Properties

Label 1134.2.g.e.163.1
Level $1134$
Weight $2$
Character 1134.163
Analytic conductor $9.055$
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] = [1134,2,Mod(163,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.g (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: \(9.05503558921\)
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 163.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.163
Dual form 1134.2.g.e.487.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(3.50000 - 6.06218i) q^{19} +3.00000 q^{20} +3.00000 q^{22} +(4.50000 - 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} +3.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(7.50000 + 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(1.50000 - 2.59808i) q^{40} +3.00000 q^{41} -1.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-4.50000 - 7.79423i) q^{46} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +(1.50000 - 2.59808i) q^{58} +(-1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(6.00000 - 5.19615i) q^{70} +12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(-0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(6.00000 - 5.19615i) q^{77} +(8.00000 - 13.8564i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(1.50000 - 2.59808i) q^{82} -9.00000 q^{83} +9.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-1.50000 + 2.59808i) q^{89} +(0.500000 + 2.59808i) q^{91} -9.00000 q^{92} +(10.5000 + 18.1865i) q^{95} -1.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 3 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - 3 q^{5} - q^{7} - 2 q^{8} + 3 q^{10} + 3 q^{11} - 2 q^{13} - 5 q^{14} - q^{16} - 3 q^{17} + 7 q^{19} + 6 q^{20} + 6 q^{22} + 9 q^{23} - 4 q^{25} - q^{26} - 4 q^{28} + 6 q^{29} - 8 q^{31} + q^{32} - 6 q^{34} + 15 q^{35} + q^{37} - 7 q^{38} + 3 q^{40} + 6 q^{41} - 2 q^{43} + 3 q^{44} - 9 q^{46} - 13 q^{49} - 8 q^{50} + q^{52} - 3 q^{53} - 18 q^{55} + q^{56} + 3 q^{58} - 2 q^{61} - 16 q^{62} + 2 q^{64} + 3 q^{65} + 4 q^{67} - 3 q^{68} + 12 q^{70} + 24 q^{71} - 11 q^{73} - q^{74} - 14 q^{76} + 12 q^{77} + 16 q^{79} - 3 q^{80} + 3 q^{82} - 18 q^{83} + 18 q^{85} - q^{86} - 3 q^{88} - 3 q^{89} + q^{91} - 18 q^{92} + 21 q^{95} - 2 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i \(-0.445720\pi\)
0.768613 0.639713i \(-0.220947\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −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
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 7.50000 + 2.59808i 1.26773 + 0.439155i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −3.50000 6.06218i −0.567775 0.983415i
\(39\) 0 0
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) −4.50000 7.79423i −0.663489 1.14920i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 0 0
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −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
\(66\) 0 0
\(67\) 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
\(69\) 0 0
\(70\) 6.00000 5.19615i 0.717137 0.621059i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) 6.00000 5.19615i 0.683763 0.592157i
\(78\) 0 0
\(79\) 8.00000 13.8564i 0.900070 1.55897i 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) 9.00000 0.976187
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) −1.50000 + 2.59808i −0.159000 + 0.275396i −0.934508 0.355942i \(-0.884160\pi\)
0.775509 + 0.631337i \(0.217494\pi\)
\(90\) 0 0
\(91\) 0.500000 + 2.59808i 0.0524142 + 0.272352i
\(92\) −9.00000 −0.938315
\(93\) 0 0
\(94\) 0 0
\(95\) 10.5000 + 18.1865i 1.07728 + 1.86590i
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) −4.50000 + 7.79423i −0.435031 + 0.753497i −0.997298 0.0734594i \(-0.976596\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 13.5000 + 23.3827i 1.25888 + 2.18045i
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) 0 0
\(124\) −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
\(129\) 0 0
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) 0 0
\(133\) −17.5000 6.06218i −1.51744 0.525657i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 0 0
\(139\) −7.00000 −0.593732 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) −1.50000 7.79423i −0.126773 0.658733i
