Properties

Label 1155.2.c.f.694.13
Level $1155$
Weight $2$
Character 1155.694
Analytic conductor $9.223$
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] = [1155,2,Mod(694,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1155.694");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.c (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: \(9.22272143346\)
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: \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + 22984 x^{4} + 3428 x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 694.13
Root \(0.792050i\) of defining polynomial
Character \(\chi\) \(=\) 1155.694
Dual form 1155.2.c.f.694.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.792050i q^{2} -1.00000i q^{3} +1.37266 q^{4} +(-0.199975 - 2.22711i) q^{5} +0.792050 q^{6} -1.00000i q^{7} +2.67131i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+0.792050i q^{2} -1.00000i q^{3} +1.37266 q^{4} +(-0.199975 - 2.22711i) q^{5} +0.792050 q^{6} -1.00000i q^{7} +2.67131i q^{8} -1.00000 q^{9} +(1.76398 - 0.158390i) q^{10} +1.00000 q^{11} -1.37266i q^{12} -6.97648i q^{13} +0.792050 q^{14} +(-2.22711 + 0.199975i) q^{15} +0.629499 q^{16} -2.01100i q^{17} -0.792050i q^{18} -6.64274 q^{19} +(-0.274497 - 3.05705i) q^{20} -1.00000 q^{21} +0.792050i q^{22} +2.05588i q^{23} +2.67131 q^{24} +(-4.92002 + 0.890732i) q^{25} +5.52572 q^{26} +1.00000i q^{27} -1.37266i q^{28} +6.58029 q^{29} +(-0.158390 - 1.76398i) q^{30} -6.71609 q^{31} +5.84122i q^{32} -1.00000i q^{33} +1.59281 q^{34} +(-2.22711 + 0.199975i) q^{35} -1.37266 q^{36} -4.53927i q^{37} -5.26138i q^{38} -6.97648 q^{39} +(5.94930 - 0.534196i) q^{40} +10.5891 q^{41} -0.792050i q^{42} +5.38354i q^{43} +1.37266 q^{44} +(0.199975 + 2.22711i) q^{45} -1.62836 q^{46} -1.71761i q^{47} -0.629499i q^{48} -1.00000 q^{49} +(-0.705505 - 3.89690i) q^{50} -2.01100 q^{51} -9.57631i q^{52} -5.42564i q^{53} -0.792050 q^{54} +(-0.199975 - 2.22711i) q^{55} +2.67131 q^{56} +6.64274i q^{57} +5.21192i q^{58} -7.79524 q^{59} +(-3.05705 + 0.274497i) q^{60} -2.21899 q^{61} -5.31948i q^{62} +1.00000i q^{63} -3.36754 q^{64} +(-15.5374 + 1.39512i) q^{65} +0.792050 q^{66} -2.45990i q^{67} -2.76041i q^{68} +2.05588 q^{69} +(-0.158390 - 1.76398i) q^{70} +6.95053 q^{71} -2.67131i q^{72} -9.73428i q^{73} +3.59533 q^{74} +(0.890732 + 4.92002i) q^{75} -9.11820 q^{76} -1.00000i q^{77} -5.52572i q^{78} +6.67029 q^{79} +(-0.125884 - 1.40196i) q^{80} +1.00000 q^{81} +8.38713i q^{82} -4.69895i q^{83} -1.37266 q^{84} +(-4.47871 + 0.402149i) q^{85} -4.26403 q^{86} -6.58029i q^{87} +2.67131i q^{88} -6.34225 q^{89} +(-1.76398 + 0.158390i) q^{90} -6.97648 q^{91} +2.82201i q^{92} +6.71609i q^{93} +1.36044 q^{94} +(1.32838 + 14.7941i) q^{95} +5.84122 q^{96} +15.0556i q^{97} -0.792050i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.792050i 0.560064i 0.959991 + 0.280032i \(0.0903451\pi\)
−0.959991 + 0.280032i \(0.909655\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.37266 0.686328
\(5\) −0.199975 2.22711i −0.0894316 0.995993i
\(6\) 0.792050 0.323353
\(7\) 1.00000i 0.377964i
\(8\) 2.67131i 0.944452i
\(9\) −1.00000 −0.333333
\(10\) 1.76398 0.158390i 0.557820 0.0500874i
\(11\) 1.00000 0.301511
\(12\) 1.37266i 0.396252i
\(13\) 6.97648i 1.93493i −0.253010 0.967464i \(-0.581421\pi\)
0.253010 0.967464i \(-0.418579\pi\)
\(14\) 0.792050 0.211684
\(15\) −2.22711 + 0.199975i −0.575037 + 0.0516333i
\(16\) 0.629499 0.157375
\(17\) 2.01100i 0.487738i −0.969808 0.243869i \(-0.921583\pi\)
0.969808 0.243869i \(-0.0784167\pi\)
\(18\) 0.792050i 0.186688i
\(19\) −6.64274 −1.52395 −0.761974 0.647607i \(-0.775770\pi\)
−0.761974 + 0.647607i \(0.775770\pi\)
\(20\) −0.274497 3.05705i −0.0613794 0.683578i
\(21\) −1.00000 −0.218218
\(22\) 0.792050i 0.168866i
\(23\) 2.05588i 0.428680i 0.976759 + 0.214340i \(0.0687600\pi\)
−0.976759 + 0.214340i \(0.931240\pi\)
\(24\) 2.67131 0.545280
\(25\) −4.92002 + 0.890732i −0.984004 + 0.178146i
\(26\) 5.52572 1.08368
\(27\) 1.00000i 0.192450i
\(28\) 1.37266i 0.259408i
\(29\) 6.58029 1.22193 0.610965 0.791658i \(-0.290782\pi\)
0.610965 + 0.791658i \(0.290782\pi\)
\(30\) −0.158390 1.76398i −0.0289180 0.322057i
\(31\) −6.71609 −1.20625 −0.603123 0.797648i \(-0.706077\pi\)
−0.603123 + 0.797648i \(0.706077\pi\)
\(32\) 5.84122i 1.03259i
\(33\) 1.00000i 0.174078i
\(34\) 1.59281 0.273165
\(35\) −2.22711 + 0.199975i −0.376450 + 0.0338020i
\(36\) −1.37266 −0.228776
\(37\) 4.53927i 0.746251i −0.927781 0.373125i \(-0.878286\pi\)
0.927781 0.373125i \(-0.121714\pi\)
\(38\) 5.26138i 0.853509i
\(39\) −6.97648 −1.11713
\(40\) 5.94930 0.534196i 0.940667 0.0844638i
\(41\) 10.5891 1.65375 0.826873 0.562389i \(-0.190118\pi\)
0.826873 + 0.562389i \(0.190118\pi\)
\(42\) 0.792050i 0.122216i
\(43\) 5.38354i 0.820982i 0.911865 + 0.410491i \(0.134643\pi\)
−0.911865 + 0.410491i \(0.865357\pi\)
\(44\) 1.37266 0.206936
\(45\) 0.199975 + 2.22711i 0.0298105 + 0.331998i
\(46\) −1.62836 −0.240088
\(47\) 1.71761i 0.250540i −0.992123 0.125270i \(-0.960020\pi\)
0.992123 0.125270i \(-0.0399796\pi\)
\(48\) 0.629499i 0.0908603i
\(49\) −1.00000 −0.142857
\(50\) −0.705505 3.89690i −0.0997734 0.551105i
\(51\) −2.01100 −0.281596
\(52\) 9.57631i 1.32800i
\(53\) 5.42564i 0.745268i −0.927978 0.372634i \(-0.878455\pi\)
0.927978 0.372634i \(-0.121545\pi\)
\(54\) −0.792050 −0.107784
\(55\) −0.199975 2.22711i −0.0269646 0.300303i
\(56\) 2.67131 0.356969
\(57\) 6.64274i 0.879852i
\(58\) 5.21192i 0.684359i
\(59\) −7.79524 −1.01485 −0.507427 0.861695i \(-0.669403\pi\)
−0.507427 + 0.861695i \(0.669403\pi\)
\(60\) −3.05705 + 0.274497i −0.394664 + 0.0354374i
\(61\) −2.21899 −0.284113 −0.142057 0.989859i \(-0.545372\pi\)
−0.142057 + 0.989859i \(0.545372\pi\)
\(62\) 5.31948i 0.675575i
\(63\) 1.00000i 0.125988i
\(64\) −3.36754 −0.420943
\(65\) −15.5374 + 1.39512i −1.92717 + 0.173044i
