Properties

Label 252.2.bf.f.19.2
Level $252$
Weight $2$
Character 252.19
Analytic conductor $2.012$
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] = [252,2,Mod(19,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bf (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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.562828176.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(1.40376 - 0.171630i\) of defining polynomial
Character \(\chi\) \(=\) 252.19
Dual form 252.2.bf.f.199.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.553244 + 1.30151i) q^{2} +(-1.38784 - 1.44010i) q^{4} +(-0.834598 - 0.481855i) q^{5} +(1.20103 - 2.35744i) q^{7} +(2.64212 - 1.00956i) q^{8} +O(q^{10})\) \(q+(-0.553244 + 1.30151i) q^{2} +(-1.38784 - 1.44010i) q^{4} +(-0.834598 - 0.481855i) q^{5} +(1.20103 - 2.35744i) q^{7} +(2.64212 - 1.00956i) q^{8} +(1.08887 - 0.819652i) q^{10} +(4.74861 - 2.74161i) q^{11} +3.75117i q^{13} +(2.40376 + 2.86739i) q^{14} +(-0.147789 + 3.99727i) q^{16} +(0.594545 - 0.343260i) q^{17} +(2.44109 - 4.22809i) q^{19} +(0.464369 + 1.87065i) q^{20} +(0.941086 + 7.69713i) q^{22} +(-1.07465 - 0.620450i) q^{23} +(-2.03563 - 3.52582i) q^{25} +(-4.88217 - 2.07531i) q^{26} +(-5.06180 + 1.54214i) q^{28} +2.48011 q^{29} +(2.41401 + 4.18119i) q^{31} +(-5.12071 - 2.40381i) q^{32} +(0.117828 + 0.963711i) q^{34} +(-2.13832 + 1.38879i) q^{35} +(1.36643 - 2.36673i) q^{37} +(4.15237 + 5.51625i) q^{38} +(-2.69157 - 0.430544i) q^{40} +9.42976i q^{41} -5.97437i q^{43} +(-10.5385 - 3.03356i) q^{44} +(1.40207 - 1.05541i) q^{46} +(-1.80752 + 3.13072i) q^{47} +(-4.11504 - 5.66272i) q^{49} +(5.71508 - 0.698752i) q^{50} +(5.40207 - 5.20603i) q^{52} +(-2.04757 - 3.54650i) q^{53} -5.28424 q^{55} +(0.793298 - 7.44115i) q^{56} +(-1.37210 + 3.22788i) q^{58} +(-6.34315 - 10.9867i) q^{59} +(9.01711 + 5.20603i) q^{61} +(-6.77738 + 0.828634i) q^{62} +(5.96158 - 5.33475i) q^{64} +(1.80752 - 3.13072i) q^{65} +(-8.17396 + 4.71924i) q^{67} +(-1.31946 - 0.379814i) q^{68} +(-0.624505 - 3.55138i) q^{70} +10.1163i q^{71} +(-5.76850 + 3.33044i) q^{73} +(2.32435 + 3.08781i) q^{74} +(-9.47672 + 2.35250i) q^{76} +(-0.759946 - 14.4873i) q^{77} +(-1.22492 - 0.707208i) q^{79} +(2.04945 - 3.26490i) q^{80} +(-12.2729 - 5.21696i) q^{82} +0.543780 q^{83} -0.661608 q^{85} +(7.77568 + 3.30528i) q^{86} +(9.77857 - 12.0377i) q^{88} +(-0.480107 - 0.277190i) q^{89} +(8.84315 + 4.50528i) q^{91} +(0.597935 + 2.40870i) q^{92} +(-3.07465 - 4.08455i) q^{94} +(-4.07465 + 2.35250i) q^{95} +10.8747i q^{97} +(9.64670 - 2.22289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.553244 + 1.30151i −0.391203 + 0.920305i
\(3\) 0 0
\(4\) −1.38784 1.44010i −0.693921 0.720051i
\(5\) −0.834598 0.481855i −0.373244 0.215492i 0.301631 0.953425i \(-0.402469\pi\)
−0.674875 + 0.737932i \(0.735802\pi\)
\(6\) 0 0
\(7\) 1.20103 2.35744i 0.453948 0.891028i
\(8\) 2.64212 1.00956i 0.934130 0.356933i
\(9\) 0 0
\(10\) 1.08887 0.819652i 0.344332 0.259197i
\(11\) 4.74861 2.74161i 1.43176 0.826626i 0.434504 0.900670i \(-0.356924\pi\)
0.997255 + 0.0740437i \(0.0235904\pi\)
\(12\) 0 0
\(13\) 3.75117i 1.04039i 0.854048 + 0.520193i \(0.174140\pi\)
−0.854048 + 0.520193i \(0.825860\pi\)
\(14\) 2.40376 + 2.86739i 0.642432 + 0.766343i
\(15\) 0 0
\(16\) −0.147789 + 3.99727i −0.0369471 + 0.999317i
\(17\) 0.594545 0.343260i 0.144198 0.0832529i −0.426165 0.904645i \(-0.640136\pi\)
0.570363 + 0.821393i \(0.306802\pi\)
\(18\) 0 0
\(19\) 2.44109 4.22809i 0.560024 0.969989i −0.437470 0.899233i \(-0.644125\pi\)
0.997494 0.0707563i \(-0.0225413\pi\)
\(20\) 0.464369 + 1.87065i 0.103836 + 0.418289i
\(21\) 0 0
\(22\) 0.941086 + 7.69713i 0.200640 + 1.64103i
\(23\) −1.07465 0.620450i −0.224080 0.129373i 0.383758 0.923434i \(-0.374630\pi\)
−0.607838 + 0.794061i \(0.707963\pi\)
\(24\) 0 0
\(25\) −2.03563 3.52582i −0.407126 0.705163i
\(26\) −4.88217 2.07531i −0.957473 0.407002i
\(27\) 0 0
\(28\) −5.06180 + 1.54214i −0.956590 + 0.291438i
\(29\) 2.48011 0.460544 0.230272 0.973126i \(-0.426038\pi\)
0.230272 + 0.973126i \(0.426038\pi\)
\(30\) 0 0
\(31\) 2.41401 + 4.18119i 0.433569 + 0.750963i 0.997178 0.0750787i \(-0.0239208\pi\)
−0.563609 + 0.826042i \(0.690587\pi\)
\(32\) −5.12071 2.40381i −0.905222 0.424938i
\(33\) 0 0
\(34\) 0.117828 + 0.963711i 0.0202073 + 0.165275i
\(35\) −2.13832 + 1.38879i −0.361443 + 0.234748i
\(36\) 0 0
\(37\) 1.36643 2.36673i 0.224640 0.389089i −0.731571 0.681765i \(-0.761213\pi\)
0.956212 + 0.292677i \(0.0945459\pi\)
\(38\) 4.15237 + 5.51625i 0.673603 + 0.894855i
\(39\) 0 0
\(40\) −2.69157 0.430544i −0.425574 0.0680749i
\(41\) 9.42976i 1.47268i 0.676611 + 0.736340i \(0.263448\pi\)
−0.676611 + 0.736340i \(0.736552\pi\)
\(42\) 0 0
\(43\) 5.97437i 0.911083i −0.890215 0.455541i \(-0.849446\pi\)
0.890215 0.455541i \(-0.150554\pi\)
\(44\) −10.5385 3.03356i −1.58874 0.457326i
\(45\) 0 0
\(46\) 1.40207 1.05541i 0.206723 0.155611i
\(47\) −1.80752 + 3.13072i −0.263654 + 0.456662i −0.967210 0.253978i \(-0.918261\pi\)
0.703556 + 0.710640i \(0.251594\pi\)
\(48\) 0 0
\(49\) −4.11504 5.66272i −0.587863 0.808960i
\(50\) 5.71508 0.698752i 0.808234 0.0988184i
\(51\) 0 0
\(52\) 5.40207 5.20603i 0.749132 0.721946i
\(53\) −2.04757 3.54650i −0.281256 0.487150i 0.690438 0.723391i \(-0.257418\pi\)
−0.971694 + 0.236242i \(0.924084\pi\)
\(54\) 0 0
\(55\) −5.28424 −0.712526
\(56\) 0.793298 7.44115i 0.106009 0.994365i
\(57\) 0 0
\(58\) −1.37210 + 3.22788i −0.180166 + 0.423841i
\(59\) −6.34315 10.9867i −0.825808 1.43034i −0.901300 0.433195i \(-0.857386\pi\)
0.0754923 0.997146i \(-0.475947\pi\)
\(60\) 0 0
\(61\) 9.01711 + 5.20603i 1.15452 + 0.666564i 0.949985 0.312295i \(-0.101098\pi\)
0.204537 + 0.978859i \(0.434431\pi\)
\(62\) −6.77738 + 0.828634i −0.860728 + 0.105237i
\(63\) 0 0
\(64\) 5.96158 5.33475i 0.745198 0.666843i
\(65\) 1.80752 3.13072i 0.224195 0.388318i
\(66\) 0 0
\(67\) −8.17396 + 4.71924i −0.998608 + 0.576546i −0.907836 0.419325i \(-0.862267\pi\)
−0.0907716 + 0.995872i \(0.528933\pi\)
\(68\) −1.31946 0.379814i −0.160009 0.0460592i
\(69\) 0 0
\(70\) −0.624505 3.55138i −0.0746427 0.424472i
\(71\) 10.1163i 1.20058i 0.799782 + 0.600291i \(0.204948\pi\)
−0.799782 + 0.600291i \(0.795052\pi\)
\(72\) 0 0
\(73\) −5.76850 + 3.33044i −0.675152 + 0.389799i −0.798026 0.602623i \(-0.794122\pi\)