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) −1.50000 2.59808i −0.125436 0.217262i
\(144\) 0 0
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) −11.0000 −0.910366
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) 3.50000 + 6.06218i 0.284826 + 0.493333i 0.972567 0.232623i \(-0.0747309\pi\)
−0.687741 + 0.725956i \(0.741398\pi\)
\(152\) −3.50000 + 6.06218i −0.283887 + 0.491708i
\(153\) 0 0
\(154\) −1.50000 7.79423i −0.120873 0.628077i
\(155\) 24.0000 1.92773
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) −3.00000 −0.237171
\(161\) −22.5000 7.79423i −1.77325 0.614271i
\(162\) 0 0
\(163\) 9.50000 16.4545i 0.744097 1.28881i −0.206518 0.978443i \(-0.566213\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) −15.0000 −1.16073 −0.580367 0.814355i \(-0.697091\pi\)
−0.580367 + 0.814355i \(0.697091\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 4.50000 7.79423i 0.345134 0.597790i
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.92820i −0.604743 + 0.523723i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 1.50000 + 2.59808i 0.112430 + 0.194734i
\(179\) 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.50000 + 0.866025i 0.185312 + 0.0641941i
\(183\) 0 0
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) 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 \(0.166667\pi\)
\(192\) 0 0
\(193\) −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
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 12.5000 + 21.6506i 0.886102 + 1.53477i 0.844446 + 0.535641i \(0.179930\pi\)
0.0416556 + 0.999132i \(0.486737\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 0 0
\(202\) −3.00000 −0.211079
\(203\) −1.50000 7.79423i −0.105279 0.547048i
\(204\) 0 0
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) −6.50000 11.2583i −0.452876 0.784405i
\(207\) 0 0
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 21.0000 1.45260
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 0 0
\(214\) 4.50000 + 7.79423i 0.307614 + 0.532803i
\(215\) 1.50000 2.59808i 0.102299 0.177187i
\(216\) 0 0
\(217\) −16.0000 + 13.8564i −1.08615 + 0.940634i
\(218\) 13.0000 0.880471
\(219\) 0 0
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) 1.50000 + 2.59808i 0.100901 + 0.174766i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) −4.50000 + 7.79423i −0.299336 + 0.518464i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 0 0
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) 27.0000 1.78033
\(231\) 0 0
\(232\) −3.00000 −0.196960
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 1.50000 + 7.79423i 0.0972306 + 0.505225i
\(239\) −3.00000 −0.194054 −0.0970269 0.995282i \(-0.530933\pi\)
−0.0970269 + 0.995282i \(0.530933\pi\)
\(240\) 0 0
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 3.00000 20.7846i 0.191663 1.32788i
\(246\) 0 0
\(247\) −3.50000 + 6.06218i −0.222700 + 0.385727i
\(248\) 4.00000 + 6.92820i 0.254000 + 0.439941i
\(249\) 0 0
\(250\) −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
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.5000 18.1865i 0.654972 1.13444i −0.326929 0.945049i \(-0.606014\pi\)
0.981901 0.189396i \(-0.0606529\pi\)
\(258\) 0 0
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) −3.00000 −0.186052
\(261\) 0 0
\(262\) 7.50000 + 12.9904i 0.463352 + 0.802548i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) −14.0000 + 12.1244i −0.858395 + 0.743392i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 0 0
\(271\) −2.50000 + 4.33013i −0.151864 + 0.263036i −0.931913 0.362682i \(-0.881861\pi\)
0.780049 + 0.625719i \(0.215194\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) 9.00000 0.543710
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 0 0
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) −3.50000 + 6.06218i −0.209916 + 0.363585i
\(279\) 0 0
\(280\) −7.50000 2.59808i −0.448211 0.155265i
\(281\) −21.0000 −1.25275 −0.626377 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) 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
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) −1.50000 7.79423i −0.0885422 0.460079i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 4.50000 + 7.79423i 0.264249 + 0.457693i
