Properties

Label 273.2.i.d.79.2
Level $273$
Weight $2$
Character 273.79
Analytic conductor $2.180$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(79,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4868829729.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} - x^{6} + 5x^{5} - 8x^{4} + 15x^{3} - 9x^{2} - 54x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(1.25184 - 1.19703i\) of defining polynomial
Character \(\chi\) \(=\) 273.79
Dual form 273.2.i.d.235.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.410741 + 0.711425i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.662583 + 1.14763i) q^{4} +(-0.910741 + 1.57745i) q^{5} +0.821482 q^{6} +(0.589259 + 2.57930i) q^{7} -2.73157 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.410741 + 0.711425i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.662583 + 1.14763i) q^{4} +(-0.910741 + 1.57745i) q^{5} +0.821482 q^{6} +(0.589259 + 2.57930i) q^{7} -2.73157 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.748158 - 1.29585i) q^{10} +(-2.57332 - 4.45713i) q^{11} +(0.662583 - 1.14763i) q^{12} -1.00000 q^{13} +(-2.07701 - 0.640210i) q^{14} +1.82148 q^{15} +(-0.203200 + 0.351952i) q^{16} +(2.43911 + 4.22466i) q^{17} +(-0.410741 - 0.711425i) q^{18} +(-3.82517 + 6.62538i) q^{19} -2.41377 q^{20} +(1.93911 - 1.79996i) q^{21} +4.22788 q^{22} +(-1.11763 + 1.93578i) q^{23} +(1.36578 + 2.36561i) q^{24} +(0.841101 + 1.45683i) q^{25} +(0.410741 - 0.711425i) q^{26} +1.00000 q^{27} +(-2.56964 + 2.38525i) q^{28} +1.82885 q^{29} +(-0.748158 + 1.29585i) q^{30} +(-0.865783 - 1.49958i) q^{31} +(-2.89849 - 5.02033i) q^{32} +(-2.57332 + 4.45713i) q^{33} -4.00737 q^{34} +(-4.60537 - 1.41955i) q^{35} -1.32517 q^{36} +(5.53711 - 9.59056i) q^{37} +(-3.14231 - 5.44264i) q^{38} +(0.500000 + 0.866025i) q^{39} +(2.48775 - 4.30891i) q^{40} +5.37453 q^{41} +(0.484066 + 2.11885i) q^{42} +11.2426 q^{43} +(3.41008 - 5.90644i) q^{44} +(-0.910741 - 1.57745i) q^{45} +(-0.918109 - 1.59021i) q^{46} +(-4.09801 + 7.09796i) q^{47} +0.406399 q^{48} +(-6.30555 + 3.03975i) q^{49} -1.38190 q^{50} +(2.43911 - 4.22466i) q^{51} +(-0.662583 - 1.14763i) q^{52} +(3.25553 + 5.63874i) q^{53} +(-0.410741 + 0.711425i) q^{54} +9.37453 q^{55} +(-1.60960 - 7.04552i) q^{56} +7.65033 q^{57} +(-0.751184 + 1.30109i) q^{58} +(-4.18727 - 7.25256i) q^{59} +(1.20688 + 2.09038i) q^{60} +(1.26059 - 2.18341i) q^{61} +1.42245 q^{62} +(-2.52837 - 0.779336i) q^{63} +3.94932 q^{64} +(0.910741 - 1.57745i) q^{65} +(-2.11394 - 3.66145i) q^{66} +(-0.248158 - 0.429822i) q^{67} +(-3.23222 + 5.59838i) q^{68} +2.23525 q^{69} +(2.90152 - 2.69331i) q^{70} -2.27580 q^{71} +(1.36578 - 2.36561i) q^{72} +(1.68727 + 2.92243i) q^{73} +(4.54864 + 7.87848i) q^{74} +(0.841101 - 1.45683i) q^{75} -10.1380 q^{76} +(9.97991 - 9.26377i) q^{77} -0.821482 q^{78} +(4.01243 - 6.94974i) q^{79} +(-0.370125 - 0.641075i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.20754 + 3.82357i) q^{82} +16.1614 q^{83} +(3.35051 + 1.03275i) q^{84} -8.88558 q^{85} +(-4.61781 + 7.99828i) q^{86} +(-0.914425 - 1.58383i) q^{87} +(7.02921 + 12.1749i) q^{88} +(-6.52468 + 11.3011i) q^{89} +1.49632 q^{90} +(-0.589259 - 2.57930i) q^{91} -2.96208 q^{92} +(-0.865783 + 1.49958i) q^{93} +(-3.36644 - 5.83085i) q^{94} +(-6.96747 - 12.0680i) q^{95} +(-2.89849 + 5.02033i) q^{96} +13.0742 q^{97} +(0.427398 - 5.73447i) q^{98} +5.14665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9} - 14 q^{10} - 4 q^{11} - 7 q^{12} - 8 q^{13} + 16 q^{14} + 6 q^{15} - 9 q^{16} - 2 q^{17} + q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21} + 40 q^{22} + 4 q^{23} + 6 q^{24} + 3 q^{25} - q^{26} + 8 q^{27} - 20 q^{28} - 26 q^{29} - 14 q^{30} - 2 q^{31} + 18 q^{32} - 4 q^{33} + 13 q^{35} + 14 q^{36} + 5 q^{37} - 11 q^{38} + 4 q^{39} - 17 q^{40} + 16 q^{41} - 17 q^{42} + 32 q^{43} + 26 q^{44} - 3 q^{45} + 29 q^{46} - 15 q^{47} + 18 q^{48} - 21 q^{49} + 48 q^{50} - 2 q^{51} + 7 q^{52} + 2 q^{53} + q^{54} + 48 q^{55} - 35 q^{56} + 12 q^{57} - q^{58} - 20 q^{59} + q^{60} - 20 q^{61} - 44 q^{62} - 3 q^{63} + 40 q^{64} + 3 q^{65} - 20 q^{66} - 10 q^{67} - 13 q^{68} - 8 q^{69} - 31 q^{70} + 4 q^{71} + 6 q^{72} + 21 q^{74} + 3 q^{75} - 86 q^{76} + 3 q^{77} + 2 q^{78} - 6 q^{79} + 21 q^{80} - 4 q^{81} - 6 q^{82} + 32 q^{83} - 2 q^{84} + 4 q^{85} + 51 q^{86} + 13 q^{87} - 39 q^{88} - 51 q^{89} + 28 q^{90} - 9 q^{91} - 8 q^{92} - 2 q^{93} - 19 q^{94} - 17 q^{95} + 18 q^{96} + 26 q^{97} + 33 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.410741 + 0.711425i −0.290438 + 0.503053i −0.973913 0.226920i \(-0.927134\pi\)
0.683475 + 0.729974i \(0.260468\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.662583 + 1.14763i 0.331292 + 0.573814i
\(5\) −0.910741 + 1.57745i −0.407296 + 0.705457i −0.994586 0.103920i \(-0.966862\pi\)
0.587290 + 0.809377i \(0.300195\pi\)
\(6\) 0.821482 0.335369
\(7\) 0.589259 + 2.57930i 0.222719 + 0.974883i
\(8\) −2.73157 −0.965754
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.748158 1.29585i −0.236588 0.409783i
\(11\) −2.57332 4.45713i −0.775887 1.34387i −0.934295 0.356501i \(-0.883970\pi\)
0.158408 0.987374i \(-0.449364\pi\)
\(12\) 0.662583 1.14763i 0.191271 0.331292i
\(13\) −1.00000 −0.277350
\(14\) −2.07701 0.640210i −0.555104 0.171103i
\(15\) 1.82148 0.470305
\(16\) −0.203200 + 0.351952i −0.0507999 + 0.0879881i
\(17\) 2.43911 + 4.22466i 0.591570 + 1.02463i 0.994021 + 0.109188i \(0.0348252\pi\)
−0.402451 + 0.915442i \(0.631841\pi\)
\(18\) −0.410741 0.711425i −0.0968126 0.167684i
\(19\) −3.82517 + 6.62538i −0.877553 + 1.51997i −0.0235358 + 0.999723i \(0.507492\pi\)
−0.854018 + 0.520244i \(0.825841\pi\)
\(20\) −2.41377 −0.539735
\(21\) 1.93911 1.79996i 0.423148 0.392784i
\(22\) 4.22788 0.901387
\(23\) −1.11763 + 1.93578i −0.233041 + 0.403639i −0.958702 0.284414i \(-0.908201\pi\)
0.725661 + 0.688053i \(0.241534\pi\)
\(24\) 1.36578 + 2.36561i 0.278789 + 0.482877i
\(25\) 0.841101 + 1.45683i 0.168220 + 0.291366i
\(26\) 0.410741 0.711425i 0.0805530 0.139522i
\(27\) 1.00000 0.192450
\(28\) −2.56964 + 2.38525i −0.485616 + 0.450770i
\(29\) 1.82885 0.339609 0.169805 0.985478i \(-0.445686\pi\)
0.169805 + 0.985478i \(0.445686\pi\)
\(30\) −0.748158 + 1.29585i −0.136594 + 0.236588i
\(31\) −0.865783 1.49958i −0.155499 0.269333i 0.777741 0.628584i \(-0.216365\pi\)
−0.933241 + 0.359252i \(0.883032\pi\)
\(32\) −2.89849 5.02033i −0.512386 0.887478i
\(33\) −2.57332 + 4.45713i −0.447958 + 0.775887i
\(34\) −4.00737 −0.687258
\(35\) −4.60537 1.41955i −0.778450 0.239947i
\(36\) −1.32517 −0.220861
\(37\) 5.53711 9.59056i 0.910296 1.57668i 0.0966498 0.995318i \(-0.469187\pi\)
0.813646 0.581360i \(-0.197479\pi\)
\(38\) −3.14231 5.44264i −0.509750 0.882912i
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 2.48775 4.30891i 0.393348 0.681298i
\(41\) 5.37453 0.839361 0.419680 0.907672i \(-0.362142\pi\)
0.419680 + 0.907672i \(0.362142\pi\)
\(42\) 0.484066 + 2.11885i 0.0746930 + 0.326945i
\(43\) 11.2426 1.71448 0.857242 0.514914i \(-0.172176\pi\)
0.857242 + 0.514914i \(0.172176\pi\)
\(44\) 3.41008 5.90644i 0.514089 0.890429i
\(45\) −0.910741 1.57745i −0.135765 0.235152i
\(46\) −0.918109 1.59021i −0.135368 0.234464i
\(47\) −4.09801 + 7.09796i −0.597756 + 1.03534i 0.395396 + 0.918511i \(0.370607\pi\)
−0.993152 + 0.116832i \(0.962726\pi\)
\(48\) 0.406399 0.0586587
\(49\) −6.30555 + 3.03975i −0.900793 + 0.434250i
\(50\) −1.38190 −0.195430
