Properties

Label 1050.2.o.f.949.2
Level $1050$
Weight $2$
Character 1050.949
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.f.499.2

$q$-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} +(1.00000 - 1.73205i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.33013 - 2.50000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(2.00000 - 1.73205i) q^{21} -2.00000i q^{22} +(4.33013 - 2.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(1.73205 + 2.00000i) q^{28} +6.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.73205 + 1.00000i) q^{33} -5.00000 q^{34} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(-3.46410 - 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +5.00000 q^{41} +(0.866025 - 2.50000i) q^{42} +(-1.00000 - 1.73205i) q^{44} +(2.50000 - 4.33013i) q^{46} +(0.866025 - 0.500000i) q^{47} +1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(2.50000 + 4.33013i) q^{51} +(-3.46410 - 2.00000i) q^{52} +(-10.3923 - 6.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} +4.00000i q^{57} +(5.19615 - 3.00000i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(-5.00000 - 8.66025i) q^{61} -11.0000i q^{62} +(-2.59808 + 0.500000i) q^{63} -1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-4.33013 + 2.50000i) q^{68} -5.00000 q^{69} -1.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(3.46410 + 4.00000i) q^{77} +4.00000i q^{78} +(4.50000 + 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.33013 - 2.50000i) q^{82} +6.00000i q^{83} +(-0.500000 - 2.59808i) q^{84} +(-5.19615 - 3.00000i) q^{87} +(-1.73205 - 1.00000i) q^{88} +(5.50000 + 9.52628i) q^{89} +(10.0000 + 3.46410i) q^{91} -5.00000i q^{92} +(-9.52628 + 5.50000i) q^{93} +(0.500000 - 0.866025i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000i q^{97} +(-6.92820 - 1.00000i) q^{98} +2.00000 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 \( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} + 4 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{19} + 8 q^{21} - 2 q^{24} - 8 q^{26} + 24 q^{29} + 22 q^{31} - 20 q^{34} + 4 q^{36} - 8 q^{39} + 20 q^{41} - 4 q^{44} + 10 q^{46} - 22 q^{49} + 10 q^{51} - 2 q^{54} + 10 q^{56} - 4 q^{59} - 20 q^{61} - 4 q^{64} - 4 q^{66} - 20 q^{69} - 4 q^{71} - 16 q^{74} - 16 q^{76} + 18 q^{79} - 2 q^{81} - 2 q^{84} + 22 q^{89} + 40 q^{91} + 2 q^{94} + 2 q^{96} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.33013 2.50000i −1.05021 0.606339i −0.127502 0.991838i \(-0.540696\pi\)
−0.922708 + 0.385499i \(0.874029\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 0 0
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) 2.00000i 0.426401i
\(23\) 4.33013 2.50000i 0.902894 0.521286i 0.0247559 0.999694i \(-0.492119\pi\)
0.878138 + 0.478407i \(0.158786\pi\)
\(24\) −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
\(28\) 1.73205 + 2.00000i 0.327327 + 0.377964i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 5.50000 9.52628i 0.987829 1.71097i 0.359211 0.933257i \(-0.383046\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −1.73205 + 1.00000i −0.301511 + 0.174078i
\(34\) −5.00000 −0.857493
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.92820 + 4.00000i −1.13899 + 0.657596i −0.946180 0.323640i \(-0.895093\pi\)
−0.192809 + 0.981236i \(0.561760\pi\)
\(38\) −3.46410 2.00000i −0.561951 0.324443i
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0.866025 2.50000i 0.133631 0.385758i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) 2.50000 4.33013i 0.368605 0.638442i
\(47\) 0.866025 0.500000i 0.126323 0.0729325i −0.435507 0.900185i \(-0.643431\pi\)
0.561830 + 0.827253i \(0.310098\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) 2.50000 + 4.33013i 0.350070 + 0.606339i
\(52\) −3.46410 2.00000i −0.480384 0.277350i
\(53\) −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i \(-0.641688\pi\)
−0.996922 + 0.0783936i \(0.975021\pi\)
\(54\) −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
\(58\) 5.19615 3.00000i 0.682288 0.393919i
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 11.0000i 1.39700i
\(63\) −2.59808 + 0.500000i −0.327327 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −4.33013 + 2.50000i −0.525105 + 0.303170i
\(69\) −5.00000 −0.601929
\(70\) 0 0
\(71\) −1.00000 −0.118678 −0.0593391 0.998238i \(-0.518899\pi\)
−0.0593391 + 0.998238i \(0.518899\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −1.73205 1.00000i −0.202721 0.117041i 0.395203 0.918594i \(-0.370674\pi\)
−0.597924 + 0.801553i \(0.704008\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 3.46410 + 4.00000i 0.394771 + 0.455842i
\(78\) 4.00000i 0.452911i
\(79\) 4.50000 + 7.79423i 0.506290 + 0.876919i 0.999974 + 0.00727784i \(0.00231663\pi\)
−0.493684 + 0.869641i \(0.664350\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.33013 2.50000i 0.478183 0.276079i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) −0.500000 2.59808i −0.0545545 0.283473i
\(85\) 0 0
\(86\) 0 0
\(87\) −5.19615 3.00000i −0.557086 0.321634i
\(88\) −1.73205 1.00000i −0.184637 0.106600i
\(89\) 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i \(0.0314541\pi\)
−0.412123 + 0.911128i \(0.635213\pi\)
\(90\) 0 0
\(91\) 10.0000 + 3.46410i 1.04828 + 0.363137i
\(92\) 5.00000i 0.521286i
\(93\) −9.52628 + 5.50000i −0.987829 + 0.570323i
\(94\) 0.500000 0.866025i 0.0515711 0.0893237i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 1.00000i 0.101535i 0.998711 + 0.0507673i \(0.0161667\pi\)
−0.998711 + 0.0507673i \(0.983833\pi\)
