Properties

Label 280.2.bf.a.109.15
Level $280$
Weight $2$
Character 280.109
Analytic conductor $2.236$
Analytic rank $0$
Dimension $88$
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] = [280,2,Mod(109,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("280.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bf (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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.15
Character \(\chi\) \(=\) 280.109
Dual form 280.2.bf.a.149.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.643189 + 1.25949i) q^{2} +(1.37008 - 2.37305i) q^{3} +(-1.17262 - 1.62018i) q^{4} +(2.18145 - 0.491206i) q^{5} +(2.10761 + 3.25192i) q^{6} +(-2.02537 - 1.70232i) q^{7} +(2.79480 - 0.434817i) q^{8} +(-2.25425 - 3.90447i) q^{9} +O(q^{10})\) \(q+(-0.643189 + 1.25949i) q^{2} +(1.37008 - 2.37305i) q^{3} +(-1.17262 - 1.62018i) q^{4} +(2.18145 - 0.491206i) q^{5} +(2.10761 + 3.25192i) q^{6} +(-2.02537 - 1.70232i) q^{7} +(2.79480 - 0.434817i) q^{8} +(-2.25425 - 3.90447i) q^{9} +(-0.784414 + 3.06344i) q^{10} +(1.84762 + 1.06672i) q^{11} +(-5.45134 + 0.562906i) q^{12} -6.08794 q^{13} +(3.44674 - 1.45601i) q^{14} +(1.82310 - 5.84968i) q^{15} +(-1.24994 + 3.79969i) q^{16} +(-0.115849 - 0.0668855i) q^{17} +(6.36754 - 0.327885i) q^{18} +(3.27805 - 1.89258i) q^{19} +(-3.35384 - 2.95833i) q^{20} +(-6.81461 + 2.47399i) q^{21} +(-2.53189 + 1.64095i) q^{22} +(2.43685 - 1.40692i) q^{23} +(2.79727 - 7.22795i) q^{24} +(4.51743 - 2.14308i) q^{25} +(3.91570 - 7.66769i) q^{26} -4.13353 q^{27} +(-0.383072 + 5.27762i) q^{28} +6.47037i q^{29} +(6.19500 + 6.05863i) q^{30} +(1.72541 - 2.98850i) q^{31} +(-3.98172 - 4.01820i) q^{32} +(5.06277 - 2.92299i) q^{33} +(0.158754 - 0.102890i) q^{34} +(-5.25443 - 2.71864i) q^{35} +(-3.68256 + 8.23073i) q^{36} +(5.51098 + 9.54530i) q^{37} +(0.275280 + 5.34595i) q^{38} +(-8.34098 + 14.4470i) q^{39} +(5.88314 - 2.32136i) q^{40} -3.79820 q^{41} +(1.26712 - 10.1742i) q^{42} +9.07301 q^{43} +(-0.438269 - 4.24432i) q^{44} +(-6.83543 - 7.41010i) q^{45} +(0.204639 + 3.97410i) q^{46} +(2.84799 - 1.64429i) q^{47} +(7.30434 + 8.17206i) q^{48} +(1.20423 + 6.89564i) q^{49} +(-0.206376 + 7.06806i) q^{50} +(-0.317446 + 0.183277i) q^{51} +(7.13882 + 9.86354i) q^{52} +(2.20436 - 3.81807i) q^{53} +(2.65864 - 5.20612i) q^{54} +(4.55446 + 1.41944i) q^{55} +(-6.40071 - 3.87698i) q^{56} -10.3720i q^{57} +(-8.14934 - 4.16167i) q^{58} +(0.601135 + 0.347066i) q^{59} +(-11.6153 + 3.90568i) q^{60} +(-6.12389 + 3.53563i) q^{61} +(2.65421 + 4.09530i) q^{62} +(-2.08097 + 11.7454i) q^{63} +(7.62187 - 2.43046i) q^{64} +(-13.2805 + 2.99044i) q^{65} +(0.425155 + 8.25653i) q^{66} +(-4.02458 + 6.97077i) q^{67} +(0.0274803 + 0.266127i) q^{68} -7.71037i q^{69} +(6.80368 - 4.86928i) q^{70} -9.63322 q^{71} +(-7.99792 - 9.93205i) q^{72} +(-8.96544 - 5.17620i) q^{73} +(-15.5668 + 0.801583i) q^{74} +(1.10361 - 13.6563i) q^{75} +(-6.91021 - 3.09174i) q^{76} +(-1.92620 - 5.30573i) q^{77} +(-12.8310 - 19.7975i) q^{78} +(0.0729440 + 0.126343i) q^{79} +(-0.860247 + 8.90281i) q^{80} +(1.09947 - 1.90435i) q^{81} +(2.44296 - 4.78379i) q^{82} +2.32247 q^{83} +(11.9992 + 8.13982i) q^{84} +(-0.285573 - 0.0890015i) q^{85} +(-5.83566 + 11.4273i) q^{86} +(15.3545 + 8.86493i) q^{87} +(5.62755 + 2.17790i) q^{88} +(-1.60348 - 2.77732i) q^{89} +(13.7294 - 3.84304i) q^{90} +(12.3303 + 10.3636i) q^{91} +(-5.13695 - 2.29836i) q^{92} +(-4.72790 - 8.18897i) q^{93} +(0.239165 + 4.64459i) q^{94} +(6.22125 - 5.73877i) q^{95} +(-14.9907 + 3.94355i) q^{96} +14.5077i q^{97} +(-9.45952 - 2.91848i) q^{98} -9.61862i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.643189 + 1.25949i −0.454803 + 0.890592i
\(3\) 1.37008 2.37305i 0.791017 1.37008i −0.134321 0.990938i \(-0.542885\pi\)
0.925338 0.379144i \(-0.123781\pi\)
\(4\) −1.17262 1.62018i −0.586308 0.810088i
\(5\) 2.18145 0.491206i 0.975573 0.219674i
\(6\) 2.10761 + 3.25192i 0.860427 + 1.32759i
\(7\) −2.02537 1.70232i −0.765517 0.643415i
\(8\) 2.79480 0.434817i 0.988113 0.153731i
\(9\) −2.25425 3.90447i −0.751416 1.30149i
\(10\) −0.784414 + 3.06344i −0.248054 + 0.968746i
\(11\) 1.84762 + 1.06672i 0.557077 + 0.321629i 0.751971 0.659196i \(-0.229103\pi\)
−0.194894 + 0.980824i \(0.562436\pi\)
\(12\) −5.45134 + 0.562906i −1.57367 + 0.162497i
\(13\) −6.08794 −1.68849 −0.844246 0.535956i \(-0.819951\pi\)
−0.844246 + 0.535956i \(0.819951\pi\)
\(14\) 3.44674 1.45601i 0.921180 0.389136i
\(15\) 1.82310 5.84968i 0.470724 1.51038i
\(16\) −1.24994 + 3.79969i −0.312485 + 0.949923i
\(17\) −0.115849 0.0668855i −0.0280975 0.0162221i 0.485885 0.874023i \(-0.338497\pi\)
−0.513983 + 0.857800i \(0.671831\pi\)
\(18\) 6.36754 0.327885i 1.50084 0.0772832i
\(19\) 3.27805 1.89258i 0.752036 0.434188i −0.0743930 0.997229i \(-0.523702\pi\)
0.826429 + 0.563041i \(0.190369\pi\)
\(20\) −3.35384 2.95833i −0.749942 0.661503i
\(21\) −6.81461 + 2.47399i −1.48707 + 0.539869i
\(22\) −2.53189 + 1.64095i −0.539800 + 0.349851i
\(23\) 2.43685 1.40692i 0.508119 0.293363i −0.223941 0.974603i \(-0.571892\pi\)
0.732060 + 0.681240i \(0.238559\pi\)
\(24\) 2.79727 7.22795i 0.570990 1.47540i
\(25\) 4.51743 2.14308i 0.903486 0.428617i
\(26\) 3.91570 7.66769i 0.767931 1.50376i
\(27\) −4.13353 −0.795498
\(28\) −0.383072 + 5.27762i −0.0723939 + 0.997376i
\(29\) 6.47037i 1.20152i 0.799431 + 0.600758i \(0.205135\pi\)
−0.799431 + 0.600758i \(0.794865\pi\)
\(30\) 6.19500 + 6.05863i 1.13105 + 1.10615i
\(31\) 1.72541 2.98850i 0.309893 0.536750i −0.668446 0.743761i \(-0.733040\pi\)
0.978339 + 0.207011i \(0.0663736\pi\)
\(32\) −3.98172 4.01820i −0.703874 0.710324i
\(33\) 5.06277 2.92299i 0.881315 0.508827i
\(34\) 0.158754 0.102890i 0.0272261 0.0176456i
\(35\) −5.25443 2.71864i −0.888160 0.459534i
\(36\) −3.68256 + 8.23073i −0.613760 + 1.37179i
\(37\) 5.51098 + 9.54530i 0.906000 + 1.56924i 0.819570 + 0.572980i \(0.194213\pi\)
0.0864300 + 0.996258i \(0.472454\pi\)
\(38\) 0.275280 + 5.34595i 0.0446563 + 0.867228i
\(39\) −8.34098 + 14.4470i −1.33563 + 2.31337i
\(40\) 5.88314 2.32136i 0.930206 0.367039i
\(41\) −3.79820 −0.593180 −0.296590 0.955005i \(-0.595849\pi\)
−0.296590 + 0.955005i \(0.595849\pi\)
\(42\) 1.26712 10.1742i 0.195521 1.56991i
\(43\) 9.07301 1.38362 0.691811 0.722079i \(-0.256813\pi\)
0.691811 + 0.722079i \(0.256813\pi\)
\(44\) −0.438269 4.24432i −0.0660715 0.639855i
\(45\) −6.83543 7.41010i −1.01897 1.10463i
\(46\) 0.204639 + 3.97410i 0.0301724 + 0.585949i
\(47\) 2.84799 1.64429i 0.415422 0.239844i −0.277695 0.960669i \(-0.589570\pi\)
0.693117 + 0.720825i \(0.256237\pi\)
\(48\) 7.30434 + 8.17206i 1.05429 + 1.17954i
\(49\) 1.20423 + 6.89564i 0.172033 + 0.985091i
\(50\) −0.206376 + 7.06806i −0.0291859 + 0.999574i
\(51\) −0.317446 + 0.183277i −0.0444513 + 0.0256640i
\(52\) 7.13882 + 9.86354i 0.989977 + 1.36783i
\(53\) 2.20436 3.81807i 0.302792 0.524452i −0.673975 0.738754i \(-0.735414\pi\)
0.976767 + 0.214302i \(0.0687478\pi\)
\(54\) 2.65864 5.20612i 0.361795 0.708464i
\(55\) 4.55446 + 1.41944i 0.614123 + 0.191397i
\(56\) −6.40071 3.87698i −0.855330 0.518083i
\(57\) 10.3720i 1.37380i
\(58\) −8.14934 4.16167i −1.07006 0.546454i
\(59\) 0.601135 + 0.347066i 0.0782611 + 0.0451841i 0.538620 0.842549i \(-0.318946\pi\)
−0.460359 + 0.887733i \(0.652279\pi\)
\(60\) −11.6153 + 3.90568i −1.49953 + 0.504222i
\(61\) −6.12389 + 3.53563i −0.784084 + 0.452691i −0.837876 0.545861i \(-0.816203\pi\)
0.0537920 + 0.998552i \(0.482869\pi\)
\(62\) 2.65421 + 4.09530i 0.337085 + 0.520103i
\(63\) −2.08097 + 11.7454i −0.262177 + 1.47979i
\(64\) 7.62187 2.43046i 0.952734 0.303807i
\(65\) −13.2805 + 2.99044i −1.64725 + 0.370918i
\(66\) 0.425155 + 8.25653i 0.0523329 + 1.01631i
\(67\) −4.02458 + 6.97077i −0.491680 + 0.851615i −0.999954 0.00958015i \(-0.996950\pi\)
0.508274 + 0.861196i \(0.330284\pi\)
\(68\) 0.0274803 + 0.266127i 0.00333248 + 0.0322726i
