Properties

Label 546.2.cg.b.271.6
Level $546$
Weight $2$
Character 546.271
Analytic conductor $4.360$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(145,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.145");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.cg (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: \(4.35983195036\)
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 271.6
Character \(\chi\) \(=\) 546.271
Dual form 546.2.cg.b.409.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.08192 - 4.03777i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.31184 - 2.29762i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.08192 - 4.03777i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.31184 - 2.29762i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.09010 - 3.62017i) q^{10} +(-0.163915 - 0.611738i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.96448 - 3.02338i) q^{13} +(0.697052 - 2.55228i) q^{14} +(1.08192 - 4.03777i) q^{15} -1.00000 q^{16} +5.91724 q^{17} +(-0.258819 + 0.965926i) q^{18} +(2.38683 + 0.639550i) q^{19} +(4.03777 - 1.08192i) q^{20} +(0.0127227 - 2.64572i) q^{21} +(0.316659 - 0.548469i) q^{22} -5.14888i q^{23} +(-0.965926 + 0.258819i) q^{24} +(-10.8029 + 6.23707i) q^{25} +(0.748759 - 3.52695i) q^{26} +1.00000i q^{27} +(2.29762 - 1.31184i) q^{28} +(-0.692966 - 1.20025i) q^{29} +(3.62017 - 2.09010i) q^{30} +(5.35833 + 1.43576i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.163915 - 0.611738i) q^{33} +(4.18412 + 4.18412i) q^{34} +(-7.85797 + 7.78276i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.59342 + 1.59342i) q^{37} +(1.23551 + 2.13997i) q^{38} +(-0.189595 - 3.60056i) q^{39} +(3.62017 + 2.09010i) q^{40} +(-1.22233 - 0.327523i) q^{41} +(1.87980 - 1.86181i) q^{42} +(-2.40764 - 1.39005i) q^{43} +(0.611738 - 0.163915i) q^{44} +(2.95585 - 2.95585i) q^{45} +(3.64081 - 3.64081i) q^{46} +(3.20911 - 0.859880i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.55814 + 6.02824i) q^{49} +(-12.0491 - 3.22855i) q^{50} +(5.12448 + 2.95862i) q^{51} +(3.02338 - 1.96448i) q^{52} +(5.96016 + 10.3233i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-2.29272 + 1.32370i) q^{55} +(2.55228 + 0.697052i) q^{56} +(1.74728 + 1.74728i) q^{57} +(0.358706 - 1.33871i) q^{58} +(8.53508 + 8.53508i) q^{59} +(4.03777 + 1.08192i) q^{60} +(-10.7264 + 6.19287i) q^{61} +(2.77367 + 4.80415i) q^{62} +(1.33388 - 2.28490i) q^{63} -1.00000i q^{64} +(-10.0823 + 11.2032i) q^{65} +(0.548469 - 0.316659i) q^{66} +(-6.13532 + 1.64395i) q^{67} +5.91724i q^{68} +(2.57444 - 4.45906i) q^{69} +(-11.0597 - 0.0531837i) q^{70} +(14.8816 - 3.98751i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(2.14685 - 8.01215i) q^{73} -2.25344 q^{74} -12.4741 q^{75} +(-0.639550 + 2.38683i) q^{76} +(-1.19051 + 1.17912i) q^{77} +(2.41192 - 2.68005i) q^{78} +(-0.213699 + 0.370137i) q^{79} +(1.08192 + 4.03777i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.632726 - 1.09591i) q^{82} +(5.72801 - 5.72801i) q^{83} +(2.64572 + 0.0127227i) q^{84} +(-6.40196 - 23.8925i) q^{85} +(-0.719544 - 2.68538i) q^{86} -1.38593i q^{87} +(0.548469 + 0.316659i) q^{88} +(-1.18693 - 1.18693i) q^{89} +4.18021 q^{90} +(-4.36951 + 8.47982i) q^{91} +5.14888 q^{92} +(3.92257 + 3.92257i) q^{93} +(2.87721 + 1.66116i) q^{94} -10.3294i q^{95} +(-0.258819 - 0.965926i) q^{96} +(-1.95617 - 7.30052i) q^{97} +(-6.77859 + 1.74662i) q^{98} +(0.447823 - 0.447823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 1.00000i 0.500000i
\(5\) −1.08192 4.03777i −0.483848 1.80575i −0.585192 0.810895i \(-0.698981\pi\)
0.101343 0.994851i \(-0.467686\pi\)
\(6\) 0.258819 + 0.965926i 0.105662 + 0.394338i
\(7\) −1.31184 2.29762i −0.495830 0.868420i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 2.09010 3.62017i 0.660949 1.14480i
\(11\) −0.163915 0.611738i −0.0494222 0.184446i 0.936802 0.349860i \(-0.113771\pi\)
−0.986224 + 0.165414i \(0.947104\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −1.96448 3.02338i −0.544848 0.838535i
\(14\) 0.697052 2.55228i 0.186295 0.682125i
\(15\) 1.08192 4.03777i 0.279350 1.04255i
\(16\) −1.00000 −0.250000
\(17\) 5.91724 1.43514 0.717570 0.696486i \(-0.245254\pi\)
0.717570 + 0.696486i \(0.245254\pi\)
\(18\) −0.258819 + 0.965926i −0.0610042 + 0.227671i
\(19\) 2.38683 + 0.639550i 0.547577 + 0.146723i 0.521993 0.852950i \(-0.325189\pi\)
0.0255840 + 0.999673i \(0.491855\pi\)
\(20\) 4.03777 1.08192i 0.902873 0.241924i
\(21\) 0.0127227 2.64572i 0.00277633 0.577344i
\(22\) 0.316659 0.548469i 0.0675119 0.116934i
\(23\) 5.14888i 1.07362i −0.843704 0.536808i \(-0.819630\pi\)
0.843704 0.536808i \(-0.180370\pi\)
\(24\) −0.965926 + 0.258819i −0.197169 + 0.0528312i
\(25\) −10.8029 + 6.23707i −2.16059 + 1.24741i
\(26\) 0.748759 3.52695i 0.146844 0.691691i
\(27\) 1.00000i 0.192450i
\(28\) 2.29762 1.31184i 0.434210 0.247915i
\(29\) −0.692966 1.20025i −0.128681 0.222881i 0.794485 0.607284i \(-0.207741\pi\)
−0.923166 + 0.384402i \(0.874408\pi\)
\(30\) 3.62017 2.09010i 0.660949 0.381599i
\(31\) 5.35833 + 1.43576i 0.962384 + 0.257870i 0.705609 0.708601i \(-0.250673\pi\)
0.256775 + 0.966471i \(0.417340\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0.163915 0.611738i 0.0285339 0.106490i
\(34\) 4.18412 + 4.18412i 0.717570 + 0.717570i
\(35\) −7.85797 + 7.78276i −1.32824 + 1.31553i
\(36\) −0.866025 + 0.500000i −0.144338 + 0.0833333i
\(37\) −1.59342 + 1.59342i −0.261957 + 0.261957i −0.825849 0.563892i \(-0.809304\pi\)
0.563892 + 0.825849i \(0.309304\pi\)
\(38\) 1.23551 + 2.13997i 0.200427 + 0.347150i
\(39\) −0.189595 3.60056i −0.0303595 0.576551i
\(40\) 3.62017 + 2.09010i 0.572399 + 0.330475i
\(41\) −1.22233 0.327523i −0.190896 0.0511505i 0.162104 0.986774i \(-0.448172\pi\)
−0.353000 + 0.935623i \(0.614839\pi\)
\(42\) 1.87980 1.86181i 0.290060 0.287284i
\(43\) −2.40764 1.39005i −0.367162 0.211981i 0.305056 0.952334i \(-0.401325\pi\)
−0.672218 + 0.740353i \(0.734658\pi\)
\(44\) 0.611738 0.163915i 0.0922230 0.0247111i
\(45\) 2.95585 2.95585i 0.440633 0.440633i
\(46\) 3.64081 3.64081i 0.536808 0.536808i
\(47\) 3.20911 0.859880i 0.468097 0.125426i −0.0170575 0.999855i \(-0.505430\pi\)
0.485155 + 0.874428i \(0.338763\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) −3.55814 + 6.02824i −0.508306 + 0.861177i
\(50\) −12.0491 3.22855i −1.70400 0.456585i
\(51\) 5.12448 + 2.95862i 0.717570 + 0.414289i
\(52\) 3.02338 1.96448i 0.419268 0.272424i
\(53\) 5.96016 + 10.3233i 0.818690 + 1.41801i 0.906647 + 0.421889i \(0.138633\pi\)
−0.0879571 + 0.996124i \(0.528034\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −2.29272 + 1.32370i −0.309150 + 0.178488i
\(56\) 2.55228 + 0.697052i 0.341062 + 0.0931475i
\(57\) 1.74728 + 1.74728i 0.231433 + 0.231433i
\(58\) 0.358706 1.33871i 0.0471003 0.175781i
\(59\) 8.53508 + 8.53508i 1.11117 + 1.11117i 0.992992 + 0.118181i \(0.0377063\pi\)
0.118181 + 0.992992i \(0.462294\pi\)
\(60\) 4.03777 + 1.08192i 0.521274 + 0.139675i
\(61\) −10.7264 + 6.19287i −1.37337 + 0.792916i −0.991351 0.131239i \(-0.958105\pi\)
−0.382020 + 0.924154i \(0.624771\pi\)
\(62\) 2.77367 + 4.80415i 0.352257 + 0.610127i
\(63\) 1.33388 2.28490i 0.168053 0.287870i
\(64\) 1.00000i 0.125000i
\(65\) −10.0823 + 11.2032i −1.25056 + 1.38958i
\(66\) 0.548469 0.316659i 0.0675119 0.0389780i
\(67\) −6.13532 + 1.64395i −0.749548 + 0.200841i −0.613318 0.789836i \(-0.710165\pi\)
−0.136231 + 0.990677i \(0.543499\pi\)
\(68\) 5.91724i 0.717570i
\(69\) 2.57444 4.45906i 0.309926 0.536808i
\(70\) −11.0597 0.0531837i −1.32188 0.00635667i
\(71\) 14.8816 3.98751i 1.76612 0.473231i 0.778178 0.628044i \(-0.216144\pi\)
0.987944 + 0.154813i \(0.0494776\pi\)
