Properties

Label 81.2.c.b.28.2
Level $81$
Weight $2$
Character 81.28
Analytic conductor $0.647$
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] = [81,2,Mod(28,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 28.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 81.28
Dual form 81.2.c.b.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.73205 q^{8} +O(q^{10})\) \(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.73205 q^{8} -3.00000 q^{10} +(-1.73205 - 3.00000i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.73205 - 3.00000i) q^{14} +(2.50000 + 4.33013i) q^{16} -5.19615 q^{17} +2.00000 q^{19} +(-0.866025 - 1.50000i) q^{20} +(3.00000 - 5.19615i) q^{22} +(1.73205 - 3.00000i) q^{23} +(1.00000 + 1.73205i) q^{25} +1.73205 q^{26} +2.00000 q^{28} +(0.866025 + 1.50000i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(-4.50000 - 7.79423i) q^{34} +3.46410 q^{35} -7.00000 q^{37} +(1.73205 + 3.00000i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-3.46410 + 6.00000i) q^{41} +(-1.00000 - 1.73205i) q^{43} +3.46410 q^{44} +6.00000 q^{46} +(3.46410 + 6.00000i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-1.73205 + 3.00000i) q^{50} +(0.500000 + 0.866025i) q^{52} +6.00000 q^{55} +(-1.73205 - 3.00000i) q^{56} +(-1.50000 + 2.59808i) q^{58} +(6.92820 - 12.0000i) q^{59} +(3.50000 + 6.06218i) q^{61} -13.8564 q^{62} +1.00000 q^{64} +(0.866025 + 1.50000i) q^{65} +(5.00000 - 8.66025i) q^{67} +(2.59808 - 4.50000i) q^{68} +(3.00000 + 5.19615i) q^{70} +10.3923 q^{71} -7.00000 q^{73} +(-6.06218 - 10.5000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-3.46410 + 6.00000i) q^{77} +(-1.00000 - 1.73205i) q^{79} -8.66025 q^{80} -12.0000 q^{82} +(-6.92820 - 12.0000i) q^{83} +(4.50000 - 7.79423i) q^{85} +(1.73205 - 3.00000i) q^{86} +(-3.00000 - 5.19615i) q^{88} +5.19615 q^{89} -2.00000 q^{91} +(1.73205 + 3.00000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(-1.73205 + 3.00000i) q^{95} +(-1.00000 - 1.73205i) q^{97} +5.19615 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} - 4 q^{7} - 12 q^{10} + 2 q^{13} + 10 q^{16} + 8 q^{19} + 12 q^{22} + 4 q^{25} + 8 q^{28} - 16 q^{31} - 18 q^{34} - 28 q^{37} - 6 q^{40} - 4 q^{43} + 24 q^{46} + 6 q^{49} + 2 q^{52} + 24 q^{55} - 6 q^{58} + 14 q^{61} + 4 q^{64} + 20 q^{67} + 12 q^{70} - 28 q^{73} - 4 q^{76} - 4 q^{79} - 48 q^{82} + 18 q^{85} - 12 q^{88} - 8 q^{91} - 24 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 1.50000i 0.612372 + 1.06066i 0.990839 + 0.135045i \(0.0431180\pi\)
−0.378467 + 0.925615i \(0.623549\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.866025 + 1.50000i −0.387298 + 0.670820i −0.992085 0.125567i \(-0.959925\pi\)
0.604787 + 0.796387i \(0.293258\pi\)
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 1.73205 0.612372
\(9\) 0 0
\(10\) −3.00000 −0.948683
\(11\) −1.73205 3.00000i −0.522233 0.904534i −0.999665 0.0258656i \(-0.991766\pi\)
0.477432 0.878668i \(-0.341568\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 1.73205 3.00000i 0.462910 0.801784i
\(15\) 0 0
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) −5.19615 −1.26025 −0.630126 0.776493i \(-0.716997\pi\)
−0.630126 + 0.776493i \(0.716997\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −0.866025 1.50000i −0.193649 0.335410i
\(21\) 0 0
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) 1.73205 3.00000i 0.361158 0.625543i −0.626994 0.779024i \(-0.715715\pi\)
0.988152 + 0.153481i \(0.0490483\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.200000 + 0.346410i
\(26\) 1.73205 0.339683
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) 0.866025 + 1.50000i 0.160817 + 0.278543i 0.935162 0.354221i \(-0.115254\pi\)
−0.774345 + 0.632764i \(0.781920\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −2.59808 + 4.50000i −0.459279 + 0.795495i
\(33\) 0 0
\(34\) −4.50000 7.79423i −0.771744 1.33670i
\(35\) 3.46410 0.585540
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 1.73205 + 3.00000i 0.280976 + 0.486664i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) −3.46410 + 6.00000i −0.541002 + 0.937043i 0.457845 + 0.889032i \(0.348621\pi\)
−0.998847 + 0.0480106i \(0.984712\pi\)
\(42\) 0 0
\(43\) −1.00000 1.73205i −0.152499 0.264135i 0.779647 0.626219i \(-0.215399\pi\)
−0.932145 + 0.362084i \(0.882065\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 3.46410 + 6.00000i 0.505291 + 0.875190i 0.999981 + 0.00612051i \(0.00194823\pi\)
−0.494690 + 0.869069i \(0.664718\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −1.73205 + 3.00000i −0.244949 + 0.424264i
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) −1.73205 3.00000i −0.231455 0.400892i
\(57\) 0 0
\(58\) −1.50000 + 2.59808i −0.196960 + 0.341144i
\(59\) 6.92820 12.0000i 0.901975 1.56227i 0.0770484 0.997027i \(-0.475450\pi\)
0.824927 0.565240i \(-0.191216\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) −13.8564 −1.75977
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.866025 + 1.50000i 0.107417 + 0.186052i
\(66\) 0 0
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) 2.59808 4.50000i 0.315063 0.545705i
\(69\) 0 0
\(70\) 3.00000 + 5.19615i 0.358569 + 0.621059i
\(71\) 10.3923 1.23334 0.616670 0.787222i \(-0.288481\pi\)
0.616670 + 0.787222i \(0.288481\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −6.06218 10.5000i −0.704714 1.22060i
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) −3.46410 + 6.00000i −0.394771 + 0.683763i
\(78\) 0 0
\(79\) −1.00000 1.73205i −0.112509 0.194871i 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) −8.66025 −0.968246
\(81\) 0 0
\(82\) −12.0000 −1.32518
