Properties

Label 507.2.j.f.361.1
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
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] = [507,2,Mod(316,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.f.316.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.09077 + 1.20711i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.91421 - 3.31552i) q^{4} +2.82843i q^{5} +(2.09077 + 1.20711i) q^{6} +(-2.44949 - 1.41421i) q^{7} +4.41421i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-2.09077 + 1.20711i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.91421 - 3.31552i) q^{4} +2.82843i q^{5} +(2.09077 + 1.20711i) q^{6} +(-2.44949 - 1.41421i) q^{7} +4.41421i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.41421 - 5.91359i) q^{10} +(1.73205 - 1.00000i) q^{11} -3.82843 q^{12} +6.82843 q^{14} +(2.44949 - 1.41421i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(-1.82843 + 3.16693i) q^{17} -2.41421i q^{18} +(-2.44949 - 1.41421i) q^{19} +(9.37769 + 5.41421i) q^{20} +2.82843i q^{21} +(-2.41421 + 4.18154i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(3.82282 - 2.20711i) q^{24} -3.00000 q^{25} +1.00000 q^{27} +(-9.37769 + 5.41421i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-3.41421 + 5.91359i) q^{30} -6.82843i q^{31} +(-1.37333 - 0.792893i) q^{32} +(-1.73205 - 1.00000i) q^{33} -8.82843i q^{34} +(4.00000 - 6.92820i) q^{35} +(1.91421 + 3.31552i) q^{36} +(-3.16693 + 1.82843i) q^{37} +6.82843 q^{38} -12.4853 q^{40} +(9.37769 - 5.41421i) q^{41} +(-3.41421 - 5.91359i) q^{42} +(4.82843 - 8.36308i) q^{43} -7.65685i q^{44} +(-2.44949 - 1.41421i) q^{45} +(8.36308 + 4.82843i) q^{46} +0.343146i q^{47} +(-1.50000 + 2.59808i) q^{48} +(0.500000 + 0.866025i) q^{49} +(6.27231 - 3.62132i) q^{50} +3.65685 q^{51} -2.00000 q^{53} +(-2.09077 + 1.20711i) q^{54} +(2.82843 + 4.89898i) q^{55} +(6.24264 - 10.8126i) q^{56} +2.82843i q^{57} +(4.18154 + 2.41421i) q^{58} +(-3.16693 - 1.82843i) q^{59} -10.8284i q^{60} +(4.65685 - 8.06591i) q^{61} +(8.24264 + 14.2767i) q^{62} +(2.44949 - 1.41421i) q^{63} +9.82843 q^{64} +4.82843 q^{66} +(1.01461 - 0.585786i) q^{67} +(7.00000 + 12.1244i) q^{68} +(-2.00000 + 3.46410i) q^{69} +19.3137i q^{70} +(-1.73205 - 1.00000i) q^{71} +(-3.82282 - 2.20711i) q^{72} -11.6569i q^{73} +(4.41421 - 7.64564i) q^{74} +(1.50000 + 2.59808i) q^{75} +(-9.37769 + 5.41421i) q^{76} -5.65685 q^{77} +11.3137 q^{79} +(7.34847 - 4.24264i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.0711 + 22.6398i) q^{82} -7.65685i q^{83} +(9.37769 + 5.41421i) q^{84} +(-8.95743 - 5.17157i) q^{85} +23.3137i q^{86} +(-1.00000 + 1.73205i) q^{87} +(4.41421 + 7.64564i) q^{88} +(-7.94282 + 4.58579i) q^{89} +6.82843 q^{90} -15.3137 q^{92} +(-5.91359 + 3.41421i) q^{93} +(-0.414214 - 0.717439i) q^{94} +(4.00000 - 6.92820i) q^{95} +1.58579i q^{96} +(6.63103 + 3.82843i) q^{97} +(-2.09077 - 1.20711i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 16 q^{10} - 8 q^{12} + 32 q^{14} - 12 q^{16} + 8 q^{17} - 8 q^{22} - 16 q^{23} - 24 q^{25} + 8 q^{27} - 8 q^{29} - 16 q^{30} + 32 q^{35} + 4 q^{36} + 32 q^{38} - 32 q^{40} - 16 q^{42} + 16 q^{43} - 12 q^{48} + 4 q^{49} - 16 q^{51} - 16 q^{53} + 16 q^{56} - 8 q^{61} + 32 q^{62} + 56 q^{64} + 16 q^{66} + 56 q^{68} - 16 q^{69} + 24 q^{74} + 12 q^{75} - 4 q^{81} - 48 q^{82} - 8 q^{87} + 24 q^{88} + 32 q^{90} - 32 q^{92} + 8 q^{94} + 32 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09077 + 1.20711i −1.47840 + 0.853553i −0.999702 0.0244272i \(-0.992224\pi\)
−0.478696 + 0.877981i \(0.658890\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 1.91421 3.31552i 0.957107 1.65776i
\(5\) 2.82843i 1.26491i 0.774597 + 0.632456i \(0.217953\pi\)
−0.774597 + 0.632456i \(0.782047\pi\)
\(6\) 2.09077 + 1.20711i 0.853553 + 0.492799i
\(7\) −2.44949 1.41421i −0.925820 0.534522i −0.0403329 0.999186i \(-0.512842\pi\)
−0.885487 + 0.464664i \(0.846175\pi\)
\(8\) 4.41421i 1.56066i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −3.41421 5.91359i −1.07967 1.87004i
\(11\) 1.73205 1.00000i 0.522233 0.301511i −0.215615 0.976478i \(-0.569176\pi\)
0.737848 + 0.674967i \(0.235842\pi\)
\(12\) −3.82843 −1.10517
\(13\) 0 0
\(14\) 6.82843 1.82497
\(15\) 2.44949 1.41421i 0.632456 0.365148i
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) −1.82843 + 3.16693i −0.443459 + 0.768093i −0.997943 0.0641009i \(-0.979582\pi\)
0.554485 + 0.832194i \(0.312915\pi\)
\(18\) 2.41421i 0.569036i
\(19\) −2.44949 1.41421i −0.561951 0.324443i 0.191977 0.981399i \(-0.438510\pi\)
−0.753928 + 0.656957i \(0.771843\pi\)
\(20\) 9.37769 + 5.41421i 2.09692 + 1.21065i
\(21\) 2.82843i 0.617213i
\(22\) −2.41421 + 4.18154i −0.514712 + 0.891507i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 3.82282 2.20711i 0.780330 0.450524i
\(25\) −3.00000 −0.600000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −9.37769 + 5.41421i −1.77222 + 1.02319i
\(29\) −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) −3.41421 + 5.91359i −0.623347 + 1.07967i
\(31\) 6.82843i 1.22642i −0.789919 0.613211i \(-0.789878\pi\)
0.789919 0.613211i \(-0.210122\pi\)
\(32\) −1.37333 0.792893i −0.242773 0.140165i
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) 8.82843i 1.51406i
\(35\) 4.00000 6.92820i 0.676123 1.17108i
\(36\) 1.91421 + 3.31552i 0.319036 + 0.552586i
\(37\) −3.16693 + 1.82843i −0.520640 + 0.300592i −0.737196 0.675679i \(-0.763851\pi\)
0.216557 + 0.976270i \(0.430517\pi\)
\(38\) 6.82843 1.10772
\(39\) 0 0
\(40\) −12.4853 −1.97410
\(41\) 9.37769 5.41421i 1.46455 0.845558i 0.465333 0.885136i \(-0.345935\pi\)
0.999217 + 0.0395775i \(0.0126012\pi\)
\(42\) −3.41421 5.91359i −0.526825 0.912487i
\(43\) 4.82843 8.36308i 0.736328 1.27536i −0.217810 0.975991i \(-0.569891\pi\)
0.954138 0.299367i \(-0.0967754\pi\)
\(44\) 7.65685i 1.15431i
\(45\) −2.44949 1.41421i −0.365148 0.210819i
\(46\) 8.36308 + 4.82843i 1.23307 + 0.711913i
\(47\) 0.343146i 0.0500530i 0.999687 + 0.0250265i \(0.00796701\pi\)
−0.999687 + 0.0250265i \(0.992033\pi\)
\(48\) −1.50000 + 2.59808i −0.216506 + 0.375000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 6.27231 3.62132i 0.887039 0.512132i
\(51\) 3.65685 0.512062
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) −2.09077 + 1.20711i −0.284518 + 0.164266i
\(55\) 2.82843 + 4.89898i 0.381385 + 0.660578i
\(56\) 6.24264 10.8126i 0.834208 1.44489i
\(57\) 2.82843i 0.374634i
\(58\) 4.18154 + 2.41421i 0.549063 + 0.317002i
\(59\) −3.16693 1.82843i −0.412299 0.238041i 0.279478 0.960152i \(-0.409839\pi\)
−0.691777 + 0.722111i \(0.743172\pi\)
\(60\) 10.8284i 1.39794i
\(61\) 4.65685 8.06591i 0.596249 1.03273i −0.397120 0.917767i \(-0.629990\pi\)
0.993369 0.114967i \(-0.0366763\pi\)
\(62\) 8.24264 + 14.2767i 1.04682 + 1.81314i
\(63\) 2.44949 1.41421i 0.308607 0.178174i
\(64\) 9.82843 1.22855
\(65\) 0 0
\(66\) 4.82843 0.594338
\(67\) 1.01461 0.585786i 0.123955 0.0715652i −0.436741 0.899587i \(-0.643867\pi\)
