Properties

Label 546.2.s.c.43.2
Level $546$
Weight $2$
Character 546.43
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(43,546)]
 
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, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.s (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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.43
Dual form 546.2.s.c.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.46410i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.46410i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.73205 - 3.00000i) q^{10} +(3.46410 + 2.00000i) q^{11} -1.00000 q^{12} +(2.59808 - 2.50000i) q^{13} -1.00000 q^{14} +(3.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.23205 + 5.59808i) q^{17} -1.00000i q^{18} +(6.46410 - 3.73205i) q^{19} +(3.00000 - 1.73205i) q^{20} -1.00000i q^{21} +(2.00000 + 3.46410i) q^{22} +(2.86603 - 4.96410i) q^{23} +(-0.866025 - 0.500000i) q^{24} -7.00000 q^{25} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(-4.00000 + 6.92820i) q^{29} +(1.73205 + 3.00000i) q^{30} -6.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.46410 + 2.00000i) q^{33} +6.46410i q^{34} +(1.73205 + 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.26795 - 2.46410i) q^{37} +7.46410 q^{38} +(0.866025 + 3.50000i) q^{39} +3.46410 q^{40} +(-6.00000 - 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.23205 + 3.86603i) q^{43} +4.00000i q^{44} +(-3.00000 + 1.73205i) q^{45} +(4.96410 - 2.86603i) q^{46} +0.535898i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-6.06218 - 3.50000i) q^{50} -6.46410 q^{51} +(3.46410 + 1.00000i) q^{52} -8.26795 q^{53} +(0.866025 + 0.500000i) q^{54} +(6.92820 - 12.0000i) q^{55} +(-0.500000 - 0.866025i) q^{56} +7.46410i q^{57} +(-6.92820 + 4.00000i) q^{58} +(-5.42820 + 3.13397i) q^{59} +3.46410i q^{60} +(2.59808 + 4.50000i) q^{61} +(3.23205 - 5.59808i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-8.66025 - 9.00000i) q^{65} -4.00000 q^{66} +(6.23205 + 3.59808i) q^{67} +(-3.23205 + 5.59808i) q^{68} +(2.86603 + 4.96410i) q^{69} +3.46410i q^{70} +(1.66987 - 0.964102i) q^{71} +(0.866025 - 0.500000i) q^{72} +10.9282i q^{73} +(-2.46410 - 4.26795i) q^{74} +(3.50000 - 6.06218i) q^{75} +(6.46410 + 3.73205i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -9.46410 q^{79} +(3.00000 + 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.46410 - 6.00000i) q^{82} +1.73205i q^{83} +(0.866025 - 0.500000i) q^{84} +(19.3923 - 11.1962i) q^{85} +4.46410i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(-10.1603 - 5.86603i) q^{89} -3.46410 q^{90} +(-1.00000 + 3.46410i) q^{91} +5.73205 q^{92} +(5.59808 + 3.23205i) q^{93} +(-0.267949 + 0.464102i) q^{94} +(-12.9282 - 22.3923i) q^{95} -1.00000i q^{96} +(10.7321 - 6.19615i) q^{97} +(0.866025 - 0.500000i) q^{98} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{12} - 4 q^{14} + 12 q^{15} - 2 q^{16} + 6 q^{17} + 12 q^{19} + 12 q^{20} + 8 q^{22} + 8 q^{23} - 28 q^{25} + 14 q^{26} + 4 q^{27} - 16 q^{29} + 2 q^{36} - 24 q^{37} + 16 q^{38} - 24 q^{41} + 2 q^{42} + 2 q^{43} - 12 q^{45} + 6 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{51} - 40 q^{53} - 2 q^{56} + 6 q^{59} + 6 q^{62} - 4 q^{64} - 16 q^{66} + 18 q^{67} - 6 q^{68} + 8 q^{69} + 24 q^{71} + 4 q^{74} + 14 q^{75} + 12 q^{76} - 16 q^{77} - 4 q^{78} - 24 q^{79} + 12 q^{80} - 2 q^{81} + 36 q^{85} - 16 q^{87} - 8 q^{88} - 6 q^{89} - 4 q^{91} + 16 q^{92} + 12 q^{93} - 8 q^{94} - 24 q^{95} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 3.46410i 1.54919i −0.632456 0.774597i \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.73205 3.00000i 0.547723 0.948683i
\(11\) 3.46410 + 2.00000i 1.04447 + 0.603023i 0.921095 0.389338i \(-0.127296\pi\)
0.123371 + 0.992361i \(0.460630\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.59808 2.50000i 0.720577 0.693375i
\(14\) −1.00000 −0.267261
\(15\) 3.00000 + 1.73205i 0.774597 + 0.447214i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.23205 + 5.59808i 0.783887 + 1.35773i 0.929661 + 0.368415i \(0.120099\pi\)
−0.145774 + 0.989318i \(0.546567\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.46410 3.73205i 1.48297 0.856191i 0.483154 0.875536i \(-0.339491\pi\)
0.999813 + 0.0193444i \(0.00615788\pi\)
\(20\) 3.00000 1.73205i 0.670820 0.387298i
\(21\) 1.00000i 0.218218i
\(22\) 2.00000 + 3.46410i 0.426401 + 0.738549i
\(23\) 2.86603 4.96410i 0.597608 1.03509i −0.395566 0.918438i \(-0.629451\pi\)
0.993173 0.116649i \(-0.0372153\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) −7.00000 −1.40000
\(26\) 3.50000 0.866025i 0.686406 0.169842i
\(27\) 1.00000 0.192450
\(28\) −0.866025 0.500000i −0.163663 0.0944911i
\(29\) −4.00000 + 6.92820i −0.742781 + 1.28654i 0.208443 + 0.978035i \(0.433160\pi\)
−0.951224 + 0.308500i \(0.900173\pi\)
\(30\) 1.73205 + 3.00000i 0.316228 + 0.547723i
\(31\) 6.46410i 1.16099i −0.814265 0.580493i \(-0.802860\pi\)
0.814265 0.580493i \(-0.197140\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −3.46410 + 2.00000i −0.603023 + 0.348155i
\(34\) 6.46410i 1.10858i
\(35\) 1.73205 + 3.00000i 0.292770 + 0.507093i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −4.26795 2.46410i −0.701647 0.405096i 0.106314 0.994333i \(-0.466095\pi\)
−0.807960 + 0.589237i \(0.799429\pi\)
\(38\) 7.46410 1.21084
\(39\) 0.866025 + 3.50000i 0.138675 + 0.560449i
\(40\) 3.46410 0.547723
\(41\) −6.00000 3.46410i −0.937043 0.541002i −0.0480106 0.998847i \(-0.515288\pi\)
−0.889032 + 0.457845i \(0.848621\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 2.23205 + 3.86603i 0.340385 + 0.589563i 0.984504 0.175361i \(-0.0561094\pi\)
−0.644120 + 0.764925i \(0.722776\pi\)
\(44\) 4.00000i 0.603023i
\(45\) −3.00000 + 1.73205i −0.447214 + 0.258199i
\(46\) 4.96410 2.86603i 0.731917 0.422572i
\(47\) 0.535898i 0.0781688i 0.999236 + 0.0390844i \(0.0124441\pi\)
−0.999236 + 0.0390844i \(0.987556\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −6.06218 3.50000i −0.857321 0.494975i
\(51\) −6.46410 −0.905155
\(52\) 3.46410 + 1.00000i 0.480384 + 0.138675i
\(53\) −8.26795 −1.13569 −0.567845 0.823135i \(-0.692223\pi\)
−0.567845 + 0.823135i \(0.692223\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 6.92820 12.0000i 0.934199 1.61808i
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 7.46410i 0.988644i
\(58\) −6.92820 + 4.00000i −0.909718 + 0.525226i
\(59\) −5.42820 + 3.13397i −0.706692 + 0.408009i −0.809835 0.586658i \(-0.800443\pi\)
0.103143 + 0.994667i \(0.467110\pi\)
\(60\) 3.46410i 0.447214i
\(61\) 2.59808 + 4.50000i 0.332650 + 0.576166i 0.983030 0.183442i \(-0.0587240\pi\)
−0.650381 + 0.759608i \(0.725391\pi\)
\(62\) 3.23205 5.59808i 0.410471 0.710956i
\(63\) 0.866025 + 0.500000i 0.109109 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) −8.66025 9.00000i −1.07417 1.11631i
\(66\) −4.00000 −0.492366
\(67\) 6.23205 + 3.59808i 0.761366 + 0.439575i 0.829786 0.558082i \(-0.188462\pi\)
−0.0684199 + 0.997657i \(0.521796\pi\)
\(68\) −3.23205 + 5.59808i −0.391944 + 0.678866i
\(69\) 2.86603 + 4.96410i 0.345029 + 0.597608i
