Properties

Label 441.2.bd.a.47.8
Level $441$
Weight $2$
Character 441.47
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(47,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([7, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bd (of order \(42\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 47.8
Character \(\chi\) \(=\) 441.47
Dual form 441.2.bd.a.122.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.58104 - 1.70396i) q^{2} +(1.73188 - 0.0242085i) q^{3} +(-0.254319 + 3.39365i) q^{4} +(-1.54809 - 1.94124i) q^{5} +(-2.77943 - 2.91278i) q^{6} +(1.62028 + 2.09157i) q^{7} +(2.55004 - 2.03359i) q^{8} +(2.99883 - 0.0838526i) q^{9} +O(q^{10})\) \(q+(-1.58104 - 1.70396i) q^{2} +(1.73188 - 0.0242085i) q^{3} +(-0.254319 + 3.39365i) q^{4} +(-1.54809 - 1.94124i) q^{5} +(-2.77943 - 2.91278i) q^{6} +(1.62028 + 2.09157i) q^{7} +(2.55004 - 2.03359i) q^{8} +(2.99883 - 0.0838526i) q^{9} +(-0.860202 + 5.70707i) q^{10} +(6.31951 - 1.44239i) q^{11} +(-0.358295 + 5.88356i) q^{12} +(0.268638 + 0.289522i) q^{13} +(1.00222 - 6.06776i) q^{14} +(-2.72810 - 3.32453i) q^{15} +(-0.766553 - 0.115539i) q^{16} +(0.246053 + 3.28335i) q^{17} +(-4.88415 - 4.97730i) q^{18} +(-4.15483 - 2.39879i) q^{19} +(6.98161 - 4.75998i) q^{20} +(2.85677 + 3.58313i) q^{21} +(-12.4492 - 8.48771i) q^{22} +(-0.796671 - 1.65430i) q^{23} +(4.36713 - 3.58367i) q^{24} +(-0.259238 + 1.13580i) q^{25} +(0.0686068 - 0.915494i) q^{26} +(5.19158 - 0.217820i) q^{27} +(-7.51014 + 4.96675i) q^{28} +(-3.60442 - 5.28672i) q^{29} +(-1.35161 + 9.90479i) q^{30} +(6.63604 + 3.83132i) q^{31} +(-2.65960 - 3.90091i) q^{32} +(10.9097 - 2.65103i) q^{33} +(5.20567 - 5.61038i) q^{34} +(1.55191 - 6.38331i) q^{35} +(-0.478092 + 10.1983i) q^{36} +(4.18839 - 2.85560i) q^{37} +(2.48152 + 10.8722i) q^{38} +(0.472257 + 0.494915i) q^{39} +(-7.89537 - 1.80207i) q^{40} +(-0.945689 + 2.40958i) q^{41} +(1.58883 - 10.5329i) q^{42} +(-3.17477 - 8.08918i) q^{43} +(3.28779 + 21.8131i) q^{44} +(-4.80523 - 5.69164i) q^{45} +(-1.55929 + 3.97302i) q^{46} +(-4.73276 + 4.39136i) q^{47} +(-1.33038 - 0.181543i) q^{48} +(-1.74936 + 6.77789i) q^{49} +(2.34521 - 1.35401i) q^{50} +(0.505620 + 5.68042i) q^{51} +(-1.05086 + 0.838031i) q^{52} +(-0.852581 + 1.25051i) q^{53} +(-8.57927 - 8.50186i) q^{54} +(-12.5832 - 10.0348i) q^{55} +(8.38518 + 2.03860i) q^{56} +(-7.25374 - 4.05384i) q^{57} +(-3.30960 + 14.5003i) q^{58} +(-3.84504 - 9.79699i) q^{59} +(11.9761 - 8.41274i) q^{60} +(1.99647 - 0.149615i) q^{61} +(-3.96345 - 17.3650i) q^{62} +(5.03434 + 6.13640i) q^{63} +(-2.78706 + 12.2109i) q^{64} +(0.146158 - 0.969697i) q^{65} +(-21.7660 - 14.3983i) q^{66} +(-0.397642 + 0.688737i) q^{67} -11.2051 q^{68} +(-1.41979 - 2.84577i) q^{69} +(-13.3305 + 7.44789i) q^{70} +(1.22407 + 2.54180i) q^{71} +(7.47660 - 6.31221i) q^{72} +(3.93163 + 12.7460i) q^{73} +(-11.4878 - 2.62202i) q^{74} +(-0.421473 + 1.97334i) q^{75} +(9.19731 - 13.4900i) q^{76} +(13.2563 + 10.8806i) q^{77} +(0.0966561 - 1.58719i) q^{78} +(-5.83054 - 10.0988i) q^{79} +(0.962402 + 1.66693i) q^{80} +(8.98594 - 0.502919i) q^{81} +(5.60099 - 2.19823i) q^{82} +(6.36258 + 5.90362i) q^{83} +(-12.8864 + 8.78364i) q^{84} +(5.99287 - 5.56057i) q^{85} +(-8.76418 + 18.1990i) q^{86} +(-6.37042 - 9.06872i) q^{87} +(13.1818 - 16.5294i) q^{88} +(2.17014 + 2.01360i) q^{89} +(-2.10104 + 17.1866i) q^{90} +(-0.170288 + 1.03098i) q^{91} +(5.81674 - 2.28290i) q^{92} +(11.5856 + 6.47475i) q^{93} +(14.9654 + 1.12150i) q^{94} +(1.77541 + 11.7791i) q^{95} +(-4.70054 - 6.69153i) q^{96} +(8.62846 + 4.98164i) q^{97} +(14.3150 - 7.73529i) q^{98} +(18.8302 - 4.85538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 18 q^{2} - 11 q^{3} - 60 q^{4} - 15 q^{5} - 22 q^{6} - 5 q^{7} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 18 q^{2} - 11 q^{3} - 60 q^{4} - 15 q^{5} - 22 q^{6} - 5 q^{7} + 13 q^{9} - 22 q^{10} - 21 q^{11} + 24 q^{12} - 10 q^{13} - 24 q^{14} - 10 q^{15} + 42 q^{16} + 9 q^{17} + 12 q^{18} - 36 q^{19} - 15 q^{20} - 38 q^{21} - 9 q^{22} - 84 q^{23} - 38 q^{24} - 97 q^{25} - 6 q^{26} - 20 q^{27} - 26 q^{28} - 123 q^{29} - q^{30} - 6 q^{31} - 30 q^{32} - 8 q^{33} - q^{34} + 70 q^{36} - 13 q^{37} - 75 q^{38} - 24 q^{39} - 7 q^{40} - 15 q^{41} - 133 q^{42} - 9 q^{43} - 51 q^{44} - 41 q^{45} - 108 q^{46} - 36 q^{47} + 15 q^{48} + 5 q^{49} - 45 q^{50} + 10 q^{51} - 35 q^{52} + 12 q^{53} - 50 q^{54} + 14 q^{55} + 33 q^{56} - 7 q^{57} + 33 q^{58} - 3 q^{59} + 180 q^{60} + 55 q^{61} - 66 q^{62} - 20 q^{63} + 64 q^{64} + 3 q^{65} + 285 q^{66} + 13 q^{67} + 6 q^{68} + 82 q^{69} + 11 q^{70} + 63 q^{71} - 21 q^{72} - 22 q^{73} - 21 q^{74} - 107 q^{75} + 21 q^{76} - 69 q^{77} + 63 q^{78} + q^{79} + 45 q^{80} - 211 q^{81} - 28 q^{82} + 9 q^{83} + 239 q^{84} - 10 q^{85} - 21 q^{86} - 109 q^{87} - 29 q^{88} - 132 q^{89} - 275 q^{90} - 13 q^{91} + 195 q^{92} + 19 q^{93} - 4 q^{94} - 129 q^{95} - 5 q^{96} - 3 q^{97} - 21 q^{98} - 148 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58104 1.70396i −1.11797 1.20488i −0.976632 0.214918i \(-0.931051\pi\)
−0.141333 0.989962i \(-0.545139\pi\)
\(3\) 1.73188 0.0242085i 0.999902 0.0139768i
\(4\) −0.254319 + 3.39365i −0.127159 + 1.69683i
\(5\) −1.54809 1.94124i −0.692327 0.868150i 0.304098 0.952641i \(-0.401645\pi\)
−0.996424 + 0.0844907i \(0.973074\pi\)
\(6\) −2.77943 2.91278i −1.13470 1.18914i
\(7\) 1.62028 + 2.09157i 0.612410 + 0.790540i
\(8\) 2.55004 2.03359i 0.901575 0.718982i
\(9\) 2.99883 0.0838526i 0.999609 0.0279509i
\(10\) −0.860202 + 5.70707i −0.272020 + 1.80473i
\(11\) 6.31951 1.44239i 1.90541 0.434896i 0.905460 0.424432i \(-0.139526\pi\)
0.999945 0.0104647i \(-0.00333108\pi\)
\(12\) −0.358295 + 5.88356i −0.103431 + 1.69844i
\(13\) 0.268638 + 0.289522i 0.0745067 + 0.0802991i 0.769205 0.639002i \(-0.220653\pi\)
−0.694698 + 0.719301i \(0.744462\pi\)
\(14\) 1.00222 6.06776i 0.267853 1.62168i
\(15\) −2.72810 3.32453i −0.704393 0.858389i
\(16\) −0.766553 0.115539i −0.191638 0.0288848i
\(17\) 0.246053 + 3.28335i 0.0596766 + 0.796329i 0.944103 + 0.329650i \(0.106931\pi\)
−0.884427 + 0.466679i \(0.845450\pi\)
\(18\) −4.88415 4.97730i −1.15121 1.17316i
\(19\) −4.15483 2.39879i −0.953183 0.550320i −0.0591146 0.998251i \(-0.518828\pi\)
−0.894068 + 0.447931i \(0.852161\pi\)
\(20\) 6.98161 4.75998i 1.56114 1.06436i
\(21\) 2.85677 + 3.58313i 0.623399 + 0.781904i
\(22\) −12.4492 8.48771i −2.65418 1.80959i
\(23\) −0.796671 1.65430i −0.166117 0.344946i 0.801248 0.598333i \(-0.204170\pi\)
−0.967365 + 0.253386i \(0.918456\pi\)
\(24\) 4.36713 3.58367i 0.891437 0.731513i
\(25\) −0.259238 + 1.13580i −0.0518476 + 0.227159i
\(26\) 0.0686068 0.915494i 0.0134549 0.179543i
\(27\) 5.19158 0.217820i 0.999121 0.0419195i
\(28\) −7.51014 + 4.96675i −1.41928 + 0.938628i
\(29\) −3.60442 5.28672i −0.669325 0.981719i −0.999288 0.0377255i \(-0.987989\pi\)
0.329963 0.943994i \(-0.392964\pi\)
\(30\) −1.35161 + 9.90479i −0.246769 + 1.80836i
\(31\) 6.63604 + 3.83132i 1.19187 + 0.688126i 0.958730 0.284318i \(-0.0917671\pi\)
0.233139 + 0.972444i \(0.425100\pi\)
\(32\) −2.65960 3.90091i −0.470154 0.689590i
\(33\) 10.9097 2.65103i 1.89914 0.461485i
\(34\) 5.20567 5.61038i 0.892765 0.962172i
\(35\) 1.55191 6.38331i 0.262320 1.07898i
\(36\) −0.478092 + 10.1983i −0.0796821 + 1.69972i
\(37\) 4.18839 2.85560i 0.688567 0.469457i −0.167802 0.985821i \(-0.553667\pi\)
0.856369 + 0.516364i \(0.172715\pi\)
\(38\) 2.48152 + 10.8722i 0.402555 + 1.76371i
\(39\) 0.472257 + 0.494915i 0.0756217 + 0.0792499i
\(40\) −7.89537 1.80207i −1.24837 0.284932i
\(41\) −0.945689 + 2.40958i −0.147692 + 0.376313i −0.985505 0.169644i \(-0.945738\pi\)
0.837814 + 0.545956i \(0.183834\pi\)
\(42\) 1.58883 10.5329i 0.245161 1.62526i
\(43\) −3.17477 8.08918i −0.484148 1.23359i −0.939276 0.343162i \(-0.888502\pi\)
0.455129 0.890426i \(-0.349593\pi\)
\(44\) 3.28779 + 21.8131i 0.495653 + 3.28844i
\(45\) −4.80523 5.69164i −0.716322 0.848460i
\(46\) −1.55929 + 3.97302i −0.229906 + 0.585790i
\(47\) −4.73276 + 4.39136i −0.690344 + 0.640546i −0.945222 0.326427i \(-0.894155\pi\)
0.254878 + 0.966973i \(0.417965\pi\)
