Properties

Label 273.2.bv.b.32.6
Level $273$
Weight $2$
Character 273.32
Analytic conductor $2.180$
Analytic rank $0$
Dimension $128$
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] = [273,2,Mod(2,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bv (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.6
Character \(\chi\) \(=\) 273.32
Dual form 273.2.bv.b.128.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.49865 - 1.49865i) q^{2} +(-1.00312 + 1.41200i) q^{3} +2.49189i q^{4} +(0.189246 - 0.706275i) q^{5} +(3.61942 - 0.612770i) q^{6} +(-2.64267 + 0.127700i) q^{7} +(0.737165 - 0.737165i) q^{8} +(-0.987501 - 2.83282i) q^{9} +O(q^{10})\) \(q+(-1.49865 - 1.49865i) q^{2} +(-1.00312 + 1.41200i) q^{3} +2.49189i q^{4} +(0.189246 - 0.706275i) q^{5} +(3.61942 - 0.612770i) q^{6} +(-2.64267 + 0.127700i) q^{7} +(0.737165 - 0.737165i) q^{8} +(-0.987501 - 2.83282i) q^{9} +(-1.34207 + 0.774844i) q^{10} +(3.26458 + 0.874742i) q^{11} +(-3.51855 - 2.49966i) q^{12} +(3.48370 + 0.929429i) q^{13} +(4.15180 + 3.76905i) q^{14} +(0.807426 + 0.975694i) q^{15} +2.77427 q^{16} +4.62710 q^{17} +(-2.76548 + 5.72531i) q^{18} +(-1.69330 - 6.31950i) q^{19} +(1.75996 + 0.471579i) q^{20} +(2.47060 - 3.85955i) q^{21} +(-3.58153 - 6.20338i) q^{22} +1.23779 q^{23} +(0.301414 + 1.78034i) q^{24} +(3.86712 + 2.23268i) q^{25} +(-3.82795 - 6.61372i) q^{26} +(4.99052 + 1.44730i) q^{27} +(-0.318214 - 6.58523i) q^{28} +(0.0742930 + 0.0428931i) q^{29} +(0.252175 - 2.67227i) q^{30} +(-1.75110 - 6.53521i) q^{31} +(-5.63199 - 5.63199i) q^{32} +(-4.50990 + 3.73212i) q^{33} +(-6.93438 - 6.93438i) q^{34} +(-0.409922 + 1.89062i) q^{35} +(7.05905 - 2.46074i) q^{36} +(3.78999 + 3.78999i) q^{37} +(-6.93303 + 12.0084i) q^{38} +(-4.80692 + 3.98666i) q^{39} +(-0.381136 - 0.660146i) q^{40} +(11.3670 - 3.04579i) q^{41} +(-9.48666 + 2.08155i) q^{42} +(-7.89663 + 4.55912i) q^{43} +(-2.17976 + 8.13497i) q^{44} +(-2.18763 + 0.161349i) q^{45} +(-1.85501 - 1.85501i) q^{46} +(1.11118 + 0.297740i) q^{47} +(-2.78293 + 3.91728i) q^{48} +(6.96739 - 0.674939i) q^{49} +(-2.44944 - 9.14144i) q^{50} +(-4.64153 + 6.53347i) q^{51} +(-2.31603 + 8.68098i) q^{52} +(-0.966555 - 0.558041i) q^{53} +(-5.31004 - 9.64803i) q^{54} +(1.23562 - 2.14015i) q^{55} +(-1.85394 + 2.04222i) q^{56} +(10.6217 + 3.94826i) q^{57} +(-0.0470574 - 0.175621i) q^{58} +(0.0904502 - 0.0904502i) q^{59} +(-2.43132 + 2.01201i) q^{60} +(0.604519 - 1.04706i) q^{61} +(-7.16968 + 12.4183i) q^{62} +(2.97139 + 7.36009i) q^{63} +11.3322i q^{64} +(1.31571 - 2.28456i) q^{65} +(12.3519 + 1.16562i) q^{66} +(7.33907 + 1.96650i) q^{67} +11.5302i q^{68} +(-1.24165 + 1.74776i) q^{69} +(3.44770 - 2.21904i) q^{70} +(-0.179939 + 0.671543i) q^{71} +(-2.81620 - 1.36030i) q^{72} +(-3.83834 + 1.02848i) q^{73} -11.3597i q^{74} +(-7.03173 + 3.22073i) q^{75} +(15.7475 - 4.21952i) q^{76} +(-8.73891 - 1.89476i) q^{77} +(13.1785 + 1.22928i) q^{78} +(7.74974 + 13.4229i) q^{79} +(0.525020 - 1.95940i) q^{80} +(-7.04968 + 5.59481i) q^{81} +(-21.5997 - 12.4706i) q^{82} +(-4.66837 - 4.66837i) q^{83} +(9.61756 + 6.15645i) q^{84} +(0.875658 - 3.26800i) q^{85} +(18.6668 + 5.00175i) q^{86} +(-0.135090 + 0.0618750i) q^{87} +(3.05136 - 1.76170i) q^{88} +(-8.63123 + 8.63123i) q^{89} +(3.52029 + 3.03668i) q^{90} +(-9.32495 - 2.01130i) q^{91} +3.08443i q^{92} +(10.9843 + 4.08303i) q^{93} +(-1.21906 - 2.11147i) q^{94} -4.78375 q^{95} +(13.6019 - 2.30282i) q^{96} +(-7.29693 - 1.95521i) q^{97} +(-11.4531 - 9.43016i) q^{98} +(-0.745794 - 10.1118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 2 q^{3} - 4 q^{6} - 16 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 2 q^{3} - 4 q^{6} - 16 q^{7} + 8 q^{9} - 12 q^{10} + 48 q^{12} - 16 q^{13} - 6 q^{15} - 64 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{21} - 8 q^{22} + 2 q^{24} - 40 q^{27} + 68 q^{28} + 18 q^{30} + 20 q^{31} - 16 q^{33} - 48 q^{34} - 60 q^{36} - 8 q^{37} + 4 q^{39} + 44 q^{40} + 2 q^{42} - 144 q^{43} - 2 q^{45} - 24 q^{46} - 64 q^{48} - 60 q^{49} - 36 q^{51} + 48 q^{52} + 14 q^{54} - 16 q^{55} + 40 q^{57} + 44 q^{58} - 58 q^{60} + 20 q^{61} + 14 q^{63} - 34 q^{66} - 84 q^{67} - 54 q^{69} - 104 q^{70} + 46 q^{72} - 48 q^{73} + 144 q^{76} + 82 q^{78} - 24 q^{79} + 24 q^{81} + 36 q^{82} + 184 q^{84} + 56 q^{85} + 4 q^{87} + 132 q^{88} + 24 q^{91} + 16 q^{93} - 16 q^{94} - 90 q^{96} + 52 q^{97} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49865 1.49865i −1.05970 1.05970i −0.998101 0.0616028i \(-0.980379\pi\)
−0.0616028 0.998101i \(-0.519621\pi\)
\(3\) −1.00312 + 1.41200i −0.579152 + 0.815220i
\(4\) 2.49189i 1.24594i
\(5\) 0.189246 0.706275i 0.0846333 0.315856i −0.910611 0.413264i \(-0.864389\pi\)
0.995244 + 0.0974084i \(0.0310553\pi\)
\(6\) 3.61942 0.612770i 1.47762 0.250162i
\(7\) −2.64267 + 0.127700i −0.998835 + 0.0482661i
\(8\) 0.737165 0.737165i 0.260627 0.260627i
\(9\) −0.987501 2.83282i −0.329167 0.944272i
\(10\) −1.34207 + 0.774844i −0.424400 + 0.245027i
\(11\) 3.26458 + 0.874742i 0.984308 + 0.263745i 0.714858 0.699270i \(-0.246491\pi\)
0.269450 + 0.963014i \(0.413158\pi\)
\(12\) −3.51855 2.49966i −1.01572 0.721590i
\(13\) 3.48370 + 0.929429i 0.966204 + 0.257777i
\(14\) 4.15180 + 3.76905i 1.10962 + 1.00732i
\(15\) 0.807426 + 0.975694i 0.208476 + 0.251923i
\(16\) 2.77427 0.693569
\(17\) 4.62710 1.12224 0.561118 0.827736i \(-0.310372\pi\)
0.561118 + 0.827736i \(0.310372\pi\)
\(18\) −2.76548 + 5.72531i −0.651829 + 1.34947i
\(19\) −1.69330 6.31950i −0.388471 1.44979i −0.832623 0.553841i \(-0.813162\pi\)
0.444152 0.895951i \(-0.353505\pi\)
\(20\) 1.75996 + 0.471579i 0.393538 + 0.105448i
\(21\) 2.47060 3.85955i 0.539129 0.842223i
\(22\) −3.58153 6.20338i −0.763584 1.32257i
\(23\) 1.23779 0.258097 0.129048 0.991638i \(-0.458808\pi\)
0.129048 + 0.991638i \(0.458808\pi\)
\(24\) 0.301414 + 1.78034i 0.0615258 + 0.363411i
\(25\) 3.86712 + 2.23268i 0.773423 + 0.446536i
\(26\) −3.82795 6.61372i −0.750723 1.29706i
\(27\) 4.99052 + 1.44730i 0.960427 + 0.278533i
\(28\) −0.318214 6.58523i −0.0601369 1.24449i
\(29\) 0.0742930 + 0.0428931i 0.0137959 + 0.00796505i 0.506882 0.862015i \(-0.330798\pi\)
−0.493086 + 0.869980i \(0.664131\pi\)
\(30\) 0.252175 2.67227i 0.0460406 0.487887i
\(31\) −1.75110 6.53521i −0.314507 1.17376i −0.924447 0.381310i \(-0.875473\pi\)
0.609940 0.792448i \(-0.291194\pi\)
\(32\) −5.63199 5.63199i −0.995604 0.995604i
\(33\) −4.50990 + 3.73212i −0.785073 + 0.649680i
\(34\) −6.93438 6.93438i −1.18924 1.18924i
\(35\) −0.409922 + 1.89062i −0.0692895 + 0.319573i
\(36\) 7.05905 2.46074i 1.17651 0.410123i
\(37\) 3.78999 + 3.78999i 0.623070 + 0.623070i 0.946315 0.323245i \(-0.104774\pi\)
−0.323245 + 0.946315i \(0.604774\pi\)
\(38\) −6.93303 + 12.0084i −1.12469 + 1.94801i
\(39\) −4.80692 + 3.98666i −0.769724 + 0.638377i
\(40\) −0.381136 0.660146i −0.0602628 0.104378i
\(41\) 11.3670 3.04579i 1.77523 0.475672i 0.785532 0.618821i \(-0.212389\pi\)
0.989701 + 0.143148i \(0.0457226\pi\)
\(42\) −9.48666 + 2.08155i −1.46382 + 0.321190i
\(43\) −7.89663 + 4.55912i −1.20423 + 0.695260i −0.961492 0.274833i \(-0.911377\pi\)
−0.242734 + 0.970093i \(0.578044\pi\)
\(44\) −2.17976 + 8.13497i −0.328611 + 1.22639i
\(45\) −2.18763 + 0.161349i −0.326112 + 0.0240524i
\(46\) −1.85501 1.85501i −0.273506 0.273506i
\(47\) 1.11118 + 0.297740i 0.162082 + 0.0434298i 0.338948 0.940805i \(-0.389929\pi\)
−0.176865 + 0.984235i \(0.556596\pi\)
\(48\) −2.78293 + 3.91728i −0.401681 + 0.565411i
\(49\) 6.96739 0.674939i 0.995341 0.0964198i
\(50\) −2.44944 9.14144i −0.346404 1.29280i
\(51\) −4.64153 + 6.53347i −0.649944 + 0.914869i
\(52\) −2.31603 + 8.68098i −0.321176 + 1.20384i
\(53\) −0.966555 0.558041i −0.132767 0.0766528i 0.432146 0.901804i \(-0.357757\pi\)
−0.564912 + 0.825151i \(0.691090\pi\)
\(54\) −5.31004 9.64803i −0.722605 1.31293i
\(55\) 1.23562 2.14015i 0.166610 0.288578i
\(56\) −1.85394 + 2.04222i −0.247744 + 0.272903i
\(57\) 10.6217 + 3.94826i 1.40688 + 0.522960i
