Properties

Label 1050.2.o.b.499.2
Level $1050$
Weight $2$
Character 1050.499
Analytic conductor $8.384$
Analytic rank $0$
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(499,1050)]
 
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([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.499");
 
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.o (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: \(0\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 499.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.499
Dual form 1050.2.o.b.949.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.866025 - 0.500000i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-0.500000 - 2.59808i) q^{21} -3.00000i q^{22} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(-2.59808 + 0.500000i) q^{28} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.59808 + 1.50000i) q^{33} +1.00000 q^{36} +(-6.92820 - 4.00000i) q^{37} +(-3.46410 + 2.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(0.866025 - 2.50000i) q^{42} +10.0000i q^{43} +(1.50000 - 2.59808i) q^{44} +(5.19615 + 3.00000i) q^{47} -1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-3.46410 + 2.00000i) q^{52} +(2.59808 - 1.50000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} -4.00000i q^{57} +(-7.79423 - 4.50000i) q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +1.00000i q^{62} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-8.66025 + 5.00000i) q^{67} -6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-1.73205 + 1.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(7.79423 - 1.50000i) q^{77} -4.00000i q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +9.00000i q^{83} +(2.00000 - 1.73205i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(7.79423 - 4.50000i) q^{87} +(2.59808 - 1.50000i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 - 3.46410i) q^{91} +(-0.866025 - 0.500000i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -1.00000i q^{97} +(-2.59808 - 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} - 6 q^{11} - 8 q^{14} - 2 q^{16} - 8 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{26} - 36 q^{29} + 2 q^{31} + 4 q^{36} - 8 q^{39} + 6 q^{44} - 22 q^{49} - 2 q^{54} - 10 q^{56} + 6 q^{59} + 20 q^{61} - 4 q^{64} + 6 q^{66} - 24 q^{71} - 16 q^{74} - 16 q^{76} - 2 q^{79} - 2 q^{81} + 8 q^{84} - 20 q^{86} + 12 q^{89} - 40 q^{91} + 12 q^{94} + 2 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −0.866025 + 2.50000i −0.327327 + 0.944911i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 0 0
\(21\) −0.500000 2.59808i −0.109109 0.566947i
\(22\) 3.00000i 0.639602i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −2.59808 + 0.500000i −0.490990 + 0.0944911i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 2.59808 + 1.50000i 0.452267 + 0.261116i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.92820 4.00000i −1.13899 0.657596i −0.192809 0.981236i \(-0.561760\pi\)
−0.946180 + 0.323640i \(0.895093\pi\)
\(38\) −3.46410 + 2.00000i −0.561951 + 0.324443i
\(39\) −2.00000 3.46410i −0.320256 0.554700i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0.866025 2.50000i 0.133631 0.385758i
\(43\) 10.0000i 1.52499i 0.646997 + 0.762493i \(0.276025\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 + 3.00000i 0.757937 + 0.437595i 0.828554 0.559908i \(-0.189164\pi\)
−0.0706177 + 0.997503i \(0.522497\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.46410 + 2.00000i −0.480384 + 0.277350i
\(53\) 2.59808 1.50000i 0.356873 0.206041i −0.310835 0.950464i \(-0.600609\pi\)
0.667708 + 0.744423i \(0.267275\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) 4.00000i 0.529813i
\(58\) −7.79423 4.50000i −1.02343 0.590879i
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 1.73205 + 2.00000i 0.218218 + 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.50000 + 2.59808i 0.184637 + 0.319801i
\(67\) −8.66025 + 5.00000i −1.05802 + 0.610847i −0.924883 0.380251i \(-0.875838\pi\)
−0.133135 + 0.991098i \(0.542504\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −1.73205 + 1.00000i −0.202721 + 0.117041i −0.597924 0.801553i \(-0.704008\pi\)
0.395203 + 0.918594i \(0.370674\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 7.79423 1.50000i 0.888235 0.170941i
\(78\) 4.00000i 0.452911i
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 9.00000i 0.987878i 0.869496 + 0.493939i \(0.164443\pi\)
−0.869496 + 0.493939i \(0.835557\pi\)
\(84\) 2.00000 1.73205i 0.218218 0.188982i
\(85\) 0 0
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 7.79423 4.50000i 0.835629 0.482451i
\(88\) 2.59808 1.50000i 0.276956 0.159901i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 0 0
\(93\) −0.866025 0.500000i −0.0898027 0.0518476i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 1.00000i 0.101535i −0.998711 0.0507673i \(-0.983833\pi\)
0.998711 0.0507673i \(-0.0161667\pi\)
\(98\) −2.59808 6.50000i −0.262445 0.656599i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) 6.92820 + 4.00000i 0.682656 + 0.394132i 0.800855 0.598858i \(-0.204379\pi\)
−0.118199 + 0.992990i \(0.537712\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) 2.59808 + 1.50000i 0.251166 + 0.145010i 0.620298 0.784366i \(-0.287012\pi\)