\(72\) −0.965926 0.258819i −0.113835 0.0305021i
\(73\) 2.14685 8.01215i 0.251270 0.937752i −0.718858 0.695157i \(-0.755335\pi\)
0.970128 0.242595i \(-0.0779985\pi\)
\(74\) −2.25344 −0.261957
\(75\) −12.4741 −1.44039
\(76\) −0.639550 + 2.38683i −0.0733614 + 0.273788i
\(77\) −1.19051 + 1.17912i −0.135672 + 0.134373i
\(78\) 2.41192 2.68005i 0.273096 0.303456i
\(79\) −0.213699 + 0.370137i −0.0240430 + 0.0416437i −0.877797 0.479034i \(-0.840987\pi\)
0.853754 + 0.520677i \(0.174321\pi\)
\(80\) 1.08192 + 4.03777i 0.120962 + 0.451437i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.632726 1.09591i −0.0698729 0.121023i
\(83\) 5.72801 5.72801i 0.628731 0.628731i −0.319018 0.947749i \(-0.603353\pi\)
0.947749 + 0.319018i \(0.103353\pi\)
\(84\) 2.64572 + 0.0127227i 0.288672 + 0.00138817i
\(85\) −6.40196 23.8925i −0.694390 2.59150i
\(86\) −0.719544 2.68538i −0.0775904 0.289571i
\(87\) 1.38593i 0.148587i
\(88\) 0.548469 + 0.316659i 0.0584670 + 0.0337560i
\(89\) −1.18693 1.18693i −0.125814 0.125814i 0.641396 0.767210i \(-0.278356\pi\)
−0.767210 + 0.641396i \(0.778356\pi\)
\(90\) 4.18021 0.440633
\(91\) −4.36951 + 8.47982i −0.458049 + 0.888927i
\(92\) 5.14888 0.536808
\(93\) 3.92257 + 3.92257i 0.406751 + 0.406751i
\(94\) 2.87721 + 1.66116i 0.296762 + 0.171336i
\(95\) 10.3294i 1.05978i
\(96\) −0.258819 0.965926i −0.0264156 0.0985844i
\(97\) −1.95617 7.30052i −0.198619 0.741256i −0.991300 0.131620i \(-0.957982\pi\)
0.792681 0.609636i \(-0.208684\pi\)
\(98\) −6.77859 + 1.74662i −0.684741 + 0.176435i
\(99\) 0.447823 0.447823i 0.0450079 0.0450079i
\(100\) −6.23707 10.8029i −0.623707 1.08029i
\(101\) 2.10015 3.63757i 0.208973 0.361951i −0.742418 0.669936i \(-0.766321\pi\)
0.951391 + 0.307985i \(0.0996547\pi\)
\(102\) 1.53149 + 5.71561i 0.151640 + 0.565930i
\(103\) −0.712002 + 1.23322i −0.0701556 + 0.121513i −0.898969 0.438011i \(-0.855683\pi\)
0.828814 + 0.559525i \(0.189016\pi\)
\(104\) 3.52695 + 0.748759i 0.345846 + 0.0734219i
\(105\) −10.6966 + 2.81108i −1.04388 + 0.274333i
\(106\) −3.08520 + 11.5141i −0.299661 + 1.11835i
\(107\) −10.9568 −1.05923 −0.529616 0.848237i \(-0.677664\pi\)
−0.529616 + 0.848237i \(0.677664\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −0.300729 + 1.12234i −0.0288046 + 0.107500i −0.978831 0.204668i \(-0.934389\pi\)
0.950027 + 0.312168i \(0.101055\pi\)
\(110\) −2.55719 0.685198i −0.243819 0.0653310i
\(111\) −2.17666 + 0.583233i −0.206599 + 0.0553581i
\(112\) 1.31184 + 2.29762i 0.123957 + 0.217105i
\(113\) −8.19504 + 14.1942i −0.770925 + 1.33528i 0.166132 + 0.986104i \(0.446872\pi\)
−0.937057 + 0.349177i \(0.886461\pi\)
\(114\) 2.47103i 0.231433i
\(115\) −20.7900 + 5.57067i −1.93868 + 0.519467i
\(116\) 1.20025 0.692966i 0.111441 0.0643403i
\(117\) 1.63609 3.21298i 0.151256 0.297040i
\(118\) 12.0704i 1.11117i
\(119\) −7.76248 13.5956i −0.711586 1.24630i
\(120\) 2.09010 + 3.62017i 0.190800 + 0.330475i
\(121\) 9.17892 5.29945i 0.834448 0.481769i
\(122\) −11.9637 3.20567i −1.08314 0.290227i
\(123\) −0.894810 0.894810i −0.0806823 0.0806823i
\(124\) −1.43576 + 5.35833i −0.128935 + 0.481192i
\(125\) 22.0925 + 22.0925i 1.97601 + 1.97601i
\(126\) 2.55886 0.672474i 0.227962 0.0599087i
\(127\) 15.9441 9.20531i 1.41481 0.816839i 0.418971 0.908000i \(-0.362391\pi\)
0.995836 + 0.0911603i \(0.0290576\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −1.39005 2.40764i −0.122387 0.211981i
\(130\) −15.0511 + 0.792548i −1.32007 + 0.0695111i
\(131\) 9.34579 + 5.39580i 0.816546 + 0.471433i 0.849224 0.528033i \(-0.177070\pi\)
−0.0326781 + 0.999466i \(0.510404\pi\)
\(132\) 0.611738 + 0.163915i 0.0532450 + 0.0142669i
\(133\) −1.66170 6.32303i −0.144088 0.548276i
\(134\) −5.50077 3.17587i −0.475195 0.274354i
\(135\) 4.03777 1.08192i 0.347516 0.0931166i
\(136\) −4.18412 + 4.18412i −0.358785 + 0.358785i
\(137\) 10.5293 10.5293i 0.899580 0.899580i −0.0958184 0.995399i \(-0.530547\pi\)
0.995399 + 0.0958184i \(0.0305468\pi\)
\(138\) 4.97344 1.33263i 0.423367 0.113441i
\(139\) 8.18822 + 4.72747i 0.694516 + 0.400979i 0.805302 0.592865i \(-0.202003\pi\)
−0.110786 + 0.993844i \(0.535337\pi\)
\(140\) −7.78276 7.85797i −0.657763 0.664120i
\(141\) 3.20911 + 0.859880i 0.270256 + 0.0724149i
\(142\) 13.3425 + 7.70329i 1.11968 + 0.646445i
\(143\) −1.52751 + 1.69732i −0.127737 + 0.141937i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.09661 + 4.09661i −0.340205 + 0.340205i
\(146\) 7.18350 4.14740i 0.594511 0.343241i
\(147\) −6.09556 + 3.44154i −0.502753 + 0.283853i
\(148\) −1.59342 1.59342i −0.130979 0.130979i
\(149\) −3.63073 + 13.5501i −0.297441 + 1.11006i 0.641819 + 0.766856i \(0.278180\pi\)
−0.939260 + 0.343207i \(0.888487\pi\)
\(150\) −8.82055 8.82055i −0.720195 0.720195i
\(151\) −7.09882 1.90212i −0.577694 0.154793i −0.0418710 0.999123i \(-0.513332\pi\)
−0.535823 + 0.844330i \(0.679999\pi\)
\(152\) −2.13997 + 1.23551i −0.173575 + 0.100213i
\(153\) 2.95862 + 5.12448i 0.239190 + 0.414289i
\(154\) −1.67558 0.00805754i −0.135022 0.000649295i
\(155\) 23.1891i 1.86259i
\(156\) 3.60056 0.189595i 0.288276 0.0151798i
\(157\) −18.5419 + 10.7052i −1.47980 + 0.854365i −0.999738 0.0228679i \(-0.992720\pi\)
−0.480065 + 0.877233i \(0.659387\pi\)
\(158\) −0.412834 + 0.110619i −0.0328433 + 0.00880035i
\(159\) 11.9203i 0.945342i
\(160\) −2.09010 + 3.62017i −0.165237 + 0.286199i
\(161\) −11.8302 + 6.75452i −0.932350 + 0.532331i
\(162\) −0.965926 + 0.258819i −0.0758903 + 0.0203347i
\(163\) 0.215258 + 0.0576783i 0.0168603 + 0.00451771i 0.267239 0.963630i \(-0.413889\pi\)
−0.250379 + 0.968148i \(0.580555\pi\)
\(164\) 0.327523 1.22233i 0.0255753 0.0954481i
\(165\) −2.64740 −0.206100
\(166\) 8.10063 0.628731
\(167\) 4.93109 18.4031i 0.381579 1.42407i −0.461909 0.886927i \(-0.652835\pi\)
0.843489 0.537147i \(-0.180498\pi\)
\(168\) 1.86181 + 1.87980i 0.143642 + 0.145030i
\(169\) −5.28167 + 11.8787i −0.406282 + 0.913748i
\(170\) 12.3676 21.4214i 0.948555 1.64295i
\(171\) 0.639550 + 2.38683i 0.0489076 + 0.182526i
\(172\) 1.39005 2.40764i 0.105991 0.183581i
\(173\) 7.60190 + 13.1669i 0.577962 + 1.00106i 0.995713 + 0.0924977i \(0.0294851\pi\)
−0.417751 + 0.908562i \(0.637182\pi\)
\(174\) 0.980002 0.980002i 0.0742937 0.0742937i
\(175\) 28.5022 + 16.6390i 2.15456 + 1.25779i
\(176\) 0.163915 + 0.611738i 0.0123555 + 0.0461115i
\(177\) 3.12406 + 11.6591i 0.234818 + 0.876354i
\(178\) 1.67857i 0.125814i
\(179\) −18.0069 10.3963i −1.34590 0.777054i −0.358232 0.933633i \(-0.616620\pi\)
−0.987666 + 0.156579i \(0.949954\pi\)
\(180\) 2.95585 + 2.95585i 0.220316 + 0.220316i
\(181\) 19.5707 1.45468 0.727340 0.686278i \(-0.240757\pi\)
0.727340 + 0.686278i \(0.240757\pi\)
\(182\) −9.08585 + 2.90643i −0.673488 + 0.215439i
\(183\) −12.3857 −0.915580
\(184\) 3.64081 + 3.64081i 0.268404 + 0.268404i
\(185\) 8.15783 + 4.70993i 0.599776 + 0.346281i
\(186\) 5.54735i 0.406751i
\(187\) −0.969922 3.61980i −0.0709278 0.264706i
\(188\) 0.859880 + 3.20911i 0.0627132 + 0.234049i
\(189\) 2.29762 1.31184i 0.167127 0.0954225i
\(190\) 7.30400 7.30400i 0.529888 0.529888i
\(191\) −2.63634 4.56628i −0.190759 0.330404i 0.754743 0.656021i \(-0.227762\pi\)
−0.945502 + 0.325616i \(0.894428\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 3.53613 + 13.1970i 0.254536 + 0.949943i 0.968348 + 0.249605i \(0.0803007\pi\)
−0.713812 + 0.700338i \(0.753033\pi\)
\(194\) 3.77903 6.54547i 0.271319 0.469937i
\(195\) −14.3331 + 4.66106i −1.02642 + 0.333785i
\(196\) −6.02824 3.55814i −0.430588 0.254153i
\(197\) 3.27692 12.2296i 0.233471 0.871325i −0.745362 0.666660i \(-0.767723\pi\)
0.978832 0.204664i \(-0.0656102\pi\)
\(198\) 0.633318 0.0450079
\(199\) −5.99676 −0.425099 −0.212549 0.977150i \(-0.568177\pi\)
−0.212549 + 0.977150i \(0.568177\pi\)
