Properties

Label 55.2.l.a.2.2
Level $55$
Weight $2$
Character 55.2
Analytic conductor $0.439$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,2,Mod(2,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.l (of order \(20\), degree \(8\), 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: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 2.2
Character \(\chi\) \(=\) 55.2
Dual form 55.2.l.a.28.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.474334 - 0.930933i) q^{2} +(-0.440550 + 2.78152i) q^{3} +(0.533928 - 0.734888i) q^{4} +(2.23541 + 0.0540419i) q^{5} +(2.79838 - 0.909249i) q^{6} +(-0.543058 + 0.0860119i) q^{7} +(-3.00128 - 0.475357i) q^{8} +(-4.68963 - 1.52375i) q^{9} +O(q^{10})\) \(q+(-0.474334 - 0.930933i) q^{2} +(-0.440550 + 2.78152i) q^{3} +(0.533928 - 0.734888i) q^{4} +(2.23541 + 0.0540419i) q^{5} +(2.79838 - 0.909249i) q^{6} +(-0.543058 + 0.0860119i) q^{7} +(-3.00128 - 0.475357i) q^{8} +(-4.68963 - 1.52375i) q^{9} +(-1.01002 - 2.10665i) q^{10} +(-3.29961 - 0.335528i) q^{11} +(1.80889 + 1.80889i) q^{12} +(2.89095 - 1.47301i) q^{13} +(0.337662 + 0.464752i) q^{14} +(-1.13513 + 6.19405i) q^{15} +(0.419681 + 1.29165i) q^{16} +(-5.04545 - 2.57079i) q^{17} +(0.805938 + 5.08849i) q^{18} +(1.25925 - 0.914902i) q^{19} +(1.23326 - 1.61393i) q^{20} -1.54842i q^{21} +(1.25276 + 3.23087i) q^{22} +(-0.803543 + 0.803543i) q^{23} +(2.64443 - 8.13873i) q^{24} +(4.99416 + 0.241612i) q^{25} +(-2.74255 - 1.99258i) q^{26} +(2.46879 - 4.84527i) q^{27} +(-0.226744 + 0.445011i) q^{28} +(3.44380 + 2.50207i) q^{29} +(6.30468 - 1.88132i) q^{30} +(-0.509209 + 1.56718i) q^{31} +(-3.29400 + 3.29400i) q^{32} +(2.38692 - 9.03013i) q^{33} +5.91638i q^{34} +(-1.21861 + 0.162924i) q^{35} +(-3.62371 + 2.63278i) q^{36} +(-0.149692 - 0.945121i) q^{37} +(-1.44902 - 0.738312i) q^{38} +(2.82361 + 8.69018i) q^{39} +(-6.68343 - 1.22481i) q^{40} +(5.25869 + 7.23797i) q^{41} +(-1.44148 + 0.734469i) q^{42} +(2.55312 + 2.55312i) q^{43} +(-2.00833 + 2.24570i) q^{44} +(-10.4009 - 3.65965i) q^{45} +(1.12919 + 0.366897i) q^{46} +(4.02160 + 0.636959i) q^{47} +(-3.77764 + 0.598319i) q^{48} +(-6.36988 + 2.06970i) q^{49} +(-2.14397 - 4.76383i) q^{50} +(9.37348 - 12.9015i) q^{51} +(0.461058 - 2.91101i) q^{52} +(-3.19821 - 6.27685i) q^{53} -5.68165 q^{54} +(-7.35786 - 0.928362i) q^{55} +1.67076 q^{56} +(1.99006 + 3.90571i) q^{57} +(0.695746 - 4.39276i) q^{58} +(3.97760 - 5.47470i) q^{59} +(3.94586 + 4.14137i) q^{60} +(-8.75080 + 2.84331i) q^{61} +(1.70048 - 0.269329i) q^{62} +(2.67780 + 0.424122i) q^{63} +(7.21224 + 2.34340i) q^{64} +(6.54208 - 3.13656i) q^{65} +(-9.53864 + 2.06123i) q^{66} +(-2.62254 - 2.62254i) q^{67} +(-4.58314 + 2.33523i) q^{68} +(-1.88107 - 2.58908i) q^{69} +(0.729699 + 1.05716i) q^{70} +(2.11802 + 6.51858i) q^{71} +(13.3506 + 6.80246i) q^{72} +(1.57837 + 9.96541i) q^{73} +(-0.808840 + 0.587656i) q^{74} +(-2.87223 + 13.7849i) q^{75} -1.41390i q^{76} +(1.82074 - 0.101594i) q^{77} +(6.75064 - 6.75064i) q^{78} +(1.28746 - 3.96241i) q^{79} +(0.868359 + 2.91005i) q^{80} +(0.421915 + 0.306539i) q^{81} +(4.24369 - 8.32870i) q^{82} +(5.14352 - 10.0947i) q^{83} +(-1.13792 - 0.826745i) q^{84} +(-11.1397 - 6.01944i) q^{85} +(1.16575 - 3.58782i) q^{86} +(-8.47673 + 8.47673i) q^{87} +(9.74357 + 2.57551i) q^{88} -3.64860i q^{89} +(1.52661 + 11.4184i) q^{90} +(-1.44326 + 1.04859i) q^{91} +(0.161481 + 1.01955i) q^{92} +(-4.13483 - 2.10680i) q^{93} +(-1.31462 - 4.04597i) q^{94} +(2.86440 - 1.97713i) q^{95} +(-7.71117 - 10.6135i) q^{96} +(14.8515 - 7.56722i) q^{97} +(4.94820 + 4.94820i) q^{98} +(14.9627 + 6.60129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8} - 24 q^{11} + 12 q^{12} - 10 q^{13} + 14 q^{15} - 8 q^{16} - 10 q^{18} + 16 q^{20} + 10 q^{22} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 50 q^{28} + 30 q^{30} - 28 q^{31} + 66 q^{33} - 10 q^{35} + 24 q^{36} - 8 q^{37} + 10 q^{38} - 50 q^{40} + 40 q^{41} - 10 q^{42} - 28 q^{45} + 60 q^{46} - 28 q^{47} - 54 q^{48} - 50 q^{50} + 20 q^{51} - 50 q^{52} - 24 q^{53} - 64 q^{55} - 80 q^{56} + 30 q^{57} - 50 q^{58} + 34 q^{60} - 60 q^{61} + 100 q^{62} - 30 q^{63} - 100 q^{66} - 8 q^{67} - 30 q^{68} + 30 q^{70} + 24 q^{71} + 80 q^{72} + 50 q^{73} + 34 q^{75} + 70 q^{77} + 60 q^{78} + 98 q^{80} - 12 q^{81} - 10 q^{82} + 90 q^{83} + 30 q^{85} + 100 q^{86} + 170 q^{88} - 20 q^{90} + 20 q^{91} - 68 q^{92} - 8 q^{93} - 40 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.474334 0.930933i −0.335405 0.658269i 0.660285 0.751015i \(-0.270435\pi\)
−0.995690 + 0.0927463i \(0.970435\pi\)
\(3\) −0.440550 + 2.78152i −0.254352 + 1.60591i 0.447966 + 0.894051i \(0.352149\pi\)
−0.702318 + 0.711863i \(0.747851\pi\)
\(4\) 0.533928 0.734888i 0.266964 0.367444i
\(5\) 2.23541 + 0.0540419i 0.999708 + 0.0241683i
\(6\) 2.79838 0.909249i 1.14243 0.371199i
\(7\) −0.543058 + 0.0860119i −0.205257 + 0.0325095i −0.258216 0.966087i \(-0.583135\pi\)
0.0529594 + 0.998597i \(0.483135\pi\)
\(8\) −3.00128 0.475357i −1.06111 0.168064i
\(9\) −4.68963 1.52375i −1.56321 0.507917i
\(10\) −1.01002 2.10665i −0.319398 0.666183i
\(11\) −3.29961 0.335528i −0.994870 0.101166i
\(12\) 1.80889 + 1.80889i 0.522181 + 0.522181i
\(13\) 2.89095 1.47301i 0.801805 0.408540i −0.00453687 0.999990i \(-0.501444\pi\)
0.806342 + 0.591450i \(0.201444\pi\)
\(14\) 0.337662 + 0.464752i 0.0902440 + 0.124210i
\(15\) −1.13513 + 6.19405i −0.293090 + 1.59930i
\(16\) 0.419681 + 1.29165i 0.104920 + 0.322912i
\(17\) −5.04545 2.57079i −1.22370 0.623507i −0.281825 0.959466i \(-0.590940\pi\)
−0.941877 + 0.335959i \(0.890940\pi\)
\(18\) 0.805938 + 5.08849i 0.189961 + 1.19937i
\(19\) 1.25925 0.914902i 0.288893 0.209893i −0.433894 0.900964i \(-0.642861\pi\)
0.722787 + 0.691071i \(0.242861\pi\)
\(20\) 1.23326 1.61393i 0.275766 0.360885i
\(21\) 1.54842i 0.337893i
\(22\) 1.25276 + 3.23087i 0.267090 + 0.688823i
\(23\) −0.803543 + 0.803543i −0.167550 + 0.167550i −0.785902 0.618351i \(-0.787801\pi\)
0.618351 + 0.785902i \(0.287801\pi\)
\(24\) 2.64443 8.13873i 0.539793 1.66131i
\(25\) 4.99416 + 0.241612i 0.998832 + 0.0483224i
\(26\) −2.74255 1.99258i −0.537858 0.390777i
\(27\) 2.46879 4.84527i 0.475119 0.932473i
\(28\) −0.226744 + 0.445011i −0.0428507 + 0.0840992i
\(29\) 3.44380 + 2.50207i 0.639498 + 0.464623i 0.859678 0.510837i \(-0.170664\pi\)
−0.220180 + 0.975459i \(0.570664\pi\)
\(30\) 6.30468 1.88132i 1.15107 0.343480i
\(31\) −0.509209 + 1.56718i −0.0914566 + 0.281475i −0.986314 0.164878i \(-0.947277\pi\)
0.894857 + 0.446352i \(0.147277\pi\)
\(32\) −3.29400 + 3.29400i −0.582302 + 0.582302i
\(33\) 2.38692 9.03013i 0.415510 1.57194i
\(34\) 5.91638i 1.01465i
\(35\) −1.21861 + 0.162924i −0.205982 + 0.0275393i
\(36\) −3.62371 + 2.63278i −0.603951 + 0.438796i
\(37\) −0.149692 0.945121i −0.0246093 0.155377i 0.972324 0.233638i \(-0.0750631\pi\)
−0.996933 + 0.0782613i \(0.975063\pi\)
\(38\) −1.44902 0.738312i −0.235062 0.119770i
\(39\) 2.82361 + 8.69018i 0.452140 + 1.39154i
\(40\) −6.68343 1.22481i −1.05674 0.193660i
\(41\) 5.25869 + 7.23797i 0.821270 + 1.13038i 0.989486 + 0.144631i \(0.0461994\pi\)
−0.168216 + 0.985750i \(0.553801\pi\)
\(42\) −1.44148 + 0.734469i −0.222425 + 0.113331i
\(43\) 2.55312 + 2.55312i 0.389348 + 0.389348i 0.874455 0.485107i \(-0.161219\pi\)
−0.485107 + 0.874455i \(0.661219\pi\)
\(44\) −2.00833 + 2.24570i −0.302767 + 0.338551i
\(45\) −10.4009 3.65965i −1.55048 0.545549i
\(46\) 1.12919 + 0.366897i 0.166490 + 0.0540960i
\(47\) 4.02160 + 0.636959i 0.586611 + 0.0929101i 0.442683 0.896678i \(-0.354027\pi\)
0.143928 + 0.989588i \(0.454027\pi\)
\(48\) −3.77764 + 0.598319i −0.545255 + 0.0863599i
\(49\) −6.36988 + 2.06970i −0.909983 + 0.295671i
\(50\) −2.14397 4.76383i −0.303204 0.673707i
\(51\) 9.37348 12.9015i 1.31255 1.80657i
\(52\) 0.461058 2.91101i 0.0639373 0.403684i
\(53\) −3.19821 6.27685i −0.439309 0.862192i −0.999429 0.0337806i \(-0.989245\pi\)
0.560121 0.828411i \(-0.310755\pi\)
\(54\) −5.68165 −0.773175
\(55\) −7.35786 0.928362i −0.992134 0.125180i
\(56\) 1.67076 0.223264
\(57\) 1.99006 + 3.90571i 0.263590 + 0.517324i
\(58\) 0.695746 4.39276i 0.0913559 0.576798i
\(59\) 3.97760 5.47470i 0.517839 0.712745i −0.467377 0.884058i \(-0.654801\pi\)
