Properties

Label 845.2.n.a.529.1
Level $845$
Weight $2$
Character 845.529
Analytic conductor $6.747$
Analytic rank $1$
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] = [845,2,Mod(484,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("845.484");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.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: \(6.74735897080\)
Analytic rank: \(1\)
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: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 529.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.529
Dual form 845.2.n.a.484.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.23205 + 0.133975i) q^{10} +(-1.00000 + 1.73205i) q^{11} -2.00000i q^{12} +(-4.46410 - 0.267949i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{18} +(-3.00000 - 5.19615i) q^{19} +(1.86603 + 1.23205i) q^{20} +(1.73205 - 1.00000i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-3.00000 + 5.19615i) q^{24} +(3.00000 - 4.00000i) q^{25} -4.00000i q^{27} +(-3.00000 + 5.19615i) q^{29} +(3.73205 + 2.46410i) q^{30} -6.00000 q^{31} +(4.33013 - 2.50000i) q^{32} +(-3.46410 + 2.00000i) q^{33} +(0.500000 - 0.866025i) q^{36} +(-5.19615 - 3.00000i) q^{37} +6.00000i q^{38} +(-3.00000 - 6.00000i) q^{40} +(-4.00000 + 6.92820i) q^{41} +(-5.19615 + 3.00000i) q^{43} +2.00000 q^{44} +(-1.86603 - 1.23205i) q^{45} +(3.00000 + 5.19615i) q^{46} -8.00000i q^{47} +(1.73205 - 1.00000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-4.59808 + 1.96410i) q^{50} +12.0000i q^{53} +(-2.00000 + 3.46410i) q^{54} +(0.267949 - 4.46410i) q^{55} -12.0000i q^{57} +(5.19615 - 3.00000i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(2.00000 + 4.00000i) q^{60} +(-3.00000 - 5.19615i) q^{61} +(5.19615 + 3.00000i) q^{62} -7.00000 q^{64} +4.00000 q^{66} +(10.3923 + 6.00000i) q^{67} +(-6.00000 - 10.3923i) q^{69} +(-1.00000 - 1.73205i) q^{71} +(-2.59808 + 1.50000i) q^{72} -6.00000i q^{73} +(3.00000 + 5.19615i) q^{74} +(9.19615 - 3.92820i) q^{75} +(-3.00000 + 5.19615i) q^{76} +(-0.133975 + 2.23205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(6.92820 - 4.00000i) q^{82} +4.00000i q^{83} +6.00000 q^{86} +(-10.3923 + 6.00000i) q^{87} +(-5.19615 - 3.00000i) q^{88} +(4.00000 - 6.92820i) q^{89} +(1.00000 + 2.00000i) q^{90} +6.00000i q^{92} +(-10.3923 - 6.00000i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(11.1962 + 7.39230i) q^{95} +10.0000 q^{96} +(5.19615 - 3.00000i) q^{97} +(6.06218 - 3.50000i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} - 8 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} - 8 q^{5} - 4 q^{6} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{15} + 2 q^{16} - 12 q^{19} + 4 q^{20} - 12 q^{24} + 12 q^{25} - 12 q^{29} + 8 q^{30} - 24 q^{31} + 2 q^{36} - 12 q^{40} - 16 q^{41} + 8 q^{44} - 4 q^{45} + 12 q^{46} - 14 q^{49} - 8 q^{50} - 8 q^{54} + 8 q^{55} - 4 q^{59} + 8 q^{60} - 12 q^{61} - 28 q^{64} + 16 q^{66} - 24 q^{69} - 4 q^{71} + 12 q^{74} + 16 q^{75} - 12 q^{76} - 4 q^{80} + 22 q^{81} + 24 q^{86} + 16 q^{89} + 4 q^{90} - 16 q^{94} + 24 q^{95} + 40 q^{96} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.161521 0.986869i \(-0.448360\pi\)
−0.773893 + 0.633316i \(0.781693\pi\)
\(3\) 1.73205 + 1.00000i 1.00000 + 0.577350i 0.908248 0.418432i \(-0.137420\pi\)
0.0917517 + 0.995782i \(0.470753\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) −1.00000 1.73205i −0.408248 0.707107i
\(7\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) 3.00000i 1.06066i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 2.23205 + 0.133975i 0.705836 + 0.0423665i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 0 0
\(14\) 0 0
\(15\) −4.46410 0.267949i −1.15263 0.0691842i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 1.86603 + 1.23205i 0.417256 + 0.275495i
\(21\) 0 0
\(22\) 1.73205 1.00000i 0.369274 0.213201i
\(23\) −5.19615 3.00000i −1.08347 0.625543i −0.151642 0.988436i \(-0.548456\pi\)
−0.931831 + 0.362892i \(0.881789\pi\)
\(24\) −3.00000 + 5.19615i −0.612372 + 1.06066i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 3.73205 + 2.46410i 0.681376 + 0.449881i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 4.33013 2.50000i 0.765466 0.441942i
\(33\) −3.46410 + 2.00000i −0.603023 + 0.348155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −5.19615 3.00000i −0.854242 0.493197i 0.00783774 0.999969i \(-0.497505\pi\)
−0.862080 + 0.506772i \(0.830838\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −3.00000 6.00000i −0.474342 0.948683i
\(41\) −4.00000 + 6.92820i −0.624695 + 1.08200i 0.363905 + 0.931436i \(0.381443\pi\)
−0.988600 + 0.150567i \(0.951890\pi\)
\(42\) 0 0
\(43\) −5.19615 + 3.00000i −0.792406 + 0.457496i −0.840809 0.541332i \(-0.817920\pi\)
0.0484030 + 0.998828i \(0.484587\pi\)
\(44\) 2.00000 0.301511
\(45\) −1.86603 1.23205i −0.278171 0.183663i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 1.73205 1.00000i 0.250000 0.144338i
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) −4.59808 + 1.96410i −0.650266 + 0.277766i
\(51\) 0 0
\(52\) 0 0
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) −2.00000 + 3.46410i −0.272166 + 0.471405i
\(55\) 0.267949 4.46410i 0.0361303 0.601939i
\(56\) 0 0
\(57\) 12.0000i 1.58944i
\(58\) 5.19615 3.00000i 0.682288 0.393919i
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) 2.00000 + 4.00000i 0.258199 + 0.516398i
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 5.19615 + 3.00000i 0.659912 + 0.381000i
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) 10.3923 + 6.00000i 1.26962 + 0.733017i 0.974916 0.222571i \(-0.0714450\pi\)
0.294706 + 0.955588i \(0.404778\pi\)
\(68\) 0 0
\(69\) −6.00000 10.3923i −0.722315 1.25109i
\(70\) 0 0
\(71\) −1.00000 1.73205i −0.118678 0.205557i 0.800566 0.599245i \(-0.204532\pi\)
−0.919244 + 0.393688i \(0.871199\pi\)
\(72\) −2.59808 + 1.50000i −0.306186 + 0.176777i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 3.00000 + 5.19615i 0.348743 + 0.604040i