\(200\) 3.22855 12.0491i 0.228293 0.852000i
\(201\) −6.13532 1.64395i −0.432752 0.115956i
\(202\) 4.05718 1.08712i 0.285462 0.0764893i
\(203\) −1.84866 + 3.16672i −0.129751 + 0.222260i
\(204\) −2.95862 + 5.12448i −0.207145 + 0.358785i
\(205\) 5.28985i 0.369459i
\(206\) −1.37548 + 0.368559i −0.0958344 + 0.0256787i
\(207\) 4.45906 2.57444i 0.309926 0.178936i
\(208\) 1.96448 + 3.02338i 0.136212 + 0.209634i
\(209\) 1.56495i 0.108250i
\(210\) −9.55136 5.57589i −0.659106 0.384773i
\(211\) 10.5594 + 18.2895i 0.726941 + 1.25910i 0.958170 + 0.286199i \(0.0923918\pi\)
−0.231230 + 0.972899i \(0.574275\pi\)
\(212\) −10.3233 + 5.96016i −0.709007 + 0.409345i
\(213\) 14.8816 + 3.98751i 1.01967 + 0.273220i
\(214\) −7.74762 7.74762i −0.529616 0.529616i
\(215\) −3.00784 + 11.2254i −0.205133 + 0.765568i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −3.73045 14.1949i −0.253239 0.963613i
\(218\) −1.00626 + 0.580963i −0.0681524 + 0.0393478i
\(219\) 5.86530 5.86530i 0.396340 0.396340i
\(220\) −1.32370 2.29272i −0.0892439 0.154575i
\(221\) −11.6243 17.8901i −0.781933 1.20342i
\(222\) −1.95154 1.12672i −0.130979 0.0756205i
\(223\) −18.8580 5.05298i −1.26282 0.338373i −0.435547 0.900166i \(-0.643445\pi\)
−0.827277 + 0.561794i \(0.810112\pi\)
\(224\) −0.697052 + 2.55228i −0.0465738 + 0.170531i
\(225\) −10.8029 6.23707i −0.720195 0.415805i
\(226\) −15.8316 + 4.24207i −1.05310 + 0.282178i
\(227\) 14.2857 14.2857i 0.948178 0.948178i −0.0505434 0.998722i \(-0.516095\pi\)
0.998722 + 0.0505434i \(0.0160953\pi\)
\(228\) −1.74728 + 1.74728i −0.115717 + 0.115717i
\(229\) −1.82487 + 0.488972i −0.120591 + 0.0323122i −0.318610 0.947886i \(-0.603216\pi\)
0.198019 + 0.980198i \(0.436549\pi\)
\(230\) −18.6398 10.7617i −1.22907 0.709606i
\(231\) −1.62057 + 0.425890i −0.106626 + 0.0280215i
\(232\) 1.33871 + 0.358706i 0.0878904 + 0.0235502i
\(233\) 0.334379 + 0.193054i 0.0219059 + 0.0126474i 0.510913 0.859632i \(-0.329307\pi\)
−0.489007 + 0.872280i \(0.662641\pi\)
\(234\) 3.42881 1.11503i 0.224148 0.0728917i
\(235\) −6.94400 12.0274i −0.452976 0.784578i
\(236\) −8.53508 + 8.53508i −0.555586 + 0.555586i
\(237\) −0.370137 + 0.213699i −0.0240430 + 0.0138812i
\(238\) 4.12462 15.1024i 0.267360 0.978945i
\(239\) 4.60738 + 4.60738i 0.298027 + 0.298027i 0.840241 0.542214i \(-0.182414\pi\)
−0.542214 + 0.840241i \(0.682414\pi\)
\(240\) −1.08192 + 4.03777i −0.0698375 + 0.260637i
\(241\) 10.5802 + 10.5802i 0.681530 + 0.681530i 0.960345 0.278815i \(-0.0899416\pi\)
−0.278815 + 0.960345i \(0.589942\pi\)
\(242\) 10.2378 + 2.74320i 0.658108 + 0.176340i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −6.19287 10.7264i −0.396458 0.686685i
\(245\) 28.1903 + 7.84490i 1.80101 + 0.501192i
\(246\) 1.26545i 0.0806823i
\(247\) −2.75527 8.47268i −0.175314 0.539104i
\(248\) −4.80415 + 2.77367i −0.305064 + 0.176129i
\(249\) 7.82461 2.09660i 0.495865 0.132867i
\(250\) 31.2435i 1.97601i
\(251\) 7.83244 13.5662i 0.494379 0.856290i −0.505600 0.862768i \(-0.668729\pi\)
0.999979 + 0.00647817i \(0.00206208\pi\)
\(252\) 2.28490 + 1.33388i 0.143935 + 0.0840265i
\(253\) −3.14977 + 0.843978i −0.198024 + 0.0530604i
\(254\) 17.7833 + 4.76502i 1.11582 + 0.298984i
\(255\) 6.40196 23.8925i 0.400907 1.49620i
\(256\) 1.00000 0.0625000
\(257\) 28.6976 1.79011 0.895055 0.445956i \(-0.147136\pi\)
0.895055 + 0.445956i \(0.147136\pi\)
\(258\) 0.719544 2.68538i 0.0447969 0.167184i
\(259\) 5.75140 + 1.57077i 0.357375 + 0.0976026i
\(260\) −11.2032 10.0823i −0.694790 0.625279i
\(261\) 0.692966 1.20025i 0.0428935 0.0742937i
\(262\) 2.79307 + 10.4239i 0.172556 + 0.643989i
\(263\) −6.02517 + 10.4359i −0.371528 + 0.643505i −0.989801 0.142458i \(-0.954499\pi\)
0.618273 + 0.785963i \(0.287833\pi\)
\(264\) 0.316659 + 0.548469i 0.0194890 + 0.0337560i
\(265\) 35.2347 35.2347i 2.16445 2.16445i
\(266\) 3.29605 5.64606i 0.202094 0.346182i
\(267\) −0.434447 1.62138i −0.0265877 0.0992268i
\(268\) −1.64395 6.13532i −0.100420 0.374774i
\(269\) 1.83319i 0.111771i −0.998437 0.0558857i \(-0.982202\pi\)
0.998437 0.0558857i \(-0.0177983\pi\)
\(270\) 3.62017 + 2.09010i 0.220316 + 0.127200i
\(271\) −10.6003 10.6003i −0.643924 0.643924i 0.307594 0.951518i \(-0.400476\pi\)
−0.951518 + 0.307594i \(0.900476\pi\)
\(272\) −5.91724 −0.358785
\(273\) −8.02402 + 5.15899i −0.485636 + 0.312236i
\(274\) 14.8907 0.899580
\(275\) 5.58621 + 5.58621i 0.336861 + 0.336861i
\(276\) 4.45906 + 2.57444i 0.268404 + 0.154963i
\(277\) 5.82993i 0.350287i −0.984543 0.175143i \(-0.943961\pi\)
0.984543 0.175143i \(-0.0560389\pi\)
\(278\) 2.44712 + 9.13277i 0.146768 + 0.547747i
\(279\) 1.43576 + 5.35833i 0.0859567 + 0.320795i
\(280\) 0.0531837 11.0597i 0.00317834 0.660941i
\(281\) −17.7789 + 17.7789i −1.06060 + 1.06060i −0.0625584 + 0.998041i \(0.519926\pi\)
−0.998041 + 0.0625584i \(0.980074\pi\)
\(282\) 1.66116 + 2.87721i 0.0989206 + 0.171336i
\(283\) −6.89348 + 11.9399i −0.409775 + 0.709751i −0.994864 0.101218i \(-0.967726\pi\)
0.585089 + 0.810969i \(0.301059\pi\)
\(284\) 3.98751 + 14.8816i 0.236615 + 0.883061i
\(285\) 5.16471 8.94554i 0.305931 0.529888i
\(286\) −2.28030 + 0.120074i −0.134837 + 0.00710013i
\(287\) 0.850983 + 3.23812i 0.0502319 + 0.191140i
\(288\) 0.258819 0.965926i 0.0152511 0.0569177i
\(289\) 18.0137 1.05963
\(290\) −5.79348 −0.340205
\(291\) 1.95617 7.30052i 0.114673 0.427964i
\(292\) 8.01215 + 2.14685i 0.468876 + 0.125635i
\(293\) −3.06465 + 0.821170i −0.179039 + 0.0479733i −0.347224 0.937782i \(-0.612876\pi\)
0.168186 + 0.985755i \(0.446209\pi\)
\(294\) −6.74374 1.87668i −0.393303 0.109450i
\(295\) 25.2285 43.6970i 1.46886 2.54414i
\(296\) 2.25344i 0.130979i
\(297\) 0.611738 0.163915i 0.0354966 0.00951130i
\(298\) −12.1486 + 7.01402i −0.703752 + 0.406311i
\(299\) −15.5670 + 10.1149i −0.900265 + 0.584957i
\(300\) 12.4741i 0.720195i
\(301\) −0.0353706 + 7.35538i −0.00203873 + 0.423957i
\(302\) −3.67462 6.36463i −0.211451 0.366243i
\(303\) 3.63757 2.10015i 0.208973 0.120650i
\(304\) −2.38683 0.639550i −0.136894 0.0366807i
\(305\) 36.6104 + 36.6104i 2.09631 + 2.09631i
\(306\) −1.53149 + 5.71561i −0.0875497 + 0.326740i
\(307\) 10.5351 + 10.5351i 0.601271 + 0.601271i 0.940650 0.339378i \(-0.110217\pi\)
−0.339378 + 0.940650i \(0.610217\pi\)
\(308\) −1.17912 1.19051i −0.0671865 0.0678358i
\(309\) −1.23322 + 0.712002i −0.0701556 + 0.0405044i
\(310\) 16.3972 16.3972i 0.931296 0.931296i
\(311\) −16.6841 28.8977i −0.946069 1.63864i −0.753596 0.657338i \(-0.771683\pi\)
−0.192473 0.981302i \(-0.561651\pi\)
\(312\) 2.68005 + 2.41192i 0.151728 + 0.136548i
\(313\) 1.72540 + 0.996161i 0.0975254 + 0.0563063i 0.547969 0.836498i \(-0.315401\pi\)
−0.450444 + 0.892805i \(0.648734\pi\)
\(314\) −20.6808 5.54140i −1.16708 0.312719i
\(315\) −10.6691 2.91382i −0.601133 0.164175i
\(316\) −0.370137 0.213699i −0.0208218 0.0120215i
\(317\) −20.4735 + 5.48586i −1.14991 + 0.308116i −0.782927 0.622113i \(-0.786274\pi\)
−0.366979 + 0.930229i \(0.619608\pi\)
\(318\) −8.42893 + 8.42893i −0.472671 + 0.472671i
\(319\) −0.620653 + 0.620653i −0.0347499 + 0.0347499i
\(320\) −4.03777 + 1.08192i −0.225718 + 0.0604810i
\(321\) −9.48886 5.47839i −0.529616 0.305774i
\(322\) −13.1414 3.58904i −0.732340 0.200009i
\(323\) 14.1234 + 3.78437i 0.785850 + 0.210568i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) 40.0791 + 20.4088i 2.22319 + 1.13208i
\(326\) 0.111426 + 0.192995i 0.00617131 + 0.0106890i
\(327\) −0.821606 + 0.821606i −0.0454349 + 0.0454349i
\(328\) 1.09591 0.632726i 0.0605117 0.0349364i
\(329\) −6.18553 6.24531i −0.341019 0.344315i
\(330\) −1.87200 1.87200i −0.103050 0.103050i
\(331\) 2.42975 9.06797i 0.133551 0.498421i −0.866448 0.499267i \(-0.833603\pi\)
1.00000 0.000846312i \(0.000269389\pi\)
