Properties

Label 462.2.bf.a.5.4
Level $462$
Weight $2$
Character 462.5
Analytic conductor $3.689$
Analytic rank $0$
Dimension $256$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(5,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 25, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.bf (of order \(30\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(32\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 462.5
Dual form 462.2.bf.a.185.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.207912 + 0.978148i) q^{2} +(-1.37785 + 1.04954i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.40395 + 2.66986i) q^{5} +(-0.740133 - 1.56595i) q^{6} +(-0.383771 + 2.61777i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.796937 - 2.89221i) q^{9} +O(q^{10})\) \(q+(-0.207912 + 0.978148i) q^{2} +(-1.37785 + 1.04954i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.40395 + 2.66986i) q^{5} +(-0.740133 - 1.56595i) q^{6} +(-0.383771 + 2.61777i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.796937 - 2.89221i) q^{9} +(-3.11133 + 1.79633i) q^{10} +(-0.0399035 + 3.31638i) q^{11} +(1.68561 - 0.398380i) q^{12} +(0.128990 - 0.0419115i) q^{13} +(-2.48078 - 0.919649i) q^{14} +(-6.11441 - 1.15562i) q^{15} +(0.669131 + 0.743145i) q^{16} +(4.29270 - 0.912441i) q^{17} +(2.66332 + 1.38085i) q^{18} +(0.847386 + 1.90326i) q^{19} +(-1.11019 - 3.41682i) q^{20} +(-2.21867 - 4.00967i) q^{21} +(-3.23562 - 0.728547i) q^{22} +(-1.84743 - 1.06661i) q^{23} +(0.0392151 + 1.73161i) q^{24} +(-0.826523 + 7.86384i) q^{25} +(0.0141770 + 0.134885i) q^{26} +(1.93743 + 4.82145i) q^{27} +(1.41534 - 2.23536i) q^{28} +(-4.23952 - 5.83519i) q^{29} +(2.40163 - 5.74053i) q^{30} +(-6.71409 - 6.04540i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.42569 - 4.61136i) q^{33} +4.38860i q^{34} +(-7.91165 + 5.26838i) q^{35} +(-1.90441 + 2.31802i) q^{36} +(0.190758 + 1.81494i) q^{37} +(-2.03785 + 0.433159i) q^{38} +(-0.133741 + 0.193128i) q^{39} +(3.57297 - 0.375534i) q^{40} +(-2.13325 - 1.54990i) q^{41} +(4.38334 - 1.33653i) q^{42} -7.85021 q^{43} +(1.38535 - 3.01344i) q^{44} +(9.63761 - 4.82503i) q^{45} +(1.42740 - 1.58529i) q^{46} +(8.12870 - 3.61913i) q^{47} +(-1.70192 - 0.321663i) q^{48} +(-6.70544 - 2.00925i) q^{49} +(-7.52015 - 2.44345i) q^{50} +(-4.95705 + 5.76256i) q^{51} +(-0.134885 - 0.0141770i) q^{52} +(5.78993 + 5.21328i) q^{53} +(-5.11890 + 0.892656i) q^{54} +(-8.95021 + 7.86590i) q^{55} +(1.89225 + 1.84916i) q^{56} +(-3.16512 - 1.73304i) q^{57} +(6.58912 - 2.93367i) q^{58} +(11.0948 + 4.93971i) q^{59} +(5.11576 + 3.54267i) q^{60} +(0.196784 - 0.177185i) q^{61} +(7.30923 - 5.31046i) q^{62} +(7.26531 + 3.19614i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.421984 + 0.243633i) q^{65} +(5.22283 - 2.39208i) q^{66} +(2.86118 + 4.95571i) q^{67} +(-4.29270 - 0.912441i) q^{68} +(3.66492 - 0.469314i) q^{69} +(-3.50833 - 8.83412i) q^{70} +(10.6343 + 3.45530i) q^{71} +(-1.87142 - 2.34474i) q^{72} +(1.61382 - 3.62469i) q^{73} +(-1.81494 - 0.190758i) q^{74} +(-7.11458 - 11.7027i) q^{75} -2.08338i q^{76} +(-8.66622 - 1.37719i) q^{77} +(-0.161101 - 0.170972i) q^{78} +(3.23727 + 0.688103i) q^{79} +(-0.375534 + 3.57297i) q^{80} +(-7.72978 - 4.60982i) q^{81} +(1.95955 - 1.76439i) q^{82} +(2.53408 - 7.79910i) q^{83} +(0.395977 + 4.56544i) q^{84} +(12.7555 + 9.26745i) q^{85} +(1.63215 - 7.67866i) q^{86} +(11.9657 + 3.59048i) q^{87} +(2.65956 + 1.98160i) q^{88} +(-5.67452 + 9.82856i) q^{89} +(2.71582 + 10.4302i) q^{90} +(0.0602119 + 0.353751i) q^{91} +(1.25388 + 1.72581i) q^{92} +(15.5959 + 1.28294i) q^{93} +(1.84999 + 8.70352i) q^{94} +(-3.04436 + 6.83775i) q^{95} +(0.668483 - 1.59785i) q^{96} +(14.9552 - 4.85925i) q^{97} +(3.35948 - 6.14116i) q^{98} +(9.55989 + 2.75836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207912 + 0.978148i −0.147016 + 0.691655i
\(3\) −1.37785 + 1.04954i −0.795502 + 0.605951i
\(4\) −0.913545 0.406737i −0.456773 0.203368i
\(5\) 2.40395 + 2.66986i 1.07508 + 1.19400i 0.980097 + 0.198520i \(0.0636133\pi\)
0.0949840 + 0.995479i \(0.469720\pi\)
\(6\) −0.740133 1.56595i −0.302158 0.639297i
\(7\) −0.383771 + 2.61777i −0.145052 + 0.989424i
\(8\) 0.587785 0.809017i 0.207813 0.286031i
\(9\) 0.796937 2.89221i 0.265646 0.964071i
\(10\) −3.11133 + 1.79633i −0.983889 + 0.568048i
\(11\) −0.0399035 + 3.31638i −0.0120314 + 0.999928i
\(12\) 1.68561 0.398380i 0.486595 0.115002i
\(13\) 0.128990 0.0419115i 0.0357755 0.0116241i −0.291075 0.956700i \(-0.594013\pi\)
0.326850 + 0.945076i \(0.394013\pi\)
\(14\) −2.48078 0.919649i −0.663015 0.245787i
\(15\) −6.11441 1.15562i −1.57873 0.298381i
\(16\) 0.669131 + 0.743145i 0.167283 + 0.185786i
\(17\) 4.29270 0.912441i 1.04113 0.221300i 0.344544 0.938770i \(-0.388034\pi\)
0.696589 + 0.717471i \(0.254700\pi\)
\(18\) 2.66332 + 1.38085i 0.627750 + 0.325469i
\(19\) 0.847386 + 1.90326i 0.194404 + 0.436638i 0.984277 0.176632i \(-0.0565203\pi\)
−0.789873 + 0.613270i \(0.789854\pi\)
\(20\) −1.11019 3.41682i −0.248246 0.764023i
\(21\) −2.21867 4.00967i −0.484154 0.874983i
\(22\) −3.23562 0.728547i −0.689836 0.155327i
\(23\) −1.84743 1.06661i −0.385215 0.222404i 0.294870 0.955537i \(-0.404724\pi\)
−0.680085 + 0.733134i \(0.738057\pi\)
\(24\) 0.0392151 + 1.73161i 0.00800476 + 0.353463i
\(25\) −0.826523 + 7.86384i −0.165305 + 1.57277i
\(26\) 0.0141770 + 0.134885i 0.00278034 + 0.0264532i
\(27\) 1.93743 + 4.82145i 0.372858 + 0.927888i
\(28\) 1.41534 2.23536i 0.267473 0.422443i
\(29\) −4.23952 5.83519i −0.787258 1.08357i −0.994444 0.105266i \(-0.966430\pi\)
0.207186 0.978302i \(-0.433570\pi\)
\(30\) 2.40163 5.74053i 0.438475 1.04807i
\(31\) −6.71409 6.04540i −1.20589 1.08579i −0.994100 0.108469i \(-0.965405\pi\)
−0.211787 0.977316i \(-0.567928\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −3.42569 4.61136i −0.596337 0.802734i
\(34\) 4.38860i 0.752639i
\(35\) −7.91165 + 5.26838i −1.33731 + 0.890519i
\(36\) −1.90441 + 2.31802i −0.317401 + 0.386337i
\(37\) 0.190758 + 1.81494i 0.0313604 + 0.298374i 0.998949 + 0.0458413i \(0.0145969\pi\)
−0.967588 + 0.252533i \(0.918736\pi\)
\(38\) −2.03785 + 0.433159i −0.330583 + 0.0702676i
\(39\) −0.133741 + 0.193128i −0.0214158 + 0.0309252i
\(40\) 3.57297 0.375534i 0.564936 0.0593772i
\(41\) −2.13325 1.54990i −0.333157 0.242053i 0.408612 0.912708i \(-0.366013\pi\)
−0.741769 + 0.670655i \(0.766013\pi\)
\(42\) 4.38334 1.33653i 0.676364 0.206231i
\(43\) −7.85021 −1.19715 −0.598573 0.801068i \(-0.704265\pi\)
−0.598573 + 0.801068i \(0.704265\pi\)
\(44\) 1.38535 3.01344i 0.208849 0.454293i
\(45\) 9.63761 4.82503i 1.43669 0.719274i
\(46\) 1.42740 1.58529i 0.210459 0.233739i
\(47\) 8.12870 3.61913i 1.18569 0.527904i 0.283389 0.959005i \(-0.408541\pi\)
0.902304 + 0.431101i \(0.141875\pi\)
\(48\) −1.70192 0.321663i −0.245651 0.0464281i
\(49\) −6.70544 2.00925i −0.957920 0.287035i
\(50\) −7.52015 2.44345i −1.06351 0.345555i
\(51\) −4.95705 + 5.76256i −0.694126 + 0.806920i
\(52\) −0.134885 0.0141770i −0.0187052 0.00196600i
\(53\) 5.78993 + 5.21328i 0.795308 + 0.716099i 0.962930 0.269753i \(-0.0869420\pi\)
−0.167622 + 0.985851i \(0.553609\pi\)
\(54\) −5.11890 + 0.892656i −0.696594 + 0.121475i
\(55\) −8.95021 + 7.86590i −1.20685 + 1.06064i
\(56\) 1.89225 + 1.84916i 0.252862 + 0.247105i
\(57\) −3.16512 1.73304i −0.419230 0.229547i
\(58\) 6.58912 2.93367i 0.865194 0.385209i
\(59\) 11.0948 + 4.93971i 1.44442 + 0.643096i 0.971290 0.237898i \(-0.0764584\pi\)
0.473127 + 0.880994i \(0.343125\pi\)
\(60\) 5.11576 + 3.54267i 0.660441 + 0.457357i
\(61\) 0.196784 0.177185i 0.0251957 0.0226863i −0.656437 0.754381i \(-0.727937\pi\)
0.681632 + 0.731695i \(0.261270\pi\)
\(62\) 7.30923 5.31046i 0.928273 0.674430i
\(63\) 7.26531 + 3.19614i 0.915342 + 0.402676i
\(64\) −0.309017 0.951057i −0.0386271 0.118882i
\(65\) 0.421984 + 0.243633i 0.0523407 + 0.0302189i
\(66\) 5.22283 2.39208i 0.642886 0.294444i
\(67\) 2.86118 + 4.95571i 0.349549 + 0.605436i 0.986169 0.165741i \(-0.0530016\pi\)
−0.636621 + 0.771177i \(0.719668\pi\)
\(68\) −4.29270 0.912441i −0.520566 0.110650i
