Properties

Label 429.2.p.b.230.12
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 230.12
Character \(\chi\) \(=\) 429.230
Dual form 429.2.p.b.263.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.964601 + 1.67074i) q^{2} +(1.18696 + 1.26140i) q^{3} +(-0.860909 - 1.49114i) q^{4} +1.71348i q^{5} +(-3.25241 + 0.766347i) q^{6} +(3.58916 - 2.07221i) q^{7} -0.536667 q^{8} +(-0.182262 + 2.99446i) q^{9} +O(q^{10})\) \(q+(-0.964601 + 1.67074i) q^{2} +(1.18696 + 1.26140i) q^{3} +(-0.860909 - 1.49114i) q^{4} +1.71348i q^{5} +(-3.25241 + 0.766347i) q^{6} +(3.58916 - 2.07221i) q^{7} -0.536667 q^{8} +(-0.182262 + 2.99446i) q^{9} +(-2.86278 - 1.65283i) q^{10} +(2.70190 + 1.92347i) q^{11} +(0.859060 - 2.85587i) q^{12} +(-3.28917 + 1.47695i) q^{13} +7.99540i q^{14} +(-2.16139 + 2.03383i) 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} +(-5.81987 + 2.65878i) q^{22} +(-4.70378 - 2.71573i) q^{23} +(-0.637002 - 0.676952i) 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} +(-1.31312 - 5.57295i) q^{30} -2.17965 q^{31} +(3.78376 + 6.55366i) q^{32} +(0.780766 + 5.69126i) q^{33} -6.31909 q^{34} +(3.55069 + 6.14998i) q^{35} +(4.62206 - 2.30618i) q^{36} +(2.26663 - 3.92591i) q^{37} -7.06662i q^{38} +(-5.76713 - 2.39589i) q^{39} -0.919571i q^{40} +(-2.05502 + 3.55940i) q^{41} +(-10.0854 + 9.49021i) q^{42} +(3.16703 - 1.82848i) q^{43} +(0.542079 - 5.68484i) q^{44} +(-5.13096 - 0.312303i) q^{45} +(9.07453 - 5.23918i) q^{46} -1.44769i q^{47} +(7.55104 - 1.77921i) 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} +(-1.70200 - 9.87888i) q^{54} +(-3.29584 + 4.62966i) 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} +(5.55096 + 11.1253i) 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} +(-2.15757 - 9.15680i) q^{69} -13.7000 q^{70} +(-3.04416 + 1.75755i) q^{71} +(0.0978141 - 1.60703i) q^{72} +10.7920i q^{73} +(4.37278 + 7.57388i) q^{74} +(2.44985 + 2.60349i) q^{75} +(5.46201 + 3.15349i) q^{76} +(13.6834 + 1.30478i) q^{77} +(9.56587 - 7.32428i) q^{78} +5.74463i q^{79} +(6.64645 + 3.83733i) q^{80} +(-8.93356 - 1.09155i) q^{81} +(-3.96455 - 6.86681i) q^{82} -7.17926 q^{83} +(-2.83464 - 12.0303i) q^{84} +(-4.86058 + 2.80625i) q^{85} +7.05503i q^{86} +(14.6714 - 3.45693i) q^{87} +(-1.45002 - 1.03227i) q^{88} +(7.81452 + 4.51171i) q^{89} +(5.47110 - 8.27124i) q^{90} +(-8.74483 + 12.1168i) q^{91} +9.35198i q^{92} +(-2.58715 - 2.74941i) 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 \(0.927744\pi\)
\(3\) 1.18696 + 1.26140i 0.685290 + 0.728270i
\(4\) −0.860909 1.49114i −0.430455 0.745569i
\(5\) 1.71348i 0.766294i 0.923687 + 0.383147i \(0.125160\pi\)
−0.923687 + 0.383147i \(0.874840\pi\)
\(6\) −3.25241 + 0.766347i −1.32779 + 0.312860i
\(7\) 3.58916 2.07221i 1.35658 0.783220i 0.367416 0.930057i \(-0.380243\pi\)
0.989161 + 0.146837i \(0.0469092\pi\)
\(8\) −0.536667 −0.189741
\(9\) −0.182262 + 2.99446i −0.0607540 + 0.998153i
\(10\) −2.86278 1.65283i −0.905292 0.522670i
\(11\) 2.70190 + 1.92347i 0.814652 + 0.579949i
\(12\) 0.859060 2.85587i 0.247989 0.824419i
\(13\) −3.28917 + 1.47695i −0.912251 + 0.409631i
\(14\) 7.99540i 2.13686i
\(15\) −2.16139 + 2.03383i −0.558069 + 0.525134i
\(16\) 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 −0.817602 0.575784i \(-0.804697\pi\)
0.0898424 + 0.995956i \(0.471364\pi\)
\(20\) 2.55504 1.47516i 0.571325 0.329855i
\(21\) 6.87407 + 2.06775i 1.50004 + 0.451221i
\(22\) −5.81987 + 2.65878i −1.24080 + 0.566853i
\(23\) −4.70378 2.71573i −0.980805 0.566268i −0.0782919 0.996930i \(-0.524947\pi\)
−0.902513 + 0.430662i \(0.858280\pi\)
\(24\) −0.637002 0.676952i −0.130027 0.138182i
\(25\) 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 \(-0.132786\pi\)
\(30\) −1.31312 5.57295i −0.239743 1.01748i
\(31\) −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
\(33\) 0.780766 + 5.69126i 0.135914 + 0.990721i
\(34\) −6.31909 −1.08371
\(35\) 3.55069 + 6.14998i 0.600176 + 1.03954i
\(36\) 4.62206 2.30618i 0.770344 0.384363i
\(37\) 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
\(39\) −5.76713 2.39589i −0.923479 0.383649i
\(40\) 0.919571i 0.145397i
\(41\) −2.05502 + 3.55940i −0.320941 + 0.555885i −0.980682 0.195607i \(-0.937332\pi\)
0.659742 + 0.751492i \(0.270666\pi\)
\(42\) −10.0854 + 9.49021i −1.55621 + 1.46437i
\(43\) 3.16703 1.82848i 0.482967 0.278841i −0.238685 0.971097i \(-0.576716\pi\)
0.721652 + 0.692256i \(0.243383\pi\)
\(44\) 0.542079 5.68484i 0.0817215 0.857022i
\(45\) −5.13096 0.312303i −0.764878 0.0465554i
\(46\) 9.07453 5.23918i 1.33797 0.772475i
\(47\) 1.44769i 0.211168i −0.994410 0.105584i \(-0.966329\pi\)
0.994410 0.105584i \(-0.0336711\pi\)
\(48\) 7.55104 1.77921i 1.08990 0.256807i
\(49\) 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 \(-0.786129\pi\)
0.782643 0.622471i \(-0.213871\pi\)
\(54\) −1.70200 9.87888i −0.231613 1.34435i
\(55\) −3.29584 + 4.62966i −0.444412 + 0.624263i
\(56\) −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 −0.958072 0.286529i \(-0.907499\pi\)
−0.230895 + 0.972979i \(0.574165\pi\)
\(60\) 4.89349 + 1.47199i 0.631747 + 0.190033i
\(61\) 2.63306 1.52020i 0.337129 0.194641i −0.321873 0.946783i \(-0.604312\pi\)
0.659002 + 0.752142i \(0.270979\pi\)
\(62\) 2.10249 3.64163i 0.267017 0.462487i
\(63\) 5.55096 + 11.1253i 0.699356 + 1.40165i
\(64\) −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
\(69\) −2.15757 9.15680i −0.259740 1.10235i