\(291\) 0 0
\(292\) −5.50000 + 9.52628i −0.321863 + 0.557483i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) 0 0
\(298\) −4.50000 7.79423i −0.260678 0.451508i
\(299\) −4.50000 + 7.79423i −0.260242 + 0.450752i
\(300\) 0 0
\(301\) 0.500000 + 2.59808i 0.0288195 + 0.149751i
\(302\) 7.00000 0.402805
\(303\) 0 0
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −7.50000 2.59808i −0.427352 0.148039i
\(309\) 0 0
\(310\) 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 \(0.595114\pi\)
\(312\) 0 0
\(313\) 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 \(0.997978\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 0 0
\(322\) −18.0000 + 15.5885i −1.00310 + 0.868711i
\(323\) −21.0000 −1.16847
\(324\) 0 0
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) −9.50000 16.4545i −0.526156 0.911330i
\(327\) 0 0
\(328\) −3.00000 −0.165647
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) 0 0
\(334\) −7.50000 + 12.9904i −0.410382 + 0.710802i
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 0 0
\(340\) −4.50000 7.79423i −0.244047 0.422701i
\(341\) 12.0000 20.7846i 0.649836 1.12555i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) −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 \(0.937721\pi\)
\(348\) 0 0
\(349\) 23.0000 1.23116 0.615581 0.788074i \(-0.288921\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 2.00000 + 10.3923i 0.106904 + 0.555492i
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 0 0
\(355\) −18.0000 + 31.1769i −0.955341 + 1.65470i
\(356\) 3.00000 0.159000
\(357\) 0 0
\(358\) 21.0000 1.10988
\(359\) −4.50000 + 7.79423i −0.237501 + 0.411364i −0.959997 0.280012i \(-0.909662\pi\)
0.722496 + 0.691375i \(0.242995\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 0 0
\(364\) 2.00000 1.73205i 0.104828 0.0907841i
\(365\) 33.0000 1.72730
\(366\) 0 0
\(367\) −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) 4.50000 + 7.79423i 0.234579 + 0.406302i
\(369\) 0 0
\(370\) 3.00000 0.155963
\(371\) −6.00000 + 5.19615i −0.311504 + 0.269771i
\(372\) 0 0
\(373\) 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i \(-0.724071\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) −4.50000 7.79423i −0.232689 0.403030i
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 0 0
\(383\) −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i \(-0.958522\pi\)
0.608290 + 0.793715i \(0.291856\pi\)
\(384\) 0 0
\(385\) 4.50000 + 23.3827i 0.229341 + 1.19169i
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) 0.500000 + 0.866025i 0.0253837 + 0.0439658i
\(389\) −13.5000 23.3827i −0.684477 1.18555i −0.973601 0.228257i \(-0.926697\pi\)
0.289124 0.957292i \(-0.406636\pi\)
\(390\) 0 0
\(391\) −27.0000 −1.36545
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 0 0
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) 24.0000 + 41.5692i 1.20757 + 2.09157i
\(396\) 0 0
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) 25.0000 1.25314
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) −1.50000 + 2.59808i −0.0746278 + 0.129259i
\(405\) 0 0
\(406\) −7.50000 2.59808i −0.372219 0.128940i
\(407\) 3.00000 0.148704
\(408\) 0 0
\(409\) 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
\(411\) 0 0
\(412\) −13.0000 −0.640464
\(413\) 0 0
\(414\) 0 0
\(415\) 13.5000 23.3827i 0.662689 1.14781i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 0 0
\(418\) 10.5000 18.1865i 0.513572 0.889532i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 35.0000 1.70580 0.852898 0.522078i \(-0.174843\pi\)
0.852898 + 0.522078i \(0.174843\pi\)
\(422\) 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
\(426\) 0 0
\(427\) 5.00000 + 1.73205i 0.241967 + 0.0838198i
\(428\) 9.00000 0.435031
\(429\) 0 0
\(430\) −1.50000 2.59808i −0.0723364 0.125290i
\(431\) −13.5000 23.3827i −0.650272 1.12630i −0.983057 0.183301i \(-0.941322\pi\)
0.332785 0.943003i \(-0.392012\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 4.00000 + 20.7846i 0.192006 + 0.997693i
\(435\) 0 0
\(436\) 6.50000 11.2583i 0.311294 0.539176i
\(437\) −31.5000 54.5596i −1.50685 2.60994i
\(438\) 0 0
\(439\) −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 \(0.840097\pi\)
\(444\) 0 0
