Properties

Label 1470.2.n.d.79.1
Level $1470$
Weight $2$
Character 1470.79
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(79,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), not 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: \(11.7380090971\)
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 79.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.d.949.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.86603 + 1.23205i) q^{10} +(-0.866025 - 0.500000i) q^{12} +2.00000i q^{13} +(2.00000 - 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(-6.92820 - 4.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000i q^{27} +8.00000 q^{29} +(-2.23205 - 0.133975i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +1.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.133975 + 2.23205i) q^{40} -10.0000 q^{41} +2.00000i q^{43} +(-1.23205 + 1.86603i) q^{45} +(4.00000 + 6.92820i) q^{46} +(5.19615 + 3.00000i) q^{47} -1.00000i q^{48} +(-4.00000 - 3.00000i) q^{50} +(1.00000 - 1.73205i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} -2.00000i q^{57} +(-6.92820 - 4.00000i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(1.86603 + 1.23205i) q^{60} +(1.00000 - 1.73205i) q^{61} -4.00000i q^{62} -1.00000 q^{64} +(0.267949 - 4.46410i) q^{65} +(12.1244 - 7.00000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +8.00000 q^{69} +6.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(3.00000 + 5.19615i) q^{74} +(-4.59808 + 1.96410i) q^{75} -2.00000 q^{76} +2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(1.23205 - 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.66025 + 5.00000i) q^{82} -12.0000i q^{83} +(4.00000 - 2.00000i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-6.92820 + 4.00000i) q^{87} +(7.00000 - 12.1244i) q^{89} +(2.00000 - 1.00000i) q^{90} -8.00000i q^{92} +(-3.46410 - 2.00000i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(2.46410 - 3.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +14.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9} + 4 q^{10} + 8 q^{15} - 2 q^{16} - 4 q^{19} - 4 q^{20} + 2 q^{24} + 6 q^{25} + 4 q^{26} + 32 q^{29} - 2 q^{30} + 8 q^{31} + 8 q^{34} + 4 q^{36} - 4 q^{39} - 4 q^{40} - 40 q^{41} + 2 q^{45} + 16 q^{46} - 16 q^{50} + 4 q^{51} + 2 q^{54} - 24 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{64} + 8 q^{65} + 32 q^{69} + 24 q^{71} + 12 q^{74} - 8 q^{75} - 8 q^{76} + 8 q^{79} - 2 q^{80} - 2 q^{81} + 16 q^{85} + 4 q^{86} + 28 q^{89} + 8 q^{90} - 12 q^{94} - 4 q^{95} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.23205 0.133975i −0.998203 0.0599153i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.86603 + 1.23205i 0.590089 + 0.389609i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) 2.00000 1.00000i 0.516398 0.258199i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.73205 + 1.00000i −0.420084 + 0.242536i −0.695113 0.718900i \(-0.744646\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.00000 2.00000i −0.223607 0.447214i
\(21\) 0 0
\(22\) 0 0
\(23\) −6.92820 4.00000i −1.44463 0.834058i −0.446476 0.894795i \(-0.647321\pi\)
−0.998154 + 0.0607377i \(0.980655\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 4.96410 + 0.598076i 0.992820 + 0.119615i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) −2.23205 0.133975i −0.407515 0.0244603i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −5.19615 3.00000i −0.854242 0.493197i 0.00783774 0.999969i \(-0.497505\pi\)
−0.862080 + 0.506772i \(0.830838\pi\)
\(38\) 1.73205 1.00000i 0.280976 0.162221i
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) −0.133975 + 2.23205i −0.0211832 + 0.352918i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 0 0
\(45\) −1.23205 + 1.86603i −0.183663 + 0.278171i
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) 5.19615 + 3.00000i 0.757937 + 0.437595i 0.828554 0.559908i \(-0.189164\pi\)
−0.0706177 + 0.997503i \(0.522497\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 1.00000 1.73205i 0.140028 0.242536i
\(52\) −1.73205 + 1.00000i −0.240192 + 0.138675i
\(53\) 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000i 0.264906i
\(58\) −6.92820 4.00000i −0.909718 0.525226i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) 1.86603 + 1.23205i 0.240903 + 0.159057i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.267949 4.46410i 0.0332350 0.553704i
\(66\) 0 0
\(67\) 12.1244 7.00000i 1.48123 0.855186i 0.481452 0.876472i \(-0.340109\pi\)
0.999773 + 0.0212861i \(0.00677610\pi\)
\(68\) −1.73205 1.00000i −0.210042 0.121268i
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 8.66025 5.00000i 1.01361 0.585206i 0.101361 0.994850i \(-0.467680\pi\)
0.912245 + 0.409644i \(0.134347\pi\)
\(74\) 3.00000 + 5.19615i 0.348743 + 0.604040i
\(75\) −4.59808 + 1.96410i −0.530940 + 0.226795i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 2.00000i 0.226455i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 1.23205 1.86603i 0.137747 0.208628i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 8.66025 + 5.00000i 0.956365 + 0.552158i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) 4.00000 2.00000i 0.433861 0.216930i
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −6.92820 + 4.00000i −0.742781 + 0.428845i
\(88\) 0 0
\(89\) 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i \(-0.567211\pi\)
0.951584 0.307389i \(-0.0994552\pi\)
\(90\) 2.00000 1.00000i 0.210819 0.105409i
\(91\) 0 0
\(92\) 8.00000i 0.834058i
\(93\) −3.46410 2.00000i −0.359211 0.207390i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 2.46410 3.73205i 0.252811 0.382900i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 14.0000i 1.42148i 0.703452 + 0.710742i \(0.251641\pi\)