\(332\) 5.72801 + 5.72801i 0.314366 + 0.314366i
\(333\) −2.17666 0.583233i −0.119280 0.0319610i
\(334\) 16.4998 9.52614i 0.902827 0.521247i
\(335\) 13.2758 + 22.9944i 0.725335 + 1.25632i
\(336\) −0.0127227 + 2.64572i −0.000694083 + 0.144336i
\(337\) 15.7627i 0.858648i −0.903151 0.429324i \(-0.858752\pi\)
0.903151 0.429324i \(-0.141248\pi\)
\(338\) −12.1342 + 4.66482i −0.660015 + 0.253733i
\(339\) −14.1942 + 8.19504i −0.770925 + 0.445094i
\(340\) 23.8925 6.40196i 1.29575 0.347195i
\(341\) 3.51324i 0.190252i
\(342\) −1.23551 + 2.13997i −0.0668090 + 0.115717i
\(343\) 18.5183 + 0.267169i 0.999896 + 0.0144258i
\(344\) 2.68538 0.719544i 0.144786 0.0387952i
\(345\) −20.7900 5.57067i −1.11930 0.299915i
\(346\) −3.93503 + 14.6857i −0.211549 + 0.789510i
\(347\) 6.89050 0.369902 0.184951 0.982748i \(-0.440787\pi\)
0.184951 + 0.982748i \(0.440787\pi\)
\(348\) 1.38593 0.0742937
\(349\) −5.86607 + 21.8925i −0.314004 + 1.17188i 0.610910 + 0.791700i \(0.290804\pi\)
−0.924913 + 0.380178i \(0.875863\pi\)
\(350\) 8.38854 + 31.9196i 0.448386 + 1.70618i
\(351\) 3.02338 1.96448i 0.161376 0.104856i
\(352\) −0.316659 + 0.548469i −0.0168780 + 0.0292335i
\(353\) 0.240340 + 0.896962i 0.0127920 + 0.0477405i 0.972027 0.234870i \(-0.0754664\pi\)
−0.959235 + 0.282610i \(0.908800\pi\)
\(354\) −6.03521 + 10.4533i −0.320768 + 0.555586i
\(355\) −32.2013 55.7744i −1.70907 2.96020i
\(356\) 1.18693 1.18693i 0.0629072 0.0629072i
\(357\) 0.0752835 15.6554i 0.00398443 0.828569i
\(358\) −5.38151 20.0841i −0.284422 1.06148i
\(359\) −1.68034 6.27110i −0.0886847 0.330976i 0.907302 0.420480i \(-0.138138\pi\)
−0.995986 + 0.0895044i \(0.971472\pi\)
\(360\) 4.18021i 0.220316i
\(361\) −11.1665 6.44701i −0.587713 0.339316i
\(362\) 13.8386 + 13.8386i 0.727340 + 0.727340i
\(363\) 10.5989 0.556298
\(364\) −8.47982 4.36951i −0.444464 0.229024i
\(365\) −34.6740 −1.81492
\(366\) −8.75804 8.75804i −0.457790 0.457790i
\(367\) 22.5233 + 13.0038i 1.17571 + 0.678794i 0.955017 0.296550i \(-0.0958361\pi\)
0.220689 + 0.975344i \(0.429169\pi\)
\(368\) 5.14888i 0.268404i
\(369\) −0.327523 1.22233i −0.0170502 0.0636321i
\(370\) 2.43804 + 9.09888i 0.126748 + 0.473028i
\(371\) 15.9002 27.2367i 0.825500 1.41406i
\(372\) −3.92257 + 3.92257i −0.203376 + 0.203376i
\(373\) 12.8602 + 22.2745i 0.665876 + 1.15333i 0.979047 + 0.203634i \(0.0652752\pi\)
−0.313172 + 0.949697i \(0.601391\pi\)
\(374\) 1.87375 3.24542i 0.0968891 0.167817i
\(375\) 8.08641 + 30.1789i 0.417581 + 1.55843i
\(376\) −1.66116 + 2.87721i −0.0856678 + 0.148381i
\(377\) −2.26751 + 4.45297i −0.116782 + 0.229339i
\(378\) 2.55228 + 0.697052i 0.131275 + 0.0358525i
\(379\) −7.60010 + 28.3640i −0.390391 + 1.45696i 0.439100 + 0.898438i \(0.355297\pi\)
−0.829491 + 0.558520i \(0.811369\pi\)
\(380\) 10.3294 0.529888
\(381\) 18.4106 0.943205
\(382\) 1.36467 5.09302i 0.0698226 0.260582i
\(383\) −12.2027 3.26972i −0.623531 0.167075i −0.0667987 0.997766i \(-0.521279\pi\)
−0.556733 + 0.830692i \(0.687945\pi\)
\(384\) 0.965926 0.258819i 0.0492922 0.0132078i
\(385\) 6.04905 + 3.53131i 0.308288 + 0.179972i
\(386\) −6.83128 + 11.8321i −0.347703 + 0.602239i
\(387\) 2.78010i 0.141321i
\(388\) 7.30052 1.95617i 0.370628 0.0993095i
\(389\) −12.5800 + 7.26305i −0.637830 + 0.368251i −0.783778 0.621041i \(-0.786710\pi\)
0.145948 + 0.989292i \(0.453377\pi\)
\(390\) −13.4309 6.83919i −0.680101 0.346316i
\(391\) 30.4672i 1.54079i
\(392\) −1.74662 6.77859i −0.0882177 0.342371i
\(393\) 5.39580 + 9.34579i 0.272182 + 0.471433i
\(394\) 10.9648 6.33052i 0.552398 0.318927i
\(395\) 1.72573 + 0.462409i 0.0868311 + 0.0232663i
\(396\) 0.447823 + 0.447823i 0.0225040 + 0.0225040i
\(397\) −1.39851 + 5.21930i −0.0701890 + 0.261949i −0.992099 0.125454i \(-0.959961\pi\)
0.921910 + 0.387403i \(0.126628\pi\)
\(398\) −4.24035 4.24035i −0.212549 0.212549i
\(399\) 1.72244 6.30675i 0.0862297 0.315733i
\(400\) 10.8029 6.23707i 0.540146 0.311854i
\(401\) −2.89768 + 2.89768i −0.144703 + 0.144703i −0.775747 0.631044i \(-0.782627\pi\)
0.631044 + 0.775747i \(0.282627\pi\)
\(402\) −3.17587 5.50077i −0.158398 0.274354i
\(403\) −6.18546 19.0208i −0.308120 0.947493i
\(404\) 3.63757 + 2.10015i 0.180976 + 0.104486i
\(405\) 4.03777 + 1.08192i 0.200638 + 0.0537609i
\(406\) −3.54641 + 0.932003i −0.176005 + 0.0462545i
\(407\) 1.23594 + 0.713572i 0.0612634 + 0.0353705i
\(408\) −5.71561 + 1.53149i −0.282965 + 0.0758202i
\(409\) 0.0881259 0.0881259i 0.00435754 0.00435754i −0.704925 0.709282i \(-0.749019\pi\)
0.709282 + 0.704925i \(0.249019\pi\)
\(410\) −3.74049 + 3.74049i −0.184730 + 0.184730i
\(411\) 14.3833 3.85400i 0.709477 0.190104i
\(412\) −1.23322 0.712002i −0.0607566 0.0350778i
\(413\) 8.41372 30.8071i 0.414012 1.51592i
\(414\) 4.97344 + 1.33263i 0.244431 + 0.0654951i
\(415\) −29.3256 16.9312i −1.43954 0.831118i
\(416\) −0.748759 + 3.52695i −0.0367109 + 0.172923i
\(417\) 4.72747 + 8.18822i 0.231505 + 0.400979i
\(418\) 1.10658 1.10658i 0.0541248 0.0541248i
\(419\) −3.80264 + 2.19546i −0.185771 + 0.107255i −0.590001 0.807402i \(-0.700873\pi\)
0.404230 + 0.914657i \(0.367539\pi\)
\(420\) −2.81108 10.6966i −0.137167 0.521940i
\(421\) −22.1184 22.1184i −1.07799 1.07799i −0.996690 0.0812959i \(-0.974094\pi\)
−0.0812959 0.996690i \(-0.525906\pi\)
\(422\) −5.46596 + 20.3992i −0.266079 + 0.993019i
\(423\) 2.34923 + 2.34923i 0.114224 + 0.114224i
\(424\) −11.5141 3.08520i −0.559176 0.149831i
\(425\) −63.9235 + 36.9062i −3.10074 + 1.79022i
\(426\) 7.70329 + 13.3425i 0.373225 + 0.646445i
\(427\) 28.3002 + 16.5211i 1.36954 + 0.799511i
\(428\) 10.9568i 0.529616i
\(429\) −2.17152 + 0.706168i −0.104842 + 0.0340941i
\(430\) −10.0644 + 5.81071i −0.485351 + 0.280217i
\(431\) 11.0657 2.96504i 0.533014 0.142821i 0.0177345 0.999843i \(-0.494355\pi\)
0.515280 + 0.857022i \(0.327688\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −5.94636 + 10.2994i −0.285764 + 0.494958i −0.972794 0.231671i \(-0.925581\pi\)
0.687030 + 0.726629i \(0.258914\pi\)
\(434\) 7.39949 12.6751i 0.355187 0.608426i
\(435\) −5.59608 + 1.49946i −0.268311 + 0.0718938i
\(436\) −1.12234 0.300729i −0.0537501 0.0144023i
\(437\) 3.29297 12.2895i 0.157524 0.587887i
\(438\) 8.29479 0.396340
\(439\) 8.61975 0.411398 0.205699 0.978615i \(-0.434053\pi\)
0.205699 + 0.978615i \(0.434053\pi\)
\(440\) 0.685198 2.55719i 0.0326655 0.121909i
\(441\) −6.99968 0.0673217i −0.333318 0.00320579i
\(442\) 4.43059 20.8698i 0.210742 0.992675i
\(443\) −4.22436 + 7.31680i −0.200705 + 0.347632i −0.948756 0.316010i \(-0.897657\pi\)
0.748051 + 0.663642i \(0.230990\pi\)
\(444\) −0.583233 2.17666i −0.0276790 0.103300i
\(445\) −3.50840 + 6.07672i −0.166314 + 0.288064i
\(446\) −9.76161 16.9076i −0.462226 0.800598i
\(447\) −9.91933 + 9.91933i −0.469168 + 0.469168i
\(448\) −2.29762 + 1.31184i −0.108552 + 0.0619787i
\(449\) −2.32879 8.69115i −0.109902 0.410161i 0.888953 0.457999i \(-0.151434\pi\)
−0.998855 + 0.0478379i \(0.984767\pi\)
\(450\) −3.22855 12.0491i −0.152195 0.568000i
\(451\) 0.801433i 0.0377380i
\(452\) −14.1942 8.19504i −0.667640 0.385462i
\(453\) −5.19670 5.19670i −0.244162 0.244162i
\(454\) 20.2031 0.948178
\(455\) 38.9670 + 8.46860i 1.82680 + 0.397014i
\(456\) −2.47103 −0.115717
\(457\) −13.0992 13.0992i −0.612755 0.612755i 0.330908 0.943663i \(-0.392645\pi\)
−0.943663 + 0.330908i \(0.892645\pi\)
\(458\) −1.63613 0.944621i −0.0764514 0.0441392i
\(459\) 5.91724i 0.276193i
\(460\) −5.57067 20.7900i −0.259734 0.969340i
\(461\) −10.7940 40.2836i −0.502725 1.87620i −0.481548 0.876420i \(-0.659925\pi\)
−0.0211769 0.999776i \(-0.506741\pi\)
\(462\) −1.44707 0.844769i −0.0673237 0.0393022i
\(463\) −12.7149 + 12.7149i −0.590912 + 0.590912i −0.937878 0.346966i \(-0.887212\pi\)