\(70\) 3.46410i 0.414039i
\(71\) 1.66987 0.964102i 0.198177 0.114418i −0.397628 0.917547i \(-0.630166\pi\)
0.595805 + 0.803129i \(0.296833\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 10.9282i 1.27905i 0.768771 + 0.639525i \(0.220869\pi\)
−0.768771 + 0.639525i \(0.779131\pi\)
\(74\) −2.46410 4.26795i −0.286446 0.496139i
\(75\) 3.50000 6.06218i 0.404145 0.700000i
\(76\) 6.46410 + 3.73205i 0.741483 + 0.428096i
\(77\) −4.00000 −0.455842
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −9.46410 −1.06479 −0.532397 0.846495i \(-0.678709\pi\)
−0.532397 + 0.846495i \(0.678709\pi\)
\(80\) 3.00000 + 1.73205i 0.335410 + 0.193649i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.46410 6.00000i −0.382546 0.662589i
\(83\) 1.73205i 0.190117i 0.995472 + 0.0950586i \(0.0303039\pi\)
−0.995472 + 0.0950586i \(0.969696\pi\)
\(84\) 0.866025 0.500000i 0.0944911 0.0545545i
\(85\) 19.3923 11.1962i 2.10339 1.21439i
\(86\) 4.46410i 0.481376i
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) −10.1603 5.86603i −1.07698 0.621797i −0.146903 0.989151i \(-0.546931\pi\)
−0.930081 + 0.367353i \(0.880264\pi\)
\(90\) −3.46410 −0.365148
\(91\) −1.00000 + 3.46410i −0.104828 + 0.363137i
\(92\) 5.73205 0.597608
\(93\) 5.59808 + 3.23205i 0.580493 + 0.335148i
\(94\) −0.267949 + 0.464102i −0.0276368 + 0.0478684i
\(95\) −12.9282 22.3923i −1.32641 2.29740i
\(96\) 1.00000i 0.102062i
\(97\) 10.7321 6.19615i 1.08967 0.629124i 0.156185 0.987728i \(-0.450080\pi\)
0.933490 + 0.358604i \(0.116747\pi\)
\(98\) 0.866025 0.500000i 0.0874818 0.0505076i
\(99\) 4.00000i 0.402015i
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −5.59808 3.23205i −0.554292 0.320021i
\(103\) −10.6603 −1.05039 −0.525193 0.850983i \(-0.676007\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) −3.46410 −0.338062
\(106\) −7.16025 4.13397i −0.695465 0.401527i
\(107\) −4.26795 + 7.39230i −0.412598 + 0.714641i −0.995173 0.0981360i \(-0.968712\pi\)
0.582575 + 0.812777i \(0.302045\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 12.0000i 1.14939i −0.818367 0.574696i \(-0.805120\pi\)
0.818367 0.574696i \(-0.194880\pi\)
\(110\) 12.0000 6.92820i 1.14416 0.660578i
\(111\) 4.26795 2.46410i 0.405096 0.233882i
\(112\) 1.00000i 0.0944911i
\(113\) 2.19615 + 3.80385i 0.206597 + 0.357836i 0.950640 0.310295i \(-0.100428\pi\)
−0.744044 + 0.668131i \(0.767095\pi\)
\(114\) −3.73205 + 6.46410i −0.349539 + 0.605419i
\(115\) −17.1962 9.92820i −1.60355 0.925810i
\(116\) −8.00000 −0.742781
\(117\) −3.46410 1.00000i −0.320256 0.0924500i
\(118\) −6.26795 −0.577011
\(119\) −5.59808 3.23205i −0.513175 0.296282i
\(120\) −1.73205 + 3.00000i −0.158114 + 0.273861i
\(121\) 2.50000 + 4.33013i 0.227273 + 0.393648i
\(122\) 5.19615i 0.470438i
\(123\) 6.00000 3.46410i 0.541002 0.312348i
\(124\) 5.59808 3.23205i 0.502722 0.290247i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) 2.53590 4.39230i 0.225025 0.389754i −0.731302 0.682054i \(-0.761087\pi\)
0.956327 + 0.292300i \(0.0944204\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −4.46410 −0.393042
\(130\) −3.00000 12.1244i −0.263117 1.06338i
\(131\) 19.0000 1.66004 0.830019 0.557735i \(-0.188330\pi\)
0.830019 + 0.557735i \(0.188330\pi\)
\(132\) −3.46410 2.00000i −0.301511 0.174078i
\(133\) −3.73205 + 6.46410i −0.323610 + 0.560509i
\(134\) 3.59808 + 6.23205i 0.310826 + 0.538367i
\(135\) 3.46410i 0.298142i
\(136\) −5.59808 + 3.23205i −0.480031 + 0.277146i
\(137\) −12.0000 + 6.92820i −1.02523 + 0.591916i −0.915614 0.402058i \(-0.868295\pi\)
−0.109615 + 0.993974i \(0.534962\pi\)
\(138\) 5.73205i 0.487945i
\(139\) −1.46410 2.53590i −0.124183 0.215092i 0.797230 0.603676i \(-0.206298\pi\)
−0.921413 + 0.388584i \(0.872964\pi\)
\(140\) −1.73205 + 3.00000i −0.146385 + 0.253546i
\(141\) −0.464102 0.267949i −0.0390844 0.0225654i
\(142\) 1.92820 0.161811
\(143\) 14.0000 3.46410i 1.17074 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 24.0000 + 13.8564i 1.99309 + 1.15071i
\(146\) −5.46410 + 9.46410i −0.452212 + 0.783255i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 4.92820i 0.405096i
\(149\) −9.99038 + 5.76795i −0.818444 + 0.472529i −0.849880 0.526977i \(-0.823325\pi\)
0.0314357 + 0.999506i \(0.489992\pi\)
\(150\) 6.06218 3.50000i 0.494975 0.285774i
\(151\) 12.0000i 0.976546i 0.872691 + 0.488273i \(0.162373\pi\)
−0.872691 + 0.488273i \(0.837627\pi\)
\(152\) 3.73205 + 6.46410i 0.302709 + 0.524308i
\(153\) 3.23205 5.59808i 0.261296 0.452578i
\(154\) −3.46410 2.00000i −0.279145 0.161165i
\(155\) −22.3923 −1.79859
\(156\) −2.59808 + 2.50000i −0.208013 + 0.200160i
\(157\) −2.92820 −0.233696 −0.116848 0.993150i \(-0.537279\pi\)
−0.116848 + 0.993150i \(0.537279\pi\)
\(158\) −8.19615 4.73205i −0.652051 0.376462i
\(159\) 4.13397 7.16025i 0.327846 0.567845i
\(160\) 1.73205 + 3.00000i 0.136931 + 0.237171i
\(161\) 5.73205i 0.451749i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) 1.16025 0.669873i 0.0908781 0.0524685i −0.453872 0.891067i \(-0.649958\pi\)
0.544750 + 0.838598i \(0.316624\pi\)
\(164\) 6.92820i 0.541002i
\(165\) 6.92820 + 12.0000i 0.539360 + 0.934199i
\(166\) −0.866025 + 1.50000i −0.0672166 + 0.116423i
\(167\) 17.3205 + 10.0000i 1.34030 + 0.773823i 0.986851 0.161630i \(-0.0516752\pi\)
0.353450 + 0.935454i \(0.385009\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 22.3923 1.71741
\(171\) −6.46410 3.73205i −0.494322 0.285397i
\(172\) −2.23205 + 3.86603i −0.170192 + 0.294782i
\(173\) 0.535898 + 0.928203i 0.0407436 + 0.0705700i 0.885678 0.464300i \(-0.153694\pi\)
−0.844934 + 0.534870i \(0.820361\pi\)
\(174\) 8.00000i 0.606478i
\(175\) 6.06218 3.50000i 0.458258 0.264575i
\(176\) −3.46410 + 2.00000i −0.261116 + 0.150756i
\(177\) 6.26795i 0.471128i
\(178\) −5.86603 10.1603i −0.439677 0.761543i
\(179\) −8.46410 + 14.6603i −0.632637 + 1.09576i 0.354374 + 0.935104i \(0.384694\pi\)
−0.987011 + 0.160655i \(0.948639\pi\)
\(180\) −3.00000 1.73205i −0.223607 0.129099i
\(181\) −24.7846 −1.84223 −0.921113 0.389296i \(-0.872718\pi\)
−0.921113 + 0.389296i \(0.872718\pi\)
\(182\) −2.59808 + 2.50000i −0.192582 + 0.185312i
\(183\) −5.19615 −0.384111
\(184\) 4.96410 + 2.86603i 0.365958 + 0.211286i
\(185\) −8.53590 + 14.7846i −0.627572 + 1.08699i
\(186\) 3.23205 + 5.59808i 0.236985 + 0.410471i
\(187\) 25.8564i 1.89081i
\(188\) −0.464102 + 0.267949i −0.0338481 + 0.0195422i
\(189\) −0.866025 + 0.500000i −0.0629941 + 0.0363696i
\(190\) 25.8564i 1.87582i
\(191\) 13.2583 + 22.9641i 0.959339 + 1.66162i 0.724110 + 0.689684i \(0.242251\pi\)
0.235229 + 0.971940i \(0.424416\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 15.4641 + 8.92820i 1.11313 + 0.642666i 0.939638 0.342169i \(-0.111162\pi\)
0.173492 + 0.984835i \(0.444495\pi\)
\(194\) 12.3923 0.889716
\(195\) 12.1244 3.00000i 0.868243 0.214834i
\(196\) 1.00000 0.0714286
\(197\) 2.25833 + 1.30385i 0.160899 + 0.0928953i 0.578288 0.815833i \(-0.303721\pi\)
−0.417388 + 0.908728i \(0.637054\pi\)
\(198\) 2.00000 3.46410i 0.142134 0.246183i
\(199\) −11.0622 19.1603i −0.784177 1.35823i −0.929489 0.368849i \(-0.879752\pi\)
0.145312 0.989386i \(-0.453581\pi\)
