Properties

Label 546.2.cg.a.271.2
Level $546$
Weight $2$
Character 546.271
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 271.2
Character \(\chi\) \(=\) 546.271
Dual form 546.2.cg.a.409.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(0.0344778 + 0.128673i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.22943 - 1.42466i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(0.0344778 + 0.128673i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.22943 - 1.42466i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.0666060 - 0.115365i) q^{10} +(1.12343 + 4.19269i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.49669 + 3.28023i) q^{13} +(-2.58383 - 0.569061i) q^{14} +(0.0344778 - 0.128673i) q^{15} -1.00000 q^{16} -3.34137 q^{17} +(0.258819 - 0.965926i) q^{18} +(3.90282 + 1.04576i) q^{19} +(-0.128673 + 0.0344778i) q^{20} +(-2.64307 + 0.119073i) q^{21} +(2.17030 - 3.75906i) q^{22} -1.46312i q^{23} +(-0.965926 + 0.258819i) q^{24} +(4.31476 - 2.49113i) q^{25} +(3.37779 - 1.26116i) q^{26} -1.00000i q^{27} +(1.42466 + 2.22943i) q^{28} +(2.15096 + 3.72557i) q^{29} +(-0.115365 + 0.0666060i) q^{30} +(2.57692 + 0.690485i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.12343 - 4.19269i) q^{33} +(2.36270 + 2.36270i) q^{34} +(0.260180 + 0.237748i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(5.09307 - 5.09307i) q^{37} +(-2.02025 - 3.49917i) q^{38} +(2.93628 - 2.09242i) q^{39} +(0.115365 + 0.0666060i) q^{40} +(11.0520 + 2.96138i) q^{41} +(1.95313 + 1.78474i) q^{42} +(9.78926 + 5.65183i) q^{43} +(-4.19269 + 1.12343i) q^{44} +(-0.0941951 + 0.0941951i) q^{45} +(-1.03458 + 1.03458i) q^{46} +(-11.3605 + 3.04405i) q^{47} +(0.866025 + 0.500000i) q^{48} +(2.94071 - 6.35234i) q^{49} +(-4.81249 - 1.28950i) q^{50} +(2.89371 + 1.67068i) q^{51} +(-3.28023 - 1.49669i) q^{52} +(-3.41047 - 5.90712i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-0.500752 + 0.289109i) q^{55} +(0.569061 - 2.58383i) q^{56} +(-2.85706 - 2.85706i) q^{57} +(1.11342 - 4.15533i) q^{58} +(-1.99005 - 1.99005i) q^{59} +(0.128673 + 0.0344778i) q^{60} +(5.17990 - 2.99062i) q^{61} +(-1.33391 - 2.31041i) q^{62} +(2.34850 + 1.21841i) q^{63} -1.00000i q^{64} +(-0.473679 - 0.0794876i) q^{65} +(-3.75906 + 2.17030i) q^{66} +(-8.21404 + 2.20095i) q^{67} -3.34137i q^{68} +(-0.731561 + 1.26710i) q^{69} +(-0.0158620 - 0.352089i) q^{70} +(12.0922 - 3.24009i) q^{71} +(0.965926 + 0.258819i) q^{72} +(2.11308 - 7.88613i) q^{73} -7.20269 q^{74} -4.98225 q^{75} +(-1.04576 + 3.90282i) q^{76} +(8.47775 + 7.74681i) q^{77} +(-3.55583 - 0.596701i) q^{78} +(-6.41891 + 11.1179i) q^{79} +(-0.0344778 - 0.128673i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.72095 - 9.90898i) q^{82} +(-8.93817 + 8.93817i) q^{83} +(-0.119073 - 2.64307i) q^{84} +(-0.115203 - 0.429943i) q^{85} +(-2.92560 - 10.9185i) q^{86} -4.30192i q^{87} +(3.75906 + 2.17030i) q^{88} +(-7.78051 - 7.78051i) q^{89} +0.133212 q^{90} +(1.33645 + 9.44531i) q^{91} +1.46312 q^{92} +(-1.88644 - 1.88644i) q^{93} +(10.1856 + 5.88065i) q^{94} +0.538243i q^{95} +(-0.258819 - 0.965926i) q^{96} +(-1.45202 - 5.41903i) q^{97} +(-6.57118 + 2.41239i) q^{98} +(-3.06926 + 3.06926i) 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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

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
\(5\) 0.0344778 + 0.128673i 0.0154189 + 0.0575443i 0.973207 0.229932i \(-0.0738504\pi\)
−0.957788 + 0.287476i \(0.907184\pi\)
\(6\) 0.258819 + 0.965926i 0.105662 + 0.394338i
\(7\) 2.22943 1.42466i 0.842645 0.538469i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0.0666060 0.115365i 0.0210627 0.0364816i
\(11\) 1.12343 + 4.19269i 0.338726 + 1.26414i 0.899772 + 0.436360i \(0.143732\pi\)
−0.561046 + 0.827785i \(0.689601\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −1.49669 + 3.28023i −0.415106 + 0.909773i
\(14\) −2.58383 0.569061i −0.690557 0.152088i
\(15\) 0.0344778 0.128673i 0.00890213 0.0332232i
\(16\) −1.00000 −0.250000
\(17\) −3.34137 −0.810401 −0.405200 0.914228i \(-0.632798\pi\)
−0.405200 + 0.914228i \(0.632798\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) 3.90282 + 1.04576i 0.895369 + 0.239913i 0.677026 0.735959i \(-0.263268\pi\)
0.218343 + 0.975872i \(0.429935\pi\)
\(20\) −0.128673 + 0.0344778i −0.0287721 + 0.00770947i
\(21\) −2.64307 + 0.119073i −0.576765 + 0.0259840i
\(22\) 2.17030 3.75906i 0.462709 0.801435i
\(23\) 1.46312i 0.305082i −0.988297 0.152541i \(-0.951254\pi\)
0.988297 0.152541i \(-0.0487456\pi\)
\(24\) −0.965926 + 0.258819i −0.197169 + 0.0528312i
\(25\) 4.31476 2.49113i 0.862952 0.498225i
\(26\) 3.37779 1.26116i 0.662440 0.247334i
\(27\) 1.00000i 0.192450i
\(28\) 1.42466 + 2.22943i 0.269235 + 0.421323i
\(29\) 2.15096 + 3.72557i 0.399423 + 0.691821i 0.993655 0.112473i \(-0.0358771\pi\)
−0.594232 + 0.804294i \(0.702544\pi\)
\(30\) −0.115365 + 0.0666060i −0.0210627 + 0.0121605i
\(31\) 2.57692 + 0.690485i 0.462829 + 0.124015i 0.482696 0.875788i \(-0.339658\pi\)
−0.0198670 + 0.999803i \(0.506324\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 1.12343 4.19269i 0.195564 0.729854i
\(34\) 2.36270 + 2.36270i 0.405200 + 0.405200i
\(35\) 0.260180 + 0.237748i 0.0439785 + 0.0401868i
\(36\) −0.866025 + 0.500000i −0.144338 + 0.0833333i
\(37\) 5.09307 5.09307i 0.837296 0.837296i −0.151207 0.988502i \(-0.548316\pi\)
0.988502 + 0.151207i \(0.0483159\pi\)
\(38\) −2.02025 3.49917i −0.327728 0.567641i
\(39\) 2.93628 2.09242i 0.470182 0.335056i
\(40\) 0.115365 + 0.0666060i 0.0182408 + 0.0105313i
\(41\) 11.0520 + 2.96138i 1.72604 + 0.462490i 0.979264 0.202589i \(-0.0649356\pi\)
0.746773 + 0.665079i \(0.231602\pi\)
\(42\) 1.95313 + 1.78474i 0.301375 + 0.275391i
\(43\) 9.78926 + 5.65183i 1.49285 + 0.861896i 0.999966 0.00819993i \(-0.00261015\pi\)
0.492882 + 0.870096i \(0.335943\pi\)
\(44\) −4.19269 + 1.12343i −0.632072 + 0.169363i
\(45\) −0.0941951 + 0.0941951i −0.0140418 + 0.0140418i
\(46\) −1.03458 + 1.03458i −0.152541 + 0.152541i
\(47\) −11.3605 + 3.04405i −1.65711 + 0.444020i −0.961590 0.274491i \(-0.911491\pi\)
−0.695515 + 0.718511i \(0.744824\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 2.94071 6.35234i 0.420102 0.907477i
\(50\) −4.81249 1.28950i −0.680589 0.182363i
\(51\) 2.89371 + 1.67068i 0.405200 + 0.233943i
\(52\) −3.28023 1.49669i −0.454887 0.207553i
\(53\) −3.41047 5.90712i −0.468465 0.811405i 0.530886 0.847443i \(-0.321859\pi\)
−0.999350 + 0.0360388i \(0.988526\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −0.500752 + 0.289109i −0.0675214 + 0.0389835i
\(56\) 0.569061 2.58383i 0.0760440 0.345279i
\(57\) −2.85706 2.85706i −0.378427 0.378427i
\(58\) 1.11342 4.15533i 0.146199 0.545622i
\(59\) −1.99005 1.99005i −0.259083 0.259083i 0.565598 0.824681i \(-0.308645\pi\)
−0.824681 + 0.565598i \(0.808645\pi\)
\(60\) 0.128673 + 0.0344778i 0.0166116 + 0.00445106i
\(61\) 5.17990 2.99062i 0.663218 0.382909i −0.130284 0.991477i \(-0.541589\pi\)
0.793502 + 0.608567i \(0.208256\pi\)
\(62\) −1.33391 2.31041i −0.169407 0.293422i
\(63\) 2.34850 + 1.21841i 0.295884 + 0.153506i
\(64\) 1.00000i 0.125000i
\(65\) −0.473679 0.0794876i −0.0587527 0.00985923i
\(66\) −3.75906 + 2.17030i −0.462709 + 0.267145i
\(67\) −8.21404 + 2.20095i −1.00350 + 0.268888i −0.722913 0.690939i \(-0.757197\pi\)
−0.280592 + 0.959827i \(0.590531\pi\)
\(68\) 3.34137i 0.405200i
\(69\) −0.731561 + 1.26710i −0.0880696 + 0.152541i
\(70\) −0.0158620 0.352089i −0.00189587 0.0420826i
\(71\) 12.0922 3.24009i 1.43508 0.384528i 0.544270 0.838910i \(-0.316807\pi\)
0.890807 + 0.454382i \(0.150140\pi\)
\(72\) 0.965926 + 0.258819i 0.113835 + 0.0305021i
\(73\) 2.11308 7.88613i 0.247318 0.923002i −0.724887 0.688868i \(-0.758108\pi\)
