Properties

Label 570.2.x.b.103.6
Level $570$
Weight $2$
Character 570.103
Analytic conductor $4.551$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(103,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.103");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 103.6
Character \(\chi\) \(=\) 570.103
Dual form 570.2.x.b.487.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.99201 - 1.01583i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.219288 + 0.219288i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.99201 - 1.01583i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.219288 + 0.219288i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.18705 - 0.465647i) q^{10} +6.33127 q^{11} +(0.707107 + 0.707107i) q^{12} +(3.59328 + 0.962817i) q^{13} +(-0.155060 + 0.268571i) q^{14} +(0.465647 - 2.18705i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.885199 + 3.30361i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(3.97083 - 1.79792i) q^{19} +(-2.23304 + 0.116269i) q^{20} +(-0.268571 - 0.155060i) q^{21} +(6.11554 - 1.63865i) q^{22} +(0.601843 - 2.24611i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.93618 + 4.04708i) q^{25} +3.72004 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.0802649 + 0.299553i) q^{28} +(-3.42716 - 5.93602i) q^{29} +(-0.116269 - 2.23304i) q^{30} +2.71491i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.63865 + 6.11554i) q^{33} +(1.71007 + 2.96193i) q^{34} +(0.659581 - 0.214064i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.817873 + 0.817873i) q^{37} +(3.37019 - 2.76439i) q^{38} +3.72004i q^{39} +(-2.12686 + 0.690261i) q^{40} +(-8.81271 - 5.08802i) q^{41} +(-0.299553 - 0.0802649i) q^{42} +(-8.44577 + 2.26304i) q^{43} +(5.48304 - 3.16563i) q^{44} +(2.23304 - 0.116269i) q^{45} -2.32534i q^{46} +(-10.1917 - 2.73086i) q^{47} +(0.965926 + 0.258819i) q^{48} +6.90383i q^{49} +(3.88359 + 3.14924i) q^{50} +(-2.96193 + 1.71007i) q^{51} +(3.59328 - 0.962817i) q^{52} +(3.96536 + 1.06251i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-12.6119 - 6.43149i) q^{55} +0.310120i q^{56} +(2.76439 + 3.37019i) q^{57} +(-4.84674 - 4.84674i) q^{58} +(0.367410 - 0.636373i) q^{59} +(-0.690261 - 2.12686i) q^{60} +(2.17131 + 3.76082i) q^{61} +(0.702670 + 2.62240i) q^{62} +(0.0802649 - 0.299553i) q^{63} -1.00000i q^{64} +(-6.17978 - 5.56810i) q^{65} +(3.16563 + 5.48304i) q^{66} +(-1.33519 + 4.98299i) q^{67} +(2.41841 + 2.41841i) q^{68} +2.32534 q^{69} +(0.581703 - 0.377482i) q^{70} +(-1.14914 - 0.663459i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(4.65396 - 1.24702i) q^{73} +(1.00169 + 0.578323i) q^{74} +(-3.14924 + 3.88359i) q^{75} +(2.53987 - 3.54246i) q^{76} +(-1.38837 + 1.38837i) q^{77} +(0.962817 + 3.59328i) q^{78} +(7.21799 - 12.5019i) q^{79} +(-1.87574 + 1.21721i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-9.82930 - 2.63375i) q^{82} +(-0.190572 - 0.190572i) q^{83} -0.310120 q^{84} +(1.59258 - 7.48002i) q^{85} +(-7.57227 + 4.37185i) q^{86} +(4.84674 - 4.84674i) q^{87} +(4.47688 - 4.47688i) q^{88} +(5.18194 + 8.97538i) q^{89} +(2.12686 - 0.690261i) q^{90} +(-0.999097 + 0.576829i) q^{91} +(-0.601843 - 2.24611i) q^{92} +(-2.62240 + 0.702670i) q^{93} -10.5512 q^{94} +(-9.73630 - 0.452208i) q^{95} +1.00000 q^{96} +(-15.9044 + 4.26158i) q^{97} +(1.78684 + 6.66858i) q^{98} +(-5.48304 + 3.16563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −1.99201 1.01583i −0.890852 0.454293i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −0.219288 + 0.219288i −0.0828830 + 0.0828830i −0.747333 0.664450i \(-0.768666\pi\)
0.664450 + 0.747333i \(0.268666\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) −2.18705 0.465647i −0.691605 0.147251i
\(11\) 6.33127 1.90895 0.954475 0.298292i \(-0.0964169\pi\)
0.954475 + 0.298292i \(0.0964169\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 3.59328 + 0.962817i 0.996597 + 0.267037i 0.720019 0.693954i \(-0.244133\pi\)
0.276578 + 0.960991i \(0.410800\pi\)
\(14\) −0.155060 + 0.268571i −0.0414415 + 0.0717787i
\(15\) 0.465647 2.18705i 0.120230 0.564693i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.885199 + 3.30361i 0.214692 + 0.801243i 0.986275 + 0.165113i \(0.0527989\pi\)
−0.771582 + 0.636129i \(0.780534\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) 3.97083 1.79792i 0.910970 0.412472i
\(20\) −2.23304 + 0.116269i −0.499324 + 0.0259985i
\(21\) −0.268571 0.155060i −0.0586071 0.0338368i
\(22\) 6.11554 1.63865i 1.30384 0.349362i
\(23\) 0.601843 2.24611i 0.125493 0.468346i −0.874364 0.485271i \(-0.838721\pi\)
0.999857 + 0.0169251i \(0.00538769\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 2.93618 + 4.04708i 0.587236 + 0.809416i
\(26\) 3.72004 0.729560
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −0.0802649 + 0.299553i −0.0151686 + 0.0566101i
\(29\) −3.42716 5.93602i −0.636408 1.10229i −0.986215 0.165469i \(-0.947086\pi\)
0.349807 0.936822i \(-0.386247\pi\)
\(30\) −0.116269 2.23304i −0.0212277 0.407696i
\(31\) 2.71491i 0.487612i 0.969824 + 0.243806i \(0.0783960\pi\)
−0.969824 + 0.243806i \(0.921604\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 1.63865 + 6.11554i 0.285253 + 1.06458i
\(34\) 1.71007 + 2.96193i 0.293275 + 0.507967i
\(35\) 0.659581 0.214064i 0.111490 0.0361833i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 0.817873 + 0.817873i 0.134457 + 0.134457i 0.771132 0.636675i \(-0.219691\pi\)
−0.636675 + 0.771132i \(0.719691\pi\)
\(38\) 3.37019 2.76439i 0.546717 0.448443i
\(39\) 3.72004i 0.595683i
\(40\) −2.12686 + 0.690261i −0.336286 + 0.109140i
\(41\) −8.81271 5.08802i −1.37631 0.794616i −0.384601 0.923083i \(-0.625661\pi\)
−0.991714 + 0.128468i \(0.958994\pi\)
\(42\) −0.299553 0.0802649i −0.0462220 0.0123851i
\(43\) −8.44577 + 2.26304i −1.28797 + 0.345110i −0.836888 0.547374i \(-0.815628\pi\)
−0.451079 + 0.892484i \(0.648961\pi\)
\(44\) 5.48304 3.16563i 0.826599 0.477237i
\(45\) 2.23304 0.116269i 0.332882 0.0173323i
\(46\) 2.32534i 0.342853i
\(47\) −10.1917 2.73086i −1.48661 0.398337i −0.578021 0.816022i \(-0.696175\pi\)
−0.908592 + 0.417685i \(0.862842\pi\)
\(48\) 0.965926 + 0.258819i 0.139419 + 0.0373573i
\(49\) 6.90383i 0.986261i
\(50\) 3.88359 + 3.14924i 0.549223 + 0.445370i
\(51\) −2.96193 + 1.71007i −0.414754 + 0.239458i
\(52\) 3.59328 0.962817i 0.498299 0.133519i
\(53\) 3.96536 + 1.06251i 0.544684 + 0.145948i 0.520660 0.853764i \(-0.325686\pi\)
0.0240232 + 0.999711i \(0.492352\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −12.6119 6.43149i −1.70059 0.867222i
\(56\) 0.310120i 0.0414415i
\(57\) 2.76439 + 3.37019i 0.366152 + 0.446392i
\(58\) −4.84674 4.84674i −0.636408 0.636408i
\(59\) 0.367410 0.636373i 0.0478327 0.0828487i −0.841118 0.540852i \(-0.818102\pi\)
0.888950 + 0.458003i \(0.151435\pi\)
\(60\) −0.690261 2.12686i −0.0891123 0.274577i
\(61\) 2.17131 + 3.76082i 0.278008 + 0.481523i 0.970890 0.239528i \(-0.0769926\pi\)
−0.692882 + 0.721051i \(0.743659\pi\)
\(62\) 0.702670 + 2.62240i 0.0892392 + 0.333045i
\(63\) 0.0802649 0.299553i 0.0101124 0.0377401i
\(64\) 1.00000i 0.125000i
\(65\) −6.17978 5.56810i −0.766508 0.690638i
\(66\) 3.16563 + 5.48304i 0.389663 + 0.674916i
\(67\) −1.33519 + 4.98299i −0.163119 + 0.608769i 0.835154 + 0.550017i \(0.185379\pi\)
−0.998273 + 0.0587518i \(0.981288\pi\)
\(68\) 2.41841 + 2.41841i 0.293275 + 0.293275i
\(69\) 2.32534 0.279938
\(70\) 0.581703 0.377482i 0.0695268 0.0451177i
\(71\) −1.14914 0.663459i −0.136378 0.0787381i 0.430258 0.902706i \(-0.358422\pi\)
−0.566637 + 0.823968i \(0.691756\pi\)
\(72\) −0.258819 + 0.965926i −0.0305021 + 0.113835i
\(73\) 4.65396 1.24702i 0.544705 0.145953i 0.0240345 0.999711i \(-0.492349\pi\)
0.520670 + 0.853758i \(0.325682\pi\)
