Properties

Label 81.2.g.a.4.7
Level $81$
Weight $2$
Character 81.4
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
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] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.g (of order \(27\), degree \(18\), 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: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 4.7
Character \(\chi\) \(=\) 81.4
Dual form 81.2.g.a.61.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.69853 + 0.198530i) q^{2} +(-1.07544 + 1.35773i) q^{3} +(0.899496 + 0.213184i) q^{4} +(1.22732 - 0.616384i) q^{5} +(-2.09621 + 2.09264i) q^{6} +(0.0889729 - 0.297190i) q^{7} +(-1.72842 - 0.629095i) q^{8} +(-0.686860 - 2.92031i) q^{9} +O(q^{10})\) \(q+(1.69853 + 0.198530i) q^{2} +(-1.07544 + 1.35773i) q^{3} +(0.899496 + 0.213184i) q^{4} +(1.22732 - 0.616384i) q^{5} +(-2.09621 + 2.09264i) q^{6} +(0.0889729 - 0.297190i) q^{7} +(-1.72842 - 0.629095i) q^{8} +(-0.686860 - 2.92031i) q^{9} +(2.20701 - 0.803287i) q^{10} +(0.140180 + 2.40680i) q^{11} +(-1.25680 + 0.992005i) q^{12} +(-2.75712 - 3.70345i) q^{13} +(0.210124 - 0.487122i) q^{14} +(-0.483027 + 2.32926i) q^{15} +(-4.46306 - 2.24143i) q^{16} +(0.161307 + 0.135352i) q^{17} +(-0.586883 - 5.09660i) q^{18} +(2.66964 - 2.24009i) q^{19} +(1.23537 - 0.292789i) q^{20} +(0.307819 + 0.440411i) q^{21} +(-0.239721 + 4.11585i) q^{22} +(2.29728 + 7.67346i) q^{23} +(2.71296 - 1.67018i) q^{24} +(-1.85940 + 2.49761i) q^{25} +(-3.94780 - 6.83779i) q^{26} +(4.70367 + 2.20805i) q^{27} +(0.143387 - 0.248354i) q^{28} +(3.29291 + 7.63382i) q^{29} +(-1.28286 + 3.86041i) q^{30} +(-0.550159 + 0.583135i) q^{31} +(-4.06213 - 2.67170i) q^{32} +(-3.41854 - 2.39804i) q^{33} +(0.247112 + 0.261924i) q^{34} +(-0.0739849 - 0.419589i) q^{35} +(0.00473728 - 2.77324i) q^{36} +(1.88786 - 10.7066i) q^{37} +(4.97918 - 3.27486i) q^{38} +(7.99340 + 0.239417i) q^{39} +(-2.50910 + 0.293272i) q^{40} +(-4.66578 + 0.545352i) q^{41} +(0.435405 + 0.809162i) q^{42} +(-6.21456 + 4.08738i) q^{43} +(-0.387001 + 2.19479i) q^{44} +(-2.64303 - 3.16079i) q^{45} +(2.37859 + 13.4897i) q^{46} +(-4.27143 - 4.52745i) q^{47} +(7.84301 - 3.64910i) q^{48} +(5.76801 + 3.79368i) q^{49} +(-3.65410 + 3.87312i) q^{50} +(-0.357247 + 0.0734475i) q^{51} +(-1.69050 - 3.91901i) q^{52} +(4.27003 - 7.39591i) q^{53} +(7.55096 + 4.68425i) q^{54} +(1.65556 + 2.86752i) q^{55} +(-0.340744 + 0.457698i) q^{56} +(0.170406 + 6.03373i) q^{57} +(4.07756 + 13.6200i) q^{58} +(0.410699 - 7.05143i) q^{59} +(-0.931042 + 1.99218i) q^{60} +(9.74699 - 2.31008i) q^{61} +(-1.05023 + 0.881248i) q^{62} +(-0.929000 - 0.0557005i) q^{63} +(1.28246 + 1.07611i) q^{64} +(-5.66662 - 2.84588i) q^{65} +(-5.33041 - 4.75183i) q^{66} +(-0.497063 + 1.15232i) q^{67} +(0.116240 + 0.156137i) q^{68} +(-12.8891 - 5.13325i) q^{69} +(-0.0423646 - 0.727373i) q^{70} +(-1.68007 + 0.611494i) q^{71} +(-0.649968 + 5.47964i) q^{72} +(-12.6834 - 4.61640i) q^{73} +(5.33215 - 17.8106i) q^{74} +(-1.39141 - 5.21060i) q^{75} +(2.87888 - 1.44583i) q^{76} +(0.727750 + 0.172480i) q^{77} +(13.5295 + 1.99358i) q^{78} +(3.14586 + 0.367698i) q^{79} -6.85919 q^{80} +(-8.05645 + 4.01169i) q^{81} -8.03324 q^{82} +(-0.796837 - 0.0931369i) q^{83} +(0.182993 + 0.461770i) q^{84} +(0.281404 + 0.0666940i) q^{85} +(-11.3671 + 5.70875i) q^{86} +(-13.9060 - 3.73883i) q^{87} +(1.27182 - 4.24816i) q^{88} +(12.2626 + 4.46322i) q^{89} +(-3.86176 - 5.89342i) q^{90} +(-1.34594 + 0.489881i) q^{91} +(0.430534 + 7.39199i) q^{92} +(-0.200076 - 1.37409i) q^{93} +(-6.35631 - 8.53801i) q^{94} +(1.89575 - 4.39484i) q^{95} +(7.99603 - 2.64202i) q^{96} +(-5.96090 - 2.99368i) q^{97} +(9.04397 + 7.58879i) q^{98} +(6.93233 - 2.06251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.69853 + 0.198530i 1.20104 + 0.140382i 0.692991 0.720946i \(-0.256292\pi\)
0.508050 + 0.861328i \(0.330367\pi\)
\(3\) −1.07544 + 1.35773i −0.620905 + 0.783886i
\(4\) 0.899496 + 0.213184i 0.449748 + 0.106592i
\(5\) 1.22732 0.616384i 0.548875 0.275655i −0.152674 0.988277i \(-0.548788\pi\)
0.701549 + 0.712621i \(0.252492\pi\)
\(6\) −2.09621 + 2.09264i −0.855776 + 0.854315i
\(7\) 0.0889729 0.297190i 0.0336286 0.112327i −0.939527 0.342474i \(-0.888735\pi\)
0.973156 + 0.230146i \(0.0739205\pi\)
\(8\) −1.72842 0.629095i −0.611091 0.222419i
\(9\) −0.686860 2.92031i −0.228953 0.973437i
\(10\) 2.20701 0.803287i 0.697918 0.254022i
\(11\) 0.140180 + 2.40680i 0.0422659 + 0.725678i 0.951169 + 0.308671i \(0.0998841\pi\)
−0.908903 + 0.417008i \(0.863079\pi\)
\(12\) −1.25680 + 0.992005i −0.362807 + 0.286367i
\(13\) −2.75712 3.70345i −0.764687 1.02715i −0.998494 0.0548697i \(-0.982526\pi\)
0.233807 0.972283i \(-0.424882\pi\)
\(14\) 0.210124 0.487122i 0.0561580 0.130189i
\(15\) −0.483027 + 2.32926i −0.124717 + 0.601411i
\(16\) −4.46306 2.24143i −1.11576 0.560358i
\(17\) 0.161307 + 0.135352i 0.0391226 + 0.0328277i 0.662139 0.749381i \(-0.269649\pi\)
−0.623017 + 0.782209i \(0.714093\pi\)
\(18\) −0.586883 5.09660i −0.138330 1.20128i
\(19\) 2.66964 2.24009i 0.612457 0.513913i −0.282965 0.959130i \(-0.591318\pi\)
0.895422 + 0.445218i \(0.146874\pi\)
\(20\) 1.23537 0.292789i 0.276238 0.0654696i
\(21\) 0.307819 + 0.440411i 0.0671716 + 0.0961056i
\(22\) −0.239721 + 4.11585i −0.0511087 + 0.877503i
\(23\) 2.29728 + 7.67346i 0.479017 + 1.60003i 0.766502 + 0.642242i \(0.221996\pi\)
−0.287485 + 0.957785i \(0.592819\pi\)
\(24\) 2.71296 1.67018i 0.553780 0.340924i
\(25\) −1.85940 + 2.49761i −0.371881 + 0.499522i
\(26\) −3.94780 6.83779i −0.774227 1.34100i
\(27\) 4.70367 + 2.20805i 0.905222 + 0.424939i
\(28\) 0.143387 0.248354i 0.0270976 0.0469344i
\(29\) 3.29291 + 7.63382i 0.611478 + 1.41756i 0.889475 + 0.456983i \(0.151070\pi\)
−0.277998 + 0.960582i \(0.589671\pi\)
\(30\) −1.28286 + 3.86041i −0.234217 + 0.704812i
\(31\) −0.550159 + 0.583135i −0.0988115 + 0.104734i −0.774892 0.632094i \(-0.782196\pi\)
0.676080 + 0.736828i \(0.263677\pi\)
\(32\) −4.06213 2.67170i −0.718090 0.472295i
\(33\) −3.41854 2.39804i −0.595092 0.417446i
\(34\) 0.247112 + 0.261924i 0.0423794 + 0.0449196i
\(35\) −0.0739849 0.419589i −0.0125057 0.0709236i
\(36\) 0.00473728 2.77324i 0.000789547 0.462206i
\(37\) 1.88786 10.7066i 0.310362 1.76015i −0.286764 0.958001i \(-0.592580\pi\)
0.597126 0.802148i \(-0.296309\pi\)
\(38\) 4.97918 3.27486i 0.807730 0.531252i
\(39\) 7.99340 + 0.239417i 1.27997 + 0.0383375i
\(40\) −2.50910 + 0.293272i −0.396723 + 0.0463703i
\(41\) −4.66578 + 0.545352i −0.728673 + 0.0851697i −0.472337 0.881418i \(-0.656589\pi\)
−0.256336 + 0.966588i \(0.582515\pi\)
\(42\) 0.435405 + 0.809162i 0.0671844 + 0.124856i
\(43\) −6.21456 + 4.08738i −0.947711 + 0.623319i −0.926435 0.376454i \(-0.877143\pi\)
−0.0212756 + 0.999774i \(0.506773\pi\)
\(44\) −0.387001 + 2.19479i −0.0583426 + 0.330877i
\(45\) −2.64303 3.16079i −0.394000 0.471183i
\(46\) 2.37859 + 13.4897i 0.350704 + 1.98894i
\(47\) −4.27143 4.52745i −0.623052 0.660397i 0.336580 0.941655i \(-0.390730\pi\)
−0.959632 + 0.281258i \(0.909248\pi\)
\(48\) 7.84301 3.64910i 1.13204 0.526702i
\(49\) 5.76801 + 3.79368i 0.824001 + 0.541954i
\(50\) −3.65410 + 3.87312i −0.516768 + 0.547742i
\(51\) −0.357247 + 0.0734475i −0.0500246 + 0.0102847i
\(52\) −1.69050 3.91901i −0.234430 0.543470i
\(53\) 4.27003 7.39591i 0.586533 1.01591i −0.408149 0.912915i \(-0.633826\pi\)
0.994682 0.102990i \(-0.0328411\pi\)
\(54\) 7.55096 + 4.68425i 1.02756 + 0.637446i
\(55\) 1.65556 + 2.86752i 0.223236 + 0.386656i
\(56\) −0.340744 + 0.457698i −0.0455338 + 0.0611625i
\(57\) 0.170406 + 6.03373i 0.0225708 + 0.799187i
\(58\) 4.07756 + 13.6200i 0.535410 + 1.78839i
\(59\) 0.410699 7.05143i 0.0534685 0.918018i −0.859793 0.510643i \(-0.829407\pi\)
0.913261 0.407375i \(-0.133556\pi\)
\(60\) −0.931042 + 1.99218i −0.120197 + 0.257190i
\(61\) 9.74699 2.31008i 1.24797 0.295775i 0.447032 0.894518i \(-0.352481\pi\)
0.800941 + 0.598743i \(0.204333\pi\)
\(62\) −1.05023 + 0.881248i −0.133379 + 0.111919i
\(63\) −0.929000 0.0557005i −0.117043 0.00701761i
\(64\) 1.28246 + 1.07611i 0.160308 + 0.134514i
\(65\) −5.66662 2.84588i −0.702858 0.352988i
\(66\) −5.33041 4.75183i −0.656128 0.584909i
