Properties

Label 294.2.e.d.67.1
Level $294$
Weight $2$
Character 294.67
Analytic conductor $2.348$
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] = [294,2,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.e (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: \(2.34760181943\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.2.e.d.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{12} -4.00000 q^{13} -4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -4.00000 q^{20} +4.00000 q^{22} +(0.500000 - 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000 q^{27} +2.00000 q^{29} +(-2.00000 - 3.46410i) q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +1.00000 q^{36} +(3.00000 + 5.19615i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-2.00000 - 3.46410i) q^{40} +4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(2.00000 - 3.46410i) q^{45} +(-4.00000 - 6.92820i) q^{47} +1.00000 q^{48} -11.0000 q^{50} +(2.00000 - 3.46410i) q^{52} +(5.00000 - 8.66025i) q^{53} +(0.500000 + 0.866025i) q^{54} +16.0000 q^{55} -4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-2.00000 - 3.46410i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-8.00000 - 13.8564i) q^{65} +(-2.00000 + 3.46410i) q^{66} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-8.00000 + 13.8564i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-5.50000 - 9.52628i) q^{75} -4.00000 q^{76} +4.00000 q^{78} +(4.00000 + 6.92820i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +(2.00000 + 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(4.00000 + 6.92820i) q^{89} +4.00000 q^{90} +(4.00000 + 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{8} - q^{9} - 4 q^{10} + 4 q^{11} - q^{12} - 8 q^{13} - 8 q^{15} - q^{16} + q^{18} + 4 q^{19} - 8 q^{20} + 8 q^{22} + q^{24} - 11 q^{25} - 4 q^{26} + 2 q^{27} + 4 q^{29} - 4 q^{30} + 8 q^{31} + q^{32} + 4 q^{33} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 8 q^{43} + 4 q^{44} + 4 q^{45} - 8 q^{47} + 2 q^{48} - 22 q^{50} + 4 q^{52} + 10 q^{53} + q^{54} + 32 q^{55} - 8 q^{57} + 2 q^{58} + 4 q^{59} + 4 q^{60} - 4 q^{61} + 16 q^{62} + 2 q^{64} - 16 q^{65} - 4 q^{66} - 4 q^{67} + 16 q^{71} + q^{72} - 16 q^{73} - 6 q^{74} - 11 q^{75} - 8 q^{76} + 8 q^{78} + 8 q^{79} + 4 q^{80} - q^{81} + 24 q^{83} + 4 q^{86} - 2 q^{87} - 4 q^{88} + 8 q^{89} + 8 q^{90} + 8 q^{93} + 8 q^{94} - 16 q^{95} + q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −2.00000 + 3.46410i −0.632456 + 1.09545i
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −4.00000 −0.894427
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −5.50000 + 9.52628i −1.10000 + 1.90526i
\(26\) −2.00000 3.46410i −0.392232 0.679366i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −2.00000 3.46410i −0.365148 0.632456i
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 2.00000 + 3.46410i 0.348155 + 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.00000 + 5.19615i 0.493197 + 0.854242i 0.999969 0.00783774i \(-0.00249486\pi\)
−0.506772 + 0.862080i \(0.669162\pi\)
\(38\) −2.00000 + 3.46410i −0.324443 + 0.561951i
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) −2.00000 3.46410i −0.316228 0.547723i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 2.00000 3.46410i 0.298142 0.516398i
\(46\) 0 0
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) −11.0000 −1.55563
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 5.00000 8.66025i 0.686803 1.18958i −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 16.0000 2.15744
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 1.00000 + 1.73205i 0.131306 + 0.227429i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 2.00000 3.46410i 0.258199 0.447214i
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.00000 13.8564i −0.992278 1.71868i
\(66\) −2.00000 + 3.46410i −0.246183 + 0.426401i
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −8.00000 + 13.8564i −0.936329 + 1.62177i −0.164083 + 0.986447i \(0.552466\pi\)
−0.772246 + 0.635323i \(0.780867\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) −5.50000 9.52628i −0.635085 1.10000i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 4.00000 + 6.92820i 0.450035 + 0.779484i 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) 2.00000 3.46410i 0.223607 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) 4.00000 + 6.92820i 0.423999 + 0.734388i 0.996326 0.0856373i \(-0.0272926\pi\)
−0.572327 + 0.820025i \(0.693959\pi\)
\(90\) 4.00000 0.421637
\(91\) 0 0
\(92\) 0 0
\(93\) 4.00000 + 6.92820i 0.414781 + 0.718421i
\(94\) 4.00000 6.92820i 0.412568 0.714590i
\(95\) −8.00000 + 13.8564i −0.820783 + 1.42164i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) −5.50000 9.52628i −0.550000 0.952628i
