Properties

Label 845.2.n.b.484.2
Level $845$
Weight $2$
Character 845.484
Analytic conductor $6.747$
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] = [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: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 484.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.484
Dual form 845.2.n.b.529.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(1.73205 - 1.00000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(1.73205 - 1.00000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23205 - 0.133975i) q^{10} +(1.00000 + 1.73205i) q^{11} +2.00000i q^{12} +(4.46410 - 0.267949i) q^{15} +(0.500000 + 0.866025i) q^{16} -1.00000i q^{18} +(3.00000 - 5.19615i) q^{19} +(-1.86603 + 1.23205i) q^{20} +(1.73205 + 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(3.00000 + 5.19615i) q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000i q^{27} +(-3.00000 - 5.19615i) q^{29} +(3.73205 - 2.46410i) q^{30} +6.00000 q^{31} +(-4.33013 - 2.50000i) q^{32} +(3.46410 + 2.00000i) q^{33} +(0.500000 + 0.866025i) q^{36} +(5.19615 - 3.00000i) q^{37} -6.00000i q^{38} +(-3.00000 + 6.00000i) q^{40} +(4.00000 + 6.92820i) q^{41} +(-5.19615 - 3.00000i) q^{43} -2.00000 q^{44} +(1.86603 - 1.23205i) q^{45} +(-3.00000 + 5.19615i) q^{46} -8.00000i q^{47} +(1.73205 + 1.00000i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(4.59808 + 1.96410i) q^{50} -12.0000i q^{53} +(2.00000 + 3.46410i) q^{54} +(0.267949 + 4.46410i) q^{55} -12.0000i q^{57} +(-5.19615 - 3.00000i) q^{58} +(1.00000 - 1.73205i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(-3.00000 + 5.19615i) q^{61} +(5.19615 - 3.00000i) q^{62} -7.00000 q^{64} +4.00000 q^{66} +(-10.3923 + 6.00000i) q^{67} +(-6.00000 + 10.3923i) q^{69} +(1.00000 - 1.73205i) q^{71} +(2.59808 + 1.50000i) q^{72} -6.00000i q^{73} +(3.00000 - 5.19615i) q^{74} +(9.19615 + 3.92820i) q^{75} +(3.00000 + 5.19615i) q^{76} +(0.133975 + 2.23205i) q^{80} +(5.50000 + 9.52628i) q^{81} +(6.92820 + 4.00000i) q^{82} +4.00000i q^{83} -6.00000 q^{86} +(-10.3923 - 6.00000i) q^{87} +(-5.19615 + 3.00000i) q^{88} +(-4.00000 - 6.92820i) q^{89} +(1.00000 - 2.00000i) q^{90} -6.00000i q^{92} +(10.3923 - 6.00000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(11.1962 - 7.39230i) q^{95} -10.0000 q^{96} +(-5.19615 - 3.00000i) q^{97} +(-6.06218 - 3.50000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i −0.161521 0.986869i \(-0.551640\pi\)
0.773893 + 0.633316i \(0.218307\pi\)
\(3\) 1.73205 1.00000i 1.00000 0.577350i 0.0917517 0.995782i \(-0.470753\pi\)
0.908248 + 0.418432i \(0.137420\pi\)
\(4\) −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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 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 \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) −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 −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) 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 −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 3.73205 2.46410i 0.681376 0.449881i
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) −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 \(-0.502495\pi\)
0.862080 + 0.506772i \(0.169162\pi\)
\(38\) 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 0.988600 + 0.150567i \(0.0481100\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) 0 0
\(43\) −5.19615 3.00000i −0.792406 0.457496i 0.0484030 0.998828i \(-0.484587\pi\)
−0.840809 + 0.541332i \(0.817920\pi\)
\(44\) −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 \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 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 \(-0.791775\pi\)