−0.369132 + 0.929377i \(0.620345\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) −1.73205 2.00000i −0.163663 0.188982i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 2.00000 3.46410i 0.187317 0.324443i
\(115\) 0 0
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 3.46410 + 2.00000i 0.320256 + 0.184900i
\(118\) 3.00000i 0.276172i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 8.66025 5.00000i 0.784063 0.452679i
\(123\) 0 0
\(124\) −0.500000 + 0.866025i −0.0449013 + 0.0777714i
\(125\) 0 0
\(126\) 0.500000 + 2.59808i 0.0445435 + 0.231455i
\(127\) 5.00000i 0.443678i 0.975083 + 0.221839i \(0.0712060\pi\)
−0.975083 + 0.221839i \(0.928794\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −5.00000 8.66025i −0.440225 0.762493i
\(130\) 0 0
\(131\) 4.50000 7.79423i 0.393167 0.680985i −0.599699 0.800226i \(-0.704713\pi\)
0.992865 + 0.119241i \(0.0380462\pi\)
\(132\) 3.00000i 0.261116i
\(133\) −6.92820 8.00000i −0.600751 0.693688i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) 15.5885 9.00000i 1.33181 0.768922i 0.346235 0.938148i \(-0.387460\pi\)
0.985577 + 0.169226i \(0.0541268\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −5.19615 3.00000i −0.436051 0.251754i
\(143\) 10.3923 6.00000i 0.869048 0.501745i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 6.92820 + 1.00000i 0.571429 + 0.0824786i
\(148\) 8.00000i 0.657596i
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i \(-0.153711\pi\)
−0.844963 + 0.534824i \(0.820378\pi\)
\(152\) −3.46410 2.00000i −0.280976 0.162221i
\(153\) 0 0
\(154\) 7.50000 + 2.59808i 0.604367 + 0.209359i
\(155\) 0 0
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) −3.46410 + 2.00000i −0.276465 + 0.159617i −0.631822 0.775113i \(-0.717693\pi\)
0.355357 + 0.934731i \(0.384359\pi\)
\(158\) −0.866025 + 0.500000i −0.0688973 + 0.0397779i
\(159\) −1.50000 + 2.59808i −0.118958 + 0.206041i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −13.8564 8.00000i −1.08532 0.626608i −0.152992 0.988227i \(-0.548891\pi\)
−0.932326 + 0.361619i \(0.882224\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 2.59808 0.500000i 0.200446 0.0385758i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) −8.66025 + 5.00000i −0.660338 + 0.381246i
\(173\) 15.5885 + 9.00000i 1.18517 + 0.684257i 0.957205 0.289412i \(-0.0934598\pi\)
0.227964 + 0.973670i \(0.426793\pi\)
\(174\) 9.00000 0.682288
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) −2.59808 1.50000i −0.195283 0.112747i
\(178\) 5.19615 3.00000i 0.389468 0.224860i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −6.92820 8.00000i −0.513553 0.592999i
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) 0 0
\(186\) −0.500000 0.866025i −0.0366618 0.0635001i
\(187\) 0 0
\(188\) 6.00000i 0.437595i
\(189\) −2.50000 0.866025i −0.181848 0.0629941i
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 16.4545 9.50000i 1.18442 0.683825i 0.227387 0.973805i \(-0.426982\pi\)
0.957033 + 0.289980i \(0.0936485\pi\)
\(194\) 0.500000 0.866025i 0.0358979 0.0621770i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) −2.59808 1.50000i −0.184637 0.106600i
\(199\) 10.0000 + 17.3205i 0.708881 + 1.22782i 0.965272 + 0.261245i \(0.0841331\pi\)
−0.256391 + 0.966573i \(0.582534\pi\)
\(200\) 0 0
\(201\) 5.00000 8.66025i 0.352673 0.610847i
\(202\) 18.0000i 1.26648i
\(203\) 7.79423 22.5000i 0.547048 1.57919i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) −3.46410 2.00000i −0.240192 0.138675i
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 2.59808 + 1.50000i 0.178437 + 0.103020i
\(213\) 5.19615 3.00000i 0.356034 0.205557i
\(214\) 1.50000 + 2.59808i 0.102538 + 0.177601i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −2.59808 + 0.500000i −0.176369 + 0.0339422i
\(218\) 14.0000i 0.948200i
\(219\) 1.00000 1.73205i 0.0675737 0.117041i
\(220\) 0 0
\(221\) 0 0
\(222\) 6.92820 + 4.00000i 0.464991 + 0.268462i
\(223\) 19.0000i 1.27233i 0.771551 + 0.636167i \(0.219481\pi\)
−0.771551 + 0.636167i \(0.780519\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −23.3827 + 13.5000i −1.55196 + 0.896026i −0.553981 + 0.832529i \(0.686892\pi\)
−0.997982 + 0.0634974i \(0.979775\pi\)
\(228\) 3.46410 2.00000i 0.229416 0.132453i
\(229\) −2.00000 + 3.46410i −0.132164 + 0.228914i −0.924510 0.381157i \(-0.875526\pi\)
0.792347 + 0.610071i \(0.208859\pi\)
\(230\) 0 0
\(231\) −6.00000 + 5.19615i −0.394771 + 0.341882i
\(232\) 9.00000i 0.590879i
\(233\) −20.7846 12.0000i −1.36165 0.786146i −0.371802 0.928312i \(-0.621260\pi\)
−0.989843 + 0.142166i \(0.954593\pi\)
\(234\) 2.00000 + 3.46410i 0.130744 + 0.226455i
\(235\) 0 0
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 1.00000i 0.0649570i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 1.73205 1.00000i 0.111340 0.0642824i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) 0 0
\(247\) −13.8564 8.00000i −0.881662 0.509028i
\(248\) −0.866025 + 0.500000i −0.0549927 + 0.0317500i
\(249\) −4.50000 7.79423i −0.285176 0.493939i
\(250\) 0 0
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) −0.866025 + 2.50000i −0.0545545 + 0.157485i
\(253\) 0 0
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.19615 3.00000i −0.324127 0.187135i 0.329104 0.944294i \(-0.393253\pi\)
−0.653231 + 0.757159i \(0.726587\pi\)
\(258\) 10.0000i 0.622573i
\(259\) 16.0000 13.8564i 0.994192 0.860995i
\(260\) 0 0
\(261\) −4.50000 + 7.79423i −0.278543 + 0.482451i