\(101\) 2.00000 3.46410i 0.199007 0.344691i −0.749199 0.662344i \(-0.769562\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) −2.00000 3.46410i −0.193347 0.334887i 0.753010 0.658009i \(-0.228601\pi\)
−0.946357 + 0.323122i \(0.895268\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i \(-0.599422\pi\)
0.977769 0.209687i \(-0.0672444\pi\)
\(110\) 8.00000 + 13.8564i 0.762770 + 1.32116i
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 0 0
\(116\) −1.00000 + 1.73205i −0.0928477 + 0.160817i
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 4.00000 0.365148
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 2.00000 3.46410i 0.181071 0.313625i
\(123\) 0 0
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) 8.00000 13.8564i 0.701646 1.21529i
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 2.00000 + 3.46410i 0.172133 + 0.298142i
\(136\) 0 0
\(137\) 5.00000 8.66025i 0.427179 0.739895i −0.569442 0.822031i \(-0.692841\pi\)
0.996621 + 0.0821359i \(0.0261741\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 4.00000 + 6.92820i 0.335673 + 0.581402i
\(143\) −8.00000 + 13.8564i −0.668994 + 1.15873i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) −16.0000 −1.32417
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 5.50000 9.52628i 0.449073 0.777817i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −2.00000 3.46410i −0.162221 0.280976i
\(153\) 0 0
\(154\) 0 0
\(155\) 32.0000 2.57030
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 5.00000 + 8.66025i 0.396526 + 0.686803i
\(160\) 4.00000 0.316228
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −6.00000 10.3923i −0.469956 0.813988i 0.529454 0.848339i \(-0.322397\pi\)
−0.999410 + 0.0343508i \(0.989064\pi\)
\(164\) 0 0
\(165\) −8.00000 + 13.8564i −0.622799 + 1.07872i
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) −2.00000 3.46410i −0.152057 0.263371i 0.779926 0.625871i \(-0.215256\pi\)
−0.931984 + 0.362500i \(0.881923\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 2.00000 + 3.46410i 0.150329 + 0.260378i
\(178\) −4.00000 + 6.92820i −0.299813 + 0.519291i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 2.00000 + 3.46410i 0.149071 + 0.258199i
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) −4.00000 + 6.92820i −0.293294 + 0.508001i
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) −16.0000 −1.16076
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −4.00000 6.92820i −0.287183 0.497416i
\(195\) 16.0000 1.14578
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −2.00000 3.46410i −0.142134 0.246183i
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 5.50000 9.52628i 0.388909 0.673610i
\(201\) −2.00000 3.46410i −0.141069 0.244339i
\(202\) 4.00000 0.281439
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 5.00000 + 8.66025i 0.343401 + 0.594789i
\(213\) −4.00000 + 6.92820i −0.274075 + 0.474713i
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) 8.00000 + 13.8564i 0.545595 + 0.944999i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) −8.00000 13.8564i −0.540590 0.936329i
\(220\) −8.00000 + 13.8564i −0.539360 + 0.934199i
\(221\) 0 0
\(222\) −3.00000 5.19615i −0.201347 0.348743i
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 11.0000 0.733333
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) 10.0000 17.3205i 0.663723 1.14960i −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 5.00000 + 8.66025i 0.327561 + 0.567352i 0.982027 0.188739i \(-0.0604400\pi\)
−0.654466 + 0.756091i \(0.727107\pi\)
\(234\) −2.00000 + 3.46410i −0.130744 + 0.226455i
\(235\) 16.0000 27.7128i 1.04372 1.80778i
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 2.00000 + 3.46410i 0.129099 + 0.223607i
\(241\) 4.00000 6.92820i 0.257663 0.446285i −0.707953 0.706260i \(-0.750381\pi\)
0.965615 + 0.259975i \(0.0837143\pi\)
\(242\) 2.50000 4.33013i 0.160706 0.278351i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) 0 0
\(247\) −8.00000 13.8564i −0.509028 0.881662i
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) −12.0000 20.7846i −0.758947 1.31453i
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.00000 + 6.92820i 0.249513 + 0.432169i 0.963391 0.268101i \(-0.0863961\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 16.0000 0.992278
\(261\) −1.00000 1.73205i −0.0618984 0.107211i
\(262\) 6.00000 10.3923i 0.370681 0.642039i
\(263\) −4.00000 + 6.92820i −0.246651 + 0.427211i −0.962594 0.270947i \(-0.912663\pi\)
0.715944 + 0.698158i \(0.245997\pi\)
\(264\) −2.00000 3.46410i −0.123091 0.213201i
\(265\) 40.0000 2.45718
\(266\) 0 0
\(267\) −8.00000 −0.489592
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) 14.0000 24.2487i 0.853595 1.47847i −0.0243472 0.999704i \(-0.507751\pi\)
0.877942 0.478766i \(-0.158916\pi\)