\(98\) −6.92820 1.00000i −0.699854 0.101015i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 4.33013 + 2.50000i 0.428746 + 0.247537i
\(103\) 11.2583 6.50000i 1.10932 0.640464i 0.170664 0.985329i \(-0.445409\pi\)
0.938652 + 0.344865i \(0.112075\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) −1.73205 + 1.00000i −0.167444 + 0.0966736i −0.581380 0.813632i \(-0.697487\pi\)
0.413936 + 0.910306i \(0.364154\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) 2.59808 0.500000i 0.245495 0.0472456i
\(113\) 5.00000i 0.470360i 0.971952 + 0.235180i \(0.0755680\pi\)
−0.971952 + 0.235180i \(0.924432\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 3.46410 2.00000i 0.320256 0.184900i
\(118\) 2.00000i 0.184115i
\(119\) 10.0000 8.66025i 0.916698 0.793884i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −8.66025 5.00000i −0.784063 0.452679i
\(123\) −4.33013 2.50000i −0.390434 0.225417i
\(124\) −5.50000 9.52628i −0.493915 0.855485i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 10.3923 2.00000i 0.901127 0.173422i
\(134\) 0 0
\(135\) 0 0
\(136\) −2.50000 + 4.33013i −0.214373 + 0.371305i
\(137\) 19.9186 + 11.5000i 1.70176 + 0.982511i 0.943981 + 0.329999i \(0.107048\pi\)
0.757778 + 0.652512i \(0.226285\pi\)
\(138\) −4.33013 + 2.50000i −0.368605 + 0.212814i
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) −0.866025 + 0.500000i −0.0726752 + 0.0419591i
\(143\) −6.92820 4.00000i −0.579365 0.334497i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 8.00000i 0.657596i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) −3.46410 + 2.00000i −0.280976 + 0.162221i
\(153\) 5.00000i 0.404226i
\(154\) 5.00000 + 1.73205i 0.402911 + 0.139573i
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −12.1244 7.00000i −0.967629 0.558661i −0.0691164 0.997609i \(-0.522018\pi\)
−0.898513 + 0.438948i \(0.855351\pi\)
\(158\) 7.79423 + 4.50000i 0.620076 + 0.358001i
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) 2.50000 + 12.9904i 0.197028 + 1.02379i
\(162\) 1.00000i 0.0785674i
\(163\) 20.7846 12.0000i 1.62798 0.939913i 0.643280 0.765631i \(-0.277573\pi\)
0.984696 0.174282i \(-0.0557604\pi\)
\(164\) 2.50000 4.33013i 0.195217 0.338126i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 16.0000i 1.23812i −0.785345 0.619059i \(-0.787514\pi\)
0.785345 0.619059i \(-0.212486\pi\)
\(168\) −1.73205 2.00000i −0.133631 0.154303i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 0 0
\(173\) −1.73205 + 1.00000i −0.131685 + 0.0760286i −0.564396 0.825505i \(-0.690891\pi\)
0.432710 + 0.901533i \(0.357557\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) 1.73205 1.00000i 0.130189 0.0751646i
\(178\) 9.52628 + 5.50000i 0.714025 + 0.412242i
\(179\) 11.0000 19.0526i 0.822179 1.42406i −0.0818780 0.996642i \(-0.526092\pi\)
0.904057 0.427413i \(-0.140575\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 10.3923 2.00000i 0.770329 0.148250i
\(183\) 10.0000i 0.739221i
\(184\) −2.50000 4.33013i −0.184302 0.319221i
\(185\) 0 0
\(186\) −5.50000 + 9.52628i −0.403280 + 0.698501i
\(187\) −8.66025 + 5.00000i −0.633300 + 0.365636i
\(188\) 1.00000i 0.0729325i
\(189\) 2.50000 + 0.866025i 0.181848 + 0.0629941i
\(190\) 0 0
\(191\) 12.5000 + 21.6506i 0.904468 + 1.56658i 0.821629 + 0.570022i \(0.193065\pi\)
0.0828388 + 0.996563i \(0.473601\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −9.52628 5.50000i −0.685717 0.395899i 0.116289 0.993215i \(-0.462900\pi\)
−0.802005 + 0.597317i \(0.796234\pi\)
\(194\) 0.500000 + 0.866025i 0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 24.0000i 1.70993i 0.518686 + 0.854965i \(0.326421\pi\)
−0.518686 + 0.854965i \(0.673579\pi\)
\(198\) 1.73205 1.00000i 0.123091 0.0710669i
\(199\) 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i \(-0.776623\pi\)
0.940927 + 0.338608i \(0.109956\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 12.0000i 0.844317i
\(203\) −5.19615 + 15.0000i −0.364698 + 1.05279i
\(204\) 5.00000 0.350070
\(205\) 0 0
\(206\) 6.50000 11.2583i 0.452876 0.784405i
\(207\) 4.33013 + 2.50000i 0.300965 + 0.173762i
\(208\) −3.46410 + 2.00000i −0.240192 + 0.138675i
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −10.3923 + 6.00000i −0.713746 + 0.412082i
\(213\) 0.866025 + 0.500000i 0.0593391 + 0.0342594i
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 19.0526 + 22.0000i 1.29337 + 1.49346i
\(218\) 4.00000i 0.270914i
\(219\) 1.00000 + 1.73205i 0.0675737 + 0.117041i
\(220\) 0 0
\(221\) −10.0000 + 17.3205i −0.672673 + 1.16510i
\(222\) 6.92820 4.00000i 0.464991 0.268462i
\(223\) 21.0000i 1.40626i 0.711059 + 0.703132i \(0.248216\pi\)
−0.711059 + 0.703132i \(0.751784\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) 2.50000 + 4.33013i 0.166298 + 0.288036i
\(227\) 15.5885 + 9.00000i 1.03464 + 0.597351i 0.918311 0.395860i \(-0.129553\pi\)
0.116331 + 0.993210i \(0.462887\pi\)
\(228\) 3.46410 + 2.00000i 0.229416 + 0.132453i
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) −1.00000 5.19615i −0.0657952 0.341882i
\(232\) 6.00000i 0.393919i
\(233\) 22.5167 13.0000i 1.47512 0.851658i 0.475509 0.879711i \(-0.342264\pi\)
0.999606 + 0.0280525i \(0.00893057\pi\)
\(234\) 2.00000 3.46410i 0.130744 0.226455i
\(235\) 0 0
\(236\) 1.00000 + 1.73205i 0.0650945 + 0.112747i
\(237\) 9.00000i 0.584613i
\(238\) 4.33013 12.5000i 0.280680 0.810255i
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) 0 0
\(241\) 3.00000 5.19615i 0.193247 0.334714i −0.753077 0.657932i \(-0.771431\pi\)
