Properties

Label 48.3.l.a.43.1
Level $48$
Weight $3$
Character 48.43
Analytic conductor $1.308$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,3,Mod(19,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), 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: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(1.84258 - 0.777752i\) of defining polynomial
Character \(\chi\) \(=\) 48.43
Dual form 48.3.l.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.84258 - 0.777752i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.79020 + 2.86614i) q^{4} +(-4.78830 - 4.78830i) q^{5} +(1.30414 + 3.20924i) q^{6} -10.3302 q^{7} +(-2.91202 - 7.45118i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.84258 - 0.777752i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.79020 + 2.86614i) q^{4} +(-4.78830 - 4.78830i) q^{5} +(1.30414 + 3.20924i) q^{6} -10.3302 q^{7} +(-2.91202 - 7.45118i) q^{8} +3.00000i q^{9} +(5.09872 + 12.5469i) q^{10} +(-0.526169 + 0.526169i) q^{11} +(0.0930056 - 6.92758i) q^{12} +(17.2840 - 17.2840i) q^{13} +(19.0343 + 8.03437i) q^{14} +11.7289i q^{15} +(-0.429536 + 15.9942i) q^{16} +4.71650 q^{17} +(2.33326 - 5.52774i) q^{18} +(-2.53604 - 2.53604i) q^{19} +(0.363618 - 27.0843i) q^{20} +(12.6519 + 12.6519i) q^{21} +(1.37874 - 0.560279i) q^{22} -12.5864 q^{23} +(-5.55931 + 12.6923i) q^{24} +20.8557i q^{25} +(-45.2897 + 18.4044i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-28.8235 - 29.6080i) q^{28} +(-2.19683 + 2.19683i) q^{29} +(9.12218 - 21.6114i) q^{30} -28.0521i q^{31} +(13.2310 - 29.1366i) q^{32} +1.28884 q^{33} +(-8.69052 - 3.66827i) q^{34} +(49.4644 + 49.4644i) q^{35} +(-8.59842 + 8.37061i) q^{36} +(-32.1128 - 32.1128i) q^{37} +(2.70044 + 6.64526i) q^{38} -42.3369 q^{39} +(-21.7349 + 49.6222i) q^{40} +23.1145i q^{41} +(-13.4721 - 33.1522i) q^{42} +(4.79441 - 4.79441i) q^{43} +(-2.97619 - 0.0399566i) q^{44} +(14.3649 - 14.3649i) q^{45} +(23.1915 + 9.78913i) q^{46} +39.0095i q^{47} +(20.1149 - 19.0628i) q^{48} +57.7141 q^{49} +(16.2206 - 38.4283i) q^{50} +(-5.77651 - 5.77651i) q^{51} +(97.7640 + 1.31252i) q^{52} +(-27.9768 - 27.9768i) q^{53} +(-9.62772 + 3.91243i) q^{54} +5.03891 q^{55} +(30.0819 + 76.9726i) q^{56} +6.21200i q^{57} +(5.75642 - 2.33924i) q^{58} +(79.8538 - 79.8538i) q^{59} +(-33.6167 + 32.7260i) q^{60} +(-36.7762 + 36.7762i) q^{61} +(-21.8176 + 51.6883i) q^{62} -30.9907i q^{63} +(-47.0402 + 43.3960i) q^{64} -165.522 q^{65} +(-2.37480 - 1.00240i) q^{66} +(-10.9869 - 10.9869i) q^{67} +(13.1600 + 13.5181i) q^{68} +(15.4152 + 15.4152i) q^{69} +(-52.6711 - 129.613i) q^{70} +52.6605 q^{71} +(22.3535 - 8.73607i) q^{72} +67.8061i q^{73} +(34.1946 + 84.1462i) q^{74} +(25.5429 - 25.5429i) q^{75} +(0.192584 - 14.3447i) q^{76} +(5.43545 - 5.43545i) q^{77} +(78.0091 + 32.9276i) q^{78} -56.4602i q^{79} +(78.6420 - 74.5285i) q^{80} -9.00000 q^{81} +(17.9773 - 42.5903i) q^{82} +(-58.3697 - 58.3697i) q^{83} +(-0.960771 + 71.5636i) q^{84} +(-22.5840 - 22.5840i) q^{85} +(-12.5629 + 5.10522i) q^{86} +5.38110 q^{87} +(5.45279 + 2.38836i) q^{88} -131.566i q^{89} +(-37.6408 + 15.2962i) q^{90} +(-178.548 + 178.548i) q^{91} +(-35.1187 - 36.0745i) q^{92} +(-34.3567 + 34.3567i) q^{93} +(30.3397 - 71.8781i) q^{94} +24.2866i q^{95} +(-51.8895 + 19.4803i) q^{96} +60.9413 q^{97} +(-106.343 - 44.8872i) q^{98} +(-1.57851 - 1.57851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84258 0.777752i −0.921290 0.388876i
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 2.79020 + 2.86614i 0.697551 + 0.716535i
\(5\) −4.78830 4.78830i −0.957661 0.957661i 0.0414785 0.999139i \(-0.486793\pi\)
−0.999139 + 0.0414785i \(0.986793\pi\)
\(6\) 1.30414 + 3.20924i 0.217357 + 0.534873i
\(7\) −10.3302 −1.47575 −0.737875 0.674937i \(-0.764171\pi\)
−0.737875 + 0.674937i \(0.764171\pi\)
\(8\) −2.91202 7.45118i −0.364003 0.931398i
\(9\) 3.00000i 0.333333i
\(10\) 5.09872 + 12.5469i 0.509872 + 1.25469i
\(11\) −0.526169 + 0.526169i −0.0478335 + 0.0478335i −0.730619 0.682785i \(-0.760768\pi\)
0.682785 + 0.730619i \(0.260768\pi\)
\(12\) 0.0930056 6.92758i 0.00775047 0.577298i
\(13\) 17.2840 17.2840i 1.32953 1.32953i 0.423761 0.905774i \(-0.360710\pi\)
0.905774 0.423761i \(-0.139290\pi\)
\(14\) 19.0343 + 8.03437i 1.35959 + 0.573884i
\(15\) 11.7289i 0.781927i
\(16\) −0.429536 + 15.9942i −0.0268460 + 0.999640i
\(17\) 4.71650 0.277441 0.138721 0.990332i \(-0.455701\pi\)
0.138721 + 0.990332i \(0.455701\pi\)
\(18\) 2.33326 5.52774i 0.129625 0.307097i
\(19\) −2.53604 2.53604i −0.133476 0.133476i 0.637213 0.770688i \(-0.280087\pi\)
−0.770688 + 0.637213i \(0.780087\pi\)
\(20\) 0.363618 27.0843i 0.0181809 1.35422i
\(21\) 12.6519 + 12.6519i 0.602472 + 0.602472i
\(22\) 1.37874 0.560279i 0.0626698 0.0254672i
\(23\) −12.5864 −0.547236 −0.273618 0.961838i \(-0.588220\pi\)
−0.273618 + 0.961838i \(0.588220\pi\)
\(24\) −5.55931 + 12.6923i −0.231638 + 0.528845i
\(25\) 20.8557i 0.834229i
\(26\) −45.2897 + 18.4044i −1.74191 + 0.707863i
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −28.8235 29.6080i −1.02941 1.05743i
\(29\) −2.19683 + 2.19683i −0.0757526 + 0.0757526i −0.743968 0.668215i \(-0.767058\pi\)
0.668215 + 0.743968i \(0.267058\pi\)
\(30\) 9.12218 21.6114i 0.304073 0.720381i
\(31\) 28.0521i 0.904908i −0.891788 0.452454i \(-0.850549\pi\)
0.891788 0.452454i \(-0.149451\pi\)
\(32\) 13.2310 29.1366i 0.413469 0.910518i
\(33\) 1.28884 0.0390559
\(34\) −8.69052 3.66827i −0.255604 0.107890i
\(35\) 49.4644 + 49.4644i 1.41327 + 1.41327i
\(36\) −8.59842 + 8.37061i −0.238845 + 0.232517i
\(37\) −32.1128 32.1128i −0.867914 0.867914i 0.124327 0.992241i \(-0.460323\pi\)
−0.992241 + 0.124327i \(0.960323\pi\)
\(38\) 2.70044 + 6.64526i 0.0710643 + 0.174875i
\(39\) −42.3369 −1.08556
\(40\) −21.7349 + 49.6222i −0.543372 + 1.24055i
\(41\) 23.1145i 0.563768i 0.959449 + 0.281884i \(0.0909593\pi\)
−0.959449 + 0.281884i \(0.909041\pi\)
\(42\) −13.4721 33.1522i −0.320765 0.789339i
\(43\) 4.79441 4.79441i 0.111498 0.111498i −0.649157 0.760655i \(-0.724878\pi\)
0.760655 + 0.649157i \(0.224878\pi\)
\(44\) −2.97619 0.0399566i −0.0676407 0.000908104i
\(45\) 14.3649 14.3649i 0.319220 0.319220i
\(46\) 23.1915 + 9.78913i 0.504163 + 0.212807i
\(47\) 39.0095i 0.829989i 0.909824 + 0.414994i \(0.136216\pi\)
−0.909824 + 0.414994i \(0.863784\pi\)
\(48\) 20.1149 19.0628i 0.419061 0.397141i
\(49\) 57.7141 1.17784
\(50\) 16.2206 38.4283i 0.324412 0.768567i
\(51\) −5.77651 5.77651i −0.113265 0.113265i
\(52\) 97.7640 + 1.31252i 1.88008 + 0.0252408i
\(53\) −27.9768 27.9768i −0.527864 0.527864i 0.392071 0.919935i \(-0.371759\pi\)
−0.919935 + 0.392071i \(0.871759\pi\)
\(54\) −9.62772 + 3.91243i −0.178291 + 0.0724524i
\(55\) 5.03891 0.0916166
\(56\) 30.0819 + 76.9726i 0.537177 + 1.37451i
\(57\) 6.21200i 0.108982i
\(58\) 5.75642 2.33924i 0.0992485 0.0403318i
\(59\) 79.8538 79.8538i 1.35345 1.35345i 0.471691 0.881764i \(-0.343644\pi\)
0.881764 0.471691i \(-0.156356\pi\)
\(60\) −33.6167 + 32.7260i −0.560278 + 0.545434i
\(61\) −36.7762 + 36.7762i −0.602888 + 0.602888i −0.941078 0.338190i \(-0.890185\pi\)
0.338190 + 0.941078i \(0.390185\pi\)
\(62\) −21.8176 + 51.6883i −0.351897 + 0.833682i
\(63\) 30.9907i 0.491917i
\(64\) −47.0402 + 43.3960i −0.735004 + 0.678063i
\(65\) −165.522 −2.54649
\(66\) −2.37480 1.00240i −0.0359818 0.0151879i
\(67\) −10.9869 10.9869i −0.163984 0.163984i 0.620345 0.784329i \(-0.286992\pi\)
−0.784329 + 0.620345i \(0.786992\pi\)