0.346966 + 0.937878i \(0.387212\pi\)
\(464\) 0.692966 + 1.20025i 0.0321701 + 0.0557203i
\(465\) 11.5945 20.0823i 0.537684 0.931296i
\(466\) 0.0999321 + 0.372952i 0.00462927 + 0.0172767i
\(467\) 0.419923 0.727328i 0.0194317 0.0336567i −0.856146 0.516734i \(-0.827148\pi\)
0.875578 + 0.483077i \(0.160481\pi\)
\(468\) 3.21298 + 1.63609i 0.148520 + 0.0756282i
\(469\) 11.8258 + 11.9400i 0.546062 + 0.551340i
\(470\) 3.59448 13.4148i 0.165801 0.618777i
\(471\) −21.4103 −0.986536
\(472\) −12.0704 −0.555586
\(473\) −0.455700 + 1.70070i −0.0209531 + 0.0781981i
\(474\) −0.412834 0.110619i −0.0189621 0.00508088i
\(475\) −29.7737 + 7.97784i −1.36611 + 0.366048i
\(476\) 13.5956 7.76248i 0.623152 0.355793i
\(477\) −5.96016 + 10.3233i −0.272897 + 0.472671i
\(478\) 6.51583i 0.298027i
\(479\) −23.9856 + 6.42692i −1.09593 + 0.293654i −0.761106 0.648627i \(-0.775343\pi\)
−0.334824 + 0.942281i \(0.608677\pi\)
\(480\) −3.62017 + 2.09010i −0.165237 + 0.0953998i
\(481\) 7.94777 + 1.68728i 0.362387 + 0.0769335i
\(482\) 14.9626i 0.681530i
\(483\) −13.6225 0.0655079i −0.619846 0.00298071i
\(484\) 5.29945 + 9.17892i 0.240884 + 0.417224i
\(485\) −27.3614 + 15.7971i −1.24242 + 0.717311i
\(486\) −0.965926 0.258819i −0.0438153 0.0117403i
\(487\) 26.5868 + 26.5868i 1.20476 + 1.20476i 0.972701 + 0.232061i \(0.0745468\pi\)
0.232061 + 0.972701i \(0.425453\pi\)
\(488\) 3.20567 11.9637i 0.145114 0.541572i
\(489\) 0.157580 + 0.157580i 0.00712601 + 0.00712601i
\(490\) 14.3863 + 25.4807i 0.649909 + 1.15110i
\(491\) −20.0647 + 11.5844i −0.905507 + 0.522795i −0.878983 0.476853i \(-0.841777\pi\)
−0.0265243 + 0.999648i \(0.508444\pi\)
\(492\) 0.894810 0.894810i 0.0403411 0.0403411i
\(493\) −4.10044 7.10218i −0.184675 0.319866i
\(494\) 4.04282 7.93936i 0.181895 0.357209i
\(495\) −2.29272 1.32370i −0.103050 0.0594959i
\(496\) −5.35833 1.43576i −0.240596 0.0644675i
\(497\) −28.6841 28.9613i −1.28666 1.29909i
\(498\) 7.01535 + 4.05032i 0.314366 + 0.181499i
\(499\) −19.1161 + 5.12214i −0.855754 + 0.229299i −0.659918 0.751338i \(-0.729409\pi\)
−0.195836 + 0.980637i \(0.562742\pi\)
\(500\) −22.0925 + 22.0925i −0.988006 + 0.988006i
\(501\) 13.4720 13.4720i 0.601884 0.601884i
\(502\) 15.1311 4.05437i 0.675335 0.180955i
\(503\) −1.87260 1.08114i −0.0834949 0.0482058i 0.457671 0.889121i \(-0.348684\pi\)
−0.541166 + 0.840916i \(0.682017\pi\)
\(504\) 0.672474 + 2.55886i 0.0299544 + 0.113981i
\(505\) −16.9599 4.54438i −0.754704 0.202222i
\(506\) −2.82400 1.63044i −0.125542 0.0724819i
\(507\) −10.5134 + 7.64644i −0.466917 + 0.339590i
\(508\) 9.20531 + 15.9441i 0.408420 + 0.707404i
\(509\) −18.5258 + 18.5258i −0.821141 + 0.821141i −0.986272 0.165130i \(-0.947196\pi\)
0.165130 + 0.986272i \(0.447196\pi\)
\(510\) 21.4214 12.3676i 0.948555 0.547649i
\(511\) −21.2252 + 5.57803i −0.938949 + 0.246757i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −0.639550 + 2.38683i −0.0282368 + 0.105381i
\(514\) 20.2923 + 20.2923i 0.895055 + 0.895055i
\(515\) 5.74980 + 1.54065i 0.253367 + 0.0678894i
\(516\) 2.40764 1.39005i 0.105991 0.0611936i
\(517\) −1.05204 1.82219i −0.0462688 0.0801399i
\(518\) 2.95616 + 5.17756i 0.129886 + 0.227489i
\(519\) 15.2038i 0.667373i
\(520\) −0.792548 15.0511i −0.0347555 0.660035i
\(521\) 6.95625 4.01619i 0.304759 0.175952i −0.339820 0.940490i \(-0.610366\pi\)
0.644579 + 0.764538i \(0.277033\pi\)
\(522\) 1.33871 0.358706i 0.0585936 0.0157001i
\(523\) 8.24678i 0.360607i −0.983611 0.180303i \(-0.942292\pi\)
0.983611 0.180303i \(-0.0577079\pi\)
\(524\) −5.39580 + 9.34579i −0.235716 + 0.408273i
\(525\) 16.3641 + 28.6609i 0.714188 + 1.25086i
\(526\) −11.6397 + 3.11886i −0.507516 + 0.135989i
\(527\) 31.7065 + 8.49573i 1.38116 + 0.370080i
\(528\) −0.163915 + 0.611738i −0.00713347 + 0.0266225i
\(529\) −3.51100 −0.152652
\(530\) 49.8294 2.16445
\(531\) −3.12406 + 11.6591i −0.135573 + 0.505963i
\(532\) 6.32303 1.66170i 0.274138 0.0720439i
\(533\) 1.41102 + 4.33899i 0.0611179 + 0.187942i
\(534\) 0.839287 1.45369i 0.0363195 0.0629072i
\(535\) 11.8543 + 44.2410i 0.512508 + 1.91271i
\(536\) 3.17587 5.50077i 0.137177 0.237597i
\(537\) −10.3963 18.0069i −0.448632 0.777054i
\(538\) 1.29626 1.29626i 0.0558857 0.0558857i
\(539\) 4.27093 + 1.18853i 0.183962 + 0.0511938i
\(540\) 1.08192 + 4.03777i 0.0465583 + 0.173758i
\(541\) 7.25962 + 27.0933i 0.312116 + 1.16483i 0.926645 + 0.375937i \(0.122679\pi\)
−0.614530 + 0.788894i \(0.710654\pi\)
\(542\) 14.9911i 0.643924i
\(543\) 16.9487 + 9.78535i 0.727340 + 0.419930i
\(544\) −4.18412 4.18412i −0.179393 0.179393i
\(545\) 4.85710 0.208055
\(546\) −9.32179 2.02588i −0.398936 0.0866997i
\(547\) 33.9957 1.45355 0.726776 0.686875i \(-0.241018\pi\)
0.726776 + 0.686875i \(0.241018\pi\)
\(548\) 10.5293 + 10.5293i 0.449790 + 0.449790i
\(549\) −10.7264 6.19287i −0.457790 0.264305i
\(550\) 7.90010i 0.336861i
\(551\) −0.886372 3.30799i −0.0377607 0.140925i
\(552\) 1.33263 + 4.97344i 0.0567205 + 0.211684i
\(553\) 1.13077 + 0.00543767i 0.0480854 + 0.000231233i
\(554\) 4.12239 4.12239i 0.175143 0.175143i
\(555\) 4.70993 + 8.15783i 0.199925 + 0.346281i
\(556\) −4.72747 + 8.18822i −0.200489 + 0.347258i
\(557\) −3.92396 14.6444i −0.166263 0.620503i −0.997876 0.0651468i \(-0.979248\pi\)
0.831612 0.555357i \(-0.187418\pi\)
\(558\) −2.77367 + 4.80415i −0.117419 + 0.203376i
\(559\) 0.527095 + 10.0099i 0.0222937 + 0.423375i
\(560\) 7.85797 7.78276i 0.332060 0.328882i
\(561\) 0.969922 3.61980i 0.0409502 0.152828i
\(562\) −25.1431 −1.06060
\(563\) 19.4232 0.818591 0.409295 0.912402i \(-0.365775\pi\)
0.409295 + 0.912402i \(0.365775\pi\)
\(564\) −0.859880 + 3.20911i −0.0362075 + 0.135128i
\(565\) 66.1794 + 17.7327i 2.78419 + 0.746021i
\(566\) −13.3172 + 3.56833i −0.559763 + 0.149988i
\(567\) 2.64572 + 0.0127227i 0.111110 + 0.000534305i
\(568\) −7.70329 + 13.3425i −0.323223 + 0.559838i
\(569\) 44.9997i 1.88649i 0.332103 + 0.943243i \(0.392242\pi\)
−0.332103 + 0.943243i \(0.607758\pi\)
\(570\) 9.97745 2.67345i 0.417910 0.111979i
\(571\) −24.2146 + 13.9803i −1.01335 + 0.585058i −0.912171 0.409810i \(-0.865595\pi\)
−0.101180 + 0.994868i \(0.532262\pi\)
\(572\) −1.69732 1.52751i −0.0709686 0.0638684i
\(573\) 5.27268i 0.220270i
\(574\) −1.68796 + 2.89143i −0.0704541 + 0.120686i
\(575\) 32.1140 + 55.6230i 1.33924 + 2.31964i
\(576\) 0.866025 0.500000i 0.0360844 0.0208333i
\(577\) −42.1222 11.2866i −1.75357 0.469868i −0.768188 0.640224i \(-0.778841\pi\)
−0.985383 + 0.170356i \(0.945508\pi\)
\(578\) 12.7376 + 12.7376i 0.529815 + 0.529815i
\(579\) −3.53613 + 13.1970i −0.146957 + 0.548450i
\(580\) −4.09661 4.09661i −0.170103 0.170103i
\(581\) −20.6751 5.64656i −0.857746 0.234259i
\(582\) 6.54547 3.77903i 0.271319 0.156646i
\(583\) 5.33819 5.33819i 0.221085 0.221085i
\(584\) 4.14740 + 7.18350i 0.171620 + 0.297255i
\(585\) −14.7434 3.12997i −0.609564 0.129408i
\(586\) −2.74769 1.58638i −0.113506 0.0655327i
\(587\) −9.26294 2.48200i −0.382322 0.102443i 0.0625387 0.998043i \(-0.480080\pi\)
−0.444861 + 0.895600i \(0.646747\pi\)
\(588\) −3.44154 6.09556i −0.141927 0.251377i
\(589\) 11.8712 + 6.85383i 0.489144 + 0.282407i
\(590\) 48.7376 13.0592i 2.00650 0.537639i
\(591\) 8.95271 8.95271i 0.368265 0.368265i
\(592\) 1.59342 1.59342i 0.0654893 0.0654893i
\(593\) 4.80089 1.28640i 0.197149 0.0528259i −0.158893 0.987296i \(-0.550793\pi\)
0.356042 + 0.934470i \(0.384126\pi\)
\(594\) 0.548469 + 0.316659i 0.0225040 + 0.0129927i
\(595\) −46.4975 + 46.0524i −1.90621 + 1.88797i
\(596\) −13.5501 3.63073i −0.555032 0.148720i
\(597\) −5.19335 2.99838i −0.212549 0.122716i
\(598\) −18.1598 3.85527i −0.742611 0.157654i
\(599\) −11.6073 20.1044i −0.474260 0.821443i 0.525305 0.850914i \(-0.323951\pi\)
