Properties

Label 342.2.bf.b.167.3
Level $342$
Weight $2$
Character 342.167
Analytic conductor $2.731$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [342,2,Mod(155,342)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(342, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([3, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("342.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.bf (of order \(18\), degree \(6\), 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: \(2.73088374913\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 167.3
Character \(\chi\) \(=\) 342.167
Dual form 342.2.bf.b.299.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 + 0.984808i) q^{2} +(-0.435623 - 1.67637i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.21351 - 0.213975i) q^{5} +(1.57526 - 0.720104i) q^{6} +0.151553 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.62047 + 1.46053i) q^{9} +O(q^{10})\) \(q+(0.173648 + 0.984808i) q^{2} +(-0.435623 - 1.67637i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.21351 - 0.213975i) q^{5} +(1.57526 - 0.720104i) q^{6} +0.151553 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.62047 + 1.46053i) q^{9} +(0.421448 + 1.15792i) q^{10} +(3.62692 + 2.09401i) q^{11} +(0.982705 + 1.42629i) q^{12} +(3.64204 - 4.34042i) q^{13} +(0.0263168 + 0.149250i) q^{14} +(-0.887335 - 1.94109i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.59461 - 4.38114i) q^{17} +(-1.89338 - 2.32704i) q^{18} +(2.66011 - 3.45309i) q^{19} +(-1.06714 + 0.616116i) q^{20} +(-0.0660197 - 0.254059i) q^{21} +(-1.43238 + 3.93544i) q^{22} +(-2.14469 - 5.89249i) q^{23} +(-1.23397 + 1.21545i) q^{24} +(-3.27164 + 1.19078i) q^{25} +(4.90691 + 2.83301i) q^{26} +(3.58994 + 3.75664i) q^{27} +(-0.142413 + 0.0518340i) q^{28} +(6.63553 + 5.56787i) q^{29} +(1.75751 - 1.21092i) q^{30} +(-7.82660 + 4.51869i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.93037 - 6.99228i) q^{33} +(4.59149 + 0.809603i) q^{34} +(0.183911 - 0.0324284i) q^{35} +(1.96290 - 2.26870i) q^{36} +3.92690i q^{37} +(3.86255 + 2.02007i) q^{38} +(-8.86272 - 4.21464i) q^{39} +(-0.792063 - 0.943944i) q^{40} +(11.2328 + 4.08841i) q^{41} +(0.238735 - 0.109134i) q^{42} +(-5.90711 - 2.15001i) q^{43} +(-4.12439 - 0.727240i) q^{44} +(-2.86745 + 2.33309i) q^{45} +(5.43055 - 3.13533i) q^{46} +(-2.03231 + 2.42202i) q^{47} +(-1.41126 - 1.00416i) q^{48} -6.97703 q^{49} +(-1.74080 - 3.01516i) q^{50} +(-8.03909 - 0.764632i) q^{51} +(-1.93789 + 5.32431i) q^{52} +(4.00225 + 3.35828i) q^{53} +(-3.07618 + 4.18773i) q^{54} +(4.84938 + 1.76503i) q^{55} +(-0.0757763 - 0.131248i) q^{56} +(-6.94748 - 2.95509i) q^{57} +(-4.33103 + 7.50157i) q^{58} +(-5.32150 + 4.46527i) q^{59} +(1.49771 + 1.52054i) q^{60} +(0.197824 - 1.12192i) q^{61} +(-5.80912 - 6.92303i) q^{62} +(-0.397138 + 0.221348i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.49092 - 6.04645i) q^{65} +(7.22126 + 0.686845i) q^{66} +(-10.8904 - 1.92027i) q^{67} +4.66232i q^{68} +(-8.94375 + 6.16221i) q^{69} +(0.0638715 + 0.175486i) q^{70} +(-1.44787 + 1.21491i) q^{71} +(2.57509 + 1.53912i) q^{72} +(1.66614 + 9.44917i) q^{73} +(-3.86724 + 0.681899i) q^{74} +(3.42139 + 4.96576i) q^{75} +(-1.31865 + 4.15465i) q^{76} +(0.549669 + 0.317352i) q^{77} +(2.61162 - 9.45994i) q^{78} +(0.395741 + 0.471626i) q^{79} +(0.792063 - 0.943944i) q^{80} +(4.73368 - 7.65456i) q^{81} +(-2.07574 + 11.7721i) q^{82} -11.5902i q^{83} +(0.148931 + 0.216157i) q^{84} +(0.997618 - 5.65777i) q^{85} +(1.09159 - 6.19071i) q^{86} +(6.44325 - 13.5491i) q^{87} -4.18801i q^{88} +(-0.130167 + 0.738215i) q^{89} +(-2.79557 - 2.41875i) q^{90} +(0.551961 - 0.657801i) q^{91} +(4.03070 + 4.80360i) q^{92} +(10.9845 + 11.1519i) q^{93} +(-2.73813 - 1.58086i) q^{94} +(2.48919 - 4.75956i) q^{95} +(0.743847 - 1.56419i) q^{96} +(6.90956 - 1.21834i) q^{97} +(-1.21155 - 6.87104i) q^{98} +(-12.5626 - 0.190026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 9 q^{3} - 3 q^{6} - 18 q^{7} - 24 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 9 q^{3} - 3 q^{6} - 18 q^{7} - 24 q^{8} - 3 q^{9} - 9 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} + 6 q^{14} + 9 q^{15} + 27 q^{17} + 9 q^{18} - 12 q^{19} - 9 q^{20} - 3 q^{21} - 9 q^{22} - 18 q^{23} - 9 q^{24} + 18 q^{25} - 18 q^{26} - 24 q^{27} + 6 q^{28} + 27 q^{30} - 36 q^{31} + 39 q^{33} + 9 q^{34} + 18 q^{35} + 9 q^{36} + 9 q^{38} + 24 q^{39} - 9 q^{40} + 36 q^{41} - 30 q^{42} - 15 q^{43} + 9 q^{44} - 9 q^{45} + 27 q^{46} - 3 q^{48} + 66 q^{49} - 3 q^{50} - 12 q^{51} - 15 q^{52} + 9 q^{55} + 9 q^{56} - 3 q^{57} - 9 q^{58} - 36 q^{59} - 21 q^{60} - 12 q^{61} + 3 q^{62} - 9 q^{63} - 24 q^{64} + 9 q^{65} - 33 q^{67} - 69 q^{69} + 18 q^{70} - 27 q^{71} + 6 q^{72} + 66 q^{73} - 39 q^{74} - 24 q^{75} - 9 q^{76} - 27 q^{77} - 6 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 9 q^{82} + 3 q^{84} - 54 q^{85} - 15 q^{86} + 63 q^{87} + 18 q^{89} + 9 q^{90} + 51 q^{91} - 18 q^{92} - 39 q^{93} + 54 q^{94} - 54 q^{95} - 3 q^{96} + 117 q^{97} - 42 q^{98} - 93 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 + 0.984808i 0.122788 + 0.696364i
\(3\) −0.435623 1.67637i −0.251507 0.967856i
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) 1.21351 0.213975i 0.542699 0.0956924i 0.104423 0.994533i \(-0.466700\pi\)
0.438276 + 0.898841i \(0.355589\pi\)
\(6\) 1.57526 0.720104i 0.643098 0.293981i
\(7\) 0.151553 0.0572815 0.0286407 0.999590i \(-0.490882\pi\)
0.0286407 + 0.999590i \(0.490882\pi\)
\(8\) −0.500000 0.866025i −0.176777 0.306186i
\(9\) −2.62047 + 1.46053i −0.873489 + 0.486845i
\(10\) 0.421448 + 1.15792i 0.133274 + 0.366166i
\(11\) 3.62692 + 2.09401i 1.09356 + 0.631366i 0.934522 0.355906i \(-0.115828\pi\)
0.159037 + 0.987273i \(0.449161\pi\)
\(12\) 0.982705 + 1.42629i 0.283683 + 0.411733i
\(13\) 3.64204 4.34042i 1.01012 1.20381i 0.0312127 0.999513i \(-0.490063\pi\)
0.978908 0.204302i \(-0.0654925\pi\)
\(14\) 0.0263168 + 0.149250i 0.00703347 + 0.0398888i
\(15\) −0.887335 1.94109i −0.229109 0.501187i
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) 1.59461 4.38114i 0.386749 1.06258i −0.581707 0.813398i \(-0.697615\pi\)
0.968456 0.249185i \(-0.0801628\pi\)
\(18\) −1.89338 2.32704i −0.446275 0.548488i
\(19\) 2.66011 3.45309i 0.610270 0.792193i
\(20\) −1.06714 + 0.616116i −0.238621 + 0.137768i
\(21\) −0.0660197 0.254059i −0.0144067 0.0554402i
\(22\) −1.43238 + 3.93544i −0.305385 + 0.839039i
\(23\) −2.14469 5.89249i −0.447199 1.22867i −0.934666 0.355528i \(-0.884301\pi\)
0.487467 0.873142i \(-0.337921\pi\)
\(24\) −1.23397 + 1.21545i −0.251883 + 0.248102i
\(25\) −3.27164 + 1.19078i −0.654328 + 0.238156i
\(26\) 4.90691 + 2.83301i 0.962324 + 0.555598i
\(27\) 3.58994 + 3.75664i 0.690884 + 0.722966i
\(28\) −0.142413 + 0.0518340i −0.0269135 + 0.00979571i
\(29\) 6.63553 + 5.56787i 1.23219 + 1.03393i 0.998094 + 0.0617125i \(0.0196562\pi\)
0.234092 + 0.972214i \(0.424788\pi\)
\(30\) 1.75751 1.21092i 0.320877 0.221083i
\(31\) −7.82660 + 4.51869i −1.40570 + 0.811581i −0.994970 0.100177i \(-0.968059\pi\)
−0.410729 + 0.911757i \(0.634726\pi\)
\(32\) 0.766044 + 0.642788i 0.135419 + 0.113630i
\(33\) 1.93037 6.99228i 0.336034 1.21720i
\(34\) 4.59149 + 0.809603i 0.787433 + 0.138846i
\(35\) 0.183911 0.0324284i 0.0310866 0.00548140i
\(36\) 1.96290 2.26870i 0.327150 0.378117i
\(37\) 3.92690i 0.645578i 0.946471 + 0.322789i \(0.104620\pi\)
−0.946471 + 0.322789i \(0.895380\pi\)
\(38\) 3.86255 + 2.02007i 0.626589 + 0.327699i
\(39\) −8.86272 4.21464i −1.41917 0.674883i
\(40\) −0.792063 0.943944i −0.125236 0.149251i
\(41\) 11.2328 + 4.08841i 1.75427 + 0.638502i 0.999840 0.0178788i \(-0.00569130\pi\)
0.754430 + 0.656381i \(0.227914\pi\)
\(42\) 0.238735 0.109134i 0.0368376 0.0168397i
\(43\) −5.90711 2.15001i −0.900825 0.327874i −0.150242 0.988649i \(-0.548005\pi\)
−0.750583 + 0.660776i \(0.770227\pi\)
\(44\) −4.12439 0.727240i −0.621774 0.109636i
\(45\) −2.86745 + 2.33309i −0.427454 + 0.347796i
\(46\) 5.43055 3.13533i 0.800691 0.462279i
\(47\) −2.03231 + 2.42202i −0.296444 + 0.353288i −0.893622 0.448821i \(-0.851844\pi\)
0.597178 + 0.802109i \(0.296289\pi\)