\(70\) −13.7000 −1.63746
\(71\) −3.04416 + 1.75755i −0.361275 + 0.208582i −0.669640 0.742686i \(-0.733552\pi\)
0.308365 + 0.951268i \(0.400218\pi\)
\(72\) 0.0978141 1.60703i 0.0115275 0.189390i
\(73\) 10.7920i 1.26311i 0.775333 + 0.631553i \(0.217582\pi\)
−0.775333 + 0.631553i \(0.782418\pi\)
\(74\) 4.37278 + 7.57388i 0.508325 + 0.880445i
\(75\) 2.44985 + 2.60349i 0.282884 + 0.300625i
\(76\) 5.46201 + 3.15349i 0.626535 + 0.361730i
\(77\) 13.6834 + 1.30478i 1.55937 + 0.148694i
\(78\) 9.56587 7.32428i 1.08312 0.829311i
\(79\) 5.74463i 0.646322i 0.946344 + 0.323161i \(0.104745\pi\)
−0.946344 + 0.323161i \(0.895255\pi\)
\(80\) 6.64645 + 3.83733i 0.743096 + 0.429027i
\(81\) −8.93356 1.09155i −0.992618 0.121284i
\(82\) −3.96455 6.86681i −0.437812 0.758312i
\(83\) −7.17926 −0.788026 −0.394013 0.919105i \(-0.628914\pi\)
−0.394013 + 0.919105i \(0.628914\pi\)
\(84\) −2.83464 12.0303i −0.309285 1.31262i
\(85\) −4.86058 + 2.80625i −0.527203 + 0.304381i
\(86\) 7.05503i 0.760764i
\(87\) 14.6714 3.45693i 1.57294 0.370622i
\(88\) −1.45002 1.03227i −0.154573 0.110040i
\(89\) 7.81452 + 4.51171i 0.828337 + 0.478241i 0.853283 0.521448i \(-0.174608\pi\)
−0.0249459 + 0.999689i \(0.507941\pi\)
\(90\) 5.47110 8.27124i 0.576705 0.871865i
\(91\) −8.74483 + 12.1168i −0.916707 + 1.27019i
\(92\) 9.35198i 0.975011i
\(93\) −2.58715 2.74941i −0.268275 0.285101i
\(94\) 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 \(0.0997034\pi\)
\(102\) −7.50049 7.97090i −0.742659 0.789237i
\(103\) 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 \(-0.0542859\pi\)
\(108\) 8.39521 + 3.09294i 0.807830 + 0.297618i
\(109\) 8.34893i 0.799683i 0.916584 + 0.399841i \(0.130935\pi\)
−0.916584 + 0.399841i \(0.869065\pi\)
\(110\) −4.55577 9.97226i −0.434376 0.950818i
\(111\) 7.64254 1.80077i 0.725398 0.170921i
\(112\) 18.5627i 1.75401i
\(113\) 6.72408 3.88215i 0.632548 0.365202i −0.149190 0.988809i \(-0.547667\pi\)
0.781738 + 0.623607i \(0.214333\pi\)
\(114\) 8.91384 8.38778i 0.834857 0.785587i
\(115\) 4.65336 8.05985i 0.433928 0.751585i
\(116\) −14.9841 −1.39124
\(117\) −3.82316 10.1185i −0.353452 0.935453i
\(118\) 20.3443i 1.87284i
\(119\) 11.7563 + 6.78750i 1.07770 + 0.622209i
\(120\) 1.15995 1.09149i 0.105888 0.0996392i
\(121\) 3.60049 + 10.3941i 0.327317 + 0.944914i
\(122\) 5.86553i 0.531041i
\(123\) −6.92906 + 1.63266i −0.624772 + 0.147212i
\(124\) 1.87648 + 3.25016i 0.168513 + 0.291873i
\(125\) 12.1040i 1.08262i
\(126\) −23.9419 1.45726i −2.13291 0.129823i
\(127\) 3.14794 + 1.81747i 0.279335 + 0.161274i 0.633122 0.774052i \(-0.281773\pi\)
−0.353787 + 0.935326i \(0.615106\pi\)
\(128\) −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 \(0.376006\pi\)
\(132\) 7.81429 6.06389i 0.680146 0.527794i
\(133\) −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 −0.449746 0.893156i \(-0.648486\pi\)
0.548623 + 0.836070i \(0.315152\pi\)
\(138\) 17.3798 + 5.22793i 1.47947 + 0.445031i
\(139\) 7.96240 4.59710i 0.675362 0.389921i −0.122743 0.992438i \(-0.539169\pi\)
0.798105 + 0.602518i \(0.205836\pi\)
\(140\) 6.11365 10.5892i 0.516698 0.894947i
\(141\) 1.82612 1.71835i 0.153787 0.144711i
\(142\) 6.78132i 0.569076i
\(143\) −11.7279 2.33608i −0.980733 0.195352i
\(144\) 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
\(147\) 17.1558 4.04232i 1.41499 0.333405i
\(148\) −7.80544 −0.641603
\(149\) 4.00350 + 6.93427i 0.327980 + 0.568077i 0.982111 0.188304i \(-0.0602990\pi\)
−0.654131 + 0.756381i \(0.726966\pi\)
\(150\) −6.71288 + 1.58172i −0.548104 + 0.129147i
\(151\) 14.4474i 1.17571i −0.808966 0.587855i \(-0.799972\pi\)
0.808966 0.587855i \(-0.200028\pi\)
\(152\) 1.70243 0.982900i 0.138086 0.0797237i
\(153\) −8.79276 + 4.38715i −0.710853 + 0.354680i
\(154\) −15.3790 + 21.6028i −1.23927 + 1.74080i
\(155\) 3.73480i 0.299986i
\(156\) 1.39237 + 10.6622i 0.111479 + 0.853661i
\(157\) −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
\(159\) 11.4325 10.7578i 0.906654 0.853147i
\(160\) −11.2296 + 6.48341i −0.887778 + 0.512559i
\(161\) −22.5102 −1.77405
\(162\) 10.4410 13.8727i 0.820324 1.08994i
\(163\) −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
\(165\) −9.75188 + 1.33783i −0.759183 + 0.104150i
\(166\) 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
\(171\) −4.90614 9.83292i −0.375182 0.751942i
\(172\) −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
\(176\) 13.5118 6.17281i 1.01849 0.465293i
\(177\) −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 −0.393926 0.919142i \(-0.628883\pi\)
−0.992963 + 0.118421i \(0.962217\pi\)
\(180\) 3.95160 + 7.91984i 0.294535 + 0.590310i
\(181\) −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
\(186\) 7.08912 1.67037i 0.519800 0.122477i
\(187\) −1.03122 + 10.8145i −0.0754104 + 0.790837i
\(188\) −2.15871 + 1.24633i −0.157440 + 0.0908981i
\(189\) −7.44468 + 20.2072i −0.541521 + 1.46986i
\(190\) 12.1085 0.878446
\(191\) −12.0014 + 6.92899i −0.868388 + 0.501364i −0.866812 0.498635i \(-0.833835\pi\)
−0.00157552 + 0.999999i \(0.500502\pi\)
\(192\) −6.69600 7.11595i −0.483242 0.513549i
\(193\) −18.2513 10.5374i −1.31376 0.758498i −0.331040 0.943617i \(-0.607400\pi\)
−0.982716 + 0.185119i \(0.940733\pi\)
\(194\) −24.3990 −1.75175
\(195\) 4.10531 9.88188i 0.293988 0.707656i
\(196\) −17.5215 −1.25153
\(197\) −1.67614 + 2.90316i −0.119420 + 0.206841i −0.919538 0.393001i \(-0.871437\pi\)