\(68\) 13.1600 + 13.5181i 0.193529 + 0.198796i
\(69\) 15.4152 + 15.4152i 0.223408 + 0.223408i
\(70\) −52.6711 129.613i −0.752444 1.85162i
\(71\) 52.6605 0.741697 0.370849 0.928693i \(-0.379067\pi\)
0.370849 + 0.928693i \(0.379067\pi\)
\(72\) 22.3535 8.73607i 0.310466 0.121334i
\(73\) 67.8061i 0.928850i 0.885612 + 0.464425i \(0.153739\pi\)
−0.885612 + 0.464425i \(0.846261\pi\)
\(74\) 34.1946 + 84.1462i 0.462089 + 1.13711i
\(75\) 25.5429 25.5429i 0.340573 0.340573i
\(76\) 0.192584 14.3447i 0.00253399 0.188746i
\(77\) 5.43545 5.43545i 0.0705903 0.0705903i
\(78\) 78.0091 + 32.9276i 1.00012 + 0.422149i
\(79\) 56.4602i 0.714686i −0.933973 0.357343i \(-0.883683\pi\)
0.933973 0.357343i \(-0.116317\pi\)
\(80\) 78.6420 74.5285i 0.983025 0.931606i
\(81\) −9.00000 −0.111111
\(82\) 17.9773 42.5903i 0.219236 0.519394i
\(83\) −58.3697 58.3697i −0.703249 0.703249i 0.261857 0.965107i \(-0.415665\pi\)
−0.965107 + 0.261857i \(0.915665\pi\)
\(84\) −0.960771 + 71.5636i −0.0114378 + 0.851948i
\(85\) −22.5840 22.5840i −0.265694 0.265694i
\(86\) −12.5629 + 5.10522i −0.146081 + 0.0593630i
\(87\) 5.38110 0.0618518
\(88\) 5.45279 + 2.38836i 0.0619636 + 0.0271405i
\(89\) 131.566i 1.47827i −0.673558 0.739135i \(-0.735235\pi\)
0.673558 0.739135i \(-0.264765\pi\)
\(90\) −37.6408 + 15.2962i −0.418232 + 0.169957i
\(91\) −178.548 + 178.548i −1.96206 + 1.96206i
\(92\) −35.1187 36.0745i −0.381725 0.392114i
\(93\) −34.3567 + 34.3567i −0.369427 + 0.369427i
\(94\) 30.3397 71.8781i 0.322763 0.764661i
\(95\) 24.2866i 0.255649i
\(96\) −51.8895 + 19.4803i −0.540515 + 0.202920i
\(97\) 60.9413 0.628261 0.314131 0.949380i \(-0.398287\pi\)
0.314131 + 0.949380i \(0.398287\pi\)
\(98\) −106.343 44.8872i −1.08513 0.458033i
\(99\) −1.57851 1.57851i −0.0159445 0.0159445i
\(100\) −59.7755 + 58.1917i −0.597755 + 0.581917i
\(101\) 109.986 + 109.986i 1.08897 + 1.08897i 0.995635 + 0.0933326i \(0.0297520\pi\)
0.0933326 + 0.995635i \(0.470248\pi\)
\(102\) 6.15098 + 15.1364i 0.0603038 + 0.148396i
\(103\) 173.295 1.68248 0.841239 0.540663i \(-0.181826\pi\)
0.841239 + 0.540663i \(0.181826\pi\)
\(104\) −179.117 78.4546i −1.72228 0.754371i
\(105\) 121.162i 1.15393i
\(106\) 29.7905 + 73.3085i 0.281042 + 0.691589i
\(107\) −25.4747 + 25.4747i −0.238081 + 0.238081i −0.816055 0.577974i \(-0.803844\pi\)
0.577974 + 0.816055i \(0.303844\pi\)
\(108\) 20.7827 + 0.279017i 0.192433 + 0.00258349i
\(109\) 33.0605 33.0605i 0.303307 0.303307i −0.538999 0.842306i \(-0.681197\pi\)
0.842306 + 0.538999i \(0.181197\pi\)
\(110\) −9.28460 3.91902i −0.0844054 0.0356275i
\(111\) 78.6600i 0.708649i
\(112\) 4.43721 165.224i 0.0396180 1.47522i
\(113\) 140.159 1.24034 0.620171 0.784466i \(-0.287063\pi\)
0.620171 + 0.784466i \(0.287063\pi\)
\(114\) 4.83139 11.4461i 0.0423806 0.100404i
\(115\) 60.2677 + 60.2677i 0.524067 + 0.524067i
\(116\) −12.4260 0.166824i −0.107121 0.00143814i
\(117\) 51.8519 + 51.8519i 0.443178 + 0.443178i
\(118\) −209.244 + 85.0306i −1.77325 + 0.720598i
\(119\) −48.7226 −0.409434
\(120\) 87.3942 34.1548i 0.728285 0.284624i
\(121\) 120.446i 0.995424i
\(122\) 96.3658 39.1603i 0.789883 0.320986i
\(123\) 28.3093 28.3093i 0.230157 0.230157i
\(124\) 80.4014 78.2712i 0.648398 0.631219i
\(125\) −19.8441 + 19.8441i −0.158752 + 0.158752i
\(126\) −24.1031 + 57.1029i −0.191295 + 0.453198i
\(127\) 40.8458i 0.321620i 0.986985 + 0.160810i \(0.0514107\pi\)
−0.986985 + 0.160810i \(0.948589\pi\)
\(128\) 120.427 43.3750i 0.940834 0.338868i
\(129\) −11.7439 −0.0910377
\(130\) 304.987 + 128.735i 2.34605 + 0.990268i
\(131\) −75.0168 75.0168i −0.572647 0.572647i 0.360220 0.932867i \(-0.382702\pi\)
−0.932867 + 0.360220i \(0.882702\pi\)
\(132\) 3.59614 + 3.69401i 0.0272435 + 0.0279849i
\(133\) 26.1979 + 26.1979i 0.196977 + 0.196977i
\(134\) 11.6992 + 28.7893i 0.0873071 + 0.214846i
\(135\) −35.1867 −0.260642
\(136\) −13.7346 35.1435i −0.100989 0.258408i
\(137\) 134.028i 0.978308i −0.872197 0.489154i \(-0.837306\pi\)
0.872197 0.489154i \(-0.162694\pi\)
\(138\) −16.4145 40.3929i −0.118946 0.292702i
\(139\) 22.8798 22.8798i 0.164603 0.164603i −0.619999 0.784602i \(-0.712867\pi\)
0.784602 + 0.619999i \(0.212867\pi\)
\(140\) −3.75626 + 279.788i −0.0268305 + 1.99848i
\(141\) 47.7767 47.7767i 0.338842 0.338842i
\(142\) −97.0312 40.9568i −0.683318 0.288428i
\(143\) 18.1885i 0.127193i
\(144\) −47.9827 1.28861i −0.333213 0.00894866i
\(145\) 21.0381 0.145091
\(146\) 52.7363 124.938i 0.361208 0.855740i
\(147\) −70.6850 70.6850i −0.480850 0.480850i
\(148\) 2.43861 181.641i 0.0164771 1.22730i
\(149\) −9.32124 9.32124i −0.0625587 0.0625587i 0.675135 0.737694i \(-0.264085\pi\)
−0.737694 + 0.675135i \(0.764085\pi\)
\(150\) −66.9310 + 27.1988i −0.446207 + 0.181326i
\(151\) −50.5403 −0.334704 −0.167352 0.985897i \(-0.553522\pi\)
−0.167352 + 0.985897i \(0.553522\pi\)
\(152\) −11.5115 + 26.2815i −0.0757334 + 0.172904i
\(153\) 14.1495i 0.0924803i
\(154\) −14.2427 + 5.78782i −0.0924850 + 0.0375833i
\(155\) −134.322 + 134.322i −0.866595 + 0.866595i
\(156\) −118.128 121.343i −0.757234 0.777843i
\(157\) −95.8844 + 95.8844i −0.610729 + 0.610729i −0.943136 0.332407i \(-0.892139\pi\)
0.332407 + 0.943136i \(0.392139\pi\)
\(158\) −43.9120 + 104.032i −0.277924 + 0.658433i
\(159\) 68.5288i 0.430999i
\(160\) −202.869 + 76.1608i −1.26793 + 0.476005i
\(161\) 130.021 0.807584
\(162\) 16.5832 + 6.99977i 0.102366 + 0.0432085i
\(163\) −140.885 140.885i −0.864324 0.864324i 0.127513 0.991837i \(-0.459301\pi\)
−0.991837 + 0.127513i \(0.959301\pi\)
\(164\) −66.2494 + 64.4941i −0.403959 + 0.393257i
\(165\) −6.17138 6.17138i −0.0374023 0.0374023i
\(166\) 62.1537 + 152.948i 0.374420 + 0.921374i
\(167\) −107.849 −0.645800 −0.322900 0.946433i \(-0.604658\pi\)
−0.322900 + 0.946433i \(0.604658\pi\)
\(168\) 57.4291 131.114i 0.341840 0.780443i
\(169\) 428.470i 2.53533i
\(170\) 24.0481 + 59.1777i 0.141459 + 0.348104i
\(171\) 7.60811 7.60811i 0.0444919 0.0444919i
\(172\) 27.1188 + 0.364082i 0.157668 + 0.00211675i
\(173\) −53.8845 + 53.8845i −0.311471 + 0.311471i −0.845479 0.534008i \(-0.820685\pi\)
0.534008 + 0.845479i \(0.320685\pi\)
\(174\) −9.91511 4.18517i −0.0569834 0.0240527i
\(175\) 215.445i 1.23111i
\(176\) −8.18965 8.64167i −0.0465321 0.0491004i
\(177\) −195.601 −1.10509
\(178\) −102.326 + 242.421i −0.574864 + 1.36191i
\(179\) 104.178 + 104.178i 0.582002 + 0.582002i 0.935453 0.353451i \(-0.114992\pi\)
−0.353451 + 0.935453i \(0.614992\pi\)
\(180\) 81.2529 + 1.09085i 0.451405 + 0.00606030i
\(181\) −205.498 205.498i −1.13535 1.13535i −0.989274 0.146073i \(-0.953336\pi\)
−0.146073 0.989274i \(-0.546664\pi\)
\(182\) 467.854 190.122i 2.57063 1.04463i
\(183\) 90.0828 0.492256
\(184\) 36.6520 + 93.7838i 0.199196 + 0.509695i
\(185\) 307.532i 1.66233i
\(186\) 90.0260 36.5840i 0.484011 0.196688i
\(187\) −2.48167 + 2.48167i −0.0132710 + 0.0132710i
\(188\) −111.807 + 108.844i −0.594716 + 0.578959i
\(189\) −37.9558 + 37.9558i −0.200824 + 0.200824i
\(190\) 18.8890 44.7501i 0.0994157 0.235527i
\(191\) 248.255i 1.29977i −0.760034 0.649883i \(-0.774818\pi\)
0.760034 0.649883i \(-0.225182\pi\)
\(192\) 110.761 + 4.46320i 0.576882 + 0.0232458i
\(193\) −129.921 −0.673166 −0.336583 0.941654i \(-0.609271\pi\)
−0.336583 + 0.941654i \(0.609271\pi\)
\(194\) −112.289 47.3973i −0.578811 0.244316i
\(195\) 202.722 + 202.722i 1.03960 + 1.03960i
\(196\) 161.034 + 165.417i 0.821602 + 0.843963i
\(197\) 237.001 + 237.001i 1.20305 + 1.20305i 0.973234 + 0.229816i \(0.0738123\pi\)
