Properties

Label 882.2.h.i.79.1
Level $882$
Weight $2$
Character 882.79
Analytic conductor $7.043$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(67,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.79
Dual form 882.2.h.i.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{10} -3.00000 q^{11} +(-1.50000 + 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} -9.00000 q^{23} +(-1.50000 - 0.866025i) q^{24} +4.00000 q^{25} +(0.500000 - 0.866025i) q^{26} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} -5.19615i q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.50000 - 2.59808i) q^{33} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{36} +(0.500000 - 0.866025i) q^{37} -7.00000 q^{38} -1.73205i q^{39} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-4.50000 - 7.79423i) q^{45} +(-4.50000 - 7.79423i) q^{46} -1.73205i q^{48} +(2.00000 + 3.46410i) q^{50} +5.19615i q^{51} +1.00000 q^{52} +(-1.50000 - 2.59808i) q^{53} +(-4.50000 + 2.59808i) q^{54} +9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} -3.00000 q^{58} +(4.50000 - 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} -5.19615i q^{66} +(2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-13.5000 - 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(5.50000 + 9.52628i) q^{73} +1.00000 q^{74} +(6.00000 + 3.46410i) q^{75} +(-3.50000 - 6.06218i) q^{76} +(1.50000 - 0.866025i) q^{78} +(8.00000 + 13.8564i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +1.00000 q^{86} +(-4.50000 + 2.59808i) q^{87} +3.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +(4.50000 - 7.79423i) q^{90} +(4.50000 - 7.79423i) q^{92} +(12.0000 - 6.92820i) q^{93} +(10.5000 - 18.1865i) q^{95} +(1.50000 - 0.866025i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} - 6 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} - 6 q^{5} - 2 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} - q^{13} - 9 q^{15} - q^{16} + 3 q^{17} - 3 q^{18} - 7 q^{19} + 3 q^{20} - 3 q^{22} - 18 q^{23} - 3 q^{24} + 8 q^{25} + q^{26} - 3 q^{29} + 8 q^{31} + q^{32} - 9 q^{33} - 3 q^{34} - 6 q^{36} + q^{37} - 14 q^{38} + 6 q^{40} + 3 q^{41} + q^{43} + 3 q^{44} - 9 q^{45} - 9 q^{46} + 4 q^{50} + 2 q^{52} - 3 q^{53} - 9 q^{54} + 18 q^{55} - 21 q^{57} - 6 q^{58} + 9 q^{60} + 2 q^{61} + 16 q^{62} + 2 q^{64} + 3 q^{65} + 4 q^{67} - 6 q^{68} - 27 q^{69} + 24 q^{71} - 3 q^{72} + 11 q^{73} + 2 q^{74} + 12 q^{75} - 7 q^{76} + 3 q^{78} + 16 q^{79} + 3 q^{80} - 9 q^{81} - 3 q^{82} - 9 q^{83} - 9 q^{85} + 2 q^{86} - 9 q^{87} + 6 q^{88} + 3 q^{89} + 9 q^{90} + 9 q^{92} + 24 q^{93} + 21 q^{95} + 3 q^{96} - q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.50000 + 0.866025i −0.433013 + 0.250000i
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −4.50000 2.59808i −1.16190 0.670820i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −9.00000 −1.87663 −0.938315 0.345782i \(-0.887614\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 4.00000 0.800000
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 5.19615i 0.948683i
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −4.50000 2.59808i −0.783349 0.452267i
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −7.00000 −1.13555
\(39\) 1.73205i 0.277350i
\(40\) 3.00000 0.474342
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) −4.50000 7.79423i −0.670820 1.16190i
\(46\) −4.50000 7.79423i −0.663489 1.14920i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 0 0
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 5.19615i 0.727607i
\(52\) 1.00000 0.138675
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −10.5000 + 6.06218i −1.39076 + 0.802955i
\(58\) −3.00000 −0.393919
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 4.50000 2.59808i 0.580948 0.335410i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.50000 + 2.59808i 0.186052 + 0.322252i
\(66\) 5.19615i 0.639602i
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −3.00000 −0.363803
\(69\) −13.5000 7.79423i −1.62521 0.938315i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −1.50000 2.59808i −0.176777 0.306186i
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 1.00000 0.116248
\(75\) 6.00000 + 3.46410i 0.692820 + 0.400000i
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 1.50000 0.866025i 0.169842 0.0980581i
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) 0 0
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) 1.00000 0.107833
\(87\) −4.50000 + 2.59808i −0.482451 + 0.278543i
\(88\) 3.00000 0.319801
\(89\) 1.50000 2.59808i 0.159000 0.275396i −0.775509 0.631337i \(-0.782506\pi\)
0.934508 + 0.355942i \(0.115840\pi\)
\(90\) 4.50000 7.79423i 0.474342 0.821584i
\(91\) 0 0
\(92\) 4.50000 7.79423i 0.469157 0.812605i
\(93\) 12.0000 6.92820i 1.24434 0.718421i
\(94\) 0 0
\(95\) 10.5000 18.1865i 1.07728 1.86590i
\(96\) 1.50000 0.866025i 0.153093 0.0883883i
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) −4.50000 7.79423i −0.452267 0.783349i
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) −4.50000 + 2.59808i −0.445566 + 0.257248i
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0.500000 + 0.866025i 0.0490290 + 0.0849208i
\(105\) 0 0
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) −4.50000 + 7.79423i −0.435031 + 0.753497i −0.997298 0.0734594i \(-0.976596\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(108\) −4.50000 2.59808i −0.433013 0.250000i
\(109\) 6.50000 + 11.2583i 0.622587 + 1.07835i 0.989002 + 0.147901i \(0.0472517\pi\)
