Properties

Label 546.2.i.i.235.1
Level $546$
Weight $2$
Character 546.235
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
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(79,546)]
 
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([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.i (of order \(3\), 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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 546.235
Dual form 546.2.i.i.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.292893 + 0.507306i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.292893 + 0.507306i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.292893 - 0.507306i) q^{10} +(0.207107 - 0.358719i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-2.62132 - 0.358719i) q^{14} +0.585786 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.20711 - 2.09077i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.08579 + 1.88064i) q^{19} -0.585786 q^{20} +(-1.00000 - 2.44949i) q^{21} -0.414214 q^{22} +(-0.707107 - 1.22474i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 2.44949i) q^{28} -1.82843 q^{29} +(-0.292893 - 0.507306i) q^{30} +(4.24264 - 7.34847i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.207107 - 0.358719i) q^{33} -2.41421 q^{34} +(1.53553 + 0.210133i) q^{35} +1.00000 q^{36} +(-0.707107 - 1.22474i) q^{37} +(1.08579 - 1.88064i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.292893 + 0.507306i) q^{40} -9.89949 q^{41} +(-1.62132 + 2.09077i) q^{42} +6.48528 q^{43} +(0.207107 + 0.358719i) q^{44} +(0.292893 - 0.507306i) q^{45} +(-0.707107 + 1.22474i) q^{46} +(-0.500000 - 0.866025i) q^{47} -1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} -4.65685 q^{50} +(-1.20711 - 2.09077i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(-4.74264 + 8.21449i) q^{53} +(0.500000 + 0.866025i) q^{54} +0.242641 q^{55} +(1.62132 - 2.09077i) q^{56} +2.17157 q^{57} +(0.914214 + 1.58346i) q^{58} +(-1.03553 + 1.79360i) q^{59} +(-0.292893 + 0.507306i) q^{60} +(2.20711 + 3.82282i) q^{61} -8.48528 q^{62} +(-2.62132 - 0.358719i) q^{63} +1.00000 q^{64} +(0.292893 + 0.507306i) q^{65} +(-0.207107 + 0.358719i) q^{66} +(-0.914214 + 1.58346i) q^{67} +(1.20711 + 2.09077i) q^{68} -1.41421 q^{69} +(-0.585786 - 1.43488i) q^{70} -5.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-0.707107 + 1.22474i) q^{73} +(-0.707107 + 1.22474i) q^{74} +(-2.32843 - 4.03295i) q^{75} -2.17157 q^{76} +(-0.414214 - 1.01461i) q^{77} -1.00000 q^{78} +(5.82843 + 10.0951i) q^{79} +(0.292893 - 0.507306i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.94975 + 8.57321i) q^{82} +7.65685 q^{83} +(2.62132 + 0.358719i) q^{84} +1.41421 q^{85} +(-3.24264 - 5.61642i) q^{86} +(-0.914214 + 1.58346i) q^{87} +(0.207107 - 0.358719i) q^{88} +(-1.29289 - 2.23936i) q^{89} -0.585786 q^{90} +(1.62132 - 2.09077i) q^{91} +1.41421 q^{92} +(-4.24264 - 7.34847i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(-0.636039 + 1.10165i) q^{95} +(0.500000 + 0.866025i) q^{96} -0.928932 q^{97} +(-5.00000 + 4.89898i) q^{98} -0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{17} - 2 q^{18} + 10 q^{19} - 8 q^{20} - 4 q^{21} + 4 q^{22} + 2 q^{24} - 2 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} + 4 q^{29} - 4 q^{30} - 2 q^{32} + 2 q^{33} - 4 q^{34} - 8 q^{35} + 4 q^{36} + 10 q^{38} + 2 q^{39} + 4 q^{40} + 2 q^{42} - 8 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{47} - 4 q^{48} + 10 q^{49} + 4 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} + 2 q^{54} - 16 q^{55} - 2 q^{56} + 20 q^{57} - 2 q^{58} + 10 q^{59} - 4 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + 4 q^{65} + 2 q^{66} + 2 q^{67} + 2 q^{68} - 8 q^{70} - 20 q^{71} - 2 q^{72} + 2 q^{75} - 20 q^{76} + 4 q^{77} - 4 q^{78} + 12 q^{79} + 4 q^{80} - 2 q^{81} + 8 q^{83} + 2 q^{84} + 4 q^{86} + 2 q^{87} - 2 q^{88} - 8 q^{89} - 8 q^{90} - 2 q^{91} - 2 q^{94} - 28 q^{95} + 2 q^{96} - 32 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.292893 + 0.507306i 0.130986 + 0.226874i 0.924057 0.382255i \(-0.124852\pi\)
−0.793071 + 0.609129i \(0.791519\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.62132 2.09077i 0.612801 0.790237i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.292893 0.507306i 0.0926210 0.160424i
\(11\) 0.207107 0.358719i 0.0624450 0.108158i −0.833113 0.553103i \(-0.813444\pi\)
0.895558 + 0.444945i \(0.146777\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 1.00000 0.277350
\(14\) −2.62132 0.358719i −0.700577 0.0958718i
\(15\) 0.585786 0.151249
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.20711 2.09077i 0.292766 0.507086i −0.681696 0.731635i \(-0.738758\pi\)
0.974463 + 0.224549i \(0.0720908\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 1.08579 + 1.88064i 0.249096 + 0.431448i 0.963275 0.268515i \(-0.0865330\pi\)
−0.714179 + 0.699963i \(0.753200\pi\)
\(20\) −0.585786 −0.130986
\(21\) −1.00000 2.44949i −0.218218 0.534522i
\(22\) −0.414214 −0.0883106
\(23\) −0.707107 1.22474i −0.147442 0.255377i 0.782839 0.622224i \(-0.213771\pi\)
−0.930281 + 0.366847i \(0.880437\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 2.32843 4.03295i 0.465685 0.806591i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) −1.00000 −0.192450
\(28\) 1.00000 + 2.44949i 0.188982 + 0.462910i
\(29\) −1.82843 −0.339530 −0.169765 0.985485i \(-0.554301\pi\)
−0.169765 + 0.985485i \(0.554301\pi\)
\(30\) −0.292893 0.507306i −0.0534747 0.0926210i
\(31\) 4.24264 7.34847i 0.762001 1.31982i −0.179817 0.983700i \(-0.557551\pi\)
0.941818 0.336124i \(-0.109116\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.207107 0.358719i −0.0360527 0.0624450i
\(34\) −2.41421 −0.414034
\(35\) 1.53553 + 0.210133i 0.259553 + 0.0355190i
\(36\) 1.00000 0.166667
\(37\) −0.707107 1.22474i −0.116248 0.201347i 0.802030 0.597284i \(-0.203753\pi\)
−0.918278 + 0.395937i \(0.870420\pi\)
\(38\) 1.08579 1.88064i 0.176138 0.305080i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0.292893 + 0.507306i 0.0463105 + 0.0802121i
\(41\) −9.89949 −1.54604 −0.773021 0.634381i \(-0.781255\pi\)
−0.773021 + 0.634381i \(0.781255\pi\)
\(42\) −1.62132 + 2.09077i −0.250175 + 0.322613i
\(43\) 6.48528 0.988996 0.494498 0.869179i \(-0.335352\pi\)
0.494498 + 0.869179i \(0.335352\pi\)
\(44\) 0.207107 + 0.358719i 0.0312225 + 0.0540790i
\(45\) 0.292893 0.507306i 0.0436619 0.0756247i
\(46\) −0.707107 + 1.22474i −0.104257 + 0.180579i
\(47\) −0.500000 0.866025i −0.0729325 0.126323i 0.827253 0.561830i \(-0.189902\pi\)
−0.900185 + 0.435507i \(0.856569\pi\)
\(48\) −1.00000 −0.144338
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) −4.65685 −0.658579
\(51\) −1.20711 2.09077i −0.169029 0.292766i
\(52\) −0.500000 + 0.866025i −0.0693375 + 0.120096i
\(53\) −4.74264 + 8.21449i −0.651452 + 1.12835i 0.331319 + 0.943519i \(0.392506\pi\)
−0.982771 + 0.184829i \(0.940827\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0.242641 0.0327177
\(56\) 1.62132 2.09077i 0.216658 0.279391i
\(57\) 2.17157 0.287632
\(58\) 0.914214 + 1.58346i 0.120042 + 0.207919i
\(59\) −1.03553 + 1.79360i −0.134815 + 0.233506i −0.925527 0.378682i \(-0.876377\pi\)
0.790712 + 0.612189i \(0.209711\pi\)
\(60\) −0.292893 + 0.507306i −0.0378124 + 0.0654929i
\(61\) 2.20711 + 3.82282i 0.282591 + 0.489462i 0.972022 0.234889i \(-0.0754727\pi\)
−0.689431 + 0.724351i \(0.742139\pi\)