\(83\) −6.92820 12.0000i −0.760469 1.31717i −0.942609 0.333899i \(-0.891636\pi\)
0.182140 0.983273i \(-0.441698\pi\)
\(84\) 0 0
\(85\) 4.50000 7.79423i 0.488094 0.845403i
\(86\) 1.73205 3.00000i 0.186772 0.323498i
\(87\) 0 0
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 5.19615 0.550791 0.275396 0.961331i \(-0.411191\pi\)
0.275396 + 0.961331i \(0.411191\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 1.73205 + 3.00000i 0.180579 + 0.312772i
\(93\) 0 0
\(94\) −6.00000 + 10.3923i −0.618853 + 1.07188i
\(95\) −1.73205 + 3.00000i −0.177705 + 0.307794i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 5.19615 0.524891
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) 3.46410 + 6.00000i 0.344691 + 0.597022i 0.985298 0.170847i \(-0.0546504\pi\)
−0.640607 + 0.767869i \(0.721317\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 0.866025 1.50000i 0.0849208 0.147087i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 5.19615 + 9.00000i 0.495434 + 0.858116i
\(111\) 0 0
\(112\) 5.00000 8.66025i 0.472456 0.818317i
\(113\) −0.866025 + 1.50000i −0.0814688 + 0.141108i −0.903881 0.427784i \(-0.859294\pi\)
0.822412 + 0.568892i \(0.192628\pi\)
\(114\) 0 0
\(115\) 3.00000 + 5.19615i 0.279751 + 0.484544i
\(116\) −1.73205 −0.160817
\(117\) 0 0
\(118\) 24.0000 2.20938
\(119\) 5.19615 + 9.00000i 0.476331 + 0.825029i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −6.06218 + 10.5000i −0.548844 + 0.950625i
\(123\) 0 0
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) −12.1244 −1.08444
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 6.06218 + 10.5000i 0.535826 + 0.928078i
\(129\) 0 0
\(130\) −1.50000 + 2.59808i −0.131559 + 0.227866i
\(131\) 1.73205 3.00000i 0.151330 0.262111i −0.780387 0.625297i \(-0.784978\pi\)
0.931717 + 0.363186i \(0.118311\pi\)
\(132\) 0 0
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 17.3205 1.49626
\(135\) 0 0
\(136\) −9.00000 −0.771744
\(137\) 0.866025 + 1.50000i 0.0739895 + 0.128154i 0.900646 0.434553i \(-0.143094\pi\)
−0.826657 + 0.562706i \(0.809760\pi\)
\(138\) 0 0
\(139\) −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i \(-0.943515\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(140\) −1.73205 + 3.00000i −0.146385 + 0.253546i
\(141\) 0 0
\(142\) 9.00000 + 15.5885i 0.755263 + 1.30815i
\(143\) −3.46410 −0.289683
\(144\) 0 0
\(145\) −3.00000 −0.249136
\(146\) −6.06218 10.5000i −0.501709 0.868986i
\(147\) 0 0
\(148\) 3.50000 6.06218i 0.287698 0.498308i
\(149\) 4.33013 7.50000i 0.354738 0.614424i −0.632335 0.774695i \(-0.717903\pi\)
0.987073 + 0.160271i \(0.0512368\pi\)
\(150\) 0 0
\(151\) −10.0000 17.3205i −0.813788 1.40952i −0.910195 0.414181i \(-0.864068\pi\)
0.0964061 0.995342i \(-0.469265\pi\)
\(152\) 3.46410 0.280976
\(153\) 0 0
\(154\) −12.0000 −0.966988
\(155\) −6.92820 12.0000i −0.556487 0.963863i
\(156\) 0 0
\(157\) −8.50000 + 14.7224i −0.678374 + 1.17498i 0.297097 + 0.954847i \(0.403982\pi\)
−0.975470 + 0.220131i \(0.929352\pi\)
\(158\) 1.73205 3.00000i 0.137795 0.238667i
\(159\) 0 0
\(160\) −4.50000 7.79423i −0.355756 0.616188i
\(161\) −6.92820 −0.546019
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) 0 0
\(166\) 12.0000 20.7846i 0.931381 1.61320i
\(167\) −8.66025 + 15.0000i −0.670151 + 1.16073i 0.307711 + 0.951480i \(0.400437\pi\)
−0.977861 + 0.209255i \(0.932896\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 15.5885 1.19558
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) −9.52628 16.5000i −0.724270 1.25447i −0.959274 0.282477i \(-0.908844\pi\)
0.235004 0.971994i \(-0.424490\pi\)
\(174\) 0 0
\(175\) 2.00000 3.46410i 0.151186 0.261861i
\(176\) 8.66025 15.0000i 0.652791 1.13067i
\(177\) 0 0
\(178\) 4.50000 + 7.79423i 0.337289 + 0.584202i
\(179\) −20.7846 −1.55351 −0.776757 0.629800i \(-0.783137\pi\)
−0.776757 + 0.629800i \(0.783137\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −1.73205 3.00000i −0.128388 0.222375i
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 6.06218 10.5000i 0.445700 0.771975i
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) −6.92820 −0.505291
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) 8.66025 + 15.0000i 0.626634 + 1.08536i 0.988222 + 0.153024i \(0.0489012\pi\)
−0.361588 + 0.932338i \(0.617765\pi\)
\(192\) 0 0
\(193\) 0.500000 0.866025i 0.0359908 0.0623379i −0.847469 0.530845i \(-0.821875\pi\)
0.883460 + 0.468507i \(0.155208\pi\)
\(194\) 1.73205 3.00000i 0.124354 0.215387i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) 5.19615 0.370211 0.185105 0.982719i \(-0.440737\pi\)
0.185105 + 0.982719i \(0.440737\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 1.73205 + 3.00000i 0.122474 + 0.212132i
\(201\) 0 0
\(202\) −6.00000 + 10.3923i −0.422159 + 0.731200i
\(203\) 1.73205 3.00000i 0.121566 0.210559i
\(204\) 0 0
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) −13.8564 −0.965422
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) −3.46410 6.00000i −0.239617 0.415029i
\(210\) 0 0
\(211\) 5.00000 8.66025i 0.344214 0.596196i −0.640996 0.767544i \(-0.721479\pi\)
0.985211 + 0.171347i \(0.0548120\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.46410 0.236250
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 9.52628 + 16.5000i 0.645201 + 1.11752i
\(219\) 0 0
\(220\) −3.00000 + 5.19615i −0.202260 + 0.350325i
\(221\) −2.59808 + 4.50000i −0.174766 + 0.302703i
\(222\) 0 0
\(223\) −1.00000 1.73205i −0.0669650 0.115987i 0.830599 0.556871i \(-0.187998\pi\)
−0.897564 + 0.440884i \(0.854665\pi\)
\(224\) 10.3923 0.694365
\(225\) 0 0
\(226\) −3.00000 −0.199557
\(227\) −1.73205 3.00000i −0.114960 0.199117i 0.802804 0.596244i \(-0.203341\pi\)