\(74\) 1.00169 + 0.578323i 0.116444 + 0.0672287i
\(75\) −3.14924 + 3.88359i −0.363643 + 0.448439i
\(76\) 2.53987 3.54246i 0.291344 0.406348i
\(77\) −1.38837 + 1.38837i −0.158219 + 0.158219i
\(78\) 0.962817 + 3.59328i 0.109018 + 0.406859i
\(79\) 7.21799 12.5019i 0.812088 1.40658i −0.0993127 0.995056i \(-0.531664\pi\)
0.911400 0.411521i \(-0.135002\pi\)
\(80\) −1.87574 + 1.21721i −0.209714 + 0.136089i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −9.82930 2.63375i −1.08546 0.290849i
\(83\) −0.190572 0.190572i −0.0209180 0.0209180i 0.696570 0.717488i \(-0.254708\pi\)
−0.717488 + 0.696570i \(0.754708\pi\)
\(84\) −0.310120 −0.0338368
\(85\) 1.59258 7.48002i 0.172740 0.811322i
\(86\) −7.57227 + 4.37185i −0.816539 + 0.471429i
\(87\) 4.84674 4.84674i 0.519625 0.519625i
\(88\) 4.47688 4.47688i 0.477237 0.477237i
\(89\) 5.18194 + 8.97538i 0.549284 + 0.951388i 0.998324 + 0.0578761i \(0.0184328\pi\)
−0.449040 + 0.893512i \(0.648234\pi\)
\(90\) 2.12686 0.690261i 0.224191 0.0727599i
\(91\) −0.999097 + 0.576829i −0.104734 + 0.0604681i
\(92\) −0.601843 2.24611i −0.0627464 0.234173i
\(93\) −2.62240 + 0.702670i −0.271930 + 0.0728635i
\(94\) −10.5512 −1.08828
\(95\) −9.73630 0.452208i −0.998923 0.0463955i
\(96\) 1.00000 0.102062
\(97\) −15.9044 + 4.26158i −1.61485 + 0.432698i −0.949484 0.313817i \(-0.898392\pi\)
−0.665368 + 0.746515i \(0.731726\pi\)
\(98\) 1.78684 + 6.66858i 0.180498 + 0.673629i
\(99\) −5.48304 + 3.16563i −0.551066 + 0.318158i
\(100\) 4.56635 + 2.03678i 0.456635 + 0.203678i
\(101\) −6.97371 12.0788i −0.693910 1.20189i −0.970547 0.240913i \(-0.922553\pi\)
0.276636 0.960975i \(-0.410780\pi\)
\(102\) −2.41841 + 2.41841i −0.239458 + 0.239458i
\(103\) −5.59928 + 5.59928i −0.551714 + 0.551714i −0.926935 0.375222i \(-0.877567\pi\)
0.375222 + 0.926935i \(0.377567\pi\)
\(104\) 3.22165 1.86002i 0.315909 0.182390i
\(105\) 0.377482 + 0.581703i 0.0368384 + 0.0567684i
\(106\) 4.10524 0.398736
\(107\) 3.36656 + 3.36656i 0.325458 + 0.325458i 0.850856 0.525399i \(-0.176084\pi\)
−0.525399 + 0.850856i \(0.676084\pi\)
\(108\) −0.965926 0.258819i −0.0929463 0.0249049i
\(109\) 5.03859 8.72710i 0.482610 0.835904i −0.517191 0.855870i \(-0.673022\pi\)
0.999801 + 0.0199656i \(0.00635567\pi\)
\(110\) −13.8468 2.94814i −1.32024 0.281094i
\(111\) −0.578323 + 1.00169i −0.0548920 + 0.0950758i
\(112\) 0.0802649 + 0.299553i 0.00758432 + 0.0283051i
\(113\) 13.8254 13.8254i 1.30059 1.30059i 0.372589 0.927997i \(-0.378470\pi\)
0.927997 0.372589i \(-0.121530\pi\)
\(114\) 3.54246 + 2.53987i 0.331782 + 0.237881i
\(115\) −3.48054 + 3.86289i −0.324562 + 0.360216i
\(116\) −5.93602 3.42716i −0.551145 0.318204i
\(117\) −3.59328 + 0.962817i −0.332199 + 0.0890125i
\(118\) 0.190185 0.709781i 0.0175080 0.0653407i
\(119\) −0.918554 0.530327i −0.0842037 0.0486150i
\(120\) −1.21721 1.87574i −0.111116 0.171231i
\(121\) 29.0850 2.64409
\(122\) 3.07070 + 3.07070i 0.278008 + 0.278008i
\(123\) 2.63375 9.82930i 0.237478 0.886278i
\(124\) 1.35745 + 2.35118i 0.121903 + 0.211142i
\(125\) −1.73774 11.0445i −0.155429 0.987847i
\(126\) 0.310120i 0.0276277i
\(127\) −3.78398 + 14.1220i −0.335774 + 1.25312i 0.567254 + 0.823543i \(0.308006\pi\)
−0.903028 + 0.429582i \(0.858661\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −4.37185 7.57227i −0.384920 0.666701i
\(130\) −7.41034 3.77893i −0.649930 0.331434i
\(131\) −1.82083 + 3.15377i −0.159087 + 0.275546i −0.934540 0.355859i \(-0.884188\pi\)
0.775453 + 0.631405i \(0.217522\pi\)
\(132\) 4.47688 + 4.47688i 0.389663 + 0.389663i
\(133\) −0.476491 + 1.26502i −0.0413170 + 0.109691i
\(134\) 5.15877i 0.445650i
\(135\) 0.690261 + 2.12686i 0.0594082 + 0.183051i
\(136\) 2.96193 + 1.71007i 0.253984 + 0.146638i
\(137\) −9.95833 2.66833i −0.850798 0.227971i −0.193031 0.981193i \(-0.561832\pi\)
−0.657766 + 0.753222i \(0.728499\pi\)
\(138\) 2.24611 0.601843i 0.191201 0.0512322i
\(139\) −17.8754 + 10.3204i −1.51617 + 0.875362i −0.516352 + 0.856376i \(0.672710\pi\)
−0.999820 + 0.0189860i \(0.993956\pi\)
\(140\) 0.464183 0.515175i 0.0392306 0.0435402i
\(141\) 10.5512i 0.888574i
\(142\) −1.28170 0.343432i −0.107558 0.0288201i
\(143\) 22.7500 + 6.09586i 1.90245 + 0.509761i
\(144\) 1.00000i 0.0833333i
\(145\) 0.796943 + 15.3060i 0.0661825 + 1.27109i
\(146\) 4.17262 2.40907i 0.345329 0.199376i
\(147\) −6.66858 + 1.78684i −0.550016 + 0.147376i
\(148\) 1.11723 + 0.299362i 0.0918361 + 0.0246074i
\(149\) −16.7440 9.66714i −1.37172 0.791963i −0.380576 0.924750i \(-0.624274\pi\)
−0.991145 + 0.132787i \(0.957607\pi\)
\(150\) −2.03678 + 4.56635i −0.166303 + 0.372841i
\(151\) 0.256188i 0.0208483i 0.999946 + 0.0104241i \(0.00331817\pi\)
−0.999946 + 0.0104241i \(0.996682\pi\)
\(152\) 1.53647 4.07912i 0.124625 0.330861i
\(153\) −2.41841 2.41841i −0.195517 0.195517i
\(154\) −0.981725 + 1.70040i −0.0791097 + 0.137022i
\(155\) 2.75788 5.40811i 0.221519 0.434390i
\(156\) 1.86002 + 3.22165i 0.148921 + 0.257938i
\(157\) 2.49533 + 9.31270i 0.199149 + 0.743234i 0.991154 + 0.132719i \(0.0423708\pi\)
−0.792005 + 0.610515i \(0.790963\pi\)
\(158\) 3.73631 13.9441i 0.297245 1.10933i
\(159\) 4.10524i 0.325567i
\(160\) −1.49679 + 1.66121i −0.118331 + 0.131331i
\(161\) 0.360567 + 0.624520i 0.0284167 + 0.0492191i
\(162\) 0.258819 0.965926i 0.0203347 0.0758903i
\(163\) −0.0203626 0.0203626i −0.00159492 0.00159492i 0.706309 0.707904i \(-0.250359\pi\)
−0.707904 + 0.706309i \(0.750359\pi\)
\(164\) −10.1760 −0.794616
\(165\) 2.94814 13.8468i 0.229512 1.07797i
\(166\) −0.233403 0.134755i −0.0181156 0.0104590i
\(167\) −0.467473 + 1.74463i −0.0361741 + 0.135004i −0.981651 0.190684i \(-0.938929\pi\)
0.945477 + 0.325688i \(0.105596\pi\)
\(168\) −0.299553 + 0.0802649i −0.0231110 + 0.00619257i
\(169\) 0.726336 + 0.419351i 0.0558720 + 0.0322577i
\(170\) −0.397656 7.63733i −0.0304988 0.585757i
\(171\) −2.53987 + 3.54246i −0.194229 + 0.270899i
\(172\) −6.18273 + 6.18273i −0.471429 + 0.471429i
\(173\) 5.96891 + 22.2763i 0.453808 + 1.69363i 0.691568 + 0.722311i \(0.256920\pi\)
−0.237760 + 0.971324i \(0.576413\pi\)
\(174\) 3.42716 5.93602i 0.259812 0.450008i
\(175\) −1.53134 0.243607i −0.115759 0.0184149i
\(176\) 3.16563 5.48304i 0.238619 0.413300i
\(177\) 0.709781 + 0.190185i 0.0533504 + 0.0142952i
\(178\) 7.32836 + 7.32836i 0.549284 + 0.549284i
\(179\) −14.9146 −1.11477 −0.557383 0.830255i \(-0.688195\pi\)
−0.557383 + 0.830255i \(0.688195\pi\)
\(180\) 1.87574 1.21721i 0.139809 0.0907257i
\(181\) 3.95519 2.28353i 0.293987 0.169733i −0.345752 0.938326i \(-0.612376\pi\)
0.639738 + 0.768593i \(0.279043\pi\)
\(182\) −0.815759 + 0.815759i −0.0604681 + 0.0604681i
\(183\) −3.07070 + 3.07070i −0.226992 + 0.226992i
\(184\) −1.16267 2.01380i −0.0857132 0.148460i
\(185\) −0.798388 2.46003i −0.0586987 0.180865i
\(186\) −2.35118 + 1.35745i −0.172397 + 0.0995334i
\(187\) 5.60443 + 20.9160i 0.409837 + 1.52953i
\(188\) −10.1917 + 2.73086i −0.743307 + 0.199168i
\(189\) 0.310120 0.0225579
\(190\) −9.52158 + 2.08314i −0.690768 + 0.151127i
\(191\) −17.4658 −1.26378 −0.631889 0.775059i \(-0.717720\pi\)
−0.631889 + 0.775059i \(0.717720\pi\)
\(192\) 0.965926 0.258819i 0.0697097 0.0186787i
\(193\) 0.458612 + 1.71156i 0.0330116 + 0.123201i 0.980465 0.196692i \(-0.0630198\pi\)
−0.947454 + 0.319893i \(0.896353\pi\)
\(194\) −14.2595 + 8.23275i −1.02378 + 0.591077i
\(195\) 3.77893 7.41034i 0.270615 0.530666i
\(196\) 3.45191 + 5.97889i 0.246565 + 0.427063i
\(197\) −4.89640 + 4.89640i −0.348854 + 0.348854i −0.859683 0.510829i \(-0.829339\pi\)
0.510829 + 0.859683i \(0.329339\pi\)
\(198\) −4.47688 + 4.47688i −0.318158 + 0.318158i
\(199\) 6.60568 3.81379i 0.468264 0.270352i −0.247249 0.968952i \(-0.579526\pi\)
0.715513 + 0.698600i \(0.246193\pi\)
\(200\) 4.93791 + 0.785525i 0.349163 + 0.0555450i
