Properties

Label 845.2.l.b.699.1
Level $845$
Weight $2$
Character 845.699
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(654,845)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.654");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.l (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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 699.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.699
Dual form 845.2.l.b.654.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.73205 - 1.00000i) q^{6} +3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.73205 - 1.00000i) q^{6} +3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.23205 - 1.86603i) q^{10} +(-1.73205 + 1.00000i) q^{11} +2.00000i q^{12} +(3.73205 + 2.46410i) q^{15} +(0.500000 + 0.866025i) q^{16} +1.00000 q^{18} +(-5.19615 - 3.00000i) q^{19} +(-2.23205 - 0.133975i) q^{20} +(-1.73205 - 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(-5.19615 + 3.00000i) q^{24} +(-3.00000 + 4.00000i) q^{25} -4.00000i q^{27} +(-3.00000 - 5.19615i) q^{29} +(-0.267949 + 4.46410i) q^{30} -6.00000i q^{31} +(2.50000 - 4.33013i) q^{32} +(2.00000 - 3.46410i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(-3.00000 - 5.19615i) q^{37} -6.00000i q^{38} +(-3.00000 - 6.00000i) q^{40} +(6.92820 - 4.00000i) q^{41} +(-5.19615 - 3.00000i) q^{43} +2.00000i q^{44} +(-2.23205 - 0.133975i) q^{45} +(-5.19615 - 3.00000i) q^{46} -8.00000 q^{47} +(-1.73205 - 1.00000i) q^{48} +(3.50000 + 6.06218i) q^{49} +(-4.96410 - 0.598076i) q^{50} +12.0000i q^{53} +(3.46410 - 2.00000i) q^{54} +(3.73205 + 2.46410i) q^{55} +12.0000 q^{57} +(3.00000 - 5.19615i) q^{58} +(1.73205 + 1.00000i) q^{59} +(4.00000 - 2.00000i) q^{60} +(-3.00000 + 5.19615i) q^{61} +(5.19615 - 3.00000i) q^{62} +7.00000 q^{64} +4.00000 q^{66} +(-6.00000 - 10.3923i) q^{67} +(6.00000 - 10.3923i) q^{69} +(-1.73205 - 1.00000i) q^{71} +(1.50000 - 2.59808i) q^{72} -6.00000 q^{73} +(3.00000 - 5.19615i) q^{74} +(1.19615 - 9.92820i) q^{75} +(-5.19615 + 3.00000i) q^{76} +(1.23205 - 1.86603i) q^{80} +(5.50000 + 9.52628i) q^{81} +(6.92820 + 4.00000i) q^{82} -4.00000 q^{83} -6.00000i q^{86} +(10.3923 + 6.00000i) q^{87} +(-5.19615 + 3.00000i) q^{88} +(6.92820 - 4.00000i) q^{89} +(-1.00000 - 2.00000i) q^{90} +6.00000i q^{92} +(6.00000 + 10.3923i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(-0.803848 + 13.3923i) q^{95} +10.0000i q^{96} +(3.00000 - 5.19615i) q^{97} +(-3.50000 + 6.06218i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 12 q^{8} + 2 q^{9} - 2 q^{10} + 8 q^{15} + 2 q^{16} + 4 q^{18} - 2 q^{20} - 12 q^{25} - 12 q^{29} - 8 q^{30} + 10 q^{32} + 8 q^{33} - 2 q^{36} - 12 q^{37} - 12 q^{40} - 2 q^{45} - 32 q^{47} + 14 q^{49} - 6 q^{50} + 8 q^{55} + 48 q^{57} + 12 q^{58} + 16 q^{60} - 12 q^{61} + 28 q^{64} + 16 q^{66} - 24 q^{67} + 24 q^{69} + 6 q^{72} - 24 q^{73} + 12 q^{74} - 16 q^{75} - 2 q^{80} + 22 q^{81} - 16 q^{83} - 4 q^{90} + 24 q^{93} - 16 q^{94} - 24 q^{95} + 12 q^{97} - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) −1.73205 + 1.00000i −1.00000 + 0.577350i −0.908248 0.418432i \(-0.862580\pi\)
−0.0917517 + 0.995782i \(0.529247\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) −1.73205 1.00000i −0.707107 0.408248i
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 3.00000 1.06066
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.23205 1.86603i 0.389609 0.590089i
\(11\) −1.73205 + 1.00000i −0.522233 + 0.301511i −0.737848 0.674967i \(-0.764158\pi\)
0.215615 + 0.976478i \(0.430824\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 0 0
\(14\) 0 0
\(15\) 3.73205 + 2.46410i 0.963611 + 0.636228i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.19615 3.00000i −1.19208 0.688247i −0.233301 0.972404i \(-0.574953\pi\)
−0.958778 + 0.284157i \(0.908286\pi\)
\(20\) −2.23205 0.133975i −0.499102 0.0299576i
\(21\) 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 \(0.548456\pi\)
\(24\) −5.19615 + 3.00000i −1.06066 + 0.612372i
\(25\) −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 \(-0.354747\pi\)
\(30\) −0.267949 + 4.46410i −0.0489206 + 0.815030i
\(31\) 6.00000i 1.07763i −0.842424 0.538816i \(-0.818872\pi\)
0.842424 0.538816i \(-0.181128\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −3.00000 6.00000i −0.474342 0.948683i
\(41\) 6.92820 4.00000i 1.08200 0.624695i 0.150567 0.988600i \(-0.451890\pi\)
0.931436 + 0.363905i \(0.118557\pi\)
\(42\) 0 0
\(43\) −5.19615 3.00000i −0.792406 0.457496i 0.0484030 0.998828i \(-0.484587\pi\)
−0.840809 + 0.541332i \(0.817920\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −2.23205 0.133975i −0.332734 0.0199718i
\(46\) −5.19615 3.00000i −0.766131 0.442326i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −1.73205 1.00000i −0.250000 0.144338i
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) −4.96410 0.598076i −0.702030 0.0845807i
\(51\) 0 0
\(52\) 0 0
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) 3.46410 2.00000i 0.471405 0.272166i
\(55\) 3.73205 + 2.46410i 0.503230 + 0.332259i
\(56\) 0 0
\(57\) 12.0000 1.58944
\(58\) 3.00000 5.19615i 0.393919 0.682288i
\(59\) 1.73205 + 1.00000i 0.225494 + 0.130189i 0.608492 0.793560i \(-0.291775\pi\)
−0.382998 + 0.923749i \(0.625108\pi\)
\(60\) 4.00000 2.00000i 0.516398 0.258199i
\(61\) −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
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 0 0
\(69\) 6.00000 10.3923i 0.722315 1.25109i
