Properties

Label 585.2.bu.c.361.1
Level $585$
Weight $2$
Character 585.361
Analytic conductor $4.671$
Analytic rank $0$
Dimension $8$
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] = [585,2,Mod(316,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bu (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(0.665665 + 1.24775i\) of defining polynomial
Character \(\chi\) \(=\) 585.361
Dual form 585.2.bu.c.316.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29515 + 0.747754i) q^{2} +(0.118272 - 0.204852i) q^{4} -1.00000i q^{5} +(-4.18016 - 2.41342i) q^{7} -2.63726i q^{8} +O(q^{10})\) \(q+(-1.29515 + 0.747754i) q^{2} +(0.118272 - 0.204852i) q^{4} -1.00000i q^{5} +(-4.18016 - 2.41342i) q^{7} -2.63726i q^{8} +(0.747754 + 1.29515i) q^{10} +(0.926118 - 0.534695i) q^{11} +(0.331331 + 3.59030i) q^{13} +7.21857 q^{14} +(2.20857 + 3.82535i) q^{16} +(-1.77944 + 3.08209i) q^{17} +(4.96410 + 2.86603i) q^{19} +(-0.204852 - 0.118272i) q^{20} +(-0.799640 + 1.38502i) q^{22} +(3.54290 + 6.13649i) q^{23} -1.00000 q^{25} +(-3.11378 - 4.40221i) q^{26} +(-0.988789 + 0.570878i) q^{28} +(0.736543 + 1.27573i) q^{29} +1.46410i q^{31} +(-1.15297 - 0.665665i) q^{32} -5.32235i q^{34} +(-2.41342 + 4.18016i) q^{35} +(-0.0219955 + 0.0126991i) q^{37} -8.57233 q^{38} -2.63726 q^{40} +(0.232051 - 0.133975i) q^{41} +(1.77944 - 3.08209i) q^{43} -0.252957i q^{44} +(-9.17716 - 5.29844i) q^{46} -6.51793i q^{47} +(8.14918 + 14.1148i) q^{49} +(1.29515 - 0.747754i) q^{50} +(0.774668 + 0.356756i) q^{52} -0.991015 q^{53} +(-0.534695 - 0.926118i) q^{55} +(-6.36482 + 11.0242i) q^{56} +(-1.90786 - 1.10151i) q^{58} +(7.55440 + 4.36153i) q^{59} +(-3.16867 + 5.48830i) q^{61} +(-1.09479 - 1.89623i) q^{62} -6.84325 q^{64} +(3.59030 - 0.331331i) q^{65} +(-4.48009 + 2.58658i) q^{67} +(0.420915 + 0.729047i) q^{68} -7.21857i q^{70} +(6.72458 + 3.88244i) q^{71} +10.1088i q^{73} +(0.0189916 - 0.0328945i) q^{74} +(1.17422 - 0.677939i) q^{76} -5.16177 q^{77} +8.78347 q^{79} +(3.82535 - 2.20857i) q^{80} +(-0.200360 + 0.347034i) q^{82} -0.725474i q^{83} +(3.08209 + 1.77944i) q^{85} +5.32235i q^{86} +(-1.41013 - 2.44242i) q^{88} +(-11.6970 + 6.75327i) q^{89} +(7.27987 - 15.8077i) q^{91} +1.67610 q^{92} +(4.87381 + 8.44168i) q^{94} +(2.86603 - 4.96410i) q^{95} +(-2.97800 - 1.71935i) q^{97} +(-21.1088 - 12.1872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29515 + 0.747754i −0.915808 + 0.528742i −0.882295 0.470696i \(-0.844003\pi\)
−0.0335125 + 0.999438i \(0.510669\pi\)
\(3\) 0 0
\(4\) 0.118272 0.204852i 0.0591358 0.102426i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −4.18016 2.41342i −1.57995 0.912187i −0.994864 0.101218i \(-0.967726\pi\)
−0.585089 0.810969i \(-0.698941\pi\)
\(8\) 2.63726i 0.932413i
\(9\) 0 0
\(10\) 0.747754 + 1.29515i 0.236461 + 0.409562i
\(11\) 0.926118 0.534695i 0.279235 0.161217i −0.353842 0.935305i \(-0.615125\pi\)
0.633077 + 0.774089i \(0.281792\pi\)
\(12\) 0 0
\(13\) 0.331331 + 3.59030i 0.0918946 + 0.995769i
\(14\) 7.21857 1.92924
\(15\) 0 0
\(16\) 2.20857 + 3.82535i 0.552142 + 0.956337i
\(17\) −1.77944 + 3.08209i −0.431579 + 0.747516i −0.997009 0.0772795i \(-0.975377\pi\)
0.565431 + 0.824796i \(0.308710\pi\)
\(18\) 0 0
\(19\) 4.96410 + 2.86603i 1.13884 + 0.657511i 0.946144 0.323747i \(-0.104943\pi\)
0.192699 + 0.981258i \(0.438276\pi\)
\(20\) −0.204852 0.118272i −0.0458064 0.0264463i
\(21\) 0 0
\(22\) −0.799640 + 1.38502i −0.170484 + 0.295287i
\(23\) 3.54290 + 6.13649i 0.738746 + 1.27955i 0.953060 + 0.302781i \(0.0979150\pi\)
−0.214314 + 0.976765i \(0.568752\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −3.11378 4.40221i −0.610662 0.863344i
\(27\) 0 0
\(28\) −0.988789 + 0.570878i −0.186864 + 0.107886i
\(29\) 0.736543 + 1.27573i 0.136773 + 0.236897i 0.926273 0.376853i \(-0.122994\pi\)
−0.789501 + 0.613750i \(0.789660\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) −1.15297 0.665665i −0.203818 0.117674i
\(33\) 0 0
\(34\) 5.32235i 0.912775i
\(35\) −2.41342 + 4.18016i −0.407942 + 0.706577i
\(36\) 0 0
\(37\) −0.0219955 + 0.0126991i −0.00361604 + 0.00208772i −0.501807 0.864980i \(-0.667331\pi\)
0.498191 + 0.867067i \(0.333998\pi\)
\(38\) −8.57233 −1.39061
\(39\) 0 0
\(40\) −2.63726 −0.416988
\(41\) 0.232051 0.133975i 0.0362402 0.0209233i −0.481770 0.876297i \(-0.660006\pi\)
0.518011 + 0.855374i \(0.326673\pi\)
\(42\) 0 0
\(43\) 1.77944 3.08209i 0.271363 0.470014i −0.697848 0.716246i \(-0.745859\pi\)
0.969211 + 0.246232i \(0.0791924\pi\)
\(44\) 0.252957i 0.0381347i
\(45\) 0 0
\(46\) −9.17716 5.29844i −1.35310 0.781212i
\(47\) 6.51793i 0.950738i −0.879787 0.475369i \(-0.842315\pi\)
0.879787 0.475369i \(-0.157685\pi\)
\(48\) 0 0
\(49\) 8.14918 + 14.1148i 1.16417 + 2.01640i
\(50\) 1.29515 0.747754i 0.183162 0.105748i
\(51\) 0 0
\(52\) 0.774668 + 0.356756i 0.107427 + 0.0494732i
\(53\) −0.991015 −0.136126 −0.0680632 0.997681i \(-0.521682\pi\)
−0.0680632 + 0.997681i \(0.521682\pi\)
\(54\) 0 0
\(55\) −0.534695 0.926118i −0.0720982 0.124878i
\(56\) −6.36482 + 11.0242i −0.850535 + 1.47317i
\(57\) 0 0
\(58\) −1.90786 1.10151i −0.250515 0.144635i
\(59\) 7.55440 + 4.36153i 0.983499 + 0.567823i 0.903325 0.428958i \(-0.141119\pi\)
0.0801741 + 0.996781i \(0.474452\pi\)
\(60\) 0 0
\(61\) −3.16867 + 5.48830i −0.405707 + 0.702704i −0.994403 0.105650i \(-0.966308\pi\)
0.588697 + 0.808354i \(0.299641\pi\)
\(62\) −1.09479 1.89623i −0.139038 0.240821i
\(63\) 0 0
\(64\) −6.84325 −0.855406
\(65\) 3.59030 0.331331i 0.445321 0.0410965i
\(66\) 0 0
\(67\) −4.48009 + 2.58658i −0.547330 + 0.316001i −0.748044 0.663649i \(-0.769007\pi\)
0.200714 + 0.979650i \(0.435674\pi\)
\(68\) 0.420915 + 0.729047i 0.0510435 + 0.0884099i
\(69\) 0 0
\(70\) 7.21857i 0.862785i
\(71\) 6.72458 + 3.88244i 0.798061 + 0.460761i 0.842793 0.538238i \(-0.180910\pi\)
−0.0447317 + 0.998999i \(0.514243\pi\)
\(72\) 0 0
\(73\) 10.1088i 1.18314i 0.806252 + 0.591572i \(0.201493\pi\)
−0.806252 + 0.591572i \(0.798507\pi\)
\(74\) 0.0189916 0.0328945i 0.00220773 0.00382391i
\(75\) 0 0
\(76\) 1.17422 0.677939i 0.134693 0.0777649i