0.972204 0.234134i \(-0.0752254\pi\)
\(74\) −7.20269 −0.837296
\(75\) −4.98225 −0.575301
\(76\) −1.04576 + 3.90282i −0.119957 + 0.447684i
\(77\) 8.47775 + 7.74681i 0.966129 + 0.882831i
\(78\) −3.55583 0.596701i −0.402619 0.0675630i
\(79\) −6.41891 + 11.1179i −0.722184 + 1.25086i 0.237939 + 0.971280i \(0.423528\pi\)
−0.960123 + 0.279579i \(0.909805\pi\)
\(80\) −0.0344778 0.128673i −0.00385473 0.0143861i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.72095 9.90898i −0.631773 1.09426i
\(83\) −8.93817 + 8.93817i −0.981092 + 0.981092i −0.999825 0.0187330i \(-0.994037\pi\)
0.0187330 + 0.999825i \(0.494037\pi\)
\(84\) −0.119073 2.64307i −0.0129920 0.288383i
\(85\) −0.115203 0.429943i −0.0124955 0.0466339i
\(86\) −2.92560 10.9185i −0.315476 1.17737i
\(87\) 4.30192i 0.461214i
\(88\) 3.75906 + 2.17030i 0.400718 + 0.231354i
\(89\) −7.78051 7.78051i −0.824733 0.824733i 0.162050 0.986783i \(-0.448189\pi\)
−0.986783 + 0.162050i \(0.948189\pi\)
\(90\) 0.133212 0.0140418
\(91\) 1.33645 + 9.44531i 0.140098 + 0.990138i
\(92\) 1.46312 0.152541
\(93\) −1.88644 1.88644i −0.195615 0.195615i
\(94\) 10.1856 + 5.88065i 1.05056 + 0.606543i
\(95\) 0.538243i 0.0552225i
\(96\) −0.258819 0.965926i −0.0264156 0.0985844i
\(97\) −1.45202 5.41903i −0.147431 0.550219i −0.999635 0.0270100i \(-0.991401\pi\)
0.852204 0.523209i \(-0.175265\pi\)
\(98\) −6.57118 + 2.41239i −0.663789 + 0.243688i
\(99\) −3.06926 + 3.06926i −0.308473 + 0.308473i
\(100\) 2.49113 + 4.31476i 0.249113 + 0.431476i
\(101\) −0.0194683 + 0.0337201i −0.00193717 + 0.00335528i −0.866992 0.498321i \(-0.833950\pi\)
0.865055 + 0.501677i \(0.167283\pi\)
\(102\) −0.864810 3.22751i −0.0856289 0.319572i
\(103\) −5.92112 + 10.2557i −0.583426 + 1.01052i 0.411644 + 0.911345i \(0.364955\pi\)
−0.995070 + 0.0991782i \(0.968379\pi\)
\(104\) 1.26116 + 3.37779i 0.123667 + 0.331220i
\(105\) −0.106449 0.335986i −0.0103883 0.0327889i
\(106\) −1.76539 + 6.58853i −0.171470 + 0.639935i
\(107\) 14.0973 1.36283 0.681417 0.731895i \(-0.261364\pi\)
0.681417 + 0.731895i \(0.261364\pi\)
\(108\) 1.00000 0.0962250
\(109\) −3.95106 + 14.7455i −0.378443 + 1.41237i 0.469807 + 0.882769i \(0.344324\pi\)
−0.848249 + 0.529597i \(0.822343\pi\)
\(110\) 0.558517 + 0.149654i 0.0532525 + 0.0142690i
\(111\) −6.95726 + 1.86419i −0.660354 + 0.176941i
\(112\) −2.22943 + 1.42466i −0.210661 + 0.134617i
\(113\) −6.28689 + 10.8892i −0.591421 + 1.02437i 0.402621 + 0.915367i \(0.368099\pi\)
−0.994041 + 0.109004i \(0.965234\pi\)
\(114\) 4.04050i 0.378427i
\(115\) 0.188264 0.0504452i 0.0175557 0.00470404i
\(116\) −3.72557 + 2.15096i −0.345911 + 0.199712i
\(117\) −3.58911 + 0.343949i −0.331813 + 0.0317981i
\(118\) 2.81436i 0.259083i
\(119\) −7.44935 + 4.76030i −0.682880 + 0.436376i
\(120\) −0.0666060 0.115365i −0.00608027 0.0105313i
\(121\) −6.79029 + 3.92038i −0.617299 + 0.356398i
\(122\) −5.77743 1.54806i −0.523064 0.140155i
\(123\) −8.09065 8.09065i −0.729509 0.729509i
\(124\) −0.690485 + 2.57692i −0.0620073 + 0.231415i
\(125\) 0.940279 + 0.940279i 0.0841011 + 0.0841011i
\(126\) −0.799093 2.52219i −0.0711889 0.224695i
\(127\) 12.4077 7.16360i 1.10101 0.635666i 0.164521 0.986374i \(-0.447392\pi\)
0.936485 + 0.350707i \(0.114059\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −5.65183 9.78926i −0.497616 0.861896i
\(130\) 0.278736 + 0.391148i 0.0244467 + 0.0343060i
\(131\) −11.6207 6.70920i −1.01530 0.586186i −0.102564 0.994726i \(-0.532704\pi\)
−0.912740 + 0.408541i \(0.866038\pi\)
\(132\) 4.19269 + 1.12343i 0.364927 + 0.0977819i
\(133\) 10.1909 3.22873i 0.883664 0.279967i
\(134\) 7.36451 + 4.25190i 0.636197 + 0.367308i
\(135\) 0.128673 0.0344778i 0.0110744 0.00296738i
\(136\) −2.36270 + 2.36270i −0.202600 + 0.202600i
\(137\) 6.57696 6.57696i 0.561908 0.561908i −0.367941 0.929849i \(-0.619937\pi\)
0.929849 + 0.367941i \(0.119937\pi\)
\(138\) 1.41327 0.378684i 0.120305 0.0322357i
\(139\) 10.2322 + 5.90757i 0.867885 + 0.501073i 0.866645 0.498926i \(-0.166272\pi\)
0.00123995 + 0.999999i \(0.499605\pi\)
\(140\) −0.237748 + 0.260180i −0.0200934 + 0.0219893i
\(141\) 11.3605 + 3.04405i 0.956730 + 0.256355i
\(142\) −10.8415 6.25937i −0.909802 0.525275i
\(143\) −15.4344 2.59003i −1.29069 0.216590i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −0.405220 + 0.405220i −0.0336517 + 0.0336517i
\(146\) −7.07051 + 4.08216i −0.585160 + 0.337842i
\(147\) −5.72290 + 4.03093i −0.472017 + 0.332466i
\(148\) 5.09307 + 5.09307i 0.418648 + 0.418648i
\(149\) 1.03623 3.86725i 0.0848910 0.316818i −0.910403 0.413724i \(-0.864228\pi\)
0.995294 + 0.0969061i \(0.0308946\pi\)
\(150\) 3.52299 + 3.52299i 0.287651 + 0.287651i
\(151\) −19.9317 5.34068i −1.62202 0.434618i −0.670425 0.741978i \(-0.733888\pi\)
−0.951594 + 0.307359i \(0.900555\pi\)
\(152\) 3.49917 2.02025i 0.283821 0.163864i
\(153\) −1.67068 2.89371i −0.135067 0.233943i
\(154\) −0.516849 11.4725i −0.0416489 0.924480i
\(155\) 0.355386i 0.0285453i
\(156\) 2.09242 + 2.93628i 0.167528 + 0.235091i
\(157\) −3.75270 + 2.16663i −0.299498 + 0.172916i −0.642218 0.766522i \(-0.721985\pi\)
0.342719 + 0.939438i \(0.388652\pi\)
\(158\) 12.4004 3.32267i 0.986522 0.264338i
\(159\) 6.82095i 0.540936i
\(160\) −0.0666060 + 0.115365i −0.00526566 + 0.00912040i
\(161\) −2.08444 3.26193i −0.164277 0.257076i
\(162\) 0.965926 0.258819i 0.0758903 0.0203347i
\(163\) −6.71018 1.79799i −0.525582 0.140829i −0.0137346 0.999906i \(-0.504372\pi\)
−0.511847 + 0.859076i \(0.671039\pi\)
\(164\) −2.96138 + 11.0520i −0.231245 + 0.863018i
\(165\) 0.578219 0.0450143
\(166\) 12.6405 0.981092
\(167\) −2.16192 + 8.06840i −0.167295 + 0.624352i 0.830442 + 0.557105i \(0.188088\pi\)
−0.997736 + 0.0672465i \(0.978579\pi\)
\(168\) −1.78474 + 1.95313i −0.137695 + 0.150687i
\(169\) −8.51986 9.81896i −0.655374 0.755304i
\(170\) −0.222555 + 0.385477i −0.0170692 + 0.0295647i
\(171\) 1.04576 + 3.90282i 0.0799711 + 0.298456i
\(172\) −5.65183 + 9.78926i −0.430948 + 0.746424i
\(173\) −3.92325 6.79528i −0.298280 0.516635i 0.677463 0.735557i \(-0.263079\pi\)
−0.975742 + 0.218922i \(0.929746\pi\)
\(174\) −3.04192 + 3.04192i −0.230607 + 0.230607i
\(175\) 6.07045 11.7008i 0.458883 0.884500i
\(176\) −1.12343 4.19269i −0.0846816 0.316036i
\(177\) 0.728411 + 2.71847i 0.0547507 + 0.204332i
\(178\) 11.0033i 0.824733i
\(179\) 4.27116 + 2.46595i 0.319241 + 0.184314i 0.651054 0.759031i \(-0.274327\pi\)
−0.331813 + 0.943345i \(0.607660\pi\)
\(180\) −0.0941951 0.0941951i −0.00702089 0.00702089i
\(181\) −0.641409 −0.0476755 −0.0238378 0.999716i \(-0.507589\pi\)
−0.0238378 + 0.999716i \(0.507589\pi\)
\(182\) 5.73383 7.62386i 0.425020 0.565118i
\(183\) −5.98123 −0.442146
\(184\) −1.03458 1.03458i −0.0762705 0.0762705i
\(185\) 0.830938 + 0.479742i 0.0610918 + 0.0352713i
\(186\) 2.66783i 0.195615i
\(187\) −3.75379 14.0093i −0.274504 1.02446i
\(188\) −3.04405 11.3605i −0.222010 0.828553i
\(189\) −1.42466 2.22943i −0.103628 0.162167i
\(190\) 0.380595 0.380595i 0.0276113 0.0276113i
\(191\) 9.29759 + 16.1039i 0.672750 + 1.16524i 0.977121 + 0.212684i \(0.0682204\pi\)
−0.304371 + 0.952554i \(0.598446\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.52328 5.68497i −0.109648 0.409213i 0.889183 0.457552i \(-0.151274\pi\)
−0.998831 + 0.0483394i \(0.984607\pi\)
\(194\) −2.80509 + 4.85857i −0.201394 + 0.348825i
\(195\) 0.370475 + 0.305678i 0.0265302 + 0.0218901i
\(196\) 6.35234 + 2.94071i 0.453739 + 0.210051i
\(197\) 2.22331 8.29752i 0.158405 0.591174i −0.840385 0.541990i \(-0.817671\pi\)
0.998790 0.0491843i \(-0.0156622\pi\)
\(198\) 4.34059 0.308473
\(199\) −14.0812 −0.998192 −0.499096 0.866547i \(-0.666335\pi\)
−0.499096 + 0.866547i \(0.666335\pi\)
\(200\) 1.28950 4.81249i 0.0911816 0.340294i
