Properties

Label 507.2.e.e.22.1
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
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] = [507,2,Mod(22,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.e.484.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.73205 - 3.00000i) q^{7} -1.73205 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.73205 - 3.00000i) q^{7} -1.73205 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.73205 + 3.00000i) q^{11} -1.00000 q^{12} +6.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(-3.00000 - 5.19615i) q^{17} +1.73205 q^{18} +(-1.73205 - 3.00000i) q^{19} -3.46410 q^{21} +(-3.00000 - 5.19615i) q^{22} +(-0.866025 + 1.50000i) q^{24} -5.00000 q^{25} -1.00000 q^{27} +(-1.73205 + 3.00000i) q^{28} +(-3.00000 + 5.19615i) q^{29} -3.46410 q^{31} +(2.59808 + 4.50000i) q^{32} +(1.73205 + 3.00000i) q^{33} +10.3923 q^{34} +(-0.500000 + 0.866025i) q^{36} +(3.46410 - 6.00000i) q^{37} +6.00000 q^{38} +(3.46410 - 6.00000i) q^{41} +(3.00000 - 5.19615i) q^{42} +(-2.00000 - 3.46410i) q^{43} +3.46410 q^{44} -3.46410 q^{47} +(-2.50000 - 4.33013i) q^{48} +(-2.50000 + 4.33013i) q^{49} +(4.33013 - 7.50000i) q^{50} -6.00000 q^{51} +6.00000 q^{53} +(0.866025 - 1.50000i) q^{54} +(3.00000 + 5.19615i) q^{56} -3.46410 q^{57} +(-5.19615 - 9.00000i) q^{58} +(5.19615 + 9.00000i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{62} +(-1.73205 + 3.00000i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(5.19615 - 9.00000i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.73205 - 3.00000i) q^{71} +(0.866025 + 1.50000i) q^{72} +(6.00000 + 10.3923i) q^{74} +(-2.50000 + 4.33013i) q^{75} +(-1.73205 + 3.00000i) q^{76} +12.0000 q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(6.00000 + 10.3923i) q^{82} -3.46410 q^{83} +(1.73205 + 3.00000i) q^{84} +6.92820 q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(-1.73205 + 3.00000i) q^{93} +(3.00000 - 5.19615i) q^{94} +5.19615 q^{96} +(6.92820 + 12.0000i) q^{97} +(-4.33013 - 7.50000i) q^{98} +3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} - 4 q^{12} + 24 q^{14} + 10 q^{16} - 12 q^{17} - 12 q^{22} - 20 q^{25} - 4 q^{27} - 12 q^{29} - 2 q^{36} + 24 q^{38} + 12 q^{42} - 8 q^{43} - 10 q^{48} - 10 q^{49} - 24 q^{51} + 24 q^{53} + 12 q^{56} + 4 q^{61} + 12 q^{62} + 4 q^{64} - 24 q^{66} - 12 q^{68} + 24 q^{74} - 10 q^{75} + 48 q^{77} - 32 q^{79} - 2 q^{81} + 24 q^{82} + 12 q^{87} + 12 q^{88} + 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 1.50000i −0.612372 + 1.06066i 0.378467 + 0.925615i \(0.376451\pi\)
−0.990839 + 0.135045i \(0.956882\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0.866025 + 1.50000i 0.353553 + 0.612372i
\(7\) −1.73205 3.00000i −0.654654 1.13389i −0.981981 0.188982i \(-0.939481\pi\)
0.327327 0.944911i \(-0.393852\pi\)
\(8\) −1.73205 −0.612372
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −1.73205 + 3.00000i −0.522233 + 0.904534i 0.477432 + 0.878668i \(0.341568\pi\)
−0.999665 + 0.0258656i \(0.991766\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 6.00000 1.60357
\(15\) 0 0
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 1.73205 0.408248
\(19\) −1.73205 3.00000i −0.397360 0.688247i 0.596040 0.802955i \(-0.296740\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) 0 0
\(21\) −3.46410 −0.755929
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −0.866025 + 1.50000i −0.176777 + 0.306186i
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.73205 + 3.00000i −0.327327 + 0.566947i
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) −3.46410 −0.622171 −0.311086 0.950382i \(-0.600693\pi\)
−0.311086 + 0.950382i \(0.600693\pi\)
\(32\) 2.59808 + 4.50000i 0.459279 + 0.795495i
\(33\) 1.73205 + 3.00000i 0.301511 + 0.522233i
\(34\) 10.3923 1.78227
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 3.46410 6.00000i 0.569495 0.986394i −0.427121 0.904194i \(-0.640472\pi\)
0.996616 0.0821995i \(-0.0261945\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) 3.46410 6.00000i 0.541002 0.937043i −0.457845 0.889032i \(-0.651379\pi\)
0.998847 0.0480106i \(-0.0152881\pi\)
\(42\) 3.00000 5.19615i 0.462910 0.801784i
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) 0 0
\(47\) −3.46410 −0.505291 −0.252646 0.967559i \(-0.581301\pi\)
−0.252646 + 0.967559i \(0.581301\pi\)
\(48\) −2.50000 4.33013i −0.360844 0.625000i
\(49\) −2.50000 + 4.33013i −0.357143 + 0.618590i
\(50\) 4.33013 7.50000i 0.612372 1.06066i
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0.866025 1.50000i 0.117851 0.204124i
\(55\) 0 0
\(56\) 3.00000 + 5.19615i 0.400892 + 0.694365i
\(57\) −3.46410 −0.458831
\(58\) −5.19615 9.00000i −0.682288 1.18176i
\(59\) 5.19615 + 9.00000i 0.676481 + 1.17170i 0.976034 + 0.217620i \(0.0698294\pi\)
−0.299552 + 0.954080i \(0.596837\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 3.00000 5.19615i 0.381000 0.659912i
\(63\) −1.73205 + 3.00000i −0.218218 + 0.377964i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) 5.19615 9.00000i 0.634811 1.09952i −0.351744 0.936096i \(-0.614411\pi\)
0.986555 0.163429i \(-0.0522554\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) −1.73205 3.00000i −0.205557 0.356034i 0.744753 0.667340i \(-0.232567\pi\)
−0.950310 + 0.311305i \(0.899234\pi\)
