Properties

Label 441.2.z.a.142.18
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
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] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.18
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.416374 + 1.06090i) q^{2} +(-0.936113 + 1.45729i) q^{3} +(0.513954 + 0.476880i) q^{4} +(-1.98165 + 0.954315i) q^{5} +(-1.15627 - 1.59990i) q^{6} +(-1.83671 + 1.90434i) q^{7} +(-2.77356 + 1.33568i) q^{8} +(-1.24739 - 2.72837i) q^{9} +O(q^{10})\) \(q+(-0.416374 + 1.06090i) q^{2} +(-0.936113 + 1.45729i) q^{3} +(0.513954 + 0.476880i) q^{4} +(-1.98165 + 0.954315i) q^{5} +(-1.15627 - 1.59990i) q^{6} +(-1.83671 + 1.90434i) q^{7} +(-2.77356 + 1.33568i) q^{8} +(-1.24739 - 2.72837i) q^{9} +(-0.187326 - 2.49970i) q^{10} +(1.60126 + 2.00792i) q^{11} +(-1.17607 + 0.302567i) q^{12} +(1.37852 - 3.51241i) q^{13} +(-1.25556 - 2.74149i) q^{14} +(0.464340 - 3.78119i) q^{15} +(-0.157397 - 2.10032i) q^{16} +(1.50025 - 1.39203i) q^{17} +(3.41392 - 0.187332i) q^{18} +(1.19584 - 2.07126i) q^{19} +(-1.47357 - 0.454537i) q^{20} +(-1.05580 - 4.45929i) q^{21} +(-2.79693 + 0.862738i) q^{22} +(-2.03038 + 8.89568i) q^{23} +(0.649899 - 5.29223i) q^{24} +(-0.101211 + 0.126914i) q^{25} +(3.15235 + 2.92496i) q^{26} +(5.14373 + 0.736265i) q^{27} +(-1.85212 + 0.102852i) q^{28} +(-4.41877 - 1.36301i) q^{29} +(3.81814 + 2.06701i) q^{30} +(1.61576 - 2.79857i) q^{31} +(-3.58955 - 1.10723i) q^{32} +(-4.42507 + 0.453863i) q^{33} +(0.852142 + 2.17122i) q^{34} +(1.82239 - 5.52654i) q^{35} +(0.660008 - 1.99711i) q^{36} +(5.05310 + 1.55867i) q^{37} +(1.69949 + 2.13109i) q^{38} +(3.82815 + 5.29692i) q^{39} +(4.22159 - 5.29370i) q^{40} +(-4.74636 - 3.23602i) q^{41} +(5.17049 + 0.736628i) q^{42} +(-0.447630 + 0.305189i) q^{43} +(-0.134560 + 1.79558i) q^{44} +(5.07561 + 4.21630i) q^{45} +(-8.59206 - 5.85797i) q^{46} +(2.06975 - 5.27363i) q^{47} +(3.20811 + 1.73676i) q^{48} +(-0.252996 - 6.99543i) q^{49} +(-0.0925022 - 0.160219i) q^{50} +(0.624184 + 3.48939i) q^{51} +(2.38350 - 1.14783i) q^{52} +(-7.50135 + 2.31386i) q^{53} +(-2.92282 + 5.15044i) q^{54} +(-5.08932 - 2.45089i) q^{55} +(2.55065 - 7.73505i) q^{56} +(1.89898 + 3.68162i) q^{57} +(3.28588 - 4.12036i) q^{58} +(-8.58751 + 5.85487i) q^{59} +(2.04182 - 1.72192i) q^{60} +(-5.50216 + 5.10526i) q^{61} +(2.29626 + 2.87942i) q^{62} +(7.48683 + 2.63579i) q^{63} +(5.29565 - 6.64054i) q^{64} +(0.620195 + 8.27593i) q^{65} +(1.36098 - 4.88355i) q^{66} +(-7.35380 + 12.7372i) q^{67} +1.43489 q^{68} +(-11.0629 - 11.2862i) q^{69} +(5.10433 + 4.23448i) q^{70} +(1.89732 - 8.31272i) q^{71} +(7.10393 + 5.90122i) q^{72} +(4.24857 + 0.640370i) q^{73} +(-3.75758 + 4.71186i) q^{74} +(-0.0902061 - 0.266299i) q^{75} +(1.60235 - 0.494260i) q^{76} +(-6.76479 - 0.638621i) q^{77} +(-7.21347 + 1.85580i) q^{78} +(1.58501 + 2.74532i) q^{79} +(2.31627 + 4.01189i) q^{80} +(-5.88806 + 6.80667i) q^{81} +(5.40937 - 3.68804i) q^{82} +(-0.331350 - 0.844267i) q^{83} +(1.58391 - 2.79536i) q^{84} +(-1.64454 + 4.19022i) q^{85} +(-0.137395 - 0.601965i) q^{86} +(6.12276 - 5.16349i) q^{87} +(-7.12312 - 3.43032i) q^{88} +(3.62553 + 9.23771i) q^{89} +(-6.58644 + 3.62918i) q^{90} +(4.15688 + 9.07645i) q^{91} +(-5.28569 + 3.60372i) q^{92} +(2.56580 + 4.97440i) q^{93} +(4.73303 + 4.39161i) q^{94} +(-0.393113 + 5.24573i) q^{95} +(4.97377 - 4.19452i) q^{96} +(-6.73800 + 11.6706i) q^{97} +(7.52682 + 2.64431i) q^{98} +(3.48096 - 6.87348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.416374 + 1.06090i −0.294421 + 0.750172i 0.704750 + 0.709456i \(0.251059\pi\)
−0.999171 + 0.0407164i \(0.987036\pi\)
\(3\) −0.936113 + 1.45729i −0.540465 + 0.841367i
\(4\) 0.513954 + 0.476880i 0.256977 + 0.238440i
\(5\) −1.98165 + 0.954315i −0.886223 + 0.426782i −0.820893 0.571081i \(-0.806524\pi\)
−0.0653293 + 0.997864i \(0.520810\pi\)
\(6\) −1.15627 1.59990i −0.472046 0.653158i
\(7\) −1.83671 + 1.90434i −0.694211 + 0.719772i
\(8\) −2.77356 + 1.33568i −0.980603 + 0.472234i
\(9\) −1.24739 2.72837i −0.415795 0.909458i
\(10\) −0.187326 2.49970i −0.0592378 0.790473i
\(11\) 1.60126 + 2.00792i 0.482798 + 0.605409i 0.962253 0.272157i \(-0.0877371\pi\)
−0.479455 + 0.877566i \(0.659166\pi\)
\(12\) −1.17607 + 0.302567i −0.339503 + 0.0873435i
\(13\) 1.37852 3.51241i 0.382333 0.974168i −0.602102 0.798419i \(-0.705670\pi\)
0.984435 0.175749i \(-0.0562348\pi\)
\(14\) −1.25556 2.74149i −0.335562 0.732694i
\(15\) 0.464340 3.78119i 0.119892 0.976299i
\(16\) −0.157397 2.10032i −0.0393492 0.525079i
\(17\) 1.50025 1.39203i 0.363863 0.337616i −0.476960 0.878925i \(-0.658261\pi\)
0.840824 + 0.541309i \(0.182071\pi\)
\(18\) 3.41392 0.187332i 0.804669 0.0441545i
\(19\) 1.19584 2.07126i 0.274345 0.475180i −0.695625 0.718406i \(-0.744872\pi\)
0.969970 + 0.243226i \(0.0782056\pi\)
\(20\) −1.47357 0.454537i −0.329501 0.101638i
\(21\) −1.05580 4.45929i −0.230395 0.973097i
\(22\) −2.79693 + 0.862738i −0.596307 + 0.183936i
\(23\) −2.03038 + 8.89568i −0.423364 + 1.85488i 0.0888874 + 0.996042i \(0.471669\pi\)
−0.512251 + 0.858836i \(0.671188\pi\)
\(24\) 0.649899 5.29223i 0.132660 1.08027i
\(25\) −0.101211 + 0.126914i −0.0202421 + 0.0253828i
\(26\) 3.15235 + 2.92496i 0.618227 + 0.573631i
\(27\) 5.14373 + 0.736265i 0.989910 + 0.141694i
\(28\) −1.85212 + 0.102852i −0.350019 + 0.0194372i
\(29\) −4.41877 1.36301i −0.820544 0.253104i −0.144067 0.989568i \(-0.546018\pi\)
−0.676477 + 0.736464i \(0.736494\pi\)
\(30\) 3.81814 + 2.06701i 0.697094 + 0.377383i
\(31\) 1.61576 2.79857i 0.290198 0.502638i −0.683658 0.729802i \(-0.739612\pi\)
0.973857 + 0.227164i \(0.0729454\pi\)
\(32\) −3.58955 1.10723i −0.634548 0.195732i
\(33\) −4.42507 + 0.453863i −0.770306 + 0.0790074i
\(34\) 0.852142 + 2.17122i 0.146141 + 0.372361i
\(35\) 1.82239 5.52654i 0.308040 0.934155i
\(36\) 0.660008 1.99711i 0.110001 0.332852i
\(37\) 5.05310 + 1.55867i 0.830724 + 0.256245i 0.680815 0.732455i \(-0.261626\pi\)
0.149909 + 0.988700i \(0.452102\pi\)
\(38\) 1.69949 + 2.13109i 0.275694 + 0.345709i
\(39\) 3.82815 + 5.29692i 0.612995 + 0.848186i
\(40\) 4.22159 5.29370i 0.667492 0.837008i
\(41\) −4.74636 3.23602i −0.741258 0.505381i 0.132836 0.991138i \(-0.457592\pi\)
−0.874094 + 0.485757i \(0.838544\pi\)
\(42\) 5.17049 + 0.736628i 0.797824 + 0.113664i
\(43\) −0.447630 + 0.305189i −0.0682629 + 0.0465408i −0.596971 0.802263i \(-0.703629\pi\)
0.528708 + 0.848804i \(0.322677\pi\)
\(44\) −0.134560 + 1.79558i −0.0202858 + 0.270695i
\(45\) 5.07561 + 4.21630i 0.756628 + 0.628529i
\(46\) −8.59206 5.85797i −1.26683 0.863710i
\(47\) 2.06975 5.27363i 0.301904 0.769238i −0.696747 0.717317i \(-0.745370\pi\)
0.998651 0.0519216i \(-0.0165346\pi\)
\(48\) 3.20811 + 1.73676i 0.463051 + 0.250680i
\(49\) −0.252996 6.99543i −0.0361423 0.999347i
\(50\) −0.0925022 0.160219i −0.0130818 0.0226583i
\(51\) 0.624184 + 3.48939i 0.0874033 + 0.488612i
\(52\) 2.38350 1.14783i 0.330531 0.159176i
\(53\) −7.50135 + 2.31386i −1.03039 + 0.317833i −0.763441 0.645878i \(-0.776492\pi\)
−0.266949 + 0.963711i \(0.586015\pi\)
\(54\) −2.92282 + 5.15044i −0.397745 + 0.700886i
\(55\) −5.08932 2.45089i −0.686244 0.330478i
\(56\) 2.55065 7.73505i 0.340845 1.03364i
\(57\) 1.89898 + 3.68162i 0.251526 + 0.487643i
\(58\) 3.28588 4.12036i 0.431457 0.541030i
\(59\) −8.58751 + 5.85487i −1.11800 + 0.762239i −0.973822 0.227313i \(-0.927006\pi\)
−0.144177 + 0.989552i \(0.546053\pi\)
\(60\) 2.04182 1.72192i 0.263598 0.222300i
\(61\) −5.50216 + 5.10526i −0.704479 + 0.653661i −0.948743 0.316048i \(-0.897644\pi\)
0.244264 + 0.969709i \(0.421454\pi\)
\(62\) 2.29626 + 2.87942i 0.291625 + 0.365686i
\(63\) 7.48683 + 2.63579i 0.943252 + 0.332078i
\(64\) 5.29565 6.64054i 0.661957 0.830067i
\(65\) 0.620195 + 8.27593i 0.0769258 + 1.02650i
\(66\) 1.36098 4.88355i 0.167525 0.601124i
\(67\) −7.35380 + 12.7372i −0.898410 + 1.55609i −0.0688823 + 0.997625i \(0.521943\pi\)
−0.829527 + 0.558466i \(0.811390\pi\)
\(68\) 1.43489 0.174006
\(69\) −11.0629 11.2862i −1.33182 1.35870i