\(67\) −0.497063 + 1.15232i −0.0607259 + 0.140778i −0.945877 0.324525i \(-0.894796\pi\)
0.885151 + 0.465303i \(0.154055\pi\)
\(68\) 0.116240 + 0.156137i 0.0140961 + 0.0189344i
\(69\) −12.8891 5.13325i −1.55166 0.617971i
\(70\) −0.0423646 0.727373i −0.00506354 0.0869377i
\(71\) −1.68007 + 0.611494i −0.199387 + 0.0725710i −0.439784 0.898104i \(-0.644945\pi\)
0.240396 + 0.970675i \(0.422723\pi\)
\(72\) −0.649968 + 5.47964i −0.0765995 + 0.645782i
\(73\) −12.6834 4.61640i −1.48448 0.540308i −0.532494 0.846434i \(-0.678745\pi\)
−0.951991 + 0.306126i \(0.900967\pi\)
\(74\) 5.33215 17.8106i 0.619850 2.07044i
\(75\) −1.39141 5.21060i −0.160666 0.601668i
\(76\) 2.87888 1.44583i 0.330230 0.165848i
\(77\) 0.727750 + 0.172480i 0.0829348 + 0.0196559i
\(78\) 13.5295 + 1.99358i 1.53191 + 0.225729i
\(79\) 3.14586 + 0.367698i 0.353937 + 0.0413693i 0.291204 0.956661i \(-0.405944\pi\)
0.0627332 + 0.998030i \(0.480018\pi\)
\(80\) −6.85919 −0.766881
\(81\) −8.05645 + 4.01169i −0.895161 + 0.445744i
\(82\) −8.03324 −0.887123
\(83\) −0.796837 0.0931369i −0.0874642 0.0102231i 0.0722482 0.997387i \(-0.476983\pi\)
−0.159712 + 0.987164i \(0.551057\pi\)
\(84\) 0.182993 + 0.461770i 0.0199662 + 0.0503833i
\(85\) 0.281404 + 0.0666940i 0.0305226 + 0.00723398i
\(86\) −11.3671 + 5.70875i −1.22574 + 0.615591i
\(87\) −13.9060 3.73883i −1.49088 0.400845i
\(88\) 1.27182 4.24816i 0.135576 0.452856i
\(89\) 12.2626 + 4.46322i 1.29983 + 0.473101i 0.896942 0.442147i \(-0.145783\pi\)
0.402891 + 0.915248i \(0.368005\pi\)
\(90\) −3.86176 5.89342i −0.407065 0.621221i
\(91\) −1.34594 + 0.489881i −0.141093 + 0.0513535i
\(92\) 0.430534 + 7.39199i 0.0448863 + 0.770668i
\(93\) −0.200076 1.37409i −0.0207470 0.142487i
\(94\) −6.35631 8.53801i −0.655604 0.880628i
\(95\) 1.89575 4.39484i 0.194500 0.450901i
\(96\) 7.99603 2.64202i 0.816091 0.269650i
\(97\) −5.96090 2.99368i −0.605237 0.303962i 0.119664 0.992814i \(-0.461818\pi\)
−0.724901 + 0.688853i \(0.758115\pi\)
\(98\) 9.04397 + 7.58879i 0.913579 + 0.766584i
\(99\) 6.93233 2.06251i 0.696725 0.207290i
\(100\) −2.20498 + 1.85020i −0.220498 + 0.185020i
\(101\) −9.06888 + 2.14936i −0.902387 + 0.213870i −0.655518 0.755179i \(-0.727550\pi\)
−0.246869 + 0.969049i \(0.579402\pi\)
\(102\) −0.621376 + 0.0538286i −0.0615254 + 0.00532983i
\(103\) 0.0763459 1.31081i 0.00752258 0.129158i −0.992456 0.122602i \(-0.960876\pi\)
0.999979 0.00655584i \(-0.00208680\pi\)
\(104\) 2.43565 + 8.13563i 0.238835 + 0.797764i
\(105\) 0.649255 + 0.350791i 0.0633608 + 0.0342337i
\(106\) 8.72107 11.7144i 0.847065 1.13781i
\(107\) 0.386855 + 0.670052i 0.0373987 + 0.0647764i 0.884119 0.467262i \(-0.154760\pi\)
−0.846720 + 0.532038i \(0.821426\pi\)
\(108\) 3.76021 + 2.98888i 0.361826 + 0.287605i
\(109\) 1.03104 1.78582i 0.0987559 0.171050i −0.812414 0.583081i \(-0.801847\pi\)
0.911170 + 0.412031i \(0.135180\pi\)
\(110\) 2.24273 + 5.19924i 0.213836 + 0.495728i
\(111\) 12.5063 + 14.0775i 1.18705 + 1.33617i
\(112\) −1.06322 + 1.12695i −0.100465 + 0.106487i
\(113\) 4.91077 + 3.22986i 0.461966 + 0.303840i 0.759074 0.651004i \(-0.225652\pi\)
−0.297108 + 0.954844i \(0.596022\pi\)
\(114\) −0.908434 + 10.2823i −0.0850827 + 0.963025i
\(115\) 7.54931 + 8.00180i 0.703977 + 0.746171i
\(116\) 1.33455 + 7.56859i 0.123909 + 0.702726i
\(117\) −8.92148 + 10.5954i −0.824791 + 0.979545i
\(118\) 2.09750 11.8955i 0.193091 1.09507i
\(119\) 0.0545773 0.0358960i 0.00500309 0.00329058i
\(120\) 2.30020 3.72207i 0.209979 0.339777i
\(121\) 5.15258 0.602250i 0.468416 0.0547500i
\(122\) 17.0142 1.98867i 1.54039 0.180046i
\(123\) 4.27733 6.92137i 0.385674 0.624079i
\(124\) −0.619181 + 0.407242i −0.0556041 + 0.0365714i
\(125\) −1.93505 + 10.9742i −0.173076 + 0.981562i
\(126\) −1.56687 0.279043i −0.139588 0.0248591i
\(127\) 1.81538 + 10.2955i 0.161089 + 0.913580i 0.953006 + 0.302951i \(0.0979720\pi\)
−0.791917 + 0.610628i \(0.790917\pi\)
\(128\) 8.63765 + 9.15537i 0.763468 + 0.809228i
\(129\) 1.13382 12.8334i 0.0998276 1.12992i
\(130\) −9.05993 5.95881i −0.794608 0.522622i
\(131\) 4.11030 4.35667i 0.359119 0.380644i −0.522473 0.852656i \(-0.674991\pi\)
0.881592 + 0.472012i \(0.156472\pi\)
\(132\) −2.56374 2.88581i −0.223145 0.251178i
\(133\) −0.428208 0.992698i −0.0371303 0.0860778i
\(134\) −1.07305 + 1.85857i −0.0926970 + 0.160556i
\(135\) 7.13393 0.189282i 0.613991 0.0162908i
\(136\) −0.193657 0.335423i −0.0166059 0.0287623i
\(137\) 0.693717 0.931823i 0.0592682 0.0796110i −0.771501 0.636228i \(-0.780494\pi\)
0.830769 + 0.556617i \(0.187901\pi\)
\(138\) −20.8734 11.2778i −1.77686 0.960033i
\(139\) −4.67728 15.6232i −0.396722 1.32514i −0.890273 0.455427i \(-0.849487\pi\)
0.493551 0.869717i \(-0.335699\pi\)
\(140\) 0.0229008 0.393191i 0.00193547 0.0332307i
\(141\) 10.7407 0.930448i 0.904532 0.0783578i
\(142\) −2.97504 + 0.705098i −0.249660 + 0.0591705i
\(143\) 8.52698 7.15499i 0.713062 0.598330i
\(144\) −3.48018 + 14.5731i −0.290015 + 1.21442i
\(145\) 8.74683 + 7.33946i 0.726384 + 0.609509i
\(146\) −20.6267 10.3591i −1.70708 0.857327i
\(147\) −11.3539 + 3.75153i −0.936457 + 0.309421i
\(148\) 3.98059 9.22805i 0.327203 0.758541i
\(149\) −5.33177 7.16181i −0.436796 0.586719i 0.528156 0.849148i \(-0.322884\pi\)
−0.964951 + 0.262429i \(0.915476\pi\)
\(150\) −1.32889 9.12658i −0.108503 0.745182i
\(151\) 0.906740 + 15.5681i 0.0737894 + 1.26692i 0.808484 + 0.588518i \(0.200288\pi\)
−0.734695 + 0.678398i \(0.762675\pi\)
\(152\) −6.02350 + 2.19238i −0.488571 + 0.177825i
\(153\) 0.284476 0.564034i 0.0229985 0.0455994i
\(154\) 1.20186 + 0.437442i 0.0968488 + 0.0352501i
\(155\) −0.315787 + 1.05480i −0.0253647 + 0.0847238i
\(156\) 7.13899 + 1.91942i 0.571577 + 0.153677i
\(157\) 10.9371 5.49283i 0.872878 0.438376i 0.0448048 0.998996i \(-0.485733\pi\)
0.828073 + 0.560620i \(0.189437\pi\)
\(158\) 5.27034 + 1.24909i 0.419285 + 0.0993725i
\(159\) 5.44948 + 13.7514i 0.432172 + 1.09056i
\(160\) −6.63234 0.775209i −0.524332 0.0612857i
\(161\) 2.48487 0.195835
\(162\) −14.4805 + 5.21453i −1.13770 + 0.409692i
\(163\) −25.0816 −1.96454 −0.982271 0.187465i \(-0.939973\pi\)
−0.982271 + 0.187465i \(0.939973\pi\)
\(164\) −4.31311 0.504131i −0.336798 0.0393660i
\(165\) −5.67377 0.836035i −0.441702 0.0650853i
\(166\) −1.33496 0.316391i −0.103613 0.0245567i
\(167\) 7.19682 3.61438i 0.556907 0.279689i −0.148002 0.988987i \(-0.547284\pi\)
0.704909 + 0.709298i \(0.250988\pi\)
\(168\) −0.254981 0.954865i −0.0196722 0.0736694i
\(169\) −2.38542 + 7.96785i −0.183494 + 0.612911i
\(170\) 0.464732 + 0.169149i 0.0356433 + 0.0129731i
\(171\) −8.37544 6.25755i −0.640486 0.478527i
\(172\) −6.46133 + 2.35173i −0.492672 + 0.179318i
\(173\) 1.03421 + 17.7567i 0.0786295 + 1.35002i 0.774830 + 0.632170i \(0.217835\pi\)
−0.696201 + 0.717847i \(0.745128\pi\)
\(174\) −22.8775 9.11126i −1.73434 0.690723i
\(175\) 0.576829 + 0.774816i 0.0436042 + 0.0585706i
\(176\) 4.76905 11.0559i 0.359481 0.833370i
\(177\) 9.13226 + 8.14101i 0.686423 + 0.611916i
\(178\) 19.9423 + 10.0154i 1.49474 + 0.750686i
\(179\) −13.5735 11.3896i −1.01453 0.851295i −0.0256035 0.999672i \(-0.508151\pi\)
−0.988931 + 0.148377i \(0.952595\pi\)
\(180\) −1.70357 3.40657i −0.126976 0.253911i
\(181\) 20.5130 17.2124i 1.52472 1.27939i 0.699377 0.714753i \(-0.253461\pi\)
0.825340 0.564636i \(-0.190983\pi\)
\(182\) −2.38337 + 0.564869i −0.176667 + 0.0418709i
\(183\) −7.34583 + 15.7181i −0.543019 + 1.16192i
\(184\) 0.856656 14.7082i 0.0631535 1.08430i
\(185\) −4.28235 14.3040i −0.314845 1.05165i
\(186\) −0.0670374 2.37366i −0.00491542 0.174045i
\(187\) −0.303154 + 0.407207i −0.0221688 + 0.0297779i
\(188\) −2.87695 4.98303i −0.209823 0.363424i
\(189\) 1.07471 1.20143i 0.0781736 0.0873910i
\(190\) 4.09249 7.08840i 0.296900 0.514246i
\(191\) −1.24181 2.87885i −0.0898545 0.208306i 0.867363 0.497677i \(-0.165813\pi\)
−0.957217 + 0.289370i \(0.906554\pi\)
\(192\) −2.84028 + 0.583941i −0.204979 + 0.0421423i
\(193\) −6.78035 + 7.18675i −0.488060 + 0.517314i −0.923860 0.382730i \(-0.874984\pi\)
0.435800 + 0.900043i \(0.356465\pi\)
\(194\) −9.53042 6.26826i −0.684244 0.450035i
\(195\) 9.95805 4.63316i 0.713111 0.331788i
\(196\) 4.37955 + 4.64205i 0.312825 + 0.331575i
