Properties

Label 1050.2.u.a.899.2
Level $1050$
Weight $2$
Character 1050.899
Analytic conductor $8.384$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,2,Mod(299,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.299");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.u (of order \(6\), 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: \(8.38429221223\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.899
Dual form 1050.2.u.a.299.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(0.866025 + 2.50000i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(0.866025 + 2.50000i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.59808 + 1.50000i) q^{11} +(1.50000 - 0.866025i) q^{12} -3.46410 q^{13} +(1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(0.866025 - 4.50000i) q^{21} -3.00000i q^{22} +(-3.00000 - 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(1.73205 + 3.00000i) q^{26} -5.19615i q^{27} +(-2.59808 - 0.500000i) q^{28} -3.00000i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.59808 - 4.50000i) q^{33} +3.46410i q^{34} -3.00000 q^{36} +(1.73205 - 1.00000i) q^{37} +(3.00000 + 1.73205i) q^{38} +(5.19615 + 3.00000i) q^{39} -6.92820 q^{41} +(-4.33013 + 1.50000i) q^{42} -8.00000i q^{43} +(-2.59808 + 1.50000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-6.00000 + 3.46410i) q^{47} +1.73205i q^{48} +(-5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(1.73205 - 3.00000i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(0.866025 + 2.50000i) q^{56} +6.00000 q^{57} +(-2.59808 + 1.50000i) q^{58} +(-0.866025 + 1.50000i) q^{59} +1.73205i q^{62} +(-5.19615 + 6.00000i) q^{63} +1.00000 q^{64} +(-2.59808 + 4.50000i) q^{66} +(1.73205 + 1.00000i) q^{67} +(3.00000 - 1.73205i) q^{68} +10.3923i q^{69} -12.0000i q^{71} +(1.50000 + 2.59808i) q^{72} +(-3.46410 + 6.00000i) q^{73} +(-1.73205 - 1.00000i) q^{74} -3.46410i q^{76} +(-1.50000 + 7.79423i) q^{77} -6.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(3.46410 + 6.00000i) q^{82} +8.66025i q^{83} +(3.46410 + 3.00000i) q^{84} +(-6.92820 + 4.00000i) q^{86} +(-2.59808 + 4.50000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +6.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(6.00000 + 3.46410i) q^{94} +(1.50000 - 0.866025i) q^{96} +5.19615 q^{97} +(6.50000 + 2.59808i) q^{98} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 4 q^{8} + 6 q^{9} + 6 q^{12} - 2 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} - 12 q^{23} - 6 q^{24} - 6 q^{31} - 2 q^{32} - 12 q^{36} + 12 q^{38} - 12 q^{46} - 24 q^{47} - 22 q^{49} + 12 q^{51} - 18 q^{53} - 18 q^{54} + 24 q^{57} + 4 q^{64} + 12 q^{68} + 6 q^{72} - 6 q^{77} - 2 q^{79} - 18 q^{81} - 12 q^{91} + 24 q^{92} + 6 q^{93} + 24 q^{94} + 6 q^{96} + 26 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 1.73205i 0.707107i
\(7\) 0.866025 + 2.50000i 0.327327 + 0.944911i
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 2.59808 + 1.50000i 0.783349 + 0.452267i 0.837616 0.546259i \(-0.183949\pi\)
−0.0542666 + 0.998526i \(0.517282\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) −3.46410 −0.960769 −0.480384 0.877058i \(-0.659503\pi\)
−0.480384 + 0.877058i \(0.659503\pi\)
\(14\) 1.73205 2.00000i 0.462910 0.534522i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 1.73205i −0.727607 0.420084i 0.0899392 0.995947i \(-0.471333\pi\)
−0.817546 + 0.575863i \(0.804666\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0.866025 4.50000i 0.188982 0.981981i
\(22\) 3.00000i 0.639602i
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 0 0
\(26\) 1.73205 + 3.00000i 0.339683 + 0.588348i
\(27\) 5.19615i 1.00000i
\(28\) −2.59808 0.500000i −0.490990 0.0944911i
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) 0 0
\(31\) −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i \(-0.383046\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.59808 4.50000i −0.452267 0.783349i
\(34\) 3.46410i 0.594089i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 1.73205 1.00000i 0.284747 0.164399i −0.350823 0.936442i \(-0.614098\pi\)
0.635571 + 0.772043i \(0.280765\pi\)
\(38\) 3.00000 + 1.73205i 0.486664 + 0.280976i
\(39\) 5.19615 + 3.00000i 0.832050 + 0.480384i
\(40\) 0 0
\(41\) −6.92820 −1.08200 −0.541002 0.841021i \(-0.681955\pi\)
−0.541002 + 0.841021i \(0.681955\pi\)
\(42\) −4.33013 + 1.50000i −0.668153 + 0.231455i
\(43\) 8.00000i 1.21999i −0.792406 0.609994i \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) −2.59808 + 1.50000i −0.391675 + 0.226134i
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −6.00000 + 3.46410i −0.875190 + 0.505291i −0.869069 0.494690i \(-0.835282\pi\)
−0.00612051 + 0.999981i \(0.501948\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 1.73205 3.00000i 0.240192 0.416025i
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) 0 0
\(56\) 0.866025 + 2.50000i 0.115728 + 0.334077i
\(57\) 6.00000 0.794719
\(58\) −2.59808 + 1.50000i −0.341144 + 0.196960i
\(59\) −0.866025 + 1.50000i −0.112747 + 0.195283i −0.916877 0.399170i \(-0.869298\pi\)
0.804130 + 0.594454i \(0.202632\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 1.73205i 0.219971i
\(63\) −5.19615 + 6.00000i −0.654654 + 0.755929i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.59808 + 4.50000i −0.319801 + 0.553912i
\(67\) 1.73205 + 1.00000i 0.211604 + 0.122169i 0.602056 0.798454i \(-0.294348\pi\)
−0.390453 + 0.920623i \(0.627682\pi\)
\(68\) 3.00000 1.73205i 0.363803 0.210042i
\(69\) 10.3923i 1.25109i
\(70\) 0 0
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) −3.46410 + 6.00000i −0.405442 + 0.702247i −0.994373 0.105937i \(-0.966216\pi\)
0.588930 + 0.808184i \(0.299549\pi\)
\(74\) −1.73205 1.00000i −0.201347 0.116248i
\(75\) 0 0
\(76\) 3.46410i 0.397360i
\(77\) −1.50000 + 7.79423i −0.170941 + 0.888235i
\(78\) 6.00000i 0.679366i
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 3.46410 + 6.00000i 0.382546 + 0.662589i
\(83\) 8.66025i 0.950586i 0.879827 + 0.475293i \(0.157658\pi\)
−0.879827 + 0.475293i \(0.842342\pi\)
\(84\) 3.46410 + 3.00000i 0.377964 + 0.327327i
\(85\) 0 0
\(86\) −6.92820 + 4.00000i −0.747087 + 0.431331i
