Properties

Label 552.2.j.d.323.1
Level $552$
Weight $2$
Character 552.323
Analytic conductor $4.408$
Analytic rank $0$
Dimension $42$
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] = [552,2,Mod(323,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.j (of order \(2\), degree \(1\), 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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(42\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.1
Character \(\chi\) \(=\) 552.323
Dual form 552.2.j.d.323.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41381 - 0.0336448i) q^{2} +(0.124259 - 1.72759i) q^{3} +(1.99774 + 0.0951350i) q^{4} +1.31688 q^{5} +(-0.233803 + 2.43831i) q^{6} +2.00880i q^{7} +(-2.82122 - 0.201717i) q^{8} +(-2.96912 - 0.429336i) q^{9} +O(q^{10})\) \(q+(-1.41381 - 0.0336448i) q^{2} +(0.124259 - 1.72759i) q^{3} +(1.99774 + 0.0951350i) q^{4} +1.31688 q^{5} +(-0.233803 + 2.43831i) q^{6} +2.00880i q^{7} +(-2.82122 - 0.201717i) q^{8} +(-2.96912 - 0.429336i) q^{9} +(-1.86182 - 0.0443062i) q^{10} -2.03998i q^{11} +(0.412590 - 3.43944i) q^{12} -2.24957i q^{13} +(0.0675859 - 2.84007i) q^{14} +(0.163634 - 2.27503i) q^{15} +(3.98190 + 0.380109i) q^{16} -5.84585i q^{17} +(4.18334 + 0.706897i) q^{18} +5.65573 q^{19} +(2.63078 + 0.125281i) q^{20} +(3.47039 + 0.249612i) q^{21} +(-0.0686347 + 2.88415i) q^{22} +1.00000 q^{23} +(-0.699045 + 4.84885i) q^{24} -3.26583 q^{25} +(-0.0756864 + 3.18047i) q^{26} +(-1.11066 + 5.07607i) q^{27} +(-0.191108 + 4.01306i) q^{28} +0.456913 q^{29} +(-0.307891 + 3.21096i) q^{30} -4.61668i q^{31} +(-5.61687 - 0.671374i) q^{32} +(-3.52424 - 0.253485i) q^{33} +(-0.196683 + 8.26495i) q^{34} +2.64536i q^{35} +(-5.89067 - 1.14017i) q^{36} -10.8770i q^{37} +(-7.99615 - 0.190286i) q^{38} +(-3.88633 - 0.279529i) q^{39} +(-3.71522 - 0.265637i) q^{40} -1.82621i q^{41} +(-4.89808 - 0.469665i) q^{42} +7.89849 q^{43} +(0.194073 - 4.07534i) q^{44} +(-3.90998 - 0.565385i) q^{45} +(-1.41381 - 0.0336448i) q^{46} +5.66287 q^{47} +(1.15146 - 6.83185i) q^{48} +2.96470 q^{49} +(4.61727 + 0.109878i) q^{50} +(-10.0992 - 0.726399i) q^{51} +(0.214013 - 4.49405i) q^{52} -10.1645 q^{53} +(1.74104 - 7.13924i) q^{54} -2.68641i q^{55} +(0.405209 - 5.66729i) q^{56} +(0.702775 - 9.77077i) q^{57} +(-0.645990 - 0.0153728i) q^{58} +9.04852i q^{59} +(0.543332 - 4.52934i) q^{60} +3.19878i q^{61} +(-0.155327 + 6.52713i) q^{62} +(0.862453 - 5.96438i) q^{63} +(7.91862 + 1.13818i) q^{64} -2.96242i q^{65} +(4.97409 + 0.476954i) q^{66} +0.607466 q^{67} +(0.556145 - 11.6785i) q^{68} +(0.124259 - 1.72759i) q^{69} +(0.0890025 - 3.74004i) q^{70} -7.64044 q^{71} +(8.28995 + 1.81017i) q^{72} -13.1992 q^{73} +(-0.365954 + 15.3780i) q^{74} +(-0.405808 + 5.64200i) q^{75} +(11.2987 + 0.538058i) q^{76} +4.09792 q^{77} +(5.48514 + 0.525957i) q^{78} -9.56833i q^{79} +(5.24369 + 0.500558i) q^{80} +(8.63134 + 2.54950i) q^{81} +(-0.0614427 + 2.58193i) q^{82} -1.39264i q^{83} +(6.90917 + 0.828814i) q^{84} -7.69829i q^{85} +(-11.1670 - 0.265743i) q^{86} +(0.0567755 - 0.789357i) q^{87} +(-0.411497 + 5.75524i) q^{88} -5.14172i q^{89} +(5.50895 + 0.930899i) q^{90} +4.51895 q^{91} +(1.99774 + 0.0951350i) q^{92} +(-7.97573 - 0.573664i) q^{93} +(-8.00624 - 0.190526i) q^{94} +7.44792 q^{95} +(-1.85780 + 9.62022i) q^{96} +0.534995 q^{97} +(-4.19154 - 0.0997469i) q^{98} +(-0.875837 + 6.05694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41381 0.0336448i −0.999717 0.0237905i
\(3\) 0.124259 1.72759i 0.0717409 0.997423i
\(4\) 1.99774 + 0.0951350i 0.998868 + 0.0475675i
\(5\) 1.31688 0.588927 0.294463 0.955663i \(-0.404859\pi\)
0.294463 + 0.955663i \(0.404859\pi\)
\(6\) −0.233803 + 2.43831i −0.0954498 + 0.995434i
\(7\) 2.00880i 0.759257i 0.925139 + 0.379628i \(0.123948\pi\)
−0.925139 + 0.379628i \(0.876052\pi\)
\(8\) −2.82122 0.201717i −0.997454 0.0713176i
\(9\) −2.96912 0.429336i −0.989706 0.143112i
\(10\) −1.86182 0.0443062i −0.588760 0.0140109i
\(11\) 2.03998i 0.615077i −0.951536 0.307538i \(-0.900495\pi\)
0.951536 0.307538i \(-0.0995052\pi\)
\(12\) 0.412590 3.43944i 0.119105 0.992882i
\(13\) 2.24957i 0.623919i −0.950095 0.311959i \(-0.899015\pi\)
0.950095 0.311959i \(-0.100985\pi\)
\(14\) 0.0675859 2.84007i 0.0180631 0.759042i
\(15\) 0.163634 2.27503i 0.0422502 0.587409i
\(16\) 3.98190 + 0.380109i 0.995475 + 0.0950273i
\(17\) 5.84585i 1.41783i −0.705295 0.708914i \(-0.749185\pi\)
0.705295 0.708914i \(-0.250815\pi\)
\(18\) 4.18334 + 0.706897i 0.986022 + 0.166617i
\(19\) 5.65573 1.29751 0.648757 0.760996i \(-0.275289\pi\)
0.648757 + 0.760996i \(0.275289\pi\)
\(20\) 2.63078 + 0.125281i 0.588260 + 0.0280138i
\(21\) 3.47039 + 0.249612i 0.757300 + 0.0544698i
\(22\) −0.0686347 + 2.88415i −0.0146330 + 0.614903i
\(23\) 1.00000 0.208514
\(24\) −0.699045 + 4.84885i −0.142692 + 0.989767i
\(25\) −3.26583 −0.653165
\(26\) −0.0756864 + 3.18047i −0.0148433 + 0.623742i
\(27\) −1.11066 + 5.07607i −0.213746 + 0.976889i
\(28\) −0.191108 + 4.01306i −0.0361159 + 0.758397i
\(29\) 0.456913 0.0848466 0.0424233 0.999100i \(-0.486492\pi\)
0.0424233 + 0.999100i \(0.486492\pi\)
\(30\) −0.307891 + 3.21096i −0.0562129 + 0.586238i
\(31\) 4.61668i 0.829181i −0.910008 0.414590i \(-0.863925\pi\)
0.910008 0.414590i \(-0.136075\pi\)
\(32\) −5.61687 0.671374i −0.992932 0.118683i
\(33\) −3.52424 0.253485i −0.613492 0.0441262i
\(34\) −0.196683 + 8.26495i −0.0337308 + 1.41743i
\(35\) 2.64536i 0.447147i
\(36\) −5.89067 1.14017i −0.981779 0.190028i
\(37\) 10.8770i 1.78816i −0.447904 0.894082i \(-0.647829\pi\)
0.447904 0.894082i \(-0.352171\pi\)
\(38\) −7.99615 0.190286i −1.29715 0.0308685i
\(39\) −3.88633 0.279529i −0.622311 0.0447605i
\(40\) −3.71522 0.265637i −0.587427 0.0420008i
\(41\) 1.82621i 0.285207i −0.989780 0.142603i \(-0.954453\pi\)
0.989780 0.142603i \(-0.0455473\pi\)
\(42\) −4.89808 0.469665i −0.755790 0.0724709i
\(43\) 7.89849 1.20451 0.602254 0.798304i \(-0.294269\pi\)
0.602254 + 0.798304i \(0.294269\pi\)
\(44\) 0.194073 4.07534i 0.0292577 0.614380i
\(45\) −3.90998 0.565385i −0.582865 0.0842826i
\(46\) −1.41381 0.0336448i −0.208455 0.00496066i
\(47\) 5.66287 0.826014 0.413007 0.910728i \(-0.364479\pi\)
0.413007 + 0.910728i \(0.364479\pi\)
\(48\) 1.15146 6.83185i 0.166199 0.986092i
\(49\) 2.96470 0.423529
\(50\) 4.61727 + 0.109878i 0.652980 + 0.0155391i
\(51\) −10.0992 0.726399i −1.41417 0.101716i
\(52\) 0.214013 4.49405i 0.0296782 0.623212i
\(53\) −10.1645 −1.39620 −0.698099 0.716002i \(-0.745970\pi\)
−0.698099 + 0.716002i \(0.745970\pi\)
\(54\) 1.74104 7.13924i 0.236926 0.971528i
\(55\) 2.68641i 0.362235i
\(56\) 0.405209 5.66729i 0.0541483 0.757323i
\(57\) 0.702775 9.77077i 0.0930848 1.29417i
\(58\) −0.645990 0.0153728i −0.0848226 0.00201854i
\(59\) 9.04852i 1.17802i 0.808127 + 0.589008i \(0.200481\pi\)
−0.808127 + 0.589008i \(0.799519\pi\)
\(60\) 0.543332 4.52934i 0.0701439 0.584735i
\(61\) 3.19878i 0.409561i 0.978808 + 0.204781i \(0.0656481\pi\)
−0.978808 + 0.204781i \(0.934352\pi\)
\(62\) −0.155327 + 6.52713i −0.0197266 + 0.828946i
\(63\) 0.862453 5.96438i 0.108659 0.751441i
\(64\) 7.91862 + 1.13818i 0.989828 + 0.142272i
\(65\) 2.96242i 0.367443i
\(66\) 4.97409 + 0.476954i 0.612268 + 0.0587089i
\(67\) 0.607466 0.0742138 0.0371069 0.999311i \(-0.488186\pi\)
