Properties

Label 546.2.cg.a.241.7
Level $546$
Weight $2$
Character 546.241
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
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: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 241.7
Character \(\chi\) \(=\) 546.241
Dual form 546.2.cg.a.145.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(1.56767 + 0.420055i) q^{5} +(0.965926 + 0.258819i) q^{6} +(2.44485 + 1.01129i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(1.56767 + 0.420055i) q^{5} +(0.965926 + 0.258819i) q^{6} +(2.44485 + 1.01129i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.811483 + 1.40553i) q^{10} +(-0.797035 - 0.213565i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.50249 + 0.855906i) q^{13} +(1.01368 + 2.44386i) q^{14} +(1.56767 - 0.420055i) q^{15} -1.00000 q^{16} +4.29436 q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.170930 - 0.637919i) q^{19} +(-0.420055 + 1.56767i) q^{20} +(2.62295 - 0.346627i) q^{21} +(-0.412576 - 0.714602i) q^{22} -0.381806i q^{23} +(-0.258819 + 0.965926i) q^{24} +(-2.04900 - 1.18299i) q^{25} +(-3.08185 - 1.87142i) q^{26} -1.00000i q^{27} +(-1.01129 + 2.44485i) q^{28} +(-0.856275 + 1.48311i) q^{29} +(1.40553 + 0.811483i) q^{30} +(-1.08690 - 4.05637i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.797035 + 0.213565i) q^{33} +(3.03657 + 3.03657i) q^{34} +(3.40792 + 2.61233i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.265780 - 0.265780i) q^{37} +(0.330211 - 0.571943i) q^{38} +(-2.60529 + 2.49248i) q^{39} +(-1.40553 + 0.811483i) q^{40} +(0.129761 + 0.484273i) q^{41} +(2.09981 + 1.60960i) q^{42} +(4.60461 - 2.65847i) q^{43} +(0.213565 - 0.797035i) q^{44} +(1.14761 - 1.14761i) q^{45} +(0.269978 - 0.269978i) q^{46} +(-3.54101 + 13.2152i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.95460 + 4.94489i) q^{49} +(-0.612360 - 2.28536i) q^{50} +(3.71902 - 2.14718i) q^{51} +(-0.855906 - 3.50249i) q^{52} +(2.29049 - 3.96724i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-1.15978 - 0.669597i) q^{55} +(-2.44386 + 1.01368i) q^{56} +(-0.466989 - 0.466989i) q^{57} +(-1.65420 + 0.443241i) q^{58} +(-1.09331 - 1.09331i) q^{59} +(0.420055 + 1.56767i) q^{60} +(-10.6052 - 6.12294i) q^{61} +(2.09973 - 3.63685i) q^{62} +(2.09823 - 1.61166i) q^{63} -1.00000i q^{64} +(-5.85026 - 0.129463i) q^{65} +(-0.714602 - 0.412576i) q^{66} +(1.94196 - 7.24748i) q^{67} +4.29436i q^{68} +(-0.190903 - 0.330654i) q^{69} +(0.562564 + 4.25696i) q^{70} +(1.09592 - 4.09004i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-11.0943 + 2.97272i) q^{73} +0.375870 q^{74} -2.36598 q^{75} +(0.637919 - 0.170930i) q^{76} +(-1.73266 - 1.32817i) q^{77} +(-3.60467 - 0.0797692i) q^{78} +(-3.74389 - 6.48461i) q^{79} +(-1.56767 - 0.420055i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.250678 + 0.434187i) q^{82} +(5.17265 - 5.17265i) q^{83} +(0.346627 + 2.62295i) q^{84} +(6.73212 + 1.80387i) q^{85} +(5.13578 + 1.37613i) q^{86} +1.71255i q^{87} +(0.714602 - 0.412576i) q^{88} +(7.47571 + 7.47571i) q^{89} +1.62297 q^{90} +(-9.42863 - 1.44945i) q^{91} +0.381806 q^{92} +(-2.96947 - 2.96947i) q^{93} +(-11.8485 + 6.84072i) q^{94} -1.07184i q^{95} +(-0.965926 - 0.258819i) q^{96} +(-15.6542 - 4.19452i) q^{97} +(0.00687020 + 7.00000i) q^{98} +(-0.583470 + 0.583470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\)

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
\(5\) 1.56767 + 0.420055i 0.701081 + 0.187854i 0.591715 0.806147i \(-0.298451\pi\)
0.109366 + 0.994001i \(0.465118\pi\)
\(6\) 0.965926 + 0.258819i 0.394338 + 0.105662i
\(7\) 2.44485 + 1.01129i 0.924067 + 0.382230i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0.811483 + 1.40553i 0.256614 + 0.444468i
\(11\) −0.797035 0.213565i −0.240315 0.0643923i 0.136651 0.990619i \(-0.456366\pi\)
−0.376966 + 0.926227i \(0.623033\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −3.50249 + 0.855906i −0.971416 + 0.237386i
\(14\) 1.01368 + 2.44386i 0.270919 + 0.653149i
\(15\) 1.56767 0.420055i 0.404770 0.108458i
\(16\) −1.00000 −0.250000
\(17\) 4.29436 1.04153 0.520767 0.853699i \(-0.325646\pi\)
0.520767 + 0.853699i \(0.325646\pi\)
\(18\) 0.965926 0.258819i 0.227671 0.0610042i
\(19\) −0.170930 0.637919i −0.0392140 0.146349i 0.943543 0.331250i \(-0.107470\pi\)
−0.982757 + 0.184901i \(0.940804\pi\)
\(20\) −0.420055 + 1.56767i −0.0939271 + 0.350541i
\(21\) 2.62295 0.346627i 0.572374 0.0756402i
\(22\) −0.412576 0.714602i −0.0879615 0.152354i
\(23\) 0.381806i 0.0796122i −0.999207 0.0398061i \(-0.987326\pi\)
0.999207 0.0398061i \(-0.0126740\pi\)
\(24\) −0.258819 + 0.965926i −0.0528312 + 0.197169i
\(25\) −2.04900 1.18299i −0.409799 0.236598i
\(26\) −3.08185 1.87142i −0.604401 0.367015i
\(27\) 1.00000i 0.192450i
\(28\) −1.01129 + 2.44485i −0.191115 + 0.462034i
\(29\) −0.856275 + 1.48311i −0.159006 + 0.275407i −0.934511 0.355935i \(-0.884162\pi\)
0.775504 + 0.631342i \(0.217496\pi\)
\(30\) 1.40553 + 0.811483i 0.256614 + 0.148156i
\(31\) −1.08690 4.05637i −0.195213 0.728546i −0.992212 0.124564i \(-0.960247\pi\)
0.796998 0.603982i \(-0.206420\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −0.797035 + 0.213565i −0.138746 + 0.0371769i
\(34\) 3.03657 + 3.03657i 0.520767 + 0.520767i
\(35\) 3.40792 + 2.61233i 0.576043 + 0.441564i
\(36\) 0.866025 + 0.500000i 0.144338 + 0.0833333i
\(37\) 0.265780 0.265780i 0.0436940 0.0436940i −0.684922 0.728616i \(-0.740164\pi\)
0.728616 + 0.684922i \(0.240164\pi\)
\(38\) 0.330211 0.571943i 0.0535673 0.0927814i
\(39\) −2.60529 + 2.49248i −0.417180 + 0.399116i
\(40\) −1.40553 + 0.811483i −0.222234 + 0.128307i
\(41\) 0.129761 + 0.484273i 0.0202652 + 0.0756307i 0.975318 0.220805i \(-0.0708685\pi\)
−0.955053 + 0.296436i \(0.904202\pi\)
\(42\) 2.09981 + 1.60960i 0.324007 + 0.248367i
\(43\) 4.60461 2.65847i 0.702196 0.405413i −0.105968 0.994369i \(-0.533794\pi\)
0.808165 + 0.588956i \(0.200461\pi\)
\(44\) 0.213565 0.797035i 0.0321961 0.120158i
\(45\) 1.14761 1.14761i 0.171076 0.171076i
\(46\) 0.269978 0.269978i 0.0398061 0.0398061i
\(47\) −3.54101 + 13.2152i −0.516510 + 1.92764i −0.194522 + 0.980898i \(0.562316\pi\)
−0.321988 + 0.946744i \(0.604351\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) 4.95460 + 4.94489i 0.707800 + 0.706412i
\(50\) −0.612360 2.28536i −0.0866008 0.323199i
\(51\) 3.71902 2.14718i 0.520767 0.300665i
\(52\) −0.855906 3.50249i −0.118693 0.485708i
\(53\) 2.29049 3.96724i 0.314623 0.544943i −0.664734 0.747080i \(-0.731455\pi\)
0.979357 + 0.202137i \(0.0647886\pi\)
\(54\) 0.707107 0.707107i 0.0962250 0.0962250i
\(55\) −1.15978 0.669597i −0.156384 0.0902884i
\(56\) −2.44386 + 1.01368i −0.326574 + 0.135459i
\(57\) −0.466989 0.466989i −0.0618542 0.0618542i
\(58\) −1.65420 + 0.443241i −0.217207 + 0.0582004i
\(59\) −1.09331 1.09331i −0.142336 0.142336i 0.632348 0.774684i \(-0.282091\pi\)
−0.774684 + 0.632348i \(0.782091\pi\)
\(60\) 0.420055 + 1.56767i 0.0542288 + 0.202385i
\(61\) −10.6052 6.12294i −1.35786 0.783962i −0.368527 0.929617i \(-0.620138\pi\)
−0.989336 + 0.145654i \(0.953471\pi\)
\(62\) 2.09973 3.63685i 0.266666 0.461880i
\(63\) 2.09823 1.61166i 0.264352 0.203050i
\(64\) 1.00000i 0.125000i
\(65\) −5.85026 0.129463i −0.725635 0.0160579i
\(66\) −0.714602 0.412576i −0.0879615 0.0507846i
\(67\) 1.94196 7.24748i 0.237248 0.885420i −0.739875 0.672744i \(-0.765115\pi\)
0.977123 0.212676i \(-0.0682179\pi\)
\(68\) 4.29436i 0.520767i
\(69\) −0.190903 0.330654i −0.0229821 0.0398061i
\(70\) 0.562564 + 4.25696i 0.0672393 + 0.508804i
\(71\) 1.09592 4.09004i 0.130062 0.485399i −0.869907 0.493215i \(-0.835821\pi\)
0.999969 + 0.00781655i \(0.00248811\pi\)
\(72\) 0.258819 + 0.965926i 0.0305021 + 0.113835i