\(87\) −2.59808 + 4.50000i −0.278543 + 0.482451i
\(88\) 2.59808 + 1.50000i 0.276956 + 0.159901i
\(89\) −5.19615 9.00000i −0.550791 0.953998i −0.998218 0.0596775i \(-0.980993\pi\)
0.447427 0.894321i \(-0.352341\pi\)
\(90\) 0 0
\(91\) −3.00000 8.66025i −0.314485 0.907841i
\(92\) 6.00000 0.625543
\(93\) 1.50000 + 2.59808i 0.155543 + 0.269408i
\(94\) 6.00000 + 3.46410i 0.618853 + 0.357295i
\(95\) 0 0
\(96\) 1.50000 0.866025i 0.153093 0.0883883i
\(97\) 5.19615 0.527589 0.263795 0.964579i \(-0.415026\pi\)
0.263795 + 0.964579i \(0.415026\pi\)
\(98\) 6.50000 + 2.59808i 0.656599 + 0.262445i
\(99\) 9.00000i 0.904534i
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) −1.73205 3.00000i −0.170664 0.295599i 0.767988 0.640464i \(-0.221258\pi\)
−0.938652 + 0.344865i \(0.887925\pi\)
\(104\) −3.46410 −0.339683
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) −3.46410 −0.328798
\(112\) 1.73205 2.00000i 0.163663 0.188982i
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) −3.00000 5.19615i −0.280976 0.486664i
\(115\) 0 0
\(116\) 2.59808 + 1.50000i 0.241225 + 0.139272i
\(117\) −5.19615 9.00000i −0.480384 0.832050i
\(118\) 1.73205 0.159448
\(119\) 1.73205 9.00000i 0.158777 0.825029i
\(120\) 0 0
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 0 0
\(123\) 10.3923 + 6.00000i 0.937043 + 0.541002i
\(124\) 1.50000 0.866025i 0.134704 0.0777714i
\(125\) 0 0
\(126\) 7.79423 + 1.50000i 0.694365 + 0.133631i
\(127\) 11.0000i 0.976092i −0.872818 0.488046i \(-0.837710\pi\)
0.872818 0.488046i \(-0.162290\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −6.92820 + 12.0000i −0.609994 + 1.05654i
\(130\) 0 0
\(131\) 2.59808 + 4.50000i 0.226995 + 0.393167i 0.956916 0.290365i \(-0.0937766\pi\)
−0.729921 + 0.683531i \(0.760443\pi\)
\(132\) 5.19615 0.452267
\(133\) −6.92820 6.00000i −0.600751 0.520266i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) −3.00000 1.73205i −0.257248 0.148522i
\(137\) −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) 9.00000 5.19615i 0.766131 0.442326i
\(139\) 17.3205i 1.46911i −0.678551 0.734553i \(-0.737392\pi\)
0.678551 0.734553i \(-0.262608\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) −10.3923 + 6.00000i −0.872103 + 0.503509i
\(143\) −9.00000 5.19615i −0.752618 0.434524i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 0 0
\(146\) 6.92820 0.573382
\(147\) 12.0000 1.73205i 0.989743 0.142857i
\(148\) 2.00000i 0.164399i
\(149\) −15.5885 + 9.00000i −1.27706 + 0.737309i −0.976306 0.216394i \(-0.930570\pi\)
−0.300750 + 0.953703i \(0.597237\pi\)
\(150\) 0 0
\(151\) −3.50000 + 6.06218i −0.284826 + 0.493333i −0.972567 0.232623i \(-0.925269\pi\)
0.687741 + 0.725956i \(0.258602\pi\)
\(152\) −3.00000 + 1.73205i −0.243332 + 0.140488i
\(153\) 10.3923i 0.840168i
\(154\) 7.50000 2.59808i 0.604367 0.209359i
\(155\) 0 0
\(156\) −5.19615 + 3.00000i −0.416025 + 0.240192i
\(157\) −10.3923 + 18.0000i −0.829396 + 1.43656i 0.0691164 + 0.997609i \(0.477982\pi\)
−0.898513 + 0.438948i \(0.855351\pi\)
\(158\) −0.500000 + 0.866025i −0.0397779 + 0.0688973i
\(159\) 13.5000 7.79423i 1.07062 0.618123i
\(160\) 0 0
\(161\) 10.3923 12.0000i 0.819028 0.945732i
\(162\) 9.00000 0.707107
\(163\) 12.1244 7.00000i 0.949653 0.548282i 0.0566798 0.998392i \(-0.481949\pi\)
0.892973 + 0.450110i \(0.148615\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) 0 0
\(166\) 7.50000 4.33013i 0.582113 0.336083i
\(167\) 17.3205i 1.34030i −0.742225 0.670151i \(-0.766230\pi\)
0.742225 0.670151i \(-0.233770\pi\)
\(168\) 0.866025 4.50000i 0.0668153 0.347183i
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) −9.00000 5.19615i −0.688247 0.397360i
\(172\) 6.92820 + 4.00000i 0.528271 + 0.304997i
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 5.19615 0.393919
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) 2.59808 1.50000i 0.195283 0.112747i
\(178\) −5.19615 + 9.00000i −0.389468 + 0.674579i
\(179\) 10.3923 + 6.00000i 0.776757 + 0.448461i 0.835280 0.549825i \(-0.185306\pi\)
−0.0585225 + 0.998286i \(0.518639\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) −6.00000 + 6.92820i −0.444750 + 0.513553i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 0 0
\(186\) 1.50000 2.59808i 0.109985 0.190500i
\(187\) −5.19615 9.00000i −0.379980 0.658145i
\(188\) 6.92820i 0.505291i
\(189\) 12.9904 4.50000i 0.944911 0.327327i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) 19.9186 + 11.5000i 1.43377 + 0.827788i 0.997406 0.0719816i \(-0.0229323\pi\)
0.436365 + 0.899770i \(0.356266\pi\)
\(194\) −2.59808 4.50000i −0.186531 0.323081i
\(195\) 0 0
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 7.79423 4.50000i 0.553912 0.319801i
\(199\) −9.00000 5.19615i −0.637993 0.368345i 0.145848 0.989307i \(-0.453409\pi\)
−0.783841 + 0.620962i \(0.786742\pi\)
\(200\) 0 0
\(201\) −1.73205 3.00000i −0.122169 0.211604i
\(202\) 0 0
\(203\) 7.50000 2.59808i 0.526397 0.182349i
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) −1.73205 + 3.00000i −0.120678 + 0.209020i
\(207\) 9.00000 15.5885i 0.625543 1.08347i
\(208\) 1.73205 + 3.00000i 0.120096 + 0.208013i
\(209\) −10.3923 −0.718851
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) −10.3923 + 18.0000i −0.712069 + 1.23334i
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) 0.866025 4.50000i 0.0587896 0.305480i
\(218\) 2.00000 0.135457
\(219\) 10.3923 6.00000i 0.702247 0.405442i
\(220\) 0 0
\(221\) 10.3923 + 6.00000i 0.699062 + 0.403604i
\(222\) 1.73205 + 3.00000i 0.116248 + 0.201347i
\(223\) 25.9808 1.73980 0.869900 0.493228i \(-0.164183\pi\)
0.869900 + 0.493228i \(0.164183\pi\)
\(224\) −2.59808 0.500000i −0.173591 0.0334077i
\(225\) 0 0
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) 4.50000 + 2.59808i 0.298675 + 0.172440i 0.641848 0.766832i \(-0.278168\pi\)
−0.343172 + 0.939272i \(0.611501\pi\)
\(228\) −3.00000 + 5.19615i −0.198680 + 0.344124i
\(229\) 12.0000 6.92820i 0.792982 0.457829i −0.0480291 0.998846i \(-0.515294\pi\)
0.841011 + 0.541017i \(0.181961\pi\)
\(230\) 0 0
\(231\) 9.00000 10.3923i 0.592157 0.683763i
\(232\) 3.00000i 0.196960i
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) −5.19615 + 9.00000i −0.339683 + 0.588348i
