Properties

Label 243.2.i.a.103.23
Level $243$
Weight $2$
Character 243.103
Analytic conductor $1.940$
Analytic rank $0$
Dimension $1404$
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] = [243,2,Mod(4,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(162))
 
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("243.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.i (of order \(81\), degree \(54\), 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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 103.23
Character \(\chi\) \(=\) 243.103
Dual form 243.2.i.a.151.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.02543 + 0.563818i) q^{2} +(-0.0981720 - 1.72927i) q^{3} +(2.07216 + 1.25056i) q^{4} +(-1.27054 + 0.0493029i) q^{5} +(0.776151 - 3.55787i) q^{6} +(4.39851 + 0.687914i) q^{7} +(0.606370 + 0.642715i) q^{8} +(-2.98072 + 0.339531i) q^{9} +O(q^{10})\) \(q+(2.02543 + 0.563818i) q^{2} +(-0.0981720 - 1.72927i) q^{3} +(2.07216 + 1.25056i) q^{4} +(-1.27054 + 0.0493029i) q^{5} +(0.776151 - 3.55787i) q^{6} +(4.39851 + 0.687914i) q^{7} +(0.606370 + 0.642715i) q^{8} +(-2.98072 + 0.339531i) q^{9} +(-2.60120 - 0.616496i) q^{10} +(0.0413646 + 0.302842i) q^{11} +(1.95912 - 3.70609i) q^{12} +(1.95043 - 2.84380i) q^{13} +(8.52104 + 3.87329i) q^{14} +(0.209990 + 2.19227i) q^{15} +(-1.39012 - 2.63908i) q^{16} +(-6.95270 + 3.49177i) q^{17} +(-6.22870 - 0.992889i) q^{18} +(0.466686 + 8.01269i) q^{19} +(-2.69443 - 1.48672i) q^{20} +(0.757777 - 7.67373i) q^{21} +(-0.0869667 + 0.636709i) q^{22} +(1.39733 - 3.61918i) q^{23} +(1.05190 - 1.11167i) q^{24} +(-3.37311 + 0.262179i) q^{25} +(5.55385 - 4.66024i) q^{26} +(0.879763 + 5.12113i) q^{27} +(8.25415 + 6.92605i) q^{28} +(2.53701 + 1.81334i) q^{29} +(-0.810721 + 4.55869i) q^{30} +(-2.85491 + 3.27137i) q^{31} +(-1.70176 - 7.85622i) q^{32} +(0.519634 - 0.101261i) q^{33} +(-16.0510 + 3.15231i) q^{34} +(-5.62241 - 0.657166i) q^{35} +(-6.60114 - 3.02400i) q^{36} +(1.50445 + 2.02083i) q^{37} +(-3.57246 + 16.4923i) q^{38} +(-5.10916 - 3.09363i) q^{39} +(-0.802107 - 0.786701i) q^{40} +(-0.728308 + 2.82746i) q^{41} +(5.86142 - 15.1154i) q^{42} +(-6.63437 - 6.02037i) q^{43} +(-0.293007 + 0.679266i) q^{44} +(3.77040 - 0.578347i) q^{45} +(4.87077 - 6.54258i) q^{46} +(-0.229710 - 0.263218i) q^{47} +(-4.42720 + 2.66297i) q^{48} +(12.2079 + 3.91431i) q^{49} +(-6.97985 - 1.37080i) q^{50} +(6.72077 + 11.6803i) q^{51} +(7.59793 - 3.45368i) q^{52} +(0.771083 - 4.37303i) q^{53} +(-1.10549 + 10.8686i) q^{54} +(-0.0674864 - 0.382735i) q^{55} +(2.22499 + 3.24412i) q^{56} +(13.8103 - 1.59365i) q^{57} +(4.11614 + 5.10322i) q^{58} +(2.57549 - 1.05221i) q^{59} +(-2.30642 + 4.80534i) q^{60} +(10.2081 - 6.16060i) q^{61} +(-7.62689 + 5.01629i) q^{62} +(-13.3443 - 0.557053i) q^{63} +(0.635797 - 10.9162i) q^{64} +(-2.33790 + 3.70933i) q^{65} +(1.10958 + 0.0878816i) q^{66} +(5.48432 - 3.91995i) q^{67} +(-18.7738 - 1.45921i) q^{68} +(-6.39571 - 2.06106i) q^{69} +(-11.0173 - 4.50107i) q^{70} +(-0.934287 - 3.12074i) q^{71} +(-2.02564 - 1.70987i) q^{72} +(-4.31382 + 1.02239i) q^{73} +(1.90779 + 4.94130i) q^{74} +(0.784523 + 5.80728i) q^{75} +(-9.05327 + 17.1872i) q^{76} +(-0.0263870 + 1.36051i) q^{77} +(-8.60402 - 9.14659i) q^{78} +(9.02377 - 8.85045i) q^{79} +(1.89632 + 3.28453i) q^{80} +(8.76944 - 2.02410i) q^{81} +(-3.06932 + 5.31621i) q^{82} +(-0.101470 - 0.393932i) q^{83} +(11.1667 - 14.9536i) q^{84} +(8.66155 - 4.77924i) q^{85} +(-10.0431 - 15.9345i) q^{86} +(2.88669 - 4.56518i) q^{87} +(-0.169559 + 0.210220i) q^{88} +(2.03708 - 6.80431i) q^{89} +(7.96278 + 0.954416i) q^{90} +(10.5353 - 11.1667i) q^{91} +(7.42149 - 5.75209i) q^{92} +(5.93734 + 4.61575i) q^{93} +(-0.316855 - 0.662646i) q^{94} +(-0.987994 - 10.1575i) q^{95} +(-13.4184 + 3.71407i) q^{96} +(-11.4753 - 0.445293i) q^{97} +(22.5194 + 14.8112i) q^{98} +(-0.226121 - 0.888644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18} - 54 q^{19} - 54 q^{20} - 54 q^{21} - 54 q^{22} - 54 q^{23} - 54 q^{24} - 54 q^{25} - 54 q^{26} - 54 q^{27} - 54 q^{28} - 54 q^{29} - 54 q^{30} - 54 q^{31} - 54 q^{32} - 54 q^{33} - 54 q^{34} - 54 q^{35} - 54 q^{36} - 54 q^{37} - 54 q^{38} - 54 q^{39} - 54 q^{40} - 54 q^{41} - 54 q^{42} - 54 q^{43} - 54 q^{44} - 54 q^{45} - 54 q^{46} - 54 q^{47} - 54 q^{48} - 54 q^{49} - 54 q^{50} - 54 q^{51} - 54 q^{52} - 54 q^{53} - 54 q^{54} - 54 q^{55} - 54 q^{56} - 54 q^{57} - 54 q^{58} - 54 q^{59} - 54 q^{60} - 54 q^{61} - 54 q^{62} - 54 q^{63} - 54 q^{64} + 54 q^{66} - 54 q^{67} + 135 q^{68} + 54 q^{69} - 54 q^{70} + 54 q^{71} + 270 q^{72} - 54 q^{73} + 162 q^{74} + 81 q^{75} - 54 q^{76} + 162 q^{77} + 162 q^{78} - 54 q^{79} + 351 q^{80} + 54 q^{81} - 27 q^{82} + 54 q^{83} + 324 q^{84} - 54 q^{85} + 162 q^{86} + 162 q^{87} - 54 q^{88} + 81 q^{89} + 162 q^{90} - 54 q^{91} + 270 q^{92} + 54 q^{93} - 54 q^{94} + 54 q^{95} + 135 q^{96} - 54 q^{97} + 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.02543 + 0.563818i 1.43220 + 0.398680i 0.895488 0.445086i \(-0.146827\pi\)
0.536711 + 0.843766i \(0.319667\pi\)
\(3\) −0.0981720 1.72927i −0.0566796 0.998392i
\(4\) 2.07216 + 1.25056i 1.03608 + 0.625278i
\(5\) −1.27054 + 0.0493029i −0.568204 + 0.0220489i −0.321277 0.946985i \(-0.604112\pi\)
−0.246927 + 0.969034i \(0.579421\pi\)
\(6\) 0.776151 3.55787i 0.316862 1.45249i
\(7\) 4.39851 + 0.687914i 1.66248 + 0.260007i 0.914757 0.404004i \(-0.132382\pi\)
0.747723 + 0.664011i \(0.231147\pi\)
\(8\) 0.606370 + 0.642715i 0.214384 + 0.227234i
\(9\) −2.98072 + 0.339531i −0.993575 + 0.113177i
\(10\) −2.60120 0.616496i −0.822572 0.194953i
\(11\) 0.0413646 + 0.302842i 0.0124719 + 0.0913103i 0.995984 0.0895324i \(-0.0285373\pi\)
−0.983512 + 0.180843i \(0.942118\pi\)
\(12\) 1.95912 3.70609i 0.565548 1.06986i
\(13\) 1.95043 2.84380i 0.540952 0.788727i −0.453793 0.891107i \(-0.649930\pi\)
0.994745 + 0.102380i \(0.0326456\pi\)
\(14\) 8.52104 + 3.87329i 2.27734 + 1.03518i
\(15\) 0.209990 + 2.19227i 0.0542191 + 0.566041i
\(16\) −1.39012 2.63908i −0.347530 0.659770i
\(17\) −6.95270 + 3.49177i −1.68628 + 0.846880i −0.694412 + 0.719577i \(0.744336\pi\)
−0.991864 + 0.127303i \(0.959368\pi\)
\(18\) −6.22870 0.992889i −1.46812 0.234026i
\(19\) 0.466686 + 8.01269i 0.107065 + 1.83824i 0.443199 + 0.896423i \(0.353843\pi\)
−0.336134 + 0.941814i \(0.609120\pi\)
\(20\) −2.69443 1.48672i −0.602492 0.332441i
\(21\) 0.757777 7.67373i 0.165360 1.67454i
\(22\) −0.0869667 + 0.636709i −0.0185414 + 0.135747i
\(23\) 1.39733 3.61918i 0.291364 0.754652i −0.707487 0.706727i \(-0.750171\pi\)
0.998851 0.0479255i \(-0.0152610\pi\)
\(24\) 1.05190 1.11167i 0.214717 0.226919i
\(25\) −3.37311 + 0.262179i −0.674623 + 0.0524358i
\(26\) 5.55385 4.66024i 1.08920 0.913948i
\(27\) 0.879763 + 5.12113i 0.169310 + 0.985563i
\(28\) 8.25415 + 6.92605i 1.55989 + 1.30890i
\(29\) 2.53701 + 1.81334i 0.471110 + 0.336729i 0.792140 0.610340i \(-0.208967\pi\)
−0.321030 + 0.947069i \(0.604029\pi\)
\(30\) −0.810721 + 4.55869i −0.148017 + 0.832299i
\(31\) −2.85491 + 3.27137i −0.512757 + 0.587555i −0.950180 0.311701i \(-0.899101\pi\)
0.437423 + 0.899256i \(0.355891\pi\)
\(32\) −1.70176 7.85622i −0.300832 1.38880i
\(33\) 0.519634 0.101261i 0.0904566 0.0176273i
\(34\) −16.0510 + 3.15231i −2.75272 + 0.540616i
\(35\) −5.62241 0.657166i −0.950361 0.111081i
\(36\) −6.60114 3.02400i −1.10019 0.504000i
\(37\) 1.50445 + 2.02083i 0.247331 + 0.332223i 0.908400 0.418102i \(-0.137305\pi\)
−0.661069 + 0.750325i \(0.729897\pi\)
\(38\) −3.57246 + 16.4923i −0.579529 + 2.67541i
\(39\) −5.10916 3.09363i −0.818120 0.495378i
\(40\) −0.802107 0.786701i −0.126824 0.124388i
\(41\) −0.728308 + 2.82746i −0.113743 + 0.441576i −0.999756 0.0220836i \(-0.992970\pi\)
0.886014 + 0.463659i \(0.153464\pi\)
\(42\) 5.86142 15.1154i 0.904436 2.33236i
\(43\) −6.63437 6.02037i −1.01173 0.918098i −0.0150828 0.999886i \(-0.504801\pi\)
−0.996650 + 0.0817879i \(0.973937\pi\)
\(44\) −0.293007 + 0.679266i −0.0441724 + 0.102403i
\(45\) 3.77040 0.578347i 0.562058 0.0862149i
\(46\) 4.87077 6.54258i 0.718156 0.964651i
\(47\) −0.229710 0.263218i −0.0335066 0.0383943i 0.736438 0.676505i \(-0.236506\pi\)
−0.769945 + 0.638111i \(0.779716\pi\)
\(48\) −4.42720 + 2.66297i −0.639011 + 0.384367i