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 4.50000 + 7.79423i 0.211897 + 0.367016i
\(452\) 4.50000 + 7.79423i 0.211662 + 0.366610i
\(453\) 0 0
\(454\) 3.00000 0.140797
\(455\) −7.50000 2.59808i −0.351605 0.121800i
\(456\) 0 0
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −6.50000 11.2583i −0.303725 0.526067i
\(459\) 0 0
\(460\) 13.5000 23.3827i 0.629441 1.09022i
\(461\) −9.00000 −0.419172 −0.209586 0.977790i \(-0.567212\pi\)
−0.209586 + 0.977790i \(0.567212\pi\)
\(462\) 0 0
\(463\) 41.0000 1.90543 0.952716 0.303863i \(-0.0982765\pi\)
0.952716 + 0.303863i \(0.0982765\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 0 0
\(466\) 1.50000 + 2.59808i 0.0694862 + 0.120354i
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 0 0
\(469\) 8.00000 6.92820i 0.369406 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.50000 2.59808i −0.0689701 0.119460i
\(474\) 0 0
\(475\) −28.0000 −1.28473
\(476\) 7.50000 + 2.59808i 0.343762 + 0.119083i
\(477\) 0 0
\(478\) −1.50000 + 2.59808i −0.0686084 + 0.118833i
\(479\) 1.50000 + 2.59808i 0.0685367 + 0.118709i 0.898257 0.439470i \(-0.144834\pi\)
−0.829721 + 0.558179i \(0.811500\pi\)
\(480\) 0 0
\(481\) −0.500000 + 0.866025i −0.0227980 + 0.0394874i
\(482\) 13.0000 0.592134
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 1.50000 2.59808i 0.0681115 0.117973i
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) −16.5000 12.9904i −0.745394 0.586846i
\(491\) 21.0000 0.947717 0.473858 0.880601i \(-0.342861\pi\)
0.473858 + 0.880601i \(0.342861\pi\)
\(492\) 0 0
\(493\) −4.50000 7.79423i −0.202670 0.351034i
\(494\) 3.50000 + 6.06218i 0.157472 + 0.272750i
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) −6.00000 31.1769i −0.269137 1.39848i
\(498\) 0 0
\(499\) 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 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
\(507\) 0 0
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i \(-0.769415\pi\)
0.948353 + 0.317217i \(0.102748\pi\)
\(510\) 0 0
\(511\) −22.0000 + 19.0526i −0.973223 + 0.842836i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −10.5000 18.1865i −0.463135 0.802174i
\(515\) 19.5000 + 33.7750i 0.859273 + 1.48830i
\(516\) 0 0
\(517\) 0 0
\(518\) −2.00000 + 1.73205i −0.0878750 + 0.0761019i
\(519\) 0 0
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) −1.50000 2.59808i −0.0657162 0.113824i 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) 0 0
\(523\) 3.50000 6.06218i 0.153044 0.265081i −0.779301 0.626650i \(-0.784426\pi\)
0.932345 + 0.361569i \(0.117759\pi\)
\(524\) 15.0000 0.655278
\(525\) 0 0
\(526\) −9.00000 −0.392419
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) 0 0
\(529\) −29.0000 50.2295i −1.26087 2.18389i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) 3.50000 + 18.1865i 0.151744 + 0.788486i
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) −13.5000 23.3827i −0.583656 1.01092i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 0 0
\(538\) −15.0000 −0.646696
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) 2.50000 + 4.33013i 0.107384 + 0.185995i
\(543\) 0 0
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) −39.0000 −1.67058
\(546\) 0 0
\(547\) 11.0000 0.470326 0.235163 0.971956i \(-0.424438\pi\)
0.235163 + 0.971956i \(0.424438\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) 0 0
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) 10.5000 18.1865i 0.447315 0.774772i
\(552\) 0 0
\(553\) −40.0000 13.8564i −1.70097 0.589234i
\(554\) 1.00000 0.0424859
\(555\) 0 0
\(556\) 3.50000 + 6.06218i 0.148433 + 0.257094i
\(557\) 4.50000 + 7.79423i 0.190671 + 0.330252i 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) 0 0
\(559\) 1.00000 0.0422955
\(560\) −6.00000 + 5.19615i −0.253546 + 0.219578i
\(561\) 0 0
\(562\) −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 \(0.0435194\pi\)
\(570\) 0 0
\(571\) −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
\(574\) −7.50000 2.59808i −0.313044 0.108442i
\(575\) −36.0000 −1.50130
\(576\) 0 0
\(577\) 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 0 0
\(580\) 9.00000 0.373705
\(581\) 4.50000 + 23.3827i 0.186691 + 0.970077i
