Properties

Label 429.2.p.b.230.11
Level $429$
Weight $2$
Character 429.230
Analytic conductor $3.426$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(230,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.230");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 230.11
Character \(\chi\) \(=\) 429.230
Dual form 429.2.p.b.263.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.964601 + 1.67074i) q^{2} +(-1.68588 - 0.397235i) q^{3} +(-0.860909 - 1.49114i) q^{4} -1.71348i q^{5} +(2.28988 - 2.43350i) q^{6} +(-3.58916 + 2.07221i) q^{7} -0.536667 q^{8} +(2.68441 + 1.33939i) q^{9} +O(q^{10})\) \(q+(-0.964601 + 1.67074i) q^{2} +(-1.68588 - 0.397235i) q^{3} +(-0.860909 - 1.49114i) q^{4} -1.71348i q^{5} +(2.28988 - 2.43350i) q^{6} +(-3.58916 + 2.07221i) q^{7} -0.536667 q^{8} +(2.68441 + 1.33939i) q^{9} +(2.86278 + 1.65283i) q^{10} +(-3.01673 - 1.37817i) q^{11} +(0.859060 + 2.85587i) q^{12} +(3.28917 - 1.47695i) q^{13} -7.99540i q^{14} +(-0.680657 + 2.88874i) q^{15} +(2.23949 - 3.87891i) q^{16} +(1.63775 + 2.83666i) q^{17} +(-4.82714 + 3.19297i) q^{18} +(3.17223 - 1.83149i) q^{19} +(-2.55504 + 1.47516i) q^{20} +(6.87407 - 2.06775i) q^{21} +(5.21250 - 3.71077i) q^{22} +(4.70378 + 2.71573i) q^{23} +(0.904759 + 0.213183i) q^{24} +2.06397 q^{25} +(-0.705145 + 6.92000i) q^{26} +(-3.99355 - 3.32439i) q^{27} +(6.17989 + 3.56796i) q^{28} +(4.35124 - 7.53656i) q^{29} +(-4.16976 - 3.92368i) q^{30} -2.17965 q^{31} +(3.78376 + 6.55366i) q^{32} +(4.53839 + 3.52179i) q^{33} -6.31909 q^{34} +(3.55069 + 6.14998i) q^{35} +(-0.313822 - 5.15591i) q^{36} +(2.26663 - 3.92591i) q^{37} +7.06662i q^{38} +(-6.13185 + 1.18339i) q^{39} +0.919571i q^{40} +(-2.05502 + 3.55940i) q^{41} +(-3.17606 + 13.4793i) q^{42} +(-3.16703 + 1.82848i) q^{43} +(0.542079 + 5.68484i) q^{44} +(2.29502 - 4.59969i) q^{45} +(-9.07453 + 5.23918i) q^{46} +1.44769i q^{47} +(-5.31636 + 5.64978i) q^{48} +(5.08807 - 8.81279i) q^{49} +(-1.99091 + 3.44835i) q^{50} +(-1.63423 - 5.43285i) q^{51} +(-5.03401 - 3.63309i) q^{52} +9.06332i q^{53} +(9.40636 - 3.46546i) q^{54} +(-2.36148 + 5.16911i) q^{55} +(1.92619 - 1.11208i) q^{56} +(-6.07554 + 1.82755i) q^{57} +(8.39441 + 14.5396i) q^{58} +(9.13262 - 5.27272i) q^{59} +(4.89349 - 1.47199i) q^{60} +(-2.63306 + 1.52020i) q^{61} +(2.10249 - 3.64163i) q^{62} +(-12.4103 + 0.755369i) q^{63} -5.64131 q^{64} +(-2.53073 - 5.63594i) q^{65} +(-10.2617 + 4.18534i) q^{66} +(7.83852 - 13.5767i) q^{67} +(2.81990 - 4.88422i) q^{68} +(-6.85124 - 6.44690i) q^{69} -13.7000 q^{70} +(3.04416 - 1.75755i) q^{71} +(-1.44063 - 0.718805i) q^{72} -10.7920i q^{73} +(4.37278 + 7.57388i) q^{74} +(-3.47961 - 0.819882i) q^{75} +(-5.46201 - 3.15349i) q^{76} +(13.6834 - 1.30478i) q^{77} +(3.93766 - 11.3862i) q^{78} -5.74463i q^{79} +(-6.64645 - 3.83733i) q^{80} +(5.41209 + 7.19091i) q^{81} +(-3.96455 - 6.86681i) q^{82} -7.17926 q^{83} +(-9.00126 - 8.47004i) q^{84} +(4.86058 - 2.80625i) q^{85} -7.05503i q^{86} +(-10.3295 + 10.9773i) q^{87} +(1.61898 + 0.739621i) q^{88} +(-7.81452 - 4.51171i) q^{89} +(5.47110 + 8.27124i) q^{90} +(-8.74483 + 12.1168i) q^{91} -9.35198i q^{92} +(3.67464 + 0.865835i) q^{93} +(-2.41871 - 1.39644i) q^{94} +(-3.13823 - 5.43557i) q^{95} +(-3.77563 - 12.5518i) q^{96} +(6.32360 + 10.9528i) q^{97} +(9.81591 + 17.0017i) q^{98} +(-6.25222 - 7.74014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9} + 28 q^{12} - 8 q^{15} - 44 q^{16} + 16 q^{22} - 56 q^{25} + 44 q^{27} - 40 q^{31} - 16 q^{33} - 56 q^{34} + 40 q^{36} + 28 q^{37} - 22 q^{42} - 10 q^{45} + 24 q^{48} - 8 q^{49} - 12 q^{55} - 16 q^{58} - 76 q^{60} + 104 q^{64} + 68 q^{66} - 24 q^{67} + 30 q^{69} + 88 q^{70} - 66 q^{75} - 28 q^{78} - 66 q^{81} + 32 q^{82} - 8 q^{88} - 80 q^{91} + 30 q^{93} - 80 q^{97} - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.964601 + 1.67074i −0.682076 + 1.18139i 0.292270 + 0.956336i \(0.405589\pi\)
−0.974346 + 0.225054i \(0.927744\pi\)
\(3\) −1.68588 0.397235i −0.973345 0.229344i
\(4\) −0.860909 1.49114i −0.430455 0.745569i
\(5\) 1.71348i 0.766294i −0.923687 0.383147i \(-0.874840\pi\)
0.923687 0.383147i \(-0.125160\pi\)
\(6\) 2.28988 2.43350i 0.934840 0.993470i
\(7\) −3.58916 + 2.07221i −1.35658 + 0.783220i −0.989161 0.146837i \(-0.953091\pi\)
−0.367416 + 0.930057i \(0.619757\pi\)
\(8\) −0.536667 −0.189741
\(9\) 2.68441 + 1.33939i 0.894803 + 0.446462i
\(10\) 2.86278 + 1.65283i 0.905292 + 0.522670i
\(11\) −3.01673 1.37817i −0.909577 0.415535i
\(12\) 0.859060 + 2.85587i 0.247989 + 0.824419i
\(13\) 3.28917 1.47695i 0.912251 0.409631i
\(14\) 7.99540i 2.13686i
\(15\) −0.680657 + 2.88874i −0.175745 + 0.745868i
\(16\) 2.23949 3.87891i 0.559872 0.969727i
\(17\) 1.63775 + 2.83666i 0.397212 + 0.687991i 0.993381 0.114868i \(-0.0366444\pi\)
−0.596169 + 0.802859i \(0.703311\pi\)
\(18\) −4.82714 + 3.19297i −1.13777 + 0.752590i
\(19\) 3.17223 1.83149i 0.727760 0.420172i −0.0898424 0.995956i \(-0.528636\pi\)
0.817602 + 0.575784i \(0.195303\pi\)
\(20\) −2.55504 + 1.47516i −0.571325 + 0.329855i
\(21\) 6.87407 2.06775i 1.50004 0.451221i
\(22\) 5.21250 3.71077i 1.11131 0.791139i
\(23\) 4.70378 + 2.71573i 0.980805 + 0.566268i 0.902513 0.430662i \(-0.141720\pi\)
0.0782919 + 0.996930i \(0.475053\pi\)
\(24\) 0.904759 + 0.213183i 0.184683 + 0.0435159i
\(25\) 2.06397 0.412794
\(26\) −0.705145 + 6.92000i −0.138290 + 1.35712i
\(27\) −3.99355 3.32439i −0.768559 0.639779i
\(28\) 6.17989 + 3.56796i 1.16789 + 0.674281i
\(29\) 4.35124 7.53656i 0.808005 1.39950i −0.106239 0.994341i \(-0.533881\pi\)
0.914244 0.405164i \(-0.132786\pi\)
\(30\) −4.16976 3.92368i −0.761290 0.716362i
\(31\) −2.17965 −0.391477 −0.195739 0.980656i \(-0.562710\pi\)
−0.195739 + 0.980656i \(0.562710\pi\)
\(32\) 3.78376 + 6.55366i 0.668880 + 1.15853i
\(33\) 4.53839 + 3.52179i 0.790032 + 0.613065i
\(34\) −6.31909 −1.08371
\(35\) 3.55069 + 6.14998i 0.600176 + 1.03954i
\(36\) −0.313822 5.15591i −0.0523037 0.859319i
\(37\) 2.26663 3.92591i 0.372631 0.645416i −0.617338 0.786698i \(-0.711789\pi\)
0.989969 + 0.141282i \(0.0451224\pi\)
\(38\) 7.06662i 1.14636i
\(39\) −6.13185 + 1.18339i −0.981882 + 0.189493i
\(40\) 0.919571i 0.145397i
\(41\) −2.05502 + 3.55940i −0.320941 + 0.555885i −0.980682 0.195607i \(-0.937332\pi\)
0.659742 + 0.751492i \(0.270666\pi\)
\(42\) −3.17606 + 13.4793i −0.490076 + 2.07990i
\(43\) −3.16703 + 1.82848i −0.482967 + 0.278841i −0.721652 0.692256i \(-0.756617\pi\)
0.238685 + 0.971097i \(0.423284\pi\)
\(44\) 0.542079 + 5.68484i 0.0817215 + 0.857022i
\(45\) 2.29502 4.59969i 0.342121 0.685682i
\(46\) −9.07453 + 5.23918i −1.33797 + 0.772475i
\(47\) 1.44769i 0.211168i 0.994410 + 0.105584i \(0.0336711\pi\)
−0.994410 + 0.105584i \(0.966329\pi\)
\(48\) −5.31636 + 5.64978i −0.767350 + 0.815476i
\(49\) 5.08807 8.81279i 0.726867 1.25897i
\(50\) −1.99091 + 3.44835i −0.281557 + 0.487671i
\(51\) −1.63423 5.43285i −0.228838 0.760751i
\(52\) −5.03401 3.63309i −0.698091 0.503819i
\(53\) 9.06332i 1.24494i 0.782643 + 0.622471i \(0.213871\pi\)
−0.782643 + 0.622471i \(0.786129\pi\)
\(54\) 9.40636 3.46546i 1.28004 0.471590i
\(55\) −2.36148 + 5.16911i −0.318422 + 0.697003i
\(56\) 1.92619 1.11208i 0.257398 0.148609i
\(57\) −6.07554 + 1.82755i −0.804725 + 0.242065i
\(58\) 8.39441 + 14.5396i 1.10224 + 1.90914i
\(59\) 9.13262 5.27272i 1.18897 0.686450i 0.230895 0.972979i \(-0.425835\pi\)
0.958072 + 0.286529i \(0.0925013\pi\)
\(60\) 4.89349 1.47199i 0.631747 0.190033i
\(61\) −2.63306 + 1.52020i −0.337129 + 0.194641i −0.659002 0.752142i \(-0.729021\pi\)
0.321873 + 0.946783i \(0.395688\pi\)
\(62\) 2.10249 3.64163i 0.267017 0.462487i
