Properties

Label 29.2.e.a.13.2
Level $29$
Weight $2$
Character 29.13
Analytic conductor $0.232$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [29,2,Mod(4,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29.e (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.231566165862\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{14})\)
Coefficient field: 12.0.7877952219361.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 13.2
Root \(0.911180 - 1.08155i\) of defining polynomial
Character \(\chi\) \(=\) 29.13
Dual form 29.2.e.a.9.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0741982 - 0.154074i) q^{2} +(-0.879032 - 0.701005i) q^{3} +(1.22875 + 1.54080i) q^{4} +(-2.54740 - 1.22676i) q^{5} +(-0.173229 + 0.0834229i) q^{6} +(-1.82432 + 2.28763i) q^{7} +(0.662012 - 0.151100i) q^{8} +(-0.386273 - 1.69237i) q^{9} +O(q^{10})\) \(q+(0.0741982 - 0.154074i) q^{2} +(-0.879032 - 0.701005i) q^{3} +(1.22875 + 1.54080i) q^{4} +(-2.54740 - 1.22676i) q^{5} +(-0.173229 + 0.0834229i) q^{6} +(-1.82432 + 2.28763i) q^{7} +(0.662012 - 0.151100i) q^{8} +(-0.386273 - 1.69237i) q^{9} +(-0.378025 + 0.301465i) q^{10} +(3.89257 + 0.888454i) q^{11} -2.21577i q^{12} +(0.625512 - 2.74055i) q^{13} +(0.217103 + 0.450819i) q^{14} +(1.37928 + 2.86411i) q^{15} +(-0.851229 + 3.72948i) q^{16} +0.482650i q^{17} +(-0.289412 - 0.0660563i) q^{18} +(2.38432 - 1.90144i) q^{19} +(-1.23991 - 5.43242i) q^{20} +(3.20728 - 0.732040i) q^{21} +(0.425710 - 0.533823i) q^{22} +(-4.96829 + 2.39260i) q^{23} +(-0.687851 - 0.331252i) q^{24} +(1.86686 + 2.34097i) q^{25} +(-0.375836 - 0.299719i) q^{26} +(-2.31029 + 4.79737i) q^{27} -5.76640 q^{28} +(-4.99718 - 2.00704i) q^{29} +0.543625 q^{30} +(-1.67239 + 3.47275i) q^{31} +(1.57324 + 1.25462i) q^{32} +(-2.79888 - 3.50969i) q^{33} +(0.0743639 + 0.0358118i) q^{34} +(7.45366 - 3.58950i) q^{35} +(2.13297 - 2.67467i) q^{36} +(11.2541 - 2.56868i) q^{37} +(-0.116049 - 0.508446i) q^{38} +(-2.47098 + 1.97054i) q^{39} +(-1.87177 - 0.427220i) q^{40} +5.10756i q^{41} +(0.125186 - 0.548475i) q^{42} +(-3.56577 - 7.40439i) q^{43} +(3.41405 + 7.08936i) q^{44} +(-1.09215 + 4.78502i) q^{45} +0.943011i q^{46} +(2.32767 + 0.531276i) q^{47} +(3.36264 - 2.68162i) q^{48} +(-0.347443 - 1.52225i) q^{49} +(0.499200 - 0.113939i) q^{50} +(0.338340 - 0.424265i) q^{51} +(4.99123 - 2.40365i) q^{52} +(0.401975 + 0.193581i) q^{53} +(0.567732 + 0.711913i) q^{54} +(-8.82602 - 7.03852i) q^{55} +(-0.862063 + 1.79009i) q^{56} -3.42881 q^{57} +(-0.680015 + 0.621017i) q^{58} +1.24537 q^{59} +(-2.71823 + 5.64445i) q^{60} +(-6.71717 - 5.35677i) q^{61} +(0.410973 + 0.515344i) q^{62} +(4.57621 + 2.20378i) q^{63} +(-6.58308 + 3.17024i) q^{64} +(-4.95544 + 6.21392i) q^{65} +(-0.748425 + 0.170823i) q^{66} +(-0.210269 - 0.921249i) q^{67} +(-0.743667 + 0.593055i) q^{68} +(6.04451 + 1.37962i) q^{69} -1.41475i q^{70} +(1.33021 - 5.82802i) q^{71} +(-0.511435 - 1.06201i) q^{72} +(0.209705 + 0.435458i) q^{73} +(0.439268 - 1.92456i) q^{74} -3.36646i q^{75} +(5.85946 + 1.33738i) q^{76} +(-9.13376 + 7.28393i) q^{77} +(0.120267 + 0.526925i) q^{78} +(1.80484 - 0.411944i) q^{79} +(6.74361 - 8.45623i) q^{80} +(0.701839 - 0.337988i) q^{81} +(0.786943 + 0.378972i) q^{82} +(2.71744 + 3.40756i) q^{83} +(5.06885 + 4.04228i) q^{84} +(0.592098 - 1.22950i) q^{85} -1.40540 q^{86} +(2.98573 + 5.26730i) q^{87} +2.71117 q^{88} +(6.75011 - 14.0167i) q^{89} +(0.656213 + 0.523312i) q^{90} +(5.12822 + 6.43058i) q^{91} +(-9.79128 - 4.71523i) q^{92} +(3.90450 - 1.88031i) q^{93} +(0.254565 - 0.319215i) q^{94} +(-8.40645 + 1.91872i) q^{95} +(-0.503437 - 2.20570i) q^{96} +(1.88941 - 1.50675i) q^{97} +(-0.260319 - 0.0594161i) q^{98} -6.93087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0741982 0.154074i 0.0524661 0.108947i −0.873088 0.487563i \(-0.837886\pi\)
0.925554 + 0.378617i \(0.123600\pi\)
\(3\) −0.879032 0.701005i −0.507509 0.404725i 0.335982 0.941869i \(-0.390932\pi\)
−0.843491 + 0.537143i \(0.819503\pi\)
\(4\) 1.22875 + 1.54080i 0.614373 + 0.770399i
\(5\) −2.54740 1.22676i −1.13923 0.548626i −0.233450 0.972369i \(-0.575002\pi\)
−0.905782 + 0.423743i \(0.860716\pi\)
\(6\) −0.173229 + 0.0834229i −0.0707206 + 0.0340572i
\(7\) −1.82432 + 2.28763i −0.689529 + 0.864642i −0.996193 0.0871757i \(-0.972216\pi\)
0.306664 + 0.951818i \(0.400787\pi\)
\(8\) 0.662012 0.151100i 0.234057 0.0534219i
\(9\) −0.386273 1.69237i −0.128758 0.564124i
\(10\) −0.378025 + 0.301465i −0.119542 + 0.0953317i
\(11\) 3.89257 + 0.888454i 1.17365 + 0.267879i 0.764523 0.644596i \(-0.222975\pi\)
0.409132 + 0.912475i \(0.365832\pi\)
\(12\) 2.21577i 0.639637i
\(13\) 0.625512 2.74055i 0.173486 0.760091i −0.811060 0.584963i \(-0.801109\pi\)
0.984546 0.175128i \(-0.0560339\pi\)
\(14\) 0.217103 + 0.450819i 0.0580232 + 0.120486i
\(15\) 1.37928 + 2.86411i 0.356129 + 0.739509i
\(16\) −0.851229 + 3.72948i −0.212807 + 0.932370i
\(17\) 0.482650i 0.117060i 0.998286 + 0.0585299i \(0.0186413\pi\)
−0.998286 + 0.0585299i \(0.981359\pi\)
\(18\) −0.289412 0.0660563i −0.0682150 0.0155696i
\(19\) 2.38432 1.90144i 0.547002 0.436219i −0.310595 0.950542i \(-0.600528\pi\)
0.857596 + 0.514323i \(0.171957\pi\)
\(20\) −1.23991 5.43242i −0.277253 1.21473i
\(21\) 3.20728 0.732040i 0.699885 0.159744i
\(22\) 0.425710 0.533823i 0.0907616 0.113811i
\(23\) −4.96829 + 2.39260i −1.03596 + 0.498892i −0.872989 0.487739i \(-0.837822\pi\)
−0.162970 + 0.986631i \(0.552107\pi\)
\(24\) −0.687851 0.331252i −0.140407 0.0676165i
\(25\) 1.86686 + 2.34097i 0.373372 + 0.468193i
\(26\) −0.375836 0.299719i −0.0737075 0.0587797i
\(27\) −2.31029 + 4.79737i −0.444616 + 0.923255i
\(28\) −5.76640 −1.08975
\(29\) −4.99718 2.00704i −0.927953 0.372698i
\(30\) 0.543625 0.0992519
\(31\) −1.67239 + 3.47275i −0.300370 + 0.623724i −0.995458 0.0952000i \(-0.969651\pi\)
0.695088 + 0.718924i \(0.255365\pi\)
\(32\) 1.57324 + 1.25462i 0.278112 + 0.221787i
\(33\) −2.79888 3.50969i −0.487223 0.610959i
\(34\) 0.0743639 + 0.0358118i 0.0127533 + 0.00614167i
\(35\) 7.45366 3.58950i 1.25990 0.606735i
\(36\) 2.13297 2.67467i 0.355496 0.445778i
\(37\) 11.2541 2.56868i 1.85016 0.422288i 0.854840 0.518891i \(-0.173655\pi\)
0.995323 + 0.0966033i \(0.0307978\pi\)
\(38\) −0.116049 0.508446i −0.0188257 0.0824808i
\(39\) −2.47098 + 1.97054i −0.395674 + 0.315539i
\(40\) −1.87177 0.427220i −0.295954 0.0675495i
\(41\) 5.10756i 0.797667i 0.917023 + 0.398833i \(0.130585\pi\)
−0.917023 + 0.398833i \(0.869415\pi\)
\(42\) 0.125186 0.548475i 0.0193166 0.0846315i
\(43\) −3.56577 7.40439i −0.543775 1.12916i −0.974023 0.226449i \(-0.927288\pi\)
0.430248 0.902711i \(-0.358426\pi\)
\(44\) 3.41405 + 7.08936i 0.514688 + 1.06876i
\(45\) −1.09215 + 4.78502i −0.162808 + 0.713309i
\(46\) 0.943011i 0.139039i
\(47\) 2.32767 + 0.531276i 0.339526 + 0.0774946i 0.388885 0.921287i \(-0.372861\pi\)
−0.0493584 + 0.998781i \(0.515718\pi\)
\(48\) 3.36264 2.68162i 0.485355 0.387058i
\(49\) −0.347443 1.52225i −0.0496347 0.217464i
\(50\) 0.499200 0.113939i 0.0705975 0.0161134i
\(51\) 0.338340 0.424265i 0.0473771 0.0594090i
\(52\) 4.99123 2.40365i 0.692159 0.333326i
\(53\) 0.401975 + 0.193581i 0.0552156 + 0.0265904i 0.461288 0.887251i \(-0.347388\pi\)
−0.406072 + 0.913841i \(0.633102\pi\)
\(54\) 0.567732 + 0.711913i 0.0772585 + 0.0968791i
\(55\) −8.82602 7.03852i −1.19010 0.949074i
\(56\) −0.862063 + 1.79009i −0.115198 + 0.239211i
\(57\) −3.42881 −0.454157
\(58\) −0.680015 + 0.621017i −0.0892904 + 0.0815436i
\(59\) 1.24537 0.162133 0.0810664 0.996709i \(-0.474167\pi\)
0.0810664 + 0.996709i \(0.474167\pi\)
\(60\) −2.71823 + 5.64445i −0.350921 + 0.728696i
\(61\) −6.71717 5.35677i −0.860046 0.685864i 0.0906856 0.995880i \(-0.471094\pi\)
−0.950731 + 0.310016i \(0.899666\pi\)
\(62\) 0.410973 + 0.515344i 0.0521936 + 0.0654487i
\(63\) 4.57621 + 2.20378i 0.576548 + 0.277651i
\(64\) −6.58308 + 3.17024i −0.822885 + 0.396280i
\(65\) −4.95544 + 6.21392i −0.614646 + 0.770742i
\(66\) −0.748425 + 0.170823i −0.0921248 + 0.0210269i
\(67\) −0.210269 0.921249i −0.0256885 0.112548i 0.960458 0.278424i \(-0.0898121\pi\)
−0.986147 + 0.165876i \(0.946955\pi\)