\(48\) −1.41126 1.00416i −0.203698 0.144939i
\(49\) −6.97703 −0.996719
\(50\) −1.74080 3.01516i −0.246187 0.426408i
\(51\) −8.03909 0.764632i −1.12570 0.107070i
\(52\) −1.93789 + 5.32431i −0.268737 + 0.738349i
\(53\) 4.00225 + 3.35828i 0.549751 + 0.461296i 0.874857 0.484382i \(-0.160955\pi\)
−0.325106 + 0.945678i \(0.605400\pi\)
\(54\) −3.07618 + 4.18773i −0.418616 + 0.569878i
\(55\) 4.84938 + 1.76503i 0.653890 + 0.237996i
\(56\) −0.0757763 0.131248i −0.0101260 0.0175388i
\(57\) −6.94748 2.95509i −0.920216 0.391411i
\(58\) −4.33103 + 7.50157i −0.568692 + 0.985004i
\(59\) −5.32150 + 4.46527i −0.692800 + 0.581328i −0.919715 0.392586i \(-0.871580\pi\)
0.226915 + 0.973915i \(0.427136\pi\)
\(60\) 1.49771 + 1.52054i 0.193354 + 0.196301i
\(61\) 0.197824 1.12192i 0.0253288 0.143647i −0.969521 0.245009i \(-0.921209\pi\)
0.994850 + 0.101362i \(0.0323202\pi\)
\(62\) −5.80912 6.92303i −0.737758 0.879226i
\(63\) −0.397138 + 0.221348i −0.0500347 + 0.0278872i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 3.49092 6.04645i 0.432995 0.749970i
\(66\) 7.22126 + 0.686845i 0.888875 + 0.0845448i
\(67\) −10.8904 1.92027i −1.33047 0.234598i −0.537194 0.843459i \(-0.680516\pi\)
−0.793277 + 0.608861i \(0.791627\pi\)
\(68\) 4.66232i 0.565389i
\(69\) −8.94375 + 6.16221i −1.07670 + 0.741843i
\(70\) 0.0638715 + 0.175486i 0.00763411 + 0.0209745i
\(71\) −1.44787 + 1.21491i −0.171830 + 0.144183i −0.724647 0.689120i \(-0.757997\pi\)
0.552817 + 0.833303i \(0.313553\pi\)
\(72\) 2.57509 + 1.53912i 0.303478 + 0.181387i
\(73\) 1.66614 + 9.44917i 0.195007 + 1.10594i 0.912408 + 0.409281i \(0.134220\pi\)
−0.717401 + 0.696660i \(0.754669\pi\)
\(74\) −3.86724 + 0.681899i −0.449558 + 0.0792692i
\(75\) 3.42139 + 4.96576i 0.395068 + 0.573397i
\(76\) −1.31865 + 4.15465i −0.151260 + 0.476571i
\(77\) 0.549669 + 0.317352i 0.0626407 + 0.0361656i
\(78\) 2.61162 9.45994i 0.295708 1.07113i
\(79\) 0.395741 + 0.471626i 0.0445244 + 0.0530621i 0.787847 0.615871i \(-0.211196\pi\)
−0.743323 + 0.668933i \(0.766751\pi\)
\(80\) 0.792063 0.943944i 0.0885554 0.105536i
\(81\) 4.73368 7.65456i 0.525965 0.850506i
\(82\) −2.07574 + 11.7721i −0.229227 + 1.30001i
\(83\) 11.5902i 1.27219i −0.771610 0.636096i \(-0.780548\pi\)
0.771610 0.636096i \(-0.219452\pi\)
\(84\) 0.148931 + 0.216157i 0.0162498 + 0.0235847i
\(85\) 0.997618 5.65777i 0.108207 0.613672i
\(86\) 1.09159 6.19071i 0.117709 0.667561i
\(87\) 6.44325 13.5491i 0.690789 1.45262i
\(88\) 4.18801i 0.446443i
\(89\) −0.130167 + 0.738215i −0.0137977 + 0.0782506i −0.990929 0.134386i \(-0.957094\pi\)
0.977131 + 0.212636i \(0.0682050\pi\)
\(90\) −2.79557 2.41875i −0.294679 0.254958i
\(91\) 0.551961 0.657801i 0.0578612 0.0689563i
\(92\) 4.03070 + 4.80360i 0.420230 + 0.500810i
\(93\) 10.9845 + 11.1519i 1.13904 + 1.15640i
\(94\) −2.73813 1.58086i −0.282417 0.163053i
\(95\) 2.48919 4.75956i 0.255386 0.488321i
\(96\) 0.743847 1.56419i 0.0759185 0.159645i
\(97\) 6.90956 1.21834i 0.701560 0.123704i 0.188521 0.982069i \(-0.439631\pi\)
0.513039 + 0.858365i \(0.328520\pi\)
\(98\) −1.21155 6.87104i −0.122385 0.694079i
\(99\) −12.5626 0.190026i −1.26259 0.0190983i
\(100\) 2.66706 2.23793i 0.266706 0.223793i
\(101\) −1.10437 3.03424i −0.109889 0.301918i 0.872543 0.488537i \(-0.162469\pi\)
−0.982432 + 0.186619i \(0.940247\pi\)
\(102\) −0.642957 8.04973i −0.0636622 0.797042i
\(103\) 0.361476i 0.0356172i −0.999841 0.0178086i \(-0.994331\pi\)
0.999841 0.0178086i \(-0.00566896\pi\)
\(104\) −5.57993 0.983892i −0.547157 0.0964786i
\(105\) −0.134478 0.294177i −0.0131237 0.0287087i
\(106\) −2.61228 + 4.52460i −0.253727 + 0.439468i
\(107\) −7.90423 + 13.6905i −0.764130 + 1.32351i 0.176575 + 0.984287i \(0.443498\pi\)
−0.940705 + 0.339225i \(0.889835\pi\)
\(108\) −4.65828 2.30226i −0.448244 0.221535i
\(109\) −7.48615 8.92164i −0.717043 0.854539i 0.277297 0.960784i \(-0.410561\pi\)
−0.994340 + 0.106246i \(0.966117\pi\)
\(110\) −0.896129 + 5.08220i −0.0854425 + 0.484569i
\(111\) 6.58296 1.71065i 0.624827 0.162367i
\(112\) 0.116096 0.0974161i 0.0109700 0.00920496i
\(113\) −3.56971 + 6.18292i −0.335810 + 0.581640i −0.983640 0.180145i \(-0.942343\pi\)
0.647830 + 0.761785i \(0.275677\pi\)
\(114\) 1.70378 7.35508i 0.159573 0.688866i
\(115\) −3.86345 6.69170i −0.360269 0.624004i
\(116\) −8.13968 2.96260i −0.755750 0.275071i
\(117\) −3.20452 + 16.6932i −0.296258 + 1.54329i
\(118\) −5.32150 4.46527i −0.489884 0.411061i
\(119\) 0.241667 0.663974i 0.0221535 0.0608664i
\(120\) −1.23736 + 1.73900i −0.112955 + 0.158748i
\(121\) 3.26972 + 5.66332i 0.297247 + 0.514847i
\(122\) 1.13922 0.103140
\(123\) 1.96044 20.6114i 0.176767 1.85847i
\(124\) 5.80912 6.92303i 0.521674 0.621707i
\(125\) −9.05109 + 5.22565i −0.809554 + 0.467396i
\(126\) −0.286947 0.352668i −0.0255633 0.0314182i
\(127\) 5.46567 + 0.963745i 0.485000 + 0.0855185i 0.410801 0.911725i \(-0.365249\pi\)
0.0741985 + 0.997243i \(0.476360\pi\)
\(128\) −0.939693 0.342020i −0.0830579 0.0302306i
\(129\) −1.03096 + 10.8391i −0.0907706 + 0.954331i
\(130\) 6.56078 + 2.38793i 0.575419 + 0.209435i
\(131\) 1.26981 + 1.51330i 0.110944 + 0.132218i 0.818659 0.574281i \(-0.194718\pi\)
−0.707714 + 0.706499i \(0.750274\pi\)
\(132\) 0.577548 + 7.23082i 0.0502691 + 0.629362i
\(133\) 0.403146 0.523325i 0.0349572 0.0453780i
\(134\) 11.0584i 0.955298i
\(135\) 5.16026 + 3.79057i 0.444124 + 0.326240i
\(136\) −4.59149 + 0.809603i −0.393717 + 0.0694229i
\(137\) 4.32076 + 0.761866i 0.369147 + 0.0650906i 0.355145 0.934811i \(-0.384432\pi\)
0.0140026 + 0.999902i \(0.495543\pi\)
\(138\) −7.62166 7.73782i −0.648799 0.658687i
\(139\) 16.7968 + 14.0942i 1.42469 + 1.19546i 0.948770 + 0.315968i \(0.102329\pi\)
0.475920 + 0.879488i \(0.342115\pi\)
\(140\) −0.161728 + 0.0933739i −0.0136685 + 0.00789154i
\(141\) 4.94553 + 2.35184i 0.416489 + 0.198060i
\(142\) −1.44787 1.21491i −0.121503 0.101953i
\(143\) 22.2983 8.11590i 1.86467 0.678686i
\(144\) −1.06858 + 2.80324i −0.0890484 + 0.233603i
\(145\) 9.24367 + 5.33683i 0.767645 + 0.443200i
\(146\) −9.01629 + 3.28166i −0.746193 + 0.271592i
\(147\) 3.03935 + 11.6961i 0.250682 + 0.964680i
\(148\) −1.34308 3.69008i −0.110400 0.303323i
\(149\) 0.672112 1.84661i 0.0550616 0.151280i −0.909113 0.416551i \(-0.863239\pi\)
0.964174 + 0.265270i \(0.0854611\pi\)
\(150\) −4.29620 + 4.23171i −0.350784 + 0.345518i
\(151\) −5.98969 + 3.45815i −0.487434 + 0.281420i −0.723509 0.690315i \(-0.757472\pi\)
0.236075 + 0.971735i \(0.424139\pi\)
\(152\) −4.32052 0.577173i −0.350440 0.0468149i
\(153\) 2.22020 + 13.8096i 0.179492 + 1.11644i
\(154\) −0.217081 + 0.596426i −0.0174929 + 0.0480614i
\(155\) −8.53078 + 7.15818i −0.685209 + 0.574959i
\(156\) 9.76973 + 0.929241i 0.782204 + 0.0743988i
\(157\) −3.26113 18.4948i −0.260266 1.47604i −0.782184 0.623048i \(-0.785894\pi\)
0.521918 0.852996i \(-0.325217\pi\)
\(158\) −0.395741 + 0.471626i −0.0314835 + 0.0375206i
\(159\) 3.88627 8.17221i 0.308202 0.648098i
\(160\) 1.06714 + 0.616116i 0.0843651 + 0.0487082i
\(161\) −0.325033 0.893022i −0.0256162 0.0703800i
\(162\) 8.36026 + 3.33257i 0.656844 + 0.261831i
\(163\) 5.76968 + 9.99338i 0.451916 + 0.782742i 0.998505 0.0546590i \(-0.0174072\pi\)
−0.546589 + 0.837401i \(0.684074\pi\)
\(164\) −11.9537 −0.933428
\(165\) 0.846352 8.89826i 0.0658884 0.692729i
\(166\) 11.4141 2.01262i 0.885908 0.156210i
\(167\) 4.12875 1.50274i 0.319492 0.116286i −0.177296 0.984158i \(-0.556735\pi\)
0.496788 + 0.867872i \(0.334513\pi\)
\(168\) −0.187012 + 0.184204i −0.0144283 + 0.0142117i
\(169\) −3.31732 18.8135i −0.255178 1.44719i
\(170\) 5.74505 0.440626
\(171\) −1.92736 + 12.9339i −0.147389 + 0.989079i
\(172\) 6.28621 0.479319
\(173\) −1.51717 8.60430i −0.115348 0.654173i −0.986577 0.163296i \(-0.947787\pi\)
0.871229 0.490877i \(-0.163324\pi\)
\(174\) 14.4621 + 3.99258i 1.09637 + 0.302677i
\(175\) −0.495825 + 0.180466i −0.0374809 + 0.0136419i
\(176\) 4.12439 0.727240i 0.310887 0.0548178i
\(177\) 9.80363 + 6.97566i 0.736886 + 0.524323i
\(178\) −0.749603 −0.0561851
\(179\) 4.37844 + 7.58368i 0.327260 + 0.566831i 0.981967 0.189052i \(-0.0605413\pi\)
−0.654707 + 0.755883i \(0.727208\pi\)