\(49\) 12.2079 + 3.91431i 1.74399 + 0.559188i
\(50\) −6.97985 1.37080i −0.987099 0.193860i
\(51\) 6.72077 + 11.6803i 0.941096 + 1.63556i
\(52\) 7.59793 3.45368i 1.05364 0.478940i
\(53\) 0.771083 4.37303i 0.105916 0.600682i −0.884934 0.465716i \(-0.845797\pi\)
0.990850 0.134965i \(-0.0430922\pi\)
\(54\) −1.10549 + 10.8686i −0.150438 + 1.47902i
\(55\) −0.0674864 0.382735i −0.00909987 0.0516079i
\(56\) 2.22499 + 3.24412i 0.297327 + 0.433513i
\(57\) 13.8103 1.59365i 1.82921 0.211084i
\(58\) 4.11614 + 5.10322i 0.540476 + 0.670085i
\(59\) 2.57549 1.05221i 0.335301 0.136985i −0.204296 0.978909i \(-0.565490\pi\)
0.539596 + 0.841924i \(0.318577\pi\)
\(60\) −2.30642 + 4.80534i −0.297758 + 0.620366i
\(61\) 10.2081 6.16060i 1.30701 0.788784i 0.319688 0.947523i \(-0.396422\pi\)
0.987321 + 0.158739i \(0.0507429\pi\)
\(62\) −7.62689 + 5.01629i −0.968617 + 0.637069i
\(63\) −13.3443 0.557053i −1.68123 0.0701821i
\(64\) 0.635797 10.9162i 0.0794747 1.36453i
\(65\) −2.33790 + 3.70933i −0.289981 + 0.460086i
\(66\) 1.10958 + 0.0878816i 0.136580 + 0.0108175i
\(67\) 5.48432 3.91995i 0.670016 0.478899i −0.194895 0.980824i \(-0.562437\pi\)
0.864911 + 0.501926i \(0.167375\pi\)
\(68\) −18.7738 1.45921i −2.27665 0.176955i
\(69\) −6.39571 2.06106i −0.769953 0.248122i
\(70\) −11.0173 4.50107i −1.31682 0.537980i
\(71\) −0.934287 3.12074i −0.110879 0.370363i 0.884481 0.466576i \(-0.154512\pi\)
−0.995361 + 0.0962123i \(0.969327\pi\)
\(72\) −2.02564 1.70987i −0.238724 0.201511i
\(73\) −4.31382 + 1.02239i −0.504895 + 0.119662i −0.475167 0.879896i \(-0.657612\pi\)
−0.0297280 + 0.999558i \(0.509464\pi\)
\(74\) 1.90779 + 4.94130i 0.221776 + 0.574415i
\(75\) 0.784523 + 5.80728i 0.0905889 + 0.670566i
\(76\) −9.05327 + 17.1872i −1.03848 + 1.97151i
\(77\) −0.0263870 + 1.36051i −0.00300708 + 0.155044i
\(78\) −8.60402 9.14659i −0.974214 1.03565i
\(79\) 9.02377 8.85045i 1.01525 0.995754i 0.0152622 0.999884i \(-0.495142\pi\)
0.999991 + 0.00412970i \(0.00131453\pi\)
\(80\) 1.89632 + 3.28453i 0.212015 + 0.367221i
\(81\) 8.76944 2.02410i 0.974382 0.224900i
\(82\) −3.06932 + 5.31621i −0.338949 + 0.587077i
\(83\) −0.101470 0.393932i −0.0111378 0.0432397i 0.962580 0.270999i \(-0.0873539\pi\)
−0.973718 + 0.227759i \(0.926860\pi\)
\(84\) 11.1667 14.9536i 1.21838 1.63157i
\(85\) 8.66155 4.77924i 0.939477 0.518381i
\(86\) −10.0431 15.9345i −1.08297 1.71826i
\(87\) 2.88669 4.56518i 0.309486 0.489438i
\(88\) −0.169559 + 0.210220i −0.0180750 + 0.0224095i
\(89\) 2.03708 6.80431i 0.215930 0.721256i −0.779555 0.626334i \(-0.784555\pi\)
0.995485 0.0949220i \(-0.0302602\pi\)
\(90\) 7.96278 + 0.954416i 0.839351 + 0.100604i
\(91\) 10.5353 11.1667i 1.10440 1.17059i
\(92\) 7.42149 5.75209i 0.773744 0.599697i
\(93\) 5.93734 + 4.61575i 0.615673 + 0.478631i
\(94\) −0.316855 0.662646i −0.0326811 0.0683467i
\(95\) −0.987994 10.1575i −0.101366 1.04213i
\(96\) −13.4184 + 3.71407i −1.36951 + 0.379065i
\(97\) −11.4753 0.445293i −1.16514 0.0452127i −0.551066 0.834462i \(-0.685779\pi\)
−0.614073 + 0.789249i \(0.710470\pi\)
\(98\) 22.5194 + 14.8112i 2.27480 + 1.49616i
\(99\) −0.226121 0.888644i −0.0227260 0.0893121i
\(100\) −7.31751 3.67499i −0.731751 0.367499i
\(101\) 0.205424 + 10.5916i 0.0204405 + 1.05391i 0.859894 + 0.510473i \(0.170530\pi\)
−0.839453 + 0.543432i \(0.817125\pi\)
\(102\) 7.02693 + 27.4469i 0.695770 + 2.71765i
\(103\) −2.96955 2.30158i −0.292598 0.226781i 0.455716 0.890125i \(-0.349383\pi\)
−0.748314 + 0.663344i \(0.769136\pi\)
\(104\) 3.01043 0.470823i 0.295197 0.0461680i
\(105\) −0.584452 + 9.78717i −0.0570366 + 0.955130i
\(106\) 4.02737 8.42253i 0.391173 0.818069i
\(107\) −12.7984 4.65825i −1.23727 0.450330i −0.361190 0.932492i \(-0.617629\pi\)
−0.876082 + 0.482162i \(0.839852\pi\)
\(108\) −4.58125 + 11.7120i −0.440831 + 1.12699i
\(109\) 0.649699 0.236471i 0.0622299 0.0226498i −0.310718 0.950502i \(-0.600569\pi\)
0.372948 + 0.927852i \(0.378347\pi\)
\(110\) 0.0791034 0.813254i 0.00754221 0.0775407i
\(111\) 3.34686 2.79999i 0.317670 0.265763i
\(112\) −4.29900 12.5643i −0.406217 1.18721i
\(113\) −3.77910 + 3.42935i −0.355508 + 0.322606i −0.830116 0.557591i \(-0.811726\pi\)
0.474608 + 0.880197i \(0.342590\pi\)
\(114\) 28.8703 + 4.55865i 2.70395 + 0.426957i
\(115\) −1.59694 + 4.66722i −0.148915 + 0.435221i
\(116\) 2.98940 + 6.93020i 0.277559 + 0.643453i
\(117\) −4.84814 + 9.13881i −0.448211 + 0.844883i
\(118\) 5.80975 0.679062i 0.534831 0.0625127i
\(119\) −32.9835 + 10.5757i −3.02360 + 0.969477i
\(120\) −1.28167 + 1.46429i −0.117000 + 0.133671i
\(121\) 10.5071 2.92484i 0.955189 0.265895i
\(122\) 24.1492 6.72240i 2.18637 0.608617i
\(123\) 4.96094 + 0.981860i 0.447313 + 0.0885314i
\(124\) −10.0069 + 3.20857i −0.898643 + 0.288138i
\(125\) 10.5873 1.23747i 0.946955 0.110683i
\(126\) −26.7140 8.65204i −2.37987 0.770785i
\(127\) 1.90220 + 4.40979i 0.168793 + 0.391306i 0.981526 0.191331i \(-0.0612804\pi\)
−0.812733 + 0.582637i \(0.802021\pi\)
\(128\) 2.23791 6.54054i 0.197805 0.578107i
\(129\) −9.75952 + 12.0636i −0.859278 + 1.06214i
\(130\) −6.82665 + 6.19485i −0.598737 + 0.543325i
\(131\) 4.74803 + 13.8766i 0.414837 + 1.21241i 0.933857 + 0.357646i \(0.116420\pi\)
−0.519020 + 0.854762i \(0.673703\pi\)
\(132\) 1.20340 + 0.440002i 0.104742 + 0.0382973i
\(133\) −3.45932 + 35.5649i −0.299961 + 3.08387i
\(134\) 13.3183 4.84745i 1.15052 0.418756i
\(135\) −1.37026 6.46325i −0.117934 0.556268i
\(136\) −6.46012 2.35129i −0.553951 0.201622i
\(137\) 7.61387 15.9231i 0.650497 1.36040i −0.267402 0.963585i \(-0.586165\pi\)
0.917899 0.396814i \(-0.129884\pi\)
\(138\) −11.7920 7.78056i −1.00380 0.662325i
\(139\) −0.742794 + 0.116171i −0.0630030 + 0.00985349i −0.185942 0.982561i \(-0.559534\pi\)
0.122939 + 0.992414i \(0.460768\pi\)
\(140\) −10.8287 8.39290i −0.915194 0.709329i
\(141\) −0.432623 + 0.423070i −0.0364335 + 0.0356289i
\(142\) −0.132809 6.84762i −0.0111451 0.574639i
\(143\) 0.941900 + 0.473040i 0.0787656 + 0.0395576i
\(144\) 5.03962 + 7.39438i 0.419968 + 0.616198i
\(145\) −3.31278 2.17885i −0.275111 0.180944i
\(146\) −9.31381 0.361418i −0.770816 0.0299112i
\(147\) 5.57042 21.4950i 0.459440 1.77288i
\(148\) 0.590307 + 6.06889i 0.0485230 + 0.498860i
\(149\) 5.05212 + 10.5656i 0.413886 + 0.865569i 0.998526 + 0.0542762i \(0.0172852\pi\)
−0.584640 + 0.811293i \(0.698764\pi\)
\(150\) −1.68525 + 12.2046i −0.137600 + 0.996500i
\(151\) −13.9478 + 10.8104i −1.13506 + 0.879736i −0.993904 0.110252i \(-0.964834\pi\)
−0.141154 + 0.989988i \(0.545081\pi\)
\(152\) −4.86689 + 5.15860i −0.394757 + 0.418418i
\(153\) 19.5385 12.7687i 1.57959 1.03229i
\(154\) −0.820525 + 2.74075i −0.0661198 + 0.220856i
\(155\) 3.46600 4.29717i 0.278396 0.345157i
\(156\) −6.71824 12.7998i −0.537890 1.02480i
\(157\) −0.227240 0.360541i −0.0181358 0.0287743i 0.836796 0.547514i \(-0.184426\pi\)
−0.854932 + 0.518740i \(0.826401\pi\)
\(158\) 23.2671 12.8382i 1.85103 1.02136i
\(159\) −7.63783 0.904099i −0.605719 0.0716997i
\(160\) 2.54950 + 9.89777i 0.201556 + 0.782487i
\(161\) 8.63587 14.9578i 0.680602 1.17884i
\(162\) 18.9031 + 0.844694i 1.48517 + 0.0663654i
\(163\) 0.971273 + 1.68229i 0.0760760 + 0.131767i 0.901554 0.432667i \(-0.142428\pi\)
−0.825478 + 0.564435i \(0.809094\pi\)
\(164\) −5.04507 + 4.94817i −0.393954 + 0.386387i
\(165\) −0.655225 + 0.154276i −0.0510092 + 0.0120104i
\(166\) 0.0165846 0.855095i 0.00128721 0.0663683i
\(167\) 6.65976 12.6433i 0.515348 0.978364i −0.479553 0.877513i \(-0.659201\pi\)
0.994901 0.100851i \(-0.0321567\pi\)
\(168\) 5.39151 4.16608i 0.415964 0.321420i
\(169\) 0.399308 + 1.03423i 0.0307160 + 0.0795565i
\(170\) 20.2380 4.79650i 1.55219 0.367875i
\(171\) −4.11162 23.7252i −0.314423 1.81431i
\(172\) −6.21868 20.7718i −0.474170 1.58384i
\(173\) 6.34793 + 2.59341i 0.482624 + 0.197174i 0.606436 0.795132i \(-0.292598\pi\)
−0.123812 + 0.992306i \(0.539512\pi\)
\(174\) 8.42073 7.61890i 0.638374 0.577587i
\(175\) −15.0170 1.16722i −1.13518 0.0882333i
\(176\) 0.741722 0.530151i 0.0559094 0.0399617i
\(177\) −2.07238 4.35042i −0.155770 0.326998i
\(178\) 7.96237 12.6332i 0.596805 0.946895i
\(179\) −0.396395 + 6.80583i −0.0296279 + 0.508692i 0.950550 + 0.310572i \(0.100521\pi\)
−0.980178 + 0.198120i \(0.936516\pi\)