0.923749 + 0.382998i \(0.125108\pi\)
\(60\) −2.00000 + 4.00000i −0.258199 + 0.516398i
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 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 \(-0.928555\pi\)
−0.294706 + 0.955588i \(0.595222\pi\)
\(68\) 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 \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(72\) 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 \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) 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 \(-0.431857\pi\)
−0.740034 + 0.672569i \(0.765191\pi\)
\(98\) −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 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) −5.19615 + 3.00000i −0.502331 + 0.290021i −0.729676 0.683793i \(-0.760329\pi\)
0.227345 + 0.973814i \(0.426996\pi\)
\(108\) −3.46410 2.00000i −0.333333 0.192450i
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −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 −0.421180 0.906977i \(-0.638384\pi\)
0.574875 + 0.818241i \(0.305051\pi\)
\(128\) 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 \(-0.360562\pi\)
−0.572161 + 0.820141i \(0.693895\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 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 0.0870170 + 0.996207i \(0.472267\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) 9.92820 1.19615i 0.810634 0.0976654i
\(151\) 18.0000 1.46482 0.732410 0.680864i \(-0.238396\pi\)
0.732410 + 0.680864i \(0.238396\pi\)
\(152\) 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 \(0.158947\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 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 \(-0.489064\pi\)
−0.848339 + 0.529454i \(0.822397\pi\)
\(164\) −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 \(-0.879152\pi\)
−0.143448 + 0.989658i \(0.545819\pi\)
\(168\) 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 0.840002 0.542583i \(-0.182554\pi\)
−0.0498898 + 0.998755i \(0.515887\pi\)
\(174\) −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 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −12.1244 + 7.00000i −0.875000 + 0.505181i
\(193\) −5.19615 + 3.00000i −0.374027 + 0.215945i −0.675216 0.737620i \(-0.735950\pi\)
0.301189 + 0.953564i \(0.402616\pi\)
\(194\) −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 \(-0.643969\pi\)
0.560431 + 0.828201i \(0.310635\pi\)
\(198\) 1.73205 1.00000i 0.123091 0.0710669i
\(199\) −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i \(0.490462\pi\)
−0.880616 + 0.473831i \(0.842871\pi\)
\(200\) −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 0.995222 0.0976347i \(-0.0311277\pi\)
−0.582165 + 0.813070i \(0.697794\pi\)
\(212\) 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 \(-0.963740\pi\)
−0.398321 + 0.917246i \(0.630407\pi\)
\(224\) 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 \(-0.375712\pi\)
−0.610535 + 0.791989i \(0.709046\pi\)
\(228\) 10.3923 + 6.00000i 0.688247 + 0.397360i
\(229\) 12.0000 0.792982 0.396491 0.918039i \(-0.370228\pi\)
0.396491 + 0.918039i \(0.370228\pi\)
\(230\) −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 \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 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 \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) 2.46410 + 3.73205i 0.159057 + 0.240903i
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 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 −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) −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 −0.331166 0.943572i \(-0.607442\pi\)
