Properties

Label 882.2.f.i.295.1
Level $882$
Weight $2$
Character 882.295
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(295,882)]
 
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([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), 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 295.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.i.589.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} -3.00000 q^{10} +(1.50000 - 2.59808i) 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} +3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{26} -5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(-4.50000 + 2.59808i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} -5.19615i q^{33} +(1.50000 - 2.59808i) q^{34} -3.00000 q^{36} -1.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} -9.00000 q^{45} +9.00000 q^{46} +1.73205i q^{48} +(2.00000 + 3.46410i) q^{50} +(4.50000 - 2.59808i) q^{51} +(0.500000 - 0.866025i) q^{52} +3.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} -9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(1.50000 + 2.59808i) q^{58} +5.19615i q^{60} +(-1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-4.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(13.5000 + 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +11.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} +6.92820i q^{75} +(3.50000 + 6.06218i) q^{76} +(1.50000 - 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} +3.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -3.00000 q^{82} +(4.50000 - 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 - 0.866025i) q^{86} +5.19615i q^{87} +(-1.50000 + 2.59808i) q^{88} +3.00000 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} - 2 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} + q^{13} - 9 q^{15} - q^{16} + 6 q^{17} - 3 q^{18} - 14 q^{19} - 3 q^{20} - 3 q^{22} + 9 q^{23} - 3 q^{24} - 4 q^{25} + 2 q^{26} - 3 q^{29} - 9 q^{30} - 8 q^{31} + q^{32} + 3 q^{34} - 6 q^{36} - 2 q^{37} - 7 q^{38} + 3 q^{39} + 3 q^{40} - 3 q^{41} + q^{43} - 6 q^{44} - 18 q^{45} + 18 q^{46} + 4 q^{50} + 9 q^{51} + q^{52} + 6 q^{53} - 9 q^{54} - 18 q^{55} - 21 q^{57} + 3 q^{58} - 2 q^{61} - 16 q^{62} + 2 q^{64} + 3 q^{65} - 9 q^{66} + 4 q^{67} - 3 q^{68} + 27 q^{69} + 24 q^{71} - 3 q^{72} + 22 q^{73} - q^{74} + 7 q^{76} + 3 q^{78} + 16 q^{79} + 6 q^{80} - 9 q^{81} - 6 q^{82} + 9 q^{83} - 9 q^{85} - q^{86} - 3 q^{88} + 6 q^{89} - 9 q^{90} + 9 q^{92} - 24 q^{93} + 21 q^{95} + 3 q^{96} + q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −3.00000 −0.948683
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) −4.50000 2.59808i −1.16190 0.670820i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 4.50000 + 7.79423i 0.938315 + 1.62521i 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 1.00000 0.196116
\(27\) 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 \(0.256518\pi\)
\(30\) −4.50000 + 2.59808i −0.821584 + 0.474342i
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 5.19615i 0.904534i
\(34\) 1.50000 2.59808i 0.257248 0.445566i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −3.50000 + 6.06218i −0.567775 + 0.983415i
\(39\) 1.50000 + 0.866025i 0.240192 + 0.138675i
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −3.00000 −0.452267
\(45\) −9.00000 −1.34164
\(46\) 9.00000 1.32698
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 0 0
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 4.50000 2.59808i 0.630126 0.363803i
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) −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
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 5.19615i 0.670820i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.50000 2.59808i 0.186052 0.322252i
\(66\) −4.50000 2.59808i −0.553912 0.319801i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 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
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 6.92820i 0.800000i
\(76\) 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 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) 3.00000 0.335410
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −3.00000 −0.331295
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 0 0
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) −0.500000 0.866025i −0.0539164 0.0933859i
\(87\) 5.19615i 0.557086i
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) −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 −0.839525 0.543321i \(-0.817167\pi\)
0.890292 + 0.455389i \(0.150500\pi\)
\(98\) 0 0
\(99\) −4.50000 7.79423i −0.452267 0.783349i
\(100\) 4.00000 0.400000