\(66\) 0.792050 0.0974946
\(67\) 2.45990i 0.300525i −0.988646 0.150263i \(-0.951988\pi\)
0.988646 0.150263i \(-0.0480119\pi\)
\(68\) 2.76041i 0.334749i
\(69\) 2.05588 0.247498
\(70\) −0.158390 1.76398i −0.0189313 0.210836i
\(71\) 6.95053 0.824876 0.412438 0.910986i \(-0.364677\pi\)
0.412438 + 0.910986i \(0.364677\pi\)
\(72\) 2.67131i 0.314817i
\(73\) 9.73428i 1.13931i −0.821883 0.569656i \(-0.807077\pi\)
0.821883 0.569656i \(-0.192923\pi\)
\(74\) 3.59533 0.417948
\(75\) 0.890732 + 4.92002i 0.102853 + 0.568115i
\(76\) −9.11820 −1.04593
\(77\) 1.00000i 0.113961i
\(78\) 5.52572i 0.625665i
\(79\) 6.67029 0.750466 0.375233 0.926931i \(-0.377563\pi\)
0.375233 + 0.926931i \(0.377563\pi\)
\(80\) −0.125884 1.40196i −0.0140743 0.156744i
\(81\) 1.00000 0.111111
\(82\) 8.38713i 0.926203i
\(83\) 4.69895i 0.515777i −0.966175 0.257888i \(-0.916973\pi\)
0.966175 0.257888i \(-0.0830267\pi\)
\(84\) −1.37266 −0.149769
\(85\) −4.47871 + 0.402149i −0.485784 + 0.0436192i
\(86\) −4.26403 −0.459802
\(87\) 6.58029i 0.705482i
\(88\) 2.67131i 0.284763i
\(89\) −6.34225 −0.672277 −0.336138 0.941813i \(-0.609121\pi\)
−0.336138 + 0.941813i \(0.609121\pi\)
\(90\) −1.76398 + 0.158390i −0.185940 + 0.0166958i
\(91\) −6.97648 −0.731334
\(92\) 2.82201i 0.294215i
\(93\) 6.71609i 0.696426i
\(94\) 1.36044 0.140318
\(95\) 1.32838 + 14.7941i 0.136289 + 1.51784i
\(96\) 5.84122 0.596167
\(97\) 15.0556i 1.52866i 0.644824 + 0.764331i \(0.276931\pi\)
−0.644824 + 0.764331i \(0.723069\pi\)
\(98\) 0.792050i 0.0800092i
\(99\) −1.00000 −0.100504
\(100\) −6.75350 + 1.22267i −0.675350 + 0.122267i
\(101\) 8.60162 0.855894 0.427947 0.903804i \(-0.359237\pi\)
0.427947 + 0.903804i \(0.359237\pi\)
\(102\) 1.59281i 0.157712i
\(103\) 4.50360i 0.443753i −0.975075 0.221877i \(-0.928782\pi\)
0.975075 0.221877i \(-0.0712182\pi\)
\(104\) 18.6364 1.82745
\(105\) 0.199975 + 2.22711i 0.0195156 + 0.217343i
\(106\) 4.29738 0.417398
\(107\) 2.90533i 0.280868i −0.990090 0.140434i \(-0.955150\pi\)
0.990090 0.140434i \(-0.0448498\pi\)
\(108\) 1.37266i 0.132084i
\(109\) 20.5935 1.97250 0.986251 0.165255i \(-0.0528446\pi\)
0.986251 + 0.165255i \(0.0528446\pi\)
\(110\) 1.76398 0.158390i 0.168189 0.0151019i
\(111\) −4.53927 −0.430848
\(112\) 0.629499i 0.0594820i
\(113\) 17.8285i 1.67716i −0.544777 0.838581i \(-0.683386\pi\)
0.544777 0.838581i \(-0.316614\pi\)
\(114\) −5.26138 −0.492774
\(115\) 4.57866 0.411124i 0.426962 0.0383375i
\(116\) 9.03248 0.838645
\(117\) 6.97648i 0.644976i
\(118\) 6.17422i 0.568383i
\(119\) −2.01100 −0.184348
\(120\) −0.534196 5.94930i −0.0487652 0.543095i
\(121\) 1.00000 0.0909091
\(122\) 1.75756i 0.159122i
\(123\) 10.5891i 0.954790i
\(124\) −9.21889 −0.827881
\(125\) 2.96764 + 10.7793i 0.265434 + 0.964129i
\(126\) −0.792050 −0.0705614
\(127\) 14.2017i 1.26020i −0.776516 0.630098i \(-0.783015\pi\)
0.776516 0.630098i \(-0.216985\pi\)
\(128\) 9.01518i 0.796837i
\(129\) 5.38354 0.473994
\(130\) −1.10501 12.3064i −0.0969155 1.07934i
\(131\) 16.7427 1.46281 0.731406 0.681942i \(-0.238864\pi\)
0.731406 + 0.681942i \(0.238864\pi\)
\(132\) 1.37266i 0.119474i
\(133\) 6.64274i 0.575998i
\(134\) 1.94837 0.168313
\(135\) 2.22711 0.199975i 0.191679 0.0172111i
\(136\) 5.37200 0.460645
\(137\) 16.4926i 1.40905i 0.709677 + 0.704527i \(0.248841\pi\)
−0.709677 + 0.704527i \(0.751159\pi\)
\(138\) 1.62836i 0.138615i
\(139\) −1.65018 −0.139966 −0.0699831 0.997548i \(-0.522295\pi\)
−0.0699831 + 0.997548i \(0.522295\pi\)
\(140\) −3.05705 + 0.274497i −0.258368 + 0.0231992i
\(141\) −1.71761 −0.144649
\(142\) 5.50517i 0.461984i
\(143\) 6.97648i 0.583402i
\(144\) −0.629499 −0.0524582
\(145\) −1.31589 14.6550i −0.109279 1.21703i
\(146\) 7.71004 0.638087
\(147\) 1.00000i 0.0824786i
\(148\) 6.23085i 0.512173i
\(149\) 6.27969 0.514452 0.257226 0.966351i \(-0.417192\pi\)
0.257226 + 0.966351i \(0.417192\pi\)
\(150\) −3.89690 + 0.705505i −0.318181 + 0.0576042i
\(151\) 15.0368 1.22368 0.611839 0.790983i \(-0.290430\pi\)
0.611839 + 0.790983i \(0.290430\pi\)
\(152\) 17.7448i 1.43930i
\(153\) 2.01100i 0.162579i
\(154\) 0.792050 0.0638252
\(155\) 1.34305 + 14.9575i 0.107876 + 1.20141i
\(156\) −9.57631 −0.766718
\(157\) 1.00596i 0.0802845i −0.999194 0.0401422i \(-0.987219\pi\)
0.999194 0.0401422i \(-0.0127811\pi\)
\(158\) 5.28320i 0.420309i
\(159\) −5.42564 −0.430281
\(160\) 13.0090 1.16810i 1.02845 0.0923463i
\(161\) 2.05588 0.162026
\(162\) 0.792050i 0.0622293i
\(163\) 7.18836i 0.563036i −0.959556 0.281518i \(-0.909162\pi\)
0.959556 0.281518i \(-0.0908379\pi\)
\(164\) 14.5352 1.13501
\(165\) −2.22711 + 0.199975i −0.173380 + 0.0155680i
\(166\) 3.72180 0.288868
\(167\) 25.3518i 1.96178i 0.194569 + 0.980889i \(0.437669\pi\)
−0.194569 + 0.980889i \(0.562331\pi\)
\(168\) 2.67131i 0.206096i
\(169\) −35.6713 −2.74394
\(170\) −0.318522 3.54736i −0.0244295 0.272070i
\(171\) 6.64274 0.507983
\(172\) 7.38975i 0.563463i
\(173\) 23.6325i 1.79674i 0.439236 + 0.898372i \(0.355249\pi\)
−0.439236 + 0.898372i \(0.644751\pi\)
\(174\) 5.21192 0.395115
\(175\) 0.890732 + 4.92002i 0.0673330 + 0.371919i
\(176\) 0.629499 0.0474502
\(177\) 7.79524i 0.585926i
\(178\) 5.02338i 0.376518i
\(179\) −4.63413 −0.346371 −0.173185 0.984889i \(-0.555406\pi\)
−0.173185 + 0.984889i \(0.555406\pi\)
\(180\) 0.274497 + 3.05705i 0.0204598 + 0.227859i
\(181\) 20.1523 1.49791 0.748954 0.662622i \(-0.230556\pi\)
0.748954 + 0.662622i \(0.230556\pi\)
\(182\) 5.52572i 0.409594i
\(183\) 2.21899i 0.164033i
\(184\) −5.49189 −0.404867
\(185\) −10.1094 + 0.907740i −0.743260 + 0.0667384i
\(186\) −5.31948 −0.390043
\(187\) 2.01100i 0.147059i
\(188\) 2.35769i 0.171952i
\(189\) 1.00000 0.0727393
\(190\) −11.7177 + 1.05215i −0.850089 + 0.0763306i
\(191\) −17.0974 −1.23712 −0.618562 0.785736i \(-0.712284\pi\)
−0.618562 + 0.785736i \(0.712284\pi\)
\(192\) 3.36754i 0.243032i
\(193\) 7.66253i 0.551561i 0.961221 + 0.275780i \(0.0889363\pi\)