−0.999566 + 0.0294711i \(0.990618\pi\)
\(600\) 8.82055 8.82055i 0.360098 0.360098i
\(601\) −29.9917 + 17.3157i −1.22339 + 0.706322i −0.965638 0.259890i \(-0.916314\pi\)
−0.257748 + 0.966212i \(0.582980\pi\)
\(602\) −5.22605 + 5.17603i −0.212998 + 0.210959i
\(603\) −4.49136 4.49136i −0.182902 0.182902i
\(604\) 1.90212 7.09882i 0.0773963 0.288847i
\(605\) −31.3288 31.3288i −1.27370 1.27370i
\(606\) 4.05718 + 1.08712i 0.164812 + 0.0441611i
\(607\) 32.4478 18.7338i 1.31702 0.760380i 0.333769 0.942655i \(-0.391679\pi\)
0.983248 + 0.182275i \(0.0583461\pi\)
\(608\) −1.23551 2.13997i −0.0501067 0.0867874i
\(609\) −3.18435 + 1.81812i −0.129036 + 0.0736741i
\(610\) 51.7750i 2.09631i
\(611\) −8.90397 8.01316i −0.360216 0.324178i
\(612\) −5.12448 + 2.95862i −0.207145 + 0.119595i
\(613\) −11.5890 + 3.10527i −0.468076 + 0.125421i −0.485145 0.874434i \(-0.661233\pi\)
0.0170688 + 0.999854i \(0.494567\pi\)
\(614\) 14.8989i 0.601271i
\(615\) −2.64493 + 4.58115i −0.106654 + 0.184730i
\(616\) 0.00805754 1.67558i 0.000324648 0.0675111i
\(617\) −1.90489 + 0.510413i −0.0766879 + 0.0205485i −0.296959 0.954890i \(-0.595972\pi\)
0.220271 + 0.975439i \(0.429306\pi\)
\(618\) −1.37548 0.368559i −0.0553300 0.0148256i
\(619\) 4.98570 18.6069i 0.200392 0.747874i −0.790413 0.612575i \(-0.790134\pi\)
0.990805 0.135299i \(-0.0431995\pi\)
\(620\) 23.1891 0.931296
\(621\) 5.14888 0.206618
\(622\) 8.63633 32.2312i 0.346285 1.29235i
\(623\) −1.17005 + 4.28419i −0.0468772 + 0.171642i
\(624\) 0.189595 + 3.60056i 0.00758989 + 0.144138i
\(625\) 34.1168 59.0920i 1.36467 2.36368i
\(626\) 0.515651 + 1.92443i 0.0206096 + 0.0769159i
\(627\) 0.782474 1.35528i 0.0312490 0.0541248i
\(628\) −10.7052 18.5419i −0.427182 0.739902i
\(629\) −9.42866 + 9.42866i −0.375945 + 0.375945i
\(630\) −5.48377 9.60454i −0.218479 0.382654i
\(631\) 8.30437 + 30.9923i 0.330592 + 1.23378i 0.908570 + 0.417733i \(0.137175\pi\)
−0.577978 + 0.816052i \(0.696158\pi\)
\(632\) −0.110619 0.412834i −0.00440017 0.0164217i
\(633\) 21.1188i 0.839399i
\(634\) −18.3560 10.5979i −0.729011 0.420895i
\(635\) −54.4191 54.4191i −2.15956 2.15956i
\(636\) −11.9203 −0.472671
\(637\) 25.2155 1.08471i 0.999076 0.0429778i
\(638\) −0.877735 −0.0347499
\(639\) 10.8941 + 10.8941i 0.430964 + 0.430964i
\(640\) −3.62017 2.09010i −0.143100 0.0826186i
\(641\) 33.7682i 1.33376i 0.745163 + 0.666882i \(0.232372\pi\)
−0.745163 + 0.666882i \(0.767628\pi\)
\(642\) −2.83583 10.5834i −0.111921 0.417695i
\(643\) −9.13754 34.1018i −0.360349 1.34484i −0.873617 0.486614i \(-0.838232\pi\)
0.513268 0.858228i \(-0.328435\pi\)
\(644\) −6.75452 11.8302i −0.266165 0.466175i
\(645\) −8.21758 + 8.21758i −0.323567 + 0.323567i
\(646\) 7.31084 + 12.6627i 0.287641 + 0.498209i
\(647\) −6.77441 + 11.7336i −0.266330 + 0.461296i −0.967911 0.251293i \(-0.919144\pi\)
0.701582 + 0.712589i \(0.252478\pi\)
\(648\) −0.258819 0.965926i −0.0101674 0.0379452i
\(649\) 3.82221 6.62026i 0.150035 0.259868i
\(650\) 13.9090 + 42.7714i 0.545557 + 1.67763i
\(651\) 3.86679 14.1584i 0.151552 0.554910i
\(652\) −0.0576783 + 0.215258i −0.00225886 + 0.00843016i
\(653\) −3.94374 −0.154330 −0.0771652 0.997018i \(-0.524587\pi\)
−0.0771652 + 0.997018i \(0.524587\pi\)
\(654\) −1.16193 −0.0454349
\(655\) 11.6756 43.5740i 0.456204 1.70258i
\(656\) 1.22233 + 0.327523i 0.0477241 + 0.0127876i
\(657\) 8.01215 2.14685i 0.312584 0.0837566i
\(658\) 0.0422690 8.78993i 0.00164782 0.342667i
\(659\) 2.53663 4.39357i 0.0988130 0.171149i −0.812381 0.583128i \(-0.801829\pi\)
0.911194 + 0.411978i \(0.135162\pi\)
\(660\) 2.64740i 0.103050i
\(661\) −42.4863 + 11.3842i −1.65252 + 0.442793i −0.960318 0.278907i \(-0.910028\pi\)
−0.692207 + 0.721699i \(0.743361\pi\)
\(662\) 8.13012 4.69393i 0.315986 0.182435i
\(663\) −1.12188 21.3054i −0.0435702 0.827433i
\(664\) 8.10063i 0.314366i
\(665\) −23.7331 + 13.5506i −0.920331 + 0.525469i
\(666\) −1.12672 1.95154i −0.0436595 0.0756205i
\(667\) −6.17996 + 3.56800i −0.239289 + 0.138154i
\(668\) 18.4031 + 4.93109i 0.712037 + 0.190790i
\(669\) −13.8050 13.8050i −0.533732 0.533732i
\(670\) −6.87207 + 25.6469i −0.265491 + 0.990826i
\(671\) 5.54662 + 5.54662i 0.214125 + 0.214125i
\(672\) −1.87980 + 1.86181i −0.0725150 + 0.0718209i
\(673\) 38.3345 22.1325i 1.47769 0.853144i 0.478006 0.878356i \(-0.341360\pi\)
0.999682 + 0.0252127i \(0.00802631\pi\)
\(674\) 11.1459 11.1459i 0.429324 0.429324i
\(675\) −6.23707 10.8029i −0.240065 0.415805i
\(676\) −11.8787 5.28167i −0.456874 0.203141i
\(677\) −28.1133 16.2312i −1.08048 0.623818i −0.149457 0.988768i \(-0.547753\pi\)
−0.931027 + 0.364951i \(0.881086\pi\)
\(678\) −15.8316 4.24207i −0.608009 0.162916i
\(679\) −14.2077 + 14.0717i −0.545240 + 0.540021i
\(680\) 21.4214 + 12.3676i 0.821473 + 0.474278i
\(681\) 19.5147 5.22895i 0.747805 0.200374i
\(682\) 2.48423 2.48423i 0.0951262 0.0951262i
\(683\) −15.6930 + 15.6930i −0.600475 + 0.600475i −0.940438 0.339964i \(-0.889585\pi\)
0.339964 + 0.940438i \(0.389585\pi\)
\(684\) −2.38683 + 0.639550i −0.0912628 + 0.0244538i
\(685\) −53.9068 31.1231i −2.05967 1.18915i
\(686\) 12.9055 + 13.2834i 0.492735 + 0.507161i
\(687\) −1.82487 0.488972i −0.0696230 0.0186554i
\(688\) 2.40764 + 1.39005i 0.0917905 + 0.0529953i
\(689\) 19.5027 38.2997i 0.742993 1.45910i
\(690\) −10.7617 18.6398i −0.409691 0.709606i
\(691\) 14.6882 14.6882i 0.558766 0.558766i −0.370190 0.928956i \(-0.620707\pi\)
0.928956 + 0.370190i \(0.120707\pi\)
\(692\) −13.1669 + 7.60190i −0.500530 + 0.288981i
\(693\) −1.61640 0.441456i −0.0614021 0.0167695i
\(694\) 4.87232 + 4.87232i 0.184951 + 0.184951i
\(695\) 10.2295 38.1769i 0.388026 1.44813i
\(696\) 0.980002 + 0.980002i 0.0371469 + 0.0371469i
\(697\) −7.23283 1.93803i −0.273963 0.0734082i
\(698\) −19.6283 + 11.3324i −0.742941 + 0.428937i
\(699\) 0.193054 + 0.334379i 0.00730198 + 0.0126474i
\(700\) −16.6390 + 28.5022i −0.628895 + 1.07728i
\(701\) 14.0967i 0.532426i −0.963914 0.266213i \(-0.914228\pi\)
0.963914 0.266213i \(-0.0857725\pi\)
\(702\) 3.52695 + 0.748759i 0.133116 + 0.0282601i
\(703\) −4.82231 + 2.78416i −0.181877 + 0.105007i
\(704\) −0.611738 + 0.163915i −0.0230557 + 0.00617777i
\(705\) 13.8880i 0.523052i
\(706\) −0.464302 + 0.804194i −0.0174742 + 0.0302662i
\(707\) −11.1128 0.0534394i −0.417941 0.00200979i
\(708\) −11.6591 + 3.12406i −0.438177 + 0.117409i
\(709\) −15.5374 4.16322i −0.583518 0.156353i −0.0450290 0.998986i \(-0.514338\pi\)
−0.538489 + 0.842632i \(0.681005\pi\)
\(710\) 16.6686 62.2082i 0.625563 2.33463i
\(711\) −0.427398 −0.0160287
\(712\) 1.67857 0.0629072
\(713\) 7.39256 27.5894i 0.276854 1.03323i
\(714\) 11.1232 11.0168i 0.416277 0.412292i
\(715\) 8.50604 + 4.33138i 0.318108 + 0.161984i
\(716\) 10.3963 18.0069i 0.388527 0.672949i
\(717\) 1.68642 + 6.29380i 0.0629805 + 0.235046i
\(718\) 3.24616 5.62251i 0.121146 0.209830i
\(719\) 26.1786 + 45.3426i 0.976296 + 1.69099i 0.675591 + 0.737277i \(0.263889\pi\)
0.300705 + 0.953717i \(0.402778\pi\)
\(720\) −2.95585 + 2.95585i −0.110158 + 0.110158i
\(721\) 3.76752 + 0.0181172i 0.140310 + 0.000674721i
\(722\) −3.33722 12.4547i −0.124198 0.463514i
\(723\) 3.87262 + 14.4528i 0.144024 + 0.537506i
\(724\) 19.5707i 0.727340i
\(725\) 14.9721 + 8.64416i 0.556051 + 0.321036i
\(726\) 7.49456 + 7.49456i 0.278149 + 0.278149i
\(727\) 14.4888 0.537359 0.268680 0.963230i \(-0.413413\pi\)
0.268680 + 0.963230i \(0.413413\pi\)
\(728\) −2.90643 9.08585i −0.107720 0.336744i
\(729\) −1.00000 −0.0370370
\(730\) −24.5182 24.5182i −0.907459 0.907459i
\(731\) −14.2466 8.22527i −0.526929 0.304223i
\(732\) 12.3857i 0.457790i
\(733\) −0.624291 2.32989i −0.0230587 0.0860563i 0.953438 0.301590i \(-0.0975175\pi\)
−0.976496 + 0.215534i \(0.930851\pi\)