0.800118 + 0.599843i \(0.204770\pi\)
\(198\) −6.90085 17.9120i −0.490422 1.27295i
\(199\) −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
\(201\) 26.4297 6.22748i 1.86421 0.439253i
\(202\) 4.04871 + 7.01257i 0.284866 + 0.493403i
\(203\) 36.0666i 2.53138i
\(204\) 9.50806 2.24033i 0.665697 0.156855i
\(205\) −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
\(210\) −16.2613 17.2812i −1.12214 1.19252i
\(211\) 8.31881 + 4.80287i 0.572690 + 0.330643i 0.758223 0.651995i \(-0.226068\pi\)
−0.185533 + 0.982638i \(0.559401\pi\)
\(212\) −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
\(219\) −13.6130 + 12.8096i −0.919882 + 0.865595i
\(220\) 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
\(225\) −0.376183 + 6.18047i −0.0250789 + 0.412031i
\(226\) 14.9789i 0.996382i
\(227\) −2.53984 4.39914i −0.168575 0.291981i 0.769344 0.638835i \(-0.220583\pi\)
−0.937919 + 0.346854i \(0.887250\pi\)
\(228\) 2.50536 + 10.6328i 0.165921 + 0.704177i
\(229\) 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
\(231\) 14.5957 + 18.8090i 0.960330 + 1.23754i
\(232\) −2.33517 + 4.04463i −0.153311 + 0.265543i
\(233\) 25.4210 1.66538 0.832692 0.553736i \(-0.186798\pi\)
0.832692 + 0.553736i \(0.186798\pi\)
\(234\) 20.5931 + 3.37278i 1.34622 + 0.220486i
\(235\) 2.48060 0.161816
\(236\) 15.7247 + 9.07867i 1.02359 + 0.590971i
\(237\) −7.24628 + 6.81864i −0.470697 + 0.442918i
\(238\) −22.6802 + 13.0944i −1.47014 + 0.848787i
\(239\) 10.3761 0.671177 0.335589 0.942009i \(-0.391065\pi\)
0.335589 + 0.942009i \(0.391065\pi\)
\(240\) 3.04865 + 12.9386i 0.196789 + 0.835182i
\(241\) −11.8170 + 6.82255i −0.761200 + 0.439479i −0.829726 0.558170i \(-0.811504\pi\)
0.0685265 + 0.997649i \(0.478170\pi\)
\(242\) −20.8388 4.01064i −1.33957 0.257814i
\(243\) −9.22688 12.5644i −0.591904 0.806008i
\(244\) −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
\(249\) −8.52148 9.05592i −0.540027 0.573896i
\(250\) −20.2226 11.6755i −1.27899 0.738426i
\(251\) 2.21624 1.27955i 0.139888 0.0807643i −0.428423 0.903578i \(-0.640931\pi\)
0.568311 + 0.822814i \(0.307597\pi\)
\(252\) 11.8105 17.8551i 0.743990 1.12477i
\(253\) −7.48548 16.3852i −0.470608 1.03013i
\(254\) −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 0.622666 0.782488i \(-0.286050\pi\)
−0.366321 + 0.930488i \(0.619383\pi\)
\(258\) −8.89922 + 8.37402i −0.554041 + 0.521344i
\(259\) 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 \(0.166234\pi\)
\(264\) −0.419012 3.05431i −0.0257884 0.187980i
\(265\) 15.5299 0.953992
\(266\) −14.6435 25.3633i −0.897850 1.55512i
\(267\) 3.58442 + 15.2124i 0.219363 + 0.930987i
\(268\) −26.9930 −1.64886
\(269\) −2.63966 + 1.52401i −0.160943 + 0.0929204i −0.578308 0.815818i \(-0.696287\pi\)
0.417365 + 0.908739i \(0.362954\pi\)
\(270\) 16.9273 2.91636i 1.03016 0.177484i
\(271\) −4.19786 2.42363i −0.255002 0.147225i 0.367051 0.930201i \(-0.380368\pi\)
−0.622052 + 0.782976i \(0.713701\pi\)
\(272\) 14.6709 0.889552
\(273\) −25.6639 + 3.35144i −1.55325 + 0.202838i
\(274\) 2.57811i 0.155749i
\(275\) 5.57663 + 3.96999i 0.336284 + 0.239400i
\(276\) −11.7966 + 11.1004i −0.710071 + 0.668166i
\(277\) 16.6384 9.60616i 0.999702 0.577178i 0.0915416 0.995801i \(-0.470821\pi\)
0.908160 + 0.418623i \(0.137487\pi\)
\(278\) 17.7374i 1.06382i
\(279\) 0.397268 6.52688i 0.0237838 0.390754i
\(280\) −1.90554 3.30049i −0.113878 0.197242i
\(281\) −6.47979 −0.386552 −0.193276 0.981144i \(-0.561911\pi\)
−0.193276 + 0.981144i \(0.561911\pi\)
\(282\) 1.10943 + 4.70849i 0.0660659 + 0.280386i
\(283\) −13.6552 7.88385i −0.811719 0.468646i 0.0358337 0.999358i \(-0.488591\pi\)
−0.847552 + 0.530712i \(0.821925\pi\)
\(284\) 5.24149 + 3.02618i 0.311025 + 0.179571i
\(285\) 3.13149 10.4104i 0.185493 0.616656i
\(286\) 15.2157 17.3408i 0.899722 1.02538i
\(287\) 17.0337i 1.00547i
\(288\) −20.3143 + 10.1358i −1.19703 + 0.597259i
\(289\) 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
\(297\) −17.1845 + 1.30067i −0.997148 + 0.0754726i
\(298\) −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
\(303\) 7.07615 1.66731i 0.406514 0.0957846i
\(304\) 16.4064i 0.940971i
\(305\) 2.60484 + 4.51171i 0.149152 + 0.258340i
\(306\) 1.15173 18.9222i 0.0658400 1.08171i
\(307\) 28.7316i 1.63980i −0.572506 0.819900i \(-0.694029\pi\)
0.572506 0.819900i \(-0.305971\pi\)
\(308\) −9.83454 21.5271i −0.560375 1.22662i
\(309\) 17.2212 + 18.3013i 0.979680 + 1.04112i
\(310\) 6.23987 + 3.60259i 0.354401 + 0.204613i
\(311\) 19.2304i 1.09046i 0.838288 + 0.545228i \(0.183557\pi\)
−0.838288 + 0.545228i \(0.816443\pi\)
\(312\) 3.09503 + 1.28579i 0.175221 + 0.0727937i
\(313\) −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
\(315\) −19.0630 + 9.51149i −1.07408 + 0.535912i
\(316\) 8.56605 4.94561i 0.481878 0.278212i
\(317\) 33.6635i 1.89073i −0.326012 0.945366i \(-0.605705\pi\)
0.326012 0.945366i \(-0.394295\pi\)
\(318\) 6.94565 + 29.4776i 0.389493 + 1.65302i
\(319\) 26.2530 11.9935i 1.46988 0.671508i
\(320\) 9.66630i 0.540362i
\(321\) 22.3123 5.25732i 1.24535 0.293435i
\(322\) 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
\(327\) −10.5313 + 9.90983i −0.582385 + 0.548015i
\(328\) 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
\(336\) 23.4150 22.0332i 1.27739 1.20201i
\(337\) 31.7148i 1.72762i 0.503821 + 0.863808i \(0.331927\pi\)
−0.503821 + 0.863808i \(0.668073\pi\)