−0.961221 + 0.275780i \(0.911064\pi\)
\(194\) −11.9248 −0.856149
\(195\) 1.39512 + 15.5374i 0.0999067 + 1.11265i
\(196\) −1.37266 −0.0980469
\(197\) 12.1159i 0.863220i 0.902060 + 0.431610i \(0.142054\pi\)
−0.902060 + 0.431610i \(0.857946\pi\)
\(198\) 0.792050i 0.0562886i
\(199\) −14.8587 −1.05330 −0.526652 0.850081i \(-0.676553\pi\)
−0.526652 + 0.850081i \(0.676553\pi\)
\(200\) −2.37942 13.1429i −0.168251 0.929344i
\(201\) −2.45990 −0.173508
\(202\) 6.81292i 0.479355i
\(203\) 6.58029i 0.461846i
\(204\) −2.76041 −0.193267
\(205\) −2.11756 23.5831i −0.147897 1.64712i
\(206\) 3.56708 0.248530
\(207\) 2.05588i 0.142893i
\(208\) 4.39168i 0.304508i
\(209\) −6.64274 −0.459488
\(210\) −1.76398 + 0.158390i −0.121726 + 0.0109300i
\(211\) 5.59506 0.385180 0.192590 0.981279i \(-0.438311\pi\)
0.192590 + 0.981279i \(0.438311\pi\)
\(212\) 7.44753i 0.511499i
\(213\) 6.95053i 0.476243i
\(214\) 2.30116 0.157304
\(215\) 11.9897 1.07657i 0.817692 0.0734217i
\(216\) −2.67131 −0.181760
\(217\) 6.71609i 0.455918i
\(218\) 16.3111i 1.10473i
\(219\) −9.73428 −0.657782
\(220\) −0.274497 3.05705i −0.0185066 0.206107i
\(221\) −14.0297 −0.943738
\(222\) 3.59533i 0.241302i
\(223\) 14.9290i 0.999721i 0.866106 + 0.499860i \(0.166615\pi\)
−0.866106 + 0.499860i \(0.833385\pi\)
\(224\) 5.84122 0.390283
\(225\) 4.92002 0.890732i 0.328001 0.0593821i
\(226\) 14.1210 0.939318
\(227\) 12.4673i 0.827486i 0.910394 + 0.413743i \(0.135779\pi\)
−0.910394 + 0.413743i \(0.864221\pi\)
\(228\) 9.11820i 0.603867i
\(229\) −11.3408 −0.749420 −0.374710 0.927142i \(-0.622258\pi\)
−0.374710 + 0.927142i \(0.622258\pi\)
\(230\) 0.325631 + 3.62653i 0.0214715 + 0.239126i
\(231\) −1.00000 −0.0657952
\(232\) 17.5780i 1.15405i
\(233\) 15.4252i 1.01054i −0.862962 0.505269i \(-0.831393\pi\)
0.862962 0.505269i \(-0.168607\pi\)
\(234\) −5.52572 −0.361228
\(235\) −3.82531 + 0.343480i −0.249536 + 0.0224061i
\(236\) −10.7002 −0.696523
\(237\) 6.67029i 0.433282i
\(238\) 1.59281i 0.103247i
\(239\) 15.6157 1.01009 0.505047 0.863092i \(-0.331475\pi\)
0.505047 + 0.863092i \(0.331475\pi\)
\(240\) −1.40196 + 0.125884i −0.0904962 + 0.00812578i
\(241\) 23.5767 1.51871 0.759353 0.650679i \(-0.225516\pi\)
0.759353 + 0.650679i \(0.225516\pi\)
\(242\) 0.792050i 0.0509149i
\(243\) 1.00000i 0.0641500i
\(244\) −3.04592 −0.194995
\(245\) 0.199975 + 2.22711i 0.0127759 + 0.142285i
\(246\) 8.38713 0.534744
\(247\) 46.3429i 2.94873i
\(248\) 17.9408i 1.13924i
\(249\) −4.69895 −0.297784
\(250\) −8.53774 + 2.35052i −0.539974 + 0.148660i
\(251\) 20.6569 1.30385 0.651925 0.758284i \(-0.273962\pi\)
0.651925 + 0.758284i \(0.273962\pi\)
\(252\) 1.37266i 0.0864692i
\(253\) 2.05588i 0.129252i
\(254\) 11.2484 0.705790
\(255\) 0.402149 + 4.47871i 0.0251836 + 0.280467i
\(256\) −13.8756 −0.867223
\(257\) 0.652452i 0.0406988i 0.999793 + 0.0203494i \(0.00647787\pi\)
−0.999793 + 0.0203494i \(0.993522\pi\)
\(258\) 4.26403i 0.265467i
\(259\) −4.53927 −0.282056
\(260\) −21.3275 + 1.91502i −1.32267 + 0.118765i
\(261\) −6.58029 −0.407310
\(262\) 13.2610i 0.819269i
\(263\) 25.3131i 1.56087i 0.625236 + 0.780436i \(0.285003\pi\)
−0.625236 + 0.780436i \(0.714997\pi\)
\(264\) 2.67131 0.164408
\(265\) −12.0835 + 1.08499i −0.742282 + 0.0666505i
\(266\) −5.26138 −0.322596
\(267\) 6.34225i 0.388139i
\(268\) 3.37660i 0.206259i
\(269\) −4.53171 −0.276303 −0.138151 0.990411i \(-0.544116\pi\)
−0.138151 + 0.990411i \(0.544116\pi\)
\(270\) 0.158390 + 1.76398i 0.00963933 + 0.107352i
\(271\) −13.1341 −0.797841 −0.398920 0.916986i \(-0.630615\pi\)
−0.398920 + 0.916986i \(0.630615\pi\)
\(272\) 1.26592i 0.0767576i
\(273\) 6.97648i 0.422236i
\(274\) −13.0629 −0.789161
\(275\) −4.92002 + 0.890732i −0.296688 + 0.0537132i
\(276\) 2.82201 0.169865
\(277\) 25.2114i 1.51481i −0.652947 0.757403i \(-0.726468\pi\)
0.652947 0.757403i \(-0.273532\pi\)
\(278\) 1.30702i 0.0783901i
\(279\) 6.71609 0.402082
\(280\) −0.534196 5.94930i −0.0319243 0.355539i
\(281\) −11.6960 −0.697725 −0.348862 0.937174i \(-0.613432\pi\)
−0.348862 + 0.937174i \(0.613432\pi\)
\(282\) 1.36044i 0.0810128i
\(283\) 18.7140i 1.11243i 0.831038 + 0.556216i \(0.187747\pi\)
−0.831038 + 0.556216i \(0.812253\pi\)
\(284\) 9.54069 0.566136
\(285\) 14.7941 1.32838i 0.876327 0.0786866i
\(286\) 5.52572 0.326743
\(287\) 10.5891i 0.625057i
\(288\) 5.84122i 0.344197i
\(289\) 12.9559 0.762111
\(290\) 11.6075 1.04225i 0.681617 0.0612033i
\(291\) 15.0556 0.882574
\(292\) 13.3618i 0.781942i
\(293\) 18.1044i 1.05767i −0.848724 0.528836i \(-0.822629\pi\)
0.848724 0.528836i \(-0.177371\pi\)
\(294\) −0.792050 −0.0461933
\(295\) 1.55885 + 17.3608i 0.0907600 + 1.01079i
\(296\) 12.1258 0.704798
\(297\) 1.00000i 0.0580259i
\(298\) 4.97383i 0.288126i
\(299\) 14.3428 0.829464
\(300\) 1.22267 + 6.75350i 0.0705908 + 0.389913i
\(301\) 5.38354 0.310302
\(302\) 11.9099i 0.685338i
\(303\) 8.60162i 0.494150i
\(304\) −4.18159 −0.239831
\(305\) 0.443744 + 4.94194i 0.0254087 + 0.282975i
\(306\) −1.59281 −0.0910549
\(307\) 11.2076i 0.639652i 0.947476 + 0.319826i \(0.103625\pi\)
−0.947476 + 0.319826i \(0.896375\pi\)
\(308\) 1.37266i 0.0782144i
\(309\) −4.50360 −0.256201
\(310\) −11.8471 + 1.06376i −0.672868 + 0.0604177i
\(311\) 16.2770 0.922982 0.461491 0.887145i \(-0.347315\pi\)
0.461491 + 0.887145i \(0.347315\pi\)
\(312\) 18.6364i 1.05508i
\(313\) 3.97432i 0.224642i 0.993672 + 0.112321i \(0.0358285\pi\)
−0.993672 + 0.112321i \(0.964172\pi\)
\(314\) 0.796772 0.0449644
\(315\) 2.22711 0.199975i 0.125483 0.0112673i
\(316\) 9.15601 0.515066
\(317\) 0.264616i 0.0148623i 0.999972 + 0.00743116i \(0.00236543\pi\)
−0.999972 + 0.00743116i \(0.997635\pi\)
\(318\) 4.29738i 0.240985i
\(319\) 6.58029 0.368426
\(320\) 0.673425 + 7.49988i 0.0376456 + 0.419256i
\(321\) −2.90533 −0.162159
\(322\) 1.62836i 0.0907448i
\(323\) 13.3585i 0.743288i
\(324\) 1.37266 0.0762587