\(70\) 5.10433 + 4.23448i 0.610084 + 0.506118i
\(71\) 1.89732 8.31272i 0.225171 0.986538i −0.728349 0.685207i \(-0.759712\pi\)
0.953519 0.301331i \(-0.0974311\pi\)
\(72\) 7.10393 + 5.90122i 0.837207 + 0.695465i
\(73\) 4.24857 + 0.640370i 0.497258 + 0.0749496i 0.392883 0.919588i \(-0.371478\pi\)
0.104375 + 0.994538i \(0.466716\pi\)
\(74\) −3.75758 + 4.71186i −0.436810 + 0.547743i
\(75\) −0.0902061 0.266299i −0.0104161 0.0307496i
\(76\) 1.60235 0.494260i 0.183802 0.0566955i
\(77\) −6.76479 0.638621i −0.770920 0.0727776i
\(78\) −7.21347 + 1.85580i −0.816764 + 0.210128i
\(79\) 1.58501 + 2.74532i 0.178328 + 0.308873i 0.941308 0.337549i \(-0.109598\pi\)
−0.762980 + 0.646422i \(0.776265\pi\)
\(80\) 2.31627 + 4.01189i 0.258967 + 0.448543i
\(81\) −5.88806 + 6.80667i −0.654229 + 0.756297i
\(82\) 5.40937 3.68804i 0.597364 0.407276i
\(83\) −0.331350 0.844267i −0.0363704 0.0926704i 0.911535 0.411223i \(-0.134898\pi\)
−0.947905 + 0.318553i \(0.896803\pi\)
\(84\) 1.58391 2.79536i 0.172819 0.304999i
\(85\) −1.64454 + 4.19022i −0.178376 + 0.454493i
\(86\) −0.137395 0.601965i −0.0148156 0.0649115i
\(87\) 6.12276 5.16349i 0.656429 0.553584i
\(88\) −7.12312 3.43032i −0.759327 0.365673i
\(89\) 3.62553 + 9.23771i 0.384306 + 0.979195i 0.983873 + 0.178871i \(0.0572444\pi\)
−0.599567 + 0.800325i \(0.704660\pi\)
\(90\) −6.58644 + 3.62918i −0.694272 + 0.382549i
\(91\) 4.15688 + 9.07645i 0.435759 + 0.951471i
\(92\) −5.28569 + 3.60372i −0.551072 + 0.375714i
\(93\) 2.56580 + 4.97440i 0.266061 + 0.515822i
\(94\) 4.73303 + 4.39161i 0.488174 + 0.452960i
\(95\) −0.393113 + 5.24573i −0.0403326 + 0.538201i
\(96\) 4.97377 4.19452i 0.507634 0.428101i
\(97\) −6.73800 + 11.6706i −0.684140 + 1.18497i 0.289566 + 0.957158i \(0.406489\pi\)
−0.973706 + 0.227808i \(0.926844\pi\)
\(98\) 7.52682 + 2.64431i 0.760323 + 0.267116i
\(99\) 3.48096 6.87348i 0.349849 0.690811i
\(100\) −0.112540 + 0.0169627i −0.0112540 + 0.00169627i
\(101\) 3.38243 1.62889i 0.336565 0.162081i −0.257966 0.966154i \(-0.583052\pi\)
0.594531 + 0.804073i \(0.297338\pi\)
\(102\) −3.96180 0.790691i −0.392277 0.0782901i
\(103\) −15.4853 + 7.45731i −1.52581 + 0.734791i −0.993720 0.111898i \(-0.964307\pi\)
−0.532089 + 0.846688i \(0.678593\pi\)
\(104\) 0.868038 + 11.5832i 0.0851182 + 1.13582i
\(105\) 6.34780 + 7.82921i 0.619482 + 0.764052i
\(106\) 0.668585 8.92164i 0.0649387 0.866547i
\(107\) 4.17064 + 10.6266i 0.403191 + 1.02731i 0.977922 + 0.208971i \(0.0670115\pi\)
−0.574731 + 0.818343i \(0.694893\pi\)
\(108\) 2.29253 + 2.83135i 0.220599 + 0.272446i
\(109\) 0.318455 0.811409i 0.0305024 0.0777189i −0.914811 0.403882i \(-0.867661\pi\)
0.945314 + 0.326163i \(0.105756\pi\)
\(110\) 4.71922 4.37880i 0.449960 0.417502i
\(111\) −7.00171 + 5.90473i −0.664573 + 0.560452i
\(112\) 4.28880 + 3.55793i 0.405254 + 0.336193i
\(113\) 1.99229 + 0.300289i 0.187419 + 0.0282488i 0.242081 0.970256i \(-0.422170\pi\)
−0.0546622 + 0.998505i \(0.517408\pi\)
\(114\) −4.69654 + 0.481706i −0.439871 + 0.0451159i
\(115\) −4.46576 19.5658i −0.416435 1.82452i
\(116\) −1.62105 2.80774i −0.150511 0.260693i
\(117\) −11.3027 + 0.620213i −1.04494 + 0.0573387i
\(118\) −2.63583 11.5483i −0.242648 1.06311i
\(119\) −0.104632 + 5.41372i −0.00959161 + 0.496275i
\(120\) 3.76258 + 11.1076i 0.343475 + 1.01398i
\(121\) 0.980037 4.29382i 0.0890943 0.390347i
\(122\) −3.12523 7.96296i −0.282945 0.720932i
\(123\) 9.15895 3.88755i 0.825834 0.350529i
\(124\) 2.16501 0.667816i 0.194423 0.0599717i
\(125\) 2.52659 11.0697i 0.225985 0.990105i
\(126\) −5.91364 + 6.84533i −0.526829 + 0.609831i
\(127\) −1.24401 5.45036i −0.110388 0.483641i −0.999655 0.0262533i \(-0.991642\pi\)
0.889267 0.457388i \(-0.151215\pi\)
\(128\) 1.08356 + 1.87679i 0.0957745 + 0.165886i
\(129\) −0.0257165 0.938017i −0.00226421 0.0825878i
\(130\) −9.03820 2.78792i −0.792703 0.244516i
\(131\) 14.5909 + 7.02661i 1.27481 + 0.613918i 0.944052 0.329796i \(-0.106980\pi\)
0.330762 + 0.943714i \(0.392694\pi\)
\(132\) −2.49072 1.87696i −0.216790 0.163369i
\(133\) 1.74796 + 6.08159i 0.151568 + 0.527341i
\(134\) −10.4510 13.1051i −0.902826 1.13211i
\(135\) −10.8957 + 3.44971i −0.937754 + 0.296904i
\(136\) −2.30173 + 5.86472i −0.197372 + 0.502896i
\(137\) 13.8854 + 6.68688i 1.18631 + 0.571298i 0.919745 0.392517i \(-0.128396\pi\)
0.266569 + 0.963816i \(0.414110\pi\)
\(138\) 16.5799 7.03740i 1.41137 0.599063i
\(139\) −7.11733 4.85252i −0.603684 0.411585i 0.222542 0.974923i \(-0.428565\pi\)
−0.826227 + 0.563338i \(0.809517\pi\)
\(140\) 3.57212 1.97133i 0.301899 0.166608i
\(141\) 5.74769 + 7.95294i 0.484043 + 0.669758i
\(142\) 8.02900 + 5.47408i 0.673779 + 0.459375i
\(143\) 9.26000 2.85633i 0.774360 0.238858i
\(144\) −5.53411 + 3.04934i −0.461176 + 0.254112i
\(145\) 10.0572 1.51588i 0.835205 0.125887i
\(146\) −2.44837 + 4.24070i −0.202628 + 0.350962i
\(147\) 10.4312 + 6.17982i 0.860350 + 0.509703i
\(148\) 1.85376 + 3.21081i 0.152378 + 0.263927i
\(149\) −6.24073 7.82562i −0.511260 0.641100i 0.457467 0.889226i \(-0.348757\pi\)
−0.968728 + 0.248126i \(0.920185\pi\)
\(150\) 0.320077 + 0.0151801i 0.0261342 + 0.00123945i
\(151\) −1.49629 + 6.55567i −0.121766 + 0.533493i 0.876843 + 0.480776i \(0.159645\pi\)
−0.998610 + 0.0527163i \(0.983212\pi\)
\(152\) −0.550210 + 7.34204i −0.0446279 + 0.595518i
\(153\) −5.66936 2.35684i −0.458340 0.190540i
\(154\) 3.49420 6.91089i 0.281571 0.556895i
\(155\) −0.531153 + 7.08774i −0.0426632 + 0.569301i
\(156\) −0.558499 + 4.54794i −0.0447157 + 0.364127i
\(157\) −16.3637 + 11.1566i −1.30597 + 0.890394i −0.998135 0.0610464i \(-0.980556\pi\)
−0.307833 + 0.951440i \(0.599604\pi\)
\(158\) −3.57248 + 0.538465i −0.284211 + 0.0428380i
\(159\) 3.65015 13.0977i 0.289475 1.03871i
\(160\) 8.16989 1.23141i 0.645886 0.0973517i
\(161\) −13.2111 20.2053i −1.04118 1.59240i
\(162\) −4.76959 9.08078i −0.374734 0.713454i
\(163\) 15.4643 10.5434i 1.21126 0.825821i 0.222438 0.974947i \(-0.428598\pi\)
0.988818 + 0.149126i \(0.0476460\pi\)
\(164\) −0.896223 3.92661i −0.0699833 0.306617i
\(165\) 8.33584 5.12231i 0.648944 0.398771i
\(166\) 1.03365 0.0802269
\(167\) −3.60535 + 3.34527i −0.278990 + 0.258865i −0.807239 0.590224i \(-0.799039\pi\)
0.528249 + 0.849090i \(0.322849\pi\)
\(168\) 8.88451 + 10.9579i 0.685455 + 0.845422i
\(169\) −0.907058 0.841627i −0.0697737 0.0647405i
\(170\) −3.76068 3.48940i −0.288431 0.267625i
\(171\) −7.14285 0.679047i −0.546228 0.0519280i
\(172\) −0.375600 0.0566125i −0.0286392 0.00431666i
\(173\) −3.65716 + 1.12809i −0.278049 + 0.0857668i −0.430643 0.902522i \(-0.641713\pi\)
0.152594 + 0.988289i \(0.451237\pi\)
\(174\) 2.92861 + 8.64560i 0.222017 + 0.655422i
\(175\) −0.0557927 0.425844i −0.00421753 0.0321908i
\(176\) 3.96522 3.67919i 0.298890 0.277329i
\(177\) −0.493355 17.9953i −0.0370829 1.35261i
\(178\) −11.3099 −0.847713
\(179\) 3.94679 3.66208i 0.294997 0.273717i −0.518763 0.854918i \(-0.673607\pi\)
0.813760 + 0.581201i \(0.197417\pi\)
\(180\) 0.597966 + 4.58744i 0.0445698 + 0.341928i
\(181\) −11.3685 + 14.2556i −0.845011 + 1.05961i 0.152444 + 0.988312i \(0.451286\pi\)
−0.997455 + 0.0712985i \(0.977286\pi\)
\(182\) −11.3601 + 0.630847i −0.842064 + 0.0467615i
\(183\) −2.28920 12.7973i −0.169222 0.946006i
\(184\) −6.25037 27.3847i −0.460784 2.01882i
\(185\) −11.5010 + 1.73349i −0.845567 + 0.127449i
\(186\) −6.34570 + 0.650854i −0.465289 + 0.0477229i
\(187\) 5.19736 + 0.783375i 0.380068 + 0.0572861i
\(188\) 3.57864 1.72338i 0.260999 0.125691i
\(189\) −10.8496 + 8.44308i −0.789194 + 0.614144i
\(190\) −5.40154 2.60124i −0.391869 0.188714i
\(191\) 10.5943 + 7.22305i 0.766574 + 0.522641i 0.882327 0.470637i \(-0.155976\pi\)
−0.115753 + 0.993278i \(0.536928\pi\)
\(192\) 4.71986 + 13.9336i 0.340626 + 1.00557i
\(193\) −1.00766 + 13.4463i −0.0725332 + 0.967889i 0.835635 + 0.549284i \(0.185100\pi\)
−0.908169 + 0.418604i \(0.862519\pi\)
\(194\) −9.57581 12.0077i −0.687503 0.862102i
\(195\) −12.6410 6.84340i −0.905241 0.490066i
\(196\) 3.20595 3.71598i 0.228996 0.265427i
\(197\) 4.14950 0.295639 0.147820 0.989014i \(-0.452774\pi\)