0.946324 + 0.323218i \(0.104765\pi\)
\(242\) 6.06218 + 3.50000i 0.389692 + 0.224989i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) −5.00000 −0.318788
\(247\) −13.8564 + 8.00000i −0.881662 + 0.509028i
\(248\) −9.52628 5.50000i −0.604919 0.349250i
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) −0.866025 + 2.50000i −0.0545545 + 0.157485i
\(253\) 10.0000i 0.628695i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 12.1244 7.00000i 0.756297 0.436648i −0.0716680 0.997429i \(-0.522832\pi\)
0.827964 + 0.560781i \(0.189499\pi\)
\(258\) 0 0
\(259\) −4.00000 20.7846i −0.248548 1.29149i
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) −5.19615 3.00000i −0.321019 0.185341i
\(263\) 18.1865 + 10.5000i 1.12143 + 0.647458i 0.941766 0.336270i \(-0.109166\pi\)
0.179664 + 0.983728i \(0.442499\pi\)
\(264\) 1.00000 + 1.73205i 0.0615457 + 0.106600i
\(265\) 0 0
\(266\) 8.00000 6.92820i 0.490511 0.424795i
\(267\) 11.0000i 0.673189i
\(268\) 0 0
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 4.50000 + 7.79423i 0.273356 + 0.473466i 0.969719 0.244224i \(-0.0785331\pi\)
−0.696363 + 0.717689i \(0.745200\pi\)
\(272\) 5.00000i 0.303170i
\(273\) −6.92820 8.00000i −0.419314 0.484182i
\(274\) 23.0000 1.38948
\(275\) 0 0
\(276\) −2.50000 + 4.33013i −0.150482 + 0.260643i
\(277\) −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i \(-0.352470\pi\)
−0.551131 + 0.834419i \(0.685804\pi\)
\(278\) −1.73205 + 1.00000i −0.103882 + 0.0599760i
\(279\) 11.0000 0.658553
\(280\) 0 0
\(281\) −29.0000 −1.72999 −0.864997 0.501776i \(-0.832680\pi\)
−0.864997 + 0.501776i \(0.832680\pi\)
\(282\) −0.866025 + 0.500000i −0.0515711 + 0.0297746i
\(283\) 22.5167 + 13.0000i 1.33848 + 0.772770i 0.986581 0.163270i \(-0.0522041\pi\)
0.351895 + 0.936039i \(0.385537\pi\)
\(284\) −0.500000 + 0.866025i −0.0296695 + 0.0513892i
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) −4.33013 + 12.5000i −0.255599 + 0.737852i
\(288\) 1.00000i 0.0589256i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 0.500000 0.866025i 0.0293105 0.0507673i
\(292\) −1.73205 + 1.00000i −0.101361 + 0.0585206i
\(293\) 18.0000i 1.05157i 0.850617 + 0.525786i \(0.176229\pi\)
−0.850617 + 0.525786i \(0.823771\pi\)
\(294\) 5.50000 + 4.33013i 0.320767 + 0.252538i
\(295\) 0 0
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) −1.73205 1.00000i −0.100504 0.0580259i
\(298\) 15.5885 + 9.00000i 0.903015 + 0.521356i
\(299\) −10.0000 17.3205i −0.578315 1.00167i
\(300\) 0 0
\(301\) 0 0
\(302\) 16.0000i 0.920697i
\(303\) 10.3923 6.00000i 0.597022 0.344691i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 0 0
\(306\) −2.50000 4.33013i −0.142915 0.247537i
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 5.19615 1.00000i 0.296078 0.0569803i
\(309\) −13.0000 −0.739544
\(310\) 0 0
\(311\) −14.5000 + 25.1147i −0.822220 + 1.42413i 0.0818063 + 0.996648i \(0.473931\pi\)
−0.904026 + 0.427478i \(0.859402\pi\)
\(312\) 3.46410 + 2.00000i 0.196116 + 0.113228i
\(313\) −0.866025 + 0.500000i −0.0489506 + 0.0282617i −0.524276 0.851549i \(-0.675664\pi\)
0.475325 + 0.879810i \(0.342331\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 9.00000 0.506290
\(317\) −3.46410 + 2.00000i −0.194563 + 0.112331i −0.594117 0.804379i \(-0.702498\pi\)
0.399554 + 0.916710i \(0.369165\pi\)
\(318\) 10.3923 + 6.00000i 0.582772 + 0.336463i
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) 8.66025 + 10.0000i 0.482617 + 0.557278i
\(323\) 20.0000i 1.11283i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 12.0000 20.7846i 0.664619 1.15115i
\(327\) −3.46410 + 2.00000i −0.191565 + 0.110600i
\(328\) 5.00000i 0.276079i
\(329\) 0.500000 + 2.59808i 0.0275659 + 0.143237i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) −6.92820 4.00000i −0.379663 0.219199i
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) 0 0
\(336\) −2.50000 0.866025i −0.136386 0.0472456i
\(337\) 13.0000i 0.708155i −0.935216 0.354078i \(-0.884795\pi\)
0.935216 0.354078i \(-0.115205\pi\)
\(338\) −2.59808 + 1.50000i −0.141317 + 0.0815892i
\(339\) 2.50000 4.33013i 0.135781 0.235180i
\(340\) 0 0
\(341\) −11.0000 19.0526i −0.595683 1.03175i
\(342\) 4.00000i 0.216295i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) −1.00000 + 1.73205i −0.0537603 + 0.0931156i
\(347\) −15.5885 9.00000i −0.836832 0.483145i 0.0193540 0.999813i \(-0.493839\pi\)
−0.856186 + 0.516667i \(0.827172\pi\)
\(348\) −5.19615 + 3.00000i −0.278543 + 0.160817i
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −1.73205 + 1.00000i −0.0923186 + 0.0533002i
\(353\) −7.79423 4.50000i −0.414845 0.239511i 0.278024 0.960574i \(-0.410320\pi\)
−0.692869 + 0.721063i \(0.743654\pi\)
\(354\) 1.00000 1.73205i 0.0531494 0.0920575i
\(355\) 0 0
\(356\) 11.0000 0.582999
\(357\) −12.9904 + 2.50000i −0.687524 + 0.132314i
\(358\) 22.0000i 1.16274i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −19.0526 + 11.0000i −1.00138 + 0.578147i
\(363\) 7.00000i 0.367405i
\(364\) 8.00000 6.92820i 0.419314 0.363137i
\(365\) 0 0
\(366\) 5.00000 + 8.66025i 0.261354 + 0.452679i
\(367\) −3.46410 2.00000i −0.180825 0.104399i 0.406855 0.913493i \(-0.366625\pi\)
−0.587680 + 0.809093i \(0.699959\pi\)
\(368\) −4.33013 2.50000i −0.225723 0.130322i
\(369\) 2.50000 + 4.33013i 0.130145 + 0.225417i
\(370\) 0 0
\(371\) 24.0000 20.7846i 1.24602 1.07908i
\(372\) 11.0000i 0.570323i
\(373\) −27.7128 + 16.0000i −1.43492 + 0.828449i −0.997490 0.0708063i \(-0.977443\pi\)
−0.437425 + 0.899255i \(0.644109\pi\)
\(374\) −5.00000 + 8.66025i −0.258544 + 0.447811i
