Properties

Label 378.2.h.a.361.1
Level $378$
Weight $2$
Character 378.361
Analytic conductor $3.018$
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] = [378,2,Mod(289,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.01834519640\)
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 378.361
Dual form 378.2.h.a.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(3.50000 + 6.06218i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +9.00000 q^{23} +4.00000 q^{25} +(0.500000 + 0.866025i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +(-7.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} -7.00000 q^{38} -3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} -1.00000 q^{52} +(1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(2.50000 - 0.866025i) q^{56} -3.00000 q^{58} +(-1.00000 + 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(1.50000 - 7.79423i) q^{70} -12.0000 q^{71} +(-5.50000 + 9.52628i) q^{73} -1.00000 q^{74} +(3.50000 - 6.06218i) q^{76} +(7.50000 - 2.59808i) q^{77} +(8.00000 - 13.8564i) q^{79} +(1.50000 - 2.59808i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.50000 + 7.79423i) q^{85} -1.00000 q^{86} +3.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(0.500000 - 2.59808i) q^{91} +(-4.50000 - 7.79423i) q^{92} +(-10.5000 - 18.1865i) q^{95} +(0.500000 + 0.866025i) q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 6 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 6 q^{5} + 5 q^{7} + 2 q^{8} + 3 q^{10} + 6 q^{11} + q^{13} - q^{14} - q^{16} + 3 q^{17} + 7 q^{19} + 3 q^{20} - 3 q^{22} + 18 q^{23} + 8 q^{25} + q^{26} - 4 q^{28} + 3 q^{29} - 8 q^{31} - q^{32} + 3 q^{34} - 15 q^{35} + q^{37} - 14 q^{38} - 6 q^{40} + 3 q^{41} + q^{43} - 3 q^{44} - 9 q^{46} + 11 q^{49} - 4 q^{50} - 2 q^{52} + 3 q^{53} - 18 q^{55} + 5 q^{56} - 6 q^{58} - 2 q^{61} + 16 q^{62} + 2 q^{64} - 3 q^{65} + 4 q^{67} - 6 q^{68} + 3 q^{70} - 24 q^{71} - 11 q^{73} - 2 q^{74} + 7 q^{76} + 15 q^{77} + 16 q^{79} + 3 q^{80} + 3 q^{82} - 9 q^{83} - 9 q^{85} - 2 q^{86} + 6 q^{88} + 3 q^{89} + q^{91} - 9 q^{92} - 21 q^{95} + q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) −0.500000 + 2.59808i −0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 1.50000 + 2.59808i 0.335410 + 0.580948i
\(21\) 0 0
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 9.00000 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) 0 0
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 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
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) −7.50000 + 2.59808i −1.26773 + 0.439155i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −7.00000 −1.13555
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −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
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 2.50000 0.866025i 0.334077 0.115728i
\(57\) 0 0
\(58\) −3.00000 −0.393919
\(59\) 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 \(0.754762\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 1.50000 7.79423i 0.179284 0.931589i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i \(0.389279\pi\)
−0.984594 + 0.174855i \(0.944054\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 3.50000 6.06218i 0.401478 0.695379i
\(77\) 7.50000 2.59808i 0.854704 0.296078i
\(78\) 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
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) 0 0
\(85\) −4.50000 + 7.79423i −0.488094 + 0.845403i
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) 1.50000 + 2.59808i 0.159000 + 0.275396i 0.934508 0.355942i \(-0.115840\pi\)
−0.775509 + 0.631337i \(0.782506\pi\)
\(90\) 0 0
\(91\) 0.500000 2.59808i 0.0524142 0.272352i
\(92\) −4.50000 7.79423i −0.469157 0.812605i
\(93\) 0 0
\(94\) 0 0
\(95\) −10.5000 18.1865i −1.07728 1.86590i
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 0.500000 0.866025i 0.0490290 0.0849208i
\(105\) 0 0
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) 4.50000 + 7.79423i 0.435031 + 0.753497i 0.997298 0.0734594i \(-0.0234039\pi\)
−0.562267 + 0.826956i \(0.690071\pi\)
\(108\) 0 0
\(109\) 6.50000 11.2583i 0.622587 1.07835i −0.366415 0.930451i \(-0.619415\pi\)
0.989002 0.147901i \(-0.0472517\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 0 0
\(112\) −0.500000 + 2.59808i −0.0472456 + 0.245495i
\(113\) −4.50000 + 7.79423i −0.423324 + 0.733219i −0.996262 0.0863794i \(-0.972470\pi\)