−0.366415 + 0.930451i \(0.619415\pi\)
\(110\) 4.50000 + 7.79423i 0.429058 + 0.743151i
\(111\) 1.50000 0.866025i 0.142374 0.0821995i
\(112\) 0 0
\(113\) 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i \(-0.0275297\pi\)
−0.572938 + 0.819599i \(0.694196\pi\)
\(114\) −10.5000 6.06218i −0.983415 0.567775i
\(115\) 27.0000 2.51776
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) 1.50000 2.59808i 0.138675 0.240192i
\(118\) 0 0
\(119\) 0 0
\(120\) 4.50000 + 2.59808i 0.410792 + 0.237171i
\(121\) −2.00000 −0.181818
\(122\) −1.00000 + 1.73205i −0.0905357 + 0.156813i
\(123\) 5.19615i 0.468521i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) −1.50000 + 2.59808i −0.131559 + 0.227866i
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 4.50000 2.59808i 0.391675 0.226134i
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 15.5885i 1.34164i
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 15.5885i 1.32698i
\(139\) −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i \(-0.262608\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) −5.50000 + 9.52628i −0.455183 + 0.788400i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) −9.00000 −0.737309 −0.368654 0.929567i \(-0.620181\pi\)
−0.368654 + 0.929567i \(0.620181\pi\)
\(150\) 6.92820i 0.565685i
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) 3.50000 6.06218i 0.283887 0.491708i
\(153\) −4.50000 + 7.79423i −0.363803 + 0.630126i
\(154\) 0 0
\(155\) −12.0000 + 20.7846i −0.963863 + 1.66946i
\(156\) 1.50000 + 0.866025i 0.120096 + 0.0693375i
\(157\) −11.0000 + 19.0526i −0.877896 + 1.52056i −0.0242497 + 0.999706i \(0.507720\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) −8.00000 + 13.8564i −0.636446 + 1.10236i
\(159\) 5.19615i 0.412082i
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) 9.50000 16.4545i 0.744097 1.28881i −0.206518 0.978443i \(-0.566213\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(164\) −3.00000 −0.234261
\(165\) 13.5000 + 7.79423i 1.05097 + 0.606780i
\(166\) −9.00000 −0.698535
\(167\) −7.50000 12.9904i −0.580367 1.00523i −0.995436 0.0954356i \(-0.969576\pi\)
0.415068 0.909790i \(-0.363758\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 4.50000 7.79423i 0.345134 0.597790i
\(171\) −21.0000 −1.60591
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) −4.50000 2.59808i −0.341144 0.196960i
\(175\) 0 0
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) 3.00000 0.224860
\(179\) 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) 9.00000 0.670820
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 3.46410i 0.256074i
\(184\) 9.00000 0.663489
\(185\) −1.50000 + 2.59808i −0.110282 + 0.191014i
\(186\) 12.0000 + 6.92820i 0.879883 + 0.508001i
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 0 0
\(189\) 0 0
\(190\) 21.0000 1.52350
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 1.50000 + 0.866025i 0.108253 + 0.0625000i
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 5.19615i 0.372104i
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 4.50000 7.79423i 0.319801 0.553912i
\(199\) −12.5000 21.6506i −0.886102 1.53477i −0.844446 0.535641i \(-0.820070\pi\)
−0.0416556 0.999132i \(-0.513263\pi\)
\(200\) −4.00000 −0.282843
\(201\) 6.00000 3.46410i 0.423207 0.244339i
\(202\) −1.50000 2.59808i −0.105540 0.182800i
\(203\) 0 0
\(204\) −4.50000 2.59808i −0.315063 0.181902i
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 6.50000 + 11.2583i 0.452876 + 0.784405i
\(207\) −13.5000 23.3827i −0.938315 1.62521i
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) 10.5000 18.1865i 0.726300 1.25799i
\(210\) 0 0
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) 3.00000 0.206041
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) −9.00000 −0.615227
\(215\) −1.50000 + 2.59808i −0.102299 + 0.177187i
\(216\) 5.19615i 0.353553i
\(217\) 0 0
\(218\) −6.50000 + 11.2583i −0.440236 + 0.762510i
\(219\) 19.0526i 1.28745i
\(220\) −4.50000 + 7.79423i −0.303390 + 0.525487i
\(221\) 1.50000 2.59808i 0.100901 0.174766i
\(222\) 1.50000 + 0.866025i 0.100673 + 0.0581238i
\(223\) −0.500000 + 0.866025i −0.0334825 + 0.0579934i −0.882281 0.470723i \(-0.843993\pi\)
0.848799 + 0.528716i \(0.177326\pi\)
\(224\) 0 0
\(225\) 6.00000 + 10.3923i 0.400000 + 0.692820i
\(226\) −4.50000 + 7.79423i −0.299336 + 0.518464i
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 12.1244i 0.802955i
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 13.5000 + 23.3827i 0.890164 + 1.54181i
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 3.00000 0.196116
\(235\) 0 0
\(236\) 0 0
\(237\) 27.7128i 1.80014i
\(238\) 0 0
\(239\) 1.50000 + 2.59808i 0.0970269 + 0.168056i 0.910453 0.413613i \(-0.135733\pi\)
−0.813426 + 0.581669i \(0.802400\pi\)
\(240\) 5.19615i 0.335410i
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −4.50000 + 2.59808i −0.286910 + 0.165647i
\(247\) 7.00000 0.445399
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) −13.5000 + 7.79423i −0.855528 + 0.493939i
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) −2.00000 3.46410i −0.125491 0.217357i
\(255\) 15.5885i 0.976187i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 1.50000 + 0.866025i 0.0933859 + 0.0539164i
\(259\) 0 0
\(260\) −3.00000 −0.186052
\(261\) −9.00000 −0.557086
\(262\) −7.50000 12.9904i −0.463352 0.802548i
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 4.50000 + 2.59808i 0.276956 + 0.159901i