0.229816 + 0.973234i \(0.426188\pi\)
\(198\) 1.68084 + 4.13621i 0.00848907 + 0.0208899i
\(199\) 246.508 1.23873 0.619366 0.785102i \(-0.287390\pi\)
0.619366 + 0.785102i \(0.287390\pi\)
\(200\) 155.400 60.7324i 0.776999 0.303662i
\(201\) 26.9123i 0.133892i
\(202\) −117.116 288.199i −0.579781 1.42673i
\(203\) 22.6938 22.6938i 0.111792 0.111792i
\(204\) 0.438661 32.6739i 0.00215030 0.160166i
\(205\) 110.679 110.679i 0.539898 0.539898i
\(206\) −319.311 134.781i −1.55005 0.654276i
\(207\) 37.7593i 0.182412i
\(208\) 269.020 + 283.868i 1.29336 + 1.36475i
\(209\) 2.66877 0.0127692
\(210\) −94.2344 + 223.252i −0.448735 + 1.06310i
\(211\) −13.4139 13.4139i −0.0635728 0.0635728i 0.674606 0.738178i \(-0.264314\pi\)
−0.738178 + 0.674606i \(0.764314\pi\)
\(212\) 2.12452 158.246i 0.0100213 0.746445i
\(213\) −64.4957 64.4957i −0.302797 0.302797i
\(214\) 66.7522 27.1262i 0.311926 0.126758i
\(215\) −45.9142 −0.213554
\(216\) −38.0769 16.6779i −0.176282 0.0772126i
\(217\) 289.786i 1.33542i
\(218\) −86.6295 + 35.2037i −0.397383 + 0.161485i
\(219\) 83.0451 83.0451i 0.379201 0.379201i
\(220\) 14.0596 + 14.4422i 0.0639072 + 0.0656465i
\(221\) 81.5197 81.5197i 0.368867 0.368867i
\(222\) 61.1780 144.937i 0.275577 0.652871i
\(223\) 295.580i 1.32547i 0.748854 + 0.662735i \(0.230604\pi\)
−0.748854 + 0.662735i \(0.769396\pi\)
\(224\) −136.680 + 300.988i −0.610177 + 1.34370i
\(225\) −62.5672 −0.278076
\(226\) −258.254 109.009i −1.14272 0.482340i
\(227\) −97.0742 97.0742i −0.427640 0.427640i 0.460184 0.887824i \(-0.347783\pi\)
−0.887824 + 0.460184i \(0.847783\pi\)
\(228\) −17.8045 + 17.3327i −0.0780897 + 0.0760207i
\(229\) 34.2565 + 34.2565i 0.149592 + 0.149592i 0.777936 0.628344i \(-0.216267\pi\)
−0.628344 + 0.777936i \(0.716267\pi\)
\(230\) −64.1747 157.921i −0.279021 0.686615i
\(231\) −13.3141 −0.0576367
\(232\) 22.7662 + 9.97174i 0.0981300 + 0.0429816i
\(233\) 62.8176i 0.269604i 0.990873 + 0.134802i \(0.0430398\pi\)
−0.990873 + 0.134802i \(0.956960\pi\)
\(234\) −55.2133 135.869i −0.235954 0.580637i
\(235\) 186.789 186.789i 0.794848 0.794848i
\(236\) 451.681 + 6.06400i 1.91390 + 0.0256949i
\(237\) −69.1493 + 69.1493i −0.291769 + 0.291769i
\(238\) 89.7753 + 37.8941i 0.377207 + 0.159219i
\(239\) 355.910i 1.48916i 0.667532 + 0.744581i \(0.267351\pi\)
−0.667532 + 0.744581i \(0.732649\pi\)
\(240\) −187.595 5.03798i −0.781645 0.0209916i
\(241\) 66.2545 0.274915 0.137458 0.990508i \(-0.456107\pi\)
0.137458 + 0.990508i \(0.456107\pi\)
\(242\) 93.6774 221.932i 0.387097 0.917074i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) −208.019 2.79274i −0.852535 0.0114456i
\(245\) −276.352 276.352i −1.12797 1.12797i
\(246\) −74.1799 + 30.1446i −0.301544 + 0.122539i
\(247\) −87.6655 −0.354921
\(248\) −209.022 + 81.6885i −0.842829 + 0.329389i
\(249\) 142.976i 0.574201i
\(250\) 51.9980 21.1305i 0.207992 0.0845220i
\(251\) 325.395 325.395i 1.29640 1.29640i 0.365638 0.930757i \(-0.380851\pi\)
0.930757 0.365638i \(-0.119149\pi\)
\(252\) 88.8239 86.4705i 0.352476 0.343137i
\(253\) 6.62259 6.62259i 0.0261762 0.0261762i
\(254\) 31.7679 75.2616i 0.125070 0.296306i
\(255\) 55.3193i 0.216939i
\(256\) −255.631 13.7402i −0.998559 0.0536726i
\(257\) −312.011 −1.21405 −0.607026 0.794682i \(-0.707638\pi\)
−0.607026 + 0.794682i \(0.707638\pi\)
\(258\) 21.6390 + 9.13381i 0.0838721 + 0.0354024i
\(259\) 331.733 + 331.733i 1.28082 + 1.28082i
\(260\) −461.839 474.409i −1.77630 1.82465i
\(261\) −6.59048 6.59048i −0.0252509 0.0252509i
\(262\) 79.8800 + 196.569i 0.304885 + 0.750263i
\(263\) −168.163 −0.639403 −0.319702 0.947518i \(-0.603583\pi\)
−0.319702 + 0.947518i \(0.603583\pi\)
\(264\) −3.75315 9.60342i −0.0142165 0.0363766i
\(265\) 267.923i 1.01103i
\(266\) −27.8962 68.6472i −0.104873 0.258072i
\(267\) −161.135 + 161.135i −0.603501 + 0.603501i
\(268\) 0.834331 62.1457i 0.00311318 0.231887i
\(269\) 212.116 212.116i 0.788535 0.788535i −0.192719 0.981254i \(-0.561731\pi\)
0.981254 + 0.192719i \(0.0617306\pi\)
\(270\) 64.8343 + 27.3665i 0.240127 + 0.101358i
\(271\) 173.450i 0.640037i −0.947411 0.320019i \(-0.896311\pi\)
0.947411 0.320019i \(-0.103689\pi\)
\(272\) −2.02590 + 75.4368i −0.00744818 + 0.277341i
\(273\) 437.350 1.60202
\(274\) −104.241 + 246.958i −0.380441 + 0.901305i
\(275\) −10.9736 10.9736i −0.0399041 0.0399041i
\(276\) −1.17061 + 87.1935i −0.00424134 + 0.315919i
\(277\) −38.4049 38.4049i −0.138646 0.138646i 0.634377 0.773023i \(-0.281257\pi\)
−0.773023 + 0.634377i \(0.781257\pi\)
\(278\) −59.9526 + 24.3630i −0.215657 + 0.0876368i
\(279\) 84.1564 0.301636
\(280\) 224.527 512.610i 0.801881 1.83075i
\(281\) 223.573i 0.795632i 0.917465 + 0.397816i \(0.130232\pi\)
−0.917465 + 0.397816i \(0.869768\pi\)
\(282\) −125.191 + 50.8739i −0.443939 + 0.180404i
\(283\) 247.755 247.755i 0.875459 0.875459i −0.117602 0.993061i \(-0.537521\pi\)
0.993061 + 0.117602i \(0.0375206\pi\)
\(284\) 146.933 + 150.932i 0.517371 + 0.531452i
\(285\) 29.7449 29.7449i 0.104368 0.104368i
\(286\) 14.1462 33.5139i 0.0494622 0.117181i
\(287\) 238.778i 0.831980i
\(288\) 87.4098 + 39.6930i 0.303506 + 0.137823i
\(289\) −266.755 −0.923026
\(290\) −38.7645 16.3625i −0.133671 0.0564223i
\(291\) −74.6376 74.6376i −0.256487 0.256487i
\(292\) −194.342 + 189.193i −0.665554 + 0.647920i
\(293\) −102.262 102.262i −0.349016 0.349016i 0.510727 0.859743i \(-0.329376\pi\)
−0.859743 + 0.510727i \(0.829376\pi\)
\(294\) 75.2674 + 185.218i 0.256011 + 0.629994i
\(295\) −764.729 −2.59230
\(296\) −145.765 + 332.792i −0.492450 + 1.12430i
\(297\) 3.86653i 0.0130186i
\(298\) 9.92552 + 24.4247i 0.0333071 + 0.0819622i
\(299\) −217.543 + 217.543i −0.727570 + 0.727570i
\(300\) 144.480 + 1.93970i 0.481599 + 0.00646566i
\(301\) −49.5275 + 49.5275i −0.164543 + 0.164543i
\(302\) 93.1246 + 39.3079i 0.308360 + 0.130158i
\(303\) 269.409i 0.889138i
\(304\) 41.6513 39.4726i 0.137011 0.129844i
\(305\) 352.191 1.15472
\(306\) 11.0048 26.0716i 0.0359634 0.0852012i
\(307\) 138.292 + 138.292i 0.450463 + 0.450463i 0.895508 0.445045i \(-0.146812\pi\)
−0.445045 + 0.895508i \(0.646812\pi\)
\(308\) 30.7448 + 0.412762i 0.0998208 + 0.00134014i
\(309\) −212.243 212.243i −0.686869 0.686869i
\(310\) 351.969 143.030i 1.13538 0.461387i
\(311\) 205.789 0.661702 0.330851 0.943683i \(-0.392664\pi\)
0.330851 + 0.943683i \(0.392664\pi\)
\(312\) 123.286 + 315.460i 0.395147 + 1.01109i
\(313\) 223.861i 0.715209i −0.933873 0.357605i \(-0.883594\pi\)
0.933873 0.357605i \(-0.116406\pi\)
\(314\) 251.249 102.100i 0.800156 0.325161i
\(315\) −148.393 + 148.393i −0.471089 + 0.471089i
\(316\) 161.823 157.535i 0.512098 0.498530i
\(317\) −176.488 + 176.488i −0.556744 + 0.556744i −0.928379 0.371635i \(-0.878797\pi\)
0.371635 + 0.928379i \(0.378797\pi\)
\(318\) 53.2985 126.270i 0.167605 0.397075i
\(319\) 2.31180i 0.00724703i
\(320\) 433.036 + 17.4495i 1.35324 + 0.0545296i
\(321\) 62.4000 0.194393
\(322\) −239.574 101.124i −0.744019 0.314050i
\(323\) −11.9612 11.9612i −0.0370316 0.0370316i
\(324\) −25.1118 25.7953i −0.0775056 0.0796150i
\(325\) 360.469 + 360.469i 1.10914 + 1.10914i
\(326\) 150.018 + 369.165i 0.460178 + 1.13241i
\(327\) −80.9813 −0.247649
\(328\) 172.230 67.3099i 0.525092 0.205213i
\(329\) 402.978i 1.22486i
\(330\) 6.57146 + 16.1711i 0.0199135 + 0.0490032i
\(331\) −183.939 + 183.939i −0.555706 + 0.555706i −0.928082 0.372376i \(-0.878543\pi\)
0.372376 + 0.928082i \(0.378543\pi\)
\(332\) 4.43252 330.159i 0.0133510 0.994455i