\(70\) 0 0
\(71\) −1.73205 1.00000i −0.205557 0.118678i 0.393688 0.919244i \(-0.371199\pi\)
−0.599245 + 0.800566i \(0.704532\pi\)
\(72\) 1.50000 2.59808i 0.176777 0.306186i
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) 1.19615 9.92820i 0.138120 1.14641i
\(76\) −5.19615 + 3.00000i −0.596040 + 0.344124i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.23205 1.86603i 0.137747 0.208628i
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 6.92820 + 4.00000i 0.765092 + 0.441726i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000i 0.646997i
\(87\) 10.3923 + 6.00000i 1.11417 + 0.643268i
\(88\) −5.19615 + 3.00000i −0.553912 + 0.319801i
\(89\) 6.92820 4.00000i 0.734388 0.423999i −0.0856373 0.996326i \(-0.527293\pi\)
0.820025 + 0.572327i \(0.193959\pi\)
\(90\) −1.00000 2.00000i −0.105409 0.210819i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 6.00000 + 10.3923i 0.622171 + 1.07763i
\(94\) −4.00000 6.92820i −0.412568 0.714590i
\(95\) −0.803848 + 13.3923i −0.0824730 + 1.37402i
\(96\) 10.0000i 1.02062i
\(97\) 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i \(-0.734809\pi\)
0.977173 + 0.212445i \(0.0681426\pi\)
\(98\) −3.50000 + 6.06218i −0.353553 + 0.612372i
\(99\) 2.00000i 0.201008i
\(100\) 1.96410 + 4.59808i 0.196410 + 0.459808i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 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
\(106\) −10.3923 + 6.00000i −1.00939 + 0.582772i
\(107\) 5.19615 3.00000i 0.502331 0.290021i −0.227345 0.973814i \(-0.573004\pi\)
0.729676 + 0.683793i \(0.239671\pi\)
\(108\) −3.46410 2.00000i −0.333333 0.192450i
\(109\) 12.0000i 1.14939i −0.818367 0.574696i \(-0.805120\pi\)
0.818367 0.574696i \(-0.194880\pi\)
\(110\) −0.267949 + 4.46410i −0.0255480 + 0.425635i
\(111\) 10.3923 + 6.00000i 0.986394 + 0.569495i
\(112\) 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
\(115\) 11.1962 + 7.39230i 1.04405 + 0.689336i
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) 11.1962 + 7.39230i 1.02206 + 0.674822i
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) −6.00000 −0.543214
\(123\) −8.00000 + 13.8564i −0.721336 + 1.24939i
\(124\) −5.19615 3.00000i −0.466628 0.269408i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 1.73205 1.00000i 0.153695 0.0887357i −0.421180 0.906977i \(-0.638384\pi\)
0.574875 + 0.818241i \(0.305051\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −2.00000 3.46410i −0.174078 0.301511i
\(133\) 0 0
\(134\) 6.00000 10.3923i 0.518321 0.897758i
\(135\) −8.00000 + 4.00000i −0.688530 + 0.344265i
\(136\) 0 0
\(137\) −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 12.0000 1.02151
\(139\) 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
\(141\) 13.8564 8.00000i 1.16692 0.673722i
\(142\) 2.00000i 0.167836i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −7.39230 + 11.1962i −0.613898 + 0.929790i
\(146\) −3.00000 5.19615i −0.248282 0.430037i
\(147\) −12.1244 7.00000i −1.00000 0.577350i
\(148\) −6.00000 −0.493197
\(149\) 17.3205 + 10.0000i 1.41895 + 0.819232i 0.996207 0.0870170i \(-0.0277334\pi\)
0.422744 + 0.906249i \(0.361067\pi\)
\(150\) 9.19615 3.92820i 0.750863 0.320736i
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) −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
\(160\) −11.1603 0.669873i −0.882296 0.0529581i
\(161\) 0 0
\(162\) −5.50000 + 9.52628i −0.432121 + 0.748455i
\(163\) −6.00000 + 10.3923i −0.469956 + 0.813988i −0.999410 0.0343508i \(-0.989064\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(164\) 8.00000i 0.624695i
\(165\) −8.92820 0.535898i −0.695060 0.0417196i
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) 8.00000 + 13.8564i 0.619059 + 1.07224i 0.989658 + 0.143448i \(0.0458190\pi\)
−0.370599 + 0.928793i \(0.620848\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) −5.19615 + 3.00000i −0.397360 + 0.229416i
\(172\) −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 \(0.515887\pi\)
\(174\) 12.0000i 0.909718i
\(175\) 0 0
\(176\) −1.73205 1.00000i −0.130558 0.0753778i
\(177\) −4.00000 −0.300658
\(178\) 6.92820 + 4.00000i 0.519291 + 0.299813i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) −1.23205 + 1.86603i −0.0918316 + 0.139085i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 12.0000i 0.887066i
\(184\) −15.5885 + 9.00000i −1.14920 + 0.663489i
\(185\) −7.39230 + 11.1962i −0.543493 + 0.823157i
\(186\) −6.00000 + 10.3923i −0.439941 + 0.762001i
\(187\) 0 0
\(188\) −4.00000 + 6.92820i −0.291730 + 0.505291i
\(189\) 0 0
\(190\) −12.0000 + 6.00000i −0.870572 + 0.435286i
\(191\) 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
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) 1.00000 + 1.73205i 0.0712470 + 0.123404i 0.899448 0.437028i \(-0.143969\pi\)
−0.828201 + 0.560431i \(0.810635\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) 12.0000 20.7846i 0.850657 1.47338i −0.0299585 0.999551i \(-0.509538\pi\)
0.880616 0.473831i \(-0.157129\pi\)
\(200\) −9.00000 + 12.0000i −0.636396 + 0.848528i
\(201\) 20.7846 + 12.0000i 1.46603 + 0.846415i
\(202\) 3.00000 5.19615i 0.211079 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) −14.9282 9.85641i −1.04263 0.688401i
\(206\) 5.19615 3.00000i 0.362033 0.209020i
\(207\) 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
\(213\) 4.00000 0.274075
\(214\) 5.19615 + 3.00000i 0.355202 + 0.205076i
\(215\) −0.803848 + 13.3923i −0.0548219 + 0.913348i
\(216\) 12.0000i 0.816497i