0.651575 + 0.758585i \(0.274109\pi\)
\(264\) −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 −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 0.535898 + 8.92820i 0.0326137 + 0.543353i
\(271\) 3.00000 + 5.19615i 0.182237 + 0.315644i 0.942642 0.333805i \(-0.108333\pi\)
−0.760405 + 0.649449i \(0.775000\pi\)
\(272\) 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 0.154172 0.988044i \(-0.450729\pi\)
−0.778585 + 0.627539i \(0.784062\pi\)
\(278\) 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 \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) −13.8564 8.00000i −0.825137 0.476393i
\(283\) 19.0526 11.0000i 1.13256 0.653882i 0.187980 0.982173i \(-0.439806\pi\)
0.944577 + 0.328291i \(0.106473\pi\)
\(284\) 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 \(-0.0587926\pi\)
0.332446 + 0.943122i \(0.392126\pi\)
\(294\) −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 \(0.0725954\pi\)
−0.974106 + 0.226093i \(0.927405\pi\)
\(314\) 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 −0.0778456 0.996965i \(-0.524804\pi\)
0.902320 0.431066i \(-0.141863\pi\)
\(332\) −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 \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 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 0.632945 0.774197i \(-0.281846\pi\)
−0.354001 + 0.935245i \(0.615179\pi\)
\(348\) 10.3923 6.00000i 0.557086 0.321634i
\(349\) 6.00000 + 10.3923i 0.321173 + 0.556287i 0.980730 0.195367i \(-0.0625897\pi\)
−0.659558 + 0.751654i \(0.729256\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) 12.1244 7.00000i 0.645314 0.372572i −0.141344 0.989960i \(-0.545142\pi\)
0.786659 + 0.617388i \(0.211809\pi\)
\(354\) −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 \(-0.483192\pi\)
0.0527780 + 0.998606i \(0.483192\pi\)
\(360\) 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 −0.848243 0.529607i \(-0.822339\pi\)
0.0345320 + 0.999404i \(0.489006\pi\)
\(368\) −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 0.407630 0.913147i \(-0.366355\pi\)
−0.586994 + 0.809591i \(0.699689\pi\)
\(374\) 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 \(-0.319642\pi\)
−0.999075 + 0.0429994i \(0.986309\pi\)
\(380\) 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 \(-0.267812\pi\)
−0.312437 + 0.949938i \(0.601145\pi\)
\(384\) 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 \(-0.184152\pi\)
−0.0549046 + 0.998492i \(0.517485\pi\)
\(398\) 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 \(-0.0358501\pi\)
−0.594163 + 0.804344i \(0.702517\pi\)
\(402\) 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 −0.400414 0.916334i \(-0.631134\pi\)
0.993776 0.111398i \(-0.0355330\pi\)
\(410\) 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 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) 36.0000 1.75453 0.877266 0.480004i \(-0.159365\pi\)
0.877266 + 0.480004i \(0.159365\pi\)
\(422\) 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 \(-0.0892433\pi\)
−0.720113 + 0.693857i \(0.755910\pi\)
\(432\) −3.46410 + 2.00000i −0.166667 + 0.0962250i
\(433\) 13.8564 + 8.00000i 0.665896 + 0.384455i 0.794520 0.607238i \(-0.207723\pi\)
−0.128624 + 0.991693i \(0.541056\pi\)
\(434\) 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 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −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 \(-0.954475\pi\)
0.989790 0.142534i \(-0.0455251\pi\)
\(444\) 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 \(-0.956564\pi\)
0.613161 + 0.789958i \(0.289898\pi\)
\(450\) 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 \(-0.419105\pi\)