\(69\) 3.66492 0.469314i 0.441205 0.0564988i
\(70\) −3.50833 8.83412i −0.419326 1.05588i
\(71\) 10.6343 + 3.45530i 1.26206 + 0.410068i 0.862228 0.506520i \(-0.169068\pi\)
0.399832 + 0.916588i \(0.369068\pi\)
\(72\) −1.87142 2.34474i −0.220549 0.276330i
\(73\) 1.61382 3.62469i 0.188883 0.424238i −0.794137 0.607739i \(-0.792077\pi\)
0.983019 + 0.183502i \(0.0587432\pi\)
\(74\) −1.81494 0.190758i −0.210982 0.0221751i
\(75\) −7.11458 11.7027i −0.821521 1.35131i
\(76\) 2.08338i 0.238980i
\(77\) −8.66622 1.37719i −0.987607 0.156945i
\(78\) −0.161101 0.170972i −0.0182411 0.0193588i
\(79\) 3.23727 + 0.688103i 0.364221 + 0.0774176i 0.386387 0.922337i \(-0.373723\pi\)
−0.0221658 + 0.999754i \(0.507056\pi\)
\(80\) −0.375534 + 3.57297i −0.0419860 + 0.399470i
\(81\) −7.72978 4.60982i −0.858865 0.512203i
\(82\) 1.95955 1.76439i 0.216397 0.194844i
\(83\) 2.53408 7.79910i 0.278152 0.856063i −0.710217 0.703983i \(-0.751403\pi\)
0.988368 0.152079i \(-0.0485970\pi\)
\(84\) 0.395977 + 4.56544i 0.0432046 + 0.498130i
\(85\) 12.7555 + 9.26745i 1.38353 + 1.00520i
\(86\) 1.63215 7.67866i 0.175999 0.828012i
\(87\) 11.9657 + 3.59048i 1.28285 + 0.384940i
\(88\) 2.65956 + 1.98160i 0.283510 + 0.211240i
\(89\) −5.67452 + 9.82856i −0.601498 + 1.04183i 0.391096 + 0.920350i \(0.372096\pi\)
−0.992594 + 0.121475i \(0.961237\pi\)
\(90\) 2.71582 + 10.4302i 0.286273 + 1.09944i
\(91\) 0.0602119 + 0.353751i 0.00631192 + 0.0370832i
\(92\) 1.25388 + 1.72581i 0.130726 + 0.179929i
\(93\) 15.5959 + 1.28294i 1.61722 + 0.133035i
\(94\) 1.84999 + 8.70352i 0.190812 + 0.897700i
\(95\) −3.04436 + 6.83775i −0.312345 + 0.701539i
\(96\) 0.668483 1.59785i 0.0682268 0.163080i
\(97\) 14.9552 4.85925i 1.51847 0.493382i 0.573132 0.819463i \(-0.305728\pi\)
0.945342 + 0.326081i \(0.105728\pi\)
\(98\) 3.35948 6.14116i 0.339359 0.620351i
\(99\) 9.55989 + 2.75836i 0.960805 + 0.277226i
\(100\) 3.95358 6.84780i 0.395358 0.684780i
\(101\) 1.69386 1.88122i 0.168545 0.187189i −0.652955 0.757397i \(-0.726471\pi\)
0.821500 + 0.570208i \(0.193138\pi\)
\(102\) −4.60601 6.04683i −0.456063 0.598725i
\(103\) −11.2924 + 1.18688i −1.11267 + 0.116947i −0.642980 0.765883i \(-0.722302\pi\)
−0.469694 + 0.882830i \(0.655636\pi\)
\(104\) 0.0419115 0.128990i 0.00410976 0.0126485i
\(105\) 5.37169 15.5626i 0.524223 1.51876i
\(106\) −6.30315 + 4.57950i −0.612216 + 0.444801i
\(107\) 5.85991 + 13.1616i 0.566499 + 1.27238i 0.938863 + 0.344290i \(0.111880\pi\)
−0.372365 + 0.928087i \(0.621453\pi\)
\(108\) 0.191130 5.19264i 0.0183915 0.499662i
\(109\) 2.31685 + 4.01291i 0.221914 + 0.384367i 0.955389 0.295350i \(-0.0954361\pi\)
−0.733475 + 0.679717i \(0.762103\pi\)
\(110\) −5.83316 10.3900i −0.556170 0.990652i
\(111\) −2.16768 2.30050i −0.205747 0.218354i
\(112\) −2.20218 + 1.46643i −0.208086 + 0.138565i
\(113\) 6.36475 8.76032i 0.598745 0.824102i −0.396848 0.917884i \(-0.629896\pi\)
0.995593 + 0.0937826i \(0.0298959\pi\)
\(114\) 2.35323 2.73563i 0.220401 0.256215i
\(115\) −1.59342 7.49645i −0.148587 0.699048i
\(116\) 1.49960 + 7.05508i 0.139235 + 0.655048i
\(117\) −0.0184197 0.406468i −0.00170291 0.0375780i
\(118\) −7.13850 + 9.82531i −0.657153 + 0.904493i
\(119\) 0.741149 + 11.5875i 0.0679410 + 1.06222i
\(120\) −4.52888 + 4.26740i −0.413428 + 0.389559i
\(121\) −10.9968 0.264671i −0.999710 0.0240610i
\(122\) 0.132400 + 0.229323i 0.0119869 + 0.0207619i
\(123\) 4.56597 0.103404i 0.411700 0.00932363i
\(124\) 3.67474 + 8.25361i 0.330002 + 0.741196i
\(125\) −8.44970 + 6.13906i −0.755764 + 0.549095i
\(126\) −4.63684 + 6.44202i −0.413083 + 0.573901i
\(127\) −1.97723 + 6.08528i −0.175450 + 0.539981i −0.999654 0.0263131i \(-0.991623\pi\)
0.824203 + 0.566294i \(0.191623\pi\)
\(128\) 0.994522 0.104528i 0.0879041 0.00923910i
\(129\) 10.8164 8.23910i 0.952331 0.725412i
\(130\) −0.326044 + 0.362109i −0.0285960 + 0.0317591i
\(131\) −6.54515 + 11.3365i −0.571852 + 0.990478i 0.424523 + 0.905417i \(0.360442\pi\)
−0.996376 + 0.0850605i \(0.972892\pi\)
\(132\) 1.25392 + 5.60604i 0.109140 + 0.487943i
\(133\) −5.30750 + 1.48785i −0.460219 + 0.129013i
\(134\) −5.44228 + 1.76831i −0.470142 + 0.152758i
\(135\) −8.21511 + 16.7632i −0.707044 + 1.44275i
\(136\) 1.78500 4.00919i 0.153063 0.343785i
\(137\) 1.26830 + 5.96688i 0.108358 + 0.509785i 0.998532 + 0.0541642i \(0.0172494\pi\)
−0.890174 + 0.455621i \(0.849417\pi\)
\(138\) −0.302922 + 3.68241i −0.0257864 + 0.313468i
\(139\) −11.1338 15.3244i −0.944360 1.29980i −0.953987 0.299847i \(-0.903064\pi\)
0.00962687 0.999954i \(-0.496936\pi\)
\(140\) 9.37050 1.59495i 0.791952 0.134798i
\(141\) −7.40170 + 13.5180i −0.623336 + 1.13842i
\(142\) −5.59079 + 9.68353i −0.469168 + 0.812624i
\(143\) 0.133847 + 0.429454i 0.0111929 + 0.0359127i
\(144\) 2.68259 1.34303i 0.223549 0.111919i
\(145\) 5.38756 25.3465i 0.447412 2.10491i
\(146\) 3.20995 + 2.33216i 0.265657 + 0.193011i
\(147\) 11.3479 4.26918i 0.935956 0.352116i
\(148\) 0.563936 1.73562i 0.0463553 0.142667i
\(149\) −12.1365 + 10.9277i −0.994259 + 0.895235i −0.994497 0.104765i \(-0.966591\pi\)
0.000237865 1.00000i \(0.499924\pi\)
\(150\) 12.9261 4.52599i 1.05541 0.369546i
\(151\) −0.0690708 + 0.657164i −0.00562090 + 0.0534793i −0.996973 0.0777510i \(-0.975226\pi\)
0.991352 + 0.131230i \(0.0418927\pi\)
\(152\) 2.03785 + 0.433159i 0.165292 + 0.0351338i
\(153\) 0.782037 13.1426i 0.0632240 1.06251i
\(154\) 3.14890 8.19051i 0.253746 0.660010i
\(155\) 32.4586i 2.60713i
\(156\) 0.200731 0.122034i 0.0160713 0.00977051i
\(157\) 16.3505 + 1.71850i 1.30491 + 0.137152i 0.731344 0.682008i \(-0.238893\pi\)
0.573565 + 0.819160i \(0.305560\pi\)
\(158\) −1.34613 + 3.02346i −0.107093 + 0.240534i
\(159\) −13.4492 1.10635i −1.06659 0.0877395i
\(160\) −3.41682 1.11019i −0.270123 0.0877683i
\(161\) 3.50113 4.42680i 0.275928 0.348881i
\(162\) 6.11620 6.60243i 0.480534 0.518736i
\(163\) 2.21660 + 0.471154i 0.173618 + 0.0369036i 0.293900 0.955836i \(-0.405047\pi\)
−0.120282 + 0.992740i \(0.538380\pi\)
\(164\) 1.31842 + 2.28357i 0.102951 + 0.178317i
\(165\) 4.07648 20.2316i 0.317354 1.57503i
\(166\) 7.10181 + 4.10023i 0.551207 + 0.318240i
\(167\) −6.91160 21.2717i −0.534836 1.64605i −0.744004 0.668175i \(-0.767076\pi\)
0.209169 0.977880i \(-0.432924\pi\)
\(168\) −4.54800 0.561884i −0.350886 0.0433503i
\(169\) −10.5023 + 7.63040i −0.807872 + 0.586954i
\(170\) −11.7170 + 10.5500i −0.898650 + 0.809148i
\(171\) 6.17995 0.934042i 0.472592 0.0714279i
\(172\) 7.17152 + 3.19297i 0.546824 + 0.243462i
\(173\) 19.0710 8.49095i 1.44994 0.645555i 0.477484 0.878641i \(-0.341549\pi\)
0.972456 + 0.233086i \(0.0748823\pi\)
\(174\) −5.99982 + 10.9577i −0.454845 + 0.830701i
\(175\) −20.2685 5.18156i −1.53216 0.391689i
\(176\) −2.49125 + 2.18944i −0.187785 + 0.165035i
\(177\) −20.4714 + 4.83822i −1.53872 + 0.363663i
\(178\) −8.43398 7.59399i −0.632154 0.569194i
\(179\) −11.9244 1.25331i −0.891275 0.0936767i −0.352190 0.935928i \(-0.614563\pi\)
−0.539084 + 0.842252i \(0.681230\pi\)
\(180\) −10.7669 + 0.487920i −0.802518 + 0.0363674i
\(181\) 22.5460 + 7.32565i 1.67583 + 0.544511i 0.984096 0.177638i \(-0.0568456\pi\)
0.691737 + 0.722149i \(0.256846\pi\)
\(182\) −0.358540 0.0146529i −0.0265767 0.00108614i
\(183\) −0.0851762 + 0.450668i −0.00629641 + 0.0333143i
\(184\) −1.94880 + 0.867660i −0.143667 + 0.0639647i
\(185\) −4.38706 + 4.87232i −0.322543 + 0.358220i
\(186\) −4.49748 + 14.9883i −0.329771 + 1.09900i
\(187\) 2.85471 + 14.2727i 0.208757 + 1.04372i
\(188\) −8.89797 −0.648951
\(189\) −13.3650 + 3.22141i −0.972159 + 0.234323i
\(190\) −6.05537 4.39949i −0.439303 0.319172i
\(191\) 8.44651 0.887764i 0.611168 0.0642363i 0.206112 0.978528i \(-0.433919\pi\)
0.405056 + 0.914292i \(0.367252\pi\)
\(192\) 1.42395 + 0.986087i 0.102765 + 0.0711647i
\(193\) 11.2119 2.38317i 0.807053 0.171544i 0.214132 0.976805i \(-0.431308\pi\)
0.592921 + 0.805260i \(0.297974\pi\)
\(194\) 1.64370 + 15.6387i 0.118010 + 1.12279i
\(195\) −0.837133 + 0.107200i −0.0599483 + 0.00767673i
\(196\) 5.30849 + 4.56289i 0.379178 + 0.325920i
\(197\) 10.1437i 0.722706i 0.932429 + 0.361353i \(0.117685\pi\)
