138283i
\(841\) −24.5550 −0.846723
\(842\) 14.7509 25.5492i 0.508348 0.880484i
\(843\) 10.6689 + 18.4791i 0.367458 + 0.636456i
\(844\) 7.82361 + 13.5509i 0.269300 + 0.466441i
\(845\) −24.2213 + 41.9525i −0.833238 + 1.44321i
\(846\) −5.48958 −0.188736
\(847\) 8.89820 21.4542i 0.305746 0.737174i
\(848\) 13.3384 0.458044
\(849\) −7.24152 + 12.5427i −0.248528 + 0.430463i
\(850\) −33.7661 58.4845i −1.15817 2.00600i
\(851\) 5.65171 + 9.78904i 0.193738 + 0.335564i
\(852\) 1.98543 3.43887i 0.0680198 0.117814i
\(853\) −6.24250 −0.213739 −0.106870 0.994273i \(-0.534083\pi\)
−0.106870 + 0.994273i \(0.534083\pi\)
\(854\) −0.790136 1.03071i −0.0270379 0.0352701i
\(855\) 22.3744 0.765189
\(856\) 18.8429 32.6369i 0.644038 1.11551i
\(857\) −10.9852 19.0270i −0.375249 0.649950i 0.615115 0.788437i \(-0.289109\pi\)
−0.990364 + 0.138487i \(0.955776\pi\)
\(858\) −0.409220 0.708791i −0.0139706 0.0241977i
\(859\) −10.1658 + 17.6078i −0.346854 + 0.600769i −0.985689 0.168575i \(-0.946083\pi\)
0.638835 + 0.769344i \(0.279417\pi\)
\(860\) 10.1835 0.347253
\(861\) −8.42164 10.9858i −0.287009 0.374394i
\(862\) −18.6585 −0.635510
\(863\) −13.8855 + 24.0503i −0.472667 + 0.818683i −0.999511 0.0312790i \(-0.990042\pi\)
0.526844 + 0.849962i \(0.323375\pi\)
\(864\) −1.58090 2.73821i −0.0537835 0.0931557i
\(865\) 4.14111 + 7.17261i 0.140802 + 0.243876i
\(866\) 0.561216 0.972054i 0.0190709 0.0330317i
\(867\) 19.7149 0.669552
\(868\) −4.73925 + 11.4266i −0.160860 + 0.387846i
\(869\) −9.64840 −0.327300
\(870\) 4.75988 8.24436i 0.161375 0.279510i
\(871\) 3.48317 + 6.03303i 0.118023 + 0.204421i
\(872\) −13.8167 23.9312i −0.467892 0.810413i
\(873\) 3.39124 5.87380i 0.114776 0.198798i
\(874\) 7.04002 0.238132
\(875\) −43.2330 + 5.67145i −1.46154 + 0.191730i
\(876\) 7.03376 0.237649
\(877\) −16.2656 + 28.1729i −0.549251 + 0.951331i 0.449075 + 0.893494i \(0.351754\pi\)
−0.998326 + 0.0578367i \(0.981580\pi\)
\(878\) 11.2305 + 19.4518i 0.379012 + 0.656468i
\(879\) −16.5993 28.7508i −0.559880 0.969741i
\(880\) 7.07407 12.2526i 0.238467 0.413037i
\(881\) 3.88986 0.131053 0.0655263 0.997851i \(-0.479127\pi\)
0.0655263 + 0.997851i \(0.479127\pi\)
\(882\) −5.89437 5.90525i −0.198474 0.198840i
\(883\) −35.6597 −1.20004 −0.600022 0.799984i \(-0.704841\pi\)
−0.600022 + 0.799984i \(0.704841\pi\)
\(884\) −0.808544 + 1.40044i −0.0271943 + 0.0471019i
\(885\) 23.2803 + 40.3226i 0.782557 + 1.35543i
\(886\) 1.51186 + 2.61861i 0.0507918 + 0.0879740i
\(887\) 23.8635 41.3328i 0.801259 1.38782i −0.117529 0.993069i \(-0.537497\pi\)
0.918788 0.394752i \(-0.129169\pi\)
\(888\) −34.7506 −1.16615
\(889\) 7.46134 0.978804i 0.250245 0.0328280i
\(890\) −73.5137 −2.46419
\(891\) 0.745201 1.29073i 0.0249652 0.0432409i
\(892\) −1.43004 2.47690i −0.0478813 0.0829328i
\(893\) −13.6010 23.5577i −0.455142 0.788328i
\(894\) −10.8777 + 18.8408i −0.363805 + 0.630129i
\(895\) 7.05002 0.235656