\(333\) 96.3384 96.3384i 0.289305 0.289305i
\(334\) 198.720 + 83.8795i 0.594969 + 0.251136i
\(335\) 105.217i 0.314081i
\(336\) −207.792 + 196.923i −0.618429 + 0.586081i
\(337\) 12.7162 0.0377336 0.0188668 0.999822i \(-0.493994\pi\)
0.0188668 + 0.999822i \(0.493994\pi\)
\(338\) −333.244 + 789.490i −0.985928 + 2.33577i
\(339\) −171.659 171.659i −0.506368 0.506368i
\(340\) 1.71500 127.743i 0.00504413 0.375715i
\(341\) 14.7602 + 14.7602i 0.0432849 + 0.0432849i
\(342\) −19.9358 + 8.10133i −0.0582917 + 0.0236881i
\(343\) −90.0184 −0.262444
\(344\) −49.6855 21.7626i −0.144435 0.0632633i
\(345\) 147.625i 0.427899i
\(346\) 141.195 57.3777i 0.408079 0.165831i
\(347\) −113.546 + 113.546i −0.327221 + 0.327221i −0.851529 0.524308i \(-0.824324\pi\)
0.524308 + 0.851529i \(0.324324\pi\)
\(348\) 15.0144 + 15.4230i 0.0431447 + 0.0443190i
\(349\) 90.9653 90.9653i 0.260645 0.260645i −0.564671 0.825316i \(-0.690997\pi\)
0.825316 + 0.564671i \(0.190997\pi\)
\(350\) −167.563 + 396.974i −0.478751 + 1.13421i
\(351\) 127.011i 0.361854i
\(352\) 8.36902 + 22.2925i 0.0237756 + 0.0633309i
\(353\) 36.2208 0.102609 0.0513043 0.998683i \(-0.483662\pi\)
0.0513043 + 0.998683i \(0.483662\pi\)
\(354\) 360.411 + 152.129i 1.01811 + 0.429744i
\(355\) −252.155 252.155i −0.710294 0.710294i
\(356\) 377.087 367.096i 1.05923 1.03117i
\(357\) 59.6727 + 59.6727i 0.167151 + 0.167151i
\(358\) −110.932 272.982i −0.309866 0.762520i
\(359\) 142.121 0.395880 0.197940 0.980214i \(-0.436575\pi\)
0.197940 + 0.980214i \(0.436575\pi\)
\(360\) −148.867 65.2046i −0.413518 0.181124i
\(361\) 348.137i 0.964369i
\(362\) 218.820 + 538.473i 0.604475 + 1.48749i
\(363\) 147.516 147.516i 0.406380 0.406380i
\(364\) −1009.93 13.5587i −2.77452 0.0372491i
\(365\) 324.676 324.676i 0.889523 0.889523i
\(366\) −165.985 70.0621i −0.453510 0.191427i
\(367\) 654.218i 1.78261i 0.453404 + 0.891305i \(0.350209\pi\)
−0.453404 + 0.891305i \(0.649791\pi\)
\(368\) 5.40633 201.310i 0.0146911 0.547039i
\(369\) −69.3434 −0.187923
\(370\) 239.184 566.652i 0.646442 1.53149i
\(371\) 289.007 + 289.007i 0.778995 + 0.778995i
\(372\) −194.333 2.60901i −0.522402 0.00701346i
\(373\) 335.277 + 335.277i 0.898867 + 0.898867i 0.995336 0.0964690i \(-0.0307549\pi\)
−0.0964690 + 0.995336i \(0.530755\pi\)
\(374\) 6.50281 2.64255i 0.0173872 0.00706565i
\(375\) 48.6078 0.129621
\(376\) 290.667 113.597i 0.773050 0.302118i
\(377\) 75.9397i 0.201432i
\(378\) 99.4567 40.4164i 0.263113 0.106922i
\(379\) −98.7497 + 98.7497i −0.260553 + 0.260553i −0.825279 0.564725i \(-0.808982\pi\)
0.564725 + 0.825279i \(0.308982\pi\)
\(380\) −69.6089 + 67.7646i −0.183181 + 0.178328i
\(381\) 50.0257 50.0257i 0.131301 0.131301i
\(382\) −193.081 + 457.430i −0.505448 + 1.19746i
\(383\) 156.144i 0.407687i −0.979003 0.203844i \(-0.934657\pi\)
0.979003 0.203844i \(-0.0653434\pi\)
\(384\) −200.615 94.3687i −0.522436 0.245752i
\(385\) −52.0532 −0.135203
\(386\) 239.390 + 101.046i 0.620181 + 0.261778i
\(387\) 14.3832 + 14.3832i 0.0371660 + 0.0371660i
\(388\) 170.039 + 174.667i 0.438244 + 0.450171i
\(389\) −391.047 391.047i −1.00526 1.00526i −0.999986 0.00527486i \(-0.998321\pi\)
−0.00527486 0.999986i \(-0.501679\pi\)
\(390\) −215.864 531.199i −0.553497 1.36205i
\(391\) −59.3639 −0.151826
\(392\) −168.065 430.038i −0.428737 1.09704i
\(393\) 183.753i 0.467565i
\(394\) −252.365 621.021i −0.640520 1.57620i
\(395\) −270.349 + 270.349i −0.684427 + 0.684427i
\(396\) 0.119870 8.92857i 0.000302701 0.0225469i
\(397\) 243.862 243.862i 0.614262 0.614262i −0.329791 0.944054i \(-0.606978\pi\)
0.944054 + 0.329791i \(0.106978\pi\)
\(398\) −454.210 191.722i −1.14123 0.481713i
\(399\) 64.1715i 0.160831i
\(400\) −333.571 8.95828i −0.833928 0.0223957i
\(401\) −175.261 −0.437059 −0.218529 0.975830i \(-0.570126\pi\)
−0.218529 + 0.975830i \(0.570126\pi\)
\(402\) 20.9311 49.5881i 0.0520674 0.123353i
\(403\) −484.852 484.852i −1.20311 1.20311i
\(404\) −8.35218 + 622.117i −0.0206737 + 1.53989i
\(405\) 43.0947 + 43.0947i 0.106407 + 0.106407i
\(406\) −59.4652 + 24.1650i −0.146466 + 0.0595196i
\(407\) 33.7935 0.0830307
\(408\) −26.2205 + 59.8631i −0.0642659 + 0.146723i
\(409\) 44.4504i 0.108681i 0.998522 + 0.0543404i \(0.0173056\pi\)
−0.998522 + 0.0543404i \(0.982694\pi\)
\(410\) −290.016 + 117.854i −0.707356 + 0.287449i
\(411\) −164.150 + 164.150i −0.399393 + 0.399393i
\(412\) 483.529 + 496.689i 1.17361 + 1.20556i
\(413\) −824.910 + 824.910i −1.99736 + 1.99736i
\(414\) −29.3674 + 69.5746i −0.0709357 + 0.168054i
\(415\) 558.984i 1.34695i
\(416\) −274.911 732.279i −0.660844 1.76029i
\(417\) −56.0438 −0.134398
\(418\) −4.91741 2.07564i −0.0117641 0.00496564i
\(419\) 14.9985 + 14.9985i 0.0357959 + 0.0357959i 0.724778 0.688982i \(-0.241942\pi\)
−0.688982 + 0.724778i \(0.741942\pi\)
\(420\) 347.269 338.068i 0.826831 0.804924i
\(421\) 312.907 + 312.907i 0.743247 + 0.743247i 0.973201 0.229954i \(-0.0738576\pi\)
−0.229954 + 0.973201i \(0.573858\pi\)
\(422\) 14.2834 + 35.1488i 0.0338470 + 0.0832909i
\(423\) −117.028 −0.276663
\(424\) −126.991 + 289.929i −0.299507 + 0.683795i
\(425\) 98.3660i 0.231449i
\(426\) 68.6768 + 169.000i 0.161213 + 0.396714i
\(427\) 379.907 379.907i 0.889712 0.889712i
\(428\) −144.094 1.93452i −0.336667 0.00451990i
\(429\) 22.2763 22.2763i 0.0519262 0.0519262i
\(430\) 84.6006 + 35.7099i 0.196746 + 0.0830462i
\(431\) 532.400i 1.23527i −0.786466 0.617633i \(-0.788092\pi\)
0.786466 0.617633i \(-0.211908\pi\)
\(432\) 57.1884 + 60.3448i 0.132380 + 0.139687i
\(433\) 553.451 1.27818 0.639089 0.769133i \(-0.279312\pi\)
0.639089 + 0.769133i \(0.279312\pi\)
\(434\) 225.381 533.953i 0.519312 1.23031i
\(435\) −25.7664 25.7664i −0.0592330 0.0592330i
\(436\) 187.001 + 2.51057i 0.428903 + 0.00575819i
\(437\) 31.9197 + 31.9197i 0.0730427 + 0.0730427i
\(438\) −217.606 + 88.4288i −0.496817 + 0.201892i
\(439\) 645.291 1.46991 0.734956 0.678115i \(-0.237203\pi\)
0.734956 + 0.678115i \(0.237203\pi\)
\(440\) −14.6734 37.5458i −0.0333487 0.0853315i
\(441\) 173.142i 0.392613i
\(442\) −213.609 + 86.8045i −0.483278 + 0.196390i
\(443\) 315.833 315.833i 0.712941 0.712941i −0.254208 0.967149i \(-0.581815\pi\)
0.967149 + 0.254208i \(0.0818149\pi\)
\(444\) −225.451 + 219.477i −0.507772 + 0.494318i
\(445\) −629.978 + 629.978i −1.41568 + 1.41568i
\(446\) 229.888 544.630i 0.515444 1.22114i
\(447\) 22.8323i 0.0510789i
\(448\) 485.937 448.292i 1.08468 1.00065i
\(449\) 218.589 0.486835 0.243417 0.969922i \(-0.421732\pi\)
0.243417 + 0.969922i \(0.421732\pi\)
\(450\) 115.285 + 48.6618i 0.256189 + 0.108137i
\(451\) −12.1621 12.1621i −0.0269670 0.0269670i
\(452\) 391.071 + 401.715i 0.865202 + 0.888749i
\(453\) 61.8990 + 61.8990i 0.136642 + 0.136642i
\(454\) 103.367 + 254.367i 0.227681 + 0.560279i
\(455\) 1709.88 3.75798
\(456\) 46.2867 18.0895i 0.101506 0.0396699i
\(457\) 296.561i 0.648930i −0.945898 0.324465i \(-0.894816\pi\)
0.945898 0.324465i \(-0.105184\pi\)
\(458\) −36.4773 89.7634i −0.0796447 0.195990i
\(459\) 17.3295 17.3295i 0.0377549 0.0377549i
\(460\) −4.57665 + 340.895i −0.00994925 + 0.741076i
\(461\) 118.061 118.061i 0.256097 0.256097i −0.567368 0.823465i \(-0.692038\pi\)
0.823465 + 0.567368i \(0.192038\pi\)
\(462\) 24.5323 + 10.3551i 0.0531001 + 0.0224135i
\(463\) 409.453i 0.884348i −0.896929 0.442174i \(-0.854207\pi\)
0.896929 0.442174i \(-0.145793\pi\)
\(464\) −34.1929 36.0802i −0.0736917 0.0777590i
\(465\) 329.021 0.707572
\(466\) 48.8565 115.747i 0.104842 0.248383i
