Properties

Label 475.2.n.b.39.10
Level $475$
Weight $2$
Character 475.39
Analytic conductor $3.793$
Analytic rank $0$
Dimension $96$
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] = [475,2,Mod(39,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.39");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.n (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 39.10
Character \(\chi\) \(=\) 475.39
Dual form 475.2.n.b.134.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.262787 - 0.361695i) q^{2} +(2.64793 + 0.860365i) q^{3} +(0.556267 - 1.71202i) q^{4} +(0.0123725 + 2.23603i) q^{5} +(-0.384652 - 1.18384i) q^{6} -4.32436i q^{7} +(-1.61580 + 0.525007i) q^{8} +(3.84426 + 2.79302i) q^{9} +O(q^{10})\) \(q+(-0.262787 - 0.361695i) q^{2} +(2.64793 + 0.860365i) q^{3} +(0.556267 - 1.71202i) q^{4} +(0.0123725 + 2.23603i) q^{5} +(-0.384652 - 1.18384i) q^{6} -4.32436i q^{7} +(-1.61580 + 0.525007i) q^{8} +(3.84426 + 2.79302i) q^{9} +(0.805512 - 0.592076i) q^{10} +(-0.742900 + 0.539748i) q^{11} +(2.94591 - 4.05470i) q^{12} +(1.76879 - 2.43454i) q^{13} +(-1.56410 + 1.13639i) q^{14} +(-1.89104 + 5.93151i) q^{15} +(-2.29815 - 1.66970i) q^{16} +(2.92059 - 0.948958i) q^{17} -2.12442i q^{18} +(0.309017 + 0.951057i) q^{19} +(3.83501 + 1.22265i) q^{20} +(3.72053 - 11.4506i) q^{21} +(0.390449 + 0.126865i) q^{22} +(3.67850 + 5.06302i) q^{23} -4.73024 q^{24} +(-4.99969 + 0.0553306i) q^{25} -1.34538 q^{26} +(2.86678 + 3.94578i) q^{27} +(-7.40337 - 2.40550i) q^{28} +(-1.90347 + 5.85826i) q^{29} +(2.64234 - 0.874742i) q^{30} +(-0.458081 - 1.40983i) q^{31} +4.66792i q^{32} +(-2.43153 + 0.790051i) q^{33} +(-1.11073 - 0.806991i) q^{34} +(9.66942 - 0.0535031i) q^{35} +(6.92012 - 5.02776i) q^{36} +(-3.89637 + 5.36289i) q^{37} +(0.262787 - 0.361695i) q^{38} +(6.77823 - 4.92467i) q^{39} +(-1.19392 - 3.60650i) q^{40} +(1.95642 + 1.42142i) q^{41} +(-5.11934 + 1.66337i) q^{42} +9.63799i q^{43} +(0.510806 + 1.57210i) q^{44} +(-6.19771 + 8.63044i) q^{45} +(0.864610 - 2.66099i) q^{46} +(-10.0778 - 3.27449i) q^{47} +(-4.64878 - 6.39850i) q^{48} -11.7001 q^{49} +(1.33387 + 1.79383i) q^{50} +8.54998 q^{51} +(-3.18404 - 4.38245i) q^{52} +(-4.90441 - 1.59354i) q^{53} +(0.673818 - 2.07380i) q^{54} +(-1.21609 - 1.65447i) q^{55} +(2.27032 + 6.98732i) q^{56} +2.78420i q^{57} +(2.61911 - 0.851001i) q^{58} +(-5.68224 - 4.12839i) q^{59} +(9.10290 + 6.53700i) q^{60} +(6.29954 - 4.57688i) q^{61} +(-0.389551 + 0.536171i) q^{62} +(12.0780 - 16.6240i) q^{63} +(-2.90793 + 2.11274i) q^{64} +(5.46559 + 3.92496i) q^{65} +(0.924732 + 0.671857i) q^{66} +(8.04870 - 2.61518i) q^{67} -5.52798i q^{68} +(5.38437 + 16.5714i) q^{69} +(-2.56035 - 3.48332i) q^{70} +(3.62351 - 11.1520i) q^{71} +(-7.67792 - 2.49471i) q^{72} +(7.55504 + 