\(338\) 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
\(341\) −5.88919 4.19250i −0.318918 0.227037i
\(342\) 21.1607 + 1.28798i 1.14424 + 0.0696458i
\(343\) 13.1632i 0.710747i
\(344\) −1.69964 + 0.981288i −0.0916385 + 0.0529075i
\(345\) 15.6900 3.69696i 0.844723 0.199037i
\(346\) 25.7074 1.38204
\(347\) −1.34141 2.32338i −0.0720105 0.124726i 0.827772 0.561065i \(-0.189608\pi\)
−0.899782 + 0.436339i \(0.856275\pi\)
\(348\) −17.7855 18.9009i −0.953402 1.01320i
\(349\) −1.10768 0.639520i −0.0592928 0.0342327i 0.470061 0.882634i \(-0.344232\pi\)
−0.529353 + 0.848401i \(0.677565\pi\)
\(350\) 16.5023i 0.882083i
\(351\) 8.22551 16.8327i 0.439045 0.898465i
\(352\) −2.38248 + 24.9853i −0.126986 + 1.33172i
\(353\) −10.2087 5.89397i −0.543352 0.313704i 0.203084 0.979161i \(-0.434903\pi\)
−0.746436 + 0.665457i \(0.768237\pi\)
\(354\) 25.6623 24.1478i 1.36394 1.28344i
\(355\) −3.01153 5.21612i −0.159835 0.276843i
\(356\) 15.5367i 0.823444i
\(357\) 5.39247 + 22.8859i 0.285400 + 1.21125i
\(358\) 35.7970 20.6674i 1.89193 1.09231i
\(359\) 18.0155 0.950822 0.475411 0.879764i \(-0.342299\pi\)
0.475411 + 0.879764i \(0.342299\pi\)
\(360\) 2.75362 + 0.167603i 0.145128 + 0.00883345i
\(361\) −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
\(366\) −7.39879 + 6.96214i −0.386741 + 0.363917i
\(367\) −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 −0.972674 0.232175i \(-0.925416\pi\)
−0.285268 + 0.958448i \(0.592083\pi\)
\(374\) −17.0735 12.1546i −0.882851 0.628500i
\(375\) −15.2680 + 14.3669i −0.788436 + 0.741906i
\(376\) 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
\(381\) 1.44392 + 6.12807i 0.0739745 + 0.313951i
\(382\) 26.7348i 1.36787i
\(383\) 16.7318 9.66011i 0.854955 0.493609i −0.00736430 0.999973i \(-0.502344\pi\)
0.862320 + 0.506364i \(0.169011\pi\)
\(384\) −7.16806 + 1.68897i −0.365793 + 0.0861899i
\(385\) −2.23573 + 23.4463i −0.113943 + 1.19493i
\(386\) 35.2104 20.3287i 1.79216 1.03471i
\(387\) 4.89809 + 9.81680i 0.248984 + 0.499016i
\(388\) 10.8881 18.8587i 0.552759 0.957407i
\(389\) 2.53818i 0.128691i 0.997928 + 0.0643455i \(0.0204960\pi\)
−0.997928 + 0.0643455i \(0.979504\pi\)
\(390\) 12.5500 + 16.3910i 0.635496 + 0.829989i
\(391\) 17.7907i 0.899714i
\(392\) −2.73060 + 4.72954i −0.137916 + 0.238878i
\(393\) 10.3184 + 10.9655i 0.520494 + 0.553138i
\(394\) −3.23361 5.60077i −0.162907 0.282163i
\(395\) −9.84334 −0.495272
\(396\) 16.9242 + 2.65937i 0.850474 + 0.133638i
\(397\) −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
\(399\) −25.5932 + 6.03038i −1.28126 + 0.301897i
\(400\) 4.62224 8.00595i 0.231112 0.400297i
\(401\) −13.8961 8.02294i −0.693940 0.400646i 0.111147 0.993804i \(-0.464548\pi\)
−0.805086 + 0.593158i \(0.797881\pi\)
\(402\) −15.0896 + 50.1641i −0.752601 + 2.50196i
\(403\) 7.16924 3.21923i 0.357125 0.160361i
\(404\) −7.22698 −0.359556
\(405\) 1.87036 15.3075i 0.0929389 0.760637i
\(406\) 60.2579 + 34.7899i 2.99055 + 1.72659i
\(407\) 13.6756 6.24761i 0.677874 0.309683i
\(408\) 0.877037 2.91563i 0.0434198 0.144345i
\(409\) −6.57086 + 3.79369i −0.324908 + 0.187586i −0.653578 0.756859i \(-0.726733\pi\)
0.328670 + 0.944445i \(0.393400\pi\)
\(410\) 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
\(414\) 14.0346 + 28.1282i 0.689762 + 1.38243i
\(415\) 12.3016i 0.603859i
\(416\) −22.1248 15.9677i −1.08476 0.782880i
\(417\) 15.2498 + 4.58722i 0.746787 + 0.224637i
\(418\) 13.5925 19.0933i 0.664829 0.933883i
\(419\) −1.76546 1.01929i −0.0862484 0.0497955i 0.456256 0.889849i \(-0.349190\pi\)
−0.542504 + 0.840053i \(0.682524\pi\)
\(420\) 20.6138 4.85712i 1.00585 0.237003i
\(421\) −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
\(423\) 4.33505 + 0.263859i 0.210777 + 0.0128293i
\(424\) 4.86399i 0.236216i
\(425\) 3.38026 + 5.85478i 0.163967 + 0.283999i
\(426\) 8.55396 8.04914i 0.414441 0.389982i
\(427\) 6.30032 10.9125i 0.304894 0.528092i
\(428\) −22.7879 −1.10149
\(429\) −10.9738 17.5664i −0.529818 0.848112i
\(430\) −12.0887 −0.582968
\(431\) −16.4501 + 28.4924i −0.792373 + 1.37243i 0.132121 + 0.991234i \(0.457821\pi\)
−0.924494 + 0.381197i \(0.875512\pi\)
\(432\) 3.95150 + 22.9355i 0.190117 + 1.10349i
\(433\) 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
\(435\) 5.92340 + 25.1392i 0.284005 + 1.20533i
\(436\) 12.4494 7.18768i 0.596219 0.344227i
\(437\) 19.8953 0.951720
\(438\) −8.27041 35.1000i −0.395175 1.67714i
\(439\) 3.84060 + 2.21737i 0.183302 + 0.105829i 0.588843 0.808247i \(-0.299584\pi\)
−0.405541 + 0.914077i \(0.632917\pi\)
\(440\) 1.76877 2.48459i 0.0843229 0.118448i
\(441\) 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 \(0.142445\pi\)
−0.901530 + 0.432716i \(0.857555\pi\)
\(444\) −9.26473 9.84579i −0.439685 0.467260i
\(445\) −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 −0.609066 0.793120i \(-0.708456\pi\)
0.382329 + 0.924026i \(0.375122\pi\)
\(450\) −9.96308 6.59019i −0.469664 0.310665i
\(451\) −12.3989 + 5.66436i −0.583840 + 0.266724i
\(452\) −11.5777 6.68436i −0.544567 0.314406i
\(453\) 18.2239 17.1484i 0.856235 0.805703i
\(454\) 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 0.922670 0.385592i \(-0.126003\pi\)
0.127403 + 0.991851i \(0.459336\pi\)
\(458\) −17.8809 + 30.9706i −0.835519 + 1.44716i
\(459\) −15.9706 5.88383i −0.745443 0.274634i
\(460\) −16.0245 −0.747145
\(461\) 8.83315 + 15.2995i 0.411401 + 0.712567i 0.995043 0.0994436i \(-0.0317063\pi\)