0.0371069 + 0.999311i \(0.488186\pi\)
\(68\) 0.556145 11.6785i 0.0674425 1.41622i
\(69\) 0.124259 1.72759i 0.0149590 0.207977i
\(70\) 0.0890025 3.74004i 0.0106378 0.447020i
\(71\) −7.64044 −0.906754 −0.453377 0.891319i \(-0.649781\pi\)
−0.453377 + 0.891319i \(0.649781\pi\)
\(72\) 8.28995 + 1.81017i 0.976980 + 0.213331i
\(73\) −13.1992 −1.54485 −0.772423 0.635108i \(-0.780955\pi\)
−0.772423 + 0.635108i \(0.780955\pi\)
\(74\) −0.365954 + 15.3780i −0.0425413 + 1.78766i
\(75\) −0.405808 + 5.64200i −0.0468586 + 0.651482i
\(76\) 11.2987 + 0.538058i 1.29605 + 0.0617195i
\(77\) 4.09792 0.467001
\(78\) 5.48514 + 0.525957i 0.621070 + 0.0595529i
\(79\) 9.56833i 1.07652i −0.842779 0.538260i \(-0.819082\pi\)
0.842779 0.538260i \(-0.180918\pi\)
\(80\) 5.24369 + 0.500558i 0.586262 + 0.0559641i
\(81\) 8.63134 + 2.54950i 0.959038 + 0.283278i
\(82\) −0.0614427 + 2.58193i −0.00678521 + 0.285126i
\(83\) 1.39264i 0.152862i −0.997075 0.0764312i \(-0.975647\pi\)
0.997075 0.0764312i \(-0.0243526\pi\)
\(84\) 6.90917 + 0.828814i 0.753852 + 0.0904310i
\(85\) 7.69829i 0.834997i
\(86\) −11.1670 0.265743i −1.20417 0.0286558i
\(87\) 0.0567755 0.789357i 0.00608697 0.0846280i
\(88\) −0.411497 + 5.75524i −0.0438658 + 0.613511i
\(89\) 5.14172i 0.545022i −0.962153 0.272511i \(-0.912146\pi\)
0.962153 0.272511i \(-0.0878541\pi\)
\(90\) 5.50895 + 0.930899i 0.580695 + 0.0981254i
\(91\) 4.51895 0.473714
\(92\) 1.99774 + 0.0951350i 0.208278 + 0.00991851i
\(93\) −7.97573 0.573664i −0.827044 0.0594862i
\(94\) −8.00624 0.190526i −0.825780 0.0196513i
\(95\) 7.44792 0.764141
\(96\) −1.85780 + 9.62022i −0.189611 + 0.981859i
\(97\) 0.534995 0.0543205 0.0271602 0.999631i \(-0.491354\pi\)
0.0271602 + 0.999631i \(0.491354\pi\)
\(98\) −4.19154 0.0997469i −0.423409 0.0100760i
\(99\) −0.875837 + 6.05694i −0.0880249 + 0.608745i
\(100\) −6.52426 0.310694i −0.652426 0.0310694i
\(101\) 7.58160 0.754398 0.377199 0.926132i \(-0.376887\pi\)
0.377199 + 0.926132i \(0.376887\pi\)
\(102\) 14.2540 + 1.36678i 1.41135 + 0.135331i
\(103\) 12.5721i 1.23877i 0.785088 + 0.619384i \(0.212617\pi\)
−0.785088 + 0.619384i \(0.787383\pi\)
\(104\) −0.453776 + 6.34655i −0.0444964 + 0.622330i
\(105\) 4.57009 + 0.328709i 0.445995 + 0.0320787i
\(106\) 14.3707 + 0.341982i 1.39580 + 0.0332162i
\(107\) 12.4602i 1.20458i 0.798279 + 0.602288i \(0.205744\pi\)
−0.798279 + 0.602288i \(0.794256\pi\)
\(108\) −2.70171 + 10.0350i −0.259972 + 0.965616i
\(109\) 12.2589i 1.17419i 0.809517 + 0.587096i \(0.199729\pi\)
−0.809517 + 0.587096i \(0.800271\pi\)
\(110\) −0.0903837 + 3.79808i −0.00861775 + 0.362133i
\(111\) −18.7909 1.35156i −1.78356 0.128284i
\(112\) −0.763565 + 7.99886i −0.0721501 + 0.755821i
\(113\) 2.67442i 0.251589i 0.992056 + 0.125794i \(0.0401479\pi\)
−0.992056 + 0.125794i \(0.959852\pi\)
\(114\) −1.32233 + 13.7904i −0.123847 + 1.29159i
\(115\) 1.31688 0.122800
\(116\) 0.912792 + 0.0434684i 0.0847506 + 0.00403594i
\(117\) −0.965822 + 6.67924i −0.0892903 + 0.617496i
\(118\) 0.304436 12.7929i 0.0280256 1.17768i
\(119\) 11.7432 1.07650
\(120\) −0.920559 + 6.38536i −0.0840352 + 0.582901i
\(121\) 6.83849 0.621681
\(122\) 0.107622 4.52247i 0.00974366 0.409445i
\(123\) −3.15495 0.226923i −0.284472 0.0204610i
\(124\) 0.439208 9.22292i 0.0394420 0.828242i
\(125\) −10.8851 −0.973593
\(126\) −1.42002 + 8.40350i −0.126505 + 0.748644i
\(127\) 15.1862i 1.34755i −0.738935 0.673777i \(-0.764671\pi\)
0.738935 0.673777i \(-0.235329\pi\)
\(128\) −11.1572 1.87559i −0.986163 0.165780i
\(129\) 0.981457 13.6453i 0.0864125 1.20140i
\(130\) −0.0996700 + 4.18830i −0.00874163 + 0.367339i
\(131\) 14.0848i 1.23060i 0.788294 + 0.615299i \(0.210965\pi\)
−0.788294 + 0.615299i \(0.789035\pi\)
\(132\) −7.01639 0.841676i −0.610698 0.0732585i
\(133\) 11.3613i 0.985146i
\(134\) −0.858844 0.0204381i −0.0741928 0.00176558i
\(135\) −1.46260 + 6.68457i −0.125881 + 0.575316i
\(136\) −1.17921 + 16.4925i −0.101116 + 1.41422i
\(137\) 3.39029i 0.289652i 0.989457 + 0.144826i \(0.0462622\pi\)
−0.989457 + 0.144826i \(0.953738\pi\)
\(138\) −0.233803 + 2.43831i −0.0199027 + 0.207562i
\(139\) 7.73381 0.655973 0.327987 0.944682i \(-0.393630\pi\)
0.327987 + 0.944682i \(0.393630\pi\)
\(140\) −0.251666 + 5.28472i −0.0212696 + 0.446641i
\(141\) 0.703661 9.78310i 0.0592590 0.823886i
\(142\) 10.8022 + 0.257061i 0.906497 + 0.0215721i
\(143\) −4.58908 −0.383758
\(144\) −11.6595 2.83816i −0.971628 0.236514i
\(145\) 0.601700 0.0499685
\(146\) 18.6612 + 0.444084i 1.54441 + 0.0367526i
\(147\) 0.368391 5.12179i 0.0303844 0.422438i
\(148\) 1.03478 21.7293i 0.0850584 1.78614i
\(149\) 18.4328 1.51007 0.755037 0.655682i \(-0.227619\pi\)
0.755037 + 0.655682i \(0.227619\pi\)
\(150\) 0.763560 7.96308i 0.0623445 0.650183i
\(151\) 12.3058i 1.00143i 0.865611 + 0.500716i \(0.166930\pi\)
−0.865611 + 0.500716i \(0.833070\pi\)
\(152\) −15.9561 1.14085i −1.29421 0.0925355i
\(153\) −2.50984 + 17.3570i −0.202908 + 1.40323i
\(154\) −5.79369 0.137874i −0.466869 0.0111102i
\(155\) 6.07962i 0.488327i
\(156\) −7.73727 0.928151i −0.619477 0.0743116i
\(157\) 4.67084i 0.372773i −0.982476 0.186387i \(-0.940322\pi\)
0.982476 0.186387i \(-0.0596777\pi\)
\(158\) −0.321925 + 13.5278i −0.0256109 + 1.07622i
\(159\) −1.26303 + 17.5600i −0.100164 + 1.39260i
\(160\) −7.39675 0.884119i −0.584765 0.0698957i
\(161\) 2.00880i 0.158316i
\(162\) −12.1173 3.89492i −0.952027 0.306014i
\(163\) −11.8718 −0.929869 −0.464935 0.885345i \(-0.653922\pi\)
−0.464935 + 0.885345i \(0.653922\pi\)
\(164\) 0.173737 3.64830i 0.0135666 0.284884i
\(165\) −4.64101 0.333810i −0.361302 0.0259871i
\(166\) −0.0468552 + 1.96894i −0.00363667 + 0.152819i
\(167\) 5.07003 0.392331 0.196165 0.980571i \(-0.437151\pi\)
0.196165 + 0.980571i \(0.437151\pi\)
\(168\) −9.74039 1.40425i −0.751487 0.108340i
\(169\) 7.93943 0.610725
\(170\) −0.259008 + 10.8839i −0.0198650 + 0.834761i
\(171\) −16.7925 2.42821i −1.28416 0.185690i
\(172\) 15.7791 + 0.751423i 1.20314 + 0.0572954i
\(173\) 23.4030 1.77930 0.889649 0.456645i \(-0.150949\pi\)
0.889649 + 0.456645i \(0.150949\pi\)
\(174\) −0.106828 + 1.11409i −0.00809859 + 0.0844592i
\(175\) 6.56040i 0.495920i
\(176\) 0.775415 8.12299i 0.0584491 0.612293i
\(177\) 15.6321 + 1.12436i 1.17498 + 0.0845120i
\(178\) −0.172992 + 7.26944i −0.0129663 + 0.544867i
\(179\) 15.0656i 1.12605i 0.826438 + 0.563027i \(0.190363\pi\)
−0.826438 + 0.563027i \(0.809637\pi\)
\(180\) −7.75731 1.50146i −0.578196 0.111913i
\(181\) 11.7169i 0.870911i 0.900210 + 0.435455i \(0.143413\pi\)
−0.900210 + 0.435455i \(0.856587\pi\)
\(182\) −6.38895 0.152039i −0.473580 0.0112699i
\(183\) 5.52617 + 0.397476i 0.408506 + 0.0293823i
\(184\) −2.82122 0.201717i −0.207983 0.0148707i
\(185\) 14.3237i 1.05310i
\(186\) 11.2569 + 1.07940i 0.825395 + 0.0791451i
\(187\) −11.9254 −0.872073
\(188\) 11.3129 + 0.538737i 0.825079 + 0.0392914i
\(189\) −10.1968 2.23109i −0.741710 0.162288i
\(190\) −10.5300 0.250584i −0.763925 0.0181793i
\(191\) 15.7455 1.13931 0.569654 0.821885i \(-0.307077\pi\)
0.569654 + 0.821885i \(0.307077\pi\)
\(192\) 2.95026 13.5387i 0.212916 0.977070i
\(193\) −14.5266 −1.04565 −0.522824 0.852440i \(-0.675122\pi\)
−0.522824 + 0.852440i \(0.675122\pi\)
\(194\) −0.756383 0.0179998i −0.0543051 0.00129231i