\(235\) 0 0
\(236\) −0.866025 1.50000i −0.0563735 0.0976417i
\(237\) 1.73205i 0.112509i
\(238\) −8.66025 + 3.00000i −0.561361 + 0.194461i
\(239\) 6.00000i 0.388108i −0.980991 0.194054i \(-0.937836\pi\)
0.980991 0.194054i \(-0.0621637\pi\)
\(240\) 0 0
\(241\) −22.5000 12.9904i −1.44935 0.836784i −0.450910 0.892570i \(-0.648900\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 0 0
\(245\) 0 0
\(246\) 12.0000i 0.765092i
\(247\) 10.3923 6.00000i 0.661247 0.381771i
\(248\) −1.50000 0.866025i −0.0952501 0.0549927i
\(249\) 7.50000 12.9904i 0.475293 0.823232i
\(250\) 0 0
\(251\) −19.0526 −1.20259 −0.601293 0.799028i \(-0.705348\pi\)
−0.601293 + 0.799028i \(0.705348\pi\)
\(252\) −2.59808 7.50000i −0.163663 0.472456i
\(253\) 18.0000i 1.13165i
\(254\) −9.52628 + 5.50000i −0.597732 + 0.345101i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −9.00000 + 5.19615i −0.561405 + 0.324127i −0.753709 0.657208i \(-0.771737\pi\)
0.192304 + 0.981335i \(0.438404\pi\)
\(258\) 13.8564 0.862662
\(259\) 4.00000 + 3.46410i 0.248548 + 0.215249i
\(260\) 0 0
\(261\) 7.79423 4.50000i 0.482451 0.278543i
\(262\) 2.59808 4.50000i 0.160510 0.278011i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) −2.59808 4.50000i −0.159901 0.276956i
\(265\) 0 0
\(266\) −1.73205 + 9.00000i −0.106199 + 0.551825i
\(267\) 18.0000i 1.10158i
\(268\) −1.73205 + 1.00000i −0.105802 + 0.0610847i
\(269\) 14.7224 25.5000i 0.897643 1.55476i 0.0671428 0.997743i \(-0.478612\pi\)
0.830500 0.557019i \(-0.188055\pi\)
\(270\) 0 0
\(271\) 4.50000 2.59808i 0.273356 0.157822i −0.357056 0.934083i \(-0.616219\pi\)
0.630412 + 0.776261i \(0.282886\pi\)
\(272\) 3.46410i 0.210042i
\(273\) −3.00000 + 15.5885i −0.181568 + 0.943456i
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) −9.00000 5.19615i −0.541736 0.312772i
\(277\) 6.92820 + 4.00000i 0.416275 + 0.240337i 0.693482 0.720473i \(-0.256075\pi\)
−0.277207 + 0.960810i \(0.589409\pi\)
\(278\) −15.0000 + 8.66025i −0.899640 + 0.519408i
\(279\) 5.19615i 0.311086i
\(280\) 0 0
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) −6.00000 10.3923i −0.357295 0.618853i
\(283\) −13.8564 + 24.0000i −0.823678 + 1.42665i 0.0792477 + 0.996855i \(0.474748\pi\)
−0.902926 + 0.429797i \(0.858585\pi\)
\(284\) 10.3923 + 6.00000i 0.616670 + 0.356034i
\(285\) 0 0
\(286\) 10.3923i 0.614510i
\(287\) −6.00000 17.3205i −0.354169 1.02240i
\(288\) −3.00000 −0.176777
\(289\) −2.50000 4.33013i −0.147059 0.254713i
\(290\) 0 0
\(291\) −7.79423 4.50000i −0.456906 0.263795i
\(292\) −3.46410 6.00000i −0.202721 0.351123i
\(293\) 19.0526i 1.11306i 0.830827 + 0.556531i \(0.187868\pi\)
−0.830827 + 0.556531i \(0.812132\pi\)
\(294\) −7.50000 9.52628i −0.437409 0.555584i
\(295\) 0 0
\(296\) 1.73205 1.00000i 0.100673 0.0581238i
\(297\) 7.79423 13.5000i 0.452267 0.783349i
\(298\) 15.5885 + 9.00000i 0.903015 + 0.521356i
\(299\) 10.3923 + 18.0000i 0.601003 + 1.04097i
\(300\) 0 0
\(301\) 20.0000 6.92820i 1.15278 0.399335i
\(302\) 7.00000 0.402805
\(303\) 0 0
\(304\) 3.00000 + 1.73205i 0.172062 + 0.0993399i
\(305\) 0 0
\(306\) −9.00000 + 5.19615i −0.514496 + 0.297044i
\(307\) −24.2487 −1.38395 −0.691974 0.721923i \(-0.743259\pi\)
−0.691974 + 0.721923i \(0.743259\pi\)
\(308\) −6.00000 5.19615i −0.341882 0.296078i
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 6.92820 12.0000i 0.392862 0.680458i −0.599963 0.800027i \(-0.704818\pi\)
0.992826 + 0.119570i \(0.0381515\pi\)
\(312\) 5.19615 + 3.00000i 0.294174 + 0.169842i
\(313\) 0.866025 + 1.50000i 0.0489506 + 0.0847850i 0.889463 0.457008i \(-0.151079\pi\)
−0.840512 + 0.541793i \(0.817746\pi\)
\(314\) 20.7846 1.17294
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) 7.50000 + 12.9904i 0.421242 + 0.729612i 0.996061 0.0886679i \(-0.0282610\pi\)
−0.574819 + 0.818280i \(0.694928\pi\)
\(318\) −13.5000 7.79423i −0.757042 0.437079i
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 0 0
\(321\) 5.19615i 0.290021i
\(322\) −15.5885 3.00000i −0.868711 0.167183i
\(323\) 12.0000 0.667698
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 0 0
\(326\) −12.1244 7.00000i −0.671506 0.387694i
\(327\) 3.00000 1.73205i 0.165900 0.0957826i
\(328\) −6.92820 −0.382546
\(329\) −13.8564 12.0000i −0.763928 0.661581i
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) −7.50000 4.33013i −0.411616 0.237647i
\(333\) 5.19615 + 3.00000i 0.284747 + 0.164399i
\(334\) −15.0000 + 8.66025i −0.820763 + 0.473868i
\(335\) 0 0
\(336\) −4.33013 + 1.50000i −0.236228 + 0.0818317i
\(337\) 13.0000i 0.708155i −0.935216 0.354078i \(-0.884795\pi\)
0.935216 0.354078i \(-0.115205\pi\)
\(338\) 0.500000 + 0.866025i 0.0271964 + 0.0471056i
\(339\) 18.0000 + 10.3923i 0.977626 + 0.564433i
\(340\) 0 0
\(341\) −2.59808 4.50000i −0.140694 0.243689i
\(342\) 10.3923i 0.561951i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 8.00000i 0.431331i
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) −2.59808 4.50000i −0.139272 0.241225i
\(349\) 10.3923i 0.556287i −0.960539 0.278144i \(-0.910281\pi\)
0.960539 0.278144i \(-0.0897191\pi\)
\(350\) 0 0
\(351\) 18.0000i 0.960769i
\(352\) −2.59808 + 1.50000i −0.138478 + 0.0799503i
\(353\) 30.0000 + 17.3205i 1.59674 + 0.921878i 0.992110 + 0.125370i \(0.0400119\pi\)
0.604629 + 0.796507i \(0.293321\pi\)
\(354\) −2.59808 1.50000i −0.138086 0.0797241i
\(355\) 0 0
\(356\) 10.3923 0.550791
\(357\) −10.3923 + 12.0000i −0.550019 + 0.635107i
\(358\) 12.0000i 0.634220i
\(359\) −5.19615 + 3.00000i −0.274242 + 0.158334i −0.630814 0.775934i \(-0.717279\pi\)
0.356572 + 0.934268i \(0.383946\pi\)
\(360\) 0 0
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) 6.00000 3.46410i 0.315353 0.182069i
\(363\) 3.46410i 0.181818i
\(364\) 9.00000 + 1.73205i 0.471728 + 0.0907841i
\(365\) 0 0
\(366\) 0 0
\(367\) −11.2583 + 19.5000i −0.587680 + 1.01789i 0.406855 + 0.913493i \(0.366625\pi\)
−0.994535 + 0.104399i \(0.966708\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) −10.3923 18.0000i −0.541002 0.937043i
\(370\) 0 0
\(371\) −23.3827 4.50000i −1.21397 0.233628i
\(372\) −3.00000 −0.155543
\(373\) 27.7128 16.0000i 1.43492 0.828449i 0.437425 0.899255i \(-0.355891\pi\)