−0.917764 + 0.397127i \(0.870007\pi\)
\(228\) 0 0
\(229\) 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i \(-0.822814\pi\)
0.882073 + 0.471113i \(0.156147\pi\)
\(230\) −5.19615 + 9.00000i −0.342624 + 0.593442i
\(231\) 0 0
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 25.9808 1.70206 0.851028 0.525120i \(-0.175980\pi\)
0.851028 + 0.525120i \(0.175980\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 6.92820 + 12.0000i 0.450988 + 0.781133i
\(237\) 0 0
\(238\) −9.00000 + 15.5885i −0.583383 + 1.01045i
\(239\) −13.8564 + 24.0000i −0.896296 + 1.55243i −0.0641045 + 0.997943i \(0.520419\pi\)
−0.832192 + 0.554488i \(0.812914\pi\)
\(240\) 0 0
\(241\) −14.5000 25.1147i −0.934027 1.61778i −0.776360 0.630290i \(-0.782936\pi\)
−0.157667 0.987492i \(-0.550397\pi\)
\(242\) −1.73205 −0.111340
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 2.59808 + 4.50000i 0.165985 + 0.287494i
\(246\) 0 0
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) −6.92820 + 12.0000i −0.439941 + 0.762001i
\(249\) 0 0
\(250\) −10.5000 18.1865i −0.664078 1.15022i
\(251\) −10.3923 −0.655956 −0.327978 0.944685i \(-0.606367\pi\)
−0.327978 + 0.944685i \(0.606367\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 1.73205 + 3.00000i 0.108679 + 0.188237i
\(255\) 0 0
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) 4.33013 7.50000i 0.270106 0.467837i −0.698783 0.715334i \(-0.746275\pi\)
0.968889 + 0.247497i \(0.0796080\pi\)
\(258\) 0 0
\(259\) 7.00000 + 12.1244i 0.434959 + 0.753371i
\(260\) −1.73205 −0.107417
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 3.46410 + 6.00000i 0.213606 + 0.369976i 0.952840 0.303472i \(-0.0981459\pi\)
−0.739235 + 0.673448i \(0.764813\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 3.46410 6.00000i 0.212398 0.367884i
\(267\) 0 0
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) 15.5885 0.950445 0.475223 0.879866i \(-0.342368\pi\)
0.475223 + 0.879866i \(0.342368\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −12.9904 22.5000i −0.787658 1.36426i
\(273\) 0 0
\(274\) −1.50000 + 2.59808i −0.0906183 + 0.156956i
\(275\) 3.46410 6.00000i 0.208893 0.361814i
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −13.8564 −0.831052
\(279\) 0 0
\(280\) 6.00000 0.358569
\(281\) 6.06218 + 10.5000i 0.361639 + 0.626377i 0.988231 0.152970i \(-0.0488839\pi\)
−0.626592 + 0.779348i \(0.715551\pi\)
\(282\) 0 0
\(283\) 14.0000 24.2487i 0.832214 1.44144i −0.0640654 0.997946i \(-0.520407\pi\)
0.896279 0.443491i \(-0.146260\pi\)
\(284\) −5.19615 + 9.00000i −0.308335 + 0.534052i
\(285\) 0 0
\(286\) −3.00000 5.19615i −0.177394 0.307255i
\(287\) 13.8564 0.817918
\(288\) 0 0
\(289\) 10.0000 0.588235
\(290\) −2.59808 4.50000i −0.152564 0.264249i
\(291\) 0 0
\(292\) 3.50000 6.06218i 0.204822 0.354762i
\(293\) 9.52628 16.5000i 0.556531 0.963940i −0.441251 0.897384i \(-0.645465\pi\)
0.997783 0.0665568i \(-0.0212014\pi\)
\(294\) 0 0
\(295\) 12.0000 + 20.7846i 0.698667 + 1.21013i
\(296\) −12.1244 −0.704714
\(297\) 0 0
\(298\) 15.0000 0.868927
\(299\) −1.73205 3.00000i −0.100167 0.173494i
\(300\) 0 0
\(301\) −2.00000 + 3.46410i −0.115278 + 0.199667i
\(302\) 17.3205 30.0000i 0.996683 1.72631i
\(303\) 0 0
\(304\) 5.00000 + 8.66025i 0.286770 + 0.496700i
\(305\) −12.1244 −0.694239
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −3.46410 6.00000i −0.197386 0.341882i
\(309\) 0 0
\(310\) 12.0000 20.7846i 0.681554 1.18049i
\(311\) −3.46410 + 6.00000i −0.196431 + 0.340229i −0.947369 0.320144i \(-0.896269\pi\)
0.750938 + 0.660373i \(0.229602\pi\)
\(312\) 0 0
\(313\) 12.5000 + 21.6506i 0.706542 + 1.22377i 0.966132 + 0.258047i \(0.0830791\pi\)
−0.259590 + 0.965719i \(0.583588\pi\)
\(314\) −29.4449 −1.66167
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) −4.33013 7.50000i −0.243204 0.421242i 0.718421 0.695609i \(-0.244865\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) −0.866025 + 1.50000i −0.0484123 + 0.0838525i
\(321\) 0 0
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) −10.3923 −0.578243
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) −13.8564 24.0000i −0.767435 1.32924i
\(327\) 0 0
\(328\) −6.00000 + 10.3923i −0.331295 + 0.573819i
\(329\) 6.92820 12.0000i 0.381964 0.661581i
\(330\) 0 0
\(331\) −1.00000 1.73205i −0.0549650 0.0952021i 0.837234 0.546845i \(-0.184171\pi\)
−0.892199 + 0.451643i \(0.850838\pi\)
\(332\) 13.8564 0.760469
\(333\) 0 0
\(334\) −30.0000 −1.64153
\(335\) 8.66025 + 15.0000i 0.473160 + 0.819538i
\(336\) 0 0
\(337\) −13.0000 + 22.5167i −0.708155 + 1.22656i 0.257386 + 0.966309i \(0.417139\pi\)
−0.965541 + 0.260252i \(0.916194\pi\)
\(338\) −10.3923 + 18.0000i −0.565267 + 0.979071i
\(339\) 0 0
\(340\) 4.50000 + 7.79423i 0.244047 + 0.422701i
\(341\) 27.7128 1.50073
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) −1.73205 3.00000i −0.0933859 0.161749i
\(345\) 0 0
\(346\) 16.5000 28.5788i 0.887045 1.53641i
\(347\) 1.73205 3.00000i 0.0929814 0.161048i −0.815783 0.578358i \(-0.803694\pi\)
0.908764 + 0.417310i \(0.137027\pi\)
\(348\) 0 0
\(349\) −1.00000 1.73205i −0.0535288 0.0927146i 0.838019 0.545640i \(-0.183714\pi\)
−0.891548 + 0.452926i \(0.850380\pi\)
\(350\) 6.92820 0.370328
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) −6.92820 12.0000i −0.368751 0.638696i 0.620620 0.784112i \(-0.286881\pi\)
−0.989371 + 0.145416i \(0.953548\pi\)
\(354\) 0 0
\(355\) −9.00000 + 15.5885i −0.477670 + 0.827349i
\(356\) −2.59808 + 4.50000i −0.137698 + 0.238500i
\(357\) 0 0
\(358\) −18.0000 31.1769i −0.951330 1.64775i
\(359\) −10.3923 −0.548485 −0.274242 0.961661i \(-0.588427\pi\)