\(217\) 0 0
\(218\) 10.3923 6.00000i 0.703856 0.406371i
\(219\) 10.3923 6.00000i 0.702247 0.405442i
\(220\) 4.00000 2.00000i 0.269680 0.134840i
\(221\) 0 0
\(222\) 12.0000i 0.805387i
\(223\) −12.0000 20.7846i −0.803579 1.39184i −0.917246 0.398321i \(-0.869593\pi\)
0.113666 0.993519i \(-0.463740\pi\)
\(224\) 0 0
\(225\) 1.96410 + 4.59808i 0.130940 + 0.306538i
\(226\) 0 0
\(227\) 2.00000 3.46410i 0.132745 0.229920i −0.791989 0.610535i \(-0.790954\pi\)
0.924734 + 0.380615i \(0.124288\pi\)
\(228\) 6.00000 10.3923i 0.397360 0.688247i
\(229\) 12.0000i 0.792982i 0.918039 + 0.396491i \(0.129772\pi\)
−0.918039 + 0.396491i \(0.870228\pi\)
\(230\) −0.803848 + 13.3923i −0.0530041 + 0.883062i
\(231\) 0 0
\(232\) −9.00000 15.5885i −0.590879 1.02343i
\(233\) 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
\(236\) 1.73205 1.00000i 0.112747 0.0650945i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0000i 0.646846i 0.946254 + 0.323423i \(0.104834\pi\)
−0.946254 + 0.323423i \(0.895166\pi\)
\(240\) −0.267949 + 4.46410i −0.0172960 + 0.288157i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −7.00000 −0.449977
\(243\) −8.66025 5.00000i −0.555556 0.320750i
\(244\) 3.00000 + 5.19615i 0.192055 + 0.332650i
\(245\) 8.62436 13.0622i 0.550990 0.834512i
\(246\) −16.0000 −1.02012
\(247\) 0 0
\(248\) 18.0000i 1.14300i
\(249\) 6.92820 4.00000i 0.439057 0.253490i
\(250\) 3.76795 + 10.5263i 0.238306 + 0.665740i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 0 0
\(253\) 6.00000 10.3923i 0.377217 0.653359i
\(254\) 1.73205 + 1.00000i 0.108679 + 0.0627456i
\(255\) 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 \(0.333333\pi\)
\(258\) 6.00000 + 10.3923i 0.373544 + 0.646997i
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) −5.19615 + 3.00000i −0.320408 + 0.184988i −0.651575 0.758585i \(-0.725891\pi\)
0.331166 + 0.943572i \(0.392558\pi\)
\(264\) 6.00000 10.3923i 0.369274 0.639602i
\(265\) 24.0000 12.0000i 1.47431 0.737154i
\(266\) 0 0
\(267\) −8.00000 + 13.8564i −0.489592 + 0.847998i
\(268\) −12.0000 −0.733017
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) −7.46410 4.92820i −0.454251 0.299921i
\(271\) −5.19615 + 3.00000i −0.315644 + 0.182237i −0.649449 0.760405i \(-0.725000\pi\)
0.333805 + 0.942642i \(0.391667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 1.19615 9.92820i 0.0721307 0.598693i
\(276\) −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 \(0.784062\pi\)
\(278\) 4.00000 0.239904
\(279\) −5.19615 3.00000i −0.311086 0.179605i
\(280\) 0 0
\(281\) 8.00000i 0.477240i −0.971113 0.238620i \(-0.923305\pi\)
0.971113 0.238620i \(-0.0766950\pi\)
\(282\) 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 \(0.106473\pi\)
\(284\) −1.73205 + 1.00000i −0.102778 + 0.0593391i
\(285\) −12.0000 24.0000i −0.710819 1.42164i
\(286\) 0 0
\(287\) 0 0
\(288\) −2.50000 4.33013i −0.147314 0.255155i
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) −13.3923 0.803848i −0.786423 0.0472036i
\(291\) 12.0000i 0.703452i
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) 13.0000 22.5167i 0.759468 1.31544i −0.183654 0.982991i \(-0.558793\pi\)
0.943122 0.332446i \(-0.107874\pi\)
\(294\) 14.0000i 0.816497i
\(295\) 0.267949 4.46410i 0.0156006 0.259910i
\(296\) −9.00000 15.5885i −0.523114 0.906061i
\(297\) 4.00000 + 6.92820i 0.232104 + 0.402015i
\(298\) 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
\(304\) 6.00000i 0.344124i
\(305\) 13.3923 + 0.803848i 0.766841 + 0.0460282i
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 6.00000 + 10.3923i 0.341328 + 0.591198i
\(310\) −11.1962 7.39230i −0.635899 0.419855i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 10.3923 6.00000i 0.586472 0.338600i
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 12.0000 20.7846i 0.672927 1.16554i
\(319\) 10.3923 + 6.00000i 0.581857 + 0.335936i
\(320\) −7.00000 14.0000i −0.391312 0.782624i
\(321\) −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
\(327\) 12.0000 + 20.7846i 0.663602 + 1.14939i
\(328\) 20.7846 12.0000i 1.14764 0.662589i
\(329\) 0 0
\(330\) −4.00000 8.00000i −0.220193 0.440386i
\(331\) −25.9808 15.0000i −1.42803 0.824475i −0.431066 0.902320i \(-0.641863\pi\)
−0.996965 + 0.0778456i \(0.975196\pi\)
\(332\) −2.00000 + 3.46410i −0.109764 + 0.190117i
\(333\) −6.00000 −0.328798
\(334\) −8.00000 + 13.8564i −0.437741 + 0.758189i
\(335\) −14.7846 + 22.3923i −0.807770 + 1.22342i
\(336\) 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
\(344\) −15.5885 9.00000i −0.840473 0.485247i
\(345\) −26.7846 1.60770i −1.44203 0.0865554i
\(346\) 12.0000i 0.645124i
\(347\) −5.19615 3.00000i −0.278944 0.161048i 0.354001 0.935245i \(-0.384821\pi\)
−0.632945 + 0.774197i \(0.718154\pi\)
\(348\) 10.3923 6.00000i 0.557086 0.321634i
\(349\) −10.3923 + 6.00000i −0.556287 + 0.321173i −0.751654 0.659558i \(-0.770744\pi\)
0.195367 + 0.980730i \(0.437410\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) 7.00000 + 12.1244i 0.372572 + 0.645314i 0.989960 0.141344i \(-0.0451425\pi\)
−0.617388 + 0.786659i \(0.711809\pi\)
\(354\) −2.00000 3.46410i −0.106299 0.184115i
\(355\) −0.267949 + 4.46410i −0.0142213 + 0.236930i
\(356\) 8.00000i 0.423999i
\(357\) 0 0
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) 2.00000i 0.105556i 0.998606 + 0.0527780i \(0.0168076\pi\)
−0.998606 + 0.0527780i \(0.983192\pi\)
\(360\) −6.69615 0.401924i −0.352918 0.0211832i
\(361\) 8.50000 + 14.7224i 0.447368 + 0.774865i