\(180\) 8.53613 + 3.51667i 0.636246 + 0.262117i
\(181\) −4.77429 + 3.14010i −0.354870 + 0.233402i −0.714409 0.699728i \(-0.753304\pi\)
0.359539 + 0.933130i \(0.382934\pi\)
\(182\) 27.6345 16.6775i 2.04841 1.23622i
\(183\) −11.6555 17.0477i −0.861596 1.26020i
\(184\) 3.17340 1.29648i 0.233946 0.0955776i
\(185\) −2.01111 2.49338i −0.147859 0.183317i
\(186\) 9.42324 + 12.6965i 0.690946 + 0.930951i
\(187\) −1.34505 1.96113i −0.0983599 0.143412i
\(188\) −0.146827 0.832695i −0.0107084 0.0607306i
\(189\) 0.346744 + 23.1306i 0.0252219 + 1.68250i
\(190\) 3.72585 21.1303i 0.270301 1.53295i
\(191\) −5.62928 + 2.55882i −0.407320 + 0.185150i −0.606983 0.794715i \(-0.707620\pi\)
0.199663 + 0.979865i \(0.436015\pi\)
\(192\) −18.9395 0.0277964i −1.36684 0.00200603i
\(193\) 4.91108 + 0.964505i 0.353507 + 0.0694266i 0.366314 0.930491i \(-0.380620\pi\)
−0.0128064 + 0.999918i \(0.504077\pi\)
\(194\) −22.9914 7.37189i −1.65068 0.529271i
\(195\) 6.64393 + 3.67870i 0.475782 + 0.263437i
\(196\) 20.4017 + 23.3778i 1.45727 + 1.66984i
\(197\) −5.70503 + 7.66319i −0.406467 + 0.545980i −0.957474 0.288521i \(-0.906836\pi\)
0.551007 + 0.834501i \(0.314244\pi\)
\(198\) 0.0430414 1.92738i 0.00305882 0.136973i
\(199\) 2.17258 5.03661i 0.154010 0.357036i −0.823690 0.567040i \(-0.808088\pi\)
0.977701 + 0.210004i \(0.0673477\pi\)
\(200\) −2.21386 2.00897i −0.156544 0.142056i
\(201\) −7.31705 9.09902i −0.516105 0.641795i
\(202\) −5.55567 + 21.5684i −0.390896 + 1.51755i
\(203\) 9.91162 + 9.72125i 0.695659 + 0.682298i
\(204\) −0.680310 + 32.6081i −0.0476312 + 2.28302i
\(205\) 0.785944 3.62832i 0.0548927 0.253413i
\(206\) −4.71696 6.33598i −0.328646 0.441448i
\(207\) −2.93624 + 11.2622i −0.204083 + 0.782779i
\(208\) −10.2163 1.19412i −0.708375 0.0827972i
\(209\) −2.40728 + 0.472774i −0.166515 + 0.0327024i
\(210\) −6.70195 + 19.4937i −0.462479 + 1.34520i
\(211\) 2.63348 + 12.1575i 0.181296 + 0.836957i 0.973857 + 0.227163i \(0.0729452\pi\)
−0.792560 + 0.609794i \(0.791252\pi\)
\(212\) 7.06652 8.09734i 0.485331 0.556127i
\(213\) −5.30486 + 1.92200i −0.363483 + 0.131693i
\(214\) −23.2960 16.6510i −1.59248 1.13824i
\(215\) 8.72608 + 7.32205i 0.595114 + 0.499360i
\(216\) −2.75797 + 3.67074i −0.187656 + 0.249762i
\(217\) −14.8078 + 12.4252i −1.00522 + 0.843478i
\(218\) 1.44925 0.112645i 0.0981556 0.00762925i
\(219\) 2.19149 + 7.35938i 0.148087 + 0.497301i
\(220\) 0.338788 0.877483i 0.0228411 0.0591599i
\(221\) −3.63085 + 26.5825i −0.244237 + 1.78813i
\(222\) 8.35753 3.78417i 0.560921 0.253977i
\(223\) −17.6050 9.71405i −1.17892 0.650501i −0.232235 0.972660i \(-0.574604\pi\)
−0.946686 + 0.322158i \(0.895592\pi\)
\(224\) −2.08082 35.7263i −0.139031 2.38707i
\(225\) 9.96531 1.92676i 0.664354 0.128451i
\(226\) −9.58785 + 4.81520i −0.637774 + 0.320302i
\(227\) −11.2474 21.3527i −0.746519 1.41723i −0.903040 0.429556i \(-0.858670\pi\)
0.156521 0.987675i \(-0.449972\pi\)
\(228\) 30.6100 + 13.9682i 2.02720 + 0.925067i
\(229\) −8.99223 4.08747i −0.594223 0.270108i 0.0940401 0.995568i \(-0.470022\pi\)
−0.688264 + 0.725461i \(0.741627\pi\)
\(230\) −5.86596 + 8.55277i −0.386790 + 0.563953i
\(231\) 2.35527 0.0879336i 0.154966 0.00578561i
\(232\) 0.372902 + 2.73013i 0.0244822 + 0.179242i
\(233\) 3.77592 + 0.894910i 0.247369 + 0.0586275i 0.352430 0.935838i \(-0.385356\pi\)
−0.105061 + 0.994466i \(0.533504\pi\)
\(234\) −14.9722 + 15.7766i −0.978764 + 1.03135i
\(235\) 0.304834 + 0.323105i 0.0198852 + 0.0210770i
\(236\) 6.65268 + 1.04046i 0.433053 + 0.0677282i
\(237\) −16.1907 14.7356i −1.05170 0.957183i
\(238\) −72.7688 + 2.82376i −4.71690 + 0.183037i
\(239\) −16.1160 9.72608i −1.04246 0.629128i −0.111318 0.993785i \(-0.535507\pi\)
−0.931142 + 0.364657i \(0.881186\pi\)
\(240\) 5.49366 3.60170i 0.354614 0.232488i
\(241\) −7.39774 2.05930i −0.476531 0.132651i 0.0215759 0.999767i \(-0.493132\pi\)
−0.498107 + 0.867116i \(0.665971\pi\)
\(242\) 22.9305 1.47403
\(243\) −4.36111 14.9660i −0.279766 0.960068i
\(244\) 28.8569 1.84738
\(245\) −15.7037 4.37142i −1.00327 0.279280i
\(246\) 9.49447 + 4.78576i 0.605345 + 0.305129i
\(247\) 23.6967 + 14.3010i 1.50778 + 0.909953i
\(248\) −3.83369 + 0.148765i −0.243439 + 0.00944656i
\(249\) −0.671252 + 0.214142i −0.0425389 + 0.0135707i
\(250\) 22.1415 + 3.46287i 1.40035 + 0.219011i
\(251\) 14.2128 + 15.0647i 0.897105 + 0.950876i 0.999035 0.0439158i \(-0.0139833\pi\)
−0.101930 + 0.994792i \(0.532502\pi\)
\(252\) −26.9549 17.8421i −1.69800 1.12395i
\(253\) 1.15384 + 0.273465i 0.0725414 + 0.0171926i
\(254\) 1.36646 + 10.0042i 0.0857392 + 0.627722i
\(255\) −9.11490 14.5089i −0.570797 0.908585i
\(256\) −4.14909 + 6.04952i −0.259318 + 0.378095i
\(257\) −5.95450 2.70665i −0.371431 0.168836i 0.219393 0.975637i \(-0.429592\pi\)
−0.590824 + 0.806800i \(0.701197\pi\)
\(258\) −26.5690 + 18.9315i −1.65411 + 1.17862i
\(259\) 5.22719 + 9.92358i 0.324802 + 0.616621i
\(260\) −9.48323 + 4.76265i −0.588125 + 0.295367i
\(261\) −8.17780 4.54368i −0.506193 0.281247i
\(262\) 1.79292 + 30.7833i 0.110767 + 1.90180i
\(263\) −4.77665 2.63564i −0.294541 0.162521i 0.328959 0.944344i \(-0.393302\pi\)
−0.623500 + 0.781823i \(0.714290\pi\)
\(264\) 0.380172 + 0.272575i 0.0233980 + 0.0167758i
\(265\) −0.764091 + 5.59414i −0.0469378 + 0.343645i
\(266\) −27.0588 + 70.0840i −1.65908 + 4.29713i
\(267\) −11.9665 2.85466i −0.732335 0.174702i
\(268\) 16.2665 1.26433i 0.993635 0.0772314i
\(269\) −14.2376 + 11.9467i −0.868079 + 0.728405i −0.963693 0.267014i \(-0.913963\pi\)
0.0956136 + 0.995419i \(0.469519\pi\)
\(270\) 0.868718 13.8635i 0.0528685 0.843704i
\(271\) 2.60029 + 2.18190i 0.157956 + 0.132541i 0.718340 0.695692i \(-0.244902\pi\)
−0.560384 + 0.828233i \(0.689347\pi\)
\(272\) 18.8802 + 13.4947i 1.14478 + 0.818238i
\(273\) −20.3445 17.1220i −1.23131 1.03627i
\(274\) 24.3991 27.9583i 1.47400 1.68902i
\(275\) −0.218926 1.01068i −0.0132018 0.0609461i
\(276\) −10.6755 12.2690i −0.642588 0.738510i
\(277\) 11.8391 2.32513i 0.711345 0.139704i 0.176065 0.984378i \(-0.443663\pi\)
0.535280 + 0.844675i \(0.320206\pi\)
\(278\) −1.56998 0.183504i −0.0941612 0.0110059i
\(279\) 7.39898 10.7204i 0.442965 0.641812i
\(280\) −2.98689 4.01209i −0.178501 0.239768i
\(281\) 4.81522 22.2295i 0.287252 1.32610i −0.574389 0.818583i \(-0.694760\pi\)
0.861640 0.507519i \(-0.169437\pi\)
\(282\) −1.11479 + 0.612980i −0.0663845 + 0.0365024i
\(283\) 1.16736 + 1.14494i 0.0693924 + 0.0680596i 0.734086 0.679056i \(-0.237611\pi\)
−0.664694 + 0.747116i \(0.731438\pi\)
\(284\) 1.96666 7.63505i 0.116700 0.453057i
\(285\) −17.4680 + 2.70568i −1.03471 + 0.160271i
\(286\) 1.64105 + 1.48917i 0.0970372 + 0.0880566i
\(287\) −5.14852 + 11.9356i −0.303908 + 0.704537i
\(288\) 7.73992 + 22.8394i 0.456079 + 1.34583i
\(289\) 25.9958 34.9184i 1.52916 2.05402i
\(290\) −5.48134 6.28092i −0.321875 0.368828i
\(291\) 0.356520 + 19.8875i 0.0208996 + 1.16583i
\(292\) −10.2175 3.27611i −0.597934 0.191720i
\(293\) 30.2253 + 5.93605i 1.76578 + 0.346788i 0.966988 0.254821i \(-0.0820165\pi\)
0.798791 + 0.601608i \(0.205473\pi\)
\(294\) 23.4018 40.3961i 1.36482 2.35595i
\(295\) −3.22040 + 1.46385i −0.187499 + 0.0852287i
\(296\) −0.386563 + 2.19231i −0.0224685 + 0.127425i
\(297\) −1.51450 + 0.478263i −0.0878804 + 0.0277516i
\(298\) 4.27566 + 24.2484i 0.247682 + 1.40467i
\(299\) −7.56682 11.0327i −0.437601 0.638037i
\(300\) −5.63666 + 13.0147i −0.325433 + 0.751404i
\(301\) −25.0399 31.0446i −1.44327 1.78938i
\(302\) −34.3455 + 14.0317i −1.97636 + 0.807432i
\(303\) 18.2956 1.39503i 1.05105 0.0801425i
\(304\) 20.4974 12.3702i 1.17560 0.709481i
\(305\) −12.6661 + 8.33059i −0.725256 + 0.477008i
\(306\) 46.7732 14.8460i 2.67384 0.848687i
\(307\) −0.327766 + 5.62752i −0.0187066 + 0.321179i 0.975954 + 0.217977i \(0.0699459\pi\)
−0.994660 + 0.103202i \(0.967091\pi\)
\(308\) −1.75607 + 2.78620i −0.100061 + 0.158758i
\(309\) −3.68851 + 5.36109i −0.209832 + 0.304982i
\(310\) 9.44298 6.74944i 0.536325 0.383342i
\(311\) −10.2693 0.798194i −0.582319 0.0452614i −0.217045 0.976162i \(-0.569642\pi\)
−0.365274 + 0.930900i \(0.619025\pi\)
\(312\) −1.10972 5.15962i −0.0628254 0.292106i
\(313\) −6.21727 2.54003i −0.351421 0.143571i 0.195614 0.980681i \(-0.437330\pi\)
−0.547035 + 0.837110i \(0.684244\pi\)