\(200\) 7.00000i 0.494975i
\(201\) −6.23205 + 3.59808i −0.439575 + 0.253789i
\(202\) 0 0
\(203\) 8.00000i 0.561490i
\(204\) −3.23205 5.59808i −0.226289 0.391944i
\(205\) −12.0000 + 20.7846i −0.838116 + 1.45166i
\(206\) −9.23205 5.33013i −0.643227 0.371368i
\(207\) −5.73205 −0.398405
\(208\) 0.866025 + 3.50000i 0.0600481 + 0.242681i
\(209\) 29.8564 2.06521
\(210\) −3.00000 1.73205i −0.207020 0.119523i
\(211\) 4.53590 7.85641i 0.312264 0.540857i −0.666588 0.745426i \(-0.732246\pi\)
0.978852 + 0.204569i \(0.0655793\pi\)
\(212\) −4.13397 7.16025i −0.283923 0.491768i
\(213\) 1.92820i 0.132118i
\(214\) −7.39230 + 4.26795i −0.505328 + 0.291751i
\(215\) 13.3923 7.73205i 0.913348 0.527321i
\(216\) 1.00000i 0.0680414i
\(217\) 3.23205 + 5.59808i 0.219406 + 0.380022i
\(218\) 6.00000 10.3923i 0.406371 0.703856i
\(219\) −9.46410 5.46410i −0.639525 0.369230i
\(220\) 13.8564 0.934199
\(221\) 22.3923 + 6.46410i 1.50627 + 0.434823i
\(222\) 4.92820 0.330759
\(223\) −6.52628 3.76795i −0.437032 0.252321i 0.265306 0.964164i \(-0.414527\pi\)
−0.702338 + 0.711844i \(0.747860\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 3.50000 + 6.06218i 0.233333 + 0.404145i
\(226\) 4.39230i 0.292172i
\(227\) −11.5359 + 6.66025i −0.765664 + 0.442057i −0.831326 0.555785i \(-0.812418\pi\)
0.0656613 + 0.997842i \(0.479084\pi\)
\(228\) −6.46410 + 3.73205i −0.428096 + 0.247161i
\(229\) 19.9282i 1.31689i −0.752628 0.658446i \(-0.771214\pi\)
0.752628 0.658446i \(-0.228786\pi\)
\(230\) −9.92820 17.1962i −0.654646 1.13388i
\(231\) 2.00000 3.46410i 0.131590 0.227921i
\(232\) −6.92820 4.00000i −0.454859 0.262613i
\(233\) −13.4641 −0.882063 −0.441031 0.897492i \(-0.645387\pi\)
−0.441031 + 0.897492i \(0.645387\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) 1.85641 0.121099
\(236\) −5.42820 3.13397i −0.353346 0.204004i
\(237\) 4.73205 8.19615i 0.307380 0.532397i
\(238\) −3.23205 5.59808i −0.209503 0.362869i
\(239\) 12.8564i 0.831612i 0.909453 + 0.415806i \(0.136500\pi\)
−0.909453 + 0.415806i \(0.863500\pi\)
\(240\) −3.00000 + 1.73205i −0.193649 + 0.111803i
\(241\) 13.7321 7.92820i 0.884559 0.510700i 0.0124002 0.999923i \(-0.496053\pi\)
0.872159 + 0.489223i \(0.162719\pi\)
\(242\) 5.00000i 0.321412i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −2.59808 + 4.50000i −0.166325 + 0.288083i
\(245\) −3.00000 1.73205i −0.191663 0.110657i
\(246\) 6.92820 0.441726
\(247\) 7.46410 25.8564i 0.474929 1.64520i
\(248\) 6.46410 0.410471
\(249\) −1.50000 0.866025i −0.0950586 0.0548821i
\(250\) −3.46410 + 6.00000i −0.219089 + 0.379473i
\(251\) −5.03590 8.72243i −0.317863 0.550555i 0.662179 0.749346i \(-0.269632\pi\)
−0.980042 + 0.198791i \(0.936299\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 19.8564 11.4641i 1.24836 0.720742i
\(254\) 4.39230 2.53590i 0.275598 0.159116i
\(255\) 22.3923i 1.40226i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.232051 0.401924i 0.0144749 0.0250713i −0.858697 0.512483i \(-0.828726\pi\)
0.873172 + 0.487412i \(0.162059\pi\)
\(258\) −3.86603 2.23205i −0.240688 0.138961i
\(259\) 4.92820 0.306224
\(260\) 3.46410 12.0000i 0.214834 0.744208i
\(261\) 8.00000 0.495188
\(262\) 16.4545 + 9.50000i 1.01656 + 0.586912i
\(263\) 8.66025 15.0000i 0.534014 0.924940i −0.465196 0.885208i \(-0.654016\pi\)
0.999210 0.0397320i \(-0.0126504\pi\)
\(264\) −2.00000 3.46410i −0.123091 0.213201i
\(265\) 28.6410i 1.75940i
\(266\) −6.46410 + 3.73205i −0.396339 + 0.228827i
\(267\) 10.1603 5.86603i 0.621797 0.358995i
\(268\) 7.19615i 0.439575i
\(269\) −11.1962 19.3923i −0.682641 1.18237i −0.974172 0.225808i \(-0.927498\pi\)
0.291530 0.956562i \(-0.405836\pi\)
\(270\) 1.73205 3.00000i 0.105409 0.182574i
\(271\) 10.7942 + 6.23205i 0.655703 + 0.378570i 0.790638 0.612284i \(-0.209749\pi\)
−0.134935 + 0.990854i \(0.543083\pi\)
\(272\) −6.46410 −0.391944
\(273\) −2.50000 2.59808i −0.151307 0.157243i
\(274\) −13.8564 −0.837096
\(275\) −24.2487 14.0000i −1.46225 0.844232i
\(276\) −2.86603 + 4.96410i −0.172514 + 0.298804i
\(277\) 3.66025 + 6.33975i 0.219923 + 0.380918i 0.954784 0.297299i \(-0.0960859\pi\)
−0.734861 + 0.678218i \(0.762753\pi\)
\(278\) 2.92820i 0.175622i
\(279\) −5.59808 + 3.23205i −0.335148 + 0.193498i
\(280\) −3.00000 + 1.73205i −0.179284 + 0.103510i
\(281\) 2.39230i 0.142713i 0.997451 + 0.0713565i \(0.0227328\pi\)
−0.997451 + 0.0713565i \(0.977267\pi\)
\(282\) −0.267949 0.464102i −0.0159561 0.0276368i
\(283\) −5.73205 + 9.92820i −0.340735 + 0.590170i −0.984569 0.174994i \(-0.944009\pi\)
0.643834 + 0.765165i \(0.277343\pi\)
\(284\) 1.66987 + 0.964102i 0.0990887 + 0.0572089i
\(285\) 25.8564 1.53160
\(286\) 13.8564 + 4.00000i 0.819346 + 0.236525i
\(287\) 6.92820 0.408959
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) −12.3923 + 21.4641i −0.728959 + 1.26259i
\(290\) 13.8564 + 24.0000i 0.813676 + 1.40933i
\(291\) 12.3923i 0.726450i
\(292\) −9.46410 + 5.46410i −0.553845 + 0.319762i
\(293\) −28.9808 + 16.7321i −1.69307 + 0.977497i −0.741062 + 0.671437i \(0.765678\pi\)
−0.952012 + 0.306060i \(0.900989\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 10.8564 + 18.8038i 0.632084 + 1.09480i
\(296\) 2.46410 4.26795i 0.143223 0.248070i
\(297\) 3.46410 + 2.00000i 0.201008 + 0.116052i
\(298\) −11.5359 −0.668257
\(299\) −4.96410 20.0622i −0.287081 1.16023i
\(300\) 7.00000 0.404145
\(301\) −3.86603 2.23205i −0.222834 0.128653i
\(302\) −6.00000 + 10.3923i −0.345261 + 0.598010i
\(303\) 0 0
\(304\) 7.46410i 0.428096i
\(305\) 15.5885 9.00000i 0.892592 0.515339i
\(306\) 5.59808 3.23205i 0.320021 0.184764i
\(307\) 22.0000i 1.25561i 0.778372 + 0.627803i \(0.216046\pi\)
−0.778372 + 0.627803i \(0.783954\pi\)
\(308\) −2.00000 3.46410i −0.113961 0.197386i
\(309\) 5.33013 9.23205i 0.303220 0.525193i
\(310\) −19.3923 11.1962i −1.10141 0.635899i
\(311\) −13.3205 −0.755337 −0.377668 0.925941i \(-0.623274\pi\)
−0.377668 + 0.925941i \(0.623274\pi\)
\(312\) −3.50000 + 0.866025i −0.198148 + 0.0490290i
\(313\) 0.679492 0.0384072 0.0192036 0.999816i \(-0.493887\pi\)
0.0192036 + 0.999816i \(0.493887\pi\)
\(314\) −2.53590 1.46410i −0.143109 0.0826240i
\(315\) 1.73205 3.00000i 0.0975900 0.169031i
\(316\) −4.73205 8.19615i −0.266199 0.461070i
\(317\) 16.4641i 0.924716i 0.886693 + 0.462358i \(0.152997\pi\)
−0.886693 + 0.462358i \(0.847003\pi\)
\(318\) 7.16025 4.13397i 0.401527 0.231822i
\(319\) −27.7128 + 16.0000i −1.55162 + 0.895828i
\(320\) 3.46410i 0.193649i
\(321\) −4.26795 7.39230i −0.238214 0.412598i
\(322\) −2.86603 + 4.96410i −0.159717 + 0.276639i
\(323\) 41.7846 + 24.1244i 2.32496 + 1.34232i
\(324\) −1.00000 −0.0555556
\(325\) −18.1865 + 17.5000i −1.00881 + 0.970725i
\(326\) 1.33975 0.0742017
\(327\) 10.3923 + 6.00000i 0.574696 + 0.331801i
\(328\) 3.46410 6.00000i 0.191273 0.331295i
\(329\) −0.267949 0.464102i −0.0147725 0.0255868i
\(330\) 13.8564i 0.762770i
\(331\) 18.4641 10.6603i 1.01488 0.585941i 0.102262 0.994757i \(-0.467392\pi\)
0.912616 + 0.408817i \(0.134059\pi\)
\(332\) −1.50000 + 0.866025i −0.0823232 + 0.0475293i
\(333\) 4.92820i 0.270064i
\(334\) 10.0000 + 17.3205i 0.547176 + 0.947736i