\(62\) −8.48528 −1.07763
\(63\) −2.62132 0.358719i −0.330255 0.0451944i
\(64\) 1.00000 0.125000
\(65\) 0.292893 + 0.507306i 0.0363289 + 0.0629236i
\(66\) −0.207107 + 0.358719i −0.0254931 + 0.0441553i
\(67\) −0.914214 + 1.58346i −0.111689 + 0.193451i −0.916451 0.400146i \(-0.868959\pi\)
0.804762 + 0.593597i \(0.202293\pi\)
\(68\) 1.20711 + 2.09077i 0.146383 + 0.253543i
\(69\) −1.41421 −0.170251
\(70\) −0.585786 1.43488i −0.0700149 0.171501i
\(71\) −5.00000 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −0.707107 + 1.22474i −0.0827606 + 0.143346i −0.904435 0.426612i \(-0.859707\pi\)
0.821674 + 0.569958i \(0.193040\pi\)
\(74\) −0.707107 + 1.22474i −0.0821995 + 0.142374i
\(75\) −2.32843 4.03295i −0.268864 0.465685i
\(76\) −2.17157 −0.249096
\(77\) −0.414214 1.01461i −0.0472040 0.115626i
\(78\) −1.00000 −0.113228
\(79\) 5.82843 + 10.0951i 0.655749 + 1.13579i 0.981705 + 0.190406i \(0.0609805\pi\)
−0.325956 + 0.945385i \(0.605686\pi\)
\(80\) 0.292893 0.507306i 0.0327465 0.0567185i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.94975 + 8.57321i 0.546608 + 0.946753i
\(83\) 7.65685 0.840449 0.420224 0.907420i \(-0.361951\pi\)
0.420224 + 0.907420i \(0.361951\pi\)
\(84\) 2.62132 + 0.358719i 0.286009 + 0.0391395i
\(85\) 1.41421 0.153393
\(86\) −3.24264 5.61642i −0.349663 0.605634i
\(87\) −0.914214 + 1.58346i −0.0980140 + 0.169765i
\(88\) 0.207107 0.358719i 0.0220777 0.0382396i
\(89\) −1.29289 2.23936i −0.137046 0.237371i 0.789331 0.613968i \(-0.210428\pi\)
−0.926377 + 0.376597i \(0.877094\pi\)
\(90\) −0.585786 −0.0617473
\(91\) 1.62132 2.09077i 0.169961 0.219172i
\(92\) 1.41421 0.147442
\(93\) −4.24264 7.34847i −0.439941 0.762001i
\(94\) −0.500000 + 0.866025i −0.0515711 + 0.0893237i
\(95\) −0.636039 + 1.10165i −0.0652562 + 0.113027i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −0.928932 −0.0943188 −0.0471594 0.998887i \(-0.515017\pi\)
−0.0471594 + 0.998887i \(0.515017\pi\)
\(98\) −5.00000 + 4.89898i −0.505076 + 0.494872i
\(99\) −0.414214 −0.0416300
\(100\) 2.32843 + 4.03295i 0.232843 + 0.403295i
\(101\) 7.41421 12.8418i 0.737742 1.27781i −0.215768 0.976445i \(-0.569226\pi\)
0.953510 0.301362i \(-0.0974412\pi\)
\(102\) −1.20711 + 2.09077i −0.119521 + 0.207017i
\(103\) 8.41421 + 14.5738i 0.829077 + 1.43600i 0.898763 + 0.438435i \(0.144467\pi\)
−0.0696860 + 0.997569i \(0.522200\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0.949747 1.22474i 0.0926859 0.119523i
\(106\) 9.48528 0.921292
\(107\) 9.65685 + 16.7262i 0.933563 + 1.61698i 0.777176 + 0.629283i \(0.216651\pi\)
0.156387 + 0.987696i \(0.450015\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.82843 8.36308i 0.462479 0.801038i −0.536604 0.843834i \(-0.680293\pi\)
0.999084 + 0.0427961i \(0.0136266\pi\)
\(110\) −0.121320 0.210133i −0.0115674 0.0200354i
\(111\) −1.41421 −0.134231
\(112\) −2.62132 0.358719i −0.247691 0.0338958i
\(113\) 4.89949 0.460906 0.230453 0.973083i \(-0.425979\pi\)
0.230453 + 0.973083i \(0.425979\pi\)
\(114\) −1.08579 1.88064i −0.101693 0.176138i
\(115\) 0.414214 0.717439i 0.0386256 0.0669015i
\(116\) 0.914214 1.58346i 0.0848826 0.147021i
\(117\) −0.500000 0.866025i −0.0462250 0.0800641i
\(118\) 2.07107 0.190657
\(119\) −2.41421 5.91359i −0.221311 0.542098i
\(120\) 0.585786 0.0534747
\(121\) 5.41421 + 9.37769i 0.492201 + 0.852518i
\(122\) 2.20711 3.82282i 0.199822 0.346102i
\(123\) −4.94975 + 8.57321i −0.446304 + 0.773021i
\(124\) 4.24264 + 7.34847i 0.381000 + 0.659912i
\(125\) 5.65685 0.505964
\(126\) 1.00000 + 2.44949i 0.0890871 + 0.218218i
\(127\) −7.89949 −0.700967 −0.350483 0.936569i \(-0.613983\pi\)
−0.350483 + 0.936569i \(0.613983\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 3.24264 5.61642i 0.285499 0.494498i
\(130\) 0.292893 0.507306i 0.0256884 0.0444937i
\(131\) 4.77817 + 8.27604i 0.417471 + 0.723081i 0.995684 0.0928046i \(-0.0295832\pi\)
−0.578213 + 0.815886i \(0.696250\pi\)
\(132\) 0.414214 0.0360527
\(133\) 5.69239 + 0.778985i 0.493593 + 0.0675466i
\(134\) 1.82843 0.157952
\(135\) −0.292893 0.507306i −0.0252082 0.0436619i
\(136\) 1.20711 2.09077i 0.103509 0.179282i
\(137\) −5.53553 + 9.58783i −0.472933 + 0.819143i −0.999520 0.0309777i \(-0.990138\pi\)
0.526587 + 0.850121i \(0.323471\pi\)
\(138\) 0.707107 + 1.22474i 0.0601929 + 0.104257i
\(139\) −13.0711 −1.10867 −0.554337 0.832292i \(-0.687028\pi\)
−0.554337 + 0.832292i \(0.687028\pi\)
\(140\) −0.949747 + 1.22474i −0.0802683 + 0.103510i
\(141\) −1.00000 −0.0842152
\(142\) 2.50000 + 4.33013i 0.209795 + 0.363376i
\(143\) 0.207107 0.358719i 0.0173191 0.0299976i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −0.535534 0.927572i −0.0444737 0.0770307i
\(146\) 1.41421 0.117041
\(147\) −6.74264 1.88064i −0.556124 0.155112i
\(148\) 1.41421 0.116248
\(149\) 2.46447 + 4.26858i 0.201897 + 0.349696i 0.949140 0.314856i \(-0.101956\pi\)
−0.747243 + 0.664551i \(0.768623\pi\)
\(150\) −2.32843 + 4.03295i −0.190115 + 0.329289i
\(151\) −2.03553 + 3.52565i −0.165649 + 0.286913i −0.936886 0.349636i \(-0.886305\pi\)
0.771236 + 0.636549i \(0.219639\pi\)
\(152\) 1.08579 + 1.88064i 0.0880689 + 0.152540i
\(153\) −2.41421 −0.195178
\(154\) −0.671573 + 0.866025i −0.0541169 + 0.0697863i
\(155\) 4.97056 0.399245
\(156\) 0.500000 + 0.866025i 0.0400320 + 0.0693375i
\(157\) −4.86396 + 8.42463i −0.388186 + 0.672358i −0.992206 0.124611i \(-0.960232\pi\)
0.604019 + 0.796970i \(0.293565\pi\)
\(158\) 5.82843 10.0951i 0.463685 0.803126i
\(159\) 4.74264 + 8.21449i 0.376116 + 0.651452i
\(160\) −0.585786 −0.0463105
\(161\) −3.70711 0.507306i −0.292161 0.0399813i
\(162\) 1.00000 0.0785674
\(163\) 9.32843 + 16.1573i 0.730659 + 1.26554i 0.956602 + 0.291398i \(0.0941203\pi\)
−0.225943 + 0.974140i \(0.572546\pi\)
\(164\) 4.94975 8.57321i 0.386510 0.669456i
\(165\) 0.121320 0.210133i 0.00944478 0.0163588i
\(166\) −3.82843 6.63103i −0.297144 0.514668i
\(167\) −0.656854 −0.0508289 −0.0254145 0.999677i \(-0.508091\pi\)
−0.0254145 + 0.999677i \(0.508091\pi\)
\(168\) −1.00000 2.44949i −0.0771517 0.188982i
\(169\) 1.00000 0.0769231
\(170\) −0.707107 1.22474i −0.0542326 0.0939336i
\(171\) 1.08579 1.88064i 0.0830322 0.143816i
\(172\) −3.24264 + 5.61642i −0.247249 + 0.428248i
\(173\) −2.74264 4.75039i −0.208519 0.361166i 0.742729 0.669592i \(-0.233531\pi\)
−0.951248 + 0.308426i \(0.900198\pi\)
\(174\) 1.82843 0.138613
\(175\) −4.65685 11.4069i −0.352025 0.862282i
\(176\) −0.414214 −0.0312225
\(177\) 1.03553 + 1.79360i 0.0778355 + 0.134815i
\(178\) −1.29289 + 2.23936i −0.0969064 + 0.167847i
\(179\) −9.82843 + 17.0233i −0.734611 + 1.27238i 0.220283 + 0.975436i \(0.429302\pi\)
−0.954894 + 0.296948i \(0.904031\pi\)
\(180\) 0.292893 + 0.507306i 0.0218310 + 0.0378124i
\(181\) 2.89949 0.215518 0.107759 0.994177i \(-0.465633\pi\)
0.107759 + 0.994177i \(0.465633\pi\)
\(182\) −2.62132 0.358719i −0.194305 0.0265901i
\(183\) 4.41421 0.326308
\(184\) −0.707107 1.22474i −0.0521286 0.0902894i
\(185\) 0.414214 0.717439i 0.0304536 0.0527472i
\(186\) −4.24264 + 7.34847i −0.311086 + 0.538816i
\(187\) −0.500000 0.866025i −0.0365636 0.0633300i
\(188\) 1.00000 0.0729325
\(189\) −1.62132 + 2.09077i −0.117934 + 0.152081i
\(190\) 1.27208 0.0922862
\(191\) 5.17157 + 8.95743i 0.374202 + 0.648137i 0.990207 0.139605i \(-0.0445834\pi\)
−0.616005 + 0.787742i \(0.711250\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 1.46447 2.53653i 0.105415 0.182583i −0.808493 0.588506i \(-0.799716\pi\)