0.147820 + 0.989014i \(0.452774\pi\)
\(198\) 5.84272 + 6.55490i 0.415224 + 0.465836i
\(199\) −12.5929 8.58571i −0.892689 0.608625i 0.0277056 0.999616i \(-0.491180\pi\)
−0.920394 + 0.390991i \(0.872132\pi\)
\(200\) 0.111198 0.487189i 0.00786287 0.0344495i
\(201\) −11.6777 22.6400i −0.823684 1.59690i
\(202\) 0.319742 + 4.26667i 0.0224970 + 0.300202i
\(203\) 10.7116 5.91137i 0.751808 0.414897i
\(204\) −1.34322 + 2.09105i −0.0940440 + 0.146403i
\(205\) 12.4938 + 1.88314i 0.872607 + 0.131524i
\(206\) −1.46383 19.5334i −0.101990 1.36096i
\(207\) 26.8034 5.55670i 1.86297 0.386218i
\(208\) −7.59415 2.34249i −0.526560 0.162422i
\(209\) 6.07377 0.915474i 0.420131 0.0633246i
\(210\) −10.9491 + 3.47453i −0.755559 + 0.239765i
\(211\) 26.4720 + 3.99002i 1.82241 + 0.274684i 0.969091 0.246704i \(-0.0793475\pi\)
0.853320 + 0.521388i \(0.174586\pi\)
\(212\) −4.95878 2.38802i −0.340571 0.164010i
\(213\) 10.3379 + 10.5466i 0.708343 + 0.722641i
\(214\) −13.0104 −0.889370
\(215\) 0.595801 1.03196i 0.0406333 0.0703790i
\(216\) −15.2499 + 4.82828i −1.03762 + 0.328523i
\(217\) 2.36175 + 8.21711i 0.160326 + 0.557814i
\(218\) 0.728231 + 0.675699i 0.0493220 + 0.0457641i
\(219\) −4.91035 + 5.59195i −0.331811 + 0.377869i
\(220\) −1.44690 3.68664i −0.0975500 0.248553i
\(221\) −2.82125 7.18843i −0.189778 0.483546i
\(222\) −3.34902 9.88672i −0.224772 0.663553i
\(223\) −4.77898 4.43424i −0.320024 0.296939i 0.503759 0.863844i \(-0.331950\pi\)
−0.823783 + 0.566905i \(0.808141\pi\)
\(224\) 8.70149 4.80205i 0.581393 0.320850i
\(225\) 0.472518 + 0.117830i 0.0315012 + 0.00785532i
\(226\) −1.14811 + 1.98859i −0.0763714 + 0.132279i
\(227\) 27.7640 1.84276 0.921382 0.388659i \(-0.127062\pi\)
0.921382 + 0.388659i \(0.127062\pi\)
\(228\) −0.779702 + 2.79777i −0.0516370 + 0.185287i
\(229\) 23.2286 + 11.1863i 1.53499 + 0.739212i 0.994754 0.102300i \(-0.0326203\pi\)
0.540237 + 0.841513i \(0.318335\pi\)
\(230\) 22.6168 + 3.40894i 1.49131 + 0.224779i
\(231\) 7.26327 9.26044i 0.477888 0.609292i
\(232\) 14.0763 2.12166i 0.924152 0.139294i
\(233\) −19.7786 6.10088i −1.29574 0.399682i −0.431202 0.902255i \(-0.641910\pi\)
−0.864534 + 0.502574i \(0.832387\pi\)
\(234\) 4.04818 12.2493i 0.264638 0.800765i
\(235\) 0.931178 + 12.4257i 0.0607433 + 0.810564i
\(236\) −7.20565 1.08608i −0.469048 0.0706976i
\(237\) −5.48448 0.260109i −0.356255 0.0168959i
\(238\) −5.69987 2.36514i −0.369468 0.153309i
\(239\) −1.91525 25.5572i −0.123887 1.65316i −0.619782 0.784774i \(-0.712779\pi\)
0.495896 0.868382i \(-0.334840\pi\)
\(240\) −8.01478 0.380112i −0.517352 0.0245361i
\(241\) 5.82003 25.4992i 0.374901 1.64255i −0.337901 0.941182i \(-0.609717\pi\)
0.712801 0.701366i \(-0.247426\pi\)
\(242\) 4.14727 + 2.82756i 0.266597 + 0.181763i
\(243\) −4.40740 14.9524i −0.282735 0.959198i
\(244\) −5.26245 −0.336894
\(245\) 7.17719 + 13.6211i 0.458534 + 0.870219i
\(246\) 0.310770 + 11.3354i 0.0198140 + 0.722721i
\(247\) −5.62663 7.05557i −0.358014 0.448935i
\(248\) −0.743412 + 9.92015i −0.0472067 + 0.629930i
\(249\) 1.54052 + 0.307456i 0.0976267 + 0.0194842i
\(250\) 10.6919 + 7.28961i 0.676215 + 0.461035i
\(251\) 19.7030 + 9.48845i 1.24364 + 0.598906i 0.935800 0.352532i \(-0.114679\pi\)
0.307841 + 0.951438i \(0.400393\pi\)
\(252\) 2.59093 + 4.92499i 0.163213 + 0.310245i
\(253\) −21.1129 + 10.1675i −1.32736 + 0.639222i
\(254\) 6.30027 + 0.949614i 0.395314 + 0.0595841i
\(255\) −4.56689 6.31909i −0.285990 0.395717i
\(256\) 14.3551 2.16369i 0.897196 0.135231i
\(257\) −2.84742 12.4753i −0.177617 0.778190i −0.982726 0.185064i \(-0.940751\pi\)
0.805110 0.593126i \(-0.202106\pi\)
\(258\) 1.00585 + 0.363283i 0.0626217 + 0.0226170i
\(259\) −12.2493 + 6.75997i −0.761135 + 0.420044i
\(260\) −3.62787 + 4.54921i −0.224991 + 0.282130i
\(261\) 1.79311 + 13.7562i 0.110990 + 0.851490i
\(262\) −13.5298 + 12.5539i −0.835876 + 0.775580i
\(263\) −12.6394 −0.779381 −0.389691 0.920946i \(-0.627418\pi\)
−0.389691 + 0.920946i \(0.627418\pi\)
\(264\) 11.6670 7.16929i 0.718055 0.441239i
\(265\) 12.6569 11.7439i 0.777509 0.721423i
\(266\) −7.17979 0.677798i −0.440221 0.0415585i
\(267\) −16.8559 3.36409i −1.03157 0.205879i
\(268\) −9.85361 + 3.03944i −0.601905 + 0.185663i
\(269\) −1.69890 0.256068i −0.103584 0.0156127i 0.0970459 0.995280i \(-0.469061\pi\)
−0.200629 + 0.979667i \(0.564299\pi\)
\(270\) 0.876883 12.9957i 0.0533654 0.790892i
\(271\) −3.15185 2.92449i −0.191461 0.177650i 0.578617 0.815599i \(-0.303593\pi\)
−0.770078 + 0.637949i \(0.779783\pi\)
\(272\) −3.15983 2.93189i −0.191593 0.177772i
\(273\) −17.1183 2.43881i −1.03605 0.147604i
\(274\) −12.8757 + 11.9469i −0.777848 + 0.721737i
\(275\) −0.416897 −0.0251399
\(276\) −0.303665 11.0763i −0.0182785 0.666714i
\(277\) 6.25160 + 27.3900i 0.375622 + 1.64571i 0.710684 + 0.703511i \(0.248386\pi\)
−0.335062 + 0.942196i \(0.608757\pi\)
\(278\) 8.11153 5.53035i 0.486497 0.331688i
\(279\) −9.65103 0.917491i −0.577792 0.0549287i
\(280\) 2.32716 + 17.7623i 0.139075 + 1.06150i
\(281\) −15.1021 + 2.27627i −0.900914 + 0.135791i −0.583136 0.812374i \(-0.698175\pi\)
−0.317778 + 0.948165i \(0.602937\pi\)
\(282\) −10.8305 + 2.78635i −0.644946 + 0.165925i
\(283\) −7.73215 + 1.16543i −0.459629 + 0.0692779i −0.374775 0.927116i \(-0.622280\pi\)
−0.0848531 + 0.996393i \(0.527042\pi\)
\(284\) 4.93931 3.36756i 0.293094 0.199828i
\(285\) −7.27655 5.48348i −0.431026 0.324813i
\(286\) −0.825331 + 11.0133i −0.0488028 + 0.651228i
\(287\) 14.8802 3.09505i 0.878348 0.182695i
\(288\) 1.45661 + 11.1748i 0.0858318 + 0.658480i
\(289\) −0.957406 + 12.7757i −0.0563180 + 0.751512i
\(290\) −2.57936 + 11.3009i −0.151465 + 0.663612i
\(291\) −10.6999 20.7442i −0.627237 1.21605i
\(292\) 1.87819 + 2.35518i 0.109913 + 0.137827i
\(293\) −4.32567 7.49228i −0.252708 0.437704i 0.711562 0.702623i \(-0.247988\pi\)
−0.964271 + 0.264919i \(0.914655\pi\)
\(294\) −10.8995 + 8.49338i −0.635670 + 0.495344i
\(295\) 11.4301 19.7975i 0.665486 1.15266i
\(296\) −16.0970 + 2.42623i −0.935618 + 0.141022i
\(297\) 6.75808 + 11.5071i 0.392144 + 0.667711i
\(298\) 10.9007 3.36242i 0.631461 0.194780i
\(299\) 28.4464 + 19.3944i 1.64510 + 1.12161i
\(300\) 0.0806309 0.179883i 0.00465523 0.0103856i
\(301\) 0.240984 1.41298i 0.0138901 0.0814428i
\(302\) −6.33192 4.31703i −0.364361 0.248417i
\(303\) −0.792569 + 6.45401i −0.0455319 + 0.370773i
\(304\) −4.53852 2.18564i −0.260302 0.125355i
\(305\) 6.03136 15.3676i 0.345354 0.879949i
\(306\) 4.86096 5.03331i 0.277882 0.287735i
\(307\) 17.3244 + 21.7241i 0.988755 + 1.23986i 0.970768 + 0.240022i \(0.0771545\pi\)
0.0179876 + 0.999838i \(0.494274\pi\)
\(308\) −3.17225 3.55422i −0.180756 0.202520i
\(309\) 3.62850 29.5474i 0.206418 1.68089i
\(310\) −7.29826 3.51465i −0.414513 0.199619i
\(311\) −4.45408 1.37390i −0.252568 0.0779068i 0.165886 0.986145i \(-0.446952\pi\)
−0.418454 + 0.908238i \(0.637428\pi\)
\(312\) −17.6926 9.57817i −1.00165 0.542257i
\(313\) −8.77619 15.2008i −0.496060 0.859201i 0.503930 0.863745i \(-0.331887\pi\)
−0.999990 + 0.00454372i \(0.998554\pi\)
\(314\) −5.02265 22.0057i −0.283445 1.24185i
\(315\) −17.3517 + 1.92156i −0.977656 + 0.108268i
\(316\) −0.494565 + 2.16683i −0.0278214 + 0.121894i
\(317\) 3.58308 1.10523i 0.201246 0.0620761i −0.192493 0.981298i \(-0.561657\pi\)
0.393739 + 0.919222i \(0.371181\pi\)
\(318\) 12.3755 + 9.32599i 0.693986 + 0.522975i
\(319\) −4.33878 11.0550i −0.242925 0.618963i
\(320\) −4.15699 + 18.2130i −0.232383 + 1.01814i
\(321\) −19.3902 3.86988i −1.08226 0.215996i
\(322\) 26.9367 5.60279i 1.50112 0.312231i
\(323\) −1.08919 4.77205i −0.0606041 0.265524i
\(324\) −6.27216 + 0.690421i −0.348453 + 0.0383567i
\(325\) 0.306254 + 0.530448i 0.0169879 + 0.0294239i
\(326\) 4.74658 + 20.7961i 0.262889 + 1.15179i
\(327\) 0.884348 + 1.22365i 0.0489046 + 0.0676680i
\(328\) 17.4866 + 2.63568i 0.965537 + 0.145531i
\(329\) 6.24124 + 13.6276i 0.344091 + 0.751315i
\(330\) 1.96345 + 10.9763i 0.108084 + 0.604227i
\(331\) −12.4345 + 11.5375i −0.683462 + 0.634160i −0.943474 0.331445i \(-0.892464\pi\)