0.997490 + 0.0708063i \(0.0225572\pi\)
\(374\) −5.19615 + 9.00000i −0.268687 + 0.465379i
\(375\) 0 0
\(376\) −6.00000 + 3.46410i −0.309426 + 0.178647i
\(377\) 10.3923i 0.535231i
\(378\) −10.3923 9.00000i −0.534522 0.462910i
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −9.52628 + 16.5000i −0.488046 + 0.845321i
\(382\) 0 0
\(383\) 3.00000 1.73205i 0.153293 0.0885037i −0.421392 0.906879i \(-0.638458\pi\)
0.574684 + 0.818375i \(0.305125\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 0 0
\(386\) 23.0000i 1.17067i
\(387\) 20.7846 12.0000i 1.05654 0.609994i
\(388\) −2.59808 + 4.50000i −0.131897 + 0.228453i
\(389\) −15.5885 9.00000i −0.790366 0.456318i 0.0497253 0.998763i \(-0.484165\pi\)
−0.840091 + 0.542445i \(0.817499\pi\)
\(390\) 0 0
\(391\) 20.7846i 1.05112i
\(392\) −5.50000 + 4.33013i −0.277792 + 0.218704i
\(393\) 9.00000i 0.453990i
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 0 0
\(396\) −7.79423 4.50000i −0.391675 0.226134i
\(397\) 13.8564 + 24.0000i 0.695433 + 1.20453i 0.970034 + 0.242967i \(0.0781208\pi\)
−0.274601 + 0.961558i \(0.588546\pi\)
\(398\) 10.3923i 0.520919i
\(399\) 5.19615 + 15.0000i 0.260133 + 0.750939i
\(400\) 0 0
\(401\) −10.3923 + 6.00000i −0.518967 + 0.299626i −0.736512 0.676425i \(-0.763528\pi\)
0.217545 + 0.976050i \(0.430195\pi\)
\(402\) −1.73205 + 3.00000i −0.0863868 + 0.149626i
\(403\) 5.19615 + 3.00000i 0.258839 + 0.149441i
\(404\) 0 0
\(405\) 0 0
\(406\) −6.00000 5.19615i −0.297775 0.257881i
\(407\) 6.00000 0.297409
\(408\) 3.00000 + 5.19615i 0.148522 + 0.257248i
\(409\) −7.50000 4.33013i −0.370851 0.214111i 0.302979 0.952997i \(-0.402019\pi\)
−0.673830 + 0.738886i \(0.735352\pi\)
\(410\) 0 0
\(411\) 27.0000 15.5885i 1.33181 0.768922i
\(412\) 3.46410 0.170664
\(413\) −4.50000 0.866025i −0.221431 0.0426143i
\(414\) −18.0000 −0.884652
\(415\) 0 0
\(416\) 1.73205 3.00000i 0.0849208 0.147087i
\(417\) −15.0000 + 25.9808i −0.734553 + 1.27228i
\(418\) 5.19615 + 9.00000i 0.254152 + 0.440204i
\(419\) 24.2487 1.18463 0.592314 0.805708i \(-0.298215\pi\)
0.592314 + 0.805708i \(0.298215\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) −18.0000 10.3923i −0.875190 0.505291i
\(424\) −4.50000 + 7.79423i −0.218539 + 0.378521i
\(425\) 0 0
\(426\) 20.7846 1.00702
\(427\) 0 0
\(428\) −3.00000 −0.145010
\(429\) 9.00000 + 15.5885i 0.434524 + 0.752618i
\(430\) 0 0
\(431\) 20.7846 + 12.0000i 1.00116 + 0.578020i 0.908591 0.417687i \(-0.137159\pi\)
0.0925683 + 0.995706i \(0.470492\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −34.6410 −1.66474 −0.832370 0.554220i \(-0.813017\pi\)
−0.832370 + 0.554220i \(0.813017\pi\)
\(434\) −4.33013 + 1.50000i −0.207853 + 0.0720023i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 18.0000 + 10.3923i 0.861057 + 0.497131i
\(438\) −10.3923 6.00000i −0.496564 0.286691i
\(439\) −31.5000 + 18.1865i −1.50341 + 0.867996i −0.503421 + 0.864041i \(0.667925\pi\)
−0.999992 + 0.00395451i \(0.998741\pi\)
\(440\) 0 0
\(441\) −19.5000 7.79423i −0.928571 0.371154i
\(442\) 12.0000i 0.570782i
\(443\) 4.50000 + 7.79423i 0.213801 + 0.370315i 0.952901 0.303281i \(-0.0980821\pi\)
−0.739100 + 0.673596i \(0.764749\pi\)
\(444\) 1.73205 3.00000i 0.0821995 0.142374i
\(445\) 0 0
\(446\) −12.9904 22.5000i −0.615112 1.06541i
\(447\) 31.1769 1.47462
\(448\) 0.866025 + 2.50000i 0.0409159 + 0.118114i
\(449\) 30.0000i 1.41579i 0.706319 + 0.707894i \(0.250354\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(450\) 0 0
\(451\) −18.0000 10.3923i −0.847587 0.489355i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) 10.5000 6.06218i 0.493333 0.284826i
\(454\) 5.19615i 0.243868i
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 4.33013 2.50000i 0.202555 0.116945i −0.395292 0.918556i \(-0.629357\pi\)
0.597847 + 0.801611i \(0.296023\pi\)
\(458\) −12.0000 6.92820i −0.560723 0.323734i
\(459\) −9.00000 + 15.5885i −0.420084 + 0.727607i
\(460\) 0 0
\(461\) 13.8564 0.645357 0.322679 0.946509i \(-0.395417\pi\)
0.322679 + 0.946509i \(0.395417\pi\)
\(462\) −13.5000 2.59808i −0.628077 0.120873i
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) −2.59808 + 1.50000i −0.120613 + 0.0696358i
\(465\) 0 0
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) 27.0000 15.5885i 1.24941 0.721348i 0.278419 0.960460i \(-0.410190\pi\)
0.970992 + 0.239112i \(0.0768563\pi\)
\(468\) 10.3923 0.480384
\(469\) −1.00000 + 5.19615i −0.0461757 + 0.239936i
\(470\) 0 0
\(471\) 31.1769 18.0000i 1.43656 0.829396i
\(472\) −0.866025 + 1.50000i −0.0398621 + 0.0690431i
\(473\) 12.0000 20.7846i 0.551761 0.955677i
\(474\) 1.50000 0.866025i 0.0688973 0.0397779i
\(475\) 0 0
\(476\) 6.92820 + 6.00000i 0.317554 + 0.275010i
\(477\) −27.0000 −1.23625
\(478\) −5.19615 + 3.00000i −0.237666 + 0.137217i
\(479\) −3.46410 + 6.00000i −0.158279 + 0.274147i −0.934248 0.356624i \(-0.883928\pi\)
0.775969 + 0.630771i \(0.217261\pi\)
\(480\) 0 0
\(481\) −6.00000 + 3.46410i −0.273576 + 0.157949i
\(482\) 25.9808i 1.18339i
\(483\) −25.9808 + 9.00000i −1.18217 + 0.409514i
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 0.866025 + 0.500000i 0.0392434 + 0.0226572i 0.519493 0.854475i \(-0.326121\pi\)
−0.480250 + 0.877132i \(0.659454\pi\)
\(488\) 0 0
\(489\) −24.2487 −1.09656
\(490\) 0 0
\(491\) 33.0000i 1.48927i 0.667472 + 0.744635i \(0.267376\pi\)
−0.667472 + 0.744635i \(0.732624\pi\)
\(492\) −10.3923 + 6.00000i −0.468521 + 0.270501i
\(493\) −5.19615 + 9.00000i −0.234023 + 0.405340i
\(494\) −10.3923 6.00000i −0.467572 0.269953i
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) 30.0000 10.3923i 1.34568 0.466159i
\(498\) −15.0000 −0.672166
\(499\) 11.0000 + 19.0526i 0.492428 + 0.852910i 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) 0 0
\(501\) −15.0000 + 25.9808i −0.670151 + 1.16073i
\(502\) 9.52628 + 16.5000i 0.425179 + 0.736431i
\(503\) 38.1051i 1.69902i −0.527570 0.849512i \(-0.676897\pi\)
0.527570 0.849512i \(-0.323103\pi\)
\(504\) −5.19615 + 6.00000i −0.231455 + 0.267261i
\(505\) 0 0
\(506\) −15.5885 + 9.00000i −0.692991 + 0.400099i
\(507\) 1.50000 + 0.866025i 0.0666173 + 0.0384615i
\(508\) 9.52628 + 5.50000i 0.422660 + 0.244023i
