Properties

Label 1045.2.b.c.419.5
Level $1045$
Weight $2$
Character 1045.419
Analytic conductor $8.344$
Analytic rank $0$
Dimension $20$
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] = [1045,2,Mod(419,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.419");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.34436701122\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + 2753 x^{4} + 276 x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.5
Root \(-1.51095i\) of defining polynomial
Character \(\chi\) \(=\) 1045.419
Dual form 1045.2.b.c.419.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.51095i q^{2} +0.900785i q^{3} -0.282982 q^{4} +(0.672383 - 2.13258i) q^{5} +1.36104 q^{6} +0.603482i q^{7} -2.59434i q^{8} +2.18859 q^{9} +O(q^{10})\) \(q-1.51095i q^{2} +0.900785i q^{3} -0.282982 q^{4} +(0.672383 - 2.13258i) q^{5} +1.36104 q^{6} +0.603482i q^{7} -2.59434i q^{8} +2.18859 q^{9} +(-3.22223 - 1.01594i) q^{10} +1.00000 q^{11} -0.254906i q^{12} +3.06772i q^{13} +0.911833 q^{14} +(1.92100 + 0.605673i) q^{15} -4.48589 q^{16} -4.08319i q^{17} -3.30685i q^{18} +1.00000 q^{19} +(-0.190272 + 0.603482i) q^{20} -0.543607 q^{21} -1.51095i q^{22} -6.19344i q^{23} +2.33694 q^{24} +(-4.09580 - 2.86782i) q^{25} +4.63519 q^{26} +4.67380i q^{27} -0.170774i q^{28} +2.92797 q^{29} +(0.915143 - 2.90254i) q^{30} +7.98044 q^{31} +1.58930i q^{32} +0.900785i q^{33} -6.16951 q^{34} +(1.28697 + 0.405771i) q^{35} -0.619330 q^{36} +10.2773i q^{37} -1.51095i q^{38} -2.76336 q^{39} +(-5.53263 - 1.74439i) q^{40} -7.31303 q^{41} +0.821366i q^{42} -0.0821817i q^{43} -0.282982 q^{44} +(1.47157 - 4.66734i) q^{45} -9.35800 q^{46} -2.77574i q^{47} -4.04082i q^{48} +6.63581 q^{49} +(-4.33315 + 6.18857i) q^{50} +3.67807 q^{51} -0.868110i q^{52} -8.01831i q^{53} +7.06190 q^{54} +(0.672383 - 2.13258i) q^{55} +1.56563 q^{56} +0.900785i q^{57} -4.42403i q^{58} -3.21020 q^{59} +(-0.543607 - 0.171394i) q^{60} -11.1879 q^{61} -12.0581i q^{62} +1.32077i q^{63} -6.57042 q^{64} +(6.54217 + 2.06269i) q^{65} +1.36104 q^{66} -3.52951i q^{67} +1.15547i q^{68} +5.57896 q^{69} +(0.613101 - 1.94456i) q^{70} +1.51928 q^{71} -5.67793i q^{72} +3.04579i q^{73} +15.5285 q^{74} +(2.58329 - 3.68944i) q^{75} -0.282982 q^{76} +0.603482i q^{77} +4.17531i q^{78} +3.57318 q^{79} +(-3.01623 + 9.56651i) q^{80} +2.35567 q^{81} +11.0497i q^{82} -9.37109i q^{83} +0.153831 q^{84} +(-8.70772 - 2.74546i) q^{85} -0.124173 q^{86} +2.63747i q^{87} -2.59434i q^{88} +0.629618 q^{89} +(-7.05213 - 2.22347i) q^{90} -1.85132 q^{91} +1.75263i q^{92} +7.18867i q^{93} -4.19402 q^{94} +(0.672383 - 2.13258i) q^{95} -1.43161 q^{96} -5.71214i q^{97} -10.0264i q^{98} +2.18859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9} - 6 q^{10} + 20 q^{11} + 24 q^{14} - 6 q^{15} - 4 q^{16} + 20 q^{19} - 6 q^{20} - 30 q^{21} + 38 q^{24} + 2 q^{25} + 8 q^{26} + 50 q^{29} - 20 q^{30} - 50 q^{31} + 28 q^{34} + 6 q^{35} - 12 q^{36} + 48 q^{39} + 12 q^{40} - 34 q^{41} - 12 q^{44} - 18 q^{45} - 36 q^{46} - 6 q^{49} + 26 q^{50} - 40 q^{51} - 6 q^{54} - 40 q^{56} + 30 q^{59} - 30 q^{60} - 14 q^{61} + 36 q^{64} + 30 q^{65} - 8 q^{66} - 12 q^{69} - 54 q^{70} - 40 q^{71} + 50 q^{74} - 8 q^{75} - 12 q^{76} + 106 q^{79} + 8 q^{80} - 30 q^{84} - 22 q^{85} + 56 q^{86} + 36 q^{89} - 64 q^{90} - 56 q^{91} + 28 q^{94} + 66 q^{96} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51095i 1.06841i −0.845356 0.534203i \(-0.820612\pi\)
0.845356 0.534203i \(-0.179388\pi\)
\(3\) 0.900785i 0.520069i 0.965599 + 0.260034i \(0.0837339\pi\)
−0.965599 + 0.260034i \(0.916266\pi\)
\(4\) −0.282982 −0.141491
\(5\) 0.672383 2.13258i 0.300699 0.953719i
\(6\) 1.36104 0.555644
\(7\) 0.603482i 0.228095i 0.993475 + 0.114047i \(0.0363816\pi\)
−0.993475 + 0.114047i \(0.963618\pi\)
\(8\) 2.59434i 0.917236i
\(9\) 2.18859 0.729529
\(10\) −3.22223 1.01594i −1.01896 0.321268i
\(11\) 1.00000 0.301511
\(12\) 0.254906i 0.0735850i
\(13\) 3.06772i 0.850833i 0.904998 + 0.425417i \(0.139872\pi\)
−0.904998 + 0.425417i \(0.860128\pi\)
\(14\) 0.911833 0.243698
\(15\) 1.92100 + 0.605673i 0.495999 + 0.156384i
\(16\) −4.48589 −1.12147
\(17\) 4.08319i 0.990318i −0.868802 0.495159i \(-0.835110\pi\)
0.868802 0.495159i \(-0.164890\pi\)
\(18\) 3.30685i 0.779433i
\(19\) 1.00000 0.229416
\(20\) −0.190272 + 0.603482i −0.0425462 + 0.134943i
\(21\) −0.543607 −0.118625
\(22\) 1.51095i 0.322136i
\(23\) 6.19344i 1.29142i −0.763582 0.645710i \(-0.776561\pi\)
0.763582 0.645710i \(-0.223439\pi\)
\(24\) 2.33694 0.477026
\(25\) −4.09580 2.86782i −0.819160 0.573564i
\(26\) 4.63519 0.909035
\(27\) 4.67380i 0.899473i
\(28\) 0.170774i 0.0322733i
\(29\) 2.92797 0.543711 0.271855 0.962338i \(-0.412363\pi\)
0.271855 + 0.962338i \(0.412363\pi\)
\(30\) 0.915143 2.90254i 0.167082 0.529929i
\(31\) 7.98044 1.43333 0.716665 0.697418i \(-0.245668\pi\)
0.716665 + 0.697418i \(0.245668\pi\)
\(32\) 1.58930i 0.280950i
\(33\) 0.900785i 0.156807i
\(34\) −6.16951 −1.05806
\(35\) 1.28697 + 0.405771i 0.217538 + 0.0685878i
\(36\) −0.619330 −0.103222
\(37\) 10.2773i 1.68957i 0.535106 + 0.844785i \(0.320272\pi\)
−0.535106 + 0.844785i \(0.679728\pi\)
\(38\) 1.51095i 0.245109i
\(39\) −2.76336 −0.442492
\(40\) −5.53263 1.74439i −0.874786 0.275812i
\(41\) −7.31303 −1.14210 −0.571052 0.820914i \(-0.693465\pi\)
−0.571052 + 0.820914i \(0.693465\pi\)
\(42\) 0.821366i 0.126740i
\(43\) 0.0821817i 0.0125326i −0.999980 0.00626629i \(-0.998005\pi\)
0.999980 0.00626629i \(-0.00199464\pi\)
\(44\) −0.282982 −0.0426611
\(45\) 1.47157 4.66734i 0.219368 0.695765i
\(46\) −9.35800 −1.37976
\(47\) 2.77574i 0.404883i −0.979294 0.202442i \(-0.935112\pi\)
0.979294 0.202442i \(-0.0648877\pi\)
\(48\) 4.04082i 0.583242i
\(49\) 6.63581 0.947973
\(50\) −4.33315 + 6.18857i −0.612800 + 0.875196i
\(51\) 3.67807 0.515033
\(52\) 0.868110i 0.120385i
\(53\) 8.01831i 1.10140i −0.834703 0.550700i \(-0.814361\pi\)
0.834703 0.550700i \(-0.185639\pi\)