\(73\) −11.0943 + 2.97272i −1.29849 + 0.347930i −0.840880 0.541222i \(-0.817962\pi\)
−0.457613 + 0.889152i \(0.651295\pi\)
\(74\) 0.375870 0.0436940
\(75\) −2.36598 −0.273200
\(76\) 0.637919 0.170930i 0.0731743 0.0196070i
\(77\) −1.73266 1.32817i −0.197455 0.151358i
\(78\) −3.60467 0.0797692i −0.408148 0.00903208i
\(79\) −3.74389 6.48461i −0.421221 0.729576i 0.574838 0.818267i \(-0.305065\pi\)
−0.996059 + 0.0886909i \(0.971732\pi\)
\(80\) −1.56767 0.420055i −0.175270 0.0469635i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.250678 + 0.434187i −0.0276828 + 0.0479480i
\(83\) 5.17265 5.17265i 0.567773 0.567773i −0.363731 0.931504i \(-0.618497\pi\)
0.931504 + 0.363731i \(0.118497\pi\)
\(84\) 0.346627 + 2.62295i 0.0378201 + 0.286187i
\(85\) 6.73212 + 1.80387i 0.730201 + 0.195657i
\(86\) 5.13578 + 1.37613i 0.553805 + 0.148392i
\(87\) 1.71255i 0.183605i
\(88\) 0.714602 0.412576i 0.0761769 0.0439807i
\(89\) 7.47571 + 7.47571i 0.792424 + 0.792424i 0.981888 0.189464i \(-0.0606749\pi\)
−0.189464 + 0.981888i \(0.560675\pi\)
\(90\) 1.62297 0.171076
\(91\) −9.42863 1.44945i −0.988389 0.151944i
\(92\) 0.381806 0.0398061
\(93\) −2.96947 2.96947i −0.307920 0.307920i
\(94\) −11.8485 + 6.84072i −1.22208 + 0.705566i
\(95\) 1.07184i 0.109969i
\(96\) −0.965926 0.258819i −0.0985844 0.0264156i
\(97\) −15.6542 4.19452i −1.58944 0.425889i −0.647608 0.761974i \(-0.724230\pi\)
−0.941832 + 0.336085i \(0.890897\pi\)
\(98\) 0.00687020 + 7.00000i 0.000693995 + 0.707106i
\(99\) −0.583470 + 0.583470i −0.0586410 + 0.0586410i
\(100\) 1.18299 2.04900i 0.118299 0.204900i
\(101\) −5.77766 10.0072i −0.574898 0.995753i −0.996053 0.0887643i \(-0.971708\pi\)
0.421154 0.906989i \(-0.361625\pi\)
\(102\) 4.14803 + 1.11146i 0.410716 + 0.110051i
\(103\) −4.29555 7.44012i −0.423253 0.733096i 0.573002 0.819554i \(-0.305779\pi\)
−0.996256 + 0.0864574i \(0.972445\pi\)
\(104\) 1.87142 3.08185i 0.183507 0.302200i
\(105\) 4.25751 + 0.558386i 0.415490 + 0.0544929i
\(106\) 4.42489 1.18564i 0.429783 0.115160i
\(107\) 9.38823 0.907594 0.453797 0.891105i \(-0.350069\pi\)
0.453797 + 0.891105i \(0.350069\pi\)
\(108\) 1.00000 0.0962250
\(109\) −5.89242 + 1.57887i −0.564392 + 0.151228i −0.529723 0.848171i \(-0.677704\pi\)
−0.0346684 + 0.999399i \(0.511038\pi\)
\(110\) −0.346609 1.29356i −0.0330479 0.123336i
\(111\) 0.0972824 0.363063i 0.00923364 0.0344604i
\(112\) −2.44485 1.01129i −0.231017 0.0955575i
\(113\) 6.40625 + 11.0959i 0.602649 + 1.04382i 0.992418 + 0.122906i \(0.0392214\pi\)
−0.389769 + 0.920912i \(0.627445\pi\)
\(114\) 0.660423i 0.0618542i
\(115\) 0.160380 0.598545i 0.0149555 0.0558146i
\(116\) −1.48311 0.856275i −0.137704 0.0795032i
\(117\) −1.01001 + 3.46120i −0.0933753 + 0.319988i
\(118\) 1.54617i 0.142336i
\(119\) 10.4991 + 4.34282i 0.962448 + 0.398106i
\(120\) −0.811483 + 1.40553i −0.0740780 + 0.128307i
\(121\) −8.93662 5.15956i −0.812420 0.469051i
\(122\) −3.16947 11.8286i −0.286950 1.07091i
\(123\) 0.354512 + 0.354512i 0.0319653 + 0.0319653i
\(124\) 4.05637 1.08690i 0.364273 0.0976067i
\(125\) −8.45328 8.45328i −0.756084 0.756084i
\(126\) 2.62329 + 0.344053i 0.233701 + 0.0306506i
\(127\) 3.94473 + 2.27749i 0.350038 + 0.202095i 0.664702 0.747108i \(-0.268558\pi\)
−0.314664 + 0.949203i \(0.601892\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 2.65847 4.60461i 0.234065 0.405413i
\(130\) −4.04521 4.22830i −0.354789 0.370847i
\(131\) −7.81287 + 4.51076i −0.682614 + 0.394107i −0.800839 0.598880i \(-0.795613\pi\)
0.118225 + 0.992987i \(0.462279\pi\)
\(132\) −0.213565 0.797035i −0.0185884 0.0693730i
\(133\) 0.227220 1.73248i 0.0197025 0.150225i
\(134\) 6.49791 3.75157i 0.561334 0.324086i
\(135\) 0.420055 1.56767i 0.0361526 0.134923i
\(136\) −3.03657 + 3.03657i −0.260384 + 0.260384i
\(137\) −1.15844 + 1.15844i −0.0989721 + 0.0989721i −0.754859 0.655887i \(-0.772295\pi\)
0.655887 + 0.754859i \(0.272295\pi\)
\(138\) 0.0988188 0.368797i 0.00841201 0.0313941i
\(139\) 8.27928 4.78004i 0.702239 0.405438i −0.105942 0.994372i \(-0.533786\pi\)
0.808181 + 0.588934i \(0.200452\pi\)
\(140\) −2.61233 + 3.40792i −0.220782 + 0.288021i
\(141\) 3.54101 + 13.2152i 0.298207 + 1.11292i
\(142\) 3.66703 2.11716i 0.307731 0.177668i
\(143\) 2.97440 + 0.0658217i 0.248732 + 0.00550429i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −1.96534 + 1.96534i −0.163213 + 0.163213i
\(146\) −9.94690 5.74285i −0.823211 0.475281i
\(147\) 6.76326 + 1.80510i 0.557824 + 0.148882i
\(148\) 0.265780 + 0.265780i 0.0218470 + 0.0218470i
\(149\) −3.68633 + 0.987748i −0.301996 + 0.0809195i −0.406635 0.913591i \(-0.633298\pi\)
0.104639 + 0.994510i \(0.466631\pi\)
\(150\) −1.67300 1.67300i −0.136600 0.136600i
\(151\) 4.55448 + 16.9975i 0.370638 + 1.38324i 0.859615 + 0.510943i \(0.170704\pi\)
−0.488977 + 0.872297i \(0.662630\pi\)
\(152\) 0.571943 + 0.330211i 0.0463907 + 0.0267837i
\(153\) 2.14718 3.71902i 0.173589 0.300665i
\(154\) −0.286020 2.16433i −0.0230481 0.174407i
\(155\) 6.81560i 0.547442i
\(156\) −2.49248 2.60529i −0.199558 0.208590i
\(157\) −13.6198 7.86337i −1.08698 0.627566i −0.154206 0.988039i \(-0.549282\pi\)
−0.932770 + 0.360473i \(0.882615\pi\)
\(158\) 1.93798 7.23265i 0.154178 0.575399i
\(159\) 4.58098i 0.363295i
\(160\) −0.811483 1.40553i −0.0641534 0.111117i
\(161\) 0.386115 0.933460i 0.0304302 0.0735670i
\(162\) 0.258819 0.965926i 0.0203347 0.0758903i
\(163\) 0.961529 + 3.58847i 0.0753128 + 0.281071i 0.993304 0.115530i \(-0.0368565\pi\)
−0.917991 + 0.396601i \(0.870190\pi\)
\(164\) −0.484273 + 0.129761i −0.0378154 + 0.0101326i
\(165\) −1.33919 −0.104256
\(166\) 7.31524 0.567773
\(167\) 13.0153 3.48744i 1.00715 0.269866i 0.282714 0.959204i \(-0.408765\pi\)
0.724440 + 0.689338i \(0.242099\pi\)
\(168\) −1.60960 + 2.09981i −0.124183 + 0.162004i
\(169\) 11.5349 5.99560i 0.887296 0.461200i
\(170\) 3.48480 + 6.03585i 0.267272 + 0.462929i
\(171\) −0.637919 0.170930i −0.0487829 0.0130713i
\(172\) 2.65847 + 4.60461i 0.202707 + 0.351098i
\(173\) −11.5406 + 19.9890i −0.877418 + 1.51973i −0.0232539 + 0.999730i \(0.507403\pi\)
−0.854164 + 0.520003i \(0.825931\pi\)
\(174\) −1.21096 + 1.21096i −0.0918023 + 0.0918023i
\(175\) −3.81316 4.96435i −0.288247 0.375270i
\(176\) 0.797035 + 0.213565i 0.0600788 + 0.0160981i
\(177\) −1.49348 0.400178i −0.112257 0.0300792i
\(178\) 10.5723i 0.792424i
\(179\) 6.07426 3.50698i 0.454012 0.262124i −0.255511 0.966806i \(-0.582244\pi\)
0.709523 + 0.704682i \(0.248910\pi\)
\(180\) 1.14761 + 1.14761i 0.0855379 + 0.0855379i
\(181\) 5.03562 0.374295 0.187147 0.982332i \(-0.440076\pi\)
0.187147 + 0.982332i \(0.440076\pi\)
\(182\) −5.64213 7.69197i −0.418223 0.570167i
\(183\) −12.2459 −0.905242
\(184\) 0.269978 + 0.269978i 0.0199030 + 0.0199030i
\(185\) 0.528297 0.305013i 0.0388412 0.0224250i
\(186\) 4.19947i 0.307920i
\(187\) −3.42276 0.917125i −0.250297 0.0670668i
\(188\) −13.2152 3.54101i −0.963821 0.258255i
\(189\) 1.01129 2.44485i 0.0735602 0.177837i
\(190\) 0.757908 0.757908i 0.0549844 0.0549844i
\(191\) 2.05415 3.55789i 0.148633 0.257440i −0.782090 0.623166i \(-0.785846\pi\)
0.930722 + 0.365726i \(0.119179\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 20.4591 + 5.48199i 1.47268 + 0.394602i 0.903848 0.427854i \(-0.140730\pi\)
0.568828 + 0.822456i \(0.307397\pi\)
\(194\) −8.10319 14.0351i −0.581775 1.00766i
\(195\) −5.13120 + 2.81301i −0.367453 + 0.201444i
\(196\) −4.94489 + 4.95460i −0.353206 + 0.353900i
\(197\) 14.8764 3.98613i 1.05990 0.284000i 0.313565 0.949567i \(-0.398477\pi\)
0.746338 + 0.665567i \(0.231810\pi\)
\(198\) −0.825152 −0.0586410
\(199\) −11.2862 −0.800056 −0.400028 0.916503i \(-0.631000\pi\)
−0.400028 + 0.916503i \(0.631000\pi\)
\(200\) 2.28536 0.612360i 0.161599 0.0433004i
\(201\) −1.94196 7.24748i −0.136975 0.511198i