\(58\) −0.0470574 0.175621i −0.00617894 0.0230601i
\(59\) 0.0904502 0.0904502i 0.0117756 0.0117756i −0.701194 0.712970i \(-0.747350\pi\)
0.712970 + 0.701194i \(0.247350\pi\)
\(60\) −2.43132 + 2.01201i −0.313882 + 0.259750i
\(61\) 0.604519 1.04706i 0.0774008 0.134062i −0.824727 0.565531i \(-0.808671\pi\)
0.902128 + 0.431469i \(0.142005\pi\)
\(62\) −7.16968 + 12.4183i −0.910551 + 1.57712i
\(63\) 2.97139 + 7.36009i 0.374360 + 0.927284i
\(64\) 11.3322i 1.41652i
\(65\) 1.31571 2.28456i 0.163193 0.283365i
\(66\) 12.3519 + 1.16562i 1.52041 + 0.143477i
\(67\) 7.33907 + 1.96650i 0.896610 + 0.240246i 0.677560 0.735468i \(-0.263038\pi\)
0.219050 + 0.975714i \(0.429704\pi\)
\(68\) 11.5302i 1.39824i
\(69\) −1.24165 + 1.74776i −0.149477 + 0.210406i
\(70\) 3.44770 2.21904i 0.412079 0.265226i
\(71\) −0.179939 + 0.671543i −0.0213549 + 0.0796975i −0.975781 0.218750i \(-0.929802\pi\)
0.954426 + 0.298447i \(0.0964688\pi\)
\(72\) −2.81620 1.36030i −0.331893 0.160313i
\(73\) −3.83834 + 1.02848i −0.449244 + 0.120374i −0.476345 0.879258i \(-0.658039\pi\)
0.0271019 + 0.999633i \(0.491372\pi\)
\(74\) 11.3597i 1.32054i
\(75\) −7.03173 + 3.22073i −0.811955 + 0.371898i
\(76\) 15.7475 4.21952i 1.80636 0.484012i
\(77\) −8.73891 1.89476i −0.995891 0.215928i
\(78\) 13.1785 + 1.22928i 1.49217 + 0.139189i
\(79\) 7.74974 + 13.4229i 0.871913 + 1.51020i 0.860015 + 0.510269i \(0.170454\pi\)
0.0118986 + 0.999929i \(0.496212\pi\)
\(80\) 0.525020 1.95940i 0.0586990 0.219068i
\(81\) −7.04968 + 5.59481i −0.783298 + 0.621646i
\(82\) −21.5997 12.4706i −2.38529 1.37715i
\(83\) −4.66837 4.66837i −0.512420 0.512420i 0.402847 0.915267i \(-0.368021\pi\)
−0.915267 + 0.402847i \(0.868021\pi\)
\(84\) 9.61756 + 6.15645i 1.04936 + 0.671724i
\(85\) 0.875658 3.26800i 0.0949785 0.354464i
\(86\) 18.6668 + 5.00175i 2.01289 + 0.539353i
\(87\) −0.135090 + 0.0618750i −0.0144832 + 0.00663369i
\(88\) 3.05136 1.76170i 0.325276 0.187798i
\(89\) −8.63123 + 8.63123i −0.914909 + 0.914909i −0.996653 0.0817446i \(-0.973951\pi\)
0.0817446 + 0.996653i \(0.473951\pi\)
\(90\) 3.52029 + 3.03668i 0.371071 + 0.320094i
\(91\) −9.32495 2.01130i −0.977520 0.210842i
\(92\) 3.08443i 0.321574i
\(93\) 10.9843 + 4.08303i 1.13902 + 0.423391i
\(94\) −1.21906 2.11147i −0.125736 0.217782i
\(95\) −4.78375 −0.490803
\(96\) 13.6019 2.30282i 1.38824 0.235031i
\(97\) −7.29693 1.95521i −0.740891 0.198521i −0.131417 0.991327i \(-0.541953\pi\)
−0.609474 + 0.792806i \(0.708619\pi\)
\(98\) −11.4531 9.43016i −1.15694 0.952590i
\(99\) −0.745794 10.1118i −0.0749552 1.01627i
\(100\) −5.56359 + 9.63642i −0.556359 + 0.963642i
\(101\) −6.10473 10.5737i −0.607443 1.05212i −0.991660 0.128879i \(-0.958862\pi\)
0.384217 0.923243i \(-0.374471\pi\)
\(102\) 16.7474 2.83535i 1.65824 0.280741i
\(103\) 3.29955 1.90500i 0.325115 0.187705i −0.328555 0.944485i \(-0.606562\pi\)
0.653670 + 0.756780i \(0.273228\pi\)
\(104\) 3.25320 1.88292i 0.319003 0.184635i
\(105\) −2.25835 2.47533i −0.220393 0.241567i
\(106\) 0.612219 + 2.28483i 0.0594639 + 0.221922i
\(107\) 3.64738i 0.352606i 0.984336 + 0.176303i \(0.0564138\pi\)
−0.984336 + 0.176303i \(0.943586\pi\)
\(108\) −3.60651 + 12.4358i −0.347036 + 1.19664i
\(109\) −1.85970 6.94049i −0.178127 0.664778i −0.995998 0.0893768i \(-0.971512\pi\)
0.817871 0.575402i \(-0.195154\pi\)
\(110\) −5.05908 + 1.35558i −0.482365 + 0.129249i
\(111\) −9.15328 + 1.54966i −0.868791 + 0.147087i
\(112\) −7.33148 + 0.354275i −0.692760 + 0.0334759i
\(113\) 6.52741 3.76860i 0.614047 0.354520i −0.160501 0.987036i \(-0.551311\pi\)
0.774548 + 0.632516i \(0.217978\pi\)
\(114\) −10.0012 21.8353i −0.936696 2.04506i
\(115\) 0.234246 0.874220i 0.0218436 0.0815214i
\(116\) −0.106885 + 0.185130i −0.00992399 + 0.0171889i
\(117\) −0.807256 10.7865i −0.0746309 0.997211i
\(118\) −0.271106 −0.0249573
\(119\) −12.2279 + 0.590881i −1.12093 + 0.0541660i
\(120\) 1.31445 + 0.124041i 0.119993 + 0.0113234i
\(121\) 0.366036 + 0.211331i 0.0332760 + 0.0192119i
\(122\) −2.47513 + 0.663210i −0.224088 + 0.0600442i
\(123\) −7.10184 + 19.1056i −0.640352 + 1.72269i
\(124\) 16.2850 4.36355i 1.46244 0.391859i
\(125\) 4.89387 4.89387i 0.437721 0.437721i
\(126\) 6.57711 15.4832i 0.585935 1.37936i
\(127\) −5.30192 3.06106i −0.470469 0.271625i 0.245967 0.969278i \(-0.420894\pi\)
−0.716436 + 0.697653i \(0.754228\pi\)
\(128\) 5.71896 5.71896i 0.505489 0.505489i
\(129\) 1.48378 15.7234i 0.130639 1.38437i
\(130\) −5.39553 + 1.45197i −0.473219 + 0.127346i
\(131\) 14.9487 8.63064i 1.30607 0.754062i 0.324636 0.945839i \(-0.394758\pi\)
0.981439 + 0.191777i \(0.0614250\pi\)
\(132\) −9.30003 11.2382i −0.809464 0.978157i
\(133\) 5.28184 + 16.4841i 0.457994 + 1.42935i
\(134\) −8.05159 13.9458i −0.695551 1.20473i
\(135\) 1.96663 3.25079i 0.169260 0.279783i
\(136\) 3.41093 3.41093i 0.292485 0.292485i
\(137\) 13.9211 13.9211i 1.18936 1.18936i 0.212120 0.977244i \(-0.431963\pi\)
0.977244 0.212120i \(-0.0680369\pi\)
\(138\) 4.48008 0.758481i 0.381369 0.0645662i
\(139\) 1.24639 + 2.15881i 0.105717 + 0.183108i 0.914031 0.405644i \(-0.132953\pi\)
−0.808314 + 0.588752i \(0.799620\pi\)
\(140\) −4.71120 1.02148i −0.398169 0.0863308i
\(141\) −1.53506 + 1.27032i −0.129275 + 0.106980i
\(142\) 1.27607 0.736740i 0.107086 0.0618259i
\(143\) 10.5598 + 6.08153i 0.883056 + 0.508563i
\(144\) −2.73960 7.85901i −0.228300 0.654917i
\(145\) 0.0443539 0.0443539i 0.00368339 0.00368339i
\(146\) 7.29364 + 4.21099i 0.603626 + 0.348504i
\(147\) −6.03611 + 10.5150i −0.497850 + 0.867263i
\(148\) −9.44422 + 9.44422i −0.776310 + 0.776310i
\(149\) 1.63726 0.438703i 0.134130 0.0359400i −0.191130 0.981565i \(-0.561215\pi\)
0.325259 + 0.945625i \(0.394548\pi\)
\(150\) 15.3648 + 5.71135i 1.25453 + 0.466329i
\(151\) 0.548192 0.146888i 0.0446113 0.0119536i −0.236444 0.971645i \(-0.575982\pi\)
0.281056 + 0.959691i \(0.409315\pi\)
\(152\) −5.90675 3.41027i −0.479101 0.276609i
\(153\) −4.56926 13.1077i −0.369403 1.05970i
\(154\) 10.2570 + 15.9361i 0.826529 + 1.28417i
\(155\) −4.94704 −0.397356
\(156\) −9.93431 11.9783i −0.795382 0.959032i
\(157\) 2.77084 4.79924i 0.221137 0.383021i −0.734016 0.679132i \(-0.762356\pi\)
0.955154 + 0.296111i \(0.0956898\pi\)
\(158\) 8.50213 31.7304i 0.676393 2.52433i
\(159\) 1.75753 0.804996i 0.139381 0.0638403i
\(160\) −5.04356 + 2.91190i −0.398729 + 0.230206i
\(161\) −3.27107 + 0.158066i −0.257796 + 0.0124573i
\(162\) 18.9496 + 2.18034i 1.48882 + 0.171303i
\(163\) 3.90119 1.04532i 0.305564 0.0818757i −0.102779 0.994704i \(-0.532773\pi\)
0.408343 + 0.912829i \(0.366107\pi\)
\(164\) 7.58976 + 28.3254i 0.592661 + 2.21184i
\(165\) 1.78243 + 3.89152i 0.138762 + 0.302954i
\(166\) 13.9925i 1.08603i
\(167\) −2.07644 7.74939i −0.160680 0.599666i −0.998552 0.0537988i \(-0.982867\pi\)
0.837872 0.545867i \(-0.183800\pi\)
\(168\) −1.02389 4.66636i −0.0789945 0.360018i
\(169\) 11.2723 + 6.47570i 0.867102 + 0.498131i
\(170\) −6.20988 + 3.58528i −0.476276 + 0.274978i
\(171\) −16.2298 + 11.0373i −1.24113 + 0.844045i
\(172\) −11.3608 19.6775i −0.866254 1.50040i
\(173\) −8.47934 + 14.6866i −0.644672 + 1.11660i 0.339705 + 0.940532i \(0.389673\pi\)
−0.984377 + 0.176073i \(0.943661\pi\)
\(174\) 0.295181 + 0.109723i 0.0223776 + 0.00831811i
\(175\) −10.5046 5.40640i −0.794075 0.408686i
\(176\) 9.05684 + 2.42677i 0.682685 + 0.182925i
\(177\) 0.0369835 + 0.218448i 0.00277985 + 0.0164196i
\(178\) 25.8703 1.93906
\(179\) 11.0600 + 19.1564i 0.826662 + 1.43182i 0.900643 + 0.434560i \(0.143096\pi\)
−0.0739812 + 0.997260i \(0.523570\pi\)
\(180\) −0.402063 5.45132i −0.0299680 0.406317i
\(181\) 10.2313i 0.760484i 0.924887 + 0.380242i \(0.124159\pi\)
−0.924887 + 0.380242i \(0.875841\pi\)
\(182\) 10.9606 + 16.9890i 0.812452 + 1.25931i
\(183\) 0.872043 + 1.90391i 0.0644633 + 0.140741i
\(184\) 0.912455 0.912455i 0.0672671 0.0672671i
\(185\) 3.39401 1.95953i 0.249533 0.144068i
\(186\) −10.3426 22.5806i −0.758353 1.65569i
\(187\) 15.1055 + 4.04751i 1.10463 + 0.295984i
\(188\) −0.741934 + 2.76893i −0.0541111 + 0.201945i