0.913908 + 0.405922i \(0.133050\pi\)
\(194\) 0.464466 + 0.804479i 0.0333467 + 0.0577582i
\(195\) 0.585786 0.0419490
\(196\) 6.74264 + 1.88064i 0.481617 + 0.134331i
\(197\) −15.5563 −1.10834 −0.554172 0.832402i \(-0.686965\pi\)
−0.554172 + 0.832402i \(0.686965\pi\)
\(198\) 0.207107 + 0.358719i 0.0147184 + 0.0254931i
\(199\) −1.36396 + 2.36245i −0.0966886 + 0.167470i −0.910312 0.413923i \(-0.864158\pi\)
0.813623 + 0.581392i \(0.197492\pi\)
\(200\) 2.32843 4.03295i 0.164645 0.285173i
\(201\) 0.914214 + 1.58346i 0.0644837 + 0.111689i
\(202\) −14.8284 −1.04332
\(203\) −2.96447 + 3.82282i −0.208065 + 0.268309i
\(204\) 2.41421 0.169029
\(205\) −2.89949 5.02207i −0.202510 0.350757i
\(206\) 8.41421 14.5738i 0.586246 1.01541i
\(207\) −0.707107 + 1.22474i −0.0491473 + 0.0851257i
\(208\) −0.500000 0.866025i −0.0346688 0.0600481i
\(209\) 0.899495 0.0622194
\(210\) −1.53553 0.210133i −0.105962 0.0145006i
\(211\) −12.9289 −0.890064 −0.445032 0.895515i \(-0.646808\pi\)
−0.445032 + 0.895515i \(0.646808\pi\)
\(212\) −4.74264 8.21449i −0.325726 0.564174i
\(213\) −2.50000 + 4.33013i −0.171297 + 0.296695i
\(214\) 9.65685 16.7262i 0.660129 1.14338i
\(215\) 1.89949 + 3.29002i 0.129544 + 0.224378i
\(216\) −1.00000 −0.0680414
\(217\) −8.48528 20.7846i −0.576018 1.41095i
\(218\) −9.65685 −0.654045
\(219\) 0.707107 + 1.22474i 0.0477818 + 0.0827606i
\(220\) −0.121320 + 0.210133i −0.00817942 + 0.0141672i
\(221\) 1.20711 2.09077i 0.0811988 0.140640i
\(222\) 0.707107 + 1.22474i 0.0474579 + 0.0821995i
\(223\) −7.92893 −0.530961 −0.265480 0.964116i \(-0.585531\pi\)
−0.265480 + 0.964116i \(0.585531\pi\)
\(224\) 1.00000 + 2.44949i 0.0668153 + 0.163663i
\(225\) −4.65685 −0.310457
\(226\) −2.44975 4.24309i −0.162955 0.282246i
\(227\) 10.5858 18.3351i 0.702603 1.21694i −0.264946 0.964263i \(-0.585354\pi\)
0.967550 0.252681i \(-0.0813125\pi\)
\(228\) −1.08579 + 1.88064i −0.0719080 + 0.124548i
\(229\) −13.2426 22.9369i −0.875098 1.51571i −0.856658 0.515885i \(-0.827463\pi\)
−0.0184404 0.999830i \(-0.505870\pi\)
\(230\) −0.828427 −0.0546249
\(231\) −1.08579 0.148586i −0.0714395 0.00977627i
\(232\) −1.82843 −0.120042
\(233\) 8.86396 + 15.3528i 0.580697 + 1.00580i 0.995397 + 0.0958390i \(0.0305534\pi\)
−0.414699 + 0.909958i \(0.636113\pi\)
\(234\) −0.500000 + 0.866025i −0.0326860 + 0.0566139i
\(235\) 0.292893 0.507306i 0.0191062 0.0330930i
\(236\) −1.03553 1.79360i −0.0674075 0.116753i
\(237\) 11.6569 0.757194
\(238\) −3.91421 + 5.04757i −0.253721 + 0.327185i
\(239\) 4.51472 0.292033 0.146016 0.989282i \(-0.453355\pi\)
0.146016 + 0.989282i \(0.453355\pi\)
\(240\) −0.292893 0.507306i −0.0189062 0.0327465i
\(241\) 1.07107 1.85514i 0.0689935 0.119500i −0.829465 0.558559i \(-0.811355\pi\)
0.898459 + 0.439058i \(0.144688\pi\)
\(242\) 5.41421 9.37769i 0.348039 0.602821i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −4.41421 −0.282591
\(245\) 2.92893 2.86976i 0.187123 0.183342i
\(246\) 9.89949 0.631169
\(247\) 1.08579 + 1.88064i 0.0690869 + 0.119662i
\(248\) 4.24264 7.34847i 0.269408 0.466628i
\(249\) 3.82843 6.63103i 0.242617 0.420224i
\(250\) −2.82843 4.89898i −0.178885 0.309839i
\(251\) 24.8284 1.56716 0.783578 0.621293i \(-0.213392\pi\)
0.783578 + 0.621293i \(0.213392\pi\)
\(252\) 1.62132 2.09077i 0.102134 0.131706i
\(253\) −0.585786 −0.0368281
\(254\) 3.94975 + 6.84116i 0.247829 + 0.429253i
\(255\) 0.707107 1.22474i 0.0442807 0.0766965i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.2426 22.9369i −0.826053 1.43077i −0.901112 0.433587i \(-0.857248\pi\)
0.0750585 0.997179i \(-0.476086\pi\)
\(258\) −6.48528 −0.403756
\(259\) −3.70711 0.507306i −0.230348 0.0315225i
\(260\) −0.585786 −0.0363289
\(261\) 0.914214 + 1.58346i 0.0565884 + 0.0980140i
\(262\) 4.77817 8.27604i 0.295197 0.511296i
\(263\) −10.2929 + 17.8278i −0.634687 + 1.09931i 0.351894 + 0.936040i \(0.385538\pi\)
−0.986581 + 0.163270i \(0.947796\pi\)
\(264\) −0.207107 0.358719i −0.0127465 0.0220777i
\(265\) −5.55635 −0.341324
\(266\) −2.17157 5.31925i −0.133148 0.326144i
\(267\) −2.58579 −0.158248
\(268\) −0.914214 1.58346i −0.0558445 0.0967255i
\(269\) 4.57107 7.91732i 0.278703 0.482728i −0.692360 0.721552i \(-0.743429\pi\)
0.971063 + 0.238825i \(0.0767622\pi\)
\(270\) −0.292893 + 0.507306i −0.0178249 + 0.0308737i
\(271\) −13.1066 22.7013i −0.796169 1.37901i −0.922094 0.386966i \(-0.873523\pi\)
0.125925 0.992040i \(-0.459810\pi\)
\(272\) −2.41421 −0.146383
\(273\) −1.00000 2.44949i −0.0605228 0.148250i
\(274\) 11.0711 0.668828
\(275\) −0.964466 1.67050i −0.0581595 0.100735i
\(276\) 0.707107 1.22474i 0.0425628 0.0737210i
\(277\) −9.03553 + 15.6500i −0.542893 + 0.940318i 0.455844 + 0.890060i \(0.349338\pi\)
−0.998736 + 0.0502577i \(0.983996\pi\)
\(278\) 6.53553 + 11.3199i 0.391975 + 0.678921i
\(279\) −8.48528 −0.508001
\(280\) 1.53553 + 0.210133i 0.0917657 + 0.0125578i
\(281\) 0.686292 0.0409407 0.0204704 0.999790i \(-0.493484\pi\)
0.0204704 + 0.999790i \(0.493484\pi\)
\(282\) 0.500000 + 0.866025i 0.0297746 + 0.0515711i
\(283\) 7.87868 13.6463i 0.468339 0.811187i −0.531006 0.847368i \(-0.678186\pi\)
0.999345 + 0.0361811i \(0.0115193\pi\)
\(284\) 2.50000 4.33013i 0.148348 0.256946i
\(285\) 0.636039 + 1.10165i 0.0376757 + 0.0652562i
\(286\) −0.414214 −0.0244930
\(287\) −16.0503 + 20.6976i −0.947416 + 1.22174i
\(288\) 1.00000 0.0589256
\(289\) 5.58579 + 9.67487i 0.328576 + 0.569110i
\(290\) −0.535534 + 0.927572i −0.0314476 + 0.0544689i
\(291\) −0.464466 + 0.804479i −0.0272275 + 0.0471594i
\(292\) −0.707107 1.22474i −0.0413803 0.0716728i
\(293\) −9.89949 −0.578335 −0.289167 0.957279i \(-0.593378\pi\)
−0.289167 + 0.957279i \(0.593378\pi\)
\(294\) 1.74264 + 6.77962i 0.101633 + 0.395395i
\(295\) −1.21320 −0.0706354
\(296\) −0.707107 1.22474i −0.0410997 0.0711868i
\(297\) −0.207107 + 0.358719i −0.0120176 + 0.0208150i
\(298\) 2.46447 4.26858i 0.142763 0.247272i
\(299\) −0.707107 1.22474i −0.0408930 0.0708288i
\(300\) 4.65685 0.268864
\(301\) 10.5147 13.5592i 0.606058 0.781541i
\(302\) 4.07107 0.234264
\(303\) −7.41421 12.8418i −0.425935 0.737742i
\(304\) 1.08579 1.88064i 0.0622741 0.107862i
\(305\) −1.29289 + 2.23936i −0.0740309 + 0.128225i
\(306\) 1.20711 + 2.09077i 0.0690057 + 0.119521i
\(307\) −28.1127 −1.60448 −0.802238 0.597004i \(-0.796358\pi\)
−0.802238 + 0.597004i \(0.796358\pi\)
\(308\) 1.08579 + 0.148586i 0.0618684 + 0.00846650i
\(309\) 16.8284 0.957336
\(310\) −2.48528 4.30463i −0.141154 0.244487i
\(311\) 4.05025 7.01524i 0.229669 0.397798i −0.728041 0.685533i \(-0.759569\pi\)
0.957710 + 0.287735i \(0.0929024\pi\)
\(312\) 0.500000 0.866025i 0.0283069 0.0490290i
\(313\) −1.75736 3.04384i −0.0993318 0.172048i 0.812076 0.583551i \(-0.198337\pi\)
−0.911408 + 0.411503i \(0.865004\pi\)
\(314\) 9.72792 0.548978
\(315\) −0.585786 1.43488i −0.0330053 0.0808462i
\(316\) −11.6569 −0.655749
\(317\) −14.8995 25.8067i −0.836839 1.44945i −0.892524 0.450999i \(-0.851068\pi\)
0.0556853 0.998448i \(-0.482266\pi\)
\(318\) 4.74264 8.21449i 0.265954 0.460646i
\(319\) −0.378680 + 0.655892i −0.0212020 + 0.0367229i
\(320\) 0.292893 + 0.507306i 0.0163732 + 0.0283593i
\(321\) 19.3137 1.07799
\(322\) 1.41421 + 3.46410i 0.0788110 + 0.193047i
\(323\) 5.24264 0.291708
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 2.32843 4.03295i 0.129158 0.223708i
\(326\) 9.32843 16.1573i 0.516654 0.894871i
