Properties

Label 546.2.l.g.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
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(211,546)]
 
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, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.g.295.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} +1.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} -1.00000 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.00000 + 1.73205i) q^{20} +1.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-4.50000 - 7.79423i) q^{29} +(-1.00000 + 1.73205i) q^{30} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +1.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} -1.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} -2.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.00000 - 1.73205i) q^{43} -1.00000 q^{44} +(-1.00000 + 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +1.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-0.500000 + 0.866025i) q^{56} -1.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-5.00000 + 8.66025i) q^{59} -2.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(1.00000 + 1.73205i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(5.00000 + 5.19615i) q^{65} -1.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-3.00000 + 5.19615i) q^{69} +2.00000 q^{70} +(4.00000 - 6.92820i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-0.500000 - 0.866025i) q^{76} +1.00000 q^{77} +(-3.50000 + 0.866025i) q^{78} +11.0000 q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} -12.0000 q^{83} +(-0.500000 + 0.866025i) q^{84} +(1.00000 - 1.73205i) q^{85} +2.00000 q^{86} +(4.50000 - 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.50000 - 9.52628i) q^{89} -2.00000 q^{90} +(3.50000 - 0.866025i) q^{91} -6.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-3.50000 - 6.06218i) q^{94} +(-1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(7.00000 - 12.1244i) q^{97} +(0.500000 - 0.866025i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} + q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + q^{11} - 2 q^{12} + 5 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} + q^{17} - 2 q^{18} - q^{19} - 2 q^{20} + 2 q^{21} - q^{22} + 6 q^{23} - q^{24} - 2 q^{25} - 2 q^{26} - 2 q^{27} + q^{28} - 9 q^{29} - 2 q^{30} + 4 q^{31} + q^{32} - q^{33} + 2 q^{34} + 2 q^{35} - q^{36} + 2 q^{37} - 2 q^{38} - 2 q^{39} - 4 q^{40} - 5 q^{41} + q^{42} + 2 q^{43} - 2 q^{44} - 2 q^{45} - 6 q^{46} - 14 q^{47} + q^{48} - q^{49} - q^{50} + 2 q^{51} - 7 q^{52} - 2 q^{53} - q^{54} + 2 q^{55} - q^{56} - 2 q^{57} + 9 q^{58} - 10 q^{59} - 4 q^{60} + 11 q^{61} + 2 q^{62} + q^{63} + 2 q^{64} + 10 q^{65} - 2 q^{66} - 2 q^{67} + q^{68} - 6 q^{69} + 4 q^{70} + 8 q^{71} + q^{72} + 16 q^{73} - 2 q^{74} - q^{75} - q^{76} + 2 q^{77} - 7 q^{78} + 22 q^{79} - 2 q^{80} - q^{81} + 5 q^{82} - 24 q^{83} - q^{84} + 2 q^{85} + 4 q^{86} + 9 q^{87} - q^{88} - 11 q^{89} - 4 q^{90} + 7 q^{91} - 12 q^{92} + 2 q^{93} - 7 q^{94} - 2 q^{95} + 2 q^{96} + 14 q^{97} + q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) 1.00000 0.267261
\(15\) 1.00000 + 1.73205i 0.258199 + 0.447214i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) −1.00000 −0.235702
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 1.00000 0.218218
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −1.00000 −0.200000
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) −1.00000 −0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) −4.50000 7.79423i −0.835629 1.44735i −0.893517 0.449029i \(-0.851770\pi\)
0.0578882 0.998323i \(-0.481563\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 1.00000 0.171499
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) −1.00000 −0.162221
\(39\) −1.00000 + 3.46410i −0.160128 + 0.554700i
\(40\) −2.00000 −0.316228
\(41\) −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i \(-0.294342\pi\)
−0.992507 + 0.122189i \(0.961009\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 1.00000 1.73205i 0.152499 0.264135i −0.779647 0.626219i \(-0.784601\pi\)
0.932145 + 0.362084i \(0.117935\pi\)
\(44\) −1.00000 −0.150756
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 1.00000 0.140028
\(52\) −3.50000 + 0.866025i −0.485363 + 0.120096i
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 1.00000 + 1.73205i 0.134840 + 0.233550i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) −1.00000 −0.132453
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −5.00000 + 8.66025i −0.650945 + 1.12747i 0.331949 + 0.943297i \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) −2.00000 −0.258199
\(61\) 5.50000 9.52628i 0.704203 1.21972i −0.262776 0.964857i \(-0.584638\pi\)
0.966978 0.254858i \(-0.0820288\pi\)
\(62\) 1.00000 + 1.73205i 0.127000 + 0.219971i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 5.00000 + 5.19615i 0.620174 + 0.644503i
\(66\) −1.00000 −0.123091
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 0.500000 + 0.866025i 0.0606339 + 0.105021i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) 2.00000 0.239046
\(71\) 4.00000 6.92820i 0.474713 0.822226i −0.524868 0.851184i \(-0.675885\pi\)
0.999581 + 0.0289572i \(0.00921865\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −0.500000 0.866025i −0.0573539 0.0993399i
\(77\) 1.00000 0.113961
\(78\) −3.50000 + 0.866025i −0.396297 + 0.0980581i
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.50000 4.33013i 0.276079 0.478183i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) 2.00000 0.215666
\(87\) 4.50000 7.79423i 0.482451 0.835629i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −5.50000 9.52628i −0.582999 1.00978i −0.995122 0.0986553i \(-0.968546\pi\)
0.412123 0.911128i \(-0.364787\pi\)
\(90\) −2.00000 −0.210819
\(91\) 3.50000 0.866025i 0.366900 0.0907841i
\(92\) −6.00000 −0.625543
\(93\) 1.00000 + 1.73205i 0.103695 + 0.179605i
\(94\) −3.50000 6.06218i −0.360997 0.625266i
\(95\) −1.00000 + 1.73205i −0.102598 + 0.177705i
\(96\) 1.00000 0.102062
\(97\) 7.00000 12.1244i 0.710742 1.23104i −0.253837 0.967247i \(-0.581693\pi\)
0.964579 0.263795i \(-0.0849741\pi\)
\(98\) 0.500000 0.866025i 0.0505076 0.0874818i
\(99\) −1.00000 −0.100504