\(63\) −12.4103 + 0.755369i −1.56355 + 0.0951675i
\(64\) −5.64131 −0.705164
\(65\) −2.53073 5.63594i −0.313898 0.699052i
\(66\) −10.2617 + 4.18534i −1.26313 + 0.515179i
\(67\) 7.83852 13.5767i 0.957628 1.65866i 0.229392 0.973334i \(-0.426326\pi\)
0.728236 0.685326i \(-0.240340\pi\)
\(68\) 2.81990 4.88422i 0.341964 0.592298i
\(69\) −6.85124 6.44690i −0.824792 0.776116i
\(70\) −13.7000 −1.63746
\(71\) 3.04416 1.75755i 0.361275 0.208582i −0.308365 0.951268i \(-0.599782\pi\)
0.669640 + 0.742686i \(0.266448\pi\)
\(72\) −1.44063 0.718805i −0.169780 0.0847119i
\(73\) 10.7920i 1.26311i −0.775333 0.631553i \(-0.782418\pi\)
0.775333 0.631553i \(-0.217582\pi\)
\(74\) 4.37278 + 7.57388i 0.508325 + 0.880445i
\(75\) −3.47961 0.819882i −0.401791 0.0946718i
\(76\) −5.46201 3.15349i −0.626535 0.361730i
\(77\) 13.6834 1.30478i 1.55937 0.148694i
\(78\) 3.93766 11.3862i 0.445852 1.28923i
\(79\) 5.74463i 0.646322i −0.946344 0.323161i \(-0.895255\pi\)
0.946344 0.323161i \(-0.104745\pi\)
\(80\) −6.64645 3.83733i −0.743096 0.429027i
\(81\) 5.41209 + 7.19091i 0.601344 + 0.798991i
\(82\) −3.96455 6.86681i −0.437812 0.758312i
\(83\) −7.17926 −0.788026 −0.394013 0.919105i \(-0.628914\pi\)
−0.394013 + 0.919105i \(0.628914\pi\)
\(84\) −9.00126 8.47004i −0.982118 0.924157i
\(85\) 4.86058 2.80625i 0.527203 0.304381i
\(86\) 7.05503i 0.760764i
\(87\) −10.3295 + 10.9773i −1.10744 + 1.17689i
\(88\) 1.61898 + 0.739621i 0.172584 + 0.0788439i
\(89\) −7.81452 4.51171i −0.828337 0.478241i 0.0249459 0.999689i \(-0.492059\pi\)
−0.853283 + 0.521448i \(0.825392\pi\)
\(90\) 5.47110 + 8.27124i 0.576705 + 0.871865i
\(91\) −8.74483 + 12.1168i −0.916707 + 1.27019i
\(92\) 9.35198i 0.975011i
\(93\) 3.67464 + 0.865835i 0.381042 + 0.0897829i
\(94\) −2.41871 1.39644i −0.249471 0.144032i
\(95\) −3.13823 5.43557i −0.321975 0.557678i
\(96\) −3.77563 12.5518i −0.385349 1.28106i
\(97\) 6.32360 + 10.9528i 0.642065 + 1.11209i 0.984971 + 0.172719i \(0.0552552\pi\)
−0.342907 + 0.939369i \(0.611411\pi\)
\(98\) 9.81591 + 17.0017i 0.991557 + 1.71743i
\(99\) −6.25222 7.74014i −0.628372 0.777913i
\(100\) −1.77689 3.07767i −0.177689 0.307767i
\(101\) 2.09865 3.63496i 0.208823 0.361692i −0.742521 0.669823i \(-0.766370\pi\)
0.951344 + 0.308131i \(0.0997034\pi\)
\(102\) 10.6532 + 2.51017i 1.05483 + 0.248543i
\(103\) 14.5087 1.42958 0.714792 0.699337i \(-0.246521\pi\)
0.714792 + 0.699337i \(0.246521\pi\)
\(104\) −1.76519 + 0.792629i −0.173091 + 0.0777237i
\(105\) −3.54306 11.7786i −0.345768 1.14947i
\(106\) −15.1424 8.74248i −1.47076 0.849145i
\(107\) 6.61739 11.4617i 0.639727 1.10804i −0.345766 0.938321i \(-0.612381\pi\)
0.985493 0.169719i \(-0.0542859\pi\)
\(108\) −1.51904 + 8.81693i −0.146170 + 0.848410i
\(109\) 8.34893i 0.799683i −0.916584 0.399841i \(-0.869065\pi\)
0.916584 0.399841i \(-0.130935\pi\)
\(110\) −6.35835 8.93155i −0.606245 0.851589i
\(111\) −5.38078 + 5.71825i −0.510721 + 0.542752i
\(112\) 18.5627i 1.75401i
\(113\) −6.72408 + 3.88215i −0.632548 + 0.365202i −0.781738 0.623607i \(-0.785667\pi\)
0.149190 + 0.988809i \(0.452333\pi\)
\(114\) 2.80711 11.9135i 0.262910 1.11580i
\(115\) 4.65336 8.05985i 0.433928 0.751585i
\(116\) −14.9841 −1.39124
\(117\) 10.8077 + 0.440738i 0.999170 + 0.0407463i
\(118\) 20.3443i 1.87284i
\(119\) −11.7563 6.78750i −1.07770 0.622209i
\(120\) 0.365286 1.55029i 0.0333459 0.141522i
\(121\) 7.20127 + 8.31515i 0.654661 + 0.755922i
\(122\) 5.86553i 0.531041i
\(123\) 4.87845 5.18441i 0.439875 0.467463i
\(124\) 1.87648 + 3.25016i 0.168513 + 0.291873i
\(125\) 12.1040i 1.08262i
\(126\) 10.7089 21.4629i 0.954027 1.91207i
\(127\) −3.14794 1.81747i −0.279335 0.161274i 0.353787 0.935326i \(-0.384894\pi\)
−0.633122 + 0.774052i \(0.718227\pi\)
\(128\) −2.12590 + 3.68217i −0.187905 + 0.325461i
\(129\) 6.06558 1.82456i 0.534045 0.160643i
\(130\) 11.8573 + 1.20825i 1.03996 + 0.105971i
\(131\) 8.69314 0.759523 0.379761 0.925084i \(-0.376006\pi\)
0.379761 + 0.925084i \(0.376006\pi\)
\(132\) 1.34434 9.79931i 0.117010 0.852921i
\(133\) −7.59044 + 13.1470i −0.658174 + 1.13999i
\(134\) 15.1221 + 26.1922i 1.30635 + 2.26266i
\(135\) −5.69629 + 6.84288i −0.490259 + 0.588942i
\(136\) −0.878925 1.52234i −0.0753672 0.130540i
\(137\) −1.15732 + 0.668179i −0.0988766 + 0.0570864i −0.548623 0.836070i \(-0.684848\pi\)
0.449746 + 0.893156i \(0.351514\pi\)
\(138\) 17.3798 5.22793i 1.47947 0.445031i
\(139\) −7.96240 + 4.59710i −0.675362 + 0.389921i −0.798105 0.602518i \(-0.794164\pi\)
0.122743 + 0.992438i \(0.460831\pi\)
\(140\) 6.11365 10.5892i 0.516698 0.894947i
\(141\) 0.575074 2.44064i 0.0484300 0.205539i
\(142\) 6.78132i 0.569076i
\(143\) −11.9580 0.0775035i −0.999979 0.00648117i
\(144\) 11.2071 7.41303i 0.933921 0.617753i
\(145\) −12.9138 7.45578i −1.07243 0.619169i
\(146\) 18.0306 + 10.4100i 1.49222 + 0.861534i
\(147\) −12.0786 + 12.8362i −0.996230 + 1.05871i
\(148\) −7.80544 −0.641603
\(149\) 4.00350 + 6.93427i 0.327980 + 0.568077i 0.982111 0.188304i \(-0.0602990\pi\)
−0.654131 + 0.756381i \(0.726966\pi\)
\(150\) 4.72625 5.02266i 0.385896 0.410099i
\(151\) 14.4474i 1.17571i 0.808966 + 0.587855i \(0.200028\pi\)
−0.808966 + 0.587855i \(0.799972\pi\)
\(152\) −1.70243 + 0.982900i −0.138086 + 0.0797237i
\(153\) 0.596998 + 9.80833i 0.0482645 + 0.792957i
\(154\) −11.0191 + 24.1199i −0.887941 + 1.94364i
\(155\) 3.73480i 0.299986i
\(156\) 7.04356 + 8.12465i 0.563936 + 0.650493i
\(157\) −22.1309 −1.76624 −0.883120 0.469148i \(-0.844561\pi\)
−0.883120 + 0.469148i \(0.844561\pi\)
\(158\) 9.59778 + 5.54128i 0.763558 + 0.440840i
\(159\) 3.60027 15.2797i 0.285520 1.21176i
\(160\) 11.2296 6.48341i 0.887778 0.512559i
\(161\) −22.5102 −1.77405
\(162\) −17.2346 + 2.10582i −1.35408 + 0.165449i
\(163\) −0.868763 1.50474i −0.0680467 0.117860i 0.829995 0.557771i \(-0.188343\pi\)
−0.898041 + 0.439911i \(0.855010\pi\)
\(164\) 7.07675 0.552602
\(165\) 6.03454 7.77646i 0.469788 0.605397i
\(166\) 6.92512 11.9947i 0.537493 0.930966i
\(167\) 3.44254 5.96265i 0.266392 0.461404i −0.701536 0.712634i \(-0.747502\pi\)
0.967927 + 0.251231i \(0.0808352\pi\)
\(168\) −3.68909 + 1.10970i −0.284619 + 0.0856149i
\(169\) 8.63726 9.71585i 0.664405 0.747373i
\(170\) 10.8277i 0.830444i
\(171\) 10.9686 0.667622i 0.838792 0.0510543i
\(172\) 5.45305 + 3.14832i 0.415791 + 0.240057i
\(173\) −6.66271 11.5402i −0.506556 0.877382i −0.999971 0.00758740i \(-0.997585\pi\)
0.493415 0.869794i \(-0.335749\pi\)
\(174\) −8.37638 27.8466i −0.635012 2.11104i
\(175\) −7.40793 + 4.27697i −0.559987 + 0.323308i
\(176\) −12.1017 + 8.61520i −0.912203 + 0.649395i
\(177\) −17.4911 + 5.26140i −1.31471 + 0.395471i
\(178\) 15.0758 8.70400i 1.12998 0.652393i
\(179\) 18.5553 + 10.7129i 1.38689 + 0.800721i 0.992963 0.118421i \(-0.0377832\pi\)
0.393926 + 0.919142i \(0.371117\pi\)
\(180\) −8.83458 + 0.537730i −0.658491 + 0.0400800i
\(181\) −9.13729 −0.679169 −0.339585 0.940575i \(-0.610287\pi\)
−0.339585 + 0.940575i \(0.610287\pi\)
\(182\) −11.8088 26.2982i −0.875325 1.94935i
\(183\) 5.04291 1.51693i 0.372782 0.112135i
\(184\) −2.52436 1.45744i −0.186098 0.107444i
\(185\) −6.72699 3.88383i −0.494578 0.285545i
\(186\) −4.99114 + 5.30417i −0.365968 + 0.388921i
\(187\) −1.03122 10.8145i −0.0754104 0.790837i
\(188\) 2.15871 1.24633i 0.157440 0.0908981i
\(189\) 21.2223 + 3.65633i 1.54370 + 0.265959i
\(190\) 12.1085 0.878446
\(191\) 12.0014 6.92899i 0.868388 0.501364i 0.00157552 0.999999i \(-0.499498\pi\)
0.866812 + 0.498635i \(0.166165\pi\)
\(192\) 9.51059 + 2.24093i 0.686368 + 0.161725i
\(193\) 18.2513 + 10.5374i 1.31376 + 0.758498i 0.982716 0.185119i \(-0.0592670\pi\)