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 5.19615i 0.514496i
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −0.500000 0.866025i −0.0490290 0.0849208i
\(105\) 0 0
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) −13.0000 −1.24517 −0.622587 0.782551i \(-0.713918\pi\)
−0.622587 + 0.782551i \(0.713918\pi\)
\(110\) −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 \(0.694196\pi\)
\(114\) 12.1244i 1.13555i
\(115\) 13.5000 23.3827i 1.25888 2.18045i
\(116\) 3.00000 0.278543
\(117\) 3.00000 0.277350
\(118\) 0 0
\(119\) 0 0
\(120\) 4.50000 + 2.59808i 0.410792 + 0.237171i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) −4.50000 2.59808i −0.405751 0.234261i
\(124\) −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
\(129\) 1.73205i 0.152499i
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) −4.50000 + 2.59808i −0.391675 + 0.226134i
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −13.5000 + 7.79423i −1.16190 + 0.670820i
\(136\) −3.00000 −0.257248
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) 13.5000 7.79423i 1.14920 0.663489i
\(139\) 3.50000 + 6.06218i 0.296866 + 0.514187i 0.975417 0.220366i \(-0.0707252\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 3.00000 0.250873
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 9.00000 0.747409
\(146\) 5.50000 9.52628i 0.455183 0.788400i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 4.50000 + 7.79423i 0.368654 + 0.638528i 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) 6.00000 + 3.46410i 0.489898 + 0.282843i
\(151\) 3.50000 6.06218i 0.284826 0.493333i −0.687741 0.725956i \(-0.741398\pi\)
0.972567 + 0.232623i \(0.0747309\pi\)
\(152\) 7.00000 0.567775
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) 0 0
\(155\) −12.0000 + 20.7846i −0.963863 + 1.66946i
\(156\) 1.73205i 0.138675i
\(157\) 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i \(0.174386\pi\)
0.0242497 + 0.999706i \(0.492280\pi\)
\(158\) −8.00000 13.8564i −0.636446 1.10236i
\(159\) 4.50000 2.59808i 0.356873 0.206041i
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) −13.5000 + 7.79423i −1.05097 + 0.606780i
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 7.50000 + 12.9904i 0.580367 + 1.00523i 0.995436 + 0.0954356i \(0.0304244\pi\)
−0.415068 + 0.909790i \(0.636242\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −9.00000 −0.690268
\(171\) −10.5000 + 18.1865i −0.802955 + 1.39076i
\(172\) −1.00000 −0.0762493
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 4.50000 + 2.59808i 0.341144 + 0.196960i
\(175\) 0 0
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) 1.50000 2.59808i 0.112430 0.194734i
\(179\) −21.0000 −1.56961 −0.784807 0.619740i \(-0.787238\pi\)
−0.784807 + 0.619740i \(0.787238\pi\)
\(180\) 4.50000 + 7.79423i 0.335410 + 0.580948i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 3.46410i 0.256074i
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 1.50000 0.866025i 0.108253 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −0.500000 0.866025i −0.0358979 0.0621770i
\(195\) 5.19615i 0.372104i
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −9.00000 −0.639602
\(199\) −25.0000 −1.77220 −0.886102 0.463491i \(-0.846597\pi\)
−0.886102 + 0.463491i \(0.846597\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 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
\(206\) 13.0000 0.905753
\(207\) 27.0000 1.87663
\(208\) −1.00000 −0.0693375
\(209\) −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 \(0.888391\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 18.0000 10.3923i 1.23334 0.712069i
\(214\) 4.50000 7.79423i 0.307614 0.532803i
\(215\) −3.00000 −0.204598
\(216\) 5.19615i 0.353553i
\(217\) 0 0
\(218\) −6.50000 + 11.2583i −0.440236 + 0.762510i
\(219\) 16.5000 9.52628i 1.11497 0.643726i
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) 1.50000 + 2.59808i 0.100901 + 0.174766i
\(222\) 1.73205i 0.116248i
\(223\) 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 0 0
\(225\) 6.00000 + 10.3923i 0.400000 + 0.692820i
\(226\) 9.00000 0.598671
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 10.5000 + 6.06218i 0.695379 + 0.401478i
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) −13.5000 23.3827i −0.890164 1.54181i
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 1.50000 2.59808i 0.0980581 0.169842i
\(235\) 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 \(0.802400\pi\)
\(240\) 4.50000 2.59808i 0.290474 0.167705i
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) 2.00000 0.128565
\(243\) −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
\(247\) −3.50000 6.06218i −0.222700 0.385727i
\(248\) 4.00000 + 6.92820i 0.254000 + 0.439941i