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 0.500000 + 0.866025i 0.0495074 + 0.0857493i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −2.50000 2.59808i −0.245145 0.254762i
\(105\) 2.00000 0.195180
\(106\) −0.500000 0.866025i −0.0485643 0.0841158i
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) −1.00000 + 1.73205i −0.0949158 + 0.164399i
\(112\) −1.00000 −0.0944911
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) −0.500000 0.866025i −0.0468293 0.0811107i
\(115\) 6.00000 + 10.3923i 0.559503 + 0.969087i
\(116\) 9.00000 0.835629
\(117\) −3.50000 + 0.866025i −0.323575 + 0.0800641i
\(118\) −10.0000 −0.920575
\(119\) −0.500000 0.866025i −0.0458349 0.0793884i
\(120\) −1.00000 1.73205i −0.0912871 0.158114i
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 11.0000 0.995893
\(123\) 2.50000 4.33013i 0.225417 0.390434i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) −12.0000 −1.07331
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 6.00000 + 10.3923i 0.532414 + 0.922168i 0.999284 + 0.0378419i \(0.0120483\pi\)
−0.466870 + 0.884326i \(0.654618\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.00000 0.176090
\(130\) −2.00000 + 6.92820i −0.175412 + 0.607644i
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −0.500000 0.866025i −0.0435194 0.0753778i
\(133\) 0.500000 + 0.866025i 0.0433555 + 0.0750939i
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) −2.00000 −0.172133
\(136\) −0.500000 + 0.866025i −0.0428746 + 0.0742611i
\(137\) 5.00000 8.66025i 0.427179 0.739895i −0.569442 0.822031i \(-0.692841\pi\)
0.996621 + 0.0821359i \(0.0261741\pi\)
\(138\) −6.00000 −0.510754
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) −3.50000 6.06218i −0.294753 0.510527i
\(142\) 8.00000 0.671345
\(143\) −1.00000 + 3.46410i −0.0836242 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) −9.00000 15.5885i −0.747409 1.29455i
\(146\) 4.00000 + 6.92820i 0.331042 + 0.573382i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) −2.00000 −0.164399
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −3.00000 −0.244137 −0.122068 0.992522i \(-0.538953\pi\)
−0.122068 + 0.992522i \(0.538953\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 0.500000 + 0.866025i 0.0404226 + 0.0700140i
\(154\) 0.500000 + 0.866025i 0.0402911 + 0.0697863i
\(155\) 4.00000 0.321288
\(156\) −2.50000 2.59808i −0.200160 0.208013i
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 5.50000 + 9.52628i 0.437557 + 0.757870i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) 1.00000 1.73205i 0.0790569 0.136931i
\(161\) 6.00000 0.472866
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i \(-0.858291\pi\)
0.824202 + 0.566296i \(0.191624\pi\)
\(164\) 5.00000 0.390434
\(165\) −1.00000 + 1.73205i −0.0778499 + 0.134840i
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 2.00000 0.153393
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i \(-0.931694\pi\)
0.672949 + 0.739689i \(0.265027\pi\)
\(174\) 9.00000 0.682288
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) 0.500000 0.866025i 0.0376889 0.0652791i
\(177\) −10.0000 −0.751646
\(178\) 5.50000 9.52628i 0.412242 0.714025i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) −1.00000 1.73205i −0.0745356 0.129099i
\(181\) −19.0000 −1.41226 −0.706129 0.708083i \(-0.749560\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 2.50000 + 2.59808i 0.185312 + 0.192582i
\(183\) 11.0000 0.813143
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) −1.00000 + 1.73205i −0.0733236 + 0.127000i
\(187\) 1.00000 0.0731272
\(188\) 3.50000 6.06218i 0.255264 0.442130i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) −2.00000 −0.145095
\(191\) −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i \(-0.879560\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i \(-0.0370998\pi\)
−0.597317 + 0.802005i \(0.703766\pi\)
\(194\) 14.0000 1.00514
\(195\) −2.00000 + 6.92820i −0.143223 + 0.496139i
\(196\) 1.00000 0.0714286
\(197\) −13.5000 23.3827i −0.961835 1.66595i −0.717888 0.696159i \(-0.754891\pi\)
−0.243947 0.969788i \(-0.578442\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.00000 1.73205i 0.0705346 0.122169i
\(202\) −1.00000 + 1.73205i −0.0703598 + 0.121867i
\(203\) −9.00000 −0.631676
\(204\) −0.500000 + 0.866025i −0.0350070 + 0.0606339i
\(205\) −5.00000 8.66025i −0.349215 0.604858i
\(206\) −7.00000 12.1244i −0.487713 0.844744i
\(207\) −6.00000 −0.417029
\(208\) 1.00000 3.46410i 0.0693375 0.240192i
\(209\) −1.00000 −0.0691714
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) 3.00000 + 5.19615i 0.206529 + 0.357718i 0.950619 0.310361i \(-0.100450\pi\)
−0.744090 + 0.668079i \(0.767117\pi\)
\(212\) 0.500000 0.866025i 0.0343401 0.0594789i
\(213\) 8.00000 0.548151
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) 1.00000 0.0680414
\(217\) 1.00000 1.73205i 0.0678844 0.117579i
\(218\) 8.00000 + 13.8564i 0.541828 + 0.938474i
\(219\) 4.00000 + 6.92820i 0.270295 + 0.468165i
\(220\) −2.00000 −0.134840
\(221\) 3.50000 0.866025i 0.235435 0.0582552i
\(222\) −2.00000 −0.134231
\(223\) −10.0000 17.3205i −0.669650 1.15987i −0.978002 0.208595i \(-0.933111\pi\)
0.308353 0.951272i \(-0.400222\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 6.00000 0.399114
\(227\) −1.00000 + 1.73205i −0.0663723 + 0.114960i −0.897302 0.441417i \(-0.854476\pi\)
0.830930 + 0.556378i \(0.187809\pi\)
\(228\) 0.500000 0.866025i 0.0331133 0.0573539i
\(229\) −23.0000 −1.51988 −0.759941 0.649992i \(-0.774772\pi\)
−0.759941 + 0.649992i \(0.774772\pi\)
\(230\) −6.00000 + 10.3923i −0.395628 + 0.685248i
\(231\) 0.500000 + 0.866025i 0.0328976 + 0.0569803i
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) −14.0000 −0.913259
\(236\) −5.00000 8.66025i −0.325472 0.563735i
\(237\) 5.50000 + 9.52628i 0.357263 + 0.618798i
\(238\) 0.500000 0.866025i 0.0324102 0.0561361i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 1.00000 1.73205i 0.0645497 0.111803i
\(241\) −8.00000 + 13.8564i −0.515325 + 0.892570i 0.484516 + 0.874782i \(0.338996\pi\)
−0.999842 + 0.0177875i \(0.994338\pi\)
\(242\) 10.0000 0.642824
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 5.50000 + 9.52628i 0.352101 + 0.609858i
\(245\) −1.00000 1.73205i −0.0638877 0.110657i
\(246\) 5.00000 0.318788
\(247\) −3.50000 + 0.866025i −0.222700 + 0.0551039i
\(248\) −2.00000 −0.127000