0.560695 + 0.828022i \(0.310534\pi\)
\(68\) 7.00000 + 12.1244i 0.848875 + 1.47029i
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) 19.3137i 2.30843i
\(71\) −1.73205 1.00000i −0.205557 0.118678i 0.393688 0.919244i \(-0.371199\pi\)
−0.599245 + 0.800566i \(0.704532\pi\)
\(72\) −3.82282 2.20711i −0.450524 0.260110i
\(73\) 11.6569i 1.36433i −0.731198 0.682166i \(-0.761038\pi\)
0.731198 0.682166i \(-0.238962\pi\)
\(74\) 4.41421 7.64564i 0.513142 0.888788i
\(75\) 1.50000 + 2.59808i 0.173205 + 0.300000i
\(76\) −9.37769 + 5.41421i −1.07570 + 0.621053i
\(77\) −5.65685 −0.644658
\(78\) 0 0
\(79\) 11.3137 1.27289 0.636446 0.771321i \(-0.280404\pi\)
0.636446 + 0.771321i \(0.280404\pi\)
\(80\) 7.34847 4.24264i 0.821584 0.474342i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −13.0711 + 22.6398i −1.44346 + 2.50014i
\(83\) 7.65685i 0.840449i −0.907420 0.420224i \(-0.861951\pi\)
0.907420 0.420224i \(-0.138049\pi\)
\(84\) 9.37769 + 5.41421i 1.02319 + 0.590739i
\(85\) −8.95743 5.17157i −0.971569 0.560936i
\(86\) 23.3137i 2.51398i
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) 4.41421 + 7.64564i 0.470557 + 0.815028i
\(89\) −7.94282 + 4.58579i −0.841937 + 0.486092i −0.857922 0.513780i \(-0.828245\pi\)
0.0159854 + 0.999872i \(0.494911\pi\)
\(90\) 6.82843 0.719779
\(91\) 0 0
\(92\) −15.3137 −1.59656
\(93\) −5.91359 + 3.41421i −0.613211 + 0.354037i
\(94\) −0.414214 0.717439i −0.0427229 0.0739982i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 1.58579i 0.161849i
\(97\) 6.63103 + 3.82843i 0.673279 + 0.388718i 0.797318 0.603559i \(-0.206251\pi\)
−0.124039 + 0.992277i \(0.539585\pi\)
\(98\) −2.09077 1.20711i −0.211200 0.121936i
\(99\) 2.00000i 0.201008i
\(100\) −5.74264 + 9.94655i −0.574264 + 0.994655i
\(101\) −1.82843 3.16693i −0.181935 0.315121i 0.760604 0.649216i \(-0.224903\pi\)
−0.942540 + 0.334095i \(0.891569\pi\)
\(102\) −7.64564 + 4.41421i −0.757031 + 0.437072i
\(103\) −13.6569 −1.34565 −0.672825 0.739802i \(-0.734919\pi\)
−0.672825 + 0.739802i \(0.734919\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 4.18154 2.41421i 0.406147 0.234489i
\(107\) −5.65685 9.79796i −0.546869 0.947204i −0.998487 0.0549930i \(-0.982486\pi\)
0.451618 0.892211i \(-0.350847\pi\)
\(108\) 1.91421 3.31552i 0.184195 0.319036i
\(109\) 17.3137i 1.65835i −0.558987 0.829176i \(-0.688810\pi\)
0.558987 0.829176i \(-0.311190\pi\)
\(110\) −11.8272 6.82843i −1.12768 0.651065i
\(111\) 3.16693 + 1.82843i 0.300592 + 0.173547i
\(112\) 8.48528i 0.801784i
\(113\) −8.65685 + 14.9941i −0.814368 + 1.41053i 0.0954122 + 0.995438i \(0.469583\pi\)
−0.909781 + 0.415090i \(0.863750\pi\)
\(114\) −3.41421 5.91359i −0.319770 0.553859i
\(115\) 9.79796 5.65685i 0.913664 0.527504i
\(116\) −7.65685 −0.710921
\(117\) 0 0
\(118\) 8.82843 0.812723
\(119\) 8.95743 5.17157i 0.821126 0.474077i
\(120\) 6.24264 + 10.8126i 0.569873 + 0.987048i
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 22.4853i 2.03572i
\(123\) −9.37769 5.41421i −0.845558 0.488183i
\(124\) −22.6398 13.0711i −2.03311 1.17382i
\(125\) 5.65685i 0.505964i
\(126\) −3.41421 + 5.91359i −0.304162 + 0.526825i
\(127\) −2.82843 4.89898i −0.250982 0.434714i 0.712814 0.701353i \(-0.247420\pi\)
−0.963797 + 0.266639i \(0.914087\pi\)
\(128\) −17.8023 + 10.2782i −1.57352 + 0.908471i
\(129\) −9.65685 −0.850239
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −6.63103 + 3.82843i −0.577157 + 0.333222i
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) −1.41421 + 2.44949i −0.122169 + 0.211604i
\(135\) 2.82843i 0.243432i
\(136\) −13.9795 8.07107i −1.19873 0.692088i
\(137\) −4.47871 2.58579i −0.382642 0.220919i 0.296325 0.955087i \(-0.404239\pi\)
−0.678967 + 0.734169i \(0.737572\pi\)
\(138\) 9.65685i 0.822046i
\(139\) −7.65685 + 13.2621i −0.649446 + 1.12487i 0.333810 + 0.942641i \(0.391666\pi\)
−0.983255 + 0.182233i \(0.941668\pi\)
\(140\) −15.3137 26.5241i −1.29424 2.24170i
\(141\) 0.297173 0.171573i 0.0250265 0.0144490i
\(142\) 4.82843 0.405193
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 4.89898 2.82843i 0.406838 0.234888i
\(146\) 14.0711 + 24.3718i 1.16453 + 2.01702i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 14.0000i 1.15079i
\(149\) 12.8418 + 7.41421i 1.05204 + 0.607396i 0.923220 0.384272i \(-0.125547\pi\)
0.128821 + 0.991668i \(0.458881\pi\)
\(150\) −6.27231 3.62132i −0.512132 0.295680i
\(151\) 20.4853i 1.66707i 0.552468 + 0.833534i \(0.313686\pi\)
−0.552468 + 0.833534i \(0.686314\pi\)
\(152\) 6.24264 10.8126i 0.506345 0.877015i
\(153\) −1.82843 3.16693i −0.147820 0.256031i
\(154\) 11.8272 6.82843i 0.953062 0.550250i
\(155\) 19.3137 1.55131
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −23.6544 + 13.6569i −1.88184 + 1.08648i
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 2.24264 3.88437i 0.177296 0.307086i
\(161\) 11.3137i 0.891645i
\(162\) 2.09077 + 1.20711i 0.164266 + 0.0948393i
\(163\) 11.4069 + 6.58579i 0.893459 + 0.515839i 0.875072 0.483992i \(-0.160814\pi\)
0.0183864 + 0.999831i \(0.494147\pi\)
\(164\) 41.4558i 3.23716i
\(165\) 2.82843 4.89898i 0.220193 0.381385i
\(166\) 9.24264 + 16.0087i 0.717368 + 1.24252i
\(167\) −6.63103 + 3.82843i −0.513125 + 0.296253i −0.734117 0.679023i \(-0.762404\pi\)
0.220993 + 0.975275i \(0.429070\pi\)
\(168\) −12.4853 −0.963260
\(169\) 0 0
\(170\) 24.9706 1.91515
\(171\) 2.44949 1.41421i 0.187317 0.108148i
\(172\) −18.4853 32.0174i −1.40949 2.44131i
\(173\) −0.171573 + 0.297173i −0.0130444 + 0.0225936i −0.872474 0.488661i \(-0.837486\pi\)
0.859429 + 0.511254i \(0.170819\pi\)
\(174\) 4.82843i 0.366042i
\(175\) 7.34847 + 4.24264i 0.555492 + 0.320713i
\(176\) −5.19615 3.00000i −0.391675 0.226134i
\(177\) 3.65685i 0.274866i
\(178\) 11.0711 19.1757i 0.829812 1.43728i
\(179\) −0.343146 0.594346i −0.0256479 0.0444235i 0.852917 0.522047i \(-0.174832\pi\)
−0.878564 + 0.477624i \(0.841498\pi\)
\(180\) −9.37769 + 5.41421i −0.698972 + 0.403552i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −9.31371 −0.688489
\(184\) 15.2913 8.82843i 1.12729 0.650840i
\(185\) −5.17157 8.95743i −0.380222 0.658563i
\(186\) 8.24264 14.2767i 0.604380 1.04682i
\(187\) 7.31371i 0.534831i
\(188\) 1.13770 + 0.656854i 0.0829757 + 0.0479060i
\(189\) −2.44949 1.41421i −0.178174 0.102869i
\(190\) 19.3137i 1.40116i
\(191\) 9.65685 16.7262i 0.698745 1.21026i −0.270156 0.962817i \(-0.587075\pi\)
0.968902 0.247446i \(-0.0795913\pi\)
\(192\) −4.91421 8.51167i −0.354653 0.614277i
\(193\) 14.9941 8.65685i 1.07930 0.623134i 0.148592 0.988899i \(-0.452526\pi\)
0.930707 + 0.365765i \(0.119192\pi\)
\(194\) −18.4853 −1.32717
\(195\) 0 0
\(196\) 3.82843 0.273459
\(197\) −14.2767 + 8.24264i −1.01717 + 0.587264i −0.913283 0.407325i \(-0.866462\pi\)
−0.103888 + 0.994589i \(0.533128\pi\)
\(198\) −2.41421 4.18154i −0.171571 0.297169i
\(199\) 5.17157 8.95743i 0.366603 0.634975i −0.622429 0.782676i \(-0.713854\pi\)
0.989032 + 0.147701i \(0.0471874\pi\)
\(200\) 13.2426i 0.936396i
\(201\) −1.01461 0.585786i −0.0715652 0.0413182i