0.260012 + 0.965605i \(0.416273\pi\)
\(332\) 0.232315 0.591929i 0.0127499 0.0324863i
\(333\) −2.05051 15.7310i −0.112367 0.862054i
\(334\) −2.04784 5.21781i −0.112053 0.285506i
\(335\) 2.41744 32.2585i 0.132079 1.76247i
\(336\) −9.19974 + 2.91940i −0.501887 + 0.159266i
\(337\) −0.304341 4.06114i −0.0165785 0.221225i −0.999339 0.0363434i \(-0.988429\pi\)
0.982761 0.184881i \(-0.0591900\pi\)
\(338\) 1.27056 0.611870i 0.0691094 0.0332813i
\(339\) −2.30261 + 2.62224i −0.125061 + 0.142420i
\(340\) −2.84345 + 1.36933i −0.154208 + 0.0742626i
\(341\) 8.20654 1.23694i 0.444409 0.0669839i
\(342\) 3.69450 7.29514i 0.199776 0.394476i
\(343\) 13.7863 + 12.3668i 0.744392 + 0.667743i
\(344\) 0.833896 1.44435i 0.0449606 0.0778741i
\(345\) 32.6935 + 11.8079i 1.76016 + 0.635715i
\(346\) 0.325958 4.34960i 0.0175236 0.233836i
\(347\) −4.15321 3.85362i −0.222956 0.206873i 0.560784 0.827962i \(-0.310500\pi\)
−0.783740 + 0.621089i \(0.786690\pi\)
\(348\) 5.60918 + 0.266023i 0.300684 + 0.0142604i
\(349\) 3.05567 2.08332i 0.163566 0.111518i −0.478771 0.877940i \(-0.658917\pi\)
0.642337 + 0.766423i \(0.277965\pi\)
\(350\) 0.475010 + 0.118120i 0.0253903 + 0.00631376i
\(351\) 9.67680 17.0519i 0.516509 0.910165i
\(352\) −3.52457 8.98047i −0.187860 0.478661i
\(353\) −4.86123 2.34104i −0.258737 0.124601i 0.300019 0.953933i \(-0.403007\pi\)
−0.558756 + 0.829332i \(0.688721\pi\)
\(354\) 19.2967 + 6.96937i 1.02561 + 0.370418i
\(355\) 4.17311 + 18.2836i 0.221486 + 0.970392i
\(356\) −2.54192 + 6.47671i −0.134721 + 0.343265i
\(357\) −7.79142 5.22034i −0.412365 0.276289i
\(358\) 2.24178 + 5.71196i 0.118482 + 0.301886i
\(359\) −8.81747 + 6.01165i −0.465368 + 0.317283i −0.773205 0.634157i \(-0.781347\pi\)
0.307836 + 0.951439i \(0.400395\pi\)
\(360\) −19.7092 4.91479i −1.03876 0.259032i
\(361\) 6.63992 + 11.5007i 0.349469 + 0.605299i
\(362\) −10.3903 17.9965i −0.546102 0.945876i
\(363\) 5.33992 + 5.44770i 0.280273 + 0.285930i
\(364\) −2.19193 + 6.64721i −0.114888 + 0.348409i
\(365\) −9.03032 + 2.78549i −0.472669 + 0.145799i
\(366\) 14.5299 + 2.89986i 0.759490 + 0.151578i
\(367\) 11.6235 14.5754i 0.606741 0.760829i −0.379671 0.925122i \(-0.623963\pi\)
0.986412 + 0.164293i \(0.0525342\pi\)
\(368\) 19.0033 + 2.86429i 0.990616 + 0.149311i
\(369\) −2.90852 + 16.9864i −0.151411 + 0.884278i
\(370\) 2.94963 12.9232i 0.153344 0.671845i
\(371\) 9.37143 18.5350i 0.486541 0.962289i
\(372\) −1.05349 + 3.78019i −0.0546209 + 0.195994i
\(373\) −8.58752 −0.444645 −0.222323 0.974973i \(-0.571364\pi\)
−0.222323 + 0.974973i \(0.571364\pi\)
\(374\) −2.99513 + 5.18772i −0.154874 + 0.268250i
\(375\) 13.7666 + 14.0445i 0.710904 + 0.725253i
\(376\) 1.30330 + 17.3913i 0.0672123 + 0.896886i
\(377\) −10.8788 + 13.6416i −0.560287 + 0.702578i
\(378\) −4.43979 15.0259i −0.228358 0.772848i
\(379\) 15.6700 + 19.6496i 0.804916 + 1.00933i 0.999595 + 0.0284655i \(0.00906206\pi\)
−0.194679 + 0.980867i \(0.562367\pi\)
\(380\) −2.70363 + 2.50860i −0.138693 + 0.128688i
\(381\) 9.10728 + 3.28927i 0.466580 + 0.168514i
\(382\) −12.0741 + 8.23200i −0.617766 + 0.421186i
\(383\) −3.34512 + 4.19464i −0.170928 + 0.214336i −0.859915 0.510436i \(-0.829484\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(384\) −3.74936 0.177819i −0.191334 0.00907428i
\(385\) 14.0149 5.19022i 0.714267 0.264518i
\(386\) −13.8457 6.66774i −0.704728 0.339379i
\(387\) 1.39104 + 0.840613i 0.0707103 + 0.0427308i
\(388\) −9.02848 + 2.78492i −0.458352 + 0.141383i
\(389\) −23.7580 + 11.4413i −1.20458 + 0.580095i −0.924978 0.380021i \(-0.875917\pi\)
−0.279602 + 0.960116i \(0.590202\pi\)
\(390\) 12.5236 10.5615i 0.634156 0.534801i
\(391\) 9.33694 + 16.1721i 0.472190 + 0.817856i
\(392\) 10.0453 + 19.0643i 0.507366 + 0.962895i
\(393\) −23.8986 + 14.6855i −1.20552 + 0.740785i
\(394\) −1.72774 + 4.40222i −0.0870424 + 0.221780i
\(395\) −5.76085 3.92768i −0.289860 0.197623i
\(396\) 5.06688 1.87266i 0.254620 0.0941045i
\(397\) −0.726604 + 9.69586i −0.0364672 + 0.486621i 0.948832 + 0.315782i \(0.102267\pi\)
−0.985299 + 0.170839i \(0.945352\pi\)
\(398\) 14.3520 9.78501i 0.719400 0.490478i
\(399\) −10.4989 3.14577i −0.525604 0.157485i
\(400\) 0.282490 + 0.192598i 0.0141245 + 0.00962992i
\(401\) 9.01343 11.3025i 0.450109 0.564419i −0.504067 0.863665i \(-0.668164\pi\)
0.954176 + 0.299245i \(0.0967349\pi\)
\(402\) 28.8812 2.96223i 1.44046 0.147743i
\(403\) −7.60239 9.53310i −0.378702 0.474877i
\(404\) 2.51520 + 0.775837i 0.125136 + 0.0385994i
\(405\) 5.17239 19.1075i 0.257018 0.949461i
\(406\) 1.81135 + 13.8253i 0.0898959 + 0.686140i
\(407\) 4.96163 + 12.6420i 0.245939 + 0.626642i
\(408\) −6.39191 8.84433i −0.316447 0.437860i
\(409\) 9.97288 + 3.07622i 0.493127 + 0.152110i 0.531338 0.847160i \(-0.321690\pi\)
−0.0382106 + 0.999270i \(0.512166\pi\)
\(410\) −7.19994 + 12.4707i −0.355580 + 0.615882i
\(411\) −22.7431 + 13.9754i −1.12183 + 0.689358i
\(412\) −11.5150 3.55189i −0.567301 0.174989i
\(413\) 4.62313 27.1072i 0.227489 1.33386i
\(414\) −5.26512 + 30.7495i −0.258767 + 1.51126i
\(415\) 1.46232 + 1.35683i 0.0717824 + 0.0666043i
\(416\) −8.83731 + 11.0816i −0.433285 + 0.543322i
\(417\) 13.7342 5.82951i 0.672564 0.285473i
\(418\) −1.55773 + 6.82487i −0.0761911 + 0.333815i
\(419\) 4.80052 1.48076i 0.234521 0.0723400i −0.175267 0.984521i \(-0.556079\pi\)
0.409788 + 0.912181i \(0.365603\pi\)
\(420\) −0.471111 + 7.05099i −0.0229879 + 0.344053i
\(421\) 23.3803 + 7.21188i 1.13949 + 0.351486i 0.806377 0.591402i \(-0.201425\pi\)
0.333111 + 0.942887i \(0.391901\pi\)
\(422\) −15.2553 + 26.4230i −0.742616 + 1.28625i
\(423\) −16.9702 + 0.931204i −0.825120 + 0.0452767i
\(424\) 17.7149 16.4370i 0.860312 0.798253i
\(425\) 0.0248268 + 0.331291i 0.00120428 + 0.0160700i
\(426\) −15.4934 + 6.57622i −0.750656 + 0.318619i
\(427\) 0.383738 19.8548i 0.0185704 0.960843i
\(428\) −2.92410 + 7.45049i −0.141342 + 0.360133i
\(429\) −4.50590 + 16.1683i −0.217547 + 0.780615i
\(430\) 0.846732 + 1.06177i 0.0408330 + 0.0512030i
\(431\) 2.79956 + 37.3575i 0.134850 + 1.79945i 0.497439 + 0.867499i \(0.334274\pi\)
−0.362589 + 0.931949i \(0.618107\pi\)
\(432\) 0.736782 10.9193i 0.0354484 0.525357i
\(433\) −16.7181 + 8.05102i −0.803421 + 0.386907i −0.790080 0.613004i \(-0.789961\pi\)
−0.0133410 + 0.999911i \(0.504247\pi\)
\(434\) −9.70093 0.915803i −0.465660 0.0439599i
\(435\) −7.20560 + 16.0753i −0.345482 + 0.770751i
\(436\) 0.550616 0.265162i 0.0263697 0.0126990i
\(437\) 15.9973 + 14.8433i 0.765253 + 0.710051i
\(438\) −3.88797 7.53775i −0.185775 0.360168i
\(439\) −12.3688 + 31.5152i −0.590330 + 1.50414i 0.253396 + 0.967363i \(0.418452\pi\)
−0.843726 + 0.536774i \(0.819643\pi\)
\(440\) 17.3892 0.828996
\(441\) −18.7706 + 9.41626i −0.893836 + 0.448393i
\(442\) 8.80092 0.418617
\(443\) −1.78404 + 4.54565i −0.0847622 + 0.215971i −0.966970 0.254889i \(-0.917961\pi\)
0.882208 + 0.470860i \(0.156056\pi\)
\(444\) −6.41441 0.304212i −0.304414 0.0144373i
\(445\) −16.0002 14.8461i −0.758484 0.703770i
\(446\) 6.69415 3.22373i 0.316977 0.152648i
\(447\) 17.2462 1.76888i 0.815718 0.0836651i
\(448\) 2.91925 + 22.2814i 0.137921 + 1.05270i
\(449\) −16.6876 + 8.03633i −0.787537 + 0.379258i −0.784020 0.620736i \(-0.786834\pi\)
−0.00351727 + 0.999994i \(0.501120\pi\)
\(450\) −0.321750 + 0.452235i −0.0151675 + 0.0213186i
\(451\) −1.10251 14.7120i −0.0519153 0.692761i
\(452\) 0.880743 + 1.10442i 0.0414267 + 0.0519474i
\(453\) −8.15281 8.31737i −0.383052 0.390784i
\(454\) −11.5602 + 29.4550i −0.542548 + 1.38239i
\(455\) −16.8993 14.0194i −0.792251 0.657241i
\(456\) −10.1844 7.67479i −0.476929 0.359405i
\(457\) −1.95714 26.1163i −0.0915513 1.22167i −0.834000 0.551764i \(-0.813955\pi\)
0.742449 0.669903i \(-0.233664\pi\)
\(458\) −21.5394 + 19.9856i −1.00647 + 0.933868i
\(459\) 8.74176 6.05562i 0.408030 0.282652i
\(460\) 7.03533 12.1856i 0.328024 0.568154i
\(461\) 4.30686 + 1.32849i 0.200590 + 0.0618739i 0.393422 0.919358i \(-0.371291\pi\)
−0.192832 + 0.981232i \(0.561767\pi\)