\(72\) 0.866025 + 1.50000i 0.102062 + 0.176777i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 6.00000 + 10.3923i 0.697486 + 1.20808i
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) −1.73205 + 3.00000i −0.198680 + 0.344124i
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 6.00000 + 10.3923i 0.662589 + 1.14764i
\(83\) −3.46410 −0.380235 −0.190117 0.981761i \(-0.560887\pi\)
−0.190117 + 0.981761i \(0.560887\pi\)
\(84\) 1.73205 + 3.00000i 0.188982 + 0.327327i
\(85\) 0 0
\(86\) 6.92820 0.747087
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) −3.46410 + 6.00000i −0.367194 + 0.635999i −0.989126 0.147073i \(-0.953015\pi\)
0.621932 + 0.783072i \(0.286348\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.73205 + 3.00000i −0.179605 + 0.311086i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) 5.19615 0.530330
\(97\) 6.92820 + 12.0000i 0.703452 + 1.21842i 0.967247 + 0.253837i \(0.0816925\pi\)
−0.263795 + 0.964579i \(0.584974\pi\)
\(98\) −4.33013 7.50000i −0.437409 0.757614i
\(99\) 3.46410 0.348155
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 5.19615 9.00000i 0.514496 0.891133i
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −5.19615 + 9.00000i −0.504695 + 0.874157i
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 6.92820 0.663602 0.331801 0.943349i \(-0.392344\pi\)
0.331801 + 0.943349i \(0.392344\pi\)
\(110\) 0 0
\(111\) −3.46410 6.00000i −0.328798 0.569495i
\(112\) −17.3205 −1.63663
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −18.0000 −1.65703
\(119\) −10.3923 + 18.0000i −0.952661 + 1.65006i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −3.46410 −0.313625
\(123\) −3.46410 6.00000i −0.312348 0.541002i
\(124\) 1.73205 + 3.00000i 0.155543 + 0.269408i
\(125\) 0 0
\(126\) −3.00000 5.19615i −0.267261 0.462910i
\(127\) −4.00000 + 6.92820i −0.354943 + 0.614779i −0.987108 0.160055i \(-0.948833\pi\)
0.632166 + 0.774833i \(0.282166\pi\)
\(128\) −6.06218 + 10.5000i −0.535826 + 0.928078i
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 1.73205 3.00000i 0.150756 0.261116i
\(133\) −6.00000 + 10.3923i −0.520266 + 0.901127i
\(134\) 9.00000 + 15.5885i 0.777482 + 1.34664i
\(135\) 0 0
\(136\) 5.19615 + 9.00000i 0.445566 + 0.771744i
\(137\) −10.3923 18.0000i −0.887875 1.53784i −0.842383 0.538879i \(-0.818848\pi\)
−0.0454914 0.998965i \(-0.514485\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) −1.73205 + 3.00000i −0.145865 + 0.252646i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) 0 0
\(146\) 0 0
\(147\) 2.50000 + 4.33013i 0.206197 + 0.357143i
\(148\) −6.92820 −0.569495
\(149\) −6.92820 12.0000i −0.567581 0.983078i −0.996804 0.0798802i \(-0.974546\pi\)
0.429224 0.903198i \(-0.358787\pi\)
\(150\) −4.33013 7.50000i −0.353553 0.612372i
\(151\) −10.3923 −0.845714 −0.422857 0.906196i \(-0.638973\pi\)
−0.422857 + 0.906196i \(0.638973\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) −3.00000 + 5.19615i −0.242536 + 0.420084i
\(154\) −10.3923 + 18.0000i −0.837436 + 1.45048i
\(155\) 0 0
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 6.92820 12.0000i 0.551178 0.954669i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) −0.866025 1.50000i −0.0680414 0.117851i
\(163\) 1.73205 + 3.00000i 0.135665 + 0.234978i 0.925851 0.377888i \(-0.123350\pi\)
−0.790186 + 0.612866i \(0.790016\pi\)
\(164\) −6.92820 −0.541002
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 8.66025 15.0000i 0.670151 1.16073i −0.307711 0.951480i \(-0.599563\pi\)
0.977861 0.209255i \(-0.0671038\pi\)
\(168\) 6.00000 0.462910
\(169\) 0 0
\(170\) 0 0
\(171\) −1.73205 + 3.00000i −0.132453 + 0.229416i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) −10.3923 −0.787839
\(175\) 8.66025 + 15.0000i 0.654654 + 1.13389i
\(176\) 8.66025 + 15.0000i 0.652791 + 1.13067i
\(177\) 10.3923 0.781133
\(178\) −6.00000 10.3923i −0.449719 0.778936i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) 20.7846 1.51992
\(188\) 1.73205 + 3.00000i 0.126323 + 0.218797i
\(189\) 1.73205 + 3.00000i 0.125988 + 0.218218i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) −24.0000 −1.72310
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(198\) −3.00000 + 5.19615i −0.213201 + 0.369274i
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) 8.66025 0.612372
\(201\) −5.19615 9.00000i −0.366508 0.634811i
\(202\) 5.19615 + 9.00000i 0.365600 + 0.633238i
\(203\) 20.7846 1.45879
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) 0 0
\(206\) 6.92820 12.0000i 0.482711 0.836080i
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) −3.46410 −0.237356
\(214\) −10.3923 18.0000i −0.710403 1.23045i
\(215\) 0 0
\(216\) 1.73205 0.117851
\(217\) 6.00000 + 10.3923i 0.407307 + 0.705476i
\(218\) −6.00000 + 10.3923i −0.406371 + 0.703856i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 12.0000 0.805387
\(223\) 1.73205 3.00000i 0.115987 0.200895i −0.802187 0.597073i \(-0.796330\pi\)
0.918174 + 0.396178i \(0.129664\pi\)
\(224\) 9.00000 15.5885i 0.601338 1.04155i
\(225\) 2.50000 + 4.33013i 0.166667 + 0.288675i
\(226\) −10.3923 −0.691286
\(227\) 8.66025 + 15.0000i 0.574801 + 0.995585i 0.996063 + 0.0886460i \(0.0282540\pi\)
−0.421262 + 0.906939i \(0.638413\pi\)
\(228\) 1.73205 + 3.00000i 0.114708 + 0.198680i
\(229\) 6.92820 0.457829 0.228914 0.973447i \(-0.426482\pi\)
0.228914 + 0.973447i \(0.426482\pi\)
\(230\) 0 0