\(249\) 15.5885i 0.987878i
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) −2.00000 + 3.46410i −0.125491 + 0.217357i
\(255\) −13.5000 7.79423i −0.845403 0.488094i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) −1.50000 0.866025i −0.0933859 0.0539164i
\(259\) 0 0
\(260\) −3.00000 −0.186052
\(261\) 4.50000 + 7.79423i 0.278543 + 0.482451i
\(262\) −15.0000 −0.926703
\(263\) −4.50000 + 7.79423i −0.277482 + 0.480613i −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 5.19615i 0.319801i
\(265\) −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
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) 15.5885i 0.948683i
\(271\) 5.00000 0.303728 0.151864 0.988401i \(-0.451472\pi\)
0.151864 + 0.988401i \(0.451472\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 15.5885i 0.938315i
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 7.00000 0.419832
\(279\) −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 \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −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
\(289\) −8.00000 −0.470588
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 1.73205i 0.101535i
\(292\) −5.50000 9.52628i −0.321863 0.557483i
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) −13.5000 7.79423i −0.783349 0.452267i
\(298\) 9.00000 0.521356
\(299\) −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
\(303\) 5.19615i 0.298511i
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) 6.00000 0.343559
\(306\) −4.50000 7.79423i −0.257248 0.445566i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 19.5000 + 11.2583i 1.10932 + 0.640464i
\(310\) 12.0000 + 20.7846i 0.681554 + 1.18049i
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) −1.50000 0.866025i −0.0849208 0.0490290i
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 5.19615i 0.291386i
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 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
\(325\) −4.00000 −0.221880
\(326\) −9.50000 + 16.4545i −0.526156 + 0.911330i
\(327\) −19.5000 + 11.2583i −1.07835 + 0.622587i
\(328\) 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 −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) −9.00000 −0.493939
\(333\) −1.50000 + 2.59808i −0.0821995 + 0.142374i
\(334\) 15.0000 0.820763
\(335\) 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 \(0.718128\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 13.5000 + 7.79423i 0.733219 + 0.423324i
\(340\) −4.50000 + 7.79423i −0.244047 + 0.422701i
\(341\) −24.0000 −1.29967
\(342\) 10.5000 + 18.1865i 0.567775 + 0.983415i
\(343\) 0 0
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 46.7654i 2.51776i
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 4.50000 2.59808i 0.241225 0.139272i
\(349\) −11.5000 + 19.9186i −0.615581 + 1.06622i 0.374701 + 0.927146i \(0.377745\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) 0 0
\(351\) 4.50000 2.59808i 0.240192 0.138675i
\(352\) 3.00000 0.159901
\(353\) −1.50000 + 2.59808i −0.0798369 + 0.138282i −0.903179 0.429263i \(-0.858773\pi\)
0.823343 + 0.567545i \(0.192107\pi\)
\(354\) 0 0
\(355\) −18.0000 31.1769i −0.955341 1.65470i
\(356\) −1.50000 2.59808i −0.0794998 0.137698i
\(357\) 0 0
\(358\) −10.5000 + 18.1865i −0.554942 + 0.961188i
\(359\) 9.00000 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) 9.00000 0.474342
\(361\) 30.0000 1.57895
\(362\) 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
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) −9.00000 −0.469157
\(369\) −9.00000 −0.468521
\(370\) 3.00000 0.155963
\(371\) 0 0
\(372\) 13.8564i 0.718421i
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) −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
\(383\) −7.50000 12.9904i −0.383232 0.663777i 0.608290 0.793715i \(-0.291856\pi\)
−0.991522 + 0.129937i \(0.958522\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) −1.00000 −0.0507673
\(389\) −13.5000 + 23.3827i −0.684477 + 1.18555i 0.289124 + 0.957292i \(0.406636\pi\)
−0.973601 + 0.228257i \(0.926697\pi\)
\(390\) −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
\(395\) −48.0000 −2.41514
\(396\) −4.50000 + 7.79423i −0.226134 + 0.391675i
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) −12.5000 + 21.6506i −0.626568 + 1.08525i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 6.00000 3.46410i 0.299253 0.172774i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 3.00000 0.149256
\(405\) −13.5000 + 23.3827i −0.670820 + 1.16190i
\(406\) 0 0
\(407\) −1.50000 + 2.59808i −0.0743522 + 0.128782i
\(408\) −4.50000 + 2.59808i −0.222783 + 0.128624i
\(409\) 17.0000 + 29.4449i 0.840596 + 1.45595i 0.889392 + 0.457146i \(0.151128\pi\)