0.985217 + 0.171313i \(0.0548010\pi\)
\(60\) 3.94586 + 4.14137i 0.509408 + 0.534649i
\(61\) −8.75080 + 2.84331i −1.12043 + 0.364048i −0.809930 0.586526i \(-0.800495\pi\)
−0.310496 + 0.950575i \(0.600495\pi\)
\(62\) 1.70048 0.269329i 0.215961 0.0342048i
\(63\) 2.67780 + 0.424122i 0.337371 + 0.0534343i
\(64\) 7.21224 + 2.34340i 0.901530 + 0.292925i
\(65\) 6.54208 3.13656i 0.811445 0.389043i
\(66\) −9.53864 + 2.06123i −1.17413 + 0.253720i
\(67\) −2.62254 2.62254i −0.320394 0.320394i 0.528524 0.848918i \(-0.322746\pi\)
−0.848918 + 0.528524i \(0.822746\pi\)
\(68\) −4.58314 + 2.33523i −0.555788 + 0.283188i
\(69\) −1.88107 2.58908i −0.226455 0.311688i
\(70\) 0.729699 + 1.05716i 0.0872157 + 0.126355i
\(71\) 2.11802 + 6.51858i 0.251362 + 0.773613i 0.994525 + 0.104502i \(0.0333250\pi\)
−0.743162 + 0.669111i \(0.766675\pi\)
\(72\) 13.3506 + 6.80246i 1.57338 + 0.801677i
\(73\) 1.57837 + 9.96541i 0.184734 + 1.16636i 0.889504 + 0.456928i \(0.151050\pi\)
−0.704770 + 0.709436i \(0.748950\pi\)
\(74\) −0.808840 + 0.587656i −0.0940257 + 0.0683137i
\(75\) −2.87223 + 13.7849i −0.331656 + 1.59175i
\(76\) 1.41390i 0.162186i
\(77\) 1.82074 0.101594i 0.207492 0.0115778i
\(78\) 6.75064 6.75064i 0.764360 0.764360i
\(79\) 1.28746 3.96241i 0.144851 0.445806i −0.852141 0.523313i \(-0.824696\pi\)
0.996992 + 0.0775069i \(0.0246960\pi\)
\(80\) 0.868359 + 2.91005i 0.0970855 + 0.325353i
\(81\) 0.421915 + 0.306539i 0.0468795 + 0.0340599i
\(82\) 4.24369 8.32870i 0.468637 0.919751i
\(83\) 5.14352 10.0947i 0.564574 1.10804i −0.415534 0.909577i \(-0.636405\pi\)
0.980109 0.198462i \(-0.0635946\pi\)
\(84\) −1.13792 0.826745i −0.124157 0.0902053i
\(85\) −11.1397 6.01944i −1.20827 0.652900i
\(86\) 1.16575 3.58782i 0.125706 0.386884i
\(87\) −8.47673 + 8.47673i −0.908801 + 0.908801i
\(88\) 9.74357 + 2.57551i 1.03867 + 0.274550i
\(89\) 3.64860i 0.386750i −0.981125 0.193375i \(-0.938057\pi\)
0.981125 0.193375i \(-0.0619435\pi\)
\(90\) 1.52661 + 11.4184i 0.160919 + 1.20361i
\(91\) −1.44326 + 1.04859i −0.151294 + 0.109922i
\(92\) 0.161481 + 1.01955i 0.0168355 + 0.106295i
\(93\) −4.13483 2.10680i −0.428762 0.218465i
\(94\) −1.31462 4.04597i −0.135592 0.417310i
\(95\) 2.86440 1.97713i 0.293881 0.202850i
\(96\) −7.71117 10.6135i −0.787018 1.08324i
\(97\) 14.8515 7.56722i 1.50794 0.768335i 0.512057 0.858952i \(-0.328884\pi\)
0.995886 + 0.0906166i \(0.0288838\pi\)
\(98\) 4.94820 + 4.94820i 0.499844 + 0.499844i
\(99\) 14.9627 + 6.60129i 1.50380 + 0.663454i
\(100\) 2.84408 3.54115i 0.284408 0.354115i
\(101\) −0.608855 0.197829i −0.0605834 0.0196847i 0.278569 0.960416i \(-0.410140\pi\)
−0.339152 + 0.940732i \(0.610140\pi\)
\(102\) −16.4566 2.60646i −1.62944 0.258078i
\(103\) −2.04060 + 0.323199i −0.201066 + 0.0318457i −0.256155 0.966636i \(-0.582456\pi\)
0.0550890 + 0.998481i \(0.482456\pi\)
\(104\) −9.37677 + 3.04670i −0.919468 + 0.298753i
\(105\) 0.0836796 3.46136i 0.00816630 0.337795i
\(106\) −4.32630 + 5.95465i −0.420208 + 0.578366i
\(107\) −1.39820 + 8.82790i −0.135169 + 0.853425i 0.823171 + 0.567794i \(0.192203\pi\)
−0.958340 + 0.285631i \(0.907797\pi\)
\(108\) −2.24258 4.40131i −0.215792 0.423516i
\(109\) −4.48044 −0.429148 −0.214574 0.976708i \(-0.568836\pi\)
−0.214574 + 0.976708i \(0.568836\pi\)
\(110\) 2.62584 + 7.29003i 0.250364 + 0.695077i
\(111\) 2.69482 0.255781
\(112\) −0.339008 0.665341i −0.0320333 0.0628688i
\(113\) −0.224599 + 1.41806i −0.0211285 + 0.133400i −0.995998 0.0893772i \(-0.971512\pi\)
0.974869 + 0.222778i \(0.0715123\pi\)
\(114\) 2.69200 3.70522i 0.252129 0.347026i
\(115\) −1.83968 + 1.75283i −0.171551 + 0.163452i
\(116\) 3.67748 1.19489i 0.341446 0.110942i
\(117\) −15.8020 + 2.50279i −1.46089 + 0.231383i
\(118\) −6.98328 1.10604i −0.642863 0.101820i
\(119\) 2.96109 + 0.962116i 0.271443 + 0.0881971i
\(120\) 6.35124 18.0505i 0.579786 1.64778i
\(121\) 10.7748 + 2.21422i 0.979531 + 0.201293i
\(122\) 6.79773 + 6.79773i 0.615438 + 0.615438i
\(123\) −22.4493 + 11.4385i −2.02419 + 1.03137i
\(124\) 0.879824 + 1.21097i 0.0790106 + 0.108749i
\(125\) 11.1510 + 0.809997i 0.997372 + 0.0724483i
\(126\) −0.875342 2.69403i −0.0779817 0.240003i
\(127\) −10.5351 5.36790i −0.934838 0.476324i −0.0809136 0.996721i \(-0.525784\pi\)
−0.853924 + 0.520397i \(0.825784\pi\)
\(128\) 0.218011 + 1.37647i 0.0192696 + 0.121664i
\(129\) −8.22635 + 5.97680i −0.724290 + 0.526228i
\(130\) −6.02306 4.60245i −0.528257 0.403662i
\(131\) 7.94436i 0.694102i −0.937846 0.347051i \(-0.887183\pi\)
0.937846 0.347051i \(-0.112817\pi\)
\(132\) −5.36169 6.57556i −0.466675 0.572329i
\(133\) −0.605156 + 0.605156i −0.0524737 + 0.0524737i
\(134\) −1.19745 + 3.68537i −0.103444 + 0.318367i
\(135\) 5.78062 10.6978i 0.497516 0.920718i
\(136\) 13.9208 + 10.1140i 1.19370 + 0.867272i
\(137\) −2.03155 + 3.98714i −0.173567 + 0.340644i −0.961359 0.275297i \(-0.911224\pi\)
0.787792 + 0.615941i \(0.211224\pi\)
\(138\) −1.51800 + 2.97924i −0.129221 + 0.253610i
\(139\) −18.2968 13.2934i −1.55192 1.12753i −0.942267 0.334862i \(-0.891310\pi\)
−0.609650 0.792671i \(-0.708690\pi\)
\(140\) −0.530917 + 0.982531i −0.0448707 + 0.0830390i
\(141\) −3.54344 + 10.9056i −0.298411 + 0.918415i
\(142\) 5.06371 5.06371i 0.424937 0.424937i
\(143\) −10.0332 + 3.89037i −0.839022 + 0.325329i
\(144\) 6.69683i 0.558069i
\(145\) 7.56311 + 5.77927i 0.628082 + 0.479942i
\(146\) 8.52846 6.19629i 0.705820 0.512808i
\(147\) −2.95067 18.6298i −0.243367 1.53656i
\(148\) −0.774483 0.394619i −0.0636621 0.0324375i
\(149\) 4.56892 + 14.0617i 0.374301 + 1.15198i 0.943949 + 0.330091i \(0.107079\pi\)
−0.569648 + 0.821888i \(0.692921\pi\)
\(150\) 14.1952 3.86481i 1.15904 0.315560i
\(151\) 3.90602 + 5.37617i 0.317867 + 0.437507i 0.937815 0.347137i \(-0.112846\pi\)
−0.619947 + 0.784644i \(0.712846\pi\)
\(152\) −4.21429 + 2.14729i −0.341824 + 0.174168i
\(153\) 19.7440 + 19.7440i 1.59621 + 1.59621i
\(154\) −0.958216 1.64680i −0.0772152 0.132703i
\(155\) −1.22299 + 3.47579i −0.0982327 + 0.279182i
\(156\) 7.89392 + 2.56489i 0.632019 + 0.205355i
\(157\) 1.59445 + 0.252536i 0.127251 + 0.0201545i 0.219735 0.975560i \(-0.429481\pi\)
−0.0924842 + 0.995714i \(0.529481\pi\)
\(158\) −4.29942 + 0.680962i −0.342044 + 0.0541744i
\(159\) 18.8682 6.13065i 1.49634 0.486192i
\(160\) −7.54147 + 7.18544i −0.596205 + 0.568059i
\(161\) 0.367256 0.505485i 0.0289438 0.0398378i
\(162\) 0.0852388 0.538177i 0.00669699 0.0422831i
\(163\) 4.59871 + 9.02548i 0.360199 + 0.706930i 0.997996 0.0632741i \(-0.0201542\pi\)
−0.637797 + 0.770204i \(0.720154\pi\)
\(164\) 8.12686 0.634601
\(165\) 5.82377 20.0571i 0.453380 1.56144i
\(166\) −11.8372 −0.918749
\(167\) −6.50021 12.7574i −0.503001 0.987195i −0.993292 0.115636i \(-0.963109\pi\)
0.490290 0.871559i \(-0.336891\pi\)
\(168\) −0.736053 + 4.64725i −0.0567877 + 0.358543i
\(169\) −1.45339 + 2.00041i −0.111799 + 0.153878i
\(170\) −0.319733 + 13.2256i −0.0245224 + 1.01436i
\(171\) −7.29952 + 2.37176i −0.558208 + 0.181373i
\(172\) 3.23944 0.513077i 0.247005 0.0391218i
\(173\) 16.3652 + 2.59199i 1.24422 + 0.197066i 0.743615 0.668608i \(-0.233110\pi\)
0.500609 + 0.865674i \(0.333110\pi\)
\(174\) 11.9121 + 3.87047i 0.903052 + 0.293419i
\(175\) −2.73290 + 0.298348i −0.206588 + 0.0225530i
\(176\) −0.951401 4.40274i −0.0717145 0.331869i
\(177\) 13.4757 + 13.4757i 1.01289 + 1.01289i
\(178\) −3.39660 + 1.73065i −0.254586 + 0.129718i
\(179\) −11.7477 16.1694i −0.878066 1.20855i −0.976953 0.213455i \(-0.931528\pi\)
0.0988868 0.995099i \(-0.468472\pi\)
\(180\) −8.24277 + 5.68952i −0.614380 + 0.424072i
\(181\) −8.30476 25.5594i −0.617288 1.89982i −0.355370 0.934726i \(-0.615645\pi\)
−0.261918 0.965090i \(-0.584355\pi\)
\(182\) 1.66075 + 0.846194i 0.123103 + 0.0627241i
\(183\) −4.05356 25.5932i −0.299648 1.89190i
\(184\) 2.79363 2.02969i 0.205949 0.149631i
\(185\) −0.283549 2.12083i −0.0208469 0.155926i
\(186\) 4.84857i 0.355515i
\(187\) 15.7854 + 10.1755i 1.15435 + 0.744105i
\(188\) 2.61534 2.61534i 0.190743 0.190743i
\(189\) −0.923944 + 2.84361i −0.0672071 + 0.206842i
\(190\) −3.19926 1.72874i −0.232099 0.125416i
\(191\) −10.4691 7.60626i −0.757519 0.550370i 0.140629 0.990062i \(-0.455087\pi\)
−0.898148 + 0.439693i \(0.855087\pi\)
\(192\) −9.69557 + 19.0286i −0.699718 + 1.37327i