\(202\) 7.64564 + 4.41421i 0.537946 + 0.310583i
\(203\) 5.65685i 0.397033i
\(204\) 7.00000 12.1244i 0.490098 0.848875i
\(205\) 15.3137 + 26.5241i 1.06956 + 1.85252i
\(206\) 28.5533 16.4853i 1.98941 1.14858i
\(207\) 4.00000 0.278019
\(208\) 0 0
\(209\) −5.65685 −0.391293
\(210\) 16.7262 9.65685i 1.15421 0.666386i
\(211\) 6.00000 + 10.3923i 0.413057 + 0.715436i 0.995222 0.0976347i \(-0.0311277\pi\)
−0.582165 + 0.813070i \(0.697794\pi\)
\(212\) −3.82843 + 6.63103i −0.262937 + 0.455421i
\(213\) 2.00000i 0.137038i
\(214\) 23.6544 + 13.6569i 1.61698 + 0.933563i
\(215\) 23.6544 + 13.6569i 1.61321 + 0.931390i
\(216\) 4.41421i 0.300349i
\(217\) −9.65685 + 16.7262i −0.655550 + 1.13545i
\(218\) 20.8995 + 36.1990i 1.41549 + 2.45170i
\(219\) −10.0951 + 5.82843i −0.682166 + 0.393849i
\(220\) 21.6569 1.46010
\(221\) 0 0
\(222\) −8.82843 −0.592525
\(223\) 3.88437 2.24264i 0.260116 0.150178i −0.364271 0.931293i \(-0.618682\pi\)
0.624388 + 0.781115i \(0.285349\pi\)
\(224\) 2.24264 + 3.88437i 0.149843 + 0.259535i
\(225\) 1.50000 2.59808i 0.100000 0.173205i
\(226\) 41.7990i 2.78043i
\(227\) −4.60181 2.65685i −0.305433 0.176342i 0.339448 0.940625i \(-0.389760\pi\)
−0.644881 + 0.764283i \(0.723093\pi\)
\(228\) 9.37769 + 5.41421i 0.621053 + 0.358565i
\(229\) 21.3137i 1.40845i −0.709977 0.704225i \(-0.751295\pi\)
0.709977 0.704225i \(-0.248705\pi\)
\(230\) −13.6569 + 23.6544i −0.900506 + 1.55972i
\(231\) 2.82843 + 4.89898i 0.186097 + 0.322329i
\(232\) 7.64564 4.41421i 0.501961 0.289807i
\(233\) 26.9706 1.76690 0.883450 0.468525i \(-0.155214\pi\)
0.883450 + 0.468525i \(0.155214\pi\)
\(234\) 0 0
\(235\) −0.970563 −0.0633125
\(236\) −12.1244 + 7.00000i −0.789228 + 0.455661i
\(237\) −5.65685 9.79796i −0.367452 0.636446i
\(238\) −12.4853 + 21.6251i −0.809301 + 1.40175i
\(239\) 2.00000i 0.129369i 0.997906 + 0.0646846i \(0.0206041\pi\)
−0.997906 + 0.0646846i \(0.979396\pi\)
\(240\) −7.34847 4.24264i −0.474342 0.273861i
\(241\) 10.0951 + 5.82843i 0.650285 + 0.375442i 0.788565 0.614951i \(-0.210824\pi\)
−0.138281 + 0.990393i \(0.544158\pi\)
\(242\) 16.8995i 1.08634i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −17.8284 30.8797i −1.14135 1.97687i
\(245\) −2.44949 + 1.41421i −0.156492 + 0.0903508i
\(246\) 26.1421 1.66676
\(247\) 0 0
\(248\) 30.1421 1.91403
\(249\) −6.63103 + 3.82843i −0.420224 + 0.242617i
\(250\) −6.82843 11.8272i −0.431868 0.748017i
\(251\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 10.8284i 0.682127i
\(253\) −6.92820 4.00000i −0.435572 0.251478i
\(254\) 11.8272 + 6.82843i 0.742103 + 0.428454i
\(255\) 10.3431i 0.647713i
\(256\) 14.9853 25.9553i 0.936580 1.62220i
\(257\) −7.82843 13.5592i −0.488324 0.845802i 0.511586 0.859232i \(-0.329058\pi\)
−0.999910 + 0.0134304i \(0.995725\pi\)
\(258\) 20.1903 11.6569i 1.25699 0.725724i
\(259\) 10.3431 0.642692
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 16.7262 9.65685i 1.03335 0.596602i
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 4.41421 7.64564i 0.271676 0.470557i
\(265\) 5.65685i 0.347498i
\(266\) −16.7262 9.65685i −1.02555 0.592100i
\(267\) 7.94282 + 4.58579i 0.486092 + 0.280646i
\(268\) 4.48528i 0.273982i
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −3.41421 5.91359i −0.207782 0.359890i
\(271\) −10.2182 + 5.89949i −0.620713 + 0.358369i −0.777147 0.629320i \(-0.783334\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(272\) 10.9706 0.665188
\(273\) 0 0
\(274\) 12.4853 0.754263
\(275\) −5.19615 + 3.00000i −0.313340 + 0.180907i
\(276\) 7.65685 + 13.2621i 0.460888 + 0.798282i
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 36.9706i 2.21735i
\(279\) 5.91359 + 3.41421i 0.354037 + 0.204404i
\(280\) 30.5826 + 17.6569i 1.82766 + 1.05520i
\(281\) 26.8284i 1.60045i −0.599700 0.800225i \(-0.704713\pi\)
0.599700 0.800225i \(-0.295287\pi\)
\(282\) −0.414214 + 0.717439i −0.0246661 + 0.0427229i
\(283\) −2.48528 4.30463i −0.147735 0.255884i 0.782655 0.622455i \(-0.213865\pi\)
−0.930390 + 0.366572i \(0.880531\pi\)
\(284\) −6.63103 + 3.82843i −0.393479 + 0.227175i
\(285\) −8.00000 −0.473879
\(286\) 0 0
\(287\) −30.6274 −1.80788
\(288\) 1.37333 0.792893i 0.0809243 0.0467217i
\(289\) 1.81371 + 3.14144i 0.106689 + 0.184790i
\(290\) −6.82843 + 11.8272i −0.400979 + 0.694516i
\(291\) 7.65685i 0.448853i
\(292\) −38.6485 22.3137i −2.26173 1.30581i
\(293\) −22.6398 13.0711i −1.32263 0.763620i −0.338481 0.940973i \(-0.609913\pi\)
−0.984147 + 0.177353i \(0.943247\pi\)
\(294\) 2.41421i 0.140800i
\(295\) 5.17157 8.95743i 0.301101 0.521522i
\(296\) −8.07107 13.9795i −0.469121 0.812542i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) −35.7990 −2.07378
\(299\) 0 0
\(300\) 11.4853 0.663103
\(301\) −23.6544 + 13.6569i −1.36341 + 0.787168i
\(302\) −24.7279 42.8300i −1.42293 2.46459i
\(303\) −1.82843 + 3.16693i −0.105040 + 0.181935i
\(304\) 8.48528i 0.486664i
\(305\) 22.8138 + 13.1716i 1.30632 + 0.754202i
\(306\) 7.64564 + 4.41421i 0.437072 + 0.252344i
\(307\) 17.1716i 0.980033i 0.871713 + 0.490017i \(0.163009\pi\)
−0.871713 + 0.490017i \(0.836991\pi\)
\(308\) −10.8284 + 18.7554i −0.617007 + 1.06869i
\(309\) 6.82843 + 11.8272i 0.388456 + 0.672825i
\(310\) −40.3805 + 23.3137i −2.29346 + 1.32413i
\(311\) −34.6274 −1.96354 −0.981770 0.190071i \(-0.939128\pi\)
−0.981770 + 0.190071i \(0.939128\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 20.9077 12.0711i 1.17989 0.681210i
\(315\) 4.00000 + 6.92820i 0.225374 + 0.390360i
\(316\) 21.6569 37.5108i 1.21829 2.11015i
\(317\) 8.48528i 0.476581i −0.971194 0.238290i \(-0.923413\pi\)
0.971194 0.238290i \(-0.0765870\pi\)
\(318\) −4.18154 2.41421i −0.234489 0.135382i
\(319\) −3.46410 2.00000i −0.193952 0.111979i
\(320\) 27.7990i 1.55401i
\(321\) −5.65685 + 9.79796i −0.315735 + 0.546869i
\(322\) −13.6569 23.6544i −0.761067 1.31821i
\(323\) 8.95743 5.17157i 0.498405 0.287754i
\(324\) −3.82843 −0.212690
\(325\) 0 0
\(326\) −31.7990 −1.76118
\(327\) −14.9941 + 8.65685i −0.829176 + 0.478725i
\(328\) 23.8995 + 41.3951i 1.31963 + 2.28566i
\(329\) 0.485281 0.840532i 0.0267544 0.0463400i
\(330\) 13.6569i 0.751785i
\(331\) 1.85514 + 1.07107i 0.101968 + 0.0588712i 0.550117 0.835088i \(-0.314583\pi\)
−0.448149 + 0.893959i \(0.647917\pi\)
\(332\) −25.3864 14.6569i −1.39326 0.804399i
\(333\) 3.65685i 0.200394i
\(334\) 9.24264 16.0087i 0.505735 0.875958i
\(335\) 1.65685 + 2.86976i 0.0905236 + 0.156792i
\(336\) 7.34847 4.24264i 0.400892 0.231455i
\(337\) 13.3137 0.725244 0.362622 0.931936i \(-0.381882\pi\)
0.362622 + 0.931936i \(0.381882\pi\)
\(338\) 0 0
\(339\) 17.3137 0.940352
\(340\) −34.2929 + 19.7990i −1.85979 + 1.07375i
\(341\) −6.82843 11.8272i −0.369780 0.640478i
\(342\) −3.41421 + 5.91359i −0.184620 + 0.319770i
\(343\) 16.9706i 0.916324i
\(344\) 36.9164 + 21.3137i 1.99040 + 1.14916i
\(345\) −9.79796 5.65685i −0.527504 0.304555i
\(346\) 0.828427i 0.0445365i
\(347\) 15.6569 27.1185i 0.840504 1.45580i −0.0489652 0.998800i \(-0.515592\pi\)