\(68\) −0.743667 + 0.593055i −0.0901829 + 0.0719184i
\(69\) 6.04451 + 1.37962i 0.727673 + 0.166087i
\(70\) 1.41475i 0.169095i
\(71\) 1.33021 5.82802i 0.157867 0.691659i −0.832597 0.553880i \(-0.813147\pi\)
0.990463 0.137779i \(-0.0439962\pi\)
\(72\) −0.511435 1.06201i −0.0602732 0.125158i
\(73\) 0.209705 + 0.435458i 0.0245442 + 0.0509665i 0.912880 0.408227i \(-0.133853\pi\)
−0.888336 + 0.459193i \(0.848138\pi\)
\(74\) 0.439268 1.92456i 0.0510639 0.223725i
\(75\) 3.36646i 0.388725i
\(76\) 5.85946 + 1.33738i 0.672126 + 0.153408i
\(77\) −9.13376 + 7.28393i −1.04089 + 0.830081i
\(78\) 0.120267 + 0.526925i 0.0136176 + 0.0596625i
\(79\) 1.80484 0.411944i 0.203061 0.0463473i −0.119781 0.992800i \(-0.538219\pi\)
0.322841 + 0.946453i \(0.395362\pi\)
\(80\) 6.74361 8.45623i 0.753959 0.945435i
\(81\) 0.701839 0.337988i 0.0779821 0.0375542i
\(82\) 0.786943 + 0.378972i 0.0869033 + 0.0418504i
\(83\) 2.71744 + 3.40756i 0.298277 + 0.374028i 0.908274 0.418376i \(-0.137401\pi\)
−0.609996 + 0.792404i \(0.708829\pi\)
\(84\) 5.06885 + 4.04228i 0.553057 + 0.441048i
\(85\) 0.592098 1.22950i 0.0642220 0.133358i
\(86\) −1.40540 −0.151548
\(87\) 2.98573 + 5.26730i 0.320104 + 0.564714i
\(88\) 2.71117 0.289012
\(89\) 6.75011 14.0167i 0.715510 1.48577i −0.152015 0.988378i \(-0.548576\pi\)
0.867525 0.497394i \(-0.165710\pi\)
\(90\) 0.656213 + 0.523312i 0.0691709 + 0.0551619i
\(91\) 5.12822 + 6.43058i 0.537583 + 0.674108i
\(92\) −9.79128 4.71523i −1.02081 0.491597i
\(93\) 3.90450 1.88031i 0.404878 0.194979i
\(94\) 0.254565 0.319215i 0.0262564 0.0329245i
\(95\) −8.40645 + 1.91872i −0.862483 + 0.196856i
\(96\) −0.503437 2.20570i −0.0513818 0.225118i
\(97\) 1.88941 1.50675i 0.191840 0.152988i −0.522859 0.852419i \(-0.675135\pi\)
0.714700 + 0.699431i \(0.246563\pi\)
\(98\) −0.260319 0.0594161i −0.0262962 0.00600193i
\(99\) 6.93087i 0.696578i
\(100\) −1.31306 + 5.75291i −0.131306 + 0.575291i
\(101\) 5.85513 + 12.1583i 0.582607 + 1.20980i 0.959018 + 0.283344i \(0.0914437\pi\)
−0.376411 + 0.926453i \(0.622842\pi\)
\(102\) −0.0402641 0.0836092i −0.00398674 0.00827854i
\(103\) −0.389459 + 1.70633i −0.0383745 + 0.168130i −0.990484 0.137627i \(-0.956052\pi\)
0.952110 + 0.305757i \(0.0989095\pi\)
\(104\) 1.90879i 0.187172i
\(105\) −9.06826 2.06977i −0.884972 0.201989i
\(106\) 0.0596517 0.0475707i 0.00579389 0.00462047i
\(107\) 0.580401 + 2.54290i 0.0561095 + 0.245832i 0.995203 0.0978294i \(-0.0311900\pi\)
−0.939094 + 0.343661i \(0.888333\pi\)
\(108\) −10.2305 + 2.33506i −0.984435 + 0.224691i
\(109\) −5.70347 + 7.15192i −0.546293 + 0.685030i −0.975958 0.217959i \(-0.930060\pi\)
0.429665 + 0.902988i \(0.358632\pi\)
\(110\) −1.73933 + 0.837617i −0.165839 + 0.0798636i
\(111\) −11.6934 5.63123i −1.10989 0.534493i
\(112\) −6.97874 8.75107i −0.659429 0.826898i
\(113\) 9.93607 + 7.92375i 0.934706 + 0.745404i 0.967186 0.254069i \(-0.0817690\pi\)
−0.0324796 + 0.999472i \(0.510340\pi\)
\(114\) −0.254412 + 0.528292i −0.0238278 + 0.0494790i
\(115\) 15.5914 1.45390
\(116\) −3.04782 10.1658i −0.282983 0.943870i
\(117\) −4.87965 −0.451123
\(118\) 0.0924039 0.191879i 0.00850647 0.0176639i
\(119\) −1.10412 0.880510i −0.101215 0.0807162i
\(120\) 1.34587 + 1.68766i 0.122860 + 0.154062i
\(121\) 4.45211 + 2.14402i 0.404737 + 0.194911i
\(122\) −1.32374 + 0.637480i −0.119846 + 0.0577148i
\(123\) 3.58042 4.48971i 0.322836 0.404823i
\(124\) −7.40575 + 1.69031i −0.665056 + 0.151795i
\(125\) 1.26196 + 5.52899i 0.112873 + 0.494528i
\(126\) 0.679093 0.541558i 0.0604984 0.0482459i
\(127\) −1.11618 0.254762i −0.0990453 0.0226064i 0.172711 0.984973i \(-0.444747\pi\)
−0.271756 + 0.962366i \(0.587604\pi\)
\(128\) 5.27401i 0.466161i
\(129\) −2.05609 + 9.00832i −0.181029 + 0.793138i
\(130\) 0.589720 + 1.22457i 0.0517219 + 0.107402i
\(131\) −7.58804 15.7567i −0.662970 1.37667i −0.912810 0.408385i \(-0.866092\pi\)
0.249840 0.968287i \(-0.419622\pi\)
\(132\) 1.96861 8.62504i 0.171345 0.750713i
\(133\) 8.92328i 0.773746i
\(134\) −0.157542 0.0359580i −0.0136096 0.00310630i
\(135\) 11.7705 9.38665i 1.01304 0.807874i
\(136\) 0.0729284 + 0.319520i 0.00625356 + 0.0273986i
\(137\) 0.925317 0.211198i 0.0790552 0.0180438i −0.182810 0.983148i \(-0.558519\pi\)
0.261866 + 0.965104i \(0.415662\pi\)
\(138\) 0.661055 0.828937i 0.0562728 0.0705638i
\(139\) −6.53941 + 3.14921i −0.554665 + 0.267113i −0.690150 0.723667i \(-0.742455\pi\)
0.135484 + 0.990779i \(0.456741\pi\)
\(140\) 14.6893 + 7.07402i 1.24148 + 0.597864i
\(141\) −1.67367 2.09872i −0.140949 0.176744i
\(142\) −0.799248 0.637379i −0.0670714 0.0534877i
\(143\) 4.86970 10.1120i 0.407225 0.845611i
\(144\) 6.64048 0.553373
\(145\) 10.2677 + 11.2431i 0.852682 + 0.933689i
\(146\) 0.0826526 0.00684038
\(147\) −0.761689 + 1.58166i −0.0628231 + 0.130453i
\(148\) 17.7863 + 14.1841i 1.46202 + 1.16592i
\(149\) −10.6334 13.3339i −0.871126 1.09236i −0.994982 0.100057i \(-0.968097\pi\)
0.123856 0.992300i \(-0.460474\pi\)
\(150\) −0.518685 0.249785i −0.0423504 0.0203949i
\(151\) −8.86929 + 4.27122i −0.721772 + 0.347587i −0.758442 0.651740i \(-0.774039\pi\)
0.0366700 + 0.999327i \(0.488325\pi\)
\(152\) 1.29114 1.61904i 0.104726 0.131322i
\(153\) 0.816824 0.186435i 0.0660363 0.0150724i
\(154\) 0.444557 + 1.94773i 0.0358234 + 0.156953i
\(155\) 8.52049 6.79487i 0.684382 0.545777i
\(156\) −6.07242 1.38599i −0.486183 0.110968i
\(157\) 2.64062i 0.210744i −0.994433 0.105372i \(-0.966397\pi\)
0.994433 0.105372i \(-0.0336034\pi\)
\(158\) 0.0704463 0.308645i 0.00560440 0.0245545i
\(159\) −0.217648 0.451951i −0.0172606 0.0358420i
\(160\) −2.46856 5.12601i −0.195157 0.405247i
\(161\) 3.59038 15.7305i 0.282961 1.23973i
\(162\) 0.133213i 0.0104662i
\(163\) −9.53190 2.17559i −0.746596 0.170406i −0.167735 0.985832i \(-0.553645\pi\)
−0.578861 + 0.815426i \(0.696502\pi\)
\(164\) −7.86972 + 6.27589i −0.614522 + 0.490065i
\(165\) 2.82432 + 12.3742i 0.219873 + 0.963327i
\(166\) 0.726646 0.165852i 0.0563987 0.0128726i
\(167\) −14.7231 + 18.4622i −1.13931 + 1.42865i −0.251847 + 0.967767i \(0.581038\pi\)
−0.887462 + 0.460881i \(0.847533\pi\)
\(168\) 2.01264 0.969238i 0.155279 0.0747784i
\(169\) 4.59326 + 2.21200i 0.353328 + 0.170154i
\(170\) −0.145502 0.182454i −0.0111595 0.0139936i
\(171\) −4.13894 3.30069i −0.316512 0.252410i
\(172\) 7.02726 14.5923i 0.535823 1.11265i
\(173\) −5.22521 −0.397265 −0.198633 0.980074i \(-0.563650\pi\)
−0.198633 + 0.980074i \(0.563650\pi\)
\(174\) 1.03309 0.0692004i 0.0783184 0.00524607i
\(175\) −8.76101 −0.662270
\(176\) −6.62694 + 13.7610i −0.499525 + 1.03727i
\(177\) −1.09472 0.873007i −0.0822839 0.0656192i
\(178\) −1.65877 2.08004i −0.124330 0.155905i
\(179\) 10.2128 + 4.91824i 0.763343 + 0.367607i 0.774700 0.632329i \(-0.217901\pi\)
−0.0113570 + 0.999936i \(0.503615\pi\)
\(180\) −8.71473 + 4.19679i −0.649557 + 0.312810i
\(181\) 6.44743 8.08482i 0.479233 0.600940i −0.482172 0.876077i \(-0.660152\pi\)
0.961405 + 0.275137i \(0.0887232\pi\)
\(182\) 1.37129 0.312988i 0.101647 0.0232002i
\(183\) 2.14949 + 9.41754i 0.158895 + 0.696164i
\(184\) −2.92754 + 2.33464i −0.215821 + 0.172112i
\(185\) −31.8199 7.26268i −2.33944 0.533963i
\(186\) 0.741098i 0.0543399i
\(187\) −0.428813 + 1.87875i −0.0313579 + 0.137388i
\(188\) 2.04153 + 4.23928i 0.148894 + 0.309181i
\(189\) −6.75988 14.0370i −0.491709 1.02104i
\(190\) −0.328119 + 1.43758i −0.0238042 + 0.104293i
\(191\) 6.30617i 0.456299i 0.973626 + 0.228149i \(0.0732675\pi\)
−0.973626 + 0.228149i \(0.926733\pi\)
\(192\) 8.00909 + 1.82802i 0.578006 + 0.131926i
\(193\) −3.20725 + 2.55769i −0.230863 + 0.184107i −0.732088 0.681210i \(-0.761454\pi\)
0.501226 + 0.865317i \(0.332883\pi\)
\(194\) −0.0919610 0.402908i −0.00660242 0.0289271i
\(195\) 8.71198 1.98845i 0.623878 0.142396i
\(196\) 1.91856 2.40580i 0.137040 0.171843i
\(197\) 18.3245 8.82462i 1.30557 0.628728i 0.353735 0.935346i \(-0.384912\pi\)
0.951833 + 0.306618i \(0.0991974\pi\)
\(198\) −1.06787 0.514258i −0.0758901 0.0365467i
\(199\) −1.22899 1.54111i −0.0871211 0.109246i 0.736360 0.676589i \(-0.236543\pi\)
−0.823482 + 0.567343i \(0.807971\pi\)