\(180\) 1.89656 3.17311i 0.141361 0.236510i
\(181\) 2.66248 + 7.31510i 0.197900 + 0.543727i 0.998457 0.0555303i \(-0.0176849\pi\)
−0.800557 + 0.599257i \(0.795463\pi\)
\(182\) 0.743655 + 0.429349i 0.0551233 + 0.0318255i
\(183\) −1.96693 + 0.157105i −0.145400 + 0.0116135i
\(184\) −4.03070 + 4.80360i −0.297147 + 0.354126i
\(185\) 0.840258 + 4.76534i 0.0617770 + 0.350355i
\(186\) −9.07502 + 12.7541i −0.665413 + 0.935175i
\(187\) 14.9577 12.5510i 1.09381 0.917817i
\(188\) 1.08137 2.97105i 0.0788672 0.216686i
\(189\) 0.544064 + 0.569329i 0.0395748 + 0.0414126i
\(190\) 5.11950 + 1.62489i 0.371407 + 0.117882i
\(191\) −15.9194 + 9.19105i −1.15188 + 0.665041i −0.949346 0.314233i \(-0.898253\pi\)
−0.202539 + 0.979274i \(0.564919\pi\)
\(192\) 1.66959 + 0.460927i 0.120493 + 0.0332646i
\(193\) −2.62862 + 7.22206i −0.189212 + 0.519855i −0.997634 0.0687476i \(-0.978100\pi\)
0.808422 + 0.588603i \(0.200322\pi\)
\(194\) 2.39967 + 6.59303i 0.172286 + 0.473352i
\(195\) −11.6568 3.21812i −0.834764 0.230454i
\(196\) 6.55627 2.38629i 0.468305 0.170449i
\(197\) −4.17254 2.40902i −0.297281 0.171635i 0.343940 0.938992i \(-0.388238\pi\)
−0.641221 + 0.767356i \(0.721572\pi\)
\(198\) −1.99433 12.4047i −0.141731 0.881566i
\(199\) −11.8378 + 4.30860i −0.839159 + 0.305429i −0.725612 0.688104i \(-0.758443\pi\)
−0.113547 + 0.993533i \(0.536221\pi\)
\(200\) 2.66706 + 2.23793i 0.188590 + 0.158246i
\(201\) 1.52501 + 19.0929i 0.107566 + 1.34671i
\(202\) 2.79637 1.61449i 0.196752 0.113595i
\(203\) 1.00563 + 0.843824i 0.0705814 + 0.0592249i
\(204\) 7.81579 2.03101i 0.547215 0.142199i
\(205\) 14.5060 + 2.55779i 1.01314 + 0.178644i
\(206\) 0.355984 0.0627696i 0.0248026 0.00437336i
\(207\) 14.2263 + 12.3087i 0.988794 + 0.855512i
\(208\) 5.66601i 0.392867i
\(209\) 16.8788 6.95382i 1.16753 0.481006i
\(210\) 0.266356 0.183518i 0.0183803 0.0126640i
\(211\) −6.74580 8.03934i −0.464400 0.553451i 0.482116 0.876108i \(-0.339868\pi\)
−0.946516 + 0.322657i \(0.895424\pi\)
\(212\) −4.90948 1.78691i −0.337185 0.122725i
\(213\) 2.66736 + 1.89793i 0.182765 + 0.130044i
\(214\) −14.8551 5.40681i −1.01547 0.369602i
\(215\) −7.62839 1.34509i −0.520252 0.0917344i
\(216\) 1.45838 4.98730i 0.0992301 0.339343i
\(217\) −1.18614 + 0.684819i −0.0805205 + 0.0464885i
\(218\) 7.48615 8.92164i 0.507026 0.604250i
\(219\) 15.1145 6.90935i 1.02135 0.466891i
\(220\) −5.16060 −0.347928
\(221\) −13.2084 22.8776i −0.888491 1.53891i
\(222\) 2.82778 + 6.18590i 0.189788 + 0.415170i
\(223\) 4.64461 12.7610i 0.311026 0.854537i −0.681424 0.731889i \(-0.738639\pi\)
0.992450 0.122648i \(-0.0391387\pi\)
\(224\) 0.116096 + 0.0974161i 0.00775699 + 0.00650889i
\(225\) 6.83404 7.89873i 0.455603 0.526582i
\(226\) −6.70886 2.44183i −0.446267 0.162428i
\(227\) −3.96772 6.87229i −0.263347 0.456130i 0.703782 0.710416i \(-0.251493\pi\)
−0.967129 + 0.254286i \(0.918160\pi\)
\(228\) 7.53919 + 0.400699i 0.499295 + 0.0265369i
\(229\) −8.53888 + 14.7898i −0.564265 + 0.977336i 0.432852 + 0.901465i \(0.357507\pi\)
−0.997118 + 0.0758711i \(0.975826\pi\)
\(230\) 5.91915 4.96676i 0.390297 0.327498i
\(231\) 0.292552 1.05970i 0.0192485 0.0697230i
\(232\) 1.50415 8.53047i 0.0987524 0.560053i
\(233\) 14.3087 + 17.0524i 0.937394 + 1.11714i 0.992932 + 0.118686i \(0.0378681\pi\)
−0.0555380 + 0.998457i \(0.517687\pi\)
\(234\) −16.9961 0.257088i −1.11107 0.0168064i
\(235\) −1.94799 + 3.37401i −0.127073 + 0.220096i
\(236\) 3.47336 6.01604i 0.226097 0.391611i
\(237\) 0.618228 0.868862i 0.0401583 0.0564386i
\(238\) 0.695851 + 0.122697i 0.0451053 + 0.00795329i
\(239\) 18.0802i 1.16951i −0.811210 0.584754i \(-0.801191\pi\)
0.811210 0.584754i \(-0.198809\pi\)
\(240\) −1.92745 0.916592i −0.124416 0.0591657i
\(241\) −4.35941 11.9774i −0.280814 0.771531i −0.997266 0.0738946i \(-0.976457\pi\)
0.716452 0.697637i \(-0.245765\pi\)
\(242\) −5.00950 + 4.20347i −0.322023 + 0.270209i
\(243\) −14.8940 4.60093i −0.955451 0.295150i
\(244\) 0.197824 + 1.12192i 0.0126644 + 0.0718233i
\(245\) −8.46671 + 1.49291i −0.540918 + 0.0953785i
\(246\) 20.6387 1.64848i 1.31588 0.105103i
\(247\) −5.29964 24.1223i −0.337208 1.53486i
\(248\) 7.82660 + 4.51869i 0.496990 + 0.286937i
\(249\) −19.4295 + 5.04896i −1.23130 + 0.319965i
\(250\) −6.71797 8.00616i −0.424882 0.506354i
\(251\) −2.31257 + 2.75602i −0.145968 + 0.173958i −0.834075 0.551652i \(-0.813998\pi\)
0.688106 + 0.725610i \(0.258442\pi\)
\(252\) 0.297483 0.343828i 0.0187396 0.0216591i
\(253\) 4.56028 25.8626i 0.286702 1.62597i
\(254\) 5.54999i 0.348237i
\(255\) −9.91914 + 0.792272i −0.621160 + 0.0496140i
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −4.94891 + 28.0667i −0.308705 + 1.75075i 0.296829 + 0.954931i \(0.404071\pi\)
−0.605533 + 0.795820i \(0.707040\pi\)
\(258\) −10.8535 + 0.866900i −0.675708 + 0.0539708i
\(259\) 0.595132i 0.0369797i
\(260\) −1.21238 + 6.87577i −0.0751888 + 0.426417i
\(261\) −25.5202 4.89900i −1.57966 0.303240i
\(262\) −1.26981 + 1.51330i −0.0784493 + 0.0934923i
\(263\) 2.73531 + 3.25981i 0.168666 + 0.201009i 0.843756 0.536727i \(-0.180340\pi\)
−0.675090 + 0.737736i \(0.735895\pi\)
\(264\) −7.02068 + 1.82439i −0.432093 + 0.112284i
\(265\) 5.57536 + 3.21894i 0.342492 + 0.197738i
\(266\) 0.585380 + 0.306147i 0.0358919 + 0.0187711i
\(267\) 1.29423 0.103374i 0.0792055 0.00632639i
\(268\) 10.8904 1.92027i 0.665236 0.117299i
\(269\) 4.10283 + 23.2683i 0.250154 + 1.41869i 0.808212 + 0.588891i \(0.200435\pi\)
−0.558058 + 0.829802i \(0.688454\pi\)
\(270\) −2.83692 + 5.74009i −0.172649 + 0.349330i
\(271\) 24.4569 20.5218i 1.48565 1.24661i 0.585770 0.810478i \(-0.300792\pi\)
0.899882 0.436132i \(-0.143652\pi\)
\(272\) −1.59461 4.38114i −0.0966872 0.265646i
\(273\) −1.34317 0.638740i −0.0812922 0.0386583i
\(274\) 4.38741i 0.265053i
\(275\) −14.3595 2.53196i −0.865909 0.152683i
\(276\) 6.29678 8.84953i 0.379021 0.532679i
\(277\) −2.15381 + 3.73051i −0.129410 + 0.224144i −0.923448 0.383723i \(-0.874642\pi\)
0.794038 + 0.607868i \(0.207975\pi\)
\(278\) −10.9634 + 18.9891i −0.657539 + 1.13889i
\(279\) 13.9096 23.2721i 0.832748 1.39326i
\(280\) −0.120039 0.143057i −0.00717371 0.00854930i
\(281\) 2.07535 11.7699i 0.123805 0.702132i −0.858206 0.513306i \(-0.828421\pi\)
0.982011 0.188826i \(-0.0604682\pi\)
\(282\) −1.45732 + 5.27879i −0.0867823 + 0.314347i
\(283\) 1.23232 1.03404i 0.0732536 0.0614671i −0.605426 0.795902i \(-0.706997\pi\)
0.678679 + 0.734435i \(0.262553\pi\)
\(284\) 0.945030 1.63684i 0.0560772 0.0971286i
\(285\) −9.06316 2.09945i −0.536855 0.124361i
\(286\) 11.8647 + 20.5502i 0.701572 + 1.21516i
\(287\) 1.70236 + 0.619609i 0.100487 + 0.0365743i
\(288\) −2.94621 0.565569i −0.173607 0.0333265i
\(289\) −3.62890 3.04501i −0.213465 0.179118i
\(290\) −3.65061 + 10.0300i −0.214371 + 0.588980i
\(291\) −5.05236 11.0523i −0.296174 0.647896i
\(292\) −4.79747 8.30946i −0.280751 0.486274i
\(293\) 4.13384 0.241502 0.120751 0.992683i \(-0.461470\pi\)
0.120751 + 0.992683i \(0.461470\pi\)
\(294\) −10.9907 + 5.02419i −0.640988 + 0.293017i
\(295\) −5.50225 + 6.55732i −0.320353 + 0.381782i
\(296\) 3.40080 1.96345i 0.197667 0.114123i
\(297\) 5.15400 + 21.1424i 0.299065 + 1.22681i
\(298\) 1.93527 + 0.341240i 0.112107 + 0.0197675i
\(299\) −33.3869 12.1518i −1.93082 0.702759i
\(300\) −4.91345 3.49611i −0.283678 0.201848i
\(301\) −0.895237 0.325840i −0.0516006 0.0187811i
\(302\) −4.44571 5.29819i −0.255822 0.304877i
\(303\) −4.60544 + 3.17313i −0.264575 + 0.182291i
\(304\) −0.181845 4.35510i −0.0104295 0.249782i
\(305\) 1.40379i 0.0803806i
\(306\) −13.2143 + 4.58448i −0.755410 + 0.262077i
\(307\) −2.00147 + 0.352914i −0.114230 + 0.0201419i −0.230471 0.973079i \(-0.574027\pi\)
0.116241 + 0.993221i \(0.462916\pi\)
\(308\) −0.625061 0.110215i −0.0356162 0.00628009i
\(309\) −0.605969 + 0.157467i −0.0344723 + 0.00895798i
\(310\) −8.53078 7.15818i −0.484516 0.406557i
\(311\) −14.6056 + 8.43256i −0.828209 + 0.478167i −0.853239 0.521520i \(-0.825365\pi\)
0.0250301 + 0.999687i \(0.492032\pi\)
\(312\) 0.781372 + 9.78266i 0.0442365 + 0.553834i
\(313\) −13.1523 11.0361i −0.743414 0.623798i 0.190338 0.981719i \(-0.439041\pi\)