\(325\) 6.21417 + 34.3244i 0.344700 + 1.90398i
\(326\) 5.69355 0.315336
\(327\) 20.5935i 1.13882i
\(328\) 28.2869i 1.56188i
\(329\) −1.71761 −0.0946951
\(330\) −0.158390 1.76398i −0.00871910 0.0971040i
\(331\) −7.36413 −0.404769 −0.202385 0.979306i \(-0.564869\pi\)
−0.202385 + 0.979306i \(0.564869\pi\)
\(332\) 6.45004i 0.353992i
\(333\) 4.53927i 0.248750i
\(334\) −20.0799 −1.09872
\(335\) −5.47847 + 0.491920i −0.299321 + 0.0268764i
\(336\) −0.629499 −0.0343420
\(337\) 18.2163i 0.992305i −0.868235 0.496152i \(-0.834746\pi\)
0.868235 0.496152i \(-0.165254\pi\)
\(338\) 28.2534i 1.53678i
\(339\) −17.8285 −0.968310
\(340\) −6.14772 + 0.552013i −0.333407 + 0.0299371i
\(341\) −6.71609 −0.363697
\(342\) 5.26138i 0.284503i
\(343\) 1.00000i 0.0539949i
\(344\) −14.3811 −0.775378
\(345\) −0.411124 4.57866i −0.0221342 0.246507i
\(346\) −18.7181 −1.00629
\(347\) 4.83663i 0.259644i −0.991537 0.129822i \(-0.958559\pi\)
0.991537 0.129822i \(-0.0414405\pi\)
\(348\) 9.03248i 0.484192i
\(349\) 26.1747 1.40110 0.700550 0.713603i \(-0.252938\pi\)
0.700550 + 0.713603i \(0.252938\pi\)
\(350\) −3.89690 + 0.705505i −0.208298 + 0.0377108i
\(351\) 6.97648 0.372377
\(352\) 5.84122i 0.311338i
\(353\) 34.1495i 1.81759i 0.417240 + 0.908796i \(0.362997\pi\)
−0.417240 + 0.908796i \(0.637003\pi\)
\(354\) −6.17422 −0.328156
\(355\) −1.38993 15.4796i −0.0737700 0.821571i
\(356\) −8.70573 −0.461403
\(357\) 2.01100i 0.106433i
\(358\) 3.67046i 0.193990i
\(359\) −36.6175 −1.93260 −0.966299 0.257422i \(-0.917127\pi\)
−0.966299 + 0.257422i \(0.917127\pi\)
\(360\) −5.94930 + 0.534196i −0.313556 + 0.0281546i
\(361\) 25.1260 1.32242
\(362\) 15.9616i 0.838924i
\(363\) 1.00000i 0.0524864i
\(364\) −9.57631 −0.501935
\(365\) −21.6793 + 1.94661i −1.13475 + 0.101890i
\(366\) −1.75756 −0.0918689
\(367\) 29.1290i 1.52052i −0.649618 0.760260i \(-0.725071\pi\)
0.649618 0.760260i \(-0.274929\pi\)
\(368\) 1.29417i 0.0674633i
\(369\) −10.5891 −0.551248
\(370\) −0.718976 8.00718i −0.0373778 0.416273i
\(371\) −5.42564 −0.281685
\(372\) 9.21889i 0.477977i
\(373\) 0.177939i 0.00921334i 0.999989 + 0.00460667i \(0.00146635\pi\)
−0.999989 + 0.00460667i \(0.998534\pi\)
\(374\) 1.59281 0.0823623
\(375\) 10.7793 2.96764i 0.556640 0.153248i
\(376\) 4.58828 0.236623
\(377\) 45.9073i 2.36435i
\(378\) 0.792050i 0.0407387i
\(379\) −0.0707006 −0.00363164 −0.00181582 0.999998i \(-0.500578\pi\)
−0.00181582 + 0.999998i \(0.500578\pi\)
\(380\) 1.82341 + 20.3072i 0.0935391 + 1.04174i
\(381\) −14.2017 −0.727574
\(382\) 13.5420i 0.692869i
\(383\) 2.25388i 0.115168i 0.998341 + 0.0575840i \(0.0183397\pi\)
−0.998341 + 0.0575840i \(0.981660\pi\)
\(384\) 9.01518 0.460054
\(385\) −2.22711 + 0.199975i −0.113504 + 0.0101917i
\(386\) −6.06911 −0.308909
\(387\) 5.38354i 0.273661i
\(388\) 20.6661i 1.04916i
\(389\) 0.181295 0.00919203 0.00459602 0.999989i \(-0.498537\pi\)
0.00459602 + 0.999989i \(0.498537\pi\)
\(390\) −12.3064 + 1.10501i −0.623158 + 0.0559542i
\(391\) 4.13436 0.209084
\(392\) 2.67131i 0.134922i
\(393\) 16.7427i 0.844555i
\(394\) −9.59638 −0.483458
\(395\) −1.33389 14.8555i −0.0671153 0.747459i
\(396\) −1.37266 −0.0689786
\(397\) 9.73781i 0.488726i 0.969684 + 0.244363i \(0.0785789\pi\)
−0.969684 + 0.244363i \(0.921421\pi\)
\(398\) 11.7688i 0.589918i
\(399\) 6.64274 0.332553
\(400\) −3.09715 + 0.560715i −0.154857 + 0.0280357i
\(401\) −10.7003 −0.534348 −0.267174 0.963648i \(-0.586090\pi\)
−0.267174 + 0.963648i \(0.586090\pi\)
\(402\) 1.94837i 0.0971758i
\(403\) 46.8547i 2.33400i
\(404\) 11.8071 0.587424
\(405\) −0.199975 2.22711i −0.00993684 0.110666i
\(406\) 5.21192 0.258663
\(407\) 4.53927i 0.225003i
\(408\) 5.37200i 0.265954i
\(409\) −31.1485 −1.54020 −0.770098 0.637926i \(-0.779793\pi\)
−0.770098 + 0.637926i \(0.779793\pi\)
\(410\) 18.6790 1.67722i 0.922492 0.0828318i
\(411\) 16.4926 0.813518
\(412\) 6.18190i 0.304560i
\(413\) 7.79524i 0.383579i
\(414\) 1.62836 0.0800294
\(415\) −10.4651 + 0.939673i −0.513710 + 0.0461267i
\(416\) 40.7512 1.99799
\(417\) 1.65018i 0.0808096i
\(418\) 5.26138i 0.257343i
\(419\) 25.2282 1.23248 0.616239 0.787559i \(-0.288655\pi\)
0.616239 + 0.787559i \(0.288655\pi\)
\(420\) 0.274497 + 3.05705i 0.0133941 + 0.149169i
\(421\) 9.09604 0.443314 0.221657 0.975125i \(-0.428853\pi\)
0.221657 + 0.975125i \(0.428853\pi\)
\(422\) 4.43157i 0.215725i
\(423\) 1.71761i 0.0835132i
\(424\) 14.4936 0.703870
\(425\) 1.79126 + 9.89414i 0.0868888 + 0.479936i
\(426\) 5.50517 0.266726
\(427\) 2.21899i 0.107385i
\(428\) 3.98801i 0.192768i
\(429\) −6.97648 −0.336828
\(430\) 0.852700 + 9.49646i 0.0411208 + 0.457960i
\(431\) 28.0128 1.34933 0.674665 0.738124i \(-0.264288\pi\)
0.674665 + 0.738124i \(0.264288\pi\)
\(432\) 0.629499i 0.0302868i
\(433\) 19.2478i 0.924988i 0.886622 + 0.462494i \(0.153045\pi\)
−0.886622 + 0.462494i \(0.846955\pi\)
\(434\) −5.31948 −0.255343
\(435\) −14.6550 + 1.31589i −0.702655 + 0.0630923i
\(436\) 28.2678 1.35378
\(437\) 13.6566i 0.653286i
\(438\) 7.71004i 0.368400i
\(439\) −31.8121 −1.51831 −0.759154 0.650911i \(-0.774387\pi\)
−0.759154 + 0.650911i \(0.774387\pi\)
\(440\) 5.94930 0.534196i 0.283622 0.0254668i
\(441\) 1.00000 0.0476190
\(442\) 11.1122i 0.528554i
\(443\) 4.63304i 0.220122i −0.993925 0.110061i \(-0.964895\pi\)
0.993925 0.110061i \(-0.0351047\pi\)
\(444\) −6.23085 −0.295703
\(445\) 1.26829 + 14.1249i 0.0601228 + 0.669583i
\(446\) −11.8245 −0.559908
\(447\) 6.27969i 0.297019i
\(448\) 3.36754i 0.159101i
\(449\) −29.2903 −1.38230 −0.691148 0.722714i \(-0.742895\pi\)
−0.691148 + 0.722714i \(0.742895\pi\)
\(450\) 0.705505 + 3.89690i 0.0332578 + 0.183702i
\(451\) 10.5891 0.498623
\(452\) 24.4724i 1.15108i
\(453\) 15.0368i 0.706490i
\(454\) −9.87475 −0.463445
\(455\) 1.39512 + 15.5374i 0.0654043 + 0.728403i
\(456\) −17.7448 −0.830978
\(457\) 31.1481i 1.45704i −0.685022 0.728522i \(-0.740207\pi\)