\(327\) −4.82843 8.36308i −0.267013 0.462479i
\(328\) −9.89949 −0.546608
\(329\) −2.62132 0.358719i −0.144518 0.0197768i
\(330\) −0.242641 −0.0133569
\(331\) 11.2426 + 19.4728i 0.617951 + 1.07032i 0.989859 + 0.142053i \(0.0453705\pi\)
−0.371908 + 0.928270i \(0.621296\pi\)
\(332\) −3.82843 + 6.63103i −0.210112 + 0.363925i
\(333\) −0.707107 + 1.22474i −0.0387492 + 0.0671156i
\(334\) 0.328427 + 0.568852i 0.0179707 + 0.0311262i
\(335\) −1.07107 −0.0585187
\(336\) −1.62132 + 2.09077i −0.0884503 + 0.114061i
\(337\) −20.3137 −1.10656 −0.553279 0.832996i \(-0.686624\pi\)
−0.553279 + 0.832996i \(0.686624\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) 2.44975 4.24309i 0.133052 0.230453i
\(340\) −0.707107 + 1.22474i −0.0383482 + 0.0664211i
\(341\) −1.75736 3.04384i −0.0951663 0.164833i
\(342\) −2.17157 −0.117425
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 6.48528 0.349663
\(345\) −0.414214 0.717439i −0.0223005 0.0386256i
\(346\) −2.74264 + 4.75039i −0.147445 + 0.255383i
\(347\) 4.36396 7.55860i 0.234270 0.405767i −0.724790 0.688969i \(-0.758063\pi\)
0.959060 + 0.283202i \(0.0913968\pi\)
\(348\) −0.914214 1.58346i −0.0490070 0.0848826i
\(349\) −6.72792 −0.360137 −0.180069 0.983654i \(-0.557632\pi\)
−0.180069 + 0.983654i \(0.557632\pi\)
\(350\) −7.55025 + 9.73641i −0.403578 + 0.520433i
\(351\) −1.00000 −0.0533761
\(352\) 0.207107 + 0.358719i 0.0110388 + 0.0191198i
\(353\) −6.31371 + 10.9357i −0.336045 + 0.582047i −0.983685 0.179900i \(-0.942423\pi\)
0.647640 + 0.761946i \(0.275756\pi\)
\(354\) 1.03553 1.79360i 0.0550380 0.0953286i
\(355\) −1.46447 2.53653i −0.0777258 0.134625i
\(356\) 2.58579 0.137046
\(357\) −6.32843 0.866025i −0.334936 0.0458349i
\(358\) 19.6569 1.03890
\(359\) 0.414214 + 0.717439i 0.0218614 + 0.0378650i 0.876749 0.480948i \(-0.159707\pi\)
−0.854888 + 0.518813i \(0.826374\pi\)
\(360\) 0.292893 0.507306i 0.0154368 0.0267374i
\(361\) 7.14214 12.3705i 0.375902 0.651081i
\(362\) −1.44975 2.51104i −0.0761970 0.131977i
\(363\) 10.8284 0.568345
\(364\) 1.00000 + 2.44949i 0.0524142 + 0.128388i
\(365\) −0.828427 −0.0433619
\(366\) −2.20711 3.82282i −0.115367 0.199822i
\(367\) −6.31371 + 10.9357i −0.329573 + 0.570837i −0.982427 0.186647i \(-0.940238\pi\)
0.652854 + 0.757484i \(0.273571\pi\)
\(368\) −0.707107 + 1.22474i −0.0368605 + 0.0638442i
\(369\) 4.94975 + 8.57321i 0.257674 + 0.446304i
\(370\) −0.828427 −0.0430679
\(371\) 9.48528 + 23.2341i 0.492451 + 1.20625i
\(372\) 8.48528 0.439941
\(373\) 2.79289 + 4.83743i 0.144611 + 0.250473i 0.929228 0.369508i \(-0.120474\pi\)
−0.784617 + 0.619981i \(0.787140\pi\)
\(374\) −0.500000 + 0.866025i −0.0258544 + 0.0447811i
\(375\) 2.82843 4.89898i 0.146059 0.252982i
\(376\) −0.500000 0.866025i −0.0257855 0.0446619i
\(377\) −1.82843 −0.0941688
\(378\) 2.62132 + 0.358719i 0.134826 + 0.0184505i
\(379\) 18.6274 0.956826 0.478413 0.878135i \(-0.341212\pi\)
0.478413 + 0.878135i \(0.341212\pi\)
\(380\) −0.636039 1.10165i −0.0326281 0.0565135i
\(381\) −3.94975 + 6.84116i −0.202352 + 0.350483i
\(382\) 5.17157 8.95743i 0.264601 0.458302i
\(383\) −5.58579 9.67487i −0.285420 0.494363i 0.687291 0.726382i \(-0.258800\pi\)
−0.972711 + 0.232020i \(0.925467\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0.393398 0.507306i 0.0200494 0.0258547i
\(386\) −2.92893 −0.149079
\(387\) −3.24264 5.61642i −0.164833 0.285499i
\(388\) 0.464466 0.804479i 0.0235797 0.0408412i
\(389\) 2.25736 3.90986i 0.114453 0.198238i −0.803108 0.595833i \(-0.796822\pi\)
0.917561 + 0.397595i \(0.130155\pi\)
\(390\) −0.292893 0.507306i −0.0148312 0.0256884i
\(391\) −3.41421 −0.172664
\(392\) −1.74264 6.77962i −0.0880166 0.342422i
\(393\) 9.55635 0.482054
\(394\) 7.77817 + 13.4722i 0.391859 + 0.678719i
\(395\) −3.41421 + 5.91359i −0.171788 + 0.297545i
\(396\) 0.207107 0.358719i 0.0104075 0.0180263i
\(397\) 4.77817 + 8.27604i 0.239810 + 0.415363i 0.960660 0.277729i \(-0.0895816\pi\)
−0.720850 + 0.693091i \(0.756248\pi\)
\(398\) 2.72792 0.136738
\(399\) 3.52082 4.54026i 0.176261 0.227297i
\(400\) −4.65685 −0.232843
\(401\) −9.94975 17.2335i −0.496867 0.860598i 0.503127 0.864213i \(-0.332183\pi\)
−0.999993 + 0.00361428i \(0.998850\pi\)
\(402\) 0.914214 1.58346i 0.0455968 0.0789760i
\(403\) 4.24264 7.34847i 0.211341 0.366053i
\(404\) 7.41421 + 12.8418i 0.368871 + 0.638903i
\(405\) −0.585786 −0.0291080
\(406\) 4.79289 + 0.655892i 0.237867 + 0.0325514i
\(407\) −0.585786 −0.0290364
\(408\) −1.20711 2.09077i −0.0597607 0.103509i
\(409\) −16.2929 + 28.2201i −0.805632 + 1.39540i 0.110232 + 0.993906i \(0.464841\pi\)
−0.915864 + 0.401489i \(0.868493\pi\)
\(410\) −2.89949 + 5.02207i −0.143196 + 0.248022i
\(411\) 5.53553 + 9.58783i 0.273048 + 0.472933i
\(412\) −16.8284 −0.829077
\(413\) 2.07107 + 5.07306i 0.101911 + 0.249629i
\(414\) 1.41421 0.0695048
\(415\) 2.24264 + 3.88437i 0.110087 + 0.190676i
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) −6.53553 + 11.3199i −0.320046 + 0.554337i
\(418\) −0.449747 0.778985i −0.0219979 0.0381014i
\(419\) 27.4558 1.34131 0.670653 0.741771i \(-0.266014\pi\)
0.670653 + 0.741771i \(0.266014\pi\)
\(420\) 0.585786 + 1.43488i 0.0285835 + 0.0700149i
\(421\) 1.07107 0.0522007 0.0261003 0.999659i \(-0.491691\pi\)
0.0261003 + 0.999659i \(0.491691\pi\)
\(422\) 6.46447 + 11.1968i 0.314685 + 0.545051i
\(423\) −0.500000 + 0.866025i −0.0243108 + 0.0421076i
\(424\) −4.74264 + 8.21449i −0.230323 + 0.398931i
\(425\) −5.62132 9.73641i −0.272674 0.472285i
\(426\) 5.00000 0.242251
\(427\) 11.5711 + 1.58346i 0.559963 + 0.0766292i
\(428\) −19.3137 −0.933563
\(429\) −0.207107 0.358719i −0.00999921 0.0173191i
\(430\) 1.89949 3.29002i 0.0916018 0.158659i
\(431\) −15.2426 + 26.4010i −0.734212 + 1.27169i 0.220856 + 0.975306i \(0.429115\pi\)
−0.955068 + 0.296386i \(0.904218\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 29.9706 1.44029 0.720147 0.693822i \(-0.244074\pi\)
0.720147 + 0.693822i \(0.244074\pi\)
\(434\) −13.7574 + 17.7408i −0.660374 + 0.851584i
\(435\) −1.07107 −0.0513538
\(436\) 4.82843 + 8.36308i 0.231240 + 0.400519i
\(437\) 1.53553 2.65962i 0.0734545 0.127227i
\(438\) 0.707107 1.22474i 0.0337869 0.0585206i
\(439\) −8.29289 14.3637i −0.395798 0.685543i 0.597405 0.801940i \(-0.296199\pi\)
−0.993203 + 0.116397i \(0.962865\pi\)
\(440\) 0.242641 0.0115674
\(441\) −5.00000 + 4.89898i −0.238095 + 0.233285i
\(442\) −2.41421 −0.114832
\(443\) 16.8492 + 29.1837i 0.800532 + 1.38656i 0.919267 + 0.393636i \(0.128783\pi\)
−0.118735 + 0.992926i \(0.537884\pi\)
\(444\) 0.707107 1.22474i 0.0335578 0.0581238i
\(445\) 0.757359 1.31178i 0.0359023 0.0621846i
\(446\) 3.96447 + 6.86666i 0.187723 + 0.325146i
\(447\) 4.92893 0.233130
\(448\) 1.62132 2.09077i 0.0766002 0.0987796i
\(449\) 24.9706 1.17843 0.589217 0.807975i \(-0.299436\pi\)
0.589217 + 0.807975i \(0.299436\pi\)
\(450\) 2.32843 + 4.03295i 0.109763 + 0.190115i
\(451\) −2.05025 + 3.55114i −0.0965426 + 0.167217i
\(452\) −2.44975 + 4.24309i −0.115226 + 0.199578i
\(453\) 2.03553 + 3.52565i 0.0956377 + 0.165649i
\(454\) −21.1716 −0.993631
\(455\) 1.53553 + 0.210133i 0.0719869 + 0.00985119i
\(456\) 2.17157 0.101693
\(457\) 1.53553 + 2.65962i 0.0718292 + 0.124412i 0.899703 0.436503i \(-0.143783\pi\)
−0.827874 + 0.560914i \(0.810450\pi\)
\(458\) −13.2426 + 22.9369i −0.618788 + 1.07177i
\(459\) −1.20711 + 2.09077i −0.0563429 + 0.0975888i
\(460\) 0.414214 + 0.717439i 0.0193128 + 0.0334508i