−0.583642 + 0.812011i \(0.698373\pi\)
\(462\) −45.5039 + 6.24254i −2.11703 + 0.290429i
\(463\) −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
\(465\) 4.71108 4.43305i 0.218471 0.205578i
\(466\) −24.5211 + 42.4718i −1.13592 + 1.96747i
\(467\) 18.9378i 0.876335i −0.898893 0.438167i \(-0.855628\pi\)
0.898893 0.438167i \(-0.144372\pi\)
\(468\) −11.7966 + 14.4120i −0.545300 + 0.666193i
\(469\) 64.9721i 3.00013i
\(470\) −2.39279 + 4.14443i −0.110371 + 0.191168i
\(471\) −26.2685 27.9159i −1.21039 1.28630i
\(472\) 4.90118 2.82970i 0.225595 0.130247i
\(473\) 12.0740 + 1.15132i 0.555164 + 0.0529378i
\(474\) −4.40238 18.6839i −0.202208 0.858180i
\(475\) −6.54739 + 3.78014i −0.300415 + 0.173445i
\(476\) 23.3737i 1.07133i
\(477\) 27.1397 + 1.65190i 1.24264 + 0.0756353i
\(478\) −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
\(483\) −26.7186 28.3943i −1.21574 1.29199i
\(484\) 12.3993 14.3172i 0.563604 0.650781i
\(485\) −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 \(-0.0879034\pi\)
\(492\) 8.39981 + 8.92662i 0.378693 + 0.402443i
\(493\) 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
\(498\) 23.3499 5.50181i 1.04633 0.246542i
\(499\) −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
\(501\) 11.6074 2.73500i 0.518582 0.122191i
\(502\) 4.93701i 0.220350i
\(503\) −15.1946 26.3178i −0.677492 1.17345i −0.975734 0.218960i \(-0.929733\pi\)
0.298242 0.954490i \(-0.403600\pi\)
\(504\) −2.97902 5.97058i −0.132696 0.265951i
\(505\) 6.22845 + 3.59600i 0.277162 + 0.160020i
\(506\) 34.5959 + 3.29890i 1.53797 + 0.146654i
\(507\) 22.5076 0.637263i 0.999599 0.0283019i
\(508\) 6.25869i 0.277685i
\(509\) 7.90008 + 4.56111i 0.350165 + 0.202168i 0.664758 0.747059i \(-0.268535\pi\)
−0.314593 + 0.949227i \(0.601868\pi\)
\(510\) 13.6580 12.8520i 0.604787 0.569095i
\(511\) 22.3632 + 38.7342i 0.989290 + 1.71350i
\(512\) 29.0873 1.28549
\(513\) 6.57987 17.8599i 0.290509 0.788532i
\(514\) −7.92808 + 4.57728i −0.349693 + 0.201895i
\(515\) 24.8604i 1.09548i
\(516\) −2.50125 10.6154i −0.110111 0.467317i
\(517\) 2.78460 3.91151i 0.122466 0.172028i
\(518\) 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 \(0.0130282\pi\)
−0.999163 + 0.0409178i \(0.986972\pi\)
\(522\) −45.0681 + 22.4867i −1.97258 + 0.984217i
\(523\) −10.4710 6.04544i −0.457865 0.264349i 0.253281 0.967393i \(-0.418490\pi\)
−0.711146 + 0.703044i \(0.751824\pi\)
\(524\) −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
\(531\) −14.1244 28.3083i −0.612948 1.22847i
\(532\) 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
\(537\) −8.51110 36.1215i −0.367281 1.55876i
\(538\) 5.88024i 0.253515i
\(539\) 30.6986 14.0245i 1.32228 0.604077i
\(540\) −5.29970 + 14.3851i −0.228063 + 0.619035i
\(541\) 19.4924i 0.838045i 0.907976 + 0.419023i \(0.137627\pi\)
−0.907976 + 0.419023i \(0.862373\pi\)
\(542\) 8.09851 4.67568i 0.347861 0.200838i
\(543\) −10.8456 11.5258i −0.465428 0.494619i
\(544\) −12.3937 + 21.4665i −0.531374 + 0.920368i
\(545\) −14.3058 −0.612792
\(546\) 19.1561 46.1105i 0.819804 1.97335i
\(547\) 9.55999i 0.408756i −0.978892 0.204378i \(-0.934483\pi\)
0.978892 0.204378i \(-0.0655171\pi\)
\(548\) −1.99270 1.15048i −0.0851238 0.0491462i
\(549\) 4.07226 + 8.16166i 0.173800 + 0.348331i
\(550\) −12.0120 + 5.48763i −0.512195 + 0.233993i
\(551\) 31.8770i 1.35800i
\(552\) 1.15789 + 4.91415i 0.0492833 + 0.209160i
\(553\) 11.9041 + 20.6184i 0.506212 + 0.876785i
\(554\) 37.0644i 1.57472i
\(555\) 3.08559 + 13.0954i 0.130976 + 0.555868i
\(556\) −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
\(561\) −14.8655 + 11.5356i −0.627621 + 0.487034i
\(562\) 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 \(0.864453\pi\)
\(570\) 14.3723 + 15.2737i 0.601991 + 0.639746i
\(571\) 3.30522i 0.138319i −0.997606 0.0691596i \(-0.977968\pi\)
0.997606 0.0691596i \(-0.0220318\pi\)
\(572\) 6.61321 + 19.4990i 0.276512 + 0.815295i
\(573\) −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
\(576\) 1.02820 16.8927i 0.0428415 0.703861i
\(577\) −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
\(579\) −8.37165 35.5296i −0.347914 1.47656i
\(580\) 25.6750i 1.06610i
\(581\) −25.7675 + 14.8769i −1.06902 + 0.617198i
\(582\) −28.9606 30.7769i −1.20046 1.27574i
\(583\) 17.4331 24.4881i 0.722004 1.01420i
\(584\) 5.79171i 0.239663i
\(585\) 17.3378 6.55093i 0.716832 0.270848i
\(586\) 61.4784 2.53965
\(587\) 4.57662 + 2.64231i 0.188897 + 0.109060i 0.591466 0.806330i \(-0.298549\pi\)
−0.402569 + 0.915390i \(0.631883\pi\)
\(588\) −20.7972 22.1016i −0.857664 0.911454i
\(589\) 6.91436 3.99201i 0.284901 0.164488i
\(590\) 34.8596 1.43515
\(591\) −5.65155 + 1.33164i −0.232474 + 0.0547764i
\(592\) −10.1522 17.5841i −0.417252 0.722701i
\(593\) −16.7919 −0.689559 −0.344779 0.938684i \(-0.612046\pi\)
−0.344779 + 0.938684i \(0.612046\pi\)
\(594\) 14.4031 29.9655i 0.590968 1.22950i
\(595\) −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 \(0.176162\pi\)
−0.850727 + 0.525607i \(0.823838\pi\)
\(600\) −1.31475 1.39721i −0.0536745 0.0570408i
\(601\) −32.7717 18.9207i −1.33678 0.771793i −0.350455 0.936579i \(-0.613973\pi\)
−0.986329 + 0.164787i \(0.947306\pi\)
\(602\) 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
\(605\) −17.8101 + 6.16939i −0.724082 + 0.250821i
\(606\) −4.04001 + 13.4307i −0.164114 + 0.545584i