\(231\) 6.00000 10.3923i 0.394771 0.683763i
\(232\) 5.19615 9.00000i 0.341144 0.590879i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.19615 9.00000i 0.338241 0.585850i
\(237\) −4.00000 + 6.92820i −0.259828 + 0.450035i
\(238\) −18.0000 31.1769i −1.16677 2.02090i
\(239\) −10.3923 −0.672222 −0.336111 0.941822i \(-0.609112\pi\)
−0.336111 + 0.941822i \(0.609112\pi\)
\(240\) 0 0
\(241\) 6.92820 + 12.0000i 0.446285 + 0.772988i 0.998141 0.0609515i \(-0.0194135\pi\)
−0.551856 + 0.833939i \(0.686080\pi\)
\(242\) 1.73205 0.111340
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 1.00000 1.73205i 0.0640184 0.110883i
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) 6.00000 0.381000
\(249\) −1.73205 + 3.00000i −0.109764 + 0.190117i
\(250\) 0 0
\(251\) −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 3.46410 0.218218
\(253\) 0 0
\(254\) −6.92820 12.0000i −0.434714 0.752947i
\(255\) 0 0
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 3.46410 6.00000i 0.215666 0.373544i
\(259\) −24.0000 −1.49129
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 10.3923 18.0000i 0.642039 1.11204i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) −3.00000 5.19615i −0.184637 0.319801i
\(265\) 0 0
\(266\) −10.3923 18.0000i −0.637193 1.10365i
\(267\) 3.46410 + 6.00000i 0.212000 + 0.367194i
\(268\) −10.3923 −0.634811
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 5.19615 9.00000i 0.315644 0.546711i −0.663930 0.747794i \(-0.731113\pi\)
0.979574 + 0.201083i \(0.0644462\pi\)
\(272\) −30.0000 −1.81902
\(273\) 0 0
\(274\) 36.0000 2.17484
\(275\) 8.66025 15.0000i 0.522233 0.904534i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) −6.92820 −0.415526
\(279\) 1.73205 + 3.00000i 0.103695 + 0.179605i
\(280\) 0 0
\(281\) −6.92820 −0.413302 −0.206651 0.978415i \(-0.566256\pi\)
−0.206651 + 0.978415i \(0.566256\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −1.73205 + 3.00000i −0.102778 + 0.178017i
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 2.59808 4.50000i 0.153093 0.265165i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 13.8564 0.812277
\(292\) 0 0
\(293\) 13.8564 + 24.0000i 0.809500 + 1.40209i 0.913211 + 0.407487i \(0.133595\pi\)
−0.103711 + 0.994607i \(0.533072\pi\)
\(294\) −8.66025 −0.505076
\(295\) 0 0
\(296\) −6.00000 + 10.3923i −0.348743 + 0.604040i
\(297\) 1.73205 3.00000i 0.100504 0.174078i
\(298\) 24.0000 1.39028
\(299\) 0 0
\(300\) 5.00000 0.288675
\(301\) −6.92820 + 12.0000i −0.399335 + 0.691669i
\(302\) 9.00000 15.5885i 0.517892 0.897015i
\(303\) −3.00000 5.19615i −0.172345 0.298511i
\(304\) −17.3205 −0.993399
\(305\) 0 0
\(306\) −5.19615 9.00000i −0.297044 0.514496i
\(307\) 10.3923 0.593120 0.296560 0.955014i \(-0.404160\pi\)
0.296560 + 0.955014i \(0.404160\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) −4.00000 + 6.92820i −0.227552 + 0.394132i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) −12.1244 + 21.0000i −0.684217 + 1.18510i
\(315\) 0 0
\(316\) 4.00000 + 6.92820i 0.225018 + 0.389742i
\(317\) 13.8564 0.778253 0.389127 0.921184i \(-0.372777\pi\)
0.389127 + 0.921184i \(0.372777\pi\)
\(318\) 5.19615 + 9.00000i 0.291386 + 0.504695i
\(319\) −10.3923 18.0000i −0.581857 1.00781i
\(320\) 0 0
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 0 0
\(323\) −10.3923 + 18.0000i −0.578243 + 1.00155i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) 3.46410 6.00000i 0.191565 0.331801i
\(328\) −6.00000 + 10.3923i −0.331295 + 0.573819i
\(329\) 6.00000 + 10.3923i 0.330791 + 0.572946i
\(330\) 0 0
\(331\) −1.73205 3.00000i −0.0952021 0.164895i 0.814491 0.580176i \(-0.197016\pi\)
−0.909693 + 0.415282i \(0.863683\pi\)
\(332\) 1.73205 + 3.00000i 0.0950586 + 0.164646i
\(333\) −6.92820 −0.379663
\(334\) 15.0000 + 25.9808i 0.820763 + 1.42160i
\(335\) 0 0
\(336\) −8.66025 + 15.0000i −0.472456 + 0.818317i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −3.00000 5.19615i −0.162221 0.280976i
\(343\) −6.92820 −0.374088
\(344\) 3.46410 + 6.00000i 0.186772 + 0.323498i
\(345\) 0 0
\(346\) 31.1769 1.67608
\(347\) −18.0000 31.1769i −0.966291 1.67366i −0.706107 0.708105i \(-0.749550\pi\)
−0.260184 0.965559i \(-0.583783\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) −3.46410 + 6.00000i −0.185429 + 0.321173i −0.943721 0.330743i \(-0.892701\pi\)
0.758292 + 0.651915i \(0.226034\pi\)
\(350\) −30.0000 −1.60357
\(351\) 0 0
\(352\) −18.0000 −0.959403
\(353\) −17.3205 + 30.0000i −0.921878 + 1.59674i −0.125370 + 0.992110i \(0.540012\pi\)
−0.796507 + 0.604629i \(0.793321\pi\)
\(354\) −9.00000 + 15.5885i −0.478345 + 0.828517i
\(355\) 0 0
\(356\) 6.92820 0.367194
\(357\) 10.3923 + 18.0000i 0.550019 + 0.952661i
\(358\) −10.3923 18.0000i −0.549250 0.951330i
\(359\) −17.3205 −0.914141 −0.457071 0.889430i \(-0.651101\pi\)
−0.457071 + 0.889430i \(0.651101\pi\)
\(360\) 0 0
\(361\) 3.50000 6.06218i 0.184211 0.319062i
\(362\) −8.66025 + 15.0000i −0.455173 + 0.788382i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 0 0
\(366\) −1.73205 + 3.00000i −0.0905357 + 0.156813i
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) 0 0
\(369\) −6.92820 −0.360668
\(370\) 0 0
\(371\) −10.3923 18.0000i −0.539542 0.934513i
\(372\) 3.46410 0.179605
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) −18.0000 + 31.1769i −0.930758 + 1.61212i