\(48\) −1.33038 0.181543i −0.192023 0.0262035i
\(49\) −1.74936 + 6.77789i −0.249908 + 0.968270i
\(50\) 2.34521 1.35401i 0.331663 0.191486i
\(51\) 0.505620 + 5.68042i 0.0708009 + 0.795417i
\(52\) −1.05086 + 0.838031i −0.145728 + 0.116214i
\(53\) −0.852581 + 1.25051i −0.117111 + 0.171770i −0.880318 0.474383i \(-0.842671\pi\)
0.763207 + 0.646154i \(0.223623\pi\)
\(54\) −8.57927 8.50186i −1.16749 1.15696i
\(55\) −12.5832 10.0348i −1.69672 1.35309i
\(56\) 8.38518 + 2.03860i 1.12052 + 0.272420i
\(57\) −7.25374 4.05384i −0.960781 0.536944i
\(58\) −3.30960 + 14.5003i −0.434572 + 1.90398i
\(59\) −3.84504 9.79699i −0.500581 1.27546i −0.928396 0.371593i \(-0.878812\pi\)
0.427814 0.903867i \(-0.359284\pi\)
\(60\) 11.9761 8.41274i 1.54611 1.08608i
\(61\) 1.99647 0.149615i 0.255622 0.0191562i 0.0536972 0.998557i \(-0.482899\pi\)
0.201925 + 0.979401i \(0.435280\pi\)
\(62\) −3.96345 17.3650i −0.503359 2.20536i
\(63\) 5.03434 + 6.13640i 0.634267 + 0.773114i
\(64\) −2.78706 + 12.2109i −0.348382 + 1.52636i
\(65\) 0.146158 0.969697i 0.0181287 0.120276i
\(66\) −21.7660 14.3983i −2.67921 1.77231i
\(67\) −0.397642 + 0.688737i −0.0485798 + 0.0841426i −0.889293 0.457338i \(-0.848803\pi\)
0.840713 + 0.541481i \(0.182136\pi\)
\(68\) −11.2051 −1.35882
\(69\) −1.41979 2.84577i −0.170922 0.342591i
\(70\) −13.3305 + 7.44789i −1.59330 + 0.890194i
\(71\) 1.22407 + 2.54180i 0.145270 + 0.301656i 0.960889 0.276933i \(-0.0893180\pi\)
−0.815619 + 0.578589i \(0.803604\pi\)
\(72\) 7.47660 6.31221i 0.881126 0.743901i
\(73\) 3.93163 + 12.7460i 0.460162 + 1.49181i 0.827363 + 0.561667i \(0.189840\pi\)
−0.367201 + 0.930142i \(0.619684\pi\)
\(74\) −11.4878 2.62202i −1.33543 0.304804i
\(75\) −0.421473 + 1.97334i −0.0486676 + 0.227862i
\(76\) 9.19731 13.4900i 1.05500 1.54741i
\(77\) 13.2563 + 10.8806i 1.51069 + 1.23996i
\(78\) 0.0966561 1.58719i 0.0109442 0.179714i
\(79\) −5.83054 10.0988i −0.655987 1.13620i −0.981645 0.190715i \(-0.938919\pi\)
0.325659 0.945487i \(-0.394414\pi\)
\(80\) 0.962402 + 1.66693i 0.107600 + 0.186368i
\(81\) 8.98594 0.502919i 0.998437 0.0558799i
\(82\) 5.60099 2.19823i 0.618526 0.242754i
\(83\) 6.36258 + 5.90362i 0.698384 + 0.648006i 0.947237 0.320535i \(-0.103863\pi\)
−0.248852 + 0.968541i \(0.580053\pi\)
\(84\) −12.8864 + 8.78364i −1.40603 + 0.958373i
\(85\) 5.99287 5.56057i 0.650018 0.603128i
\(86\) −8.76418 + 18.1990i −0.945065 + 1.96245i
\(87\) −6.37042 9.06872i −0.682981 0.972268i
\(88\) 13.1818 16.5294i 1.40518 1.76204i
\(89\) 2.17014 + 2.01360i 0.230035 + 0.213441i 0.786766 0.617252i \(-0.211754\pi\)
−0.556731 + 0.830693i \(0.687945\pi\)
\(90\) −2.10104 + 17.1866i −0.221470 + 1.81163i
\(91\) −0.170288 + 1.03098i −0.0178511 + 0.108076i
\(92\) 5.81674 2.28290i 0.606437 0.238009i
\(93\) 11.5856 + 6.47475i 1.20137 + 0.671400i
\(94\) 14.9654 + 1.12150i 1.54356 + 0.115674i
\(95\) 1.77541 + 11.7791i 0.182153 + 1.20851i
\(96\) −4.70054 6.69153i −0.479747 0.682951i
\(97\) 8.62846 + 4.98164i 0.876087 + 0.505809i 0.869366 0.494168i \(-0.164527\pi\)
0.00672098 + 0.999977i \(0.497861\pi\)
\(98\) 14.3150 7.73529i 1.44604 0.781382i
\(99\) 18.8302 4.85538i 1.89251 0.487984i
\(100\) −3.78856 1.16862i −0.378856 0.116862i
\(101\) −4.08846 5.12676i −0.406817 0.510132i 0.535646 0.844442i \(-0.320068\pi\)
−0.942463 + 0.334310i \(0.891497\pi\)
\(102\) 8.87979 9.84253i 0.879230 0.974556i
\(103\) −9.16003 + 7.30488i −0.902564 + 0.719771i −0.960421 0.278554i \(-0.910145\pi\)
0.0578562 + 0.998325i \(0.481574\pi\)
\(104\) 1.27381 + 0.191995i 0.124907 + 0.0188267i
\(105\) 2.53319 11.0927i 0.247214 1.08254i
\(106\) 3.47878 0.524341i 0.337889 0.0509285i
\(107\) −0.851993 + 0.918230i −0.0823653 + 0.0887687i −0.772890 0.634541i \(-0.781189\pi\)
0.690524 + 0.723309i \(0.257380\pi\)
\(108\) −0.581114 + 17.6738i −0.0559177 + 1.70066i
\(109\) −7.52127 + 6.97871i −0.720407 + 0.668440i −0.952598 0.304230i \(-0.901601\pi\)
0.232192 + 0.972670i \(0.425410\pi\)
\(110\) 2.79575 + 37.3066i 0.266564 + 3.55705i
\(111\) 7.18467 5.04695i 0.681938 0.479035i
\(112\) −1.00037 1.79051i −0.0945265 0.169187i
\(113\) 4.15519 + 13.4708i 0.390887 + 1.26722i 0.910744 + 0.412971i \(0.135509\pi\)
−0.519857 + 0.854253i \(0.674015\pi\)
\(114\) 4.56090 + 18.7694i 0.427167 + 1.75791i
\(115\) −1.97809 + 4.10754i −0.184458 + 0.383030i
\(116\) 18.8580 10.8876i 1.75092 1.01089i
\(117\) 0.829875 + 0.845702i 0.0767220 + 0.0781852i
\(118\) −10.6145 + 22.0412i −0.977144 + 2.02906i
\(119\) −6.46869 + 5.83460i −0.592984 + 0.534857i
\(120\) −13.7175 2.92983i −1.25223 0.267456i
\(121\) 27.9451 13.4577i 2.54047 1.22342i
\(122\) −3.41144 3.16535i −0.308857 0.286578i
\(123\) −1.57949 + 4.19599i −0.142418 + 0.378340i
\(124\) −14.6898 + 21.5460i −1.31919 + 1.93489i
\(125\) −8.57909 + 4.13147i −0.767337 + 0.369530i
\(126\) 2.49667 18.2802i 0.222421 1.62853i
\(127\) −12.3855 5.96454i −1.09903 0.529267i −0.205680 0.978619i \(-0.565941\pi\)
−0.893355 + 0.449352i \(0.851655\pi\)
\(128\) 17.0358 9.83562i 1.50577 0.869354i
\(129\) −5.69415 13.9326i −0.501342 1.22670i
\(130\) −1.88341 + 1.28408i −0.165186 + 0.112622i
\(131\) 2.93208 3.67672i 0.256177 0.321236i −0.637066 0.770809i \(-0.719852\pi\)
0.893244 + 0.449573i \(0.148424\pi\)
\(132\) 6.22212 + 37.6980i 0.541566 + 3.28119i
\(133\) −1.71476 12.5768i −0.148688 1.09055i
\(134\) 1.80227 0.411356i 0.155692 0.0355357i
\(135\) −8.45988 9.74092i −0.728110 0.838365i
\(136\) 7.30442 + 7.87230i 0.626349 + 0.675044i
\(137\) 0.663356 + 0.529009i 0.0566744 + 0.0451963i 0.651417 0.758720i \(-0.274175\pi\)
−0.594743 + 0.803916i \(0.702746\pi\)
\(138\) −2.60433 + 6.91855i −0.221696 + 0.588946i
\(139\) 20.7592 + 8.14738i 1.76077 + 0.691051i 0.999070 + 0.0431220i \(0.0137304\pi\)
0.761700 + 0.647929i \(0.224365\pi\)
\(140\) 21.2680 + 6.89003i 1.79748 + 0.582313i
\(141\) −8.09027 + 7.71989i −0.681324 + 0.650132i
\(142\) 2.39582 6.10444i 0.201053 0.512274i
\(143\) 2.11526 + 1.44216i 0.176887 + 0.120600i
\(144\) −2.30845 0.282205i −0.192371 0.0235171i
\(145\) −4.68284 + 15.1814i −0.388888 + 1.26074i
\(146\) 15.5026 26.8513i 1.28301 2.22223i
\(147\) −2.86560 + 11.7808i −0.236350 + 0.971668i
\(148\) 8.62571 + 14.9402i 0.709029 + 1.22807i
\(149\) −10.0143 + 2.28570i −0.820406 + 0.187252i −0.612068 0.790805i \(-0.709662\pi\)
−0.208337 + 0.978057i \(0.566805\pi\)
\(150\) 4.02885 2.40176i 0.328955 0.196103i
\(151\) 2.26430 1.09043i 0.184266 0.0887379i −0.339476 0.940615i \(-0.610250\pi\)
0.523742 + 0.851877i \(0.324535\pi\)
\(152\) −15.4731 + 2.33220i −1.25504 + 0.189166i
\(153\) 1.01319 + 9.82557i 0.0819114 + 0.794350i
\(154\) −2.41855 39.7909i −0.194892 3.20644i
\(155\) −2.83566 18.8134i −0.227766 1.51113i
\(156\) −1.79967 + 1.47681i −0.144089 + 0.118239i
\(157\) −2.19083 + 0.859836i −0.174847 + 0.0686224i −0.451150 0.892448i \(-0.648986\pi\)
0.276303 + 0.961071i \(0.410891\pi\)
\(158\) −7.98958 + 25.9016i −0.635617 + 2.06062i
\(159\) −1.44630 + 2.18637i −0.114699 + 0.173390i
\(160\) −3.45532 + 11.2019i −0.273167 + 0.885586i
\(161\) 2.16927 4.34674i 0.170962 0.342571i
\(162\) −15.0641 14.5165i −1.18355 1.14053i
\(163\) 2.20951 + 5.62974i 0.173062 + 0.440955i 0.990918 0.134468i \(-0.0429325\pi\)
−0.817856 + 0.575423i \(0.804837\pi\)
\(164\) −7.93675 3.82214i −0.619756 0.298459i
\(165\) −22.0355 17.0744i −1.71546 1.32924i
\(166\) 20.1754i 1.56592i
\(167\) 1.39695 + 18.6410i 0.108099 + 1.44249i 0.742689 + 0.669637i \(0.233550\pi\)
−0.634589 + 0.772849i \(0.718831\pi\)
\(168\) 14.5715 + 3.32762i 1.12422 + 0.256732i
\(169\) 0.959834 12.8081i 0.0738334 0.985238i
\(170\) −18.9500 1.42010i −1.45339 0.108917i
\(171\) −12.6608 6.84517i −0.968192 0.523463i
\(172\) 28.2592 8.71682i 2.15475 0.664651i
\(173\) −17.8952 12.2007i −1.36054 0.927603i −0.360556 0.932737i \(-0.617413\pi\)
−0.999987 + 0.00513480i \(0.998366\pi\)
\(174\) −5.38081 + 25.1929i −0.407918 + 1.90987i
\(175\) −2.79564 + 1.29810i −0.211330 + 0.0981269i
\(176\) −5.01089 + 0.375514i −0.377710 + 0.0283055i
\(177\) −6.89632 16.8742i −0.518359 1.26834i
\(178\) 6.88141i 0.515784i
\(179\) −21.0352 + 1.57637i −1.57225 + 0.117824i −0.832102 0.554623i \(-0.812863\pi\)
−0.740146 + 0.672446i \(0.765244\pi\)