\(197\) 0.354010 + 2.00769i 0.0252221 + 0.143042i 0.994818 0.101669i \(-0.0324182\pi\)
−0.969596 + 0.244711i \(0.921307\pi\)
\(198\) 12.1842 2.12695i 0.865895 0.151156i
\(199\) −2.26949 + 12.8709i −0.160880 + 0.912396i 0.792331 + 0.610091i \(0.208867\pi\)
−0.953211 + 0.302305i \(0.902244\pi\)
\(200\) 4.78507 3.14719i 0.338356 0.222540i
\(201\) −1.02998 1.91413i −0.0726492 0.135012i
\(202\) −15.8305 + 1.85032i −1.11383 + 0.130188i
\(203\) 2.56168 0.299417i 0.179794 0.0210149i
\(204\) −0.337000 0.0100938i −0.0235947 0.000706707i
\(205\) −5.39027 + 3.54524i −0.376473 + 0.247610i
\(206\) 0.389910 2.21129i 0.0271663 0.154068i
\(207\) 20.8310 11.9794i 1.44785 0.832624i
\(208\) 4.00414 + 22.7086i 0.277637 + 1.57456i
\(209\) 5.76569 + 6.11128i 0.398821 + 0.422726i
\(210\) 1.03314 + 0.724726i 0.0712932 + 0.0500108i
\(211\) 13.2622 + 8.72269i 0.913008 + 0.600495i 0.916734 0.399498i \(-0.130816\pi\)
−0.00372605 + 0.999993i \(0.501186\pi\)
\(212\) 5.41756 5.74228i 0.372080 0.394382i
\(213\) 0.976566 2.93870i 0.0669132 0.201357i
\(214\) 0.524059 + 1.21491i 0.0358239 + 0.0830492i
\(215\) −5.10787 + 8.84708i −0.348354 + 0.603366i
\(216\) −6.74087 6.77550i −0.458658 0.461015i
\(217\) 0.124353 + 0.215385i 0.00844160 + 0.0146213i
\(218\) 2.10579 2.82857i 0.142622 0.191575i
\(219\) 19.9081 12.2560i 1.34526 0.828186i
\(220\) 0.877861 + 2.93226i 0.0591854 + 0.197693i
\(221\) 0.0565295 0.970573i 0.00380258 0.0652878i
\(222\) 18.4476 + 26.3939i 1.23812 + 1.77144i
\(223\) −1.84454 + 0.437163i −0.123519 + 0.0292746i −0.291910 0.956446i \(-0.594291\pi\)
0.168391 + 0.985720i \(0.446143\pi\)
\(224\) −1.15542 + 0.969515i −0.0772000 + 0.0647785i
\(225\) 8.57096 + 3.71453i 0.571397 + 0.247635i
\(226\) 7.69986 + 6.46095i 0.512187 + 0.429776i
\(227\) −22.8390 11.4702i −1.51588 0.761301i −0.520186 0.854053i \(-0.674138\pi\)
−0.995689 + 0.0927514i \(0.970434\pi\)
\(228\) −1.13302 + 5.46364i −0.0750360 + 0.361839i
\(229\) −1.85823 + 4.30787i −0.122795 + 0.284672i −0.968515 0.248956i \(-0.919912\pi\)
0.845719 + 0.533628i \(0.179172\pi\)
\(230\) 11.2341 + 15.0900i 0.740756 + 0.995008i
\(231\) −1.01683 + 0.802596i −0.0669026 + 0.0528070i
\(232\) −0.889146 15.2660i −0.0583753 1.00226i
\(233\) −10.7706 + 3.92018i −0.705605 + 0.256819i −0.669802 0.742540i \(-0.733621\pi\)
−0.0358031 + 0.999359i \(0.511399\pi\)
\(234\) −17.2569 + 16.2254i −1.12812 + 1.06069i
\(235\) −8.03307 2.92380i −0.524020 0.190728i
\(236\) 1.87268 6.25518i 0.121901 0.407178i
\(237\) −3.88242 + 3.87579i −0.252190 + 0.251760i
\(238\) 0.0998275 0.0501352i 0.00647085 0.00324978i
\(239\) −11.4299 2.70892i −0.739336 0.175226i −0.156343 0.987703i \(-0.549970\pi\)
−0.582993 + 0.812477i \(0.698119\pi\)
\(240\) 7.37665 9.31293i 0.476160 0.601147i
\(241\) −4.38905 0.513006i −0.282723 0.0330456i −0.0264506 0.999650i \(-0.508420\pi\)
−0.256273 + 0.966605i \(0.582495\pi\)
\(242\) 8.87136 0.570273
\(243\) 3.21743 15.2528i 0.206398 0.978468i
\(244\) 9.25985 0.592801
\(245\) 9.41757 + 1.10076i 0.601666 + 0.0703247i
\(246\) 8.63926 10.9070i 0.550819 0.695403i
\(247\) −15.6566 3.71068i −0.996205 0.236105i
\(248\) 1.31776 0.661802i 0.0836776 0.0420245i
\(249\) 0.983404 0.981726i 0.0623207 0.0622143i
\(250\) −5.46543 + 18.2558i −0.345664 + 1.15460i
\(251\) −5.90077 2.14770i −0.372453 0.135562i 0.149010 0.988836i \(-0.452391\pi\)
−0.521463 + 0.853274i \(0.674614\pi\)
\(252\) −0.823757 0.248151i −0.0518918 0.0156320i
\(253\) −18.1465 + 6.60477i −1.14086 + 0.415239i
\(254\) 1.03951 + 17.8476i 0.0652245 + 1.11986i
\(255\) −0.393186 + 0.310345i −0.0246222 + 0.0194346i
\(256\) 10.8542 + 14.5798i 0.678390 + 0.911236i
\(257\) −0.936302 + 2.17059i −0.0584049 + 0.135398i −0.944919 0.327303i \(-0.893860\pi\)
0.886515 + 0.462701i \(0.153120\pi\)
\(258\) 4.47364 21.5728i 0.278517 1.34307i
\(259\) −3.01392 1.51365i −0.187276 0.0940534i
\(260\) −4.49040 3.76790i −0.278483 0.233675i
\(261\) 20.0314 14.8597i 1.23991 0.919792i
\(262\) 7.84639 6.58390i 0.484752 0.406755i
\(263\) −13.6191 + 3.22778i −0.839787 + 0.199033i −0.627932 0.778268i \(-0.716098\pi\)
−0.211855 + 0.977301i \(0.567950\pi\)
\(264\) 4.40010 + 6.29543i 0.270807 + 0.387457i
\(265\) 0.681979 11.7091i 0.0418937 0.719286i
\(266\) −0.530244 1.77114i −0.0325113 0.108595i
\(267\) −19.2475 + 11.8494i −1.17793 + 0.725170i
\(268\) −0.692763 + 0.930542i −0.0423172 + 0.0568419i
\(269\) 12.8630 + 22.2793i 0.784268 + 1.35839i 0.929435 + 0.368985i \(0.120295\pi\)
−0.145167 + 0.989407i \(0.546372\pi\)
\(270\) 12.1548 + 1.09479i 0.739715 + 0.0666270i
\(271\) −6.52248 + 11.2973i −0.396212 + 0.686260i −0.993255 0.115950i \(-0.963009\pi\)
0.597043 + 0.802209i \(0.296342\pi\)
\(272\) −0.416538 0.965643i −0.0252563 0.0585507i
\(273\) 0.782348 2.35426i 0.0473499 0.142486i
\(274\) 1.36329 1.44501i 0.0823595 0.0872959i
\(275\) −6.27191 4.12510i −0.378210 0.248753i
\(276\) −10.4993 7.36509i −0.631986 0.443326i
\(277\) −3.58097 3.79560i −0.215159 0.228056i 0.610800 0.791785i \(-0.290848\pi\)
−0.825960 + 0.563729i \(0.809366\pi\)
\(278\) −4.84283 27.4651i −0.290454 1.64725i
\(279\) 2.08082 + 1.20610i 0.124575 + 0.0722076i
\(280\) −0.136084 + 0.771772i −0.00813259 + 0.0461222i
\(281\) 4.74552 3.12118i 0.283094 0.186194i −0.400019 0.916507i \(-0.630996\pi\)
0.683112 + 0.730313i \(0.260626\pi\)
\(282\) 18.4281 + 0.551957i 1.09738 + 0.0328686i
\(283\) 11.2778 1.31819i 0.670396 0.0783580i 0.225916 0.974147i \(-0.427463\pi\)
0.444480 + 0.895789i \(0.353388\pi\)
\(284\) −1.64157 + 0.191872i −0.0974095 + 0.0113855i
\(285\) 3.92824 + 7.30030i 0.232689 + 0.432432i
\(286\) 15.9038 10.4601i 0.940412 0.618518i
\(287\) −0.253055 + 1.43515i −0.0149374 + 0.0847140i
\(288\) −5.01210 + 13.6978i −0.295341 + 0.807149i
\(289\) −2.94432 16.6981i −0.173195 0.982239i
\(290\) 13.3996 + 14.2028i 0.786854 + 0.834016i
\(291\) 10.4752 4.87377i 0.614066 0.285706i
\(292\) −10.4246 6.85634i −0.610051 0.401237i
\(293\) −11.8588 + 12.5696i −0.692799 + 0.734324i −0.974304 0.225236i \(-0.927685\pi\)
0.281506 + 0.959560i \(0.409166\pi\)
\(294\) −20.0298 + 4.11798i −1.16816 + 0.240166i
\(295\) −3.84233 8.90753i −0.223709 0.518616i
\(296\) −9.99847 + 17.3179i −0.581149 + 1.00658i
\(297\) −4.65497 + 11.6303i −0.270109 + 0.674860i
\(298\) −7.63434 13.2231i −0.442245 0.765991i
\(299\) 22.0844 29.6645i 1.27717 1.71554i
\(300\) −0.140746 4.98354i −0.00812598 0.287725i
\(301\) 0.661801 + 2.21057i 0.0381456 + 0.127415i
\(302\) −1.55061 + 26.6229i −0.0892275 + 1.53198i
\(303\) 6.83477 14.6246i 0.392648 0.840161i
\(304\) −16.9358 + 4.01385i −0.971333 + 0.230210i
\(305\) 10.5388 8.84310i 0.603450 0.506354i
\(306\) 0.595168 0.901550i 0.0340235 0.0515382i
\(307\) −6.44460 5.40766i −0.367812 0.308631i 0.440083 0.897957i \(-0.354949\pi\)
−0.807895 + 0.589326i \(0.799393\pi\)
\(308\) 0.617838 + 0.310290i 0.0352046 + 0.0176804i
\(309\) 1.69762 + 1.51335i 0.0965741 + 0.0860916i
\(310\) −0.745784 + 1.72892i −0.0423577 + 0.0981961i
\(311\) 3.91461 + 5.25824i 0.221977 + 0.298167i 0.899136 0.437670i \(-0.144196\pi\)
−0.677158 + 0.735837i \(0.736789\pi\)
\(312\) −13.6654 5.44243i −0.773650 0.308117i
\(313\) −0.317011 5.44287i −0.0179185 0.307649i −0.995345 0.0963741i \(-0.969275\pi\)
0.977427 0.211275i \(-0.0677616\pi\)
\(314\) 19.6675 7.15839i 1.10990 0.403971i
\(315\) −1.17451 + 0.504258i −0.0661764 + 0.0284117i
\(316\) 2.75130 + 1.00139i 0.154773 + 0.0563327i
\(317\) 1.03115 3.44428i 0.0579151 0.193450i −0.924136 0.382063i \(-0.875214\pi\)
0.982052 + 0.188613i \(0.0603991\pi\)
\(318\) 6.52605 + 24.4390i 0.365963 + 1.37047i
\(319\) −17.9115 + 8.99549i −1.00285 + 0.503651i
\(320\) 2.23729 + 0.530248i 0.125068 + 0.0296417i
\(321\) −1.32579 0.195356i −0.0739983 0.0109037i
\(322\) 4.22063 + 0.493321i 0.235206 + 0.0274917i
\(323\) 0.733832 0.0408315
\(324\) −8.10197 + 1.89099i −0.450109 + 0.105055i
\(325\) 14.3764 0.797458
\(326\) −42.6018 4.97944i −2.35950 0.275786i
\(327\) 1.31583 + 3.32042i 0.0727658 + 0.183619i
\(328\) 8.40754 + 1.99262i 0.464229 + 0.110024i
\(329\) −1.72555 + 0.866606i −0.0951329 + 0.0477775i
\(330\) −9.47108 2.54644i −0.521366 0.140177i
\(331\) 7.68837 25.6809i 0.422591 1.41155i −0.436488 0.899710i \(-0.643778\pi\)