\(51\) 2.43911 4.22466i 0.341543 0.591570i
\(52\) −0.662583 1.14763i −0.0918838 0.159147i
\(53\) 3.25553 + 5.63874i 0.447181 + 0.774540i 0.998201 0.0599517i \(-0.0190947\pi\)
−0.551020 + 0.834492i \(0.685761\pi\)
\(54\) −0.410741 + 0.711425i −0.0558948 + 0.0968126i
\(55\) 9.37453 1.26406
\(56\) −1.60960 7.04552i −0.215092 0.941497i
\(57\) 7.65033 1.01331
\(58\) −0.751184 + 1.30109i −0.0986353 + 0.170841i
\(59\) −4.18727 7.25256i −0.545136 0.944202i −0.998598 0.0529273i \(-0.983145\pi\)
0.453463 0.891275i \(-0.350188\pi\)
\(60\) 1.20688 + 2.09038i 0.155808 + 0.269867i
\(61\) 1.26059 2.18341i 0.161402 0.279556i −0.773970 0.633223i \(-0.781732\pi\)
0.935372 + 0.353666i \(0.115065\pi\)
\(62\) 1.42245 0.180651
\(63\) −2.52837 0.779336i −0.318544 0.0981870i
\(64\) 3.94932 0.493665
\(65\) 0.910741 1.57745i 0.112964 0.195659i
\(66\) −2.11394 3.66145i −0.260208 0.450694i
\(67\) −0.248158 0.429822i −0.0303173 0.0525111i 0.850469 0.526026i \(-0.176318\pi\)
−0.880786 + 0.473515i \(0.842985\pi\)
\(68\) −3.23222 + 5.59838i −0.391965 + 0.678903i
\(69\) 2.23525 0.269092
\(70\) 2.90152 2.69331i 0.346798 0.321912i
\(71\) −2.27580 −0.270088 −0.135044 0.990840i \(-0.543118\pi\)
−0.135044 + 0.990840i \(0.543118\pi\)
\(72\) 1.36578 2.36561i 0.160959 0.278789i
\(73\) 1.68727 + 2.92243i 0.197479 + 0.342045i 0.947711 0.319131i \(-0.103391\pi\)
−0.750231 + 0.661176i \(0.770058\pi\)
\(74\) 4.54864 + 7.87848i 0.528769 + 0.915855i
\(75\) 0.841101 1.45683i 0.0971220 0.168220i
\(76\) −10.1380 −1.16290
\(77\) 9.97991 9.26377i 1.13732 1.05570i
\(78\) −0.821482 −0.0930146
\(79\) 4.01243 6.94974i 0.451434 0.781906i −0.547041 0.837105i \(-0.684246\pi\)
0.998475 + 0.0551991i \(0.0175793\pi\)
\(80\) −0.370125 0.641075i −0.0413812 0.0716744i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.20754 + 3.82357i −0.243782 + 0.422243i
\(83\) 16.1614 1.77394 0.886971 0.461825i \(-0.152805\pi\)
0.886971 + 0.461825i \(0.152805\pi\)
\(84\) 3.35051 + 1.03275i 0.365570 + 0.112682i
\(85\) −8.88558 −0.963777
\(86\) −4.61781 + 7.99828i −0.497951 + 0.862476i
\(87\) −0.914425 1.58383i −0.0980367 0.169805i
\(88\) 7.02921 + 12.1749i 0.749316 + 1.29785i
\(89\) −6.52468 + 11.3011i −0.691615 + 1.19791i 0.279694 + 0.960089i \(0.409767\pi\)
−0.971309 + 0.237823i \(0.923566\pi\)
\(90\) 1.49632 0.157726
\(91\) −0.589259 2.57930i −0.0617711 0.270384i
\(92\) −2.96208 −0.308818
\(93\) −0.865783 + 1.49958i −0.0897775 + 0.155499i
\(94\) −3.36644 5.83085i −0.347222 0.601406i
\(95\) −6.96747 12.0680i −0.714848 1.23815i
\(96\) −2.89849 + 5.02033i −0.295826 + 0.512386i
\(97\) 13.0742 1.32749 0.663743 0.747960i \(-0.268967\pi\)
0.663743 + 0.747960i \(0.268967\pi\)
\(98\) 0.427398 5.73447i 0.0431737 0.579269i
\(99\) 5.14665 0.517258
\(100\) −1.11460 + 1.93054i −0.111460 + 0.193054i
\(101\) 5.10675 + 8.84516i 0.508141 + 0.880126i 0.999956 + 0.00942616i \(0.00300049\pi\)
−0.491814 + 0.870700i \(0.663666\pi\)
\(102\) 2.00368 + 3.47048i 0.198394 + 0.343629i
\(103\) 2.27284 3.93667i 0.223950 0.387892i −0.732054 0.681246i \(-0.761438\pi\)
0.956004 + 0.293354i \(0.0947716\pi\)
\(104\) 2.73157 0.267852
\(105\) 1.07332 + 4.69814i 0.104746 + 0.458492i
\(106\) −5.34872 −0.519513
\(107\) 3.25691 5.64113i 0.314857 0.545348i −0.664550 0.747244i \(-0.731377\pi\)
0.979407 + 0.201895i \(0.0647101\pi\)
\(108\) 0.662583 + 1.14763i 0.0637571 + 0.110431i
\(109\) −1.80048 3.11853i −0.172455 0.298701i 0.766823 0.641859i \(-0.221837\pi\)
−0.939278 + 0.343158i \(0.888503\pi\)
\(110\) −3.85051 + 6.66927i −0.367131 + 0.635890i
\(111\) −11.0742 −1.05112
\(112\) −1.02753 0.316722i −0.0970922 0.0299274i
\(113\) −0.396272 −0.0372781 −0.0186391 0.999826i \(-0.505933\pi\)
−0.0186391 + 0.999826i \(0.505933\pi\)
\(114\) −3.14231 + 5.44264i −0.294304 + 0.509750i
\(115\) −2.03573 3.52600i −0.189833 0.328801i
\(116\) 1.21177 + 2.09884i 0.112510 + 0.194872i
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) 6.87953 0.633312
\(119\) −9.45938 + 8.78060i −0.867140 + 0.804916i
\(120\) −4.97550 −0.454199
\(121\) −7.74400 + 13.4130i −0.704000 + 1.21936i
\(122\) 1.03555 + 1.79363i 0.0937545 + 0.162388i
\(123\) −2.68727 4.65448i −0.242303 0.419680i
\(124\) 1.14731 1.98719i 0.103031 0.178455i
\(125\) −12.1715 −1.08865
\(126\) 1.59294 1.47864i 0.141911 0.131727i
\(127\) −15.8132 −1.40319 −0.701596 0.712575i \(-0.747529\pi\)
−0.701596 + 0.712575i \(0.747529\pi\)
\(128\) 4.17483 7.23102i 0.369007 0.639138i
\(129\) −5.62131 9.73639i −0.494929 0.857242i
\(130\) 0.748158 + 1.29585i 0.0656178 + 0.113653i
\(131\) −1.10585 + 1.91539i −0.0966186 + 0.167348i −0.910283 0.413987i \(-0.864136\pi\)
0.813664 + 0.581335i \(0.197469\pi\)
\(132\) −6.82017 −0.593619
\(133\) −19.3428 5.96218i −1.67724 0.516986i
\(134\) 0.407715 0.0352212
\(135\) −0.910741 + 1.57745i −0.0783841 + 0.135765i
\(136\) −6.66258 11.5399i −0.571312 0.989541i
\(137\) 10.3210 + 17.8765i 0.881783 + 1.52729i 0.849357 + 0.527819i \(0.176990\pi\)
0.0324262 + 0.999474i \(0.489677\pi\)
\(138\) −0.918109 + 1.59021i −0.0781547 + 0.135368i
\(139\) −10.0249 −0.850298 −0.425149 0.905123i \(-0.639778\pi\)
−0.425149 + 0.905123i \(0.639778\pi\)
\(140\) −1.42233 6.22582i −0.120209 0.526178i
\(141\) 8.19601 0.690229
\(142\) 0.934766 1.61906i 0.0784438 0.135869i
\(143\) 2.57332 + 4.45713i 0.215192 + 0.372724i
\(144\) −0.203200 0.351952i −0.0169333 0.0293294i
\(145\) −1.66561 + 2.88492i −0.138321 + 0.239580i
\(146\) −2.77212 −0.229422
\(147\) 5.78527 + 3.94089i 0.477161 + 0.325039i
\(148\) 14.6752 1.20629
\(149\) −2.22788 + 3.85880i −0.182515 + 0.316126i −0.942736 0.333539i \(-0.891757\pi\)
0.760221 + 0.649664i \(0.225091\pi\)
\(150\) 0.690950 + 1.19676i 0.0564158 + 0.0977150i
\(151\) −8.10537 14.0389i −0.659606 1.14247i −0.980718 0.195430i \(-0.937390\pi\)
0.321112 0.947041i \(-0.395944\pi\)
\(152\) 10.4487 18.0977i 0.847501 1.46791i
\(153\) −4.87822 −0.394380
\(154\) 2.49132 + 10.9050i 0.200756 + 0.878747i
\(155\) 3.15402 0.253337
\(156\) −0.662583 + 1.14763i −0.0530491 + 0.0918838i
\(157\) 1.00875 + 1.74720i 0.0805069 + 0.139442i 0.903468 0.428656i \(-0.141013\pi\)
−0.822961 + 0.568098i \(0.807679\pi\)
\(158\) 3.29614 + 5.70909i 0.262227 + 0.454191i
\(159\) 3.25553 5.63874i 0.258180 0.447181i
\(160\) 10.5591 0.834770
\(161\) −5.65153 1.74201i −0.445403 0.137290i
\(162\) 0.821482 0.0645418
\(163\) −6.97688 + 12.0843i −0.546471 + 0.946516i 0.452041 + 0.891997i \(0.350696\pi\)
−0.998513 + 0.0545192i \(0.982637\pi\)
\(164\) 3.56107 + 6.16796i 0.278073 + 0.481637i
\(165\) −4.68727 8.11858i −0.364903 0.632031i
\(166\) −6.63815 + 11.4976i −0.515220 + 0.892387i
\(167\) −5.65033 −0.437236 −0.218618 0.975811i \(-0.570155\pi\)
−0.218618 + 0.975811i \(0.570155\pi\)
\(168\) −5.29680 + 4.91671i −0.408657 + 0.379333i
\(169\) 1.00000 0.0769231
\(170\) 3.64968 6.32142i 0.279917 0.484831i
\(171\) −3.82517 6.62538i −0.292518 0.506656i
\(172\) 7.44917 + 12.9023i 0.567994 + 0.983794i
\(173\) 3.99632 6.92182i 0.303834 0.526256i −0.673167 0.739491i \(-0.735066\pi\)
0.977001 + 0.213234i \(0.0683998\pi\)
\(174\) 1.50237 0.113894
\(175\) −3.26197 + 3.02790i −0.246582 + 0.228888i
\(176\) 2.09160 0.157660
\(177\) −4.18727 + 7.25256i −0.314734 + 0.545136i
\(178\) −5.35991 9.28364i −0.401742 0.695838i
\(179\) 5.44786 + 9.43596i 0.407192 + 0.705277i 0.994574 0.104033i \(-0.0331747\pi\)
−0.587382 + 0.809310i \(0.699841\pi\)
\(180\) 1.20688 2.09038i 0.0899558 0.155808i