−0.933752 + 0.357920i \(0.883486\pi\)
\(314\) 17.6475 6.42317i 0.995906 0.362480i
\(315\) −0.434569 + 0.353585i −0.0244852 + 0.0199223i
\(316\) −0.533181 0.307832i −0.0299938 0.0173169i
\(317\) 29.9396 10.8971i 1.68158 0.612044i 0.688052 0.725661i \(-0.258466\pi\)
0.993525 + 0.113617i \(0.0362438\pi\)
\(318\) 8.72290 + 2.40814i 0.489156 + 0.135042i
\(319\) 12.4074 + 34.0891i 0.694681 + 1.90862i
\(320\) −0.421448 + 1.15792i −0.0235597 + 0.0647296i
\(321\) 26.3937 + 7.28655i 1.47315 + 0.406695i
\(322\) 0.823014 0.475167i 0.0458648 0.0264800i
\(323\) −10.8867 17.1606i −0.605750 0.954843i
\(324\) −1.83019 + 8.81195i −0.101677 + 0.489553i
\(325\) −6.74697 + 18.5371i −0.374254 + 1.02826i
\(326\) −8.83967 + 7.41736i −0.489584 + 0.410810i
\(327\) −11.6949 + 16.4361i −0.646729 + 0.908916i
\(328\) −2.07574 11.7721i −0.114614 0.650006i
\(329\) −0.308002 + 0.367063i −0.0169807 + 0.0202368i
\(330\) 8.91004 0.711673i 0.490482 0.0391763i
\(331\) 27.0602 + 15.6232i 1.48736 + 0.858728i 0.999896 0.0144149i \(-0.00458856\pi\)
0.487464 + 0.873143i \(0.337922\pi\)
\(332\) 3.96409 + 10.8912i 0.217558 + 0.597734i
\(333\) −5.73537 10.2903i −0.314296 0.563905i
\(334\) 2.19686 + 3.80508i 0.120207 + 0.208205i
\(335\) −13.6265 −0.744494
\(336\) −0.213880 0.152184i −0.0116681 0.00830230i
\(337\) 24.2172 4.27015i 1.31920 0.232610i 0.530653 0.847589i \(-0.321947\pi\)
0.788543 + 0.614979i \(0.210836\pi\)
\(338\) 17.9516 6.53384i 0.976438 0.355394i
\(339\) 11.9199 + 3.29075i 0.647402 + 0.178729i
\(340\) 0.997618 + 5.65777i 0.0541034 + 0.306836i
\(341\) −37.8486 −2.04962
\(342\) −13.0721 + 0.347865i −0.706857 + 0.0188104i
\(343\) −2.11825 −0.114375
\(344\) 1.09159 + 6.19071i 0.0588545 + 0.333781i
\(345\) −9.53478 + 9.39165i −0.513336 + 0.505629i
\(346\) 8.21013 2.98824i 0.441379 0.160649i
\(347\) −20.9391 + 3.69212i −1.12407 + 0.198203i −0.704626 0.709579i \(-0.748885\pi\)
−0.419442 + 0.907782i \(0.637774\pi\)
\(348\) −1.42060 + 14.9357i −0.0761522 + 0.800639i
\(349\) −28.0360 −1.50073 −0.750367 0.661022i \(-0.770123\pi\)
−0.750367 + 0.661022i \(0.770123\pi\)
\(350\) −0.263823 0.456955i −0.0141019 0.0244253i
\(351\) 29.3801 1.89997i 1.56819 0.101413i
\(352\) 1.43238 + 3.93544i 0.0763463 + 0.209760i
\(353\) 8.26849 + 4.77382i 0.440088 + 0.254085i 0.703635 0.710562i \(-0.251559\pi\)
−0.263547 + 0.964646i \(0.584892\pi\)
\(354\) −5.16730 + 10.8660i −0.274639 + 0.577521i
\(355\) −1.49705 + 1.78411i −0.0794550 + 0.0946908i
\(356\) −0.130167 0.738215i −0.00689884 0.0391253i
\(357\) −1.21834 0.115882i −0.0644816 0.00613312i
\(358\) −6.70816 + 5.62882i −0.354537 + 0.297492i
\(359\) 1.81305 4.98132i 0.0956893 0.262904i −0.882608 0.470109i \(-0.844215\pi\)
0.978298 + 0.207205i \(0.0664368\pi\)
\(360\) 3.45424 + 1.31674i 0.182054 + 0.0693982i
\(361\) −4.84768 18.3712i −0.255141 0.966904i
\(362\) −6.74163 + 3.89228i −0.354332 + 0.204574i
\(363\) 8.06948 7.94834i 0.423538 0.417180i
\(364\) −0.293692 + 0.806913i −0.0153937 + 0.0422937i
\(365\) 4.04377 + 11.1102i 0.211660 + 0.581532i
\(366\) −0.496271 1.90977i −0.0259405 0.0998250i
\(367\) 1.97741 0.719720i 0.103220 0.0375691i −0.289894 0.957059i \(-0.593620\pi\)
0.393114 + 0.919490i \(0.371398\pi\)
\(368\) −5.43055 3.13533i −0.283087 0.163440i
\(369\) −35.4064 + 5.69236i −1.84319 + 0.296332i
\(370\) −4.54703 + 1.65498i −0.236389 + 0.0860385i
\(371\) 0.606551 + 0.508956i 0.0314905 + 0.0264237i
\(372\) −14.1362 6.72243i −0.732927 0.348542i
\(373\) −2.70068 + 1.55924i −0.139836 + 0.0807342i −0.568286 0.822831i \(-0.692393\pi\)
0.428450 + 0.903566i \(0.359060\pi\)
\(374\) 14.9577 + 12.5510i 0.773442 + 0.648995i
\(375\) 12.7030 + 12.8966i 0.655981 + 0.665978i
\(376\) 3.11369 + 0.549027i 0.160576 + 0.0283139i
\(377\) 48.3337 8.52254i 2.48931 0.438933i
\(378\) −0.466204 + 0.634661i −0.0239789 + 0.0326435i
\(379\) 21.1889i 1.08840i 0.838955 + 0.544201i \(0.183167\pi\)
−0.838955 + 0.544201i \(0.816833\pi\)
\(380\) −0.711211 + 5.32388i −0.0364844 + 0.273109i
\(381\) −0.765371 9.58234i −0.0392111 0.490918i
\(382\) −11.8158 14.0815i −0.604548 0.720473i
\(383\) −2.18013 0.793502i −0.111399 0.0405460i 0.285719 0.958313i \(-0.407768\pi\)
−0.397118 + 0.917767i \(0.629990\pi\)
\(384\) −0.164003 + 1.72427i −0.00836923 + 0.0879912i
\(385\) 0.734935 + 0.267495i 0.0374558 + 0.0136328i
\(386\) −7.56880 1.33458i −0.385242 0.0679285i
\(387\) 18.6195 2.99350i 0.946484 0.152168i
\(388\) −6.07617 + 3.50808i −0.308471 + 0.178096i
\(389\) 11.1404 13.2766i 0.564842 0.673153i −0.405722 0.913997i \(-0.632980\pi\)
0.970564 + 0.240844i \(0.0774242\pi\)
\(390\) 1.14504 12.0386i 0.0579814 0.609597i
\(391\) −29.2358 −1.47852
\(392\) 3.48852 + 6.04229i 0.176197 + 0.305182i
\(393\) 1.98371 2.78791i 0.100065 0.140632i
\(394\) 1.64786 4.52747i 0.0830182 0.228091i
\(395\) 0.581153 + 0.487645i 0.0292410 + 0.0245361i
\(396\) 11.8700 4.11809i 0.596488 0.206942i
\(397\) −33.5646 12.2165i −1.68456 0.613129i −0.690635 0.723203i \(-0.742669\pi\)
−0.993923 + 0.110074i \(0.964891\pi\)
\(398\) −6.29876 10.9098i −0.315728 0.546857i
\(399\) −1.05291 0.447851i −0.0527113 0.0224206i
\(400\) −1.74080 + 3.01516i −0.0870401 + 0.150758i
\(401\) −1.63438 + 1.37141i −0.0816173 + 0.0684850i −0.682684 0.730714i \(-0.739187\pi\)
0.601066 + 0.799199i \(0.294743\pi\)
\(402\) −18.5380 + 4.81728i −0.924591 + 0.240264i
\(403\) −8.89181 + 50.4280i −0.442933 + 2.51200i
\(404\) 2.07554 + 2.47354i 0.103262 + 0.123063i
\(405\) 4.10650 10.3018i 0.204053 0.511900i
\(406\) −0.656379 + 1.13688i −0.0325755 + 0.0564225i
\(407\) −8.22295 + 14.2426i −0.407596 + 0.705978i
\(408\) 3.35735 + 7.34437i 0.166214 + 0.363600i
\(409\) −1.20787 0.212980i −0.0597253 0.0105312i 0.143706 0.989620i \(-0.454098\pi\)
−0.203431 + 0.979089i \(0.565209\pi\)
\(410\) 14.7297i 0.727450i
\(411\) −0.605047 7.57510i −0.0298447 0.373652i
\(412\) 0.123632 + 0.339676i 0.00609091 + 0.0167346i
\(413\) −0.806487 + 0.676723i −0.0396846 + 0.0332994i
\(414\) −9.65132 + 16.1475i −0.474336 + 0.793607i
\(415\) −2.48001 14.0649i −0.121739 0.690417i
\(416\) 5.57993 0.983892i 0.273579 0.0482393i
\(417\) 16.3101 34.2976i 0.798710 1.67956i
\(418\) 9.77915 + 15.4148i 0.478314 + 0.753965i
\(419\) 6.61242 + 3.81768i 0.323038 + 0.186506i 0.652746 0.757577i \(-0.273617\pi\)
−0.329708 + 0.944083i \(0.606950\pi\)
\(420\) 0.226982 + 0.230442i 0.0110756 + 0.0112444i
\(421\) −12.4583 14.8472i −0.607181 0.723610i 0.371629 0.928381i \(-0.378799\pi\)
−0.978810 + 0.204772i \(0.934355\pi\)
\(422\) 6.74580 8.03934i 0.328381 0.391349i
\(423\) 1.78817 9.31508i 0.0869439 0.452915i
\(424\) 0.907236 5.14519i 0.0440593 0.249872i
\(425\) 16.2323i 0.787384i
\(426\) −1.40591 + 2.95641i −0.0681168 + 0.143239i
\(427\) 0.0299807 0.170029i 0.00145087 0.00822829i
\(428\) 2.74511 15.5683i 0.132690 0.752521i
\(429\) −23.3189 33.8448i −1.12585 1.63404i
\(430\) 7.74607i 0.373549i
\(431\) 4.06994 23.0818i 0.196042 1.11181i −0.714885 0.699242i \(-0.753521\pi\)
0.910927 0.412568i \(-0.135368\pi\)
\(432\) 5.16477 + 0.570188i 0.248490 + 0.0274332i
\(433\) 0.835652 0.995891i 0.0401589 0.0478595i −0.745591 0.666404i \(-0.767833\pi\)
0.785750 + 0.618544i \(0.212277\pi\)
\(434\) −0.880386 1.04920i −0.0422599 0.0503634i
\(435\) 4.91978 17.8207i 0.235886 0.854437i
\(436\) 10.0861 + 5.82319i 0.483035 + 0.278880i
\(437\) −26.0524 8.26883i −1.24626 0.395552i
\(438\) 9.42899 + 13.6851i 0.450535 + 0.653900i
\(439\) 4.77876 0.842624i 0.228078 0.0402163i −0.0584411 0.998291i \(-0.518613\pi\)
0.286519 + 0.958075i \(0.407502\pi\)
\(440\) −0.896129 5.08220i −0.0427213 0.242284i
\(441\) 18.2831 10.1902i 0.870623 0.485247i
\(442\) 20.2364 16.9803i 0.962547 0.807673i
\(443\) −5.05432 13.8866i −0.240138 0.659774i −0.999954 0.00963524i \(-0.996933\pi\)
0.759815 0.650139i \(-0.225289\pi\)
\(444\) −5.60088 + 3.85899i −0.265806 + 0.183139i
\(445\) 0.923684i 0.0437868i
\(446\) 13.3736 + 2.35813i 0.633259 + 0.111661i
\(447\) −3.38840 0.322286i −0.160266 0.0152436i
\(448\) −0.0757763 + 0.131248i −0.00358009 + 0.00620090i
\(449\) −3.14402 + 5.44561i −0.148376 + 0.256994i −0.930627 0.365968i \(-0.880738\pi\)