0.889469 0.456995i \(-0.151074\pi\)
\(348\) 3.82843 + 6.63103i 0.205225 + 0.355461i
\(349\) 6.63103 3.82843i 0.354951 0.204931i −0.311913 0.950111i \(-0.600970\pi\)
0.666864 + 0.745180i \(0.267636\pi\)
\(350\) −20.4853 −1.09498
\(351\) 0 0
\(352\) −3.17157 −0.169045
\(353\) 15.1172 8.72792i 0.804608 0.464540i −0.0404722 0.999181i \(-0.512886\pi\)
0.845080 + 0.534640i \(0.179553\pi\)
\(354\) −4.41421 7.64564i −0.234613 0.406361i
\(355\) 2.82843 4.89898i 0.150117 0.260011i
\(356\) 35.1127i 1.86097i
\(357\) −8.95743 5.17157i −0.474077 0.273709i
\(358\) 1.43488 + 0.828427i 0.0758357 + 0.0437837i
\(359\) 1.02944i 0.0543316i −0.999631 0.0271658i \(-0.991352\pi\)
0.999631 0.0271658i \(-0.00864821\pi\)
\(360\) 6.24264 10.8126i 0.329016 0.569873i
\(361\) −5.50000 9.52628i −0.289474 0.501383i
\(362\) 29.2708 16.8995i 1.53844 0.888218i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 32.9706 1.72576
\(366\) 19.4728 11.2426i 1.01786 0.587662i
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) −6.00000 + 10.3923i −0.312772 + 0.541736i
\(369\) 10.8284i 0.563705i
\(370\) 21.6251 + 12.4853i 1.12424 + 0.649079i
\(371\) 4.89898 + 2.82843i 0.254342 + 0.146845i
\(372\) 26.1421i 1.35541i
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) −8.82843 15.2913i −0.456507 0.790693i
\(375\) 4.89898 2.82843i 0.252982 0.146059i
\(376\) −1.51472 −0.0781156
\(377\) 0 0
\(378\) 6.82843 0.351216
\(379\) −14.2767 + 8.24264i −0.733343 + 0.423396i −0.819644 0.572873i \(-0.805829\pi\)
0.0863007 + 0.996269i \(0.472495\pi\)
\(380\) −15.3137 26.5241i −0.785577 1.36066i
\(381\) −2.82843 + 4.89898i −0.144905 + 0.250982i
\(382\) 46.6274i 2.38567i
\(383\) 2.57258 + 1.48528i 0.131453 + 0.0758943i 0.564284 0.825581i \(-0.309152\pi\)
−0.432832 + 0.901475i \(0.642485\pi\)
\(384\) 17.8023 + 10.2782i 0.908471 + 0.524506i
\(385\) 16.0000i 0.815436i
\(386\) −20.8995 + 36.1990i −1.06376 + 1.84248i
\(387\) 4.82843 + 8.36308i 0.245443 + 0.425119i
\(388\) 25.3864 14.6569i 1.28880 0.744089i
\(389\) −6.97056 −0.353422 −0.176711 0.984263i \(-0.556546\pi\)
−0.176711 + 0.984263i \(0.556546\pi\)
\(390\) 0 0
\(391\) 14.6274 0.739740
\(392\) −3.82282 + 2.20711i −0.193082 + 0.111476i
\(393\) 4.00000 + 6.92820i 0.201773 + 0.349482i
\(394\) 19.8995 34.4669i 1.00252 1.73642i
\(395\) 32.0000i 1.61009i
\(396\) 6.63103 + 3.82843i 0.333222 + 0.192386i
\(397\) −2.57258 1.48528i −0.129114 0.0745441i 0.434052 0.900888i \(-0.357083\pi\)
−0.563166 + 0.826344i \(0.690417\pi\)
\(398\) 24.9706i 1.25166i
\(399\) 4.00000 6.92820i 0.200250 0.346844i
\(400\) 4.50000 + 7.79423i 0.225000 + 0.389711i
\(401\) 1.85514 1.07107i 0.0926415 0.0534866i −0.452964 0.891529i \(-0.649633\pi\)
0.545605 + 0.838042i \(0.316300\pi\)
\(402\) 2.82843 0.141069
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) 2.44949 1.41421i 0.121716 0.0702728i
\(406\) −6.82843 11.8272i −0.338889 0.586973i
\(407\) −3.65685 + 6.33386i −0.181264 + 0.313958i
\(408\) 16.1421i 0.799155i
\(409\) 0.891519 + 0.514719i 0.0440828 + 0.0254512i 0.521879 0.853019i \(-0.325231\pi\)
−0.477797 + 0.878470i \(0.658564\pi\)
\(410\) −64.0349 36.9706i −3.16246 1.82585i
\(411\) 5.17157i 0.255095i
\(412\) −26.1421 + 45.2795i −1.28793 + 2.23076i
\(413\) 5.17157 + 8.95743i 0.254476 + 0.440766i
\(414\) −8.36308 + 4.82843i −0.411023 + 0.237304i
\(415\) 21.6569 1.06309
\(416\) 0 0
\(417\) 15.3137 0.749916
\(418\) 11.8272 6.82843i 0.578486 0.333989i
\(419\) 15.3137 + 26.5241i 0.748124 + 1.29579i 0.948721 + 0.316114i \(0.102378\pi\)
−0.200597 + 0.979674i \(0.564288\pi\)
\(420\) −15.3137 + 26.5241i −0.747232 + 1.29424i
\(421\) 14.6863i 0.715766i 0.933766 + 0.357883i \(0.116501\pi\)
−0.933766 + 0.357883i \(0.883499\pi\)
\(422\) −25.0892 14.4853i −1.22133 0.705132i
\(423\) −0.297173 0.171573i −0.0144490 0.00834216i
\(424\) 8.82843i 0.428746i
\(425\) 5.48528 9.50079i 0.266075 0.460856i
\(426\) −2.41421 4.18154i −0.116969 0.202596i
\(427\) −22.8138 + 13.1716i −1.10404 + 0.637417i
\(428\) −43.3137 −2.09365
\(429\) 0 0
\(430\) −65.9411 −3.17996
\(431\) 17.0233 9.82843i 0.819985 0.473419i −0.0304262 0.999537i \(-0.509686\pi\)
0.850411 + 0.526118i \(0.176353\pi\)
\(432\) −1.50000 2.59808i −0.0721688 0.125000i
\(433\) 0.656854 1.13770i 0.0315664 0.0546746i −0.849811 0.527088i \(-0.823284\pi\)
0.881377 + 0.472414i \(0.156617\pi\)
\(434\) 46.6274i 2.23819i
\(435\) −4.89898 2.82843i −0.234888 0.135613i
\(436\) −57.4039 33.1421i −2.74915 1.58722i
\(437\) 11.3137i 0.541208i
\(438\) 14.0711 24.3718i 0.672342 1.16453i
\(439\) −8.48528 14.6969i −0.404980 0.701447i 0.589339 0.807886i \(-0.299388\pi\)
−0.994319 + 0.106439i \(0.966055\pi\)
\(440\) −21.6251 + 12.4853i −1.03094 + 0.595212i
\(441\) −1.00000 −0.0476190
\(442\) 0 0
\(443\) 41.9411 1.99268 0.996342 0.0854611i \(-0.0272364\pi\)
0.996342 + 0.0854611i \(0.0272364\pi\)
\(444\) 12.1244 7.00000i 0.575396 0.332205i
\(445\) −12.9706 22.4657i −0.614864 1.06498i
\(446\) −5.41421 + 9.37769i −0.256370 + 0.444047i
\(447\) 14.8284i 0.701361i
\(448\) −24.0746 13.8995i −1.13742 0.656689i
\(449\) 6.75412 + 3.89949i 0.318747 + 0.184029i 0.650834 0.759220i \(-0.274419\pi\)
−0.332087 + 0.943249i \(0.607753\pi\)
\(450\) 7.24264i 0.341421i
\(451\) 10.8284 18.7554i 0.509891 0.883157i
\(452\) 33.1421 + 57.4039i 1.55887 + 2.70005i
\(453\) 17.7408 10.2426i 0.833534 0.481241i
\(454\) 12.8284 0.602068
\(455\) 0 0
\(456\) −12.4853 −0.584677
\(457\) 3.16693 1.82843i 0.148143 0.0855302i −0.424096 0.905617i \(-0.639408\pi\)
0.572239 + 0.820087i \(0.306075\pi\)
\(458\) 25.7279 + 44.5621i 1.20219 + 2.08225i
\(459\) −1.82843 + 3.16693i −0.0853437 + 0.147820i
\(460\) 43.3137i 2.01951i
\(461\) −9.37769 5.41421i −0.436763 0.252165i 0.265461 0.964122i \(-0.414476\pi\)
−0.702223 + 0.711957i \(0.747809\pi\)
\(462\) −11.8272 6.82843i −0.550250 0.317687i
\(463\) 7.51472i 0.349239i 0.984636 + 0.174619i \(0.0558695\pi\)
−0.984636 + 0.174619i \(0.944131\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) −9.65685 16.7262i −0.447826 0.775657i
\(466\) −56.3893 + 32.5563i −2.61218 + 1.50814i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 0 0
\(469\) −3.31371 −0.153013
\(470\) 2.02922 1.17157i 0.0936011 0.0540406i
\(471\) 5.00000 + 8.66025i 0.230388 + 0.399043i
\(472\) 8.07107 13.9795i 0.371501 0.643459i
\(473\) 19.3137i 0.888045i
\(474\) 23.6544 + 13.6569i 1.08648 + 0.627280i
\(475\) 7.34847 + 4.24264i 0.337171 + 0.194666i
\(476\) 39.5980i 1.81497i
\(477\) 1.00000 1.73205i 0.0457869 0.0793052i
\(478\) −2.41421 4.18154i −0.110424 0.191259i
\(479\) −2.32640 + 1.34315i −0.106296 + 0.0613699i −0.552205 0.833708i \(-0.686214\pi\)
0.445910 + 0.895078i \(0.352880\pi\)
\(480\) −4.48528 −0.204724
\(481\) 0 0
\(482\) −28.1421 −1.28184
\(483\) 9.79796 5.65685i 0.445823 0.257396i
\(484\) 13.3995 + 23.2086i 0.609068 + 1.05494i
\(485\) −10.8284 + 18.7554i −0.491694 + 0.851638i
\(486\) 2.41421i 0.109511i