\(180\) 20.5375 14.8598i 1.53078 1.10758i
\(181\) −8.12648 1.85482i −0.604037 0.137867i −0.0904440 0.995902i \(-0.528829\pi\)
−0.513593 + 0.858034i \(0.671686\pi\)
\(182\) 2.02599 1.33986i 0.150176 0.0993174i
\(183\) 3.45403 0.307447i 0.255329 0.0227271i
\(184\) −5.39571 2.59844i −0.397777 0.191559i
\(185\) −12.0274 3.70996i −0.884273 0.272762i
\(186\) −7.28461 29.9782i −0.534134 2.19811i
\(187\) 6.29080 + 20.3943i 0.460029 + 1.49138i
\(188\) −13.6991 17.1781i −0.999110 1.25284i
\(189\) 8.86743 + 10.5057i 0.645011 + 0.764174i
\(190\) 17.2640 21.6484i 1.25247 1.57054i
\(191\) −1.00521 0.394514i −0.0727342 0.0285461i 0.328695 0.944436i \(-0.393391\pi\)
−0.401429 + 0.915890i \(0.631486\pi\)
\(192\) −4.53124 + 21.2153i −0.327014 + 1.53108i
\(193\) −0.263118 + 0.0396586i −0.0189396 + 0.00285469i −0.158505 0.987358i \(-0.550667\pi\)
0.139566 + 0.990213i \(0.455429\pi\)
\(194\) −5.15345 22.5787i −0.369996 1.62106i
\(195\) 0.229654 1.68294i 0.0164459 0.120518i
\(196\) −22.5569 7.66045i −1.61121 0.547175i
\(197\) 14.6588i 1.04440i 0.852824 + 0.522199i \(0.174888\pi\)
−0.852824 + 0.522199i \(0.825112\pi\)
\(198\) −38.0447 24.4093i −2.70372 1.73469i
\(199\) 12.1157 + 4.75507i 0.858860 + 0.337078i 0.753573 0.657364i \(-0.228329\pi\)
0.105287 + 0.994442i \(0.466424\pi\)
\(200\) 1.64867 + 3.42351i 0.116579 + 0.242078i
\(201\) −0.671996 + 1.20244i −0.0473990 + 0.0848134i
\(202\) −2.27177 + 15.0722i −0.159841 + 1.06048i
\(203\) 5.21737 16.1049i 0.366188 1.13034i
\(204\) −19.4059 + 0.271259i −1.35869 + 0.0189920i
\(205\) 6.14158 1.89443i 0.428947 0.132313i
\(206\) 26.9296 + 4.05898i 1.87627 + 0.282803i
\(207\) −2.52780 4.89417i −0.175694 0.340168i
\(208\) −0.172474 0.252972i −0.0119589 0.0175405i
\(209\) −29.7165 9.16632i −2.05553 0.634048i
\(210\) −22.9066 + 13.2216i −1.58070 + 0.912376i
\(211\) −23.4596 + 7.23634i −1.61503 + 0.498170i −0.965112 0.261836i \(-0.915672\pi\)
−0.649916 + 0.760006i \(0.725196\pi\)
\(212\) −4.02695 3.21139i −0.276572 0.220559i
\(213\) 2.18147 + 4.37246i 0.149472 + 0.299596i
\(214\) 2.91166 0.199037
\(215\) −10.7882 + 18.6858i −0.735751 + 1.27436i
\(216\) 12.7958 11.1130i 0.870643 0.756143i
\(217\) 2.73879 + 20.0876i 0.185921 + 1.36364i
\(218\) 23.7829 + 1.78228i 1.61078 + 0.120711i
\(219\) 7.11768 + 21.9794i 0.480968 + 1.48523i
\(220\) 37.2546 40.1510i 2.51171 2.70698i
\(221\) −0.884504 + 0.953269i −0.0594982 + 0.0641238i
\(222\) −19.9590 4.26293i −1.33956 0.286109i
\(223\) 9.86491 + 0.739273i 0.660603 + 0.0495054i 0.400813 0.916160i \(-0.368728\pi\)
0.259790 + 0.965665i \(0.416347\pi\)
\(224\) 3.84974 11.8833i 0.257221 0.793988i
\(225\) −0.682171 + 3.42779i −0.0454780 + 0.228520i
\(226\) 16.3841 28.3781i 1.08986 1.88769i
\(227\) 11.1384 0.739281 0.369640 0.929175i \(-0.379481\pi\)
0.369640 + 0.929175i \(0.379481\pi\)
\(228\) 15.6021 23.5857i 1.03327 1.56200i
\(229\) −3.00027 2.39263i −0.198263 0.158110i 0.519326 0.854576i \(-0.326183\pi\)
−0.717589 + 0.696467i \(0.754754\pi\)
\(230\) 10.1265 3.12362i 0.667723 0.205965i
\(231\) 23.2217 + 18.5231i 1.52788 + 1.21873i
\(232\) −19.9424 6.15142i −1.30928 0.403861i
\(233\) −9.13957 13.4053i −0.598753 0.878209i 0.400522 0.916287i \(-0.368829\pi\)
−0.999275 + 0.0380779i \(0.987876\pi\)
\(234\) 0.128973 2.75116i 0.00843126 0.179849i
\(235\) 15.8514 + 2.38922i 1.03403 + 0.155855i
\(236\) 34.2254 10.5572i 2.22789 0.687212i
\(237\) −10.3423 17.3488i −0.671803 1.12692i
\(238\) 20.1692 + 1.79763i 1.30737 + 0.116523i
\(239\) −0.660613 + 4.38288i −0.0427315 + 0.283505i −0.999983 0.00575029i \(-0.998170\pi\)
0.957252 + 0.289255i \(0.0934077\pi\)
\(240\) 1.70712 + 2.86363i 0.110194 + 0.184846i
\(241\) −6.43288 13.3580i −0.414379 0.860466i −0.998798 0.0490142i \(-0.984392\pi\)
0.584420 0.811452i \(-0.301322\pi\)
\(242\) −67.1137 26.3402i −4.31423 1.69321i
\(243\) 15.5504 1.08853i 0.997559 0.0698294i
\(244\) 6.81337i 0.436182i
\(245\) 15.8657 7.09685i 1.01362 0.453401i
\(246\) 9.64704 3.94266i 0.615073 0.251375i
\(247\) −0.421639 1.84732i −0.0268283 0.117542i
\(248\) 24.7135 3.72496i 1.56931 0.236535i
\(249\) 11.1622 + 10.0703i 0.707373 + 0.638182i
\(250\) 20.6038 + 8.08638i 1.30310 + 0.511428i
\(251\) 2.39110 2.99834i 0.150925 0.189254i −0.700622 0.713533i \(-0.747094\pi\)
0.851546 + 0.524279i \(0.175665\pi\)
\(252\) −22.1051 + 15.5242i −1.39249 + 0.977931i
\(253\) −7.42072 9.30529i −0.466537 0.585019i
\(254\) 9.41866 + 30.5345i 0.590979 + 1.91591i
\(255\) 10.2443 9.77532i 0.641524 0.612155i
\(256\) −19.7568 6.09418i −1.23480 0.380886i
\(257\) 4.48426 + 2.15951i 0.279720 + 0.134706i 0.568484 0.822694i \(-0.307530\pi\)
−0.288764 + 0.957400i \(0.593244\pi\)
\(258\) −14.7379 + 31.7307i −0.917544 + 1.97547i
\(259\) 12.7591 + 4.13345i 0.792810 + 0.256840i
\(260\) 3.25364 + 0.742623i 0.201782 + 0.0460555i
\(261\) −11.2524 15.5517i −0.696503 0.962627i
\(262\) −10.9007 + 0.816896i −0.673448 + 0.0504680i
\(263\) 17.5791i 1.08397i 0.840388 + 0.541986i \(0.182327\pi\)
−0.840388 + 0.541986i \(0.817673\pi\)
\(264\) 22.4291 28.9461i 1.38042 1.78151i
\(265\) 3.74741 0.280829i 0.230201 0.0172512i
\(266\) −18.7193 + 22.8064i −1.14776 + 1.39835i
\(267\) 3.80717 + 3.43478i 0.232995 + 0.210205i
\(268\) −2.23620 1.52462i −0.136598 0.0931309i
\(269\) 4.66714 1.43962i 0.284560 0.0877753i −0.149189 0.988809i \(-0.547666\pi\)
0.433750 + 0.901033i \(0.357190\pi\)
\(270\) −3.22270 + 29.8161i −0.196127 + 1.81455i
\(271\) −24.1617 1.81067i −1.46772 0.109990i −0.683262 0.730173i \(-0.739440\pi\)
−0.784458 + 0.620182i \(0.787059\pi\)
\(272\) 0.190743 2.54529i 0.0115655 0.154331i
\(273\) −0.269960 + 1.78966i −0.0163387 + 0.108315i
\(274\) −0.147385 1.96672i −0.00890386 0.118814i
\(275\) 7.55160i 0.455379i
\(276\) 10.0186 4.09453i 0.603051 0.246462i
\(277\) −15.9504 7.68133i −0.958370 0.461526i −0.111757 0.993736i \(-0.535648\pi\)
−0.846613 + 0.532209i \(0.821362\pi\)
\(278\) −18.9383 48.2541i −1.13585 2.89409i
\(279\) 20.2216 + 10.9330i 1.21064 + 0.654543i
\(280\) −9.02359 19.4336i −0.539263 1.16138i
\(281\) −4.64702 + 15.0653i −0.277218 + 0.898720i 0.704715 + 0.709491i \(0.251075\pi\)
−0.981933 + 0.189229i \(0.939401\pi\)
\(282\) 25.9454 + 1.58002i 1.54503 + 0.0940886i
\(283\) −3.33334 + 10.8064i −0.198147 + 0.642376i 0.800903 + 0.598794i \(0.204353\pi\)
−0.999050 + 0.0435819i \(0.986123\pi\)
\(284\) −8.93728 + 3.50762i −0.530330 + 0.208139i
\(285\) 3.35995 + 20.3570i 0.199026 + 1.20584i
\(286\) −0.886936 5.88444i −0.0524456 0.347954i
\(287\) −6.57209 + 1.92622i −0.387938 + 0.113701i
\(288\) −8.30277 11.4751i −0.489245 0.676179i
\(289\) 6.09028 0.917962i 0.358252 0.0539978i
\(290\) 33.2722 16.0230i 1.95381 0.940906i
\(291\) 15.0641 + 8.41873i 0.883071 + 0.493515i
\(292\) −44.2554 + 10.1010i −2.58985 + 0.591117i
\(293\) −9.55253 16.5455i −0.558065 0.966597i −0.997658 0.0683996i \(-0.978211\pi\)
0.439593 0.898197i \(-0.355123\pi\)
\(294\) 24.6047 13.7432i 1.43498 0.801517i
\(295\) −13.0659 + 22.6308i −0.760725 + 1.31761i
\(296\) 4.87345 15.7993i 0.283264 0.918318i
\(297\) 32.4941 8.86480i 1.88550 0.514388i
\(298\) 19.7278 + 13.4502i 1.14280 + 0.779149i
\(299\) 0.264943 0.675063i 0.0153220 0.0390399i
\(300\) −6.58964 1.93219i −0.380453 0.111555i
\(301\) 11.7751 19.7470i 0.678704 1.13820i
\(302\) −5.43800 2.13426i −0.312922 0.122813i
\(303\) −7.20483 8.77997i −0.413907 0.504396i
\(304\) 2.90774 + 2.31885i 0.166770 + 0.132995i
\(305\) −3.38115 3.64402i −0.193604 0.208656i
\(306\) 15.1405 17.2611i 0.865523 0.986750i
\(307\) −3.71723 + 0.848434i −0.212154 + 0.0484227i −0.327277 0.944929i \(-0.606131\pi\)
0.115123 + 0.993351i \(0.463274\pi\)
\(308\) −40.2964 + 42.2200i −2.29610 + 2.40571i
\(309\) −15.6872 + 12.8729i −0.892416 + 0.732316i
\(310\) −27.5739 + 34.5766i −1.56609 + 1.96382i
\(311\) −21.1155 + 14.3963i −1.19735 + 0.816339i −0.986911 0.161268i \(-0.948442\pi\)
−0.210439 + 0.977607i \(0.567489\pi\)
\(312\) 2.21073 + 0.301676i 0.125158 + 0.0170790i
\(313\) −6.51130 + 3.75930i −0.368041 + 0.212488i −0.672602 0.740004i \(-0.734823\pi\)
0.304562 + 0.952493i \(0.401490\pi\)
\(314\) 4.92891 + 2.37364i 0.278155 + 0.133952i