0.782252 + 0.622963i \(0.214071\pi\)
\(450\) 8.96545 + 5.35862i 0.422636 + 0.252608i
\(451\) 32.1794 + 38.3499i 1.51527 + 1.80583i
\(452\) 1.23975 7.03096i 0.0583128 0.330709i
\(453\) 8.40639 + 8.53451i 0.394967 + 0.400986i
\(454\) 6.07890 5.10080i 0.285297 0.239393i
\(455\) 0.529058 0.916355i 0.0248026 0.0429594i
\(456\) 0.914556 + 7.49424i 0.0428280 + 0.350950i
\(457\) −2.08364 3.60897i −0.0974685 0.168820i 0.813168 0.582030i \(-0.197741\pi\)
−0.910636 + 0.413209i \(0.864408\pi\)
\(458\) −16.0478 5.84094i −0.749867 0.272929i
\(459\) 22.1829 9.73766i 1.03541 0.454515i
\(460\) 5.91915 + 4.96676i 0.275982 + 0.231576i
\(461\) −1.93086 + 5.30498i −0.0899289 + 0.247078i −0.976501 0.215513i \(-0.930858\pi\)
0.886572 + 0.462590i \(0.153080\pi\)
\(462\) 1.09440 + 0.104093i 0.0509161 + 0.00484285i
\(463\) −1.28617 2.22771i −0.0597734 0.103531i 0.834590 0.550871i \(-0.185704\pi\)
−0.894364 + 0.447341i \(0.852371\pi\)
\(464\) 8.66206 0.402126
\(465\) 15.7160 + 11.1825i 0.728812 + 0.518577i
\(466\) −14.3087 + 17.0524i −0.662838 + 0.789939i
\(467\) 16.9075 9.76155i 0.782386 0.451711i −0.0548891 0.998492i \(-0.517481\pi\)
0.837275 + 0.546782i \(0.184147\pi\)
\(468\) −2.69816 16.7825i −0.124722 0.775772i
\(469\) −1.65046 0.291021i −0.0762114 0.0134381i
\(470\) −3.66102 1.33250i −0.168870 0.0614637i
\(471\) −29.5836 + 13.5236i −1.36314 + 0.623135i
\(472\) 6.52779 + 2.37592i 0.300466 + 0.109361i
\(473\) −16.9225 20.1674i −0.778097 0.927300i
\(474\) 0.963016 + 0.457960i 0.0442328 + 0.0210348i
\(475\) −4.59104 + 14.4649i −0.210651 + 0.663693i
\(476\) 0.706586i 0.0323863i
\(477\) −15.3926 2.95485i −0.704780 0.135293i
\(478\) 17.8055 3.13959i 0.814404 0.143601i
\(479\) 12.9662 + 2.28629i 0.592441 + 0.104463i 0.461827 0.886970i \(-0.347194\pi\)
0.130614 + 0.991433i \(0.458305\pi\)
\(480\) 0.567969 2.05733i 0.0259241 0.0939037i
\(481\) 17.0444 + 14.3019i 0.777157 + 0.652112i
\(482\) 11.0384 6.37304i 0.502786 0.290284i
\(483\) −1.35545 + 0.933899i −0.0616750 + 0.0424939i
\(484\) −5.00950 4.20347i −0.227704 0.191067i
\(485\) 8.12414 2.95694i 0.368898 0.134268i
\(486\) 1.94471 15.4667i 0.0882140 0.701583i
\(487\) 0.979574 + 0.565557i 0.0443887 + 0.0256278i 0.522030 0.852927i \(-0.325175\pi\)
−0.477641 + 0.878555i \(0.658508\pi\)
\(488\) −1.07052 + 0.389637i −0.0484602 + 0.0176381i
\(489\) 14.2393 14.0255i 0.643921 0.634255i
\(490\) −2.94046 8.07884i −0.132836 0.364965i
\(491\) 6.03935 16.5930i 0.272552 0.748831i −0.725603 0.688114i \(-0.758439\pi\)
0.998155 0.0607172i \(-0.0193388\pi\)
\(492\) 5.20730 + 20.0389i 0.234763 + 0.903423i
\(493\) 34.9747 20.1926i 1.57518 0.909431i
\(494\) 22.8355 9.40791i 1.02742 0.423282i
\(495\) −15.2855 + 2.45748i −0.687033 + 0.110456i
\(496\) −3.09097 + 8.49236i −0.138788 + 0.381318i
\(497\) −0.219428 + 0.184122i −0.00984270 + 0.00825901i
\(498\) −8.34616 18.2576i −0.374000 0.818144i
\(499\) −1.60738 9.11592i −0.0719564 0.408085i −0.999416 0.0341623i \(-0.989124\pi\)
0.927460 0.373923i \(-0.121987\pi\)
\(500\) 6.71797 8.00616i 0.300437 0.358046i
\(501\) −4.31774 6.26671i −0.192902 0.279976i
\(502\) −3.11572 1.79886i −0.139062 0.0802872i
\(503\) 6.58007 + 18.0786i 0.293391 + 0.806084i 0.995565 + 0.0940790i \(0.0299906\pi\)
−0.702174 + 0.712005i \(0.747787\pi\)
\(504\) 0.390262 + 0.233258i 0.0173836 + 0.0103901i
\(505\) −1.98942 3.44578i −0.0885281 0.153335i
\(506\) 26.2616 1.16747
\(507\) −30.0933 + 13.7566i −1.33649 + 0.610954i
\(508\) −5.46567 + 0.963745i −0.242500 + 0.0427593i
\(509\) −10.5636 + 3.84485i −0.468224 + 0.170420i −0.565348 0.824853i \(-0.691258\pi\)
0.0971234 + 0.995272i \(0.469036\pi\)
\(510\) −2.50268 9.63086i −0.110820 0.426462i
\(511\) 0.252508 + 1.43204i 0.0111703 + 0.0633499i
\(512\) 1.00000 0.0441942
\(513\) 22.5216 2.40331i 0.994355 0.106109i
\(514\) −28.4996 −1.25707
\(515\) −0.0773467 0.438655i −0.00340830 0.0193294i
\(516\) −2.73842 10.5380i −0.120552 0.463912i
\(517\) −12.4428 + 4.52880i −0.547232 + 0.199176i
\(518\) −0.586090 + 0.103344i −0.0257513 + 0.00454065i
\(519\) −13.7631 + 6.29158i −0.604134 + 0.276170i
\(520\) −6.98184 −0.306174
\(521\) −11.7751 20.3951i −0.515876 0.893524i −0.999830 0.0184307i \(-0.994133\pi\)
0.483954 0.875094i \(-0.339200\pi\)
\(522\) 0.393030 25.9832i 0.0172025 1.13725i
\(523\) 3.98784 + 10.9565i 0.174376 + 0.479094i 0.995835 0.0911733i \(-0.0290617\pi\)
−0.821459 + 0.570268i \(0.806839\pi\)
\(524\) −1.71081 0.987739i −0.0747373 0.0431496i
\(525\) 0.518521 + 0.752574i 0.0226301 + 0.0328450i
\(526\) −2.73531 + 3.25981i −0.119265 + 0.142135i
\(527\) 7.31669 + 41.4950i 0.318720 + 1.80755i
\(528\) −3.01580 6.59721i −0.131246 0.287107i
\(529\) −12.5027 + 10.4910i −0.543597 + 0.456132i
\(530\) −2.20188 + 6.04962i −0.0956436 + 0.262779i
\(531\) 7.42313 19.4733i 0.322137 0.845070i
\(532\) −0.199845 + 0.629648i −0.00866440 + 0.0272987i
\(533\) 58.6557 33.8649i 2.54066 1.46685i
\(534\) 0.326544 + 1.25662i 0.0141309 + 0.0543791i
\(535\) −6.66244 + 18.3049i −0.288042 + 0.791390i
\(536\) 3.78219 + 10.3915i 0.163366 + 0.448843i
\(537\) 10.8058 10.6435i 0.466303 0.459302i
\(538\) −22.2023 + 8.08099i −0.957211 + 0.348396i
\(539\) −25.3052 14.6099i −1.08997 0.629295i
\(540\) −6.14551 1.79706i −0.264460 0.0773332i
\(541\) 3.57328 1.30057i 0.153628 0.0559158i −0.264062 0.964506i \(-0.585062\pi\)
0.417689 + 0.908590i \(0.362840\pi\)
\(542\) 24.4569 + 20.5218i 1.05051 + 0.881486i
\(543\) 11.1030 7.64993i 0.476476 0.328290i
\(544\) 4.03768 2.33116i 0.173114 0.0999476i
\(545\) −10.9935 9.22467i −0.470911 0.395141i
\(546\) 0.395797 1.43368i 0.0169386 0.0613558i
\(547\) 41.7067 + 7.35402i 1.78325 + 0.314435i 0.965356 0.260935i \(-0.0840307\pi\)
0.817894 + 0.575370i \(0.195142\pi\)
\(548\) −4.32076 + 0.761866i −0.184574 + 0.0325453i
\(549\) 1.12020 + 3.22887i 0.0478092 + 0.137805i
\(550\) 14.5810i 0.621736i
\(551\) 36.8775 8.10196i 1.57104 0.345155i
\(552\) 9.80850 + 4.66441i 0.417478 + 0.198530i
\(553\) 0.0599756 + 0.0714761i 0.00255042 + 0.00303948i
\(554\) −4.04784 1.47329i −0.171976 0.0625942i
\(555\) 7.62246 3.48448i 0.323555 0.147908i
\(556\) −20.6044 7.49938i −0.873821 0.318045i
\(557\) −3.13180 0.552221i −0.132699 0.0233984i 0.106904 0.994269i \(-0.465906\pi\)
−0.239603 + 0.970871i \(0.577017\pi\)
\(558\) 25.3339 + 9.65717i 1.07247 + 0.408821i
\(559\) −30.8459 + 17.8089i −1.30464 + 0.753235i
\(560\) 0.120039 0.143057i 0.00507258 0.00604527i
\(561\) −27.5560 19.6072i −1.16342 0.827815i
\(562\) 11.9514 0.504141
\(563\) 13.7502 + 23.8160i 0.579501 + 1.00372i 0.995537 + 0.0943765i \(0.0300858\pi\)
−0.416036 + 0.909348i \(0.636581\pi\)
\(564\) −5.45166 0.518531i −0.229556 0.0218341i
\(565\) −3.00890 + 8.26687i −0.126585 + 0.347790i
\(566\) 1.23232 + 1.03404i 0.0517981 + 0.0434638i
\(567\) 0.717402 1.16007i 0.0301280 0.0487183i
\(568\) 1.77607 + 0.646438i 0.0745224 + 0.0271240i
\(569\) 7.69616 + 13.3301i 0.322640 + 0.558829i 0.981032 0.193846i \(-0.0620963\pi\)
−0.658392 + 0.752675i \(0.728763\pi\)
\(570\) 0.493754 9.29003i 0.0206811 0.389117i
\(571\) 10.1606 17.5988i 0.425210 0.736485i −0.571230 0.820790i \(-0.693534\pi\)
0.996440 + 0.0843049i \(0.0268670\pi\)
\(572\) −18.1777 + 15.2529i −0.760048 + 0.637756i
\(573\) 22.3425 + 22.6830i 0.933371 + 0.947596i
\(574\) −0.314584 + 1.78409i −0.0131305 + 0.0744666i
\(575\) 14.0333 + 16.7242i 0.585230 + 0.697449i
\(576\) 0.0453738 2.99966i 0.00189057 0.124986i
\(577\) 1.95568 3.38733i 0.0814158 0.141016i −0.822442 0.568848i \(-0.807389\pi\)
0.903858 + 0.427832i \(0.140722\pi\)
\(578\) 2.36860 4.10253i 0.0985206 0.170643i
\(579\) 13.2520 + 1.26045i 0.550733 + 0.0523826i
\(580\) −10.5115 1.85346i −0.436467 0.0769609i
\(581\) 1.75653i 0.0728730i
\(582\) 10.0070 6.89481i 0.414805 0.285799i
\(583\) 7.48358 + 20.5610i 0.309938 + 0.851548i
\(584\) 7.35015 6.16750i 0.304151 0.255213i
\(585\) −0.316792 + 20.9431i −0.0130978 + 0.865891i
\(586\) 0.717834 + 4.07104i 0.0296534 + 0.168173i
\(587\) −16.9108 + 2.98183i −0.697983 + 0.123073i −0.511371 0.859360i \(-0.670862\pi\)
−0.186613 + 0.982434i \(0.559751\pi\)
\(588\) −6.85637 9.95124i −0.282752 0.410382i