\(195\) −5.11783 0.368107i −0.366496 0.0263607i
\(196\) 5.92270 + 0.282047i 0.423050 + 0.0201462i
\(197\) 17.5727 1.25200 0.626001 0.779822i \(-0.284690\pi\)
0.626001 + 0.779822i \(0.284690\pi\)
\(198\) 1.44205 8.53392i 0.102482 0.606479i
\(199\) 17.0863i 1.21122i 0.795763 + 0.605609i \(0.207070\pi\)
−0.795763 + 0.605609i \(0.792930\pi\)
\(200\) 9.21363 + 0.658771i 0.651502 + 0.0465821i
\(201\) 0.0754831 1.04945i 0.00532416 0.0740226i
\(202\) −10.7190 0.255082i −0.754184 0.0179475i
\(203\) 0.917849i 0.0644204i
\(204\) −20.1065 2.41194i −1.40774 0.168870i
\(205\) 2.40491i 0.167966i
\(206\) 0.422987 17.7746i 0.0294709 1.23842i
\(207\) −2.96912 0.429336i −0.206368 0.0298409i
\(208\) 0.855082 8.95756i 0.0592893 0.621095i
\(209\) 11.5376i 0.798071i
\(210\) −6.45019 0.618493i −0.445105 0.0426801i
\(211\) 2.15666 0.148471 0.0742354 0.997241i \(-0.476348\pi\)
0.0742354 + 0.997241i \(0.476348\pi\)
\(212\) −20.3059 0.966996i −1.39462 0.0664136i
\(213\) −0.949393 + 13.1995i −0.0650513 + 0.904417i
\(214\) 0.419222 17.6164i 0.0286574 1.20423i
\(215\) 10.4014 0.709367
\(216\) 4.15734 14.0967i 0.282871 0.959158i
\(217\) 9.27402 0.629561
\(218\) 0.412449 17.3318i 0.0279346 1.17386i
\(219\) −1.64011 + 22.8027i −0.110829 + 1.54087i
\(220\) 0.255571 5.36674i 0.0172306 0.361825i
\(221\) −13.1507 −0.884609
\(222\) 26.5214 + 2.54307i 1.78000 + 0.170680i
\(223\) 20.3814i 1.36484i 0.730961 + 0.682419i \(0.239072\pi\)
−0.730961 + 0.682419i \(0.760928\pi\)
\(224\) 1.34866 11.2832i 0.0901110 0.753890i
\(225\) 9.69662 + 1.40214i 0.646442 + 0.0934758i
\(226\) 0.0899805 3.78114i 0.00598542 0.251517i
\(227\) 15.8343i 1.05096i −0.850806 0.525481i \(-0.823886\pi\)
0.850806 0.525481i \(-0.176114\pi\)
\(228\) 2.33350 19.4526i 0.154540 1.28828i
\(229\) 11.7168i 0.774269i 0.922023 + 0.387135i \(0.126535\pi\)
−0.922023 + 0.387135i \(0.873465\pi\)
\(230\) −1.86182 0.0443062i −0.122765 0.00292146i
\(231\) 0.509203 7.07951i 0.0335031 0.465798i
\(232\) −1.28905 0.0921669i −0.0846306 0.00605105i
\(233\) 23.0711i 1.51144i −0.654897 0.755719i \(-0.727288\pi\)
0.654897 0.755719i \(-0.272712\pi\)
\(234\) 1.59021 9.41071i 0.103956 0.615197i
\(235\) 7.45732 0.486462
\(236\) −0.860830 + 18.0765i −0.0560353 + 1.17668i
\(237\) −16.5301 1.18895i −1.07375 0.0772306i
\(238\) −16.6027 0.395097i −1.07619 0.0256103i
\(239\) −13.1778 −0.852401 −0.426201 0.904629i \(-0.640148\pi\)
−0.426201 + 0.904629i \(0.640148\pi\)
\(240\) 1.51633 8.99673i 0.0978789 0.580736i
\(241\) −5.44379 −0.350666 −0.175333 0.984509i \(-0.556100\pi\)
−0.175333 + 0.984509i \(0.556100\pi\)
\(242\) −9.66834 0.230080i −0.621505 0.0147901i
\(243\) 5.47701 14.5946i 0.351350 0.936244i
\(244\) −0.304316 + 6.39031i −0.0194818 + 0.409098i
\(245\) 3.90416 0.249428
\(246\) 4.45287 + 0.426975i 0.283905 + 0.0272229i
\(247\) 12.7230i 0.809543i
\(248\) −0.931261 + 13.0247i −0.0591352 + 0.827069i
\(249\) −2.40591 0.173048i −0.152469 0.0109665i
\(250\) 15.3895 + 0.366227i 0.973318 + 0.0231623i
\(251\) 10.8606i 0.685517i −0.939424 0.342758i \(-0.888639\pi\)
0.939424 0.342758i \(-0.111361\pi\)
\(252\) 2.29037 11.8332i 0.144280 0.745422i
\(253\) 2.03998i 0.128252i
\(254\) −0.510935 + 21.4704i −0.0320589 + 1.34717i
\(255\) −13.2995 0.956581i −0.832846 0.0599034i
\(256\) 15.7110 + 3.02711i 0.981940 + 0.189195i
\(257\) 1.45048i 0.0904784i 0.998976 + 0.0452392i \(0.0144050\pi\)
−0.998976 + 0.0452392i \(0.985595\pi\)
\(258\) −1.84669 + 19.2589i −0.114970 + 1.19901i
\(259\) 21.8497 1.35768
\(260\) 0.281829 5.91813i 0.0174783 0.367027i
\(261\) −1.35663 0.196169i −0.0839732 0.0121426i
\(262\) 0.473882 19.9133i 0.0292765 1.23025i
\(263\) 5.61383 0.346164 0.173082 0.984907i \(-0.444627\pi\)
0.173082 + 0.984907i \(0.444627\pi\)
\(264\) 9.89155 + 1.42604i 0.608783 + 0.0877665i
\(265\) −13.3854 −0.822258
\(266\) 0.382247 16.0627i 0.0234371 0.984867i
\(267\) −8.88278 0.638905i −0.543617 0.0391003i
\(268\) 1.21356 + 0.0577913i 0.0741298 + 0.00353016i
\(269\) −2.95147 −0.179954 −0.0899772 0.995944i \(-0.528679\pi\)
−0.0899772 + 0.995944i \(0.528679\pi\)
\(270\) 2.29275 9.40153i 0.139532 0.572159i
\(271\) 8.48737i 0.515571i −0.966202 0.257785i \(-0.917007\pi\)
0.966202 0.257785i \(-0.0829928\pi\)
\(272\) 2.22206 23.2776i 0.134732 1.41141i
\(273\) 0.561519 7.80688i 0.0339847 0.472494i
\(274\) 0.114066 4.79323i 0.00689095 0.289570i
\(275\) 6.66221i 0.401747i
\(276\) 0.412590 3.43944i 0.0248350 0.207030i
\(277\) 31.0685i 1.86673i −0.358935 0.933363i \(-0.616860\pi\)
0.358935 0.933363i \(-0.383140\pi\)
\(278\) −10.9342 0.260203i −0.655788 0.0156059i
\(279\) −1.98211 + 13.7075i −0.118666 + 0.820646i
\(280\) 0.533612 7.46314i 0.0318894 0.446008i
\(281\) 19.5511i 1.16632i 0.812357 + 0.583161i \(0.198184\pi\)
−0.812357 + 0.583161i \(0.801816\pi\)
\(282\) −1.32400 + 13.8078i −0.0788428 + 0.822243i
\(283\) −4.97196 −0.295553 −0.147776 0.989021i \(-0.547212\pi\)
−0.147776 + 0.989021i \(0.547212\pi\)
\(284\) −15.2636 0.726873i −0.905727 0.0431320i
\(285\) 0.925471 12.8669i 0.0548202 0.762172i
\(286\) 6.48810 + 0.154399i 0.383649 + 0.00912978i
\(287\) 3.66851 0.216545
\(288\) 16.3889 + 4.40492i 0.965726 + 0.259562i
\(289\) −17.1740 −1.01024
\(290\) −0.850691 0.0202441i −0.0499543 0.00118877i
\(291\) 0.0664778 0.924250i 0.00389700 0.0541805i
\(292\) −26.3685 1.25570i −1.54310 0.0734845i
\(293\) −3.48481 −0.203585 −0.101792 0.994806i \(-0.532458\pi\)
−0.101792 + 0.994806i \(0.532458\pi\)
\(294\) −0.693157 + 7.22886i −0.0404258 + 0.421595i
\(295\) 11.9158i 0.693766i
\(296\) −2.19407 + 30.6864i −0.127527 + 1.78361i
\(297\) 10.3551 + 2.26571i 0.600862 + 0.131470i
\(298\) −26.0606 0.620169i −1.50965 0.0359254i
\(299\) 2.24957i 0.130096i
\(300\) −1.34745 + 11.2326i −0.0777950 + 0.648516i
\(301\) 15.8665i 0.914531i
\(302\) 0.414027 17.3981i 0.0238246 1.00115i
\(303\) 0.942082 13.0979i 0.0541212 0.752454i
\(304\) 22.5206 + 2.14980i 1.29164 + 0.123299i
\(305\) 4.21241i 0.241202i
\(306\) 4.13242 24.4552i 0.236234 1.39801i
\(307\) 28.0776 1.60247 0.801237 0.598347i \(-0.204175\pi\)
0.801237 + 0.598347i \(0.204175\pi\)
\(308\) 8.18656 + 0.389855i 0.466473 + 0.0222141i
\(309\) 21.7194 + 1.56220i 1.23558 + 0.0888703i
\(310\) −0.204548 + 8.59545i −0.0116175 + 0.488189i
\(311\) −20.3473 −1.15379 −0.576894 0.816819i \(-0.695736\pi\)
−0.576894 + 0.816819i \(0.695736\pi\)
\(312\) 10.9078 + 1.57255i 0.617534 + 0.0890282i
\(313\) −20.8538 −1.17873 −0.589363 0.807868i \(-0.700621\pi\)
−0.589363 + 0.807868i \(0.700621\pi\)
\(314\) −0.157149 + 6.60369i −0.00886845 + 0.372668i
\(315\) 1.13575 7.85438i 0.0639921 0.442544i
\(316\) 0.910282 19.1150i 0.0512074 1.07530i
\(317\) −7.34290 −0.412418 −0.206209 0.978508i \(-0.566113\pi\)
−0.206209 + 0.978508i \(0.566113\pi\)
\(318\) 2.37649 24.7841i 0.133267 1.38982i
\(319\) 0.932093i 0.0521872i
\(320\) 10.4279 + 1.49884i 0.582936 + 0.0837878i
\(321\) 21.5261 + 1.54829i 1.20147 + 0.0864173i
\(322\) 0.0675859 2.84007i 0.00376641 0.158271i
\(323\) 33.0626i 1.83965i
\(324\) 17.0006 + 5.91437i 0.944477 + 0.328576i
\(325\) 7.34670i 0.407522i
\(326\) 16.7845 + 0.399424i 0.929606 + 0.0221220i
\(327\) 21.1784 + 1.52328i 1.17117 + 0.0842376i
\(328\) −0.368378 + 5.15216i −0.0203403 + 0.284481i
\(329\) 11.3756i 0.627157i