−0.0487958 + 0.998809i \(0.515538\pi\)
\(410\) 4.50000 + 7.79423i 0.222239 + 0.384930i
\(411\) 15.5885i 0.768922i
\(412\) 6.50000 11.2583i 0.320232 0.554658i
\(413\) 0 0
\(414\) 13.5000 23.3827i 0.663489 1.14920i
\(415\) −27.0000 −1.32538
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 10.5000 + 6.06218i 0.514187 + 0.296866i
\(418\) 10.5000 + 18.1865i 0.513572 + 0.889532i
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 0 0
\(421\) −17.5000 + 30.3109i −0.852898 + 1.47726i 0.0256838 + 0.999670i \(0.491824\pi\)
−0.878582 + 0.477592i \(0.841510\pi\)
\(422\) −5.00000 −0.243396
\(423\) 0 0
\(424\) −3.00000 −0.145693
\(425\) −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
\(429\) 4.50000 2.59808i 0.217262 0.125436i
\(430\) −1.50000 + 2.59808i −0.0723364 + 0.125290i
\(431\) 27.0000 1.30054 0.650272 0.759701i \(-0.274655\pi\)
0.650272 + 0.759701i \(0.274655\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 13.5000 7.79423i 0.647275 0.373705i
\(436\) 6.50000 + 11.2583i 0.311294 + 0.539176i
\(437\) −31.5000 54.5596i −1.50685 2.60994i
\(438\) 19.0526i 0.910366i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 3.00000 0.142695
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 1.50000 + 0.866025i 0.0711868 + 0.0410997i
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) −0.500000 0.866025i −0.0236757 0.0410075i
\(447\) 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 \(0.454782\pi\)
\(450\) 12.0000 0.565685
\(451\) −9.00000 −0.423793
\(452\) 4.50000 7.79423i 0.211662 0.366610i
\(453\) 12.1244i 0.569652i
\(454\) −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 −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) 13.0000 0.607450
\(459\) 15.5885i 0.727607i
\(460\) −27.0000 −1.25888
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) −20.5000 35.5070i −0.952716 1.65015i −0.739511 0.673145i \(-0.764943\pi\)
−0.213205 0.977007i \(-0.568390\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 41.5692i 1.92773i
\(466\) 1.50000 2.59808i 0.0694862 0.120354i
\(467\) −3.00000 −0.138823 −0.0694117 0.997588i \(-0.522112\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) −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
\(478\) 3.00000 0.137217
\(479\) 1.50000 2.59808i 0.0685367 0.118709i −0.829721 0.558179i \(-0.811500\pi\)
0.898257 + 0.439470i \(0.144834\pi\)
\(480\) 5.19615i 0.237171i
\(481\) −0.500000 0.866025i −0.0227980 0.0394874i
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −3.00000 −0.136223
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) −25.0000 −1.13286 −0.566429 0.824110i \(-0.691675\pi\)
−0.566429 + 0.824110i \(0.691675\pi\)
\(488\) 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 \(0.990472\pi\)
\(492\) 5.19615i 0.234261i
\(493\) −4.50000 + 7.79423i −0.202670 + 0.351034i
\(494\) −7.00000 −0.314945
\(495\) −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
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 22.5000 + 12.9904i 1.00523 + 0.580367i
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 13.5000 23.3827i 0.600148 1.03949i
\(507\) 20.7846i 0.923077i
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) 4.50000 + 7.79423i 0.199459 + 0.345473i 0.948353 0.317217i \(-0.102748\pi\)
−0.748894 + 0.662690i \(0.769415\pi\)
\(510\) −13.5000 + 7.79423i −0.597790 + 0.345134i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 36.3731i 1.60591i
\(514\) 21.0000 0.926270
\(515\) 19.5000 33.7750i 0.859273 1.48830i
\(516\) −1.50000 + 0.866025i −0.0660338 + 0.0381246i
\(517\) 0 0
\(518\) 0 0
\(519\) 10.3923i 0.456172i
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 9.00000 0.393919
\(523\) −7.00000 −0.306089 −0.153044 0.988219i \(-0.548908\pi\)
−0.153044 + 0.988219i \(0.548908\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) 4.50000 + 7.79423i 0.196209 + 0.339845i
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 4.50000 + 2.59808i 0.195837 + 0.113067i
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) −9.00000 −0.390935
\(531\) 0 0
\(532\) 0 0
\(533\) 1.50000 2.59808i 0.0649722 0.112535i
\(534\) 5.19615i 0.224860i
\(535\) −13.5000 23.3827i −0.583656 1.01092i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) −31.5000 + 18.1865i −1.35933 + 0.784807i
\(538\) 7.50000 12.9904i 0.323348 0.560055i
\(539\) 0 0
\(540\) 13.5000 + 7.79423i 0.580948 + 0.335410i
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) 2.50000 4.33013i 0.107384 0.185995i
\(543\) 3.00000 1.73205i 0.128742 0.0743294i
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 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 \(0.242229\pi\)
\(548\) −9.00000 −0.384461