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 5.50000 + 9.52628i 0.227592 + 0.394200i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 3.00000 0.123823 0.0619116 0.998082i \(-0.480280\pi\)
0.0619116 + 0.998082i \(0.480280\pi\)
\(588\) 0 0
\(589\) −56.0000 −2.30744
\(590\) 0 0
\(591\) 0 0
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) −19.5000 + 33.7750i −0.800769 + 1.38697i 0.118342 + 0.992973i \(0.462242\pi\)
−0.919111 + 0.394000i \(0.871091\pi\)
\(594\) 0 0
\(595\) −4.50000 23.3827i −0.184482 0.958597i
\(596\) −9.00000 −0.368654
\(597\) 0 0
\(598\) 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 \(0.670218\pi\)
\(600\) 0 0
\(601\) −25.0000 −1.01977 −0.509886 0.860242i \(-0.670312\pi\)
−0.509886 + 0.860242i \(0.670312\pi\)
\(602\) 2.50000 + 0.866025i 0.101892 + 0.0352966i
\(603\) 0 0
\(604\) 3.50000 6.06218i 0.142413 0.246667i
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) 0 0
\(607\) 6.50000 11.2583i 0.263827 0.456962i −0.703429 0.710766i \(-0.748349\pi\)
0.967256 + 0.253804i \(0.0816819\pi\)
\(608\) 7.00000 0.283887
\(609\) 0 0
\(610\) −6.00000 −0.242933
\(611\) 0 0
\(612\) 0 0
\(613\) −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
\(615\) 0 0
\(616\) −6.00000 + 5.19615i −0.241747 + 0.209359i
\(617\) −45.0000 −1.81163 −0.905816 0.423672i \(-0.860741\pi\)
−0.905816 + 0.423672i \(0.860741\pi\)
\(618\) 0 0
\(619\) −8.50000 14.7224i −0.341644 0.591744i 0.643094 0.765787i \(-0.277650\pi\)
−0.984738 + 0.174042i \(0.944317\pi\)
\(620\) −12.0000 20.7846i −0.481932 0.834730i
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 7.50000 + 2.59808i 0.300481 + 0.104090i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 6.00000 10.3923i 0.238103 0.412406i
\(636\) 0 0
\(637\) 6.50000 2.59808i 0.257539 0.102940i
\(638\) 9.00000 0.356313
\(639\) 0 0
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) 0 0
\(643\) 29.0000 1.14365 0.571824 0.820376i \(-0.306236\pi\)
0.571824 + 0.820376i \(0.306236\pi\)
\(644\) 4.50000 + 23.3827i 0.177325 + 0.921407i
\(645\) 0 0
\(646\) −10.5000 + 18.1865i −0.413117 + 0.715540i
\(647\) 10.5000 + 18.1865i 0.412798 + 0.714986i 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 4.00000 0.156893
\(651\) 0 0
\(652\) −19.0000 −0.744097
\(653\) −7.50000 + 12.9904i −0.293498 + 0.508353i −0.974634 0.223803i \(-0.928153\pi\)
0.681137 + 0.732156i \(0.261486\pi\)
\(654\) 0 0
\(655\) −22.5000 38.9711i −0.879148 1.52273i
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 0 0
\(658\) 0 0
\(659\) 3.00000 0.116863 0.0584317 0.998291i \(-0.481390\pi\)
0.0584317 + 0.998291i \(0.481390\pi\)
\(660\) 0 0
\(661\) 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
\(663\) 0 0
\(664\) 9.00000 0.349268
\(665\) 42.0000 36.3731i 1.62869 1.41049i
\(666\) 0 0
\(667\) 13.5000 23.3827i 0.522722 0.905381i
\(668\) 7.50000 + 12.9904i 0.290184 + 0.502613i
\(669\) 0 0
\(670\) −6.00000 + 10.3923i −0.231800 + 0.401490i
\(671\) −6.00000 −0.231627
\(672\) 0 0
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) −6.50000 + 11.2583i −0.250371 + 0.433655i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 15.0000 25.9808i 0.576497 0.998522i −0.419380 0.907811i \(-0.637753\pi\)
0.995877 0.0907112i \(-0.0289140\pi\)
\(678\) 0 0
\(679\) 0.500000 + 2.59808i 0.0191882 + 0.0997050i
\(680\) −9.00000 −0.345134
\(681\) 0 0
\(682\) −12.0000 20.7846i −0.459504 0.795884i
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 0 0
\(685\) −27.0000 −1.03162
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 0 0
\(688\) 0.500000 0.866025i 0.0190623 0.0330169i
\(689\) 1.50000 + 2.59808i 0.0571454 + 0.0989788i
\(690\) 0 0
\(691\) −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
\(696\) 0 0
\(697\) −4.50000 7.79423i −0.170450 0.295227i
\(698\) 11.5000 19.9186i 0.435281 0.753930i
\(699\) 0 0
\(700\) 10.0000 + 3.46410i 0.377964 + 0.130931i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −3.50000 6.06218i −0.132005 0.228639i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −3.00000 −0.112906
\(707\) −6.00000 + 5.19615i −0.225653 + 0.195421i
\(708\) 0 0
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 18.0000 + 31.1769i 0.675528 + 1.17005i
\(711\) 0 0
\(712\) 1.50000 2.59808i 0.0562149 0.0973670i