\(201\) 8.21404 + 2.20095i 0.579374 + 0.155243i
\(202\) 0.0376099 0.0100775i 0.00264622 0.000709054i
\(203\) 10.1031 + 5.24152i 0.709096 + 0.367883i
\(204\) −1.67068 + 2.89371i −0.116971 + 0.202600i
\(205\) 1.52420i 0.106455i
\(206\) 11.4387 3.06500i 0.796974 0.213549i
\(207\) 1.26710 0.731561i 0.0880696 0.0508470i
\(208\) 1.49669 3.28023i 0.103776 0.227443i
\(209\) 17.5382i 1.21314i
\(210\) −0.162307 + 0.312849i −0.0112003 + 0.0215886i
\(211\) 5.74753 + 9.95501i 0.395676 + 0.685331i 0.993187 0.116530i \(-0.0371770\pi\)
−0.597511 + 0.801861i \(0.703844\pi\)
\(212\) 5.90712 3.41047i 0.405702 0.234232i
\(213\) −12.0922 3.24009i −0.828542 0.222007i
\(214\) −9.96828 9.96828i −0.681417 0.681417i
\(215\) −0.389725 + 1.45447i −0.0265790 + 0.0991944i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 6.72877 2.13184i 0.456779 0.144719i
\(218\) 13.2205 7.63285i 0.895405 0.516962i
\(219\) −5.77305 + 5.77305i −0.390106 + 0.390106i
\(220\) −0.289109 0.500752i −0.0194918 0.0337607i
\(221\) 5.00098 10.9605i 0.336402 0.737281i
\(222\) 6.23771 + 3.60134i 0.418648 + 0.241706i
\(223\) −23.9774 6.42474i −1.60565 0.430232i −0.658906 0.752225i \(-0.728981\pi\)
−0.946742 + 0.321993i \(0.895647\pi\)
\(224\) 2.58383 + 0.569061i 0.172639 + 0.0380220i
\(225\) 4.31476 + 2.49113i 0.287651 + 0.166075i
\(226\) 12.1453 3.25433i 0.807896 0.216475i
\(227\) 17.3523 17.3523i 1.15171 1.15171i 0.165501 0.986210i \(-0.447076\pi\)
0.986210 0.165501i \(-0.0529240\pi\)
\(228\) 2.85706 2.85706i 0.189214 0.189214i
\(229\) 10.9064 2.92237i 0.720718 0.193116i 0.120226 0.992747i \(-0.461638\pi\)
0.600492 + 0.799631i \(0.294971\pi\)
\(230\) −0.168793 0.0974526i −0.0111299 0.00642584i
\(231\) −3.46854 10.9478i −0.228213 0.720313i
\(232\) 4.15533 + 1.11342i 0.272811 + 0.0730995i
\(233\) 1.29629 + 0.748411i 0.0849225 + 0.0490300i 0.541860 0.840469i \(-0.317720\pi\)
−0.456937 + 0.889499i \(0.651054\pi\)
\(234\) 2.78109 + 2.29467i 0.181806 + 0.150008i
\(235\) −0.783373 1.35684i −0.0511016 0.0885106i
\(236\) 1.99005 1.99005i 0.129542 0.129542i
\(237\) 11.1179 6.41891i 0.722184 0.416953i
\(238\) 8.63352 + 1.90144i 0.559628 + 0.123252i
\(239\) 6.71829 + 6.71829i 0.434570 + 0.434570i 0.890180 0.455610i \(-0.150579\pi\)
−0.455610 + 0.890180i \(0.650579\pi\)
\(240\) −0.0344778 + 0.128673i −0.00222553 + 0.00830580i
\(241\) −2.24834 2.24834i −0.144829 0.144829i 0.630975 0.775803i \(-0.282655\pi\)
−0.775803 + 0.630975i \(0.782655\pi\)
\(242\) 7.57359 + 2.02934i 0.486849 + 0.130451i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 2.99062 + 5.17990i 0.191455 + 0.331609i
\(245\) 0.918763 + 0.159375i 0.0586976 + 0.0101821i
\(246\) 11.4419i 0.729509i
\(247\) −9.27163 + 11.2370i −0.589940 + 0.714993i
\(248\) 2.31041 1.33391i 0.146711 0.0847036i
\(249\) 12.2098 3.27160i 0.773763 0.207329i
\(250\) 1.32976i 0.0841011i
\(251\) −6.52293 + 11.2981i −0.411724 + 0.713127i −0.995078 0.0990910i \(-0.968407\pi\)
0.583354 + 0.812218i \(0.301740\pi\)
\(252\) −1.21841 + 2.34850i −0.0767529 + 0.147942i
\(253\) 6.13442 1.64371i 0.385667 0.103339i
\(254\) −13.8390 3.70815i −0.868336 0.232670i
\(255\) −0.115203 + 0.429943i −0.00721429 + 0.0269241i
\(256\) 1.00000 0.0625000
\(257\) −8.11285 −0.506065 −0.253033 0.967458i \(-0.581428\pi\)
−0.253033 + 0.967458i \(0.581428\pi\)
\(258\) −2.92560 + 10.9185i −0.182140 + 0.679756i
\(259\) 4.09877 18.6105i 0.254685 1.15640i
\(260\) 0.0794876 0.473679i 0.00492961 0.0293764i
\(261\) −2.15096 + 3.72557i −0.133141 + 0.230607i
\(262\) 3.47294 + 12.9612i 0.214559 + 0.800745i
\(263\) 6.41984 11.1195i 0.395864 0.685657i −0.597347 0.801983i \(-0.703778\pi\)
0.993211 + 0.116326i \(0.0371118\pi\)
\(264\) −2.17030 3.75906i −0.133573 0.231354i
\(265\) 0.642500 0.642500i 0.0394685 0.0394685i
\(266\) −9.48912 4.92300i −0.581816 0.301849i
\(267\) 2.84786 + 10.6284i 0.174286 + 0.650446i
\(268\) −2.20095 8.21404i −0.134444 0.501752i
\(269\) 10.2406i 0.624377i −0.950020 0.312189i \(-0.898938\pi\)
0.950020 0.312189i \(-0.101062\pi\)
\(270\) −0.115365 0.0666060i −0.00702089 0.00405351i
\(271\) −17.2875 17.2875i −1.05014 1.05014i −0.998675 0.0514655i \(-0.983611\pi\)
−0.0514655 0.998675i \(-0.516389\pi\)
\(272\) 3.34137 0.202600
\(273\) 3.56526 8.84810i 0.215779 0.535512i
\(274\) −9.30123 −0.561908
\(275\) 15.2919 + 15.2919i 0.922133 + 0.922133i
\(276\) −1.26710 0.731561i −0.0762705 0.0440348i
\(277\) 4.22131i 0.253634i −0.991926 0.126817i \(-0.959524\pi\)
0.991926 0.126817i \(-0.0404761\pi\)
\(278\) −3.05798 11.4125i −0.183406 0.684479i
\(279\) 0.690485 + 2.57692i 0.0413382 + 0.154276i
\(280\) 0.352089 0.0158620i 0.0210413 0.000947936i
\(281\) −1.40963 + 1.40963i −0.0840912 + 0.0840912i −0.747901 0.663810i \(-0.768938\pi\)
0.663810 + 0.747901i \(0.268938\pi\)
\(282\) −5.88065 10.1856i −0.350188 0.606543i
\(283\) 2.75252 4.76750i 0.163620 0.283399i −0.772544 0.634961i \(-0.781016\pi\)
0.936164 + 0.351562i \(0.114349\pi\)
\(284\) 3.24009 + 12.0922i 0.192264 + 0.717539i
\(285\) 0.269121 0.466132i 0.0159414 0.0276113i
\(286\) 9.08236 + 12.7452i 0.537051 + 0.753641i
\(287\) 28.8587 9.14314i 1.70347 0.539703i
\(288\) −0.258819 + 0.965926i −0.0152511 + 0.0569177i
\(289\) −5.83526 −0.343250
\(290\) 0.573067 0.0336517
\(291\) −1.45202 + 5.41903i −0.0851192 + 0.317669i
\(292\) 7.88613 + 2.11308i 0.461501 + 0.123659i
\(293\) −4.70508 + 1.26072i −0.274874 + 0.0736522i −0.393623 0.919272i \(-0.628778\pi\)
0.118749 + 0.992924i \(0.462112\pi\)
\(294\) 6.89700 + 1.19640i 0.402241 + 0.0697756i
\(295\) 0.187453 0.324679i 0.0109140 0.0189035i
\(296\) 7.20269i 0.418648i
\(297\) 4.19269 1.12343i 0.243285 0.0651879i
\(298\) −3.46728 + 2.00184i −0.200854 + 0.115963i
\(299\) 4.79938 + 2.18983i 0.277555 + 0.126641i
\(300\) 4.98225i 0.287651i
\(301\) 29.8764 1.34597i 1.72205 0.0775802i
\(302\) 10.3174 + 17.8703i 0.593700 + 1.02832i
\(303\) 0.0337201 0.0194683i 0.00193717 0.00111843i
\(304\) −3.90282 1.04576i −0.223842 0.0599783i
\(305\) 0.563403 + 0.563403i 0.0322604 + 0.0322604i
\(306\) −0.864810 + 3.22751i −0.0494379 + 0.184505i
\(307\) −9.12772 9.12772i −0.520947 0.520947i 0.396911 0.917857i \(-0.370082\pi\)
−0.917857 + 0.396911i \(0.870082\pi\)
\(308\) −7.74681 + 8.47775i −0.441416 + 0.483064i
\(309\) 10.2557 5.92112i 0.583426 0.336841i
\(310\) 0.251296 0.251296i 0.0142727 0.0142727i
\(311\) 2.52062 + 4.36584i 0.142931 + 0.247564i 0.928599 0.371084i \(-0.121014\pi\)
−0.785668 + 0.618648i \(0.787681\pi\)
\(312\) 0.596701 3.55583i 0.0337815 0.201309i
\(313\) −14.9827 8.65025i −0.846871 0.488941i 0.0127230 0.999919i \(-0.495950\pi\)
−0.859594 + 0.510978i \(0.829283\pi\)
\(314\) 4.18560 + 1.12153i 0.236207 + 0.0632915i
\(315\) −0.0758057 + 0.344197i −0.00427117 + 0.0193933i
\(316\) −11.1179 6.41891i −0.625430 0.361092i
\(317\) −6.23606 + 1.67095i −0.350252 + 0.0938497i −0.429656 0.902993i \(-0.641365\pi\)
0.0794037 + 0.996843i \(0.474698\pi\)
\(318\) 4.82314 4.82314i 0.270468 0.270468i
\(319\) −13.2037 + 13.2037i −0.739267 + 0.739267i
\(320\) 0.128673 0.0344778i 0.00719303 0.00192737i
\(321\) −12.2086 7.04864i −0.681417 0.393416i
\(322\) −0.832605 + 3.78045i −0.0463993 + 0.210676i
\(323\) −13.0408 3.49426i −0.725608 0.194426i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) 1.71364 + 17.8819i 0.0950557 + 0.991907i
\(326\) 3.47344 + 6.01618i 0.192376 + 0.333206i
\(327\) 10.7945 10.7945i 0.596936 0.596936i
\(328\) 9.90898 5.72095i 0.547132 0.315887i
\(329\) −20.9908 + 22.9713i −1.15726 + 1.26645i
\(330\) −0.408863 0.408863i −0.0225071 0.0225071i
\(331\) −6.02078 + 22.4698i −0.330932 + 1.23505i 0.577281 + 0.816546i \(0.304114\pi\)
−0.908213 + 0.418509i \(0.862553\pi\)
\(332\) −8.93817 8.93817i −0.490546 0.490546i
\(333\) 6.95726 + 1.86419i 0.381256 + 0.102157i