\(330\) 6.55029 + 0.628091i 0.360581 + 0.0345753i
\(331\) 19.9784 1.09811 0.549056 0.835786i \(-0.314988\pi\)
0.549056 + 0.835786i \(0.314988\pi\)
\(332\) 0.132489 2.78213i 0.00727128 0.152689i
\(333\) −4.66988 + 32.2950i −0.255908 + 1.76976i
\(334\) −7.16808 0.170580i −0.392220 0.00933373i
\(335\) 0.799960 0.0437065
\(336\) 13.7238 + 2.31305i 0.748697 + 0.126187i
\(337\) −29.8819 −1.62777 −0.813887 0.581024i \(-0.802652\pi\)
−0.813887 + 0.581024i \(0.802652\pi\)
\(338\) −11.2249 0.267121i −0.610553 0.0145294i
\(339\) 4.62030 + 0.332321i 0.250940 + 0.0180492i
\(340\) 0.732377 15.3792i 0.0397187 0.834052i
\(341\) −9.41794 −0.510010
\(342\) 23.6598 + 3.99802i 1.27938 + 0.216188i
\(343\) 20.0171i 1.08082i
\(344\) −22.2834 1.59326i −1.20144 0.0859026i
\(345\) 0.163634 2.27503i 0.00880977 0.122483i
\(346\) −33.0875 0.787390i −1.77879 0.0423303i
\(347\) 20.6960i 1.11102i −0.831509 0.555511i \(-0.812523\pi\)
0.831509 0.555511i \(-0.187477\pi\)
\(348\) 0.188518 1.57153i 0.0101056 0.0842426i
\(349\) 3.85538i 0.206374i 0.994662 + 0.103187i \(0.0329040\pi\)
−0.994662 + 0.103187i \(0.967096\pi\)
\(350\) −0.220724 + 9.27519i −0.0117982 + 0.495780i
\(351\) 11.4190 + 2.49850i 0.609499 + 0.133360i
\(352\) −1.36959 + 11.4583i −0.0729993 + 0.610729i
\(353\) 17.3265i 0.922198i 0.887349 + 0.461099i \(0.152545\pi\)
−0.887349 + 0.461099i \(0.847455\pi\)
\(354\) −22.0631 2.11557i −1.17264 0.112441i
\(355\) −10.0616 −0.534012
\(356\) 0.489158 10.2718i 0.0259253 0.544405i
\(357\) 1.45919 20.2874i 0.0772288 1.07372i
\(358\) 0.506879 21.2999i 0.0267894 1.12574i
\(359\) −6.12585 −0.323310 −0.161655 0.986847i \(-0.551683\pi\)
−0.161655 + 0.986847i \(0.551683\pi\)
\(360\) 10.9169 + 2.38378i 0.575370 + 0.125636i
\(361\) 12.9873 0.683542
\(362\) 0.394213 16.5655i 0.0207194 0.870664i
\(363\) 0.849743 11.8141i 0.0445999 0.620079i
\(364\) 9.02767 + 0.429910i 0.473178 + 0.0225334i
\(365\) −17.3817 −0.909802
\(366\) −7.79960 0.747884i −0.407691 0.0390925i
\(367\) 18.2451i 0.952389i −0.879340 0.476194i \(-0.842016\pi\)
0.879340 0.476194i \(-0.157984\pi\)
\(368\) 3.98190 + 0.380109i 0.207571 + 0.0198146i
\(369\) −0.784060 + 5.42225i −0.0408165 + 0.282271i
\(370\) −0.481917 + 20.2510i −0.0250537 + 1.05280i
\(371\) 20.4184i 1.06007i
\(372\) −15.8788 1.90480i −0.823278 0.0987593i
\(373\) 26.3578i 1.36476i 0.730999 + 0.682378i \(0.239054\pi\)
−0.730999 + 0.682378i \(0.760946\pi\)
\(374\) 16.8603 + 0.401228i 0.871826 + 0.0207470i
\(375\) −1.35257 + 18.8050i −0.0698465 + 0.971085i
\(376\) −15.9762 1.14229i −0.823911 0.0589093i
\(377\) 1.02786i 0.0529374i
\(378\) 14.3413 + 3.49742i 0.737639 + 0.179888i
\(379\) −4.98877 −0.256256 −0.128128 0.991758i \(-0.540897\pi\)
−0.128128 + 0.991758i \(0.540897\pi\)
\(380\) 14.8790 + 0.708558i 0.763276 + 0.0363483i
\(381\) −26.2354 1.88701i −1.34408 0.0966747i
\(382\) −22.2613 0.529756i −1.13899 0.0271047i
\(383\) −6.02210 −0.307715 −0.153857 0.988093i \(-0.549170\pi\)
−0.153857 + 0.988093i \(0.549170\pi\)
\(384\) −4.62662 + 19.0419i −0.236101 + 0.971728i
\(385\) 5.39647 0.275030
\(386\) 20.5379 + 0.488745i 1.04535 + 0.0248765i
\(387\) −23.4516 3.39111i −1.19211 0.172380i
\(388\) 1.06878 + 0.0508967i 0.0542590 + 0.00258389i
\(389\) 11.5392 0.585061 0.292531 0.956256i \(-0.405503\pi\)
0.292531 + 0.956256i \(0.405503\pi\)
\(390\) 7.22328 + 0.692623i 0.365765 + 0.0350723i
\(391\) 5.84585i 0.295638i
\(392\) −8.36410 0.598030i −0.422451 0.0302051i
\(393\) 24.3328 + 1.75017i 1.22743 + 0.0882842i
\(394\) −24.8445 0.591230i −1.25165 0.0297857i
\(395\) 12.6003i 0.633992i
\(396\) −2.32592 + 12.0168i −0.116882 + 0.603869i
\(397\) 24.0649i 1.20778i 0.797066 + 0.603892i \(0.206384\pi\)
−0.797066 + 0.603892i \(0.793616\pi\)
\(398\) 0.574866 24.1569i 0.0288154 1.21087i
\(399\) 19.6276 + 1.41174i 0.982608 + 0.0706753i
\(400\) −13.0042 1.24137i −0.650209 0.0620685i
\(401\) 25.0724i 1.25205i 0.779801 + 0.626027i \(0.215320\pi\)
−0.779801 + 0.626027i \(0.784680\pi\)
\(402\) −0.142028 + 1.48119i −0.00708369 + 0.0738749i
\(403\) −10.3856 −0.517341
\(404\) 15.1460 + 0.721276i 0.753544 + 0.0358848i
\(405\) 11.3664 + 3.35739i 0.564803 + 0.166830i
\(406\) 0.0308809 1.29767i 0.00153259 0.0644021i
\(407\) −22.1888 −1.09986
\(408\) 28.3457 + 4.08652i 1.40332 + 0.202313i
\(409\) −26.2389 −1.29743 −0.648716 0.761031i \(-0.724694\pi\)
−0.648716 + 0.761031i \(0.724694\pi\)
\(410\) −0.0809127 + 3.40009i −0.00399599 + 0.167918i
\(411\) 5.85702 + 0.421273i 0.288905 + 0.0207799i
\(412\) −1.19605 + 25.1158i −0.0589251 + 1.23737i
\(413\) −18.1767 −0.894417
\(414\) 4.18334 + 0.706897i 0.205600 + 0.0347421i
\(415\) 1.83395i 0.0900248i
\(416\) −1.51030 + 12.6356i −0.0740487 + 0.619509i
\(417\) 0.960995 13.3608i 0.0470601 0.654283i
\(418\) −0.388179 + 16.3120i −0.0189865 + 0.797845i
\(419\) 5.67054i 0.277024i −0.990361 0.138512i \(-0.955768\pi\)
0.990361 0.138512i \(-0.0442320\pi\)
\(420\) 9.09855 + 1.09145i 0.443964 + 0.0532572i
\(421\) 39.0265i 1.90204i −0.309133 0.951019i \(-0.600039\pi\)
0.309133 0.951019i \(-0.399961\pi\)
\(422\) −3.04912 0.0725605i −0.148429 0.00353219i
\(423\) −16.8137 2.43127i −0.817511 0.118213i
\(424\) 28.6763 + 2.05034i 1.39264 + 0.0995734i
\(425\) 19.0915i 0.926076i
\(426\) 1.78636 18.6297i 0.0865494 0.902614i
\(427\) −6.42572 −0.310962
\(428\) −1.18540 + 24.8922i −0.0572986 + 1.20321i
\(429\) −0.570234 + 7.92803i −0.0275311 + 0.382769i
\(430\) −14.7056 0.349952i −0.709167 0.0168762i
\(431\) −36.3903 −1.75286 −0.876431 0.481528i \(-0.840082\pi\)
−0.876431 + 0.481528i \(0.840082\pi\)
\(432\) −6.35198 + 19.7902i −0.305610 + 0.952157i
\(433\) 5.92766 0.284865 0.142433 0.989804i \(-0.454508\pi\)
0.142433 + 0.989804i \(0.454508\pi\)
\(434\) −13.1117 0.312023i −0.629383 0.0149776i
\(435\) 0.0747666 1.03949i 0.00358478 0.0498397i
\(436\) −1.16625 + 24.4901i −0.0558534 + 1.17286i
\(437\) 5.65573 0.270550
\(438\) 3.08601 32.1836i 0.147455 1.53779i
\(439\) 11.6261i 0.554885i −0.960742 0.277442i \(-0.910513\pi\)
0.960742 0.277442i \(-0.0894867\pi\)
\(440\) −0.541893 + 7.57896i −0.0258337 + 0.361313i
\(441\) −8.80256 1.27286i −0.419170 0.0606121i
\(442\) 18.5926 + 0.442452i 0.884359 + 0.0210453i
\(443\) 21.8676i 1.03896i 0.854483 + 0.519480i \(0.173874\pi\)
−0.854483 + 0.519480i \(0.826126\pi\)
\(444\) −37.4107 4.48774i −1.77543 0.212978i
\(445\) 6.77104i 0.320978i
\(446\) 0.685728 28.8155i 0.0324701 1.36445i
\(447\) 2.29044 31.8443i 0.108334 1.50618i
\(448\) −2.28637 + 15.9070i −0.108021 + 0.751533i
\(449\) 37.9704i 1.79194i 0.444119 + 0.895968i \(0.353517\pi\)
−0.444119 + 0.895968i \(0.646483\pi\)
\(450\) −13.6620 2.30860i −0.644035 0.108829i
\(451\) −3.72544 −0.175424
\(452\) −0.254431 + 5.34279i −0.0119674 + 0.251304i
\(453\) 21.2594 + 1.52911i 0.998853 + 0.0718437i
\(454\) −0.532743 + 22.3868i −0.0250029 + 1.05066i
\(455\) 5.95092 0.278983
\(456\) −3.95361 + 27.4238i −0.185145 + 1.28424i
\(457\) −4.91821 −0.230064 −0.115032 0.993362i \(-0.536697\pi\)
−0.115032 + 0.993362i \(0.536697\pi\)
\(458\) 0.394210 16.5654i 0.0184202 0.774050i
\(459\) 29.6739 + 6.49273i 1.38506 + 0.303055i
\(460\) 2.63078 + 0.125281i 0.122661 + 0.00584128i
\(461\) 12.9620 0.603701 0.301851 0.953355i \(-0.402396\pi\)
0.301851 + 0.953355i \(0.402396\pi\)