\(713\) −72.0000 −2.69642
\(714\) 0 0
\(715\) 9.00000 0.336581
\(716\) 10.5000 18.1865i 0.392403 0.679663i
\(717\) 0 0
\(718\) 4.50000 + 7.79423i 0.167939 + 0.290878i
\(719\) 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 0 0
\(721\) −32.5000 11.2583i −1.21036 0.419282i
\(722\) −30.0000 −1.11648
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −6.00000 10.3923i −0.222834 0.385961i
\(726\) 0 0
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) −0.500000 2.59808i −0.0185312 0.0962911i
\(729\) 0 0
\(730\) 16.5000 28.5788i 0.610692 1.05775i
\(731\) 1.50000 + 2.59808i 0.0554795 + 0.0960933i
\(732\) 0 0
\(733\) 0.500000 0.866025i 0.0184679 0.0319874i −0.856644 0.515908i \(-0.827454\pi\)
0.875112 + 0.483921i \(0.160788\pi\)
\(734\) −17.0000 −0.627481
\(735\) 0 0
\(736\) 9.00000 0.331744
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) 0 0
\(739\) −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
\(741\) 0 0
\(742\) 1.50000 + 7.79423i 0.0550667 + 0.286135i
\(743\) 21.0000 0.770415 0.385208 0.922830i \(-0.374130\pi\)
0.385208 + 0.922830i \(0.374130\pi\)
\(744\) 0 0
\(745\) 13.5000 + 23.3827i 0.494602 + 0.856675i
\(746\) −6.50000 11.2583i −0.237982 0.412197i
\(747\) 0 0
\(748\) −9.00000 −0.329073
\(749\) 22.5000 + 7.79423i 0.822132 + 0.284795i
\(750\) 0 0
\(751\) 6.50000 11.2583i 0.237188 0.410822i −0.722718 0.691143i \(-0.757107\pi\)
0.959906 + 0.280321i \(0.0904408\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −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
\(759\) 0 0
\(760\) −10.5000 18.1865i −0.380875 0.659695i
\(761\) 22.5000 38.9711i 0.815624 1.41270i −0.0932544 0.995642i \(-0.529727\pi\)
0.908879 0.417061i \(-0.136940\pi\)
\(762\) 0 0
\(763\) 26.0000 22.5167i 0.941263 0.815158i
\(764\) 0 0
\(765\) 0 0
\(766\) 7.50000 + 12.9904i 0.270986 + 0.469362i
\(767\) 0 0
\(768\) 0 0
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) 22.5000 + 7.79423i 0.810844 + 0.280885i
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −13.5000 23.3827i −0.485561 0.841017i 0.514301 0.857610i \(-0.328051\pi\)
−0.999862 + 0.0165929i \(0.994718\pi\)
\(774\) 0 0
\(775\) −16.0000 + 27.7128i −0.574737 + 0.995474i
\(776\) 1.00000 0.0358979
\(777\) 0 0
\(778\) −27.0000 −0.967997
\(779\) 10.5000 18.1865i 0.376202 0.651600i
\(780\) 0 0
\(781\) 18.0000 + 31.1769i 0.644091 + 1.11560i
\(782\) −13.5000 + 23.3827i −0.482759 + 0.836163i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) −66.0000 −2.35564
\(786\) 0 0
\(787\) 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
\(789\) 0 0
\(790\) 48.0000 1.70776
\(791\) 4.50000 + 23.3827i 0.160002 + 0.831393i
\(792\) 0 0
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) −6.50000 11.2583i −0.230676 0.399543i
\(795\) 0 0
\(796\) 12.5000 21.6506i 0.443051 0.767386i
\(797\) −21.0000 −0.743858 −0.371929 0.928261i \(-0.621304\pi\)
−0.371929 + 0.928261i \(0.621304\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.00000 3.46410i 0.0707107 0.122474i
\(801\) 0 0
\(802\) 13.5000 + 23.3827i 0.476702 + 0.825671i
\(803\) 16.5000 28.5788i 0.582272 1.00853i
\(804\) 0 0
\(805\) 54.0000 46.7654i 1.90325 1.64826i
\(806\) 8.00000 0.281788
\(807\) 0 0
\(808\) 1.50000 + 2.59808i 0.0527698 + 0.0914000i
\(809\) 16.5000 + 28.5788i 0.580109 + 1.00478i 0.995466 + 0.0951198i \(0.0303234\pi\)
−0.415357 + 0.909659i \(0.636343\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −6.00000 + 5.19615i −0.210559 + 0.182349i
\(813\) 0 0
\(814\) 1.50000 2.59808i 0.0525750 0.0910625i
\(815\) 28.5000 + 49.3634i 0.998311 + 1.72913i
\(816\) 0 0
\(817\) −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 \(-0.0951694\pi\)
\(822\) 0 0
\(823\) 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
\(825\) 0 0
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) −5.50000 9.52628i −0.191023 0.330861i 0.754567 0.656223i \(-0.227847\pi\)
−0.945589 + 0.325362i \(0.894514\pi\)
\(830\) −13.5000 23.3827i −0.468592 0.811625i
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) 16.5000 + 12.9904i 0.571691 + 0.450090i
\(834\) 0 0
\(835\) 22.5000 38.9711i 0.778645 1.34865i
\(836\) −10.5000 18.1865i −0.363150 0.628994i
\(837\) 0 0
\(838\) 4.50000 7.79423i 0.155450 0.269247i