−0.274242 + 0.961661i \(0.588427\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 1.73205 + 3.00000i 0.0910346 + 0.157676i
\(363\) 0 0
\(364\) 1.00000 1.73205i 0.0524142 0.0907841i
\(365\) 6.06218 10.5000i 0.317309 0.549595i
\(366\) 0 0
\(367\) −10.0000 17.3205i −0.521996 0.904123i −0.999673 0.0255875i \(-0.991854\pi\)
0.477677 0.878536i \(-0.341479\pi\)
\(368\) 17.3205 0.902894
\(369\) 0 0
\(370\) 21.0000 1.09174
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) −15.5885 + 27.0000i −0.806060 + 1.39614i
\(375\) 0 0
\(376\) 6.00000 + 10.3923i 0.309426 + 0.535942i
\(377\) 1.73205 0.0892052
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −1.73205 3.00000i −0.0888523 0.153897i
\(381\) 0 0
\(382\) −15.0000 + 25.9808i −0.767467 + 1.32929i
\(383\) −8.66025 + 15.0000i −0.442518 + 0.766464i −0.997876 0.0651476i \(-0.979248\pi\)
0.555357 + 0.831612i \(0.312581\pi\)
\(384\) 0 0
\(385\) −6.00000 10.3923i −0.305788 0.529641i
\(386\) 1.73205 0.0881591
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) 13.8564 + 24.0000i 0.702548 + 1.21685i 0.967569 + 0.252606i \(0.0812876\pi\)
−0.265022 + 0.964242i \(0.585379\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) 2.59808 4.50000i 0.131223 0.227284i
\(393\) 0 0
\(394\) 4.50000 + 7.79423i 0.226707 + 0.392668i
\(395\) 3.46410 0.174298
\(396\) 0 0
\(397\) 29.0000 1.45547 0.727734 0.685859i \(-0.240573\pi\)
0.727734 + 0.685859i \(0.240573\pi\)
\(398\) 17.3205 + 30.0000i 0.868199 + 1.50376i
\(399\) 0 0
\(400\) −5.00000 + 8.66025i −0.250000 + 0.433013i
\(401\) −6.06218 + 10.5000i −0.302731 + 0.524345i −0.976753 0.214366i \(-0.931232\pi\)
0.674023 + 0.738711i \(0.264565\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) −6.92820 −0.344691
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 12.1244 + 21.0000i 0.600982 + 1.04093i
\(408\) 0 0
\(409\) 9.50000 16.4545i 0.469745 0.813622i −0.529657 0.848212i \(-0.677679\pi\)
0.999402 + 0.0345902i \(0.0110126\pi\)
\(410\) 10.3923 18.0000i 0.513239 0.888957i
\(411\) 0 0
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) −27.7128 −1.36366
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) 2.59808 + 4.50000i 0.127381 + 0.220631i
\(417\) 0 0
\(418\) 6.00000 10.3923i 0.293470 0.508304i
\(419\) −3.46410 + 6.00000i −0.169232 + 0.293119i −0.938150 0.346228i \(-0.887462\pi\)
0.768918 + 0.639348i \(0.220796\pi\)
\(420\) 0 0
\(421\) 12.5000 + 21.6506i 0.609213 + 1.05519i 0.991370 + 0.131090i \(0.0418478\pi\)
−0.382158 + 0.924097i \(0.624819\pi\)
\(422\) 17.3205 0.843149
\(423\) 0 0
\(424\) 0 0
\(425\) −5.19615 9.00000i −0.252050 0.436564i
\(426\) 0 0
\(427\) 7.00000 12.1244i 0.338754 0.586739i
\(428\) 0 0
\(429\) 0 0
\(430\) 3.00000 + 5.19615i 0.144673 + 0.250581i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) 13.8564 + 24.0000i 0.665129 + 1.15204i
\(435\) 0 0
\(436\) −5.50000 + 9.52628i −0.263402 + 0.456226i
\(437\) 3.46410 6.00000i 0.165710 0.287019i
\(438\) 0 0
\(439\) −10.0000 17.3205i −0.477274 0.826663i 0.522387 0.852709i \(-0.325042\pi\)
−0.999661 + 0.0260459i \(0.991708\pi\)
\(440\) 10.3923 0.495434
\(441\) 0 0
\(442\) −9.00000 −0.428086
\(443\) −17.3205 30.0000i −0.822922 1.42534i −0.903497 0.428594i \(-0.859009\pi\)
0.0805748 0.996749i \(-0.474324\pi\)
\(444\) 0 0
\(445\) −4.50000 + 7.79423i −0.213320 + 0.369482i
\(446\) 1.73205 3.00000i 0.0820150 0.142054i
\(447\) 0 0
\(448\) −1.00000 1.73205i −0.0472456 0.0818317i
\(449\) −20.7846 −0.980886 −0.490443 0.871473i \(-0.663165\pi\)
−0.490443 + 0.871473i \(0.663165\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) −0.866025 1.50000i −0.0407344 0.0705541i
\(453\) 0 0
\(454\) 3.00000 5.19615i 0.140797 0.243868i
\(455\) 1.73205 3.00000i 0.0811998 0.140642i
\(456\) 0 0
\(457\) −14.5000 25.1147i −0.678281 1.17482i −0.975498 0.220008i \(-0.929392\pi\)
0.297217 0.954810i \(-0.403942\pi\)
\(458\) 1.73205 0.0809334
\(459\) 0 0
\(460\) −6.00000 −0.279751
\(461\) −6.92820 12.0000i −0.322679 0.558896i 0.658361 0.752702i \(-0.271250\pi\)
−0.981040 + 0.193806i \(0.937917\pi\)
\(462\) 0 0
\(463\) −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i \(-0.892852\pi\)
0.757982 + 0.652275i \(0.226185\pi\)
\(464\) −4.33013 + 7.50000i −0.201021 + 0.348179i
\(465\) 0 0
\(466\) 22.5000 + 38.9711i 1.04229 + 1.80530i
\(467\) 20.7846 0.961797 0.480899 0.876776i \(-0.340311\pi\)
0.480899 + 0.876776i \(0.340311\pi\)
\(468\) 0 0
\(469\) −20.0000 −0.923514
\(470\) −10.3923 18.0000i −0.479361 0.830278i
\(471\) 0 0
\(472\) 12.0000 20.7846i 0.552345 0.956689i
\(473\) −3.46410 + 6.00000i −0.159280 + 0.275880i
\(474\) 0 0
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) −10.3923 −0.476331
\(477\) 0 0
\(478\) −48.0000 −2.19547
\(479\) −12.1244 21.0000i −0.553976 0.959514i −0.997982 0.0634909i \(-0.979777\pi\)
0.444006 0.896024i \(-0.353557\pi\)
\(480\) 0 0
\(481\) −3.50000 + 6.06218i −0.159586 + 0.276412i
\(482\) 25.1147 43.5000i 1.14394 1.98137i
\(483\) 0 0
\(484\) −0.500000 0.866025i −0.0227273 0.0393648i
\(485\) 3.46410 0.157297
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 6.06218 + 10.5000i 0.274422 + 0.475313i
\(489\) 0 0
\(490\) −4.50000 + 7.79423i −0.203289 + 0.352107i
\(491\) −8.66025 + 15.0000i −0.390832 + 0.676941i −0.992559 0.121761i \(-0.961146\pi\)
0.601728 + 0.798701i \(0.294479\pi\)
\(492\) 0 0
\(493\) −4.50000 7.79423i −0.202670 0.351034i
\(494\) 3.46410 0.155857
\(495\) 0 0
\(496\) −40.0000 −1.79605
\(497\) −10.3923 18.0000i −0.466159 0.807410i
\(498\) 0 0
\(499\) 5.00000 8.66025i 0.223831 0.387686i −0.732137 0.681157i \(-0.761477\pi\)
0.955968 + 0.293471i \(0.0948104\pi\)
\(500\) 6.06218 10.5000i 0.271109 0.469574i
\(501\) 0 0