\(362\) −1.00000 1.73205i −0.0525588 0.0910346i
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 6.00000 + 12.0000i 0.314054 + 0.628109i
\(366\) 10.3923 6.00000i 0.543214 0.313625i
\(367\) 15.5885 9.00000i 0.813711 0.469796i −0.0345320 0.999404i \(-0.510994\pi\)
0.848243 + 0.529607i \(0.177661\pi\)
\(368\) −5.19615 3.00000i −0.270868 0.156386i
\(369\) 8.00000i 0.416463i
\(370\) −13.3923 0.803848i −0.696233 0.0417900i
\(371\) 0 0
\(372\) 12.0000 0.622171
\(373\) 3.46410 + 2.00000i 0.179364 + 0.103556i 0.586994 0.809591i \(-0.300311\pi\)
−0.407630 + 0.913147i \(0.633645\pi\)
\(374\) 0 0
\(375\) −21.0526 + 7.53590i −1.08715 + 0.389152i
\(376\) −24.0000 −1.23771
\(377\) 0 0
\(378\) 0 0
\(379\) −15.5885 + 9.00000i −0.800725 + 0.462299i −0.843725 0.536776i \(-0.819642\pi\)
0.0429994 + 0.999075i \(0.486309\pi\)
\(380\) 11.1962 + 7.39230i 0.574351 + 0.379217i
\(381\) −2.00000 + 3.46410i −0.102463 + 0.177471i
\(382\) 0 0
\(383\) −4.00000 + 6.92820i −0.204390 + 0.354015i −0.949938 0.312437i \(-0.898855\pi\)
0.745548 + 0.666452i \(0.232188\pi\)
\(384\) 5.19615 + 3.00000i 0.265165 + 0.153093i
\(385\) 0 0
\(386\) −3.00000 + 5.19615i −0.152696 + 0.264477i
\(387\) −5.19615 + 3.00000i −0.264135 + 0.152499i
\(388\) −3.00000 5.19615i −0.152302 0.263795i
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 10.5000 + 18.1865i 0.530330 + 0.918559i
\(393\) 20.7846 12.0000i 1.04844 0.605320i
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) 1.73205 + 1.00000i 0.0870388 + 0.0502519i
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) 24.0000 1.20301
\(399\) 0 0
\(400\) −4.96410 0.598076i −0.248205 0.0299038i
\(401\) −13.8564 + 8.00000i −0.691956 + 0.399501i −0.804344 0.594163i \(-0.797483\pi\)
0.112388 + 0.993664i \(0.464150\pi\)
\(402\) 24.0000i 1.19701i
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 13.5526 20.5263i 0.673432 1.01996i
\(406\) 0 0
\(407\) 10.3923 + 6.00000i 0.515127 + 0.297409i
\(408\) 0 0
\(409\) −20.7846 12.0000i −1.02773 0.593362i −0.111398 0.993776i \(-0.535533\pi\)
−0.916334 + 0.400414i \(0.868866\pi\)
\(410\) 1.07180 17.8564i 0.0529323 0.881865i
\(411\) 4.00000i 0.197305i
\(412\) −5.19615 3.00000i −0.255996 0.147799i
\(413\) 0 0
\(414\) −5.19615 + 3.00000i −0.255377 + 0.147442i
\(415\) 4.00000 + 8.00000i 0.196352 + 0.392705i
\(416\) 0 0
\(417\) 8.00000i 0.391762i
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) 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
\(421\) 36.0000i 1.75453i −0.480004 0.877266i \(-0.659365\pi\)
0.480004 0.877266i \(-0.340635\pi\)
\(422\) −6.00000 + 10.3923i −0.292075 + 0.505889i
\(423\) −4.00000 + 6.92820i −0.194487 + 0.336861i
\(424\) 36.0000i 1.74831i
\(425\) 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
\(431\) 8.66025 5.00000i 0.417150 0.240842i −0.276707 0.960954i \(-0.589243\pi\)
0.693857 + 0.720113i \(0.255910\pi\)
\(432\) 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
\(435\) 1.60770 26.7846i 0.0770831 1.28422i
\(436\) −10.3923 6.00000i −0.497701 0.287348i
\(437\) 36.0000 1.72211
\(438\) 10.3923 + 6.00000i 0.496564 + 0.286691i
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 11.1962 + 7.39230i 0.533756 + 0.352414i
\(441\) 7.00000 0.333333
\(442\) 0 0
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) 10.3923 6.00000i 0.493197 0.284747i
\(445\) −14.9282 9.85641i −0.707665 0.467238i
\(446\) 12.0000 20.7846i 0.568216 0.984180i
\(447\) −40.0000 −1.89194
\(448\) 0 0
\(449\) −13.8564 8.00000i −0.653924 0.377543i 0.136034 0.990704i \(-0.456564\pi\)
−0.789958 + 0.613161i \(0.789898\pi\)
\(450\) −3.00000 + 4.00000i −0.141421 + 0.188562i
\(451\) −8.00000 + 13.8564i −0.376705 + 0.652473i
\(452\) 0 0
\(453\) −18.0000 31.1769i −0.845714 1.46482i
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) 15.0000 + 25.9808i 0.701670 + 1.21533i 0.967880 + 0.251414i \(0.0808954\pi\)
−0.266209 + 0.963915i \(0.585771\pi\)
\(458\) −10.3923 + 6.00000i −0.485601 + 0.280362i
\(459\) 0 0
\(460\) 12.0000 6.00000i 0.559503 0.279751i
\(461\) −3.46410 2.00000i −0.161339 0.0931493i 0.417156 0.908835i \(-0.363027\pi\)
−0.578496 + 0.815685i \(0.696360\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 14.7846 22.3923i 0.685620 1.03842i
\(466\) −20.7846 + 12.0000i −0.962828 + 0.555889i
\(467\) 18.0000i 0.832941i −0.909149 0.416470i \(-0.863267\pi\)
0.909149 0.416470i \(-0.136733\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.85641 + 14.9282i −0.454642 + 0.688587i
\(471\) 12.0000 + 20.7846i 0.552931 + 0.957704i
\(472\) 5.19615 + 3.00000i 0.239172 + 0.138086i
\(473\) 12.0000 0.551761
\(474\) 0 0
\(475\) 27.5885 11.7846i 1.26585 0.540715i
\(476\) 0 0
\(477\) 10.3923 + 6.00000i 0.475831 + 0.274721i
\(478\) −8.66025 + 5.00000i −0.396111 + 0.228695i
\(479\) −19.0526 + 11.0000i −0.870534 + 0.502603i −0.867526 0.497393i \(-0.834291\pi\)
−0.00300810 + 0.999995i \(0.500958\pi\)
\(480\) 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
\(485\) −13.3923 0.803848i −0.608113 0.0365008i
\(486\) 10.0000i 0.453609i
\(487\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(488\) −9.00000 + 15.5885i −0.407411 + 0.705656i
\(489\) 24.0000i 1.08532i
\(490\) 15.6244 + 0.937822i 0.705836 + 0.0423665i
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 8.00000 + 13.8564i 0.360668 + 0.624695i
\(493\) 0 0
\(494\) 0 0
\(495\) 4.00000 2.00000i 0.179787 0.0898933i
\(496\) 5.19615 3.00000i 0.233314 0.134704i