\(54\) 7.06190 0.961003
\(55\) 0.672383 2.13258i 0.0906641 0.287557i
\(56\) 1.56563 0.209217
\(57\) 0.900785i 0.119312i
\(58\) 4.42403i 0.580904i
\(59\) −3.21020 −0.417933 −0.208966 0.977923i \(-0.567010\pi\)
−0.208966 + 0.977923i \(0.567010\pi\)
\(60\) −0.543607 0.171394i −0.0701794 0.0221269i
\(61\) −11.1879 −1.43247 −0.716233 0.697862i \(-0.754135\pi\)
−0.716233 + 0.697862i \(0.754135\pi\)
\(62\) 12.0581i 1.53138i
\(63\) 1.32077i 0.166402i
\(64\) −6.57042 −0.821302
\(65\) 6.54217 + 2.06269i 0.811456 + 0.255845i
\(66\) 1.36104 0.167533
\(67\) 3.52951i 0.431198i −0.976482 0.215599i \(-0.930830\pi\)
0.976482 0.215599i \(-0.0691704\pi\)
\(68\) 1.15547i 0.140121i
\(69\) 5.57896 0.671627
\(70\) 0.613101 1.94456i 0.0732796 0.232419i
\(71\) 1.51928 0.180305 0.0901525 0.995928i \(-0.471265\pi\)
0.0901525 + 0.995928i \(0.471265\pi\)
\(72\) 5.67793i 0.669150i
\(73\) 3.04579i 0.356483i 0.983987 + 0.178242i \(0.0570409\pi\)
−0.983987 + 0.178242i \(0.942959\pi\)
\(74\) 15.5285 1.80515
\(75\) 2.58329 3.68944i 0.298293 0.426020i
\(76\) −0.282982 −0.0324603
\(77\) 0.603482i 0.0687731i
\(78\) 4.17531i 0.472761i
\(79\) 3.57318 0.402014 0.201007 0.979590i \(-0.435579\pi\)
0.201007 + 0.979590i \(0.435579\pi\)
\(80\) −3.01623 + 9.56651i −0.337225 + 1.06957i
\(81\) 2.35567 0.261741
\(82\) 11.0497i 1.22023i
\(83\) 9.37109i 1.02861i −0.857607 0.514305i \(-0.828050\pi\)
0.857607 0.514305i \(-0.171950\pi\)
\(84\) 0.153831 0.0167843
\(85\) −8.70772 2.74546i −0.944485 0.297787i
\(86\) −0.124173 −0.0133899
\(87\) 2.63747i 0.282767i
\(88\) 2.59434i 0.276557i
\(89\) 0.629618 0.0667394 0.0333697 0.999443i \(-0.489376\pi\)
0.0333697 + 0.999443i \(0.489376\pi\)
\(90\) −7.05213 2.22347i −0.743360 0.234374i
\(91\) −1.85132 −0.194071
\(92\) 1.75263i 0.182724i
\(93\) 7.18867i 0.745430i
\(94\) −4.19402 −0.432580
\(95\) 0.672383 2.13258i 0.0689850 0.218798i
\(96\) −1.43161 −0.146113
\(97\) 5.71214i 0.579980i −0.957030 0.289990i \(-0.906348\pi\)
0.957030 0.289990i \(-0.0936520\pi\)
\(98\) 10.0264i 1.01282i
\(99\) 2.18859 0.219961
\(100\) 1.15904 + 0.811542i 0.115904 + 0.0811542i
\(101\) −15.0319 −1.49573 −0.747865 0.663850i \(-0.768921\pi\)
−0.747865 + 0.663850i \(0.768921\pi\)
\(102\) 5.55740i 0.550264i
\(103\) 15.9710i 1.57367i −0.617162 0.786836i \(-0.711718\pi\)
0.617162 0.786836i \(-0.288282\pi\)
\(104\) 7.95870 0.780415
\(105\) −0.365512 + 1.15929i −0.0356704 + 0.113135i
\(106\) −12.1153 −1.17674
\(107\) 0.124523i 0.0120381i 0.999982 + 0.00601903i \(0.00191593\pi\)
−0.999982 + 0.00601903i \(0.998084\pi\)
\(108\) 1.32260i 0.127267i
\(109\) 14.3549 1.37495 0.687477 0.726206i \(-0.258718\pi\)
0.687477 + 0.726206i \(0.258718\pi\)
\(110\) −3.22223 1.01594i −0.307228 0.0968661i
\(111\) −9.25760 −0.878692
\(112\) 2.70715i 0.255802i
\(113\) 11.5904i 1.09033i 0.838328 + 0.545166i \(0.183533\pi\)
−0.838328 + 0.545166i \(0.816467\pi\)
\(114\) 1.36104 0.127474
\(115\) −13.2080 4.16436i −1.23165 0.388329i
\(116\) −0.828563 −0.0769302
\(117\) 6.71398i 0.620707i
\(118\) 4.85047i 0.446522i
\(119\) 2.46413 0.225886
\(120\) 1.57132 4.98371i 0.143441 0.454948i
\(121\) 1.00000 0.0909091
\(122\) 16.9044i 1.53045i
\(123\) 6.58747i 0.593972i
\(124\) −2.25832 −0.202803
\(125\) −8.86981 + 6.80635i −0.793340 + 0.608779i
\(126\) 1.99563 0.177784
\(127\) 18.8000i 1.66823i 0.551591 + 0.834115i \(0.314021\pi\)
−0.551591 + 0.834115i \(0.685979\pi\)
\(128\) 13.1062i 1.15843i
\(129\) 0.0740280 0.00651780
\(130\) 3.11662 9.88492i 0.273346 0.866965i
\(131\) 16.2223 1.41735 0.708674 0.705537i \(-0.249294\pi\)
0.708674 + 0.705537i \(0.249294\pi\)
\(132\) 0.254906i 0.0221867i
\(133\) 0.603482i 0.0523285i
\(134\) −5.33292 −0.460694
\(135\) 9.96726 + 3.14258i 0.857845 + 0.270471i
\(136\) −10.5932 −0.908355
\(137\) 21.2561i 1.81603i 0.418932 + 0.908017i \(0.362404\pi\)
−0.418932 + 0.908017i \(0.637596\pi\)
\(138\) 8.42955i 0.717571i
\(139\) −21.9041 −1.85788 −0.928942 0.370226i \(-0.879280\pi\)
−0.928942 + 0.370226i \(0.879280\pi\)
\(140\) −0.364190 0.114826i −0.0307797 0.00970455i
\(141\) 2.50035 0.210567
\(142\) 2.29556i 0.192639i
\(143\) 3.06772i 0.256536i
\(144\) −9.81775 −0.818145
\(145\) 1.96872 6.24414i 0.163493 0.518547i
\(146\) 4.60206 0.380869
\(147\) 5.97744i 0.493011i
\(148\) 2.90828i 0.239059i
\(149\) −11.0150 −0.902388 −0.451194 0.892426i \(-0.649002\pi\)
−0.451194 + 0.892426i \(0.649002\pi\)
\(150\) −5.57457 3.90323i −0.455162 0.318698i
\(151\) 15.7653 1.28296 0.641481 0.767139i \(-0.278320\pi\)
0.641481 + 0.767139i \(0.278320\pi\)
\(152\) 2.59434i 0.210428i
\(153\) 8.93640i 0.722465i
\(154\) 0.911833 0.0734776
\(155\) 5.36591 17.0189i 0.431001 1.36699i
\(156\) 0.781981 0.0626086
\(157\) 23.8820i 1.90599i 0.302981 + 0.952997i \(0.402018\pi\)
−0.302981 + 0.952997i \(0.597982\pi\)
\(158\) 5.39890i 0.429514i
\(159\) 7.22277 0.572803
\(160\) 3.38930 + 1.06862i 0.267948 + 0.0844814i
\(161\) 3.73763 0.294566
\(162\) 3.55930i 0.279645i
\(163\) 18.1018i 1.41784i 0.705290 + 0.708919i \(0.250817\pi\)
−0.705290 + 0.708919i \(0.749183\pi\)
\(164\) 2.06946 0.161597
\(165\) 1.92100 + 0.605673i 0.149549 + 0.0471515i
\(166\) −14.1593 −1.09897
\(167\) 8.11307i 0.627808i 0.949455 + 0.313904i \(0.101637\pi\)
−0.949455 + 0.313904i \(0.898363\pi\)
\(168\) 1.41030i 0.108807i
\(169\) 3.58907 0.276082
\(170\) −4.14827 + 13.1570i −0.318158 + 1.00909i
\(171\) 2.18859 0.167365
\(172\) 0.0232559i 0.00177325i
\(173\) 17.9368i 1.36371i 0.731489 + 0.681853i \(0.238826\pi\)
−0.731489 + 0.681853i \(0.761174\pi\)
\(174\) 3.98510 0.302110
\(175\) 1.73068 2.47174i 0.130827 0.186846i
\(176\) −4.48589 −0.338136
\(177\) 2.89170i 0.217354i
\(178\) 0.951324i 0.0713048i
\(179\) 22.6454 1.69260 0.846300 0.532707i \(-0.178825\pi\)
0.846300 + 0.532707i \(0.178825\pi\)
\(180\) −0.416427 + 1.32077i −0.0310386 + 0.0984445i
\(181\) −2.12283 −0.157789 −0.0788943 0.996883i \(-0.525139\pi\)
−0.0788943 + 0.996883i \(0.525139\pi\)