\(75\) 9.19615 3.92820i 1.06188 0.453590i
\(76\) −3.00000 + 5.19615i −0.344124 + 0.596040i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −0.133975 + 2.23205i −0.0149788 + 0.249551i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 6.92820 4.00000i 0.765092 0.441726i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000 0.646997
\(87\) −10.3923 + 6.00000i −1.11417 + 0.643268i
\(88\) −5.19615 3.00000i −0.553912 0.319801i
\(89\) 4.00000 6.92820i 0.423999 0.734388i −0.572327 0.820025i \(-0.693959\pi\)
0.996326 + 0.0856373i \(0.0272926\pi\)
\(90\) 1.00000 + 2.00000i 0.105409 + 0.210819i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) −10.3923 6.00000i −1.07763 0.622171i
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) 11.1962 + 7.39230i 1.14870 + 0.758434i
\(96\) 10.0000 1.02062
\(97\) 5.19615 3.00000i 0.527589 0.304604i −0.212445 0.977173i \(-0.568143\pi\)
0.740034 + 0.672569i \(0.234809\pi\)
\(98\) 6.06218 3.50000i 0.612372 0.353553i
\(99\) −2.00000 −0.201008
\(100\) −4.96410 0.598076i −0.496410 0.0598076i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) −5.19615 3.00000i −0.502331 0.290021i 0.227345 0.973814i \(-0.426996\pi\)
−0.729676 + 0.683793i \(0.760329\pi\)
\(108\) −3.46410 + 2.00000i −0.333333 + 0.192450i
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) −2.46410 + 3.73205i −0.234943 + 0.355837i
\(111\) −6.00000 10.3923i −0.569495 0.986394i
\(112\) 0 0
\(113\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) −6.00000 + 10.3923i −0.561951 + 0.973329i
\(115\) 13.3923 + 0.803848i 1.24884 + 0.0749592i
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) 0.803848 13.3923i 0.0733809 1.22254i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 6.00000i 0.543214i
\(123\) −13.8564 + 8.00000i −1.24939 + 0.721336i
\(124\) 3.00000 + 5.19615i 0.269408 + 0.466628i
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 1.73205 + 1.00000i 0.153695 + 0.0887357i 0.574875 0.818241i \(-0.305051\pi\)
−0.421180 + 0.906977i \(0.638384\pi\)
\(128\) −2.59808 1.50000i −0.229640 0.132583i
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 3.46410 + 2.00000i 0.301511 + 0.174078i
\(133\) 0 0
\(134\) −6.00000 10.3923i −0.518321 0.897758i
\(135\) 4.00000 + 8.00000i 0.344265 + 0.688530i
\(136\) 0 0
\(137\) 1.73205 1.00000i 0.147979 0.0854358i −0.424182 0.905577i \(-0.639438\pi\)
0.572161 + 0.820141i \(0.306105\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 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
\(141\) 8.00000 13.8564i 0.673722 1.16692i
\(142\) 2.00000i 0.167836i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0.803848 13.3923i 0.0667559 1.11217i
\(146\) −3.00000 + 5.19615i −0.248282 + 0.430037i
\(147\) −12.1244 + 7.00000i −1.00000 + 0.577350i
\(148\) 6.00000i 0.493197i
\(149\) 10.0000 + 17.3205i 0.819232 + 1.41895i 0.906249 + 0.422744i \(0.138933\pi\)
−0.0870170 + 0.996207i \(0.527733\pi\)
\(150\) −9.92820 1.19615i −0.810634 0.0976654i
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 15.5885 9.00000i 1.26439 0.729996i
\(153\) 0 0
\(154\) 0 0
\(155\) 12.0000 6.00000i 0.963863 0.481932i
\(156\) 0 0
\(157\) 12.0000i 0.957704i −0.877896 0.478852i \(-0.841053\pi\)
0.877896 0.478852i \(-0.158947\pi\)
\(158\) 0 0
\(159\) −12.0000 + 20.7846i −0.951662 + 1.64833i
\(160\) −6.16025 + 9.33013i −0.487011 + 0.737611i
\(161\) 0 0
\(162\) −9.52628 + 5.50000i −0.748455 + 0.432121i
\(163\) 10.3923 6.00000i 0.813988 0.469956i −0.0343508 0.999410i \(-0.510936\pi\)
0.848339 + 0.529454i \(0.177603\pi\)
\(164\) 8.00000 0.624695
\(165\) 4.92820 7.46410i 0.383660 0.581080i
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) 13.8564 + 8.00000i 1.07224 + 0.619059i 0.928793 0.370599i \(-0.120848\pi\)
0.143448 + 0.989658i \(0.454181\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 3.00000 5.19615i 0.229416 0.397360i
\(172\) 5.19615 + 3.00000i 0.396203 + 0.228748i
\(173\) 10.3923 6.00000i 0.790112 0.456172i −0.0498898 0.998755i \(-0.515887\pi\)
0.840002 + 0.542583i \(0.182554\pi\)
\(174\) 12.0000 0.909718
\(175\) 0 0
\(176\) 1.00000 + 1.73205i 0.0753778 + 0.130558i
\(177\) 4.00000i 0.300658i
\(178\) −6.92820 + 4.00000i −0.519291 + 0.299813i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) −0.133975 + 2.23205i −0.00998588 + 0.166367i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 12.0000i 0.887066i
\(184\) 9.00000 15.5885i 0.663489 1.14920i
\(185\) 13.3923 + 0.803848i 0.984622 + 0.0591000i
\(186\) 6.00000 + 10.3923i 0.439941 + 0.762001i
\(187\) 0 0
\(188\) −6.92820 + 4.00000i −0.505291 + 0.291730i
\(189\) 0 0
\(190\) −6.00000 12.0000i −0.435286 0.870572i
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) −12.1244 7.00000i −0.875000 0.505181i
\(193\) 5.19615 + 3.00000i 0.374027 + 0.215945i 0.675216 0.737620i \(-0.264050\pi\)
−0.301189 + 0.953564i \(0.597384\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) −1.73205 1.00000i −0.123404 0.0712470i 0.437028 0.899448i \(-0.356031\pi\)
−0.560431 + 0.828201i \(0.689365\pi\)
\(198\) 1.73205 + 1.00000i 0.123091 + 0.0710669i
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 12.0000 + 9.00000i 0.848528 + 0.636396i
\(201\) 12.0000 + 20.7846i 0.846415 + 1.46603i
\(202\) −5.19615 + 3.00000i −0.365600 + 0.211079i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.07180 17.8564i 0.0748575 1.24715i
\(206\) 3.00000 5.19615i 0.209020 0.362033i
\(207\) 6.00000i 0.417029i
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) 10.3923 6.00000i 0.713746 0.412082i
\(213\) 4.00000i 0.274075i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 7.39230 11.1962i 0.504151 0.763571i
\(216\) 12.0000 0.816497
\(217\) 0 0
\(218\) 10.3923 + 6.00000i 0.703856 + 0.406371i
\(219\) 6.00000 10.3923i 0.405442 0.702247i
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) 0 0
\(222\) 12.0000i 0.805387i
\(223\) 20.7846 + 12.0000i 1.39184 + 0.803579i 0.993519 0.113666i \(-0.0362595\pi\)