\(334\) 7.23393 4.17651i 0.395823 0.228529i
\(335\) −0.566404 0.981040i −0.0309460 0.0536000i
\(336\) 2.64307 0.119073i 0.144191 0.00649599i
\(337\) 16.6393i 0.906401i −0.891409 0.453200i \(-0.850282\pi\)
0.891409 0.453200i \(-0.149718\pi\)
\(338\) −0.918598 + 12.9675i −0.0499652 + 0.705339i
\(339\) 10.8892 6.28689i 0.591421 0.341457i
\(340\) 0.429943 0.115203i 0.0233170 0.00624776i
\(341\) 11.5800i 0.627090i
\(342\) 2.02025 3.49917i 0.109243 0.189214i
\(343\) −2.49379 18.3516i −0.134652 0.990893i
\(344\) 10.9185 2.92560i 0.588686 0.157738i
\(345\) −0.188264 0.0504452i −0.0101358 0.00271588i
\(346\) −2.03083 + 7.57915i −0.109178 + 0.407457i
\(347\) 27.1302 1.45642 0.728212 0.685352i \(-0.240352\pi\)
0.728212 + 0.685352i \(0.240352\pi\)
\(348\) 4.30192 0.230607
\(349\) −0.102175 + 0.381321i −0.00546929 + 0.0204117i −0.968607 0.248599i \(-0.920030\pi\)
0.963137 + 0.269010i \(0.0866966\pi\)
\(350\) −12.5662 + 3.98129i −0.671692 + 0.212809i
\(351\) 3.28023 + 1.49669i 0.175086 + 0.0798872i
\(352\) −2.17030 + 3.75906i −0.115677 + 0.200359i
\(353\) 0.963251 + 3.59490i 0.0512687 + 0.191337i 0.986811 0.161878i \(-0.0517550\pi\)
−0.935542 + 0.353215i \(0.885088\pi\)
\(354\) 1.40718 2.43731i 0.0747908 0.129542i
\(355\) 0.833823 + 1.44422i 0.0442547 + 0.0766514i
\(356\) 7.78051 7.78051i 0.412366 0.412366i
\(357\) 8.83147 0.397868i 0.467411 0.0210574i
\(358\) −1.27647 4.76386i −0.0674636 0.251778i
\(359\) −9.48820 35.4104i −0.500768 1.86889i −0.494974 0.868908i \(-0.664822\pi\)
−0.00579429 0.999983i \(-0.501844\pi\)
\(360\) 0.133212i 0.00702089i
\(361\) −2.31607 1.33718i −0.121898 0.0703781i
\(362\) 0.453544 + 0.453544i 0.0238378 + 0.0238378i
\(363\) 7.84076 0.411533
\(364\) −9.44531 + 1.33645i −0.495069 + 0.0700489i
\(365\) 1.08759 0.0569268
\(366\) 4.22937 + 4.22937i 0.221073 + 0.221073i
\(367\) 26.7283 + 15.4316i 1.39520 + 0.805521i 0.993885 0.110418i \(-0.0352189\pi\)
0.401318 + 0.915939i \(0.368552\pi\)
\(368\) 1.46312i 0.0762705i
\(369\) 2.96138 + 11.0520i 0.154163 + 0.575346i
\(370\) −0.248333 0.926791i −0.0129102 0.0481816i
\(371\) −16.0190 8.31074i −0.831666 0.431472i
\(372\) 1.88644 1.88644i 0.0978073 0.0978073i
\(373\) 9.21429 + 15.9596i 0.477098 + 0.826358i 0.999656 0.0262461i \(-0.00835536\pi\)
−0.522558 + 0.852604i \(0.675022\pi\)
\(374\) −7.25176 + 12.5604i −0.374980 + 0.649484i
\(375\) −0.344166 1.28445i −0.0177727 0.0663285i
\(376\) −5.88065 + 10.1856i −0.303271 + 0.525281i
\(377\) −15.4401 + 1.47964i −0.795203 + 0.0762053i
\(378\) −0.569061 + 2.58383i −0.0292693 + 0.132898i
\(379\) 1.60912 6.00531i 0.0826548 0.308472i −0.912205 0.409734i \(-0.865621\pi\)
0.994860 + 0.101262i \(0.0322881\pi\)
\(380\) −0.538243 −0.0276113
\(381\) −14.3272 −0.734004
\(382\) 4.81279 17.9616i 0.246244 0.918994i
\(383\) 9.57092 + 2.56452i 0.489051 + 0.131041i 0.494914 0.868942i \(-0.335200\pi\)
−0.00586294 + 0.999983i \(0.501866\pi\)
\(384\) 0.965926 0.258819i 0.0492922 0.0132078i
\(385\) −0.704510 + 1.35795i −0.0359052 + 0.0692075i
\(386\) −2.94276 + 5.09700i −0.149782 + 0.259431i
\(387\) 11.3037i 0.574598i
\(388\) 5.41903 1.45202i 0.275109 0.0737153i
\(389\) 21.1408 12.2056i 1.07188 0.618851i 0.143186 0.989696i \(-0.454265\pi\)
0.928695 + 0.370845i \(0.120932\pi\)
\(390\) −0.0458181 0.478112i −0.00232009 0.0242101i
\(391\) 4.88883i 0.247239i
\(392\) −2.41239 6.57118i −0.121844 0.331895i
\(393\) 6.70920 + 11.6207i 0.338435 + 0.586186i
\(394\) −7.43936 + 4.29511i −0.374789 + 0.216385i
\(395\) −1.65188 0.442620i −0.0831151 0.0222706i
\(396\) −3.06926 3.06926i −0.154236 0.154236i
\(397\) 2.69845 10.0707i 0.135431 0.505436i −0.864565 0.502522i \(-0.832406\pi\)
0.999996 0.00291412i \(-0.000927595\pi\)
\(398\) 9.95694 + 9.95694i 0.499096 + 0.499096i
\(399\) −10.4400 2.29929i −0.522652 0.115108i
\(400\) −4.31476 + 2.49113i −0.215738 + 0.124556i
\(401\) −0.647442 + 0.647442i −0.0323317 + 0.0323317i −0.723088 0.690756i \(-0.757278\pi\)
0.690756 + 0.723088i \(0.257278\pi\)
\(402\) −4.25190 7.36451i −0.212066 0.367308i
\(403\) −6.12179 + 7.41947i −0.304948 + 0.369590i
\(404\) −0.0337201 0.0194683i −0.00167764 0.000968585i
\(405\) −0.128673 0.0344778i −0.00639381 0.00171322i
\(406\) −3.43763 10.8503i −0.170607 0.538490i
\(407\) 27.0754 + 15.6320i 1.34208 + 0.774848i
\(408\) 3.22751 0.864810i 0.159786 0.0428145i
\(409\) −2.38229 + 2.38229i −0.117796 + 0.117796i −0.763548 0.645751i \(-0.776544\pi\)
0.645751 + 0.763548i \(0.276544\pi\)
\(410\) 1.07777 1.07777i 0.0532273 0.0532273i
\(411\) −8.98430 + 2.40733i −0.443163 + 0.118745i
\(412\) −10.2557 5.92112i −0.505261 0.291713i
\(413\) −7.27183 1.60154i −0.357823 0.0788068i
\(414\) −1.41327 0.378684i −0.0694583 0.0186113i
\(415\) −1.45827 0.841932i −0.0715836 0.0413288i
\(416\) −3.37779 + 1.26116i −0.165610 + 0.0618334i
\(417\) −5.90757 10.2322i −0.289295 0.501073i
\(418\) 12.4014 12.4014i 0.606570 0.606570i
\(419\) 12.9360 7.46860i 0.631965 0.364865i −0.149548 0.988755i \(-0.547782\pi\)
0.781513 + 0.623889i \(0.214448\pi\)
\(420\) 0.335986 0.106449i 0.0163944 0.00519417i
\(421\) −19.8845 19.8845i −0.969109 0.969109i 0.0304275 0.999537i \(-0.490313\pi\)
−0.999537 + 0.0304275i \(0.990313\pi\)
\(422\) 2.97514 11.1034i 0.144828 0.540504i
\(423\) −8.31649 8.31649i −0.404362 0.404362i
\(424\) −6.58853 1.76539i −0.319967 0.0857350i
\(425\) −14.4172 + 8.32377i −0.699337 + 0.403762i
\(426\) 6.25937 + 10.8415i 0.303267 + 0.525275i
\(427\) 7.28762 14.0469i 0.352673 0.679779i
\(428\) 14.0973i 0.681417i
\(429\) 12.0716 + 9.96025i 0.582822 + 0.480885i
\(430\) 1.30405 0.752892i 0.0628867 0.0363077i
\(431\) −30.4523 + 8.15967i −1.46684 + 0.393038i −0.901845 0.432059i \(-0.857787\pi\)
−0.564991 + 0.825097i \(0.691120\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −12.7366 + 22.0605i −0.612083 + 1.06016i 0.378806 + 0.925476i \(0.376335\pi\)
−0.990889 + 0.134682i \(0.956999\pi\)
\(434\) −6.26540 3.25052i −0.300749 0.156030i
\(435\) 0.553540 0.148321i 0.0265402 0.00711143i
\(436\) −14.7455 3.95106i −0.706183 0.189221i
\(437\) 1.53007 5.71030i 0.0731932 0.273161i
\(438\) 8.16432 0.390106
\(439\) −26.8403 −1.28102 −0.640509 0.767950i \(-0.721277\pi\)
−0.640509 + 0.767950i \(0.721277\pi\)
\(440\) −0.149654 + 0.558517i −0.00713448 + 0.0266262i
\(441\) 6.97164 0.629439i 0.331983 0.0299733i
\(442\) −11.2864 + 4.21400i −0.536842 + 0.200439i
\(443\) 6.95881 12.0530i 0.330623 0.572656i −0.652011 0.758209i \(-0.726074\pi\)
0.982634 + 0.185553i \(0.0594078\pi\)
\(444\) −1.86419 6.95726i −0.0884707 0.330177i
\(445\) 0.732886 1.26940i 0.0347421 0.0601751i
\(446\) 12.4116 + 21.4976i 0.587708 + 1.01794i
\(447\) −2.83102 + 2.83102i −0.133903 + 0.133903i
\(448\) −1.42466 2.22943i −0.0673087 0.105331i
\(449\) −3.68798 13.7637i −0.174047 0.649550i −0.996712 0.0810249i \(-0.974181\pi\)
0.822666 0.568526i \(-0.192486\pi\)
\(450\) −1.28950 4.81249i −0.0607877 0.226863i
\(451\) 49.6646i 2.33862i
\(452\) −10.8892 6.28689i −0.512185 0.295710i
\(453\) 14.5910 + 14.5910i 0.685545 + 0.685545i
\(454\) −24.5398 −1.15171
\(455\) −1.16928 + 0.497618i −0.0548166 + 0.0233287i
\(456\) −4.04050 −0.189214
\(457\) −0.187430 0.187430i −0.00876761 0.00876761i 0.702709 0.711477i \(-0.251973\pi\)
−0.711477 + 0.702709i \(0.751973\pi\)
\(458\) −9.77845 5.64559i −0.456917 0.263801i
\(459\) 3.34137i 0.155962i
\(460\) 0.0504452 + 0.188264i 0.00235202 + 0.00877785i
\(461\) −9.81634 36.6351i −0.457192 1.70626i −0.681562 0.731761i \(-0.738699\pi\)
0.224369 0.974504i \(-0.427968\pi\)
\(462\) −5.28864 + 10.1939i −0.246050 + 0.474263i
\(463\) 5.29794 5.29794i 0.246216 0.246216i −0.573200 0.819416i \(-0.694298\pi\)
0.819416 + 0.573200i \(0.194298\pi\)