−0.703452 + 0.710742i \(0.748359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.96410 + 4.59808i 0.196410 + 0.459808i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) −1.73205 + 1.00000i −0.171499 + 0.0990148i
\(103\) −3.46410 2.00000i −0.341328 0.197066i 0.319531 0.947576i \(-0.396475\pi\)
−0.660859 + 0.750510i \(0.729808\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 10.0000i 0.940721i 0.882474 + 0.470360i \(0.155876\pi\)
−0.882474 + 0.470360i \(0.844124\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) 14.9282 + 9.85641i 1.39206 + 0.919115i
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) 1.73205 + 1.00000i 0.160128 + 0.0924500i
\(118\) 12.0000i 1.10469i
\(119\) 0 0
\(120\) −1.00000 2.00000i −0.0912871 0.182574i
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) −1.73205 + 1.00000i −0.156813 + 0.0905357i
\(123\) 8.66025 5.00000i 0.780869 0.450835i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 0 0
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −1.00000 1.73205i −0.0880451 0.152499i
\(130\) −2.46410 + 3.73205i −0.216116 + 0.327323i
\(131\) 4.00000 6.92820i 0.349482 0.605320i −0.636676 0.771132i \(-0.719691\pi\)
0.986157 + 0.165812i \(0.0530244\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −14.0000 −1.20942
\(135\) 0.133975 2.23205i 0.0115307 0.192104i
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) 1.73205 1.00000i 0.147979 0.0854358i −0.424182 0.905577i \(-0.639438\pi\)
0.572161 + 0.820141i \(0.306105\pi\)
\(138\) −6.92820 4.00000i −0.589768 0.340503i
\(139\) 22.0000 1.86602 0.933008 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −5.19615 3.00000i −0.436051 0.251754i
\(143\) 0 0
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −17.8564 1.07180i −1.48289 0.0890079i
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 10.0000 17.3205i 0.819232 1.41895i −0.0870170 0.996207i \(-0.527733\pi\)
0.906249 0.422744i \(-0.138933\pi\)
\(150\) 4.96410 + 0.598076i 0.405317 + 0.0488327i
\(151\) −10.0000 17.3205i −0.813788 1.40952i −0.910195 0.414181i \(-0.864068\pi\)
0.0964061 0.995342i \(-0.469265\pi\)
\(152\) 1.73205 + 1.00000i 0.140488 + 0.0811107i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) −4.00000 8.00000i −0.321288 0.642575i
\(156\) 1.00000 1.73205i 0.0800641 0.138675i
\(157\) 1.73205 1.00000i 0.138233 0.0798087i −0.429289 0.903167i \(-0.641236\pi\)
0.567521 + 0.823359i \(0.307902\pi\)
\(158\) −3.46410 + 2.00000i −0.275589 + 0.159111i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −1.73205 1.00000i −0.135665 0.0783260i 0.430632 0.902528i \(-0.358291\pi\)
−0.566296 + 0.824202i \(0.691624\pi\)
\(164\) −5.00000 8.66025i −0.390434 0.676252i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 2.00000i 0.154765i −0.997001 0.0773823i \(-0.975344\pi\)
0.997001 0.0773823i \(-0.0246562\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −4.46410 0.267949i −0.342381 0.0205508i
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) −1.73205 + 1.00000i −0.132068 + 0.0762493i
\(173\) 10.3923 + 6.00000i 0.790112 + 0.456172i 0.840002 0.542583i \(-0.182554\pi\)
−0.0498898 + 0.998755i \(0.515887\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) 0 0
\(177\) 10.3923 + 6.00000i 0.781133 + 0.450988i
\(178\) −12.1244 + 7.00000i −0.908759 + 0.524672i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −2.23205 0.133975i −0.166367 0.00998588i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) −4.00000 + 6.92820i −0.294884 + 0.510754i
\(185\) 11.1962 + 7.39230i 0.823157 + 0.543493i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 0 0
\(188\) 6.00000i 0.437595i
\(189\) 0 0
\(190\) −4.00000 + 2.00000i −0.290191 + 0.145095i
\(191\) −11.0000 + 19.0526i −0.795932 + 1.37859i 0.126314 + 0.991990i \(0.459685\pi\)
−0.922246 + 0.386604i \(0.873648\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −17.3205 + 10.0000i −1.24676 + 0.719816i −0.970461 0.241257i \(-0.922440\pi\)
−0.276296 + 0.961073i \(0.589107\pi\)
\(194\) 7.00000 12.1244i 0.502571 0.870478i
\(195\) 2.00000 + 4.00000i 0.143223 + 0.286446i
\(196\) 0 0
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 0 0
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 0.598076 4.96410i 0.0422904 0.351015i
\(201\) −7.00000 + 12.1244i −0.493742 + 0.855186i
\(202\) 6.00000i 0.422159i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 22.3205 + 1.33975i 1.55893 + 0.0935719i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) −6.92820 + 4.00000i −0.481543 + 0.278019i
\(208\) −1.73205 1.00000i −0.120096 0.0693375i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 5.19615 + 3.00000i 0.356873 + 0.206041i
\(213\) −5.19615 + 3.00000i −0.356034 + 0.205557i
\(214\) 0 0
\(215\) 0.267949 4.46410i 0.0182740 0.304449i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 2.00000i 0.135457i
\(219\) −5.00000 + 8.66025i −0.337869 + 0.585206i
\(220\) 0 0
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) −5.19615 3.00000i −0.348743 0.201347i
\(223\) 20.0000i 1.33930i −0.742677 0.669650i \(-0.766444\pi\)
0.742677 0.669650i \(-0.233556\pi\)
\(224\) 0 0
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) −13.8564 + 8.00000i −0.919682 + 0.530979i −0.883534 0.468368i \(-0.844842\pi\)
−0.0361484 + 0.999346i \(0.511509\pi\)
\(228\) 1.73205 1.00000i 0.114708 0.0662266i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) −8.00000 16.0000i −0.527504 1.05501i
\(231\) 0 0
\(232\) 8.00000i 0.525226i
\(233\) 12.1244 + 7.00000i 0.794293 + 0.458585i 0.841472 0.540301i \(-0.181690\pi\)
−0.0471787 + 0.998886i \(0.515023\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) −11.1962 7.39230i −0.730356 0.482221i