\(502\) −9.00000 15.5885i −0.401690 0.695747i
\(503\) −20.7846 −0.926740 −0.463370 0.886165i \(-0.653360\pi\)
−0.463370 + 0.886165i \(0.653360\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) −10.3923 18.0000i −0.461994 0.800198i
\(507\) 0 0
\(508\) −1.00000 + 1.73205i −0.0443678 + 0.0768473i
\(509\) −13.8564 + 24.0000i −0.614174 + 1.06378i 0.376354 + 0.926476i \(0.377178\pi\)
−0.990529 + 0.137305i \(0.956156\pi\)
\(510\) 0 0
\(511\) 7.00000 + 12.1244i 0.309662 + 0.536350i
\(512\) −8.66025 −0.382733
\(513\) 0 0
\(514\) 15.0000 0.661622
\(515\) −6.92820 12.0000i −0.305293 0.528783i
\(516\) 0 0
\(517\) 12.0000 20.7846i 0.527759 0.914106i
\(518\) −12.1244 + 21.0000i −0.532714 + 0.922687i
\(519\) 0 0
\(520\) 1.50000 + 2.59808i 0.0657794 + 0.113933i
\(521\) 20.7846 0.910590 0.455295 0.890341i \(-0.349534\pi\)
0.455295 + 0.890341i \(0.349534\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) 1.73205 + 3.00000i 0.0756650 + 0.131056i
\(525\) 0 0
\(526\) −6.00000 + 10.3923i −0.261612 + 0.453126i
\(527\) 20.7846 36.0000i 0.905392 1.56818i
\(528\) 0 0
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 0 0
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 3.46410 + 6.00000i 0.150047 + 0.259889i
\(534\) 0 0
\(535\) 0 0
\(536\) 8.66025 15.0000i 0.374066 0.647901i
\(537\) 0 0
\(538\) 13.5000 + 23.3827i 0.582026 + 1.00810i
\(539\) −10.3923 −0.447628
\(540\) 0 0
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) 1.73205 + 3.00000i 0.0743980 + 0.128861i
\(543\) 0 0
\(544\) 13.5000 23.3827i 0.578808 1.00252i
\(545\) −9.52628 + 16.5000i −0.408061 + 0.706782i
\(546\) 0 0
\(547\) −10.0000 17.3205i −0.427569 0.740571i 0.569087 0.822277i \(-0.307297\pi\)
−0.996657 + 0.0817056i \(0.973963\pi\)
\(548\) −1.73205 −0.0739895
\(549\) 0 0
\(550\) 12.0000 0.511682
\(551\) 1.73205 + 3.00000i 0.0737878 + 0.127804i
\(552\) 0 0
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) 1.73205 3.00000i 0.0735878 0.127458i
\(555\) 0 0
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) −36.3731 −1.54118 −0.770588 0.637333i \(-0.780037\pi\)
−0.770588 + 0.637333i \(0.780037\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 8.66025 + 15.0000i 0.365963 + 0.633866i
\(561\) 0 0
\(562\) −10.5000 + 18.1865i −0.442916 + 0.767153i
\(563\) 17.3205 30.0000i 0.729972 1.26435i −0.226922 0.973913i \(-0.572866\pi\)
0.956894 0.290436i \(-0.0938004\pi\)
\(564\) 0 0
\(565\) −1.50000 2.59808i −0.0631055 0.109302i
\(566\) 48.4974 2.03850
\(567\) 0 0
\(568\) 18.0000 0.755263
\(569\) 16.4545 + 28.5000i 0.689808 + 1.19478i 0.971900 + 0.235395i \(0.0756383\pi\)
−0.282092 + 0.959387i \(0.591028\pi\)
\(570\) 0 0
\(571\) −4.00000 + 6.92820i −0.167395 + 0.289936i −0.937503 0.347977i \(-0.886869\pi\)
0.770108 + 0.637913i \(0.220202\pi\)
\(572\) 1.73205 3.00000i 0.0724207 0.125436i
\(573\) 0 0
\(574\) 12.0000 + 20.7846i 0.500870 + 0.867533i
\(575\) 6.92820 0.288926
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 8.66025 + 15.0000i 0.360219 + 0.623918i
\(579\) 0 0
\(580\) 1.50000 2.59808i 0.0622841 0.107879i
\(581\) −13.8564 + 24.0000i −0.574861 + 0.995688i
\(582\) 0 0
\(583\) 0 0
\(584\) −12.1244 −0.501709
\(585\) 0 0
\(586\) 33.0000 1.36322
\(587\) 19.0526 + 33.0000i 0.786383 + 1.36206i 0.928169 + 0.372158i \(0.121382\pi\)
−0.141786 + 0.989897i \(0.545284\pi\)
\(588\) 0 0
\(589\) −8.00000 + 13.8564i −0.329634 + 0.570943i
\(590\) −20.7846 + 36.0000i −0.855689 + 1.48210i
\(591\) 0 0
\(592\) −17.5000 30.3109i −0.719246 1.24577i
\(593\) −15.5885 −0.640141 −0.320071 0.947394i \(-0.603707\pi\)
−0.320071 + 0.947394i \(0.603707\pi\)
\(594\) 0 0
\(595\) −18.0000 −0.737928
\(596\) 4.33013 + 7.50000i 0.177369 + 0.307212i
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) 6.92820 12.0000i 0.283079 0.490307i −0.689063 0.724702i \(-0.741978\pi\)
0.972141 + 0.234395i \(0.0753109\pi\)
\(600\) 0 0
\(601\) 12.5000 + 21.6506i 0.509886 + 0.883148i 0.999934 + 0.0114528i \(0.00364562\pi\)
−0.490049 + 0.871695i \(0.663021\pi\)
\(602\) −6.92820 −0.282372
\(603\) 0 0
\(604\) 20.0000 0.813788
\(605\) −0.866025 1.50000i −0.0352089 0.0609837i
\(606\) 0 0
\(607\) −13.0000 + 22.5167i −0.527654 + 0.913923i 0.471827 + 0.881691i \(0.343595\pi\)
−0.999480 + 0.0322317i \(0.989739\pi\)
\(608\) −5.19615 + 9.00000i −0.210732 + 0.364998i
\(609\) 0 0
\(610\) −10.5000 18.1865i −0.425133 0.736351i
\(611\) 6.92820 0.280285
\(612\) 0 0
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) −13.8564 24.0000i −0.559199 0.968561i
\(615\) 0 0
\(616\) −6.00000 + 10.3923i −0.241747 + 0.418718i
\(617\) −6.06218 + 10.5000i −0.244054 + 0.422714i −0.961865 0.273524i \(-0.911811\pi\)
0.717811 + 0.696238i \(0.245144\pi\)
\(618\) 0 0
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 13.8564 0.556487
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) −5.19615 9.00000i −0.208179 0.360577i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −21.6506 + 37.5000i −0.865333 + 1.49880i
\(627\) 0 0
\(628\) −8.50000 14.7224i −0.339187 0.587489i
\(629\) 36.3731 1.45029
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −1.73205 3.00000i −0.0688973 0.119334i
\(633\) 0 0
\(634\) 7.50000 12.9904i 0.297863 0.515914i
\(635\) −1.73205 + 3.00000i −0.0687343 + 0.119051i
\(636\) 0 0
\(637\) −1.50000 2.59808i −0.0594322 0.102940i
\(638\) 10.3923 0.411435
\(639\) 0 0
\(640\) −21.0000 −0.830098
\(641\) 11.2583 + 19.5000i 0.444677 + 0.770204i 0.998030 0.0627436i \(-0.0199850\pi\)
−0.553352 + 0.832947i \(0.686652\pi\)
\(642\) 0 0
\(643\) −4.00000 + 6.92820i −0.157745 + 0.273222i −0.934055 0.357129i \(-0.883756\pi\)
0.776310 + 0.630351i \(0.217089\pi\)