−0.932429 + 0.361353i \(0.882315\pi\)
\(198\) −4.68570 + 8.77749i −0.332998 + 0.623789i
\(199\) 5.62200 3.24586i 0.398533 0.230093i −0.287318 0.957835i \(-0.592764\pi\)
0.685851 + 0.727742i \(0.259430\pi\)
\(200\) 5.87616 + 5.29092i 0.415507 + 0.374125i
\(201\) −9.14348 3.82530i −0.644931 0.269816i
\(202\) 1.48794 + 2.04797i 0.104691 + 0.144095i
\(203\) 16.9022 8.85870i 1.18630 0.621759i
\(204\) 6.87234 3.24815i 0.481160 0.227416i
\(205\) −0.990225 9.42136i −0.0691603 0.658016i
\(206\) 1.18688 11.2924i 0.0826938 0.786779i
\(207\) −4.55715 + 4.49312i −0.316744 + 0.312294i
\(208\) 0.117458 + 0.0678142i 0.00814422 + 0.00470207i
\(209\) −6.34576 + 2.73431i −0.438945 + 0.189136i
\(210\) 14.1057 + 8.48996i 0.973386 + 0.585863i
\(211\) −8.87569 27.3166i −0.611028 1.88055i −0.448311 0.893878i \(-0.647974\pi\)
−0.162717 0.986673i \(-0.552026\pi\)
\(212\) −3.16893 7.11754i −0.217643 0.488835i
\(213\) −18.2789 + 6.40024i −1.25245 + 0.438537i
\(214\) −14.0923 + 2.99541i −0.963330 + 0.204762i
\(215\) −18.8715 20.9590i −1.28703 1.42939i
\(216\) 5.03943 + 1.26656i 0.342890 + 0.0861787i
\(217\) 18.4021 15.2559i 1.24922 1.03564i
\(218\) −4.40692 + 1.43189i −0.298474 + 0.0969802i
\(219\) 1.58066 + 6.68804i 0.106811 + 0.451936i
\(220\) 11.3758 3.54548i 0.766955 0.239036i
\(221\) 0.515474 0.297609i 0.0346746 0.0200194i
\(222\) 2.70092 1.64201i 0.181274 0.110205i
\(223\) 6.44688 8.87337i 0.431715 0.594205i −0.536631 0.843817i \(-0.680303\pi\)
0.968346 + 0.249613i \(0.0803032\pi\)
\(224\) −0.976530 2.45894i −0.0652471 0.164295i
\(225\) 22.0852 + 8.65746i 1.47235 + 0.577164i
\(226\) 7.24558 + 8.04704i 0.481969 + 0.535281i
\(227\) 2.32583 + 1.03553i 0.154371 + 0.0687304i 0.482468 0.875914i \(-0.339741\pi\)
−0.328097 + 0.944644i \(0.606407\pi\)
\(228\) 2.18659 + 2.87058i 0.144810 + 0.190109i
\(229\) −1.36050 + 6.40065i −0.0899043 + 0.422967i 0.910060 + 0.414477i \(0.136036\pi\)
−0.999964 + 0.00848927i \(0.997298\pi\)
\(230\) 7.66393 0.505345
\(231\) 13.3862 7.19797i 0.880744 0.473592i
\(232\) −7.21269 −0.473537
\(233\) 1.81542 8.54087i 0.118932 0.559531i −0.877819 0.478992i \(-0.841002\pi\)
0.996751 0.0805393i \(-0.0256643\pi\)
\(234\) 0.401415 + 0.0664922i 0.0262413 + 0.00434673i
\(235\) 29.2036 + 13.0023i 1.90503 + 0.848175i
\(236\) −8.12642 9.02531i −0.528985 0.587497i
\(237\) −5.18266 + 2.44954i −0.336650 + 0.159115i
\(238\) −11.4883 1.68422i −0.744679 0.109172i
\(239\) −12.4991 + 17.2036i −0.808502 + 1.11281i 0.183050 + 0.983104i \(0.441403\pi\)
−0.991553 + 0.129704i \(0.958597\pi\)
\(240\) −3.23254 5.31715i −0.208660 0.343221i
\(241\) −12.5972 + 7.27299i −0.811456 + 0.468494i −0.847461 0.530857i \(-0.821870\pi\)
0.0360053 + 0.999352i \(0.488537\pi\)
\(242\) 2.54525 10.7015i 0.163615 0.687917i
\(243\) 15.4887 1.76106i 0.993598 0.112972i
\(244\) −0.251839 + 0.0818275i −0.0161224 + 0.00523847i
\(245\) −10.7552 22.7327i −0.687122 1.45234i
\(246\) −0.848174 + 4.48769i −0.0540776 + 0.286125i
\(247\) 0.189073 + 0.209987i 0.0120304 + 0.0133611i
\(248\) −8.83727 + 1.87842i −0.561167 + 0.119280i
\(249\) 4.69388 + 13.4056i 0.297462 + 0.849546i
\(250\) −4.24812 9.54143i −0.268675 0.603453i
\(251\) 4.17665 + 12.8544i 0.263628 + 0.811364i 0.992006 + 0.126189i \(0.0402744\pi\)
−0.728378 + 0.685175i \(0.759726\pi\)
\(252\) −5.33720 5.87489i −0.336212 0.370083i
\(253\) 3.61101 6.08421i 0.227022 0.382511i
\(254\) −5.54121 3.19922i −0.347686 0.200737i
\(255\) −27.3018 + 0.618294i −1.70970 + 0.0387191i
\(256\) −0.104528 + 0.994522i −0.00653303 + 0.0621576i
\(257\) 0.921368 + 8.76623i 0.0574734 + 0.546822i 0.984938 + 0.172910i \(0.0553171\pi\)
−0.927464 + 0.373912i \(0.878016\pi\)
\(258\) 5.81020 + 12.2930i 0.361727 + 0.765332i
\(259\) −4.82430 0.197160i −0.299767 0.0122510i
\(260\) −0.286408 0.394206i −0.0177622 0.0244476i
\(261\) −20.2552 + 7.61130i −1.25377 + 0.471127i
\(262\) −9.72799 8.75912i −0.600997 0.541140i
\(263\) −2.81687 + 1.62632i −0.173695 + 0.100283i −0.584327 0.811518i \(-0.698642\pi\)
0.410632 + 0.911801i \(0.365308\pi\)
\(264\) −5.74424 + 0.0609553i −0.353533 + 0.00375154i
\(265\) 27.9908i 1.71946i
\(266\) −0.351842 5.50086i −0.0215728 0.337279i
\(267\) −2.49682 19.4979i −0.152803 1.19325i
\(268\) −0.598149 5.69101i −0.0365378 0.347634i
\(269\) 6.29580 1.33821i 0.383862 0.0815924i −0.0119390 0.999929i \(-0.503800\pi\)
0.395801 + 0.918336i \(0.370467\pi\)
\(270\) −14.6889 11.5209i −0.893936 0.701137i
\(271\) 3.80854 0.400294i 0.231352 0.0243161i 0.0118573 0.999930i \(-0.496226\pi\)
0.219495 + 0.975614i \(0.429559\pi\)
\(272\) 3.55045 + 2.57955i 0.215278 + 0.156408i
\(273\) −0.454238 0.424221i −0.0274918 0.0256750i
\(274\) −6.10019 −0.368526
\(275\) −26.0465 3.05486i −1.57067 0.184215i
\(276\) −3.53896 1.06192i −0.213020 0.0639200i
\(277\) −11.6449 + 12.9330i −0.699675 + 0.777068i −0.983324 0.181860i \(-0.941788\pi\)
0.283650 + 0.958928i \(0.408455\pi\)
\(278\) 17.3044 7.70442i 1.03785 0.462080i
\(279\) −22.8353 + 14.6008i −1.36711 + 0.874126i
\(280\) −0.388139 + 9.49734i −0.0231958 + 0.567575i
\(281\) −13.0434 4.23806i −0.778105 0.252822i −0.107074 0.994251i \(-0.534148\pi\)
−0.671031 + 0.741429i \(0.734148\pi\)
\(282\) −11.6837 10.0505i −0.695754 0.598499i
\(283\) −24.2105 2.54463i −1.43917 0.151262i −0.647429 0.762125i \(-0.724156\pi\)
−0.791736 + 0.610863i \(0.790823\pi\)
\(284\) −8.30953 7.48193i −0.493080 0.443971i
\(285\) −2.98181 12.6166i −0.176627 0.747341i
\(286\) −0.447897 + 0.0416341i −0.0264847 + 0.00246187i
\(287\) 4.87595 4.98955i 0.287818 0.294524i
\(288\) 0.755938 + 2.90320i 0.0445441 + 0.171073i
\(289\) 2.06445 0.919150i 0.121438 0.0540677i
\(290\) 23.6724 + 10.5396i 1.39009 + 0.618909i
\(291\) −15.5061 + 22.3914i −0.908983 + 1.31261i
\(292\) −2.94859 + 2.65492i −0.172553 + 0.155367i
\(293\) 11.8043 8.57629i 0.689612 0.501032i −0.186921 0.982375i \(-0.559851\pi\)
0.876532 + 0.481343i \(0.159851\pi\)
\(294\) 1.81653 + 11.9875i 0.105942 + 0.699125i
\(295\) 13.4830 + 41.4964i 0.785010 + 2.41601i
\(296\) 1.58044 + 0.912468i 0.0918612 + 0.0530361i
\(297\) −16.0671 + 6.23287i −0.932307 + 0.361668i
\(298\) −8.16562 14.1433i −0.473022 0.819298i
\(299\) −0.283003 0.0601542i −0.0163665 0.00347880i
\(300\) 1.73959 + 13.5847i 0.100436 + 0.784311i
\(301\) 3.01268 20.5500i 0.173648 1.18448i
\(302\) −0.628443 0.204194i −0.0361628 0.0117500i
\(303\) −0.359468 + 4.36981i −0.0206509 + 0.251039i
\(304\) −0.847386 + 1.90326i −0.0486009 + 0.109159i
\(305\) 0.946121 + 0.0994413i 0.0541747 + 0.00569399i
\(306\) 12.6928 + 3.49744i 0.725597 + 0.199935i
\(307\) 5.17001i 0.295068i −0.989057 0.147534i \(-0.952866\pi\)
0.989057 0.147534i \(-0.0471336\pi\)
\(308\) 7.35683 + 4.78299i 0.419194 + 0.272536i
\(309\) 14.3136 13.4872i 0.814270 0.767258i
\(310\) 31.7493 + 6.74851i 1.80324 + 0.383290i
\(311\) 0.943611 8.97786i 0.0535073 0.509088i −0.934642 0.355591i \(-0.884280\pi\)
0.988149 0.153497i \(-0.0490536\pi\)
\(312\) 0.0776325 + 0.221717i 0.00439508 + 0.0125522i
\(313\) −23.8919 + 21.5124i −1.35045 + 1.21595i −0.395759 + 0.918354i \(0.629519\pi\)
−0.954692 + 0.297597i \(0.903815\pi\)
\(314\) −5.08040 + 15.6359i −0.286704 + 0.882384i
\(315\) 8.93220 + 27.0807i 0.503272 + 1.52583i
\(316\) −2.67752 1.94533i −0.150622 0.109433i
\(317\) 1.79420 8.44103i 0.100772 0.474096i −0.898603 0.438762i \(-0.855417\pi\)
0.999376 0.0353338i \(-0.0112494\pi\)
\(318\) 3.87842 12.9253i 0.217491 0.724813i
\(319\) 19.5209 13.8270i 1.09296 0.774165i
\(320\) 1.79633 3.11133i 0.100418 0.173929i
\(321\) −21.8876 11.9845i −1.22165 0.668907i
\(322\) 3.60214 + 4.34501i 0.200739 + 0.242138i
\(323\) 5.37419 + 7.39693i 0.299028 + 0.411576i
\(324\) 5.18652 + 7.35527i 0.288140 + 0.408626i
\(325\) 0.222972 + 1.04900i 0.0123682 + 0.0581880i
\(326\) −0.921716 + 2.07021i −0.0510491 + 0.114658i
\(327\) −7.40398 3.09756i −0.409441 0.171295i
\(328\) −2.50778 + 0.814829i −0.138469 + 0.0449914i
\(329\) 6.35449 + 22.6680i 0.350334 + 1.24973i
\(330\) 18.9420 + 8.19379i 1.04272 + 0.451053i
\(331\) 14.2009 24.5966i 0.780551 1.35195i −0.151070 0.988523i \(-0.548272\pi\)