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 4.00000i 0.259828i
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −0.133975 + 2.23205i −0.00864802 + 0.144078i
\(241\) 12.0000 + 20.7846i 0.772988 + 1.33885i 0.935918 + 0.352217i \(0.114572\pi\)
−0.162930 + 0.986638i \(0.552095\pi\)
\(242\) −9.52628 + 5.50000i −0.612372 + 0.353553i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −10.0000 −0.637577
\(247\) −3.46410 2.00000i −0.220416 0.127257i
\(248\) 3.46410 2.00000i 0.219971 0.127000i
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 8.52628 + 7.23205i 0.539249 + 0.457395i
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) −2.46410 + 3.73205i −0.154308 + 0.233710i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 25.9808 + 15.0000i 1.62064 + 0.935674i 0.986750 + 0.162247i \(0.0518742\pi\)
0.633885 + 0.773427i \(0.281459\pi\)
\(258\) 2.00000i 0.124515i
\(259\) 0 0
\(260\) 4.00000 2.00000i 0.248069 0.124035i
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) −6.92820 + 4.00000i −0.428026 + 0.247121i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) −12.0000 + 6.00000i −0.737154 + 0.368577i
\(266\) 0 0
\(267\) 14.0000i 0.856786i
\(268\) 12.1244 + 7.00000i 0.740613 + 0.427593i
\(269\) −15.0000 25.9808i −0.914566 1.58408i −0.807535 0.589819i \(-0.799199\pi\)
−0.107031 0.994256i \(-0.534134\pi\)
\(270\) −1.23205 + 1.86603i −0.0749802 + 0.113563i
\(271\) −10.0000 + 17.3205i −0.607457 + 1.05215i 0.384201 + 0.923249i \(0.374477\pi\)
−0.991658 + 0.128897i \(0.958856\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) 4.00000 + 6.92820i 0.240772 + 0.417029i
\(277\) 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i \(-0.647530\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(278\) −19.0526 11.0000i −1.14270 0.659736i
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 5.19615 + 3.00000i 0.309426 + 0.178647i
\(283\) 17.3205 10.0000i 1.02960 0.594438i 0.112728 0.993626i \(-0.464041\pi\)
0.916869 + 0.399188i \(0.130708\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) −0.267949 + 4.46410i −0.0158719 + 0.264431i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 14.9282 + 9.85641i 0.876614 + 0.578788i
\(291\) −7.00000 12.1244i −0.410347 0.710742i
\(292\) 8.66025 + 5.00000i 0.506803 + 0.292603i
\(293\) 24.0000i 1.40209i −0.713115 0.701047i \(-0.752716\pi\)
0.713115 0.701047i \(-0.247284\pi\)
\(294\) 0 0
\(295\) 12.0000 + 24.0000i 0.698667 + 1.39733i
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) 0 0
\(298\) −17.3205 + 10.0000i −1.00335 + 0.579284i
\(299\) 8.00000 13.8564i 0.462652 0.801337i
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 0 0
\(302\) 20.0000i 1.15087i
\(303\) 5.19615 + 3.00000i 0.298511 + 0.172345i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) −2.46410 + 3.73205i −0.141094 + 0.213697i
\(306\) 1.00000 1.73205i 0.0571662 0.0990148i
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) −0.535898 + 8.92820i −0.0304370 + 0.507088i
\(311\) 4.00000 + 6.92820i 0.226819 + 0.392862i 0.956864 0.290537i \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) −1.73205 + 1.00000i −0.0980581 + 0.0566139i
\(313\) −5.19615 3.00000i −0.293704 0.169570i 0.345907 0.938269i \(-0.387571\pi\)
−0.639611 + 0.768699i \(0.720905\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 29.4449 + 17.0000i 1.65379 + 0.954815i 0.975494 + 0.220024i \(0.0706137\pi\)
0.678294 + 0.734791i \(0.262720\pi\)
\(318\) 5.19615 3.00000i 0.291386 0.168232i
\(319\) 0 0
\(320\) 2.23205 + 0.133975i 0.124775 + 0.00748941i
\(321\) 0 0
\(322\) 0 0
\(323\) 4.00000i 0.222566i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −1.19615 + 9.92820i −0.0663506 + 0.550718i
\(326\) 1.00000 + 1.73205i 0.0553849 + 0.0959294i
\(327\) 1.73205 + 1.00000i 0.0957826 + 0.0553001i
\(328\) 10.0000i 0.552158i
\(329\) 0 0
\(330\) 0 0
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) 10.3923 6.00000i 0.570352 0.329293i
\(333\) −5.19615 + 3.00000i −0.284747 + 0.164399i
\(334\) −1.00000 + 1.73205i −0.0547176 + 0.0947736i
\(335\) −28.0000 + 14.0000i −1.52980 + 0.764902i
\(336\) 0 0
\(337\) 12.0000i 0.653682i 0.945079 + 0.326841i \(0.105984\pi\)
−0.945079 + 0.326841i \(0.894016\pi\)
\(338\) −7.79423 4.50000i −0.423950 0.244768i
\(339\) −5.00000 8.66025i −0.271563 0.470360i
\(340\) 3.73205 + 2.46410i 0.202399 + 0.133635i
\(341\) 0 0
\(342\) 2.00000i 0.108148i
\(343\) 0 0
\(344\) 2.00000 0.107833
\(345\) −17.8564 1.07180i −0.961357 0.0577036i
\(346\) −6.00000 10.3923i −0.322562 0.558694i
\(347\) −24.2487 + 14.0000i −1.30174 + 0.751559i −0.980702 0.195507i \(-0.937365\pi\)
−0.321037 + 0.947067i \(0.604031\pi\)
\(348\) −6.92820 4.00000i −0.371391 0.214423i
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) 5.19615 3.00000i 0.276563 0.159674i −0.355303 0.934751i \(-0.615622\pi\)
0.631867 + 0.775077i \(0.282289\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) −13.3923 0.803848i −0.710790 0.0426638i
\(356\) 14.0000 0.741999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) −7.00000 + 12.1244i −0.369446 + 0.639899i −0.989479 0.144677i \(-0.953786\pi\)
0.620033 + 0.784576i \(0.287119\pi\)
\(360\) 1.86603 + 1.23205i 0.0983482 + 0.0649348i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 1.73205 + 1.00000i 0.0910346 + 0.0525588i
\(363\) 11.0000i 0.577350i
\(364\) 0 0
\(365\) −20.0000 + 10.0000i −1.04685 + 0.523424i
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) −13.8564 + 8.00000i −0.723299 + 0.417597i −0.815966 0.578101i \(-0.803794\pi\)
0.0926670 + 0.995697i \(0.470461\pi\)
\(368\) 6.92820 4.00000i 0.361158 0.208514i
\(369\) −5.00000 + 8.66025i −0.260290 + 0.450835i
\(370\) −6.00000 12.0000i −0.311925 0.623850i