0.398321 + 0.917246i \(0.369593\pi\)
\(224\) 0 0
\(225\) 4.96410 + 0.598076i 0.330940 + 0.0398717i
\(226\) 0 0
\(227\) 3.46410 2.00000i 0.229920 0.132745i −0.380615 0.924734i \(-0.624288\pi\)
0.610535 + 0.791989i \(0.290954\pi\)
\(228\) −10.3923 + 6.00000i −0.688247 + 0.397360i
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) −11.1962 7.39230i −0.738252 0.487434i
\(231\) 0 0
\(232\) −15.5885 9.00000i −1.02343 0.590879i
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 0 0
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) −1.00000 + 1.73205i −0.0650945 + 0.112747i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0000 0.646846 0.323423 0.946254i \(-0.395166\pi\)
0.323423 + 0.946254i \(0.395166\pi\)
\(240\) −2.46410 + 3.73205i −0.159057 + 0.240903i
\(241\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 8.66025 5.00000i 0.555556 0.320750i
\(244\) −3.00000 + 5.19615i −0.192055 + 0.332650i
\(245\) 0.937822 15.6244i 0.0599153 0.998203i
\(246\) 16.0000 1.02012
\(247\) 0 0
\(248\) 18.0000i 1.14300i
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) 7.23205 8.52628i 0.457395 0.539249i
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 0 0
\(253\) 10.3923 6.00000i 0.653359 0.377217i
\(254\) −1.00000 1.73205i −0.0627456 0.108679i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 10.3923 + 6.00000i 0.646997 + 0.373544i
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 10.3923 + 6.00000i 0.642039 + 0.370681i
\(263\) 5.19615 + 3.00000i 0.320408 + 0.184988i 0.651575 0.758585i \(-0.274109\pi\)
−0.331166 + 0.943572i \(0.607442\pi\)
\(264\) −6.00000 10.3923i −0.369274 0.639602i
\(265\) −12.0000 24.0000i −0.737154 1.47431i
\(266\) 0 0
\(267\) 13.8564 8.00000i 0.847998 0.489592i
\(268\) 12.0000i 0.733017i
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0.535898 8.92820i 0.0326137 0.543353i
\(271\) −3.00000 + 5.19615i −0.182237 + 0.315644i −0.942642 0.333805i \(-0.891667\pi\)
0.760405 + 0.649449i \(0.225000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 3.92820 + 9.19615i 0.236880 + 0.554549i
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) −10.3923 + 6.00000i −0.624413 + 0.360505i −0.778585 0.627539i \(-0.784062\pi\)
0.154172 + 0.988044i \(0.450729\pi\)
\(278\) 4.00000i 0.239904i
\(279\) −3.00000 5.19615i −0.179605 0.311086i
\(280\) 0 0
\(281\) 8.00000 0.477240 0.238620 0.971113i \(-0.423305\pi\)
0.238620 + 0.971113i \(0.423305\pi\)
\(282\) −13.8564 + 8.00000i −0.825137 + 0.476393i
\(283\) 19.0526 + 11.0000i 1.13256 + 0.653882i 0.944577 0.328291i \(-0.106473\pi\)
0.187980 + 0.982173i \(0.439806\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 12.0000 + 24.0000i 0.710819 + 1.42164i
\(286\) 0 0
\(287\) 0 0
\(288\) 4.33013 + 2.50000i 0.255155 + 0.147314i
\(289\) −8.50000 + 14.7224i −0.500000 + 0.866025i
\(290\) −7.39230 + 11.1962i −0.434091 + 0.657461i
\(291\) 12.0000 0.703452
\(292\) −5.19615 + 3.00000i −0.304082 + 0.175562i
\(293\) −22.5167 + 13.0000i −1.31544 + 0.759468i −0.982991 0.183654i \(-0.941207\pi\)
−0.332446 + 0.943122i \(0.607874\pi\)
\(294\) 14.0000 0.816497
\(295\) 3.73205 + 2.46410i 0.217288 + 0.143466i
\(296\) 9.00000 15.5885i 0.523114 0.906061i
\(297\) 6.92820 + 4.00000i 0.402015 + 0.232104i
\(298\) 20.0000i 1.15857i
\(299\) 0 0
\(300\) −8.00000 6.00000i −0.461880 0.346410i
\(301\) 0 0
\(302\) 15.5885 + 9.00000i 0.897015 + 0.517892i
\(303\) 10.3923 6.00000i 0.597022 0.344691i
\(304\) −6.00000 −0.344124
\(305\) 11.1962 + 7.39230i 0.641090 + 0.423282i
\(306\) 0 0
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 0 0
\(309\) −6.00000 + 10.3923i −0.341328 + 0.591198i
\(310\) −13.3923 0.803848i −0.760632 0.0456555i
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) −6.00000 + 10.3923i −0.338600 + 0.586472i
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 20.7846 12.0000i 1.16554 0.672927i
\(319\) −6.00000 10.3923i −0.335936 0.581857i
\(320\) 14.0000 7.00000i 0.782624 0.391312i
\(321\) −6.00000 10.3923i −0.334887 0.580042i
\(322\) 0 0
\(323\) 0 0
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −12.0000 −0.664619
\(327\) −20.7846 12.0000i −1.14939 0.663602i
\(328\) −20.7846 12.0000i −1.14764 0.662589i
\(329\) 0 0
\(330\) −8.00000 + 4.00000i −0.440386 + 0.220193i
\(331\) −15.0000 25.9808i −0.824475 1.42803i −0.902320 0.431066i \(-0.858137\pi\)
0.0778456 0.996965i \(-0.475196\pi\)
\(332\) 3.46410 2.00000i 0.190117 0.109764i
\(333\) 6.00000i 0.328798i
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) −26.7846 1.60770i −1.46340 0.0878378i
\(336\) 0 0
\(337\) 32.0000i 1.74315i 0.490261 + 0.871576i \(0.336901\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −5.19615 + 3.00000i −0.280976 + 0.162221i
\(343\) 0 0
\(344\) −9.00000 15.5885i −0.485247 0.840473i
\(345\) 22.3923 + 14.7846i 1.20556 + 0.795977i
\(346\) −12.0000 −0.645124
\(347\) 5.19615 3.00000i 0.278944 0.161048i −0.354001 0.935245i \(-0.615179\pi\)
0.632945 + 0.774197i \(0.281846\pi\)
\(348\) 10.3923 + 6.00000i 0.557086 + 0.321634i
\(349\) −6.00000 + 10.3923i −0.321173 + 0.556287i −0.980730 0.195367i \(-0.937410\pi\)
0.659558 + 0.751654i \(0.270744\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) −12.1244 7.00000i −0.645314 0.372572i 0.141344 0.989960i \(-0.454858\pi\)
−0.786659 + 0.617388i \(0.788191\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 3.73205 + 2.46410i 0.198077 + 0.130781i
\(356\) −8.00000 −0.423999
\(357\) 0 0
\(358\) 10.3923 6.00000i 0.549250 0.317110i
\(359\) −2.00000 −0.105556 −0.0527780 0.998606i \(-0.516808\pi\)
−0.0527780 + 0.998606i \(0.516808\pi\)
\(360\) 3.69615 5.59808i 0.194804 0.295045i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −1.73205 1.00000i −0.0910346 0.0525588i
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 6.00000 + 12.0000i 0.314054 + 0.628109i
\(366\) −6.00000 + 10.3923i −0.313625 + 0.543214i