\(462\) 6.80020 + 11.5614i 0.316374 + 0.537887i
\(463\) 25.6078 7.89895i 1.19009 0.367095i 0.364416 0.931236i \(-0.381269\pi\)
0.825678 + 0.564141i \(0.190793\pi\)
\(464\) −2.16725 + 9.49534i −0.100612 + 0.440810i
\(465\) −9.83167 7.40897i −0.455933 0.343583i
\(466\) 14.7077 18.4429i 0.681322 0.854351i
\(467\) 9.92612 + 9.21010i 0.459326 + 0.426193i 0.875593 0.483050i \(-0.160471\pi\)
−0.416266 + 0.909243i \(0.636662\pi\)
\(468\) −6.10485 5.07128i −0.282197 0.234420i
\(469\) −10.7490 37.3986i −0.496344 1.72691i
\(470\) −13.5702 4.18585i −0.625946 0.193079i
\(471\) −0.940102 34.2905i −0.0433176 1.58002i
\(472\) 15.9978 27.7090i 0.736358 1.27541i
\(473\) −1.32956 0.410116i −0.0611334 0.0188572i
\(474\) 2.55955 5.71020i 0.117564 0.262278i
\(475\) 0.141840 + 0.361403i 0.00650808 + 0.0165823i
\(476\) −2.63547 + 2.73251i −0.120797 + 0.125244i
\(477\) 15.6702 + 17.5802i 0.717487 + 0.804943i
\(478\) 27.9112 + 8.60945i 1.27663 + 0.393787i
\(479\) 18.6800 + 23.4240i 0.853511 + 1.07027i 0.996748 + 0.0805810i \(0.0256776\pi\)
−0.143237 + 0.989688i \(0.545751\pi\)
\(480\) −5.85341 + 13.0586i −0.267170 + 0.596042i
\(481\) 12.4405 15.5999i 0.567239 0.711295i
\(482\) 24.6289 + 16.7917i 1.12182 + 0.764841i
\(483\) 41.8121 0.338022i 1.90252 0.0153805i
\(484\) 2.55133 1.73947i 0.115970 0.0790667i
\(485\) 2.21501 29.5572i 0.100578 1.34212i
\(486\) 17.6982 + 1.54997i 0.802807 + 0.0703080i
\(487\) 1.05122 + 0.716707i 0.0476352 + 0.0324771i 0.586904 0.809657i \(-0.300347\pi\)
−0.539268 + 0.842134i \(0.681299\pi\)
\(488\) 8.44161 21.5089i 0.382134 0.973661i
\(489\) 0.888429 + 32.4057i 0.0401761 + 1.46544i
\(490\) −17.4391 + 1.94284i −0.787816 + 0.0877687i
\(491\) 11.5683 + 20.0368i 0.522068 + 0.904248i 0.999670 + 0.0256722i \(0.00817260\pi\)
−0.477602 + 0.878576i \(0.658494\pi\)
\(492\) 6.56117 + 2.36969i 0.295801 + 0.106834i
\(493\) −8.52659 + 4.10619i −0.384018 + 0.184933i
\(494\) 9.82807 3.03156i 0.442186 0.136396i
\(495\) −0.338595 + 16.9428i −0.0152187 + 0.761522i
\(496\) −6.13220 2.95311i −0.275344 0.132599i
\(497\) 12.3454 + 18.8812i 0.553766 + 0.846937i
\(498\) −0.967615 + 1.50633i −0.0433599 + 0.0675003i
\(499\) −6.33248 + 7.94068i −0.283481 + 0.355474i −0.903101 0.429428i \(-0.858715\pi\)
0.619620 + 0.784902i \(0.287287\pi\)
\(500\) 6.57747 4.48445i 0.294154 0.200551i
\(501\) −1.50002 8.38559i −0.0670160 0.374641i
\(502\) −18.2701 + 16.9522i −0.815437 + 0.756615i
\(503\) −14.8789 18.6575i −0.663417 0.831899i 0.330293 0.943878i \(-0.392852\pi\)
−0.993711 + 0.111979i \(0.964281\pi\)
\(504\) −24.2858 + 2.68946i −1.08177 + 0.119798i
\(505\) −5.14834 + 6.45581i −0.229098 + 0.287280i
\(506\) −1.99581 26.6323i −0.0887247 1.18395i
\(507\) 2.07560 0.533988i 0.0921807 0.0237153i
\(508\) 1.95980 3.39448i 0.0869521 0.150605i
\(509\) 3.62417 0.160638 0.0803192 0.996769i \(-0.474406\pi\)
0.0803192 + 0.996769i \(0.474406\pi\)
\(510\) 8.60549 2.21393i 0.381057 0.0980343i
\(511\) −9.02288 + 6.91454i −0.399149 + 0.305881i
\(512\) −4.64611 + 20.3559i −0.205331 + 0.899613i
\(513\) 7.67608 9.77354i 0.338907 0.431512i
\(514\) 14.4207 + 2.17357i 0.636071 + 0.0958723i
\(515\) 23.5698 29.5556i 1.03861 1.30238i
\(516\) 0.434104 0.494362i 0.0191104 0.0217631i
\(517\) 13.9032 4.28857i 0.611462 0.188611i
\(518\) −2.07138 15.8100i −0.0910112 0.694652i
\(519\) 1.77957 6.38556i 0.0781145 0.280295i
\(520\) −12.7741 22.1255i −0.560183 0.970265i
\(521\) 1.22160 + 2.11588i 0.0535195 + 0.0926984i 0.891544 0.452934i \(-0.149623\pi\)
−0.838024 + 0.545633i \(0.816289\pi\)
\(522\) −15.3407 3.82543i −0.671442 0.167435i
\(523\) −28.9548 + 19.7411i −1.26611 + 0.863217i −0.995053 0.0993478i \(-0.968324\pi\)
−0.271053 + 0.962564i \(0.587372\pi\)
\(524\) 4.14821 + 10.5695i 0.181215 + 0.461730i
\(525\) 0.672806 + 0.317332i 0.0293636 + 0.0138495i
\(526\) 5.26273 13.4092i 0.229466 0.584670i
\(527\) −1.47165 6.44773i −0.0641061 0.280867i
\(528\) 1.64975 + 9.22261i 0.0717961 + 0.401363i
\(529\) −54.2884 26.1439i −2.36036 1.13669i
\(530\) 7.18915 + 18.3177i 0.312277 + 0.795668i
\(531\) 26.6862 + 16.1267i 1.15808 + 0.699838i
\(532\) −2.00182 + 3.95923i −0.0867897 + 0.171654i
\(533\) −17.9092 + 12.2103i −0.775733 + 0.528886i
\(534\) 10.5873 16.4818i 0.458159 0.713237i
\(535\) −18.4059 17.0782i −0.795757 0.738354i
\(536\) 3.38350 45.1496i 0.146145 1.95017i
\(537\) 1.64208 + 9.17974i 0.0708609 + 0.396135i
\(538\) 0.979040 1.69575i 0.0422094 0.0731088i
\(539\) 13.6411 11.7095i 0.587564 0.504363i
\(540\) −7.24500 3.42295i −0.311775 0.147300i
\(541\) −1.49234 + 0.224934i −0.0641608 + 0.00967068i −0.181044 0.983475i \(-0.557948\pi\)
0.116883 + 0.993146i \(0.462710\pi\)
\(542\) 4.41495 2.12613i 0.189638 0.0913250i
\(543\) −10.1324 29.9120i −0.434822 1.28365i
\(544\) −6.92650 + 3.33563i −0.296971 + 0.143014i
\(545\) 0.143272 + 1.91184i 0.00613712 + 0.0818941i
\(546\) 9.71497 17.1454i 0.415762 0.733757i
\(547\) 0.248375 3.31434i 0.0106198 0.141711i −0.989373 0.145397i \(-0.953554\pi\)
0.999993 + 0.00368573i \(0.00117321\pi\)
\(548\) 3.94765 + 10.0584i 0.168635 + 0.429675i
\(549\) 20.7924 + 8.64373i 0.887396 + 0.368905i
\(550\) 0.173585 0.442288i 0.00740170 0.0188592i
\(551\) −8.10730 + 7.52247i −0.345382 + 0.320468i
\(552\) 45.7585 + 16.5265i 1.94761 + 0.703416i
\(553\) −8.13922 2.02396i −0.346115 0.0860676i
\(554\) −31.6612 4.77216i −1.34516 0.202750i
\(555\) 8.24000 18.3830i 0.349768 0.780314i
\(556\) −1.34392 5.88809i −0.0569948 0.249710i
\(557\) 22.1323 + 38.3342i 0.937775 + 1.62427i 0.769609 + 0.638515i \(0.220451\pi\)
0.168165 + 0.985759i \(0.446216\pi\)
\(558\) 4.99181 9.85679i 0.211320 0.417271i
\(559\) 0.454882 + 1.99297i 0.0192395 + 0.0842936i
\(560\) −11.8943 2.95773i −0.502626 0.124987i
\(561\) −6.00692 + 6.84072i −0.253612 + 0.288816i
\(562\) 3.87321 16.9696i 0.163381 0.715820i
\(563\) −11.6083 29.5774i −0.489231 1.24654i −0.936035 0.351908i \(-0.885533\pi\)
0.446804 0.894632i \(-0.352562\pi\)
\(564\) −0.838545 + 6.82840i −0.0353091 + 0.287528i
\(565\) −4.23460 + 1.30620i −0.178151 + 0.0549522i
\(566\) 1.98305 8.68832i 0.0833539 0.365197i
\(567\) −2.14754 23.7147i −0.0901882 0.995925i
\(568\) 5.84077 + 25.5901i 0.245073 + 1.07374i
\(569\) −13.7700 23.8504i −0.577270 0.999861i −0.995791 0.0916541i \(-0.970785\pi\)
0.418521 0.908207i \(-0.362549\pi\)
\(570\) 8.84721 5.43655i 0.370569 0.227712i
\(571\) 31.7345 + 9.78879i 1.32805 + 0.409648i 0.875985 0.482339i \(-0.160213\pi\)
0.452061 + 0.891987i \(0.350689\pi\)
\(572\) 6.12134 + 2.94788i 0.255946 + 0.123257i
\(573\) −20.4435 + 8.67732i −0.854039 + 0.362500i
\(574\) −2.91216 + 17.0751i −0.121551 + 0.712702i
\(575\) −0.923491 1.15802i −0.0385123 0.0482928i
\(576\) −24.7236 6.16521i −1.03015 0.256884i
\(577\) 11.8149 30.1039i 0.491860 1.25324i −0.442455 0.896791i \(-0.645892\pi\)
0.934315 0.356449i \(-0.116013\pi\)
\(578\) −13.1551 6.33518i −0.547182 0.263509i
\(579\) −18.6519 14.0558i −0.775148 0.584137i
\(580\) 5.89184 + 4.01699i 0.244645 + 0.166796i
\(581\) 2.21636 + 0.919671i 0.0919502 + 0.0381544i
\(582\) 26.4627 2.71418i 1.09692 0.112506i
\(583\) −16.6576 11.3570i −0.689889 0.470358i
\(584\) −12.6390 + 3.89862i −0.523006 + 0.161326i
\(585\) 21.8062 12.0154i 0.901576 0.496776i
\(586\) 9.74969 1.46953i 0.402756 0.0607057i
\(587\) 17.8716 30.9544i 0.737638 1.27763i −0.215918 0.976411i \(-0.569274\pi\)
0.953556 0.301215i \(-0.0973922\pi\)
\(588\) 2.41413 + 8.15057i 0.0995569 + 0.336124i
\(589\) −3.86438 6.69331i −0.159229 0.275793i
\(590\) 16.2441 + 20.3694i 0.668757 + 0.838595i
\(591\) −3.88440 + 6.04702i −0.159783 + 0.248741i
\(592\) 2.47837 10.8584i 0.101860 0.446279i
\(593\) −0.306850 + 4.09462i −0.0126008 + 0.168146i 0.987353 + 0.158537i \(0.0506777\pi\)
−0.999954 + 0.00960899i \(0.996941\pi\)
\(594\) −15.0218 + 2.37841i −0.616353 + 0.0975873i
\(595\) −4.95905 10.8280i −0.203301 0.443904i
\(596\) 0.524434 6.99809i 0.0214817 0.286653i
\(597\) 24.3003 10.3143i 0.994544 0.422138i
\(598\) −32.4199 + 22.1035i −1.32575 + 0.903881i