\(589\) −5.21614 + 39.0462i −0.214927 + 1.60887i
\(590\) −7.41316 4.27999i −0.305195 0.176204i
\(591\) −2.22076 + 8.04416i −0.0913499 + 0.330893i
\(592\) 2.52416 + 3.00818i 0.103742 + 0.123635i
\(593\) 10.5095 12.5247i 0.431573 0.514329i −0.505802 0.862649i \(-0.668803\pi\)
0.937376 + 0.348320i \(0.113248\pi\)
\(594\) −19.9262 + 8.74703i −0.817583 + 0.358895i
\(595\) 0.151192 0.857450i 0.00619825 0.0351520i
\(596\) 1.96513i 0.0804947i
\(597\) 12.3796 + 17.9677i 0.506665 + 0.735367i
\(598\) 6.16965 34.9898i 0.252296 1.43084i
\(599\) −3.09275 + 17.5399i −0.126366 + 0.716660i 0.854120 + 0.520075i \(0.174096\pi\)
−0.980487 + 0.196585i \(0.937015\pi\)
\(600\) 2.58978 5.44589i 0.105727 0.222328i
\(601\) 30.8806i 1.25965i 0.776738 + 0.629824i \(0.216873\pi\)
−0.776738 + 0.629824i \(0.783127\pi\)
\(602\) 0.165433 0.938218i 0.00674255 0.0382389i
\(603\) 31.3425 10.8738i 1.27636 0.442814i
\(604\) 4.44571 5.29819i 0.180893 0.215580i
\(605\) 5.17965 + 6.17286i 0.210583 + 0.250962i
\(606\) −3.92465 3.98446i −0.159428 0.161858i
\(607\) −2.03226 1.17332i −0.0824867 0.0476237i 0.458189 0.888855i \(-0.348498\pi\)
−0.540676 + 0.841231i \(0.681832\pi\)
\(608\) 4.25736 0.935338i 0.172659 0.0379330i
\(609\) 0.976491 2.05340i 0.0395694 0.0832081i
\(610\) 1.38246 0.243765i 0.0559742 0.00986976i
\(611\) 3.11079 + 17.6422i 0.125849 + 0.713726i
\(612\) −6.80947 12.2174i −0.275256 0.493861i
\(613\) −20.2198 + 16.9664i −0.816670 + 0.685268i −0.952190 0.305507i \(-0.901174\pi\)
0.135520 + 0.990775i \(0.456730\pi\)
\(614\) −0.695105 1.90978i −0.0280521 0.0770726i
\(615\) −2.03130 25.4317i −0.0819101 1.02550i
\(616\) 0.634704i 0.0255729i
\(617\) −30.6875 5.41103i −1.23543 0.217840i −0.482475 0.875910i \(-0.660262\pi\)
−0.752957 + 0.658070i \(0.771373\pi\)
\(618\) −0.260300 0.569419i −0.0104708 0.0229054i
\(619\) −18.6411 + 32.2873i −0.749247 + 1.29773i 0.198937 + 0.980012i \(0.436251\pi\)
−0.948184 + 0.317722i \(0.897082\pi\)
\(620\) 5.56807 9.64419i 0.223619 0.387320i
\(621\) 14.4367 29.2105i 0.579324 1.17218i
\(622\) −10.8407 12.9194i −0.434672 0.518022i
\(623\) −0.0197272 + 0.111878i −0.000790352 + 0.00448231i
\(624\) −9.49836 + 2.46824i −0.380239 + 0.0988088i
\(625\) 3.46987 2.91157i 0.138795 0.116463i
\(626\) 8.58458 14.8689i 0.343109 0.594282i
\(627\) −19.0100 25.2659i −0.759186 1.00902i
\(628\) 9.39004 + 16.2640i 0.374703 + 0.649005i
\(629\) 17.2043 + 6.26186i 0.685981 + 0.249677i
\(630\) −0.423676 0.366567i −0.0168796 0.0146044i
\(631\) −27.1796 22.8064i −1.08200 0.907908i −0.0859172 0.996302i \(-0.527382\pi\)
−0.996086 + 0.0883941i \(0.971826\pi\)
\(632\) 0.210570 0.578535i 0.00837601 0.0230129i
\(633\) −10.5383 + 14.8106i −0.418860 + 0.588669i
\(634\) 15.9305 + 27.5925i 0.632683 + 1.09584i
\(635\) 6.83887 0.271392
\(636\) −0.856842 + 9.00855i −0.0339760 + 0.357212i
\(637\) −25.4106 + 30.2832i −1.00681 + 1.19986i
\(638\) −31.4166 + 18.1384i −1.24380 + 0.718106i
\(639\) 2.01968 5.29828i 0.0798973 0.209597i
\(640\) −1.21351 0.213975i −0.0479682 0.00845810i
\(641\) −35.8841 13.0607i −1.41734 0.515868i −0.484062 0.875034i \(-0.660839\pi\)
−0.933274 + 0.359166i \(0.883061\pi\)
\(642\) −2.59263 + 27.2580i −0.102323 + 1.07579i
\(643\) 40.8231 + 14.8584i 1.60991 + 0.585958i 0.981422 0.191864i \(-0.0614532\pi\)
0.628485 + 0.777822i \(0.283675\pi\)
\(644\) 0.610863 + 0.727998i 0.0240714 + 0.0286871i
\(645\) 1.06822 + 13.3740i 0.0420612 + 0.526600i
\(646\) 15.0095 13.7012i 0.590540 0.539066i
\(647\) 28.4430i 1.11821i −0.829097 0.559104i \(-0.811145\pi\)
0.829097 0.559104i \(-0.188855\pi\)
\(648\) −8.99588 0.272212i −0.353392 0.0106935i
\(649\) −28.6510 + 5.05194i −1.12465 + 0.198306i
\(650\) −19.4271 3.42552i −0.761994 0.134360i
\(651\) 1.66472 + 1.69009i 0.0652456 + 0.0662400i
\(652\) −8.83967 7.41736i −0.346188 0.290486i
\(653\) 27.8912 16.1030i 1.09147 0.630158i 0.157500 0.987519i \(-0.449657\pi\)
0.933966 + 0.357361i \(0.116323\pi\)
\(654\) −18.2172 8.66312i −0.712347 0.338755i
\(655\) 1.86474 + 1.56470i 0.0728615 + 0.0611381i
\(656\) 11.2328 4.08841i 0.438567 0.159626i
\(657\) −18.1669 22.3278i −0.708758 0.871089i
\(658\) −0.414971 0.239583i −0.0161772 0.00933993i
\(659\) −31.1905 + 11.3524i −1.21501 + 0.442227i −0.868438 0.495797i \(-0.834876\pi\)
−0.346570 + 0.938024i \(0.612654\pi\)
\(660\) 2.24807 + 8.65110i 0.0875062 + 0.336744i
\(661\) −9.69428 26.6348i −0.377064 1.03597i −0.972567 0.232622i \(-0.925270\pi\)
0.595503 0.803353i \(-0.296953\pi\)
\(662\) −10.6869 + 29.3620i −0.415358 + 1.14119i
\(663\) −32.5975 + 32.1082i −1.26598 + 1.24698i
\(664\) −10.0374 + 5.79511i −0.389527 + 0.224894i
\(665\) 0.377244 0.721324i 0.0146289 0.0279717i
\(666\) 9.13804 7.43513i 0.354092 0.288105i
\(667\) 18.5775 51.0411i 0.719322 1.97632i
\(668\) −3.36579 + 2.82423i −0.130226 + 0.109273i
\(669\) −23.4154 2.22714i −0.905293 0.0861064i
\(670\) −2.36621 13.4195i −0.0914148 0.518439i
\(671\) 3.06679 3.65486i 0.118392 0.141094i
\(672\) 0.112732 0.237057i 0.00434873 0.00914467i
\(673\) 40.1515 + 23.1815i 1.54773 + 0.893581i 0.998315 + 0.0580305i \(0.0184821\pi\)
0.549413 + 0.835551i \(0.314851\pi\)
\(674\) 8.41055 + 23.1078i 0.323962 + 0.890079i
\(675\) −16.2183 8.01555i −0.624243 0.308519i
\(676\) 9.55184 + 16.5443i 0.367378 + 0.636318i
\(677\) −31.6194 −1.21523 −0.607617 0.794230i \(-0.707874\pi\)
−0.607617 + 0.794230i \(0.707874\pi\)
\(678\) −1.17088 + 12.3103i −0.0449675 + 0.472774i
\(679\) 1.04716 0.184643i 0.0401864 0.00708594i
\(680\) −5.39858 + 1.96492i −0.207026 + 0.0753514i
\(681\) −9.79211 + 9.64511i −0.375234 + 0.369601i
\(682\) −6.57235 37.2736i −0.251668 1.42728i
\(683\) 9.45932 0.361951 0.180975 0.983488i \(-0.442075\pi\)
0.180975 + 0.983488i \(0.442075\pi\)
\(684\) −2.61252 12.8131i −0.0998923 0.489920i
\(685\) 5.40631 0.206565
\(686\) −0.367831 2.08607i −0.0140439 0.0796467i
\(687\) 28.5129 + 7.87161i 1.08784 + 0.300321i
\(688\) −5.90711 + 2.15001i −0.225206 + 0.0819684i
\(689\) 29.1527 5.14041i 1.11063 0.195834i
\(690\) −10.9047 7.75909i −0.415134 0.295383i
\(691\) −39.5236 −1.50355 −0.751775 0.659420i \(-0.770802\pi\)
−0.751775 + 0.659420i \(0.770802\pi\)
\(692\) 4.36852 + 7.56650i 0.166066 + 0.287635i
\(693\) −1.90389 0.0287989i −0.0723229 0.00109398i
\(694\) −7.27206 19.9798i −0.276044 0.758424i
\(695\) 23.3990 + 13.5094i 0.887574 + 0.512441i
\(696\) −14.9555 + 1.19454i −0.566887 + 0.0452790i
\(697\) 35.8238 42.6932i 1.35692 1.61712i
\(698\) −4.86840 27.6101i −0.184272 1.04506i
\(699\) 22.3531 31.4152i 0.845472 1.18823i
\(700\) 0.404200 0.339164i 0.0152773 0.0128192i
\(701\) −7.11248 + 19.5414i −0.268634 + 0.738067i 0.729880 + 0.683576i \(0.239576\pi\)
−0.998514 + 0.0544916i \(0.982646\pi\)
\(702\) 6.97290 + 28.6038i 0.263175 + 1.07958i
\(703\) 13.5599 + 10.4460i 0.511423 + 0.393977i
\(704\) −3.62692 + 2.09401i −0.136695 + 0.0789208i
\(705\) 6.50469 + 1.79576i 0.244981 + 0.0676322i
\(706\) −3.26548 + 8.97184i −0.122898 + 0.337660i
\(707\) −0.167371 0.459847i −0.00629462 0.0172943i
\(708\) −11.5982 3.20193i −0.435888 0.120336i
\(709\) 40.3486 14.6857i 1.51532 0.551533i 0.555349 0.831618i \(-0.312585\pi\)
0.959975 + 0.280085i \(0.0903625\pi\)
\(710\) −2.01697 1.16450i −0.0756954 0.0437027i
\(711\) −1.72585 0.657887i −0.0647245 0.0246727i
\(712\) 0.704396 0.256379i 0.0263984 0.00960822i
\(713\) 43.4120 + 36.4270i 1.62579 + 1.36420i
\(714\) −0.0974418 1.21996i −0.00364667 0.0456558i
\(715\) 25.3226 14.6200i 0.947011 0.546757i
\(716\) −6.70816 5.62882i −0.250696 0.210359i
\(717\) −30.3091 + 7.87613i −1.13192 + 0.294139i
\(718\) 5.22048 + 0.920511i 0.194826 + 0.0343532i
\(719\) −2.15331 + 0.379686i −0.0803048 + 0.0141599i −0.213656 0.976909i \(-0.568537\pi\)
0.133351 + 0.991069i \(0.457426\pi\)
\(720\) −0.696913 + 3.63041i −0.0259724 + 0.135297i
\(721\) 0.0547825i 0.00204021i
\(722\) 17.2503 7.96415i 0.641989 0.296395i
\(723\) −18.1795 + 12.5256i −0.676104 + 0.465833i
\(724\) −5.00382 5.96332i −0.185966 0.221625i
\(725\) −28.3391 10.3146i −1.05249 0.383075i
\(726\) 9.22884 + 6.56667i 0.342514 + 0.243712i
\(727\) −5.96682 2.17174i −0.221297 0.0805455i 0.228992 0.973428i \(-0.426457\pi\)