0.931621 0.363431i \(-0.118395\pi\)
\(332\) −5.48718 + 6.09413i −0.301148 + 0.334459i
\(333\) 5.40121 + 0.894680i 0.295984 + 0.0490282i
\(334\) 22.2439 2.33793i 1.21713 0.127926i
\(335\) −6.35291 + 19.5522i −0.347096 + 1.06825i
\(336\) 1.49519 4.33179i 0.0815692 0.236319i
\(337\) −9.46724 + 6.87835i −0.515713 + 0.374688i −0.814987 0.579480i \(-0.803256\pi\)
0.299273 + 0.954167i \(0.403256\pi\)
\(338\) −5.28009 11.8593i −0.287199 0.645060i
\(339\) 0.424636 + 18.7505i 0.0230630 + 1.01838i
\(340\) −7.88336 13.6544i −0.427535 0.740513i
\(341\) 20.3168 22.0253i 1.10022 1.19274i
\(342\) −0.371253 + 6.23910i −0.0200750 + 0.337372i
\(343\) 7.83310 16.7822i 0.422948 0.906154i
\(344\) −4.61424 + 6.35095i −0.248783 + 0.342420i
\(345\) 10.0633 + 8.65663i 0.541790 + 0.466057i
\(346\) 4.34032 + 20.4196i 0.233337 + 1.09776i
\(347\) −0.951803 4.47788i −0.0510955 0.240385i 0.945187 0.326529i \(-0.105879\pi\)
−0.996283 + 0.0861434i \(0.972546\pi\)
\(348\) −9.47081 8.14695i −0.507689 0.436722i
\(349\) 8.57284 11.7995i 0.458894 0.631613i −0.515385 0.856959i \(-0.672351\pi\)
0.974279 + 0.225346i \(0.0723511\pi\)
\(350\) 9.28239 18.7483i 0.496165 1.00214i
\(351\) 0.451983 + 0.540719i 0.0241251 + 0.0288615i
\(352\) −1.62363 2.89203i −0.0865400 0.154145i
\(353\) 5.74609 + 9.95253i 0.305834 + 0.529720i 0.977447 0.211183i \(-0.0677315\pi\)
−0.671613 + 0.740902i \(0.734398\pi\)
\(354\) −0.476258 21.0299i −0.0253128 1.11773i
\(355\) 16.3392 + 36.6985i 0.867196 + 1.94775i
\(356\) 9.18157 6.67080i 0.486622 0.353552i
\(357\) −13.1827 15.1879i −0.697702 0.803830i
\(358\) 3.70515 11.4033i 0.195823 0.602682i
\(359\) 11.8785 1.24848i 0.626921 0.0658920i 0.214260 0.976777i \(-0.431266\pi\)
0.412661 + 0.910885i \(0.364599\pi\)
\(360\) 1.76131 10.6331i 0.0928291 0.560412i
\(361\) 9.80914 10.8942i 0.516271 0.573377i
\(362\) −11.8531 + 20.5303i −0.622988 + 1.07905i
\(363\) 15.4297 11.1769i 0.809851 0.586635i
\(364\) 0.0888772 0.347658i 0.00465843 0.0182222i
\(365\) 13.5570 4.40492i 0.709603 0.230564i
\(366\) −0.423110 0.177014i −0.0221163 0.00925267i
\(367\) −10.1988 + 22.9068i −0.532372 + 1.19573i 0.424556 + 0.905402i \(0.360430\pi\)
−0.956928 + 0.290325i \(0.906237\pi\)
\(368\) −0.443522 2.08661i −0.0231202 0.108772i
\(369\) −6.18269 + 4.93464i −0.321858 + 0.256887i
\(370\) −3.85373 5.30421i −0.200346 0.275753i
\(371\) −15.8692 + 13.1560i −0.823886 + 0.683026i
\(372\) −13.7257 7.51545i −0.711646 0.389658i
\(373\) 12.5537 21.7436i 0.650006 1.12584i −0.333115 0.942886i \(-0.608100\pi\)
0.983121 0.182957i \(-0.0585669\pi\)
\(374\) −14.5543 0.175121i −0.752584 0.00905527i
\(375\) 5.19922 17.3270i 0.268487 0.894762i
\(376\) 1.84999 8.70352i 0.0954060 0.448850i
\(377\) −0.791418 0.574998i −0.0407601 0.0296139i
\(378\) −0.372283 13.7427i −0.0191482 0.706847i
\(379\) 9.00339 27.7096i 0.462473 1.42335i −0.399660 0.916663i \(-0.630872\pi\)
0.862133 0.506682i \(-0.169128\pi\)
\(380\) 5.56233 5.00834i 0.285342 0.256923i
\(381\) −3.66241 10.4598i −0.187631 0.535870i
\(382\) −0.887764 + 8.44651i −0.0454219 + 0.432161i
\(383\) 25.1874 + 5.35375i 1.28702 + 0.273564i 0.800091 0.599879i \(-0.204785\pi\)
0.486927 + 0.873443i \(0.338118\pi\)
\(384\) −1.26059 + 1.18781i −0.0643294 + 0.0606154i
\(385\) −17.1563 26.4483i −0.874365 1.34793i
\(386\) 11.4624i 0.583422i
\(387\) −6.25612 + 22.7045i −0.318017 + 1.15413i
\(388\) −15.6387 1.64370i −0.793936 0.0834460i
\(389\) −0.908772 + 2.04114i −0.0460766 + 0.103490i −0.935117 0.354339i \(-0.884706\pi\)
0.889041 + 0.457829i \(0.151373\pi\)
\(390\) 0.0691926 0.841128i 0.00350370 0.0425922i
\(391\) −8.90366 2.89297i −0.450278 0.146304i
\(392\) −5.56687 + 4.24381i −0.281170 + 0.214345i
\(393\) −2.87990 22.4894i −0.145272 1.13444i
\(394\) −9.92200 2.10899i −0.499863 0.106249i
\(395\) 5.94511 + 10.2972i 0.299131 + 0.518110i
\(396\) −7.61147 6.40824i −0.382491 0.322026i
\(397\) 5.09935 + 2.94411i 0.255929 + 0.147761i 0.622476 0.782639i \(-0.286127\pi\)
−0.366547 + 0.930400i \(0.619460\pi\)
\(398\) 2.00605 + 6.17399i 0.100554 + 0.309474i
\(399\) 5.75138 7.62045i 0.287929 0.381500i
\(400\) −6.39702 + 4.64771i −0.319851 + 0.232385i
\(401\) 3.16147 2.84660i 0.157876 0.142153i −0.586407 0.810017i \(-0.699458\pi\)
0.744283 + 0.667864i \(0.232791\pi\)
\(402\) 5.64274 8.14835i 0.281434 0.406403i
\(403\) −1.11942 0.498400i −0.0557625 0.0248270i
\(404\) −2.31258 + 1.02963i −0.115055 + 0.0512259i
\(405\) −6.27445 31.7192i −0.311780 1.57614i
\(406\) 5.15095 + 18.3747i 0.255638 + 0.911920i
\(407\) −6.02664 + 0.560203i −0.298730 + 0.0277683i
\(408\) 1.74833 + 7.39749i 0.0865552 + 0.366230i
\(409\) 11.2471 + 10.1270i 0.556135 + 0.500746i 0.898591 0.438788i \(-0.144592\pi\)
−0.342456 + 0.939534i \(0.611259\pi\)
\(410\) 9.42136 + 0.990225i 0.465288 + 0.0489037i
\(411\) −8.01000 6.89034i −0.395104 0.339875i
\(412\) 10.7989 + 3.50877i 0.532022 + 0.172865i
\(413\) −17.1889 + 27.1479i −0.845810 + 1.33586i
\(414\) −3.44745 5.39174i −0.169433 0.264989i
\(415\) 26.9143 11.9830i 1.32117 0.588224i
\(416\) −0.0907531 + 0.100792i −0.00444954 + 0.00494171i
\(417\) 31.4243 + 9.42934i 1.53886 + 0.461757i
\(418\) −1.35520 6.77558i −0.0662852 0.331405i
\(419\) 12.1453 0.593339 0.296669 0.954980i \(-0.404124\pi\)
0.296669 + 0.954980i \(0.404124\pi\)
\(420\) −11.2372 + 12.0323i −0.548318 + 0.587116i
\(421\) −9.63976 7.00369i −0.469813 0.341339i 0.327555 0.944832i \(-0.393775\pi\)
−0.797368 + 0.603493i \(0.793775\pi\)
\(422\) 28.5650 3.00230i 1.39052 0.146150i
\(423\) −3.98923 26.3941i −0.193963 1.28333i
\(424\) 7.62086 1.61986i 0.370102 0.0786676i
\(425\) 3.62728 + 34.5113i 0.175949 + 1.67404i
\(426\) −2.45997 19.2102i −0.119186 0.930737i
\(427\) 0.388311 + 0.583135i 0.0187917 + 0.0282199i
\(428\) 14.4071i 0.696395i
\(429\) −0.635150 0.451244i −0.0306653 0.0217863i
\(430\) 24.4246 14.1015i 1.17786 0.680037i
\(431\) 7.81330 + 7.03513i 0.376353 + 0.338870i 0.835500 0.549490i \(-0.185178\pi\)
−0.459147 + 0.888361i \(0.651845\pi\)
\(432\) −2.28664 + 4.66597i −0.110016 + 0.224492i
\(433\) −1.60967 2.21552i −0.0773557 0.106471i 0.768586 0.639747i \(-0.220961\pi\)
−0.845941 + 0.533276i \(0.820961\pi\)
\(434\) 11.0965 + 21.1719i 0.532649 + 1.01628i
\(435\) 19.1788 + 40.5780i 0.919555 + 1.94557i
\(436\) −0.484354 4.60832i −0.0231964 0.220699i
\(437\) 0.464557 4.41996i 0.0222228 0.211436i
\(438\) −6.87052 + 0.155595i −0.328286 + 0.00743460i
\(439\) 26.8106 + 15.4791i 1.27960 + 0.738778i 0.976775 0.214267i \(-0.0687364\pi\)
0.302826 + 0.953046i \(0.402070\pi\)
\(440\) 1.10284 + 11.8643i 0.0525760 + 0.565610i
\(441\) −11.1550 + 17.7923i −0.531190 + 0.847253i
\(442\) 0.183933 + 0.566087i 0.00874879 + 0.0269260i
\(443\) 8.40843 + 18.8856i 0.399496 + 0.897284i 0.995541 + 0.0943322i \(0.0300716\pi\)
−0.596044 + 0.802952i \(0.703262\pi\)
\(444\) 1.04458 + 2.98329i 0.0495735 + 0.141581i
\(445\) −39.8822 + 8.47722i −1.89060 + 0.401859i
\(446\) 7.33908 + 8.15087i 0.347516 + 0.385955i
\(447\) 5.25316 27.7945i 0.248466 1.31463i
\(448\) 2.60824 0.443948i 0.123228 0.0209746i
\(449\) −20.9320 + 6.80123i −0.987844 + 0.320970i −0.757998 0.652257i \(-0.773822\pi\)
−0.229846 + 0.973227i \(0.573822\pi\)
\(450\) −13.0601 + 19.8026i −0.615657 + 0.933504i
\(451\) 5.22518 7.01283i 0.246044 0.330221i
\(452\) −9.37763 + 5.41418i −0.441087 + 0.254661i
\(453\) −0.594550 0.977966i −0.0279344 0.0459489i
\(454\) −1.49647 + 2.05971i −0.0702326 + 0.0966669i
\(455\) −0.799720 + 1.01116i −0.0374914 + 0.0474039i
\(456\) −3.26247 + 1.54198i −0.152779 + 0.0722097i
\(457\) −23.9040 26.5481i −1.11818 1.24187i −0.967388 0.253300i \(-0.918484\pi\)
−0.150793 0.988565i \(-0.548183\pi\)
\(458\) −5.97791 2.66154i −0.279330 0.124366i
\(459\) 12.7161 + 18.9292i 0.593536 + 0.883541i
\(460\) −1.59342 + 7.49645i −0.0742936 + 0.349524i
\(461\) 14.9546 0.696505 0.348252 0.937401i \(-0.386775\pi\)
0.348252 + 0.937401i \(0.386775\pi\)
\(462\) 4.25754 + 14.5902i 0.198079 + 0.678797i
\(463\) −2.65847 −0.123550 −0.0617749 0.998090i \(-0.519676\pi\)