\(200\) 1.58960 + 1.26767i 0.112402 + 0.0896375i
\(201\) −0.460967 + 0.957207i −0.0325141 + 0.0675162i
\(202\) 2.30772 0.162371
\(203\) 13.7078 7.77019i 0.962101 0.545361i
\(204\) 1.06944 0.0748758
\(205\) 6.26577 13.0110i 0.437620 0.908728i
\(206\) 0.234004 + 0.186612i 0.0163038 + 0.0130019i
\(207\) 5.96829 + 7.48399i 0.414825 + 0.520173i
\(208\) 9.68836 + 4.66567i 0.671767 + 0.323506i
\(209\) 10.9705 5.28311i 0.758845 0.365440i
\(210\) −0.991747 + 1.24361i −0.0684371 + 0.0858174i
\(211\) −17.3534 + 3.96080i −1.19466 + 0.272673i −0.773192 0.634172i \(-0.781341\pi\)
−0.421466 + 0.906844i \(0.638484\pi\)
\(212\) 0.195656 + 0.857226i 0.0134377 + 0.0588745i
\(213\) −5.25476 + 4.19053i −0.360050 + 0.287131i
\(214\) 0.434861 + 0.0992541i 0.0297265 + 0.00678487i
\(215\) 23.2363i 1.58470i
\(216\) −0.804559 + 3.52500i −0.0547433 + 0.239846i
\(217\) −4.89339 10.1612i −0.332185 0.689789i
\(218\) 0.678739 + 1.40942i 0.0459700 + 0.0954577i
\(219\) 0.120920 0.529786i 0.00817103 0.0357996i
\(220\) 22.2477i 1.49994i
\(221\) 1.32273 + 0.301904i 0.0889762 + 0.0203082i
\(222\) −1.73526 + 1.38382i −0.116463 + 0.0928759i
\(223\) 4.22512 + 18.5115i 0.282935 + 1.23962i 0.894010 + 0.448047i \(0.147880\pi\)
−0.611075 + 0.791572i \(0.709263\pi\)
\(224\) −5.74020 + 1.31016i −0.383533 + 0.0875390i
\(225\) 3.24067 4.06367i 0.216045 0.270911i
\(226\) 1.95808 0.942963i 0.130250 0.0627250i
\(227\) −0.0933811 0.0449699i −0.00619792 0.00298476i 0.430782 0.902456i \(-0.358238\pi\)
−0.436980 + 0.899471i \(0.643952\pi\)
\(228\) −4.21314 5.28311i −0.279022 0.349883i
\(229\) 10.3207 + 8.23049i 0.682012 + 0.543886i 0.902064 0.431602i \(-0.142051\pi\)
−0.220053 + 0.975488i \(0.570623\pi\)
\(230\) 1.15685 2.40223i 0.0762806 0.158398i
\(231\) 13.1349 0.864215
\(232\) −3.61146 0.573612i −0.237104 0.0376595i
\(233\) −2.18750 −0.143308 −0.0716538 0.997430i \(-0.522828\pi\)
−0.0716538 + 0.997430i \(0.522828\pi\)
\(234\) −0.362061 + 0.751828i −0.0236687 + 0.0491485i
\(235\) −5.27777 4.20888i −0.344284 0.274557i
\(236\) 1.53024 + 1.91886i 0.0996100 + 0.124907i
\(237\) −1.87529 0.903092i −0.121813 0.0586621i
\(238\) −0.217588 + 0.104785i −0.0141041 + 0.00679219i
\(239\) 9.54386 11.9676i 0.617341 0.774121i −0.370627 0.928782i \(-0.620857\pi\)
0.987968 + 0.154661i \(0.0494285\pi\)
\(240\) −11.8557 + 2.70599i −0.765283 + 0.174671i
\(241\) −3.02515 13.2541i −0.194867 0.853768i −0.973935 0.226829i \(-0.927164\pi\)
0.779068 0.626940i \(-0.215693\pi\)
\(242\) 0.660677 0.526872i 0.0424699 0.0338686i
\(243\) 14.7197 + 3.35967i 0.944267 + 0.215523i
\(244\) 16.9319i 1.08395i
\(245\) −0.982362 + 4.30401i −0.0627608 + 0.274973i
\(246\) −0.426087 0.884779i −0.0271663 0.0564115i
\(247\) −3.71955 7.72373i −0.236669 0.491449i
\(248\) −0.582409 + 2.55170i −0.0369830 + 0.162033i
\(249\) 4.90029i 0.310543i
\(250\) 0.945510 + 0.215807i 0.0597993 + 0.0136488i
\(251\) −16.0564 + 12.8046i −1.01347 + 0.808216i −0.981537 0.191274i \(-0.938738\pi\)
−0.0319344 + 0.999490i \(0.510167\pi\)
\(252\) 2.22741 + 9.75890i 0.140313 + 0.614753i
\(253\) −21.4651 + 4.89927i −1.34950 + 0.308015i
\(254\) −0.122071 + 0.153072i −0.00765942 + 0.00960461i
\(255\) −1.38236 + 0.665710i −0.0865668 + 0.0416884i
\(256\) −12.3536 5.94916i −0.772098 0.371823i
\(257\) 12.3518 + 15.4887i 0.770486 + 0.966159i 0.999974 0.00715224i \(-0.00227665\pi\)
−0.229488 + 0.973311i \(0.573705\pi\)
\(258\) 1.23539 + 0.985192i 0.0769121 + 0.0613354i
\(259\) −14.6549 + 30.4313i −0.910614 + 1.89091i
\(260\) −15.6634 −0.971401
\(261\) −1.46639 + 9.23235i −0.0907671 + 0.571468i
\(262\) −2.99072 −0.184768
\(263\) 6.45116 13.3960i 0.397796 0.826031i −0.601829 0.798625i \(-0.705561\pi\)
0.999624 0.0274060i \(-0.00872469\pi\)
\(264\) −2.38321 1.90055i −0.146676 0.116971i
\(265\) −0.786515 0.986258i −0.0483152 0.0605854i
\(266\) 1.37485 + 0.662091i 0.0842973 + 0.0405954i
\(267\) −15.7594 + 7.58931i −0.964458 + 0.464458i
\(268\) 1.16109 1.45596i 0.0709250 0.0889371i
\(269\) −1.51784 + 0.346436i −0.0925441 + 0.0211226i −0.268542 0.963268i \(-0.586542\pi\)
0.175998 + 0.984391i \(0.443685\pi\)
\(270\) −0.572892 2.51000i −0.0348651 0.152754i
\(271\) 9.50030 7.57624i 0.577102 0.460224i −0.290921 0.956747i \(-0.593962\pi\)
0.868023 + 0.496523i \(0.165390\pi\)
\(272\) −1.80003 0.410846i −0.109143 0.0249112i
\(273\) 9.24759i 0.559690i
\(274\) 0.0361168 0.158238i 0.00218189 0.00955950i
\(275\) 5.18704 + 10.7710i 0.312790 + 0.649516i
\(276\) 5.30145 + 11.0086i 0.319110 + 0.662638i
\(277\) 2.67977 11.7409i 0.161012 0.705439i −0.828380 0.560167i \(-0.810737\pi\)
0.989392 0.145272i \(-0.0464059\pi\)
\(278\) 1.24122i 0.0744434i
\(279\) 6.52319 + 1.48887i 0.390533 + 0.0891366i
\(280\) 4.39204 3.50254i 0.262475 0.209317i
\(281\) −3.04306 13.3325i −0.181534 0.795351i −0.980901 0.194508i \(-0.937689\pi\)
0.799367 0.600843i \(-0.205168\pi\)
\(282\) −0.447542 + 0.102149i −0.0266507 + 0.00608286i
\(283\) 16.2063 20.3221i 0.963367 1.20802i −0.0147331 0.999891i \(-0.504690\pi\)
0.978101 0.208133i \(-0.0667387\pi\)
\(284\) 10.6143 5.11157i 0.629842 0.303316i
\(285\) 8.73456 + 4.20634i 0.517391 + 0.249162i
\(286\) −1.19668 1.50059i −0.0707613 0.0887318i
\(287\) −11.6842 9.31784i −0.689696 0.550015i
\(288\) 1.51558 3.14714i 0.0893065 0.185447i
\(289\) 16.7670 0.986297
\(290\) 2.49411 0.747763i 0.146459 0.0439101i
\(291\) −2.71709 −0.159279
\(292\) −0.413278 + 0.858181i −0.0241853 + 0.0502212i
\(293\) −4.47701 3.57030i −0.261550 0.208579i 0.483931 0.875106i \(-0.339209\pi\)
−0.745481 + 0.666527i \(0.767780\pi\)
\(294\) 0.187178 + 0.234713i 0.0109164 + 0.0136888i
\(295\) −3.17245 1.52777i −0.184707 0.0889502i
\(296\) 7.06223 3.40099i 0.410483 0.197678i
\(297\) −13.2552 + 16.6215i −0.769146 + 0.964479i
\(298\) −2.84340 + 0.648987i −0.164714 + 0.0375948i
\(299\) 3.44931 + 15.1124i 0.199479 + 0.873974i
\(300\) 5.18704 4.13653i 0.299474 0.238822i
\(301\) 23.4436 + 5.35085i 1.35127 + 0.308418i
\(302\) 1.68345i 0.0968714i
\(303\) 3.37618 14.7920i 0.193956 0.849779i
\(304\) 5.06176 + 10.5108i 0.290312 + 0.602838i
\(305\) 10.5398 + 21.8862i 0.603510 + 1.25320i
\(306\) 0.0318821 0.139685i 0.00182258 0.00798524i
\(307\) 12.7599i 0.728244i 0.931351 + 0.364122i \(0.118631\pi\)
−0.931351 + 0.364122i \(0.881369\pi\)
\(308\) −22.4461 5.12319i −1.27899 0.291921i
\(309\) 1.53849 1.22691i 0.0875217 0.0697963i
\(310\) −0.414708 1.81695i −0.0235538 0.103196i
\(311\) 12.2017 2.78495i 0.691893 0.157920i 0.137906 0.990445i \(-0.455963\pi\)
0.553987 + 0.832525i \(0.313106\pi\)
\(312\) −1.33807 + 1.67789i −0.0757533 + 0.0949917i
\(313\) −23.2978 + 11.2196i −1.31687 + 0.634171i −0.954597 0.297900i \(-0.903714\pi\)
−0.362274 + 0.932072i \(0.617999\pi\)
\(314\) −0.406851 0.195929i −0.0229599 0.0110569i
\(315\) −8.95391 11.2279i −0.504496 0.632618i
\(316\) 2.85242 + 2.27473i 0.160461 + 0.127963i
\(317\) 11.7612 24.4225i 0.660577 1.37170i −0.253966 0.967213i \(-0.581735\pi\)
0.914543 0.404489i \(-0.132551\pi\)
\(318\) −0.0857831 −0.00481047
\(319\) −17.6687 12.2523i −0.989258 0.685998i
\(320\) 20.6589 1.15487
\(321\) 1.27240 2.64216i 0.0710182 0.147471i
\(322\) −2.15726 1.72036i −0.120219 0.0958717i
\(323\) 0.917728 + 1.15079i 0.0510638 + 0.0640319i
\(324\) 1.38315 + 0.666092i 0.0768419 + 0.0370051i
\(325\) 7.58327 3.65191i 0.420644 0.202572i
\(326\) −1.04245 + 1.30719i −0.0577361 + 0.0723988i
\(327\) 10.0271 2.28861i 0.554498 0.126560i
\(328\) 0.771752 + 3.38127i 0.0426129 + 0.186699i
\(329\) −5.46179 + 4.35563i −0.301118 + 0.240134i
\(330\) 2.11610 + 0.482986i 0.116487 + 0.0265875i
\(331\) 10.9792i 0.603470i 0.953392 + 0.301735i \(0.0975658\pi\)
−0.953392 + 0.301735i \(0.902434\pi\)
\(332\) −1.91132 + 8.37405i −0.104897 + 0.459586i
\(333\) −8.69431 18.0539i −0.476445 0.989349i
\(334\) 1.75212 + 3.63831i 0.0958717 + 0.199080i
\(335\) −0.594515 + 2.60474i −0.0324819 + 0.142312i
\(336\) 12.5846i 0.686546i
\(337\) 16.7612 + 3.82563i 0.913040 + 0.208395i 0.653137 0.757240i \(-0.273452\pi\)
0.259902 + 0.965635i \(0.416310\pi\)
\(338\) 0.681623 0.543576i 0.0370754 0.0295667i
\(339\) −3.17954 13.9305i −0.172689 0.756599i
