Properties

Label 546.2.bg.a.467.17
Level $546$
Weight $2$
Character 546.467
Analytic conductor $4.360$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(311,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.311");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bg (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 467.17
Character \(\chi\) \(=\) 546.467
Dual form 546.2.bg.a.311.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.71668 + 0.230243i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00187 - 0.578432i) q^{5} +(-1.05774 + 1.37157i) q^{6} +(0.296298 - 2.62911i) q^{7} +1.00000 q^{8} +(2.89398 + 0.790508i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.71668 + 0.230243i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00187 - 0.578432i) q^{5} +(-1.05774 + 1.37157i) q^{6} +(0.296298 - 2.62911i) q^{7} +1.00000 q^{8} +(2.89398 + 0.790508i) q^{9} +(1.00187 - 0.578432i) q^{10} +(-1.85690 - 3.21624i) q^{11} +(-0.658943 - 1.60181i) q^{12} +(0.361803 - 3.58735i) q^{13} +(2.12873 + 1.57116i) q^{14} +(-1.58672 - 1.22366i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0128016 + 0.0221731i) q^{17} +(-2.13159 + 2.11100i) q^{18} +(0.122255 - 0.211752i) q^{19} +1.15686i q^{20} +(1.11398 - 4.44511i) q^{21} +3.71379 q^{22} +(2.36531 + 1.36561i) q^{23} +(1.71668 + 0.230243i) q^{24} +(-1.83083 - 3.17109i) q^{25} +(2.92584 + 2.10701i) q^{26} +(4.78602 + 2.02337i) q^{27} +(-2.42502 + 1.05795i) q^{28} -3.51946i q^{29} +(1.85308 - 0.762308i) q^{30} +(2.24622 + 3.89056i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.44718 - 5.94879i) q^{33} -0.0256033 q^{34} +(-1.81761 + 2.46265i) q^{35} +(-0.762388 - 2.90151i) q^{36} +(8.29815 + 4.79094i) q^{37} +(0.122255 + 0.211752i) q^{38} +(1.44706 - 6.07503i) q^{39} +(-1.00187 - 0.578432i) q^{40} -0.471512i q^{41} +(3.29259 + 3.18729i) q^{42} -1.24061 q^{43} +(-1.85690 + 3.21624i) q^{44} +(-2.44214 - 2.46596i) q^{45} +(-2.36531 + 1.36561i) q^{46} +(-0.203606 - 0.117552i) q^{47} +(-1.05774 + 1.37157i) q^{48} +(-6.82442 - 1.55800i) q^{49} +3.66166 q^{50} +(0.0168711 + 0.0410116i) q^{51} +(-3.28764 + 1.48035i) q^{52} +(-6.44560 + 3.72137i) q^{53} +(-4.14530 + 3.13313i) q^{54} +4.29635i q^{55} +(0.296298 - 2.62911i) q^{56} +(0.258628 - 0.335362i) q^{57} +(3.04794 + 1.75973i) q^{58} +(-2.80431 + 1.61907i) q^{59} +(-0.266360 + 1.98597i) q^{60} +(10.2453 + 5.91511i) q^{61} -4.49243 q^{62} +(2.93581 - 7.37435i) q^{63} +1.00000 q^{64} +(-2.43752 + 3.38480i) q^{65} +(6.37539 + 0.855076i) q^{66} +(-6.24108 + 3.60329i) q^{67} +(0.0128016 - 0.0221731i) q^{68} +(3.74606 + 2.88892i) q^{69} +(-1.22391 - 2.80542i) q^{70} +14.6757 q^{71} +(2.89398 + 0.790508i) q^{72} +(0.784266 + 1.35839i) q^{73} +(-8.29815 + 4.79094i) q^{74} +(-2.41283 - 5.86529i) q^{75} -0.244511 q^{76} +(-9.00603 + 3.92901i) q^{77} +(4.53760 + 4.29071i) q^{78} +(3.01266 - 5.21808i) q^{79} +(1.00187 - 0.578432i) q^{80} +(7.75019 + 4.57542i) q^{81} +(0.408341 + 0.235756i) q^{82} +3.64267i q^{83} +(-4.40657 + 1.25782i) q^{84} -0.0296195i q^{85} +(0.620304 - 1.07440i) q^{86} +(0.810333 - 6.04179i) q^{87} +(-1.85690 - 3.21624i) q^{88} +(-8.11911 - 4.68757i) q^{89} +(3.35666 - 0.881980i) q^{90} +(-9.32434 - 2.01414i) q^{91} -2.73122i q^{92} +(2.96026 + 7.19602i) q^{93} +(0.203606 - 0.117552i) q^{94} +(-0.244969 + 0.141433i) q^{95} +(-0.658943 - 1.60181i) q^{96} +12.7955 q^{97} +(4.76147 - 5.13112i) q^{98} +(-2.83135 - 10.7756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 1.71668 + 0.230243i 0.991125 + 0.132931i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00187 0.578432i −0.448052 0.258683i 0.258955 0.965889i \(-0.416622\pi\)
−0.707007 + 0.707206i \(0.749955\pi\)
\(6\) −1.05774 + 1.37157i −0.431819 + 0.559940i
\(7\) 0.296298 2.62911i 0.111990 0.993709i
\(8\) 1.00000 0.353553
\(9\) 2.89398 + 0.790508i 0.964659 + 0.263503i
\(10\) 1.00187 0.578432i 0.316820 0.182916i
\(11\) −1.85690 3.21624i −0.559875 0.969732i −0.997506 0.0705774i \(-0.977516\pi\)
0.437631 0.899155i \(-0.355818\pi\)
\(12\) −0.658943 1.60181i −0.190220 0.462403i
\(13\) 0.361803 3.58735i 0.100346 0.994953i
\(14\) 2.12873 + 1.57116i 0.568926 + 0.419909i
\(15\) −1.58672 1.22366i −0.409688 0.315947i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.0128016 + 0.0221731i 0.00310485 + 0.00537776i 0.867574 0.497309i \(-0.165678\pi\)
−0.864469 + 0.502686i \(0.832345\pi\)
\(18\) −2.13159 + 2.11100i −0.502420 + 0.497568i
\(19\) 0.122255 0.211752i 0.0280473 0.0485793i −0.851661 0.524093i \(-0.824404\pi\)
0.879708 + 0.475514i \(0.157738\pi\)
\(20\) 1.15686i 0.258683i
\(21\) 1.11398 4.44511i 0.243091 0.970003i
\(22\) 3.71379 0.791783
\(23\) 2.36531 + 1.36561i 0.493201 + 0.284750i 0.725902 0.687799i \(-0.241423\pi\)
−0.232700 + 0.972548i \(0.574756\pi\)
\(24\) 1.71668 + 0.230243i 0.350416 + 0.0469982i
\(25\) −1.83083 3.17109i −0.366166 0.634219i
\(26\) 2.92584 + 2.10701i 0.573804 + 0.413218i
\(27\) 4.78602 + 2.02337i 0.921070 + 0.389397i
\(28\) −2.42502 + 1.05795i −0.458286 + 0.199934i
\(29\) 3.51946i 0.653548i −0.945103 0.326774i \(-0.894038\pi\)
0.945103 0.326774i \(-0.105962\pi\)
\(30\) 1.85308 0.762308i 0.338324 0.139178i
\(31\) 2.24622 + 3.89056i 0.403432 + 0.698765i 0.994138 0.108122i \(-0.0344838\pi\)
−0.590705 + 0.806887i \(0.701150\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.44718 5.94879i −0.425999 1.03555i
\(34\) −0.0256033 −0.00439092
\(35\) −1.81761 + 2.46265i −0.307233 + 0.416263i
\(36\) −0.762388 2.90151i −0.127065 0.483585i
\(37\) 8.29815 + 4.79094i 1.36421 + 0.787625i 0.990181 0.139793i \(-0.0446437\pi\)
0.374026 + 0.927418i \(0.377977\pi\)
\(38\) 0.122255 + 0.211752i 0.0198324 + 0.0343508i
\(39\) 1.44706 6.07503i 0.231716 0.972784i
\(40\) −1.00187 0.578432i −0.158410 0.0914582i
\(41\) 0.471512i 0.0736377i −0.999322 0.0368189i \(-0.988278\pi\)
0.999322 0.0368189i \(-0.0117225\pi\)
\(42\) 3.29259 + 3.18729i 0.508058 + 0.491810i
\(43\) −1.24061 −0.189191 −0.0945955 0.995516i \(-0.530156\pi\)
−0.0945955 + 0.995516i \(0.530156\pi\)
\(44\) −1.85690 + 3.21624i −0.279937 + 0.484866i
\(45\) −2.44214 2.46596i −0.364053 0.367603i
\(46\) −2.36531 + 1.36561i −0.348746 + 0.201349i
\(47\) −0.203606 0.117552i −0.0296990 0.0171467i 0.485077 0.874471i \(-0.338792\pi\)
−0.514776 + 0.857325i \(0.672125\pi\)
\(48\) −1.05774 + 1.37157i −0.152671 + 0.197969i
\(49\) −6.82442 1.55800i −0.974916 0.222571i
\(50\) 3.66166 0.517837
\(51\) 0.0168711 + 0.0410116i 0.00236243 + 0.00574277i
\(52\) −3.28764 + 1.48035i −0.455914 + 0.205287i
\(53\) −6.44560 + 3.72137i −0.885372 + 0.511170i −0.872426 0.488747i \(-0.837454\pi\)
−0.0129459 + 0.999916i \(0.504121\pi\)
\(54\) −4.14530 + 3.13313i −0.564104 + 0.426365i
\(55\) 4.29635i 0.579320i
\(56\) 0.296298 2.62911i 0.0395945 0.351329i
\(57\) 0.258628 0.335362i 0.0342561 0.0444198i
\(58\) 3.04794 + 1.75973i 0.400215 + 0.231064i
\(59\) −2.80431 + 1.61907i −0.365090 + 0.210785i −0.671311 0.741176i \(-0.734269\pi\)
0.306221 + 0.951960i \(0.400935\pi\)
\(60\) −0.266360 + 1.98597i −0.0343870 + 0.256387i
\(61\) 10.2453 + 5.91511i 1.31177 + 0.757353i 0.982390 0.186844i \(-0.0598258\pi\)
0.329384 + 0.944196i \(0.393159\pi\)
\(62\) −4.49243 −0.570539
\(63\) 2.93581 7.37435i 0.369877 0.929081i
\(64\) 1.00000 0.125000
\(65\) −2.43752 + 3.38480i −0.302337 + 0.419833i
\(66\) 6.37539 + 0.855076i 0.784756 + 0.105253i
\(67\) −6.24108 + 3.60329i −0.762469 + 0.440212i −0.830182 0.557493i \(-0.811763\pi\)
0.0677122 + 0.997705i \(0.478430\pi\)
\(68\) 0.0128016 0.0221731i 0.00155243 0.00268888i
\(69\) 3.74606 + 2.88892i 0.450972 + 0.347785i
\(70\) −1.22391 2.80542i −0.146285 0.335312i
\(71\) 14.6757 1.74168 0.870841 0.491564i \(-0.163575\pi\)