\(371\) 0 0
\(372\) 4.00000i 0.207390i
\(373\) 19.0526 + 11.0000i 0.986504 + 0.569558i 0.904227 0.427051i \(-0.140448\pi\)
0.0822766 + 0.996610i \(0.473781\pi\)
\(374\) 0 0
\(375\) 10.5263 3.76795i 0.543575 0.194576i
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 16.0000i 0.824042i
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 4.46410 + 0.267949i 0.229004 + 0.0137455i
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 19.0526 11.0000i 0.974814 0.562809i
\(383\) 22.5167 + 13.0000i 1.15055 + 0.664269i 0.949021 0.315214i \(-0.102076\pi\)
0.201527 + 0.979483i \(0.435410\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) 1.73205 + 1.00000i 0.0880451 + 0.0508329i
\(388\) −12.1244 + 7.00000i −0.615521 + 0.355371i
\(389\) −2.00000 3.46410i −0.101404 0.175637i 0.810859 0.585241i \(-0.199000\pi\)
−0.912263 + 0.409604i \(0.865667\pi\)
\(390\) 0.267949 4.46410i 0.0135681 0.226049i
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 8.00000i 0.403547i
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) −4.92820 + 7.46410i −0.247965 + 0.375560i
\(396\) 0 0
\(397\) −32.9090 19.0000i −1.65165 0.953583i −0.976392 0.216004i \(-0.930698\pi\)
−0.675261 0.737579i \(-0.735969\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i \(-0.913661\pi\)
0.713751 + 0.700399i \(0.246995\pi\)
\(402\) 12.1244 7.00000i 0.604708 0.349128i
\(403\) −6.92820 + 4.00000i −0.345118 + 0.199254i
\(404\) 3.00000 5.19615i 0.149256 0.258518i
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) 0 0
\(407\) 0 0
\(408\) −1.73205 1.00000i −0.0857493 0.0495074i
\(409\) −12.0000 20.7846i −0.593362 1.02773i −0.993776 0.111398i \(-0.964467\pi\)
0.400414 0.916334i \(-0.368866\pi\)
\(410\) −18.6603 12.3205i −0.921564 0.608467i
\(411\) −1.00000 + 1.73205i −0.0493264 + 0.0854358i
\(412\) 4.00000i 0.197066i
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −1.60770 + 26.7846i −0.0789187 + 1.31480i
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) −19.0526 + 11.0000i −0.933008 + 0.538672i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 3.46410 + 2.00000i 0.168630 + 0.0973585i
\(423\) 5.19615 3.00000i 0.252646 0.145865i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) −9.19615 + 3.92820i −0.446079 + 0.190546i
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −2.46410 + 3.73205i −0.118830 + 0.179975i
\(431\) 5.00000 + 8.66025i 0.240842 + 0.417150i 0.960954 0.276707i \(-0.0892433\pi\)
−0.720113 + 0.693857i \(0.755910\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 14.0000i 0.672797i −0.941720 0.336399i \(-0.890791\pi\)
0.941720 0.336399i \(-0.109209\pi\)
\(434\) 0 0
\(435\) 16.0000 8.00000i 0.767141 0.383571i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 13.8564 8.00000i 0.662842 0.382692i
\(438\) 8.66025 5.00000i 0.413803 0.238909i
\(439\) 18.0000 31.1769i 0.859093 1.48799i −0.0137020 0.999906i \(-0.504362\pi\)
0.872795 0.488087i \(-0.162305\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.00000i 0.190261i
\(443\) 3.46410 + 2.00000i 0.164584 + 0.0950229i 0.580030 0.814595i \(-0.303041\pi\)
−0.415445 + 0.909618i \(0.636374\pi\)
\(444\) 3.00000 + 5.19615i 0.142374 + 0.246598i
\(445\) −17.2487 + 26.1244i −0.817667 + 1.23841i
\(446\) −10.0000 + 17.3205i −0.473514 + 0.820150i
\(447\) 20.0000i 0.945968i
\(448\) 0 0
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) −4.59808 + 1.96410i −0.216755 + 0.0925886i
\(451\) 0 0
\(452\) −8.66025 + 5.00000i −0.407344 + 0.235180i
\(453\) 17.3205 + 10.0000i 0.813788 + 0.469841i
\(454\) 16.0000 0.750917
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −27.7128 16.0000i −1.29635 0.748448i −0.316579 0.948566i \(-0.602534\pi\)
−0.979772 + 0.200118i \(0.935868\pi\)
\(458\) −8.66025 + 5.00000i −0.404667 + 0.233635i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) −1.07180 + 17.8564i −0.0499728 + 0.832559i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) −4.00000 + 6.92820i −0.185695 + 0.321634i
\(465\) 7.46410 + 4.92820i 0.346139 + 0.228540i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) −31.1769 18.0000i −1.44270 0.832941i −0.444667 0.895696i \(-0.646678\pi\)
−0.998029 + 0.0627555i \(0.980011\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 0 0
\(470\) 6.00000 + 12.0000i 0.276759 + 0.553519i
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) −10.3923 + 6.00000i −0.478345 + 0.276172i
\(473\) 0 0
\(474\) 2.00000 3.46410i 0.0918630 0.159111i
\(475\) −6.00000 + 8.00000i −0.275299 + 0.367065i
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) 15.5885 + 9.00000i 0.712999 + 0.411650i
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) 1.23205 1.86603i 0.0562352 0.0851720i
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) 24.0000i 1.09317i
\(483\) 0 0
\(484\) 11.0000 0.500000
\(485\) 1.87564 31.2487i 0.0851686 1.41893i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 27.7128 16.0000i 1.25579 0.725029i 0.283535 0.958962i \(-0.408493\pi\)
0.972253 + 0.233933i \(0.0751596\pi\)
\(488\) −1.73205 1.00000i −0.0784063 0.0452679i
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 8.66025 + 5.00000i 0.390434 + 0.225417i
\(493\) −13.8564 + 8.00000i −0.624061 + 0.360302i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 12.0000i 0.537733i
\(499\) −6.00000 + 10.3923i −0.268597 + 0.465223i −0.968500 0.249015i \(-0.919893\pi\)
0.699903 + 0.714238i \(0.253227\pi\)
\(500\) −3.76795 10.5263i −0.168508 0.470750i
\(501\) 1.00000 + 1.73205i 0.0446767 + 0.0773823i
\(502\) 20.7846 + 12.0000i 0.927663 + 0.535586i
\(503\) 26.0000i 1.15928i 0.814872 + 0.579641i \(0.196807\pi\)
−0.814872 + 0.579641i \(0.803193\pi\)
\(504\) 0 0