\(69\) 7.71037i 0.928219i
\(70\) 6.80368 4.86928i 0.813196 0.581990i
\(71\) −9.63322 −1.14325 −0.571627 0.820514i \(-0.693687\pi\)
−0.571627 + 0.820514i \(0.693687\pi\)
\(72\) −7.99792 9.93205i −0.942563 1.17050i
\(73\) −8.96544 5.17620i −1.04932 0.605828i −0.126865 0.991920i \(-0.540491\pi\)
−0.922460 + 0.386092i \(0.873825\pi\)
\(74\) −15.5668 + 0.801583i −1.80960 + 0.0931821i
\(75\) 1.10361 13.6563i 0.127433 1.57689i
\(76\) −6.91021 3.09174i −0.792656 0.354647i
\(77\) −1.92620 5.30573i −0.219511 0.604644i
\(78\) −12.8310 19.7975i −1.45282 2.24163i
\(79\) 0.0729440 + 0.126343i 0.00820685 + 0.0142147i 0.870100 0.492876i \(-0.164054\pi\)
−0.861893 + 0.507090i \(0.830721\pi\)
\(80\) −0.860247 + 8.90281i −0.0961785 + 0.995364i
\(81\) 1.09947 1.90435i 0.122164 0.211594i
\(82\) 2.44296 4.78379i 0.269780 0.528281i
\(83\) 2.32247 0.254924 0.127462 0.991843i \(-0.459317\pi\)
0.127462 + 0.991843i \(0.459317\pi\)
\(84\) 11.9992 + 8.13982i 1.30922 + 0.888127i
\(85\) −0.285573 0.0890015i −0.0309748 0.00965356i
\(86\) −5.83566 + 11.4273i −0.629275 + 1.23224i
\(87\) 15.3545 + 8.86493i 1.64618 + 0.950420i
\(88\) 5.62755 + 2.17790i 0.599899 + 0.232165i
\(89\) −1.60348 2.77732i −0.169969 0.294395i 0.768440 0.639922i \(-0.221033\pi\)
−0.938409 + 0.345527i \(0.887700\pi\)
\(90\) 13.7294 3.84304i 1.44721 0.405092i
\(91\) 12.3303 + 10.3636i 1.29257 + 1.08640i
\(92\) −5.13695 2.29836i −0.535564 0.239620i
\(93\) −4.72790 8.18897i −0.490261 0.849157i
\(94\) 0.239165 + 4.64459i 0.0246680 + 0.479053i
\(95\) 6.22125 5.73877i 0.638286 0.588785i
\(96\) −14.9907 + 3.94355i −1.52998 + 0.402487i
\(97\) 14.5077i 1.47304i 0.676417 + 0.736519i \(0.263532\pi\)
−0.676417 + 0.736519i \(0.736468\pi\)
\(98\) −9.45952 2.91848i −0.955556 0.294811i
\(99\) 9.61862i 0.966707i
\(100\) −8.76939 4.80602i −0.876939 0.480602i
\(101\) 9.50967 + 5.49041i 0.946247 + 0.546316i 0.891913 0.452207i \(-0.149363\pi\)
0.0543342 + 0.998523i \(0.482696\pi\)
\(102\) −0.0266580 0.517701i −0.00263954 0.0512600i
\(103\) −4.65961 + 2.69023i −0.459125 + 0.265076i −0.711676 0.702507i \(-0.752064\pi\)
0.252551 + 0.967584i \(0.418730\pi\)
\(104\) −17.0146 + 2.64714i −1.66842 + 0.259574i
\(105\) −13.6505 + 8.74426i −1.33215 + 0.853352i
\(106\) 3.39099 + 5.23210i 0.329362 + 0.508187i
\(107\) 2.01974 + 3.49830i 0.195256 + 0.338194i 0.946984 0.321279i \(-0.104113\pi\)
−0.751728 + 0.659473i \(0.770780\pi\)
\(108\) 4.84704 + 6.69704i 0.466407 + 0.644423i
\(109\) 5.65776 + 3.26651i 0.541915 + 0.312875i 0.745855 0.666109i \(-0.232041\pi\)
−0.203940 + 0.978983i \(0.565375\pi\)
\(110\) −4.71714 + 4.82332i −0.449761 + 0.459885i
\(111\) 30.2020 2.86664
\(112\) 8.99987 5.56798i 0.850408 0.526125i
\(113\) 1.87629i 0.176506i 0.996098 + 0.0882530i \(0.0281284\pi\)
−0.996098 + 0.0882530i \(0.971872\pi\)
\(114\) 13.0634 + 6.67114i 1.22350 + 0.624809i
\(115\) 4.62478 4.26612i 0.431263 0.397817i
\(116\) 10.4831 7.58726i 0.973334 0.704459i
\(117\) 13.7237 + 23.7702i 1.26876 + 2.19756i
\(118\) −0.823768 + 0.533893i −0.0758340 + 0.0491489i
\(119\) 0.120777 + 0.332680i 0.0110716 + 0.0304967i
\(120\) 2.55168 17.1414i 0.232935 1.56479i
\(121\) −3.22421 5.58450i −0.293110 0.507682i
\(122\) −0.514264 9.98704i −0.0465593 0.904184i
\(123\) −5.20385 + 9.01333i −0.469215 + 0.812705i
\(124\) −6.86513 + 0.708894i −0.616507 + 0.0636606i
\(125\) 8.80185 6.89402i 0.787261 0.616620i
\(126\) −13.4548 10.1755i −1.19865 0.906504i
\(127\) 4.14125i 0.367476i −0.982975 0.183738i \(-0.941180\pi\)
0.982975 0.183738i \(-0.0588199\pi\)
\(128\) −1.84117 + 11.1629i −0.162738 + 0.986669i
\(129\) 12.4308 21.5307i 1.09447 1.89567i
\(130\) 4.77547 18.6501i 0.418836 1.63572i
\(131\) −9.39337 + 5.42327i −0.820703 + 0.473833i −0.850659 0.525718i \(-0.823797\pi\)
0.0299559 + 0.999551i \(0.490463\pi\)
\(132\) −10.6724 4.77503i −0.928917 0.415613i
\(133\) −9.86103 1.74710i −0.855060 0.151493i
\(134\) −6.19104 9.55243i −0.534824 0.825204i
\(135\) −9.01707 + 2.03041i −0.776066 + 0.174750i
\(136\) −0.352859 0.136559i −0.0302574 0.0117098i
\(137\) 14.1556 + 8.17276i 1.20940 + 0.698246i 0.962628 0.270828i \(-0.0872976\pi\)
0.246770 + 0.969074i \(0.420631\pi\)
\(138\) 9.71111 + 4.95922i 0.826665 + 0.422157i
\(139\) 1.23998i 0.105174i 0.998616 + 0.0525870i \(0.0167467\pi\)
−0.998616 + 0.0525870i \(0.983253\pi\)
\(140\) 1.75675 + 11.7010i 0.148472 + 0.988917i
\(141\) 9.01123i 0.758883i
\(142\) 6.19598 12.1329i 0.519955 1.01817i
\(143\) −11.2482 6.49414i −0.940620 0.543067i
\(144\) 17.6535 3.68509i 1.47112 0.307091i
\(145\) 3.17829 + 14.1148i 0.263942 + 1.17217i
\(146\) 12.2858 7.96258i 1.01678 0.658988i
\(147\) 18.0136 + 6.58988i 1.48574 + 0.543524i
\(148\) 9.00279 20.1217i 0.740025 1.65400i
\(149\) −6.60567 + 3.81378i −0.541158 + 0.312437i −0.745548 0.666452i \(-0.767812\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(150\) 16.4901 + 10.1736i 1.34641 + 0.830667i
\(151\) −8.80697 + 15.2541i −0.716701 + 1.24136i 0.245599 + 0.969371i \(0.421015\pi\)
−0.962300 + 0.271991i \(0.912318\pi\)
\(152\) 8.33858 6.71475i 0.676348 0.544638i
\(153\) 0.603106i 0.0487583i
\(154\) 7.92141 + 0.986556i 0.638326 + 0.0794990i
\(155\) 2.29592 7.36678i 0.184413 0.591714i
\(156\) 33.1874 3.42694i 2.65712 0.274375i
\(157\) 3.92236 6.79374i 0.313039 0.542199i −0.665980 0.745970i \(-0.731986\pi\)
0.979019 + 0.203771i \(0.0653197\pi\)
\(158\) −0.206044 + 0.0106099i −0.0163920 + 0.000844074i
\(159\) −6.04031 10.4621i −0.479028 0.829701i
\(160\) −10.6597 6.80965i −0.842721 0.538350i
\(161\) −7.33055 1.29877i −0.577728 0.102357i
\(162\) 1.69133 + 2.60963i 0.132883 + 0.205032i
\(163\) 0.618575 + 1.07140i 0.0484506 + 0.0839189i 0.889234 0.457453i \(-0.151238\pi\)
−0.840783 + 0.541372i \(0.817905\pi\)
\(164\) 4.45384 + 6.15376i 0.347786 + 0.480528i
\(165\) 9.60837 8.86322i 0.748011 0.690001i
\(166\) −1.49378 + 2.92512i −0.115940 + 0.227033i
\(167\) 16.3669i 1.26651i −0.773944 0.633254i \(-0.781719\pi\)
0.773944 0.633254i \(-0.218281\pi\)
\(168\) −17.9698 + 9.87742i −1.38640 + 0.762060i
\(169\) 24.0630 1.85100
\(170\) 0.295774 0.302431i 0.0226848 0.0231954i
\(171\) −14.7791 8.53270i −1.13018 0.652512i
\(172\) −10.6392 14.6999i −0.811229 1.12086i
\(173\) −1.99421 3.45407i −0.151617 0.262608i 0.780205 0.625524i \(-0.215115\pi\)
−0.931822 + 0.362916i \(0.881781\pi\)
\(174\) −21.0411 + 13.6370i −1.59512 + 1.03382i
\(175\) −12.7977 3.34957i −0.967413 0.253204i
\(176\) −6.36262 + 5.68703i −0.479600 + 0.428676i
\(177\) 1.64721 0.951016i 0.123812 0.0714828i
\(178\) 4.52934 0.233230i 0.339488 0.0174813i
\(179\) −16.6595 9.61835i −1.24519 0.718909i −0.275042 0.961432i \(-0.588692\pi\)
−0.970146 + 0.242523i \(0.922025\pi\)
\(180\) −3.99033 + 19.7638i −0.297422 + 1.47311i
\(181\) 5.06441i 0.376435i −0.982127 0.188217i \(-0.939729\pi\)
0.982127 0.188217i \(-0.0602709\pi\)
\(182\) −20.9836 + 8.86413i −1.55540 + 0.657053i
\(183\) 19.3764i 1.43234i
\(184\) 6.19878 4.99165i 0.456980 0.367989i
\(185\) 16.7106 + 18.1155i 1.22859 + 1.33188i
\(186\) 13.3548 0.687683i 0.979224 0.0504233i
\(187\) −0.142696 0.247157i −0.0104350 0.0180739i
\(188\) −6.00364 2.68613i −0.437860 0.195906i
\(189\) 8.37191 + 7.03657i 0.608967 + 0.511835i
\(190\) 3.22647 + 11.5267i 0.234073 + 0.836234i
\(191\) −7.26612 12.5853i −0.525758 0.910639i −0.999550 0.0300025i \(-0.990448\pi\)
0.473792 0.880637i \(-0.342885\pi\)
\(192\) 4.67498 21.4170i 0.337388 1.54564i
\(193\) −4.34743 2.50999i −0.312935 0.180673i 0.335304 0.942110i \(-0.391161\pi\)
−0.648239 + 0.761437i \(0.724494\pi\)
\(194\) −18.2723 9.33121i −1.31188 0.669942i
\(195\) −11.0990 + 35.6125i −0.794813 + 2.55027i
\(196\) 9.76004 10.0370i 0.697146 0.716929i
\(197\) −21.1781 −1.50888 −0.754440 0.656369i \(-0.772091\pi\)
−0.754440 + 0.656369i \(0.772091\pi\)
\(198\) 12.1145 + 6.18659i 0.860942 + 0.439661i