0.685022 0.728522i \(-0.259793\pi\)
\(458\) 8.98248i 0.419723i
\(459\) 2.01100 0.0938653
\(460\) 6.28492 0.564332i 0.293036 0.0263121i
\(461\) 5.07279 0.236263 0.118132 0.992998i \(-0.462310\pi\)
0.118132 + 0.992998i \(0.462310\pi\)
\(462\) 0.792050i 0.0368495i
\(463\) 26.6104i 1.23669i 0.785906 + 0.618346i \(0.212197\pi\)
−0.785906 + 0.618346i \(0.787803\pi\)
\(464\) 4.14229 0.192301
\(465\) 14.9575 1.34305i 0.693636 0.0622825i
\(466\) 12.2175 0.565966
\(467\) 14.2806i 0.660828i −0.943836 0.330414i \(-0.892812\pi\)
0.943836 0.330414i \(-0.107188\pi\)
\(468\) 9.57631i 0.442665i
\(469\) −2.45990 −0.113588
\(470\) −0.272053 3.02984i −0.0125489 0.139756i
\(471\) −1.00596 −0.0463523
\(472\) 20.8235i 0.958481i
\(473\) 5.38354i 0.247535i
\(474\) 5.28320 0.242666
\(475\) 32.6824 5.91690i 1.49957 0.271486i
\(476\) −2.76041 −0.126523
\(477\) 5.42564i 0.248423i
\(478\) 12.3684i 0.565718i
\(479\) −18.8608 −0.861773 −0.430887 0.902406i \(-0.641799\pi\)
−0.430887 + 0.902406i \(0.641799\pi\)
\(480\) −1.16810 13.0090i −0.0533162 0.593778i
\(481\) −31.6681 −1.44394
\(482\) 18.6739i 0.850573i
\(483\) 2.05588i 0.0935456i
\(484\) 1.37266 0.0623935
\(485\) 33.5304 3.01074i 1.52254 0.136711i
\(486\) 0.792050 0.0359281
\(487\) 39.5539i 1.79236i −0.443691 0.896180i \(-0.646331\pi\)
0.443691 0.896180i \(-0.353669\pi\)
\(488\) 5.92763i 0.268331i
\(489\) −7.18836 −0.325069
\(490\) −1.76398 + 0.158390i −0.0796886 + 0.00715534i
\(491\) −9.52713 −0.429953 −0.214977 0.976619i \(-0.568968\pi\)
−0.214977 + 0.976619i \(0.568968\pi\)
\(492\) 14.5352i 0.655299i
\(493\) 13.2329i 0.595982i
\(494\) −36.7059 −1.65148
\(495\) 0.199975 + 2.22711i 0.00898821 + 0.100101i
\(496\) −4.22777 −0.189833
\(497\) 6.95053i 0.311774i
\(498\) 3.72180i 0.166778i
\(499\) 14.3007 0.640187 0.320094 0.947386i \(-0.396286\pi\)
0.320094 + 0.947386i \(0.396286\pi\)
\(500\) 4.07355 + 14.7963i 0.182175 + 0.661709i
\(501\) 25.3518 1.13263
\(502\) 16.3613i 0.730239i
\(503\) 3.16460i 0.141102i −0.997508 0.0705512i \(-0.977524\pi\)
0.997508 0.0705512i \(-0.0224758\pi\)
\(504\) −2.67131 −0.118990
\(505\) −1.72011 19.1567i −0.0765439 0.852464i
\(506\) −1.62836 −0.0723893
\(507\) 35.6713i 1.58422i
\(508\) 19.4940i 0.864908i
\(509\) 16.5587 0.733952 0.366976 0.930231i \(-0.380393\pi\)
0.366976 + 0.930231i \(0.380393\pi\)
\(510\) −3.54736 + 0.318522i −0.157080 + 0.0141044i
\(511\) −9.73428 −0.430619
\(512\) 7.04022i 0.311137i
\(513\) 6.64274i 0.293284i
\(514\) −0.516775 −0.0227940
\(515\) −10.0300 + 0.900608i −0.441975 + 0.0396855i
\(516\) 7.38975 0.325315
\(517\) 1.71761i 0.0755405i
\(518\) 3.59533i 0.157970i
\(519\) 23.6325 1.03735
\(520\) −3.72681 41.5052i −0.163431 1.82012i
\(521\) 0.0943128 0.00413192 0.00206596 0.999998i \(-0.499342\pi\)
0.00206596 + 0.999998i \(0.499342\pi\)
\(522\) 5.21192i 0.228120i
\(523\) 39.1138i 1.71033i 0.518358 + 0.855164i \(0.326544\pi\)
−0.518358 + 0.855164i \(0.673456\pi\)
\(524\) 22.9819 1.00397
\(525\) 4.92002 0.890732i 0.214727 0.0388747i
\(526\) −20.0492 −0.874188
\(527\) 13.5060i 0.588332i
\(528\) 0.629499i 0.0273954i
\(529\) 18.7734 0.816234
\(530\) −0.859368 9.57072i −0.0373286 0.415726i
\(531\) 7.79524 0.338285
\(532\) 9.11820i 0.395324i
\(533\) 73.8749i 3.19988i
\(534\) −5.02338 −0.217383
\(535\) −6.47047 + 0.580993i −0.279743 + 0.0251185i
\(536\) 6.57118 0.283832
\(537\) 4.63413i 0.199977i
\(538\) 3.58934i 0.154747i
\(539\) −1.00000 −0.0430730
\(540\) 3.05705 0.274497i 0.131555 0.0118125i
\(541\) −4.25392 −0.182890 −0.0914451 0.995810i \(-0.529149\pi\)
−0.0914451 + 0.995810i \(0.529149\pi\)
\(542\) 10.4029i 0.446842i
\(543\) 20.1523i 0.864817i
\(544\) 11.7467 0.503635
\(545\) −4.11819 45.8640i −0.176404 1.96460i
\(546\) −5.52572 −0.236479
\(547\) 0.274019i 0.0117162i −0.999983 0.00585810i \(-0.998135\pi\)
0.999983 0.00585810i \(-0.00186470\pi\)
\(548\) 22.6386i 0.967074i
\(549\) 2.21899 0.0947044
\(550\) −0.705505 3.89690i −0.0300828 0.166165i
\(551\) −43.7112 −1.86216
\(552\) 5.49189i 0.233750i
\(553\) 6.67029i 0.283649i
\(554\) 19.9687 0.848389
\(555\) 0.907740 + 10.1094i 0.0385314 + 0.429122i
\(556\) −2.26513 −0.0960628
\(557\) 23.2359i 0.984538i 0.870443 + 0.492269i \(0.163832\pi\)
−0.870443 + 0.492269i \(0.836168\pi\)
\(558\) 5.31948i 0.225192i
\(559\) 37.5581 1.58854
\(560\) −1.40196 + 0.125884i −0.0592437 + 0.00531957i
\(561\) −2.01100 −0.0849043
\(562\) 9.26382i 0.390771i
\(563\) 26.3095i 1.10881i −0.832246 0.554407i \(-0.812945\pi\)
0.832246 0.554407i \(-0.187055\pi\)
\(564\) −2.35769 −0.0992768
\(565\) −39.7059 + 3.56525i −1.67044 + 0.149991i
\(566\) −14.8224 −0.623033
\(567\) 1.00000i 0.0419961i
\(568\) 18.5670i 0.779056i
\(569\) −11.5720 −0.485123 −0.242562 0.970136i \(-0.577988\pi\)
−0.242562 + 0.970136i \(0.577988\pi\)
\(570\) 1.05215 + 11.7177i 0.0440695 + 0.490799i
\(571\) −16.6267 −0.695804 −0.347902 0.937531i \(-0.613106\pi\)
−0.347902 + 0.937531i \(0.613106\pi\)
\(572\) 9.57631i 0.400406i
\(573\) 17.0974i 0.714254i
\(574\) 8.38713 0.350072
\(575\) −1.83123 10.1150i −0.0763678 0.421823i
\(576\) 3.36754 0.140314
\(577\) 26.8828i 1.11915i −0.828781 0.559573i \(-0.810965\pi\)
0.828781 0.559573i \(-0.189035\pi\)
\(578\) 10.2617i 0.426831i
\(579\) 7.66253 0.318444
\(580\) −1.80627 20.1163i −0.0750013 0.835284i
\(581\) −4.69895 −0.194945
\(582\) 11.9248i 0.494298i
\(583\) 5.42564i 0.224707i
\(584\) 26.0033 1.07602
\(585\) 15.5374 1.39512i 0.642391 0.0576812i
\(586\) 14.3396 0.592364
\(587\) 9.63552i 0.397701i −0.980030 0.198850i \(-0.936279\pi\)
0.980030 0.198850i \(-0.0637208\pi\)
\(588\) 1.37266i 0.0566074i
\(589\) 44.6132 1.83826
\(590\) −13.7507 + 1.23469i −0.566106 + 0.0508314i
\(591\) 12.1159 0.498380
\(592\) 2.85746i 0.117441i
\(593\) 5.93289i 0.243635i 0.992553 + 0.121817i \(0.0388722\pi\)
−0.992553 + 0.121817i \(0.961128\pi\)
\(594\) −0.792050 −0.0324982
\(595\) 0.402149 + 4.47871i 0.0164865 + 0.183609i