0.870841 + 0.491564i \(0.163575\pi\)
\(72\) 2.89398 + 0.790508i 0.341058 + 0.0931623i
\(73\) 0.784266 + 1.35839i 0.0917914 + 0.158987i 0.908265 0.418395i \(-0.137407\pi\)
−0.816474 + 0.577383i \(0.804074\pi\)
\(74\) −8.29815 + 4.79094i −0.964640 + 0.556935i
\(75\) −2.41283 5.86529i −0.278609 0.677265i
\(76\) −0.244511 −0.0280473
\(77\) −9.00603 + 3.92901i −1.02633 + 0.447753i
\(78\) 4.53760 + 4.29071i 0.513782 + 0.485827i
\(79\) 3.01266 5.21808i 0.338951 0.587080i −0.645285 0.763942i \(-0.723261\pi\)
0.984236 + 0.176862i \(0.0565946\pi\)
\(80\) 1.00187 0.578432i 0.112013 0.0646707i
\(81\) 7.75019 + 4.57542i 0.861133 + 0.508380i
\(82\) 0.408341 + 0.235756i 0.0450937 + 0.0260349i
\(83\) 3.64267i 0.399835i 0.979813 + 0.199917i \(0.0640673\pi\)
−0.979813 + 0.199917i \(0.935933\pi\)
\(84\) −4.40657 + 1.25782i −0.480797 + 0.137239i
\(85\) 0.0296195i 0.00321269i
\(86\) 0.620304 1.07440i 0.0668891 0.115855i
\(87\) 0.810333 6.04179i 0.0868768 0.647748i
\(88\) −1.85690 3.21624i −0.197946 0.342852i
\(89\) −8.11911 4.68757i −0.860623 0.496881i 0.00359755 0.999994i \(-0.498855\pi\)
−0.864221 + 0.503112i \(0.832188\pi\)
\(90\) 3.35666 0.881980i 0.353823 0.0929688i
\(91\) −9.32434 2.01414i −0.977456 0.211140i
\(92\) 2.73122i 0.284750i
\(93\) 2.96026 + 7.19602i 0.306964 + 0.746193i
\(94\) 0.203606 0.117552i 0.0210004 0.0121246i
\(95\) −0.244969 + 0.141433i −0.0251333 + 0.0145107i
\(96\) −0.658943 1.60181i −0.0672531 0.163484i
\(97\) 12.7955 1.29918 0.649591 0.760284i \(-0.274940\pi\)
0.649591 + 0.760284i \(0.274940\pi\)
\(98\) 4.76147 5.13112i 0.480981 0.518321i
\(99\) −2.83135 10.7756i −0.284561 1.08299i
\(100\) −1.83083 + 3.17109i −0.183083 + 0.317109i
\(101\) −5.03494 8.72077i −0.500995 0.867749i −0.999999 0.00114938i \(-0.999634\pi\)
0.499004 0.866600i \(-0.333699\pi\)
\(102\) −0.0439526 0.00589498i −0.00435196 0.000583690i
\(103\) 8.82256 + 5.09371i 0.869313 + 0.501898i 0.867120 0.498099i \(-0.165969\pi\)
0.00219314 + 0.999998i \(0.499302\pi\)
\(104\) 0.361803 3.58735i 0.0354777 0.351769i
\(105\) −3.68727 + 3.80908i −0.359841 + 0.371728i
\(106\) 7.44274i 0.722903i
\(107\) −15.7423 9.08881i −1.52186 0.878648i −0.999667 0.0258233i \(-0.991779\pi\)
−0.522197 0.852825i \(-0.674887\pi\)
\(108\) −0.640722 5.15650i −0.0616535 0.496184i
\(109\) −2.40616 + 1.38920i −0.230469 + 0.133061i −0.610788 0.791794i \(-0.709147\pi\)
0.380320 + 0.924855i \(0.375814\pi\)
\(110\) −3.72075 2.14818i −0.354760 0.204821i
\(111\) 13.1422 + 10.1351i 1.24740 + 0.961981i
\(112\) 2.12873 + 1.57116i 0.201146 + 0.148460i
\(113\) 18.6367i 1.75319i 0.481229 + 0.876595i \(0.340191\pi\)
−0.481229 + 0.876595i \(0.659809\pi\)
\(114\) 0.161119 + 0.391659i 0.0150901 + 0.0366823i
\(115\) −1.57983 2.73634i −0.147320 0.255165i
\(116\) −3.04794 + 1.75973i −0.282995 + 0.163387i
\(117\) 3.88288 10.0957i 0.358972 0.933348i
\(118\) 3.23814i 0.298095i
\(119\) 0.0620885 0.0270870i 0.00569164 0.00248306i
\(120\) −1.58672 1.22366i −0.144847 0.111704i
\(121\) −1.39612 + 2.41815i −0.126920 + 0.219832i
\(122\) −10.2453 + 5.91511i −0.927564 + 0.535529i
\(123\) 0.108562 0.809434i 0.00978874 0.0729842i
\(124\) 2.24622 3.89056i 0.201716 0.349383i
\(125\) 10.0204i 0.896249i
\(126\) 4.91847 + 6.22966i 0.438172 + 0.554982i
\(127\) −8.83042 −0.783573 −0.391787 0.920056i \(-0.628143\pi\)
−0.391787 + 0.920056i \(0.628143\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −2.12973 0.285642i −0.187512 0.0251494i
\(130\) −1.71256 3.80335i −0.150201 0.333576i
\(131\) −7.07051 + 12.2465i −0.617753 + 1.06998i 0.372141 + 0.928176i \(0.378624\pi\)
−0.989895 + 0.141804i \(0.954710\pi\)
\(132\) −3.92821 + 5.09371i −0.341907 + 0.443351i
\(133\) −0.520496 0.384164i −0.0451327 0.0333113i
\(134\) 7.20658i 0.622554i
\(135\) −3.62461 4.79555i −0.311957 0.412735i
\(136\) 0.0128016 + 0.0221731i 0.00109773 + 0.00190133i
\(137\) −6.70701 11.6169i −0.573019 0.992498i −0.996254 0.0864777i \(-0.972439\pi\)
0.423235 0.906020i \(-0.360894\pi\)
\(138\) −4.37490 + 1.79972i −0.372416 + 0.153202i
\(139\) 15.0565i 1.27708i 0.769589 + 0.638539i \(0.220461\pi\)
−0.769589 + 0.638539i \(0.779539\pi\)
\(140\) 3.04152 + 0.342777i 0.257056 + 0.0289699i
\(141\) −0.322461 0.248678i −0.0271561 0.0209425i
\(142\) −7.33784 + 12.7095i −0.615778 + 1.06656i
\(143\) −12.2096 + 5.49769i −1.02102 + 0.459740i
\(144\) −2.13159 + 2.11100i −0.177632 + 0.175917i
\(145\) −2.03577 + 3.52606i −0.169062 + 0.292823i
\(146\) −1.56853 −0.129813
\(147\) −11.3566 4.24586i −0.936678 0.350193i
\(148\) 9.58187i 0.787625i
\(149\) 4.72601 8.18569i 0.387170 0.670598i −0.604898 0.796303i \(-0.706786\pi\)
0.992068 + 0.125705i \(0.0401193\pi\)
\(150\) 6.28590 + 0.843074i 0.513242 + 0.0688367i
\(151\) −12.9798 + 7.49388i −1.05628 + 0.609843i −0.924401 0.381423i \(-0.875434\pi\)
−0.131878 + 0.991266i \(0.542101\pi\)
\(152\) 0.122255 0.211752i 0.00991621 0.0171754i
\(153\) 0.0195196 + 0.0742882i 0.00157807 + 0.00600584i
\(154\) 1.10039 9.76396i 0.0886718 0.786802i
\(155\) 5.19714i 0.417444i
\(156\) −5.98466 + 1.78432i −0.479157 + 0.142860i
\(157\) 1.50376 0.868197i 0.120013 0.0692896i −0.438792 0.898589i \(-0.644593\pi\)
0.558805 + 0.829299i \(0.311260\pi\)
\(158\) 3.01266 + 5.21808i 0.239674 + 0.415128i
\(159\) −11.9219 + 4.90434i −0.945465 + 0.388940i
\(160\) 1.15686i 0.0914582i
\(161\) 4.29118 5.81403i 0.338192 0.458210i
\(162\) −7.83753 + 4.42415i −0.615774 + 0.347594i
\(163\) −11.0173 6.36085i −0.862943 0.498221i 0.00205345 0.999998i \(-0.499346\pi\)
−0.864997 + 0.501777i \(0.832680\pi\)
\(164\) −0.408341 + 0.235756i −0.0318861 + 0.0184094i
\(165\) −0.989207 + 7.37546i −0.0770097 + 0.574179i
\(166\) −3.15464 1.82133i −0.244848 0.141363i
\(167\) 6.85544i 0.530490i 0.964181 + 0.265245i \(0.0854528\pi\)
−0.964181 + 0.265245i \(0.914547\pi\)
\(168\) 1.11398 4.44511i 0.0859457 0.342948i
\(169\) −12.7382 2.59583i −0.979861 0.199679i
\(170\) 0.0256513 + 0.0148098i 0.00196736 + 0.00113586i
\(171\) 0.521196 0.516163i 0.0398568 0.0394719i
\(172\) 0.620304 + 1.07440i 0.0472977 + 0.0819221i
\(173\) 7.79711 13.5050i 0.592803 1.02677i −0.401049 0.916056i \(-0.631354\pi\)
0.993853 0.110709i \(-0.0353122\pi\)
\(174\) 4.82718 + 3.72266i 0.365947 + 0.282214i
\(175\) −8.87962 + 3.87387i −0.671236 + 0.292837i
\(176\) 3.71379 0.279937
\(177\) −5.18688 + 2.13375i −0.389870 + 0.160382i
\(178\) 8.11911 4.68757i 0.608553 0.351348i
\(179\) 3.42830 1.97933i 0.256243 0.147942i −0.366377 0.930467i \(-0.619402\pi\)
0.622620 + 0.782525i \(0.286068\pi\)
\(180\) −0.914511 + 3.34794i −0.0681636 + 0.249541i
\(181\) 0.429161i 0.0318992i 0.999873 + 0.0159496i \(0.00507714\pi\)
−0.999873 + 0.0159496i \(0.994923\pi\)
\(182\) 6.40647 7.06804i 0.474879 0.523918i
\(183\) 16.2259 + 12.5133i 1.19946 + 0.925007i
\(184\) 2.36531 + 1.36561i 0.174373 + 0.100674i
\(185\) −5.54247 9.59983i −0.407490 0.705794i
\(186\) −7.71207 1.03435i −0.565476 0.0758424i
\(187\) 0.0475426 0.0823462i 0.00347666 0.00602175i
\(188\) 0.235104i 0.0171467i
\(189\) 6.73774 11.9834i 0.490098 0.871667i
\(190\) 0.282866i 0.0205212i
\(191\) −1.57425 0.908893i −0.113909 0.0657652i 0.441963 0.897033i \(-0.354282\pi\)
−0.555872 + 0.831268i \(0.687615\pi\)
\(192\) 1.71668 + 0.230243i 0.123891 + 0.0166164i
\(193\) 17.1426 9.89729i 1.23395 0.712422i 0.266100 0.963945i \(-0.414265\pi\)
0.967851 + 0.251523i \(0.0809315\pi\)
\(194\) −6.39773 + 11.0812i −0.459330 + 0.795583i
\(195\) −4.96377 + 5.24939i −0.355463 + 0.375917i
\(196\) 2.06294 + 6.68912i 0.147353 + 0.477794i
\(197\) 25.2444 1.79859 0.899296 0.437341i \(-0.144080\pi\)
0.899296 + 0.437341i \(0.144080\pi\)
\(198\) 10.7476 + 2.93578i 0.763800 + 0.208637i