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 12.0000 0.511682
\(551\) 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
\(556\) 3.50000 6.06218i 0.148433 0.257094i
\(557\) −9.00000 −0.381342 −0.190671 0.981654i \(-0.561066\pi\)
−0.190671 + 0.981654i \(0.561066\pi\)
\(558\) −12.0000 + 20.7846i −0.508001 + 0.879883i
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) 15.5885i 0.658145i
\(562\) −10.5000 18.1865i −0.442916 0.767153i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 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 −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 31.5000 18.1865i 1.31939 0.761750i
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −1.50000 2.59808i −0.0627182 0.108631i
\(573\) 0 0
\(574\) 0 0
\(575\) −36.0000 −1.50130
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −25.0000 −1.04076 −0.520382 0.853934i \(-0.674210\pi\)
−0.520382 + 0.853934i \(0.674210\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) −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
\(584\) −11.0000 −0.455183
\(585\) −4.50000 7.79423i −0.186052 0.322252i
\(586\) 9.00000 0.371787
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 0 0
\(589\) 28.0000 + 48.4974i 1.15372 + 1.99830i
\(590\) 0 0
\(591\) 27.0000 15.5885i 1.11063 0.641223i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) 39.0000 1.60154 0.800769 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) −13.5000 + 7.79423i −0.553912 + 0.319801i
\(595\) 0 0
\(596\) 4.50000 7.79423i 0.184327 0.319264i
\(597\) −37.5000 + 21.6506i −1.53477 + 0.886102i
\(598\) 4.50000 + 7.79423i 0.184019 + 0.318730i
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 6.92820i 0.282843i
\(601\) 12.5000 21.6506i 0.509886 0.883148i −0.490049 0.871695i \(-0.663021\pi\)
0.999934 0.0114528i \(-0.00364562\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) −7.00000 −0.284826
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 4.50000 + 2.59808i 0.182800 + 0.105540i
\(607\) 6.50000 + 11.2583i 0.263827 + 0.456962i 0.967256 0.253804i \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 0 0
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) 0 0
\(612\) −9.00000 −0.363803
\(613\) 23.0000 0.928961 0.464481 0.885583i \(-0.346241\pi\)
0.464481 + 0.885583i \(0.346241\pi\)
\(614\) −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 \(0.472592\pi\)
\(618\) 19.5000 11.2583i 0.784405 0.452876i
\(619\) −8.50000 + 14.7224i −0.341644 + 0.591744i −0.984738 0.174042i \(-0.944317\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 24.0000 0.963863
\(621\) 40.5000 23.3827i 1.62521 0.938315i
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) −1.50000 + 0.866025i −0.0600481 + 0.0346688i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) 36.3731i 1.45260i
\(628\) 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
\(633\) −7.50000 4.33013i −0.298098 0.172107i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) −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
\(640\) −3.00000 −0.118585
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 15.5885i 0.615227i
\(643\) −14.5000 25.1147i −0.571824 0.990429i −0.996379 0.0850262i \(-0.972903\pi\)
0.424555 0.905402i \(-0.360431\pi\)
\(644\) 0 0
\(645\) −4.50000 + 2.59808i −0.177187 + 0.102299i
\(646\) −10.5000 + 18.1865i −0.413117 + 0.715540i
\(647\) −21.0000 −0.825595 −0.412798 0.910823i \(-0.635448\pi\)
−0.412798 + 0.910823i \(0.635448\pi\)
\(648\) 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
\(653\) −7.50000 12.9904i −0.293498 0.508353i 0.681137 0.732156i \(-0.261486\pi\)
−0.974634 + 0.223803i \(0.928153\pi\)
\(654\) 22.5167i 0.880471i
\(655\) −22.5000 + 38.9711i −0.879148 + 1.52273i
\(656\) 3.00000 0.117130
\(657\) 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 \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 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
\(667\) −27.0000 −1.04544
\(668\) 7.50000 12.9904i 0.290184 0.502613i
\(669\) 1.73205i 0.0669650i
\(670\) −6.00000 10.3923i −0.231800 0.401490i
\(671\) 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 \(0.930993\pi\)
\(674\) 13.0000 0.500741
\(675\) 18.0000 + 10.3923i 0.692820 + 0.400000i
\(676\) −12.0000 −0.461538
\(677\) 15.0000 25.9808i 0.576497 0.998522i −0.419380 0.907811i \(-0.637753\pi\)
0.995877 0.0907112i \(-0.0289140\pi\)
\(678\) 13.5000 7.79423i 0.518464 0.299336i
\(679\) 0 0
\(680\) 4.50000 + 7.79423i 0.172567 + 0.298895i
\(681\) 5.19615i 0.199117i
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 21.0000 0.802955
\(685\) −27.0000 −1.03162
\(686\) 0 0
\(687\) 19.5000 + 11.2583i 0.743971 + 0.429532i