\(340\) 2.62196 0.598444i 0.142196 0.0324552i
\(341\) −9.59527 + 12.0321i −0.519613 + 0.651574i
\(342\) −0.815653 + 0.392798i −0.0441055 + 0.0212401i
\(343\) −14.3374 6.90451i −0.774145 0.372809i
\(344\) −3.47938 4.36301i −0.187596 0.235238i
\(345\) −13.7053 10.9296i −0.737870 0.588431i
\(346\) −0.387701 + 0.805070i −0.0208429 + 0.0432808i
\(347\) −31.2968 −1.68010 −0.840049 0.542510i \(-0.817474\pi\)
−0.840049 + 0.542510i \(0.817474\pi\)
\(348\) −4.44714 + 11.0726i −0.238392 + 0.593553i
\(349\) −16.8395 −0.901398 −0.450699 0.892676i \(-0.648825\pi\)
−0.450699 + 0.892676i \(0.648825\pi\)
\(350\) −0.650051 + 1.34985i −0.0347467 + 0.0721523i
\(351\) 11.7023 + 9.33228i 0.624623 + 0.498120i
\(352\) 5.00929 + 6.28145i 0.266996 + 0.334802i
\(353\) −24.0306 11.5725i −1.27902 0.615944i −0.333883 0.942615i \(-0.608359\pi\)
−0.945138 + 0.326671i \(0.894073\pi\)
\(354\) −0.215734 + 0.103892i −0.0114661 + 0.00552179i
\(355\) −10.5382 + 13.2145i −0.559308 + 0.701350i
\(356\) 29.8912 6.82246i 1.58423 0.361590i
\(357\) 0.353319 + 1.54799i 0.0186996 + 0.0819284i
\(358\) 1.51555 1.20861i 0.0800992 0.0638770i
\(359\) −11.7911 2.69123i −0.622308 0.142038i −0.100270 0.994960i \(-0.531971\pi\)
−0.522038 + 0.852923i \(0.674828\pi\)
\(360\) 3.33276i 0.175652i
\(361\) −2.15835 + 9.45635i −0.113597 + 0.497703i
\(362\) −0.767274 1.59326i −0.0403270 0.0837400i
\(363\) −2.41058 5.00561i −0.126522 0.262727i
\(364\) −3.60696 + 15.8031i −0.189056 + 0.828308i
\(365\) 1.36655i 0.0715282i
\(366\) 1.61049 + 0.367583i 0.0841816 + 0.0192139i
\(367\) 26.5559 21.1776i 1.38621 1.10546i 0.404612 0.914488i \(-0.367406\pi\)
0.981595 0.190975i \(-0.0611650\pi\)
\(368\) −4.69400 20.5658i −0.244692 1.07206i
\(369\) 8.64389 1.97291i 0.449983 0.102706i
\(370\) −3.47997 + 4.36375i −0.180915 + 0.226860i
\(371\) −1.17617 + 0.566416i −0.0610639 + 0.0294068i
\(372\) 7.69481 + 3.70563i 0.398957 + 0.192128i
\(373\) 3.86240 + 4.84329i 0.199987 + 0.250776i 0.871705 0.490031i \(-0.163015\pi\)
−0.671718 + 0.740807i \(0.734443\pi\)
\(374\) 0.257650 + 0.205469i 0.0133228 + 0.0106245i
\(375\) 2.76655 5.74480i 0.142864 0.296660i
\(376\) 1.62122 0.0836082
\(377\) −8.62619 + 12.4396i −0.444271 + 0.640671i
\(378\) −2.66432 −0.137038
\(379\) −11.3223 + 23.5109i −0.581585 + 1.20767i 0.377882 + 0.925854i \(0.376652\pi\)
−0.959467 + 0.281820i \(0.909062\pi\)
\(380\) −13.2857 10.5950i −0.681544 0.543513i
\(381\) 0.802572 + 1.00639i 0.0411170 + 0.0515591i
\(382\) 0.971619 + 0.467907i 0.0497123 + 0.0239402i
\(383\) 18.8120 9.05940i 0.961250 0.462914i 0.113633 0.993523i \(-0.463751\pi\)
0.847617 + 0.530609i \(0.178037\pi\)
\(384\) 3.69711 4.63603i 0.188667 0.236581i
\(385\) 32.2030 7.35013i 1.64122 0.374597i
\(386\) 0.156103 + 0.683930i 0.00794541 + 0.0348111i
\(387\) −11.1536 + 8.89473i −0.566971 + 0.452144i
\(388\) 4.64321 + 1.05978i 0.235723 + 0.0538023i
\(389\) 15.7075i 0.796400i −0.917299 0.398200i \(-0.869635\pi\)
0.917299 0.398200i \(-0.130365\pi\)
\(390\) 0.340044 1.48983i 0.0172188 0.0754405i
\(391\) −1.15479 2.39794i −0.0584002 0.121269i
\(392\) −0.460023 0.955248i −0.0232347 0.0482473i
\(393\) −4.37541 + 19.1699i −0.220710 + 0.966995i
\(394\) 3.47811i 0.175224i
\(395\) −5.10302 1.16473i −0.256761 0.0586040i
\(396\) 10.6791 8.51628i 0.536644 0.427959i
\(397\) −2.57280 11.2722i −0.129125 0.565734i −0.997553 0.0699182i \(-0.977726\pi\)
0.868428 0.495816i \(-0.165131\pi\)
\(398\) −0.328634 + 0.0750087i −0.0164730 + 0.00375984i
\(399\) 6.25526 7.84385i 0.313155 0.392684i
\(400\) −10.3197 + 4.96971i −0.515985 + 0.248485i
\(401\) 4.33830 + 2.08921i 0.216644 + 0.104330i 0.539059 0.842268i \(-0.318780\pi\)
−0.322414 + 0.946599i \(0.604494\pi\)
\(402\) 0.113278 + 0.142046i 0.00564979 + 0.00708462i
\(403\) 8.47114 + 6.75551i 0.421978 + 0.336516i
\(404\) −11.5390 + 23.9610i −0.574088 + 1.19211i
\(405\) −2.20250 −0.109443
\(406\) −0.180090 2.68856i −0.00893771 0.133431i
\(407\) 46.0896 2.28457
\(408\) 0.159879 0.331992i 0.00791518 0.0164360i
\(409\) 18.6701 + 14.8889i 0.923177 + 0.736209i 0.964817 0.262924i \(-0.0846868\pi\)
−0.0416399 + 0.999133i \(0.513258\pi\)
\(410\) −1.53975 1.93079i −0.0760429 0.0953548i
\(411\) −0.961434 0.463002i −0.0474240 0.0228382i
\(412\) −3.10766 + 1.49657i −0.153103 + 0.0737306i
\(413\) −2.27195 + 2.84893i −0.111795 + 0.140187i
\(414\) 1.59593 0.364260i 0.0784355 0.0179024i
\(415\) −2.74213 12.0141i −0.134606 0.589748i
\(416\) 4.42242 3.52676i 0.216827 0.172914i
\(417\) 7.95596 + 1.81590i 0.389605 + 0.0889248i
\(418\) 2.08227i 0.101847i
\(419\) 6.86486 30.0769i 0.335370 1.46935i −0.473200 0.880955i \(-0.656901\pi\)
0.808571 0.588399i \(-0.200242\pi\)
\(420\) −7.95349 16.5156i −0.388091 0.805878i
\(421\) 4.52434 + 9.39489i 0.220503 + 0.457879i 0.981648 0.190703i \(-0.0610767\pi\)
−0.761145 + 0.648582i \(0.775362\pi\)
\(422\) −0.677335 + 2.96760i −0.0329721 + 0.144460i
\(423\) 4.14451i 0.201513i
\(424\) 0.295363 + 0.0674146i 0.0143441 + 0.00327394i
\(425\) −1.12987 + 0.901039i −0.0548066 + 0.0437068i
\(426\) 0.255759 + 1.12055i 0.0123916 + 0.0542910i
\(427\) 24.5086 5.59392i 1.18605 0.270709i
\(428\) −3.20494 + 4.01886i −0.154916 + 0.194259i
\(429\) −11.3692 + 5.47512i −0.548911 + 0.264341i
\(430\) 3.58012 + 1.72409i 0.172649 + 0.0831432i
\(431\) 6.65691 + 8.34750i 0.320652 + 0.402085i 0.915867 0.401482i \(-0.131505\pi\)
−0.595215 + 0.803566i \(0.702933\pi\)
\(432\) −15.9251 12.6999i −0.766197 0.611022i
\(433\) −11.9500 + 24.8145i −0.574282 + 1.19251i 0.388303 + 0.921532i \(0.373061\pi\)
−0.962586 + 0.270978i \(0.912653\pi\)
\(434\) −1.92866 −0.0925788
\(435\) −1.14413 17.0807i −0.0548569 0.818958i
\(436\) −18.0278 −0.863374
\(437\) −7.29663 + 15.1516i −0.349045 + 0.724800i
\(438\) −0.0726543 0.0579398i −0.00347155 0.00276847i
\(439\) −16.1160 20.2088i −0.769173 0.964512i 0.230791 0.973003i \(-0.425869\pi\)
−0.999964 + 0.00849123i \(0.997297\pi\)
\(440\) −6.90645 3.32597i −0.329252 0.158559i
\(441\) −2.44200 + 1.17601i −0.116286 + 0.0560003i
\(442\) 0.144659 0.181397i 0.00688075 0.00862819i
\(443\) −13.7606 + 3.14077i −0.653786 + 0.149222i −0.536533 0.843880i \(-0.680266\pi\)
−0.117254 + 0.993102i \(0.537409\pi\)
\(444\) −5.69159 24.9365i −0.270111 1.18343i
\(445\) −34.3905 + 27.4255i −1.63027 + 1.30009i
\(446\) 3.16563 + 0.722535i 0.149897 + 0.0342130i
\(447\) 19.1750i 0.906948i
\(448\) 4.75732 20.8432i 0.224762 0.984748i
\(449\) 9.59709 + 19.9286i 0.452915 + 0.940487i 0.994973 + 0.100146i \(0.0319310\pi\)
−0.542058 + 0.840341i \(0.682355\pi\)
\(450\) −0.385655 0.800821i −0.0181800 0.0377511i
\(451\) −4.53783 + 19.8815i −0.213678 + 0.936185i
\(452\) 25.0458i 1.17805i
\(453\) 10.7905 + 2.46287i 0.506983 + 0.115716i
\(454\) −0.0138574 + 0.0110509i −0.000650361 + 0.000518645i
\(455\) −5.17483 22.6724i −0.242600 1.06290i
\(456\) −2.26991 + 0.518093i −0.106299 + 0.0242619i
\(457\) 6.08500 7.63035i 0.284644 0.356933i −0.618868 0.785495i \(-0.712408\pi\)
0.903512 + 0.428562i \(0.140980\pi\)
\(458\) 2.03388 0.979467i 0.0950372 0.0457675i
\(459\) −2.31545 1.11506i −0.108076 0.0520467i
\(460\) 19.1578 + 24.0232i 0.893239 + 1.12009i
\(461\) 15.7515 + 12.5614i 0.733621 + 0.585043i 0.917420 0.397921i \(-0.130268\pi\)
−0.183799 + 0.982964i \(0.558840\pi\)
\(462\) 0.974589 2.02375i 0.0453420 0.0941536i
\(463\) −15.7776 −0.733249 −0.366624 0.930369i \(-0.619487\pi\)
−0.366624 + 0.930369i \(0.619487\pi\)
\(464\) 11.7390 16.9284i 0.544968 0.785882i
\(465\) −12.2530 −0.568220
\(466\) −0.162308 + 0.337037i −0.00751879 + 0.0156129i
\(467\) −30.6532 24.4451i −1.41846 1.13119i −0.971613 0.236577i \(-0.923975\pi\)
−0.446849 0.894609i \(-0.647454\pi\)
\(468\) −5.99585 7.51855i −0.277158 0.347545i
\(469\) 2.49107 + 1.19964i 0.115027 + 0.0553941i
\(470\) −1.04008 + 0.500877i −0.0479754 + 0.0231037i
\(471\) −1.85109 + 2.32119i −0.0852935 + 0.106955i
\(472\) 0.824447 0.188175i 0.0379482 0.00866144i
\(473\) −7.30155 31.9902i −0.335725 1.47091i
\(474\) −0.278286 + 0.221926i −0.0127821 + 0.0101934i
\(475\) 8.90239 + 2.03191i 0.408470 + 0.0932305i
\(476\) 2.78316i 0.127566i
\(477\) 0.172339 0.755067i 0.00789087 0.0345722i