\(487\) −27.5387 15.8995i −1.24790 0.720475i −0.277209 0.960810i \(-0.589409\pi\)
−0.970690 + 0.240335i \(0.922743\pi\)
\(488\) 35.6046 + 20.5563i 1.61175 + 0.930542i
\(489\) 13.1716i 0.595639i
\(490\) 3.41421 5.91359i 0.154238 0.267149i
\(491\) −7.31371 12.6677i −0.330063 0.571686i 0.652461 0.757822i \(-0.273737\pi\)
−0.982524 + 0.186136i \(0.940403\pi\)
\(492\) −35.9018 + 20.7279i −1.61858 + 0.934487i
\(493\) 7.31371 0.329393
\(494\) 0 0
\(495\) −5.65685 −0.254257
\(496\) −17.7408 + 10.2426i −0.796584 + 0.459908i
\(497\) 2.82843 + 4.89898i 0.126872 + 0.219749i
\(498\) 9.24264 16.0087i 0.414173 0.717368i
\(499\) 2.14214i 0.0958952i −0.998850 0.0479476i \(-0.984732\pi\)
0.998850 0.0479476i \(-0.0152680\pi\)
\(500\) 18.7554 + 10.8284i 0.838766 + 0.484262i
\(501\) 6.63103 + 3.82843i 0.296253 + 0.171042i
\(502\) 0 0
\(503\) −7.65685 + 13.2621i −0.341402 + 0.591326i −0.984693 0.174296i \(-0.944235\pi\)
0.643291 + 0.765622i \(0.277569\pi\)
\(504\) 6.24264 + 10.8126i 0.278069 + 0.481630i
\(505\) 8.95743 5.17157i 0.398600 0.230132i
\(506\) 19.3137 0.858599
\(507\) 0 0
\(508\) −21.6569 −0.960868
\(509\) −24.0746 + 13.8995i −1.06709 + 0.616084i −0.927385 0.374109i \(-0.877949\pi\)
−0.139705 + 0.990193i \(0.544615\pi\)
\(510\) −12.4853 21.6251i −0.552858 0.957577i
\(511\) −16.4853 + 28.5533i −0.729266 + 1.26313i
\(512\) 31.2426i 1.38074i
\(513\) −2.44949 1.41421i −0.108148 0.0624391i
\(514\) 32.7349 + 18.8995i 1.44387 + 0.833621i
\(515\) 38.6274i 1.70213i
\(516\) −18.4853 + 32.0174i −0.813769 + 1.40949i
\(517\) 0.343146 + 0.594346i 0.0150915 + 0.0261393i
\(518\) −21.6251 + 12.4853i −0.950154 + 0.548572i
\(519\) 0.343146 0.0150624
\(520\) 0 0
\(521\) 2.68629 0.117689 0.0588443 0.998267i \(-0.481258\pi\)
0.0588443 + 0.998267i \(0.481258\pi\)
\(522\) −4.18154 + 2.41421i −0.183021 + 0.105667i
\(523\) −3.65685 6.33386i −0.159903 0.276960i 0.774930 0.632046i \(-0.217785\pi\)
−0.934834 + 0.355086i \(0.884452\pi\)
\(524\) −15.3137 + 26.5241i −0.668982 + 1.15871i
\(525\) 8.48528i 0.370328i
\(526\) 25.0892 + 14.4853i 1.09394 + 0.631588i
\(527\) 21.6251 + 12.4853i 0.942006 + 0.543867i
\(528\) 6.00000i 0.261116i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 6.82843 + 11.8272i 0.296608 + 0.513740i
\(531\) 3.16693 1.82843i 0.137433 0.0793470i
\(532\) 30.6274 1.32787
\(533\) 0 0
\(534\) −22.1421 −0.958184
\(535\) 27.7128 16.0000i 1.19813 0.691740i
\(536\) 2.58579 + 4.47871i 0.111689 + 0.193451i
\(537\) −0.343146 + 0.594346i −0.0148078 + 0.0256479i
\(538\) 43.4558i 1.87351i
\(539\) 1.73205 + 1.00000i 0.0746047 + 0.0430730i
\(540\) 9.37769 + 5.41421i 0.403552 + 0.232991i
\(541\) 10.0000i 0.429934i −0.976621 0.214967i \(-0.931036\pi\)
0.976621 0.214967i \(-0.0689643\pi\)
\(542\) 14.2426 24.6690i 0.611774 1.05962i
\(543\) 7.00000 + 12.1244i 0.300399 + 0.520306i
\(544\) 5.02207 2.89949i 0.215320 0.124315i
\(545\) 48.9706 2.09767
\(546\) 0 0
\(547\) 0.686292 0.0293437 0.0146719 0.999892i \(-0.495330\pi\)
0.0146719 + 0.999892i \(0.495330\pi\)
\(548\) −17.1464 + 9.89949i −0.732459 + 0.422885i
\(549\) 4.65685 + 8.06591i 0.198750 + 0.344245i
\(550\) 7.24264 12.5446i 0.308827 0.534904i
\(551\) 5.65685i 0.240990i
\(552\) −15.2913 8.82843i −0.650840 0.375763i
\(553\) −27.7128 16.0000i −1.17847 0.680389i
\(554\) 4.82843i 0.205140i
\(555\) −5.17157 + 8.95743i −0.219521 + 0.380222i
\(556\) 29.3137 + 50.7728i 1.24318 + 2.15325i
\(557\) −27.5387 + 15.8995i −1.16685 + 0.673683i −0.952937 0.303169i \(-0.901955\pi\)
−0.213917 + 0.976852i \(0.568622\pi\)
\(558\) −16.4853 −0.697878
\(559\) 0 0
\(560\) −24.0000 −1.01419
\(561\) 6.33386 3.65685i 0.267416 0.154393i
\(562\) 32.3848 + 56.0921i 1.36607 + 2.36610i
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 1.31371i 0.0553171i
\(565\) −42.4098 24.4853i −1.78419 1.03010i
\(566\) 10.3923 + 6.00000i 0.436821 + 0.252199i
\(567\) 2.82843i 0.118783i
\(568\) 4.41421 7.64564i 0.185216 0.320804i
\(569\) −4.51472 7.81972i −0.189267 0.327820i 0.755739 0.654873i \(-0.227278\pi\)
−0.945006 + 0.327053i \(0.893944\pi\)
\(570\) 16.7262 9.65685i 0.700582 0.404481i
\(571\) −20.9706 −0.877591 −0.438795 0.898587i \(-0.644595\pi\)
−0.438795 + 0.898587i \(0.644595\pi\)
\(572\) 0 0
\(573\) −19.3137 −0.806842
\(574\) 64.0349 36.9706i 2.67276 1.54312i
\(575\) 6.00000 + 10.3923i 0.250217 + 0.433389i
\(576\) −4.91421 + 8.51167i −0.204759 + 0.354653i
\(577\) 35.9411i 1.49625i 0.663559 + 0.748124i \(0.269045\pi\)
−0.663559 + 0.748124i \(0.730955\pi\)
\(578\) −7.58410 4.37868i −0.315457 0.182129i
\(579\) −14.9941 8.65685i −0.623134 0.359767i
\(580\) 21.6569i 0.899252i
\(581\) −10.8284 + 18.7554i −0.449239 + 0.778105i
\(582\) 9.24264 + 16.0087i 0.383120 + 0.663583i
\(583\) −3.46410 + 2.00000i −0.143468 + 0.0828315i
\(584\) 51.4558 2.12926
\(585\) 0 0
\(586\) 63.1127 2.60716
\(587\) 19.8931 11.4853i 0.821076 0.474048i −0.0297116 0.999559i \(-0.509459\pi\)
0.850787 + 0.525510i \(0.176126\pi\)
\(588\) −1.91421 3.31552i −0.0789408 0.136730i
\(589\) −9.65685 + 16.7262i −0.397904 + 0.689190i
\(590\) 24.9706i 1.02802i
\(591\) 14.2767 + 8.24264i 0.587264 + 0.339057i
\(592\) 9.50079 + 5.48528i 0.390480 + 0.225444i
\(593\) 3.51472i 0.144332i 0.997393 + 0.0721661i \(0.0229912\pi\)
−0.997393 + 0.0721661i \(0.977009\pi\)
\(594\) −2.41421 + 4.18154i −0.0990564 + 0.171571i
\(595\) 14.6274 + 25.3354i 0.599666 + 1.03865i
\(596\) 49.1639 28.3848i 2.01383 1.16269i
\(597\) −10.3431 −0.423317
\(598\) 0 0
\(599\) −0.686292 −0.0280411 −0.0140206 0.999902i \(-0.504463\pi\)
−0.0140206 + 0.999902i \(0.504463\pi\)
\(600\) −11.4685 + 6.62132i −0.468198 + 0.270314i
\(601\) −22.3137 38.6485i −0.910195 1.57650i −0.813788 0.581162i \(-0.802598\pi\)
−0.0964075 0.995342i \(-0.530735\pi\)
\(602\) 32.9706 57.1067i 1.34378 2.32749i
\(603\) 1.17157i 0.0477101i
\(604\) 67.9193 + 39.2132i 2.76360 + 1.59556i
\(605\) −17.1464 9.89949i −0.697101 0.402472i
\(606\) 8.82843i 0.358630i
\(607\) 12.9706 22.4657i 0.526459 0.911854i −0.473066 0.881027i \(-0.656853\pi\)
0.999525 0.0308265i \(-0.00981393\pi\)
\(608\) 2.24264 + 3.88437i 0.0909511 + 0.157532i
\(609\) 4.89898 2.82843i 0.198517 0.114614i
\(610\) −63.5980 −2.57501
\(611\) 0 0
\(612\) −14.0000 −0.565916
\(613\) −31.4741 + 18.1716i −1.27123 + 0.733943i −0.975219 0.221243i \(-0.928989\pi\)
−0.296008 + 0.955186i \(0.595655\pi\)
\(614\) −20.7279 35.9018i −0.836511 1.44888i
\(615\) 15.3137 26.5241i 0.617508 1.06956i
\(616\) 24.9706i 1.00609i
\(617\) 25.2633 + 14.5858i 1.01706 + 0.587202i 0.913252 0.407395i \(-0.133563\pi\)
0.103811 + 0.994597i \(0.466896\pi\)
\(618\) −28.5533 16.4853i −1.14858 0.663135i
\(619\) 15.7990i 0.635015i 0.948256 + 0.317508i \(0.102846\pi\)
−0.948256 + 0.317508i \(0.897154\pi\)
\(620\) 36.9706 64.0349i 1.48477 2.57170i
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 72.3980 41.7990i 2.90289 1.67599i
\(623\) 25.9411 1.03931
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) −12.5446 + 7.24264i −0.501384 + 0.289474i