\(199\) −1.83165 + 3.17251i −0.129842 + 0.224893i −0.923615 0.383321i \(-0.874780\pi\)
0.793773 + 0.608214i \(0.208114\pi\)
\(200\) 11.6935 7.95376i 0.826855 0.562415i
\(201\) 11.0280 + 19.1011i 0.777855 + 1.34728i
\(202\) −13.0316 + 8.44594i −0.916901 + 0.594254i
\(203\) 11.0146 13.1049i 0.773074 0.919782i
\(204\) 0.669183 + 0.299404i 0.0468522 + 0.0209624i
\(205\) −8.28559 + 1.86570i −0.578690 + 0.130306i
\(206\) −0.391299 7.59905i −0.0272631 0.529451i
\(207\) −10.9865 6.34308i −0.763618 0.440875i
\(208\) 7.60956 23.1323i 0.527628 1.60394i
\(209\) 8.07543 0.558589
\(210\) −2.23345 22.8168i −0.154123 1.57451i
\(211\) 1.82414i 0.125579i 0.998027 + 0.0627895i \(0.0199997\pi\)
−0.998027 + 0.0627895i \(0.980000\pi\)
\(212\) −8.77081 + 0.905675i −0.602382 + 0.0622020i
\(213\) −13.1983 + 22.8601i −0.904333 + 1.56635i
\(214\) −5.70514 + 0.293776i −0.389996 + 0.0200821i
\(215\) 19.7923 4.45672i 1.34982 0.303946i
\(216\) −11.5524 + 1.79733i −0.786041 + 0.122293i
\(217\) −8.58196 + 3.11561i −0.582581 + 0.211502i
\(218\) −7.75313 + 5.02489i −0.525108 + 0.340329i
\(219\) −24.5668 + 14.1836i −1.66007 + 0.958441i
\(220\) −3.04090 9.04348i −0.205017 0.609711i
\(221\) 0.705283 + 0.407195i 0.0474425 + 0.0273909i
\(222\) −19.4256 + 38.0390i −1.30376 + 2.55301i
\(223\) 18.9721i 1.27047i −0.772319 0.635234i \(-0.780904\pi\)
0.772319 0.635234i \(-0.219096\pi\)
\(224\) 1.22419 + 14.9165i 0.0817944 + 0.996649i
\(225\) −18.5510 12.8071i −1.23673 0.853810i
\(226\) −2.36316 1.20681i −0.157195 0.0802755i
\(227\) −3.42574 + 5.93355i −0.227374 + 0.393823i −0.957029 0.289992i \(-0.906347\pi\)
0.729655 + 0.683815i \(0.239681\pi\)
\(228\) −16.8044 + 12.1623i −1.11290 + 0.805471i
\(229\) 11.1597 6.44308i 0.737456 0.425771i −0.0836874 0.996492i \(-0.526670\pi\)
0.821144 + 0.570721i \(0.193336\pi\)
\(230\) 2.39851 + 8.56877i 0.158153 + 0.565008i
\(231\) −15.2298 2.69830i −1.00205 0.177535i
\(232\) 2.81343 + 18.0834i 0.184710 + 1.18723i
\(233\) 0.0279737 0.0161506i 0.00183262 0.00105806i −0.499083 0.866554i \(-0.666330\pi\)
0.500916 + 0.865496i \(0.332997\pi\)
\(234\) −38.7652 + 1.99614i −2.53416 + 0.130492i
\(235\) 5.40506 4.98588i 0.352587 0.325243i
\(236\) −0.142594 1.38092i −0.00928207 0.0898902i
\(237\) 0.399757 0.0259670
\(238\) −0.496688 0.0618590i −0.0321955 0.00400973i
\(239\) 4.82580 0.312155 0.156077 0.987745i \(-0.450115\pi\)
0.156077 + 0.987745i \(0.450115\pi\)
\(240\) 19.9482 + 14.2390i 1.28765 + 0.919122i
\(241\) −10.7989 + 18.7042i −0.695618 + 1.20485i 0.274354 + 0.961629i \(0.411536\pi\)
−0.969972 + 0.243216i \(0.921797\pi\)
\(242\) 9.10738 0.468968i 0.585445 0.0301464i
\(243\) −9.21303 15.9574i −0.591016 1.02367i
\(244\) 12.9093 + 5.77584i 0.826434 + 0.369760i
\(245\) 6.01415 + 14.4509i 0.384230 + 0.923237i
\(246\) −8.00512 12.3515i −0.510388 0.787500i
\(247\) −19.9566 + 11.5219i −1.26981 + 0.733123i
\(248\) 3.52273 9.10250i 0.223694 0.578009i
\(249\) 3.18197 5.51133i 0.201649 0.349266i
\(250\) 3.02168 + 15.5200i 0.191108 + 0.981569i
\(251\) 29.4788i 1.86068i −0.366693 0.930342i \(-0.619510\pi\)
0.366693 0.930342i \(-0.380490\pi\)
\(252\) 21.4699 10.4014i 1.35247 0.655224i
\(253\) 6.00316 0.377415
\(254\) 5.21585 + 2.66360i 0.327272 + 0.167129i
\(255\) −0.602464 + 0.555741i −0.0377278 + 0.0348019i
\(256\) −12.8753 9.49877i −0.804706 0.593673i
\(257\) 3.05932 1.76630i 0.190835 0.110179i −0.401538 0.915842i \(-0.631524\pi\)
0.592373 + 0.805663i \(0.298191\pi\)
\(258\) 19.1223 + 29.5047i 1.19051 + 1.83688i
\(259\) 5.08736 28.7142i 0.316113 1.78421i
\(260\) 20.4180 + 18.0102i 1.26627 + 1.11694i
\(261\) 25.2634 14.5858i 1.56376 0.902839i
\(262\) −0.788825 15.3190i −0.0487337 0.946412i
\(263\) 2.31205 + 1.33486i 0.142567 + 0.0823112i 0.569587 0.821931i \(-0.307103\pi\)
−0.427020 + 0.904242i \(0.640437\pi\)
\(264\) 12.8785 10.3706i 0.792616 0.638264i
\(265\) 2.93324 9.41171i 0.180188 0.578157i
\(266\) 8.54296 11.2961i 0.523802 0.692610i
\(267\) −8.78762 −0.537794
\(268\) 16.0132 1.65352i 0.978160 0.101005i
\(269\) 19.5980 + 11.3149i 1.19491 + 0.689883i 0.959416 0.281993i \(-0.0909955\pi\)
0.235495 + 0.971876i \(0.424329\pi\)
\(270\) 3.24240 12.6628i 0.197326 0.770635i
\(271\) −4.23600 7.33697i −0.257319 0.445689i 0.708204 0.706008i \(-0.249506\pi\)
−0.965523 + 0.260319i \(0.916172\pi\)
\(272\) 0.398949 0.356588i 0.0241898 0.0216213i
\(273\) 41.4869 15.0615i 2.51090 0.911564i
\(274\) −19.3982 + 12.5722i −1.17189 + 0.759515i
\(275\) 10.6325 + 0.859248i 0.641167 + 0.0518146i
\(276\) −12.4922 + 9.04131i −0.751939 + 0.544223i
\(277\) 1.62592 2.81617i 0.0976918 0.169207i −0.813037 0.582212i \(-0.802187\pi\)
0.910729 + 0.413005i \(0.135521\pi\)
\(278\) −1.56174 0.797543i −0.0936671 0.0478334i
\(279\) −15.5580 −0.931433
\(280\) −15.8672 5.31336i −0.948247 0.317534i
\(281\) −16.4018 −0.978451 −0.489225 0.872157i \(-0.662720\pi\)
−0.489225 + 0.872157i \(0.662720\pi\)
\(282\) 11.3495 + 5.79592i 0.675855 + 0.345142i
\(283\) −8.26884 + 14.3221i −0.491532 + 0.851358i −0.999952 0.00975110i \(-0.996896\pi\)
0.508421 + 0.861109i \(0.330229\pi\)
\(284\) 11.2961 + 15.6075i 0.670299 + 0.926136i
\(285\) −5.09478 22.6259i −0.301789 1.34024i
\(286\) 15.4140 9.98998i 0.911448 0.590720i
\(287\) 7.69276 + 6.46575i 0.454089 + 0.381661i
\(288\) −6.71318 + 24.6045i −0.395578 + 1.44984i
\(289\) −8.49105 14.7069i −0.499474 0.865114i
\(290\) −19.8216 5.07545i −1.16396 0.298041i
\(291\) 34.4276 + 19.8768i 2.01818 + 1.16520i
\(292\) 2.12667 + 20.5953i 0.124454 + 1.20525i
\(293\) 24.7886 1.44817 0.724084 0.689712i \(-0.242263\pi\)
0.724084 + 0.689712i \(0.242263\pi\)
\(294\) −19.8860 + 18.4494i −1.15978 + 1.07599i
\(295\) 1.48183 + 0.461824i 0.0862752 + 0.0268884i
\(296\) 19.5526 + 24.2810i 1.13647 + 1.41130i
\(297\) −7.63717 4.40932i −0.443153 0.255855i
\(298\) −0.554722 10.7727i −0.0321342 0.624048i
\(299\) −14.8354 + 8.56523i −0.857955 + 0.495340i
\(300\) −23.4197 + 14.2256i −1.35214 + 0.821313i
\(301\) −18.3762 15.4451i −1.05919 0.890243i
\(302\) −13.5478 20.9035i −0.779589 1.20286i
\(303\) 26.0580 15.0446i 1.49700 0.864291i
\(304\) 3.09386 + 14.8212i 0.177445 + 0.850054i
\(305\) −11.6222 + 10.7209i −0.665486 + 0.613876i
\(306\) −0.759605 0.387911i −0.0434237 0.0221754i
\(307\) 12.1238 0.691940 0.345970 0.938246i \(-0.387550\pi\)
0.345970 + 0.938246i \(0.387550\pi\)
\(308\) −6.33752 + 9.34238i −0.361114 + 0.532331i
\(309\) 14.7433i 0.838719i
\(310\) 7.80166 + 7.62992i 0.443104 + 0.433350i
\(311\) 13.8034 23.9081i 0.782717 1.35571i −0.147637 0.989042i \(-0.547167\pi\)
0.930353 0.366664i \(-0.119500\pi\)
\(312\) −17.0296 + 44.0033i −0.964111 + 2.49120i
\(313\) −28.4805 + 16.4432i −1.60981 + 0.929427i −0.620404 + 0.784282i \(0.713032\pi\)
−0.989410 + 0.145145i \(0.953635\pi\)
\(314\) 6.03380 + 9.30982i 0.340507 + 0.525384i
\(315\) 1.22991 + 26.6443i 0.0692978 + 1.50123i
\(316\) 0.119162 0.266334i 0.00670339 0.0149824i
\(317\) −8.08482 14.0033i −0.454089 0.786505i 0.544547 0.838731i \(-0.316702\pi\)
−0.998635 + 0.0522259i \(0.983368\pi\)
\(318\) 17.0620 0.878575i 0.956788 0.0492681i
\(319\) −6.90208 + 11.9547i −0.386442 + 0.669337i
\(320\) 15.4329 9.04583i 0.862723 0.505677i
\(321\) 11.0689 0.617804
\(322\) 6.35071 8.39738i 0.353911 0.467967i
\(323\) −0.506346 −0.0281738
\(324\) −4.37464 + 0.451726i −0.243035 + 0.0250959i
\(325\) −27.5019 + 13.0470i −1.52553 + 0.723715i
\(326\) −1.74728 + 0.0899730i −0.0967729 + 0.00498314i
\(327\) 15.5032 8.95077i 0.857328 0.494979i
\(328\) −10.6152 + 1.65152i −0.586129 + 0.0911902i
\(329\) −8.56733 1.51789i −0.472332 0.0836842i
\(330\) 4.98311 + 17.8023i 0.274311 + 0.979987i
\(331\) −23.2696 + 13.4347i −1.27901 + 0.738438i −0.976667 0.214761i \(-0.931103\pi\)
−0.302345 + 0.953198i \(0.597770\pi\)
\(332\) −2.72336 3.76280i −0.149464 0.206511i
\(333\) 24.8462 43.0349i 1.36157 2.35830i
\(334\) 20.6139 + 10.5270i 1.12794 + 0.576012i