\(315\) 4.11864 19.2726i 0.232059 1.08589i
\(316\) 35.7546 17.2185i 2.01135 0.968616i
\(317\) −13.7912 + 20.2280i −0.774592 + 1.13612i 0.212687 + 0.977120i \(0.431779\pi\)
−0.987279 + 0.158998i \(0.949174\pi\)
\(318\) 6.01214 0.992313i 0.337144 0.0556461i
\(319\) −30.4037 28.2105i −1.70228 1.57949i
\(320\) 28.0189 13.4932i 1.56631 0.754293i
\(321\) −1.45332 + 1.61089i −0.0811165 + 0.0899112i
\(322\) −10.8364 + 3.17604i −0.603887 + 0.176994i
\(323\) 6.85376 14.2320i 0.381354 0.791889i
\(324\) −0.578563 + 30.6230i −0.0321424 + 1.70128i
\(325\) −0.398479 + 0.230062i −0.0221037 + 0.0127616i
\(326\) 6.09951 12.6658i 0.337821 0.701492i
\(327\) −12.8570 + 12.2684i −0.710994 + 0.678443i
\(328\) 2.48854 + 8.06765i 0.137407 + 0.445462i
\(329\) −16.8533 2.78366i −0.929151 0.153468i
\(330\) 5.74504 + 64.5430i 0.316254 + 3.55297i
\(331\) −1.27375 16.9970i −0.0700117 0.934241i −0.916036 0.401097i \(-0.868629\pi\)
0.846024 0.533145i \(-0.178990\pi\)
\(332\) −21.6529 + 20.0910i −1.18836 + 1.10264i
\(333\) 12.3208 8.91465i 0.675176 0.488520i
\(334\) 29.5549 31.8526i 1.61717 1.74290i
\(335\) 1.95259 0.294306i 0.106681 0.0160796i
\(336\) −1.77588 3.07673i −0.0968820 0.167849i
\(337\) 5.30860 + 0.800143i 0.289178 + 0.0435866i 0.292029 0.956409i \(-0.405670\pi\)
−0.00285132 + 0.999996i \(0.500908\pi\)
\(338\) −23.3420 + 18.6146i −1.26964 + 1.01250i
\(339\) 7.52240 + 23.2292i 0.408561 + 1.26164i
\(340\) 17.3465 + 21.7519i 0.940748 + 1.17966i
\(341\) 47.4628 + 14.6403i 2.57026 + 0.792819i
\(342\) 8.35331 + 32.3959i 0.451695 + 1.75177i
\(343\) −17.0109 + 7.32319i −0.918502 + 0.395415i
\(344\) −24.5458 14.1715i −1.32342 0.764078i
\(345\) −3.32638 + 7.16167i −0.179086 + 0.385571i
\(346\) 7.50349 + 49.7824i 0.403390 + 2.67632i
\(347\) −6.83068 0.511889i −0.366690 0.0274796i −0.109889 0.993944i \(-0.535050\pi\)
−0.256801 + 0.966464i \(0.582669\pi\)
\(348\) 32.3962 19.3126i 1.73662 1.03527i
\(349\) −5.44455 + 2.13683i −0.291440 + 0.114382i −0.506557 0.862207i \(-0.669082\pi\)
0.215117 + 0.976588i \(0.430987\pi\)
\(350\) 6.63192 + 2.71131i 0.354491 + 0.144925i
\(351\) 1.45772 + 1.44457i 0.0778073 + 0.0771052i
\(352\) −22.4340 20.8157i −1.19573 1.10948i
\(353\) −11.0910 + 13.9077i −0.590315 + 0.740232i −0.983834 0.179085i \(-0.942686\pi\)
0.393519 + 0.919317i \(0.371258\pi\)
\(354\) −17.8495 + 38.4298i −0.948689 + 2.04252i
\(355\) 3.03928 6.31114i 0.161308 0.334960i
\(356\) −7.38535 + 6.85261i −0.391423 + 0.363187i
\(357\) −11.0618 + 10.2614i −0.585450 + 0.543093i
\(358\) 35.9437 + 33.3509i 1.89968 + 1.76265i
\(359\) 15.0747 5.91637i 0.795611 0.312254i 0.0675050 0.997719i \(-0.478496\pi\)
0.728106 + 0.685465i \(0.240401\pi\)
\(360\) −23.8280 4.74204i −1.25584 0.249928i
\(361\) 2.00840 + 3.47864i 0.105705 + 0.183086i
\(362\) 9.68778 + 16.7797i 0.509178 + 0.881923i
\(363\) 48.0718 23.9836i 2.52312 1.25881i
\(364\) −3.45549 0.840097i −0.181117 0.0440331i
\(365\) 18.6566 27.3642i 0.976532 1.43231i
\(366\) −5.98484 5.39943i −0.312833 0.282233i
\(367\) −7.87988 1.79853i −0.411326 0.0938826i 0.0118502 0.999930i \(-0.496228\pi\)
−0.423177 + 0.906047i \(0.639085\pi\)
\(368\) 0.419553 + 1.36016i 0.0218707 + 0.0709031i
\(369\) −2.63391 + 7.30520i −0.137116 + 0.380294i
\(370\) 12.6942 + 26.3598i 0.659941 + 1.37038i
\(371\) −3.99695 + 0.242941i −0.207511 + 0.0126129i
\(372\) −24.9195 + 37.6708i −1.29201 + 1.95314i
\(373\) −22.4288 −1.16132 −0.580659 0.814147i \(-0.697205\pi\)
−0.580659 + 0.814147i \(0.697205\pi\)
\(374\) 24.8050 42.9635i 1.28263 2.22159i
\(375\) −14.7580 + 7.36291i −0.762098 + 0.380219i
\(376\) −3.13850 + 20.8226i −0.161856 + 1.07384i
\(377\) 0.562340 2.46377i 0.0289620 0.126891i
\(378\) 3.88141 31.7196i 0.199638 1.63148i
\(379\) −1.42258 6.23271i −0.0730728 0.320153i 0.925160 0.379577i \(-0.123931\pi\)
−0.998233 + 0.0594245i \(0.981073\pi\)
\(380\) −40.4256 + 3.02948i −2.07379 + 0.155409i
\(381\) −21.5946 10.0300i −1.10632 0.513854i
\(382\) 0.917037 + 2.33657i 0.0469197 + 0.119549i
\(383\) 0.887283 3.88744i 0.0453380 0.198639i −0.947187 0.320683i \(-0.896088\pi\)
0.992525 + 0.122044i \(0.0389448\pi\)
\(384\) 29.2659 17.4465i 1.49347 0.890315i
\(385\) 0.600089 42.5779i 0.0305834 2.16997i
\(386\) 0.483577 + 0.385640i 0.0246134 + 0.0196285i
\(387\) −10.1989 23.9918i −0.518438 1.21957i
\(388\) −19.1003 + 28.0151i −0.969673 + 1.42225i
\(389\) 21.0777 16.8089i 1.06868 0.852247i 0.0791955 0.996859i \(-0.474765\pi\)
0.989488 + 0.144612i \(0.0461934\pi\)
\(390\) −3.23075 + 2.26948i −0.163595 + 0.114919i
\(391\) 5.23564 3.02280i 0.264778 0.152869i
\(392\) 9.32250 + 20.8413i 0.470857 + 1.05265i
\(393\) 4.98901 6.43862i 0.251662 0.324785i
\(394\) 24.9780 23.1762i 1.25837 1.16760i
\(395\) −10.5780 + 26.9523i −0.532237 + 1.35612i
\(396\) 11.6886 + 65.1379i 0.587374 + 3.27330i
\(397\) −2.26729 15.0425i −0.113792 0.754961i −0.970841 0.239726i \(-0.922943\pi\)
0.857049 0.515236i \(-0.172296\pi\)
\(398\) −11.0530 28.1626i −0.554037 1.41166i
\(399\) −3.27422 21.7401i −0.163916 1.08837i
\(400\) 0.329948 0.840695i 0.0164974 0.0420347i
\(401\) 37.1201 + 8.47241i 1.85369 + 0.423092i 0.995864 0.0908535i \(-0.0289595\pi\)
0.857823 + 0.513946i \(0.171817\pi\)
\(402\) 3.11136 0.756050i 0.155180 0.0377083i
\(403\) 0.673437 + 2.95052i 0.0335463 + 0.146976i
\(404\) 18.4382 12.5710i 0.917336 0.625429i
\(405\) −14.8873 16.6653i −0.739757 0.828107i
\(406\) −35.6910 + 16.5724i −1.77131 + 0.822472i
\(407\) 22.3497 24.0873i 1.10783 1.19396i
\(408\) 12.8410 + 13.4571i 0.635723 + 0.666224i
\(409\) −2.39008 3.50560i −0.118182 0.173341i 0.762590 0.646883i \(-0.223928\pi\)
−0.880771 + 0.473542i \(0.842975\pi\)
\(410\) −12.9381 7.46983i −0.638968 0.368909i
\(411\) 1.16166 + 0.900122i 0.0573005 + 0.0443998i
\(412\) −22.4606 32.9437i −1.10656 1.62302i
\(413\) 14.2611 23.9161i 0.701742 1.17683i
\(414\) −4.34291 + 12.0452i −0.213442 + 0.591987i
\(415\) 1.61050 21.4906i 0.0790564 1.05493i
\(416\) 0.414934 1.81794i 0.0203438 0.0891320i
\(417\) 36.1497 + 13.6077i 1.77026 + 0.666374i
\(418\) 31.3640 + 65.1280i 1.53406 + 3.18551i
\(419\) −10.4288 7.11026i −0.509482 0.347359i 0.281137 0.959668i \(-0.409289\pi\)
−0.790619 + 0.612309i \(0.790241\pi\)
\(420\) 37.0005 + 11.4178i 1.80544 + 0.557134i
\(421\) 25.6879 17.5137i 1.25195 0.853565i 0.258299 0.966065i \(-0.416838\pi\)
0.993652 + 0.112500i \(0.0358857\pi\)
\(422\) 49.4211 + 28.5333i 2.40578 + 1.38898i
\(423\) −13.8245 + 13.5658i −0.672171 + 0.659591i
\(424\) 0.368901 + 4.92264i 0.0179154 + 0.239064i
\(425\) −3.79300 0.571703i −0.183988 0.0277317i
\(426\) 4.00149 10.6302i 0.193873 0.515034i
\(427\) 3.54778 + 3.93335i 0.171689 + 0.190348i
\(428\) −2.89947 3.12489i −0.140151 0.151047i
\(429\) 3.69830 + 2.44645i 0.178555 + 0.118116i
\(430\) 48.8964 11.1603i 2.35799 0.538197i
\(431\) −1.11780 + 7.41614i −0.0538427 + 0.357223i 0.945644 + 0.325202i \(0.105432\pi\)
−0.999487 + 0.0320208i \(0.989806\pi\)
\(432\) −4.00479 0.432861i −0.192681 0.0208260i
\(433\) 8.59410 6.85357i 0.413006 0.329361i −0.394845 0.918748i \(-0.629202\pi\)
0.807851 + 0.589386i \(0.200630\pi\)
\(434\) 29.8983 36.4261i 1.43516 1.74851i
\(435\) −7.74260 + 26.4057i −0.371229 + 1.26606i
\(436\) −21.7705 27.2994i −1.04262 1.30740i
\(437\) −0.658300 + 8.78440i −0.0314907 + 0.420215i
\(438\) 26.1987 46.8786i 1.25182 2.23995i
\(439\) 14.0833 + 15.1782i 0.672160 + 0.724416i 0.973395 0.229134i \(-0.0735893\pi\)
−0.301235 + 0.953550i \(0.597399\pi\)
\(440\) −52.4942 −2.50256
\(441\) −4.67768 + 20.4724i −0.222747 + 0.974876i
\(442\) 3.02277 0.143778
\(443\) 5.74353 + 6.19005i 0.272883 + 0.294098i 0.854593 0.519298i \(-0.173807\pi\)
−0.581710 + 0.813396i \(0.697616\pi\)
\(444\) 15.3004 + 25.6658i 0.726124 + 1.21804i
\(445\) 0.549307 7.33000i 0.0260397 0.347475i
\(446\) −14.3371 17.9782i −0.678884 0.851293i
\(447\) −17.2883 + 4.20100i −0.817708 + 0.198701i
\(448\) −30.0558 + 13.9558i −1.42000 + 0.659349i
\(449\) −16.6216 + 13.2553i −0.784422 + 0.625555i −0.931571 0.363559i \(-0.881562\pi\)
0.147150 + 0.989114i \(0.452990\pi\)
\(450\) 6.91936 4.25710i 0.326182 0.200681i
\(451\) −2.50075 + 16.5914i −0.117756 + 0.781258i