0.963915 + 0.266209i \(0.0857713\pi\)
\(458\) 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 \(-0.803640\pi\)
0.908835 + 0.417156i \(0.136973\pi\)
\(462\) 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 \(-0.863267\pi\)
0.909149 0.416470i \(-0.136733\pi\)
\(468\) 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 0.999995 + 0.00300810i \(0.000957509\pi\)
−0.497393 + 0.867526i \(0.665709\pi\)
\(480\) −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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) −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 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) −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 \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) −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 0.379664 0.925124i \(-0.376040\pi\)
−0.611349 + 0.791361i \(0.709373\pi\)
\(504\) 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 \(-0.0204948\pi\)
−0.554686 + 0.832060i \(0.687161\pi\)
\(510\) 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 0.597259 0.802048i \(-0.296256\pi\)
0.993224 0.116218i \(-0.0370770\pi\)
\(524\) 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 \(-0.583050\pi\)
−0.257960 + 0.966156i \(0.583050\pi\)
\(542\) 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 \(0.125734\pi\)
−0.922995 + 0.384812i \(0.874266\pi\)
\(548\) 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 \(-0.570814\pi\)
0.734364 + 0.678756i \(0.237481\pi\)
\(558\) 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 −0.160066 0.987106i \(-0.551171\pi\)
−0.934892 + 0.354932i \(0.884504\pi\)
\(564\) 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 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) −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 \(-0.802096\pi\)
0.0979766 + 0.995189i \(0.468763\pi\)
\(588\) 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 0.920703 0.390264i \(-0.127616\pi\)
−0.798330 + 0.602220i \(0.794283\pi\)
\(602\) 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 0.781803 0.623525i \(-0.214300\pi\)
−0.149087 + 0.988824i \(0.547634\pi\)
\(608\) −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 \(-0.873831\pi\)
−0.126885 + 0.991917i \(0.540498\pi\)
\(614\) 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 \(-0.0934001\pi\)
0.228147 + 0.973627i \(0.426733\pi\)
\(618\) −10.3923 6.00000i −0.418040 0.241355i
\(619\) −18.0000 −0.723481 −0.361741 0.932279i \(-0.617817\pi\)
−0.361741 + 0.932279i \(0.617817\pi\)
\(620\) −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 −0.396100 0.918207i \(-0.629637\pi\)
0.993241 0.116071i \(-0.0370299\pi\)
\(632\) 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 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 12.0000i 0.473602i
\(643\) −31.1769 18.0000i −1.22950 0.709851i −0.262573 0.964912i \(-0.584571\pi\)
−0.966925 + 0.255062i \(0.917904\pi\)
\(644\) 0 0
\(645\) −24.0000 12.0000i −0.944999 0.472500i
\(646\) 0 0
\(647\) −5.19615 + 3.00000i −0.204282 + 0.117942i −0.598651 0.801010i \(-0.704296\pi\)
0.394369 + 0.918952i \(0.370963\pi\)
\(648\) −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 −0.964928 0.262515i \(-0.915448\pi\)
−0.255119 + 0.966910i \(0.582115\pi\)
\(654\) 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 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) −8.92820 + 0.535898i −0.347530 + 0.0208598i
\(661\) −6.00000 10.3923i −0.233373 0.404214i 0.725426 0.688301i \(-0.241643\pi\)
−0.958799 + 0.284087i \(0.908310\pi\)
\(662\) 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 −0.611365 + 0.791349i \(0.709379\pi\)