\(265\) 4.50000 + 7.79423i 0.276433 + 0.478796i
\(266\) 0 0
\(267\) 4.50000 2.59808i 0.275396 0.159000i
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) 7.50000 + 12.9904i 0.457283 + 0.792038i 0.998816 0.0486418i \(-0.0154893\pi\)
−0.541533 + 0.840679i \(0.682156\pi\)
\(270\) 13.5000 7.79423i 0.821584 0.474342i
\(271\) 2.50000 4.33013i 0.151864 0.263036i −0.780049 0.625719i \(-0.784806\pi\)
0.931913 + 0.362682i \(0.118139\pi\)
\(272\) 1.50000 2.59808i 0.0909509 0.157532i
\(273\) 0 0
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) −12.0000 −0.723627
\(276\) 13.5000 7.79423i 0.812605 0.469157i
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) 3.50000 6.06218i 0.209916 0.363585i
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 10.5000 18.1865i 0.626377 1.08492i −0.361895 0.932219i \(-0.617870\pi\)
0.988273 0.152699i \(-0.0487965\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 31.5000 18.1865i 1.86590 1.07728i
\(286\) −1.50000 + 2.59808i −0.0886969 + 0.153627i
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 9.00000 0.528498
\(291\) −1.50000 + 0.866025i −0.0879316 + 0.0507673i
\(292\) −11.0000 −0.643726
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) 15.5885i 0.904534i
\(298\) −4.50000 7.79423i −0.260678 0.451508i
\(299\) 4.50000 + 7.79423i 0.260242 + 0.450752i
\(300\) −6.00000 + 3.46410i −0.346410 + 0.200000i
\(301\) 0 0
\(302\) −3.50000 6.06218i −0.201402 0.348839i
\(303\) −4.50000 2.59808i −0.258518 0.149256i
\(304\) 7.00000 0.401478
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) −9.00000 −0.514496
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 19.5000 + 11.2583i 1.10932 + 0.640464i
\(310\) −24.0000 −1.36311
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 1.73205i 0.0980581i
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 4.50000 2.59808i 0.252347 0.145693i
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) −3.00000 −0.167705
\(321\) −13.5000 + 7.79423i −0.753497 + 0.435031i
\(322\) 0 0
\(323\) −21.0000 −1.16847
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) 19.0000 1.05231
\(327\) 22.5167i 1.24517i
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) 0 0
\(330\) 15.5885i 0.858116i
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −4.50000 7.79423i −0.246970 0.427764i
\(333\) 3.00000 0.164399
\(334\) 7.50000 12.9904i 0.410382 0.710802i
\(335\) −6.00000 + 10.3923i −0.327815 + 0.567792i
\(336\) 0 0
\(337\) 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i \(-0.0514616\pi\)
−0.632882 + 0.774248i \(0.718128\pi\)
\(338\) 12.0000 0.652714
\(339\) 15.5885i 0.846649i
\(340\) 9.00000 0.488094
\(341\) −12.0000 + 20.7846i −0.649836 + 1.12555i
\(342\) −10.5000 18.1865i −0.567775 0.983415i
\(343\) 0 0
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 40.5000 + 23.3827i 2.18045 + 1.25888i
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 5.19615i 0.278543i
\(349\) 11.5000 19.9186i 0.615581 1.06622i −0.374701 0.927146i \(-0.622255\pi\)
0.990282 0.139072i \(-0.0444119\pi\)
\(350\) 0 0
\(351\) 4.50000 2.59808i 0.240192 0.138675i
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 0 0
\(355\) −36.0000 −1.91068
\(356\) 1.50000 + 2.59808i 0.0794998 + 0.137698i
\(357\) 0 0
\(358\) −10.5000 + 18.1865i −0.554942 + 0.961188i
\(359\) −4.50000 + 7.79423i −0.237501 + 0.411364i −0.959997 0.280012i \(-0.909662\pi\)
0.722496 + 0.691375i \(0.242995\pi\)
\(360\) 4.50000 + 7.79423i 0.237171 + 0.410792i
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) −1.00000 1.73205i −0.0525588 0.0910346i
\(363\) −3.00000 1.73205i −0.157459 0.0909091i
\(364\) 0 0
\(365\) −16.5000 28.5788i −0.863649 1.49588i
\(366\) −3.00000 + 1.73205i −0.156813 + 0.0905357i
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 4.50000 + 7.79423i 0.234579 + 0.406302i
\(369\) −4.50000 + 7.79423i −0.234261 + 0.405751i
\(370\) −3.00000 −0.155963
\(371\) 0 0
\(372\) 13.8564i 0.718421i
\(373\) −13.0000 −0.673114 −0.336557 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 4.50000 7.79423i 0.232689 0.403030i
\(375\) 4.50000 + 2.59808i 0.232379 + 0.134164i
\(376\) 0 0
\(377\) 3.00000 0.154508
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 10.5000 + 18.1865i 0.538639 + 0.932949i
\(381\) −6.00000 3.46410i −0.307389 0.177471i
\(382\) 0 0
\(383\) −15.0000 −0.766464 −0.383232 0.923652i \(-0.625189\pi\)
−0.383232 + 0.923652i \(0.625189\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 3.00000 0.152499
\(388\) −0.500000 0.866025i −0.0253837 0.0439658i
\(389\) 27.0000 1.36895 0.684477 0.729034i \(-0.260031\pi\)
0.684477 + 0.729034i \(0.260031\pi\)
\(390\) −4.50000 + 2.59808i −0.227866 + 0.131559i
\(391\) −13.5000 23.3827i −0.682724 1.18251i
\(392\) 0 0
\(393\) −22.5000 12.9904i −1.13497 0.655278i
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) −24.0000 41.5692i −1.20757 2.09157i
\(396\) 9.00000 0.452267
\(397\) −6.50000 + 11.2583i −0.326226 + 0.565039i −0.981760 0.190126i \(-0.939110\pi\)
0.655534 + 0.755166i \(0.272444\pi\)
\(398\) 12.5000 21.6506i 0.626568 1.08525i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 27.0000 1.34832 0.674158 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) 6.00000 + 3.46410i 0.299253 + 0.172774i
\(403\) −8.00000 −0.398508
\(404\) 1.50000 2.59808i 0.0746278 0.129259i
\(405\) 13.5000 23.3827i 0.670820 1.16190i
\(406\) 0 0
\(407\) −1.50000 + 2.59808i −0.0743522 + 0.128782i
\(408\) 5.19615i 0.257248i