\(607\) −15.9973 + 9.23603i −0.649309 + 0.374879i −0.788192 0.615430i \(-0.788982\pi\)
0.138882 + 0.990309i \(0.455649\pi\)
\(608\) −24.0059 13.8598i −0.973568 0.562090i
\(609\) 45.4945 42.8096i 1.84353 1.73473i
\(610\) −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 0.391304 0.920261i \(-0.372024\pi\)
−0.601318 + 0.799010i \(0.705357\pi\)
\(614\) 48.0030 + 27.7145i 1.93724 + 1.11847i
\(615\) −2.79753 11.8728i −0.112807 0.478759i
\(616\) −7.34343 0.700234i −0.295875 0.0282132i
\(617\) −7.05118 + 4.07100i −0.283870 + 0.163892i −0.635174 0.772369i \(-0.719072\pi\)
0.351304 + 0.936261i \(0.385738\pi\)
\(618\) −47.1882 + 11.1187i −1.89819 + 0.447260i
\(619\) −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
\(621\) 27.8129 4.79180i 1.11609 0.192288i
\(622\) −32.1290 18.5497i −1.28825 0.743774i
\(623\) 37.3968 1.49827
\(624\) −22.2088 + 17.0046i −0.889065 + 0.680728i
\(625\) −10.4202 −0.416807
\(626\) 16.7197 28.9593i 0.668252 1.15745i
\(627\) −12.9002 16.6240i −0.515186 0.663899i
\(628\) 19.0527 + 33.0003i 0.760286 + 1.31685i
\(629\) 14.8486 0.592054
\(630\) 2.49699 41.0241i 0.0994825 1.63444i
\(631\) −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
\(633\) 3.81574 + 16.1941i 0.151662 + 0.643660i
\(634\) 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
\(639\) −4.70806 9.43594i −0.186248 0.373280i
\(640\) −6.30935 3.64271i −0.249399 0.143991i
\(641\) −1.65745 + 0.956932i −0.0654655 + 0.0377965i −0.532375 0.846508i \(-0.678701\pi\)
0.466910 + 0.884305i \(0.345367\pi\)
\(642\) −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 0.196983 0.980407i \(-0.436885\pi\)
−0.750566 + 0.660796i \(0.770219\pi\)
\(648\) 4.79435 + 0.585801i 0.188340 + 0.0230124i
\(649\) −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 0.982050 0.188619i \(-0.0604011\pi\)
0.327677 + 0.944790i \(0.393734\pi\)
\(654\) −6.39818 27.1542i −0.250189 1.06181i
\(655\) 14.8956i 0.582018i
\(656\) 9.20440 + 15.9425i 0.359371 + 0.622449i
\(657\) −32.3162 1.96697i −1.26077 0.0767388i
\(658\) 11.5749 0.451236
\(659\) 11.0405 + 19.1227i 0.430077 + 0.744915i 0.996879 0.0789387i \(-0.0251531\pi\)
−0.566803 + 0.823854i \(0.691820\pi\)
\(660\) 10.3904 + 13.3897i 0.404445 + 0.521192i
\(661\) 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
\(663\) −2.64878 20.2832i −0.102870 0.787736i
\(664\) 3.85287 0.149521
\(665\) −22.5272 13.0061i −0.873568 0.504355i
\(666\) −23.4766 + 11.7137i −0.909702 + 0.453896i
\(667\) −40.9345 + 23.6335i −1.58499 + 0.915094i
\(668\) −11.8549 −0.458678
\(669\) −13.9245 + 3.28095i −0.538351 + 0.126849i
\(670\) −44.8800 + 25.9115i −1.73387 + 1.00105i
\(671\) 10.0383 + 0.957206i 0.387525 + 0.0369525i
\(672\) 12.4585 + 52.8742i 0.480595 + 2.03967i
\(673\) −30.5284 17.6256i −1.17678 0.679416i −0.221515 0.975157i \(-0.571100\pi\)
−0.955268 + 0.295741i \(0.904433\pi\)
\(674\) −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 \(0.488181\pi\)
\(678\) −18.8944 + 17.7793i −0.725635 + 0.682811i
\(679\) 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
\(682\) 12.6853 5.79520i 0.485745 0.221910i
\(683\) 5.46171 3.15332i 0.208987 0.120658i −0.391854 0.920028i \(-0.628166\pi\)
0.600840 + 0.799369i \(0.294833\pi\)
\(684\) −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
\(687\) 22.0028 + 23.3827i 0.839457 + 0.892106i
\(688\) 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
\(693\) −6.40108 + 40.7365i −0.243157 + 1.54745i
\(694\) 5.17569 0.196466
\(695\) 7.87705 + 13.6435i 0.298794 + 0.517526i
\(696\) −7.87364 + 1.85522i −0.298450 + 0.0703220i
\(697\) −13.4624 −0.509926
\(698\) 2.13694 1.23376i 0.0808844 0.0466986i
\(699\) 30.1736 + 32.0660i 1.14127 + 1.21285i
\(700\) −12.7551 7.36417i −0.482098 0.278339i
\(701\) −35.6093 −1.34494 −0.672472 0.740123i \(-0.734767\pi\)
−0.672472 + 0.740123i \(0.734767\pi\)
\(702\) 20.1888 + 29.9795i 0.761975 + 1.13150i
\(703\) 16.6052i 0.626277i
\(704\) −15.2422 10.8509i −0.574463 0.408959i
\(705\) 2.94436 + 3.12903i 0.110891 + 0.117846i
\(706\) 19.6946 11.3707i 0.741214 0.427940i
\(707\) 17.3953i 0.654218i
\(708\) 7.21274 + 30.6112i 0.271071 + 1.15044i
\(709\) 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
\(711\) −17.2021 1.04703i −0.645128 0.0392666i
\(712\) −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
\(715\) 4.00283 20.0955i 0.149697 0.751530i
\(716\) 36.8914i 1.37870i
\(717\) 12.3161 + 13.0885i 0.459951 + 0.488798i
\(718\) −17.3778 + 30.0992i −0.648533 + 1.12329i
\(719\) 10.9779 6.33810i 0.409407 0.236371i −0.281128 0.959670i \(-0.590709\pi\)
0.690535 + 0.723299i \(0.257375\pi\)
\(720\) −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
\(726\) −19.6757 31.0465i −0.730235 1.15224i
\(727\) 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
\(732\) −2.07953 8.82562i −0.0768617 0.326204i
\(733\) 1.45846i 0.0538696i 0.999637 + 0.0269348i \(0.00857465\pi\)
−0.999637 + 0.0269348i \(0.991425\pi\)
\(734\) −5.24167 9.07883i −0.193473 0.335106i
\(735\) 6.92646 + 29.3962i 0.255486 + 1.08429i
\(736\) 41.1026i 1.51506i
\(737\) 47.2934 21.6057i 1.74207 0.795856i
\(738\) 21.2850 10.6201i 0.783510 0.390932i
\(739\) −20.8762 12.0529i −0.767945 0.443373i 0.0641961 0.997937i \(-0.479552\pi\)
−0.832141 + 0.554564i \(0.812885\pi\)
\(740\) 13.3745i 0.491657i
\(741\) 22.6827 2.96212i 0.833269 0.108816i
\(742\) 72.4649 2.66027
\(743\) 4.88608 8.46294i 0.179253 0.310475i −0.762372 0.647139i \(-0.775965\pi\)