\(77\) −5.16177 −0.588238
\(78\) 0 0
\(79\) 8.78347 0.988218 0.494109 0.869400i \(-0.335494\pi\)
0.494109 + 0.869400i \(0.335494\pi\)
\(80\) 3.82535 2.20857i 0.427687 0.246925i
\(81\) 0 0
\(82\) −0.200360 + 0.347034i −0.0221261 + 0.0383235i
\(83\) 0.725474i 0.0796311i −0.999207 0.0398155i \(-0.987323\pi\)
0.999207 0.0398155i \(-0.0126770\pi\)
\(84\) 0 0
\(85\) 3.08209 + 1.77944i 0.334299 + 0.193008i
\(86\) 5.32235i 0.573923i
\(87\) 0 0
\(88\) −1.41013 2.44242i −0.150320 0.260363i
\(89\) −11.6970 + 6.75327i −1.23988 + 0.715845i −0.969070 0.246788i \(-0.920625\pi\)
−0.270810 + 0.962633i \(0.587292\pi\)
\(90\) 0 0
\(91\) 7.27987 15.8077i 0.763138 1.65709i
\(92\) 1.67610 0.174745
\(93\) 0 0
\(94\) 4.87381 + 8.44168i 0.502695 + 0.870693i
\(95\) 2.86603 4.96410i 0.294048 0.509306i
\(96\) 0 0
\(97\) −2.97800 1.71935i −0.302371 0.174574i 0.341137 0.940014i \(-0.389188\pi\)
−0.643507 + 0.765440i \(0.722521\pi\)
\(98\) −21.1088 12.1872i −2.13231 1.23109i
\(99\) 0 0
\(100\) −0.118272 + 0.204852i −0.0118272 + 0.0204852i
\(101\) −1.42763 2.47273i −0.142055 0.246046i 0.786215 0.617953i \(-0.212038\pi\)
−0.928270 + 0.371906i \(0.878704\pi\)
\(102\) 0 0
\(103\) 5.54488 0.546354 0.273177 0.961964i \(-0.411926\pi\)
0.273177 + 0.961964i \(0.411926\pi\)
\(104\) 9.46855 0.873806i 0.928468 0.0856838i
\(105\) 0 0
\(106\) 1.28351 0.741035i 0.124666 0.0719757i
\(107\) −2.22056 3.84611i −0.214669 0.371818i 0.738501 0.674252i \(-0.235534\pi\)
−0.953170 + 0.302434i \(0.902201\pi\)
\(108\) 0 0
\(109\) 13.7804i 1.31993i −0.751298 0.659963i \(-0.770572\pi\)
0.751298 0.659963i \(-0.229428\pi\)
\(110\) 1.38502 + 0.799640i 0.132056 + 0.0762427i
\(111\) 0 0
\(112\) 21.3208i 2.01463i
\(113\) −4.02200 + 6.96630i −0.378358 + 0.655334i −0.990823 0.135163i \(-0.956844\pi\)
0.612466 + 0.790497i \(0.290178\pi\)
\(114\) 0 0
\(115\) 6.13649 3.54290i 0.572230 0.330377i
\(116\) 0.348448 0.0323526
\(117\) 0 0
\(118\) −13.0454 −1.20093
\(119\) 14.8767 8.58909i 1.36375 0.787361i
\(120\) 0 0
\(121\) −4.92820 + 8.53590i −0.448018 + 0.775991i
\(122\) 9.47754i 0.858056i
\(123\) 0 0
\(124\) 0.299925 + 0.173162i 0.0269340 + 0.0155504i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 0.353326 + 0.611979i 0.0313526 + 0.0543044i 0.881276 0.472602i \(-0.156685\pi\)
−0.849923 + 0.526906i \(0.823352\pi\)
\(128\) 11.1690 6.44840i 0.987205 0.569963i
\(129\) 0 0
\(130\) −4.40221 + 3.11378i −0.386099 + 0.273097i
\(131\) −6.26554 −0.547423 −0.273711 0.961812i \(-0.588251\pi\)
−0.273711 + 0.961812i \(0.588251\pi\)
\(132\) 0 0
\(133\) −13.8338 23.9609i −1.19955 2.07767i
\(134\) 3.86825 6.70001i 0.334166 0.578793i
\(135\) 0 0
\(136\) 8.12828 + 4.69286i 0.696994 + 0.402410i
\(137\) 14.1212 + 8.15290i 1.20646 + 0.696549i 0.961984 0.273107i \(-0.0880511\pi\)
0.244475 + 0.969656i \(0.421384\pi\)
\(138\) 0 0
\(139\) 3.41264 5.91087i 0.289456 0.501353i −0.684224 0.729272i \(-0.739859\pi\)
0.973680 + 0.227919i \(0.0731921\pi\)
\(140\) 0.570878 + 0.988789i 0.0482480 + 0.0835680i
\(141\) 0 0
\(142\) −11.6124 −0.974494
\(143\) 2.22656 + 3.14788i 0.186195 + 0.263239i
\(144\) 0 0
\(145\) 1.27573 0.736543i 0.105944 0.0611666i
\(146\) −7.55889 13.0924i −0.625578 1.08353i
\(147\) 0 0
\(148\) 0.00600778i 0.000493837i
\(149\) 7.30887 + 4.21978i 0.598766 + 0.345698i 0.768556 0.639783i \(-0.220976\pi\)
−0.169790 + 0.985480i \(0.554309\pi\)
\(150\) 0 0
\(151\) 1.37017i 0.111503i −0.998445 0.0557513i \(-0.982245\pi\)
0.998445 0.0557513i \(-0.0177554\pi\)
\(152\) 7.55846 13.0916i 0.613072 1.06187i
\(153\) 0 0
\(154\) 6.68525 3.85973i 0.538713 0.311026i
\(155\) 1.46410 0.117599
\(156\) 0 0
\(157\) 11.9700 0.955311 0.477656 0.878547i \(-0.341487\pi\)
0.477656 + 0.878547i \(0.341487\pi\)
\(158\) −11.3759 + 6.56787i −0.905017 + 0.522512i
\(159\) 0 0
\(160\) −0.665665 + 1.15297i −0.0526255 + 0.0911500i
\(161\) 34.2020i 2.69550i
\(162\) 0 0
\(163\) 19.5474 + 11.2857i 1.53107 + 0.883962i 0.999313 + 0.0370630i \(0.0118002\pi\)
0.531754 + 0.846899i \(0.321533\pi\)
\(164\) 0.0633815i 0.00494927i
\(165\) 0 0
\(166\) 0.542476 + 0.939595i 0.0421043 + 0.0729267i
\(167\) −7.09881 + 4.09850i −0.549323 + 0.317152i −0.748849 0.662741i \(-0.769393\pi\)
0.199526 + 0.979893i \(0.436060\pi\)
\(168\) 0 0
\(169\) −12.7804 + 2.37915i −0.983111 + 0.183012i
\(170\) −5.32235 −0.408205
\(171\) 0 0
\(172\) −0.420915 0.729047i −0.0320945 0.0555893i
\(173\) 4.58386 7.93948i 0.348505 0.603628i −0.637479 0.770467i \(-0.720023\pi\)
0.985984 + 0.166840i \(0.0533563\pi\)
\(174\) 0 0
\(175\) 4.18016 + 2.41342i 0.315991 + 0.182437i
\(176\) 4.09079 + 2.36182i 0.308355 + 0.178029i
\(177\) 0 0
\(178\) 10.0996 17.4930i 0.756994 1.31115i
\(179\) 5.01850 + 8.69229i 0.375100 + 0.649693i 0.990342 0.138646i \(-0.0442750\pi\)
−0.615242 + 0.788338i \(0.710942\pi\)
\(180\) 0 0
\(181\) −17.0238 −1.26537 −0.632686 0.774408i \(-0.718048\pi\)
−0.632686 + 0.774408i \(0.718048\pi\)
\(182\) 2.39174 + 25.9168i 0.177287 + 1.92108i
\(183\) 0 0
\(184\) 16.1835 9.34356i 1.19307 0.688817i
\(185\) 0.0126991 + 0.0219955i 0.000933659 + 0.00161714i
\(186\) 0 0
\(187\) 3.80584i 0.278310i
\(188\) −1.33521 0.770886i −0.0973804 0.0562226i
\(189\) 0 0
\(190\) 8.57233i 0.621902i
\(191\) −1.93870 + 3.35793i −0.140280 + 0.242971i −0.927602 0.373570i \(-0.878133\pi\)
0.787322 + 0.616542i \(0.211467\pi\)
\(192\) 0 0
\(193\) 1.08595 0.626972i 0.0781681 0.0451304i −0.460406 0.887708i \(-0.652296\pi\)
0.538575 + 0.842578i \(0.318963\pi\)
\(194\) 5.14261 0.369218
\(195\) 0 0
\(196\) 3.85527 0.275376
\(197\) −13.2346 + 7.64098i −0.942923 + 0.544397i −0.890876 0.454247i \(-0.849908\pi\)
−0.0520479 + 0.998645i \(0.516575\pi\)
\(198\) 0 0
\(199\) −6.61480 + 11.4572i −0.468911 + 0.812177i −0.999368 0.0355340i \(-0.988687\pi\)
0.530458 + 0.847711i \(0.322020\pi\)
\(200\) 2.63726i 0.186483i
\(201\) 0 0
\(202\) 3.69799 + 2.13504i 0.260190 + 0.150221i
\(203\) 7.11035i 0.499049i
\(204\) 0 0
\(205\) −0.133975 0.232051i −0.00935719 0.0162071i
\(206\) −7.18144 + 4.14621i −0.500355 + 0.288880i
\(207\) 0 0