0.859079 0.511842i \(-0.171037\pi\)
\(332\) −0.696896 0.253649i −0.0382471 0.0139208i
\(333\) −32.5632 + 1.84078i −1.78445 + 0.100874i
\(334\) 12.9416 4.71034i 0.708131 0.257739i
\(335\) 0.100216 + 1.72065i 0.00547541 + 0.0940092i
\(336\) −0.386662 2.65553i −0.0210941 0.144871i
\(337\) 12.9090 + 17.3398i 0.703198 + 0.944559i 0.999946 0.0103968i \(-0.00330947\pi\)
−0.296748 + 0.954956i \(0.595902\pi\)
\(338\) −5.63355 + 13.0600i −0.306425 + 0.710372i
\(339\) −9.66651 + 3.19397i −0.525013 + 0.173473i
\(340\) 0.238904 + 0.119982i 0.0129564 + 0.00650693i
\(341\) −1.48061 1.24238i −0.0801796 0.0672787i
\(342\) −12.9836 12.2914i −0.702073 0.664643i
\(343\) 3.30415 2.77251i 0.178407 0.149702i
\(344\) 13.3127 3.15518i 0.717775 0.170116i
\(345\) −18.9831 + 1.64447i −1.02202 + 0.0885353i
\(346\) −1.76859 + 30.3656i −0.0950802 + 1.63246i
\(347\) −4.83041 16.1347i −0.259310 0.866156i −0.984165 0.177254i \(-0.943278\pi\)
0.724855 0.688901i \(-0.241907\pi\)
\(348\) −11.7113 6.32760i −0.627793 0.339195i
\(349\) −1.17716 + 1.58120i −0.0630118 + 0.0846396i −0.832512 0.554007i \(-0.813098\pi\)
0.769500 + 0.638647i \(0.220505\pi\)
\(350\) 0.825937 + 1.43056i 0.0441482 + 0.0764669i
\(351\) −4.79117 23.5077i −0.255734 1.25475i
\(352\) 5.86083 10.1513i 0.312384 0.541064i
\(353\) 2.30243 + 5.33762i 0.122546 + 0.284093i 0.968435 0.249265i \(-0.0801890\pi\)
−0.845889 + 0.533358i \(0.820930\pi\)
\(354\) 13.8952 + 15.6408i 0.738520 + 0.831297i
\(355\) −1.68507 + 1.78607i −0.0894341 + 0.0947946i
\(356\) 10.0787 + 6.62885i 0.534168 + 0.351328i
\(357\) −0.00995743 + 0.112705i −0.000527003 + 0.00596499i
\(358\) −20.7939 22.0402i −1.09899 1.16486i
\(359\) 3.38611 + 19.2036i 0.178712 + 1.01353i 0.933771 + 0.357871i \(0.116497\pi\)
−0.755059 + 0.655657i \(0.772392\pi\)
\(360\) 2.57984 + 7.12591i 0.135970 + 0.375569i
\(361\) −1.19036 + 6.75087i −0.0626506 + 0.355309i
\(362\) 38.2590 25.1634i 2.01085 1.32256i
\(363\) −4.72359 + 7.64349i −0.247924 + 0.401179i
\(364\) −1.31510 + 0.153713i −0.0689300 + 0.00805676i
\(365\) −18.4121 + 2.15207i −0.963736 + 0.112645i
\(366\) −15.5976 + 25.2393i −0.815300 + 1.31928i
\(367\) 15.7834 10.3809i 0.823885 0.541878i −0.0661288 0.997811i \(-0.521065\pi\)
0.890014 + 0.455933i \(0.150694\pi\)
\(368\) 6.94663 39.3963i 0.362118 2.05367i
\(369\) 4.79734 + 13.2510i 0.249740 + 0.689818i
\(370\) −4.43392 25.1460i −0.230509 1.30728i
\(371\) −1.81807 1.92704i −0.0943897 0.100047i
\(372\) 0.112967 1.27864i 0.00585709 0.0662946i
\(373\) 18.6275 + 12.2515i 0.964495 + 0.634359i 0.930976 0.365079i \(-0.118958\pi\)
0.0335191 + 0.999438i \(0.489329\pi\)
\(374\) −0.595759 + 0.631467i −0.0308059 + 0.0326524i
\(375\) −12.8190 14.4294i −0.661968 0.745128i
\(376\) 4.53465 + 10.5125i 0.233857 + 0.542141i
\(377\) 19.1926 33.2425i 0.988467 1.71207i
\(378\) 2.06394 1.82730i 0.106158 0.0939861i
\(379\) 5.97107 + 10.3422i 0.306713 + 0.531243i 0.977641 0.210280i \(-0.0674374\pi\)
−0.670928 + 0.741522i \(0.734104\pi\)
\(380\) 2.64213 3.54899i 0.135538 0.182060i
\(381\) −15.9309 8.60742i −0.816163 0.440971i
\(382\) −1.53772 5.13634i −0.0786766 0.262798i
\(383\) −1.21579 + 20.8743i −0.0621238 + 1.06662i 0.812856 + 0.582465i \(0.197912\pi\)
−0.874980 + 0.484160i \(0.839125\pi\)
\(384\) −21.7198 + 1.88154i −1.10838 + 0.0960171i
\(385\) 0.999498 0.236885i 0.0509391 0.0120728i
\(386\) −12.9434 + 10.8608i −0.658802 + 0.552800i
\(387\) 16.2049 + 15.3410i 0.823744 + 0.779826i
\(388\) −4.72360 3.96357i −0.239804 0.201220i
\(389\) 8.58044 + 4.30926i 0.435046 + 0.218488i 0.652823 0.757510i \(-0.273584\pi\)
−0.217778 + 0.975998i \(0.569881\pi\)
\(390\) 17.8339 5.89260i 0.903052 0.298383i
\(391\) −0.668054 + 1.54872i −0.0337849 + 0.0783222i
\(392\) −7.58299 10.1857i −0.382999 0.514456i
\(393\) 1.49479 + 10.2660i 0.0754024 + 0.517852i
\(394\) 0.202710 + 3.48040i 0.0102124 + 0.175340i
\(395\) 4.08763 1.48777i 0.205671 0.0748581i
\(396\) 6.67530 0.377351i 0.335446 0.0189626i
\(397\) 1.93277 + 0.703471i 0.0970030 + 0.0353062i 0.390066 0.920787i \(-0.372452\pi\)
−0.293063 + 0.956093i \(0.594674\pi\)
\(398\) −6.41005 + 21.4111i −0.321307 + 1.07324i
\(399\) 1.80833 + 0.486195i 0.0905296 + 0.0243402i
\(400\) 13.8969 6.97926i 0.694843 0.348963i
\(401\) 0.658673 + 0.156108i 0.0328925 + 0.00779568i 0.247029 0.969008i \(-0.420546\pi\)
−0.214137 + 0.976804i \(0.568694\pi\)
\(402\) −1.36944 3.45568i −0.0683014 0.172354i
\(403\) 3.67646 + 0.429717i 0.183138 + 0.0214057i
\(404\) −8.61563 −0.428644
\(405\) −7.41511 + 9.88950i −0.368460 + 0.491413i
\(406\) 4.41052 0.218891
\(407\) 26.0332 + 3.04285i 1.29042 + 0.150828i
\(408\) 0.663681 + 0.0977940i 0.0328571 + 0.00484152i
\(409\) 16.6911 + 3.95585i 0.825319 + 0.195604i 0.621510 0.783406i \(-0.286520\pi\)
0.203810 + 0.979011i \(0.434668\pi\)
\(410\) −9.85937 + 4.95156i −0.486920 + 0.244540i
\(411\) 0.519114 + 1.94400i 0.0256060 + 0.0958904i
\(412\) 0.348117 1.16279i 0.0171505 0.0572866i
\(413\) −2.05907 0.749442i −0.101320 0.0368776i
\(414\) 37.7603 16.2118i 1.85582 0.796764i
\(415\) −1.03538 + 0.376849i −0.0508250 + 0.0184988i
\(416\) 1.30524 + 22.4101i 0.0639947 + 1.09875i
\(417\) 26.2422 + 10.4513i 1.28509 + 0.511804i
\(418\) 8.57992 + 11.5248i 0.419658 + 0.563698i
\(419\) −11.1249 + 25.7904i −0.543486 + 1.25994i 0.396282 + 0.918129i \(0.370300\pi\)
−0.939768 + 0.341813i \(0.888959\pi\)
\(420\) 0.509219 + 0.453947i 0.0248474 + 0.0221503i
\(421\) −8.98026 4.51006i −0.437671 0.219807i 0.216299 0.976327i \(-0.430601\pi\)
−0.653970 + 0.756521i \(0.726898\pi\)
\(422\) 20.7945 + 17.4487i 1.01226 + 0.849388i
\(423\) −10.2877 + 15.5836i −0.500205 + 0.757702i
\(424\) −12.0332 + 10.0970i −0.584382 + 0.490354i
\(425\) −0.637991 + 0.151207i −0.0309471 + 0.00733460i
\(426\) 2.24214 4.79759i 0.108632 0.232444i
\(427\) 0.180685 3.10224i 0.00874396 0.150128i
\(428\) 0.205130 + 0.685181i 0.00991532 + 0.0331195i
\(429\) 0.544287 + 19.2721i 0.0262784 + 0.930466i
\(430\) −10.4323 + 14.0130i −0.503088 + 0.675765i
\(431\) −2.67380 4.63116i −0.128792 0.223075i 0.794417 0.607373i \(-0.207777\pi\)
−0.923209 + 0.384298i \(0.874443\pi\)
\(432\) −16.0436 20.3976i −0.771896 0.981380i
\(433\) 3.44686 5.97014i 0.165646 0.286906i −0.771239 0.636546i \(-0.780363\pi\)
0.936884 + 0.349639i \(0.113696\pi\)
\(434\) 0.168456 + 0.390525i 0.00808615 + 0.0187458i
\(435\) −19.3717 + 3.98268i −0.928801 + 0.190955i
\(436\) 1.30813 1.38653i 0.0626479 0.0664029i
\(437\) 23.3222 + 15.3392i 1.11565 + 0.733775i
\(438\) 36.2477 16.8649i 1.73198 0.805835i
\(439\) −10.6865 11.3270i −0.510039 0.540610i 0.420264 0.907402i \(-0.361937\pi\)
−0.930303 + 0.366792i \(0.880456\pi\)
\(440\) −1.05757 5.99779i −0.0504178 0.285934i
\(441\) 7.11691 19.4501i 0.338901 0.926196i
\(442\) 0.288704 1.63732i 0.0137323 0.0778796i
\(443\) 23.3555 15.3611i 1.10965 0.729830i 0.143977 0.989581i \(-0.454011\pi\)
0.965675 + 0.259751i \(0.0836407\pi\)
\(444\) 8.24831 + 15.3288i 0.391448 + 0.727472i
\(445\) 17.8012 2.08066i 0.843859 0.0986330i
\(446\) −3.21979 + 0.376339i −0.152461 + 0.0178202i
\(447\) 15.4578 + 0.462990i 0.731129 + 0.0218987i
\(448\) 0.433914 0.285390i 0.0205005 0.0134834i
\(449\) −1.89891 + 10.7693i −0.0896152 + 0.508233i 0.906650 + 0.421884i \(0.138631\pi\)
−0.996265 + 0.0863489i \(0.972480\pi\)
\(450\) 13.8206 + 8.01082i 0.651508 + 0.377634i
\(451\) −1.96661 11.1532i −0.0926038 0.525182i
\(452\) 3.72866 + 3.95215i 0.175381 + 0.185893i
\(453\) −22.1124 15.5115i −1.03893 0.728792i
\(454\) −36.5155 24.0166i −1.71376 1.12716i
\(455\) −1.34994 + 1.43086i −0.0632864 + 0.0670796i
\(456\) 3.50126 10.5361i 0.163961 0.493396i
\(457\) −6.50790 15.0870i −0.304427 0.705740i 0.695492 0.718534i \(-0.255187\pi\)
−0.999918 + 0.0127940i \(0.995927\pi\)
\(458\) −4.01150 + 6.94812i −0.187445 + 0.324664i
\(459\) 0.459869 + 0.992825i 0.0214648 + 0.0463411i
\(460\) 5.08471 + 8.80698i 0.237076 + 0.410627i
\(461\) −14.9299 + 20.0543i −0.695355 + 0.934024i −0.999829 0.0184970i \(-0.994112\pi\)
0.304474 + 0.952521i \(0.401519\pi\)
\(462\) −1.88646 + 1.16136i −0.0877660 + 0.0540314i
\(463\) −3.89051 12.9952i −0.180807 0.603938i −0.999556 0.0297865i \(-0.990517\pi\)