\(375\) 0 0
\(376\) −0.500000 0.866025i −0.0257855 0.0446619i
\(377\) 24.0000i 1.23606i
\(378\) 2.59808 0.500000i 0.133631 0.0257172i
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 21.6506 + 12.5000i 1.10774 + 0.639556i
\(383\) 2.59808 1.50000i 0.132755 0.0766464i −0.432151 0.901801i \(-0.642245\pi\)
0.564907 + 0.825155i \(0.308912\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −11.0000 −0.559885
\(387\) 0 0
\(388\) 0.866025 + 0.500000i 0.0439658 + 0.0253837i
\(389\) 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i \(-0.625135\pi\)
0.991500 0.130105i \(-0.0415314\pi\)
\(390\) 0 0
\(391\) −25.0000 −1.26430
\(392\) −4.33013 + 5.50000i −0.218704 + 0.277792i
\(393\) 6.00000i 0.302660i
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) 0 0
\(396\) 1.00000 1.73205i 0.0502519 0.0870388i
\(397\) 29.4449 17.0000i 1.47780 0.853206i 0.478110 0.878300i \(-0.341322\pi\)
0.999685 + 0.0250943i \(0.00798860\pi\)
\(398\) 5.00000i 0.250627i
\(399\) −10.0000 3.46410i −0.500626 0.173422i
\(400\) 0 0
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 0 0
\(403\) −38.1051 22.0000i −1.89815 1.09590i
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 0 0
\(406\) 3.00000 + 15.5885i 0.148888 + 0.773642i
\(407\) 16.0000i 0.793091i
\(408\) 4.33013 2.50000i 0.214373 0.123768i
\(409\) −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i \(0.499551\pi\)
−0.866730 + 0.498778i \(0.833782\pi\)
\(410\) 0 0
\(411\) −11.5000 19.9186i −0.567253 0.982511i
\(412\) 13.0000i 0.640464i
\(413\) −3.46410 4.00000i −0.170457 0.196827i
\(414\) 5.00000 0.245737
\(415\) 0 0
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) 1.73205 + 1.00000i 0.0848189 + 0.0489702i
\(418\) −6.92820 + 4.00000i −0.338869 + 0.195646i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) −13.8564 + 8.00000i −0.674519 + 0.389434i
\(423\) 0.866025 + 0.500000i 0.0421076 + 0.0243108i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 0 0
\(426\) 1.00000 0.0484502
\(427\) 25.9808 5.00000i 1.25730 0.241967i
\(428\) 2.00000i 0.0966736i
\(429\) 4.00000 + 6.92820i 0.193122 + 0.334497i
\(430\) 0 0
\(431\) 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i \(-0.810315\pi\)
0.899888 + 0.436121i \(0.143648\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 9.00000i 0.432512i −0.976337 0.216256i \(-0.930615\pi\)
0.976337 0.216256i \(-0.0693846\pi\)
\(434\) 27.5000 + 9.52628i 1.32004 + 0.457276i
\(435\) 0 0
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) −17.3205 10.0000i −0.828552 0.478365i
\(438\) 1.73205 + 1.00000i 0.0827606 + 0.0477818i
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 20.0000i 0.951303i
\(443\) −6.92820 + 4.00000i −0.329169 + 0.190046i −0.655472 0.755219i \(-0.727530\pi\)
0.326303 + 0.945265i \(0.394197\pi\)
\(444\) 4.00000 6.92820i 0.189832 0.328798i
\(445\) 0 0
\(446\) 10.5000 + 18.1865i 0.497189 + 0.861157i
\(447\) 18.0000i 0.851371i
\(448\) 0.866025 2.50000i 0.0409159 0.118114i
\(449\) −37.0000 −1.74614 −0.873069 0.487597i \(-0.837874\pi\)
−0.873069 + 0.487597i \(0.837874\pi\)
\(450\) 0 0
\(451\) 5.00000 8.66025i 0.235441 0.407795i
\(452\) 4.33013 + 2.50000i 0.203672 + 0.117590i
\(453\) −13.8564 + 8.00000i −0.651031 + 0.375873i
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −12.1244 + 7.00000i −0.567153 + 0.327446i −0.756012 0.654558i \(-0.772855\pi\)
0.188858 + 0.982004i \(0.439521\pi\)
\(458\) −12.1244 7.00000i −0.566534 0.327089i
\(459\) −2.50000 + 4.33013i −0.116690 + 0.202113i
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) −3.46410 4.00000i −0.161165 0.186097i
\(463\) 13.0000i 0.604161i 0.953282 + 0.302081i \(0.0976812\pi\)
−0.953282 + 0.302081i \(0.902319\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) 13.0000 22.5167i 0.602213 1.04306i
\(467\) 29.4449 17.0000i 1.36255 0.786666i 0.372584 0.927999i \(-0.378472\pi\)
0.989962 + 0.141332i \(0.0451386\pi\)
\(468\) 4.00000i 0.184900i
\(469\) 0 0
\(470\) 0 0
\(471\) 7.00000 + 12.1244i 0.322543 + 0.558661i
\(472\) 1.73205 + 1.00000i 0.0797241 + 0.0460287i
\(473\) 0 0
\(474\) −4.50000 7.79423i −0.206692 0.358001i
\(475\) 0 0
\(476\) −2.50000 12.9904i −0.114587 0.595413i
\(477\) 12.0000i 0.549442i
\(478\) −9.52628 + 5.50000i −0.435722 + 0.251564i
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) 6.00000i 0.273293i
\(483\) 4.33013 12.5000i 0.197028 0.568770i
\(484\) 7.00000 0.318182
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −33.7750 19.5000i −1.53049 0.883629i −0.999339 0.0363527i \(-0.988426\pi\)
−0.531152 0.847277i \(-0.678241\pi\)
\(488\) −8.66025 + 5.00000i −0.392031 + 0.226339i
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −4.33013 + 2.50000i −0.195217 + 0.112709i
\(493\) −25.9808 15.0000i −1.17011 0.675566i
\(494\) −8.00000 + 13.8564i −0.359937 + 0.623429i
\(495\) 0 0
\(496\) −11.0000 −0.493915
\(497\) 0.866025 2.50000i 0.0388465 0.112140i
\(498\) 6.00000i 0.268866i
\(499\) 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
\(501\) −8.00000 + 13.8564i −0.357414 + 0.619059i
\(502\) −6.92820 + 4.00000i −0.309221 + 0.178529i
\(503\) 8.00000i 0.356702i 0.983967 + 0.178351i \(0.0570763\pi\)
−0.983967 + 0.178351i \(0.942924\pi\)
\(504\) 0.500000 + 2.59808i 0.0222718 + 0.115728i
\(505\) 0 0
\(506\) −5.00000 8.66025i −0.222277 0.384995i
\(507\) 2.59808 + 1.50000i 0.115385 + 0.0666173i
\(508\) 0 0
\(509\) 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i \(-0.152553\pi\)
−0.843012 + 0.537895i \(0.819220\pi\)
\(510\) 0 0