\(505\) 6.00000 + 12.0000i 0.266996 + 0.533993i
\(506\) 0 0
\(507\) −7.79423 + 4.50000i −0.346154 + 0.199852i
\(508\) 6.92820 4.00000i 0.307389 0.177471i
\(509\) −7.00000 + 12.1244i −0.310270 + 0.537403i −0.978421 0.206623i \(-0.933753\pi\)
0.668151 + 0.744026i \(0.267086\pi\)
\(510\) 4.00000 2.00000i 0.177123 0.0885615i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −1.73205 1.00000i −0.0764719 0.0441511i
\(514\) −15.0000 25.9808i −0.661622 1.14596i
\(515\) 7.46410 + 4.92820i 0.328908 + 0.217163i
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) 0 0
\(518\) 0 0
\(519\) −12.0000 −0.526742
\(520\) −4.46410 0.267949i −0.195764 0.0117503i
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) −6.92820 + 4.00000i −0.303239 + 0.175075i
\(523\) 3.46410 + 2.00000i 0.151475 + 0.0874539i 0.573822 0.818980i \(-0.305460\pi\)
−0.422347 + 0.906434i \(0.638794\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) 0 0
\(527\) −6.92820 4.00000i −0.301797 0.174243i
\(528\) 0 0
\(529\) 20.5000 + 35.5070i 0.891304 + 1.54378i
\(530\) 13.3923 + 0.803848i 0.581725 + 0.0349169i
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 20.0000i 0.866296i
\(534\) 7.00000 12.1244i 0.302920 0.524672i
\(535\) 0 0
\(536\) −7.00000 12.1244i −0.302354 0.523692i
\(537\) 10.3923 + 6.00000i 0.448461 + 0.258919i
\(538\) 30.0000i 1.29339i
\(539\) 0 0
\(540\) 2.00000 1.00000i 0.0860663 0.0430331i
\(541\) 15.0000 25.9808i 0.644900 1.11700i −0.339424 0.940633i \(-0.610232\pi\)
0.984325 0.176367i \(-0.0564345\pi\)
\(542\) 17.3205 10.0000i 0.743980 0.429537i
\(543\) 1.73205 1.00000i 0.0743294 0.0429141i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 2.00000 + 4.00000i 0.0856706 + 0.171341i
\(546\) 0 0
\(547\) 26.0000i 1.11168i −0.831289 0.555840i \(-0.812397\pi\)
0.831289 0.555840i \(-0.187603\pi\)
\(548\) 1.73205 + 1.00000i 0.0739895 + 0.0427179i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) −8.00000 + 13.8564i −0.340811 + 0.590303i
\(552\) 8.00000i 0.340503i
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) −13.3923 0.803848i −0.568472 0.0341214i
\(556\) 11.0000 + 19.0526i 0.466504 + 0.808008i
\(557\) −15.5885 + 9.00000i −0.660504 + 0.381342i −0.792469 0.609912i \(-0.791205\pi\)
0.131965 + 0.991254i \(0.457871\pi\)
\(558\) −3.46410 2.00000i −0.146647 0.0846668i
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −15.5885 9.00000i −0.657559 0.379642i
\(563\) 20.7846 12.0000i 0.875967 0.505740i 0.00664037 0.999978i \(-0.497886\pi\)
0.869326 + 0.494238i \(0.164553\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 1.33975 22.3205i 0.0563635 0.939031i
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 5.00000 8.66025i 0.209611 0.363057i −0.741981 0.670421i \(-0.766114\pi\)
0.951592 + 0.307364i \(0.0994469\pi\)
\(570\) 2.46410 3.73205i 0.103210 0.156318i
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 0 0
\(573\) 22.0000i 0.919063i
\(574\) 0 0
\(575\) −32.0000 24.0000i −1.33449 1.00087i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 22.5167 13.0000i 0.937381 0.541197i 0.0482425 0.998836i \(-0.484638\pi\)
0.889138 + 0.457639i \(0.151305\pi\)
\(578\) 11.2583 6.50000i 0.468285 0.270364i
\(579\) 10.0000 17.3205i 0.415586 0.719816i
\(580\) −8.00000 16.0000i −0.332182 0.664364i
\(581\) 0 0
\(582\) 14.0000i 0.580319i
\(583\) 0 0
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) −3.73205 2.46410i −0.154301 0.101878i
\(586\) −12.0000 + 20.7846i −0.495715 + 0.858604i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 1.60770 26.7846i 0.0661878 1.10270i
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 5.19615 3.00000i 0.213561 0.123299i
\(593\) 12.1244 + 7.00000i 0.497888 + 0.287456i 0.727841 0.685746i \(-0.240524\pi\)
−0.229953 + 0.973202i \(0.573857\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.0000 0.819232
\(597\) 13.8564 + 8.00000i 0.567105 + 0.327418i
\(598\) −13.8564 + 8.00000i −0.566631 + 0.327144i
\(599\) −17.0000 29.4449i −0.694601 1.20308i −0.970315 0.241845i \(-0.922248\pi\)
0.275714 0.961240i \(-0.411086\pi\)
\(600\) 1.96410 + 4.59808i 0.0801841 + 0.187716i
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) 14.0000i 0.570124i
\(604\) 10.0000 17.3205i 0.406894 0.704761i
\(605\) −13.5526 + 20.5263i −0.550990 + 0.834512i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) −10.3923 6.00000i −0.421811 0.243532i 0.274041 0.961718i \(-0.411640\pi\)
−0.695852 + 0.718186i \(0.744973\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) 4.00000 2.00000i 0.161955 0.0809776i
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) −1.73205 + 1.00000i −0.0700140 + 0.0404226i
\(613\) 8.66025 5.00000i 0.349784 0.201948i −0.314806 0.949156i \(-0.601939\pi\)
0.664590 + 0.747208i \(0.268606\pi\)
\(614\) −6.00000 + 10.3923i −0.242140 + 0.419399i
\(615\) −20.0000 + 10.0000i −0.806478 + 0.403239i
\(616\) 0 0
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) −3.46410 2.00000i −0.139347 0.0804518i
\(619\) 11.0000 + 19.0526i 0.442127 + 0.765787i 0.997847 0.0655827i \(-0.0208906\pi\)
−0.555720 + 0.831370i \(0.687557\pi\)
\(620\) 4.92820 7.46410i 0.197921 0.299766i
\(621\) 4.00000 6.92820i 0.160514 0.278019i
\(622\) 8.00000i 0.320771i
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 0 0
\(628\) 1.73205 + 1.00000i 0.0691164 + 0.0399043i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) −3.46410 2.00000i −0.137795 0.0795557i
\(633\) 3.46410 2.00000i 0.137686 0.0794929i
\(634\) −17.0000 29.4449i −0.675156 1.16940i
\(635\) −1.07180 + 17.8564i −0.0425330 + 0.708610i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) −1.86603 1.23205i −0.0737611 0.0487011i
\(641\) 21.0000 + 36.3731i 0.829450 + 1.43665i 0.898470 + 0.439034i \(0.144679\pi\)