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) −6.00000 −0.308607
\(379\) −8.66025 + 15.0000i −0.444847 + 0.770498i −0.998042 0.0625541i \(-0.980075\pi\)
0.553194 + 0.833052i \(0.313409\pi\)
\(380\) 0 0
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 41.5692 2.12687
\(383\) −1.73205 3.00000i −0.0885037 0.153293i 0.818375 0.574684i \(-0.194875\pi\)
−0.906879 + 0.421392i \(0.861542\pi\)
\(384\) 6.06218 + 10.5000i 0.309359 + 0.535826i
\(385\) 0 0
\(386\) 0 0
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) 6.92820 12.0000i 0.351726 0.609208i
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 4.33013 7.50000i 0.218704 0.378807i
\(393\) −6.00000 + 10.3923i −0.302660 + 0.524222i
\(394\) 0 0
\(395\) 0 0
\(396\) −1.73205 3.00000i −0.0870388 0.150756i
\(397\) −17.3205 30.0000i −0.869291 1.50566i −0.862722 0.505678i \(-0.831242\pi\)
−0.00656933 0.999978i \(-0.502091\pi\)
\(398\) −27.7128 −1.38912
\(399\) 6.00000 + 10.3923i 0.300376 + 0.520266i
\(400\) −12.5000 + 21.6506i −0.625000 + 1.08253i
\(401\) 3.46410 6.00000i 0.172989 0.299626i −0.766475 0.642275i \(-0.777991\pi\)
0.939463 + 0.342649i \(0.111324\pi\)
\(402\) 18.0000 0.897758
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −18.0000 + 31.1769i −0.893325 + 1.54728i
\(407\) 12.0000 + 20.7846i 0.594818 + 1.03025i
\(408\) 10.3923 0.514496
\(409\) −13.8564 24.0000i −0.685155 1.18672i −0.973388 0.229163i \(-0.926401\pi\)
0.288233 0.957560i \(-0.406932\pi\)
\(410\) 0 0
\(411\) −20.7846 −1.02523
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) 18.0000 31.1769i 0.885722 1.53412i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) −10.3923 + 18.0000i −0.508304 + 0.880409i
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) −34.6410 −1.68830 −0.844150 0.536107i \(-0.819894\pi\)
−0.844150 + 0.536107i \(0.819894\pi\)
\(422\) 17.3205 + 30.0000i 0.843149 + 1.46038i
\(423\) 1.73205 + 3.00000i 0.0842152 + 0.145865i
\(424\) −10.3923 −0.504695
\(425\) 15.0000 + 25.9808i 0.727607 + 1.26025i
\(426\) 3.00000 5.19615i 0.145350 0.251754i
\(427\) 3.46410 6.00000i 0.167640 0.290360i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 12.1244 21.0000i 0.584010 1.01153i −0.410988 0.911641i \(-0.634816\pi\)
0.994998 0.0998939i \(-0.0318503\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) 17.0000 + 29.4449i 0.816968 + 1.41503i 0.907906 + 0.419173i \(0.137680\pi\)
−0.0909384 + 0.995857i \(0.528987\pi\)
\(434\) −20.7846 −0.997693
\(435\) 0 0
\(436\) −3.46410 6.00000i −0.165900 0.287348i
\(437\) 0 0
\(438\) 0 0
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) −3.46410 + 6.00000i −0.164399 + 0.284747i
\(445\) 0 0
\(446\) 3.00000 + 5.19615i 0.142054 + 0.246045i
\(447\) −13.8564 −0.655386
\(448\) −1.73205 3.00000i −0.0818317 0.141737i
\(449\) 3.46410 + 6.00000i 0.163481 + 0.283158i 0.936115 0.351694i \(-0.114394\pi\)
−0.772634 + 0.634852i \(0.781061\pi\)
\(450\) −8.66025 −0.408248
\(451\) 12.0000 + 20.7846i 0.565058 + 0.978709i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) −5.19615 + 9.00000i −0.244137 + 0.422857i
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 13.8564 24.0000i 0.648175 1.12267i −0.335383 0.942082i \(-0.608866\pi\)
0.983558 0.180591i \(-0.0578010\pi\)
\(458\) −6.00000 + 10.3923i −0.280362 + 0.485601i
\(459\) 3.00000 + 5.19615i 0.140028 + 0.242536i
\(460\) 0 0
\(461\) 6.92820 + 12.0000i 0.322679 + 0.558896i 0.981040 0.193806i \(-0.0620834\pi\)
−0.658361 + 0.752702i \(0.728750\pi\)
\(462\) 10.3923 + 18.0000i 0.483494 + 0.837436i
\(463\) 17.3205 0.804952 0.402476 0.915430i \(-0.368150\pi\)
0.402476 + 0.915430i \(0.368150\pi\)
\(464\) 15.0000 + 25.9808i 0.696358 + 1.20613i
\(465\) 0 0
\(466\) −5.19615 + 9.00000i −0.240707 + 0.416917i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) −9.00000 15.5885i −0.414259 0.717517i
\(473\) 13.8564 0.637118
\(474\) −6.92820 12.0000i −0.318223 0.551178i
\(475\) 8.66025 + 15.0000i 0.397360 + 0.688247i
\(476\) 20.7846 0.952661
\(477\) −3.00000 5.19615i −0.137361 0.237915i
\(478\) 9.00000 15.5885i 0.411650 0.712999i
\(479\) −5.19615 + 9.00000i −0.237418 + 0.411220i −0.959973 0.280094i \(-0.909635\pi\)
0.722554 + 0.691314i \(0.242968\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −24.0000 −1.09317
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 0 0
\(486\) −1.73205 −0.0785674
\(487\) −19.0526 33.0000i −0.863354 1.49537i −0.868672 0.495387i \(-0.835026\pi\)
0.00531860 0.999986i \(-0.498307\pi\)
\(488\) −1.73205 3.00000i −0.0784063 0.135804i
\(489\) 3.46410 0.156652
\(490\) 0 0
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) −3.46410 + 6.00000i −0.156174 + 0.270501i
\(493\) 36.0000 1.62136
\(494\) 0 0
\(495\) 0 0
\(496\) −8.66025 + 15.0000i −0.388857 + 0.673520i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) −10.3923 −0.465223 −0.232612 0.972570i \(-0.574727\pi\)
−0.232612 + 0.972570i \(0.574727\pi\)
\(500\) 0 0
\(501\) −8.66025 15.0000i −0.386912 0.670151i
\(502\) 20.7846 0.927663
\(503\) −12.0000 20.7846i −0.535054 0.926740i −0.999161 0.0409609i \(-0.986958\pi\)
0.464107 0.885779i \(-0.346375\pi\)
\(504\) 3.00000 5.19615i 0.133631 0.231455i
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) 20.7846 36.0000i 0.921262 1.59567i 0.123796 0.992308i \(-0.460493\pi\)