0.572938 + 0.819599i \(0.305804\pi\)
\(114\) 0 0
\(115\) −27.0000 −2.51776
\(116\) 1.50000 2.59808i 0.139272 0.241225i
\(117\) 0 0
\(118\) 0 0
\(119\) 1.50000 7.79423i 0.137505 0.714496i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −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
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0 0
\(133\) 14.0000 + 12.1244i 1.21395 + 1.05131i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) 0 0
\(139\) 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i \(-0.737392\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 6.00000 + 5.19615i 0.507093 + 0.439155i
\(141\) 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
\(146\) −5.50000 9.52628i −0.455183 0.788400i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.0410997 0.0711868i
\(149\) 9.00000 0.737309 0.368654 0.929567i \(-0.379819\pi\)
0.368654 + 0.929567i \(0.379819\pi\)
\(150\) 0 0
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 0 0
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) 12.0000 + 20.7846i 0.963863 + 1.66946i
\(156\) 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
\(160\) 1.50000 + 2.59808i 0.118585 + 0.205396i
\(161\) 22.5000 7.79423i 1.77325 0.614271i
\(162\) 0 0
\(163\) 9.50000 + 16.4545i 0.744097 + 1.28881i 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) −7.50000 + 12.9904i −0.580367 + 1.00523i 0.415068 + 0.909790i \(0.363758\pi\)
−0.995436 + 0.0954356i \(0.969576\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) −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 −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) 10.0000 3.46410i 0.755929 0.261861i
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 0 0
\(178\) −3.00000 −0.224860
\(179\) −10.5000 + 18.1865i −0.784807 + 1.35933i 0.144308 + 0.989533i \(0.453905\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.00000 + 1.73205i 0.148250 + 0.128388i
\(183\) 0 0
\(184\) 9.00000 0.663489
\(185\) −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 \(-0.334758\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 12.5000 21.6506i 0.886102 1.53477i 0.0416556 0.999132i \(-0.486737\pi\)
0.844446 0.535641i \(-0.179930\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) 1.50000 2.59808i 0.105540 0.182800i
\(203\) 6.00000 + 5.19615i 0.421117 + 0.364698i
\(204\) 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
\(209\) 10.5000 + 18.1865i 0.726300 + 1.25799i
\(210\) 0 0
\(211\) −2.50000 + 4.33013i −0.172107 + 0.298098i −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) −3.00000 −0.206041
\(213\) 0 0
\(214\) −9.00000 −0.615227
\(215\) −1.50000 2.59808i −0.102299 0.177187i
\(216\) 0 0
\(217\) −16.0000 13.8564i −1.08615 0.940634i
\(218\) 6.50000 + 11.2583i 0.440236 + 0.762510i
\(219\) 0 0
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) −1.50000 2.59808i −0.100901 0.174766i
\(222\) 0 0
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) −2.00000 1.73205i −0.133631 0.115728i
\(225\) 0 0
\(226\) −4.50000 7.79423i −0.299336 0.518464i
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 0 0
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) 13.5000 23.3827i 0.890164 1.54181i
\(231\) 0 0
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 1.50000 + 2.59808i 0.0982683 + 0.170206i 0.910968 0.412477i \(-0.135336\pi\)
−0.812700 + 0.582683i \(0.802003\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 6.00000 + 5.19615i 0.388922 + 0.336817i
\(239\) −1.50000 + 2.59808i −0.0970269 + 0.168056i −0.910453 0.413613i \(-0.864267\pi\)
0.813426 + 0.581669i \(0.197600\pi\)
\(240\) 0 0
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −16.5000 + 12.9904i −1.05415 + 0.829925i
\(246\) 0 0
\(247\) 7.00000 0.445399
\(248\) −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 \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 2.00000 3.46410i 0.125491 0.217357i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 0 0
\(259\) 2.00000 + 1.73205i 0.124274 + 0.107624i
\(260\) 3.00000 0.186052
\(261\) 0 0
\(262\) 7.50000 12.9904i 0.463352 0.802548i
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) −17.5000 + 6.06218i −1.07299 + 0.371696i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 7.50000 12.9904i 0.457283 0.792038i −0.541533 0.840679i \(-0.682156\pi\)
0.998816 + 0.0486418i \(0.0154893\pi\)
\(270\) 0 0