\(270\) −2.00000 + 3.46410i −0.121716 + 0.210819i
\(271\) −16.0000 27.7128i −0.971931 1.68343i −0.689713 0.724083i \(-0.742263\pi\)
−0.282218 0.959350i \(-0.591070\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 22.0000 + 38.1051i 1.32665 + 2.29783i
\(276\) 0 0
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) −6.00000 10.3923i −0.359856 0.623289i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 4.00000 + 6.92820i 0.238197 + 0.412568i
\(283\) −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) −4.00000 + 6.92820i −0.237356 + 0.411113i
\(285\) −8.00000 13.8564i −0.473879 0.820783i
\(286\) −16.0000 −0.946100
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −4.00000 + 6.92820i −0.234888 + 0.406838i
\(291\) 4.00000 6.92820i 0.234484 0.406138i
\(292\) −8.00000 13.8564i −0.468165 0.810885i
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 16.0000 0.931556
\(296\) −3.00000 5.19615i −0.174371 0.302020i
\(297\) 2.00000 3.46410i 0.116052 0.201008i
\(298\) −5.00000 + 8.66025i −0.289642 + 0.501675i
\(299\) 0 0
\(300\) 11.0000 0.635085
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 2.00000 + 3.46410i 0.114897 + 0.199007i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 8.00000 13.8564i 0.458079 0.793416i
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 16.0000 + 27.7128i 0.908739 + 1.57398i
\(311\) 16.0000 27.7128i 0.907277 1.57145i 0.0894452 0.995992i \(-0.471491\pi\)
0.817832 0.575458i \(-0.195176\pi\)
\(312\) −2.00000 + 3.46410i −0.113228 + 0.196116i
\(313\) 12.0000 + 20.7846i 0.678280 + 1.17482i 0.975499 + 0.220006i \(0.0706077\pi\)
−0.297218 + 0.954810i \(0.596059\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) −5.00000 + 8.66025i −0.280386 + 0.485643i
\(319\) 4.00000 6.92820i 0.223957 0.387905i
\(320\) 2.00000 + 3.46410i 0.111803 + 0.193649i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 22.0000 38.1051i 1.22034 2.11369i
\(326\) 6.00000 10.3923i 0.332309 0.575577i
\(327\) 7.00000 + 12.1244i 0.387101 + 0.670478i
\(328\) 0 0
\(329\) 0 0
\(330\) −16.0000 −0.880771
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) −6.00000 + 10.3923i −0.329293 + 0.570352i
\(333\) 3.00000 5.19615i 0.164399 0.284747i
\(334\) −4.00000 6.92820i −0.218870 0.379094i
\(335\) −16.0000 −0.874173
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 1.50000 + 2.59808i 0.0815892 + 0.141317i
\(339\) 7.00000 12.1244i 0.380188 0.658505i
\(340\) 0 0
\(341\) −16.0000 27.7128i −0.866449 1.50073i
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 2.00000 3.46410i 0.107521 0.186231i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) −1.00000 1.73205i −0.0536056 0.0928477i
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −2.00000 3.46410i −0.106600 0.184637i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 16.0000 + 27.7128i 0.849192 + 1.47084i
\(356\) −8.00000 −0.423999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i \(-0.305417\pi\)
−0.996157 + 0.0875892i \(0.972084\pi\)
\(360\) −2.00000 + 3.46410i −0.105409 + 0.182574i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −10.0000 17.3205i −0.525588 0.910346i
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) −64.0000 −3.34991
\(366\) 2.00000 + 3.46410i 0.104542 + 0.181071i
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 0 0
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 4.00000 + 6.92820i 0.206284 + 0.357295i
\(377\) −8.00000 −0.412021
\(378\) 0 0
\(379\) 36.0000 1.84920 0.924598 0.380945i \(-0.124401\pi\)
0.924598 + 0.380945i \(0.124401\pi\)
\(380\) −8.00000 13.8564i −0.410391 0.710819i
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) 0 0
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) −2.00000 3.46410i −0.101666 0.176090i
\(388\) 4.00000 6.92820i 0.203069 0.351726i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 8.00000 + 13.8564i 0.405096 + 0.701646i
\(391\) 0 0
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) −16.0000 + 27.7128i −0.805047 + 1.39438i
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) 2.00000 + 3.46410i 0.100377 + 0.173858i 0.911840 0.410546i \(-0.134662\pi\)
−0.811463 + 0.584404i \(0.801328\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 2.00000 3.46410i 0.0997509 0.172774i
\(403\) −16.0000 + 27.7128i −0.797017 + 1.38047i
\(404\) 2.00000 + 3.46410i 0.0995037 + 0.172345i
\(405\) −4.00000 −0.198762
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −12.0000 + 20.7846i −0.593362 + 1.02773i 0.400414 + 0.916334i \(0.368866\pi\)
−0.993776 + 0.111398i \(0.964467\pi\)
\(410\) 0 0
\(411\) 5.00000 + 8.66025i 0.246632 + 0.427179i
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) 24.0000 + 41.5692i 1.17811 + 2.04055i