0.122874 + 0.992422i \(0.460789\pi\)
\(74\) 2.32435 + 3.08781i 0.270200 + 0.358950i
\(75\) 0 0
\(76\) −9.47672 + 2.35250i −1.08705 + 0.269850i
\(77\) −0.759946 14.4873i −0.0866039 1.65098i
\(78\) 0 0
\(79\) −1.22492 0.707208i −0.137814 0.0795671i 0.429508 0.903063i \(-0.358687\pi\)
−0.567322 + 0.823496i \(0.692020\pi\)
\(80\) 2.04945 3.26490i 0.229135 0.365027i
\(81\) 0 0
\(82\) −12.2729 5.21696i −1.35531 0.576117i
\(83\) 0.543780 0.0596876 0.0298438 0.999555i \(-0.490499\pi\)
0.0298438 + 0.999555i \(0.490499\pi\)
\(84\) 0 0
\(85\) −0.661608 −0.0717614
\(86\) 7.77568 + 3.30528i 0.838474 + 0.356418i
\(87\) 0 0
\(88\) 9.77857 12.0377i 1.04240 1.28322i
\(89\) −0.480107 0.277190i −0.0508912 0.0293821i 0.474339 0.880343i \(-0.342687\pi\)
−0.525230 + 0.850960i \(0.676021\pi\)
\(90\) 0 0
\(91\) 8.84315 + 4.50528i 0.927014 + 0.472281i
\(92\) 0.597935 + 2.40870i 0.0623390 + 0.251124i
\(93\) 0 0
\(94\) −3.07465 4.08455i −0.317126 0.421289i
\(95\) −4.07465 + 2.35250i −0.418050 + 0.241362i
\(96\) 0 0
\(97\) 10.8747i 1.10416i 0.833790 + 0.552081i \(0.186166\pi\)
−0.833790 + 0.552081i \(0.813834\pi\)
\(98\) 9.64670 2.22289i 0.974464 0.224546i
\(99\) 0 0
\(100\) −2.25240 + 7.82479i −0.225240 + 0.782479i
\(101\) −12.4972 + 7.21527i −1.24352 + 0.717946i −0.969809 0.243866i \(-0.921584\pi\)
−0.273710 + 0.961812i \(0.588251\pi\)
\(102\) 0 0
\(103\) −7.51235 + 13.0118i −0.740214 + 1.28209i 0.212184 + 0.977230i \(0.431942\pi\)
−0.952398 + 0.304858i \(0.901391\pi\)
\(104\) 3.78702 + 9.91103i 0.371348 + 0.971857i
\(105\) 0 0
\(106\) 5.74861 0.702851i 0.558354 0.0682669i
\(107\) 10.4925 + 6.05782i 1.01434 + 0.585632i 0.912461 0.409165i \(-0.134180\pi\)
0.101883 + 0.994796i \(0.467513\pi\)
\(108\) 0 0
\(109\) 3.03563 + 5.25787i 0.290761 + 0.503612i 0.973990 0.226592i \(-0.0727583\pi\)
−0.683229 + 0.730204i \(0.739425\pi\)
\(110\) 2.92347 6.87747i 0.278742 0.655741i
\(111\) 0 0
\(112\) 9.24582 + 5.14925i 0.873648 + 0.486559i
\(113\) 7.37939 0.694194 0.347097 0.937829i \(-0.387167\pi\)
0.347097 + 0.937829i \(0.387167\pi\)
\(114\) 0 0
\(115\) 0.597935 + 1.03565i 0.0557577 + 0.0965752i
\(116\) −3.44200 3.57161i −0.319581 0.331615i
\(117\) 0 0
\(118\) 17.8085 2.17735i 1.63941 0.200442i
\(119\) −0.0951483 1.81387i −0.00872223 0.166277i
\(120\) 0 0
\(121\) 9.53284 16.5114i 0.866622 1.50103i
\(122\) −11.7643 + 8.85562i −1.06509 + 0.801751i
\(123\) 0 0
\(124\) 2.67107 9.27924i 0.239869 0.833301i
\(125\) 8.74207i 0.781915i
\(126\) 0 0
\(127\) 11.6431i 1.03316i 0.856240 + 0.516578i \(0.172794\pi\)
−0.856240 + 0.516578i \(0.827206\pi\)
\(128\) 3.64500 + 10.7105i 0.322176 + 0.946680i
\(129\) 0 0
\(130\) 3.07465 + 4.08455i 0.269665 + 0.358239i
\(131\) 4.63078 8.02074i 0.404593 0.700776i −0.589681 0.807636i \(-0.700747\pi\)
0.994274 + 0.106861i \(0.0340798\pi\)
\(132\) 0 0
\(133\) −7.03563 10.8328i −0.610067 0.939321i
\(134\) −1.61993 13.2494i −0.139940 1.14457i
\(135\) 0 0
\(136\) 1.22432 1.50716i 0.104984 0.129238i
\(137\) 3.61504 + 6.26144i 0.308854 + 0.534951i 0.978112 0.208080i \(-0.0667213\pi\)
−0.669258 + 0.743030i \(0.733388\pi\)
\(138\) 0 0
\(139\) 5.30812 0.450229 0.225115 0.974332i \(-0.427724\pi\)
0.225115 + 0.974332i \(0.427724\pi\)
\(140\) 4.96766 + 1.15198i 0.419844 + 0.0973604i
\(141\) 0 0
\(142\) −13.1664 5.59677i −1.10490 0.469671i
\(143\) 10.2842 + 17.8128i 0.860011 + 1.48958i
\(144\) 0 0
\(145\) −2.06989 1.19505i −0.171895 0.0992438i
\(146\) −1.14321 9.35029i −0.0946127 0.773836i
\(147\) 0 0
\(148\) −5.30473 + 1.31685i −0.436046 + 0.108244i
\(149\) 2.33080 4.03707i 0.190947 0.330730i −0.754617 0.656165i \(-0.772178\pi\)
0.945564 + 0.325435i \(0.105511\pi\)
\(150\) 0 0
\(151\) 10.5709 6.10309i 0.860244 0.496662i −0.00384988 0.999993i \(-0.501225\pi\)
0.864094 + 0.503330i \(0.167892\pi\)
\(152\) 2.18114 13.6355i 0.176914 1.10599i
\(153\) 0 0
\(154\) 19.2758 + 7.02594i 1.55329 + 0.566167i
\(155\) 4.65281i 0.373723i
\(156\) 0 0
\(157\) −18.9944 + 10.9664i −1.51592 + 0.875217i −0.516095 + 0.856531i \(0.672615\pi\)
−0.999825 + 0.0186856i \(0.994052\pi\)
\(158\) 1.59812 1.20298i 0.127139 0.0957042i
\(159\) 0 0
\(160\) 3.11545 + 4.47366i 0.246298 + 0.353674i
\(161\) −2.75337 + 1.78824i −0.216996 + 0.140933i
\(162\) 0 0
\(163\) −3.48011 2.00924i −0.272583 0.157376i 0.357478 0.933922i \(-0.383637\pi\)
−0.630061 + 0.776546i \(0.716970\pi\)
\(164\) 13.5798 13.0870i 1.06041 1.02192i
\(165\) 0 0
\(166\) −0.300843 + 0.707734i −0.0233499 + 0.0549308i
\(167\) −14.7178 −1.13890 −0.569448 0.822027i \(-0.692843\pi\)
−0.569448 + 0.822027i \(0.692843\pi\)
\(168\) 0 0
\(169\) −1.07126 −0.0824047
\(170\) 0.366030 0.861087i 0.0280733 0.0660424i
\(171\) 0 0
\(172\) −8.60370 + 8.29148i −0.656026 + 0.632219i
\(173\) 10.0918 + 5.82648i 0.767262 + 0.442979i 0.831897 0.554930i \(-0.187255\pi\)
−0.0646349 + 0.997909i \(0.520588\pi\)
\(174\) 0 0
\(175\) −10.7568 + 0.564256i −0.813134 + 0.0426538i
\(176\) 10.2572 + 19.3866i 0.773163 + 1.46132i
\(177\) 0 0
\(178\) 0.626381 0.471509i 0.0469492 0.0353411i
\(179\) 2.24663 1.29709i 0.167921 0.0969494i −0.413684 0.910421i \(-0.635758\pi\)
0.581605 + 0.813471i \(0.302425\pi\)
\(180\) 0 0
\(181\) 9.53343i 0.708615i −0.935129 0.354307i \(-0.884717\pi\)
0.935129 0.354307i \(-0.115283\pi\)
\(182\) −10.7561 + 9.01691i −0.797293 + 0.668378i
\(183\) 0 0
\(184\) −3.46574 0.554380i −0.255498 0.0408694i
\(185\) −2.28085 + 1.31685i −0.167691 + 0.0968166i
\(186\) 0 0
\(187\) 1.88217 3.26002i 0.137638 0.238396i
\(188\) 7.01711 1.74193i 0.511775 0.127043i
\(189\) 0 0
\(190\) −0.807521 6.60470i −0.0585837 0.479155i
\(191\) −7.21637 4.16637i −0.522158 0.301468i 0.215659 0.976469i \(-0.430810\pi\)
−0.737817 + 0.675001i \(0.764143\pi\)
\(192\) 0 0
\(193\) 6.18630 + 10.7150i 0.445300 + 0.771282i 0.998073 0.0620498i \(-0.0197638\pi\)
−0.552773 + 0.833332i \(0.686430\pi\)
\(194\) −14.1536 6.01639i −1.01617 0.431951i
\(195\) 0 0
\(196\) −2.44387 + 13.7850i −0.174562 + 0.984646i
\(197\) −3.23686 −0.230617 −0.115308 0.993330i \(-0.536786\pi\)
−0.115308 + 0.993330i \(0.536786\pi\)
\(198\) 0 0
\(199\) −9.61504 16.6537i −0.681592 1.18055i −0.974495 0.224410i \(-0.927955\pi\)
0.292903 0.956142i \(-0.405379\pi\)
\(200\) −8.93790 7.26054i −0.632005 0.513397i
\(201\) 0 0
\(202\) −2.47672 20.2570i −0.174261 1.42528i
\(203\) 2.97869 5.84670i 0.209063 0.410358i