\(734\) 6.73128 + 25.1215i 0.248456 + 0.927250i
\(735\) 20.4910 + 20.8890i 0.755823 + 0.770503i
\(736\) −3.64081 + 3.64081i −0.134202 + 0.134202i
\(737\) 2.01134 + 3.48374i 0.0740886 + 0.128325i
\(738\) 0.632726 1.09591i 0.0232910 0.0403411i
\(739\) −9.09911 33.9583i −0.334716 1.24918i −0.904176 0.427159i \(-0.859514\pi\)
0.569460 0.822019i \(-0.307152\pi\)
\(740\) −4.70993 + 8.15783i −0.173140 + 0.299888i
\(741\) 1.85021 8.71519i 0.0679690 0.320161i
\(742\) 30.5024 8.01610i 1.11978 0.294280i
\(743\) −4.80877 + 17.9466i −0.176417 + 0.658396i 0.819889 + 0.572522i \(0.194035\pi\)
−0.996306 + 0.0858740i \(0.972632\pi\)
\(744\) −5.54735 −0.203376
\(745\) 58.6402 2.14841
\(746\) −6.65693 + 24.8440i −0.243727 + 0.909603i
\(747\) 7.82461 + 2.09660i 0.286288 + 0.0767105i
\(748\) 3.61980 0.969922i 0.132353 0.0354639i
\(749\) 14.3736 + 25.1746i 0.525199 + 0.919859i
\(750\) −15.6217 + 27.0577i −0.570426 + 0.988006i
\(751\) 16.1289i 0.588552i 0.955721 + 0.294276i \(0.0950785\pi\)
−0.955721 + 0.294276i \(0.904922\pi\)
\(752\) −3.20911 + 0.859880i −0.117024 + 0.0313566i
\(753\) 13.5662 7.83244i 0.494379 0.285430i
\(754\) −4.75209 + 1.54535i −0.173061 + 0.0562785i
\(755\) 30.7214i 1.11806i
\(756\) 1.31184 + 2.29762i 0.0477112 + 0.0835637i
\(757\) −0.821968 1.42369i −0.0298749 0.0517449i 0.850701 0.525649i \(-0.176178\pi\)
−0.880576 + 0.473904i \(0.842844\pi\)
\(758\) −25.4304 + 14.6823i −0.923675 + 0.533284i
\(759\) −3.14977 0.843978i −0.114329 0.0306345i
\(760\) 7.30400 + 7.30400i 0.264944 + 0.264944i
\(761\) 13.7057 51.1504i 0.496832 1.85420i −0.0226867 0.999743i \(-0.507222\pi\)
0.519519 0.854459i \(-0.326111\pi\)
\(762\) 13.0183 + 13.0183i 0.471602 + 0.471602i
\(763\) 2.97321 0.781365i 0.107637 0.0282873i
\(764\) 4.56628 2.63634i 0.165202 0.0953795i
\(765\) 17.4905 17.4905i 0.632370 0.632370i
\(766\) −6.31661 10.9407i −0.228228 0.395303i
\(767\) 9.03784 42.5718i 0.326338 1.53718i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 2.73506 + 0.732858i 0.0986289 + 0.0264275i 0.307796 0.951452i \(-0.400409\pi\)
−0.209167 + 0.977880i \(0.567075\pi\)
\(770\) 1.78031 + 6.77434i 0.0641578 + 0.244130i
\(771\) 24.8529 + 14.3488i 0.895055 + 0.516760i
\(772\) −13.1970 + 3.53613i −0.474971 + 0.127268i
\(773\) −9.14714 + 9.14714i −0.329000 + 0.329000i −0.852206 0.523206i \(-0.824736\pi\)
0.523206 + 0.852206i \(0.324736\pi\)
\(774\) 1.96583 1.96583i 0.0706603 0.0706603i
\(775\) −66.8406 + 17.9099i −2.40098 + 0.643342i
\(776\) 6.54547 + 3.77903i 0.234969 + 0.135659i
\(777\) 4.19548 + 4.23602i 0.150512 + 0.151967i
\(778\) −14.0311 3.75963i −0.503041 0.134789i
\(779\) −2.70803 1.56348i −0.0970254 0.0560177i
\(780\) −4.66106 14.3331i −0.166893 0.513208i
\(781\) −4.87863 8.45003i −0.174571 0.302366i
\(782\) 21.5435 21.5435i 0.770395 0.770395i
\(783\) 1.20025 0.692966i 0.0428935 0.0247646i
\(784\) 3.55814 6.02824i 0.127076 0.215294i
\(785\) 63.2858 + 63.2858i 2.25877 + 2.25877i
\(786\) −2.79307 + 10.4239i −0.0996255 + 0.371807i
\(787\) −37.0580 37.0580i −1.32097 1.32097i −0.912988 0.407987i \(-0.866231\pi\)
−0.407987 0.912988i \(-0.633769\pi\)
\(788\) 12.2296 + 3.27692i 0.435662 + 0.116735i
\(789\) −10.4359 + 6.02517i −0.371528 + 0.214502i
\(790\) 0.893306 + 1.54725i 0.0317824 + 0.0550487i
\(791\) 43.3636 + 0.208527i 1.54183 + 0.00741436i
\(792\) 0.633318i 0.0225040i
\(793\) 39.7951 + 20.2641i 1.41317 + 0.719601i
\(794\) −4.67949 + 2.70171i −0.166069 + 0.0958800i
\(795\) 48.1315 12.8968i 1.70705 0.457402i
\(796\) 5.99676i 0.212549i
\(797\) 18.1260 31.3952i 0.642057 1.11208i −0.342916 0.939366i \(-0.611415\pi\)
0.984973 0.172709i \(-0.0552521\pi\)
\(798\) 5.67749 3.24160i 0.200981 0.114751i
\(799\) 18.9891 5.08811i 0.671786 0.180004i
\(800\) 12.0491 + 3.22855i 0.426000 + 0.114146i
\(801\) 0.434447 1.62138i 0.0153504 0.0572886i
\(802\) −4.09793 −0.144703
\(803\) −5.25324 −0.185383
\(804\) 1.64395 6.13532i 0.0579778 0.216376i
\(805\) 40.0725 + 40.4598i 1.41237 + 1.42602i
\(806\) 9.07595 17.8235i 0.319687 0.627806i
\(807\) 0.916594 1.58759i 0.0322656 0.0558857i
\(808\) 1.08712 + 4.05718i 0.0382447 + 0.142731i
\(809\) 12.1469 21.0391i 0.427064 0.739696i −0.569547 0.821959i \(-0.692881\pi\)
0.996611 + 0.0822628i \(0.0262147\pi\)
\(810\) 2.09010 + 3.62017i 0.0734388 + 0.127200i
\(811\) −14.0616 + 14.0616i −0.493771 + 0.493771i −0.909492 0.415721i \(-0.863529\pi\)
0.415721 + 0.909492i \(0.363529\pi\)
\(812\) −3.16672 1.84866i −0.111130 0.0648754i
\(813\) −3.87999 14.4803i −0.136077 0.507847i
\(814\) 0.369372 + 1.37852i 0.0129465 + 0.0483169i
\(815\) 0.931567i 0.0326314i
\(816\) −5.12448 2.95862i −0.179393 0.103572i
\(817\) −4.85763 4.85763i −0.169947 0.169947i
\(818\) 0.124629 0.00435754
\(819\) −9.52850 + 0.455807i −0.332953 + 0.0159272i
\(820\) −5.28985 −0.184730
\(821\) 18.4886 + 18.4886i 0.645257 + 0.645257i 0.951843 0.306586i \(-0.0991867\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(822\) 12.8957 + 7.44535i 0.449790 + 0.259687i
\(823\) 38.1095i 1.32841i 0.747549 + 0.664207i \(0.231231\pi\)
−0.747549 + 0.664207i \(0.768769\pi\)
\(824\) −0.368559 1.37548i −0.0128394 0.0479172i
\(825\) 2.04470 + 7.63091i 0.0711872 + 0.265674i
\(826\) 27.7333 15.8345i 0.964965 0.550953i
\(827\) 5.83374 5.83374i 0.202859 0.202859i −0.598365 0.801224i \(-0.704183\pi\)
0.801224 + 0.598365i \(0.204183\pi\)
\(828\) 2.57444 + 4.45906i 0.0894680 + 0.154963i
\(829\) −5.69060 + 9.85640i −0.197643 + 0.342327i −0.947764 0.318974i \(-0.896662\pi\)
0.750121 + 0.661301i \(0.229995\pi\)
\(830\) −8.76422 32.7085i −0.304210 1.13533i
\(831\) 2.91497 5.04887i 0.101119 0.175143i
\(832\) −3.02338 + 1.96448i −0.104817 + 0.0681059i
\(833\) −21.0544 + 35.6705i −0.729490 + 1.23591i
\(834\) −2.44712 + 9.13277i −0.0847368 + 0.316242i
\(835\) −79.6425 −2.75614
\(836\) 1.56495 0.0541248
\(837\) −1.43576 + 5.35833i −0.0496271 + 0.185211i
\(838\) −4.24130 1.13645i −0.146513 0.0392581i
\(839\) −22.2461 + 5.96083i −0.768021 + 0.205791i −0.621497 0.783416i \(-0.713475\pi\)
−0.146524 + 0.989207i \(0.546809\pi\)
\(840\) 5.57589 9.55136i 0.192387 0.329553i
\(841\) 13.5396 23.4513i 0.466883 0.808664i
\(842\) 31.2802i 1.07799i
\(843\) −24.2864 + 6.50753i −0.836469 + 0.224131i
\(844\) −18.2895 + 10.5594i −0.629549 + 0.363470i
\(845\) 53.6779 + 8.47438i 1.84658 + 0.291528i
\(846\) 3.32232i 0.114224i
\(847\) −24.2174 14.1377i −0.832121 0.485776i
\(848\) −5.96016 10.3233i −0.204673 0.354503i
\(849\) −11.9399 + 6.89348i −0.409775 + 0.236584i
\(850\) −71.2974 19.1041i −2.44548 0.655264i
\(851\) 8.20435 + 8.20435i 0.281241 + 0.281241i
\(852\) −3.98751 + 14.8816i −0.136610 + 0.509835i
\(853\) −23.4705 23.4705i −0.803613 0.803613i 0.180045 0.983658i \(-0.442376\pi\)
−0.983658 + 0.180045i \(0.942376\pi\)
\(854\) 8.32908 + 31.6934i 0.285015 + 1.08453i
\(855\) 8.94554 5.16471i 0.305931 0.176629i
\(856\) 7.74762 7.74762i 0.264808 0.264808i
\(857\) 9.42125 + 16.3181i 0.321824 + 0.557415i 0.980864 0.194692i \(-0.0623708\pi\)
−0.659041 + 0.752107i \(0.729038\pi\)
\(858\) −2.03484 1.03616i −0.0694681 0.0353740i
\(859\) 25.2668 + 14.5878i 0.862094 + 0.497730i 0.864713 0.502267i \(-0.167500\pi\)
−0.00261917 + 0.999997i \(0.500834\pi\)
\(860\) −11.2254 3.00784i −0.382784 0.102567i
\(861\) −0.882086 + 3.22978i −0.0300614 + 0.110071i
\(862\) 9.92121 + 5.72801i 0.337918 + 0.195097i
\(863\) 23.7880 6.37398i 0.809753 0.216973i 0.169892 0.985463i \(-0.445658\pi\)
0.639862 + 0.768490i \(0.278992\pi\)
\(864\) 0.707107 0.707107i 0.0240563 0.0240563i
\(865\) 44.9402 44.9402i 1.52801 1.52801i
\(866\) −11.4875 + 3.07806i −0.390361 + 0.104597i
\(867\) 15.6003 + 9.00685i 0.529815 + 0.305889i
\(868\) 14.1949 3.73045i 0.481807 0.126620i
\(869\) 0.261455 + 0.0700568i 0.00886927 + 0.00237651i