−0.991011 + 0.133783i \(0.957287\pi\)
\(674\) −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 \(0.243180\pi\)
−0.722093 + 0.691796i \(0.756820\pi\)
\(678\) 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 \(-0.0148256\pi\)
0.459136 + 0.888366i \(0.348159\pi\)
\(684\) 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 −0.920348 0.391102i \(-0.872094\pi\)
0.121470 0.992595i \(-0.461239\pi\)
\(692\) −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 \(-0.905681\pi\)
0.731085 + 0.682286i \(0.239014\pi\)
\(710\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 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 \(0.160142\pi\)
−0.876092 + 0.482143i \(0.839858\pi\)
\(728\) 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 \(-0.201866\pi\)
−0.915914 + 0.401374i \(0.868533\pi\)
\(740\) −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 \(-0.571849\pi\)
0.732152 + 0.681141i \(0.238516\pi\)
\(744\) 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 −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) 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 −0.151043 0.988527i \(-0.548263\pi\)
0.780568 + 0.625071i \(0.214930\pi\)
\(758\) −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 0.233975 + 0.972243i \(0.424827\pi\)
−0.958974 + 0.283493i \(0.908507\pi\)
\(762\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) 32.9090 + 19.0000i 1.18365 + 0.683383i 0.956857 0.290560i \(-0.0938415\pi\)
0.226796 + 0.973942i \(0.427175\pi\)
\(774\) −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 \(-0.401942\pi\)
−0.673653 + 0.739048i \(0.735276\pi\)
\(788\) 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 0.672634 0.739975i \(-0.265163\pi\)
−0.304520 + 0.952506i \(0.598496\pi\)
\(798\) 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 0.999491 + 0.0319002i \(0.0101559\pi\)
−0.472119 + 0.881535i \(0.656511\pi\)
\(810\) 13.5526 + 20.5263i 0.476188 + 0.721220i
\(811\) −30.0000 −1.05344 −0.526721 0.850038i \(-0.676579\pi\)
−0.526721 + 0.850038i \(0.676579\pi\)
\(812\) 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 \(-0.280146\pi\)
−0.986073 + 0.166316i \(0.946813\pi\)
\(822\) −3.46410 + 2.00000i −0.120824 + 0.0697580i
\(823\) −36.3731 21.0000i −1.26789 0.732014i −0.293298 0.956021i \(-0.594753\pi\)
−0.974588 + 0.224007i \(0.928086\pi\)
\(824\) 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 0.913409 0.407044i \(-0.133440\pi\)
−0.809214 + 0.587513i \(0.800107\pi\)
\(830\) 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 −0.129394 0.991593i \(-0.541303\pi\)
0.923442 0.383738i \(-0.125364\pi\)
\(840\) 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 \(-0.865559\pi\)
0.912125 0.409912i \(-0.134441\pi\)
\(858\) 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 \(-0.301032\pi\)
−0.409697 + 0.912222i \(0.634366\pi\)
\(878\) 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 0.965779 + 0.259367i \(0.0835140\pi\)
−0.258271 + 0.966073i \(0.583153\pi\)
\(882\) −6.06218 + 3.50000i −0.204124 + 0.117851i
\(883\) 2.00000i 0.0673054i −0.999434 0.0336527i \(-0.989286\pi\)
0.999434 0.0336527i \(-0.0107140\pi\)
\(884\) 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 −0.965193 0.261540i \(-0.915770\pi\)
−0.256096 + 0.966651i \(0.582436\pi\)
\(888\) 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 −0.636841 0.770996i \(-0.719759\pi\)
0.349281 + 0.937018i \(0.386426\pi\)
\(908\) 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 −0.993208 0.116348i \(-0.962881\pi\)
0.597365 + 0.801970i \(0.296214\pi\)
\(920\) −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 \(-0.917871\pi\)
0.704427 + 0.709777i \(0.251204\pi\)