\(896\) −4.19859 + 10.1231i −0.140265 + 0.338189i
\(897\) 0.460711 0.0153827
\(898\) 20.4292 35.3844i 0.681731 1.18079i
\(899\) 8.50866 + 14.7374i 0.283780 + 0.491521i
\(900\) 2.70825 + 4.69082i 0.0902749 + 0.156361i
\(901\) 16.1262 27.9315i 0.537243 0.930532i
\(902\) −9.29437 −0.309469
\(903\) −7.46987 9.74422i −0.248582 0.324267i
\(904\) −18.6966 −0.621840
\(905\) −27.4393 + 47.5262i −0.912113 + 1.57983i
\(906\) 1.74718 + 3.02621i 0.0580462 + 0.100539i
\(907\) 4.94034 + 8.55693i 0.164041 + 0.284128i 0.936314 0.351163i \(-0.114214\pi\)
−0.772273 + 0.635291i \(0.780880\pi\)
\(908\) 3.31846 5.74774i 0.110127 0.190746i
\(909\) −2.43744 −0.0808448
\(910\) −3.34852 4.36804i −0.111002 0.144799i
\(911\) −22.5568 −0.747339 −0.373669 0.927562i \(-0.621901\pi\)
−0.373669 + 0.927562i \(0.621901\pi\)
\(912\) −7.40033 + 12.8178i −0.245049 + 0.424438i
\(913\) −3.48768 6.04084i −0.115425 0.199923i
\(914\) 8.99114 + 15.5731i 0.297400 + 0.515113i
\(915\) 0.780037 1.35106i 0.0257872 0.0446648i
\(916\) 5.62644 0.185903
\(917\) −10.0640 + 24.2650i −0.332343 + 0.801302i
\(918\) 7.22231 0.238372
\(919\) −17.5510 + 30.3992i −0.578954 + 1.00278i 0.416646 + 0.909069i \(0.363206\pi\)
−0.995600 + 0.0937089i \(0.970128\pi\)
\(920\) 5.82312 + 10.0859i 0.191983 + 0.332524i
\(921\) −15.7412 27.2645i −0.518689 0.898396i
\(922\) −9.30100 + 16.1098i −0.306312 + 0.530548i
\(923\) −3.15813 −0.103951
\(924\) 2.26481 0.297105i 0.0745067 0.00977403i
\(925\) 105.692 3.47515
\(926\) −3.72968 + 6.45999i −0.122565 + 0.212288i
\(927\) −2.90373 5.02940i −0.0953709 0.165187i
\(928\) −3.33306 5.77303i −0.109413 0.189509i
\(929\) 23.8750 41.3527i 0.783314 1.35674i −0.146688 0.989183i \(-0.546861\pi\)
0.930001 0.367556i \(-0.119805\pi\)
\(930\) 36.4453 1.19509
\(931\) 10.7375 39.9257i 0.351909 1.30851i
\(932\) −5.17112 −0.169386
\(933\) 9.10379 15.7682i 0.298045 0.516229i
\(934\) −5.22254 9.04571i −0.170887 0.295985i
\(935\) −17.1052 29.6270i −0.559399 0.968908i
\(936\) −0.708193 + 1.22663i −0.0231480 + 0.0400935i
\(937\) 16.1702 0.528258 0.264129 0.964487i \(-0.414916\pi\)
0.264129 + 0.964487i \(0.414916\pi\)
\(938\) 47.2797 6.20231i 1.54374 0.202513i
\(939\) 21.4552 0.700164
\(940\) 5.05325 8.75249i 0.164819 0.285475i
\(941\) 23.8793 + 41.3601i 0.778441 + 1.34830i 0.932840 + 0.360291i \(0.117323\pi\)
−0.154398 + 0.988009i \(0.549344\pi\)
\(942\) −10.0108 17.3393i −0.326171 0.564945i
\(943\) 2.61596 4.53098i 0.0851875 0.147549i
\(944\) −30.7998 −1.00245
\(945\) 3.83977 9.25795i 0.124908 0.301161i
\(946\) −8.24397 −0.268034
\(947\) −2.44092 + 4.22780i −0.0793192 + 0.137385i −0.902956 0.429732i \(-0.858608\pi\)
0.823637 + 0.567117i \(0.191941\pi\)
\(948\) 1.87502 + 3.24763i 0.0608978 + 0.105478i
\(949\) −2.79707 4.84466i −0.0907966 0.157264i
\(950\) 32.9138 57.0084i 1.06786 1.84960i
\(951\) −2.80865 −0.0910767
\(952\) 29.9853 + 39.1150i 0.971830 + 1.26772i