\(262\) 7.79423 4.50000i 0.481529 0.278011i
\(263\) 5.19615 3.00000i 0.320408 0.184988i −0.331166 0.943572i \(-0.607442\pi\)
0.651575 + 0.758585i \(0.274109\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) −2.00000 10.3923i −0.122628 0.637193i
\(267\) 6.00000i 0.367194i
\(268\) −8.66025 5.00000i −0.529009 0.305424i
\(269\) 10.5000 + 18.1865i 0.640196 + 1.10885i 0.985389 + 0.170321i \(0.0544803\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 0 0
\(273\) 10.3923 2.00000i 0.628971 0.121046i
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 6.92820 4.00000i 0.416275 0.240337i −0.277207 0.960810i \(-0.589409\pi\)
0.693482 + 0.720473i \(0.256075\pi\)
\(278\) −1.73205 1.00000i −0.103882 0.0599760i
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −5.19615 3.00000i −0.309426 0.178647i
\(283\) −12.1244 + 7.00000i −0.720718 + 0.416107i −0.815017 0.579437i \(-0.803272\pi\)
0.0942988 + 0.995544i \(0.469939\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −8.50000 + 14.7224i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0.500000 + 0.866025i 0.0293105 + 0.0507673i
\(292\) −1.73205 1.00000i −0.101361 0.0585206i
\(293\) 33.0000i 1.92788i −0.266119 0.963940i \(-0.585741\pi\)
0.266119 0.963940i \(-0.414259\pi\)
\(294\) 5.50000 + 4.33013i 0.320767 + 0.252538i
\(295\) 0 0
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 2.59808 1.50000i 0.150756 0.0870388i
\(298\) 15.5885 9.00000i 0.903015 0.521356i
\(299\) 0 0
\(300\) 0 0
\(301\) −25.0000 8.66025i −1.44098 0.499169i
\(302\) 1.00000i 0.0575435i
\(303\) −15.5885 9.00000i −0.895533 0.517036i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 8.00000i 0.456584i 0.973593 + 0.228292i \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) 5.19615 + 6.00000i 0.296078 + 0.341882i
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 3.46410 2.00000i 0.196116 0.113228i
\(313\) −26.8468 15.5000i −1.51747 0.876112i −0.999789 0.0205381i \(-0.993462\pi\)
−0.517681 0.855574i \(-0.673205\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −7.79423 4.50000i −0.437767 0.252745i 0.264883 0.964281i \(-0.414667\pi\)
−0.702650 + 0.711535i \(0.748000\pi\)
\(318\) −2.59808 + 1.50000i −0.145693 + 0.0841158i
\(319\) 13.5000 + 23.3827i 0.755855 + 1.30918i
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) −12.1244 7.00000i −0.670478 0.387101i
\(328\) 0 0
\(329\) −12.0000 + 10.3923i −0.661581 + 0.572946i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) −7.79423 + 4.50000i −0.427764 + 0.246970i
\(333\) −6.92820 + 4.00000i −0.379663 + 0.219199i
\(334\) −3.00000 + 5.19615i −0.164153 + 0.284321i
\(335\) 0 0
\(336\) 2.50000 + 0.866025i 0.136386 + 0.0472456i
\(337\) 7.00000i 0.381314i −0.981657 0.190657i \(-0.938938\pi\)
0.981657 0.190657i \(-0.0610619\pi\)
\(338\) −2.59808 1.50000i −0.141317 0.0815892i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.50000 2.59808i 0.0812296 0.140694i
\(342\) 4.00000i 0.216295i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 9.00000 + 15.5885i 0.483843 + 0.838041i
\(347\) 10.3923 6.00000i 0.557888 0.322097i −0.194409 0.980921i \(-0.562279\pi\)
0.752297 + 0.658824i \(0.228946\pi\)
\(348\) 7.79423 + 4.50000i 0.417815 + 0.241225i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 2.59808 + 1.50000i 0.138478 + 0.0799503i
\(353\) −20.7846 + 12.0000i −1.10625 + 0.638696i −0.937856 0.347024i \(-0.887192\pi\)
−0.168397 + 0.985719i \(0.553859\pi\)
\(354\) −1.50000 2.59808i −0.0797241 0.138086i
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) 15.0000 25.9808i 0.791670 1.37121i −0.133263 0.991081i \(-0.542545\pi\)
0.924932 0.380131i \(-0.124121\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 6.92820 + 4.00000i 0.364138 + 0.210235i
\(363\) 2.00000i 0.104973i
\(364\) −2.00000 10.3923i −0.104828 0.544705i
\(365\) 0 0
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) −16.4545 + 9.50000i −0.858917 + 0.495896i −0.863649 0.504093i \(-0.831827\pi\)
0.00473247 + 0.999989i \(0.498494\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.50000 + 7.79423i 0.0778761 + 0.404656i
\(372\) 1.00000i 0.0518476i
\(373\) 6.92820 + 4.00000i 0.358729 + 0.207112i 0.668523 0.743691i \(-0.266927\pi\)
−0.309794 + 0.950804i \(0.600260\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 36.0000i 1.85409i
\(378\) −1.73205 2.00000i −0.0890871 0.102869i
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) 0 0
\(383\) 15.5885 + 9.00000i 0.796533 + 0.459879i 0.842257 0.539076i \(-0.181226\pi\)
−0.0457244 + 0.998954i \(0.514560\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 19.0000 0.967075
\(387\) 8.66025 + 5.00000i 0.440225 + 0.254164i
\(388\) 0.866025 0.500000i 0.0439658 0.0253837i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 4.33013 5.50000i 0.218704 0.277792i
\(393\) 9.00000i 0.453990i
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) 3.46410 + 2.00000i 0.173858 + 0.100377i 0.584404 0.811463i \(-0.301328\pi\)
−0.410546 + 0.911840i \(0.634662\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 10.0000 + 3.46410i 0.500626 + 0.173422i
\(400\) 0 0
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) 8.66025 5.00000i 0.431934 0.249377i
\(403\) −3.46410 + 2.00000i −0.172559 + 0.0996271i
\(404\) −9.00000 + 15.5885i −0.447767 + 0.775555i
\(405\) 0 0
\(406\) 18.0000 15.5885i 0.893325 0.773642i