\(314\) −0.256981 0.858375i −0.0145023 0.0484409i
\(315\) 16.9820 + 0.0498472i 0.956827 + 0.00280857i
\(316\) 29.7667 7.05484i 1.67451 0.396866i
\(317\) 7.94335 + 20.5738i 0.446143 + 1.15554i 0.955502 + 0.294985i \(0.0953148\pi\)
−0.509359 + 0.860554i \(0.670117\pi\)
\(318\) −14.9602 6.13754i −0.838925 0.344176i
\(319\) −0.444214 + 0.843320i −0.0248712 + 0.0472169i
\(320\) −0.269607 + 13.9009i −0.0150715 + 0.777082i
\(321\) −6.79891 + 22.5892i −0.379478 + 1.26081i
\(322\) 25.9249 25.4269i 1.44474 1.41699i
\(323\) −31.2232 54.0802i −1.73731 3.00910i
\(324\) 20.7029 + 6.77242i 1.15016 + 0.376245i
\(325\) −5.83344 + 10.1038i −0.323581 + 0.560459i
\(326\) 1.01874 + 3.95500i 0.0564229 + 0.219047i
\(327\) −0.472704 1.10029i −0.0261406 0.0608460i
\(328\) −2.25888 + 1.24640i −0.124726 + 0.0688207i
\(329\) −0.829309 1.31579i −0.0457213 0.0725418i
\(330\) −1.41410 0.0569521i −0.0778436 0.00313511i
\(331\) −2.89324 + 3.58705i −0.159027 + 0.197162i −0.851610 0.524175i \(-0.824374\pi\)
0.692584 + 0.721338i \(0.256472\pi\)
\(332\) 0.282371 0.943186i 0.0154971 0.0517640i
\(333\) −5.17050 5.51273i −0.283341 0.302096i
\(334\) 20.6174 21.8532i 1.12813 1.19575i
\(335\) −6.77480 + 5.25086i −0.370147 + 0.286885i
\(336\) −21.3050 + 8.66758i −1.16228 + 0.472855i
\(337\) −5.52792 11.5607i −0.301125 0.629750i 0.694872 0.719133i \(-0.255461\pi\)
−0.995997 + 0.0893836i \(0.971510\pi\)
\(338\) 0.225653 + 2.31991i 0.0122739 + 0.126187i
\(339\) 6.30126 + 6.19840i 0.342237 + 0.336651i
\(340\) 23.9248 + 0.928392i 1.29751 + 0.0503491i
\(341\) −1.10880 0.729269i −0.0600449 0.0394921i
\(342\) 5.04887 50.3720i 0.273012 2.72381i
\(343\) 23.1549 + 11.6288i 1.25025 + 0.627899i
\(344\) −0.153503 7.91458i −0.00827633 0.426726i
\(345\) 8.22765 + 2.30334i 0.442962 + 0.124008i
\(346\) 11.3951 + 8.83187i 0.612605 + 0.474804i
\(347\) 29.6350 4.63483i 1.59089 0.248811i 0.703798 0.710400i \(-0.251486\pi\)
0.887094 + 0.461589i \(0.152721\pi\)
\(348\) 11.6907 5.84982i 0.626687 0.313583i
\(349\) 3.49423 7.30757i 0.187042 0.391165i −0.787191 0.616709i \(-0.788465\pi\)
0.974233 + 0.225544i \(0.0724160\pi\)
\(350\) −29.7579 10.8310i −1.59063 0.578941i
\(351\) 16.2794 + 7.48655i 0.868929 + 0.399602i
\(352\) 2.30880 0.840335i 0.123060 0.0447900i
\(353\) −1.94929 + 20.0405i −0.103750 + 1.06665i 0.788478 + 0.615063i \(0.210869\pi\)
−0.892229 + 0.451584i \(0.850859\pi\)
\(354\) −1.74463 9.97994i −0.0927262 0.530428i
\(355\) 1.34091 + 3.91897i 0.0711683 + 0.207997i
\(356\) 12.7303 11.5522i 0.674706 0.612263i
\(357\) 21.5263 + 55.9991i 1.13929 + 2.96379i
\(358\) −4.64012 + 13.5613i −0.245238 + 0.716736i
\(359\) 3.83515 + 8.89089i 0.202412 + 0.469243i 0.988941 0.148310i \(-0.0473833\pi\)
−0.786529 + 0.617553i \(0.788124\pi\)
\(360\) 2.65797 + 2.07260i 0.140087 + 0.109236i
\(361\) −45.1139 + 5.27306i −2.37441 + 0.277529i
\(362\) −11.4405 + 3.66823i −0.601297 + 0.192798i
\(363\) −6.08934 17.8824i −0.319607 0.938582i
\(364\) 35.7954 9.96434i 1.87619 0.522273i
\(365\) 5.43049 1.51168i 0.284245 0.0791250i
\(366\) −13.9956 41.1005i −0.731561 2.14836i
\(367\) −2.14957 + 0.689233i −0.112207 + 0.0359777i −0.360899 0.932605i \(-0.617530\pi\)
0.248692 + 0.968583i \(0.419999\pi\)
\(368\) −11.4938 + 1.34343i −0.599154 + 0.0700311i
\(369\) 1.21087 8.67517i 0.0630355 0.451612i
\(370\) −2.66755 6.18408i −0.138679 0.321495i
\(371\) 6.39988 18.7044i 0.332265 0.971082i
\(372\) 6.53087 + 16.9895i 0.338610 + 0.880867i
\(373\) 2.71982 2.46810i 0.140827 0.127793i −0.598550 0.801086i \(-0.704256\pi\)
0.739377 + 0.673292i \(0.235120\pi\)
\(374\) −1.61859 4.73051i −0.0836954 0.244609i
\(375\) −3.17930 18.1867i −0.164178 0.939159i
\(376\) 0.0298851 0.307245i 0.00154121 0.0158450i
\(377\) 10.1050 3.67793i 0.520435 0.189423i
\(378\) −12.3391 + 47.0449i −0.634656 + 2.41973i
\(379\) −25.0947 9.13373i −1.28903 0.469168i −0.395620 0.918414i \(-0.629470\pi\)
−0.893408 + 0.449246i \(0.851693\pi\)
\(380\) 10.6552 22.2834i 0.546600 1.14312i
\(381\) 7.43896 3.72232i 0.381109 0.190700i
\(382\) −12.8444 + 2.00884i −0.657179 + 0.102781i
\(383\) 14.8230 + 11.4887i 0.757420 + 0.587045i 0.916413 0.400235i \(-0.131072\pi\)
−0.158993 + 0.987280i \(0.550825\pi\)
\(384\) −11.5300 3.22784i −0.588389 0.164720i
\(385\) −0.0335511 1.72989i −0.00170992 0.0881632i
\(386\) 9.40327 + 4.72250i 0.478614 + 0.240369i
\(387\) 21.8193 + 15.6925i 1.10914 + 0.797695i
\(388\) −23.2218 15.2732i −1.17891 0.775379i
\(389\) 28.8247 + 1.11853i 1.46147 + 0.0567116i 0.757182 0.653204i \(-0.226576\pi\)
0.704286 + 0.709916i \(0.251267\pi\)
\(390\) 11.3827 + 11.1969i 0.576387 + 0.566979i
\(391\) 2.92214 + 30.0423i 0.147779 + 1.51930i
\(392\) 4.88673 + 10.2197i 0.246817 + 0.516175i
\(393\) 23.5303 9.57290i 1.18695 0.482889i
\(394\) −15.8758 + 12.3047i −0.799812 + 0.619901i
\(395\) −11.0287 + 11.6898i −0.554916 + 0.588177i
\(396\) 0.642741 2.12419i 0.0322989 0.106745i
\(397\) 10.7257 35.8263i 0.538307 1.79807i −0.0617229 0.998093i \(-0.519660\pi\)
0.600030 0.799978i \(-0.295155\pi\)
\(398\) 7.24016 8.97639i 0.362916 0.449946i
\(399\) 61.8409 + 2.49061i 3.09592 + 0.124686i
\(400\) 5.38095 + 8.53746i 0.269047 + 0.426873i
\(401\) −3.41840 + 1.88620i −0.170707 + 0.0941921i −0.566165 0.824292i \(-0.691574\pi\)
0.395458 + 0.918484i \(0.370586\pi\)
\(402\) −9.69002 22.5549i −0.483294 1.12494i
\(403\) 3.73479 + 14.4994i 0.186043 + 0.722265i
\(404\) −12.8197 + 22.2044i −0.637806 + 1.10471i
\(405\) −11.0422 + 3.00406i −0.548689 + 0.149273i
\(406\) 14.5943 + 25.2781i 0.724304 + 1.25453i
\(407\) −0.549762 + 0.539203i −0.0272507 + 0.0267273i
\(408\) −3.43181 + 11.4021i −0.169900 + 0.564488i
\(409\) 0.497713 25.6619i 0.0246103 1.26890i −0.760415 0.649438i \(-0.775004\pi\)
0.785025 0.619464i \(-0.212650\pi\)
\(410\) 3.63759 6.90580i 0.179648 0.341053i
\(411\) −28.2827 11.6032i −1.39508 0.572344i
\(412\) −3.27514 8.48282i −0.161355 0.417919i
\(413\) 12.0522 2.85642i 0.593048 0.140555i
\(414\) −12.2970 + 21.1554i −0.604365 + 1.03973i
\(415\) 0.148345 + 0.495505i 0.00728195 + 0.0243234i
\(416\) −25.6607 10.4835i −1.25812 0.513998i
\(417\) 0.273812 + 1.27308i 0.0134086 + 0.0623432i
\(418\) −5.14234 0.399694i −0.251520 0.0195497i
\(419\) −14.1957 + 10.1465i −0.693507 + 0.495689i −0.872782 0.488110i \(-0.837686\pi\)
0.179275 + 0.983799i \(0.442625\pi\)
\(420\) −13.4505 + 19.5497i −0.656316 + 0.953928i
\(421\) −5.35349 + 8.49389i −0.260913 + 0.413967i −0.950731 0.310016i \(-0.899666\pi\)
0.689818 + 0.723982i \(0.257690\pi\)
\(422\) −1.52068 + 26.1090i −0.0740255 + 1.27097i
\(423\) 0.774072 + 0.706587i 0.0376367 + 0.0343555i
\(424\) 3.27817 2.15609i 0.159202 0.104709i
\(425\) 22.5368 13.6010i 1.09319 0.659746i
\(426\) −11.8283 + 0.901907i −0.573084 + 0.0436975i
\(427\) 49.1382 20.0752i 2.37797 0.971506i
\(428\) −20.6950 25.6578i −1.00033 1.24022i
\(429\) 0.725544 1.67524i 0.0350296 0.0808811i
\(430\) 13.5458 + 19.7503i 0.653237 + 0.952442i
\(431\) −2.16526 12.2798i −0.104297 0.591498i −0.991499 0.130116i \(-0.958465\pi\)
0.887202 0.461382i \(-0.152646\pi\)
\(432\) 12.2921 9.44076i 0.591404 0.454219i
\(433\) −6.71847 + 38.1024i −0.322869 + 1.83108i 0.201375 + 0.979514i \(0.435459\pi\)
−0.524244 + 0.851568i \(0.675652\pi\)
\(434\) −36.9977 + 16.8175i −1.77595 + 0.807268i
\(435\) −3.44259 + 5.94258i −0.165059 + 0.284925i
\(436\) 1.64200 + 0.322479i 0.0786376 + 0.0154439i
\(437\) 29.6515 + 9.50738i 1.41842 + 0.454800i
\(438\) 0.289367 + 16.1415i 0.0138265 + 0.771273i
\(439\) 7.64117 + 8.75581i 0.364693 + 0.417892i 0.906230 0.422785i \(-0.138947\pi\)
−0.541537 + 0.840677i \(0.682157\pi\)
\(440\) 0.205067 0.275453i 0.00977620 0.0131317i
\(441\) −37.7175 7.52252i −1.79607 0.358215i
\(442\) −22.3418 + 51.7940i −1.06269 + 2.46359i
\(443\) −0.240326 0.218084i −0.0114182 0.0103615i 0.666279 0.745703i \(-0.267886\pi\)
−0.677697 + 0.735341i \(0.737022\pi\)
\(444\) 10.4368 1.61659i 0.495308 0.0767201i
\(445\) −2.25272 + 8.74561i −0.106789 + 0.414582i
\(446\) −30.1809 29.6012i −1.42911 1.40166i
\(447\) 17.7748 9.77371i 0.840719 0.462281i
\(448\) 10.3060 47.5777i 0.486912 2.24784i
\(449\) 9.28761 + 12.4754i 0.438310 + 0.588752i 0.965308 0.261114i \(-0.0840900\pi\)
−0.526998 + 0.849866i \(0.676683\pi\)