\(204\) 0 0
\(205\) 4.54378 7.87006i 0.317351 0.549669i
\(206\) −12.7787 16.9761i −0.890338 1.18278i
\(207\) 0 0
\(208\) −14.9944 0.554380i −1.03968 0.0384393i
\(209\) 26.7700i 1.85172i
\(210\) 0 0
\(211\) 9.24637i 0.636546i −0.947999 0.318273i \(-0.896897\pi\)
0.947999 0.318273i \(-0.103103\pi\)
\(212\) −2.26562 + 7.87070i −0.155603 + 0.540562i
\(213\) 0 0
\(214\) −13.6892 + 10.3046i −0.935773 + 0.704405i
\(215\) −2.87878 + 4.98620i −0.196331 + 0.340056i
\(216\) 0 0
\(217\) 12.7562 0.669139i 0.865947 0.0454241i
\(218\) −8.52260 + 1.04201i −0.577223 + 0.0705740i
\(219\) 0 0
\(220\) 7.33369 + 7.60984i 0.494437 + 0.513055i
\(221\) 1.28763 + 2.23024i 0.0866152 + 0.150022i
\(222\) 0 0
\(223\) 1.94585 0.130303 0.0651517 0.997875i \(-0.479247\pi\)
0.0651517 + 0.997875i \(0.479247\pi\)
\(224\) −11.8170 + 9.18471i −0.789556 + 0.613679i
\(225\) 0 0
\(226\) −4.08260 + 9.60432i −0.271571 + 0.638870i
\(227\) −4.32265 7.48706i −0.286905 0.496933i 0.686165 0.727446i \(-0.259293\pi\)
−0.973069 + 0.230513i \(0.925960\pi\)
\(228\) 0 0
\(229\) 14.5396 + 8.39446i 0.960805 + 0.554721i 0.896421 0.443204i \(-0.146158\pi\)
0.0643846 + 0.997925i \(0.479492\pi\)
\(230\) −1.67871 + 0.205247i −0.110691 + 0.0135336i
\(231\) 0 0
\(232\) 6.55274 2.50381i 0.430208 0.164383i
\(233\) −0.523283 + 0.906353i −0.0342814 + 0.0593772i −0.882657 0.470018i \(-0.844248\pi\)
0.848376 + 0.529395i \(0.177581\pi\)
\(234\) 0 0
\(235\) 3.01711 1.74193i 0.196814 0.113631i
\(236\) −7.01862 + 24.3825i −0.456873 + 1.58717i
\(237\) 0 0
\(238\) 2.41340 + 0.879676i 0.156438 + 0.0570210i
\(239\) 19.2479i 1.24505i −0.782602 0.622523i \(-0.786108\pi\)
0.782602 0.622523i \(-0.213892\pi\)
\(240\) 0 0
\(241\) −2.38754 + 1.37844i −0.153795 + 0.0887934i −0.574922 0.818208i \(-0.694968\pi\)
0.421128 + 0.907001i \(0.361634\pi\)
\(242\) 16.2157 + 21.5419i 1.04238 + 1.38476i
\(243\) 0 0
\(244\) −5.01711 20.2107i −0.321187 1.29386i
\(245\) 0.705792 + 6.70895i 0.0450914 + 0.428619i
\(246\) 0 0
\(247\) 15.8603 + 9.15692i 1.00916 + 0.582641i
\(248\) 10.5992 + 8.61011i 0.673053 + 0.546742i
\(249\) 0 0
\(250\) −11.3779 4.83650i −0.719600 0.305887i
\(251\) 20.7493 1.30968 0.654841 0.755767i \(-0.272736\pi\)
0.654841 + 0.755767i \(0.272736\pi\)
\(252\) 0 0
\(253\) −6.80413 −0.427772
\(254\) −15.1536 6.44147i −0.950819 0.404173i
\(255\) 0 0
\(256\) −15.9563 1.18150i −0.997270 0.0738438i
\(257\) −6.45283 3.72554i −0.402516 0.232393i 0.285053 0.958512i \(-0.407989\pi\)
−0.687569 + 0.726119i \(0.741322\pi\)
\(258\) 0 0
\(259\) −3.93830 6.06381i −0.244714 0.376787i
\(260\) −7.01711 + 1.74193i −0.435182 + 0.108030i
\(261\) 0 0
\(262\) 7.87711 + 10.4644i 0.486649 + 0.646494i
\(263\) −25.7034 + 14.8399i −1.58494 + 0.915066i −0.590818 + 0.806805i \(0.701195\pi\)
−0.994123 + 0.108260i \(0.965472\pi\)
\(264\) 0 0
\(265\) 3.94654i 0.242434i
\(266\) 17.9914 3.16375i 1.10312 0.193982i
\(267\) 0 0
\(268\) 18.1403 + 5.22178i 1.10810 + 0.318971i
\(269\) 3.73727 2.15771i 0.227865 0.131558i −0.381722 0.924277i \(-0.624669\pi\)
0.609587 + 0.792719i \(0.291335\pi\)
\(270\) 0 0
\(271\) 6.79142 11.7631i 0.412550 0.714557i −0.582618 0.812746i \(-0.697972\pi\)
0.995168 + 0.0981892i \(0.0313050\pi\)
\(272\) 1.28424 + 2.42728i 0.0778683 + 0.147176i
\(273\) 0 0
\(274\) −10.1493 + 1.24090i −0.613142 + 0.0749656i
\(275\) −19.3328 11.1618i −1.16581 0.673082i
\(276\) 0 0
\(277\) −1.03563 1.79376i −0.0622250 0.107777i 0.833235 0.552920i \(-0.186486\pi\)
−0.895460 + 0.445143i \(0.853153\pi\)
\(278\) −2.93669 + 6.90856i −0.176131 + 0.414348i
\(279\) 0 0
\(280\) −4.24764 + 5.82811i −0.253845 + 0.348296i
\(281\) −23.7122 −1.41455 −0.707276 0.706938i \(-0.750076\pi\)
−0.707276 + 0.706938i \(0.750076\pi\)
\(282\) 0 0
\(283\) −6.12739 10.6129i −0.364235 0.630874i 0.624418 0.781091i \(-0.285336\pi\)
−0.988653 + 0.150216i \(0.952003\pi\)
\(284\) 14.5685 14.0398i 0.864480 0.833109i
\(285\) 0 0
\(286\) −28.8732 + 3.53017i −1.70731 + 0.208743i
\(287\) 22.2301 + 11.3254i 1.31220 + 0.668520i
\(288\) 0 0
\(289\) −8.26434 + 14.3143i −0.486138 + 0.842016i
\(290\) 2.70053 2.03282i 0.158580 0.119372i
\(291\) 0 0
\(292\) 12.8019 + 3.68510i 0.749177 + 0.215654i
\(293\) 10.7090i 0.625626i 0.949815 + 0.312813i \(0.101271\pi\)
−0.949815 + 0.312813i \(0.898729\pi\)
\(294\) 0 0
\(295\) 12.2259i 0.711821i
\(296\) 1.22093 7.63269i 0.0709649 0.443641i
\(297\) 0 0
\(298\) 3.96477 + 5.26704i 0.229673 + 0.305112i
\(299\) 2.32741 4.03120i 0.134598 0.233130i
\(300\) 0 0
\(301\) −14.0842 7.17541i −0.811801 0.413584i
\(302\) 2.09495 + 17.1345i 0.120551 + 0.985982i
\(303\) 0 0
\(304\) 16.5400 + 10.3825i 0.948636 + 0.595480i
\(305\) −5.01711 8.68988i −0.287279 0.497581i
\(306\) 0 0
\(307\) 4.22056 0.240880 0.120440 0.992721i \(-0.461569\pi\)
0.120440 + 0.992721i \(0.461569\pi\)
\(308\) −19.8085 + 21.2005i −1.12870 + 1.20801i
\(309\) 0 0
\(310\) 6.05567 + 2.57414i 0.343939 + 0.146201i
\(311\) 4.85070 + 8.40165i 0.275058 + 0.476414i 0.970150 0.242507i \(-0.0779697\pi\)
−0.695092 + 0.718921i \(0.744636\pi\)
\(312\) 0 0
\(313\) 11.8328 + 6.83168i 0.668831 + 0.386149i 0.795633 0.605778i \(-0.207138\pi\)
−0.126803 + 0.991928i \(0.540472\pi\)
\(314\) −3.76434 30.7885i −0.212434 1.73750i
\(315\) 0 0
\(316\) 0.681544 + 2.74550i 0.0383398 + 0.154447i
\(317\) 10.0442 17.3970i 0.564138 0.977115i −0.432992 0.901398i \(-0.642542\pi\)
0.997129 0.0757171i \(-0.0241246\pi\)
\(318\) 0 0
\(319\) 11.7771 6.79948i 0.659388 0.380698i
\(320\) −7.54610 + 1.57975i −0.421840 + 0.0883106i
\(321\) 0 0
\(322\) −0.804130 4.57286i −0.0448124 0.254836i
\(323\) 3.35171i 0.186494i
\(324\) 0 0
\(325\) 13.2259 7.63599i 0.733642 0.423569i
\(326\) 4.54039 3.41778i 0.251469 0.189294i
\(327\) 0 0
\(328\) 9.51989 + 24.9145i 0.525648 + 1.37568i
\(329\) 5.20959 + 8.02121i 0.287214 + 0.442224i
\(330\) 0 0
\(331\) 8.15886 + 4.71052i 0.448452 + 0.258914i 0.707176 0.707037i \(-0.249969\pi\)
−0.258724 + 0.965951i \(0.583302\pi\)
\(332\) −0.754681 0.783099i −0.0414185 0.0429781i
\(333\) 0 0
\(334\) 8.14252 19.1553i 0.445539 1.04813i
\(335\) 9.09596 0.496965
\(336\) 0 0
\(337\) −13.4411 −0.732185 −0.366092 0.930578i \(-0.619305\pi\)
−0.366092 + 0.930578i \(0.619305\pi\)
\(338\) 0.592669 1.39425i 0.0322369 0.0758374i
\(339\) 0 0
\(340\) 0.918207 + 0.952783i 0.0497968 + 0.0516719i