−0.0617749 + 0.998090i \(0.519676\pi\)
\(464\) 1.49960 7.05508i 0.0696173 0.327524i
\(465\) 34.0665 + 44.7230i 1.57980 + 2.07398i
\(466\) 7.97679 + 3.55149i 0.369517 + 0.164520i
\(467\) 3.24762 + 3.60685i 0.150282 + 0.166905i 0.813585 0.581446i \(-0.197513\pi\)
−0.663303 + 0.748351i \(0.730846\pi\)
\(468\) −0.148498 + 0.378819i −0.00686433 + 0.0175109i
\(469\) −14.0709 + 5.58805i −0.649735 + 0.258032i
\(470\) −18.7899 + 25.8621i −0.866714 + 1.19293i
\(471\) −24.3321 + 14.7926i −1.12117 + 0.681608i
\(472\) 10.5177 6.07237i 0.484115 0.279504i
\(473\) 0.313251 26.0343i 0.0144033 1.19706i
\(474\) −1.31847 5.57870i −0.0605595 0.256238i
\(475\) −15.6673 + 5.09062i −0.718866 + 0.233574i
\(476\) 4.03597 10.8871i 0.184989 0.499011i
\(477\) 19.6921 12.5911i 0.901640 0.576505i
\(478\) −14.2289 15.8028i −0.650816 0.722805i
\(479\) 29.8316 6.34091i 1.36304 0.289723i 0.532382 0.846504i \(-0.321297\pi\)
0.830660 + 0.556781i \(0.187964\pi\)
\(480\) 5.87305 2.05640i 0.268067 0.0938616i
\(481\) 0.100673 + 0.226114i 0.00459027 + 0.0103099i
\(482\) −4.49495 13.8340i −0.204740 0.630123i
\(483\) −0.177933 + 9.77404i −0.00809625 + 0.444734i
\(484\) 9.93844 + 4.71460i 0.451747 + 0.214300i
\(485\) 48.9252 + 28.2470i 2.22158 + 1.28263i
\(486\) −1.49769 + 15.5163i −0.0679367 + 0.703836i
\(487\) 1.83655 17.4736i 0.0832222 0.791806i −0.870713 0.491792i \(-0.836342\pi\)
0.953935 0.300014i \(-0.0969913\pi\)
\(488\) −0.0276791 0.263349i −0.00125297 0.0119212i
\(489\) −3.54864 + 1.67723i −0.160475 + 0.0758471i
\(490\) 24.4721 5.79373i 1.10554 0.261734i
\(491\) −18.1435 24.9724i −0.818806 1.12699i −0.989904 0.141736i \(-0.954731\pi\)
0.171098 0.985254i \(-0.445269\pi\)
\(492\) −4.21328 1.76268i −0.189949 0.0794679i
\(493\) −23.5232 21.1804i −1.05943 0.953918i
\(494\) −0.244709 + 0.141283i −0.0110100 + 0.00635660i
\(495\) 15.6171 + 32.1545i 0.701936 + 1.44524i
\(496\) 9.03470i 0.405670i
\(497\) −13.1263 + 26.5121i −0.588795 + 1.18923i
\(498\) −14.0886 + 1.80412i −0.631324 + 0.0808446i
\(499\) 0.763348 + 7.26277i 0.0341722 + 0.325126i 0.998232 + 0.0594406i \(0.0189317\pi\)
−0.964060 + 0.265686i \(0.914402\pi\)
\(500\) 10.2162 2.17151i 0.456881 0.0971130i
\(501\) 31.8486 + 22.0552i 1.42289 + 0.985355i
\(502\) −13.4419 + 1.41280i −0.599941 + 0.0630564i
\(503\) −18.0042 13.0808i −0.802768 0.583245i 0.108957 0.994046i \(-0.465249\pi\)
−0.911725 + 0.410801i \(0.865249\pi\)
\(504\) 6.85617 3.99911i 0.305398 0.178134i
\(505\) 9.09456 0.404703
\(506\) 5.20048 + 4.79708i 0.231190 + 0.213256i
\(507\) 6.46224 21.5361i 0.286998 0.956454i
\(508\) 4.28139 4.75497i 0.189956 0.210967i
\(509\) −5.20749 + 2.31852i −0.230818 + 0.102767i −0.518887 0.854843i \(-0.673653\pi\)
0.288069 + 0.957610i \(0.406987\pi\)
\(510\) 5.07157 26.8337i 0.224573 1.18822i
\(511\) 8.86927 + 5.61565i 0.392353 + 0.248422i
\(512\) −0.951057 0.309017i −0.0420312 0.0136568i
\(513\) −7.53472 + 7.77306i −0.332666 + 0.343189i
\(514\) −8.76623 0.921368i −0.386662 0.0406398i
\(515\) −30.3152 27.2960i −1.33585 1.20280i
\(516\) −13.2324 + 3.12736i −0.582525 + 0.137674i
\(517\) 11.6781 + 27.1023i 0.513600 + 1.19196i
\(518\) 1.19588 4.67788i 0.0525439 0.205534i
\(519\) −17.3654 + 31.7150i −0.762255 + 1.39213i
\(520\) 0.445139 0.198189i 0.0195206 0.00869115i
\(521\) −34.6817 15.4413i −1.51943 0.676496i −0.533834 0.845589i \(-0.679249\pi\)
−0.985600 + 0.169094i \(0.945916\pi\)
\(522\) −3.23367 21.3951i −0.141534 0.936438i
\(523\) 24.8884 22.4096i 1.08829 0.979905i 0.0884251 0.996083i \(-0.471817\pi\)
0.999869 + 0.0161783i \(0.00514994\pi\)
\(524\) 10.5903 7.69429i 0.462638 0.336126i
\(525\) 33.3652 14.1332i 1.45618 0.616823i
\(526\) −1.00512 3.09344i −0.0438253 0.134880i
\(527\) −34.3376 19.8249i −1.49577 0.863584i
\(528\) 1.13467 5.63139i 0.0493802 0.245075i
\(529\) −9.22468 15.9776i −0.401073 0.694679i
\(530\) −27.3791 5.81961i −1.18927 0.252788i
\(531\) 23.1285 28.1518i 1.00369 1.22168i
\(532\) 5.45380 + 0.799540i 0.236452 + 0.0346644i
\(533\) −0.340127 0.110514i −0.0147325 0.00478689i
\(534\) 19.5909 + 1.61159i 0.847783 + 0.0697401i
\(535\) −21.0526 + 47.2849i −0.910184 + 2.04431i
\(536\) 5.69101 + 0.598149i 0.245814 + 0.0258361i
\(537\) 17.7455 10.7883i 0.765774 0.465549i
\(538\) 6.43646i 0.277495i
\(539\) 6.93101 22.1576i 0.298540 0.954397i
\(540\) 14.3231 11.9726i 0.616368 0.515217i
\(541\) −17.0660 3.62748i −0.733723 0.155958i −0.174127 0.984723i \(-0.555710\pi\)
−0.559596 + 0.828766i \(0.689044\pi\)
\(542\) −0.400294 + 3.80854i −0.0171941 + 0.163591i
\(543\) −38.7536 + 13.5693i −1.66308 + 0.582314i
\(544\) −3.26137 + 2.93655i −0.139830 + 0.125903i
\(545\) −5.14430 + 15.8325i −0.220358 + 0.678191i
\(546\) 0.509392 0.356112i 0.0218000 0.0152402i
\(547\) 18.2154 + 13.2343i 0.778834 + 0.565856i 0.904629 0.426200i \(-0.140148\pi\)
−0.125795 + 0.992056i \(0.540148\pi\)
\(548\) 1.26830 5.96688i 0.0541791 0.254893i
\(549\) −0.355633 0.710348i −0.0151781 0.0303169i
\(550\) 8.40349 24.8422i 0.358326 1.05928i
\(551\) 7.51338 13.0136i 0.320081 0.554396i
\(552\) 1.77450 3.24084i 0.0755279 0.137939i
\(553\) −3.04367 + 8.21036i −0.129430 + 0.349140i
\(554\) −10.2293 14.0794i −0.434599 0.598175i
\(555\) 0.931015 11.3177i 0.0395194 0.480410i
\(556\) 3.93827 + 18.5281i 0.167020 + 0.785766i
\(557\) 4.35322 9.77748i 0.184452 0.414285i −0.797525 0.603285i \(-0.793858\pi\)
0.981977 + 0.189000i \(0.0605247\pi\)
\(558\) −9.53400 25.3719i −0.403606 1.07408i
\(559\) −1.01260 + 0.329014i −0.0428284 + 0.0139158i
\(560\) −9.20910 2.35427i −0.389156 0.0994859i
\(561\) −18.9131 16.6694i −0.798510 0.703784i
\(562\) 6.85733 11.8772i 0.289259 0.501011i
\(563\) 10.8014 11.9962i 0.455226 0.505580i −0.471216 0.882018i \(-0.656185\pi\)
0.926442 + 0.376438i \(0.122851\pi\)
\(564\) 12.2601 9.33876i 0.516241 0.393233i
\(565\) 38.6894 4.06642i 1.62768 0.171076i
\(566\) 7.52267 23.1524i 0.316201 0.973168i
\(567\) 15.0339 18.4657i 0.631365 0.775486i
\(568\) 9.04608 6.57236i 0.379565 0.275770i
\(569\) 12.7640 + 28.6683i 0.535093 + 1.20184i 0.955632 + 0.294564i \(0.0951744\pi\)
−0.420539 + 0.907275i \(0.638159\pi\)
\(570\) 12.9608 0.293520i 0.542869 0.0122942i
\(571\) −16.2378 28.1246i −0.679529 1.17698i −0.975123 0.221665i \(-0.928851\pi\)
0.295594 0.955314i \(-0.404482\pi\)
\(572\) 0.0523989 0.446766i 0.00219091 0.0186802i
\(573\) −10.7063 + 10.0881i −0.447261 + 0.421438i
\(574\) 3.86675 + 5.80678i 0.161395 + 0.242371i
\(575\) 9.91460 13.6463i 0.413467 0.569089i
\(576\) −2.99692 + 0.135810i −0.124872 + 0.00565877i
\(577\) 3.29944 + 15.5227i 0.137358 + 0.646217i 0.991920 + 0.126868i \(0.0404923\pi\)
−0.854562 + 0.519349i \(0.826174\pi\)
\(578\) 0.469842 + 2.21043i 0.0195429 + 0.0919420i
\(579\) −12.9471 + 15.0510i −0.538065 + 0.625499i
\(580\) −15.2311 + 20.9638i −0.632437 + 0.870475i
\(581\) 19.4437 + 9.62671i 0.806663 + 0.399383i
\(582\) −18.6782 19.8227i −0.774237 0.821676i
\(583\) −17.5203 + 18.9936i −0.725615 + 0.786635i
\(584\) −1.98386 3.43614i −0.0820926 0.142189i
\(585\) 1.04093 1.02631i 0.0430373 0.0424326i
\(586\) 5.93464 + 13.3294i 0.245158 + 0.550633i
\(587\) 11.3149 8.22077i 0.467017 0.339308i −0.329261 0.944239i \(-0.606800\pi\)
0.796277 + 0.604932i \(0.206800\pi\)
\(588\) −12.1032 0.715505i −0.499129 0.0295069i
\(589\) 5.81653 17.9015i 0.239666 0.737616i
\(590\) −43.3928 + 4.56077i −1.78646 + 0.187764i
\(591\) −10.6462 13.9764i −0.437925 0.574914i
\(592\) −1.22112 + 1.35619i −0.0501877 + 0.0557391i
\(593\) −6.97419 + 12.0797i −0.286396 + 0.496052i −0.972947 0.231030i \(-0.925791\pi\)
0.686551 + 0.727082i \(0.259124\pi\)
\(594\) −2.75613 17.0119i −0.113085 0.698006i
\(595\) −29.1552 + 29.8345i −1.19525 + 1.22310i
\(596\) 15.5319 5.04663i 0.636213 0.206718i
\(597\) −4.33961 + 10.3728i −0.177608 + 0.424531i
\(598\) 0.117679 0.264312i 0.00481226 0.0108085i
\(599\) −9.57760 45.0590i −0.391330 1.84106i −0.526414 0.850228i \(-0.676464\pi\)
0.135084 0.990834i \(-0.456870\pi\)
\(600\) −13.6495 1.12283i −0.557238 0.0458394i
\(601\) −4.92688 6.78127i −0.200972 0.276614i 0.696621 0.717439i \(-0.254686\pi\)