\(208\) −13.0024 + 9.19686i −0.901552 + 0.637688i
\(209\) 6.12979 0.424007
\(210\) 0 0
\(211\) 2.40521 + 4.16595i 0.165582 + 0.286796i 0.936862 0.349700i \(-0.113717\pi\)
−0.771280 + 0.636496i \(0.780383\pi\)
\(212\) −0.117209 + 0.203012i −0.00804994 + 0.0139429i
\(213\) 0 0
\(214\) 5.75189 + 3.32086i 0.393191 + 0.227009i
\(215\) −3.08209 1.77944i −0.210197 0.121357i
\(216\) 0 0
\(217\) 3.53349 6.12019i 0.239869 0.415465i
\(218\) 10.3044 + 17.8477i 0.697900 + 1.20880i
\(219\) 0 0
\(220\) −0.252957 −0.0170543
\(221\) −11.6552 5.36754i −0.784013 0.361060i
\(222\) 0 0
\(223\) −12.7420 + 7.35661i −0.853269 + 0.492635i −0.861753 0.507329i \(-0.830633\pi\)
0.00848317 + 0.999964i \(0.497300\pi\)
\(224\) 3.21306 + 5.56518i 0.214682 + 0.371839i
\(225\) 0 0
\(226\) 12.0299i 0.800214i
\(227\) −12.9062 7.45140i −0.856615 0.494567i 0.00626222 0.999980i \(-0.498007\pi\)
−0.862877 + 0.505413i \(0.831340\pi\)
\(228\) 0 0
\(229\) 19.3074i 1.27587i −0.770092 0.637933i \(-0.779790\pi\)
0.770092 0.637933i \(-0.220210\pi\)
\(230\) −5.29844 + 9.17716i −0.349369 + 0.605124i
\(231\) 0 0
\(232\) 3.36444 1.94246i 0.220886 0.127529i
\(233\) −21.1937 −1.38845 −0.694224 0.719759i \(-0.744252\pi\)
−0.694224 + 0.719759i \(0.744252\pi\)
\(234\) 0 0
\(235\) −6.51793 −0.425183
\(236\) 1.78694 1.03169i 0.116320 0.0671573i
\(237\) 0 0
\(238\) −12.8451 + 22.2483i −0.832621 + 1.44214i
\(239\) 14.8971i 0.963612i −0.876278 0.481806i \(-0.839981\pi\)
0.876278 0.481806i \(-0.160019\pi\)
\(240\) 0 0
\(241\) −8.13343 4.69584i −0.523921 0.302486i 0.214617 0.976698i \(-0.431150\pi\)
−0.738537 + 0.674213i \(0.764483\pi\)
\(242\) 14.7403i 0.947544i
\(243\) 0 0
\(244\) 0.749527 + 1.29822i 0.0479835 + 0.0831099i
\(245\) 14.1148 8.14918i 0.901762 0.520632i
\(246\) 0 0
\(247\) −8.64512 + 18.7722i −0.550076 + 1.19445i
\(248\) 3.86122 0.245188
\(249\) 0 0
\(250\) −0.747754 1.29515i −0.0472921 0.0819123i
\(251\) −5.65817 + 9.80024i −0.357140 + 0.618585i −0.987482 0.157733i \(-0.949582\pi\)
0.630341 + 0.776318i \(0.282915\pi\)
\(252\) 0 0
\(253\) 6.56229 + 3.78874i 0.412568 + 0.238196i
\(254\) −0.915219 0.528402i −0.0574260 0.0331549i
\(255\) 0 0
\(256\) −2.80038 + 4.85040i −0.175024 + 0.303150i
\(257\) 13.2660 + 22.9773i 0.827508 + 1.43329i 0.899987 + 0.435917i \(0.143576\pi\)
−0.0724788 + 0.997370i \(0.523091\pi\)
\(258\) 0 0
\(259\) 0.122593 0.00761758
\(260\) 0.356756 0.774668i 0.0221251 0.0480428i
\(261\) 0 0
\(262\) 8.11480 4.68508i 0.501334 0.289445i
\(263\) −7.07038 12.2463i −0.435979 0.755137i 0.561396 0.827547i \(-0.310264\pi\)
−0.997375 + 0.0724100i \(0.976931\pi\)
\(264\) 0 0
\(265\) 0.991015i 0.0608776i
\(266\) 35.8337 + 20.6886i 2.19711 + 1.26850i
\(267\) 0 0
\(268\) 1.22368i 0.0747479i
\(269\) 12.3872 21.4553i 0.755264 1.30815i −0.189980 0.981788i \(-0.560842\pi\)
0.945243 0.326367i \(-0.105824\pi\)
\(270\) 0 0
\(271\) 16.2095 9.35856i 0.984657 0.568492i 0.0809839 0.996715i \(-0.474194\pi\)
0.903673 + 0.428224i \(0.140860\pi\)
\(272\) −15.7201 −0.953170
\(273\) 0 0
\(274\) −24.3854 −1.47318
\(275\) −0.926118 + 0.534695i −0.0558470 + 0.0322433i
\(276\) 0 0
\(277\) −11.3323 + 19.6282i −0.680893 + 1.17934i 0.293815 + 0.955862i \(0.405075\pi\)
−0.974709 + 0.223480i \(0.928258\pi\)
\(278\) 10.2073i 0.612191i
\(279\) 0 0
\(280\) 11.0242 + 6.36482i 0.658822 + 0.380371i
\(281\) 27.8384i 1.66070i 0.557241 + 0.830351i \(0.311860\pi\)
−0.557241 + 0.830351i \(0.688140\pi\)
\(282\) 0 0
\(283\) 3.96004 + 6.85898i 0.235400 + 0.407724i 0.959389 0.282087i \(-0.0910268\pi\)
−0.723989 + 0.689811i \(0.757693\pi\)
\(284\) 1.59065 0.918364i 0.0943879 0.0544949i
\(285\) 0 0
\(286\) −5.23757 2.41204i −0.309704 0.142627i
\(287\) −1.29335 −0.0763439
\(288\) 0 0
\(289\) 2.16715 + 3.75362i 0.127480 + 0.220801i
\(290\) −1.10151 + 1.90786i −0.0646827 + 0.112034i
\(291\) 0 0
\(292\) 2.07081 + 1.19558i 0.121185 + 0.0699662i
\(293\) −0.236400 0.136485i −0.0138106 0.00797356i 0.493079 0.869985i \(-0.335871\pi\)
−0.506889 + 0.862011i \(0.669205\pi\)
\(294\) 0 0
\(295\) 4.36153 7.55440i 0.253938 0.439834i
\(296\) 0.0334909 + 0.0580080i 0.00194662 + 0.00337165i
\(297\) 0 0
\(298\) −12.6214 −0.731139
\(299\) −20.8579 + 14.7533i −1.20624 + 0.853204i
\(300\) 0 0
\(301\) −14.8767 + 8.58909i −0.857481 + 0.495067i
\(302\) 1.02455 + 1.77457i 0.0589560 + 0.102115i
\(303\) 0 0
\(304\) 25.3192i 1.45216i
\(305\) 5.48830 + 3.16867i 0.314259 + 0.181437i
\(306\) 0 0
\(307\) 6.85224i 0.391078i 0.980696 + 0.195539i \(0.0626456\pi\)
−0.980696 + 0.195539i \(0.937354\pi\)
\(308\) −0.610491 + 1.05740i −0.0347859 + 0.0602510i
\(309\) 0 0
\(310\) −1.89623 + 1.09479i −0.107698 + 0.0621798i
\(311\) 10.6447 0.603605 0.301803 0.953370i \(-0.402412\pi\)
0.301803 + 0.953370i \(0.402412\pi\)
\(312\) 0 0
\(313\) 17.8236 1.00745 0.503724 0.863865i \(-0.331963\pi\)
0.503724 + 0.863865i \(0.331963\pi\)
\(314\) −15.5029 + 8.95062i −0.874881 + 0.505113i
\(315\) 0 0
\(316\) 1.03883 1.79931i 0.0584390 0.101219i
\(317\) 8.17161i 0.458963i 0.973313 + 0.229482i \(0.0737031\pi\)
−0.973313 + 0.229482i \(0.926297\pi\)
\(318\) 0 0
\(319\) 1.36425 + 0.787651i 0.0763835 + 0.0441000i
\(320\) 6.84325i 0.382549i
\(321\) 0 0
\(322\) 25.5747 + 44.2967i 1.42522 + 2.46856i
\(323\) −17.6667 + 10.1999i −0.983001 + 0.567536i
\(324\) 0 0
\(325\) −0.331331 3.59030i −0.0183789 0.199154i
\(326\) −33.7556 −1.86955
\(327\) 0 0
\(328\) −0.353326 0.611979i −0.0195092 0.0337909i
\(329\) −15.7305 + 27.2460i −0.867250 + 1.50212i
\(330\) 0 0
\(331\) 21.5983 + 12.4698i 1.18715 + 0.685400i 0.957657 0.287911i \(-0.0929608\pi\)
0.229490 + 0.973311i \(0.426294\pi\)
\(332\) −0.148615 0.0858029i −0.00815631 0.00470905i
\(333\) 0 0
\(334\) 6.12934 10.6163i 0.335383 0.580900i
\(335\) 2.58658 + 4.48009i 0.141320 + 0.244773i
\(336\) 0 0
\(337\) 19.6057 1.06799 0.533996 0.845487i \(-0.320690\pi\)
0.533996 + 0.845487i \(0.320690\pi\)
\(338\) 14.7735 12.6380i 0.803575 0.687415i
\(339\) 0 0
\(340\) 0.729047 0.420915i 0.0395381 0.0228273i
\(341\) 0.782847 + 1.35593i 0.0423936 + 0.0734278i
\(342\) 0 0