\(335\) 12.4641 21.5885i 0.680987 1.17950i
\(336\) 0.866025 + 0.500000i 0.0472456 + 0.0272772i
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 6.92820 11.0000i 0.376845 0.598321i
\(339\) −4.39230 −0.238557
\(340\) 19.3923 + 11.1962i 1.05170 + 0.607197i
\(341\) 12.9282 22.3923i 0.700101 1.21261i
\(342\) −3.73205 6.46410i −0.201806 0.349539i
\(343\) 1.00000i 0.0539949i
\(344\) −3.86603 + 2.23205i −0.208442 + 0.120344i
\(345\) 17.1962 9.92820i 0.925810 0.534516i
\(346\) 1.07180i 0.0576202i
\(347\) −12.8564 22.2679i −0.690168 1.19541i −0.971783 0.235879i \(-0.924203\pi\)
0.281614 0.959528i \(-0.409130\pi\)
\(348\) 4.00000 6.92820i 0.214423 0.371391i
\(349\) −30.8660 17.8205i −1.65222 0.953910i −0.976157 0.217067i \(-0.930351\pi\)
−0.676064 0.736843i \(-0.736316\pi\)
\(350\) 7.00000 0.374166
\(351\) 2.59808 2.50000i 0.138675 0.133440i
\(352\) −4.00000 −0.213201
\(353\) 8.08846 + 4.66987i 0.430505 + 0.248552i 0.699562 0.714572i \(-0.253379\pi\)
−0.269057 + 0.963124i \(0.586712\pi\)
\(354\) 3.13397 5.42820i 0.166569 0.288506i
\(355\) −3.33975 5.78461i −0.177255 0.307015i
\(356\) 11.7321i 0.621797i
\(357\) 5.59808 3.23205i 0.296282 0.171058i
\(358\) −14.6603 + 8.46410i −0.774819 + 0.447342i
\(359\) 8.00000i 0.422224i 0.977462 + 0.211112i \(0.0677085\pi\)
−0.977462 + 0.211112i \(0.932292\pi\)
\(360\) −1.73205 3.00000i −0.0912871 0.158114i
\(361\) 18.3564 31.7942i 0.966127 1.67338i
\(362\) −21.4641 12.3923i −1.12813 0.651325i
\(363\) −5.00000 −0.262432
\(364\) −3.50000 + 0.866025i −0.183450 + 0.0453921i
\(365\) 37.8564 1.98149
\(366\) −4.50000 2.59808i −0.235219 0.135804i
\(367\) 16.5263 28.6244i 0.862665 1.49418i −0.00668260 0.999978i \(-0.502127\pi\)
0.869347 0.494202i \(-0.164540\pi\)
\(368\) 2.86603 + 4.96410i 0.149402 + 0.258772i
\(369\) 6.92820i 0.360668i
\(370\) −14.7846 + 8.53590i −0.768615 + 0.443760i
\(371\) 7.16025 4.13397i 0.371742 0.214625i
\(372\) 6.46410i 0.335148i
\(373\) 13.1244 + 22.7321i 0.679553 + 1.17702i 0.975116 + 0.221697i \(0.0711597\pi\)
−0.295562 + 0.955324i \(0.595507\pi\)
\(374\) −12.9282 + 22.3923i −0.668501 + 1.15788i
\(375\) −6.00000 3.46410i −0.309839 0.178885i
\(376\) −0.535898 −0.0276368
\(377\) 6.92820 + 28.0000i 0.356821 + 1.44207i
\(378\) −1.00000 −0.0514344
\(379\) −8.32051 4.80385i −0.427396 0.246757i 0.270841 0.962624i \(-0.412698\pi\)
−0.698237 + 0.715867i \(0.746032\pi\)
\(380\) 12.9282 22.3923i 0.663203 1.14870i
\(381\) 2.53590 + 4.39230i 0.129918 + 0.225025i
\(382\) 26.5167i 1.35671i
\(383\) 6.33975 3.66025i 0.323946 0.187030i −0.329204 0.944259i \(-0.606780\pi\)
0.653150 + 0.757229i \(0.273447\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 13.8564i 0.706188i
\(386\) 8.92820 + 15.4641i 0.454434 + 0.787102i
\(387\) 2.23205 3.86603i 0.113462 0.196521i
\(388\) 10.7321 + 6.19615i 0.544837 + 0.314562i
\(389\) 14.6603 0.743304 0.371652 0.928372i \(-0.378791\pi\)
0.371652 + 0.928372i \(0.378791\pi\)
\(390\) 12.0000 + 3.46410i 0.607644 + 0.175412i
\(391\) 37.0526 1.87383
\(392\) 0.866025 + 0.500000i 0.0437409 + 0.0252538i
\(393\) −9.50000 + 16.4545i −0.479212 + 0.830019i
\(394\) 1.30385 + 2.25833i 0.0656869 + 0.113773i
\(395\) 32.7846i 1.64957i
\(396\) 3.46410 2.00000i 0.174078 0.100504i
\(397\) −25.7942 + 14.8923i −1.29458 + 0.747423i −0.979462 0.201631i \(-0.935376\pi\)
−0.315114 + 0.949054i \(0.602043\pi\)
\(398\) 22.1244i 1.10899i
\(399\) −3.73205 6.46410i −0.186836 0.323610i
\(400\) 3.50000 6.06218i 0.175000 0.303109i
\(401\) −14.1962 8.19615i −0.708922 0.409296i 0.101740 0.994811i \(-0.467559\pi\)
−0.810662 + 0.585515i \(0.800892\pi\)
\(402\) −7.19615 −0.358911
\(403\) −16.1603 16.7942i −0.805000 0.836580i
\(404\) 0 0
\(405\) 3.00000 + 1.73205i 0.149071 + 0.0860663i
\(406\) 4.00000 6.92820i 0.198517 0.343841i
\(407\) −9.85641 17.0718i −0.488564 0.846218i
\(408\) 6.46410i 0.320021i
\(409\) 5.53590 3.19615i 0.273733 0.158040i −0.356850 0.934162i \(-0.616149\pi\)
0.630583 + 0.776122i \(0.282816\pi\)
\(410\) −20.7846 + 12.0000i −1.02648 + 0.592638i
\(411\) 13.8564i 0.683486i
\(412\) −5.33013 9.23205i −0.262597 0.454830i
\(413\) 3.13397 5.42820i 0.154213 0.267104i
\(414\) −4.96410 2.86603i −0.243972 0.140857i
\(415\) 6.00000 0.294528
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) 2.92820 0.143395
\(418\) 25.8564 + 14.9282i 1.26468 + 0.730162i
\(419\) 2.50000 4.33013i 0.122133 0.211541i −0.798476 0.602027i \(-0.794360\pi\)
0.920609 + 0.390487i \(0.127693\pi\)
\(420\) −1.73205 3.00000i −0.0845154 0.146385i
\(421\) 1.60770i 0.0783543i −0.999232 0.0391771i \(-0.987526\pi\)
0.999232 0.0391771i \(-0.0124737\pi\)
\(422\) 7.85641 4.53590i 0.382444 0.220804i
\(423\) 0.464102 0.267949i 0.0225654 0.0130281i
\(424\) 8.26795i 0.401527i
\(425\) −22.6244 39.1865i −1.09744 1.90083i
\(426\) −0.964102 + 1.66987i −0.0467109 + 0.0809056i
\(427\) −4.50000 2.59808i −0.217770 0.125730i
\(428\) −8.53590 −0.412598
\(429\) −4.00000 + 13.8564i −0.193122 + 0.668994i
\(430\) 15.4641 0.745745
\(431\) 4.20577 + 2.42820i 0.202585 + 0.116962i 0.597861 0.801600i \(-0.296018\pi\)
−0.395276 + 0.918563i \(0.629351\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 4.92820 + 8.53590i 0.236834 + 0.410209i 0.959804 0.280670i \(-0.0905568\pi\)
−0.722970 + 0.690880i \(0.757223\pi\)
\(434\) 6.46410i 0.310287i
\(435\) −24.0000 + 13.8564i −1.15071 + 0.664364i
\(436\) 10.3923 6.00000i 0.497701 0.287348i
\(437\) 42.7846i 2.04667i
\(438\) −5.46410 9.46410i −0.261085 0.452212i
\(439\) −6.80385 + 11.7846i −0.324730 + 0.562449i −0.981458 0.191679i \(-0.938607\pi\)
0.656728 + 0.754128i \(0.271940\pi\)
\(440\) 12.0000 + 6.92820i 0.572078 + 0.330289i
\(441\) −1.00000 −0.0476190
\(442\) 16.1603 + 16.7942i 0.768665 + 0.798820i
\(443\) −22.3923 −1.06389 −0.531945 0.846779i \(-0.678539\pi\)
−0.531945 + 0.846779i \(0.678539\pi\)
\(444\) 4.26795 + 2.46410i 0.202548 + 0.116941i
\(445\) −20.3205 + 35.1962i −0.963284 + 1.66846i
\(446\) −3.76795 6.52628i −0.178418 0.309028i
\(447\) 11.5359i 0.545629i
\(448\) 0.866025 0.500000i 0.0409159 0.0236228i
\(449\) 15.5885 9.00000i 0.735665 0.424736i −0.0848262 0.996396i \(-0.527033\pi\)
0.820491 + 0.571660i \(0.193700\pi\)
\(450\) 7.00000i 0.329983i
\(451\) −13.8564 24.0000i −0.652473 1.13012i
\(452\) −2.19615 + 3.80385i −0.103298 + 0.178918i
\(453\) −10.3923 6.00000i −0.488273 0.281905i
\(454\) −13.3205 −0.625162
\(455\) 12.0000 + 3.46410i 0.562569 + 0.162400i
\(456\) −7.46410 −0.349539
\(457\) 1.03590 + 0.598076i 0.0484573 + 0.0279768i 0.524033 0.851698i \(-0.324427\pi\)
−0.475576 + 0.879675i \(0.657760\pi\)
\(458\) 9.96410 17.2583i 0.465592 0.806429i
\(459\) 3.23205 + 5.59808i 0.150859 + 0.261296i
\(460\) 19.8564i 0.925810i
\(461\) −4.39230 + 2.53590i −0.204570 + 0.118109i −0.598785 0.800910i \(-0.704350\pi\)
0.394215 + 0.919018i \(0.371016\pi\)
\(462\) 3.46410 2.00000i 0.161165 0.0930484i
\(463\) 8.24871i 0.383350i −0.981458 0.191675i \(-0.938608\pi\)
0.981458 0.191675i \(-0.0613920\pi\)
\(464\) −4.00000 6.92820i −0.185695 0.321634i
\(465\) 11.1962 19.3923i 0.519209 0.899297i