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0 0
\(411\) −9.00000 + 15.5885i −0.443937 + 0.768922i
\(412\) 8.00000i 0.394132i
\(413\) −7.79423 + 1.50000i −0.383529 + 0.0738102i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 1.73205 1.00000i 0.0848189 0.0489702i
\(418\) 10.3923 + 6.00000i 0.508304 + 0.293470i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 12.1244 + 7.00000i 0.590204 + 0.340755i
\(423\) 5.19615 3.00000i 0.252646 0.145865i
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 17.3205 + 20.0000i 0.838198 + 0.967868i
\(428\) 3.00000i 0.145010i
\(429\) −6.00000 + 10.3923i −0.289683 + 0.501745i
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 34.0000i 1.63394i 0.576683 + 0.816968i \(0.304347\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) −2.50000 0.866025i −0.120004 0.0415705i
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 0 0
\(438\) 1.73205 1.00000i 0.0827606 0.0477818i
\(439\) 17.5000 30.3109i 0.835229 1.44666i −0.0586141 0.998281i \(-0.518668\pi\)
0.893843 0.448379i \(-0.147999\pi\)
\(440\) 0 0
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) −28.5788 16.5000i −1.35782 0.783939i −0.368492 0.929631i \(-0.620126\pi\)
−0.989330 + 0.145692i \(0.953459\pi\)
\(444\) 4.00000 + 6.92820i 0.189832 + 0.328798i
\(445\) 0 0
\(446\) −9.50000 + 16.4545i −0.449838 + 0.779142i
\(447\) 18.0000i 0.851371i
\(448\) 0.866025 2.50000i 0.0409159 0.118114i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.866025 0.500000i −0.0406894 0.0234920i
\(454\) −27.0000 −1.26717
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 0.866025 + 0.500000i 0.0405110 + 0.0233890i 0.520119 0.854094i \(-0.325888\pi\)
−0.479608 + 0.877483i \(0.659221\pi\)
\(458\) −3.46410 + 2.00000i −0.161867 + 0.0934539i
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) −7.79423 + 1.50000i −0.362620 + 0.0697863i
\(463\) 8.00000i 0.371792i −0.982569 0.185896i \(-0.940481\pi\)
0.982569 0.185896i \(-0.0595187\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −31.1769 18.0000i −1.44270 0.832941i −0.444667 0.895696i \(-0.646678\pi\)
−0.998029 + 0.0627555i \(0.980011\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −5.00000 25.9808i −0.230879 1.19968i
\(470\) 0 0
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) −2.59808 + 1.50000i −0.119586 + 0.0690431i
\(473\) 25.9808 15.0000i 1.19460 0.689701i
\(474\) 0.500000 0.866025i 0.0229658 0.0397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 3.00000i 0.137361i
\(478\) 20.7846 + 12.0000i 0.950666 + 0.548867i
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0 0
\(481\) 16.0000 27.7128i 0.729537 1.26360i
\(482\) 1.00000i 0.0455488i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 35.5070 20.5000i 1.60898 0.928944i 0.619378 0.785093i \(-0.287385\pi\)
0.989599 0.143851i \(-0.0459486\pi\)
\(488\) 8.66025 + 5.00000i 0.392031 + 0.226339i
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 13.8564i −0.359937 0.623429i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 5.19615 15.0000i 0.233079 0.672842i
\(498\) 9.00000i 0.403300i
\(499\) 1.00000 1.73205i 0.0447661 0.0775372i −0.842774 0.538267i \(-0.819079\pi\)
0.887540 + 0.460730i \(0.152412\pi\)
\(500\) 0 0
\(501\) −3.00000 5.19615i −0.134030 0.232147i
\(502\) 23.3827 + 13.5000i 1.04362 + 0.602534i
\(503\) 12.0000i 0.535054i 0.963550 + 0.267527i \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) −2.00000 + 1.73205i −0.0890871 + 0.0771517i
\(505\) 0 0
\(506\) 0 0
\(507\) 2.59808 1.50000i 0.115385 0.0666173i
\(508\) −4.33013 + 2.50000i −0.192118 + 0.110920i
\(509\) −1.50000 + 2.59808i −0.0664863 + 0.115158i −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) −1.00000 5.19615i −0.0442374 0.229864i
\(512\) 1.00000i 0.0441942i
\(513\) −3.46410 2.00000i −0.152944 0.0883022i
\(514\) −3.00000 5.19615i −0.132324 0.229192i
\(515\) 0 0
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) 18.0000i 0.791639i
\(518\) 20.7846 4.00000i 0.913223 0.175750i
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) −7.79423 + 4.50000i −0.341144 + 0.196960i
\(523\) −3.46410 2.00000i −0.151475 0.0874539i 0.422347 0.906434i \(-0.361206\pi\)
−0.573822 + 0.818980i \(0.694540\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 6.00000 0.261612
\(527\) 0 0
\(528\) −2.59808 + 1.50000i −0.113067 + 0.0652791i
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 0 0
\(531\) 3.00000 0.130189
\(532\) 3.46410 10.0000i 0.150188 0.433555i
\(533\) 0 0
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0 0
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) −10.3923 6.00000i −0.448461 0.258919i
\(538\) 21.0000i 0.905374i
\(539\) −3.00000 + 20.7846i −0.129219 + 0.895257i
\(540\) 0 0
\(541\) −13.0000 + 22.5167i −0.558914 + 0.968067i 0.438674 + 0.898646i \(0.355448\pi\)
−0.997587 + 0.0694205i \(0.977885\pi\)
\(542\) −9.52628 + 5.50000i −0.409189 + 0.236245i
\(543\) −6.92820 + 4.00000i −0.297318 + 0.171656i
\(544\) 0 0
\(545\) 0 0
\(546\) 10.0000 + 3.46410i 0.427960 + 0.148250i
\(547\) 8.00000i 0.342055i 0.985266 + 0.171028i \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) 15.5885 + 9.00000i 0.665906 + 0.384461i
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) 0 0
\(551\) 18.0000 31.1769i 0.766826 1.32818i
\(552\) 0 0