−0.0690201 + 0.997615i \(0.521987\pi\)
\(642\) 0 0
\(643\) 36.0000i 1.41970i −0.704352 0.709851i \(-0.748762\pi\)
0.704352 0.709851i \(-0.251238\pi\)
\(644\) 0 0
\(645\) 2.00000 + 4.00000i 0.0787499 + 0.157500i
\(646\) −2.00000 + 3.46410i −0.0786889 + 0.136293i
\(647\) −12.1244 + 7.00000i −0.476658 + 0.275198i −0.719023 0.694987i \(-0.755410\pi\)
0.242365 + 0.970185i \(0.422077\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 0 0
\(650\) 6.00000 8.00000i 0.235339 0.313786i
\(651\) 0 0
\(652\) 2.00000i 0.0783260i
\(653\) −12.1244 7.00000i −0.474463 0.273931i 0.243643 0.969865i \(-0.421657\pi\)
−0.718106 + 0.695934i \(0.754991\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) −9.85641 + 14.9282i −0.385122 + 0.583293i
\(656\) 5.00000 8.66025i 0.195217 0.338126i
\(657\) 10.0000i 0.390137i
\(658\) 0 0
\(659\) −16.0000 −0.623272 −0.311636 0.950202i \(-0.600877\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(660\) 0 0
\(661\) −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i \(-0.307396\pi\)
−0.996682 + 0.0813955i \(0.974062\pi\)
\(662\) 24.2487 14.0000i 0.942453 0.544125i
\(663\) 3.46410 + 2.00000i 0.134535 + 0.0776736i
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −55.4256 32.0000i −2.14609 1.23904i
\(668\) 1.73205 1.00000i 0.0670151 0.0386912i
\(669\) 10.0000 + 17.3205i 0.386622 + 0.669650i
\(670\) 31.2487 + 1.87564i 1.20724 + 0.0724625i
\(671\) 0 0
\(672\) 0 0
\(673\) 20.0000i 0.770943i −0.922720 0.385472i \(-0.874039\pi\)
0.922720 0.385472i \(-0.125961\pi\)
\(674\) 6.00000 10.3923i 0.231111 0.400297i
\(675\) −0.598076 + 4.96410i −0.0230200 + 0.191068i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −10.3923 6.00000i −0.399409 0.230599i 0.286820 0.957984i \(-0.407402\pi\)
−0.686229 + 0.727386i \(0.740735\pi\)
\(678\) 10.0000i 0.384048i
\(679\) 0 0
\(680\) −2.00000 4.00000i −0.0766965 0.153393i
\(681\) 8.00000 13.8564i 0.306561 0.530979i
\(682\) 0 0
\(683\) 20.7846 12.0000i 0.795301 0.459167i −0.0465244 0.998917i \(-0.514815\pi\)
0.841825 + 0.539750i \(0.181481\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) −4.00000 + 2.00000i −0.152832 + 0.0764161i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) −1.73205 1.00000i −0.0660338 0.0381246i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 14.9282 + 9.85641i 0.568307 + 0.375227i
\(691\) 17.0000 29.4449i 0.646710 1.12014i −0.337193 0.941435i \(-0.609478\pi\)
0.983904 0.178700i \(-0.0571891\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) −49.1051 2.94744i −1.86266 0.111803i
\(696\) 4.00000 + 6.92820i 0.151620 + 0.262613i
\(697\) 17.3205 10.0000i 0.656061 0.378777i
\(698\) −25.9808 15.0000i −0.983386 0.567758i
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 1.73205 + 1.00000i 0.0653720 + 0.0377426i
\(703\) 10.3923 6.00000i 0.391953 0.226294i
\(704\) 0 0
\(705\) 13.3923 + 0.803848i 0.504383 + 0.0302747i
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) 12.0000i 0.450988i
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) 11.1962 + 7.39230i 0.420184 + 0.277428i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −12.1244 7.00000i −0.454379 0.262336i
\(713\) 32.0000i 1.19841i
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 15.5885 9.00000i 0.582162 0.336111i
\(718\) 12.1244 7.00000i 0.452477 0.261238i
\(719\) −4.00000 + 6.92820i −0.149175 + 0.258378i −0.930923 0.365216i \(-0.880995\pi\)
0.781748 + 0.623595i \(0.214328\pi\)
\(720\) −1.00000 2.00000i −0.0372678 0.0745356i
\(721\) 0 0
\(722\) 15.0000i 0.558242i
\(723\) −20.7846 12.0000i −0.772988 0.446285i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 39.7128 + 4.78461i 1.47490 + 0.177696i
\(726\) 5.50000 9.52628i 0.204124 0.353553i
\(727\) 36.0000i 1.33517i −0.744535 0.667583i \(-0.767329\pi\)
0.744535 0.667583i \(-0.232671\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 22.3205 + 1.33975i 0.826119 + 0.0495862i
\(731\) −2.00000 3.46410i −0.0739727 0.128124i
\(732\) −1.73205 + 1.00000i −0.0640184 + 0.0369611i
\(733\) −1.73205 1.00000i −0.0639748 0.0369358i 0.467671 0.883902i \(-0.345093\pi\)
−0.531646 + 0.846967i \(0.678426\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 0 0
\(738\) 8.66025 5.00000i 0.318788 0.184053i
\(739\) −2.00000 3.46410i −0.0735712 0.127429i 0.826893 0.562360i \(-0.190106\pi\)
−0.900464 + 0.434930i \(0.856773\pi\)
\(740\) −0.803848 + 13.3923i −0.0295500 + 0.492311i
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) 32.0000i 1.17397i −0.809599 0.586983i \(-0.800316\pi\)
0.809599 0.586983i \(-0.199684\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) −24.6410 + 37.3205i −0.902777 + 1.36732i
\(746\) −11.0000 19.0526i −0.402739 0.697564i
\(747\) −10.3923 6.00000i −0.380235 0.219529i
\(748\) 0 0
\(749\) 0 0
\(750\) −11.0000 2.00000i −0.401663 0.0730297i
\(751\) 12.0000 20.7846i 0.437886 0.758441i −0.559640 0.828736i \(-0.689061\pi\)
0.997526 + 0.0702946i \(0.0223939\pi\)
\(752\) −5.19615 + 3.00000i −0.189484 + 0.109399i
\(753\) 20.7846 12.0000i 0.757433 0.437304i
\(754\) 8.00000 13.8564i 0.291343 0.504621i
\(755\) 20.0000 + 40.0000i 0.727875 + 1.45575i
\(756\) 0 0
\(757\) 34.0000i 1.23575i −0.786276 0.617876i \(-0.787994\pi\)
0.786276 0.617876i \(-0.212006\pi\)
\(758\) 10.3923 + 6.00000i 0.377466 + 0.217930i
\(759\) 0 0
\(760\) −3.73205 2.46410i −0.135376 0.0893824i
\(761\) −17.0000 + 29.4449i −0.616250 + 1.06738i 0.373914 + 0.927463i \(0.378015\pi\)
−0.990164 + 0.139912i \(0.955318\pi\)
\(762\) 8.00000i 0.289809i
\(763\) 0 0
\(764\) −22.0000 −0.795932
\(765\) 0.267949 4.46410i 0.00968772 0.161400i
\(766\) −13.0000 22.5167i −0.469709 0.813560i
\(767\) 20.7846 12.0000i 0.750489 0.433295i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) −17.3205 10.0000i −0.623379 0.359908i