\(193\) 3.40398 6.68068i 0.245024 0.480886i −0.735439 0.677591i \(-0.763024\pi\)
0.980463 + 0.196705i \(0.0630241\pi\)
\(194\) −14.0892 10.2364i −1.01154 0.734928i
\(195\) 5.84231 + 19.5788i 0.418376 + 1.40206i
\(196\) −1.88006 + 5.78622i −0.134290 + 0.413301i
\(197\) −2.73095 + 2.73095i −0.194572 + 0.194572i −0.797668 0.603096i \(-0.793933\pi\)
0.603096 + 0.797668i \(0.293933\pi\)
\(198\) −0.951948 17.0605i −0.0676520 1.21243i
\(199\) 12.3835i 0.877842i 0.898526 + 0.438921i \(0.144639\pi\)
−0.898526 + 0.438921i \(0.855361\pi\)
\(200\) −14.8740 3.09915i −1.05175 0.219143i
\(201\) 8.45002 6.13930i 0.596018 0.433033i
\(202\) 0.104635 + 0.660640i 0.00736210 + 0.0464825i
\(203\) −2.08539 1.06256i −0.146366 0.0745771i
\(204\) −4.47639 13.7769i −0.313410 0.964577i
\(205\) 11.3642 + 16.4641i 0.793710 + 1.14990i
\(206\) 1.26880 + 1.74635i 0.0884015 + 0.121674i
\(207\) 4.99272 2.54392i 0.347018 0.176814i
\(208\) 3.11589 + 3.11589i 0.216048 + 0.216048i
\(209\) −4.46202 + 2.59630i −0.308645 + 0.179590i
\(210\) −3.26199 + 1.56394i −0.225099 + 0.107922i
\(211\) 12.8931 + 4.18923i 0.887599 + 0.288398i 0.717109 0.696961i \(-0.245465\pi\)
0.170490 + 0.985359i \(0.445465\pi\)
\(212\) −6.32040 1.00105i −0.434087 0.0687526i
\(213\) −19.0647 + 3.01955i −1.30629 + 0.206896i
\(214\) 8.88139 2.88574i 0.607119 0.197265i
\(215\) 5.56931 + 5.84527i 0.379824 + 0.398644i
\(216\) −9.71277 + 13.3685i −0.660870 + 0.909610i
\(217\) 0.141733 0.894870i 0.00962149 0.0607477i
\(218\) 2.12522 + 4.17099i 0.143938 + 0.282495i
\(219\) −28.4144 −1.92007
\(220\) −4.61081 + 4.91153i −0.310861 + 0.331135i
\(221\) −18.3729 −1.23590
\(222\) −1.27825 2.50870i −0.0857903 0.168373i
\(223\) −0.819786 + 5.17593i −0.0548969 + 0.346606i 0.944917 + 0.327310i \(0.106142\pi\)
−0.999814 + 0.0192953i \(0.993858\pi\)
\(224\) 1.50551 2.07216i 0.100591 0.138452i
\(225\) −23.0526 8.74293i −1.53684 0.582862i
\(226\) 1.42666 0.463549i 0.0948999 0.0308348i
\(227\) 14.8855 2.35763i 0.987984 0.156481i 0.358530 0.933518i \(-0.383278\pi\)
0.629455 + 0.777037i \(0.283278\pi\)
\(228\) 3.93281 + 0.622895i 0.260456 + 0.0412522i
\(229\) −14.1396 4.59424i −0.934371 0.303596i −0.198022 0.980198i \(-0.563452\pi\)
−0.736349 + 0.676602i \(0.763452\pi\)
\(230\) 2.50438 + 0.881190i 0.165134 + 0.0581040i
\(231\) −0.519539 + 5.10919i −0.0341832 + 0.336160i
\(232\) −9.14646 9.14646i −0.600494 0.600494i
\(233\) 4.93530 2.51466i 0.323322 0.164741i −0.284794 0.958589i \(-0.591925\pi\)
0.608117 + 0.793848i \(0.291925\pi\)
\(234\) 9.82534 + 13.5234i 0.642302 + 0.884054i
\(235\) 8.95553 + 1.64120i 0.584194 + 0.107060i
\(236\) −1.89954 5.84618i −0.123649 0.380554i
\(237\) 10.4543 + 5.32676i 0.679083 + 0.346010i
\(238\) −0.508880 3.21294i −0.0329858 0.208264i
\(239\) 19.9985 14.5297i 1.29359 0.939850i 0.293721 0.955891i \(-0.405106\pi\)
0.999871 + 0.0160415i \(0.00510638\pi\)
\(240\) −8.47692 + 1.13334i −0.547183 + 0.0731568i
\(241\) 5.19700i 0.334768i −0.985892 0.167384i \(-0.946468\pi\)
0.985892 0.167384i \(-0.0535320\pi\)
\(242\) −3.04958 11.0809i −0.196034 0.712309i
\(243\) 10.4972 10.4972i 0.673394 0.673394i
\(244\) −2.58278 + 7.94898i −0.165346 + 0.508882i
\(245\) −14.3512 + 4.28240i −0.916863 + 0.273592i
\(246\) 21.2969 + 15.4731i 1.35784 + 0.986531i
\(247\) 2.29278 4.49983i 0.145886 0.286318i
\(248\) 2.27325 4.46151i 0.144352 0.283306i
\(249\) 25.8127 + 18.7540i 1.63582 + 1.18849i
\(250\) −4.53523 10.7650i −0.286833 0.680838i
\(251\) 3.85860 11.8755i 0.243553 0.749578i −0.752319 0.658799i \(-0.771065\pi\)
0.995871 0.0907782i \(-0.0289354\pi\)
\(252\) 1.74143 1.74143i 0.109700 0.109700i
\(253\) 2.92099 2.38177i 0.183641 0.149740i
\(254\) 12.3536i 0.775136i
\(255\) 21.6508 28.3336i 1.35583 1.77432i
\(256\) 13.4482 9.77068i 0.840511 0.610667i
\(257\) 1.99537 + 12.5983i 0.124468 + 0.785859i 0.968399 + 0.249407i \(0.0802357\pi\)
−0.843931 + 0.536452i \(0.819764\pi\)
\(258\) 9.46603 + 4.82319i 0.589330 + 0.300278i
\(259\) 0.162583 + 0.500380i 0.0101024 + 0.0310921i
\(260\) 1.18797 6.48239i 0.0736749 0.402021i
\(261\) −12.3376 16.9813i −0.763679 1.05111i
\(262\) −7.39566 + 3.76828i −0.456906 + 0.232805i
\(263\) −13.6161 13.6161i −0.839605 0.839605i 0.149202 0.988807i \(-0.452330\pi\)
−0.988807 + 0.149202i \(0.952330\pi\)
\(264\) −11.4564 + 25.9673i −0.705091 + 1.59818i
\(265\) −6.81012 14.2042i −0.418343 0.872557i
\(266\) 0.850405 + 0.276313i 0.0521417 + 0.0169419i
\(267\) 10.1487 + 1.60739i 0.621088 + 0.0983707i
\(268\) −3.32752 + 0.527027i −0.203261 + 0.0321933i
\(269\) 16.5446 5.37566i 1.00874 0.327760i 0.242387 0.970180i \(-0.422070\pi\)
0.766353 + 0.642420i \(0.222070\pi\)
\(270\) −12.7008 0.307047i −0.772949 0.0186863i
\(271\) −18.6755 + 25.7046i −1.13445 + 1.56144i −0.355133 + 0.934816i \(0.615564\pi\)
−0.779321 + 0.626625i \(0.784436\pi\)
\(272\) 1.20306 7.59585i 0.0729465 0.460566i
\(273\) −2.28084 4.47641i −0.138043 0.270925i
\(274\) 4.67539 0.282451
\(275\) −16.3977 2.47291i −0.988819 0.149122i
\(276\) −2.90704 −0.174983
\(277\) 3.29581 + 6.46840i 0.198026 + 0.388649i 0.968571 0.248738i \(-0.0800157\pi\)
−0.770545 + 0.637386i \(0.780016\pi\)
\(278\) −3.69648 + 23.3386i −0.221700 + 1.39976i
\(279\) 4.77600 6.57360i 0.285932 0.393551i
\(280\) 3.73484 + 0.0902909i 0.223199 + 0.00539591i
\(281\) −5.27301 + 1.71330i −0.314561 + 0.102207i −0.462043 0.886858i \(-0.652883\pi\)
0.147481 + 0.989065i \(0.452883\pi\)
\(282\) 11.8331 1.87418i 0.704653 0.111606i
\(283\) −13.6503 2.16199i −0.811425 0.128517i −0.263085 0.964773i \(-0.584740\pi\)
−0.548340 + 0.836255i \(0.684740\pi\)
\(284\) 5.92130 + 1.92395i 0.351364 + 0.114165i
\(285\) 4.23753 + 8.83842i 0.251010 + 0.523543i
\(286\) 8.38078 + 7.49494i 0.495566 + 0.443185i
\(287\) −3.47833 3.47833i −0.205319 0.205319i
\(288\) 20.4669 10.4284i 1.20602 0.614499i
\(289\) 8.85528 + 12.1882i 0.520899 + 0.716956i
\(290\) 1.79267 9.78205i 0.105269 0.574422i
\(291\) 14.5056 + 44.6436i 0.850332 + 2.61705i
\(292\) 8.16620 + 4.16089i 0.477891 + 0.243497i
\(293\) 1.06366 + 6.71571i 0.0621400 + 0.392336i 0.999082 + 0.0428502i \(0.0136438\pi\)
−0.936942 + 0.349486i \(0.886356\pi\)
\(294\) −15.9435 + 11.5836i −0.929843 + 0.675570i
\(295\) 9.18745 12.0233i 0.534914 0.700021i
\(296\) 2.90773i 0.169009i
\(297\) −9.77176 + 15.1592i −0.567015 + 0.879623i
\(298\) 10.9233 10.9233i 0.632770 0.632770i
\(299\) −1.13937 + 3.50663i −0.0658917 + 0.202794i
\(300\) 8.59682 + 9.47092i 0.496338 + 0.546804i
\(301\) −1.60609 1.16689i −0.0925737 0.0672587i
\(302\) 3.15210 6.18634i 0.181383 0.355984i
\(303\) 0.818498 1.60639i 0.0470215 0.0922848i
\(304\) 1.71022 + 1.24254i 0.0980876 + 0.0712648i
\(305\) −19.7153 + 5.88306i −1.12890 + 0.336863i
\(306\) 9.01510 27.7456i 0.515359 1.58611i
\(307\) −5.54209 + 5.54209i −0.316304 + 0.316304i −0.847346 0.531042i \(-0.821801\pi\)
0.531042 + 0.847346i \(0.321801\pi\)
\(308\) 0.897482 1.39228i 0.0511388 0.0793327i
\(309\) 5.81836i 0.330995i
\(310\) 3.81583 0.510166i 0.216725 0.0289755i
\(311\) −13.4223 + 9.75186i −0.761108 + 0.552977i −0.899250 0.437435i \(-0.855887\pi\)
0.138142 + 0.990412i \(0.455887\pi\)
\(312\) −4.34353 27.4239i −0.245904 1.55257i
\(313\) 8.48544 + 4.32355i 0.479625 + 0.244381i 0.677050 0.735937i \(-0.263258\pi\)
−0.197425 + 0.980318i \(0.563258\pi\)
\(314\) −0.521207 1.60411i −0.0294134 0.0905251i
\(315\) 5.96307 + 1.09280i 0.335981 + 0.0615724i
\(316\) −2.22451 3.06178i −0.125139 0.172239i
\(317\) −21.4887 + 10.9490i −1.20693 + 0.614960i −0.937474 0.348054i \(-0.886843\pi\)
−0.269452 + 0.963014i \(0.586843\pi\)
\(318\) −14.6570 14.6570i −0.821926 0.821926i
\(319\) −10.5237 9.41134i −0.589213 0.526934i
\(320\) 15.9957 + 5.62823i 0.894187 + 0.314628i
\(321\) −23.9390 7.77826i −1.33615 0.434140i
\(322\) −0.644774 0.102122i −0.0359319 0.00569105i
\(323\) −8.70552 + 1.37882i −0.484388 + 0.0767196i
\(324\) 0.450544 0.146391i 0.0250302 0.00813282i
\(325\) 14.7938 6.65797i 0.820610 0.369318i
\(326\) 6.22079 8.56218i 0.344538 0.474215i
\(327\) 1.97386 12.4625i 0.109155 0.689175i
\(328\) −12.3422 24.2230i −0.681485 1.33749i
\(329\) −2.23875 −0.123426
\(330\) −21.4342 + 4.09222i −1.17991 + 0.225269i
\(331\) 12.5641 0.690587 0.345294 0.938495i \(-0.387779\pi\)