\(461\) −4.48528 −0.208900 −0.104450 0.994530i \(-0.533308\pi\)
−0.104450 + 0.994530i \(0.533308\pi\)
\(462\) 0.414214 + 1.01461i 0.0192710 + 0.0472040i
\(463\) −20.9706 −0.974585 −0.487292 0.873239i \(-0.662015\pi\)
−0.487292 + 0.873239i \(0.662015\pi\)
\(464\) 0.914214 + 1.58346i 0.0424413 + 0.0735105i
\(465\) 2.48528 4.30463i 0.115252 0.199623i
\(466\) 8.86396 15.3528i 0.410615 0.711206i
\(467\) 5.70711 + 9.88500i 0.264093 + 0.457423i 0.967326 0.253537i \(-0.0815939\pi\)
−0.703232 + 0.710960i \(0.748261\pi\)
\(468\) 1.00000 0.0462250
\(469\) 1.82843 + 4.47871i 0.0844289 + 0.206808i
\(470\) −0.585786 −0.0270203
\(471\) 4.86396 + 8.42463i 0.224119 + 0.388186i
\(472\) −1.03553 + 1.79360i −0.0476643 + 0.0825570i
\(473\) 1.34315 2.32640i 0.0617579 0.106968i
\(474\) −5.82843 10.0951i −0.267709 0.463685i
\(475\) 10.1127 0.464002
\(476\) 6.32843 + 0.866025i 0.290063 + 0.0396942i
\(477\) 9.48528 0.434301
\(478\) −2.25736 3.90986i −0.103249 0.178833i
\(479\) 16.0563 27.8104i 0.733633 1.27069i −0.221687 0.975118i \(-0.571156\pi\)
0.955320 0.295572i \(-0.0955103\pi\)
\(480\) −0.292893 + 0.507306i −0.0133687 + 0.0231552i
\(481\) −0.707107 1.22474i −0.0322413 0.0558436i
\(482\) −2.14214 −0.0975716
\(483\) −2.29289 + 2.95680i −0.104330 + 0.134539i
\(484\) −10.8284 −0.492201
\(485\) −0.272078 0.471253i −0.0123544 0.0213985i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −8.10660 + 14.0410i −0.367345 + 0.636261i −0.989150 0.146912i \(-0.953067\pi\)
0.621804 + 0.783173i \(0.286400\pi\)
\(488\) 2.20711 + 3.82282i 0.0999110 + 0.173051i
\(489\) 18.6569 0.843692
\(490\) −3.94975 1.10165i −0.178431 0.0497676i
\(491\) 23.6569 1.06762 0.533809 0.845605i \(-0.320760\pi\)
0.533809 + 0.845605i \(0.320760\pi\)
\(492\) −4.94975 8.57321i −0.223152 0.386510i
\(493\) −2.20711 + 3.82282i −0.0994031 + 0.172171i
\(494\) 1.08579 1.88064i 0.0488518 0.0846139i
\(495\) −0.121320 0.210133i −0.00545294 0.00944478i
\(496\) −8.48528 −0.381000
\(497\) −8.10660 + 10.4539i −0.363631 + 0.468919i
\(498\) −7.65685 −0.343112
\(499\) −1.82843 3.16693i −0.0818516 0.141771i 0.822194 0.569208i \(-0.192750\pi\)
−0.904045 + 0.427437i \(0.859417\pi\)
\(500\) −2.82843 + 4.89898i −0.126491 + 0.219089i
\(501\) −0.328427 + 0.568852i −0.0146730 + 0.0254145i
\(502\) −12.4142 21.5020i −0.554073 0.959683i
\(503\) 26.1421 1.16562 0.582810 0.812608i \(-0.301953\pi\)
0.582810 + 0.812608i \(0.301953\pi\)
\(504\) −2.62132 0.358719i −0.116763 0.0159786i
\(505\) 8.68629 0.386535
\(506\) 0.292893 + 0.507306i 0.0130207 + 0.0225525i
\(507\) 0.500000 0.866025i 0.0222058 0.0384615i
\(508\) 3.94975 6.84116i 0.175242 0.303528i
\(509\) −5.31371 9.20361i −0.235526 0.407943i 0.723899 0.689906i \(-0.242348\pi\)
−0.959425 + 0.281963i \(0.909015\pi\)
\(510\) −1.41421 −0.0626224
\(511\) 1.41421 + 3.46410i 0.0625611 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) −1.08579 1.88064i −0.0479386 0.0830322i
\(514\) −13.2426 + 22.9369i −0.584108 + 1.01170i
\(515\) −4.92893 + 8.53716i −0.217195 + 0.376192i
\(516\) 3.24264 + 5.61642i 0.142749 + 0.247249i
\(517\) −0.414214 −0.0182171
\(518\) 1.41421 + 3.46410i 0.0621370 + 0.152204i
\(519\) −5.48528 −0.240777
\(520\) 0.292893 + 0.507306i 0.0128442 + 0.0222468i
\(521\) −20.3137 + 35.1844i −0.889960 + 1.54146i −0.0500384 + 0.998747i \(0.515934\pi\)
−0.839921 + 0.542708i \(0.817399\pi\)
\(522\) 0.914214 1.58346i 0.0400140 0.0693064i
\(523\) 8.41421 + 14.5738i 0.367928 + 0.637270i 0.989241 0.146292i \(-0.0467340\pi\)
−0.621314 + 0.783562i \(0.713401\pi\)
\(524\) −9.55635 −0.417471
\(525\) −12.2071 1.67050i −0.532762 0.0729068i
\(526\) 20.5858 0.897583
\(527\) −10.2426 17.7408i −0.446176 0.772800i
\(528\) −0.207107 + 0.358719i −0.00901317 + 0.0156113i
\(529\) 10.5000 18.1865i 0.456522 0.790719i
\(530\) 2.77817 + 4.81194i 0.120676 + 0.209017i
\(531\) 2.07107 0.0898767
\(532\) −3.52082 + 4.54026i −0.152647 + 0.196845i
\(533\) −9.89949 −0.428795
\(534\) 1.29289 + 2.23936i 0.0559490 + 0.0969064i
\(535\) −5.65685 + 9.79796i −0.244567 + 0.423603i
\(536\) −0.914214 + 1.58346i −0.0394880 + 0.0683952i
\(537\) 9.82843 + 17.0233i 0.424128 + 0.734611i
\(538\) −9.14214 −0.394145
\(539\) −2.79289 0.778985i −0.120298 0.0335533i
\(540\) 0.585786 0.0252082
\(541\) −11.5355 19.9801i −0.495951 0.859013i 0.504038 0.863682i \(-0.331847\pi\)
−0.999989 + 0.00466870i \(0.998514\pi\)
\(542\) −13.1066 + 22.7013i −0.562977 + 0.975104i
\(543\) 1.44975 2.51104i 0.0622146 0.107759i
\(544\) 1.20711 + 2.09077i 0.0517543 + 0.0896410i
\(545\) 5.65685 0.242313
\(546\) −1.62132 + 2.09077i −0.0693861 + 0.0894767i
\(547\) −30.8701 −1.31991 −0.659954 0.751306i \(-0.729424\pi\)
−0.659954 + 0.751306i \(0.729424\pi\)
\(548\) −5.53553 9.58783i −0.236466 0.409572i
\(549\) 2.20711 3.82282i 0.0941970 0.163154i
\(550\) −0.964466 + 1.67050i −0.0411250 + 0.0712305i
\(551\) −1.98528 3.43861i −0.0845758 0.146490i
\(552\) −1.41421 −0.0601929
\(553\) 30.5563 + 4.18154i 1.29939 + 0.177817i
\(554\) 18.0711 0.767766
\(555\) −0.414214 0.717439i −0.0175824 0.0304536i
\(556\) 6.53553 11.3199i 0.277168 0.480070i
\(557\) 16.3137 28.2562i 0.691234 1.19725i −0.280200 0.959942i \(-0.590401\pi\)
0.971434 0.237311i \(-0.0762660\pi\)
\(558\) 4.24264 + 7.34847i 0.179605 + 0.311086i
\(559\) 6.48528 0.274298
\(560\) −0.585786 1.43488i −0.0247540 0.0606347i
\(561\) −1.00000 −0.0422200
\(562\) −0.343146 0.594346i −0.0144747 0.0250710i
\(563\) 16.3848 28.3793i 0.690536 1.19604i −0.281126 0.959671i \(-0.590708\pi\)
0.971662 0.236373i \(-0.0759586\pi\)
\(564\) 0.500000 0.866025i 0.0210538 0.0364662i
\(565\) 1.43503 + 2.48554i 0.0603721 + 0.104568i
\(566\) −15.7574 −0.662331
\(567\) 1.00000 + 2.44949i 0.0419961 + 0.102869i
\(568\) −5.00000 −0.209795
\(569\) −11.8640 20.5490i −0.497363 0.861458i 0.502632 0.864500i \(-0.332365\pi\)
−0.999995 + 0.00304214i \(0.999032\pi\)
\(570\) 0.636039 1.10165i 0.0266407 0.0461431i
\(571\) 15.6569 27.1185i 0.655219 1.13487i −0.326620 0.945156i \(-0.605910\pi\)
0.981839 0.189717i \(-0.0607570\pi\)
\(572\) 0.207107 + 0.358719i 0.00865957 + 0.0149988i
\(573\) 10.3431 0.432091
\(574\) 25.9497 + 3.55114i 1.08312 + 0.148222i
\(575\) −6.58579 −0.274646
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −8.17157 + 14.1536i −0.340187 + 0.589221i −0.984467 0.175568i \(-0.943824\pi\)
0.644280 + 0.764790i \(0.277157\pi\)
\(578\) 5.58579 9.67487i 0.232338 0.402421i
\(579\) −1.46447 2.53653i −0.0608611 0.105415i
\(580\) 1.07107 0.0444737
\(581\) 12.4142 16.0087i 0.515028 0.664154i
\(582\) 0.928932 0.0385055
\(583\) 1.96447 + 3.40256i 0.0813599 + 0.140919i
\(584\) −0.707107 + 1.22474i −0.0292603 + 0.0506803i
\(585\) 0.292893 0.507306i 0.0121096 0.0209745i
\(586\) 4.94975 + 8.57321i 0.204472 + 0.354156i
\(587\) −1.58579 −0.0654524 −0.0327262 0.999464i \(-0.510419\pi\)
−0.0327262 + 0.999464i \(0.510419\pi\)
\(588\) 5.00000 4.89898i 0.206197 0.202031i
\(589\) 18.4264 0.759247
\(590\) 0.606602 + 1.05066i 0.0249734 + 0.0432552i
\(591\) −7.77817 + 13.4722i −0.319951 + 0.554172i
\(592\) −0.707107 + 1.22474i −0.0290619 + 0.0503367i
\(593\) 17.1924 + 29.7781i 0.706007 + 1.22284i 0.966327 + 0.257317i \(0.0828385\pi\)
−0.260320 + 0.965522i \(0.583828\pi\)
\(594\) 0.414214 0.0169954
\(595\) 2.29289 2.95680i 0.0939995 0.121217i
\(596\) −4.92893 −0.201897
\(597\) 1.36396 + 2.36245i 0.0558232 + 0.0966886i
\(598\) −0.707107 + 1.22474i −0.0289157 + 0.0500835i