0.797466 0.603364i \(-0.206173\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 8.66025 0.382733
\(513\) 1.73205 + 3.00000i 0.0764719 + 0.132453i
\(514\) 15.5885 + 27.0000i 0.687577 + 1.19092i
\(515\) 0 0
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 6.00000 10.3923i 0.263880 0.457053i
\(518\) 20.7846 36.0000i 0.913223 1.58175i
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −5.19615 + 9.00000i −0.227429 + 0.393919i
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) 17.3205 0.755929
\(526\) 20.7846 + 36.0000i 0.906252 + 1.56967i
\(527\) 10.3923 + 18.0000i 0.452696 + 0.784092i
\(528\) 17.3205 0.753778
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 5.19615 9.00000i 0.225494 0.390567i
\(532\) 12.0000 0.520266
\(533\) 0 0
\(534\) −12.0000 −0.519291
\(535\) 0 0
\(536\) −9.00000 + 15.5885i −0.388741 + 0.673319i
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 10.3923 0.448044
\(539\) −8.66025 15.0000i −0.373024 0.646096i
\(540\) 0 0
\(541\) −6.92820 −0.297867 −0.148933 0.988847i \(-0.547584\pi\)
−0.148933 + 0.988847i \(0.547584\pi\)
\(542\) 9.00000 + 15.5885i 0.386583 + 0.669582i
\(543\) 5.00000 8.66025i 0.214571 0.371647i
\(544\) 15.5885 27.0000i 0.668350 1.15762i
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −10.3923 + 18.0000i −0.443937 + 0.768922i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 15.0000 + 25.9808i 0.639602 + 1.10782i
\(551\) 20.7846 0.885454
\(552\) 0 0
\(553\) 13.8564 + 24.0000i 0.589234 + 1.02058i
\(554\) 17.3205 0.735878
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 6.92820 12.0000i 0.293557 0.508456i −0.681091 0.732199i \(-0.738494\pi\)
0.974648 + 0.223743i \(0.0718275\pi\)
\(558\) −6.00000 −0.254000
\(559\) 0 0
\(560\) 0 0
\(561\) 10.3923 18.0000i 0.438763 0.759961i
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 3.46410 0.145865
\(565\) 0 0
\(566\) 3.46410 + 6.00000i 0.145607 + 0.252199i
\(567\) 3.46410 0.145479
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 20.7846 36.0000i 0.867533 1.50261i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −16.4545 28.5000i −0.684416 1.18544i
\(579\) 0 0
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) −12.0000 + 20.7846i −0.497416 + 0.861550i
\(583\) −10.3923 + 18.0000i −0.430405 + 0.745484i
\(584\) 0 0
\(585\) 0 0
\(586\) −48.0000 −1.98286
\(587\) −5.19615 + 9.00000i −0.214468 + 0.371470i −0.953108 0.302631i \(-0.902135\pi\)
0.738640 + 0.674100i \(0.235468\pi\)
\(588\) 2.50000 4.33013i 0.103098 0.178571i
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) 0 0
\(591\) 0 0
\(592\) −17.3205 30.0000i −0.711868 1.23299i
\(593\) −6.92820 −0.284507 −0.142254 0.989830i \(-0.545435\pi\)
−0.142254 + 0.989830i \(0.545435\pi\)
\(594\) 3.00000 + 5.19615i 0.123091 + 0.213201i
\(595\) 0 0
\(596\) −6.92820 + 12.0000i −0.283790 + 0.491539i
\(597\) 16.0000 0.654836
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 4.33013 7.50000i 0.176777 0.306186i
\(601\) −5.00000 + 8.66025i −0.203954 + 0.353259i −0.949799 0.312861i \(-0.898713\pi\)
0.745845 + 0.666120i \(0.232046\pi\)
\(602\) −12.0000 20.7846i −0.489083 0.847117i
\(603\) −10.3923 −0.423207
\(604\) 5.19615 + 9.00000i 0.211428 + 0.366205i
\(605\) 0 0
\(606\) 10.3923 0.422159
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 9.00000 15.5885i 0.364998 0.632195i
\(609\) 10.3923 18.0000i 0.421117 0.729397i
\(610\) 0 0
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) 10.3923 18.0000i 0.419741 0.727013i −0.576172 0.817328i \(-0.695454\pi\)
0.995913 + 0.0903153i \(0.0287875\pi\)
\(614\) −9.00000 + 15.5885i −0.363210 + 0.629099i
\(615\) 0 0
\(616\) −20.7846 −0.837436
\(617\) 3.46410 + 6.00000i 0.139459 + 0.241551i 0.927292 0.374338i \(-0.122130\pi\)
−0.787833 + 0.615889i \(0.788797\pi\)
\(618\) −6.92820 12.0000i −0.278693 0.482711i
\(619\) −31.1769 −1.25311 −0.626553 0.779379i \(-0.715535\pi\)
−0.626553 + 0.779379i \(0.715535\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24.0000 0.961540
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −8.66025 + 15.0000i −0.346133 + 0.599521i
\(627\) 6.00000 10.3923i 0.239617 0.415029i
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) −41.5692 −1.65747
\(630\) 0 0
\(631\) 19.0526 + 33.0000i 0.758470 + 1.31371i 0.943630 + 0.331001i \(0.107386\pi\)
−0.185160 + 0.982708i \(0.559280\pi\)
\(632\) 13.8564 0.551178
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) −12.0000 + 20.7846i −0.476581 + 0.825462i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 36.0000 1.42525
\(639\) −1.73205 + 3.00000i −0.0685189 + 0.118678i
\(640\) 0 0
\(641\) −3.00000 5.19615i −0.118493 0.205236i 0.800678 0.599095i \(-0.204473\pi\)
−0.919171 + 0.393860i \(0.871140\pi\)
\(642\) −20.7846 −0.820303
\(643\) 5.19615 + 9.00000i 0.204916 + 0.354925i 0.950106 0.311927i \(-0.100974\pi\)
−0.745190 + 0.666852i \(0.767641\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −18.0000 31.1769i −0.708201 1.22664i
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) 0.866025 1.50000i 0.0340207 0.0589256i
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) 1.73205 3.00000i 0.0678323 0.117489i
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 6.00000 + 10.3923i 0.234619 + 0.406371i
\(655\) 0 0
\(656\) −17.3205 30.0000i −0.676252 1.17130i
\(657\) 0 0
\(658\) −20.7846 −0.810268