\(341\) 22.9264 + 13.2365i 1.24153 + 0.716799i
\(342\) 0 0
\(343\) −18.2918 + 2.89985i −0.987666 + 0.156577i
\(344\) −6.03148 15.7850i −0.325195 0.851070i
\(345\) 0 0
\(346\) −13.1664 + 9.91103i −0.707831 + 0.532820i
\(347\) 19.5890 11.3097i 1.05159 0.607136i 0.128497 0.991710i \(-0.458985\pi\)
0.923094 + 0.384574i \(0.125651\pi\)
\(348\) 0 0
\(349\) 2.48180i 0.132848i −0.997791 0.0664239i \(-0.978841\pi\)
0.997791 0.0664239i \(-0.0211590\pi\)
\(350\) 5.21673 14.3122i 0.278846 0.765018i
\(351\) 0 0
\(352\) −30.9066 + 2.62423i −1.64733 + 0.139872i
\(353\) 7.89315 4.55711i 0.420110 0.242551i −0.275014 0.961440i \(-0.588683\pi\)
0.695124 + 0.718889i \(0.255349\pi\)
\(354\) 0 0
\(355\) 4.87458 8.44303i 0.258716 0.448109i
\(356\) 0.267131 + 1.07610i 0.0141579 + 0.0570331i
\(357\) 0 0
\(358\) 0.445241 + 3.64162i 0.0235317 + 0.192466i
\(359\) 6.00000 + 3.46410i 0.316668 + 0.182828i 0.649906 0.760014i \(-0.274808\pi\)
−0.333238 + 0.942843i \(0.608141\pi\)
\(360\) 0 0
\(361\) −2.41780 4.18776i −0.127253 0.220408i
\(362\) 12.4078 + 5.27431i 0.652141 + 0.277212i
\(363\) 0 0
\(364\) −5.78484 18.9877i −0.303208 0.995223i
\(365\) 6.41917 0.335995
\(366\) 0 0
\(367\) −1.91680 3.31999i −0.100056 0.173302i 0.811652 0.584142i \(-0.198569\pi\)
−0.911707 + 0.410840i \(0.865235\pi\)
\(368\) 2.63893 4.20398i 0.137564 0.219147i
\(369\) 0 0
\(370\) −0.452022 3.69708i −0.0234995 0.192202i
\(371\) −10.8199 + 0.567567i −0.561740 + 0.0294666i
\(372\) 0 0
\(373\) 13.4150 23.2355i 0.694603 1.20309i −0.275711 0.961241i \(-0.588913\pi\)
0.970314 0.241848i \(-0.0777534\pi\)
\(374\) 3.20164 + 4.25325i 0.165553 + 0.219930i
\(375\) 0 0
\(376\) −1.61504 + 10.0965i −0.0832894 + 0.520689i
\(377\) 9.30330i 0.479144i
\(378\) 0 0
\(379\) 6.93692i 0.356325i −0.984001 0.178163i \(-0.942985\pi\)
0.984001 0.178163i \(-0.0570153\pi\)
\(380\) 9.04282 + 2.60301i 0.463887 + 0.133532i
\(381\) 0 0
\(382\) 9.41497 7.08713i 0.481712 0.362609i
\(383\) −1.12881 + 1.95515i −0.0576793 + 0.0999035i −0.893423 0.449216i \(-0.851703\pi\)
0.835744 + 0.549119i \(0.185037\pi\)
\(384\) 0 0
\(385\) −6.34654 + 12.4573i −0.323450 + 0.634881i
\(386\) −17.3682 + 2.12351i −0.884017 + 0.108084i
\(387\) 0 0
\(388\) 15.6607 15.0924i 0.795054 0.766202i
\(389\) 15.3047 + 26.5086i 0.775981 + 1.34404i 0.934242 + 0.356641i \(0.116078\pi\)
−0.158261 + 0.987397i \(0.550589\pi\)
\(390\) 0 0
\(391\) −0.851904 −0.0430827
\(392\) −16.5893 10.8072i −0.837885 0.545847i
\(393\) 0 0
\(394\) 1.79078 4.21280i 0.0902179 0.212238i
\(395\) 0.681544 + 1.18047i 0.0342922 + 0.0593958i
\(396\) 0 0
\(397\) −12.0368 6.94947i −0.604112 0.348784i 0.166546 0.986034i \(-0.446739\pi\)
−0.770657 + 0.637250i \(0.780072\pi\)
\(398\) 26.9944 3.30046i 1.35311 0.165437i
\(399\) 0 0
\(400\) 14.3945 7.61589i 0.719724 0.380794i
\(401\) −5.13832 + 8.89984i −0.256596 + 0.444437i −0.965328 0.261041i \(-0.915934\pi\)
0.708732 + 0.705478i \(0.249268\pi\)
\(402\) 0 0
\(403\) −15.6843 + 9.05535i −0.781292 + 0.451079i
\(404\) 27.7349 + 7.98361i 1.37986 + 0.397199i
\(405\) 0 0
\(406\) 5.96158 + 7.11144i 0.295868 + 0.352935i
\(407\) 14.9849i 0.742775i
\(408\) 0 0
\(409\) 10.5342 6.08193i 0.520883 0.300732i −0.216413 0.976302i \(-0.569436\pi\)
0.737296 + 0.675570i \(0.236102\pi\)
\(410\) 7.72912 + 10.2678i 0.381714 + 0.507092i
\(411\) 0 0
\(412\) 29.1642 7.23973i 1.43682 0.356676i
\(413\) −33.5187 + 1.75826i −1.64935 + 0.0865182i
\(414\) 0 0
\(415\) −0.453838 0.262023i −0.0222780 0.0128622i
\(416\) 9.01711 19.2086i 0.442100 0.941781i
\(417\) 0 0
\(418\) 34.8414 + 14.8104i 1.70415 + 0.724398i
\(419\) −16.2245 −0.792619 −0.396310 0.918117i \(-0.629709\pi\)
−0.396310 + 0.918117i \(0.629709\pi\)
\(420\) 0 0
\(421\) −9.58477 −0.467133 −0.233567 0.972341i \(-0.575040\pi\)
−0.233567 + 0.972341i \(0.575040\pi\)
\(422\) 12.0342 + 5.11550i 0.585816 + 0.249019i
\(423\) 0 0
\(424\) −8.99034 7.30313i −0.436609 0.354672i
\(425\) −2.42055 1.39750i −0.117414 0.0677889i
\(426\) 0 0
\(427\) 23.1027 15.0047i 1.11802 0.726127i
\(428\) −5.83799 23.5175i −0.282190 1.13676i
\(429\) 0 0
\(430\) −4.89690 6.50534i −0.236150 0.313715i
\(431\) 0.131544 0.0759470i 0.00633626 0.00365824i −0.496829 0.867849i \(-0.665502\pi\)
0.503165 + 0.864190i \(0.332169\pi\)
\(432\) 0 0
\(433\) 9.46997i 0.455098i −0.973767 0.227549i \(-0.926929\pi\)
0.973767 0.227549i \(-0.0730711\pi\)
\(434\) −6.18640 + 16.9725i −0.296957 + 0.814705i
\(435\) 0 0
\(436\) 3.35889 11.6687i 0.160862 0.558830i
\(437\) −5.24663 + 3.02915i −0.250981 + 0.144904i
\(438\) 0 0
\(439\) −16.7373 + 28.9898i −0.798826 + 1.38361i 0.121555 + 0.992585i \(0.461212\pi\)
−0.920381 + 0.391023i \(0.872121\pi\)
\(440\) −13.9616 + 5.33475i −0.665592 + 0.254324i
\(441\) 0 0
\(442\) −3.61504 + 0.441992i −0.171950 + 0.0210234i
\(443\) 22.6513 + 13.0777i 1.07619 + 0.621341i 0.929867 0.367895i \(-0.119921\pi\)
0.146327 + 0.989236i \(0.453255\pi\)
\(444\) 0 0
\(445\) 0.267131 + 0.462684i 0.0126632 + 0.0219333i
\(446\) −1.07653 + 2.53253i −0.0509750 + 0.119919i
\(447\) 0 0
\(448\) −5.41629 20.4613i −0.255896 0.966704i
\(449\) −10.2918 −0.485701 −0.242851 0.970064i \(-0.578082\pi\)
−0.242851 + 0.970064i \(0.578082\pi\)
\(450\) 0 0
\(451\) 25.8527 + 44.7782i 1.21736 + 2.10852i
\(452\) −10.2414 10.6271i −0.481716 0.499855i
\(453\) 0 0
\(454\) 12.1359 1.48380i 0.569568 0.0696380i
\(455\) −5.20959 8.02121i −0.244229 0.376040i
\(456\) 0 0
\(457\) −5.96574 + 10.3330i −0.279065 + 0.483356i −0.971153 0.238458i \(-0.923358\pi\)
0.692087 + 0.721814i \(0.256691\pi\)
\(458\) −18.9694 + 14.2792i −0.886382 + 0.667225i
\(459\) 0 0
\(460\) 0.661608 2.29841i 0.0308476 0.107164i
\(461\) 30.0093i 1.39767i −0.715281 0.698837i \(-0.753701\pi\)
0.715281 0.698837i \(-0.246299\pi\)
\(462\) 0 0
\(463\) 13.2736i 0.616875i 0.951245 + 0.308437i \(0.0998060\pi\)
−0.951245 + 0.308437i \(0.900194\pi\)
\(464\) −0.366532 + 9.91365i −0.0170158 + 0.460230i
\(465\) 0 0
\(466\) −0.890122 1.18249i −0.0412341 0.0547778i
\(467\) −14.8246 + 25.6770i −0.686002 + 1.18819i 0.287119 + 0.957895i \(0.407303\pi\)
−0.973121 + 0.230295i \(0.926031\pi\)
\(468\) 0 0
\(469\) 1.30812 + 24.9376i 0.0604036 + 1.15151i
\(470\) 0.597935 + 4.89050i 0.0275807 + 0.225582i
\(471\) 0 0
\(472\) −27.8510 22.6243i −1.28195 1.04137i
\(473\) −16.3794 28.3699i −0.753125 1.30445i
\(474\) 0 0
\(475\) −19.8766 −0.912001