0.818749 0.574151i \(-0.194668\pi\)
\(464\) 2.41425 41.4510i 0.112079 1.92431i
\(465\) −1.09253 1.56313i −0.0506648 0.0724885i
\(466\) −19.0724 + 4.52025i −0.883514 + 0.209397i
\(467\) −26.2848 + 22.0556i −1.21632 + 1.02061i −0.217308 + 0.976103i \(0.569728\pi\)
−0.999009 + 0.0445082i \(0.985828\pi\)
\(468\) −10.2836 + 7.62860i −0.475360 + 0.352632i
\(469\) 0.298233 + 0.250247i 0.0137711 + 0.0115554i
\(470\) −13.0639 6.56096i −0.602595 0.302634i
\(471\) −4.30444 + 20.7569i −0.198338 + 0.956426i
\(472\) −5.14589 + 11.9295i −0.236859 + 0.549100i
\(473\) −10.7087 14.3842i −0.492385 0.661388i
\(474\) −7.36386 + 5.81237i −0.338233 + 0.266971i
\(475\) 0.630948 + 10.8330i 0.0289499 + 0.497050i
\(476\) 0.0567445 0.0206533i 0.00260088 0.000946643i
\(477\) −24.5313 7.38986i −1.12321 0.338359i
\(478\) −18.8761 6.87035i −0.863374 0.314242i
\(479\) 6.21271 20.7519i 0.283866 0.948178i −0.690523 0.723310i \(-0.742620\pi\)
0.974389 0.224868i \(-0.0721951\pi\)
\(480\) 8.18520 8.17123i 0.373602 0.372964i
\(481\) −44.8563 + 22.5277i −2.04527 + 1.02717i
\(482\) −7.35307 1.74271i −0.334923 0.0793783i
\(483\) −2.67233 + 3.37379i −0.121595 + 0.153513i
\(484\) 4.76311 + 0.556728i 0.216505 + 0.0253058i
\(485\) −9.16119 −0.415988
\(486\) 8.49302 25.2686i 0.385251 1.14621i
\(487\) 38.8502 1.76047 0.880235 0.474538i \(-0.157385\pi\)
0.880235 + 0.474538i \(0.157385\pi\)
\(488\) −18.3002 2.13899i −0.828411 0.0968273i
\(489\) 26.9737 34.0540i 1.21979 1.53998i
\(490\) 15.7775 + 3.73933i 0.712754 + 0.168926i
\(491\) 26.1680 13.1421i 1.18095 0.593093i 0.253604 0.967308i \(-0.418384\pi\)
0.927342 + 0.374215i \(0.122088\pi\)
\(492\) 5.32297 5.31388i 0.239978 0.239568i
\(493\) −0.502087 + 1.67709i −0.0226129 + 0.0755322i
\(494\) −25.8565 9.41099i −1.16334 0.423420i
\(495\) 7.23690 6.80434i 0.325275 0.305832i
\(496\) 3.76245 1.36942i 0.168939 0.0614887i
\(497\) 0.0322497 + 0.553706i 0.00144660 + 0.0248371i
\(498\) 1.86524 1.47225i 0.0835835 0.0659733i
\(499\) −16.4063 22.0374i −0.734445 0.986531i −0.999750 0.0223667i \(-0.992880\pi\)
0.265304 0.964165i \(-0.414528\pi\)
\(500\) −4.08009 + 9.45872i −0.182467 + 0.423007i
\(501\) −2.83239 + 13.6584i −0.126542 + 0.610211i
\(502\) −9.59624 4.81941i −0.428301 0.215101i
\(503\) −25.2177 21.1601i −1.12440 0.943484i −0.125583 0.992083i \(-0.540080\pi\)
−0.998818 + 0.0485988i \(0.984524\pi\)
\(504\) 1.57067 + 0.680704i 0.0699630 + 0.0303209i
\(505\) −9.80560 + 8.22788i −0.436343 + 0.366136i
\(506\) −32.1335 + 7.61579i −1.42851 + 0.338563i
\(507\) −8.25281 11.8077i −0.366520 0.524398i
\(508\) −0.561920 + 9.64779i −0.0249312 + 0.428051i
\(509\) −1.47242 4.91823i −0.0652639 0.217997i 0.919137 0.393939i \(-0.128888\pi\)
−0.984400 + 0.175942i \(0.943703\pi\)
\(510\) −0.729450 + 0.449072i −0.0323006 + 0.0198852i
\(511\) −2.50043 + 3.35866i −0.110612 + 0.148578i
\(512\) 2.95483 + 5.11791i 0.130586 + 0.226182i
\(513\) 17.5033 4.64197i 0.772791 0.204948i
\(514\) −2.02126 + 3.50093i −0.0891541 + 0.154419i
\(515\) −0.714261 1.65584i −0.0314741 0.0729651i
\(516\) 3.75575 11.3019i 0.165338 0.497538i
\(517\) 10.2979 10.9151i 0.452902 0.480048i
\(518\) −4.81872 3.16932i −0.211722 0.139252i
\(519\) −25.2210 17.6921i −1.10708 0.776596i
\(520\) 8.00400 + 8.48374i 0.350999 + 0.372037i
\(521\) −1.32353 7.50611i −0.0579849 0.328849i 0.941992 0.335635i \(-0.108951\pi\)
−0.999977 + 0.00678637i \(0.997840\pi\)
\(522\) 36.9739 21.2628i 1.61831 0.930647i
\(523\) −1.93766 + 10.9890i −0.0847279 + 0.480516i 0.912687 + 0.408659i \(0.134004\pi\)
−0.997415 + 0.0718566i \(0.977108\pi\)
\(524\) 4.62597 3.04255i 0.202087 0.132914i
\(525\) −1.67234 0.0500896i −0.0729867 0.00218609i
\(526\) −23.7732 + 2.77868i −1.03656 + 0.121156i
\(527\) −0.167673 + 0.0195981i −0.00730395 + 0.000853709i
\(528\) 9.88210 + 18.3650i 0.430063 + 0.799236i
\(529\) −34.3883 + 22.6175i −1.49514 + 0.983370i
\(530\) 3.48297 19.7529i 0.151291 0.858012i
\(531\) −20.8745 + 3.64398i −0.905875 + 0.158135i
\(532\) −0.173544 0.984215i −0.00752407 0.0426711i
\(533\) 14.8838 + 15.7759i 0.644689 + 0.683331i
\(534\) −35.0449 + 16.3053i −1.51654 + 0.705599i
\(535\) 0.887805 + 0.583919i 0.0383832 + 0.0252450i
\(536\) 1.58406 1.67900i 0.0684208 0.0725218i
\(537\) 30.0615 6.18043i 1.29725 0.266705i
\(538\) 17.4250 + 40.3957i 0.751245 + 1.74158i
\(539\) −8.32207 + 14.4143i −0.358457 + 0.620866i
\(540\) 6.45729 + 1.35058i 0.277877 + 0.0581198i
\(541\) 12.8996 + 22.3428i 0.554598 + 0.960592i 0.997935 + 0.0642366i \(0.0204612\pi\)
−0.443337 + 0.896355i \(0.646205\pi\)
\(542\) −13.3215 + 17.8938i −0.572206 + 0.768605i
\(543\) 1.30937 + 46.3620i 0.0561902 + 1.98958i
\(544\) −0.293627 0.980782i −0.0125891 0.0420507i
\(545\) 0.164671 2.82729i 0.00705373 0.121108i
\(546\) 1.79623 3.84346i 0.0768716 0.164485i
\(547\) 35.1748 8.33659i 1.50397 0.356447i 0.605628 0.795748i \(-0.292922\pi\)
0.898340 + 0.439301i \(0.144774\pi\)
\(548\) 0.822645 0.690281i 0.0351417 0.0294874i
\(549\) −13.4410 26.8775i −0.573646 1.14711i
\(550\) −9.83406 8.25176i −0.419326 0.351856i
\(551\) 25.8913 + 13.0031i 1.10301 + 0.553952i
\(552\) 19.0485 + 16.9809i 0.810758 + 0.722755i
\(553\) 0.389173 0.902203i 0.0165493 0.0383656i
\(554\) −5.32884 7.15787i −0.226401 0.304109i
\(555\) 24.0264 + 9.56886i 1.01987 + 0.406176i
\(556\) −0.876571 15.0501i −0.0371749 0.638268i
\(557\) 31.3174 11.3986i 1.32696 0.482974i 0.421278 0.906931i \(-0.361582\pi\)
0.905682 + 0.423957i \(0.139359\pi\)
\(558\) 3.29488 + 2.46171i 0.139483 + 0.104212i
\(559\) 32.2717 + 11.7459i 1.36495 + 0.496800i
\(560\) −0.610282 + 2.03848i −0.0257891 + 0.0861417i
\(561\) −0.226853 0.849528i −0.00957773 0.0358671i
\(562\) 8.68004 4.35928i 0.366145 0.183885i
\(563\) 33.7166 + 7.99099i 1.42099 + 0.336780i 0.868064 0.496453i \(-0.165364\pi\)
0.552923 + 0.833233i \(0.313512\pi\)
\(564\) 9.85959 + 1.45282i 0.415164 + 0.0611748i
\(565\) 8.01793 + 0.937162i 0.337317 + 0.0394267i
\(566\) 19.4174 0.816173
\(567\) 0.475430 + 2.75123i 0.0199662 + 0.115541i
\(568\) 3.28856 0.137985
\(569\) −32.6401 3.81508i −1.36834 0.159936i −0.600013 0.799990i \(-0.704838\pi\)
−0.768330 + 0.640054i \(0.778912\pi\)
\(570\) 5.22290 + 13.1796i 0.218763 + 0.552034i
\(571\) −14.8522 3.52004i −0.621545 0.147309i −0.0922351 0.995737i \(-0.529401\pi\)
−0.529310 + 0.848428i \(0.677549\pi\)
\(572\) 9.19532 4.61806i 0.384476 0.193091i
\(573\) 5.24419 + 1.40998i 0.219079 + 0.0589027i
\(574\) −0.714740 + 2.38740i −0.0298327 + 0.0996481i
\(575\) −23.4369 8.53034i −0.977386 0.355740i
\(576\) 2.26171 4.48432i 0.0942380 0.186847i
\(577\) 9.00255 3.27666i 0.374781 0.136409i −0.147760 0.989023i \(-0.547206\pi\)
0.522541 + 0.852614i \(0.324984\pi\)
\(578\) −1.68595 28.9467i −0.0701264 1.20402i
\(579\) −2.46581 16.9348i −0.102476 0.703786i
\(580\) 6.30308 + 8.46650i 0.261721 + 0.351552i
\(581\) −0.0985762 + 0.228525i −0.00408963 + 0.00948083i
\(582\) 18.7600 6.19861i 0.777627 0.256940i
\(583\) 18.3991 + 9.24035i 0.762011 + 0.382696i
\(584\) 19.0182 + 15.9582i 0.786980 + 0.660355i
\(585\) −4.41869 + 18.5030i −0.182691 + 0.765006i
\(586\) −22.6380 + 18.9955i −0.935165 + 0.784697i
\(587\) −27.7523 + 6.57742i −1.14546 + 0.271479i −0.759166 0.650897i \(-0.774393\pi\)
−0.386294 + 0.922376i \(0.626245\pi\)
\(588\) −11.0126 + 0.953999i −0.454151 + 0.0393423i
\(589\) −0.162450 + 2.78917i −0.00669365 + 0.114926i
\(590\) −4.75790 15.8925i −0.195880 0.654284i
\(591\) −3.10661 1.67850i −0.127789 0.0690442i
\(592\) −32.4237 + 43.5525i −1.33260 + 1.79000i
\(593\) −21.1230 36.5862i −0.867419 1.50241i −0.864625 0.502418i \(-0.832444\pi\)
−0.00279478 0.999996i \(-0.500890\pi\)
\(594\) −10.2156 + 18.8303i −0.419150 + 0.772617i
\(595\) 0.0448581 0.0776966i 0.00183900 0.00318525i
\(596\) −3.26912 7.57867i −0.133908 0.310434i
\(597\) −15.0345 16.9233i −0.615323 0.692623i
\(598\) 43.4003 46.0016i 1.77477 1.88115i
\(599\) 14.9593 + 9.83888i 0.611220 + 0.402006i 0.817037 0.576585i \(-0.195615\pi\)
−0.205818 + 0.978590i \(0.565985\pi\)
\(600\) −0.873020 + 9.88145i −0.0356409 + 0.403409i
\(601\) 6.88063 + 7.29305i 0.280667 + 0.297490i 0.852336 0.522995i \(-0.175185\pi\)
−0.571669 + 0.820484i \(0.693704\pi\)