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) 4.00000 6.92820i 0.252478 0.437304i −0.711730 0.702454i \(-0.752088\pi\)
0.964207 + 0.265149i \(0.0854212\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −3.00000 + 5.19615i −0.188608 + 0.326679i
\(254\) −6.00000 + 10.3923i −0.376473 + 0.652071i
\(255\) 2.00000 0.125245
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.50000 + 7.79423i 0.280702 + 0.486191i 0.971558 0.236802i \(-0.0760993\pi\)
−0.690856 + 0.722993i \(0.742766\pi\)
\(258\) 1.00000 + 1.73205i 0.0622573 + 0.107833i
\(259\) 2.00000 0.124274
\(260\) −7.00000 + 1.73205i −0.434122 + 0.107417i
\(261\) 9.00000 0.557086
\(262\) −4.00000 6.92820i −0.247121 0.428026i
\(263\) 14.0000 + 24.2487i 0.863277 + 1.49524i 0.868748 + 0.495255i \(0.164925\pi\)
−0.00547092 + 0.999985i \(0.501741\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) −2.00000 −0.122859
\(266\) −0.500000 + 0.866025i −0.0306570 + 0.0530994i
\(267\) 5.50000 9.52628i 0.336595 0.582999i
\(268\) 2.00000 0.122169
\(269\) −8.00000 + 13.8564i −0.487769 + 0.844840i −0.999901 0.0140665i \(-0.995522\pi\)
0.512132 + 0.858906i \(0.328856\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 2.50000 + 2.59808i 0.151307 + 0.157243i
\(274\) 10.0000 0.604122
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) −3.00000 5.19615i −0.180579 0.312772i
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 9.00000 0.539784
\(279\) −1.00000 + 1.73205i −0.0598684 + 0.103695i
\(280\) −1.00000 + 1.73205i −0.0597614 + 0.103510i
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) 3.50000 6.06218i 0.208422 0.360997i
\(283\) 14.0000 + 24.2487i 0.832214 + 1.44144i 0.896279 + 0.443491i \(0.146260\pi\)
−0.0640654 + 0.997946i \(0.520407\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) −2.00000 −0.118470
\(286\) −3.50000 + 0.866025i −0.206959 + 0.0512092i
\(287\) −5.00000 −0.295141
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 9.00000 15.5885i 0.528498 0.915386i
\(291\) 14.0000 0.820695
\(292\) −4.00000 + 6.92820i −0.234082 + 0.405442i
\(293\) −10.0000 + 17.3205i −0.584206 + 1.01187i 0.410768 + 0.911740i \(0.365261\pi\)
−0.994974 + 0.100135i \(0.968073\pi\)
\(294\) 1.00000 0.0583212
\(295\) −10.0000 + 17.3205i −0.582223 + 1.00844i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) −6.00000 −0.347571
\(299\) −6.00000 + 20.7846i −0.346989 + 1.20201i
\(300\) 1.00000 0.0577350
\(301\) −1.00000 1.73205i −0.0576390 0.0998337i
\(302\) −1.50000 2.59808i −0.0863153 0.149502i
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 1.00000 0.0573539
\(305\) 11.0000 19.0526i 0.629858 1.09095i
\(306\) −0.500000 + 0.866025i −0.0285831 + 0.0495074i
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) −0.500000 + 0.866025i −0.0284901 + 0.0493464i
\(309\) −7.00000 12.1244i −0.398216 0.689730i
\(310\) 2.00000 + 3.46410i 0.113592 + 0.196748i
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 1.00000 3.46410i 0.0566139 0.196116i
\(313\) −12.0000 −0.678280 −0.339140 0.940736i \(-0.610136\pi\)
−0.339140 + 0.940736i \(0.610136\pi\)
\(314\) 1.00000 + 1.73205i 0.0564333 + 0.0977453i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) −5.50000 + 9.52628i −0.309399 + 0.535895i
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 0.500000 0.866025i 0.0280386 0.0485643i
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 2.00000 0.111803
\(321\) 1.50000 2.59808i 0.0837218 0.145010i
\(322\) 3.00000 + 5.19615i 0.167183 + 0.289570i
\(323\) 0.500000 + 0.866025i 0.0278207 + 0.0481869i
\(324\) 1.00000 0.0555556
\(325\) −2.50000 2.59808i −0.138675 0.144115i
\(326\) −2.00000 −0.110770
\(327\) 8.00000 + 13.8564i 0.442401 + 0.766261i
\(328\) 2.50000 + 4.33013i 0.138039 + 0.239091i
\(329\) −3.50000 + 6.06218i −0.192961 + 0.334219i
\(330\) −2.00000 −0.110096
\(331\) −13.0000 + 22.5167i −0.714545 + 1.23763i 0.248590 + 0.968609i \(0.420033\pi\)
−0.963135 + 0.269019i \(0.913301\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −33.0000 −1.79762 −0.898812 0.438334i \(-0.855569\pi\)
−0.898812 + 0.438334i \(0.855569\pi\)
\(338\) −11.5000 + 6.06218i −0.625518 + 0.329739i
\(339\) 6.00000 0.325875
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 1.00000 + 1.73205i 0.0541530 + 0.0937958i
\(342\) 0.500000 0.866025i 0.0270369 0.0468293i
\(343\) −1.00000 −0.0539949
\(344\) −1.00000 + 1.73205i −0.0539164 + 0.0933859i
\(345\) −6.00000 + 10.3923i −0.323029 + 0.559503i
\(346\) −8.00000 −0.430083
\(347\) 1.50000 2.59808i 0.0805242 0.139472i −0.822951 0.568112i \(-0.807674\pi\)
0.903475 + 0.428640i \(0.141007\pi\)
\(348\) 4.50000 + 7.79423i 0.241225 + 0.417815i
\(349\) 3.00000 + 5.19615i 0.160586 + 0.278144i 0.935079 0.354439i \(-0.115328\pi\)
−0.774493 + 0.632583i \(0.781995\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −2.50000 2.59808i −0.133440 0.138675i
\(352\) 1.00000 0.0533002
\(353\) −13.0000 22.5167i −0.691920 1.19844i −0.971208 0.238233i \(-0.923432\pi\)
0.279288 0.960207i \(-0.409902\pi\)
\(354\) −5.00000 8.66025i −0.265747 0.460287i
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) 11.0000 0.582999
\(357\) 0.500000 0.866025i 0.0264628 0.0458349i
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 1.00000 1.73205i 0.0527046 0.0912871i
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −9.50000 16.4545i −0.499309 0.864828i
\(363\) 10.0000 0.524864
\(364\) −1.00000 + 3.46410i −0.0524142 + 0.181568i
\(365\) 16.0000 0.837478
\(366\) 5.50000 + 9.52628i 0.287490 + 0.497947i
\(367\) 7.00000 + 12.1244i 0.365397 + 0.632886i 0.988840 0.148983i \(-0.0475999\pi\)
−0.623443 + 0.781869i \(0.714267\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 5.00000 0.260290
\(370\) −2.00000 + 3.46410i −0.103975 + 0.180090i
\(371\) −0.500000 + 0.866025i −0.0259587 + 0.0449618i
\(372\) −2.00000 −0.103695
\(373\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(374\) 0.500000 + 0.866025i 0.0258544 + 0.0447811i
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 7.00000 0.360997
\(377\) 9.00000 31.1769i 0.463524 1.60569i
\(378\) −1.00000 −0.0514344
\(379\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(380\) −1.00000 1.73205i −0.0512989 0.0888523i
\(381\) −6.00000 + 10.3923i −0.307389 + 0.532414i
\(382\) −4.00000 −0.204658
\(383\) −4.50000 + 7.79423i −0.229939 + 0.398266i −0.957790 0.287469i \(-0.907186\pi\)