\(452\) −46.7719 + 10.6754i −2.19996 + 0.502128i
\(453\) 3.89510 1.94331i 0.183008 0.0913047i
\(454\) −17.6103 18.9794i −0.826491 0.890745i
\(455\) 2.26501 1.26548i 0.106185 0.0593268i
\(456\) −26.7412 + 4.41367i −1.25227 + 0.206689i
\(457\) −37.2040 5.60761i −1.74033 0.262313i −0.799373 0.600835i \(-0.794835\pi\)
−0.940958 + 0.338522i \(0.890073\pi\)
\(458\) 0.666602 + 8.89518i 0.0311482 + 0.415644i
\(459\) 1.99258 + 16.9922i 0.0930059 + 0.793128i
\(460\) −13.4365 7.75757i −0.626480 0.361698i
\(461\) −1.77082 + 1.20732i −0.0824751 + 0.0562306i −0.603856 0.797094i \(-0.706370\pi\)
0.521380 + 0.853324i \(0.325417\pi\)
\(462\) −5.15192 68.8546i −0.239689 3.20340i
\(463\) 6.50140 + 4.43258i 0.302146 + 0.205999i 0.704896 0.709310i \(-0.250993\pi\)
−0.402751 + 0.915310i \(0.631946\pi\)
\(464\) 2.15216 + 4.46900i 0.0999114 + 0.207468i
\(465\) −5.36648 32.5139i −0.248865 1.50780i
\(466\) −8.39200 + 36.7678i −0.388752 + 1.70323i
\(467\) 1.07657 14.3658i 0.0498175 0.664769i −0.915270 0.402841i \(-0.868023\pi\)
0.965087 0.261928i \(-0.0843582\pi\)
\(468\) −3.08107 + 2.60123i −0.142423 + 0.120242i
\(469\) −2.08484 + 0.284251i −0.0962688 + 0.0131255i
\(470\) −20.9907 30.7876i −0.968227 1.42013i
\(471\) −3.77344 + 1.54217i −0.173871 + 0.0710595i
\(472\) −29.7280 17.1635i −1.36834 0.790014i
\(473\) −31.7307 46.5404i −1.45898 2.13993i
\(474\) −13.2100 + 45.0519i −0.606754 + 2.06930i
\(475\) 3.80163 4.09718i 0.174431 0.187991i
\(476\) −18.1555 23.4363i −0.832155 1.07420i
\(477\) −2.45188 + 3.82154i −0.112264 + 0.174977i
\(478\) 8.51271 5.80387i 0.389362 0.265463i
\(479\) 3.55593 + 15.5795i 0.162475 + 0.711848i 0.988873 + 0.148762i \(0.0475288\pi\)
−0.826398 + 0.563086i \(0.809614\pi\)
\(480\) −5.71303 + 19.4840i −0.260763 + 0.889318i
\(481\) 1.95192 + 0.445513i 0.0889998 + 0.0203136i
\(482\) −12.5908 + 32.0810i −0.573497 + 1.46125i
\(483\) 3.65168 7.58055i 0.166157 0.344927i
\(484\) 38.5636 + 98.2585i 1.75289 + 4.46630i
\(485\) −3.68705 24.4620i −0.167420 1.11076i
\(486\) −26.4407 24.7762i −1.19937 1.12387i
\(487\) 1.26841 3.23184i 0.0574769 0.146449i −0.899251 0.437433i \(-0.855888\pi\)
0.956728 + 0.290985i \(0.0939828\pi\)
\(488\) 4.78682 4.44152i 0.216689 0.201058i
\(489\) 3.96290 + 9.69656i 0.179208 + 0.438493i
\(490\) −37.1770 15.8140i −1.67949 0.714406i
\(491\) 36.6568 21.1638i 1.65430 0.955108i 0.679020 0.734120i \(-0.262405\pi\)
0.975276 0.220989i \(-0.0709284\pi\)
\(492\) −13.8380 6.42735i −0.623867 0.289768i
\(493\) 16.4713 13.1354i 0.741829 0.591589i
\(494\) −2.48113 + 3.63915i −0.111631 + 0.163733i
\(495\) −38.5763 29.0374i −1.73388 1.30513i
\(496\) −4.64421 3.70363i −0.208531 0.166298i
\(497\) −3.33302 + 6.67866i −0.149506 + 0.299579i
\(498\) −0.488418 34.9415i −0.0218865 1.56577i
\(499\) −6.53746 + 28.6425i −0.292657 + 1.28221i 0.588155 + 0.808748i \(0.299854\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(500\) −11.8390 30.1652i −0.529454 1.34903i
\(501\) 2.87063 + 32.2502i 0.128250 + 1.44083i
\(502\) −8.88948 + 0.666174i −0.396757 + 0.0297328i
\(503\) 8.96602 + 39.2827i 0.399775 + 1.75153i 0.628281 + 0.777987i \(0.283759\pi\)
−0.228505 + 0.973543i \(0.573384\pi\)
\(504\) 25.3167 + 5.41030i 1.12769 + 0.240994i
\(505\) −3.62299 + 15.8734i −0.161221 + 0.706356i
\(506\) −4.12335 + 27.3567i −0.183305 + 1.21615i
\(507\) 1.35225 22.2053i 0.0600557 0.986174i
\(508\) 23.3914 40.5151i 1.03783 1.79757i
\(509\) −18.6219 −0.825402 −0.412701 0.910867i \(-0.635415\pi\)
−0.412701 + 0.910867i \(0.635415\pi\)
\(510\) −32.8534 2.00070i −1.45478 0.0885924i
\(511\) −20.2889 + 28.8755i −0.897527 + 1.27738i
\(512\) 3.78211 + 7.85364i 0.167147 + 0.347085i
\(513\) −22.0926 11.5485i −0.975414 0.509880i
\(514\) −3.41010 11.0553i −0.150413 0.487627i
\(515\) 28.3611 + 6.47323i 1.24974 + 0.285245i
\(516\) 48.7306 15.7806i 2.14525 0.694703i
\(517\) −23.5747 + 34.5777i −1.03681 + 1.52073i
\(518\) −13.1294 28.2761i −0.576873 1.24238i
\(519\) −31.2876 20.6970i −1.37338 0.908496i
\(520\) −1.59926 2.76999i −0.0701320 0.121472i
\(521\) 5.83362 + 10.1041i 0.255575 + 0.442670i 0.965052 0.262060i \(-0.0844018\pi\)
−0.709476 + 0.704729i \(0.751068\pi\)
\(522\) −8.70904 + 43.7615i −0.381184 + 1.91539i
\(523\) 6.42076 2.51996i 0.280760 0.110190i −0.220783 0.975323i \(-0.570861\pi\)
0.501543 + 0.865133i \(0.332766\pi\)
\(524\) 11.7318 + 10.8855i 0.512506 + 0.475536i
\(525\) −4.81029 + 2.31583i −0.209938 + 0.101071i
\(526\) 29.9540 27.7932i 1.30606 1.21184i
\(527\) −10.9468 + 22.7312i −0.476848 + 0.990185i
\(528\) −8.66918 + 0.771653i −0.377278 + 0.0335819i
\(529\) 12.2382 15.3463i 0.532097 0.667228i
\(530\) −6.40333 5.94142i −0.278143 0.258079i
\(531\) −12.3521 29.0571i −0.536036 1.26097i
\(532\) 43.1175 2.62075i 1.86938 0.113624i
\(533\) −0.951674 + 0.373504i −0.0412216 + 0.0161783i
\(534\) −0.166589 11.9178i −0.00720900 0.515733i
\(535\) 3.10147 + 0.232423i 0.134088 + 0.0100485i
\(536\) 0.386603 + 2.56495i 0.0166987 + 0.110789i
\(537\) −36.3924 + 3.23932i −1.57045 + 0.139787i
\(538\) −9.83200 5.67651i −0.423887 0.244732i
\(539\) −1.27875 + 45.3562i −0.0550796 + 1.95363i
\(540\) 35.2088 26.2326i 1.51515 1.12887i
\(541\) 32.9703 + 10.1700i 1.41750 + 0.437242i 0.906452 0.422309i \(-0.138780\pi\)
0.511051 + 0.859550i \(0.329256\pi\)
\(542\) 35.1154 + 44.0333i 1.50834 + 1.89139i
\(543\) −14.1190 3.01559i −0.605905 0.129411i
\(544\) 12.1537 9.69221i 0.521083 0.415550i
\(545\) 25.1910 + 3.79693i 1.07906 + 0.162643i
\(546\) 3.47633 2.36953i 0.148773 0.101407i
\(547\) −0.367258 + 0.0553553i −0.0157028 + 0.00236682i −0.156889 0.987616i \(-0.550146\pi\)
0.141186 + 0.989983i \(0.454908\pi\)
\(548\) −1.96398 + 2.11666i −0.0838969 + 0.0904194i
\(549\) 5.97453 0.616078i 0.254987 0.0262936i
\(550\) 12.8676 11.9394i 0.548677 0.509097i
\(551\) 2.29403 + 30.6117i 0.0977289 + 1.30410i
\(552\) −9.40764 4.36957i −0.400416 0.185981i
\(553\) 11.6752 28.5579i 0.496481 1.21441i
\(554\) 12.1297 + 39.3234i 0.515340 + 1.67069i
\(555\) −20.9199 6.13405i −0.887999 0.260376i
\(556\) −32.9288 + 68.3774i −1.39649 + 2.89985i
\(557\) 17.4010 10.0465i 0.737303 0.425682i −0.0837847 0.996484i \(-0.526701\pi\)
0.821088 + 0.570802i \(0.193367\pi\)
\(558\) −13.3418 51.7424i −0.564804 2.19043i
\(559\) 1.48914 3.09222i 0.0629838 0.130787i
\(560\) −1.92714 + 4.71384i −0.0814365 + 0.199196i
\(561\) 11.3886 + 35.1682i 0.480829 + 1.48480i
\(562\) 33.0178 15.9005i 1.39277 0.670723i
\(563\) −0.811390 0.752860i −0.0341960 0.0317293i 0.662890 0.748717i \(-0.269330\pi\)
−0.697086 + 0.716988i \(0.745520\pi\)
\(564\) −24.1411 29.4189i −1.01652 1.23876i
\(565\) 19.7175 28.9202i 0.829520 1.21668i
\(566\) 23.6839 11.4055i 0.995507 0.479411i
\(567\) 15.6117 + 17.9799i 0.655628 + 0.755084i
\(568\) 8.29038 + 3.99244i 0.347857 + 0.167519i
\(569\) 11.5932 6.69333i 0.486012 0.280599i −0.236907 0.971532i \(-0.576134\pi\)
0.722918 + 0.690933i \(0.242800\pi\)
\(570\) 29.3752 37.9105i 1.23039 1.58789i
\(571\) −32.9512 + 22.4657i −1.37896 + 0.940162i −0.379074 + 0.925366i \(0.623757\pi\)
−0.999891 + 0.0147956i \(0.995290\pi\)
\(572\) −5.43215 + 6.81169i −0.227129 + 0.284811i
\(573\) −1.75045 0.658918i −0.0731260 0.0275267i
\(574\) 13.6729 + 8.15313i 0.570698 + 0.340305i
\(575\) 2.08548 0.475997i 0.0869705 0.0198504i
\(576\) −7.33399 + 36.8521i −0.305583 + 1.53550i
\(577\) −17.5489 18.9132i −0.730570 0.787368i 0.253082 0.967445i \(-0.418556\pi\)
−0.983652 + 0.180077i \(0.942365\pi\)
\(578\) −11.1932 8.92624i −0.465574 0.371283i
\(579\) −0.454729 + 0.0750537i −0.0188979 + 0.00311913i
\(580\) −50.3294 19.7528i −2.08981 0.820191i
\(581\) −2.03865 + 22.8733i −0.0845774 + 0.948946i
\(582\) −9.47176 38.9789i −0.392617 1.61573i
\(583\) −3.58418 + 9.13235i −0.148442 + 0.378223i
\(584\) 35.9460 + 24.5075i 1.48745 + 1.01413i
\(585\) 0.356992 2.92021i 0.0147598 0.120736i
\(586\) −13.0898 + 42.4362i −0.540736 + 1.75302i
\(587\) −5.75513 + 9.96817i −0.237540 + 0.411431i −0.960008 0.279974i \(-0.909674\pi\)
0.722468 + 0.691404i \(0.243008\pi\)
\(588\) −39.2513 12.7209i −1.61870 0.524602i
\(589\) −18.3811 31.8370i −0.757379 1.31182i