\(466\) −11.6603 6.73205i −0.540151 0.311856i
\(467\) 39.6410 1.83437 0.917184 0.398465i \(-0.130457\pi\)
0.917184 + 0.398465i \(0.130457\pi\)
\(468\) −0.866025 3.50000i −0.0400320 0.161788i
\(469\) −7.19615 −0.332287
\(470\) 1.60770 + 0.928203i 0.0741574 + 0.0428148i
\(471\) 1.46410 2.53590i 0.0674622 0.116848i
\(472\) −3.13397 5.42820i −0.144253 0.249853i
\(473\) 17.8564i 0.821038i
\(474\) 8.19615 4.73205i 0.376462 0.217350i
\(475\) −45.2487 + 26.1244i −2.07615 + 1.19867i
\(476\) 6.46410i 0.296282i
\(477\) 4.13397 + 7.16025i 0.189282 + 0.327846i
\(478\) −6.42820 + 11.1340i −0.294019 + 0.509256i
\(479\) −3.80385 2.19615i −0.173802 0.100345i 0.410575 0.911827i \(-0.365328\pi\)
−0.584377 + 0.811482i \(0.698661\pi\)
\(480\) −3.46410 −0.158114
\(481\) −17.2487 + 4.26795i −0.786474 + 0.194602i
\(482\) 15.8564 0.722240
\(483\) −4.96410 2.86603i −0.225874 0.130409i
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) −21.4641 37.1769i −0.974635 1.68812i
\(486\) 1.00000i 0.0453609i
\(487\) 0.339746 0.196152i 0.0153954 0.00888851i −0.492283 0.870435i \(-0.663837\pi\)
0.507678 + 0.861547i \(0.330504\pi\)
\(488\) −4.50000 + 2.59808i −0.203705 + 0.117609i
\(489\) 1.33975i 0.0605854i
\(490\) −1.73205 3.00000i −0.0782461 0.135526i
\(491\) −4.92820 + 8.53590i −0.222407 + 0.385220i −0.955538 0.294867i \(-0.904725\pi\)
0.733132 + 0.680087i \(0.238058\pi\)
\(492\) 6.00000 + 3.46410i 0.270501 + 0.156174i
\(493\) −51.7128 −2.32903
\(494\) 19.3923 18.6603i 0.872501 0.839565i
\(495\) −13.8564 −0.622799
\(496\) 5.59808 + 3.23205i 0.251361 + 0.145123i
\(497\) −0.964102 + 1.66987i −0.0432459 + 0.0749040i
\(498\) −0.866025 1.50000i −0.0388075 0.0672166i
\(499\) 0.267949i 0.0119951i −0.999982 0.00599753i \(-0.998091\pi\)
0.999982 0.00599753i \(-0.00190908\pi\)
\(500\) −6.00000 + 3.46410i −0.268328 + 0.154919i
\(501\) −17.3205 + 10.0000i −0.773823 + 0.446767i
\(502\) 10.0718i 0.449526i
\(503\) 3.46410 + 6.00000i 0.154457 + 0.267527i 0.932861 0.360236i \(-0.117304\pi\)
−0.778404 + 0.627763i \(0.783971\pi\)
\(504\) −0.500000 + 0.866025i −0.0222718 + 0.0385758i
\(505\) 0 0
\(506\) 22.9282 1.01928
\(507\) 11.0000 + 6.92820i 0.488527 + 0.307692i
\(508\) 5.07180 0.225025
\(509\) −29.6603 17.1244i −1.31467 0.759024i −0.331802 0.943349i \(-0.607657\pi\)
−0.982865 + 0.184325i \(0.940990\pi\)
\(510\) −11.1962 + 19.3923i −0.495774 + 0.858706i
\(511\) −5.46410 9.46410i −0.241718 0.418667i
\(512\) 1.00000i 0.0441942i
\(513\) 6.46410 3.73205i 0.285397 0.164774i
\(514\) 0.401924 0.232051i 0.0177281 0.0102353i
\(515\) 36.9282i 1.62725i
\(516\) −2.23205 3.86603i −0.0982606 0.170192i
\(517\) −1.07180 + 1.85641i −0.0471376 + 0.0816447i
\(518\) 4.26795 + 2.46410i 0.187523 + 0.108266i
\(519\) −1.07180 −0.0470467
\(520\) 9.00000 8.66025i 0.394676 0.379777i
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 6.92820 + 4.00000i 0.303239 + 0.175075i
\(523\) −7.46410 + 12.9282i −0.326382 + 0.565311i −0.981791 0.189963i \(-0.939163\pi\)
0.655409 + 0.755274i \(0.272496\pi\)
\(524\) 9.50000 + 16.4545i 0.415009 + 0.718817i
\(525\) 7.00000i 0.305505i
\(526\) 15.0000 8.66025i 0.654031 0.377605i
\(527\) 36.1865 20.8923i 1.57631 0.910083i
\(528\) 4.00000i 0.174078i
\(529\) −4.92820 8.53590i −0.214270 0.371126i
\(530\) −14.3205 + 24.8038i −0.622043 + 1.07741i
\(531\) 5.42820 + 3.13397i 0.235564 + 0.136003i
\(532\) −7.46410 −0.323610
\(533\) −24.2487 + 6.00000i −1.05033 + 0.259889i
\(534\) 11.7321 0.507695
\(535\) 25.6077 + 14.7846i 1.10712 + 0.639194i
\(536\) −3.59808 + 6.23205i −0.155413 + 0.269184i
\(537\) −8.46410 14.6603i −0.365253 0.632637i
\(538\) 22.3923i 0.965401i
\(539\) 3.46410 2.00000i 0.149209 0.0861461i
\(540\) 3.00000 1.73205i 0.129099 0.0745356i
\(541\) 17.3205i 0.744667i 0.928099 + 0.372333i \(0.121442\pi\)
−0.928099 + 0.372333i \(0.878558\pi\)
\(542\) 6.23205 + 10.7942i 0.267690 + 0.463652i
\(543\) 12.3923 21.4641i 0.531805 0.921113i
\(544\) −5.59808 3.23205i −0.240016 0.138573i
\(545\) −41.5692 −1.78063
\(546\) −0.866025 3.50000i −0.0370625 0.149786i
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −12.0000 6.92820i −0.512615 0.295958i
\(549\) 2.59808 4.50000i 0.110883 0.192055i
\(550\) −14.0000 24.2487i −0.596962 1.03397i
\(551\) 59.7128i 2.54385i
\(552\) −4.96410 + 2.86603i −0.211286 + 0.121986i
\(553\) 8.19615 4.73205i 0.348536 0.201227i
\(554\) 7.32051i 0.311019i
\(555\) −8.53590 14.7846i −0.362329 0.627572i
\(556\) 1.46410 2.53590i 0.0620917 0.107546i
\(557\) 21.3109 + 12.3038i 0.902971 + 0.521331i 0.878163 0.478361i \(-0.158769\pi\)
0.0248083 + 0.999692i \(0.492102\pi\)
\(558\) −6.46410 −0.273647
\(559\) 15.4641 + 4.46410i 0.654062 + 0.188811i
\(560\) −3.46410 −0.146385
\(561\) −22.3923 12.9282i −0.945404 0.545829i
\(562\) −1.19615 + 2.07180i −0.0504566 + 0.0873935i
\(563\) −6.92820 12.0000i −0.291989 0.505740i 0.682291 0.731081i \(-0.260984\pi\)
−0.974280 + 0.225341i \(0.927650\pi\)
\(564\) 0.535898i 0.0225654i
\(565\) 13.1769 7.60770i 0.554357 0.320058i
\(566\) −9.92820 + 5.73205i −0.417314 + 0.240936i
\(567\) 1.00000i 0.0419961i
\(568\) 0.964102 + 1.66987i 0.0404528 + 0.0700663i
\(569\) 7.73205 13.3923i 0.324144 0.561435i −0.657194 0.753721i \(-0.728257\pi\)
0.981339 + 0.192286i \(0.0615903\pi\)
\(570\) 22.3923 + 12.9282i 0.937910 + 0.541503i
\(571\) 3.39230 0.141964 0.0709818 0.997478i \(-0.477387\pi\)
0.0709818 + 0.997478i \(0.477387\pi\)
\(572\) 10.0000 + 10.3923i 0.418121 + 0.434524i
\(573\) −26.5167 −1.10775
\(574\) 6.00000 + 3.46410i 0.250435 + 0.144589i
\(575\) −20.0622 + 34.7487i −0.836651 + 1.44912i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 1.21539i 0.0505974i 0.999680 + 0.0252987i \(0.00805368\pi\)
−0.999680 + 0.0252987i \(0.991946\pi\)
\(578\) −21.4641 + 12.3923i −0.892789 + 0.515452i
\(579\) −15.4641 + 8.92820i −0.642666 + 0.371043i
\(580\) 27.7128i 1.15071i
\(581\) −0.866025 1.50000i −0.0359288 0.0622305i
\(582\) −6.19615 + 10.7321i −0.256839 + 0.444858i
\(583\) −28.6410 16.5359i −1.18619 0.684847i
\(584\) −10.9282 −0.452212
\(585\) −3.46410 + 12.0000i −0.143223 + 0.496139i
\(586\) −33.4641 −1.38239
\(587\) 7.03590 + 4.06218i 0.290403 + 0.167664i 0.638123 0.769934i \(-0.279711\pi\)
−0.347721 + 0.937598i \(0.613044\pi\)
\(588\) −0.500000 + 0.866025i −0.0206197 + 0.0357143i
\(589\) −24.1244 41.7846i −0.994027 1.72170i
\(590\) 21.7128i 0.893902i
\(591\) −2.25833 + 1.30385i −0.0928953 + 0.0536331i
\(592\) 4.26795 2.46410i 0.175412 0.101274i
\(593\) 4.26795i 0.175264i −0.996153 0.0876318i \(-0.972070\pi\)
0.996153 0.0876318i \(-0.0279299\pi\)
\(594\) 2.00000 + 3.46410i 0.0820610 + 0.142134i
\(595\) −11.1962 + 19.3923i −0.458997 + 0.795007i
\(596\) −9.99038 5.76795i −0.409222 0.236264i
\(597\) 22.1244 0.905490
\(598\) 5.73205 19.8564i 0.234401 0.811989i
\(599\) −19.0526 −0.778466 −0.389233 0.921139i \(-0.627260\pi\)
−0.389233 + 0.921139i \(0.627260\pi\)
\(600\) 6.06218 + 3.50000i 0.247487 + 0.142887i
\(601\) 12.1244 21.0000i 0.494563 0.856608i −0.505418 0.862875i \(-0.668662\pi\)
0.999980 + 0.00626702i \(0.00199487\pi\)
\(602\) −2.23205 3.86603i −0.0909716 0.157567i