\(627\) 2.82843 + 4.89898i 0.112956 + 0.195646i
\(628\) −19.1421 + 33.1552i −0.763854 + 1.32303i
\(629\) 13.3726i 0.533200i
\(630\) −16.7262 9.65685i −0.666386 0.384738i
\(631\) −16.5521 9.55635i −0.658928 0.380432i 0.132940 0.991124i \(-0.457558\pi\)
−0.791868 + 0.610692i \(0.790891\pi\)
\(632\) 49.9411i 1.98655i
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) 10.2426 + 17.7408i 0.406787 + 0.704576i
\(635\) 13.8564 8.00000i 0.549875 0.317470i
\(636\) 7.65685 0.303614
\(637\) 0 0
\(638\) 9.65685 0.382319
\(639\) 1.73205 1.00000i 0.0685189 0.0395594i
\(640\) −29.0711 50.3526i −1.14913 1.99036i
\(641\) −13.1421 + 22.7628i −0.519083 + 0.899078i 0.480671 + 0.876901i \(0.340393\pi\)
−0.999754 + 0.0221773i \(0.992940\pi\)
\(642\) 27.3137i 1.07799i
\(643\) −14.8710 8.58579i −0.586456 0.338590i 0.177239 0.984168i \(-0.443283\pi\)
−0.763695 + 0.645577i \(0.776617\pi\)
\(644\) 37.5108 + 21.6569i 1.47813 + 0.853400i
\(645\) 27.3137i 1.07548i
\(646\) −12.4853 + 21.6251i −0.491227 + 0.850830i
\(647\) −5.65685 9.79796i −0.222394 0.385198i 0.733140 0.680077i \(-0.238054\pi\)
−0.955534 + 0.294880i \(0.904720\pi\)
\(648\) 3.82282 2.20711i 0.150175 0.0867033i
\(649\) −7.31371 −0.287088
\(650\) 0 0
\(651\) 19.3137 0.756964
\(652\) 43.6705 25.2132i 1.71027 0.987425i
\(653\) 1.34315 + 2.32640i 0.0525614 + 0.0910389i 0.891109 0.453789i \(-0.149928\pi\)
−0.838548 + 0.544828i \(0.816595\pi\)
\(654\) 20.8995 36.1990i 0.817235 1.41549i
\(655\) 22.6274i 0.884126i
\(656\) −28.1331 16.2426i −1.09841 0.634169i
\(657\) 10.0951 + 5.82843i 0.393849 + 0.227389i
\(658\) 2.34315i 0.0913453i
\(659\) 12.3431 21.3790i 0.480821 0.832806i −0.518937 0.854812i \(-0.673672\pi\)
0.999758 + 0.0220065i \(0.00700546\pi\)
\(660\) −10.8284 18.7554i −0.421496 0.730052i
\(661\) 0.891519 0.514719i 0.0346761 0.0200202i −0.482562 0.875862i \(-0.660294\pi\)
0.517238 + 0.855842i \(0.326960\pi\)
\(662\) −5.17157 −0.200999
\(663\) 0 0
\(664\) 33.7990 1.31166
\(665\) −19.5959 + 11.3137i −0.759897 + 0.438727i
\(666\) 4.41421 + 7.64564i 0.171047 + 0.296263i
\(667\) −4.00000 + 6.92820i −0.154881 + 0.268261i
\(668\) 29.3137i 1.13418i
\(669\) −3.88437 2.24264i −0.150178 0.0867055i
\(670\) −6.92820 4.00000i −0.267660 0.154533i
\(671\) 18.6274i 0.719103i
\(672\) 2.24264 3.88437i 0.0865117 0.149843i
\(673\) −14.3137 24.7921i −0.551753 0.955664i −0.998148 0.0608282i \(-0.980626\pi\)
0.446395 0.894836i \(-0.352708\pi\)
\(674\) −27.8359 + 16.0711i −1.07220 + 0.619034i
\(675\) −3.00000 −0.115470
\(676\) 0 0
\(677\) 49.3137 1.89528 0.947640 0.319341i \(-0.103462\pi\)
0.947640 + 0.319341i \(0.103462\pi\)
\(678\) −36.1990 + 20.8995i −1.39021 + 0.802640i
\(679\) −10.8284 18.7554i −0.415557 0.719766i
\(680\) 22.8284 39.5400i 0.875430 1.51629i
\(681\) 5.31371i 0.203622i
\(682\) 28.5533 + 16.4853i 1.09336 + 0.631254i
\(683\) −17.2695 9.97056i −0.660800 0.381513i 0.131782 0.991279i \(-0.457930\pi\)
−0.792582 + 0.609766i \(0.791264\pi\)
\(684\) 10.8284i 0.414035i
\(685\) 7.31371 12.6677i 0.279442 0.484008i
\(686\) −20.4853 35.4815i −0.782132 1.35469i
\(687\) −18.4582 + 10.6569i −0.704225 + 0.406584i
\(688\) −28.9706 −1.10449
\(689\) 0 0
\(690\) 27.3137 1.03982
\(691\) −29.5680 + 17.0711i −1.12482 + 0.649414i −0.942627 0.333849i \(-0.891652\pi\)
−0.182192 + 0.983263i \(0.558319\pi\)
\(692\) 0.656854 + 1.13770i 0.0249699 + 0.0432491i
\(693\) 2.82843 4.89898i 0.107443 0.186097i
\(694\) 75.5980i 2.86966i
\(695\) −37.5108 21.6569i −1.42286 0.821491i
\(696\) −7.64564 4.41421i −0.289807 0.167320i
\(697\) 39.5980i 1.49988i
\(698\) −9.24264 + 16.0087i −0.349839 + 0.605939i
\(699\) −13.4853 23.3572i −0.510060 0.883450i
\(700\) 28.1331 16.2426i 1.06333 0.613914i
\(701\) −38.9706 −1.47190 −0.735949 0.677037i \(-0.763264\pi\)
−0.735949 + 0.677037i \(0.763264\pi\)
\(702\) 0 0
\(703\) 10.3431 0.390099
\(704\) 17.0233 9.82843i 0.641591 0.370423i
\(705\) 0.485281 + 0.840532i 0.0182768 + 0.0316563i
\(706\) −21.0711 + 36.4962i −0.793020 + 1.37355i
\(707\) 10.3431i 0.388994i
\(708\) 12.1244 + 7.00000i 0.455661 + 0.263076i
\(709\) 35.1844 + 20.3137i 1.32138 + 0.762897i 0.983948 0.178454i \(-0.0571095\pi\)
0.337429 + 0.941351i \(0.390443\pi\)
\(710\) 13.6569i 0.512533i
\(711\) −5.65685 + 9.79796i −0.212149 + 0.367452i
\(712\) −20.2426 35.0613i −0.758625 1.31398i
\(713\) −23.6544 + 13.6569i −0.885863 + 0.511453i
\(714\) 24.9706 0.934500
\(715\) 0 0
\(716\) −2.62742 −0.0981912
\(717\) 1.73205 1.00000i 0.0646846 0.0373457i
\(718\) 1.24264 + 2.15232i 0.0463749 + 0.0803237i
\(719\) 18.9706 32.8580i 0.707483 1.22540i −0.258305 0.966063i \(-0.583164\pi\)
0.965788 0.259333i \(-0.0835026\pi\)
\(720\) 8.48528i 0.316228i
\(721\) 33.4523 + 19.3137i 1.24583 + 0.719280i
\(722\) 22.9985 + 13.2782i 0.855915 + 0.494162i
\(723\) 11.6569i 0.433523i
\(724\) −26.7990 + 46.4172i −0.995977 + 1.72508i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) −14.6354 + 8.44975i −0.543170 + 0.313600i
\(727\) 21.6569 0.803208 0.401604 0.915813i \(-0.368453\pi\)
0.401604 + 0.915813i \(0.368453\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −68.9339 + 39.7990i −2.55136 + 1.47303i
\(731\) 17.6569 + 30.5826i 0.653062 + 1.13114i
\(732\) −17.8284 + 30.8797i −0.658958 + 1.14135i
\(733\) 8.62742i 0.318661i 0.987225 + 0.159330i \(0.0509335\pi\)
−0.987225 + 0.159330i \(0.949066\pi\)
\(734\) −50.1785 28.9706i −1.85212 1.06932i
\(735\) 2.44949 + 1.41421i 0.0903508 + 0.0521641i
\(736\) 6.34315i 0.233811i
\(737\) 1.17157 2.02922i 0.0431554 0.0747474i
\(738\) −13.0711 22.6398i −0.481153 0.833381i
\(739\) −8.78335 + 5.07107i −0.323101 + 0.186542i −0.652774 0.757553i \(-0.726395\pi\)
0.329673 + 0.944095i \(0.393061\pi\)
\(740\) −39.5980 −1.45565
\(741\) 0 0
\(742\) −13.6569 −0.501359
\(743\) 1.73205 1.00000i 0.0635428 0.0366864i −0.467892 0.883786i \(-0.654986\pi\)
0.531435 + 0.847099i \(0.321653\pi\)
\(744\) −15.0711 26.1039i −0.552532 0.957014i
\(745\) −20.9706 + 36.3221i −0.768302 + 1.33074i
\(746\) 24.1421i 0.883906i
\(747\) 6.63103 + 3.82843i 0.242617 + 0.140075i
\(748\) 24.2487 + 14.0000i 0.886621 + 0.511891i
\(749\) 32.0000i 1.16925i
\(750\) −6.82843 + 11.8272i −0.249339 + 0.431868i
\(751\) 16.4853 + 28.5533i 0.601556 + 1.04193i 0.992586 + 0.121548i \(0.0387858\pi\)
−0.391029 + 0.920378i \(0.627881\pi\)
\(752\) 0.891519 0.514719i 0.0325103 0.0187699i
\(753\) 0 0
\(754\) 0 0
\(755\) −57.9411 −2.10869
\(756\) −9.37769 + 5.41421i −0.341063 + 0.196913i
\(757\) 7.97056 + 13.8054i 0.289695 + 0.501767i 0.973737 0.227676i \(-0.0731128\pi\)
−0.684042 + 0.729443i \(0.739779\pi\)
\(758\) 19.8995 34.4669i 0.722782 1.25190i
\(759\) 8.00000i 0.290382i
\(760\) 30.5826 + 17.6569i 1.10935 + 0.640481i
\(761\) 13.4361 + 7.75736i 0.487060 + 0.281204i 0.723354 0.690478i \(-0.242600\pi\)
−0.236294 + 0.971682i \(0.575933\pi\)
\(762\) 13.6569i 0.494736i
\(763\) −24.4853 + 42.4098i −0.886427 + 1.53534i
\(764\) −36.9706 64.0349i −1.33755 2.31670i
\(765\) 8.95743 5.17157i 0.323856 0.186979i