\(202\) 2.99074 11.1616i 0.210427 0.785326i
\(203\) −3.59332 + 2.76005i −0.252201 + 0.193718i
\(204\) 2.14718 + 3.71902i 0.150333 + 0.260384i
\(205\) 0.813685i 0.0568302i
\(206\) 2.22354 8.29837i 0.154922 0.578175i
\(207\) −0.330654 0.190903i −0.0229821 0.0132687i
\(208\) 3.50249 0.855906i 0.242854 0.0593464i
\(209\) 0.544949i 0.0376949i
\(210\) 2.61567 + 3.40535i 0.180499 + 0.234991i
\(211\) 6.20836 10.7532i 0.427401 0.740280i −0.569240 0.822171i \(-0.692763\pi\)
0.996641 + 0.0818911i \(0.0260960\pi\)
\(212\) 3.96724 + 2.29049i 0.272471 + 0.157311i
\(213\) −1.09592 4.09004i −0.0750915 0.280245i
\(214\) 6.63848 + 6.63848i 0.453797 + 0.453797i
\(215\) 8.33519 2.23341i 0.568456 0.152317i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 1.44484 11.0164i 0.0980820 0.747842i
\(218\) −5.28300 3.05014i −0.357810 0.206582i
\(219\) −8.12161 + 8.12161i −0.548807 + 0.548807i
\(220\) 0.669597 1.15978i 0.0451442 0.0781921i
\(221\) −15.0409 + 3.67557i −1.01176 + 0.247245i
\(222\) 0.325513 0.187935i 0.0218470 0.0126134i
\(223\) 3.07026 + 11.4584i 0.205600 + 0.767308i 0.989266 + 0.146126i \(0.0466805\pi\)
−0.783666 + 0.621182i \(0.786653\pi\)
\(224\) −1.01368 2.44386i −0.0677297 0.163287i
\(225\) −2.04900 + 1.18299i −0.136600 + 0.0788659i
\(226\) −3.31612 + 12.3759i −0.220585 + 0.823234i
\(227\) 10.3723 10.3723i 0.688437 0.688437i −0.273450 0.961886i \(-0.588165\pi\)
0.961886 + 0.273450i \(0.0881647\pi\)
\(228\) 0.466989 0.466989i 0.0309271 0.0309271i
\(229\) −4.17662 + 15.5874i −0.275999 + 1.03004i 0.679170 + 0.733981i \(0.262340\pi\)
−0.955169 + 0.296061i \(0.904327\pi\)
\(230\) 0.536641 0.309830i 0.0353850 0.0204296i
\(231\) −2.16461 0.283896i −0.142421 0.0186790i
\(232\) −0.443241 1.65420i −0.0291002 0.108603i
\(233\) −11.1322 + 6.42720i −0.729297 + 0.421060i −0.818165 0.574984i \(-0.805008\pi\)
0.0888681 + 0.996043i \(0.471675\pi\)
\(234\) −3.16162 + 1.73325i −0.206682 + 0.113306i
\(235\) −11.1023 + 19.2297i −0.724231 + 1.25441i
\(236\) 1.09331 1.09331i 0.0711682 0.0711682i
\(237\) −6.48461 3.74389i −0.421221 0.243192i
\(238\) 4.35313 + 10.4948i 0.282171 + 0.680277i
\(239\) 13.5059 + 13.5059i 0.873627 + 0.873627i 0.992866 0.119239i \(-0.0380454\pi\)
−0.119239 + 0.992866i \(0.538045\pi\)
\(240\) −1.56767 + 0.420055i −0.101192 + 0.0271144i
\(241\) 6.92996 + 6.92996i 0.446398 + 0.446398i 0.894155 0.447757i \(-0.147777\pi\)
−0.447757 + 0.894155i \(0.647777\pi\)
\(242\) −2.67079 9.96751i −0.171685 0.640736i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 6.12294 10.6052i 0.391981 0.678931i
\(245\) 5.69004 + 9.83313i 0.363523 + 0.628216i
\(246\) 0.501356i 0.0319653i
\(247\) 1.14468 + 2.08800i 0.0728342 + 0.132857i
\(248\) 3.63685 + 2.09973i 0.230940 + 0.133333i
\(249\) 1.89332 7.06598i 0.119984 0.447788i
\(250\) 11.9547i 0.756084i
\(251\) 9.22525 + 15.9786i 0.582293 + 1.00856i 0.995207 + 0.0977909i \(0.0311777\pi\)
−0.412914 + 0.910770i \(0.635489\pi\)
\(252\) 1.61166 + 2.09823i 0.101525 + 0.132176i
\(253\) −0.0815405 + 0.304313i −0.00512641 + 0.0191320i
\(254\) 1.17892 + 4.39978i 0.0739718 + 0.276067i
\(255\) 6.73212 1.80387i 0.421582 0.112962i
\(256\) 1.00000 0.0625000
\(257\) −22.3159 −1.39203 −0.696013 0.718029i \(-0.745044\pi\)
−0.696013 + 0.718029i \(0.745044\pi\)
\(258\) 5.13578 1.37613i 0.319739 0.0856739i
\(259\) 0.918574 0.381014i 0.0570774 0.0236751i
\(260\) 0.129463 5.85026i 0.00802894 0.362818i
\(261\) 0.856275 + 1.48311i 0.0530021 + 0.0918023i
\(262\) −8.71412 2.33494i −0.538360 0.144253i
\(263\) 8.20565 + 14.2126i 0.505982 + 0.876386i 0.999976 + 0.00692122i \(0.00220311\pi\)
−0.493994 + 0.869465i \(0.664464\pi\)
\(264\) 0.412576 0.714602i 0.0253923 0.0439807i
\(265\) 5.25718 5.25718i 0.322946 0.322946i
\(266\) 1.38572 1.06438i 0.0849636 0.0652612i
\(267\) 10.2120 + 2.73630i 0.624965 + 0.167459i
\(268\) 7.24748 + 1.94196i 0.442710 + 0.118624i
\(269\) 16.8220i 1.02565i 0.858492 + 0.512827i \(0.171402\pi\)
−0.858492 + 0.512827i \(0.828598\pi\)
\(270\) 1.40553 0.811483i 0.0855379 0.0493853i
\(271\) 3.01068 + 3.01068i 0.182886 + 0.182886i 0.792612 0.609726i \(-0.208721\pi\)
−0.609726 + 0.792612i \(0.708721\pi\)
\(272\) −4.29436 −0.260384
\(273\) −8.89016 + 3.45905i −0.538057 + 0.209351i
\(274\) −1.63828 −0.0989721
\(275\) 1.38048 + 1.38048i 0.0832460 + 0.0832460i
\(276\) 0.330654 0.190903i 0.0199030 0.0114910i
\(277\) 22.5571i 1.35533i 0.735372 + 0.677663i \(0.237007\pi\)
−0.735372 + 0.677663i \(0.762993\pi\)
\(278\) 9.23434 + 2.47433i 0.553839 + 0.148401i
\(279\) −4.05637 1.08690i −0.242849 0.0650711i
\(280\) −4.25696 + 0.562564i −0.254402 + 0.0336196i
\(281\) 7.38947 7.38947i 0.440819 0.440819i −0.451468 0.892287i \(-0.649100\pi\)
0.892287 + 0.451468i \(0.149100\pi\)
\(282\) −6.84072 + 11.8485i −0.407359 + 0.705566i
\(283\) 8.75973 + 15.1723i 0.520712 + 0.901899i 0.999710 + 0.0240834i \(0.00766672\pi\)
−0.478998 + 0.877816i \(0.659000\pi\)
\(284\) 4.09004 + 1.09592i 0.242699 + 0.0650311i
\(285\) −0.535922 0.928244i −0.0317453 0.0549844i
\(286\) 2.05667 + 2.14976i 0.121614 + 0.127118i
\(287\) −0.172493 + 1.31520i −0.0101819 + 0.0776338i
\(288\) −0.965926 + 0.258819i −0.0569177 + 0.0152511i
\(289\) 1.44152 0.0847951
\(290\) −2.77941 −0.163213
\(291\) −15.6542 + 4.19452i −0.917663 + 0.245887i
\(292\) −2.97272 11.0943i −0.173965 0.649246i
\(293\) 1.28663 4.80175i 0.0751655 0.280522i −0.918105 0.396337i \(-0.870281\pi\)
0.993271 + 0.115815i \(0.0369480\pi\)
\(294\) 3.50595 + 6.05874i 0.204471 + 0.353353i
\(295\) −1.25469 2.17319i −0.0730509 0.126528i
\(296\) 0.375870i 0.0218470i
\(297\) −0.213565 + 0.797035i −0.0123923 + 0.0462487i
\(298\) −3.30507 1.90818i −0.191458 0.110538i
\(299\) 0.326790 + 1.33727i 0.0188988 + 0.0773365i
\(300\) 2.36598i 0.136600i
\(301\) 13.9461 1.84300i 0.803838 0.106229i
\(302\) −8.79857 + 15.2396i −0.506301 + 0.876939i
\(303\) −10.0072 5.77766i −0.574898 0.331918i
\(304\) 0.170930 + 0.637919i 0.00980350 + 0.0365872i
\(305\) −14.0535 14.0535i −0.804702 0.804702i
\(306\) 4.14803 1.11146i 0.237127 0.0635380i
\(307\) 17.8871 + 17.8871i 1.02087 + 1.02087i 0.999778 + 0.0210932i \(0.00671468\pi\)
0.0210932 + 0.999778i \(0.493285\pi\)
\(308\) 1.32817 1.73266i 0.0756792 0.0987274i
\(309\) −7.44012 4.29555i −0.423253 0.244365i
\(310\) 4.81935 4.81935i 0.273721 0.273721i
\(311\) −2.73172 + 4.73148i −0.154902 + 0.268298i −0.933023 0.359816i \(-0.882839\pi\)
0.778122 + 0.628114i \(0.216173\pi\)
\(312\) 0.0797692 3.60467i 0.00451604 0.204074i
\(313\) −20.8623 + 12.0448i −1.17921 + 0.680815i −0.955831 0.293917i \(-0.905041\pi\)
−0.223375 + 0.974732i \(0.571708\pi\)
\(314\) −4.07038 15.1909i −0.229705 0.857270i
\(315\) 3.96630 1.64518i 0.223476 0.0926952i
\(316\) 6.48461 3.74389i 0.364788 0.210610i
\(317\) 0.902659 3.36877i 0.0506984 0.189209i −0.935933 0.352179i \(-0.885441\pi\)
0.986631 + 0.162970i \(0.0521075\pi\)
\(318\) 3.23924 3.23924i 0.181648 0.181648i
\(319\) 0.999223 0.999223i 0.0559457 0.0559457i
\(320\) 0.420055 1.56767i 0.0234818 0.0876352i
\(321\) 8.13045 4.69411i 0.453797 0.262000i
\(322\) 0.933081 0.387031i 0.0519986 0.0215684i
\(323\) −0.734034 2.73945i −0.0408428 0.152427i
\(324\) 0.866025 0.500000i 0.0481125 0.0277778i
\(325\) 8.18912 + 2.38966i 0.454250 + 0.132554i
\(326\) −1.85753 + 3.21734i −0.102879 + 0.178192i
\(327\) −4.31355 + 4.31355i −0.238540 + 0.238540i
\(328\) −0.434187 0.250678i −0.0239740 0.0138414i
\(329\) −22.0216 + 28.7283i −1.21409 + 1.58384i
\(330\) −0.946953 0.946953i −0.0521281 0.0521281i
\(331\) 4.77070 1.27830i 0.262221 0.0702620i −0.125313 0.992117i \(-0.539994\pi\)
0.387534 + 0.921855i \(0.373327\pi\)
\(332\) 5.17265 + 5.17265i 0.283886 + 0.283886i
\(333\) −0.0972824 0.363063i −0.00533104 0.0198957i