0.941625 + 0.336664i \(0.109299\pi\)
\(744\) 1.38844 + 1.47552i 0.0509027 + 0.0540952i
\(745\) −11.8818 + 6.85994i −0.435314 + 0.251329i
\(746\) 54.1205i 1.98149i
\(747\) 1.30851 21.4980i 0.0478758 0.786570i
\(748\) 17.0138 7.77264i 0.622085 0.284196i
\(749\) 54.8503i 2.00419i
\(750\) −9.27587 39.3672i −0.338707 1.43749i
\(751\) −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
\(756\) 36.5410 6.29554i 1.32898 0.228967i
\(757\) 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
\(765\) −7.51731 15.0663i −0.271789 0.544722i
\(766\) 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 0.874662 0.484734i \(-0.161083\pi\)
0.0175394 + 0.999846i \(0.494417\pi\)
\(770\) −37.0160 26.3516i −1.33396 0.949646i
\(771\) 1.88498 + 7.99995i 0.0678860 + 0.288111i
\(772\) 36.2869i 1.30600i
\(773\) −18.5994 + 10.7384i −0.668975 + 0.386233i −0.795688 0.605706i \(-0.792891\pi\)
0.126713 + 0.991939i \(0.459557\pi\)
\(774\) −21.1260 1.28586i −0.759358 0.0462194i
\(775\) −4.49874 −0.161599
\(776\) −3.39367 5.87801i −0.121826 0.211008i
\(777\) 23.6988 22.3002i 0.850188 0.800014i
\(778\) −4.24064 2.44833i −0.152034 0.0877771i
\(779\) 15.0550i 0.539401i
\(780\) −18.2696 + 2.38581i −0.654155 + 0.0854258i
\(781\) −11.6056 1.10665i −0.415281 0.0395992i
\(782\) 29.7236 + 17.1609i 1.06291 + 0.613673i
\(783\) 7.67760 + 44.5628i 0.274375 + 1.59255i
\(784\) −22.7893 39.4723i −0.813905 1.40973i
\(785\) 37.9210i 1.35346i
\(786\) −28.2736 + 6.66196i −1.00849 + 0.237624i
\(787\) −15.9266 + 9.19525i −0.567723 + 0.327775i −0.756240 0.654295i \(-0.772966\pi\)
0.188516 + 0.982070i \(0.439632\pi\)
\(788\) 5.77201 0.205619
\(789\) 0.0743129 0.0175099i 0.00264561 0.000623371i
\(790\) 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
\(795\) 18.4333 + 19.5894i 0.653761 + 0.694763i
\(796\) −3.23776 + 5.60796i −0.114759 + 0.198769i
\(797\) −17.2948 + 9.98516i −0.612614 + 0.353693i −0.773988 0.633201i \(-0.781741\pi\)
0.161374 + 0.986893i \(0.448407\pi\)
\(798\) 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
\(803\) −20.7581 + 29.1588i −0.732538 + 1.02899i
\(804\) −32.0396 34.0490i −1.12995 1.20082i
\(805\) 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 \(0.840537\pi\)
\(810\) 23.7707 + 17.8905i 0.835217 + 0.628609i
\(811\) 19.0035i 0.667303i −0.942697 0.333651i \(-0.891719\pi\)
0.942697 0.333651i \(-0.108281\pi\)
\(812\) −53.7804 + 31.0501i −1.88732 + 1.08964i
\(813\) −1.92551 8.17193i −0.0675304 0.286602i
\(814\) −2.75336 + 28.8748i −0.0965052 + 1.01206i
\(815\) 2.57835 1.48861i 0.0903157 0.0521438i
\(816\) 17.4137 + 18.5058i 0.609601 + 0.647834i
\(817\) −6.69769 + 11.6007i −0.234323 + 0.405859i
\(818\) 14.6376i 0.511791i
\(819\) −34.6895 28.3945i −1.21215 0.992183i
\(820\) 12.1259i 0.423455i
\(821\) 3.60701 6.24752i 0.125885 0.218040i −0.796193 0.605042i \(-0.793156\pi\)
0.922079 + 0.387002i \(0.126489\pi\)
\(822\) −3.25202 + 3.06010i −0.113427 + 0.106733i
\(823\) −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
\(825\) 1.61148 + 11.7466i 0.0561044 + 0.408964i
\(826\) −42.1575 73.0190i −1.46685 2.54066i
\(827\) −37.3026 −1.29714 −0.648569 0.761156i \(-0.724632\pi\)
−0.648569 + 0.761156i \(0.724632\pi\)
\(828\) −28.0041 1.70451i −0.973210 0.0592358i
\(829\) 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
\(834\) −22.3740 + 21.0536i −0.774749 + 0.729027i
\(835\) 10.2169 + 5.89874i 0.353571 + 0.204134i
\(836\) 8.69212 + 19.0264i 0.300623 + 0.658043i
\(837\) 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 −0.139051 0.990285i \(-0.544405\pi\)
0.788087 + 0.615564i \(0.211072\pi\)
\(840\) 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
\(843\) −7.69124 8.17361i −0.264900 0.281514i
\(844\) 16.5393i 0.569307i
\(845\) 16.6480 + 14.7998i 0.572707 + 0.509129i
\(846\) −4.62243 + 6.98822i −0.158923 + 0.240260i
\(847\) 34.4614 + 29.8450i 1.18411 + 1.02549i
\(848\) −35.1558 20.2972i −1.20725 0.697009i
\(849\) −6.26349 26.5825i −0.214962 0.912309i
\(850\) −13.0424 −0.447351
\(851\) −21.3234 + 12.3111i −0.730957 + 0.422018i
\(852\) 2.40421 + 10.2036i 0.0823668 + 0.349568i
\(853\) 3.69558i 0.126534i 0.997997 + 0.0632671i \(0.0201520\pi\)
−0.997997 + 0.0632671i \(0.979848\pi\)
\(854\) 12.1546 + 21.0524i 0.415922 + 0.720397i
\(855\) 16.8486 8.40659i 0.576209 0.287499i
\(856\) −3.55134 + 6.15109i −0.121382 + 0.210240i
\(857\) −10.5639 −0.360857 −0.180429 0.983588i \(-0.557748\pi\)
−0.180429 + 0.983588i \(0.557748\pi\)
\(858\) 39.9341 1.38974i 1.36333 0.0474450i
\(859\) −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
\(861\) −21.4863 + 20.2183i −0.732252 + 0.689038i
\(862\) −31.7355 54.9676i −1.08092 1.87220i
\(863\) 6.66363i 0.226833i −0.993548 0.113416i \(-0.963821\pi\)
0.993548 0.113416i \(-0.0361794\pi\)
\(864\) −36.8975 13.5937i −1.25528 0.462466i
\(865\) 19.7739 11.4165i 0.672332 0.388171i
\(866\) −7.01154 −0.238262
\(867\) 10.5724 2.49112i 0.359058 0.0846028i
\(868\) 13.4700 + 7.77691i 0.457202 + 0.263966i
\(869\) −11.0497 + 15.5214i −0.374834 + 0.526528i
\(870\) −47.7146 14.3528i −1.61768 0.486606i
\(871\) −5.73014 + 56.2332i −0.194158 + 1.90539i
\(872\) 4.48060i 0.151732i
\(873\) −33.9503 + 16.9395i −1.14904 + 0.573315i
\(874\) −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 −0.244334 0.969691i \(-0.578569\pi\)
0.717610 + 0.696445i \(0.245236\pi\)
\(878\) −7.40929 + 4.27775i −0.250051 + 0.144367i