\(199\) −5.33963 + 3.08284i −0.378517 + 0.218537i −0.677173 0.735824i \(-0.736795\pi\)
0.298656 + 0.954361i \(0.403462\pi\)
\(200\) −1.83083 3.17109i −0.129459 0.224230i
\(201\) −11.5436 + 4.74873i −0.814221 + 0.334949i
\(202\) 10.0699 0.708514
\(203\) −9.25305 1.04281i −0.649437 0.0731909i
\(204\) 0.0270815 0.0351166i 0.00189608 0.00245865i
\(205\) −0.272738 + 0.472395i −0.0190488 + 0.0329935i
\(206\) −8.82256 + 5.09371i −0.614697 + 0.354896i
\(207\) 5.76562 + 5.82185i 0.400738 + 0.404646i
\(208\) 2.92584 + 2.10701i 0.202870 + 0.146095i
\(209\) −0.908061 −0.0628119
\(210\) −1.45513 5.09781i −0.100413 0.351782i
\(211\) −3.98179 −0.274117 −0.137059 0.990563i \(-0.543765\pi\)
−0.137059 + 0.990563i \(0.543765\pi\)
\(212\) 6.44560 + 3.72137i 0.442686 + 0.255585i
\(213\) 25.1934 + 3.37898i 1.72623 + 0.231524i
\(214\) 15.7423 9.08881i 1.07612 0.621298i
\(215\) 1.24293 + 0.717608i 0.0847673 + 0.0489405i
\(216\) 4.78602 + 2.02337i 0.325647 + 0.137673i
\(217\) 10.8943 4.75278i 0.739550 0.322640i
\(218\) 2.77840i 0.188177i
\(219\) 1.03357 + 2.51249i 0.0698425 + 0.169778i
\(220\) 3.72075 2.14818i 0.250853 0.144830i
\(221\) 0.0841743 0.0379017i 0.00566218 0.00254954i
\(222\) −15.3483 + 6.31391i −1.03011 + 0.423762i
\(223\) −2.03477 −0.136258 −0.0681291 0.997677i \(-0.521703\pi\)
−0.0681291 + 0.997677i \(0.521703\pi\)
\(224\) −2.42502 + 1.05795i −0.162029 + 0.0706874i
\(225\) −2.79161 10.6244i −0.186107 0.708290i
\(226\) −16.1398 9.31833i −1.07361 0.619846i
\(227\) −15.6005 + 9.00694i −1.03544 + 0.597812i −0.918538 0.395332i \(-0.870630\pi\)
−0.116902 + 0.993143i \(0.537296\pi\)
\(228\) −0.419746 0.0562970i −0.0277984 0.00372836i
\(229\) −9.36691 + 16.2240i −0.618983 + 1.07211i 0.370688 + 0.928757i \(0.379122\pi\)
−0.989672 + 0.143353i \(0.954212\pi\)
\(230\) 3.15966 0.208342
\(231\) −16.3651 + 4.67128i −1.07674 + 0.307348i
\(232\) 3.51946i 0.231064i
\(233\) 17.0834 + 9.86309i 1.11917 + 0.646152i 0.941189 0.337882i \(-0.109710\pi\)
0.177980 + 0.984034i \(0.443044\pi\)
\(234\) 6.80170 + 8.41052i 0.444641 + 0.549813i
\(235\) 0.135992 + 0.235545i 0.00887112 + 0.0153652i
\(236\) 2.80431 + 1.61907i 0.182545 + 0.105392i
\(237\) 6.37320 8.26413i 0.413984 0.536813i
\(238\) −0.00758619 + 0.0673137i −0.000491740 + 0.00436330i
\(239\) 20.1417 1.30286 0.651428 0.758711i \(-0.274170\pi\)
0.651428 + 0.758711i \(0.274170\pi\)
\(240\) 1.85308 0.762308i 0.119616 0.0492068i
\(241\) 11.1359 + 19.2880i 0.717327 + 1.24245i 0.962055 + 0.272855i \(0.0879678\pi\)
−0.244729 + 0.969592i \(0.578699\pi\)
\(242\) −1.39612 2.41815i −0.0897460 0.155445i
\(243\) 12.2511 + 9.63897i 0.785911 + 0.618340i
\(244\) 11.8302i 0.757353i
\(245\) 5.93601 + 5.50838i 0.379238 + 0.351918i
\(246\) 0.646709 + 0.498735i 0.0412327 + 0.0317982i
\(247\) −0.715398 0.515185i −0.0455197 0.0327805i
\(248\) 2.24622 + 3.89056i 0.142635 + 0.247051i
\(249\) −0.838700 + 6.25329i −0.0531504 + 0.396286i
\(250\) −8.67790 5.01019i −0.548838 0.316872i
\(251\) 20.5563 1.29750 0.648752 0.761000i \(-0.275291\pi\)
0.648752 + 0.761000i \(0.275291\pi\)
\(252\) −7.85428 + 1.14469i −0.494773 + 0.0721086i
\(253\) 10.1432i 0.637697i
\(254\) 4.41521 7.64737i 0.277035 0.479839i
\(255\) 0.00681970 0.0508472i 0.000427066 0.00318418i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.10857 8.84830i 0.318664 0.551942i −0.661546 0.749905i \(-0.730099\pi\)
0.980210 + 0.197963i \(0.0634326\pi\)
\(258\) 1.31224 1.70158i 0.0816963 0.105936i
\(259\) 15.0546 20.3972i 0.935448 1.26742i
\(260\) 4.15008 + 0.418557i 0.257377 + 0.0259578i
\(261\) 2.78216 10.1852i 0.172212 0.630451i
\(262\) −7.07051 12.2465i −0.436818 0.756590i
\(263\) 24.3841 14.0782i 1.50359 0.868097i 0.503598 0.863938i \(-0.332009\pi\)
0.999991 0.00415905i \(-0.00132387\pi\)
\(264\) −2.44718 5.94879i −0.150613 0.366122i
\(265\) 8.61025 0.528923
\(266\) 0.592944 0.258681i 0.0363557 0.0158607i
\(267\) −12.8586 9.91642i −0.786935 0.606875i
\(268\) 6.24108 + 3.60329i 0.381235 + 0.220106i
\(269\) 14.6822 + 25.4302i 0.895187 + 1.55051i 0.833573 + 0.552409i \(0.186291\pi\)
0.0616140 + 0.998100i \(0.480375\pi\)
\(270\) 5.96537 0.741228i 0.363041 0.0451097i
\(271\) −14.2082 + 24.6093i −0.863085 + 1.49491i 0.00585211 + 0.999983i \(0.498137\pi\)
−0.868937 + 0.494923i \(0.835196\pi\)
\(272\) −0.0256033 −0.00155243
\(273\) −15.5432 5.60450i −0.940714 0.339200i
\(274\) 13.4140 0.810371
\(275\) −6.79933 + 11.7768i −0.410015 + 0.710166i
\(276\) 0.628846 4.68864i 0.0378521 0.282223i
\(277\) −13.8268 23.9486i −0.830769 1.43893i −0.897429 0.441159i \(-0.854567\pi\)
0.0666595 0.997776i \(-0.478766\pi\)
\(278\) −13.0393 7.52827i −0.782048 0.451516i
\(279\) 3.42498 + 13.0348i 0.205048 + 0.780375i
\(280\) −1.81761 + 2.46265i −0.108623 + 0.147171i
\(281\) 12.3610 0.737394 0.368697 0.929550i \(-0.379804\pi\)
0.368697 + 0.929550i \(0.379804\pi\)
\(282\) 0.376592 0.154920i 0.0224257 0.00922536i
\(283\) 11.8406 6.83616i 0.703849 0.406367i −0.104930 0.994480i \(-0.533462\pi\)
0.808779 + 0.588112i \(0.200129\pi\)
\(284\) −7.33784 12.7095i −0.435421 0.754171i
\(285\) −0.453097 + 0.186392i −0.0268391 + 0.0110409i
\(286\) 1.34366 13.3227i 0.0794523 0.787786i
\(287\) −1.23965 0.139708i −0.0731745 0.00824669i
\(288\) −0.762388 2.90151i −0.0449241 0.170973i
\(289\) 8.49967 14.7219i 0.499981 0.865992i
\(290\) −2.03577 3.52606i −0.119545 0.207057i
\(291\) 21.9657 + 2.94607i 1.28765 + 0.172702i
\(292\) 0.784266 1.35839i 0.0458957 0.0794937i
\(293\) 4.20649i 0.245746i −0.992422 0.122873i \(-0.960789\pi\)
0.992422 0.122873i \(-0.0392107\pi\)
\(294\) 9.35533 7.71219i 0.545614 0.449784i
\(295\) 3.74609 0.218106
\(296\) 8.29815 + 4.79094i 0.482320 + 0.278468i
\(297\) −2.37951 19.1502i −0.138073 1.11120i
\(298\) 4.72601 + 8.18569i 0.273771 + 0.474184i
\(299\) 5.75471 7.99112i 0.332803 0.462138i
\(300\) −3.87307 + 5.02221i −0.223612 + 0.289958i
\(301\) −0.367590 + 3.26169i −0.0211875 + 0.188001i
\(302\) 14.9878i 0.862448i
\(303\) −6.63547 16.1300i −0.381198 0.926646i
\(304\) 0.122255 + 0.211752i 0.00701182 + 0.0121448i
\(305\) −6.84299 11.8524i −0.391828 0.678666i
\(306\) −0.0740952 0.0202396i −0.00423574 0.00115702i
\(307\) −21.1492 −1.20705 −0.603524 0.797345i \(-0.706237\pi\)
−0.603524 + 0.797345i \(0.706237\pi\)
\(308\) 7.90564 + 5.83494i 0.450466 + 0.332477i
\(309\) 13.9727 + 10.7756i 0.794880 + 0.613003i
\(310\) 4.50085 + 2.59857i 0.255631 + 0.147589i
\(311\) 15.6755 + 27.1507i 0.888874 + 1.53957i 0.841208 + 0.540711i \(0.181845\pi\)
0.0476652 + 0.998863i \(0.484822\pi\)
\(312\) 1.44706 6.07503i 0.0819238 0.343931i
\(313\) 28.3855 + 16.3884i 1.60444 + 0.926325i 0.990584 + 0.136908i \(0.0437165\pi\)
0.613858 + 0.789417i \(0.289617\pi\)
\(314\) 1.73639i 0.0979903i
\(315\) −7.20687 + 5.69000i −0.406061 + 0.320595i
\(316\) −6.02532 −0.338951
\(317\) 11.1137 19.2495i 0.624209 1.08116i −0.364484 0.931210i \(-0.618755\pi\)
0.988693 0.149952i \(-0.0479120\pi\)
\(318\) 1.71364 12.7768i 0.0960963 0.716487i
\(319\) −11.3194 + 6.53528i −0.633766 + 0.365905i
\(320\) −1.00187 0.578432i −0.0560065 0.0323354i
\(321\) −24.9318 19.2271i −1.39156 1.07315i
\(322\) 2.88951 + 6.62328i 0.161026 + 0.369101i
\(323\) 0.00626027 0.000348331
\(324\) 0.0873358 8.99958i 0.00485199 0.499976i
\(325\) −12.0382 + 5.42053i −0.667761 + 0.300677i
\(326\) 11.0173 6.36085i 0.610193 0.352295i
\(327\) −4.45046 + 1.83081i −0.246111 + 0.101244i
\(328\) 0.471512i 0.0260349i
\(329\) −0.369385 + 0.500472i −0.0203648 + 0.0275919i
\(330\) −5.89273 4.54441i −0.324384 0.250161i
\(331\) −16.0419 9.26179i −0.881742 0.509074i −0.0105099 0.999945i \(-0.503345\pi\)
−0.871233 + 0.490871i \(0.836679\pi\)
\(332\) 3.15464 1.82133i 0.173133 0.0999586i
\(333\) 20.2274 + 20.4246i 1.10845 + 1.11926i