\(467\) 494.764 + 494.764i 1.05945 + 1.05945i 0.998117 + 0.0613343i \(0.0195356\pi\)
0.0613343 + 0.998117i \(0.480464\pi\)
\(468\) −3.93757 + 293.292i −0.00841360 + 0.626692i
\(469\) 113.497 + 113.497i 0.241999 + 0.241999i
\(470\) −489.450 + 198.898i −1.04138 + 0.423188i
\(471\) 234.868 0.498658
\(472\) −827.542 362.469i −1.75327 0.767943i
\(473\) 5.04534i 0.0106667i
\(474\) 181.194 73.6321i 0.382266 0.155342i
\(475\) 52.8909 52.8909i 0.111349 0.111349i
\(476\) −135.946 139.646i −0.285601 0.293374i
\(477\) 83.9303 83.9303i 0.175955 0.175955i
\(478\) 276.810 655.792i 0.579100 1.37195i
\(479\) 558.806i 1.16661i 0.812254 + 0.583305i \(0.198241\pi\)
−0.812254 + 0.583305i \(0.801759\pi\)
\(480\) 341.740 + 155.185i 0.711959 + 0.323302i
\(481\) −1110.07 −2.30784
\(482\) −122.079 51.5296i −0.253277 0.106908i
\(483\) −159.243 159.243i −0.329695 0.329695i
\(484\) −345.216 + 336.070i −0.713256 + 0.694359i
\(485\) −291.806 291.806i −0.601661 0.601661i
\(486\) −11.7373 28.8831i −0.0241508 0.0594303i
\(487\) −361.328 −0.741946 −0.370973 0.928644i \(-0.620976\pi\)
−0.370973 + 0.928644i \(0.620976\pi\)
\(488\) 381.119 + 166.933i 0.780981 + 0.342075i
\(489\) 345.096i 0.705718i
\(490\) 294.268 + 724.135i 0.600547 + 1.47783i
\(491\) −488.975 + 488.975i −0.995876 + 0.995876i −0.999992 0.00411514i \(-0.998690\pi\)
0.00411514 + 0.999992i \(0.498690\pi\)
\(492\) 160.127 + 2.14978i 0.325462 + 0.00436946i
\(493\) −10.3613 + 10.3613i −0.0210169 + 0.0210169i
\(494\) 161.531 + 68.1820i 0.326985 + 0.138020i
\(495\) 15.1167i 0.0305389i
\(496\) 448.672 + 12.0494i 0.904582 + 0.0242931i
\(497\) −543.996 −1.09456
\(498\) 111.200 263.445i 0.223293 0.529005i
\(499\) −102.895 102.895i −0.206203 0.206203i 0.596448 0.802652i \(-0.296578\pi\)
−0.802652 + 0.596448i \(0.796578\pi\)
\(500\) −112.245 1.50693i −0.224490 0.00301387i
\(501\) 132.087 + 132.087i 0.263647 + 0.263647i
\(502\) −852.643 + 346.490i −1.69849 + 0.690219i
\(503\) −881.975 −1.75343 −0.876715 0.481011i \(-0.840270\pi\)
−0.876715 + 0.481011i \(0.840270\pi\)
\(504\) −230.918 + 90.2458i −0.458170 + 0.179059i
\(505\) 1053.29i 2.08572i
\(506\) −17.3534 + 7.05192i −0.0342952 + 0.0139366i
\(507\) −524.767 + 524.767i −1.03504 + 1.03504i
\(508\) −117.070 + 113.968i −0.230452 + 0.224346i
\(509\) 161.639 161.639i 0.317563 0.317563i −0.530268 0.847830i \(-0.677909\pi\)
0.847830 + 0.530268i \(0.177909\pi\)
\(510\) 43.0247 101.930i 0.0843622 0.199863i
\(511\) 700.454i 1.37075i
\(512\) 460.334 + 224.135i 0.899090 + 0.437764i
\(513\) −18.6360 −0.0363275
\(514\) 574.906 + 242.668i 1.11849 + 0.472116i
\(515\) −829.791 829.791i −1.61124 1.61124i
\(516\) −32.7678 33.6596i −0.0635034 0.0652317i
\(517\) −20.5256 20.5256i −0.0397013 0.0397013i
\(518\) −353.239 869.252i −0.681928 1.67809i
\(519\) 131.989 0.254315
\(520\) 482.003 + 1233.33i 0.926929 + 2.37179i
\(521\) 763.931i 1.46628i −0.680078 0.733140i \(-0.738054\pi\)
0.680078 0.733140i \(-0.261946\pi\)
\(522\) 7.01773 + 17.2692i 0.0134439 + 0.0330828i
\(523\) 295.573 295.573i 0.565150 0.565150i −0.365616 0.930766i \(-0.619142\pi\)
0.930766 + 0.365616i \(0.119142\pi\)
\(524\) 5.69668 424.321i 0.0108715 0.809773i
\(525\) −263.865 + 263.865i −0.502600 + 0.502600i
\(526\) 309.854 + 130.789i 0.589076 + 0.248649i
\(527\) 132.308i 0.251059i
\(528\) −0.553605 + 20.6141i −0.00104849 + 0.0390418i
\(529\) −370.582 −0.700532
\(530\) 208.377 493.669i 0.393165 0.931451i
\(531\) 239.561 + 239.561i 0.451152 + 0.451152i
\(532\) −1.98944 + 148.184i −0.00373954 + 0.278542i
\(533\) 399.509 + 399.509i 0.749549 + 0.749549i
\(534\) 422.227 171.581i 0.790686 0.321312i
\(535\) 243.961 0.456002
\(536\) −49.8713 + 113.859i −0.0930434 + 0.212424i
\(537\) 255.184i 0.475203i
\(538\) −555.814 + 225.867i −1.03311 + 0.419827i
\(539\) −30.3673 + 30.3673i −0.0563401 + 0.0563401i
\(540\) −98.1781 100.850i −0.181811 0.186759i
\(541\) 243.037 243.037i 0.449236 0.449236i −0.445865 0.895100i \(-0.647104\pi\)
0.895100 + 0.445865i \(0.147104\pi\)
\(542\) −134.901 + 319.596i −0.248895 + 0.589660i
\(543\) 503.365i 0.927007i
\(544\) 62.4040 137.423i 0.114713 0.252615i
\(545\) −316.607 −0.580931
\(546\) −805.853 340.150i −1.47592 0.622986i
\(547\) 424.574 + 424.574i 0.776187 + 0.776187i 0.979180 0.202993i \(-0.0650669\pi\)
−0.202993 + 0.979180i \(0.565067\pi\)
\(548\) 384.144 373.966i 0.700992 0.682419i
\(549\) −110.328 110.328i −0.200963 0.200963i
\(550\) 11.6850 + 28.7545i 0.0212455 + 0.0522810i
\(551\) 11.1425 0.0202223
\(552\) 69.9719 159.751i 0.126761 0.289403i
\(553\) 583.248i 1.05470i
\(554\) 40.8946 + 100.634i 0.0738171 + 0.181649i
\(555\) 376.648 376.648i 0.678645 0.678645i
\(556\) 129.416 + 1.73746i 0.232763 + 0.00312493i
\(557\) −445.773 + 445.773i −0.800311 + 0.800311i −0.983144 0.182833i \(-0.941473\pi\)
0.182833 + 0.983144i \(0.441473\pi\)
\(558\) −155.065 65.4528i −0.277894 0.117299i
\(559\) 165.733i 0.296481i
\(560\) −812.392 + 769.898i −1.45070 + 1.37482i
\(561\) 6.07883 0.0108357
\(562\) 173.884 411.951i 0.309402 0.733008i
\(563\) −529.295 529.295i −0.940133 0.940133i 0.0581732 0.998307i \(-0.481472\pi\)
−0.998307 + 0.0581732i \(0.981472\pi\)
\(564\) 270.241 + 3.62810i 0.479151 + 0.00643280i
\(565\) −671.123 671.123i −1.18783 1.18783i
\(566\) −649.200 + 263.816i −1.14700 + 0.466107i
\(567\) 92.9722 0.163972
\(568\) −153.349 392.383i −0.269980 0.690815i
\(569\) 346.814i 0.609516i 0.952430 + 0.304758i \(0.0985755\pi\)
−0.952430 + 0.304758i \(0.901424\pi\)
\(570\) −77.9416 + 31.6732i −0.136740 + 0.0555671i
\(571\) −155.711 + 155.711i −0.272699 + 0.272699i −0.830186 0.557487i \(-0.811766\pi\)
0.557487 + 0.830186i \(0.311766\pi\)
\(572\) −52.1309 + 50.7497i −0.0911380 + 0.0887233i
\(573\) −304.049 + 304.049i −0.530627 + 0.530627i
\(574\) −185.710 + 439.968i −0.323537 + 0.766495i
\(575\) 262.499i 0.456520i
\(576\) −130.188 141.121i −0.226021 0.245001i
\(577\) 620.510 1.07541 0.537704 0.843134i \(-0.319292\pi\)
0.537704 + 0.843134i \(0.319292\pi\)
\(578\) 491.517 + 207.469i 0.850375 + 0.358943i
\(579\) 159.120 + 159.120i 0.274819 + 0.274819i
\(580\) 58.7007 + 60.2983i 0.101208 + 0.103963i
\(581\) 602.974 + 602.974i 1.03782 + 1.03782i
\(582\) 79.4762 + 195.575i 0.136557 + 0.336040i
\(583\) 29.4410 0.0504992
\(584\) 505.235 197.453i 0.865129 0.338104i
\(585\) 496.565i 0.848829i
\(586\) 108.891 + 267.960i 0.185821 + 0.457269i
\(587\) 561.656 561.656i 0.956825 0.956825i −0.0422810 0.999106i \(-0.513462\pi\)
0.999106 + 0.0422810i \(0.0134625\pi\)
\(588\) 5.36773 399.819i 0.00912880 0.679964i
\(589\) −71.1413 + 71.1413i −0.120783 + 0.120783i
\(590\) 1409.07 + 594.770i 2.38826 + 1.00808i
\(591\) 580.531i 0.982286i
\(592\) 527.413 499.826i 0.890901 0.844301i
\(593\) 851.739 1.43632 0.718161 0.695877i \(-0.244984\pi\)
0.718161 + 0.695877i \(0.244984\pi\)
\(594\) 3.00721 7.12440i 0.00506263 0.0119939i
\(595\) 233.299 + 233.299i 0.392099 + 0.392099i
\(596\) 0.707843 52.7241i 0.00118766 0.0884633i
\(597\) −301.909 301.909i −0.505710 0.505710i
\(598\) 570.036 231.646i 0.953237 0.387368i
\(599\) −1001.69 −1.67228 −0.836138 0.548519i \(-0.815192\pi\)
−0.836138 + 0.548519i \(0.815192\pi\)
\(600\) −264.707 115.943i −0.441178 0.193239i
\(601\) 955.182i 1.58932i 0.607054 + 0.794661i \(0.292351\pi\)
−0.607054 + 0.794661i \(0.707649\pi\)
\(602\) 129.778 52.7382i 0.215579 0.0876050i
\(603\) 32.9607 32.9607i 0.0546612 0.0546612i
\(604\) −141.018 144.856i −0.233473 0.239827i
\(605\) 576.734 576.734i 0.953279 0.953279i