\(367\) −15.5885 9.00000i −0.813711 0.469796i 0.0345320 0.999404i \(-0.489006\pi\)
−0.848243 + 0.529607i \(0.822339\pi\)
\(368\) −5.19615 + 3.00000i −0.270868 + 0.156386i
\(369\) −8.00000 −0.416463
\(370\) −11.1962 7.39230i −0.582060 0.384308i
\(371\) 0 0
\(372\) 12.0000i 0.622171i
\(373\) −3.46410 + 2.00000i −0.179364 + 0.103556i −0.586994 0.809591i \(-0.699689\pi\)
0.407630 + 0.913147i \(0.366355\pi\)
\(374\) 0 0
\(375\) −14.4641 + 17.0526i −0.746923 + 0.880590i
\(376\) 24.0000 1.23771
\(377\) 0 0
\(378\) 0 0
\(379\) 9.00000 15.5885i 0.462299 0.800725i −0.536776 0.843725i \(-0.680358\pi\)
0.999075 + 0.0429994i \(0.0136914\pi\)
\(380\) 0.803848 13.3923i 0.0412365 0.687011i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 0 0
\(383\) −6.92820 + 4.00000i −0.354015 + 0.204390i −0.666452 0.745548i \(-0.732188\pi\)
0.312437 + 0.949938i \(0.398855\pi\)
\(384\) −3.00000 5.19615i −0.153093 0.265165i
\(385\) 0 0
\(386\) −3.00000 5.19615i −0.152696 0.264477i
\(387\) −5.19615 3.00000i −0.264135 0.152499i
\(388\) −5.19615 3.00000i −0.263795 0.152302i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −18.1865 10.5000i −0.918559 0.530330i
\(393\) −20.7846 12.0000i −1.04844 0.605320i
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) 1.00000 + 1.73205i 0.0502519 + 0.0870388i
\(397\) −15.5885 + 9.00000i −0.782362 + 0.451697i −0.837267 0.546795i \(-0.815848\pi\)
0.0549046 + 0.998492i \(0.482515\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 0 0
\(400\) −1.96410 4.59808i −0.0982051 0.229904i
\(401\) −8.00000 + 13.8564i −0.399501 + 0.691956i −0.993664 0.112388i \(-0.964150\pi\)
0.594163 + 0.804344i \(0.297483\pi\)
\(402\) 24.0000i 1.19701i
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) −1.47372 + 24.5526i −0.0732298 + 1.22003i
\(406\) 0 0
\(407\) 10.3923 6.00000i 0.515127 0.297409i
\(408\) 0 0
\(409\) −12.0000 20.7846i −0.593362 1.02773i −0.993776 0.111398i \(-0.964467\pi\)
0.400414 0.916334i \(-0.368866\pi\)
\(410\) −9.85641 + 14.9282i −0.486773 + 0.737251i
\(411\) 4.00000 0.197305
\(412\) 5.19615 3.00000i 0.255996 0.147799i
\(413\) 0 0
\(414\) −3.00000 + 5.19615i −0.147442 + 0.255377i
\(415\) −4.00000 8.00000i −0.196352 0.392705i
\(416\) 0 0
\(417\) 8.00000i 0.391762i
\(418\) −10.3923 6.00000i −0.508304 0.293470i
\(419\) 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
\(421\) −36.0000 −1.75453 −0.877266 0.480004i \(-0.840635\pi\)
−0.877266 + 0.480004i \(0.840635\pi\)
\(422\) −10.3923 + 6.00000i −0.505889 + 0.292075i
\(423\) 6.92820 4.00000i 0.336861 0.194487i
\(424\) −36.0000 −1.74831
\(425\) 0 0
\(426\) −2.00000 + 3.46410i −0.0969003 + 0.167836i
\(427\) 0 0
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) −12.0000 + 6.00000i −0.578691 + 0.289346i
\(431\) −5.00000 + 8.66025i −0.240842 + 0.417150i −0.960954 0.276707i \(-0.910757\pi\)
0.720113 + 0.693857i \(0.244090\pi\)
\(432\) −3.46410 2.00000i −0.166667 0.0962250i
\(433\) 13.8564 8.00000i 0.665896 0.384455i −0.128624 0.991693i \(-0.541056\pi\)
0.794520 + 0.607238i \(0.207723\pi\)
\(434\) 0 0
\(435\) 14.7846 22.3923i 0.708868 1.07363i
\(436\) 6.00000 + 10.3923i 0.287348 + 0.497701i
\(437\) 36.0000i 1.72211i
\(438\) −10.3923 + 6.00000i −0.496564 + 0.286691i
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 13.3923 + 0.803848i 0.638453 + 0.0383219i
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) −6.00000 + 10.3923i −0.284747 + 0.493197i
\(445\) −1.07180 + 17.8564i −0.0508080 + 0.846475i
\(446\) −12.0000 20.7846i −0.568216 0.984180i
\(447\) 40.0000i 1.89194i
\(448\) 0 0
\(449\) 8.00000 + 13.8564i 0.377543 + 0.653924i 0.990704 0.136034i \(-0.0434356\pi\)
−0.613161 + 0.789958i \(0.710102\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) −8.00000 13.8564i −0.376705 0.652473i
\(452\) 0 0
\(453\) −31.1769 18.0000i −1.46482 0.845714i
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) −25.9808 15.0000i −1.21533 0.701670i −0.251414 0.967880i \(-0.580895\pi\)
−0.963915 + 0.266209i \(0.914229\pi\)
\(458\) 10.3923 + 6.00000i 0.485601 + 0.280362i
\(459\) 0 0
\(460\) −6.00000 12.0000i −0.279751 0.559503i
\(461\) −2.00000 3.46410i −0.0931493 0.161339i 0.815685 0.578496i \(-0.196360\pi\)
−0.908835 + 0.417156i \(0.863027\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 26.7846 + 1.60770i 1.24211 + 0.0745551i
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 18.0000i 0.832941i 0.909149 + 0.416470i \(0.136733\pi\)
−0.909149 + 0.416470i \(0.863267\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.07180 17.8564i 0.0494383 0.823655i
\(471\) 12.0000 20.7846i 0.552931 0.957704i
\(472\) 5.19615 3.00000i 0.239172 0.138086i
\(473\) 12.0000i 0.551761i
\(474\) 0 0
\(475\) −29.7846 3.58846i −1.36661 0.164650i
\(476\) 0 0
\(477\) −10.3923 + 6.00000i −0.475831 + 0.274721i
\(478\) −8.66025 5.00000i −0.396111 0.228695i
\(479\) −11.0000 + 19.0526i −0.502603 + 0.870534i 0.497393 + 0.867526i \(0.334291\pi\)
−0.999995 + 0.00300810i \(0.999042\pi\)
\(480\) −20.0000 + 10.0000i −0.912871 + 0.456435i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) −7.39230 + 11.1962i −0.335667 + 0.508391i
\(486\) −10.0000 −0.453609
\(487\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 15.5885 9.00000i 0.705656 0.407411i
\(489\) 24.0000 1.08532
\(490\) −8.62436 + 13.0622i −0.389609 + 0.590089i
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 13.8564 + 8.00000i 0.624695 + 0.360668i
\(493\) 0 0
\(494\) 0 0
\(495\) 4.00000 2.00000i 0.179787 0.0898933i
\(496\) −3.00000 + 5.19615i −0.134704 + 0.233314i
\(497\) 0 0
\(498\) 6.92820 4.00000i 0.310460 0.179244i
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 10.5263 3.76795i 0.470750 0.168508i
\(501\) 16.0000 + 27.7128i 0.714827 + 1.23812i
\(502\) 12.0000i 0.535586i
\(503\) −5.19615 + 3.00000i −0.231685 + 0.133763i −0.611349 0.791361i \(-0.709373\pi\)
0.379664 + 0.925124i \(0.376040\pi\)
\(504\) 0 0
\(505\) −0.803848 + 13.3923i −0.0357707 + 0.595950i