\(450\) 21.2704 + 1.71609i 1.00270 + 0.0808975i
\(451\) −0.886401 0.103605i −0.0417390 0.00487859i
\(452\) −12.1195 + 2.38019i −0.570053 + 0.111955i
\(453\) 20.0633 + 23.0582i 0.942656 + 1.08337i
\(454\) −10.7419 49.5901i −0.504142 2.32738i
\(455\) −12.8350 + 14.7072i −0.601713 + 0.689486i
\(456\) 9.39839 + 7.90972i 0.440120 + 0.370406i
\(457\) 24.5294 + 17.5325i 1.14743 + 0.820137i 0.986000 0.166746i \(-0.0533261\pi\)
0.161435 + 0.986883i \(0.448388\pi\)
\(458\) −15.9086 13.3489i −0.743360 0.623753i
\(459\) −23.9986 32.5338i −1.12016 1.51855i
\(460\) −9.14573 + 7.67418i −0.426422 + 0.357811i
\(461\) 33.6136 2.61265i 1.56554 0.121683i 0.734777 0.678309i \(-0.237287\pi\)
0.830764 + 0.556625i \(0.187904\pi\)
\(462\) 4.82003 + 1.14984i 0.224248 + 0.0534955i
\(463\) −7.72979 + 20.0207i −0.359234 + 0.930439i 0.628989 + 0.777414i \(0.283469\pi\)
−0.988222 + 0.153024i \(0.951099\pi\)
\(464\) 1.25881 9.21612i 0.0584388 0.427848i
\(465\) −7.77121 5.57178i −0.360381 0.258385i
\(466\) 7.14332 + 3.94151i 0.330908 + 0.182587i
\(467\) 2.07111 + 35.5596i 0.0958397 + 1.64550i 0.613339 + 0.789820i \(0.289826\pi\)
−0.517499 + 0.855684i \(0.673137\pi\)
\(468\) −21.4747 + 12.8742i −0.992669 + 0.595111i
\(469\) 26.8194 13.4692i 1.23841 0.621951i
\(470\) 0.435248 + 0.826299i 0.0200765 + 0.0381143i
\(471\) −0.601163 + 0.428354i −0.0277001 + 0.0197375i
\(472\) 2.23797 + 1.01728i 0.103011 + 0.0468242i
\(473\) 1.54879 2.25820i 0.0712136 0.103832i
\(474\) −24.4849 38.9747i −1.12463 1.79017i
\(475\) −3.67495 26.9054i −0.168618 1.23450i
\(476\) −81.5728 19.3331i −3.73888 0.886131i
\(477\) −0.813607 + 13.2966i −0.0372525 + 0.608809i
\(478\) −27.1582 28.7860i −1.24219 1.31664i
\(479\) −38.9663 6.09422i −1.78042 0.278452i −0.823184 0.567775i \(-0.807804\pi\)
−0.957231 + 0.289323i \(0.906570\pi\)
\(480\) 16.8656 5.38045i 0.769805 0.245583i
\(481\) 8.68116 0.336869i 0.395827 0.0153599i
\(482\) −13.8226 8.34197i −0.629601 0.379966i
\(483\) −26.7138 13.4653i −1.21552 0.612692i
\(484\) 25.4300 + 7.07894i 1.15591 + 0.321770i
\(485\) 14.6018 0.663034
\(486\) −0.395058 32.7715i −0.0179202 1.48655i
\(487\) −43.1512 −1.95537 −0.977684 0.210079i \(-0.932628\pi\)
−0.977684 + 0.210079i \(0.932628\pi\)
\(488\) 10.1494 + 2.82527i 0.459440 + 0.127894i
\(489\) 2.81378 1.84474i 0.127244 0.0834222i
\(490\) −29.3421 17.7081i −1.32554 0.799968i
\(491\) 39.3080 1.52533i 1.77394 0.0688371i 0.869115 0.494611i \(-0.164689\pi\)
0.904830 + 0.425773i \(0.139998\pi\)
\(492\) 9.05199 + 8.23850i 0.408095 + 0.371420i
\(493\) −23.9708 3.74897i −1.07959 0.168845i
\(494\) 39.9329 + 42.3264i 1.79667 + 1.90436i
\(495\) 0.331109 + 1.11791i 0.0148822 + 0.0502464i
\(496\) 12.6021 + 2.98674i 0.565849 + 0.134109i
\(497\) −1.96267 14.3693i −0.0880379 0.644551i
\(498\) −1.48032 + 0.0552673i −0.0663345 + 0.00247659i
\(499\) −8.60295 + 12.5434i −0.385121 + 0.561520i −0.967972 0.251059i \(-0.919221\pi\)
0.582851 + 0.812579i \(0.301937\pi\)
\(500\) 23.4861 + 10.6757i 1.05033 + 0.477433i
\(501\) −22.5174 10.2753i −1.00600 0.459066i
\(502\) 20.2934 + 38.5260i 0.905738 + 1.71950i
\(503\) 25.5520 12.8327i 1.13931 0.572181i 0.223861 0.974621i \(-0.428134\pi\)
0.915446 + 0.402440i \(0.131838\pi\)
\(504\) −7.73356 8.91437i −0.344480 0.397077i
\(505\) −0.783197 13.4470i −0.0348518 0.598383i
\(506\) 2.18285 + 1.20444i 0.0970393 + 0.0535440i
\(507\) 1.74927 0.792044i 0.0776877 0.0351759i
\(508\) −1.57303 + 11.5166i −0.0697918 + 0.510967i
\(509\) −0.820458 + 2.12504i −0.0363662 + 0.0941907i −0.949877 0.312623i \(-0.898792\pi\)
0.913511 + 0.406814i \(0.133360\pi\)
\(510\) −10.2812 34.5260i −0.455261 1.52884i
\(511\) −19.6777 + 1.52947i −0.870491 + 0.0676599i
\(512\) −22.4056 + 18.8005i −0.990196 + 0.830873i
\(513\) −40.6235 + 9.43923i −1.79357 + 0.416752i
\(514\) −10.5344 8.83940i −0.464652 0.389889i
\(515\) 3.88642 + 2.77784i 0.171256 + 0.122406i
\(516\) −35.3095 + 12.7930i −1.55442 + 0.563179i
\(517\) 0.0702117 0.0804537i 0.00308791 0.00353835i
\(518\) 4.99224 + 23.0468i 0.219347 + 1.01262i
\(519\) 3.86152 11.2319i 0.169502 0.493024i
\(520\) −3.80167 + 0.746624i −0.166714 + 0.0327416i
\(521\) −18.3527 2.14512i −0.804046 0.0939795i −0.295865 0.955230i \(-0.595608\pi\)
−0.508181 + 0.861250i \(0.669682\pi\)
\(522\) −14.0018 13.8137i −0.612842 0.604610i
\(523\) 9.24118 + 12.4131i 0.404089 + 0.542785i 0.956861 0.290547i \(-0.0938374\pi\)
−0.552772 + 0.833333i \(0.686430\pi\)
\(524\) −7.51483 + 34.6923i −0.328287 + 1.51554i
\(525\) −0.544176 + 26.0830i −0.0237498 + 1.13836i
\(526\) −8.18877 8.03148i −0.357047 0.350189i
\(527\) 8.42646 32.7135i 0.367062 1.42502i
\(528\) −0.989589 1.23059i −0.0430663 0.0535545i
\(529\) 5.88656 + 5.34177i 0.255937 + 0.232251i
\(530\) −4.70169 + 10.8998i −0.204229 + 0.473455i
\(531\) −7.31958 + 4.01079i −0.317643 + 0.174054i
\(532\) −51.6442 + 69.3702i −2.23906 + 3.00758i
\(533\) 6.62022 + 7.58593i 0.286754 + 0.328583i
\(534\) −22.6278 12.5288i −0.979199 0.542176i
\(535\) 16.4906 + 5.28751i 0.712952 + 0.228599i
\(536\) 5.84494 + 1.14791i 0.252463 + 0.0495821i
\(537\) 11.8080 + 0.0173300i 0.509553 + 0.000747843i
\(538\) −35.5730 + 16.1699i −1.53366 + 0.697135i
\(539\) −0.680444 + 3.85899i −0.0293088 + 0.166218i
\(540\) 5.24324 15.1065i 0.225633 0.650080i
\(541\) −1.99478 11.3130i −0.0857624 0.486383i −0.997189 0.0749210i \(-0.976130\pi\)
0.911427 0.411462i \(-0.134982\pi\)
\(542\) 4.03652 + 5.88538i 0.173383 + 0.252799i
\(543\) 5.89877 + 7.94775i 0.253140 + 0.341070i
\(544\) 39.2640 + 48.6797i 1.68343 + 2.08713i
\(545\) −0.813812 + 0.332479i −0.0348599 + 0.0142418i
\(546\) −31.5528 46.1502i −1.35034 1.97505i
\(547\) −27.5720 + 16.6398i −1.17889 + 0.711465i −0.964190 0.265214i \(-0.914557\pi\)
−0.214703 + 0.976679i \(0.568878\pi\)
\(548\) 35.6898 23.4736i 1.52459 1.00274i
\(549\) −28.3357 + 21.8290i −1.20934 + 0.931639i
\(550\) 0.126417 2.17049i 0.00539043 0.0925502i
\(551\) −13.3458 + 21.1745i −0.568549 + 0.902064i
\(552\) −2.55349 5.36038i −0.108684 0.228153i
\(553\) 45.7795 32.7212i 1.94674 1.39145i
\(554\) 25.2904 + 1.96572i 1.07448 + 0.0835155i
\(555\) −4.11428 + 3.72252i −0.174642 + 0.158012i
\(556\) −1.68447 0.688181i −0.0714373 0.0291854i
\(557\) −4.91838 16.4285i −0.208399 0.696100i −0.996727 0.0808446i \(-0.974238\pi\)
0.788328 0.615255i \(-0.210947\pi\)
\(558\) 21.0305 17.5417i 0.890291 0.742601i
\(559\) −30.0606 + 7.12449i −1.27143 + 0.301334i
\(560\) 6.08152 + 15.7515i 0.256991 + 0.665624i
\(561\) −3.25928 + 2.51848i −0.137607 + 0.106330i
\(562\) 22.2863 42.3095i 0.940092 1.78472i
\(563\) −0.112124 + 5.78111i −0.00472548 + 0.243645i 0.990000 + 0.141069i \(0.0450540\pi\)
−0.994725 + 0.102576i \(0.967292\pi\)
\(564\) −1.42554 + 0.335650i −0.0600260 + 0.0141334i
\(565\) 4.63243 4.54346i 0.194888 0.191145i
\(566\) 1.71888 + 2.97718i 0.0722497 + 0.125140i
\(567\) 39.9649 2.87039i 1.67837 0.120545i
\(568\) 1.43922 2.49280i 0.0603883 0.104596i
\(569\) 5.48878 + 21.3088i 0.230102 + 0.893310i 0.974282 + 0.225331i \(0.0723464\pi\)
−0.744181 + 0.667979i \(0.767160\pi\)
\(570\) −36.9057 4.36858i −1.54581 0.182979i
\(571\) 21.2092 11.7027i 0.887577 0.489744i 0.0273326 0.999626i \(-0.491299\pi\)
0.860244 + 0.509882i \(0.170311\pi\)
\(572\) 1.36021 + 2.15811i 0.0568731 + 0.0902353i
\(573\) 4.97752 + 9.48332i 0.207939 + 0.396171i
\(574\) −17.1575 + 21.2720i −0.716141 + 0.887875i
\(575\) −3.76449 + 12.5743i −0.156990 + 0.524384i
\(576\) 1.81126 + 32.7541i 0.0754690 + 1.36475i
\(577\) −18.8099 + 19.9374i −0.783068 + 0.830003i −0.988900 0.148584i \(-0.952528\pi\)
0.205832 + 0.978587i \(0.434010\pi\)
\(578\) 72.3404 56.0680i 3.00896 2.33212i
\(579\) 1.18576 8.58725i 0.0492783 0.356874i
\(580\) −4.13984 8.65774i −0.171897 0.359493i
\(581\) −0.175327 1.80252i −0.00727379 0.0747811i
\(582\) −10.4908 + 40.4819i −0.434860 + 1.67803i
\(583\) 1.35623 + 0.0526280i 0.0561694 + 0.00217963i
\(584\) −3.27288 2.15261i −0.135433 0.0890755i
\(585\) 5.70920 11.8503i 0.236046 0.489949i
\(586\) 57.8725 + 29.0646i 2.39069 + 1.20065i
\(587\) −0.0957648 4.93761i −0.00395264 0.203797i −0.996582 0.0826081i \(-0.973675\pi\)
0.992629 0.121189i \(-0.0386707\pi\)
\(588\) 38.4235 37.5751i 1.58456 1.54957i
\(589\) −27.5448 21.3488i −1.13496 0.879663i