\(343\) 44.8817i 2.42339i
\(344\) −8.12828 4.69286i −0.438247 0.253022i
\(345\) 0 0
\(346\) 13.7104i 0.737076i
\(347\) 8.54049 14.7926i 0.458478 0.794107i −0.540403 0.841406i \(-0.681728\pi\)
0.998881 + 0.0472996i \(0.0150615\pi\)
\(348\) 0 0
\(349\) −24.5708 + 14.1860i −1.31525 + 0.759357i −0.982960 0.183822i \(-0.941153\pi\)
−0.332286 + 0.943179i \(0.607820\pi\)
\(350\) −7.21857 −0.385849
\(351\) 0 0
\(352\) −1.42371 −0.0758840
\(353\) 18.4047 10.6260i 0.979586 0.565564i 0.0774407 0.996997i \(-0.475325\pi\)
0.902145 + 0.431433i \(0.141992\pi\)
\(354\) 0 0
\(355\) 3.88244 6.72458i 0.206058 0.356904i
\(356\) 3.19488i 0.169328i
\(357\) 0 0
\(358\) −12.9994 7.50520i −0.687039 0.396662i
\(359\) 32.6519i 1.72330i −0.507502 0.861650i \(-0.669431\pi\)
0.507502 0.861650i \(-0.330569\pi\)
\(360\) 0 0
\(361\) 6.92820 + 12.0000i 0.364642 + 0.631579i
\(362\) 22.0484 12.7296i 1.15884 0.669055i
\(363\) 0 0
\(364\) −2.37724 3.36090i −0.124601 0.176159i
\(365\) 10.1088 0.529118
\(366\) 0 0
\(367\) 2.95918 + 5.12546i 0.154468 + 0.267547i 0.932865 0.360226i \(-0.117300\pi\)
−0.778397 + 0.627772i \(0.783967\pi\)
\(368\) −15.6495 + 27.1057i −0.815785 + 1.41298i
\(369\) 0 0
\(370\) −0.0328945 0.0189916i −0.00171010 0.000987329i
\(371\) 4.14261 + 2.39174i 0.215073 + 0.124173i
\(372\) 0 0
\(373\) 6.65926 11.5342i 0.344803 0.597217i −0.640515 0.767946i \(-0.721279\pi\)
0.985318 + 0.170729i \(0.0546123\pi\)
\(374\) −2.84583 4.92912i −0.147154 0.254879i
\(375\) 0 0
\(376\) −17.1895 −0.886480
\(377\) −4.33621 + 3.06710i −0.223326 + 0.157963i
\(378\) 0 0
\(379\) −22.0131 + 12.7093i −1.13074 + 0.652832i −0.944120 0.329601i \(-0.893086\pi\)
−0.186617 + 0.982433i \(0.559752\pi\)
\(380\) −0.677939 1.17422i −0.0347775 0.0602364i
\(381\) 0 0
\(382\) 5.79869i 0.296687i
\(383\) 9.37632 + 5.41342i 0.479107 + 0.276613i 0.720044 0.693928i \(-0.244121\pi\)
−0.240937 + 0.970541i \(0.577455\pi\)
\(384\) 0 0
\(385\) 5.16177i 0.263068i
\(386\) −0.937641 + 1.62404i −0.0477247 + 0.0826615i
\(387\) 0 0
\(388\) −0.704427 + 0.406701i −0.0357618 + 0.0206471i
\(389\) −23.0370 −1.16802 −0.584011 0.811746i \(-0.698518\pi\)
−0.584011 + 0.811746i \(0.698518\pi\)
\(390\) 0 0
\(391\) −25.2176 −1.27531
\(392\) 37.2244 21.4915i 1.88012 1.08549i
\(393\) 0 0
\(394\) 11.4271 19.7924i 0.575691 0.997126i
\(395\) 8.78347i 0.441944i
\(396\) 0 0
\(397\) −18.2614 10.5432i −0.916512 0.529149i −0.0339917 0.999422i \(-0.510822\pi\)
−0.882521 + 0.470273i \(0.844155\pi\)
\(398\) 19.7850i 0.991731i
\(399\) 0 0
\(400\) −2.20857 3.82535i −0.110428 0.191267i
\(401\) 17.1273 9.88845i 0.855296 0.493805i −0.00713812 0.999975i \(-0.502272\pi\)
0.862434 + 0.506169i \(0.168939\pi\)
\(402\) 0 0
\(403\) −5.25656 + 0.485102i −0.261848 + 0.0241646i
\(404\) −0.675394 −0.0336021
\(405\) 0 0
\(406\) 5.31679 + 9.20895i 0.263868 + 0.457033i
\(407\) −0.0135803 + 0.0235218i −0.000673151 + 0.00116593i
\(408\) 0 0
\(409\) −27.6096 15.9404i −1.36521 0.788204i −0.374897 0.927066i \(-0.622322\pi\)
−0.990312 + 0.138862i \(0.955655\pi\)
\(410\) 0.347034 + 0.200360i 0.0171388 + 0.00989508i
\(411\) 0 0
\(412\) 0.655802 1.13588i 0.0323090 0.0559609i
\(413\) −21.0524 36.4639i −1.03592 1.79427i
\(414\) 0 0
\(415\) −0.725474 −0.0356121
\(416\) 2.00792 4.36004i 0.0984465 0.213769i
\(417\) 0 0
\(418\) −7.93899 + 4.58358i −0.388309 + 0.224190i
\(419\) 15.3648 + 26.6127i 0.750621 + 1.30011i 0.947522 + 0.319690i \(0.103579\pi\)
−0.196902 + 0.980423i \(0.563088\pi\)
\(420\) 0 0
\(421\) 17.9820i 0.876391i −0.898880 0.438195i \(-0.855618\pi\)
0.898880 0.438195i \(-0.144382\pi\)
\(422\) −6.23021 3.59701i −0.303282 0.175100i
\(423\) 0 0
\(424\) 2.61357i 0.126926i
\(425\) 1.77944 3.08209i 0.0863157 0.149503i
\(426\) 0 0
\(427\) 26.4911 15.2947i 1.28200 0.740160i
\(428\) −1.05051 −0.0507785
\(429\) 0 0
\(430\) 5.32235 0.256666
\(431\) 4.24308 2.44974i 0.204382 0.118000i −0.394316 0.918975i \(-0.629018\pi\)
0.598698 + 0.800975i \(0.295685\pi\)
\(432\) 0 0
\(433\) −9.61972 + 16.6618i −0.462294 + 0.800717i −0.999075 0.0430048i \(-0.986307\pi\)
0.536781 + 0.843722i \(0.319640\pi\)
\(434\) 10.5687i 0.507315i
\(435\) 0 0
\(436\) −2.82296 1.62983i −0.135195 0.0780549i
\(437\) 40.6162i 1.94294i
\(438\) 0 0
\(439\) −4.27987 7.41295i −0.204267 0.353801i 0.745632 0.666358i \(-0.232148\pi\)
−0.949899 + 0.312557i \(0.898814\pi\)
\(440\) −2.44242 + 1.41013i −0.116438 + 0.0672253i
\(441\) 0 0
\(442\) 19.1088 1.76346i 0.908913 0.0838791i
\(443\) 37.9652 1.80378 0.901891 0.431965i \(-0.142179\pi\)
0.901891 + 0.431965i \(0.142179\pi\)
\(444\) 0 0
\(445\) 6.75327 + 11.6970i 0.320136 + 0.554491i
\(446\) 11.0019 19.0558i 0.520954 0.902318i
\(447\) 0 0
\(448\) 28.6059 + 16.5156i 1.35150 + 0.780290i
\(449\) −23.1283 13.3531i −1.09149 0.630173i −0.157518 0.987516i \(-0.550349\pi\)
−0.933973 + 0.357344i \(0.883683\pi\)
\(450\) 0 0
\(451\) 0.143271 0.248153i 0.00674637 0.0116851i
\(452\) 0.951375 + 1.64783i 0.0447489 + 0.0775074i
\(453\) 0 0
\(454\) 22.2873 1.04599
\(455\) −15.8077 7.27987i −0.741075 0.341286i
\(456\) 0 0
\(457\) 3.69903 2.13563i 0.173033 0.0999007i −0.410982 0.911643i \(-0.634814\pi\)
0.584015 + 0.811743i \(0.301481\pi\)
\(458\) 14.4371 + 25.0059i 0.674604 + 1.16845i
\(459\) 0 0
\(460\) 1.67610i 0.0781485i
\(461\) −17.8767 10.3211i −0.832603 0.480704i 0.0221401 0.999755i \(-0.492952\pi\)
−0.854743 + 0.519051i \(0.826285\pi\)
\(462\) 0 0
\(463\) 32.1040i 1.49200i −0.665947 0.745999i \(-0.731972\pi\)
0.665947 0.745999i \(-0.268028\pi\)
\(464\) −3.25341 + 5.63507i −0.151036 + 0.261602i
\(465\) 0 0
\(466\) 27.4490 15.8477i 1.27155 0.734131i
\(467\) 23.3774 1.08178 0.540888 0.841095i \(-0.318088\pi\)
0.540888 + 0.841095i \(0.318088\pi\)
\(468\) 0 0
\(469\) 24.9700 1.15301
\(470\) 8.44168 4.87381i 0.389386 0.224812i
\(471\) 0 0
\(472\) 11.5025 19.9229i 0.529446 0.917027i
\(473\) 3.80584i 0.174993i
\(474\) 0 0
\(475\) −4.96410 2.86603i −0.227769 0.131502i
\(476\) 4.06338i 0.186245i
\(477\) 0 0
\(478\) 11.1393 + 19.2939i 0.509502 + 0.882483i