\(334\) −5.93699 3.42772i −0.324857 0.187557i
\(335\) 8.33704 0.455501
\(336\) 3.29259 + 3.18729i 0.179626 + 0.173881i
\(337\) −17.9572 −0.978191 −0.489095 0.872230i \(-0.662673\pi\)
−0.489095 + 0.872230i \(0.662673\pi\)
\(338\) 8.61715 9.73369i 0.468711 0.529443i
\(339\) −4.29097 + 31.9932i −0.233053 + 1.73763i
\(340\) −0.0256513 + 0.0148098i −0.00139113 + 0.000803172i
\(341\) 8.34198 14.4487i 0.451743 0.782442i
\(342\) 0.186412 + 0.709450i 0.0100800 + 0.0383627i
\(343\) −6.11820 + 17.4805i −0.330352 + 0.943858i
\(344\) −1.24061 −0.0668891
\(345\) −2.08203 5.06117i −0.112093 0.272484i
\(346\) 7.79711 + 13.5050i 0.419175 + 0.726033i
\(347\) 0.436830 0.252204i 0.0234503 0.0135390i −0.488229 0.872716i \(-0.662357\pi\)
0.511679 + 0.859177i \(0.329024\pi\)
\(348\) −5.63751 + 2.31913i −0.302202 + 0.124318i
\(349\) 22.5405 1.20656 0.603282 0.797528i \(-0.293859\pi\)
0.603282 + 0.797528i \(0.293859\pi\)
\(350\) 1.08494 9.62691i 0.0579927 0.514580i
\(351\) 8.99013 16.4371i 0.479858 0.877346i
\(352\) −1.85690 + 3.21624i −0.0989728 + 0.171426i
\(353\) −13.8668 + 8.00600i −0.738055 + 0.426116i −0.821362 0.570408i \(-0.806785\pi\)
0.0833068 + 0.996524i \(0.473452\pi\)
\(354\) 0.745560 5.55884i 0.0396260 0.295449i
\(355\) −14.7032 8.48889i −0.780364 0.450543i
\(356\) 9.37514i 0.496881i
\(357\) 0.112823 0.0322043i 0.00597121 0.00170443i
\(358\) 3.95866i 0.209222i
\(359\) −7.67875 + 13.3000i −0.405269 + 0.701947i −0.994353 0.106125i \(-0.966156\pi\)
0.589084 + 0.808072i \(0.299489\pi\)
\(360\) −2.44214 2.46596i −0.128712 0.129967i
\(361\) 9.47011 + 16.4027i 0.498427 + 0.863300i
\(362\) −0.371664 0.214580i −0.0195342 0.0112781i
\(363\) −2.95345 + 3.82974i −0.155016 + 0.201009i
\(364\) 2.91787 + 9.08218i 0.152938 + 0.476036i
\(365\) 1.81458i 0.0949795i
\(366\) −18.9498 + 7.79545i −0.990520 + 0.407474i
\(367\) −27.0095 + 15.5939i −1.40988 + 0.813996i −0.995376 0.0960509i \(-0.969379\pi\)
−0.414506 + 0.910047i \(0.636045\pi\)
\(368\) −2.36531 + 1.36561i −0.123300 + 0.0711875i
\(369\) 0.372734 1.36454i 0.0194037 0.0710353i
\(370\) 11.0849 0.576278
\(371\) 7.87407 + 18.0488i 0.408801 + 0.937048i
\(372\) 4.75181 6.16167i 0.246370 0.319468i
\(373\) 2.30810 3.99775i 0.119509 0.206996i −0.800064 0.599914i \(-0.795201\pi\)
0.919573 + 0.392919i \(0.128535\pi\)
\(374\) 0.0475426 + 0.0823462i 0.00245837 + 0.00425802i
\(375\) −2.30712 + 17.2018i −0.119139 + 0.888296i
\(376\) −0.203606 0.117552i −0.0105002 0.00606228i
\(377\) −12.6256 1.27335i −0.650249 0.0655809i
\(378\) 7.00909 + 11.8268i 0.360509 + 0.608304i
\(379\) 3.52362i 0.180996i −0.995897 0.0904982i \(-0.971154\pi\)
0.995897 0.0904982i \(-0.0288459\pi\)
\(380\) 0.244969 + 0.141433i 0.0125666 + 0.00725535i
\(381\) −15.1590 2.03315i −0.776619 0.104161i
\(382\) 1.57425 0.908893i 0.0805456 0.0465030i
\(383\) 1.24813 + 0.720607i 0.0637763 + 0.0368213i 0.531549 0.847027i \(-0.321610\pi\)
−0.467773 + 0.883849i \(0.654943\pi\)
\(384\) −1.05774 + 1.37157i −0.0539774 + 0.0699924i
\(385\) 11.2956 + 1.27300i 0.575676 + 0.0648781i
\(386\) 19.7946i 1.00752i
\(387\) −3.59029 0.980711i −0.182505 0.0498523i
\(388\) −6.39773 11.0812i −0.324795 0.562562i
\(389\) −7.08963 + 4.09320i −0.359459 + 0.207533i −0.668843 0.743403i \(-0.733210\pi\)
0.309385 + 0.950937i \(0.399877\pi\)
\(390\) −2.06422 6.92345i −0.104526 0.350582i
\(391\) 0.0699283i 0.00353643i
\(392\) −6.82442 1.55800i −0.344685 0.0786908i
\(393\) −14.9575 + 19.3953i −0.754505 + 0.978366i
\(394\) −12.6222 + 21.8623i −0.635898 + 1.10141i
\(395\) −6.03661 + 3.48524i −0.303735 + 0.175362i
\(396\) −7.91627 + 7.83982i −0.397808 + 0.393966i
\(397\) 6.43999 11.1544i 0.323214 0.559823i −0.657935 0.753074i \(-0.728570\pi\)
0.981149 + 0.193252i \(0.0619034\pi\)
\(398\) 6.16568i 0.309058i
\(399\) −0.805073 0.779327i −0.0403041 0.0390152i
\(400\) 3.66166 0.183083
\(401\) 4.27201 7.39934i 0.213334 0.369505i −0.739422 0.673242i \(-0.764901\pi\)
0.952756 + 0.303737i \(0.0982344\pi\)
\(402\) 1.65927 12.3714i 0.0827567 0.617029i
\(403\) 14.7695 6.65035i 0.735721 0.331278i
\(404\) −5.03494 + 8.72077i −0.250498 + 0.433874i
\(405\) −5.11815 9.06696i −0.254323 0.450541i
\(406\) 5.52962 7.49197i 0.274431 0.371820i
\(407\) 35.5851i 1.76389i
\(408\) 0.0168711 + 0.0410116i 0.000835244 + 0.00203037i
\(409\) −10.1026 17.4982i −0.499542 0.865232i 0.500458 0.865761i \(-0.333165\pi\)
−1.00000 0.000529035i \(0.999832\pi\)
\(410\) −0.272738 0.472395i −0.0134695 0.0233299i
\(411\) −8.83908 21.4867i −0.436000 1.05986i
\(412\) 10.1874i 0.501898i
\(413\) 3.42579 + 7.85256i 0.168572 + 0.386399i
\(414\) −7.92468 + 2.08225i −0.389477 + 0.102337i
\(415\) 2.10704 3.64949i 0.103430 0.179147i
\(416\) −3.28764 + 1.48035i −0.161190 + 0.0725799i
\(417\) −3.46667 + 25.8472i −0.169763 + 1.26575i
\(418\) 0.454031 0.786404i 0.0222074 0.0384643i
\(419\) 2.16600 0.105816 0.0529081 0.998599i \(-0.483151\pi\)
0.0529081 + 0.998599i \(0.483151\pi\)
\(420\) 5.14240 + 1.28873i 0.250923 + 0.0628835i
\(421\) 14.2671i 0.695334i 0.937618 + 0.347667i \(0.113026\pi\)
−0.937618 + 0.347667i \(0.886974\pi\)
\(422\) 1.99089 3.44833i 0.0969152 0.167862i
\(423\) −0.496305 0.501145i −0.0241312 0.0243665i
\(424\) −6.44560 + 3.72137i −0.313026 + 0.180726i
\(425\) 0.0468753 0.0811904i 0.00227379 0.00393831i
\(426\) −15.5230 + 20.1287i −0.752092 + 0.975237i
\(427\) 18.5871 25.1833i 0.899494 1.21871i
\(428\) 18.1776i 0.878648i
\(429\) −22.2258 + 6.62660i −1.07307 + 0.319935i
\(430\) −1.24293 + 0.717608i −0.0599396 + 0.0346061i
\(431\) −17.2738 29.9190i −0.832048 1.44115i −0.896412 0.443222i \(-0.853835\pi\)
0.0643642 0.997926i \(-0.479498\pi\)
\(432\) −4.14530 + 3.13313i −0.199441 + 0.150743i
\(433\) 0.715483i 0.0343839i 0.999852 + 0.0171920i \(0.00547264\pi\)
−0.999852 + 0.0171920i \(0.994527\pi\)
\(434\) −1.33110 + 11.8111i −0.0638947 + 0.566950i
\(435\) −4.30662 + 5.58439i −0.206487 + 0.267751i
\(436\) 2.40616 + 1.38920i 0.115234 + 0.0665306i
\(437\) 0.578343 0.333907i 0.0276659 0.0159729i
\(438\) −2.69267 0.361144i −0.128661 0.0172561i
\(439\) 15.5035 + 8.95097i 0.739944 + 0.427207i 0.822049 0.569417i \(-0.192831\pi\)
−0.0821052 + 0.996624i \(0.526164\pi\)
\(440\) 4.29635i 0.204821i
\(441\) −18.5181 9.90356i −0.881813 0.471598i
\(442\) −0.00926333 + 0.0918479i −0.000440612 + 0.00436876i
\(443\) −14.3289 8.27278i −0.680785 0.393052i 0.119366 0.992850i \(-0.461914\pi\)
−0.800151 + 0.599799i \(0.795247\pi\)
\(444\) 2.20616 16.4490i 0.104700 0.780635i
\(445\) 5.42288 + 9.39271i 0.257069 + 0.445257i
\(446\) 1.01738 1.76216i 0.0481745 0.0834407i
\(447\) 9.99775 12.9641i 0.472877 0.613180i
\(448\) 0.296298 2.62911i 0.0139988 0.124214i
\(449\) −26.7037 −1.26023 −0.630113 0.776503i \(-0.716991\pi\)
−0.630113 + 0.776503i \(0.716991\pi\)
\(450\) 10.5968 + 2.89458i 0.499536 + 0.136452i
\(451\) −1.51649 + 0.875548i −0.0714089 + 0.0412279i
\(452\) 16.1398 9.31833i 0.759153 0.438297i
\(453\) −24.0075 + 9.87608i −1.12797 + 0.464019i
\(454\) 18.0139i 0.845433i
\(455\) 8.17677 + 7.41142i 0.383333 + 0.347453i
\(456\) 0.258628 0.335362i 0.0121114 0.0157048i
\(457\) 32.4759 + 18.7500i 1.51916 + 0.877087i 0.999745 + 0.0225635i \(0.00718280\pi\)
0.519413 + 0.854523i \(0.326151\pi\)
\(458\) −9.36691 16.2240i −0.437687 0.758096i
\(459\) 0.0164046 + 0.132023i 0.000765700 + 0.00616232i
\(460\) −1.57983 + 2.73634i −0.0736599 + 0.127583i
\(461\) 8.31097i 0.387080i 0.981092 + 0.193540i \(0.0619970\pi\)
−0.981092 + 0.193540i \(0.938003\pi\)
\(462\) 4.13710 16.5082i 0.192475 0.768032i
\(463\) 28.8122i 1.33902i −0.742805 0.669508i \(-0.766505\pi\)
0.742805 0.669508i \(-0.233495\pi\)
\(464\) 3.04794 + 1.75973i 0.141497 + 0.0816935i