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) 1.50000 + 2.59808i 0.0571454 + 0.0989788i
\(690\) −40.5000 23.3827i −1.54181 0.890164i
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 10.5000 18.1865i 0.398288 0.689855i
\(696\) 5.19615i 0.196960i
\(697\) −4.50000 7.79423i −0.170450 0.295227i
\(698\) 11.5000 + 19.9186i 0.435281 + 0.753930i
\(699\) 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 \(0.610402\pi\)
\(702\) 5.19615i 0.196116i
\(703\) 7.00000 0.264010
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 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 −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) −36.0000 −1.35106
\(711\) −24.0000 41.5692i −0.900070 1.55897i
\(712\) −3.00000 −0.112430
\(713\) 36.0000 62.3538i 1.34821 2.33517i
\(714\) 0 0
\(715\) −4.50000 7.79423i −0.168290 0.291488i
\(716\) 10.5000 + 18.1865i 0.392403 + 0.679663i
\(717\) 4.50000 + 2.59808i 0.168056 + 0.0970269i
\(718\) 4.50000 7.79423i 0.167939 0.290878i
\(719\) −15.0000 −0.559406 −0.279703 0.960087i \(-0.590236\pi\)
−0.279703 + 0.960087i \(0.590236\pi\)
\(720\) 4.50000 7.79423i 0.167705 0.290474i
\(721\) 0 0
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 22.5167i 0.837404i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −6.00000 10.3923i −0.222834 0.385961i
\(726\) 3.00000 1.73205i 0.111340 0.0642824i
\(727\) 6.50000 11.2583i 0.241072 0.417548i −0.719948 0.694028i \(-0.755834\pi\)
0.961020 + 0.276479i \(0.0891678\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −33.0000 −1.22138
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 3.00000 1.73205i 0.110883 0.0640184i
\(733\) 0.500000 + 0.866025i 0.0184679 + 0.0319874i 0.875112 0.483921i \(-0.160788\pi\)
−0.856644 + 0.515908i \(0.827454\pi\)
\(734\) 8.50000 + 14.7224i 0.313741 + 0.543415i
\(735\) 0 0
\(736\) −4.50000 + 7.79423i −0.165872 + 0.287299i
\(737\) 12.0000 0.442026
\(738\) −4.50000 + 7.79423i −0.165647 + 0.286910i
\(739\) 23.0000 0.846069 0.423034 0.906114i \(-0.360965\pi\)
0.423034 + 0.906114i \(0.360965\pi\)
\(740\) 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
\(745\) 13.5000 23.3827i 0.494602 0.856675i
\(746\) 13.0000 0.475964
\(747\) −13.5000 23.3827i −0.493939 0.855528i
\(748\) −9.00000 −0.329073
\(749\) 0 0
\(750\) 5.19615i 0.189737i
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 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
\(761\) 22.5000 + 38.9711i 0.815624 + 1.41270i 0.908879 + 0.417061i \(0.136940\pi\)
−0.0932544 + 0.995642i \(0.529727\pi\)
\(762\) 6.92820i 0.250982i
\(763\) 0 0
\(764\) 0 0
\(765\) −27.0000 −0.976187
\(766\) −15.0000 −0.541972
\(767\) 0 0
\(768\) −1.50000 0.866025i −0.0541266 0.0312500i
\(769\) −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i \(-0.302780\pi\)
−0.995397 + 0.0958377i \(0.969447\pi\)
\(770\) 0 0
\(771\) 31.5000 + 18.1865i 1.13444 + 0.654972i
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 27.0000 0.971123 0.485561 0.874203i \(-0.338615\pi\)
0.485561 + 0.874203i \(0.338615\pi\)
\(774\) −3.00000 −0.107833
\(775\) 32.0000 1.14947
\(776\) −0.500000 + 0.866025i −0.0179490 + 0.0310885i
\(777\) 0 0
\(778\) 13.5000 + 23.3827i 0.483998 + 0.838310i
\(779\) 10.5000 + 18.1865i 0.376202 + 0.651600i
\(780\) −4.50000 + 2.59808i −0.161126 + 0.0930261i
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 27.0000 0.965518
\(783\) 13.5000 + 7.79423i 0.482451 + 0.278543i
\(784\) 0 0
\(785\) 33.0000 57.1577i 1.17782 2.04004i
\(786\) −22.5000 + 12.9904i −0.802548 + 0.463352i
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) −9.00000 15.5885i −0.320612 0.555316i
\(789\) 15.5885i 0.554964i
\(790\) −24.0000 + 41.5692i −0.853882 + 1.47897i
\(791\) 0 0
\(792\) 4.50000 + 7.79423i 0.159901 + 0.276956i
\(793\) −2.00000 −0.0710221
\(794\) −6.50000 + 11.2583i −0.230676 + 0.399543i
\(795\) −13.5000 7.79423i −0.478796 0.276433i
\(796\) 12.5000 + 21.6506i 0.443051 + 0.767386i
\(797\) 10.5000 + 18.1865i 0.371929 + 0.644200i 0.989862 0.142031i \(-0.0453631\pi\)
−0.617933 + 0.786231i \(0.712030\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −4.00000 −0.141421
\(801\) 4.50000 7.79423i 0.159000 0.275396i
\(802\) −27.0000 −0.953403
\(803\) 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
\(807\) 22.5000 12.9904i 0.792038 0.457283i
\(808\) 1.50000 2.59808i 0.0527698 0.0914000i
\(809\) −33.0000 −1.16022 −0.580109 0.814539i \(-0.696990\pi\)
−0.580109 + 0.814539i \(0.696990\pi\)
\(810\) 13.5000 + 23.3827i 0.474342 + 0.821584i
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 7.50000 4.33013i 0.263036 0.151864i
\(814\) 1.50000 + 2.59808i 0.0525750 + 0.0910625i
\(815\) 28.5000 + 49.3634i 0.998311 + 1.72913i
\(816\) 5.19615i 0.181902i