\(599\) −20.1916 + 3.04339i −0.825007 + 0.124350i −0.547958 0.836506i \(-0.684595\pi\)
−0.277049 + 0.960856i \(0.589356\pi\)
\(600\) 0.605882 + 0.618112i 0.0247350 + 0.0252343i
\(601\) 23.5521 3.54991i 0.960712 0.144804i 0.350081 0.936719i \(-0.386154\pi\)
0.610631 + 0.791915i \(0.290916\pi\)
\(602\) 1.39870 + 0.843989i 0.0570066 + 0.0343984i
\(603\) 43.9248 + 4.17578i 1.78875 + 0.170051i
\(604\) −3.89529 + 2.65576i −0.158497 + 0.108061i
\(605\) 2.15556 + 9.44414i 0.0876361 + 0.383959i
\(606\) −6.51708 3.52812i −0.264738 0.143320i
\(607\) −36.1946 −1.46909 −0.734547 0.678558i \(-0.762605\pi\)
−0.734547 + 0.678558i \(0.762605\pi\)
\(608\) −6.58589 + 6.11082i −0.267093 + 0.247826i
\(609\) −1.41271 + 21.1436i −0.0572459 + 0.856783i
\(610\) 13.7923 + 12.7974i 0.558433 + 0.518151i
\(611\) −15.6700 14.5396i −0.633940 0.588210i
\(612\) −1.78986 3.91491i −0.0723507 0.158251i
\(613\) −29.0192 4.37395i −1.17208 0.176662i −0.465991 0.884789i \(-0.654302\pi\)
−0.706085 + 0.708127i \(0.749540\pi\)
\(614\) −30.2606 + 9.33416i −1.22122 + 0.376696i
\(615\) −14.4399 + 16.4443i −0.582274 + 0.663098i
\(616\) 19.6156 7.26433i 0.790334 0.292688i
\(617\) 34.3322 31.8556i 1.38216 1.28246i 0.464232 0.885714i \(-0.346330\pi\)
0.917929 0.396745i \(-0.129860\pi\)
\(618\) 29.8361 + 16.1523i 1.20019 + 0.649739i
\(619\) −1.02212 −0.0410825 −0.0205412 0.999789i \(-0.506539\pi\)
−0.0205412 + 0.999789i \(0.506539\pi\)
\(620\) −3.65299 + 3.38948i −0.146708 + 0.136125i
\(621\) −16.9933 + 44.2620i −0.681918 + 1.77617i
\(622\) 3.31214 4.15329i 0.132805 0.166532i
\(623\) −24.2508 10.0628i −0.971586 0.403156i
\(624\) 10.5227 8.87405i 0.421244 0.355246i
\(625\) 5.37655 + 23.5562i 0.215062 + 0.942248i
\(626\) 19.7808 2.98147i 0.790599 0.119164i
\(627\) −4.35162 + 9.70823i −0.173787 + 0.387709i
\(628\) −13.7306 2.06955i −0.547909 0.0825841i
\(629\) 9.75061 4.69565i 0.388782 0.187228i
\(630\) 5.18619 19.2086i 0.206623 0.765287i
\(631\) −36.3801 17.5197i −1.44827 0.697450i −0.465976 0.884797i \(-0.654297\pi\)
−0.982294 + 0.187347i \(0.940011\pi\)
\(632\) −8.06300 5.49726i −0.320729 0.218669i
\(633\) −30.5954 + 34.8423i −1.21606 + 1.38486i
\(634\) −0.319355 + 4.26150i −0.0126832 + 0.169246i
\(635\) 7.66655 + 9.61355i 0.304238 + 0.381502i
\(636\) 8.12203 4.99092i 0.322059 0.197903i
\(637\) −24.9196 8.75471i −0.987350 0.346874i
\(638\) 13.5349 0.535851
\(639\) −25.0469 + 5.19256i −0.990840 + 0.205414i
\(640\) −3.93830 2.68509i −0.155675 0.106137i
\(641\) −0.0173105 + 0.0758422i −0.000683723 + 0.00299559i −0.975269 0.221023i \(-0.929060\pi\)
0.974585 + 0.224018i \(0.0719176\pi\)
\(642\) 12.1792 18.9599i 0.480673 0.748286i
\(643\) −0.241043 3.21650i −0.00950582 0.126846i 0.990432 0.138002i \(-0.0440680\pi\)
−0.999938 + 0.0111556i \(0.996449\pi\)
\(644\) 2.84558 16.6847i 0.112131 0.657471i
\(645\) 0.946124 + 1.83428i 0.0372536 + 0.0722249i
\(646\) 5.51619 + 0.831432i 0.217032 + 0.0327123i
\(647\) 1.60958 + 21.4783i 0.0632789 + 0.844399i 0.935057 + 0.354498i \(0.115348\pi\)
−0.871778 + 0.489901i \(0.837033\pi\)
\(648\) 7.23939 26.7433i 0.284390 1.05058i
\(649\) −25.5069 7.86784i −1.00123 0.308840i
\(650\) −0.690270 + 0.104041i −0.0270746 + 0.00408084i
\(651\) −14.1856 4.25039i −0.555976 0.166586i
\(652\) 12.9759 + 1.95580i 0.508174 + 0.0765949i
\(653\) 27.4646 + 13.2262i 1.07477 + 0.517582i 0.885641 0.464370i \(-0.153719\pi\)
0.189130 + 0.981952i \(0.439433\pi\)
\(654\) −1.66640 + 0.428712i −0.0651612 + 0.0167640i
\(655\) −35.6198 −1.39178
\(656\) −6.04959 + 10.4782i −0.236197 + 0.409105i
\(657\) −3.55244 12.3905i −0.138594 0.483399i
\(658\) −17.0563 + 0.947170i −0.664923 + 0.0369245i
\(659\) −26.5500 24.6348i −1.03424 0.959634i −0.0350301 0.999386i \(-0.511153\pi\)
−0.999210 + 0.0397521i \(0.987343\pi\)
\(660\) 6.72697 + 1.34256i 0.261847 + 0.0522591i
\(661\) 13.1863 + 33.5981i 0.512886 + 1.30681i 0.919456 + 0.393193i \(0.128630\pi\)
−0.406570 + 0.913620i \(0.633275\pi\)
\(662\) −7.06281 17.9957i −0.274504 0.699424i
\(663\) 13.1166 + 2.61780i 0.509408 + 0.101667i
\(664\) 2.04669 + 1.89905i 0.0794270 + 0.0736975i
\(665\) −9.26761 10.3835i −0.359382 0.402655i
\(666\) 17.5429 + 4.37459i 0.679773 + 0.169512i
\(667\) 21.0967 36.5405i 0.816866 1.41485i
\(668\) −3.44828 −0.133418
\(669\) 10.9356 2.81340i 0.422796 0.108772i
\(670\) 33.2166 + 15.9963i 1.28327 + 0.617990i
\(671\) −19.0613 2.87303i −0.735853 0.110912i
\(672\) −1.14760 + 17.1759i −0.0442697 + 0.662573i
\(673\) 11.4707 1.72893i 0.442162 0.0666452i 0.0758116 0.997122i \(-0.475845\pi\)
0.366350 + 0.930477i \(0.380607\pi\)
\(674\) 4.43520 + 1.36808i 0.170838 + 0.0526964i
\(675\) −0.614042 + 0.578294i −0.0236345 + 0.0222585i
\(676\) −0.0648314 0.865115i −0.00249352 0.0332737i
\(677\) −8.56775 1.29138i −0.329285 0.0496318i −0.0176809 0.999844i \(-0.505628\pi\)
−0.311605 + 0.950212i \(0.600866\pi\)
\(678\) −1.82319 3.53468i −0.0700192 0.135749i
\(679\) −9.84893 34.2669i −0.377967 1.31504i
\(680\) −1.03555 13.8184i −0.0397115 0.529913i
\(681\) −25.9903 + 40.4602i −0.995949 + 1.55044i
\(682\) −2.10472 + 9.22138i −0.0805939 + 0.353105i
\(683\) 13.8713 + 9.45726i 0.530769 + 0.361872i 0.798856 0.601523i \(-0.205439\pi\)
−0.268087 + 0.963395i \(0.586391\pi\)
\(684\) −3.34728 3.75528i −0.127986 0.143587i
\(685\) −33.8975 −1.29516
\(686\) −18.8602 + 9.47676i −0.720087 + 0.361825i
\(687\) −38.0463 + 23.3792i −1.45156 + 0.891971i
\(688\) 0.711448 + 0.892128i 0.0271237 + 0.0340121i
\(689\) −2.21353 + 29.5376i −0.0843289 + 1.12529i
\(690\) −26.1397 + 29.7681i −0.995123 + 1.13325i
\(691\) −24.7452 16.8710i −0.941352 0.641803i −0.00769454 0.999970i \(-0.502449\pi\)
−0.933657 + 0.358168i \(0.883402\pi\)
\(692\) −2.41758 1.16424i −0.0919024 0.0442579i
\(693\) 6.69591 + 19.2535i 0.254357 + 0.731380i
\(694\) 5.81761 2.80161i 0.220834 0.106348i
\(695\) 18.7349 + 2.82384i 0.710656 + 0.107114i
\(696\) −10.0851 + 22.4993i −0.382275 + 0.852834i
\(697\) −11.6253 + 1.75224i −0.440341 + 0.0663708i
\(698\) 0.937900 + 4.10921i 0.0355000 + 0.155536i
\(699\) 27.4057 23.1120i 1.03658 0.874175i
\(700\) 0.174401 0.245471i 0.00659175 0.00927791i
\(701\) −5.09046 + 6.38323i −0.192264 + 0.241091i −0.868614 0.495489i \(-0.834989\pi\)
0.676351 + 0.736580i \(0.263560\pi\)
\(702\) 14.0613 + 17.3661i 0.530709 + 0.655443i
\(703\) 9.27113 8.60236i 0.349667 0.324444i
\(704\) 21.8133 0.822122
\(705\) −18.9795 10.2749i −0.714811 0.386974i
\(706\) 4.50771 4.18254i 0.169650 0.157412i
\(707\) −3.11059 + 9.43310i −0.116986 + 0.354768i
\(708\) 8.32804 9.48403i 0.312987 0.356432i
\(709\) 34.7124 10.7074i 1.30365 0.402124i 0.436293 0.899805i \(-0.356291\pi\)
0.867360 + 0.497681i \(0.165815\pi\)
\(710\) −21.1347 3.18554i −0.793171 0.119551i
\(711\) 5.51315 7.74898i 0.206759 0.290610i
\(712\) −22.3943 20.7788i −0.839260 0.778720i
\(713\) 21.6146 + 20.0554i 0.809473 + 0.751081i
\(714\) 8.78242 6.09233i 0.328674 0.228000i
\(715\) −15.6243 + 14.4972i −0.584315 + 0.542165i
\(716\) 3.77484 0.141072
\(717\) 39.0371 + 21.1333i 1.45787 + 0.789239i
\(718\) −2.70642 11.8576i −0.101003 0.442521i
\(719\) −13.9134 + 9.48597i −0.518881 + 0.353767i −0.794269 0.607566i \(-0.792146\pi\)
0.275388 + 0.961333i \(0.411194\pi\)
\(720\) 8.05667 11.3240i 0.300254 0.422022i
\(721\) 14.2407 43.1861i 0.530352 1.60833i
\(722\) −14.9658 + 2.25573i −0.556969 + 0.0839496i
\(723\) 31.7115 + 32.3516i 1.17936 + 1.20317i
\(724\) −12.6411 + 1.90534i −0.469802 + 0.0708113i
\(725\) 0.620211 0.422853i 0.0230341 0.0157044i
\(726\) −8.00289 + 3.39686i −0.297015 + 0.126069i
\(727\) 0.303669 4.05219i 0.0112625 0.150287i −0.988737 0.149661i \(-0.952182\pi\)
1.00000 0.000626012i \(-0.000199266\pi\)
\(728\) −23.6526 19.6219i −0.876623 0.727235i
\(729\) 25.9158 + 7.57429i 0.959845 + 0.280529i
\(730\) 0.804860 10.7401i 0.0297892 0.397509i
\(731\) −0.246725 + 1.08097i −0.00912544 + 0.0399811i
\(732\) 4.92625 7.66891i 0.182079 0.283451i
\(733\) −23.1307 29.0050i −0.854353 1.07133i −0.996673 0.0815044i \(-0.974028\pi\)
0.142320 0.989821i \(-0.454544\pi\)