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) 6.00000 10.3923i 0.293821 0.508913i
\(418\) 8.00000 + 13.8564i 0.391293 + 0.677739i
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) −14.0000 24.2487i −0.681509 1.18041i
\(423\) −4.00000 + 6.92820i −0.194487 + 0.336861i
\(424\) −5.00000 + 8.66025i −0.242821 + 0.420579i
\(425\) 0 0
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) −8.00000 13.8564i −0.386244 0.668994i
\(430\) −8.00000 + 13.8564i −0.385794 + 0.668215i
\(431\) −20.0000 + 34.6410i −0.963366 + 1.66860i −0.249424 + 0.968394i \(0.580241\pi\)
−0.713942 + 0.700205i \(0.753092\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 8.00000 0.384455 0.192228 0.981350i \(-0.438429\pi\)
0.192228 + 0.981350i \(0.438429\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) 0 0
\(438\) 8.00000 13.8564i 0.382255 0.662085i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −16.0000 −0.762770
\(441\) 0 0
\(442\) 0 0
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 3.00000 5.19615i 0.142374 0.246598i
\(445\) −16.0000 + 27.7128i −0.758473 + 1.31371i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 5.50000 + 9.52628i 0.259272 + 0.449073i
\(451\) 0 0
\(452\) 7.00000 12.1244i 0.329252 0.570282i
\(453\) 4.00000 + 6.92820i 0.187936 + 0.325515i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) −2.00000 + 3.46410i −0.0934539 + 0.161867i
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −1.00000 1.73205i −0.0464238 0.0804084i
\(465\) −16.0000 + 27.7128i −0.741982 + 1.28515i
\(466\) −5.00000 + 8.66025i −0.231621 + 0.401179i
\(467\) 10.0000 + 17.3205i 0.462745 + 0.801498i 0.999097 0.0424970i \(-0.0135313\pi\)
−0.536352 + 0.843995i \(0.680198\pi\)
\(468\) −4.00000 −0.184900
\(469\) 0 0
\(470\) 32.0000 1.47605
\(471\) 2.00000 + 3.46410i 0.0921551 + 0.159617i
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) −4.00000 6.92820i −0.183726 0.318223i
\(475\) −44.0000 −2.01886
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) −12.0000 20.7846i −0.548867 0.950666i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) −2.00000 + 3.46410i −0.0912871 + 0.158114i
\(481\) −12.0000 20.7846i −0.547153 0.947697i
\(482\) 8.00000 0.364390
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) −16.0000 27.7128i −0.726523 1.25837i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i \(-0.775317\pi\)
0.942309 + 0.334744i \(0.108650\pi\)
\(488\) 2.00000 + 3.46410i 0.0905357 + 0.156813i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 8.00000 13.8564i 0.359937 0.623429i
\(495\) −8.00000 13.8564i −0.359573 0.622799i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 6.00000 + 10.3923i 0.268597 + 0.465223i 0.968500 0.249015i \(-0.0801067\pi\)
−0.699903 + 0.714238i \(0.746773\pi\)
\(500\) 12.0000 20.7846i 0.536656 0.929516i
\(501\) 4.00000 6.92820i 0.178707 0.309529i
\(502\) 10.0000 + 17.3205i 0.446322 + 0.773052i
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 16.0000 0.711991
\(506\) 0 0
\(507\) −1.50000 + 2.59808i −0.0666173 + 0.115385i
\(508\) 8.00000 13.8564i 0.354943 0.614779i
\(509\) −2.00000 3.46410i −0.0886484 0.153544i 0.818292 0.574803i \(-0.194921\pi\)
−0.906940 + 0.421260i \(0.861588\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) −4.00000 + 6.92820i −0.176432 + 0.305590i
\(515\) 16.0000 27.7128i 0.705044 1.22117i
\(516\) −2.00000 3.46410i −0.0880451 0.152499i
\(517\) −32.0000 −1.40736
\(518\) 0 0
\(519\) 4.00000 0.175581
\(520\) 8.00000 + 13.8564i 0.350823 + 0.607644i
\(521\) 16.0000 27.7128i 0.700973 1.21412i −0.267153 0.963654i \(-0.586083\pi\)
0.968125 0.250466i \(-0.0805839\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) 0 0
\(528\) 2.00000 3.46410i 0.0870388 0.150756i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 20.0000 + 34.6410i 0.868744 + 1.50471i
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 0 0
\(534\) −4.00000 6.92820i −0.173097 0.299813i
\(535\) 8.00000 13.8564i 0.345870 0.599065i
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 28.0000 1.20717
\(539\) 0 0
\(540\) −4.00000 −0.172133
\(541\) 1.00000 + 1.73205i 0.0429934 + 0.0744667i 0.886721 0.462304i \(-0.152977\pi\)
−0.843728 + 0.536771i \(0.819644\pi\)
\(542\) 16.0000 27.7128i 0.687259 1.19037i
\(543\) 10.0000 17.3205i 0.429141 0.743294i
\(544\) 0 0
\(545\) 56.0000 2.39878
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 5.00000 + 8.66025i 0.213589 + 0.369948i
\(549\) −2.00000 + 3.46410i −0.0853579 + 0.147844i
\(550\) −22.0000 + 38.1051i −0.938083 + 1.62481i
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) −22.0000 −0.934690
\(555\) −12.0000 20.7846i −0.509372 0.882258i
\(556\) 6.00000 10.3923i 0.254457 0.440732i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) −4.00000 6.92820i −0.169334 0.293294i