\(478\) −1.13576 2.35844i −0.0519487 0.107872i
\(479\) 18.3393 + 38.0820i 0.837945 + 1.74001i 0.653141 + 0.757236i \(0.273451\pi\)
0.184805 + 0.982775i \(0.440835\pi\)
\(480\) −1.42342 + 6.23640i −0.0649698 + 0.284651i
\(481\) 32.4492i 1.47955i
\(482\) −2.26657 0.517329i −0.103239 0.0235637i
\(483\) −14.1832 + 11.3107i −0.645357 + 0.514655i
\(484\) 2.16700 + 9.49426i 0.0985002 + 0.431557i
\(485\) −6.66151 + 1.52045i −0.302484 + 0.0690399i
\(486\) 1.60981 2.01864i 0.0730225 0.0915674i
\(487\) 12.2269 5.88815i 0.554052 0.266817i −0.135839 0.990731i \(-0.543373\pi\)
0.689891 + 0.723914i \(0.257659\pi\)
\(488\) −5.25625 2.53128i −0.237939 0.114586i
\(489\) 6.85374 + 8.59432i 0.309937 + 0.388649i
\(490\) 0.590247 + 0.470706i 0.0266646 + 0.0212643i
\(491\) −1.77332 + 3.68233i −0.0800287 + 0.166181i −0.937144 0.348944i \(-0.886540\pi\)
0.857115 + 0.515125i \(0.172255\pi\)
\(492\) 11.3172 0.510217
\(493\) 0.968699 2.41189i 0.0436280 0.108626i
\(494\) −1.46601 −0.0659590
\(495\) −8.50254 + 17.6557i −0.382161 + 0.793565i
\(496\) −11.5280 9.19325i −0.517621 0.412789i
\(497\) 10.9056 + 13.6752i 0.489184 + 0.613417i
\(498\) −0.755008 0.363593i −0.0338327 0.0162930i
\(499\) 11.2754 5.42993i 0.504755 0.243077i −0.164136 0.986438i \(-0.552484\pi\)
0.668891 + 0.743361i \(0.266769\pi\)
\(500\) −6.96844 + 8.73815i −0.311638 + 0.390782i
\(501\) 25.8842 5.90790i 1.15642 0.263945i
\(502\) 0.781495 + 3.42395i 0.0348798 + 0.152818i
\(503\) 20.1194 16.0447i 0.897080 0.715398i −0.0621370 0.998068i \(-0.519792\pi\)
0.959217 + 0.282670i \(0.0912201\pi\)
\(504\) 3.36249 + 0.767467i 0.149777 + 0.0341857i
\(505\) 38.1549i 1.69787i
\(506\) −0.837822 + 3.67074i −0.0372457 + 0.163184i
\(507\) −2.48700 5.16431i −0.110452 0.229355i
\(508\) −0.978970 2.03285i −0.0434348 0.0901932i
\(509\) −3.53552 + 15.4901i −0.156709 + 0.686588i 0.834133 + 0.551563i \(0.185968\pi\)
−0.990842 + 0.135024i \(0.956889\pi\)
\(510\) 0.262381i 0.0116184i
\(511\) −1.37874 0.314687i −0.0609917 0.0139210i
\(512\) −10.0800 + 8.03853i −0.445477 + 0.355256i
\(513\) 3.61341 + 15.8314i 0.159536 + 0.698972i
\(514\) 3.30290 0.753864i 0.145684 0.0332515i
\(515\) 3.08537 3.86893i 0.135958 0.170486i
\(516\) −16.4064 + 7.90092i −0.722253 + 0.347818i
\(517\) 8.58862 + 4.13606i 0.377727 + 0.181904i
\(518\) 3.60131 + 4.51590i 0.158232 + 0.198417i
\(519\) 4.59313 + 3.66289i 0.201616 + 0.160783i
\(520\) −2.34164 + 4.86246i −0.102688 + 0.213233i
\(521\) −22.1399 −0.969965 −0.484982 0.874524i \(-0.661174\pi\)
−0.484982 + 0.874524i \(0.661174\pi\)
\(522\) 1.31366 + 0.910957i 0.0574975 + 0.0398715i
\(523\) 31.1728 1.36309 0.681546 0.731775i \(-0.261308\pi\)
0.681546 + 0.731775i \(0.261308\pi\)
\(524\) 14.9542 31.0527i 0.653276 1.35654i
\(525\) 7.70121 + 6.14151i 0.336108 + 0.268037i
\(526\) −1.58531 1.98792i −0.0691228 0.0866772i
\(527\) −1.67612 0.807179i −0.0730131 0.0351613i
\(528\) 15.4718 7.45083i 0.673324 0.324256i
\(529\) 4.61906 5.79212i 0.200829 0.251831i
\(530\) −0.210315 + 0.0480030i −0.00913550 + 0.00208512i
\(531\) −0.481051 2.10762i −0.0208758 0.0914630i
\(532\) −13.7490 + 10.9644i −0.596094 + 0.475369i
\(533\) 13.9975 + 3.19484i 0.606300 + 0.138384i
\(534\) 2.99123i 0.129443i
\(535\) 1.64103 7.18981i 0.0709478 0.310843i
\(536\) −0.278401 0.578106i −0.0120251 0.0249704i
\(537\) −5.52970 11.4825i −0.238624 0.495508i
\(538\) −0.0592439 + 0.259564i −0.00255419 + 0.0111906i
\(539\) 6.23415i 0.268524i
\(540\) 28.9259 + 6.60214i 1.24477 + 0.284111i
\(541\) −0.559338 + 0.446058i −0.0240478 + 0.0191775i −0.635440 0.772150i \(-0.719181\pi\)
0.611392 + 0.791328i \(0.290610\pi\)
\(542\) −0.462397 2.02589i −0.0198617 0.0870196i
\(543\) −11.3350 + 2.58714i −0.486431 + 0.111025i
\(544\) −0.605542 + 0.759325i −0.0259624 + 0.0325558i
\(545\) 23.3027 11.2220i 0.998180 0.480698i
\(546\) −1.42482 0.686155i −0.0609765 0.0293647i
\(547\) −25.7613 32.3036i −1.10147 1.38120i −0.917247 0.398318i \(-0.869594\pi\)
−0.184225 0.982884i \(-0.558977\pi\)
\(548\) 1.46239 + 1.16622i 0.0624703 + 0.0498184i
\(549\) −6.47098 + 13.4371i −0.276175 + 0.573483i
\(550\) 2.04440 0.0871736
\(551\) −15.7312 + 4.71637i −0.670170 + 0.200924i
\(552\) 4.21000 0.179189
\(553\) −2.35024 + 4.88033i −0.0999425 + 0.207533i
\(554\) −1.61013 1.28403i −0.0684078 0.0545534i
\(555\) 22.8795 + 28.6900i 0.971182 + 1.21782i
\(556\) −12.8876 6.20633i −0.546555 0.263207i
\(557\) −19.1398 + 9.21726i −0.810981 + 0.390548i −0.792948 0.609290i \(-0.791455\pi\)
−0.0180332 + 0.999837i \(0.505740\pi\)
\(558\) 0.713406 0.894583i 0.0302009 0.0378707i
\(559\) −22.5225 + 5.14062i −0.952601 + 0.217425i
\(560\) 7.04217 + 30.8538i 0.297586 + 1.30381i
\(561\) 1.69395 1.35088i 0.0715187 0.0570343i
\(562\) −2.27998 0.520392i −0.0961753 0.0219514i
\(563\) 14.3265i 0.603790i 0.953341 + 0.301895i \(0.0976193\pi\)
−0.953341 + 0.301895i \(0.902381\pi\)
\(564\) 1.17719 5.15759i 0.0495684 0.217174i
\(565\) −15.5906 32.3742i −0.655901 1.36199i
\(566\) −1.92863 4.00485i −0.0810664 0.168336i
\(567\) −0.507190 + 2.22215i −0.0213000 + 0.0933214i
\(568\) 4.05921i 0.170321i
\(569\) −16.7463 3.82222i −0.702039 0.160236i −0.143422 0.989662i \(-0.545811\pi\)
−0.558617 + 0.829426i \(0.688668\pi\)
\(570\) 1.29618 1.03367i 0.0542909 0.0432956i
\(571\) −0.918962 4.02624i −0.0384574 0.168493i 0.952052 0.305935i \(-0.0989690\pi\)
−0.990510 + 0.137442i \(0.956112\pi\)
\(572\) 21.5642 4.92190i 0.901647 0.205795i
\(573\) 4.42066 5.54333i 0.184676 0.231576i
\(574\) −2.30259 + 1.10887i −0.0961080 + 0.0462832i
\(575\) −14.8761 7.16394i −0.620375 0.298757i
\(576\) 7.90810 + 9.91644i 0.329504 + 0.413185i
\(577\) −35.6466 28.4272i −1.48399 1.18344i −0.938479 0.345338i \(-0.887764\pi\)
−0.545510 0.838104i \(-0.683664\pi\)
\(578\) 1.24409 2.58337i 0.0517471 0.107454i
\(579\) 4.61223 0.191678
\(580\) −4.70702 + 29.6353i −0.195448 + 1.23054i
\(581\) −12.7527 −0.529071
\(582\) −0.201603 + 0.418634i −0.00835673 + 0.0173529i
\(583\) 1.39273 + 1.11067i 0.0576810 + 0.0459991i
\(584\) 0.204625 + 0.256592i 0.00846745 + 0.0106178i
\(585\) 12.4304 + 5.98618i 0.513935 + 0.247498i
\(586\) −0.882277 + 0.424882i −0.0364465 + 0.0175517i
\(587\) −12.0226 + 15.0759i −0.496227 + 0.622249i −0.965374 0.260871i \(-0.915990\pi\)
0.469147 + 0.883120i \(0.344562\pi\)
\(588\) −3.37295 + 0.769853i −0.139098 + 0.0317482i
\(589\) 2.61569 + 11.4601i 0.107778 + 0.472205i
\(590\) −0.470780 + 0.375434i −0.0193817 + 0.0154564i
\(591\) −22.2939 5.08844i −0.917050 0.209311i
\(592\) 44.1585i 1.81490i
\(593\) −7.52102 + 32.9517i −0.308851 + 1.35317i 0.547514 + 0.836796i \(0.315574\pi\)
−0.856366 + 0.516370i \(0.827283\pi\)
\(594\) 1.57743 + 3.27558i 0.0647229 + 0.134399i
\(595\) 1.73247 + 3.59751i 0.0710244 + 0.147484i
\(596\) 7.47909 32.7680i 0.306355 1.34223i
\(597\) 2.21622i 0.0907036i
\(598\) 2.58437 + 0.589865i 0.105683 + 0.0241214i
\(599\) 15.1458 12.0784i 0.618841 0.493509i −0.263163 0.964751i \(-0.584766\pi\)
0.882004 + 0.471242i \(0.156194\pi\)
\(600\) −0.508672 2.22864i −0.0207664 0.0909837i
\(601\) −16.6470 + 3.79958i −0.679047 + 0.154988i −0.548114 0.836403i \(-0.684654\pi\)
−0.130932 + 0.991391i \(0.541797\pi\)
\(602\) 2.56390 3.21503i 0.104497 0.131035i
\(603\) −1.47788 + 0.711707i −0.0601837 + 0.0289830i
\(604\) −17.4792 8.41754i −0.711218 0.342505i
\(605\) −8.71110 10.9234i −0.354157 0.444098i
\(606\) −2.02856 1.61772i −0.0824046 0.0657155i
\(607\) 17.9395 37.2517i 0.728140 1.51200i −0.126042 0.992025i \(-0.540228\pi\)
0.854182 0.519973i \(-0.174058\pi\)
\(608\) 6.13669 0.248876
\(609\) −17.4966 2.77900i −0.708996 0.112611i
\(610\) 4.15414 0.168196
\(611\) 2.91198 6.04678i 0.117806 0.244627i
\(612\) 1.29093 + 1.02948i 0.0521827 + 0.0416143i
\(613\) 6.00843 + 7.53434i 0.242678 + 0.304309i 0.888222 0.459414i \(-0.151941\pi\)
−0.645544 + 0.763723i \(0.723369\pi\)
\(614\) 1.96597 + 0.946759i 0.0793399 + 0.0382081i
\(615\) −14.6286 + 7.04476i −0.589882 + 0.284072i
\(616\) −4.94606 + 6.20216i −0.199282 + 0.249892i
\(617\) 12.1657 2.77673i 0.489771 0.111787i 0.0294988 0.999565i \(-0.490609\pi\)