\(596\) 8.61985 0.353083
\(597\) 14.8587i 0.608126i
\(598\) 11.3602i 0.464553i
\(599\) 24.2153 0.989411 0.494705 0.869061i \(-0.335276\pi\)
0.494705 + 0.869061i \(0.335276\pi\)
\(600\) −13.1429 + 2.37942i −0.536557 + 0.0971396i
\(601\) 43.6346 1.77989 0.889947 0.456065i \(-0.150741\pi\)
0.889947 + 0.456065i \(0.150741\pi\)
\(602\) 4.26403i 0.173789i
\(603\) 2.45990i 0.100175i
\(604\) 20.6404 0.839844
\(605\) −0.199975 2.22711i −0.00813014 0.0905448i
\(606\) 6.81292 0.276756
\(607\) 11.0521i 0.448592i 0.974521 + 0.224296i \(0.0720082\pi\)
−0.974521 + 0.224296i \(0.927992\pi\)
\(608\) 38.8017i 1.57362i
\(609\) −6.58029 −0.266647
\(610\) −3.91427 + 0.351467i −0.158484 + 0.0142305i
\(611\) −11.9829 −0.484776
\(612\) 2.76041i 0.111583i
\(613\) 9.26989i 0.374407i −0.982321 0.187204i \(-0.940058\pi\)
0.982321 0.187204i \(-0.0599424\pi\)
\(614\) −8.87699 −0.358246
\(615\) −23.5831 + 2.11756i −0.950964 + 0.0853884i
\(616\) 2.67131 0.107630
\(617\) 14.8200i 0.596630i −0.954467 0.298315i \(-0.903575\pi\)
0.954467 0.298315i \(-0.0964246\pi\)
\(618\) 3.56708i 0.143489i
\(619\) −8.04117 −0.323202 −0.161601 0.986856i \(-0.551666\pi\)
−0.161601 + 0.986856i \(0.551666\pi\)
\(620\) 1.84355 + 20.5315i 0.0740387 + 0.824563i
\(621\) −2.05588 −0.0824995
\(622\) 12.8922i 0.516929i
\(623\) 6.34225i 0.254097i
\(624\) −4.39168 −0.175808
\(625\) 23.4132 8.76484i 0.936528 0.350594i
\(626\) −3.14786 −0.125814
\(627\) 6.64274i 0.265285i
\(628\) 1.38084i 0.0551015i
\(629\) −9.12845 −0.363975
\(630\) 0.158390 + 1.76398i 0.00631042 + 0.0702787i
\(631\) 28.2050 1.12283 0.561413 0.827536i \(-0.310258\pi\)
0.561413 + 0.827536i \(0.310258\pi\)
\(632\) 17.8184i 0.708779i
\(633\) 5.59506i 0.222384i
\(634\) −0.209589 −0.00832385
\(635\) −31.6287 + 2.83998i −1.25515 + 0.112701i
\(636\) −7.44753 −0.295314
\(637\) 6.97648i 0.276418i
\(638\) 5.21192i 0.206342i
\(639\) −6.95053 −0.274959
\(640\) 20.0778 1.80281i 0.793644 0.0712624i
\(641\) 2.00498 0.0791919 0.0395959 0.999216i \(-0.487393\pi\)
0.0395959 + 0.999216i \(0.487393\pi\)
\(642\) 2.30116i 0.0908197i
\(643\) 7.10193i 0.280073i −0.990146 0.140036i \(-0.955278\pi\)
0.990146 0.140036i \(-0.0447220\pi\)
\(644\) 2.82201 0.111203
\(645\) −1.07657 11.9897i −0.0423900 0.472095i
\(646\) −10.5806 −0.416289
\(647\) 6.36568i 0.250261i 0.992140 + 0.125130i \(0.0399349\pi\)
−0.992140 + 0.125130i \(0.960065\pi\)
\(648\) 2.67131i 0.104939i
\(649\) −7.79524 −0.305990
\(650\) −27.1867 + 4.92194i −1.06635 + 0.193054i
\(651\) 6.71609 0.263224
\(652\) 9.86715i 0.386428i
\(653\) 2.88871i 0.113044i 0.998401 + 0.0565220i \(0.0180011\pi\)
−0.998401 + 0.0565220i \(0.981999\pi\)
\(654\) 16.3111 0.637815
\(655\) −3.34811 37.2877i −0.130822 1.45695i
\(656\) 6.66585 0.260258
\(657\) 9.73428i 0.379770i
\(658\) 1.36044i 0.0530353i
\(659\) 5.34350 0.208153 0.104077 0.994569i \(-0.466811\pi\)
0.104077 + 0.994569i \(0.466811\pi\)
\(660\) −3.05705 + 0.274497i −0.118996 + 0.0106848i
\(661\) 24.6815 0.959997 0.479999 0.877269i \(-0.340637\pi\)
0.479999 + 0.877269i \(0.340637\pi\)
\(662\) 5.83276i 0.226697i
\(663\) 14.0297i 0.544867i
\(664\) 12.5524 0.487126
\(665\) 14.7941 1.32838i 0.573690 0.0515124i
\(666\) −3.59533 −0.139316
\(667\) 13.5283i 0.523817i
\(668\) 34.7993i 1.34642i
\(669\) 14.9290 0.577189
\(670\) −0.389625 4.33923i −0.0150525 0.167639i
\(671\) −2.21899 −0.0856633
\(672\) 5.84122i 0.225330i
\(673\) 7.79045i 0.300300i −0.988663 0.150150i \(-0.952024\pi\)
0.988663 0.150150i \(-0.0479756\pi\)
\(674\) 14.4282 0.555754
\(675\) −0.890732 4.92002i −0.0342843 0.189372i
\(676\) −48.9644 −1.88325
\(677\) 7.81878i 0.300500i 0.988648 + 0.150250i \(0.0480079\pi\)
−0.988648 + 0.150250i \(0.951992\pi\)
\(678\) 14.1210i 0.542315i
\(679\) 15.0556 0.577780
\(680\) −1.07427 11.9640i −0.0411962 0.458799i
\(681\) 12.4673 0.477749
\(682\) 5.31948i 0.203694i
\(683\) 35.5185i 1.35908i 0.733640 + 0.679538i \(0.237820\pi\)
−0.733640 + 0.679538i \(0.762180\pi\)
\(684\) 9.11820 0.348643
\(685\) 36.7307 3.29810i 1.40341 0.126014i
\(686\) −0.792050 −0.0302406
\(687\) 11.3408i 0.432678i
\(688\) 3.38893i 0.129202i
\(689\) −37.8518 −1.44204
\(690\) 3.62653 0.325631i 0.138060 0.0123966i
\(691\) 37.5400 1.42809 0.714045 0.700100i \(-0.246861\pi\)
0.714045 + 0.700100i \(0.246861\pi\)
\(692\) 32.4393i 1.23316i
\(693\) 1.00000i 0.0379869i
\(694\) 3.83085 0.145417
\(695\) 0.329994 + 3.67512i 0.0125174 + 0.139405i
\(696\) 17.5780 0.666293
\(697\) 21.2947i 0.806595i
\(698\) 20.7317i 0.784706i
\(699\) −15.4252 −0.583435
\(700\) 1.22267 + 6.75350i 0.0462125 + 0.255258i
\(701\) 11.3900 0.430194 0.215097 0.976593i \(-0.430993\pi\)
0.215097 + 0.976593i \(0.430993\pi\)
\(702\) 5.52572i 0.208555i
\(703\) 30.1532i 1.13725i
\(704\) −3.36754 −0.126919
\(705\) 0.343480 + 3.82531i 0.0129362 + 0.144069i
\(706\) −27.0481 −1.01797
\(707\) 8.60162i 0.323497i
\(708\) 10.7002i 0.402138i
\(709\) −43.6935 −1.64094 −0.820471 0.571688i \(-0.806289\pi\)
−0.820471 + 0.571688i \(0.806289\pi\)
\(710\) 12.2606 1.10090i 0.460132 0.0413159i
\(711\) −6.67029 −0.250155
\(712\) 16.9421i 0.634933i
\(713\) 13.8075i 0.517093i
\(714\) −1.59281 −0.0596094
\(715\) −15.5374 + 1.39512i −0.581065 + 0.0521746i
\(716\) −6.36106 −0.237724
\(717\) 15.6157i 0.583178i
\(718\) 29.0029i 1.08238i
\(719\) 32.3812 1.20761 0.603807 0.797130i \(-0.293650\pi\)
0.603807 + 0.797130i \(0.293650\pi\)
\(720\) 0.125884 + 1.40196i 0.00469142 + 0.0522480i
\(721\) −4.50360 −0.167723
\(722\) 19.9010i 0.740640i
\(723\) 23.5767i 0.876825i
\(724\) 27.6622 1.02806
\(725\) −32.3752 + 5.86128i −1.20238 + 0.217682i
\(726\) 0.792050 0.0293957
\(727\) 0.0109599i 0.000406481i −1.00000 0.000203240i \(-0.999935\pi\)
1.00000 0.000203240i \(-6.46934e-5\pi\)
\(728\) 18.6364i 0.690710i
\(729\) −1.00000 −0.0370370
\(730\) −1.54182 17.1711i −0.0570651 0.635531i
\(731\) 10.8263 0.400424