\(335\) −5.35532 + 17.1833i −0.292592 + 0.938823i
\(336\) −0.882545 28.9857i −0.0481468 1.58130i
\(337\) 13.5015i 0.735475i −0.929930 0.367738i \(-0.880132\pi\)
0.929930 0.367738i \(-0.119868\pi\)
\(338\) −15.4771 + 30.3071i −0.841842 + 1.64849i
\(339\) 4.45252 + 2.57066i 0.241828 + 0.139619i
\(340\) 0.190670 + 0.567044i 0.0103405 + 0.0307523i
\(341\) 6.37579 3.68106i 0.345268 0.199341i
\(342\) 20.2526 13.1259i 1.09513 0.709768i
\(343\) 9.29955 16.0162i 0.502128 0.864793i
\(344\) 25.3573 3.94510i 1.36717 0.212706i
\(345\) −3.78738 16.8198i −0.203906 0.905546i
\(346\) 5.63300 0.290061i 0.302832 0.0155938i
\(347\) −11.4913 + 19.9036i −0.616887 + 1.06848i 0.373163 + 0.927766i \(0.378273\pi\)
−0.990050 + 0.140714i \(0.955060\pi\)
\(348\) −3.64221 35.2722i −0.195243 1.89079i
\(349\) 9.42601i 0.504563i −0.967654 0.252281i \(-0.918819\pi\)
0.967654 0.252281i \(-0.0811808\pi\)
\(350\) 12.4501 13.9641i 0.665484 0.746412i
\(351\) 25.1647 1.34319
\(352\) −3.07038 11.6715i −0.163652 0.622091i
\(353\) −16.4675 9.50750i −0.876475 0.506033i −0.00698041 0.999976i \(-0.502222\pi\)
−0.869495 + 0.493943i \(0.835555\pi\)
\(354\) 0.138327 + 2.68632i 0.00735201 + 0.142776i
\(355\) −21.0144 + 4.73190i −1.11533 + 0.251143i
\(356\) −2.61947 + 5.85465i −0.138832 + 0.310296i
\(357\) 0.954940 + 0.169189i 0.0505408 + 0.00895443i
\(358\) 22.8294 14.7960i 1.20657 0.781992i
\(359\) 0.0924791 + 0.160179i 0.00488086 + 0.00845390i 0.868456 0.495767i \(-0.165113\pi\)
−0.863575 + 0.504221i \(0.831780\pi\)
\(360\) −22.3257 17.7376i −1.17667 0.934855i
\(361\) −2.33626 + 4.04652i −0.122961 + 0.212975i
\(362\) 6.37856 + 3.25737i 0.335250 + 0.171204i
\(363\) −17.6697 −0.927421
\(364\) 2.33212 32.1298i 0.122236 1.68406i
\(365\) −22.1002 6.88772i −1.15678 0.360520i
\(366\) −24.4043 12.4627i −1.27563 0.651435i
\(367\) 4.03222 + 2.32800i 0.210480 + 0.121521i 0.601534 0.798847i \(-0.294556\pi\)
−0.391054 + 0.920368i \(0.627890\pi\)
\(368\) 2.29993 + 11.0179i 0.119892 + 0.574345i
\(369\) 8.56209 + 14.8300i 0.445725 + 0.772018i
\(370\) −33.5644 + 9.39512i −1.74493 + 0.488429i
\(371\) −10.9642 + 3.98047i −0.569233 + 0.206656i
\(372\) −7.72355 + 17.2626i −0.400447 + 0.895022i
\(373\) 6.50449 + 11.2661i 0.336790 + 0.583337i 0.983827 0.179121i \(-0.0573255\pi\)
−0.647037 + 0.762458i \(0.723992\pi\)
\(374\) 0.403072 0.0207555i 0.0208424 0.00107324i
\(375\) −4.30060 30.3326i −0.222082 1.56637i
\(376\) 7.24461 5.83382i 0.373612 0.300856i
\(377\) 39.3912i 2.02875i
\(378\) −14.2472 + 6.01848i −0.732797 + 0.309557i
\(379\) 27.2688i 1.40070i 0.713797 + 0.700352i \(0.246974\pi\)
−0.713797 + 0.700352i \(0.753026\pi\)
\(380\) −16.5930 3.35014i −0.851201 0.171858i
\(381\) −9.82739 5.67385i −0.503473 0.290680i
\(382\) 20.5245 1.05687i 1.05012 0.0540742i
\(383\) −6.35810 + 3.67085i −0.324884 + 0.187572i −0.653567 0.756868i \(-0.726728\pi\)
0.328683 + 0.944440i \(0.393395\pi\)
\(384\) 23.9676 + 19.6633i 1.22309 + 1.00344i
\(385\) −6.80812 10.6280i −0.346974 0.541654i
\(386\) 5.95752 3.86114i 0.303230 0.196527i
\(387\) −20.4528 35.4253i −1.03968 1.80077i
\(388\) 23.5051 17.0120i 1.19329 0.863654i
\(389\) −0.175410 0.101273i −0.00889366 0.00513475i 0.495547 0.868581i \(-0.334968\pi\)
−0.504440 + 0.863447i \(0.668301\pi\)
\(390\) −37.7148 36.8846i −1.90976 1.86772i
\(391\) −0.376410 −0.0190359
\(392\) 6.36394 + 18.7483i 0.321427 + 0.946934i
\(393\) 29.7213i 1.49924i
\(394\) 13.6215 26.6736i 0.686243 1.34380i
\(395\) 0.221184 + 0.239780i 0.0111290 + 0.0120646i
\(396\) −15.5839 + 11.2790i −0.783118 + 0.566789i
\(397\) −0.182428 0.315975i −0.00915580 0.0158583i 0.861411 0.507908i \(-0.169581\pi\)
−0.870567 + 0.492050i \(0.836248\pi\)
\(398\) −2.81764 4.34746i −0.141235 0.217918i
\(399\) −17.6564 + 21.0071i −0.883925 + 1.05167i
\(400\) 2.49653 + 19.8436i 0.124827 + 0.992179i
\(401\) 18.1863 + 31.4996i 0.908181 + 1.57302i 0.816589 + 0.577219i \(0.195862\pi\)
0.0915915 + 0.995797i \(0.470805\pi\)
\(402\) −31.1506 + 1.60404i −1.55365 + 0.0800024i
\(403\) −10.5042 + 18.1938i −0.523251 + 0.906297i
\(404\) −2.25577 21.8455i −0.112229 1.08685i
\(405\) 1.46302 4.69430i 0.0726981 0.233262i
\(406\) 9.42095 + 22.3017i 0.467554 + 1.10681i
\(407\) 23.5147i 1.16558i
\(408\) −0.807506 + 0.650255i −0.0399775 + 0.0321924i
\(409\) 5.40114 9.35504i 0.267069 0.462577i −0.701035 0.713127i \(-0.747278\pi\)
0.968104 + 0.250550i \(0.0806115\pi\)
\(410\) 2.97937 11.6356i 0.147140 0.574641i
\(411\) 38.7887 22.3947i 1.91331 1.10465i
\(412\) 9.82258 + 4.39478i 0.483924 + 0.216516i
\(413\) −0.626704 1.72626i −0.0308381 0.0849436i
\(414\) 15.0555 9.75761i 0.739935 0.479561i
\(415\) 5.06634 1.14081i 0.248697 0.0560002i
\(416\) 24.2405 + 24.4626i 1.18849 + 1.19938i
\(417\) 2.94254 + 1.69888i 0.144097 + 0.0831944i
\(418\) −5.19403 + 10.1709i −0.254048 + 0.497475i
\(419\) 18.6727i 0.912219i −0.889924 0.456110i \(-0.849243\pi\)
0.889924 0.456110i \(-0.150757\pi\)
\(420\) 30.1740 + 11.8625i 1.47234 + 0.578831i
\(421\) 16.6714i 0.812516i 0.913758 + 0.406258i \(0.133167\pi\)
−0.913758 + 0.406258i \(0.866833\pi\)
\(422\) −2.29748 1.17327i −0.111840 0.0571137i
\(423\) −12.8402 7.41326i −0.624310 0.360445i
\(424\) 4.50060 11.6292i 0.218569 0.564766i
\(425\) −0.666682 0.0538766i −0.0323388 0.00261340i
\(426\) −20.3031 31.3265i −0.983686 1.51777i
\(427\) 18.4219 + 3.26385i 0.891498 + 0.157949i
\(428\) 3.29948 7.37451i 0.159486 0.356460i
\(429\) −30.8218 + 17.7950i −1.48809 + 0.859151i
\(430\) −7.11700 + 27.7947i −0.343212 + 1.34038i
\(431\) 2.95698 5.12165i 0.142433 0.246701i −0.785979 0.618253i \(-0.787841\pi\)
0.928412 + 0.371552i \(0.121174\pi\)
\(432\) 5.16666 15.7061i 0.248581 0.755661i
\(433\) 25.3998i 1.22064i 0.792157 + 0.610318i \(0.208958\pi\)
−0.792157 + 0.610318i \(0.791042\pi\)
\(434\) 1.59574 12.8128i 0.0765981 0.615034i
\(435\) 37.8496 + 11.7962i 1.81475 + 0.565582i
\(436\) −1.34206 12.9969i −0.0642732 0.622440i
\(437\) 5.32542 9.22389i 0.254749 0.441239i
\(438\) −2.06304 40.0643i −0.0985757 1.91434i
\(439\) 12.5963 + 21.8175i 0.601190 + 1.04129i 0.992641 + 0.121093i \(0.0386398\pi\)
−0.391451 + 0.920199i \(0.628027\pi\)
\(440\) 13.3460 + 1.98669i 0.636246 + 0.0947118i
\(441\) 24.2092 20.2464i 1.15282 0.964113i
\(442\) −0.966487 + 0.626391i −0.0459711 + 0.0297944i
\(443\) −11.7718 20.3894i −0.559295 0.968728i −0.997555 0.0698797i \(-0.977738\pi\)
0.438260 0.898848i \(-0.355595\pi\)
\(444\) −35.4153 48.9325i −1.68074 2.32223i
\(445\) −4.86215 5.27093i −0.230488 0.249866i
\(446\) 23.8952 + 12.2027i 1.13147 + 0.577813i
\(447\) 20.9008i 0.988573i
\(448\) −19.5745 8.05226i −0.924808 0.380434i
\(449\) −5.21146 −0.245944 −0.122972 0.992410i \(-0.539243\pi\)
−0.122972 + 0.992410i \(0.539243\pi\)
\(450\) 28.0622 15.1274i 1.32287 0.713111i
\(451\) −7.01762 4.05162i −0.330447 0.190784i
\(452\) 3.03991 2.20016i 0.142985 0.103487i
\(453\) 24.1325 + 41.7988i 1.13384 + 1.96388i
\(454\) −5.26983 8.13106i −0.247326 0.381610i
\(455\) 31.9886 + 16.5509i 1.49965 + 0.775920i
\(456\) −4.50991 28.9876i −0.211196 1.35747i
\(457\) 6.73451 3.88817i 0.315027 0.181881i −0.334147 0.942521i \(-0.608448\pi\)
0.649174 + 0.760640i \(0.275115\pi\)
\(458\) 0.937158 + 18.1997i 0.0437905 + 0.850414i
\(459\) 0.478865 + 0.276473i 0.0223515 + 0.0129047i
\(460\) −12.3350 2.49044i −0.575120 0.116117i
\(461\) 31.3778i 1.46141i 0.682693 + 0.730706i \(0.260809\pi\)
−0.682693 + 0.730706i \(0.739191\pi\)
\(462\) 13.1941 17.4463i 0.613847 0.811673i
\(463\) 34.1001i 1.58477i 0.610023 + 0.792384i \(0.291160\pi\)
−0.610023 + 0.792384i \(0.708840\pi\)
\(464\) −24.5854 8.08757i −1.14135 0.375456i
\(465\) −14.3362 15.5414i −0.664823 0.720717i
\(466\) 0.00234914 + 0.0456204i 0.000108822 + 0.00211332i
\(467\) 10.8078 + 18.7196i 0.500124 + 0.866239i 1.00000 0.000142626i \(4.53993e-5\pi\)
−0.499876 + 0.866097i \(0.666621\pi\)