\(766\) −7.17157 −0.259119
\(767\) 0 0
\(768\) −29.9706 −1.08147
\(769\) 36.3731 21.0000i 1.31165 0.757279i 0.329278 0.944233i \(-0.393195\pi\)
0.982369 + 0.186954i \(0.0598615\pi\)
\(770\) 19.3137 + 33.4523i 0.696018 + 1.20554i
\(771\) −7.82843 + 13.5592i −0.281934 + 0.488324i
\(772\) 66.2843i 2.38562i
\(773\) −5.07306 2.92893i −0.182465 0.105346i 0.405985 0.913880i \(-0.366928\pi\)
−0.588450 + 0.808533i \(0.700262\pi\)
\(774\) −20.1903 11.6569i −0.725724 0.418997i
\(775\) 20.4853i 0.735853i
\(776\) −16.8995 + 29.2708i −0.606657 + 1.05076i
\(777\) −5.17157 8.95743i −0.185529 0.321346i
\(778\) 14.5738 8.41421i 0.522498 0.301664i
\(779\) −30.6274 −1.09734
\(780\) 0 0
\(781\) −4.00000 −0.143131
\(782\) −30.5826 + 17.6569i −1.09363 + 0.631408i
\(783\) −1.00000 1.73205i −0.0357371 0.0618984i
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i
\(785\) 28.2843i 1.00951i
\(786\) −16.7262 9.65685i −0.596602 0.344449i
\(787\) 28.3793 + 16.3848i 1.01161 + 0.584054i 0.911663 0.410938i \(-0.134799\pi\)
0.0999484 + 0.994993i \(0.468132\pi\)
\(788\) 63.1127i 2.24830i
\(789\) −6.00000 + 10.3923i −0.213606 + 0.369976i
\(790\) −38.6274 66.9046i −1.37430 2.38036i
\(791\) 42.4098 24.4853i 1.50792 0.870596i
\(792\) −8.82843 −0.313704
\(793\) 0 0
\(794\) 7.17157 0.254510
\(795\) −4.89898 + 2.82843i −0.173749 + 0.100314i
\(796\) −19.7990 34.2929i −0.701757 1.21548i
\(797\) 17.8284 30.8797i 0.631515 1.09382i −0.355727 0.934590i \(-0.615767\pi\)
0.987242 0.159227i \(-0.0509000\pi\)
\(798\) 19.3137i 0.683698i
\(799\) −1.08672 0.627417i −0.0384453 0.0221964i
\(800\) 4.11999 + 2.37868i 0.145664 + 0.0840990i
\(801\) 9.17157i 0.324062i
\(802\) −2.58579 + 4.47871i −0.0913073 + 0.158149i
\(803\) −11.6569 20.1903i −0.411361 0.712499i
\(804\) −3.88437 + 2.24264i −0.136991 + 0.0790918i
\(805\) −32.0000 −1.12785
\(806\) 0 0
\(807\) 18.0000 0.633630
\(808\) 13.9795 8.07107i 0.491797 0.283939i
\(809\) −20.6569 35.7787i −0.726256 1.25791i −0.958455 0.285244i \(-0.907925\pi\)
0.232198 0.972668i \(-0.425408\pi\)
\(810\) −3.41421 + 5.91359i −0.119963 + 0.207782i
\(811\) 1.85786i 0.0652384i −0.999468 0.0326192i \(-0.989615\pi\)
0.999468 0.0326192i \(-0.0103849\pi\)
\(812\) 18.7554 + 10.8284i 0.658185 + 0.380003i
\(813\) 10.2182 + 5.89949i 0.358369 + 0.206904i
\(814\) 17.6569i 0.618872i
\(815\) −18.6274 + 32.2636i −0.652490 + 1.13015i
\(816\) −5.48528 9.50079i −0.192023 0.332594i
\(817\) −23.6544 + 13.6569i −0.827561 + 0.477793i
\(818\) −2.48528 −0.0868958
\(819\) 0 0
\(820\) 117.255 4.09472
\(821\) 13.6823 7.89949i 0.477516 0.275694i −0.241864 0.970310i \(-0.577759\pi\)
0.719381 + 0.694616i \(0.244426\pi\)
\(822\) −6.24264 10.8126i −0.217737 0.377132i
\(823\) 24.4853 42.4098i 0.853503 1.47831i −0.0245234 0.999699i \(-0.507807\pi\)
0.878027 0.478612i \(-0.158860\pi\)
\(824\) 60.2843i 2.10010i
\(825\) 5.19615 + 3.00000i 0.180907 + 0.104447i
\(826\) −21.6251 12.4853i −0.752435 0.434418i
\(827\) 26.0000i 0.904109i 0.891990 + 0.452054i \(0.149309\pi\)
−0.891990 + 0.452054i \(0.850691\pi\)
\(828\) 7.65685 13.2621i 0.266094 0.460888i
\(829\) 2.65685 + 4.60181i 0.0922764 + 0.159827i 0.908469 0.417953i \(-0.137252\pi\)
−0.816192 + 0.577780i \(0.803919\pi\)
\(830\) −45.2795 + 26.1421i −1.57167 + 0.907407i
\(831\) 2.00000 0.0693792
\(832\) 0 0
\(833\) −3.65685 −0.126702
\(834\) −32.0174 + 18.4853i −1.10867 + 0.640093i
\(835\) −10.8284 18.7554i −0.374733 0.649057i
\(836\) −10.8284 + 18.7554i −0.374509 + 0.648669i
\(837\) 6.82843i 0.236025i
\(838\) −64.0349 36.9706i −2.21205 1.27713i
\(839\) −40.9239 23.6274i −1.41285 0.815709i −0.417194 0.908818i \(-0.636986\pi\)
−0.995656 + 0.0931087i \(0.970320\pi\)
\(840\) 35.3137i 1.21844i
\(841\) 12.5000 21.6506i 0.431034 0.746574i
\(842\) −17.7279 30.7057i −0.610945 1.05819i
\(843\) −23.2341 + 13.4142i −0.800225 + 0.462010i
\(844\) 45.9411 1.58136
\(845\) 0 0
\(846\) 0.828427 0.0284819
\(847\) 17.1464 9.89949i 0.589158 0.340151i
\(848\) 3.00000 + 5.19615i 0.103020 + 0.178437i
\(849\) −2.48528 + 4.30463i −0.0852946 + 0.147735i
\(850\) 26.4853i 0.908438i
\(851\) 12.6677 + 7.31371i 0.434244 + 0.250711i
\(852\) 6.63103 + 3.82843i 0.227175 + 0.131160i
\(853\) 7.65685i 0.262166i 0.991371 + 0.131083i \(0.0418454\pi\)
−0.991371 + 0.131083i \(0.958155\pi\)
\(854\) 31.7990 55.0775i 1.08814 1.88471i
\(855\) 4.00000 + 6.92820i 0.136797 + 0.236940i
\(856\) 43.2503 24.9706i 1.47826 0.853476i
\(857\) −29.5980 −1.01105 −0.505524 0.862813i \(-0.668701\pi\)
−0.505524 + 0.862813i \(0.668701\pi\)
\(858\) 0 0
\(859\) −23.3137 −0.795453 −0.397727 0.917504i \(-0.630201\pi\)
−0.397727 + 0.917504i \(0.630201\pi\)
\(860\) 90.5590 52.2843i 3.08804 1.78288i
\(861\) 15.3137 + 26.5241i 0.521890 + 0.903940i
\(862\) −23.7279 + 41.0980i −0.808176 + 1.39980i
\(863\) 39.6569i 1.34994i −0.737847 0.674968i \(-0.764158\pi\)
0.737847 0.674968i \(-0.235842\pi\)
\(864\) −1.37333 0.792893i −0.0467217 0.0269748i
\(865\) −0.840532 0.485281i −0.0285789 0.0165001i
\(866\) 3.17157i 0.107774i
\(867\) 1.81371 3.14144i 0.0615968 0.106689i
\(868\) 36.9706 + 64.0349i 1.25486 + 2.17349i
\(869\) 19.5959 11.3137i 0.664746 0.383791i
\(870\) 13.6569 0.463011
\(871\) 0 0
\(872\) 76.4264 2.58812
\(873\) −6.63103 + 3.82843i −0.224426 + 0.129573i
\(874\) −13.6569 23.6544i −0.461950 0.800121i
\(875\) 8.00000 13.8564i 0.270449 0.468432i
\(876\) 44.6274i 1.50782i
\(877\) 12.3705 + 7.14214i 0.417724 + 0.241173i 0.694103 0.719876i \(-0.255801\pi\)
−0.276379 + 0.961049i \(0.589135\pi\)
\(878\) 35.4815 + 20.4853i 1.19744 + 0.691345i
\(879\) 26.1421i 0.881752i
\(880\) 8.48528 14.6969i 0.286039 0.495434i
\(881\) 26.7990 + 46.4172i 0.902881 + 1.56384i 0.823737 + 0.566972i \(0.191885\pi\)
0.0791441 + 0.996863i \(0.474781\pi\)
\(882\) 2.09077 1.20711i 0.0703999 0.0406454i
\(883\) 51.5980 1.73641 0.868205 0.496205i \(-0.165274\pi\)
0.868205 + 0.496205i \(0.165274\pi\)
\(884\) 0 0
\(885\) −10.3431 −0.347681
\(886\) −87.6893 + 50.6274i −2.94598 + 1.70086i
\(887\) 4.00000 + 6.92820i 0.134307 + 0.232626i 0.925332 0.379157i \(-0.123786\pi\)
−0.791026 + 0.611783i \(0.790453\pi\)
\(888\) −8.07107 + 13.9795i −0.270847 + 0.469121i
\(889\) 16.0000i 0.536623i
\(890\) 54.2369 + 31.3137i 1.81803 + 1.04964i
\(891\) −1.73205 1.00000i −0.0580259 0.0335013i
\(892\) 17.1716i 0.574947i
\(893\) 0.485281 0.840532i 0.0162393 0.0281273i
\(894\) 17.8995 + 31.0028i 0.598649 + 1.03689i
\(895\) 1.68106 0.970563i 0.0561918 0.0324423i
\(896\) 58.1421 1.94239
\(897\) 0 0
\(898\) −18.8284 −0.628313
\(899\) −11.8272 + 6.82843i −0.394459 + 0.227741i
\(900\) −5.74264 9.94655i −0.191421 0.331552i
\(901\) 3.65685 6.33386i 0.121827 0.211011i
\(902\) 52.2843i 1.74088i
\(903\) 23.6544 + 13.6569i 0.787168 + 0.454472i
\(904\) −66.1872 38.2132i −2.20135 1.27095i
\(905\) 39.5980i 1.31628i
\(906\) −24.7279 + 42.8300i −0.821530 + 1.42293i
\(907\) 10.4853 + 18.1610i 0.348158 + 0.603027i 0.985922 0.167204i \(-0.0534739\pi\)