\(182\) 2.79725i 0.207346i
\(183\) 10.0779i 0.744980i
\(184\) −16.0679 −1.18454
\(185\) 21.9171 + 6.91025i 1.61138 + 0.508052i
\(186\) 10.8617 0.796422
\(187\) 4.08319i 0.298592i
\(188\) 0.785485i 0.0572873i
\(189\) −2.82055 −0.205165
\(190\) −3.22223 1.01594i −0.233765 0.0737040i
\(191\) −5.41877 −0.392088 −0.196044 0.980595i \(-0.562810\pi\)
−0.196044 + 0.980595i \(0.562810\pi\)
\(192\) 5.91854i 0.427133i
\(193\) 2.89582i 0.208446i 0.994554 + 0.104223i \(0.0332356\pi\)
−0.994554 + 0.104223i \(0.966764\pi\)
\(194\) −8.63078 −0.619654
\(195\) −1.85804 + 5.89309i −0.133057 + 0.422013i
\(196\) −1.87781 −0.134130
\(197\) 3.06581i 0.218430i 0.994018 + 0.109215i \(0.0348337\pi\)
−0.994018 + 0.109215i \(0.965166\pi\)
\(198\) 3.30685i 0.235008i
\(199\) 23.6145 1.67399 0.836993 0.547214i \(-0.184312\pi\)
0.836993 + 0.547214i \(0.184312\pi\)
\(200\) −7.44009 + 10.6259i −0.526094 + 0.751363i
\(201\) 3.17933 0.224252
\(202\) 22.7125i 1.59805i
\(203\) 1.76698i 0.124018i
\(204\) −1.04083 −0.0728725
\(205\) −4.91716 + 15.5956i −0.343429 + 1.08925i
\(206\) −24.1315 −1.68132
\(207\) 13.5549i 0.942129i
\(208\) 13.7615i 0.954185i
\(209\) 1.00000 0.0691714
\(210\) 1.75163 + 0.552272i 0.120874 + 0.0381104i
\(211\) −11.5535 −0.795377 −0.397688 0.917521i \(-0.630187\pi\)
−0.397688 + 0.917521i \(0.630187\pi\)
\(212\) 2.26904i 0.155838i
\(213\) 1.36854i 0.0937709i
\(214\) 0.188148 0.0128615
\(215\) −0.175259 0.0552576i −0.0119526 0.00376853i
\(216\) 12.1254 0.825030
\(217\) 4.81605i 0.326935i
\(218\) 21.6897i 1.46901i
\(219\) −2.74361 −0.185396
\(220\) −0.190272 + 0.603482i −0.0128282 + 0.0406867i
\(221\) 12.5261 0.842596
\(222\) 13.9878i 0.938800i
\(223\) 9.59966i 0.642841i −0.946937 0.321420i \(-0.895840\pi\)
0.946937 0.321420i \(-0.104160\pi\)
\(224\) −0.959111 −0.0640833
\(225\) −8.96402 6.27648i −0.597601 0.418432i
\(226\) 17.5125 1.16492
\(227\) 5.29283i 0.351298i 0.984453 + 0.175649i \(0.0562023\pi\)
−0.984453 + 0.175649i \(0.943798\pi\)
\(228\) 0.254906i 0.0168816i
\(229\) 1.45160 0.0959243 0.0479622 0.998849i \(-0.484727\pi\)
0.0479622 + 0.998849i \(0.484727\pi\)
\(230\) −6.29216 + 19.9567i −0.414893 + 1.31591i
\(231\) −0.543607 −0.0357667
\(232\) 7.59614i 0.498711i
\(233\) 25.0472i 1.64090i 0.571721 + 0.820448i \(0.306276\pi\)
−0.571721 + 0.820448i \(0.693724\pi\)
\(234\) 10.1445 0.663167
\(235\) −5.91949 1.86636i −0.386145 0.121748i
\(236\) 0.908429 0.0591337
\(237\) 3.21866i 0.209075i
\(238\) 3.72318i 0.241338i
\(239\) −1.53900 −0.0995499 −0.0497749 0.998760i \(-0.515850\pi\)
−0.0497749 + 0.998760i \(0.515850\pi\)
\(240\) −8.61737 2.71698i −0.556249 0.175380i
\(241\) −4.82341 −0.310703 −0.155352 0.987859i \(-0.549651\pi\)
−0.155352 + 0.987859i \(0.549651\pi\)
\(242\) 1.51095i 0.0971278i
\(243\) 16.1434i 1.03560i
\(244\) 3.16598 0.202681
\(245\) 4.46181 14.1514i 0.285054 0.904100i
\(246\) −9.95337 −0.634603
\(247\) 3.06772i 0.195195i
\(248\) 20.7039i 1.31470i
\(249\) 8.44134 0.534948
\(250\) 10.2841 + 13.4019i 0.650423 + 0.847609i
\(251\) −11.4453 −0.722423 −0.361211 0.932484i \(-0.617637\pi\)
−0.361211 + 0.932484i \(0.617637\pi\)
\(252\) 0.373755i 0.0235443i
\(253\) 6.19344i 0.389378i
\(254\) 28.4059 1.78235
\(255\) 2.47307 7.84379i 0.154870 0.491197i
\(256\) 6.66201 0.416376
\(257\) 4.14766i 0.258724i 0.991597 + 0.129362i \(0.0412929\pi\)
−0.991597 + 0.129362i \(0.958707\pi\)
\(258\) 0.111853i 0.00696366i
\(259\) −6.20214 −0.385382
\(260\) −1.85132 0.583703i −0.114814 0.0361997i
\(261\) 6.40812 0.396653
\(262\) 24.5111i 1.51430i
\(263\) 4.43431i 0.273431i 0.990610 + 0.136716i \(0.0436546\pi\)
−0.990610 + 0.136716i \(0.956345\pi\)
\(264\) 2.33694 0.143829
\(265\) −17.0997 5.39137i −1.05043 0.331189i
\(266\) 0.911833 0.0559081
\(267\) 0.567151i 0.0347091i
\(268\) 0.998787i 0.0610106i
\(269\) −4.65270 −0.283680 −0.141840 0.989890i \(-0.545302\pi\)
−0.141840 + 0.989890i \(0.545302\pi\)
\(270\) 4.74830 15.0601i 0.288972 0.916527i
\(271\) −19.7128 −1.19746 −0.598732 0.800949i \(-0.704329\pi\)
−0.598732 + 0.800949i \(0.704329\pi\)
\(272\) 18.3167i 1.11061i
\(273\) 1.66764i 0.100930i
\(274\) 32.1171 1.94026
\(275\) −4.09580 2.86782i −0.246986 0.172936i
\(276\) −1.57874 −0.0950292
\(277\) 21.9425i 1.31840i −0.751970 0.659198i \(-0.770896\pi\)
0.751970 0.659198i \(-0.229104\pi\)
\(278\) 33.0961i 1.98497i
\(279\) 17.4659 1.04566
\(280\) 1.05271 3.33884i 0.0629112 0.199534i
\(281\) −4.67060 −0.278625 −0.139312 0.990248i \(-0.544489\pi\)
−0.139312 + 0.990248i \(0.544489\pi\)
\(282\) 3.77791i 0.224971i
\(283\) 10.2046i 0.606598i 0.952895 + 0.303299i \(0.0980881\pi\)
−0.952895 + 0.303299i \(0.901912\pi\)
\(284\) −0.429928 −0.0255115
\(285\) 1.92100 + 0.605673i 0.113790 + 0.0358769i
\(286\) 4.63519 0.274084
\(287\) 4.41328i 0.260508i
\(288\) 3.47831i 0.204961i
\(289\) 0.327596 0.0192703
\(290\) −9.43461 2.97464i −0.554019 0.174677i
\(291\) 5.14541 0.301629
\(292\) 0.861905i 0.0504392i
\(293\) 19.0508i 1.11296i 0.830862 + 0.556478i \(0.187848\pi\)
−0.830862 + 0.556478i \(0.812152\pi\)
\(294\) 9.03164 0.526736
\(295\) −2.15848 + 6.84601i −0.125672 + 0.398590i
\(296\) 26.6626 1.54973
\(297\) 4.67380i 0.271201i
\(298\) 16.6432i 0.964117i
\(299\) 18.9998 1.09878
\(300\) −0.731025 + 1.04404i −0.0422057 + 0.0602779i
\(301\) 0.0495951 0.00285862
\(302\) 23.8206i 1.37072i
\(303\) 13.5405i 0.777883i
\(304\) −4.48589 −0.257283
\(305\) −7.52256 + 23.8591i −0.430741 + 1.36617i
\(306\) −13.5025 −0.771886
\(307\) 1.26498i 0.0721961i 0.999348 + 0.0360981i \(0.0114929\pi\)
−0.999348 + 0.0360981i \(0.988507\pi\)
\(308\) 0.170774i 0.00973078i
\(309\) 14.3865 0.818417
\(310\) −25.7148 8.10765i −1.46050 0.460484i
\(311\) 34.2924 1.94455 0.972273 0.233849i \(-0.0751322\pi\)
0.972273 + 0.233849i \(0.0751322\pi\)
\(312\) 7.16908i 0.405869i
\(313\) 0.755401i 0.0426978i −0.999772 0.0213489i \(-0.993204\pi\)
0.999772 0.0213489i \(-0.00679608\pi\)
\(314\) 36.0846 2.03637