\(773\) −20.7846 + 12.0000i −0.747570 + 0.431610i −0.824815 0.565402i \(-0.808721\pi\)
0.0772449 + 0.997012i \(0.475388\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 7.85641 + 18.3923i 0.282210 + 0.660671i
\(776\) 14.0000 0.502571
\(777\) 0 0
\(778\) 4.00000i 0.143407i
\(779\) 10.0000 17.3205i 0.358287 0.620572i
\(780\) −2.46410 + 3.73205i −0.0882290 + 0.133629i
\(781\) 0 0
\(782\) −13.8564 8.00000i −0.495504 0.286079i
\(783\) 8.00000i 0.285897i
\(784\) 0 0
\(785\) −4.00000 + 2.00000i −0.142766 + 0.0713831i
\(786\) 4.00000 6.92820i 0.142675 0.247121i
\(787\) 24.2487 14.0000i 0.864373 0.499046i −0.00110111 0.999999i \(-0.500350\pi\)
0.865474 + 0.500953i \(0.167017\pi\)
\(788\) −5.19615 + 3.00000i −0.185105 + 0.106871i
\(789\) 0 0
\(790\) 8.00000 4.00000i 0.284627 0.142314i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.46410 + 2.00000i 0.123014 + 0.0710221i
\(794\) 19.0000 + 32.9090i 0.674285 + 1.16790i
\(795\) 7.39230 11.1962i 0.262178 0.397087i
\(796\) 8.00000 13.8564i 0.283552 0.491127i
\(797\) 20.0000i 0.708436i 0.935163 + 0.354218i \(0.115253\pi\)
−0.935163 + 0.354218i \(0.884747\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 4.59808 1.96410i 0.162567 0.0694415i
\(801\) −7.00000 12.1244i −0.247333 0.428393i
\(802\) 8.66025 5.00000i 0.305804 0.176556i
\(803\) 0 0
\(804\) −14.0000 −0.493742
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 25.9808 + 15.0000i 0.914566 + 0.528025i
\(808\) −5.19615 + 3.00000i −0.182800 + 0.105540i
\(809\) 9.00000 + 15.5885i 0.316423 + 0.548061i 0.979739 0.200279i \(-0.0641847\pi\)
−0.663316 + 0.748340i \(0.730851\pi\)
\(810\) 0.133975 2.23205i 0.00470739 0.0784263i
\(811\) −22.0000 −0.772524 −0.386262 0.922389i \(-0.626234\pi\)
−0.386262 + 0.922389i \(0.626234\pi\)
\(812\) 0 0
\(813\) 20.0000i 0.701431i
\(814\) 0 0
\(815\) 3.73205 + 2.46410i 0.130728 + 0.0863137i
\(816\) 1.00000 + 1.73205i 0.0350070 + 0.0606339i
\(817\) −3.46410 2.00000i −0.121194 0.0699711i
\(818\) 24.0000i 0.839140i
\(819\) 0 0
\(820\) 10.0000 + 20.0000i 0.349215 + 0.698430i
\(821\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(822\) 1.73205 1.00000i 0.0604122 0.0348790i
\(823\) −3.46410 + 2.00000i −0.120751 + 0.0697156i −0.559159 0.829060i \(-0.688876\pi\)
0.438408 + 0.898776i \(0.355543\pi\)
\(824\) −2.00000 + 3.46410i −0.0696733 + 0.120678i
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000i 0.417281i 0.977992 + 0.208640i \(0.0669038\pi\)
−0.977992 + 0.208640i \(0.933096\pi\)
\(828\) −6.92820 4.00000i −0.240772 0.139010i
\(829\) −11.0000 19.0526i −0.382046 0.661723i 0.609309 0.792933i \(-0.291447\pi\)
−0.991355 + 0.131210i \(0.958114\pi\)
\(830\) 14.7846 22.3923i 0.513181 0.777248i
\(831\) −1.00000 + 1.73205i −0.0346896 + 0.0600842i
\(832\) 2.00000i 0.0693375i
\(833\) 0 0
\(834\) 22.0000 0.761798
\(835\) −0.267949 + 4.46410i −0.00927276 + 0.154487i
\(836\) 0 0
\(837\) −3.46410 + 2.00000i −0.119737 + 0.0691301i
\(838\) −10.3923 6.00000i −0.358996 0.207267i
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 15.5885 + 9.00000i 0.537214 + 0.310160i
\(843\) −15.5885 + 9.00000i −0.536895 + 0.309976i
\(844\) −2.00000 3.46410i −0.0688428 0.119239i
\(845\) −20.0885 1.20577i −0.691064 0.0414798i
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) 6.00000i 0.206041i
\(849\) −10.0000 + 17.3205i −0.343199 + 0.594438i
\(850\) 9.92820 + 1.19615i 0.340535 + 0.0410277i
\(851\) 24.0000 + 41.5692i 0.822709 + 1.42497i
\(852\) −5.19615 3.00000i −0.178017 0.102778i
\(853\) 10.0000i 0.342393i 0.985237 + 0.171197i \(0.0547634\pi\)
−0.985237 + 0.171197i \(0.945237\pi\)
\(854\) 0 0
\(855\) −2.00000 4.00000i −0.0683986 0.136797i
\(856\) 0 0
\(857\) 8.66025 5.00000i 0.295829 0.170797i −0.344739 0.938699i \(-0.612033\pi\)
0.640567 + 0.767902i \(0.278699\pi\)
\(858\) 0 0
\(859\) −21.0000 + 36.3731i −0.716511 + 1.24103i 0.245863 + 0.969305i \(0.420929\pi\)
−0.962374 + 0.271728i \(0.912405\pi\)
\(860\) 4.00000 2.00000i 0.136399 0.0681994i
\(861\) 0 0
\(862\) 10.0000i 0.340601i
\(863\) −27.7128 16.0000i −0.943355 0.544646i −0.0523446 0.998629i \(-0.516669\pi\)
−0.891010 + 0.453983i \(0.850003\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) −22.3923 14.7846i −0.761361 0.502692i
\(866\) −7.00000 + 12.1244i −0.237870 + 0.412002i
\(867\) 13.0000i 0.441503i
\(868\) 0 0
\(869\) 0 0
\(870\) −17.8564 1.07180i −0.605389 0.0363373i
\(871\) 14.0000 + 24.2487i 0.474372 + 0.821636i
\(872\) −1.73205 + 1.00000i −0.0586546 + 0.0338643i
\(873\) 12.1244 + 7.00000i 0.410347 + 0.236914i
\(874\) −16.0000 −0.541208
\(875\) 0 0
\(876\) −10.0000 −0.337869
\(877\) −36.3731 21.0000i −1.22823 0.709120i −0.261571 0.965184i \(-0.584241\pi\)
−0.966660 + 0.256064i \(0.917574\pi\)
\(878\) −31.1769 + 18.0000i −1.05217 + 0.607471i
\(879\) 12.0000 + 20.7846i 0.404750 + 0.701047i
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 10.0000i 0.336527i 0.985742 + 0.168263i \(0.0538159\pi\)
−0.985742 + 0.168263i \(0.946184\pi\)
\(884\) 2.00000 3.46410i 0.0672673 0.116510i
\(885\) −22.3923 14.7846i −0.752709 0.496979i
\(886\) −2.00000 3.46410i −0.0671913 0.116379i
\(887\) −25.9808 15.0000i −0.872349 0.503651i −0.00422062 0.999991i \(-0.501343\pi\)
−0.868128 + 0.496340i \(0.834677\pi\)
\(888\) 6.00000i 0.201347i
\(889\) 0 0
\(890\) 28.0000 14.0000i 0.938562 0.469281i
\(891\) 0 0
\(892\) 17.3205 10.0000i 0.579934 0.334825i
\(893\) −10.3923 + 6.00000i −0.347765 + 0.200782i
\(894\) 10.0000 17.3205i 0.334450 0.579284i
\(895\) 12.0000 + 24.0000i 0.401116 + 0.802232i
\(896\) 0 0
\(897\) 16.0000i 0.534224i
\(898\) −22.5167 13.0000i −0.751391 0.433816i
\(899\) 16.0000 + 27.7128i 0.533630 + 0.924274i