\(817\) −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 −0.222731 0.974880i \(-0.571497\pi\)
0.955636 0.294549i \(-0.0951694\pi\)
\(822\) −13.5000 7.79423i −0.470867 0.271855i
\(823\) 20.0000 + 34.6410i 0.697156 + 1.20751i 0.969448 + 0.245295i \(0.0788849\pi\)
−0.272292 + 0.962215i \(0.587782\pi\)
\(824\) −6.50000 11.2583i −0.226438 0.392203i
\(825\) 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 \(0.284723\pi\)
\(828\) −13.5000 23.3827i −0.469157 0.812605i
\(829\) 11.0000 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(830\) −13.5000 + 23.3827i −0.468592 + 0.811625i
\(831\) 1.73205i 0.0600842i
\(832\) 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
\(836\) 21.0000 0.726300
\(837\) −36.0000 + 20.7846i −1.24434 + 0.718421i
\(838\) −9.00000 −0.310900
\(839\) −7.50000 + 12.9904i −0.258929 + 0.448478i −0.965955 0.258709i \(-0.916703\pi\)
0.707026 + 0.707187i \(0.250036\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) 17.5000 + 30.3109i 0.603090 + 1.04458i
\(843\) 36.3731i 1.25275i
\(844\) −2.50000 + 4.33013i −0.0860535 + 0.149049i
\(845\) −36.0000 −1.23844
\(846\) 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 −0.857339 0.514753i \(-0.827884\pi\)
0.874458 + 0.485101i \(0.161217\pi\)
\(854\) 0 0
\(855\) 63.0000 2.15455
\(856\) −9.00000 −0.307614
\(857\) −1.50000 + 2.59808i −0.0512390 + 0.0887486i −0.890507 0.454969i \(-0.849650\pi\)
0.839268 + 0.543718i \(0.182984\pi\)
\(858\) 5.19615i 0.177394i
\(859\) 12.5000 + 21.6506i 0.426494 + 0.738710i 0.996559 0.0828900i \(-0.0264150\pi\)
−0.570064 + 0.821600i \(0.693082\pi\)
\(860\) 1.50000 + 2.59808i 0.0511496 + 0.0885937i
\(861\) 0 0
\(862\) 13.5000 23.3827i 0.459812 0.796417i
\(863\) −51.0000 −1.73606 −0.868030 0.496512i \(-0.834614\pi\)
−0.868030 + 0.496512i \(0.834614\pi\)
\(864\) 4.50000 2.59808i 0.153093 0.0883883i
\(865\) −18.0000 −0.612018
\(866\) 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
\(870\) 15.5885i 0.528498i
\(871\) −2.00000 + 3.46410i −0.0677674 + 0.117377i
\(872\) 13.0000 0.440236
\(873\) −1.50000 2.59808i −0.0507673 0.0879316i
\(874\) −63.0000 −2.13101
\(875\) 0 0
\(876\) −16.5000 9.52628i −0.557483 0.321863i
\(877\) −23.5000 40.7032i −0.793539 1.37445i −0.923763 0.382965i \(-0.874903\pi\)
0.130224 0.991485i \(-0.458430\pi\)
\(878\) 4.00000 + 6.92820i 0.134993 + 0.233816i
\(879\) 13.5000 + 7.79423i 0.455344 + 0.262893i
\(880\) 4.50000 7.79423i 0.151695 0.262743i
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 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
\(887\) 16.5000 + 28.5788i 0.554016 + 0.959583i 0.997979 + 0.0635387i \(0.0202386\pi\)
−0.443964 + 0.896045i \(0.646428\pi\)
\(888\) 1.50000 0.866025i 0.0503367 0.0290619i
\(889\) 0 0
\(890\) −9.00000 −0.301681
\(891\) −27.0000 −0.904534
\(892\) −1.00000 −0.0334825
\(893\) 0 0
\(894\) 13.5000 7.79423i 0.451508 0.260678i
\(895\) 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
\(899\) 24.0000 0.800445
\(900\) 6.00000 10.3923i 0.200000 0.346410i
\(901\) 9.00000 0.299833
\(902\) −4.50000 + 7.79423i −0.149834 + 0.259519i
\(903\) 0 0
\(904\) −4.50000 7.79423i −0.149668 0.259232i
\(905\) −3.00000 5.19615i −0.0997234 0.172726i
\(906\) −10.5000 6.06218i −0.348839 0.201402i
\(907\) 21.5000 37.2391i 0.713896 1.23650i −0.249488 0.968378i \(-0.580262\pi\)
0.963384 0.268126i \(-0.0864043\pi\)
\(908\) −3.00000 −0.0995585
\(909\) 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 \(0.943081\pi\)
\(912\) 12.1244i 0.401478i
\(913\) −13.5000 23.3827i −0.446785 0.773854i
\(914\) −5.00000 8.66025i −0.165385 0.286456i
\(915\) 9.00000 5.19615i 0.297531 0.171780i
\(916\) 6.50000 11.2583i 0.214766 0.371986i
\(917\) 0 0
\(918\) −13.5000 7.79423i −0.445566 0.257248i
\(919\) 53.0000 1.74831 0.874154 0.485648i \(-0.161416\pi\)
0.874154 + 0.485648i \(0.161416\pi\)
\(920\) −13.5000 + 23.3827i −0.445082 + 0.770904i
\(921\) −42.0000 + 24.2487i −1.38395 + 0.799022i
\(922\) −4.50000 7.79423i −0.148200 0.256689i
\(923\) 6.00000 + 10.3923i 0.197492 + 0.342067i
\(924\) 0 0
\(925\) 2.00000 3.46410i 0.0657596 0.113899i
\(926\) −41.0000 −1.34734
\(927\) 39.0000 1.28093
\(928\) −3.00000 −0.0984798
\(929\) −9.00000 + 15.5885i −0.295280 + 0.511441i −0.975050 0.221985i \(-0.928746\pi\)
0.679770 + 0.733426i \(0.262080\pi\)
\(930\) 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
\(934\) −1.50000 + 2.59808i −0.0490815 + 0.0850117i
\(935\) −27.0000 −0.882994
\(936\) −3.00000 −0.0980581
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) 17.3205i 0.565233i
\(940\) 0 0
\(941\) 3.00000 + 5.19615i 0.0977972 + 0.169390i 0.910773 0.412908i \(-0.135487\pi\)
−0.812975 + 0.582298i \(0.802154\pi\)