0.331040 + 0.943617i \(0.392600\pi\)
\(194\) −24.3990 −1.75175
\(195\) 2.02771 + 10.5068i 0.145208 + 0.752410i
\(196\) −17.5215 −1.25153
\(197\) −1.67614 + 2.90316i −0.119420 + 0.206841i −0.919538 0.393001i \(-0.871437\pi\)
0.800118 + 0.599843i \(0.204770\pi\)
\(198\) 18.9626 2.97967i 1.34762 0.211756i
\(199\) −1.88043 3.25700i −0.133300 0.230882i 0.791647 0.610979i \(-0.209224\pi\)
−0.924947 + 0.380097i \(0.875891\pi\)
\(200\) −1.10767 −0.0783238
\(201\) −18.6080 + 19.7750i −1.31251 + 1.39482i
\(202\) 4.04871 + 7.01257i 0.284866 + 0.493403i
\(203\) 36.0666i 2.53138i
\(204\) −6.69421 + 7.11406i −0.468689 + 0.498084i
\(205\) 6.09898 + 3.52125i 0.425971 + 0.245935i
\(206\) −13.9951 + 24.2402i −0.975085 + 1.68890i
\(207\) 8.98945 + 13.5903i 0.624810 + 0.944590i
\(208\) 1.63712 16.0660i 0.113514 1.11398i
\(209\) −12.0939 + 1.15321i −0.836550 + 0.0797694i
\(210\) 23.0966 + 5.44213i 1.59382 + 0.375542i
\(211\) −8.31881 4.80287i −0.572690 0.330643i 0.185533 0.982638i \(-0.440599\pi\)
−0.758223 + 0.651995i \(0.773932\pi\)
\(212\) 13.5147 7.80270i 0.928191 0.535891i
\(213\) −5.83026 + 1.75377i −0.399483 + 0.120166i
\(214\) 12.7663 + 22.1118i 0.872685 + 1.51153i
\(215\) 3.13308 + 5.42665i 0.213674 + 0.370095i
\(216\) 2.14321 + 1.78409i 0.145827 + 0.121392i
\(217\) 7.82313 4.51669i 0.531069 0.306613i
\(218\) 13.9489 + 8.05339i 0.944737 + 0.545444i
\(219\) −4.28696 + 18.1940i −0.289686 + 1.22944i
\(220\) 9.74089 0.928845i 0.656731 0.0626227i
\(221\) 9.57642 + 6.91139i 0.644180 + 0.464911i
\(222\) −4.36339 14.5057i −0.292851 0.973559i
\(223\) −4.12973 + 7.15290i −0.276547 + 0.478993i −0.970524 0.241003i \(-0.922523\pi\)
0.693977 + 0.719997i \(0.255857\pi\)
\(224\) −27.1611 15.6814i −1.81477 1.04776i
\(225\) 5.54054 + 2.76445i 0.369369 + 0.184297i
\(226\) 14.9789i 0.996382i
\(227\) −2.53984 4.39914i −0.168575 0.291981i 0.769344 0.638835i \(-0.220583\pi\)
−0.937919 + 0.346854i \(0.887250\pi\)
\(228\) 7.95563 + 7.48612i 0.526874 + 0.495780i
\(229\) 18.5371 1.22497 0.612483 0.790484i \(-0.290171\pi\)
0.612483 + 0.790484i \(0.290171\pi\)
\(230\) 8.97726 + 15.5491i 0.591943 + 1.02528i
\(231\) −23.5869 3.23581i −1.55190 0.212901i
\(232\) −2.33517 + 4.04463i −0.153311 + 0.265543i
\(233\) 25.4210 1.66538 0.832692 0.553736i \(-0.186798\pi\)
0.832692 + 0.553736i \(0.186798\pi\)
\(234\) −11.1614 + 17.6316i −0.729647 + 1.15262i
\(235\) 2.48060 0.161816
\(236\) −15.7247 9.07867i −1.02359 0.590971i
\(237\) −2.28197 + 9.68478i −0.148230 + 0.629094i
\(238\) 22.6802 13.0944i 1.47014 0.848787i
\(239\) 10.3761 0.671177 0.335589 0.942009i \(-0.391065\pi\)
0.335589 + 0.942009i \(0.391065\pi\)
\(240\) 9.68082 + 9.10950i 0.624894 + 0.588016i
\(241\) 11.8170 6.82255i 0.761200 0.439479i −0.0685265 0.997649i \(-0.521830\pi\)
0.829726 + 0.558170i \(0.188496\pi\)
\(242\) −20.8388 + 4.01064i −1.33957 + 0.257814i
\(243\) −6.26767 14.2729i −0.402071 0.915608i
\(244\) 4.53365 + 2.61750i 0.290237 + 0.167569i
\(245\) −15.1006 8.71833i −0.964741 0.556994i
\(246\) 3.95604 + 13.1515i 0.252228 + 0.838509i
\(247\) 7.72899 10.7093i 0.491784 0.681416i
\(248\) 1.16975 0.0742791
\(249\) 12.1034 + 2.85186i 0.767021 + 0.180729i
\(250\) 20.2226 + 11.6755i 1.27899 + 0.738426i
\(251\) −2.21624 + 1.27955i −0.139888 + 0.0807643i −0.568311 0.822814i \(-0.692403\pi\)
0.428423 + 0.903578i \(0.359069\pi\)
\(252\) 11.8105 + 17.8551i 0.743990 + 1.12477i
\(253\) −10.4473 14.6752i −0.656814 0.922623i
\(254\) 6.07302 3.50626i 0.381055 0.220002i
\(255\) −9.30911 + 2.80023i −0.582959 + 0.175357i
\(256\) −9.74261 16.8747i −0.608913 1.05467i
\(257\) −4.10951 2.37263i −0.256344 0.148000i 0.366321 0.930488i \(-0.380617\pi\)
−0.622666 + 0.782488i \(0.713950\pi\)
\(258\) −2.80251 + 11.8940i −0.174477 + 0.740486i
\(259\) 18.7877i 1.16741i
\(260\) −6.22524 + 8.62570i −0.386073 + 0.534943i
\(261\) 21.7749 14.4032i 1.34783 0.891537i
\(262\) −8.38541 + 14.5239i −0.518052 + 0.897293i
\(263\) 0.0220398 0.0381740i 0.00135903 0.00235391i −0.865345 0.501176i \(-0.832901\pi\)
0.866704 + 0.498823i \(0.166234\pi\)
\(264\) −2.43561 1.89003i −0.149901 0.116323i
\(265\) 15.5299 0.953992
\(266\) −14.6435 25.3633i −0.897850 1.55512i
\(267\) 11.3822 + 10.7104i 0.696576 + 0.655467i
\(268\) −26.9930 −1.64886
\(269\) 2.63966 1.52401i 0.160943 0.0929204i −0.417365 0.908739i \(-0.637046\pi\)
0.578308 + 0.815818i \(0.303713\pi\)
\(270\) −5.93802 16.1177i −0.361376 0.980890i
\(271\) 4.19786 + 2.42363i 0.255002 + 0.147225i 0.622052 0.782976i \(-0.286299\pi\)
−0.367051 + 0.930201i \(0.619632\pi\)
\(272\) 14.6709 0.889552
\(273\) 19.5560 16.9538i 1.18358 1.02609i
\(274\) 2.57811i 0.155749i
\(275\) −6.22643 2.84451i −0.375468 0.171530i
\(276\) −3.71494 + 15.7663i −0.223613 + 0.949022i
\(277\) −16.6384 + 9.60616i −0.999702 + 0.577178i −0.908160 0.418623i \(-0.862513\pi\)
−0.0915416 + 0.995801i \(0.529179\pi\)
\(278\) 17.7374i 1.06382i
\(279\) −5.85107 2.91939i −0.350295 0.174780i
\(280\) −1.90554 3.30049i −0.113878 0.197242i
\(281\) −6.47979 −0.386552 −0.193276 0.981144i \(-0.561911\pi\)
−0.193276 + 0.981144i \(0.561911\pi\)
\(282\) 3.52295 + 3.31504i 0.209789 + 0.197408i
\(283\) 13.6552 + 7.88385i 0.811719 + 0.468646i 0.847552 0.530712i \(-0.178075\pi\)
−0.0358337 + 0.999358i \(0.511409\pi\)
\(284\) −5.24149 3.02618i −0.311025 0.179571i
\(285\) 3.13149 + 10.4104i 0.185493 + 0.616656i
\(286\) 11.6642 19.9039i 0.689718 1.17694i
\(287\) 17.0337i 1.00547i
\(288\) 1.37927 + 22.6606i 0.0812743 + 1.33529i
\(289\) 3.13557 5.43097i 0.184445 0.319469i
\(290\) 24.9133 14.3837i 1.46296 0.844640i
\(291\) −6.31002 20.9771i −0.369900 1.22970i
\(292\) −16.0924 + 9.29092i −0.941734 + 0.543710i
\(293\) −15.9337 27.5979i −0.930854 1.61229i −0.781866 0.623447i \(-0.785732\pi\)
−0.148988 0.988839i \(-0.547602\pi\)
\(294\) −9.79482 32.5620i −0.571246 1.89906i
\(295\) −9.03473 15.6486i −0.526022 0.911098i
\(296\) −1.21642 + 2.10691i −0.0707032 + 0.122462i
\(297\) 7.46585 + 15.5326i 0.433213 + 0.901292i
\(298\) −15.4471 −0.894828
\(299\) 19.4825 + 1.98526i 1.12670 + 0.114810i
\(300\) 1.77307 + 5.89443i 0.102368 + 0.340315i
\(301\) 7.57799 13.1255i 0.436788 0.756539i
\(302\) −24.1378 13.9359i −1.38897 0.801924i
\(303\) −4.98201 + 5.29447i −0.286209 + 0.304159i
\(304\) 16.4064i 0.940971i
\(305\) 2.60484 + 4.51171i 0.149152 + 0.258340i
\(306\) −16.9630 8.46370i −0.969711 0.483837i
\(307\) 28.7316i 1.63980i 0.572506 + 0.819900i \(0.305971\pi\)
−0.572506 + 0.819900i \(0.694029\pi\)
\(308\) −13.7258 19.2805i −0.782098 1.09861i
\(309\) −24.4600 5.76337i −1.39148 0.327866i
\(310\) −6.23987 3.60259i −0.354401 0.204613i
\(311\) 19.2304i 1.09046i −0.838288 0.545228i \(-0.816443\pi\)
0.838288 0.545228i \(-0.183557\pi\)
\(312\) 3.29076 0.635084i 0.186303 0.0359546i
\(313\) −17.3332 −0.979733 −0.489866 0.871798i \(-0.662954\pi\)
−0.489866 + 0.871798i \(0.662954\pi\)
\(314\) 21.3475 36.9749i 1.20471 2.08662i
\(315\) 1.29431 + 21.2648i 0.0729263 + 1.19814i
\(316\) −8.56605 + 4.94561i −0.481878 + 0.278212i
\(317\) 33.6635i 1.89073i 0.326012 + 0.945366i \(0.394295\pi\)
−0.326012 + 0.945366i \(0.605705\pi\)
\(318\) 22.0555 + 20.7539i 1.23681 + 1.16382i
\(319\) −23.5132 + 16.7390i −1.31649 + 0.937203i
\(320\) 9.66630i 0.540362i
\(321\) −15.7091 + 16.6944i −0.876798 + 0.931788i
\(322\) 21.7133 37.6086i 1.21004 2.09584i
\(323\) 10.3906 + 5.99903i 0.578150 + 0.333795i
\(324\) 6.06333 14.2609i 0.336852 0.792273i
\(325\) 6.78874 3.04837i 0.376572 0.169093i
\(326\) 3.35204 0.185652
\(327\) −3.31649 + 14.0753i −0.183402 + 0.778368i