−0.897593 + 0.440825i \(0.854686\pi\)
\(602\) 19.4746 + 7.21944i 0.793726 + 0.294242i
\(603\) 16.6131 4.32575i 0.676539 0.176158i
\(604\) 0.330392 0.572256i 0.0134435 0.0232848i
\(605\) −25.7292 29.9962i −1.04604 1.21952i
\(606\) −4.19958 1.26015i −0.170596 0.0511900i
\(607\) 4.08022 19.1959i 0.165611 0.779139i −0.814417 0.580280i \(-0.802943\pi\)
0.980028 0.198859i \(-0.0637236\pi\)
\(608\) −1.68549 1.22458i −0.0683556 0.0496632i
\(609\) −13.9911 + 29.9455i −0.566949 + 1.21345i
\(610\) −0.293978 + 0.904771i −0.0119028 + 0.0366331i
\(611\) 0.896839 0.807518i 0.0362822 0.0326687i
\(612\) −6.05999 + 11.6882i −0.244960 + 0.472469i
\(613\) −1.06977 + 10.1782i −0.0432077 + 0.411094i 0.951445 + 0.307819i \(0.0995990\pi\)
−0.994653 + 0.103276i \(0.967068\pi\)
\(614\) 5.05703 + 1.07491i 0.204085 + 0.0433797i
\(615\) 11.2525 + 11.9419i 0.453743 + 0.481545i
\(616\) −6.20805 + 6.20163i −0.250129 + 0.249871i
\(617\) 7.42318i 0.298846i 0.988773 + 0.149423i \(0.0477416\pi\)
−0.988773 + 0.149423i \(0.952258\pi\)
\(618\) 10.2165 + 16.8049i 0.410967 + 0.675993i
\(619\) −10.6282 1.11707i −0.427183 0.0448987i −0.111502 0.993764i \(-0.535566\pi\)
−0.315681 + 0.948865i \(0.602233\pi\)
\(620\) −13.2021 + 29.6524i −0.530208 + 1.19087i
\(621\) 1.56336 10.9738i 0.0627353 0.440361i
\(622\) 8.58549 + 2.78959i 0.344247 + 0.111853i
\(623\) −23.5512 18.6265i −0.943558 0.746255i
\(624\) −0.233012 + 0.0298386i −0.00932796 + 0.00119450i
\(625\) 1.96869 + 0.418458i 0.0787476 + 0.0167383i
\(626\) −16.0749 27.8425i −0.642481 1.11281i
\(627\) 5.87373 10.4276i 0.234574 0.416438i
\(628\) −14.2379 8.22027i −0.568155 0.328024i
\(629\) 2.47489 + 7.61693i 0.0986803 + 0.303707i
\(630\) −28.3461 + 3.10660i −1.12933 + 0.123770i
\(631\) −4.36971 + 3.17478i −0.173955 + 0.126386i −0.671356 0.741135i \(-0.734288\pi\)
0.497401 + 0.867521i \(0.334288\pi\)
\(632\) 2.45951 2.21455i 0.0978339 0.0880901i
\(633\) 40.8992 + 28.3227i 1.62560 + 1.12573i
\(634\) 7.88354 + 3.50998i 0.313095 + 0.139399i
\(635\) −21.0000 + 9.34980i −0.833360 + 0.371036i
\(636\) 11.8364 + 6.48098i 0.469346 + 0.256988i
\(637\) −0.949147 + 0.0218616i −0.0376066 + 0.000866186i
\(638\) 9.46624 + 21.9691i 0.374772 + 0.869766i
\(639\) 18.4683 28.0030i 0.730596 1.10778i
\(640\) 2.66986 + 2.40395i 0.105536 + 0.0950246i
\(641\) −4.65713 0.489484i −0.183946 0.0193335i 0.0121078 0.999927i \(-0.496146\pi\)
−0.196053 + 0.980593i \(0.562813\pi\)
\(642\) 16.2733 18.9176i 0.642255 0.746620i
\(643\) −6.52633 2.12053i −0.257373 0.0836256i 0.177488 0.984123i \(-0.443203\pi\)
−0.434862 + 0.900497i \(0.643203\pi\)
\(644\) −4.99898 + 2.62004i −0.196988 + 0.103244i
\(645\) 47.9994 + 9.07189i 1.88997 + 0.357205i
\(646\) −8.35265 + 3.71884i −0.328631 + 0.146316i
\(647\) 10.1996 11.3279i 0.400989 0.445344i −0.508506 0.861059i \(-0.669802\pi\)
0.909495 + 0.415715i \(0.136469\pi\)
\(648\) −8.27288 + 3.54394i −0.324989 + 0.139219i
\(649\) −16.8247 + 36.5974i −0.660428 + 1.43658i
\(650\) −1.07243 −0.0420643
\(651\) −9.34370 + 40.3341i −0.366208 + 1.58082i
\(652\) −1.83333 1.33199i −0.0717989 0.0521649i
\(653\) −7.30762 + 0.768062i −0.285969 + 0.0300566i −0.246427 0.969161i \(-0.579257\pi\)
−0.0395422 + 0.999218i \(0.512590\pi\)
\(654\) 4.56924 6.59817i 0.178671 0.258009i
\(655\) −46.0012 + 9.77786i −1.79742 + 0.382053i
\(656\) −0.275625 2.62240i −0.0107613 0.102387i
\(657\) −9.19726 7.55615i −0.358819 0.294793i
\(658\) −23.4938 + 1.50269i −0.915884 + 0.0585811i
\(659\) 25.6136i 0.997766i 0.866669 + 0.498883i \(0.166256\pi\)
−0.866669 + 0.498883i \(0.833744\pi\)
\(660\) −11.9530 + 16.8245i −0.465270 + 0.654891i
\(661\) 0.145629 0.0840790i 0.00566432 0.00327030i −0.497165 0.867656i \(-0.665626\pi\)
0.502829 + 0.864386i \(0.332292\pi\)
\(662\) 21.1066 + 19.0045i 0.820332 + 0.738630i
\(663\) −0.397894 + 0.951071i −0.0154529 + 0.0369365i
\(664\) −4.82011 6.63431i −0.187057 0.257461i
\(665\) −16.7313 10.5936i −0.648813 0.410801i
\(666\) −1.99810 + 5.09716i −0.0774249 + 0.197511i
\(667\) 1.60830 + 15.3020i 0.0622738 + 0.592496i
\(668\) −2.33793 + 22.2439i −0.0904571 + 0.860641i
\(669\) 0.430115 + 18.9924i 0.0166292 + 0.734289i
\(670\) −17.8041 10.2792i −0.687834 0.397121i
\(671\) 0.579763 + 0.659683i 0.0223815 + 0.0254668i
\(672\) 3.92626 + 2.36314i 0.151459 + 0.0911603i
\(673\) 3.73624 + 11.4990i 0.144021 + 0.443252i 0.996884 0.0788834i \(-0.0251355\pi\)
−0.852862 + 0.522136i \(0.825135\pi\)
\(674\) −4.75969 10.6904i −0.183337 0.411781i
\(675\) −39.5164 + 11.2506i −1.52099 + 0.433036i
\(676\) 12.6979 2.69903i 0.488382 0.103809i
\(677\) −11.2429 12.4865i −0.432099 0.479895i 0.487292 0.873239i \(-0.337985\pi\)
−0.919391 + 0.393344i \(0.871318\pi\)
\(678\) −18.4290 3.48308i −0.707761 0.133767i
\(679\) 6.98102 + 41.0142i 0.267907 + 1.57398i
\(680\) 14.9950 4.87218i 0.575034 0.186840i
\(681\) −4.29147 + 1.01425i −0.164450 + 0.0388662i
\(682\) 17.3199 + 24.4521i 0.663213 + 0.936320i
\(683\) −5.41293 + 3.12516i −0.207120 + 0.119581i −0.599972 0.800021i \(-0.704822\pi\)
0.392852 + 0.919602i \(0.371488\pi\)
\(684\) −6.02557 1.66032i −0.230393 0.0634840i
\(685\) −12.8818 + 17.7303i −0.492189 + 0.677440i
\(686\) 14.7869 + 11.1511i 0.564566 + 0.425753i
\(687\) −4.84316 10.2470i −0.184778 0.390948i
\(688\) −5.25282 5.83384i −0.200262 0.222413i
\(689\) 0.965340 + 0.429797i 0.0367765 + 0.0163740i
\(690\) −10.5597 + 8.04359i −0.402002 + 0.306214i
\(691\) 0.150244 0.706842i 0.00571555 0.0268895i −0.975197 0.221337i \(-0.928958\pi\)
0.980913 + 0.194447i \(0.0622913\pi\)
\(692\) −20.8758 −0.793578
\(693\) −10.8896 + 23.9670i −0.413660 + 0.910431i
\(694\) 4.57792 0.173775
\(695\) 14.1488 66.5650i 0.536696 2.52496i
\(696\) 9.93801 7.57000i 0.376699 0.286940i
\(697\) −10.5716 4.70677i −0.400427 0.178282i
\(698\) 9.75927 + 10.8388i 0.369394 + 0.410253i
\(699\) 6.46260 + 13.6734i 0.244438 + 0.517175i
\(700\) 16.4087 + 12.9775i 0.620190 + 0.490505i
\(701\) 9.76813 13.4447i 0.368937 0.507799i −0.583674 0.811988i \(-0.698385\pi\)
0.952612 + 0.304189i \(0.0983855\pi\)
\(702\) −0.622876 + 0.329685i −0.0235089 + 0.0124431i
\(703\) −3.29265 + 1.90101i −0.124185 + 0.0716981i
\(704\) 3.16640 0.986869i 0.119338 0.0371940i
\(705\) −53.8845 + 12.7351i −2.02941 + 0.479632i
\(706\) −10.9297 + 3.55128i −0.411345 + 0.133654i
\(707\) 4.27455 + 5.15609i 0.160761 + 0.193915i
\(708\) 20.6694 + 3.90652i 0.776803 + 0.146816i
\(709\) 28.5916 + 31.7541i 1.07378 + 1.19255i 0.980420 + 0.196919i \(0.0630937\pi\)
0.0933589 + 0.995633i \(0.470240\pi\)
\(710\) −39.2937 + 8.35213i −1.47467 + 0.313450i
\(711\) 4.57004 8.81450i 0.171390 0.330569i
\(712\) 4.61607 + 10.3679i 0.172995 + 0.388552i
\(713\) 5.95569 + 18.3297i 0.223043 + 0.686454i
\(714\) 17.5969 9.73687i 0.658546 0.364393i
\(715\) −0.824819 + 1.38974i −0.0308465 + 0.0519734i
\(716\) 10.3838 + 5.99506i 0.388059 + 0.224046i
\(717\) −0.833903 36.8223i −0.0311427 1.37515i
\(718\) −1.24848 + 11.8785i −0.0465927 + 0.443300i
\(719\) −0.0250490 0.238326i −0.000934172 0.00888805i 0.994045 0.108971i \(-0.0347557\pi\)
−0.994979 + 0.100083i \(0.968089\pi\)
\(720\) 10.0345 + 3.93356i 0.373964 + 0.146595i
\(721\) 1.22672 30.0164i 0.0456853 1.11787i
\(722\) 8.61666 + 11.8598i 0.320679 + 0.441377i
\(723\) 9.72374 23.2423i 0.361630 0.864391i
\(724\) −17.6172 15.8626i −0.654739 0.589529i
\(725\) 49.3911 28.5159i 1.83434 1.05906i
\(726\) 7.72464 + 17.4164i 0.286688 + 0.646382i
\(727\) 18.2514i 0.676906i 0.940983 + 0.338453i \(0.109904\pi\)
−0.940983 + 0.338453i \(0.890096\pi\)
\(728\) 0.321582 + 0.159217i 0.0119186 + 0.00590098i
\(729\) −19.4927 + 18.6824i −0.721953 + 0.691942i
\(730\) 1.49001 + 14.1765i 0.0551479 + 0.524697i
\(731\) −33.6986 + 7.16286i −1.24639 + 0.264928i
\(732\) 0.261115 0.377061i 0.00965110 0.0139366i
\(733\) −9.03354 + 0.949463i −0.333661 + 0.0350692i −0.269878 0.962895i \(-0.586983\pi\)
−0.0637834 + 0.997964i \(0.520317\pi\)
\(734\) −20.2858 14.7385i −0.748763 0.544008i
\(735\) 38.6779 + 20.0343i 1.42665 + 0.738977i
\(736\) 2.13322 0.0786316
\(737\) −16.5492 + 9.29102i −0.609598 + 0.342239i