\(497\) 0 0
\(498\) 6.92820 + 4.00000i 0.310460 + 0.179244i
\(499\) 6.00000i 0.268597i 0.990941 + 0.134298i \(0.0428781\pi\)
−0.990941 + 0.134298i \(0.957122\pi\)
\(500\) 7.23205 8.52628i 0.323427 0.381307i
\(501\) −27.7128 16.0000i −1.23812 0.714827i
\(502\) −12.0000 −0.535586
\(503\) 5.19615 + 3.00000i 0.231685 + 0.133763i 0.611349 0.791361i \(-0.290627\pi\)
−0.379664 + 0.925124i \(0.623960\pi\)
\(504\) 0 0
\(505\) −7.39230 + 11.1962i −0.328953 + 0.498222i
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) 2.00000i 0.0887357i
\(509\) 17.3205 10.0000i 0.767718 0.443242i −0.0643419 0.997928i \(-0.520495\pi\)
0.832060 + 0.554686i \(0.187161\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) −12.0000 + 20.7846i −0.529813 + 0.917663i
\(514\) 0 0
\(515\) −12.0000 + 6.00000i −0.528783 + 0.264392i
\(516\) 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 \(0.728243\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) −36.3731 + 21.0000i −1.59048 + 0.918266i −0.597259 + 0.802048i \(0.703744\pi\)
−0.993224 + 0.116218i \(0.962923\pi\)
\(524\) −6.00000 + 10.3923i −0.262111 + 0.453990i
\(525\) 0 0
\(526\) −5.19615 3.00000i −0.226563 0.130806i
\(527\) 0 0
\(528\) 4.00000 0.174078
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 22.3923 + 14.7846i 0.972660 + 0.642202i
\(531\) 1.73205 1.00000i 0.0751646 0.0433963i
\(532\) 0 0
\(533\) 0 0
\(534\) −16.0000 −0.692388
\(535\) −11.1962 7.39230i −0.484052 0.319597i
\(536\) −18.0000 31.1769i −0.777482 1.34664i
\(537\) −20.7846 12.0000i −0.896922 0.517838i
\(538\) 18.0000 0.776035
\(539\) −12.1244 7.00000i −0.522233 0.301511i
\(540\) −0.535898 + 8.92820i −0.0230614 + 0.384209i
\(541\) 12.0000i 0.515920i −0.966156 0.257960i \(-0.916950\pi\)
0.966156 0.257960i \(-0.0830503\pi\)
\(542\) −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 \(-0.125734\pi\)
\(548\) 1.00000 + 1.73205i 0.0427179 + 0.0739895i
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 9.19615 3.92820i 0.392125 0.167499i
\(551\) 36.0000i 1.53365i
\(552\) 18.0000 31.1769i 0.766131 1.32698i
\(553\) 0 0
\(554\) 12.0000i 0.509831i
\(555\) 1.60770 26.7846i 0.0682429 1.13694i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) −7.00000 12.1244i −0.296600 0.513725i 0.678756 0.734364i \(-0.262519\pi\)
−0.975356 + 0.220638i \(0.929186\pi\)
\(558\) 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 \(0.884504\pi\)
\(564\) 16.0000i 0.673722i
\(565\) 0 0
\(566\) 19.0526 + 11.0000i 0.800839 + 0.462364i
\(567\) 0 0
\(568\) −5.19615 3.00000i −0.218026 0.125877i
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 14.7846 22.3923i 0.619259 0.937910i
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.58846 29.7846i 0.149649 1.24210i
\(576\) 3.50000 6.06218i 0.145833 0.252591i
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 8.50000 14.7224i 0.353553 0.612372i
\(579\) −10.3923 6.00000i −0.431889 0.249351i
\(580\) 6.00000 + 12.0000i 0.249136 + 0.498273i
\(581\) 0 0
\(582\) −10.3923 + 6.00000i −0.430775 + 0.248708i
\(583\) −12.0000 20.7846i −0.496989 0.860811i
\(584\) −18.0000 −0.744845
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) −10.0000 17.3205i −0.412744 0.714894i 0.582445 0.812870i \(-0.302096\pi\)
−0.995189 + 0.0979766i \(0.968763\pi\)
\(588\) −12.1244 + 7.00000i −0.500000 + 0.288675i
\(589\) −18.0000 + 31.1769i −0.741677 + 1.28462i
\(590\) 4.00000 2.00000i 0.164677 0.0823387i
\(591\) −3.46410 2.00000i −0.142494 0.0822690i
\(592\) 3.00000 5.19615i 0.123299 0.213561i
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) −4.00000 + 6.92820i −0.164122 + 0.284268i
\(595\) 0 0
\(596\) 17.3205 10.0000i 0.709476 0.409616i
\(597\) 48.0000i 1.96451i
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 3.58846 29.7846i 0.146498 1.21595i
\(601\) 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
\(603\) −12.0000 −0.488678
\(604\) 15.5885 + 9.00000i 0.634285 + 0.366205i
\(605\) 15.6244 + 0.937822i 0.635220 + 0.0381279i
\(606\) 12.0000i 0.487467i
\(607\) −15.5885 9.00000i −0.632716 0.365299i 0.149087 0.988824i \(-0.452366\pi\)
−0.781803 + 0.623525i \(0.785700\pi\)
\(608\) −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
\(613\) −15.0000 25.9808i −0.605844 1.04935i −0.991917 0.126885i \(-0.959502\pi\)
0.386073 0.922468i \(-0.373831\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) 35.7128 + 2.14359i 1.44008 + 0.0864380i
\(616\) 0 0
\(617\) −17.0000 + 29.4449i −0.684394 + 1.18541i 0.289233 + 0.957259i \(0.406600\pi\)
−0.973627 + 0.228147i \(0.926733\pi\)
\(618\) −6.00000 + 10.3923i −0.241355 + 0.418040i
\(619\) 18.0000i 0.723481i −0.932279 0.361741i \(-0.882183\pi\)
0.932279 0.361741i \(-0.117817\pi\)
\(620\) −0.803848 + 13.3923i −0.0322833 + 0.537848i
\(621\) 12.0000 + 20.7846i 0.481543 + 0.834058i
\(622\) 12.0000 + 20.7846i 0.481156 + 0.833387i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 6.92820 4.00000i 0.276907 0.159872i
\(627\) −20.7846 + 12.0000i −0.830057 + 0.479234i
\(628\) −10.3923 6.00000i −0.414698 0.239426i
\(629\) 0 0
\(630\) 0 0
\(631\) 25.9808 + 15.0000i 1.03428 + 0.597141i 0.918207 0.396100i \(-0.129637\pi\)
0.116071 + 0.993241i \(0.462970\pi\)
\(632\) 0 0
\(633\) −20.7846 12.0000i −0.826114 0.476957i
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) −3.73205 2.46410i −0.148102 0.0977849i
\(636\) −24.0000 −0.951662
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) −1.73205 + 1.00000i −0.0685189 + 0.0395594i