\(476\) −2.48011 + 2.65439i −0.113676 + 0.121664i
\(477\) 0 0
\(478\) 25.0513 + 10.6488i 1.14582 + 0.487065i
\(479\) 5.76773 + 9.99001i 0.263535 + 0.456455i 0.967179 0.254097i \(-0.0817784\pi\)
−0.703644 + 0.710553i \(0.748445\pi\)
\(480\) 0 0
\(481\) 8.87802 + 5.12573i 0.404803 + 0.233713i
\(482\) −0.473165 3.87001i −0.0215521 0.176274i
\(483\) 0 0
\(484\) −37.0081 + 9.18691i −1.68219 + 0.417587i
\(485\) 5.24005 9.07604i 0.237939 0.412122i
\(486\) 0 0
\(487\) −8.44822 + 4.87758i −0.382825 + 0.221024i −0.679047 0.734095i \(-0.737607\pi\)
0.296221 + 0.955119i \(0.404273\pi\)
\(488\) 29.0801 + 4.65165i 1.31639 + 0.210570i
\(489\) 0 0
\(490\) −9.12223 2.79310i −0.412100 0.126179i
\(491\) 40.4736i 1.82655i 0.407346 + 0.913274i \(0.366454\pi\)
−0.407346 + 0.913274i \(0.633546\pi\)
\(492\) 0 0
\(493\) 1.47453 0.851323i 0.0664097 0.0383416i
\(494\) −20.6924 + 15.5762i −0.930995 + 0.700808i
\(495\) 0 0
\(496\) −17.0701 + 9.03151i −0.766470 + 0.405527i
\(497\) 23.8485 + 12.1500i 1.06975 + 0.545001i
\(498\) 0 0
\(499\) −27.6827 15.9826i −1.23925 0.715480i −0.270307 0.962774i \(-0.587125\pi\)
−0.968941 + 0.247294i \(0.920459\pi\)
\(500\) 12.5895 12.1326i 0.563019 0.542587i
\(501\) 0 0
\(502\) −11.4794 + 27.0053i −0.512351 + 1.20531i
\(503\) −22.7110 −1.01263 −0.506317 0.862348i \(-0.668993\pi\)
−0.506317 + 0.862348i \(0.668993\pi\)
\(504\) 0 0
\(505\) 13.9069 0.618847
\(506\) 3.76434 8.85562i 0.167346 0.393681i
\(507\) 0 0
\(508\) 16.7672 16.1588i 0.743925 0.716929i
\(509\) 1.98947 + 1.14862i 0.0881819 + 0.0509118i 0.543443 0.839446i \(-0.317121\pi\)
−0.455261 + 0.890358i \(0.650454\pi\)
\(510\) 0 0
\(511\) 0.923166 + 17.5989i 0.0408384 + 0.778528i
\(512\) 10.3655 20.1136i 0.458093 0.888904i
\(513\) 0 0
\(514\) 8.41881 6.33727i 0.371338 0.279525i
\(515\) 12.5396 7.23973i 0.552560 0.319021i
\(516\) 0 0
\(517\) 19.8221i 0.871773i
\(518\) 10.0709 1.77096i 0.442491 0.0778114i
\(519\) 0 0
\(520\) 1.61504 10.0965i 0.0708242 0.442762i
\(521\) 32.5712 18.8050i 1.42697 0.823862i 0.430090 0.902786i \(-0.358482\pi\)
0.996881 + 0.0789240i \(0.0251485\pi\)
\(522\) 0 0
\(523\) −17.8444 + 30.9073i −0.780279 + 1.35148i 0.151500 + 0.988457i \(0.451590\pi\)
−0.931779 + 0.363026i \(0.881744\pi\)
\(524\) −17.9775 + 4.46273i −0.785350 + 0.194955i
\(525\) 0 0
\(526\) −5.09394 41.6632i −0.222106 1.81660i
\(527\) 2.87047 + 1.65727i 0.125040 + 0.0721917i
\(528\) 0 0
\(529\) −10.7301 18.5850i −0.466525 0.808046i
\(530\) −5.13645 2.18340i −0.223113 0.0948408i
\(531\) 0 0
\(532\) −5.83597 + 25.1662i −0.253021 + 1.09109i
\(533\) −35.3726 −1.53216
\(534\) 0 0
\(535\) −5.83799 10.1117i −0.252398 0.437167i
\(536\) −16.8322 + 20.7209i −0.727041 + 0.895005i
\(537\) 0 0
\(538\) 0.740657 + 6.05782i 0.0319320 + 0.261171i
\(539\) −35.0657 15.6082i −1.51039 0.672293i
\(540\) 0 0
\(541\) −18.5102 + 32.0605i −0.795814 + 1.37839i 0.126507 + 0.991966i \(0.459623\pi\)
−0.922321 + 0.386425i \(0.873710\pi\)
\(542\) 11.5524 + 15.3469i 0.496219 + 0.659208i
\(543\) 0 0
\(544\) −3.86963 + 0.328564i −0.165909 + 0.0140871i
\(545\) 5.85094i 0.250627i
\(546\) 0 0
\(547\) 2.09106i 0.0894073i −0.999000 0.0447036i \(-0.985766\pi\)
0.999000 0.0447036i \(-0.0142344\pi\)
\(548\) 4.00000 13.8959i 0.170872 0.593604i
\(549\) 0 0
\(550\) 25.2229 18.9866i 1.07551 0.809591i
\(551\) 6.05415 10.4861i 0.257916 0.446723i
\(552\) 0 0
\(553\) −3.13837 + 2.03829i −0.133457 + 0.0866771i
\(554\) 2.90755 0.355491i 0.123530 0.0151034i
\(555\) 0 0
\(556\) −7.36684 7.64424i −0.312424 0.324188i
\(557\) −8.39887 14.5473i −0.355872 0.616388i 0.631395 0.775461i \(-0.282483\pi\)
−0.987267 + 0.159073i \(0.949149\pi\)
\(558\) 0 0
\(559\) 22.4109 0.947878
\(560\) −5.23535 8.75271i −0.221234 0.369869i
\(561\) 0 0
\(562\) 13.1186 30.8616i 0.553376 1.30182i
\(563\) −8.69784 15.0651i −0.366570 0.634918i 0.622456 0.782654i \(-0.286135\pi\)
−0.989027 + 0.147736i \(0.952801\pi\)
\(564\) 0 0
\(565\) −6.15882 3.55580i −0.259104 0.149594i
\(566\) 17.2028 2.10329i 0.723086 0.0884079i
\(567\) 0 0
\(568\) 10.2130 + 26.7284i 0.428527 + 1.12150i
\(569\) −17.1425 + 29.6917i −0.718652 + 1.24474i 0.242882 + 0.970056i \(0.421907\pi\)
−0.961534 + 0.274686i \(0.911426\pi\)
\(570\) 0 0
\(571\) 5.14176 2.96860i 0.215176 0.124232i −0.388539 0.921432i \(-0.627020\pi\)
0.603715 + 0.797201i \(0.293687\pi\)
\(572\) 11.3794 39.5317i 0.475796 1.65290i
\(573\) 0 0
\(574\) −27.0388 + 22.6669i −1.12858 + 0.946097i
\(575\) 5.05203i 0.210684i
\(576\) 0 0
\(577\) 33.7930 19.5104i 1.40682 0.812229i 0.411742 0.911300i \(-0.364920\pi\)
0.995080 + 0.0990712i \(0.0315871\pi\)
\(578\) −14.0579 18.6754i −0.584732 0.776794i
\(579\) 0 0
\(580\) 1.15169 + 4.63940i 0.0478211 + 0.192641i
\(581\) 0.653097 1.28193i 0.0270950 0.0531833i
\(582\) 0 0
\(583\) −19.4462 11.2273i −0.805381 0.464987i
\(584\) −11.8788 + 14.6231i −0.491547 + 0.605107i
\(585\) 0 0
\(586\) −13.9378 5.92469i −0.575767 0.244747i
\(587\) 7.71931 0.318610 0.159305 0.987229i \(-0.449075\pi\)
0.159305 + 0.987229i \(0.449075\pi\)
\(588\) 0 0
\(589\) 23.5712 0.971235
\(590\) −15.9121 6.76392i −0.655092 0.278466i
\(591\) 0 0
\(592\) 9.25853 + 5.81178i 0.380523 + 0.238863i
\(593\) −0.336377 0.194207i −0.0138133 0.00797513i 0.493077 0.869985i \(-0.335872\pi\)
−0.506891 + 0.862010i \(0.669205\pi\)
\(594\) 0 0
\(595\) −0.794612 + 1.55970i −0.0325759 + 0.0639415i
\(596\) −9.04858 + 2.24622i −0.370644 + 0.0920088i
\(597\) 0 0
\(598\) 3.95901 + 5.25938i 0.161896 + 0.215072i
\(599\) −18.0000 + 10.3923i −0.735460 + 0.424618i −0.820416 0.571767i \(-0.806258\pi\)
0.0849563 + 0.996385i \(0.472925\pi\)
\(600\) 0 0
\(601\) 26.4110i 1.07733i −0.842521 0.538664i \(-0.818929\pi\)
0.842521 0.538664i \(-0.181071\pi\)
\(602\) 17.1309 14.3610i 0.698202 0.585309i
\(603\) 0 0
\(604\) −23.4598 6.75299i −0.954564 0.274775i
\(605\) −15.9122 + 9.18691i −0.646922 + 0.373501i
\(606\) 0 0
\(607\) 20.3531 35.2526i 0.826106 1.43086i −0.0749655 0.997186i \(-0.523885\pi\)
0.901071 0.433671i \(-0.142782\pi\)
\(608\) −22.6636 + 15.7829i −0.919131 + 0.640081i
\(609\) 0 0
\(610\) 14.0856 1.72217i 0.570310 0.0697288i
\(611\) −11.7438 6.78031i −0.475105 0.274302i
\(612\) 0 0
\(613\) −8.66920 15.0155i −0.350146 0.606470i 0.636129 0.771583i \(-0.280535\pi\)
−0.986275 + 0.165113i \(0.947201\pi\)
\(614\) −2.33500 + 5.49310i −0.0942330 + 0.221683i