\(328\) 1.10286 1.91022i 0.0608954 0.105474i
\(329\) −2.99991 5.19600i −0.165391 0.286465i
\(330\) 7.17151 + 17.5833i 0.394779 + 0.967929i
\(331\) 11.1119 + 19.2463i 0.610764 + 1.05787i 0.991112 + 0.133030i \(0.0424707\pi\)
−0.380348 + 0.924843i \(0.624196\pi\)
\(332\) 6.18069 + 10.7053i 0.339210 + 0.587528i
\(333\) 11.3429 7.50286i 0.621585 0.411154i
\(334\) 6.64135 + 11.5032i 0.363399 + 0.629425i
\(335\) −23.2635 13.4312i −1.27102 0.733824i
\(336\) 7.37377 31.2946i 0.402272 1.70726i
\(337\) 31.7148i 1.72762i −0.503821 0.863808i \(-0.668073\pi\)
0.503821 0.863808i \(-0.331927\pi\)
\(338\) 7.90113 + 23.8025i 0.429765 + 1.29469i
\(339\) 12.8781 3.87381i 0.699445 0.210397i
\(340\) −8.36903 4.83186i −0.453874 0.262045i
\(341\) 6.57541 + 3.00394i 0.356079 + 0.162672i
\(342\) −9.46493 + 18.9697i −0.511805 + 1.02576i
\(343\) 13.1632i 0.710747i
\(344\) 1.69964 0.981288i 0.0916385 0.0529075i
\(345\) −11.0467 + 11.7395i −0.594733 + 0.632033i
\(346\) 25.7074 1.38204
\(347\) −1.34141 2.32338i −0.0720105 0.124726i 0.827772 0.561065i \(-0.189608\pi\)
−0.899782 + 0.436339i \(0.856275\pi\)
\(348\) 25.2614 + 5.95221i 1.35415 + 0.319072i
\(349\) 1.10768 + 0.639520i 0.0592928 + 0.0342327i 0.529353 0.848401i \(-0.322435\pi\)
−0.470061 + 0.882634i \(0.655768\pi\)
\(350\) 16.5023i 0.882083i
\(351\) −18.0454 5.03622i −0.963192 0.268814i
\(352\) −2.38248 24.9853i −0.126986 1.33172i
\(353\) 10.2087 + 5.89397i 0.543352 + 0.313704i 0.746436 0.665457i \(-0.231763\pi\)
−0.203084 + 0.979161i \(0.565097\pi\)
\(354\) 8.08147 34.2981i 0.429526 1.82292i
\(355\) −3.01153 5.21612i −0.159835 0.276843i
\(356\) 15.5367i 0.823444i
\(357\) 17.1235 + 16.1129i 0.906272 + 0.852787i
\(358\) −35.7970 + 20.6674i −1.89193 + 1.09231i
\(359\) 18.0155 0.950822 0.475411 0.879764i \(-0.342299\pi\)
0.475411 + 0.879764i \(0.342299\pi\)
\(360\) −1.23166 + 2.46850i −0.0649142 + 0.130102i
\(361\) −2.79130 + 4.83468i −0.146911 + 0.254457i
\(362\) 8.81384 15.2660i 0.463245 0.802364i
\(363\) −8.83744 16.8790i −0.463845 0.885916i
\(364\) 25.5964 + 2.60826i 1.34162 + 0.136710i
\(365\) −18.4919 −0.967911
\(366\) −2.33000 + 9.88861i −0.121791 + 0.516886i
\(367\) −2.71701 + 4.70601i −0.141827 + 0.245651i −0.928185 0.372120i \(-0.878631\pi\)
0.786358 + 0.617771i \(0.211964\pi\)
\(368\) 21.0681 12.1637i 1.09825 0.634075i
\(369\) −10.2839 + 6.80242i −0.535360 + 0.354120i
\(370\) 12.9777 7.49269i 0.674680 0.389526i
\(371\) −18.7811 32.5297i −0.975064 1.68886i
\(372\) −1.87245 6.22480i −0.0970821 0.322741i
\(373\) 24.2949 14.0267i 1.25794 0.726273i 0.285268 0.958448i \(-0.407917\pi\)
0.972674 + 0.232175i \(0.0745841\pi\)
\(374\) 19.0630 + 8.70880i 0.985722 + 0.450321i
\(375\) −4.80814 + 20.4059i −0.248291 + 1.05376i
\(376\) 0.776929i 0.0400671i
\(377\) 3.18085 31.2156i 0.163822 1.60768i
\(378\) −26.5798 + 31.9300i −1.36712 + 1.64230i
\(379\) −12.6903 + 21.9802i −0.651856 + 1.12905i 0.330817 + 0.943695i \(0.392676\pi\)
−0.982672 + 0.185352i \(0.940658\pi\)
\(380\) −5.40346 + 9.35906i −0.277192 + 0.480110i
\(381\) 4.58510 + 4.31451i 0.234902 + 0.221039i
\(382\) 26.7348i 1.36787i
\(383\) −16.7318 + 9.66011i −0.854955 + 0.493609i −0.862320 0.506364i \(-0.830989\pi\)
0.00736430 + 0.999973i \(0.497656\pi\)
\(384\) 5.04672 5.36323i 0.257539 0.273691i
\(385\) −2.23573 23.4463i −0.113943 1.19493i
\(386\) −35.2104 + 20.3287i −1.79216 + 1.03471i
\(387\) −10.9506 + 0.666527i −0.556652 + 0.0338815i
\(388\) 10.8881 18.8587i 0.552759 0.957407i
\(389\) 2.53818i 0.128691i −0.997928 0.0643455i \(-0.979504\pi\)
0.997928 0.0643455i \(-0.0204960\pi\)
\(390\) −19.5101 6.74712i −0.987932 0.341654i
\(391\) 17.7907i 0.899714i
\(392\) −2.73060 + 4.72954i −0.137916 + 0.238878i
\(393\) −14.6556 3.45322i −0.739278 0.174192i
\(394\) −3.23361 5.60077i −0.162907 0.282163i
\(395\) −9.84334 −0.495272
\(396\) −6.15903 + 15.9865i −0.309503 + 0.803351i
\(397\) −1.96766 3.40809i −0.0987542 0.171047i 0.812415 0.583080i \(-0.198152\pi\)
−0.911169 + 0.412032i \(0.864819\pi\)
\(398\) 7.25545 0.363683
\(399\) 18.0191 19.1492i 0.902081 0.958657i
\(400\) 4.62224 8.00595i 0.231112 0.400297i
\(401\) 13.8961 + 8.02294i 0.693940 + 0.400646i 0.805086 0.593158i \(-0.202119\pi\)
−0.111147 + 0.993804i \(0.535452\pi\)
\(402\) −15.0896 50.1641i −0.752601 2.50196i
\(403\) −7.16924 + 3.21923i −0.357125 + 0.160361i
\(404\) −7.22698 −0.359556
\(405\) 12.3215 9.27354i 0.612261 0.460806i
\(406\) −60.2579 34.7899i −2.99055 1.72659i
\(407\) −12.2484 + 8.71960i −0.607130 + 0.432214i
\(408\) 0.877037 + 2.91563i 0.0434198 + 0.144345i
\(409\) 6.57086 3.79369i 0.324908 0.187586i −0.328670 0.944445i \(-0.606600\pi\)
0.653578 + 0.756859i \(0.273267\pi\)
\(410\) −11.7662 + 6.79320i −0.581090 + 0.335492i
\(411\) 2.21653 0.666744i 0.109333 0.0328881i
\(412\) −12.4907 21.6345i −0.615371 1.06585i
\(413\) −21.8523 + 37.8493i −1.07528 + 1.86244i
\(414\) −31.3770 + 1.90981i −1.54210 + 0.0938620i
\(415\) 12.3016i 0.603859i
\(416\) 22.1248 + 15.9677i 1.08476 + 0.782880i
\(417\) 15.2498 4.58722i 0.746787 0.224637i
\(418\) 9.73903 21.3181i 0.476352 1.04270i
\(419\) 1.76546 + 1.01929i 0.0862484 + 0.0497955i 0.542504 0.840053i \(-0.317476\pi\)
−0.456256 + 0.889849i \(0.650810\pi\)
\(420\) −14.5133 + 15.4235i −0.708176 + 0.752591i
\(421\) −17.8359 −0.869267 −0.434633 0.900607i \(-0.643122\pi\)
−0.434633 + 0.900607i \(0.643122\pi\)
\(422\) 16.0487 9.26570i 0.781237 0.451047i
\(423\) −1.93902 + 3.88620i −0.0942783 + 0.188953i
\(424\) 4.86399i 0.236216i
\(425\) 3.38026 + 5.85478i 0.163967 + 0.283999i
\(426\) 2.69378 11.4325i 0.130514 0.553907i
\(427\) 6.30032 10.9125i 0.304894 0.528092i
\(428\) −22.7879 −1.10149
\(429\) 20.1290 + 4.88081i 0.971839 + 0.235648i
\(430\) −12.0887 −0.582968
\(431\) −16.4501 + 28.4924i −0.792373 + 1.37243i 0.132121 + 0.991234i \(0.457821\pi\)
−0.924494 + 0.381197i \(0.875512\pi\)
\(432\) −21.8385 + 8.04567i −1.05071 + 0.387098i
\(433\) 1.81721 + 3.14751i 0.0873297 + 0.151259i 0.906382 0.422460i \(-0.138833\pi\)
−0.819052 + 0.573719i \(0.805500\pi\)
\(434\) 17.4272i 0.836532i
\(435\) 18.8094 + 17.6994i 0.901844 + 0.848621i
\(436\) −12.4494 + 7.18768i −0.596219 + 0.344227i
\(437\) 19.8953 0.951720
\(438\) −26.2623 24.7124i −1.25486 1.18080i
\(439\) −3.84060 2.21737i −0.183302 0.105829i 0.405541 0.914077i \(-0.367083\pi\)
−0.588843 + 0.808247i \(0.700416\pi\)
\(440\) 1.26733 2.77410i 0.0604176 0.132250i
\(441\) 25.4622 16.8422i 1.21248 0.802012i
\(442\) −20.7845 + 9.33295i −0.988620 + 0.443923i
\(443\) 18.2152i 0.865432i −0.901530 0.432716i \(-0.857555\pi\)
0.901530 0.432716i \(-0.142445\pi\)
\(444\) 13.1591 + 3.10060i 0.624502 + 0.147148i
\(445\) −7.73075 + 13.3901i −0.366473 + 0.634749i
\(446\) −7.96708 13.7994i −0.377252 0.653420i
\(447\) −3.99490 13.2807i −0.188952 0.628156i
\(448\) 20.2476 11.6899i 0.956609 0.552298i
\(449\) 4.80448 2.77387i 0.226737 0.130907i −0.382329 0.924026i \(-0.624878\pi\)
0.609066 + 0.793120i \(0.291544\pi\)
\(450\) −9.96308 + 6.59019i −0.469664 + 0.310665i
\(451\) 11.1049 7.90557i 0.522910 0.372259i
\(452\) 11.5777 + 6.68436i 0.544567 + 0.314406i
\(453\) 5.73901 24.3566i 0.269642 1.14437i
\(454\) 9.79974 0.459925
\(455\) 20.7620 + 14.9841i 0.973338 + 0.702467i
\(456\) 3.26055 0.980788i 0.152689 0.0459296i
\(457\) −22.4480 12.9603i −1.05007 0.606259i −0.127403 0.991851i \(-0.540664\pi\)
−0.922670 + 0.385592i \(0.873997\pi\)
\(458\) −17.8809 + 30.9706i −0.835519 + 1.44716i
\(459\) 2.88975 16.7729i 0.134882 0.782890i
\(460\) −16.0245 −0.747145
\(461\) 8.83315 + 15.2995i 0.411401 + 0.712567i 0.995043 0.0994436i \(-0.0317063\pi\)