\(603\) 7.19615i 0.293050i
\(604\) −10.3923 + 6.00000i −0.422857 + 0.244137i
\(605\) 15.0000 8.66025i 0.609837 0.352089i
\(606\) 0 0
\(607\) 7.59808 + 13.1603i 0.308396 + 0.534158i 0.978012 0.208550i \(-0.0668744\pi\)
−0.669615 + 0.742708i \(0.733541\pi\)
\(608\) −3.73205 + 6.46410i −0.151355 + 0.262154i
\(609\) 6.92820 + 4.00000i 0.280745 + 0.162088i
\(610\) 18.0000 0.728799
\(611\) 1.33975 + 1.39230i 0.0542003 + 0.0563266i
\(612\) 6.46410 0.261296
\(613\) 29.7846 + 17.1962i 1.20299 + 0.694546i 0.961219 0.275787i \(-0.0889386\pi\)
0.241770 + 0.970333i \(0.422272\pi\)
\(614\) −11.0000 + 19.0526i −0.443924 + 0.768899i
\(615\) −12.0000 20.7846i −0.483887 0.838116i
\(616\) 4.00000i 0.161165i
\(617\) −5.07180 + 2.92820i −0.204183 + 0.117885i −0.598605 0.801044i \(-0.704278\pi\)
0.394422 + 0.918929i \(0.370945\pi\)
\(618\) 9.23205 5.33013i 0.371368 0.214409i
\(619\) 30.7846i 1.23734i −0.785652 0.618669i \(-0.787672\pi\)
0.785652 0.618669i \(-0.212328\pi\)
\(620\) −11.1962 19.3923i −0.449648 0.778814i
\(621\) 2.86603 4.96410i 0.115010 0.199203i
\(622\) −11.5359 6.66025i −0.462547 0.267052i
\(623\) 11.7321 0.470035
\(624\) −3.46410 1.00000i −0.138675 0.0400320i
\(625\) −11.0000 −0.440000
\(626\) 0.588457 + 0.339746i 0.0235195 + 0.0135790i
\(627\) −14.9282 + 25.8564i −0.596175 + 1.03261i
\(628\) −1.46410 2.53590i −0.0584240 0.101193i
\(629\) 31.8564i 1.27020i
\(630\) 3.00000 1.73205i 0.119523 0.0690066i
\(631\) 30.2487 17.4641i 1.20418 0.695235i 0.242700 0.970101i \(-0.421967\pi\)
0.961482 + 0.274867i \(0.0886337\pi\)
\(632\) 9.46410i 0.376462i
\(633\) 4.53590 + 7.85641i 0.180286 + 0.312264i
\(634\) −8.23205 + 14.2583i −0.326937 + 0.566271i
\(635\) −15.2154 8.78461i −0.603804 0.348607i
\(636\) 8.26795 0.327846
\(637\) −0.866025 3.50000i −0.0343132 0.138675i
\(638\) −32.0000 −1.26689
\(639\) −1.66987 0.964102i −0.0660592 0.0381393i
\(640\) −1.73205 + 3.00000i −0.0684653 + 0.118585i
\(641\) −13.3205 23.0718i −0.526128 0.911281i −0.999537 0.0304380i \(-0.990310\pi\)
0.473408 0.880843i \(-0.343024\pi\)
\(642\) 8.53590i 0.336885i
\(643\) −17.5359 + 10.1244i −0.691548 + 0.399266i −0.804192 0.594370i \(-0.797402\pi\)
0.112643 + 0.993635i \(0.464068\pi\)
\(644\) −4.96410 + 2.86603i −0.195613 + 0.112937i
\(645\) 15.4641i 0.608898i
\(646\) 24.1244 + 41.7846i 0.949160 + 1.64399i
\(647\) 18.6603 32.3205i 0.733610 1.27065i −0.221720 0.975110i \(-0.571167\pi\)
0.955330 0.295540i \(-0.0954995\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −25.0718 −0.984154
\(650\) −24.5000 + 6.06218i −0.960969 + 0.237778i
\(651\) −6.46410 −0.253348
\(652\) 1.16025 + 0.669873i 0.0454391 + 0.0262343i
\(653\) 18.7942 32.5526i 0.735475 1.27388i −0.219040 0.975716i \(-0.570292\pi\)
0.954515 0.298164i \(-0.0963743\pi\)
\(654\) 6.00000 + 10.3923i 0.234619 + 0.406371i
\(655\) 65.8179i 2.57172i
\(656\) 6.00000 3.46410i 0.234261 0.135250i
\(657\) 9.46410 5.46410i 0.369230 0.213175i
\(658\) 0.535898i 0.0208915i
\(659\) −0.803848 1.39230i −0.0313135 0.0542365i 0.849944 0.526873i \(-0.176636\pi\)
−0.881257 + 0.472637i \(0.843302\pi\)
\(660\) −6.92820 + 12.0000i −0.269680 + 0.467099i
\(661\) 43.9186 + 25.3564i 1.70823 + 0.986250i 0.936748 + 0.350005i \(0.113820\pi\)
0.771487 + 0.636245i \(0.219513\pi\)
\(662\) 21.3205 0.828645
\(663\) −16.7942 + 16.1603i −0.652234 + 0.627612i
\(664\) −1.73205 −0.0672166
\(665\) 22.3923 + 12.9282i 0.868336 + 0.501334i
\(666\) −2.46410 + 4.26795i −0.0954820 + 0.165380i
\(667\) 22.9282 + 39.7128i 0.887784 + 1.53769i
\(668\) 20.0000i 0.773823i
\(669\) 6.52628 3.76795i 0.252321 0.145677i
\(670\) 21.5885 12.4641i 0.834035 0.481530i
\(671\) 20.7846i 0.802381i
\(672\) 0.500000 + 0.866025i 0.0192879 + 0.0334077i
\(673\) 19.8205 34.3301i 0.764024 1.32333i −0.176736 0.984258i \(-0.556554\pi\)
0.940761 0.339071i \(-0.110113\pi\)
\(674\) −5.19615 3.00000i −0.200148 0.115556i
\(675\) −7.00000 −0.269430
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 1.07180 0.0411925 0.0205962 0.999788i \(-0.493444\pi\)
0.0205962 + 0.999788i \(0.493444\pi\)
\(678\) −3.80385 2.19615i −0.146086 0.0843427i
\(679\) −6.19615 + 10.7321i −0.237787 + 0.411858i
\(680\) 11.1962 + 19.3923i 0.429353 + 0.743661i
\(681\) 13.3205i 0.510443i
\(682\) 22.3923 12.9282i 0.857446 0.495046i
\(683\) 44.3205 25.5885i 1.69588 0.979115i 0.746285 0.665626i \(-0.231836\pi\)
0.949592 0.313489i \(-0.101498\pi\)
\(684\) 7.46410i 0.285397i
\(685\) 24.0000 + 41.5692i 0.916993 + 1.58828i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 17.2583 + 9.96410i 0.658446 + 0.380154i
\(688\) −4.46410 −0.170192
\(689\) −21.4808 + 20.6699i −0.818352 + 0.787459i
\(690\) 19.8564 0.755920
\(691\) −35.6603 20.5885i −1.35658 0.783222i −0.367419 0.930056i \(-0.619758\pi\)
−0.989161 + 0.146834i \(0.953092\pi\)
\(692\) −0.535898 + 0.928203i −0.0203718 + 0.0352850i
\(693\) 2.00000 + 3.46410i 0.0759737 + 0.131590i
\(694\) 25.7128i 0.976045i
\(695\) −8.78461 + 5.07180i −0.333219 + 0.192384i
\(696\) 6.92820 4.00000i 0.262613 0.151620i
\(697\) 44.7846i 1.69634i
\(698\) −17.8205 30.8660i −0.674516 1.16830i
\(699\) 6.73205 11.6603i 0.254630 0.441031i
\(700\) 6.06218 + 3.50000i 0.229129 + 0.132288i
\(701\) 2.12436 0.0802358 0.0401179 0.999195i \(-0.487227\pi\)
0.0401179 + 0.999195i \(0.487227\pi\)
\(702\) 3.50000 0.866025i 0.132099 0.0326860i
\(703\) −36.7846 −1.38736
\(704\) −3.46410 2.00000i −0.130558 0.0753778i
\(705\) −0.928203 + 1.60770i −0.0349582 + 0.0605493i
\(706\) 4.66987 + 8.08846i 0.175753 + 0.304413i
\(707\) 0 0
\(708\) 5.42820 3.13397i 0.204004 0.117782i
\(709\) −6.67949 + 3.85641i −0.250854 + 0.144830i −0.620155 0.784479i \(-0.712930\pi\)
0.369301 + 0.929310i \(0.379597\pi\)
\(710\) 6.67949i 0.250677i
\(711\) 4.73205 + 8.19615i 0.177466 + 0.307380i
\(712\) 5.86603 10.1603i 0.219839 0.380772i
\(713\) −32.0885 18.5263i −1.20172 0.693815i
\(714\) 6.46410 0.241913
\(715\) −12.0000 48.4974i −0.448775 1.81370i
\(716\) −16.9282 −0.632637
\(717\) −11.1340 6.42820i −0.415806 0.240066i
\(718\) −4.00000 + 6.92820i −0.149279 + 0.258558i
\(719\) 17.2679 + 29.9090i 0.643986 + 1.11542i 0.984535 + 0.175189i \(0.0560538\pi\)
−0.340549 + 0.940227i \(0.610613\pi\)
\(720\) 3.46410i 0.129099i
\(721\) 9.23205 5.33013i 0.343820 0.198504i
\(722\) 31.7942 18.3564i 1.18326 0.683155i
\(723\) 15.8564i 0.589706i
\(724\) −12.3923 21.4641i −0.460556 0.797707i
\(725\) 28.0000 48.4974i 1.03989 1.80115i
\(726\) −4.33013 2.50000i −0.160706 0.0927837i
\(727\) 22.9090 0.849646 0.424823 0.905276i \(-0.360336\pi\)
0.424823 + 0.905276i \(0.360336\pi\)
\(728\) −3.46410 1.00000i −0.128388 0.0370625i
\(729\) 1.00000 0.0370370
\(730\) 32.7846 + 18.9282i 1.21341 + 0.700564i
\(731\) −14.4282 + 24.9904i −0.533646 + 0.924303i
\(732\) −2.59808 4.50000i −0.0960277 0.166325i
\(733\) 4.85641i 0.179375i 0.995970 + 0.0896877i \(0.0285869\pi\)
−0.995970 + 0.0896877i \(0.971413\pi\)
\(734\) 28.6244 16.5263i 1.05654 0.609996i
\(735\) 3.00000 1.73205i 0.110657 0.0638877i
\(736\) 5.73205i 0.211286i
\(737\) 14.3923 + 24.9282i 0.530147 + 0.918242i
\(738\) −3.46410 + 6.00000i −0.127515 + 0.220863i