\(465\) 1.19661 8.92182i 0.0554913 0.413739i
\(466\) −17.0834 + 9.86309i −0.791372 + 0.456899i
\(467\) −10.3800 + 17.9787i −0.480328 + 0.831953i −0.999745 0.0225677i \(-0.992816\pi\)
0.519417 + 0.854521i \(0.326149\pi\)
\(468\) −10.6846 + 1.68518i −0.493895 + 0.0778974i
\(469\) 7.62422 + 17.4761i 0.352054 + 0.806972i
\(470\) −0.271983 −0.0125457
\(471\) 2.78137 1.14418i 0.128159 0.0527212i
\(472\) −2.80431 + 1.61907i −0.129079 + 0.0745237i
\(473\) 2.30368 + 3.99009i 0.105923 + 0.183465i
\(474\) 3.97034 + 9.65142i 0.182364 + 0.443304i
\(475\) −0.895316 −0.0410799
\(476\) −0.0545023 0.0402267i −0.00249811 0.00184379i
\(477\) −21.5952 + 5.67426i −0.988776 + 0.259806i
\(478\) −10.0708 + 17.4432i −0.460629 + 0.797833i
\(479\) 15.1644 8.75519i 0.692881 0.400035i −0.111809 0.993730i \(-0.535665\pi\)
0.804690 + 0.593695i \(0.202331\pi\)
\(480\) −0.266360 + 1.98597i −0.0121576 + 0.0906465i
\(481\) 20.1891 28.0350i 0.920542 1.27829i
\(482\) −22.2718 −1.01445
\(483\) 8.70522 8.99280i 0.396101 0.409187i
\(484\) 2.79224 0.126920
\(485\) −12.8194 7.40130i −0.582101 0.336076i
\(486\) −14.4732 + 5.79031i −0.656516 + 0.262654i
\(487\) 0.122893 0.0709520i 0.00556879 0.00321514i −0.497213 0.867628i \(-0.665643\pi\)
0.502782 + 0.864413i \(0.332310\pi\)
\(488\) 10.2453 + 5.91511i 0.463782 + 0.267765i
\(489\) −17.4487 13.4562i −0.789056 0.608511i
\(490\) −7.73840 + 2.38654i −0.349585 + 0.107813i
\(491\) 10.0187i 0.452138i 0.974111 + 0.226069i \(0.0725875\pi\)
−0.974111 + 0.226069i \(0.927413\pi\)
\(492\) −0.755272 + 0.310699i −0.0340503 + 0.0140074i
\(493\) 0.0780373 0.0450549i 0.00351463 0.00202917i
\(494\) 0.803863 0.361960i 0.0361675 0.0162854i
\(495\) −3.39630 + 12.4335i −0.152652 + 0.558846i
\(496\) −4.49243 −0.201716
\(497\) 4.34837 38.5839i 0.195051 1.73073i
\(498\) −4.99616 3.85298i −0.223883 0.172656i
\(499\) −9.05469 5.22772i −0.405343 0.234025i 0.283444 0.958989i \(-0.408523\pi\)
−0.688787 + 0.724964i \(0.741856\pi\)
\(500\) 8.67790 5.01019i 0.388087 0.224062i
\(501\) −1.57842 + 11.7686i −0.0705186 + 0.525782i
\(502\) −10.2782 + 17.8023i −0.458737 + 0.794556i
\(503\) −13.6155 −0.607083 −0.303542 0.952818i \(-0.598169\pi\)
−0.303542 + 0.952818i \(0.598169\pi\)
\(504\) 2.93581 7.37435i 0.130771 0.328480i
\(505\) 11.6495i 0.518395i
\(506\) 8.78427 + 5.07160i 0.390508 + 0.225460i
\(507\) −21.2697 7.38909i −0.944622 0.328161i
\(508\) 4.41521 + 7.64737i 0.195893 + 0.339297i
\(509\) 8.06558 + 4.65666i 0.357500 + 0.206403i 0.667984 0.744176i \(-0.267158\pi\)
−0.310483 + 0.950579i \(0.600491\pi\)
\(510\) 0.0406251 + 0.0313296i 0.00179891 + 0.00138730i
\(511\) 3.80373 1.65943i 0.168267 0.0734090i
\(512\) 1.00000 0.0441942
\(513\) 1.01357 0.766084i 0.0447502 0.0338234i
\(514\) 5.10857 + 8.84830i 0.225329 + 0.390282i
\(515\) −5.89273 10.2065i −0.259665 0.449753i
\(516\) 0.817490 + 1.98722i 0.0359880 + 0.0874824i
\(517\) 0.873127i 0.0384001i
\(518\) 10.1372 + 23.2363i 0.445401 + 1.02094i
\(519\) 16.4946 21.3885i 0.724032 0.938851i
\(520\) −2.43752 + 3.38480i −0.106892 + 0.148433i
\(521\) 6.86110 + 11.8838i 0.300590 + 0.520637i 0.976270 0.216558i \(-0.0694830\pi\)
−0.675680 + 0.737195i \(0.736150\pi\)
\(522\) 7.42960 + 7.50205i 0.325185 + 0.328356i
\(523\) −23.6617 13.6611i −1.03465 0.597358i −0.116340 0.993209i \(-0.537116\pi\)
−0.918315 + 0.395851i \(0.870450\pi\)
\(524\) 14.1410 0.617753
\(525\) −16.1354 + 4.60571i −0.704206 + 0.201010i
\(526\) 28.1563i 1.22768i
\(527\) −0.0575105 + 0.0996111i −0.00250520 + 0.00433913i
\(528\) 6.37539 + 0.855076i 0.277453 + 0.0372124i
\(529\) −7.77021 13.4584i −0.337835 0.585147i
\(530\) −4.30512 + 7.45669i −0.187003 + 0.323898i
\(531\) −9.39549 + 2.46872i −0.407729 + 0.107133i
\(532\) −0.0724480 + 0.642845i −0.00314102 + 0.0278709i
\(533\) −1.69148 0.170594i −0.0732661 0.00738925i
\(534\) 15.0172 6.17768i 0.649857 0.267334i
\(535\) 10.5145 + 18.2117i 0.454582 + 0.787360i
\(536\) −6.24108 + 3.60329i −0.269574 + 0.155638i
\(537\) 6.34101 2.60853i 0.273635 0.112566i
\(538\) −29.3643 −1.26599
\(539\) 7.66133 + 24.8420i 0.329997 + 1.07002i
\(540\) −2.34076 + 5.53678i −0.100730 + 0.238265i
\(541\) 5.89940 + 3.40602i 0.253635 + 0.146436i 0.621428 0.783472i \(-0.286553\pi\)
−0.367793 + 0.929908i \(0.619886\pi\)
\(542\) −14.2082 24.6093i −0.610293 1.05706i
\(543\) −0.0988114 + 0.736731i −0.00424040 + 0.0316162i
\(544\) 0.0128016 0.0221731i 0.000548866 0.000950663i
\(545\) 3.21423 0.137682
\(546\) 12.6252 10.6585i 0.540309 0.456142i
\(547\) 14.2644 0.609901 0.304951 0.952368i \(-0.401360\pi\)
0.304951 + 0.952368i \(0.401360\pi\)
\(548\) −6.70701 + 11.6169i −0.286509 + 0.496249i
\(549\) 24.9736 + 25.2172i 1.06585 + 1.07624i
\(550\) −6.79933 11.7768i −0.289924 0.502164i
\(551\) −0.745255 0.430273i −0.0317489 0.0183302i
\(552\) 3.74606 + 2.88892i 0.159443 + 0.122960i
\(553\) −12.8263 9.46672i −0.545428 0.402566i
\(554\) 27.6535 1.17489
\(555\) −7.30434 17.7559i −0.310052 0.753698i
\(556\) 13.0393 7.52827i 0.552991 0.319270i
\(557\) −10.8866 18.8561i −0.461279 0.798958i 0.537746 0.843107i \(-0.319276\pi\)
−0.999025 + 0.0441487i \(0.985942\pi\)
\(558\) −13.0010 3.55130i −0.550376 0.150339i
\(559\) −0.448855 + 4.45050i −0.0189846 + 0.188236i
\(560\) −1.22391 2.80542i −0.0517195 0.118551i
\(561\) 0.100575 0.130416i 0.00424628 0.00550615i
\(562\) −6.18049 + 10.7049i −0.260708 + 0.451560i
\(563\) 5.19862 + 9.00428i 0.219096 + 0.379485i 0.954532 0.298109i \(-0.0963560\pi\)
−0.735436 + 0.677594i \(0.763023\pi\)
\(564\) −0.0541311 + 0.403598i −0.00227933 + 0.0169945i
\(565\) 10.7800 18.6716i 0.453520 0.785520i
\(566\) 13.6723i 0.574690i
\(567\) 14.3256 19.0204i 0.601621 0.798782i
\(568\) 14.6757 0.615778
\(569\) −14.6618 8.46500i −0.614655 0.354871i 0.160130 0.987096i \(-0.448809\pi\)
−0.774785 + 0.632225i \(0.782142\pi\)
\(570\) 0.0651280 0.485590i 0.00272791 0.0203391i
\(571\) 8.19990 + 14.2026i 0.343155 + 0.594362i 0.985017 0.172458i \(-0.0551710\pi\)
−0.641862 + 0.766820i \(0.721838\pi\)
\(572\) 10.8659 + 7.82498i 0.454328 + 0.327179i
\(573\) −2.49321 1.92274i −0.104156 0.0803236i
\(574\) 0.740818 1.00372i 0.0309211 0.0418944i
\(575\) 10.0008i 0.417063i
\(576\) 2.89398 + 0.790508i 0.120582 + 0.0329378i
\(577\) 11.8397 + 20.5070i 0.492894 + 0.853718i 0.999966 0.00818553i \(-0.00260556\pi\)
−0.507072 + 0.861904i \(0.669272\pi\)
\(578\) 8.49967 + 14.7219i 0.353540 + 0.612349i
\(579\) 31.7071 13.0435i 1.31770 0.542069i
\(580\) 4.07154 0.169062
\(581\) 9.57696 + 1.07931i 0.397319 + 0.0447775i
\(582\) −13.5342 + 17.5498i −0.561011 + 0.727463i
\(583\) 23.9376 + 13.8204i 0.991395 + 0.572382i
\(584\) 0.784266 + 1.35839i 0.0324532 + 0.0562106i
\(585\) −9.72984 + 7.86864i −0.402279 + 0.325328i
\(586\) 3.64292 + 2.10324i 0.150488 + 0.0868842i
\(587\) 43.3060i 1.78743i −0.448633 0.893716i \(-0.648089\pi\)
0.448633 0.893716i \(-0.351911\pi\)
\(588\) 2.00128 + 11.9580i 0.0825316 + 0.493141i
\(589\) 1.09845 0.0452607
\(590\) −1.87304 + 3.24421i −0.0771120 + 0.133562i
\(591\) 43.3366 + 5.81236i 1.78263 + 0.239089i
\(592\) −8.29815 + 4.79094i −0.341052 + 0.196906i
\(593\) 18.9754 + 10.9554i 0.779226 + 0.449886i 0.836156 0.548492i \(-0.184798\pi\)
−0.0569301 + 0.998378i \(0.518131\pi\)
\(594\) 17.7743 + 7.51436i 0.729287 + 0.308318i
\(595\) −0.0778729 0.00877620i −0.00319248 0.000359789i
\(596\) −9.45202 −0.387170
\(597\) −9.87624 + 4.06283i −0.404208 + 0.166281i
\(598\) 4.04316 + 8.97928i 0.165337 + 0.367190i
\(599\) −39.3065 + 22.6936i −1.60602 + 0.927237i −0.615773 + 0.787923i \(0.711156\pi\)
−0.990248 + 0.139314i \(0.955510\pi\)
\(600\) −2.41283 5.86529i −0.0985033 0.239449i
\(601\) 8.20455i 0.334671i −0.985900 0.167335i \(-0.946484\pi\)