−0.583642 + 0.812011i \(0.698373\pi\)
\(462\) 28.1581 36.2863i 1.31004 1.68819i
\(463\) −30.0204 −1.39517 −0.697583 0.716504i \(-0.745741\pi\)
−0.697583 + 0.716504i \(0.745741\pi\)
\(464\) −19.4891 33.7561i −0.904758 1.56709i
\(465\) 1.48359 6.29644i 0.0688001 0.291990i
\(466\) −24.5211 + 42.4718i −1.13592 + 1.96747i
\(467\) 18.9378i 0.876335i 0.898893 + 0.438167i \(0.144372\pi\)
−0.898893 + 0.438167i \(0.855628\pi\)
\(468\) −8.64722 16.4952i −0.399718 0.762490i
\(469\) 64.9721i 3.00013i
\(470\) −2.39279 + 4.14443i −0.110371 + 0.191168i
\(471\) 37.3101 + 8.79118i 1.71916 + 0.405076i
\(472\) −4.90118 + 2.82970i −0.225595 + 0.130247i
\(473\) 12.0740 1.15132i 0.555164 0.0529378i
\(474\) −13.9795 13.1545i −0.642102 0.604207i
\(475\) 6.54739 3.78014i 0.300415 0.173445i
\(476\) 23.3737i 1.07133i
\(477\) −12.1393 + 24.3296i −0.555819 + 1.11398i
\(478\) −10.0088 + 17.3358i −0.457794 + 0.792922i
\(479\) 19.8678 34.4121i 0.907785 1.57233i 0.0906509 0.995883i \(-0.471105\pi\)
0.817134 0.576447i \(-0.195561\pi\)
\(480\) −21.5072 + 6.46948i −0.981667 + 0.295290i
\(481\) 1.65695 16.2607i 0.0755506 0.741423i
\(482\) 26.3241i 1.19903i
\(483\) 37.9495 + 8.94184i 1.72676 + 0.406868i
\(484\) 6.19939 17.8967i 0.281791 0.813486i
\(485\) 18.7675 10.8354i 0.852186 0.492010i
\(486\) 29.8921 + 3.29603i 1.35593 + 0.149511i
\(487\) −12.8327 22.2269i −0.581505 1.00720i −0.995301 0.0968261i \(-0.969131\pi\)
0.413797 0.910369i \(-0.364202\pi\)
\(488\) 1.41308 0.815840i 0.0639670 0.0369314i
\(489\) 0.866896 + 2.88192i 0.0392024 + 0.130325i
\(490\) 29.1321 16.8194i 1.31605 0.759824i
\(491\) 15.8918 27.5254i 0.717186 1.24220i −0.244925 0.969542i \(-0.578763\pi\)
0.962110 0.272660i \(-0.0879034\pi\)
\(492\) −11.9306 2.81114i −0.537872 0.126736i
\(493\) 28.5049 1.28380
\(494\) 10.4370 + 23.2433i 0.469584 + 1.04577i
\(495\) −13.2626 + 10.7131i −0.596110 + 0.481517i
\(496\) −4.88131 + 8.45467i −0.219177 + 0.379626i
\(497\) −7.28399 + 12.6162i −0.326732 + 0.565916i
\(498\) −16.4396 + 17.4707i −0.736678 + 0.782881i
\(499\) −6.35324 −0.284410 −0.142205 0.989837i \(-0.545419\pi\)
−0.142205 + 0.989837i \(0.545419\pi\)
\(500\) −18.0488 + 10.4205i −0.807165 + 0.466017i
\(501\) −8.17230 + 8.68484i −0.365111 + 0.388010i
\(502\) 4.93701i 0.220350i
\(503\) −15.1946 26.3178i −0.677492 1.17345i −0.975734 0.218960i \(-0.929733\pi\)
0.298242 0.954490i \(-0.403600\pi\)
\(504\) 6.66018 0.405382i 0.296668 0.0180571i
\(505\) −6.22845 3.59600i −0.277162 0.160020i
\(506\) 34.5959 3.29890i 1.53797 0.146654i
\(507\) −18.4209 + 12.9488i −0.818101 + 0.575075i
\(508\) 6.25869i 0.277685i
\(509\) −7.90008 4.56111i −0.350165 0.202168i 0.314593 0.949227i \(-0.398132\pi\)
−0.664758 + 0.747059i \(0.731465\pi\)
\(510\) 4.30113 18.2542i 0.190457 0.808309i
\(511\) 22.3632 + 38.7342i 0.989290 + 1.71350i
\(512\) 29.0873 1.28549
\(513\) −18.7570 3.23160i −0.828143 0.142678i
\(514\) 7.92808 4.57728i 0.349693 0.201895i
\(515\) 24.8604i 1.09548i
\(516\) −7.94258 7.47384i −0.349653 0.329018i
\(517\) 1.99517 4.36729i 0.0877475 0.192073i
\(518\) −31.3893 18.1226i −1.37916 0.796261i
\(519\) 6.64840 + 22.1020i 0.291832 + 0.970171i
\(520\) 1.35816 + 3.02463i 0.0595592 + 0.132639i
\(521\) 1.86793i 0.0818355i −0.999163 0.0409178i \(-0.986972\pi\)
0.999163 0.0409178i \(-0.0130282\pi\)
\(522\) 3.05997 + 50.2734i 0.133931 + 2.20041i
\(523\) 10.4710 + 6.04544i 0.457865 + 0.264349i 0.711146 0.703044i \(-0.248176\pi\)
−0.253281 + 0.967393i \(0.581510\pi\)
\(524\) −7.48400 12.9627i −0.326940 0.566277i
\(525\) 14.1879 4.26778i 0.619209 0.186261i
\(526\) 0.0425191 + 0.0736453i 0.00185392 + 0.00321109i
\(527\) −3.56972 6.18293i −0.155499 0.269333i
\(528\) 23.8244 9.71699i 1.03682 0.422878i
\(529\) 3.25033 + 5.62974i 0.141319 + 0.244771i
\(530\) −14.9801 + 25.9463i −0.650695 + 1.12704i
\(531\) 31.5779 1.92204i 1.37036 0.0834092i
\(532\) 26.1387 1.13326
\(533\) −1.50227 + 14.7426i −0.0650704 + 0.638574i
\(534\) −28.8735 + 8.68531i −1.24948 + 0.375850i
\(535\) −19.6394 11.3388i −0.849084 0.490219i
\(536\) −4.20668 + 7.28618i −0.181701 + 0.314715i
\(537\) −27.0266 25.4316i −1.16628 1.09745i
\(538\) 5.88024i 0.253515i
\(539\) −27.4949 + 19.5735i −1.18429 + 0.843092i
\(540\) 15.1077 + 2.60286i 0.650131 + 0.112009i
\(541\) 19.4924i 0.838045i −0.907976 0.419023i \(-0.862373\pi\)
0.907976 0.419023i \(-0.137627\pi\)
\(542\) −8.09851 + 4.67568i −0.347861 + 0.200838i
\(543\) 15.4044 + 3.62965i 0.661066 + 0.155763i
\(544\) −12.3937 + 21.4665i −0.531374 + 0.920368i
\(545\) −14.3058 −0.612792
\(546\) 9.46164 + 49.0266i 0.404921 + 2.09815i
\(547\) 9.55999i 0.408756i 0.978892 + 0.204378i \(0.0655171\pi\)
−0.978892 + 0.204378i \(0.934483\pi\)
\(548\) 1.99270 + 1.15048i 0.0851238 + 0.0491462i
\(549\) −9.10434 + 0.554149i −0.388564 + 0.0236505i
\(550\) 10.7584 7.65892i 0.458742 0.326577i
\(551\) 31.8770i 1.35800i
\(552\) 3.67683 + 3.45984i 0.156496 + 0.147261i
\(553\) 11.9041 + 20.6184i 0.506212 + 0.876785i
\(554\) 37.0644i 1.57472i
\(555\) 9.79813 + 9.21989i 0.415907 + 0.391362i
\(556\) 13.7098 + 7.91537i 0.581426 + 0.335686i
\(557\) 1.16163 2.01200i 0.0492199 0.0852513i −0.840366 0.542020i \(-0.817660\pi\)
0.889586 + 0.456768i \(0.150993\pi\)
\(558\) 10.5215 6.95956i 0.445410 0.294622i
\(559\) −7.71632 + 10.6917i −0.326365 + 0.452212i
\(560\) 31.8069 1.34409
\(561\) −2.55739 + 18.6417i −0.107973 + 0.787052i
\(562\) 6.25041 10.8260i 0.263658 0.456669i
\(563\) −4.14745 7.18359i −0.174794 0.302752i 0.765296 0.643679i \(-0.222593\pi\)
−0.940090 + 0.340926i \(0.889259\pi\)
\(564\) −4.13442 + 1.24365i −0.174090 + 0.0523673i
\(565\) 6.65201 + 11.5216i 0.279852 + 0.484718i
\(566\) −26.3437 + 15.2095i −1.10731 + 0.639304i
\(567\) −34.3259 14.5944i −1.44155 0.612908i
\(568\) −1.63370 + 0.943218i −0.0685486 + 0.0395765i
\(569\) −19.3951 + 33.5933i −0.813086 + 1.40831i 0.0976083 + 0.995225i \(0.468881\pi\)
−0.910694 + 0.413081i \(0.864453\pi\)
\(570\) −20.4136 4.80994i −0.855032 0.201466i
\(571\) 3.30522i 0.138319i 0.997606 + 0.0691596i \(0.0220318\pi\)
−0.997606 + 0.0691596i \(0.977968\pi\)
\(572\) 10.1792 + 17.8978i 0.425614 + 0.748344i
\(573\) −22.9853 + 6.91410i −0.960226 + 0.288841i
\(574\) 28.4589 + 16.4307i 1.18785 + 0.685805i
\(575\) 9.70845 + 5.60518i 0.404870 + 0.233752i
\(576\) −15.1436 7.55589i −0.630982 0.314829i
\(577\) −3.78483 −0.157565 −0.0787824 0.996892i \(-0.525103\pi\)
−0.0787824 + 0.996892i \(0.525103\pi\)
\(578\) 6.04915 + 10.4774i 0.251611 + 0.435804i
\(579\) −26.5837 25.0149i −1.10478 1.03958i
\(580\) 25.6750i 1.06610i
\(581\) 25.7675 14.8769i 1.06902 0.617198i
\(582\) 41.1339 + 9.69215i 1.70505 + 0.401753i
\(583\) 12.4908 27.3415i 0.517317 1.13237i
\(584\) 5.79171i 0.239663i
\(585\) 0.755198 18.5188i 0.0312236 0.765657i
\(586\) 61.4784 2.53965
\(587\) −4.57662 2.64231i −0.188897 0.109060i 0.402569 0.915390i \(-0.368117\pi\)
−0.591466 + 0.806330i \(0.701451\pi\)
\(588\) 29.5392 + 6.96015i 1.21817 + 0.287032i
\(589\) −6.91436 + 3.99201i −0.284901 + 0.164488i
\(590\) 34.8596 1.43515
\(591\) 3.97901 4.22856i 0.163675 0.173940i
\(592\) −10.1522 17.5841i −0.417252 0.722701i
\(593\) −16.7919 −0.689559 −0.344779 0.938684i \(-0.612046\pi\)
−0.344779 + 0.938684i \(0.612046\pi\)
\(594\) −33.1524 2.50926i −1.36026 0.102956i
\(595\) −11.6303 + 20.1442i −0.476795 + 0.825832i
\(596\) 6.89330 11.9396i 0.282361 0.489063i
\(597\) 1.87639 + 6.23789i 0.0767955 + 0.255300i
\(598\) −22.1097 + 30.6352i −0.904132 + 1.25276i
\(599\) 25.7279i 1.05121i −0.850727 0.525607i \(-0.823838\pi\)
0.850727 0.525607i \(-0.176162\pi\)