\(509\) 9.52628 + 16.5000i 0.422245 + 0.731350i 0.996159 0.0875661i \(-0.0279089\pi\)
−0.573914 + 0.818916i \(0.694576\pi\)
\(510\) 0 0
\(511\) −18.0000 3.46410i −0.796273 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 9.00000 + 15.5885i 0.397360 + 0.688247i
\(514\) 9.00000 + 5.19615i 0.396973 + 0.229192i
\(515\) 0 0
\(516\) −6.92820 12.0000i −0.304997 0.528271i
\(517\) −20.7846 −0.914106
\(518\) 1.00000 5.19615i 0.0439375 0.228306i
\(519\) 0 0
\(520\) 0 0
\(521\) 13.8564 24.0000i 0.607060 1.05146i −0.384662 0.923057i \(-0.625682\pi\)
0.991722 0.128402i \(-0.0409847\pi\)
\(522\) −7.79423 4.50000i −0.341144 0.196960i
\(523\) −19.0526 33.0000i −0.833110 1.44299i −0.895560 0.444941i \(-0.853225\pi\)
0.0624496 0.998048i \(-0.480109\pi\)
\(524\) −5.19615 −0.226995
\(525\) 0 0
\(526\) 0 0
\(527\) 3.00000 + 5.19615i 0.130682 + 0.226348i
\(528\) −2.59808 + 4.50000i −0.113067 + 0.195837i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −5.19615 −0.225494
\(532\) 8.66025 3.00000i 0.375470 0.130066i
\(533\) 24.0000 1.03956
\(534\) 15.5885 9.00000i 0.674579 0.389468i
\(535\) 0 0
\(536\) 1.73205 + 1.00000i 0.0748132 + 0.0431934i
\(537\) −10.3923 18.0000i −0.448461 0.776757i
\(538\) −29.4449 −1.26946
\(539\) −20.7846 + 3.00000i −0.895257 + 0.129219i
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) −4.50000 2.59808i −0.193292 0.111597i
\(543\) 6.00000 10.3923i 0.257485 0.445976i
\(544\) 3.00000 1.73205i 0.128624 0.0742611i
\(545\) 0 0
\(546\) 15.0000 5.19615i 0.641941 0.222375i
\(547\) 2.00000i 0.0855138i −0.999086 0.0427569i \(-0.986386\pi\)
0.999086 0.0427569i \(-0.0136141\pi\)
\(548\) −9.00000 15.5885i −0.384461 0.665906i
\(549\) 0 0
\(550\) 0 0
\(551\) 5.19615 + 9.00000i 0.221364 + 0.383413i
\(552\) 10.3923i 0.442326i
\(553\) 1.73205 2.00000i 0.0736543 0.0850487i
\(554\) 8.00000i 0.339887i
\(555\) 0 0
\(556\) 15.0000 + 8.66025i 0.636142 + 0.367277i
\(557\) 1.50000 2.59808i 0.0635570 0.110084i −0.832496 0.554031i \(-0.813089\pi\)
0.896053 + 0.443947i \(0.146422\pi\)
\(558\) −4.50000 + 2.59808i −0.190500 + 0.109985i
\(559\) 27.7128i 1.17213i
\(560\) 0 0
\(561\) 18.0000i 0.759961i
\(562\) 25.9808 15.0000i 1.09593 0.632737i
\(563\) 22.5000 + 12.9904i 0.948262 + 0.547479i 0.892541 0.450967i \(-0.148921\pi\)
0.0557214 + 0.998446i \(0.482254\pi\)
\(564\) −6.00000 + 10.3923i −0.252646 + 0.437595i
\(565\) 0 0
\(566\) 27.7128 1.16486
\(567\) −23.3827 4.50000i −0.981981 0.188982i
\(568\) 12.0000i 0.503509i
\(569\) 5.19615 3.00000i 0.217834 0.125767i −0.387113 0.922032i \(-0.626528\pi\)
0.604947 + 0.796266i \(0.293194\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 9.00000 5.19615i 0.376309 0.217262i
\(573\) 0 0
\(574\) −12.0000 + 13.8564i −0.500870 + 0.578355i
\(575\) 0 0
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −0.866025 + 1.50000i −0.0360531 + 0.0624458i −0.883489 0.468452i \(-0.844812\pi\)
0.847436 + 0.530898i \(0.178145\pi\)
\(578\) −2.50000 + 4.33013i −0.103986 + 0.180110i
\(579\) −19.9186 34.5000i −0.827788 1.43377i
\(580\) 0 0
\(581\) −21.6506 + 7.50000i −0.898220 + 0.311152i
\(582\) 9.00000i 0.373062i
\(583\) −23.3827 + 13.5000i −0.968412 + 0.559113i
\(584\) −3.46410 + 6.00000i −0.143346 + 0.248282i
\(585\) 0 0
\(586\) 16.5000 9.52628i 0.681609 0.393527i
\(587\) 15.5885i 0.643404i −0.946841 0.321702i \(-0.895745\pi\)
0.946841 0.321702i \(-0.104255\pi\)
\(588\) −4.50000 + 11.2583i −0.185577 + 0.464286i
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 27.0000 + 15.5885i 1.11063 + 0.641223i
\(592\) −1.73205 1.00000i −0.0711868 0.0410997i
\(593\) −33.0000 + 19.0526i −1.35515 + 0.782395i −0.988965 0.148148i \(-0.952669\pi\)
−0.366182 + 0.930543i \(0.619335\pi\)
\(594\) −15.5885 −0.639602
\(595\) 0 0
\(596\) 18.0000i 0.737309i
\(597\) 9.00000 + 15.5885i 0.368345 + 0.637993i
\(598\) 10.3923 18.0000i 0.424973 0.736075i
\(599\) 25.9808 + 15.0000i 1.06155 + 0.612883i 0.925859 0.377869i \(-0.123343\pi\)
0.135686 + 0.990752i \(0.456676\pi\)
\(600\) 0 0
\(601\) 29.4449i 1.20108i −0.799594 0.600541i \(-0.794952\pi\)
0.799594 0.600541i \(-0.205048\pi\)
\(602\) −16.0000 13.8564i −0.652111 0.564745i
\(603\) 6.00000i 0.244339i
\(604\) −3.50000 6.06218i −0.142413 0.246667i
\(605\) 0 0
\(606\) 0 0
\(607\) −11.2583 19.5000i −0.456962 0.791481i 0.541837 0.840484i \(-0.317729\pi\)
−0.998799 + 0.0490029i \(0.984396\pi\)
\(608\) 3.46410i 0.140488i
\(609\) −13.5000 2.59808i −0.547048 0.105279i
\(610\) 0 0
\(611\) 20.7846 12.0000i 0.840855 0.485468i
\(612\) 9.00000 + 5.19615i 0.363803 + 0.210042i
\(613\) −1.73205 1.00000i −0.0699569 0.0403896i 0.464614 0.885514i \(-0.346193\pi\)
−0.534570 + 0.845124i \(0.679527\pi\)
\(614\) 12.1244 + 21.0000i 0.489299 + 0.847491i
\(615\) 0 0
\(616\) −1.50000 + 7.79423i −0.0604367 + 0.314038i
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 5.19615 3.00000i 0.209020 0.120678i
\(619\) −6.00000 3.46410i −0.241160 0.139234i 0.374550 0.927207i \(-0.377797\pi\)
−0.615710 + 0.787973i \(0.711131\pi\)
\(620\) 0 0
\(621\) −27.0000 + 15.5885i −1.08347 + 0.625543i
\(622\) −13.8564 −0.555591
\(623\) 18.0000 20.7846i 0.721155 0.832718i
\(624\) 6.00000i 0.240192i
\(625\) 0 0
\(626\) 0.866025 1.50000i 0.0346133 0.0599521i
\(627\) 15.5885 + 9.00000i 0.622543 + 0.359425i
\(628\) −10.3923 18.0000i −0.414698 0.718278i
\(629\) −6.92820 −0.276246
\(630\) 0 0
\(631\) −31.0000 −1.23409 −0.617045 0.786928i \(-0.711670\pi\)
−0.617045 + 0.786928i \(0.711670\pi\)
\(632\) −0.500000 0.866025i −0.0198889 0.0344486i
\(633\) −6.00000 3.46410i −0.238479 0.137686i
\(634\) 7.50000 12.9904i 0.297863 0.515914i
\(635\) 0 0
\(636\) 15.5885i 0.618123i
\(637\) 19.0526 15.0000i 0.754890 0.594322i
\(638\) −9.00000 −0.356313
\(639\) 31.1769 18.0000i 1.23334 0.712069i
\(640\) 0 0
\(641\) −20.7846 12.0000i −0.820943 0.473972i 0.0297987 0.999556i \(-0.490513\pi\)
−0.850741 + 0.525584i \(0.823847\pi\)
\(642\) −4.50000 + 2.59808i −0.177601 + 0.102538i
\(643\) 17.3205 0.683054 0.341527 0.939872i \(-0.389056\pi\)
0.341527 + 0.939872i \(0.389056\pi\)
\(644\) 5.19615 + 15.0000i 0.204757 + 0.591083i
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) −4.50000 + 2.59808i −0.176640 + 0.101983i