\(181\) −3.80579 −0.282882 −0.141441 0.989947i \(-0.545174\pi\)
−0.141441 + 0.989947i \(0.545174\pi\)
\(182\) 2.07701 + 0.640210i 0.153958 + 0.0474556i
\(183\) −2.52118 −0.186371
\(184\) 3.05287 5.28772i 0.225060 0.389816i
\(185\) 10.0858 + 17.4690i 0.741520 + 1.28435i
\(186\) −0.711226 1.23188i −0.0521496 0.0903257i
\(187\) 12.5532 21.7428i 0.917983 1.58999i
\(188\) −10.8611 −0.792126
\(189\) 0.589259 + 2.57930i 0.0428623 + 0.187616i
\(190\) 11.4473 0.830476
\(191\) 7.50434 12.9979i 0.542995 0.940495i −0.455735 0.890115i \(-0.650624\pi\)
0.998730 0.0503796i \(-0.0160431\pi\)
\(192\) −1.97466 3.42021i −0.142509 0.246833i
\(193\) 10.8747 + 18.8356i 0.782779 + 1.35581i 0.930317 + 0.366757i \(0.119532\pi\)
−0.147538 + 0.989056i \(0.547135\pi\)
\(194\) −5.37012 + 9.30133i −0.385552 + 0.667796i
\(195\) −1.82148 −0.130439
\(196\) −7.66645 5.22234i −0.547604 0.373024i
\(197\) 2.12359 0.151300 0.0756499 0.997134i \(-0.475897\pi\)
0.0756499 + 0.997134i \(0.475897\pi\)
\(198\) −2.11394 + 3.66145i −0.150231 + 0.260208i
\(199\) −0.976040 1.69055i −0.0691896 0.119840i 0.829355 0.558722i \(-0.188708\pi\)
−0.898545 + 0.438882i \(0.855375\pi\)
\(200\) −2.29752 3.97943i −0.162459 0.281388i
\(201\) −0.248158 + 0.429822i −0.0175037 + 0.0303173i
\(202\) −8.39022 −0.590334
\(203\) 1.07767 + 4.71715i 0.0756373 + 0.331079i
\(204\) 6.46445 0.452602
\(205\) −4.89481 + 8.47805i −0.341868 + 0.592133i
\(206\) 1.86710 + 3.23391i 0.130087 + 0.225317i
\(207\) −1.11763 1.93578i −0.0776803 0.134546i
\(208\) 0.203200 0.351952i 0.0140894 0.0244035i
\(209\) 39.3736 2.72353
\(210\) −3.78323 1.16613i −0.261068 0.0804708i
\(211\) −0.481943 −0.0331783 −0.0165892 0.999862i \(-0.505281\pi\)
−0.0165892 + 0.999862i \(0.505281\pi\)
\(212\) −4.31411 + 7.47227i −0.296295 + 0.513197i
\(213\) 1.13790 + 1.97090i 0.0779677 + 0.135044i
\(214\) 2.67549 + 4.63409i 0.182893 + 0.316780i
\(215\) −10.2391 + 17.7347i −0.698302 + 1.20949i
\(216\) −2.73157 −0.185860
\(217\) 3.35769 3.11675i 0.227935 0.211579i
\(218\) 2.95813 0.200350
\(219\) 1.68727 2.92243i 0.114015 0.197479i
\(220\) 6.21141 + 10.7585i 0.418773 + 0.725336i
\(221\) −2.43911 4.22466i −0.164072 0.284181i
\(222\) 4.54864 7.87848i 0.305285 0.528769i
\(223\) −12.2061 −0.817384 −0.408692 0.912672i \(-0.634015\pi\)
−0.408692 + 0.912672i \(0.634015\pi\)
\(224\) 11.2410 10.4343i 0.751069 0.697174i
\(225\) −1.68220 −0.112147
\(226\) 0.162765 0.281917i 0.0108270 0.0187529i
\(227\) 0.503684 + 0.872406i 0.0334307 + 0.0579036i 0.882257 0.470769i \(-0.156023\pi\)
−0.848826 + 0.528672i \(0.822690\pi\)
\(228\) 5.06898 + 8.77974i 0.335702 + 0.581452i
\(229\) −10.0191 + 17.3537i −0.662084 + 1.14676i 0.317984 + 0.948096i \(0.396994\pi\)
−0.980067 + 0.198666i \(0.936339\pi\)
\(230\) 3.34464 0.220539
\(231\) −13.0126 4.01097i −0.856167 0.263902i
\(232\) −4.99563 −0.327979
\(233\) 10.8704 18.8280i 0.712142 1.23347i −0.251910 0.967751i \(-0.581059\pi\)
0.964052 0.265715i \(-0.0856080\pi\)
\(234\) 0.410741 + 0.711425i 0.0268510 + 0.0465073i
\(235\) −7.46445 12.9288i −0.486927 0.843382i
\(236\) 5.54882 9.61085i 0.361198 0.625613i
\(237\) −8.02486 −0.521271
\(238\) −2.36138 10.3362i −0.153065 0.669996i
\(239\) 3.43534 0.222214 0.111107 0.993808i \(-0.464560\pi\)
0.111107 + 0.993808i \(0.464560\pi\)
\(240\) −0.370125 + 0.641075i −0.0238915 + 0.0413812i
\(241\) −2.26041 3.91514i −0.145606 0.252196i 0.783993 0.620770i \(-0.213180\pi\)
−0.929599 + 0.368573i \(0.879846\pi\)
\(242\) −6.36156 11.0185i −0.408936 0.708299i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.34098 0.213885
\(245\) 0.947674 12.7151i 0.0605446 0.812339i
\(246\) 4.41508 0.281495
\(247\) 3.82517 6.62538i 0.243390 0.421563i
\(248\) 2.36494 + 4.09620i 0.150174 + 0.260109i
\(249\) −8.08069 13.9962i −0.512093 0.886971i
\(250\) 4.99934 8.65911i 0.316186 0.547651i
\(251\) −11.3343 −0.715417 −0.357709 0.933833i \(-0.616442\pi\)
−0.357709 + 0.933833i \(0.616442\pi\)
\(252\) −0.780866 3.41800i −0.0491899 0.215314i
\(253\) 11.5040 0.723253
\(254\) 6.49512 11.2499i 0.407540 0.705880i
\(255\) 4.44279 + 7.69514i 0.278218 + 0.481888i
\(256\) 7.37887 + 12.7806i 0.461180 + 0.798786i
\(257\) 5.59450 9.68997i 0.348976 0.604443i −0.637092 0.770788i \(-0.719863\pi\)
0.986068 + 0.166344i \(0.0531963\pi\)
\(258\) 9.23561 0.574984
\(259\) 27.9997 + 8.63054i 1.73982 + 0.536276i
\(260\) 2.41377 0.149696
\(261\) −0.914425 + 1.58383i −0.0566015 + 0.0980367i
\(262\) −0.908437 1.57346i −0.0561234 0.0972086i
\(263\) −2.34110 4.05491i −0.144358 0.250036i 0.784775 0.619781i \(-0.212779\pi\)
−0.929133 + 0.369745i \(0.879445\pi\)
\(264\) 7.02921 12.1749i 0.432618 0.749316i
\(265\) −11.8598 −0.728540
\(266\) 12.1865 11.3121i 0.747205 0.693587i
\(267\) 13.0494 0.798608
\(268\) 0.328851 0.569586i 0.0200877 0.0347930i
\(269\) −9.67942 16.7652i −0.590165 1.02220i −0.994210 0.107456i \(-0.965729\pi\)
0.404045 0.914739i \(-0.367604\pi\)
\(270\) −0.748158 1.29585i −0.0455314 0.0788628i
\(271\) 8.68238 15.0383i 0.527417 0.913513i −0.472072 0.881560i \(-0.656494\pi\)
0.999489 0.0319535i \(-0.0101729\pi\)
\(272\) −1.98250 −0.120207
\(273\) −1.93911 + 1.79996i −0.117360 + 0.108939i
\(274\) −16.9571 −1.02441
\(275\) 4.32885 7.49779i 0.261040 0.452134i
\(276\) 1.48104 + 2.56524i 0.0891481 + 0.154409i
\(277\) −1.15890 2.00727i −0.0696315 0.120605i 0.829108 0.559089i \(-0.188849\pi\)
−0.898739 + 0.438484i \(0.855516\pi\)
\(278\) 4.11763 7.13194i 0.246959 0.427745i
\(279\) 1.73157 0.103666
\(280\) 12.5799 + 3.87758i 0.751792 + 0.231730i
\(281\) −26.8071 −1.59918 −0.799589 0.600548i \(-0.794949\pi\)
−0.799589 + 0.600548i \(0.794949\pi\)
\(282\) −3.36644 + 5.83085i −0.200469 + 0.347222i
\(283\) −7.36090 12.7495i −0.437560 0.757876i 0.559941 0.828533i \(-0.310824\pi\)
−0.997501 + 0.0706564i \(0.977491\pi\)
\(284\) −1.50791 2.61177i −0.0894779 0.154980i
\(285\) −6.96747 + 12.0680i −0.412718 + 0.714848i
\(286\) −4.22788 −0.250000
\(287\) 3.16699 + 13.8625i 0.186941 + 0.818278i
\(288\) 5.79698 0.341590
\(289\) −3.39849 + 5.88636i −0.199911 + 0.346256i
\(290\) −1.36827 2.36991i −0.0803475 0.139166i
\(291\) −6.53711 11.3226i −0.383212 0.663743i
\(292\) −2.23591 + 3.87271i −0.130847 + 0.226633i
\(293\) −10.0599 −0.587703 −0.293852 0.955851i \(-0.594937\pi\)
−0.293852 + 0.955851i \(0.594937\pi\)
\(294\) −5.17990 + 2.49710i −0.302098 + 0.145634i
\(295\) 15.2541 0.888126
\(296\) −15.1250 + 26.1973i −0.879122 + 1.52268i
\(297\) −2.57332 4.45713i −0.149319 0.258629i
\(298\) −1.83017 3.16994i −0.106019 0.183630i
\(299\) 1.11763 1.93578i 0.0646339 0.111949i
\(300\) 2.22920 0.128703
\(301\) 6.62481 + 28.9981i 0.381848 + 1.67142i
\(302\) 13.3168 0.766298
\(303\) 5.10675 8.84516i 0.293375 0.508141i
\(304\) −1.55455 2.69255i −0.0891593 0.154428i
\(305\) 2.29614 + 3.97704i 0.131477 + 0.227724i
\(306\) 2.00368 3.47048i 0.114543 0.198394i
\(307\) 9.33398 0.532718 0.266359 0.963874i \(-0.414179\pi\)
0.266359 + 0.963874i \(0.414179\pi\)
\(308\) 17.2439 + 5.31520i 0.982561 + 0.302862i
\(309\) −4.54568 −0.258595
\(310\) −1.29548 + 2.24385i −0.0735786 + 0.127442i
\(311\) 7.67574 + 13.2948i 0.435251 + 0.753877i 0.997316 0.0732160i \(-0.0233262\pi\)
−0.562065 + 0.827093i \(0.689993\pi\)
\(312\) −1.36578 2.36561i −0.0773222 0.133926i
\(313\) 5.64617 9.77946i 0.319141 0.552768i −0.661168 0.750238i \(-0.729939\pi\)
0.980309 + 0.197470i \(0.0632725\pi\)
\(314\) −1.65734 −0.0935290
\(315\) 3.53205 3.27860i 0.199008 0.184728i