\(553\) −1.73205 2.00000i −0.0736543 0.0850487i
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) 2.59808 1.50000i 0.110084 0.0635570i −0.443947 0.896053i \(-0.646422\pi\)
0.554031 + 0.832496i \(0.313089\pi\)
\(558\) 0.866025 + 0.500000i 0.0366618 + 0.0211667i
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) 5.19615 + 3.00000i 0.219186 + 0.126547i
\(563\) −33.7750 + 19.5000i −1.42345 + 0.821827i −0.996592 0.0824933i \(-0.973712\pi\)
−0.426855 + 0.904320i \(0.640378\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 2.59808 0.500000i 0.109109 0.0209980i
\(568\) 6.00000i 0.251754i
\(569\) −18.0000 + 31.1769i −0.754599 + 1.30700i 0.190974 + 0.981595i \(0.438835\pi\)
−0.945573 + 0.325409i \(0.894498\pi\)
\(570\) 0 0
\(571\) 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i \(0.0852845\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(572\) 10.3923 + 6.00000i 0.434524 + 0.250873i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 19.9186 11.5000i 0.829222 0.478751i −0.0243645 0.999703i \(-0.507756\pi\)
0.853586 + 0.520952i \(0.174423\pi\)
\(578\) −14.7224 + 8.50000i −0.612372 + 0.353553i
\(579\) −9.50000 + 16.4545i −0.394807 + 0.683825i
\(580\) 0 0
\(581\) −22.5000 7.79423i −0.933457 0.323359i
\(582\) 1.00000i 0.0414513i
\(583\) −7.79423 4.50000i −0.322804 0.186371i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) 16.5000 28.5788i 0.681609 1.18058i
\(587\) 21.0000i 0.866763i 0.901211 + 0.433381i \(0.142680\pi\)
−0.901211 + 0.433381i \(0.857320\pi\)
\(588\) 2.59808 + 6.50000i 0.107143 + 0.268055i
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 6.92820 4.00000i 0.284747 0.164399i
\(593\) 20.7846 + 12.0000i 0.853522 + 0.492781i 0.861838 0.507184i \(-0.169314\pi\)
−0.00831589 + 0.999965i \(0.502647\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −17.3205 10.0000i −0.708881 0.409273i
\(598\) 0 0
\(599\) −9.00000 15.5885i −0.367730 0.636927i 0.621480 0.783430i \(-0.286532\pi\)
−0.989210 + 0.146503i \(0.953198\pi\)
\(600\) 0 0
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) −17.3205 20.0000i −0.705931 0.815139i
\(603\) 10.0000i 0.407231i
\(604\) −0.500000 + 0.866025i −0.0203447 + 0.0352381i
\(605\) 0 0
\(606\) −9.00000 15.5885i −0.365600 0.633238i
\(607\) 6.06218 + 3.50000i 0.246056 + 0.142061i 0.617957 0.786212i \(-0.287961\pi\)
−0.371901 + 0.928272i \(0.621294\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 4.50000 + 23.3827i 0.182349 + 0.947514i
\(610\) 0 0
\(611\) −12.0000 + 20.7846i −0.485468 + 0.840855i
\(612\) 0 0
\(613\) 13.8564 8.00000i 0.559655 0.323117i −0.193352 0.981129i \(-0.561936\pi\)
0.753007 + 0.658012i \(0.228603\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 0 0
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) 6.00000i 0.241551i −0.992680 0.120775i \(-0.961462\pi\)
0.992680 0.120775i \(-0.0385381\pi\)
\(618\) −6.92820 4.00000i −0.278693 0.160904i
\(619\) −17.0000 29.4449i −0.683288 1.18349i −0.973972 0.226670i \(-0.927216\pi\)
0.290684 0.956819i \(-0.406117\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 10.3923 + 12.0000i 0.416359 + 0.480770i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) −15.5000 26.8468i −0.619505 1.07301i
\(627\) −10.3923 + 6.00000i −0.415029 + 0.239617i
\(628\) −3.46410 2.00000i −0.138233 0.0798087i
\(629\) 0 0
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −0.866025 0.500000i −0.0344486 0.0198889i
\(633\) −12.1244 + 7.00000i −0.481900 + 0.278225i
\(634\) −4.50000 7.79423i −0.178718 0.309548i
\(635\) 0 0
\(636\) −3.00000 −0.118958
\(637\) 17.3205 22.0000i 0.686264 0.871672i
\(638\) 27.0000i 1.06894i
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) −2.59808 1.50000i −0.102538 0.0592003i
\(643\) 34.0000i 1.34083i 0.741987 + 0.670415i \(0.233884\pi\)
−0.741987 + 0.670415i \(0.766116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.5885 + 9.00000i −0.612845 + 0.353827i −0.774078 0.633090i \(-0.781786\pi\)
0.161233 + 0.986916i \(0.448453\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 4.50000 7.79423i 0.176640 0.305950i
\(650\) 0 0
\(651\) 2.00000 1.73205i 0.0783862 0.0678844i
\(652\) 16.0000i 0.626608i
\(653\) 2.59808 + 1.50000i 0.101671 + 0.0586995i 0.549973 0.835182i \(-0.314638\pi\)
−0.448303 + 0.893882i \(0.647971\pi\)
\(654\) −7.00000 12.1244i −0.273722 0.474100i
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000i 0.0780274i
\(658\) −15.5885 + 3.00000i −0.607701 + 0.116952i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −17.3205 + 10.0000i −0.673181 + 0.388661i
\(663\) 0 0
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 0 0
\(668\) −5.19615 + 3.00000i −0.201045 + 0.116073i
\(669\) −9.50000 16.4545i −0.367291 0.636167i
\(670\) 0 0
\(671\) −30.0000 −1.15814
\(672\) 1.73205 + 2.00000i 0.0668153 + 0.0771517i
\(673\) 29.0000i 1.11787i −0.829212 0.558934i \(-0.811211\pi\)
0.829212 0.558934i \(-0.188789\pi\)
\(674\) 3.50000 6.06218i 0.134815 0.233506i
\(675\) 0 0
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 28.5788 + 16.5000i 1.09837 + 0.634147i 0.935793 0.352549i \(-0.114685\pi\)
0.162581 + 0.986695i \(0.448018\pi\)
\(678\) 0 0
\(679\) 2.50000 + 0.866025i 0.0959412 + 0.0332350i
\(680\) 0 0
\(681\) 13.5000 23.3827i 0.517321 0.896026i
\(682\) 2.59808 1.50000i 0.0994855 0.0574380i
\(683\) −28.5788 + 16.5000i −1.09354 + 0.631355i −0.934516 0.355920i \(-0.884168\pi\)