\(644\) 3.46410 6.00000i 0.136505 0.236433i
\(645\) 0 0
\(646\) −9.00000 15.5885i −0.354100 0.613320i
\(647\) 31.1769 1.22569 0.612845 0.790203i \(-0.290025\pi\)
0.612845 + 0.790203i \(0.290025\pi\)
\(648\) 0 0
\(649\) −48.0000 −1.88416
\(650\) 1.73205 + 3.00000i 0.0679366 + 0.117670i
\(651\) 0 0
\(652\) 8.00000 13.8564i 0.313304 0.542659i
\(653\) 6.92820 12.0000i 0.271122 0.469596i −0.698028 0.716071i \(-0.745939\pi\)
0.969149 + 0.246474i \(0.0792721\pi\)
\(654\) 0 0
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) −34.6410 −1.35250
\(657\) 0 0
\(658\) 24.0000 0.935617
\(659\) −1.73205 3.00000i −0.0674711 0.116863i 0.830316 0.557292i \(-0.188160\pi\)
−0.897787 + 0.440429i \(0.854826\pi\)
\(660\) 0 0
\(661\) −8.50000 + 14.7224i −0.330612 + 0.572636i −0.982632 0.185565i \(-0.940588\pi\)
0.652020 + 0.758202i \(0.273922\pi\)
\(662\) 1.73205 3.00000i 0.0673181 0.116598i
\(663\) 0 0
\(664\) −12.0000 20.7846i −0.465690 0.806599i
\(665\) 6.92820 0.268664
\(666\) 0 0
\(667\) 6.00000 0.232321
\(668\) −8.66025 15.0000i −0.335075 0.580367i
\(669\) 0 0
\(670\) −15.0000 + 25.9808i −0.579501 + 1.00372i
\(671\) 12.1244 21.0000i 0.468056 0.810696i
\(672\) 0 0
\(673\) 12.5000 + 21.6506i 0.481840 + 0.834571i 0.999783 0.0208444i \(-0.00663546\pi\)
−0.517943 + 0.855415i \(0.673302\pi\)
\(674\) −45.0333 −1.73462
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −6.92820 12.0000i −0.266272 0.461197i 0.701624 0.712548i \(-0.252459\pi\)
−0.967896 + 0.251350i \(0.919125\pi\)
\(678\) 0 0
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 7.79423 13.5000i 0.298895 0.517701i
\(681\) 0 0
\(682\) 24.0000 + 41.5692i 0.919007 + 1.59177i
\(683\) 20.7846 0.795301 0.397650 0.917537i \(-0.369826\pi\)
0.397650 + 0.917537i \(0.369826\pi\)
\(684\) 0 0
\(685\) −3.00000 −0.114624
\(686\) −17.3205 30.0000i −0.661300 1.14541i
\(687\) 0 0
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.00000 1.73205i −0.0380418 0.0658903i 0.846378 0.532583i \(-0.178779\pi\)
−0.884419 + 0.466693i \(0.845445\pi\)
\(692\) 19.0526 0.724270
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) −6.92820 12.0000i −0.262802 0.455186i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 1.73205 3.00000i 0.0655591 0.113552i
\(699\) 0 0
\(700\) 2.00000 + 3.46410i 0.0755929 + 0.130931i
\(701\) −46.7654 −1.76630 −0.883152 0.469087i \(-0.844583\pi\)
−0.883152 + 0.469087i \(0.844583\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) −1.73205 3.00000i −0.0652791 0.113067i
\(705\) 0 0
\(706\) 12.0000 20.7846i 0.451626 0.782239i
\(707\) 6.92820 12.0000i 0.260562 0.451306i
\(708\) 0 0
\(709\) 12.5000 + 21.6506i 0.469447 + 0.813107i 0.999390 0.0349269i \(-0.0111198\pi\)
−0.529943 + 0.848034i \(0.677787\pi\)
\(710\) −31.1769 −1.17005
\(711\) 0 0
\(712\) 9.00000 0.337289
\(713\) 13.8564 + 24.0000i 0.518927 + 0.898807i
\(714\) 0 0
\(715\) 3.00000 5.19615i 0.112194 0.194325i
\(716\) 10.3923 18.0000i 0.388379 0.672692i
\(717\) 0 0
\(718\) −9.00000 15.5885i −0.335877 0.581756i
\(719\) 10.3923 0.387568 0.193784 0.981044i \(-0.437924\pi\)
0.193784 + 0.981044i \(0.437924\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) −12.9904 22.5000i −0.483452 0.837363i
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −1.73205 + 3.00000i −0.0643268 + 0.111417i
\(726\) 0 0
\(727\) 17.0000 + 29.4449i 0.630495 + 1.09205i 0.987451 + 0.157928i \(0.0504814\pi\)
−0.356956 + 0.934121i \(0.616185\pi\)
\(728\) −3.46410 −0.128388
\(729\) 0 0
\(730\) 21.0000 0.777245
\(731\) 5.19615 + 9.00000i 0.192187 + 0.332877i
\(732\) 0 0
\(733\) 23.0000 39.8372i 0.849524 1.47142i −0.0321090 0.999484i \(-0.510222\pi\)
0.881633 0.471935i \(-0.156444\pi\)
\(734\) 17.3205 30.0000i 0.639312 1.10732i
\(735\) 0 0
\(736\) 9.00000 + 15.5885i 0.331744 + 0.574598i
\(737\) −34.6410 −1.27602
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 6.06218 + 10.5000i 0.222850 + 0.385988i
\(741\) 0 0
\(742\) 0 0
\(743\) −3.46410 + 6.00000i −0.127086 + 0.220119i −0.922546 0.385887i \(-0.873896\pi\)
0.795461 + 0.606005i \(0.207229\pi\)
\(744\) 0 0
\(745\) 7.50000 + 12.9904i 0.274779 + 0.475931i
\(746\) 17.3205 0.634149
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) 0 0
\(750\) 0 0
\(751\) 5.00000 8.66025i 0.182453 0.316017i −0.760263 0.649616i \(-0.774930\pi\)
0.942715 + 0.333599i \(0.108263\pi\)
\(752\) −17.3205 + 30.0000i −0.631614 + 1.09399i
\(753\) 0 0
\(754\) 1.50000 + 2.59808i 0.0546268 + 0.0946164i
\(755\) 34.6410 1.26072
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −13.8564 24.0000i −0.503287 0.871719i
\(759\) 0 0
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) 14.7224 25.5000i 0.533688 0.924374i −0.465538 0.885028i \(-0.654139\pi\)
0.999226 0.0393463i \(-0.0125276\pi\)
\(762\) 0 0
\(763\) −11.0000 19.0526i −0.398227 0.689749i
\(764\) −17.3205 −0.626634
\(765\) 0 0
\(766\) −30.0000 −1.08394
\(767\) −6.92820 12.0000i −0.250163 0.433295i
\(768\) 0 0
\(769\) 0.500000 0.866025i 0.0180305 0.0312297i −0.856869 0.515534i \(-0.827594\pi\)
0.874900 + 0.484304i \(0.160927\pi\)
\(770\) 10.3923 18.0000i 0.374513 0.648675i
\(771\) 0 0
\(772\) 0.500000 + 0.866025i 0.0179954 + 0.0311689i
\(773\) 25.9808 0.934463 0.467232 0.884135i \(-0.345251\pi\)
0.467232 + 0.884135i \(0.345251\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) −1.73205 3.00000i −0.0621770 0.107694i
\(777\) 0 0
\(778\) −24.0000 + 41.5692i −0.860442 + 1.49033i
\(779\) −6.92820 + 12.0000i −0.248229 + 0.429945i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) −31.1769 −1.11488
\(783\) 0 0
\(784\) 15.0000 0.535714
\(785\) −14.7224 25.5000i −0.525466 0.910134i
\(786\) 0 0