0.985900 0.167335i \(-0.0535163\pi\)
\(602\) −2.64091 1.94919i −0.107636 0.0794430i
\(603\) −20.9100 + 5.49421i −0.851520 + 0.223741i
\(604\) 12.9798 + 7.49388i 0.528140 + 0.304922i
\(605\) 2.79747 1.61512i 0.113733 0.0656640i
\(606\) 17.2867 + 2.31852i 0.702226 + 0.0941835i
\(607\) −24.0464 13.8832i −0.976012 0.563501i −0.0749481 0.997187i \(-0.523879\pi\)
−0.901064 + 0.433687i \(0.857212\pi\)
\(608\) −0.244511 −0.00991621
\(609\) −15.6444 3.92062i −0.633944 0.158872i
\(610\) 13.6860 0.554129
\(611\) −0.495366 + 0.687876i −0.0200403 + 0.0278285i
\(612\) 0.0545756 0.0540486i 0.00220609 0.00218478i
\(613\) 15.8517 9.15200i 0.640245 0.369646i −0.144464 0.989510i \(-0.546146\pi\)
0.784709 + 0.619864i \(0.212812\pi\)
\(614\) 10.5746 18.3157i 0.426756 0.739163i
\(615\) −0.576969 + 0.748155i −0.0232656 + 0.0301685i
\(616\) −9.00603 + 3.92901i −0.362863 + 0.158304i
\(617\) −22.1693 −0.892502 −0.446251 0.894908i \(-0.647241\pi\)
−0.446251 + 0.894908i \(0.647241\pi\)
\(618\) −16.3183 + 6.71293i −0.656419 + 0.270034i
\(619\) −19.7675 34.2384i −0.794525 1.37616i −0.923140 0.384463i \(-0.874387\pi\)
0.128616 0.991695i \(-0.458947\pi\)
\(620\) −4.50085 + 2.59857i −0.180759 + 0.104361i
\(621\) 8.55728 + 11.3217i 0.343392 + 0.454326i
\(622\) −31.3509 −1.25706
\(623\) −14.7298 + 19.9571i −0.590137 + 0.799564i
\(624\) 4.53760 + 4.29071i 0.181649 + 0.171766i
\(625\) −3.35805 + 5.81632i −0.134322 + 0.232653i
\(626\) −28.3855 + 16.3884i −1.13451 + 0.655011i
\(627\) −1.55885 0.209075i −0.0622545 0.00834965i
\(628\) −1.50376 0.868197i −0.0600066 0.0346448i
\(629\) 0.245327i 0.00978184i
\(630\) −1.32425 9.08634i −0.0527594 0.362008i
\(631\) 38.3301i 1.52590i 0.646460 + 0.762948i \(0.276249\pi\)
−0.646460 + 0.762948i \(0.723751\pi\)
\(632\) 3.01266 5.21808i 0.119837 0.207564i
\(633\) −6.83545 0.916780i −0.271685 0.0364387i
\(634\) 11.1137 + 19.2495i 0.441382 + 0.764497i
\(635\) 8.84697 + 5.10780i 0.351081 + 0.202697i
\(636\) 10.2082 + 7.87246i 0.404782 + 0.312163i
\(637\) −8.05818 + 23.9179i −0.319277 + 0.947662i
\(638\) 13.0706i 0.517468i
\(639\) 42.4711 + 11.6012i 1.68013 + 0.458938i
\(640\) 1.00187 0.578432i 0.0396026 0.0228645i
\(641\) 13.7967 7.96553i 0.544937 0.314620i −0.202140 0.979357i \(-0.564790\pi\)
0.747077 + 0.664737i \(0.231456\pi\)
\(642\) 29.1171 11.9780i 1.14916 0.472734i
\(643\) −20.5219 −0.809303 −0.404652 0.914471i \(-0.632607\pi\)
−0.404652 + 0.914471i \(0.632607\pi\)
\(644\) −7.18068 0.809256i −0.282959 0.0318892i
\(645\) 1.96849 + 1.51808i 0.0775094 + 0.0597743i
\(646\) −0.00313014 + 0.00542155i −0.000123154 + 0.000213308i
\(647\) −17.2187 29.8237i −0.676938 1.17249i −0.975898 0.218226i \(-0.929973\pi\)
0.298960 0.954266i \(-0.403360\pi\)
\(648\) 7.75019 + 4.57542i 0.304456 + 0.179740i
\(649\) 10.4146 + 6.01288i 0.408809 + 0.236026i
\(650\) 1.32480 13.1357i 0.0519629 0.515224i
\(651\) 19.7962 5.65067i 0.775875 0.221467i
\(652\) 12.7217i 0.498221i
\(653\) −15.3842 8.88210i −0.602032 0.347583i 0.167808 0.985820i \(-0.446331\pi\)
−0.769841 + 0.638236i \(0.779664\pi\)
\(654\) 0.639708 4.76962i 0.0250145 0.186507i
\(655\) 14.1675 8.17963i 0.553571 0.319604i
\(656\) 0.408341 + 0.235756i 0.0159430 + 0.00920472i
\(657\) 1.19583 + 4.55112i 0.0466538 + 0.177556i
\(658\) −0.248729 0.570132i −0.00969646 0.0222261i
\(659\) 9.50676i 0.370331i 0.982707 + 0.185165i \(0.0592821\pi\)
−0.982707 + 0.185165i \(0.940718\pi\)
\(660\) 6.88194 2.83105i 0.267879 0.110199i
\(661\) −17.2613 29.8975i −0.671387 1.16288i −0.977511 0.210885i \(-0.932366\pi\)
0.306124 0.951992i \(-0.400968\pi\)
\(662\) 16.0419 9.26179i 0.623486 0.359970i
\(663\) 0.153227 0.0456845i 0.00595084 0.00177424i
\(664\) 3.64267i 0.141363i
\(665\) 0.299258 + 0.685956i 0.0116047 + 0.0266002i
\(666\) −27.8019 + 7.30510i −1.07730 + 0.283067i
\(667\) 4.80622 8.32462i 0.186098 0.322331i
\(668\) 5.93699 3.42772i 0.229709 0.132622i
\(669\) −3.49304 0.468492i −0.135049 0.0181129i
\(670\) −4.16852 + 7.22009i −0.161044 + 0.278936i
\(671\) 43.9350i 1.69609i
\(672\) −4.40657 + 1.25782i −0.169987 + 0.0485214i
\(673\) −30.8952 −1.19092 −0.595460 0.803385i \(-0.703030\pi\)
−0.595460 + 0.803385i \(0.703030\pi\)
\(674\) 8.97860 15.5514i 0.345843 0.599017i
\(675\) −2.34611 18.8814i −0.0903017 0.726744i
\(676\) 4.12105 + 12.3295i 0.158502 + 0.474212i
\(677\) 23.5469 40.7844i 0.904979 1.56747i 0.0840345 0.996463i \(-0.473219\pi\)
0.820945 0.571007i \(-0.193447\pi\)
\(678\) −25.5614 19.7127i −0.981680 0.757061i
\(679\) 3.79127 33.6406i 0.145495 1.29101i
\(680\) 0.0296195i 0.00113586i
\(681\) −28.8548 + 11.8701i −1.10572 + 0.454864i
\(682\) 8.34198 + 14.4487i 0.319431 + 0.553270i
\(683\) −7.64632 13.2438i −0.292578 0.506760i 0.681840 0.731501i \(-0.261180\pi\)
−0.974419 + 0.224741i \(0.927847\pi\)
\(684\) −0.707608 0.193288i −0.0270561 0.00739054i
\(685\) 15.5182i 0.592920i
\(686\) −12.0794 14.0388i −0.461195 0.536003i
\(687\) −19.8155 + 25.6947i −0.756007 + 0.980313i
\(688\) 0.620304 1.07440i 0.0236489 0.0409610i
\(689\) 11.0178 + 24.4691i 0.419746 + 0.932197i
\(690\) 5.42412 + 0.727490i 0.206493 + 0.0276951i
\(691\) 6.72191 11.6427i 0.255713 0.442909i −0.709376 0.704831i \(-0.751023\pi\)
0.965089 + 0.261922i \(0.0843563\pi\)
\(692\) −15.5942 −0.592803
\(693\) −29.1691 + 4.25113i −1.10804 + 0.161487i
\(694\) 0.504408i 0.0191471i
\(695\) 8.70919 15.0848i 0.330358 0.572197i
\(696\) 0.810333 6.04179i 0.0307156 0.229013i
\(697\) 0.0104549 0.00603612i 0.000396006 0.000228634i
\(698\) −11.2702 + 19.5206i −0.426585 + 0.738866i
\(699\) 27.0558 + 20.8651i 1.02334 + 0.789190i
\(700\) 7.79468 + 5.75304i 0.294611 + 0.217445i
\(701\) 44.2310i 1.67058i 0.549809 + 0.835290i \(0.314700\pi\)
−0.549809 + 0.835290i \(0.685300\pi\)
\(702\) 9.73986 + 16.0042i 0.367607 + 0.604040i
\(703\) 2.02898 1.17143i 0.0765246 0.0441815i
\(704\) −1.85690 3.21624i −0.0699844 0.121216i
\(705\) 0.179222 + 0.435666i 0.00674988 + 0.0164081i
\(706\) 16.0120i 0.602619i
\(707\) −24.4197 + 10.6534i −0.918397 + 0.400664i
\(708\) 4.44132 + 3.42509i 0.166915 + 0.128723i
\(709\) −34.4905 19.9131i −1.29532 0.747852i −0.315726 0.948850i \(-0.602248\pi\)
−0.979592 + 0.200998i \(0.935581\pi\)
\(710\) 14.7032 8.48889i 0.551801 0.318582i
\(711\) 12.8435 12.7195i 0.481669 0.477017i
\(712\) −8.11911 4.68757i −0.304276 0.175674i
\(713\) 12.2698i 0.459509i
\(714\) −0.0285216 + 0.113809i −0.00106739 + 0.00425921i
\(715\) 15.4125 + 1.55443i 0.576396 + 0.0581325i
\(716\) −3.42830 1.97933i −0.128121 0.0739710i
\(717\) 34.5768 + 4.63748i 1.29129 + 0.173190i
\(718\) −7.67875 13.3000i −0.286569 0.496351i
\(719\) −13.8793 + 24.0396i −0.517609 + 0.896525i 0.482182 + 0.876071i \(0.339845\pi\)
−0.999791 + 0.0204540i \(0.993489\pi\)
\(720\) 3.35666 0.881980i 0.125095 0.0328694i
\(721\) 16.0060 21.6862i 0.596095 0.807637i
\(722\) −18.9402 −0.704882
\(723\) 14.6759 + 35.6752i 0.545801 + 1.32677i
\(724\) 0.371664 0.214580i 0.0138128 0.00797481i
\(725\) −11.1605 + 6.44355i −0.414492 + 0.239307i
\(726\) −1.83993 4.47264i −0.0682861 0.165995i
\(727\) 34.8578i 1.29281i 0.762996 + 0.646403i \(0.223727\pi\)
−0.762996 + 0.646403i \(0.776273\pi\)
\(728\) −9.32434 2.01414i −0.345583 0.0746491i
\(729\) 18.8120 + 19.3678i 0.696739 + 0.717324i
\(730\) 1.57147 + 0.907290i 0.0581628 + 0.0335803i
\(731\) −0.0158818 0.0275081i −0.000587410 0.00101742i
\(732\) 2.72383 20.3087i 0.100676 0.750631i
\(733\) 17.9806 31.1434i 0.664130 1.15031i −0.315390 0.948962i \(-0.602135\pi\)
0.979520 0.201345i \(-0.0645312\pi\)
\(734\) 31.1878i 1.15116i
\(735\) 8.92196 + 10.8229i 0.329091 + 0.399207i
\(736\) 2.73122i 0.100674i
\(737\) 23.1781 + 13.3819i 0.853775 + 0.492927i
\(738\) 0.995362 + 1.00507i 0.0366398 + 0.0369971i