\(409\) −17.0000 + 29.4449i −0.840596 + 1.45595i 0.0487958 + 0.998809i \(0.484462\pi\)
−0.889392 + 0.457146i \(0.848872\pi\)
\(410\) 4.50000 7.79423i 0.222239 0.384930i
\(411\) −13.5000 7.79423i −0.665906 0.384461i
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) 0 0
\(414\) 13.5000 23.3827i 0.663489 1.14920i
\(415\) 13.5000 23.3827i 0.662689 1.14781i
\(416\) −1.00000 −0.0490290
\(417\) 12.1244i 0.593732i
\(418\) 21.0000 1.02714
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 0 0
\(421\) −17.5000 + 30.3109i −0.852898 + 1.47726i 0.0256838 + 0.999670i \(0.491824\pi\)
−0.878582 + 0.477592i \(0.841510\pi\)
\(422\) 2.50000 4.33013i 0.121698 0.210787i
\(423\) 0 0
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 20.7846i 1.00702i
\(427\) 0 0
\(428\) −4.50000 7.79423i −0.217516 0.376748i
\(429\) 5.19615i 0.250873i
\(430\) −3.00000 −0.144673
\(431\) −13.5000 23.3827i −0.650272 1.12630i −0.983057 0.183301i \(-0.941322\pi\)
0.332785 0.943003i \(-0.392012\pi\)
\(432\) 4.50000 2.59808i 0.216506 0.125000i
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 13.5000 7.79423i 0.647275 0.373705i
\(436\) −13.0000 −0.622587
\(437\) 31.5000 54.5596i 1.50685 2.60994i
\(438\) −16.5000 + 9.52628i −0.788400 + 0.455183i
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 3.00000 0.142695
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 1.73205i 0.0821995i
\(445\) −4.50000 + 7.79423i −0.213320 + 0.369482i
\(446\) −1.00000 −0.0473514
\(447\) −13.5000 7.79423i −0.638528 0.368654i
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −6.00000 + 10.3923i −0.282843 + 0.489898i
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) −9.00000 −0.423324
\(453\) −10.5000 6.06218i −0.493333 0.284826i
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 0 0
\(456\) 10.5000 6.06218i 0.491708 0.283887i
\(457\) 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) 6.50000 + 11.2583i 0.303725 + 0.526067i
\(459\) −13.5000 + 7.79423i −0.630126 + 0.363803i
\(460\) −13.5000 + 23.3827i −0.629441 + 1.09022i
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) 0 0
\(463\) −20.5000 35.5070i −0.952716 1.65015i −0.739511 0.673145i \(-0.764943\pi\)
−0.213205 0.977007i \(-0.568390\pi\)
\(464\) 3.00000 0.139272
\(465\) −36.0000 + 20.7846i −1.66946 + 0.963863i
\(466\) −3.00000 −0.138972
\(467\) −1.50000 + 2.59808i −0.0694117 + 0.120225i −0.898642 0.438682i \(-0.855446\pi\)
0.829231 + 0.558906i \(0.188779\pi\)
\(468\) 1.50000 + 2.59808i 0.0693375 + 0.120096i
\(469\) 0 0
\(470\) 0 0
\(471\) −33.0000 + 19.0526i −1.52056 + 0.877896i
\(472\) 0 0
\(473\) −1.50000 + 2.59808i −0.0689701 + 0.119460i
\(474\) −24.0000 + 13.8564i −1.10236 + 0.636446i
\(475\) −14.0000 + 24.2487i −0.642364 + 1.11261i
\(476\) 0 0
\(477\) 4.50000 7.79423i 0.206041 0.356873i
\(478\) −1.50000 + 2.59808i −0.0686084 + 0.118833i
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) −4.50000 + 2.59808i −0.205396 + 0.118585i
\(481\) −1.00000 −0.0455961
\(482\) 6.50000 + 11.2583i 0.296067 + 0.512803i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 1.50000 2.59808i 0.0681115 0.117973i
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 12.5000 + 21.6506i 0.566429 + 0.981084i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) 28.5000 16.4545i 1.28881 0.744097i
\(490\) 0 0
\(491\) −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i \(-0.323806\pi\)
−0.999552 + 0.0299272i \(0.990472\pi\)
\(492\) −4.50000 2.59808i −0.202876 0.117130i
\(493\) −9.00000 −0.405340
\(494\) 3.50000 + 6.06218i 0.157472 + 0.272750i
\(495\) 13.5000 + 23.3827i 0.606780 + 1.05097i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) −13.5000 7.79423i −0.604949 0.349268i
\(499\) −25.0000 −1.11915 −0.559577 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 25.9808i 1.16073i
\(502\) −6.00000 10.3923i −0.267793 0.463831i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 13.5000 + 23.3827i 0.600148 + 1.03949i
\(507\) 18.0000 10.3923i 0.799408 0.461538i
\(508\) 2.00000 3.46410i 0.0887357 0.153695i
\(509\) 9.00000 0.398918 0.199459 0.979906i \(-0.436082\pi\)
0.199459 + 0.979906i \(0.436082\pi\)
\(510\) 13.5000 7.79423i 0.597790 0.345134i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −31.5000 18.1865i −1.39076 0.802955i
\(514\) 10.5000 + 18.1865i 0.463135 + 0.802174i
\(515\) −39.0000 −1.71855
\(516\) 1.73205i 0.0762493i
\(517\) 0 0
\(518\) 0 0
\(519\) 10.3923i 0.456172i
\(520\) −1.50000 2.59808i −0.0657794 0.113933i
\(521\) 1.50000 + 2.59808i 0.0657162 + 0.113824i 0.897011 0.442007i \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) −3.50000 + 6.06218i −0.153044 + 0.265081i −0.932345 0.361569i \(-0.882241\pi\)
0.779301 + 0.626650i \(0.215574\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 0 0
\(526\) 4.50000 + 7.79423i 0.196209 + 0.339845i
\(527\) 24.0000 1.04546
\(528\) 5.19615i 0.226134i
\(529\) 58.0000 2.52174
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.50000 2.59808i 0.0649722 0.112535i
\(534\) 4.50000 + 2.59808i 0.194734 + 0.112430i
\(535\) 13.5000 23.3827i 0.583656 1.01092i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 36.3731i 1.56961i
\(538\) −7.50000 + 12.9904i −0.323348 + 0.560055i
\(539\) 0 0
\(540\) 13.5000 + 7.79423i 0.580948 + 0.335410i
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) 5.00000 0.214768
\(543\) −3.00000 1.73205i −0.128742 0.0743294i
\(544\) 3.00000 0.128624
\(545\) −19.5000 33.7750i −0.835288 1.44676i
\(546\) 0 0