0.345294 + 0.938495i \(0.387779\pi\)
\(332\) −4.67222 9.16976i −0.256422 0.503256i
\(333\) −0.738128 + 4.66036i −0.0404492 + 0.255386i
\(334\) −8.79299 + 12.1025i −0.481131 + 0.662220i
\(335\) −5.72074 6.00419i −0.312557 0.328044i
\(336\) 2.00001 0.649844i 0.109110 0.0354519i
\(337\) −16.2727 + 2.57734i −0.886430 + 0.140397i −0.583015 0.812462i \(-0.698127\pi\)
−0.303415 + 0.952858i \(0.598127\pi\)
\(338\) 2.55164 + 0.404140i 0.138791 + 0.0219823i
\(339\) −3.84544 1.24946i −0.208855 0.0678612i
\(340\) −10.3714 + 4.97252i −0.562470 + 0.269673i
\(341\) 2.20603 5.00024i 0.119463 0.270778i
\(342\) 5.67035 + 5.67035i 0.306618 + 0.306618i
\(343\) 6.71049 3.41917i 0.362333 0.184618i
\(344\) −6.44901 8.87630i −0.347707 0.478578i
\(345\) −4.06506 5.88931i −0.218856 0.317070i
\(346\) −5.34960 16.4644i −0.287596 0.885130i
\(347\) 12.6879 + 6.46480i 0.681121 + 0.347049i 0.760080 0.649829i \(-0.225160\pi\)
−0.0789590 + 0.996878i \(0.525160\pi\)
\(348\) 1.70349 + 10.7554i 0.0913167 + 0.576551i
\(349\) 13.4408 9.76528i 0.719467 0.522724i −0.166747 0.986000i \(-0.553326\pi\)
0.886214 + 0.463276i \(0.153326\pi\)
\(350\) 1.57405 + 2.40263i 0.0841364 + 0.128426i
\(351\) 17.6440i 0.941767i
\(352\) 11.9741 9.76368i 0.638224 0.520406i
\(353\) 7.78082 7.78082i 0.414131 0.414131i −0.469044 0.883175i \(-0.655401\pi\)
0.883175 + 0.469044i \(0.155401\pi\)
\(354\) 6.15297 18.9369i 0.327027 1.00649i
\(355\) 4.38237 + 14.6862i 0.232592 + 0.779462i
\(356\) −2.68131 1.94809i −0.142109 0.103248i
\(357\) −3.98066 + 7.81248i −0.210679 + 0.413481i
\(358\) −9.48024 + 18.6060i −0.501046 + 0.983358i
\(359\) 10.6626 + 7.74686i 0.562753 + 0.408864i 0.832465 0.554077i \(-0.186929\pi\)
−0.269713 + 0.962941i \(0.586929\pi\)
\(360\) 29.4765 + 15.9278i 1.55355 + 0.839469i
\(361\) −5.12265 + 15.7659i −0.269613 + 0.829783i
\(362\) −19.8549 + 19.8549i −1.04355 + 1.04355i
\(363\) −10.9058 + 28.9950i −0.572405 + 1.52184i
\(364\) 1.62050i 0.0849374i
\(365\) 2.98975 + 22.3621i 0.156491 + 1.17049i
\(366\) −21.9028 + 15.9133i −1.14488 + 0.831802i
\(367\) 4.34925 + 27.4601i 0.227029 + 1.43341i 0.793121 + 0.609064i \(0.208455\pi\)
−0.566092 + 0.824342i \(0.691545\pi\)
\(368\) −1.37513 0.700661i −0.0716834 0.0365245i
\(369\) −13.6324 41.9563i −0.709676 2.18416i
\(370\) −1.83985 + 1.26994i −0.0956493 + 0.0660213i
\(371\) 2.27670 + 3.13361i 0.118200 + 0.162689i
\(372\) −3.75596 + 1.91376i −0.194738 + 0.0992238i
\(373\) 6.02155 + 6.02155i 0.311784 + 0.311784i 0.845600 0.533816i \(-0.179243\pi\)
−0.533816 + 0.845600i \(0.679243\pi\)
\(374\) 1.98511 19.5218i 0.102648 1.00945i
\(375\) −7.16558 + 30.6598i −0.370029 + 1.58327i
\(376\) −11.7672 3.82339i −0.606847 0.197176i
\(377\) 13.6414 + 2.16059i 0.702570 + 0.111276i
\(378\) 3.08547 0.488690i 0.158699 0.0251355i
\(379\) −4.14195 + 1.34580i −0.212758 + 0.0691292i −0.413457 0.910524i \(-0.635679\pi\)
0.200699 + 0.979653i \(0.435679\pi\)
\(380\) 0.0764100 3.16066i 0.00391975 0.162138i
\(381\) 19.5722 26.9388i 1.00271 1.38012i
\(382\) −2.11506 + 13.3540i −0.108216 + 0.683248i
\(383\) 3.08002 + 6.04488i 0.157382 + 0.308879i 0.956211 0.292679i \(-0.0945468\pi\)
−0.798829 + 0.601558i \(0.794547\pi\)
\(384\) −3.92473 −0.200283
\(385\) 4.07560 0.128710i 0.207712 0.00655965i
\(386\) −7.83388 −0.398734
\(387\) −8.08287 15.8635i −0.410875 0.806388i
\(388\) 2.36857 14.9545i 0.120246 0.759202i
\(389\) −14.4727 + 19.9200i −0.733797 + 1.00998i 0.265155 + 0.964206i \(0.414577\pi\)
−0.998952 + 0.0457786i \(0.985423\pi\)
\(390\) 15.4553 14.7257i 0.782609 0.745663i
\(391\) 6.11997 1.98850i 0.309500 0.100563i
\(392\) 20.1017 3.18379i 1.01529 0.160806i
\(393\) 22.0974 + 3.49989i 1.11467 + 0.176546i
\(394\) 3.83771 + 1.24695i 0.193341 + 0.0628203i
\(395\) 3.09215 8.78805i 0.155583 0.442175i
\(396\) 12.8402 7.47128i 0.645244 0.375446i
\(397\) −20.7876 20.7876i −1.04330 1.04330i −0.999019 0.0442826i \(-0.985900\pi\)
−0.0442826 0.999019i \(-0.514100\pi\)
\(398\) 11.5282 5.87390i 0.577856 0.294432i
\(399\) −1.41665 1.94986i −0.0709214 0.0976149i
\(400\) 1.78388 + 6.55209i 0.0891939 + 0.327604i
\(401\) 7.65264 + 23.5524i 0.382155 + 1.17615i 0.938523 + 0.345216i \(0.112194\pi\)
−0.556369 + 0.830935i \(0.687806\pi\)
\(402\) −9.72340 4.95432i −0.484959 0.247099i
\(403\) 0.836384 + 5.28072i 0.0416633 + 0.263051i
\(404\) −0.470467 + 0.341814i −0.0234066 + 0.0170059i
\(405\) 0.926589 + 0.708044i 0.0460426 + 0.0351830i
\(406\) 2.44537i 0.121362i
\(407\) 0.176812 + 3.16876i 0.00876424 + 0.157069i
\(408\) −34.2653 + 34.2653i −1.69638 + 1.69638i
\(409\) 3.09442 9.52366i 0.153009 0.470915i −0.844944 0.534854i \(-0.820367\pi\)
0.997954 + 0.0639396i \(0.0203665\pi\)
\(410\) 9.93650 18.3888i 0.490729 0.908156i
\(411\) −10.1953 7.40734i −0.502898 0.365377i
\(412\) −0.852016 + 1.67218i −0.0419758 + 0.0823822i
\(413\) −1.68918 + 3.31520i −0.0831190 + 0.163130i
\(414\) −4.73643 3.44122i −0.232783 0.169127i
\(415\) 12.0434 22.2879i 0.591189 1.09407i
\(416\) −4.67068 + 14.3749i −0.228999 + 0.704787i
\(417\) 45.0367 45.0367i 2.20545 2.20545i
\(418\) 4.53347 + 2.92233i 0.221739 + 0.142936i
\(419\) 7.65743i 0.374090i 0.982351 + 0.187045i \(0.0598910\pi\)
−0.982351 + 0.187045i \(0.940109\pi\)
\(420\) −2.49904 1.90961i −0.121941 0.0931796i
\(421\) 17.5332 12.7386i 0.854517 0.620843i −0.0718707 0.997414i \(-0.522897\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(422\) −2.21575 13.9897i −0.107861 0.681009i
\(423\) −17.8892 9.11503i −0.869805 0.443188i
\(424\) 6.61501 + 20.3589i 0.321253 + 0.988716i
\(425\) −24.5766 14.0580i −1.19214 0.681911i
\(426\) 11.8540 + 16.3157i 0.574329 + 0.790497i
\(427\) 4.50764 2.29676i 0.218140 0.111148i
\(428\) 5.74098 + 5.74098i 0.277501 + 0.277501i
\(429\) −6.40101 29.6216i −0.309044 1.43014i
\(430\) 2.79983 7.95726i 0.135020 0.383733i
\(431\) 27.0858 + 8.80070i 1.30468 + 0.423915i 0.877206 0.480115i \(-0.159405\pi\)
0.427470 + 0.904030i \(0.359405\pi\)
\(432\) 7.29448 + 1.15533i 0.350956 + 0.0555860i
\(433\) 12.3180 1.95098i 0.591966 0.0937582i 0.146738 0.989175i \(-0.453123\pi\)
0.445228 + 0.895417i \(0.353123\pi\)
\(434\) −0.900293 + 0.292523i −0.0432154 + 0.0140415i
\(435\) −19.4071 + 18.4909i −0.930500 + 0.886572i
\(436\) −2.39223 + 3.29262i −0.114567 + 0.157688i
\(437\) −0.276702 + 1.74703i −0.0132365 + 0.0835717i
\(438\) 13.4779 + 26.4519i 0.643999 + 1.26392i
\(439\) 16.9147 0.807294 0.403647 0.914915i \(-0.367742\pi\)
0.403647 + 0.914915i \(0.367742\pi\)
\(440\) 21.6417 + 6.28389i 1.03173 + 0.299573i
\(441\) 33.0261 1.57267
\(442\) 8.71491 + 17.1040i 0.414526 + 0.813553i
\(443\) 1.73048 10.9258i 0.0822176 0.519102i −0.911866 0.410487i \(-0.865359\pi\)
0.994084 0.108614i \(-0.0346414\pi\)
\(444\) 1.43884 1.98039i 0.0682844 0.0939854i
\(445\) 0.197177 8.15613i 0.00934709 0.386637i
\(446\) 5.20729 1.69195i 0.246572 0.0801162i
\(447\) −41.1258 + 6.51369i −1.94518 + 0.308087i
\(448\) −4.11822 0.652263i −0.194568 0.0308165i
\(449\) −4.29754 1.39635i −0.202813 0.0658980i 0.205849 0.978584i \(-0.434005\pi\)
−0.408662 + 0.912686i \(0.634005\pi\)
\(450\) 2.79554 + 25.6075i 0.131783 + 1.20715i
\(451\) −14.9231 25.6469i −0.702701 1.20767i
\(452\) 0.922199 + 0.922199i 0.0433766 + 0.0433766i
\(453\) −16.6748 + 8.49621i −0.783449 + 0.399187i
\(454\) −9.25549 12.7391i −0.434381 0.597875i
\(455\) −3.28294 + 2.26603i −0.153907 + 0.106233i
\(456\) −4.11612 12.6681i −0.192755 0.593240i
\(457\) −29.0702 14.8120i −1.35985 0.692877i −0.386517 0.922282i \(-0.626322\pi\)
−0.973331 + 0.229405i \(0.926322\pi\)
\(458\) 2.42997 + 15.3422i 0.113545 + 0.716895i
\(459\) −24.9123 + 18.0998i −1.16281 + 0.844829i
\(460\) 0.305878 + 2.28784i 0.0142616 + 0.106671i
\(461\) 23.4279i 1.09114i 0.838064 + 0.545572i \(0.183688\pi\)
−0.838064 + 0.545572i \(0.816312\pi\)
\(462\) 5.00274 1.93980i 0.232749 0.0902479i
\(463\) −29.2123 + 29.2123i −1.35761 + 1.35761i −0.480762 + 0.876851i \(0.659640\pi\)
−0.876851 + 0.480762i \(0.840360\pi\)
\(464\) −1.78649 + 5.49825i −0.0829356 + 0.255250i
\(465\) −9.12920 4.93303i −0.423357 0.228764i
\(466\) −4.68196 3.40165i −0.216888 0.157578i
\(467\) 12.8965 25.3107i 0.596777 1.17124i −0.373133 0.927778i \(-0.621716\pi\)