\(650\) 0 0
\(651\) −5.19615 + 6.00000i −0.203653 + 0.235159i
\(652\) 14.0000i 0.548282i
\(653\) −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) −3.00000 1.73205i −0.117309 0.0677285i
\(655\) 0 0
\(656\) 3.46410 + 6.00000i 0.135250 + 0.234261i
\(657\) −20.7846 −0.810885
\(658\) −3.46410 + 18.0000i −0.135045 + 0.701713i
\(659\) 12.0000i 0.467454i −0.972302 0.233727i \(-0.924908\pi\)
0.972302 0.233727i \(-0.0750921\pi\)
\(660\) 0 0
\(661\) −6.00000 3.46410i −0.233373 0.134738i 0.378754 0.925497i \(-0.376353\pi\)
−0.612127 + 0.790759i \(0.709686\pi\)
\(662\) 4.00000 6.92820i 0.155464 0.269272i
\(663\) −10.3923 18.0000i −0.403604 0.699062i
\(664\) 8.66025i 0.336083i
\(665\) 0 0
\(666\) 6.00000i 0.232495i
\(667\) −15.5885 + 9.00000i −0.603587 + 0.348481i
\(668\) 15.0000 + 8.66025i 0.580367 + 0.335075i
\(669\) −38.9711 22.5000i −1.50671 0.869900i
\(670\) 0 0
\(671\) 0 0
\(672\) 3.46410 + 3.00000i 0.133631 + 0.115728i
\(673\) 41.0000i 1.58043i −0.612827 0.790217i \(-0.709968\pi\)
0.612827 0.790217i \(-0.290032\pi\)
\(674\) −11.2583 + 6.50000i −0.433655 + 0.250371i
\(675\) 0 0
\(676\) 0.500000 0.866025i 0.0192308 0.0333087i
\(677\) 4.50000 2.59808i 0.172949 0.0998522i −0.411027 0.911623i \(-0.634830\pi\)
0.583976 + 0.811771i \(0.301496\pi\)
\(678\) 20.7846i 0.798228i
\(679\) 4.50000 + 12.9904i 0.172694 + 0.498525i
\(680\) 0 0
\(681\) −4.50000 7.79423i −0.172440 0.298675i
\(682\) −2.59808 + 4.50000i −0.0994855 + 0.172314i
\(683\) −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i \(-0.964939\pi\)
0.592168 + 0.805814i \(0.298272\pi\)
\(684\) 9.00000 5.19615i 0.344124 0.198680i
\(685\) 0 0
\(686\) −0.866025 + 18.5000i −0.0330650 + 0.706333i
\(687\) −24.0000 −0.915657
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 15.5885 27.0000i 0.593873 1.02862i
\(690\) 0 0
\(691\) −6.00000 + 3.46410i −0.228251 + 0.131781i −0.609765 0.792582i \(-0.708736\pi\)
0.381514 + 0.924363i \(0.375403\pi\)
\(692\) 0 0
\(693\) −22.5000 + 7.79423i −0.854704 + 0.296078i
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) −2.59808 + 4.50000i −0.0984798 + 0.170572i
\(697\) 20.7846 + 12.0000i 0.787273 + 0.454532i
\(698\) −9.00000 + 5.19615i −0.340655 + 0.196677i
\(699\) 31.1769i 1.17922i
\(700\) 0 0
\(701\) 3.00000i 0.113308i −0.998394 0.0566542i \(-0.981957\pi\)
0.998394 0.0566542i \(-0.0180433\pi\)
\(702\) 15.5885 9.00000i 0.588348 0.339683i
\(703\) −3.46410 + 6.00000i −0.130651 + 0.226294i
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) 34.6410i 1.30373i
\(707\) 0 0
\(708\) 3.00000i 0.112747i
\(709\) −19.0000 32.9090i −0.713560 1.23592i −0.963512 0.267664i \(-0.913748\pi\)
0.249952 0.968258i \(-0.419585\pi\)
\(710\) 0 0
\(711\) 1.50000 2.59808i 0.0562544 0.0974355i
\(712\) −5.19615 9.00000i −0.194734 0.337289i
\(713\) 10.3923i 0.389195i
\(714\) 15.5885 + 3.00000i 0.583383 + 0.112272i
\(715\) 0 0
\(716\) −10.3923 + 6.00000i −0.388379 + 0.224231i
\(717\) −5.19615 + 9.00000i −0.194054 + 0.336111i
\(718\) 5.19615 + 3.00000i 0.193919 + 0.111959i
\(719\) 22.5167 + 39.0000i 0.839730 + 1.45445i 0.890121 + 0.455725i \(0.150620\pi\)
−0.0503909 + 0.998730i \(0.516047\pi\)
\(720\) 0 0
\(721\) 6.00000 6.92820i 0.223452 0.258020i
\(722\) 7.00000 0.260513
\(723\) 22.5000 + 38.9711i 0.836784 + 1.44935i
\(724\) −6.00000 3.46410i −0.222988 0.128742i
\(725\) 0 0
\(726\) 3.00000 1.73205i 0.111340 0.0642824i
\(727\) 29.4449 1.09205 0.546025 0.837769i \(-0.316140\pi\)
0.546025 + 0.837769i \(0.316140\pi\)
\(728\) −3.00000 8.66025i −0.111187 0.320970i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −13.8564 + 24.0000i −0.512498 + 0.887672i
\(732\) 0 0
\(733\) 17.3205 + 30.0000i 0.639748 + 1.10808i 0.985488 + 0.169745i \(0.0542944\pi\)
−0.345740 + 0.938330i \(0.612372\pi\)
\(734\) 22.5167 0.831105
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) −10.3923 + 18.0000i −0.382546 + 0.662589i
\(739\) −5.00000 + 8.66025i −0.183928 + 0.318573i −0.943215 0.332184i \(-0.892215\pi\)
0.759287 + 0.650756i \(0.225548\pi\)
\(740\) 0 0
\(741\) −20.7846 −0.763542
\(742\) 7.79423 + 22.5000i 0.286135 + 0.826001i
\(743\) 18.0000 0.660356 0.330178 0.943919i \(-0.392891\pi\)
0.330178 + 0.943919i \(0.392891\pi\)
\(744\) 1.50000 + 2.59808i 0.0549927 + 0.0952501i
\(745\) 0 0
\(746\) −27.7128 16.0000i −1.01464 0.585802i
\(747\) −22.5000 + 12.9904i −0.823232 + 0.475293i
\(748\) 10.3923 0.379980
\(749\) −5.19615 + 6.00000i −0.189863 + 0.219235i
\(750\) 0 0
\(751\) 5.50000 + 9.52628i 0.200698 + 0.347619i 0.948753 0.316017i \(-0.102346\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(752\) 6.00000 + 3.46410i 0.218797 + 0.126323i
\(753\) 28.5788 + 16.5000i 1.04147 + 0.601293i
\(754\) 9.00000 5.19615i 0.327761 0.189233i
\(755\) 0 0
\(756\) −2.59808 + 13.5000i −0.0944911 + 0.490990i
\(757\) 4.00000i 0.145382i −0.997354 0.0726912i \(-0.976841\pi\)
0.997354 0.0726912i \(-0.0231588\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) −15.5885 + 27.0000i −0.565825 + 0.980038i
\(760\) 0 0
\(761\) 8.66025 + 15.0000i 0.313934 + 0.543750i 0.979210 0.202848i \(-0.0650196\pi\)
−0.665276 + 0.746597i \(0.731686\pi\)
\(762\) 19.0526 0.690201
\(763\) −5.19615 1.00000i −0.188113 0.0362024i
\(764\) 0 0
\(765\) 0 0
\(766\) −3.00000 1.73205i −0.108394 0.0625815i
\(767\) 3.00000 5.19615i 0.108324 0.187622i
\(768\) 1.50000 0.866025i 0.0541266 0.0312500i
\(769\) 19.0526i 0.687053i −0.939143 0.343526i \(-0.888379\pi\)
0.939143 0.343526i \(-0.111621\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −19.9186 + 11.5000i −0.716886 + 0.413894i
\(773\) −24.0000 13.8564i −0.863220 0.498380i 0.00186926 0.999998i \(-0.499405\pi\)
−0.865089 + 0.501618i \(0.832738\pi\)
\(774\) −20.7846 12.0000i −0.747087 0.431331i
\(775\) 0 0
\(776\) 5.19615 0.186531
\(777\) −3.00000 8.66025i −0.107624 0.310685i
\(778\) 18.0000i 0.645331i
\(779\) 20.7846 12.0000i 0.744686 0.429945i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 18.0000 10.3923i 0.643679 0.371628i
\(783\) −15.5885 −0.557086
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i
\(785\) 0 0
\(786\) −7.79423 + 4.50000i −0.278011 + 0.160510i