\(732\) 3.04592i 0.112580i
\(733\) 42.6165i 1.57408i −0.616903 0.787039i \(-0.711613\pi\)
0.616903 0.787039i \(-0.288387\pi\)
\(734\) 23.0716 0.851589
\(735\) 2.22711 0.199975i 0.0821481 0.00737619i
\(736\) −12.0088 −0.442651
\(737\) 2.45990i 0.0906118i
\(738\) 8.38713i 0.308734i
\(739\) −13.4478 −0.494685 −0.247343 0.968928i \(-0.579557\pi\)
−0.247343 + 0.968928i \(0.579557\pi\)
\(740\) −13.8768 + 1.24601i −0.510121 + 0.0458044i
\(741\) 46.3429 1.70245
\(742\) 4.29738i 0.157762i
\(743\) 31.3424i 1.14984i −0.818209 0.574921i \(-0.805033\pi\)
0.818209 0.574921i \(-0.194967\pi\)
\(744\) −17.9408 −0.657741
\(745\) −1.25578 13.9855i −0.0460082 0.512390i
\(746\) −0.140937 −0.00516006
\(747\) 4.69895i 0.171926i
\(748\) 2.76041i 0.100930i
\(749\) −2.90533 −0.106158
\(750\) 2.35052 + 8.53774i 0.0858288 + 0.311754i
\(751\) −43.3436 −1.58163 −0.790816 0.612054i \(-0.790343\pi\)
−0.790816 + 0.612054i \(0.790343\pi\)
\(752\) 1.08123i 0.0394286i
\(753\) 20.6569i 0.752778i
\(754\) 36.3609 1.32418
\(755\) −3.00698 33.4886i −0.109435 1.21877i
\(756\) 1.37266 0.0499230
\(757\) 37.9384i 1.37890i −0.724336 0.689448i \(-0.757853\pi\)
0.724336 0.689448i \(-0.242147\pi\)
\(758\) 0.0559984i 0.00203395i
\(759\) 2.05588 0.0746236
\(760\) −39.5197 + 3.54852i −1.43353 + 0.128719i
\(761\) −26.3508 −0.955215 −0.477607 0.878573i \(-0.658496\pi\)
−0.477607 + 0.878573i \(0.658496\pi\)
\(762\) 11.2484i 0.407488i
\(763\) 20.5935i 0.745536i
\(764\) −23.4688 −0.849073
\(765\) 4.47871 0.402149i 0.161928 0.0145397i
\(766\) −1.78519 −0.0645014
\(767\) 54.3833i 1.96367i
\(768\) 13.8756i 0.500691i
\(769\) −13.3491 −0.481381 −0.240690 0.970602i \(-0.577374\pi\)
−0.240690 + 0.970602i \(0.577374\pi\)
\(770\) −0.158390 1.76398i −0.00570799 0.0635695i
\(771\) 0.652452 0.0234975
\(772\) 10.5180i 0.378552i
\(773\) 4.65893i 0.167570i 0.996484 + 0.0837851i \(0.0267009\pi\)
−0.996484 + 0.0837851i \(0.973299\pi\)
\(774\) 4.26403 0.153267
\(775\) 33.0433 5.98224i 1.18695 0.214888i
\(776\) −40.2182 −1.44375
\(777\) 4.53927i 0.162845i
\(778\) 0.143595i 0.00514813i
\(779\) −70.3409 −2.52022
\(780\) 1.91502 + 21.3275i 0.0685688 + 0.763646i
\(781\) 6.95053 0.248710
\(782\) 3.27462i 0.117100i
\(783\) 6.58029i 0.235161i
\(784\) −0.629499 −0.0224821
\(785\) −2.24038 + 0.201167i −0.0799628 + 0.00717997i
\(786\) 13.2610 0.473005
\(787\) 18.0636i 0.643897i 0.946757 + 0.321948i \(0.104338\pi\)
−0.946757 + 0.321948i \(0.895662\pi\)
\(788\) 16.6309i 0.592452i
\(789\) 25.3131 0.901170
\(790\) 11.7663 1.05651i 0.418625 0.0375889i
\(791\) −17.8285 −0.633908
\(792\) 2.67131i 0.0949210i
\(793\) 15.4808i 0.549738i
\(794\) −7.71283 −0.273718
\(795\) 1.08499 + 12.0835i 0.0384807 + 0.428557i
\(796\) −20.3959 −0.722913
\(797\) 30.8679i 1.09340i 0.837330 + 0.546698i \(0.184115\pi\)
−0.837330 + 0.546698i \(0.815885\pi\)
\(798\) 5.26138i 0.186251i
\(799\) −3.45411 −0.122198
\(800\) −5.20296 28.7389i −0.183953 1.01607i
\(801\) 6.34225 0.224092
\(802\) 8.47519i 0.299269i
\(803\) 9.73428i 0.343515i
\(804\) −3.37660 −0.119084
\(805\) −0.411124 4.57866i −0.0144902 0.161376i
\(806\) −37.1113 −1.30719
\(807\) 4.53171i 0.159524i
\(808\) 22.9776i 0.808350i
\(809\) −3.33569 −0.117276 −0.0586382 0.998279i \(-0.518676\pi\)
−0.0586382 + 0.998279i \(0.518676\pi\)
\(810\) 1.76398 0.158390i 0.0619800 0.00556527i
\(811\) −28.9946 −1.01814 −0.509068 0.860726i \(-0.670010\pi\)
−0.509068 + 0.860726i \(0.670010\pi\)
\(812\) 9.03248i 0.316978i
\(813\) 13.1341i 0.460634i
\(814\) 3.59533 0.126016
\(815\) −16.0093 + 1.43749i −0.560780 + 0.0503532i
\(816\) −1.26592 −0.0443160
\(817\) 35.7614i 1.25113i
\(818\) 24.6712i 0.862609i
\(819\) 6.97648 0.243778
\(820\) −2.90669 32.3716i −0.101506 1.13046i
\(821\) −5.47236 −0.190987 −0.0954934 0.995430i \(-0.530443\pi\)
−0.0954934 + 0.995430i \(0.530443\pi\)
\(822\) 13.0629i 0.455622i
\(823\) 8.28403i 0.288763i 0.989522 + 0.144382i \(0.0461193\pi\)
−0.989522 + 0.144382i \(0.953881\pi\)
\(824\) 12.0305 0.419103
\(825\) 0.890732 + 4.92002i 0.0310113 + 0.171293i
\(826\) −6.17422 −0.214829
\(827\) 18.6467i 0.648409i −0.945987 0.324204i \(-0.894903\pi\)
0.945987 0.324204i \(-0.105097\pi\)
\(828\) 2.82201i 0.0980717i
\(829\) −20.1059 −0.698307 −0.349153 0.937066i \(-0.613531\pi\)
−0.349153 + 0.937066i \(0.613531\pi\)
\(830\) −0.744268 8.28886i −0.0258339 0.287711i
\(831\) −25.2114 −0.874574
\(832\) 23.4936i 0.814494i
\(833\) 2.01100i 0.0696769i
\(834\) −1.30702 −0.0452585
\(835\) 56.4611 5.06972i 1.95392 0.175445i
\(836\) −9.11820 −0.315359
\(837\) 6.71609i 0.232142i
\(838\) 19.9820i 0.690267i
\(839\) −8.85969 −0.305871 −0.152935 0.988236i \(-0.548873\pi\)
−0.152935 + 0.988236i \(0.548873\pi\)
\(840\) −5.94930 + 0.534196i −0.205270 + 0.0184315i
\(841\) 14.3003 0.493113
\(842\) 7.20452i 0.248284i
\(843\) 11.6960i 0.402832i
\(844\) 7.68009 0.264360
\(845\) 7.13336 + 79.4437i 0.245395 + 2.73295i
\(846\) −1.36044 −0.0467727
\(847\) 1.00000i 0.0343604i
\(848\) 3.41543i 0.117286i
\(849\) 18.7140 0.642263
\(850\) −7.83666 + 1.41877i −0.268795 + 0.0486633i
\(851\) 9.33217 0.319903
\(852\) 9.54069i 0.326859i
\(853\) 1.18696i 0.0406409i −0.999794 0.0203204i \(-0.993531\pi\)
0.999794 0.0203204i \(-0.00646864\pi\)
\(854\) −1.75756 −0.0601423
\(855\) −1.32838 14.7941i −0.0454297 0.505947i
\(856\) 7.76103 0.265267
\(857\) 42.4639i 1.45054i −0.688466 0.725269i \(-0.741715\pi\)
0.688466 0.725269i \(-0.258285\pi\)
\(858\) 5.52572i 0.188645i
\(859\) 7.06518 0.241061 0.120530 0.992710i \(-0.461540\pi\)
0.120530 + 0.992710i \(0.461540\pi\)
\(860\) 16.4578 1.47777i 0.561205 0.0503914i
\(861\) −10.5891 −0.360877
\(862\) 22.1876i 0.755711i
\(863\) 44.1199i 1.50186i 0.660382 + 0.750930i \(0.270395\pi\)
−0.660382 + 0.750930i \(0.729605\pi\)
\(864\) −5.84122 −0.198722
\(865\) 52.6321 4.72591i 1.78954 0.160686i
\(866\) −15.2452 −0.518053
\(867\) 12.9559i 0.440005i