\(462\) −0.958107 + 9.99198i −0.0445752 + 0.464869i
\(463\) 9.88660i 0.459469i 0.973253 + 0.229735i \(0.0737858\pi\)
−0.973253 + 0.229735i \(0.926214\pi\)
\(464\) 1.81938 + 0.173677i 0.0844626 + 0.00806274i
\(465\) −10.5031 0.755447i −0.487069 0.0350330i
\(466\) −0.776222 + 32.6182i −0.0359578 + 1.51101i
\(467\) 38.1940i 1.76741i 0.468048 + 0.883703i \(0.344957\pi\)
−0.468048 + 0.883703i \(0.655043\pi\)
\(468\) −2.56489 + 13.2515i −0.118562 + 0.612550i
\(469\) 1.22028i 0.0563473i
\(470\) −10.5433 0.250900i −0.486324 0.0115732i
\(471\) −8.06928 0.580393i −0.371813 0.0267431i
\(472\) 1.82524 25.5279i 0.0840133 1.17502i
\(473\) 16.1127i 0.740865i
\(474\) 23.3305 + 2.23711i 1.07161 + 0.102754i
\(475\) −18.4706 −0.847491
\(476\) 23.4598 + 1.11719i 1.07528 + 0.0512062i
\(477\) 30.1795 + 4.36398i 1.38183 + 0.199813i
\(478\) 18.6310 + 0.443365i 0.852160 + 0.0202790i
\(479\) 41.3560 1.88960 0.944802 0.327642i \(-0.106254\pi\)
0.944802 + 0.327642i \(0.106254\pi\)
\(480\) −2.44651 + 12.6687i −0.111667 + 0.578243i
\(481\) −24.4685 −1.11567
\(482\) 7.69651 + 0.183155i 0.350566 + 0.00834250i
\(483\) 3.47039 + 0.249612i 0.157908 + 0.0113577i
\(484\) 13.6615 + 0.650579i 0.620977 + 0.0295718i
\(485\) 0.704524 0.0319908
\(486\) −8.23450 + 20.4498i −0.373525 + 0.927620i
\(487\) 6.12249i 0.277436i 0.990332 + 0.138718i \(0.0442982\pi\)
−0.990332 + 0.138718i \(0.955702\pi\)
\(488\) 0.645246 9.02447i 0.0292089 0.408519i
\(489\) −1.47517 + 20.5095i −0.0667097 + 0.927473i
\(490\) −5.51976 0.131355i −0.249357 0.00593400i
\(491\) 17.7014i 0.798853i −0.916765 0.399427i \(-0.869209\pi\)
0.916765 0.399427i \(-0.130791\pi\)
\(492\) −6.28116 0.753479i −0.283177 0.0339694i
\(493\) 2.67105i 0.120298i
\(494\) −0.428062 + 17.9879i −0.0192594 + 0.809314i
\(495\) −1.15337 + 7.97627i −0.0518402 + 0.358507i
\(496\) 1.75484 18.3832i 0.0787948 0.825429i
\(497\) 15.3482i 0.688459i
\(498\) 3.39569 + 0.325605i 0.152165 + 0.0145907i
\(499\) 20.6853 0.926000 0.463000 0.886358i \(-0.346773\pi\)
0.463000 + 0.886358i \(0.346773\pi\)
\(500\) −21.7456 1.03555i −0.972491 0.0463114i
\(501\) 0.629996 8.75892i 0.0281462 0.391320i
\(502\) −0.365404 + 15.3549i −0.0163088 + 0.685323i
\(503\) 26.2288 1.16949 0.584743 0.811219i \(-0.301195\pi\)
0.584743 + 0.811219i \(0.301195\pi\)
\(504\) −3.63629 + 16.6529i −0.161973 + 0.741779i
\(505\) 9.98407 0.444285
\(506\) −0.0686347 + 2.88415i −0.00305118 + 0.128216i
\(507\) 0.986545 13.7161i 0.0438140 0.609152i
\(508\) 1.44473 30.3379i 0.0640997 1.34603i
\(509\) 12.1329 0.537782 0.268891 0.963171i \(-0.413343\pi\)
0.268891 + 0.963171i \(0.413343\pi\)
\(510\) 18.7708 + 1.79989i 0.831185 + 0.0797003i
\(511\) 26.5146i 1.17294i
\(512\) −22.1106 4.80837i −0.977161 0.212502i
\(513\) −6.28157 + 28.7089i −0.277338 + 1.26753i
\(514\) 0.0488011 2.05071i 0.00215252 0.0904528i
\(515\) 16.5560i 0.729544i
\(516\) 3.25884 27.1664i 0.143462 1.19593i
\(517\) 11.5521i 0.508062i
\(518\) −30.8914 0.735130i −1.35729 0.0322997i
\(519\) 2.90803 40.4308i 0.127648 1.77471i
\(520\) −0.597568 + 8.35764i −0.0262051 + 0.366507i
\(521\) 22.1658i 0.971102i 0.874208 + 0.485551i \(0.161381\pi\)
−0.874208 + 0.485551i \(0.838619\pi\)
\(522\) 1.91142 + 0.322990i 0.0836606 + 0.0141369i
\(523\) 24.0306 1.05078 0.525392 0.850860i \(-0.323919\pi\)
0.525392 + 0.850860i \(0.323919\pi\)
\(524\) −1.33996 + 28.1378i −0.0585364 + 1.22920i
\(525\) −11.3337 0.815189i −0.494642 0.0355777i
\(526\) −7.93691 0.188876i −0.346066 0.00823540i
\(527\) −26.9885 −1.17564
\(528\) −13.9368 2.34895i −0.606522 0.102225i
\(529\) 1.00000 0.0434783
\(530\) 18.9244 + 0.450349i 0.822025 + 0.0195619i
\(531\) 3.88486 26.8661i 0.168588 1.16589i
\(532\) −1.08085 + 22.6968i −0.0468609 + 0.984031i
\(533\) −4.10820 −0.177946
\(534\) 12.5371 + 1.20215i 0.542533 + 0.0520222i
\(535\) 16.4086i 0.709407i
\(536\) −1.71380 0.122536i −0.0740248 0.00529275i
\(537\) 26.0271 + 1.87203i 1.12315 + 0.0807842i
\(538\) 4.17283 + 0.0993017i 0.179903 + 0.00428120i
\(539\) 6.04793i 0.260503i
\(540\) −3.55783 + 13.2149i −0.153105 + 0.568677i
\(541\) 41.0300i 1.76402i −0.471231 0.882010i \(-0.656190\pi\)
0.471231 0.882010i \(-0.343810\pi\)
\(542\) −0.285556 + 11.9996i −0.0122657 + 0.515425i
\(543\) 20.2420 + 1.45593i 0.868666 + 0.0624799i
\(544\) −3.92475 + 32.8354i −0.168272 + 1.40781i
\(545\) 16.1435i 0.691513i
\(546\) −1.05654 + 11.0186i −0.0452159 + 0.471552i
\(547\) −20.2874 −0.867425 −0.433712 0.901051i \(-0.642797\pi\)
−0.433712 + 0.901051i \(0.642797\pi\)
\(548\) −0.322535 + 6.77290i −0.0137780 + 0.289324i
\(549\) 1.37335 9.49755i 0.0586132 0.405346i
\(550\) 0.224149 9.41913i 0.00955774 0.401633i
\(551\) 2.58418 0.110090
\(552\) −0.699045 + 4.84885i −0.0297533 + 0.206381i
\(553\) 19.2209 0.817356
\(554\) −1.04529 + 43.9251i −0.0444103 + 1.86620i
\(555\) −24.7454 1.77984i −1.05038 0.0755502i
\(556\) 15.4501 + 0.735756i 0.655231 + 0.0312030i
\(557\) −2.82028 −0.119499 −0.0597495 0.998213i \(-0.519030\pi\)
−0.0597495 + 0.998213i \(0.519030\pi\)
\(558\) 3.26352 19.3131i 0.138156 0.817590i
\(559\) 17.7682i 0.751515i
\(560\) −1.00552 + 10.5335i −0.0424911 + 0.445123i
\(561\) −1.48184 + 20.6022i −0.0625633 + 0.869826i
\(562\) 0.657794 27.6416i 0.0277474 1.16599i
\(563\) 13.0757i 0.551075i −0.961290 0.275538i \(-0.911144\pi\)
0.961290 0.275538i \(-0.0888558\pi\)
\(564\) 2.33644 19.4771i 0.0983821 0.820134i
\(565\) 3.52190i 0.148167i
\(566\) 7.02943 + 0.167281i 0.295469 + 0.00703134i
\(567\) −5.12145 + 17.3387i −0.215081 + 0.728156i
\(568\) 21.5554 + 1.54120i 0.904445 + 0.0646675i
\(569\) 0.331551i 0.0138993i 0.999976 + 0.00694966i \(0.00221216\pi\)
−0.999976 + 0.00694966i \(0.997788\pi\)
\(570\) −1.74135 + 18.1603i −0.0729371 + 0.760652i
\(571\) 28.3372 1.18587 0.592937 0.805249i \(-0.297968\pi\)
0.592937 + 0.805249i \(0.297968\pi\)
\(572\) −9.16776 0.436582i −0.383323 0.0182544i
\(573\) 1.95652 27.2018i 0.0817350 1.13637i
\(574\) −5.18659 0.123426i −0.216484 0.00515171i
\(575\) −3.26583 −0.136194
\(576\) −23.0227 6.77913i −0.959278 0.282464i
\(577\) −12.4432 −0.518018 −0.259009 0.965875i \(-0.583396\pi\)
−0.259009 + 0.965875i \(0.583396\pi\)
\(578\) 24.2808 + 0.577816i 1.00995 + 0.0240340i
\(579\) −1.80506 + 25.0960i −0.0750158 + 1.04295i
\(580\) 1.20204 + 0.0572427i 0.0499119 + 0.00237687i
\(581\) 2.79755 0.116062
\(582\) −0.125083 + 1.30448i −0.00518488 + 0.0540725i
\(583\) 20.7353i 0.858768i
\(584\) 37.2378 + 2.66249i 1.54091 + 0.110175i
\(585\) −1.27187 + 8.79577i −0.0525855 + 0.363660i
\(586\) 4.92687 + 0.117246i 0.203527 + 0.00484338i
\(587\) 40.2414i 1.66094i 0.557062 + 0.830471i \(0.311928\pi\)
−0.557062 + 0.830471i \(0.688072\pi\)
\(588\) 1.22321 10.1969i 0.0504443 0.420514i
\(589\) 26.1107i 1.07587i
\(590\) 0.400906 16.8467i 0.0165050 0.693569i
\(591\) 2.18356 30.3584i 0.0898198 1.24878i
\(592\) 4.13444 43.3110i 0.169924 1.78007i
\(593\) 44.8082i 1.84005i −0.391857 0.920026i \(-0.628167\pi\)
0.391857 0.920026i \(-0.371833\pi\)
\(594\) −14.5639 3.55169i −0.597564 0.145728i
\(595\) 15.4644 0.633977
\(596\) 36.8239 + 1.75361i 1.50837 + 0.0718305i
\(597\) 29.5181 + 2.12313i 1.20810 + 0.0868938i
\(598\) −0.0756864 + 3.18047i −0.00309505 + 0.130059i
\(599\) −31.2851 −1.27828 −0.639138 0.769092i \(-0.720709\pi\)