\(739\) −23.0900 + 13.3310i −0.849378 + 0.490389i −0.860441 0.509550i \(-0.829812\pi\)
0.0110630 + 0.999939i \(0.496478\pi\)
\(740\) −5.54247 + 9.59983i −0.203745 + 0.352897i
\(741\) −1.10949 1.04912i −0.0407582 0.0385405i
\(742\) −19.5678 2.20527i −0.718355 0.0809579i
\(743\) 24.5770 0.901644 0.450822 0.892614i \(-0.351131\pi\)
0.450822 + 0.892614i \(0.351131\pi\)
\(744\) 2.96026 + 7.19602i 0.108528 + 0.263819i
\(745\) −9.46974 + 5.46736i −0.346944 + 0.200308i
\(746\) 2.30810 + 3.99775i 0.0845057 + 0.146368i
\(747\) −2.87956 + 10.5418i −0.105357 + 0.385704i
\(748\) −0.0950852 −0.00347666
\(749\) −28.5599 + 38.6951i −1.04355 + 1.41389i
\(750\) −13.7436 10.5989i −0.501846 0.387018i
\(751\) −0.764556 + 1.32425i −0.0278990 + 0.0483226i −0.879638 0.475644i \(-0.842215\pi\)
0.851739 + 0.523967i \(0.175548\pi\)
\(752\) 0.203606 0.117552i 0.00742475 0.00428668i
\(753\) 35.2886 + 4.73296i 1.28599 + 0.172479i
\(754\) 7.41553 10.2974i 0.270058 0.375008i
\(755\) 17.3388 0.631024
\(756\) −13.7468 + 0.156667i −0.499968 + 0.00569793i
\(757\) −20.0619 −0.729164 −0.364582 0.931171i \(-0.618788\pi\)
−0.364582 + 0.931171i \(0.618788\pi\)
\(758\) 3.05155 + 1.76181i 0.110837 + 0.0639919i
\(759\) 2.33540 17.4126i 0.0847698 0.632038i
\(760\) −0.244969 + 0.141433i −0.00888596 + 0.00513031i
\(761\) 19.1290 + 11.0442i 0.693427 + 0.400350i 0.804895 0.593418i \(-0.202222\pi\)
−0.111468 + 0.993768i \(0.535555\pi\)
\(762\) 9.34026 12.1115i 0.338362 0.438754i
\(763\) 2.93941 + 6.73768i 0.106414 + 0.243920i
\(764\) 1.81779i 0.0657652i
\(765\) 0.0234145 0.0857182i 0.000846552 0.00309915i
\(766\) −1.24813 + 0.720607i −0.0450967 + 0.0260366i
\(767\) 4.79356 + 10.6458i 0.173086 + 0.384399i
\(768\) −0.658943 1.60181i −0.0237776 0.0578003i
\(769\) −33.5491 −1.20981 −0.604906 0.796297i \(-0.706789\pi\)
−0.604906 + 0.796297i \(0.706789\pi\)
\(770\) −6.75024 + 9.14576i −0.243262 + 0.329590i
\(771\) 10.8070 14.0135i 0.389206 0.504683i
\(772\) −17.1426 9.89729i −0.616976 0.356211i
\(773\) −39.2647 + 22.6695i −1.41225 + 0.815365i −0.995601 0.0936997i \(-0.970131\pi\)
−0.416654 + 0.909065i \(0.636797\pi\)
\(774\) 2.64447 2.61893i 0.0950533 0.0941354i
\(775\) 8.22489 14.2459i 0.295447 0.511729i
\(776\) 12.7955 0.459330
\(777\) 30.5403 31.5492i 1.09563 1.13182i
\(778\) 8.18640i 0.293497i
\(779\) −0.0998437 0.0576448i −0.00357727 0.00206534i
\(780\) 7.02799 + 1.67406i 0.251642 + 0.0599408i
\(781\) −27.2512 47.2005i −0.975125 1.68897i
\(782\) −0.0605597 0.0349641i −0.00216561 0.00125032i
\(783\) 7.12117 16.8442i 0.254490 0.601963i
\(784\) 4.76147 5.13112i 0.170053 0.183254i
\(785\) −2.00877 −0.0716962
\(786\) −9.31813 22.6512i −0.332367 0.807943i
\(787\) −16.3431 28.3071i −0.582568 1.00904i −0.995174 0.0981280i \(-0.968715\pi\)
0.412606 0.910910i \(-0.364619\pi\)
\(788\) −12.6222 21.8623i −0.449648 0.778813i
\(789\) 45.1011 18.5534i 1.60564 0.660520i
\(790\) 6.97048i 0.247999i
\(791\) 48.9978 + 5.52200i 1.74216 + 0.196340i
\(792\) −2.83135 10.7756i −0.100608 0.382894i
\(793\) 24.9264 34.6133i 0.885161 1.22915i
\(794\) 6.43999 + 11.1544i 0.228547 + 0.395854i
\(795\) 14.7810 + 1.98245i 0.524229 + 0.0703103i
\(796\) 5.33963 + 3.08284i 0.189258 + 0.109268i
\(797\) −26.9293 −0.953884 −0.476942 0.878935i \(-0.658255\pi\)
−0.476942 + 0.878935i \(0.658255\pi\)
\(798\) 1.07745 0.307550i 0.0381415 0.0108872i
\(799\) 0.00601943i 0.000212952i
\(800\) −1.83083 + 3.17109i −0.0647297 + 0.112115i
\(801\) −19.7909 19.9839i −0.699278 0.706097i
\(802\) 4.27201 + 7.39934i 0.150850 + 0.261280i
\(803\) 2.91260 5.04477i 0.102783 0.178026i
\(804\) 9.88430 + 7.62266i 0.348592 + 0.268831i
\(805\) −7.66224 + 3.34277i −0.270059 + 0.117817i
\(806\) −1.62537 + 16.1159i −0.0572514 + 0.567660i
\(807\) 19.3494 + 47.0360i 0.681132 + 1.65575i
\(808\) −5.03494 8.72077i −0.177129 0.306796i
\(809\) −4.33969 + 2.50552i −0.152575 + 0.0880894i −0.574344 0.818614i \(-0.694743\pi\)
0.421769 + 0.906703i \(0.361409\pi\)
\(810\) 10.4113 + 0.101036i 0.365816 + 0.00355003i
\(811\) 40.9851 1.43918 0.719590 0.694399i \(-0.244330\pi\)
0.719590 + 0.694399i \(0.244330\pi\)
\(812\) 3.72343 + 8.53478i 0.130667 + 0.299512i
\(813\) −30.0570 + 38.9749i −1.05414 + 1.36691i
\(814\) 30.8176 + 17.7925i 1.08016 + 0.623628i
\(815\) 7.35865 + 12.7456i 0.257762 + 0.446457i
\(816\) −0.0439526 0.00589498i −0.00153865 0.000206366i
\(817\) −0.151671 + 0.262702i −0.00530629 + 0.00919077i
\(818\) 20.2052 0.706459
\(819\) −25.3922 13.1998i −0.887275 0.461240i
\(820\) 0.545475 0.0190488
\(821\) 1.96031 3.39536i 0.0684154 0.118499i −0.829789 0.558078i \(-0.811539\pi\)
0.898204 + 0.439579i \(0.144872\pi\)
\(822\) 23.0276 + 3.08849i 0.803179 + 0.107723i
\(823\) 0.415511 + 0.719686i 0.0144838 + 0.0250867i 0.873176 0.487404i \(-0.162056\pi\)
−0.858693 + 0.512491i \(0.828723\pi\)
\(824\) 8.82256 + 5.09371i 0.307349 + 0.177448i
\(825\) −14.3838 + 18.6515i −0.500779 + 0.649360i
\(826\) −8.51341 0.959453i −0.296219 0.0333836i
\(827\) −44.4483 −1.54562 −0.772810 0.634637i \(-0.781149\pi\)
−0.772810 + 0.634637i \(0.781149\pi\)
\(828\) 2.15906 7.90410i 0.0750324 0.274686i
\(829\) 36.1389 20.8648i 1.25515 0.724664i 0.283026 0.959112i \(-0.408662\pi\)
0.972129 + 0.234448i \(0.0753284\pi\)
\(830\) 2.10704 + 3.64949i 0.0731363 + 0.126676i
\(831\) −18.2221 44.2957i −0.632117 1.53660i
\(832\) 0.361803 3.58735i 0.0125433 0.124369i
\(833\) −0.0528181 0.171263i −0.00183004 0.00593392i
\(834\) −20.6510 15.9258i −0.715087 0.551467i
\(835\) 3.96541 6.86829i 0.137229 0.237687i
\(836\) 0.454031 + 0.786404i 0.0157030 + 0.0271984i
\(837\) 2.87840 + 23.1652i 0.0994920 + 0.800707i
\(838\) −1.08300 + 1.87581i −0.0374117 + 0.0647989i
\(839\) 44.3088i 1.52971i 0.644203 + 0.764855i \(0.277189\pi\)
−0.644203 + 0.764855i \(0.722811\pi\)
\(840\) −3.68727 + 3.80908i −0.127223 + 0.131426i
\(841\) 16.6134 0.572875
\(842\) −12.3556 7.13353i −0.425803 0.245838i
\(843\) 21.2198 + 2.84603i 0.730850 + 0.0980226i
\(844\) 1.99089 + 3.44833i 0.0685294 + 0.118696i
\(845\) 11.2606 + 9.96888i 0.387375 + 0.342940i
\(846\) 0.682157 0.179240i 0.0234530 0.00616241i
\(847\) 5.94391 + 4.38704i 0.204235 + 0.150741i
\(848\) 7.44274i 0.255585i
\(849\) 21.9004 9.00928i 0.751621 0.309198i
\(850\) 0.0468753 + 0.0811904i 0.00160781 + 0.00278481i
\(851\) 13.0851 + 22.6641i 0.448552 + 0.776915i
\(852\) −9.67044 23.5076i −0.331304 0.805359i
\(853\) −39.9111 −1.36653 −0.683264 0.730171i \(-0.739440\pi\)
−0.683264 + 0.730171i \(0.739440\pi\)
\(854\) 12.5158 + 28.6886i 0.428282 + 0.981703i
\(855\) −0.820738 + 0.215653i −0.0280686 + 0.00737519i
\(856\) −15.7423 9.08881i −0.538060 0.310649i
\(857\) −17.9784 31.1395i −0.614131 1.06371i −0.990536 0.137250i \(-0.956173\pi\)
0.376406 0.926455i \(-0.377160\pi\)
\(858\) 5.37409 22.5614i 0.183468 0.770233i
\(859\) 14.9743 + 8.64539i 0.510915 + 0.294977i 0.733210 0.680003i \(-0.238021\pi\)
−0.222295 + 0.974980i \(0.571355\pi\)
\(860\) 1.43522i 0.0489405i
\(861\) −2.09592 0.525256i −0.0714289 0.0179007i
\(862\) 34.5475 1.17669
\(863\) 24.7603 42.8861i 0.842851 1.45986i −0.0446227 0.999004i \(-0.514209\pi\)
0.887474 0.460858i \(-0.152458\pi\)
\(864\) −0.640722 5.15650i −0.0217978 0.175428i
\(865\) −15.6235 + 9.02020i −0.531213 + 0.306696i
\(866\) −0.619627 0.357742i −0.0210558 0.0121566i
\(867\) 17.9808 23.3157i 0.610661 0.791844i
\(868\) −9.56315 7.05831i −0.324595 0.239575i
\(869\) −22.3768 −0.759080
\(870\) −2.68292 6.52184i −0.0909593 0.221111i
\(871\) 10.6682 + 23.6926i 0.361479 + 0.802795i
\(872\) −2.40616 + 1.38920i −0.0814830 + 0.0470442i
\(873\) 37.0297 + 10.1149i 1.25327 + 0.342338i
\(874\) 0.667813i 0.0225891i
\(875\) 26.3446 + 2.96902i 0.890611 + 0.100371i