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) 2.00000i 0.0887357i
\(509\) −10.0000 + 17.3205i −0.443242 + 0.767718i −0.997928 0.0643419i \(-0.979505\pi\)
0.554686 + 0.832060i \(0.312839\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000i 0.486136i
\(513\) −20.7846 + 12.0000i −0.917663 + 0.529813i
\(514\) 0 0
\(515\) −6.00000 12.0000i −0.264392 0.528783i
\(516\) 6.00000 + 10.3923i 0.264135 + 0.457496i
\(517\) 13.8564 + 8.00000i 0.609404 + 0.351840i
\(518\) 0 0
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 5.19615 + 3.00000i 0.227429 + 0.131306i
\(523\) 36.3731 + 21.0000i 1.59048 + 0.918266i 0.993224 + 0.116218i \(0.0370770\pi\)
0.597259 + 0.802048i \(0.296256\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) 0 0
\(526\) −3.00000 5.19615i −0.130806 0.226563i
\(527\) 0 0
\(528\) 4.00000i 0.174078i
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) −1.60770 + 26.7846i −0.0698338 + 1.16345i
\(531\) 1.00000 1.73205i 0.0433963 0.0751646i
\(532\) 0 0
\(533\) 0 0
\(534\) −16.0000 −0.692388
\(535\) 13.3923 + 0.803848i 0.579000 + 0.0347534i
\(536\) −18.0000 + 31.1769i −0.777482 + 1.34664i
\(537\) −20.7846 + 12.0000i −0.896922 + 0.517838i
\(538\) 18.0000i 0.776035i
\(539\) −7.00000 12.1244i −0.301511 0.522233i
\(540\) 4.92820 7.46410i 0.212076 0.321204i
\(541\) 12.0000 0.515920 0.257960 0.966156i \(-0.416950\pi\)
0.257960 + 0.966156i \(0.416950\pi\)
\(542\) 5.19615 3.00000i 0.223194 0.128861i
\(543\) 3.46410 + 2.00000i 0.148659 + 0.0858282i
\(544\) 0 0
\(545\) 24.0000 12.0000i 1.02805 0.514024i
\(546\) 0 0
\(547\) 18.0000i 0.769624i −0.922995 0.384812i \(-0.874266\pi\)
0.922995 0.384812i \(-0.125734\pi\)
\(548\) −1.73205 1.00000i −0.0739895 0.0427179i
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 1.19615 9.92820i 0.0510041 0.423340i
\(551\) 36.0000 1.53365
\(552\) 31.1769 18.0000i 1.32698 0.766131i
\(553\) 0 0
\(554\) 12.0000 0.509831
\(555\) 22.3923 + 14.7846i 0.950500 + 0.627572i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −12.1244 7.00000i −0.513725 0.296600i 0.220638 0.975356i \(-0.429186\pi\)
−0.734364 + 0.678756i \(0.762519\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −6.92820 4.00000i −0.292249 0.168730i
\(563\) −25.9808 + 15.0000i −1.09496 + 0.632175i −0.934892 0.354932i \(-0.884504\pi\)
−0.160066 + 0.987106i \(0.551171\pi\)
\(564\) −16.0000 −0.673722
\(565\) 0 0
\(566\) −11.0000 19.0526i −0.462364 0.800839i
\(567\) 0 0
\(568\) 5.19615 3.00000i 0.218026 0.125877i
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 1.60770 26.7846i 0.0673389 1.12188i
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −27.5885 + 11.7846i −1.15052 + 0.491452i
\(576\) −3.50000 6.06218i −0.145833 0.252591i
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 14.7224 8.50000i 0.612372 0.353553i
\(579\) 6.00000 + 10.3923i 0.249351 + 0.431889i
\(580\) −12.0000 + 6.00000i −0.498273 + 0.249136i
\(581\) 0 0
\(582\) −10.3923 6.00000i −0.430775 0.248708i
\(583\) −20.7846 12.0000i −0.860811 0.496989i
\(584\) 18.0000 0.744845
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) 17.3205 + 10.0000i 0.714894 + 0.412744i 0.812870 0.582445i \(-0.197904\pi\)
−0.0979766 + 0.995189i \(0.531237\pi\)
\(588\) 12.1244 + 7.00000i 0.500000 + 0.288675i
\(589\) 18.0000 + 31.1769i 0.741677 + 1.28462i
\(590\) −2.00000 4.00000i −0.0823387 0.164677i
\(591\) −2.00000 3.46410i −0.0822690 0.142494i
\(592\) −5.19615 + 3.00000i −0.213561 + 0.123299i
\(593\) 22.0000i 0.903432i −0.892162 0.451716i \(-0.850812\pi\)
0.892162 0.451716i \(-0.149188\pi\)
\(594\) −4.00000 6.92820i −0.164122 0.284268i
\(595\) 0 0
\(596\) 10.0000 17.3205i 0.409616 0.709476i
\(597\) 48.0000i 1.96451i
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 11.7846 + 27.5885i 0.481105 + 1.12629i
\(601\) 3.00000 5.19615i 0.122373 0.211955i −0.798330 0.602220i \(-0.794283\pi\)
0.920703 + 0.390264i \(0.127616\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) 9.00000 + 15.5885i 0.366205 + 0.634285i
\(605\) −13.0622 8.62436i −0.531053 0.350630i
\(606\) −12.0000 −0.487467
\(607\) 15.5885 9.00000i 0.632716 0.365299i −0.149087 0.988824i \(-0.547634\pi\)
0.781803 + 0.623525i \(0.214300\pi\)
\(608\) −25.9808 15.0000i −1.05366 0.608330i
\(609\) 0 0
\(610\) −6.00000 12.0000i −0.242933 0.485866i
\(611\) 0 0
\(612\) 0 0
\(613\) 25.9808 + 15.0000i 1.04935 + 0.605844i 0.922468 0.386073i \(-0.126169\pi\)
0.126885 + 0.991917i \(0.459502\pi\)
\(614\) 6.00000 10.3923i 0.242140 0.419399i
\(615\) 19.7128 29.8564i 0.794897 1.20393i
\(616\) 0 0
\(617\) −29.4449 + 17.0000i −1.18541 + 0.684394i −0.957259 0.289233i \(-0.906600\pi\)
−0.228147 + 0.973627i \(0.573267\pi\)
\(618\) 10.3923 6.00000i 0.418040 0.241355i
\(619\) 18.0000 0.723481 0.361741 0.932279i \(-0.382183\pi\)
0.361741 + 0.932279i \(0.382183\pi\)
\(620\) −11.1962 7.39230i −0.449648 0.296882i
\(621\) −12.0000 + 20.7846i −0.481543 + 0.834058i
\(622\) 20.7846 + 12.0000i 0.833387 + 0.481156i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −4.00000 + 6.92820i −0.159872 + 0.276907i
\(627\) 20.7846 + 12.0000i 0.830057 + 0.479234i
\(628\) −10.3923 + 6.00000i −0.414698 + 0.239426i
\(629\) 0 0
\(630\) 0 0
\(631\) −15.0000 25.9808i −0.597141 1.03428i −0.993241 0.116071i \(-0.962970\pi\)
0.396100 0.918207i \(-0.370363\pi\)
\(632\) 0 0
\(633\) 20.7846 12.0000i 0.826114 0.476957i
\(634\) 1.00000 1.73205i 0.0397151 0.0687885i
\(635\) −4.46410 0.267949i −0.177152 0.0106332i
\(636\) 24.0000 0.951662
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) 1.00000 1.73205i 0.0395594 0.0685189i
\(640\) 6.69615 + 0.401924i 0.264689 + 0.0158874i
\(641\) −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 31.1769 18.0000i 1.22950 0.709851i 0.262573 0.964912i \(-0.415429\pi\)
0.966925 + 0.255062i \(0.0820957\pi\)
\(644\) 0 0
\(645\) 24.0000 12.0000i 0.944999 0.472500i
\(646\) 0 0
\(647\) −5.19615 3.00000i −0.204282 0.117942i 0.394369 0.918952i \(-0.370963\pi\)
−0.598651 + 0.801010i \(0.704296\pi\)