\(271\) −2.50000 4.33013i −0.151864 0.263036i 0.780049 0.625719i \(-0.215194\pi\)
−0.931913 + 0.362682i \(0.881861\pi\)
\(272\) 1.50000 + 2.59808i 0.0909509 + 0.157532i
\(273\) 0 0
\(274\) −4.50000 + 7.79423i −0.271855 + 0.470867i
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) 3.50000 + 6.06218i 0.209916 + 0.363585i
\(279\) 0 0
\(280\) −7.50000 + 2.59808i −0.448211 + 0.155265i
\(281\) −10.5000 18.1865i −0.626377 1.08492i −0.988273 0.152699i \(-0.951204\pi\)
0.361895 0.932219i \(-0.382130\pi\)
\(282\) 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
\(286\) 1.50000 + 2.59808i 0.0886969 + 0.153627i
\(287\) 1.50000 7.79423i 0.0885422 0.460079i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 9.00000 0.528498
\(291\) 0 0
\(292\) 11.0000 0.643726
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) 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
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 3.50000 6.06218i 0.201402 0.348839i
\(303\) 0 0
\(304\) −7.00000 −0.401478
\(305\) 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 \(0.794649\pi\)
\(308\) −6.00000 5.19615i −0.341882 0.296078i
\(309\) 0 0
\(310\) −24.0000 −1.36311
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 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 \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) −3.00000 −0.167705
\(321\) 0 0
\(322\) −4.50000 + 23.3827i −0.250775 + 1.30307i
\(323\) 21.0000 1.16847
\(324\) 0 0
\(325\) 2.00000 3.46410i 0.110940 0.192154i
\(326\) −19.0000 −1.05231
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 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
\(335\) −6.00000 10.3923i −0.327815 0.567792i
\(336\) 0 0
\(337\) 6.50000 11.2583i 0.354078 0.613280i −0.632882 0.774248i \(-0.718128\pi\)
0.986960 + 0.160968i \(0.0514616\pi\)
\(338\) −12.0000 −0.652714
\(339\) 0 0
\(340\) 9.00000 0.488094
\(341\) −12.0000 20.7846i −0.649836 1.12555i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) −11.5000 19.9186i −0.615581 1.06622i −0.990282 0.139072i \(-0.955588\pi\)
0.374701 0.927146i \(-0.377745\pi\)
\(350\) −2.00000 + 10.3923i −0.106904 + 0.555492i
\(351\) 0 0
\(352\) −1.50000 2.59808i −0.0799503 0.138478i
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 0 0
\(355\) 36.0000 1.91068
\(356\) 1.50000 2.59808i 0.0794998 0.137698i
\(357\) 0 0
\(358\) −10.5000 18.1865i −0.554942 0.961188i
\(359\) 4.50000 + 7.79423i 0.237501 + 0.411364i 0.959997 0.280012i \(-0.0903384\pi\)
−0.722496 + 0.691375i \(0.757005\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) −2.50000 + 0.866025i −0.131036 + 0.0453921i
\(365\) 16.5000 28.5788i 0.863649 1.49588i
\(366\) 0 0
\(367\) 17.0000 0.887393 0.443696 0.896177i \(-0.353667\pi\)
0.443696 + 0.896177i \(0.353667\pi\)
\(368\) −4.50000 + 7.79423i −0.234579 + 0.406302i
\(369\) 0 0
\(370\) 3.00000 0.155963
\(371\) 1.50000 7.79423i 0.0778761 0.404656i
\(372\) 0 0
\(373\) −13.0000 −0.673114 −0.336557 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 4.50000 + 7.79423i 0.232689 + 0.403030i
\(375\) 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
\(383\) −15.0000 −0.766464 −0.383232 0.923652i \(-0.625189\pi\)
−0.383232 + 0.923652i \(0.625189\pi\)
\(384\) 0 0
\(385\) −22.5000 + 7.79423i −1.14671 + 0.397231i
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) 0.500000 0.866025i 0.0253837 0.0439658i
\(389\) −27.0000 −1.36895 −0.684477 0.729034i \(-0.739969\pi\)
−0.684477 + 0.729034i \(0.739969\pi\)
\(390\) 0 0
\(391\) 13.5000 23.3827i 0.682724 1.18251i
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) 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 0.981760 0.190126i \(-0.0608897\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(398\) 12.5000 + 21.6506i 0.626568 + 1.08525i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −27.0000 −1.34832 −0.674158 0.738587i \(-0.735493\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 1.50000 + 2.59808i 0.0746278 + 0.129259i
\(405\) 0 0
\(406\) −7.50000 + 2.59808i −0.372219 + 0.128940i
\(407\) 1.50000 + 2.59808i 0.0743522 + 0.128782i
\(408\) 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
\(412\) 6.50000 + 11.2583i 0.320232 + 0.554658i
\(413\) 0 0
\(414\) 0 0
\(415\) 13.5000 + 23.3827i 0.662689 + 1.14781i
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) −21.0000 −1.02714
\(419\) 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i \(-0.762780\pi\)