−0.639138 + 0.769092i \(0.720709\pi\)
\(600\) 2.28296 15.8355i 0.0932014 0.646481i
\(601\) 16.9810 0.692670 0.346335 0.938111i \(-0.387426\pi\)
0.346335 + 0.938111i \(0.387426\pi\)
\(602\) 0.533826 22.4323i 0.0217571 0.914272i
\(603\) −1.80364 0.260807i −0.0734499 0.0106209i
\(604\) −1.17071 + 24.5838i −0.0476356 + 1.00030i
\(605\) 9.00547 0.366125
\(606\) −1.77260 + 18.4863i −0.0720071 + 0.750953i
\(607\) 25.5425i 1.03674i −0.855157 0.518368i \(-0.826540\pi\)
0.855157 0.518368i \(-0.173460\pi\)
\(608\) −31.7675 3.79711i −1.28834 0.153993i
\(609\) 1.58566 + 0.114051i 0.0642544 + 0.00462157i
\(610\) 0.141726 5.95556i 0.00573830 0.241133i
\(611\) 12.7390i 0.515366i
\(612\) −6.66525 + 34.4360i −0.269427 + 1.39199i
\(613\) 8.59550i 0.347169i 0.984819 + 0.173584i \(0.0555350\pi\)
−0.984819 + 0.173584i \(0.944465\pi\)
\(614\) −39.6965 0.944667i −1.60202 0.0381236i
\(615\) −4.15469 0.298831i −0.167533 0.0120500i
\(616\) −11.5612 0.826618i −0.465812 0.0333054i
\(617\) 24.6671i 0.993060i 0.868020 + 0.496530i \(0.165393\pi\)
−0.868020 + 0.496530i \(0.834607\pi\)
\(618\) −30.6547 2.93940i −1.23311 0.118240i
\(619\) −21.9073 −0.880530 −0.440265 0.897868i \(-0.645116\pi\)
−0.440265 + 0.897868i \(0.645116\pi\)
\(620\) 0.578385 12.1455i 0.0232285 0.487774i
\(621\) −1.11066 + 5.07607i −0.0445691 + 0.203696i
\(622\) 28.7673 + 0.684581i 1.15346 + 0.0274492i
\(623\) 10.3287 0.413811
\(624\) −15.3687 2.59029i −0.615241 0.103694i
\(625\) 1.99474 0.0797895
\(626\) 29.4834 + 0.701622i 1.17839 + 0.0280424i
\(627\) −19.9322 1.43365i −0.796014 0.0572543i
\(628\) 0.444360 9.33110i 0.0177319 0.372351i
\(629\) −63.5852 −2.53531
\(630\) −1.86999 + 11.0664i −0.0745023 + 0.440896i
\(631\) 27.7857i 1.10613i −0.833138 0.553065i \(-0.813458\pi\)
0.833138 0.553065i \(-0.186542\pi\)
\(632\) −1.93009 + 26.9944i −0.0767748 + 1.07378i
\(633\) 0.267985 3.72583i 0.0106514 0.148088i
\(634\) 10.3815 + 0.247051i 0.412302 + 0.00981163i
\(635\) 19.9984i 0.793611i
\(636\) −4.19376 + 34.9601i −0.166294 + 1.38626i
\(637\) 6.66931i 0.264248i
\(638\) −0.0313601 + 1.31781i −0.00124156 + 0.0521724i
\(639\) 22.6854 + 3.28032i 0.897420 + 0.129767i
\(640\) −14.6926 2.46993i −0.580778 0.0976324i
\(641\) 31.4114i 1.24068i −0.784334 0.620338i \(-0.786995\pi\)
0.784334 0.620338i \(-0.213005\pi\)
\(642\) −30.3818 2.91324i −1.19908 0.114976i
\(643\) −18.4633 −0.728122 −0.364061 0.931375i \(-0.618610\pi\)
−0.364061 + 0.931375i \(0.618610\pi\)
\(644\) −0.191108 + 4.01306i −0.00753069 + 0.158137i
\(645\) 1.29246 17.9693i 0.0508907 0.707540i
\(646\) −1.11238 + 46.7443i −0.0437662 + 1.83913i
\(647\) 8.07781 0.317571 0.158786 0.987313i \(-0.449242\pi\)
0.158786 + 0.987313i \(0.449242\pi\)
\(648\) −23.8367 8.93380i −0.936393 0.350953i
\(649\) 18.4588 0.724571
\(650\) 0.247179 10.3869i 0.00969514 0.407407i
\(651\) 1.15238 16.0217i 0.0451653 0.627939i
\(652\) −23.7167 1.12942i −0.928817 0.0442315i
\(653\) 17.8146 0.697139 0.348569 0.937283i \(-0.386668\pi\)
0.348569 + 0.937283i \(0.386668\pi\)
\(654\) −29.8910 2.86618i −1.16883 0.112076i
\(655\) 18.5481i 0.724732i
\(656\) 0.694161 7.27180i 0.0271024 0.283916i
\(657\) 39.1899 + 5.66688i 1.52894 + 0.221086i
\(658\) 0.382730 16.0830i 0.0149204 0.626979i
\(659\) 16.9195i 0.659089i −0.944140 0.329545i \(-0.893105\pi\)
0.944140 0.329545i \(-0.106895\pi\)
\(660\) −9.23975 1.10839i −0.359657 0.0431439i
\(661\) 0.802060i 0.0311965i −0.999878 0.0155983i \(-0.995035\pi\)
0.999878 0.0155983i \(-0.00496528\pi\)
\(662\) −28.2457 0.672169i −1.09780 0.0261246i
\(663\) −1.63409 + 22.7189i −0.0634627 + 0.882330i
\(664\) −0.280919 + 3.92896i −0.0109018 + 0.152473i
\(665\) 14.9614i 0.580179i
\(666\) 7.68890 45.5020i 0.297939 1.76317i
\(667\) 0.456913 0.0176917
\(668\) 10.1286 + 0.482337i 0.391887 + 0.0186622i
\(669\) 35.2106 + 2.53257i 1.36132 + 0.0979147i
\(670\) −1.13099 0.0269145i −0.0436941 0.00103980i
\(671\) 6.52544 0.251912
\(672\) −19.3251 3.73196i −0.745483 0.143964i
\(673\) 45.4230 1.75093 0.875464 0.483284i \(-0.160556\pi\)
0.875464 + 0.483284i \(0.160556\pi\)
\(674\) 42.2475 + 1.00537i 1.62731 + 0.0387255i
\(675\) 3.62721 16.5775i 0.139611 0.638070i
\(676\) 15.8609 + 0.755318i 0.610034 + 0.0290507i
\(677\) −39.1422 −1.50436 −0.752179 0.658959i \(-0.770997\pi\)
−0.752179 + 0.658959i \(0.770997\pi\)
\(678\) −6.52107 0.625289i −0.250440 0.0240141i
\(679\) 1.07470i 0.0412432i
\(680\) −1.55287 + 21.7186i −0.0595500 + 0.832871i
\(681\) −27.3552 1.96756i −1.04825 0.0753969i
\(682\) 13.3152 + 0.316865i 0.509865 + 0.0121334i
\(683\) 21.7015i 0.830386i −0.909733 0.415193i \(-0.863714\pi\)
0.909733 0.415193i \(-0.136286\pi\)
\(684\) −33.3161 6.44848i −1.27387 0.246564i
\(685\) 4.46460i 0.170584i
\(686\) 0.673473 28.3005i 0.0257133 1.08052i
\(687\) 20.2418 + 1.45592i 0.772274 + 0.0555468i
\(688\) 31.4510 + 3.00229i 1.19906 + 0.114461i
\(689\) 22.8657i 0.871113i
\(690\) −0.307891 + 3.21096i −0.0117212 + 0.122239i
\(691\) −36.7240 −1.39705 −0.698523 0.715588i \(-0.746159\pi\)
−0.698523 + 0.715588i \(0.746159\pi\)
\(692\) 46.7530 + 2.22644i 1.77728 + 0.0846367i
\(693\) −12.1672 1.75939i −0.462194 0.0668335i
\(694\) −0.696314 + 29.2603i −0.0264317 + 1.11071i
\(695\) 10.1845 0.386320
\(696\) −0.319403 + 2.21550i −0.0121069 + 0.0839784i
\(697\) −10.6758 −0.404374
\(698\) 0.129714 5.45079i 0.00490973 0.206315i
\(699\) −39.8573 2.86679i −1.50754 0.108432i
\(700\) 0.624124 13.1060i 0.0235897 0.495359i
\(701\) −16.0748 −0.607136 −0.303568 0.952810i \(-0.598178\pi\)
−0.303568 + 0.952810i \(0.598178\pi\)
\(702\) −16.0602 3.91660i −0.606154 0.147823i
\(703\) 61.5172i 2.32017i
\(704\) 2.32185 16.1538i 0.0875082 0.608820i
\(705\) 0.926638 12.8832i 0.0348992 0.485208i
\(706\) 0.582948 24.4965i 0.0219395 0.921937i
\(707\) 15.2300i 0.572782i
\(708\) 31.1219 + 3.73333i 1.16963 + 0.140307i
\(709\) 14.8490i 0.557666i 0.960340 + 0.278833i \(0.0899475\pi\)
−0.960340 + 0.278833i \(0.910052\pi\)
\(710\) 14.2252 + 0.338519i 0.533861 + 0.0127044i
\(711\) −4.10803 + 28.4095i −0.154063 + 1.06544i
\(712\) −1.03717 + 14.5060i −0.0388696 + 0.543634i
\(713\) 4.61668i 0.172896i
\(714\) −2.74559 + 28.6335i −0.102751 + 1.07158i
\(715\) −6.04327 −0.226005
\(716\) −1.43326 + 30.0971i −0.0535636 + 1.12478i
\(717\) −1.63746 + 22.7658i −0.0611520 + 0.850205i
\(718\) 8.66080 + 0.206103i 0.323218 + 0.00769169i
\(719\) −45.7333 −1.70557 −0.852783 0.522266i \(-0.825087\pi\)
−0.852783 + 0.522266i \(0.825087\pi\)
\(720\) −15.3542 3.73752i −0.572218 0.139289i
\(721\) −25.2549 −0.940543
\(722\) −18.3616 0.436955i −0.683349 0.0162618i
\(723\) −0.676440 + 9.40463i −0.0251571 + 0.349762i
\(724\) −1.11469 + 23.4073i −0.0414270 + 0.869925i
\(725\) −1.49220 −0.0554188
\(726\) −1.59886 + 16.6743i −0.0593393 + 0.618842i
\(727\) 22.2095i 0.823706i 0.911250 + 0.411853i \(0.135118\pi\)
−0.911250 + 0.411853i \(0.864882\pi\)
\(728\) −12.7490 0.911547i −0.472508 0.0337842i
\(729\) −24.5329 11.2755i −0.908625 0.417612i
\(730\) 24.5745 + 0.584805i 0.909544 + 0.0216446i
\(731\) 46.1734i 1.70779i
\(732\) 11.0020 + 1.31978i 0.406646 + 0.0487807i
\(733\) 25.0905i 0.926739i −0.886165 0.463369i \(-0.846640\pi\)
0.886165 0.463369i \(-0.153360\pi\)
\(734\) −0.613855 + 25.7952i −0.0226578 + 0.952119i