\(334\) 11.6692 + 6.73721i 0.638510 + 0.368644i
\(335\) 6.08867 10.5459i 0.332660 0.576184i
\(336\) −2.62295 + 0.346627i −0.143093 + 0.0189101i
\(337\) 27.7323i 1.51067i −0.655336 0.755337i \(-0.727473\pi\)
0.655336 0.755337i \(-0.272527\pi\)
\(338\) 12.3959 + 3.91684i 0.674248 + 0.213048i
\(339\) 11.0959 + 6.40625i 0.602649 + 0.347940i
\(340\) −1.80387 + 6.73212i −0.0978284 + 0.365100i
\(341\) 3.46520i 0.187651i
\(342\) −0.330211 0.571943i −0.0178558 0.0309271i
\(343\) 7.11258 + 17.1000i 0.384043 + 0.923315i
\(344\) −1.37613 + 5.13578i −0.0741958 + 0.276902i
\(345\) −0.160380 0.598545i −0.00863455 0.0322246i
\(346\) −22.2948 + 5.97387i −1.19858 + 0.321157i
\(347\) −3.19116 −0.171311 −0.0856553 0.996325i \(-0.527298\pi\)
−0.0856553 + 0.996325i \(0.527298\pi\)
\(348\) −1.71255 −0.0918023
\(349\) 2.67590 0.717004i 0.143237 0.0383803i −0.186488 0.982457i \(-0.559711\pi\)
0.329725 + 0.944077i \(0.393044\pi\)
\(350\) 0.814021 6.20664i 0.0435112 0.331759i
\(351\) 0.855906 + 3.50249i 0.0456849 + 0.186949i
\(352\) 0.412576 + 0.714602i 0.0219904 + 0.0380884i
\(353\) 23.1542 + 6.20415i 1.23237 + 0.330214i 0.815504 0.578752i \(-0.196460\pi\)
0.416871 + 0.908966i \(0.363127\pi\)
\(354\) −0.773085 1.33902i −0.0410890 0.0711682i
\(355\) 3.43608 5.95147i 0.182368 0.315871i
\(356\) −7.47571 + 7.47571i −0.396212 + 0.396212i
\(357\) 11.2639 1.48854i 0.596147 0.0787819i
\(358\) 6.77496 + 1.81534i 0.358068 + 0.0959439i
\(359\) 9.20478 + 2.46641i 0.485810 + 0.130172i 0.493407 0.869799i \(-0.335751\pi\)
−0.00759675 + 0.999971i \(0.502418\pi\)
\(360\) 1.62297i 0.0855379i
\(361\) 16.0768 9.28192i 0.846145 0.488522i
\(362\) 3.56072 + 3.56072i 0.187147 + 0.187147i
\(363\) −10.3191 −0.541614
\(364\) 1.44945 9.42863i 0.0759720 0.494195i
\(365\) −18.6409 −0.975709
\(366\) −8.65915 8.65915i −0.452621 0.452621i
\(367\) 12.1022 6.98720i 0.631729 0.364729i −0.149693 0.988733i \(-0.547828\pi\)
0.781421 + 0.624004i \(0.214495\pi\)
\(368\) 0.381806i 0.0199030i
\(369\) 0.484273 + 0.129761i 0.0252102 + 0.00675506i
\(370\) 0.589239 + 0.157886i 0.0306331 + 0.00820811i
\(371\) 9.61192 7.38299i 0.499026 0.383305i
\(372\) 2.96947 2.96947i 0.153960 0.153960i
\(373\) 3.93347 6.81297i 0.203667 0.352762i −0.746040 0.665901i \(-0.768047\pi\)
0.949707 + 0.313139i \(0.101381\pi\)
\(374\) −1.77175 3.06876i −0.0916150 0.158682i
\(375\) −11.5474 3.09411i −0.596305 0.159779i
\(376\) −6.84072 11.8485i −0.352783 0.611038i
\(377\) 1.72969 5.92747i 0.0890836 0.305280i
\(378\) 2.44386 1.01368i 0.125699 0.0521383i
\(379\) 17.0033 4.55602i 0.873401 0.234027i 0.205843 0.978585i \(-0.434006\pi\)
0.667558 + 0.744558i \(0.267340\pi\)
\(380\) 1.07184 0.0549844
\(381\) 4.55498 0.233359
\(382\) 3.96831 1.06330i 0.203036 0.0544034i
\(383\) 1.64423 + 6.13635i 0.0840162 + 0.313553i 0.995126 0.0986108i \(-0.0314399\pi\)
−0.911110 + 0.412164i \(0.864773\pi\)
\(384\) 0.258819 0.965926i 0.0132078 0.0492922i
\(385\) −2.15833 2.80993i −0.109999 0.143207i
\(386\) 10.5904 + 18.3431i 0.539037 + 0.933639i
\(387\) 5.31695i 0.270276i
\(388\) 4.19452 15.6542i 0.212945 0.794720i
\(389\) −30.5671 17.6479i −1.54981 0.894785i −0.998155 0.0607150i \(-0.980662\pi\)
−0.551658 0.834070i \(-0.686005\pi\)
\(390\) −5.61741 1.63921i −0.284449 0.0830046i
\(391\) 1.63961i 0.0829188i
\(392\) −7.00000 + 0.00687020i −0.353553 + 0.000346998i
\(393\) −4.51076 + 7.81287i −0.227538 + 0.394107i
\(394\) 13.3379 + 7.70062i 0.671952 + 0.387951i
\(395\) −3.14528 11.7383i −0.158256 0.590620i
\(396\) −0.583470 0.583470i −0.0293205 0.0293205i
\(397\) 7.09877 1.90211i 0.356277 0.0954642i −0.0762409 0.997089i \(-0.524292\pi\)
0.432518 + 0.901625i \(0.357625\pi\)
\(398\) −7.98053 7.98053i −0.400028 0.400028i
\(399\) −0.669460 1.61398i −0.0335149 0.0808000i
\(400\) 2.04900 + 1.18299i 0.102450 + 0.0591495i
\(401\) −20.8949 + 20.8949i −1.04344 + 1.04344i −0.0444275 + 0.999013i \(0.514146\pi\)
−0.999013 + 0.0444275i \(0.985854\pi\)
\(402\) 3.75157 6.49791i 0.187111 0.324086i
\(403\) 7.27874 + 13.2771i 0.362580 + 0.661380i
\(404\) 10.0072 5.77766i 0.497877 0.287449i
\(405\) −0.420055 1.56767i −0.0208727 0.0778979i
\(406\) −4.49251 0.589207i −0.222959 0.0292419i
\(407\) −0.268598 + 0.155075i −0.0133139 + 0.00768678i
\(408\) −1.11146 + 4.14803i −0.0550256 + 0.205358i
\(409\) −6.14465 + 6.14465i −0.303834 + 0.303834i −0.842512 0.538678i \(-0.818924\pi\)
0.538678 + 0.842512i \(0.318924\pi\)
\(410\) −0.575362 + 0.575362i −0.0284151 + 0.0284151i
\(411\) −0.424018 + 1.58246i −0.0209153 + 0.0780568i
\(412\) 7.44012 4.29555i 0.366548 0.211627i
\(413\) −1.56733 3.77862i −0.0771232 0.185934i
\(414\) −0.0988188 0.368797i −0.00485668 0.0181254i
\(415\) 10.2818 5.93619i 0.504713 0.291396i
\(416\) 3.08185 + 1.87142i 0.151100 + 0.0917537i
\(417\) 4.78004 8.27928i 0.234080 0.405438i
\(418\) −0.385337 + 0.385337i −0.0188474 + 0.0188474i
\(419\) 6.14618 + 3.54850i 0.300261 + 0.173355i 0.642560 0.766235i \(-0.277872\pi\)
−0.342299 + 0.939591i \(0.611206\pi\)
\(420\) −0.558386 + 4.25751i −0.0272464 + 0.207745i
\(421\) 19.9117 + 19.9117i 0.970435 + 0.970435i 0.999575 0.0291399i \(-0.00927684\pi\)
−0.0291399 + 0.999575i \(0.509277\pi\)
\(422\) 11.9936 3.21368i 0.583840 0.156440i
\(423\) 9.67423 + 9.67423i 0.470377 + 0.470377i
\(424\) 1.18564 + 4.42489i 0.0575800 + 0.214891i
\(425\) −8.79913 5.08018i −0.426820 0.246425i
\(426\) 2.11716 3.66703i 0.102577 0.177668i
\(427\) −19.7362 25.6946i −0.955103 1.24345i
\(428\) 9.38823i 0.453797i
\(429\) 2.60882 1.43020i 0.125955 0.0690505i
\(430\) 7.47313 + 4.31461i 0.360386 + 0.208069i
\(431\) 9.11889 34.0322i 0.439242 1.63927i −0.291466 0.956581i \(-0.594143\pi\)
0.730707 0.682691i \(-0.239190\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −10.4769 18.1465i −0.503488 0.872068i −0.999992 0.00403277i \(-0.998716\pi\)
0.496503 0.868035i \(-0.334617\pi\)
\(434\) 8.81143 6.76812i 0.422962 0.324880i
\(435\) −0.719365 + 2.68471i −0.0344909 + 0.128722i
\(436\) −1.57887 5.89242i −0.0756141 0.282196i
\(437\) −0.243562 + 0.0652622i −0.0116511 + 0.00312191i
\(438\) −11.4857 −0.548807
\(439\) 11.5304 0.550318 0.275159 0.961399i \(-0.411269\pi\)
0.275159 + 0.961399i \(0.411269\pi\)
\(440\) 1.29356 0.346609i 0.0616682 0.0165239i
\(441\) 6.75970 1.81837i 0.321890 0.0865890i
\(442\) −13.2346 8.03653i −0.629504 0.382259i
\(443\) −20.2056 34.9971i −0.959995 1.66276i −0.722499 0.691372i \(-0.757006\pi\)
−0.237497 0.971388i \(-0.576327\pi\)
\(444\) 0.363063 + 0.0972824i 0.0172302 + 0.00461682i
\(445\) 8.57921 + 14.8596i 0.406694 + 0.704414i
\(446\) −5.93128 + 10.2733i −0.280854 + 0.486454i
\(447\) −2.69858 + 2.69858i −0.127638 + 0.127638i
\(448\) 1.01129 2.44485i 0.0477788 0.115508i
\(449\) 30.8308 + 8.26109i 1.45500 + 0.389865i 0.897758 0.440488i \(-0.145195\pi\)
0.557237 + 0.830353i \(0.311861\pi\)
\(450\) −2.28536 0.612360i −0.107733 0.0288669i
\(451\) 0.413695i 0.0194801i
\(452\) −11.0959 + 6.40625i −0.521909 + 0.301324i
\(453\) 12.4431 + 12.4431i 0.584626 + 0.584626i
\(454\) 14.6687 0.688437
\(455\) −14.1721 6.23280i −0.664398 0.292198i
\(456\) 0.660423 0.0309271
\(457\) −19.7641 19.7641i −0.924525 0.924525i 0.0728198 0.997345i \(-0.476800\pi\)
−0.997345 + 0.0728198i \(0.976800\pi\)
\(458\) −13.9752 + 8.06861i −0.653020 + 0.377021i
\(459\) 4.29436i 0.200443i
\(460\) 0.598545 + 0.160380i 0.0279073 + 0.00747774i
\(461\) −29.5044 7.90568i −1.37416 0.368204i −0.505162 0.863025i \(-0.668567\pi\)
−0.868995 + 0.494820i \(0.835234\pi\)
\(462\) −1.32987 1.73135i −0.0618709 0.0805499i
\(463\) −18.6854 + 18.6854i −0.868386 + 0.868386i −0.992294 0.123907i \(-0.960457\pi\)
0.123907 + 0.992294i \(0.460457\pi\)
\(464\) 0.856275 1.48311i 0.0397516 0.0688518i