\(870\) −5.01730 2.89674i −0.170103 0.0982088i
\(871\) 17.0230 + 15.3199i 0.576802 + 0.519095i
\(872\) −0.580963 1.00626i −0.0196739 0.0340762i
\(873\) 5.34435 5.34435i 0.180879 0.180879i
\(874\) 11.0185 6.36152i 0.372706 0.215182i
\(875\) 21.7783 79.7421i 0.736242 2.69577i
\(876\) 5.86530 + 5.86530i 0.198170 + 0.198170i
\(877\) 7.99081 29.8221i 0.269831 1.00702i −0.689396 0.724384i \(-0.742124\pi\)
0.959227 0.282637i \(-0.0912092\pi\)
\(878\) 6.09509 + 6.09509i 0.205699 + 0.205699i
\(879\) −3.06465 0.821170i −0.103368 0.0276974i
\(880\) 2.29272 1.32370i 0.0772875 0.0446219i
\(881\) −10.9949 19.0437i −0.370428 0.641600i 0.619203 0.785231i \(-0.287456\pi\)
−0.989631 + 0.143631i \(0.954122\pi\)
\(882\) −4.90191 4.99712i −0.165056 0.168262i
\(883\) 4.16764i 0.140252i 0.997538 + 0.0701262i \(0.0223402\pi\)
−0.997538 + 0.0701262i \(0.977660\pi\)
\(884\) 17.8901 11.6243i 0.601708 0.390967i
\(885\) 43.6970 25.2285i 1.46886 0.848045i
\(886\) −8.16083 + 2.18669i −0.274169 + 0.0734632i
\(887\) 44.3768i 1.49003i −0.667050 0.745013i \(-0.732443\pi\)
0.667050 0.745013i \(-0.267557\pi\)
\(888\) 1.12672 1.95154i 0.0378103 0.0654893i
\(889\) −42.0664 24.5575i −1.41086 0.823633i
\(890\) −6.77770 + 1.81608i −0.227189 + 0.0608751i
\(891\) 0.611738 + 0.163915i 0.0204940 + 0.00549135i
\(892\) 5.05298 18.8580i 0.169186 0.631412i
\(893\) 8.20955 0.274722
\(894\) −14.0280 −0.469168
\(895\) −22.4958 + 83.9556i −0.751953 + 2.80633i
\(896\) −2.55228 0.697052i −0.0852656 0.0232869i
\(897\) −18.5389 + 0.976204i −0.618995 + 0.0325945i
\(898\) 4.49887 7.79227i 0.150129 0.260032i
\(899\) −1.98987 7.42628i −0.0663657 0.247680i
\(900\) 6.23707 10.8029i 0.207902 0.360098i
\(901\) 35.2677 + 61.0854i 1.17494 + 2.03505i
\(902\) −0.566699 + 0.566699i −0.0188690 + 0.0188690i
\(903\) −3.70832 + 6.35226i −0.123405 + 0.211390i
\(904\) −4.24207 15.8316i −0.141089 0.526551i
\(905\) −21.1739 79.0221i −0.703844 2.62678i
\(906\) 7.34924i 0.244162i
\(907\) 7.72303 + 4.45890i 0.256439 + 0.148055i 0.622709 0.782453i \(-0.286032\pi\)
−0.366270 + 0.930509i \(0.619365\pi\)
\(908\) 14.2857 + 14.2857i 0.474089 + 0.474089i
\(909\) 4.20030 0.139315
\(910\) 21.5657 + 33.5421i 0.714894 + 1.11191i
\(911\) −28.1929 −0.934072 −0.467036 0.884238i \(-0.654678\pi\)
−0.467036 + 0.884238i \(0.654678\pi\)
\(912\) −1.74728 1.74728i −0.0578583 0.0578583i
\(913\) −4.44295 2.56514i −0.147040 0.0848937i
\(914\) 18.5251i 0.612755i
\(915\) 13.4004 + 50.0108i 0.443002 + 1.65331i
\(916\) −0.488972 1.82487i −0.0161561 0.0602953i
\(917\) 0.137299 28.5515i 0.00453400 0.942855i
\(918\) −4.18412 + 4.18412i −0.138096 + 0.138096i
\(919\) 5.59640 + 9.69325i 0.184608 + 0.319751i 0.943444 0.331531i \(-0.107565\pi\)
−0.758836 + 0.651281i \(0.774232\pi\)
\(920\) 10.7617 18.6398i 0.354803 0.614537i
\(921\) 3.85612 + 14.3912i 0.127064 + 0.474208i
\(922\) 20.8523 36.1173i 0.686735 1.18946i
\(923\) −41.2903 37.1594i −1.35909 1.22312i
\(924\) −0.425890 1.62057i −0.0140107 0.0533130i
\(925\) 7.27534 27.1519i 0.239212 0.892750i
\(926\) −17.9816 −0.590912
\(927\) −1.42400 −0.0467704
\(928\) −0.358706 + 1.33871i −0.0117751 + 0.0439452i
\(929\) 21.2250 + 5.68722i 0.696370 + 0.186592i 0.589604 0.807692i \(-0.299284\pi\)
0.106766 + 0.994284i \(0.465950\pi\)
\(930\) 22.3989 6.00178i 0.734490 0.196806i
\(931\) −12.3480 + 12.1128i −0.404691 + 0.396980i
\(932\) −0.193054 + 0.334379i −0.00632370 + 0.0109530i
\(933\) 33.3682i 1.09243i
\(934\) 0.811229 0.217368i 0.0265442 0.00711251i
\(935\) −13.5665 + 7.83265i −0.443674 + 0.256155i
\(936\) 1.11503 + 3.42881i 0.0364459 + 0.112074i
\(937\) 26.1389i 0.853920i 0.904270 + 0.426960i \(0.140416\pi\)
−0.904270 + 0.426960i \(0.859584\pi\)
\(938\) −0.0808117 + 16.8050i −0.00263859 + 0.548701i
\(939\) 0.996161 + 1.72540i 0.0325085 + 0.0563063i
\(940\) 12.0274 6.94400i 0.392289 0.226488i
\(941\) −6.95414 1.86336i −0.226699 0.0607437i 0.143682 0.989624i \(-0.454106\pi\)
−0.370380 + 0.928880i \(0.620773\pi\)
\(942\) −15.1394 15.1394i −0.493268 0.493268i
\(943\) −1.68638 + 6.29365i −0.0549160 + 0.204949i
\(944\) −8.53508 8.53508i −0.277793 0.277793i
\(945\) −7.78276 7.85797i −0.253173 0.255620i
\(946\) −1.52480 + 0.880345i −0.0495756 + 0.0286225i
\(947\) 7.36706 7.36706i 0.239397 0.239397i −0.577203 0.816601i \(-0.695856\pi\)
0.816601 + 0.577203i \(0.195856\pi\)
\(948\) −0.213699 0.370137i −0.00694061 0.0120215i
\(949\) −28.4412 + 9.24893i −0.923241 + 0.300233i
\(950\) −26.6944 15.4120i −0.866079 0.500031i
\(951\) −20.4735 5.48586i −0.663898 0.177891i
\(952\) 15.1024 + 4.12462i 0.489473 + 0.133680i
\(953\) 12.2353 + 7.06405i 0.396340 + 0.228827i 0.684904 0.728634i \(-0.259844\pi\)
−0.288563 + 0.957461i \(0.593178\pi\)
\(954\) −11.5141 + 3.08520i −0.372784 + 0.0998872i
\(955\) −15.5853 + 15.5853i −0.504328 + 0.504328i
\(956\) −4.60738 + 4.60738i −0.149013 + 0.149013i
\(957\) −0.847827 + 0.227175i −0.0274064 + 0.00734351i
\(958\) −21.5049 12.4159i −0.694792 0.401138i
\(959\) −38.0052 10.3796i −1.22725 0.335175i
\(960\) −4.03777 1.08192i −0.130319 0.0349187i
\(961\) −0.196509 0.113454i −0.00633899 0.00365982i
\(962\) 4.42683 + 6.81301i 0.142727 + 0.219660i
\(963\) −5.47839 9.48886i −0.176539 0.305774i
\(964\) −10.5802 + 10.5802i −0.340765 + 0.340765i
\(965\) 49.4608 28.5562i 1.59220 0.919256i
\(966\) −9.58625 9.67889i −0.308432 0.311413i
\(967\) 6.47081 + 6.47081i 0.208087 + 0.208087i 0.803454 0.595367i \(-0.202993\pi\)
−0.595367 + 0.803454i \(0.702993\pi\)
\(968\) −2.74320 + 10.2378i −0.0881698 + 0.329054i
\(969\) 10.3391 + 10.3391i 0.332139 + 0.332139i
\(970\) −30.5177 8.17720i −0.979865 0.262554i
\(971\) 11.1381 6.43060i 0.357440 0.206368i −0.310517 0.950568i \(-0.600502\pi\)
0.667957 + 0.744200i \(0.267169\pi\)
\(972\) −0.500000 0.866025i −0.0160375 0.0277778i
\(973\) 0.120293 25.0151i 0.00385641 0.801949i
\(974\) 37.5994i 1.20476i
\(975\) 24.5052 + 37.7141i 0.784793 + 1.20782i
\(976\) 10.7264 6.19287i 0.343343 0.198229i
\(977\) −16.5044 + 4.42235i −0.528024 + 0.141483i −0.512975 0.858403i \(-0.671457\pi\)
−0.0150481 + 0.999887i \(0.504790\pi\)
\(978\) 0.222852i 0.00712601i
\(979\) −0.531536 + 0.920647i −0.0169880 + 0.0294240i
\(980\) −7.84490 + 28.1903i −0.250596 + 0.900505i
\(981\) −1.12234 + 0.300729i −0.0358334 + 0.00960153i
\(982\) −22.3793 5.99651i −0.714151 0.191356i
\(983\) 10.7386 40.0769i 0.342507 1.27826i −0.552990 0.833188i \(-0.686513\pi\)
0.895497 0.445067i \(-0.146820\pi\)
\(984\) 1.26545 0.0403411
\(985\) −52.9258 −1.68636
\(986\) 2.12255 7.92145i 0.0675956 0.252270i
\(987\) −2.23417 8.50136i −0.0711145 0.270601i
\(988\) 8.47268 2.75527i 0.269552 0.0876568i
\(989\) −7.15722 + 12.3967i −0.227586 + 0.394191i
\(990\) −0.685198 2.55719i −0.0217770 0.0812729i
\(991\) 10.0195 17.3543i 0.318280 0.551277i −0.661850 0.749637i \(-0.730228\pi\)
0.980129 + 0.198360i \(0.0635616\pi\)
\(992\) −2.77367 4.80415i −0.0880643 0.152532i
\(993\) 6.63821 6.63821i 0.210657 0.210657i
\(994\) 0.196014 40.7615i 0.00621718 1.29288i
\(995\) 6.48800 + 24.2135i 0.205683 + 0.767621i
\(996\) 2.09660 + 7.82461i 0.0664333 + 0.247932i
\(997\) 14.4532i 0.457737i −0.973457 0.228868i \(-0.926497\pi\)
0.973457 0.228868i \(-0.0735025\pi\)
\(998\) −17.1390 9.89522i −0.542526 0.313228i
\(999\) −1.59342 1.59342i −0.0504137 0.0504137i
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 546.2.cg.b.271.6 yes 40
7.3 odd 6 546.2.by.b.115.1 yes 40
13.6 odd 12 546.2.by.b.19.1 40
91.45 even 12 inner 546.2.cg.b.409.6 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.by.b.19.1 40 13.6 odd 12
546.2.by.b.115.1 yes 40 7.3 odd 6
546.2.cg.b.271.6 yes 40 1.1 even 1 trivial
546.2.cg.b.409.6 yes 40 91.45 even 12 inner