\(868\) 9.21889i 0.312909i
\(869\) 6.67029 0.226274
\(870\) −1.04225 11.6075i −0.0353357 0.393532i
\(871\) −17.1615 −0.581494
\(872\) 55.0118i 1.86293i
\(873\) 15.0556i 0.509554i
\(874\) 10.8167 0.365882
\(875\) 10.7793 2.96764i 0.364407 0.100324i
\(876\) −13.3618 −0.451454
\(877\) 16.2216i 0.547763i 0.961763 + 0.273882i \(0.0883077\pi\)
−0.961763 + 0.273882i \(0.911692\pi\)
\(878\) 25.1968i 0.850350i
\(879\) −18.1044 −0.610647
\(880\) −0.125884 1.40196i −0.00424355 0.0472601i
\(881\) −36.1694 −1.21858 −0.609290 0.792948i \(-0.708545\pi\)
−0.609290 + 0.792948i \(0.708545\pi\)
\(882\) 0.792050i 0.0266697i
\(883\) 13.0357i 0.438685i −0.975648 0.219343i \(-0.929609\pi\)
0.975648 0.219343i \(-0.0703912\pi\)
\(884\) −19.2579 −0.647714
\(885\) 17.3608 1.55885i 0.583578 0.0524003i
\(886\) 3.66960 0.123283
\(887\) 35.7631i 1.20081i −0.799697 0.600403i \(-0.795007\pi\)
0.799697 0.600403i \(-0.204993\pi\)
\(888\) 12.1258i 0.406915i
\(889\) −14.2017 −0.476309
\(890\) −11.1876 + 1.00455i −0.375009 + 0.0336726i
\(891\) 1.00000 0.0335013
\(892\) 20.4924i 0.686137i
\(893\) 11.4097i 0.381809i
\(894\) 4.97383 0.166350
\(895\) 0.926710 + 10.3207i 0.0309765 + 0.344983i
\(896\) 9.01518 0.301176
\(897\) 14.3428i 0.478891i
\(898\) 23.1994i 0.774174i
\(899\) −44.1939 −1.47395
\(900\) 6.75350 1.22267i 0.225117 0.0407556i
\(901\) −10.9109 −0.363496
\(902\) 8.38713i 0.279261i
\(903\) 5.38354i 0.179153i
\(904\) 47.6254 1.58400
\(905\) −4.02995 44.8813i −0.133960 1.49191i
\(906\) 11.9099 0.395680
\(907\) 9.68421i 0.321559i −0.986990 0.160779i \(-0.948599\pi\)
0.986990 0.160779i \(-0.0514008\pi\)
\(908\) 17.1134i 0.567927i
\(909\) −8.60162 −0.285298
\(910\) −12.3064 + 1.10501i −0.407953 + 0.0366306i
\(911\) −12.9132 −0.427835 −0.213917 0.976852i \(-0.568622\pi\)
−0.213917 + 0.976852i \(0.568622\pi\)
\(912\) 4.18159i 0.138466i
\(913\) 4.69895i 0.155513i
\(914\) 24.6708 0.816038
\(915\) 4.94194 0.443744i 0.163376 0.0146697i
\(916\) −15.5670 −0.514348
\(917\) 16.7427i 0.552891i
\(918\) 1.59281i 0.0525706i
\(919\) 20.4704 0.675256 0.337628 0.941280i \(-0.390375\pi\)
0.337628 + 0.941280i \(0.390375\pi\)
\(920\) 1.09824 + 12.2310i 0.0362079 + 0.403245i
\(921\) 11.2076 0.369303
\(922\) 4.01790i 0.132323i
\(923\) 48.4902i 1.59608i
\(924\) −1.37266 −0.0451571
\(925\) 4.04327 + 22.3333i 0.132942 + 0.734314i
\(926\) −21.0768 −0.692627
\(927\) 4.50360i 0.147918i
\(928\) 38.4370i 1.26175i
\(929\) −18.7464 −0.615048 −0.307524 0.951540i \(-0.599500\pi\)
−0.307524 + 0.951540i \(0.599500\pi\)
\(930\) 1.06376 + 11.8471i 0.0348822 + 0.388481i
\(931\) 6.64274 0.217707
\(932\) 21.1735i 0.693561i
\(933\) 16.2770i 0.532884i
\(934\) 11.3110 0.370106
\(935\) −4.47871 + 0.402149i −0.146469 + 0.0131517i
\(936\) −18.6364 −0.609149
\(937\) 47.9357i 1.56599i −0.622027 0.782996i \(-0.713690\pi\)
0.622027 0.782996i \(-0.286310\pi\)
\(938\) 1.94837i 0.0636165i
\(939\) 3.97432 0.129697
\(940\) −5.25084 + 0.471480i −0.171263 + 0.0153780i
\(941\) −40.2901 −1.31342 −0.656709 0.754144i \(-0.728052\pi\)
−0.656709 + 0.754144i \(0.728052\pi\)
\(942\) 0.796772i 0.0259602i
\(943\) 21.7699i 0.708927i
\(944\) −4.90709 −0.159712
\(945\) −0.199975 2.22711i −0.00650519 0.0724478i
\(946\) −4.26403 −0.138636
\(947\) 3.95361i 0.128475i −0.997935 0.0642375i \(-0.979538\pi\)
0.997935 0.0642375i \(-0.0204615\pi\)
\(948\) 9.15601i 0.297374i
\(949\) −67.9110 −2.20448
\(950\) 4.68648 + 25.8861i 0.152050 + 0.839856i
\(951\) 0.264616 0.00858076
\(952\) 5.37200i 0.174108i
\(953\) 11.1167i 0.360106i −0.983657 0.180053i \(-0.942373\pi\)
0.983657 0.180053i \(-0.0576269\pi\)
\(954\) −4.29738 −0.139133
\(955\) 3.41905 + 38.0777i 0.110638 + 1.23217i
\(956\) 21.4350 0.693256
\(957\) 6.58029i 0.212711i
\(958\) 14.9387i 0.482648i
\(959\) 16.4926 0.532572
\(960\) 7.49988 0.673425i 0.242058 0.0217347i
\(961\) 14.1059 0.455029
\(962\) 25.0827i 0.808699i
\(963\) 2.90533i 0.0936228i
\(964\) 32.3627 1.04233
\(965\) 17.0653 1.53231i 0.549351 0.0493269i
\(966\) 1.62836 0.0523915
\(967\) 23.7486i 0.763702i 0.924224 + 0.381851i \(0.124713\pi\)
−0.924224 + 0.381851i \(0.875287\pi\)
\(968\) 2.67131i 0.0858593i
\(969\) 13.3585 0.429138
\(970\) 2.38466 + 26.5578i 0.0765667 + 0.852718i
\(971\) −6.78652 −0.217790 −0.108895 0.994053i \(-0.534731\pi\)
−0.108895 + 0.994053i \(0.534731\pi\)
\(972\) 1.37266i 0.0440280i
\(973\) 1.65018i 0.0529023i
\(974\) 31.3287 1.00384
\(975\) 34.3244 6.21417i 1.09926 0.199013i
\(976\) −1.39685 −0.0447122
\(977\) 3.56837i 0.114162i −0.998370 0.0570812i \(-0.981821\pi\)
0.998370 0.0570812i \(-0.0181794\pi\)
\(978\) 5.69355i 0.182059i
\(979\) −6.34225 −0.202699
\(980\) 0.274497 + 3.05705i 0.00876849 + 0.0976540i
\(981\) −20.5935 −0.657501
\(982\) 7.54596i 0.240801i
\(983\) 14.5740i 0.464837i −0.972616 0.232419i \(-0.925336\pi\)
0.972616 0.232419i \(-0.0746639\pi\)
\(984\) 28.2869 0.901753
\(985\) 26.9833 2.42287i 0.859761 0.0771991i
\(986\) 10.4812 0.333788
\(987\) 1.71761i 0.0546722i
\(988\) 63.6129i 2.02380i
\(989\) −11.0679 −0.351938
\(990\) −1.76398 + 0.158390i −0.0560630 + 0.00503397i
\(991\) −29.1681 −0.926555 −0.463277 0.886213i \(-0.653327\pi\)
−0.463277 + 0.886213i \(0.653327\pi\)
\(992\) 39.2302i 1.24556i
\(993\) 7.36413i 0.233693i
\(994\) 5.50517 0.174613
\(995\) 2.97137 + 33.0919i 0.0941987 + 1.04908i
\(996\) −6.45004 −0.204377
\(997\) 58.0260i 1.83770i 0.394605 + 0.918851i \(0.370881\pi\)
−0.394605 + 0.918851i \(0.629119\pi\)
\(998\) 11.3269i 0.358546i
\(999\) 4.53927 0.143616
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 1155.2.c.f.694.13 yes 20
5.2 odd 4 5775.2.a.cn.1.5 10
5.3 odd 4 5775.2.a.co.1.6 10
5.4 even 2 inner 1155.2.c.f.694.8 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.c.f.694.8 20 5.4 even 2 inner
1155.2.c.f.694.13 yes 20 1.1 even 1 trivial
5775.2.a.cn.1.5 10 5.2 odd 4
5775.2.a.co.1.6 10 5.3 odd 4