\(599\) −0.778175 + 1.34784i −0.0317954 + 0.0550712i −0.881485 0.472212i \(-0.843456\pi\)
0.849690 + 0.527283i \(0.176789\pi\)
\(600\) −2.32843 4.03295i −0.0950576 0.164645i
\(601\) 1.20101 0.0489902 0.0244951 0.999700i \(-0.492202\pi\)
0.0244951 + 0.999700i \(0.492202\pi\)
\(602\) −17.0000 2.32640i −0.692868 0.0948169i
\(603\) 1.82843 0.0744593
\(604\) −2.03553 3.52565i −0.0828247 0.143457i
\(605\) −3.17157 + 5.49333i −0.128943 + 0.223335i
\(606\) −7.41421 + 12.8418i −0.301182 + 0.521662i
\(607\) −17.2635 29.9012i −0.700702 1.21365i −0.968220 0.250099i \(-0.919537\pi\)
0.267518 0.963553i \(-0.413796\pi\)
\(608\) −2.17157 −0.0880689
\(609\) 1.82843 + 4.47871i 0.0740916 + 0.181487i
\(610\) 2.58579 0.104695
\(611\) −0.500000 0.866025i −0.0202278 0.0350356i
\(612\) 1.20711 2.09077i 0.0487944 0.0845144i
\(613\) 3.89949 6.75412i 0.157499 0.272796i −0.776467 0.630158i \(-0.782990\pi\)
0.933966 + 0.357361i \(0.116324\pi\)
\(614\) 14.0563 + 24.3463i 0.567268 + 0.982537i
\(615\) −5.79899 −0.233838
\(616\) −0.414214 1.01461i −0.0166891 0.0408799i
\(617\) −24.1421 −0.971926 −0.485963 0.873979i \(-0.661531\pi\)
−0.485963 + 0.873979i \(0.661531\pi\)
\(618\) −8.41421 14.5738i −0.338469 0.586246i
\(619\) −10.4142 + 18.0379i −0.418583 + 0.725006i −0.995797 0.0915862i \(-0.970806\pi\)
0.577215 + 0.816593i \(0.304140\pi\)
\(620\) −2.48528 + 4.30463i −0.0998113 + 0.172878i
\(621\) 0.707107 + 1.22474i 0.0283752 + 0.0491473i
\(622\) −8.10051 −0.324801
\(623\) −6.77817 0.927572i −0.271562 0.0371624i
\(624\) −1.00000 −0.0400320
\(625\) −9.98528 17.2950i −0.399411 0.691801i
\(626\) −1.75736 + 3.04384i −0.0702382 + 0.121656i
\(627\) 0.449747 0.778985i 0.0179612 0.0311097i
\(628\) −4.86396 8.42463i −0.194093 0.336179i
\(629\) −3.41421 −0.136134
\(630\) −0.949747 + 1.22474i −0.0378388 + 0.0487950i
\(631\) 32.6274 1.29888 0.649438 0.760414i \(-0.275004\pi\)
0.649438 + 0.760414i \(0.275004\pi\)
\(632\) 5.82843 + 10.0951i 0.231842 + 0.401563i
\(633\) −6.46447 + 11.1968i −0.256939 + 0.445032i
\(634\) −14.8995 + 25.8067i −0.591735 + 1.02491i
\(635\) −2.31371 4.00746i −0.0918167 0.159031i
\(636\) −9.48528 −0.376116
\(637\) −1.74264 6.77962i −0.0690459 0.268618i
\(638\) 0.757359 0.0299841
\(639\) 2.50000 + 4.33013i 0.0988985 + 0.171297i
\(640\) 0.292893 0.507306i 0.0115776 0.0200530i
\(641\) −15.8995 + 27.5387i −0.627992 + 1.08771i 0.359962 + 0.932967i \(0.382790\pi\)
−0.987954 + 0.154748i \(0.950544\pi\)
\(642\) −9.65685 16.7262i −0.381126 0.660129i
\(643\) −2.51472 −0.0991708 −0.0495854 0.998770i \(-0.515790\pi\)
−0.0495854 + 0.998770i \(0.515790\pi\)
\(644\) 2.29289 2.95680i 0.0903527 0.116514i
\(645\) 3.79899 0.149585
\(646\) −2.62132 4.54026i −0.103134 0.178634i
\(647\) 4.51472 7.81972i 0.177492 0.307425i −0.763529 0.645774i \(-0.776535\pi\)
0.941021 + 0.338349i \(0.109868\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0.428932 + 0.742932i 0.0168371 + 0.0291626i
\(650\) −4.65685 −0.182657
\(651\) −22.2426 3.04384i −0.871758 0.119297i
\(652\) −18.6569 −0.730659
\(653\) −11.0711 19.1757i −0.433244 0.750401i 0.563906 0.825839i \(-0.309298\pi\)
−0.997151 + 0.0754376i \(0.975965\pi\)
\(654\) −4.82843 + 8.36308i −0.188806 + 0.327022i
\(655\) −2.79899 + 4.84799i −0.109366 + 0.189427i
\(656\) 4.94975 + 8.57321i 0.193255 + 0.334728i
\(657\) 1.41421 0.0551737
\(658\) 1.00000 + 2.44949i 0.0389841 + 0.0954911i
\(659\) 10.5858 0.412364 0.206182 0.978514i \(-0.433896\pi\)
0.206182 + 0.978514i \(0.433896\pi\)
\(660\) 0.121320 + 0.210133i 0.00472239 + 0.00817942i
\(661\) −20.1213 + 34.8511i −0.782629 + 1.35555i 0.147777 + 0.989021i \(0.452788\pi\)
−0.930405 + 0.366532i \(0.880545\pi\)
\(662\) 11.2426 19.4728i 0.436958 0.756833i
\(663\) −1.20711 2.09077i −0.0468801 0.0811988i
\(664\) 7.65685 0.297144
\(665\) 1.27208 + 3.11594i 0.0493291 + 0.120831i
\(666\) 1.41421 0.0547997
\(667\) 1.29289 + 2.23936i 0.0500610 + 0.0867082i
\(668\) 0.328427 0.568852i 0.0127072 0.0220096i
\(669\) −3.96447 + 6.86666i −0.153275 + 0.265480i
\(670\) 0.535534 + 0.927572i 0.0206895 + 0.0358352i
\(671\) 1.82843 0.0705856
\(672\) 2.62132 + 0.358719i 0.101120 + 0.0138379i
\(673\) 42.1421 1.62446 0.812230 0.583337i \(-0.198253\pi\)
0.812230 + 0.583337i \(0.198253\pi\)
\(674\) 10.1569 + 17.5922i 0.391227 + 0.677626i
\(675\) −2.32843 + 4.03295i −0.0896212 + 0.155228i
\(676\) −0.500000 + 0.866025i −0.0192308 + 0.0333087i
\(677\) −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i \(-0.259740\pi\)
−0.973392 + 0.229147i \(0.926406\pi\)
\(678\) −4.89949 −0.188164
\(679\) −1.50610 + 1.94218i −0.0577987 + 0.0745342i
\(680\) 1.41421 0.0542326
\(681\) −10.5858 18.3351i −0.405648 0.702603i
\(682\) −1.75736 + 3.04384i −0.0672928 + 0.116554i
\(683\) 7.07107 12.2474i 0.270567 0.468636i −0.698440 0.715668i \(-0.746122\pi\)
0.969007 + 0.247033i \(0.0794555\pi\)
\(684\) 1.08579 + 1.88064i 0.0415161 + 0.0719080i
\(685\) −6.48528 −0.247790
\(686\) 2.13604 + 18.3967i 0.0815543 + 0.702388i
\(687\) −26.4853 −1.01048
\(688\) −3.24264 5.61642i −0.123625 0.214124i
\(689\) −4.74264 + 8.21449i −0.180680 + 0.312947i
\(690\) −0.414214 + 0.717439i −0.0157688 + 0.0273124i
\(691\) 10.3284 + 17.8894i 0.392912 + 0.680543i 0.992832 0.119516i \(-0.0381344\pi\)
−0.599920 + 0.800060i \(0.704801\pi\)
\(692\) 5.48528 0.208519
\(693\) −0.671573 + 0.866025i −0.0255109 + 0.0328976i
\(694\) −8.72792 −0.331307
\(695\) −3.82843 6.63103i −0.145221 0.251529i
\(696\) −0.914214 + 1.58346i −0.0346532 + 0.0600211i
\(697\) −11.9497 + 20.6976i −0.452629 + 0.783976i
\(698\) 3.36396 + 5.82655i 0.127328 + 0.220538i
\(699\) 17.7279 0.670532
\(700\) 12.2071 + 1.67050i 0.461385 + 0.0631391i
\(701\) −29.1716 −1.10180 −0.550898 0.834573i \(-0.685715\pi\)
−0.550898 + 0.834573i \(0.685715\pi\)
\(702\) 0.500000 + 0.866025i 0.0188713 + 0.0326860i
\(703\) 1.53553 2.65962i 0.0579138 0.100310i
\(704\) 0.207107 0.358719i 0.00780563 0.0135197i
\(705\) −0.292893 0.507306i −0.0110310 0.0191062i
\(706\) 12.6274 0.475239
\(707\) −14.8284 36.3221i −0.557680 1.36603i
\(708\) −2.07107 −0.0778355
\(709\) 18.4350 + 31.9304i 0.692342 + 1.19917i 0.971069 + 0.238801i \(0.0767544\pi\)
−0.278726 + 0.960371i \(0.589912\pi\)
\(710\) −1.46447 + 2.53653i −0.0549604 + 0.0951943i
\(711\) 5.82843 10.0951i 0.218583 0.378597i
\(712\) −1.29289 2.23936i −0.0484532 0.0839234i
\(713\) −12.0000 −0.449404
\(714\) 2.41421 + 5.91359i 0.0903497 + 0.221311i
\(715\) 0.242641 0.00907425
\(716\) −9.82843 17.0233i −0.367306 0.636192i
\(717\) 2.25736 3.90986i 0.0843026 0.146016i
\(718\) 0.414214 0.717439i 0.0154583 0.0267746i
\(719\) −4.65685 8.06591i −0.173671 0.300808i 0.766029 0.642806i \(-0.222230\pi\)
−0.939701 + 0.341998i \(0.888896\pi\)
\(720\) −0.585786 −0.0218310
\(721\) 44.1127 + 6.03668i 1.64284 + 0.224818i
\(722\) −14.2843 −0.531606
\(723\) −1.07107 1.85514i −0.0398334 0.0689935i
\(724\) −1.44975 + 2.51104i −0.0538794 + 0.0933219i
\(725\) −4.25736 + 7.37396i −0.158114 + 0.273862i
\(726\) −5.41421 9.37769i −0.200940 0.348039i
\(727\) −50.4264 −1.87021 −0.935106 0.354368i \(-0.884696\pi\)
−0.935106 + 0.354368i \(0.884696\pi\)
\(728\) 1.62132 2.09077i 0.0600901 0.0774891i
\(729\) 1.00000 0.0370370
\(730\) 0.414214 + 0.717439i 0.0153307 + 0.0265536i
\(731\) 7.82843 13.5592i 0.289545 0.501506i
\(732\) −2.20711 + 3.82282i −0.0815770 + 0.141296i