\(189\) −13.3731 3.18744i −0.972751 0.231852i
\(190\) 7.16916 + 7.16916i 0.520105 + 0.520105i
\(191\) −18.8520 10.8842i −1.36408 0.787552i −0.373916 0.927463i \(-0.621985\pi\)
−0.990164 + 0.139911i \(0.955318\pi\)
\(192\) −16.0011 11.3675i −1.15478 0.820381i
\(193\) 0.977573 3.64835i 0.0703673 0.262614i −0.921776 0.387724i \(-0.873262\pi\)
0.992143 + 0.125109i \(0.0399282\pi\)
\(194\) 8.00536 + 13.8657i 0.574752 + 0.995499i
\(195\) 1.90599 + 4.14947i 0.136491 + 0.297150i
\(196\) 1.68187 + 17.3619i 0.120134 + 1.24014i
\(197\) −17.8050 + 4.77082i −1.26855 + 0.339907i −0.829475 0.558543i \(-0.811360\pi\)
−0.439075 + 0.898450i \(0.644694\pi\)
\(198\) −14.0363 + 16.2716i −0.997515 + 1.15638i
\(199\) 25.8677i 1.83371i −0.399216 0.916857i \(-0.630718\pi\)
0.399216 0.916857i \(-0.369282\pi\)
\(200\) 4.49655 1.20485i 0.317954 0.0851956i
\(201\) −10.1387 + 8.39015i −0.715126 + 0.591795i
\(202\) −6.69741 + 24.9951i −0.471228 + 1.75865i
\(203\) −0.201809 0.103865i −0.0141642 0.00728989i
\(204\) −16.2807 11.5662i −1.13987 0.809794i
\(205\) 8.60466i 0.600975i
\(206\) −7.79979 2.08995i −0.543437 0.145613i
\(207\) −1.22232 3.50643i −0.0849570 0.243714i
\(208\) 9.66474 + 2.57849i 0.670129 + 0.178786i
\(209\) 22.1117i 1.52950i
\(210\) −0.325165 + 7.09412i −0.0224385 + 0.489541i
\(211\) 7.09306 12.2855i 0.488307 0.845772i −0.511603 0.859222i \(-0.670948\pi\)
0.999910 + 0.0134501i \(0.00428143\pi\)
\(212\) 1.39057 2.40855i 0.0955050 0.165420i
\(213\) −0.767719 0.927713i −0.0526033 0.0635658i
\(214\) 5.46614 5.46614i 0.373658 0.373658i
\(215\) 1.72559 + 6.43999i 0.117684 + 0.439204i
\(216\) 4.74574 2.61194i 0.322906 0.177720i
\(217\) 5.46213 + 17.0468i 0.370794 + 1.15721i
\(218\) −7.61431 + 13.1884i −0.515706 + 0.893230i
\(219\) 2.39810 6.45143i 0.162048 0.435947i
\(220\) 5.33301 + 3.07902i 0.359552 + 0.207587i
\(221\) 16.1194 + 4.30056i 1.08431 + 0.289287i
\(222\) 16.0399 + 11.3951i 1.07653 + 0.764792i
\(223\) 2.87666 + 10.7358i 0.192635 + 0.718924i 0.992866 + 0.119233i \(0.0380434\pi\)
−0.800231 + 0.599692i \(0.795290\pi\)
\(224\) 15.6027 + 14.1643i 1.04250 + 0.946390i
\(225\) 2.50599 13.1596i 0.167066 0.877307i
\(226\) −15.4301 4.13448i −1.02639 0.275021i
\(227\) −1.40183 1.40183i −0.0930428 0.0930428i 0.659053 0.752096i \(-0.270957\pi\)
−0.752096 + 0.659053i \(0.770957\pi\)
\(228\) −9.83863 + 26.4681i −0.651579 + 1.75290i
\(229\) −3.92459 + 14.6468i −0.259344 + 0.967885i 0.706278 + 0.707934i \(0.250373\pi\)
−0.965622 + 0.259950i \(0.916294\pi\)
\(230\) −1.66120 + 0.959094i −0.109536 + 0.0632408i
\(231\) 11.4416 10.4387i 0.752801 0.686815i
\(232\) 0.0863854 0.0231469i 0.00567148 0.00151967i
\(233\) −10.4655 18.1268i −0.685619 1.18753i −0.973242 0.229783i \(-0.926198\pi\)
0.287623 0.957744i \(-0.407135\pi\)
\(234\) −14.9553 + 17.3749i −0.977662 + 1.13583i
\(235\) 0.420572 0.728452i 0.0274351 0.0475190i
\(236\) 0.225392 + 0.225392i 0.0146717 + 0.0146717i
\(237\) −26.7271 2.52217i −1.73611 0.163833i
\(238\) 19.2108 + 17.4397i 1.24525 + 1.13045i
\(239\) 15.0244 + 15.0244i 0.971849 + 0.971849i 0.999614 0.0277652i \(-0.00883906\pi\)
−0.0277652 + 0.999614i \(0.508839\pi\)
\(240\) 2.24002 + 2.70684i 0.144593 + 0.174726i
\(241\) −5.83002 5.83002i −0.375545 0.375545i 0.493947 0.869492i \(-0.335554\pi\)
−0.869492 + 0.493947i \(0.835554\pi\)
\(242\) −0.231849 0.865270i −0.0149038 0.0556217i
\(243\) −0.828212 15.5664i −0.0531298 0.998588i
\(244\) 2.60915 + 1.50639i 0.167034 + 0.0964370i
\(245\) 0.841856 5.04862i 0.0537842 0.322544i
\(246\) 39.2757 17.9894i 2.50413 1.14696i
\(247\) −0.0254408 23.5890i −0.00161876 1.50093i
\(248\) −6.10837 3.52667i −0.387882 0.223944i
\(249\) 11.2747 1.90881i 0.714504 0.120966i
\(250\) −14.6684 −0.927709
\(251\) 9.58699 + 16.6052i 0.605126 + 1.04811i 0.992032 + 0.125989i \(0.0402105\pi\)
−0.386906 + 0.922119i \(0.626456\pi\)
\(252\) −18.3405 + 7.40436i −1.15534 + 0.466431i
\(253\) 4.04086 + 1.08275i 0.254047 + 0.0680717i
\(254\) 3.35825 + 12.5332i 0.210715 + 0.786400i
\(255\) 3.73603 + 4.51463i 0.233960 + 0.282717i
\(256\) 5.52295 0.345184
\(257\) 6.33686 0.395283 0.197641 0.980274i \(-0.436672\pi\)
0.197641 + 0.980274i \(0.436672\pi\)
\(258\) −25.7875 + 21.3402i −1.60546 + 1.32858i
\(259\) −10.4997 9.53169i −0.652417 0.592271i
\(260\) 5.69286 + 3.27859i 0.353056 + 0.203330i
\(261\) 0.0481438 0.252815i 0.00298003 0.0156489i
\(262\) −35.3371 9.46855i −2.18313 0.584969i
\(263\) −21.0813 + 12.1713i −1.29993 + 0.750514i −0.980392 0.197060i \(-0.936861\pi\)
−0.319537 + 0.947574i \(0.603527\pi\)
\(264\) −0.573351 + 6.07573i −0.0352873 + 0.373935i
\(265\) −0.577047 + 0.577047i −0.0354477 + 0.0354477i
\(266\) 16.7882 32.6195i 1.02935 2.00003i
\(267\) −3.52916 20.8455i −0.215981 1.27572i
\(268\) −4.90029 + 18.2881i −0.299333 + 1.11712i
\(269\) 10.9722i 0.668985i 0.942398 + 0.334493i \(0.108565\pi\)
−0.942398 + 0.334493i \(0.891435\pi\)
\(270\) −7.81906 + 1.92450i −0.475853 + 0.117121i
\(271\) −5.74281 5.74281i −0.348851 0.348851i 0.510831 0.859681i \(-0.329338\pi\)
−0.859681 + 0.510831i \(0.829338\pi\)
\(272\) 12.8368 0.778347
\(273\) 12.1940 11.1493i 0.738015 0.674785i
\(274\) −41.7258 −2.52075
\(275\) 10.6715 + 10.6715i 0.643515 + 0.643515i
\(276\) −4.35522 3.09405i −0.262154 0.186240i
\(277\) 0.443387i 0.0266406i 0.999911 + 0.0133203i \(0.00424010\pi\)
−0.999911 + 0.0133203i \(0.995760\pi\)
\(278\) 1.36739 5.10318i 0.0820108 0.306069i
\(279\) −16.7838 + 11.4141i −1.00482 + 0.683343i
\(280\) 1.09152 + 1.69588i 0.0652305 + 0.101348i
\(281\) −9.34921 + 9.34921i −0.557727 + 0.557727i −0.928660 0.370933i \(-0.879038\pi\)
0.370933 + 0.928660i \(0.379038\pi\)
\(282\) 4.20427 + 0.396746i 0.250361 + 0.0236259i
\(283\) −8.16911 + 4.71644i −0.485603 + 0.280363i −0.722749 0.691111i \(-0.757122\pi\)
0.237145 + 0.971474i \(0.423788\pi\)
\(284\) −1.67341 0.448389i −0.0992985 0.0266070i
\(285\) 4.79868 6.75467i 0.284249 0.400112i
\(286\) −6.71136 24.9395i −0.396851 1.47470i
\(287\) −29.6504 + 9.50058i −1.75021 + 0.560802i
\(288\) −10.3928 + 21.5160i −0.612401 + 1.26784i
\(289\) 4.41001 0.259412
\(290\) −0.132942 −0.00780661
\(291\) 10.0805 8.34198i 0.590927 0.489015i
\(292\) −2.56285 9.56470i −0.149980 0.559732i
\(293\) −3.23244 0.866128i −0.188841 0.0505998i 0.163159 0.986600i \(-0.447832\pi\)
−0.352000 + 0.936000i \(0.614498\pi\)
\(294\) 24.8043 6.71229i 1.44662 0.391469i
\(295\) −0.0467654 0.0810000i −0.00272279 0.00471600i
\(296\) 5.58769 0.324778
\(297\) 15.0260 + 9.09025i 0.871894 + 0.527470i
\(298\) −3.11114 1.79622i −0.180223 0.104052i
\(299\) 4.31209 + 1.15044i 0.249374 + 0.0665315i
\(300\) −8.02570 17.5223i −0.463364 1.01165i
\(301\) 20.2860 13.0567i 1.16926 0.752573i
\(302\) −1.04168 0.601414i −0.0599419 0.0346075i
\(303\) 21.0539 + 1.98680i 1.20951 + 0.114139i
\(304\) −4.69769 17.5320i −0.269431 1.00553i
\(305\) −0.625108 0.625108i −0.0357936 0.0357936i
\(306\) −12.7961 + 26.4915i −0.731505 + 1.51442i
\(307\) 3.71140 + 3.71140i 0.211821 + 0.211821i 0.805041 0.593220i \(-0.202143\pi\)
−0.593220 + 0.805041i \(0.702143\pi\)
\(308\) 4.72154 21.7764i 0.269035 1.24082i
\(309\) −0.619986 + 6.56992i −0.0352698 + 0.373750i
\(310\) 7.41387 + 7.41387i 0.421080 + 0.421080i
\(311\) −7.27077 + 12.5933i −0.412288 + 0.714103i −0.995140 0.0984752i \(-0.968603\pi\)
0.582852 + 0.812578i \(0.301937\pi\)
\(312\) −0.604667 + 6.48232i −0.0342325 + 0.366989i
\(313\) −5.16579 8.94742i −0.291988 0.505738i 0.682292 0.731080i \(-0.260983\pi\)
−0.974280 + 0.225342i \(0.927650\pi\)
\(314\) −11.3449 + 3.03985i −0.640228 + 0.171549i
\(315\) 5.76057 0.705751i 0.324571 0.0397646i
\(316\) −33.4484 + 19.3115i −1.88162 + 1.08635i
\(317\) −6.76020 + 25.2294i −0.379691 + 1.41703i 0.466678 + 0.884428i \(0.345451\pi\)
−0.846368 + 0.532598i \(0.821216\pi\)
\(318\) −3.84032 1.42751i −0.215354 0.0800505i
\(319\) 0.205015 + 0.205015i 0.0114786 + 0.0114786i
\(320\) 8.00363 + 2.14457i 0.447417 + 0.119885i
\(321\) −5.15011 3.65876i −0.287451 0.204212i