\(640\) −3.69615 + 5.59808i −0.146103 + 0.221283i
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) −12.0000 −0.473602
\(643\) 18.0000 31.1769i 0.709851 1.22950i −0.255062 0.966925i \(-0.582096\pi\)
0.964912 0.262573i \(-0.0845709\pi\)
\(644\) 0 0
\(645\) −12.0000 24.0000i −0.472500 0.944999i
\(646\) 0 0
\(647\) −5.19615 + 3.00000i −0.204282 + 0.117942i −0.598651 0.801010i \(-0.704296\pi\)
0.394369 + 0.918952i \(0.370963\pi\)
\(648\) 16.5000 + 28.5788i 0.648181 + 1.12268i
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) 6.00000 + 10.3923i 0.234978 + 0.406994i
\(653\) 31.1769 18.0000i 1.22005 0.704394i 0.255119 0.966910i \(-0.417885\pi\)
0.964928 + 0.262515i \(0.0845520\pi\)
\(654\) −12.0000 + 20.7846i −0.469237 + 0.812743i
\(655\) 12.0000 + 24.0000i 0.468879 + 0.937758i
\(656\) 6.92820 + 4.00000i 0.270501 + 0.156174i
\(657\) −3.00000 + 5.19615i −0.117041 + 0.202721i
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) −4.92820 + 7.46410i −0.191830 + 0.290540i
\(661\) 10.3923 6.00000i 0.404214 0.233373i −0.284087 0.958799i \(-0.591690\pi\)
0.688301 + 0.725426i \(0.258357\pi\)
\(662\) 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
\(668\) 16.0000 0.619059
\(669\) 41.5692 + 24.0000i 1.60716 + 0.927894i
\(670\) −26.7846 1.60770i −1.03478 0.0621107i
\(671\) 12.0000i 0.463255i
\(672\) 0 0
\(673\) −41.5692 + 24.0000i −1.60238 + 0.925132i −0.611365 + 0.791349i \(0.709379\pi\)
−0.991011 + 0.133783i \(0.957287\pi\)
\(674\) 27.7128 16.0000i 1.06746 0.616297i
\(675\) 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
\(681\) 8.00000i 0.306561i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) 22.0000 38.1051i 0.841807 1.45805i −0.0465592 0.998916i \(-0.514826\pi\)
0.888366 0.459136i \(-0.151841\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 4.46410 + 0.267949i 0.170565 + 0.0102378i
\(686\) 0 0
\(687\) −12.0000 20.7846i −0.457829 0.792982i
\(688\) 6.00000i 0.228748i
\(689\) 0 0
\(690\) −12.0000 24.0000i −0.456832 0.913664i
\(691\) −36.3731 + 21.0000i −1.38370 + 0.798878i −0.992595 0.121470i \(-0.961239\pi\)
−0.391102 + 0.920348i \(0.627906\pi\)
\(692\) 10.3923 6.00000i 0.395056 0.228086i
\(693\) 0 0
\(694\) 6.00000i 0.227757i
\(695\) −8.92820 0.535898i −0.338666 0.0203278i
\(696\) 31.1769 + 18.0000i 1.18176 + 0.682288i
\(697\) 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 \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 36.0000i 1.35777i
\(704\) −12.1244 + 7.00000i −0.456954 + 0.263822i
\(705\) −29.8564 19.7128i −1.12446 0.742427i
\(706\) −7.00000 + 12.1244i −0.263448 + 0.456306i
\(707\) 0 0
\(708\) −2.00000 + 3.46410i −0.0751646 + 0.130189i
\(709\) −10.3923 6.00000i −0.390291 0.225335i 0.291995 0.956420i \(-0.405681\pi\)
−0.682286 + 0.731085i \(0.739014\pi\)
\(710\) −4.00000 + 2.00000i −0.150117 + 0.0750587i
\(711\) 0 0
\(712\) 20.7846 12.0000i 0.778936 0.449719i
\(713\) 18.0000 + 31.1769i 0.674105 + 1.16758i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −10.0000 17.3205i −0.373457 0.646846i
\(718\) −1.73205 + 1.00000i −0.0646396 + 0.0373197i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) −1.00000 2.00000i −0.0372678 0.0745356i
\(721\) 0 0
\(722\) −8.50000 + 14.7224i −0.316337 + 0.547912i
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 29.7846 + 3.58846i 1.10617 + 0.133272i
\(726\) 12.1244 7.00000i 0.449977 0.259794i
\(727\) 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
\(730\) −7.39230 + 11.1962i −0.273601 + 0.414388i
\(731\) 0 0
\(732\) −10.3923 6.00000i −0.384111 0.221766i
\(733\) −42.0000 −1.55131 −0.775653 0.631160i \(-0.782579\pi\)
−0.775653 + 0.631160i \(0.782579\pi\)
\(734\) 15.5885 + 9.00000i 0.575380 + 0.332196i
\(735\) −1.87564 + 31.2487i −0.0691842 + 1.15263i
\(736\) 30.0000i 1.10581i
\(737\) 20.7846 + 12.0000i 0.765611 + 0.442026i
\(738\) 6.92820 4.00000i 0.255031 0.147242i
\(739\) 5.19615 3.00000i 0.191144 0.110357i −0.401374 0.915914i \(-0.631467\pi\)
0.592518 + 0.805557i \(0.298134\pi\)
\(740\) 6.00000 + 12.0000i 0.220564 + 0.441129i
\(741\) 0 0
\(742\) 0 0
\(743\) 8.00000 + 13.8564i 0.293492 + 0.508342i 0.974633 0.223810i \(-0.0718494\pi\)
−0.681141 + 0.732152i \(0.738516\pi\)
\(744\) 18.0000 + 31.1769i 0.659912 + 1.14300i
\(745\) 2.67949 44.6410i 0.0981690 1.63552i
\(746\) 4.00000i 0.146450i
\(747\) −2.00000 + 3.46410i −0.0731762 + 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) −17.0526 14.4641i −0.622671 0.528154i
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −4.00000 6.92820i −0.145865 0.252646i
\(753\) 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 \(-0.785070\pi\)
0.151043 + 0.988527i \(0.451737\pi\)
\(758\) −15.5885 9.00000i −0.566198 0.326895i
\(759\) 24.0000i 0.871145i
\(760\) −2.41154 + 40.1769i −0.0874758 + 1.45737i
\(761\) −34.6410 20.0000i −1.25574 0.724999i −0.283493 0.958974i \(-0.591493\pi\)
−0.972243 + 0.233975i \(0.924827\pi\)
\(762\) −4.00000 −0.144905
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) 0 0
\(768\) 34.0000i 1.22687i
\(769\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000 0.215945
\(773\) −19.0000 + 32.9090i −0.683383 + 1.18365i 0.290560 + 0.956857i \(0.406159\pi\)
−0.973942 + 0.226796i \(0.927175\pi\)
\(774\) −5.19615 3.00000i −0.186772 0.107833i
\(775\) 24.0000 + 18.0000i 0.862105 + 0.646579i
\(776\) 9.00000 15.5885i 0.323081 0.559593i
\(777\) 0 0
\(778\) 3.00000 + 5.19615i 0.107555 + 0.186291i