0.954759 + 0.297382i \(0.0961133\pi\)
\(420\) 0 0
\(421\) −17.5000 30.3109i −0.852898 1.47726i −0.878582 0.477592i \(-0.841510\pi\)
0.0256838 0.999670i \(-0.491824\pi\)
\(422\) −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
\(427\) −1.00000 + 5.19615i −0.0483934 + 0.251459i
\(428\) 4.50000 7.79423i 0.217516 0.376748i
\(429\) 0 0
\(430\) 3.00000 0.144673
\(431\) 13.5000 23.3827i 0.650272 1.12630i −0.332785 0.943003i \(-0.607988\pi\)
0.983057 0.183301i \(-0.0586785\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 20.0000 6.92820i 0.960031 0.332564i
\(435\) 0 0
\(436\) −13.0000 −0.622587
\(437\) 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 \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) 0 0
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 9.00000 0.423324
\(453\) 0 0
\(454\) −1.50000 + 2.59808i −0.0703985 + 0.121934i
\(455\) −1.50000 + 7.79423i −0.0703211 + 0.365399i
\(456\) 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
\(461\) −4.50000 7.79423i −0.209586 0.363013i 0.741998 0.670402i \(-0.233878\pi\)
−0.951584 + 0.307388i \(0.900545\pi\)
\(462\) 0 0
\(463\) −20.5000 + 35.5070i −0.952716 + 1.65015i −0.213205 + 0.977007i \(0.568390\pi\)
−0.739511 + 0.673145i \(0.764943\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) −3.00000 −0.138972
\(467\) −1.50000 2.59808i −0.0694117 0.120225i 0.829231 0.558906i \(-0.188779\pi\)
−0.898642 + 0.438682i \(0.855446\pi\)
\(468\) 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
\(475\) 14.0000 + 24.2487i 0.642364 + 1.11261i
\(476\) −7.50000 + 2.59808i −0.343762 + 0.119083i
\(477\) 0 0
\(478\) −1.50000 2.59808i −0.0686084 0.118833i
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) 0 0
\(481\) 1.00000 0.0455961
\(482\) 6.50000 11.2583i 0.296067 0.512803i
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) −1.50000 2.59808i −0.0681115 0.117973i
\(486\) 0 0
\(487\) 12.5000 21.6506i 0.566429 0.981084i −0.430486 0.902597i \(-0.641658\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) 0 0
\(490\) −3.00000 20.7846i −0.135526 0.938953i
\(491\) 10.5000 18.1865i 0.473858 0.820747i −0.525694 0.850674i \(-0.676194\pi\)
0.999552 + 0.0299272i \(0.00952753\pi\)
\(492\) 0 0
\(493\) 9.00000 0.405340
\(494\) −3.50000 + 6.06218i −0.157472 + 0.272750i
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) −30.0000 + 10.3923i −1.34568 + 0.466159i
\(498\) 0 0
\(499\) −25.0000 −1.11915 −0.559577 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) −13.5000 + 23.3827i −0.600148 + 1.03949i
\(507\) 0 0
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) 9.00000 0.398918 0.199459 0.979906i \(-0.436082\pi\)
0.199459 + 0.979906i \(0.436082\pi\)
\(510\) 0 0
\(511\) −5.50000 + 28.5788i −0.243306 + 1.26425i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −10.5000 + 18.1865i −0.463135 + 0.802174i
\(515\) 39.0000 1.71855
\(516\) 0 0
\(517\) 0 0
\(518\) −2.50000 + 0.866025i −0.109844 + 0.0380510i
\(519\) 0 0
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) 1.50000 2.59808i 0.0657162 0.113824i −0.831295 0.555831i \(-0.812400\pi\)
0.897011 + 0.442007i \(0.145733\pi\)
\(522\) 0 0
\(523\) 3.50000 + 6.06218i 0.153044 + 0.265081i 0.932345 0.361569i \(-0.117759\pi\)
−0.779301 + 0.626650i \(0.784426\pi\)
\(524\) 7.50000 + 12.9904i 0.327639 + 0.567487i
\(525\) 0 0
\(526\) 4.50000 7.79423i 0.196209 0.339845i
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) 58.0000 2.52174
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) 3.50000 18.1865i 0.151744 0.788486i
\(533\) −1.50000 2.59808i −0.0649722 0.112535i
\(534\) 0 0
\(535\) −13.5000 23.3827i −0.583656 1.01092i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) 7.50000 + 12.9904i 0.323348 + 0.560055i
\(539\) 16.5000 12.9904i 0.710705 0.559535i
\(540\) 0 0
\(541\) −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) 5.00000 0.214768
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) −19.5000 + 33.7750i −0.835288 + 1.44676i
\(546\) 0 0
\(547\) −5.50000 9.52628i −0.235163 0.407314i 0.724157 0.689635i \(-0.242229\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(548\) −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
\(553\) 8.00000 41.5692i 0.340195 1.76770i
\(554\) 0.500000 0.866025i 0.0212430 0.0367939i
\(555\) 0 0
\(556\) −7.00000 −0.296866
\(557\) −4.50000 + 7.79423i −0.190671 + 0.330252i −0.945473 0.325701i \(-0.894400\pi\)