\(615\) 0 0
\(616\) −16.6337 37.5100i −0.670189 1.51132i
\(617\) 46.4753 1.87103 0.935513 0.353291i \(-0.114938\pi\)
0.935513 + 0.353291i \(0.114938\pi\)
\(618\) 0 0
\(619\) 13.1911 + 22.8476i 0.530194 + 0.918322i 0.999379 + 0.0352227i \(0.0112141\pi\)
−0.469186 + 0.883099i \(0.655453\pi\)
\(620\) −6.70053 + 6.45737i −0.269100 + 0.259334i
\(621\) 0 0
\(622\) −13.6184 + 1.66505i −0.546049 + 0.0667625i
\(623\) −1.23008 + 0.798909i −0.0492822 + 0.0320076i
\(624\) 0 0
\(625\) −5.96574 + 10.3330i −0.238630 + 0.413318i
\(626\) −15.4379 + 11.6209i −0.617023 + 0.464465i
\(627\) 0 0
\(628\) 42.1541 + 12.1342i 1.68213 + 0.484209i
\(629\) 1.87617i 0.0748079i
\(630\) 0 0
\(631\) 41.0696i 1.63495i −0.575961 0.817477i \(-0.695372\pi\)
0.575961 0.817477i \(-0.304628\pi\)
\(632\) −3.95035 0.631898i −0.157137 0.0251356i
\(633\) 0 0
\(634\) 17.0855 + 22.6974i 0.678551 + 0.901428i
\(635\) 5.61028 9.71729i 0.222637 0.385619i
\(636\) 0 0
\(637\) 21.2418 15.4362i 0.841632 0.611605i
\(638\) 2.33399 + 19.0897i 0.0924037 + 0.755768i
\(639\) 0 0
\(640\) 2.11878 10.6953i 0.0837522 0.422769i
\(641\) 22.7239 + 39.3590i 0.897540 + 1.55459i 0.830629 + 0.556827i \(0.187981\pi\)
0.0669115 + 0.997759i \(0.478685\pi\)
\(642\) 0 0
\(643\) −30.5534 −1.20491 −0.602454 0.798154i \(-0.705810\pi\)
−0.602454 + 0.798154i \(0.705810\pi\)
\(644\) 6.39649 + 1.48333i 0.252057 + 0.0584513i
\(645\) 0 0
\(646\) 4.36228 + 1.85432i 0.171632 + 0.0729571i
\(647\) −18.0896 31.3321i −0.711175 1.23179i −0.964417 0.264388i \(-0.914830\pi\)
0.253242 0.967403i \(-0.418503\pi\)
\(648\) 0 0
\(649\) −60.2423 34.7809i −2.36472 1.36527i
\(650\) 2.62113 + 21.4382i 0.102809 + 0.840876i
\(651\) 0 0
\(652\) 1.93633 + 7.80022i 0.0758324 + 0.305480i
\(653\) −4.11545 + 7.12816i −0.161050 + 0.278946i −0.935245 0.354000i \(-0.884821\pi\)
0.774196 + 0.632946i \(0.218155\pi\)
\(654\) 0 0
\(655\) −7.72968 + 4.46273i −0.302024 + 0.174373i
\(656\) −37.6933 1.39361i −1.47168 0.0544114i
\(657\) 0 0
\(658\) −13.3218 + 2.34262i −0.519339 + 0.0913250i
\(659\) 22.8837i 0.891422i 0.895177 + 0.445711i \(0.147049\pi\)
−0.895177 + 0.445711i \(0.852951\pi\)
\(660\) 0 0
\(661\) −17.7212 + 10.2313i −0.689275 + 0.397953i −0.803340 0.595520i \(-0.796946\pi\)
0.114065 + 0.993473i \(0.463613\pi\)
\(662\) −10.6446 + 8.01275i −0.413715 + 0.311424i
\(663\) 0 0
\(664\) 1.43673 0.548978i 0.0557560 0.0213045i
\(665\) 0.652090 + 12.4312i 0.0252870 + 0.482060i
\(666\) 0 0
\(667\) −2.66525 1.53878i −0.103199 0.0595819i
\(668\) 20.4260 + 21.1951i 0.790304 + 0.820063i
\(669\) 0 0
\(670\) −5.03228 + 11.8385i −0.194414 + 0.457359i
\(671\) 57.0916 2.20400
\(672\) 0 0
\(673\) 4.23008 0.163058 0.0815289 0.996671i \(-0.474020\pi\)
0.0815289 + 0.996671i \(0.474020\pi\)
\(674\) 7.43622 17.4937i 0.286433 0.673833i
\(675\) 0 0
\(676\) 1.48674 + 1.54273i 0.0571824 + 0.0593356i
\(677\) −20.7962 12.0067i −0.799262 0.461454i 0.0439511 0.999034i \(-0.486005\pi\)
−0.843213 + 0.537580i \(0.819339\pi\)
\(678\) 0 0
\(679\) 25.6365 + 13.0609i 0.983840 + 0.501232i
\(680\) −1.74805 + 0.667932i −0.0670345 + 0.0256140i
\(681\) 0 0
\(682\) −29.9113 + 22.5158i −1.14536 + 0.862174i
\(683\) 7.09951 4.09890i 0.271655 0.156840i −0.357984 0.933728i \(-0.616536\pi\)
0.629640 + 0.776887i \(0.283203\pi\)
\(684\) 0 0
\(685\) 6.96771i 0.266222i
\(686\) 6.34567 25.4113i 0.242279 0.970207i
\(687\) 0 0
\(688\) 23.8812 + 0.882944i 0.910461 + 0.0336619i
\(689\) 13.3035 7.68079i 0.506824 0.292615i
\(690\) 0 0
\(691\) 17.9925 31.1638i 0.684465 1.18553i −0.289139 0.957287i \(-0.593369\pi\)
0.973605 0.228242i \(-0.0732976\pi\)
\(692\) −5.61504 22.6194i −0.213452 0.859860i
\(693\) 0 0
\(694\) 3.88217 + 31.7522i 0.147365 + 1.20530i
\(695\) −4.43015 2.55775i −0.168045 0.0970209i
\(696\) 0 0
\(697\) 3.23686 + 5.60641i 0.122605 + 0.212358i
\(698\) 3.23008 + 1.37304i 0.122260 + 0.0519704i
\(699\) 0 0
\(700\) 15.7413 + 14.7077i 0.594964 + 0.555900i
\(701\) 12.9471 0.489003 0.244502 0.969649i \(-0.421376\pi\)
0.244502 + 0.969649i \(0.421376\pi\)
\(702\) 0 0
\(703\) −6.67117 11.5548i −0.251608 0.435798i
\(704\) 13.6834 41.6769i 0.515713 1.57076i
\(705\) 0 0
\(706\) 1.56428 + 12.7942i 0.0588723 + 0.481516i
\(707\) 2.00000 + 38.1272i 0.0752177 + 1.43392i
\(708\) 0 0
\(709\) −6.65603 + 11.5286i −0.249973 + 0.432965i −0.963518 0.267644i \(-0.913755\pi\)
0.713545 + 0.700609i \(0.247088\pi\)
\(710\) 8.29183 + 11.0154i 0.311187 + 0.413399i
\(711\) 0 0
\(712\) −1.54834 0.247673i −0.0580265 0.00928192i
\(713\) 5.99109i 0.224368i
\(714\) 0 0
\(715\) 19.8221i 0.741303i
\(716\) −4.98592 1.43522i −0.186333 0.0536367i
\(717\) 0 0
\(718\) −7.82802 + 5.89255i −0.292139 + 0.219908i
\(719\) 23.7520 41.1397i 0.885800 1.53425i 0.0410056 0.999159i \(-0.486944\pi\)
0.844794 0.535091i \(-0.179723\pi\)
\(720\) 0 0
\(721\) 21.6519 + 33.3375i 0.806358 + 1.24155i
\(722\) 6.78803 0.829936i 0.252624 0.0308870i
\(723\) 0 0
\(724\) −13.7291 + 13.2309i −0.510239 + 0.491723i
\(725\) −5.04858 8.74440i −0.187500 0.324759i
\(726\) 0 0
\(727\) 24.3567 0.903340 0.451670 0.892185i \(-0.350828\pi\)
0.451670 + 0.892185i \(0.350828\pi\)
\(728\) 27.9130 + 2.97579i 1.03452 + 0.110290i
\(729\) 0 0
\(730\) −3.55137 + 8.35460i −0.131442 + 0.309218i
\(731\) −2.05076 3.55203i −0.0758503 0.131377i
\(732\) 0 0
\(733\) 3.35812 + 1.93881i 0.124035 + 0.0716117i 0.560734 0.827996i \(-0.310519\pi\)
−0.436699 + 0.899608i \(0.643852\pi\)
\(734\) 5.38144 0.657960i 0.198633 0.0242857i
\(735\) 0 0
\(736\) 4.01153 + 5.76041i 0.147867 + 0.212331i
\(737\) −25.8766 + 44.8196i −0.953177 + 1.65095i
\(738\) 0 0
\(739\) −7.46497 + 4.30990i −0.274603 + 0.158542i −0.630978 0.775801i \(-0.717346\pi\)
0.356374 + 0.934343i \(0.384013\pi\)
\(740\) 5.06185 + 1.45708i 0.186077 + 0.0535632i
\(741\) 0 0
\(742\) 5.24733 14.3961i 0.192636 0.528499i
\(743\) 6.12929i 0.224862i −0.993660 0.112431i \(-0.964136\pi\)
0.993660 0.112431i \(-0.0358637\pi\)
\(744\) 0 0
\(745\) −3.89057 + 2.24622i −0.142539 + 0.0822952i
\(746\) 22.8194 + 30.3146i 0.835477 + 1.10990i
\(747\) 0 0
\(748\) −7.30692 + 1.81387i −0.267167 + 0.0663216i
\(749\) 26.8827 17.4597i 0.982273 0.637963i
\(750\) 0 0
\(751\) 30.7146 + 17.7331i 1.12079 + 0.647090i 0.941603 0.336725i \(-0.109319\pi\)
0.179190 + 0.983815i \(0.442652\pi\)
\(752\) −12.2472 7.68783i −0.446609 0.280346i