\(316\) 10.6343 0.598225
\(317\) −12.3166 + 21.3330i −0.691769 + 1.19818i 0.279489 + 0.960149i \(0.409835\pi\)
−0.971258 + 0.238030i \(0.923498\pi\)
\(318\) 2.67436 + 4.63212i 0.149971 + 0.259757i
\(319\) −4.70623 8.15142i −0.263498 0.456392i
\(320\) −3.59681 + 6.22986i −0.201068 + 0.348260i
\(321\) −6.51381 −0.363566
\(322\) 3.56063 3.30512i 0.198426 0.184187i
\(323\) −37.3200 −2.07654
\(324\) 0.662583 1.14763i 0.0368102 0.0637571i
\(325\) −0.841101 1.45683i −0.0466559 0.0808104i
\(326\) −5.73138 9.92705i −0.317432 0.549808i
\(327\) −1.80048 + 3.11853i −0.0995670 + 0.172455i
\(328\) −14.6809 −0.810616
\(329\) −20.7225 6.38744i −1.14247 0.352151i
\(330\) 7.70101 0.423927
\(331\) 13.7774 23.8632i 0.757276 1.31164i −0.186959 0.982368i \(-0.559863\pi\)
0.944235 0.329273i \(-0.106804\pi\)
\(332\) 10.7083 + 18.5473i 0.587692 + 1.01791i
\(333\) 5.53711 + 9.59056i 0.303432 + 0.525560i
\(334\) 2.32082 4.01979i 0.126990 0.219953i
\(335\) 0.904031 0.0493925
\(336\) 0.239474 + 1.04823i 0.0130644 + 0.0571854i
\(337\) −25.3034 −1.37837 −0.689183 0.724588i \(-0.742030\pi\)
−0.689183 + 0.724588i \(0.742030\pi\)
\(338\) −0.410741 + 0.711425i −0.0223414 + 0.0386964i
\(339\) 0.198136 + 0.343181i 0.0107613 + 0.0186391i
\(340\) −5.88744 10.1973i −0.319291 0.553029i
\(341\) −4.45588 + 7.71781i −0.241300 + 0.417943i
\(342\) 6.28461 0.339833
\(343\) −11.5560 14.4727i −0.623966 0.781452i
\(344\) −30.7100 −1.65577
\(345\) −2.03573 + 3.52600i −0.109600 + 0.189833i
\(346\) 3.28290 + 5.68616i 0.176490 + 0.305690i
\(347\) 9.17502 + 15.8916i 0.492541 + 0.853105i 0.999963 0.00859203i \(-0.00273496\pi\)
−0.507422 + 0.861697i \(0.669402\pi\)
\(348\) 1.21177 2.09884i 0.0649575 0.112510i
\(349\) 28.0427 1.50109 0.750546 0.660818i \(-0.229790\pi\)
0.750546 + 0.660818i \(0.229790\pi\)
\(350\) −0.814296 3.56433i −0.0435260 0.190521i
\(351\) −1.00000 −0.0533761
\(352\) −14.9175 + 25.8379i −0.795106 + 1.37716i
\(353\) 9.32010 + 16.1429i 0.496059 + 0.859199i 0.999990 0.00454470i \(-0.00144663\pi\)
−0.503931 + 0.863744i \(0.668113\pi\)
\(354\) −3.43977 5.95785i −0.182821 0.316656i
\(355\) 2.07267 3.58996i 0.110006 0.190536i
\(356\) −17.2926 −0.916505
\(357\) 12.3339 + 3.80177i 0.652780 + 0.201211i
\(358\) −8.95064 −0.473056
\(359\) 17.4434 30.2129i 0.920630 1.59458i 0.122187 0.992507i \(-0.461009\pi\)
0.798443 0.602071i \(-0.205658\pi\)
\(360\) 2.48775 + 4.30891i 0.131116 + 0.227099i
\(361\) −19.7638 34.2319i −1.04020 1.80168i
\(362\) 1.56320 2.70754i 0.0821598 0.142305i
\(363\) 15.4880 0.812909
\(364\) 2.56964 2.38525i 0.134686 0.125021i
\(365\) −6.14665 −0.321730
\(366\) 1.03555 1.79363i 0.0541292 0.0937545i
\(367\) 12.7077 + 22.0104i 0.663338 + 1.14893i 0.979733 + 0.200307i \(0.0641940\pi\)
−0.316395 + 0.948627i \(0.602473\pi\)
\(368\) −0.454202 0.786701i −0.0236769 0.0410096i
\(369\) −2.68727 + 4.65448i −0.139893 + 0.242303i
\(370\) −16.5705 −0.861462
\(371\) −12.6256 + 11.7196i −0.655490 + 0.608454i
\(372\) −2.29461 −0.118970
\(373\) −5.29974 + 9.17942i −0.274410 + 0.475292i −0.969986 0.243160i \(-0.921816\pi\)
0.695576 + 0.718453i \(0.255149\pi\)
\(374\) 10.3123 + 17.8614i 0.533234 + 0.923589i
\(375\) 6.08576 + 10.5408i 0.314267 + 0.544327i
\(376\) 11.1940 19.3885i 0.577285 0.999887i
\(377\) −1.82885 −0.0941906
\(378\) −2.07701 0.640210i −0.106830 0.0329289i
\(379\) 27.7743 1.42667 0.713335 0.700824i \(-0.247184\pi\)
0.713335 + 0.700824i \(0.247184\pi\)
\(380\) 9.23306 15.9921i 0.473646 0.820379i
\(381\) 7.90658 + 13.6946i 0.405066 + 0.701596i
\(382\) 6.16469 + 10.6775i 0.315413 + 0.546311i
\(383\) −3.81732 + 6.61180i −0.195056 + 0.337847i −0.946919 0.321473i \(-0.895822\pi\)
0.751863 + 0.659320i \(0.229156\pi\)
\(384\) −8.34967 −0.426092
\(385\) 5.52402 + 24.1797i 0.281530 + 1.23231i
\(386\) −17.8668 −0.909395
\(387\) −5.62131 + 9.73639i −0.285747 + 0.494929i
\(388\) 8.66277 + 15.0043i 0.439785 + 0.761730i
\(389\) −1.43845 2.49147i −0.0729323 0.126322i 0.827253 0.561830i \(-0.189902\pi\)
−0.900185 + 0.435507i \(0.856569\pi\)
\(390\) 0.748158 1.29585i 0.0378845 0.0656178i
\(391\) −10.9040 −0.551441
\(392\) 17.2240 8.30327i 0.869944 0.419378i
\(393\) 2.21170 0.111566
\(394\) −0.872247 + 1.51078i −0.0439432 + 0.0761118i
\(395\) 7.30857 + 12.6588i 0.367734 + 0.636934i
\(396\) 3.41008 + 5.90644i 0.171363 + 0.296810i
\(397\) 13.3899 23.1920i 0.672021 1.16397i −0.305309 0.952253i \(-0.598760\pi\)
0.977330 0.211721i \(-0.0679069\pi\)
\(398\) 1.60360 0.0803812
\(399\) 4.50803 + 19.7325i 0.225684 + 0.987860i
\(400\) −0.683646 −0.0341823
\(401\) 2.32076 4.01967i 0.115893 0.200733i −0.802243 0.596997i \(-0.796360\pi\)
0.918136 + 0.396264i \(0.129694\pi\)
\(402\) −0.203857 0.353091i −0.0101675 0.0176106i
\(403\) 0.865783 + 1.49958i 0.0431277 + 0.0746994i
\(404\) −6.76730 + 11.7213i −0.336686 + 0.583157i
\(405\) 1.82148 0.0905102
\(406\) −3.79854 1.17085i −0.188518 0.0581083i
\(407\) −56.9952 −2.82515
\(408\) −6.66258 + 11.5399i −0.329847 + 0.571312i
\(409\) −3.01153 5.21612i −0.148910 0.257921i 0.781915 0.623386i \(-0.214243\pi\)
−0.930825 + 0.365465i \(0.880910\pi\)
\(410\) −4.02100 6.96457i −0.198583 0.343956i
\(411\) 10.3210 17.8765i 0.509098 0.881783i
\(412\) 6.02378 0.296771
\(413\) 16.2391 15.0738i 0.799075 0.741735i
\(414\) 1.83622 0.0902452
\(415\) −14.7188 + 25.4938i −0.722519 + 1.25144i
\(416\) 2.89849 + 5.02033i 0.142110 + 0.246142i
\(417\) 5.01243 + 8.68179i 0.245460 + 0.425149i
\(418\) −16.1724 + 28.0113i −0.791016 + 1.37008i
\(419\) 6.96718 0.340369 0.170185 0.985412i \(-0.445564\pi\)
0.170185 + 0.985412i \(0.445564\pi\)
\(420\) −4.68056 + 4.34469i −0.228388 + 0.211999i
\(421\) −5.53279 −0.269652 −0.134826 0.990869i \(-0.543048\pi\)
−0.134826 + 0.990869i \(0.543048\pi\)
\(422\) 0.197954 0.342866i 0.00963625 0.0166905i
\(423\) −4.09801 7.09796i −0.199252 0.345114i
\(424\) −8.89268 15.4026i −0.431867 0.748015i
\(425\) −4.10307 + 7.10673i −0.199028 + 0.344727i
\(426\) −1.86953 −0.0905791
\(427\) 6.37447 + 1.96485i 0.308482 + 0.0950855i
\(428\) 8.63189 0.417238
\(429\) 2.57332 4.45713i 0.124241 0.215192i
\(430\) −8.41125 14.5687i −0.405627 0.702566i
\(431\) 9.51612 + 16.4824i 0.458375 + 0.793929i 0.998875 0.0474148i \(-0.0150983\pi\)
−0.540500 + 0.841344i \(0.681765\pi\)
\(432\) −0.203200 + 0.351952i −0.00977645 + 0.0169333i
\(433\) 24.1903 1.16251 0.581256 0.813720i \(-0.302561\pi\)
0.581256 + 0.813720i \(0.302561\pi\)
\(434\) 0.838192 + 3.66892i 0.0402345 + 0.176114i
\(435\) 3.33122 0.159720
\(436\) 2.38594 4.13257i 0.114266 0.197914i
\(437\) −8.55020 14.8094i −0.409012 0.708429i
\(438\) 1.38606 + 2.40072i 0.0662285 + 0.114711i
\(439\) −7.03277 + 12.1811i −0.335656 + 0.581373i −0.983611 0.180306i \(-0.942291\pi\)
0.647955 + 0.761679i \(0.275625\pi\)
\(440\) −25.6072 −1.22077
\(441\) 0.520276 6.98064i 0.0247750 0.332411i
\(442\) 4.00737 0.190611
\(443\) 5.26197 9.11400i 0.250004 0.433019i −0.713523 0.700632i \(-0.752901\pi\)
0.963527 + 0.267613i \(0.0862348\pi\)
\(444\) −7.33760 12.7091i −0.348227 0.603147i
\(445\) −11.8846 20.5847i −0.563384 0.975809i
\(446\) 5.01357 8.68375i 0.237399 0.411187i
\(447\) 4.45576 0.210750
\(448\) 2.32717 + 10.1865i 0.109949 + 0.481266i
\(449\) 12.7159 0.600099 0.300050 0.953924i \(-0.402997\pi\)
0.300050 + 0.953924i \(0.402997\pi\)
\(450\) 0.690950 1.19676i 0.0325717 0.0564158i
\(451\) −13.8304 23.9550i −0.651249 1.12800i
\(452\) −0.262563 0.454772i −0.0123499 0.0213907i