\(468\) 22.4192 50.1082i 1.03633 2.31625i
\(469\) 20.0177 7.26727i 0.924332 0.335572i
\(470\) 2.80318 + 10.0145i 0.129301 + 0.461933i
\(471\) −10.7479 18.6159i −0.495238 0.857778i
\(472\) 1.83097 + 0.708597i 0.0842770 + 0.0326158i
\(473\) 16.7634 + 9.67837i 0.770784 + 0.445012i
\(474\) −0.257119 + 0.503489i −0.0118099 + 0.0231260i
\(475\) 10.7524 15.5747i 0.493354 0.714618i
\(476\) 0.397375 0.585785i 0.0182136 0.0268494i
\(477\) −19.8767 −0.910092
\(478\) −3.10390 + 6.07803i −0.141969 + 0.278003i
\(479\) −1.43986 + 2.49392i −0.0657891 + 0.113950i −0.897044 0.441942i \(-0.854290\pi\)
0.831255 + 0.555892i \(0.187623\pi\)
\(480\) −30.7643 + 15.9662i −1.40419 + 0.728752i
\(481\) −33.5505 58.1112i −1.52977 2.64964i
\(482\) −16.6120 25.6314i −0.756656 1.16748i
\(483\) −13.1255 + 15.6163i −0.597231 + 0.710568i
\(484\) −5.26711 + 11.7723i −0.239414 + 0.535103i
\(485\) 7.12630 + 31.6479i 0.323588 + 1.43706i
\(486\) 26.0239 1.34005i 1.18047 0.0607860i
\(487\) −10.3485 5.97470i −0.468935 0.270740i 0.246859 0.969051i \(-0.420602\pi\)
−0.715794 + 0.698312i \(0.753935\pi\)
\(488\) −15.5777 + 12.5442i −0.705170 + 0.567848i
\(489\) 3.39000 0.153301
\(490\) −22.0690 1.71994i −0.996977 0.0776988i
\(491\) 16.6670i 0.752173i −0.926584 0.376087i \(-0.877269\pi\)
0.926584 0.376087i \(-0.122731\pi\)
\(492\) 20.7053 2.13803i 0.933467 0.0963899i
\(493\) 0.432774 0.749586i 0.0194912 0.0337597i
\(494\) −1.67589 32.5458i −0.0754017 1.46431i
\(495\) −4.72473 20.9825i −0.212361 0.943094i
\(496\) 9.19870 + 10.2915i 0.413034 + 0.462100i
\(497\) 19.5108 + 16.3988i 0.875180 + 0.735587i
\(498\) 4.89484 + 7.55247i 0.219343 + 0.338434i
\(499\) 37.1045 21.4223i 1.66103 0.958994i 0.688799 0.724952i \(-0.258138\pi\)
0.972227 0.234042i \(-0.0751952\pi\)
\(500\) −21.4907 6.17650i −0.961094 0.276222i
\(501\) −38.8395 22.4240i −1.73522 1.00183i
\(502\) 37.1281 + 18.9604i 1.65711 + 0.846245i
\(503\) 32.6248i 1.45467i −0.686283 0.727334i \(-0.740759\pi\)
0.686283 0.727334i \(-0.259241\pi\)
\(504\) −0.708778 + 33.7311i −0.0315715 + 1.50250i
\(505\) 23.4418 + 7.30583i 1.04315 + 0.325105i
\(506\) −3.86116 + 7.56090i −0.171650 + 0.336123i
\(507\) 32.9683 57.1028i 1.46417 2.53603i
\(508\) −6.70955 + 4.85610i −0.297688 + 0.215454i
\(509\) −8.82639 + 5.09592i −0.391223 + 0.225873i −0.682690 0.730708i \(-0.739190\pi\)
0.291467 + 0.956581i \(0.405857\pi\)
\(510\) −0.312451 1.11624i −0.0138356 0.0494280i
\(511\) 9.34678 + 25.7457i 0.413477 + 1.13892i
\(512\) 20.2448 10.1068i 0.894703 0.446661i
\(513\) −13.5499 + 7.82304i −0.598243 + 0.345396i
\(514\) 0.256912 + 4.98924i 0.0113319 + 0.220066i
\(515\) −8.84325 + 8.15743i −0.389680 + 0.359459i
\(516\) −49.4601 + 5.10725i −2.17736 + 0.224834i
\(517\) 7.01599 0.308563
\(518\) 32.8930 + 24.8761i 1.44524 + 1.09299i
\(519\) −10.9289 −0.479726
\(520\) −35.8162 + 14.1323i −1.57064 + 0.619742i
\(521\) 0.101242 0.175356i 0.00443548 0.00768248i −0.863799 0.503836i \(-0.831921\pi\)
0.868235 + 0.496154i \(0.165255\pi\)
\(522\) 2.12153 + 41.2003i 0.0928570 + 1.80329i
\(523\) −10.0334 17.3783i −0.438729 0.759902i 0.558862 0.829260i \(-0.311238\pi\)
−0.997592 + 0.0693587i \(0.977905\pi\)
\(524\) 19.8015 + 8.85950i 0.865031 + 0.387029i
\(525\) −25.4826 + 25.7803i −1.11215 + 1.12515i
\(526\) −3.16833 + 2.05343i −0.138146 + 0.0895338i
\(527\) −0.399774 + 0.230810i −0.0174144 + 0.0100542i
\(528\) 4.77830 + 22.8905i 0.207949 + 0.996182i
\(529\) −7.54116 + 13.0617i −0.327877 + 0.567899i
\(530\) 9.96731 + 9.74789i 0.432952 + 0.423421i
\(531\) 3.12949i 0.135808i
\(532\) 8.73260 + 18.0253i 0.378606 + 0.781495i
\(533\) 23.1232 1.00158
\(534\) 5.65210 11.0679i 0.244590 0.478955i
\(535\) 6.12436 + 6.63925i 0.264779 + 0.287040i
\(536\) −8.21690 + 21.2319i −0.354916 + 0.917079i
\(537\) −45.6497 + 26.3559i −1.96993 + 1.13734i
\(538\) −26.8562 + 17.4058i −1.15785 + 0.750418i
\(539\) −5.13076 + 14.0251i −0.220998 + 0.604102i
\(540\) 13.8632 + 12.2283i 0.596577 + 0.526224i
\(541\) 31.4204 18.1406i 1.35087 0.779924i 0.362497 0.931985i \(-0.381924\pi\)
0.988371 + 0.152061i \(0.0485909\pi\)
\(542\) 11.9654 0.616135i 0.513957 0.0264652i
\(543\) −12.0181 6.93865i −0.515746 0.297766i
\(544\) 0.192519 + 0.731824i 0.00825417 + 0.0313767i
\(545\) 13.9466 + 4.34659i 0.597408 + 0.186188i
\(546\) −7.71415 + 61.9396i −0.330135 + 2.65077i
\(547\) −13.3940 −0.572687 −0.286343 0.958127i \(-0.592440\pi\)
−0.286343 + 0.958127i \(0.592440\pi\)
\(548\) −3.35783 32.5181i −0.143439 1.38911i
\(549\) 27.6095 + 15.9404i 1.17835 + 0.680318i
\(550\) −7.92095 + 12.8389i −0.337750 + 0.547453i
\(551\) 12.2457 + 21.2102i 0.521685 + 0.903584i
\(552\) −3.35260 21.5490i −0.142696 0.917185i
\(553\) 0.0673369 0.380065i 0.00286346 0.0161620i
\(554\) 2.50116 + 3.85915i 0.106264 + 0.163960i
\(555\) 65.8841 14.8354i 2.79662 0.629728i
\(556\) 2.00899 1.45402i 0.0852001 0.0616644i
\(557\) 1.09992 1.90513i 0.0466053 0.0807227i −0.841782 0.539818i \(-0.818493\pi\)
0.888387 + 0.459095i \(0.151826\pi\)
\(558\) 10.0067 19.5951i 0.423619 0.829527i
\(559\) −55.2360 −2.33623
\(560\) 16.8977 16.5671i 0.714059 0.700086i
\(561\) −0.782023 −0.0330170
\(562\) 10.5495 20.6579i 0.445002 0.871400i
\(563\) 10.3121 17.8611i 0.434603 0.752755i −0.562660 0.826688i \(-0.690222\pi\)
0.997263 + 0.0739336i \(0.0235553\pi\)
\(564\) −14.5998 + 10.5667i −0.614762 + 0.444939i
\(565\) 0.921644 + 4.09302i 0.0387738 + 0.172195i
\(566\) −12.7200 19.6263i −0.534662 0.824954i
\(567\) −5.46864 + 1.98535i −0.229661 + 0.0833768i
\(568\) −26.9230 + 4.18869i −1.12966 + 0.175754i
\(569\) 11.4607 + 19.8506i 0.480459 + 0.832180i 0.999749 0.0224188i \(-0.00713672\pi\)
−0.519290 + 0.854598i \(0.673803\pi\)
\(570\) 31.7740 + 8.13592i 1.33086 + 0.340776i
\(571\) 15.6853 + 9.05590i 0.656408 + 0.378978i 0.790907 0.611936i \(-0.209609\pi\)
−0.134499 + 0.990914i \(0.542942\pi\)
\(572\) 2.66815 + 25.8392i 0.111561 + 1.08039i
\(573\) −39.8207 −1.66353
\(574\) −13.0914 + 5.53024i −0.546425 + 0.230828i
\(575\) 7.99318 11.5780i 0.333339 0.482837i
\(576\) −26.6712 24.2805i −1.11130 1.01169i
\(577\) 4.99051 + 2.88127i 0.207758 + 0.119949i 0.600269 0.799798i \(-0.295060\pi\)
−0.392511 + 0.919747i \(0.628394\pi\)
\(578\) 23.9845 1.23504i 0.997626 0.0513709i
\(579\) −11.9127 + 6.87778i −0.495074 + 0.285831i
\(580\) 19.1415 21.7006i 0.794807 0.901068i
\(581\) −4.70385 3.95357i −0.195148 0.164022i
\(582\) −47.1780 + 30.5766i −1.95559 + 1.26744i
\(583\) 8.14563 4.70288i 0.337357 0.194773i
\(584\) −27.3073 10.5681i −1.12999 0.437312i
\(585\) 41.6137 + 45.1123i 1.72051 + 1.86516i
\(586\) −15.9438 + 31.2210i −0.658631 + 1.28973i
\(587\) −38.0279 −1.56958 −0.784791 0.619761i \(-0.787230\pi\)
−0.784791 + 0.619761i \(0.787230\pi\)
\(588\) −10.4463 36.9126i −0.430797 1.52225i
\(589\) 13.0619i 0.538207i
\(590\) −1.53476 + 1.56930i −0.0631849 + 0.0646071i
\(591\) −29.0158 + 50.2568i −1.19355 + 2.06729i
\(592\) −43.1576 + 9.00897i −1.77377 + 0.370266i
\(593\) 10.0001 5.77354i 0.410654 0.237091i −0.280417 0.959878i \(-0.590473\pi\)
0.691071 + 0.722787i \(0.257139\pi\)
\(594\) 10.4656 6.78289i 0.429410 0.278305i
\(595\) 0.426883 + 0.666397i 0.0175005 + 0.0273196i
\(596\) 13.9249 + 6.23024i 0.570387 + 0.255200i
\(597\) 5.01902 + 8.69319i 0.205415 + 0.355789i
\(598\) −1.24583 24.1941i −0.0509458 0.989370i
\(599\) 17.5545 30.4052i 0.717256 1.24232i −0.244827 0.969567i \(-0.578731\pi\)
0.962083 0.272757i \(-0.0879355\pi\)
\(600\) −2.85363 38.6466i −0.116499 1.57774i
\(601\) −21.5369 −0.878508 −0.439254 0.898363i \(-0.644757\pi\)
−0.439254 + 0.898363i \(0.644757\pi\)
\(602\) 31.2723 13.2104i 1.27456 0.538417i
\(603\) 36.2896 1.47783
\(604\) 35.0415 3.61839i 1.42582 0.147230i
\(605\) −9.77659 10.5985i −0.397475 0.430892i
\(606\) 2.18827 + 42.4963i 0.0888924 + 1.72629i
\(607\) −9.17528 + 5.29735i −0.372413 + 0.215013i −0.674512 0.738264i \(-0.735646\pi\)