−0.450289 + 0.892883i \(0.648679\pi\)
\(728\) −0.845653 0.149111i −0.0313420 0.00552644i
\(729\) −1.22472 + 26.9722i −0.0453599 + 0.998971i
\(730\) −10.2392 + 5.91159i −0.378969 + 0.218798i
\(731\) −18.8390 + 22.4515i −0.696786 + 0.830397i
\(732\) 1.79458 0.820359i 0.0663294 0.0303213i
\(733\) −44.1884 −1.63214 −0.816068 0.577957i \(-0.803850\pi\)
−0.816068 + 0.577957i \(0.803850\pi\)
\(734\) 1.05216 + 1.82239i 0.0388359 + 0.0672658i
\(735\) 6.19096 + 13.5430i 0.228357 + 0.499542i
\(736\) 2.14469 5.89249i 0.0790544 0.217200i
\(737\) −35.4775 29.7692i −1.30683 1.09656i
\(738\) −11.7541 33.8801i −0.432676 1.24714i
\(739\) 2.11001 + 0.767982i 0.0776181 + 0.0282507i 0.380537 0.924766i \(-0.375739\pi\)
−0.302919 + 0.953016i \(0.597961\pi\)
\(740\) −2.41943 4.19057i −0.0889399 0.154048i
\(741\) −38.1293 + 19.3924i −1.40072 + 0.712397i
\(742\) −0.395898 + 0.685715i −0.0145339 + 0.0251734i
\(743\) 24.8554 20.8561i 0.911854 0.765137i −0.0606165 0.998161i \(-0.519307\pi\)
0.972471 + 0.233024i \(0.0748622\pi\)
\(744\) 4.16557 15.0888i 0.152717 0.553181i
\(745\) 0.420487 2.38470i 0.0154055 0.0873687i
\(746\) −2.00452 2.38889i −0.0733905 0.0874634i
\(747\) 16.9279 + 30.3718i 0.619359 + 1.11124i
\(748\) −9.76291 + 16.9099i −0.356968 + 0.618286i
\(749\) −1.19791 + 2.07483i −0.0437705 + 0.0758127i
\(750\) −10.4948 + 14.7495i −0.383217 + 0.538576i
\(751\) −28.3950 5.00681i −1.03615 0.182701i −0.370397 0.928874i \(-0.620778\pi\)
−0.665753 + 0.746173i \(0.731889\pi\)
\(752\) 3.16172i 0.115296i
\(753\) 5.62753 + 2.67616i 0.205079 + 0.0975246i
\(754\) 16.7861 + 46.1195i 0.611315 + 1.67957i
\(755\) −6.52860 + 5.47814i −0.237600 + 0.199370i
\(756\) −0.705975 0.348913i −0.0256761 0.0126898i
\(757\) −6.92406 39.2683i −0.251659 1.42723i −0.804505 0.593946i \(-0.797569\pi\)
0.552846 0.833284i \(-0.313542\pi\)
\(758\) −20.8670 + 3.67942i −0.757925 + 0.133643i
\(759\) −45.3420 + 3.62161i −1.64581 + 0.131456i
\(760\) −5.36650 + 0.224075i −0.194663 + 0.00812807i
\(761\) 23.2754 + 13.4381i 0.843734 + 0.487130i 0.858532 0.512761i \(-0.171377\pi\)
−0.0147980 + 0.999891i \(0.504711\pi\)
\(762\) 9.30386 2.41770i 0.337043 0.0875840i
\(763\) −1.13454 1.35210i −0.0410733 0.0489492i
\(764\) 11.8158 14.0815i 0.427480 0.509451i
\(765\) 5.64914 + 16.2831i 0.204245 + 0.588715i
\(766\) 0.402871 2.28480i 0.0145563 0.0825531i
\(767\) 39.3602i 1.42122i
\(768\) −1.72655 + 0.137905i −0.0623016 + 0.00497622i
\(769\) 3.30147 18.7236i 0.119054 0.675189i −0.865609 0.500721i \(-0.833068\pi\)
0.984663 0.174468i \(-0.0558205\pi\)
\(770\) −0.135811 + 0.770220i −0.00489427 + 0.0277568i
\(771\) 49.2061 3.93024i 1.77211 0.141544i
\(772\) 7.68556i 0.276609i
\(773\) −8.41729 + 47.7368i −0.302749 + 1.71698i 0.331166 + 0.943572i \(0.392558\pi\)
−0.633915 + 0.773403i \(0.718553\pi\)
\(774\) 6.18127 + 17.8168i 0.222181 + 0.640413i
\(775\) 20.2250 24.1033i 0.726505 0.865815i
\(776\) −4.50990 5.37468i −0.161896 0.192940i
\(777\) 0.997664 0.259253i 0.0357910 0.00930064i
\(778\) 15.0095 + 8.66572i 0.538115 + 0.310681i
\(779\) 43.9981 27.9123i 1.57640 1.00006i
\(780\) 12.0545 0.962831i 0.431621 0.0344749i
\(781\) −7.79533 + 1.37453i −0.278939 + 0.0491845i
\(782\) −5.07674 28.7916i −0.181544 1.02959i
\(783\) 2.90463 + 44.9156i 0.103803 + 1.60515i
\(784\) −5.34472 + 4.48475i −0.190883 + 0.160170i
\(785\) −7.91483 21.7458i −0.282492 0.776142i
\(786\) 3.09003 + 1.46945i 0.110218 + 0.0524137i
\(787\) 21.1601i 0.754275i −0.926157 0.377137i \(-0.876908\pi\)
0.926157 0.377137i \(-0.123092\pi\)
\(788\) 4.74483 + 0.836642i 0.169028 + 0.0298042i
\(789\) 4.27311 6.00545i 0.152127 0.213800i
\(790\) −0.379321 + 0.657002i −0.0134956 + 0.0233751i
\(791\) −0.540999 + 0.937038i −0.0192357 + 0.0333172i
\(792\) 6.11673 + 10.9745i 0.217349 + 0.389963i
\(793\) −4.14910 4.94470i −0.147339 0.175592i
\(794\) 6.20249 35.1761i 0.220118 1.24835i
\(795\) 2.96739 10.7486i 0.105242 0.381215i
\(796\) 9.65026 8.09753i 0.342044 0.287009i
\(797\) 3.34795 5.79881i 0.118590 0.205404i −0.800619 0.599174i \(-0.795496\pi\)
0.919209 + 0.393769i \(0.128829\pi\)
\(798\) 0.258212 1.11468i 0.00914060 0.0394593i
\(799\) 7.37047 + 12.7660i 0.260748 + 0.451630i
\(800\) −3.27164 1.19078i −0.115670 0.0421004i
\(801\) −0.737089 2.12458i −0.0260437 0.0750683i
\(802\) −1.63438 1.37141i −0.0577121 0.0484262i
\(803\) −13.7436 + 37.7603i −0.485002 + 1.33253i
\(804\) −7.96318 17.4198i −0.280840 0.614350i
\(805\) −0.585516 1.01414i −0.0206367 0.0357439i
\(806\) −51.2059 −1.80365
\(807\) 37.2191 17.0141i 1.31017 0.598924i
\(808\) −2.07554 + 2.47354i −0.0730174 + 0.0870187i
\(809\) 0.239238 0.138124i 0.00841116 0.00485619i −0.495789 0.868443i \(-0.665121\pi\)
0.504200 + 0.863587i \(0.331788\pi\)
\(810\) 10.8584 + 2.25522i 0.381524 + 0.0792405i
\(811\) −15.6274 2.75553i −0.548752 0.0967597i −0.107603 0.994194i \(-0.534318\pi\)
−0.441148 + 0.897434i \(0.645429\pi\)
\(812\) −1.23359 0.448990i −0.0432905 0.0157564i
\(813\) −45.0562 32.0592i −1.58019 1.12437i
\(814\) −15.4541 5.62483i −0.541666 0.197150i
\(815\) 9.13991 + 10.8925i 0.320157 + 0.381548i
\(816\) −6.64979 + 4.58168i −0.232789 + 0.160391i
\(817\) −23.1377 + 14.6785i −0.809486 + 0.513536i
\(818\) 1.22650i 0.0428837i
\(819\) −0.485654 + 2.52990i −0.0169701 + 0.0884019i
\(820\) −14.5060 + 2.55779i −0.506570 + 0.0893220i
\(821\) −33.5466 5.91517i −1.17078 0.206441i −0.445752 0.895157i \(-0.647064\pi\)
−0.725031 + 0.688716i \(0.758175\pi\)
\(822\) 7.35495 1.91126i 0.256533 0.0666627i
\(823\) 0.656381 + 0.550769i 0.0228800 + 0.0191986i 0.654156 0.756360i \(-0.273024\pi\)
−0.631276 + 0.775558i \(0.717468\pi\)
\(824\) −0.313047 + 0.180738i −0.0109055 + 0.00629630i
\(825\) 2.01079 + 25.1749i 0.0700068 + 0.876476i
\(826\) −0.806487 0.676723i −0.0280613 0.0235462i
\(827\) −25.1865 + 9.16712i −0.875819 + 0.318772i −0.740521 0.672033i \(-0.765421\pi\)
−0.135298 + 0.990805i \(0.543199\pi\)
\(828\) −17.5781 6.70070i −0.610883 0.232866i
\(829\) −11.5202 6.65117i −0.400112 0.231005i 0.286420 0.958104i \(-0.407535\pi\)
−0.686532 + 0.727099i \(0.740868\pi\)
\(830\) 13.4205 4.88467i 0.465833 0.169549i
\(831\) 7.19197 + 1.98550i 0.249487 + 0.0688762i
\(832\) 1.93789 + 5.32431i 0.0671842 + 0.184587i
\(833\) −11.1256 + 30.5674i −0.385480 + 1.05910i
\(834\) 36.6087 + 10.1066i 1.26766 + 0.349964i
\(835\) 4.68874 2.70704i 0.162260 0.0936811i
\(836\) −13.4825 + 12.3073i −0.466303 + 0.425658i
\(837\) −45.0721 13.1799i −1.55792 0.455565i
\(838\) −2.61145 + 7.17489i −0.0902110 + 0.247853i
\(839\) 12.4762 10.4688i 0.430727 0.361423i −0.401499 0.915859i \(-0.631511\pi\)
0.832226 + 0.554437i \(0.187066\pi\)
\(840\) −0.187526 + 0.263550i −0.00647025 + 0.00909333i
\(841\) 7.99326 + 45.3320i 0.275630 + 1.56317i
\(842\) 12.4583 14.8472i 0.429342 0.511669i
\(843\) −20.6348 + 1.64816i −0.710700 + 0.0567658i
\(844\) 9.08860 + 5.24730i 0.312842 + 0.180620i
\(845\) −8.05121 22.1205i −0.276970 0.760969i
\(846\) 9.48408 + 0.143459i 0.326069 + 0.00493223i
\(847\) 0.495534 + 0.858290i 0.0170267 + 0.0294912i
\(848\) 5.22456 0.179412
\(849\) −2.27026 1.61538i −0.0779151 0.0554395i
\(850\) −15.9857 + 2.81872i −0.548306 + 0.0966812i
\(851\) 23.1392 8.42199i 0.793202 0.288702i
\(852\) −3.15563 0.871180i −0.108110 0.0298461i
\(853\) −6.57869 37.3096i −0.225250 1.27746i −0.862207 0.506557i \(-0.830918\pi\)
0.636957 0.770900i \(-0.280193\pi\)
\(854\) 0.172652 0.00590804
\(855\) 0.428651 + 16.1078i 0.0146595 + 0.550876i
\(856\) 15.8085 0.540322
\(857\) −5.35564 30.3734i −0.182945 1.03753i −0.928567 0.371165i \(-0.878958\pi\)
0.745622 0.666370i \(-0.232153\pi\)
\(858\) 29.2813 28.8417i 0.999647 0.984641i
\(859\) 18.7388 6.82035i 0.639358 0.232707i −0.00194129 0.999998i \(-0.500618\pi\)
0.641299 + 0.767291i \(0.278396\pi\)
\(860\) 7.62839 1.34509i 0.260126 0.0458672i
\(861\) 0.297110 3.12371i 0.0101255 0.106456i
\(862\) 23.4379 0.798297
\(863\) 1.51655 + 2.62674i 0.0516240 + 0.0894154i 0.890683 0.454626i \(-0.150227\pi\)
−0.839059 + 0.544041i \(0.816894\pi\)
\(864\) 0.335328 + 5.18532i 0.0114081 + 0.176408i
\(865\) −3.68221 10.1168i −0.125199 0.343981i