\(600\) 1.86739 + 0.440004i 0.0762361 + 0.0179631i
\(601\) 32.7717 + 18.9207i 1.33678 + 0.771793i 0.986329 0.164787i \(-0.0526935\pi\)
0.350455 + 0.936579i \(0.386027\pi\)
\(602\) 14.6195 + 25.3217i 0.595845 + 1.03203i
\(603\) 39.2263 25.9467i 1.59742 1.05663i
\(604\) 21.5430 12.4379i 0.876574 0.506090i
\(605\) 14.2479 12.3393i 0.579259 0.501663i
\(606\) −4.04001 13.4307i −0.164114 0.545584i
\(607\) 15.9973 9.23603i 0.649309 0.374879i −0.138882 0.990309i \(-0.544351\pi\)
0.788192 + 0.615430i \(0.211018\pi\)
\(608\) 24.0059 + 13.8598i 0.973568 + 0.562090i
\(609\) 14.3269 60.8041i 0.580557 2.46391i
\(610\) −10.0505 −0.406933
\(611\) 2.13816 + 4.76170i 0.0865008 + 0.192638i
\(612\) 14.1116 9.33429i 0.570428 0.377316i
\(613\) 5.19968 + 3.00204i 0.210013 + 0.121251i 0.601318 0.799010i \(-0.294643\pi\)
−0.391304 + 0.920261i \(0.627976\pi\)
\(614\) −48.0030 27.7145i −1.93724 1.11847i
\(615\) −8.88341 8.35915i −0.358214 0.337073i
\(616\) −7.34343 + 0.700234i −0.295875 + 0.0282132i
\(617\) 7.05118 4.07100i 0.283870 0.163892i −0.351304 0.936261i \(-0.614262\pi\)
0.635174 + 0.772369i \(0.280928\pi\)
\(618\) 33.2232 35.3068i 1.33643 1.42025i
\(619\) −35.5739 −1.42984 −0.714918 0.699208i \(-0.753536\pi\)
−0.714918 + 0.699208i \(0.753536\pi\)
\(620\) 5.56911 3.21532i 0.223661 0.129131i
\(621\) −9.75662 26.4826i −0.391520 1.06271i
\(622\) 32.1290 + 18.5497i 1.28825 + 0.743774i
\(623\) 37.3968 1.49827
\(624\) −9.14197 + 26.4351i −0.365972 + 1.05825i
\(625\) −10.4202 −0.416807
\(626\) 16.7197 28.9593i 0.668252 1.15745i
\(627\) 20.8469 + 2.85993i 0.832546 + 0.114214i
\(628\) 19.0527 + 33.0003i 0.760286 + 1.31685i
\(629\) 14.8486 0.592054
\(630\) −36.7764 18.3496i −1.46521 0.731065i
\(631\) −4.31785 7.47874i −0.171891 0.297724i 0.767190 0.641420i \(-0.221654\pi\)
−0.939081 + 0.343696i \(0.888321\pi\)
\(632\) 3.08296i 0.122633i
\(633\) 12.1167 + 11.4016i 0.481595 + 0.453173i
\(634\) −56.2429 32.4719i −2.23369 1.28962i
\(635\) −3.11420 + 5.39395i −0.123583 + 0.214052i
\(636\) −25.8837 + 7.78593i −1.02635 + 0.308732i
\(637\) 3.71949 36.5016i 0.147372 1.44624i
\(638\) −5.28562 55.4308i −0.209260 2.19453i
\(639\) 10.5258 0.640668i 0.416394 0.0253444i
\(640\) 6.30935 + 3.64271i 0.249399 + 0.143991i
\(641\) 1.65745 0.956932i 0.0654655 0.0377965i −0.466910 0.884305i \(-0.654633\pi\)
0.532375 + 0.846508i \(0.321299\pi\)
\(642\) −12.7388 42.3492i −0.502762 1.67139i
\(643\) −9.79884 16.9721i −0.386429 0.669314i 0.605538 0.795817i \(-0.292958\pi\)
−0.991966 + 0.126503i \(0.959625\pi\)
\(644\) 19.3792 + 33.5658i 0.763648 + 1.32268i
\(645\) −3.12635 10.3933i −0.123100 0.409235i
\(646\) −20.0456 + 11.5733i −0.788684 + 0.455347i
\(647\) 14.0810 + 8.12968i 0.553582 + 0.319611i 0.750566 0.660796i \(-0.229781\pi\)
−0.196983 + 0.980407i \(0.563115\pi\)
\(648\) −2.90449 3.85913i −0.114099 0.151601i
\(649\) −34.8174 + 3.32002i −1.36670 + 0.130322i
\(650\) −1.45540 + 14.2827i −0.0570854 + 0.560213i
\(651\) −14.9831 + 4.50698i −0.587233 + 0.176643i
\(652\) −1.49585 + 2.59089i −0.0585821 + 0.101467i
\(653\) −33.4686 19.3231i −1.30973 0.756171i −0.327677 0.944790i \(-0.606266\pi\)
−0.982050 + 0.188619i \(0.939599\pi\)
\(654\) −20.3171 19.1181i −0.794461 0.747576i
\(655\) 14.8956i 0.582018i
\(656\) 9.20440 + 15.9425i 0.359371 + 0.622449i
\(657\) 14.4546 28.9701i 0.563929 1.13023i
\(658\) 11.5749 0.451236
\(659\) 11.0405 + 19.1227i 0.430077 + 0.744915i 0.996879 0.0789387i \(-0.0251531\pi\)
−0.566803 + 0.823854i \(0.691820\pi\)
\(660\) −16.7910 2.30350i −0.653588 0.0896637i
\(661\) 2.38985 4.13934i 0.0929545 0.161002i −0.815799 0.578336i \(-0.803702\pi\)
0.908753 + 0.417334i \(0.137036\pi\)
\(662\) −42.8741 −1.66635
\(663\) −13.3993 15.4559i −0.520385 0.600257i
\(664\) 3.85287 0.149521
\(665\) 22.5272 + 13.0061i 0.873568 + 0.504355i
\(666\) 1.59398 + 26.1882i 0.0617656 + 1.01477i
\(667\) 40.9345 23.6335i 1.58499 0.915094i
\(668\) −11.8549 −0.458678
\(669\) 9.80362 10.4185i 0.379030 0.402802i
\(670\) 44.8800 25.9115i 1.73387 1.00105i
\(671\) 10.0383 0.957206i 0.387525 0.0369525i
\(672\) 39.5612 + 37.2264i 1.52611 + 1.43604i
\(673\) 30.5284 + 17.6256i 1.17678 + 0.679416i 0.955268 0.295741i \(-0.0955665\pi\)
0.221515 + 0.975157i \(0.428900\pi\)
\(674\) 52.9871 + 30.5921i 2.04099 + 1.17837i
\(675\) −8.24256 6.86144i −0.317256 0.264097i
\(676\) −21.9236 4.51489i −0.843215 0.173649i
\(677\) 1.93182 0.0742457 0.0371229 0.999311i \(-0.488181\pi\)
0.0371229 + 0.999311i \(0.488181\pi\)
\(678\) −5.95015 + 25.2527i −0.228514 + 0.969824i
\(679\) −45.3929 26.2076i −1.74202 1.00576i
\(680\) −2.60851 + 1.50603i −0.100032 + 0.0577534i
\(681\) 2.53439 + 8.42535i 0.0971180 + 0.322860i
\(682\) −11.3614 + 8.08819i −0.435052 + 0.309713i
\(683\) −5.46171 + 3.15332i −0.208987 + 0.120658i −0.600840 0.799369i \(-0.705167\pi\)
0.391854 + 0.920028i \(0.371834\pi\)
\(684\) −10.4385 15.7810i −0.399127 0.603401i
\(685\) 1.14492 + 1.98305i 0.0437450 + 0.0757685i
\(686\) −21.9923 12.6972i −0.839669 0.484783i
\(687\) −31.2514 7.36359i −1.19231 0.280939i
\(688\) 16.3795i 0.624462i
\(689\) 13.3860 + 29.8108i 0.509967 + 1.13570i
\(690\) −8.95797 29.7800i −0.341024 1.13371i
\(691\) 18.8097 32.5793i 0.715555 1.23938i −0.247191 0.968967i \(-0.579507\pi\)
0.962745 0.270410i \(-0.0871592\pi\)
\(692\) −11.4720 + 19.8701i −0.436099 + 0.755346i
\(693\) 38.4794 + 14.8248i 1.46171 + 0.563146i
\(694\) 5.17569 0.196466
\(695\) 7.87705 + 13.6435i 0.298794 + 0.517526i
\(696\) 5.54349 5.89116i 0.210125 0.223304i
\(697\) −13.4624 −0.509926
\(698\) −2.13694 + 1.23376i −0.0808844 + 0.0466986i
\(699\) −42.8568 10.0981i −1.62099 0.381946i
\(700\) 12.7551 + 7.36417i 0.482098 + 0.278339i
\(701\) −35.6093 −1.34494 −0.672472 0.740123i \(-0.734767\pi\)
−0.672472 + 0.740123i \(0.734767\pi\)
\(702\) 25.8208 25.2912i 0.974544 0.954554i
\(703\) 16.6052i 0.626277i
\(704\) 17.0183 + 7.77470i 0.641401 + 0.293020i
\(705\) −4.18200 0.985381i −0.157503 0.0371116i
\(706\) −19.6946 + 11.3707i −0.741214 + 0.427940i
\(707\) 17.3953i 0.654218i
\(708\) 22.9037 + 21.5520i 0.860773 + 0.809974i
\(709\) 25.8235 + 44.7276i 0.969822 + 1.67978i 0.696059 + 0.717985i \(0.254935\pi\)
0.273763 + 0.961797i \(0.411731\pi\)
\(710\) 11.6197 0.436079
\(711\) 7.69428 15.4209i 0.288558 0.578330i
\(712\) 4.19380 + 2.42129i 0.157169 + 0.0907416i
\(713\) −10.2526 5.91934i −0.383963 0.221681i
\(714\) −43.4378 + 13.0663i −1.62562 + 0.488995i
\(715\) −0.132801 + 20.4899i −0.00496648 + 0.766278i
\(716\) 36.8914i 1.37870i
\(717\) −17.4930 4.12177i −0.653287 0.153930i
\(718\) −17.3778 + 30.0992i −0.648533 + 1.12329i
\(719\) −10.9779 + 6.33810i −0.409407 + 0.236371i −0.690535 0.723299i \(-0.742625\pi\)
0.281128 + 0.959670i \(0.409291\pi\)
\(720\) −12.7021 19.2031i −0.473380 0.715658i
\(721\) −52.0741 + 30.0650i −1.93934 + 1.11968i
\(722\) −5.38499 9.32707i −0.200408 0.347118i
\(723\) −22.6322 + 6.80789i −0.841702 + 0.253188i
\(724\) 7.86638 + 13.6250i 0.292352 + 0.506368i
\(725\) 8.98082 15.5552i 0.333539 0.577707i
\(726\) 36.7249 + 1.51643i 1.36299 + 0.0562799i
\(727\) 10.3708 0.384630 0.192315 0.981333i \(-0.438400\pi\)
0.192315 + 0.981333i \(0.438400\pi\)
\(728\) 4.69307 6.50271i 0.173937 0.241006i
\(729\) 4.89686 + 26.5522i 0.181365 + 0.983416i
\(730\) 17.8373 30.8951i 0.660188 1.14348i
\(731\) −10.3736 5.98919i −0.383681 0.221518i
\(732\) −6.60344 6.21374i −0.244070 0.229666i
\(733\) 1.45846i 0.0538696i −0.999637 0.0269348i \(-0.991425\pi\)
0.999637 0.0269348i \(-0.00857465\pi\)
\(734\) −5.24167 9.07883i −0.193473 0.335106i
\(735\) 21.9946 + 20.6966i 0.811283 + 0.763405i