\(547\) −5.50000 + 9.52628i −0.235163 + 0.407314i −0.959320 0.282321i \(-0.908896\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) −10.5000 18.1865i −0.447315 0.774772i
\(552\) 13.5000 + 7.79423i 0.574598 + 0.331744i
\(553\) 0 0
\(554\) −0.500000 0.866025i −0.0212430 0.0367939i
\(555\) −4.50000 + 2.59808i −0.191014 + 0.110282i
\(556\) 7.00000 0.296866
\(557\) 4.50000 + 7.79423i 0.190671 + 0.330252i 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) 12.0000 + 20.7846i 0.508001 + 0.879883i
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 15.5885i 0.658145i
\(562\) 21.0000 0.885832
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) −13.5000 23.3827i −0.567949 0.983717i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) 31.5000 + 18.1865i 1.31939 + 0.761750i
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) 0 0
\(575\) −36.0000 −1.50130
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −12.5000 21.6506i −0.520382 0.901328i −0.999719 0.0236970i \(-0.992456\pi\)
0.479337 0.877631i \(-0.340877\pi\)
\(578\) 8.00000 0.332756
\(579\) −21.0000 + 12.1244i −0.872730 + 0.503871i
\(580\) 4.50000 + 7.79423i 0.186852 + 0.323638i
\(581\) 0 0
\(582\) −1.50000 0.866025i −0.0621770 0.0358979i
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) −5.50000 9.52628i −0.227592 0.394200i
\(585\) −4.50000 + 7.79423i −0.186052 + 0.322252i
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) 1.50000 2.59808i 0.0619116 0.107234i −0.833408 0.552658i \(-0.813614\pi\)
0.895320 + 0.445424i \(0.146947\pi\)
\(588\) 0 0
\(589\) 28.0000 + 48.4974i 1.15372 + 1.99830i
\(590\) 0 0
\(591\) 27.0000 + 15.5885i 1.11063 + 0.641223i
\(592\) −1.00000 −0.0410997
\(593\) 19.5000 33.7750i 0.800769 1.38697i −0.118342 0.992973i \(-0.537758\pi\)
0.919111 0.394000i \(-0.128909\pi\)
\(594\) 13.5000 7.79423i 0.553912 0.319801i
\(595\) 0 0
\(596\) 4.50000 7.79423i 0.184327 0.319264i
\(597\) 43.3013i 1.77220i
\(598\) −4.50000 + 7.79423i −0.184019 + 0.318730i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) −6.00000 3.46410i −0.244949 0.141421i
\(601\) −12.5000 + 21.6506i −0.509886 + 0.883148i 0.490049 + 0.871695i \(0.336979\pi\)
−0.999934 + 0.0114528i \(0.996354\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 3.50000 6.06218i 0.142413 0.246667i
\(605\) 6.00000 0.243935
\(606\) 5.19615i 0.211079i
\(607\) 13.0000 0.527654 0.263827 0.964570i \(-0.415015\pi\)
0.263827 + 0.964570i \(0.415015\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) 0 0
\(612\) −4.50000 7.79423i −0.181902 0.315063i
\(613\) −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 15.5885i 0.628587i
\(616\) 0 0
\(617\) 22.5000 + 38.9711i 0.905816 + 1.56892i 0.819818 + 0.572624i \(0.194074\pi\)
0.0859976 + 0.996295i \(0.472592\pi\)
\(618\) 22.5167i 0.905753i
\(619\) −17.0000 −0.683288 −0.341644 0.939829i \(-0.610984\pi\)
−0.341644 + 0.939829i \(0.610984\pi\)
\(620\) −12.0000 20.7846i −0.481932 0.834730i
\(621\) 46.7654i 1.87663i
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −1.50000 + 0.866025i −0.0600481 + 0.0346688i
\(625\) −29.0000 −1.16000
\(626\) 5.00000 8.66025i 0.199840 0.346133i
\(627\) 31.5000 18.1865i 1.25799 0.726300i
\(628\) −11.0000 19.0526i −0.438948 0.760280i
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −8.00000 13.8564i −0.318223 0.551178i
\(633\) 8.66025i 0.344214i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 12.0000 0.476205
\(636\) 4.50000 + 2.59808i 0.178437 + 0.103020i
\(637\) 0 0
\(638\) 9.00000 0.356313
\(639\) 18.0000 + 31.1769i 0.712069 + 1.23334i
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) −13.5000 7.79423i −0.532803 0.307614i
\(643\) 14.5000 + 25.1147i 0.571824 + 0.990429i 0.996379 + 0.0850262i \(0.0270974\pi\)
−0.424555 + 0.905402i \(0.639569\pi\)
\(644\) 0 0
\(645\) −4.50000 + 2.59808i −0.177187 + 0.102299i
\(646\) −10.5000 18.1865i −0.413117 0.715540i
\(647\) −10.5000 18.1865i −0.412798 0.714986i 0.582397 0.812905i \(-0.302115\pi\)
−0.995194 + 0.0979182i \(0.968782\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) 0 0
\(650\) 2.00000 3.46410i 0.0784465 0.135873i
\(651\) 0 0
\(652\) 9.50000 + 16.4545i 0.372049 + 0.644407i
\(653\) 15.0000 0.586995 0.293498 0.955960i \(-0.405181\pi\)
0.293498 + 0.955960i \(0.405181\pi\)
\(654\) −19.5000 + 11.2583i −0.762510 + 0.440236i
\(655\) 45.0000 1.75830
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) −16.5000 + 28.5788i −0.643726 + 1.11497i
\(658\) 0 0
\(659\) −1.50000 + 2.59808i −0.0584317 + 0.101207i −0.893762 0.448542i \(-0.851943\pi\)
0.835330 + 0.549749i \(0.185277\pi\)
\(660\) −13.5000 + 7.79423i −0.525487 + 0.303390i
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) 4.00000 6.92820i 0.155464 0.269272i
\(663\) 4.50000 2.59808i 0.174766 0.100901i
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 0 0
\(666\) 1.50000 + 2.59808i 0.0581238 + 0.100673i
\(667\) 13.5000 23.3827i 0.522722 0.905381i
\(668\) 15.0000 0.580367
\(669\) −1.50000 + 0.866025i −0.0579934 + 0.0334825i
\(670\) −12.0000 −0.463600
\(671\) −3.00000 5.19615i −0.115814 0.200595i
\(672\) 0 0
\(673\) −17.5000 + 30.3109i −0.674575 + 1.16840i 0.302017 + 0.953302i \(0.402340\pi\)
−0.976593 + 0.215096i \(0.930993\pi\)
\(674\) −6.50000 + 11.2583i −0.250371 + 0.433655i
\(675\) 20.7846i 0.800000i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −15.0000 25.9808i −0.576497 0.998522i −0.995877 0.0907112i \(-0.971086\pi\)
0.419380 0.907811i \(-0.362247\pi\)
\(678\) −13.5000 + 7.79423i −0.518464 + 0.299336i