0.727851 + 0.685736i \(0.240519\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 2.00000 0.101929
\(386\) −5.50000 + 9.52628i −0.279943 + 0.484875i
\(387\) 1.00000 + 1.73205i 0.0508329 + 0.0880451i
\(388\) 7.00000 + 12.1244i 0.355371 + 0.615521i
\(389\) 22.0000 1.11544 0.557722 0.830028i \(-0.311675\pi\)
0.557722 + 0.830028i \(0.311675\pi\)
\(390\) −7.00000 + 1.73205i −0.354459 + 0.0877058i
\(391\) 6.00000 0.303433
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) −4.00000 6.92820i −0.201773 0.349482i
\(394\) 13.5000 23.3827i 0.680120 1.17800i
\(395\) 22.0000 1.10694
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 10.5000 18.1865i 0.526980 0.912756i −0.472526 0.881317i \(-0.656658\pi\)
0.999506 0.0314391i \(-0.0100090\pi\)
\(398\) −10.0000 −0.501255
\(399\) −0.500000 + 0.866025i −0.0250313 + 0.0433555i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −3.00000 5.19615i −0.149813 0.259483i 0.781345 0.624099i \(-0.214534\pi\)
−0.931158 + 0.364615i \(0.881200\pi\)
\(402\) 2.00000 0.0997509
\(403\) 5.00000 + 5.19615i 0.249068 + 0.258839i
\(404\) −2.00000 −0.0995037
\(405\) −1.00000 1.73205i −0.0496904 0.0860663i
\(406\) −4.50000 7.79423i −0.223331 0.386821i
\(407\) −1.00000 + 1.73205i −0.0495682 + 0.0858546i
\(408\) −1.00000 −0.0495074
\(409\) −10.0000 + 17.3205i −0.494468 + 0.856444i −0.999980 0.00637586i \(-0.997970\pi\)
0.505511 + 0.862820i \(0.331304\pi\)
\(410\) 5.00000 8.66025i 0.246932 0.427699i
\(411\) 10.0000 0.493264
\(412\) 7.00000 12.1244i 0.344865 0.597324i
\(413\) 5.00000 + 8.66025i 0.246034 + 0.426143i
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) −24.0000 −1.17811
\(416\) 3.50000 0.866025i 0.171602 0.0424604i
\(417\) 9.00000 0.440732
\(418\) −0.500000 0.866025i −0.0244558 0.0423587i
\(419\) 10.0000 + 17.3205i 0.488532 + 0.846162i 0.999913 0.0131919i \(-0.00419923\pi\)
−0.511381 + 0.859354i \(0.670866\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) −3.00000 + 5.19615i −0.146038 + 0.252945i
\(423\) 3.50000 6.06218i 0.170176 0.294753i
\(424\) 1.00000 0.0485643
\(425\) −0.500000 + 0.866025i −0.0242536 + 0.0420084i
\(426\) 4.00000 + 6.92820i 0.193801 + 0.335673i
\(427\) −5.50000 9.52628i −0.266164 0.461009i
\(428\) 3.00000 0.145010
\(429\) −3.50000 + 0.866025i −0.168982 + 0.0418121i
\(430\) 4.00000 0.192897
\(431\) −14.0000 24.2487i −0.674356 1.16802i −0.976657 0.214807i \(-0.931088\pi\)
0.302300 0.953213i \(-0.402245\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 9.00000 15.5885i 0.432512 0.749133i −0.564577 0.825381i \(-0.690961\pi\)
0.997089 + 0.0762473i \(0.0242938\pi\)
\(434\) 2.00000 0.0960031
\(435\) 9.00000 15.5885i 0.431517 0.747409i
\(436\) −8.00000 + 13.8564i −0.383131 + 0.663602i
\(437\) −6.00000 −0.287019
\(438\) −4.00000 + 6.92820i −0.191127 + 0.331042i
\(439\) 10.0000 + 17.3205i 0.477274 + 0.826663i 0.999661 0.0260459i \(-0.00829161\pi\)
−0.522387 + 0.852709i \(0.674958\pi\)
\(440\) −1.00000 1.73205i −0.0476731 0.0825723i
\(441\) 1.00000 0.0476190
\(442\) 2.50000 + 2.59808i 0.118913 + 0.123578i
\(443\) 35.0000 1.66290 0.831450 0.555599i \(-0.187511\pi\)
0.831450 + 0.555599i \(0.187511\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) −11.0000 19.0526i −0.521450 0.903178i
\(446\) 10.0000 17.3205i 0.473514 0.820150i
\(447\) −6.00000 −0.283790
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) 15.0000 25.9808i 0.707894 1.22611i −0.257743 0.966213i \(-0.582979\pi\)
0.965637 0.259895i \(-0.0836878\pi\)
\(450\) 1.00000 0.0471405
\(451\) 2.50000 4.33013i 0.117720 0.203898i
\(452\) 3.00000 + 5.19615i 0.141108 + 0.244406i
\(453\) −1.50000 2.59808i −0.0704761 0.122068i
\(454\) −2.00000 −0.0938647
\(455\) 7.00000 1.73205i 0.328165 0.0811998i
\(456\) 1.00000 0.0468293
\(457\) 3.00000 + 5.19615i 0.140334 + 0.243066i 0.927622 0.373519i \(-0.121849\pi\)
−0.787288 + 0.616585i \(0.788516\pi\)
\(458\) −11.5000 19.9186i −0.537360 0.930734i
\(459\) −0.500000 + 0.866025i −0.0233380 + 0.0404226i
\(460\) −12.0000 −0.559503
\(461\) 12.0000 20.7846i 0.558896 0.968036i −0.438693 0.898637i \(-0.644559\pi\)
0.997589 0.0693989i \(-0.0221081\pi\)
\(462\) −0.500000 + 0.866025i −0.0232621 + 0.0402911i
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 2.00000 + 3.46410i 0.0927478 + 0.160644i
\(466\) 9.00000 + 15.5885i 0.416917 + 0.722121i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 1.00000 3.46410i 0.0462250 0.160128i
\(469\) −2.00000 −0.0923514
\(470\) −7.00000 12.1244i −0.322886 0.559255i
\(471\) 1.00000 + 1.73205i 0.0460776 + 0.0798087i
\(472\) 5.00000 8.66025i 0.230144 0.398621i
\(473\) 2.00000 0.0919601
\(474\) −5.50000 + 9.52628i −0.252623 + 0.437557i
\(475\) 0.500000 0.866025i 0.0229416 0.0397360i
\(476\) 1.00000 0.0458349
\(477\) 0.500000 0.866025i 0.0228934 0.0396526i
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) −5.50000 9.52628i −0.251301 0.435267i 0.712583 0.701588i \(-0.247525\pi\)
−0.963884 + 0.266321i \(0.914192\pi\)
\(480\) 2.00000 0.0912871
\(481\) −2.00000 + 6.92820i −0.0911922 + 0.315899i
\(482\) −16.0000 −0.728780
\(483\) 3.00000 + 5.19615i 0.136505 + 0.236433i
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 14.0000 24.2487i 0.635707 1.10108i
\(486\) 1.00000 0.0453609
\(487\) 14.5000 25.1147i 0.657058 1.13806i −0.324316 0.945949i \(-0.605134\pi\)
0.981374 0.192109i \(-0.0615326\pi\)
\(488\) −5.50000 + 9.52628i −0.248973 + 0.431234i
\(489\) −2.00000 −0.0904431
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 2.50000 + 4.33013i 0.112709 + 0.195217i
\(493\) −9.00000 −0.405340
\(494\) −2.50000 2.59808i −0.112480 0.116893i
\(495\) −2.00000 −0.0898933
\(496\) −1.00000 1.73205i −0.0449013 0.0777714i
\(497\) −4.00000 6.92820i −0.179425 0.310772i
\(498\) 6.00000 10.3923i 0.268866 0.465690i
\(499\) −30.0000 −1.34298 −0.671492 0.741012i \(-0.734346\pi\)
−0.671492 + 0.741012i \(0.734346\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 0 0
\(502\) 8.00000 0.357057
\(503\) 4.00000 6.92820i 0.178351 0.308913i −0.762965 0.646440i \(-0.776257\pi\)
0.941316 + 0.337527i \(0.109590\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 2.00000 + 3.46410i 0.0889988 + 0.154150i
\(506\) −6.00000 −0.266733
\(507\) −11.5000 + 6.06218i −0.510733 + 0.269231i
\(508\) −12.0000 −0.532414