10.3986i) q^{73} +2.96365 q^{74} +(-13.2864 - 4.15505i) q^{75} +1.80012 q^{76} +(2.33407 + 3.21257i) q^{77} +(-3.56246 - 1.15751i) q^{78} +(3.35067 - 10.3123i) q^{79} +(3.70508 - 5.15940i) q^{80} +(-0.208911 - 0.642961i) q^{81} -1.08116i q^{82} +(-10.0710 + 3.27228i) q^{83} +(-17.5340 - 12.7392i) q^{84} +(2.15804 + 6.51880i) q^{85} +(3.48602 - 2.53274i) q^{86} +(-10.0805 + 13.8746i) q^{87} +(0.917010 - 1.26216i) q^{88} +(-3.85580 + 2.80140i) q^{89} +(4.75027 - 0.0262843i) q^{90} +(-10.5278 - 7.64890i) q^{91} +(10.7142 - 3.48126i) q^{92} -4.12724i q^{93} +(1.46396 + 4.50560i) q^{94} +(-2.12277 + 0.702739i) q^{95} +(-4.01611 + 12.3603i) q^{96} +(-0.493676 - 0.160405i) q^{97} +(3.07464 + 4.23187i) q^{98} -4.36342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.262787 0.361695i −0.185819 0.255757i 0.705937 0.708275i \(-0.250526\pi\)
−0.891756 + 0.452517i \(0.850526\pi\)
\(3\) 2.64793 + 0.860365i 1.52878 + 0.496732i 0.948255 0.317509i \(-0.102846\pi\)
0.580528 + 0.814240i \(0.302846\pi\)
\(4\) 0.556267 1.71202i 0.278134 0.856008i
\(5\) 0.0123725 + 2.23603i 0.00553315 + 0.999985i
\(6\) −0.384652 1.18384i −0.157033 0.483299i
\(7\) 4.32436i 1.63445i −0.576315 0.817227i \(-0.695510\pi\)
0.576315 0.817227i \(-0.304490\pi\)
\(8\) −1.61580 + 0.525007i −0.571273 + 0.185618i
\(9\) 3.84426 + 2.79302i 1.28142 + 0.931005i
\(10\) 0.805512 0.592076i 0.254725 0.187231i
\(11\) −0.742900 + 0.539748i −0.223993 + 0.162740i −0.694122 0.719857i \(-0.744207\pi\)
0.470129 + 0.882598i \(0.344207\pi\)
\(12\) 2.94591 4.05470i 0.850412 1.17049i
\(13\) 1.76879 2.43454i 0.490575 0.675219i −0.489919 0.871768i \(-0.662974\pi\)
0.980494 + 0.196549i \(0.0629736\pi\)
\(14\) −1.56410 + 1.13639i −0.418024 + 0.303712i
\(15\) −1.89104 + 5.93151i −0.488265 + 1.53151i
\(16\) −2.29815 1.66970i −0.574537 0.417426i
\(17\) 2.92059 0.948958i 0.708348 0.230156i 0.0673839 0.997727i \(-0.478535\pi\)
0.640964 + 0.767571i \(0.278535\pi\)
\(18\) 2.12442i 0.500730i
\(19\) 0.309017 + 0.951057i 0.0708934 + 0.218187i
\(20\) 3.83501 + 1.22265i 0.857533 + 0.273393i
\(21\) 3.72053 11.4506i 0.811886 2.49873i
\(22\) 0.390449 + 0.126865i 0.0832440 + 0.0270476i
\(23\) 3.67850 + 5.06302i 0.767021 + 1.05571i 0.996597 + 0.0824230i \(0.0262658\pi\)
−0.229577 + 0.973291i \(0.573734\pi\)
\(24\) −4.73024 −0.965555
\(25\) −4.99969 + 0.0553306i −0.999939 + 0.0110661i
\(26\) −1.34538 −0.263850
\(27\) 2.86678 + 3.94578i 0.551711 + 0.759365i
\(28\) −7.40337 2.40550i −1.39911 0.454597i
\(29\) −1.90347 + 5.85826i −0.353465 + 1.08785i 0.603430 + 0.797416i \(0.293800\pi\)
−0.956894 + 0.290436i \(0.906200\pi\)
\(30\) 2.64234 0.874742i 0.482423 0.159705i
\(31\) −0.458081 1.40983i −0.0822738 0.253213i 0.901455 0.432873i \(-0.142500\pi\)
−0.983729 + 0.179660i \(0.942500\pi\)