−0.159022 + 0.987275i \(0.550834\pi\)
\(684\) −2.00000 + 3.46410i −0.0764719 + 0.132453i
\(685\) 0 0
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 4.00000i 0.152610i
\(688\) −8.66025 5.00000i −0.330169 0.190623i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 2.59808 7.50000i 0.0986928 0.284901i
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) 4.50000 + 7.79423i 0.170572 + 0.295439i
\(697\) 0 0
\(698\) −22.5167 13.0000i −0.852268 0.492057i
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) −3.46410 2.00000i −0.130744 0.0754851i
\(703\) 27.7128 16.0000i 1.04521 0.603451i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) −46.7654 + 9.00000i −1.75879 + 0.338480i
\(708\) 3.00000i 0.112747i
\(709\) −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 5.19615 + 3.00000i 0.194734 + 0.112430i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) −20.7846 + 12.0000i −0.776215 + 0.448148i
\(718\) 25.9808 15.0000i 0.969593 0.559795i
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 0 0
\(721\) −16.0000 + 13.8564i −0.595871 + 0.516040i
\(722\) 3.00000i 0.111648i
\(723\) −0.866025 0.500000i −0.0322078 0.0185952i
\(724\) 4.00000 + 6.92820i 0.148659 + 0.257485i
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) 13.0000i 0.482143i −0.970507 0.241072i \(-0.922501\pi\)
0.970507 0.241072i \(-0.0774989\pi\)
\(728\) 3.46410 10.0000i 0.128388 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −8.66025 + 5.00000i −0.320092 + 0.184805i
\(733\) −8.66025 5.00000i −0.319874 0.184679i 0.331463 0.943468i \(-0.392458\pi\)
−0.651336 + 0.758789i \(0.725791\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 0 0
\(737\) 25.9808 + 15.0000i 0.957014 + 0.552532i
\(738\) 0 0
\(739\) 25.0000 + 43.3013i 0.919640 + 1.59286i 0.799962 + 0.600050i \(0.204853\pi\)
0.119677 + 0.992813i \(0.461814\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) −2.59808 + 7.50000i −0.0953784 + 0.275334i
\(743\) 42.0000i 1.54083i −0.637542 0.770415i \(-0.720049\pi\)
0.637542 0.770415i \(-0.279951\pi\)
\(744\) 0.500000 0.866025i 0.0183309 0.0317500i
\(745\) 0 0
\(746\) 4.00000 + 6.92820i 0.146450 + 0.253660i
\(747\) 7.79423 + 4.50000i 0.285176 + 0.164646i
\(748\) 0 0
\(749\) −6.00000 + 5.19615i −0.219235 + 0.189863i
\(750\) 0 0
\(751\) 3.50000 6.06218i 0.127717 0.221212i −0.795075 0.606511i \(-0.792568\pi\)
0.922792 + 0.385299i \(0.125902\pi\)
\(752\) −5.19615 + 3.00000i −0.189484 + 0.109399i
\(753\) −23.3827 + 13.5000i −0.852112 + 0.491967i
\(754\) 18.0000 31.1769i 0.655521 1.13540i
\(755\) 0 0
\(756\) −0.500000 2.59808i −0.0181848 0.0944911i
\(757\) 38.0000i 1.38113i 0.723269 + 0.690567i \(0.242639\pi\)
−0.723269 + 0.690567i \(0.757361\pi\)
\(758\) −6.92820 4.00000i −0.251644 0.145287i
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 + 10.3923i −0.217500 + 0.376721i −0.954043 0.299670i \(-0.903123\pi\)
0.736543 + 0.676391i \(0.236457\pi\)
\(762\) 5.00000i 0.181131i
\(763\) −36.3731 + 7.00000i −1.31679 + 0.253417i
\(764\) 0 0
\(765\) 0 0
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) −10.3923 + 6.00000i −0.375244 + 0.216647i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 19.0000 0.685158 0.342579 0.939489i \(-0.388700\pi\)
0.342579 + 0.939489i \(0.388700\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 16.4545 + 9.50000i 0.592210 + 0.341912i
\(773\) −5.19615 + 3.00000i −0.186893 + 0.107903i −0.590527 0.807018i \(-0.701080\pi\)
0.403634 + 0.914920i \(0.367747\pi\)
\(774\) 5.00000 + 8.66025i 0.179721 + 0.311286i
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) −6.92820 + 20.0000i −0.248548 + 0.717496i
\(778\) 6.00000i 0.215110i
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 0 0
\(783\) 9.00000i 0.321634i
\(784\) 6.50000 2.59808i 0.232143 0.0927884i
\(785\) 0 0
\(786\) −4.50000 + 7.79423i −0.160510 + 0.278011i
\(787\) 43.3013 25.0000i 1.54352 0.891154i 0.544911 0.838494i \(-0.316563\pi\)
0.998613 0.0526599i \(-0.0167699\pi\)
\(788\) −5.19615 + 3.00000i −0.185105 + 0.106871i
\(789\) −3.00000 + 5.19615i −0.106803 + 0.184988i
\(790\) 0 0
\(791\) 0 0
\(792\) 3.00000i 0.106600i
\(793\) 34.6410 + 20.0000i 1.23014 + 0.710221i
\(794\) 2.00000 + 3.46410i 0.0709773 + 0.122936i
\(795\) 0 0
\(796\) −10.0000 + 17.3205i −0.354441 + 0.613909i
\(797\) 33.0000i 1.16892i −0.811423 0.584460i \(-0.801306\pi\)
0.811423 0.584460i \(-0.198694\pi\)
\(798\) 6.92820 + 8.00000i 0.245256 + 0.283197i
\(799\) 0 0
\(800\) 0 0
\(801\) −3.00000 5.19615i −0.106000 0.183597i
\(802\) −20.7846 + 12.0000i −0.733930 + 0.423735i
\(803\) 5.19615 + 3.00000i 0.183368 + 0.105868i
\(804\) 10.0000 0.352673
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −18.1865 10.5000i −0.640196 0.369618i
\(808\) −15.5885 + 9.00000i −0.548400 + 0.316619i
\(809\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) 23.3827 4.50000i 0.820571 0.157919i
\(813\) 11.0000i 0.385787i
\(814\) −12.0000 + 20.7846i −0.420600 + 0.728500i
\(815\) 0 0
\(816\) 0 0
\(817\) −34.6410 20.0000i −1.21194 0.699711i
\(818\) 25.0000i 0.874105i
\(819\) −8.00000 + 6.92820i −0.279543 + 0.242091i
\(820\) 0 0
\(821\) 1.50000 2.59808i 0.0523504 0.0906735i −0.838663 0.544651i \(-0.816662\pi\)
0.891013 + 0.453978i \(0.149995\pi\)
\(822\) −15.5885 + 9.00000i −0.543710 + 0.313911i
\(823\) 34.6410 20.0000i 1.20751 0.697156i 0.245295 0.969448i \(-0.421115\pi\)