\(606\) −209.533 + 496.407i −0.345765 + 0.819154i
\(607\) 291.885i 0.480865i −0.970666 0.240432i \(-0.922711\pi\)
0.970666 0.240432i \(-0.0772892\pi\)
\(608\) −107.446 + 40.3371i −0.176720 + 0.0663440i
\(609\) −55.5881 −0.0912777
\(610\) −648.940 273.917i −1.06384 0.449045i
\(611\) 674.238 + 674.238i 1.10350 + 1.10350i
\(612\) −40.5544 + 39.4800i −0.0662654 + 0.0645097i
\(613\) −332.933 332.933i −0.543121 0.543121i 0.381322 0.924442i \(-0.375469\pi\)
−0.924442 + 0.381322i \(0.875469\pi\)
\(614\) −147.257 362.371i −0.239833 0.590181i
\(615\) −271.107 −0.440825
\(616\) −56.3287 24.6724i −0.0914427 0.0400526i
\(617\) 970.864i 1.57352i 0.617257 + 0.786762i \(0.288244\pi\)
−0.617257 + 0.786762i \(0.711756\pi\)
\(618\) 226.002 + 556.146i 0.365699 + 0.899913i
\(619\) −696.761 + 696.761i −1.12562 + 1.12562i −0.134744 + 0.990881i \(0.543021\pi\)
−0.990881 + 0.134744i \(0.956979\pi\)
\(620\) −759.773 10.2003i −1.22544 0.0164520i
\(621\) −46.2455 + 46.2455i −0.0744694 + 0.0744694i
\(622\) −379.183 160.053i −0.609619 0.257320i
\(623\) 1359.11i 2.18156i
\(624\) 18.1852 677.146i 0.0291430 1.08517i
\(625\) 711.432 1.13829
\(626\) −174.108 + 412.481i −0.278128 + 0.658915i
\(627\) −3.26856 3.26856i −0.00521301 0.00521301i
\(628\) −542.355 7.28135i −0.863623 0.0115945i
\(629\) −151.460 151.460i −0.240795 0.240795i
\(630\) 388.839 158.013i 0.617205 0.250815i
\(631\) −377.591 −0.598401 −0.299200 0.954190i \(-0.596720\pi\)
−0.299200 + 0.954190i \(0.596720\pi\)
\(632\) −420.695 + 164.413i −0.665657 + 0.260148i
\(633\) 32.8571i 0.0519069i
\(634\) 462.457 187.929i 0.729427 0.296418i
\(635\) 195.582 195.582i 0.308003 0.308003i
\(636\) −196.413 + 191.209i −0.308826 + 0.300644i
\(637\) 997.527 997.527i 1.56598 1.56598i
\(638\) −1.79801 + 4.25968i −0.00281820 + 0.00667661i
\(639\) 157.981i 0.247232i
\(640\) −784.333 368.947i −1.22552 0.576480i
\(641\) 729.200 1.13760 0.568799 0.822477i \(-0.307408\pi\)
0.568799 + 0.822477i \(0.307408\pi\)
\(642\) −114.977 48.5317i −0.179092 0.0755946i
\(643\) 243.958 + 243.958i 0.379406 + 0.379406i 0.870888 0.491482i \(-0.163545\pi\)
−0.491482 + 0.870888i \(0.663545\pi\)
\(644\) 362.785 + 372.659i 0.563331 + 0.578663i
\(645\) 56.2332 + 56.2332i 0.0871832 + 0.0871832i
\(646\) 12.7366 + 31.3423i 0.0197161 + 0.0485176i
\(647\) −281.594 −0.435230 −0.217615 0.976035i \(-0.569828\pi\)
−0.217615 + 0.976035i \(0.569828\pi\)
\(648\) 26.2082 + 67.0606i 0.0404448 + 0.103489i
\(649\) 84.0331i 0.129481i
\(650\) −383.838 944.549i −0.590520 1.45315i
\(651\) 354.913 354.913i 0.545182 0.545182i
\(652\) 10.6986 796.893i 0.0164089 1.22223i
\(653\) 323.704 323.704i 0.495718 0.495718i −0.414384 0.910102i \(-0.636003\pi\)
0.910102 + 0.414384i \(0.136003\pi\)
\(654\) 149.215 + 62.9834i 0.228157 + 0.0963049i
\(655\) 718.407i 1.09680i
\(656\) −369.698 9.92850i −0.563564 0.0151349i
\(657\) −203.418 −0.309617
\(658\) −313.417 + 742.519i −0.476317 + 1.12845i
\(659\) 507.811 + 507.811i 0.770578 + 0.770578i 0.978208 0.207629i \(-0.0665748\pi\)
−0.207629 + 0.978208i \(0.566575\pi\)
\(660\) 0.468647 34.9075i 0.000710071 0.0528901i
\(661\) 57.1593 + 57.1593i 0.0864741 + 0.0864741i 0.749021 0.662547i \(-0.230524\pi\)
−0.662547 + 0.749021i \(0.730524\pi\)
\(662\) 481.981 195.863i 0.728068 0.295866i
\(663\) −199.682 −0.301179
\(664\) −264.949 + 604.897i −0.399020 + 0.910990i
\(665\) 250.887i 0.377274i
\(666\) −252.439 + 102.584i −0.379037 + 0.154030i
\(667\) 27.6502 27.6502i 0.0414546 0.0414546i
\(668\) −300.919 309.109i −0.450478 0.462739i
\(669\) 362.010 362.010i 0.541121 0.541121i
\(670\) 81.8329 193.871i 0.122139 0.289360i
\(671\) 38.7009i 0.0576765i
\(672\) 536.031 201.236i 0.797666 0.299458i
\(673\) 1110.84 1.65059 0.825293 0.564705i \(-0.191010\pi\)
0.825293 + 0.564705i \(0.191010\pi\)
\(674\) −23.4307 9.89007i −0.0347636 0.0146737i
\(675\) 76.6288 + 76.6288i 0.113524 + 0.113524i
\(676\) 1228.06 1195.52i 1.81665 1.76852i
\(677\) 397.465 + 397.465i 0.587097 + 0.587097i 0.936844 0.349747i \(-0.113732\pi\)
−0.349747 + 0.936844i \(0.613732\pi\)
\(678\) 182.787 + 449.803i 0.269597 + 0.663426i
\(679\) −629.539 −0.927156
\(680\) −102.512 + 234.043i −0.150754 + 0.344181i
\(681\) 237.782i 0.349166i
\(682\) −15.7170 38.6765i −0.0230455 0.0567104i
\(683\) −238.015 + 238.015i −0.348485 + 0.348485i −0.859545 0.511060i \(-0.829253\pi\)
0.511060 + 0.859545i \(0.329253\pi\)
\(684\) 43.0341 + 0.577751i 0.0629153 + 0.000844665i
\(685\) −641.768 + 641.768i −0.936887 + 0.936887i
\(686\) 165.866 + 70.0120i 0.241787 + 0.102058i
\(687\) 83.9109i 0.122141i
\(688\) 74.6236 + 78.7423i 0.108464 + 0.114451i
\(689\) −967.099 −1.40363
\(690\) −114.816 + 272.011i −0.166400 + 0.394219i
\(691\) −685.172 685.172i −0.991565 0.991565i 0.00839951 0.999965i \(-0.497326\pi\)
−0.999965 + 0.00839951i \(0.997326\pi\)
\(692\) −304.789 4.09192i −0.440447 0.00591318i
\(693\) 16.3064 + 16.3064i 0.0235301 + 0.0235301i
\(694\) 297.528 120.907i 0.428714 0.174217i
\(695\) −219.111 −0.315267
\(696\) −15.6699 40.0956i −0.0225142 0.0576086i
\(697\) 109.019i 0.156412i
\(698\) −238.359 + 96.8624i −0.341489 + 0.138771i
\(699\) 76.9356 76.9356i 0.110065 0.110065i
\(700\) 617.495 601.135i 0.882136 0.858764i
\(701\) 543.074 543.074i 0.774713 0.774713i −0.204214 0.978926i \(-0.565464\pi\)
0.978926 + 0.204214i \(0.0654637\pi\)
\(702\) −98.7828 + 234.027i −0.140716 + 0.333372i
\(703\) 162.879i 0.231691i
\(704\) 1.91746 47.5847i 0.00272366 0.0675919i
\(705\) −457.538 −0.648991
\(706\) −66.7398 28.1708i −0.0945323 0.0399020i
\(707\) −1136.18 1136.18i −1.60704 1.60704i
\(708\) −545.767 560.621i −0.770857 0.791837i
\(709\) −488.019 488.019i −0.688320 0.688320i 0.273541 0.961860i \(-0.411805\pi\)
−0.961860 + 0.273541i \(0.911805\pi\)
\(710\) 268.501 + 660.729i 0.378171 + 0.930604i
\(711\) 169.381 0.238229
\(712\) −980.322 + 383.123i −1.37686 + 0.538094i
\(713\) 353.076i 0.495198i
\(714\) −63.5412 156.362i −0.0889933 0.218995i
\(715\) 87.0923 87.0923i 0.121807 0.121807i
\(716\) −7.91118 + 589.269i −0.0110491 + 0.823002i
\(717\) 435.899 435.899i 0.607948 0.607948i
\(718\) −261.869 110.535i −0.364721 0.153948i
\(719\) 297.369i 0.413587i −0.978385 0.206793i \(-0.933697\pi\)
0.978385 0.206793i \(-0.0663028\pi\)
\(720\) 223.586 + 235.926i 0.310535 + 0.327675i
\(721\) −1790.18 −2.48292
\(722\) −270.764 + 641.470i −0.375020 + 0.888463i
\(723\) −81.1449 81.1449i −0.112234 0.112234i
\(724\) 15.6053 1162.37i 0.0215542 1.60548i
\(725\) −45.8164 45.8164i −0.0631950 0.0631950i
\(726\) −386.541 + 157.079i −0.532425 + 0.216362i
\(727\) 1158.85 1.59402 0.797009 0.603967i \(-0.206414\pi\)
0.797009 + 0.603967i \(0.206414\pi\)
\(728\) 1850.33 + 810.456i 2.54166 + 1.11326i
\(729\) 27.0000i 0.0370370i
\(730\) −850.759 + 345.724i −1.16542 + 0.473595i
\(731\) 22.6128 22.6128i 0.0309341 0.0309341i
\(732\) 251.349 + 258.190i 0.343373 + 0.352719i
\(733\) −348.835 + 348.835i −0.475901 + 0.475901i −0.903818 0.427917i \(-0.859248\pi\)
0.427917 + 0.903818i \(0.359248\pi\)
\(734\) 508.819 1205.45i 0.693215 1.64230i
\(735\) 676.923i 0.920983i
\(736\) −166.531 + 366.726i −0.226265 + 0.498269i
\(737\) 11.5619 0.0156878
\(738\) 127.771 + 53.9320i 0.173131 + 0.0730786i
\(739\) 825.489 + 825.489i 1.11703 + 1.11703i 0.992174 + 0.124860i \(0.0398482\pi\)
0.124860 + 0.992174i \(0.460152\pi\)
\(740\) −881.430 + 858.076i −1.19112 + 1.15956i
\(741\) 107.368 + 107.368i 0.144896 + 0.144896i
\(742\) −307.743 757.295i −0.414748 1.02061i