\(322\) 5.13906 + 4.66529i 0.286389 + 0.259986i
\(323\) −7.83508 29.2409i −0.435955 1.62701i
\(324\) −13.9416 17.5670i −0.774536 0.975945i
\(325\) 11.3968 + 11.3722i 0.632178 + 0.630816i
\(326\) −7.41307 4.27994i −0.410572 0.237044i
\(327\) 11.6655 + 4.33624i 0.645103 + 0.239795i
\(328\) 6.13413 10.6246i 0.338701 0.586647i
\(329\) −2.97450 0.644929i −0.163990 0.0355561i
\(330\) 3.16079 8.50324i 0.173996 0.468088i
\(331\) 1.17988 + 4.40338i 0.0648523 + 0.242032i 0.990741 0.135764i \(-0.0433488\pi\)
−0.925889 + 0.377796i \(0.876682\pi\)
\(332\) 11.6331 11.6331i 0.638447 0.638447i
\(333\) 6.99372 14.4789i 0.383253 0.793441i
\(334\) −8.50175 + 14.7255i −0.465195 + 0.805741i
\(335\) 2.77777 4.81125i 0.151766 0.262867i
\(336\) 6.85412 10.7075i 0.373923 0.584139i
\(337\) 23.2811i 1.26820i −0.773250 0.634102i \(-0.781370\pi\)
0.773250 0.634102i \(-0.218630\pi\)
\(338\) −7.18845 26.5980i −0.391000 1.44674i
\(339\) −1.22650 + 12.9971i −0.0666143 + 0.705904i
\(340\) 8.14349 + 2.18204i 0.441643 + 0.118338i
\(341\) 22.8665i 1.23829i
\(342\) 40.8638 + 7.78173i 2.20966 + 0.420788i
\(343\) −18.3263 + 2.67337i −0.989527 + 0.144349i
\(344\) −2.46029 + 9.18194i −0.132650 + 0.495057i
\(345\) 0.999423 + 1.20770i 0.0538071 + 0.0650206i
\(346\) 34.7176 9.30256i 1.86643 0.500109i
\(347\) 20.6263i 1.10728i 0.832757 + 0.553639i \(0.186761\pi\)
−0.832757 + 0.553639i \(0.813239\pi\)
\(348\) −0.154185 0.336629i −0.00826521 0.0180452i
\(349\) 17.9128 4.79971i 0.958849 0.256923i 0.254736 0.967011i \(-0.418011\pi\)
0.704113 + 0.710088i \(0.251345\pi\)
\(350\) 7.64043 + 23.8450i 0.408398 + 1.27457i
\(351\) 16.0403 + 9.68029i 0.856169 + 0.516696i
\(352\) −13.4595 23.3126i −0.717396 1.24257i
\(353\) 6.48087 24.1869i 0.344942 1.28734i −0.547738 0.836650i \(-0.684511\pi\)
0.892680 0.450691i \(-0.148822\pi\)
\(354\) 0.271952 0.382802i 0.0144541 0.0203457i
\(355\) 0.440241 + 0.254173i 0.0233656 + 0.0134901i
\(356\) −21.5081 21.5081i −1.13992 1.13992i
\(357\) 11.4317 17.8585i 0.605030 0.945173i
\(358\) 12.1337 45.2838i 0.641288 2.39332i
\(359\) 5.13386 + 1.37561i 0.270955 + 0.0726021i 0.391738 0.920077i \(-0.371874\pi\)
−0.120783 + 0.992679i \(0.538541\pi\)
\(360\) −1.49370 + 1.73158i −0.0787249 + 0.0912624i
\(361\) −20.6143 + 11.9017i −1.08496 + 0.626403i
\(362\) 15.3331 15.3331i 0.805887 0.805887i
\(363\) −0.665579 + 0.304854i −0.0349338 + 0.0160007i
\(364\) 5.01194 23.2367i 0.262697 1.21793i
\(365\) 2.90556i 0.152084i
\(366\) 1.54640 4.16017i 0.0808317 0.217456i
\(367\) 3.04387 + 5.27213i 0.158889 + 0.275203i 0.934468 0.356047i \(-0.115876\pi\)
−0.775580 + 0.631250i \(0.782542\pi\)
\(368\) 3.43397 0.179008
\(369\) −19.8531 29.1930i −1.03351 1.51973i
\(370\) −8.02308 2.14978i −0.417100 0.111762i
\(371\) 2.62555 + 1.35129i 0.136312 + 0.0701553i
\(372\) −10.1745 + 27.3716i −0.527521 + 1.41915i
\(373\) −4.52998 + 7.84616i −0.234553 + 0.406259i −0.959143 0.282922i \(-0.908696\pi\)
0.724589 + 0.689181i \(0.242029\pi\)
\(374\) −16.5721 28.7037i −0.856921 1.48423i
\(375\) 2.00102 + 11.8193i 0.103332 + 0.610345i
\(376\) 1.03861 0.599639i 0.0535620 0.0309240i
\(377\) 0.218948 + 0.218477i 0.0112764 + 0.0112521i
\(378\) 15.2647 + 24.8184i 0.785133 + 1.27652i
\(379\) 8.65669 + 32.3072i 0.444664 + 1.65951i 0.716822 + 0.697256i \(0.245596\pi\)
−0.272158 + 0.962253i \(0.587737\pi\)
\(380\) 11.9206i 0.611512i
\(381\) 9.64068 4.41570i 0.493907 0.226223i
\(382\) 11.9409 + 44.5640i 0.610949 + 2.28009i
\(383\) −32.7748 + 8.78199i −1.67471 + 0.448738i −0.966376 0.257134i \(-0.917222\pi\)
−0.708339 + 0.705872i \(0.750555\pi\)
\(384\) 2.33838 + 13.8120i 0.119330 + 0.704840i
\(385\) −2.99203 + 5.81349i −0.152488 + 0.296283i
\(386\) −6.93263 + 4.00256i −0.352862 + 0.203725i
\(387\) 20.7131 + 17.8676i 1.05291 + 0.908260i
\(388\) 4.87216 18.1831i 0.247346 0.923109i
\(389\) −10.6989 + 18.5310i −0.542455 + 0.939559i 0.456308 + 0.889822i \(0.349172\pi\)
−0.998762 + 0.0497371i \(0.984162\pi\)
\(390\) 3.36218 9.07500i 0.170251 0.459530i
\(391\) 5.72737 0.289646
\(392\) 4.63857 5.63365i 0.234283 0.284542i
\(393\) −2.80886 + 29.7652i −0.141688 + 1.50145i
\(394\) 33.8331 + 19.5336i 1.70449 + 0.984087i
\(395\) 10.9469 2.93321i 0.550798 0.147586i
\(396\) 25.1974 1.85844i 1.26622 0.0933899i
\(397\) 16.7692 4.49328i 0.841620 0.225511i 0.187843 0.982199i \(-0.439850\pi\)
0.653777 + 0.756688i \(0.273184\pi\)
\(398\) −38.7666 + 38.7666i −1.94319 + 1.94319i
\(399\) −28.5739 9.07755i −1.43048 0.454446i
\(400\) 10.7284 + 6.19407i 0.536422 + 0.309703i
\(401\) −11.4524 + 11.4524i −0.571905 + 0.571905i −0.932660 0.360755i \(-0.882519\pi\)
0.360755 + 0.932660i \(0.382519\pi\)
\(402\) 27.7681 + 2.62041i 1.38495 + 0.130694i
\(403\) −0.0263092 24.3942i −0.00131055 1.21516i
\(404\) 26.3484 15.2123i 1.31088 0.756839i
\(405\) 2.61735 + 6.03781i 0.130057 + 0.300021i
\(406\) 0.146784 + 0.458098i 0.00728476 + 0.0227350i
\(407\) 9.05746 + 15.6880i 0.448962 + 0.777624i
\(408\) 1.39467 + 8.23781i 0.0690464 + 0.407833i
\(409\) −20.9626 + 20.9626i −1.03653 + 1.03653i −0.0372265 + 0.999307i \(0.511852\pi\)
−0.999307 + 0.0372265i \(0.988148\pi\)
\(410\) −12.8953 + 12.8953i −0.636856 + 0.636856i
\(411\) 5.69211 + 33.6213i 0.280771 + 1.65841i
\(412\) 4.74704 + 8.22211i 0.233870 + 0.405075i
\(413\) −0.227479 + 0.250580i −0.0111935 + 0.0123303i
\(414\) −3.42308 + 7.08672i −0.168235 + 0.348294i
\(415\) −4.18062 + 2.41368i −0.205219 + 0.118483i
\(416\) −14.3856 24.8547i −0.705313 1.21860i
\(417\) −4.29852 0.405640i −0.210499 0.0198643i
\(418\) −33.1377 + 33.1377i −1.62082 + 1.62082i
\(419\) 6.66420 + 3.84758i 0.325567 + 0.187966i 0.653871 0.756606i \(-0.273144\pi\)
−0.328304 + 0.944572i \(0.606477\pi\)
\(420\) 6.16823 5.62756i 0.300979 0.274597i
\(421\) −18.0124 + 18.0124i −0.877871 + 0.877871i −0.993314 0.115443i \(-0.963171\pi\)
0.115443 + 0.993314i \(0.463171\pi\)
\(422\) −29.0417 + 7.78170i −1.41373 + 0.378807i
\(423\) −0.253849 3.44179i −0.0123426 0.167345i
\(424\) −1.12388 + 0.301142i −0.0545803 + 0.0146248i
\(425\) 17.8935 + 10.3308i 0.867963 + 0.501119i
\(426\) −0.239774 + 2.54085i −0.0116171 + 0.123105i
\(427\) −1.46383 + 2.84422i −0.0708399 + 0.137642i
\(428\) −9.08887 −0.439327
\(429\) −19.1799 + 8.80997i −0.926014 + 0.425349i
\(430\) 7.06522 12.2373i 0.340715 0.590136i
\(431\) 6.35822 23.7292i 0.306265 1.14299i −0.625587 0.780155i \(-0.715140\pi\)
0.931851 0.362840i \(-0.118193\pi\)
\(432\) 13.8451 + 4.01521i 0.666122 + 0.193182i
\(433\) 29.7044 17.1498i 1.42750 0.824168i 0.430577 0.902554i \(-0.358310\pi\)
0.996923 + 0.0783862i \(0.0249767\pi\)
\(434\) 17.3613 33.7329i 0.833368 1.61923i
\(435\) 0.0181355 + 0.107120i 0.000869533 + 0.00513602i
\(436\) 17.2949 4.63416i 0.828276 0.221936i
\(437\) −2.09595 7.82221i −0.100263 0.374187i
\(438\) −13.2623 + 6.07452i −0.633698 + 0.290252i
\(439\) 17.0630i 0.814370i −0.913346 0.407185i \(-0.866510\pi\)
0.913346 0.407185i \(-0.133490\pi\)
\(440\) −0.666790 2.48850i −0.0317880 0.118634i
\(441\) −8.79227 19.0708i −0.418680 0.908134i
\(442\) −17.7123 30.6023i −0.842488 1.45560i
\(443\) 14.6489 8.45757i 0.695992 0.401831i −0.109861 0.993947i \(-0.535041\pi\)
0.805853 + 0.592116i \(0.201707\pi\)
\(444\) −3.86157 22.8089i −0.183262 1.08246i
\(445\) 4.46260 + 7.72945i 0.211547 + 0.366411i
\(446\) 11.7781 20.4003i 0.557710 0.965983i
\(447\) −1.02292 + 2.75189i −0.0483825 + 0.130160i
\(448\) −1.44712 29.9472i −0.0683701 1.41487i
\(449\) 5.19161 + 1.39109i 0.245007 + 0.0656495i 0.379233 0.925301i \(-0.376188\pi\)
−0.134226 + 0.990951i \(0.542855\pi\)
\(450\) −23.4772 + 15.9660i −1.10673 + 0.752645i
\(451\) 39.7729 1.87283
\(452\) 9.39092 + 16.2656i 0.441712 + 0.765067i
\(453\) −0.342497 + 0.921395i −0.0160919 + 0.0432909i
\(454\) 4.20170i 0.197196i
\(455\) −3.18524 + 6.20535i −0.149326 + 0.290911i
\(456\) 10.7405 4.91944i 0.502969 0.230374i
\(457\) 16.7676 16.7676i 0.784354 0.784354i −0.196208 0.980562i \(-0.562863\pi\)
0.980562 + 0.196208i \(0.0628628\pi\)