0.962215 + 0.272292i \(0.0877817\pi\)
\(824\) −4.00000 + 6.92820i −0.139347 + 0.241355i
\(825\) 0 0
\(826\) −7.50000 2.59808i −0.260958 0.0903986i
\(827\) 15.0000i 0.521601i 0.965393 + 0.260801i \(0.0839865\pi\)
−0.965393 + 0.260801i \(0.916014\pi\)
\(828\) 0 0
\(829\) −2.00000 3.46410i −0.0694629 0.120313i 0.829202 0.558949i \(-0.188795\pi\)
−0.898665 + 0.438636i \(0.855462\pi\)
\(830\) 0 0
\(831\) −4.00000 + 6.92820i −0.138758 + 0.240337i
\(832\) 4.00000i 0.138675i
\(833\) 0 0
\(834\) 2.00000 0.0692543
\(835\) 0 0
\(836\) 6.00000 + 10.3923i 0.207514 + 0.359425i
\(837\) −0.866025 + 0.500000i −0.0299342 + 0.0172825i
\(838\) 0 0
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) −19.0526 11.0000i −0.656595 0.379085i
\(843\) −5.19615 + 3.00000i −0.178965 + 0.103325i
\(844\) 7.00000 + 12.1244i 0.240950 + 0.417338i
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) 3.46410 + 4.00000i 0.119028 + 0.137442i
\(848\) 3.00000i 0.103020i
\(849\) 7.00000 12.1244i 0.240239 0.416107i
\(850\) 0 0
\(851\) 0 0
\(852\) 5.19615 + 3.00000i 0.178017 + 0.102778i
\(853\) 10.0000i 0.342393i 0.985237 + 0.171197i \(0.0547634\pi\)
−0.985237 + 0.171197i \(0.945237\pi\)
\(854\) 5.00000 + 25.9808i 0.171096 + 0.889043i
\(855\) 0 0
\(856\) −1.50000 + 2.59808i −0.0512689 + 0.0888004i
\(857\) −36.3731 + 21.0000i −1.24248 + 0.717346i −0.969599 0.244701i \(-0.921310\pi\)
−0.272882 + 0.962048i \(0.587977\pi\)
\(858\) −10.3923 + 6.00000i −0.354787 + 0.204837i
\(859\) 25.0000 43.3013i 0.852989 1.47742i −0.0255092 0.999675i \(-0.508121\pi\)
0.878498 0.477746i \(-0.158546\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 12.0000i 0.408722i
\(863\) 5.19615 + 3.00000i 0.176879 + 0.102121i 0.585826 0.810437i \(-0.300770\pi\)
−0.408946 + 0.912558i \(0.634104\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) 0 0
\(866\) −17.0000 + 29.4449i −0.577684 + 1.00058i
\(867\) 17.0000i 0.577350i
\(868\) −1.73205 2.00000i −0.0587896 0.0678844i
\(869\) 3.00000 0.101768
\(870\) 0 0
\(871\) −20.0000 34.6410i −0.677674 1.17377i
\(872\) −12.1244 + 7.00000i −0.410582 + 0.237050i
\(873\) −0.866025 0.500000i −0.0293105 0.0169224i
\(874\) 0 0
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −27.7128 16.0000i −0.935795 0.540282i −0.0471555 0.998888i \(-0.515016\pi\)
−0.888640 + 0.458606i \(0.848349\pi\)
\(878\) 30.3109 17.5000i 1.02294 0.590596i
\(879\) 16.5000 + 28.5788i 0.556531 + 0.963940i
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) −6.92820 1.00000i −0.233285 0.0336718i
\(883\) 32.0000i 1.07689i −0.842662 0.538443i \(-0.819013\pi\)
0.842662 0.538443i \(-0.180987\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −16.5000 28.5788i −0.554328 0.960125i
\(887\) 20.7846 + 12.0000i 0.697879 + 0.402921i 0.806557 0.591156i \(-0.201328\pi\)
−0.108678 + 0.994077i \(0.534662\pi\)
\(888\) 8.00000i 0.268462i
\(889\) −12.5000 4.33013i −0.419237 0.145228i
\(890\) 0 0
\(891\) −1.50000 + 2.59808i −0.0502519 + 0.0870388i
\(892\) −16.4545 + 9.50000i −0.550937 + 0.318084i
\(893\) −20.7846 + 12.0000i −0.695530 + 0.401565i
\(894\) −9.00000 + 15.5885i −0.301005 + 0.521356i
\(895\) 0 0
\(896\) 2.00000 1.73205i 0.0668153 0.0578638i
\(897\) 0 0
\(898\) −10.3923 6.00000i −0.346796 0.200223i
\(899\) −4.50000 7.79423i −0.150083 0.259952i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 25.9808 5.00000i 0.864586 0.166390i
\(904\) 0 0
\(905\) 0 0
\(906\) −0.500000 0.866025i −0.0166114 0.0287718i
\(907\) 6.92820 4.00000i 0.230047 0.132818i −0.380547 0.924762i \(-0.624264\pi\)
0.610594 + 0.791944i \(0.290931\pi\)
\(908\) −23.3827 13.5000i −0.775982 0.448013i
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 6.00000 0.198789 0.0993944 0.995048i \(-0.468309\pi\)
0.0993944 + 0.995048i \(0.468309\pi\)
\(912\) 3.46410 + 2.00000i 0.114708 + 0.0662266i
\(913\) 23.3827 13.5000i 0.773854 0.446785i
\(914\) 0.500000 + 0.866025i 0.0165385 + 0.0286456i
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) 15.5885 + 18.0000i 0.514776 + 0.594412i
\(918\) 0 0
\(919\) 4.00000 6.92820i 0.131948 0.228540i −0.792480 0.609898i \(-0.791210\pi\)
0.924427 + 0.381358i \(0.124544\pi\)
\(920\) 0 0
\(921\) −4.00000 6.92820i −0.131804 0.228292i
\(922\) 25.9808 + 15.0000i 0.855631 + 0.493999i
\(923\) 24.0000i 0.789970i
\(924\) −7.50000 2.59808i −0.246732 0.0854704i
\(925\) 0 0
\(926\) 4.00000 6.92820i 0.131448 0.227675i
\(927\) 6.92820 4.00000i 0.227552 0.131377i
\(928\) 7.79423 4.50000i 0.255858 0.147720i
\(929\) −3.00000 + 5.19615i −0.0984268 + 0.170480i −0.911034 0.412332i \(-0.864714\pi\)
0.812607 + 0.582812i \(0.198048\pi\)
\(930\) 0 0
\(931\) 26.0000 10.3923i 0.852116 0.340594i
\(932\) 24.0000i 0.786146i
\(933\) 20.7846 + 12.0000i 0.680458 + 0.392862i
\(934\) −18.0000 31.1769i −0.588978 1.02014i
\(935\) 0 0
\(936\) −2.00000 + 3.46410i −0.0653720 + 0.113228i
\(937\) 35.0000i 1.14340i 0.820463 + 0.571700i \(0.193716\pi\)
−0.820463 + 0.571700i \(0.806284\pi\)
\(938\) 8.66025 25.0000i 0.282767 0.816279i
\(939\) 31.0000 1.01165
\(940\) 0 0
\(941\) 4.50000 + 7.79423i 0.146696 + 0.254085i 0.930004 0.367549i \(-0.119803\pi\)
−0.783309 + 0.621633i \(0.786469\pi\)
\(942\) 3.46410 2.00000i 0.112867 0.0651635i
\(943\) 0 0
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 30.0000 0.975384