\(743\) −899.725 −1.21094 −0.605468 0.795870i \(-0.707014\pi\)
−0.605468 + 0.795870i \(0.707014\pi\)
\(744\) 356.046 + 155.951i 0.478556 + 0.209611i
\(745\) 89.2659i 0.119820i
\(746\) −357.013 878.538i −0.478569 1.17767i
\(747\) 175.109 175.109i 0.234416 0.234416i
\(748\) −14.0372 0.188455i −0.0187663 0.000251945i
\(749\) 263.160 263.160i 0.351348 0.351348i
\(750\) −89.5638 37.8048i −0.119418 0.0504065i
\(751\) 80.4386i 0.107109i 0.998565 + 0.0535543i \(0.0170550\pi\)
−0.998565 + 0.0535543i \(0.982945\pi\)
\(752\) −623.927 16.7560i −0.829690 0.0222819i
\(753\) −797.052 −1.05850
\(754\) 59.0623 139.925i 0.0783319 0.185577i
\(755\) 242.003 + 242.003i 0.320533 + 0.320533i
\(756\) −214.691 2.88231i −0.283983 0.00381258i
\(757\) 233.298 + 233.298i 0.308187 + 0.308187i 0.844206 0.536019i \(-0.180072\pi\)
−0.536019 + 0.844206i \(0.680072\pi\)
\(758\) 258.757 105.151i 0.341368 0.138722i
\(759\) −16.2220 −0.0213728
\(760\) 180.964 70.7233i 0.238111 0.0930569i
\(761\) 56.1906i 0.0738378i 0.999318 + 0.0369189i \(0.0117543\pi\)
−0.999318 + 0.0369189i \(0.988246\pi\)
\(762\) −131.084 + 53.2687i −0.172026 + 0.0699064i
\(763\) −341.523 + 341.523i −0.447606 + 0.447606i
\(764\) 711.535 692.682i 0.931328 0.906652i
\(765\) 67.7521 67.7521i 0.0885648 0.0885648i
\(766\) −121.441 + 287.708i −0.158540 + 0.375598i
\(767\) 2760.38i 3.59893i
\(768\) 296.255 + 329.911i 0.385748 + 0.429572i
\(769\) 517.343 0.672748 0.336374 0.941728i \(-0.390799\pi\)
0.336374 + 0.941728i \(0.390799\pi\)
\(770\) 95.9122 + 40.4845i 0.124561 + 0.0525773i
\(771\) 382.134 + 382.134i 0.495635 + 0.495635i
\(772\) −362.506 372.372i −0.469567 0.482347i
\(773\) −523.925 523.925i −0.677781 0.677781i 0.281716 0.959498i \(-0.409096\pi\)
−0.959498 + 0.281716i \(0.909096\pi\)
\(774\) −15.3157 37.6888i −0.0197877 0.0486936i
\(775\) 585.048 0.754900
\(776\) −177.463 454.085i −0.228689 0.585161i
\(777\) 812.578i 1.04579i
\(778\) 416.397 + 1024.67i 0.535215 + 1.31706i
\(779\) 58.6192 58.6192i 0.0752492 0.0752492i
\(780\) −15.3944 + 1146.66i −0.0197365 + 1.47008i
\(781\) −27.7083 + 27.7083i −0.0354780 + 0.0354780i
\(782\) 109.383 + 46.1704i 0.139876 + 0.0590414i
\(783\) 16.1433i 0.0206173i
\(784\) −24.7903 + 923.092i −0.0316202 + 1.17741i
\(785\) 918.248 1.16974
\(786\) 142.914 338.579i 0.181825 0.430763i
\(787\) −46.6965 46.6965i −0.0593348 0.0593348i 0.676817 0.736152i \(-0.263359\pi\)
−0.736152 + 0.676817i \(0.763359\pi\)
\(788\) −17.9975 + 1340.56i −0.0228395 + 1.70122i
\(789\) 205.957 + 205.957i 0.261035 + 0.261035i
\(790\) 708.403 287.875i 0.896713 0.364398i
\(791\) −1447.87 −1.83044
\(792\) −7.16509 + 16.3584i −0.00904683 + 0.0206545i
\(793\) 1271.27i 1.60312i
\(794\) −639.000 + 259.671i −0.804786 + 0.327042i
\(795\) 328.137 328.137i 0.412751 0.412751i
\(796\) 687.806 + 706.526i 0.864078 + 0.887595i
\(797\) 127.126 127.126i 0.159505 0.159505i −0.622842 0.782348i \(-0.714022\pi\)
0.782348 + 0.622842i \(0.214022\pi\)
\(798\) −49.9095 + 118.241i −0.0625432 + 0.148172i
\(799\) 183.988i 0.230273i
\(800\) 607.665 + 275.942i 0.759581 + 0.344928i
\(801\) 394.698 0.492756
\(802\) 322.932 + 136.309i 0.402658 + 0.169962i
\(803\) −35.6774 35.6774i −0.0444302 0.0444302i
\(804\) −77.1344 + 75.0908i −0.0959384 + 0.0933965i
\(805\) −622.580 622.580i −0.773392 0.773392i
\(806\) 516.284 + 1270.47i 0.640551 + 1.57627i
\(807\) −519.576 −0.643836
\(808\) 499.243 1139.80i 0.617874 1.41065i
\(809\) 1047.16i 1.29439i −0.762325 0.647194i \(-0.775942\pi\)
0.762325 0.647194i \(-0.224058\pi\)
\(810\) −45.8885 112.923i −0.0566524 0.139411i
\(811\) −112.206 + 112.206i −0.138356 + 0.138356i −0.772893 0.634537i \(-0.781191\pi\)
0.634537 + 0.772893i \(0.281191\pi\)
\(812\) 128.364 + 1.72334i 0.158083 + 0.00212234i
\(813\) −212.432 + 212.432i −0.261294 + 0.261294i
\(814\) −62.2672 26.2830i −0.0764954 0.0322887i
\(815\) 1349.20i 1.65546i
\(816\) 94.8720 89.9096i 0.116265 0.110183i
\(817\) −24.3176 −0.0297645
\(818\) 34.5714 81.9035i 0.0422633 0.100126i
\(819\) −535.643 535.643i −0.654020 0.654020i
\(820\) 626.039 + 8.40484i 0.763463 + 0.0102498i
\(821\) −7.63080 7.63080i −0.00929452 0.00929452i 0.702444 0.711739i \(-0.252092\pi\)
−0.711739 + 0.702444i \(0.752092\pi\)
\(822\) 430.128 174.792i 0.523271 0.212642i
\(823\) 1316.28 1.59937 0.799687 0.600417i \(-0.204999\pi\)
0.799687 + 0.600417i \(0.204999\pi\)
\(824\) −504.640 1291.26i −0.612427 1.56706i
\(825\) 26.8798i 0.0325816i
\(826\) 2161.54 878.387i 2.61687 1.06342i
\(827\) 341.515 341.515i 0.412957 0.412957i −0.469810 0.882767i \(-0.655678\pi\)
0.882767 + 0.469810i \(0.155678\pi\)
\(828\) 108.224 105.356i 0.130705 0.127242i
\(829\) −621.672 + 621.672i −0.749905 + 0.749905i −0.974461 0.224556i \(-0.927907\pi\)
0.224556 + 0.974461i \(0.427907\pi\)
\(830\) 434.751 1029.97i 0.523796 1.24093i
\(831\) 94.0725i 0.113204i
\(832\) −62.9859 + 1563.10i −0.0757042 + 1.87872i
\(833\) 272.208 0.326781
\(834\) 103.265 + 43.5882i 0.123819 + 0.0522640i
\(835\) 516.412 + 516.412i 0.618457 + 0.618457i
\(836\) 7.44640 + 7.64906i 0.00890717 + 0.00914959i
\(837\) −103.070 103.070i −0.123142 0.123142i
\(838\) −15.9708 39.3010i −0.0190582 0.0468986i
\(839\) 1440.49 1.71692 0.858459 0.512883i \(-0.171422\pi\)
0.858459 + 0.512883i \(0.171422\pi\)
\(840\) −902.804 + 352.828i −1.07477 + 0.420033i
\(841\) 831.348i 0.988523i
\(842\) −333.192 819.921i −0.395715 0.973778i
\(843\) 273.820 273.820i 0.324816 0.324816i
\(844\) 1.01863 75.8734i 0.00120691 0.0898974i
\(845\) −2051.65 + 2051.65i −2.42798 + 2.42798i
\(846\) 215.634 + 91.0191i 0.254887 + 0.107588i
\(847\) 1244.24i 1.46900i
\(848\) 459.484 435.450i 0.541845 0.513503i
\(849\) −606.873 −0.714809
\(850\) 76.5043 181.247i 0.0900051 0.213232i
\(851\) 404.186 + 404.186i 0.474954 + 0.474954i
\(852\) 4.89772 364.810i 0.00574850 0.428180i
\(853\) −625.193 625.193i −0.732934 0.732934i 0.238266 0.971200i \(-0.423421\pi\)
−0.971200 + 0.238266i \(0.923421\pi\)
\(854\) −995.482 + 404.535i −1.16567 + 0.473695i
\(855\) −72.8599 −0.0852163
\(856\) 264.000 + 115.634i 0.308411 + 0.135086i
\(857\) 1105.18i 1.28959i −0.764356 0.644794i \(-0.776943\pi\)
0.764356 0.644794i \(-0.223057\pi\)
\(858\) −58.3714 + 23.7205i −0.0680319 + 0.0276462i
\(859\) 379.841 379.841i 0.442190 0.442190i −0.450558 0.892747i \(-0.648775\pi\)
0.892747 + 0.450558i \(0.148775\pi\)
\(860\) −128.110 131.597i −0.148965 0.153019i
\(861\) −292.442 + 292.442i −0.339654 + 0.339654i
\(862\) −414.075 + 980.989i −0.480365 + 1.13804i
\(863\) 381.969i 0.442606i 0.975205 + 0.221303i \(0.0710311\pi\)
−0.975205 + 0.221303i \(0.928969\pi\)
\(864\) −58.4408 155.668i −0.0676398 0.180172i
\(865\) 516.031 0.596567
\(866\) −1019.78 430.448i −1.17757 0.497053i
\(867\) 326.706 + 326.706i 0.376824 + 0.376824i
\(868\) −830.567 + 808.561i −0.956874 + 0.931521i
\(869\) 29.7076 + 29.7076i 0.0341859 + 0.0341859i
\(870\) 27.4367 + 67.5164i 0.0315365 + 0.0776051i
\(871\) −379.794 −0.436044
\(872\) −342.613 150.067i −0.392904 0.172095i
\(873\) 182.824i 0.209420i
\(874\) −33.9890 83.6401i −0.0388890 0.0956981i
\(875\) 204.994 204.994i 0.234279 0.234279i
\(876\) 469.732 + 6.30634i 0.536224 + 0.00719902i
\(877\) 638.602 638.602i 0.728166 0.728166i −0.242088 0.970254i \(-0.577832\pi\)
0.970254 + 0.242088i \(0.0778323\pi\)
\(878\) −1189.00 501.877i −1.35421 0.571614i
\(879\) 250.489i 0.284971i
\(880\) −2.16439 + 80.5935i −0.00245954 + 0.0915835i