\(453\) −8.10537 + 14.0389i −0.380824 + 0.659606i
\(454\) −0.827535 −0.0388382
\(455\) 4.60537 + 1.41955i 0.215903 + 0.0665493i
\(456\) −20.8974 −0.978610
\(457\) −0.960106 + 1.66295i −0.0449118 + 0.0777896i −0.887607 0.460601i \(-0.847634\pi\)
0.842696 + 0.538390i \(0.180967\pi\)
\(458\) −8.23055 14.2557i −0.384588 0.666127i
\(459\) 2.43911 + 4.22466i 0.113848 + 0.197190i
\(460\) 2.69769 4.67253i 0.125780 0.217858i
\(461\) 24.8320 1.15654 0.578270 0.815845i \(-0.303728\pi\)
0.578270 + 0.815845i \(0.303728\pi\)
\(462\) 8.19832 7.61003i 0.381420 0.354050i
\(463\) 9.05949 0.421030 0.210515 0.977591i \(-0.432486\pi\)
0.210515 + 0.977591i \(0.432486\pi\)
\(464\) −0.371622 + 0.643668i −0.0172521 + 0.0298815i
\(465\) −1.57701 2.73146i −0.0731320 0.126668i
\(466\) 8.92982 + 15.4669i 0.413666 + 0.716490i
\(467\) 4.03253 6.98454i 0.186603 0.323206i −0.757512 0.652821i \(-0.773586\pi\)
0.944116 + 0.329615i \(0.106919\pi\)
\(468\) 1.32517 0.0612558
\(469\) 0.962410 0.893350i 0.0444400 0.0412511i
\(470\) 12.2638 0.565688
\(471\) 1.00875 1.74720i 0.0464807 0.0805069i
\(472\) 11.4378 + 19.8108i 0.526467 + 0.911868i
\(473\) −28.9309 50.1098i −1.33024 2.30405i
\(474\) 3.29614 5.70909i 0.151397 0.262227i
\(475\) −12.8694 −0.590489
\(476\) −16.3445 5.03797i −0.749149 0.230915i
\(477\) −6.51105 −0.298121
\(478\) −1.41104 + 2.44398i −0.0645392 + 0.111785i
\(479\) −4.73941 8.20890i −0.216549 0.375074i 0.737202 0.675673i \(-0.236147\pi\)
−0.953751 + 0.300599i \(0.902813\pi\)
\(480\) −5.27955 9.14445i −0.240977 0.417385i
\(481\) −5.53711 + 9.59056i −0.252471 + 0.437292i
\(482\) 3.71377 0.169158
\(483\) 1.31714 + 5.76537i 0.0599320 + 0.262334i
\(484\) −20.5242 −0.932917
\(485\) −11.9072 + 20.6239i −0.540680 + 0.936485i
\(486\) −0.410741 0.711425i −0.0186316 0.0322709i
\(487\) 8.41008 + 14.5667i 0.381097 + 0.660080i 0.991219 0.132228i \(-0.0422130\pi\)
−0.610122 + 0.792307i \(0.708880\pi\)
\(488\) −3.44338 + 5.96412i −0.155875 + 0.269983i
\(489\) 13.9538 0.631011
\(490\) 8.65659 + 5.89682i 0.391065 + 0.266391i
\(491\) −14.8117 −0.668443 −0.334222 0.942494i \(-0.608473\pi\)
−0.334222 + 0.942494i \(0.608473\pi\)
\(492\) 3.56107 6.16796i 0.160546 0.278073i
\(493\) 4.46076 + 7.72627i 0.200903 + 0.347974i
\(494\) 3.14231 + 5.44264i 0.141379 + 0.244876i
\(495\) −4.68727 + 8.11858i −0.210677 + 0.364903i
\(496\) 0.703708 0.0315974
\(497\) −1.34104 5.86997i −0.0601537 0.263304i
\(498\) 13.2763 0.594925
\(499\) −19.4893 + 33.7565i −0.872461 + 1.51115i −0.0130188 + 0.999915i \(0.504144\pi\)
−0.859443 + 0.511232i \(0.829189\pi\)
\(500\) −8.06464 13.9684i −0.360662 0.624684i
\(501\) 2.82517 + 4.89333i 0.126219 + 0.218618i
\(502\) 4.65548 8.06353i 0.207784 0.359893i
\(503\) −27.7246 −1.23618 −0.618089 0.786108i \(-0.712093\pi\)
−0.618089 + 0.786108i \(0.712093\pi\)
\(504\) 6.90640 + 2.12881i 0.307635 + 0.0948246i
\(505\) −18.6037 −0.827855
\(506\) −4.72519 + 8.18426i −0.210060 + 0.363835i
\(507\) −0.500000 0.866025i −0.0222058 0.0384615i
\(508\) −10.4775 18.1476i −0.464866 0.805171i
\(509\) 15.5011 26.8487i 0.687074 1.19005i −0.285707 0.958317i \(-0.592228\pi\)
0.972780 0.231729i \(-0.0744383\pi\)
\(510\) −7.29935 −0.323221
\(511\) −6.54358 + 6.07403i −0.289471 + 0.268699i
\(512\) 4.57610 0.202237
\(513\) −3.82517 + 6.62538i −0.168885 + 0.292518i
\(514\) 4.59579 + 7.96014i 0.202711 + 0.351107i
\(515\) 4.13994 + 7.17058i 0.182427 + 0.315974i
\(516\) 7.44917 12.9023i 0.327931 0.567994i
\(517\) 42.1820 1.85516
\(518\) −17.6406 + 16.3748i −0.775084 + 0.719466i
\(519\) −7.99263 −0.350838
\(520\) −2.48775 + 4.30891i −0.109095 + 0.188958i
\(521\) −5.43983 9.42206i −0.238323 0.412788i 0.721910 0.691987i \(-0.243264\pi\)
−0.960233 + 0.279199i \(0.909931\pi\)
\(522\) −0.751184 1.30109i −0.0328784 0.0569471i
\(523\) −5.11347 + 8.85678i −0.223596 + 0.387280i −0.955897 0.293701i \(-0.905113\pi\)
0.732301 + 0.680981i \(0.238446\pi\)
\(524\) −2.93087 −0.128036
\(525\) 4.25322 + 1.31100i 0.185626 + 0.0572167i
\(526\) 3.84635 0.167709
\(527\) 4.22348 7.31527i 0.183977 0.318658i
\(528\) −1.04580 1.81137i −0.0455125 0.0788300i
\(529\) 9.00183 + 15.5916i 0.391384 + 0.677897i
\(530\) 4.87130 8.43733i 0.211596 0.366494i
\(531\) 8.37453 0.363424
\(532\) −5.97389 26.1488i −0.259001 1.13370i
\(533\) −5.37453 −0.232797
\(534\) −5.35991 + 9.28364i −0.231946 + 0.401742i
\(535\) 5.93240 + 10.2752i 0.256480 + 0.444236i
\(536\) 0.677860 + 1.17409i 0.0292791 + 0.0507129i
\(537\) 5.44786 9.43596i 0.235092 0.407192i
\(538\) 15.9030 0.685625
\(539\) 29.7748 + 20.2824i 1.28249 + 0.873624i
\(540\) −2.41377 −0.103872
\(541\) 0.200420 0.347137i 0.00861671 0.0149246i −0.861685 0.507444i \(-0.830591\pi\)
0.870302 + 0.492519i \(0.163924\pi\)
\(542\) 7.13243 + 12.3537i 0.306364 + 0.530638i
\(543\) 1.90290 + 3.29591i 0.0816611 + 0.141441i
\(544\) 14.1395 24.4903i 0.606224 1.05001i
\(545\) 6.55910 0.280961
\(546\) −0.484066 2.11885i −0.0207161 0.0906783i
\(547\) 45.5549 1.94779 0.973893 0.227010i \(-0.0728949\pi\)
0.973893 + 0.227010i \(0.0728949\pi\)
\(548\) −13.6771 + 23.6894i −0.584255 + 1.01196i
\(549\) 1.26059 + 2.18341i 0.0538007 + 0.0931855i
\(550\) 3.55607 + 6.15930i 0.151632 + 0.262634i
\(551\) −6.99566 + 12.1168i −0.298025 + 0.516195i
\(552\) −6.10573 −0.259877
\(553\) 20.2898 + 6.25406i 0.862810 + 0.265950i
\(554\) 1.90403 0.0808945
\(555\) 10.0858 17.4690i 0.428117 0.741520i
\(556\) −6.64231 11.5048i −0.281697 0.487913i
\(557\) 8.36276 + 14.4847i 0.354341 + 0.613737i 0.987005 0.160689i \(-0.0513718\pi\)
−0.632664 + 0.774427i \(0.718038\pi\)
\(558\) −0.711226 + 1.23188i −0.0301086 + 0.0521496i
\(559\) −11.2426 −0.475512
\(560\) 1.43542 1.33242i 0.0606577 0.0563051i
\(561\) −25.1065 −1.06000
\(562\) 11.0108 19.0712i 0.464462 0.804472i
\(563\) −12.7080 22.0108i −0.535577 0.927647i −0.999135 0.0415802i \(-0.986761\pi\)
0.463558 0.886067i \(-0.346573\pi\)
\(564\) 5.43054 + 9.40597i 0.228667 + 0.396063i
\(565\) 0.360901 0.625099i 0.0151832 0.0262981i
\(566\) 12.0937 0.508336
\(567\) 1.93911 1.79996i 0.0814349 0.0755913i
\(568\) 6.21650 0.260839
\(569\) 10.0903 17.4770i 0.423009 0.732674i −0.573223 0.819399i \(-0.694307\pi\)
0.996232 + 0.0867259i \(0.0276404\pi\)
\(570\) −5.72366 9.91367i −0.239738 0.415238i
\(571\) −13.0255 22.5609i −0.545101 0.944143i −0.998601 0.0528863i \(-0.983158\pi\)
0.453499 0.891257i \(-0.350175\pi\)
\(572\) −3.41008 + 5.90644i −0.142583 + 0.246961i
\(573\) −15.0087 −0.626997
\(574\) −11.1629 3.44083i −0.465932 0.143618i
\(575\) −3.76014 −0.156809
\(576\) −1.97466 + 3.42021i −0.0822775 + 0.142509i
\(577\) 2.75553 + 4.77271i 0.114714 + 0.198691i 0.917665 0.397354i \(-0.130071\pi\)
−0.802951 + 0.596045i \(0.796738\pi\)
\(578\) −2.79180 4.83554i −0.116124 0.201132i
\(579\) 10.8747 18.8356i 0.451938 0.782779i
\(580\) −4.41442 −0.183299
\(581\) 9.52324 + 41.6850i 0.395090 + 1.72939i
\(582\) 10.7402 0.445198
\(583\) 16.7551 29.0206i 0.693923 1.20191i
\(584\) −4.60888 7.98281i −0.190717 0.330331i
\(585\) 0.910741 + 1.57745i 0.0376545 + 0.0652195i
\(586\) 4.13200 7.15683i 0.170691 0.295646i
\(587\) −10.7694 −0.444499 −0.222249 0.974990i \(-0.571340\pi\)
−0.222249 + 0.974990i \(0.571340\pi\)
\(588\) −0.689452 + 9.25051i −0.0284325 + 0.381485i
\(589\) 13.2471 0.545835
\(590\) −6.26547 + 10.8521i −0.257945 + 0.446775i
\(591\) −1.06180 1.83909i −0.0436765 0.0756499i
\(592\) 2.25028 + 3.89760i 0.0924860 + 0.160190i