\(201\) −5.15877 −0.363871
\(202\) −9.86232 9.86232i −0.693910 0.693910i
\(203\) 2.05323 + 0.550161i 0.144108 + 0.0386137i
\(204\) −1.71007 + 2.96193i −0.119729 + 0.207377i
\(205\) 12.3864 + 19.0876i 0.865105 + 1.33314i
\(206\) −3.95929 + 6.85769i −0.275857 + 0.477798i
\(207\) 0.601843 + 2.24611i 0.0418310 + 0.156115i
\(208\) 2.63047 2.63047i 0.182390 0.182390i
\(209\) 25.1404 11.3831i 1.73900 0.787388i
\(210\) 0.515175 + 0.464183i 0.0355505 + 0.0320316i
\(211\) −0.170890 0.0986634i −0.0117646 0.00679227i 0.494106 0.869402i \(-0.335495\pi\)
−0.505871 + 0.862609i \(0.668829\pi\)
\(212\) 3.96536 1.06251i 0.272342 0.0729738i
\(213\) 0.343432 1.28170i 0.0235315 0.0878209i
\(214\) 4.12318 + 2.38052i 0.281855 + 0.162729i
\(215\) 19.1229 + 4.07148i 1.30417 + 0.277673i
\(216\) −1.00000 −0.0680414
\(217\) −0.595346 0.595346i −0.0404147 0.0404147i
\(218\) 2.60817 9.73381i 0.176647 0.659257i
\(219\) 2.40907 + 4.17262i 0.162790 + 0.281960i
\(220\) −14.1380 + 0.736129i −0.953183 + 0.0496298i
\(221\) 12.7231i 0.855847i
\(222\) −0.299362 + 1.11723i −0.0200919 + 0.0749839i
\(223\) −3.25559 12.1500i −0.218010 0.813625i −0.985085 0.172067i \(-0.944955\pi\)
0.767075 0.641557i \(-0.221711\pi\)
\(224\) 0.155060 + 0.268571i 0.0103604 + 0.0179447i
\(225\) −4.56635 2.03678i −0.304423 0.135786i
\(226\) 9.77604 16.9326i 0.650293 1.12634i
\(227\) 3.56929 + 3.56929i 0.236902 + 0.236902i 0.815566 0.578664i \(-0.196426\pi\)
−0.578664 + 0.815566i \(0.696426\pi\)
\(228\) 4.07912 + 1.53647i 0.270147 + 0.101755i
\(229\) 22.9254i 1.51495i −0.652862 0.757476i \(-0.726432\pi\)
0.652862 0.757476i \(-0.273568\pi\)
\(230\) −2.36215 + 4.63209i −0.155756 + 0.305431i
\(231\) −1.70040 0.981725i −0.111878 0.0645928i
\(232\) −6.62077 1.77403i −0.434675 0.116471i
\(233\) 6.05339 1.62200i 0.396571 0.106261i −0.0550216 0.998485i \(-0.517523\pi\)
0.451592 + 0.892224i \(0.350856\pi\)
\(234\) −3.22165 + 1.86002i −0.210606 + 0.121593i
\(235\) 17.5279 + 15.7929i 1.14339 + 1.03022i
\(236\) 0.734820i 0.0478327i
\(237\) 13.9441 + 3.73631i 0.905766 + 0.242699i
\(238\) −1.02451 0.274518i −0.0664093 0.0177943i
\(239\) 22.5950i 1.46155i −0.682618 0.730775i \(-0.739159\pi\)
0.682618 0.730775i \(-0.260841\pi\)
\(240\) −1.66121 1.49679i −0.107231 0.0966171i
\(241\) −0.0802518 + 0.0463334i −0.00516947 + 0.00298460i −0.502583 0.864529i \(-0.667617\pi\)
0.497413 + 0.867514i \(0.334283\pi\)
\(242\) 28.0939 7.52774i 1.80595 0.483902i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) 3.76082 + 2.17131i 0.240762 + 0.139004i
\(245\) 7.01311 13.7525i 0.448051 0.878613i
\(246\) 10.1760i 0.648801i
\(247\) 15.9994 2.63727i 1.01802 0.167806i
\(248\) 1.91973 + 1.91973i 0.121903 + 0.121903i
\(249\) 0.134755 0.233403i 0.00853975 0.0147913i
\(250\) −4.53705 10.2184i −0.286948 0.646267i
\(251\) 4.59120 + 7.95219i 0.289794 + 0.501938i 0.973760 0.227576i \(-0.0730799\pi\)
−0.683966 + 0.729514i \(0.739747\pi\)
\(252\) −0.0802649 0.299553i −0.00505621 0.0188700i
\(253\) 3.81043 14.2207i 0.239559 0.894048i
\(254\) 14.6202i 0.917351i
\(255\) 7.63733 0.397656i 0.478268 0.0249022i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.08691 7.78847i 0.130178 0.485831i −0.869793 0.493417i \(-0.835748\pi\)
0.999971 + 0.00758535i \(0.00241451\pi\)
\(258\) −6.18273 6.18273i −0.384920 0.384920i
\(259\) −0.358699 −0.0222885
\(260\) −8.13590 1.73223i −0.504567 0.107428i
\(261\) 5.93602 + 3.42716i 0.367430 + 0.212136i
\(262\) −0.942531 + 3.51757i −0.0582297 + 0.217316i
\(263\) −14.4774 + 3.87921i −0.892715 + 0.239202i −0.675885 0.737007i \(-0.736238\pi\)
−0.216830 + 0.976209i \(0.569572\pi\)
\(264\) 5.48304 + 3.16563i 0.337458 + 0.194831i
\(265\) −6.81968 6.14466i −0.418930 0.377464i
\(266\) −0.132844 + 1.34524i −0.00814522 + 0.0824818i
\(267\) −7.32836 + 7.32836i −0.448489 + 0.448489i
\(268\) 1.33519 + 4.98299i 0.0815595 + 0.304384i
\(269\) 0.866982 1.50166i 0.0528608 0.0915576i −0.838384 0.545080i \(-0.816499\pi\)
0.891245 + 0.453522i \(0.149833\pi\)
\(270\) 1.21721 + 1.87574i 0.0740772 + 0.114154i
\(271\) −0.460704 + 0.797963i −0.0279858 + 0.0484728i −0.879679 0.475568i \(-0.842243\pi\)
0.851693 + 0.524041i \(0.175576\pi\)
\(272\) 3.30361 + 0.885199i 0.200311 + 0.0536731i
\(273\) −0.815759 0.815759i −0.0493720 0.0493720i
\(274\) −10.3096 −0.622827
\(275\) 18.5897 + 25.6231i 1.12100 + 1.54513i
\(276\) 2.01380 1.16267i 0.121217 0.0699845i
\(277\) 1.31226 1.31226i 0.0788458 0.0788458i −0.666584 0.745430i \(-0.732244\pi\)
0.745430 + 0.666584i \(0.232244\pi\)
\(278\) −14.5952 + 14.5952i −0.875362 + 0.875362i
\(279\) −1.35745 2.35118i −0.0812687 0.140761i
\(280\) 0.315029 0.617760i 0.0188266 0.0369182i
\(281\) 17.2366 9.95154i 1.02825 0.593659i 0.111766 0.993735i \(-0.464349\pi\)
0.916482 + 0.400075i \(0.131016\pi\)
\(282\) −2.73086 10.1917i −0.162620 0.606907i
\(283\) −30.2967 + 8.11799i −1.80095 + 0.482564i −0.994127 0.108222i \(-0.965484\pi\)
−0.806828 + 0.590786i \(0.798818\pi\)
\(284\) −1.32692 −0.0787381
\(285\) −2.08314 9.52158i −0.123395 0.564010i
\(286\) 23.5526 1.39269
\(287\) 3.04826 0.816779i 0.179933 0.0482129i
\(288\) 0.258819 + 0.965926i 0.0152511 + 0.0569177i
\(289\) 4.59219 2.65130i 0.270129 0.155959i
\(290\) 4.73127 + 14.5782i 0.277830 + 0.856061i
\(291\) −8.23275 14.2595i −0.482612 0.835909i
\(292\) 3.40693 3.40693i 0.199376 0.199376i
\(293\) −8.23657 + 8.23657i −0.481185 + 0.481185i −0.905510 0.424325i \(-0.860511\pi\)
0.424325 + 0.905510i \(0.360511\pi\)
\(294\) −5.97889 + 3.45191i −0.348696 + 0.201320i
\(295\) −1.37833 + 0.894432i −0.0802494 + 0.0520759i
\(296\) 1.15665 0.0672287
\(297\) −4.47688 4.47688i −0.259775 0.259775i
\(298\) −18.6755 5.00408i −1.08184 0.289879i
\(299\) 4.32518 7.49143i 0.250132 0.433241i
\(300\) −0.785525 + 4.93791i −0.0453523 + 0.285090i
\(301\) 1.35580 2.34831i 0.0781468 0.135354i
\(302\) 0.0663064 + 0.247459i 0.00381550 + 0.0142397i
\(303\) 9.86232 9.86232i 0.566576 0.566576i
\(304\) 0.428365 4.33780i 0.0245684 0.248790i
\(305\) −0.504911 9.69725i −0.0289111 0.555263i
\(306\) −2.96193 1.71007i −0.169322 0.0977584i
\(307\) 4.07756 1.09258i 0.232719 0.0623568i −0.140575 0.990070i \(-0.544895\pi\)
0.373294 + 0.927713i \(0.378228\pi\)
\(308\) −0.508178 + 1.89655i −0.0289562 + 0.108066i
\(309\) −6.85769 3.95929i −0.390120 0.225236i
\(310\) 1.26419 5.93763i 0.0718011 0.337235i
\(311\) −11.0780 −0.628178 −0.314089 0.949393i \(-0.601699\pi\)
−0.314089 + 0.949393i \(0.601699\pi\)
\(312\) 2.63047 + 2.63047i 0.148921 + 0.148921i
\(313\) 5.84492 21.8136i 0.330375 1.23297i −0.578423 0.815737i \(-0.696332\pi\)
0.908797 0.417238i \(-0.137002\pi\)
\(314\) 4.82061 + 8.34953i 0.272043 + 0.471191i
\(315\) −0.464183 + 0.515175i −0.0261537 + 0.0290268i
\(316\) 14.4360i 0.812088i
\(317\) −4.74943 + 17.7251i −0.266755 + 0.995543i 0.694413 + 0.719577i \(0.255664\pi\)
−0.961168 + 0.275966i \(0.911002\pi\)
\(318\) 1.06251 + 3.96536i 0.0595828 + 0.222366i
\(319\) −21.6983 37.5825i −1.21487 2.10422i
\(320\) −1.01583 + 1.99201i −0.0567866 + 0.111357i
\(321\) −2.38052 + 4.12318i −0.132868 + 0.230133i
\(322\) 0.509919 + 0.509919i 0.0284167 + 0.0284167i
\(323\) 9.45461 + 11.5265i 0.526068 + 0.641353i
\(324\) 1.00000i 0.0555556i
\(325\) 6.65393 + 17.3693i 0.369093 + 0.963476i
\(326\) −0.0249390 0.0143985i −0.00138124 0.000797461i
\(327\) 9.73381 + 2.60817i 0.538281 + 0.144232i
\(328\) −9.82930 + 2.63375i −0.542732 + 0.145425i
\(329\) 2.83376 1.63607i 0.156230 0.0901996i
\(330\) −0.736129 14.1380i −0.0405225 0.778271i
\(331\) 1.63560i 0.0899008i −0.998989 0.0449504i \(-0.985687\pi\)
0.998989 0.0449504i \(-0.0143130\pi\)
\(332\) −0.260327 0.0697543i −0.0142873 0.00382827i
\(333\) −1.11723 0.299362i −0.0612241 0.0164049i
\(334\) 1.80618i 0.0988295i