\(779\) −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
\(785\) −24.0000 + 12.0000i −0.856597 + 0.428298i
\(786\) 20.7846 + 12.0000i 0.741362 + 0.428026i
\(787\) −6.00000 + 10.3923i −0.213877 + 0.370446i −0.952925 0.303207i \(-0.901942\pi\)
0.739048 + 0.673653i \(0.235276\pi\)
\(788\) 2.00000 0.0712470
\(789\) 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
\(795\) −29.5692 + 44.7846i −1.04871 + 1.58835i
\(796\) −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
\(800\) 9.82051 + 22.9904i 0.347207 + 0.812833i
\(801\) 8.00000i 0.282666i
\(802\) −13.8564 8.00000i −0.489287 0.282490i
\(803\) 10.3923 6.00000i 0.366736 0.211735i
\(804\) 20.7846 12.0000i 0.733017 0.423207i
\(805\) 0 0
\(806\) 0 0
\(807\) 36.0000i 1.26726i
\(808\) −9.00000 15.5885i −0.316619 0.548400i
\(809\) 15.0000 + 25.9808i 0.527372 + 0.913435i 0.999491 + 0.0319002i \(0.0101559\pi\)
−0.472119 + 0.881535i \(0.656511\pi\)
\(810\) 24.5526 + 1.47372i 0.862689 + 0.0517813i
\(811\) 30.0000i 1.05344i 0.850038 + 0.526721i \(0.176579\pi\)
−0.850038 + 0.526721i \(0.823421\pi\)
\(812\) 0 0
\(813\) 6.00000 10.3923i 0.210429 0.364474i
\(814\) 12.0000i 0.420600i
\(815\) 26.7846 + 1.60770i 0.938224 + 0.0563151i
\(816\) 0 0
\(817\) 18.0000 + 31.1769i 0.629740 + 1.09074i
\(818\) 24.0000i 0.839140i
\(819\) 0 0
\(820\) −16.0000 + 8.00000i −0.558744 + 0.279372i
\(821\) −17.3205 + 10.0000i −0.604490 + 0.349002i −0.770806 0.637070i \(-0.780146\pi\)
0.166316 + 0.986073i \(0.446813\pi\)
\(822\) 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 \(0.928086\pi\)
\(824\) 18.0000i 0.627060i
\(825\) 7.85641 + 18.3923i 0.273525 + 0.640338i
\(826\) 0 0
\(827\) 4.00000 0.139094 0.0695468 0.997579i \(-0.477845\pi\)
0.0695468 + 0.997579i \(0.477845\pi\)
\(828\) 5.19615 + 3.00000i 0.180579 + 0.104257i
\(829\) −3.00000 5.19615i −0.104194 0.180470i 0.809214 0.587513i \(-0.199893\pi\)
−0.913409 + 0.407044i \(0.866560\pi\)
\(830\) −4.92820 + 7.46410i −0.171060 + 0.259083i
\(831\) 24.0000 0.832551
\(832\) 0 0
\(833\) 0 0
\(834\) −6.92820 + 4.00000i −0.239904 + 0.138509i
\(835\) 19.7128 29.8564i 0.682190 1.03322i
\(836\) 6.00000 10.3923i 0.207514 0.359425i
\(837\) −24.0000 −0.829561
\(838\) −6.00000 + 10.3923i −0.207267 + 0.358996i
\(839\) 39.8372 + 23.0000i 1.37533 + 0.794048i 0.991593 0.129394i \(-0.0413031\pi\)
0.383738 + 0.923442i \(0.374636\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 31.1769 18.0000i 1.07443 0.620321i
\(843\) 8.00000 + 13.8564i 0.275535 + 0.477240i
\(844\) 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
\(851\) 31.1769 + 18.0000i 1.06873 + 0.617032i
\(852\) 2.00000 3.46410i 0.0685189 0.118678i
\(853\) 54.0000 1.84892 0.924462 0.381273i \(-0.124514\pi\)
0.924462 + 0.381273i \(0.124514\pi\)
\(854\) 0 0
\(855\) 11.1962 + 7.39230i 0.382900 + 0.252811i
\(856\) 15.5885 9.00000i 0.532803 0.307614i
\(857\) 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 \(0.710502\pi\)
\(860\) 11.1962 + 7.39230i 0.381786 + 0.252076i
\(861\) 0 0
\(862\) 8.66025 + 5.00000i 0.294969 + 0.170301i
\(863\) −8.00000 −0.272323 −0.136162 0.990687i \(-0.543477\pi\)
−0.136162 + 0.990687i \(0.543477\pi\)
\(864\) −17.3205 10.0000i −0.589256 0.340207i
\(865\) 1.60770 26.7846i 0.0546633 0.910704i
\(866\) 16.0000i 0.543702i
\(867\) 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
\(873\) −3.00000 5.19615i −0.101535 0.175863i
\(874\) 18.0000 + 31.1769i 0.608859 + 1.05457i
\(875\) 0 0
\(876\) 12.0000i 0.405442i
\(877\) −3.00000 + 5.19615i −0.101303 + 0.175462i −0.912222 0.409697i \(-0.865634\pi\)
0.810919 + 0.585159i \(0.198968\pi\)
\(878\) 4.00000 6.92820i 0.134993 0.233816i
\(879\) 52.0000i 1.75392i
\(880\) −0.267949 + 4.46410i −0.00903257 + 0.150485i
\(881\) −21.0000 36.3731i −0.707508 1.22544i −0.965779 0.259367i \(-0.916486\pi\)
0.258271 0.966073i \(-0.416847\pi\)
\(882\) 3.50000 + 6.06218i 0.117851 + 0.204124i
\(883\) 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
\(886\) −5.19615 + 3.00000i −0.174568 + 0.100787i
\(887\) 36.3731 21.0000i 1.22129 0.705111i 0.256096 0.966651i \(-0.417564\pi\)
0.965193 + 0.261540i \(0.0842305\pi\)
\(888\) 31.1769 + 18.0000i 1.04623 + 0.604040i
\(889\) 0 0
\(890\) 1.07180 17.8564i 0.0359267 0.598548i
\(891\) −19.0526 11.0000i −0.638285 0.368514i
\(892\) −24.0000 −0.803579
\(893\) 41.5692 + 24.0000i 1.39106 + 0.803129i
\(894\) −20.0000 34.6410i −0.668900 1.15857i
\(895\) 14.7846 22.3923i 0.494195 0.748492i
\(896\) 0 0
\(897\) 0 0
\(898\) 16.0000i 0.533927i
\(899\) −31.1769 + 18.0000i −1.03981 + 0.600334i
\(900\) 4.96410 + 0.598076i 0.165470 + 0.0199359i
\(901\) 0 0
\(902\) −16.0000 −0.532742
\(903\) 0 0
\(904\) 0 0
\(905\) 2.00000 + 4.00000i 0.0664822 + 0.132964i
\(906\) 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 \(0.386426\pi\)
\(908\) −2.00000 3.46410i −0.0663723 0.114960i
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 6.00000 + 10.3923i 0.198680 + 0.344124i
\(913\) 6.92820 4.00000i 0.229290 0.132381i
\(914\) −15.0000 + 25.9808i −0.496156 + 0.859367i
\(915\) −24.0000 + 12.0000i −0.793416 + 0.396708i
\(916\) 10.3923 + 6.00000i 0.343371 + 0.198246i
\(917\) 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 \(0.296214\pi\)
\(920\) 33.5885 + 22.1769i 1.10738 + 0.731151i
\(921\) −20.7846 + 12.0000i −0.684876 + 0.395413i
\(922\) 4.00000i 0.131733i
\(923\) 0 0
\(924\) 0 0
\(925\) 29.7846 + 3.58846i 0.979312 + 0.117988i
\(926\) −12.0000 20.7846i −0.394344 0.683025i