0.969910 0.243463i \(-0.0782835\pi\)
\(468\) −6.59784 + 12.9490i −0.304985 + 0.598567i
\(469\) 1.64976 + 1.19862i 0.0761789 + 0.0553472i
\(470\) −2.72006 9.11547i −0.125467 0.420465i
\(471\) −1.40487 + 4.32374i −0.0647329 + 0.199227i
\(472\) −14.5403 + 14.5403i −0.669273 + 0.669273i
\(473\) −7.56766 9.28095i −0.347962 0.426739i
\(474\) 12.2590i 0.563072i
\(475\) 6.50997 4.26491i 0.298698 0.195688i
\(476\) 2.28806 1.66237i 0.104873 0.0761946i
\(477\) 5.43407 + 34.3094i 0.248809 + 1.57092i
\(478\) −23.0121 11.7253i −1.05255 0.536301i
\(479\) 9.69547 + 29.8396i 0.442998 + 1.36341i 0.884665 + 0.466227i \(0.154387\pi\)
−0.441667 + 0.897179i \(0.645613\pi\)
\(480\) −16.6641 24.1423i −0.760608 1.10194i
\(481\) −1.82493 2.51180i −0.0832096 0.114528i
\(482\) −4.83806 + 2.46511i −0.220367 + 0.112283i
\(483\) 1.24422 + 1.24422i 0.0566141 + 0.0566141i
\(484\) 7.38019 6.73607i 0.335463 0.306185i
\(485\) 33.6082 16.1133i 1.52607 0.731666i
\(486\) −14.7513 4.79299i −0.669133 0.217415i
\(487\) −6.78843 1.07518i −0.307613 0.0487211i 0.000719535 1.00000i \(-0.499771\pi\)
−0.308333 + 0.951279i \(0.599771\pi\)
\(488\) 27.6152 4.37382i 1.25008 0.197994i
\(489\) −27.1306 + 8.81525i −1.22689 + 0.398640i
\(490\) 10.7939 + 11.3287i 0.487618 + 0.511778i
\(491\) 8.65794 11.9166i 0.390728 0.537790i −0.567659 0.823264i \(-0.692151\pi\)
0.958387 + 0.285473i \(0.0921508\pi\)
\(492\) −3.58029 + 22.6051i −0.161412 + 1.01911i
\(493\) −10.9433 21.4773i −0.492859 0.967291i
\(494\) −5.27658 −0.237405
\(495\) 33.0910 + 15.5652i 1.48733 + 0.699605i
\(496\) −2.23795 −0.100487
\(497\) −1.71088 3.35779i −0.0767435 0.150618i
\(498\) 5.21490 32.9256i 0.233685 1.47543i
\(499\) 15.5610 21.4179i 0.696607 0.958797i −0.303376 0.952871i \(-0.598114\pi\)
0.999982 0.00592589i \(-0.00188628\pi\)
\(500\) 6.54906 7.76223i 0.292883 0.347137i
\(501\) 38.3486 12.4602i 1.71329 0.556682i
\(502\) −12.8856 + 2.04088i −0.575112 + 0.0910888i
\(503\) −30.0639 4.76166i −1.34049 0.212312i −0.555340 0.831624i \(-0.687412\pi\)
−0.785145 + 0.619312i \(0.787412\pi\)
\(504\) −7.83523 2.54582i −0.349009 0.113400i
\(505\) −1.35035 0.475134i −0.0600899 0.0211432i
\(506\) −3.60279 1.58949i −0.160163 0.0706615i
\(507\) −4.92391 4.92391i −0.218678 0.218678i
\(508\) −9.56978 + 4.87604i −0.424590 + 0.216339i
\(509\) 2.38516 + 3.28290i 0.105721 + 0.145512i 0.858599 0.512648i \(-0.171335\pi\)
−0.752879 + 0.658159i \(0.771335\pi\)
\(510\) −36.6464 6.71587i −1.62273 0.297384i
\(511\) −1.71429 5.27604i −0.0758357 0.233398i
\(512\) −12.9913 6.61940i −0.574140 0.292539i
\(513\) −1.32411 8.36013i −0.0584611 0.369109i
\(514\) 10.7817 7.83334i 0.475559 0.345514i
\(515\) −4.57905 + 0.612206i −0.201777 + 0.0269770i
\(516\) 9.23663i 0.406620i
\(517\) −13.0560 3.45108i −0.574202 0.151778i
\(518\) 0.388701 0.388701i 0.0170786 0.0170786i
\(519\) −14.4194 + 44.3783i −0.632941 + 1.94799i
\(520\) −21.1256 + 6.30389i −0.926420 + 0.276444i
\(521\) −14.1602 10.2880i −0.620370 0.450725i 0.232681 0.972553i \(-0.425250\pi\)
−0.853051 + 0.521828i \(0.825250\pi\)
\(522\) −9.95627 + 19.5403i −0.435774 + 0.855255i
\(523\) 7.88844 15.4819i 0.344938 0.676978i −0.651739 0.758444i \(-0.725960\pi\)
0.996676 + 0.0814656i \(0.0259601\pi\)
\(524\) −5.83821 4.24171i −0.255044 0.185300i
\(525\) 0.374117 7.73306i 0.0163278 0.337499i
\(526\) −6.21710 + 19.1343i −0.271078 + 0.834293i
\(527\) 6.59808 6.59808i 0.287417 0.287417i
\(528\) 12.6655 0.706715i 0.551194 0.0307558i
\(529\) 21.7086i 0.943854i
\(530\) −9.99288 + 13.0773i −0.434063 + 0.568042i
\(531\) −26.9955 + 19.6134i −1.17151 + 0.851149i
\(532\) 0.121612 + 0.767831i 0.00527257 + 0.0332897i
\(533\) 25.8642 + 13.1785i 1.12030 + 0.570823i
\(534\) −3.31748 10.2102i −0.143561 0.441837i
\(535\) −3.60264 + 19.6584i −0.155756 + 0.849909i
\(536\) 6.62435 + 9.11763i 0.286128 + 0.393822i
\(537\) 50.1509 25.5532i 2.16417 1.10270i
\(538\) −12.8520 12.8520i −0.554090 0.554090i
\(539\) 21.7126 4.69193i 0.935226 0.202096i
\(540\) −4.77524 9.95994i −0.205494 0.428608i
\(541\) −35.0319 11.3826i −1.50614 0.489375i −0.564339 0.825543i \(-0.690869\pi\)
−0.941802 + 0.336169i \(0.890869\pi\)
\(542\) 32.7876 + 5.19305i 1.40835 + 0.223061i
\(543\) 74.7528 11.8397i 3.20795 0.508089i
\(544\) 25.0879 8.15154i 1.07563 0.349495i
\(545\) −10.0156 0.242131i −0.429023 0.0103718i
\(546\) −3.08535 + 4.24662i −0.132041 + 0.181739i
\(547\) 1.35549 8.55820i 0.0579564 0.365922i −0.941616 0.336688i \(-0.890693\pi\)
0.999573 0.0292340i \(-0.00930681\pi\)
\(548\) 1.84540 + 3.62180i 0.0788316 + 0.154716i
\(549\) 45.3705 1.93637
\(550\) 5.47588 + 16.4381i 0.233492 + 0.700925i
\(551\) 6.62577 0.282267
\(552\) 4.41490 + 8.66473i 0.187911 + 0.368796i
\(553\) −0.358354 + 2.26256i −0.0152387 + 0.0962136i
\(554\) 4.45833 6.13636i 0.189416 0.260709i
\(555\) 6.02405 + 0.145633i 0.255707 + 0.00618179i
\(556\) −19.5384 + 6.34840i −0.828611 + 0.269232i
\(557\) 8.27356 1.31040i 0.350562 0.0555236i 0.0213297 0.999772i \(-0.493210\pi\)
0.329232 + 0.944249i \(0.393210\pi\)
\(558\) −8.38500 1.32805i −0.354965 0.0562210i
\(559\) 11.1417 + 3.62017i 0.471245 + 0.153117i
\(560\) −0.721868 1.50563i −0.0305045 0.0636247i
\(561\) −35.2576 + 39.4248i −1.48858 + 1.66452i
\(562\) 4.09614 + 4.09614i 0.172785 + 0.172785i
\(563\) 26.8581 13.6849i 1.13193 0.576748i 0.215327 0.976542i \(-0.430918\pi\)
0.916605 + 0.399794i \(0.130918\pi\)
\(564\) 6.12244 + 8.42682i 0.257801 + 0.354833i
\(565\) −0.578708 + 3.15783i −0.0243464 + 0.132851i
\(566\) 4.46212 + 13.7330i 0.187557 + 0.577241i
\(567\) −0.255490 0.130179i −0.0107296 0.00546700i
\(568\) −3.25812 20.5709i −0.136708 0.863137i
\(569\) −21.9297 + 15.9329i −0.919341 + 0.667940i −0.943360 0.331771i \(-0.892354\pi\)
0.0240192 + 0.999711i \(0.492354\pi\)
\(570\) 6.21797 8.13722i 0.260442 0.340831i
\(571\) 6.30511i 0.263861i −0.991259 0.131930i \(-0.957883\pi\)
0.991259 0.131930i \(-0.0421175\pi\)
\(572\) −2.49804 + 9.45049i −0.104448 + 0.395145i
\(573\) 25.7692 25.7692i 1.07652 1.07652i
\(574\) −1.58820 + 4.88797i −0.0662902 + 0.204020i
\(575\) −4.20717 + 3.81888i −0.175451 + 0.159258i
\(576\) −30.2519 21.9793i −1.26050 0.915805i
\(577\) −10.7963 + 21.1889i −0.449456 + 0.882107i 0.549458 + 0.835521i \(0.314834\pi\)
−0.998914 + 0.0465858i \(0.985166\pi\)
\(578\) 7.14608 14.0250i 0.297238 0.583362i
\(579\) 17.0829 + 12.4114i 0.709939 + 0.515801i
\(580\) 8.28527 2.47233i 0.344027 0.102658i
\(581\) −1.92496 + 5.92442i −0.0798608 + 0.245786i
\(582\) 34.6797 34.6797i 1.43752 1.43752i
\(583\) 8.44680 + 21.7842i 0.349831 + 0.902211i
\(584\) 30.6593i 1.26869i
\(585\) −35.4592 + 4.74080i −1.46606 + 0.196008i
\(586\) 5.74735 4.17569i 0.237421 0.172496i
\(587\) 1.70730 + 10.7795i 0.0704680 + 0.444917i 0.997544 + 0.0700437i \(0.0223139\pi\)
−0.927076 + 0.374874i \(0.877686\pi\)
\(588\) −15.2663 7.77855i −0.629570 0.320782i
\(589\) 0.792596 + 2.43936i 0.0326584 + 0.100512i
\(590\) −15.5508 2.84986i −0.640215 0.117327i
\(591\) −6.39308 8.79931i −0.262976 0.361955i
\(592\) 1.15794 0.589999i 0.0475910 0.0242488i
\(593\) −26.5198 26.5198i −1.08904 1.08904i −0.995628 0.0934112i \(-0.970223\pi\)
−0.0934112 0.995628i \(-0.529777\pi\)
\(594\) 18.7472 + 1.90635i 0.769208 + 0.0782187i
\(595\) 6.56727 + 2.31075i 0.269232 + 0.0947316i
\(596\) 12.7732 + 4.15028i 0.523213 + 0.170002i
\(597\) −34.4450 5.45554i −1.40974 0.223281i
\(598\) 3.80488 0.602634i 0.155593 0.0246435i
\(599\) −42.0288 + 13.6560i −1.71725 + 0.557968i −0.991513 0.130006i \(-0.958500\pi\)
−0.725735 + 0.687974i \(0.758500\pi\)
\(600\) 15.1731 40.0072i 0.619441 1.63329i
\(601\) 21.8365 30.0554i 0.890730 1.22599i −0.0826012 0.996583i \(-0.526323\pi\)
0.973332 0.229403i \(-0.0736772\pi\)
\(602\) −0.324476 + 2.04866i −0.0132247 + 0.0834972i
\(603\) 8.30263 + 16.2948i 0.338109 + 0.663577i
\(604\) 6.03642 0.245618
\(605\) 23.9666 + 5.53200i 0.974380 + 0.224908i
\(606\) −1.88368 −0.0765194
\(607\) 20.5058 + 40.2449i 0.832306 + 1.63349i 0.772269 + 0.635295i \(0.219122\pi\)
0.0600364 + 0.998196i \(0.480878\pi\)
\(608\) −1.13430 + 7.16167i −0.0460018 + 0.290444i
\(609\) 3.87426 5.33246i 0.156993 0.216082i
\(610\) 14.8284 + 15.5631i 0.600384 + 0.630132i
\(611\) 12.5645 4.08245i 0.508305 0.165158i