\(32\) 4.66792i 0.825180i
\(33\) −2.43153 + 0.790051i −0.423275 + 0.137530i
\(34\) −1.11073 0.806991i −0.190488 0.138398i
\(35\) 9.66942 0.0535031i 1.63443 0.00904368i
\(36\) 6.92012 5.02776i 1.15335 0.837960i
\(37\) −3.89637 + 5.36289i −0.640559 + 0.881653i −0.998645 0.0520350i \(-0.983429\pi\)
0.358087 + 0.933688i \(0.383429\pi\)
\(38\) 0.262787 0.361695i 0.0426297 0.0586747i
\(39\) 6.77823 4.92467i 1.08539 0.788579i
\(40\) −1.19392 3.60650i −0.188776 0.570237i
\(41\) 1.95642 + 1.42142i 0.305541 + 0.221989i 0.729981 0.683467i \(-0.239529\pi\)
−0.424440 + 0.905456i \(0.639529\pi\)
\(42\) −5.11934 + 1.66337i −0.789931 + 0.256664i
\(43\) 9.63799i 1.46978i 0.678186 + 0.734890i \(0.262766\pi\)
−0.678186 + 0.734890i \(0.737234\pi\)
\(44\) 0.510806 + 1.57210i 0.0770070 + 0.237003i
\(45\) −6.19771 + 8.63044i −0.923901 + 1.28655i
\(46\) 0.864610 2.66099i 0.127480 0.392342i
\(47\) −10.0778 3.27449i −1.47000 0.477633i −0.538894 0.842374i \(-0.681158\pi\)
−0.931109 + 0.364741i \(0.881158\pi\)
\(48\) −4.64878 6.39850i −0.670994 0.923544i
\(49\) −11.7001 −1.67144
\(50\) 1.33387 + 1.79383i 0.188637 + 0.253685i
\(51\) 8.54998 1.19724
\(52\) −3.18404 4.38245i −0.441547 0.607737i
\(53\) −4.90441 1.59354i −0.673673 0.218890i −0.0478496 0.998855i \(-0.515237\pi\)
−0.625823 + 0.779965i \(0.715237\pi\)
\(54\) 0.673818 2.07380i 0.0916951 0.282208i
\(55\) −1.21609 1.65447i −0.163977 0.223089i
\(56\) 2.27032 + 6.98732i 0.303384 + 0.933720i
\(57\) 2.78420i 0.368776i
\(58\) 2.61911 0.851001i 0.343906 0.111742i
\(59\) −5.68224 4.12839i −0.739764 0.537470i 0.152873 0.988246i \(-0.451147\pi\)
−0.892637 + 0.450776i \(0.851147\pi\)
\(60\) 9.10290 + 6.53700i 1.17518 + 0.843923i
\(61\) 6.29954 4.57688i 0.806573 0.586010i −0.106262 0.994338i \(-0.533888\pi\)
0.912835 + 0.408329i \(0.133888\pi\)
\(62\) −0.389551 + 0.536171i −0.0494730 + 0.0680937i
\(63\) 12.0780 16.6240i 1.52169 2.09442i
\(64\) −2.90793 + 2.11274i −0.363492 + 0.264092i
\(65\) 5.46559 + 3.92496i 0.677923 + 0.486831i
\(66\) 0.924732 + 0.671857i 0.113827 + 0.0826999i
\(67\) 8.04870 2.61518i 0.983305 0.319495i 0.227130 0.973864i \(-0.427066\pi\)
0.756175 + 0.654369i \(0.227066\pi\)
\(68\) 5.52798i 0.670365i
\(69\) 5.38437 + 16.5714i 0.648202 + 1.99496i
\(70\) −2.56035 3.48332i −0.306020 0.416337i
\(71\) 3.62351 11.1520i 0.430031 1.32350i −0.468063 0.883695i \(-0.655048\pi\)
0.898094 0.439804i \(-0.144952\pi\)
\(72\) −7.67792 2.49471i −0.904851 0.294004i
\(73\) 7.55504 + 10.3986i 0.884250 + 1.21707i 0.975226 + 0.221213i \(0.0710015\pi\)
−0.0909755 + 0.995853i \(0.528999\pi\)
\(74\) 2.96365 0.344517
\(75\) −13.2864 4.15505i −1.53419 0.479784i
\(76\) 1.80012 0.206488
\(77\) 2.33407 + 3.21257i 0.265992 + 0.366106i