0.302099 + 0.953277i \(0.402313\pi\)
\(608\) −20.6570 5.63614i −0.837754 0.228576i
\(609\) −16.0076 44.0930i −0.648661 1.78674i
\(610\) −6.02754 21.5336i −0.244048 0.871870i
\(611\) −17.3384 + 10.0103i −0.701436 + 0.404974i
\(612\) 0.977138 0.707213i 0.0394985 0.0285874i
\(613\) −15.4694 + 26.7937i −0.624802 + 1.08219i 0.363777 + 0.931486i \(0.381487\pi\)
−0.988579 + 0.150702i \(0.951846\pi\)
\(614\) −7.79787 + 15.2697i −0.314696 + 0.616236i
\(615\) −6.92452 + 22.2183i −0.279224 + 0.895928i
\(616\) −7.69039 13.9909i −0.309854 0.563711i
\(617\) 2.10027i 0.0845538i 0.999106 + 0.0422769i \(0.0134612\pi\)
−0.999106 + 0.0422769i \(0.986539\pi\)
\(618\) −18.5690 9.48274i −0.746956 0.381452i
\(619\) 38.1487 + 22.0252i 1.53333 + 0.885267i 0.999205 + 0.0398593i \(0.0126910\pi\)
0.534122 + 0.845408i \(0.320642\pi\)
\(620\) −14.6277 + 4.91861i −0.587463 + 0.197536i
\(621\) −10.0728 + 5.81553i −0.404207 + 0.233369i
\(622\) 21.2338 + 32.7626i 0.851399 + 1.31366i
\(623\) −1.48023 + 8.35473i −0.0593040 + 0.334725i
\(624\) −44.4684 49.7510i −1.78016 1.99163i
\(625\) 15.8144 19.3625i 0.632576 0.774499i
\(626\) −2.39170 46.4470i −0.0955916 1.85639i
\(627\) 11.0640 19.1634i 0.441854 0.765313i
\(628\) −15.6065 + 1.61153i −0.622766 + 0.0643069i
\(629\) 1.47442i 0.0587890i
\(630\) −34.3492 15.5882i −1.36850 0.621050i
\(631\) 29.3294 1.16758 0.583792 0.811903i \(-0.301568\pi\)
0.583792 + 0.811903i \(0.301568\pi\)
\(632\) 0.258800 + 0.321386i 0.0102945 + 0.0127841i
\(633\) 4.32878 + 2.49922i 0.172054 + 0.0993351i
\(634\) 22.8371 1.17595i 0.906976 0.0467030i
\(635\) −2.03421 9.03392i −0.0807251 0.358500i
\(636\) −9.86752 + 22.0544i −0.391273 + 0.874515i
\(637\) −7.33130 41.9802i −0.290477 1.66332i
\(638\) −10.6175 16.3822i −0.420351 0.648579i
\(639\) 21.7157 + 37.6127i 0.859059 + 1.48793i
\(640\) 1.46687 + 25.2557i 0.0579832 + 0.998318i
\(641\) 8.49533 14.7144i 0.335546 0.581182i −0.648044 0.761603i \(-0.724413\pi\)
0.983589 + 0.180421i \(0.0577460\pi\)
\(642\) −7.11937 + 13.9411i −0.280979 + 0.550211i
\(643\) 9.47205 0.373541 0.186771 0.982404i \(-0.440198\pi\)
0.186771 + 0.982404i \(0.440198\pi\)
\(644\) 6.49168 + 13.3997i 0.255808 + 0.528023i
\(645\) 16.5410 53.0742i 0.651303 2.08980i
\(646\) 0.325676 0.637736i 0.0128135 0.0250914i
\(647\) −38.7747 22.3866i −1.52439 0.880107i −0.999583 0.0288861i \(-0.990804\pi\)
−0.524807 0.851221i \(-0.675863\pi\)
\(648\) 2.24478 5.80035i 0.0881831 0.227859i
\(649\) 0.740444 + 1.28249i 0.0290650 + 0.0503420i
\(650\) 1.25640 43.0299i 0.0492801 1.68777i
\(651\) −4.36448 + 24.6341i −0.171057 + 0.965485i
\(652\) 1.01051 2.25855i 0.0395747 0.0884515i
\(653\) 9.50325 + 16.4601i 0.371891 + 0.644134i 0.989856 0.142071i \(-0.0453762\pi\)
−0.617966 + 0.786205i \(0.712043\pi\)
\(654\) 1.30191 + 25.2831i 0.0509086 + 0.988647i
\(655\) −17.8272 + 16.4447i −0.696567 + 0.642546i
\(656\) 4.74753 14.4320i 0.185360 0.563475i
\(657\) 46.6737i 1.82092i
\(658\) 7.42218 9.81415i 0.289347 0.382595i
\(659\) 35.4688i 1.38167i −0.723013 0.690835i \(-0.757243\pi\)
0.723013 0.690835i \(-0.242757\pi\)
\(660\) −25.6269 5.17410i −0.997526 0.201402i
\(661\) −15.4781 8.93629i −0.602029 0.347581i 0.167811 0.985819i \(-0.446330\pi\)
−0.769839 + 0.638238i \(0.779664\pi\)
\(662\) −1.95410 37.9488i −0.0759484 1.47492i
\(663\) 1.93259 1.11578i 0.0750556 0.0433334i
\(664\) 6.49084 1.00985i 0.251893 0.0391897i
\(665\) −22.3695 + 1.03259i −0.867453 + 0.0400421i
\(666\) 38.2212 + 58.9731i 1.48104 + 2.28516i
\(667\) 9.10327 + 15.7673i 0.352480 + 0.610514i
\(668\) −26.5172 + 19.1921i −1.02598 + 0.742564i
\(669\) −45.0219 25.9934i −1.74065 1.00496i
\(670\) −18.1976 17.7970i −0.703036 0.687560i
\(671\) −15.0861 −0.582393
\(672\) 37.0748 + 17.5317i 1.43019 + 0.676302i
\(673\) 22.0936i 0.851645i −0.904807 0.425822i \(-0.859985\pi\)
0.904807 0.425822i \(-0.140015\pi\)
\(674\) 17.0050 + 8.68403i 0.655009 + 0.334496i
\(675\) −18.6729 + 8.85849i −0.718721 + 0.340963i
\(676\) −28.2167 38.9863i −1.08526 1.49947i
\(677\) −8.47585 14.6806i −0.325754 0.564222i 0.655911 0.754838i \(-0.272285\pi\)
−0.981665 + 0.190617i \(0.938951\pi\)
\(678\) −6.10153 + 3.95447i −0.234328 + 0.151871i
\(679\) 24.6968 29.3835i 0.947775 1.12764i
\(680\) −0.836821 0.124569i −0.0320906 0.00477702i
\(681\) 9.38708 + 16.2589i 0.359714 + 0.623042i
\(682\) 0.535417 + 10.3978i 0.0205022 + 0.398154i
\(683\) −11.6719 + 20.2163i −0.446613 + 0.773557i −0.998163 0.0605852i \(-0.980703\pi\)
0.551550 + 0.834142i \(0.314037\pi\)
\(684\) 3.50571 + 33.9503i 0.134044 + 1.29812i
\(685\) 34.8943 + 10.8751i 1.33324 + 0.415517i
\(686\) 14.1908 + 22.0141i 0.541808 + 0.840502i
\(687\) 35.3102i 1.34717i
\(688\) −11.3407 + 34.4746i −0.432361 + 1.31433i
\(689\) −13.4200 + 23.2442i −0.511262 + 0.885532i
\(690\) 23.6203 + 6.04813i 0.899209 + 0.230248i
\(691\) −26.6149 + 15.3661i −1.01248 + 0.584555i −0.911917 0.410375i \(-0.865398\pi\)
−0.100563 + 0.994931i \(0.532064\pi\)
\(692\) −3.25776 + 7.28126i −0.123841 + 0.276792i
\(693\) −16.3739 + 19.4812i −0.621994 + 0.740031i
\(694\) −17.6772 27.2749i −0.671018 1.03534i
\(695\) 0.609087 + 2.70496i 0.0231040 + 0.102605i
\(696\) 46.7675 + 18.0993i 1.77272 + 0.686054i
\(697\) 0.440019 + 0.254045i 0.0166669 + 0.00962264i
\(698\) 11.8719 + 6.06270i 0.449360 + 0.229477i
\(699\) 0.0885107i 0.00334778i
\(700\) 9.57987 + 24.6622i 0.362085 + 0.932145i
\(701\) 46.2468i 1.74672i 0.487076 + 0.873360i \(0.338063\pi\)
−0.487076 + 0.873360i \(0.661937\pi\)
\(702\) −16.1856 + 31.6946i −0.610887 + 1.19623i
\(703\) 36.1305 + 20.8600i 1.36269 + 0.786749i
\(704\) 16.6749 + 3.63986i 0.628459 + 0.137182i
\(705\) −4.42638 19.6575i −0.166707 0.740346i
\(706\) 22.5663 14.6255i 0.849292 0.550436i
\(707\) −9.91416 27.3086i −0.372861 1.02704i
\(708\) −3.47236 1.55359i −0.130499 0.0583875i
\(709\) −29.6911 + 17.1422i −1.11507 + 0.643787i −0.940138 0.340793i \(-0.889304\pi\)
−0.174934 + 0.984580i \(0.555971\pi\)
\(710\) 7.55644 29.5109i 0.283588 1.10752i
\(711\) 0.328868 0.569616i 0.0123335 0.0213623i
\(712\) −5.68905 7.06483i −0.213206 0.264766i
\(713\) 9.71004i 0.363644i
\(714\) −0.827298 + 1.09391i −0.0309609 + 0.0409387i
\(715\) −27.7273 8.64145i −1.03694 0.323172i
\(716\) 3.95176 + 38.2699i 0.147684 + 1.43021i
\(717\) 6.61173 11.4519i 0.246920 0.427678i
\(718\) −0.261224 + 0.0134513i −0.00974881 + 0.000501997i
\(719\) 12.8833 + 22.3145i 0.480465 + 0.832190i 0.999749 0.0224116i \(-0.00713443\pi\)
−0.519283 + 0.854602i \(0.673801\pi\)
\(720\) 36.7000 16.7103i 1.36773 0.622757i
\(721\) 14.0171 + 2.48343i 0.522022 + 0.0924879i
\(722\) −3.59389 5.54517i −0.133751 0.206370i
\(723\) 29.5907 + 51.2526i 1.10049 + 1.90611i
\(724\) −8.20523 + 5.93861i −0.304945 + 0.220707i
\(725\) 13.8665 + 29.2294i 0.514990 + 1.08555i
\(726\) 11.3650 22.2548i 0.421794 0.825953i
\(727\) 37.7082i 1.39852i 0.714867 + 0.699260i \(0.246487\pi\)
−0.714867 + 0.699260i \(0.753513\pi\)
\(728\) 38.9671 + 23.6028i 1.44422 + 0.874779i
\(729\) −43.8936 −1.62569
\(730\) 22.8896 23.4048i 0.847182 0.866252i
\(731\) −1.05110 0.606853i −0.0388764 0.0224453i
\(732\) 31.3932 22.7211i 1.16033 0.839796i
\(733\) 1.98974 + 3.44633i 0.0734927 + 0.127293i 0.900430 0.435001i \(-0.143252\pi\)
−0.826937 + 0.562294i \(0.809919\pi\)
\(734\) −5.52557 + 3.58118i −0.203952 + 0.132184i
\(735\) 42.5327 + 5.52709i 1.56884 + 0.203870i
\(736\) −15.3561 4.18982i −0.566035 0.154439i
\(737\) −14.8717 + 8.58620i −0.547808 + 0.316277i
\(738\) −24.1852 + 1.24537i −0.890270 + 0.0458428i
\(739\) 6.04586 + 3.49058i 0.222400 + 0.128403i 0.607061 0.794655i \(-0.292348\pi\)
−0.384661 + 0.923058i \(0.625682\pi\)
\(740\) 9.75520 48.3168i 0.358608 1.77616i
\(741\) 63.1440i 2.31965i
\(742\) 2.03870 16.3695i 0.0748431 0.600942i
\(743\) 1.57992i 0.0579618i 0.999580 + 0.0289809i \(0.00922619\pi\)
−0.999580 + 0.0289809i \(0.990774\pi\)