\(590\) −7.34806 + 1.14922i −0.302515 + 0.0473124i
\(591\) 13.8118 + 9.11321i 0.568140 + 0.374867i
\(592\) 3.24176 6.77957i 0.133236 0.278639i
\(593\) 6.11543 + 2.22584i 0.251131 + 0.0914041i 0.464518 0.885564i \(-0.346227\pi\)
−0.213388 + 0.976968i \(0.568450\pi\)
\(594\) −3.33718 + 0.114785i −0.136926 + 0.00470968i
\(595\) 41.3856 15.0631i 1.69664 0.617528i
\(596\) −2.74408 + 28.2116i −0.112402 + 1.15559i
\(597\) −8.92293 3.26252i −0.365191 0.133526i
\(598\) −9.10567 26.6123i −0.372359 1.08826i
\(599\) −15.9256 + 14.4517i −0.650703 + 0.590481i −0.929030 0.370005i \(-0.879356\pi\)
0.278327 + 0.960486i \(0.410220\pi\)
\(600\) −3.25671 + 4.02558i −0.132955 + 0.164344i
\(601\) −12.2625 + 35.8386i −0.500199 + 1.46189i 0.350666 + 0.936501i \(0.385955\pi\)
−0.850865 + 0.525385i \(0.823921\pi\)
\(602\) −33.2131 76.9966i −1.35367 3.13815i
\(603\) −15.0163 + 13.5464i −0.611511 + 0.551652i
\(604\) −42.4211 + 4.95832i −1.72609 + 0.201751i
\(605\) −13.2055 + 4.23417i −0.536880 + 0.172144i
\(606\) 37.8430 + 7.48982i 1.53727 + 0.304253i
\(607\) 9.64724 2.68549i 0.391569 0.109001i −0.0667916 0.997767i \(-0.521276\pi\)
0.458361 + 0.888766i \(0.348437\pi\)
\(608\) 62.1553 17.3021i 2.52073 0.701693i
\(609\) 15.8376 18.0942i 0.641771 0.733213i
\(610\) −30.3512 + 9.73172i −1.22888 + 0.394026i
\(611\) −1.19657 + 0.139859i −0.0484081 + 0.00565810i
\(612\) 56.4549 2.02476i 2.28205 0.0818462i
\(613\) 6.03527 + 13.9913i 0.243762 + 0.565105i 0.995543 0.0943087i \(-0.0300641\pi\)
−0.751781 + 0.659413i \(0.770805\pi\)
\(614\) −3.83676 + 11.2134i −0.154839 + 0.452535i
\(615\) −6.35150 1.00291i −0.256117 0.0404411i
\(616\) −0.890419 + 0.808012i −0.0358760 + 0.0325557i
\(617\) −7.19187 21.0190i −0.289534 0.846195i −0.991044 0.133535i \(-0.957367\pi\)
0.701510 0.712660i \(-0.252510\pi\)
\(618\) −10.4935 + 8.77890i −0.422111 + 0.353139i
\(619\) 0.0117882 0.121193i 0.000473808 0.00487117i −0.995063 0.0992462i \(-0.968357\pi\)
0.995537 + 0.0943750i \(0.0300853\pi\)
\(620\) 12.5560 4.57000i 0.504260 0.183535i
\(621\) 19.7637 + 3.97191i 0.793088 + 0.159387i
\(622\) −20.3498 7.40672i −0.815952 0.296982i
\(623\) 13.6409 28.5275i 0.546511 1.14293i
\(624\) −1.06199 + 17.7840i −0.0425137 + 0.711930i
\(625\) 3.32270 0.519660i 0.132908 0.0207864i
\(626\) −11.1605 8.65008i −0.446065 0.345727i
\(627\) 1.05388 + 4.11641i 0.0420878 + 0.164393i
\(628\) −0.0200016 1.03128i −0.000798150 0.0411524i
\(629\) −17.5163 8.79701i −0.698420 0.350760i
\(630\) 34.3678 + 9.67572i 1.36925 + 0.385490i
\(631\) 8.64926 + 5.68870i 0.344321 + 0.226464i 0.709877 0.704326i \(-0.248751\pi\)
−0.365555 + 0.930790i \(0.619121\pi\)
\(632\) 11.1601 + 0.433061i 0.443923 + 0.0172262i
\(633\) 20.7650 5.74752i 0.825336 0.228443i
\(634\) 4.48886 + 46.1495i 0.178275 + 1.83283i
\(635\) −2.63424 5.50905i −0.104537 0.218620i
\(636\) −14.6962 11.4250i −0.582742 0.453030i
\(637\) 34.9422 27.0823i 1.38446 1.07304i
\(638\) −1.37521 + 1.45763i −0.0544449 + 0.0577083i
\(639\) 3.84444 + 8.98484i 0.152084 + 0.355435i
\(640\) −2.52089 + 8.42037i −0.0996471 + 0.332844i
\(641\) 2.63182 3.26294i 0.103951 0.128878i −0.723718 0.690096i \(-0.757568\pi\)
0.827668 + 0.561218i \(0.189667\pi\)
\(642\) −26.5070 + 41.9196i −1.04615 + 1.65444i
\(643\) −1.99798 3.17001i −0.0787925 0.125013i 0.804278 0.594253i \(-0.202552\pi\)
−0.883070 + 0.469241i \(0.844528\pi\)
\(644\) 36.6005 20.1953i 1.44226 0.795805i
\(645\) 11.8051 15.8085i 0.464826 0.622461i
\(646\) −32.7492 127.140i −1.28850 5.00226i
\(647\) −23.3221 + 40.3951i −0.916887 + 1.58809i −0.112772 + 0.993621i \(0.535973\pi\)
−0.804115 + 0.594474i \(0.797360\pi\)
\(648\) 6.61844 + 4.40889i 0.259997 + 0.173198i
\(649\) 0.425186 + 0.736444i 0.0166900 + 0.0289080i
\(650\) −17.5120 + 17.1756i −0.686876 + 0.673683i
\(651\) 22.9402 + 24.3868i 0.899097 + 0.955794i
\(652\) −0.0911684 + 4.70062i −0.00357043 + 0.184090i
\(653\) 17.7554 33.7078i 0.694822 1.31909i −0.242340 0.970191i \(-0.577915\pi\)
0.937162 0.348895i \(-0.113443\pi\)
\(654\) −0.337068 2.49508i −0.0131804 0.0975653i
\(655\) −6.71673 17.3968i −0.262445 0.679748i
\(656\) 8.47434 2.00845i 0.330867 0.0784170i
\(657\) 12.5112 4.51215i 0.488108 0.176036i
\(658\) −0.937846 3.13262i −0.0365610 0.122122i
\(659\) −12.1664 4.97052i −0.473935 0.193624i 0.128631 0.991692i \(-0.458942\pi\)
−0.602567 + 0.798069i \(0.705855\pi\)
\(660\) −1.55066 0.499711i −0.0603594 0.0194512i
\(661\) −16.9129 1.31458i −0.657837 0.0511312i −0.255765 0.966739i \(-0.582327\pi\)
−0.402073 + 0.915608i \(0.631710\pi\)
\(662\) −7.88251 + 5.63408i −0.306363 + 0.218975i
\(663\) 46.3247 + 3.66905i 1.79910 + 0.142494i
\(664\) 0.191657 0.304085i 0.00743775 0.0118008i
\(665\) 2.64176 45.3574i 0.102443 1.75888i
\(666\) −7.36432 14.0809i −0.285362 0.545624i
\(667\) 10.1079 6.64805i 0.391378 0.257413i
\(668\) 29.6112 17.8704i 1.14569 0.691428i
\(669\) −15.0699 + 31.3975i −0.582635 + 1.21390i
\(670\) −16.6824 + 6.81553i −0.644499 + 0.263307i
\(671\) 2.28794 + 2.83660i 0.0883249 + 0.109506i
\(672\) −61.5761 + 7.10562i −2.37535 + 0.274105i
\(673\) −11.0433 16.1015i −0.425688 0.620669i 0.551212 0.834365i \(-0.314166\pi\)
−0.976900 + 0.213697i \(0.931450\pi\)
\(674\) −4.67833 26.5321i −0.180202 1.02198i
\(675\) −4.31020 17.0435i −0.165900 0.656005i
\(676\) −0.465937 + 2.64246i −0.0179206 + 0.101633i
\(677\) 41.2654 18.7574i 1.58596 0.720906i 0.589723 0.807606i \(-0.299237\pi\)
0.996234 + 0.0866996i \(0.0276320\pi\)
\(678\) 9.26802 + 16.1072i 0.355936 + 0.618594i
\(679\) −50.1678 9.85264i −1.92526 0.378110i
\(680\) 8.32379 + 2.66892i 0.319203 + 0.102348i
\(681\) −35.8204 + 21.5461i −1.37264 + 0.825647i
\(682\) −1.83463 2.10225i −0.0702515 0.0804992i
\(683\) 3.50729 4.71111i 0.134203 0.180266i −0.729942 0.683509i \(-0.760453\pi\)
0.864145 + 0.503244i \(0.167860\pi\)
\(684\) 21.1497 54.3042i 0.808679 2.07637i
\(685\) −8.88870 + 20.6063i −0.339620 + 0.787327i
\(686\) 40.3423 + 36.6087i 1.54027 + 1.39772i
\(687\) −6.18554 + 15.9512i −0.235993 + 0.608578i
\(688\) −6.66566 + 25.8777i −0.254126 + 0.986577i
\(689\) −10.9321 10.7221i −0.416478 0.408479i
\(690\) 15.3659 + 9.30416i 0.584970 + 0.354203i
\(691\) −0.420680 + 1.94208i −0.0160034 + 0.0738800i −0.984637 0.174613i \(-0.944133\pi\)
0.968634 + 0.248493i \(0.0799352\pi\)
\(692\) 9.91073 + 13.3124i 0.376749 + 0.506062i
\(693\) −0.383282 4.06426i −0.0145597 0.154389i
\(694\) 62.6370 + 7.32122i 2.37767 + 0.277910i
\(695\) 0.938025 0.184222i 0.0355813 0.00698794i
\(696\) 4.68451 0.912869i 0.177566 0.0346022i
\(697\) −4.80917 22.2016i −0.182160 0.840945i
\(698\) 11.1975 12.8309i 0.423831 0.485656i
\(699\) 1.17685 6.61743i 0.0445125 0.250294i
\(700\) −29.6581 21.1983i −1.12097 0.801220i
\(701\) −6.38533 5.35793i −0.241171 0.202366i 0.514189 0.857677i \(-0.328093\pi\)
−0.755359 + 0.655311i \(0.772538\pi\)
\(702\) 28.7518 + 24.3421i 1.08517 + 0.918734i
\(703\) −15.4902 + 12.9978i −0.584224 + 0.490222i
\(704\) 3.33219 0.258998i 0.125587 0.00976136i
\(705\) 0.528808 0.558858i 0.0199161 0.0210478i
\(706\) −15.2474 + 39.4916i −0.573842 + 1.48629i
\(707\) −6.38256 + 46.7286i −0.240041 + 1.75741i
\(708\) 1.14613 11.6064i 0.0430741 0.436195i
\(709\) 20.2204 + 11.1571i 0.759392 + 0.419015i 0.815017 0.579437i \(-0.196728\pi\)
−0.0556253 + 0.998452i \(0.517715\pi\)
\(710\) 0.506347 + 8.69365i 0.0190029 + 0.326267i
\(711\) −23.8924 + 29.4446i −0.896034 + 1.10426i
\(712\) 5.60846 2.81667i 0.210186 0.105559i
\(713\) 7.85041 + 14.9036i 0.294000 + 0.558146i
\(714\) 12.0269 + 125.559i 0.450095 + 4.69894i
\(715\) −1.22005 0.554579i −0.0456272 0.0207401i
\(716\) −9.33247 + 13.6071i −0.348771 + 0.508520i
\(717\) −15.2368 + 28.8237i −0.569030 + 1.07644i
\(718\) 2.75501 + 20.1702i 0.102816 + 0.752747i
\(719\) −50.4503 11.9569i −1.88148 0.445919i −0.881809 0.471607i \(-0.843674\pi\)
−0.999670 + 0.0256879i \(0.991822\pi\)
\(720\) −6.76761 9.14641i −0.252214 0.340867i
\(721\) −11.4783 12.1663i −0.427475 0.453097i
\(722\) −94.3483 14.7558i −3.51128 0.549154i
\(723\) −2.83483 + 12.9948i −0.105429 + 0.483283i
\(724\) −13.8200 + 0.536277i −0.513615 + 0.0199306i
\(725\) −9.03303 5.45146i −0.335478 0.202462i
\(726\) −2.25113 39.6529i −0.0835473 1.47166i