\(648\) 28.5788 + 16.5000i 1.12268 + 0.648181i
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) −10.3923 6.00000i −0.406994 0.234978i
\(653\) −31.1769 18.0000i −1.22005 0.704394i −0.255119 0.966910i \(-0.582115\pi\)
−0.964928 + 0.262515i \(0.915448\pi\)
\(654\) 12.0000 + 20.7846i 0.469237 + 0.812743i
\(655\) 24.0000 12.0000i 0.937758 0.468879i
\(656\) 4.00000 + 6.92820i 0.156174 + 0.270501i
\(657\) 5.19615 3.00000i 0.202721 0.117041i
\(658\) 0 0
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) −8.92820 0.535898i −0.347530 0.0208598i
\(661\) 6.00000 10.3923i 0.233373 0.404214i −0.725426 0.688301i \(-0.758357\pi\)
0.958799 + 0.284087i \(0.0916904\pi\)
\(662\) 30.0000i 1.16598i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −3.00000 + 5.19615i −0.116248 + 0.201347i
\(667\) 31.1769 18.0000i 1.20717 0.696963i
\(668\) 16.0000i 0.619059i
\(669\) 24.0000 + 41.5692i 0.927894 + 1.60716i
\(670\) 22.3923 + 14.7846i 0.865090 + 0.571179i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) −41.5692 24.0000i −1.60238 0.925132i −0.991011 0.133783i \(-0.957287\pi\)
−0.611365 0.791349i \(-0.709379\pi\)
\(674\) 16.0000 27.7128i 0.616297 1.06746i
\(675\) −16.0000 12.0000i −0.615840 0.461880i
\(676\) 0 0
\(677\) 36.0000i 1.38359i −0.722093 0.691796i \(-0.756820\pi\)
0.722093 0.691796i \(-0.243180\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 8.00000 0.306561
\(682\) −10.3923 + 6.00000i −0.397942 + 0.229752i
\(683\) −38.1051 + 22.0000i −1.45805 + 0.841807i −0.998916 0.0465592i \(-0.985174\pi\)
−0.459136 + 0.888366i \(0.651841\pi\)
\(684\) −6.00000 −0.229416
\(685\) −2.46410 + 3.73205i −0.0941485 + 0.142594i
\(686\) 0 0
\(687\) −20.7846 12.0000i −0.792982 0.457829i
\(688\) 6.00000i 0.228748i
\(689\) 0 0
\(690\) −12.0000 24.0000i −0.456832 0.913664i
\(691\) 21.0000 36.3731i 0.798878 1.38370i −0.121470 0.992595i \(-0.538761\pi\)
0.920348 0.391102i \(-0.127906\pi\)
\(692\) −10.3923 6.00000i −0.395056 0.228086i
\(693\) 0 0
\(694\) −6.00000 −0.227757
\(695\) −7.46410 4.92820i −0.283130 0.186937i
\(696\) −18.0000 31.1769i −0.682288 1.18176i
\(697\) 0 0
\(698\) 10.3923 6.00000i 0.393355 0.227103i
\(699\) 24.0000 41.5692i 0.907763 1.57229i
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 36.0000i 1.35777i
\(704\) 7.00000 12.1244i 0.263822 0.456954i
\(705\) −2.14359 + 35.7128i −0.0807324 + 1.34502i
\(706\) 7.00000 + 12.1244i 0.263448 + 0.456306i
\(707\) 0 0
\(708\) −3.46410 + 2.00000i −0.130189 + 0.0751646i
\(709\) 6.00000 + 10.3923i 0.225335 + 0.390291i 0.956420 0.291995i \(-0.0943191\pi\)
−0.731085 + 0.682286i \(0.760986\pi\)
\(710\) −2.00000 4.00000i −0.0750587 0.150117i
\(711\) 0 0
\(712\) 20.7846 + 12.0000i 0.778936 + 0.449719i
\(713\) 31.1769 + 18.0000i 1.16758 + 0.674105i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 17.3205 + 10.0000i 0.646846 + 0.373457i
\(718\) 1.73205 + 1.00000i 0.0646396 + 0.0373197i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) 0 0
\(722\) 14.7224 8.50000i 0.547912 0.316337i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 11.7846 + 27.5885i 0.437669 + 1.02461i
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) 26.0000i 0.964287i −0.876092 0.482143i \(-0.839858\pi\)
0.876092 0.482143i \(-0.160142\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0.803848 13.3923i 0.0297517 0.495671i
\(731\) 0 0
\(732\) −10.3923 + 6.00000i −0.384111 + 0.221766i
\(733\) 42.0000i 1.55131i 0.631160 + 0.775653i \(0.282579\pi\)
−0.631160 + 0.775653i \(0.717421\pi\)
\(734\) 9.00000 + 15.5885i 0.332196 + 0.575380i
\(735\) 17.2487 26.1244i 0.636228 0.963611i
\(736\) −30.0000 −1.10581
\(737\) −20.7846 + 12.0000i −0.765611 + 0.442026i
\(738\) 6.92820 + 4.00000i 0.255031 + 0.147242i
\(739\) 3.00000 5.19615i 0.110357 0.191144i −0.805557 0.592518i \(-0.798134\pi\)
0.915914 + 0.401374i \(0.131467\pi\)
\(740\) −6.00000 12.0000i −0.220564 0.441129i
\(741\) 0 0
\(742\) 0 0
\(743\) −13.8564 8.00000i −0.508342 0.293492i 0.223810 0.974633i \(-0.428151\pi\)
−0.732152 + 0.681141i \(0.761484\pi\)
\(744\) 18.0000 31.1769i 0.659912 1.14300i
\(745\) −37.3205 24.6410i −1.36732 0.902777i
\(746\) 4.00000 0.146450
\(747\) −3.46410 + 2.00000i −0.126745 + 0.0731762i
\(748\) 0 0
\(749\) 0 0
\(750\) 21.0526 7.53590i 0.768731 0.275172i
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) −6.92820 4.00000i −0.252646 0.145865i
\(753\) 24.0000i 0.874609i
\(754\) 0 0
\(755\) 36.0000 18.0000i 1.31017 0.655087i
\(756\) 0 0
\(757\) 17.3205 + 10.0000i 0.629525 + 0.363456i 0.780568 0.625071i \(-0.214930\pi\)
−0.151043 + 0.988527i \(0.548263\pi\)
\(758\) −15.5885 + 9.00000i −0.566198 + 0.326895i
\(759\) 24.0000 0.871145
\(760\) −22.1769 + 33.5885i −0.804441 + 1.21838i
\(761\) 20.0000 + 34.6410i 0.724999 + 1.25574i 0.958974 + 0.283493i \(0.0914933\pi\)
−0.233975 + 0.972243i \(0.575173\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 8.00000 0.289052
\(767\) 0 0
\(768\) 34.0000i 1.22687i
\(769\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) −32.9090 + 19.0000i −1.18365 + 0.683383i −0.956857 0.290560i \(-0.906159\pi\)
−0.226796 + 0.973942i \(0.572825\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) −18.0000 + 24.0000i −0.646579 + 0.862105i
\(776\) 9.00000 + 15.5885i 0.323081 + 0.559593i
\(777\) 0 0
\(778\) 5.19615 + 3.00000i 0.186291 + 0.107555i
\(779\) 48.0000 1.71978
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 20.7846 + 12.0000i 0.742781 + 0.428845i
\(784\) 3.50000 + 6.06218i 0.125000 + 0.216506i
\(785\) 12.0000 + 24.0000i 0.428298 + 0.856597i
\(786\) 12.0000 + 20.7846i 0.428026 + 0.741362i
\(787\) 10.3923 6.00000i 0.370446 0.213877i −0.303207 0.952925i \(-0.598058\pi\)
0.673653 + 0.739048i \(0.264724\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 6.00000 + 10.3923i 0.213606 + 0.369976i
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000i 0.213201i
\(793\) 0 0
\(794\) 18.0000 0.638796
\(795\) 3.21539 53.5692i 0.114038 1.89990i