\(733\) 14.2929 + 24.7560i 0.527920 + 0.914384i 0.999470 + 0.0325451i \(0.0103613\pi\)
−0.471550 + 0.881839i \(0.656305\pi\)
\(734\) 12.6274 0.466086
\(735\) −1.02082 3.97141i −0.0376533 0.146488i
\(736\) 1.41421 0.0521286
\(737\) 0.378680 + 0.655892i 0.0139488 + 0.0241601i
\(738\) 4.94975 8.57321i 0.182203 0.315584i
\(739\) 15.0000 25.9808i 0.551784 0.955718i −0.446362 0.894852i \(-0.647281\pi\)
0.998146 0.0608653i \(-0.0193860\pi\)
\(740\) 0.414214 + 0.717439i 0.0152268 + 0.0263736i
\(741\) 2.17157 0.0797747
\(742\) 15.3787 19.8315i 0.564569 0.728039i
\(743\) 12.1716 0.446532 0.223266 0.974758i \(-0.428328\pi\)
0.223266 + 0.974758i \(0.428328\pi\)
\(744\) −4.24264 7.34847i −0.155543 0.269408i
\(745\) −1.44365 + 2.50048i −0.0528913 + 0.0916104i
\(746\) 2.79289 4.83743i 0.102255 0.177111i
\(747\) −3.82843 6.63103i −0.140075 0.242617i
\(748\) 1.00000 0.0365636
\(749\) 50.6274 + 6.92820i 1.84989 + 0.253151i
\(750\) −5.65685 −0.206559
\(751\) 9.65685 + 16.7262i 0.352384 + 0.610346i 0.986667 0.162755i \(-0.0520379\pi\)
−0.634283 + 0.773101i \(0.718705\pi\)
\(752\) −0.500000 + 0.866025i −0.0182331 + 0.0315807i
\(753\) 12.4142 21.5020i 0.452399 0.783578i
\(754\) 0.914214 + 1.58346i 0.0332937 + 0.0576664i
\(755\) −2.38478 −0.0867909
\(756\) −1.00000 2.44949i −0.0363696 0.0890871i
\(757\) −30.7574 −1.11790 −0.558948 0.829203i \(-0.688795\pi\)
−0.558948 + 0.829203i \(0.688795\pi\)
\(758\) −9.31371 16.1318i −0.338289 0.585934i
\(759\) −0.292893 + 0.507306i −0.0106314 + 0.0184140i
\(760\) −0.636039 + 1.10165i −0.0230716 + 0.0399611i
\(761\) −21.5563 37.3367i −0.781417 1.35345i −0.931116 0.364722i \(-0.881164\pi\)
0.149699 0.988732i \(-0.452169\pi\)
\(762\) 7.89949 0.286169
\(763\) −9.65685 23.6544i −0.349602 0.856346i
\(764\) −10.3431 −0.374202
\(765\) −0.707107 1.22474i −0.0255655 0.0442807i
\(766\) −5.58579 + 9.67487i −0.201823 + 0.349567i
\(767\) −1.03553 + 1.79360i −0.0373910 + 0.0647630i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 9.89949 0.356985 0.178492 0.983941i \(-0.442878\pi\)
0.178492 + 0.983941i \(0.442878\pi\)
\(770\) −0.636039 0.0870399i −0.0229213 0.00313670i
\(771\) −26.4853 −0.953844
\(772\) 1.46447 + 2.53653i 0.0527073 + 0.0912917i
\(773\) −9.48528 + 16.4290i −0.341162 + 0.590910i −0.984649 0.174547i \(-0.944154\pi\)
0.643487 + 0.765457i \(0.277487\pi\)
\(774\) −3.24264 + 5.61642i −0.116554 + 0.201878i
\(775\) −19.7574 34.2208i −0.709705 1.22925i
\(776\) −0.928932 −0.0333467
\(777\) −2.29289 + 2.95680i −0.0822571 + 0.106074i
\(778\) −4.51472 −0.161861
\(779\) −10.7487 18.6174i −0.385113 0.667036i
\(780\) −0.292893 + 0.507306i −0.0104873 + 0.0181645i
\(781\) −1.03553 + 1.79360i −0.0370543 + 0.0641800i
\(782\) 1.70711 + 2.95680i 0.0610460 + 0.105735i
\(783\) 1.82843 0.0653427
\(784\) −5.00000 + 4.89898i −0.178571 + 0.174964i
\(785\) −5.69848 −0.203388
\(786\) −4.77817 8.27604i −0.170432 0.295197i
\(787\) 13.1569 22.7883i 0.468991 0.812317i −0.530380 0.847760i \(-0.677951\pi\)
0.999372 + 0.0354431i \(0.0112843\pi\)
\(788\) 7.77817 13.4722i 0.277086 0.479927i
\(789\) 10.2929 + 17.8278i 0.366437 + 0.634687i
\(790\) 6.82843 0.242945
\(791\) 7.94365 10.2437i 0.282444 0.364225i
\(792\) −0.414214 −0.0147184
\(793\) 2.20711 + 3.82282i 0.0783767 + 0.135752i
\(794\) 4.77817 8.27604i 0.169571 0.293706i
\(795\) −2.77817 + 4.81194i −0.0985317 + 0.170662i
\(796\) −1.36396 2.36245i −0.0483443 0.0837348i
\(797\) 34.3431 1.21650 0.608248 0.793747i \(-0.291872\pi\)
0.608248 + 0.793747i \(0.291872\pi\)
\(798\) −5.69239 0.778985i −0.201508 0.0275758i
\(799\) −2.41421 −0.0854087
\(800\) 2.32843 + 4.03295i 0.0823223 + 0.142586i
\(801\) −1.29289 + 2.23936i −0.0456821 + 0.0791238i
\(802\) −9.94975 + 17.2335i −0.351338 + 0.608535i
\(803\) 0.292893 + 0.507306i 0.0103360 + 0.0179024i
\(804\) −1.82843 −0.0644837
\(805\) −0.828427 2.02922i −0.0291982 0.0715207i
\(806\) −8.48528 −0.298881
\(807\) −4.57107 7.91732i −0.160909 0.278703i
\(808\) 7.41421 12.8418i 0.260831 0.451773i
\(809\) 8.79289 15.2297i 0.309142 0.535449i −0.669033 0.743233i \(-0.733292\pi\)
0.978175 + 0.207783i \(0.0666249\pi\)
\(810\) 0.292893 + 0.507306i 0.0102912 + 0.0178249i
\(811\) 55.4558 1.94732 0.973659 0.228009i \(-0.0732216\pi\)
0.973659 + 0.228009i \(0.0732216\pi\)
\(812\) −1.82843 4.47871i −0.0641652 0.157172i
\(813\) −26.2132 −0.919337
\(814\) 0.292893 + 0.507306i 0.0102659 + 0.0177811i
\(815\) −5.46447 + 9.46473i −0.191412 + 0.331535i
\(816\) −1.20711 + 2.09077i −0.0422572 + 0.0731916i
\(817\) 7.04163 + 12.1965i 0.246355 + 0.426700i
\(818\) 32.5858 1.13934
\(819\) −2.62132 0.358719i −0.0915963 0.0125347i
\(820\) 5.79899 0.202510
\(821\) −23.9497 41.4822i −0.835852 1.44774i −0.893335 0.449392i \(-0.851641\pi\)
0.0574829 0.998346i \(-0.481693\pi\)
\(822\) 5.53553 9.58783i 0.193074 0.334414i
\(823\) 21.9203 37.9671i 0.764094 1.32345i −0.176630 0.984277i \(-0.556520\pi\)
0.940724 0.339172i \(-0.110147\pi\)
\(824\) 8.41421 + 14.5738i 0.293123 + 0.507704i
\(825\) −1.92893 −0.0671568
\(826\) 3.35786 4.33013i 0.116835 0.150664i
\(827\) 46.3553 1.61193 0.805967 0.591961i \(-0.201646\pi\)
0.805967 + 0.591961i \(0.201646\pi\)
\(828\) −0.707107 1.22474i −0.0245737 0.0425628i
\(829\) 13.3492 23.1216i 0.463638 0.803045i −0.535501 0.844535i \(-0.679877\pi\)
0.999139 + 0.0414897i \(0.0132104\pi\)
\(830\) 2.24264 3.88437i 0.0778432 0.134828i
\(831\) 9.03553 + 15.6500i 0.313439 + 0.542893i
\(832\) 1.00000 0.0346688
\(833\) −16.2782 4.54026i −0.564005 0.157311i
\(834\) 13.0711 0.452614
\(835\) −0.192388 0.333226i −0.00665787 0.0115318i
\(836\) −0.449747 + 0.778985i −0.0155548 + 0.0269418i
\(837\) −4.24264 + 7.34847i −0.146647 + 0.254000i
\(838\) −13.7279 23.7775i −0.474223 0.821379i
\(839\) −31.8284 −1.09884 −0.549420 0.835547i \(-0.685151\pi\)
−0.549420 + 0.835547i \(0.685151\pi\)
\(840\) 0.949747 1.22474i 0.0327694 0.0422577i
\(841\) −25.6569 −0.884719
\(842\) −0.535534 0.927572i −0.0184557 0.0319662i
\(843\) 0.343146 0.594346i 0.0118186 0.0204704i
\(844\) 6.46447 11.1968i 0.222516 0.385409i
\(845\) 0.292893 + 0.507306i 0.0100758 + 0.0174519i
\(846\) 1.00000 0.0343807
\(847\) 28.3848 + 3.88437i 0.975312 + 0.133468i
\(848\) 9.48528 0.325726
\(849\) −7.87868 13.6463i −0.270396 0.468339i
\(850\) −5.62132 + 9.73641i −0.192810 + 0.333956i
\(851\) −1.00000 + 1.73205i −0.0342796 + 0.0593739i
\(852\) −2.50000 4.33013i −0.0856486 0.148348i
\(853\) 6.72792 0.230360 0.115180 0.993345i \(-0.463256\pi\)
0.115180 + 0.993345i \(0.463256\pi\)
\(854\) −4.41421 10.8126i −0.151051 0.369999i
\(855\) 1.27208 0.0435041
\(856\) 9.65685 + 16.7262i 0.330064 + 0.571688i
\(857\) −10.2782 + 17.8023i −0.351096 + 0.608116i −0.986442 0.164112i \(-0.947524\pi\)
0.635346 + 0.772228i \(0.280858\pi\)
\(858\) −0.207107 + 0.358719i −0.00707051 + 0.0122465i
\(859\) 5.89949 + 10.2182i 0.201288 + 0.348641i 0.948944 0.315445i \(-0.102154\pi\)
−0.747656 + 0.664087i \(0.768821\pi\)
\(860\) −3.79899 −0.129544
\(861\) 9.89949 + 24.2487i 0.337374 + 0.826394i
\(862\) 30.4853 1.03833
\(863\) −19.6569 34.0467i −0.669127 1.15896i −0.978149 0.207907i \(-0.933335\pi\)
0.309021 0.951055i \(-0.399998\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 1.60660 2.78272i 0.0546261 0.0946152i
\(866\) −14.9853 25.9553i −0.509221 0.881996i
\(867\) 11.1716 0.379407
\(868\) 22.2426 + 3.04384i 0.754964 + 0.103315i
\(869\) 4.82843 0.163793
\(870\) 0.535534 + 0.927572i 0.0181563 + 0.0314476i