\(465\) −3.40780 5.90248i −0.158033 0.273721i
\(466\) −12.4164 3.32696i −0.575178 0.154119i
\(467\) −8.85664 15.3402i −0.409837 0.709858i 0.585035 0.811008i \(-0.301081\pi\)
−0.994871 + 0.101151i \(0.967748\pi\)
\(468\) −3.46120 1.01001i −0.159994 0.0466876i
\(469\) 12.0771 15.7551i 0.557667 0.727504i
\(470\) −21.4479 + 5.74695i −0.989318 + 0.265087i
\(471\) −15.7267 −0.724650
\(472\) 1.54617 0.0711682
\(473\) −4.23779 + 1.13551i −0.194854 + 0.0522110i
\(474\) −1.93798 7.23265i −0.0890145 0.332207i
\(475\) −0.404416 + 1.50930i −0.0185559 + 0.0692516i
\(476\) −4.34282 + 10.4991i −0.199053 + 0.481224i
\(477\) −2.29049 3.96724i −0.104874 0.181648i
\(478\) 19.1003i 0.873627i
\(479\) −9.04785 + 33.7670i −0.413407 + 1.54285i 0.374599 + 0.927187i \(0.377780\pi\)
−0.788006 + 0.615668i \(0.788886\pi\)
\(480\) −1.40553 0.811483i −0.0641534 0.0370390i
\(481\) −0.703410 + 1.15838i −0.0320727 + 0.0528174i
\(482\) 9.80044i 0.446398i
\(483\) −0.132344 1.00146i −0.00602188 0.0455679i
\(484\) 5.15956 8.93662i 0.234526 0.406210i
\(485\) −22.7786 13.1512i −1.03432 0.597166i
\(486\) −0.258819 0.965926i −0.0117403 0.0438153i
\(487\) 27.3697 + 27.3697i 1.24024 + 1.24024i 0.959901 + 0.280341i \(0.0904475\pi\)
0.280341 + 0.959901i \(0.409553\pi\)
\(488\) 11.8286 3.16947i 0.535456 0.143475i
\(489\) 2.62695 + 2.62695i 0.118795 + 0.118795i
\(490\) −2.92961 + 10.9765i −0.132346 + 0.495870i
\(491\) −29.8739 17.2477i −1.34819 0.778379i −0.360199 0.932875i \(-0.617291\pi\)
−0.987993 + 0.154496i \(0.950625\pi\)
\(492\) −0.354512 + 0.354512i −0.0159827 + 0.0159827i
\(493\) −3.67715 + 6.36902i −0.165611 + 0.286846i
\(494\) −0.667032 + 2.28585i −0.0300112 + 0.102845i
\(495\) −1.15978 + 0.669597i −0.0521281 + 0.0300961i
\(496\) 1.08690 + 4.05637i 0.0488033 + 0.182137i
\(497\) 6.81557 8.89126i 0.305720 0.398827i
\(498\) 6.33518 3.65762i 0.283886 0.163902i
\(499\) 4.43740 16.5606i 0.198645 0.741354i −0.792648 0.609680i \(-0.791298\pi\)
0.991293 0.131674i \(-0.0420352\pi\)
\(500\) 8.45328 8.45328i 0.378042 0.378042i
\(501\) 9.52786 9.52786i 0.425673 0.425673i
\(502\) −4.77534 + 17.8218i −0.213134 + 0.795427i
\(503\) 14.1495 8.16924i 0.630897 0.364248i −0.150203 0.988655i \(-0.547993\pi\)
0.781099 + 0.624407i \(0.214659\pi\)
\(504\) −0.344053 + 2.62329i −0.0153253 + 0.116850i
\(505\) −4.85387 18.1149i −0.215994 0.806101i
\(506\) −0.272840 + 0.157524i −0.0121292 + 0.00700280i
\(507\) 6.99167 10.9598i 0.310511 0.486740i
\(508\) −2.27749 + 3.94473i −0.101047 + 0.175019i
\(509\) −23.8779 + 23.8779i −1.05837 + 1.05837i −0.0601828 + 0.998187i \(0.519168\pi\)
−0.998187 + 0.0601828i \(0.980832\pi\)
\(510\) 6.03585 + 3.48480i 0.267272 + 0.154310i
\(511\) −30.1302 3.95168i −1.33288 0.174812i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −0.637919 + 0.170930i −0.0281648 + 0.00754674i
\(514\) −15.7797 15.7797i −0.696013 0.696013i
\(515\) −3.60874 13.4680i −0.159020 0.593470i
\(516\) 4.60461 + 2.65847i 0.202707 + 0.117033i
\(517\) 5.64463 9.77678i 0.248250 0.429982i
\(518\) 0.918947 + 0.380112i 0.0403762 + 0.0167012i
\(519\) 23.0813i 1.01316i
\(520\) 4.22830 4.04521i 0.185423 0.177394i
\(521\) 16.8569 + 9.73236i 0.738516 + 0.426382i 0.821530 0.570166i \(-0.193121\pi\)
−0.0830135 + 0.996548i \(0.526454\pi\)
\(522\) −0.443241 + 1.65420i −0.0194001 + 0.0724022i
\(523\) 40.8287i 1.78531i −0.450737 0.892657i \(-0.648839\pi\)
0.450737 0.892657i \(-0.351161\pi\)
\(524\) −4.51076 7.81287i −0.197054 0.341307i
\(525\) −5.78447 2.39268i −0.252455 0.104425i
\(526\) −4.24756 + 15.8521i −0.185202 + 0.691184i
\(527\) −4.66755 17.4195i −0.203322 0.758806i
\(528\) 0.797035 0.213565i 0.0346865 0.00929422i
\(529\) 22.8542 0.993662
\(530\) 7.43478 0.322946
\(531\) −1.49348 + 0.400178i −0.0648117 + 0.0173663i
\(532\) 1.73248 + 0.227220i 0.0751124 + 0.00985124i
\(533\) −0.868977 1.58510i −0.0376396 0.0686582i
\(534\) 5.28613 + 9.15584i 0.228753 + 0.396212i
\(535\) 14.7176 + 3.94357i 0.636298 + 0.170495i
\(536\) 3.75157 + 6.49791i 0.162043 + 0.280667i
\(537\) 3.50698 6.07426i 0.151337 0.262124i
\(538\) −11.8949 + 11.8949i −0.512827 + 0.512827i
\(539\) −2.89294 4.99938i −0.124608 0.215339i
\(540\) 1.56767 + 0.420055i 0.0674616 + 0.0180763i
\(541\) 27.3075 + 7.31703i 1.17404 + 0.314583i 0.792561 0.609793i \(-0.208747\pi\)
0.381481 + 0.924377i \(0.375414\pi\)
\(542\) 4.25774i 0.182886i
\(543\) 4.36097 2.51781i 0.187147 0.108050i
\(544\) −3.03657 3.03657i −0.130192 0.130192i
\(545\) −9.90056 −0.424093
\(546\) −8.73221 3.84037i −0.373704 0.164353i
\(547\) −32.6461 −1.39584 −0.697922 0.716173i \(-0.745892\pi\)
−0.697922 + 0.716173i \(0.745892\pi\)
\(548\) −1.15844 1.15844i −0.0494861 0.0494861i
\(549\) −10.6052 + 6.12294i −0.452621 + 0.261321i
\(550\) 1.95229i 0.0832460i
\(551\) 1.09247 + 0.292726i 0.0465407 + 0.0124706i
\(552\) 0.368797 + 0.0988188i 0.0156970 + 0.00420601i
\(553\) −2.59547 19.6401i −0.110371 0.835181i
\(554\) −15.9503 + 15.9503i −0.677663 + 0.677663i
\(555\) 0.305013 0.528297i 0.0129471 0.0224250i
\(556\) 4.78004 + 8.27928i 0.202719 + 0.351120i
\(557\) −26.5061 7.10228i −1.12310 0.300933i −0.350962 0.936390i \(-0.614145\pi\)
−0.772137 + 0.635456i \(0.780812\pi\)
\(558\) −2.09973 3.63685i −0.0888888 0.153960i
\(559\) −13.8522 + 13.2524i −0.585885 + 0.560516i
\(560\) −3.40792 2.61233i −0.144011 0.110391i
\(561\) −3.42276 + 0.917125i −0.144509 + 0.0387210i
\(562\) 10.4503 0.440819
\(563\) 21.1871 0.892930 0.446465 0.894801i \(-0.352683\pi\)
0.446465 + 0.894801i \(0.352683\pi\)
\(564\) −13.2152 + 3.54101i −0.556462 + 0.149104i
\(565\) 5.38195 + 20.0857i 0.226420 + 0.845012i
\(566\) −4.53437 + 16.9225i −0.190594 + 0.711306i
\(567\) −0.346627 2.62295i −0.0145570 0.110153i
\(568\) 2.11716 + 3.66703i 0.0888342 + 0.153865i
\(569\) 34.8300i 1.46015i 0.683367 + 0.730075i \(0.260515\pi\)
−0.683367 + 0.730075i \(0.739485\pi\)
\(570\) 0.277414 1.03532i 0.0116196 0.0433649i
\(571\) −19.8627 11.4677i −0.831228 0.479910i 0.0230452 0.999734i \(-0.492664\pi\)
−0.854273 + 0.519825i \(0.825997\pi\)
\(572\) −0.0658217 + 2.97440i −0.00275214 + 0.124366i
\(573\) 4.10829i 0.171626i
\(574\) −1.05196 + 0.808016i −0.0439079 + 0.0337260i
\(575\) −0.451673 + 0.782320i −0.0188361 + 0.0326250i
\(576\) −0.866025 0.500000i −0.0360844 0.0208333i
\(577\) −3.77797 14.0996i −0.157279 0.586973i −0.998899 0.0469033i \(-0.985065\pi\)
0.841621 0.540069i \(-0.181602\pi\)
\(578\) 1.01931 + 1.01931i 0.0423976 + 0.0423976i
\(579\) 20.4591 5.48199i 0.850250 0.227824i
\(580\) −1.96534 1.96534i −0.0816064 0.0816064i
\(581\) 17.8774 7.41534i 0.741680 0.307640i
\(582\) −14.0351 8.10319i −0.581775 0.335888i
\(583\) −2.67287 + 2.67287i −0.110699 + 0.110699i
\(584\) 5.74285 9.94690i 0.237641 0.411606i
\(585\) −3.03725 + 5.00174i −0.125575 + 0.206797i
\(586\) 4.30514 2.48557i 0.177844 0.102678i
\(587\) 3.79127 + 14.1492i 0.156482 + 0.584001i 0.998974 + 0.0452907i \(0.0144214\pi\)
−0.842491 + 0.538710i \(0.818912\pi\)
\(588\) −1.80510 + 6.76326i −0.0744409 + 0.278912i
\(589\) −2.40185 + 1.38671i −0.0989667 + 0.0571384i
\(590\) 0.649476 2.42388i 0.0267385 0.0997894i
\(591\) 10.8903 10.8903i 0.447968 0.447968i
\(592\) −0.265780 + 0.265780i −0.0109235 + 0.0109235i
\(593\) 8.53339 31.8471i 0.350425 1.30780i −0.535721 0.844395i \(-0.679960\pi\)
0.886146 0.463407i \(-0.153373\pi\)
\(594\) −0.714602 + 0.412576i −0.0293205 + 0.0169282i
\(595\) 14.6348 + 11.2183i 0.599969 + 0.459905i
\(596\) −0.987748 3.68633i −0.0404597 0.150998i
\(597\) −9.77412 + 5.64309i −0.400028 + 0.230956i
\(598\) −0.714519 + 1.17667i −0.0292189 + 0.0481176i
\(599\) −11.8719 + 20.5628i −0.485075 + 0.840174i −0.999853 0.0171493i \(-0.994541\pi\)
0.514778 + 0.857323i \(0.327874\pi\)