\(659\) −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) −10.3923 + 18.0000i −0.404214 + 0.700119i −0.994230 0.107273i \(-0.965788\pi\)
0.590016 + 0.807392i \(0.299121\pi\)
\(662\) 6.00000 0.233197
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 6.00000 10.3923i 0.232495 0.402694i
\(667\) 0 0
\(668\) −17.3205 −0.670151
\(669\) −1.73205 3.00000i −0.0669650 0.115987i
\(670\) 0 0
\(671\) −6.92820 −0.267460
\(672\) −9.00000 15.5885i −0.347183 0.601338i
\(673\) −23.0000 + 39.8372i −0.886585 + 1.53561i −0.0426985 + 0.999088i \(0.513595\pi\)
−0.843886 + 0.536522i \(0.819738\pi\)
\(674\) −12.1244 + 21.0000i −0.467013 + 0.808890i
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) −5.19615 + 9.00000i −0.199557 + 0.345643i
\(679\) 24.0000 41.5692i 0.921035 1.59528i
\(680\) 0 0
\(681\) 17.3205 0.663723
\(682\) 10.3923 + 18.0000i 0.397942 + 0.689256i
\(683\) −15.5885 27.0000i −0.596476 1.03313i −0.993337 0.115248i \(-0.963234\pi\)
0.396861 0.917879i \(-0.370099\pi\)
\(684\) 3.46410 0.132453
\(685\) 0 0
\(686\) 6.00000 10.3923i 0.229081 0.396780i
\(687\) 3.46410 6.00000i 0.132164 0.228914i
\(688\) −20.0000 −0.762493
\(689\) 0 0
\(690\) 0 0
\(691\) −22.5167 + 39.0000i −0.856574 + 1.48363i 0.0186028 + 0.999827i \(0.494078\pi\)
−0.875177 + 0.483803i \(0.839255\pi\)
\(692\) −9.00000 + 15.5885i −0.342129 + 0.592584i
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) 62.3538 2.36692
\(695\) 0 0
\(696\) −5.19615 9.00000i −0.196960 0.341144i
\(697\) −41.5692 −1.57455
\(698\) −6.00000 10.3923i −0.227103 0.393355i
\(699\) 3.00000 5.19615i 0.113470 0.196537i
\(700\) 8.66025 15.0000i 0.327327 0.566947i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) −1.73205 + 3.00000i −0.0652791 + 0.113067i
\(705\) 0 0
\(706\) −30.0000 51.9615i −1.12906 1.95560i
\(707\) −20.7846 −0.781686
\(708\) −5.19615 9.00000i −0.195283 0.338241i
\(709\) −3.46410 6.00000i −0.130097 0.225335i 0.793617 0.608418i \(-0.208196\pi\)
−0.923714 + 0.383083i \(0.874862\pi\)
\(710\) 0 0
\(711\) 4.00000 + 6.92820i 0.150012 + 0.259828i
\(712\) 6.00000 10.3923i 0.224860 0.389468i
\(713\) 0 0
\(714\) −36.0000 −1.34727
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −5.19615 + 9.00000i −0.194054 + 0.336111i
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) 12.0000 + 20.7846i 0.447524 + 0.775135i 0.998224 0.0595683i \(-0.0189724\pi\)
−0.550700 + 0.834703i \(0.685639\pi\)
\(720\) 0 0
\(721\) 13.8564 + 24.0000i 0.516040 + 0.893807i
\(722\) 6.06218 + 10.5000i 0.225611 + 0.390770i
\(723\) 13.8564 0.515325
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) 15.0000 25.9808i 0.557086 0.964901i
\(726\) 0.866025 1.50000i 0.0321412 0.0556702i
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) 34.6410 1.27950 0.639748 0.768585i \(-0.279039\pi\)
0.639748 + 0.768585i \(0.279039\pi\)
\(734\) 13.8564 + 24.0000i 0.511449 + 0.885856i
\(735\) 0 0
\(736\) 0 0
\(737\) 18.0000 + 31.1769i 0.663039 + 1.14842i
\(738\) 6.00000 10.3923i 0.220863 0.382546i
\(739\) −19.0526 + 33.0000i −0.700860 + 1.21392i 0.267305 + 0.963612i \(0.413867\pi\)
−0.968165 + 0.250313i \(0.919467\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 36.0000 1.32160
\(743\) −1.73205 + 3.00000i −0.0635428 + 0.110059i −0.896047 0.443960i \(-0.853573\pi\)
0.832504 + 0.554019i \(0.186907\pi\)
\(744\) 3.00000 5.19615i 0.109985 0.190500i
\(745\) 0 0
\(746\) 38.1051 1.39513
\(747\) 1.73205 + 3.00000i 0.0633724 + 0.109764i
\(748\) −10.3923 18.0000i −0.379980 0.658145i
\(749\) 41.5692 1.51891
\(750\) 0 0
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) −8.66025 + 15.0000i −0.315807 + 0.546994i
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 0 0
\(756\) 1.73205 3.00000i 0.0629941 0.109109i
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) −15.0000 25.9808i −0.544825 0.943664i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.2487 42.0000i −0.879015 1.52250i −0.852423 0.522852i \(-0.824868\pi\)
−0.0265919 0.999646i \(-0.508465\pi\)
\(762\) −13.8564 −0.501965
\(763\) −12.0000 20.7846i −0.434429 0.752453i
\(764\) −12.0000 + 20.7846i −0.434145 + 0.751961i
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) −19.0000 −0.685603
\(769\) −13.8564 + 24.0000i −0.499675 + 0.865462i −1.00000 0.000375472i \(-0.999880\pi\)
0.500325 + 0.865838i \(0.333214\pi\)
\(770\) 0 0
\(771\) −9.00000 15.5885i −0.324127 0.561405i
\(772\) 0 0
\(773\) 6.92820 + 12.0000i 0.249190 + 0.431610i 0.963301 0.268422i \(-0.0865023\pi\)
−0.714111 + 0.700032i \(0.753169\pi\)
\(774\) −3.46410 6.00000i −0.124515 0.215666i
\(775\) 17.3205 0.622171
\(776\) −12.0000 20.7846i −0.430775 0.746124i
\(777\) −12.0000 + 20.7846i −0.430498 + 0.745644i
\(778\) −15.5885 + 27.0000i −0.558873 + 0.967997i
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 3.00000 5.19615i 0.107211 0.185695i
\(784\) 12.5000 + 21.6506i 0.446429 + 0.773237i
\(785\) 0 0
\(786\) −10.3923 18.0000i −0.370681 0.642039i
\(787\) −5.19615 9.00000i −0.185223 0.320815i 0.758429 0.651756i \(-0.225967\pi\)
−0.943652 + 0.330941i \(0.892634\pi\)
\(788\) 0 0
\(789\) −12.0000 20.7846i −0.427211 0.739952i
\(790\) 0 0
\(791\) 10.3923 18.0000i 0.369508 0.640006i
\(792\) −6.00000 −0.213201
\(793\) 0 0
\(794\) 60.0000 2.12932
\(795\) 0 0
\(796\) 8.00000 13.8564i 0.283552 0.491127i
\(797\) −21.0000 36.3731i −0.743858 1.28840i −0.950726 0.310031i \(-0.899660\pi\)