\(335\) 7.72157 8.56982i 0.421874 0.468219i
\(336\) −0.268571 + 0.155060i −0.0146518 + 0.00845921i
\(337\) 0.514208 0.137782i 0.0280107 0.00750545i −0.244786 0.969577i \(-0.578718\pi\)
0.272797 + 0.962072i \(0.412051\pi\)
\(338\) 0.810123 + 0.217072i 0.0440649 + 0.0118072i
\(339\) 16.9326 + 9.77604i 0.919653 + 0.530962i
\(340\) −2.36079 7.27418i −0.128032 0.394498i
\(341\) 17.1888i 0.930826i
\(342\) −1.53647 + 4.07912i −0.0830830 + 0.220574i
\(343\) −3.04894 3.04894i −0.164627 0.164627i
\(344\) −4.37185 + 7.57227i −0.235714 + 0.408269i
\(345\) −4.63209 2.36215i −0.249384 0.127174i
\(346\) 11.5311 + 19.9724i 0.619913 + 1.07372i
\(347\) 0.501655 + 1.87220i 0.0269303 + 0.100505i 0.978083 0.208216i \(-0.0667657\pi\)
−0.951153 + 0.308721i \(0.900099\pi\)
\(348\) 1.77403 6.62077i 0.0950979 0.354910i
\(349\) 21.3205i 1.14126i 0.821208 + 0.570629i \(0.193301\pi\)
−0.821208 + 0.570629i \(0.806699\pi\)
\(350\) −1.54221 + 0.161035i −0.0824348 + 0.00860766i
\(351\) −1.86002 3.22165i −0.0992805 0.171959i
\(352\) 1.63865 6.11554i 0.0873405 0.325959i
\(353\) 18.3308 + 18.3308i 0.975651 + 0.975651i 0.999711 0.0240595i \(-0.00765912\pi\)
−0.0240595 + 0.999711i \(0.507659\pi\)
\(354\) 0.734820 0.0390552
\(355\) 1.61514 + 2.48895i 0.0857228 + 0.132100i
\(356\) 8.97538 + 5.18194i 0.475694 + 0.274642i
\(357\) 0.274518 1.02451i 0.0145290 0.0542230i
\(358\) −14.4064 + 3.86017i −0.761400 + 0.204016i
\(359\) −26.9383 15.5528i −1.42175 0.820847i −0.425300 0.905053i \(-0.639831\pi\)
−0.996448 + 0.0842061i \(0.973165\pi\)
\(360\) 1.49679 1.66121i 0.0788875 0.0875537i
\(361\) 12.5349 14.2785i 0.659733 0.751500i
\(362\) 3.22940 3.22940i 0.169733 0.169733i
\(363\) 7.52774 + 28.0939i 0.395104 + 1.47455i
\(364\) −0.576829 + 0.999097i −0.0302340 + 0.0523669i
\(365\) −10.5375 2.24355i −0.551557 0.117433i
\(366\) −2.17131 + 3.76082i −0.113496 + 0.196581i
\(367\) 28.8125 + 7.72029i 1.50400 + 0.402996i 0.914438 0.404726i \(-0.132633\pi\)
0.589563 + 0.807722i \(0.299300\pi\)
\(368\) −1.64426 1.64426i −0.0857132 0.0857132i
\(369\) 10.1760 0.529744
\(370\) −1.40789 2.16957i −0.0731925 0.112790i
\(371\) −1.10255 + 0.636558i −0.0572416 + 0.0330484i
\(372\) −1.91973 + 1.91973i −0.0995334 + 0.0995334i
\(373\) 13.3691 13.3691i 0.692226 0.692226i −0.270495 0.962721i \(-0.587187\pi\)
0.962721 + 0.270495i \(0.0871874\pi\)
\(374\) 10.8269 + 18.7528i 0.559847 + 0.969684i
\(375\) 10.2184 4.53705i 0.527675 0.234292i
\(376\) −9.13763 + 5.27562i −0.471237 + 0.272069i
\(377\) −6.59946 24.6295i −0.339889 1.26848i
\(378\) 0.299553 0.0802649i 0.0154073 0.00412838i
\(379\) 32.1397 1.65091 0.825453 0.564471i \(-0.190920\pi\)
0.825453 + 0.564471i \(0.190920\pi\)
\(380\) −8.65799 + 4.47653i −0.444145 + 0.229641i
\(381\) −14.6202 −0.749014
\(382\) −16.8706 + 4.52047i −0.863177 + 0.231288i
\(383\) 0.941979 + 3.51551i 0.0481329 + 0.179634i 0.985807 0.167880i \(-0.0536923\pi\)
−0.937674 + 0.347515i \(0.887026\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 4.17599 1.35529i 0.212828 0.0690722i
\(386\) 0.885971 + 1.53455i 0.0450947 + 0.0781063i
\(387\) 6.18273 6.18273i 0.314286 0.314286i
\(388\) −11.6429 + 11.6429i −0.591077 + 0.591077i
\(389\) 12.1029 6.98763i 0.613642 0.354287i −0.160747 0.986996i \(-0.551390\pi\)
0.774390 + 0.632709i \(0.218057\pi\)
\(390\) 1.73223 8.13590i 0.0877147 0.411977i
\(391\) 7.95301 0.402201
\(392\) 4.88174 + 4.88174i 0.246565 + 0.246565i
\(393\) −3.51757 0.942531i −0.177438 0.0475444i
\(394\) −3.46228 + 5.99684i −0.174427 + 0.302116i
\(395\) −27.0781 + 17.5717i −1.36245 + 0.884127i
\(396\) −3.16563 + 5.48304i −0.159079 + 0.275533i
\(397\) −1.08210 4.03846i −0.0543091 0.202684i 0.933440 0.358733i \(-0.116791\pi\)
−0.987749 + 0.156048i \(0.950124\pi\)
\(398\) 5.39351 5.39351i 0.270352 0.270352i
\(399\) −1.34524 0.132844i −0.0673461 0.00665054i
\(400\) 4.97296 0.519266i 0.248648 0.0259633i
\(401\) 26.2536 + 15.1575i 1.31104 + 0.756931i 0.982269 0.187477i \(-0.0600310\pi\)
0.328775 + 0.944408i \(0.393364\pi\)
\(402\) −4.98299 + 1.33519i −0.248529 + 0.0665931i
\(403\) −2.61396 + 9.75543i −0.130211 + 0.485953i
\(404\) −12.0788 6.97371i −0.600944 0.346955i
\(405\) −1.87574 + 1.21721i −0.0932062 + 0.0604838i
\(406\) 2.12566 0.105495
\(407\) 5.17817 + 5.17817i 0.256672 + 0.256672i
\(408\) −0.885199 + 3.30361i −0.0438239 + 0.163553i
\(409\) −6.92849 12.0005i −0.342592 0.593387i 0.642321 0.766435i \(-0.277971\pi\)
−0.984913 + 0.173049i \(0.944638\pi\)
\(410\) 16.9046 + 15.2314i 0.834858 + 0.752223i
\(411\) 10.3096i 0.508536i
\(412\) −2.04948 + 7.64876i −0.100971 + 0.376827i
\(413\) 0.0589802 + 0.220117i 0.00290223 + 0.0108313i
\(414\) 1.16267 + 2.01380i 0.0571421 + 0.0989731i
\(415\) 0.186032 + 0.573211i 0.00913197 + 0.0281378i
\(416\) 1.86002 3.22165i 0.0911950 0.157954i
\(417\) −14.5952 14.5952i −0.714730 0.714730i
\(418\) 21.3376 17.5021i 1.04365 0.856055i
\(419\) 34.6356i 1.69206i 0.533135 + 0.846030i \(0.321014\pi\)
−0.533135 + 0.846030i \(0.678986\pi\)
\(420\) 0.617760 + 0.315029i 0.0301436 + 0.0153718i
\(421\) −11.2641 6.50334i −0.548979 0.316953i 0.199731 0.979851i \(-0.435993\pi\)
−0.748710 + 0.662898i \(0.769326\pi\)
\(422\) −0.190603 0.0510720i −0.00927842 0.00248614i
\(423\) 10.1917 2.73086i 0.495538 0.132779i
\(424\) 3.55524 2.05262i 0.172658 0.0996840i
\(425\) −10.7709 + 13.2825i −0.522463 + 0.644294i
\(426\) 1.32692i 0.0642894i
\(427\) −1.30084 0.348560i −0.0629522 0.0168680i
\(428\) 4.59881 + 1.23225i 0.222292 + 0.0595629i
\(429\) 23.5526i 1.13713i
\(430\) 19.5251 1.01662i 0.941582 0.0490257i
\(431\) 19.2452 11.1112i 0.927007 0.535208i 0.0411431 0.999153i \(-0.486900\pi\)
0.885864 + 0.463946i \(0.153567\pi\)
\(432\) −0.965926 + 0.258819i −0.0464731 + 0.0124524i
\(433\) 11.1720 + 2.99353i 0.536892 + 0.143860i 0.517069 0.855944i \(-0.327023\pi\)
0.0198230 + 0.999804i \(0.493690\pi\)
\(434\) −0.729147 0.420973i −0.0350002 0.0202074i
\(435\) −14.5782 + 4.73127i −0.698971 + 0.226847i
\(436\) 10.0772i 0.482610i
\(437\) −1.64852 10.0010i −0.0788593 0.478411i
\(438\) 3.40693 + 3.40693i 0.162790 + 0.162790i
\(439\) −5.66009 + 9.80357i −0.270141 + 0.467899i −0.968898 0.247461i \(-0.920404\pi\)
0.698756 + 0.715360i \(0.253737\pi\)
\(440\) −13.4657 + 4.37023i −0.641954 + 0.208342i
\(441\) −3.45191 5.97889i −0.164377 0.284709i
\(442\) 3.29298 + 12.2896i 0.156631 + 0.584554i
\(443\) −9.60294 + 35.8387i −0.456250 + 1.70275i 0.228138 + 0.973629i \(0.426736\pi\)
−0.684388 + 0.729118i \(0.739931\pi\)
\(444\) 1.15665i 0.0548920i
\(445\) −1.20499 23.1430i −0.0571222 1.09708i
\(446\) −6.28931 10.8934i −0.297807 0.515817i
\(447\) 5.00408 18.6755i 0.236685 0.883320i
\(448\) 0.219288 + 0.219288i 0.0103604 + 0.0103604i
\(449\) 27.2788 1.28737 0.643683 0.765292i \(-0.277406\pi\)
0.643683 + 0.765292i \(0.277406\pi\)
\(450\) −4.93791 0.785525i −0.232775 0.0370300i
\(451\) −55.7956 32.2136i −2.62731 1.51688i
\(452\) 5.06045 18.8859i 0.238024 0.888316i
\(453\) −0.247459 + 0.0663064i −0.0116266 + 0.00311535i
\(454\) 4.37146 + 2.52387i 0.205163 + 0.118451i
\(455\) 2.57617 0.134134i 0.120773 0.00628831i
\(456\) 4.33780 + 0.428365i 0.203136 + 0.0200600i
\(457\) −9.33785 + 9.33785i −0.436806 + 0.436806i −0.890936 0.454129i \(-0.849950\pi\)
0.454129 + 0.890936i \(0.349950\pi\)
\(458\) −5.93353 22.1442i −0.277256 1.03473i
\(459\) 1.71007 2.96193i 0.0798194 0.138251i
\(460\) −1.08279 + 5.08563i −0.0504853 + 0.237119i
\(461\) −5.69535 + 9.86464i −0.265259 + 0.459442i −0.967631 0.252368i \(-0.918791\pi\)
0.702372 + 0.711810i \(0.252124\pi\)
\(462\) −1.89655 0.508178i −0.0882354 0.0236426i
\(463\) −20.8423 20.8423i −0.968626 0.968626i 0.0308970 0.999523i \(-0.490164\pi\)
−0.999523 + 0.0308970i \(0.990164\pi\)
\(464\) −6.85432 −0.318204