\(736\) 41.1026i 1.51506i
\(737\) −42.3578 + 30.1544i −1.56027 + 1.11075i
\(738\) −1.44518 23.7434i −0.0531976 0.874006i
\(739\) 20.8762 + 12.0529i 0.767945 + 0.443373i 0.832141 0.554564i \(-0.187115\pi\)
−0.0641961 + 0.997937i \(0.520448\pi\)
\(740\) 13.3745i 0.491657i
\(741\) −17.2843 + 14.9844i −0.634954 + 0.550465i
\(742\) 72.4649 2.66027
\(743\) 4.88608 8.46294i 0.179253 0.310475i −0.762372 0.647139i \(-0.775965\pi\)
0.941625 + 0.336664i \(0.109299\pi\)
\(744\) −1.97206 0.464665i −0.0722992 0.0170355i
\(745\) 11.8818 6.85994i 0.435314 0.251329i
\(746\) 54.1205i 1.98149i
\(747\) −19.2721 9.61579i −0.705128 0.351824i
\(748\) −15.2382 + 10.8480i −0.557163 + 0.396643i
\(749\) 54.8503i 2.00419i
\(750\) −29.4550 27.7167i −1.07555 1.01207i
\(751\) −25.8225 + 44.7258i −0.942275 + 1.63207i −0.181157 + 0.983454i \(0.557984\pi\)
−0.761118 + 0.648614i \(0.775349\pi\)
\(752\) 5.61546 + 3.24209i 0.204775 + 0.118227i
\(753\) 4.24461 1.27680i 0.154682 0.0465291i
\(754\) 49.0848 + 35.4249i 1.78756 + 1.29010i
\(755\) 24.7554 0.900940
\(756\) −12.8184 34.7932i −0.466201 1.26542i
\(757\) 7.89389 13.6726i 0.286908 0.496940i −0.686162 0.727449i \(-0.740706\pi\)
0.973070 + 0.230509i \(0.0740392\pi\)
\(758\) −24.4821 42.4042i −0.889230 1.54019i
\(759\) 11.7833 + 28.8907i 0.427708 + 1.04867i
\(760\) 1.68418 + 2.91709i 0.0610918 + 0.105814i
\(761\) 5.22100 + 9.04303i 0.189261 + 0.327810i 0.945004 0.327059i \(-0.106057\pi\)
−0.755743 + 0.654868i \(0.772724\pi\)
\(762\) −11.6312 + 3.49873i −0.421354 + 0.126745i
\(763\) 17.3007 + 29.9657i 0.626328 + 1.08483i
\(764\) −20.6642 11.9305i −0.747603 0.431629i
\(765\) 16.8064 1.02295i 0.607638 0.0369847i
\(766\) 37.2726i 1.34671i
\(767\) 22.2512 30.8313i 0.803445 1.11325i
\(768\) 9.72168 + 32.3189i 0.350801 + 1.16621i
\(769\) −24.7415 14.2845i −0.892201 0.515113i −0.0175394 0.999846i \(-0.505583\pi\)
−0.874662 + 0.484734i \(0.838917\pi\)
\(770\) 41.3292 + 18.8810i 1.48940 + 0.680423i
\(771\) 5.98567 + 5.63242i 0.215569 + 0.202847i
\(772\) 36.2869i 1.30600i
\(773\) 18.5994 10.7384i 0.668975 0.386233i −0.126713 0.991939i \(-0.540443\pi\)
0.795688 + 0.605706i \(0.207109\pi\)
\(774\) 9.44941 18.9386i 0.339652 0.680733i
\(775\) −4.49874 −0.161599
\(776\) −3.39367 5.87801i −0.121826 0.211008i
\(777\) 7.46312 31.6738i 0.267738 1.13629i
\(778\) 4.24064 + 2.44833i 0.152034 + 0.0877771i
\(779\) 15.0550i 0.539401i
\(780\) 13.9215 12.0690i 0.498469 0.432141i
\(781\) −11.6056 + 1.10665i −0.415281 + 0.0395992i
\(782\) −29.7236 17.1609i −1.06291 0.613673i
\(783\) −42.4314 + 15.6324i −1.51637 + 0.558657i
\(784\) −22.7893 39.4723i −0.813905 1.40973i
\(785\) 37.9210i 1.35346i
\(786\) 19.9062 21.1547i 0.710032 0.754563i
\(787\) 15.9266 9.19525i 0.567723 0.327775i −0.188516 0.982070i \(-0.560368\pi\)
0.756240 + 0.654295i \(0.227034\pi\)
\(788\) 5.77201 0.205619
\(789\) −0.0523205 + 0.0556019i −0.00186266 + 0.00197948i
\(790\) 9.49490 16.4456i 0.337813 0.585110i
\(791\) 16.0892 27.8674i 0.572067 0.990849i
\(792\) 3.35536 + 4.15388i 0.119228 + 0.147602i
\(793\) −6.41533 + 8.88907i −0.227815 + 0.315660i
\(794\) 7.59204 0.269431
\(795\) −26.1815 6.16901i −0.928563 0.218792i
\(796\) −3.23776 + 5.60796i −0.114759 + 0.198769i
\(797\) 17.2948 9.98516i 0.612614 0.353693i −0.161374 0.986893i \(-0.551593\pi\)
0.773988 + 0.633201i \(0.218259\pi\)
\(798\) 14.6120 + 48.5764i 0.517260 + 1.71959i
\(799\) −4.10661 + 2.37095i −0.145281 + 0.0838783i
\(800\) 7.80956 + 13.5266i 0.276110 + 0.478236i
\(801\) −14.9344 22.5779i −0.527682 0.797752i
\(802\) −26.8084 + 15.4779i −0.946639 + 0.546542i
\(803\) −14.8732 + 32.5565i −0.524865 + 1.14889i
\(804\) 45.5071 + 10.7226i 1.60491 + 0.378157i
\(805\) 38.5708i 1.35944i
\(806\) 1.53697 15.0832i 0.0541375 0.531283i
\(807\) −5.05555 + 1.52073i −0.177964 + 0.0535324i
\(808\) −1.12627 + 1.95077i −0.0396222 + 0.0686277i
\(809\) −24.3042 + 42.0960i −0.854489 + 1.48002i 0.0226301 + 0.999744i \(0.492796\pi\)
−0.877119 + 0.480274i \(0.840537\pi\)
\(810\) 3.60830 + 29.5313i 0.126783 + 1.03762i
\(811\) 19.0035i 0.667303i 0.942697 + 0.333651i \(0.108281\pi\)
−0.942697 + 0.333651i \(0.891719\pi\)
\(812\) 53.7804 31.0501i 1.88732 1.08964i
\(813\) −6.11434 5.75350i −0.214439 0.201784i
\(814\) −2.75336 28.8748i −0.0965052 1.01206i
\(815\) −2.57835 + 1.48861i −0.0903157 + 0.0521438i
\(816\) −24.7334 5.82779i −0.865841 0.204013i
\(817\) −6.69769 + 11.6007i −0.234323 + 0.405859i
\(818\) 14.6376i 0.511791i
\(819\) −39.7038 + 20.8138i −1.38736 + 0.727294i
\(820\) 12.1259i 0.423455i
\(821\) 3.60701 6.24752i 0.125885 0.218040i −0.796193 0.605042i \(-0.793156\pi\)
0.922079 + 0.387002i \(0.126489\pi\)
\(822\) −1.02411 + 4.34639i −0.0357201 + 0.151598i
\(823\) −2.69247 4.66349i −0.0938535 0.162559i 0.815276 0.579073i \(-0.196585\pi\)
−0.909130 + 0.416514i \(0.863252\pi\)
\(824\) −7.78634 −0.271250
\(825\) 9.36710 + 7.26887i 0.326121 + 0.253070i
\(826\) −42.1575 73.0190i −1.46685 2.54066i
\(827\) −37.3026 −1.29714 −0.648569 0.761156i \(-0.724632\pi\)
−0.648569 + 0.761156i \(0.724632\pi\)
\(828\) 12.5259 25.1045i 0.435305 0.872442i
\(829\) 5.16945 8.95376i 0.179543 0.310977i −0.762181 0.647364i \(-0.775872\pi\)
0.941724 + 0.336387i \(0.109205\pi\)
\(830\) −20.5527 11.8661i −0.713393 0.411878i
\(831\) 31.8662 9.58552i 1.10543 0.332518i
\(832\) −18.5552 + 8.33191i −0.643286 + 0.288857i
\(833\) 33.3319 1.15488
\(834\) −7.04594 + 29.9033i −0.243981 + 1.03547i
\(835\) −10.2169 5.89874i −0.353571 0.204134i
\(836\) 12.1313 + 17.0408i 0.419570 + 0.589369i
\(837\) 8.70454 + 7.24601i 0.300873 + 0.250459i
\(838\) −3.40593 + 1.96641i −0.117656 + 0.0679286i
\(839\) −18.7996 + 10.8540i −0.649036 + 0.374721i −0.788087 0.615564i \(-0.788928\pi\)
0.139051 + 0.990285i \(0.455595\pi\)
\(840\) 1.90145 + 6.32120i 0.0656062 + 0.218102i
\(841\) −23.3665 40.4720i −0.805743 1.39559i
\(842\) 17.2045 29.7991i 0.592906 1.02694i
\(843\) 10.9242 + 2.57400i 0.376249 + 0.0886534i
\(844\) 16.5393i 0.569307i
\(845\) −16.6480 14.7998i −0.572707 0.509129i
\(846\) −4.62243 6.98822i −0.158923 0.240260i
\(847\) −43.0772 14.9219i −1.48015 0.512723i
\(848\) 35.1558 + 20.2972i 1.20725 + 0.697009i
\(849\) −19.8894 18.7156i −0.682602 0.642317i
\(850\) −13.0424 −0.447351
\(851\) 21.3234 12.3111i 0.730957 0.422018i
\(852\) 7.63444 + 7.18389i 0.261552 + 0.246116i
\(853\) 3.69558i 0.126534i −0.997997 0.0632671i \(-0.979848\pi\)
0.997997 0.0632671i \(-0.0201520\pi\)
\(854\) 12.1546 + 21.0524i 0.415922 + 0.720397i
\(855\) −1.14396 18.7946i −0.0391226 0.642761i
\(856\) −3.55134 + 6.15109i −0.121382 + 0.210240i
\(857\) −10.5639 −0.360857 −0.180429 0.983588i \(-0.557748\pi\)
−0.180429 + 0.983588i \(0.557748\pi\)
\(858\) −27.5710 + 28.9223i −0.941259 + 0.987391i
\(859\) −48.7450 −1.66316 −0.831579 0.555406i \(-0.812563\pi\)
−0.831579 + 0.555406i \(0.812563\pi\)
\(860\) 5.39460 9.34372i 0.183954 0.318618i
\(861\) −6.76639 + 28.7169i −0.230598 + 0.978668i
\(862\) −31.7355 54.9676i −1.08092 1.87220i
\(863\) 6.66363i 0.226833i 0.993548 + 0.113416i \(0.0361794\pi\)
−0.993548 + 0.113416i \(0.963821\pi\)
\(864\) 6.67631 38.7511i 0.227133 1.31834i
\(865\) −19.7739 + 11.4165i −0.672332 + 0.388171i
\(866\) −7.01154 −0.238262
\(867\) −7.44358 + 7.91042i −0.252797 + 0.268652i
\(868\) −13.4700 7.77691i −0.457202 0.263966i
\(869\) −7.91710 + 17.3300i −0.268569 + 0.587880i
\(870\) −47.7146 + 14.3528i −1.61768 + 0.486606i
\(871\) 5.73014 56.2332i 0.194158 1.90539i
\(872\) 4.48060i 0.151732i
\(873\) 2.30511 + 37.8715i 0.0780160 + 1.28176i
\(874\) −19.1910 + 33.2398i −0.649145 + 1.12435i