\(738\) −3.54135 7.07356i −0.130359 0.260381i
\(739\) −33.9311 + 37.6843i −1.24818 + 1.38624i −0.356041 + 0.934470i \(0.615874\pi\)
−0.892135 + 0.451770i \(0.850793\pi\)
\(740\) 5.98953 2.66671i 0.220180 0.0980303i
\(741\) −0.480903 0.0908908i −0.0176664 0.00333896i
\(742\) −9.56913 18.2577i −0.351294 0.670260i
\(743\) −27.6648 8.98885i −1.01492 0.329769i −0.246111 0.969242i \(-0.579153\pi\)
−0.768814 + 0.639473i \(0.779153\pi\)
\(744\) 10.2050 11.8632i 0.374132 0.434927i
\(745\) −58.3511 6.13295i −2.13782 0.224694i
\(746\) 18.6584 + 16.8001i 0.683134 + 0.615096i
\(747\) −20.5372 13.5445i −0.751415 0.495567i
\(748\) 3.19730 14.1998i 0.116905 0.519197i
\(749\) −36.7028 + 10.2889i −1.34109 + 0.375947i
\(750\) 15.8674 + 8.68809i 0.579395 + 0.317244i
\(751\) −41.9330 + 18.6698i −1.53016 + 0.681270i −0.987346 0.158583i \(-0.949307\pi\)
−0.542813 + 0.839854i \(0.682641\pi\)
\(752\) 8.12870 + 3.61913i 0.296423 + 0.131976i
\(753\) −19.2460 13.3279i −0.701364 0.485695i
\(754\) 0.726978 0.654574i 0.0264750 0.0238382i
\(755\) −1.92058 + 1.39538i −0.0698971 + 0.0507832i
\(756\) 13.5198 + 2.49312i 0.491710 + 0.0906738i
\(757\) −2.61417 8.04560i −0.0950138 0.292422i 0.892244 0.451555i \(-0.149130\pi\)
−0.987257 + 0.159132i \(0.949130\pi\)
\(758\) 25.2321 + 14.5678i 0.916473 + 0.529126i
\(759\) 1.41018 + 12.1730i 0.0511864 + 0.441853i
\(760\) 3.74243 + 6.48207i 0.135752 + 0.235130i
\(761\) −2.43321 0.517196i −0.0882040 0.0187483i 0.163598 0.986527i \(-0.447690\pi\)
−0.251802 + 0.967779i \(0.581023\pi\)
\(762\) 10.9927 1.40767i 0.398222 0.0509946i
\(763\) −11.3940 + 4.52495i −0.412491 + 0.163814i
\(764\) −8.07735 2.62449i −0.292228 0.0949508i
\(765\) 36.9688 29.5062i 1.33661 1.06680i
\(766\) −10.4735 + 23.5239i −0.378424 + 0.849954i
\(767\) 1.63815 + 0.172176i 0.0591501 + 0.00621693i
\(768\) −0.899765 1.48001i −0.0324675 0.0534052i
\(769\) 1.14600i 0.0413257i 0.999787 + 0.0206629i \(0.00657766\pi\)
−0.999787 + 0.0206629i \(0.993422\pi\)
\(770\) 29.4373 11.2825i 1.06085 0.406592i
\(771\) −10.4700 11.1115i −0.377068 0.400172i
\(772\) −11.2119 2.38317i −0.403527 0.0857722i
\(773\) 4.23009 40.2466i 0.152146 1.44757i −0.605989 0.795473i \(-0.707222\pi\)
0.758135 0.652098i \(-0.226111\pi\)
\(774\) −20.9076 10.8399i −0.751508 0.389634i
\(775\) 53.0894 47.8019i 1.90703 1.71709i
\(776\) 4.85925 14.9552i 0.174437 0.536862i
\(777\) 6.85408 4.79163i 0.245889 0.171899i
\(778\) −1.80759 1.31329i −0.0648052 0.0470837i
\(779\) 1.14217 5.37349i 0.0409225 0.192525i
\(780\) 0.808361 + 0.242561i 0.0289440 + 0.00868507i
\(781\) −11.8834 + 35.1296i −0.425223 + 1.25704i
\(782\) 4.68093 8.10761i 0.167390 0.289928i
\(783\) 19.9203 31.7459i 0.711894 1.13451i
\(784\) −2.99365 6.32756i −0.106916 0.225984i
\(785\) 34.7176 + 47.7847i 1.23912 + 1.70551i
\(786\) 22.5967 + 1.85885i 0.805999 + 0.0663029i
\(787\) 5.12017 + 24.0885i 0.182514 + 0.858663i 0.970147 + 0.242518i \(0.0779732\pi\)
−0.787633 + 0.616145i \(0.788693\pi\)
\(788\) 4.12580 9.26670i 0.146976 0.330113i
\(789\) 2.17433 5.19723i 0.0774083 0.185026i
\(790\) −11.3083 + 3.67428i −0.402330 + 0.130725i
\(791\) 20.4899 + 20.0234i 0.728537 + 0.711950i
\(792\) 7.85072 6.11279i 0.278963 0.217208i
\(793\) 0.0179572 0.0311027i 0.000637677 0.00110449i
\(794\) −3.93999 + 4.37580i −0.139825 + 0.155291i
\(795\) −29.3774 38.5671i −1.04191 1.36783i
\(796\) −6.45616 + 0.678570i −0.228832 + 0.0240513i
\(797\) −7.36553 + 22.6688i −0.260901 + 0.802969i 0.731709 + 0.681617i \(0.238723\pi\)
−0.992610 + 0.121352i \(0.961277\pi\)
\(798\) 6.25815 + 7.21008i 0.221536 + 0.255234i
\(799\) 31.5918 22.9528i 1.11764 0.812011i
\(800\) −3.21613 7.22355i −0.113707 0.255391i
\(801\) 23.9040 + 24.2447i 0.844608 + 0.856643i
\(802\) 2.12709 + 3.68423i 0.0751102 + 0.130095i
\(803\) 11.9565 + 5.49667i 0.421935 + 0.193973i
\(804\) 6.79709 + 7.21357i 0.239715 + 0.254403i
\(805\) 20.2355 1.29429i 0.713208 0.0456177i
\(806\) 0.720250 0.991338i 0.0253697 0.0349184i
\(807\) −7.27016 + 8.45155i −0.255922 + 0.297509i
\(808\) −0.526315 2.47612i −0.0185157 0.0871095i
\(809\) 0.638462 + 3.00373i 0.0224471 + 0.105605i 0.987945 0.154806i \(-0.0494752\pi\)
−0.965498 + 0.260411i \(0.916142\pi\)
\(810\) 32.3306 + 0.457461i 1.13598 + 0.0160735i
\(811\) 13.7490 18.9239i 0.482794 0.664509i −0.496245 0.868183i \(-0.665288\pi\)
0.979039 + 0.203674i \(0.0652882\pi\)
\(812\) −19.0441 + 1.21808i −0.668316 + 0.0427464i
\(813\) −4.82747 + 4.54876i −0.169307 + 0.159532i
\(814\) 0.705048 6.01142i 0.0247119 0.210700i
\(815\) 4.07070 + 7.05066i 0.142590 + 0.246974i
\(816\) −7.59933 + 0.172100i −0.266030 + 0.00602469i
\(817\) −6.65216 14.9410i −0.232730 0.522719i
\(818\) −12.2441 + 8.89584i −0.428104 + 0.311036i
\(819\) 1.07111 + 0.107772i 0.0374276 + 0.00376585i
\(820\) −2.92740 + 9.00960i −0.102229 + 0.314629i
\(821\) −41.4782 + 4.35954i −1.44760 + 0.152149i −0.795486 0.605972i \(-0.792784\pi\)
−0.652114 + 0.758121i \(0.726118\pi\)
\(822\) 8.40514 6.40238i 0.293163 0.223309i
\(823\) 9.11752 10.1260i 0.317817 0.352971i −0.562976 0.826473i \(-0.690344\pi\)
0.880793 + 0.473502i \(0.157010\pi\)
\(824\) −5.67730 + 9.83338i −0.197778 + 0.342562i
\(825\) 39.0944 23.1277i 1.36109 0.805203i
\(826\) −22.9808 22.4576i −0.799606 0.781401i
\(827\) 43.8101 14.2348i 1.52343 0.494992i 0.576681 0.816970i \(-0.304348\pi\)
0.946747 + 0.321978i \(0.104348\pi\)
\(828\) 5.99068 2.25111i 0.208191 0.0782316i
\(829\) 6.50331 14.6067i 0.225869 0.507310i −0.764690 0.644399i \(-0.777108\pi\)
0.990559 + 0.137088i \(0.0437744\pi\)
\(830\) 6.12537 + 28.8176i 0.212615 + 1.00027i
\(831\) 2.47126 30.0415i 0.0857272 1.04213i
\(832\) −0.0797203 0.109726i −0.00276381 0.00380405i
\(833\) −30.6178 2.50677i −1.06084 0.0868545i
\(834\) −15.7568 + 28.7772i −0.545613 + 0.996472i
\(835\) 40.1774 69.5892i 1.39039 2.40823i
\(836\) 6.90928 + 0.0831341i 0.238963 + 0.00287525i
\(837\) 16.1395 44.0842i 0.557862 1.52377i
\(838\) −2.52516 + 11.8799i −0.0872302 + 0.410386i
\(839\) −40.3922 29.3467i −1.39449 1.01316i −0.995355 0.0962696i \(-0.969309\pi\)
−0.399140 0.916890i \(-0.630691\pi\)
\(840\) −9.43303 13.4933i −0.325470 0.465562i
\(841\) −7.11449 + 21.8961i −0.245327 + 0.755039i
\(842\) 8.85486 7.97295i 0.305159 0.274766i
\(843\) 22.4199 7.85016i 0.772182 0.270374i
\(844\) −3.00230 + 28.5650i −0.103344 + 0.983248i
\(845\) −45.6192 9.69667i −1.56935 0.333576i
\(846\) 26.6468 + 1.58559i 0.916135 + 0.0545139i
\(847\) 4.91310 28.6856i 0.168816 0.985648i
\(848\) 7.79112i 0.267548i
\(849\) 36.0291 21.9038i 1.23652 0.751735i
\(850\) −34.5113 3.62728i −1.18373 0.124415i
\(851\) 1.58342 3.55643i 0.0542790 0.121913i
\(852\) 19.3019 + 1.58780i 0.661271 + 0.0543973i
\(853\) 21.6618 + 7.03834i 0.741685 + 0.240988i 0.655400 0.755282i \(-0.272500\pi\)
0.0862858 + 0.996270i \(0.472500\pi\)
\(854\) −0.651126 + 0.258585i −0.0222811 + 0.00884858i
\(855\) 17.3501 + 14.2542i 0.593360 + 0.487484i
\(856\) 14.0923 + 2.99541i 0.481665 + 0.102381i
\(857\) −10.1592 17.5962i −0.347031 0.601076i 0.638689 0.769465i \(-0.279477\pi\)
−0.985721 + 0.168389i \(0.946144\pi\)
\(858\) 0.573439 0.527451i 0.0195769 0.0180069i
\(859\) 8.18421 + 4.72516i 0.279242 + 0.161220i 0.633080 0.774086i \(-0.281790\pi\)
−0.353838 + 0.935307i \(0.615124\pi\)
\(860\) 8.71523 + 26.8227i 0.297187 + 0.914647i
\(861\) −1.48160 + 11.9923i −0.0504927 + 0.408698i
\(862\) −8.50587 + 6.17988i −0.289711 + 0.210487i
\(863\) 22.6266 20.3731i 0.770218 0.693508i −0.187165 0.982329i \(-0.559930\pi\)
0.957383 + 0.288821i \(0.0932632\pi\)
\(864\) −4.08859 3.20678i −0.139097 0.109097i
\(865\) 68.5154 + 30.5050i 2.32959 + 1.03720i
\(866\) 2.50177 1.11386i 0.0850137 0.0378505i
\(867\) −1.87981 + 3.43317i −0.0638417 + 0.116596i
\(868\) −23.0163 + 6.45214i −0.781225 + 0.219000i
\(869\) −2.41119 + 10.7086i −0.0817941 + 0.363264i
\(870\) −43.6788 + 10.3231i −1.48085 + 0.349986i
\(871\) 0.576765 + 0.519321i 0.0195429 + 0.0175965i
\(872\) 4.60832 + 0.484354i 0.156058 + 0.0164023i
\(873\) −2.13560 47.1262i −0.0722791 1.59498i
\(874\) 4.22679 + 1.37337i 0.142973 + 0.0464548i