\(600\) 1.67300 1.67300i 0.0682999 0.0682999i
\(601\) 11.9640 + 6.90744i 0.488023 + 0.281760i 0.723754 0.690058i \(-0.242415\pi\)
−0.235731 + 0.971818i \(0.575748\pi\)
\(602\) 11.1646 + 8.55816i 0.455033 + 0.348805i
\(603\) −5.30552 5.30552i −0.216057 0.216057i
\(604\) −16.9975 + 4.55448i −0.691620 + 0.185319i
\(605\) −11.8423 11.8423i −0.481460 0.481460i
\(606\) −2.99074 11.1616i −0.121490 0.453408i
\(607\) 11.9562 + 6.90292i 0.485287 + 0.280181i 0.722617 0.691248i \(-0.242939\pi\)
−0.237330 + 0.971429i \(0.576272\pi\)
\(608\) −0.330211 + 0.571943i −0.0133918 + 0.0231953i
\(609\) −1.73188 + 4.18693i −0.0701792 + 0.169663i
\(610\) 19.8747i 0.804702i
\(611\) 1.09136 49.3170i 0.0441516 1.99515i
\(612\) 3.71902 + 2.14718i 0.150333 + 0.0867946i
\(613\) −1.59295 + 5.94498i −0.0643387 + 0.240115i −0.990605 0.136754i \(-0.956333\pi\)
0.926266 + 0.376870i \(0.123000\pi\)
\(614\) 25.2962i 1.02087i
\(615\) 0.406842 + 0.704672i 0.0164055 + 0.0284151i
\(616\) 2.16433 0.286020i 0.0872033 0.0115241i
\(617\) 4.00262 14.9380i 0.161139 0.601381i −0.837362 0.546649i \(-0.815903\pi\)
0.998501 0.0547314i \(-0.0174303\pi\)
\(618\) −2.22354 8.29837i −0.0894440 0.333809i
\(619\) −41.6279 + 11.1542i −1.67317 + 0.448323i −0.965961 0.258686i \(-0.916710\pi\)
−0.707204 + 0.707010i \(0.750044\pi\)
\(620\) 6.81560 0.273721
\(621\) −0.381806 −0.0153214
\(622\) −5.27728 + 1.41404i −0.211600 + 0.0566979i
\(623\) 10.7169 + 25.8371i 0.429365 + 1.03514i
\(624\) 2.60529 2.49248i 0.104295 0.0997791i
\(625\) −3.78613 6.55777i −0.151445 0.262311i
\(626\) −23.2689 6.23487i −0.930011 0.249196i
\(627\) 0.272474 + 0.471940i 0.0108816 + 0.0188474i
\(628\) 7.86337 13.6198i 0.313783 0.543488i
\(629\) 1.14136 1.14136i 0.0455089 0.0455089i
\(630\) 3.96791 + 1.64128i 0.158085 + 0.0653903i
\(631\) −6.97794 1.86973i −0.277787 0.0744329i 0.117236 0.993104i \(-0.462597\pi\)
−0.395023 + 0.918671i \(0.629263\pi\)
\(632\) 7.23265 + 1.93798i 0.287699 + 0.0770888i
\(633\) 12.4167i 0.493520i
\(634\) 3.02036 1.74380i 0.119954 0.0692553i
\(635\) 5.22735 + 5.22735i 0.207441 + 0.207441i
\(636\) 4.58098 0.181648
\(637\) −21.5858 13.0787i −0.855260 0.518198i
\(638\) 1.41311 0.0559457
\(639\) −2.99412 2.99412i −0.118446 0.118446i
\(640\) 1.40553 0.811483i 0.0555585 0.0320767i
\(641\) 6.19839i 0.244822i 0.992480 + 0.122411i \(0.0390626\pi\)
−0.992480 + 0.122411i \(0.960937\pi\)
\(642\) 9.06833 + 2.42985i 0.357899 + 0.0958986i
\(643\) −6.46325 1.73182i −0.254886 0.0682964i 0.129114 0.991630i \(-0.458787\pi\)
−0.383999 + 0.923333i \(0.625453\pi\)
\(644\) 0.933460 + 0.386115i 0.0367835 + 0.0152151i
\(645\) 6.10179 6.10179i 0.240258 0.240258i
\(646\) 1.41805 2.45613i 0.0557923 0.0966350i
\(647\) 1.69327 + 2.93282i 0.0665692 + 0.115301i 0.897389 0.441240i \(-0.145461\pi\)
−0.830820 + 0.556542i \(0.812128\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) 0.637912 + 1.10490i 0.0250402 + 0.0433710i
\(650\) 4.10084 + 7.48032i 0.160848 + 0.293402i
\(651\) −4.25694 10.2629i −0.166842 0.402235i
\(652\) −3.58847 + 0.961529i −0.140536 + 0.0376564i
\(653\) 8.37502 0.327740 0.163870 0.986482i \(-0.447602\pi\)
0.163870 + 0.986482i \(0.447602\pi\)
\(654\) −6.10028 −0.238540
\(655\) −14.1427 + 3.78953i −0.552602 + 0.148069i
\(656\) −0.129761 0.484273i −0.00506630 0.0189077i
\(657\) −2.97272 + 11.0943i −0.115977 + 0.432831i
\(658\) −35.8857 + 4.74235i −1.39897 + 0.184876i
\(659\) −5.81421 10.0705i −0.226489 0.392291i 0.730276 0.683152i \(-0.239392\pi\)
−0.956765 + 0.290861i \(0.906058\pi\)
\(660\) 1.33919i 0.0521281i
\(661\) −9.86844 + 36.8295i −0.383838 + 1.43250i 0.456153 + 0.889902i \(0.349227\pi\)
−0.839991 + 0.542601i \(0.817440\pi\)
\(662\) 4.27729 + 2.46950i 0.166242 + 0.0959797i
\(663\) −11.1881 + 10.7036i −0.434508 + 0.415694i
\(664\) 7.31524i 0.283886i
\(665\) 1.08394 2.62050i 0.0420334 0.101619i
\(666\) 0.187935 0.325513i 0.00728234 0.0126134i
\(667\) 0.566262 + 0.326931i 0.0219257 + 0.0126588i
\(668\) 3.48744 + 13.0153i 0.134933 + 0.503577i
\(669\) 8.38810 + 8.38810i 0.324303 + 0.324303i
\(670\) 11.7624 3.15173i 0.454422 0.121762i
\(671\) 7.14511 + 7.14511i 0.275834 + 0.275834i
\(672\) −2.09981 1.60960i −0.0810018 0.0620917i
\(673\) −22.0840 12.7502i −0.851277 0.491485i 0.00980485 0.999952i \(-0.496879\pi\)
−0.861081 + 0.508467i \(0.830212\pi\)
\(674\) 19.6097 19.6097i 0.755337 0.755337i
\(675\) −1.18299 + 2.04900i −0.0455333 + 0.0788659i
\(676\) 5.99560 + 11.5349i 0.230600 + 0.443648i
\(677\) 21.0666 12.1628i 0.809654 0.467454i −0.0371820 0.999309i \(-0.511838\pi\)
0.846836 + 0.531855i \(0.178505\pi\)
\(678\) 3.31612 + 12.3759i 0.127355 + 0.475294i
\(679\) −34.0303 26.0858i −1.30596 1.00108i
\(680\) −6.03585 + 3.48480i −0.231464 + 0.133636i
\(681\) 3.79654 14.1689i 0.145484 0.542953i
\(682\) −2.45026 + 2.45026i −0.0938255 + 0.0938255i
\(683\) 32.6233 32.6233i 1.24830 1.24830i 0.291823 0.956472i \(-0.405738\pi\)
0.956472 0.291823i \(-0.0942617\pi\)
\(684\) 0.170930 0.637919i 0.00653567 0.0243914i
\(685\) −2.30265 + 1.32944i −0.0879798 + 0.0507952i
\(686\) −7.06220 + 17.1209i −0.269636 + 0.653679i
\(687\) 4.17662 + 15.5874i 0.159348 + 0.594695i
\(688\) −4.60461 + 2.65847i −0.175549 + 0.101353i
\(689\) −4.62682 + 15.8557i −0.176268 + 0.604053i
\(690\) 0.309830 0.536641i 0.0117950 0.0204296i
\(691\) 23.4337 23.4337i 0.891459 0.891459i −0.103201 0.994661i \(-0.532908\pi\)
0.994661 + 0.103201i \(0.0329085\pi\)
\(692\) −19.9890 11.5406i −0.759866 0.438709i
\(693\) −2.01655 + 0.836444i −0.0766026 + 0.0317739i
\(694\) −2.25649 2.25649i −0.0856553 0.0856553i
\(695\) 14.9870 4.01576i 0.568490 0.152326i
\(696\) −1.21096 1.21096i −0.0459012 0.0459012i
\(697\) 0.557238 + 2.07964i 0.0211069 + 0.0787720i
\(698\) 2.39914 + 1.38515i 0.0908089 + 0.0524285i
\(699\) −6.42720 + 11.1322i −0.243099 + 0.421060i
\(700\) 4.96435 3.81316i 0.187635 0.144124i
\(701\) 15.7207i 0.593761i −0.954915 0.296880i \(-0.904054\pi\)
0.954915 0.296880i \(-0.0959463\pi\)
\(702\) −1.87142 + 3.08185i −0.0706321 + 0.116317i
\(703\) −0.214976 0.124117i −0.00810798 0.00468115i
\(704\) −0.213565 + 0.797035i −0.00804903 + 0.0300394i
\(705\) 22.2045i 0.836270i
\(706\) 11.9855 + 20.7595i 0.451080 + 0.781294i
\(707\) −4.00538 30.3090i −0.150638 1.13989i
\(708\) 0.400178 1.49348i 0.0150396 0.0561286i
\(709\) −1.94388 7.25466i −0.0730040 0.272454i 0.919769 0.392459i \(-0.128376\pi\)
−0.992773 + 0.120005i \(0.961709\pi\)
\(710\) 6.63801 1.77865i 0.249120 0.0667515i
\(711\) −7.48779 −0.280814
\(712\) −10.5723 −0.396212
\(713\) −1.54875 + 0.414986i −0.0580011 + 0.0155414i
\(714\) 9.01732 + 6.91220i 0.337465 + 0.258683i
\(715\) 4.63521 + 1.35260i 0.173347 + 0.0505843i
\(716\) 3.50698 + 6.07426i 0.131062 + 0.227006i
\(717\) 18.4495 + 4.94352i 0.689008 + 0.184619i
\(718\) 4.76475 + 8.25278i 0.177819 + 0.307991i
\(719\) 18.3004 31.6973i 0.682491 1.18211i −0.291728 0.956501i \(-0.594230\pi\)
0.974218 0.225607i \(-0.0724365\pi\)
\(720\) −1.14761 + 1.14761i −0.0427689 + 0.0427689i
\(721\) −2.97791 22.5340i −0.110903 0.839211i
\(722\) 17.9313 + 4.80468i 0.667334 + 0.178812i
\(723\) 9.46650 + 2.53654i 0.352063 + 0.0943349i
\(724\) 5.03562i 0.187147i
\(725\) 3.50901 2.02593i 0.130321 0.0752411i
\(726\) −7.29672 7.29672i −0.270807 0.270807i
\(727\) −21.7594 −0.807011 −0.403506 0.914977i \(-0.632208\pi\)
−0.403506 + 0.914977i \(0.632208\pi\)
\(728\) 7.69197 5.64213i 0.285083 0.209111i
\(729\) −1.00000 −0.0370370
\(730\) −13.1811 13.1811i −0.487855 0.487855i
\(731\) 19.7738 11.4164i 0.731362 0.422252i
\(732\) 12.2459i 0.452621i
\(733\) 5.07883 + 1.36087i 0.187591 + 0.0502649i 0.351391 0.936229i \(-0.385709\pi\)
−0.163800 + 0.986494i \(0.552375\pi\)
\(734\) 13.4982 + 3.61684i 0.498229 + 0.133500i