\(593\) 19.0491 32.9940i 0.782252 1.35490i −0.148376 0.988931i \(-0.547404\pi\)
0.930627 0.365968i \(-0.119262\pi\)
\(594\) 4.22788 0.173472
\(595\) −5.23591 22.9186i −0.214651 0.939569i
\(596\) −5.90463 −0.241863
\(597\) −0.976040 + 1.69055i −0.0399467 + 0.0691896i
\(598\) 0.918109 + 1.59021i 0.0375443 + 0.0650286i
\(599\) 8.80073 + 15.2433i 0.359588 + 0.622825i 0.987892 0.155143i \(-0.0495839\pi\)
−0.628304 + 0.777968i \(0.716251\pi\)
\(600\) −2.29752 + 3.97943i −0.0937960 + 0.162459i
\(601\) 16.9127 0.689884 0.344942 0.938624i \(-0.387899\pi\)
0.344942 + 0.938624i \(0.387899\pi\)
\(602\) −23.3510 7.19764i −0.951716 0.293354i
\(603\) 0.496316 0.0202115
\(604\) 10.7410 18.6039i 0.437044 0.756982i
\(605\) −14.1056 24.4315i −0.573472 0.993283i
\(606\) 4.19511 + 7.26614i 0.170415 + 0.295167i
\(607\) −12.2398 + 21.1999i −0.496797 + 0.860478i −0.999993 0.00369446i \(-0.998824\pi\)
0.503196 + 0.864172i \(0.332157\pi\)
\(608\) 44.3488 1.79858
\(609\) 3.54634 3.29186i 0.143705 0.133393i
\(610\) −3.77248 −0.152743
\(611\) 4.09801 7.09796i 0.165788 0.287153i
\(612\) −3.23222 5.59838i −0.130655 0.226301i
\(613\) −16.5097 28.5956i −0.666819 1.15496i −0.978789 0.204872i \(-0.934322\pi\)
0.311970 0.950092i \(-0.399011\pi\)
\(614\) −3.83385 + 6.64042i −0.154722 + 0.267986i
\(615\) 9.78961 0.394755
\(616\) −27.2608 + 25.3046i −1.09837 + 1.01955i
\(617\) 2.65783 0.107000 0.0535001 0.998568i \(-0.482962\pi\)
0.0535001 + 0.998568i \(0.482962\pi\)
\(618\) 1.86710 3.23391i 0.0751057 0.130087i
\(619\) 5.26942 + 9.12691i 0.211796 + 0.366841i 0.952277 0.305236i \(-0.0987354\pi\)
−0.740481 + 0.672078i \(0.765402\pi\)
\(620\) 2.08980 + 3.61964i 0.0839283 + 0.145368i
\(621\) −1.11763 + 1.93578i −0.0448487 + 0.0776803i
\(622\) −12.6110 −0.505654
\(623\) −32.9936 10.1698i −1.32186 0.407446i
\(624\) −0.406399 −0.0162690
\(625\) 6.87959 11.9158i 0.275184 0.476632i
\(626\) 4.63823 + 8.03365i 0.185381 + 0.321089i
\(627\) −19.6868 34.0985i −0.786215 1.36176i
\(628\) −1.33676 + 2.31533i −0.0533425 + 0.0923919i
\(629\) 54.0225 2.15402
\(630\) 0.881717 + 3.85944i 0.0351285 + 0.153764i
\(631\) 7.56729 0.301249 0.150625 0.988591i \(-0.451872\pi\)
0.150625 + 0.988591i \(0.451872\pi\)
\(632\) −10.9602 + 18.9837i −0.435974 + 0.755130i
\(633\) 0.240972 + 0.417375i 0.00957776 + 0.0165892i
\(634\) −10.1179 17.5247i −0.401832 0.695993i
\(635\) 14.4017 24.9445i 0.571514 0.989891i
\(636\) 8.62823 0.342132
\(637\) 6.30555 3.03975i 0.249835 0.120439i
\(638\) 7.73216 0.306119
\(639\) 1.13790 1.97090i 0.0450147 0.0779677i
\(640\) 7.60439 + 13.1712i 0.300590 + 0.520637i
\(641\) 2.39047 + 4.14041i 0.0944177 + 0.163536i 0.909365 0.415998i \(-0.136568\pi\)
−0.814948 + 0.579534i \(0.803234\pi\)
\(642\) 2.67549 4.63409i 0.105593 0.182893i
\(643\) −20.9917 −0.827831 −0.413916 0.910315i \(-0.635839\pi\)
−0.413916 + 0.910315i \(0.635839\pi\)
\(644\) −1.74543 7.64008i −0.0687796 0.301061i
\(645\) 20.4782 0.806330
\(646\) 15.3289 26.5503i 0.603106 1.04461i
\(647\) 10.1738 + 17.6216i 0.399974 + 0.692775i 0.993722 0.111876i \(-0.0356858\pi\)
−0.593748 + 0.804651i \(0.702352\pi\)
\(648\) 1.36578 + 2.36561i 0.0536530 + 0.0929298i
\(649\) −21.5504 + 37.3264i −0.845927 + 1.46519i
\(650\) 1.38190 0.0542025
\(651\) −4.37803 1.34947i −0.171589 0.0528899i
\(652\) −18.4911 −0.724166
\(653\) −0.816419 + 1.41408i −0.0319489 + 0.0553372i −0.881558 0.472076i \(-0.843505\pi\)
0.849609 + 0.527413i \(0.176838\pi\)
\(654\) −1.47907 2.56182i −0.0578361 0.100175i
\(655\) −2.01429 3.48885i −0.0787047 0.136321i
\(656\) −1.09210 + 1.89158i −0.0426395 + 0.0738537i
\(657\) −3.37453 −0.131653
\(658\) 13.0558 12.1189i 0.508967 0.472445i
\(659\) 14.5692 0.567537 0.283768 0.958893i \(-0.408415\pi\)
0.283768 + 0.958893i \(0.408415\pi\)
\(660\) 6.21141 10.7585i 0.241779 0.418773i
\(661\) 3.34135 + 5.78738i 0.129963 + 0.225103i 0.923662 0.383208i \(-0.125181\pi\)
−0.793699 + 0.608311i \(0.791847\pi\)
\(662\) 11.3179 + 19.6032i 0.439883 + 0.761900i
\(663\) −2.43911 + 4.22466i −0.0947271 + 0.164072i
\(664\) −44.1459 −1.71319
\(665\) 27.0214 25.0824i 1.04784 0.972653i
\(666\) −9.09728 −0.352513
\(667\) −2.04397 + 3.54026i −0.0791428 + 0.137079i
\(668\) −3.74382 6.48448i −0.144853 0.250892i
\(669\) 6.10307 + 10.5708i 0.235958 + 0.408692i
\(670\) −0.371323 + 0.643150i −0.0143454 + 0.0248470i
\(671\) −12.9756 −0.500919
\(672\) −14.6569 4.51779i −0.565402 0.174278i
\(673\) −6.76051 −0.260598 −0.130299 0.991475i \(-0.541594\pi\)
−0.130299 + 0.991475i \(0.541594\pi\)
\(674\) 10.3932 18.0015i 0.400330 0.693391i
\(675\) 0.841101 + 1.45683i 0.0323740 + 0.0560734i
\(676\) 0.662583 + 1.14763i 0.0254840 + 0.0441395i
\(677\) 0.548460 0.949961i 0.0210790 0.0365100i −0.855293 0.518144i \(-0.826623\pi\)
0.876373 + 0.481634i \(0.159957\pi\)
\(678\) −0.325530 −0.0125019
\(679\) 7.70410 + 33.7223i 0.295656 + 1.29414i
\(680\) 24.2716 0.930772
\(681\) 0.503684 0.872406i 0.0193012 0.0334307i
\(682\) −3.66043 6.34005i −0.140165 0.242773i
\(683\) −9.68245 16.7705i −0.370489 0.641705i 0.619152 0.785271i \(-0.287476\pi\)
−0.989641 + 0.143566i \(0.954143\pi\)
\(684\) 5.06898 8.77974i 0.193817 0.335702i
\(685\) −37.5991 −1.43659
\(686\) 15.0428 2.27670i 0.574335 0.0869249i
\(687\) 20.0383 0.764508
\(688\) −2.28450 + 3.95687i −0.0870956 + 0.150854i
\(689\) −3.25553 5.63874i −0.124026 0.214819i
\(690\) −1.67232 2.89654i −0.0636641 0.110270i
\(691\) 10.7499 18.6194i 0.408946 0.708314i −0.585826 0.810437i \(-0.699230\pi\)
0.994772 + 0.102122i \(0.0325633\pi\)
\(692\) 10.5916 0.402631
\(693\) 3.03271 + 13.2747i 0.115203 + 0.504266i
\(694\) −15.0742 −0.572210
\(695\) 9.13006 15.8137i 0.346323 0.599849i
\(696\) 2.49781 + 4.32634i 0.0946794 + 0.163989i
\(697\) 13.1091 + 22.7056i 0.496541 + 0.860034i
\(698\) −11.5183 + 19.9503i −0.435974 + 0.755129i
\(699\) −21.7407 −0.822310
\(700\) −5.63623 1.73729i −0.213029 0.0656635i
\(701\) −24.7988 −0.936637 −0.468319 0.883560i \(-0.655140\pi\)
−0.468319 + 0.883560i \(0.655140\pi\)
\(702\) 0.410741 0.711425i 0.0155024 0.0268510i
\(703\) 42.3608 + 73.3710i 1.59767 + 2.76724i
\(704\) −10.1629 17.6026i −0.383028 0.663424i
\(705\) −7.46445 + 12.9288i −0.281127 + 0.486927i
\(706\) −15.3126 −0.576297
\(707\) −19.8051 + 18.3839i −0.744847 + 0.691399i
\(708\) −11.0976 −0.417075
\(709\) 10.2389 17.7342i 0.384529 0.666023i −0.607175 0.794568i \(-0.707697\pi\)
0.991704 + 0.128545i \(0.0410306\pi\)
\(710\) 1.70266 + 2.94909i 0.0638997 + 0.110677i
\(711\) 4.01243 + 6.94974i 0.150478 + 0.260635i
\(712\) 17.8226 30.8696i 0.667930 1.15689i
\(713\) 3.87048 0.144951
\(714\) −7.77072 + 7.21311i −0.290812 + 0.269944i
\(715\) −9.37453 −0.350588
\(716\) −7.21932 + 12.5042i −0.269799 + 0.467305i
\(717\) −1.71767 2.97509i −0.0641475 0.111107i
\(718\) 14.3295 + 24.8194i 0.534772 + 0.926252i
\(719\) 7.00581 12.1344i 0.261272 0.452537i −0.705308 0.708901i \(-0.749191\pi\)
0.966580 + 0.256364i \(0.0825246\pi\)
\(720\) 0.740250 0.0275875
\(721\) 11.4931 + 3.54261i 0.428027 + 0.131934i
\(722\) 32.4712 1.20845
\(723\) −2.26041 + 3.91514i −0.0840655 + 0.145606i
\(724\) −2.52166 4.36764i −0.0937166 0.162322i
\(725\) 1.53825 + 2.66432i 0.0571291 + 0.0989505i
\(726\) −6.36156 + 11.0185i −0.236100 + 0.408936i
\(727\) −23.9523 −0.888342 −0.444171 0.895942i \(-0.646502\pi\)
−0.444171 + 0.895942i \(0.646502\pi\)
\(728\) 1.60960 + 7.04552i 0.0596557 + 0.261124i
\(729\) 1.00000 0.0370370
\(730\) 2.52468 4.37288i 0.0934427 0.161847i