\(753\) 0 0
\(754\) −12.1083 5.14699i −0.440959 0.187442i
\(755\) −11.7632 −0.428108
\(756\) 0 0
\(757\) 29.4204 1.06930 0.534651 0.845073i \(-0.320443\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(758\) 9.02845 + 3.83781i 0.327928 + 0.139395i
\(759\) 0 0
\(760\) −8.39073 + 10.3292i −0.304364 + 0.374679i
\(761\) −43.5568 25.1475i −1.57893 0.911597i −0.995009 0.0997877i \(-0.968184\pi\)
−0.583923 0.811809i \(-0.698483\pi\)
\(762\) 0 0
\(763\) 16.0410 0.841446i 0.580723 0.0304624i
\(764\) 4.01518 + 16.1746i 0.145264 + 0.585175i
\(765\) 0 0
\(766\) −1.92014 2.55082i −0.0693774 0.0921650i
\(767\) 41.2128 23.7942i 1.48811 0.859160i
\(768\) 0 0
\(769\) 20.2817i 0.731377i −0.930737 0.365689i \(-0.880833\pi\)
0.930737 0.365689i \(-0.119167\pi\)
\(770\) −12.7020 15.1520i −0.457750 0.546039i
\(771\) 0 0
\(772\) 6.84507 23.7796i 0.246359 0.855847i
\(773\) 18.8149 10.8628i 0.676723 0.390706i −0.121896 0.992543i \(-0.538897\pi\)
0.798619 + 0.601836i \(0.205564\pi\)
\(774\) 0 0
\(775\) 9.82806 17.0227i 0.353034 0.611473i
\(776\) 10.9787 + 28.7324i 0.394112 + 1.03143i
\(777\) 0 0
\(778\) −42.9684 + 5.25351i −1.54049 + 0.188347i
\(779\) 39.8698 + 23.0189i 1.42848 + 0.824736i
\(780\) 0 0
\(781\) 27.7349 + 48.0382i 0.992432 + 1.71894i
\(782\) 0.471311 1.10876i 0.0168540 0.0396492i
\(783\) 0 0
\(784\) 23.2436 15.6120i 0.830128 0.557573i
\(785\) 21.1369 0.754410
\(786\) 0 0
\(787\) 0.299328 + 0.518452i 0.0106699 + 0.0184808i 0.871311 0.490731i \(-0.163270\pi\)
−0.860641 + 0.509212i \(0.829937\pi\)
\(788\) 4.49225 + 4.66141i 0.160030 + 0.166056i
\(789\) 0 0
\(790\) −1.91345 + 0.233947i −0.0680774 + 0.00832346i
\(791\) 8.86288 17.3965i 0.315128 0.618547i
\(792\) 0 0
\(793\) −19.5287 + 33.8247i −0.693484 + 1.20115i
\(794\) 15.7041 11.8213i 0.557318 0.419521i
\(795\) 0 0
\(796\) −10.6389 + 36.9594i −0.377087 + 1.30999i
\(797\) 36.1789i 1.28152i 0.767741 + 0.640760i \(0.221381\pi\)
−0.767741 + 0.640760i \(0.778619\pi\)
\(798\) 0 0
\(799\) 2.48180i 0.0877998i
\(800\) 1.94847 + 22.9480i 0.0688890 + 0.811333i
\(801\) 0 0
\(802\) −8.74046 11.6113i −0.308636 0.410011i
\(803\) −18.2616 + 31.6299i −0.644436 + 1.11620i
\(804\) 0 0
\(805\) 3.15963 0.165741i 0.111362 0.00584162i
\(806\) −3.10834 25.4231i −0.109487 0.895490i
\(807\) 0 0
\(808\) −25.7349 + 31.6803i −0.905350 + 1.11451i
\(809\) −15.0603 26.0852i −0.529491 0.917106i −0.999408 0.0343953i \(-0.989049\pi\)
0.469917 0.882711i \(-0.344284\pi\)
\(810\) 0 0
\(811\) 21.5947 0.758292 0.379146 0.925337i \(-0.376218\pi\)
0.379146 + 0.925337i \(0.376218\pi\)
\(812\) −12.5538 + 3.82468i −0.440552 + 0.134220i
\(813\) 0 0
\(814\) 19.5030 + 8.29032i 0.683579 + 0.290575i
\(815\) 1.93633 + 3.35382i 0.0678266 + 0.117479i
\(816\) 0 0
\(817\) −25.2601 14.5839i −0.883740 0.510228i
\(818\) 2.08769 + 17.0751i 0.0729942 + 0.597018i
\(819\) 0 0
\(820\) −17.6397 + 4.37889i −0.616006 + 0.152917i
\(821\) 25.1264 43.5202i 0.876918 1.51887i 0.0222131 0.999753i \(-0.492929\pi\)
0.854705 0.519114i \(-0.173738\pi\)
\(822\) 0 0
\(823\) 2.87338 1.65894i 0.100160 0.0578272i −0.449084 0.893490i \(-0.648249\pi\)
0.549243 + 0.835663i \(0.314916\pi\)
\(824\) −6.71237 + 41.9628i −0.233837 + 1.46184i
\(825\) 0 0
\(826\) 16.2556 44.5976i 0.565606 1.55175i
\(827\) 29.3948i 1.02216i −0.859534 0.511078i \(-0.829246\pi\)
0.859534 0.511078i \(-0.170754\pi\)
\(828\) 0 0
\(829\) 28.2980 16.3379i 0.982830 0.567437i 0.0797067 0.996818i \(-0.474602\pi\)
0.903123 + 0.429381i \(0.141268\pi\)
\(830\) 0.592108 0.445710i 0.0205524 0.0154708i
\(831\) 0 0
\(832\) 20.0115 + 22.3629i 0.693775 + 0.775294i
\(833\) −4.39036 1.95421i −0.152117 0.0677094i
\(834\) 0 0
\(835\) 12.2834 + 7.09184i 0.425086 + 0.245423i
\(836\) −38.5516 + 37.1526i −1.33333 + 1.28495i
\(837\) 0 0
\(838\) 8.97611 21.1163i 0.310075 0.729451i
\(839\) −8.66161 −0.299032 −0.149516 0.988759i \(-0.547772\pi\)
−0.149516 + 0.988759i \(0.547772\pi\)
\(840\) 0 0
\(841\) −22.8491 −0.787899
\(842\) 5.30272 12.4747i 0.182744 0.429905i
\(843\) 0 0
\(844\) −13.3157 + 12.8325i −0.458346 + 0.441713i
\(845\) 0.894073 + 0.516193i 0.0307570 + 0.0177576i
\(846\) 0 0
\(847\) −27.4753 42.3038i −0.944062 1.45358i
\(848\) 14.4789 7.66057i 0.497209 0.263065i
\(849\) 0 0
\(850\) 3.15801 2.37720i 0.108319 0.0815372i
\(851\) −2.93688 + 1.69561i −0.100675 + 0.0581248i
\(852\) 0 0
\(853\) 7.17809i 0.245773i 0.992421 + 0.122887i \(0.0392151\pi\)
−0.992421 + 0.122887i \(0.960785\pi\)
\(854\) 6.74724 + 38.3696i 0.230886 + 1.31298i
\(855\) 0 0
\(856\) 33.8380 + 5.41274i 1.15656 + 0.185004i
\(857\) −39.5334 + 22.8246i −1.35044 + 0.779675i −0.988311 0.152454i \(-0.951282\pi\)
−0.362126 + 0.932129i \(0.617949\pi\)
\(858\) 0 0
\(859\) −6.77944 + 11.7423i −0.231311 + 0.400643i −0.958194 0.286118i \(-0.907635\pi\)
0.726883 + 0.686761i \(0.240968\pi\)
\(860\) 11.1759 2.77431i 0.381096 0.0946033i
\(861\) 0 0
\(862\) 0.0260696 + 0.213223i 0.000887934 + 0.00726240i
\(863\) −36.0550 20.8163i −1.22733 0.708597i −0.260856 0.965378i \(-0.584005\pi\)
−0.966470 + 0.256781i \(0.917338\pi\)
\(864\) 0 0
\(865\) −5.61504 9.72554i −0.190917 0.330678i
\(866\) 12.3252 + 5.23920i 0.418828 + 0.178035i
\(867\) 0 0
\(868\) −18.6672 17.4416i −0.633607 0.592005i
\(869\) −7.75555 −0.263089
\(870\) 0 0
\(871\) −17.7026 30.6619i −0.599831 1.03894i
\(872\) 13.3286 + 10.8273i 0.451364 + 0.366657i
\(873\) 0 0
\(874\) −1.03979 8.50439i −0.0351713 0.287665i
\(875\) 20.6089 + 10.4995i 0.696708 + 0.354948i
\(876\) 0 0
\(877\) 9.84239 17.0475i 0.332354 0.575654i −0.650619 0.759404i \(-0.725491\pi\)
0.982973 + 0.183751i \(0.0588239\pi\)
\(878\) −28.4706 37.8221i −0.960837 1.27643i
\(879\) 0 0
\(880\) 0.780950 21.1225i 0.0263258 0.712040i
\(881\) 7.24606i 0.244126i 0.992522 + 0.122063i \(0.0389510\pi\)
−0.992522 + 0.122063i \(0.961049\pi\)
\(882\) 0 0
\(883\) 35.4533i 1.19310i 0.802577 + 0.596549i \(0.203462\pi\)
−0.802577 + 0.596549i \(0.796538\pi\)
\(884\) 1.42474 4.94953i 0.0479193 0.166471i
\(885\) 0 0
\(886\) −29.5524 + 22.2456i −0.992833 + 0.747357i
\(887\) −8.98684 + 15.5657i −0.301749 + 0.522644i −0.976532 0.215372i \(-0.930904\pi\)
0.674784 + 0.738016i \(0.264237\pi\)
\(888\) 0 0
\(889\) 27.4479 + 13.9837i 0.920572 + 0.468999i
\(890\) −0.749976 + 0.0916955i −0.0251392 + 0.00307364i
\(891\) 0 0