\(930\) 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 \(-0.632411\pi\)
0.404088 0.914720i \(-0.367589\pi\)
\(938\) 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 \(-0.349143\pi\)
0.456387 + 0.889781i \(0.349143\pi\)
\(942\) 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 \(-0.516328\pi\)
0.839250 + 0.543746i \(0.182994\pi\)
\(948\) 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 0.797318 0.603559i \(-0.206251\pi\)
−0.124039 + 0.992277i \(0.539585\pi\)
\(954\) −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 −0.946094 0.323891i \(-0.895009\pi\)
0.753545 + 0.657396i \(0.228342\pi\)
\(972\) −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 \(-0.849711\pi\)
−0.0514302 + 0.998677i \(0.516378\pi\)
\(978\) −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 0.964658 0.263504i \(-0.0848781\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(992\) −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 0.978777 + 0.204927i \(0.0656958\pi\)
0.666861 + 0.745182i \(0.267638\pi\)
\(998\) −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.b.484.2 4
5.4 even 2 inner 845.2.n.b.484.1 4
13.2 odd 12 65.2.d.b.64.2 yes 2
13.3 even 3 845.2.b.b.339.2 2
13.4 even 6 845.2.n.a.529.2 4
13.5 odd 4 845.2.l.a.699.2 4
13.6 odd 12 845.2.l.a.654.1 4
13.7 odd 12 845.2.l.b.654.1 4
13.8 odd 4 845.2.l.b.699.2 4
13.9 even 3 inner 845.2.n.b.529.1 4
13.10 even 6 845.2.b.a.339.1 2
13.11 odd 12 65.2.d.a.64.2 yes 2
13.12 even 2 845.2.n.a.484.1 4
39.2 even 12 585.2.h.b.64.2 2
39.11 even 12 585.2.h.c.64.1 2
52.11 even 12 1040.2.f.a.129.1 2
52.15 even 12 1040.2.f.b.129.1 2
65.2 even 12 325.2.c.e.51.2 2
65.3 odd 12 4225.2.a.k.1.1 1
65.4 even 6 845.2.n.a.529.1 4
65.9 even 6 inner 845.2.n.b.529.2 4
65.19 odd 12 845.2.l.b.654.2 4
65.23 odd 12 4225.2.a.e.1.1 1
65.24 odd 12 65.2.d.b.64.1 yes 2
65.28 even 12 325.2.c.b.51.1 2
65.29 even 6 845.2.b.b.339.1 2
65.34 odd 4 845.2.l.a.699.1 4
65.37 even 12 325.2.c.e.51.1 2
65.42 odd 12 4225.2.a.h.1.1 1
65.44 odd 4 845.2.l.b.699.1 4
65.49 even 6 845.2.b.a.339.2 2
65.54 odd 12 65.2.d.a.64.1 2
65.59 odd 12 845.2.l.a.654.2 4
65.62 odd 12 4225.2.a.m.1.1 1
65.63 even 12 325.2.c.b.51.2 2
65.64 even 2 845.2.n.a.484.2 4
195.89 even 12 585.2.h.b.64.1 2
195.119 even 12 585.2.h.c.64.2 2
260.119 even 12 1040.2.f.a.129.2 2
260.219 even 12 1040.2.f.b.129.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.d.a.64.1 2 65.54 odd 12
65.2.d.a.64.2 yes 2 13.11 odd 12
65.2.d.b.64.1 yes 2 65.24 odd 12
65.2.d.b.64.2 yes 2 13.2 odd 12
325.2.c.b.51.1 2 65.28 even 12
325.2.c.b.51.2 2 65.63 even 12
325.2.c.e.51.1 2 65.37 even 12
325.2.c.e.51.2 2 65.2 even 12
585.2.h.b.64.1 2 195.89 even 12
585.2.h.b.64.2 2 39.2 even 12
585.2.h.c.64.1 2 39.11 even 12
585.2.h.c.64.2 2 195.119 even 12
845.2.b.a.339.1 2 13.10 even 6
845.2.b.a.339.2 2 65.49 even 6
845.2.b.b.339.1 2 65.29 even 6
845.2.b.b.339.2 2 13.3 even 3
845.2.l.a.654.1 4 13.6 odd 12
845.2.l.a.654.2 4 65.59 odd 12
845.2.l.a.699.1 4 65.34 odd 4
845.2.l.a.699.2 4 13.5 odd 4
845.2.l.b.654.1 4 13.7 odd 12
845.2.l.b.654.2 4 65.19 odd 12
845.2.l.b.699.1 4 65.44 odd 4
845.2.l.b.699.2 4 13.8 odd 4
845.2.n.a.484.1 4 13.12 even 2
845.2.n.a.484.2 4 65.64 even 2
845.2.n.a.529.1 4 65.4 even 6
845.2.n.a.529.2 4 13.4 even 6
845.2.n.b.484.1 4 5.4 even 2 inner
845.2.n.b.484.2 4 1.1 even 1 trivial
845.2.n.b.529.1 4 13.9 even 3 inner
845.2.n.b.529.2 4 65.9 even 6 inner
1040.2.f.a.129.1 2 52.11 even 12
1040.2.f.a.129.2 2 260.119 even 12
1040.2.f.b.129.1 2 52.15 even 12
1040.2.f.b.129.2 2 260.219 even 12
4225.2.a.e.1.1 1 65.23 odd 12
4225.2.a.h.1.1 1 65.42 odd 12
4225.2.a.k.1.1 1 65.3 odd 12
4225.2.a.m.1.1 1 65.62 odd 12