\(731\) 27.4220 + 47.4962i 1.01424 + 1.75671i
\(732\) −1.67049 2.89338i −0.0617431 0.106942i
\(733\) 6.08419 10.5381i 0.224725 0.389235i −0.731512 0.681829i \(-0.761185\pi\)
0.956237 + 0.292594i \(0.0945183\pi\)
\(734\) −20.8783 −0.770634
\(735\) −11.4854 + 5.53685i −0.423647 + 0.204230i
\(736\) 12.9577 0.477627
\(737\) −1.27718 + 2.21214i −0.0470456 + 0.0814854i
\(738\) −2.20754 3.82357i −0.0812607 0.140748i
\(739\) −11.8531 20.5301i −0.436022 0.755212i 0.561357 0.827574i \(-0.310280\pi\)
−0.997378 + 0.0723622i \(0.976946\pi\)
\(740\) −13.3653 + 23.1494i −0.491318 + 0.850989i
\(741\) −7.65033 −0.281042
\(742\) −3.15178 13.7959i −0.115705 0.506464i
\(743\) 43.8078 1.60715 0.803577 0.595201i \(-0.202928\pi\)
0.803577 + 0.595201i \(0.202928\pi\)
\(744\) 2.36494 4.09620i 0.0867030 0.150174i
\(745\) −4.05805 7.02875i −0.148675 0.257513i
\(746\) −4.35364 7.54073i −0.159398 0.276086i
\(747\) −8.08069 + 13.9962i −0.295657 + 0.512093i
\(748\) 33.2702 1.21648
\(749\) 16.4693 + 5.07645i 0.601775 + 0.185489i
\(750\) −9.99868 −0.365100
\(751\) −5.43423 + 9.41235i −0.198298 + 0.343462i −0.947977 0.318340i \(-0.896875\pi\)
0.749679 + 0.661802i \(0.230208\pi\)
\(752\) −1.66543 2.88461i −0.0607319 0.105191i
\(753\) 5.66717 + 9.81583i 0.206523 + 0.357709i
\(754\) 0.751184 1.30109i 0.0273565 0.0473829i
\(755\) 29.5276 1.07462
\(756\) −2.56964 + 2.38525i −0.0934569 + 0.0867507i
\(757\) −17.6451 −0.641323 −0.320662 0.947194i \(-0.603905\pi\)
−0.320662 + 0.947194i \(0.603905\pi\)
\(758\) −11.4080 + 19.7593i −0.414359 + 0.717691i
\(759\) −5.75202 9.96280i −0.208785 0.361627i
\(760\) 19.0321 + 32.9646i 0.690367 + 1.19575i
\(761\) 5.48919 9.50756i 0.198983 0.344649i −0.749216 0.662326i \(-0.769569\pi\)
0.948199 + 0.317677i \(0.102903\pi\)
\(762\) −12.9902 −0.470587
\(763\) 6.98267 6.48161i 0.252789 0.234650i
\(764\) 19.8890 0.719559
\(765\) 4.44279 7.69514i 0.160629 0.278218i
\(766\) −3.13586 5.43148i −0.113303 0.196247i
\(767\) 4.18727 + 7.25256i 0.151193 + 0.261875i
\(768\) 7.37887 12.7806i 0.266262 0.461180i
\(769\) −1.58755 −0.0572484 −0.0286242 0.999590i \(-0.509113\pi\)
−0.0286242 + 0.999590i \(0.509113\pi\)
\(770\) −19.4710 6.00167i −0.701685 0.216285i
\(771\) −11.1890 −0.402962
\(772\) −14.4108 + 24.9602i −0.518656 + 0.898339i
\(773\) −22.0386 38.1720i −0.792674 1.37295i −0.924306 0.381653i \(-0.875355\pi\)
0.131632 0.991299i \(-0.457978\pi\)
\(774\) −4.61781 7.99828i −0.165984 0.287492i
\(775\) 1.45642 2.52260i 0.0523162 0.0906143i
\(776\) −35.7131 −1.28203
\(777\) −6.52559 28.5637i −0.234104 1.02472i
\(778\) 2.36332 0.0847292
\(779\) −20.5585 + 35.6083i −0.736584 + 1.27580i
\(780\) −1.20688 2.09038i −0.0432134 0.0748478i
\(781\) 5.85638 + 10.1435i 0.209558 + 0.362965i
\(782\) 4.47874 7.75740i 0.160159 0.277404i
\(783\) 1.82885 0.0653578
\(784\) 0.211440 2.83693i 0.00755143 0.101319i
\(785\) −3.67483 −0.131160
\(786\) −0.908437 + 1.57346i −0.0324029 + 0.0561234i
\(787\) −16.5191 28.6118i −0.588841 1.01990i −0.994385 0.105827i \(-0.966251\pi\)
0.405544 0.914076i \(-0.367082\pi\)
\(788\) 1.40706 + 2.43709i 0.0501243 + 0.0868179i
\(789\) −2.34110 + 4.05491i −0.0833454 + 0.144358i
\(790\) −12.0077 −0.427216
\(791\) −0.233507 1.02210i −0.00830254 0.0363418i
\(792\) −14.0584 −0.499544
\(793\) −1.26059 + 2.18341i −0.0447649 + 0.0775350i
\(794\) 10.9996 + 19.0518i 0.390361 + 0.676125i
\(795\) 5.92988 + 10.2709i 0.210311 + 0.364270i
\(796\) 1.29342 2.24026i 0.0458439 0.0794040i
\(797\) −9.81448 −0.347647 −0.173823 0.984777i \(-0.555612\pi\)
−0.173823 + 0.984777i \(0.555612\pi\)
\(798\) −15.8898 4.89782i −0.562493 0.173381i
\(799\) −39.9819 −1.41446
\(800\) 4.87585 8.44521i 0.172387 0.298583i
\(801\) −6.52468 11.3011i −0.230538 0.399304i
\(802\) 1.90646 + 3.30209i 0.0673196 + 0.116601i
\(803\) 8.68376 15.0407i 0.306443 0.530775i
\(804\) −0.657701 −0.0231953
\(805\) 7.89502 7.32849i 0.278263 0.258295i
\(806\) −1.42245 −0.0501037
\(807\) −9.67942 + 16.7652i −0.340732 + 0.590165i
\(808\) −13.9494 24.1611i −0.490740 0.849986i
\(809\) 23.6464 + 40.9567i 0.831362 + 1.43996i 0.896959 + 0.442114i \(0.145771\pi\)
−0.0655972 + 0.997846i \(0.520895\pi\)
\(810\) −0.748158 + 1.29585i −0.0262876 + 0.0455314i
\(811\) 18.8003 0.660167 0.330083 0.943952i \(-0.392923\pi\)
0.330083 + 0.943952i \(0.392923\pi\)
\(812\) −4.69949 + 4.36226i −0.164920 + 0.153085i
\(813\) −17.3648 −0.609009
\(814\) 23.4103 40.5478i 0.820529 1.42120i
\(815\) −12.7083 22.0114i −0.445151 0.771024i
\(816\) 0.991252 + 1.71690i 0.0347008 + 0.0601035i
\(817\) −43.0049 + 74.4866i −1.50455 + 2.60596i
\(818\) 4.94784 0.172997
\(819\) 2.52837 + 0.779336i 0.0883483 + 0.0272322i
\(820\) −12.9729 −0.453032
\(821\) 10.5865 18.3363i 0.369471 0.639942i −0.620012 0.784592i \(-0.712872\pi\)
0.989483 + 0.144650i \(0.0462057\pi\)
\(822\) 8.47853 + 14.6852i 0.295723 + 0.512206i
\(823\) −6.64140 11.5032i −0.231505 0.400978i 0.726746 0.686906i \(-0.241032\pi\)
−0.958251 + 0.285928i \(0.907698\pi\)
\(824\) −6.20841 + 10.7533i −0.216280 + 0.374608i
\(825\) −8.65770 −0.301422
\(826\) 4.05382 + 17.7444i 0.141051 + 0.617405i
\(827\) 14.0291 0.487840 0.243920 0.969795i \(-0.421567\pi\)
0.243920 + 0.969795i \(0.421567\pi\)
\(828\) 1.48104 2.56524i 0.0514697 0.0891481i
\(829\) 5.41786 + 9.38401i 0.188170 + 0.325920i 0.944640 0.328108i \(-0.106411\pi\)
−0.756470 + 0.654028i \(0.773078\pi\)
\(830\) −12.0913 20.9427i −0.419694 0.726931i
\(831\) −1.15890 + 2.00727i −0.0402018 + 0.0696315i
\(832\) −3.94932 −0.136918
\(833\) −28.2218 19.2245i −0.977827 0.666090i
\(834\) −8.23525 −0.285163
\(835\) 5.14599 8.91312i 0.178084 0.308451i
\(836\) 26.0883 + 45.1862i 0.902282 + 1.56280i
\(837\) −0.865783 1.49958i −0.0299258 0.0518331i
\(838\) −2.86171 + 4.95662i −0.0988561 + 0.171224i
\(839\) 1.76051 0.0607794 0.0303897 0.999538i \(-0.490325\pi\)
0.0303897 + 0.999538i \(0.490325\pi\)
\(840\) −2.93186 12.8333i −0.101159 0.442791i
\(841\) −25.6553 −0.884666
\(842\) 2.27255 3.93617i 0.0783171 0.135649i
\(843\) 13.4036 + 23.2156i 0.461643 + 0.799589i
\(844\) −0.319328 0.553092i −0.0109917 0.0190382i
\(845\) −0.910741 + 1.57745i −0.0313305 + 0.0542659i
\(846\) 6.73288 0.231481
\(847\) −39.1593 12.0703i −1.34553 0.414742i
\(848\) −2.64609 −0.0908670
\(849\) −7.36090 + 12.7495i −0.252625 + 0.437560i
\(850\) −3.37060 5.83805i −0.115611 0.200244i
\(851\) 12.3768 + 21.4373i 0.424272 + 0.734861i
\(852\) −1.50791 + 2.61177i −0.0516601 + 0.0894779i
\(853\) 11.7754 0.403181 0.201590 0.979470i \(-0.435389\pi\)
0.201590 + 0.979470i \(0.435389\pi\)
\(854\) −4.01610 + 3.72791i −0.137428 + 0.127566i
\(855\) 13.9349 0.476565
\(856\) −8.89645 + 15.4091i −0.304075 + 0.526673i
\(857\) −0.157584 0.272943i −0.00538296 0.00932356i 0.863321 0.504655i \(-0.168380\pi\)
−0.868704 + 0.495331i \(0.835047\pi\)
\(858\) 2.11394 + 3.66145i 0.0721688 + 0.125000i
\(859\) −28.0707 + 48.6199i −0.957761 + 1.65889i −0.229841 + 0.973228i \(0.573821\pi\)
−0.727920 + 0.685662i \(0.759513\pi\)
\(860\) −27.1371 −0.925366
\(861\) 10.4218 9.67395i 0.355174 0.329687i
\(862\) −15.6346 −0.532518
\(863\) −26.1297 + 45.2579i −0.889465 + 1.54060i −0.0489551 + 0.998801i \(0.515589\pi\)
−0.840509 + 0.541797i \(0.817744\pi\)
\(864\) −2.89849 5.02033i −0.0986087 0.170795i
\(865\) 7.27922 + 12.6080i 0.247501 + 0.428684i
\(866\) −9.93596 + 17.2096i −0.337638 + 0.584806i
\(867\) 6.79698 0.230838
\(868\) 5.80162 + 1.78827i 0.196920 + 0.0606980i