0.460272 + 0.887778i \(0.347752\pi\)
\(618\) −0.0748812 0.328076i −0.00301217 0.0131972i
\(619\) 24.5785 19.6007i 0.987892 0.787818i 0.0106499 0.999943i \(-0.496610\pi\)
0.977242 + 0.212125i \(0.0680385\pi\)
\(620\) 20.9390 + 4.77920i 0.840932 + 0.191937i
\(621\) 29.3623i 1.17827i
\(622\) 0.476253 2.08660i 0.0190960 0.0836651i
\(623\) 19.7507 + 41.0128i 0.791296 + 1.64314i
\(624\) −5.24572 10.8929i −0.209997 0.436063i
\(625\) 6.89943 30.2284i 0.275977 1.20914i
\(626\) 4.42207i 0.176741i
\(627\) −13.3469 3.04634i −0.533024 0.121659i
\(628\) 4.06866 3.24465i 0.162357 0.129476i
\(629\) 1.23977 + 5.43180i 0.0494329 + 0.216580i
\(630\) −2.39429 + 0.546480i −0.0953907 + 0.0217723i
\(631\) 2.93725 3.68320i 0.116930 0.146626i −0.719922 0.694055i \(-0.755822\pi\)
0.836852 + 0.547430i \(0.184394\pi\)
\(632\) 1.13258 0.545423i 0.0450517 0.0216958i
\(633\) 18.0307 + 8.68315i 0.716658 + 0.345124i
\(634\) −2.89021 3.62421i −0.114785 0.143936i
\(635\) 2.53084 + 2.01827i 0.100433 + 0.0800928i
\(636\) 0.428931 0.890685i 0.0170082 0.0353179i
\(637\) −4.38912 −0.173903
\(638\) −3.19875 + 1.81319i −0.126640 + 0.0717850i
\(639\) −10.3770 −0.410508
\(640\) 6.46997 13.4350i 0.255748 0.531066i
\(641\) 22.8183 + 18.1970i 0.901268 + 0.718738i 0.960137 0.279528i \(-0.0901780\pi\)
−0.0588691 + 0.998266i \(0.518749\pi\)
\(642\) −0.312679 0.392087i −0.0123404 0.0154744i
\(643\) 11.9567 + 5.75803i 0.471526 + 0.227075i 0.654528 0.756038i \(-0.272867\pi\)
−0.183003 + 0.983112i \(0.558582\pi\)
\(644\) 28.6491 13.7967i 1.12893 0.543666i
\(645\) 16.2888 20.4255i 0.641370 0.804252i
\(646\) 0.245402 0.0560113i 0.00965519 0.00220374i
\(647\) 7.64780 + 33.5072i 0.300666 + 1.31730i 0.869125 + 0.494592i \(0.164683\pi\)
−0.568459 + 0.822712i \(0.692460\pi\)
\(648\) 0.413556 0.329800i 0.0162460 0.0129558i
\(649\) 4.84767 + 1.10645i 0.190288 + 0.0434320i
\(650\) 1.43935i 0.0564560i
\(651\) −2.82162 + 12.3623i −0.110588 + 0.484518i
\(652\) −8.36013 17.3600i −0.327408 0.679870i
\(653\) 12.5243 + 26.0069i 0.490112 + 1.01773i 0.988563 + 0.150810i \(0.0481882\pi\)
−0.498451 + 0.866918i \(0.666098\pi\)
\(654\) 0.391374 1.71472i 0.0153039 0.0670509i
\(655\) 49.4475i 1.93207i
\(656\) −19.0485 4.34770i −0.743721 0.169749i
\(657\) 0.655953 0.523105i 0.0255912 0.0204083i
\(658\) 0.265835 + 1.16470i 0.0103633 + 0.0454048i
\(659\) −32.7737 + 7.48039i −1.27668 + 0.291395i −0.806532 0.591191i \(-0.798658\pi\)
−0.470152 + 0.882585i \(0.655801\pi\)
\(660\) −15.5957 + 19.5564i −0.607063 + 0.761233i
\(661\) 16.8358 8.10769i 0.654836 0.315353i −0.0768012 0.997046i \(-0.524471\pi\)
0.731638 + 0.681694i \(0.238756\pi\)
\(662\) 1.69161 + 0.814636i 0.0657462 + 0.0316617i
\(663\) −0.951083 1.19262i −0.0369370 0.0463175i
\(664\) 2.31386 + 1.84524i 0.0897951 + 0.0716092i
\(665\) 10.9468 22.7312i 0.424497 0.881477i
\(666\) −3.42675 −0.132784
\(667\) 29.6295 1.98469i 1.14726 0.0768476i
\(668\) −46.5375 −1.80059
\(669\) 9.26260 19.2340i 0.358113 0.743629i
\(670\) 0.357212 + 0.284867i 0.0138003 + 0.0110054i
\(671\) −21.3878 26.8195i −0.825668 1.03536i
\(672\) 5.96425 + 2.87223i 0.230076 + 0.110799i
\(673\) −28.7262 + 13.8338i −1.10731 + 0.533254i −0.895951 0.444153i \(-0.853505\pi\)
−0.211363 + 0.977408i \(0.567790\pi\)
\(674\) 1.83308 2.29861i 0.0706076 0.0885392i
\(675\) −15.5435 + 3.54770i −0.598269 + 0.136551i
\(676\) 2.23571 + 9.79527i 0.0859887 + 0.376741i
\(677\) 29.5275 23.5474i 1.13483 0.905000i 0.138484 0.990365i \(-0.455777\pi\)
0.996350 + 0.0853646i \(0.0272055\pi\)
\(678\) −2.38224 0.543731i −0.0914894 0.0208819i
\(679\) 7.07107i 0.271363i
\(680\) 0.206198 0.903412i 0.00790733 0.0346443i
\(681\) 0.0505608 + 0.104991i 0.00193749 + 0.00402325i
\(682\) 1.14188 + 2.37114i 0.0437249 + 0.0907958i
\(683\) 3.52930 15.4629i 0.135045 0.591671i −0.861437 0.507864i \(-0.830435\pi\)
0.996482 0.0838066i \(-0.0267078\pi\)
\(684\) 10.4330i 0.398915i
\(685\) −2.61624 0.597141i −0.0999615 0.0228156i
\(686\) −2.12762 + 1.69672i −0.0812327 + 0.0647809i
\(687\) −3.30262 14.4697i −0.126003 0.552055i
\(688\) 30.6498 6.99562i 1.16851 0.266706i
\(689\) 0.781959 0.980546i 0.0297903 0.0373558i
\(690\) −2.70088 + 1.30068i −0.102821 + 0.0495159i
\(691\) 26.4855 + 12.7548i 1.00756 + 0.485214i 0.863496 0.504355i \(-0.168270\pi\)
0.144061 + 0.989569i \(0.453984\pi\)
\(692\) −6.42045 8.05099i −0.244069 0.306053i
\(693\) 15.8552 + 12.6441i 0.602291 + 0.480311i
\(694\) −2.32216 + 4.82202i −0.0881482 + 0.183042i
\(695\) 20.5218 0.778438
\(696\) 2.77248 + 3.03587i 0.105091 + 0.115074i
\(697\) −2.46516 −0.0933748
\(698\) −1.24946 + 2.59453i −0.0472928 + 0.0982045i
\(699\) 1.92288 + 1.53344i 0.0727299 + 0.0580002i
\(700\) −10.7651 13.4990i −0.406881 0.510213i
\(701\) −9.93285 4.78341i −0.375159 0.180667i 0.236797 0.971559i \(-0.423902\pi\)
−0.611955 + 0.790892i \(0.709617\pi\)
\(702\) 2.30615 1.11059i 0.0870402 0.0419164i
\(703\) 21.9493 27.5235i 0.827832 1.03807i
\(704\) −28.4417 + 6.49164i −1.07194 + 0.244663i
\(705\) 1.68888 + 7.39948i 0.0636070 + 0.278681i
\(706\) −3.56606 + 2.84384i −0.134210 + 0.107029i
\(707\) −38.4953 8.78630i −1.44777 0.330443i
\(708\) 2.75944i 0.103706i
\(709\) −7.44065 + 32.5996i −0.279439 + 1.22430i 0.619065 + 0.785340i \(0.287512\pi\)
−0.898505 + 0.438964i \(0.855346\pi\)
\(710\) 1.25409 + 2.60415i 0.0470653 + 0.0977320i
\(711\) −1.39432 2.89534i −0.0522912 0.108584i
\(712\) 2.35072 10.2992i 0.0880971 0.385979i
\(713\) 21.2550i 0.796005i
\(714\) 0.264721 + 0.0604209i 0.00990695 + 0.00226120i
\(715\) −24.8102 + 19.7855i −0.927848 + 0.739934i
\(716\) 4.97096 + 21.7792i 0.185773 + 0.813927i
\(717\) −16.7787 + 3.82963i −0.626613 + 0.143020i
\(718\) −1.28952 + 1.61701i −0.0481246 + 0.0603464i
\(719\) −44.2582 + 21.3136i −1.65055 + 0.794864i −0.651199 + 0.758907i \(0.725734\pi\)
−0.999353 + 0.0359569i \(0.988552\pi\)
\(720\) −16.9160 8.14630i −0.630421 0.303595i
\(721\) −3.19295 4.00383i −0.118912 0.149111i
\(722\) 1.29683 + 1.03419i 0.0482632 + 0.0384886i
\(723\) −6.63195 + 13.7714i −0.246645 + 0.512163i
\(724\) 20.3793 0.757392
\(725\) −4.63061 15.4451i −0.171976 0.573616i
\(726\) −0.950096 −0.0352614
\(727\) −15.3329 + 31.8392i −0.568667 + 1.18085i 0.396213 + 0.918159i \(0.370324\pi\)
−0.964880 + 0.262691i \(0.915390\pi\)
\(728\) 4.36660 + 3.48225i 0.161837 + 0.129061i
\(729\) −12.0410 15.0989i −0.445962 0.559219i
\(730\) −0.210549 0.101395i −0.00779278 0.00375281i
\(731\) 3.57373 1.72102i 0.132179 0.0636542i
\(732\) −11.8694 + 14.8837i −0.438704 + 0.550117i
\(733\) −16.5129 + 3.76896i −0.609918 + 0.139210i −0.516314 0.856400i \(-0.672696\pi\)
−0.0936046 + 0.995609i \(0.529839\pi\)
\(734\) −1.29253 5.66292i −0.0477080 0.209022i
\(735\) 3.88066 3.09472i 0.143140 0.114150i
\(736\) −10.8181 2.46916i −0.398761 0.0910146i
\(737\) 3.77284i 0.138974i
\(738\) 0.337387 1.47819i 0.0124194 0.0544128i
\(739\) 14.8159 + 30.7656i 0.545012 + 1.13173i 0.973607 + 0.228233i \(0.0732947\pi\)
−0.428594 + 0.903497i \(0.640991\pi\)
\(740\) −27.9082 57.9520i −1.02593 2.13036i
\(741\) −2.14476 + 9.39682i −0.0787899 + 0.345201i
\(742\) 0.223245i 0.00819559i
\(743\) 26.8583 + 6.13024i 0.985337 + 0.224897i 0.684686 0.728838i \(-0.259939\pi\)
0.300650 + 0.953734i \(0.402796\pi\)
\(744\) 2.30071 1.83475i 0.0843481 0.0672654i
\(745\) 10.7301 + 47.0116i 0.393120 + 1.72237i
\(746\) 1.03281 0.235732i 0.0378138 0.00863076i
\(747\) 4.71719 5.91516i 0.172593 0.216424i
\(748\) −3.42168 + 1.64779i −0.125109 + 0.0602493i
\(749\) −6.87606 3.31133i −0.251246 0.120994i
\(750\) −0.679853 0.852508i −0.0248247 0.0311292i
\(751\) 4.50823 + 3.59519i 0.164508 + 0.131190i 0.702284 0.711897i \(-0.252164\pi\)
−0.537776 + 0.843088i \(0.680735\pi\)
\(752\) −3.96277 + 8.22877i −0.144507 + 0.300072i
\(753\) 23.0901 0.841452
\(754\) 1.27657 + 2.25207i 0.0464899 + 0.0820155i
\(755\) 27.8334 1.01296
\(756\) 13.3221 27.6636i 0.484519 1.00611i
\(757\) 3.55347 + 2.83380i 0.129153 + 0.102996i 0.685936 0.727662i \(-0.259393\pi\)
−0.556783 + 0.830658i \(0.687964\pi\)
\(758\) 2.78233 + 3.48893i 0.101059 + 0.126724i
\(759\) 22.3029 + 10.7405i 0.809546 + 0.389857i