\(900\) 4.96410 + 0.598076i 0.165470 + 0.0199359i
\(901\) −6.00000 + 10.3923i −0.199889 + 0.346218i
\(902\) 0 0
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) 4.46410 + 0.267949i 0.148392 + 0.00890693i
\(906\) −10.0000 17.3205i −0.332228 0.575435i
\(907\) 32.9090 19.0000i 1.09272 0.630885i 0.158424 0.987371i \(-0.449359\pi\)
0.934300 + 0.356487i \(0.116025\pi\)
\(908\) −13.8564 8.00000i −0.459841 0.265489i
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 22.0000 0.728893 0.364446 0.931224i \(-0.381258\pi\)
0.364446 + 0.931224i \(0.381258\pi\)
\(912\) 1.73205 + 1.00000i 0.0573539 + 0.0331133i
\(913\) 0 0
\(914\) 16.0000 + 27.7128i 0.529233 + 0.916658i
\(915\) 0.267949 4.46410i 0.00885813 0.147579i
\(916\) 10.0000 0.330409
\(917\) 0 0
\(918\) 2.00000i 0.0660098i
\(919\) −8.00000 + 13.8564i −0.263896 + 0.457081i −0.967274 0.253735i \(-0.918341\pi\)
0.703378 + 0.710816i \(0.251674\pi\)
\(920\) 9.85641 14.9282i 0.324956 0.492168i
\(921\) 6.00000 + 10.3923i 0.197707 + 0.342438i
\(922\) −12.1244 7.00000i −0.399294 0.230533i
\(923\) 12.0000i 0.394985i
\(924\) 0 0
\(925\) −24.0000 18.0000i −0.789115 0.591836i
\(926\) −2.00000 + 3.46410i −0.0657241 + 0.113837i
\(927\) −3.46410 + 2.00000i −0.113776 + 0.0656886i
\(928\) 6.92820 4.00000i 0.227429 0.131306i
\(929\) −11.0000 + 19.0526i −0.360898 + 0.625094i −0.988109 0.153755i \(-0.950863\pi\)
0.627211 + 0.778850i \(0.284197\pi\)
\(930\) −4.00000 8.00000i −0.131165 0.262330i
\(931\) 0 0
\(932\) 14.0000i 0.458585i
\(933\) −6.92820 4.00000i −0.226819 0.130954i
\(934\) 18.0000 + 31.1769i 0.588978 + 1.02014i
\(935\) 0 0
\(936\) 1.00000 1.73205i 0.0326860 0.0566139i
\(937\) 42.0000i 1.37208i 0.727564 + 0.686040i \(0.240653\pi\)
−0.727564 + 0.686040i \(0.759347\pi\)
\(938\) 0 0
\(939\) 6.00000 0.195803
\(940\) 0.803848 13.3923i 0.0262186 0.436809i
\(941\) 7.00000 + 12.1244i 0.228193 + 0.395243i 0.957273 0.289187i \(-0.0933848\pi\)
−0.729079 + 0.684429i \(0.760051\pi\)
\(942\) 1.73205 1.00000i 0.0564333 0.0325818i
\(943\) 69.2820 + 40.0000i 2.25613 + 1.30258i
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 0 0
\(947\) 20.7846 + 12.0000i 0.675409 + 0.389948i 0.798123 0.602494i \(-0.205826\pi\)
−0.122714 + 0.992442i \(0.539160\pi\)
\(948\) −3.46410 + 2.00000i −0.112509 + 0.0649570i
\(949\) 10.0000 + 17.3205i 0.324614 + 0.562247i
\(950\) 9.19615 3.92820i 0.298363 0.127448i
\(951\) −34.0000 −1.10253
\(952\) 0 0
\(953\) 34.0000i 1.10137i 0.834714 + 0.550684i \(0.185633\pi\)
−0.834714 + 0.550684i \(0.814367\pi\)
\(954\) −3.00000 + 5.19615i −0.0971286 + 0.168232i
\(955\) 27.1051 41.0526i 0.877101 1.32843i
\(956\) −9.00000 15.5885i −0.291081 0.504167i
\(957\) 0 0
\(958\) 24.0000i 0.775405i
\(959\) 0 0
\(960\) −2.00000 + 1.00000i −0.0645497 + 0.0322749i
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) −10.3923 + 6.00000i −0.335061 + 0.193448i
\(963\) 0 0
\(964\) −12.0000 + 20.7846i −0.386494 + 0.669427i
\(965\) 40.0000 20.0000i 1.28765 0.643823i
\(966\) 0 0
\(967\) 32.0000i 1.02905i −0.857475 0.514525i \(-0.827968\pi\)
0.857475 0.514525i \(-0.172032\pi\)
\(968\) −9.52628 5.50000i −0.306186 0.176777i
\(969\) 2.00000 + 3.46410i 0.0642493 + 0.111283i
\(970\) −17.2487 + 26.1244i −0.553823 + 0.838803i
\(971\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) −32.0000 −1.02535
\(975\) −3.92820 9.19615i −0.125803 0.294513i
\(976\) 1.00000 + 1.73205i 0.0320092 + 0.0554416i
\(977\) −29.4449 + 17.0000i −0.942025 + 0.543878i −0.890594 0.454798i \(-0.849711\pi\)
−0.0514302 + 0.998677i \(0.516378\pi\)
\(978\) −1.73205 1.00000i −0.0553849 0.0319765i
\(979\) 0 0
\(980\) 0 0
\(981\) −2.00000 −0.0638551
\(982\) 3.46410 + 2.00000i 0.110544 + 0.0638226i
\(983\) −15.5885 + 9.00000i −0.497195 + 0.287055i −0.727554 0.686050i \(-0.759343\pi\)
0.230360 + 0.973106i \(0.426010\pi\)
\(984\) −5.00000 8.66025i −0.159394 0.276079i
\(985\) 0.803848 13.3923i 0.0256127 0.426714i
\(986\) 16.0000 0.509544
\(987\) 0 0
\(988\) 4.00000i 0.127257i
\(989\) 8.00000 13.8564i 0.254385 0.440608i
\(990\) 0 0
\(991\) −8.00000 13.8564i −0.254128 0.440163i 0.710530 0.703667i \(-0.248455\pi\)
−0.964658 + 0.263504i \(0.915122\pi\)
\(992\) 3.46410 + 2.00000i 0.109985 + 0.0635001i
\(993\) 28.0000i 0.888553i
\(994\) 0 0
\(995\) 16.0000 + 32.0000i 0.507234 + 1.01447i
\(996\) −6.00000 + 10.3923i −0.190117 + 0.329293i
\(997\) 5.19615 3.00000i 0.164564 0.0950110i −0.415456 0.909613i \(-0.636378\pi\)
0.580020 + 0.814602i \(0.303045\pi\)
\(998\) 10.3923 6.00000i 0.328963 0.189927i
\(999\) 3.00000 5.19615i 0.0949158 0.164399i
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 1470.2.n.d.79.1 4
5.4 even 2 inner 1470.2.n.d.79.2 4
7.2 even 3 1470.2.g.d.589.2 yes 2
7.3 odd 6 1470.2.n.e.949.2 4
7.4 even 3 inner 1470.2.n.d.949.2 4
7.5 odd 6 1470.2.g.c.589.2 yes 2
7.6 odd 2 1470.2.n.e.79.1 4
35.2 odd 12 7350.2.a.m.1.1 1
35.4 even 6 inner 1470.2.n.d.949.1 4
35.9 even 6 1470.2.g.d.589.1 yes 2
35.12 even 12 7350.2.a.bc.1.1 1
35.19 odd 6 1470.2.g.c.589.1 2
35.23 odd 12 7350.2.a.cr.1.1 1
35.24 odd 6 1470.2.n.e.949.1 4
35.33 even 12 7350.2.a.bx.1.1 1
35.34 odd 2 1470.2.n.e.79.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.c.589.1 2 35.19 odd 6
1470.2.g.c.589.2 yes 2 7.5 odd 6
1470.2.g.d.589.1 yes 2 35.9 even 6
1470.2.g.d.589.2 yes 2 7.2 even 3
1470.2.n.d.79.1 4 1.1 even 1 trivial
1470.2.n.d.79.2 4 5.4 even 2 inner
1470.2.n.d.949.1 4 35.4 even 6 inner
1470.2.n.d.949.2 4 7.4 even 3 inner
1470.2.n.e.79.1 4 7.6 odd 2
1470.2.n.e.79.2 4 35.34 odd 2
1470.2.n.e.949.1 4 35.24 odd 6
1470.2.n.e.949.2 4 7.3 odd 6
7350.2.a.m.1.1 1 35.2 odd 12
7350.2.a.bc.1.1 1 35.12 even 12
7350.2.a.bx.1.1 1 35.33 even 12
7350.2.a.cr.1.1 1 35.23 odd 12