\(727\) 45.4706 + 12.6576i 1.68641 + 0.469445i 0.972905 0.231203i \(-0.0742662\pi\)
0.713507 + 0.700648i \(0.247106\pi\)
\(728\) 13.5653 0.502763
\(729\) −25.4520 + 9.01077i −0.942668 + 0.333732i
\(730\) 11.8514 0.438641
\(731\) 67.1486 + 18.6921i 2.48358 + 0.691352i
\(732\) −2.83294 49.9013i −0.104708 1.84441i
\(733\) −31.4336 18.9703i −1.16103 0.700683i −0.200724 0.979648i \(-0.564330\pi\)
−0.960301 + 0.278965i \(0.910009\pi\)
\(734\) −4.74242 + 0.184028i −0.175046 + 0.00679258i
\(735\) −6.01769 + 27.5850i −0.221966 + 1.01749i
\(736\) −30.8110 4.81876i −1.13571 0.177622i
\(737\) 1.41398 + 1.49873i 0.0520847 + 0.0552066i
\(738\) 7.34377 16.8883i 0.270328 0.621666i
\(739\) −31.3668 7.43407i −1.15385 0.273467i −0.391215 0.920299i \(-0.627945\pi\)
−0.762632 + 0.646833i \(0.776093\pi\)
\(740\) −1.04922 7.68169i −0.0385703 0.282384i
\(741\) 22.4039 42.3819i 0.823029 1.55694i
\(742\) 23.5084 34.2761i 0.863021 1.25832i
\(743\) 22.8905 + 10.4050i 0.839771 + 0.381723i 0.787052 0.616887i \(-0.211606\pi\)
0.0527187 + 0.998609i \(0.483211\pi\)
\(744\) 0.633614 + 6.61486i 0.0232294 + 0.242513i
\(745\) −6.93986 13.1750i −0.254257 0.482694i
\(746\) 6.90037 3.46550i 0.252640 0.126881i
\(747\) 0.436208 + 1.13975i 0.0159600 + 0.0417013i
\(748\) −0.334657 5.74585i −0.0122363 0.210089i
\(749\) −53.0896 29.2936i −1.93985 1.07036i
\(750\) 3.81455 38.6286i 0.139288 1.41052i
\(751\) −3.73259 + 27.3274i −0.136204 + 0.997191i 0.788104 + 0.615543i \(0.211063\pi\)
−0.924308 + 0.381648i \(0.875357\pi\)
\(752\) −0.375329 + 0.972127i −0.0136869 + 0.0354498i
\(753\) 24.6556 26.0567i 0.898500 0.949558i
\(754\) 22.5408 1.75201i 0.820886 0.0638043i
\(755\) 17.1883 14.4227i 0.625547 0.524896i
\(756\) −28.2075 + 48.3639i −1.02590 + 1.75898i
\(757\) −6.23353 5.23055i −0.226561 0.190108i 0.522440 0.852676i \(-0.325022\pi\)
−0.749001 + 0.662569i \(0.769466\pi\)
\(758\) −45.6779 32.6486i −1.65910 1.18585i
\(759\) 0.359620 2.02215i 0.0130534 0.0733992i
\(760\) 5.92926 6.79418i 0.215077 0.246451i
\(761\) −2.91446 13.4546i −0.105649 0.487730i −0.999245 0.0388574i \(-0.987628\pi\)
0.893596 0.448873i \(-0.148174\pi\)
\(762\) 17.1658 3.34510i 0.621853 0.121180i
\(763\) 3.02038 0.593183i 0.109345 0.0214747i
\(764\) −14.8647 1.73744i −0.537787 0.0628583i
\(765\) −24.1950 + 17.1865i −0.874772 + 0.621378i
\(766\) 23.5455 + 31.6271i 0.850733 + 1.14273i
\(767\) 2.03106 9.37644i 0.0733375 0.338563i
\(768\) 10.8686 + 6.58099i 0.392185 + 0.237471i
\(769\) 0.938893 + 0.920860i 0.0338574 + 0.0332071i 0.716949 0.697125i \(-0.245538\pi\)
−0.683092 + 0.730333i \(0.739365\pi\)
\(770\) 0.907386 3.52269i 0.0326999 0.126949i
\(771\) −4.09596 + 10.5626i −0.147512 + 0.380404i
\(772\) 8.97038 + 8.14019i 0.322851 + 0.292972i
\(773\) 9.31617 21.5973i 0.335079 0.776801i −0.664485 0.747301i \(-0.731349\pi\)
0.999565 0.0295001i \(-0.00939153\pi\)
\(774\) 35.3459 + 44.0863i 1.27048 + 1.58465i
\(775\) 8.77226 11.7832i 0.315109 0.423265i
\(776\) −6.67207 7.64534i −0.239513 0.274452i
\(777\) 16.6474 10.0134i 0.597220 0.359230i
\(778\) 57.7518 + 18.5174i 2.07050 + 0.663880i
\(779\) −22.9955 4.51617i −0.823899 0.161808i
\(780\) 9.16689 + 15.9315i 0.328227 + 0.570438i
\(781\) 0.906444 0.412029i 0.0324351 0.0147436i
\(782\) −11.0198 + 62.4962i −0.394066 + 2.23486i
\(783\) −7.05441 + 14.5877i −0.252104 + 0.521320i
\(784\) −6.64031 37.6591i −0.237154 1.34497i
\(785\) 0.306494 + 0.446880i 0.0109393 + 0.0159498i
\(786\) 53.0564 6.12249i 1.89246 0.218382i
\(787\) 10.1607 + 12.5973i 0.362191 + 0.449046i 0.926375 0.376603i \(-0.122908\pi\)
−0.564184 + 0.825649i \(0.690809\pi\)
\(788\) −21.4050 + 8.74490i −0.762521 + 0.311524i
\(789\) −4.08880 + 8.51884i −0.145565 + 0.303279i
\(790\) −28.9289 + 17.4587i −1.02924 + 0.621152i
\(791\) −18.9815 + 12.4843i −0.674904 + 0.443892i
\(792\) 0.434032 0.684178i 0.0154227 0.0243112i
\(793\) 2.39063 41.0455i 0.0848936 1.45757i
\(794\) 41.9237 66.5165i 1.48782 2.36058i
\(795\) 9.74877 + 0.772130i 0.345753 + 0.0273846i
\(796\) 10.8005 7.71974i 0.382814 0.273619i
\(797\) −39.3305 3.05701i −1.39316 0.108285i −0.641138 0.767425i \(-0.721537\pi\)
−0.752020 + 0.659141i \(0.770920\pi\)
\(798\) 123.850 + 39.9116i 4.38426 + 1.41285i
\(799\) 2.51620 + 1.02798i 0.0890168 + 0.0363674i
\(800\) 7.79999 + 26.0538i 0.275771 + 0.921140i
\(801\) −3.76169 + 20.9734i −0.132913 + 0.741060i
\(802\) −7.98723 + 1.89301i −0.282039 + 0.0668444i
\(803\) −0.488063 1.26412i −0.0172234 0.0446097i
\(804\) −3.78328 28.0050i −0.133426 0.987660i
\(805\) −10.2348 + 19.4303i −0.360729 + 0.684827i
\(806\) −0.610423 + 31.4733i −0.0215012 + 1.10860i
\(807\) 22.0568 + 23.4477i 0.776436 + 0.825398i
\(808\) −6.68282 + 6.55447i −0.235101 + 0.230585i
\(809\) 22.3619 + 38.7319i 0.786202 + 1.36174i 0.928279 + 0.371886i \(0.121289\pi\)
−0.142077 + 0.989856i \(0.545378\pi\)
\(810\) −24.0589 0.141241i −0.845344 0.00496271i
\(811\) 13.4063 23.2204i 0.470759 0.815378i −0.528682 0.848820i \(-0.677314\pi\)
0.999441 + 0.0334420i \(0.0106469\pi\)
\(812\) 8.38151 + 32.5390i 0.294133 + 1.14190i
\(813\) 3.51781 4.71079i 0.123375 0.165215i
\(814\) −1.41752 + 0.782154i −0.0496840 + 0.0274145i
\(815\) −1.31699 2.08954i −0.0461320 0.0731935i
\(816\) 21.4825 33.9736i 0.752037 1.18931i
\(817\) 45.1432 55.9688i 1.57936 1.95810i
\(818\) 15.4768 51.6960i 0.541132 1.80751i
\(819\) −27.6113 + 36.8620i −0.964817 + 1.28806i
\(820\) 6.16602 6.53560i 0.215327 0.228233i
\(821\) −12.8394 + 9.95130i −0.448099 + 0.347303i −0.811522 0.584321i \(-0.801361\pi\)
0.363424 + 0.931624i \(0.381608\pi\)
\(822\) −50.7426 39.4479i −1.76985 1.37590i
\(823\) −20.8116 43.5237i −0.725446 1.51714i −0.851063 0.525064i \(-0.824042\pi\)
0.125617 0.992079i \(-0.459909\pi\)
\(824\) −0.321390 3.30418i −0.0111962 0.115107i
\(825\) −1.72624 + 0.477802i −0.0600998 + 0.0166349i
\(826\) 26.0214 + 1.00975i 0.905399 + 0.0351336i
\(827\) −36.8029 24.2057i −1.27976 0.841713i −0.286555 0.958064i \(-0.592510\pi\)
−0.993208 + 0.116351i \(0.962880\pi\)
\(828\) −20.1684 + 19.6652i −0.700901 + 0.683414i
\(829\) −7.68253 3.85831i −0.266825 0.134005i 0.310357 0.950620i \(-0.399551\pi\)
−0.577182 + 0.816615i \(0.695848\pi\)
\(830\) 0.0210873 + 1.08725i 0.000731949 + 0.0377391i
\(831\) −5.18304 20.2448i −0.179798 0.702283i
\(832\) −29.8034 23.0994i −1.03325 0.800827i
\(833\) −98.5459 + 15.4123i −3.41441 + 0.534004i
\(834\) −0.163200 + 2.73293i −0.00565115 + 0.0946336i
\(835\) −7.83817 + 16.3921i −0.271251 + 0.567274i
\(836\) −5.57949 2.03077i −0.192971 0.0702356i
\(837\) −19.2648 11.7424i −0.665887 0.405875i
\(838\) −34.4733 + 12.5473i −1.19086 + 0.433438i
\(839\) 1.31599 13.5296i 0.0454330 0.467092i −0.944798 0.327654i \(-0.893742\pi\)
0.990231 0.139438i \(-0.0445297\pi\)
\(840\) −6.64475 + 5.55901i −0.229266 + 0.191804i
\(841\) −6.24010 18.2374i −0.215176 0.628875i
\(842\) −15.6322 + 14.1854i −0.538720 + 0.488862i
\(843\) −38.9135 6.14448i −1.34025 0.211627i
\(844\) −9.74664 + 28.4856i −0.335493 + 0.980516i
\(845\) −0.558329 1.29435i −0.0192071 0.0445271i
\(846\) 1.16945 + 1.86758i 0.0402064 + 0.0642088i
\(847\) 48.2275 5.63699i 1.65712 0.193689i
\(848\) −12.6127 + 4.04409i −0.433121 + 0.138875i
\(849\) 1.86530 2.13108i 0.0640171 0.0731385i
\(850\) 53.3153 14.8413i 1.82870 0.509053i
\(851\) 9.41598 2.62112i 0.322776 0.0898508i
\(852\) −13.3961 2.65133i −0.458943 0.0908332i
\(853\) 1.82662 0.585681i 0.0625421 0.0200533i −0.273890 0.961761i \(-0.588311\pi\)
0.336432 + 0.941708i \(0.390780\pi\)
\(854\) 110.845 12.9559i 3.79304 0.443343i
\(855\) 6.39371 + 29.9411i 0.218660 + 1.02397i
\(856\) −4.76666 11.0504i −0.162921 0.377694i
\(857\) −2.74607 + 8.02568i −0.0938038 + 0.274152i −0.983068 0.183242i \(-0.941341\pi\)
0.889264 + 0.457394i \(0.151217\pi\)
\(858\) 2.41407 2.98400i 0.0824150 0.101872i
\(859\) −11.7803 + 10.6900i −0.401938 + 0.364739i −0.847758 0.530383i \(-0.822048\pi\)
0.445820 + 0.895123i \(0.352912\pi\)
\(860\) 8.92521 + 26.0849i 0.304347 + 0.889488i
\(861\) 21.1453 + 7.73142i 0.720630 + 0.263486i
\(862\) 2.53799 26.0928i 0.0864442 0.888724i
\(863\) 26.8817 9.78413i 0.915063 0.333056i 0.158790 0.987312i \(-0.449241\pi\)
0.756272 + 0.654257i \(0.227018\pi\)
\(864\) 38.7356 15.6266i 1.31781 0.531627i