\(590\) 59.2196 13.5165i 2.43803 0.556465i
\(591\) 0.354868 + 25.3873i 0.0145973 + 1.04429i
\(592\) −3.54055 + 1.70504i −0.145516 + 0.0700768i
\(593\) 10.8794 1.63980i 0.446762 0.0673385i 0.0781914 0.996938i \(-0.475085\pi\)
0.368570 + 0.929600i \(0.379847\pi\)
\(594\) −66.4798 41.3530i −2.72770 1.69673i
\(595\) 21.3405 + 3.52482i 0.874875 + 0.144504i
\(596\) −5.21005 34.5664i −0.213412 1.41590i
\(597\) 21.0981 + 7.94191i 0.863487 + 0.325041i
\(598\) −1.56916 + 0.615851i −0.0641679 + 0.0251840i
\(599\) 8.17027 26.4874i 0.333828 1.08224i −0.620681 0.784063i \(-0.713144\pi\)
0.954509 0.298181i \(-0.0963799\pi\)
\(600\) 2.93818 + 5.88919i 0.119951 + 0.240425i
\(601\) 13.0337 42.2543i 0.531657 1.72359i −0.147003 0.989136i \(-0.546963\pi\)
0.678660 0.734453i \(-0.262561\pi\)
\(602\) −52.2650 + 11.1566i −2.13016 + 0.454711i
\(603\) −1.13471 + 2.09875i −0.0462089 + 0.0854676i
\(604\) 3.12468 + 7.96156i 0.127142 + 0.323951i
\(605\) −69.3861 33.4146i −2.82095 1.35850i
\(606\) −3.56956 + 26.1582i −0.145003 + 1.06261i
\(607\) 2.60165i 0.105598i 0.998605 + 0.0527989i \(0.0168142\pi\)
−0.998605 + 0.0527989i \(0.983186\pi\)
\(608\) 1.69269 + 22.5874i 0.0686478 + 0.916041i
\(609\) 8.64599 28.0181i 0.350353 1.13535i
\(610\) −0.863506 + 11.5227i −0.0349623 + 0.466540i
\(611\) −2.54279 0.190556i −0.102870 0.00770908i
\(612\) −33.6022 + 0.939578i −1.35829 + 0.0379802i
\(613\) −5.49898 + 1.69621i −0.222102 + 0.0685093i −0.403809 0.914843i \(-0.632314\pi\)
0.181707 + 0.983353i \(0.441838\pi\)
\(614\) 7.32279 + 4.99260i 0.295524 + 0.201485i
\(615\) 10.5906 3.42960i 0.427056 0.138295i
\(616\) 55.9307 + 0.788283i 2.25351 + 0.0317608i
\(617\) 7.60983 0.570278i 0.306360 0.0229585i 0.0793369 0.996848i \(-0.474720\pi\)
0.227023 + 0.973889i \(0.427101\pi\)
\(618\) 46.7371 + 6.37775i 1.88004 + 0.256551i
\(619\) 19.8701i 0.798648i 0.916810 + 0.399324i \(0.130755\pi\)
−0.916810 + 0.399324i \(0.869245\pi\)
\(620\) 64.5673 4.83865i 2.59308 0.194325i
\(621\) −4.49633 8.41493i −0.180431 0.337680i
\(622\) 57.9152 + 13.2188i 2.32219 + 0.530024i
\(623\) −0.695339 + 7.80161i −0.0278582 + 0.312565i
\(624\) −0.304828 0.433943i −0.0122029 0.0173716i
\(625\) 26.5496 + 12.7856i 1.06198 + 0.511424i
\(626\) 16.7003 + 5.15137i 0.667480 + 0.205890i
\(627\) −51.6873 15.1556i −2.06419 0.605256i
\(628\) −2.36081 7.65357i −0.0942068 0.305411i
\(629\) 10.4065 + 13.0493i 0.414934 + 0.520311i
\(630\) −39.3514 + 23.4528i −1.56780 + 0.934380i
\(631\) 22.6144 28.3576i 0.900266 1.12890i −0.0908453 0.995865i \(-0.528957\pi\)
0.991112 0.133033i \(-0.0424717\pi\)
\(632\) −35.4049 13.8954i −1.40833 0.552729i
\(633\) −40.4541 + 13.1004i −1.60791 + 0.520694i
\(634\) 56.2722 8.48167i 2.23485 0.336850i
\(635\) 7.59523 + 33.2769i 0.301408 + 1.32055i
\(636\) −7.05195 5.46426i −0.279628 0.216672i
\(637\) −2.43229 + 1.31432i −0.0963710 + 0.0520751i
\(638\) 96.4087i 3.81686i
\(639\) 3.88390 + 7.51977i 0.153645 + 0.297478i
\(640\) −45.4663 17.8442i −1.79721 0.705354i
\(641\) −13.5029 28.0391i −0.533332 1.10748i −0.977384 0.211475i \(-0.932173\pi\)
0.444051 0.896001i \(-0.353541\pi\)
\(642\) 5.04266 0.0704870i 0.199018 0.00278190i
\(643\) 1.70086 11.2845i 0.0670755 0.445017i −0.929933 0.367728i \(-0.880136\pi\)
0.997009 0.0772885i \(-0.0246262\pi\)
\(644\) 14.1996 + 8.46719i 0.559544 + 0.333654i
\(645\) −18.2316 + 32.6227i −0.717868 + 1.28452i
\(646\) −35.0868 + 10.8228i −1.38047 + 0.425819i
\(647\) 21.7393 + 3.27666i 0.854658 + 0.128819i 0.561735 0.827317i \(-0.310134\pi\)
0.292923 + 0.956136i \(0.405372\pi\)
\(648\) 21.8918 19.5562i 0.859989 0.768238i
\(649\) −38.4298 56.3662i −1.50850 2.21257i
\(650\) 1.02203 + 0.315254i 0.0400873 + 0.0123653i
\(651\) 5.22955 + 34.7230i 0.204962 + 1.36090i
\(652\) −19.6673 + 6.06656i −0.770231 + 0.237585i
\(653\) 19.8740 + 15.8490i 0.777730 + 0.620219i 0.929764 0.368157i \(-0.120011\pi\)
−0.152034 + 0.988375i \(0.548582\pi\)
\(654\) 41.2323 + 2.51095i 1.61231 + 0.0981859i
\(655\) −11.6765 −0.456240
\(656\) 1.00332 1.73780i 0.0391731 0.0678498i
\(657\) 12.8591 + 37.8935i 0.501680 + 1.47836i
\(658\) 21.9025 + 33.1184i 0.853848 + 1.29109i
\(659\) −14.3171 1.07292i −0.557716 0.0417951i −0.207109 0.978318i \(-0.566406\pi\)
−0.350607 + 0.936523i \(0.614025\pi\)
\(660\) 63.5486 70.4386i 2.47363 2.74182i
\(661\) −16.6237 + 17.9160i −0.646585 + 0.696853i −0.968245 0.250002i \(-0.919569\pi\)
0.321660 + 0.946855i \(0.395759\pi\)
\(662\) −26.9484 + 29.0434i −1.04738 + 1.12881i
\(663\) −1.50878 + 1.67236i −0.0585962 + 0.0649492i
\(664\) 28.2304 + 2.11557i 1.09555 + 0.0821001i
\(665\) −21.7601 + 22.7988i −0.843821 + 0.884101i
\(666\) −34.6699 6.89971i −1.34343 0.267358i
\(667\) −5.87430 + 10.1746i −0.227454 + 0.393962i
\(668\) −63.6164 −2.46139
\(669\) 17.1028 + 1.04152i 0.661231 + 0.0402674i
\(670\) −3.58861 2.86182i −0.138640 0.110562i
\(671\) 12.4009 3.82518i 0.478732 0.147669i
\(672\) 6.37961 20.6737i 0.246099 0.797505i
\(673\) 25.8385 + 7.97012i 0.996000 + 0.307225i 0.749563 0.661933i \(-0.230264\pi\)
0.246438 + 0.969159i \(0.420740\pi\)
\(674\) −7.02971 10.3107i −0.270774 0.397153i
\(675\) −1.09846 + 5.95305i −0.0422796 + 0.229133i
\(676\) 43.2221 + 6.51468i 1.66239 + 0.250565i
\(677\) −2.04272 + 0.630097i −0.0785083 + 0.0242166i −0.333761 0.942658i \(-0.608318\pi\)
0.255252 + 0.966875i \(0.417841\pi\)
\(678\) 27.6884 49.5442i 1.06337 1.90273i
\(679\) 3.56109 + 26.1187i 0.136662 + 1.00235i
\(680\) 3.97414 26.3667i 0.152401 1.01112i
\(681\) 19.2904 0.269644i 0.739209 0.0103328i
\(682\) −50.0942 104.022i −1.91821 3.98320i
\(683\) 38.3570 + 15.0540i 1.46769 + 0.576027i 0.958618 0.284696i \(-0.0918928\pi\)
0.509074 + 0.860723i \(0.329988\pi\)
\(684\) 26.4500 41.2253i 1.01134 1.57629i
\(685\) 2.10669i 0.0804925i
\(686\) 39.3734 + 17.4076i 1.50328 + 0.664625i
\(687\) −5.25403 4.07112i −0.200454 0.155323i
\(688\) 1.49901 + 6.56759i 0.0571492 + 0.250387i
\(689\) −0.591085 + 0.0890917i −0.0225185 + 0.00339412i
\(690\) 17.4623 5.65489i 0.664779 0.215278i
\(691\) −5.23088 2.05297i −0.198992 0.0780987i 0.263752 0.964591i \(-0.415040\pi\)
−0.462744 + 0.886492i \(0.653135\pi\)
\(692\) 45.9560 57.6270i 1.74699 2.19065i
\(693\) 40.6656 + 31.5176i 1.54476 + 1.19726i
\(694\) 9.92736 + 12.4485i 0.376838 + 0.472539i
\(695\) −16.3210 52.9115i −0.619092 2.00705i
\(696\) −34.6868 10.1708i −1.31480 0.385522i
\(697\) −8.14417 2.51214i −0.308482 0.0951542i
\(698\) 12.2491 + 5.89887i 0.463636 + 0.223275i
\(699\) −16.1532 22.9951i −0.610969 0.869755i
\(700\) −3.69430 9.81755i −0.139632 0.371069i
\(701\) −4.86749 1.11097i −0.183842 0.0419608i 0.129608 0.991565i \(-0.458628\pi\)
−0.313451 + 0.949604i \(0.601485\pi\)
\(702\) 0.156765 4.76781i 0.00591672 0.179949i
\(703\) −24.2520 + 1.81744i −0.914682 + 0.0685460i
\(704\) 81.1869i 3.05985i
\(705\) 27.5106 + 3.75411i 1.03611 + 0.141388i
\(706\) 41.2335 3.09002i 1.55184 0.116295i
\(707\) 4.09854 16.8581i 0.154141 0.634015i
\(708\) 59.0188 19.1123i 2.21806 0.718284i
\(709\) 31.0024 + 21.1371i 1.16432 + 0.793820i 0.981900 0.189400i \(-0.0606543\pi\)
0.182421 + 0.983221i \(0.441607\pi\)
\(710\) −15.5591 + 4.79936i −0.583924 + 0.180117i
\(711\) −18.3316 29.7956i −0.687488 1.11742i
\(712\) 9.62877 + 0.721576i 0.360853 + 0.0270422i
\(713\) 1.05143 14.0303i 0.0393763 0.525440i
\(714\) 34.9742 + 2.62502i 1.30887 + 0.0982390i
\(715\) −0.475030 6.33883i −0.0177651 0.237059i
\(716\) 71.7872i 2.68281i
\(717\) −1.03800 + 7.60663i −0.0387649 + 0.284075i
\(718\) −33.9149 16.3326i −1.26569 0.609526i
\(719\) −12.2770 31.2814i −0.457856 1.16660i −0.954385 0.298578i \(-0.903488\pi\)
0.496529 0.868020i \(-0.334607\pi\)
\(720\) 3.02586 + 4.91814i 0.112767 + 0.183288i
\(721\) −30.1205 7.32289i −1.12175 0.272719i
\(722\) 2.75210 8.92210i 0.102423 0.332046i
\(723\) −11.4644 22.9788i −0.426365 0.854590i
\(724\) 8.36132 27.1067i 0.310746 1.00741i
\(725\) 6.93904 2.72337i 0.257709 0.101143i
\(726\) −116.871 43.9934i −4.33748 1.63275i
\(727\) 0.196917 + 1.30646i 0.00730323 + 0.0484538i 0.992186 0.124771i \(-0.0398195\pi\)
−0.984882 + 0.173224i \(0.944581\pi\)
\(728\) 1.66235 + 2.97534i 0.0616110 + 0.110274i