\(511\) 4.00000 3.46410i 0.176950 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) −3.46410 + 2.00000i −0.152944 + 0.0883022i
\(514\) 7.00000 12.1244i 0.308757 0.534782i
\(515\) 0 0
\(516\) 0 0
\(517\) 2.00000i 0.0879599i
\(518\) −13.8564 16.0000i −0.608816 0.703000i
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) 1.50000 2.59808i 0.0657162 0.113824i −0.831295 0.555831i \(-0.812400\pi\)
0.897011 + 0.442007i \(0.145733\pi\)
\(522\) 5.19615 + 3.00000i 0.227429 + 0.131306i
\(523\) −12.1244 + 7.00000i −0.530161 + 0.306089i −0.741082 0.671414i \(-0.765687\pi\)
0.210921 + 0.977503i \(0.432354\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) 21.0000 0.915644
\(527\) −47.6314 + 27.5000i −2.07486 + 1.19792i
\(528\) 1.73205 + 1.00000i 0.0753778 + 0.0435194i
\(529\) 1.00000 1.73205i 0.0434783 0.0753066i
\(530\) 0 0
\(531\) −2.00000 −0.0867926
\(532\) 3.46410 10.0000i 0.150188 0.433555i
\(533\) 20.0000i 0.866296i
\(534\) −5.50000 9.52628i −0.238008 0.412242i
\(535\) 0 0
\(536\) 0 0
\(537\) −19.0526 + 11.0000i −0.822179 + 0.474685i
\(538\) 24.0000i 1.03471i
\(539\) −13.0000 + 5.19615i −0.559950 + 0.223814i
\(540\) 0 0
\(541\) 2.00000 + 3.46410i 0.0859867 + 0.148933i 0.905811 0.423681i \(-0.139262\pi\)
−0.819825 + 0.572615i \(0.805929\pi\)
\(542\) 7.79423 + 4.50000i 0.334791 + 0.193292i
\(543\) 19.0526 + 11.0000i 0.817624 + 0.472055i
\(544\) 2.50000 + 4.33013i 0.107187 + 0.185653i
\(545\) 0 0
\(546\) −10.0000 3.46410i −0.427960 0.148250i
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 19.9186 11.5000i 0.850880 0.491256i
\(549\) 5.00000 8.66025i 0.213395 0.369611i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 5.00000i 0.212814i
\(553\) −23.3827 + 4.50000i −0.994333 + 0.191359i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 32.9090 + 19.0000i 1.39440 + 0.805056i 0.993798 0.111198i \(-0.0354686\pi\)
0.400599 + 0.916253i \(0.368802\pi\)
\(558\) 9.52628 5.50000i 0.403280 0.232834i
\(559\) 0 0
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) −25.1147 + 14.5000i −1.05940 + 0.611646i
\(563\) 31.1769 + 18.0000i 1.31395 + 0.758610i 0.982748 0.184950i \(-0.0592124\pi\)
0.331202 + 0.943560i \(0.392546\pi\)
\(564\) −0.500000 + 0.866025i −0.0210538 + 0.0364662i
\(565\) 0 0
\(566\) 26.0000 1.09286
\(567\) −1.73205 2.00000i −0.0727393 0.0839921i
\(568\) 1.00000i 0.0419591i
\(569\) 4.50000 + 7.79423i 0.188650 + 0.326751i 0.944800 0.327647i \(-0.106256\pi\)
−0.756151 + 0.654398i \(0.772922\pi\)
\(570\) 0 0
\(571\) 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i \(-0.460975\pi\)
0.798379 0.602155i \(-0.205691\pi\)
\(572\) −6.92820 + 4.00000i −0.289683 + 0.167248i
\(573\) 25.0000i 1.04439i
\(574\) 2.50000 + 12.9904i 0.104348 + 0.542208i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −1.73205 1.00000i −0.0721062 0.0416305i 0.463513 0.886090i \(-0.346589\pi\)
−0.535620 + 0.844459i \(0.679922\pi\)
\(578\) 6.92820 + 4.00000i 0.288175 + 0.166378i
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 0 0
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 1.00000i 0.0414513i
\(583\) −20.7846 + 12.0000i −0.860811 + 0.496989i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 6.00000i 0.247647i −0.992304 0.123823i \(-0.960484\pi\)
0.992304 0.123823i \(-0.0395156\pi\)
\(588\) 6.92820 + 1.00000i 0.285714 + 0.0412393i
\(589\) −44.0000 −1.81299
\(590\) 0 0
\(591\) 12.0000 20.7846i 0.493614 0.854965i
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) 7.79423 4.50000i 0.320071 0.184793i −0.331353 0.943507i \(-0.607505\pi\)
0.651424 + 0.758714i \(0.274172\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −4.33013 + 2.50000i −0.177220 + 0.102318i
\(598\) −17.3205 10.0000i −0.708288 0.408930i
\(599\) 8.50000 14.7224i 0.347301 0.601542i −0.638468 0.769648i \(-0.720432\pi\)
0.985769 + 0.168106i \(0.0537650\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) 0 0
\(606\) 6.00000 10.3923i 0.243733 0.422159i
\(607\) 23.3827 13.5000i 0.949074 0.547948i 0.0562808 0.998415i \(-0.482076\pi\)
0.892793 + 0.450467i \(0.148742\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 12.0000 10.3923i 0.486265 0.421117i
\(610\) 0 0
\(611\) −2.00000 3.46410i −0.0809113 0.140143i
\(612\) −4.33013 2.50000i −0.175035 0.101057i
\(613\) −29.4449 17.0000i −1.18927 0.686624i −0.231127 0.972924i \(-0.574241\pi\)
−0.958140 + 0.286300i \(0.907575\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) 0 0
\(616\) 4.00000 3.46410i 0.161165 0.139573i
\(617\) 29.0000i 1.16750i −0.811935 0.583748i \(-0.801586\pi\)
0.811935 0.583748i \(-0.198414\pi\)
\(618\) −11.2583 + 6.50000i −0.452876 + 0.261468i
\(619\) −7.00000 + 12.1244i −0.281354 + 0.487319i −0.971718 0.236143i \(-0.924117\pi\)
0.690365 + 0.723462i \(0.257450\pi\)
\(620\) 0 0
\(621\) −2.50000 4.33013i −0.100322 0.173762i
\(622\) 29.0000i 1.16279i
\(623\) −28.5788 + 5.50000i −1.14499 + 0.220353i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) −0.500000 + 0.866025i −0.0199840 + 0.0346133i
\(627\) 6.92820 + 4.00000i 0.276686 + 0.159745i
\(628\) −12.1244 + 7.00000i −0.483814 + 0.279330i
\(629\) 40.0000 1.59490
\(630\) 0 0
\(631\) 33.0000 1.31371 0.656855 0.754017i \(-0.271887\pi\)
0.656855 + 0.754017i \(0.271887\pi\)
\(632\) 7.79423 4.50000i 0.310038 0.179000i
\(633\) 13.8564 + 8.00000i 0.550743 + 0.317971i
\(634\) −2.00000 + 3.46410i −0.0794301 + 0.137577i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) −17.3205 + 22.0000i −0.686264 + 0.871672i
\(638\) 12.0000i 0.475085i