\(787\) −13.0000 + 22.5167i −0.463400 + 0.802632i −0.999128 0.0417585i \(-0.986704\pi\)
0.535728 + 0.844391i \(0.320037\pi\)
\(788\) −2.59808 + 4.50000i −0.0925526 + 0.160306i
\(789\) 0 0
\(790\) 3.00000 + 5.19615i 0.106735 + 0.184871i
\(791\) 3.46410 0.123169
\(792\) 0 0
\(793\) 7.00000 0.248577
\(794\) 25.1147 + 43.5000i 0.891289 + 1.54376i
\(795\) 0 0
\(796\) −10.0000 + 17.3205i −0.354441 + 0.613909i
\(797\) −26.8468 + 46.5000i −0.950962 + 1.64711i −0.207613 + 0.978211i \(0.566569\pi\)
−0.743349 + 0.668903i \(0.766764\pi\)
\(798\) 0 0
\(799\) −18.0000 31.1769i −0.636794 1.10296i
\(800\) −10.3923 −0.367423
\(801\) 0 0
\(802\) −21.0000 −0.741536
\(803\) 12.1244 + 21.0000i 0.427859 + 0.741074i
\(804\) 0 0
\(805\) 6.00000 10.3923i 0.211472 0.366281i
\(806\) −6.92820 + 12.0000i −0.244036 + 0.422682i
\(807\) 0 0
\(808\) 6.00000 + 10.3923i 0.211079 + 0.365600i
\(809\) 46.7654 1.64418 0.822091 0.569355i \(-0.192807\pi\)
0.822091 + 0.569355i \(0.192807\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 1.73205 + 3.00000i 0.0607831 + 0.105279i
\(813\) 0 0
\(814\) −21.0000 + 36.3731i −0.736050 + 1.27488i
\(815\) 13.8564 24.0000i 0.485369 0.840683i
\(816\) 0 0
\(817\) −2.00000 3.46410i −0.0699711 0.121194i
\(818\) 32.9090 1.15063
\(819\) 0 0
\(820\) 12.0000 0.419058
\(821\) 6.06218 + 10.5000i 0.211571 + 0.366453i 0.952207 0.305455i \(-0.0988086\pi\)
−0.740635 + 0.671908i \(0.765475\pi\)
\(822\) 0 0
\(823\) 14.0000 24.2487i 0.488009 0.845257i −0.511896 0.859048i \(-0.671057\pi\)
0.999905 + 0.0137907i \(0.00438987\pi\)
\(824\) −6.92820 + 12.0000i −0.241355 + 0.418040i
\(825\) 0 0
\(826\) −24.0000 41.5692i −0.835067 1.44638i
\(827\) 10.3923 0.361376 0.180688 0.983540i \(-0.442168\pi\)
0.180688 + 0.983540i \(0.442168\pi\)
\(828\) 0 0
\(829\) 2.00000 0.0694629 0.0347314 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 20.7846 + 36.0000i 0.721444 + 1.24958i
\(831\) 0 0
\(832\) 0.500000 0.866025i 0.0173344 0.0300240i
\(833\) −7.79423 + 13.5000i −0.270054 + 0.467747i
\(834\) 0 0
\(835\) −15.0000 25.9808i −0.519096 0.899101i
\(836\) 6.92820 0.239617
\(837\) 0 0
\(838\) −12.0000 −0.414533
\(839\) −22.5167 39.0000i −0.777361 1.34643i −0.933458 0.358688i \(-0.883224\pi\)
0.156096 0.987742i \(-0.450109\pi\)
\(840\) 0 0
\(841\) 13.0000 22.5167i 0.448276 0.776437i
\(842\) −21.6506 + 37.5000i −0.746130 + 1.29234i
\(843\) 0 0
\(844\) 5.00000 + 8.66025i 0.172107 + 0.298098i
\(845\) −20.7846 −0.715012
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 0 0
\(849\) 0 0
\(850\) 9.00000 15.5885i 0.308697 0.534680i
\(851\) −12.1244 + 21.0000i −0.415618 + 0.719871i
\(852\) 0 0
\(853\) 17.0000 + 29.4449i 0.582069 + 1.00817i 0.995234 + 0.0975167i \(0.0310899\pi\)
−0.413165 + 0.910656i \(0.635577\pi\)
\(854\) 24.2487 0.829774
\(855\) 0 0
\(856\) 0 0
\(857\) 11.2583 + 19.5000i 0.384577 + 0.666107i 0.991710 0.128493i \(-0.0410139\pi\)
−0.607133 + 0.794600i \(0.707681\pi\)
\(858\) 0 0
\(859\) −22.0000 + 38.1051i −0.750630 + 1.30013i 0.196887 + 0.980426i \(0.436917\pi\)
−0.947518 + 0.319704i \(0.896417\pi\)
\(860\) −1.73205 + 3.00000i −0.0590624 + 0.102299i
\(861\) 0 0
\(862\) 0 0
\(863\) −31.1769 −1.06127 −0.530637 0.847599i \(-0.678047\pi\)
−0.530637 + 0.847599i \(0.678047\pi\)
\(864\) 0 0
\(865\) 33.0000 1.12203
\(866\) 9.52628 + 16.5000i 0.323716 + 0.560693i
\(867\) 0 0
\(868\) −8.00000 + 13.8564i −0.271538 + 0.470317i
\(869\) −3.46410 + 6.00000i −0.117512 + 0.203536i
\(870\) 0 0
\(871\) −5.00000 8.66025i −0.169419 0.293442i
\(872\) 19.0526 0.645201
\(873\) 0 0
\(874\) 12.0000 0.405906
\(875\) 12.1244 + 21.0000i 0.409878 + 0.709930i
\(876\) 0 0
\(877\) −26.5000 + 45.8993i −0.894841 + 1.54991i −0.0608407 + 0.998147i \(0.519378\pi\)
−0.834001 + 0.551763i \(0.813955\pi\)
\(878\) 17.3205 30.0000i 0.584539 1.01245i
\(879\) 0 0
\(880\) 15.0000 + 25.9808i 0.505650 + 0.875811i
\(881\) −20.7846 −0.700251 −0.350126 0.936703i \(-0.613861\pi\)
−0.350126 + 0.936703i \(0.613861\pi\)
\(882\) 0 0
\(883\) 56.0000 1.88455 0.942275 0.334840i \(-0.108682\pi\)
0.942275 + 0.334840i \(0.108682\pi\)
\(884\) −2.59808 4.50000i −0.0873828 0.151351i
\(885\) 0 0
\(886\) 30.0000 51.9615i 1.00787 1.74568i
\(887\) 1.73205 3.00000i 0.0581566 0.100730i −0.835481 0.549519i \(-0.814811\pi\)
0.893638 + 0.448789i \(0.148144\pi\)
\(888\) 0 0
\(889\) −2.00000 3.46410i −0.0670778 0.116182i
\(890\) −15.5885 −0.522526
\(891\) 0 0
\(892\) 2.00000 0.0669650
\(893\) 6.92820 + 12.0000i 0.231843 + 0.401565i
\(894\) 0 0
\(895\) 18.0000 31.1769i 0.601674 1.04213i
\(896\) 12.1244 21.0000i 0.405046 0.701561i
\(897\) 0 0
\(898\) −18.0000 31.1769i −0.600668 1.04039i
\(899\) −13.8564 −0.462137
\(900\) 0 0
\(901\) 0 0
\(902\) 20.7846 + 36.0000i 0.692052 + 1.19867i
\(903\) 0 0
\(904\) −1.50000 + 2.59808i −0.0498893 + 0.0864107i
\(905\) −1.73205 + 3.00000i −0.0575753 + 0.0997234i
\(906\) 0 0
\(907\) 26.0000 + 45.0333i 0.863316 + 1.49531i 0.868710 + 0.495321i \(0.164950\pi\)
−0.00539395 + 0.999985i \(0.501717\pi\)
\(908\) 3.46410 0.114960
\(909\) 0 0
\(910\) 6.00000 0.198898
\(911\) −12.1244 21.0000i −0.401698 0.695761i 0.592233 0.805767i \(-0.298246\pi\)
−0.993931 + 0.110006i \(0.964913\pi\)
\(912\) 0 0
\(913\) −24.0000 + 41.5692i −0.794284 + 1.37574i
\(914\) 25.1147 43.5000i 0.830722 1.43885i
\(915\) 0 0
\(916\) 0.500000 + 0.866025i 0.0165205 + 0.0286143i
\(917\) −6.92820 −0.228789
\(918\) 0 0
\(919\) 2.00000 0.0659739 0.0329870 0.999456i \(-0.489498\pi\)
0.0329870 + 0.999456i \(0.489498\pi\)
\(920\) 5.19615 + 9.00000i 0.171312 + 0.296721i
\(921\) 0 0
\(922\) 12.0000 20.7846i 0.395199 0.684505i
\(923\) 5.19615 9.00000i 0.171033 0.296239i
\(924\) 0 0