\(869\) −41.3012 −1.40105
\(870\) −1.36827 + 2.36991i −0.0463887 + 0.0803475i
\(871\) 0.248158 + 0.429822i 0.00840851 + 0.0145640i
\(872\) 4.91814 + 8.51847i 0.166549 + 0.288472i
\(873\) −6.53711 + 11.3226i −0.221248 + 0.383212i
\(874\) 14.0477 0.475170
\(875\) −7.17217 31.3939i −0.242464 1.06131i
\(876\) 4.47182 0.151089
\(877\) 6.22734 10.7861i 0.210282 0.364220i −0.741520 0.670930i \(-0.765895\pi\)
0.951803 + 0.306710i \(0.0992283\pi\)
\(878\) −5.77730 10.0066i −0.194974 0.337706i
\(879\) 5.02993 + 8.71209i 0.169655 + 0.293852i
\(880\) −1.90490 + 3.29939i −0.0642142 + 0.111222i
\(881\) 42.2647 1.42393 0.711967 0.702213i \(-0.247804\pi\)
0.711967 + 0.702213i \(0.247804\pi\)
\(882\) 4.75250 + 3.23737i 0.160025 + 0.109008i
\(883\) 24.4690 0.823448 0.411724 0.911309i \(-0.364927\pi\)
0.411724 + 0.911309i \(0.364927\pi\)
\(884\) 3.23222 5.59838i 0.108711 0.188294i
\(885\) −7.62703 13.2104i −0.256380 0.444063i
\(886\) 4.32262 + 7.48699i 0.145221 + 0.251530i
\(887\) 6.09057 10.5492i 0.204501 0.354207i −0.745472 0.666537i \(-0.767776\pi\)
0.949974 + 0.312330i \(0.101109\pi\)
\(888\) 30.2500 1.01512
\(889\) −9.31804 40.7868i −0.312517 1.36795i
\(890\) 19.5260 0.654512
\(891\) −2.57332 + 4.45713i −0.0862096 + 0.149319i
\(892\) −8.08759 14.0081i −0.270792 0.469026i
\(893\) −31.3511 54.3017i −1.04913 1.81714i
\(894\) −1.83017 + 3.16994i −0.0612099 + 0.106019i
\(895\) −19.8463 −0.663390
\(896\) 21.1110 + 6.50719i 0.705270 + 0.217390i
\(897\) −2.23525 −0.0746328
\(898\) −5.22294 + 9.04639i −0.174292 + 0.301882i
\(899\) −1.58339 2.74251i −0.0528089 0.0914678i
\(900\) −1.11460 1.93054i −0.0371533 0.0643514i
\(901\) −15.8812 + 27.5070i −0.529078 + 0.916390i
\(902\) 22.7229 0.756589
\(903\) 21.8006 20.2363i 0.725480 0.673421i
\(904\) 1.08244 0.0360015
\(905\) 3.46609 6.00345i 0.115217 0.199561i
\(906\) −6.65842 11.5327i −0.221211 0.383149i
\(907\) 2.87537 + 4.98029i 0.0954751 + 0.165368i 0.909807 0.415032i \(-0.136230\pi\)
−0.814332 + 0.580400i \(0.802896\pi\)
\(908\) −0.667465 + 1.15608i −0.0221506 + 0.0383660i
\(909\) −10.2135 −0.338761
\(910\) −2.90152 + 2.69331i −0.0961844 + 0.0892824i
\(911\) 47.9209 1.58769 0.793846 0.608119i \(-0.208076\pi\)
0.793846 + 0.608119i \(0.208076\pi\)
\(912\) −1.55455 + 2.69255i −0.0514762 + 0.0891593i
\(913\) −41.5885 72.0334i −1.37638 2.38396i
\(914\) −0.788710 1.36609i −0.0260882 0.0451861i
\(915\) 2.29614 3.97704i 0.0759081 0.131477i
\(916\) −26.5541 −0.877371
\(917\) −5.59199 1.72366i −0.184664 0.0569202i
\(918\) −4.00737 −0.132263
\(919\) −15.4236 + 26.7145i −0.508778 + 0.881229i 0.491171 + 0.871063i \(0.336569\pi\)
−0.999948 + 0.0101654i \(0.996764\pi\)
\(920\) 5.56074 + 9.63149i 0.183332 + 0.317541i
\(921\) −4.66699 8.08346i −0.153783 0.266359i
\(922\) −10.1995 + 17.6661i −0.335903 + 0.581801i
\(923\) 2.27580 0.0749089
\(924\) −4.01884 17.5912i −0.132210 0.578709i
\(925\) 18.6291 0.612521
\(926\) −3.72111 + 6.44515i −0.122283 + 0.211801i
\(927\) 2.27284 + 3.93667i 0.0746499 + 0.129297i
\(928\) −5.30091 9.18144i −0.174011 0.301396i
\(929\) −4.85631 + 8.41138i −0.159330 + 0.275968i −0.934627 0.355628i \(-0.884267\pi\)
0.775297 + 0.631597i \(0.217600\pi\)
\(930\) 2.59097 0.0849612
\(931\) 3.98028 53.4042i 0.130449 1.75025i
\(932\) 28.8101 0.943706
\(933\) 7.67574 13.2948i 0.251292 0.435251i
\(934\) 3.31265 + 5.73768i 0.108393 + 0.187743i
\(935\) 22.8655 + 39.6042i 0.747781 + 1.29520i
\(936\) −1.36578 + 2.36561i −0.0446420 + 0.0773222i
\(937\) −55.4352 −1.81099 −0.905495 0.424356i \(-0.860500\pi\)
−0.905495 + 0.424356i \(0.860500\pi\)
\(938\) 0.240250 + 1.05162i 0.00784443 + 0.0343365i
\(939\) −11.2923 −0.368512
\(940\) 9.89164 17.1328i 0.322630 0.558811i
\(941\) 12.2114 + 21.1508i 0.398081 + 0.689496i 0.993489 0.113927i \(-0.0363431\pi\)
−0.595409 + 0.803423i \(0.703010\pi\)
\(942\) 0.828669 + 1.43530i 0.0269995 + 0.0467645i
\(943\) −6.00671 + 10.4039i −0.195605 + 0.338799i
\(944\) 3.40341 0.110771
\(945\) −4.60537 1.41955i −0.149813 0.0461778i
\(946\) 47.5325 1.54541
\(947\) −8.32185 + 14.4139i −0.270424 + 0.468388i −0.968970 0.247177i \(-0.920497\pi\)
0.698547 + 0.715564i \(0.253830\pi\)
\(948\) −5.31714 9.20956i −0.172693 0.299113i
\(949\) −1.68727 2.92243i −0.0547710 0.0948661i
\(950\) 5.28599 9.15561i 0.171500 0.297047i
\(951\) 24.6332 0.798786
\(952\) 25.8389 23.9848i 0.837445 0.777351i
\(953\) 44.7918 1.45095 0.725475 0.688249i \(-0.241620\pi\)
0.725475 + 0.688249i \(0.241620\pi\)
\(954\) 2.67436 4.63212i 0.0865855 0.149971i
\(955\) 13.6690 + 23.6754i 0.442319 + 0.766120i
\(956\) 2.27620 + 3.94249i 0.0736175 + 0.127509i
\(957\) −4.70623 + 8.15142i −0.152131 + 0.263498i
\(958\) 7.78668 0.251576
\(959\) −40.0271 + 37.1548i −1.29254 + 1.19979i
\(960\) 7.19362 0.232173
\(961\) 14.0008 24.2502i 0.451640 0.782263i
\(962\) −4.54864 7.87848i −0.146654 0.254012i
\(963\) 3.25691 + 5.64113i 0.104952 + 0.181783i
\(964\) 2.99542 5.18821i 0.0964759 0.167101i
\(965\) −39.6162 −1.27529
\(966\) −4.64263 1.43103i −0.149374 0.0460427i
\(967\) 54.1765 1.74220 0.871099 0.491107i \(-0.163408\pi\)
0.871099 + 0.491107i \(0.163408\pi\)
\(968\) 21.1532 36.6385i 0.679891 1.17761i
\(969\) 18.6600 + 32.3200i 0.599445 + 1.03827i
\(970\) −9.78159 16.9422i −0.314068 0.543982i
\(971\) −16.7999 + 29.0984i −0.539136 + 0.933811i 0.459815 + 0.888015i \(0.347916\pi\)
−0.998951 + 0.0457959i \(0.985418\pi\)
\(972\) −1.32517 −0.0425047
\(973\) −5.90724 25.8571i −0.189377 0.828941i
\(974\) −13.8175 −0.442740
\(975\) −0.841101 + 1.45683i −0.0269368 + 0.0466559i
\(976\) 0.512303 + 0.887335i 0.0163984 + 0.0284029i
\(977\) 27.9356 + 48.3859i 0.893739 + 1.54800i 0.835357 + 0.549707i \(0.185261\pi\)
0.0583819 + 0.998294i \(0.481406\pi\)
\(978\) −5.73138 + 9.92705i −0.183269 + 0.317432i
\(979\) 67.1605 2.14646
\(980\) 15.2201 7.33724i 0.486189 0.234380i
\(981\) 3.60097 0.114970
\(982\) 6.08378 10.5374i 0.194141 0.336263i
\(983\) −26.0283 45.0823i −0.830172 1.43790i −0.897901 0.440197i \(-0.854909\pi\)
0.0677289 0.997704i \(-0.478425\pi\)
\(984\) 7.34044 + 12.7140i 0.234005 + 0.405308i
\(985\) −1.93404 + 3.34986i −0.0616238 + 0.106735i
\(986\) −7.32888 −0.233399
\(987\) 4.82957 + 21.1400i 0.153727 + 0.672892i
\(988\) 10.1380 0.322532
\(989\) −12.5650 + 21.7633i −0.399545 + 0.692032i
\(990\) −3.85051 6.66927i −0.122377 0.211963i
\(991\) −7.15402 12.3911i −0.227255 0.393617i 0.729739 0.683726i \(-0.239642\pi\)
−0.956994 + 0.290109i \(0.906308\pi\)
\(992\) −5.01893 + 8.69304i −0.159351 + 0.276004i
\(993\) −27.5549 −0.874427
\(994\) 4.72686 + 1.45699i 0.149927 + 0.0462130i
\(995\) 3.55568 0.112723
\(996\) 10.7083 18.5473i 0.339304 0.587692i
\(997\) −28.3864 49.1667i −0.899006 1.55712i −0.828766 0.559595i \(-0.810957\pi\)
−0.0702399 0.997530i \(-0.522376\pi\)
\(998\) −16.0101 27.7304i −0.506792 0.877789i
\(999\) 5.53711 9.59056i 0.175187 0.303432i
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 273.2.i.d.79.2 8
3.2 odd 2 819.2.j.f.352.3 8
7.2 even 3 1911.2.a.r.1.3 4
7.4 even 3 inner 273.2.i.d.235.2 yes 8
7.5 odd 6 1911.2.a.q.1.3 4
21.2 odd 6 5733.2.a.bj.1.2 4
21.5 even 6 5733.2.a.bk.1.2 4
21.11 odd 6 819.2.j.f.235.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.i.d.79.2 8 1.1 even 1 trivial
273.2.i.d.235.2 yes 8 7.4 even 3 inner
819.2.j.f.235.3 8 21.11 odd 6
819.2.j.f.352.3 8 3.2 odd 2
1911.2.a.q.1.3 4 7.5 odd 6
1911.2.a.r.1.3 4 7.2 even 3
5733.2.a.bj.1.2 4 21.2 odd 6
5733.2.a.bk.1.2 4 21.5 even 6