\(875\) −12.8279 24.4754i −0.433663 0.827418i
\(876\) 1.27627 6.75274i 0.0431211 0.228154i
\(877\) 10.7434 4.78328i 0.362779 0.161520i −0.217249 0.976116i \(-0.569708\pi\)
0.580028 + 0.814596i \(0.303042\pi\)
\(878\) −20.7151 + 23.0065i −0.699101 + 0.776430i
\(879\) −7.26333 + 24.2059i −0.244986 + 0.816443i
\(880\) −11.8344 1.38799i −0.398936 0.0467892i
\(881\) 29.3602 0.989171 0.494586 0.869129i \(-0.335320\pi\)
0.494586 + 0.869129i \(0.335320\pi\)
\(882\) −15.0843 14.6105i −0.507913 0.491959i
\(883\) −33.9917 24.6965i −1.14391 0.831102i −0.156254 0.987717i \(-0.549942\pi\)
−0.987660 + 0.156615i \(0.949942\pi\)
\(884\) −0.591958 + 0.0622173i −0.0199097 + 0.00209259i
\(885\) −62.1296 43.0248i −2.08846 1.44626i
\(886\) −20.2212 + 4.29814i −0.679343 + 0.144399i
\(887\) 1.96245 + 18.6715i 0.0658927 + 0.626927i 0.976776 + 0.214263i \(0.0687350\pi\)
−0.910883 + 0.412664i \(0.864598\pi\)
\(888\) −3.13528 + 0.401490i −0.105213 + 0.0134731i
\(889\) −15.1711 7.51127i −0.508821 0.251920i
\(890\) 40.7732i 1.36672i
\(891\) 15.5964 25.4510i 0.522499 0.852640i
\(892\) −9.49864 + 5.48404i −0.318038 + 0.183619i
\(893\) 13.7763 + 12.4042i 0.461006 + 0.415092i
\(894\) 26.0949 + 10.9172i 0.872744 + 0.365124i
\(895\) −25.3196 34.8495i −0.846342 1.16489i
\(896\) −0.108037 + 2.64354i −0.00360926 + 0.0883146i
\(897\) 0.453070 0.214139i 0.0151276 0.00714990i
\(898\) −2.30059 21.8887i −0.0767718 0.730435i
\(899\) −6.81155 + 64.8076i −0.227178 + 2.16145i
\(900\) −16.6545 16.8918i −0.555151 0.563062i
\(901\) 29.6112 + 17.0961i 0.986493 + 0.569552i
\(902\) 5.77321 + 6.56904i 0.192227 + 0.218725i
\(903\) 17.4170 + 31.4768i 0.579603 + 1.04748i
\(904\) −3.34615 10.2984i −0.111291 0.342519i
\(905\) 34.6412 + 77.8053i 1.15151 + 2.58634i
\(906\) 1.08021 0.378227i 0.0358875 0.0125658i
\(907\) 8.29563 1.76329i 0.275452 0.0585491i −0.0681145 0.997678i \(-0.521698\pi\)
0.343566 + 0.939128i \(0.388365\pi\)
\(908\) −1.70357 1.89200i −0.0565349 0.0627883i
\(909\) −4.09099 6.39822i −0.135690 0.212216i
\(910\) −0.822792 0.992476i −0.0272753 0.0329003i
\(911\) 38.5237 12.5171i 1.27635 0.414711i 0.409056 0.912509i \(-0.365858\pi\)
0.867292 + 0.497799i \(0.165858\pi\)
\(912\) −0.829975 3.51177i −0.0274832 0.116286i
\(913\) 25.7637 + 8.71520i 0.852654 + 0.288431i
\(914\) 30.9378 17.8620i 1.02333 0.590821i
\(915\) −1.40798 + 0.855976i −0.0465464 + 0.0282977i
\(916\) 3.84626 5.29392i 0.127084 0.174916i
\(917\) −27.1646 21.4843i −0.897054 0.709475i
\(918\) −21.1594 + 8.50260i −0.698365 + 0.280628i
\(919\) −1.40871 1.56453i −0.0464691 0.0516091i 0.719462 0.694532i \(-0.244388\pi\)
−0.765931 + 0.642923i \(0.777722\pi\)
\(920\) −7.00135 3.11720i −0.230828 0.102771i
\(921\) 5.42613 + 7.12350i 0.178797 + 0.234727i
\(922\) −3.10923 + 14.6278i −0.102397 + 0.481741i
\(923\) 1.51654 0.0499175
\(924\) −15.1565 + 1.13103i −0.498614 + 0.0372083i
\(925\) −14.4300 −0.474457
\(926\) 0.552728 2.60038i 0.0181638 0.0854538i
\(927\) −5.56663 + 33.6059i −0.182832 + 1.10376i
\(928\) 6.58912 + 2.93367i 0.216299 + 0.0963023i
\(929\) −38.2826 42.5171i −1.25601 1.39494i −0.884519 0.466504i \(-0.845513\pi\)
−0.371491 0.928436i \(-0.621153\pi\)
\(930\) −50.8285 + 24.0236i −1.66673 + 0.787766i
\(931\) −1.85798 14.4648i −0.0608927 0.474065i
\(932\) −5.13235 + 7.06408i −0.168116 + 0.231392i
\(933\) 8.12246 + 13.3605i 0.265917 + 0.437403i
\(934\) −4.20325 + 2.42675i −0.137534 + 0.0794055i
\(935\) −31.2434 + 41.9325i −1.02177 + 1.37134i
\(936\) −0.339666 0.224014i −0.0111023 0.00732212i
\(937\) −25.1987 + 8.18757i −0.823207 + 0.267476i −0.690181 0.723637i \(-0.742469\pi\)
−0.133025 + 0.991113i \(0.542469\pi\)
\(938\) −2.54043 14.9253i −0.0829479 0.487327i
\(939\) 10.3414 54.7163i 0.337478 1.78560i
\(940\) −21.3903 23.7563i −0.697675 0.774846i
\(941\) −16.5454 + 3.51683i −0.539364 + 0.114645i −0.469535 0.882914i \(-0.655579\pi\)
−0.0698287 + 0.997559i \(0.522245\pi\)
\(942\) −9.41043 26.8760i −0.306608 0.875666i
\(943\) 2.28788 + 5.13866i 0.0745037 + 0.167338i
\(944\) 3.75293 + 11.5503i 0.122148 + 0.375932i
\(945\) −40.7295 27.9385i −1.32493 0.908839i
\(946\) 25.4003 + 5.71924i 0.825834 + 0.185949i
\(947\) −48.8372 28.1962i −1.58700 0.916253i −0.993798 0.111196i \(-0.964532\pi\)
−0.593198 0.805057i \(-0.702135\pi\)
\(948\) 5.73091 0.129786i 0.186131 0.00421526i
\(949\) 0.0562504 0.535187i 0.00182597 0.0173729i
\(950\) −1.72196 16.3833i −0.0558677 0.531546i
\(951\) 6.38706 + 13.5135i 0.207114 + 0.438207i
\(952\) 9.81010 + 6.21134i 0.317947 + 0.201311i
\(953\) 33.6447 + 46.3079i 1.08986 + 1.50006i 0.848183 + 0.529703i \(0.177696\pi\)
0.241674 + 0.970358i \(0.422304\pi\)
\(954\) 8.22169 + 21.8796i 0.266187 + 0.708379i
\(955\) 22.6752 + 20.4169i 0.733753 + 0.660674i
\(956\) 18.4159 10.6324i 0.595612 0.343877i
\(957\) −12.3849 + 39.5395i −0.400347 + 1.27813i
\(958\) 30.4981i 0.985348i
\(959\) −16.1067 + 1.03020i −0.520111 + 0.0332670i
\(960\) 0.790393 + 6.17226i 0.0255098 + 0.199209i
\(961\) 5.29184 + 50.3485i 0.170705 + 1.62415i
\(962\) −0.242104 + 0.0514608i −0.00780575 + 0.00165916i
\(963\) 42.7360 6.45915i 1.37715 0.208143i
\(964\) 14.4663 1.52047i 0.465928 0.0489710i
\(965\) 33.3157 + 24.2053i 1.07247 + 0.779196i
\(966\) −9.52346 2.20618i −0.306412 0.0709827i
\(967\) 49.1395 1.58022 0.790110 0.612965i \(-0.210023\pi\)
0.790110 + 0.612965i \(0.210023\pi\)
\(968\) −6.67789 + 8.74104i −0.214635 + 0.280948i
\(969\) −15.1682 4.55144i −0.487272 0.146213i
\(970\) −37.8019 + 41.9832i −1.21374 + 1.34800i
\(971\) 31.5976 14.0682i 1.01402 0.451469i 0.168661 0.985674i \(-0.446056\pi\)
0.845355 + 0.534205i \(0.179389\pi\)
\(972\) −14.8659 4.69099i −0.476824 0.150464i
\(973\) 44.3887 23.2648i 1.42304 0.745835i
\(974\) 16.7100 + 5.42939i 0.535421 + 0.173969i
\(975\) −1.40819 1.21135i −0.0450981 0.0387941i
\(976\) 0.263349 + 0.0276791i 0.00842959 + 0.000885986i
\(977\) −7.82119 7.04223i −0.250222 0.225301i 0.534469 0.845188i \(-0.320512\pi\)
−0.784691 + 0.619887i \(0.787178\pi\)
\(978\) −0.902778 3.81981i −0.0288676 0.122144i
\(979\) −32.3688 19.2111i −1.03451 0.613989i
\(980\) 0.579090 + 25.1419i 0.0184983 + 0.803129i
\(981\) 13.4526 3.50280i 0.429508 0.111836i
\(982\) 28.1990 12.5550i 0.899866 0.400646i
\(983\) 9.07308 + 4.03960i 0.289386 + 0.128843i 0.546296 0.837592i \(-0.316038\pi\)
−0.256909 + 0.966436i \(0.582704\pi\)
\(984\) 2.60015 3.75473i 0.0828899 0.119696i
\(985\) −27.0822 + 24.3849i −0.862910 + 0.776968i
\(986\) 25.6083 18.6055i 0.815535 0.592521i
\(987\) −32.5464 24.5638i −1.03596 0.781873i
\(988\) −0.0873174 0.268735i −0.00277794 0.00854961i
\(989\) 14.5027 + 8.37312i 0.461158 + 0.266250i
\(990\) −34.6989 + 8.59052i −1.10280 + 0.273025i
\(991\) −26.5055 45.9090i −0.841976 1.45835i −0.888221 0.459416i \(-0.848059\pi\)
0.0462449 0.998930i \(-0.485275\pi\)
\(992\) 8.83727 + 1.87842i 0.280584 + 0.0596399i
\(993\) 6.24846 + 48.7948i 0.198289 + 1.54846i
\(994\) −23.2037 18.3516i −0.735976 0.582079i
\(995\) 22.1810 + 7.20705i 0.703186 + 0.228479i
\(996\) 1.16448 14.1558i 0.0368980 0.448544i
\(997\) 18.0230 40.4803i 0.570794 1.28202i −0.365501 0.930811i \(-0.619102\pi\)
0.936295 0.351213i \(-0.114231\pi\)
\(998\) −7.26277 0.763348i −0.229899 0.0241634i
\(999\) −8.38105 + 4.43604i −0.265165 + 0.140350i
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 462.2.bf.a.5.4 256
3.2 odd 2 inner 462.2.bf.a.5.21 yes 256
7.3 odd 6 inner 462.2.bf.a.269.3 yes 256
11.9 even 5 inner 462.2.bf.a.383.27 yes 256
21.17 even 6 inner 462.2.bf.a.269.27 yes 256
33.20 odd 10 inner 462.2.bf.a.383.3 yes 256
77.31 odd 30 inner 462.2.bf.a.185.21 yes 256
231.185 even 30 inner 462.2.bf.a.185.4 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.bf.a.5.4 256 1.1 even 1 trivial
462.2.bf.a.5.21 yes 256 3.2 odd 2 inner
462.2.bf.a.185.4 yes 256 231.185 even 30 inner
462.2.bf.a.185.21 yes 256 77.31 odd 30 inner
462.2.bf.a.269.3 yes 256 7.3 odd 6 inner
462.2.bf.a.269.27 yes 256 21.17 even 6 inner
462.2.bf.a.383.3 yes 256 33.20 odd 10 inner
462.2.bf.a.383.27 yes 256 11.9 even 5 inner