\(925\) −7.00000 12.1244i −0.230159 0.398646i
\(926\) −13.8564 −0.455350
\(927\) 0 0
\(928\) −9.00000 −0.295439
\(929\) −25.1147 43.5000i −0.823988 1.42719i −0.902690 0.430291i \(-0.858411\pi\)
0.0787027 0.996898i \(-0.474922\pi\)
\(930\) 0 0
\(931\) 3.00000 5.19615i 0.0983210 0.170297i
\(932\) −12.9904 + 22.5000i −0.425514 + 0.737012i
\(933\) 0 0
\(934\) 18.0000 + 31.1769i 0.588978 + 1.02014i
\(935\) −31.1769 −1.01959
\(936\) 0 0
\(937\) −25.0000 −0.816714 −0.408357 0.912822i \(-0.633898\pi\)
−0.408357 + 0.912822i \(0.633898\pi\)
\(938\) −17.3205 30.0000i −0.565535 0.979535i
\(939\) 0 0
\(940\) 6.00000 10.3923i 0.195698 0.338960i
\(941\) 25.1147 43.5000i 0.818717 1.41806i −0.0879109 0.996128i \(-0.528019\pi\)
0.906628 0.421931i \(-0.138648\pi\)
\(942\) 0 0
\(943\) 12.0000 + 20.7846i 0.390774 + 0.676840i
\(944\) 69.2820 2.25494
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) 8.66025 + 15.0000i 0.281420 + 0.487435i 0.971735 0.236075i \(-0.0758611\pi\)
−0.690314 + 0.723510i \(0.742528\pi\)
\(948\) 0 0
\(949\) −3.50000 + 6.06218i −0.113615 + 0.196787i
\(950\) −3.46410 + 6.00000i −0.112390 + 0.194666i
\(951\) 0 0
\(952\) 9.00000 + 15.5885i 0.291692 + 0.505225i
\(953\) 5.19615 0.168320 0.0841599 0.996452i \(-0.473179\pi\)
0.0841599 + 0.996452i \(0.473179\pi\)
\(954\) 0 0
\(955\) −30.0000 −0.970777
\(956\) −13.8564 24.0000i −0.448148 0.776215i
\(957\) 0 0
\(958\) 21.0000 36.3731i 0.678479 1.17516i
\(959\) 1.73205 3.00000i 0.0559308 0.0968751i
\(960\) 0 0
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) −12.1244 −0.390905
\(963\) 0 0
\(964\) 29.0000 0.934027
\(965\) 0.866025 + 1.50000i 0.0278783 + 0.0482867i
\(966\) 0 0
\(967\) 23.0000 39.8372i 0.739630 1.28108i −0.213032 0.977045i \(-0.568334\pi\)
0.952662 0.304032i \(-0.0983329\pi\)
\(968\) −0.866025 + 1.50000i −0.0278351 + 0.0482118i
\(969\) 0 0
\(970\) 3.00000 + 5.19615i 0.0963242 + 0.166838i
\(971\) −31.1769 −1.00051 −0.500257 0.865877i \(-0.666761\pi\)
−0.500257 + 0.865877i \(0.666761\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) −13.8564 24.0000i −0.443988 0.769010i
\(975\) 0 0
\(976\) −17.5000 + 30.3109i −0.560161 + 0.970228i
\(977\) −24.2487 + 42.0000i −0.775785 + 1.34370i 0.158567 + 0.987348i \(0.449313\pi\)
−0.934352 + 0.356351i \(0.884021\pi\)
\(978\) 0 0
\(979\) −9.00000 15.5885i −0.287641 0.498209i
\(980\) −5.19615 −0.165985
\(981\) 0 0
\(982\) −30.0000 −0.957338
\(983\) −17.3205 30.0000i −0.552438 0.956851i −0.998098 0.0616488i \(-0.980364\pi\)
0.445659 0.895203i \(-0.352969\pi\)
\(984\) 0 0
\(985\) −4.50000 + 7.79423i −0.143382 + 0.248345i
\(986\) 7.79423 13.5000i 0.248219 0.429928i
\(987\) 0 0
\(988\) 1.00000 + 1.73205i 0.0318142 + 0.0551039i
\(989\) −6.92820 −0.220304
\(990\) 0 0
\(991\) −34.0000 −1.08005 −0.540023 0.841650i \(-0.681584\pi\)
−0.540023 + 0.841650i \(0.681584\pi\)
\(992\) −20.7846 36.0000i −0.659912 1.14300i
\(993\) 0 0
\(994\) 18.0000 31.1769i 0.570925 0.988872i
\(995\) −17.3205 + 30.0000i −0.549097 + 0.951064i
\(996\) 0 0
\(997\) 3.50000 + 6.06218i 0.110846 + 0.191991i 0.916112 0.400923i \(-0.131311\pi\)
−0.805266 + 0.592914i \(0.797977\pi\)
\(998\) 17.3205 0.548271
\(999\) 0 0
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 81.2.c.b.28.2 4
3.2 odd 2 inner 81.2.c.b.28.1 4
4.3 odd 2 1296.2.i.s.433.1 4
9.2 odd 6 inner 81.2.c.b.55.1 4
9.4 even 3 81.2.a.a.1.1 2
9.5 odd 6 81.2.a.a.1.2 yes 2
9.7 even 3 inner 81.2.c.b.55.2 4
12.11 even 2 1296.2.i.s.433.2 4
27.2 odd 18 729.2.e.o.82.2 12
27.4 even 9 729.2.e.o.649.1 12
27.5 odd 18 729.2.e.o.163.1 12
27.7 even 9 729.2.e.o.568.2 12
27.11 odd 18 729.2.e.o.325.2 12
27.13 even 9 729.2.e.o.406.1 12
27.14 odd 18 729.2.e.o.406.2 12
27.16 even 9 729.2.e.o.325.1 12
27.20 odd 18 729.2.e.o.568.1 12
27.22 even 9 729.2.e.o.163.2 12
27.23 odd 18 729.2.e.o.649.2 12
27.25 even 9 729.2.e.o.82.1 12
36.7 odd 6 1296.2.i.s.865.1 4
36.11 even 6 1296.2.i.s.865.2 4
36.23 even 6 1296.2.a.o.1.1 2
36.31 odd 6 1296.2.a.o.1.2 2
45.4 even 6 2025.2.a.j.1.2 2
45.13 odd 12 2025.2.b.k.649.3 4
45.14 odd 6 2025.2.a.j.1.1 2
45.22 odd 12 2025.2.b.k.649.2 4
45.23 even 12 2025.2.b.k.649.1 4
45.32 even 12 2025.2.b.k.649.4 4
63.13 odd 6 3969.2.a.i.1.1 2
63.41 even 6 3969.2.a.i.1.2 2
72.5 odd 6 5184.2.a.br.1.2 2
72.13 even 6 5184.2.a.br.1.1 2
72.59 even 6 5184.2.a.bq.1.2 2
72.67 odd 6 5184.2.a.bq.1.1 2
99.32 even 6 9801.2.a.v.1.1 2
99.76 odd 6 9801.2.a.v.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.a.a.1.1 2 9.4 even 3
81.2.a.a.1.2 yes 2 9.5 odd 6
81.2.c.b.28.1 4 3.2 odd 2 inner
81.2.c.b.28.2 4 1.1 even 1 trivial
81.2.c.b.55.1 4 9.2 odd 6 inner
81.2.c.b.55.2 4 9.7 even 3 inner
729.2.e.o.82.1 12 27.25 even 9
729.2.e.o.82.2 12 27.2 odd 18
729.2.e.o.163.1 12 27.5 odd 18
729.2.e.o.163.2 12 27.22 even 9
729.2.e.o.325.1 12 27.16 even 9
729.2.e.o.325.2 12 27.11 odd 18
729.2.e.o.406.1 12 27.13 even 9
729.2.e.o.406.2 12 27.14 odd 18
729.2.e.o.568.1 12 27.20 odd 18
729.2.e.o.568.2 12 27.7 even 9
729.2.e.o.649.1 12 27.4 even 9
729.2.e.o.649.2 12 27.23 odd 18
1296.2.a.o.1.1 2 36.23 even 6
1296.2.a.o.1.2 2 36.31 odd 6
1296.2.i.s.433.1 4 4.3 odd 2
1296.2.i.s.433.2 4 12.11 even 2
1296.2.i.s.865.1 4 36.7 odd 6
1296.2.i.s.865.2 4 36.11 even 6
2025.2.a.j.1.1 2 45.14 odd 6
2025.2.a.j.1.2 2 45.4 even 6
2025.2.b.k.649.1 4 45.23 even 12
2025.2.b.k.649.2 4 45.22 odd 12
2025.2.b.k.649.3 4 45.13 odd 12
2025.2.b.k.649.4 4 45.32 even 12
3969.2.a.i.1.1 2 63.13 odd 6
3969.2.a.i.1.2 2 63.41 even 6
5184.2.a.bq.1.1 2 72.67 odd 6
5184.2.a.bq.1.2 2 72.59 even 6
5184.2.a.br.1.1 2 72.13 even 6
5184.2.a.br.1.2 2 72.5 odd 6
9801.2.a.v.1.1 2 99.32 even 6
9801.2.a.v.1.2 2 99.76 odd 6