\(744\) −16.7743 20.8308i −0.614975 0.763694i
\(745\) −12.5366 + 11.5643i −0.459304 + 0.423684i
\(746\) −18.3731 + 0.946091i −0.672688 + 0.0346388i
\(747\) −5.23541 9.06800i −0.191554 0.331781i
\(748\) −0.233110 + 0.521014i −0.00852336 + 0.0190502i
\(749\) 1.86449 10.5236i 0.0681270 0.384524i
\(750\) 40.9696 + 14.0930i 1.49600 + 0.514605i
\(751\) −14.0937 24.4110i −0.514286 0.890770i −0.999863 0.0165756i \(-0.994724\pi\)
0.485576 0.874194i \(-0.338610\pi\)
\(752\) 2.68797 + 12.8767i 0.0980201 + 0.469566i
\(753\) −69.9546 40.3883i −2.54929 1.47183i
\(754\) 49.6127 + 25.3360i 1.80679 + 0.922682i
\(755\) −11.7190 + 37.6021i −0.426499 + 1.36848i
\(756\) 1.58344 21.8152i 0.0575892 0.793410i
\(757\) −20.0301 −0.728005 −0.364002 0.931398i \(-0.618590\pi\)
−0.364002 + 0.931398i \(0.618590\pi\)
\(758\) −34.3447 17.5390i −1.24746 0.637045i
\(759\) 8.22482 14.2458i 0.298542 0.517090i
\(760\) 14.8919 18.7438i 0.540184 0.679911i
\(761\) −3.42583 5.93371i −0.124186 0.215097i 0.797228 0.603678i \(-0.206299\pi\)
−0.921415 + 0.388581i \(0.872965\pi\)
\(762\) 13.4670 8.72812i 0.487858 0.316187i
\(763\) −5.89841 16.2472i −0.213537 0.588188i
\(764\) −11.8700 + 26.5301i −0.429442 + 0.959825i
\(765\) 0.296250 + 1.31565i 0.0107109 + 0.0475672i
\(766\) −0.533933 10.3690i −0.0192918 0.374647i
\(767\) −3.65968 2.11291i −0.132143 0.0762929i
\(768\) −40.1813 + 17.5397i −1.44992 + 0.632908i
\(769\) 30.9952 1.11772 0.558858 0.829264i \(-0.311240\pi\)
0.558858 + 0.829264i \(0.311240\pi\)
\(770\) 17.7648 1.73893i 0.640197 0.0626666i
\(771\) 9.67990i 0.348613i
\(772\) 1.03124 + 9.98686i 0.0371153 + 0.359435i
\(773\) 19.6576 34.0479i 0.707033 1.22462i −0.258920 0.965899i \(-0.583367\pi\)
0.965953 0.258718i \(-0.0833001\pi\)
\(774\) 57.7728 2.97490i 2.07660 0.106931i
\(775\) 1.38982 17.1980i 0.0499240 0.617771i
\(776\) 6.30821 + 40.5463i 0.226452 + 1.45553i
\(777\) −61.1701 51.4133i −2.19447 1.84444i
\(778\) 0.240374 0.155789i 0.00861783 0.00558532i
\(779\) −12.4507 + 7.18842i −0.446093 + 0.257552i
\(780\) 70.7134 23.7776i 2.53194 0.851374i
\(781\) −17.7985 10.2760i −0.636880 0.367703i
\(782\) 0.242102 0.474083i 0.00865757 0.0169532i
\(783\) 26.7454i 0.955804i
\(784\) −27.7065 4.04342i −0.989518 0.144408i
\(785\) 5.21931 16.7469i 0.186285 0.597722i
\(786\) −37.4336 19.1164i −1.33521 0.681859i
\(787\) −0.739671 + 1.28115i −0.0263664 + 0.0456680i −0.878908 0.476992i \(-0.841727\pi\)
0.852541 + 0.522660i \(0.175060\pi\)
\(788\) 24.8338 + 34.3123i 0.884669 + 1.22233i
\(789\) 6.33540 3.65774i 0.225546 0.130219i
\(790\) −0.444263 + 0.124355i −0.0158062 + 0.00442435i
\(791\) 3.19403 3.80017i 0.113567 0.135118i
\(792\) −4.18234 26.8822i −0.148613 0.955216i
\(793\) 37.2819 21.5247i 1.32392 0.764365i
\(794\) 0.515302 0.0265345i 0.0182874 0.000941674i
\(795\) −18.3157 19.8556i −0.649591 0.704204i
\(796\) 7.28784 0.752543i 0.258311 0.0266732i
\(797\) 22.9420 0.812646 0.406323 0.913730i \(-0.366811\pi\)
0.406323 + 0.913730i \(0.366811\pi\)
\(798\) −15.1017 35.7495i −0.534596 1.26552i
\(799\) −0.439916 −0.0155631
\(800\) −26.5985 9.61881i −0.940398 0.340076i
\(801\) −7.22930 + 12.5215i −0.255435 + 0.442426i
\(802\) −51.3706 + 2.64523i −1.81396 + 0.0934065i
\(803\) −11.0431 19.1272i −0.389703 0.674986i
\(804\) 18.0155 40.2655i 0.635356 1.42006i
\(805\) −16.6292 + 0.767612i −0.586101 + 0.0270548i
\(806\) −16.1587 24.9319i −0.569165 0.878190i
\(807\) 53.7017 31.0047i 1.89039 1.09142i
\(808\) 28.9650 + 11.2097i 1.01898 + 0.394354i
\(809\) 17.7624 30.7653i 0.624492 1.08165i −0.364147 0.931341i \(-0.618639\pi\)
0.988639 0.150310i \(-0.0480272\pi\)
\(810\) 4.97142 + 4.86198i 0.174678 + 0.170832i
\(811\) 16.9327i 0.594588i 0.954786 + 0.297294i \(0.0960841\pi\)
−0.954786 + 0.297294i \(0.903916\pi\)
\(812\) −34.1481 2.47862i −1.19836 0.0869825i
\(813\) −23.2147 −0.814174
\(814\) −29.6165 15.1244i −1.03806 0.530110i
\(815\) 1.87567 + 2.03336i 0.0657019 + 0.0712256i
\(816\) −0.299609 1.43528i −0.0104884 0.0502449i
\(817\) 29.7418 17.1714i 1.04053 0.600752i
\(818\) 8.30861 + 12.8197i 0.290504 + 0.448231i
\(819\) 12.6688 71.5056i 0.442684 2.49861i
\(820\) 12.7386 + 11.2364i 0.444851 + 0.392390i
\(821\) 21.0726 12.1663i 0.735440 0.424606i −0.0849691 0.996384i \(-0.527079\pi\)
0.820409 + 0.571777i \(0.193746\pi\)
\(822\) 3.25735 + 63.2579i 0.113613 + 2.20637i
\(823\) 27.8187 + 16.0611i 0.969698 + 0.559856i 0.899144 0.437652i \(-0.144190\pi\)
0.0705541 + 0.997508i \(0.477523\pi\)
\(824\) −11.8529 + 9.54474i −0.412917 + 0.332507i
\(825\) 16.6065 24.0543i 0.578164 0.837465i
\(826\) 2.57729 + 0.320983i 0.0896754 + 0.0111684i
\(827\) 18.8774 0.656431 0.328215 0.944603i \(-0.393553\pi\)
0.328215 + 0.944603i \(0.393553\pi\)
\(828\) 2.60609 + 25.2381i 0.0905680 + 0.877086i
\(829\) −13.1796 7.60926i −0.457747 0.264280i 0.253349 0.967375i \(-0.418468\pi\)
−0.711096 + 0.703094i \(0.751801\pi\)
\(830\) −1.82178 + 7.11474i −0.0632347 + 0.246956i
\(831\) −4.45528 7.71676i −0.154552 0.267692i
\(832\) −46.4015 + 14.7965i −1.60868 + 0.512976i
\(833\) 0.321709 0.879399i 0.0111466 0.0304694i
\(834\) −4.03232 + 2.61340i −0.139628 + 0.0904945i
\(835\) −8.03952 35.7035i −0.278219 1.23557i
\(836\) −9.46939 13.0836i −0.327506 0.452507i
\(837\) −7.13203 + 12.3530i −0.246519 + 0.426983i
\(838\) 23.5180 + 12.0100i 0.812415 + 0.414880i
\(839\) 42.1502 1.45519 0.727593 0.686009i \(-0.240639\pi\)
0.727593 + 0.686009i \(0.240639\pi\)
\(840\) −34.3482 + 30.3740i −1.18513 + 1.04800i
\(841\) −12.8656 −0.443643
\(842\) −20.9975 10.7229i −0.723621 0.369535i
\(843\) −22.4718 + 38.9224i −0.773971 + 1.34056i
\(844\) 2.95543 2.13902i 0.101730 0.0736280i
\(845\) 52.4923 11.8199i 1.80579 0.406618i
\(846\) 17.5956 11.4039i 0.604948 0.392073i
\(847\) −2.97637 + 16.7993i −0.102269 + 0.577231i
\(848\) 11.7522 + 13.1483i 0.403571 + 0.451513i
\(849\) 22.6580 + 39.2448i 0.777620 + 1.34688i
\(850\) 0.496659 0.805025i 0.0170353 0.0276121i
\(851\) 26.8589 + 15.5070i 0.920711 + 0.531573i
\(852\) 52.5140 5.42260i 1.79910 0.185775i
\(853\) −17.3097 −0.592675 −0.296337 0.955083i \(-0.595765\pi\)
−0.296337 + 0.955083i \(0.595765\pi\)
\(854\) −15.9595 + 21.1029i −0.546124 + 0.722125i
\(855\) −36.4311 11.3541i −1.24592 0.388301i
\(856\) 7.16591 + 8.89885i 0.244926 + 0.304156i
\(857\) 5.34286 + 3.08470i 0.182509 + 0.105371i 0.588471 0.808518i \(-0.299730\pi\)
−0.405962 + 0.913890i \(0.633063\pi\)
\(858\) −2.58832 50.2653i −0.0883637 1.71603i
\(859\) −17.6408 + 10.1849i −0.601897 + 0.347505i −0.769788 0.638300i \(-0.779638\pi\)
0.167890 + 0.985806i \(0.446305\pi\)
\(860\) −30.4295 26.8410i −1.03764 0.915270i
\(861\) 25.8833 9.39672i 0.882099 0.320239i
\(862\) 4.54875 + 7.01847i 0.154931 + 0.239050i
\(863\) −24.6744 + 14.2458i −0.839926 + 0.484932i −0.857239 0.514918i \(-0.827822\pi\)
0.0173129 + 0.999850i \(0.494489\pi\)
\(864\) 16.4585 + 16.6093i 0.559930 + 0.565061i
\(865\) −6.04692 6.55530i −0.205601 0.222887i
\(866\) −31.9907 16.3368i −1.08709 0.555149i
\(867\) −46.5337 −1.58037
\(868\) 15.1112 + 10.2509i 0.512907 + 0.347937i
\(869\) 0.311244i 0.0105582i
\(870\) −39.2015 + 40.0839i −1.32906 + 1.35897i
\(871\) 24.5014 42.4377i 0.830198 1.43795i
\(872\) 17.2327 + 6.66916i 0.583572 + 0.225846i
\(873\) 56.6451 32.7040i 1.91715 1.10686i
\(874\) 8.19213 + 12.6400i 0.277103 + 0.427554i
\(875\) −29.5628 1.02062i −0.999405 0.0345031i
\(876\) 51.7874 + 23.1705i 1.74973 + 0.782859i
\(877\) −17.4347 30.1978i −0.588729 1.01971i −0.994399 0.105689i \(-0.966295\pi\)
0.405671 0.914019i \(-0.367038\pi\)
\(878\) −35.5807 + 1.83216i −1.20079 + 0.0618324i
\(879\) 33.9625 58.8247i 1.14553 1.98411i
\(880\) −11.0862 + 15.5313i −0.373716 + 0.523561i
\(881\) −19.8680 −0.669371 −0.334685 0.942330i \(-0.608630\pi\)
−0.334685 + 0.942330i \(0.608630\pi\)
\(882\) 9.92898 + 43.5134i 0.334326 + 1.46517i