\(735\) 9.84428 + 5.67073i 0.363112 + 0.209168i
\(736\) −0.269978 + 0.269978i −0.00995152 + 0.00995152i
\(737\) −3.09561 + 5.36176i −0.114028 + 0.197503i
\(738\) 0.250678 + 0.434187i 0.00922759 + 0.0159827i
\(739\) −15.8606 4.24984i −0.583443 0.156333i −0.0449881 0.998988i \(-0.514325\pi\)
−0.538455 + 0.842655i \(0.680992\pi\)
\(740\) 0.305013 + 0.528297i 0.0112125 + 0.0194206i
\(741\) 2.03532 + 1.23593i 0.0747695 + 0.0454029i
\(742\) 12.0172 + 1.57610i 0.441166 + 0.0578604i
\(743\) −10.5714 + 2.83260i −0.387827 + 0.103918i −0.447463 0.894302i \(-0.647672\pi\)
0.0596366 + 0.998220i \(0.481006\pi\)
\(744\) 4.19947 0.153960
\(745\) −6.19384 −0.226925
\(746\) 7.59888 2.03611i 0.278215 0.0745474i
\(747\) −1.89332 7.06598i −0.0692731 0.258531i
\(748\) 0.917125 3.42276i 0.0335334 0.125148i
\(749\) 22.9528 + 9.49418i 0.838678 + 0.346910i
\(750\) −5.97737 10.3531i −0.218263 0.378042i
\(751\) 50.9903i 1.86066i 0.366719 + 0.930332i \(0.380481\pi\)
−0.366719 + 0.930332i \(0.619519\pi\)
\(752\) 3.54101 13.2152i 0.129128 0.481910i
\(753\) 15.9786 + 9.22525i 0.582293 + 0.336187i
\(754\) 5.41443 2.96828i 0.197182 0.108098i
\(755\) 28.5596i 1.03939i
\(756\) 2.44485 + 1.01129i 0.0889184 + 0.0367801i
\(757\) 21.6738 37.5401i 0.787748 1.36442i −0.139595 0.990209i \(-0.544580\pi\)
0.927343 0.374211i \(-0.122087\pi\)
\(758\) 15.2447 + 8.80156i 0.553714 + 0.319687i
\(759\) 0.0815405 + 0.304313i 0.00295973 + 0.0110459i
\(760\) 0.757908 + 0.757908i 0.0274922 + 0.0274922i
\(761\) −7.31737 + 1.96068i −0.265254 + 0.0710747i −0.388995 0.921240i \(-0.627178\pi\)
0.123741 + 0.992315i \(0.460511\pi\)
\(762\) 3.22086 + 3.22086i 0.116679 + 0.116679i
\(763\) −16.0028 2.09882i −0.579340 0.0759823i
\(764\) 3.55789 + 2.05415i 0.128720 + 0.0743164i
\(765\) 4.92825 4.92825i 0.178181 0.178181i
\(766\) −3.17641 + 5.50170i −0.114768 + 0.198785i
\(767\) 4.76506 + 2.89353i 0.172056 + 0.104479i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 5.01814 + 18.7279i 0.180959 + 0.675347i 0.995460 + 0.0951848i \(0.0303442\pi\)
−0.814501 + 0.580162i \(0.802989\pi\)
\(770\) 0.460753 3.51309i 0.0166044 0.126603i
\(771\) −19.3261 + 11.1579i −0.696013 + 0.401843i
\(772\) −5.48199 + 20.4591i −0.197301 + 0.736338i
\(773\) 27.8227 27.8227i 1.00071 1.00071i 0.000712815 1.00000i \(-0.499773\pi\)
1.00000 0.000712815i \(-0.000226896\pi\)
\(774\) 3.75965 3.75965i 0.135138 0.135138i
\(775\) −2.57159 + 9.59729i −0.0923741 + 0.344745i
\(776\) 14.0351 8.10319i 0.503832 0.290888i
\(777\) 0.605001 0.789255i 0.0217043 0.0283143i
\(778\) −9.13524 34.0932i −0.327514 1.22230i
\(779\) 0.286747 0.165553i 0.0102738 0.00593157i
\(780\) −2.81301 5.13120i −0.100722 0.183727i
\(781\) −1.74698 + 3.02586i −0.0625119 + 0.108274i
\(782\) 1.15938 1.15938i 0.0414594 0.0414594i
\(783\) 1.48311 + 0.856275i 0.0530021 + 0.0306008i
\(784\) −4.95460 4.94489i −0.176950 0.176603i
\(785\) −18.0482 18.0482i −0.644167 0.644167i
\(786\) −8.71412 + 2.33494i −0.310823 + 0.0832846i
\(787\) −20.4080 20.4080i −0.727465 0.727465i 0.242649 0.970114i \(-0.421984\pi\)
−0.970114 + 0.242649i \(0.921984\pi\)
\(788\) 3.98613 + 14.8764i 0.142000 + 0.529952i
\(789\) 14.2126 + 8.20565i 0.505982 + 0.292129i
\(790\) 6.07622 10.5243i 0.216182 0.374438i
\(791\) 4.44116 + 33.6065i 0.157909 + 1.19491i
\(792\) 0.825152i 0.0293205i
\(793\) 42.3854 + 12.3684i 1.50515 + 0.439216i
\(794\) 6.36459 + 3.67460i 0.225871 + 0.130407i
\(795\) 1.92426 7.18144i 0.0682465 0.254700i
\(796\) 11.2862i 0.400028i
\(797\) 27.6580 + 47.9051i 0.979697 + 1.69688i 0.663474 + 0.748199i \(0.269081\pi\)
0.316223 + 0.948685i \(0.397585\pi\)
\(798\) 0.667876 1.61464i 0.0236425 0.0571575i
\(799\) −15.2064 + 56.7510i −0.537963 + 2.00771i
\(800\) 0.612360 + 2.28536i 0.0216502 + 0.0807997i
\(801\) 10.2120 2.73630i 0.360824 0.0966824i
\(802\) −29.5498 −1.04344
\(803\) 9.47744 0.334452
\(804\) 7.24748 1.94196i 0.255599 0.0684875i
\(805\) 0.997404 1.30116i 0.0351539 0.0458600i
\(806\) −4.24150 + 14.5352i −0.149400 + 0.511980i
\(807\) 8.41099 + 14.5683i 0.296081 + 0.512827i
\(808\) 11.1616 + 2.99074i 0.392663 + 0.105214i
\(809\) 9.97055 + 17.2695i 0.350546 + 0.607163i 0.986345 0.164691i \(-0.0526628\pi\)
−0.635799 + 0.771854i \(0.719329\pi\)
\(810\) 0.811483 1.40553i 0.0285126 0.0493853i
\(811\) −19.0450 + 19.0450i −0.668759 + 0.668759i −0.957429 0.288670i \(-0.906787\pi\)
0.288670 + 0.957429i \(0.406787\pi\)
\(812\) −2.76005 3.59332i −0.0968588 0.126101i
\(813\) 4.11266 + 1.10198i 0.144237 + 0.0386483i
\(814\) −0.299582 0.0802727i −0.0105003 0.00281356i
\(815\) 6.02942i 0.211201i
\(816\) −3.71902 + 2.14718i −0.130192 + 0.0751663i
\(817\) −2.48296 2.48296i −0.0868677 0.0868677i
\(818\) −8.68985 −0.303834
\(819\) −5.96958 + 7.44071i −0.208594 + 0.259999i
\(820\) −0.813685 −0.0284151
\(821\) 17.2092 + 17.2092i 0.600607 + 0.600607i 0.940474 0.339867i \(-0.110382\pi\)
−0.339867 + 0.940474i \(0.610382\pi\)
\(822\) −1.41879 + 0.819140i −0.0494861 + 0.0285708i
\(823\) 30.6407i 1.06807i −0.845463 0.534034i \(-0.820675\pi\)
0.845463 0.534034i \(-0.179325\pi\)
\(824\) 8.29837 + 2.22354i 0.289087 + 0.0774608i
\(825\) 1.88577 + 0.505290i 0.0656540 + 0.0175919i
\(826\) 1.56362 3.78016i 0.0544053 0.131528i
\(827\) 20.5897 20.5897i 0.715975 0.715975i −0.251803 0.967778i \(-0.581024\pi\)
0.967778 + 0.251803i \(0.0810235\pi\)
\(828\) 0.190903 0.330654i 0.00663435 0.0114910i
\(829\) 23.3116 + 40.3769i 0.809645 + 1.40235i 0.913110 + 0.407714i \(0.133674\pi\)
−0.103465 + 0.994633i \(0.532993\pi\)
\(830\) 11.4678 + 3.07280i 0.398055 + 0.106658i
\(831\) 11.2786 + 19.5350i 0.391249 + 0.677663i
\(832\) 0.855906 + 3.50249i 0.0296732 + 0.121427i
\(833\) 21.2768 + 21.2351i 0.737199 + 0.735753i
\(834\) 9.23434 2.47433i 0.319759 0.0856791i
\(835\) 21.8685 0.756792
\(836\) −0.544949 −0.0188474
\(837\) −4.05637 + 1.08690i −0.140209 + 0.0375688i
\(838\) 1.83684 + 6.85517i 0.0634525 + 0.236808i
\(839\) −10.3499 + 38.6264i −0.357319 + 1.33353i 0.520222 + 0.854031i \(0.325849\pi\)
−0.877541 + 0.479502i \(0.840817\pi\)
\(840\) −3.40535 + 2.61567i −0.117496 + 0.0902493i
\(841\) 13.0336 + 22.5748i 0.449434 + 0.778442i
\(842\) 28.1594i 0.970435i
\(843\) 2.70473 10.0942i 0.0931560 0.347663i
\(844\) 10.7532 + 6.20836i 0.370140 + 0.213700i
\(845\) 20.6013 4.55383i 0.708705 0.156656i
\(846\) 13.6814i 0.470377i
\(847\) −16.6309 21.6518i −0.571446 0.743966i
\(848\) −2.29049 + 3.96724i −0.0786557 + 0.136236i
\(849\) 15.1723 + 8.75973i 0.520712 + 0.300633i
\(850\) −2.62969 9.81415i −0.0901978 0.336623i
\(851\) −0.101477 0.101477i −0.00347858 0.00347858i
\(852\) 4.09004 1.09592i 0.140123 0.0375457i
\(853\) −7.00618 7.00618i −0.239887 0.239887i 0.576916 0.816803i \(-0.304256\pi\)
−0.816803 + 0.576916i \(0.804256\pi\)
\(854\) 4.21323 32.1245i 0.144174 1.09928i
\(855\) −0.928244 0.535922i −0.0317453 0.0183281i
\(856\) −6.63848 + 6.63848i −0.226899 + 0.226899i
\(857\) 9.17115 15.8849i 0.313280 0.542618i −0.665790 0.746139i \(-0.731905\pi\)
0.979070 + 0.203521i \(0.0652387\pi\)
\(858\) 2.85601 + 0.833410i 0.0975027 + 0.0284521i
\(859\) −16.5211 + 9.53844i −0.563691 + 0.325447i −0.754626 0.656155i \(-0.772182\pi\)
0.190934 + 0.981603i \(0.438848\pi\)
\(860\) 2.23341 + 8.33519i 0.0761586 + 0.284228i
\(861\) 0.508217 + 1.22524i 0.0173200 + 0.0417562i
\(862\) 30.5124 17.6163i 1.03926 0.600015i
\(863\) −8.15636 + 30.4400i −0.277646 + 1.03619i 0.676402 + 0.736533i \(0.263538\pi\)
−0.954047 + 0.299656i \(0.903128\pi\)
\(864\) −0.707107 + 0.707107i −0.0240563 + 0.0240563i
\(865\) −26.4883 + 26.4883i −0.900630 + 0.900630i
\(866\) 5.42325 20.2398i 0.184290 0.687778i
\(867\) 1.24839 0.720758i 0.0423976 0.0244782i
\(868\) 11.0164 + 1.44484i 0.373921 + 0.0490410i