\(679\) 0 0
\(680\) 4.50000 + 7.79423i 0.172567 + 0.298895i
\(681\) 4.50000 + 2.59808i 0.172440 + 0.0995585i
\(682\) −24.0000 −0.919007
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 10.5000 18.1865i 0.401478 0.695379i
\(685\) 27.0000 1.03162
\(686\) 0 0
\(687\) 19.5000 + 11.2583i 0.743971 + 0.429532i
\(688\) −1.00000 −0.0381246
\(689\) −1.50000 + 2.59808i −0.0571454 + 0.0989788i
\(690\) 46.7654i 1.78033i
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 10.5000 + 18.1865i 0.398288 + 0.689855i
\(696\) 4.50000 2.59808i 0.170572 0.0984798i
\(697\) −4.50000 + 7.79423i −0.170450 + 0.295227i
\(698\) 23.0000 0.870563
\(699\) −4.50000 + 2.59808i −0.170206 + 0.0982683i
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 4.50000 + 2.59808i 0.169842 + 0.0980581i
\(703\) 3.50000 + 6.06218i 0.132005 + 0.228639i
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) −1.50000 2.59808i −0.0564532 0.0977799i
\(707\) 0 0
\(708\) 0 0
\(709\) −13.0000 22.5167i −0.488225 0.845631i 0.511683 0.859174i \(-0.329022\pi\)
−0.999908 + 0.0135434i \(0.995689\pi\)
\(710\) −18.0000 31.1769i −0.675528 1.17005i
\(711\) −24.0000 + 41.5692i −0.900070 + 1.55897i
\(712\) −1.50000 + 2.59808i −0.0562149 + 0.0973670i
\(713\) −36.0000 + 62.3538i −1.34821 + 2.33517i
\(714\) 0 0
\(715\) −4.50000 7.79423i −0.168290 0.291488i
\(716\) −21.0000 −0.784807
\(717\) 5.19615i 0.194054i
\(718\) −9.00000 −0.335877
\(719\) −7.50000 + 12.9904i −0.279703 + 0.484459i −0.971311 0.237814i \(-0.923569\pi\)
0.691608 + 0.722273i \(0.256903\pi\)
\(720\) −4.50000 + 7.79423i −0.167705 + 0.290474i
\(721\) 0 0
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 19.5000 + 11.2583i 0.725213 + 0.418702i
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 3.46410i 0.128565i
\(727\) −6.50000 + 11.2583i −0.241072 + 0.417548i −0.961020 0.276479i \(-0.910832\pi\)
0.719948 + 0.694028i \(0.244166\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 16.5000 28.5788i 0.610692 1.05775i
\(731\) 3.00000 0.110959
\(732\) −3.00000 1.73205i −0.110883 0.0640184i
\(733\) 1.00000 0.0369358 0.0184679 0.999829i \(-0.494121\pi\)
0.0184679 + 0.999829i \(0.494121\pi\)
\(734\) −8.50000 14.7224i −0.313741 0.543415i
\(735\) 0 0
\(736\) −4.50000 + 7.79423i −0.165872 + 0.287299i
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) −9.00000 −0.331295
\(739\) −11.5000 19.9186i −0.423034 0.732717i 0.573200 0.819415i \(-0.305702\pi\)
−0.996235 + 0.0866983i \(0.972368\pi\)
\(740\) −1.50000 2.59808i −0.0551411 0.0955072i
\(741\) 10.5000 + 6.06218i 0.385727 + 0.222700i
\(742\) 0 0
\(743\) −10.5000 18.1865i −0.385208 0.667199i 0.606590 0.795015i \(-0.292537\pi\)
−0.991798 + 0.127815i \(0.959204\pi\)
\(744\) −12.0000 + 6.92820i −0.439941 + 0.254000i
\(745\) 27.0000 0.989203
\(746\) −6.50000 11.2583i −0.237982 0.412197i
\(747\) −27.0000 −0.987878
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) 5.19615i 0.189737i
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 0 0
\(753\) −18.0000 10.3923i −0.655956 0.378717i
\(754\) 1.50000 + 2.59808i 0.0546268 + 0.0946164i
\(755\) 21.0000 0.764268
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) 40.5000 + 23.3827i 1.47006 + 0.848738i
\(760\) −10.5000 + 18.1865i −0.380875 + 0.659695i
\(761\) 45.0000 1.63125 0.815624 0.578582i \(-0.196394\pi\)
0.815624 + 0.578582i \(0.196394\pi\)
\(762\) 6.92820i 0.250982i
\(763\) 0 0
\(764\) 0 0
\(765\) 13.5000 23.3827i 0.488094 0.845403i
\(766\) −7.50000 12.9904i −0.270986 0.469362i
\(767\) 0 0
\(768\) −1.50000 + 0.866025i −0.0541266 + 0.0312500i
\(769\) 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) 0 0
\(771\) 31.5000 + 18.1865i 1.13444 + 0.654972i
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) 13.5000 + 23.3827i 0.485561 + 0.841017i 0.999862 0.0165929i \(-0.00528194\pi\)
−0.514301 + 0.857610i \(0.671949\pi\)
\(774\) 1.50000 + 2.59808i 0.0539164 + 0.0933859i
\(775\) 16.0000 27.7128i 0.574737 0.995474i
\(776\) 0.500000 0.866025i 0.0179490 0.0310885i
\(777\) 0 0
\(778\) 13.5000 + 23.3827i 0.483998 + 0.838310i
\(779\) −21.0000 −0.752403
\(780\) −4.50000 2.59808i −0.161126 0.0930261i
\(781\) −36.0000 −1.28818
\(782\) 13.5000 23.3827i 0.482759 0.836163i
\(783\) −13.5000 7.79423i −0.482451 0.278543i
\(784\) 0 0
\(785\) 33.0000 57.1577i 1.17782 2.04004i
\(786\) 25.9808i 0.926703i
\(787\) −14.0000 + 24.2487i −0.499046 + 0.864373i −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) −9.00000 + 15.5885i −0.320612 + 0.555316i
\(789\) 13.5000 + 7.79423i 0.480613 + 0.277482i
\(790\) 24.0000 41.5692i 0.853882 1.47897i
\(791\) 0 0
\(792\) 4.50000 + 7.79423i 0.159901 + 0.276956i
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) −13.0000 −0.461353
\(795\) 15.5885i 0.552866i
\(796\) 25.0000 0.886102
\(797\) −10.5000 18.1865i −0.371929 0.644200i 0.617933 0.786231i \(-0.287970\pi\)
−0.989862 + 0.142031i \(0.954637\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.00000 3.46410i 0.0707107 0.122474i
\(801\) 9.00000 0.317999
\(802\) 13.5000 + 23.3827i 0.476702 + 0.825671i
\(803\) −16.5000 28.5788i −0.582272 1.00853i
\(804\) 6.92820i 0.244339i
\(805\) 0 0
\(806\) −4.00000 6.92820i −0.140894 0.244036i
\(807\) 25.9808i 0.914566i
\(808\) 3.00000 0.105540
\(809\) 16.5000 + 28.5788i 0.580109 + 1.00478i 0.995466 + 0.0951198i \(0.0303234\pi\)
−0.415357 + 0.909659i \(0.636343\pi\)
\(810\) 27.0000 0.948683
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 7.50000 4.33013i 0.263036 0.151864i