\(735\) 0.485127 6.74478i 0.0178942 0.248785i
\(736\) −5.61687 0.671374i −0.207041 0.0247472i
\(737\) 1.23922i 0.0456472i
\(738\) 1.29095 7.63967i 0.0475204 0.281220i
\(739\) 43.4830 1.59955 0.799774 0.600302i \(-0.204953\pi\)
0.799774 + 0.600302i \(0.204953\pi\)
\(740\) 1.36268 28.6149i 0.0500932 1.05191i
\(741\) −21.9800 1.58094i −0.807457 0.0580774i
\(742\) −0.686974 + 28.8678i −0.0252196 + 1.05977i
\(743\) 32.9745 1.20972 0.604859 0.796333i \(-0.293229\pi\)
0.604859 + 0.796333i \(0.293229\pi\)
\(744\) 22.3856 + 3.22727i 0.820696 + 0.118317i
\(745\) 24.2738 0.889324
\(746\) 0.886804 37.2650i 0.0324682 1.36437i
\(747\) −0.597912 + 4.13492i −0.0218765 + 0.151289i
\(748\) −23.8238 1.13452i −0.871086 0.0414823i
\(749\) −25.0302 −0.914582
\(750\) 2.54497 26.5412i 0.0929293 0.969148i
\(751\) 38.3311i 1.39872i 0.714769 + 0.699361i \(0.246532\pi\)
−0.714769 + 0.699361i \(0.753468\pi\)
\(752\) 22.5490 + 2.15251i 0.822276 + 0.0784939i
\(753\) −18.7627 1.34953i −0.683751 0.0491796i
\(754\) −0.0345821 + 1.45320i −0.00125941 + 0.0529224i
\(755\) 16.2053i 0.589771i
\(756\) −20.1583 5.42720i −0.733151 0.197385i
\(757\) 15.5710i 0.565939i −0.959129 0.282970i \(-0.908680\pi\)
0.959129 0.282970i \(-0.0913196\pi\)
\(758\) 7.05320 + 0.167846i 0.256184 + 0.00609646i
\(759\) −3.52424 0.253485i −0.127922 0.00920094i
\(760\) −21.0123 1.50237i −0.762195 0.0544967i
\(761\) 42.7482i 1.54962i −0.632194 0.774810i \(-0.717846\pi\)
0.632194 0.774810i \(-0.282154\pi\)
\(762\) 37.0285 + 3.55057i 1.34140 + 0.128624i
\(763\) −24.6258 −0.891513
\(764\) 31.4554 + 1.49795i 1.13802 + 0.0541940i
\(765\) −3.30516 + 22.8572i −0.119498 + 0.826402i
\(766\) 8.51412 + 0.202612i 0.307628 + 0.00732068i
\(767\) 20.3553 0.734987
\(768\) 7.18184 26.7660i 0.259152 0.965836i
\(769\) −33.1519 −1.19549 −0.597743 0.801688i \(-0.703936\pi\)
−0.597743 + 0.801688i \(0.703936\pi\)
\(770\) −7.62960 0.181563i −0.274952 0.00654308i
\(771\) 2.50583 + 0.180235i 0.0902453 + 0.00649100i
\(772\) −29.0203 1.38199i −1.04447 0.0497389i
\(773\) −28.0896 −1.01031 −0.505156 0.863028i \(-0.668565\pi\)
−0.505156 + 0.863028i \(0.668565\pi\)
\(774\) 33.0420 + 5.58342i 1.18767 + 0.200692i
\(775\) 15.0773i 0.541592i
\(776\) −1.50934 0.107917i −0.0541822 0.00387400i
\(777\) 2.71502 37.7473i 0.0974008 1.35418i
\(778\) −16.3143 0.388235i −0.584896 0.0139189i
\(779\) 10.3286i 0.370060i
\(780\) −10.1891 1.22226i −0.364827 0.0437641i
\(781\) 15.5863i 0.557723i
\(782\) −0.196683 + 8.26495i −0.00703336 + 0.295554i
\(783\) −0.507473 + 2.31932i −0.0181356 + 0.0828857i
\(784\) 11.8052 + 1.12691i 0.421613 + 0.0402468i
\(785\) 6.15093i 0.219536i
\(786\) −34.3431 3.29308i −1.22498 0.117460i
\(787\) −14.8016 −0.527621 −0.263811 0.964574i \(-0.584979\pi\)
−0.263811 + 0.964574i \(0.584979\pi\)
\(788\) 35.1056 + 1.67178i 1.25059 + 0.0595546i
\(789\) 0.697569 9.69839i 0.0248341 0.345272i
\(790\) −0.423936 + 17.8145i −0.0150830 + 0.633813i
\(791\) −5.37240 −0.191020
\(792\) 3.69272 16.9113i 0.131215 0.600918i
\(793\) 7.19587 0.255533
\(794\) 0.809660 34.0233i 0.0287338 1.20744i
\(795\) −1.66325 + 23.1244i −0.0589895 + 0.820139i
\(796\) −1.62551 + 34.1340i −0.0576146 + 1.20985i
\(797\) 28.4561 1.00797 0.503983 0.863714i \(-0.331867\pi\)
0.503983 + 0.863714i \(0.331867\pi\)
\(798\) −27.7022 2.65630i −0.980648 0.0940320i
\(799\) 33.1043i 1.17115i
\(800\) 18.3437 + 2.19259i 0.648549 + 0.0775197i
\(801\) −2.20753 + 15.2664i −0.0779992 + 0.539411i
\(802\) 0.843556 35.4477i 0.0297870 1.25170i
\(803\) 26.9260i 0.950199i
\(804\) 0.250635 2.08934i 0.00883920 0.0736855i
\(805\) 2.64536i 0.0932366i
\(806\) 14.6832 + 0.349420i 0.517195 + 0.0123078i
\(807\) −0.366746 + 5.09892i −0.0129101 + 0.179491i
\(808\) −21.3894 1.52934i −0.752477 0.0538018i
\(809\) 47.7099i 1.67739i 0.544601 + 0.838696i \(0.316681\pi\)
−0.544601 + 0.838696i \(0.683319\pi\)
\(810\) −15.9571 5.12914i −0.560674 0.180220i
\(811\) 0.565059 0.0198419 0.00992094 0.999951i \(-0.496842\pi\)
0.00992094 + 0.999951i \(0.496842\pi\)
\(812\) −0.0873195 + 1.83362i −0.00306431 + 0.0643474i
\(813\) −14.6627 1.05463i −0.514242 0.0369875i
\(814\) 31.3708 + 0.746538i 1.09955 + 0.0261661i
\(815\) −15.6337 −0.547625
\(816\) −39.9380 6.73126i −1.39811 0.235641i
\(817\) 44.6717 1.56287
\(818\) 37.0970 + 0.882804i 1.29706 + 0.0308665i
\(819\) −13.4173 1.94015i −0.468838 0.0677943i
\(820\) 0.228791 4.80437i 0.00798972 0.167776i
\(821\) 42.6322 1.48788 0.743938 0.668249i \(-0.232956\pi\)
0.743938 + 0.668249i \(0.232956\pi\)
\(822\) −8.26655 0.792660i −0.288329 0.0276472i
\(823\) 16.8841i 0.588543i 0.955722 + 0.294271i \(0.0950770\pi\)
−0.955722 + 0.294271i \(0.904923\pi\)
\(824\) 2.53600 35.4688i 0.0883459 1.23561i
\(825\) 11.5096 + 0.827839i 0.400711 + 0.0288217i
\(826\) 25.6985 + 0.611552i 0.894164 + 0.0212786i
\(827\) 13.4702i 0.468405i 0.972188 + 0.234202i \(0.0752478\pi\)
−0.972188 + 0.234202i \(0.924752\pi\)
\(828\) −5.89067 1.14017i −0.204715 0.0396236i
\(829\) 40.6857i 1.41307i −0.707677 0.706536i \(-0.750257\pi\)
0.707677 0.706536i \(-0.249743\pi\)
\(830\) −0.0617028 + 2.59286i −0.00214173 + 0.0899994i
\(831\) −53.6736 3.86054i −1.86192 0.133921i
\(832\) 2.56041 17.8135i 0.0887661 0.617572i
\(833\) 17.3312i 0.600491i
\(834\) −1.80819 + 18.8574i −0.0626125 + 0.652978i
\(835\) 6.67662 0.231054
\(836\) 1.09763 23.0490i 0.0379622 0.797167i
\(837\) 23.4346 + 5.12755i 0.810018 + 0.177234i
\(838\) −0.190784 + 8.01709i −0.00659054 + 0.276946i
\(839\) −34.8626 −1.20359 −0.601795 0.798650i \(-0.705548\pi\)
−0.601795 + 0.798650i \(0.705548\pi\)
\(840\) −12.8269 1.84922i −0.442571 0.0638043i
\(841\) −28.7912 −0.992801
\(842\) −1.31304 + 55.1763i −0.0452504 + 1.90150i
\(843\) 33.7763 + 2.42940i 1.16332 + 0.0836730i
\(844\) 4.30844 + 0.205174i 0.148303 + 0.00706238i
\(845\) 10.4553 0.359673
\(846\) 23.6897 + 4.00306i 0.814468 + 0.137628i
\(847\) 13.7372i 0.472015i
\(848\) −40.4739 3.86361i −1.38988 0.132677i
\(849\) −0.617811 + 8.58950i −0.0212032 + 0.294791i
\(850\) 0.642331 26.9919i 0.0220318 0.925813i
\(851\) 10.8770i 0.372858i
\(852\) −3.15237 + 26.2789i −0.107999 + 0.900299i
\(853\) 20.3449i 0.696597i 0.937384 + 0.348299i \(0.113240\pi\)
−0.937384 + 0.348299i \(0.886760\pi\)
\(854\) 9.08477 + 0.216192i 0.310874 + 0.00739794i
\(855\) −22.1138 3.19766i −0.756275 0.109358i
\(856\) 2.51343 35.1531i 0.0859074 1.20151i
\(857\) 11.5616i 0.394938i −0.980309 0.197469i \(-0.936728\pi\)
0.980309 0.197469i \(-0.0632722\pi\)
\(858\) 1.07294 11.1896i 0.0366296 0.382006i
\(859\) −12.3481 −0.421310 −0.210655 0.977560i \(-0.567560\pi\)
−0.210655 + 0.977560i \(0.567560\pi\)
\(860\) 20.7792 + 0.989534i 0.708564 + 0.0337428i
\(861\) 0.455845 6.33767i 0.0155351 0.215987i
\(862\) 51.4491 + 1.22435i 1.75236 + 0.0417014i
\(863\) −19.4082 −0.660662 −0.330331 0.943865i \(-0.607160\pi\)
−0.330331 + 0.943865i \(0.607160\pi\)
\(864\) 9.64635 27.7659i 0.328175 0.944617i
\(865\) 30.8190 1.04788
\(866\) −8.38061 0.199435i −0.284785 0.00677708i
\(867\) −2.13402 + 29.6696i −0.0724752 + 1.00763i
\(868\) 18.5270 + 0.882283i 0.628849 + 0.0299466i
\(869\) −19.5192 −0.662143
\(870\) −0.140679 + 1.46713i −0.00476948 + 0.0497403i
\(871\) 1.36654i 0.0463034i
\(872\) 2.47283 34.5852i 0.0837405 1.17120i