\(796\) −12.0000 + 20.7846i −0.425329 + 0.736691i
\(797\) 10.3923 6.00000i 0.368114 0.212531i −0.304520 0.952506i \(-0.598496\pi\)
0.672634 + 0.739975i \(0.265163\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.99038 24.8205i 0.105726 0.877537i
\(801\) 8.00000 0.282666
\(802\) 13.8564 8.00000i 0.489287 0.282490i
\(803\) 10.3923 + 6.00000i 0.366736 + 0.211735i
\(804\) 12.0000 20.7846i 0.423207 0.733017i
\(805\) 0 0
\(806\) 0 0
\(807\) 36.0000i 1.26726i
\(808\) 15.5885 + 9.00000i 0.548400 + 0.316619i
\(809\) 15.0000 25.9808i 0.527372 0.913435i −0.472119 0.881535i \(-0.656511\pi\)
0.999491 0.0319002i \(-0.0101559\pi\)
\(810\) 13.5526 20.5263i 0.476188 0.721220i
\(811\) 30.0000 1.05344 0.526721 0.850038i \(-0.323421\pi\)
0.526721 + 0.850038i \(0.323421\pi\)
\(812\) 0 0
\(813\) −10.3923 + 6.00000i −0.364474 + 0.210429i
\(814\) −12.0000 −0.420600
\(815\) −14.7846 + 22.3923i −0.517882 + 0.784368i
\(816\) 0 0
\(817\) 31.1769 + 18.0000i 1.09074 + 0.629740i
\(818\) 24.0000i 0.839140i
\(819\) 0 0
\(820\) −16.0000 + 8.00000i −0.558744 + 0.279372i
\(821\) 10.0000 17.3205i 0.349002 0.604490i −0.637070 0.770806i \(-0.719854\pi\)
0.986073 + 0.166316i \(0.0531872\pi\)
\(822\) −3.46410 2.00000i −0.120824 0.0697580i
\(823\) −36.3731 + 21.0000i −1.26789 + 0.732014i −0.974588 0.224007i \(-0.928086\pi\)
−0.293298 + 0.956021i \(0.594753\pi\)
\(824\) −18.0000 −0.627060
\(825\) −2.39230 + 19.8564i −0.0832894 + 0.691311i
\(826\) 0 0
\(827\) 4.00000i 0.139094i 0.997579 + 0.0695468i \(0.0221553\pi\)
−0.997579 + 0.0695468i \(0.977845\pi\)
\(828\) −5.19615 + 3.00000i −0.180579 + 0.104257i
\(829\) 3.00000 5.19615i 0.104194 0.180470i −0.809214 0.587513i \(-0.800107\pi\)
0.913409 + 0.407044i \(0.133440\pi\)
\(830\) −0.535898 + 8.92820i −0.0186013 + 0.309902i
\(831\) −24.0000 −0.832551
\(832\) 0 0
\(833\) 0 0
\(834\) 4.00000 6.92820i 0.138509 0.239904i
\(835\) −35.7128 2.14359i −1.23589 0.0741821i
\(836\) −6.00000 10.3923i −0.207514 0.359425i
\(837\) 24.0000i 0.829561i
\(838\) −10.3923 + 6.00000i −0.358996 + 0.207267i
\(839\) −23.0000 39.8372i −0.794048 1.37533i −0.923442 0.383738i \(-0.874636\pi\)
0.129394 0.991593i \(-0.458697\pi\)
\(840\) 0 0
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) 31.1769 + 18.0000i 1.07443 + 0.620321i
\(843\) 13.8564 + 8.00000i 0.477240 + 0.275535i
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) −8.00000 −0.275046
\(847\) 0 0
\(848\) 10.3923 + 6.00000i 0.356873 + 0.206041i
\(849\) 22.0000 + 38.1051i 0.755038 + 1.30776i
\(850\) 0 0
\(851\) 18.0000 + 31.1769i 0.617032 + 1.06873i
\(852\) −3.46410 + 2.00000i −0.118678 + 0.0685189i
\(853\) 54.0000i 1.84892i 0.381273 + 0.924462i \(0.375486\pi\)
−0.381273 + 0.924462i \(0.624514\pi\)
\(854\) 0 0
\(855\) −0.803848 + 13.3923i −0.0274910 + 0.458007i
\(856\) 9.00000 15.5885i 0.307614 0.532803i
\(857\) 24.0000i 0.819824i 0.912125 + 0.409912i \(0.134441\pi\)
−0.912125 + 0.409912i \(0.865559\pi\)
\(858\) 0 0
\(859\) −36.0000 −1.22830 −0.614152 0.789188i \(-0.710502\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(860\) −13.3923 0.803848i −0.456674 0.0274110i
\(861\) 0 0
\(862\) 8.66025 5.00000i 0.294969 0.170301i
\(863\) 8.00000i 0.272323i 0.990687 + 0.136162i \(0.0434766\pi\)
−0.990687 + 0.136162i \(0.956523\pi\)
\(864\) −10.0000 17.3205i −0.340207 0.589256i
\(865\) −14.7846 + 22.3923i −0.502692 + 0.761361i
\(866\) −16.0000 −0.543702
\(867\) −29.4449 + 17.0000i −1.00000 + 0.577350i
\(868\) 0 0
\(869\) 0 0
\(870\) −24.0000 + 12.0000i −0.813676 + 0.406838i
\(871\) 0 0
\(872\) 36.0000i 1.21911i
\(873\) 5.19615 + 3.00000i 0.175863 + 0.101535i
\(874\) 18.0000 31.1769i 0.608859 1.05457i
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) −5.19615 + 3.00000i −0.175462 + 0.101303i −0.585159 0.810919i \(-0.698968\pi\)
0.409697 + 0.912222i \(0.365634\pi\)
\(878\) −6.92820 + 4.00000i −0.233816 + 0.134993i
\(879\) −52.0000 −1.75392
\(880\) −3.73205 2.46410i −0.125807 0.0830648i
\(881\) 21.0000 36.3731i 0.707508 1.22544i −0.258271 0.966073i \(-0.583153\pi\)
0.965779 0.259367i \(-0.0835140\pi\)
\(882\) 6.06218 + 3.50000i 0.204124 + 0.117851i
\(883\) 2.00000i 0.0673054i 0.999434 + 0.0336527i \(0.0107140\pi\)
−0.999434 + 0.0336527i \(0.989286\pi\)
\(884\) 0 0
\(885\) 4.00000 + 8.00000i 0.134459 + 0.268917i
\(886\) 3.00000 5.19615i 0.100787 0.174568i
\(887\) −36.3731 21.0000i −1.22129 0.705111i −0.256096 0.966651i \(-0.582436\pi\)
−0.965193 + 0.261540i \(0.915770\pi\)
\(888\) 31.1769 18.0000i 1.04623 0.604040i
\(889\) 0 0
\(890\) 9.85641 14.9282i 0.330387 0.500395i
\(891\) 11.0000 + 19.0526i 0.368514 + 0.638285i
\(892\) 24.0000i 0.803579i
\(893\) −41.5692 + 24.0000i −1.39106 + 0.803129i
\(894\) 20.0000 34.6410i 0.668900 1.15857i
\(895\) 1.60770 26.7846i 0.0537393 0.895311i
\(896\) 0 0
\(897\) 0 0
\(898\) 16.0000i 0.533927i
\(899\) 18.0000 31.1769i 0.600334 1.03981i
\(900\) −1.96410 4.59808i −0.0654701 0.153269i
\(901\) 0 0
\(902\) 16.0000i 0.532742i
\(903\) 0 0
\(904\) 0 0
\(905\) −4.00000 + 2.00000i −0.132964 + 0.0664822i
\(906\) 18.0000 + 31.1769i 0.598010 + 1.03578i
\(907\) −8.66025 5.00000i −0.287559 0.166022i 0.349281 0.937018i \(-0.386426\pi\)
−0.636841 + 0.770996i \(0.719759\pi\)
\(908\) −3.46410 2.00000i −0.114960 0.0663723i
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) −10.3923 6.00000i −0.344124 0.198680i
\(913\) −6.92820 4.00000i −0.229290 0.132381i
\(914\) 15.0000 + 25.9808i 0.496156 + 0.859367i
\(915\) 12.0000 + 24.0000i 0.396708 + 0.793416i
\(916\) 6.00000 + 10.3923i 0.198246 + 0.343371i
\(917\) 0 0
\(918\) 0 0
\(919\) −12.0000 20.7846i −0.395843 0.685621i 0.597365 0.801970i \(-0.296214\pi\)
−0.993208 + 0.116348i \(0.962881\pi\)
\(920\) −2.41154 + 40.1769i −0.0795062 + 1.32459i
\(921\) −12.0000 + 20.7846i −0.395413 + 0.684876i
\(922\) 4.00000i 0.131733i
\(923\) 0 0
\(924\) 0 0
\(925\) −27.5885 + 11.7846i −0.907103 + 0.387476i
\(926\) −12.0000 + 20.7846i −0.394344 + 0.683025i