\(315\) 2.81665 + 0.888065i 0.158700 + 0.0500368i
\(316\) −1.01114 −0.0568813
\(317\) 19.4248i 1.09101i −0.838108 0.545504i \(-0.816338\pi\)
0.838108 0.545504i \(-0.183662\pi\)
\(318\) 10.9133i 0.611986i
\(319\) 2.92797 0.163935
\(320\) −4.41784 + 14.0119i −0.246965 + 0.783292i
\(321\) −0.112168 −0.00626062
\(322\) 5.64738i 0.314716i
\(323\) 4.08319i 0.227195i
\(324\) −0.666611 −0.0370340
\(325\) 8.79769 12.5648i 0.488008 0.696969i
\(326\) 27.3509 1.51483
\(327\) 12.9307i 0.715071i
\(328\) 18.9725i 1.04758i
\(329\) 1.67511 0.0923518
\(330\) 0.915143 2.90254i 0.0503770 0.159779i
\(331\) 26.3233 1.44686 0.723429 0.690399i \(-0.242565\pi\)
0.723429 + 0.690399i \(0.242565\pi\)
\(332\) 2.65185i 0.145539i
\(333\) 22.4927i 1.23259i
\(334\) 12.2585 0.670754
\(335\) −7.52696 2.37318i −0.411242 0.129661i
\(336\) 2.43856 0.133034
\(337\) 28.4082i 1.54749i −0.633495 0.773746i \(-0.718380\pi\)
0.633495 0.773746i \(-0.281620\pi\)
\(338\) 5.42292i 0.294968i
\(339\) −10.4404 −0.567047
\(340\) 2.46413 + 0.776917i 0.133636 + 0.0421342i
\(341\) 7.98044 0.432165
\(342\) 3.30685i 0.178814i
\(343\) 8.22896i 0.444322i
\(344\) −0.213207 −0.0114953
\(345\) 3.75120 11.8976i 0.201958 0.640544i
\(346\) 27.1016 1.45699
\(347\) 15.4328i 0.828475i −0.910169 0.414237i \(-0.864048\pi\)
0.910169 0.414237i \(-0.135952\pi\)
\(348\) 0.746358i 0.0400090i
\(349\) −9.55388 −0.511408 −0.255704 0.966755i \(-0.582307\pi\)
−0.255704 + 0.966755i \(0.582307\pi\)
\(350\) −3.73469 2.61498i −0.199628 0.139776i
\(351\) −14.3379 −0.765302
\(352\) 1.58930i 0.0847097i
\(353\) 6.07556i 0.323370i 0.986842 + 0.161685i \(0.0516928\pi\)
−0.986842 + 0.161685i \(0.948307\pi\)
\(354\) −4.36923 −0.232222
\(355\) 1.02154 3.23998i 0.0542175 0.171960i
\(356\) −0.178171 −0.00944302
\(357\) 2.21965i 0.117476i
\(358\) 34.2162i 1.80838i
\(359\) −19.9636 −1.05364 −0.526820 0.849977i \(-0.676616\pi\)
−0.526820 + 0.849977i \(0.676616\pi\)
\(360\) −12.1086 3.81774i −0.638181 0.201213i
\(361\) 1.00000 0.0526316
\(362\) 3.20750i 0.168582i
\(363\) 0.900785i 0.0472790i
\(364\) 0.523889 0.0274592
\(365\) 6.49540 + 2.04794i 0.339985 + 0.107194i
\(366\) −15.2273 −0.795941
\(367\) 0.193444i 0.0100977i −0.999987 0.00504886i \(-0.998393\pi\)
0.999987 0.00504886i \(-0.00160711\pi\)
\(368\) 27.7830i 1.44829i
\(369\) −16.0052 −0.833198
\(370\) 10.4411 33.1157i 0.542805 1.72160i
\(371\) 4.83890 0.251223
\(372\) 2.03426i 0.105472i
\(373\) 33.8918i 1.75485i 0.479712 + 0.877426i \(0.340741\pi\)
−0.479712 + 0.877426i \(0.659259\pi\)
\(374\) −6.16951 −0.319018
\(375\) −6.13106 7.98979i −0.316607 0.412591i
\(376\) −7.20120 −0.371374
\(377\) 8.98221i 0.462607i
\(378\) 4.26173i 0.219200i
\(379\) 9.70742 0.498637 0.249318 0.968422i \(-0.419793\pi\)
0.249318 + 0.968422i \(0.419793\pi\)
\(380\) −0.190272 + 0.603482i −0.00976076 + 0.0309580i
\(381\) −16.9348 −0.867594
\(382\) 8.18751i 0.418909i
\(383\) 12.2664i 0.626783i −0.949624 0.313391i \(-0.898535\pi\)
0.949624 0.313391i \(-0.101465\pi\)
\(384\) −11.8059 −0.602465
\(385\) 1.28697 + 0.405771i 0.0655903 + 0.0206800i
\(386\) 4.37546 0.222705
\(387\) 0.179862i 0.00914288i
\(388\) 1.61643i 0.0820619i
\(389\) −22.1011 −1.12057 −0.560285 0.828300i \(-0.689308\pi\)
−0.560285 + 0.828300i \(0.689308\pi\)
\(390\) 8.90419 + 2.80741i 0.450881 + 0.142159i
\(391\) −25.2890 −1.27892
\(392\) 17.2155i 0.869515i
\(393\) 14.6128i 0.737118i
\(394\) 4.63229 0.233372
\(395\) 2.40254 7.62009i 0.120885 0.383408i
\(396\) −0.619330 −0.0311225
\(397\) 1.76411i 0.0885380i 0.999020 + 0.0442690i \(0.0140959\pi\)
−0.999020 + 0.0442690i \(0.985904\pi\)
\(398\) 35.6804i 1.78850i
\(399\) −0.543607 −0.0272144
\(400\) 18.3733 + 12.8647i 0.918665 + 0.643236i
\(401\) −37.7407 −1.88468 −0.942339 0.334659i \(-0.891379\pi\)
−0.942339 + 0.334659i \(0.891379\pi\)
\(402\) 4.80382i 0.239593i
\(403\) 24.4818i 1.21953i
\(404\) 4.25376 0.211632
\(405\) 1.58391 5.02365i 0.0787051 0.249627i
\(406\) 2.66982 0.132501
\(407\) 10.2773i 0.509425i
\(408\) 9.54215i 0.472407i
\(409\) 15.2172 0.752440 0.376220 0.926530i \(-0.377224\pi\)
0.376220 + 0.926530i \(0.377224\pi\)
\(410\) 23.5643 + 7.42960i 1.16376 + 0.366922i
\(411\) −19.1472 −0.944463
\(412\) 4.51951i 0.222660i
\(413\) 1.93730i 0.0953282i
\(414\) −20.4808 −1.00658
\(415\) −19.9846 6.30096i −0.981005 0.309302i
\(416\) −4.87552 −0.239042
\(417\) 19.7309i 0.966227i
\(418\) 1.51095i 0.0739032i
\(419\) 23.6883 1.15725 0.578624 0.815595i \(-0.303590\pi\)
0.578624 + 0.815595i \(0.303590\pi\)
\(420\) 0.103433 0.328057i 0.00504703 0.0160076i
\(421\) −14.2242 −0.693244 −0.346622 0.938005i \(-0.612671\pi\)
−0.346622 + 0.938005i \(0.612671\pi\)
\(422\) 17.4568i 0.849785i
\(423\) 6.07495i 0.295374i
\(424\) −20.8022 −1.01024
\(425\) −11.7098 + 16.7239i −0.568011 + 0.811229i
\(426\) 2.06780 0.100185
\(427\) 6.75170i 0.326738i
\(428\) 0.0352377i 0.00170328i
\(429\) −2.76336 −0.133416
\(430\) −0.0834916 + 0.264808i −0.00402632 + 0.0127702i
\(431\) −23.9472 −1.15350 −0.576749 0.816922i \(-0.695679\pi\)
−0.576749 + 0.816922i \(0.695679\pi\)
\(432\) 20.9661i 1.00873i
\(433\) 26.4436i 1.27080i 0.772185 + 0.635398i \(0.219164\pi\)
−0.772185 + 0.635398i \(0.780836\pi\)
\(434\) 7.27683 0.349299
\(435\) 5.62463 + 1.77339i 0.269680 + 0.0850277i
\(436\) −4.06219 −0.194544
\(437\) 6.19344i 0.296272i
\(438\) 4.14546i 0.198078i
\(439\) −22.3823 −1.06825 −0.534124 0.845406i \(-0.679359\pi\)
−0.534124 + 0.845406i \(0.679359\pi\)
\(440\) −5.53263 1.74439i −0.263758 0.0831604i
\(441\) 14.5230 0.691573
\(442\) 18.9263i 0.900234i
\(443\) 10.3295i 0.490771i 0.969426 + 0.245386i \(0.0789146\pi\)
−0.969426 + 0.245386i \(0.921085\pi\)
\(444\) 2.61973 0.124327
\(445\) 0.423345 1.34271i 0.0200685 0.0636506i
\(446\) −14.5046 −0.686815
\(447\) 9.92219i 0.469304i
\(448\) 3.96513i 0.187335i
\(449\) 14.4952 0.684068 0.342034 0.939687i \(-0.388884\pi\)
0.342034 + 0.939687i \(0.388884\pi\)
\(450\) −9.48347 + 13.5442i −0.447055 + 0.638480i