\(873\) −1.58846 0.229693i −0.0537613 0.00777392i
\(874\) −7.99615 0.190286i −0.270474 0.00643652i
\(875\) 21.8661i 0.739207i
\(876\) −5.44585 + 45.3978i −0.183998 + 1.53385i
\(877\) 42.3177i 1.42897i 0.699652 + 0.714484i \(0.253338\pi\)
−0.699652 + 0.714484i \(0.746662\pi\)
\(878\) −0.391159 + 16.4372i −0.0132010 + 0.554728i
\(879\) −0.433018 + 6.02031i −0.0146053 + 0.203060i
\(880\) 1.02113 10.6970i 0.0344222 0.360596i
\(881\) 5.20976i 0.175521i −0.996142 0.0877606i \(-0.972029\pi\)
0.996142 0.0877606i \(-0.0279711\pi\)
\(882\) 12.4024 + 2.09574i 0.417609 + 0.0705672i
\(883\) 13.5991 0.457647 0.228824 0.973468i \(-0.426512\pi\)
0.228824 + 0.973468i \(0.426512\pi\)
\(884\) −26.2716 1.25109i −0.883608 0.0420786i
\(885\) 20.5856 + 1.48065i 0.691978 + 0.0497714i
\(886\) 0.735730 30.9167i 0.0247173 1.03867i
\(887\) 31.3869 1.05387 0.526935 0.849906i \(-0.323341\pi\)
0.526935 + 0.849906i \(0.323341\pi\)
\(888\) 52.7408 + 7.60350i 1.76987 + 0.255157i
\(889\) 30.5060 1.02314
\(890\) −0.227810 + 9.57298i −0.00763622 + 0.320887i
\(891\) 5.20093 17.6078i 0.174238 0.589882i
\(892\) −1.93898 + 40.7166i −0.0649219 + 1.36329i
\(893\) 32.0277 1.07176
\(894\) −4.30965 + 44.9448i −0.144136 + 1.50318i
\(895\) 19.8396i 0.663164i
\(896\) 3.76769 22.4126i 0.125870 0.748751i
\(897\) −3.88633 0.279529i −0.129761 0.00933321i
\(898\) 1.27751 53.6831i 0.0426310 1.79143i
\(899\) 2.10942i 0.0703532i
\(900\) 19.2379 + 3.72359i 0.641263 + 0.124120i
\(901\) 59.4200i 1.97957i
\(902\) 5.26708 + 0.125342i 0.175374 + 0.00417342i
\(903\) 27.4108 + 1.97156i 0.912175 + 0.0656093i
\(904\) 0.539476 7.54515i 0.0179427 0.250948i
\(905\) 15.4298i 0.512903i
\(906\) −30.0053 2.87714i −0.996861 0.0955865i
\(907\) 5.42672 0.180191 0.0900956 0.995933i \(-0.471283\pi\)
0.0900956 + 0.995933i \(0.471283\pi\)
\(908\) 1.50640 31.6328i 0.0499916 1.04977i
\(909\) −22.5107 3.25506i −0.746632 0.107963i
\(910\) −8.41348 0.200217i −0.278904 0.00663714i
\(911\) 5.57731 0.184784 0.0923922 0.995723i \(-0.470549\pi\)
0.0923922 + 0.995723i \(0.470549\pi\)
\(912\) 6.51234 38.6391i 0.215645 1.27947i
\(913\) −2.84096 −0.0940222
\(914\) 6.95343 + 0.165472i 0.229999 + 0.00547334i
\(915\) 7.27730 + 0.523429i 0.240580 + 0.0173040i
\(916\) −1.11468 + 23.4071i −0.0368301 + 0.773393i
\(917\) −28.2937 −0.934340
\(918\) −41.7350 10.1779i −1.37746 0.335920i
\(919\) 31.7977i 1.04891i 0.851439 + 0.524454i \(0.175731\pi\)
−0.851439 + 0.524454i \(0.824269\pi\)
\(920\) −3.71522 0.265637i −0.122487 0.00875778i
\(921\) 3.48889 48.5066i 0.114963 1.59835i
\(922\) −18.3259 0.436105i −0.603530 0.0143623i
\(923\) 17.1877i 0.565741i
\(924\) 1.69076 14.0946i 0.0556220 0.463677i
\(925\) 35.5223i 1.16797i
\(926\) 0.332633 13.9778i 0.0109310 0.459339i
\(927\) 5.39767 37.3281i 0.177283 1.22602i
\(928\) −2.56642 0.306759i −0.0842469 0.0100699i
\(929\) 8.03771i 0.263709i −0.991269 0.131854i \(-0.957907\pi\)
0.991269 0.131854i \(-0.0420931\pi\)
\(930\) 14.8240 + 1.42144i 0.486097 + 0.0466107i
\(931\) 16.7676 0.549535
\(932\) 2.19487 46.0899i 0.0718953 1.50973i
\(933\) −2.52833 + 35.1517i −0.0827738 + 1.15082i
\(934\) 1.28503 53.9991i 0.0420474 1.76691i
\(935\) −15.7044 −0.513587
\(936\) 4.07212 18.6488i 0.133101 0.609556i
\(937\) −11.4972 −0.375599 −0.187799 0.982207i \(-0.560135\pi\)
−0.187799 + 0.982207i \(0.560135\pi\)
\(938\) 0.0410561 1.72525i 0.00134053 0.0563314i
\(939\) −2.59127 + 36.0267i −0.0845628 + 1.17569i
\(940\) 14.8978 + 0.709452i 0.485911 + 0.0231398i
\(941\) 36.9281 1.20382 0.601911 0.798563i \(-0.294406\pi\)
0.601911 + 0.798563i \(0.294406\pi\)
\(942\) 11.3889 + 1.09206i 0.371071 + 0.0355811i
\(943\) 1.82621i 0.0594697i
\(944\) −3.43942 + 36.0303i −0.111944 + 1.17269i
\(945\) −13.4280 2.93808i −0.436813 0.0955757i
\(946\) −0.542110 + 22.7804i −0.0176255 + 0.740655i
\(947\) 18.6243i 0.605210i 0.953116 + 0.302605i \(0.0978563\pi\)
−0.953116 + 0.302605i \(0.902144\pi\)
\(948\) −32.9097 3.94780i −1.06886 0.128219i
\(949\) 29.6925i 0.963858i
\(950\) 26.1140 + 0.621441i 0.847251 + 0.0201622i
\(951\) −0.912421 + 12.6855i −0.0295873 + 0.411356i
\(952\) −33.1301 2.36879i −1.07375 0.0767730i
\(953\) 6.28063i 0.203450i −0.994813 0.101725i \(-0.967564\pi\)
0.994813 0.101725i \(-0.0324361\pi\)
\(954\) −42.5214 7.18523i −1.37668 0.232630i
\(955\) 20.7350 0.670969
\(956\) −26.3258 1.25367i −0.851436 0.0405466i
\(957\) −1.61027 0.115821i −0.0520527 0.00374395i
\(958\) −58.4697 1.39142i −1.88907 0.0449546i
\(959\) −6.81042 −0.219920
\(960\) 3.88514 17.8288i 0.125392 0.575423i
\(961\) 9.68623 0.312459
\(962\) 34.5939 + 0.823239i 1.11535 + 0.0265423i
\(963\) 5.34963 36.9959i 0.172389 1.19218i
\(964\) −10.8753 0.517895i −0.350269 0.0166803i
\(965\) −19.1298 −0.615811
\(966\) −4.89808 0.469665i −0.157593 0.0151112i
\(967\) 57.5475i 1.85060i 0.379233 + 0.925301i \(0.376188\pi\)
−0.379233 + 0.925301i \(0.623812\pi\)
\(968\) −19.2929 1.37944i −0.620098 0.0443368i
\(969\) −57.1185 4.10832i −1.83491 0.131978i
\(970\) −0.996066 0.0237036i −0.0319817 0.000761076i
\(971\) 33.7961i 1.08457i −0.840195 0.542284i \(-0.817560\pi\)
0.840195 0.542284i \(-0.182440\pi\)
\(972\) 12.3301 28.6351i 0.395487 0.918471i
\(973\) 15.5357i 0.498052i
\(974\) 0.205990 8.65606i 0.00660034 0.277358i
\(975\) 12.6921 + 0.912893i 0.406472 + 0.0292360i
\(976\) −1.21588 + 12.7372i −0.0389195 + 0.407708i
\(977\) 52.2944i 1.67305i −0.547932 0.836523i \(-0.684585\pi\)
0.547932 0.836523i \(-0.315415\pi\)
\(978\) 2.77566 28.9470i 0.0887558 0.925624i
\(979\) −10.4890 −0.335230
\(980\) 7.79948 + 0.371422i 0.249145 + 0.0118647i
\(981\) 5.26320 36.3982i 0.168041 1.16211i
\(982\) −0.595560 + 25.0265i −0.0190051 + 0.798627i
\(983\) 2.31390 0.0738018 0.0369009 0.999319i \(-0.488251\pi\)
0.0369009 + 0.999319i \(0.488251\pi\)
\(984\) 8.85504 + 1.27661i 0.282288 + 0.0406967i
\(985\) 23.1411 0.737338
\(986\) −0.0898669 + 3.77636i −0.00286194 + 0.120264i
\(987\) 19.6523 + 1.41352i 0.625541 + 0.0449928i
\(988\) 1.21040 25.4171i 0.0385079 0.808627i
\(989\) 7.89849 0.251157
\(990\) 1.89901 11.2381i 0.0603546 0.357172i
\(991\) 38.2038i 1.21359i −0.794860 0.606793i \(-0.792456\pi\)
0.794860 0.606793i \(-0.207544\pi\)
\(992\) −3.09952 + 25.9313i −0.0984098 + 0.823320i
\(993\) 2.48249 34.5144i 0.0787795 1.09528i
\(994\) −0.516386 + 21.6994i −0.0163788 + 0.688264i
\(995\) 22.5007i 0.713319i
\(996\) −4.78992 0.574591i −0.151774 0.0182066i
\(997\) 6.82163i 0.216043i 0.994149 + 0.108022i \(0.0344516\pi\)
−0.994149 + 0.108022i \(0.965548\pi\)
\(998\) −29.2451 0.695952i −0.925738 0.0220300i
\(999\) 55.2122 + 12.0806i 1.74684 + 0.382212i
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 552.2.j.d.323.1 yes 42
3.2 odd 2 552.2.j.c.323.42 yes 42
4.3 odd 2 2208.2.j.d.47.22 42
8.3 odd 2 552.2.j.c.323.41 42
8.5 even 2 2208.2.j.c.47.22 42
12.11 even 2 2208.2.j.c.47.21 42
24.5 odd 2 2208.2.j.d.47.21 42
24.11 even 2 inner 552.2.j.d.323.2 yes 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.j.c.323.41 42 8.3 odd 2
552.2.j.c.323.42 yes 42 3.2 odd 2
552.2.j.d.323.1 yes 42 1.1 even 1 trivial
552.2.j.d.323.2 yes 42 24.11 even 2 inner
2208.2.j.c.47.21 42 12.11 even 2
2208.2.j.c.47.22 42 8.5 even 2
2208.2.j.d.47.21 42 24.5 odd 2
2208.2.j.d.47.22 42 4.3 odd 2