\(509\) 6.00000 + 10.3923i 0.265945 + 0.460631i 0.967811 0.251679i \(-0.0809826\pi\)
−0.701866 + 0.712309i \(0.747649\pi\)
\(510\) 1.00000 + 1.73205i 0.0442807 + 0.0766965i
\(511\) 4.00000 6.92820i 0.176950 0.306486i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) −4.50000 + 7.79423i −0.198486 + 0.343789i
\(515\) −28.0000 −1.23383
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) −3.50000 6.06218i −0.153930 0.266614i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) −8.00000 −0.351161
\(520\) −5.00000 5.19615i −0.219265 0.227866i
\(521\) 19.0000 0.832405 0.416203 0.909272i \(-0.363361\pi\)
0.416203 + 0.909272i \(0.363361\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) 5.50000 + 9.52628i 0.240498 + 0.416555i 0.960856 0.277047i \(-0.0893559\pi\)
−0.720358 + 0.693602i \(0.756023\pi\)
\(524\) 4.00000 6.92820i 0.174741 0.302660i
\(525\) −1.00000 −0.0436436
\(526\) −14.0000 + 24.2487i −0.610429 + 1.05729i
\(527\) 1.00000 1.73205i 0.0435607 0.0754493i
\(528\) 1.00000 0.0435194
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −1.00000 1.73205i −0.0434372 0.0752355i
\(531\) −5.00000 8.66025i −0.216982 0.375823i
\(532\) −1.00000 −0.0433555
\(533\) 5.00000 17.3205i 0.216574 0.750234i
\(534\) 11.0000 0.476017
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) −16.0000 −0.689809
\(539\) 0.500000 0.866025i 0.0215365 0.0373024i
\(540\) 1.00000 1.73205i 0.0430331 0.0745356i
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 1.00000 1.73205i 0.0429537 0.0743980i
\(543\) −9.50000 16.4545i −0.407684 0.706129i
\(544\) −0.500000 0.866025i −0.0214373 0.0371305i
\(545\) 32.0000 1.37073
\(546\) −1.00000 + 3.46410i −0.0427960 + 0.148250i
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 5.00000 + 8.66025i 0.213589 + 0.369948i
\(549\) 5.50000 + 9.52628i 0.234734 + 0.406572i
\(550\) 0.500000 0.866025i 0.0213201 0.0369274i
\(551\) 9.00000 0.383413
\(552\) 3.00000 5.19615i 0.127688 0.221163i
\(553\) 5.50000 9.52628i 0.233884 0.405099i
\(554\) 2.00000 0.0849719
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 4.50000 + 7.79423i 0.190843 + 0.330549i
\(557\) 1.50000 + 2.59808i 0.0635570 + 0.110084i 0.896053 0.443947i \(-0.146422\pi\)
−0.832496 + 0.554031i \(0.813089\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 7.00000 1.73205i 0.296068 0.0732579i
\(560\) −2.00000 −0.0845154
\(561\) 0.500000 + 0.866025i 0.0211100 + 0.0365636i
\(562\) −10.0000 17.3205i −0.421825 0.730622i
\(563\) −17.0000 + 29.4449i −0.716465 + 1.24095i 0.245927 + 0.969288i \(0.420908\pi\)
−0.962392 + 0.271665i \(0.912426\pi\)
\(564\) 7.00000 0.294753
\(565\) 6.00000 10.3923i 0.252422 0.437208i
\(566\) −14.0000 + 24.2487i −0.588464 + 1.01925i
\(567\) −1.00000 −0.0419961
\(568\) −4.00000 + 6.92820i −0.167836 + 0.290701i
\(569\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) −1.00000 1.73205i −0.0418854 0.0725476i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) −2.50000 2.59808i −0.104530 0.108631i
\(573\) −4.00000 −0.167102
\(574\) −2.50000 4.33013i −0.104348 0.180736i
\(575\) −3.00000 5.19615i −0.125109 0.216695i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 12.0000 0.499567 0.249783 0.968302i \(-0.419641\pi\)
0.249783 + 0.968302i \(0.419641\pi\)
\(578\) −8.00000 + 13.8564i −0.332756 + 0.576351i
\(579\) −5.50000 + 9.52628i −0.228572 + 0.395899i
\(580\) 18.0000 0.747409
\(581\) −6.00000 + 10.3923i −0.248922 + 0.431145i
\(582\) 7.00000 + 12.1244i 0.290159 + 0.502571i
\(583\) −0.500000 0.866025i −0.0207079 0.0358671i
\(584\) −8.00000 −0.331042
\(585\) −7.00000 + 1.73205i −0.289414 + 0.0716115i
\(586\) −20.0000 −0.826192
\(587\) 13.0000 + 22.5167i 0.536567 + 0.929362i 0.999086 + 0.0427523i \(0.0136126\pi\)
−0.462518 + 0.886610i \(0.653054\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) −1.00000 + 1.73205i −0.0412043 + 0.0713679i
\(590\) −20.0000 −0.823387
\(591\) 13.5000 23.3827i 0.555316 0.961835i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −3.00000 −0.123195 −0.0615976 0.998101i \(-0.519620\pi\)
−0.0615976 + 0.998101i \(0.519620\pi\)
\(594\) 0.500000 0.866025i 0.0205152 0.0355335i
\(595\) −1.00000 1.73205i −0.0409960 0.0710072i
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) −10.0000 −0.409273
\(598\) −21.0000 + 5.19615i −0.858754 + 0.212486i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) −1.00000 1.73205i −0.0407909 0.0706518i 0.844909 0.534910i \(-0.179654\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) 1.00000 1.73205i 0.0407570 0.0705931i
\(603\) 2.00000 0.0814463
\(604\) 1.50000 2.59808i 0.0610341 0.105714i
\(605\) 10.0000 17.3205i 0.406558 0.704179i
\(606\) −2.00000 −0.0812444
\(607\) 23.0000 39.8372i 0.933541 1.61694i 0.156326 0.987705i \(-0.450035\pi\)
0.777215 0.629235i \(-0.216632\pi\)
\(608\) 0.500000 + 0.866025i 0.0202777 + 0.0351220i
\(609\) −4.50000 7.79423i −0.182349 0.315838i
\(610\) 22.0000 0.890754
\(611\) −17.5000 18.1865i −0.707974 0.735748i
\(612\) −1.00000 −0.0404226
\(613\) −14.0000 24.2487i −0.565455 0.979396i −0.997007 0.0773084i \(-0.975367\pi\)
0.431553 0.902088i \(-0.357966\pi\)
\(614\) 9.50000 + 16.4545i 0.383389 + 0.664049i
\(615\) 5.00000 8.66025i 0.201619 0.349215i
\(616\) −1.00000 −0.0402911
\(617\) 6.00000 10.3923i 0.241551 0.418378i −0.719605 0.694383i \(-0.755677\pi\)
0.961156 + 0.276005i \(0.0890106\pi\)
\(618\) 7.00000 12.1244i 0.281581 0.487713i
\(619\) 11.0000 0.442127 0.221064 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) −7.50000 12.9904i −0.300723 0.520867i
\(623\) −11.0000 −0.440706
\(624\) 3.50000 0.866025i 0.140112 0.0346688i
\(625\) −19.0000 −0.760000
\(626\) −6.00000 10.3923i −0.239808 0.415360i
\(627\) −0.500000 0.866025i −0.0199681 0.0345857i
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) 2.00000 0.0797452
\(630\) −1.00000 + 1.73205i −0.0398410 + 0.0690066i
\(631\) 16.5000 28.5788i 0.656855 1.13771i −0.324571 0.945861i \(-0.605220\pi\)
0.981425 0.191844i \(-0.0614468\pi\)
\(632\) −11.0000 −0.437557
\(633\) −3.00000 + 5.19615i −0.119239 + 0.206529i
\(634\) 15.0000 + 25.9808i 0.595726 + 1.03183i
\(635\) 12.0000 + 20.7846i 0.476205 + 0.824812i
\(636\) 1.00000 0.0396526
\(637\) 1.00000 3.46410i 0.0396214 0.137253i
\(638\) 9.00000 0.356313
\(639\) 4.00000 + 6.92820i 0.158238 + 0.274075i
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 3.00000 0.118401