\(78\) −3.56246 1.15751i −0.403369 0.131063i
\(79\) 3.35067 10.3123i 0.376980 1.16023i −0.565153 0.824986i \(-0.691183\pi\)
0.942133 0.335239i \(-0.108817\pi\)
\(80\) 3.70508 5.15940i 0.414240 0.576838i
\(81\) −0.208911 0.642961i −0.0232123 0.0714401i
\(82\) 1.08116i 0.119394i
\(83\) −10.0710 + 3.27228i −1.10544 + 0.359179i −0.804194 0.594367i \(-0.797403\pi\)
−0.301246 + 0.953546i \(0.597403\pi\)
\(84\) −17.5340 12.7392i −1.91312 1.38996i
\(85\) 2.15804 + 6.51880i 0.234072 + 0.707064i
\(86\) 3.48602 2.53274i 0.375907 0.273112i
\(87\) −10.0805 + 13.8746i −1.08074 + 1.48751i
\(88\) 0.917010 1.26216i 0.0977536 0.134546i
\(89\) −3.85580 + 2.80140i −0.408714 + 0.296948i −0.773081 0.634307i \(-0.781285\pi\)
0.364367 + 0.931256i \(0.381285\pi\)
\(90\) 4.75027 0.0262843i 0.500722 0.00277061i
\(91\) −10.5278 7.64890i −1.10361 0.801823i
\(92\) 10.7142 3.48126i 1.11703 0.362946i
\(93\) 4.12724i 0.427975i
\(94\) 1.46396 + 4.50560i 0.150996 + 0.464717i
\(95\) −2.12277 + 0.702739i −0.217792 + 0.0720995i
\(96\) −4.01611 + 12.3603i −0.409893 + 1.26152i
\(97\) −0.493676 0.160405i −0.0501252 0.0162867i 0.283847 0.958870i \(-0.408389\pi\)
−0.333972 + 0.942583i \(0.608389\pi\)
\(98\) 3.07464 + 4.23187i 0.310585 + 0.427484i
\(99\) −4.36342 −0.438541
\(100\) −2.68644 + 8.59033i −0.268644 + 0.859033i
\(101\) −14.8247 −1.47511 −0.737557 0.675284i \(-0.764021\pi\)
−0.737557 + 0.675284i \(0.764021\pi\)
\(102\) −2.24682 3.09249i −0.222469 0.306202i
\(103\) 3.98724 + 1.29553i 0.392875 + 0.127653i 0.498791 0.866722i \(-0.333778\pi\)
−0.105916 + 0.994375i \(0.533778\pi\)
\(104\) −1.57988 + 4.86236i −0.154920 + 0.476794i
\(105\) 25.6500 + 8.17755i 2.50318 + 0.798047i
\(106\) 0.712440 + 2.19266i 0.0691983 + 0.212970i
\(107\) 2.34479i 0.226679i 0.993556 + 0.113340i \(0.0361548\pi\)
−0.993556 + 0.113340i \(0.963845\pi\)
\(108\) 8.34993 2.71306i 0.803472 0.261064i
\(109\) −6.43598 4.67601i −0.616455 0.447881i 0.235226 0.971941i \(-0.424417\pi\)
−0.851682 + 0.524060i \(0.824417\pi\)
\(110\) −0.278843 + 0.874627i −0.0265866 + 0.0833924i
\(111\) −14.9313 + 10.8483i −1.41722 + 1.02967i
\(112\) −7.22040 + 9.93803i −0.682264 + 0.939055i
\(113\) 3.18196 4.37959i 0.299334 0.411997i −0.632684 0.774410i \(-0.718047\pi\)
0.932018 + 0.362413i \(0.118047\pi\)
\(114\) 1.00703 0.731651i 0.0943172 0.0685254i
\(115\) −11.2756 + 8.28790i −1.05145 + 0.772850i
\(116\) 8.97060 + 6.51752i 0.832899 + 0.605137i
\(117\) 13.5994 4.41871i 1.25726 0.408510i
\(118\) 3.14013i 0.289072i
\(119\) −4.10364 12.6297i −0.376180 1.15776i
\(120\) −0.0585248 10.5770i −0.00534256 0.965540i
\(121\) −3.13861 + 9.65966i −0.285329 + 0.878151i
\(122\) −3.31087 1.07577i −0.299752 0.0973955i
\(123\) 3.95752 + 5.44706i 0.356838 + 0.491145i
\(124\) −2.66846 −0.239635