\(639\) −0.500000 0.866025i −0.0197797 0.0342594i
\(640\) 0 0
\(641\) 7.50000 12.9904i 0.296232 0.513089i −0.679039 0.734103i \(-0.737603\pi\)
0.975271 + 0.221013i \(0.0709364\pi\)
\(642\) 1.73205 1.00000i 0.0683586 0.0394669i
\(643\) 26.0000i 1.02534i 0.858586 + 0.512670i \(0.171344\pi\)
−0.858586 + 0.512670i \(0.828656\pi\)
\(644\) 12.5000 + 4.33013i 0.492569 + 0.170631i
\(645\) 0 0
\(646\) 10.0000 + 17.3205i 0.393445 + 0.681466i
\(647\) −24.2487 14.0000i −0.953315 0.550397i −0.0592060 0.998246i \(-0.518857\pi\)
−0.894109 + 0.447849i \(0.852190\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 2.00000 + 3.46410i 0.0785069 + 0.135978i
\(650\) 0 0
\(651\) −5.50000 28.5788i −0.215562 1.12009i
\(652\) 24.0000i 0.939913i
\(653\) 24.2487 14.0000i 0.948925 0.547862i 0.0561784 0.998421i \(-0.482108\pi\)
0.892747 + 0.450558i \(0.148775\pi\)
\(654\) −2.00000 + 3.46410i −0.0782062 + 0.135457i
\(655\) 0 0
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) 2.00000i 0.0780274i
\(658\) 1.73205 + 2.00000i 0.0675224 + 0.0779681i
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −8.66025 5.00000i −0.336590 0.194331i
\(663\) 17.3205 10.0000i 0.672673 0.388368i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 25.9808 15.0000i 1.00598 0.580802i
\(668\) −13.8564 8.00000i −0.536120 0.309529i
\(669\) 10.5000 18.1865i 0.405953 0.703132i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) −2.59808 + 0.500000i −0.100223 + 0.0192879i
\(673\) 19.0000i 0.732396i 0.930537 + 0.366198i \(0.119341\pi\)
−0.930537 + 0.366198i \(0.880659\pi\)
\(674\) −6.50000 11.2583i −0.250371 0.433655i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 15.5885 9.00000i 0.599113 0.345898i −0.169580 0.985517i \(-0.554241\pi\)
0.768693 + 0.639618i \(0.220908\pi\)
\(678\) 5.00000i 0.192024i
\(679\) −2.50000 0.866025i −0.0959412 0.0332350i
\(680\) 0 0
\(681\) −9.00000 15.5885i −0.344881 0.597351i
\(682\) −19.0526 11.0000i −0.729560 0.421212i
\(683\) 1.73205 + 1.00000i 0.0662751 + 0.0382639i 0.532771 0.846259i \(-0.321151\pi\)
−0.466496 + 0.884523i \(0.654484\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 14.0000i 0.534133i
\(688\) 0 0
\(689\) −24.0000 + 41.5692i −0.914327 + 1.58366i
\(690\) 0 0
\(691\) 1.00000 + 1.73205i 0.0380418 + 0.0658903i 0.884419 0.466693i \(-0.154555\pi\)
−0.846378 + 0.532583i \(0.821221\pi\)
\(692\) 2.00000i 0.0760286i
\(693\) −1.73205 + 5.00000i −0.0657952 + 0.189934i
\(694\) −18.0000 −0.683271
\(695\) 0 0
\(696\) −3.00000 + 5.19615i −0.113715 + 0.196960i
\(697\) −21.6506 12.5000i −0.820076 0.473471i
\(698\) 3.46410 2.00000i 0.131118 0.0757011i
\(699\) −26.0000 −0.983410
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −3.46410 + 2.00000i −0.130744 + 0.0754851i
\(703\) 27.7128 + 16.0000i 1.04521 + 0.603451i
\(704\) −1.00000 + 1.73205i −0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) −9.00000 −0.338719
\(707\) −20.7846 24.0000i −0.781686 0.902613i
\(708\) 2.00000i 0.0751646i
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −4.50000 + 7.79423i −0.168763 + 0.292306i
\(712\) 9.52628 5.50000i 0.357012 0.206121i
\(713\) 55.0000i 2.05977i
\(714\) −10.0000 + 8.66025i −0.374241 + 0.324102i
\(715\) 0 0
\(716\) −11.0000 19.0526i −0.411089 0.712028i
\(717\) 9.52628 + 5.50000i 0.355765 + 0.205401i
\(718\) −17.3205 10.0000i −0.646396 0.373197i
\(719\) −1.50000 2.59808i −0.0559406 0.0968919i 0.836699 0.547663i \(-0.184482\pi\)
−0.892640 + 0.450771i \(0.851149\pi\)
\(720\) 0 0
\(721\) 6.50000 + 33.7750i 0.242073 + 1.25785i
\(722\) 3.00000i 0.111648i
\(723\) −5.19615 + 3.00000i −0.193247 + 0.111571i
\(724\) −11.0000 + 19.0526i −0.408812 + 0.708083i
\(725\) 0 0
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) 33.0000i 1.22390i 0.790896 + 0.611951i \(0.209615\pi\)
−0.790896 + 0.611951i \(0.790385\pi\)
\(728\) 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
\(733\) 25.9808 15.0000i 0.959621 0.554038i 0.0635649 0.997978i \(-0.479753\pi\)
0.896056 + 0.443940i \(0.146420\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 0 0
\(738\) 4.33013 + 2.50000i 0.159394 + 0.0920263i
\(739\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 10.3923 30.0000i 0.381514 1.10133i
\(743\) 33.0000i 1.21065i −0.795977 0.605326i \(-0.793043\pi\)
0.795977 0.605326i \(-0.206957\pi\)
\(744\) 5.50000 + 9.52628i 0.201640 + 0.349250i
\(745\) 0 0
\(746\) −16.0000 + 27.7128i −0.585802 + 1.01464i
\(747\) −5.19615 + 3.00000i −0.190117 + 0.109764i
\(748\) 10.0000i 0.365636i
\(749\) −1.00000 5.19615i −0.0365392 0.189863i
\(750\) 0 0
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −0.866025 0.500000i −0.0315807 0.0182331i
\(753\) 6.92820 + 4.00000i 0.252478 + 0.145768i
\(754\) −12.0000 20.7846i −0.437014 0.756931i
\(755\) 0 0
\(756\) 2.00000 1.73205i 0.0727393 0.0629941i
\(757\) 28.0000i 1.01768i −0.860862 0.508839i \(-0.830075\pi\)
0.860862 0.508839i \(-0.169925\pi\)
\(758\) 1.73205 1.00000i 0.0629109 0.0363216i
\(759\) −5.00000 + 8.66025i −0.181489 + 0.314347i
\(760\) 0 0
\(761\) −8.50000 14.7224i −0.308125 0.533688i 0.669827 0.742517i \(-0.266368\pi\)
−0.977952 + 0.208829i \(0.933035\pi\)
\(762\) 0 0
\(763\) 6.92820 + 8.00000i 0.250818 + 0.289619i
\(764\) 25.0000 0.904468
\(765\) 0 0
\(766\) 1.50000 2.59808i 0.0541972 0.0938723i
\(767\) 6.92820 + 4.00000i 0.250163 + 0.144432i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) −9.52628 + 5.50000i −0.342858 + 0.197949i
\(773\) 3.46410 + 2.00000i 0.124595 + 0.0719350i 0.561002 0.827814i \(-0.310416\pi\)