\(612\) 25.0515 3.96777i 1.01265 0.160388i
\(613\) −13.9243 2.20539i −0.562397 0.0890749i −0.131238 0.991351i \(-0.541895\pi\)
−0.431159 + 0.902276i \(0.641895\pi\)
\(614\) 7.78811 + 2.53051i 0.314302 + 0.102123i
\(615\) −50.8017 + 24.3566i −2.04852 + 0.982152i
\(616\) −5.51285 0.560586i −0.222119 0.0225867i
\(617\) −17.9495 17.9495i −0.722618 0.722618i 0.246520 0.969138i \(-0.420713\pi\)
−0.969138 + 0.246520i \(0.920713\pi\)
\(618\) −5.41650 + 2.75984i −0.217884 + 0.111017i
\(619\) −15.8217 21.7768i −0.635930 0.875282i 0.362461 0.931999i \(-0.381937\pi\)
−0.998390 + 0.0567171i \(0.981937\pi\)
\(620\) 1.90133 + 2.75458i 0.0763592 + 0.110627i
\(621\) 1.90961 + 5.87716i 0.0766298 + 0.235842i
\(622\) 15.4450 + 7.86961i 0.619287 + 0.315543i
\(623\) 0.313823 + 1.98140i 0.0125730 + 0.0793831i
\(624\) −10.0396 + 7.29421i −0.401907 + 0.292002i
\(625\) 24.8832 + 2.41330i 0.995330 + 0.0965319i
\(626\) 9.95017i 0.397689i
\(627\) −5.25594 13.5550i −0.209902 0.541336i
\(628\) 1.03690 1.03690i 0.0413770 0.0413770i
\(629\) −1.67444 + 5.15339i −0.0667642 + 0.205479i
\(630\) −1.81116 6.06957i −0.0721584 0.241818i
\(631\) 4.56785 + 3.31874i 0.181843 + 0.132117i 0.674983 0.737833i \(-0.264151\pi\)
−0.493140 + 0.869950i \(0.664151\pi\)
\(632\) −5.74761 + 11.2803i −0.228628 + 0.448707i
\(633\) −17.3325 + 34.0170i −0.688905 + 1.35205i
\(634\) 20.3857 + 14.8110i 0.809618 + 0.588222i
\(635\) −23.2602 12.5688i −0.923053 0.498778i
\(636\) 5.56891 17.1393i 0.220821 0.679619i
\(637\) −15.3663 + 15.3663i −0.608835 + 0.608835i
\(638\) −3.76958 + 14.2610i −0.149239 + 0.564597i
\(639\) 33.7970i 1.33699i
\(640\) 0.412958 + 3.08876i 0.0163236 + 0.122094i
\(641\) −27.9714 + 20.3224i −1.10480 + 0.802686i −0.981837 0.189725i \(-0.939240\pi\)
−0.122965 + 0.992411i \(0.539240\pi\)
\(642\) 4.11405 + 25.9751i 0.162369 + 1.02516i
\(643\) 17.2668 + 8.79786i 0.680935 + 0.346954i 0.760007 0.649915i \(-0.225196\pi\)
−0.0790717 + 0.996869i \(0.525196\pi\)
\(644\) −0.175387 0.539784i −0.00691120 0.0212705i
\(645\) −18.7123 + 12.9161i −0.736797 + 0.508569i
\(646\) 5.41291 + 7.45023i 0.212968 + 0.293126i
\(647\) −18.4816 + 9.41683i −0.726586 + 0.370214i −0.777832 0.628472i \(-0.783681\pi\)
0.0512465 + 0.998686i \(0.483681\pi\)
\(648\) −1.12057 1.12057i −0.0440202 0.0440202i
\(649\) −14.9614 + 16.7298i −0.587288 + 0.656700i
\(650\) −13.2153 10.6139i −0.518347 0.416311i
\(651\) 2.42666 + 0.788470i 0.0951084 + 0.0309026i
\(652\) 9.08810 + 1.43941i 0.355917 + 0.0563718i
\(653\) −32.3979 + 5.13133i −1.26783 + 0.200804i −0.753877 0.657015i \(-0.771819\pi\)
−0.513951 + 0.857820i \(0.671819\pi\)
\(654\) −12.5380 + 4.07383i −0.490273 + 0.159299i
\(655\) 0.429328 17.7589i 0.0167752 0.693899i
\(656\) −7.14192 + 9.83001i −0.278845 + 0.383797i
\(657\) 7.78287 49.1391i 0.303639 1.91710i
\(658\) 1.06191 + 2.08413i 0.0413978 + 0.0812477i
\(659\) 3.99211 0.155511 0.0777553 0.996972i \(-0.475225\pi\)
0.0777553 + 0.996972i \(0.475225\pi\)
\(660\) −11.6302 14.9889i −0.452707 0.583440i
\(661\) 42.4892 1.65264 0.826318 0.563204i \(-0.190431\pi\)
0.826318 + 0.563204i \(0.190431\pi\)
\(662\) −5.95960 11.6964i −0.231626 0.454592i
\(663\) 8.09420 51.1048i 0.314353 1.98475i
\(664\) −20.2358 + 27.8521i −0.785299 + 1.08087i
\(665\) −1.38548 + 1.32007i −0.0537265 + 0.0511901i
\(666\) 4.68860 1.52342i 0.181679 0.0590312i
\(667\) −4.77776 + 0.756723i −0.184996 + 0.0293004i
\(668\) −12.8459 2.03459i −0.497022 0.0787206i
\(669\) −14.0358 4.56051i −0.542656 0.176320i
\(670\) −2.87596 + 8.17361i −0.111108 + 0.315774i
\(671\) 29.8282 6.44567i 1.15151 0.248832i
\(672\) 5.10050 + 5.10050i 0.196756 + 0.196756i
\(673\) 0.563270 0.287000i 0.0217125 0.0110631i −0.443101 0.896472i \(-0.646122\pi\)
0.464813 + 0.885409i \(0.346122\pi\)
\(674\) 10.1180 + 13.9263i 0.389731 + 0.536419i
\(675\) 13.5002 23.6016i 0.519623 0.908425i
\(676\) 0.694078 + 2.13615i 0.0266953 + 0.0821597i
\(677\) 4.26823 + 2.17477i 0.164041 + 0.0835833i 0.534084 0.845432i \(-0.320657\pi\)
−0.370042 + 0.929015i \(0.620657\pi\)
\(678\) 0.660859 + 4.17250i 0.0253801 + 0.160244i
\(679\) −7.41436 + 5.38685i −0.284537 + 0.206728i
\(680\) 30.5722 + 23.3614i 1.17239 + 0.895869i
\(681\) 42.4430i 1.62642i
\(682\) −5.70128 + 0.318123i −0.218313 + 0.0121816i
\(683\) −6.48359 + 6.48359i −0.248088 + 0.248088i −0.820186 0.572098i \(-0.806130\pi\)
0.572098 + 0.820186i \(0.306130\pi\)
\(684\) −2.15444 + 6.63067i −0.0823769 + 0.253530i
\(685\) −4.75683 + 8.80312i −0.181749 + 0.336350i
\(686\) −6.36603 4.62519i −0.243056 0.176591i
\(687\) 19.0082 37.3057i 0.725208 1.42330i
\(688\) −2.22623 + 4.36923i −0.0848744 + 0.166575i
\(689\) −18.4918 13.4350i −0.704480 0.511834i
\(690\) −3.55436 + 6.57780i −0.135312 + 0.250413i
\(691\) 9.76613 30.0571i 0.371521 1.14342i −0.574275 0.818663i \(-0.694716\pi\)
0.945796 0.324762i \(-0.105284\pi\)
\(692\) 10.6427 10.6427i 0.404573 0.404573i
\(693\) −8.69339 2.29791i −0.330234 0.0872905i
\(694\) 14.8780i 0.564762i
\(695\) −40.1826 30.7051i −1.52421 1.16471i
\(696\) 29.4706 21.4116i 1.11708 0.811605i
\(697\) −7.92520 50.0378i −0.300189 1.89532i
\(698\) −15.4662 7.88044i −0.585405 0.298279i
\(699\) 4.82035 + 14.8355i 0.182322 + 0.561130i
\(700\) −1.23992 + 2.16767i −0.0468645 + 0.0819303i
\(701\) 9.60255 + 13.2168i 0.362683 + 0.499191i 0.950894 0.309517i \(-0.100167\pi\)
−0.588211 + 0.808708i \(0.700167\pi\)
\(702\) −16.4254 + 8.36914i −0.619936 + 0.315873i
\(703\) −1.05319 1.05319i −0.0397220 0.0397220i
\(704\) −23.0113 10.1522i −0.867271 0.382626i
\(705\) −8.51041 + 24.1870i −0.320521 + 0.910935i
\(706\) −10.9341 3.55271i −0.411511 0.133708i
\(707\) 0.347659 + 0.0550638i 0.0130751 + 0.00207089i
\(708\) 17.0981 2.70808i 0.642587 0.101776i
\(709\) −18.1917 + 5.91083i −0.683202 + 0.221986i −0.629997 0.776598i \(-0.716944\pi\)
−0.0532052 + 0.998584i \(0.516944\pi\)
\(710\) 11.5932 11.0458i 0.435083 0.414543i
\(711\) −12.0755 + 16.6204i −0.452865 + 0.623315i
\(712\) −1.73438 + 10.9505i −0.0649988 + 0.410386i
\(713\) −0.850128 1.66847i −0.0318376 0.0624847i
\(714\) 9.16106 0.342844
\(715\) −22.6387 + 8.15438i −0.846639 + 0.304956i
\(716\) −18.1551 −0.678488
\(717\) 31.6045 + 62.0273i 1.18029 + 2.31645i
\(718\) 2.15415 13.6008i 0.0803923 0.507577i
\(719\) 8.94663 12.3140i 0.333653 0.459234i −0.608921 0.793231i \(-0.708397\pi\)
0.942574 + 0.333997i \(0.108397\pi\)
\(720\) 0.361909 14.9702i 0.0134876 0.557906i
\(721\) 1.08036 0.351031i 0.0402348 0.0130731i
\(722\) 17.1068 2.70945i 0.636650 0.100835i
\(723\) 14.4556 + 2.28954i 0.537609 + 0.0851489i
\(724\) −23.2174 7.54381i −0.862870 0.280363i
\(725\) 16.5944 + 13.3278i 0.616299 + 0.494982i
\(726\) 32.1654 3.60077i 1.19377 0.133637i
\(727\) 5.98783 + 5.98783i 0.222076 + 0.222076i 0.809372 0.587296i \(-0.199808\pi\)
−0.587296 + 0.809372i \(0.699808\pi\)
\(728\) 4.83008 2.46105i 0.179015 0.0912125i
\(729\) 25.4932 + 35.0884i 0.944193 + 1.29957i
\(730\) 19.3995 13.3904i 0.718008 0.495600i
\(731\) −6.31812 19.4452i −0.233684 0.719206i
\(732\) −20.9725 10.6860i −0.775164 0.394966i
\(733\) −4.57591 28.8912i −0.169015 1.06712i −0.915677 0.401915i \(-0.868345\pi\)
0.746662 0.665204i \(-0.231655\pi\)
\(734\) 23.5005 17.0741i 0.867420 0.630217i
\(735\) −5.58918 41.8048i −0.206160 1.54199i
\(736\) 5.29374i 0.195130i
\(737\) 7.77342 + 9.53329i 0.286338 + 0.351163i
\(738\) −32.5922 + 32.5922i −1.19973 + 1.19973i
\(739\) 13.4702 41.4569i 0.495508 1.52502i −0.320656 0.947196i \(-0.603903\pi\)
0.816164 0.577821i \(-0.196097\pi\)
\(740\) −1.70997 0.923991i −0.0628596 0.0339666i
\(741\) 11.5063 + 8.35982i 0.422695 + 0.307106i
\(742\) 1.83726 3.60583i 0.0674480 0.132374i
\(743\) −20.8901 + 40.9991i −0.766384 + 1.50411i 0.0946199 + 0.995513i \(0.469836\pi\)
−0.861004 + 0.508599i \(0.830164\pi\)
\(744\) 11.4083 + 8.28863i 0.418249 + 0.303876i
\(745\) 9.45352 + 31.6806i 0.346350 + 1.16069i
\(746\) 2.74943 8.46188i 0.100664 0.309811i
\(747\) −39.5030 + 39.5030i −1.44534 + 1.44534i
\(748\) 15.9061 6.16757i 0.581585 0.225509i
\(749\) 4.91432i 0.179565i
\(750\) 31.9411 7.87232i 1.16632 0.287456i
\(751\) 2.65295 1.92748i 0.0968077 0.0703349i −0.538328 0.842735i \(-0.680944\pi\)
0.635136 + 0.772400i \(0.280944\pi\)