\(734\) 10.6234 + 18.4002i 0.392116 + 0.679164i
\(735\) −26.5685 2.29163i −0.979994 0.0845279i
\(736\) 17.1377 29.6834i 0.631704 1.09414i
\(737\) −37.3505 + 5.62968i −1.37582 + 0.207372i
\(738\) −16.8099 10.1584i −0.618782 0.373935i
\(739\) 16.2666 5.01758i 0.598376 0.184575i 0.0192528 0.999815i \(-0.493871\pi\)
0.579123 + 0.815240i \(0.303395\pi\)
\(740\) −6.73763 4.59364i −0.247680 0.168866i
\(741\) 15.5492 1.59482i 0.571213 0.0585871i
\(742\) 15.7618 + 17.6597i 0.578635 + 0.648307i
\(743\) 26.6118 + 18.1436i 0.976293 + 0.665625i 0.942641 0.333809i \(-0.108334\pi\)
0.0336517 + 0.999434i \(0.489286\pi\)
\(744\) −13.7606 10.3697i −0.504489 0.380173i
\(745\) 19.8351 + 9.55207i 0.726701 + 0.349961i
\(746\) 3.57562 9.11054i 0.130913 0.333560i
\(747\) −1.89016 + 1.95717i −0.0691572 + 0.0716093i
\(748\) 2.29763 + 2.88113i 0.0840096 + 0.105345i
\(749\) −27.8969 11.5757i −1.01933 0.422967i
\(750\) −20.6319 + 8.75729i −0.753370 + 0.319771i
\(751\) 12.2247 + 5.88709i 0.446084 + 0.214823i 0.643420 0.765513i \(-0.277515\pi\)
−0.197336 + 0.980336i \(0.563229\pi\)
\(752\) −11.4021 3.51707i −0.415790 0.128254i
\(753\) −32.2716 + 19.8307i −1.17604 + 0.722670i
\(754\) −9.94277 17.2214i −0.362094 0.627166i
\(755\) −3.29104 14.4190i −0.119773 0.524761i
\(756\) −9.60255 0.834611i −0.349241 0.0303545i
\(757\) 2.63602 11.5491i 0.0958077 0.419761i −0.904165 0.427184i \(-0.859506\pi\)
0.999972 + 0.00742296i \(0.00236282\pi\)
\(758\) −27.3709 + 8.44282i −0.994157 + 0.306657i
\(759\) 4.94717 40.2855i 0.179571 1.46227i
\(760\) −5.91629 15.0745i −0.214606 0.546808i
\(761\) −1.65809 + 7.26458i −0.0601058 + 0.263341i −0.996048 0.0888118i \(-0.971693\pi\)
0.935943 + 0.352153i \(0.114550\pi\)
\(762\) −7.28163 + 8.29238i −0.263786 + 0.300401i
\(763\) 0.960287 + 2.09677i 0.0347647 + 0.0759081i
\(764\) 2.00044 + 8.76451i 0.0723734 + 0.317089i
\(765\) 13.4839 0.739898i 0.487511 0.0267511i
\(766\) −3.05729 5.29539i −0.110465 0.191330i
\(767\) 8.72665 + 38.2339i 0.315101 + 1.38055i
\(768\) −10.2849 + 22.9451i −0.371125 + 0.827958i
\(769\) 48.0483 + 7.24211i 1.73267 + 0.261157i 0.938185 0.346133i \(-0.112505\pi\)
0.794480 + 0.607290i \(0.207744\pi\)
\(770\) −0.329134 + 17.0296i −0.0118612 + 0.613703i
\(771\) 20.8457 + 7.52882i 0.750739 + 0.271144i
\(772\) −6.93018 + 6.43027i −0.249423 + 0.231430i
\(773\) −2.31385 + 5.89558i −0.0832232 + 0.212049i −0.966428 0.256939i \(-0.917286\pi\)
0.883204 + 0.468988i \(0.155381\pi\)
\(774\) −1.47100 + 1.12575i −0.0528741 + 0.0404641i
\(775\) 0.191647 + 0.488308i 0.00688415 + 0.0175405i
\(776\) 3.10017 41.3689i 0.111290 1.48506i
\(777\) 1.61551 24.1789i 0.0579561 0.867413i
\(778\) −2.24585 29.9688i −0.0805177 1.07443i
\(779\) −12.3785 + 5.96119i −0.443507 + 0.213582i
\(780\) −3.23342 9.54544i −0.115775 0.341781i
\(781\) 19.7293 9.50115i 0.705971 0.339978i
\(782\) −21.0447 + 3.17197i −0.752556 + 0.113430i
\(783\) −21.7254 10.2643i −0.776402 0.366817i
\(784\) −14.6528 + 1.63243i −0.523314 + 0.0583011i
\(785\) 21.7804 37.7247i 0.777374 1.34645i
\(786\) −5.62915 31.4687i −0.200785 1.12245i
\(787\) −2.10261 + 28.0574i −0.0749501 + 1.00014i 0.825280 + 0.564724i \(0.191017\pi\)
−0.900230 + 0.435415i \(0.856602\pi\)
\(788\) 2.13265 + 1.97881i 0.0759725 + 0.0704922i
\(789\) 11.8319 18.4193i 0.421228 0.655745i
\(790\) 6.56556 4.47632i 0.233592 0.159260i
\(791\) −4.23110 + 3.24244i −0.150441 + 0.115288i
\(792\) −0.473905 + 23.7135i −0.0168395 + 0.842622i
\(793\) 10.3469 + 26.3636i 0.367430 + 0.936197i
\(794\) −9.98383 4.80796i −0.354313 0.170628i
\(795\) 5.26597 + 29.4385i 0.186765 + 1.04407i
\(796\) −2.37783 10.4180i −0.0842801 0.369255i
\(797\) −7.44067 + 18.9585i −0.263562 + 0.671545i −0.999988 0.00497343i \(-0.998417\pi\)
0.736426 + 0.676519i \(0.236512\pi\)
\(798\) 7.70884 9.82854i 0.272890 0.347926i
\(799\) −4.23590 10.7929i −0.149855 0.381825i
\(800\) 0.503823 0.343501i 0.0178128 0.0121446i
\(801\) 20.6815 21.4148i 0.730745 0.756655i
\(802\) 8.23789 + 14.2684i 0.290890 + 0.503836i
\(803\) 5.51726 + 9.55618i 0.194700 + 0.337230i
\(804\) 4.79475 17.2048i 0.169098 0.606767i
\(805\) 45.4622 + 27.4323i 1.60233 + 0.966863i
\(806\) 13.2791 4.09607i 0.467738 0.144278i
\(807\) 1.96352 2.23608i 0.0691193 0.0787136i
\(808\) −7.20572 + 9.03569i −0.253496 + 0.317874i
\(809\) 36.6328 + 5.52151i 1.28794 + 0.194126i 0.757074 0.653329i \(-0.226628\pi\)
0.530868 + 0.847455i \(0.321866\pi\)
\(810\) 18.1176 + 13.4433i 0.636588 + 0.472349i
\(811\) 2.10023 9.20169i 0.0737489 0.323115i −0.924574 0.381002i \(-0.875579\pi\)
0.998323 + 0.0578869i \(0.0184363\pi\)
\(812\) 8.32429 + 2.06998i 0.292125 + 0.0726421i
\(813\) 7.21231 1.85551i 0.252947 0.0650754i
\(814\) −15.4779 −0.542499
\(815\) −20.5832 + 35.6511i −0.720997 + 1.24880i
\(816\) 7.23057 1.86020i 0.253121 0.0651201i
\(817\) 0.0968307 + 1.29212i 0.00338768 + 0.0452054i
\(818\) −7.41603 + 9.29940i −0.259295 + 0.325146i
\(819\) 19.5787 22.6634i 0.684136 0.791922i
\(820\) 5.52323 + 6.92591i 0.192879 + 0.241863i
\(821\) −12.3420 + 11.4517i −0.430740 + 0.399668i −0.865525 0.500866i \(-0.833015\pi\)
0.434785 + 0.900534i \(0.356824\pi\)
\(822\) −5.35698 29.9472i −0.186846 1.04453i
\(823\) 31.7894 21.6736i 1.10811 0.755495i 0.136159 0.990687i \(-0.456524\pi\)
0.971949 + 0.235192i \(0.0755718\pi\)
\(824\) 32.9888 41.3667i 1.14922 1.44108i
\(825\) 0.390263 0.607540i 0.0135872 0.0211518i
\(826\) 26.8332 + 16.1914i 0.933646 + 0.563372i
\(827\) 42.3344 + 20.3872i 1.47211 + 0.708932i 0.986274 0.165118i \(-0.0528004\pi\)
0.485838 + 0.874049i \(0.338515\pi\)
\(828\) 16.4256 + 9.92612i 0.570829 + 0.344956i
\(829\) 7.69029 2.37214i 0.267095 0.0823879i −0.158315 0.987389i \(-0.550606\pi\)
0.425410 + 0.905001i \(0.360130\pi\)
\(830\) −2.04834 + 0.986429i −0.0710989 + 0.0342394i
\(831\) −45.7674 16.5298i −1.58765 0.573412i
\(832\) −16.0242 27.7546i −0.555537 0.962219i
\(833\) −10.1174 10.1427i −0.350546 0.351423i
\(834\) 0.466010 + 16.9979i 0.0161366 + 0.588588i
\(835\) 3.95211 10.0698i 0.136768 0.348480i
\(836\) 3.55821 + 2.42595i 0.123063 + 0.0839031i
\(837\) 10.3715 13.2055i 0.358491 0.456448i
\(838\) −0.427863 + 5.70944i −0.0147803 + 0.197229i
\(839\) −19.0942 + 13.0182i −0.659206 + 0.449439i −0.846159 0.532930i \(-0.821091\pi\)
0.186954 + 0.982369i \(0.440139\pi\)
\(840\) −28.0633 13.2362i −0.968277 0.456692i
\(841\) −6.29323 4.29065i −0.217008 0.147953i
\(842\) −17.3861 + 21.8015i −0.599164 + 0.751328i
\(843\) 10.8201 24.1389i 0.372663 0.831389i
\(844\) 11.7027 + 14.6747i 0.402822 + 0.505123i
\(845\) 2.60065 + 0.802195i 0.0894652 + 0.0275963i
\(846\) 6.07804 18.3915i 0.208967 0.632313i
\(847\) 6.37684 + 9.75282i 0.219111 + 0.335111i
\(848\) 6.04053 + 15.3910i 0.207433 + 0.528530i
\(849\) 5.53979 12.3590i 0.190125 0.424158i
\(850\) −0.361805 0.111602i −0.0124098 0.00382791i
\(851\) −24.1252 + 41.7860i −0.827001 + 1.43241i
\(852\) 0.283765 + 10.3504i 0.00972162 + 0.354599i
\(853\) −13.2044 4.07301i −0.452110 0.139457i 0.0603340 0.998178i \(-0.480783\pi\)
−0.512444 + 0.858721i \(0.671260\pi\)
\(854\) 20.9043 + 8.67415i 0.715330 + 0.296823i
\(855\) 14.8027 5.47089i 0.506241 0.187101i
\(856\) −25.7613 23.9030i −0.880502 0.816987i
\(857\) 0.870221 1.09122i 0.0297262 0.0372754i −0.766746 0.641950i \(-0.778126\pi\)
0.796472 + 0.604675i \(0.206697\pi\)
\(858\) −15.2769 11.5124i −0.521545 0.393027i
\(859\) −6.96637 + 30.5216i −0.237689 + 1.04139i 0.705391 + 0.708819i \(0.250772\pi\)
−0.943080 + 0.332566i \(0.892085\pi\)
\(860\) 0.798335 0.246254i 0.0272230 0.00839718i
\(861\) −9.41912 + 24.5820i −0.321003 + 0.837753i
\(862\) −40.7984 12.5846i −1.38960 0.428634i
\(863\) 11.8269 20.4847i 0.402591 0.697309i −0.591446 0.806344i \(-0.701443\pi\)
0.994038 + 0.109035i \(0.0347762\pi\)
\(864\) −17.6484 8.33814i −0.600412 0.283669i
\(865\) 6.17069 5.72556i 0.209810 0.194675i
\(866\) −1.58037 21.0885i −0.0537031 0.716618i
\(867\) −17.7217 13.3547i −0.601859 0.453550i
\(868\) −2.70474 + 5.34949i −0.0918050 + 0.181573i
\(869\) −2.97436 + 7.57854i −0.100898 + 0.257084i