\(875\) 25.0820 + 43.4433i 0.847926 + 1.46865i
\(876\) 30.8205 9.27096i 1.04133 0.313237i
\(877\) −14.0157 + 8.09196i −0.473276 + 0.273246i −0.717610 0.696445i \(-0.754764\pi\)
0.244334 + 0.969691i \(0.421431\pi\)
\(878\) 7.40929 4.27775i 0.250051 0.144367i
\(879\) 15.8994 + 52.8562i 0.536274 + 1.78280i
\(880\) 14.7620 + 20.7361i 0.497627 + 0.699015i
\(881\) −38.1631 22.0335i −1.28575 0.742326i −0.307854 0.951434i \(-0.599611\pi\)
−0.977893 + 0.209107i \(0.932944\pi\)
\(882\) 3.57814 + 58.7867i 0.120482 + 1.97945i
\(883\) 57.2309 1.92597 0.962986 0.269552i \(-0.0868756\pi\)
0.962986 + 0.269552i \(0.0868756\pi\)
\(884\) 2.06141 20.2299i 0.0693328 0.680404i
\(885\) 9.01532 + 29.9707i 0.303047 + 1.00745i
\(886\) 30.4329 + 17.5704i 1.02241 + 0.590290i
\(887\) −0.507853 + 0.879627i −0.0170520 + 0.0295350i −0.874426 0.485160i \(-0.838761\pi\)
0.857373 + 0.514695i \(0.172095\pi\)
\(888\) 2.88769 3.06880i 0.0969045 0.102982i
\(889\) 15.0646 0.505252
\(890\) −14.9142 25.8321i −0.499924 0.865894i
\(891\) −6.41647 29.1518i −0.214960 0.976623i
\(892\) 14.2213 0.476164
\(893\) 2.65143 + 4.59241i 0.0887267 + 0.153679i
\(894\) 26.0420 + 6.13614i 0.870976 + 0.205223i
\(895\) 18.3564 31.7943i 0.613588 1.06276i
\(896\) 17.6212i 0.588684i
\(897\) −32.0566 11.0860i −1.07034 0.370152i
\(898\) 10.7027i 0.357153i
\(899\) −9.48418 + 16.4271i −0.316315 + 0.547874i
\(900\) −0.647720 10.6417i −0.0215907 0.354722i
\(901\) −25.7096 + 14.8434i −0.856510 + 0.494506i
\(902\) 2.49632 + 26.1791i 0.0831182 + 0.871669i
\(903\) −17.9895 + 19.1178i −0.598653 + 0.636199i
\(904\) 3.60860 2.08342i 0.120020 0.0692936i
\(905\) 15.6566i 0.520443i
\(906\) 35.1576 + 33.0828i 1.16803 + 1.09910i
\(907\) 9.74671 16.8818i 0.323634 0.560551i −0.657601 0.753367i \(-0.728429\pi\)
0.981235 + 0.192816i \(0.0617620\pi\)
\(908\) −4.37315 + 7.57452i −0.145128 + 0.251369i
\(909\) 10.5022 6.94682i 0.348337 0.230412i
\(910\) −45.0616 + 20.2342i −1.49378 + 0.670756i
\(911\) 22.8242i 0.756198i 0.925765 + 0.378099i \(0.123422\pi\)
−0.925765 + 0.378099i \(0.876578\pi\)
\(912\) −6.51720 + 27.6593i −0.215806 + 0.915890i
\(913\) 21.6579 + 9.89427i 0.716770 + 0.327452i
\(914\) 43.3067 25.0031i 1.43246 0.827030i
\(915\) −2.59924 8.64095i −0.0859282 0.285661i
\(916\) −15.9588 27.6414i −0.527292 0.913297i
\(917\) −31.2011 + 18.0140i −1.03035 + 0.594873i
\(918\) 25.2356 + 21.0071i 0.832898 + 0.693338i
\(919\) 20.4576 11.8112i 0.674833 0.389615i −0.123073 0.992398i \(-0.539275\pi\)
0.797905 + 0.602783i \(0.205941\pi\)
\(920\) −2.49730 + 4.32546i −0.0823337 + 0.142606i
\(921\) 11.4132 48.4382i 0.376078 1.59609i
\(922\) −34.0819 −1.12243
\(923\) 7.41695 10.2769i 0.244132 0.338269i
\(924\) 15.4811 + 37.9571i 0.509292 + 1.24870i
\(925\) 4.67825 8.10296i 0.153820 0.266424i
\(926\) 28.9577 50.1562i 0.951609 1.64823i
\(927\) 38.9472 + 19.4327i 1.27920 + 0.638255i
\(928\) 65.8561 2.16183
\(929\) 37.4887 21.6441i 1.22997 0.710121i 0.262943 0.964811i \(-0.415307\pi\)
0.967023 + 0.254690i \(0.0819736\pi\)
\(930\) 9.08862 + 8.55225i 0.298028 + 0.280439i
\(931\) 37.2749i 1.22164i
\(932\) −21.8852 37.9062i −0.716873 1.24166i
\(933\) −7.63900 + 32.4202i −0.250090 + 1.06139i
\(934\) −31.6400 18.2674i −1.03529 0.597727i
\(935\) −18.5305 + 1.76698i −0.606013 + 0.0577865i
\(936\) −5.80012 0.236530i −0.189583 0.00773122i
\(937\) 55.6524i 1.81808i −0.416704 0.909042i \(-0.636815\pi\)
0.416704 0.909042i \(-0.363185\pi\)
\(938\) −108.551 62.6722i −3.54433 2.04632i
\(939\) 29.2218 + 6.88538i 0.953618 + 0.224696i
\(940\) −2.13557 3.69892i −0.0696546 0.120645i
\(941\) −9.25699 −0.301769 −0.150885 0.988551i \(-0.548212\pi\)
−0.150885 + 0.988551i \(0.548212\pi\)
\(942\) −50.6772 + 53.8555i −1.65115 + 1.75471i
\(943\) −19.3327 + 11.1618i −0.629560 + 0.363477i
\(944\) 47.2328i 1.53730i
\(945\) 6.26507 36.3641i 0.203803 1.18293i
\(946\) −9.72306 + 21.2831i −0.316124 + 0.691973i
\(947\) 31.4410 + 18.1525i 1.02170 + 0.589876i 0.914595 0.404372i \(-0.132510\pi\)
0.107101 + 0.994248i \(0.465843\pi\)
\(948\) 16.4059 4.93498i 0.532840 0.160281i
\(949\) −15.9392 35.4967i −0.517408 1.15227i
\(950\) 14.5853i 0.473209i
\(951\) 13.3723 56.7528i 0.433628 1.84033i
\(952\) 6.30922 + 3.64263i 0.204483 + 0.118058i
\(953\) −11.3686 19.6910i −0.368265 0.637854i 0.621029 0.783788i \(-0.286715\pi\)
−0.989294 + 0.145933i \(0.953382\pi\)
\(954\) −28.9389 43.7499i −0.936931 1.41646i
\(955\) −11.8727 20.5641i −0.384192 0.665440i
\(956\) −8.93292 15.4723i −0.288911 0.500409i
\(957\) 46.2898 18.8797i 1.49634 0.610295i
\(958\) 38.3291 + 66.3879i 1.23836 + 2.14490i
\(959\) 2.76921 4.79641i 0.0894224 0.154884i
\(960\) 3.83980 16.2963i 0.123929 0.525959i
\(961\) −26.2491 −0.846746
\(962\) 25.5690 + 18.4534i 0.824378 + 0.594961i
\(963\) 33.1153 21.9045i 1.06713 0.705863i
\(964\) −20.3467 11.7472i −0.655324 0.378352i
\(965\) 18.0557 31.2733i 0.581232 1.00672i
\(966\) −51.5456 + 54.7784i −1.65845 + 1.76247i
\(967\) 16.0880i 0.517356i −0.965964 0.258678i \(-0.916713\pi\)
0.965964 0.258678i \(-0.0832869\pi\)
\(968\) −3.86469 4.46247i −0.124216 0.143429i
\(969\) −15.1344 14.2412i −0.486185 0.457493i
\(970\) 41.8073i 1.34235i
\(971\) −11.2948 + 6.52107i −0.362468 + 0.209271i −0.670163 0.742214i \(-0.733776\pi\)
0.307695 + 0.951485i \(0.400442\pi\)
\(972\) −15.8870 + 21.6337i −0.509576 + 0.693900i
\(973\) 19.0522 32.9995i 0.610787 1.05791i
\(974\) 49.5137 1.58652
\(975\) −12.6560 + 2.44247i −0.405315 + 0.0782217i
\(976\) 13.6179i 0.435897i
\(977\) −21.6654 12.5085i −0.693138 0.400183i 0.111649 0.993748i \(-0.464387\pi\)
−0.804786 + 0.593564i \(0.797720\pi\)
\(978\) −5.65114 1.33155i −0.180704 0.0425782i
\(979\) 17.3563 + 24.3804i 0.554711 + 0.779200i
\(980\) 30.0228i 0.959042i
\(981\) 11.1824 22.4119i 0.357028 0.715558i
\(982\) 30.6584 + 53.1020i 0.978350 + 1.69455i
\(983\) 13.4470i 0.428891i 0.976736 + 0.214446i \(0.0687945\pi\)
−0.976736 + 0.214446i \(0.931206\pi\)
\(984\) −2.61810 + 2.78230i −0.0834621 + 0.0886966i
\(985\) 4.97451 + 2.87204i 0.158501 + 0.0915107i
\(986\) −27.4959 + 47.6242i −0.875646 + 1.51666i
\(987\) 2.99347 + 9.95153i 0.0952832 + 0.316761i
\(988\) −22.6230 2.30527i −0.719733 0.0733405i
\(989\) −19.8627 −0.631596
\(990\) −5.10562 32.4922i −0.162267 1.03267i
\(991\) 25.1960 43.6407i 0.800376 1.38629i −0.118992 0.992895i \(-0.537966\pi\)
0.919369 0.393397i \(-0.128700\pi\)
\(992\) −8.24727 14.2847i −0.261851 0.453540i
\(993\) −11.0880 36.8611i −0.351867 1.16975i
\(994\) −14.0523 24.3393i −0.445712 0.771995i
\(995\) −5.58082 + 3.22209i −0.176924 + 0.102147i
\(996\) −6.16741 20.5030i −0.195422 0.649663i
\(997\) −39.8364 + 22.9996i −1.26163 + 0.728403i −0.973390 0.229155i \(-0.926404\pi\)
−0.288241 + 0.957558i \(0.593071\pi\)
\(998\) 6.12834 10.6146i 0.193989 0.335999i
\(999\) −22.1031 + 8.14317i −0.699313 + 0.257638i
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 429.2.p.b.230.11 96
3.2 odd 2 inner 429.2.p.b.230.38 yes 96
11.10 odd 2 inner 429.2.p.b.230.37 yes 96
13.3 even 3 inner 429.2.p.b.263.12 yes 96
33.32 even 2 inner 429.2.p.b.230.12 yes 96
39.29 odd 6 inner 429.2.p.b.263.37 yes 96
143.120 odd 6 inner 429.2.p.b.263.38 yes 96
429.263 even 6 inner 429.2.p.b.263.11 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.p.b.230.11 96 1.1 even 1 trivial
429.2.p.b.230.12 yes 96 33.32 even 2 inner
429.2.p.b.230.37 yes 96 11.10 odd 2 inner
429.2.p.b.230.38 yes 96 3.2 odd 2 inner
429.2.p.b.263.11 yes 96 429.263 even 6 inner
429.2.p.b.263.12 yes 96 13.3 even 3 inner
429.2.p.b.263.37 yes 96 39.29 odd 6 inner
429.2.p.b.263.38 yes 96 143.120 odd 6 inner