\(602\) 0.685225 + 3.88610i 0.0279277 + 0.158386i
\(603\) 3.70655 + 0.660095i 0.150942 + 0.0268812i
\(604\) −2.50327 + 14.1968i −0.101857 + 0.577658i
\(605\) 5.95265 3.91512i 0.242010 0.159172i
\(606\) 14.5125 23.4834i 0.589529 0.953948i
\(607\) 11.8705 1.38747i 0.481811 0.0563156i 0.128279 0.991738i \(-0.459055\pi\)
0.353532 + 0.935423i \(0.384981\pi\)
\(608\) −16.8293 + 1.96706i −0.682518 + 0.0797749i
\(609\) −2.34840 + 3.80007i −0.0951619 + 0.153987i
\(610\) 19.6561 12.9280i 0.795851 0.523439i
\(611\) −4.99036 + 28.3018i −0.201888 + 1.14497i
\(612\) 0.376128 0.446700i 0.0152041 0.0180568i
\(613\) −6.82305 38.6954i −0.275580 1.56289i −0.737112 0.675771i \(-0.763811\pi\)
0.461532 0.887124i \(-0.347300\pi\)
\(614\) −9.87275 10.4645i −0.398432 0.422313i
\(615\) 0.983437 11.1312i 0.0396560 0.448854i
\(616\) −1.14936 0.755943i −0.0463088 0.0304578i
\(617\) 28.0503 29.7316i 1.12926 1.19695i 0.151230 0.988499i \(-0.451677\pi\)
0.978033 0.208450i \(-0.0668419\pi\)
\(618\) 2.58301 + 2.90750i 0.103904 + 0.116957i
\(619\) 10.1196 + 23.4598i 0.406740 + 0.942928i 0.991305 + 0.131582i \(0.0420057\pi\)
−0.584566 + 0.811346i \(0.698735\pi\)
\(620\) −0.508917 + 0.881470i −0.0204386 + 0.0354007i
\(621\) −6.13771 + 41.1659i −0.246298 + 1.65193i
\(622\) 5.60517 + 9.70843i 0.224747 + 0.389273i
\(623\) 2.41746 3.24722i 0.0968537 0.130097i
\(624\) −35.1384 18.9852i −1.40666 0.760016i
\(625\) −0.0757739 0.253102i −0.00303095 0.0101241i
\(626\) 0.542118 9.30781i 0.0216674 0.372015i
\(627\) −14.4981 + 1.25594i −0.578999 + 0.0501576i
\(628\) 11.0089 2.60915i 0.439303 0.104117i
\(629\) 1.75368 1.47151i 0.0699239 0.0586731i
\(630\) −2.09506 + 0.623321i −0.0834691 + 0.0248337i
\(631\) −3.09592 2.59779i −0.123247 0.103416i 0.579081 0.815270i \(-0.303411\pi\)
−0.702328 + 0.711854i \(0.747856\pi\)
\(632\) −5.20607 2.61459i −0.207086 0.104003i
\(633\) −26.1058 + 8.62577i −1.03761 + 0.342843i
\(634\) 2.43523 5.64549i 0.0967152 0.224211i
\(635\) 8.57405 + 11.5170i 0.340251 + 0.457036i
\(636\) 1.97021 + 13.5311i 0.0781237 + 0.536542i
\(637\) −1.85337 31.8212i −0.0734333 1.26080i
\(638\) −32.2091 + 11.7231i −1.27517 + 0.464123i
\(639\) 2.93972 + 4.48631i 0.116294 + 0.177476i
\(640\) 16.2444 + 5.91248i 0.642116 + 0.233711i
\(641\) −3.39146 + 11.3283i −0.133955 + 0.447440i −0.998478 0.0551528i \(-0.982435\pi\)
0.864523 + 0.502593i \(0.167621\pi\)
\(642\) −2.21311 0.595027i −0.0873443 0.0234838i
\(643\) −18.1003 + 9.09029i −0.713804 + 0.358486i −0.768354 0.640025i \(-0.778924\pi\)
0.0545496 + 0.998511i \(0.482628\pi\)
\(644\) 2.23513 + 0.529736i 0.0880766 + 0.0208745i
\(645\) −6.51875 16.4496i −0.256675 0.647702i
\(646\) 1.24643 + 0.145687i 0.0490403 + 0.00573199i
\(647\) 25.4173 0.999257 0.499629 0.866240i \(-0.333470\pi\)
0.499629 + 0.866240i \(0.333470\pi\)
\(648\) 16.4487 1.86564i 0.646166 0.0732891i
\(649\) 17.0290 0.668446
\(650\) 24.4187 + 2.85414i 0.957780 + 0.111948i
\(651\) −0.426168 0.0627963i −0.0167029 0.00246118i
\(652\) −22.5608 5.34701i −0.883549 0.209405i
\(653\) 5.84284 2.93439i 0.228648 0.114831i −0.330787 0.943705i \(-0.607314\pi\)
0.559435 + 0.828874i \(0.311018\pi\)
\(654\) 1.57578 + 5.90105i 0.0616179 + 0.230749i
\(655\) 2.35928 7.88056i 0.0921848 0.307919i
\(656\) 22.0460 + 8.02410i 0.860753 + 0.313289i
\(657\) −4.76957 + 40.2104i −0.186078 + 1.56876i
\(658\) −3.10295 + 1.12938i −0.120966 + 0.0440279i
\(659\) 1.45025 + 24.8998i 0.0564936 + 0.969958i 0.900838 + 0.434156i \(0.142953\pi\)
−0.844344 + 0.535802i \(0.820010\pi\)
\(660\) −4.92530 1.96157i −0.191717 0.0763540i
\(661\) −26.8875 36.1162i −1.04580 1.40476i −0.910285 0.413982i \(-0.864138\pi\)
−0.135518 0.990775i \(-0.543270\pi\)
\(662\) 18.1573 42.0934i 0.705705 1.63601i
\(663\) 1.25698 + 1.12054i 0.0488171 + 0.0435183i
\(664\) 1.31868 + 0.662266i 0.0511747 + 0.0257009i
\(665\) −1.13743 0.954419i −0.0441077 0.0370108i
\(666\) −55.6750 3.33814i −2.15736 0.129350i
\(667\) −51.0131 + 42.8051i −1.97523 + 1.65742i
\(668\) 7.24404 1.71687i 0.280280 0.0664276i
\(669\) 1.39014 2.97452i 0.0537458 0.115002i
\(670\) −0.171379 + 2.94247i −0.00662096 + 0.113678i
\(671\) 6.92624 + 23.1352i 0.267384 + 0.893126i
\(672\) −0.0737520 2.61141i −0.00284504 0.100737i
\(673\) 7.24462 9.73122i 0.279260 0.375111i −0.640258 0.768160i \(-0.721172\pi\)
0.919517 + 0.393049i \(0.128580\pi\)
\(674\) 18.4838 + 32.0150i 0.711971 + 1.23317i
\(675\) −14.2609 + 7.64229i −0.548901 + 0.294152i
\(676\) −3.84429 + 6.65851i −0.147857 + 0.256097i
\(677\) −2.36922 5.49247i −0.0910566 0.211093i 0.866602 0.499001i \(-0.166300\pi\)
−0.957658 + 0.287908i \(0.907040\pi\)
\(678\) −17.0529 + 3.50597i −0.654915 + 0.134646i
\(679\) −1.42005 + 1.50516i −0.0544965 + 0.0577629i
\(680\) −0.444429 0.292306i −0.0170431 0.0112094i
\(681\) 40.1353 18.6737i 1.53799 0.715577i
\(682\) −2.26821 2.40416i −0.0868543 0.0920602i
\(683\) 4.79324 + 27.1838i 0.183408 + 1.04016i 0.927984 + 0.372621i \(0.121541\pi\)
−0.744575 + 0.667538i \(0.767348\pi\)
\(684\) −6.19966 7.41415i −0.237050 0.283487i
\(685\) 0.277053 1.57124i 0.0105856 0.0600341i
\(686\) 6.16262 4.05322i 0.235290 0.154753i
\(687\) −3.85050 7.15583i −0.146906 0.273012i
\(688\) 36.8975 4.31270i 1.40670 0.164420i
\(689\) −39.1634 + 4.57754i −1.49200 + 0.174390i
\(690\) −32.5698 0.975527i −1.23991 0.0371377i
\(691\) 24.5061 16.1179i 0.932254 0.613153i 0.0100889 0.999949i \(-0.496789\pi\)
0.922165 + 0.386796i \(0.126418\pi\)
\(692\) −2.85518 + 16.1926i −0.108538 + 0.615549i
\(693\) 0.00383277 2.24373i 0.000145595 0.0852321i
\(694\) −5.00138 28.3642i −0.189850 1.07669i
\(695\) −15.3704 16.2917i −0.583034 0.617980i
\(696\) 21.6834 + 15.2105i 0.821906 + 0.576552i
\(697\) −0.826436 0.543556i −0.0313035 0.0205886i
\(698\) −2.31335 + 2.45201i −0.0875617 + 0.0928099i
\(699\) 6.26058 18.8395i 0.236797 0.712574i
\(700\) 0.353677 + 0.819915i 0.0133677 + 0.0309899i
\(701\) −1.45226 + 2.51539i −0.0548512 + 0.0950051i −0.892147 0.451745i \(-0.850802\pi\)
0.837296 + 0.546750i \(0.184135\pi\)
\(702\) −3.47098 40.8796i −0.131004 1.54290i
\(703\) −18.9438 32.8116i −0.714479 1.23751i
\(704\) −2.41021 + 3.23748i −0.0908383 + 0.122017i
\(705\) 12.6088 7.76237i 0.474875 0.292348i
\(706\) 2.85106 + 9.52321i 0.107301 + 0.358411i
\(707\) −0.168115 + 2.88642i −0.00632260 + 0.108555i
\(708\) 6.47889 + 9.26966i 0.243492 + 0.348375i
\(709\) −24.0474 + 5.69934i −0.903119 + 0.214043i −0.655839 0.754901i \(-0.727685\pi\)
−0.247280 + 0.968944i \(0.579537\pi\)
\(710\) −3.21672 + 2.69915i −0.120721 + 0.101297i
\(711\) −1.08697 9.43945i −0.0407646 0.354007i
\(712\) −18.3872 15.4287i −0.689089 0.578215i
\(713\) −5.73853 2.88200i −0.214910 0.107932i
\(714\) −0.0392883 + 0.189456i −0.00147033 + 0.00709022i
\(715\) 6.05513 14.0374i 0.226449 0.524968i
\(716\) −9.78127 13.1385i −0.365543 0.491010i
\(717\) 15.9701 12.6054i 0.596414 0.470756i
\(718\) 1.93893 + 33.2901i 0.0723602 + 1.24238i
\(719\) 23.8425 8.67796i 0.889175 0.323633i 0.143269 0.989684i \(-0.454239\pi\)
0.745907 + 0.666051i \(0.232017\pi\)
\(720\) 4.71131 + 20.0310i 0.175580 + 0.746511i
\(721\) −0.382767 0.139316i −0.0142550 0.00518838i
\(722\) −3.36211 + 11.2302i −0.125125 + 0.417946i
\(723\) 5.41668 5.40743i 0.201448 0.201105i
\(724\) 22.1207 11.1095i 0.822111 0.412880i
\(725\) −25.1892 5.96994i −0.935502 0.221718i
\(726\) −9.54061 + 12.0449i −0.354085 + 0.447029i
\(727\) −17.6415 2.06200i −0.654288 0.0764754i −0.217529 0.976054i \(-0.569800\pi\)
−0.436759 + 0.899578i \(0.643874\pi\)
\(728\) 2.63453 0.0976424
\(729\) 17.2490 + 20.7719i 0.638853 + 0.769328i
\(730\) −31.7008 −1.17330
\(731\) −1.55568 0.181833i −0.0575391 0.00672535i
\(732\) −9.95840 + 12.5724i −0.368073 + 0.464688i
\(733\) 9.01202 + 2.13589i 0.332866 + 0.0788908i 0.393651 0.919260i \(-0.371212\pi\)
−0.0607842 + 0.998151i \(0.519360\pi\)
\(734\) 28.8694 14.4988i 1.06559 0.535159i
\(735\) −11.6226 + 11.6027i −0.428704 + 0.427973i
\(736\) 11.1694 37.3083i 0.411708 1.37520i
\(737\) −2.84309 1.03480i −0.104726 0.0381173i
\(738\) 5.51771 + 23.4596i 0.203110 + 0.863558i
\(739\) 5.02496 1.82894i 0.184846 0.0672785i −0.247939 0.968776i \(-0.579753\pi\)