\(947\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 0.866025 0.500000i 0.0281272 0.0162392i
\(949\) −4.00000 6.92820i −0.129845 0.224899i
\(950\) 0 0
\(951\) 9.00000 0.291845
\(952\) 0 0
\(953\) 6.00000i 0.194359i 0.995267 + 0.0971795i \(0.0309821\pi\)
−0.995267 + 0.0971795i \(0.969018\pi\)
\(954\) 1.50000 2.59808i 0.0485643 0.0841158i
\(955\) 0 0
\(956\) 12.0000 + 20.7846i 0.388108 + 0.672222i
\(957\) −23.3827 13.5000i −0.755855 0.436393i
\(958\) 18.0000i 0.581554i
\(959\) 9.00000 + 46.7654i 0.290625 + 1.51013i
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) 27.7128 16.0000i 0.893497 0.515861i
\(963\) 2.59808 1.50000i 0.0837218 0.0483368i
\(964\) −0.500000 + 0.866025i −0.0161039 + 0.0278928i
\(965\) 0 0
\(966\) 0 0
\(967\) 1.00000i 0.0321578i −0.999871 0.0160789i \(-0.994882\pi\)
0.999871 0.0160789i \(-0.00511830\pi\)
\(968\) 1.73205 + 1.00000i 0.0556702 + 0.0321412i
\(969\) 0 0
\(970\) 0 0
\(971\) 19.5000 33.7750i 0.625785 1.08389i −0.362604 0.931943i \(-0.618112\pi\)
0.988389 0.151948i \(-0.0485545\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 1.73205 5.00000i 0.0555270 0.160293i
\(974\) 41.0000 1.31372
\(975\) 0 0
\(976\) 5.00000 + 8.66025i 0.160046 + 0.277208i
\(977\) 36.3731 21.0000i 1.16368 0.671850i 0.211495 0.977379i \(-0.432167\pi\)
0.952183 + 0.305530i \(0.0988335\pi\)
\(978\) 13.8564 + 8.00000i 0.443079 + 0.255812i
\(979\) −18.0000 −0.575282
\(980\) 0 0
\(981\) 14.0000 0.446986
\(982\) −28.5788 16.5000i −0.911987 0.526536i
\(983\) −31.1769 + 18.0000i −0.994389 + 0.574111i −0.906583 0.422027i \(-0.861319\pi\)
−0.0878058 + 0.996138i \(0.527985\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 5.19615 15.0000i 0.165395 0.477455i
\(988\) 16.0000i 0.509028i
\(989\) 0 0
\(990\) 0 0
\(991\) 6.50000 + 11.2583i 0.206479 + 0.357633i 0.950603 0.310409i \(-0.100466\pi\)
−0.744124 + 0.668042i \(0.767133\pi\)
\(992\) −0.866025 0.500000i −0.0274963 0.0158750i
\(993\) 20.0000i 0.634681i
\(994\) 12.0000 10.3923i 0.380617 0.329624i
\(995\) 0 0
\(996\) 4.50000 7.79423i 0.142588 0.246970i
\(997\) 12.1244 7.00000i 0.383982 0.221692i −0.295567 0.955322i \(-0.595509\pi\)
0.679549 + 0.733630i \(0.262175\pi\)
\(998\) 1.73205 1.00000i 0.0548271 0.0316544i
\(999\) 4.00000 6.92820i 0.126554 0.219199i
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.o.b.499.2 4
5.2 odd 4 1050.2.i.e.751.1 2
5.3 odd 4 42.2.e.b.37.1 yes 2
5.4 even 2 inner 1050.2.o.b.499.1 4
7.4 even 3 inner 1050.2.o.b.949.1 4
15.8 even 4 126.2.g.b.37.1 2
20.3 even 4 336.2.q.d.289.1 2
35.2 odd 12 7350.2.a.ce.1.1 1
35.3 even 12 294.2.e.f.67.1 2
35.4 even 6 inner 1050.2.o.b.949.2 4
35.12 even 12 7350.2.a.cw.1.1 1
35.13 even 4 294.2.e.f.79.1 2
35.18 odd 12 42.2.e.b.25.1 2
35.23 odd 12 294.2.a.d.1.1 1
35.32 odd 12 1050.2.i.e.151.1 2
35.33 even 12 294.2.a.a.1.1 1
40.3 even 4 1344.2.q.j.961.1 2
40.13 odd 4 1344.2.q.v.961.1 2
45.13 odd 12 1134.2.h.p.541.1 2
45.23 even 12 1134.2.h.a.541.1 2
45.38 even 12 1134.2.e.p.919.1 2
45.43 odd 12 1134.2.e.a.919.1 2
60.23 odd 4 1008.2.s.n.289.1 2
105.23 even 12 882.2.a.g.1.1 1
105.38 odd 12 882.2.g.b.361.1 2
105.53 even 12 126.2.g.b.109.1 2
105.68 odd 12 882.2.a.k.1.1 1
105.83 odd 4 882.2.g.b.667.1 2
140.3 odd 12 2352.2.q.m.1537.1 2
140.23 even 12 2352.2.a.m.1.1 1
140.83 odd 4 2352.2.q.m.961.1 2
140.103 odd 12 2352.2.a.n.1.1 1
140.123 even 12 336.2.q.d.193.1 2
280.53 odd 12 1344.2.q.v.193.1 2
280.93 odd 12 9408.2.a.d.1.1 1
280.123 even 12 1344.2.q.j.193.1 2
280.163 even 12 9408.2.a.bu.1.1 1
280.173 even 12 9408.2.a.db.1.1 1
280.243 odd 12 9408.2.a.bm.1.1 1
315.88 odd 12 1134.2.h.p.109.1 2
315.158 even 12 1134.2.e.p.865.1 2
315.193 odd 12 1134.2.e.a.865.1 2
315.263 even 12 1134.2.h.a.109.1 2
420.23 odd 12 7056.2.a.g.1.1 1
420.263 odd 12 1008.2.s.n.865.1 2
420.383 even 12 7056.2.a.bz.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.e.b.25.1 2 35.18 odd 12
42.2.e.b.37.1 yes 2 5.3 odd 4
126.2.g.b.37.1 2 15.8 even 4
126.2.g.b.109.1 2 105.53 even 12
294.2.a.a.1.1 1 35.33 even 12
294.2.a.d.1.1 1 35.23 odd 12
294.2.e.f.67.1 2 35.3 even 12
294.2.e.f.79.1 2 35.13 even 4
336.2.q.d.193.1 2 140.123 even 12
336.2.q.d.289.1 2 20.3 even 4
882.2.a.g.1.1 1 105.23 even 12
882.2.a.k.1.1 1 105.68 odd 12
882.2.g.b.361.1 2 105.38 odd 12
882.2.g.b.667.1 2 105.83 odd 4
1008.2.s.n.289.1 2 60.23 odd 4
1008.2.s.n.865.1 2 420.263 odd 12
1050.2.i.e.151.1 2 35.32 odd 12
1050.2.i.e.751.1 2 5.2 odd 4
1050.2.o.b.499.1 4 5.4 even 2 inner
1050.2.o.b.499.2 4 1.1 even 1 trivial
1050.2.o.b.949.1 4 7.4 even 3 inner
1050.2.o.b.949.2 4 35.4 even 6 inner
1134.2.e.a.865.1 2 315.193 odd 12
1134.2.e.a.919.1 2 45.43 odd 12
1134.2.e.p.865.1 2 315.158 even 12
1134.2.e.p.919.1 2 45.38 even 12
1134.2.h.a.109.1 2 315.263 even 12
1134.2.h.a.541.1 2 45.23 even 12
1134.2.h.p.109.1 2 315.88 odd 12
1134.2.h.p.541.1 2 45.13 odd 12
1344.2.q.j.193.1 2 280.123 even 12
1344.2.q.j.961.1 2 40.3 even 4
1344.2.q.v.193.1 2 280.53 odd 12
1344.2.q.v.961.1 2 40.13 odd 4
2352.2.a.m.1.1 1 140.23 even 12
2352.2.a.n.1.1 1 140.103 odd 12
2352.2.q.m.961.1 2 140.83 odd 4
2352.2.q.m.1537.1 2 140.3 odd 12
7056.2.a.g.1.1 1 420.23 odd 12
7056.2.a.bz.1.1 1 420.383 even 12
7350.2.a.ce.1.1 1 35.2 odd 12
7350.2.a.cw.1.1 1 35.12 even 12
9408.2.a.d.1.1 1 280.93 odd 12
9408.2.a.bm.1.1 1 280.243 odd 12
9408.2.a.bu.1.1 1 280.163 even 12
9408.2.a.db.1.1 1 280.173 even 12