\(465\) 5.93763 + 1.26419i 0.275351 + 0.0586254i
\(466\) 5.42732 3.13347i 0.251416 0.145155i
\(467\) −14.6449 + 14.6449i −0.677687 + 0.677687i −0.959476 0.281790i \(-0.909072\pi\)
0.281790 + 0.959476i \(0.409072\pi\)
\(468\) −2.63047 + 2.63047i −0.121593 + 0.121593i
\(469\) −0.799917 1.38550i −0.0369368 0.0639763i
\(470\) 21.0181 + 10.7183i 0.969494 + 0.494396i
\(471\) −8.34953 + 4.82061i −0.384726 + 0.222122i
\(472\) −0.190185 0.709781i −0.00875399 0.0326703i
\(473\) −53.4724 + 14.3279i −2.45866 + 0.658797i
\(474\) 14.4360 0.663067
\(475\) 18.9354 + 10.7912i 0.868816 + 0.495135i
\(476\) −1.06065 −0.0486150
\(477\) −3.96536 + 1.06251i −0.181561 + 0.0486492i
\(478\) −5.84802 21.8251i −0.267482 0.998257i
\(479\) −1.00693 + 0.581352i −0.0460079 + 0.0265627i −0.522828 0.852438i \(-0.675123\pi\)
0.476820 + 0.879001i \(0.341789\pi\)
\(480\) −1.99201 1.01583i −0.0909222 0.0463661i
\(481\) 2.15139 + 3.72631i 0.0980948 + 0.169905i
\(482\) −0.0655253 + 0.0655253i −0.00298460 + 0.00298460i
\(483\) −0.509919 + 0.509919i −0.0232021 + 0.0232021i
\(484\) 25.1883 14.5425i 1.14492 0.661022i
\(485\) 36.0108 + 7.66711i 1.63517 + 0.348146i
\(486\) 1.00000 0.0453609
\(487\) −5.04003 5.04003i −0.228386 0.228386i 0.583632 0.812018i \(-0.301631\pi\)
−0.812018 + 0.583632i \(0.801631\pi\)
\(488\) 4.19465 + 1.12395i 0.189883 + 0.0508789i
\(489\) 0.0143985 0.0249390i 0.000651124 0.00112778i
\(490\) 3.21475 15.0990i 0.145227 0.682103i
\(491\) 6.22692 10.7853i 0.281017 0.486736i −0.690618 0.723219i \(-0.742662\pi\)
0.971636 + 0.236483i \(0.0759949\pi\)
\(492\) −2.63375 9.82930i −0.118739 0.443139i
\(493\) 16.5765 16.5765i 0.746570 0.746570i
\(494\) 14.7716 6.68835i 0.664607 0.300923i
\(495\) 14.1380 0.736129i 0.635456 0.0330865i
\(496\) 2.35118 + 1.35745i 0.105571 + 0.0609515i
\(497\) 0.397482 0.106505i 0.0178295 0.00477740i
\(498\) 0.0697543 0.260327i 0.00312577 0.0116655i
\(499\) −18.2705 10.5485i −0.817900 0.472215i 0.0317917 0.999495i \(-0.489879\pi\)
−0.849692 + 0.527280i \(0.823212\pi\)
\(500\) −7.02716 8.69592i −0.314264 0.388893i
\(501\) −1.80618 −0.0806940
\(502\) 6.49294 + 6.49294i 0.289794 + 0.289794i
\(503\) −6.18413 + 23.0795i −0.275737 + 1.02906i 0.679610 + 0.733574i \(0.262149\pi\)
−0.955346 + 0.295489i \(0.904517\pi\)
\(504\) −0.155060 0.268571i −0.00690691 0.0119631i
\(505\) 1.62165 + 31.1452i 0.0721625 + 1.38594i
\(506\) 14.7224i 0.654489i
\(507\) −0.217072 + 0.810123i −0.00964050 + 0.0359788i
\(508\) 3.78398 + 14.1220i 0.167887 + 0.626562i
\(509\) −4.73071 8.19383i −0.209685 0.363185i 0.741930 0.670477i \(-0.233911\pi\)
−0.951615 + 0.307292i \(0.900577\pi\)
\(510\) 7.27418 2.36079i 0.322106 0.104538i
\(511\) −0.747099 + 1.29401i −0.0330497 + 0.0572438i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −4.07912 1.53647i −0.180098 0.0678370i
\(514\) 8.06321i 0.355653i
\(515\) 16.8417 5.46589i 0.742135 0.240856i
\(516\) −7.57227 4.37185i −0.333351 0.192460i
\(517\) −64.5264 17.2898i −2.83787 0.760405i
\(518\) −0.346476 + 0.0928381i −0.0152233 + 0.00407907i
\(519\) −19.9724 + 11.5311i −0.876690 + 0.506157i
\(520\) −8.30701 + 0.432524i −0.364287 + 0.0189674i
\(521\) 38.6070i 1.69140i 0.533656 + 0.845702i \(0.320818\pi\)
−0.533656 + 0.845702i \(0.679182\pi\)
\(522\) 6.62077 + 1.77403i 0.289783 + 0.0776471i
\(523\) −36.8220 9.86642i −1.61011 0.431428i −0.662037 0.749472i \(-0.730308\pi\)
−0.948076 + 0.318043i \(0.896974\pi\)
\(524\) 3.64166i 0.159087i
\(525\) −0.161035 1.54221i −0.00702813 0.0673077i
\(526\) −12.9801 + 7.49405i −0.565959 + 0.326756i
\(527\) −8.96899 + 2.40323i −0.390695 + 0.104687i
\(528\) 6.11554 + 1.63865i 0.266145 + 0.0713132i
\(529\) 15.2358 + 8.79639i 0.662426 + 0.382452i
\(530\) −8.17766 4.17022i −0.355215 0.181143i
\(531\) 0.734820i 0.0318885i
\(532\) 0.219855 + 1.33378i 0.00953192 + 0.0578268i
\(533\) −26.7677 26.7677i −1.15944 1.15944i
\(534\) −5.18194 + 8.97538i −0.224244 + 0.388402i
\(535\) −3.28636 10.1261i −0.142082 0.437788i
\(536\) 2.57938 + 4.46762i 0.111412 + 0.192972i
\(537\) −3.86017 14.4064i −0.166579 0.621680i
\(538\) 0.448783 1.67488i 0.0193484 0.0722092i
\(539\) 43.7100i 1.88272i
\(540\) 1.66121 + 1.49679i 0.0714873 + 0.0644114i
\(541\) 22.8304 + 39.5434i 0.981554 + 1.70010i 0.656347 + 0.754459i \(0.272101\pi\)
0.325208 + 0.945643i \(0.394566\pi\)
\(542\) −0.238478 + 0.890012i −0.0102435 + 0.0382293i
\(543\) 3.22940 + 3.22940i 0.138587 + 0.138587i
\(544\) 3.42015 0.146638
\(545\) −18.9022 + 12.2661i −0.809679 + 0.525421i
\(546\) −0.999097 0.576829i −0.0427574 0.0246860i
\(547\) 11.5754 43.2001i 0.494930 1.84710i −0.0354931 0.999370i \(-0.511300\pi\)
0.530423 0.847733i \(-0.322033\pi\)
\(548\) −9.95833 + 2.66833i −0.425399 + 0.113985i
\(549\) −3.76082 2.17131i −0.160508 0.0926692i
\(550\) 24.5881 + 19.9387i 1.04844 + 0.850188i
\(551\) −24.2812 17.4091i −1.03441 0.741653i
\(552\) 1.64426 1.64426i 0.0699845 0.0699845i
\(553\) 1.15870 + 4.32434i 0.0492730 + 0.183889i
\(554\) 0.927905 1.60718i 0.0394229 0.0682825i
\(555\) 2.16957 1.40789i 0.0920929 0.0597614i
\(556\) −10.3204 + 17.8754i −0.437681 + 0.758086i
\(557\) 18.4394 + 4.94082i 0.781302 + 0.209349i 0.627359 0.778730i \(-0.284136\pi\)
0.153943 + 0.988080i \(0.450803\pi\)
\(558\) −1.91973 1.91973i −0.0812687 0.0812687i
\(559\) −32.5269 −1.37574
\(560\) 0.144406 0.678246i 0.00610228 0.0286611i
\(561\) −18.7528 + 10.8269i −0.791744 + 0.457113i
\(562\) 14.0736 14.0736i 0.593659 0.593659i
\(563\) 22.6314 22.6314i 0.953800 0.953800i −0.0451787 0.998979i \(-0.514386\pi\)
0.998979 + 0.0451787i \(0.0143857\pi\)
\(564\) −5.27562 9.13763i −0.222143 0.384764i
\(565\) −41.5846 + 13.4960i −1.74948 + 0.567783i
\(566\) −27.1633 + 15.6828i −1.14176 + 0.659195i
\(567\) 0.0802649 + 0.299553i 0.00337081 + 0.0125800i
\(568\) −1.28170 + 0.343432i −0.0537791 + 0.0144101i
\(569\) −21.8851 −0.917470 −0.458735 0.888573i \(-0.651697\pi\)
−0.458735 + 0.888573i \(0.651697\pi\)
\(570\) −4.47653 8.65799i −0.187501 0.362643i
\(571\) −7.33723 −0.307053 −0.153527 0.988145i \(-0.549063\pi\)
−0.153527 + 0.988145i \(0.549063\pi\)
\(572\) 22.7500 6.09586i 0.951227 0.254881i
\(573\) −4.52047 16.8706i −0.188846 0.704781i
\(574\) 2.73300 1.57790i 0.114073 0.0658601i
\(575\) 10.8573 4.15927i 0.452780 0.173453i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 18.6090 18.6090i 0.774705 0.774705i −0.204220 0.978925i \(-0.565466\pi\)
0.978925 + 0.204220i \(0.0654659\pi\)
\(578\) 3.74950 3.74950i 0.155959 0.155959i
\(579\) −1.53455 + 0.885971i −0.0637736 + 0.0368197i
\(580\) 8.34317 + 12.8569i 0.346431 + 0.533854i
\(581\) 0.0835804 0.00346750
\(582\) −11.6429 11.6429i −0.482612 0.482612i
\(583\) 25.1057 + 6.72706i 1.03977 + 0.278606i
\(584\) 2.40907 4.17262i 0.0996879 0.172664i
\(585\) 8.13590 + 1.73223i 0.336378 + 0.0716187i
\(586\) −5.82413 + 10.0877i −0.240593 + 0.416719i
\(587\) −9.65810 36.0445i −0.398632 1.48772i −0.815504 0.578751i \(-0.803540\pi\)
0.416872 0.908965i \(-0.363126\pi\)
\(588\) −4.88174 + 4.88174i −0.201320 + 0.201320i
\(589\) 4.88120 + 10.7804i 0.201126 + 0.444200i
\(590\) −1.09987 + 1.22069i −0.0452808 + 0.0502551i
\(591\) −5.99684 3.46228i −0.246677 0.142419i
\(592\) 1.11723 0.299362i 0.0459181 0.0123037i
\(593\) 6.25662 23.3500i 0.256929 0.958871i −0.710079 0.704122i \(-0.751341\pi\)
0.967007 0.254749i \(-0.0819927\pi\)
\(594\) −5.48304 3.16563i −0.224972 0.129888i
\(595\) 1.29104 + 1.98951i 0.0529276 + 0.0815619i
\(596\) −19.3343 −0.791963
\(597\) 5.39351 + 5.39351i 0.220742 + 0.220742i
\(598\) 2.23888 8.35561i 0.0915546 0.341686i
\(599\) 9.76934 + 16.9210i 0.399165 + 0.691373i 0.993623 0.112753i \(-0.0359669\pi\)
−0.594459 + 0.804126i \(0.702634\pi\)
\(600\) 0.519266 + 4.97296i 0.0211990 + 0.203020i