\(451\) −7.31303 −0.344357
\(452\) 3.27987i 0.154272i
\(453\) 14.2012i 0.667228i
\(454\) 7.99723 0.375328
\(455\) −1.24479 + 3.94808i −0.0583568 + 0.185089i
\(456\) 2.33694 0.109437
\(457\) 16.8399i 0.787737i −0.919167 0.393869i \(-0.871136\pi\)
0.919167 0.393869i \(-0.128864\pi\)
\(458\) 2.19330i 0.102486i
\(459\) 19.0840 0.890765
\(460\) 3.73763 + 1.17844i 0.174268 + 0.0549450i
\(461\) 10.7768 0.501928 0.250964 0.967996i \(-0.419252\pi\)
0.250964 + 0.967996i \(0.419252\pi\)
\(462\) 0.821366i 0.0382134i
\(463\) 13.0560i 0.606764i −0.952869 0.303382i \(-0.901884\pi\)
0.952869 0.303382i \(-0.0981159\pi\)
\(464\) −13.1345 −0.609756
\(465\) 15.3304 + 4.83354i 0.710931 + 0.224150i
\(466\) 37.8451 1.75314
\(467\) 13.1491i 0.608470i 0.952597 + 0.304235i \(0.0984008\pi\)
−0.952597 + 0.304235i \(0.901599\pi\)
\(468\) 1.89993i 0.0878245i
\(469\) 2.12999 0.0983540
\(470\) −2.81999 + 8.94408i −0.130076 + 0.412560i
\(471\) −21.5126 −0.991247
\(472\) 8.32834i 0.383343i
\(473\) 0.0821817i 0.00377872i
\(474\) 4.86325 0.223377
\(475\) −4.09580 2.86782i −0.187928 0.131585i
\(476\) −0.697304 −0.0319609
\(477\) 17.5488i 0.803502i
\(478\) 2.32536i 0.106360i
\(479\) −6.76244 −0.308984 −0.154492 0.987994i \(-0.549374\pi\)
−0.154492 + 0.987994i \(0.549374\pi\)
\(480\) −0.962593 + 3.05303i −0.0439361 + 0.139351i
\(481\) −31.5278 −1.43754
\(482\) 7.28795i 0.331957i
\(483\) 3.36680i 0.153195i
\(484\) −0.282982 −0.0128628
\(485\) −12.1816 3.84074i −0.553138 0.174399i
\(486\) 24.3919 1.10644
\(487\) 28.4833i 1.29070i −0.763886 0.645351i \(-0.776711\pi\)
0.763886 0.645351i \(-0.223289\pi\)
\(488\) 29.0252i 1.31391i
\(489\) −16.3058 −0.737373
\(490\) −21.3821 6.74158i −0.965946 0.304554i
\(491\) −0.746198 −0.0336754 −0.0168377 0.999858i \(-0.505360\pi\)
−0.0168377 + 0.999858i \(0.505360\pi\)
\(492\) 1.86414i 0.0840417i
\(493\) 11.9555i 0.538447i
\(494\) 4.63519 0.208547
\(495\) 1.47157 4.66734i 0.0661421 0.209781i
\(496\) −35.7994 −1.60744
\(497\) 0.916856i 0.0411266i
\(498\) 12.7545i 0.571541i
\(499\) 10.7995 0.483452 0.241726 0.970345i \(-0.422287\pi\)
0.241726 + 0.970345i \(0.422287\pi\)
\(500\) 2.51000 1.92608i 0.112250 0.0861367i
\(501\) −7.30813 −0.326503
\(502\) 17.2934i 0.771841i
\(503\) 23.2195i 1.03530i −0.855591 0.517652i \(-0.826806\pi\)
0.855591 0.517652i \(-0.173194\pi\)
\(504\) 3.42653 0.152630
\(505\) −10.1072 + 32.0568i −0.449764 + 1.42651i
\(506\) −9.35800 −0.416014
\(507\) 3.23298i 0.143582i
\(508\) 5.32006i 0.236039i
\(509\) −35.1577 −1.55834 −0.779169 0.626814i \(-0.784359\pi\)
−0.779169 + 0.626814i \(0.784359\pi\)
\(510\) −11.8516 3.73670i −0.524798 0.165464i
\(511\) −1.83808 −0.0813119
\(512\) 16.1464i 0.713576i
\(513\) 4.67380i 0.206353i
\(514\) 6.26692 0.276422
\(515\) −34.0595 10.7386i −1.50084 0.473201i
\(516\) −0.0209486 −0.000922211
\(517\) 2.77574i 0.122077i
\(518\) 9.37114i 0.411744i
\(519\) −16.1572 −0.709221
\(520\) 5.35130 16.9726i 0.234670 0.744297i
\(521\) −6.74136 −0.295344 −0.147672 0.989036i \(-0.547178\pi\)
−0.147672 + 0.989036i \(0.547178\pi\)
\(522\) 9.68237i 0.423786i
\(523\) 17.7769i 0.777329i −0.921379 0.388664i \(-0.872937\pi\)
0.921379 0.388664i \(-0.127063\pi\)
\(524\) −4.59061 −0.200542
\(525\) 2.22651 + 1.55897i 0.0971728 + 0.0680390i
\(526\) 6.70004 0.292135
\(527\) 32.5856i 1.41945i
\(528\) 4.04082i 0.175854i
\(529\) −15.3587 −0.667768
\(530\) −8.14612 + 25.8368i −0.353845 + 1.12228i
\(531\) −7.02580 −0.304894
\(532\) 0.170774i 0.00740401i
\(533\) 22.4344i 0.971740i
\(534\) 0.856939 0.0370834
\(535\) 0.265555 + 0.0837270i 0.0114809 + 0.00361983i
\(536\) −9.15673 −0.395510
\(537\) 20.3987i 0.880268i
\(538\) 7.03001i 0.303085i
\(539\) 6.63581 0.285825
\(540\) −2.82055 0.889295i −0.121377 0.0382691i
\(541\) 8.59351 0.369464 0.184732 0.982789i \(-0.440858\pi\)
0.184732 + 0.982789i \(0.440858\pi\)
\(542\) 29.7851i 1.27938i
\(543\) 1.91221i 0.0820609i
\(544\) 6.48939 0.278230
\(545\) 9.65202 30.6131i 0.413447 1.31132i
\(546\) −2.51972 −0.107834
\(547\) 8.81086i 0.376725i −0.982100 0.188363i \(-0.939682\pi\)
0.982100 0.188363i \(-0.0603180\pi\)
\(548\) 6.01510i 0.256953i
\(549\) −24.4857 −1.04502
\(550\) −4.33315 + 6.18857i −0.184766 + 0.263881i
\(551\) 2.92797 0.124736
\(552\) 14.4737i 0.616041i
\(553\) 2.15635i 0.0916972i
\(554\) −33.1541 −1.40858
\(555\) −6.22465 + 19.7426i −0.264222 + 0.838026i
\(556\) 6.19847 0.262874
\(557\) 27.6651i 1.17221i −0.810235 0.586105i \(-0.800661\pi\)
0.810235 0.586105i \(-0.199339\pi\)
\(558\) 26.3902i 1.11718i
\(559\) 0.252111 0.0106631
\(560\) −5.77322 1.82024i −0.243963 0.0769192i
\(561\) 3.67807 0.155288
\(562\) 7.05707i 0.297684i
\(563\) 9.49474i 0.400156i 0.979780 + 0.200078i \(0.0641195\pi\)
−0.979780 + 0.200078i \(0.935880\pi\)
\(564\) −0.707553 −0.0297933
\(565\) 24.7174 + 7.79318i 1.03987 + 0.327861i
\(566\) 15.4186 0.648093
\(567\) 1.42160i 0.0597017i
\(568\) 3.94151i 0.165382i
\(569\) −0.862737 −0.0361678 −0.0180839 0.999836i \(-0.505757\pi\)
−0.0180839 + 0.999836i \(0.505757\pi\)
\(570\) 0.915143 2.90254i 0.0383311 0.121574i
\(571\) −31.5625 −1.32085 −0.660424 0.750892i \(-0.729624\pi\)
−0.660424 + 0.750892i \(0.729624\pi\)
\(572\) 0.868110i 0.0362975i
\(573\) 4.88114i 0.203913i
\(574\) −6.66827 −0.278328
\(575\) −17.7617 + 25.3671i −0.740713 + 1.05788i
\(576\) −14.3799 −0.599164
\(577\) 19.9673i 0.831250i −0.909536 0.415625i \(-0.863563\pi\)
0.909536 0.415625i \(-0.136437\pi\)
\(578\) 0.494982i 0.0205886i
\(579\) −2.60851 −0.108406
\(580\) −0.557112 + 1.76698i −0.0231328 + 0.0733698i
\(581\) 5.65528 0.234621
\(582\) 7.77448i 0.322262i
\(583\) 8.01831i 0.332084i
\(584\) 7.90181 0.326979
\(585\) 14.3181 + 4.51436i 0.591981 + 0.186646i
\(586\) 28.7848 1.18909
\(587\) 33.3785i 1.37768i 0.724913 + 0.688840i \(0.241880\pi\)
−0.724913 + 0.688840i \(0.758120\pi\)
\(588\) 1.69151i 0.0697566i
\(589\) 7.98044 0.328828
\(590\) 10.3440 + 3.26137i 0.425856 + 0.134268i