\(927\) −5.19615 3.00000i −0.170664 0.0985329i
\(928\) −30.0000 −0.984798
\(929\) 13.8564 + 8.00000i 0.454614 + 0.262471i 0.709777 0.704427i \(-0.248796\pi\)
−0.255163 + 0.966898i \(0.582129\pi\)
\(930\) 26.7846 + 1.60770i 0.878302 + 0.0527184i
\(931\) 42.0000i 1.37649i
\(932\) 20.7846 + 12.0000i 0.680823 + 0.393073i
\(933\) −41.5692 + 24.0000i −1.36092 + 0.785725i
\(934\) 15.5885 9.00000i 0.510070 0.294489i
\(935\) 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
\(940\) 17.8564 + 1.07180i 0.582412 + 0.0349582i
\(941\) 28.0000i 0.912774i −0.889781 0.456387i \(-0.849143\pi\)
0.889781 0.456387i \(-0.150857\pi\)
\(942\) −12.0000 + 20.7846i −0.390981 + 0.677199i
\(943\) −24.0000 + 41.5692i −0.781548 + 1.35368i
\(944\) 2.00000i 0.0650945i
\(945\) 0 0
\(946\) 6.00000 + 10.3923i 0.195077 + 0.337883i
\(947\) −14.0000 24.2487i −0.454939 0.787977i 0.543746 0.839250i \(-0.317006\pi\)
−0.998685 + 0.0512727i \(0.983672\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 24.0000 + 18.0000i 0.778663 + 0.583997i
\(951\) 3.46410 2.00000i 0.112331 0.0648544i
\(952\) 0 0
\(953\) 20.7846 + 12.0000i 0.673280 + 0.388718i 0.797318 0.603559i \(-0.206251\pi\)
−0.124039 + 0.992277i \(0.539585\pi\)
\(954\) 12.0000i 0.388514i
\(955\) 0 0
\(956\) 8.66025 + 5.00000i 0.280093 + 0.161712i
\(957\) −24.0000 −0.775810
\(958\) −19.0526 11.0000i −0.615560 0.355394i
\(959\) 0 0
\(960\) 26.1244 + 17.2487i 0.843160 + 0.556700i
\(961\) −5.00000 −0.161290
\(962\) 0 0
\(963\) 6.00000i 0.193347i
\(964\) 0 0
\(965\) 7.39230 11.1962i 0.237967 0.360417i
\(966\) 0 0
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) −10.5000 + 18.1865i −0.337483 + 0.584537i
\(969\) 0 0
\(970\) −6.00000 12.0000i −0.192648 0.385297i
\(971\) −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
\(977\) −17.0000 29.4449i −0.543878 0.942025i −0.998677 0.0514302i \(-0.983622\pi\)
0.454798 0.890594i \(-0.349711\pi\)
\(978\) 20.7846 12.0000i 0.664619 0.383718i
\(979\) −8.00000 + 13.8564i −0.255681 + 0.442853i
\(980\) −7.00000 14.0000i −0.223607 0.447214i
\(981\) −10.3923 6.00000i −0.331801 0.191565i
\(982\) 6.00000 10.3923i 0.191468 0.331632i
\(983\) 16.0000 0.510321 0.255160 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) −24.0000 + 41.5692i −0.765092 + 1.32518i
\(985\) 2.46410 3.73205i 0.0785128 0.118913i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 36.0000 1.14473
\(990\) 3.73205 + 2.46410i 0.118612 + 0.0783143i
\(991\) 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
\(993\) 60.0000 1.90404
\(994\) 0 0
\(995\) −53.5692 3.21539i −1.69826 0.101935i
\(996\) 8.00000i 0.253490i
\(997\) −51.9615 30.0000i −1.64564 0.950110i −0.978777 0.204927i \(-0.934304\pi\)
−0.666861 0.745182i \(-0.732362\pi\)
\(998\) −5.19615 + 3.00000i −0.164481 + 0.0949633i
\(999\) −20.7846 + 12.0000i −0.657596 + 0.379663i
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.l.b.699.1 4
5.4 even 2 845.2.l.a.699.2 4
13.2 odd 12 845.2.b.a.339.2 2
13.3 even 3 65.2.d.a.64.1 2
13.4 even 6 845.2.l.a.654.2 4
13.5 odd 4 845.2.n.a.484.2 4
13.6 odd 12 845.2.n.a.529.1 4
13.7 odd 12 845.2.n.b.529.2 4
13.8 odd 4 845.2.n.b.484.1 4
13.9 even 3 inner 845.2.l.b.654.2 4
13.10 even 6 65.2.d.b.64.1 yes 2
13.11 odd 12 845.2.b.b.339.1 2
13.12 even 2 845.2.l.a.699.1 4
39.23 odd 6 585.2.h.b.64.1 2
39.29 odd 6 585.2.h.c.64.2 2
52.3 odd 6 1040.2.f.a.129.2 2
52.23 odd 6 1040.2.f.b.129.2 2
65.2 even 12 4225.2.a.e.1.1 1
65.3 odd 12 325.2.c.e.51.2 2
65.4 even 6 inner 845.2.l.b.654.1 4
65.9 even 6 845.2.l.a.654.1 4
65.19 odd 12 845.2.n.a.529.2 4
65.23 odd 12 325.2.c.e.51.1 2
65.24 odd 12 845.2.b.b.339.2 2
65.28 even 12 4225.2.a.m.1.1 1
65.29 even 6 65.2.d.b.64.2 yes 2
65.34 odd 4 845.2.n.b.484.2 4
65.37 even 12 4225.2.a.k.1.1 1
65.42 odd 12 325.2.c.b.51.1 2
65.44 odd 4 845.2.n.a.484.1 4
65.49 even 6 65.2.d.a.64.2 yes 2
65.54 odd 12 845.2.b.a.339.1 2
65.59 odd 12 845.2.n.b.529.1 4
65.62 odd 12 325.2.c.b.51.2 2
65.63 even 12 4225.2.a.h.1.1 1
65.64 even 2 inner 845.2.l.b.699.2 4
195.29 odd 6 585.2.h.b.64.2 2
195.179 odd 6 585.2.h.c.64.1 2
260.159 odd 6 1040.2.f.b.129.1 2
260.179 odd 6 1040.2.f.a.129.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.d.a.64.1 2 13.3 even 3
65.2.d.a.64.2 yes 2 65.49 even 6
65.2.d.b.64.1 yes 2 13.10 even 6
65.2.d.b.64.2 yes 2 65.29 even 6
325.2.c.b.51.1 2 65.42 odd 12
325.2.c.b.51.2 2 65.62 odd 12
325.2.c.e.51.1 2 65.23 odd 12
325.2.c.e.51.2 2 65.3 odd 12
585.2.h.b.64.1 2 39.23 odd 6
585.2.h.b.64.2 2 195.29 odd 6
585.2.h.c.64.1 2 195.179 odd 6
585.2.h.c.64.2 2 39.29 odd 6
845.2.b.a.339.1 2 65.54 odd 12
845.2.b.a.339.2 2 13.2 odd 12
845.2.b.b.339.1 2 13.11 odd 12
845.2.b.b.339.2 2 65.24 odd 12
845.2.l.a.654.1 4 65.9 even 6
845.2.l.a.654.2 4 13.4 even 6
845.2.l.a.699.1 4 13.12 even 2
845.2.l.a.699.2 4 5.4 even 2
845.2.l.b.654.1 4 65.4 even 6 inner
845.2.l.b.654.2 4 13.9 even 3 inner
845.2.l.b.699.1 4 1.1 even 1 trivial
845.2.l.b.699.2 4 65.64 even 2 inner
845.2.n.a.484.1 4 65.44 odd 4
845.2.n.a.484.2 4 13.5 odd 4
845.2.n.a.529.1 4 13.6 odd 12
845.2.n.a.529.2 4 65.19 odd 12
845.2.n.b.484.1 4 13.8 odd 4
845.2.n.b.484.2 4 65.34 odd 4
845.2.n.b.529.1 4 65.59 odd 12
845.2.n.b.529.2 4 13.7 odd 12
1040.2.f.a.129.1 2 260.179 odd 6
1040.2.f.a.129.2 2 52.3 odd 6
1040.2.f.b.129.1 2 260.159 odd 6
1040.2.f.b.129.2 2 52.23 odd 6
4225.2.a.e.1.1 1 65.2 even 12
4225.2.a.h.1.1 1 65.63 even 12
4225.2.a.k.1.1 1 65.37 even 12
4225.2.a.m.1.1 1 65.28 even 12