\(479\) 4.48198 2.58767i 0.204787 0.118234i −0.394100 0.919068i \(-0.628943\pi\)
0.598886 + 0.800834i \(0.295610\pi\)
\(480\) 0 0
\(481\) −0.0528814 0.0747629i −0.00241119 0.00340889i
\(482\) 14.0453 0.639747
\(483\) 0 0
\(484\) 1.16573 + 2.01911i 0.0529879 + 0.0917777i
\(485\) −1.71935 + 2.97800i −0.0780717 + 0.135224i
\(486\) 0 0
\(487\) −26.6501 15.3865i −1.20763 0.697227i −0.245391 0.969424i \(-0.578917\pi\)
−0.962242 + 0.272197i \(0.912250\pi\)
\(488\) 14.4741 + 8.35661i 0.655211 + 0.378286i
\(489\) 0 0
\(490\) −12.1872 + 21.1088i −0.550560 + 0.953598i
\(491\) −17.8992 31.0023i −0.807778 1.39911i −0.914400 0.404813i \(-0.867337\pi\)
0.106622 0.994300i \(-0.465997\pi\)
\(492\) 0 0
\(493\) −5.24255 −0.236113
\(494\) −2.84028 30.7772i −0.127790 1.38473i
\(495\) 0 0
\(496\) −5.60070 + 3.23357i −0.251479 + 0.145191i
\(497\) −18.7399 32.4585i −0.840600 1.45596i
\(498\) 0 0
\(499\) 28.8971i 1.29361i −0.762655 0.646805i \(-0.776105\pi\)
0.762655 0.646805i \(-0.223895\pi\)
\(500\) 0.204852 + 0.118272i 0.00916128 + 0.00528927i
\(501\) 0 0
\(502\) 16.9237i 0.755340i
\(503\) −3.93161 + 6.80974i −0.175302 + 0.303631i −0.940266 0.340442i \(-0.889423\pi\)
0.764964 + 0.644073i \(0.222757\pi\)
\(504\) 0 0
\(505\) −2.47273 + 1.42763i −0.110035 + 0.0635289i
\(506\) −11.3322 −0.503777
\(507\) 0 0
\(508\) 0.167154 0.00741625
\(509\) −24.2585 + 14.0057i −1.07524 + 0.620790i −0.929608 0.368549i \(-0.879855\pi\)
−0.145631 + 0.989339i \(0.546521\pi\)
\(510\) 0 0
\(511\) 24.3968 42.2564i 1.07925 1.86931i
\(512\) 17.4176i 0.769757i
\(513\) 0 0
\(514\) −34.3628 19.8394i −1.51568 0.875076i
\(515\) 5.54488i 0.244337i
\(516\) 0 0
\(517\) −3.48510 6.03637i −0.153275 0.265479i
\(518\) −0.158776 + 0.0916696i −0.00697623 + 0.00402773i
\(519\) 0 0
\(520\) −0.873806 9.46855i −0.0383189 0.415224i
\(521\) 37.5609 1.64557 0.822786 0.568351i \(-0.192419\pi\)
0.822786 + 0.568351i \(0.192419\pi\)
\(522\) 0 0
\(523\) 22.6553 + 39.2401i 0.990647 + 1.71585i 0.613493 + 0.789700i \(0.289764\pi\)
0.377154 + 0.926151i \(0.376903\pi\)
\(524\) −0.741035 + 1.28351i −0.0323723 + 0.0560704i
\(525\) 0 0
\(526\) 18.3144 + 10.5738i 0.798545 + 0.461040i
\(527\) −4.51249 2.60529i −0.196567 0.113488i
\(528\) 0 0
\(529\) −13.6043 + 23.5633i −0.591491 + 1.02449i
\(530\) −0.741035 1.28351i −0.0321885 0.0557522i
\(531\) 0 0
\(532\) −6.54460 −0.283744
\(533\) 0.557894 + 0.788741i 0.0241651 + 0.0341642i
\(534\) 0 0
\(535\) −3.84611 + 2.22056i −0.166282 + 0.0960030i
\(536\) 6.82149 + 11.8152i 0.294644 + 0.510338i
\(537\) 0 0
\(538\) 37.0504i 1.59736i
\(539\) 15.0942 + 8.71465i 0.650154 + 0.375367i
\(540\) 0 0
\(541\) 19.7445i 0.848882i 0.905456 + 0.424441i \(0.139529\pi\)
−0.905456 + 0.424441i \(0.860471\pi\)
\(542\) −13.9958 + 24.2414i −0.601171 + 1.04126i
\(543\) 0 0
\(544\) 4.10328 2.36903i 0.175927 0.101571i
\(545\) −13.7804 −0.590289
\(546\) 0 0
\(547\) −11.8312 −0.505867 −0.252934 0.967484i \(-0.581395\pi\)
−0.252934 + 0.967484i \(0.581395\pi\)
\(548\) 3.34028 1.92851i 0.142690 0.0823820i
\(549\) 0 0
\(550\) 0.799640 1.38502i 0.0340968 0.0590573i
\(551\) 8.44381i 0.359718i
\(552\) 0 0
\(553\) −36.7164 21.1982i −1.56134 0.901439i
\(554\) 33.8952i 1.44007i
\(555\) 0 0
\(556\) −0.807237 1.39818i −0.0342345 0.0592958i
\(557\) 3.50412 2.02310i 0.148474 0.0857217i −0.423922 0.905699i \(-0.639347\pi\)
0.572397 + 0.819977i \(0.306014\pi\)
\(558\) 0 0
\(559\) 11.6552 + 5.36754i 0.492962 + 0.227023i
\(560\) −21.3208 −0.900968
\(561\) 0 0
\(562\) −20.8163 36.0549i −0.878083 1.52088i
\(563\) −1.94963 + 3.37686i −0.0821671 + 0.142318i −0.904181 0.427151i \(-0.859517\pi\)
0.822013 + 0.569468i \(0.192851\pi\)
\(564\) 0 0
\(565\) 6.96630 + 4.02200i 0.293074 + 0.169207i
\(566\) −10.2577 5.92226i −0.431162 0.248931i
\(567\) 0 0
\(568\) 10.2390 17.7345i 0.429619 0.744123i
\(569\) 8.66778 + 15.0130i 0.363372 + 0.629379i 0.988514 0.151133i \(-0.0482920\pi\)
−0.625141 + 0.780512i \(0.714959\pi\)
\(570\) 0 0
\(571\) −29.5118 −1.23503 −0.617515 0.786559i \(-0.711860\pi\)
−0.617515 + 0.786559i \(0.711860\pi\)
\(572\) 0.908189 0.0838123i 0.0379733 0.00350437i
\(573\) 0 0
\(574\) 1.67508 0.967106i 0.0699163 0.0403662i
\(575\) −3.54290 6.13649i −0.147749 0.255909i
\(576\) 0 0
\(577\) 28.3684i 1.18099i 0.807041 + 0.590496i \(0.201068\pi\)
−0.807041 + 0.590496i \(0.798932\pi\)
\(578\) −5.61357 3.24100i −0.233494 0.134808i
\(579\) 0 0
\(580\) 0.348448i 0.0144685i
\(581\) −1.75087 + 3.03260i −0.0726384 + 0.125813i
\(582\) 0 0
\(583\) −0.917797 + 0.529891i −0.0380113 + 0.0219458i
\(584\) 26.6595 1.10318
\(585\) 0 0
\(586\) 0.408230 0.0168638
\(587\) −29.7806 + 17.1939i −1.22918 + 0.709667i −0.966858 0.255314i \(-0.917821\pi\)
−0.262320 + 0.964981i \(0.584488\pi\)
\(588\) 0 0
\(589\) −4.19615 + 7.26795i −0.172899 + 0.299471i
\(590\) 13.0454i 0.537071i
\(591\) 0 0
\(592\) −0.0971572 0.0560937i −0.00399314 0.00230544i
\(593\) 5.47612i 0.224877i 0.993659 + 0.112439i \(0.0358662\pi\)
−0.993659 + 0.112439i \(0.964134\pi\)
\(594\) 0 0
\(595\) −8.58909 14.8767i −0.352118 0.609887i
\(596\) 1.72886 0.998159i 0.0708170 0.0408862i
\(597\) 0 0
\(598\) 15.9823 34.7043i 0.653564 1.41916i
\(599\) −38.6039 −1.57731 −0.788657 0.614833i \(-0.789223\pi\)
−0.788657 + 0.614833i \(0.789223\pi\)
\(600\) 0 0
\(601\) −3.28948 5.69754i −0.134181 0.232408i 0.791104 0.611682i \(-0.209507\pi\)
−0.925284 + 0.379275i \(0.876174\pi\)
\(602\) 12.8451 22.2483i 0.523525 0.906772i
\(603\) 0 0
\(604\) −0.280682 0.162052i −0.0114208 0.00659379i
\(605\) 8.53590 + 4.92820i 0.347034 + 0.200360i
\(606\) 0 0
\(607\) 8.38318 14.5201i 0.340263 0.589352i −0.644219 0.764841i \(-0.722817\pi\)
0.984481 + 0.175489i \(0.0561507\pi\)
\(608\) −3.81563 6.60886i −0.154744 0.268025i
\(609\) 0 0
\(610\) −9.47754 −0.383734
\(611\) 23.4013 2.15959i 0.946715 0.0873677i
\(612\) 0 0
\(613\) 24.9232 14.3894i 1.00664 0.581184i 0.0964341 0.995339i \(-0.469256\pi\)
0.910206 + 0.414155i \(0.135923\pi\)
\(614\) −5.12379 8.87466i −0.206779 0.358152i
\(615\) 0 0
\(616\) 13.6129i 0.548481i
\(617\) −32.3279 18.6645i −1.30147 0.751406i −0.320817 0.947141i \(-0.603957\pi\)