\(591\) −2.76163 −0.113598
\(592\) 46.1026i 1.89480i
\(593\) 30.5439i 1.25429i −0.778904 0.627143i \(-0.784224\pi\)
0.778904 0.627143i \(-0.215776\pi\)
\(594\) 7.06190 0.289753
\(595\) 1.65684 5.25495i 0.0679237 0.215432i
\(596\) 3.11706 0.127680
\(597\) 21.2716i 0.870587i
\(598\) 28.7078i 1.17395i
\(599\) 0.919784 0.0375814 0.0187907 0.999823i \(-0.494018\pi\)
0.0187907 + 0.999823i \(0.494018\pi\)
\(600\) −9.57164 6.70192i −0.390761 0.273605i
\(601\) −21.5390 −0.878592 −0.439296 0.898342i \(-0.644772\pi\)
−0.439296 + 0.898342i \(0.644772\pi\)
\(602\) 0.0749360i 0.00305416i
\(603\) 7.72463i 0.314571i
\(604\) −4.46130 −0.181528
\(605\) 0.672383 2.13258i 0.0273363 0.0867017i
\(606\) −20.4591 −0.831094
\(607\) 21.9638i 0.891485i −0.895161 0.445742i \(-0.852940\pi\)
0.895161 0.445742i \(-0.147060\pi\)
\(608\) 1.58930i 0.0644544i
\(609\) −1.59167 −0.0644976
\(610\) 36.0500 + 11.3662i 1.45962 + 0.460206i
\(611\) 8.51521 0.344488
\(612\) 2.52884i 0.102222i
\(613\) 34.6490i 1.39946i −0.714408 0.699730i \(-0.753304\pi\)
0.714408 0.699730i \(-0.246696\pi\)
\(614\) 1.91132 0.0771347
\(615\) −14.0483 4.42930i −0.566483 0.178607i
\(616\) 1.56563 0.0630812
\(617\) 10.0214i 0.403448i −0.979442 0.201724i \(-0.935346\pi\)
0.979442 0.201724i \(-0.0646544\pi\)
\(618\) 21.7373i 0.874402i
\(619\) 41.5032 1.66815 0.834077 0.551648i \(-0.186001\pi\)
0.834077 + 0.551648i \(0.186001\pi\)
\(620\) −1.51846 + 4.81605i −0.0609827 + 0.193417i
\(621\) 28.9469 1.16160
\(622\) 51.8143i 2.07756i
\(623\) 0.379963i 0.0152229i
\(624\) 12.3961 0.496242
\(625\) 8.55119 + 23.4921i 0.342048 + 0.939683i
\(626\) −1.14138 −0.0456186
\(627\) 0.900785i 0.0359739i
\(628\) 6.75818i 0.269681i
\(629\) 41.9639 1.67321
\(630\) 1.34182 4.25583i 0.0534596 0.169556i
\(631\) −38.1373 −1.51822 −0.759112 0.650960i \(-0.774367\pi\)
−0.759112 + 0.650960i \(0.774367\pi\)
\(632\) 9.27002i 0.368741i
\(633\) 10.4072i 0.413650i
\(634\) −29.3500 −1.16564
\(635\) 40.0925 + 12.6408i 1.59102 + 0.501635i
\(636\) −2.04391 −0.0810465
\(637\) 20.3568i 0.806567i
\(638\) 4.42403i 0.175149i
\(639\) 3.32507 0.131538
\(640\) 27.9500 + 8.81238i 1.10482 + 0.348340i
\(641\) 35.1370 1.38783 0.693914 0.720058i \(-0.255885\pi\)
0.693914 + 0.720058i \(0.255885\pi\)
\(642\) 0.169481i 0.00668888i
\(643\) 32.6958i 1.28940i 0.764437 + 0.644698i \(0.223017\pi\)
−0.764437 + 0.644698i \(0.776983\pi\)
\(644\) −1.05768 −0.0416785
\(645\) 0.0497752 0.157871i 0.00195990 0.00621616i
\(646\) −6.16951 −0.242736
\(647\) 6.81340i 0.267863i −0.990991 0.133931i \(-0.957240\pi\)
0.990991 0.133931i \(-0.0427601\pi\)
\(648\) 6.11139i 0.240078i
\(649\) −3.21020 −0.126011
\(650\) −18.9848 13.2929i −0.744646 0.521390i
\(651\) −4.33823 −0.170029
\(652\) 5.12247i 0.200611i
\(653\) 19.1447i 0.749190i 0.927188 + 0.374595i \(0.122218\pi\)
−0.927188 + 0.374595i \(0.877782\pi\)
\(654\) 19.5377 0.763986
\(655\) 10.9076 34.5953i 0.426195 1.35175i
\(656\) 32.8054 1.28084
\(657\) 6.66598i 0.260065i
\(658\) 2.53101i 0.0986692i
\(659\) 10.4111 0.405559 0.202779 0.979224i \(-0.435003\pi\)
0.202779 + 0.979224i \(0.435003\pi\)
\(660\) −0.543607 0.171394i −0.0211599 0.00667152i
\(661\) −18.8172 −0.731903 −0.365951 0.930634i \(-0.619256\pi\)
−0.365951 + 0.930634i \(0.619256\pi\)
\(662\) 39.7733i 1.54583i
\(663\) 11.2833i 0.438208i
\(664\) −24.3117 −0.943479
\(665\) 1.28697 + 0.405771i 0.0499067 + 0.0157351i
\(666\) 33.9854 1.31691
\(667\) 18.1342i 0.702160i
\(668\) 2.29585i 0.0888292i
\(669\) 8.64723 0.334321
\(670\) −3.58577 + 11.3729i −0.138530 + 0.439373i
\(671\) −11.1879 −0.431905
\(672\) 0.863953i 0.0333277i
\(673\) 48.1251i 1.85508i 0.373718 + 0.927542i \(0.378083\pi\)
−0.373718 + 0.927542i \(0.621917\pi\)
\(674\) −42.9235 −1.65335
\(675\) 13.4036 19.1430i 0.515906 0.736813i
\(676\) −1.01564 −0.0390632
\(677\) 35.9017i 1.37981i 0.723898 + 0.689907i \(0.242349\pi\)
−0.723898 + 0.689907i \(0.757651\pi\)
\(678\) 15.7750i 0.605837i
\(679\) 3.44717 0.132290
\(680\) −7.12266 + 22.5908i −0.273141 + 0.866316i
\(681\) −4.76771 −0.182699
\(682\) 12.0581i 0.461728i
\(683\) 10.6585i 0.407837i −0.978988 0.203918i \(-0.934632\pi\)
0.978988 0.203918i \(-0.0653677\pi\)
\(684\) −0.619330 −0.0236807
\(685\) 45.3304 + 14.2923i 1.73199 + 0.546080i
\(686\) 12.4336 0.474716
\(687\) 1.30758i 0.0498872i
\(688\) 0.368658i 0.0140549i
\(689\) 24.5980 0.937108
\(690\) −17.9767 5.66788i −0.684361 0.215773i
\(691\) −4.88607 −0.185875 −0.0929375 0.995672i \(-0.529626\pi\)
−0.0929375 + 0.995672i \(0.529626\pi\)
\(692\) 5.07578i 0.192952i
\(693\) 1.32077i 0.0501720i
\(694\) −23.3182 −0.885147
\(695\) −14.7280 + 46.7123i −0.558663 + 1.77190i
\(696\) 6.84249 0.259364
\(697\) 29.8605i 1.13105i
\(698\) 14.4355i 0.546391i
\(699\) −22.5621 −0.853378
\(700\) −0.489751 + 0.699458i −0.0185108 + 0.0264370i
\(701\) 22.9415 0.866490 0.433245 0.901276i \(-0.357368\pi\)
0.433245 + 0.901276i \(0.357368\pi\)
\(702\) 21.6640i 0.817653i
\(703\) 10.2773i 0.387614i
\(704\) −6.57042 −0.247632
\(705\) 1.68119 5.33219i 0.0633173 0.200822i
\(706\) 9.17990 0.345490
\(707\) 9.07148i 0.341168i
\(708\) 0.818299i 0.0307536i
\(709\) 35.0072 1.31472 0.657361 0.753576i \(-0.271673\pi\)
0.657361 + 0.753576i \(0.271673\pi\)
\(710\) −4.89546 1.54349i −0.183723 0.0579263i
\(711\) 7.82020 0.293281
\(712\) 1.63344i 0.0612158i
\(713\) 49.4264i 1.85103i
\(714\) 3.35379 0.125512
\(715\) 6.54217 + 2.06269i 0.244663 + 0.0771401i
\(716\) −6.40825 −0.239487
\(717\) 1.38631i 0.0517728i
\(718\) 30.1641i 1.12571i
\(719\) −48.2732 −1.80029 −0.900144 0.435592i \(-0.856539\pi\)
−0.900144 + 0.435592i \(0.856539\pi\)
\(720\) −6.60128 + 20.9371i −0.246015 + 0.780281i
\(721\) 9.63822 0.358946
\(722\) 1.51095i 0.0562319i
\(723\) 4.34486i 0.161587i
\(724\) 0.600722 0.0223257
\(725\) −11.9924 8.39690i −0.445386 0.311853i
\(726\) 1.36104 0.0505131
\(727\) 14.0424i 0.520803i −0.965500 0.260402i \(-0.916145\pi\)