\(464\) −2.15096 3.72557i −0.0998558 0.172955i
\(465\) 0.177693 0.307774i 0.00824033 0.0142727i
\(466\) −0.387406 1.44582i −0.0179462 0.0669763i
\(467\) 0.323895 0.561003i 0.0149881 0.0259601i −0.858434 0.512924i \(-0.828562\pi\)
0.873422 + 0.486964i \(0.161896\pi\)
\(468\) −0.343949 3.58911i −0.0158990 0.165907i
\(469\) −15.1770 + 16.6090i −0.700810 + 0.766934i
\(470\) −0.405504 + 1.51336i −0.0187045 + 0.0698061i
\(471\) 4.33325 0.199666
\(472\) −2.81436 −0.129542
\(473\) −12.6989 + 47.3928i −0.583894 + 2.17912i
\(474\) −12.4004 3.32267i −0.569568 0.152615i
\(475\) 19.4449 5.21023i 0.892191 0.239062i
\(476\) −4.76030 7.44935i −0.218188 0.341440i
\(477\) 3.41047 5.90712i 0.156155 0.270468i
\(478\) 9.50110i 0.434570i
\(479\) −24.4386 + 6.54830i −1.11663 + 0.299199i −0.769518 0.638625i \(-0.779503\pi\)
−0.347110 + 0.937825i \(0.612837\pi\)
\(480\) 0.115365 0.0666060i 0.00526566 0.00304013i
\(481\) 9.08373 + 24.3292i 0.414183 + 1.10932i
\(482\) 3.17964i 0.144829i
\(483\) 0.174219 + 3.86713i 0.00792723 + 0.175961i
\(484\) −3.92038 6.79029i −0.178199 0.308650i
\(485\) 0.647219 0.373672i 0.0293887 0.0169676i
\(486\) −0.965926 0.258819i −0.0438153 0.0117403i
\(487\) 1.09116 + 1.09116i 0.0494452 + 0.0494452i 0.731397 0.681952i \(-0.238869\pi\)
−0.681952 + 0.731397i \(0.738869\pi\)
\(488\) 1.54806 5.77743i 0.0700773 0.261532i
\(489\) 4.91219 + 4.91219i 0.222137 + 0.222137i
\(490\) −0.536968 0.762359i −0.0242578 0.0344399i
\(491\) −11.2592 + 6.50052i −0.508122 + 0.293364i −0.732061 0.681239i \(-0.761442\pi\)
0.223939 + 0.974603i \(0.428108\pi\)
\(492\) 8.09065 8.09065i 0.364754 0.364754i
\(493\) −7.18715 12.4485i −0.323693 0.560653i
\(494\) 14.5018 1.38972i 0.652466 0.0625267i
\(495\) −0.500752 0.289109i −0.0225071 0.0129945i
\(496\) −2.57692 0.690485i −0.115707 0.0310037i
\(497\) 22.3426 24.4507i 1.00220 1.09677i
\(498\) −10.9470 6.32024i −0.490546 0.283217i
\(499\) 2.49214 0.667766i 0.111563 0.0298933i −0.202605 0.979260i \(-0.564941\pi\)
0.314169 + 0.949367i \(0.398274\pi\)
\(500\) −0.940279 + 0.940279i −0.0420506 + 0.0420506i
\(501\) 5.90648 5.90648i 0.263882 0.263882i
\(502\) 12.6013 3.37652i 0.562425 0.150701i
\(503\) −3.22228 1.86038i −0.143674 0.0829504i 0.426440 0.904516i \(-0.359768\pi\)
−0.570114 + 0.821566i \(0.693101\pi\)
\(504\) 2.52219 0.799093i 0.112347 0.0355944i
\(505\) −0.00501009 0.00134245i −0.000222946 5.97382e-5i
\(506\) −5.49997 3.17541i −0.244503 0.141164i
\(507\) 2.46894 + 12.7634i 0.109649 + 0.566842i
\(508\) 7.16360 + 12.4077i 0.317833 + 0.550503i
\(509\) −26.7355 + 26.7355i −1.18503 + 1.18503i −0.206608 + 0.978424i \(0.566243\pi\)
−0.978424 + 0.206608i \(0.933757\pi\)
\(510\) 0.385477 0.222555i 0.0170692 0.00985491i
\(511\) −6.52405 20.5920i −0.288607 0.910936i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 1.04576 3.90282i 0.0461713 0.172314i
\(514\) 5.73665 + 5.73665i 0.253033 + 0.253033i
\(515\) −1.52378 0.408295i −0.0671456 0.0179916i
\(516\) 9.78926 5.65183i 0.430948 0.248808i
\(517\) −25.5255 44.2115i −1.12261 1.94442i
\(518\) −16.0579 + 10.2614i −0.705543 + 0.450858i
\(519\) 7.84651i 0.344424i
\(520\) −0.391148 + 0.278736i −0.0171530 + 0.0122234i
\(521\) 30.7500 17.7535i 1.34718 0.777796i 0.359333 0.933209i \(-0.383004\pi\)
0.987850 + 0.155413i \(0.0496709\pi\)
\(522\) 4.15533 1.11342i 0.181874 0.0487330i
\(523\) 23.8894i 1.04461i 0.852758 + 0.522305i \(0.174928\pi\)
−0.852758 + 0.522305i \(0.825072\pi\)
\(524\) 6.70920 11.6207i 0.293093 0.507652i
\(525\) −11.1076 + 7.09800i −0.484775 + 0.309782i
\(526\) −12.4022 + 3.32315i −0.540761 + 0.144896i
\(527\) −8.61045 2.30716i −0.375077 0.100502i
\(528\) −1.12343 + 4.19269i −0.0488909 + 0.182463i
\(529\) 20.8593 0.906925
\(530\) −0.908632 −0.0394685
\(531\) 0.728411 2.71847i 0.0316103 0.117971i
\(532\) 3.22873 + 10.1909i 0.139983 + 0.441832i
\(533\) −26.2554 + 31.8210i −1.13725 + 1.37832i
\(534\) 5.50165 9.52914i 0.238080 0.412366i
\(535\) 0.486043 + 1.81394i 0.0210135 + 0.0784233i
\(536\) −4.25190 + 7.36451i −0.183654 + 0.318098i
\(537\) −2.46595 4.27116i −0.106414 0.184314i
\(538\) −7.24116 + 7.24116i −0.312189 + 0.312189i
\(539\) 29.9371 + 5.19310i 1.28948 + 0.223683i
\(540\) 0.0344778 + 0.128673i 0.00148369 + 0.00553720i
\(541\) −10.2573 38.2807i −0.440995 1.64582i −0.726300 0.687378i \(-0.758761\pi\)
0.285305 0.958437i \(-0.407905\pi\)
\(542\) 24.4482i 1.05014i
\(543\) 0.555476 + 0.320704i 0.0238378 + 0.0137627i
\(544\) −2.36270 2.36270i −0.101300 0.101300i
\(545\) −2.03357 −0.0871088
\(546\) −8.77757 + 3.73554i −0.375645 + 0.159866i
\(547\) −29.0577 −1.24242 −0.621209 0.783645i \(-0.713358\pi\)
−0.621209 + 0.783645i \(0.713358\pi\)
\(548\) 6.57696 + 6.57696i 0.280954 + 0.280954i
\(549\) 5.17990 + 2.99062i 0.221073 + 0.127636i
\(550\) 21.6259i 0.922133i
\(551\) 4.49877 + 16.7896i 0.191654 + 0.715262i
\(552\) 0.378684 + 1.41327i 0.0161178 + 0.0601526i
\(553\) 1.52864 + 33.9313i 0.0650045 + 1.44290i
\(554\) −2.98492 + 2.98492i −0.126817 + 0.126817i
\(555\) −0.479742 0.830938i −0.0203639 0.0352713i
\(556\) −5.90757 + 10.2322i −0.250537 + 0.433942i
\(557\) −5.25539 19.6134i −0.222678 0.831046i −0.983321 0.181876i \(-0.941783\pi\)
0.760643 0.649170i \(-0.224884\pi\)
\(558\) 1.33391 2.31041i 0.0564691 0.0978073i
\(559\) −33.1908 + 23.6520i −1.40382 + 1.00037i
\(560\) −0.260180 0.237748i −0.0109946 0.0100467i
\(561\) −3.75379 + 14.0093i −0.158485 + 0.591474i
\(562\) 1.99351 0.0840912
\(563\) −11.8161 −0.497989 −0.248995 0.968505i \(-0.580100\pi\)
−0.248995 + 0.968505i \(0.580100\pi\)
\(564\) −3.04405 + 11.3605i −0.128178 + 0.478365i
\(565\) −1.61790 0.433516i −0.0680657 0.0182382i
\(566\) −5.31746 + 1.42481i −0.223509 + 0.0598892i
\(567\) 0.119073 + 2.64307i 0.00500061 + 0.110999i
\(568\) 6.25937 10.8415i 0.262637 0.454901i
\(569\) 27.0496i 1.13398i 0.823725 + 0.566990i \(0.191892\pi\)
−0.823725 + 0.566990i \(0.808108\pi\)
\(570\) −0.519903 + 0.139307i −0.0217763 + 0.00583495i
\(571\) −0.632370 + 0.365099i −0.0264639 + 0.0152789i −0.513174 0.858285i \(-0.671530\pi\)
0.486710 + 0.873564i \(0.338197\pi\)
\(572\) 2.59003 15.4344i 0.108295 0.645346i
\(573\) 18.5952i 0.776825i
\(574\) −26.8713 13.9410i −1.12159 0.581885i
\(575\) −3.64482 6.31302i −0.152000 0.263271i
\(576\) 0.866025 0.500000i 0.0360844 0.0208333i
\(577\) 45.1679 + 12.1027i 1.88036 + 0.503842i 0.999538 + 0.0303997i \(0.00967802\pi\)
0.880825 + 0.473442i \(0.156989\pi\)
\(578\) 4.12615 + 4.12615i 0.171625 + 0.171625i
\(579\) −1.52328 + 5.68497i −0.0633055 + 0.236259i
\(580\) −0.405220 0.405220i −0.0168258 0.0168258i
\(581\) −7.19320 + 32.6608i −0.298424 + 1.35500i
\(582\) 4.85857 2.80509i 0.201394 0.116275i
\(583\) 20.9353 20.9353i 0.867051 0.867051i
\(584\) −4.08216 7.07051i −0.168921 0.292580i
\(585\) −0.168001 0.449962i −0.00694600 0.0186037i
\(586\) 4.21846 + 2.43553i 0.174263 + 0.100611i
\(587\) 24.4744 + 6.55790i 1.01017 + 0.270674i 0.725700 0.688012i \(-0.241516\pi\)
0.284468 + 0.958685i \(0.408183\pi\)
\(588\) −4.03093 5.72290i −0.166233 0.236008i
\(589\) 9.33519 + 5.38968i 0.384650 + 0.222078i
\(590\) −0.362132 + 0.0970330i −0.0149087 + 0.00399479i
\(591\) −6.07421 + 6.07421i −0.249860 + 0.249860i
\(592\) −5.09307 + 5.09307i −0.209324 + 0.209324i
\(593\) 12.1103 3.24493i 0.497309 0.133253i −0.00144199 0.999999i \(-0.500459\pi\)
0.498751 + 0.866745i \(0.333792\pi\)
\(594\) −3.75906 2.17030i −0.154236 0.0890484i
\(595\) −0.869359 0.794404i −0.0356402 0.0325674i
\(596\) 3.86725 + 1.03623i 0.158409 + 0.0424455i
\(597\) 12.1947 + 7.04062i 0.499096 + 0.288153i
\(598\) −1.84523 4.94212i −0.0754570 0.202098i
\(599\) −9.43306 16.3385i −0.385424 0.667574i 0.606404 0.795157i \(-0.292612\pi\)
−0.991828 + 0.127582i \(0.959278\pi\)