−0.436407 + 0.899749i \(0.643749\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) −6.92820 + 20.0000i −0.248548 + 0.717496i
\(778\) 24.0000i 0.860442i
\(779\) −10.0000 17.3205i −0.358287 0.620572i
\(780\) 0 0
\(781\) −1.00000 + 1.73205i −0.0357828 + 0.0619777i
\(782\) −21.6506 + 12.5000i −0.774225 + 0.446999i
\(783\) 6.00000i 0.214423i
\(784\) −1.00000 + 6.92820i −0.0357143 + 0.247436i
\(785\) 0 0
\(786\) 3.00000 + 5.19615i 0.107006 + 0.185341i
\(787\) 34.6410 + 20.0000i 1.23482 + 0.712923i 0.968031 0.250832i \(-0.0807042\pi\)
0.266788 + 0.963755i \(0.414038\pi\)
\(788\) 20.7846 + 12.0000i 0.740421 + 0.427482i
\(789\) −10.5000 18.1865i −0.373810 0.647458i
\(790\) 0 0
\(791\) −12.5000 4.33013i −0.444449 0.153962i
\(792\) 2.00000i 0.0710669i
\(793\) −34.6410 + 20.0000i −1.23014 + 0.710221i
\(794\) 17.0000 29.4449i 0.603307 1.04496i
\(795\) 0 0
\(796\) −2.50000 4.33013i −0.0886102 0.153477i
\(797\) 42.0000i 1.48772i −0.668338 0.743858i \(-0.732994\pi\)
0.668338 0.743858i \(-0.267006\pi\)
\(798\) −10.3923 + 2.00000i −0.367884 + 0.0707992i
\(799\) −5.00000 −0.176887
\(800\) 0 0
\(801\) −5.50000 + 9.52628i −0.194333 + 0.336595i
\(802\) 5.19615 + 3.00000i 0.183483 + 0.105934i
\(803\) −3.46410 + 2.00000i −0.122245 + 0.0705785i
\(804\) 0 0
\(805\) 0 0
\(806\) −44.0000 −1.54983
\(807\) 20.7846 12.0000i 0.731653 0.422420i
\(808\) 10.3923 + 6.00000i 0.365600 + 0.211079i
\(809\) 5.00000 8.66025i 0.175791 0.304478i −0.764644 0.644453i \(-0.777085\pi\)
0.940435 + 0.339975i \(0.110418\pi\)
\(810\) 0 0
\(811\) −48.0000 −1.68551 −0.842754 0.538299i \(-0.819067\pi\)
−0.842754 + 0.538299i \(0.819067\pi\)
\(812\) 10.3923 + 12.0000i 0.364698 + 0.421117i
\(813\) 9.00000i 0.315644i
\(814\) 8.00000 + 13.8564i 0.280400 + 0.485667i
\(815\) 0 0
\(816\) 2.50000 4.33013i 0.0875175 0.151585i
\(817\) 0 0
\(818\) 35.0000i 1.22375i
\(819\) 2.00000 + 10.3923i 0.0698857 + 0.363137i
\(820\) 0 0
\(821\) −26.0000 45.0333i −0.907406 1.57167i −0.817654 0.575710i \(-0.804726\pi\)
−0.0897520 0.995964i \(-0.528607\pi\)
\(822\) −19.9186 11.5000i −0.694740 0.401109i
\(823\) −17.3205 10.0000i −0.603755 0.348578i 0.166762 0.985997i \(-0.446669\pi\)
−0.770517 + 0.637419i \(0.780002\pi\)
\(824\) −6.50000 11.2583i −0.226438 0.392203i
\(825\) 0 0
\(826\) −5.00000 1.73205i −0.173972 0.0602658i
\(827\) 30.0000i 1.04320i 0.853189 + 0.521601i \(0.174665\pi\)
−0.853189 + 0.521601i \(0.825335\pi\)
\(828\) 4.33013 2.50000i 0.150482 0.0868810i
\(829\) 13.0000 22.5167i 0.451509 0.782036i −0.546971 0.837151i \(-0.684219\pi\)
0.998480 + 0.0551154i \(0.0175527\pi\)
\(830\) 0 0
\(831\) 1.00000 + 1.73205i 0.0346896 + 0.0600842i
\(832\) 4.00000i 0.138675i
\(833\) 12.9904 + 32.5000i 0.450090 + 1.12606i
\(834\) 2.00000 0.0692543
\(835\) 0 0
\(836\) −4.00000 + 6.92820i −0.138343 + 0.239617i
\(837\) −9.52628 5.50000i −0.329276 0.190108i
\(838\) 0 0
\(839\) 9.00000 0.310715 0.155357 0.987858i \(-0.450347\pi\)
0.155357 + 0.987858i \(0.450347\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 24.2487 14.0000i 0.835666 0.482472i
\(843\) 25.1147 + 14.5000i 0.864997 + 0.499407i
\(844\) −8.00000 + 13.8564i −0.275371 + 0.476957i
\(845\) 0 0
\(846\) 1.00000 0.0343807
\(847\) −18.1865 + 3.50000i −0.624897 + 0.120261i
\(848\) 12.0000i 0.412082i
\(849\) −13.0000 22.5167i −0.446159 0.772770i
\(850\) 0 0
\(851\) −20.0000 + 34.6410i −0.685591 + 1.18748i
\(852\) 0.866025 0.500000i 0.0296695 0.0171297i
\(853\) 20.0000i 0.684787i 0.939557 + 0.342393i \(0.111238\pi\)
−0.939557 + 0.342393i \(0.888762\pi\)
\(854\) 20.0000 17.3205i 0.684386 0.592696i
\(855\) 0 0
\(856\) 1.00000 + 1.73205i 0.0341793 + 0.0592003i
\(857\) 50.2295 + 29.0000i 1.71581 + 0.990621i 0.926222 + 0.376979i \(0.123037\pi\)
0.789584 + 0.613642i \(0.210296\pi\)
\(858\) 6.92820 + 4.00000i 0.236525 + 0.136558i
\(859\) −5.00000 8.66025i −0.170598 0.295484i 0.768031 0.640412i \(-0.221237\pi\)
−0.938629 + 0.344928i \(0.887903\pi\)
\(860\) 0 0
\(861\) 10.0000 8.66025i 0.340799 0.295141i
\(862\) 3.00000i 0.102180i
\(863\) 44.1673 25.5000i 1.50347 0.868030i 0.503480 0.864007i \(-0.332053\pi\)
0.999992 0.00402340i \(-0.00128069\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) 0 0
\(866\) −4.50000 7.79423i −0.152916 0.264859i
\(867\) 8.00000i 0.271694i
\(868\) 28.5788 5.50000i 0.970029 0.186682i
\(869\) 18.0000 0.610608
\(870\) 0 0
\(871\) 0 0
\(872\) −3.46410 2.00000i −0.117309 0.0677285i
\(873\) −0.866025 + 0.500000i −0.0293105 + 0.0169224i
\(874\) −20.0000 −0.676510
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −19.0526 + 11.0000i −0.643359 + 0.371444i −0.785907 0.618344i \(-0.787804\pi\)
0.142548 + 0.989788i \(0.454470\pi\)
\(878\) 30.3109 + 17.5000i 1.02294 + 0.590596i
\(879\) 9.00000 15.5885i 0.303562 0.525786i
\(880\) 0 0
\(881\) 39.0000 1.31394 0.656972 0.753915i \(-0.271837\pi\)
0.656972 + 0.753915i \(0.271837\pi\)
\(882\) −2.59808 6.50000i −0.0874818 0.218866i
\(883\) 2.00000i 0.0673054i 0.999434 + 0.0336527i \(0.0107140\pi\)
−0.999434 + 0.0336527i \(0.989286\pi\)
\(884\) 10.0000 + 17.3205i 0.336336 + 0.582552i
\(885\) 0 0
\(886\) −4.00000 + 6.92820i −0.134383 + 0.232758i
\(887\) −48.4974 + 28.0000i −1.62838 + 0.940148i −0.643809 + 0.765186i \(0.722647\pi\)
−0.984575 + 0.174962i \(0.944020\pi\)
\(888\) 8.00000i 0.268462i
\(889\) 0 0
\(890\) 0 0
\(891\) 1.00000 + 1.73205i 0.0335013 + 0.0580259i
\(892\) 18.1865 + 10.5000i 0.608930 + 0.351566i
\(893\) −3.46410 2.00000i −0.115922 0.0669274i
\(894\) −9.00000 15.5885i −0.301005 0.521356i