\(892\) −2.70053 2.80222i −0.0904203 0.0938251i
\(893\) 8.82463 + 15.2847i 0.295305 + 0.511483i
\(894\) 0 0
\(895\) −2.50005 −0.0835674
\(896\) 29.6270 + 4.27074i 0.989770 + 0.142675i
\(897\) 0 0
\(898\) 5.69389 13.3949i 0.190008 0.446993i
\(899\) 5.98700 + 10.3698i 0.199678 + 0.345852i
\(900\) 0 0
\(901\) −2.43475 1.40570i −0.0811132 0.0468307i
\(902\) −72.5820 + 8.87421i −2.41672 + 0.295479i
\(903\) 0 0
\(904\) 19.4972 7.44992i 0.648468 0.247781i
\(905\) −4.59374 + 7.95658i −0.152701 + 0.264486i
\(906\) 0 0
\(907\) −7.60870 + 4.39289i −0.252643 + 0.145863i −0.620974 0.783831i \(-0.713263\pi\)
0.368331 + 0.929695i \(0.379929\pi\)
\(908\) −4.78297 + 16.6159i −0.158728 + 0.551419i
\(909\) 0 0
\(910\) 13.3218 2.34262i 0.441615 0.0776573i
\(911\) 21.5478i 0.713911i −0.934121 0.356955i \(-0.883815\pi\)
0.934121 0.356955i \(-0.116185\pi\)
\(912\) 0 0
\(913\) 2.58220 1.49083i 0.0854582 0.0493393i
\(914\) −10.1479 13.4811i −0.335663 0.445915i
\(915\) 0 0
\(916\) −8.08983 32.5887i −0.267295 1.07676i
\(917\) −13.3467 20.5500i −0.440747 0.678619i
\(918\) 0 0
\(919\) −27.5939 15.9314i −0.910240 0.525527i −0.0297316 0.999558i \(-0.509465\pi\)
−0.880508 + 0.474031i \(0.842799\pi\)
\(920\) 2.62537 + 2.13267i 0.0865558 + 0.0703120i
\(921\) 0 0
\(922\) 39.0574 + 16.6025i 1.28629 + 0.546774i
\(923\) −37.9479 −1.24907
\(924\) 0 0
\(925\) −11.1262 −0.365828
\(926\) −17.2756 7.34352i −0.567713 0.241323i
\(927\) 0 0
\(928\) −12.6999 5.96171i −0.416895 0.195703i
\(929\) −44.1750 25.5044i −1.44933 0.836773i −0.450892 0.892579i \(-0.648894\pi\)
−0.998442 + 0.0558058i \(0.982227\pi\)
\(930\) 0 0
\(931\) −33.9876 + 3.57555i −1.11390 + 0.117184i
\(932\) 2.03148 0.504294i 0.0665432 0.0165187i
\(933\) 0 0
\(934\) −25.2172 33.5000i −0.825131 1.09615i
\(935\) −3.14171 + 1.81387i −0.102745 + 0.0593199i
\(936\) 0 0
\(937\) 2.65742i 0.0868141i −0.999057 0.0434071i \(-0.986179\pi\)
0.999057 0.0434071i \(-0.0138212\pi\)
\(938\) −33.1801 12.0940i −1.08337 0.394884i
\(939\) 0 0
\(940\) −6.69582 1.92742i −0.218394 0.0628656i
\(941\) −26.2920 + 15.1797i −0.857096 + 0.494844i −0.863039 0.505138i \(-0.831442\pi\)
0.00594304 + 0.999982i \(0.498108\pi\)
\(942\) 0 0
\(943\) 5.85070 10.1337i 0.190525 0.329999i
\(944\) 44.8541 23.7316i 1.45988 0.772397i
\(945\) 0 0
\(946\) 45.9855 5.62240i 1.49512 0.182800i
\(947\) −37.6505 21.7375i −1.22348 0.706374i −0.257818 0.966193i \(-0.583004\pi\)
−0.965657 + 0.259819i \(0.916337\pi\)
\(948\) 0 0
\(949\) −12.4931 21.6386i −0.405542 0.702419i
\(950\) 10.9966 25.8695i 0.356777 0.839319i
\(951\) 0 0
\(952\) −2.08260 4.69640i −0.0674975 0.152211i
\(953\) 53.8683 1.74497 0.872483 0.488645i \(-0.162509\pi\)
0.872483 + 0.488645i \(0.162509\pi\)
\(954\) 0 0
\(955\) 4.01518 + 6.95449i 0.129928 + 0.225042i
\(956\) −27.7190 + 26.7131i −0.896496 + 0.863963i
\(957\) 0 0
\(958\) −16.1930 + 1.97984i −0.523173 + 0.0639656i
\(959\) 19.1027 1.00205i 0.616860 0.0323580i
\(960\) 0 0
\(961\) 3.84512 6.65995i 0.124036 0.214837i
\(962\) −11.5829 + 8.71903i −0.373447 + 0.281113i
\(963\) 0 0
\(964\) 5.29862 + 1.52523i 0.170657 + 0.0491244i
\(965\) 11.9236i 0.383835i
\(966\) 0 0
\(967\) 44.9529i 1.44559i 0.691064 + 0.722794i \(0.257142\pi\)
−0.691064 + 0.722794i \(0.742858\pi\)
\(968\) 8.51771 53.2490i 0.273770 1.71149i
\(969\) 0 0
\(970\) 8.91350 + 11.8412i 0.286195 + 0.380199i
\(971\) −0.641758 + 1.11156i −0.0205950 + 0.0356716i −0.876139 0.482058i \(-0.839889\pi\)
0.855544 + 0.517730i \(0.173223\pi\)
\(972\) 0 0
\(973\) 6.37523 12.5136i 0.204381 0.401167i
\(974\) −1.67428 13.6939i −0.0536474 0.438781i
\(975\) 0 0
\(976\) −22.1425 + 35.2744i −0.708765 + 1.12911i
\(977\) 9.67678 + 16.7607i 0.309588 + 0.536222i 0.978272 0.207325i \(-0.0664756\pi\)
−0.668684 + 0.743546i \(0.733142\pi\)
\(978\) 0 0
\(979\) −3.03979 −0.0971520
\(980\) 8.68205 10.3274i 0.277338 0.329896i
\(981\) 0 0
\(982\) −52.6767 22.3918i −1.68098 0.714550i
\(983\) 4.21637 + 7.30296i 0.134481 + 0.232928i 0.925399 0.378994i \(-0.123730\pi\)
−0.790918 + 0.611922i \(0.790397\pi\)
\(984\) 0 0
\(985\) 2.70148 + 1.55970i 0.0860763 + 0.0496962i
\(986\) 0.292225 + 2.39011i 0.00930635 + 0.0761165i
\(987\) 0 0
\(988\) −8.82463 35.5488i −0.280749 1.13096i
\(989\) −3.70680 + 6.42036i −0.117869 + 0.204156i
\(990\) 0 0
\(991\) 21.1967 12.2379i 0.673334 0.388750i −0.124005 0.992282i \(-0.539574\pi\)
0.797339 + 0.603532i \(0.206240\pi\)
\(992\) −2.31065 27.2135i −0.0733633 0.864029i
\(993\) 0 0
\(994\) −29.0073 + 24.3171i −0.920057 + 0.771292i
\(995\) 18.5322i 0.587511i
\(996\) 0 0
\(997\) −29.0273 + 16.7589i −0.919304 + 0.530761i −0.883413 0.468595i \(-0.844760\pi\)
−0.0358914 + 0.999356i \(0.511427\pi\)
\(998\) 36.1168 27.1870i 1.14326 0.860588i
\(999\) 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 252.2.bf.f.19.2 8
3.2 odd 2 84.2.o.b.19.3 yes 8
4.3 odd 2 252.2.bf.g.19.2 8
7.2 even 3 1764.2.b.j.1567.7 8
7.3 odd 6 252.2.bf.g.199.2 8
7.5 odd 6 1764.2.b.i.1567.7 8
12.11 even 2 84.2.o.a.19.3 8
21.2 odd 6 588.2.b.a.391.2 8
21.5 even 6 588.2.b.b.391.2 8
21.11 odd 6 588.2.o.d.31.3 8
21.17 even 6 84.2.o.a.31.3 yes 8
21.20 even 2 588.2.o.b.19.3 8
24.5 odd 2 1344.2.bl.i.1279.2 8
24.11 even 2 1344.2.bl.j.1279.2 8
28.3 even 6 inner 252.2.bf.f.199.2 8
28.19 even 6 1764.2.b.j.1567.8 8
28.23 odd 6 1764.2.b.i.1567.8 8
84.11 even 6 588.2.o.b.31.3 8
84.23 even 6 588.2.b.b.391.1 8
84.47 odd 6 588.2.b.a.391.1 8
84.59 odd 6 84.2.o.b.31.3 yes 8
84.83 odd 2 588.2.o.d.19.3 8
168.59 odd 6 1344.2.bl.i.703.2 8
168.101 even 6 1344.2.bl.j.703.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.o.a.19.3 8 12.11 even 2
84.2.o.a.31.3 yes 8 21.17 even 6
84.2.o.b.19.3 yes 8 3.2 odd 2
84.2.o.b.31.3 yes 8 84.59 odd 6
252.2.bf.f.19.2 8 1.1 even 1 trivial
252.2.bf.f.199.2 8 28.3 even 6 inner
252.2.bf.g.19.2 8 4.3 odd 2
252.2.bf.g.199.2 8 7.3 odd 6
588.2.b.a.391.1 8 84.47 odd 6
588.2.b.a.391.2 8 21.2 odd 6
588.2.b.b.391.1 8 84.23 even 6
588.2.b.b.391.2 8 21.5 even 6
588.2.o.b.19.3 8 21.20 even 2
588.2.o.b.31.3 8 84.11 even 6
588.2.o.d.19.3 8 84.83 odd 2
588.2.o.d.31.3 8 21.11 odd 6
1344.2.bl.i.703.2 8 168.59 odd 6
1344.2.bl.i.1279.2 8 24.5 odd 2
1344.2.bl.j.703.2 8 168.101 even 6
1344.2.bl.j.1279.2 8 24.11 even 2
1764.2.b.i.1567.7 8 7.5 odd 6
1764.2.b.i.1567.8 8 28.23 odd 6
1764.2.b.j.1567.7 8 7.2 even 3
1764.2.b.j.1567.8 8 28.19 even 6