\(814\) −3.00000 −0.105150
\(815\) −28.5000 + 49.3634i −0.998311 + 1.72913i
\(816\) 4.50000 2.59808i 0.157532 0.0909509i
\(817\) 3.50000 + 6.06218i 0.122449 + 0.212089i
\(818\) −34.0000 −1.18878
\(819\) 0 0
\(820\) 9.00000 0.314294
\(821\) 21.0000 + 36.3731i 0.732905 + 1.26943i 0.955636 + 0.294549i \(0.0951694\pi\)
−0.222731 + 0.974880i \(0.571497\pi\)
\(822\) 15.5885i 0.543710i
\(823\) 20.0000 34.6410i 0.697156 1.20751i −0.272292 0.962215i \(-0.587782\pi\)
0.969448 0.245295i \(-0.0788849\pi\)
\(824\) −13.0000 −0.452876
\(825\) −18.0000 10.3923i −0.626680 0.361814i
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 27.0000 0.938315
\(829\) 5.50000 + 9.52628i 0.191023 + 0.330861i 0.945589 0.325362i \(-0.105486\pi\)
−0.754567 + 0.656223i \(0.772153\pi\)
\(830\) 27.0000 0.937184
\(831\) −1.50000 0.866025i −0.0520344 0.0300421i
\(832\) −0.500000 0.866025i −0.0173344 0.0300240i
\(833\) 0 0
\(834\) 10.5000 6.06218i 0.363585 0.209916i
\(835\) 22.5000 + 38.9711i 0.778645 + 1.34865i
\(836\) 10.5000 + 18.1865i 0.363150 + 0.628994i
\(837\) 36.0000 + 20.7846i 1.24434 + 0.718421i
\(838\) −4.50000 + 7.79423i −0.155450 + 0.269247i
\(839\) 7.50000 12.9904i 0.258929 0.448478i −0.707026 0.707187i \(-0.749964\pi\)
0.965955 + 0.258709i \(0.0832972\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) −35.0000 −1.20618
\(843\) 31.5000 18.1865i 1.08492 0.626377i
\(844\) 5.00000 0.172107
\(845\) −18.0000 + 31.1769i −0.619219 + 1.07252i
\(846\) 0 0
\(847\) 0 0
\(848\) −1.50000 + 2.59808i −0.0515102 + 0.0892183i
\(849\) −6.00000 + 3.46410i −0.205919 + 0.118888i
\(850\) −6.00000 + 10.3923i −0.205798 + 0.356453i
\(851\) −4.50000 + 7.79423i −0.154258 + 0.267183i
\(852\) −18.0000 + 10.3923i −0.616670 + 0.356034i
\(853\) −0.500000 + 0.866025i −0.0171197 + 0.0296521i −0.874458 0.485101i \(-0.838783\pi\)
0.857339 + 0.514753i \(0.172116\pi\)
\(854\) 0 0
\(855\) 63.0000 2.15455
\(856\) 4.50000 7.79423i 0.153807 0.266401i
\(857\) −3.00000 −0.102478 −0.0512390 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) −4.50000 + 2.59808i −0.153627 + 0.0886969i
\(859\) 25.0000 0.852989 0.426494 0.904490i \(-0.359748\pi\)
0.426494 + 0.904490i \(0.359748\pi\)
\(860\) −1.50000 2.59808i −0.0511496 0.0885937i
\(861\) 0 0
\(862\) 13.5000 23.3827i 0.459812 0.796417i
\(863\) 25.5000 44.1673i 0.868030 1.50347i 0.00402340 0.999992i \(-0.498719\pi\)
0.864007 0.503480i \(-0.167947\pi\)
\(864\) 4.50000 + 2.59808i 0.153093 + 0.0883883i
\(865\) 9.00000 + 15.5885i 0.306009 + 0.530023i
\(866\) −1.00000 1.73205i −0.0339814 0.0588575i
\(867\) 12.0000 6.92820i 0.407541 0.235294i
\(868\) 0 0
\(869\) −24.0000 41.5692i −0.814144 1.41014i
\(870\) 13.5000 + 7.79423i 0.457693 + 0.264249i
\(871\) −4.00000 −0.135535
\(872\) −6.50000 11.2583i −0.220118 0.381255i
\(873\) −3.00000 −0.101535
\(874\) 63.0000 2.13101
\(875\) 0 0
\(876\) −16.5000 9.52628i −0.557483 0.321863i
\(877\) 47.0000 1.58708 0.793539 0.608520i \(-0.208236\pi\)
0.793539 + 0.608520i \(0.208236\pi\)
\(878\) −4.00000 + 6.92820i −0.134993 + 0.233816i
\(879\) 15.5885i 0.525786i
\(880\) −4.50000 7.79423i −0.151695 0.262743i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 1.50000 + 2.59808i 0.0504505 + 0.0873828i
\(885\) 0 0
\(886\) 18.0000 31.1769i 0.604722 1.04741i
\(887\) 33.0000 1.10803 0.554016 0.832506i \(-0.313095\pi\)
0.554016 + 0.832506i \(0.313095\pi\)
\(888\) −1.50000 + 0.866025i −0.0503367 + 0.0290619i
\(889\) 0 0
\(890\) −9.00000 −0.301681
\(891\) 13.5000 23.3827i 0.452267 0.783349i
\(892\) −0.500000 0.866025i −0.0167412 0.0289967i
\(893\) 0 0
\(894\) 15.5885i 0.521356i
\(895\) −31.5000 54.5596i −1.05293 1.82373i
\(896\) 0 0
\(897\) 15.5885i 0.520483i
\(898\) 3.00000 + 5.19615i 0.100111 + 0.173398i
\(899\) 12.0000 + 20.7846i 0.400222 + 0.693206i
\(900\) −12.0000 −0.400000
\(901\) 4.50000 7.79423i 0.149917 0.259663i
\(902\) 4.50000 7.79423i 0.149834 0.259519i
\(903\) 0 0
\(904\) −4.50000 7.79423i −0.149668 0.259232i
\(905\) 6.00000 0.199447
\(906\) 12.1244i 0.402805i
\(907\) −43.0000 −1.42779 −0.713896 0.700252i \(-0.753071\pi\)
−0.713896 + 0.700252i \(0.753071\pi\)
\(908\) −1.50000 + 2.59808i −0.0497792 + 0.0862202i
\(909\) −4.50000 7.79423i −0.149256 0.258518i
\(910\) 0 0
\(911\) −19.5000 + 33.7750i −0.646064 + 1.11902i 0.337991 + 0.941149i \(0.390253\pi\)
−0.984055 + 0.177866i \(0.943081\pi\)
\(912\) 10.5000 + 6.06218i 0.347690 + 0.200739i
\(913\) 13.5000 23.3827i 0.446785 0.773854i
\(914\) −5.00000 + 8.66025i −0.165385 + 0.286456i
\(915\) 10.3923i 0.343559i
\(916\) −6.50000 + 11.2583i −0.214766 + 0.371986i
\(917\) 0 0
\(918\) −13.5000 7.79423i −0.445566 0.257248i
\(919\) −26.5000 + 45.8993i −0.874154 + 1.51408i −0.0164935 + 0.999864i \(0.505250\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) −27.0000 −0.890164
\(921\) 42.0000 + 24.2487i 1.38395 + 0.799022i
\(922\) −9.00000 −0.296399
\(923\) −6.00000 10.3923i −0.197492 0.342067i
\(924\) 0 0
\(925\) 2.00000 3.46410i 0.0657596 0.113899i
\(926\) 20.5000 35.5070i 0.673672 1.16683i
\(927\) 19.5000 + 33.7750i 0.640464 + 1.10932i
\(928\) 1.50000 + 2.59808i 0.0492399 + 0.0852860i
\(929\) 9.00000 + 15.5885i 0.295280 + 0.511441i 0.975050 0.221985i \(-0.0712536\pi\)
−0.679770 + 0.733426i \(0.737920\pi\)
\(930\) −36.0000 20.7846i −1.18049 0.681554i
\(931\) 0 0
\(932\) −1.50000 2.59808i −0.0491341 0.0851028i
\(933\) −36.0000 + 20.7846i −1.17859 + 0.680458i
\(934\) −3.00000 −0.0981630
\(935\) 13.5000 + 23.3827i 0.441497 + 0.764696i