\(942\) 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 −0.946892 0.321552i \(-0.895796\pi\)
0.751918 + 0.659256i \(0.229129\pi\)
\(948\) −24.0000 + 13.8564i −0.779484 + 0.450035i
\(949\) 5.50000 + 9.52628i 0.178538 + 0.309236i
\(950\) −14.0000 24.2487i −0.454220 0.786732i
\(951\) 31.1769i 1.01098i
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) −4.50000 7.79423i −0.145693 0.252347i
\(955\) 0 0
\(956\) 1.50000 2.59808i 0.0485135 0.0840278i
\(957\) 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
\(962\) −1.00000 −0.0322413
\(963\) 13.5000 23.3827i 0.435031 0.753497i
\(964\) −13.0000 −0.418702
\(965\) −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 \(-0.395787\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) −31.5000 + 18.1865i −1.01193 + 0.584236i
\(970\) −1.50000 + 2.59808i −0.0481621 + 0.0834192i
\(971\) 33.0000 1.05902 0.529510 0.848304i \(-0.322376\pi\)
0.529510 + 0.848304i \(0.322376\pi\)
\(972\) 15.5885i 0.500000i
\(973\) 0 0
\(974\) −12.5000 + 21.6506i −0.400526 + 0.693731i
\(975\) −6.00000 + 3.46410i −0.192154 + 0.110940i
\(976\) −1.00000 1.73205i −0.0320092 0.0554416i
\(977\) 15.0000 + 25.9808i 0.479893 + 0.831198i 0.999734 0.0230645i \(-0.00734232\pi\)
−0.519841 + 0.854263i \(0.674009\pi\)
\(978\) 32.9090i 1.05231i
\(979\) 4.50000 7.79423i 0.143821 0.249105i
\(980\) 0 0
\(981\) −19.5000 + 33.7750i −0.622587 + 1.07835i
\(982\) −21.0000 −0.670137
\(983\) 7.50000 12.9904i 0.239213 0.414329i −0.721276 0.692648i \(-0.756444\pi\)
0.960489 + 0.278319i \(0.0897773\pi\)
\(984\) 4.50000 + 2.59808i 0.143455 + 0.0828236i
\(985\) −27.0000 46.7654i −0.860292 1.49007i
\(986\) 4.50000 + 7.79423i 0.143309 + 0.248219i
\(987\) 0 0
\(988\) −3.50000 + 6.06218i −0.111350 + 0.192864i
\(989\) 9.00000 0.286183
\(990\) 13.5000 + 23.3827i 0.429058 + 0.743151i
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) 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
\(996\) −13.5000 + 7.79423i −0.427764 + 0.246970i
\(997\) 6.50000 11.2583i 0.205857 0.356555i −0.744548 0.667568i \(-0.767335\pi\)
0.950405 + 0.311014i \(0.100668\pi\)
\(998\) 25.0000 0.791361
\(999\) 5.19615i 0.164399i
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.f.i.295.1 2
3.2 odd 2 2646.2.f.d.883.1 2
7.2 even 3 126.2.e.a.25.1 2
7.3 odd 6 882.2.h.i.79.1 2
7.4 even 3 126.2.h.b.79.1 yes 2
7.5 odd 6 882.2.e.c.655.1 2
7.6 odd 2 882.2.f.g.295.1 2
9.2 odd 6 7938.2.a.t.1.1 1
9.4 even 3 inner 882.2.f.i.589.1 2
9.5 odd 6 2646.2.f.d.1765.1 2
9.7 even 3 7938.2.a.m.1.1 1
21.2 odd 6 378.2.e.b.235.1 2
21.5 even 6 2646.2.e.g.2125.1 2
21.11 odd 6 378.2.h.a.289.1 2
21.17 even 6 2646.2.h.d.667.1 2
21.20 even 2 2646.2.f.a.883.1 2
28.11 odd 6 1008.2.t.f.961.1 2
28.23 odd 6 1008.2.q.a.529.1 2
63.2 odd 6 1134.2.g.c.487.1 2
63.4 even 3 126.2.e.a.121.1 yes 2
63.5 even 6 2646.2.h.d.361.1 2
63.11 odd 6 1134.2.g.c.163.1 2
63.13 odd 6 882.2.f.g.589.1 2
63.16 even 3 1134.2.g.e.487.1 2
63.20 even 6 7938.2.a.be.1.1 1
63.23 odd 6 378.2.h.a.361.1 2
63.25 even 3 1134.2.g.e.163.1 2
63.31 odd 6 882.2.e.c.373.1 2
63.32 odd 6 378.2.e.b.37.1 2
63.34 odd 6 7938.2.a.b.1.1 1
63.40 odd 6 882.2.h.i.67.1 2
63.41 even 6 2646.2.f.a.1765.1 2
63.58 even 3 126.2.h.b.67.1 yes 2
63.59 even 6 2646.2.e.g.1549.1 2
84.11 even 6 3024.2.t.a.289.1 2
84.23 even 6 3024.2.q.f.2881.1 2
252.23 even 6 3024.2.t.a.1873.1 2
252.67 odd 6 1008.2.q.a.625.1 2
252.95 even 6 3024.2.q.f.2305.1 2
252.247 odd 6 1008.2.t.f.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.a.25.1 2 7.2 even 3
126.2.e.a.121.1 yes 2 63.4 even 3
126.2.h.b.67.1 yes 2 63.58 even 3
126.2.h.b.79.1 yes 2 7.4 even 3
378.2.e.b.37.1 2 63.32 odd 6
378.2.e.b.235.1 2 21.2 odd 6
378.2.h.a.289.1 2 21.11 odd 6
378.2.h.a.361.1 2 63.23 odd 6
882.2.e.c.373.1 2 63.31 odd 6
882.2.e.c.655.1 2 7.5 odd 6
882.2.f.g.295.1 2 7.6 odd 2
882.2.f.g.589.1 2 63.13 odd 6
882.2.f.i.295.1 2 1.1 even 1 trivial
882.2.f.i.589.1 2 9.4 even 3 inner
882.2.h.i.67.1 2 63.40 odd 6
882.2.h.i.79.1 2 7.3 odd 6
1008.2.q.a.529.1 2 28.23 odd 6
1008.2.q.a.625.1 2 252.67 odd 6
1008.2.t.f.193.1 2 252.247 odd 6
1008.2.t.f.961.1 2 28.11 odd 6
1134.2.g.c.163.1 2 63.11 odd 6
1134.2.g.c.487.1 2 63.2 odd 6
1134.2.g.e.163.1 2 63.25 even 3
1134.2.g.e.487.1 2 63.16 even 3
2646.2.e.g.1549.1 2 63.59 even 6
2646.2.e.g.2125.1 2 21.5 even 6
2646.2.f.a.883.1 2 21.20 even 2
2646.2.f.a.1765.1 2 63.41 even 6
2646.2.f.d.883.1 2 3.2 odd 2
2646.2.f.d.1765.1 2 9.5 odd 6
2646.2.h.d.361.1 2 63.5 even 6
2646.2.h.d.667.1 2 21.17 even 6
3024.2.q.f.2305.1 2 252.95 even 6
3024.2.q.f.2881.1 2 84.23 even 6
3024.2.t.a.289.1 2 84.11 even 6
3024.2.t.a.1873.1 2 252.23 even 6
7938.2.a.b.1.1 1 63.34 odd 6
7938.2.a.m.1.1 1 9.7 even 3
7938.2.a.t.1.1 1 9.2 odd 6
7938.2.a.be.1.1 1 63.20 even 6