\(729\) 26.9051 2.26166i 0.996486 0.0837652i
\(730\) −76.1244 + 11.4739i −2.81749 + 0.424668i
\(731\) 25.7784 12.4142i 0.953450 0.459157i
\(732\) 0.164942 + 11.8000i 0.00609642 + 0.436139i
\(733\) −11.8581 + 2.70652i −0.437987 + 0.0999677i −0.435828 0.900030i \(-0.643544\pi\)
−0.00215919 + 0.999998i \(0.500687\pi\)
\(734\) 9.39380 + 16.2705i 0.346731 + 0.600556i
\(735\) 27.3057 12.6750i 1.00719 0.467524i
\(736\) −4.33447 + 7.50752i −0.159771 + 0.276731i
\(737\) −1.51948 + 4.92604i −0.0559708 + 0.181453i
\(738\) 16.6121 7.06176i 0.611499 0.259947i
\(739\) −23.0715 15.7299i −0.848699 0.578633i 0.0589988 0.998258i \(-0.481209\pi\)
−0.907698 + 0.419625i \(0.862162\pi\)
\(740\) 15.6491 39.8733i 0.575273 1.46577i
\(741\) −0.774950 3.18913i −0.0284685 0.117156i
\(742\) 6.73331 + 6.42653i 0.247187 + 0.235925i
\(743\) 24.9555 + 9.79432i 0.915529 + 0.359319i 0.775879 0.630882i \(-0.217307\pi\)
0.139650 + 0.990201i \(0.455402\pi\)
\(744\) 42.7107 7.04947i 1.56585 0.258446i
\(745\) 19.9402 + 15.9018i 0.730552 + 0.582596i
\(746\) 35.4608 + 38.2177i 1.29831 + 1.39925i
\(747\) 19.5753 + 17.1704i 0.716224 + 0.628232i
\(748\) −70.8109 + 16.1621i −2.58910 + 0.590946i
\(749\) −3.30102 0.294212i −0.120617 0.0107503i
\(750\) 35.8790 + 13.5059i 1.31012 + 0.493165i
\(751\) 13.3889 16.7892i 0.488569 0.612647i −0.475039 0.879965i \(-0.657566\pi\)
0.963608 + 0.267318i \(0.0861374\pi\)
\(752\) 4.13528 2.81939i 0.150798 0.102813i
\(753\) 4.06851 5.25066i 0.148265 0.191345i
\(754\) −5.08725 + 2.93713i −0.185267 + 0.106964i
\(755\) −5.62213 2.70747i −0.204610 0.0985351i
\(756\) −37.9077 + 27.4212i −1.37869 + 0.997299i
\(757\) 43.9870 21.1830i 1.59874 0.769911i 0.599207 0.800594i \(-0.295483\pi\)
0.999529 + 0.0306836i \(0.00976844\pi\)
\(758\) −8.37112 + 12.2782i −0.304053 + 0.445964i
\(759\) −13.0771 15.9360i −0.474668 0.578441i
\(760\) 28.4811 + 26.4266i 1.03312 + 0.958595i
\(761\) 23.4497 11.2928i 0.850052 0.409363i 0.0424551 0.999098i \(-0.486482\pi\)
0.807597 + 0.589735i \(0.200768\pi\)
\(762\) 17.0512 + 52.6542i 0.617700 + 1.90746i
\(763\) −26.7831 4.42378i −0.969613 0.160151i
\(764\) 1.59449 3.31099i 0.0576865 0.119787i
\(765\) 17.5053 17.1777i 0.632906 0.621061i
\(766\) −8.02687 + 4.63431i −0.290022 + 0.167445i
\(767\) 1.80353 3.74507i 0.0651216 0.135226i
\(768\) −34.3640 10.0761i −1.24001 0.363590i
\(769\) 3.35142 + 10.8650i 0.120855 + 0.391803i 0.995704 0.0925932i \(-0.0295156\pi\)
−0.874849 + 0.484396i \(0.839039\pi\)
\(770\) −73.4996 + 66.2949i −2.64874 + 2.38910i
\(771\) 7.81849 + 3.63145i 0.281576 + 0.130784i
\(772\) −0.0676717 0.903016i −0.00243556 0.0325003i
\(773\) −21.4280 + 19.8823i −0.770713 + 0.715117i −0.963964 0.266032i \(-0.914287\pi\)
0.193251 + 0.981149i \(0.438097\pi\)
\(774\) −24.7562 + 55.3106i −0.889844 + 1.98810i
\(775\) −6.07191 + 6.54397i −0.218110 + 0.235066i
\(776\) 32.1335 4.84335i 1.15353 0.173866i
\(777\) 22.1973 + 6.84976i 0.796322 + 0.245734i
\(778\) −61.9665 9.33995i −2.22161 0.334853i
\(779\) 9.70924 7.74286i 0.347870 0.277417i
\(780\) 5.65290 + 1.20737i 0.202406 + 0.0432308i
\(781\) 11.4018 + 14.2973i 0.407987 + 0.511599i
\(782\) −13.4285 4.14214i −0.480201 0.148123i
\(783\) −19.8642 26.6613i −0.709890 0.952799i
\(784\) 2.12409 4.99349i 0.0758602 0.178339i
\(785\) 5.06075 + 2.92182i 0.180626 + 0.104284i
\(786\) −18.8590 + 1.67866i −0.672677 + 0.0598757i
\(787\) −1.64145 10.8903i −0.0585113 0.388197i −0.998849 0.0479560i \(-0.984729\pi\)
0.940338 0.340241i \(-0.110509\pi\)
\(788\) −49.7469 3.72801i −1.77216 0.132805i
\(789\) 0.425563 + 30.4449i 0.0151505 + 1.08387i
\(790\) 62.6499 24.5883i 2.22898 0.874811i
\(791\) −21.4426 + 30.5174i −0.762409 + 1.08507i
\(792\) 38.1439 50.6742i 1.35538 1.80063i
\(793\) 0.579644 + 0.537831i 0.0205838 + 0.0190989i
\(794\) −22.0471 + 27.6462i −0.782422 + 0.981126i
\(795\) 6.48327 0.577082i 0.229938 0.0204670i
\(796\) −19.2183 + 39.9072i −0.681174 + 1.41447i
\(797\) −8.57919 + 7.96032i −0.303890 + 0.281969i −0.817346 0.576147i \(-0.804556\pi\)
0.513456 + 0.858116i \(0.328365\pi\)
\(798\) −31.8675 + 39.9512i −1.12810 + 1.41426i
\(799\) −15.5829 14.4588i −0.551283 0.511516i
\(800\) 5.12010 2.00949i 0.181023 0.0710463i
\(801\) 6.67673 + 5.85646i 0.235910 + 0.206928i
\(802\) −44.2517 76.6463i −1.56258 2.70647i
\(803\) 43.2307 + 74.8777i 1.52558 + 2.64238i
\(804\) −3.90975 2.58632i −0.137886 0.0912126i
\(805\) −11.7963 + 2.51807i −0.415765 + 0.0887503i
\(806\) 3.96283 5.81241i 0.139585 0.204733i
\(807\) 8.04808 2.60624i 0.283306 0.0917439i
\(808\) −20.8514 4.75921i −0.733551 0.167428i
\(809\) −0.0144668 0.0469002i −0.000508626 0.00164892i 0.955318 0.295580i \(-0.0955127\pi\)
−0.955827 + 0.293931i \(0.905037\pi\)
\(810\) −4.85953 + 51.7159i −0.170746 + 1.81711i
\(811\) −17.9558 37.2855i −0.630512 1.30927i −0.934285 0.356527i \(-0.883961\pi\)
0.303773 0.952744i \(-0.401753\pi\)
\(812\) 53.3276 + 21.8017i 1.87143 + 0.765090i
\(813\) −41.8891 2.55095i −1.46911 0.0894656i
\(814\) −76.3795 −2.67710
\(815\) 7.50818 13.0045i 0.263000 0.455529i
\(816\) 0.268727 4.41276i 0.00940732 0.154477i
\(817\) −6.21363 + 41.2247i −0.217387 + 1.44227i
\(818\) −2.19458 + 9.61509i −0.0767318 + 0.336184i
\(819\) −0.424214 + 3.10602i −0.0148232 + 0.108533i
\(820\) 4.86710 + 21.3242i 0.169967 + 0.744673i
\(821\) 20.2362 1.51649i 0.706249 0.0529260i 0.283237 0.959050i \(-0.408592\pi\)
0.423012 + 0.906124i \(0.360973\pi\)
\(822\) −0.302865 3.40255i −0.0105636 0.118678i
\(823\) −5.27812 13.4484i −0.183984 0.468783i 0.808889 0.587961i \(-0.200069\pi\)
−0.992873 + 0.119178i \(0.961974\pi\)
\(824\) −8.50331 + 37.2554i −0.296227 + 1.29785i
\(825\) 0.182813 + 13.0785i 0.00636473 + 0.455334i
\(826\) −63.2994 + 13.5121i −2.20247 + 0.470145i
\(827\) −30.7684 24.5370i −1.06992 0.853234i −0.0802773 0.996773i \(-0.525581\pi\)
−0.989645 + 0.143538i \(0.954152\pi\)
\(828\) 17.2520 7.33378i 0.599548 0.254866i
\(829\) −6.19179 + 9.08168i −0.215050 + 0.315420i −0.918572 0.395253i \(-0.870657\pi\)
0.703523 + 0.710673i \(0.251609\pi\)
\(830\) −39.1654 + 31.2334i −1.35945 + 1.08413i
\(831\) −27.8102 12.9170i −0.964727 0.448086i
\(832\) −4.28404 + 2.47339i −0.148522 + 0.0857493i
\(833\) −22.6846 4.07603i −0.785975 0.141226i
\(834\) −33.9671 83.1119i −1.17619 2.87793i
\(835\) 34.0242 31.5698i 1.17745 1.09252i
\(836\) 38.6648 98.5162i 1.33725 3.40725i
\(837\) 35.2861 + 18.4452i 1.21967 + 0.637558i
\(838\) 4.37285 + 29.0119i 0.151057 + 1.00220i
\(839\) −8.95014 22.8046i −0.308993 0.787302i −0.998040 0.0625845i \(-0.980066\pi\)
0.689047 0.724717i \(-0.258030\pi\)
\(840\) −16.0983 33.4383i −0.555443 1.15373i
\(841\) −4.36264 + 11.1158i −0.150436 + 0.383304i
\(842\) −70.4562 16.0812i −2.42808 0.554194i
\(843\) −7.68339 + 26.2038i −0.264630 + 0.902506i
\(844\) −18.5914 81.4542i −0.639942 2.80377i
\(845\) −26.3495 + 17.9648i −0.906452 + 0.618008i
\(846\) 44.9727 + 2.10830i 1.54619 + 0.0724849i
\(847\) 73.4267 + 36.6440i 2.52297 + 1.25910i
\(848\) 0.798031 0.860072i 0.0274045 0.0295350i
\(849\) −5.51135 + 18.7962i −0.189149 + 0.645083i
\(850\) 5.02274 + 7.36700i 0.172278 + 0.252686i
\(851\) −8.06079 4.65390i −0.276320 0.159534i
\(852\) −15.3934 + 6.29115i −0.527369 + 0.215531i
\(853\) −3.39775 4.98358i −0.116337 0.170635i 0.763654 0.645626i \(-0.223404\pi\)
−0.879990 + 0.474992i \(0.842451\pi\)
\(854\) 1.09307 12.2641i 0.0374040 0.419667i
\(855\) 6.31185 + 35.1745i 0.215861 + 1.20294i
\(856\) −0.305313 + 4.07412i −0.0104354 + 0.139251i
\(857\) 8.61403 37.7405i 0.294250 1.28919i −0.584299 0.811539i \(-0.698630\pi\)
0.878548 0.477654i \(-0.158513\pi\)
\(858\) −1.67852 10.1697i −0.0573038 0.347187i
\(859\) 4.04164 + 8.39256i 0.137899 + 0.286350i 0.958469 0.285195i \(-0.0920584\pi\)
−0.820570 + 0.571545i \(0.806344\pi\)
\(860\) −60.6693 41.3636i −2.06881 1.41049i
\(861\) −11.3354 + 3.49509i −0.386311 + 0.119112i
\(862\) 14.4041 9.82054i 0.490605 0.334489i
\(863\) 24.6534 + 14.2336i 0.839211 + 0.484519i 0.856996 0.515323i \(-0.172328\pi\)
−0.0177849 + 0.999842i \(0.505661\pi\)
\(864\) −14.6572 19.6726i −0.498648 0.669275i
\(865\) 4.01876 + 53.6266i 0.136642 + 1.82336i