\(752\) 0.865065 + 5.46181i 0.0315457 + 0.199172i
\(753\) 31.3322 + 15.9646i 1.14181 + 0.581781i
\(754\) −4.45923 13.7241i −0.162396 0.499802i
\(755\) 8.44103 + 12.2291i 0.307201 + 0.445061i
\(756\) 1.59642 + 2.19728i 0.0580611 + 0.0799142i
\(757\) −16.6423 + 8.47970i −0.604876 + 0.308200i −0.729475 0.684007i \(-0.760236\pi\)
0.124599 + 0.992207i \(0.460236\pi\)
\(758\) 3.21752 + 3.21752i 0.116866 + 0.116866i
\(759\) 5.33810 + 9.17409i 0.193761 + 0.332998i
\(760\) −9.53672 + 4.57233i −0.345933 + 0.165856i
\(761\) −3.30619 1.07424i −0.119849 0.0389413i 0.248478 0.968637i \(-0.420069\pi\)
−0.368328 + 0.929696i \(0.620069\pi\)
\(762\) −34.3619 5.44240i −1.24480 0.197157i
\(763\) 2.43314 0.385371i 0.0880855 0.0139514i
\(764\) −11.1795 + 3.63244i −0.404460 + 0.131417i
\(765\) 43.0691 + 45.2031i 1.55717 + 1.63432i
\(766\) 4.16642 5.73459i 0.150539 0.207199i
\(767\) 3.43474 21.6861i 0.124021 0.783040i
\(768\) 21.2528 + 41.7109i 0.766894 + 1.50511i
\(769\) 40.6658 1.46645 0.733223 0.679989i \(-0.238015\pi\)
0.733223 + 0.679989i \(0.238015\pi\)
\(770\) −2.05301 3.73305i −0.0739855 0.134530i
\(771\) −35.9215 −1.29368
\(772\) −3.09208 6.06854i −0.111286 0.218412i
\(773\) −6.74385 + 42.5790i −0.242559 + 1.53146i 0.502568 + 0.864538i \(0.332389\pi\)
−0.745128 + 0.666922i \(0.767611\pi\)
\(774\) −10.9339 + 15.0492i −0.393011 + 0.540933i
\(775\) −2.92172 + 7.70374i −0.104951 + 0.276726i
\(776\) −48.1707 + 15.6516i −1.72923 + 0.561861i
\(777\) −1.46345 + 0.231787i −0.0525008 + 0.00831531i
\(778\) 25.4091 + 4.02440i 0.910960 + 0.144282i
\(779\) 13.2441 + 4.30326i 0.474518 + 0.154180i
\(780\) 17.5076 + 6.16019i 0.626871 + 0.220570i
\(781\) −4.80146 22.2194i −0.171810 0.795074i
\(782\) −4.75407 4.75407i −0.170005 0.170005i
\(783\) 20.6252 10.5091i 0.737085 0.375564i
\(784\) −5.34664 7.35902i −0.190951 0.262822i
\(785\) 3.55060 + 0.650689i 0.126726 + 0.0232241i
\(786\) −7.22340 22.2313i −0.257650 0.792965i
\(787\) 23.4179 + 11.9320i 0.834758 + 0.425331i 0.818479 0.574537i \(-0.194818\pi\)
0.0162795 + 0.999867i \(0.494818\pi\)
\(788\) 0.548813 + 3.46507i 0.0195506 + 0.123438i
\(789\) 43.8721 31.8750i 1.56189 1.13478i
\(790\) −9.64780 + 1.28988i −0.343253 + 0.0458920i
\(791\) 0.789410i 0.0280682i
\(792\) −41.7693 26.9250i −1.48421 0.956736i
\(793\) −21.1099 + 21.1099i −0.749635 + 0.749635i
\(794\) −9.49161 + 29.2122i −0.336845 + 1.03670i
\(795\) 42.5095 12.6849i 1.50766 0.449886i
\(796\) 9.10047 + 6.61188i 0.322558 + 0.234352i
\(797\) 20.2679 39.7780i 0.717925 1.40901i −0.186534 0.982448i \(-0.559725\pi\)
0.904459 0.426560i \(-0.140275\pi\)
\(798\) −1.14322 + 2.24369i −0.0404695 + 0.0794259i
\(799\) −18.6533 13.5524i −0.659907 0.479450i
\(800\) −17.2466 + 15.6549i −0.609760 + 0.553484i
\(801\) −5.55955 + 17.1105i −0.196437 + 0.604572i
\(802\) 18.2958 18.2958i 0.646047 0.646047i
\(803\) −1.86432 33.4116i −0.0657902 1.17907i
\(804\) 9.48776i 0.334607i
\(805\) 0.848287 1.11012i 0.0298982 0.0391266i
\(806\) 4.51927 3.28344i 0.159185 0.115654i
\(807\) 7.66381 + 48.3874i 0.269779 + 1.70332i
\(808\) 1.73331 + 0.883165i 0.0609776 + 0.0310696i
\(809\) −17.0236 52.3932i −0.598517 1.84205i −0.536376 0.843979i \(-0.680207\pi\)
−0.0621416 0.998067i \(-0.519793\pi\)
\(810\) 0.219628 1.19844i 0.00771695 0.0421089i
\(811\) 7.83988 + 10.7907i 0.275295 + 0.378912i 0.924168 0.381985i \(-0.124759\pi\)
−0.648873 + 0.760897i \(0.724759\pi\)
\(812\) −1.89431 + 0.965200i −0.0664773 + 0.0338719i
\(813\) −63.2704 63.2704i −2.21899 2.21899i
\(814\) 2.86603 1.66765i 0.100454 0.0584510i
\(815\) 9.79228 + 20.4242i 0.343008 + 0.715429i
\(816\) 20.5980 + 6.69270i 0.721075 + 0.234292i
\(817\) 5.55089 + 0.879175i 0.194201 + 0.0307584i
\(818\) −10.3337 + 1.63669i −0.361309 + 0.0572256i
\(819\) 8.36612 2.71832i 0.292336 0.0949857i
\(820\) 18.1669 + 0.439191i 0.634416 + 0.0153372i
\(821\) −4.26813 + 5.87458i −0.148959 + 0.205024i −0.876975 0.480535i \(-0.840442\pi\)
0.728016 + 0.685560i \(0.240442\pi\)
\(822\) −2.05974 + 13.0047i −0.0718418 + 0.453591i
\(823\) 21.8556 + 42.8940i 0.761837 + 1.49519i 0.865681 + 0.500596i \(0.166886\pi\)
−0.103844 + 0.994594i \(0.533114\pi\)
\(824\) 6.27805 0.218706
\(825\) 14.1025 44.5212i 0.490985 1.55003i
\(826\) 3.88746 0.135262
\(827\) −16.7916 32.9554i −0.583901 1.14597i −0.974285 0.225318i \(-0.927658\pi\)
0.390384 0.920652i \(-0.372342\pi\)
\(828\) 0.796255 5.02735i 0.0276718 0.174713i
\(829\) −12.5416 + 17.2620i −0.435586 + 0.599533i −0.969224 0.246180i \(-0.920825\pi\)
0.533638 + 0.845713i \(0.320825\pi\)
\(830\) −26.4612 0.639707i −0.918480 0.0222046i
\(831\) −19.4440 + 6.31774i −0.674505 + 0.219160i
\(832\) 24.3021 3.84907i 0.842523 0.133442i
\(833\) 37.4597 + 5.93303i 1.29790 + 0.205567i
\(834\) −63.2885 20.5637i −2.19150 0.712062i
\(835\) −13.8412 28.8693i −0.478995 0.999064i
\(836\) −0.474404 + 4.66533i −0.0164076 + 0.161354i
\(837\) 6.33630 + 6.33630i 0.219015 + 0.219015i
\(838\) 7.12855 3.63218i 0.246252 0.125471i
\(839\) −12.5857 17.3228i −0.434507 0.598048i 0.534473 0.845186i \(-0.320510\pi\)
−0.968980 + 0.247137i \(0.920510\pi\)
\(840\) −1.89653 + 10.3488i −0.0654365 + 0.357066i
\(841\) −3.36207 10.3474i −0.115933 0.356806i
\(842\) −20.1754 10.2799i −0.695291 0.354268i
\(843\) −2.44257 15.4218i −0.0841267 0.531155i
\(844\) 9.96260 7.23825i 0.342927 0.249151i
\(845\) −3.35702 + 4.39321i −0.115485 + 0.151131i
\(846\) 20.9772i 0.721213i
\(847\) −6.04181 0.275687i −0.207599 0.00947272i
\(848\) 6.76524 6.76524i 0.232319 0.232319i
\(849\) 12.0273 37.0161i 0.412775 1.27039i
\(850\) −1.42947 + 29.5474i −0.0490304 + 1.01347i
\(851\) 0.879730 + 0.639161i 0.0301567 + 0.0219102i
\(852\) −7.96013 + 15.6226i −0.272710 + 0.535223i
\(853\) 13.3142 26.1306i 0.455871 0.894696i −0.542631 0.839971i \(-0.682572\pi\)
0.998501 0.0547251i \(-0.0174283\pi\)
\(854\) −4.27625 3.10688i −0.146330 0.106315i
\(855\) −16.4456 + 4.90738i −0.562428 + 0.167829i
\(856\) 8.39280 25.8304i 0.286860 0.882864i
\(857\) 14.3622 14.3622i 0.490604 0.490604i −0.417893 0.908496i \(-0.637231\pi\)
0.908496 + 0.417893i \(0.137231\pi\)
\(858\) −24.5395 + 20.0094i −0.837765 + 0.683111i
\(859\) 21.7404i 0.741772i 0.928678 + 0.370886i \(0.120946\pi\)
−0.928678 + 0.370886i \(0.879054\pi\)
\(860\) 7.26923 0.971875i 0.247879 0.0331407i
\(861\) 11.2074 8.14267i 0.381948 0.277502i
\(862\) −4.65484 29.3895i −0.158544 1.00101i
\(863\) 22.9709 + 11.7043i 0.781938 + 0.398417i 0.798919 0.601438i \(-0.205405\pi\)
−0.0169810 + 0.999856i \(0.505405\pi\)
\(864\) 7.82813 + 24.0925i 0.266318 + 0.819644i
\(865\) 36.4429 + 6.67859i 1.23910 + 0.227079i
\(866\) −7.65908 10.5418i −0.260266 0.358226i
\(867\) −37.8031 + 19.2616i −1.28386 + 0.654160i
\(868\) −0.581954 0.581954i −0.0197528 0.0197528i
\(869\) −5.57763 + 12.6424i −0.189208 + 0.428865i
\(870\) 26.4193 + 9.29585i 0.895697 + 0.315159i
\(871\) −11.4447 3.71860i −0.387788 0.126000i
\(872\) 13.4471 + 2.12981i 0.455375 + 0.0721244i
\(873\) −81.1786 + 12.8574i −2.74748 + 0.435158i
\(874\) 1.75761 0.571084i 0.0594522 0.0193172i
\(875\) −6.12529 + 0.519240i −0.207072 + 0.0175535i
\(876\) −15.1712 + 20.8814i −0.512588 + 0.705517i
\(877\) −7.20614 + 45.4978i −0.243334 + 1.53635i 0.499167 + 0.866506i \(0.333639\pi\)
−0.742501 + 0.669845i \(0.766361\pi\)
\(878\) −8.02321 15.7464i −0.270770 0.531417i
\(879\) −19.1485 −0.645864
\(880\) −1.88884 9.89337i −0.0636729 0.333505i
\(881\) 3.73181 0.125728 0.0628640 0.998022i \(-0.479977\pi\)
0.0628640 + 0.998022i \(0.479977\pi\)
\(882\) −15.6654 30.7450i −0.527481 1.03524i
\(883\) −3.92144 + 24.7590i −0.131967 + 0.833207i 0.829544 + 0.558441i \(0.188600\pi\)
−0.961511 + 0.274766i \(0.911400\pi\)
\(884\) −9.80982 + 13.5021i −0.329940 + 0.454123i
\(885\) 29.3955 + 30.8520i 0.988117 + 1.03708i
\(886\) −10.9920 + 3.57153i −0.369285 + 0.119988i
\(887\) −14.0482 + 2.22501i −0.471692 + 0.0747087i −0.387755 0.921762i \(-0.626749\pi\)
−0.0839369 + 0.996471i \(0.526749\pi\)
\(888\) −8.08793 1.28100i −0.271413 0.0429876i
\(889\) 6.18287 + 2.00893i 0.207367 + 0.0673775i
\(890\) −7.68633 + 3.68517i −0.257646 + 0.123527i
\(891\) −1.28930 1.15302i −0.0431933 0.0386278i
\(892\) 3.36602 + 3.36602i 0.112703 + 0.112703i