−0.980657 + 0.195735i \(0.937291\pi\)
\(618\) 0 0
\(619\) 12.7535i 0.512606i −0.966597 0.256303i \(-0.917496\pi\)
0.966597 0.256303i \(-0.0825045\pi\)
\(620\) 0.173162 0.299925i 0.00695434 0.0120453i
\(621\) 0 0
\(622\) −13.7864 + 7.95961i −0.552786 + 0.319151i
\(623\) 65.1939 2.61194
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −23.0842 + 13.3276i −0.922629 + 0.532680i
\(627\) 0 0
\(628\) 1.41571 2.45209i 0.0564931 0.0978489i
\(629\) 0.0903896i 0.00360407i
\(630\) 0 0
\(631\) 24.8759 + 14.3621i 0.990294 + 0.571746i 0.905362 0.424641i \(-0.139600\pi\)
0.0849315 + 0.996387i \(0.472933\pi\)
\(632\) 23.1643i 0.921427i
\(633\) 0 0
\(634\) −6.11035 10.5834i −0.242673 0.420322i
\(635\) 0.611979 0.353326i 0.0242856 0.0140213i
\(636\) 0 0
\(637\) −47.9762 + 33.9346i −1.90089 + 1.34454i
\(638\) −2.35588 −0.0932701
\(639\) 0 0
\(640\) −6.44840 11.1690i −0.254895 0.441492i
\(641\) 11.1985 19.3964i 0.442315 0.766112i −0.555546 0.831486i \(-0.687491\pi\)
0.997861 + 0.0653739i \(0.0208240\pi\)
\(642\) 0 0
\(643\) 12.2665 + 7.08209i 0.483745 + 0.279290i 0.721976 0.691918i \(-0.243234\pi\)
−0.238231 + 0.971209i \(0.576567\pi\)
\(644\) −7.00637 4.04513i −0.276090 0.159400i
\(645\) 0 0
\(646\) 15.2540 26.4207i 0.600160 1.03951i
\(647\) 11.8048 + 20.4466i 0.464096 + 0.803838i 0.999160 0.0409732i \(-0.0130458\pi\)
−0.535064 + 0.844812i \(0.679713\pi\)
\(648\) 0 0
\(649\) 9.32835 0.366170
\(650\) 3.11378 + 4.40221i 0.122132 + 0.172669i
\(651\) 0 0
\(652\) 4.62379 2.66955i 0.181082 0.104548i
\(653\) 16.6383 + 28.8183i 0.651105 + 1.12775i 0.982855 + 0.184380i \(0.0590277\pi\)
−0.331750 + 0.943367i \(0.607639\pi\)
\(654\) 0 0
\(655\) 6.26554i 0.244815i
\(656\) 1.02500 + 0.591784i 0.0400195 + 0.0231053i
\(657\) 0 0
\(658\) 47.0502i 1.83421i
\(659\) 11.5454 19.9972i 0.449745 0.778982i −0.548624 0.836069i \(-0.684848\pi\)
0.998369 + 0.0570875i \(0.0181814\pi\)
\(660\) 0 0
\(661\) 11.6364 6.71826i 0.452602 0.261310i −0.256326 0.966590i \(-0.582512\pi\)
0.708929 + 0.705280i \(0.249179\pi\)
\(662\) −37.2972 −1.44960
\(663\) 0 0
\(664\) −1.91326 −0.0742491
\(665\) −23.9609 + 13.8338i −0.929164 + 0.536453i
\(666\) 0 0
\(667\) −5.21900 + 9.03957i −0.202080 + 0.350014i
\(668\) 1.93895i 0.0750200i
\(669\) 0 0
\(670\) −6.70001 3.86825i −0.258844 0.149444i
\(671\) 6.77708i 0.261626i
\(672\) 0 0
\(673\) −0.972620 1.68463i −0.0374918 0.0649376i 0.846671 0.532117i \(-0.178603\pi\)
−0.884162 + 0.467180i \(0.845270\pi\)
\(674\) −25.3923 + 14.6603i −0.978075 + 0.564692i
\(675\) 0 0
\(676\) −1.02419 + 2.89949i −0.0393919 + 0.111519i
\(677\) −24.8683 −0.955768 −0.477884 0.878423i \(-0.658596\pi\)
−0.477884 + 0.878423i \(0.658596\pi\)
\(678\) 0 0
\(679\) 8.29903 + 14.3743i 0.318488 + 0.551637i
\(680\) 4.69286 8.12828i 0.179963 0.311705i
\(681\) 0 0
\(682\) −2.02781 1.17075i −0.0776487 0.0448305i
\(683\) 12.6631 + 7.31107i 0.484542 + 0.279750i 0.722307 0.691572i \(-0.243082\pi\)
−0.237766 + 0.971323i \(0.576415\pi\)
\(684\) 0 0
\(685\) 8.15290 14.1212i 0.311506 0.539545i
\(686\) 33.5605 + 58.1285i 1.28135 + 2.21935i
\(687\) 0 0
\(688\) 15.7201 0.599323
\(689\) −0.328354 3.55804i −0.0125093 0.135550i
\(690\) 0 0
\(691\) −3.05231 + 1.76225i −0.116115 + 0.0670393i −0.556933 0.830558i \(-0.688022\pi\)
0.440817 + 0.897597i \(0.354689\pi\)
\(692\) −1.08428 1.87803i −0.0412182 0.0713920i
\(693\) 0 0
\(694\) 25.5447i 0.969665i
\(695\) −5.91087 3.41264i −0.224212 0.129449i
\(696\) 0 0
\(697\) 0.953601i 0.0361202i
\(698\) 21.2152 36.7458i 0.803008 1.39085i
\(699\) 0 0
\(700\) 0.988789 0.570878i 0.0373727 0.0215772i
\(701\) −1.53457 −0.0579599 −0.0289800 0.999580i \(-0.509226\pi\)
−0.0289800 + 0.999580i \(0.509226\pi\)
\(702\) 0 0
\(703\) −0.145584 −0.00549081
\(704\) −6.33766 + 3.65905i −0.238860 + 0.137906i
\(705\) 0 0
\(706\) −15.8912 + 27.5244i −0.598075 + 1.03590i
\(707\) 13.7819i 0.518322i
\(708\) 0 0
\(709\) 12.1289 + 7.00262i 0.455510 + 0.262989i 0.710155 0.704046i \(-0.248625\pi\)
−0.254644 + 0.967035i \(0.581958\pi\)
\(710\) 11.6124i 0.435807i
\(711\) 0 0
\(712\) 17.8101 + 30.8481i 0.667463 + 1.15608i
\(713\) −8.98444 + 5.18717i −0.336470 + 0.194261i
\(714\) 0 0
\(715\) 3.14788 2.22656i 0.117724 0.0832687i
\(716\) 2.37418 0.0887274
\(717\) 0 0
\(718\) 24.4156 + 42.2890i 0.911181 + 1.57821i
\(719\) −11.2381 + 19.4649i −0.419109 + 0.725918i −0.995850 0.0910091i \(-0.970991\pi\)
0.576741 + 0.816927i \(0.304324\pi\)
\(720\) 0 0
\(721\) −23.1785 13.3821i −0.863213 0.498376i
\(722\) −17.9461 10.3612i −0.667884 0.385603i
\(723\) 0 0
\(724\) −2.01344 + 3.48737i −0.0748288 + 0.129607i
\(725\) −0.736543 1.27573i −0.0273545 0.0473794i
\(726\) 0 0
\(727\) 10.3421 0.383566 0.191783 0.981437i \(-0.438573\pi\)
0.191783 + 0.981437i \(0.438573\pi\)
\(728\) −41.6890 19.1989i −1.54510 0.711560i
\(729\) 0 0
\(730\) −13.0924 + 7.55889i −0.484571 + 0.279767i
\(731\) 6.33285 + 10.9688i 0.234229 + 0.405696i
\(732\) 0 0
\(733\) 27.3533i 1.01032i 0.863026 + 0.505159i \(0.168566\pi\)
−0.863026 + 0.505159i \(0.831434\pi\)
\(734\) −7.66516 4.42548i −0.282926 0.163348i
\(735\) 0 0
\(736\) 9.43355i 0.347725i
\(737\) −2.76606 + 4.79096i −0.101889 + 0.176477i
\(738\) 0 0
\(739\) 11.6495 6.72583i 0.428533 0.247413i −0.270189 0.962807i \(-0.587086\pi\)
0.698721 + 0.715394i \(0.253753\pi\)
\(740\) 0.00600778 0.000220851
\(741\) 0 0
\(742\) −7.15372 −0.262621
\(743\) −14.1964 + 8.19632i −0.520817 + 0.300694i −0.737269 0.675599i \(-0.763885\pi\)
0.216452 + 0.976293i \(0.430552\pi\)
\(744\) 0 0
\(745\) 4.21978 7.30887i 0.154601 0.267776i
\(746\) 19.9179i 0.729248i
\(747\) 0 0
\(748\) 0.779635 + 0.450122i 0.0285063 + 0.0164581i
\(749\) 21.4365i 0.783274i
\(750\) 0 0
\(751\) −13.8328 23.9590i −0.504764 0.874277i −0.999985 0.00551009i \(-0.998246\pi\)
0.495221 0.868767i \(-0.335087\pi\)
\(752\) 24.9334 14.3953i 0.909226 0.524942i
\(753\) 0 0
\(754\) 3.32260 7.21476i 0.121002 0.262746i
\(755\) −1.37017 −0.0498654
\(756\) 0 0
\(757\) −11.4989 19.9167i −0.417935 0.723885i 0.577797 0.816181i \(-0.303913\pi\)