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 3.00000 + 5.19615i 0.126547 + 0.219186i
\(563\) −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) −4.00000 + 6.92820i −0.168430 + 0.291730i
\(565\) −28.0000 48.4974i −1.17797 2.04030i
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 8.00000 13.8564i 0.335083 0.580381i
\(571\) −18.0000 + 31.1769i −0.753277 + 1.30471i 0.192950 + 0.981209i \(0.438194\pi\)
−0.946227 + 0.323505i \(0.895139\pi\)
\(572\) −8.00000 13.8564i −0.334497 0.579365i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −8.00000 + 13.8564i −0.333044 + 0.576850i −0.983107 0.183031i \(-0.941409\pi\)
0.650063 + 0.759880i \(0.274743\pi\)
\(578\) −8.50000 + 14.7224i −0.353553 + 0.612372i
\(579\) −1.00000 1.73205i −0.0415586 0.0719816i
\(580\) −8.00000 −0.332182
\(581\) 0 0
\(582\) 8.00000 0.331611
\(583\) −20.0000 34.6410i −0.828315 1.43468i
\(584\) 8.00000 13.8564i 0.331042 0.573382i
\(585\) −8.00000 + 13.8564i −0.330759 + 0.572892i
\(586\) 6.00000 + 10.3923i 0.247858 + 0.429302i
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 8.00000 + 13.8564i 0.329355 + 0.570459i
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) 3.00000 5.19615i 0.123299 0.213561i
\(593\) −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i \(-0.330686\pi\)
−0.999965 + 0.00831589i \(0.997353\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 4.00000 + 6.92820i 0.163709 + 0.283552i
\(598\) 0 0
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 5.50000 + 9.52628i 0.224537 + 0.388909i
\(601\) 32.0000 1.30531 0.652654 0.757656i \(-0.273656\pi\)
0.652654 + 0.757656i \(0.273656\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 4.00000 + 6.92820i 0.162758 + 0.281905i
\(605\) 10.0000 17.3205i 0.406558 0.704179i
\(606\) −2.00000 + 3.46410i −0.0812444 + 0.140720i
\(607\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 16.0000 0.647821
\(611\) 16.0000 + 27.7128i 0.647291 + 1.12114i
\(612\) 0 0
\(613\) −13.0000 + 22.5167i −0.525065 + 0.909439i 0.474509 + 0.880251i \(0.342626\pi\)
−0.999574 + 0.0291886i \(0.990708\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) −16.0000 + 27.7128i −0.642575 + 1.11297i
\(621\) 0 0
\(622\) 32.0000 1.28308
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) −20.5000 35.5070i −0.820000 1.42028i
\(626\) −12.0000 + 20.7846i −0.479616 + 0.830720i
\(627\) −8.00000 + 13.8564i −0.319489 + 0.553372i
\(628\) 2.00000 + 3.46410i 0.0798087 + 0.138233i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) 14.0000 24.2487i 0.556450 0.963800i
\(634\) 15.0000 25.9808i 0.595726 1.03183i
\(635\) −32.0000 55.4256i −1.26988 2.19950i
\(636\) −10.0000 −0.396526
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) −4.00000 6.92820i −0.158238 0.274075i
\(640\) −2.00000 + 3.46410i −0.0790569 + 0.136931i
\(641\) 1.00000 1.73205i 0.0394976 0.0684119i −0.845601 0.533816i \(-0.820758\pi\)
0.885098 + 0.465404i \(0.154091\pi\)
\(642\) 2.00000 + 3.46410i 0.0789337 + 0.136717i
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) −16.0000 −0.629999
\(646\) 0 0
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −8.00000 13.8564i −0.314027 0.543912i
\(650\) 44.0000 1.72582
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 23.0000 + 39.8372i 0.900060 + 1.55895i 0.827415 + 0.561591i \(0.189811\pi\)
0.0726446 + 0.997358i \(0.476856\pi\)
\(654\) −7.00000 + 12.1244i −0.273722 + 0.474100i
\(655\) 24.0000 41.5692i 0.937758 1.62424i
\(656\) 0 0
\(657\) 16.0000 0.624219
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) −8.00000 13.8564i −0.311400 0.539360i
\(661\) 14.0000 24.2487i 0.544537 0.943166i −0.454099 0.890951i \(-0.650039\pi\)
0.998636 0.0522143i \(-0.0166279\pi\)
\(662\) 10.0000 17.3205i 0.388661 0.673181i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) 4.00000 6.92820i 0.154765 0.268060i
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) −8.00000 13.8564i −0.309067 0.535320i
\(671\) −16.0000 −0.617673
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) −5.50000 + 9.52628i −0.211695 + 0.366667i
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i \(-0.0925982\pi\)
−0.727386 + 0.686229i \(0.759265\pi\)
\(678\) 14.0000 0.537667
\(679\) 0 0
\(680\) 0 0
\(681\) 10.0000 + 17.3205i 0.383201 + 0.663723i
\(682\) 16.0000 27.7128i 0.612672 1.06118i
\(683\) 22.0000 38.1051i 0.841807 1.45805i −0.0465592 0.998916i \(-0.514826\pi\)
0.888366 0.459136i \(-0.151841\pi\)
\(684\) 2.00000 + 3.46410i 0.0764719 + 0.132453i
\(685\) 40.0000 1.52832
\(686\) 0 0
\(687\) −4.00000 −0.152610
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −20.0000 + 34.6410i −0.761939 + 1.31972i
\(690\) 0 0
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 4.00000 0.152057