\(787\) 20.7846 36.0000i 0.740891 1.28326i −0.211199 0.977443i \(-0.567737\pi\)
0.952090 0.305818i \(-0.0989300\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 0 0
\(790\) 0 0
\(791\) −10.3923 30.0000i −0.369508 1.06668i
\(792\) 9.00000i 0.319801i
\(793\) 0 0
\(794\) 13.8564 24.0000i 0.491745 0.851728i
\(795\) 0 0
\(796\) 9.00000 5.19615i 0.318997 0.184173i
\(797\) 25.9808i 0.920286i −0.887845 0.460143i \(-0.847798\pi\)
0.887845 0.460143i \(-0.152202\pi\)
\(798\) 10.3923 12.0000i 0.367884 0.424795i
\(799\) 24.0000 0.849059
\(800\) 0 0
\(801\) 15.5885 27.0000i 0.550791 0.953998i
\(802\) 10.3923 + 6.00000i 0.366965 + 0.211867i
\(803\) −18.0000 + 10.3923i −0.635206 + 0.366736i
\(804\) 3.46410 0.122169
\(805\) 0 0
\(806\) 6.00000i 0.211341i
\(807\) −44.1673 + 25.5000i −1.55476 + 0.897643i
\(808\) 0 0
\(809\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 0 0
\(811\) 31.1769i 1.09477i 0.836881 + 0.547385i \(0.184377\pi\)
−0.836881 + 0.547385i \(0.815623\pi\)
\(812\) −1.50000 + 7.79423i −0.0526397 + 0.273524i
\(813\) −9.00000 −0.315644
\(814\) −3.00000 5.19615i −0.105150 0.182125i
\(815\) 0 0
\(816\) 3.00000 5.19615i 0.105021 0.181902i
\(817\) 13.8564 + 24.0000i 0.484774 + 0.839654i
\(818\) 8.66025i 0.302799i
\(819\) 18.0000 20.7846i 0.628971 0.726273i
\(820\) 0 0
\(821\) 2.59808 1.50000i 0.0906735 0.0523504i −0.453978 0.891013i \(-0.649995\pi\)
0.544651 + 0.838663i \(0.316662\pi\)
\(822\) −27.0000 15.5885i −0.941733 0.543710i
\(823\) −6.92820 4.00000i −0.241502 0.139431i 0.374365 0.927281i \(-0.377861\pi\)
−0.615867 + 0.787850i \(0.711194\pi\)
\(824\) −1.73205 3.00000i −0.0603388 0.104510i
\(825\) 0 0
\(826\) 1.50000 + 4.33013i 0.0521917 + 0.150664i
\(827\) −9.00000 −0.312961 −0.156480 0.987681i \(-0.550015\pi\)
−0.156480 + 0.987681i \(0.550015\pi\)
\(828\) 9.00000 + 15.5885i 0.312772 + 0.541736i
\(829\) 15.0000 + 8.66025i 0.520972 + 0.300783i 0.737332 0.675530i \(-0.236085\pi\)
−0.216361 + 0.976314i \(0.569419\pi\)
\(830\) 0 0
\(831\) −6.92820 12.0000i −0.240337 0.416275i
\(832\) −3.46410 −0.120096
\(833\) 24.0000 3.46410i 0.831551 0.120024i
\(834\) 30.0000 1.03882
\(835\) 0 0
\(836\) 5.19615 9.00000i 0.179713 0.311272i
\(837\) −4.50000 + 7.79423i −0.155543 + 0.269408i
\(838\) −12.1244 21.0000i −0.418829 0.725433i
\(839\) 3.46410 0.119594 0.0597970 0.998211i \(-0.480955\pi\)
0.0597970 + 0.998211i \(0.480955\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) −16.0000 27.7128i −0.551396 0.955047i
\(843\) 25.9808 45.0000i 0.894825 1.54988i
\(844\) −2.00000 + 3.46410i −0.0688428 + 0.119239i
\(845\) 0 0
\(846\) 20.7846i 0.714590i
\(847\) 3.46410 4.00000i 0.119028 0.137442i
\(848\) 9.00000 0.309061
\(849\) 41.5692 24.0000i 1.42665 0.823678i
\(850\) 0 0
\(851\) −10.3923 6.00000i −0.356244 0.205677i
\(852\) −10.3923 18.0000i −0.356034 0.616670i
\(853\) 24.2487 0.830260 0.415130 0.909762i \(-0.363736\pi\)
0.415130 + 0.909762i \(0.363736\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.50000 + 2.59808i 0.0512689 + 0.0888004i
\(857\) −12.0000 6.92820i −0.409912 0.236663i 0.280840 0.959755i \(-0.409387\pi\)
−0.690752 + 0.723092i \(0.742720\pi\)
\(858\) 9.00000 15.5885i 0.307255 0.532181i
\(859\) 18.0000 10.3923i 0.614152 0.354581i −0.160437 0.987046i \(-0.551290\pi\)
0.774589 + 0.632465i \(0.217957\pi\)
\(860\) 0 0
\(861\) −6.00000 + 31.1769i −0.204479 + 1.06251i
\(862\) 24.0000i 0.817443i
\(863\) −27.0000 46.7654i −0.919091 1.59191i −0.800799 0.598933i \(-0.795592\pi\)
−0.118291 0.992979i \(-0.537742\pi\)
\(864\) 4.50000 + 2.59808i 0.153093 + 0.0883883i
\(865\) 0 0
\(866\) 17.3205 + 30.0000i 0.588575 + 1.01944i
\(867\) 8.66025i 0.294118i
\(868\) 3.46410 + 3.00000i 0.117579 + 0.101827i
\(869\) 3.00000i 0.101768i
\(870\) 0 0
\(871\) −6.00000 3.46410i −0.203302 0.117377i
\(872\) −1.00000 + 1.73205i −0.0338643 + 0.0586546i
\(873\) 7.79423 + 13.5000i 0.263795 + 0.456906i
\(874\) 20.7846i 0.703050i
\(875\) 0 0
\(876\) 12.0000i 0.405442i
\(877\) −38.1051 + 22.0000i −1.28672 + 0.742887i −0.978068 0.208288i \(-0.933211\pi\)
−0.308651 + 0.951175i \(0.599877\pi\)
\(878\) 31.5000 + 18.1865i 1.06307 + 0.613766i
\(879\) 16.5000 28.5788i 0.556531 0.963940i
\(880\) 0 0
\(881\) −10.3923 −0.350126 −0.175063 0.984557i \(-0.556013\pi\)
−0.175063 + 0.984557i \(0.556013\pi\)
\(882\) 3.00000 + 20.7846i 0.101015 + 0.699854i
\(883\) 52.0000i 1.74994i 0.484178 + 0.874970i \(0.339119\pi\)
−0.484178 + 0.874970i \(0.660881\pi\)
\(884\) −10.3923 + 6.00000i −0.349531 + 0.201802i
\(885\) 0 0
\(886\) 4.50000 7.79423i 0.151180 0.261852i
\(887\) 21.0000 12.1244i 0.705111 0.407096i −0.104137 0.994563i \(-0.533208\pi\)
0.809248 + 0.587467i \(0.199875\pi\)
\(888\) −3.46410 −0.116248
\(889\) 27.5000 9.52628i 0.922320 0.319501i
\(890\) 0 0
\(891\) −23.3827 + 13.5000i −0.783349 + 0.452267i
\(892\) −12.9904 + 22.5000i −0.434950 + 0.753356i
\(893\) 12.0000 20.7846i 0.401565 0.695530i
\(894\) −15.5885 27.0000i −0.521356 0.903015i
\(895\) 0 0
\(896\) 1.73205 2.00000i 0.0578638 0.0668153i
\(897\) 36.0000i 1.20201i
\(898\) 25.9808 15.0000i 0.866989 0.500556i
\(899\) −2.59808 + 4.50000i −0.0866507 + 0.150083i
\(900\) 0 0
\(901\) 27.0000 15.5885i 0.899500 0.519327i
\(902\) 20.7846i 0.692052i
\(903\) −36.0000 6.92820i −1.19800 0.230556i
\(904\) −12.0000 −0.399114
\(905\) 0 0
\(906\) −10.5000 6.06218i −0.348839 0.201402i
\(907\) −22.5167 13.0000i −0.747653 0.431658i 0.0771920 0.997016i \(-0.475405\pi\)
−0.824845 + 0.565358i \(0.808738\pi\)
\(908\) −4.50000 + 2.59808i −0.149338 + 0.0862202i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −3.00000 5.19615i −0.0993399 0.172062i
\(913\) −12.9904 + 22.5000i −0.429919 + 0.744641i
\(914\) −4.33013 2.50000i −0.143228 0.0826927i
\(915\) 0 0
\(916\) 13.8564i 0.457829i
\(917\) −9.00000 + 10.3923i −0.297206 + 0.343184i
\(918\) 18.0000 0.594089
\(919\) −10.0000 17.3205i −0.329870 0.571351i 0.652616 0.757689i \(-0.273671\pi\)
−0.982486 + 0.186338i \(0.940338\pi\)
\(920\) 0 0
\(921\) 36.3731 + 21.0000i 1.19853 + 0.691974i
\(922\) −6.92820 12.0000i −0.228168 0.395199i
\(923\) 41.5692i 1.36827i
\(924\) 4.50000 + 12.9904i 0.148039 + 0.427352i
\(925\) 0 0
\(926\) −3.46410 + 2.00000i −0.113837 + 0.0657241i