\(601\) 22.9520i 0.936231i 0.883667 + 0.468116i \(0.155067\pi\)
−0.883667 + 0.468116i \(0.844933\pi\)
\(602\) 0.701812 2.61920i 0.0286037 0.106751i
\(603\) −1.33519 4.98299i −0.0543730 0.202923i
\(604\) 0.128094 + 0.221865i 0.00521207 + 0.00902758i
\(605\) −57.9374 29.5454i −2.35549 1.20119i
\(606\) 6.97371 12.0788i 0.283288 0.490669i
\(607\) −11.8605 11.8605i −0.481402 0.481402i 0.424177 0.905579i \(-0.360563\pi\)
−0.905579 + 0.424177i \(0.860563\pi\)
\(608\) −0.708936 4.30086i −0.0287512 0.174423i
\(609\) 2.12566i 0.0861361i
\(610\) −2.99754 9.23615i −0.121367 0.373961i
\(611\) −33.9924 19.6255i −1.37518 0.793963i
\(612\) −3.30361 0.885199i −0.133540 0.0357820i
\(613\) −26.3007 + 7.04726i −1.06228 + 0.284636i −0.747316 0.664468i \(-0.768658\pi\)
−0.314961 + 0.949105i \(0.601991\pi\)
\(614\) 3.65584 2.11070i 0.147538 0.0851810i
\(615\) −15.2314 + 16.9046i −0.614188 + 0.681659i
\(616\) 1.96345i 0.0791097i
\(617\) −24.5872 6.58811i −0.989842 0.265227i −0.272658 0.962111i \(-0.587903\pi\)
−0.717184 + 0.696884i \(0.754569\pi\)
\(618\) −7.64876 2.04948i −0.307678 0.0824421i
\(619\) 4.00889i 0.161131i 0.996749 + 0.0805654i \(0.0256726\pi\)
−0.996749 + 0.0805654i \(0.974327\pi\)
\(620\) −0.315659 6.06251i −0.0126772 0.243476i
\(621\) −2.01380 + 1.16267i −0.0808112 + 0.0466564i
\(622\) −10.7006 + 2.86721i −0.429054 + 0.114965i
\(623\) −3.10452 0.831855i −0.124380 0.0333276i
\(624\) 3.22165 + 1.86002i 0.128969 + 0.0744604i
\(625\) −7.75770 + 23.7659i −0.310308 + 0.950636i
\(626\) 22.5831i 0.902600i
\(627\) 17.5021 + 21.3376i 0.698966 + 0.852140i
\(628\) 6.81737 + 6.81737i 0.272043 + 0.272043i
\(629\) −1.97795 + 3.42591i −0.0788661 + 0.136600i
\(630\) −0.315029 + 0.617760i −0.0125510 + 0.0246122i
\(631\) −5.52757 9.57403i −0.220049 0.381136i 0.734774 0.678312i \(-0.237288\pi\)
−0.954823 + 0.297176i \(0.903955\pi\)
\(632\) −3.73631 13.9441i −0.148622 0.554666i
\(633\) 0.0510720 0.190603i 0.00202993 0.00757579i
\(634\) 18.3504i 0.728788i
\(635\) 21.8833 24.2872i 0.868411 0.963810i
\(636\) 2.05262 + 3.55524i 0.0813917 + 0.140974i
\(637\) −6.64712 + 24.8074i −0.263369 + 0.982905i
\(638\) −30.6860 30.6860i −1.21487 1.21487i
\(639\) 1.32692 0.0524921
\(640\) −0.465647 + 2.18705i −0.0184063 + 0.0864506i
\(641\) −38.7197 22.3548i −1.52934 0.882963i −0.999390 0.0349331i \(-0.988878\pi\)
−0.529948 0.848030i \(-0.677788\pi\)
\(642\) −1.23225 + 4.59881i −0.0486329 + 0.181500i
\(643\) −22.9781 + 6.15697i −0.906169 + 0.242807i −0.681664 0.731666i \(-0.738743\pi\)
−0.224505 + 0.974473i \(0.572077\pi\)
\(644\) 0.624520 + 0.360567i 0.0246095 + 0.0142083i
\(645\) 1.01662 + 19.5251i 0.0400293 + 0.768799i
\(646\) 12.1157 + 8.68674i 0.476687 + 0.341775i
\(647\) 20.9244 20.9244i 0.822622 0.822622i −0.163862 0.986483i \(-0.552395\pi\)
0.986483 + 0.163862i \(0.0523951\pi\)
\(648\) −0.258819 0.965926i −0.0101674 0.0379452i
\(649\) 2.32617 4.02905i 0.0913102 0.158154i
\(650\) 10.9227 + 15.0553i 0.428424 + 0.590517i
\(651\) 0.420973 0.729147i 0.0164992 0.0285775i
\(652\) −0.0278158 0.00745323i −0.00108935 0.000291891i
\(653\) 30.2481 + 30.2481i 1.18370 + 1.18370i 0.978779 + 0.204920i \(0.0656935\pi\)
0.204920 + 0.978779i \(0.434306\pi\)
\(654\) 10.0772 0.394049
\(655\) 6.83080 4.43267i 0.266901 0.173199i
\(656\) −8.81271 + 5.08802i −0.344079 + 0.198654i
\(657\) −3.40693 + 3.40693i −0.132917 + 0.132917i
\(658\) 2.31375 2.31375i 0.0901996 0.0901996i
\(659\) 13.4067 + 23.2211i 0.522252 + 0.904567i 0.999665 + 0.0258876i \(0.00824120\pi\)
−0.477413 + 0.878679i \(0.658425\pi\)
\(660\) −4.37023 13.4657i −0.170111 0.524153i
\(661\) 7.07026 4.08202i 0.275001 0.158772i −0.356157 0.934426i \(-0.615913\pi\)
0.631158 + 0.775654i \(0.282580\pi\)
\(662\) −0.423325 1.57987i −0.0164530 0.0614034i
\(663\) −12.2896 + 3.29298i −0.477287 + 0.127889i
\(664\) −0.269510 −0.0104590
\(665\) 2.23421 2.03589i 0.0866391 0.0789483i
\(666\) −1.15665 −0.0448192
\(667\) −15.3955 + 4.12522i −0.596118 + 0.159729i
\(668\) 0.467473 + 1.74463i 0.0180871 + 0.0675018i
\(669\) 10.8934 6.28931i 0.421163 0.243159i
\(670\) 5.24043 10.2763i 0.202455 0.397008i
\(671\) 13.7471 + 23.8108i 0.530703 + 0.919204i
\(672\) −0.219288 + 0.219288i −0.00845921 + 0.00845921i
\(673\) 19.6072 19.6072i 0.755803 0.755803i −0.219752 0.975556i \(-0.570525\pi\)
0.975556 + 0.219752i \(0.0705249\pi\)
\(674\) 0.461027 0.266174i 0.0177581 0.0102526i
\(675\) 0.785525 4.93791i 0.0302349 0.190060i
\(676\) 0.838701 0.0322577
\(677\) −17.7081 17.7081i −0.680577 0.680577i 0.279553 0.960130i \(-0.409814\pi\)
−0.960130 + 0.279553i \(0.909814\pi\)
\(678\) 18.8859 + 5.06045i 0.725307 + 0.194345i
\(679\) 2.55314 4.42216i 0.0979804 0.169707i
\(680\) −4.16305 6.41530i −0.159646 0.246015i
\(681\) −2.52387 + 4.37146i −0.0967148 + 0.167515i
\(682\) 4.44879 + 16.6031i 0.170353 + 0.635766i
\(683\) 26.8964 26.8964i 1.02916 1.02916i 0.0295985 0.999562i \(-0.490577\pi\)
0.999562 0.0295985i \(-0.00942286\pi\)
\(684\) −0.428365 + 4.33780i −0.0163790 + 0.165860i
\(685\) 17.1265 + 15.4313i 0.654370 + 0.589599i
\(686\) −3.73417 2.15592i −0.142571 0.0823136i
\(687\) 22.1442 5.93353i 0.844855 0.226378i
\(688\) −2.26304 + 8.44577i −0.0862775 + 0.321992i
\(689\) 13.2256 + 7.63583i 0.503857 + 0.290902i
\(690\) −5.08563 1.08279i −0.193607 0.0412211i
\(691\) 10.0289 0.381516 0.190758 0.981637i \(-0.438905\pi\)
0.190758 + 0.981637i \(0.438905\pi\)
\(692\) 16.3074 + 16.3074i 0.619913 + 0.619913i
\(693\) 0.508178 1.89655i 0.0193041 0.0720439i
\(694\) 0.969124 + 1.67857i 0.0367874 + 0.0637177i
\(695\) 46.0917 2.39987i 1.74836 0.0910324i
\(696\) 6.85432i 0.259812i
\(697\) 9.00782 33.6177i 0.341196 1.27336i
\(698\) 5.51814 + 20.5940i 0.208865 + 0.779494i
\(699\) 3.13347 + 5.42732i 0.118519 + 0.205280i
\(700\) −1.44799 + 0.554702i −0.0547287 + 0.0209658i
\(701\) −18.8206 + 32.5983i −0.710845 + 1.23122i 0.253696 + 0.967284i \(0.418354\pi\)
−0.964540 + 0.263935i \(0.914980\pi\)
\(702\) −2.63047 2.63047i −0.0992805 0.0992805i
\(703\) 4.71810 + 1.77716i 0.177947 + 0.0670268i
\(704\) 6.33127i 0.238619i
\(705\) −10.7183 + 21.0181i −0.403673 + 0.791588i
\(706\) 22.4506 + 12.9618i 0.844939 + 0.487826i
\(707\) 4.17799 + 1.11949i 0.157129 + 0.0421027i
\(708\) 0.709781 0.190185i 0.0266752 0.00714760i
\(709\) 0.257513 0.148675i 0.00967110 0.00558361i −0.495157 0.868804i \(-0.664889\pi\)
0.504828 + 0.863220i \(0.331556\pi\)
\(710\) 2.20429 + 1.98611i 0.0827257 + 0.0745374i
\(711\) 14.4360i 0.541392i
\(712\) 10.0107 + 2.68237i 0.375168 + 0.100526i
\(713\) 6.09797 + 1.63395i 0.228371 + 0.0611918i
\(714\) 1.06065i 0.0396940i
\(715\) −39.1259 35.2532i −1.46322 1.31839i
\(716\) −12.9164 + 7.45728i −0.482708 + 0.278692i
\(717\) 21.8251 5.84802i 0.815074 0.218398i
\(718\) −30.0457 8.05073i −1.12130 0.300451i
\(719\) 10.2040 + 5.89129i 0.380546 + 0.219708i 0.678056 0.735011i \(-0.262823\pi\)
−0.297510 + 0.954719i \(0.596156\pi\)
\(720\) 1.01583 1.99201i 0.0378577 0.0742377i
\(721\) 2.45571i 0.0914553i
\(722\) 8.41227 17.0362i 0.313072 0.634023i
\(723\) −0.0655253 0.0655253i −0.00243691 0.00243691i
\(724\) 2.28353 3.95519i 0.0848667 0.146993i
\(725\) 13.9608 31.2992i 0.518490 1.16242i
\(726\) 14.5425 + 25.1883i 0.539722 + 0.934826i
\(727\) −0.862014 3.21708i −0.0319703 0.119315i 0.948097 0.317982i \(-0.103005\pi\)
−0.980067 + 0.198668i \(0.936339\pi\)
\(728\) −0.298589 + 1.11435i −0.0110664 + 0.0413005i
\(729\) 1.00000i 0.0370370i
\(730\) −10.7591 + 0.560198i −0.398212 + 0.0207339i
\(731\) −14.9524 25.8983i −0.553033 0.957882i
\(732\) −1.12395 + 4.19465i −0.0415425 + 0.155039i
\(733\) −2.34690 2.34690i −0.0866846 0.0866846i 0.662435 0.749120i \(-0.269523\pi\)
−0.749120 + 0.662435i \(0.769523\pi\)
\(734\) 29.8289 1.10101