\(643\) 21.5000 37.2391i 0.847877 1.46857i −0.0352216 0.999380i \(-0.511214\pi\)
0.883099 0.469187i \(-0.155453\pi\)
\(644\) −3.00000 + 5.19615i −0.118217 + 0.204757i
\(645\) 4.00000 0.157500
\(646\) −0.500000 + 0.866025i −0.0196722 + 0.0340733i
\(647\) −19.5000 33.7750i −0.766624 1.32783i −0.939384 0.342868i \(-0.888602\pi\)
0.172760 0.984964i \(-0.444732\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −10.0000 −0.392534
\(650\) 1.00000 3.46410i 0.0392232 0.135873i
\(651\) 2.00000 0.0783862
\(652\) −1.00000 1.73205i −0.0391630 0.0678323i
\(653\) 24.5000 + 42.4352i 0.958759 + 1.66062i 0.725521 + 0.688200i \(0.241599\pi\)
0.233238 + 0.972420i \(0.425068\pi\)
\(654\) −8.00000 + 13.8564i −0.312825 + 0.541828i
\(655\) −16.0000 −0.625172
\(656\) −2.50000 + 4.33013i −0.0976086 + 0.169063i
\(657\) −4.00000 + 6.92820i −0.156055 + 0.270295i
\(658\) −7.00000 −0.272888
\(659\) −4.50000 + 7.79423i −0.175295 + 0.303620i −0.940263 0.340448i \(-0.889421\pi\)
0.764968 + 0.644068i \(0.222755\pi\)
\(660\) −1.00000 1.73205i −0.0389249 0.0674200i
\(661\) 13.0000 + 22.5167i 0.505641 + 0.875797i 0.999979 + 0.00652642i \(0.00207744\pi\)
−0.494337 + 0.869270i \(0.664589\pi\)
\(662\) −26.0000 −1.01052
\(663\) 2.50000 + 2.59808i 0.0970920 + 0.100901i
\(664\) 12.0000 0.465690
\(665\) 1.00000 + 1.73205i 0.0387783 + 0.0671660i
\(666\) −1.00000 1.73205i −0.0387492 0.0671156i
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 0 0
\(669\) 10.0000 17.3205i 0.386622 0.669650i
\(670\) 2.00000 3.46410i 0.0772667 0.133830i
\(671\) 11.0000 0.424650
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 20.5000 + 35.5070i 0.790217 + 1.36870i 0.925832 + 0.377934i \(0.123365\pi\)
−0.135615 + 0.990762i \(0.543301\pi\)
\(674\) −16.5000 28.5788i −0.635556 1.10082i
\(675\) 1.00000 0.0384900
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) −4.00000 −0.153732 −0.0768662 0.997041i \(-0.524491\pi\)
−0.0768662 + 0.997041i \(0.524491\pi\)
\(678\) 3.00000 + 5.19615i 0.115214 + 0.199557i
\(679\) −7.00000 12.1244i −0.268635 0.465290i
\(680\) −1.00000 + 1.73205i −0.0383482 + 0.0664211i
\(681\) −2.00000 −0.0766402
\(682\) −1.00000 + 1.73205i −0.0382920 + 0.0663237i
\(683\) 2.00000 3.46410i 0.0765279 0.132550i −0.825222 0.564809i \(-0.808950\pi\)
0.901750 + 0.432259i \(0.142283\pi\)
\(684\) 1.00000 0.0382360
\(685\) 10.0000 17.3205i 0.382080 0.661783i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −11.5000 19.9186i −0.438752 0.759941i
\(688\) −2.00000 −0.0762493
\(689\) −2.50000 2.59808i −0.0952424 0.0989788i
\(690\) −12.0000 −0.456832
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) −4.00000 6.92820i −0.152057 0.263371i
\(693\) −0.500000 + 0.866025i −0.0189934 + 0.0328976i
\(694\) 3.00000 0.113878
\(695\) 9.00000 15.5885i 0.341389 0.591304i
\(696\) −4.50000 + 7.79423i −0.170572 + 0.295439i
\(697\) −5.00000 −0.189389
\(698\) −3.00000 + 5.19615i −0.113552 + 0.196677i
\(699\) 9.00000 + 15.5885i 0.340411 + 0.589610i
\(700\) −0.500000 0.866025i −0.0188982 0.0327327i
\(701\) 1.00000 0.0377695 0.0188847 0.999822i \(-0.493988\pi\)
0.0188847 + 0.999822i \(0.493988\pi\)
\(702\) 1.00000 3.46410i 0.0377426 0.130744i
\(703\) −2.00000 −0.0754314
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) −7.00000 12.1244i −0.263635 0.456630i
\(706\) 13.0000 22.5167i 0.489261 0.847426i
\(707\) 2.00000 0.0752177
\(708\) 5.00000 8.66025i 0.187912 0.325472i
\(709\) −12.0000 + 20.7846i −0.450669 + 0.780582i −0.998428 0.0560542i \(-0.982148\pi\)
0.547758 + 0.836637i \(0.315481\pi\)
\(710\) 16.0000 0.600469
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 5.50000 + 9.52628i 0.206121 + 0.357012i
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) 1.00000 0.0374241
\(715\) −2.00000 + 6.92820i −0.0747958 + 0.259100i
\(716\) −12.0000 −0.448461
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) −15.0000 25.9808i −0.559795 0.969593i
\(719\) −7.50000 + 12.9904i −0.279703 + 0.484459i −0.971311 0.237814i \(-0.923569\pi\)
0.691608 + 0.722273i \(0.256903\pi\)
\(720\) 2.00000 0.0745356
\(721\) −7.00000 + 12.1244i −0.260694 + 0.451535i
\(722\) −9.00000 + 15.5885i −0.334945 + 0.580142i
\(723\) −16.0000 −0.595046
\(724\) 9.50000 16.4545i 0.353065 0.611526i
\(725\) 4.50000 + 7.79423i 0.167126 + 0.289470i
\(726\) 5.00000 + 8.66025i 0.185567 + 0.321412i
\(727\) −52.0000 −1.92857 −0.964287 0.264861i \(-0.914674\pi\)
−0.964287 + 0.264861i \(0.914674\pi\)
\(728\) −3.50000 + 0.866025i −0.129719 + 0.0320970i
\(729\) 1.00000 0.0370370
\(730\) 8.00000 + 13.8564i 0.296093 + 0.512849i
\(731\) −1.00000 1.73205i −0.0369863 0.0640622i
\(732\) −5.50000 + 9.52628i −0.203286 + 0.352101i
\(733\) 43.0000 1.58824 0.794121 0.607760i \(-0.207932\pi\)
0.794121 + 0.607760i \(0.207932\pi\)
\(734\) −7.00000 + 12.1244i −0.258375 + 0.447518i
\(735\) 1.00000 1.73205i 0.0368856 0.0638877i
\(736\) 6.00000 0.221163
\(737\) 1.00000 1.73205i 0.0368355 0.0638009i
\(738\) 2.50000 + 4.33013i 0.0920263 + 0.159394i
\(739\) 19.0000 + 32.9090i 0.698926 + 1.21058i 0.968839 + 0.247691i \(0.0796718\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(740\) −4.00000 −0.147043
\(741\) −2.50000 2.59808i −0.0918398 0.0954427i
\(742\) −1.00000 −0.0367112
\(743\) 21.0000 + 36.3731i 0.770415 + 1.33440i 0.937336 + 0.348428i \(0.113284\pi\)
−0.166920 + 0.985970i \(0.553382\pi\)
\(744\) −1.00000 1.73205i −0.0366618 0.0635001i
\(745\) −6.00000 + 10.3923i −0.219823 + 0.380745i
\(746\) 0 0
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) −0.500000 + 0.866025i −0.0182818 + 0.0316650i
\(749\) −3.00000 −0.109618
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) −11.5000 19.9186i −0.419641 0.726839i 0.576262 0.817265i \(-0.304511\pi\)
−0.995903 + 0.0904254i \(0.971177\pi\)
\(752\) 3.50000 + 6.06218i 0.127632 + 0.221065i
\(753\) 8.00000 0.291536
\(754\) 31.5000 7.79423i 1.14716 0.283849i
\(755\) −6.00000 −0.218362
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) 18.0000 + 31.1769i 0.654221 + 1.13314i 0.982088 + 0.188420i \(0.0603368\pi\)
−0.327867 + 0.944724i \(0.606330\pi\)
\(758\) 0 0
\(759\) −6.00000 −0.217786
\(760\) 1.00000 1.73205i 0.0362738 0.0628281i
\(761\) −5.00000 + 8.66025i −0.181250 + 0.313934i −0.942306 0.334752i \(-0.891348\pi\)
0.761057 + 0.648686i \(0.224681\pi\)