\(839\) 15.0000 0.517858 0.258929 0.965896i \(-0.416631\pi\)
0.258929 + 0.965896i \(0.416631\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 17.5000 30.3109i 0.603090 1.04458i
\(843\) 0 0
\(844\) −2.50000 4.33013i −0.0860535 0.149049i
\(845\) 18.0000 31.1769i 0.619219 1.07252i
\(846\) 0 0
\(847\) −5.00000 1.73205i −0.171802 0.0595140i
\(848\) 3.00000 0.103020
\(849\) 0 0
\(850\) 6.00000 + 10.3923i 0.205798 + 0.356453i
\(851\) −4.50000 7.79423i −0.154258 0.267183i
\(852\) 0 0
\(853\) −1.00000 −0.0342393 −0.0171197 0.999853i \(-0.505450\pi\)
−0.0171197 + 0.999853i \(0.505450\pi\)
\(854\) 4.00000 3.46410i 0.136877 0.118539i
\(855\) 0 0
\(856\) 4.50000 7.79423i 0.153807 0.266401i
\(857\) −1.50000 2.59808i −0.0512390 0.0887486i 0.839268 0.543718i \(-0.182984\pi\)
−0.890507 + 0.454969i \(0.849650\pi\)
\(858\) 0 0
\(859\) 12.5000 21.6506i 0.426494 0.738710i −0.570064 0.821600i \(-0.693082\pi\)
0.996559 + 0.0828900i \(0.0264150\pi\)
\(860\) −3.00000 −0.102299
\(861\) 0 0
\(862\) −27.0000 −0.919624
\(863\) 25.5000 44.1673i 0.868030 1.50347i 0.00402340 0.999992i \(-0.498719\pi\)
0.864007 0.503480i \(-0.167947\pi\)
\(864\) 0 0
\(865\) 9.00000 + 15.5885i 0.306009 + 0.530023i
\(866\) 1.00000 1.73205i 0.0339814 0.0588575i
\(867\) 0 0
\(868\) 20.0000 + 6.92820i 0.678844 + 0.235159i
\(869\) 48.0000 1.62829
\(870\) 0 0
\(871\) −2.00000 3.46410i −0.0677674 0.117377i
\(872\) −6.50000 11.2583i −0.220118 0.381255i
\(873\) 0 0
\(874\) −63.0000 −2.13101
\(875\) 1.50000 + 7.79423i 0.0507093 + 0.263493i
\(876\) 0 0
\(877\) −23.5000 + 40.7032i −0.793539 + 1.37445i 0.130224 + 0.991485i \(0.458430\pi\)
−0.923763 + 0.382965i \(0.874903\pi\)
\(878\) 4.00000 + 6.92820i 0.134993 + 0.233816i
\(879\) 0 0
\(880\) 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 −0.443964 0.896045i \(-0.646428\pi\)
0.997979 0.0635387i \(-0.0202386\pi\)
\(888\) 0 0
\(889\) 2.00000 + 10.3923i 0.0670778 + 0.348547i
\(890\) −9.00000 −0.301681
\(891\) 0 0
\(892\) 0.500000 + 0.866025i 0.0167412 + 0.0289967i
\(893\) 0 0
\(894\) 0 0
\(895\) −63.0000 −2.10586
\(896\) −2.50000 0.866025i −0.0835191 0.0289319i
\(897\) 0 0
\(898\) 3.00000 5.19615i 0.100111 0.173398i
\(899\) −12.0000 20.7846i −0.400222 0.693206i
\(900\) 0 0
\(901\) −4.50000 + 7.79423i −0.149917 + 0.259663i
\(902\) 9.00000 0.299667
\(903\) 0 0
\(904\) 9.00000 0.299336
\(905\) −3.00000 + 5.19615i −0.0997234 + 0.172726i
\(906\) 0 0
\(907\) 21.5000 + 37.2391i 0.713896 + 1.23650i 0.963384 + 0.268126i \(0.0864043\pi\)
−0.249488 + 0.968378i \(0.580262\pi\)
\(908\) 1.50000 2.59808i 0.0497792 0.0862202i
\(909\) 0 0
\(910\) −6.00000 + 5.19615i −0.198898 + 0.172251i
\(911\) 39.0000 1.29213 0.646064 0.763283i \(-0.276414\pi\)
0.646064 + 0.763283i \(0.276414\pi\)
\(912\) 0 0
\(913\) −13.5000 23.3827i −0.446785 0.773854i
\(914\) −5.00000 8.66025i −0.165385 0.286456i
\(915\) 0 0
\(916\) −13.0000 −0.429532
\(917\) 37.5000 + 12.9904i 1.23836 + 0.428980i
\(918\) 0 0
\(919\) −26.5000 + 45.8993i −0.874154 + 1.51408i −0.0164935 + 0.999864i \(0.505250\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) −13.5000 23.3827i −0.445082 0.770904i
\(921\) 0 0
\(922\) −4.50000 + 7.79423i −0.148200 + 0.256689i
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 20.5000 35.5070i 0.673672 1.16683i
\(927\) 0 0
\(928\) 1.50000 + 2.59808i 0.0492399 + 0.0852860i
\(929\) −9.00000 + 15.5885i −0.295280 + 0.511441i −0.975050 0.221985i \(-0.928746\pi\)
0.679770 + 0.733426i \(0.262080\pi\)
\(930\) 0 0
\(931\) −7.00000 + 48.4974i −0.229416 + 1.58944i
\(932\) 3.00000 0.0982683
\(933\) 0 0
\(934\) −1.50000 2.59808i −0.0490815 0.0850117i
\(935\) 13.5000 + 23.3827i 0.441497 + 0.764696i
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) −2.00000 10.3923i −0.0653023 0.339321i
\(939\) 0 0
\(940\) 0 0
\(941\) 3.00000 + 5.19615i 0.0977972 + 0.169390i 0.910773 0.412908i \(-0.135487\pi\)
−0.812975 + 0.582298i \(0.802154\pi\)
\(942\) 0 0
\(943\) 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 \(0.229129\pi\)
\(948\) 0 0
\(949\) 5.50000 + 9.52628i 0.178538 + 0.309236i
\(950\) −14.0000 + 24.2487i −0.454220 + 0.786732i
\(951\) 0 0
\(952\) 6.00000 5.19615i 0.194461 0.168408i