0.754802 + 0.655953i \(0.227733\pi\)
\(558\) 0 0
\(559\) 1.00000 0.0422955
\(560\) 1.50000 7.79423i 0.0633866 0.329366i
\(561\) 0 0
\(562\) 21.0000 0.885832
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 0 0
\(565\) 13.5000 23.3827i 0.567949 0.983717i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) 6.00000 + 5.19615i 0.250435 + 0.216883i
\(575\) 36.0000 1.50130
\(576\) 0 0
\(577\) 12.5000 21.6506i 0.520382 0.901328i −0.479337 0.877631i \(-0.659123\pi\)
0.999719 0.0236970i \(-0.00754370\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) −4.50000 + 7.79423i −0.186852 + 0.323638i
\(581\) −18.0000 15.5885i −0.746766 0.646718i
\(582\) 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
\(587\) 1.50000 + 2.59808i 0.0619116 + 0.107234i 0.895320 0.445424i \(-0.146947\pi\)
−0.833408 + 0.552658i \(0.813614\pi\)
\(588\) 0 0
\(589\) 28.0000 48.4974i 1.15372 1.99830i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) 19.5000 + 33.7750i 0.800769 + 1.38697i 0.919111 + 0.394000i \(0.128909\pi\)
−0.118342 + 0.992973i \(0.537758\pi\)
\(594\) 0 0
\(595\) −4.50000 + 23.3827i −0.184482 + 0.958597i
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) 0 0
\(598\) 4.50000 + 7.79423i 0.184019 + 0.318730i
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 0 0
\(601\) 12.5000 + 21.6506i 0.509886 + 0.883148i 0.999934 + 0.0114528i \(0.00364562\pi\)
−0.490049 + 0.871695i \(0.663021\pi\)
\(602\) −2.50000 + 0.866025i −0.101892 + 0.0352966i
\(603\) 0 0
\(604\) 3.50000 + 6.06218i 0.142413 + 0.246667i
\(605\) 6.00000 0.243935
\(606\) 0 0
\(607\) −13.0000 −0.527654 −0.263827 0.964570i \(-0.584985\pi\)
−0.263827 + 0.964570i \(0.584985\pi\)
\(608\) 3.50000 6.06218i 0.141944 0.245854i
\(609\) 0 0
\(610\) 3.00000 + 5.19615i 0.121466 + 0.210386i
\(611\) 0 0
\(612\) 0 0
\(613\) −11.5000 + 19.9186i −0.464481 + 0.804504i −0.999178 0.0405396i \(-0.987092\pi\)
0.534697 + 0.845044i \(0.320426\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) 0 0
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) −22.5000 + 38.9711i −0.905816 + 1.56892i −0.0859976 + 0.996295i \(0.527408\pi\)
−0.819818 + 0.572624i \(0.805926\pi\)
\(618\) 0 0
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 12.0000 20.7846i 0.481932 0.834730i
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 6.00000 + 5.19615i 0.240385 + 0.208179i
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 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
\(635\) 12.0000 0.476205
\(636\) 0 0
\(637\) −1.00000 6.92820i −0.0396214 0.274505i
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) 33.0000 1.30342 0.651711 0.758468i \(-0.274052\pi\)
0.651711 + 0.758468i \(0.274052\pi\)
\(642\) 0 0
\(643\) −14.5000 + 25.1147i −0.571824 + 0.990429i 0.424555 + 0.905402i \(0.360431\pi\)
−0.996379 + 0.0850262i \(0.972903\pi\)
\(644\) −18.0000 15.5885i −0.709299 0.614271i
\(645\) 0 0
\(646\) −10.5000 + 18.1865i −0.413117 + 0.715540i
\(647\) −10.5000 + 18.1865i −0.412798 + 0.714986i −0.995194 0.0979182i \(-0.968782\pi\)
0.582397 + 0.812905i \(0.302115\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 2.00000 + 3.46410i 0.0784465 + 0.135873i
\(651\) 0 0
\(652\) 9.50000 16.4545i 0.372049 0.644407i
\(653\) −15.0000 −0.586995 −0.293498 0.955960i \(-0.594819\pi\)
−0.293498 + 0.955960i \(0.594819\pi\)
\(654\) 0 0
\(655\) 45.0000 1.75830
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.50000 + 2.59808i 0.0584317 + 0.101207i 0.893762 0.448542i \(-0.148057\pi\)
−0.835330 + 0.549749i \(0.814723\pi\)
\(660\) 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
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) −42.0000 36.3731i −1.62869 1.41049i
\(666\) 0 0
\(667\) 13.5000 + 23.3827i 0.522722 + 0.905381i
\(668\) 15.0000 0.580367
\(669\) 0 0
\(670\) 12.0000 0.463600
\(671\) −3.00000 + 5.19615i −0.115814 + 0.200595i
\(672\) 0 0
\(673\) −17.5000 30.3109i −0.674575 1.16840i −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) 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 \(0.362247\pi\)
−0.995877 + 0.0907112i \(0.971086\pi\)
\(678\) 0 0
\(679\) 2.00000 + 1.73205i 0.0767530 + 0.0664700i
\(680\) −4.50000 + 7.79423i −0.172567 + 0.298895i
\(681\) 0 0
\(682\) 24.0000 0.919007
\(683\) −4.50000 + 7.79423i −0.172188 + 0.298238i −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 0 0
\(685\) −27.0000 −1.03162