\(927\) −5.19615 + 3.00000i −0.170664 + 0.0985329i
\(928\) 30.0000i 0.984798i
\(929\) 8.00000 + 13.8564i 0.262471 + 0.454614i 0.966898 0.255163i \(-0.0821291\pi\)
−0.704427 + 0.709777i \(0.748796\pi\)
\(930\) −22.3923 14.7846i −0.734273 0.484806i
\(931\) 42.0000 1.37649
\(932\) −20.7846 + 12.0000i −0.680823 + 0.393073i
\(933\) −41.5692 24.0000i −1.36092 0.785725i
\(934\) 9.00000 15.5885i 0.294489 0.510070i
\(935\) 0 0
\(936\) 0 0
\(937\) 56.0000i 1.82944i 0.404088 + 0.914720i \(0.367589\pi\)
−0.404088 + 0.914720i \(0.632411\pi\)
\(938\) 0 0
\(939\) 8.00000 13.8564i 0.261070 0.452187i
\(940\) 9.85641 14.9282i 0.321481 0.486904i
\(941\) −28.0000 −0.912774 −0.456387 0.889781i \(-0.650857\pi\)
−0.456387 + 0.889781i \(0.650857\pi\)
\(942\) −20.7846 + 12.0000i −0.677199 + 0.390981i
\(943\) 41.5692 24.0000i 1.35368 0.781548i
\(944\) −2.00000 −0.0650945
\(945\) 0 0
\(946\) −6.00000 + 10.3923i −0.195077 + 0.337883i
\(947\) −24.2487 14.0000i −0.787977 0.454939i 0.0512727 0.998685i \(-0.483672\pi\)
−0.839250 + 0.543746i \(0.817006\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 24.0000 + 18.0000i 0.778663 + 0.583997i
\(951\) −2.00000 + 3.46410i −0.0648544 + 0.112331i
\(952\) 0 0
\(953\) 20.7846 12.0000i 0.673280 0.388718i −0.124039 0.992277i \(-0.539585\pi\)
0.797318 + 0.603559i \(0.206251\pi\)
\(954\) 12.0000 0.388514
\(955\) 0 0
\(956\) −5.00000 8.66025i −0.161712 0.280093i
\(957\) 24.0000i 0.775810i
\(958\) 19.0526 11.0000i 0.615560 0.355394i
\(959\) 0 0
\(960\) 31.2487 + 1.87564i 1.00855 + 0.0605362i
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 6.00000i 0.193347i
\(964\) 0 0
\(965\) −13.3923 0.803848i −0.431114 0.0258768i
\(966\) 0 0
\(967\) 48.0000i 1.54358i −0.635880 0.771788i \(-0.719363\pi\)
0.635880 0.771788i \(-0.280637\pi\)
\(968\) −18.1865 + 10.5000i −0.584537 + 0.337483i
\(969\) 0 0
\(970\) 12.0000 6.00000i 0.385297 0.192648i
\(971\) −6.00000 10.3923i −0.192549 0.333505i 0.753545 0.657396i \(-0.228342\pi\)
−0.946094 + 0.323891i \(0.895009\pi\)
\(972\) −8.66025 5.00000i −0.277778 0.160375i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −6.00000 −0.192055
\(977\) 29.4449 + 17.0000i 0.942025 + 0.543878i 0.890594 0.454798i \(-0.150289\pi\)
0.0514302 + 0.998677i \(0.483622\pi\)
\(978\) −20.7846 12.0000i −0.664619 0.383718i
\(979\) 8.00000 + 13.8564i 0.255681 + 0.442853i
\(980\) −14.0000 + 7.00000i −0.447214 + 0.223607i
\(981\) −6.00000 10.3923i −0.191565 0.331801i
\(982\) −10.3923 + 6.00000i −0.331632 + 0.191468i
\(983\) 16.0000i 0.510321i 0.966899 + 0.255160i \(0.0821283\pi\)
−0.966899 + 0.255160i \(0.917872\pi\)
\(984\) −24.0000 41.5692i −0.765092 1.32518i
\(985\) 4.46410 + 0.267949i 0.142238 + 0.00853757i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 36.0000 1.14473
\(990\) −4.46410 0.267949i −0.141878 0.00851598i
\(991\) 8.00000 13.8564i 0.254128 0.440163i −0.710530 0.703667i \(-0.751545\pi\)
0.964658 + 0.263504i \(0.0848781\pi\)
\(992\) −25.9808 + 15.0000i −0.824890 + 0.476250i
\(993\) 60.0000i 1.90404i
\(994\) 0 0
\(995\) 44.7846 + 29.5692i 1.41977 + 0.937407i
\(996\) 8.00000 0.253490
\(997\) 51.9615 30.0000i 1.64564 0.950110i 0.666861 0.745182i \(-0.267638\pi\)
0.978777 0.204927i \(-0.0656958\pi\)
\(998\) −5.19615 3.00000i −0.164481 0.0949633i
\(999\) −12.0000 + 20.7846i −0.379663 + 0.657596i
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 845.2.n.a.529.1 4
5.4 even 2 inner 845.2.n.a.529.2 4
13.2 odd 12 845.2.l.a.699.1 4
13.3 even 3 inner 845.2.n.a.484.2 4
13.4 even 6 845.2.b.b.339.1 2
13.5 odd 4 845.2.l.a.654.2 4
13.6 odd 12 65.2.d.b.64.1 yes 2
13.7 odd 12 65.2.d.a.64.1 2
13.8 odd 4 845.2.l.b.654.2 4
13.9 even 3 845.2.b.a.339.2 2
13.10 even 6 845.2.n.b.484.1 4
13.11 odd 12 845.2.l.b.699.1 4
13.12 even 2 845.2.n.b.529.2 4
39.20 even 12 585.2.h.c.64.2 2
39.32 even 12 585.2.h.b.64.1 2
52.7 even 12 1040.2.f.a.129.2 2
52.19 even 12 1040.2.f.b.129.2 2
65.4 even 6 845.2.b.b.339.2 2
65.7 even 12 325.2.c.b.51.1 2
65.9 even 6 845.2.b.a.339.1 2
65.17 odd 12 4225.2.a.k.1.1 1
65.19 odd 12 65.2.d.a.64.2 yes 2
65.22 odd 12 4225.2.a.e.1.1 1
65.24 odd 12 845.2.l.a.699.2 4
65.29 even 6 inner 845.2.n.a.484.1 4
65.32 even 12 325.2.c.b.51.2 2
65.33 even 12 325.2.c.e.51.2 2
65.34 odd 4 845.2.l.a.654.1 4
65.43 odd 12 4225.2.a.h.1.1 1
65.44 odd 4 845.2.l.b.654.1 4
65.48 odd 12 4225.2.a.m.1.1 1
65.49 even 6 845.2.n.b.484.2 4
65.54 odd 12 845.2.l.b.699.2 4
65.58 even 12 325.2.c.e.51.1 2
65.59 odd 12 65.2.d.b.64.2 yes 2
65.64 even 2 845.2.n.b.529.1 4
195.59 even 12 585.2.h.b.64.2 2
195.149 even 12 585.2.h.c.64.1 2
260.19 even 12 1040.2.f.a.129.1 2
260.59 even 12 1040.2.f.b.129.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.d.a.64.1 2 13.7 odd 12
65.2.d.a.64.2 yes 2 65.19 odd 12
65.2.d.b.64.1 yes 2 13.6 odd 12
65.2.d.b.64.2 yes 2 65.59 odd 12
325.2.c.b.51.1 2 65.7 even 12
325.2.c.b.51.2 2 65.32 even 12
325.2.c.e.51.1 2 65.58 even 12
325.2.c.e.51.2 2 65.33 even 12
585.2.h.b.64.1 2 39.32 even 12
585.2.h.b.64.2 2 195.59 even 12
585.2.h.c.64.1 2 195.149 even 12
585.2.h.c.64.2 2 39.20 even 12
845.2.b.a.339.1 2 65.9 even 6
845.2.b.a.339.2 2 13.9 even 3
845.2.b.b.339.1 2 13.4 even 6
845.2.b.b.339.2 2 65.4 even 6
845.2.l.a.654.1 4 65.34 odd 4
845.2.l.a.654.2 4 13.5 odd 4
845.2.l.a.699.1 4 13.2 odd 12
845.2.l.a.699.2 4 65.24 odd 12
845.2.l.b.654.1 4 65.44 odd 4
845.2.l.b.654.2 4 13.8 odd 4
845.2.l.b.699.1 4 13.11 odd 12
845.2.l.b.699.2 4 65.54 odd 12
845.2.n.a.484.1 4 65.29 even 6 inner
845.2.n.a.484.2 4 13.3 even 3 inner
845.2.n.a.529.1 4 1.1 even 1 trivial
845.2.n.a.529.2 4 5.4 even 2 inner
845.2.n.b.484.1 4 13.10 even 6
845.2.n.b.484.2 4 65.49 even 6
845.2.n.b.529.1 4 65.64 even 2
845.2.n.b.529.2 4 13.12 even 2
1040.2.f.a.129.1 2 260.19 even 12
1040.2.f.a.129.2 2 52.7 even 12
1040.2.f.b.129.1 2 260.59 even 12
1040.2.f.b.129.2 2 52.19 even 12
4225.2.a.e.1.1 1 65.22 odd 12
4225.2.a.h.1.1 1 65.43 odd 12
4225.2.a.k.1.1 1 65.17 odd 12
4225.2.a.m.1.1 1 65.48 odd 12