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −24.0000 41.5692i −0.910372 1.57681i
\(696\) 1.00000 1.73205i 0.0379049 0.0656532i
\(697\) 0 0
\(698\) 6.00000 + 10.3923i 0.227103 + 0.393355i
\(699\) −10.0000 −0.378235
\(700\) 0 0
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) −2.00000 3.46410i −0.0754851 0.130744i
\(703\) −12.0000 + 20.7846i −0.452589 + 0.783906i
\(704\) 2.00000 3.46410i 0.0753778 0.130558i
\(705\) 16.0000 + 27.7128i 0.602595 + 1.04372i
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) 19.0000 + 32.9090i 0.713560 + 1.23592i 0.963512 + 0.267664i \(0.0862517\pi\)
−0.249952 + 0.968258i \(0.580415\pi\)
\(710\) −16.0000 + 27.7128i −0.600469 + 1.04004i
\(711\) 4.00000 6.92820i 0.150012 0.259828i
\(712\) −4.00000 6.92820i −0.149906 0.259645i
\(713\) 0 0
\(714\) 0 0
\(715\) −64.0000 −2.39346
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 12.0000 20.7846i 0.448148 0.776215i
\(718\) 8.00000 13.8564i 0.298557 0.517116i
\(719\) −12.0000 20.7846i −0.447524 0.775135i 0.550700 0.834703i \(-0.314361\pi\)
−0.998224 + 0.0595683i \(0.981028\pi\)
\(720\) −4.00000 −0.149071
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 4.00000 + 6.92820i 0.148762 + 0.257663i
\(724\) 10.0000 17.3205i 0.371647 0.643712i
\(725\) −11.0000 + 19.0526i −0.408530 + 0.707594i
\(726\) 2.50000 + 4.33013i 0.0927837 + 0.160706i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −32.0000 55.4256i −1.18437 2.05139i
\(731\) 0 0
\(732\) −2.00000 + 3.46410i −0.0739221 + 0.128037i
\(733\) −2.00000 3.46410i −0.0738717 0.127950i 0.826723 0.562609i \(-0.190202\pi\)
−0.900595 + 0.434659i \(0.856869\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 0 0
\(737\) 8.00000 + 13.8564i 0.294684 + 0.510407i
\(738\) 0 0
\(739\) 10.0000 17.3205i 0.367856 0.637145i −0.621374 0.783514i \(-0.713425\pi\)
0.989230 + 0.146369i \(0.0467586\pi\)
\(740\) −12.0000 20.7846i −0.441129 0.764057i
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) −4.00000 6.92820i −0.146647 0.254000i
\(745\) −20.0000 + 34.6410i −0.732743 + 1.26915i
\(746\) 11.0000 19.0526i 0.402739 0.697564i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 0 0
\(749\) 0 0
\(750\) 24.0000 0.876356
\(751\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) −4.00000 + 6.92820i −0.145865 + 0.252646i
\(753\) −10.0000 + 17.3205i −0.364420 + 0.631194i
\(754\) −4.00000 6.92820i −0.145671 0.252310i
\(755\) 32.0000 1.16460
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 18.0000 + 31.1769i 0.653789 + 1.13240i
\(759\) 0 0
\(760\) 8.00000 13.8564i 0.290191 0.502625i
\(761\) 8.00000 + 13.8564i 0.290000 + 0.502294i 0.973809 0.227366i \(-0.0730114\pi\)
−0.683810 + 0.729661i \(0.739678\pi\)
\(762\) 16.0000 0.579619
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −12.0000 + 20.7846i −0.433578 + 0.750978i
\(767\) −8.00000 + 13.8564i −0.288863 + 0.500326i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −40.0000 −1.44244 −0.721218 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 0 0
\(771\) −8.00000 −0.288113
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) 18.0000 31.1769i 0.647415 1.12136i −0.336323 0.941747i \(-0.609183\pi\)
0.983738 0.179609i \(-0.0574833\pi\)
\(774\) 2.00000 3.46410i 0.0718885 0.124515i
\(775\) 44.0000 + 76.2102i 1.58053 + 2.73755i
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 0 0
\(780\) −8.00000 + 13.8564i −0.286446 + 0.496139i
\(781\) 16.0000 27.7128i 0.572525 0.991642i
\(782\) 0 0
\(783\) 2.00000 0.0714742
\(784\) 0 0
\(785\) 16.0000 0.571064
\(786\) 6.00000 + 10.3923i 0.214013 + 0.370681i
\(787\) 10.0000 17.3205i 0.356462 0.617409i −0.630905 0.775860i \(-0.717316\pi\)
0.987367 + 0.158450i \(0.0506498\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) −4.00000 6.92820i −0.142404 0.246651i
\(790\) −32.0000 −1.13851
\(791\) 0 0
\(792\) 4.00000 0.142134
\(793\) 8.00000 + 13.8564i 0.284088 + 0.492055i
\(794\) −2.00000 + 3.46410i −0.0709773 + 0.122936i
\(795\) −20.0000 + 34.6410i −0.709327 + 1.22859i
\(796\) 4.00000 + 6.92820i 0.141776 + 0.245564i
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 5.50000 + 9.52628i 0.194454 + 0.336805i
\(801\) 4.00000 6.92820i 0.141333 0.244796i
\(802\) −9.00000 + 15.5885i −0.317801 + 0.550448i
\(803\) 32.0000 + 55.4256i 1.12926 + 1.95593i
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) −32.0000 −1.12715
\(807\) 14.0000 + 24.2487i 0.492823 + 0.853595i
\(808\) −2.00000 + 3.46410i −0.0703598 + 0.121867i
\(809\) −21.0000 + 36.3731i −0.738321 + 1.27881i 0.214930 + 0.976629i \(0.431048\pi\)
−0.953251 + 0.302180i \(0.902286\pi\)
\(810\) −2.00000 3.46410i −0.0702728 0.121716i
\(811\) 44.0000 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) 0 0
\(813\) 32.0000 1.12229