\(458\) 27.8319 16.0687i 1.30050 0.750843i
\(459\) 23.0916 + 6.69679i 1.07782 + 0.312580i
\(460\) 2.17846 + 0.583716i 0.101571 + 0.0272159i
\(461\) 8.82574 32.9381i 0.411056 1.53408i −0.381551 0.924348i \(-0.624610\pi\)
0.792607 0.609733i \(-0.208723\pi\)
\(462\) −32.7908 1.50300i −1.52557 0.0699257i
\(463\) −17.8769 17.8769i −0.830809 0.830809i 0.156819 0.987627i \(-0.449876\pi\)
−0.987627 + 0.156819i \(0.949876\pi\)
\(464\) 0.206109 + 0.118997i 0.00956838 + 0.00552430i
\(465\) 4.96248 6.98523i 0.230129 0.323932i
\(466\) −11.4816 + 42.8498i −0.531874 + 1.98498i
\(467\) 2.68938 + 4.65814i 0.124450 + 0.215553i 0.921518 0.388336i \(-0.126950\pi\)
−0.797068 + 0.603889i \(0.793617\pi\)
\(468\) 26.8787 2.01159i 1.24247 0.0929858i
\(469\) −19.6458 4.25960i −0.907160 0.196690i
\(470\) −1.72198 + 0.461404i −0.0794291 + 0.0212830i
\(471\) 3.99705 + 8.72664i 0.184174 + 0.402103i
\(472\) 0.133353i 0.00613809i
\(473\) −29.7673 + 7.97611i −1.36870 + 0.366742i
\(474\) 36.2747 + 43.8344i 1.66615 + 2.01338i
\(475\) 7.56122 28.2188i 0.346932 1.29477i
\(476\) −1.47241 30.4705i −0.0674877 1.39661i
\(477\) −0.626353 + 3.28914i −0.0286787 + 0.150599i
\(478\) 45.0326i 2.05974i
\(479\) −39.8136 10.6680i −1.81913 0.487435i −0.822449 0.568838i \(-0.807393\pi\)
−0.996681 + 0.0814037i \(0.974060\pi\)
\(480\) 0.947685 10.0425i 0.0432557 0.458376i
\(481\) 9.68065 + 16.7257i 0.441400 + 0.762626i
\(482\) 17.4743i 0.795932i
\(483\) 3.05808 4.77731i 0.139148 0.217375i
\(484\) −0.526614 + 0.912121i −0.0239370 + 0.0414601i
\(485\) −2.76183 + 4.78363i −0.125408 + 0.217213i
\(486\) −22.0874 + 24.5698i −1.00190 + 1.11451i
\(487\) −21.7024 + 21.7024i −0.983428 + 0.983428i −0.999865 0.0164372i \(-0.994768\pi\)
0.0164372 + 0.999865i \(0.494768\pi\)
\(488\) −0.326224 1.21748i −0.0147675 0.0551129i
\(489\) −2.43736 + 6.55706i −0.110221 + 0.296521i
\(490\) −8.82774 + 6.30445i −0.398797 + 0.284806i
\(491\) 6.96387 12.0618i 0.314275 0.544340i −0.665008 0.746836i \(-0.731572\pi\)
0.979283 + 0.202496i \(0.0649053\pi\)
\(492\) −47.6089 17.6970i −2.14638 0.797842i
\(493\) 0.343761 + 0.198470i 0.0154822 + 0.00893866i
\(494\) −35.3135 + 35.3898i −1.58883 + 1.59226i
\(495\) −7.28282 1.38687i −0.327339 0.0623353i
\(496\) −4.85804 18.1305i −0.218132 0.814082i
\(497\) 0.389764 1.79764i 0.0174833 0.0806353i
\(498\) −19.7574 14.0361i −0.885351 0.628974i
\(499\) 0.520510 + 0.139470i 0.0233012 + 0.00624355i 0.270451 0.962734i \(-0.412827\pi\)
−0.247150 + 0.968977i \(0.579494\pi\)
\(500\) 12.1950 + 12.1950i 0.545375 + 0.545375i
\(501\) 13.0251 + 4.84163i 0.581917 + 0.216308i
\(502\) 10.5178 39.2528i 0.469430 1.75194i
\(503\) 5.22046 3.01403i 0.232769 0.134389i −0.379080 0.925364i \(-0.623759\pi\)
0.611849 + 0.790975i \(0.290426\pi\)
\(504\) 7.61600 + 3.23519i 0.339243 + 0.144107i
\(505\) −8.62323 + 2.31059i −0.383729 + 0.102820i
\(506\) −4.43318 7.67849i −0.197079 0.341350i
\(507\) −20.4512 + 9.42064i −0.908270 + 0.418385i
\(508\) 7.62782 13.2118i 0.338430 0.586178i
\(509\) 5.82687 + 5.82687i 0.258272 + 0.258272i 0.824351 0.566079i \(-0.191540\pi\)
−0.566079 + 0.824351i \(0.691540\pi\)
\(510\) 1.16684 12.3648i 0.0516684 0.547524i
\(511\) 10.0121 3.20809i 0.442910 0.141917i
\(512\) −19.7149 19.7149i −0.871282 0.871282i
\(513\) 0.695734 33.9883i 0.0307174 1.50062i
\(514\) −9.49672 9.49672i −0.418882 0.418882i
\(515\) −0.721026 2.69091i −0.0317722 0.118575i
\(516\) 39.1810 + 3.69741i 1.72485 + 0.162769i
\(517\) 3.36709 + 1.94399i 0.148084 + 0.0854966i
\(518\) 1.45064 + 30.0199i 0.0637373 + 1.31900i
\(519\) −12.2318 26.7053i −0.536915 1.17223i
\(520\) −0.714203 2.65399i −0.0313199 0.116385i
\(521\) 1.69103 + 0.976318i 0.0740855 + 0.0427733i 0.536585 0.843846i \(-0.319714\pi\)
−0.462500 + 0.886619i \(0.653047\pi\)
\(522\) −0.451031 + 0.306730i −0.0197411 + 0.0134252i
\(523\) −20.1558 −0.881350 −0.440675 0.897667i \(-0.645261\pi\)
−0.440675 + 0.897667i \(0.645261\pi\)
\(524\) 21.5066 + 37.2505i 0.939519 + 1.62729i
\(525\) 18.1712 9.40928i 0.793058 0.410654i
\(526\) 49.8339 + 13.3530i 2.17286 + 0.582217i
\(527\) −8.10252 30.2390i −0.352951 1.31723i
\(528\) −12.5117 + 10.3539i −0.544502 + 0.450597i
\(529\) −21.4679 −0.933386
\(530\) 1.72958 0.0751281
\(531\) −0.345548 0.166909i −0.0149955 0.00724324i
\(532\) −41.0765 + 13.1617i −1.78089 + 0.570634i
\(533\) 42.4302 0.0457610i 1.83786 0.00198213i
\(534\) −25.9511 + 36.5290i −1.12301 + 1.58076i
\(535\) 2.57606 + 0.690252i 0.111373 + 0.0298422i
\(536\) 6.85973 3.96047i 0.296295 0.171066i
\(537\) −38.1434 3.59950i −1.64601 0.155330i
\(538\) 16.4434 16.4434i 0.708926 0.708926i
\(539\) 23.3360 + 3.89127i 1.00515 + 0.167609i
\(540\) 8.10059 + 4.90061i 0.348594 + 0.210889i
\(541\) −9.27497 + 34.6146i −0.398762 + 1.48820i 0.416515 + 0.909129i \(0.363251\pi\)
−0.815277 + 0.579071i \(0.803415\pi\)
\(542\) 17.2129i 0.739357i
\(543\) −14.4466 10.2632i −0.619962 0.440435i
\(544\) −26.0597 26.0597i −1.11730 1.11730i
\(545\) −5.25383 −0.225050
\(546\) −34.9833 1.56569i −1.49715 0.0670052i
\(547\) −32.5673 −1.39248 −0.696238 0.717811i \(-0.745144\pi\)
−0.696238 + 0.717811i \(0.745144\pi\)
\(548\) 34.6899 + 34.6899i 1.48188 + 1.48188i
\(549\) −3.56309 0.678521i −0.152069 0.0289586i
\(550\) 31.9856i 1.36387i
\(551\) 0.145262 0.542125i 0.00618837 0.0230953i
\(552\) 0.373087 + 2.20369i 0.0158796 + 0.0937953i
\(553\) −22.1941 34.4827i −0.943789 1.46635i
\(554\) 0.664481 0.664481i 0.0282311 0.0282311i
\(555\) −0.637735 + 6.75800i −0.0270703 + 0.286861i
\(556\) −5.37950 + 3.10586i −0.228142 + 0.131718i
\(557\) 23.3051 + 6.24457i 0.987467 + 0.264591i 0.716186 0.697909i \(-0.245886\pi\)
0.271281 + 0.962500i \(0.412553\pi\)
\(558\) 42.2587 + 8.04735i 1.78895 + 0.340672i
\(559\) −31.7469 + 8.54326i −1.34275 + 0.361341i
\(560\) −1.13724 + 5.24509i −0.0480570 + 0.221645i
\(561\) −20.8678 + 17.2689i −0.881037 + 0.729093i
\(562\) 28.0223 1.18205
\(563\) 21.6650 0.913072 0.456536 0.889705i \(-0.349090\pi\)
0.456536 + 0.889705i \(0.349090\pi\)
\(564\) −3.16549 3.82518i −0.133291 0.161069i
\(565\) −1.42638 5.32334i −0.0600084 0.223954i
\(566\) 19.3109 + 5.17434i 0.811697 + 0.217494i
\(567\) 17.9155 15.6855i 0.752381 0.658728i
\(568\) 0.362393 + 0.627683i 0.0152057 + 0.0263370i
\(569\) 8.89470 0.372885 0.186443 0.982466i \(-0.440304\pi\)
0.186443 + 0.982466i \(0.440304\pi\)
\(570\) −17.3144 + 2.93134i −0.725220 + 0.122780i
\(571\) −2.58932 1.49495i −0.108360 0.0625616i 0.444841 0.895610i \(-0.353260\pi\)
−0.553200 + 0.833048i \(0.686594\pi\)
\(572\) −15.1545 + 26.3138i −0.633641 + 1.10024i
\(573\) 34.2793 15.7009i 1.43204 0.655913i
\(574\) 58.6735 + 30.1974i 2.44898 + 1.26042i
\(575\) 4.78668 + 2.76359i 0.199618 + 0.115250i
\(576\) 32.1020 11.1905i 1.33758 0.466272i
\(577\) 7.00616 + 26.1473i 0.291670 + 1.08853i 0.943826 + 0.330443i \(0.107198\pi\)
−0.652156 + 0.758085i \(0.726135\pi\)
\(578\) −6.60905 6.60905i −0.274900 0.274900i
\(579\) 4.17086 + 5.04007i 0.173335 + 0.209458i
\(580\) 0.110525 + 0.110525i 0.00458930 + 0.00458930i
\(581\) 12.9331 + 11.7408i 0.536556 + 0.487091i
\(582\) −27.6087 2.60536i −1.14442 0.107996i
\(583\) −2.66726 2.66726i −0.110466 0.110466i
\(584\) −2.07133 + 3.58765i −0.0857122 + 0.148458i
\(585\) −7.77100 1.47115i −0.321291 0.0608247i
\(586\) 3.54626 + 6.14230i 0.146495 + 0.253736i
\(587\) −11.3759 + 3.04816i −0.469534 + 0.125811i −0.485825 0.874056i \(-0.661481\pi\)
0.0162914 + 0.999867i \(0.494814\pi\)
\(588\) −26.2022 15.0413i −1.08056 0.620293i
\(589\) −38.3341 + 22.1322i −1.57953 + 0.911941i
\(590\) −0.0513057 + 0.191475i −0.00211222 + 0.00788291i
\(591\) 11.1241 29.9263i 0.457584 1.23101i
\(592\) 10.5145 + 10.5145i 0.432142 + 0.432142i
\(593\) −30.4230 8.15183i −1.24932 0.334756i −0.427249 0.904134i \(-0.640517\pi\)
−0.822076 + 0.569378i \(0.807184\pi\)
\(594\) −8.89553 36.1417i −0.364988 1.48291i
\(595\) −1.89675 + 8.74806i −0.0777591 + 0.358636i
\(596\) 1.09320 + 4.07987i 0.0447792 + 0.167118i
\(597\) 36.5253 + 25.9484i 1.49488 + 1.06200i