\(927\) 5.19615 9.00000i 0.170664 0.295599i
\(928\) 2.59808 + 1.50000i 0.0852860 + 0.0492399i
\(929\) 24.2487 + 42.0000i 0.795574 + 1.37798i 0.922474 + 0.386060i \(0.126164\pi\)
−0.126899 + 0.991916i \(0.540503\pi\)
\(930\) 0 0
\(931\) 9.00000 22.5167i 0.294963 0.737954i
\(932\) 18.0000 0.589610
\(933\) −20.7846 + 12.0000i −0.680458 + 0.392862i
\(934\) −27.0000 15.5885i −0.883467 0.510070i
\(935\) 0 0
\(936\) −5.19615 9.00000i −0.169842 0.294174i
\(937\) 22.5167 0.735587 0.367794 0.929907i \(-0.380113\pi\)
0.367794 + 0.929907i \(0.380113\pi\)
\(938\) 5.00000 1.73205i 0.163256 0.0565535i
\(939\) 3.00000i 0.0979013i
\(940\) 0 0
\(941\) 16.4545 28.5000i 0.536401 0.929073i −0.462693 0.886518i \(-0.653117\pi\)
0.999094 0.0425550i \(-0.0135498\pi\)
\(942\) −31.1769 18.0000i −1.01580 0.586472i
\(943\) 20.7846 + 36.0000i 0.676840 + 1.17232i
\(944\) 1.73205 0.0563735
\(945\) 0 0
\(946\) −24.0000 −0.780307
\(947\) 6.00000 + 10.3923i 0.194974 + 0.337705i 0.946892 0.321552i \(-0.104204\pi\)
−0.751918 + 0.659256i \(0.770871\pi\)
\(948\) −1.50000 0.866025i −0.0487177 0.0281272i
\(949\) 12.0000 20.7846i 0.389536 0.674697i
\(950\) 0 0
\(951\) 25.9808i 0.842484i
\(952\) 1.73205 9.00000i 0.0561361 0.291692i
\(953\) −24.0000 −0.777436 −0.388718 0.921357i \(-0.627082\pi\)
−0.388718 + 0.921357i \(0.627082\pi\)
\(954\) 13.5000 + 23.3827i 0.437079 + 0.757042i
\(955\) 0 0
\(956\) 5.19615 + 3.00000i 0.168056 + 0.0970269i
\(957\) −13.5000 + 7.79423i −0.436393 + 0.251952i
\(958\) 6.92820 0.223840
\(959\) −46.7654 9.00000i −1.51013 0.290625i
\(960\) 0 0
\(961\) −14.0000 24.2487i −0.451613 0.782216i
\(962\) 6.00000 + 3.46410i 0.193448 + 0.111687i
\(963\) −4.50000 + 7.79423i −0.145010 + 0.251166i
\(964\) 22.5000 12.9904i 0.724676 0.418392i
\(965\) 0 0
\(966\) 20.7846 + 18.0000i 0.668734 + 0.579141i
\(967\) 7.00000i 0.225105i 0.993646 + 0.112552i \(0.0359026\pi\)
−0.993646 + 0.112552i \(0.964097\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) −18.0000 10.3923i −0.578243 0.333849i
\(970\) 0 0
\(971\) −4.33013 7.50000i −0.138960 0.240686i 0.788143 0.615492i \(-0.211043\pi\)
−0.927103 + 0.374806i \(0.877709\pi\)
\(972\) 15.5885i 0.500000i
\(973\) 43.3013 15.0000i 1.38817 0.480878i
\(974\) 1.00000i 0.0320421i
\(975\) 0 0
\(976\) 0 0
\(977\) 12.0000 20.7846i 0.383914 0.664959i −0.607704 0.794164i \(-0.707909\pi\)
0.991618 + 0.129205i \(0.0412426\pi\)
\(978\) 12.1244 + 21.0000i 0.387694 + 0.671506i
\(979\) 31.1769i 0.996419i
\(980\) 0 0
\(981\) −6.00000 −0.191565
\(982\) 28.5788 16.5000i 0.911987 0.526536i
\(983\) −12.0000 6.92820i −0.382741 0.220975i 0.296269 0.955104i \(-0.404257\pi\)
−0.679010 + 0.734129i \(0.737591\pi\)
\(984\) 10.3923 + 6.00000i 0.331295 + 0.191273i
\(985\) 0 0
\(986\) 10.3923 0.330958
\(987\) 10.3923 + 30.0000i 0.330791 + 0.954911i
\(988\) 12.0000i 0.381771i
\(989\) −41.5692 + 24.0000i −1.32182 + 0.763156i
\(990\) 0 0
\(991\) 23.5000 40.7032i 0.746502 1.29298i −0.202988 0.979181i \(-0.565065\pi\)
0.949490 0.313798i \(-0.101602\pi\)
\(992\) 1.50000 0.866025i 0.0476250 0.0274963i
\(993\) 13.8564i 0.439720i
\(994\) −24.0000 20.7846i −0.761234 0.659248i
\(995\) 0 0
\(996\) 7.50000 + 12.9904i 0.237647 + 0.411616i
\(997\) 8.66025 15.0000i 0.274273 0.475055i −0.695678 0.718353i \(-0.744896\pi\)
0.969951 + 0.243299i \(0.0782295\pi\)
\(998\) 11.0000 19.0526i 0.348199 0.603098i
\(999\) −5.19615 9.00000i −0.164399 0.284747i
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 1050.2.u.a.899.2 4
3.2 odd 2 1050.2.u.d.899.2 4
5.2 odd 4 42.2.f.a.17.2 yes 4
5.3 odd 4 1050.2.s.b.101.1 4
5.4 even 2 1050.2.u.d.899.1 4
7.5 odd 6 inner 1050.2.u.a.299.1 4
15.2 even 4 42.2.f.a.17.1 yes 4
15.8 even 4 1050.2.s.b.101.2 4
15.14 odd 2 inner 1050.2.u.a.899.1 4
20.7 even 4 336.2.bc.e.17.2 4
21.5 even 6 1050.2.u.d.299.1 4
35.2 odd 12 294.2.f.a.215.1 4
35.12 even 12 42.2.f.a.5.1 4
35.17 even 12 294.2.d.a.293.3 4
35.19 odd 6 1050.2.u.d.299.2 4
35.27 even 4 294.2.f.a.227.2 4
35.32 odd 12 294.2.d.a.293.4 4
35.33 even 12 1050.2.s.b.551.2 4
45.2 even 12 1134.2.t.d.1025.2 4
45.7 odd 12 1134.2.t.d.1025.1 4
45.22 odd 12 1134.2.l.c.269.2 4
45.32 even 12 1134.2.l.c.269.1 4
60.47 odd 4 336.2.bc.e.17.1 4
105.2 even 12 294.2.f.a.215.2 4
105.17 odd 12 294.2.d.a.293.2 4
105.32 even 12 294.2.d.a.293.1 4
105.47 odd 12 42.2.f.a.5.2 yes 4
105.62 odd 4 294.2.f.a.227.1 4
105.68 odd 12 1050.2.s.b.551.1 4
105.89 even 6 inner 1050.2.u.a.299.2 4
140.47 odd 12 336.2.bc.e.257.1 4
140.67 even 12 2352.2.k.e.881.2 4
140.87 odd 12 2352.2.k.e.881.4 4
315.47 odd 12 1134.2.l.c.215.1 4
315.187 even 12 1134.2.l.c.215.2 4
315.257 odd 12 1134.2.t.d.593.1 4
315.292 even 12 1134.2.t.d.593.2 4
420.47 even 12 336.2.bc.e.257.2 4
420.227 even 12 2352.2.k.e.881.1 4
420.347 odd 12 2352.2.k.e.881.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.f.a.5.1 4 35.12 even 12
42.2.f.a.5.2 yes 4 105.47 odd 12
42.2.f.a.17.1 yes 4 15.2 even 4
42.2.f.a.17.2 yes 4 5.2 odd 4
294.2.d.a.293.1 4 105.32 even 12
294.2.d.a.293.2 4 105.17 odd 12
294.2.d.a.293.3 4 35.17 even 12
294.2.d.a.293.4 4 35.32 odd 12
294.2.f.a.215.1 4 35.2 odd 12
294.2.f.a.215.2 4 105.2 even 12
294.2.f.a.227.1 4 105.62 odd 4
294.2.f.a.227.2 4 35.27 even 4
336.2.bc.e.17.1 4 60.47 odd 4
336.2.bc.e.17.2 4 20.7 even 4
336.2.bc.e.257.1 4 140.47 odd 12
336.2.bc.e.257.2 4 420.47 even 12
1050.2.s.b.101.1 4 5.3 odd 4
1050.2.s.b.101.2 4 15.8 even 4
1050.2.s.b.551.1 4 105.68 odd 12
1050.2.s.b.551.2 4 35.33 even 12
1050.2.u.a.299.1 4 7.5 odd 6 inner
1050.2.u.a.299.2 4 105.89 even 6 inner
1050.2.u.a.899.1 4 15.14 odd 2 inner
1050.2.u.a.899.2 4 1.1 even 1 trivial
1050.2.u.d.299.1 4 21.5 even 6
1050.2.u.d.299.2 4 35.19 odd 6
1050.2.u.d.899.1 4 5.4 even 2
1050.2.u.d.899.2 4 3.2 odd 2
1134.2.l.c.215.1 4 315.47 odd 12
1134.2.l.c.215.2 4 315.187 even 12
1134.2.l.c.269.1 4 45.32 even 12
1134.2.l.c.269.2 4 45.22 odd 12
1134.2.t.d.593.1 4 315.257 odd 12
1134.2.t.d.593.2 4 315.292 even 12
1134.2.t.d.1025.1 4 45.7 odd 12
1134.2.t.d.1025.2 4 45.2 even 12
2352.2.k.e.881.1 4 420.227 even 12
2352.2.k.e.881.2 4 140.67 even 12
2352.2.k.e.881.3 4 420.347 odd 12
2352.2.k.e.881.4 4 140.87 odd 12