\(866\) 1.12587 + 0.650022i 0.0382587 + 0.0220886i
\(867\) −3.52374 + 7.40987i −0.119673 + 0.251652i
\(868\) 0.880386 1.04920i 0.0298823 0.0356123i
\(869\) 0.447736 + 2.53924i 0.0151884 + 0.0861377i
\(870\) 18.4043 + 1.75051i 0.623963 + 0.0593479i
\(871\) −47.9980 + 40.2751i −1.62635 + 1.36467i
\(872\) −3.98330 + 10.9440i −0.134891 + 0.370611i
\(873\) −16.3268 + 13.2843i −0.552580 + 0.449604i
\(874\) 3.61926 27.0925i 0.122423 0.916417i
\(875\) −1.37172 + 0.791961i −0.0463725 + 0.0267732i
\(876\) −11.8399 + 11.6621i −0.400032 + 0.394027i
\(877\) 14.4218 39.6235i 0.486989 1.33799i −0.416404 0.909179i \(-0.636710\pi\)
0.903394 0.428812i \(-0.141068\pi\)
\(878\) 1.65965 + 4.55984i 0.0560103 + 0.153887i
\(879\) −1.80079 6.92987i −0.0607393 0.233739i
\(880\) 4.84938 1.76503i 0.163472 0.0594991i
\(881\) 39.3323 + 22.7085i 1.32514 + 0.765069i 0.984543 0.175141i \(-0.0560381\pi\)
0.340595 + 0.940210i \(0.389371\pi\)
\(882\) 13.2102 + 16.2358i 0.444811 + 0.546688i
\(883\) −25.2236 + 9.18064i −0.848842 + 0.308953i −0.729568 0.683908i \(-0.760279\pi\)
−0.119274 + 0.992861i \(0.538057\pi\)
\(884\) 20.2364 + 16.9803i 0.680624 + 0.571111i
\(885\) 13.3894 + 6.36731i 0.450081 + 0.214035i
\(886\) 12.7980 7.38893i 0.429957 0.248236i
\(887\) −30.8448 25.8818i −1.03567 0.869027i −0.0441521 0.999025i \(-0.514059\pi\)
−0.991514 + 0.129997i \(0.958503\pi\)
\(888\) −4.77294 4.84568i −0.160169 0.162611i
\(889\) 0.828336 + 0.146058i 0.0277815 + 0.00489863i
\(890\) −0.909651 + 0.160396i −0.0304916 + 0.00537649i
\(891\) 33.1974 17.8501i 1.11215 0.598002i
\(892\) 13.5799i 0.454690i
\(893\) 2.95728 + 13.4606i 0.0989615 + 0.450442i
\(894\) −0.271001 3.39289i −0.00906362 0.113475i
\(895\) 6.93601 + 8.26601i 0.231845 + 0.276302i
\(896\) −0.142413 0.0518340i −0.00475768 0.00173165i
\(897\) −5.82695 + 61.2626i −0.194556 + 2.04550i
\(898\) −5.90883 2.15064i −0.197180 0.0717678i
\(899\) −77.0931 13.5936i −2.57120 0.453372i
\(900\) −3.72037 + 9.75976i −0.124012 + 0.325325i
\(901\) 21.0951 12.1793i 0.702781 0.405751i
\(902\) −32.1794 + 38.3499i −1.07146 + 1.27691i
\(903\) −0.156244 + 1.64270i −0.00519947 + 0.0546655i
\(904\) 7.13942 0.237454
\(905\) 4.79619 + 8.30725i 0.159431 + 0.276142i
\(906\) −6.94510 + 9.76069i −0.230736 + 0.324277i
\(907\) 18.5078 50.8497i 0.614541 1.68844i −0.105423 0.994427i \(-0.533620\pi\)
0.719965 0.694011i \(-0.244158\pi\)
\(908\) 6.07890 + 5.10080i 0.201735 + 0.169276i
\(909\) 7.32559 + 6.33815i 0.242974 + 0.210223i
\(910\) 0.994303 + 0.361897i 0.0329608 + 0.0119968i
\(911\) −21.1475 36.6286i −0.700648 1.21356i −0.968239 0.250026i \(-0.919561\pi\)
0.267591 0.963533i \(-0.413772\pi\)
\(912\) −7.22157 + 2.20202i −0.239130 + 0.0729162i
\(913\) 24.2700 42.0368i 0.803219 1.39122i
\(914\) 3.19232 2.67867i 0.105593 0.0886027i
\(915\) −2.35327 + 0.611521i −0.0777968 + 0.0202163i
\(916\) 2.96552 16.8183i 0.0979836 0.555693i
\(917\) 0.192443 + 0.229345i 0.00635504 + 0.00757364i
\(918\) 13.4418 + 20.1550i 0.443644 + 0.665214i
\(919\) 6.68902 11.5857i 0.220650 0.382178i −0.734355 0.678765i \(-0.762515\pi\)
0.955006 + 0.296588i \(0.0958487\pi\)
\(920\) −3.86345 + 6.69170i −0.127374 + 0.220619i
\(921\) 1.46350 + 3.20148i 0.0482241 + 0.105492i
\(922\) −5.55968 0.980321i −0.183098 0.0322852i
\(923\) 10.7091i 0.352494i
\(924\) 0.0875288 + 1.09585i 0.00287949 + 0.0360508i
\(925\) −4.67607 12.8474i −0.153748 0.422420i
\(926\) 1.97053 1.65347i 0.0647555 0.0543363i
\(927\) 0.527947 + 0.947234i 0.0173401 + 0.0311113i
\(928\) 1.50415 + 8.53047i 0.0493762 + 0.280026i
\(929\) −2.22452 + 0.392242i −0.0729840 + 0.0128691i −0.210021 0.977697i \(-0.567353\pi\)
0.137037 + 0.990566i \(0.456242\pi\)
\(930\) −8.28359 + 17.4191i −0.271630 + 0.571193i
\(931\) −18.5596 + 24.0923i −0.608268 + 0.789594i
\(932\) −19.2781 11.1302i −0.631474 0.364581i
\(933\) 20.4987 + 20.8111i 0.671096 + 0.681324i
\(934\) 12.5492 + 14.9556i 0.410623 + 0.489361i
\(935\) 15.4657 18.4313i 0.505782 0.602768i
\(936\) 16.0590 5.57142i 0.524906 0.182108i
\(937\) −4.45373 + 25.2583i −0.145497 + 0.825154i 0.821470 + 0.570252i \(0.193154\pi\)
−0.966967 + 0.254902i \(0.917957\pi\)
\(938\) 1.67593i 0.0547209i
\(939\) −12.7712 + 26.8558i −0.416773 + 0.876407i
\(940\) 0.676528 3.83678i 0.0220659 0.125142i
\(941\) 7.49046 42.4805i 0.244182 1.38482i −0.578203 0.815893i \(-0.696246\pi\)
0.822385 0.568932i \(-0.192643\pi\)
\(942\) −18.4553 26.7858i −0.601306 0.872727i
\(943\) 74.9576i 2.44096i
\(944\) −1.20629 + 6.84119i −0.0392613 + 0.222662i
\(945\) 0.782050 + 0.574471i 0.0254401 + 0.0186875i
\(946\) 16.9225 20.1674i 0.550198 0.655700i
\(947\) −17.5830 20.9546i −0.571370 0.680932i 0.400542 0.916279i \(-0.368822\pi\)
−0.971912 + 0.235346i \(0.924378\pi\)
\(948\) −0.283776 + 1.02791i −0.00921663 + 0.0333850i
\(949\) 47.0815 + 27.1825i 1.52833 + 0.882381i
\(950\) −15.0423 2.00949i −0.488038 0.0651965i
\(951\) −31.3101 45.4430i −1.01530 1.47359i
\(952\) −0.695851 + 0.122697i −0.0225527 + 0.00397664i
\(953\) 0.280284 + 1.58957i 0.00907930 + 0.0514913i 0.989011 0.147843i \(-0.0472331\pi\)
−0.979932 + 0.199334i \(0.936122\pi\)
\(954\) 0.237058 15.6719i 0.00767504 0.507396i
\(955\) −17.3517 + 14.5598i −0.561487 + 0.471144i
\(956\) 6.18378 + 16.9898i 0.199998 + 0.549489i
\(957\) 51.7411 35.6494i 1.67255 1.15238i
\(958\) 13.1662i 0.425382i
\(959\) 0.654822 + 0.115463i 0.0211453 + 0.00372849i
\(960\) 2.12470 + 0.202089i 0.0685744 + 0.00652240i
\(961\) 25.3371 43.8852i 0.817326 1.41565i
\(962\) −11.1249 + 19.2689i −0.358682 + 0.621256i
\(963\) 0.717289 47.4199i 0.0231143 1.52809i
\(964\) 8.19302 + 9.76406i 0.263879 + 0.314479i
\(965\) −1.64452 + 9.32651i −0.0529388 + 0.300231i
\(966\) −1.15508 1.17269i −0.0371641 0.0377305i
\(967\) 3.51047 2.94563i 0.112889 0.0947252i −0.584596 0.811325i \(-0.698747\pi\)
0.697485 + 0.716600i \(0.254302\pi\)
\(968\) 3.26972 5.66332i 0.105093 0.182026i
\(969\) −24.0252 + 25.7257i −0.771799 + 0.826428i
\(970\) 4.32276 + 7.48724i 0.138796 + 0.240401i
\(971\) 34.5382 + 12.5709i 1.10838 + 0.403419i 0.830401 0.557167i \(-0.188112\pi\)
0.277984 + 0.960586i \(0.410334\pi\)
\(972\) 15.5694 0.770590i 0.499389 0.0247167i
\(973\) 2.54560 + 2.13602i 0.0816083 + 0.0684775i
\(974\) −0.386864 + 1.06290i −0.0123959 + 0.0340575i
\(975\) 34.0143 + 3.23525i 1.08933 + 0.103611i
\(976\) −0.569612 0.986596i −0.0182328 0.0315802i
\(977\) 14.0044 0.448040 0.224020 0.974585i \(-0.428082\pi\)
0.224020 + 0.974585i \(0.428082\pi\)
\(978\) 16.2850 + 11.5874i 0.520738 + 0.370525i
\(979\) −2.01793 + 2.40488i −0.0644934 + 0.0768602i
\(980\) 7.44550 4.29866i 0.237838 0.137316i
\(981\) 32.6476 + 12.4451i 1.04236 + 0.397341i
\(982\) 17.3896 + 3.06626i 0.554925 + 0.0978483i
\(983\) 20.8618 + 7.59308i 0.665389 + 0.242182i 0.652561 0.757736i \(-0.273695\pi\)
0.0128276 + 0.999918i \(0.495917\pi\)
\(984\) −18.8302 + 8.60791i −0.600285 + 0.274410i
\(985\) −5.57889 2.03055i −0.177758 0.0646987i
\(986\) 25.9592 + 30.9369i 0.826708 + 0.985232i
\(987\) 0.749508 + 0.356427i 0.0238571 + 0.0113452i
\(988\) 13.2303 + 20.8549i 0.420913 + 0.663484i
\(989\) 39.4187i 1.25344i
\(990\) −5.07445 14.6266i −0.161277 0.464862i
\(991\) 15.9705 2.81603i 0.507319 0.0894541i 0.0858707 0.996306i \(-0.472633\pi\)
0.421449 + 0.906852i \(0.361522\pi\)
\(992\) −8.90008 1.56932i −0.282578 0.0498261i
\(993\) 14.4023 52.1688i 0.457043 1.65553i
\(994\) −0.219428 0.184122i −0.00695984 0.00584000i
\(995\) −13.4434 + 7.76153i −0.426183 + 0.246057i
\(996\) 16.5310 11.3898i 0.523803 0.360898i
\(997\) −33.0621 27.7424i −1.04709 0.878610i −0.0543019 0.998525i \(-0.517293\pi\)
−0.992784 + 0.119915i \(0.961738\pi\)
\(998\) 8.69831 3.16593i 0.275340 0.100216i
\(999\) −14.7520 + 14.0973i −0.466731 + 0.446019i
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 342.2.bf.b.167.3 yes 48
9.2 odd 6 342.2.x.b.281.5 yes 48
19.14 odd 18 342.2.x.b.185.5 48
171.128 even 18 inner 342.2.bf.b.299.3 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
342.2.x.b.185.5 48 19.14 odd 18
342.2.x.b.281.5 yes 48 9.2 odd 6
342.2.bf.b.167.3 yes 48 1.1 even 1 trivial
342.2.bf.b.299.3 yes 48 171.128 even 18 inner