\(865\) −8.19318 2.98207i −0.278577 0.101394i
\(866\) −35.0906 + 73.3858i −1.19243 + 2.49375i
\(867\) −62.9353 41.5256i −2.13739 1.41028i
\(868\) −46.2225 + 7.22907i −1.56889 + 0.245371i
\(869\) 3.05355 + 2.36668i 0.103585 + 0.0802842i
\(870\) −10.3233 + 10.0953i −0.349992 + 0.342263i
\(871\) −0.450776 23.2419i −0.0152740 0.787521i
\(872\) 0.545941 + 0.274182i 0.0184879 + 0.00928497i
\(873\) 34.3558 2.56892i 1.16277 0.0869447i
\(874\) 54.6968 + 35.9746i 1.85015 + 1.21686i
\(875\) 47.4195 + 1.84009i 1.60307 + 0.0622065i
\(876\) −4.66219 + 17.9904i −0.157521 + 0.607839i
\(877\) 3.40405 + 34.9967i 0.114947 + 1.18175i 0.858405 + 0.512973i \(0.171456\pi\)
−0.743458 + 0.668782i \(0.766816\pi\)
\(878\) 10.5400 + 22.0425i 0.355708 + 0.743900i
\(879\) 7.29774 52.8503i 0.246147 1.78260i
\(880\) −0.916253 + 0.710149i −0.0308869 + 0.0239391i
\(881\) 22.4854 23.8332i 0.757554 0.802960i −0.227759 0.973717i \(-0.573140\pi\)
0.985313 + 0.170757i \(0.0546214\pi\)
\(882\) −72.1530 36.5022i −2.42952 1.22909i
\(883\) 9.66049 32.2683i 0.325102 1.08591i −0.626715 0.779248i \(-0.715601\pi\)
0.951817 0.306667i \(-0.0992136\pi\)
\(884\) −40.7666 + 50.5427i −1.37113 + 1.69993i
\(885\) 2.84754 + 5.42522i 0.0957191 + 0.182367i
\(886\) −0.363804 0.577215i −0.0122222 0.0193919i
\(887\) −14.3318 + 7.90796i −0.481215 + 0.265523i −0.705120 0.709088i \(-0.749107\pi\)
0.223905 + 0.974611i \(0.428119\pi\)
\(888\) 3.82903 + 0.453247i 0.128494 + 0.0152100i
\(889\) 5.33328 + 20.7051i 0.178872 + 0.694425i
\(890\) −9.49368 + 16.4435i −0.318229 + 0.551189i
\(891\) 0.975725 + 2.57203i 0.0326880 + 0.0861662i
\(892\) −24.3325 42.1452i −0.814713 1.41112i
\(893\) 2.00188 1.96343i 0.0669905 0.0657038i
\(894\) 41.5123 9.77426i 1.38838 0.326900i
\(895\) 0.168089 8.66665i 0.00561861 0.289694i
\(896\) 14.3428 27.2291i 0.479159 0.909661i
\(897\) −18.3356 + 14.1682i −0.612209 + 0.473061i
\(898\) 11.7776 + 30.5047i 0.393023 + 1.01796i
\(899\) −13.1750 + 3.12254i −0.439412 + 0.104143i
\(900\) 23.0592 + 8.46961i 0.768642 + 0.282320i
\(901\) 9.90853 + 33.0968i 0.330101 + 1.10261i
\(902\) −1.73693 0.709615i −0.0578336 0.0236276i
\(903\) −51.2261 + 46.3483i −1.70470 + 1.54237i
\(904\) −4.49562 0.349428i −0.149522 0.0116218i
\(905\) 5.91112 4.22502i 0.196492 0.140444i
\(906\) 27.6363 + 58.0150i 0.918154 + 1.92742i
\(907\) 18.2033 28.8815i 0.604430 0.958993i −0.394762 0.918784i \(-0.629173\pi\)
0.999191 0.0402094i \(-0.0128025\pi\)
\(908\) 3.39628 58.3119i 0.112709 1.93515i
\(909\) −4.20849 31.5009i −0.139587 1.04482i
\(910\) −34.2886 + 22.5520i −1.13666 + 0.747591i
\(911\) 31.5283 19.0274i 1.04458 0.630407i 0.112869 0.993610i \(-0.463996\pi\)
0.931710 + 0.363203i \(0.118317\pi\)
\(912\) −23.4037 34.2310i −0.774973 1.13350i
\(913\) 0.115102 0.0470243i 0.00380932 0.00155628i
\(914\) 39.7974 + 49.3411i 1.31638 + 1.63206i
\(915\) 15.6493 + 21.0851i 0.517349 + 0.697053i
\(916\) −13.5217 19.7152i −0.446771 0.651408i
\(917\) 11.3383 + 64.3028i 0.374424 + 2.12346i
\(918\) −30.2644 79.4258i −0.998875 2.62144i
\(919\) 2.21386 12.5555i 0.0730287 0.414166i −0.926275 0.376849i \(-0.877008\pi\)
0.999303 0.0373174i \(-0.0118812\pi\)
\(920\) −3.96803 + 1.80369i −0.130822 + 0.0594659i
\(921\) 9.76365 + 0.0143296i 0.321723 + 0.000472175i
\(922\) 69.5552 + 13.6602i 2.29068 + 0.449874i
\(923\) −10.6970 3.42986i −0.352096 0.112895i
\(924\) 4.99047 + 2.76319i 0.164174 + 0.0909022i
\(925\) −5.60451 6.42206i −0.184275 0.211156i
\(926\) −26.9442 + 36.1923i −0.885441 + 1.18935i
\(927\) 9.63287 + 5.85211i 0.316385 + 0.192208i
\(928\) 9.92863 23.0172i 0.325923 0.755575i
\(929\) −30.7346 27.8901i −1.00837 0.915046i −0.0119778 0.999928i \(-0.503813\pi\)
−0.996391 + 0.0848824i \(0.972949\pi\)
\(930\) −12.5986 15.6668i −0.413125 0.513735i
\(931\) −25.6669 + 99.6451i −0.841199 + 3.26574i
\(932\) 6.70518 + 6.57640i 0.219636 + 0.215417i
\(933\) −0.372132 + 17.8367i −0.0121830 + 0.583949i
\(934\) −15.8543 + 73.1914i −0.518767 + 2.39490i
\(935\) 1.80564 + 2.42539i 0.0590506 + 0.0793187i
\(936\) −8.81341 + 2.42553i −0.288075 + 0.0792809i
\(937\) −20.7457 2.42483i −0.677733 0.0792156i −0.229739 0.973252i \(-0.573787\pi\)
−0.447994 + 0.894037i \(0.647861\pi\)
\(938\) 61.9152 12.1597i 2.02160 0.397030i
\(939\) −3.78203 + 11.0007i −0.123422 + 0.358993i
\(940\) 0.227604 + 1.05074i 0.00742362 + 0.0342713i
\(941\) 16.2050 18.5689i 0.528267 0.605327i −0.425838 0.904800i \(-0.640021\pi\)
0.954105 + 0.299472i \(0.0968106\pi\)
\(942\) −1.45913 + 0.528656i −0.0475411 + 0.0172246i
\(943\) 9.21543 + 6.58679i 0.300096 + 0.214495i
\(944\) −6.35710 5.33424i −0.206906 0.173615i
\(945\) −1.58096 29.3713i −0.0514285 0.955448i
\(946\) 4.41020 3.70059i 0.143388 0.120317i
\(947\) −12.0534 + 0.936861i −0.391681 + 0.0304439i −0.271823 0.962347i \(-0.587627\pi\)
−0.119858 + 0.992791i \(0.538244\pi\)
\(948\) −15.1219 50.7820i −0.491138 1.64932i
\(949\) −5.50633 + 14.2617i −0.178743 + 0.462956i
\(950\) 7.72638 56.5671i 0.250677 1.83528i
\(951\) 34.7978 15.7559i 1.12839 0.510921i
\(952\) −26.7974 14.7862i −0.868509 0.479223i
\(953\) 1.61763 + 27.7737i 0.0524002 + 0.899677i 0.917415 + 0.397931i \(0.130272\pi\)
−0.865015 + 0.501746i \(0.832691\pi\)
\(954\) −9.14477 + 26.4727i −0.296073 + 0.857084i
\(955\) 7.02609 3.52863i 0.227359 0.114184i
\(956\) −21.2320 40.3080i −0.686693 1.30365i
\(957\) 1.50193 + 0.685375i 0.0485506 + 0.0221550i
\(958\) −75.4876 34.3133i −2.43890 1.10861i
\(959\) 44.4434 64.8001i 1.43515 2.09250i
\(960\) 24.0648 0.898453i 0.776688 0.0289975i
\(961\) 1.64396 + 12.0359i 0.0530308 + 0.388254i
\(962\) 17.7731 + 4.21229i 0.573027 + 0.135810i
\(963\) 39.7302 + 9.53949i 1.28029 + 0.307406i
\(964\) −12.7540 13.5185i −0.410780 0.435402i
\(965\) −6.28729 0.983315i −0.202395 0.0316540i
\(966\) −46.5150 42.3348i −1.49660 1.36210i
\(967\) 13.2525 0.514259i 0.426173 0.0165375i 0.175203 0.984532i \(-0.443942\pi\)
0.250970 + 0.967995i \(0.419250\pi\)
\(968\) 8.25102 + 4.97951i 0.265198 + 0.160048i
\(969\) −90.4539 + 59.3025i −2.90580 + 1.90507i
\(970\) 29.5750 + 8.23276i 0.949596 + 0.264338i
\(971\) −34.4989 −1.10712 −0.553561 0.832808i \(-0.686732\pi\)
−0.553561 + 0.832808i \(0.686732\pi\)
\(972\) 9.67886 36.4657i 0.310450 1.16964i
\(973\) −3.34710 −0.107303
\(974\) −87.4000 24.3295i −2.80048 0.779566i
\(975\) 18.0449 + 9.09566i 0.577898 + 0.291294i
\(976\) −30.4487 18.3759i −0.974640 0.588198i
\(977\) 35.8742 1.39208i 1.14772 0.0445367i 0.542116 0.840304i \(-0.317623\pi\)
0.605603 + 0.795767i \(0.292932\pi\)
\(978\) 6.73924 2.14995i 0.215497 0.0687477i
\(979\) 2.14490 + 0.335456i 0.0685512 + 0.0107212i
\(980\) −27.0739 28.6966i −0.864843 0.916680i
\(981\) −1.85628 + 0.925448i −0.0592666 + 0.0295473i
\(982\) 80.4758 + 19.0731i 2.56808 + 0.608647i
\(983\) −0.626154 4.58426i −0.0199712 0.146215i 0.978114 0.208070i \(-0.0667182\pi\)
−0.998085 + 0.0618548i \(0.980298\pi\)
\(984\) 2.37711 + 3.78384i 0.0757794 + 0.120624i
\(985\) 6.87067 10.0177i 0.218918 0.319190i
\(986\) −46.4376 21.1085i −1.47887 0.672231i
\(987\) −2.19393 + 1.56327i −0.0698337 + 0.0497594i
\(988\) 31.2191 + 59.2681i 0.993213 + 1.88557i
\(989\) −31.0593 + 15.5986i −0.987627 + 0.496005i
\(990\) 0.0403395 + 2.45094i 0.00128207 + 0.0778961i
\(991\) −0.113620 1.95078i −0.00360926 0.0619685i 0.996023 0.0891011i \(-0.0283994\pi\)
−0.999632 + 0.0271326i \(0.991362\pi\)
\(992\) 30.5590 + 16.8617i 0.970248 + 0.535360i
\(993\) 6.48700 + 4.65103i 0.205859 + 0.147596i
\(994\) 4.12641 30.2107i 0.130882 0.958224i
\(995\) −2.51204 + 6.50635i −0.0796370 + 0.206265i
\(996\) −1.65874 0.395701i −0.0525592 0.0125383i
\(997\) −37.4385 + 2.90995i −1.18569 + 0.0921591i −0.655149 0.755500i \(-0.727394\pi\)
−0.530541 + 0.847659i \(0.678011\pi\)
\(998\) −24.4969 + 20.5553i −0.775436 + 0.650668i
\(999\) −9.02539 + 9.48236i −0.285551 + 0.300009i
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 243.2.i.a.103.23 1404
3.2 odd 2 729.2.i.a.685.4 1404
243.92 odd 162 729.2.i.a.613.4 1404
243.151 even 81 inner 243.2.i.a.151.23 yes 1404
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.i.a.103.23 1404 1.1 even 1 trivial
243.2.i.a.151.23 yes 1404 243.151 even 81 inner
729.2.i.a.613.4 1404 243.92 odd 162
729.2.i.a.685.4 1404 3.2 odd 2