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) −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
\(698\) 23.0000 0.870563
\(699\) 0 0
\(700\) −8.00000 6.92820i −0.302372 0.261861i
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 1.50000 2.59808i 0.0564532 0.0977799i
\(707\) −7.50000 + 2.59808i −0.282067 + 0.0977107i
\(708\) 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
\(713\) −36.0000 62.3538i −1.34821 2.33517i
\(714\) 0 0
\(715\) −4.50000 + 7.79423i −0.168290 + 0.291488i
\(716\) 21.0000 0.784807
\(717\) 0 0
\(718\) −9.00000 −0.335877
\(719\) −7.50000 12.9904i −0.279703 0.484459i 0.691608 0.722273i \(-0.256903\pi\)
−0.971311 + 0.237814i \(0.923569\pi\)
\(720\) 0 0
\(721\) −32.5000 + 11.2583i −1.21036 + 0.419282i
\(722\) −15.0000 25.9808i −0.558242 0.966904i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 6.00000 + 10.3923i 0.222834 + 0.385961i
\(726\) 0 0
\(727\) 6.50000 + 11.2583i 0.241072 + 0.417548i 0.961020 0.276479i \(-0.0891678\pi\)
−0.719948 + 0.694028i \(0.755834\pi\)
\(728\) 0.500000 2.59808i 0.0185312 0.0962911i
\(729\) 0 0
\(730\) 16.5000 + 28.5788i 0.610692 + 1.05775i
\(731\) 3.00000 0.110959
\(732\) 0 0
\(733\) −1.00000 −0.0369358 −0.0184679 0.999829i \(-0.505879\pi\)
−0.0184679 + 0.999829i \(0.505879\pi\)
\(734\) −8.50000 + 14.7224i −0.313741 + 0.543415i
\(735\) 0 0
\(736\) −4.50000 7.79423i −0.165872 0.287299i
\(737\) 6.00000 + 10.3923i 0.221013 + 0.382805i
\(738\) 0 0
\(739\) −11.5000 + 19.9186i −0.423034 + 0.732717i −0.996235 0.0866983i \(-0.972368\pi\)
0.573200 + 0.819415i \(0.305702\pi\)
\(740\) −1.50000 + 2.59808i −0.0551411 + 0.0955072i
\(741\) 0 0
\(742\) 6.00000 + 5.19615i 0.220267 + 0.190757i
\(743\) 10.5000 18.1865i 0.385208 0.667199i −0.606590 0.795015i \(-0.707463\pi\)
0.991798 + 0.127815i \(0.0407965\pi\)
\(744\) 0 0
\(745\) −27.0000 −0.989203
\(746\) 6.50000 11.2583i 0.237982 0.412197i
\(747\) 0 0
\(748\) −9.00000 −0.329073
\(749\) 18.0000 + 15.5885i 0.657706 + 0.569590i
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 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
\(761\) 45.0000 1.63125 0.815624 0.578582i \(-0.196394\pi\)
0.815624 + 0.578582i \(0.196394\pi\)
\(762\) 0 0
\(763\) 6.50000 33.7750i 0.235316 1.22274i
\(764\) 0 0
\(765\) 0 0
\(766\) 7.50000 12.9904i 0.270986 0.469362i
\(767\) 0 0
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 4.50000 23.3827i 0.162169 0.842654i
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 13.5000 23.3827i 0.485561 0.841017i −0.514301 0.857610i \(-0.671949\pi\)
0.999862 + 0.0165929i \(0.00528194\pi\)
\(774\) 0 0
\(775\) −16.0000 27.7128i −0.574737 0.995474i
\(776\) 0.500000 + 0.866025i 0.0179490 + 0.0310885i
\(777\) 0 0
\(778\) 13.5000 23.3827i 0.483998 0.838310i
\(779\) 21.0000 0.752403
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) 13.5000 + 23.3827i 0.482759 + 0.836163i
\(783\) 0 0
\(784\) 1.00000 + 6.92820i 0.0357143 + 0.247436i
\(785\) −33.0000 57.1577i −1.17782 2.04004i
\(786\) 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
\(790\) −24.0000 41.5692i −0.853882 1.47897i
\(791\) −4.50000 + 23.3827i −0.160002 + 0.831393i
\(792\) 0 0
\(793\) 1.00000 + 1.73205i 0.0355110 + 0.0615069i
\(794\) −13.0000 −0.461353
\(795\) 0 0
\(796\) −25.0000 −0.886102
\(797\) −10.5000 + 18.1865i −0.371929 + 0.644200i −0.989862 0.142031i \(-0.954637\pi\)
0.617933 + 0.786231i \(0.287970\pi\)
\(798\) 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
\(805\) −67.5000 + 23.3827i −2.37906 + 0.824131i
\(806\) 4.00000 6.92820i 0.140894 0.244036i
\(807\) 0 0
\(808\) −3.00000 −0.105540
\(809\) −16.5000 + 28.5788i −0.580109 + 1.00478i 0.415357 + 0.909659i \(0.363657\pi\)
−0.995466 + 0.0951198i \(0.969677\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 1.50000 7.79423i 0.0526397 0.273524i
\(813\) 0 0
\(814\) −3.00000 −0.105150
\(815\) −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 \(0.428503\pi\)
−0.955636 + 0.294549i \(0.904831\pi\)
\(822\) 0 0
\(823\) 20.0000 + 34.6410i 0.697156 + 1.20751i 0.969448 + 0.245295i \(0.0788849\pi\)
−0.272292 + 0.962215i \(0.587782\pi\)
\(824\) −13.0000 −0.452876
\(825\) 0 0
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 0 0
\(829\) −5.50000 + 9.52628i −0.191023 + 0.330861i −0.945589 0.325362i \(-0.894514\pi\)
0.754567 + 0.656223i \(0.227847\pi\)
\(830\) −27.0000 −0.937184
\(831\) 0 0
\(832\) 0.500000 0.866025i 0.0173344 0.0300240i