0.432785 + 0.901497i \(0.357531\pi\)
\(740\) −0.802557 13.7794i −0.0295026 0.506540i
\(741\) 21.8758 17.2668i 0.803628 0.634312i
\(742\) −2.70547 3.63408i −0.0993211 0.133411i
\(743\) −10.3074 + 23.8952i −0.378141 + 0.876629i 0.617776 + 0.786354i \(0.288034\pi\)
−0.995917 + 0.0902752i \(0.971225\pi\)
\(744\) −0.518619 + 2.50088i −0.0190135 + 0.0916869i
\(745\) −10.9582 5.50343i −0.401478 0.201630i
\(746\) 29.2071 + 24.5076i 1.06935 + 0.897288i
\(747\) 0.275327 + 2.39098i 0.0100737 + 0.0874815i
\(748\) −0.359496 + 0.301653i −0.0131445 + 0.0110295i
\(749\) 0.233553 0.0553530i 0.00853382 0.00202255i
\(750\) −18.9087 27.0536i −0.690449 0.987858i
\(751\) 0.211970 3.63939i 0.00773490 0.132803i −0.992230 0.124418i \(-0.960294\pi\)
0.999965 0.00838551i \(-0.00266922\pi\)
\(752\) 8.91566 + 29.7804i 0.325121 + 1.08598i
\(753\) 9.26192 5.70192i 0.337523 0.207790i
\(754\) 39.1987 52.6530i 1.42753 1.91751i
\(755\) 10.7088 + 18.5482i 0.389733 + 0.675038i
\(756\) 1.22282 0.851568i 0.0444736 0.0309712i
\(757\) −5.44196 + 9.42576i −0.197792 + 0.342585i −0.947812 0.318830i \(-0.896710\pi\)
0.750021 + 0.661415i \(0.230044\pi\)
\(758\) 8.08880 + 18.7519i 0.293798 + 0.681101i
\(759\) 10.5479 31.7410i 0.382866 1.15213i
\(760\) −6.04143 + 6.40354i −0.219146 + 0.232281i
\(761\) −20.6250 13.5653i −0.747655 0.491740i 0.117607 0.993060i \(-0.462478\pi\)
−0.865262 + 0.501320i \(0.832848\pi\)
\(762\) −25.3502 17.7827i −0.918341 0.644199i
\(763\) −0.438992 0.465305i −0.0158926 0.0168452i
\(764\) −0.503281 2.85425i −0.0182081 0.103263i
\(765\) 0.00148204 0.867597i 5.35834e−5 0.0313680i
\(766\) −6.20921 + 35.2142i −0.224348 + 1.27234i
\(767\) −27.2470 + 17.9206i −0.983832 + 0.647076i
\(768\) −31.4685 0.942540i −1.13552 0.0340110i
\(769\) −31.0819 + 3.63295i −1.12084 + 0.131008i −0.656269 0.754527i \(-0.727866\pi\)
−0.464573 + 0.885535i \(0.653792\pi\)
\(770\) 1.74470 0.203927i 0.0628748 0.00734901i
\(771\) −1.94014 3.60559i −0.0698725 0.129852i
\(772\) −7.63100 + 5.01899i −0.274646 + 0.180637i
\(773\) 2.32846 13.2054i 0.0837490 0.474964i −0.913871 0.406006i \(-0.866921\pi\)
0.997620 0.0689585i \(-0.0219676\pi\)
\(774\) 24.4789 + 29.2743i 0.879877 + 1.05224i
\(775\) −0.433476 2.45837i −0.0155709 0.0883071i
\(776\) 8.41966 + 8.92431i 0.302248 + 0.320364i
\(777\) 5.29641 2.46425i 0.190008 0.0884045i
\(778\) 13.7186 + 9.02287i 0.491836 + 0.323486i
\(779\) −11.2343 + 11.9077i −0.402511 + 0.426637i
\(780\) 9.94494 2.04461i 0.356086 0.0732088i
\(781\) −1.70726 3.95787i −0.0610905 0.141624i
\(782\) −1.44218 + 2.49792i −0.0515721 + 0.0893255i
\(783\) −1.36709 + 43.1779i −0.0488557 + 1.54305i
\(784\) −17.2397 29.8600i −0.615703 1.06643i
\(785\) 10.0377 13.4830i 0.358260 0.481227i
\(786\) 0.500844 + 17.7339i 0.0178645 + 0.632546i
\(787\) −5.98854 20.0031i −0.213468 0.713034i −0.995913 0.0903142i \(-0.971213\pi\)
0.782445 0.622720i \(-0.213972\pi\)
\(788\) −0.109578 + 1.88138i −0.00390354 + 0.0670213i
\(789\) 10.2640 21.9623i 0.365409 0.781878i
\(790\) 7.23832 1.71551i 0.257528 0.0610352i
\(791\) 1.39681 1.17206i 0.0496648 0.0416737i
\(792\) −13.2795 0.796208i −0.471867 0.0282920i
\(793\) −35.4289 29.7283i −1.25812 1.05568i
\(794\) 3.14321 + 1.57858i 0.111548 + 0.0560216i
\(795\) 15.1644 + 13.5184i 0.537826 + 0.479449i
\(796\) −4.78528 + 11.0935i −0.169610 + 0.393199i
\(797\) 31.0967 + 41.7701i 1.10150 + 1.47957i 0.860778 + 0.508980i \(0.169977\pi\)
0.240724 + 0.970594i \(0.422615\pi\)
\(798\) 2.97497 + 1.18482i 0.105313 + 0.0419423i
\(799\) −0.0762088 1.30846i −0.00269608 0.0462898i
\(800\) 14.2260 5.17785i 0.502966 0.183065i
\(801\) 4.61131 38.8762i 0.162933 1.37362i
\(802\) 1.08778 + 0.395920i 0.0384109 + 0.0139804i
\(803\) 9.33278 31.1737i 0.329347 1.10009i
\(804\) −0.518400 1.94133i −0.0182826 0.0684653i
\(805\) 3.04974 1.53164i 0.107489 0.0539831i
\(806\) 6.15927 + 1.45977i 0.216951 + 0.0514183i
\(807\) −44.0826 6.49561i −1.55178 0.228656i
\(808\) 17.0270 + 1.99017i 0.599009 + 0.0700141i
\(809\) −41.7858 −1.46911 −0.734554 0.678550i \(-0.762609\pi\)
−0.734554 + 0.678550i \(0.762609\pi\)
\(810\) −14.5581 + 15.3255i −0.511521 + 0.538483i
\(811\) 5.44750 0.191287 0.0956437 0.995416i \(-0.469509\pi\)
0.0956437 + 0.995416i \(0.469509\pi\)
\(812\) 2.36805 + 0.276785i 0.0831022 + 0.00971325i
\(813\) −8.32410 21.0053i −0.291939 0.736687i
\(814\) 43.6141 + 10.3367i 1.52867 + 0.362302i
\(815\) −30.7832 + 15.4599i −1.07829 + 0.541537i
\(816\) 1.75904 + 0.472945i 0.0615788 + 0.0165564i
\(817\) −7.43451 + 24.8330i −0.260101 + 0.868797i
\(818\) 27.5649 + 10.0328i 0.963783 + 0.350788i
\(819\) 2.35508 + 3.59408i 0.0822931 + 0.125587i
\(820\) −5.60432 + 2.03981i −0.195711 + 0.0712331i
\(821\) −1.78967 30.7275i −0.0624600 1.07240i −0.873317 0.487152i \(-0.838036\pi\)
0.810857 0.585244i \(-0.199001\pi\)
\(822\) 0.495788 + 3.40500i 0.0172926 + 0.118763i
\(823\) 11.1564 + 14.9856i 0.388886 + 0.522365i 0.952853 0.303433i \(-0.0981327\pi\)
−0.563967 + 0.825798i \(0.690725\pi\)
\(824\) −0.956581 + 2.21760i −0.0333241 + 0.0772539i
\(825\) 12.3458 4.07926i 0.429827 0.142022i
\(826\) −3.34861 1.68174i −0.116513 0.0585151i
\(827\) −1.28456 1.07787i −0.0446686 0.0374814i 0.620180 0.784459i \(-0.287060\pi\)
−0.664849 + 0.746978i \(0.731504\pi\)
\(828\) 21.2912 6.33456i 0.739921 0.220141i
\(829\) 23.5451 19.7567i 0.817755 0.686178i −0.134690 0.990888i \(-0.543004\pi\)
0.952445 + 0.304710i \(0.0985595\pi\)
\(830\) −1.83344 + 0.434534i −0.0636398 + 0.0150829i
\(831\) 9.00452 0.780044i 0.312363 0.0270594i
\(832\) 0.449435 7.71650i 0.0155813 0.267521i
\(833\) 0.416935 + 1.39266i 0.0144459 + 0.0482528i
\(834\) 42.4983 + 22.9618i 1.47160 + 0.795101i
\(835\) 6.60497 8.87201i 0.228574 0.307029i
\(836\) 3.88339 + 6.72622i 0.134310 + 0.232631i
\(837\) −3.87536 + 1.52810i −0.133952 + 0.0528187i
\(838\) −24.0161 + 41.5971i −0.829622 + 1.43695i
\(839\) −4.82744 11.1913i −0.166662 0.386366i 0.814333 0.580397i \(-0.197103\pi\)
−0.980995 + 0.194032i \(0.937844\pi\)
\(840\) −0.901508 1.01476i −0.0311050 0.0350126i
\(841\) −27.5310 + 29.1811i −0.949343 + 1.00625i
\(842\) −14.3579 9.44331i −0.494804 0.325438i
\(843\) −0.865803 + 9.79976i −0.0298198 + 0.337522i
\(844\) 10.0698 + 10.6733i 0.346615 + 0.367391i
\(845\) 1.98358 + 11.2494i 0.0682373 + 0.386993i
\(846\) −20.5678 + 24.4268i −0.707134 + 0.839812i
\(847\) 0.279457 1.58488i 0.00960225 0.0544571i
\(848\) −35.6348 + 23.4374i −1.22370 + 0.804843i
\(849\) −10.3389 + 16.7298i −0.354828 + 0.574166i
\(850\) −1.11367 + 0.130169i −0.0381984 + 0.00446475i
\(851\) 86.4934 10.1096i 2.96495 0.346553i
\(852\) 1.50490 2.43516i 0.0515571 0.0834272i
\(853\) 7.58261 4.98716i 0.259624 0.170757i −0.413024 0.910720i \(-0.635527\pi\)
0.672647 + 0.739963i \(0.265157\pi\)
\(854\) 0.922785 5.23338i 0.0315771 0.179082i
\(855\) −14.1364 2.51754i −0.483455 0.0860980i
\(856\) −0.247123 1.40150i −0.00844649 0.0479024i
\(857\) −17.4250 18.4695i −0.595228 0.630905i 0.357796 0.933800i \(-0.383528\pi\)
−0.953024 + 0.302895i \(0.902047\pi\)
\(858\) −2.90159 + 32.8423i −0.0990588 + 1.12122i
\(859\) 0.357616 + 0.235208i 0.0122017 + 0.00802519i 0.555595 0.831453i \(-0.312490\pi\)
−0.543393 + 0.839478i \(0.682861\pi\)
\(860\) −6.48056 + 6.86900i −0.220985 + 0.234231i
\(861\) −1.67640 1.88699i −0.0571314 0.0643086i
\(862\) −3.62210 8.39698i −0.123369 0.286002i
\(863\) 20.6116 35.7004i 0.701628 1.21526i −0.266267 0.963899i \(-0.585790\pi\)
0.967895 0.251356i \(-0.0808764\pi\)
\(864\) −13.2077 21.5362i −0.449334 0.732676i
\(865\) 12.2143 + 21.1557i 0.415297 + 0.719316i
\(866\) 7.03984 9.45614i 0.239223 0.321333i
\(867\) 25.8379 + 13.9602i 0.877501 + 0.474112i
\(868\) 0.0659379 + 0.220248i 0.00223808 + 0.00747570i
\(869\) −0.443990 + 7.62301i −0.0150613 + 0.258593i
\(870\) −33.6940 + 2.91885i −1.14233 + 0.0989583i
\(871\) 5.63803 1.33624i 0.191037 0.0452767i
\(872\) −2.90553 + 2.43803i −0.0983936 + 0.0825620i
\(873\) −4.64816 + 19.4639i −0.157316 + 0.658754i
\(874\) 36.5681 + 30.6843i 1.23693 + 1.03791i
\(875\) 3.08926 + 1.55148i 0.104436 + 0.0524497i
\(876\) 20.5200 6.78016i 0.693308 0.229080i
\(877\) −14.9215 + 34.5918i −0.503862 + 1.16808i 0.456600 + 0.889672i \(0.349067\pi\)