\(762\) −12.0000 −0.434714
\(763\) 8.00000 13.8564i 0.289619 0.501636i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) −9.00000 −0.325183
\(767\) −35.0000 + 8.66025i −1.26378 + 0.312704i
\(768\) −1.00000 −0.0360844
\(769\) 23.0000 + 39.8372i 0.829401 + 1.43657i 0.898509 + 0.438956i \(0.144652\pi\)
−0.0691074 + 0.997609i \(0.522015\pi\)
\(770\) 1.00000 + 1.73205i 0.0360375 + 0.0624188i
\(771\) −4.50000 + 7.79423i −0.162064 + 0.280702i
\(772\) −11.0000 −0.395899
\(773\) −27.0000 + 46.7654i −0.971123 + 1.68203i −0.278944 + 0.960307i \(0.589984\pi\)
−0.692179 + 0.721726i \(0.743349\pi\)
\(774\) −1.00000 + 1.73205i −0.0359443 + 0.0622573i
\(775\) −2.00000 −0.0718421
\(776\) −7.00000 + 12.1244i −0.251285 + 0.435239i
\(777\) 1.00000 + 1.73205i 0.0358748 + 0.0621370i
\(778\) 11.0000 + 19.0526i 0.394369 + 0.683067i
\(779\) 5.00000 0.179144
\(780\) −5.00000 5.19615i −0.179029 0.186052i
\(781\) 8.00000 0.286263
\(782\) 3.00000 + 5.19615i 0.107280 + 0.185814i
\(783\) 4.50000 + 7.79423i 0.160817 + 0.278543i
\(784\) −0.500000 + 0.866025i −0.0178571 + 0.0309295i
\(785\) 4.00000 0.142766
\(786\) 4.00000 6.92820i 0.142675 0.247121i
\(787\) 14.5000 25.1147i 0.516869 0.895244i −0.482939 0.875654i \(-0.660431\pi\)
0.999808 0.0195896i \(-0.00623598\pi\)
\(788\) 27.0000 0.961835
\(789\) −14.0000 + 24.2487i −0.498413 + 0.863277i
\(790\) 11.0000 + 19.0526i 0.391362 + 0.677860i
\(791\) −3.00000 5.19615i −0.106668 0.184754i
\(792\) 1.00000 0.0355335
\(793\) 38.5000 9.52628i 1.36718 0.338288i
\(794\) 21.0000 0.745262
\(795\) −1.00000 1.73205i −0.0354663 0.0614295i
\(796\) −5.00000 8.66025i −0.177220 0.306955i
\(797\) −26.0000 + 45.0333i −0.920967 + 1.59516i −0.123045 + 0.992401i \(0.539266\pi\)
−0.797922 + 0.602761i \(0.794067\pi\)
\(798\) −1.00000 −0.0353996
\(799\) −3.50000 + 6.06218i −0.123821 + 0.214464i
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) 11.0000 0.388666
\(802\) 3.00000 5.19615i 0.105934 0.183483i
\(803\) 4.00000 + 6.92820i 0.141157 + 0.244491i
\(804\) 1.00000 + 1.73205i 0.0352673 + 0.0610847i
\(805\) 12.0000 0.422944
\(806\) −2.00000 + 6.92820i −0.0704470 + 0.244036i
\(807\) −16.0000 −0.563227
\(808\) −1.00000 1.73205i −0.0351799 0.0609333i
\(809\) 14.0000 + 24.2487i 0.492214 + 0.852539i 0.999960 0.00896753i \(-0.00285449\pi\)
−0.507746 + 0.861507i \(0.669521\pi\)
\(810\) 1.00000 1.73205i 0.0351364 0.0608581i
\(811\) −36.0000 −1.26413 −0.632065 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) 4.50000 7.79423i 0.157919 0.273524i
\(813\) 1.00000 1.73205i 0.0350715 0.0607457i
\(814\) −2.00000 −0.0701000
\(815\) −2.00000 + 3.46410i −0.0700569 + 0.121342i
\(816\) −0.500000 0.866025i −0.0175035 0.0303170i
\(817\) 1.00000 + 1.73205i 0.0349856 + 0.0605968i
\(818\) −20.0000 −0.699284
\(819\) −1.00000 + 3.46410i −0.0349428 + 0.121046i
\(820\) 10.0000 0.349215
\(821\) 22.5000 + 38.9711i 0.785255 + 1.36010i 0.928846 + 0.370465i \(0.120802\pi\)
−0.143591 + 0.989637i \(0.545865\pi\)
\(822\) 5.00000 + 8.66025i 0.174395 + 0.302061i
\(823\) 8.00000 13.8564i 0.278862 0.483004i −0.692240 0.721668i \(-0.743376\pi\)
0.971102 + 0.238664i \(0.0767093\pi\)
\(824\) 14.0000 0.487713
\(825\) 0.500000 0.866025i 0.0174078 0.0301511i
\(826\) −5.00000 + 8.66025i −0.173972 + 0.301329i
\(827\) 16.0000 0.556375 0.278187 0.960527i \(-0.410266\pi\)
0.278187 + 0.960527i \(0.410266\pi\)
\(828\) 3.00000 5.19615i 0.104257 0.180579i
\(829\) −9.50000 16.4545i −0.329949 0.571488i 0.652553 0.757743i \(-0.273698\pi\)
−0.982501 + 0.186256i \(0.940365\pi\)
\(830\) −12.0000 20.7846i −0.416526 0.721444i
\(831\) 2.00000 0.0693792
\(832\) 2.50000 + 2.59808i 0.0866719 + 0.0900721i
\(833\) −1.00000 −0.0346479
\(834\) 4.50000 + 7.79423i 0.155822 + 0.269892i
\(835\) 0 0
\(836\) 0.500000 0.866025i 0.0172929 0.0299521i
\(837\) −2.00000 −0.0691301
\(838\) −10.0000 + 17.3205i −0.345444 + 0.598327i
\(839\) −4.00000 + 6.92820i −0.138095 + 0.239188i −0.926776 0.375615i \(-0.877431\pi\)
0.788680 + 0.614804i \(0.210765\pi\)
\(840\) −2.00000 −0.0690066
\(841\) −26.0000 + 45.0333i −0.896552 + 1.55287i
\(842\) −13.0000 22.5167i −0.448010 0.775975i
\(843\) −10.0000 17.3205i −0.344418 0.596550i
\(844\) −6.00000 −0.206529
\(845\) −1.00000 + 25.9808i −0.0344010 + 0.893765i
\(846\) 7.00000 0.240665
\(847\) −5.00000 8.66025i −0.171802 0.297570i
\(848\) 0.500000 + 0.866025i 0.0171701 + 0.0297394i
\(849\) −14.0000 + 24.2487i −0.480479 + 0.832214i
\(850\) −1.00000 −0.0342997
\(851\) −6.00000 + 10.3923i −0.205677 + 0.356244i
\(852\) −4.00000 + 6.92820i −0.137038 + 0.237356i
\(853\) −53.0000 −1.81469 −0.907343 0.420392i \(-0.861893\pi\)
−0.907343 + 0.420392i \(0.861893\pi\)
\(854\) 5.50000 9.52628i 0.188206 0.325983i
\(855\) −1.00000 1.73205i −0.0341993 0.0592349i
\(856\) 1.50000 + 2.59808i 0.0512689 + 0.0888004i
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) −2.50000 2.59808i −0.0853486 0.0886969i
\(859\) 49.0000 1.67186 0.835929 0.548837i \(-0.184929\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(860\) 2.00000 + 3.46410i 0.0681994 + 0.118125i
\(861\) −2.50000 4.33013i −0.0851998 0.147570i
\(862\) 14.0000 24.2487i 0.476842 0.825914i
\(863\) −50.0000 −1.70202 −0.851010 0.525150i \(-0.824009\pi\)
−0.851010 + 0.525150i \(0.824009\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) −8.00000 + 13.8564i −0.272008 + 0.471132i
\(866\) 18.0000 0.611665
\(867\) −8.00000 + 13.8564i −0.271694 + 0.470588i
\(868\) 1.00000 + 1.73205i 0.0339422 + 0.0587896i
\(869\) 5.50000 + 9.52628i 0.186575 + 0.323157i
\(870\) 18.0000 0.610257
\(871\) 2.00000 6.92820i 0.0677674 0.234753i
\(872\) −16.0000 −0.541828
\(873\) 7.00000 + 12.1244i 0.236914 + 0.410347i
\(874\) −3.00000 5.19615i −0.101477 0.175762i
\(875\) −6.00000 + 10.3923i −0.202837 + 0.351324i
\(876\) −8.00000 −0.270295
\(877\) 10.0000 17.3205i 0.337676 0.584872i −0.646319 0.763067i \(-0.723693\pi\)
0.983995 + 0.178195i \(0.0570259\pi\)
\(878\) −10.0000 + 17.3205i −0.337484 + 0.584539i
\(879\) −20.0000 −0.674583
\(880\) 1.00000 1.73205i 0.0337100 0.0583874i
\(881\) −1.00000 1.73205i −0.0336909 0.0583543i 0.848688 0.528893i \(-0.177393\pi\)
−0.882379 + 0.470539i \(0.844059\pi\)
\(882\) 0.500000 + 0.866025i 0.0168359 + 0.0291606i
\(883\) 46.0000 1.54802 0.774012 0.633171i \(-0.218247\pi\)
0.774012 + 0.633171i \(0.218247\pi\)