\(833\) −3.00000 20.7846i −0.103944 0.720144i
\(834\) 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
\(839\) 7.50000 + 12.9904i 0.258929 + 0.448478i 0.965955 0.258709i \(-0.0832972\pi\)
−0.707026 + 0.707187i \(0.749964\pi\)
\(840\) 0 0
\(841\) 10.0000 17.3205i 0.344828 0.597259i
\(842\) 35.0000 1.20618
\(843\) 0 0
\(844\) 5.00000 0.172107
\(845\) −18.0000 31.1769i −0.619219 1.07252i
\(846\) 0 0
\(847\) −5.00000 + 1.73205i −0.171802 + 0.0595140i
\(848\) 1.50000 + 2.59808i 0.0515102 + 0.0892183i
\(849\) 0 0
\(850\) 6.00000 + 10.3923i 0.205798 + 0.356453i
\(851\) 4.50000 + 7.79423i 0.154258 + 0.267183i
\(852\) 0 0
\(853\) 0.500000 + 0.866025i 0.0171197 + 0.0296521i 0.874458 0.485101i \(-0.161217\pi\)
−0.857339 + 0.514753i \(0.827884\pi\)
\(854\) −4.00000 3.46410i −0.136877 0.118539i
\(855\) 0 0
\(856\) 4.50000 + 7.79423i 0.153807 + 0.266401i
\(857\) −3.00000 −0.102478 −0.0512390 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) 0 0
\(859\) −25.0000 −0.852989 −0.426494 0.904490i \(-0.640252\pi\)
−0.426494 + 0.904490i \(0.640252\pi\)
\(860\) −1.50000 + 2.59808i −0.0511496 + 0.0885937i
\(861\) 0 0
\(862\) 13.5000 + 23.3827i 0.459812 + 0.796417i
\(863\) −25.5000 44.1673i −0.868030 1.50347i −0.864007 0.503480i \(-0.832053\pi\)
−0.00402340 0.999992i \(-0.501281\pi\)
\(864\) 0 0
\(865\) 9.00000 15.5885i 0.306009 0.530023i
\(866\) −1.00000 + 1.73205i −0.0339814 + 0.0588575i
\(867\) 0 0
\(868\) −4.00000 + 20.7846i −0.135769 + 0.705476i
\(869\) 24.0000 41.5692i 0.814144 1.41014i
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 6.50000 11.2583i 0.220118 0.381255i
\(873\) 0 0
\(874\) −63.0000 −2.13101
\(875\) 7.50000 2.59808i 0.253546 0.0878310i
\(876\) 0 0
\(877\) 47.0000 1.58708 0.793539 0.608520i \(-0.208236\pi\)
0.793539 + 0.608520i \(0.208236\pi\)
\(878\) −4.00000 6.92820i −0.134993 0.233816i
\(879\) 0 0
\(880\) 4.50000 7.79423i 0.151695 0.262743i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −1.50000 + 2.59808i −0.0504505 + 0.0873828i
\(885\) 0 0
\(886\) 18.0000 + 31.1769i 0.604722 + 1.04741i
\(887\) 33.0000 1.10803 0.554016 0.832506i \(-0.313095\pi\)
0.554016 + 0.832506i \(0.313095\pi\)
\(888\) 0 0
\(889\) −10.0000 + 3.46410i −0.335389 + 0.116182i
\(890\) 9.00000 0.301681
\(891\) 0 0
\(892\) 0.500000 0.866025i 0.0167412 0.0289967i
\(893\) 0 0
\(894\) 0 0
\(895\) 31.5000 54.5596i 1.05293 1.82373i
\(896\) −0.500000 + 2.59808i −0.0167038 + 0.0867956i
\(897\) 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
\(902\) 4.50000 + 7.79423i 0.149834 + 0.259519i
\(903\) 0 0
\(904\) −4.50000 + 7.79423i −0.149668 + 0.259232i
\(905\) −6.00000 −0.199447
\(906\) 0 0
\(907\) −43.0000 −1.42779 −0.713896 0.700252i \(-0.753071\pi\)
−0.713896 + 0.700252i \(0.753071\pi\)
\(908\) −1.50000 2.59808i −0.0497792 0.0862202i
\(909\) 0 0
\(910\) −6.00000 5.19615i −0.198898 0.172251i
\(911\) 19.5000 + 33.7750i 0.646064 + 1.11902i 0.984055 + 0.177866i \(0.0569194\pi\)
−0.337991 + 0.941149i \(0.609747\pi\)
\(912\) 0 0
\(913\) −13.5000 23.3827i −0.446785 0.773854i
\(914\) 5.00000 + 8.66025i 0.165385 + 0.286456i
\(915\) 0 0
\(916\) 6.50000 + 11.2583i 0.214766 + 0.371986i
\(917\) −37.5000 + 12.9904i −1.23836 + 0.428980i
\(918\) 0 0
\(919\) −26.5000 45.8993i −0.874154 1.51408i −0.857661 0.514216i \(-0.828083\pi\)
−0.0164935 0.999864i \(-0.505250\pi\)
\(920\) −27.0000 −0.890164
\(921\) 0 0
\(922\) 9.00000 0.296399
\(923\) −6.00000 + 10.3923i −0.197492 + 0.342067i
\(924\) 0 0
\(925\) 2.00000 + 3.46410i 0.0657596 + 0.113899i
\(926\) −20.5000 35.5070i −0.673672 1.16683i
\(927\) 0 0
\(928\) 1.50000 2.59808i 0.0492399 0.0852860i
\(929\) 9.00000 15.5885i 0.295280 0.511441i −0.679770 0.733426i \(-0.737920\pi\)
0.975050 + 0.221985i \(0.0712536\pi\)
\(930\) 0 0
\(931\) 45.5000 + 18.1865i 1.49120 + 0.596040i
\(932\) 1.50000 2.59808i 0.0491341 0.0851028i
\(933\) 0 0
\(934\) 3.00000 0.0981630
\(935\) −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 \(0.360383\pi\)
\(938\) −10.0000 + 3.46410i −0.326512 + 0.113107i
\(939\) 0 0
\(940\) 0 0
\(941\) −3.00000 5.19615i −0.0977972 0.169390i 0.812975 0.582298i \(-0.197846\pi\)
−0.910773 + 0.412908i \(0.864513\pi\)
\(942\) 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 −0.751918 0.659256i \(-0.770871\pi\)
0.946892 + 0.321552i \(0.104204\pi\)
\(948\) 0 0
\(949\) 5.50000 + 9.52628i 0.178538 + 0.309236i
\(950\) −28.0000 −0.908440
\(951\) 0 0