\(869\) 1.59913 + 5.96803i 0.0542468 + 0.202452i
\(870\) −2.40704 + 1.38971i −0.0816064 + 0.0471155i
\(871\) −0.598519 + 27.0463i −0.0202801 + 0.916430i
\(872\) 3.05014 5.28300i 0.103291 0.178905i
\(873\) −11.4596 + 11.4596i −0.387850 + 0.387850i
\(874\) −0.218371 0.126077i −0.00738652 0.00426461i
\(875\) −12.1183 29.2157i −0.409674 0.987671i
\(876\) −8.12161 8.12161i −0.274404 0.274404i
\(877\) 30.4828 8.16784i 1.02933 0.275808i 0.295646 0.955298i \(-0.404465\pi\)
0.733685 + 0.679489i \(0.237799\pi\)
\(878\) 8.15326 + 8.15326i 0.275159 + 0.275159i
\(879\) −1.28663 4.80175i −0.0433968 0.161959i
\(880\) 1.15978 + 0.669597i 0.0390960 + 0.0225721i
\(881\) 0.445778 0.772110i 0.0150186 0.0260131i −0.858418 0.512950i \(-0.828553\pi\)
0.873437 + 0.486937i \(0.161886\pi\)
\(882\) 6.06561 + 3.49405i 0.204240 + 0.117651i
\(883\) 23.7074i 0.797818i 0.916990 + 0.398909i \(0.130611\pi\)
−0.916990 + 0.398909i \(0.869389\pi\)
\(884\) −3.67557 15.0409i −0.123623 0.505882i
\(885\) −2.17319 1.25469i −0.0730509 0.0421760i
\(886\) 10.4592 39.0342i 0.351383 1.31138i
\(887\) 0.392486i 0.0131784i 0.999978 + 0.00658920i \(0.00209742\pi\)
−0.999978 + 0.00658920i \(0.997903\pi\)
\(888\) 0.187935 + 0.325513i 0.00630669 + 0.0109235i
\(889\) 7.34109 + 9.55738i 0.246212 + 0.320544i
\(890\) −4.44093 + 16.5738i −0.148860 + 0.555554i
\(891\) 0.213565 + 0.797035i 0.00715470 + 0.0267017i
\(892\) −11.4584 + 3.07026i −0.383654 + 0.102800i
\(893\) 9.03552 0.302362
\(894\) −3.81637 −0.127638
\(895\) 10.9955 2.94624i 0.367540 0.0984821i
\(896\) 2.44386 1.01368i 0.0816436 0.0338648i
\(897\) 0.951645 + 0.994717i 0.0317745 + 0.0332126i
\(898\) 15.9592 + 27.6421i 0.532565 + 0.922430i
\(899\) 6.94674 + 1.86137i 0.231687 + 0.0620803i
\(900\) −1.18299 2.04900i −0.0394330 0.0682999i
\(901\) 9.83618 17.0368i 0.327691 0.567577i
\(902\) 0.292527 0.292527i 0.00974007 0.00974007i
\(903\) 11.1561 8.56912i 0.371253 0.285162i
\(904\) −12.3759 3.31612i −0.411617 0.110292i
\(905\) 7.89417 + 2.11524i 0.262411 + 0.0703128i
\(906\) 17.5971i 0.584626i
\(907\) 9.55936 5.51910i 0.317413 0.183259i −0.332826 0.942988i \(-0.608002\pi\)
0.650239 + 0.759730i \(0.274669\pi\)
\(908\) 10.3723 + 10.3723i 0.344218 + 0.344218i
\(909\) −11.5553 −0.383266
\(910\) −5.61393 14.4284i −0.186100 0.478298i
\(911\) −59.8158 −1.98178 −0.990892 0.134657i \(-0.957007\pi\)
−0.990892 + 0.134657i \(0.957007\pi\)
\(912\) 0.466989 + 0.466989i 0.0154636 + 0.0154636i
\(913\) −5.22749 + 3.01809i −0.173005 + 0.0998842i
\(914\) 27.9507i 0.924525i
\(915\) −19.1975 5.14394i −0.634648 0.170053i
\(916\) −15.5874 4.17662i −0.515021 0.137999i
\(917\) −23.6630 + 3.12710i −0.781421 + 0.103266i
\(918\) 3.03657 3.03657i 0.100222 0.100222i
\(919\) −13.2386 + 22.9299i −0.436701 + 0.756388i −0.997433 0.0716097i \(-0.977186\pi\)
0.560732 + 0.827997i \(0.310520\pi\)
\(920\) 0.309830 + 0.536641i 0.0102148 + 0.0176925i
\(921\) 24.4342 + 6.54713i 0.805135 + 0.215735i
\(922\) −15.2726 26.4529i −0.502976 0.871181i
\(923\) −0.337769 + 15.2633i −0.0111178 + 0.502399i
\(924\) 0.283896 2.16461i 0.00933948 0.0712104i
\(925\) −0.858999 + 0.230168i −0.0282437 + 0.00756788i
\(926\) −26.4252 −0.868386
\(927\) −8.59111 −0.282169
\(928\) 1.65420 0.443241i 0.0543017 0.0145501i
\(929\) 7.01300 + 26.1729i 0.230089 + 0.858704i 0.980301 + 0.197507i \(0.0632846\pi\)
−0.750212 + 0.661197i \(0.770049\pi\)
\(930\) 1.76401 6.58336i 0.0578440 0.215877i
\(931\) 2.30755 4.00587i 0.0756268 0.131287i
\(932\) −6.42720 11.1322i −0.210530 0.364648i
\(933\) 5.46344i 0.178865i
\(934\) 4.58454 17.1097i 0.150011 0.559847i
\(935\) −4.98049 2.87549i −0.162880 0.0940386i
\(936\) −1.73325 3.16162i −0.0566531 0.103341i
\(937\) 19.1418i 0.625336i −0.949862 0.312668i \(-0.898777\pi\)
0.949862 0.312668i \(-0.101223\pi\)
\(938\) 19.6803 2.60079i 0.642586 0.0849188i
\(939\) −12.0448 + 20.8623i −0.393069 + 0.680815i
\(940\) −19.2297 11.1023i −0.627203 0.362116i
\(941\) −11.3247 42.2645i −0.369176 1.37778i −0.861670 0.507469i \(-0.830581\pi\)
0.492494 0.870316i \(-0.336085\pi\)
\(942\) −11.1205 11.1205i −0.362325 0.362325i
\(943\) 0.184899 0.0495434i 0.00602113 0.00161336i
\(944\) 1.09331 + 1.09331i 0.0355841 + 0.0355841i
\(945\) 2.61233 3.40792i 0.0849791 0.110859i
\(946\) −3.79950 2.19364i −0.123532 0.0713215i
\(947\) −41.5008 + 41.5008i −1.34859 + 1.34859i −0.461404 + 0.887190i \(0.652654\pi\)
−0.887190 + 0.461404i \(0.847346\pi\)
\(948\) 3.74389 6.48461i 0.121596 0.210610i
\(949\) 36.3134 19.9076i 1.17878 0.646228i
\(950\) −1.35320 + 0.781273i −0.0439037 + 0.0253478i
\(951\) −0.902659 3.36877i −0.0292707 0.109240i
\(952\) −10.4948 + 4.35313i −0.340139 + 0.141086i
\(953\) 3.29385 1.90170i 0.106698 0.0616022i −0.445701 0.895182i \(-0.647046\pi\)
0.552399 + 0.833580i \(0.313712\pi\)
\(954\) 1.18564 4.42489i 0.0383867 0.143261i
\(955\) 4.71472 4.71472i 0.152565 0.152565i
\(956\) −13.5059 + 13.5059i −0.436813 + 0.436813i
\(957\) 0.365741 1.36496i 0.0118227 0.0441230i
\(958\) −30.2747 + 17.4791i −0.978131 + 0.564724i
\(959\) −4.00372 + 1.66070i −0.129287 + 0.0536268i
\(960\) −0.420055 1.56767i −0.0135572 0.0505962i
\(961\) 11.5740 6.68224i 0.373354 0.215556i
\(962\) −1.31648 + 0.321710i −0.0424451 + 0.0103723i
\(963\) 4.69411 8.13045i 0.151266 0.262000i
\(964\) −6.92996 + 6.92996i −0.223199 + 0.223199i
\(965\) 29.7702 + 17.1879i 0.958338 + 0.553297i
\(966\) 0.614556 0.801719i 0.0197730 0.0257949i
\(967\) −22.5652 22.5652i −0.725647 0.725647i 0.244102 0.969749i \(-0.421507\pi\)
−0.969749 + 0.244102i \(0.921507\pi\)
\(968\) 9.96751 2.67079i 0.320368 0.0858423i
\(969\) −2.00542 2.00542i −0.0644233 0.0644233i
\(970\) −6.80757 25.4062i −0.218578 0.815744i
\(971\) −40.4365 23.3460i −1.29767 0.749210i −0.317668 0.948202i \(-0.602900\pi\)
−0.980001 + 0.198992i \(0.936233\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) 25.0756 3.31378i 0.803887 0.106235i
\(974\) 38.7067i 1.24024i
\(975\) 8.28681 2.02505i 0.265390 0.0648536i
\(976\) 10.6052 + 6.12294i 0.339466 + 0.195991i
\(977\) 8.19576 30.5870i 0.262206 0.978565i −0.701733 0.712440i \(-0.747590\pi\)
0.963939 0.266125i \(-0.0857434\pi\)
\(978\) 3.71506i 0.118795i
\(979\) −4.36186 7.55496i −0.139406 0.241458i
\(980\) −9.83313 + 5.69004i −0.314108 + 0.181762i
\(981\) −1.57887 + 5.89242i −0.0504094 + 0.188131i
\(982\) −8.92808 33.3201i −0.284907 1.06329i
\(983\) 6.25562 1.67619i 0.199523 0.0534621i −0.157673 0.987491i \(-0.550399\pi\)
0.357197 + 0.934029i \(0.383733\pi\)
\(984\) −0.501356 −0.0159827
\(985\) 24.9957 0.796429
\(986\) −7.10371 + 1.90343i −0.226228 + 0.0606177i
\(987\) −4.70713 + 35.8903i −0.149830 + 1.14240i
\(988\) −2.08800 + 1.14468i −0.0664283 + 0.0364171i
\(989\) −1.01502 1.75807i −0.0322758 0.0559034i
\(990\) −1.29356 0.346609i −0.0411121 0.0110160i
\(991\) 1.79039 + 3.10104i 0.0568735 + 0.0985079i 0.893060 0.449937i \(-0.148553\pi\)
−0.836187 + 0.548445i \(0.815220\pi\)
\(992\) −2.09973 + 3.63685i −0.0666666 + 0.115470i
\(993\) 3.49239 3.49239i 0.110828 0.110828i
\(994\) 11.1064 1.46773i 0.352274 0.0465536i
\(995\) −17.6930 4.74081i −0.560904 0.150294i
\(996\) 7.06598 + 1.89332i 0.223894 + 0.0599922i
\(997\) 8.76573i 0.277614i −0.990319 0.138807i \(-0.955673\pi\)
0.990319 0.138807i \(-0.0443267\pi\)
\(998\) 14.8478 8.57239i 0.469999 0.271354i
\(999\) −0.265780 0.265780i −0.00840892 0.00840892i
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.a.241.7 yes 32
7.5 odd 6 546.2.by.a.397.7 32
13.2 odd 12 546.2.by.a.535.7 yes 32
91.54 even 12 inner 546.2.cg.a.145.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.by.a.397.7 32 7.5 odd 6
546.2.by.a.535.7 yes 32 13.2 odd 12
546.2.cg.a.145.7 yes 32 91.54 even 12 inner
546.2.cg.a.241.7 yes 32 1.1 even 1 trivial