\(598\) −4.73820 8.18640i −0.193759 0.334767i
\(599\) 38.0326 + 21.9581i 1.55397 + 0.897185i 0.997813 + 0.0661072i \(0.0210579\pi\)
0.556157 + 0.831077i \(0.312275\pi\)
\(600\) −2.80934 + 7.55775i −0.114691 + 0.308544i
\(601\) −3.50137 + 6.06455i −0.142824 + 0.247378i −0.928559 0.371185i \(-0.878952\pi\)
0.785735 + 0.618563i \(0.212285\pi\)
\(602\) −49.9688 10.8342i −2.03658 0.441570i
\(603\) −1.67661 22.7321i −0.0682769 0.925724i
\(604\) 0.366028 + 1.36603i 0.0148935 + 0.0555831i
\(605\) 0.218529 0.218529i 0.00888446 0.00888446i
\(606\) −28.5748 34.5298i −1.16077 1.40268i
\(607\) −4.12251 + 7.14039i −0.167327 + 0.289819i −0.937479 0.348041i \(-0.886847\pi\)
0.770152 + 0.637860i \(0.220180\pi\)
\(608\) −26.0547 + 45.1280i −1.05666 + 1.83018i
\(609\) 0.349096 0.180766i 0.0141461 0.00732501i
\(610\) 1.87363i 0.0758612i
\(611\) 3.59429 + 2.07000i 0.145409 + 0.0837432i
\(612\) 32.6629 11.3861i 1.32032 0.460255i
\(613\) −41.7472 11.1861i −1.68615 0.451803i −0.716760 0.697320i \(-0.754376\pi\)
−0.969392 + 0.245516i \(0.921042\pi\)
\(614\) 11.1242i 0.448935i
\(615\) 12.1498 + 8.63150i 0.489927 + 0.348056i
\(616\) −7.83877 + 5.04526i −0.315833 + 0.203279i
\(617\) −11.1128 + 41.4737i −0.447386 + 1.66967i 0.262173 + 0.965021i \(0.415561\pi\)
−0.709559 + 0.704646i \(0.751106\pi\)
\(618\) 10.7751 8.91685i 0.433439 0.358688i
\(619\) −17.5737 + 4.70885i −0.706345 + 0.189265i −0.594071 0.804413i \(-0.702480\pi\)
−0.112274 + 0.993677i \(0.535814\pi\)
\(620\) 12.3275i 0.495083i
\(621\) 6.17722 + 1.79145i 0.247883 + 0.0718885i
\(622\) 29.7693 7.97666i 1.19364 0.319835i
\(623\) 21.7073 23.9117i 0.869683 0.958002i
\(624\) −13.3357 + 11.0601i −0.533856 + 0.442758i
\(625\) 8.63313 + 14.9530i 0.345325 + 0.598121i
\(626\) −5.66732 + 21.1507i −0.226512 + 0.845353i
\(627\) 31.2218 + 22.1807i 1.24688 + 0.885812i
\(628\) 11.9592 + 6.90462i 0.477222 + 0.275524i
\(629\) 17.5366 + 17.5366i 0.699231 + 0.699231i
\(630\) −9.69073 7.57538i −0.386088 0.301811i
\(631\) −5.81585 + 21.7050i −0.231525 + 0.864064i 0.748159 + 0.663519i \(0.230938\pi\)
−0.979684 + 0.200545i \(0.935729\pi\)
\(632\) 15.6077 + 4.18208i 0.620843 + 0.166354i
\(633\) 10.2320 + 22.3393i 0.406687 + 0.887907i
\(634\) 47.9412 27.6788i 1.90399 1.09927i
\(635\) −3.16532 + 3.16532i −0.125612 + 0.125612i
\(636\) 2.00596 + 4.37955i 0.0795414 + 0.173661i
\(637\) 24.8996 + 4.12440i 0.986557 + 0.163415i
\(638\) 0.614491i 0.0243279i
\(639\) 2.08005 0.153414i 0.0822854 0.00606897i
\(640\) −2.95687 5.12145i −0.116880 0.202443i
\(641\) −17.8697 −0.705813 −0.352906 0.935659i \(-0.614807\pi\)
−0.352906 + 0.935659i \(0.614807\pi\)
\(642\) 2.23501 + 13.2014i 0.0882088 + 0.521018i
\(643\) 13.6671 + 3.66210i 0.538979 + 0.144419i 0.518031 0.855362i \(-0.326665\pi\)
0.0209476 + 0.999781i \(0.493332\pi\)
\(644\) −0.393883 8.15113i −0.0155211 0.321199i
\(645\) −10.8243 4.02355i −0.426205 0.158427i
\(646\) −32.0798 + 55.5638i −1.26216 + 2.18613i
\(647\) −7.12070 12.3334i −0.279943 0.484876i 0.691427 0.722446i \(-0.256982\pi\)
−0.971370 + 0.237570i \(0.923649\pi\)
\(648\) −1.07248 + 9.32108i −0.0421309 + 0.366166i
\(649\) 0.374403 0.216161i 0.0146966 0.00848508i
\(650\) −0.0368013 34.1226i −0.00144347 1.33840i
\(651\) −29.5492 9.38741i −1.15813 0.367921i
\(652\) 2.60482 + 9.72131i 0.102013 + 0.380716i
\(653\) 22.1580i 0.867110i −0.901127 0.433555i \(-0.857259\pi\)
0.901127 0.433555i \(-0.142741\pi\)
\(654\) −10.9839 23.9810i −0.429506 0.937729i
\(655\) −3.26662 12.1912i −0.127638 0.476350i
\(656\) 31.5353 8.44985i 1.23125 0.329911i
\(657\) 6.70385 + 9.85768i 0.261542 + 0.384585i
\(658\) 3.49121 + 5.42425i 0.136101 + 0.211459i
\(659\) 5.24635 3.02898i 0.204369 0.117992i −0.394323 0.918972i \(-0.629021\pi\)
0.598692 + 0.800980i \(0.295687\pi\)
\(660\) −9.69723 + 4.44160i −0.377464 + 0.172889i
\(661\) −4.00469 + 14.9457i −0.155764 + 0.581320i 0.843274 + 0.537483i \(0.180625\pi\)
−0.999039 + 0.0438368i \(0.986042\pi\)
\(662\) 4.83089 8.36735i 0.187758 0.325206i
\(663\) −22.2421 + 18.4467i −0.863811 + 0.716409i
\(664\) −6.88272 −0.267101
\(665\) 12.6419 0.610886i 0.490231 0.0236892i
\(666\) −32.1799 + 11.2177i −1.24695 + 0.434678i
\(667\) 0.0919591 + 0.0530926i 0.00356067 + 0.00205575i
\(668\) 19.3106 5.17426i 0.747150 0.200198i
\(669\) −18.0446 6.70748i −0.697646 0.259326i
\(670\) −11.3733 + 3.04746i −0.439388 + 0.117734i
\(671\) 2.88941 2.88941i 0.111544 0.111544i
\(672\) −35.6513 + 7.82256i −1.37528 + 0.301762i
\(673\) 28.9412 + 16.7092i 1.11560 + 0.644092i 0.940274 0.340418i \(-0.110569\pi\)
0.175327 + 0.984510i \(0.443902\pi\)
\(674\) −34.8902 + 34.8902i −1.34392 + 1.34392i
\(675\) 16.0676 + 16.7391i 0.618441 + 0.644289i
\(676\) −16.1367 + 28.0894i −0.620643 + 1.08036i
\(677\) −8.18026 + 4.72287i −0.314393 + 0.181515i −0.648891 0.760882i \(-0.724767\pi\)
0.334498 + 0.942397i \(0.391433\pi\)
\(678\) 21.3161 17.6399i 0.818640 0.677458i
\(679\) 19.5330 + 4.23514i 0.749610 + 0.162530i
\(680\) −1.76355 3.05456i −0.0676291 0.117137i
\(681\) 3.38559 0.573184i 0.129736 0.0219645i
\(682\) −34.2688 + 34.2688i −1.31222 + 1.31222i
\(683\) −11.3328 + 11.3328i −0.433636 + 0.433636i −0.889863 0.456227i \(-0.849200\pi\)
0.456227 + 0.889863i \(0.349200\pi\)
\(684\) −27.5038 40.4429i −1.05163 1.54637i
\(685\) −7.19764 12.4667i −0.275008 0.476327i
\(686\) 31.4711 + 23.4582i 1.20157 + 0.895638i
\(687\) −16.7444 20.2340i −0.638839 0.771974i
\(688\) −21.9074 + 12.6483i −0.835213 + 0.482210i
\(689\) −2.84853 2.84239i −0.108520 0.108286i
\(690\) 0.312140 3.30770i 0.0118829 0.125922i
\(691\) −5.69907 + 5.69907i −0.216803 + 0.216803i −0.807150 0.590347i \(-0.798991\pi\)
0.590347 + 0.807150i \(0.298991\pi\)
\(692\) −36.5974 21.1295i −1.39123 0.803225i
\(693\) 3.26216 + 26.6268i 0.123919 + 1.01147i
\(694\) 30.9116 30.9116i 1.17339 1.17339i
\(695\) 1.76058 0.471747i 0.0667828 0.0178944i
\(696\) −0.0539715 + 0.145196i −0.00204578 + 0.00550362i
\(697\) 52.5964 14.0932i 1.99223 0.533816i
\(698\) −34.0380 19.6519i −1.28836 0.743834i
\(699\) 36.0933 + 3.40603i 1.36517 + 0.128828i
\(700\) 13.4721 26.1763i 0.509199 0.989372i
\(701\) −26.0188 −0.982718 −0.491359 0.870957i \(-0.663500\pi\)
−0.491359 + 0.870957i \(0.663500\pi\)
\(702\) −9.53144 38.5461i −0.359741 1.45483i
\(703\) 17.5332 30.3684i 0.661277 1.14537i
\(704\) −9.91273 + 36.9948i −0.373600 + 1.39429i
\(705\) 0.606692 + 1.32457i 0.0228493 + 0.0498863i
\(706\) −45.9602 + 26.5351i −1.72974 + 0.998663i
\(707\) 17.4830 + 27.1632i 0.657517 + 1.02158i
\(708\) −0.544348 + 0.0921587i −0.0204579 + 0.00346354i
\(709\) −21.5867 + 5.78414i −0.810705 + 0.217228i −0.640279 0.768143i \(-0.721181\pi\)
−0.170427 + 0.985370i \(0.554515\pi\)
\(710\) −0.278850 1.04068i −0.0104651 0.0390561i
\(711\) 30.3718 35.2087i 1.13903 1.32043i
\(712\) 12.7253i 0.476900i
\(713\) −2.16750 8.08921i −0.0811734 0.302943i
\(714\) −43.8957 + 9.63152i −1.64275 + 0.360451i
\(715\) 6.29363 6.30722i 0.235369 0.235877i
\(716\) −47.7357 + 27.5602i −1.78397 + 1.02997i
\(717\) −36.2858 + 6.14322i −1.35512 + 0.229423i
\(718\) −5.63229 9.75540i −0.210195 0.364068i
\(719\) 17.7947 30.8213i 0.663631 1.14944i −0.316024 0.948751i \(-0.602348\pi\)
0.979655 0.200691i \(-0.0643187\pi\)
\(720\) −6.06908 + 0.447625i −0.226181 + 0.0166820i
\(721\) −8.47636 + 5.45563i −0.315676 + 0.203178i
\(722\) 48.7299 + 13.0571i 1.81354 + 0.485936i
\(723\) 14.0802 2.38379i 0.523649 0.0886542i
\(724\) −25.4951 −0.947520
\(725\) 0.191533 + 0.331745i 0.00711336 + 0.0123207i
\(726\) 1.45434 + 0.540599i 0.0539755 + 0.0200635i
\(727\) 21.5268i 0.798387i 0.916867 + 0.399193i \(0.130710\pi\)
−0.916867 + 0.399193i \(0.869290\pi\)
\(728\) −8.35668 + 5.39136i −0.309719 + 0.199817i
\(729\) 22.8106 + 14.4456i 0.844839 + 0.535021i
\(730\) 4.35441 4.35441i 0.161164 0.161164i
\(731\) −36.5385 + 21.0955i −1.35142 + 0.780245i
\(732\) −4.74432 + 2.17303i −0.175355 + 0.0803176i
\(733\) 13.4259 + 3.59745i 0.495895 + 0.132875i 0.498094 0.867123i \(-0.334033\pi\)