0.206868 0.978369i \(-0.433673\pi\)
\(798\) −20.7846 −0.735767
\(799\) 10.3923 + 18.0000i 0.367653 + 0.636794i
\(800\) −12.9904 22.5000i −0.459279 0.795495i
\(801\) 6.92820 0.244796
\(802\) 6.00000 + 10.3923i 0.211867 + 0.366965i
\(803\) 0 0
\(804\) −5.19615 + 9.00000i −0.183254 + 0.317406i
\(805\) 0 0
\(806\) 0 0
\(807\) −6.00000 −0.211210
\(808\) −5.19615 + 9.00000i −0.182800 + 0.316619i
\(809\) 15.0000 25.9808i 0.527372 0.913435i −0.472119 0.881535i \(-0.656511\pi\)
0.999491 0.0319002i \(-0.0101559\pi\)
\(810\) 0 0
\(811\) −38.1051 −1.33805 −0.669026 0.743239i \(-0.733288\pi\)
−0.669026 + 0.743239i \(0.733288\pi\)
\(812\) −10.3923 18.0000i −0.364698 0.631676i
\(813\) −5.19615 9.00000i −0.182237 0.315644i
\(814\) −41.5692 −1.45700
\(815\) 0 0
\(816\) −15.0000 + 25.9808i −0.525105 + 0.909509i
\(817\) −6.92820 + 12.0000i −0.242387 + 0.419827i
\(818\) 48.0000 1.67828
\(819\) 0 0
\(820\) 0 0
\(821\) −6.92820 + 12.0000i −0.241796 + 0.418803i −0.961226 0.275762i \(-0.911070\pi\)
0.719430 + 0.694565i \(0.244403\pi\)
\(822\) 18.0000 31.1769i 0.627822 1.08742i
\(823\) −20.0000 34.6410i −0.697156 1.20751i −0.969448 0.245295i \(-0.921115\pi\)
0.272292 0.962215i \(-0.412218\pi\)
\(824\) 13.8564 0.482711
\(825\) −8.66025 15.0000i −0.301511 0.522233i
\(826\) 31.1769 + 54.0000i 1.08478 + 1.87890i
\(827\) −24.2487 −0.843210 −0.421605 0.906780i \(-0.638533\pi\)
−0.421605 + 0.906780i \(0.638533\pi\)
\(828\) 0 0
\(829\) −1.00000 + 1.73205i −0.0347314 + 0.0601566i −0.882869 0.469620i \(-0.844391\pi\)
0.848137 + 0.529777i \(0.177724\pi\)
\(830\) 0 0
\(831\) −10.0000 −0.346896
\(832\) 0 0
\(833\) 30.0000 1.03944
\(834\) −3.46410 + 6.00000i −0.119952 + 0.207763i
\(835\) 0 0
\(836\) −6.00000 10.3923i −0.207514 0.359425i
\(837\) 3.46410 0.119737
\(838\) 10.3923 + 18.0000i 0.358996 + 0.621800i
\(839\) 1.73205 + 3.00000i 0.0597970 + 0.103572i 0.894374 0.447320i \(-0.147621\pi\)
−0.834577 + 0.550891i \(0.814288\pi\)
\(840\) 0 0
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) 30.0000 51.9615i 1.03387 1.79071i
\(843\) −3.46410 + 6.00000i −0.119310 + 0.206651i
\(844\) −20.0000 −0.688428
\(845\) 0 0
\(846\) −6.00000 −0.206284
\(847\) −1.73205 + 3.00000i −0.0595140 + 0.103081i
\(848\) 15.0000 25.9808i 0.515102 0.892183i
\(849\) −2.00000 3.46410i −0.0686398 0.118888i
\(850\) −51.9615 −1.78227
\(851\) 0 0
\(852\) 1.73205 + 3.00000i 0.0593391 + 0.102778i
\(853\) 20.7846 0.711651 0.355826 0.934552i \(-0.384200\pi\)
0.355826 + 0.934552i \(0.384200\pi\)
\(854\) 6.00000 + 10.3923i 0.205316 + 0.355617i
\(855\) 0 0
\(856\) 10.3923 18.0000i 0.355202 0.615227i
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) −12.0000 + 20.7846i −0.408959 + 0.708338i
\(862\) 21.0000 + 36.3731i 0.715263 + 1.23887i
\(863\) 31.1769 1.06127 0.530637 0.847599i \(-0.321953\pi\)
0.530637 + 0.847599i \(0.321953\pi\)
\(864\) −2.59808 4.50000i −0.0883883 0.153093i
\(865\) 0 0
\(866\) −58.8897 −2.00115
\(867\) 9.50000 + 16.4545i 0.322637 + 0.558824i
\(868\) 6.00000 10.3923i 0.203653 0.352738i
\(869\) 13.8564 24.0000i 0.470046 0.814144i
\(870\) 0 0
\(871\) 0 0
\(872\) −12.0000 −0.406371
\(873\) 6.92820 12.0000i 0.234484 0.406138i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −24.2487 42.0000i −0.818821 1.41824i −0.906552 0.422095i \(-0.861295\pi\)
0.0877308 0.996144i \(-0.472038\pi\)
\(878\) 6.92820 + 12.0000i 0.233816 + 0.404980i
\(879\) 27.7128 0.934730
\(880\) 0 0
\(881\) 9.00000 15.5885i 0.303218 0.525188i −0.673645 0.739055i \(-0.735272\pi\)
0.976863 + 0.213866i \(0.0686057\pi\)
\(882\) −4.33013 + 7.50000i −0.145803 + 0.252538i
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 31.1769 54.0000i 1.04741 1.81417i
\(887\) −24.0000 + 41.5692i −0.805841 + 1.39576i 0.109881 + 0.993945i \(0.464953\pi\)
−0.915722 + 0.401813i \(0.868380\pi\)
\(888\) 6.00000 + 10.3923i 0.201347 + 0.348743i
\(889\) 27.7128 0.929458
\(890\) 0 0
\(891\) −1.73205 3.00000i −0.0580259 0.100504i
\(892\) −3.46410 −0.115987
\(893\) 6.00000 + 10.3923i 0.200782 + 0.347765i
\(894\) 12.0000 20.7846i 0.401340 0.695141i
\(895\) 0 0
\(896\) 42.0000 1.40312
\(897\) 0 0
\(898\) −12.0000 −0.400445
\(899\) 10.3923 18.0000i 0.346603 0.600334i
\(900\) 2.50000 4.33013i 0.0833333 0.144338i
\(901\) −18.0000 31.1769i −0.599667 1.03865i
\(902\) −41.5692 −1.38410
\(903\) 6.92820 + 12.0000i 0.230556 + 0.399335i
\(904\) −5.19615 9.00000i −0.172821 0.299336i
\(905\) 0 0
\(906\) −9.00000 15.5885i −0.299005 0.517892i
\(907\) −22.0000 + 38.1051i −0.730498 + 1.26526i 0.226173 + 0.974087i \(0.427379\pi\)
−0.956671 + 0.291172i \(0.905955\pi\)
\(908\) 8.66025 15.0000i 0.287401 0.497792i
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) −8.66025 + 15.0000i −0.286770 + 0.496700i
\(913\) 6.00000 10.3923i 0.198571 0.343935i
\(914\) 24.0000 + 41.5692i 0.793849 + 1.37499i
\(915\) 0 0
\(916\) −3.46410 6.00000i −0.114457 0.198246i
\(917\) 20.7846 + 36.0000i 0.686368 + 1.18882i
\(918\) −10.3923 −0.342997
\(919\) 16.0000 + 27.7128i 0.527791 + 0.914161i 0.999475 + 0.0323936i \(0.0103130\pi\)
−0.471684 + 0.881768i \(0.656354\pi\)
\(920\) 0 0
\(921\) 5.19615 9.00000i 0.171219 0.296560i
\(922\) −24.0000 −0.790398
\(923\) 0 0
\(924\) −12.0000 −0.394771
\(925\) −17.3205 + 30.0000i −0.569495 + 0.986394i
\(926\) −15.0000 + 25.9808i −0.492931 + 0.853781i