\(125\) −0.185580 11.1788i −0.0165988 0.999862i
\(126\) −9.18675 −0.818421
\(127\) 5.13130 + 7.06262i 0.455329 + 0.626706i 0.973532 0.228551i \(-0.0733988\pi\)
−0.518203 + 0.855258i \(0.673399\pi\)
\(128\) 10.4072 + 3.38152i 0.919880 + 0.298887i
\(129\) −8.29219 + 25.5207i −0.730087 + 2.24698i
\(130\) −0.0166457 3.00831i −0.00145992 0.263846i
\(131\) 0.623982 + 1.92042i 0.0545176 + 0.167788i 0.974608 0.223918i \(-0.0718849\pi\)
−0.920090 + 0.391706i \(0.871885\pi\)
\(132\) 4.60229i 0.400578i
\(133\) 4.11271 1.33630i 0.356617 0.115872i
\(134\) −3.06099 2.22394i −0.264430 0.192119i
\(135\) −8.78743 + 6.45903i −0.756301 + 0.555905i
\(136\) −4.22090 + 3.06666i −0.361939 + 0.262964i
\(137\) −10.9877 + 15.1233i −0.938744 + 1.29207i 0.0176055 + 0.999845i \(0.494396\pi\)
−0.956350 + 0.292225i \(0.905604\pi\)
\(138\) 4.57885 6.30225i 0.389778 0.536483i
\(139\) 13.6831 9.94137i 1.16059 0.843216i 0.170735 0.985317i \(-0.445386\pi\)
0.989852 + 0.142101i \(0.0453857\pi\)
\(140\) 5.28718 16.5840i 0.446849 1.40160i
\(141\) −23.8681 17.3412i −2.01006 1.46039i
\(142\) −4.98584 + 1.62000i −0.418402 + 0.135947i
\(143\) 2.76332i 0.231080i
\(144\) −4.17117 12.8375i −0.347597 1.06979i
\(145\) −13.1228 4.18373i −1.08979 0.347440i
\(146\) 1.77577 5.46524i 0.146963 0.452307i
\(147\) −30.9811 10.0664i −2.55527 0.830259i
\(148\) 7.01392 + 9.65384i 0.576541 + 0.793541i
\(149\) −2.74494 −0.224874 −0.112437 0.993659i \(-0.535866\pi\)
−0.112437 + 0.993659i \(0.535866\pi\)
\(150\) 1.98864 + 5.89754i 0.162372 + 0.481532i
\(151\) −16.7075 −1.35964 −0.679818 0.733380i \(-0.737941\pi\)
−0.679818 + 0.733380i \(0.737941\pi\)
\(152\) −0.998622 1.37449i −0.0809990 0.111486i
\(153\) 13.8780 + 4.50922i 1.12197 + 0.364549i
\(154\) 0.548608 1.68844i 0.0442081 0.136059i
\(155\) 3.14676 1.04173i 0.252754 0.0836736i
\(156\) −4.66061 14.3439i −0.373147 1.14843i
\(157\) 2.41292i 0.192572i −0.995354 0.0962859i \(-0.969304\pi\)
0.995354 0.0962859i \(-0.0306963\pi\)
\(158\) −4.61043 + 1.49802i −0.366786 + 0.119176i
\(159\) −11.6155 8.43916i −0.921170 0.669269i
\(160\) −10.4376 + 0.0577538i −0.825167 + 0.00456584i
\(161\) 21.8943 15.9072i 1.72552 1.25366i
\(162\) −0.177657 + 0.244524i −0.0139581 + 0.0192116i
\(163\) −8.97603 + 12.3544i −0.703057 + 0.967675i 0.296862 + 0.954920i \(0.404060\pi\)
−0.999919 + 0.0127543i \(0.995940\pi\)
\(164\) 3.52179 2.55873i 0.275005 0.199803i
\(165\) −1.79667 5.42720i −0.139870 0.422507i
\(166\) 3.83011 + 2.78274i 0.297274 + 0.215982i
\(167\) 21.7786 7.07628i 1.68528 0.547579i 0.699352 0.714777i \(-0.253472\pi\)
0.985923 + 0.167198i \(0.0534720\pi\)
\(168\) 20.4552i 1.57816i
\(169\) 1.21889 + 3.75135i 0.0937607 + 0.288566i
\(170\) 1.79072 2.49361i 0.137342 0.191251i
\(171\) −1.46837 + 4.51919i −0.112289 + 0.345591i