\(884\) −1.00000 + 3.46410i −0.0336336 + 0.116510i
\(885\) −20.0000 −0.672293
\(886\) 17.5000 + 30.3109i 0.587924 + 1.01831i
\(887\) 10.5000 + 18.1865i 0.352555 + 0.610644i 0.986696 0.162573i \(-0.0519794\pi\)
−0.634141 + 0.773217i \(0.718646\pi\)
\(888\) 1.00000 1.73205i 0.0335578 0.0581238i
\(889\) 12.0000 0.402467
\(890\) 11.0000 19.0526i 0.368721 0.638643i
\(891\) 0.500000 0.866025i 0.0167506 0.0290129i
\(892\) 20.0000 0.669650
\(893\) 3.50000 6.06218i 0.117123 0.202863i
\(894\) −3.00000 5.19615i −0.100335 0.173785i
\(895\) 12.0000 + 20.7846i 0.401116 + 0.694753i
\(896\) 1.00000 0.0334077
\(897\) −21.0000 + 5.19615i −0.701170 + 0.173494i
\(898\) 30.0000 1.00111
\(899\) −9.00000 15.5885i −0.300167 0.519904i
\(900\) 0.500000 + 0.866025i 0.0166667 + 0.0288675i
\(901\) −0.500000 + 0.866025i −0.0166574 + 0.0288515i
\(902\) 5.00000 0.166482
\(903\) 1.00000 1.73205i 0.0332779 0.0576390i
\(904\) −3.00000 + 5.19615i −0.0997785 + 0.172821i
\(905\) −38.0000 −1.26316
\(906\) 1.50000 2.59808i 0.0498342 0.0863153i
\(907\) −17.0000 29.4449i −0.564476 0.977701i −0.997098 0.0761255i \(-0.975745\pi\)
0.432623 0.901575i \(-0.357588\pi\)
\(908\) −1.00000 1.73205i −0.0331862 0.0574801i
\(909\) −2.00000 −0.0663358
\(910\) 5.00000 + 5.19615i 0.165748 + 0.172251i
\(911\) 40.0000 1.32526 0.662630 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) 0.500000 + 0.866025i 0.0165567 + 0.0286770i
\(913\) −6.00000 10.3923i −0.198571 0.343935i
\(914\) −3.00000 + 5.19615i −0.0992312 + 0.171873i
\(915\) 22.0000 0.727298
\(916\) 11.5000 19.9186i 0.379971 0.658129i
\(917\) −4.00000 + 6.92820i −0.132092 + 0.228789i
\(918\) −1.00000 −0.0330049
\(919\) −14.5000 + 25.1147i −0.478311 + 0.828459i −0.999691 0.0248659i \(-0.992084\pi\)
0.521380 + 0.853325i \(0.325417\pi\)
\(920\) −6.00000 10.3923i −0.197814 0.342624i
\(921\) 9.50000 + 16.4545i 0.313036 + 0.542194i
\(922\) 24.0000 0.790398
\(923\) 28.0000 6.92820i 0.921631 0.228045i
\(924\) −1.00000 −0.0328976
\(925\) −1.00000 1.73205i −0.0328798 0.0569495i
\(926\) 0.500000 + 0.866025i 0.0164310 + 0.0284594i
\(927\) 7.00000 12.1244i 0.229910 0.398216i
\(928\) −9.00000 −0.295439
\(929\) −6.50000 + 11.2583i −0.213258 + 0.369374i −0.952732 0.303811i \(-0.901741\pi\)
0.739474 + 0.673185i \(0.235074\pi\)
\(930\) −2.00000 + 3.46410i −0.0655826 + 0.113592i
\(931\) 1.00000 0.0327737
\(932\) −9.00000 + 15.5885i −0.294805 + 0.510617i
\(933\) −7.50000 12.9904i −0.245539 0.425286i
\(934\) 4.00000 + 6.92820i 0.130884 + 0.226698i
\(935\) 2.00000 0.0654070
\(936\) 3.50000 0.866025i 0.114401 0.0283069i
\(937\) −4.00000 −0.130674 −0.0653372 0.997863i \(-0.520812\pi\)
−0.0653372 + 0.997863i \(0.520812\pi\)
\(938\) −1.00000 1.73205i −0.0326512 0.0565535i
\(939\) −6.00000 10.3923i −0.195803 0.339140i
\(940\) 7.00000 12.1244i 0.228315 0.395453i
\(941\) 32.0000 1.04317 0.521585 0.853199i \(-0.325341\pi\)
0.521585 + 0.853199i \(0.325341\pi\)
\(942\) −1.00000 + 1.73205i −0.0325818 + 0.0564333i
\(943\) 15.0000 25.9808i 0.488467 0.846050i
\(944\) 10.0000 0.325472
\(945\) −1.00000 + 1.73205i −0.0325300 + 0.0563436i
\(946\) 1.00000 + 1.73205i 0.0325128 + 0.0563138i
\(947\) 9.50000 + 16.4545i 0.308709 + 0.534699i 0.978080 0.208229i \(-0.0667699\pi\)
−0.669372 + 0.742928i \(0.733437\pi\)
\(948\) −11.0000 −0.357263
\(949\) 20.0000 + 20.7846i 0.649227 + 0.674697i
\(950\) 1.00000 0.0324443
\(951\) 15.0000 + 25.9808i 0.486408 + 0.842484i
\(952\) 0.500000 + 0.866025i 0.0162051 + 0.0280680i
\(953\) 15.0000 25.9808i 0.485898 0.841599i −0.513971 0.857808i \(-0.671826\pi\)
0.999869 + 0.0162081i \(0.00515944\pi\)
\(954\) 1.00000 0.0323762
\(955\) −4.00000 + 6.92820i −0.129437 + 0.224191i
\(956\) 6.00000 10.3923i 0.194054 0.336111i
\(957\) 9.00000 0.290929
\(958\) 5.50000 9.52628i 0.177697 0.307780i
\(959\) −5.00000 8.66025i −0.161458 0.279654i
\(960\) 1.00000 + 1.73205i 0.0322749 + 0.0559017i
\(961\) −27.0000 −0.870968
\(962\) −7.00000 + 1.73205i −0.225689 + 0.0558436i
\(963\) 3.00000 0.0966736
\(964\) −8.00000 13.8564i −0.257663 0.446285i
\(965\) 11.0000 + 19.0526i 0.354103 + 0.613324i
\(966\) −3.00000 + 5.19615i −0.0965234 + 0.167183i
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) −5.00000 + 8.66025i −0.160706 + 0.278351i
\(969\) −0.500000 + 0.866025i −0.0160623 + 0.0278207i
\(970\) 28.0000 0.899026
\(971\) 29.0000 50.2295i 0.930654 1.61194i 0.148449 0.988920i \(-0.452572\pi\)
0.782206 0.623020i \(-0.214095\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) −4.50000 7.79423i −0.144263 0.249871i
\(974\) 29.0000 0.929220
\(975\) 1.00000 3.46410i 0.0320256 0.110940i
\(976\) −11.0000 −0.352101
\(977\) −18.0000 31.1769i −0.575871 0.997438i −0.995946 0.0899487i \(-0.971330\pi\)
0.420075 0.907489i \(-0.362004\pi\)
\(978\) −1.00000 1.73205i −0.0319765 0.0553849i
\(979\) 5.50000 9.52628i 0.175781 0.304461i
\(980\) 2.00000 0.0638877
\(981\) −8.00000 + 13.8564i −0.255420 + 0.442401i
\(982\) 0 0
\(983\) −48.0000 −1.53096 −0.765481 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) −2.50000 + 4.33013i −0.0796971 + 0.138039i
\(985\) −27.0000 46.7654i −0.860292 1.49007i
\(986\) −4.50000 7.79423i −0.143309 0.248219i
\(987\) −7.00000 −0.222812
\(988\) 1.00000 3.46410i 0.0318142 0.110208i
\(989\) 12.0000 0.381578
\(990\) −1.00000 1.73205i −0.0317821 0.0550482i
\(991\) −22.5000 38.9711i −0.714736 1.23796i −0.963061 0.269282i \(-0.913213\pi\)
0.248325 0.968677i \(-0.420120\pi\)
\(992\) 1.00000 1.73205i 0.0317500 0.0549927i
\(993\) −26.0000 −0.825085
\(994\) 4.00000 6.92820i 0.126872 0.219749i
\(995\) −10.0000 + 17.3205i −0.317021 + 0.549097i
\(996\) 12.0000 0.380235
\(997\) 17.5000 30.3109i 0.554231 0.959955i −0.443732 0.896159i \(-0.646346\pi\)
0.997963 0.0637961i \(-0.0203207\pi\)
\(998\) −15.0000 25.9808i −0.474817 0.822407i
\(999\) −1.00000 1.73205i −0.0316386 0.0547997i
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.l.g.211.1 2
3.2 odd 2 1638.2.r.d.757.1 2
13.3 even 3 7098.2.a.e.1.1 1
13.9 even 3 inner 546.2.l.g.295.1 yes 2
13.10 even 6 7098.2.a.r.1.1 1
39.35 odd 6 1638.2.r.d.1387.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.l.g.211.1 2 1.1 even 1 trivial
546.2.l.g.295.1 yes 2 13.9 even 3 inner
1638.2.r.d.757.1 2 3.2 odd 2
1638.2.r.d.1387.1 2 39.35 odd 6
7098.2.a.e.1.1 1 13.3 even 3
7098.2.a.r.1.1 1 13.10 even 6