−0.960462 + 0.278411i \(0.910192\pi\)
\(878\) −15.9026 21.3609i −0.536686 0.720894i
\(879\) −4.31269 29.6189i −0.145463 0.999020i
\(880\) −0.961523 16.5087i −0.0324129 0.556509i
\(881\) 2.94091 1.07040i 0.0990817 0.0360628i −0.292004 0.956417i \(-0.594322\pi\)
0.391085 + 0.920354i \(0.372100\pi\)
\(882\) 15.9497 31.6237i 0.537054 1.06482i
\(883\) 46.2681 + 16.8402i 1.55705 + 0.566719i 0.970057 0.242876i \(-0.0780909\pi\)
0.586989 + 0.809595i \(0.300313\pi\)
\(884\) 0.257759 0.860976i 0.00866938 0.0289577i
\(885\) 16.2262 + 4.36266i 0.545438 + 0.146649i
\(886\) 42.7196 21.4546i 1.43519 0.720781i
\(887\) −52.8516 12.5261i −1.77458 0.420584i −0.792629 0.609704i \(-0.791288\pi\)
−0.981954 + 0.189121i \(0.939436\pi\)
\(888\) −12.7602 32.1995i −0.428205 1.08055i
\(889\) 3.22125 + 0.376510i 0.108037 + 0.0126277i
\(890\) 30.6490 1.02736
\(891\) −10.7847 18.8279i −0.361301 0.630759i
\(892\) −1.75235 −0.0586730
\(893\) −21.5451 2.51826i −0.720979 0.0842703i
\(894\) 26.1636 + 3.85523i 0.875042 + 0.128938i
\(895\) −23.6795 5.61213i −0.791517 0.187593i
\(896\) 3.48940 1.75244i 0.116573 0.0585450i
\(897\) 16.5259 + 61.8871i 0.551785 + 2.06635i
\(898\) −5.36337 + 17.9149i −0.178978 + 0.597828i
\(899\) −6.26317 2.27961i −0.208888 0.0760291i
\(900\) 6.91766 + 5.16840i 0.230589 + 0.172280i
\(901\) 1.68984 0.615050i 0.0562966 0.0204903i
\(902\) −1.12610 19.3344i −0.0374951 0.643766i
\(903\) −3.71308 1.47879i −0.123564 0.0492109i
\(904\) −6.45600 8.67192i −0.214723 0.288424i
\(905\) 14.5665 33.7691i 0.484208 1.12252i
\(906\) −34.4791 30.7366i −1.14549 1.02116i
\(907\) 42.0616 + 21.1241i 1.39663 + 0.701415i 0.978360 0.206908i \(-0.0663400\pi\)
0.418271 + 0.908322i \(0.362636\pi\)
\(908\) −18.0983 15.1863i −0.600613 0.503974i
\(909\) 12.5059 + 25.0076i 0.414793 + 0.829451i
\(910\) −2.57699 + 2.16235i −0.0854263 + 0.0716811i
\(911\) 50.3668 11.9372i 1.66873 0.395496i 0.715707 0.698400i \(-0.246105\pi\)
0.953021 + 0.302905i \(0.0979564\pi\)
\(912\) 12.7637 27.3108i 0.422647 0.904352i
\(913\) 0.112461 1.93088i 0.00372192 0.0639029i
\(914\) −8.05864 26.9177i −0.266556 0.890359i
\(915\) 0.672703 + 23.8191i 0.0222389 + 0.787434i
\(916\) −2.58984 + 3.47876i −0.0855708 + 0.114942i
\(917\) −0.929052 1.60917i −0.0306800 0.0531393i
\(918\) 0.583995 + 1.77764i 0.0192747 + 0.0586709i
\(919\) −6.58049 + 11.3977i −0.217070 + 0.375977i −0.953911 0.300090i \(-0.902983\pi\)
0.736841 + 0.676066i \(0.236317\pi\)
\(920\) −8.01452 18.5797i −0.264231 0.612556i
\(921\) 14.2729 2.93441i 0.470308 0.0966921i
\(922\) −29.3402 + 31.0988i −0.966270 + 1.02419i
\(923\) 6.89678 + 4.53608i 0.227010 + 0.149307i
\(924\) −1.08574 + 0.505159i −0.0357181 + 0.0166185i
\(925\) 23.2306 + 24.6230i 0.763816 + 0.809598i
\(926\) −4.02821 22.8451i −0.132375 0.750736i
\(927\) −3.88041 + 0.677388i −0.127449 + 0.0222483i
\(928\) 7.01909 39.8072i 0.230413 1.30674i
\(929\) −14.3922 + 9.46587i −0.472191 + 0.310565i −0.763208 0.646153i \(-0.776377\pi\)
0.291017 + 0.956718i \(0.406006\pi\)
\(930\) −1.54536 2.87192i −0.0506744 0.0941740i
\(931\) 23.8967 2.79312i 0.783182 0.0915409i
\(932\) −10.5238 + 1.23006i −0.344719 + 0.0402919i
\(933\) −11.3492 0.339930i −0.371556 0.0111288i
\(934\) −49.0242 + 32.2437i −1.60412 + 1.05505i
\(935\) −0.121072 + 0.686633i −0.00395948 + 0.0224553i
\(936\) 22.0856 12.7009i 0.721891 0.415142i
\(937\) 6.62799 + 37.5892i 0.216527 + 1.22799i 0.878237 + 0.478226i \(0.158720\pi\)
−0.661710 + 0.749760i \(0.730169\pi\)
\(938\) 0.456876 + 0.484261i 0.0149175 + 0.0158117i
\(939\) 7.73087 + 5.42306i 0.252287 + 0.176975i
\(940\) −6.60240 4.34247i −0.215347 0.141636i
\(941\) 14.6033 15.4786i 0.476053 0.504586i −0.444191 0.895932i \(-0.646509\pi\)
0.920244 + 0.391346i \(0.127990\pi\)
\(942\) −11.4321 + 34.4016i −0.372477 + 1.12086i
\(943\) −14.9034 34.5499i −0.485320 1.12510i
\(944\) −17.6383 + 30.5504i −0.574077 + 0.994331i
\(945\) 0.578473 2.13697i 0.0188177 0.0695157i
\(946\) −15.3333 26.5580i −0.498528 0.863476i
\(947\) −4.64962 + 6.24553i −0.151092 + 0.202952i −0.871225 0.490884i \(-0.836674\pi\)
0.720132 + 0.693837i \(0.244081\pi\)
\(948\) −4.31848 + 2.65859i −0.140258 + 0.0863469i
\(949\) 17.8731 + 59.7005i 0.580187 + 1.93796i
\(950\) −1.07898 + 18.5253i −0.0350067 + 0.601042i
\(951\) 3.56746 + 5.10413i 0.115683 + 0.165513i
\(952\) −0.116915 + 0.0277093i −0.00378923 + 0.000898064i
\(953\) 29.0892 24.4088i 0.942292 0.790677i −0.0356905 0.999363i \(-0.511363\pi\)
0.977983 + 0.208686i \(0.0669186\pi\)
\(954\) −40.1999 17.4221i −1.30152 0.564060i
\(955\) −3.29858 2.76784i −0.106740 0.0895652i
\(956\) −9.70360 4.87333i −0.313837 0.157615i
\(957\) 7.04928 33.9931i 0.227871 1.09884i
\(958\) 14.6723 34.0143i 0.474041 1.09895i
\(959\) −0.215207 0.289073i −0.00694939 0.00933464i
\(960\) −3.12600 + 2.46739i −0.100891 + 0.0796346i
\(961\) 1.76512 + 30.3059i 0.0569393 + 0.977610i
\(962\) −80.6621 + 29.3586i −2.60065 + 0.946560i
\(963\) 1.69105 1.58997i 0.0544932 0.0512360i
\(964\) −3.83856 1.39712i −0.123632 0.0449983i
\(965\) −3.89187 + 12.9998i −0.125284 + 0.418477i
\(966\) −5.20882 + 5.19993i −0.167591 + 0.167305i
\(967\) −4.84104 + 2.43126i −0.155677 + 0.0781841i −0.524932 0.851144i \(-0.675909\pi\)
0.369255 + 0.929328i \(0.379613\pi\)
\(968\) −9.28471 2.20052i −0.298422 0.0707273i
\(969\) −0.789192 + 0.996345i −0.0253525 + 0.0320072i
\(970\) −15.5606 1.81877i −0.499619 0.0583971i
\(971\) −45.8419 −1.47114 −0.735568 0.677451i \(-0.763085\pi\)
−0.735568 + 0.677451i \(0.763085\pi\)
\(972\) 6.14572 13.0339i 0.197124 0.418064i
\(973\) −5.05922 −0.162191
\(974\) 65.9882 + 7.71291i 2.11440 + 0.247138i
\(975\) −15.4609 + 19.5192i −0.495146 + 0.625116i
\(976\) −48.6792 11.5372i −1.55818 0.369297i
\(977\) −45.3323 + 22.7667i −1.45031 + 0.728372i −0.987431 0.158050i \(-0.949479\pi\)
−0.462877 + 0.886422i \(0.653183\pi\)
\(978\) 52.5764 52.4867i 1.68121 1.67834i
\(979\) −9.02312 + 30.1393i −0.288380 + 0.963257i
\(980\) 8.23640 + 2.99780i 0.263102 + 0.0957613i
\(981\) −5.92333 1.78436i −0.189117 0.0569702i
\(982\) 47.0562 17.1271i 1.50162 0.546546i
\(983\) 2.05422 + 35.2695i 0.0655193 + 1.12492i 0.857536 + 0.514424i \(0.171994\pi\)
−0.792017 + 0.610499i \(0.790969\pi\)
\(984\) −11.7472 + 9.27222i −0.374488 + 0.295588i
\(985\) 1.67199 + 2.24587i 0.0532741 + 0.0715595i
\(986\) −1.18576 + 2.74890i −0.0377623 + 0.0875429i
\(987\) 0.679113 3.27482i 0.0216164 0.104239i
\(988\) −13.2920 6.67548i −0.422874 0.212375i
\(989\) −45.6409 38.2973i −1.45130 1.21778i
\(990\) 13.6430 10.1206i 0.433601 0.321655i
\(991\) −3.21935 + 2.70136i −0.102266 + 0.0858114i −0.692487 0.721430i \(-0.743485\pi\)
0.590221 + 0.807242i \(0.299041\pi\)
\(992\) 3.79278 0.898906i 0.120421 0.0285403i
\(993\) 26.5994 + 38.0570i 0.844107 + 1.20770i
\(994\) −0.0551499 + 0.946887i −0.00174925 + 0.0300334i
\(995\) 5.14804 + 17.1956i 0.163204 + 0.545139i
\(996\) 1.09386 0.673412i 0.0346602 0.0213379i
\(997\) 4.11126 5.52238i 0.130205 0.174896i −0.732240 0.681047i \(-0.761525\pi\)
0.862445 + 0.506151i \(0.168932\pi\)
\(998\) −23.4914 40.6884i −0.743608 1.28797i
\(999\) 32.5205 46.1917i 1.02890 1.46144i
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 81.2.g.a.4.7 144
3.2 odd 2 243.2.g.a.64.2 144
9.2 odd 6 729.2.g.a.676.7 144
9.4 even 3 729.2.g.c.190.2 144
9.5 odd 6 729.2.g.b.190.7 144
9.7 even 3 729.2.g.d.676.2 144
81.7 even 27 729.2.g.d.55.2 144
81.20 odd 54 243.2.g.a.19.2 144
81.34 even 27 729.2.g.c.541.2 144
81.40 even 27 6561.2.a.c.1.18 72
81.41 odd 54 6561.2.a.d.1.55 72
81.47 odd 54 729.2.g.b.541.7 144
81.61 even 27 inner 81.2.g.a.61.7 yes 144
81.74 odd 54 729.2.g.a.55.7 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.4.7 144 1.1 even 1 trivial
81.2.g.a.61.7 yes 144 81.61 even 27 inner
243.2.g.a.19.2 144 81.20 odd 54
243.2.g.a.64.2 144 3.2 odd 2
729.2.g.a.55.7 144 81.74 odd 54
729.2.g.a.676.7 144 9.2 odd 6
729.2.g.b.190.7 144 9.5 odd 6
729.2.g.b.541.7 144 81.47 odd 54
729.2.g.c.190.2 144 9.4 even 3
729.2.g.c.541.2 144 81.34 even 27
729.2.g.d.55.2 144 81.7 even 27
729.2.g.d.676.2 144 9.7 even 3
6561.2.a.c.1.18 72 81.40 even 27
6561.2.a.d.1.55 72 81.41 odd 54