\(814\) 12.0000 + 20.7846i 0.420600 + 0.728500i
\(815\) 24.0000 41.5692i 0.840683 1.45611i
\(816\) 0 0
\(817\) 8.00000 + 13.8564i 0.279885 + 0.484774i
\(818\) −24.0000 −0.839140
\(819\) 0 0
\(820\) 0 0
\(821\) 5.00000 + 8.66025i 0.174501 + 0.302245i 0.939989 0.341206i \(-0.110835\pi\)
−0.765487 + 0.643451i \(0.777502\pi\)
\(822\) −5.00000 + 8.66025i −0.174395 + 0.302061i
\(823\) −8.00000 + 13.8564i −0.278862 + 0.483004i −0.971102 0.238664i \(-0.923291\pi\)
0.692240 + 0.721668i \(0.256624\pi\)
\(824\) 4.00000 + 6.92820i 0.139347 + 0.241355i
\(825\) −44.0000 −1.53188
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) −26.0000 + 45.0333i −0.903017 + 1.56407i −0.0794606 + 0.996838i \(0.525320\pi\)
−0.823557 + 0.567234i \(0.808014\pi\)
\(830\) −24.0000 + 41.5692i −0.833052 + 1.44289i
\(831\) −11.0000 19.0526i −0.381586 0.660926i
\(832\) −4.00000 −0.138675
\(833\) 0 0
\(834\) 12.0000 0.415526
\(835\) −16.0000 27.7128i −0.553703 0.959041i
\(836\) −8.00000 + 13.8564i −0.276686 + 0.479234i
\(837\) 4.00000 6.92820i 0.138260 0.239474i
\(838\) −14.0000 24.2487i −0.483622 0.837658i
\(839\) −24.0000 −0.828572 −0.414286 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 3.00000 + 5.19615i 0.103387 + 0.179071i
\(843\) −3.00000 + 5.19615i −0.103325 + 0.178965i
\(844\) 14.0000 24.2487i 0.481900 0.834675i
\(845\) 6.00000 + 10.3923i 0.206406 + 0.357506i
\(846\) −8.00000 −0.275046
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) −14.0000 24.2487i −0.480479 0.832214i
\(850\) 0 0
\(851\) 0 0
\(852\) −4.00000 6.92820i −0.137038 0.237356i
\(853\) −52.0000 −1.78045 −0.890223 0.455525i \(-0.849452\pi\)
−0.890223 + 0.455525i \(0.849452\pi\)
\(854\) 0 0
\(855\) 16.0000 0.547188
\(856\) 2.00000 + 3.46410i 0.0683586 + 0.118401i
\(857\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(858\) 8.00000 13.8564i 0.273115 0.473050i
\(859\) −18.0000 31.1769i −0.614152 1.06374i −0.990533 0.137277i \(-0.956165\pi\)
0.376381 0.926465i \(-0.377169\pi\)
\(860\) −16.0000 −0.545595
\(861\) 0 0
\(862\) −40.0000 −1.36241
\(863\) −24.0000 41.5692i −0.816970 1.41503i −0.907905 0.419176i \(-0.862319\pi\)
0.0909355 0.995857i \(-0.471014\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 8.00000 13.8564i 0.272008 0.471132i
\(866\) 4.00000 + 6.92820i 0.135926 + 0.235430i
\(867\) −17.0000 −0.577350
\(868\) 0 0
\(869\) 32.0000 1.08553
\(870\) −4.00000 6.92820i −0.135613 0.234888i
\(871\) 8.00000 13.8564i 0.271070 0.469506i
\(872\) −7.00000 + 12.1244i −0.237050 + 0.410582i
\(873\) 4.00000 + 6.92820i 0.135379 + 0.234484i
\(874\) 0 0
\(875\) 0 0
\(876\) 16.0000 0.540590
\(877\) −9.00000 15.5885i −0.303908 0.526385i 0.673109 0.739543i \(-0.264958\pi\)
−0.977018 + 0.213158i \(0.931625\pi\)
\(878\) 0 0
\(879\) −6.00000 + 10.3923i −0.202375 + 0.350524i
\(880\) −8.00000 13.8564i −0.269680 0.467099i
\(881\) 8.00000 0.269527 0.134763 0.990878i \(-0.456973\pi\)
0.134763 + 0.990878i \(0.456973\pi\)
\(882\) 0 0
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 0 0
\(885\) −8.00000 + 13.8564i −0.268917 + 0.465778i
\(886\) −6.00000 + 10.3923i −0.201574 + 0.349136i
\(887\) 12.0000 + 20.7846i 0.402921 + 0.697879i 0.994077 0.108678i \(-0.0346618\pi\)
−0.591156 + 0.806557i \(0.701328\pi\)
\(888\) 6.00000 0.201347
\(889\) 0 0
\(890\) −32.0000 −1.07264
\(891\) 2.00000 + 3.46410i 0.0670025 + 0.116052i
\(892\) −8.00000 + 13.8564i −0.267860 + 0.463947i
\(893\) 16.0000 27.7128i 0.535420 0.927374i
\(894\) −5.00000 8.66025i −0.167225 0.289642i
\(895\) −48.0000 −1.60446
\(896\) 0 0
\(897\) 0 0
\(898\) −15.0000 25.9808i −0.500556 0.866989i
\(899\) 8.00000 13.8564i 0.266815 0.462137i
\(900\) −5.50000 + 9.52628i −0.183333 + 0.317543i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 14.0000 0.465633
\(905\) −40.0000 69.2820i −1.32964 2.30301i
\(906\) −4.00000 + 6.92820i −0.132891 + 0.230174i
\(907\) 10.0000 17.3205i 0.332045 0.575118i −0.650868 0.759191i \(-0.725595\pi\)
0.982913 + 0.184073i \(0.0589282\pi\)
\(908\) 10.0000 + 17.3205i 0.331862 + 0.574801i
\(909\) −4.00000 −0.132672
\(910\) 0 0
\(911\) −8.00000 −0.265052 −0.132526 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) 2.00000 + 3.46410i 0.0662266 + 0.114708i
\(913\) 24.0000 41.5692i 0.794284 1.37574i
\(914\) −11.0000 + 19.0526i −0.363848 + 0.630203i
\(915\) 8.00000 + 13.8564i 0.264472 + 0.458079i
\(916\) −4.00000 −0.132164
\(917\) 0 0
\(918\) 0 0
\(919\) 24.0000 + 41.5692i 0.791687 + 1.37124i 0.924922 + 0.380158i \(0.124130\pi\)
−0.133235 + 0.991084i \(0.542536\pi\)
\(920\) 0 0
\(921\) 10.0000 17.3205i 0.329511 0.570730i
\(922\) −6.00000 10.3923i −0.197599 0.342252i
\(923\) −32.0000 −1.05329
\(924\) 0 0
\(925\) −66.0000 −2.17007
\(926\) 4.00000 + 6.92820i 0.131448 + 0.227675i
\(927\) −4.00000 + 6.92820i −0.131377 + 0.227552i