\(739\) 6.69615 + 3.86603i 0.246322 + 0.142214i 0.618079 0.786116i \(-0.287911\pi\)
−0.371757 + 0.928330i \(0.621245\pi\)
\(740\) −17.0718 −0.627572
\(741\) 18.6603 + 19.3923i 0.685502 + 0.712394i
\(742\) 8.26795 0.303526
\(743\) 1.54552 + 0.892305i 0.0566995 + 0.0327355i 0.528082 0.849194i \(-0.322911\pi\)
−0.471382 + 0.881929i \(0.656245\pi\)
\(744\) −3.23205 + 5.59808i −0.118493 + 0.205235i
\(745\) 19.9808 + 34.6077i 0.732038 + 1.26793i
\(746\) 26.2487i 0.961034i
\(747\) 1.50000 0.866025i 0.0548821 0.0316862i
\(748\) −22.3923 + 12.9282i −0.818744 + 0.472702i
\(749\) 8.53590i 0.311895i
\(750\) −3.46410 6.00000i −0.126491 0.219089i
\(751\) 14.6603 25.3923i 0.534960 0.926578i −0.464205 0.885728i \(-0.653660\pi\)
0.999165 0.0408506i \(-0.0130068\pi\)
\(752\) −0.464102 0.267949i −0.0169240 0.00977110i
\(753\) 10.0718 0.367037
\(754\) −8.00000 + 27.7128i −0.291343 + 1.00924i
\(755\) 41.5692 1.51286
\(756\) −0.866025 0.500000i −0.0314970 0.0181848i
\(757\) −9.92820 + 17.1962i −0.360847 + 0.625005i −0.988100 0.153810i \(-0.950846\pi\)
0.627254 + 0.778815i \(0.284179\pi\)
\(758\) −4.80385 8.32051i −0.174484 0.302214i
\(759\) 22.9282i 0.832241i
\(760\) 22.3923 12.9282i 0.812254 0.468955i
\(761\) 6.00000 3.46410i 0.217500 0.125574i −0.387292 0.921957i \(-0.626590\pi\)
0.604792 + 0.796383i \(0.293256\pi\)
\(762\) 5.07180i 0.183732i
\(763\) 6.00000 + 10.3923i 0.217215 + 0.376227i
\(764\) −13.2583 + 22.9641i −0.479670 + 0.830812i
\(765\) −19.3923 11.1962i −0.701130 0.404798i
\(766\) 7.32051 0.264501
\(767\) −6.26795 + 21.7128i −0.226323 + 0.784004i
\(768\) 1.00000 0.0360844
\(769\) 36.9282 + 21.3205i 1.33167 + 0.768837i 0.985555 0.169357i \(-0.0541690\pi\)
0.346110 + 0.938194i \(0.387502\pi\)
\(770\) −6.92820 + 12.0000i −0.249675 + 0.432450i
\(771\) 0.232051 + 0.401924i 0.00835711 + 0.0144749i
\(772\) 17.8564i 0.642666i
\(773\) 11.1962 6.46410i 0.402698 0.232498i −0.284950 0.958542i \(-0.591977\pi\)
0.687647 + 0.726045i \(0.258644\pi\)
\(774\) 3.86603 2.23205i 0.138961 0.0802294i
\(775\) 45.2487i 1.62538i
\(776\) 6.19615 + 10.7321i 0.222429 + 0.385258i
\(777\) −2.46410 + 4.26795i −0.0883992 + 0.153112i
\(778\) 12.6962 + 7.33013i 0.455179 + 0.262798i
\(779\) −51.7128 −1.85280
\(780\) 8.66025 + 9.00000i 0.310087 + 0.322252i
\(781\) 7.71281 0.275986
\(782\) 32.0885 + 18.5263i 1.14748 + 0.662498i
\(783\) −4.00000 + 6.92820i −0.142948 + 0.247594i
\(784\) 0.500000 + 0.866025i 0.0178571 + 0.0309295i
\(785\) 10.1436i 0.362040i
\(786\) −16.4545 + 9.50000i −0.586912 + 0.338854i
\(787\) −7.26795 + 4.19615i −0.259074 + 0.149577i −0.623912 0.781494i \(-0.714458\pi\)
0.364838 + 0.931071i \(0.381124\pi\)
\(788\) 2.60770i 0.0928953i
\(789\) 8.66025 + 15.0000i 0.308313 + 0.534014i
\(790\) −16.3923 + 28.3923i −0.583212 + 1.01015i
\(791\) −3.80385 2.19615i −0.135249 0.0780862i
\(792\) 4.00000 0.142134
\(793\) 18.0000 + 5.19615i 0.639199 + 0.184521i
\(794\) −29.7846 −1.05702
\(795\) −24.8038 14.3205i −0.879702 0.507896i
\(796\) 11.0622 19.1603i 0.392088 0.679117i
\(797\) 21.1244 + 36.5885i 0.748263 + 1.29603i 0.948655 + 0.316314i \(0.102445\pi\)
−0.200392 + 0.979716i \(0.564221\pi\)
\(798\) 7.46410i 0.264226i
\(799\) −3.00000 + 1.73205i −0.106132 + 0.0612756i
\(800\) 6.06218 3.50000i 0.214330 0.123744i
\(801\) 11.7321i 0.414532i
\(802\) −8.19615 14.1962i −0.289416 0.501284i
\(803\) −21.8564 + 37.8564i −0.771296 + 1.33592i
\(804\) −6.23205 3.59808i −0.219787 0.126894i
\(805\) 19.8564 0.699846
\(806\) −5.59808 22.6244i −0.197184 0.796909i
\(807\) 22.3923 0.788246
\(808\) 0 0
\(809\) −7.85641 + 13.6077i −0.276217 + 0.478421i −0.970441 0.241337i \(-0.922414\pi\)
0.694225 + 0.719758i \(0.255747\pi\)
\(810\) 1.73205 + 3.00000i 0.0608581 + 0.105409i
\(811\) 2.14359i 0.0752717i 0.999292 + 0.0376359i \(0.0119827\pi\)
−0.999292 + 0.0376359i \(0.988017\pi\)
\(812\) 6.92820 4.00000i 0.243132 0.140372i
\(813\) −10.7942 + 6.23205i −0.378570 + 0.218568i
\(814\) 19.7128i 0.690934i
\(815\) −2.32051 4.01924i −0.0812839 0.140788i
\(816\) 3.23205 5.59808i 0.113144 0.195972i
\(817\) 28.8564 + 16.6603i 1.00956 + 0.582869i
\(818\) 6.39230 0.223502
\(819\) 3.50000 0.866025i 0.122300 0.0302614i
\(820\) −24.0000 −0.838116
\(821\) 27.0622 + 15.6244i 0.944477 + 0.545294i 0.891361 0.453295i \(-0.149751\pi\)
0.0531158 + 0.998588i \(0.483085\pi\)
\(822\) 6.92820 12.0000i 0.241649 0.418548i
\(823\) 11.8038 + 20.4449i 0.411456 + 0.712663i 0.995049 0.0993832i \(-0.0316870\pi\)
−0.583593 + 0.812046i \(0.698354\pi\)
\(824\) 10.6603i 0.371368i
\(825\) 24.2487 14.0000i 0.844232 0.487417i
\(826\) 5.42820 3.13397i 0.188871 0.109045i
\(827\) 36.3923i 1.26548i −0.774363 0.632742i \(-0.781929\pi\)
0.774363 0.632742i \(-0.218071\pi\)
\(828\) −2.86603 4.96410i −0.0996013 0.172514i
\(829\) 3.60770 6.24871i 0.125300 0.217027i −0.796550 0.604573i \(-0.793344\pi\)
0.921850 + 0.387546i \(0.126677\pi\)
\(830\) 5.19615 + 3.00000i 0.180361 + 0.104132i
\(831\) −7.32051 −0.253946
\(832\) −2.59808 + 2.50000i −0.0900721 + 0.0866719i
\(833\) 6.46410 0.223968
\(834\) 2.53590 + 1.46410i 0.0878110 + 0.0506977i
\(835\) 34.6410 60.0000i 1.19880 2.07639i
\(836\) 14.9282 + 25.8564i 0.516303 + 0.894263i
\(837\) 6.46410i 0.223432i
\(838\) 4.33013 2.50000i 0.149582 0.0863611i
\(839\) −1.39230 + 0.803848i −0.0480677 + 0.0277519i −0.523841 0.851816i \(-0.675502\pi\)
0.475774 + 0.879568i \(0.342168\pi\)
\(840\) 3.46410i 0.119523i
\(841\) −17.5000 30.3109i −0.603448 1.04520i
\(842\) 0.803848 1.39230i 0.0277024 0.0479820i
\(843\) −2.07180 1.19615i −0.0713565 0.0411977i
\(844\) 9.07180 0.312264
\(845\) −45.0000 1.73205i −1.54805 0.0595844i
\(846\) 0.535898 0.0184246
\(847\) −4.33013 2.50000i −0.148785 0.0859010i
\(848\) 4.13397 7.16025i 0.141961 0.245884i
\(849\) −5.73205 9.92820i −0.196723 0.340735i
\(850\) 45.2487i 1.55202i
\(851\) −24.4641 + 14.1244i −0.838619 + 0.484177i
\(852\) −1.66987 + 0.964102i −0.0572089 + 0.0330296i
\(853\) 47.6410i 1.63120i −0.578618 0.815599i \(-0.696408\pi\)
0.578618 0.815599i \(-0.303592\pi\)
\(854\) −2.59808 4.50000i −0.0889043 0.153987i
\(855\) −12.9282 + 22.3923i −0.442135 + 0.765801i
\(856\) −7.39230 4.26795i −0.252664 0.145876i
\(857\) 33.7128 1.15161 0.575804 0.817588i \(-0.304689\pi\)
0.575804 + 0.817588i \(0.304689\pi\)
\(858\) −10.3923 + 10.0000i −0.354787 + 0.341394i
\(859\) −15.8564 −0.541014 −0.270507 0.962718i \(-0.587191\pi\)
−0.270507 + 0.962718i \(0.587191\pi\)
\(860\) 13.3923 + 7.73205i 0.456674 + 0.263661i
\(861\) −3.46410 + 6.00000i −0.118056 + 0.204479i
\(862\) 2.42820 + 4.20577i 0.0827049 + 0.143249i
\(863\) 42.9282i 1.46129i 0.682756 + 0.730647i \(0.260781\pi\)
−0.682756 + 0.730647i \(0.739219\pi\)
\(864\) −0.866025 + 0.500000i −0.0294628 + 0.0170103i
\(865\) 3.21539 1.85641i 0.109327 0.0631197i
\(866\) 9.85641i 0.334934i
\(867\) −12.3923 21.4641i −0.420865 0.728959i
\(868\) −3.23205 + 5.59808i −0.109703 + 0.190011i
\(869\) −32.7846 18.9282i −1.11214 0.642095i
\(870\) −27.7128 −0.939552
\(871\) 25.1865 6.23205i 0.853413 0.211165i
\(872\) 12.0000 0.406371
\(873\) −10.7321 6.19615i −0.363225 0.209708i