\(735\) 15.0990 + 3.21475i 0.556935 + 0.118578i
\(736\) −2.01380 1.16267i −0.0742298 0.0428566i
\(737\) −8.45343 + 31.5486i −0.311386 + 1.16211i
\(738\) 9.82930 2.63375i 0.361822 0.0969498i
\(739\) 28.6071 + 16.5163i 1.05233 + 0.607562i 0.923300 0.384079i \(-0.125481\pi\)
0.129028 + 0.991641i \(0.458814\pi\)
\(740\) −1.92144 1.73125i −0.0706335 0.0636421i
\(741\) 6.68835 + 14.7716i 0.245703 + 0.542650i
\(742\) −0.900228 + 0.900228i −0.0330484 + 0.0330484i
\(743\) −5.70483 21.2907i −0.209290 0.781081i −0.988099 0.153820i \(-0.950843\pi\)
0.778809 0.627261i \(-0.215824\pi\)
\(744\) −1.35745 + 2.35118i −0.0497667 + 0.0861984i
\(745\) 23.5339 + 36.2660i 0.862217 + 1.32868i
\(746\) 9.45339 16.3737i 0.346113 0.599486i
\(747\) 0.260327 + 0.0697543i 0.00952486 + 0.00255218i
\(748\) 15.3116 + 15.3116i 0.559847 + 0.559847i
\(749\) −1.47649 −0.0539498
\(750\) 8.69592 7.02716i 0.317530 0.256596i
\(751\) 40.4682 23.3643i 1.47671 0.852577i 0.477053 0.878875i \(-0.341705\pi\)
0.999654 + 0.0262976i \(0.00837175\pi\)
\(752\) −7.46085 + 7.46085i −0.272069 + 0.272069i
\(753\) −6.49294 + 6.49294i −0.236616 + 0.236616i
\(754\) −12.7492 22.0822i −0.464298 0.804187i
\(755\) 0.260244 0.510329i 0.00947123 0.0185728i
\(756\) 0.268571 0.155060i 0.00976785 0.00563947i
\(757\) −0.0205442 0.0766719i −0.000746691 0.00278669i 0.965551 0.260212i \(-0.0837925\pi\)
−0.966298 + 0.257425i \(0.917126\pi\)
\(758\) 31.0446 8.31837i 1.12759 0.302137i
\(759\) 14.7224 0.534388
\(760\) −7.20436 + 6.56484i −0.261330 + 0.238132i
\(761\) 18.4883 0.670201 0.335101 0.942182i \(-0.391230\pi\)
0.335101 + 0.942182i \(0.391230\pi\)
\(762\) −14.1220 + 3.78398i −0.511586 + 0.137079i
\(763\) 0.808844 + 3.01865i 0.0292821 + 0.109282i
\(764\) −15.1258 + 8.73289i −0.547232 + 0.315945i
\(765\) 2.36079 + 7.27418i 0.0853547 + 0.262998i
\(766\) 1.81976 + 3.15192i 0.0657508 + 0.113884i
\(767\) 1.93292 1.93292i 0.0697936 0.0697936i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −10.6383 + 6.14205i −0.383628 + 0.221488i −0.679396 0.733772i \(-0.737758\pi\)
0.295767 + 0.955260i \(0.404425\pi\)
\(770\) 3.68292 2.38994i 0.132723 0.0861274i
\(771\) 8.06321 0.290390
\(772\) 1.25295 + 1.25295i 0.0450947 + 0.0450947i
\(773\) −2.96842 0.795386i −0.106767 0.0286081i 0.205040 0.978754i \(-0.434268\pi\)
−0.311807 + 0.950146i \(0.600934\pi\)
\(774\) 4.37185 7.57227i 0.157143 0.272180i
\(775\) −10.9874 + 7.97146i −0.394681 + 0.286343i
\(776\) −8.23275 + 14.2595i −0.295538 + 0.511888i
\(777\) −0.0928381 0.346476i −0.00333055 0.0124298i
\(778\) 9.88199 9.88199i 0.354287 0.354287i
\(779\) −44.1416 4.35906i −1.58154 0.156180i
\(780\) −0.432524 8.30701i −0.0154869 0.297439i
\(781\) −7.27554 4.20054i −0.260339 0.150307i
\(782\) 7.68201 2.05839i 0.274708 0.0736079i
\(783\) −1.77403 + 6.62077i −0.0633986 + 0.236607i
\(784\) 5.97889 + 3.45191i 0.213532 + 0.123283i
\(785\) 4.48940 21.0858i 0.160234 0.752584i
\(786\) −3.64166 −0.129894
\(787\) −16.0590 16.0590i −0.572443 0.572443i 0.360367 0.932810i \(-0.382651\pi\)
−0.932810 + 0.360367i \(0.882651\pi\)
\(788\) −1.79221 + 6.68860i −0.0638447 + 0.238272i
\(789\) −7.49405 12.9801i −0.266795 0.462103i
\(790\) −21.6076 + 23.9813i −0.768763 + 0.853215i
\(791\) 6.06348i 0.215593i
\(792\) −1.63865 + 6.11554i −0.0582270 + 0.217306i
\(793\) 4.18115 + 15.6043i 0.148477 + 0.554123i
\(794\) −2.09046 3.62078i −0.0741876 0.128497i
\(795\) 4.17022 8.17766i 0.147903 0.290032i
\(796\) 3.81379 6.60568i 0.135176 0.234132i
\(797\) 21.2908 + 21.2908i 0.754160 + 0.754160i 0.975253 0.221093i \(-0.0709624\pi\)
−0.221093 + 0.975253i \(0.570962\pi\)
\(798\) −1.33378 + 0.219855i −0.0472154 + 0.00778278i
\(799\) 36.0867i 1.27666i
\(800\) 4.66912 1.78867i 0.165078 0.0632390i
\(801\) −8.97538 5.18194i −0.317129 0.183095i
\(802\) 29.2821 + 7.84612i 1.03399 + 0.277056i
\(803\) 29.4655 7.89525i 1.03981 0.278617i
\(804\) −4.46762 + 2.57938i −0.157561 + 0.0909678i
\(805\) −0.0838453 1.61032i −0.00295516 0.0567564i
\(806\) 10.0996i 0.355742i
\(807\) 1.67488 + 0.448783i 0.0589586 + 0.0157979i
\(808\) −13.4722 3.60986i −0.473950 0.126994i
\(809\) 10.3294i 0.363162i 0.983376 + 0.181581i \(0.0581215\pi\)
−0.983376 + 0.181581i \(0.941878\pi\)
\(810\) −1.49679 + 1.66121i −0.0525917 + 0.0583691i
\(811\) 6.89851 3.98286i 0.242240 0.139857i −0.373966 0.927442i \(-0.622002\pi\)
0.616206 + 0.787585i \(0.288669\pi\)
\(812\) 2.05323 0.550161i 0.0720542 0.0193069i
\(813\) −0.890012 0.238478i −0.0312141 0.00836379i
\(814\) 6.34194 + 3.66152i 0.222285 + 0.128336i
\(815\) 0.0198775 + 0.0612474i 0.000696278 + 0.00214540i
\(816\) 3.42015i 0.119729i
\(817\) −29.4679 + 24.1710i −1.03095 + 0.845636i
\(818\) −9.79837 9.79837i −0.342592 0.342592i
\(819\) 0.576829 0.999097i 0.0201560 0.0349113i
\(820\) 20.2707 + 10.3371i 0.707885 + 0.360988i
\(821\) 12.0173 + 20.8146i 0.419407 + 0.726434i 0.995880 0.0906824i \(-0.0289048\pi\)
−0.576473 + 0.817116i \(0.695571\pi\)
\(822\) −2.66833 9.95833i −0.0930686 0.347337i
\(823\) −7.23439 + 26.9991i −0.252175 + 0.941129i 0.717466 + 0.696594i \(0.245302\pi\)
−0.969640 + 0.244535i \(0.921365\pi\)
\(824\) 7.91858i 0.275857i
\(825\) −19.9387 + 24.5881i −0.694176 + 0.856047i
\(826\) 0.113941 + 0.197352i 0.00396451 + 0.00686674i
\(827\) −12.2954 + 45.8870i −0.427552 + 1.59565i 0.330733 + 0.943724i \(0.392704\pi\)
−0.758285 + 0.651923i \(0.773963\pi\)
\(828\) 1.64426 + 1.64426i 0.0571421 + 0.0571421i
\(829\) −10.6170 −0.368745 −0.184373 0.982856i \(-0.559025\pi\)
−0.184373 + 0.982856i \(0.559025\pi\)
\(830\) 0.328051 + 0.505530i 0.0113868 + 0.0175472i
\(831\) 1.60718 + 0.927905i 0.0557524 + 0.0321887i
\(832\) 0.962817 3.59328i 0.0333797 0.124575i
\(833\) −22.8075 + 6.11126i −0.790234 + 0.211743i
\(834\) −17.8754 10.3204i −0.618975 0.357365i
\(835\) 2.70346 3.00045i 0.0935570 0.103835i
\(836\) 16.0806 22.4283i 0.556160 0.775698i
\(837\) 1.91973 1.91973i 0.0663556 0.0663556i
\(838\) 8.96436 + 33.4554i 0.309669 + 1.15570i
\(839\) −6.26045 + 10.8434i −0.216135 + 0.374357i −0.953623 0.301003i \(-0.902678\pi\)
0.737488 + 0.675360i \(0.236012\pi\)
\(840\) 0.678246 + 0.144406i 0.0234017 + 0.00498249i
\(841\) −8.99086 + 15.5726i −0.310030 + 0.536987i
\(842\) −12.5635 3.36637i −0.432966 0.116013i
\(843\) 14.0736 + 14.0736i 0.484721 + 0.484721i
\(844\) −0.197327 −0.00679227
\(845\) −1.02088 1.57318i −0.0351193 0.0541191i
\(846\) 9.13763 5.27562i 0.314158 0.181379i
\(847\) −6.37797 + 6.37797i −0.219150 + 0.219150i
\(848\) 2.90284 2.90284i 0.0996840 0.0996840i
\(849\) −15.6828 27.1633i −0.538231 0.932243i
\(850\) −6.96610 + 15.6176i −0.238935 + 0.535678i
\(851\) 2.32926 1.34480i 0.0798460 0.0460991i
\(852\) −0.343432 1.28170i −0.0117658 0.0439105i
\(853\) 26.9951 7.23330i 0.924293 0.247664i 0.234874 0.972026i \(-0.424532\pi\)
0.689419 + 0.724362i \(0.257866\pi\)
\(854\) −1.34673 −0.0460842
\(855\) 8.65799 4.47653i 0.296097 0.153094i
\(856\) 4.76103 0.162729
\(857\) 35.8049 9.59390i 1.22307 0.327721i 0.411195 0.911548i \(-0.365112\pi\)
0.811879 + 0.583826i \(0.198445\pi\)
\(858\) 6.09586 + 22.7500i 0.208109 + 0.776674i
\(859\) −29.0736 + 16.7857i −0.991979 + 0.572719i −0.905865 0.423566i \(-0.860778\pi\)
−0.0861135 + 0.996285i \(0.527445\pi\)
\(860\) 18.5966 6.03544i 0.634140 0.205807i
\(861\) 1.57790 + 2.73300i 0.0537745 + 0.0931402i
\(862\) 15.7136 15.7136i 0.535208 0.535208i
\(863\) 0.511254 0.511254i 0.0174033 0.0174033i −0.698352 0.715755i \(-0.746083\pi\)
0.715755 + 0.698352i \(0.246083\pi\)
\(864\) −0.866025 + 0.500000i −0.0294628 + 0.0170103i
\(865\) 10.7388 50.4379i 0.365130 1.71494i
\(866\) 11.5661 0.393032
\(867\) 3.74950 + 3.74950i 0.127340 + 0.127340i
\(868\) −0.813258 0.217912i −0.0276038 0.00739641i
\(869\) 45.6991 79.1531i 1.55023 2.68508i