−0.00219907 + 0.999998i \(0.500700\pi\)
\(734\) 3.33938 12.4627i 0.123259 0.460008i
\(735\) 6.28418 + 6.25307i 0.231795 + 0.230648i
\(736\) −6.97122 6.97122i −0.256962 0.256962i
\(737\) 22.2388 + 12.8396i 0.819177 + 0.472952i
\(738\) −13.9972 + 73.5028i −0.515244 + 2.70568i
\(739\) 13.0058 48.5383i 0.478426 1.78551i −0.129571 0.991570i \(-0.541360\pi\)
0.607997 0.793940i \(-0.291973\pi\)
\(740\) 4.88294 + 8.45749i 0.179500 + 0.310904i
\(741\) 33.3333 + 23.6267i 1.22453 + 0.867949i
\(742\) −1.90966 5.95987i −0.0701060 0.218794i
\(743\) −11.1097 + 2.97684i −0.407575 + 0.109209i −0.456781 0.889579i \(-0.650998\pi\)
0.0492056 + 0.998789i \(0.484331\pi\)
\(744\) 11.1071 5.08736i 0.407206 0.186512i
\(745\) 1.23938i 0.0454074i
\(746\) 18.5475 4.96978i 0.679071 0.181956i
\(747\) −8.61461 + 17.8347i −0.315192 + 0.652536i
\(748\) −10.0859 + 37.6413i −0.368779 + 1.37630i
\(749\) −0.465772 9.63882i −0.0170189 0.352195i
\(750\) 14.7141 20.7118i 0.537284 0.756287i
\(751\) 6.28993i 0.229523i 0.993393 + 0.114761i \(0.0366104\pi\)
−0.993393 + 0.114761i \(0.963390\pi\)
\(752\) 3.08272 + 0.826012i 0.112415 + 0.0301215i
\(753\) −33.0634 3.12011i −1.20490 0.113703i
\(754\) −0.000707007 0.655546i −2.57477e−5 0.0238736i
\(755\) 0.414972i 0.0151024i
\(756\) 7.94274 33.3243i 0.288875 1.21199i
\(757\) 6.93177 12.0062i 0.251940 0.436372i −0.712120 0.702058i \(-0.752265\pi\)
0.964060 + 0.265685i \(0.0855982\pi\)
\(758\) 35.4438 61.3904i 1.28738 2.22980i
\(759\) −5.58231 + 4.61959i −0.202625 + 0.167680i
\(760\) −3.52641 + 3.52641i −0.127916 + 0.127916i
\(761\) 2.48344 + 9.26831i 0.0900245 + 0.335976i 0.996218 0.0868868i \(-0.0276919\pi\)
−0.906194 + 0.422863i \(0.861025\pi\)
\(762\) −21.0656 7.83040i −0.763125 0.283665i
\(763\) 5.80087 + 18.1039i 0.210006 + 0.655406i
\(764\) 27.1222 46.9770i 0.981245 1.69957i
\(765\) −10.1224 + 0.746576i −0.365975 + 0.0269925i
\(766\) 62.2790 + 35.9568i 2.25023 + 1.29917i
\(767\) 0.399168 0.231034i 0.0144131 0.00834217i
\(768\) −5.54018 + 7.79842i −0.199914 + 0.281401i
\(769\) −4.78937 17.8742i −0.172709 0.644559i −0.996931 0.0782915i \(-0.975054\pi\)
0.824221 0.566268i \(-0.191613\pi\)
\(770\) 13.1964 4.22839i 0.475564 0.152380i
\(771\) −6.35663 + 8.94766i −0.228929 + 0.322242i
\(772\) 9.09128 + 2.43600i 0.327202 + 0.0876736i
\(773\) 26.8965 + 26.8965i 0.967401 + 0.967401i 0.999485 0.0320840i \(-0.0102144\pi\)
−0.0320840 + 0.999485i \(0.510214\pi\)
\(774\) −4.26443 57.8188i −0.153282 2.07825i
\(775\) 7.81931 29.1821i 0.280878 1.04825i
\(776\) −6.82035 + 3.93773i −0.244836 + 0.141356i
\(777\) 23.9912 5.26411i 0.860679 0.188849i
\(778\) 43.8053 11.7376i 1.57050 0.420813i
\(779\) −38.4957 66.6765i −1.37925 2.38893i
\(780\) −10.3400 + 4.74951i −0.370232 + 0.170060i
\(781\) −1.17485 + 2.03491i −0.0420396 + 0.0728147i
\(782\) −8.58331 8.58331i −0.306938 0.306938i
\(783\) 0.308682 + 0.321583i 0.0110314 + 0.0114924i
\(784\) 19.3294 1.87246i 0.690337 0.0668737i
\(785\) −2.86521 2.86521i −0.102264 0.102264i
\(786\) 48.8170 40.3980i 1.74124 1.44095i
\(787\) 5.57088 + 5.57088i 0.198580 + 0.198580i 0.799391 0.600811i \(-0.205155\pi\)
−0.600811 + 0.799391i \(0.705155\pi\)
\(788\) −11.8884 44.3679i −0.423505 1.58054i
\(789\) 3.96118 41.9761i 0.141022 1.49439i
\(790\) −20.8014 12.0097i −0.740080 0.427285i
\(791\) −16.7685 + 10.7927i −0.596220 + 0.383745i
\(792\) −8.00381 6.90426i −0.284403 0.245332i
\(793\) 3.07913 3.08578i 0.109343 0.109579i
\(794\) −31.8649 18.3972i −1.13084 0.652892i
\(795\) −0.235944 1.39364i −0.00836808 0.0494273i
\(796\) 64.4594 2.28470
\(797\) −13.5393 23.4507i −0.479585 0.830666i 0.520141 0.854081i \(-0.325879\pi\)
−0.999726 + 0.0234148i \(0.992546\pi\)
\(798\) 29.2181 + 56.4262i 1.03431 + 1.99747i
\(799\) 5.14153 + 1.37767i 0.181894 + 0.0487385i
\(800\) −9.20512 34.3540i −0.325450 1.21460i
\(801\) 32.9740 + 15.9273i 1.16508 + 0.562765i
\(802\) 34.3262 1.21210
\(803\) −13.4302 −0.473942
\(804\) −20.9073 25.2644i −0.737343 0.891007i
\(805\) −0.507398 + 2.34019i −0.0178834 + 0.0824807i
\(806\) −36.5189 + 36.5978i −1.28632 + 1.28910i
\(807\) −15.4927 11.0064i −0.545370 0.387444i
\(808\) −12.2947 3.29437i −0.432527 0.115895i
\(809\) 14.3892 8.30762i 0.505898 0.292080i −0.225248 0.974301i \(-0.572319\pi\)
0.731146 + 0.682221i \(0.238986\pi\)
\(810\) 5.12606 12.9710i 0.180111 0.455756i
\(811\) −18.8866 + 18.8866i −0.663197 + 0.663197i −0.956132 0.292935i \(-0.905368\pi\)
0.292935 + 0.956132i \(0.405368\pi\)
\(812\) 0.258820 0.502886i 0.00908279 0.0176478i
\(813\) 13.8696 2.34813i 0.486428 0.0823526i
\(814\) 9.93681 37.0847i 0.348285 1.29982i
\(815\) 2.95313i 0.103444i
\(816\) −12.8769 + 18.1256i −0.450781 + 0.634524i
\(817\) 42.1828 + 42.1828i 1.47579 + 1.47579i
\(818\) 62.8311 2.19684
\(819\) 3.51075 + 28.4020i 0.122675 + 0.992447i
\(820\) 21.4418 0.748781
\(821\) −13.1593 13.1593i −0.459263 0.459263i 0.439151 0.898413i \(-0.355279\pi\)
−0.898413 + 0.439151i \(0.855279\pi\)
\(822\) 41.8560 58.9169i 1.45989 2.05496i
\(823\) 3.32649i 0.115954i 0.998318 + 0.0579771i \(0.0184650\pi\)
−0.998318 + 0.0579771i \(0.981535\pi\)
\(824\) 1.02802 3.83661i 0.0358127 0.133655i
\(825\) −25.7730 + 4.36339i −0.897300 + 0.151914i
\(826\) 0.716443 0.0346203i 0.0249282 0.00120459i
\(827\) 33.0646 33.0646i 1.14977 1.14977i 0.163169 0.986598i \(-0.447828\pi\)
0.986598 0.163169i \(-0.0521717\pi\)
\(828\) 8.73762 3.04588i 0.303653 0.105852i
\(829\) −37.3853 + 21.5844i −1.29845 + 0.749659i −0.980136 0.198328i \(-0.936449\pi\)
−0.318311 + 0.947986i \(0.603116\pi\)
\(830\) 9.88254 + 2.64802i 0.343028 + 0.0919141i
\(831\) −0.626064 0.444771i −0.0217179 0.0154289i
\(832\) −10.5324 + 39.4779i −0.365147 + 1.36865i
\(833\) 32.2388 3.12300i 1.11701 0.108206i
\(834\) 5.83405 + 7.04987i 0.202017 + 0.244117i
\(835\) −5.86616 −0.203007
\(836\) 55.0999 1.90567
\(837\) 0.719483 35.1485i 0.0248690 1.21491i
\(838\) −4.22112 15.7534i −0.145816 0.544194i
\(839\) −2.71003 0.726151i −0.0935607 0.0250695i 0.211735 0.977327i \(-0.432089\pi\)
−0.305296 + 0.952258i \(0.598755\pi\)
\(840\) −3.48950 0.159945i −0.120399 0.00551861i
\(841\) −14.4963 25.1084i −0.499873 0.865806i
\(842\) 53.9885 1.86057
\(843\) −3.82273 22.5795i −0.131662 0.777679i
\(844\) 30.6142 + 17.6751i 1.05378 + 0.608402i
\(845\) 6.70686 6.73586i 0.230723 0.231721i
\(846\) −4.77759 + 5.53845i −0.164257 + 0.190416i
\(847\) −0.994300 0.511735i −0.0341645 0.0175834i
\(848\) −2.68149 1.54816i −0.0920827 0.0531640i
\(849\) 1.53498 16.2660i 0.0526802 0.558246i
\(850\) −11.3338 42.2983i −0.388746 1.45082i
\(851\) 4.69121 + 4.69121i 0.160812 + 0.160812i
\(852\) 2.31176 1.91307i 0.0791994 0.0655407i
\(853\) −29.4036 29.4036i −1.00676 1.00676i −0.999977 0.00678201i \(-0.997841\pi\)
−0.00678201 0.999977i \(-0.502159\pi\)
\(854\) 6.45626 2.06872i 0.220929 0.0707901i
\(855\) 4.72396 + 13.5515i 0.161556 + 0.463451i
\(856\) 2.68872 + 2.68872i 0.0918986 + 0.0918986i
\(857\) −2.43678 + 4.22062i −0.0832388 + 0.144174i −0.904639 0.426178i \(-0.859860\pi\)
0.821401 + 0.570352i \(0.193193\pi\)
\(858\) 41.9469 + 15.5409i 1.43204 + 0.530556i
\(859\) −4.56467 7.90624i −0.155745 0.269758i 0.777585 0.628777i \(-0.216444\pi\)
−0.933330 + 0.359020i \(0.883111\pi\)
\(860\) −16.0477 + 4.29998i −0.547223 + 0.146628i
\(861\) 16.3280 51.3966i 0.556458 1.75159i
\(862\) −45.0904 + 26.0330i −1.53579 + 0.886686i
\(863\) −10.1300 + 37.8057i −0.344829 + 1.28692i 0.547982 + 0.836490i \(0.315396\pi\)
−0.892812 + 0.450430i \(0.851271\pi\)
\(864\) −19.9554 36.2577i −0.678896 1.23351i
\(865\) 8.76813 + 8.76813i 0.298125 + 0.298125i
\(866\) −70.2179 18.8148i −2.38610 0.639354i
\(867\) −4.42377 + 6.22694i −0.150239 + 0.211478i
\(868\) −42.4786 + 13.6110i −1.44182 + 0.461988i
\(869\) 13.5580 + 50.5993i 0.459925 + 1.71646i
\(870\) 0.133357 0.187714i 0.00452121 0.00636411i
\(871\) 23.7394 + 13.6718i 0.804378 + 0.463252i
\(872\) −6.48719 3.74538i −0.219684 0.126835i
\(873\) 1.66699 + 22.6016i 0.0564189 + 0.764949i