\(881\) −1362.97 −1.54707 −0.773533 0.633756i \(-0.781512\pi\)
−0.773533 + 0.633756i \(0.781512\pi\)
\(882\) 134.662 319.028i 0.152678 0.361710i
\(883\) −897.988 897.988i −1.01697 1.01697i −0.999853 0.0171209i \(-0.994550\pi\)
−0.0171209 0.999853i \(-0.505450\pi\)
\(884\) 461.104 + 6.19051i 0.521610 + 0.00700284i
\(885\) 936.598 + 936.598i 1.05830 + 1.05830i
\(886\) −827.587 + 336.308i −0.934071 + 0.379580i
\(887\) 1343.56 1.51472 0.757359 0.652998i \(-0.226489\pi\)
0.757359 + 0.652998i \(0.226489\pi\)
\(888\) 586.110 229.060i 0.660034 0.257950i
\(889\) 421.947i 0.474631i
\(890\) 1650.75 670.818i 1.85478 0.753728i
\(891\) 4.73552 4.73552i 0.00531483 0.00531483i
\(892\) −847.174 + 824.728i −0.949746 + 0.924583i
\(893\) 98.9295 98.9295i 0.110783 0.110783i
\(894\) 17.7579 42.0703i 0.0198634 0.0470585i
\(895\) 997.676i 1.11472i
\(896\) −1244.04 + 448.075i −1.38844 + 0.500084i
\(897\) 532.870 0.594058
\(898\) −402.767 170.008i −0.448516 0.189318i
\(899\) 61.6257 + 61.6257i 0.0685491 + 0.0685491i
\(900\) −174.575 179.326i −0.193972 0.199252i
\(901\) −131.952 131.952i −0.146451 0.146451i
\(902\) 12.9506 + 31.8688i 0.0143576 + 0.0353312i
\(903\) 121.317 0.134349
\(904\) −408.146 1044.35i −0.451488 1.15525i
\(905\) 1967.97i 2.17456i
\(906\) −65.9118 162.196i −0.0727503 0.179024i
\(907\) −671.651 + 671.651i −0.740519 + 0.740519i −0.972678 0.232159i \(-0.925421\pi\)
0.232159 + 0.972678i \(0.425421\pi\)
\(908\) 7.37170 549.085i 0.00811861 0.604720i
\(909\) −329.957 + 329.957i −0.362989 + 0.362989i
\(910\) −3150.59 1329.86i −3.46219 1.46139i
\(911\) 770.729i 0.846025i 0.906124 + 0.423012i \(0.139027\pi\)
−0.906124 + 0.423012i \(0.860973\pi\)
\(912\) −99.3561 2.66828i −0.108943 0.00292574i
\(913\) 61.4246 0.0672778
\(914\) −230.651 + 546.438i −0.252354 + 0.597853i
\(915\) −431.344 431.344i −0.471414 0.471414i
\(916\) −2.60140 + 193.767i −0.00283995 + 0.211536i
\(917\) 774.942 + 774.942i 0.845084 + 0.845084i
\(918\) −45.4091 + 18.4530i −0.0494652 + 0.0201013i
\(919\) −1153.98 −1.25569 −0.627843 0.778340i \(-0.716062\pi\)
−0.627843 + 0.778340i \(0.716062\pi\)
\(920\) 273.565 624.567i 0.297353 0.678877i
\(921\) 338.745i 0.367801i
\(922\) −309.358 + 125.714i −0.335529 + 0.136350i
\(923\) 910.182 910.182i 0.986112 0.986112i
\(924\) −37.1490 38.1601i −0.0402045 0.0412988i
\(925\) 669.736 669.736i 0.724039 0.724039i
\(926\) −318.453 + 754.450i −0.343902 + 0.814741i
\(927\) 519.886i 0.560826i
\(928\) 34.9418 + 93.0742i 0.0376528 + 0.100296i
\(929\) −652.736 −0.702622 −0.351311 0.936259i \(-0.614264\pi\)
−0.351311 + 0.936259i \(0.614264\pi\)
\(930\) −606.247 255.897i −0.651879 0.275158i
\(931\) −146.365 146.365i −0.157213 0.157213i
\(932\) −180.044 + 175.274i −0.193180 + 0.188062i
\(933\) −252.039 252.039i −0.270139 0.270139i
\(934\) −526.838 1296.45i −0.564067 1.38806i
\(935\) 23.7660 0.0254182
\(936\) 235.364 537.352i 0.251457 0.574094i
\(937\) 644.074i 0.687378i −0.939083 0.343689i \(-0.888323\pi\)
0.939083 0.343689i \(-0.111677\pi\)
\(938\) −120.855 297.401i −0.128843 0.317059i
\(939\) −274.172 + 274.172i −0.291983 + 0.291983i
\(940\) 1056.54 + 14.1845i 1.12398 + 0.0150899i
\(941\) 171.348 171.348i 0.182092 0.182092i −0.610175 0.792267i \(-0.708901\pi\)
0.792267 + 0.610175i \(0.208901\pi\)
\(942\) −432.763 182.669i −0.459409 0.193916i
\(943\) 290.929i 0.308514i
\(944\) 1242.90 + 1311.50i 1.31663 + 1.38930i
\(945\) 363.487 0.384643
\(946\) 3.92402 9.29644i 0.00414801 0.00982710i
\(947\) 731.249 + 731.249i 0.772174 + 0.772174i 0.978486 0.206312i \(-0.0661461\pi\)
−0.206312 + 0.978486i \(0.566146\pi\)
\(948\) −391.132 5.25111i −0.412587 0.00553915i
\(949\) 1171.96 + 1171.96i 1.23494 + 1.23494i
\(950\) −138.592 + 56.3197i −0.145886 + 0.0592839i
\(951\) 432.305 0.454580
\(952\) 141.881 + 363.041i 0.149035 + 0.381345i
\(953\) 1745.08i 1.83115i −0.402152 0.915573i \(-0.631738\pi\)
0.402152 0.915573i \(-0.368262\pi\)
\(954\) −219.925 + 89.3714i −0.230530 + 0.0936807i
\(955\) −1188.72 + 1188.72i −1.24473 + 1.24473i
\(956\) −1020.09 + 993.060i −1.06704 + 1.03877i
\(957\) −2.83137 + 2.83137i −0.00295859 + 0.00295859i
\(958\) 434.612 1029.64i 0.453666 1.07479i
\(959\) 1384.54i 1.44374i
\(960\) −508.988 551.730i −0.530196 0.574719i
\(961\) 174.077 0.181142
\(962\) 2045.40 + 863.362i 2.12619 + 0.897465i
\(963\) −76.4241 76.4241i −0.0793604 0.0793604i
\(964\) 184.864 + 189.895i 0.191767 + 0.196986i
\(965\) 622.102 + 622.102i 0.644665 + 0.644665i
\(966\) 169.566 + 417.269i 0.175534 + 0.431955i
\(967\) 904.237 0.935095 0.467548 0.883968i \(-0.345138\pi\)
0.467548 + 0.883968i \(0.345138\pi\)
\(968\) 897.467 350.743i 0.927136 0.362337i
\(969\) 29.2989i 0.0302362i
\(970\) 310.723 + 764.628i 0.320333 + 0.788276i
\(971\) −1010.37 + 1010.37i −1.04055 + 1.04055i −0.0414029 + 0.999143i \(0.513183\pi\)
−0.999143 + 0.0414029i \(0.986817\pi\)
\(972\) −0.837051 + 62.3482i −0.000861163 + 0.0641442i
\(973\) −236.354 + 236.354i −0.242913 + 0.242913i
\(974\) 665.775 + 281.023i 0.683547 + 0.288525i
\(975\) 882.966i 0.905606i
\(976\) −572.410 604.003i −0.586485 0.618856i
\(977\) −396.922 −0.406266 −0.203133 0.979151i \(-0.565112\pi\)
−0.203133 + 0.979151i \(0.565112\pi\)
\(978\) 268.399 635.867i 0.274437 0.650171i
\(979\) 69.2259 + 69.2259i 0.0707108 + 0.0707108i
\(980\) 20.9859 1563.14i 0.0214142 1.59505i
\(981\) 99.1815 + 99.1815i 0.101102 + 0.101102i
\(982\) 1281.28 520.675i 1.30476 0.530218i
\(983\) 1672.52 1.70145 0.850724 0.525612i \(-0.176164\pi\)
0.850724 + 0.525612i \(0.176164\pi\)
\(984\) −293.375 128.501i −0.298146 0.130590i
\(985\) 2269.66i 2.30423i
\(986\) 27.1501 11.0330i 0.0275356 0.0111897i
\(987\) −493.545 + 493.545i −0.500045 + 0.500045i
\(988\) −244.604 251.262i −0.247575 0.254313i
\(989\) −60.3446 + 60.3446i −0.0610157 + 0.0610157i
\(990\) 11.7571 27.8538i 0.0118758 0.0281351i
\(991\) 775.801i 0.782847i 0.920211 + 0.391423i \(0.128017\pi\)
−0.920211 + 0.391423i \(0.871983\pi\)
\(992\) −817.343 371.158i −0.823935 0.374151i
\(993\) 450.556 0.453732
\(994\) 1002.36 + 423.094i 1.00841 + 0.425648i
\(995\) −1180.35 1180.35i −1.18629 1.18629i
\(996\) −409.789 + 398.932i −0.411435 + 0.400534i
\(997\) 201.495 + 201.495i 0.202101 + 0.202101i 0.800900 0.598799i \(-0.204355\pi\)
−0.598799 + 0.800900i \(0.704355\pi\)
\(998\) 109.566 + 269.620i 0.109786 + 0.270161i
\(999\) −235.980 −0.236216
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 48.3.l.a.43.1 yes 16
3.2 odd 2 144.3.m.c.91.8 16
4.3 odd 2 192.3.l.a.79.5 16
8.3 odd 2 384.3.l.b.31.4 16
8.5 even 2 384.3.l.a.31.8 16
12.11 even 2 576.3.m.c.271.7 16
16.3 odd 4 inner 48.3.l.a.19.1 16
16.5 even 4 384.3.l.b.223.4 16
16.11 odd 4 384.3.l.a.223.8 16
16.13 even 4 192.3.l.a.175.5 16
24.5 odd 2 1152.3.m.f.415.2 16
24.11 even 2 1152.3.m.c.415.2 16
48.5 odd 4 1152.3.m.c.991.2 16
48.11 even 4 1152.3.m.f.991.2 16
48.29 odd 4 576.3.m.c.559.7 16
48.35 even 4 144.3.m.c.19.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.3.l.a.19.1 16 16.3 odd 4 inner
48.3.l.a.43.1 yes 16 1.1 even 1 trivial
144.3.m.c.19.8 16 48.35 even 4
144.3.m.c.91.8 16 3.2 odd 2
192.3.l.a.79.5 16 4.3 odd 2
192.3.l.a.175.5 16 16.13 even 4
384.3.l.a.31.8 16 8.5 even 2
384.3.l.a.223.8 16 16.11 odd 4
384.3.l.b.31.4 16 8.3 odd 2
384.3.l.b.223.4 16 16.5 even 4
576.3.m.c.271.7 16 12.11 even 2
576.3.m.c.559.7 16 48.29 odd 4
1152.3.m.c.415.2 16 24.11 even 2
1152.3.m.c.991.2 16 48.5 odd 4
1152.3.m.f.415.2 16 24.5 odd 2
1152.3.m.f.991.2 16 48.11 even 4