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 1.50000 + 2.59808i 0.0485135 + 0.0840278i
\(957\) 0 0
\(958\) 3.00000 0.0969256
\(959\) 18.0000 15.5885i 0.581250 0.503378i
\(960\) 0 0
\(961\) −16.5000 + 28.5788i −0.532258 + 0.921898i
\(962\) 0.500000 + 0.866025i 0.0161206 + 0.0279218i
\(963\) 0 0
\(964\) 6.50000 11.2583i 0.209351 0.362606i
\(965\) 42.0000 1.35203
\(966\) 0 0
\(967\) 41.0000 1.31847 0.659236 0.751936i \(-0.270880\pi\)
0.659236 + 0.751936i \(0.270880\pi\)
\(968\) −1.00000 + 1.73205i −0.0321412 + 0.0556702i
\(969\) 0 0
\(970\) −1.50000 2.59808i −0.0481621 0.0834192i
\(971\) −16.5000 + 28.5788i −0.529510 + 0.917139i 0.469897 + 0.882721i \(0.344291\pi\)
−0.999408 + 0.0344175i \(0.989042\pi\)
\(972\) 0 0
\(973\) 3.50000 + 18.1865i 0.112205 + 0.583033i
\(974\) 25.0000 0.801052
\(975\) 0 0
\(976\) −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 \(0.674009\pi\)
\(978\) 0 0
\(979\) −9.00000 −0.287641
\(980\) −19.5000 + 7.79423i −0.622905 + 0.248978i
\(981\) 0 0
\(982\) 10.5000 18.1865i 0.335068 0.580356i
\(983\) 7.50000 + 12.9904i 0.239213 + 0.414329i 0.960489 0.278319i \(-0.0897773\pi\)
−0.721276 + 0.692648i \(0.756444\pi\)
\(984\) 0 0
\(985\) −27.0000 + 46.7654i −0.860292 + 1.49007i
\(986\) −9.00000 −0.286618
\(987\) 0 0
\(988\) 7.00000 0.222700
\(989\) −4.50000 + 7.79423i −0.143092 + 0.247842i
\(990\) 0 0
\(991\) 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
\(993\) 0 0
\(994\) −30.0000 10.3923i −0.951542 0.329624i
\(995\) −75.0000 −2.37766
\(996\) 0 0
\(997\) 6.50000 + 11.2583i 0.205857 + 0.356555i 0.950405 0.311014i \(-0.100668\pi\)
−0.744548 + 0.667568i \(0.767335\pi\)
\(998\) −12.5000 21.6506i −0.395681 0.685339i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1134.2.g.e.163.1 2
3.2 odd 2 1134.2.g.c.163.1 2
7.2 even 3 7938.2.a.m.1.1 1
7.4 even 3 inner 1134.2.g.e.487.1 2
7.5 odd 6 7938.2.a.b.1.1 1
9.2 odd 6 378.2.e.b.37.1 2
9.4 even 3 126.2.h.b.79.1 yes 2
9.5 odd 6 378.2.h.a.289.1 2
9.7 even 3 126.2.e.a.121.1 yes 2
21.2 odd 6 7938.2.a.t.1.1 1
21.5 even 6 7938.2.a.be.1.1 1
21.11 odd 6 1134.2.g.c.487.1 2
36.7 odd 6 1008.2.q.a.625.1 2
36.11 even 6 3024.2.q.f.2305.1 2
36.23 even 6 3024.2.t.a.289.1 2
36.31 odd 6 1008.2.t.f.961.1 2
63.2 odd 6 2646.2.f.d.1765.1 2
63.4 even 3 126.2.e.a.25.1 2
63.5 even 6 2646.2.f.a.883.1 2
63.11 odd 6 378.2.h.a.361.1 2
63.13 odd 6 882.2.h.i.79.1 2
63.16 even 3 882.2.f.i.589.1 2
63.20 even 6 2646.2.e.g.1549.1 2
63.23 odd 6 2646.2.f.d.883.1 2
63.25 even 3 126.2.h.b.67.1 yes 2
63.31 odd 6 882.2.e.c.655.1 2
63.32 odd 6 378.2.e.b.235.1 2
63.34 odd 6 882.2.e.c.373.1 2
63.38 even 6 2646.2.h.d.361.1 2
63.40 odd 6 882.2.f.g.295.1 2
63.41 even 6 2646.2.h.d.667.1 2
63.47 even 6 2646.2.f.a.1765.1 2
63.52 odd 6 882.2.h.i.67.1 2
63.58 even 3 882.2.f.i.295.1 2
63.59 even 6 2646.2.e.g.2125.1 2
63.61 odd 6 882.2.f.g.589.1 2
252.11 even 6 3024.2.t.a.1873.1 2
252.67 odd 6 1008.2.q.a.529.1 2
252.95 even 6 3024.2.q.f.2881.1 2
252.151 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 63.4 even 3
126.2.e.a.121.1 yes 2 9.7 even 3
126.2.h.b.67.1 yes 2 63.25 even 3
126.2.h.b.79.1 yes 2 9.4 even 3
378.2.e.b.37.1 2 9.2 odd 6
378.2.e.b.235.1 2 63.32 odd 6
378.2.h.a.289.1 2 9.5 odd 6
378.2.h.a.361.1 2 63.11 odd 6
882.2.e.c.373.1 2 63.34 odd 6
882.2.e.c.655.1 2 63.31 odd 6
882.2.f.g.295.1 2 63.40 odd 6
882.2.f.g.589.1 2 63.61 odd 6
882.2.f.i.295.1 2 63.58 even 3
882.2.f.i.589.1 2 63.16 even 3
882.2.h.i.67.1 2 63.52 odd 6
882.2.h.i.79.1 2 63.13 odd 6
1008.2.q.a.529.1 2 252.67 odd 6
1008.2.q.a.625.1 2 36.7 odd 6
1008.2.t.f.193.1 2 252.151 odd 6
1008.2.t.f.961.1 2 36.31 odd 6
1134.2.g.c.163.1 2 3.2 odd 2
1134.2.g.c.487.1 2 21.11 odd 6
1134.2.g.e.163.1 2 1.1 even 1 trivial
1134.2.g.e.487.1 2 7.4 even 3 inner
2646.2.e.g.1549.1 2 63.20 even 6
2646.2.e.g.2125.1 2 63.59 even 6
2646.2.f.a.883.1 2 63.5 even 6
2646.2.f.a.1765.1 2 63.47 even 6
2646.2.f.d.883.1 2 63.23 odd 6
2646.2.f.d.1765.1 2 63.2 odd 6
2646.2.h.d.361.1 2 63.38 even 6
2646.2.h.d.667.1 2 63.41 even 6
3024.2.q.f.2305.1 2 36.11 even 6
3024.2.q.f.2881.1 2 252.95 even 6
3024.2.t.a.289.1 2 36.23 even 6
3024.2.t.a.1873.1 2 252.11 even 6
7938.2.a.b.1.1 1 7.5 odd 6
7938.2.a.m.1.1 1 7.2 even 3
7938.2.a.t.1.1 1 21.2 odd 6
7938.2.a.be.1.1 1 21.5 even 6