\(870\) −14.0541 14.3378i −0.476479 0.486097i
\(871\) 34.6008 + 43.3880i 1.17240 + 1.47015i
\(872\) 0.200527 + 2.67585i 0.00679070 + 0.0906156i
\(873\) 40.2466 + 3.82611i 1.36214 + 0.129494i
\(874\) −22.4081 + 10.7912i −0.757967 + 0.365017i
\(875\) 16.4398 + 25.1433i 0.555768 + 0.850000i
\(876\) −5.19038 + 0.532357i −0.175367 + 0.0179867i
\(877\) 3.49960 1.68532i 0.118173 0.0569091i −0.373863 0.927484i \(-0.621967\pi\)
0.492036 + 0.870575i \(0.336253\pi\)
\(878\) −28.2845 26.2442i −0.954556 0.885698i
\(879\) 14.9677 + 0.709866i 0.504849 + 0.0239432i
\(880\) −4.34660 + 11.0750i −0.146524 + 0.373337i
\(881\) −44.8121 −1.50976 −0.754880 0.655863i \(-0.772305\pi\)
−0.754880 + 0.655863i \(0.772305\pi\)
\(882\) −2.17417 23.8344i −0.0732083 0.802548i
\(883\) 0.606426 0.0204079 0.0102039 0.999948i \(-0.496752\pi\)
0.0102039 + 0.999948i \(0.496752\pi\)
\(884\) 1.97802 5.03992i 0.0665281 0.169511i
\(885\) 18.1508 + 35.1897i 0.610134 + 1.18289i
\(886\) −4.07967 3.78538i −0.137059 0.127172i
\(887\) 21.9600 10.5754i 0.737344 0.355086i −0.0272236 0.999629i \(-0.508667\pi\)
0.764568 + 0.644543i \(0.222952\pi\)
\(888\) 11.5329 25.7292i 0.387018 0.863415i
\(889\) 12.6642 + 7.64171i 0.424743 + 0.256295i
\(890\) 22.4123 10.7932i 0.751263 0.361789i
\(891\) −23.0955 0.923480i −0.773729 0.0309377i
\(892\) −0.341575 4.55800i −0.0114368 0.152613i
\(893\) −8.44797 10.5934i −0.282701 0.354495i
\(894\) −5.30427 + 19.0331i −0.177401 + 0.636562i
\(895\) −4.32639 + 11.0235i −0.144615 + 0.368474i
\(896\) −5.56423 1.38364i −0.185888 0.0462243i
\(897\) −54.8923 + 23.2993i −1.83280 + 0.777940i
\(898\) −1.57748 21.0501i −0.0526413 0.702450i
\(899\) −10.9541 + 10.1639i −0.365341 + 0.338987i
\(900\) 0.186662 + 0.285893i 0.00622207 + 0.00952978i
\(901\) −8.03293 + 13.9134i −0.267616 + 0.463524i
\(902\) 16.0671 + 4.95604i 0.534975 + 0.165018i
\(903\) 1.83353 + 1.67389i 0.0610162 + 0.0557036i
\(904\) −5.92683 + 1.82818i −0.197123 + 0.0608045i
\(905\) 8.92404 39.0988i 0.296645 1.29969i
\(906\) 12.2185 5.18621i 0.405934 0.172300i
\(907\) −29.0950 + 36.4840i −0.966083 + 1.21143i 0.0112961 + 0.999936i \(0.496404\pi\)
−0.977379 + 0.211494i \(0.932167\pi\)
\(908\) 14.2694 + 13.2401i 0.473548 + 0.439388i
\(909\) −8.66343 7.19669i −0.287348 0.238699i
\(910\) 21.9097 12.0912i 0.726299 0.400819i
\(911\) 20.1098 + 6.20306i 0.666269 + 0.205517i 0.609398 0.792865i \(-0.291411\pi\)
0.0568712 + 0.998382i \(0.481888\pi\)
\(912\) 7.43368 4.56794i 0.246154 0.151260i
\(913\) 1.16464 2.01721i 0.0385439 0.0667600i
\(914\) 28.5217 + 8.79779i 0.943415 + 0.291005i
\(915\) 16.7491 + 23.1753i 0.553707 + 0.766151i
\(916\) 6.60392 + 16.8265i 0.218200 + 0.555964i
\(917\) −40.1803 + 14.8802i −1.32687 + 0.491386i
\(918\) 2.78459 + 11.7956i 0.0919051 + 0.389312i
\(919\) 28.6701 + 8.84355i 0.945738 + 0.291722i 0.729004 0.684509i \(-0.239983\pi\)
0.216734 + 0.976231i \(0.430460\pi\)
\(920\) 38.5197 + 48.3021i 1.26996 + 1.59247i
\(921\) −47.8759 + 4.91045i −1.57756 + 0.161805i
\(922\) −3.20266 + 4.01601i −0.105474 + 0.132260i
\(923\) −26.5822 18.1234i −0.874964 0.596540i
\(924\) 8.14911 1.29574i 0.268086 0.0426267i
\(925\) −0.709245 + 0.483555i −0.0233198 + 0.0158992i
\(926\) −2.28238 + 30.4563i −0.0750038 + 1.00086i
\(927\) 39.6624 + 32.9475i 1.30269 + 1.08214i
\(928\) 14.3522 + 9.78517i 0.471134 + 0.321214i
\(929\) 19.7577 50.3418i 0.648230 1.65166i −0.105453 0.994424i \(-0.533629\pi\)
0.753683 0.657238i \(-0.228275\pi\)
\(930\) 11.9539 7.34556i 0.391983 0.240870i
\(931\) −14.7919 7.84141i −0.484785 0.256992i
\(932\) −7.25589 12.5676i −0.237674 0.411664i
\(933\) 6.17169 5.20476i 0.202052 0.170396i
\(934\) −13.9040 + 6.69582i −0.454953 + 0.219094i
\(935\) −11.0469 + 3.40753i −0.361274 + 0.111438i
\(936\) 30.5204 16.8170i 0.997592 0.549681i
\(937\) 50.2070 + 24.1784i 1.64019 + 0.789874i 0.999761 + 0.0218578i \(0.00695810\pi\)
0.640430 + 0.768017i \(0.278756\pi\)
\(938\) 44.1519 + 4.16810i 1.44161 + 0.136093i
\(939\) 30.3675 + 1.44022i 0.991006 + 0.0469998i
\(940\) −5.44699 + 6.83030i −0.177661 + 0.222780i
\(941\) −25.9178 + 17.6704i −0.844896 + 0.576040i −0.906570 0.422056i \(-0.861309\pi\)
0.0616739 + 0.998096i \(0.480356\pi\)
\(942\) 36.7704 + 13.2803i 1.19804 + 0.432697i
\(943\) 38.4235 35.6518i 1.25124 1.16098i
\(944\) 13.6487 + 17.1149i 0.444228 + 0.557044i
\(945\) 13.4429 27.0852i 0.437296 0.881082i
\(946\) 0.988690 1.23978i 0.0321451 0.0403087i
\(947\) −3.76634 50.2583i −0.122390 1.63317i −0.633559 0.773695i \(-0.718407\pi\)
0.511169 0.859480i \(-0.329213\pi\)
\(948\) −2.69473 2.74912i −0.0875208 0.0892873i
\(949\) 8.10599 14.0400i 0.263132 0.455757i
\(950\) −0.442473 −0.0143557
\(951\) −1.74352 + 6.25621i −0.0565376 + 0.202872i
\(952\) −6.94079 15.1551i −0.224952 0.491178i
\(953\) 4.85496 21.2710i 0.157267 0.689034i −0.833393 0.552681i \(-0.813605\pi\)
0.990660 0.136353i \(-0.0435381\pi\)
\(954\) −25.1756 + 9.30458i −0.815089 + 0.301247i
\(955\) −27.8872 4.20332i −0.902409 0.136016i
\(956\) 11.2034 14.0486i 0.362342 0.454363i
\(957\) 20.1720 + 4.02590i 0.652067 + 0.130139i
\(958\) −32.6285 + 10.0646i −1.05418 + 0.325171i
\(959\) −38.2376 + 14.1607i −1.23476 + 0.457273i
\(960\) −22.6502 23.1073i −0.731031 0.745786i
\(961\) 10.2787 + 17.8032i 0.331570 + 0.574296i
\(962\) 11.3701 + 19.6936i 0.366587 + 0.634947i
\(963\) 23.7910 24.6346i 0.766654 0.793838i
\(964\) 15.1513 10.3300i 0.487990 0.332706i
\(965\) −10.8352 27.6076i −0.348797 0.888721i
\(966\) −17.0509 + 44.4994i −0.548603 + 1.43174i
\(967\) 5.95934 15.1842i 0.191640 0.488290i −0.802467 0.596696i \(-0.796480\pi\)
0.994107 + 0.108407i \(0.0345749\pi\)
\(968\) 3.01697 + 13.2182i 0.0969691 + 0.424849i
\(969\) 7.97386 + 2.87991i 0.256157 + 0.0925161i
\(970\) 30.4351 + 14.6568i 0.977211 + 0.470600i
\(971\) −3.93915 10.0368i −0.126413 0.322096i 0.853630 0.520880i \(-0.174396\pi\)
−0.980043 + 0.198784i \(0.936301\pi\)
\(972\) 4.86530 9.78666i 0.156055 0.313907i
\(973\) 22.3133 4.64114i 0.715332 0.148788i
\(974\) −1.19806 + 0.816821i −0.0383882 + 0.0261726i
\(975\) −1.05970 0.0502580i −0.0339377 0.00160954i
\(976\) 11.5887 + 10.7527i 0.370944 + 0.344186i
\(977\) −1.23443 + 16.4724i −0.0394931 + 0.526998i 0.942014 + 0.335573i \(0.108930\pi\)
−0.981507 + 0.191425i \(0.938689\pi\)
\(978\) −34.7493 12.5504i −1.11116 0.401317i
\(979\) −12.7431 + 22.0717i −0.407272 + 0.705416i
\(980\) −2.80687 + 10.4233i −0.0896622 + 0.332959i
\(981\) −2.61106 + 0.143276i −0.0833648 + 0.00457446i
\(982\) −26.0738 + 3.93000i −0.832050 + 0.125411i
\(983\) −11.4391 + 5.50879i −0.364851 + 0.175703i −0.607322 0.794455i \(-0.707756\pi\)
0.242471 + 0.970159i \(0.422042\pi\)
\(984\) −20.2104 + 23.0158i −0.644284 + 0.733716i
\(985\) −8.22287 + 3.95992i −0.262002 + 0.126174i
\(986\) −0.806021 10.7556i −0.0256689 0.342528i
\(987\) −25.7019 3.66170i −0.818101 0.116553i
\(988\) 0.472829 6.30947i 0.0150427 0.200731i
\(989\) −1.80600 4.60162i −0.0574275 0.146323i
\(990\) −17.8337 7.41376i −0.566792 0.235625i
\(991\) −17.0896 + 43.5437i −0.542871 + 1.38321i 0.351628 + 0.936140i \(0.385628\pi\)
−0.894498 + 0.447072i \(0.852467\pi\)
\(992\) −8.89849 + 8.25660i −0.282527 + 0.262147i
\(993\) −5.17343 28.9211i −0.164174 0.917783i
\(994\) −25.1714 + 5.23563i −0.798389 + 0.166064i
\(995\) 33.1483 + 4.99630i 1.05087 + 0.158393i
\(996\) 0.645139 + 0.892663i 0.0204420 + 0.0282851i
\(997\) −2.34024 10.2532i −0.0741161 0.324724i 0.924255 0.381775i \(-0.124687\pi\)
−0.998371 + 0.0570516i \(0.981830\pi\)
\(998\) −5.78762 10.0244i −0.183204 0.317318i
\(999\) 24.8442 + 11.7378i 0.786034 + 0.371368i
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 441.2.z.a.142.18 yes 648
9.4 even 3 441.2.y.a.436.18 yes 648
49.39 even 21 441.2.y.a.88.18 648
441.382 even 21 inner 441.2.z.a.382.18 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.18 648 49.39 even 21
441.2.y.a.436.18 yes 648 9.4 even 3
441.2.z.a.142.18 yes 648 1.1 even 1 trivial
441.2.z.a.382.18 yes 648 441.382 even 21 inner