\(928\) 1.00000 1.73205i 0.0328266 0.0568574i
\(929\) 24.0000 + 41.5692i 0.787414 + 1.36384i 0.927546 + 0.373709i \(0.121914\pi\)
−0.140132 + 0.990133i \(0.544753\pi\)
\(930\) −32.0000 −1.04932
\(931\) 0 0
\(932\) −10.0000 −0.327561
\(933\) 16.0000 + 27.7128i 0.523816 + 0.907277i
\(934\) −10.0000 + 17.3205i −0.327210 + 0.566744i
\(935\) 0 0
\(936\) −2.00000 3.46410i −0.0653720 0.113228i
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) −24.0000 −0.783210
\(940\) 16.0000 + 27.7128i 0.521862 + 0.903892i
\(941\) −6.00000 + 10.3923i −0.195594 + 0.338779i −0.947095 0.320953i \(-0.895997\pi\)
0.751501 + 0.659732i \(0.229330\pi\)
\(942\) −2.00000 + 3.46410i −0.0651635 + 0.112867i
\(943\) 0 0
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) 14.0000 + 24.2487i 0.454939 + 0.787977i 0.998685 0.0512727i \(-0.0163278\pi\)
−0.543746 + 0.839250i \(0.682994\pi\)
\(948\) 4.00000 6.92820i 0.129914 0.225018i
\(949\) 32.0000 55.4256i 1.03876 1.79919i
\(950\) −22.0000 38.1051i −0.713774 1.23629i
\(951\) 30.0000 0.972817
\(952\) 0 0
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) −5.00000 8.66025i −0.161881 0.280386i
\(955\) 0 0
\(956\) 12.0000 20.7846i 0.388108 0.672222i
\(957\) 4.00000 + 6.92820i 0.129302 + 0.223957i
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) −4.00000 −0.129099
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) 12.0000 20.7846i 0.386896 0.670123i
\(963\) −2.00000 + 3.46410i −0.0644491 + 0.111629i
\(964\) 4.00000 + 6.92820i 0.128831 + 0.223142i
\(965\) −8.00000 −0.257529
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 2.50000 + 4.33013i 0.0803530 + 0.139176i
\(969\) 0 0
\(970\) 16.0000 27.7128i 0.513729 0.889805i
\(971\) 2.00000 + 3.46410i 0.0641831 + 0.111168i 0.896331 0.443385i \(-0.146223\pi\)
−0.832148 + 0.554553i \(0.812889\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) 8.00000 0.256337
\(975\) 22.0000 + 38.1051i 0.704564 + 1.22034i
\(976\) −2.00000 + 3.46410i −0.0640184 + 0.110883i
\(977\) −7.00000 + 12.1244i −0.223950 + 0.387893i −0.956004 0.293354i \(-0.905229\pi\)
0.732054 + 0.681247i \(0.238562\pi\)
\(978\) 6.00000 + 10.3923i 0.191859 + 0.332309i
\(979\) 32.0000 1.02272
\(980\) 0 0
\(981\) −14.0000 −0.446986
\(982\) −6.00000 10.3923i −0.191468 0.331632i
\(983\) −4.00000 + 6.92820i −0.127580 + 0.220975i −0.922739 0.385426i \(-0.874054\pi\)
0.795158 + 0.606402i \(0.207388\pi\)
\(984\) 0 0
\(985\) 12.0000 + 20.7846i 0.382352 + 0.662253i
\(986\) 0 0
\(987\) 0 0
\(988\) 16.0000 0.509028
\(989\) 0 0
\(990\) 8.00000 13.8564i 0.254257 0.440386i
\(991\) −4.00000 + 6.92820i −0.127064 + 0.220082i −0.922538 0.385906i \(-0.873889\pi\)
0.795474 + 0.605988i \(0.207222\pi\)
\(992\) −4.00000 6.92820i −0.127000 0.219971i
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) 32.0000 1.01447
\(996\) −6.00000 10.3923i −0.190117 0.329293i
\(997\) 14.0000 24.2487i 0.443384 0.767964i −0.554554 0.832148i \(-0.687111\pi\)
0.997938 + 0.0641836i \(0.0204443\pi\)
\(998\) −6.00000 + 10.3923i −0.189927 + 0.328963i
\(999\) 3.00000 + 5.19615i 0.0949158 + 0.164399i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 294.2.e.d.67.1 2
3.2 odd 2 882.2.g.a.361.1 2
4.3 odd 2 2352.2.q.y.1537.1 2
7.2 even 3 inner 294.2.e.d.79.1 2
7.3 odd 6 294.2.a.b.1.1 1
7.4 even 3 294.2.a.c.1.1 yes 1
7.5 odd 6 294.2.e.e.79.1 2
7.6 odd 2 294.2.e.e.67.1 2
21.2 odd 6 882.2.g.a.667.1 2
21.5 even 6 882.2.g.f.667.1 2
21.11 odd 6 882.2.a.l.1.1 1
21.17 even 6 882.2.a.f.1.1 1
21.20 even 2 882.2.g.f.361.1 2
28.3 even 6 2352.2.a.y.1.1 1
28.11 odd 6 2352.2.a.b.1.1 1
28.19 even 6 2352.2.q.a.961.1 2
28.23 odd 6 2352.2.q.y.961.1 2
28.27 even 2 2352.2.q.a.1537.1 2
35.4 even 6 7350.2.a.br.1.1 1
35.24 odd 6 7350.2.a.cj.1.1 1
56.3 even 6 9408.2.a.b.1.1 1
56.11 odd 6 9408.2.a.de.1.1 1
56.45 odd 6 9408.2.a.br.1.1 1
56.53 even 6 9408.2.a.bo.1.1 1
84.11 even 6 7056.2.a.ca.1.1 1
84.59 odd 6 7056.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.2.a.b.1.1 1 7.3 odd 6
294.2.a.c.1.1 yes 1 7.4 even 3
294.2.e.d.67.1 2 1.1 even 1 trivial
294.2.e.d.79.1 2 7.2 even 3 inner
294.2.e.e.67.1 2 7.6 odd 2
294.2.e.e.79.1 2 7.5 odd 6
882.2.a.f.1.1 1 21.17 even 6
882.2.a.l.1.1 1 21.11 odd 6
882.2.g.a.361.1 2 3.2 odd 2
882.2.g.a.667.1 2 21.2 odd 6
882.2.g.f.361.1 2 21.20 even 2
882.2.g.f.667.1 2 21.5 even 6
2352.2.a.b.1.1 1 28.11 odd 6
2352.2.a.y.1.1 1 28.3 even 6
2352.2.q.a.961.1 2 28.19 even 6
2352.2.q.a.1537.1 2 28.27 even 2
2352.2.q.y.961.1 2 28.23 odd 6
2352.2.q.y.1537.1 2 4.3 odd 2
7056.2.a.a.1.1 1 84.59 odd 6
7056.2.a.ca.1.1 1 84.11 even 6
7350.2.a.br.1.1 1 35.4 even 6
7350.2.a.cj.1.1 1 35.24 odd 6
9408.2.a.b.1.1 1 56.3 even 6
9408.2.a.bo.1.1 1 56.53 even 6
9408.2.a.br.1.1 1 56.45 odd 6
9408.2.a.de.1.1 1 56.11 odd 6