\(936\) −1.50000 + 2.59808i −0.0490290 + 0.0849208i
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 0 0
\(939\) 17.3205i 0.565233i
\(940\) 0 0
\(941\) −3.00000 + 5.19615i −0.0977972 + 0.169390i −0.910773 0.412908i \(-0.864513\pi\)
0.812975 + 0.582298i \(0.197846\pi\)
\(942\) −33.0000 19.0526i −1.07520 0.620766i
\(943\) −13.5000 23.3827i −0.439620 0.761445i
\(944\) 0 0
\(945\) 0 0
\(946\) −3.00000 −0.0975384
\(947\) −6.00000 10.3923i −0.194974 0.337705i 0.751918 0.659256i \(-0.229129\pi\)
−0.946892 + 0.321552i \(0.895796\pi\)
\(948\) −24.0000 13.8564i −0.779484 0.450035i
\(949\) 5.50000 9.52628i 0.178538 0.309236i
\(950\) −28.0000 −0.908440
\(951\) 31.1769i 1.01098i
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 9.00000 0.291386
\(955\) 0 0
\(956\) −3.00000 −0.0970269
\(957\) 13.5000 7.79423i 0.436393 0.251952i
\(958\) 1.50000 + 2.59808i 0.0484628 + 0.0839400i
\(959\) 0 0
\(960\) −4.50000 2.59808i −0.145237 0.0838525i
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) −0.500000 0.866025i −0.0161206 0.0279218i
\(963\) −27.0000 −0.870063
\(964\) −6.50000 + 11.2583i −0.209351 + 0.362606i
\(965\) 21.0000 36.3731i 0.676014 1.17089i
\(966\) 0 0
\(967\) −20.5000 35.5070i −0.659236 1.14183i −0.980814 0.194946i \(-0.937547\pi\)
0.321578 0.946883i \(-0.395787\pi\)
\(968\) 2.00000 0.0642824
\(969\) −31.5000 18.1865i −1.01193 0.584236i
\(970\) 3.00000 0.0963242
\(971\) 16.5000 28.5788i 0.529510 0.917139i −0.469897 0.882721i \(-0.655709\pi\)
0.999408 0.0344175i \(-0.0109576\pi\)
\(972\) 15.5885i 0.500000i
\(973\) 0 0
\(974\) −12.5000 + 21.6506i −0.400526 + 0.693731i
\(975\) 6.92820i 0.221880i
\(976\) 1.00000 1.73205i 0.0320092 0.0554416i
\(977\) 15.0000 25.9808i 0.479893 0.831198i −0.519841 0.854263i \(-0.674009\pi\)
0.999734 + 0.0230645i \(0.00734232\pi\)
\(978\) 28.5000 + 16.4545i 0.911330 + 0.526156i
\(979\) −4.50000 + 7.79423i −0.143821 + 0.249105i
\(980\) 0 0
\(981\) −19.5000 + 33.7750i −0.622587 + 1.07835i
\(982\) 10.5000 18.1865i 0.335068 0.580356i
\(983\) 15.0000 0.478426 0.239213 0.970967i \(-0.423111\pi\)
0.239213 + 0.970967i \(0.423111\pi\)
\(984\) 5.19615i 0.165647i
\(985\) −54.0000 −1.72058
\(986\) −4.50000 7.79423i −0.143309 0.248219i
\(987\) 0 0
\(988\) −3.50000 + 6.06218i −0.111350 + 0.192864i
\(989\) −4.50000 + 7.79423i −0.143092 + 0.247842i
\(990\) −13.5000 + 23.3827i −0.429058 + 0.743151i
\(991\) 12.5000 + 21.6506i 0.397076 + 0.687755i 0.993364 0.115015i \(-0.0366917\pi\)
−0.596288 + 0.802771i \(0.703358\pi\)
\(992\) −4.00000 6.92820i −0.127000 0.219971i
\(993\) 13.8564i 0.439720i
\(994\) 0 0
\(995\) 37.5000 + 64.9519i 1.18883 + 2.05911i
\(996\) 15.5885i 0.493939i
\(997\) 13.0000 0.411714 0.205857 0.978582i \(-0.434002\pi\)
0.205857 + 0.978582i \(0.434002\pi\)
\(998\) −12.5000 21.6506i −0.395681 0.685339i
\(999\) 4.50000 + 2.59808i 0.142374 + 0.0821995i
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 882.2.h.i.79.1 2
3.2 odd 2 2646.2.h.d.667.1 2
7.2 even 3 882.2.f.g.295.1 2
7.3 odd 6 126.2.e.a.25.1 2
7.4 even 3 882.2.e.c.655.1 2
7.5 odd 6 882.2.f.i.295.1 2
7.6 odd 2 126.2.h.b.79.1 yes 2
9.4 even 3 882.2.e.c.373.1 2
9.5 odd 6 2646.2.e.g.1549.1 2
21.2 odd 6 2646.2.f.a.883.1 2
21.5 even 6 2646.2.f.d.883.1 2
21.11 odd 6 2646.2.e.g.2125.1 2
21.17 even 6 378.2.e.b.235.1 2
21.20 even 2 378.2.h.a.289.1 2
28.3 even 6 1008.2.q.a.529.1 2
28.27 even 2 1008.2.t.f.961.1 2
63.2 odd 6 7938.2.a.be.1.1 1
63.4 even 3 inner 882.2.h.i.67.1 2
63.5 even 6 2646.2.f.d.1765.1 2
63.13 odd 6 126.2.e.a.121.1 yes 2
63.16 even 3 7938.2.a.b.1.1 1
63.20 even 6 1134.2.g.c.163.1 2
63.23 odd 6 2646.2.f.a.1765.1 2
63.31 odd 6 126.2.h.b.67.1 yes 2
63.32 odd 6 2646.2.h.d.361.1 2
63.34 odd 6 1134.2.g.e.163.1 2
63.38 even 6 1134.2.g.c.487.1 2
63.40 odd 6 882.2.f.i.589.1 2
63.41 even 6 378.2.e.b.37.1 2
63.47 even 6 7938.2.a.t.1.1 1
63.52 odd 6 1134.2.g.e.487.1 2
63.58 even 3 882.2.f.g.589.1 2
63.59 even 6 378.2.h.a.361.1 2
63.61 odd 6 7938.2.a.m.1.1 1
84.59 odd 6 3024.2.q.f.2881.1 2
84.83 odd 2 3024.2.t.a.289.1 2
252.31 even 6 1008.2.t.f.193.1 2
252.59 odd 6 3024.2.t.a.1873.1 2
252.139 even 6 1008.2.q.a.625.1 2
252.167 odd 6 3024.2.q.f.2305.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.a.25.1 2 7.3 odd 6
126.2.e.a.121.1 yes 2 63.13 odd 6
126.2.h.b.67.1 yes 2 63.31 odd 6
126.2.h.b.79.1 yes 2 7.6 odd 2
378.2.e.b.37.1 2 63.41 even 6
378.2.e.b.235.1 2 21.17 even 6
378.2.h.a.289.1 2 21.20 even 2
378.2.h.a.361.1 2 63.59 even 6
882.2.e.c.373.1 2 9.4 even 3
882.2.e.c.655.1 2 7.4 even 3
882.2.f.g.295.1 2 7.2 even 3
882.2.f.g.589.1 2 63.58 even 3
882.2.f.i.295.1 2 7.5 odd 6
882.2.f.i.589.1 2 63.40 odd 6
882.2.h.i.67.1 2 63.4 even 3 inner
882.2.h.i.79.1 2 1.1 even 1 trivial
1008.2.q.a.529.1 2 28.3 even 6
1008.2.q.a.625.1 2 252.139 even 6
1008.2.t.f.193.1 2 252.31 even 6
1008.2.t.f.961.1 2 28.27 even 2
1134.2.g.c.163.1 2 63.20 even 6
1134.2.g.c.487.1 2 63.38 even 6
1134.2.g.e.163.1 2 63.34 odd 6
1134.2.g.e.487.1 2 63.52 odd 6
2646.2.e.g.1549.1 2 9.5 odd 6
2646.2.e.g.2125.1 2 21.11 odd 6
2646.2.f.a.883.1 2 21.2 odd 6
2646.2.f.a.1765.1 2 63.23 odd 6
2646.2.f.d.883.1 2 21.5 even 6
2646.2.f.d.1765.1 2 63.5 even 6
2646.2.h.d.361.1 2 63.32 odd 6
2646.2.h.d.667.1 2 3.2 odd 2
3024.2.q.f.2305.1 2 252.167 odd 6
3024.2.q.f.2881.1 2 84.59 odd 6
3024.2.t.a.289.1 2 84.83 odd 2
3024.2.t.a.1873.1 2 252.59 odd 6
7938.2.a.b.1.1 1 63.16 even 3
7938.2.a.m.1.1 1 63.61 odd 6
7938.2.a.t.1.1 1 63.47 even 6
7938.2.a.be.1.1 1 63.2 odd 6