−0.995732 + 0.0922961i \(0.970579\pi\)
\(758\) 19.0068 32.9208i 0.690359 1.19574i
\(759\) 0 0
\(760\) −13.0916 7.55846i −0.474884 0.274174i
\(761\) −6.63759 3.83221i −0.240612 0.138918i 0.374846 0.927087i \(-0.377696\pi\)
−0.615458 + 0.788170i \(0.711029\pi\)
\(762\) 0 0
\(763\) −33.2580 + 57.6045i −1.20402 + 2.08542i
\(764\) 0.458587 + 0.794296i 0.0165911 + 0.0287366i
\(765\) 0 0
\(766\) −16.1916 −0.585027
\(767\) −13.1562 + 28.5676i −0.475042 + 1.03152i
\(768\) 0 0
\(769\) 6.26219 3.61548i 0.225820 0.130377i −0.382822 0.923822i \(-0.625048\pi\)
0.608642 + 0.793445i \(0.291714\pi\)
\(770\) −3.85973 6.68525i −0.139095 0.240920i
\(771\) 0 0
\(772\) 0.296612i 0.0106753i
\(773\) 29.0981 + 16.7998i 1.04658 + 0.604246i 0.921691 0.387924i \(-0.126808\pi\)
0.124893 + 0.992170i \(0.460141\pi\)
\(774\) 0 0
\(775\) 1.46410i 0.0525921i
\(776\) −4.53438 + 7.85378i −0.162775 + 0.281934i
\(777\) 0 0
\(778\) 29.8363 17.2260i 1.06968 0.617582i
\(779\) 1.53590 0.0550293
\(780\) 0 0
\(781\) 8.30368 0.297129
\(782\) 32.6605 18.8565i 1.16794 0.674309i
\(783\) 0 0
\(784\) −35.9960 + 62.3470i −1.28557 + 2.22668i
\(785\) 11.9700i 0.427228i
\(786\) 0 0
\(787\) 2.57355 + 1.48584i 0.0917371 + 0.0529645i 0.545167 0.838328i \(-0.316466\pi\)
−0.453430 + 0.891292i \(0.649800\pi\)
\(788\) 3.61484i 0.128773i
\(789\) 0 0
\(790\) 6.56787 + 11.3759i 0.233674 + 0.404736i
\(791\) 33.6252 19.4135i 1.19557 0.690265i
\(792\) 0 0
\(793\) −20.7545 9.55802i −0.737013 0.339415i
\(794\) 31.5349 1.11913
\(795\) 0 0
\(796\) 1.56469 + 2.71012i 0.0554588 + 0.0960575i
\(797\) 11.2875 19.5506i 0.399825 0.692517i −0.593879 0.804554i \(-0.702404\pi\)
0.993704 + 0.112037i \(0.0357375\pi\)
\(798\) 0 0
\(799\) 20.0888 + 11.5983i 0.710692 + 0.410318i
\(800\) 1.15297 + 0.665665i 0.0407635 + 0.0235348i
\(801\) 0 0
\(802\) −14.7882 + 25.6140i −0.522191 + 0.904462i
\(803\) 5.40512 + 9.36194i 0.190742 + 0.330376i
\(804\) 0 0
\(805\) −34.2020 −1.20546
\(806\) 6.44528 4.55889i 0.227025 0.160580i
\(807\) 0 0
\(808\) −6.52125 + 3.76505i −0.229417 + 0.132454i
\(809\) 6.82921 + 11.8285i 0.240102 + 0.415869i 0.960743 0.277439i \(-0.0894857\pi\)
−0.720641 + 0.693308i \(0.756152\pi\)
\(810\) 0 0
\(811\) 14.1147i 0.495636i −0.968807 0.247818i \(-0.920287\pi\)
0.968807 0.247818i \(-0.0797135\pi\)
\(812\) −1.45657 0.840952i −0.0511157 0.0295116i
\(813\) 0 0
\(814\) 0.0406189i 0.00142369i
\(815\) 11.2857 19.5474i 0.395320 0.684714i
\(816\) 0 0
\(817\) 17.6667 10.1999i 0.618079 0.356848i
\(818\) 47.6781 1.66703
\(819\) 0 0
\(820\) −0.0633815 −0.00221338
\(821\) 1.37318 0.792808i 0.0479244 0.0276692i −0.475846 0.879528i \(-0.657858\pi\)
0.523771 + 0.851859i \(0.324525\pi\)
\(822\) 0 0
\(823\) 9.28238 16.0776i 0.323563 0.560428i −0.657657 0.753317i \(-0.728452\pi\)
0.981221 + 0.192889i \(0.0617857\pi\)
\(824\) 14.6233i 0.509427i
\(825\) 0 0
\(826\) 54.5320 + 31.4840i 1.89741 + 1.09547i
\(827\) 9.01023i 0.313316i −0.987653 0.156658i \(-0.949928\pi\)
0.987653 0.156658i \(-0.0500721\pi\)
\(828\) 0 0
\(829\) 23.5588 + 40.8051i 0.818233 + 1.41722i 0.906983 + 0.421167i \(0.138379\pi\)
−0.0887506 + 0.996054i \(0.528287\pi\)
\(830\) 0.939595 0.542476i 0.0326138 0.0188296i
\(831\) 0 0
\(832\) −2.26738 24.5693i −0.0786072 0.851787i
\(833\) −58.0041 −2.00972
\(834\) 0 0
\(835\) 4.09850 + 7.09881i 0.141835 + 0.245665i
\(836\) 0.724980 1.25570i 0.0250740 0.0434294i
\(837\) 0 0
\(838\) −39.7994 22.9782i −1.37485 0.793769i
\(839\) −46.3121 26.7383i −1.59887 0.923108i −0.991705 0.128531i \(-0.958974\pi\)
−0.607164 0.794576i \(-0.707693\pi\)
\(840\) 0 0
\(841\) 13.4150 23.2355i 0.462586 0.801223i
\(842\) 13.4461 + 23.2894i 0.463384 + 0.802605i
\(843\) 0 0
\(844\) 1.13787 0.0391672
\(845\) 2.37915 + 12.7804i 0.0818453 + 0.439660i
\(846\) 0 0
\(847\) 41.2014 23.7876i 1.41570 0.817353i
\(848\) −2.18872 3.79098i −0.0751611 0.130183i
\(849\) 0 0
\(850\) 5.32235i 0.182555i
\(851\) −0.155856 0.0899835i −0.00534268 0.00308460i
\(852\) 0 0
\(853\) 27.7756i 0.951019i 0.879711 + 0.475510i \(0.157736\pi\)
−0.879711 + 0.475510i \(0.842264\pi\)
\(854\) −22.8733 + 39.6177i −0.782707 + 1.35569i
\(855\) 0 0
\(856\) −10.1432 + 5.85619i −0.346688 + 0.200160i
\(857\) 53.6917 1.83407 0.917037 0.398801i \(-0.130574\pi\)
0.917037 + 0.398801i \(0.130574\pi\)
\(858\) 0 0
\(859\) 2.08958 0.0712955 0.0356477 0.999364i \(-0.488651\pi\)
0.0356477 + 0.999364i \(0.488651\pi\)
\(860\) −0.729047 + 0.420915i −0.0248603 + 0.0143531i
\(861\) 0 0
\(862\) −3.66361 + 6.34556i −0.124783 + 0.216131i
\(863\) 1.75413i 0.0597113i 0.999554 + 0.0298557i \(0.00950476\pi\)
−0.999554 + 0.0298557i \(0.990495\pi\)
\(864\) 0 0
\(865\) −7.93948 4.58386i −0.269950 0.155856i
\(866\) 28.7727i 0.977737i
\(867\) 0 0
\(868\) −0.835823 1.44769i −0.0283697 0.0491377i
\(869\) 8.13453 4.69647i 0.275945 0.159317i
\(870\) 0 0
\(871\) −10.7710 15.2278i −0.364961 0.515975i
\(872\) −36.3426 −1.23072
\(873\) 0 0
\(874\) −30.3709 52.6040i −1.02731 1.77936i
\(875\) 2.41342 4.18016i 0.0815885 0.141315i
\(876\) 0 0
\(877\) −18.6777 10.7836i −0.630702 0.364136i 0.150322 0.988637i \(-0.451969\pi\)
−0.781024 + 0.624501i \(0.785302\pi\)
\(878\) 11.0861 + 6.40058i 0.374139 + 0.216009i
\(879\) 0 0
\(880\) 2.36182 4.09079i 0.0796169 0.137900i
\(881\) −12.5132 21.6734i −0.421579 0.730196i 0.574515 0.818494i \(-0.305191\pi\)
−0.996094 + 0.0882978i \(0.971857\pi\)
\(882\) 0 0
\(883\) 48.7832 1.64169 0.820843 0.571154i \(-0.193504\pi\)
0.820843 + 0.571154i \(0.193504\pi\)
\(884\) −2.47803 + 1.75277i −0.0833452 + 0.0589519i
\(885\) 0 0
\(886\) −49.1705 + 28.3886i −1.65192 + 0.953734i
\(887\) −16.8967 29.2659i −0.567334 0.982651i −0.996828 0.0795819i \(-0.974641\pi\)
0.429494 0.903070i \(-0.358692\pi\)
\(888\) 0 0
\(889\) 3.41090i 0.114398i
\(890\) −17.4930 10.0996i −0.586365 0.338538i
\(891\) 0 0
\(892\) 3.48031i 0.116530i
\(893\) 18.6806 32.3557i 0.625121 1.08274i
\(894\) 0 0
\(895\) 8.69229 5.01850i 0.290551 0.167750i
\(896\) −62.2508 −2.07965
\(897\) 0 0
\(898\) 39.9394 1.33279