\(952\) 1.50000 7.79423i 0.0486153 0.252612i
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 3.00000 0.0970269
\(957\) 0 0
\(958\) −1.50000 + 2.59808i −0.0484628 + 0.0839400i
\(959\) 22.5000 7.79423i 0.726563 0.251689i
\(960\) 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
\(965\) 21.0000 + 36.3731i 0.676014 + 1.17089i
\(966\) 0 0
\(967\) −20.5000 + 35.5070i −0.659236 + 1.14183i 0.321578 + 0.946883i \(0.395787\pi\)
−0.980814 + 0.194946i \(0.937547\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) 3.00000 0.0963242
\(971\) 16.5000 + 28.5788i 0.529510 + 0.917139i 0.999408 + 0.0344175i \(0.0109576\pi\)
−0.469897 + 0.882721i \(0.655709\pi\)
\(972\) 0 0
\(973\) 3.50000 18.1865i 0.112205 0.583033i
\(974\) 12.5000 + 21.6506i 0.400526 + 0.693731i
\(975\) 0 0
\(976\) −1.00000 1.73205i −0.0320092 0.0554416i
\(977\) −15.0000 25.9808i −0.479893 0.831198i 0.519841 0.854263i \(-0.325991\pi\)
−0.999734 + 0.0230645i \(0.992658\pi\)
\(978\) 0 0
\(979\) 4.50000 + 7.79423i 0.143821 + 0.249105i
\(980\) 19.5000 + 7.79423i 0.622905 + 0.248978i
\(981\) 0 0
\(982\) 10.5000 + 18.1865i 0.335068 + 0.580356i
\(983\) 15.0000 0.478426 0.239213 0.970967i \(-0.423111\pi\)
0.239213 + 0.970967i \(0.423111\pi\)
\(984\) 0 0
\(985\) 54.0000 1.72058
\(986\) −4.50000 + 7.79423i −0.143309 + 0.248219i
\(987\) 0 0
\(988\) −3.50000 6.06218i −0.111350 0.192864i
\(989\) 4.50000 + 7.79423i 0.143092 + 0.247842i
\(990\) 0 0
\(991\) 12.5000 21.6506i 0.397076 0.687755i −0.596288 0.802771i \(-0.703358\pi\)
0.993364 + 0.115015i \(0.0366917\pi\)
\(992\) −4.00000 + 6.92820i −0.127000 + 0.219971i
\(993\) 0 0
\(994\) 6.00000 31.1769i 0.190308 0.988872i
\(995\) −37.5000 + 64.9519i −1.18883 + 2.05911i
\(996\) 0 0
\(997\) −13.0000 −0.411714 −0.205857 0.978582i \(-0.565998\pi\)
−0.205857 + 0.978582i \(0.565998\pi\)
\(998\) 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 378.2.h.a.361.1 2
3.2 odd 2 126.2.h.b.67.1 yes 2
4.3 odd 2 3024.2.t.a.1873.1 2
7.2 even 3 378.2.e.b.37.1 2
7.3 odd 6 2646.2.f.a.1765.1 2
7.4 even 3 2646.2.f.d.1765.1 2
7.5 odd 6 2646.2.e.g.1549.1 2
7.6 odd 2 2646.2.h.d.361.1 2
9.2 odd 6 126.2.e.a.25.1 2
9.4 even 3 1134.2.g.c.487.1 2
9.5 odd 6 1134.2.g.e.487.1 2
9.7 even 3 378.2.e.b.235.1 2
12.11 even 2 1008.2.t.f.193.1 2
21.2 odd 6 126.2.e.a.121.1 yes 2
21.5 even 6 882.2.e.c.373.1 2
21.11 odd 6 882.2.f.i.589.1 2
21.17 even 6 882.2.f.g.589.1 2
21.20 even 2 882.2.h.i.67.1 2
28.23 odd 6 3024.2.q.f.2305.1 2
36.7 odd 6 3024.2.q.f.2881.1 2
36.11 even 6 1008.2.q.a.529.1 2
63.2 odd 6 126.2.h.b.79.1 yes 2
63.4 even 3 7938.2.a.t.1.1 1
63.11 odd 6 882.2.f.i.295.1 2
63.16 even 3 inner 378.2.h.a.289.1 2
63.20 even 6 882.2.e.c.655.1 2
63.23 odd 6 1134.2.g.e.163.1 2
63.25 even 3 2646.2.f.d.883.1 2
63.31 odd 6 7938.2.a.be.1.1 1
63.32 odd 6 7938.2.a.m.1.1 1
63.34 odd 6 2646.2.e.g.2125.1 2
63.38 even 6 882.2.f.g.295.1 2
63.47 even 6 882.2.h.i.79.1 2
63.52 odd 6 2646.2.f.a.883.1 2
63.58 even 3 1134.2.g.c.163.1 2
63.59 even 6 7938.2.a.b.1.1 1
63.61 odd 6 2646.2.h.d.667.1 2
84.23 even 6 1008.2.q.a.625.1 2
252.79 odd 6 3024.2.t.a.289.1 2
252.191 even 6 1008.2.t.f.961.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.a.25.1 2 9.2 odd 6
126.2.e.a.121.1 yes 2 21.2 odd 6
126.2.h.b.67.1 yes 2 3.2 odd 2
126.2.h.b.79.1 yes 2 63.2 odd 6
378.2.e.b.37.1 2 7.2 even 3
378.2.e.b.235.1 2 9.7 even 3
378.2.h.a.289.1 2 63.16 even 3 inner
378.2.h.a.361.1 2 1.1 even 1 trivial
882.2.e.c.373.1 2 21.5 even 6
882.2.e.c.655.1 2 63.20 even 6
882.2.f.g.295.1 2 63.38 even 6
882.2.f.g.589.1 2 21.17 even 6
882.2.f.i.295.1 2 63.11 odd 6
882.2.f.i.589.1 2 21.11 odd 6
882.2.h.i.67.1 2 21.20 even 2
882.2.h.i.79.1 2 63.47 even 6
1008.2.q.a.529.1 2 36.11 even 6
1008.2.q.a.625.1 2 84.23 even 6
1008.2.t.f.193.1 2 12.11 even 2
1008.2.t.f.961.1 2 252.191 even 6
1134.2.g.c.163.1 2 63.58 even 3
1134.2.g.c.487.1 2 9.4 even 3
1134.2.g.e.163.1 2 63.23 odd 6
1134.2.g.e.487.1 2 9.5 odd 6
2646.2.e.g.1549.1 2 7.5 odd 6
2646.2.e.g.2125.1 2 63.34 odd 6
2646.2.f.a.883.1 2 63.52 odd 6
2646.2.f.a.1765.1 2 7.3 odd 6
2646.2.f.d.883.1 2 63.25 even 3
2646.2.f.d.1765.1 2 7.4 even 3
2646.2.h.d.361.1 2 7.6 odd 2
2646.2.h.d.667.1 2 63.61 odd 6
3024.2.q.f.2305.1 2 28.23 odd 6
3024.2.q.f.2881.1 2 36.7 odd 6
3024.2.t.a.289.1 2 252.79 odd 6
3024.2.t.a.1873.1 2 4.3 odd 2
7938.2.a.b.1.1 1 63.59 even 6
7938.2.a.m.1.1 1 63.32 odd 6
7938.2.a.t.1.1 1 63.4 even 3
7938.2.a.be.1.1 1 63.31 odd 6