\(760\) −5.27525 + 2.54043i −0.191353 + 0.0921509i
\(761\) 22.6200 28.3646i 0.819974 1.02822i −0.179041 0.983842i \(-0.557299\pi\)
0.999015 0.0443736i \(-0.0141292\pi\)
\(762\) 0.214609 0.0489830i 0.00777445 0.00177447i
\(763\) −5.95597 26.0948i −0.215621 0.944696i
\(764\) −9.71655 + 7.74869i −0.351532 + 0.280338i
\(765\) −2.30949 0.527126i −0.0834998 0.0190583i
\(766\) 3.57064i 0.129012i
\(767\) 0.778991 3.41298i 0.0281277 0.123236i
\(768\) 6.68879 + 13.8894i 0.241361 + 0.501191i
\(769\) −14.7542 30.6375i −0.532052 1.10482i −0.977777 0.209647i \(-0.932768\pi\)
0.445725 0.895170i \(-0.352946\pi\)
\(770\) 1.25694 5.50702i 0.0452970 0.198459i
\(771\) 22.2738i 0.802170i
\(772\) −7.88178 1.79897i −0.283672 0.0647462i
\(773\) 5.50787 4.39238i 0.198104 0.157983i −0.519414 0.854523i \(-0.673850\pi\)
0.717518 + 0.696540i \(0.245278\pi\)
\(774\) 0.542868 + 2.37846i 0.0195130 + 0.0854920i
\(775\) −11.2517 + 2.56813i −0.404173 + 0.0922499i
\(776\) 1.02314 1.28298i 0.0367286 0.0460562i
\(777\) 34.2146 16.4769i 1.22744 0.591106i
\(778\) −2.42011 1.16547i −0.0867653 0.0417840i
\(779\) 9.71169 + 12.1781i 0.347958 + 0.436325i
\(780\) 13.7686 + 10.9801i 0.492995 + 0.393151i
\(781\) 10.3559 21.5042i 0.370562 0.769479i
\(782\) −0.455145 −0.0162759
\(783\) 21.1735 19.3365i 0.756678 0.691029i
\(784\) 5.97294 0.213319
\(785\) −3.23942 + 6.72672i −0.115620 + 0.240087i
\(786\) 2.62894 + 2.09651i 0.0937713 + 0.0747801i
\(787\) 30.6610 + 38.4477i 1.09295 + 1.37051i 0.922884 + 0.385077i \(0.125825\pi\)
0.170062 + 0.985433i \(0.445603\pi\)
\(788\) 36.1131 + 17.3912i 1.28648 + 0.619535i
\(789\) −15.0614 + 7.25320i −0.536201 + 0.258221i
\(790\) −0.558090 + 0.699823i −0.0198559 + 0.0248986i
\(791\) −36.2532 + 8.27455i −1.28901 + 0.294209i
\(792\) −1.04725 4.58832i −0.0372125 0.163039i
\(793\) −18.8821 + 15.0580i −0.670525 + 0.534726i
\(794\) −1.92765 0.439973i −0.0684097 0.0156141i
\(795\) 1.41830i 0.0503020i
\(796\) 0.864418 3.78726i 0.0306385 0.134236i
\(797\) −15.0982 31.3518i −0.534806 1.11054i −0.976925 0.213581i \(-0.931487\pi\)
0.442119 0.896956i \(-0.354227\pi\)
\(798\) −0.744405 1.54577i −0.0263517 0.0547198i
\(799\) −0.256421 + 1.12345i −0.00907151 + 0.0397449i
\(800\) 6.02510i 0.213019i
\(801\) −26.3289 6.00941i −0.930287 0.212332i
\(802\) 0.643788 0.513404i 0.0227329 0.0181289i
\(803\) 0.429409 + 1.88136i 0.0151535 + 0.0663919i
\(804\) −2.04127 + 0.465908i −0.0719902 + 0.0164313i
\(805\) −28.4437 + 35.6673i −1.00251 + 1.25711i
\(806\) 1.66939 0.803937i 0.0588019 0.0283175i
\(807\) 1.57708 + 0.759482i 0.0555159 + 0.0267350i
\(808\) 5.71328 + 7.16423i 0.200993 + 0.252037i
\(809\) 39.3593 + 31.3880i 1.38380 + 1.10354i 0.982223 + 0.187717i \(0.0601088\pi\)
0.401576 + 0.915826i \(0.368463\pi\)
\(810\) −0.163421 + 0.339348i −0.00574205 + 0.0119235i
\(811\) 8.56424 0.300731 0.150366 0.988630i \(-0.451955\pi\)
0.150366 + 0.988630i \(0.451955\pi\)
\(812\) 28.8157 + 11.5734i 1.01123 + 0.406147i
\(813\) −13.6620 −0.479149
\(814\) 3.41976 7.10121i 0.119863 0.248897i
\(815\) 21.6126 + 17.2355i 0.757058 + 0.603733i
\(816\) 1.29428 + 1.62298i 0.0453089 + 0.0568156i
\(817\) −22.5809 10.8744i −0.790007 0.380447i
\(818\) 3.67928 1.77185i 0.128643 0.0619513i
\(819\) 8.90205 11.1628i 0.311063 0.390060i
\(820\) 27.7464 6.33293i 0.968946 0.221156i
\(821\) −7.23124 31.6821i −0.252372 1.10571i −0.929201 0.369574i \(-0.879504\pi\)
0.676829 0.736140i \(-0.263354\pi\)
\(822\) −0.142673 + 0.113778i −0.00497630 + 0.00396847i
\(823\) −34.0344 7.76814i −1.18637 0.270780i −0.416590 0.909094i \(-0.636775\pi\)
−0.769776 + 0.638314i \(0.779632\pi\)
\(824\) 1.18846i 0.0414019i
\(825\) 2.99095 13.1042i 0.104131 0.456229i
\(826\) 0.270372 + 0.561434i 0.00940746 + 0.0195348i
\(827\) −18.3769 38.1600i −0.639027 1.32695i −0.929057 0.369936i \(-0.879380\pi\)
0.290030 0.957018i \(-0.406335\pi\)
\(828\) −4.19782 + 18.3919i −0.145884 + 0.639161i
\(829\) 23.0078i 0.799094i −0.916713 0.399547i \(-0.869167\pi\)
0.916713 0.399547i \(-0.130833\pi\)
\(830\) −2.05452 0.468931i −0.0713134 0.0162768i
\(831\) −10.5860 + 8.44205i −0.367224 + 0.292852i
\(832\) 4.57041 + 20.0243i 0.158450 + 0.694217i
\(833\) 0.734713 0.167693i 0.0254563 0.00581023i
\(834\) 0.870101 1.09107i 0.0301291 0.0377807i
\(835\) 60.1545 28.9689i 2.08173 1.00251i
\(836\) 21.6202 + 10.4117i 0.747749 + 0.360097i
\(837\) −12.7964 16.0461i −0.442307 0.554636i
\(838\) −4.12472 3.28935i −0.142486 0.113629i
\(839\) 1.67573 3.47970i 0.0578528 0.120132i −0.870038 0.492985i \(-0.835906\pi\)
0.927891 + 0.372852i \(0.121620\pi\)
\(840\) −6.31604 −0.217924
\(841\) 20.9436 + 20.0591i 0.722192 + 0.691693i
\(842\) 1.78321 0.0614534
\(843\) −6.67120 + 13.8529i −0.229768 + 0.477119i
\(844\) −27.4257 21.8713i −0.944033 0.752841i
\(845\) −8.98728 11.2697i −0.309172 0.387689i
\(846\) −0.638562 0.307515i −0.0219542 0.0105726i
\(847\) −13.0268 + 6.27338i −0.447606 + 0.215556i
\(848\) −1.06413 + 1.33438i −0.0365424 + 0.0458227i
\(849\) −28.4918 + 6.50307i −0.977836 + 0.223185i
\(850\) 0.0549927 + 0.240939i 0.00188624 + 0.00826414i
\(851\) −49.7678 + 39.6885i −1.70602 + 1.36050i
\(852\) −12.9135 2.94743i −0.442411 0.100977i
\(853\) 3.55963i 0.121879i −0.998141 0.0609397i \(-0.980590\pi\)
0.998141 0.0609397i \(-0.0194097\pi\)
\(854\) 0.956614 4.19120i 0.0327346 0.143420i
\(855\) 6.49437 + 13.4857i 0.222103 + 0.461201i
\(856\) 0.768465 + 1.59573i 0.0262656 + 0.0545411i
\(857\) 4.27323 18.7222i 0.145971 0.639540i −0.848010 0.529981i \(-0.822199\pi\)
0.993980 0.109559i \(-0.0349438\pi\)
\(858\) 2.15795i 0.0736711i
\(859\) 13.6690 + 3.11986i 0.466380 + 0.106448i 0.449252 0.893405i \(-0.351691\pi\)
0.0171282 + 0.999853i \(0.494548\pi\)
\(860\) −35.8025 + 28.5515i −1.22086 + 0.973600i
\(861\) 3.73894 + 16.3814i 0.127423 + 0.558275i
\(862\) 1.78006 0.406288i 0.0606292 0.0138382i
\(863\) 0.523014 0.655839i 0.0178036 0.0223250i −0.772850 0.634589i \(-0.781169\pi\)
0.790654 + 0.612264i \(0.209741\pi\)
\(864\) −9.65352 + 4.64889i −0.328419 + 0.158158i
\(865\) 13.3107 + 6.41010i 0.452578 + 0.217950i
\(866\) 2.93661 + 3.68239i 0.0997899 + 0.125133i
\(867\) −14.7388 11.7538i −0.500555 0.399179i
\(868\) 9.64367 20.0253i 0.327327 0.679702i
\(869\) 7.39147 0.250739
\(870\) −2.71659 1.09108i −0.0921011 0.0369910i
\(871\) −2.65625 −0.0900037
\(872\) −2.69511 + 5.59645i −0.0912679 + 0.189520i
\(873\) −3.27982 2.61557i −0.111005 0.0885235i
\(874\) 1.79307 + 2.24844i 0.0606517 + 0.0760548i
\(875\) −14.9505 7.19978i −0.505419 0.243397i
\(876\) 0.964873 0.464659i 0.0326001 0.0156994i
\(877\) −32.4944 + 40.7467i −1.09726 + 1.37592i −0.177182 + 0.984178i \(0.556698\pi\)
−0.920076 + 0.391739i \(0.871873\pi\)
\(878\) −4.30943 + 0.983598i −0.145436 + 0.0331948i
\(879\) 1.43264 + 6.27681i 0.0483218 + 0.211712i
\(880\) 33.7630 26.9251i 1.13815 0.907644i
\(881\) −6.55060 1.49513i −0.220695 0.0503722i 0.110743 0.993849i \(-0.464677\pi\)
−0.331439 + 0.943477i \(0.607534\pi\)
\(882\) 0.463507i 0.0156071i
\(883\) −3.79146 + 16.6115i −0.127593 + 0.559020i 0.870205 + 0.492690i \(0.163986\pi\)
−0.997798 + 0.0663303i \(0.978871\pi\)
\(884\) 1.16012 + 2.40902i 0.0390191 + 0.0810240i
\(885\) 1.71771 + 3.56686i 0.0577401 + 0.119899i
\(886\) −0.537101 + 2.35320i −0.0180443 + 0.0790571i
\(887\) 15.9991i 0.537197i −0.963252 0.268598i \(-0.913440\pi\)
0.963252 0.268598i \(-0.0865604\pi\)
\(888\) −8.59203 1.96107i −0.288330 0.0658094i
\(889\) 2.61908 2.08865i 0.0878411 0.0700509i
\(890\) 1.67385 + 7.33361i 0.0561075 + 0.245823i
\(891\) 3.03225 0.692091i 0.101584 0.0231859i
\(892\) −23.3308 + 29.2559i −0.781174 + 0.979561i
\(893\) 6.56012 3.15919i 0.219526 0.105718i
\(894\) 2.95438 + 1.42275i 0.0988092 + 0.0475840i
\(895\) −19.9827 25.0575i −0.667947 0.837579i
\(896\) −12.0650 9.62150i −0.403063 0.321432i
\(897\) 7.56182 15.7023i 0.252482 0.524284i
\(898\) 3.78256 0.126226
\(899\) 15.3272 13.9974i 0.511190 0.466839i
\(900\) 10.2433 0.341442
\(901\) −0.0934320 + 0.194014i −0.00311267 + 0.00646353i
\(902\) 2.72653 + 2.17434i 0.0907837 + 0.0723975i
\(903\) −16.8567 21.1377i −0.560956 0.703417i