\(600\) −3.52299 + 3.52299i −0.143825 + 0.143825i
\(601\) 37.2197 21.4888i 1.51822 0.876546i 0.518451 0.855107i \(-0.326509\pi\)
0.999770 0.0214384i \(-0.00682457\pi\)
\(602\) −22.0775 20.1740i −0.899813 0.822233i
\(603\) −6.01310 6.01310i −0.244872 0.244872i
\(604\) 5.34068 19.9317i 0.217309 0.811009i
\(605\) −0.738561 0.738561i −0.0300268 0.0300268i
\(606\) −0.0376099 0.0100775i −0.00152780 0.000409372i
\(607\) −2.85682 + 1.64939i −0.115955 + 0.0669466i −0.556856 0.830609i \(-0.687992\pi\)
0.440901 + 0.897556i \(0.354659\pi\)
\(608\) 2.02025 + 3.49917i 0.0819319 + 0.141910i
\(609\) −6.12875 9.59083i −0.248350 0.388640i
\(610\) 0.796772i 0.0322604i
\(611\) 7.01797 41.8212i 0.283917 1.69190i
\(612\) 2.89371 1.67068i 0.116971 0.0675334i
\(613\) −24.5674 + 6.58282i −0.992269 + 0.265878i −0.718203 0.695833i \(-0.755035\pi\)
−0.274065 + 0.961711i \(0.588368\pi\)
\(614\) 12.9085i 0.520947i
\(615\) 0.762099 1.31999i 0.0307308 0.0532273i
\(616\) 11.4725 0.516849i 0.462240 0.0208245i
\(617\) −28.5840 + 7.65907i −1.15075 + 0.308343i −0.783266 0.621687i \(-0.786448\pi\)
−0.367485 + 0.930030i \(0.619781\pi\)
\(618\) −11.4387 3.06500i −0.460133 0.123292i
\(619\) −5.91111 + 22.0606i −0.237588 + 0.886689i 0.739378 + 0.673291i \(0.235120\pi\)
−0.976965 + 0.213398i \(0.931547\pi\)
\(620\) −0.355386 −0.0142727
\(621\) −1.46312 −0.0587130
\(622\) 1.30477 4.86946i 0.0523164 0.195248i
\(623\) −28.4307 6.26155i −1.13905 0.250864i
\(624\) −2.93628 + 2.09242i −0.117545 + 0.0837639i
\(625\) 12.3671 21.4204i 0.494683 0.856816i
\(626\) 4.47770 + 16.7110i 0.178965 + 0.667906i
\(627\) 8.76908 15.1885i 0.350203 0.606570i
\(628\) −2.16663 3.75270i −0.0864578 0.149749i
\(629\) −17.0178 + 17.0178i −0.678545 + 0.678545i
\(630\) 0.296987 0.189781i 0.0118322 0.00756106i
\(631\) −8.61757 32.1612i −0.343060 1.28032i −0.894862 0.446342i \(-0.852726\pi\)
0.551802 0.833975i \(-0.313940\pi\)
\(632\) 3.32267 + 12.4004i 0.132169 + 0.493261i
\(633\) 11.4951i 0.456887i
\(634\) 5.59110 + 3.22802i 0.222051 + 0.128201i
\(635\) 1.34955 + 1.34955i 0.0535553 + 0.0535553i
\(636\) −6.82095 −0.270468
\(637\) 16.4358 + 19.1537i 0.651212 + 0.758896i
\(638\) 18.6729 0.739267
\(639\) 8.85209 + 8.85209i 0.350183 + 0.350183i
\(640\) −0.115365 0.0666060i −0.00456020 0.00263283i
\(641\) 4.73161i 0.186887i 0.995625 + 0.0934437i \(0.0297875\pi\)
−0.995625 + 0.0934437i \(0.970212\pi\)
\(642\) 3.64864 + 13.6169i 0.144000 + 0.537417i
\(643\) 7.51513 + 28.0468i 0.296368 + 1.10606i 0.940125 + 0.340830i \(0.110708\pi\)
−0.643757 + 0.765230i \(0.722625\pi\)
\(644\) 3.26193 2.08444i 0.128538 0.0821386i
\(645\) 1.06475 1.06475i 0.0419245 0.0419245i
\(646\) 6.75040 + 11.6920i 0.265591 + 0.460017i
\(647\) 23.9556 41.4923i 0.941791 1.63123i 0.179740 0.983714i \(-0.442474\pi\)
0.762052 0.647516i \(-0.224192\pi\)
\(648\) 0.258819 + 0.965926i 0.0101674 + 0.0379452i
\(649\) 6.10800 10.5794i 0.239760 0.415277i
\(650\) 11.4327 13.8561i 0.448425 0.543481i
\(651\) −6.89321 1.51816i −0.270166 0.0595012i
\(652\) 1.79799 6.71018i 0.0704146 0.262791i
\(653\) 1.65411 0.0647303 0.0323651 0.999476i \(-0.489696\pi\)
0.0323651 + 0.999476i \(0.489696\pi\)
\(654\) −15.2657 −0.596936
\(655\) 0.462637 1.72658i 0.0180767 0.0674633i
\(656\) −11.0520 2.96138i −0.431509 0.115623i
\(657\) 7.88613 2.11308i 0.307667 0.0824392i
\(658\) 31.0859 1.40046i 1.21186 0.0545955i
\(659\) 13.3063 23.0472i 0.518341 0.897793i −0.481432 0.876483i \(-0.659883\pi\)
0.999773 0.0213095i \(-0.00678353\pi\)
\(660\) 0.578219i 0.0225071i
\(661\) 38.1147 10.2128i 1.48249 0.397232i 0.575297 0.817945i \(-0.304887\pi\)
0.907194 + 0.420713i \(0.138220\pi\)
\(662\) 20.1459 11.6312i 0.782993 0.452061i
\(663\) −9.81121 + 6.99156i −0.381036 + 0.271530i
\(664\) 12.6405i 0.490546i
\(665\) 0.766811 + 1.19997i 0.0297356 + 0.0465330i
\(666\) −3.60134 6.23771i −0.139549 0.241706i
\(667\) 5.45096 3.14711i 0.211062 0.121857i
\(668\) −8.06840 2.16192i −0.312176 0.0836473i
\(669\) 17.5527 + 17.5527i 0.678627 + 0.678627i
\(670\) −0.293192 + 1.09421i −0.0113270 + 0.0422730i
\(671\) 18.3580 + 18.3580i 0.708702 + 0.708702i
\(672\) −1.95313 1.78474i −0.0753437 0.0688477i
\(673\) −2.01759 + 1.16486i −0.0777725 + 0.0449020i −0.538382 0.842701i \(-0.680964\pi\)
0.460609 + 0.887603i \(0.347631\pi\)
\(674\) −11.7658 + 11.7658i −0.453200 + 0.453200i
\(675\) −2.49113 4.31476i −0.0958835 0.166075i
\(676\) 9.81896 8.51986i 0.377652 0.327687i
\(677\) −22.7294 13.1229i −0.873564 0.504352i −0.00503283 0.999987i \(-0.501602\pi\)
−0.868531 + 0.495635i \(0.834935\pi\)
\(678\) −12.1453 3.25433i −0.466439 0.124982i
\(679\) −10.9574 10.0127i −0.420508 0.384252i
\(680\) −0.385477 0.222555i −0.0147824 0.00853460i
\(681\) −23.7036 + 6.35137i −0.908325 + 0.243385i
\(682\) 8.18826 8.18826i 0.313545 0.313545i
\(683\) 17.0486 17.0486i 0.652347 0.652347i −0.301211 0.953558i \(-0.597391\pi\)
0.953558 + 0.301211i \(0.0973907\pi\)
\(684\) −3.90282 + 1.04576i −0.149228 + 0.0399856i
\(685\) 1.07304 + 0.619517i 0.0409986 + 0.0236705i
\(686\) −11.2132 + 14.7399i −0.428120 + 0.562772i
\(687\) −10.9064 2.92237i −0.416107 0.111495i
\(688\) −9.78926 5.65183i −0.373212 0.215474i
\(689\) 24.4811 2.34606i 0.932657 0.0893777i
\(690\) 0.0974526 + 0.168793i 0.00370996 + 0.00642584i
\(691\) 15.3094 15.3094i 0.582397 0.582397i −0.353164 0.935561i \(-0.614894\pi\)
0.935561 + 0.353164i \(0.114894\pi\)
\(692\) 6.79528 3.92325i 0.258318 0.149140i
\(693\) −2.47006 + 11.2154i −0.0938299 + 0.426036i
\(694\) −19.1839 19.1839i −0.728212 0.728212i
\(695\) −0.407360 + 1.52029i −0.0154520 + 0.0576678i
\(696\) −3.04192 3.04192i −0.115304 0.115304i
\(697\) −36.9289 9.89507i −1.39878 0.374802i
\(698\) 0.341883 0.197386i 0.0129405 0.00747119i
\(699\) −0.748411 1.29629i −0.0283075 0.0490300i
\(700\) 11.7008 + 6.07045i 0.442250 + 0.229442i
\(701\) 6.76434i 0.255486i 0.991807 + 0.127743i \(0.0407732\pi\)
−0.991807 + 0.127743i \(0.959227\pi\)
\(702\) −1.26116 3.37779i −0.0475994 0.127487i
\(703\) 25.2035 14.5512i 0.950567 0.548810i
\(704\) 4.19269 1.12343i 0.158018 0.0423408i
\(705\) 1.56675i 0.0590070i
\(706\) 1.86086 3.22310i 0.0700343 0.121303i
\(707\) 0.00463632 + 0.102912i 0.000174367 + 0.00387042i
\(708\) −2.71847 + 0.728411i −0.102166 + 0.0273753i
\(709\) −5.65449 1.51512i −0.212359 0.0569014i 0.151071 0.988523i \(-0.451728\pi\)
−0.363430 + 0.931622i \(0.618394\pi\)
\(710\) 0.431618 1.61082i 0.0161984 0.0604531i
\(711\) −12.8378 −0.481456
\(712\) −11.0033 −0.412366
\(713\) 1.01026 3.77035i 0.0378346 0.141201i
\(714\) −6.52613 5.96346i −0.244234 0.223177i
\(715\) −0.198878 2.07529i −0.00743761 0.0776115i
\(716\) −2.46595 + 4.27116i −0.0921570 + 0.159621i
\(717\) −2.45907 9.17736i −0.0918355 0.342735i
\(718\) −18.3298 + 31.7481i −0.684062 + 1.18483i
\(719\) −5.05902 8.76249i −0.188670 0.326786i 0.756137 0.654413i \(-0.227084\pi\)
−0.944807 + 0.327627i \(0.893751\pi\)
\(720\) 0.0941951 0.0941951i 0.00351044 0.00351044i
\(721\) 1.41010 + 31.2999i 0.0525148 + 1.16567i
\(722\) 0.692177 + 2.58324i 0.0257602 + 0.0961382i
\(723\) 0.822951 + 3.07130i 0.0306059 + 0.114223i
\(724\) 0.641409i 0.0238378i
\(725\) 18.5617 + 10.7166i 0.689366 + 0.398006i
\(726\) −5.54425 5.54425i −0.205766 0.205766i
\(727\) 23.7007 0.879009 0.439505 0.898240i \(-0.355154\pi\)
0.439505 + 0.898240i \(0.355154\pi\)
\(728\) 7.62386 + 5.73383i 0.282559 + 0.212510i
\(729\) −1.00000 −0.0370370
\(730\) −0.769039 0.769039i −0.0284634 0.0284634i
\(731\) −32.7095 18.8849i −1.20981 0.698482i
\(732\) 5.98123i 0.221073i
\(733\) 1.33654 + 4.98805i 0.0493664 + 0.184238i 0.986206 0.165520i \(-0.0529304\pi\)
−0.936840 + 0.349758i \(0.886264\pi\)
\(734\) −7.98796 29.8115i −0.294841 1.10036i