\(874\) −8.58163 + 14.8638i −0.290278 + 0.502776i
\(875\) −12.3079 + 13.5578i −0.416084 + 0.458338i
\(876\) 16.0762 + 5.97579i 0.543166 + 0.201903i
\(877\) −1.32594 4.94847i −0.0447738 0.167098i 0.939919 0.341398i \(-0.110900\pi\)
−0.984693 + 0.174300i \(0.944234\pi\)
\(878\) −25.5713 + 25.5713i −0.862991 + 0.862991i
\(879\) 4.46550 3.69538i 0.150617 0.124642i
\(880\) 3.42794 5.93736i 0.115556 0.200148i
\(881\) 13.5444 23.4597i 0.456324 0.790376i −0.542439 0.840095i \(-0.682499\pi\)
0.998763 + 0.0497189i \(0.0158325\pi\)
\(882\) −15.4039 + 41.7569i −0.518676 + 1.40603i
\(883\) 1.71194i 0.0576115i −0.999585 0.0288058i \(-0.990830\pi\)
0.999585 0.0288058i \(-0.00917043\pi\)
\(884\) −10.7165 + 40.1677i −0.360435 + 1.35099i
\(885\) 0.161284 + 0.0152199i 0.00542149 + 0.000511612i
\(886\) −34.6285 9.27868i −1.16337 0.311723i
\(887\) 40.5767i 1.36243i −0.732082 0.681217i \(-0.761451\pi\)
0.732082 0.681217i \(-0.238549\pi\)
\(888\) −5.60512 + 7.88983i −0.188096 + 0.264765i
\(889\) 14.4021 + 7.41231i 0.483031 + 0.248601i
\(890\) 4.89585 18.2716i 0.164109 0.612465i
\(891\) −27.9083 + 12.0981i −0.934963 + 0.405301i
\(892\) −26.7525 + 7.16830i −0.895739 + 0.240012i
\(893\) 7.52626i 0.251857i
\(894\) 5.65711 2.59111i 0.189202 0.0866598i
\(895\) 15.6228 4.18611i 0.522212 0.139926i
\(896\) −14.3830 + 15.8436i −0.480502 + 0.529298i
\(897\) −5.94996 + 4.93465i −0.198663 + 0.164763i
\(898\) −5.69564 9.86514i −0.190066 0.329204i
\(899\) 0.150220 0.560630i 0.00501013 0.0186981i
\(900\) 32.7922 + 6.24465i 1.09307 + 0.208155i
\(901\) −4.47234 2.58211i −0.148995 0.0860225i
\(902\) −59.6055 59.6055i −1.98465 1.98465i
\(903\) −1.91325 + 41.7412i −0.0636689 + 1.38906i
\(904\) 2.03369 7.58985i 0.0676397 0.252435i
\(905\) 7.22608 + 1.93622i 0.240203 + 0.0643622i
\(906\) 1.89413 0.867564i 0.0629282 0.0288229i
\(907\) 3.94728 2.27896i 0.131067 0.0756716i −0.433033 0.901378i \(-0.642557\pi\)
0.564100 + 0.825707i \(0.309223\pi\)
\(908\) 3.49320 3.49320i 0.115926 0.115926i
\(909\) −23.9249 + 27.7351i −0.793539 + 0.919915i
\(910\) 14.0732 4.52608i 0.466521 0.150038i
\(911\) 48.9686i 1.62240i −0.584767 0.811202i \(-0.698814\pi\)
0.584767 0.811202i \(-0.301186\pi\)
\(912\) 29.4676 + 10.9536i 0.975769 + 0.362709i
\(913\) −11.1567 19.3239i −0.369231 0.639528i
\(914\) −50.2574 −1.66237
\(915\) 1.50971 0.255596i 0.0499096 0.00844973i
\(916\) −36.4980 9.77962i −1.20593 0.323128i
\(917\) −38.4023 + 24.7169i −1.26816 + 0.816223i
\(918\) −24.5701 44.6423i −0.810933 1.47342i
\(919\) 9.49195 16.4405i 0.313111 0.542323i −0.665923 0.746020i \(-0.731962\pi\)
0.979034 + 0.203697i \(0.0652956\pi\)
\(920\) −0.471766 0.817122i −0.0155537 0.0269397i
\(921\) −8.96349 + 1.51753i −0.295357 + 0.0500042i
\(922\) −62.5893 + 36.1359i −2.06127 + 1.19007i
\(923\) −1.25101 + 2.17221i −0.0411774 + 0.0714993i
\(924\) 26.0120 + 28.5111i 0.855732 + 0.937947i
\(925\) 6.19449 + 23.1182i 0.203674 + 0.760120i
\(926\) 53.5822i 1.76082i
\(927\) −8.65482 7.46584i −0.284262 0.245210i
\(928\) −0.176844 0.659990i −0.00580519 0.0216652i
\(929\) −16.1082 + 4.31617i −0.528492 + 0.141609i −0.513192 0.858274i \(-0.671537\pi\)
−0.0153002 + 0.999883i \(0.504870\pi\)
\(930\) −17.9054 + 3.03140i −0.587141 + 0.0994035i
\(931\) −16.0632 42.8875i −0.526449 1.40558i
\(932\) 45.1700 26.0789i 1.47959 0.854242i
\(933\) −10.4884 22.8990i −0.343374 0.749679i
\(934\) 2.95048 11.0113i 0.0965426 0.360302i
\(935\) 5.71731 9.90268i 0.186976 0.323852i
\(936\) −8.54650 7.35634i −0.279351 0.240449i
\(937\) 37.2586 1.21719 0.608593 0.793483i \(-0.291734\pi\)
0.608593 + 0.793483i \(0.291734\pi\)
\(938\) 23.0585 + 35.8258i 0.752888 + 1.16975i
\(939\) 17.8157 + 1.68122i 0.581393 + 0.0548645i
\(940\) 1.81522 + 1.04802i 0.0592060 + 0.0341826i
\(941\) 11.8534 3.17612i 0.386411 0.103538i −0.0603833 0.998175i \(-0.519232\pi\)
0.446794 + 0.894637i \(0.352566\pi\)
\(942\) 7.08800 19.0683i 0.230939 0.621280i
\(943\) 14.0700 3.77005i 0.458182 0.122770i
\(944\) 0.250934 0.250934i 0.00816720 0.00816720i
\(945\) −4.78202 + 8.84189i −0.155559 + 0.287627i
\(946\) 56.5640 + 32.6572i 1.83905 + 1.06178i
\(947\) 28.4447 28.4447i 0.924327 0.924327i −0.0730043 0.997332i \(-0.523259\pi\)
0.997332 + 0.0730043i \(0.0232587\pi\)
\(948\) 6.28496 66.6010i 0.204126 2.16310i
\(949\) −14.3275 + 0.0154522i −0.465091 + 0.000501601i
\(950\) −53.6217 + 30.9585i −1.73972 + 1.00443i
\(951\) −28.8427 34.8536i −0.935289 1.13020i
\(952\) −8.57838 + 9.44953i −0.278027 + 0.306261i
\(953\) −26.4924 45.8861i −0.858172 1.48640i −0.873671 0.486517i \(-0.838267\pi\)
0.0154992 0.999880i \(-0.495066\pi\)
\(954\) 5.86794 3.99058i 0.189982 0.129200i
\(955\) −11.2549 + 11.2549i −0.364199 + 0.364199i
\(956\) −37.4392 + 37.4392i −1.21087 + 1.21087i
\(957\) −0.495137 + 0.0838271i −0.0160055 + 0.00270974i
\(958\) 43.6790 + 75.6542i 1.41120 + 2.44428i
\(959\) −35.0112 + 38.5667i −1.13057 + 1.24538i
\(960\) −11.0567 + 9.14989i −0.356855 + 0.295311i
\(961\) −12.7958 + 7.38765i −0.412767 + 0.238311i
\(962\) 10.5580 39.5738i 0.340405 1.27591i
\(963\) 10.3324 3.60179i 0.332956 0.116066i
\(964\) 14.5278 14.5278i 0.467908 0.467908i
\(965\) −2.39174 1.38087i −0.0769928 0.0444518i
\(966\) −11.7425 + 2.57652i −0.377809 + 0.0828982i
\(967\) 28.2397 28.2397i 0.908127 0.908127i −0.0879936 0.996121i \(-0.528045\pi\)
0.996121 + 0.0879936i \(0.0280455\pi\)
\(968\) 0.425615 0.114043i 0.0136798 0.00366549i
\(969\) 49.1478 + 18.2690i 1.57885 + 0.586885i
\(970\) 11.3080 3.02996i 0.363077 0.0972862i
\(971\) 19.8225 + 11.4445i 0.636134 + 0.367272i 0.783124 0.621866i \(-0.213625\pi\)
−0.146990 + 0.989138i \(0.546959\pi\)
\(972\) 38.7898 2.06381i 1.24418 0.0661968i
\(973\) −3.56947 5.54584i −0.114432 0.177792i
\(974\) 65.0484 2.08428
\(975\) −27.4899 + 4.68456i −0.880381 + 0.150026i
\(976\) 1.67710 2.90483i 0.0536827 0.0929812i
\(977\) −10.7000 + 39.9329i −0.342323 + 1.27757i 0.553386 + 0.832925i \(0.313335\pi\)
−0.895709 + 0.444641i \(0.853331\pi\)
\(978\) 13.4795 6.17398i 0.431026 0.197422i
\(979\) −35.7275 + 20.6273i −1.14185 + 0.659250i
\(980\) 12.5806 + 2.09781i 0.401872 + 0.0670121i
\(981\) −17.8247 + 12.1219i −0.569098 + 0.387023i
\(982\) −28.5127 + 7.63996i −0.909877 + 0.243801i
\(983\) −13.6194 50.8284i −0.434392 1.62117i −0.742516 0.669828i \(-0.766368\pi\)
0.308124 0.951346i \(-0.400299\pi\)
\(984\) 8.84873 + 19.3192i 0.282087 + 0.615873i
\(985\) 13.4781i 0.429446i
\(986\) −0.217739 0.812613i −0.00693422 0.0258789i
\(987\) 3.89442 3.55306i 0.123961 0.113095i
\(988\) 58.7812 0.0633956i 1.87008 0.00201688i
\(989\) −9.77437 + 5.64324i −0.310807 + 0.179444i
\(990\) 8.83595 + 12.9928i 0.280825 + 0.412939i
\(991\) −14.5415 25.1866i −0.461925 0.800077i 0.537132 0.843498i \(-0.319508\pi\)
−0.999057 + 0.0434210i \(0.986174\pi\)
\(992\) −26.9440 + 46.6684i −0.855473 + 1.48172i
\(993\) −7.40115 2.75112i −0.234868 0.0873043i
\(994\) −3.27815 + 2.10991i −0.103977 + 0.0669224i
\(995\) −18.2697 4.89536i −0.579189 0.155193i
\(996\) 4.75655 + 28.0952i 0.150717 + 0.890232i
\(997\) −19.5926 −0.620504 −0.310252 0.950654i \(-0.600413\pi\)
−0.310252 + 0.950654i \(0.600413\pi\)
\(998\) −0.571045 0.989078i −0.0180761 0.0313087i
\(999\) 13.4288 + 24.3993i 0.424867 + 0.771959i
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 273.2.bv.b.32.6 128
3.2 odd 2 inner 273.2.bv.b.32.27 yes 128
7.2 even 3 273.2.bw.b.149.6 yes 128
13.11 odd 12 273.2.bw.b.11.27 yes 128
21.2 odd 6 273.2.bw.b.149.27 yes 128
39.11 even 12 273.2.bw.b.11.6 yes 128
91.37 odd 12 inner 273.2.bv.b.128.27 yes 128
273.128 even 12 inner 273.2.bv.b.128.6 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bv.b.32.6 128 1.1 even 1 trivial
273.2.bv.b.32.27 yes 128 3.2 odd 2 inner
273.2.bv.b.128.6 yes 128 273.128 even 12 inner
273.2.bv.b.128.27 yes 128 91.37 odd 12 inner
273.2.bw.b.11.6 yes 128 39.11 even 12
273.2.bw.b.11.27 yes 128 13.11 odd 12
273.2.bw.b.149.6 yes 128 7.2 even 3
273.2.bw.b.149.27 yes 128 21.2 odd 6