0.965500 0.260402i \(-0.0838550\pi\)
\(728\) 4.80293i 0.178009i
\(729\) −7.47469 −0.276840
\(730\) 3.09434 9.81426i 0.114527 0.363242i
\(731\) −0.335563 −0.0124112
\(732\) 2.85186i 0.105408i
\(733\) 41.9169i 1.54824i −0.633040 0.774119i \(-0.718193\pi\)
0.633040 0.774119i \(-0.281807\pi\)
\(734\) −0.292286 −0.0107885
\(735\) 12.7474 + 4.01913i 0.470194 + 0.148248i
\(736\) 9.84320 0.362825
\(737\) 3.52951i 0.130011i
\(738\) 24.1831i 0.890193i
\(739\) 43.9013 1.61493 0.807467 0.589912i \(-0.200838\pi\)
0.807467 + 0.589912i \(0.200838\pi\)
\(740\) −6.20214 1.95548i −0.227995 0.0718847i
\(741\) −2.76336 −0.101515
\(742\) 7.31136i 0.268409i
\(743\) 16.7953i 0.616161i 0.951360 + 0.308080i \(0.0996866\pi\)
−0.951360 + 0.308080i \(0.900313\pi\)
\(744\) 18.6498 0.683735
\(745\) −7.40633 + 23.4905i −0.271347 + 0.860625i
\(746\) 51.2090 1.87489
\(747\) 20.5094i 0.750401i
\(748\) 1.15547i 0.0422481i
\(749\) −0.0751472 −0.00274582
\(750\) −12.0722 + 9.26375i −0.440815 + 0.338264i
\(751\) −31.0266 −1.13218 −0.566089 0.824344i \(-0.691544\pi\)
−0.566089 + 0.824344i \(0.691544\pi\)
\(752\) 12.4517i 0.454065i
\(753\) 10.3098i 0.375709i
\(754\) 13.5717 0.494252
\(755\) 10.6003 33.6208i 0.385785 1.22359i
\(756\) 0.798166 0.0290290
\(757\) 37.0243i 1.34567i −0.739793 0.672835i \(-0.765076\pi\)
0.739793 0.672835i \(-0.234924\pi\)
\(758\) 14.6675i 0.532746i
\(759\) 5.57896 0.202503
\(760\) −5.53263 1.74439i −0.200690 0.0632756i
\(761\) −5.37641 −0.194895 −0.0974473 0.995241i \(-0.531068\pi\)
−0.0974473 + 0.995241i \(0.531068\pi\)
\(762\) 25.5876i 0.926942i
\(763\) 8.66295i 0.313620i
\(764\) 1.53341 0.0554769
\(765\) −19.0576 6.00869i −0.689029 0.217244i
\(766\) −18.5339 −0.669658
\(767\) 9.84801i 0.355591i
\(768\) 6.00104i 0.216544i
\(769\) 45.0438 1.62432 0.812161 0.583433i \(-0.198291\pi\)
0.812161 + 0.583433i \(0.198291\pi\)
\(770\) 0.613101 1.94456i 0.0220946 0.0700770i
\(771\) −3.73615 −0.134554
\(772\) 0.819466i 0.0294932i
\(773\) 8.86055i 0.318692i 0.987223 + 0.159346i \(0.0509385\pi\)
−0.987223 + 0.159346i \(0.949061\pi\)
\(774\) −0.271763 −0.00976831
\(775\) −32.6863 22.8865i −1.17413 0.822107i
\(776\) −14.8192 −0.531978
\(777\) 5.58679i 0.200425i
\(778\) 33.3937i 1.19722i
\(779\) −7.31303 −0.262017
\(780\) 0.525791 1.66764i 0.0188263 0.0597110i
\(781\) 1.51928 0.0543640
\(782\) 38.2104i 1.36640i
\(783\) 13.6848i 0.489054i
\(784\) −29.7675 −1.06312
\(785\) 50.9303 + 16.0579i 1.81778 + 0.573130i
\(786\) 22.0793 0.787541
\(787\) 7.51142i 0.267753i −0.990998 0.133877i \(-0.957257\pi\)
0.990998 0.133877i \(-0.0427426\pi\)
\(788\) 0.867568i 0.0309058i
\(789\) −3.99436 −0.142203
\(790\) −11.5136 3.63013i −0.409636 0.129154i
\(791\) −6.99459 −0.248699
\(792\) 5.67793i 0.201756i
\(793\) 34.3214i 1.21879i
\(794\) 2.66548 0.0945945
\(795\) 4.85647 15.4031i 0.172241 0.546293i
\(796\) −6.68247 −0.236854
\(797\) 20.2219i 0.716295i 0.933665 + 0.358148i \(0.116592\pi\)
−0.933665 + 0.358148i \(0.883408\pi\)
\(798\) 0.821366i 0.0290760i
\(799\) −11.3339 −0.400963
\(800\) 4.55782 6.50944i 0.161143 0.230143i
\(801\) 1.37797 0.0486883
\(802\) 57.0244i 2.01360i
\(803\) 3.04579i 0.107484i
\(804\) −0.899692 −0.0317297
\(805\) 2.51312 7.97079i 0.0885757 0.280933i
\(806\) 36.9909 1.30295
\(807\) 4.19108i 0.147533i
\(808\) 38.9978i 1.37194i
\(809\) 27.4034 0.963453 0.481727 0.876322i \(-0.340010\pi\)
0.481727 + 0.876322i \(0.340010\pi\)
\(810\) −7.59051 2.39322i −0.266703 0.0840890i
\(811\) −27.4966 −0.965535 −0.482768 0.875748i \(-0.660368\pi\)
−0.482768 + 0.875748i \(0.660368\pi\)
\(812\) 0.500023i 0.0175474i
\(813\) 17.7570i 0.622764i
\(814\) 15.5285 0.544272
\(815\) 38.6034 + 12.1713i 1.35222 + 0.426342i
\(816\) −16.4994 −0.577595
\(817\) 0.0821817i 0.00287517i
\(818\) 22.9924i 0.803911i
\(819\) −4.05176 −0.141580
\(820\) 1.39147 4.41328i 0.0485921 0.154119i
\(821\) 24.3693 0.850495 0.425247 0.905077i \(-0.360187\pi\)
0.425247 + 0.905077i \(0.360187\pi\)
\(822\) 28.9306i 1.00907i
\(823\) 38.8757i 1.35512i −0.735467 0.677561i \(-0.763037\pi\)
0.735467 0.677561i \(-0.236963\pi\)
\(824\) −41.4342 −1.44343
\(825\) 2.58329 3.68944i 0.0899387 0.128450i
\(826\) −2.92717 −0.101849
\(827\) 33.7426i 1.17335i −0.809824 0.586673i \(-0.800437\pi\)
0.809824 0.586673i \(-0.199563\pi\)
\(828\) 3.83578i 0.133303i
\(829\) −0.348062 −0.0120887 −0.00604435 0.999982i \(-0.501924\pi\)
−0.00604435 + 0.999982i \(0.501924\pi\)
\(830\) −9.52046 + 30.1958i −0.330460 + 1.04811i
\(831\) 19.7655 0.685656
\(832\) 20.1562i 0.698791i
\(833\) 27.0952i 0.938794i
\(834\) −29.8125 −1.03232
\(835\) 17.3018 + 5.45509i 0.598753 + 0.188781i
\(836\) −0.282982 −0.00978713
\(837\) 37.2990i 1.28924i
\(838\) 35.7919i 1.23641i
\(839\) −16.5097 −0.569979 −0.284989 0.958531i \(-0.591990\pi\)
−0.284989 + 0.958531i \(0.591990\pi\)
\(840\) 3.00758 + 0.948262i 0.103771 + 0.0327181i
\(841\) −20.4270 −0.704378
\(842\) 21.4921i 0.740666i
\(843\) 4.20721i 0.144904i
\(844\) 3.26944 0.112539
\(845\) 2.41323 7.65398i 0.0830176 0.263305i
\(846\) −9.17897 −0.315579
\(847\) 0.603482i 0.0207359i
\(848\) 35.9692i 1.23519i
\(849\) −9.19212 −0.315473
\(850\) 25.2691 + 17.6930i 0.866722 + 0.606866i
\(851\) 63.6515 2.18195
\(852\) 0.387273i 0.0132677i
\(853\) 7.46786i 0.255695i 0.991794 + 0.127847i \(0.0408068\pi\)
−0.991794 + 0.127847i \(0.959193\pi\)
\(854\) −10.2015 −0.349088
\(855\) 1.47157 4.66734i 0.0503266 0.159620i
\(856\) 0.323054 0.0110418
\(857\) 11.9526i 0.408294i 0.978940 + 0.204147i \(0.0654421\pi\)
−0.978940 + 0.204147i \(0.934558\pi\)
\(858\) 4.17531i 0.142543i
\(859\) −33.9395 −1.15800 −0.579001 0.815327i \(-0.696557\pi\)
−0.579001 + 0.815327i \(0.696557\pi\)
\(860\) 0.0495951 + 0.0156369i 0.00169118 + 0.000533214i
\(861\) 3.97542 0.135482
\(862\) 36.1832i 1.23240i
\(863\) 42.3256i 1.44078i 0.693569 + 0.720391i \(0.256037\pi\)
−0.693569 + 0.720391i \(0.743963\pi\)
\(864\) −7.42805 −0.252707
\(865\) 38.2516 + 12.0604i 1.30059 + 0.410065i