\(953\) 17.0472 0.552212 0.276106 0.961127i \(-0.410956\pi\)
0.276106 + 0.961127i \(0.410956\pi\)
\(954\) 3.17225 5.49450i 0.102705 0.177891i
\(955\) 37.6045 + 65.1329i 1.21685 + 2.10765i
\(956\) 4.26490 + 7.38702i 0.137937 + 0.238913i
\(957\) 1.57113 2.72127i 0.0507873 0.0879662i
\(958\) −18.8043 −0.607540
\(959\) 19.3818 + 25.2830i 0.625872 + 0.816432i
\(960\) −33.2623 −1.07353
\(961\) −17.0744 + 29.5738i −0.550788 + 0.953993i
\(962\) 3.10358 + 5.37557i 0.100064 + 0.173315i
\(963\) −6.12909 10.6159i −0.197507 0.342092i
\(964\) −7.08653 + 12.2742i −0.228242 + 0.395326i
\(965\) −5.90538 −0.190101
\(966\) 1.20817 2.91297i 0.0388721 0.0937234i
\(967\) 23.3640 0.751335 0.375667 0.926755i \(-0.377413\pi\)
0.375667 + 0.926755i \(0.377413\pi\)
\(968\) −13.4944 + 23.3730i −0.433726 + 0.751235i
\(969\) 17.8941 + 30.9935i 0.574841 + 0.995653i
\(970\) −15.3125 26.5221i −0.491656 0.851573i
\(971\) −18.4523 + 31.9603i −0.592162 + 1.02565i 0.401779 + 0.915737i \(0.368392\pi\)
−0.993941 + 0.109918i \(0.964941\pi\)
\(972\) −0.579274 −0.0185802
\(973\) −3.97523 + 0.521483i −0.127440 + 0.0167180i
\(974\) 48.3635 1.54967
\(975\) 2.15394 3.73073i 0.0689812 0.119479i
\(976\) 0.515994 + 0.893727i 0.0165166 + 0.0286075i
\(977\) −0.274426 0.475320i −0.00877967 0.0152068i 0.861602 0.507584i \(-0.169461\pi\)
−0.870382 + 0.492377i \(0.836128\pi\)
\(978\) 2.17517 3.76750i 0.0695542 0.120471i
\(979\) −24.2652 −0.775518
\(980\) 14.8411 3.96199i 0.474082 0.126561i
\(981\) −8.98838 −0.286977
\(982\) −5.59607 + 9.69268i −0.178578 + 0.309306i
\(983\) −3.48677 6.03926i −0.111211 0.192623i 0.805048 0.593210i \(-0.202140\pi\)
−0.916259 + 0.400587i \(0.868806\pi\)
\(984\) 8.04238 + 13.9298i 0.256382 + 0.444066i
\(985\) −4.69928 + 8.13940i −0.149732 + 0.259343i
\(986\) 15.2270 0.484926
\(987\) −12.0817 + 1.58492i −0.384565 + 0.0504485i
\(988\) −1.57627 −0.0501479
\(989\) 2.32032 4.01891i 0.0737819 0.127794i
\(990\) −3.36482 5.82804i −0.106941 0.185227i
\(991\) 15.6563 + 27.1174i 0.497337 + 0.861413i 0.999995 0.00307193i \(-0.000977828\pi\)
−0.502658 + 0.864485i \(0.667644\pi\)
\(992\) 12.7602 22.1014i 0.405138 0.701720i
\(993\) −27.0983 −0.859937
\(994\) −8.28187 + 19.9681i −0.262685 + 0.633351i
\(995\) 20.0489 0.635593
\(996\) −1.35556 + 2.34789i −0.0429524 + 0.0743957i
\(997\) −22.6062 39.1551i −0.715947 1.24006i −0.962593 0.270950i \(-0.912662\pi\)
0.246647 0.969105i \(-0.420671\pi\)
\(998\) −11.3700 19.6933i −0.359910 0.623382i
\(999\) −5.65171 + 9.78904i −0.178812 + 0.309712i
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 483.2.i.g.415.4 yes 16
7.2 even 3 3381.2.a.bf.1.5 8
7.4 even 3 inner 483.2.i.g.277.4 16
7.5 odd 6 3381.2.a.be.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.i.g.277.4 16 7.4 even 3 inner
483.2.i.g.415.4 yes 16 1.1 even 1 trivial
3381.2.a.be.1.5 8 7.5 odd 6
3381.2.a.bf.1.5 8 7.2 even 3