\(927\) 4.00000 + 6.92820i 0.131377 + 0.227552i
\(928\) −31.1769 −1.02343
\(929\) 10.3923 + 18.0000i 0.340960 + 0.590561i 0.984611 0.174758i \(-0.0559144\pi\)
−0.643651 + 0.765319i \(0.722581\pi\)
\(930\) 0 0
\(931\) 17.3205 0.567657
\(932\) −3.00000 5.19615i −0.0982683 0.170206i
\(933\) 0 0
\(934\) 10.3923 18.0000i 0.340047 0.588978i
\(935\) 0 0
\(936\) 0 0
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 31.1769 54.0000i 1.01796 1.76316i
\(939\) 5.00000 8.66025i 0.163169 0.282617i
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 12.1244 + 21.0000i 0.395033 + 0.684217i
\(943\) 0 0
\(944\) 51.9615 1.69120
\(945\) 0 0
\(946\) −12.0000 + 20.7846i −0.390154 + 0.675766i
\(947\) 25.9808 45.0000i 0.844261 1.46230i −0.0419998 0.999118i \(-0.513373\pi\)
0.886261 0.463186i \(-0.153294\pi\)
\(948\) 8.00000 0.259828
\(949\) 0 0
\(950\) −30.0000 −0.973329
\(951\) 6.92820 12.0000i 0.224662 0.389127i
\(952\) 18.0000 31.1769i 0.583383 1.01045i
\(953\) 21.0000 + 36.3731i 0.680257 + 1.17824i 0.974902 + 0.222633i \(0.0714650\pi\)
−0.294646 + 0.955607i \(0.595202\pi\)
\(954\) 10.3923 0.336463
\(955\) 0 0
\(956\) 5.19615 + 9.00000i 0.168056 + 0.291081i
\(957\) −20.7846 −0.671871
\(958\) −9.00000 15.5885i −0.290777 0.503640i
\(959\) −36.0000 + 62.3538i −1.16250 + 2.01351i
\(960\) 0 0
\(961\) −19.0000 −0.612903
\(962\) 0 0
\(963\) 12.0000 0.386695
\(964\) 6.92820 12.0000i 0.223142 0.386494i
\(965\) 0 0
\(966\) 0 0
\(967\) 10.3923 0.334194 0.167097 0.985940i \(-0.446561\pi\)
0.167097 + 0.985940i \(0.446561\pi\)
\(968\) 0.866025 + 1.50000i 0.0278351 + 0.0482118i
\(969\) 10.3923 + 18.0000i 0.333849 + 0.578243i
\(970\) 0 0
\(971\) 6.00000 + 10.3923i 0.192549 + 0.333505i 0.946094 0.323891i \(-0.104991\pi\)
−0.753545 + 0.657396i \(0.771658\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) 6.92820 12.0000i 0.222108 0.384702i
\(974\) 66.0000 2.11478
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) −24.2487 + 42.0000i −0.775785 + 1.34370i 0.158567 + 0.987348i \(0.449313\pi\)
−0.934352 + 0.356351i \(0.884021\pi\)
\(978\) −3.00000 + 5.19615i −0.0959294 + 0.166155i
\(979\) −12.0000 20.7846i −0.383522 0.664279i
\(980\) 0 0
\(981\) −3.46410 6.00000i −0.110600 0.191565i
\(982\) −10.3923 18.0000i −0.331632 0.574403i
\(983\) 51.9615 1.65732 0.828658 0.559756i \(-0.189105\pi\)
0.828658 + 0.559756i \(0.189105\pi\)
\(984\) 6.00000 + 10.3923i 0.191273 + 0.331295i
\(985\) 0 0
\(986\) −31.1769 + 54.0000i −0.992875 + 1.71971i
\(987\) 12.0000 0.381964
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −16.0000 + 27.7128i −0.508257 + 0.880327i 0.491698 + 0.870766i \(0.336377\pi\)
−0.999954 + 0.00956046i \(0.996957\pi\)
\(992\) −9.00000 15.5885i −0.285750 0.494934i
\(993\) −3.46410 −0.109930
\(994\) −10.3923 18.0000i −0.329624 0.570925i
\(995\) 0 0
\(996\) 3.46410 0.109764
\(997\) −19.0000 32.9090i −0.601736 1.04224i −0.992558 0.121771i \(-0.961143\pi\)
0.390822 0.920466i \(-0.372191\pi\)
\(998\) 9.00000 15.5885i 0.284890 0.493444i
\(999\) −3.46410 + 6.00000i −0.109599 + 0.189832i
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 507.2.e.e.22.1 4
13.2 odd 12 507.2.j.a.361.1 2
13.3 even 3 inner 507.2.e.e.484.1 4
13.4 even 6 507.2.a.f.1.1 2
13.5 odd 4 507.2.j.c.316.1 2
13.6 odd 12 39.2.b.a.25.1 2
13.7 odd 12 39.2.b.a.25.2 yes 2
13.8 odd 4 507.2.j.a.316.1 2
13.9 even 3 507.2.a.f.1.2 2
13.10 even 6 inner 507.2.e.e.484.2 4
13.11 odd 12 507.2.j.c.361.1 2
13.12 even 2 inner 507.2.e.e.22.2 4
39.17 odd 6 1521.2.a.l.1.2 2
39.20 even 12 117.2.b.a.64.1 2
39.32 even 12 117.2.b.a.64.2 2
39.35 odd 6 1521.2.a.l.1.1 2
52.7 even 12 624.2.c.e.337.2 2
52.19 even 12 624.2.c.e.337.1 2
52.35 odd 6 8112.2.a.bv.1.1 2
52.43 odd 6 8112.2.a.bv.1.2 2
65.7 even 12 975.2.h.f.649.2 4
65.19 odd 12 975.2.b.d.376.2 2
65.32 even 12 975.2.h.f.649.4 4
65.33 even 12 975.2.h.f.649.3 4
65.58 even 12 975.2.h.f.649.1 4
65.59 odd 12 975.2.b.d.376.1 2
91.6 even 12 1911.2.c.d.883.1 2
91.20 even 12 1911.2.c.d.883.2 2
104.19 even 12 2496.2.c.d.961.1 2
104.45 odd 12 2496.2.c.k.961.2 2
104.59 even 12 2496.2.c.d.961.2 2
104.85 odd 12 2496.2.c.k.961.1 2
156.59 odd 12 1872.2.c.e.1585.2 2
156.71 odd 12 1872.2.c.e.1585.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.b.a.25.1 2 13.6 odd 12
39.2.b.a.25.2 yes 2 13.7 odd 12
117.2.b.a.64.1 2 39.20 even 12
117.2.b.a.64.2 2 39.32 even 12
507.2.a.f.1.1 2 13.4 even 6
507.2.a.f.1.2 2 13.9 even 3
507.2.e.e.22.1 4 1.1 even 1 trivial
507.2.e.e.22.2 4 13.12 even 2 inner
507.2.e.e.484.1 4 13.3 even 3 inner
507.2.e.e.484.2 4 13.10 even 6 inner
507.2.j.a.316.1 2 13.8 odd 4
507.2.j.a.361.1 2 13.2 odd 12
507.2.j.c.316.1 2 13.5 odd 4
507.2.j.c.361.1 2 13.11 odd 12
624.2.c.e.337.1 2 52.19 even 12
624.2.c.e.337.2 2 52.7 even 12
975.2.b.d.376.1 2 65.59 odd 12
975.2.b.d.376.2 2 65.19 odd 12
975.2.h.f.649.1 4 65.58 even 12
975.2.h.f.649.2 4 65.7 even 12
975.2.h.f.649.3 4 65.33 even 12
975.2.h.f.649.4 4 65.32 even 12
1521.2.a.l.1.1 2 39.35 odd 6
1521.2.a.l.1.2 2 39.17 odd 6
1872.2.c.e.1585.1 2 156.71 odd 12
1872.2.c.e.1585.2 2 156.59 odd 12
1911.2.c.d.883.1 2 91.6 even 12
1911.2.c.d.883.2 2 91.20 even 12
2496.2.c.d.961.1 2 104.19 even 12
2496.2.c.d.961.2 2 104.59 even 12
2496.2.c.k.961.1 2 104.85 odd 12
2496.2.c.k.961.2 2 104.45 odd 12
8112.2.a.bv.1.1 2 52.35 odd 6
8112.2.a.bv.1.2 2 52.43 odd 6