\(899\) −1.86780 + 1.07837i −0.0622946 + 0.0359658i
\(900\) 0 0
\(901\) 1.76346 3.05440i 0.0587493 0.101757i
\(902\) 0.428526i 0.0142683i
\(903\) 0 0
\(904\) 18.3720 + 10.6071i 0.611043 + 0.352786i
\(905\) 17.0238i 0.565892i
\(906\) 0 0
\(907\) −17.3135 29.9879i −0.574885 0.995731i −0.996054 0.0887485i \(-0.971713\pi\)
0.421169 0.906982i \(-0.361620\pi\)
\(908\) −3.05288 + 1.76258i −0.101313 + 0.0584932i
\(909\) 0 0
\(910\) 25.9168 2.39174i 0.859134 0.0792853i
\(911\) −31.1865 −1.03326 −0.516628 0.856210i \(-0.672813\pi\)
−0.516628 + 0.856210i \(0.672813\pi\)
\(912\) 0 0
\(913\) −0.387907 0.671874i −0.0128378 0.0222358i
\(914\) −3.19386 + 5.53192i −0.105643 + 0.182980i
\(915\) 0 0
\(916\) −3.95516 2.28351i −0.130682 0.0754493i
\(917\) 26.1910 + 15.1214i 0.864903 + 0.499352i
\(918\) 0 0
\(919\) 25.9610 44.9658i 0.856374 1.48328i −0.0189904 0.999820i \(-0.506045\pi\)
0.875364 0.483464i \(-0.160621\pi\)
\(920\) −9.34356 16.1835i −0.308048 0.533555i
\(921\) 0 0
\(922\) 30.8707 1.01667
\(923\) −11.7110 + 25.4296i −0.385474 + 0.837026i
\(924\) 0 0
\(925\) 0.0219955 0.0126991i 0.000723209 0.000417545i
\(926\) 24.0059 + 41.5794i 0.788882 + 1.36638i
\(927\) 0 0
\(928\) 1.96117i 0.0643784i
\(929\) 17.7462 + 10.2457i 0.582232 + 0.336152i 0.762020 0.647553i \(-0.224208\pi\)
−0.179788 + 0.983705i \(0.557541\pi\)
\(930\) 0 0
\(931\) 93.4231i 3.06182i
\(932\) −2.50662 + 4.34159i −0.0821070 + 0.142213i
\(933\) 0 0
\(934\) −30.2771 + 17.4805i −0.990698 + 0.571980i
\(935\) 3.80584 0.124464
\(936\) 0 0
\(937\) −39.6806 −1.29631 −0.648154 0.761510i \(-0.724459\pi\)
−0.648154 + 0.761510i \(0.724459\pi\)
\(938\) −32.3399 + 18.6714i −1.05593 + 0.609644i
\(939\) 0 0
\(940\) −0.770886 + 1.33521i −0.0251435 + 0.0435499i
\(941\) 19.6189i 0.639557i 0.947492 + 0.319779i \(0.103609\pi\)
−0.947492 + 0.319779i \(0.896391\pi\)
\(942\) 0 0
\(943\) 1.64427 + 0.949318i 0.0535447 + 0.0309140i
\(944\) 38.5309i 1.25408i
\(945\) 0 0
\(946\) 2.84583 + 4.92912i 0.0925259 + 0.160260i
\(947\) 49.5474 28.6062i 1.61007 0.929576i 0.620721 0.784032i \(-0.286840\pi\)
0.989352 0.145544i \(-0.0464933\pi\)
\(948\) 0 0
\(949\) −36.2936 + 3.34935i −1.17814 + 0.108725i
\(950\) 8.57233 0.278123
\(951\) 0 0
\(952\) −22.6517 39.2339i −0.734146 1.27158i
\(953\) −13.7385 + 23.7958i −0.445033 + 0.770820i −0.998055 0.0623470i \(-0.980141\pi\)
0.553021 + 0.833167i \(0.313475\pi\)
\(954\) 0 0
\(955\) 3.35793 + 1.93870i 0.108660 + 0.0627350i
\(956\) −3.05170 1.76190i −0.0986991 0.0569840i
\(957\) 0 0
\(958\) −3.86988 + 6.70283i −0.125030 + 0.216559i
\(959\) −39.3527 68.1609i −1.27077 2.20103i
\(960\) 0 0
\(961\) 28.8564 0.930852
\(962\) 0.124393 + 0.0572867i 0.00401061 + 0.00184700i
\(963\) 0 0
\(964\) −1.92391 + 1.11077i −0.0619649 + 0.0357755i
\(965\) −0.626972 1.08595i −0.0201829 0.0349579i
\(966\) 0 0
\(967\) 10.3643i 0.333293i −0.986017 0.166647i \(-0.946706\pi\)
0.986017 0.166647i \(-0.0532939\pi\)
\(968\) 22.5114 + 12.9970i 0.723544 + 0.417738i
\(969\) 0 0
\(970\) 5.14261i 0.165119i
\(971\) 20.8758 36.1579i 0.669935 1.16036i −0.307987 0.951391i \(-0.599655\pi\)
0.977922 0.208971i \(-0.0670113\pi\)
\(972\) 0 0
\(973\) −28.5308 + 16.4723i −0.914656 + 0.528077i
\(974\) 46.0212 1.47461
\(975\) 0 0
\(976\) −27.9929 −0.896030
\(977\) 11.9458 6.89691i 0.382180 0.220652i −0.296586 0.955006i \(-0.595848\pi\)
0.678766 + 0.734354i \(0.262515\pi\)
\(978\) 0 0
\(979\) −7.22187 + 12.5087i −0.230812 + 0.399778i
\(980\) 3.85527i 0.123152i
\(981\) 0 0
\(982\) 46.3641 + 26.7683i 1.47954 + 0.854212i
\(983\) 37.9997i 1.21200i 0.795463 + 0.606002i \(0.207227\pi\)
−0.795463 + 0.606002i \(0.792773\pi\)
\(984\) 0 0
\(985\) 7.64098 + 13.2346i 0.243462 + 0.421688i
\(986\) 6.78988 3.92014i 0.216234 0.124843i
\(987\) 0 0
\(988\) 2.82306 + 3.99119i 0.0898134 + 0.126977i
\(989\) 25.2176 0.801873
\(990\) 0 0
\(991\) 26.2765 + 45.5122i 0.834700 + 1.44574i 0.894275 + 0.447519i \(0.147692\pi\)
−0.0595748 + 0.998224i \(0.518974\pi\)
\(992\) 0.974602 1.68806i 0.0309436 0.0535960i
\(993\) 0 0
\(994\) 48.5419 + 28.0257i 1.53966 + 0.888920i
\(995\) 11.4572 + 6.61480i 0.363217 + 0.209703i
\(996\) 0 0
\(997\) −9.29497 + 16.0994i −0.294375 + 0.509872i −0.974839 0.222909i \(-0.928445\pi\)
0.680465 + 0.732781i \(0.261778\pi\)
\(998\) 21.6079 + 37.4260i 0.683986 + 1.18470i
\(999\) 0 0
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 585.2.bu.c.361.1 8
3.2 odd 2 65.2.m.a.36.4 8
12.11 even 2 1040.2.da.b.881.3 8
13.2 odd 12 7605.2.a.cj.1.1 4
13.4 even 6 inner 585.2.bu.c.316.1 8
13.11 odd 12 7605.2.a.cf.1.4 4
15.2 even 4 325.2.m.b.49.4 8
15.8 even 4 325.2.m.c.49.1 8
15.14 odd 2 325.2.n.d.101.1 8
39.2 even 12 845.2.a.l.1.4 4
39.5 even 4 845.2.e.n.146.1 8
39.8 even 4 845.2.e.m.146.4 8
39.11 even 12 845.2.a.m.1.1 4
39.17 odd 6 65.2.m.a.56.4 yes 8
39.20 even 12 845.2.e.m.191.4 8
39.23 odd 6 845.2.c.g.506.2 8
39.29 odd 6 845.2.c.g.506.7 8
39.32 even 12 845.2.e.n.191.1 8
39.35 odd 6 845.2.m.g.316.1 8
39.38 odd 2 845.2.m.g.361.1 8
156.95 even 6 1040.2.da.b.641.3 8
195.17 even 12 325.2.m.c.199.1 8
195.89 even 12 4225.2.a.bi.1.4 4
195.119 even 12 4225.2.a.bl.1.1 4
195.134 odd 6 325.2.n.d.251.1 8
195.173 even 12 325.2.m.b.199.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.m.a.36.4 8 3.2 odd 2
65.2.m.a.56.4 yes 8 39.17 odd 6
325.2.m.b.49.4 8 15.2 even 4
325.2.m.b.199.4 8 195.173 even 12
325.2.m.c.49.1 8 15.8 even 4
325.2.m.c.199.1 8 195.17 even 12
325.2.n.d.101.1 8 15.14 odd 2
325.2.n.d.251.1 8 195.134 odd 6
585.2.bu.c.316.1 8 13.4 even 6 inner
585.2.bu.c.361.1 8 1.1 even 1 trivial
845.2.a.l.1.4 4 39.2 even 12
845.2.a.m.1.1 4 39.11 even 12
845.2.c.g.506.2 8 39.23 odd 6
845.2.c.g.506.7 8 39.29 odd 6
845.2.e.m.146.4 8 39.8 even 4
845.2.e.m.191.4 8 39.20 even 12
845.2.e.n.146.1 8 39.5 even 4
845.2.e.n.191.1 8 39.32 even 12
845.2.m.g.316.1 8 39.35 odd 6
845.2.m.g.361.1 8 39.38 odd 2
1040.2.da.b.641.3 8 156.95 even 6
1040.2.da.b.881.3 8 12.11 even 2
4225.2.a.bi.1.4 4 195.89 even 12
4225.2.a.bl.1.1 4 195.119 even 12
7605.2.a.cf.1.4 4 13.11 odd 12
7605.2.a.cj.1.1 4 13.2 odd 12