\(876\) 1.65909 2.15135i 0.0560556 0.0726873i
\(877\) −39.8181 22.9890i −1.34456 0.776283i −0.357088 0.934071i \(-0.616230\pi\)
−0.987473 + 0.157788i \(0.949564\pi\)
\(878\) −15.5035 + 8.95097i −0.523219 + 0.302081i
\(879\) 0.968516 7.22119i 0.0326672 0.243565i
\(880\) −3.72075 2.14818i −0.125426 0.0724150i
\(881\) −3.09185 −0.104167 −0.0520835 0.998643i \(-0.516586\pi\)
−0.0520835 + 0.998643i \(0.516586\pi\)
\(882\) 17.8358 11.0853i 0.600562 0.373263i
\(883\) −23.5637 −0.792981 −0.396490 0.918039i \(-0.629772\pi\)
−0.396490 + 0.918039i \(0.629772\pi\)
\(884\) −0.0749110 0.0539463i −0.00251953 0.00181441i
\(885\) 6.43083 + 0.862512i 0.216170 + 0.0289930i
\(886\) 14.3289 8.27278i 0.481388 0.277929i
\(887\) −0.0628493 + 0.108858i −0.00211027 + 0.00365510i −0.867079 0.498171i \(-0.834005\pi\)
0.864968 + 0.501826i \(0.167338\pi\)
\(888\) 13.1422 + 10.1351i 0.441022 + 0.340112i
\(889\) −2.61644 + 23.2161i −0.0877524 + 0.778644i
\(890\) −10.8458 −0.363551
\(891\) 0.324347 33.4225i 0.0108660 1.11970i
\(892\) 1.01738 + 1.76216i 0.0340645 + 0.0590015i
\(893\) −0.0497838 + 0.0287427i −0.00166595 + 0.000961838i
\(894\) 6.22835 + 15.1403i 0.208307 + 0.506369i
\(895\) −4.57963 −0.153080
\(896\) 2.12873 + 1.57116i 0.0711157 + 0.0524886i
\(897\) 11.7189 12.3932i 0.391282 0.413797i
\(898\) 13.3519 23.1261i 0.445557 0.771728i
\(899\) 13.6927 7.90548i 0.456677 0.263662i
\(900\) −7.80516 + 7.72978i −0.260172 + 0.257659i
\(901\) −0.165029 0.0952793i −0.00549790 0.00317421i
\(902\) 1.75110i 0.0583051i
\(903\) −1.38202 + 5.51464i −0.0459906 + 0.183516i
\(904\) 18.6367i 0.619846i
\(905\) 0.248240 0.429965i 0.00825179 0.0142925i
\(906\) 3.45083 25.7292i 0.114646 0.854794i
\(907\) −7.59458 13.1542i −0.252174 0.436778i 0.711950 0.702230i \(-0.247812\pi\)
−0.964124 + 0.265452i \(0.914479\pi\)
\(908\) 15.6005 + 9.00694i 0.517720 + 0.298906i
\(909\) −7.67715 29.2179i −0.254635 0.969095i
\(910\) −10.5069 + 3.37558i −0.348299 + 0.111899i
\(911\) 46.3110i 1.53435i −0.641437 0.767176i \(-0.721661\pi\)
0.641437 0.767176i \(-0.278339\pi\)
\(912\) 0.161119 + 0.391659i 0.00533517 + 0.0129691i
\(913\) 11.7157 6.76405i 0.387732 0.223857i
\(914\) −32.4759 + 18.7500i −1.07421 + 0.620194i
\(915\) −9.01828 21.9223i −0.298135 0.724730i
\(916\) 18.7338 0.618983
\(917\) 30.1024 + 22.2177i 0.994067 + 0.733695i
\(918\) −0.122538 0.0518048i −0.00404435 0.00170981i
\(919\) 1.13972 1.97406i 0.0375960 0.0651181i −0.846615 0.532206i \(-0.821363\pi\)
0.884211 + 0.467087i \(0.154697\pi\)
\(920\) −1.57983 2.73634i −0.0520854 0.0902146i
\(921\) −36.3064 4.86946i −1.19634 0.160454i
\(922\) −7.19751 4.15548i −0.237037 0.136854i
\(923\) 5.30970 52.6468i 0.174771 1.73289i
\(924\) 12.2280 + 11.8369i 0.402271 + 0.389407i
\(925\) 35.0856i 1.15361i
\(926\) 24.9521 + 14.4061i 0.819976 + 0.473414i
\(927\) 21.5057 + 21.7154i 0.706339 + 0.713227i
\(928\) −3.04794 + 1.75973i −0.100054 + 0.0577660i
\(929\) −14.3151 8.26482i −0.469663 0.271160i 0.246436 0.969159i \(-0.420741\pi\)
−0.716099 + 0.697999i \(0.754074\pi\)
\(930\) 7.12822 + 5.49720i 0.233743 + 0.180260i
\(931\) −1.16423 + 1.25461i −0.0381561 + 0.0411183i
\(932\) 19.7262i 0.646152i
\(933\) 20.6585 + 50.2182i 0.676328 + 1.64407i
\(934\) −10.3800 17.9787i −0.339644 0.588280i
\(935\) −0.0952634 + 0.0550003i −0.00311545 + 0.00179870i
\(936\) 3.88288 10.0957i 0.126916 0.329988i
\(937\) 22.3954i 0.731626i −0.930688 0.365813i \(-0.880791\pi\)
0.930688 0.365813i \(-0.119209\pi\)
\(938\) −18.9469 2.13529i −0.618637 0.0697198i
\(939\) 44.9554 + 34.6691i 1.46707 + 1.13138i
\(940\) 0.135992 0.235545i 0.00443556 0.00768262i
\(941\) −12.5819 + 7.26415i −0.410158 + 0.236805i −0.690857 0.722991i \(-0.742767\pi\)
0.280700 + 0.959796i \(0.409433\pi\)
\(942\) −0.399793 + 2.98083i −0.0130260 + 0.0971207i
\(943\) 0.643902 1.11527i 0.0209683 0.0363182i
\(944\) 3.23814i 0.105392i
\(945\) −13.6820 + 8.10857i −0.445075 + 0.263772i
\(946\) −4.60736 −0.149798
\(947\) 1.30451 2.25948i 0.0423910 0.0734233i −0.844051 0.536262i \(-0.819836\pi\)
0.886442 + 0.462839i \(0.153169\pi\)
\(948\) −10.3435 1.38729i −0.335943 0.0450571i
\(949\) 5.15677 2.32197i 0.167396 0.0753744i
\(950\) 0.447658 0.775366i 0.0145239 0.0251562i
\(951\) 23.5108 30.4864i 0.762389 0.988590i
\(952\) 0.0620885 0.0270870i 0.00201230 0.000877896i
\(953\) 24.6984i 0.800061i 0.916502 + 0.400030i \(0.131000\pi\)
−0.916502 + 0.400030i \(0.869000\pi\)
\(954\) 5.88355 21.5391i 0.190487 0.697355i
\(955\) 1.05147 + 1.82119i 0.0340247 + 0.0589324i
\(956\) −10.0708 17.4432i −0.325714 0.564153i
\(957\) −20.9365 + 8.61275i −0.676782 + 0.278411i
\(958\) 17.5104i 0.565735i
\(959\) −32.5293 + 14.1914i −1.05043 + 0.458264i
\(960\) −1.58672 1.22366i −0.0512111 0.0394934i
\(961\) 5.40903 9.36871i 0.174485 0.302216i
\(962\) 14.1845 + 31.5017i 0.457326 + 1.01566i
\(963\) −38.3730 38.7472i −1.23655 1.24861i
\(964\) 11.1359 19.2880i 0.358663 0.621223i
\(965\) −22.8996 −0.737166
\(966\) 3.43539 + 12.0353i 0.110532 + 0.387231i
\(967\) 24.8951i 0.800571i 0.916390 + 0.400286i \(0.131089\pi\)
−0.916390 + 0.400286i \(0.868911\pi\)
\(968\) −1.39612 + 2.41815i −0.0448730 + 0.0777223i
\(969\) 0.0107469 + 0.00144139i 0.000345239 + 4.63040e-5i
\(970\) 12.8194 7.40130i 0.411607 0.237642i
\(971\) −13.4579 + 23.3098i −0.431885 + 0.748047i −0.997036 0.0769409i \(-0.975485\pi\)
0.565151 + 0.824988i \(0.308818\pi\)
\(972\) 2.22202 15.4293i 0.0712713 0.494894i
\(973\) 39.5853 + 4.46122i 1.26905 + 0.143020i
\(974\) 0.141904i 0.00454690i
\(975\) −21.9138 + 6.53359i −0.701804 + 0.209242i
\(976\) −10.2453 + 5.91511i −0.327943 + 0.189338i
\(977\) 24.1168 + 41.7715i 0.771564 + 1.33639i 0.936705 + 0.350119i \(0.113859\pi\)
−0.165141 + 0.986270i \(0.552808\pi\)
\(978\) 20.3778 8.38288i 0.651609 0.268055i
\(979\) 34.8173i 1.11277i
\(980\) 1.80239 7.89493i 0.0575753 0.252194i
\(981\) −8.06155 + 2.11822i −0.257385 + 0.0676294i
\(982\) −8.67645 5.00935i −0.276877 0.159855i
\(983\) −11.9049 + 6.87329i −0.379707 + 0.219224i −0.677691 0.735347i \(-0.737019\pi\)
0.297984 + 0.954571i \(0.403686\pi\)
\(984\) 0.108562 0.809434i 0.00346084 0.0258038i
\(985\) −25.2918 14.6022i −0.805862 0.465265i
\(986\) 0.0901098i 0.00286968i
\(987\) −0.749346 + 0.774101i −0.0238519 + 0.0246399i
\(988\) −0.0884646 + 0.877146i −0.00281443 + 0.0279057i
\(989\) −2.93442 1.69419i −0.0933092 0.0538721i
\(990\) −9.06961 9.15806i −0.288251 0.291062i
\(991\) 13.4020 + 23.2129i 0.425729 + 0.737384i 0.996488 0.0837336i \(-0.0266845\pi\)
−0.570760 + 0.821117i \(0.693351\pi\)
\(992\) 2.24622 3.89056i 0.0713174 0.123525i
\(993\) −25.4063 19.5931i −0.806245 0.621767i
\(994\) 31.2405 + 23.0578i 0.990888 + 0.731348i
\(995\) 7.13286 0.226127
\(996\) 5.83486 2.40031i 0.184885 0.0760567i
\(997\) 10.4342 6.02421i 0.330455 0.190789i −0.325588 0.945512i \(-0.605562\pi\)
0.656043 + 0.754723i \(0.272229\pi\)
\(998\) 9.05469 5.22772i 0.286621 0.165481i
\(999\) 30.0213 + 39.7197i 0.949831 + 1.25668i
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.bg.a.467.17 yes 36
3.2 odd 2 546.2.bg.b.467.11 yes 36
7.3 odd 6 inner 546.2.bg.a.311.11 36
13.12 even 2 546.2.bg.b.467.17 yes 36
21.17 even 6 546.2.bg.b.311.17 yes 36
39.38 odd 2 inner 546.2.bg.a.467.11 yes 36
91.38 odd 6 546.2.bg.b.311.11 yes 36
273.38 even 6 inner 546.2.bg.a.311.17 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bg.a.311.11 36 7.3 odd 6 inner
546.2.bg.a.311.17 yes 36 273.38 even 6 inner
546.2.bg.a.467.11 yes 36 39.38 odd 2 inner
546.2.bg.a.467.17 yes 36 1.1 even 1 trivial
546.2.bg.b.311.11 yes 36 91.38 odd 6
546.2.bg.b.311.17 yes 36 21.17 even 6
546.2.bg.b.467.11 yes 36 3.2 odd 2
546.2.bg.b.467.17 yes 36 13.12 even 2