\(883\) −22.4507 −0.755525 −0.377763 0.925902i \(-0.623306\pi\)
−0.377763 + 0.925902i \(0.623306\pi\)
\(884\) −0.167299 1.62017i −0.00562686 0.0544921i
\(885\) 3.12615 2.88371i 0.105085 0.0969349i
\(886\) 33.2516 1.71223i 1.11711 0.0575235i
\(887\) −4.32682 + 2.49809i −0.145280 + 0.0838777i −0.570878 0.821035i \(-0.693397\pi\)
0.425598 + 0.904912i \(0.360064\pi\)
\(888\) 84.4086 13.1323i 2.83257 0.440692i
\(889\) −7.04972 + 8.38755i −0.236440 + 0.281310i
\(890\) 9.76595 2.73362i 0.327355 0.0916311i
\(891\) 4.06281 2.34567i 0.136109 0.0785828i
\(892\) −30.7382 + 22.2471i −1.02919 + 0.744886i
\(893\) 6.22390 10.7801i 0.208275 0.360743i
\(894\) −26.3243 13.4431i −0.880416 0.449606i
\(895\) −41.0664 12.7987i −1.37270 0.427813i
\(896\) 22.7318 19.4747i 0.759417 0.650604i
\(897\) 46.9403i 1.56729i
\(898\) 3.35195 6.56376i 0.111856 0.219036i
\(899\) 19.3367 + 11.1640i 0.644914 + 0.372341i
\(900\) 1.00340 + 45.0738i 0.0334468 + 1.50246i
\(901\) −0.510747 + 0.294880i −0.0170154 + 0.00982387i
\(902\) 9.61662 6.23264i 0.320199 0.207524i
\(903\) −61.8290 + 22.4465i −2.05754 + 0.746974i
\(904\) 0.815841 + 5.24385i 0.0271345 + 0.174408i
\(905\) −2.48767 11.0477i −0.0826930 0.367240i
\(906\) −68.1668 + 3.51012i −2.26469 + 0.116616i
\(907\) 5.67005 9.82082i 0.188271 0.326095i −0.756403 0.654106i \(-0.773045\pi\)
0.944674 + 0.328011i \(0.106378\pi\)
\(908\) 13.6305 1.40748i 0.452343 0.0467090i
\(909\) 49.5070i 1.64204i
\(910\) −41.4204 + 29.6439i −1.37307 + 0.982686i
\(911\) −50.0834 −1.65934 −0.829669 0.558256i \(-0.811471\pi\)
−0.829669 + 0.558256i \(0.811471\pi\)
\(912\) 39.4103 + 12.9643i 1.30501 + 0.429292i
\(913\) 4.29102 + 2.47742i 0.142012 + 0.0819907i
\(914\) 0.565542 + 10.9829i 0.0187065 + 0.363281i
\(915\) 9.51781 + 42.2686i 0.314649 + 1.39736i
\(916\) −23.5250 10.5255i −0.777288 0.347772i
\(917\) 28.2572 + 5.00639i 0.933134 + 0.165325i
\(918\) −0.656215 + 0.425301i −0.0216583 + 0.0140370i
\(919\) 8.64229 + 14.9689i 0.285083 + 0.493778i 0.972629 0.232362i \(-0.0746455\pi\)
−0.687546 + 0.726140i \(0.741312\pi\)
\(920\) 11.0704 13.9339i 0.364980 0.459387i
\(921\) 16.6105 28.7703i 0.547336 0.948014i
\(922\) −39.5200 20.1819i −1.30152 0.664654i
\(923\) 58.6465 1.93037
\(924\) 13.4870 + 27.8391i 0.443690 + 0.915838i
\(925\) 45.3519 + 31.3098i 1.49116 + 1.02946i
\(926\) −42.9487 21.9328i −1.41138 0.720757i
\(927\) 21.0078 + 12.1289i 0.689988 + 0.398365i
\(928\) 25.9992 25.7632i 0.853467 0.845717i
\(929\) −10.1998 17.6666i −0.334646 0.579624i 0.648771 0.760984i \(-0.275283\pi\)
−0.983417 + 0.181360i \(0.941950\pi\)
\(930\) 28.7951 8.06013i 0.944228 0.264302i
\(931\) 16.9981 + 20.3251i 0.557090 + 0.666129i
\(932\) −0.0589693 0.0263838i −0.00193160 0.000864231i
\(933\) −37.8235 65.5122i −1.23828 2.14477i
\(934\) −30.5285 + 1.57201i −0.998924 + 0.0514377i
\(935\) −0.432690 0.469068i −0.0141505 0.0153402i
\(936\) 48.6908 + 60.4658i 1.59151 + 1.97639i
\(937\) 47.6656i 1.55717i −0.627542 0.778583i \(-0.715939\pi\)
0.627542 0.778583i \(-0.284061\pi\)
\(938\) −3.72213 + 29.8863i −0.121532 + 0.975822i
\(939\) 90.1144i 2.94077i
\(940\) −14.4161 2.91062i −0.470200 0.0949339i
\(941\) 7.62940 + 4.40484i 0.248711 + 0.143594i 0.619174 0.785254i \(-0.287468\pi\)
−0.370463 + 0.928847i \(0.620801\pi\)
\(942\) 30.3595 1.56331i 0.989166 0.0509353i
\(943\) −9.25567 + 5.34376i −0.301406 + 0.174017i
\(944\) −2.07012 + 1.85032i −0.0673768 + 0.0602227i
\(945\) 21.7193 + 11.2376i 0.706529 + 0.365559i
\(946\) −22.9718 + 14.8883i −0.746879 + 0.484061i
\(947\) 7.49920 + 12.9890i 0.243691 + 0.422085i 0.961763 0.273884i \(-0.0883084\pi\)
−0.718072 + 0.695969i \(0.754975\pi\)
\(948\) −0.468762 0.647677i −0.0152247 0.0210356i
\(949\) 54.5810 + 31.5124i 1.77178 + 1.02294i
\(950\) 12.7004 + 23.5600i 0.412054 + 0.764388i
\(951\) −44.3075 −1.43677
\(952\) 0.482202 + 0.877259i 0.0156283 + 0.0284321i
\(953\) 50.0012i 1.61970i −0.586639 0.809849i \(-0.699549\pi\)
0.586639 0.809849i \(-0.300451\pi\)
\(954\) 12.7845 25.0345i 0.413913 0.810521i
\(955\) −22.0326 23.8850i −0.712959 0.772900i
\(956\) −5.65881 7.81864i −0.183019 0.252873i
\(957\) 18.9128 + 32.7580i 0.611365 + 1.05891i
\(958\) −2.21495 3.41755i −0.0715619 0.110416i
\(959\) −14.7577 40.6502i −0.476552 1.31266i
\(960\) −0.321946 49.0165i −0.0103908 1.58200i
\(961\) 9.54593 + 16.5340i 0.307933 + 0.533356i
\(962\) 94.7697 4.87999i 3.05550 0.157337i
\(963\) 9.10601 15.7721i 0.293437 0.508248i
\(964\) 42.9671 4.43679i 1.38388 0.142899i
\(965\) −10.7166 3.33993i −0.344980 0.107516i
\(966\) −11.2264 26.5756i −0.361204 0.855057i
\(967\) 51.5791i 1.65867i −0.558749 0.829337i \(-0.688719\pi\)
0.558749 0.829337i \(-0.311281\pi\)
\(968\) −11.4393 14.2056i −0.367672 0.456587i
\(969\) −0.693735 + 1.20158i −0.0222860 + 0.0386004i
\(970\) −44.4437 11.3801i −1.42700 0.365392i
\(971\) 23.9189 13.8096i 0.767595 0.443171i −0.0644213 0.997923i \(-0.520520\pi\)
0.832016 + 0.554752i \(0.187187\pi\)
\(972\) −15.0505 + 33.6387i −0.482745 + 1.07896i
\(973\) 2.11084 2.51142i 0.0676705 0.0805125i
\(974\) 14.1811 9.19093i 0.454391 0.294496i
\(975\) −6.71869 + 83.1387i −0.215170 + 2.66257i
\(976\) −5.77980 27.6882i −0.185007 0.886278i
\(977\) 15.0445 + 8.68594i 0.481316 + 0.277888i 0.720965 0.692972i \(-0.243699\pi\)
−0.239649 + 0.970860i \(0.577032\pi\)
\(978\) −2.18041 + 4.26966i −0.0697217 + 0.136529i
\(979\) 6.84188i 0.218668i
\(980\) 16.3608 26.6894i 0.522626 0.852562i
\(981\) 29.4541i 0.940397i
\(982\) 20.9919 + 10.7201i 0.669880 + 0.342091i
\(983\) 17.1607 + 9.90771i 0.547340 + 0.316007i 0.748048 0.663644i \(-0.230991\pi\)
−0.200708 + 0.979651i \(0.564324\pi\)
\(984\) −10.6246 + 27.4532i −0.338700 + 0.875177i
\(985\) −46.1990 + 10.4028i −1.47202 + 0.331462i
\(986\) 0.665739 + 1.02720i 0.0212015 + 0.0327127i
\(987\) −15.3400 + 18.2511i −0.488277 + 0.580938i
\(988\) 42.0690 + 18.8223i 1.33839 + 0.598819i
\(989\) 22.1096 12.7650i 0.703044 0.405903i
\(990\) 29.4661 + 7.54498i 0.936494 + 0.239795i
\(991\) −3.94337 + 6.83011i −0.125265 + 0.216966i −0.921837 0.387579i \(-0.873311\pi\)
0.796571 + 0.604544i \(0.206645\pi\)
\(992\) −18.8785 + 4.96630i −0.599392 + 0.157680i
\(993\) 73.6266i 2.33647i
\(994\) −33.2032 + 14.0261i −1.05314 + 0.444881i
\(995\) −2.43729 + 7.82038i −0.0772673 + 0.247923i
\(996\) −12.6605 + 1.30733i −0.401165 + 0.0414243i
\(997\) −14.6263 + 25.3335i −0.463219 + 0.802319i −0.999119 0.0419627i \(-0.986639\pi\)
0.535900 + 0.844281i \(0.319972\pi\)
\(998\) 3.11591 + 60.5112i 0.0986325 + 1.91545i
\(999\) −22.7798 39.4557i −0.720721 1.24832i
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 280.2.bf.a.109.15 yes 88
4.3 odd 2 1120.2.bv.a.529.5 88
5.4 even 2 inner 280.2.bf.a.109.30 yes 88
7.2 even 3 inner 280.2.bf.a.149.44 yes 88
8.3 odd 2 1120.2.bv.a.529.40 88
8.5 even 2 inner 280.2.bf.a.109.1 88
20.19 odd 2 1120.2.bv.a.529.39 88
28.23 odd 6 1120.2.bv.a.849.6 88
35.9 even 6 inner 280.2.bf.a.149.1 yes 88
40.19 odd 2 1120.2.bv.a.529.6 88
40.29 even 2 inner 280.2.bf.a.109.44 yes 88
56.37 even 6 inner 280.2.bf.a.149.30 yes 88
56.51 odd 6 1120.2.bv.a.849.39 88
140.79 odd 6 1120.2.bv.a.849.40 88
280.149 even 6 inner 280.2.bf.a.149.15 yes 88
280.219 odd 6 1120.2.bv.a.849.5 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.bf.a.109.1 88 8.5 even 2 inner
280.2.bf.a.109.15 yes 88 1.1 even 1 trivial
280.2.bf.a.109.30 yes 88 5.4 even 2 inner
280.2.bf.a.109.44 yes 88 40.29 even 2 inner
280.2.bf.a.149.1 yes 88 35.9 even 6 inner
280.2.bf.a.149.15 yes 88 280.149 even 6 inner
280.2.bf.a.149.30 yes 88 56.37 even 6 inner
280.2.bf.a.149.44 yes 88 7.2 even 3 inner
1120.2.bv.a.529.5 88 4.3 odd 2
1120.2.bv.a.529.6 88 40.19 odd 2
1120.2.bv.a.529.39 88 20.19 odd 2
1120.2.bv.a.529.40 88 8.3 odd 2
1120.2.bv.a.849.5 88 280.219 odd 6
1120.2.bv.a.849.6 88 28.23 odd 6
1120.2.bv.a.849.39 88 56.51 odd 6
1120.2.bv.a.849.40 88 140.79 odd 6