\(866\) −25.2658 3.80821i −0.858568 0.129408i
\(867\) 10.5254 1.73724i 0.357462 0.0589997i
\(868\) −68.8668 + 4.18583i −2.33749 + 0.142076i
\(869\) −51.4125 55.4095i −1.74405 1.87964i
\(870\) 57.2356 28.5555i 1.94047 0.968122i
\(871\) −0.306226 + 0.0698942i −0.0103761 + 0.00236827i
\(872\) −4.98769 + 33.0911i −0.168904 + 1.12061i
\(873\) 26.2930 + 14.2156i 0.889883 + 0.481124i
\(874\) 16.0090 12.7668i 0.541514 0.431843i
\(875\) −22.5418 11.2496i −0.762054 0.380307i
\(876\) −76.4007 + 18.5651i −2.58134 + 0.627257i
\(877\) 18.9939 + 23.8177i 0.641380 + 0.804265i 0.991175 0.132561i \(-0.0423201\pi\)
−0.349795 + 0.936826i \(0.613749\pi\)
\(878\) 3.59671 47.9948i 0.121383 1.61974i
\(879\) −16.9444 28.4235i −0.571520 0.958702i
\(880\) 8.48628 + 9.14603i 0.286072 + 0.308313i
\(881\) −47.7427 −1.60849 −0.804246 0.594297i \(-0.797430\pi\)
−0.804246 + 0.594297i \(0.797430\pi\)
\(882\) 42.2797 24.3972i 1.42363 0.821495i
\(883\) −49.6123 −1.66959 −0.834793 0.550564i \(-0.814413\pi\)
−0.834793 + 0.550564i \(0.814413\pi\)
\(884\) −3.01012 3.24413i −0.101241 0.109112i
\(885\) −22.0807 + 39.5101i −0.742235 + 1.32812i
\(886\) 1.46683 19.5735i 0.0492791 0.657583i
\(887\) 22.3781 + 28.0612i 0.751381 + 0.942203i 0.999649 0.0264889i \(-0.00843266\pi\)
−0.248268 + 0.968691i \(0.579861\pi\)
\(888\) 8.05776 27.4806i 0.270401 0.922187i
\(889\) −7.59275 35.5694i −0.254653 1.19296i
\(890\) −13.3585 + 10.6530i −0.447778 + 0.357091i
\(891\) 56.0614 16.1394i 1.87813 0.540691i
\(892\) −5.01767 + 33.2900i −0.168004 + 1.11463i
\(893\) 30.1978 6.89244i 1.01053 0.230647i
\(894\) 34.4919 + 22.8166i 1.15358 + 0.763100i
\(895\) 35.6246 + 38.3941i 1.19080 + 1.28337i
\(896\) 48.1747 + 19.6951i 1.60941 + 0.657967i
\(897\) 0.442507 1.17554i 0.0147749 0.0392502i
\(898\) 48.8659 + 7.36535i 1.63068 + 0.245785i
\(899\) −3.66400 48.8926i −0.122201 1.63066i
\(900\) −11.4592 3.18680i −0.381975 0.106227i
\(901\) −4.31563 2.49163i −0.143774 0.0830082i
\(902\) 32.2248 21.9705i 1.07297 0.731538i
\(903\) 19.9150 34.4846i 0.662730 1.14757i
\(904\) 37.9899 + 25.9011i 1.26353 + 0.861457i
\(905\) 8.97987 + 18.6469i 0.298501 + 0.619844i
\(906\) −9.46964 3.56464i −0.314608 0.118427i
\(907\) −3.74176 + 16.3937i −0.124243 + 0.544344i 0.874045 + 0.485846i \(0.161488\pi\)
−0.998288 + 0.0584981i \(0.981369\pi\)
\(908\) −2.83270 + 37.7998i −0.0940066 + 1.25443i
\(909\) −12.6905 15.0315i −0.420916 0.498562i
\(910\) −5.73741 1.85870i −0.190193 0.0616153i
\(911\) 0.231674 + 0.339803i 0.00767570 + 0.0112582i 0.830057 0.557678i \(-0.188308\pi\)
−0.822382 + 0.568936i \(0.807355\pi\)
\(912\) 5.09200 + 3.94557i 0.168613 + 0.130651i
\(913\) 48.7237 + 28.1307i 1.61252 + 0.930989i
\(914\) 49.2660 + 72.2600i 1.62958 + 2.39015i
\(915\) −5.94397 6.22915i −0.196502 0.205929i
\(916\) 8.88278 9.57336i 0.293495 0.316313i
\(917\) 12.4409 + 0.175341i 0.410836 + 0.00579028i
\(918\) 25.8036 30.2607i 0.851647 0.998750i
\(919\) −4.48678 + 3.05904i −0.148005 + 0.100908i −0.635059 0.772464i \(-0.719024\pi\)
0.487053 + 0.873372i \(0.338072\pi\)
\(920\) 3.30885 + 14.4970i 0.109089 + 0.477952i
\(921\) −6.41726 + 1.55938i −0.211456 + 0.0513832i
\(922\) 4.85696 + 1.10857i 0.159955 + 0.0365088i
\(923\) −0.407078 + 1.03722i −0.0133991 + 0.0341404i
\(924\) −68.7666 + 74.0956i −2.26225 + 2.43756i
\(925\) 2.15758 + 5.49743i 0.0709409 + 0.180755i
\(926\) −2.72606 18.0862i −0.0895838 0.594349i
\(927\) −26.8568 + 22.6742i −0.882094 + 0.744717i
\(928\) −11.0367 + 28.1211i −0.362298 + 0.923119i
\(929\) 15.9432 14.7932i 0.523081 0.485348i −0.373868 0.927482i \(-0.621969\pi\)
0.896949 + 0.442134i \(0.145778\pi\)
\(930\) −46.9178 + 60.5502i −1.53849 + 1.98552i
\(931\) 23.5270 23.9646i 0.771067 0.785408i
\(932\) 47.8172 27.6073i 1.56631 0.904307i
\(933\) −36.2210 + 25.4439i −1.18582 + 0.832995i
\(934\) −26.1808 + 20.8785i −0.856661 + 0.683165i
\(935\) 29.8515 43.7841i 0.976249 1.43189i
\(936\) 3.83602 + 0.468949i 0.125384 + 0.0153281i
\(937\) 4.60550 + 3.67276i 0.150455 + 0.119984i 0.695824 0.718212i \(-0.255039\pi\)
−0.545369 + 0.838196i \(0.683611\pi\)
\(938\) 3.78057 + 3.10306i 0.123440 + 0.101319i
\(939\) −11.1858 + 6.66829i −0.365035 + 0.217612i
\(940\) −12.1395 + 53.1866i −0.395947 + 1.73476i
\(941\) −2.61197 6.65519i −0.0851477 0.216953i 0.881958 0.471328i \(-0.156225\pi\)
−0.967106 + 0.254375i \(0.918130\pi\)
\(942\) 8.59376 + 3.99154i 0.280000 + 0.130051i
\(943\) 4.73957 0.355182i 0.154342 0.0115663i
\(944\) 1.81549 + 7.95416i 0.0590890 + 0.258886i
\(945\) 6.66644 33.4775i 0.216859 1.08902i
\(946\) −29.1353 + 127.650i −0.947271 + 4.15027i
\(947\) −0.367101 + 2.43556i −0.0119292 + 0.0791450i −0.994003 0.109350i \(-0.965123\pi\)
0.982074 + 0.188495i \(0.0603610\pi\)
\(948\) 61.5058 30.6860i 1.99762 0.996634i
\(949\) −2.63408 + 4.56236i −0.0855058 + 0.148100i
\(950\) −12.9919 −0.421514
\(951\) −23.3951 + 35.3664i −0.758637 + 1.14683i
\(952\) −4.63024 + 28.0331i −0.150067 + 0.908558i
\(953\) −24.5389 50.9556i −0.794893 1.65061i −0.758853 0.651262i \(-0.774240\pi\)
−0.0360402 0.999350i \(-0.511474\pi\)
\(954\) 10.3883 1.86411i 0.336333 0.0603529i
\(955\) 0.790301 + 2.56209i 0.0255735 + 0.0829074i
\(956\) −14.7060 3.35654i −0.475625 0.108558i
\(957\) −53.3386 48.1213i −1.72419 1.55554i
\(958\) 20.9248 30.6911i 0.676050 0.991584i
\(959\) −0.0316353 + 2.24460i −0.00102156 + 0.0724820i
\(960\) 48.1988 24.0469i 1.55561 0.776111i
\(961\) 13.8581 + 24.0029i 0.447034 + 0.774286i
\(962\) −2.32693 4.03036i −0.0750232 0.129944i
\(963\) −2.47798 + 2.82506i −0.0798519 + 0.0910362i
\(964\) 46.9685 18.4338i 1.51275 0.593712i
\(965\) 0.484317 + 0.449380i 0.0155907 + 0.0144661i
\(966\) −18.6904 + 5.76286i −0.601354 + 0.185417i
\(967\) 0.774350 0.718491i 0.0249014 0.0231051i −0.667624 0.744499i \(-0.732689\pi\)
0.692525 + 0.721394i \(0.256498\pi\)
\(968\) 43.8938 91.1464i 1.41080 2.92956i
\(969\) 11.5254 24.8140i 0.370248 0.797141i
\(970\) −35.8528 + 44.9580i −1.15116 + 1.44351i
\(971\) 44.4260 + 41.2213i 1.42570 + 1.32285i 0.871435 + 0.490511i \(0.163190\pi\)
0.554262 + 0.832342i \(0.313001\pi\)
\(972\) −0.260665 + 53.0495i −0.00836082 + 1.70156i
\(973\) 16.5949 + 56.6204i 0.532009 + 1.81517i
\(974\) −7.51233 + 2.94837i −0.240711 + 0.0944719i
\(975\) −0.684550 + 0.408087i −0.0219231 + 0.0130692i
\(976\) −1.54769 0.115983i −0.0495402 0.00371253i
\(977\) 1.79616 + 11.9168i 0.0574643 + 0.381251i 0.999015 + 0.0443788i \(0.0141308\pi\)
−0.941550 + 0.336872i \(0.890631\pi\)
\(978\) 10.2570 22.0833i 0.327983 0.706145i
\(979\) 16.6186 + 9.59477i 0.531134 + 0.306650i
\(980\) 20.0493 + 55.6475i 0.640451 + 1.77759i
\(981\) −21.9698 + 21.5586i −0.701442 + 0.688314i
\(982\) −94.0181 29.0007i −3.00024 0.925451i
\(983\) −28.5093 35.7495i −0.909305 1.14023i −0.989655 0.143466i \(-0.954175\pi\)
0.0803503 0.996767i \(-0.474396\pi\)
\(984\) 4.50516 + 13.9120i 0.143619 + 0.443498i
\(985\) 28.4563 22.6932i 0.906693 0.723064i
\(986\) −48.4239 7.29874i −1.54213 0.232439i
\(987\) −29.2553 4.41298i −0.931205 0.140467i
\(988\) 6.37639 0.961087i 0.202860 0.0305762i
\(989\) −10.8527 + 11.6964i −0.345096 + 0.371925i
\(990\) 11.5122 + 111.642i 0.365882 + 3.54821i
\(991\) 22.9216 21.2681i 0.728128 0.675604i −0.226296 0.974059i \(-0.572662\pi\)
0.954424 + 0.298455i \(0.0964711\pi\)
\(992\) −2.70355 36.0764i −0.0858378 1.14543i
\(993\) −2.61746 29.4060i −0.0830626 0.933171i
\(994\) 16.6498 4.87991i 0.528100 0.154781i
\(995\) −9.52546 30.8808i −0.301978 0.978987i
\(996\) −37.0140 + 35.3194i −1.17283 + 1.11914i
\(997\) 5.48745 11.3948i 0.173789 0.360877i −0.795821 0.605532i \(-0.792960\pi\)
0.969610 + 0.244655i \(0.0786746\pi\)
\(998\) 59.1416 34.1454i 1.87209 1.08085i
\(999\) 21.1224 15.7374i 0.668282 0.497909i
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 441.2.bd.a.47.8 648
9.5 odd 6 441.2.bn.a.194.8 yes 648
49.24 odd 42 441.2.bn.a.416.8 yes 648
441.122 even 42 inner 441.2.bd.a.122.8 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bd.a.47.8 648 1.1 even 1 trivial
441.2.bd.a.122.8 yes 648 441.122 even 42 inner
441.2.bn.a.194.8 yes 648 9.5 odd 6
441.2.bn.a.416.8 yes 648 49.24 odd 42