\(735\) −0.715984 0.597404i −0.0264095 0.0220356i
\(736\) 1.03458 1.03458i 0.0381352 0.0381352i
\(737\) −18.4558 31.9663i −0.679827 1.17750i
\(738\) 5.72095 9.90898i 0.210591 0.364754i
\(739\) 13.6205 + 50.8325i 0.501039 + 1.86990i 0.493170 + 0.869933i \(0.335838\pi\)
0.00786870 + 0.999969i \(0.497495\pi\)
\(740\) −0.479742 + 0.830938i −0.0176357 + 0.0305459i
\(741\) 13.6480 5.09571i 0.501371 0.187196i
\(742\) 5.45057 + 17.2037i 0.200097 + 0.631569i
\(743\) 9.88631 36.8962i 0.362693 1.35359i −0.507828 0.861459i \(-0.669551\pi\)
0.870521 0.492131i \(-0.163782\pi\)
\(744\) −2.66783 −0.0978073
\(745\) 0.533337 0.0195400
\(746\) 4.76967 17.8006i 0.174630 0.651728i
\(747\) −12.2098 3.27160i −0.446732 0.119701i
\(748\) 14.0093 3.75379i 0.512232 0.137252i
\(749\) 31.4289 20.0838i 1.14839 0.733845i
\(750\) −0.664878 + 1.15160i −0.0242779 + 0.0420506i
\(751\) 46.1388i 1.68363i 0.539766 + 0.841815i \(0.318513\pi\)
−0.539766 + 0.841815i \(0.681487\pi\)
\(752\) 11.3605 3.04405i 0.414276 0.111005i
\(753\) 11.2981 6.52293i 0.411724 0.237709i
\(754\) 11.9640 + 9.87150i 0.435704 + 0.359499i
\(755\) 2.74880i 0.100039i
\(756\) 2.22943 1.42466i 0.0810836 0.0518142i
\(757\) −2.10566 3.64711i −0.0765316 0.132557i 0.825220 0.564812i \(-0.191051\pi\)
−0.901751 + 0.432255i \(0.857718\pi\)
\(758\) −5.38421 + 3.10858i −0.195563 + 0.112909i
\(759\) −6.13442 1.64371i −0.222665 0.0596630i
\(760\) 0.380595 + 0.380595i 0.0138056 + 0.0138056i
\(761\) 0.574723 2.14490i 0.0208337 0.0777524i −0.954726 0.297486i \(-0.903852\pi\)
0.975560 + 0.219733i \(0.0705187\pi\)
\(762\) 10.1309 + 10.1309i 0.367002 + 0.367002i
\(763\) 12.1987 + 38.5030i 0.441623 + 1.39390i
\(764\) −16.1039 + 9.29759i −0.582619 + 0.336375i
\(765\) 0.314740 0.314740i 0.0113795 0.0113795i
\(766\) −4.95427 8.58105i −0.179005 0.310046i
\(767\) 9.50633 3.54936i 0.343254 0.128160i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −33.9231 9.08967i −1.22330 0.327782i −0.411332 0.911486i \(-0.634936\pi\)
−0.811967 + 0.583704i \(0.801603\pi\)
\(770\) 1.45838 0.462051i 0.0525563 0.0166512i
\(771\) 7.02593 + 4.05642i 0.253033 + 0.146089i
\(772\) 5.68497 1.52328i 0.204606 0.0548241i
\(773\) −15.6174 + 15.6174i −0.561717 + 0.561717i −0.929795 0.368078i \(-0.880016\pi\)
0.368078 + 0.929795i \(0.380016\pi\)
\(774\) 7.99290 7.99290i 0.287299 0.287299i
\(775\) 12.8389 3.44017i 0.461186 0.123575i
\(776\) −4.85857 2.80509i −0.174412 0.100697i
\(777\) −12.8549 + 14.0678i −0.461167 + 0.504679i
\(778\) −23.5795 6.31811i −0.845366 0.226515i
\(779\) 40.0372 + 23.1155i 1.43448 + 0.828199i
\(780\) −0.305678 + 0.370475i −0.0109450 + 0.0132651i
\(781\) 27.1694 + 47.0588i 0.972197 + 1.68389i
\(782\) 3.45692 3.45692i 0.123619 0.123619i
\(783\) 3.72557 2.15096i 0.133141 0.0768690i
\(784\) −2.94071 + 6.35234i −0.105025 + 0.226869i
\(785\) −0.408171 0.408171i −0.0145682 0.0145682i
\(786\) 3.47294 12.9612i 0.123876 0.462310i
\(787\) 4.26772 + 4.26772i 0.152128 + 0.152128i 0.779068 0.626940i \(-0.215693\pi\)
−0.626940 + 0.779068i \(0.715693\pi\)
\(788\) 8.29752 + 2.22331i 0.295587 + 0.0792023i
\(789\) −11.1195 + 6.41984i −0.395864 + 0.228552i
\(790\) 0.855076 + 1.48103i 0.0304222 + 0.0526928i
\(791\) 1.49720 + 33.2334i 0.0532344 + 1.18164i
\(792\) 4.34059i 0.154236i
\(793\) 2.05724 + 21.4673i 0.0730547 + 0.762326i
\(794\) −9.02917 + 5.21300i −0.320433 + 0.185002i
\(795\) −0.877671 + 0.235171i −0.0311278 + 0.00834067i
\(796\) 14.0812i 0.499096i
\(797\) 23.5531 40.7952i 0.834295 1.44504i −0.0603090 0.998180i \(-0.519209\pi\)
0.894604 0.446861i \(-0.147458\pi\)
\(798\) 5.75632 + 9.00801i 0.203772 + 0.318880i
\(799\) 37.9598 10.1713i 1.34292 0.359834i
\(800\) 4.81249 + 1.28950i 0.170147 + 0.0455908i
\(801\) 2.84786 10.6284i 0.100624 0.375535i
\(802\) 0.915622 0.0323317
\(803\) 35.4380 1.25058
\(804\) −2.20095 + 8.21404i −0.0776214 + 0.289687i
\(805\) 0.347854 0.380675i 0.0122603 0.0134170i
\(806\) 9.57512 0.917596i 0.337269 0.0323209i
\(807\) −5.12028 + 8.86858i −0.180242 + 0.312189i
\(808\) 0.0100775 + 0.0376099i 0.000354527 + 0.00132311i
\(809\) 0.813607 1.40921i 0.0286049 0.0495451i −0.851369 0.524568i \(-0.824227\pi\)
0.879973 + 0.475023i \(0.157560\pi\)
\(810\) 0.0666060 + 0.115365i 0.00234030 + 0.00405351i
\(811\) 30.9201 30.9201i 1.08575 1.08575i 0.0897926 0.995960i \(-0.471380\pi\)
0.995960 0.0897926i \(-0.0286204\pi\)
\(812\) −5.24152 + 10.1031i −0.183941 + 0.354548i
\(813\) 6.32766 + 23.6152i 0.221921 + 0.828220i
\(814\) −8.09171 30.1987i −0.283614 1.05846i
\(815\) 0.925409i 0.0324157i
\(816\) −2.89371 1.67068i −0.101300 0.0584857i
\(817\) 32.2953 + 32.2953i 1.12987 + 1.12987i
\(818\) 3.36906 0.117796
\(819\) −7.51166 + 5.88005i −0.262478 + 0.205466i
\(820\) −1.52420 −0.0532273
\(821\) 13.0387 + 13.0387i 0.455055 + 0.455055i 0.897028 0.441973i \(-0.145721\pi\)
−0.441973 + 0.897028i \(0.645721\pi\)
\(822\) 8.05510 + 4.65061i 0.280954 + 0.162209i
\(823\) 10.5970i 0.369387i 0.982796 + 0.184693i \(0.0591292\pi\)
−0.982796 + 0.184693i \(0.940871\pi\)
\(824\) 3.06500 + 11.4387i 0.106774 + 0.398487i
\(825\) −5.59721 20.8891i −0.194870 0.727264i
\(826\) 4.00950 + 6.27442i 0.139508 + 0.218315i
\(827\) −4.38155 + 4.38155i −0.152361 + 0.152361i −0.779172 0.626810i \(-0.784360\pi\)
0.626810 + 0.779172i \(0.284360\pi\)
\(828\) 0.731561 + 1.26710i 0.0254235 + 0.0440348i
\(829\) −2.22587 + 3.85531i −0.0773075 + 0.133901i −0.902087 0.431553i \(-0.857966\pi\)
0.824780 + 0.565454i \(0.191299\pi\)
\(830\) 0.435816 + 1.62649i 0.0151274 + 0.0564562i
\(831\) −2.11065 + 3.65576i −0.0732178 + 0.126817i
\(832\) 3.28023 + 1.49669i 0.113722 + 0.0518882i
\(833\) −9.82600 + 21.2255i −0.340451 + 0.735420i
\(834\) −3.05798 + 11.4125i −0.105889 + 0.395184i
\(835\) −1.11272 −0.0385074
\(836\) −17.5382 −0.606570
\(837\) 0.690485 2.57692i 0.0238666 0.0890715i
\(838\) −14.4282 3.86603i −0.498415 0.133550i
\(839\) 4.10963 1.10117i 0.141880 0.0380167i −0.187180 0.982326i \(-0.559935\pi\)
0.329060 + 0.944309i \(0.393268\pi\)
\(840\) −0.312849 0.162307i −0.0107943 0.00560014i
\(841\) 5.24675 9.08763i 0.180922 0.313367i
\(842\) 28.1209i 0.969109i
\(843\) 1.92558 0.515959i 0.0663206 0.0177706i
\(844\) −9.95501 + 5.74753i −0.342666 + 0.197838i
\(845\) 0.969687 1.43481i 0.0333583 0.0493590i
\(846\) 11.7613i 0.404362i
\(847\) −9.55329 + 18.4140i −0.328255 + 0.632714i
\(848\) 3.41047 + 5.90712i 0.117116 + 0.202851i
\(849\) −4.76750 + 2.75252i −0.163620 + 0.0944662i
\(850\) 16.0803 + 4.30870i 0.551550 + 0.147787i
\(851\) −7.45178 7.45178i −0.255444 0.255444i
\(852\) 3.24009 12.0922i 0.111004 0.414271i
\(853\) −11.5036 11.5036i −0.393875 0.393875i 0.482191 0.876066i \(-0.339841\pi\)
−0.876066 + 0.482191i \(0.839841\pi\)
\(854\) −15.0858 + 4.77956i −0.516226 + 0.163553i
\(855\) −0.466132 + 0.269121i −0.0159414 + 0.00920376i
\(856\) 9.96828 9.96828i 0.340709 0.340709i
\(857\) −3.43120 5.94301i −0.117207 0.203009i 0.801453 0.598058i \(-0.204061\pi\)
−0.918660 + 0.395049i \(0.870728\pi\)
\(858\) −1.49294 15.5789i −0.0509682 0.531854i
\(859\) 28.2527 + 16.3117i 0.963971 + 0.556549i 0.897393 0.441232i \(-0.145459\pi\)
0.0665781 + 0.997781i \(0.478792\pi\)
\(860\) −1.45447 0.389725i −0.0495972 0.0132895i
\(861\) −29.5639 6.51114i −1.00754 0.221899i
\(862\) 27.3028 + 15.7633i 0.929937 + 0.536899i
\(863\) −25.1027 + 6.72624i −0.854505 + 0.228964i −0.659376 0.751814i \(-0.729179\pi\)
−0.195129 + 0.980778i \(0.562513\pi\)
\(864\) 0.707107 0.707107i 0.0240563 0.0240563i
\(865\) 0.739103 0.739103i 0.0251302 0.0251302i
\(866\) 24.6053 6.59296i 0.836121 0.224038i
\(867\) 5.05348 + 2.91763i 0.171625 + 0.0990878i
\(868\) 2.13184 + 6.72877i 0.0723594 + 0.228389i
\(869\) −53.8250 14.4224i −1.82589 0.489245i