−0.637764 + 0.770232i \(0.720141\pi\)
\(908\) −17.6177 + 10.1716i −0.584663 + 0.337556i
\(909\) 3.65685 0.121290
\(910\) 0 0
\(911\) −40.0000 −1.32526 −0.662630 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 7.34847 4.24264i 0.243332 0.140488i
\(913\) −7.65685 13.2621i −0.253405 0.438910i
\(914\) −4.41421 + 7.64564i −0.146009 + 0.252895i
\(915\) 26.3431i 0.870878i
\(916\) −70.6659 40.7990i −2.33487 1.34804i
\(917\) 19.5959 + 11.3137i 0.647114 + 0.373612i
\(918\) 8.82843i 0.291382i
\(919\) 9.65685 16.7262i 0.318550 0.551745i −0.661636 0.749826i \(-0.730137\pi\)
0.980186 + 0.198080i \(0.0634707\pi\)
\(920\) 24.9706 + 43.2503i 0.823255 + 1.42592i
\(921\) 14.8710 8.58579i 0.490017 0.282911i
\(922\) 26.1421 0.860945
\(923\) 0 0
\(924\) 21.6569 0.712458
\(925\) 9.50079 5.48528i 0.312384 0.180355i
\(926\) −9.07107 15.7116i −0.298094 0.516314i
\(927\) 6.82843 11.8272i 0.224275 0.388456i
\(928\) 3.17157i 0.104112i
\(929\) 24.0746 + 13.8995i 0.789863 + 0.456028i 0.839914 0.542719i \(-0.182605\pi\)
−0.0500513 + 0.998747i \(0.515938\pi\)
\(930\) 40.3805 + 23.3137i 1.32413 + 0.764487i
\(931\) 2.82843i 0.0926980i
\(932\) 51.6274 89.4213i 1.69111 2.92909i
\(933\) 17.3137 + 29.9882i 0.566825 + 0.981770i
\(934\) −16.7262 + 9.65685i −0.547297 + 0.315982i
\(935\) −20.6863 −0.676514
\(936\) 0 0
\(937\) 1.31371 0.0429170 0.0214585 0.999770i \(-0.493169\pi\)
0.0214585 + 0.999770i \(0.493169\pi\)
\(938\) 6.92820 4.00000i 0.226214 0.130605i
\(939\) −3.00000 5.19615i −0.0979013 0.169570i
\(940\) −1.85786 + 3.21792i −0.0605969 + 0.104957i
\(941\) 5.85786i 0.190961i 0.995431 + 0.0954805i \(0.0304387\pi\)
−0.995431 + 0.0954805i \(0.969561\pi\)
\(942\) −20.9077 12.0711i −0.681210 0.393297i
\(943\) −37.5108 21.6569i −1.22152 0.705244i
\(944\) 10.9706i 0.357061i
\(945\) 4.00000 6.92820i 0.130120 0.225374i
\(946\) 23.3137 + 40.3805i 0.757994 + 1.31288i
\(947\) 47.6059 27.4853i 1.54698 0.893152i 0.548614 0.836076i \(-0.315156\pi\)
0.998370 0.0570760i \(-0.0181777\pi\)
\(948\) −43.3137 −1.40676
\(949\) 0 0
\(950\) −20.4853 −0.664630
\(951\) −7.34847 + 4.24264i −0.238290 + 0.137577i
\(952\) 22.8284 + 39.5400i 0.739874 + 1.28150i
\(953\) 25.8284 44.7361i 0.836665 1.44915i −0.0560029 0.998431i \(-0.517836\pi\)
0.892668 0.450715i \(-0.148831\pi\)
\(954\) 4.82843i 0.156326i
\(955\) 47.3087 + 27.3137i 1.53087 + 0.883851i
\(956\) 6.63103 + 3.82843i 0.214463 + 0.123820i
\(957\) 4.00000i 0.129302i
\(958\) 3.24264 5.61642i 0.104765 0.181458i
\(959\) 7.31371 + 12.6677i 0.236172 + 0.409062i
\(960\) 24.0746 13.8995i 0.777005 0.448604i
\(961\) −15.6274 −0.504110
\(962\) 0 0
\(963\) 11.3137 0.364579
\(964\) 38.6485 22.3137i 1.24478 0.718676i
\(965\) 24.4853 + 42.4098i 0.788209 + 1.36522i
\(966\) −13.6569 + 23.6544i −0.439402 + 0.761067i
\(967\) 10.1421i 0.326149i −0.986614 0.163075i \(-0.947859\pi\)
0.986614 0.163075i \(-0.0521411\pi\)
\(968\) −26.7597 15.4497i −0.860091 0.496574i
\(969\) −8.95743 5.17157i −0.287754 0.166135i
\(970\) 52.2843i 1.67875i
\(971\) −3.65685 + 6.33386i −0.117354 + 0.203263i −0.918718 0.394913i \(-0.870775\pi\)
0.801364 + 0.598177i \(0.204108\pi\)
\(972\) 1.91421 + 3.31552i 0.0613984 + 0.106345i
\(973\) 37.5108 21.6569i 1.20254 0.694287i
\(974\) 76.7696 2.45986
\(975\) 0 0
\(976\) −27.9411 −0.894374
\(977\) 12.0013 6.92893i 0.383954 0.221676i −0.295583 0.955317i \(-0.595514\pi\)
0.679537 + 0.733641i \(0.262181\pi\)
\(978\) 15.8995 + 27.5387i 0.508410 + 0.880592i
\(979\) −9.17157 + 15.8856i −0.293125 + 0.507707i
\(980\) 10.8284i 0.345901i
\(981\) 14.9941 + 8.65685i 0.478725 + 0.276392i
\(982\) 30.5826 + 17.6569i 0.975929 + 0.563453i
\(983\) 2.68629i 0.0856794i −0.999082 0.0428397i \(-0.986360\pi\)
0.999082 0.0428397i \(-0.0136405\pi\)
\(984\) 23.8995 41.3951i 0.761888 1.31963i
\(985\) −23.3137 40.3805i −0.742837 1.28663i
\(986\) −15.2913 + 8.82843i −0.486974 + 0.281154i
\(987\) −0.970563 −0.0308934
\(988\) 0 0
\(989\) −38.6274 −1.22828
\(990\) 11.8272 6.82843i 0.375893 0.217022i
\(991\) −13.6569 23.6544i −0.433824 0.751406i 0.563375 0.826202i \(-0.309503\pi\)
−0.997199 + 0.0747959i \(0.976169\pi\)
\(992\) −5.41421 + 9.37769i −0.171901 + 0.297742i
\(993\) 2.14214i 0.0679786i
\(994\) −11.8272 6.82843i −0.375135 0.216585i
\(995\) 25.3354 + 14.6274i 0.803187 + 0.463720i
\(996\) 29.3137i 0.928840i
\(997\) −25.6274 + 44.3880i −0.811628 + 1.40578i 0.100095 + 0.994978i \(0.468085\pi\)
−0.911724 + 0.410804i \(0.865248\pi\)
\(998\) 2.58579 + 4.47871i 0.0818516 + 0.141771i
\(999\) −3.16693 + 1.82843i −0.100197 + 0.0578489i
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 507.2.j.f.361.1 8
13.2 odd 12 39.2.a.b.1.1 2
13.3 even 3 507.2.b.e.337.1 4
13.4 even 6 inner 507.2.j.f.316.1 8
13.5 odd 4 507.2.e.h.484.2 4
13.6 odd 12 507.2.e.h.22.2 4
13.7 odd 12 507.2.e.d.22.1 4
13.8 odd 4 507.2.e.d.484.1 4
13.9 even 3 inner 507.2.j.f.316.4 8
13.10 even 6 507.2.b.e.337.4 4
13.11 odd 12 507.2.a.h.1.2 2
13.12 even 2 inner 507.2.j.f.361.4 8
39.2 even 12 117.2.a.c.1.2 2
39.11 even 12 1521.2.a.f.1.1 2
39.23 odd 6 1521.2.b.j.1351.1 4
39.29 odd 6 1521.2.b.j.1351.4 4
52.11 even 12 8112.2.a.bm.1.1 2
52.15 even 12 624.2.a.k.1.2 2
65.2 even 12 975.2.c.h.274.1 4
65.28 even 12 975.2.c.h.274.4 4
65.54 odd 12 975.2.a.l.1.2 2
91.41 even 12 1911.2.a.h.1.1 2
104.67 even 12 2496.2.a.bi.1.1 2
104.93 odd 12 2496.2.a.bf.1.1 2
117.2 even 12 1053.2.e.e.352.1 4
117.41 even 12 1053.2.e.e.703.1 4
117.67 odd 12 1053.2.e.m.703.2 4
117.106 odd 12 1053.2.e.m.352.2 4
143.54 even 12 4719.2.a.p.1.2 2
156.119 odd 12 1872.2.a.w.1.1 2
195.2 odd 12 2925.2.c.u.2224.4 4
195.119 even 12 2925.2.a.v.1.1 2
195.158 odd 12 2925.2.c.u.2224.1 4
273.41 odd 12 5733.2.a.u.1.2 2
312.197 even 12 7488.2.a.cl.1.2 2
312.275 odd 12 7488.2.a.co.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.a.b.1.1 2 13.2 odd 12
117.2.a.c.1.2 2 39.2 even 12
507.2.a.h.1.2 2 13.11 odd 12
507.2.b.e.337.1 4 13.3 even 3
507.2.b.e.337.4 4 13.10 even 6
507.2.e.d.22.1 4 13.7 odd 12
507.2.e.d.484.1 4 13.8 odd 4
507.2.e.h.22.2 4 13.6 odd 12
507.2.e.h.484.2 4 13.5 odd 4
507.2.j.f.316.1 8 13.4 even 6 inner
507.2.j.f.316.4 8 13.9 even 3 inner
507.2.j.f.361.1 8 1.1 even 1 trivial
507.2.j.f.361.4 8 13.12 even 2 inner
624.2.a.k.1.2 2 52.15 even 12
975.2.a.l.1.2 2 65.54 odd 12
975.2.c.h.274.1 4 65.2 even 12
975.2.c.h.274.4 4 65.28 even 12
1053.2.e.e.352.1 4 117.2 even 12
1053.2.e.e.703.1 4 117.41 even 12
1053.2.e.m.352.2 4 117.106 odd 12
1053.2.e.m.703.2 4 117.67 odd 12
1521.2.a.f.1.1 2 39.11 even 12
1521.2.b.j.1351.1 4 39.23 odd 6
1521.2.b.j.1351.4 4 39.29 odd 6
1872.2.a.w.1.1 2 156.119 odd 12
1911.2.a.h.1.1 2 91.41 even 12
2496.2.a.bf.1.1 2 104.93 odd 12
2496.2.a.bi.1.1 2 104.67 even 12
2925.2.a.v.1.1 2 195.119 even 12
2925.2.c.u.2224.1 4 195.158 odd 12
2925.2.c.u.2224.4 4 195.2 odd 12
4719.2.a.p.1.2 2 143.54 even 12
5733.2.a.u.1.2 2 273.41 odd 12
7488.2.a.cl.1.2 2 312.197 even 12
7488.2.a.co.1.2 2 312.275 odd 12
8112.2.a.bm.1.1 2 52.11 even 12