\(871\) −0.914214 + 1.58346i −0.0309769 + 0.0536536i
\(872\) 4.82843 8.36308i 0.163511 0.283210i
\(873\) 0.464466 + 0.804479i 0.0157198 + 0.0272275i
\(874\) −3.07107 −0.103880
\(875\) 9.17157 11.8272i 0.310056 0.399832i
\(876\) −1.41421 −0.0477818
\(877\) 20.0208 + 34.6771i 0.676055 + 1.17096i 0.976159 + 0.217055i \(0.0696451\pi\)
−0.300104 + 0.953906i \(0.597022\pi\)
\(878\) −8.29289 + 14.3637i −0.279872 + 0.484752i
\(879\) −4.94975 + 8.57321i −0.166951 + 0.289167i
\(880\) −0.121320 0.210133i −0.00408971 0.00708358i
\(881\) 18.4853 0.622785 0.311392 0.950281i \(-0.399205\pi\)
0.311392 + 0.950281i \(0.399205\pi\)
\(882\) 6.74264 + 1.88064i 0.227037 + 0.0633244i
\(883\) −9.75736 −0.328361 −0.164181 0.986430i \(-0.552498\pi\)
−0.164181 + 0.986430i \(0.552498\pi\)
\(884\) 1.20711 + 2.09077i 0.0405994 + 0.0703202i
\(885\) −0.606602 + 1.05066i −0.0203907 + 0.0353177i
\(886\) 16.8492 29.1837i 0.566061 0.980447i
\(887\) −24.4558 42.3588i −0.821147 1.42227i −0.904829 0.425776i \(-0.860001\pi\)
0.0836819 0.996493i \(-0.473332\pi\)
\(888\) −1.41421 −0.0474579
\(889\) −12.8076 + 16.5160i −0.429554 + 0.553930i
\(890\) −1.51472 −0.0507735
\(891\) 0.207107 + 0.358719i 0.00693834 + 0.0120176i
\(892\) 3.96447 6.86666i 0.132740 0.229913i
\(893\) 1.08579 1.88064i 0.0363345 0.0629331i
\(894\) −2.46447 4.26858i −0.0824241 0.142763i
\(895\) −11.5147 −0.384895
\(896\) −2.62132 0.358719i −0.0875722 0.0119840i
\(897\) −1.41421 −0.0472192
\(898\) −12.4853 21.6251i −0.416639 0.721640i
\(899\) −7.75736 + 13.4361i −0.258722 + 0.448120i
\(900\) 2.32843 4.03295i 0.0776142 0.134432i
\(901\) 11.4497 + 19.8315i 0.381446 + 0.660685i
\(902\) 4.10051 0.136532
\(903\) −6.48528 15.8856i −0.215817 0.528641i
\(904\) 4.89949 0.162955
\(905\) 0.849242 + 1.47093i 0.0282298 + 0.0488954i
\(906\) 2.03553 3.52565i 0.0676261 0.117132i
\(907\) −27.1924 + 47.0986i −0.902908 + 1.56388i −0.0792080 + 0.996858i \(0.525239\pi\)
−0.823700 + 0.567025i \(0.808094\pi\)
\(908\) 10.5858 + 18.3351i 0.351302 + 0.608472i
\(909\) −14.8284 −0.491828
\(910\) −0.585786 1.43488i −0.0194186 0.0475657i
\(911\) −4.34315 −0.143895 −0.0719474 0.997408i \(-0.522921\pi\)
−0.0719474 + 0.997408i \(0.522921\pi\)
\(912\) −1.08579 1.88064i −0.0359540 0.0622741i
\(913\) 1.58579 2.74666i 0.0524819 0.0909013i
\(914\) 1.53553 2.65962i 0.0507909 0.0879725i
\(915\) 1.29289 + 2.23936i 0.0427417 + 0.0740309i
\(916\) 26.4853 0.875098
\(917\) 25.0503 + 3.42805i 0.827232 + 0.113204i
\(918\) 2.41421 0.0796809
\(919\) −0.899495 1.55797i −0.0296716 0.0513927i 0.850808 0.525476i \(-0.176113\pi\)
−0.880480 + 0.474083i \(0.842779\pi\)
\(920\) 0.414214 0.717439i 0.0136562 0.0236533i
\(921\) −14.0563 + 24.3463i −0.463172 + 0.802238i
\(922\) 2.24264 + 3.88437i 0.0738574 + 0.127925i
\(923\) −5.00000 −0.164577
\(924\) 0.671573 0.866025i 0.0220931 0.0284901i
\(925\) −6.58579 −0.216539
\(926\) 10.4853 + 18.1610i 0.344568 + 0.596809i
\(927\) 8.41421 14.5738i 0.276359 0.478668i
\(928\) 0.914214 1.58346i 0.0300105 0.0519798i
\(929\) −17.3431 30.0392i −0.569010 0.985554i −0.996664 0.0816120i \(-0.973993\pi\)
0.427654 0.903942i \(-0.359340\pi\)
\(930\) −4.97056 −0.162991
\(931\) 10.8579 10.6385i 0.355852 0.348662i
\(932\) −17.7279 −0.580697
\(933\) −4.05025 7.01524i −0.132599 0.229669i
\(934\) 5.70711 9.88500i 0.186742 0.323447i
\(935\) 0.292893 0.507306i 0.00957863 0.0165907i
\(936\) −0.500000 0.866025i −0.0163430 0.0283069i
\(937\) 42.6569 1.39354 0.696769 0.717295i \(-0.254620\pi\)
0.696769 + 0.717295i \(0.254620\pi\)
\(938\) 2.96447 3.82282i 0.0967932 0.124820i
\(939\) −3.51472 −0.114699
\(940\) 0.292893 + 0.507306i 0.00955312 + 0.0165465i
\(941\) 6.48528 11.2328i 0.211414 0.366180i −0.740743 0.671788i \(-0.765526\pi\)
0.952157 + 0.305608i \(0.0988598\pi\)
\(942\) 4.86396 8.42463i 0.158476 0.274489i
\(943\) 7.00000 + 12.1244i 0.227951 + 0.394823i
\(944\) 2.07107 0.0674075
\(945\) −1.53553 0.210133i −0.0499509 0.00683563i
\(946\) −2.68629 −0.0873389
\(947\) −4.20711 7.28692i −0.136713 0.236793i 0.789538 0.613702i \(-0.210320\pi\)
−0.926250 + 0.376909i \(0.876987\pi\)
\(948\) −5.82843 + 10.0951i −0.189299 + 0.327875i
\(949\) −0.707107 + 1.22474i −0.0229537 + 0.0397569i
\(950\) −5.05635 8.75785i −0.164050 0.284142i
\(951\) −29.7990 −0.966298
\(952\) −2.41421 5.91359i −0.0782451 0.191661i
\(953\) −41.5858 −1.34710 −0.673548 0.739144i \(-0.735230\pi\)
−0.673548 + 0.739144i \(0.735230\pi\)
\(954\) −4.74264 8.21449i −0.153549 0.265954i
\(955\) −3.02944 + 5.24714i −0.0980303 + 0.169793i
\(956\) −2.25736 + 3.90986i −0.0730082 + 0.126454i
\(957\) 0.378680 + 0.655892i 0.0122410 + 0.0212020i
\(958\) −32.1127 −1.03751
\(959\) 11.0711 + 27.1185i 0.357503 + 0.875701i
\(960\) 0.585786 0.0189062
\(961\) −20.5000 35.5070i −0.661290 1.14539i
\(962\) −0.707107 + 1.22474i −0.0227980 + 0.0394874i
\(963\) 9.65685 16.7262i 0.311188 0.538993i
\(964\) 1.07107 + 1.85514i 0.0344968 + 0.0597502i
\(965\) 1.71573 0.0552313
\(966\) 3.70711 + 0.507306i 0.119274 + 0.0163223i
\(967\) −13.5858 −0.436889 −0.218445 0.975849i \(-0.570098\pi\)
−0.218445 + 0.975849i \(0.570098\pi\)
\(968\) 5.41421 + 9.37769i 0.174019 + 0.301410i
\(969\) 2.62132 4.54026i 0.0842089 0.145854i
\(970\) −0.272078 + 0.471253i −0.00873590 + 0.0151310i
\(971\) 16.2635 + 28.1691i 0.521919 + 0.903990i 0.999675 + 0.0254978i \(0.00811707\pi\)
−0.477756 + 0.878493i \(0.658550\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −21.1924 + 27.3286i −0.679397 + 0.876115i
\(974\) 16.2132 0.519505
\(975\) −2.32843 4.03295i −0.0745693 0.129158i
\(976\) 2.20711 3.82282i 0.0706478 0.122366i
\(977\) −21.5858 + 37.3877i −0.690590 + 1.19614i 0.281054 + 0.959692i \(0.409316\pi\)
−0.971645 + 0.236446i \(0.924017\pi\)
\(978\) −9.32843 16.1573i −0.298290 0.516654i
\(979\) −1.07107 −0.0342315
\(980\) 1.02082 + 3.97141i 0.0326087 + 0.126862i
\(981\) −9.65685 −0.308320
\(982\) −11.8284 20.4874i −0.377460 0.653780i
\(983\) 14.7426 25.5350i 0.470217 0.814440i −0.529203 0.848495i \(-0.677509\pi\)
0.999420 + 0.0340553i \(0.0108422\pi\)
\(984\) −4.94975 + 8.57321i −0.157792 + 0.273304i
\(985\) −4.55635 7.89183i −0.145177 0.251455i
\(986\) 4.41421 0.140577
\(987\) −1.62132 + 2.09077i −0.0516072 + 0.0665500i
\(988\) −2.17157 −0.0690869
\(989\) −4.58579 7.94282i −0.145820 0.252567i
\(990\) −0.121320 + 0.210133i −0.00385581 + 0.00667847i
\(991\) 0.343146 0.594346i 0.0109004 0.0188800i −0.860524 0.509410i \(-0.829864\pi\)
0.871424 + 0.490530i \(0.163197\pi\)
\(992\) 4.24264 + 7.34847i 0.134704 + 0.233314i
\(993\) 22.4853 0.713549
\(994\) 13.1066 + 1.79360i 0.415716 + 0.0568895i
\(995\) −1.59798 −0.0506594
\(996\) 3.82843 + 6.63103i 0.121308 + 0.210112i
\(997\) −26.2487 + 45.4641i −0.831306 + 1.43986i 0.0656972 + 0.997840i \(0.479073\pi\)
−0.897003 + 0.442024i \(0.854260\pi\)
\(998\) −1.82843 + 3.16693i −0.0578778 + 0.100247i
\(999\) 0.707107 + 1.22474i 0.0223719 + 0.0387492i
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.i.i.235.1 yes 4
3.2 odd 2 1638.2.j.m.235.2 4
7.2 even 3 inner 546.2.i.i.79.1 4
7.3 odd 6 3822.2.a.bu.1.1 2
7.4 even 3 3822.2.a.bn.1.2 2
21.2 odd 6 1638.2.j.m.1171.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.i.i.79.1 4 7.2 even 3 inner
546.2.i.i.235.1 yes 4 1.1 even 1 trivial
1638.2.j.m.235.2 4 3.2 odd 2
1638.2.j.m.1171.2 4 21.2 odd 6
3822.2.a.bn.1.2 2 7.4 even 3
3822.2.a.bu.1.1 2 7.3 odd 6