\(870\) −0.496291 0.286534i −0.0168258 0.00971440i
\(871\) 5.07422 30.2381i 0.171933 1.02458i
\(872\) 7.63285 + 13.2205i 0.258481 + 0.447702i
\(873\) 3.96700 3.96700i 0.134263 0.134263i
\(874\) −5.11972 + 2.95587i −0.173177 + 0.0999838i
\(875\) 3.43586 + 0.756712i 0.116153 + 0.0255815i
\(876\) −5.77305 5.77305i −0.195053 0.195053i
\(877\) −10.4590 + 39.0336i −0.353176 + 1.31807i 0.529587 + 0.848255i \(0.322347\pi\)
−0.882764 + 0.469817i \(0.844320\pi\)
\(878\) 18.9790 + 18.9790i 0.640509 + 0.640509i
\(879\) 4.70508 + 1.26072i 0.158698 + 0.0425231i
\(880\) 0.500752 0.289109i 0.0168804 0.00974588i
\(881\) −3.94323 6.82987i −0.132851 0.230104i 0.791924 0.610620i \(-0.209080\pi\)
−0.924774 + 0.380516i \(0.875746\pi\)
\(882\) −5.37478 4.48462i −0.180978 0.151005i
\(883\) 17.8741i 0.601513i −0.953701 0.300756i \(-0.902761\pi\)
0.953701 0.300756i \(-0.0972391\pi\)
\(884\) 10.9605 + 5.00098i 0.368640 + 0.168201i
\(885\) −0.324679 + 0.187453i −0.0109140 + 0.00630118i
\(886\) −13.4434 + 3.60215i −0.451640 + 0.121016i
\(887\) 49.3131i 1.65577i −0.560895 0.827887i \(-0.689543\pi\)
0.560895 0.827887i \(-0.310457\pi\)
\(888\) −3.60134 + 6.23771i −0.120853 + 0.209324i
\(889\) 17.4565 33.6475i 0.585471 1.12850i
\(890\) −1.41583 + 0.379370i −0.0474586 + 0.0127165i
\(891\) −4.19269 1.12343i −0.140460 0.0376363i
\(892\) 6.42474 23.9774i 0.215116 0.802824i
\(893\) −47.5215 −1.59025
\(894\) 4.00367 0.133903
\(895\) −0.170041 + 0.634603i −0.00568385 + 0.0212124i
\(896\) −0.569061 + 2.58383i −0.0190110 + 0.0863197i
\(897\) −3.06147 4.29614i −0.102219 0.143444i
\(898\) −7.12463 + 12.3402i −0.237752 + 0.411799i
\(899\) 2.97041 + 11.0857i 0.0990687 + 0.369729i
\(900\) −2.49113 + 4.31476i −0.0830376 + 0.143825i
\(901\) 11.3957 + 19.7379i 0.379644 + 0.657563i
\(902\) 35.1182 35.1182i 1.16931 1.16931i
\(903\) −26.5467 13.7725i −0.883418 0.458322i
\(904\) 3.25433 + 12.1453i 0.108237 + 0.403948i
\(905\) −0.0221143 0.0825319i −0.000735106 0.00274345i
\(906\) 20.6348i 0.685545i
\(907\) −39.8691 23.0185i −1.32383 0.764315i −0.339495 0.940608i \(-0.610256\pi\)
−0.984338 + 0.176293i \(0.943589\pi\)
\(908\) 17.3523 + 17.3523i 0.575855 + 0.575855i
\(909\) −0.0389367 −0.00129145
\(910\) 1.17867 + 0.474935i 0.0390726 + 0.0157439i
\(911\) 3.09215 0.102448 0.0512238 0.998687i \(-0.483688\pi\)
0.0512238 + 0.998687i \(0.483688\pi\)
\(912\) 2.85706 + 2.85706i 0.0946069 + 0.0946069i
\(913\) −47.5164 27.4336i −1.57256 0.907920i
\(914\) 0.265066i 0.00876761i
\(915\) −0.206220 0.769623i −0.00681741 0.0254429i
\(916\) 2.92237 + 10.9064i 0.0965579 + 0.360359i
\(917\) −35.4658 + 1.59778i −1.17118 + 0.0527632i
\(918\) 2.36270 2.36270i 0.0779809 0.0779809i
\(919\) −18.9763 32.8679i −0.625969 1.08421i −0.988353 0.152182i \(-0.951370\pi\)
0.362383 0.932029i \(-0.381963\pi\)
\(920\) 0.0974526 0.168793i 0.00321292 0.00556494i
\(921\) 3.34098 + 12.4687i 0.110089 + 0.410858i
\(922\) −18.9637 + 32.8461i −0.624536 + 1.08173i
\(923\) −7.46994 + 44.5145i −0.245876 + 1.46521i
\(924\) 10.9478 3.46854i 0.360156 0.114107i
\(925\) 9.28788 34.6629i 0.305384 1.13971i
\(926\) −7.49241 −0.246216
\(927\) −11.8422 −0.388950
\(928\) −1.11342 + 4.15533i −0.0365498 + 0.136406i
\(929\) 53.8194 + 14.4209i 1.76576 + 0.473133i 0.987872 0.155272i \(-0.0496254\pi\)
0.777886 + 0.628405i \(0.216292\pi\)
\(930\) −0.343277 + 0.0919808i −0.0112565 + 0.00301617i
\(931\) 18.1201 21.7168i 0.593862 0.711739i
\(932\) −0.748411 + 1.29629i −0.0245150 + 0.0424613i
\(933\) 5.04124i 0.165043i
\(934\) −0.625717 + 0.167660i −0.0204741 + 0.00548601i
\(935\) 1.67320 0.966021i 0.0547194 0.0315923i
\(936\) −2.29467 + 2.78109i −0.0750038 + 0.0909028i
\(937\) 2.71210i 0.0886004i 0.999018 + 0.0443002i \(0.0141058\pi\)
−0.999018 + 0.0443002i \(0.985894\pi\)
\(938\) 22.4761 1.01258i 0.733872 0.0330618i
\(939\) 8.65025 + 14.9827i 0.282290 + 0.488941i
\(940\) 1.35684 0.783373i 0.0442553 0.0255508i
\(941\) −19.1927 5.14266i −0.625663 0.167646i −0.0679619 0.997688i \(-0.521650\pi\)
−0.557701 + 0.830042i \(0.688316\pi\)
\(942\) −3.06407 3.06407i −0.0998328 0.0998328i
\(943\) 4.33286 16.1705i 0.141097 0.526582i
\(944\) 1.99005 + 1.99005i 0.0647708 + 0.0647708i
\(945\) 0.237748 0.260180i 0.00773395 0.00846367i
\(946\) 42.4912 24.5323i 1.38151 0.797614i
\(947\) −13.8027 + 13.8027i −0.448527 + 0.448527i −0.894865 0.446338i \(-0.852728\pi\)
0.446338 + 0.894865i \(0.352728\pi\)
\(948\) 6.41891 + 11.1179i 0.208477 + 0.361092i
\(949\) 22.7057 + 18.7345i 0.737059 + 0.608146i
\(950\) −17.4338 10.0654i −0.565627 0.326565i
\(951\) 6.23606 + 1.67095i 0.202218 + 0.0541842i
\(952\) −1.90144 + 8.63352i −0.0616261 + 0.279814i
\(953\) −37.8786 21.8692i −1.22701 0.708413i −0.260605 0.965445i \(-0.583922\pi\)
−0.966403 + 0.257032i \(0.917255\pi\)
\(954\) −6.58853 + 1.76539i −0.213312 + 0.0571567i
\(955\) −1.75157 + 1.75157i −0.0566796 + 0.0566796i
\(956\) −6.71829 + 6.71829i −0.217285 + 0.217285i
\(957\) 18.0366 4.83290i 0.583041 0.156225i
\(958\) 21.9110 + 12.6503i 0.707913 + 0.408714i
\(959\) 5.29296 24.0328i 0.170919 0.776059i
\(960\) −0.128673 0.0344778i −0.00415290 0.00111277i
\(961\) −20.6830 11.9413i −0.667194 0.385205i
\(962\) 10.7802 23.6265i 0.347566 0.761749i
\(963\) 7.04864 + 12.2086i 0.227139 + 0.393416i
\(964\) 2.24834 2.24834i 0.0724143 0.0724143i
\(965\) 0.678982 0.392010i 0.0218572 0.0126193i
\(966\) 2.61128 2.85767i 0.0840167 0.0919439i
\(967\) 16.3348 + 16.3348i 0.525292 + 0.525292i 0.919165 0.393873i \(-0.128865\pi\)
−0.393873 + 0.919165i \(0.628865\pi\)
\(968\) −2.02934 + 7.57359i −0.0652254 + 0.243424i
\(969\) 9.54651 + 9.54651i 0.306678 + 0.306678i
\(970\) −0.721879 0.193427i −0.0231781 0.00621057i
\(971\) −12.2423 + 7.06812i −0.392875 + 0.226827i −0.683405 0.730039i \(-0.739502\pi\)
0.290530 + 0.956866i \(0.406168\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) 31.2282 1.40687i 1.00113 0.0451022i
\(974\) 1.54313i 0.0494452i
\(975\) 7.45687 16.3430i 0.238811 0.523394i
\(976\) −5.17990 + 2.99062i −0.165805 + 0.0957273i
\(977\) 10.4893 2.81059i 0.335581 0.0899186i −0.0870938 0.996200i \(-0.527758\pi\)
0.422675 + 0.906281i \(0.361091\pi\)
\(978\) 6.94689i 0.222137i
\(979\) 23.8804 41.3621i 0.763222 1.32194i
\(980\) −0.159375 + 0.918763i −0.00509105 + 0.0293488i
\(981\) −14.7455 + 3.95106i −0.470789 + 0.126148i
\(982\) 12.5580 + 3.36492i 0.400743 + 0.107379i
\(983\) −7.46820 + 27.8717i −0.238199 + 0.888969i 0.738482 + 0.674273i \(0.235543\pi\)
−0.976681 + 0.214696i \(0.931124\pi\)
\(984\) −11.4419 −0.364754
\(985\) 1.14432 0.0364611
\(986\) −3.72034 + 13.8845i −0.118480 + 0.442173i
\(987\) 29.6642 9.39837i 0.944223 0.299153i
\(988\) −11.2370 9.27163i −0.357497 0.294970i
\(989\) 8.26932 14.3229i 0.262949 0.455441i
\(990\) 0.149654 + 0.558517i 0.00475632 + 0.0177508i
\(991\) −21.9777 + 38.0664i −0.698143 + 1.20922i 0.270966 + 0.962589i \(0.412657\pi\)
−0.969109 + 0.246631i \(0.920676\pi\)
\(992\) 1.33391 + 2.31041i 0.0423518 + 0.0733555i
\(993\) 16.4491 16.4491i 0.521995 0.521995i
\(994\) −33.0879 + 1.49065i −1.04948 + 0.0472805i
\(995\) −0.485490 1.81187i −0.0153911 0.0574402i
\(996\) 3.27160 + 12.2098i 0.103665 + 0.386881i
\(997\) 14.9431i 0.473253i 0.971601 + 0.236626i \(0.0760417\pi\)
−0.971601 + 0.236626i \(0.923958\pi\)
\(998\) −2.23439 1.29002i −0.0707283 0.0408350i
\(999\) −5.09307 5.09307i −0.161138 0.161138i
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.271.2 yes 32
7.3 odd 6 546.2.by.a.115.6 yes 32
13.6 odd 12 546.2.by.a.19.6 32
91.45 even 12 inner 546.2.cg.a.409.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.by.a.19.6 32 13.6 odd 12
546.2.by.a.115.6 yes 32 7.3 odd 6
546.2.cg.a.271.2 yes 32 1.1 even 1 trivial
546.2.cg.a.409.2 yes 32 91.45 even 12 inner