\(895\) 0 0
\(896\) −0.500000 2.59808i −0.0167038 0.0867956i
\(897\) 20.0000i 0.667781i
\(898\) −32.0429 + 18.5000i −1.06929 + 0.617353i
\(899\) 33.0000 57.1577i 1.10061 1.90632i
\(900\) 0 0
\(901\) 30.0000 + 51.9615i 0.999445 + 1.73109i
\(902\) 10.0000i 0.332964i
\(903\) 0 0
\(904\) 5.00000 0.166298
\(905\) 0 0
\(906\) −8.00000 + 13.8564i −0.265782 + 0.460348i
\(907\) 15.5885 + 9.00000i 0.517606 + 0.298840i 0.735955 0.677031i \(-0.236734\pi\)
−0.218348 + 0.975871i \(0.570067\pi\)
\(908\) 15.5885 9.00000i 0.517321 0.298675i
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 51.0000 1.68971 0.844853 0.534999i \(-0.179688\pi\)
0.844853 + 0.534999i \(0.179688\pi\)
\(912\) 3.46410 2.00000i 0.114708 0.0662266i
\(913\) 10.3923 + 6.00000i 0.343935 + 0.198571i
\(914\) −7.00000 + 12.1244i −0.231539 + 0.401038i
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 15.5885 3.00000i 0.514776 0.0990687i
\(918\) 5.00000i 0.165025i
\(919\) 21.5000 + 37.2391i 0.709220 + 1.22840i 0.965147 + 0.261708i \(0.0842858\pi\)
−0.255927 + 0.966696i \(0.582381\pi\)
\(920\) 0 0
\(921\) −14.0000 + 24.2487i −0.461316 + 0.799022i
\(922\) 17.3205 10.0000i 0.570421 0.329332i
\(923\) 4.00000i 0.131662i
\(924\) −5.00000 1.73205i −0.164488 0.0569803i
\(925\) 0 0
\(926\) 6.50000 + 11.2583i 0.213603 + 0.369972i
\(927\) 11.2583 + 6.50000i 0.369772 + 0.213488i
\(928\) −5.19615 3.00000i −0.170572 0.0984798i
\(929\) 17.0000 + 29.4449i 0.557752 + 0.966055i 0.997684 + 0.0680235i \(0.0216693\pi\)
−0.439932 + 0.898031i \(0.644997\pi\)
\(930\) 0 0
\(931\) −4.00000 + 27.7128i −0.131095 + 0.908251i
\(932\) 26.0000i 0.851658i
\(933\) 25.1147 14.5000i 0.822220 0.474709i
\(934\) 17.0000 29.4449i 0.556257 0.963465i
\(935\) 0 0
\(936\) −2.00000 3.46410i −0.0653720 0.113228i
\(937\) 30.0000i 0.980057i 0.871706 + 0.490029i \(0.163014\pi\)
−0.871706 + 0.490029i \(0.836986\pi\)
\(938\) 0 0
\(939\) 1.00000 0.0326338
\(940\) 0 0
\(941\) −18.0000 + 31.1769i −0.586783 + 1.01634i 0.407867 + 0.913041i \(0.366273\pi\)
−0.994651 + 0.103297i \(0.967061\pi\)
\(942\) 12.1244 + 7.00000i 0.395033 + 0.228072i
\(943\) 21.6506 12.5000i 0.705042 0.407056i
\(944\) 2.00000 0.0650945
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) −7.79423 4.50000i −0.253145 0.146153i
\(949\) −4.00000 + 6.92820i −0.129845 + 0.224899i
\(950\) 0 0
\(951\) 4.00000 0.129709
\(952\) −8.66025 10.0000i −0.280680 0.324102i
\(953\) 6.00000i 0.194359i −0.995267 0.0971795i \(-0.969018\pi\)
0.995267 0.0971795i \(-0.0309821\pi\)
\(954\) −6.00000 10.3923i −0.194257 0.336463i
\(955\) 0 0
\(956\) −5.50000 + 9.52628i −0.177883 + 0.308102i
\(957\) −10.3923 + 6.00000i −0.335936 + 0.193952i
\(958\) 3.00000i 0.0969256i
\(959\) −46.0000 + 39.8372i −1.48542 + 1.28641i
\(960\) 0 0
\(961\) −45.0000 77.9423i −1.45161 2.51427i
\(962\) 27.7128 + 16.0000i 0.893497 + 0.515861i
\(963\) −1.73205 1.00000i −0.0558146 0.0322245i
\(964\) −3.00000 5.19615i −0.0966235 0.167357i
\(965\) 0 0
\(966\) −2.50000 12.9904i −0.0804362 0.417959i
\(967\) 1.00000i 0.0321578i 0.999871 + 0.0160789i \(0.00511830\pi\)
−0.999871 + 0.0160789i \(0.994882\pi\)
\(968\) 6.06218 3.50000i 0.194846 0.112494i
\(969\) 10.0000 17.3205i 0.321246 0.556415i
\(970\) 0 0
\(971\) −3.00000 5.19615i −0.0962746 0.166752i 0.813865 0.581054i \(-0.197359\pi\)
−0.910140 + 0.414301i \(0.864026\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 1.73205 5.00000i 0.0555270 0.160293i
\(974\) −39.0000 −1.24964
\(975\) 0 0
\(976\) −5.00000 + 8.66025i −0.160046 + 0.277208i
\(977\) −28.5788 16.5000i −0.914318 0.527882i −0.0325001 0.999472i \(-0.510347\pi\)
−0.881818 + 0.471590i \(0.843680\pi\)
\(978\) −20.7846 + 12.0000i −0.664619 + 0.383718i
\(979\) 22.0000 0.703123
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) 10.3923 6.00000i 0.331632 0.191468i
\(983\) −13.8564 8.00000i −0.441951 0.255160i 0.262474 0.964939i \(-0.415462\pi\)
−0.704425 + 0.709779i \(0.748795\pi\)
\(984\) −2.50000 + 4.33013i −0.0796971 + 0.138039i
\(985\) 0 0
\(986\) −30.0000 −0.955395
\(987\) 0.866025 2.50000i 0.0275659 0.0795759i
\(988\) 16.0000i 0.509028i
\(989\) 0 0
\(990\) 0 0
\(991\) −18.5000 + 32.0429i −0.587672 + 1.01788i 0.406865 + 0.913488i \(0.366622\pi\)
−0.994537 + 0.104389i \(0.966711\pi\)
\(992\) −9.52628 + 5.50000i −0.302460 + 0.174625i
\(993\) 10.0000i 0.317340i
\(994\) −0.500000 2.59808i −0.0158590 0.0824060i
\(995\) 0 0
\(996\) −3.00000 5.19615i −0.0950586 0.164646i
\(997\) 3.46410 + 2.00000i 0.109709 + 0.0633406i 0.553851 0.832616i \(-0.313158\pi\)
−0.444141 + 0.895957i \(0.646491\pi\)
\(998\) 19.0526 + 11.0000i 0.603098 + 0.348199i
\(999\) 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.f.949.2 4
5.2 odd 4 1050.2.i.k.151.1 yes 2
5.3 odd 4 1050.2.i.j.151.1 2
5.4 even 2 inner 1050.2.o.f.949.1 4
7.2 even 3 inner 1050.2.o.f.499.1 4
35.2 odd 12 1050.2.i.k.751.1 yes 2
35.3 even 12 7350.2.a.cn.1.1 1
35.9 even 6 inner 1050.2.o.f.499.2 4
35.17 even 12 7350.2.a.h.1.1 1
35.18 odd 12 7350.2.a.bt.1.1 1
35.23 odd 12 1050.2.i.j.751.1 yes 2
35.32 odd 12 7350.2.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.j.151.1 2 5.3 odd 4
1050.2.i.j.751.1 yes 2 35.23 odd 12
1050.2.i.k.151.1 yes 2 5.2 odd 4
1050.2.i.k.751.1 yes 2 35.2 odd 12
1050.2.o.f.499.1 4 7.2 even 3 inner
1050.2.o.f.499.2 4 35.9 even 6 inner
1050.2.o.f.949.1 4 5.4 even 2 inner
1050.2.o.f.949.2 4 1.1 even 1 trivial
7350.2.a.h.1.1 1 35.17 even 12
7350.2.a.z.1.1 1 35.32 odd 12
7350.2.a.bt.1.1 1 35.18 odd 12
7350.2.a.cn.1.1 1 35.3 even 12