\(874\) 21.3923 37.0526i 0.723606 1.25332i
\(875\) −3.46410 6.00000i −0.117108 0.202837i
\(876\) 10.9282i 0.369230i
\(877\) 22.2679 12.8564i 0.751935 0.434130i −0.0744575 0.997224i \(-0.523723\pi\)
0.826393 + 0.563094i \(0.190389\pi\)
\(878\) −11.7846 + 6.80385i −0.397711 + 0.229619i
\(879\) 33.4641i 1.12872i
\(880\) 6.92820 + 12.0000i 0.233550 + 0.404520i
\(881\) 16.0167 27.7417i 0.539615 0.934641i −0.459310 0.888276i \(-0.651903\pi\)
0.998925 0.0463644i \(-0.0147635\pi\)
\(882\) −0.866025 0.500000i −0.0291606 0.0168359i
\(883\) 0.320508 0.0107860 0.00539298 0.999985i \(-0.498283\pi\)
0.00539298 + 0.999985i \(0.498283\pi\)
\(884\) 5.59808 + 22.6244i 0.188284 + 0.760939i
\(885\) −21.7128 −0.729868
\(886\) −19.3923 11.1962i −0.651497 0.376142i
\(887\) −5.92820 + 10.2679i −0.199050 + 0.344764i −0.948221 0.317613i \(-0.897119\pi\)
0.749171 + 0.662377i \(0.230452\pi\)
\(888\) 2.46410 + 4.26795i 0.0826898 + 0.143223i
\(889\) 5.07180i 0.170103i
\(890\) −35.1962 + 20.3205i −1.17978 + 0.681145i
\(891\) −3.46410 + 2.00000i −0.116052 + 0.0670025i
\(892\) 7.53590i 0.252321i
\(893\) 2.00000 + 3.46410i 0.0669274 + 0.115922i
\(894\) 5.76795 9.99038i 0.192909 0.334128i
\(895\) 50.7846 + 29.3205i 1.69754 + 0.980076i
\(896\) 1.00000 0.0334077
\(897\) 19.8564 + 5.73205i 0.662986 + 0.191388i
\(898\) 18.0000 0.600668
\(899\) 44.7846 + 25.8564i 1.49365 + 0.862359i
\(900\) −3.50000 + 6.06218i −0.116667 + 0.202073i
\(901\) −26.7224 46.2846i −0.890253 1.54196i
\(902\) 27.7128i 0.922736i
\(903\) 3.86603 2.23205i 0.128653 0.0742780i
\(904\) −3.80385 + 2.19615i −0.126514 + 0.0730429i
\(905\) 85.8564i 2.85396i
\(906\) −6.00000 10.3923i −0.199337 0.345261i
\(907\) −9.23205 + 15.9904i −0.306545 + 0.530952i −0.977604 0.210452i \(-0.932506\pi\)
0.671059 + 0.741404i \(0.265840\pi\)
\(908\) −11.5359 6.66025i −0.382832 0.221028i
\(909\) 0 0
\(910\) 8.66025 + 9.00000i 0.287085 + 0.298347i
\(911\) 27.1769 0.900411 0.450206 0.892925i \(-0.351351\pi\)
0.450206 + 0.892925i \(0.351351\pi\)
\(912\) −6.46410 3.73205i −0.214048 0.123581i
\(913\) −3.46410 + 6.00000i −0.114645 + 0.198571i
\(914\) 0.598076 + 1.03590i 0.0197826 + 0.0342645i
\(915\) 18.0000i 0.595062i
\(916\) 17.2583 9.96410i 0.570231 0.329223i
\(917\) −16.4545 + 9.50000i −0.543375 + 0.313718i
\(918\) 6.46410i 0.213347i
\(919\) 13.0000 + 22.5167i 0.428830 + 0.742756i 0.996770 0.0803145i \(-0.0255924\pi\)
−0.567939 + 0.823071i \(0.692259\pi\)
\(920\) 9.92820 17.1962i 0.327323 0.566940i
\(921\) −19.0526 11.0000i −0.627803 0.362462i
\(922\) −5.07180 −0.167031
\(923\) 1.92820 6.67949i 0.0634676 0.219858i
\(924\) 4.00000 0.131590
\(925\) 29.8756 + 17.2487i 0.982305 + 0.567134i
\(926\) 4.12436 7.14359i 0.135535 0.234753i
\(927\) 5.33013 + 9.23205i 0.175064 + 0.303220i
\(928\) 8.00000i 0.262613i
\(929\) 5.08846 2.93782i 0.166947 0.0963868i −0.414199 0.910187i \(-0.635938\pi\)
0.581145 + 0.813800i \(0.302605\pi\)
\(930\) 19.3923 11.1962i 0.635899 0.367136i
\(931\) 7.46410i 0.244626i
\(932\) −6.73205 11.6603i −0.220516 0.381944i
\(933\) 6.66025 11.5359i 0.218047 0.377668i
\(934\) 34.3301 + 19.8205i 1.12332 + 0.648547i
\(935\) 89.5692 2.92923
\(936\) 1.00000 3.46410i 0.0326860 0.113228i
\(937\) −44.9282 −1.46774 −0.733870 0.679290i \(-0.762288\pi\)
−0.733870 + 0.679290i \(0.762288\pi\)
\(938\) −6.23205 3.59808i −0.203484 0.117481i
\(939\) −0.339746 + 0.588457i −0.0110872 + 0.0192036i
\(940\) 0.928203 + 1.60770i 0.0302747 + 0.0524372i
\(941\) 19.6077i 0.639193i −0.947554 0.319596i \(-0.896453\pi\)
0.947554 0.319596i \(-0.103547\pi\)
\(942\) 2.53590 1.46410i 0.0826240 0.0477030i
\(943\) −34.3923 + 19.8564i −1.11997 + 0.646614i
\(944\) 6.26795i 0.204004i
\(945\) 1.73205 + 3.00000i 0.0563436 + 0.0975900i
\(946\) −8.92820 + 15.4641i −0.290281 + 0.502781i
\(947\) 26.1962 + 15.1244i 0.851261 + 0.491476i 0.861076 0.508476i \(-0.169791\pi\)
−0.00981541 + 0.999952i \(0.503124\pi\)
\(948\) 9.46410 0.307380
\(949\) 27.3205 + 28.3923i 0.886861 + 0.921653i
\(950\) −52.2487 −1.69517
\(951\) −14.2583 8.23205i −0.462358 0.266943i
\(952\) 3.23205 5.59808i 0.104751 0.181435i
\(953\) 15.0000 + 25.9808i 0.485898 + 0.841599i 0.999869 0.0162081i \(-0.00515944\pi\)
−0.513971 + 0.857808i \(0.671826\pi\)
\(954\) 8.26795i 0.267685i
\(955\) 79.5500 45.9282i 2.57418 1.48620i
\(956\) −11.1340 + 6.42820i −0.360098 + 0.207903i
\(957\) 32.0000i 1.03441i
\(958\) −2.19615 3.80385i −0.0709545 0.122897i
\(959\) 6.92820 12.0000i 0.223723 0.387500i
\(960\) −3.00000 1.73205i −0.0968246 0.0559017i
\(961\) −10.7846 −0.347891
\(962\) −17.0718 4.92820i −0.550417 0.158892i
\(963\) 8.53590 0.275065
\(964\) 13.7321 + 7.92820i 0.442280 + 0.255350i
\(965\) 30.9282 53.5692i 0.995614 1.72445i
\(966\) −2.86603 4.96410i −0.0922129 0.159717i
\(967\) 16.5359i 0.531759i 0.964006 + 0.265879i \(0.0856623\pi\)
−0.964006 + 0.265879i \(0.914338\pi\)
\(968\) −4.33013 + 2.50000i −0.139176 + 0.0803530i
\(969\) −41.7846 + 24.1244i −1.34232 + 0.774986i
\(970\) 42.9282i 1.37834i
\(971\) −11.9641 20.7224i −0.383946 0.665014i 0.607676 0.794185i \(-0.292102\pi\)
−0.991622 + 0.129170i \(0.958769\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) 2.53590 + 1.46410i 0.0812972 + 0.0469369i
\(974\) 0.392305 0.0125703
\(975\) −6.06218 24.5000i −0.194145 0.784628i
\(976\) −5.19615 −0.166325
\(977\) −22.3923 12.9282i −0.716393 0.413610i 0.0970305 0.995281i \(-0.469066\pi\)
−0.813424 + 0.581672i \(0.802399\pi\)
\(978\) −0.669873 + 1.16025i −0.0214202 + 0.0371008i
\(979\) −23.4641 40.6410i −0.749916 1.29889i
\(980\) 3.46410i 0.110657i
\(981\) −10.3923 + 6.00000i −0.331801 + 0.191565i
\(982\) −8.53590 + 4.92820i −0.272391 + 0.157265i
\(983\) 19.0718i 0.608296i −0.952625 0.304148i \(-0.901628\pi\)
0.952625 0.304148i \(-0.0983717\pi\)
\(984\) 3.46410 + 6.00000i 0.110432 + 0.191273i
\(985\) 4.51666 7.82309i 0.143913 0.249264i
\(986\) −44.7846 25.8564i −1.42623 0.823436i
\(987\) 0.535898 0.0170578
\(988\) 26.1244 6.46410i 0.831126 0.205650i
\(989\) 25.5885 0.813666
\(990\) −12.0000 6.92820i −0.381385 0.220193i
\(991\) −0.0717968 + 0.124356i −0.00228070 + 0.00395029i −0.867164 0.498024i \(-0.834059\pi\)
0.864883 + 0.501974i \(0.167393\pi\)
\(992\) 3.23205 + 5.59808i 0.102618 + 0.177739i
\(993\) 21.3205i 0.676586i
\(994\) −1.66987 + 0.964102i −0.0529652 + 0.0305794i
\(995\) −66.3731 + 38.3205i −2.10417 + 1.21484i
\(996\) 1.73205i 0.0548821i
\(997\) −16.9904 29.4282i −0.538091 0.932001i −0.999007 0.0445568i \(-0.985812\pi\)
0.460916 0.887444i \(-0.347521\pi\)
\(998\) 0.133975 0.232051i 0.00424089 0.00734544i
\(999\) −4.26795 2.46410i −0.135032 0.0779607i
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.s.c.43.2 4
3.2 odd 2 1638.2.bj.e.1135.1 4
13.6 odd 12 7098.2.a.bn.1.1 2
13.7 odd 12 7098.2.a.bz.1.2 2
13.10 even 6 inner 546.2.s.c.127.2 yes 4
39.23 odd 6 1638.2.bj.e.127.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.s.c.43.2 4 1.1 even 1 trivial
546.2.s.c.127.2 yes 4 13.10 even 6 inner
1638.2.bj.e.127.1 4 39.23 odd 6
1638.2.bj.e.1135.1 4 3.2 odd 2
7098.2.a.bn.1.1 2 13.6 odd 12
7098.2.a.bz.1.2 2 13.7 odd 12