\(870\) −12.8569 + 8.34317i −0.435890 + 0.282860i
\(871\) −9.59541 + 16.6197i −0.325128 + 0.563138i
\(872\) −2.60817 9.73381i −0.0883237 0.329628i
\(873\) 11.6429 11.6429i 0.394051 0.394051i
\(874\) −4.18079 9.23353i −0.141417 0.312329i
\(875\) 2.80298 + 2.04085i 0.0947581 + 0.0689933i
\(876\) 4.17262 + 2.40907i 0.140980 + 0.0813948i
\(877\) 44.1152 11.8206i 1.48966 0.399154i 0.580040 0.814588i \(-0.303037\pi\)
0.909623 + 0.415434i \(0.136370\pi\)
\(878\) −2.92988 + 10.9345i −0.0988786 + 0.369020i
\(879\) −10.0877 5.82413i −0.340249 0.196443i
\(880\) −11.8758 + 7.70650i −0.400333 + 0.259786i
\(881\) −5.08922 −0.171460 −0.0857301 0.996318i \(-0.527322\pi\)
−0.0857301 + 0.996318i \(0.527322\pi\)
\(882\) −4.88174 4.88174i −0.164377 0.164377i
\(883\) −1.61124 + 6.01323i −0.0542225 + 0.202361i −0.987723 0.156215i \(-0.950071\pi\)
0.933501 + 0.358576i \(0.116738\pi\)
\(884\) 6.36154 + 11.0185i 0.213962 + 0.370593i
\(885\) −1.22069 1.09987i −0.0410331 0.0369716i
\(886\) 37.1029i 1.24650i
\(887\) 12.5570 46.8634i 0.421623 1.57352i −0.349564 0.936912i \(-0.613670\pi\)
0.771188 0.636608i \(-0.219663\pi\)
\(888\) 0.299362 + 1.11723i 0.0100459 + 0.0374920i
\(889\) −2.26700 3.92656i −0.0760328 0.131693i
\(890\) −7.15378 22.0425i −0.239795 0.738867i
\(891\) 3.16563 5.48304i 0.106053 0.183689i
\(892\) −8.89442 8.89442i −0.297807 0.297807i
\(893\) −45.3794 + 7.48015i −1.51856 + 0.250314i
\(894\) 19.3343i 0.646635i
\(895\) 29.7099 + 15.1507i 0.993092 + 0.506430i
\(896\) 0.268571 + 0.155060i 0.00897234 + 0.00518018i
\(897\) 8.35561 + 2.23888i 0.278986 + 0.0747540i
\(898\) 26.3493 7.06027i 0.879287 0.235604i
\(899\) 16.1157 9.30443i 0.537490 0.310320i
\(900\) −4.97296 + 0.519266i −0.165765 + 0.0173089i
\(901\) 14.0405i 0.467757i
\(902\) −62.2320 16.6750i −2.07210 0.555217i
\(903\) 2.61920 + 0.701812i 0.0871615 + 0.0233548i
\(904\) 19.5521i 0.650293i
\(905\) −10.1984 + 0.531006i −0.339008 + 0.0176512i
\(906\) −0.221865 + 0.128094i −0.00737099 + 0.00425564i
\(907\) 14.2766 3.82540i 0.474046 0.127020i −0.0138828 0.999904i \(-0.504419\pi\)
0.487929 + 0.872883i \(0.337753\pi\)
\(908\) 4.87573 + 1.30645i 0.161807 + 0.0433560i
\(909\) 12.0788 + 6.97371i 0.400629 + 0.231303i
\(910\) 2.45367 0.796325i 0.0813384 0.0263979i
\(911\) 40.7085i 1.34873i 0.738397 + 0.674366i \(0.235583\pi\)
−0.738397 + 0.674366i \(0.764417\pi\)
\(912\) 4.30086 0.708936i 0.142416 0.0234752i
\(913\) −1.20656 1.20656i −0.0399315 0.0399315i
\(914\) −6.60286 + 11.4365i −0.218403 + 0.378285i
\(915\) 9.23615 2.99754i 0.305338 0.0990956i
\(916\) −11.4627 19.8540i −0.378738 0.655994i
\(917\) −0.292297 1.09087i −0.00965250 0.0360236i
\(918\) 0.885199 3.30361i 0.0292159 0.109035i
\(919\) 23.2487i 0.766905i −0.923561 0.383453i \(-0.874735\pi\)
0.923561 0.383453i \(-0.125265\pi\)
\(920\) 0.270364 + 5.19259i 0.00891365 + 0.171195i
\(921\) 2.11070 + 3.65584i 0.0695500 + 0.120464i
\(922\) −2.94813 + 11.0026i −0.0970916 + 0.362351i
\(923\) −3.49041 3.49041i −0.114888 0.114888i
\(924\) −1.96345 −0.0645928
\(925\) −0.908575 + 5.71142i −0.0298738 + 0.187790i
\(926\) −25.5265 14.7378i −0.838854 0.484313i
\(927\) 2.04948 7.64876i 0.0673137 0.251218i
\(928\) −6.62077 + 1.77403i −0.217337 + 0.0582354i
\(929\) 17.4209 + 10.0580i 0.571563 + 0.329992i 0.757773 0.652518i \(-0.226287\pi\)
−0.186211 + 0.982510i \(0.559621\pi\)
\(930\) 6.06251 0.315659i 0.198797 0.0103509i
\(931\) 12.4126 + 27.4139i 0.406805 + 0.898454i
\(932\) 4.43139 4.43139i 0.145155 0.145155i
\(933\) −2.86721 10.7006i −0.0938682 0.350321i
\(934\) −10.3555 + 17.9363i −0.338843 + 0.586894i
\(935\) 10.0831 47.3580i 0.329751 1.54877i
\(936\) −1.86002 + 3.22165i −0.0607967 + 0.105303i
\(937\) 44.9305 + 12.0391i 1.46782 + 0.393300i 0.902182 0.431355i \(-0.141964\pi\)
0.565635 + 0.824656i \(0.308631\pi\)
\(938\) −1.13125 1.13125i −0.0369368 0.0369368i
\(939\) 22.5831 0.736970
\(940\) 23.0760 + 4.91315i 0.752657 + 0.160249i
\(941\) 22.8383 13.1857i 0.744508 0.429842i −0.0791980 0.996859i \(-0.525236\pi\)
0.823706 + 0.567017i \(0.191903\pi\)
\(942\) −6.81737 + 6.81737i −0.222122 + 0.222122i
\(943\) −16.7321 + 16.7321i −0.544872 + 0.544872i
\(944\) −0.367410 0.636373i −0.0119582 0.0207122i
\(945\) −0.617760 0.315029i −0.0200957 0.0102479i
\(946\) −47.9421 + 27.6794i −1.55873 + 0.899934i
\(947\) −3.47159 12.9561i −0.112812 0.421018i 0.886302 0.463107i \(-0.153265\pi\)
−0.999114 + 0.0420887i \(0.986599\pi\)
\(948\) 13.9441 3.73631i 0.452883 0.121350i
\(949\) 17.9236 0.581826
\(950\) 21.0832 + 5.52268i 0.684028 + 0.179179i
\(951\) −18.3504 −0.595053
\(952\) −1.02451 + 0.274518i −0.0332047 + 0.00889717i
\(953\) −7.83734 29.2494i −0.253876 0.947480i −0.968712 0.248187i \(-0.920165\pi\)
0.714836 0.699292i \(-0.246501\pi\)
\(954\) −3.55524 + 2.05262i −0.115105 + 0.0664560i
\(955\) 34.7919 + 17.7423i 1.12584 + 0.574126i
\(956\) −11.2975 19.5679i −0.365388 0.632870i
\(957\) 30.6860 30.6860i 0.991937 0.991937i
\(958\) −0.822156 + 0.822156i −0.0265627 + 0.0265627i
\(959\) 2.76887 1.59861i 0.0894115 0.0516217i
\(960\) −2.18705 0.465647i −0.0705866 0.0150287i
\(961\) 23.6293 0.762235
\(962\) 3.04252 + 3.04252i 0.0980948 + 0.0980948i
\(963\) −4.59881 1.23225i −0.148194 0.0397086i
\(964\) −0.0463334 + 0.0802518i −0.00149230 + 0.00258474i
\(965\) 0.825099 3.87532i 0.0265609 0.124751i
\(966\) −0.360567 + 0.624520i −0.0116011 + 0.0200936i
\(967\) −0.603511 2.25233i −0.0194076 0.0724302i 0.955543 0.294852i \(-0.0952704\pi\)
−0.974950 + 0.222422i \(0.928604\pi\)
\(968\) 20.5662 20.5662i 0.661022 0.661022i
\(969\) −8.68674 + 12.1157i −0.279058 + 0.389214i
\(970\) 36.7682 1.91442i 1.18055 0.0614684i
\(971\) 1.20002 + 0.692830i 0.0385103 + 0.0222340i 0.519132 0.854694i \(-0.326255\pi\)
−0.480621 + 0.876928i \(0.659589\pi\)
\(972\) 0.965926 0.258819i 0.0309821 0.00830162i
\(973\) 1.65673 6.18299i 0.0531122 0.198217i
\(974\) −6.17275 3.56384i −0.197788 0.114193i
\(975\) −15.0553 + 10.9227i −0.482155 + 0.349807i
\(976\) 4.34262 0.139004
\(977\) −3.89608 3.89608i −0.124647 0.124647i 0.642032 0.766678i \(-0.278092\pi\)
−0.766678 + 0.642032i \(0.778092\pi\)
\(978\) 0.00745323 0.0278158i 0.000238328 0.000889453i
\(979\) 32.8082 + 56.8255i 1.04856 + 1.81615i
\(980\) −0.802699 15.4165i −0.0256413 0.492463i
\(981\) 10.0772i 0.321740i
\(982\) 3.22329 12.0295i 0.102859 0.383877i
\(983\) 0.266143 + 0.993259i 0.00848865 + 0.0316801i 0.970040 0.242944i \(-0.0781132\pi\)
−0.961552 + 0.274624i \(0.911447\pi\)
\(984\) −5.08802 8.81271i −0.162200 0.280939i
\(985\) 14.7276 4.77975i 0.469259 0.152295i
\(986\) 11.7214 20.3020i 0.373285 0.646549i
\(987\) 2.31375 + 2.31375i 0.0736476 + 0.0736476i
\(988\) 12.5372 10.2836i 0.398863 0.327166i
\(989\) 20.3321i 0.646523i
\(990\) 13.4657 4.37023i 0.427969 0.138895i
\(991\) 22.6210 + 13.0602i 0.718579 + 0.414872i 0.814230 0.580543i \(-0.197160\pi\)
−0.0956503 + 0.995415i \(0.530493\pi\)
\(992\) 2.62240 + 0.702670i 0.0832613 + 0.0223098i
\(993\) 1.57987 0.423325i 0.0501357 0.0134338i
\(994\) 0.356372 0.205752i 0.0113034 0.00652604i
\(995\) −17.0327 + 0.886849i −0.539973 + 0.0281150i
\(996\) 0.269510i 0.00853975i
\(997\) 0.0108030 + 0.00289465i 0.000342133 + 9.16743e-5i 0.258990 0.965880i \(-0.416610\pi\)
−0.258648 + 0.965972i \(0.583277\pi\)
\(998\) −20.3781 5.46030i −0.645058 0.172843i
\(999\) 1.15665i 0.0365947i
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 570.2.x.b.103.6 40
5.2 odd 4 inner 570.2.x.b.217.9 yes 40
19.12 odd 6 inner 570.2.x.b.373.9 yes 40
95.12 even 12 inner 570.2.x.b.487.6 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.x.b.103.6 40 1.1 even 1 trivial
570.2.x.b.217.9 yes 40 5.2 odd 4 inner
570.2.x.b.373.9 yes 40 19.12 odd 6 inner
570.2.x.b.487.6 yes 40 95.12 even 12 inner