\(866\) 39.9550 1.35773
\(867\) 0.295094i 0.0100219i
\(868\) 1.36286i 0.0462583i
\(869\) 3.57318 0.121212
\(870\) 2.67951 8.49855i 0.0908441 0.288128i
\(871\) 10.8276 0.366878
\(872\) 37.2416i 1.26116i
\(873\) 12.5015i 0.423112i
\(874\) −9.35800 −0.316539
\(875\) −4.10751 5.35277i −0.138859 0.180957i
\(876\) 0.776391 0.0262318
\(877\) 24.5946i 0.830501i 0.909707 + 0.415251i \(0.136306\pi\)
−0.909707 + 0.415251i \(0.863694\pi\)
\(878\) 33.8186i 1.14132i
\(879\) −17.1606 −0.578814
\(880\) −3.01623 + 9.56651i −0.101677 + 0.322487i
\(881\) −11.3838 −0.383529 −0.191765 0.981441i \(-0.561421\pi\)
−0.191765 + 0.981441i \(0.561421\pi\)
\(882\) 21.9436i 0.738881i
\(883\) 32.2722i 1.08605i 0.839717 + 0.543024i \(0.182721\pi\)
−0.839717 + 0.543024i \(0.817279\pi\)
\(884\) −3.54466 −0.119220
\(885\) −6.16679 1.94433i −0.207294 0.0653580i
\(886\) 15.6075 0.524343
\(887\) 29.2459i 0.981980i 0.871165 + 0.490990i \(0.163365\pi\)
−0.871165 + 0.490990i \(0.836635\pi\)
\(888\) 24.0173i 0.805968i
\(889\) −11.3455 −0.380514
\(890\) −2.02878 0.639654i −0.0680047 0.0214413i
\(891\) 2.35567 0.0789178
\(892\) 2.71653i 0.0909562i
\(893\) 2.77574i 0.0928866i
\(894\) −14.9920 −0.501407
\(895\) 15.2264 48.2932i 0.508963 1.61426i
\(896\) −7.90935 −0.264233
\(897\) 17.1147i 0.571443i
\(898\) 21.9015i 0.730863i
\(899\) 23.3665 0.779317
\(900\) 2.53665 + 1.77613i 0.0845551 + 0.0592043i
\(901\) −32.7402 −1.09074
\(902\) 11.0497i 0.367913i
\(903\) 0.0446746i 0.00148668i
\(904\) 30.0693 1.00009
\(905\) −1.42735 + 4.52710i −0.0474468 + 0.150486i
\(906\) 21.4573 0.712871
\(907\) 24.0627i 0.798990i −0.916735 0.399495i \(-0.869185\pi\)
0.916735 0.399495i \(-0.130815\pi\)
\(908\) 1.49778i 0.0497054i
\(909\) −32.8986 −1.09118
\(910\) 5.96537 + 1.88083i 0.197750 + 0.0623487i
\(911\) −8.77047 −0.290579 −0.145289 0.989389i \(-0.546411\pi\)
−0.145289 + 0.989389i \(0.546411\pi\)
\(912\) 4.04082i 0.133805i
\(913\) 9.37109i 0.310138i
\(914\) −25.4443 −0.841623
\(915\) −21.4919 6.77621i −0.710502 0.224015i
\(916\) −0.410776 −0.0135724
\(917\) 9.78985i 0.323289i
\(918\) 28.8350i 0.951698i
\(919\) 9.19702 0.303382 0.151691 0.988428i \(-0.451528\pi\)
0.151691 + 0.988428i \(0.451528\pi\)
\(920\) −10.8038 + 34.2660i −0.356189 + 1.12972i
\(921\) −1.13947 −0.0375469
\(922\) 16.2833i 0.536263i
\(923\) 4.66072i 0.153410i
\(924\) 0.153831 0.00506067
\(925\) 29.4733 42.0936i 0.969077 1.38403i
\(926\) −19.7270 −0.648270
\(927\) 34.9540i 1.14804i
\(928\) 4.65341i 0.152756i
\(929\) −40.7749 −1.33778 −0.668891 0.743360i \(-0.733231\pi\)
−0.668891 + 0.743360i \(0.733231\pi\)
\(930\) 7.30325 23.1635i 0.239483 0.759563i
\(931\) 6.63581 0.217480
\(932\) 7.08790i 0.232172i
\(933\) 30.8901i 1.01130i
\(934\) 19.8678 0.650093
\(935\) −8.70772 2.74546i −0.284773 0.0897863i
\(936\) 17.4183 0.569335
\(937\) 18.4291i 0.602052i −0.953616 0.301026i \(-0.902671\pi\)
0.953616 0.301026i \(-0.0973291\pi\)
\(938\) 3.21832i 0.105082i
\(939\) 0.680454 0.0222058
\(940\) 1.67511 + 0.528146i 0.0546360 + 0.0172262i
\(941\) −36.4393 −1.18789 −0.593943 0.804507i \(-0.702430\pi\)
−0.593943 + 0.804507i \(0.702430\pi\)
\(942\) 32.5045i 1.05905i
\(943\) 45.2928i 1.47494i
\(944\) 14.4006 0.468699
\(945\) −1.89649 + 6.01506i −0.0616929 + 0.195670i
\(946\) −0.124173 −0.00403720
\(947\) 35.2476i 1.14539i −0.819767 0.572697i \(-0.805897\pi\)
0.819767 0.572697i \(-0.194103\pi\)
\(948\) 0.910824i 0.0295822i
\(949\) −9.34366 −0.303308
\(950\) −4.33315 + 6.18857i −0.140586 + 0.200784i
\(951\) 17.4976 0.567399
\(952\) 6.39278i 0.207191i
\(953\) 21.0701i 0.682527i −0.939968 0.341263i \(-0.889145\pi\)
0.939968 0.341263i \(-0.110855\pi\)
\(954\) −26.5154 −0.858467
\(955\) −3.64349 + 11.5560i −0.117900 + 0.373942i
\(956\) 0.435510 0.0140854
\(957\) 2.63747i 0.0852574i
\(958\) 10.2177i 0.330120i
\(959\) −12.8277 −0.414228
\(960\) −12.6218 3.97952i −0.407365 0.128439i
\(961\) 32.6875 1.05443
\(962\) 47.6370i 1.53588i
\(963\) 0.272529i 0.00878212i
\(964\) 1.36494 0.0439617
\(965\) 6.17558 + 1.94710i 0.198799 + 0.0626794i
\(966\) 5.08708 0.163674
\(967\) 3.18321i 0.102365i 0.998689 + 0.0511826i \(0.0162991\pi\)
−0.998689 + 0.0511826i \(0.983701\pi\)
\(968\) 2.59434i 0.0833851i
\(969\) 3.67807 0.118157
\(970\) −5.80319 + 18.4058i −0.186329 + 0.590976i
\(971\) −3.50130 −0.112362 −0.0561810 0.998421i \(-0.517892\pi\)
−0.0561810 + 0.998421i \(0.517892\pi\)
\(972\) 4.56828i 0.146528i
\(973\) 13.2187i 0.423773i
\(974\) −43.0370 −1.37899
\(975\) 11.3182 + 7.92483i 0.362472 + 0.253798i
\(976\) 50.1877 1.60647
\(977\) 19.0989i 0.611027i −0.952188 0.305514i \(-0.901172\pi\)
0.952188 0.305514i \(-0.0988282\pi\)
\(978\) 24.6373i 0.787814i
\(979\) 0.629618 0.0201227
\(980\) −1.26261 + 4.00459i −0.0403326 + 0.127922i
\(981\) 31.4170 1.00307
\(982\) 1.12747i 0.0359790i
\(983\) 48.2760i 1.53976i −0.638186 0.769882i \(-0.720315\pi\)
0.638186 0.769882i \(-0.279685\pi\)
\(984\) −17.0901 −0.544813
\(985\) 6.53808 + 2.06140i 0.208321 + 0.0656816i
\(986\) −18.0641 −0.575280
\(987\) 1.50891i 0.0480293i
\(988\) 0.868110i 0.0276183i
\(989\) −0.508987 −0.0161848
\(990\) −7.05213 2.22347i −0.224131 0.0706666i
\(991\) 23.8140 0.756477 0.378238 0.925708i \(-0.376530\pi\)
0.378238 + 0.925708i \(0.376530\pi\)
\(992\) 12.6833i 0.402695i
\(993\) 23.7116i 0.752465i
\(994\) 1.38533 0.0439399
\(995\) 15.8780 50.3598i 0.503365 1.59651i
\(996\) −2.38875 −0.0756903
\(997\) 1.80923i 0.0572988i −0.999590 0.0286494i \(-0.990879\pi\)
0.999590 0.0286494i \(-0.00912063\pi\)
\(998\) 16.3175i 0.516522i
\(999\) −48.0338 −1.51972
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 1045.2.b.c.419.5 20
5.2 odd 4 5225.2.a.ba.1.16 20
5.3 odd 4 5225.2.a.ba.1.5 20
5.4 even 2 inner 1045.2.b.c.419.16 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.c.419.5 20 1.1 even 1 trivial
1045.2.b.c.419.16 yes 20 5.4 even 2 inner
5225.2.a.ba.1.5 20 5.3 odd 4
5225.2.a.ba.1.16 20 5.2 odd 4