\(904\) 7.77507 + 3.74428i 0.258595 + 0.124533i
\(905\) −26.3424 + 12.6858i −0.875649 + 0.421691i
\(906\) 1.18010 1.47980i 0.0392063 0.0491631i
\(907\) −1.50979 + 0.344600i −0.0501318 + 0.0114422i −0.247513 0.968885i \(-0.579613\pi\)
0.197381 + 0.980327i \(0.436756\pi\)
\(908\) −0.0454520 0.199138i −0.00150838 0.00660863i
\(909\) 18.3147 14.6055i 0.607460 0.484433i
\(910\) −3.87719 0.884944i −0.128528 0.0293356i
\(911\) 19.4756i 0.645256i 0.946526 + 0.322628i \(0.104566\pi\)
−0.946526 + 0.322628i \(0.895434\pi\)
\(912\) 2.91871 12.7877i 0.0966480 0.423443i
\(913\) 7.55036 + 15.6785i 0.249880 + 0.518882i
\(914\) −0.724144 1.50370i −0.0239525 0.0497380i
\(915\) 6.07748 26.6272i 0.200915 0.880267i
\(916\) 26.0153i 0.859570i
\(917\) 49.8886 + 11.3867i 1.64747 + 0.376023i
\(918\) −0.343605 + 0.274016i −0.0113407 + 0.00904387i
\(919\) −9.23637 40.4672i −0.304680 1.33489i −0.862975 0.505247i \(-0.831401\pi\)
0.558295 0.829642i \(-0.311456\pi\)
\(920\) 10.3217 2.35586i 0.340296 0.0776703i
\(921\) 8.94473 11.2163i 0.294739 0.369591i
\(922\) 3.10412 1.49487i 0.102229 0.0492308i
\(923\) −15.1399 7.29099i −0.498336 0.239986i
\(924\) 16.1395 + 20.2383i 0.530951 + 0.665791i
\(925\) 27.0230 + 21.5501i 0.888511 + 0.708564i
\(926\) −1.17067 + 2.43093i −0.0384707 + 0.0798852i
\(927\) 3.03818 0.0997870
\(928\) −5.34370 9.42711i −0.175415 0.309460i
\(929\) −12.1373 −0.398211 −0.199105 0.979978i \(-0.563804\pi\)
−0.199105 + 0.979978i \(0.563804\pi\)
\(930\) −0.909152 + 1.88787i −0.0298123 + 0.0619058i
\(931\) −3.72287 2.96889i −0.122012 0.0973015i
\(932\) −2.68788 3.37049i −0.0880443 0.110404i
\(933\) −12.6779 6.10536i −0.415056 0.199881i
\(934\) −6.04078 + 2.90909i −0.197660 + 0.0951882i
\(935\) 3.39714 4.25988i 0.111098 0.139313i
\(936\) −3.23038 + 0.737314i −0.105588 + 0.0240999i
\(937\) 11.9126 + 52.1927i 0.389169 + 1.70506i 0.667530 + 0.744583i \(0.267352\pi\)
−0.278361 + 0.960477i \(0.589791\pi\)
\(938\) 0.369667 0.294799i 0.0120700 0.00962554i
\(939\) 28.3445 + 6.46946i 0.924989 + 0.211123i
\(940\) 13.3036i 0.433917i
\(941\) 3.25236 14.2495i 0.106024 0.464521i −0.893846 0.448375i \(-0.852003\pi\)
0.999870 0.0161466i \(-0.00513986\pi\)
\(942\) 0.220288 + 0.457433i 0.00717737 + 0.0149040i
\(943\) −12.2203 25.3758i −0.397949 0.826350i
\(944\) −1.06009 + 4.64456i −0.0345030 + 0.151168i
\(945\) 44.0508i 1.43297i
\(946\) −5.47062 1.24863i −0.177865 0.0405966i
\(947\) 11.2593 8.97899i 0.365878 0.291778i −0.423242 0.906016i \(-0.639108\pi\)
0.789120 + 0.614239i \(0.210537\pi\)
\(948\) −0.912772 3.99911i −0.0296454 0.129885i
\(949\) 1.32457 0.302324i 0.0429972 0.00981384i
\(950\) 0.973607 1.22086i 0.0315880 0.0396101i
\(951\) −27.4588 + 13.2234i −0.890411 + 0.428799i
\(952\) −0.863988 0.416075i −0.0280020 0.0134851i
\(953\) 4.15499 + 5.21020i 0.134593 + 0.168775i 0.844561 0.535460i \(-0.179862\pi\)
−0.709967 + 0.704235i \(0.751290\pi\)
\(954\) −0.103549 0.0825777i −0.00335253 0.00267355i
\(955\) 7.73619 16.0644i 0.250337 0.519831i
\(956\) 30.1667 0.975660
\(957\) 6.94243 + 23.1560i 0.224417 + 0.748528i
\(958\) 7.22820 0.233533
\(959\) −1.20494 + 2.50207i −0.0389094 + 0.0807962i
\(960\) −18.1598 14.4820i −0.586106 0.467404i
\(961\) 10.0651 + 12.6212i 0.324680 + 0.407135i
\(962\) −4.99958 2.40767i −0.161193 0.0776264i
\(963\) 4.07935 1.96451i 0.131455 0.0633055i
\(964\) 16.7047 20.9470i 0.538022 0.674658i
\(965\) 11.3078 2.58094i 0.364012 0.0830834i
\(966\) 0.690322 + 3.02450i 0.0222107 + 0.0973116i
\(967\) 13.9834 11.1514i 0.449677 0.358605i −0.372313 0.928107i \(-0.621435\pi\)
0.821990 + 0.569502i \(0.192864\pi\)
\(968\) 3.27131 + 0.746655i 0.105144 + 0.0239984i
\(969\) 1.65492i 0.0531636i
\(970\) −0.260011 + 1.13918i −0.00834845 + 0.0365769i
\(971\) −13.2900 27.5969i −0.426495 0.885627i −0.997889 0.0649502i \(-0.979311\pi\)
0.571393 0.820676i \(-0.306403\pi\)
\(972\) 12.9102 + 26.8082i 0.414094 + 0.859874i
\(973\) 4.72576 20.7049i 0.151501 0.663769i
\(974\) 2.32073i 0.0743611i
\(975\) −9.22595 2.10576i −0.295467 0.0674384i
\(976\) 25.6958 20.4917i 0.822503 0.655924i
\(977\) 6.02069 + 26.3784i 0.192619 + 0.843919i 0.975192 + 0.221360i \(0.0710497\pi\)
−0.782573 + 0.622559i \(0.786093\pi\)
\(978\) 1.83270 0.418302i 0.0586032 0.0133758i
\(979\) 38.7285 48.5640i 1.23777 1.55211i
\(980\) −7.83868 + 3.77491i −0.250398 + 0.120585i
\(981\) 14.3068 + 6.88979i 0.456781 + 0.219974i
\(982\) 0.435775 + 0.546445i 0.0139062 + 0.0174378i
\(983\) −24.8942 19.8524i −0.794001 0.633195i 0.140127 0.990134i \(-0.455249\pi\)
−0.934128 + 0.356939i \(0.883820\pi\)
\(984\) 1.69189 3.51324i 0.0539354 0.111998i
\(985\) −57.5056 −1.83228
\(986\) −0.299734 0.328209i −0.00954548 0.0104523i
\(987\) 7.85441 0.250009
\(988\) 7.33033 15.2216i 0.233209 0.484263i
\(989\) 35.4315 + 28.2557i 1.12666 + 0.898479i
\(990\) 2.08942 + 2.62004i 0.0664060 + 0.0832705i
\(991\) 21.9543 + 10.5726i 0.697401 + 0.335851i 0.748771 0.662829i \(-0.230644\pi\)
−0.0513697 + 0.998680i \(0.516359\pi\)
\(992\) −6.98805 + 3.36527i −0.221871 + 0.106847i
\(993\) 7.69646 9.65105i 0.244240 0.306267i
\(994\) 2.91617 0.665598i 0.0924954 0.0211115i
\(995\) 1.24016 + 5.43351i 0.0393158 + 0.172254i
\(996\) 7.55036 6.02121i 0.239242 0.190789i
\(997\) −24.5985 5.61446i −0.779044 0.177812i −0.185533 0.982638i \(-0.559401\pi\)
−0.593510 + 0.804826i \(0.702258\pi\)
\(998\) 2.14013i 0.0677448i
\(999\) −13.6774 + 59.9245i −0.432733 + 1.89593i
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 29.2.e.a.13.2 yes 12
3.2 odd 2 261.2.o.a.100.1 12
4.3 odd 2 464.2.y.d.129.2 12
5.2 odd 4 725.2.p.a.274.3 24
5.3 odd 4 725.2.p.a.274.2 24
5.4 even 2 725.2.q.a.651.1 12
29.2 odd 28 841.2.d.l.574.3 24
29.3 odd 28 841.2.a.k.1.7 12
29.4 even 14 841.2.e.a.63.2 12
29.5 even 14 841.2.e.h.267.1 12
29.6 even 14 841.2.e.e.236.2 12
29.7 even 7 841.2.b.e.840.7 12
29.8 odd 28 841.2.d.m.571.3 24
29.9 even 14 inner 29.2.e.a.9.2 12
29.10 odd 28 841.2.d.l.778.2 24
29.11 odd 28 841.2.d.k.645.2 24
29.12 odd 4 841.2.d.m.190.3 24
29.13 even 14 841.2.e.f.196.1 12
29.14 odd 28 841.2.d.k.605.2 24
29.15 odd 28 841.2.d.k.605.3 24
29.16 even 7 841.2.e.e.196.2 12
29.17 odd 4 841.2.d.m.190.2 24
29.18 odd 28 841.2.d.k.645.3 24
29.19 odd 28 841.2.d.l.778.3 24
29.20 even 7 841.2.e.i.270.1 12
29.21 odd 28 841.2.d.m.571.2 24
29.22 even 14 841.2.b.e.840.6 12
29.23 even 7 841.2.e.f.236.1 12
29.24 even 7 841.2.e.a.267.2 12
29.25 even 7 841.2.e.h.63.1 12
29.26 odd 28 841.2.a.k.1.6 12
29.27 odd 28 841.2.d.l.574.2 24
29.28 even 2 841.2.e.i.651.1 12
87.26 even 28 7569.2.a.bp.1.7 12
87.32 even 28 7569.2.a.bp.1.6 12
87.38 odd 14 261.2.o.a.154.1 12
116.67 odd 14 464.2.y.d.241.2 12
145.9 even 14 725.2.q.a.676.1 12
145.38 odd 28 725.2.p.a.299.3 24
145.67 odd 28 725.2.p.a.299.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.e.a.9.2 12 29.9 even 14 inner
29.2.e.a.13.2 yes 12 1.1 even 1 trivial
261.2.o.a.100.1 12 3.2 odd 2
261.2.o.a.154.1 12 87.38 odd 14
464.2.y.d.129.2 12 4.3 odd 2
464.2.y.d.241.2 12 116.67 odd 14
725.2.p.a.274.2 24 5.3 odd 4
725.2.p.a.274.3 24 5.2 odd 4
725.2.p.a.299.2 24 145.67 odd 28
725.2.p.a.299.3 24 145.38 odd 28
725.2.q.a.651.1 12 5.4 even 2
725.2.q.a.676.1 12 145.9 even 14
841.2.a.k.1.6 12 29.26 odd 28
841.2.a.k.1.7 12 29.3 odd 28
841.2.b.e.840.6 12 29.22 even 14
841.2.b.e.840.7 12 29.7 even 7
841.2.d.k.605.2 24 29.14 odd 28
841.2.d.k.605.3 24 29.15 odd 28
841.2.d.k.645.2 24 29.11 odd 28
841.2.d.k.645.3 24 29.18 odd 28
841.2.d.l.574.2 24 29.27 odd 28
841.2.d.l.574.3 24 29.2 odd 28
841.2.d.l.778.2 24 29.10 odd 28
841.2.d.l.778.3 24 29.19 odd 28
841.2.d.m.190.2 24 29.17 odd 4
841.2.d.m.190.3 24 29.12 odd 4
841.2.d.m.571.2 24 29.21 odd 28
841.2.d.m.571.3 24 29.8 odd 28
841.2.e.a.63.2 12 29.4 even 14
841.2.e.a.267.2 12 29.24 even 7
841.2.e.e.196.2 12 29.16 even 7
841.2.e.e.236.2 12 29.6 even 14
841.2.e.f.196.1 12 29.13 even 14
841.2.e.f.236.1 12 29.23 even 7
841.2.e.h.63.1 12 29.25 even 7
841.2.e.h.267.1 12 29.5 even 14
841.2.e.i.270.1 12 29.20 even 7
841.2.e.i.651.1 12 29.28 even 2
7569.2.a.bp.1.6 12 87.32 even 28
7569.2.a.bp.1.7 12 87.26 even 28