\(893\) 5.64698 2.87728i 0.188969 0.0962845i
\(894\) 25.5712 + 35.1957i 0.855228 + 1.17712i
\(895\) −25.3872 36.7801i −0.848601 1.22942i
\(896\) −0.236785 0.728751i −0.00791045 0.0243458i
\(897\) −9.25183 4.71404i −0.308910 0.157397i
\(898\) 0.738556 + 4.66306i 0.0246459 + 0.155608i
\(899\) −5.67482 + 4.12300i −0.189266 + 0.137510i
\(900\) −18.7335 + 12.2730i −0.624449 + 0.409099i
\(901\) 39.8915i 1.32898i
\(902\) −16.7970 + 26.0576i −0.559279 + 0.867623i
\(903\) 3.95331 3.95331i 0.131558 0.131558i
\(904\) 1.34817 4.14925i 0.0448396 0.138002i
\(905\) −17.1833 57.5847i −0.571192 1.91418i
\(906\) 15.8188 + 11.4930i 0.525545 + 0.381831i
\(907\) −22.3342 + 43.8334i −0.741597 + 1.45547i 0.143301 + 0.989679i \(0.454228\pi\)
−0.884897 + 0.465786i \(0.845772\pi\)
\(908\) 6.21518 12.1980i 0.206258 0.404804i
\(909\) 2.55386 + 1.85549i 0.0847062 + 0.0615427i
\(910\) 3.66673 + 1.98134i 0.121551 + 0.0656809i
\(911\) 13.4007 41.2430i 0.443984 1.36644i −0.439610 0.898189i \(-0.644883\pi\)
0.883594 0.468254i \(-0.155117\pi\)
\(912\) −4.20960 + 4.20960i −0.139394 + 0.139394i
\(913\) −20.3587 + 31.5828i −0.673773 + 1.04524i
\(914\) 34.0883i 1.12754i
\(915\) −7.67829 57.4305i −0.253837 1.89859i
\(916\) −10.9258 + 7.93804i −0.360998 + 0.262280i
\(917\) 0.683310 + 4.31425i 0.0225649 + 0.142469i
\(918\) 28.6665 + 14.6063i 0.946135 + 0.482080i
\(919\) −7.23415 22.2644i −0.238633 0.734435i −0.996619 0.0821649i \(-0.973817\pi\)
0.757986 0.652271i \(-0.226183\pi\)
\(920\) 6.35461 4.38623i 0.209505 0.144610i
\(921\) −12.9739 17.8570i −0.427504 0.588409i
\(922\) 21.8098 11.1126i 0.718267 0.365975i
\(923\) 15.7250 + 15.7250i 0.517596 + 0.517596i
\(924\) 3.47728 + 3.10974i 0.114394 + 0.102303i
\(925\) −0.519235 4.75625i −0.0170723 0.156385i
\(926\) 41.0511 + 13.3383i 1.34902 + 0.438324i
\(927\) 10.0621 + 1.59368i 0.330483 + 0.0523434i
\(928\) −19.5857 + 3.10207i −0.642932 + 0.101830i
\(929\) 12.0399 3.91200i 0.395017 0.128349i −0.104772 0.994496i \(-0.533411\pi\)
0.499788 + 0.866148i \(0.333411\pi\)
\(930\) −0.262026 + 10.8386i −0.00859218 + 0.355411i
\(931\) −6.12773 + 8.43410i −0.200828 + 0.276416i
\(932\) 0.787098 4.96954i 0.0257823 0.162783i
\(933\) −21.2119 41.6306i −0.694445 1.36293i
\(934\) −29.6798 −0.971153
\(935\) 34.7371 + 23.5995i 1.13602 + 0.771786i
\(936\) 48.6159 1.58906
\(937\) −12.0732 23.6950i −0.394414 0.774082i 0.605346 0.795962i \(-0.293035\pi\)
−0.999761 + 0.0218805i \(0.993035\pi\)
\(938\) 0.333298 2.10436i 0.0108826 0.0687099i
\(939\) −15.7643 + 21.6977i −0.514449 + 0.708078i
\(940\) 5.98770 5.70503i 0.195297 0.186078i
\(941\) 22.7044 7.37710i 0.740141 0.240487i 0.0854076 0.996346i \(-0.472781\pi\)
0.654734 + 0.755860i \(0.272781\pi\)
\(942\) 4.69149 0.743059i 0.152857 0.0242102i
\(943\) −10.0416 1.59043i −0.327000 0.0517916i
\(944\) 8.74069 + 2.84002i 0.284485 + 0.0924349i
\(945\) −2.21907 + 6.30671i −0.0721865 + 0.205157i
\(946\) −5.05034 + 11.4473i −0.164201 + 0.372182i
\(947\) 38.6416 + 38.6416i 1.25568 + 1.25568i 0.953134 + 0.302548i \(0.0978374\pi\)
0.302548 + 0.953134i \(0.402163\pi\)
\(948\) 9.49643 4.83867i 0.308430 0.157153i
\(949\) 19.2422 + 26.4846i 0.624627 + 0.859725i
\(950\) −7.05825 4.03735i −0.229000 0.130989i
\(951\) −20.9882 64.5950i −0.680589 2.09464i
\(952\) −8.42973 4.29516i −0.273209 0.139207i
\(953\) 2.50247 + 15.8000i 0.0810628 + 0.511811i 0.994492 + 0.104813i \(0.0334243\pi\)
−0.913429 + 0.406998i \(0.866576\pi\)
\(954\) 29.3621 21.3328i 0.950634 0.690676i
\(955\) −22.9918 17.5689i −0.743996 0.568517i
\(956\) 22.4544i 0.726229i
\(957\) 30.8141 25.1257i 0.996078 0.812199i
\(958\) 23.1798 23.1798i 0.748904 0.748904i
\(959\) 0.760307 2.33998i 0.0245516 0.0755620i
\(960\) −22.7020 + 42.0129i −0.732703 + 1.35596i
\(961\) 22.8828 + 16.6253i 0.738153 + 0.536300i
\(962\) −1.47269 + 2.89032i −0.0474814 + 0.0931875i
\(963\) 20.0086 39.2690i 0.644767 1.26543i
\(964\) −3.81921 2.77482i −0.123009 0.0893710i
\(965\) 7.97033 14.7501i 0.256574 0.474824i
\(966\) 0.568111 1.74847i 0.0182787 0.0562560i
\(967\) 37.1649 37.1649i 1.19514 1.19514i 0.219539 0.975604i \(-0.429545\pi\)
0.975604 0.219539i \(-0.0704554\pi\)
\(968\) −31.2858 11.7674i −1.00556 0.378219i
\(969\) 24.8221i 0.797400i
\(970\) −30.9419 23.6439i −0.993485 0.759161i
\(971\) −17.7106 + 12.8675i −0.568359 + 0.412937i −0.834509 0.550994i \(-0.814249\pi\)
0.266149 + 0.963932i \(0.414249\pi\)
\(972\) −2.10952 13.3190i −0.0676628 0.427206i
\(973\) 11.0796 + 5.64535i 0.355197 + 0.180982i
\(974\) 2.21906 + 6.82956i 0.0711033 + 0.218833i
\(975\) 12.0019 + 44.0824i 0.384369 + 1.41177i
\(976\) −7.34510 10.1097i −0.235111 0.323602i
\(977\) 0.0913420 0.0465411i 0.00292229 0.00148898i −0.452529 0.891750i \(-0.649478\pi\)
0.455451 + 0.890261i \(0.349478\pi\)
\(978\) 21.0754 + 21.0754i 0.673915 + 0.673915i
\(979\) −1.22421 + 12.0389i −0.0391258 + 0.384766i
\(980\) −4.51541 + 12.8330i −0.144239 + 0.409935i
\(981\) 21.0116 + 6.82708i 0.670848 + 0.217972i
\(982\) −15.2003 2.40750i −0.485062 0.0768264i
\(983\) 44.9211 7.11481i 1.43276 0.226927i 0.608688 0.793410i \(-0.291696\pi\)
0.824074 + 0.566483i \(0.191696\pi\)
\(984\) 72.8141 23.6587i 2.32123 0.754213i
\(985\) −6.25238 + 5.95721i −0.199217 + 0.189813i
\(986\) −14.8032 + 20.3749i −0.471430 + 0.648868i
\(987\) 0.986282 6.22714i 0.0313937 0.198212i
\(988\) −2.08270 4.08752i −0.0662594 0.130041i
\(989\) −4.10309 −0.130471
\(990\) −1.20602 38.1886i −0.0383298 1.21371i
\(991\) −7.25030 −0.230313 −0.115157 0.993347i \(-0.536737\pi\)
−0.115157 + 0.993347i \(0.536737\pi\)
\(992\) −3.48497 6.83964i −0.110648 0.217159i
\(993\) −5.53513 + 34.9475i −0.175652 + 1.10902i
\(994\) −2.31435 + 3.18543i −0.0734067 + 0.101036i
\(995\) −0.669227 + 27.6822i −0.0212159 + 0.877585i
\(996\) 27.5643 8.95617i 0.873407 0.283787i
\(997\) 27.5642 4.36575i 0.872968 0.138265i 0.296154 0.955140i \(-0.404296\pi\)
0.576814 + 0.816876i \(0.304296\pi\)
\(998\) −27.3197 4.32702i −0.864791 0.136969i
\(999\) −4.94893 1.60800i −0.156577 0.0508750i
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 55.2.l.a.2.2 32
3.2 odd 2 495.2.bj.a.442.3 32
4.3 odd 2 880.2.cm.a.497.4 32
5.2 odd 4 275.2.bm.b.68.3 32
5.3 odd 4 inner 55.2.l.a.13.2 yes 32
5.4 even 2 275.2.bm.b.57.3 32
11.2 odd 10 605.2.m.d.602.3 32
11.3 even 5 605.2.m.d.282.2 32
11.4 even 5 605.2.e.b.362.11 32
11.5 even 5 605.2.m.e.457.3 32
11.6 odd 10 inner 55.2.l.a.17.2 yes 32
11.7 odd 10 605.2.e.b.362.6 32
11.8 odd 10 605.2.m.c.282.3 32
11.9 even 5 605.2.m.c.602.2 32
11.10 odd 2 605.2.m.e.112.3 32
15.8 even 4 495.2.bj.a.343.3 32
20.3 even 4 880.2.cm.a.673.4 32
33.17 even 10 495.2.bj.a.127.3 32
44.39 even 10 880.2.cm.a.17.4 32
55.3 odd 20 605.2.m.d.403.3 32
55.8 even 20 605.2.m.c.403.2 32
55.13 even 20 605.2.m.d.118.2 32
55.17 even 20 275.2.bm.b.193.3 32
55.18 even 20 605.2.e.b.483.11 32
55.28 even 20 inner 55.2.l.a.28.2 yes 32
55.38 odd 20 605.2.m.e.578.3 32
55.39 odd 10 275.2.bm.b.182.3 32
55.43 even 4 605.2.m.e.233.3 32
55.48 odd 20 605.2.e.b.483.6 32
55.53 odd 20 605.2.m.c.118.3 32
165.83 odd 20 495.2.bj.a.28.3 32
220.83 odd 20 880.2.cm.a.193.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.l.a.2.2 32 1.1 even 1 trivial
55.2.l.a.13.2 yes 32 5.3 odd 4 inner
55.2.l.a.17.2 yes 32 11.6 odd 10 inner
55.2.l.a.28.2 yes 32 55.28 even 20 inner
275.2.bm.b.57.3 32 5.4 even 2
275.2.bm.b.68.3 32 5.2 odd 4
275.2.bm.b.182.3 32 55.39 odd 10
275.2.bm.b.193.3 32 55.17 even 20
495.2.bj.a.28.3 32 165.83 odd 20
495.2.bj.a.127.3 32 33.17 even 10
495.2.bj.a.343.3 32 15.8 even 4
495.2.bj.a.442.3 32 3.2 odd 2
605.2.e.b.362.6 32 11.7 odd 10
605.2.e.b.362.11 32 11.4 even 5
605.2.e.b.483.6 32 55.48 odd 20
605.2.e.b.483.11 32 55.18 even 20
605.2.m.c.118.3 32 55.53 odd 20
605.2.m.c.282.3 32 11.8 odd 10
605.2.m.c.403.2 32 55.8 even 20
605.2.m.c.602.2 32 11.9 even 5
605.2.m.d.118.2 32 55.13 even 20
605.2.m.d.282.2 32 11.3 even 5
605.2.m.d.403.3 32 55.3 odd 20
605.2.m.d.602.3 32 11.2 odd 10
605.2.m.e.112.3 32 11.10 odd 2
605.2.m.e.233.3 32 55.43 even 4
605.2.m.e.457.3 32 11.5 even 5
605.2.m.e.578.3 32 55.38 odd 20
880.2.cm.a.17.4 32 44.39 even 10
880.2.cm.a.193.4 32 220.83 odd 20
880.2.cm.a.497.4 32 4.3 odd 2
880.2.cm.a.673.4 32 20.3 even 4