\(879\) 15.8994 52.8562i 0.536274 1.78280i
\(880\) 10.5770 + 23.1523i 0.356551 + 0.780465i
\(881\) 38.1631 + 22.0335i 1.28575 + 0.742326i 0.977893 0.209107i \(-0.0670558\pi\)
0.307854 + 0.951434i \(0.400389\pi\)
\(882\) −52.6998 + 26.2946i −1.77450 + 0.885384i
\(883\) 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 \(0.172095\pi\)
\(888\) −4.10150 + 0.966414i −0.137637 + 0.0324307i
\(889\) 15.0646 0.505252
\(890\) −14.9142 25.8321i −0.499924 0.865894i
\(891\) −22.0380 20.1327i −0.738300 0.674472i
\(892\) 14.2213 0.476164
\(893\) 2.65143 + 4.59241i 0.0887267 + 0.153679i
\(894\) −18.3351 19.4850i −0.613217 0.651676i
\(895\) 18.3564 31.7943i 0.613588 1.06276i
\(896\) 17.6212i 0.588684i
\(897\) 20.6207 + 26.9316i 0.688505 + 0.899221i
\(898\) 10.7027i 0.357153i
\(899\) −9.48418 + 16.4271i −0.316315 + 0.547874i
\(900\) 9.53980 4.75988i 0.317993 0.158663i
\(901\) 25.7096 14.8434i 0.856510 0.494506i
\(902\) 2.49632 26.1791i 0.0831182 0.871669i
\(903\) 25.5512 6.02049i 0.850291 0.200349i
\(904\) −3.60860 + 2.08342i −0.120020 + 0.0692936i
\(905\) 15.6566i 0.520443i
\(906\) 11.0717 + 46.9888i 0.367833 + 1.56110i
\(907\) 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 \(-0.876578\pi\)
0.925765 0.378099i \(-0.123422\pi\)
\(912\) −20.6950 + 19.4737i −0.685281 + 0.644838i
\(913\) −19.3976 13.8091i −0.641967 0.457015i
\(914\) −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 −0.797905 0.602783i \(-0.794059\pi\)
0.123073 + 0.992398i \(0.460725\pi\)
\(920\) −2.49730 + 4.32546i −0.0823337 + 0.142606i
\(921\) 36.2421 34.1032i 1.19422 1.12374i
\(922\) −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
\(927\) −2.64438 + 43.4457i −0.0868530 + 1.42694i
\(928\) 65.8561 2.16183
\(929\) −37.4887 + 21.6441i −1.22997 + 0.710121i −0.967023 0.254690i \(-0.918026\pi\)
−0.262943 + 0.964811i \(0.584693\pi\)
\(930\) 2.86215 + 12.1471i 0.0938537 + 0.398319i
\(931\) 37.2749i 1.22164i
\(932\) −21.8852 37.9062i −0.716873 1.24166i
\(933\) −24.2572 + 22.8257i −0.794146 + 0.747279i
\(934\) 31.6400 + 18.2674i 1.03529 + 0.597727i
\(935\) −18.5305 1.76698i −0.606013 0.0577865i
\(936\) 2.05177 + 5.43025i 0.0670641 + 0.177493i
\(937\) 55.6524i 1.81808i 0.416704 + 0.909042i \(0.363185\pi\)
−0.416704 + 0.909042i \(0.636815\pi\)
\(938\) 108.551 + 62.6722i 3.54433 + 2.04632i
\(939\) −20.5738 21.8642i −0.671401 0.713510i
\(940\) −2.13557 3.69892i −0.0696546 0.120645i
\(941\) −9.25699 −0.301769 −0.150885 0.988551i \(-0.548212\pi\)
−0.150885 + 0.988551i \(0.548212\pi\)
\(942\) 71.9788 16.9600i 2.34520 0.552585i
\(943\) 19.3327 11.1618i 0.629560 0.363477i
\(944\) 47.2328i 1.53730i
\(945\) −34.6248 12.7564i −1.12634 0.414964i
\(946\) −13.5702 + 19.0620i −0.441204 + 0.619758i
\(947\) −31.4410 18.1525i −1.02170 0.589876i −0.107101 0.994248i \(-0.534157\pi\)
−0.914595 + 0.404372i \(0.867490\pi\)
\(948\) 16.4059 + 4.93498i 0.532840 + 0.160281i
\(949\) −15.9392 35.4967i −0.517408 1.15227i
\(950\) 14.5853i 0.473209i
\(951\) 42.4632 39.9572i 1.37696 1.29570i
\(952\) −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
\(960\) 12.1931 11.4735i 0.393530 0.370305i
\(961\) −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
\(966\) 73.2123 17.2506i 2.35557 0.555029i
\(967\) 16.0880i 0.517356i 0.965964 + 0.258678i \(0.0832869\pi\)
−0.965964 + 0.258678i \(0.916713\pi\)
\(968\) −1.93227 5.57815i −0.0621054 0.179289i
\(969\) −4.76605 20.2273i −0.153108 0.649795i
\(970\) 41.8073i 1.34235i
\(971\) 11.2948 6.52107i 0.362468 0.209271i −0.307695 0.951485i \(-0.599558\pi\)
0.670163 + 0.742214i \(0.266224\pi\)
\(972\) −10.7918 + 24.5754i −0.346147 + 0.788256i
\(973\) 19.0522 32.9995i 0.610787 1.05791i
\(974\) 49.5137 1.58652
\(975\) −11.9032 4.94504i −0.381207 0.158368i
\(976\) 13.6179i 0.435897i
\(977\) 21.6654 + 12.5085i 0.693138 + 0.400183i 0.804786 0.593564i \(-0.202280\pi\)
−0.111649 + 0.993748i \(0.535613\pi\)
\(978\) 3.97873 + 4.22826i 0.127226 + 0.135205i
\(979\) 12.4358 + 27.2212i 0.397451 + 0.869993i
\(980\) 30.0228i 0.959042i
\(981\) −25.0005 1.52169i −0.798206 0.0485840i
\(982\) 30.6584 + 53.1020i 0.978350 + 1.69455i
\(983\) 13.4470i 0.428891i −0.976736 0.214446i \(-0.931206\pi\)
0.976736 0.214446i \(-0.0687945\pi\)
\(984\) 3.71860 0.876193i 0.118545 0.0279320i
\(985\) −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
\(990\) 30.6919 11.8245i 0.975452 0.375807i
\(991\) 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 0.288241 0.957558i \(-0.406929\pi\)
0.973390 + 0.229155i \(0.0735961\pi\)
\(998\) 6.12834 10.6146i 0.193989 0.335999i
\(999\) 3.99938 + 23.2135i 0.126535 + 0.734442i
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.230.12 yes 96
3.2 odd 2 inner 429.2.p.b.230.37 yes 96
11.10 odd 2 inner 429.2.p.b.230.38 yes 96
13.3 even 3 inner 429.2.p.b.263.11 yes 96
33.32 even 2 inner 429.2.p.b.230.11 96
39.29 odd 6 inner 429.2.p.b.263.38 yes 96
143.120 odd 6 inner 429.2.p.b.263.37 yes 96
429.263 even 6 inner 429.2.p.b.263.12 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.p.b.230.11 96 33.32 even 2 inner
429.2.p.b.230.12 yes 96 1.1 even 1 trivial
429.2.p.b.230.37 yes 96 3.2 odd 2 inner
429.2.p.b.230.38 yes 96 11.10 odd 2 inner
429.2.p.b.263.11 yes 96 13.3 even 3 inner
429.2.p.b.263.12 yes 96 429.263 even 6 inner
429.2.p.b.263.37 yes 96 143.120 odd 6 inner
429.2.p.b.263.38 yes 96 39.29 odd 6 inner