\(172\) 16.5004 + 5.36130i 1.25814 + 0.408796i
\(173\) 4.16344 + 5.73048i 0.316540 + 0.435681i 0.937407 0.348236i \(-0.113219\pi\)
−0.620867 + 0.783916i \(0.713219\pi\)
\(174\) 7.66740 0.581264
\(175\) 0.239270 + 21.6205i 0.0180871 + 1.63435i
\(176\) 2.60851 0.196624
\(177\) −11.4942 15.8205i −0.863961 1.18914i
\(178\) 2.02651 + 0.658453i 0.151893 + 0.0493531i
\(179\) 0.217238 0.668589i 0.0162371 0.0499727i −0.942610 0.333897i \(-0.891636\pi\)
0.958847 + 0.283924i \(0.0916363\pi\)
\(180\) 11.3279 + 15.4114i 0.844329 + 1.14870i
\(181\) 2.23789 + 6.88752i 0.166341 + 0.511945i 0.999133 0.0416414i \(-0.0132587\pi\)
−0.832791 + 0.553587i \(0.813259\pi\)
\(182\) 5.81789i 0.431251i
\(183\) 20.6185 6.69936i 1.52416 0.495231i
\(184\) −8.60186 6.24962i −0.634138 0.460728i
\(185\) −12.0398 8.64605i −0.885184 0.635671i
\(186\) −1.49281 + 1.08459i −0.109458 + 0.0795257i
\(187\) −1.65751 + 2.28137i −0.121209 + 0.166830i
\(188\) −11.2119 + 15.4319i −0.817715 + 1.12549i
\(189\) 17.0630 12.3970i 1.24115 0.901747i
\(190\) 0.812014 + 0.583126i 0.0589097 + 0.0423044i
\(191\) −0.408127 0.296522i −0.0295310 0.0214556i 0.572922 0.819610i \(-0.305810\pi\)
−0.602453 + 0.798154i \(0.705810\pi\)
\(192\) −9.51773 + 3.09250i −0.686883 + 0.223182i
\(193\) 23.3193i 1.67856i −0.543700 0.839280i \(-0.682977\pi\)
0.543700 0.839280i \(-0.317023\pi\)
\(194\) 0.0717140 + 0.220713i 0.00514876 + 0.0158463i
\(195\) 11.0956 + 15.0954i 0.794572 + 1.08101i
\(196\) −6.50839 + 20.0308i −0.464885 + 1.43077i
\(197\) 7.55921 + 2.45614i 0.538572 + 0.174993i 0.565657 0.824641i \(-0.308623\pi\)
−0.0270854 + 0.999633i \(0.508623\pi\)
\(198\) 1.14665 + 1.57823i 0.0814890 + 0.112160i
\(199\) 4.56505 0.323608 0.161804 0.986823i \(-0.448269\pi\)
0.161804 + 0.986823i \(0.448269\pi\)
\(200\) 8.04948 2.71428i 0.569184 0.191928i
\(201\) 23.5624 1.66196
\(202\) 3.89575 + 5.36203i 0.274104 + 0.377271i
\(203\) 25.3333 + 8.23127i 1.77805 + 0.577722i
\(204\) 4.75607 14.6377i 0.332992 1.02484i
\(205\) −3.15414 + 4.39221i −0.220295 + 0.306765i
\(206\) −0.579207 1.78262i −0.0403553 0.124201i
\(207\) 29.7377i 2.06691i
\(208\) −8.12990 + 2.64157i −0.563707 + 0.183160i
\(209\) −0.742900 0.539748i −0.0513875 0.0373352i
\(210\) −3.78270 11.4264i −0.261031 0.788499i
\(211\) 9.74433 7.07967i 0.670828 0.487385i −0.199474 0.979903i \(-0.563924\pi\)
0.870302 + 0.492518i \(0.163924\pi\)
\(212\) −5.45633 + 7.50999i −0.374742 + 0.515788i
\(213\) 19.1896 26.4122i 1.31485 1.80973i
\(214\) 0.848099 0.616180i 0.0579748 0.0421212i
\(215\) −21.5509 + 0.119246i −1.46976 + 0.00813251i
\(216\) −6.70371 4.87053i −0.456130 0.331398i
\(217\) −6.09661 + 1.98091i −0.413865 + 0.134473i
\(218\) 3.55666i 0.240887i
\(219\) 11.0586 + 34.0349i 0.747271 + 2.29986i
\(220\) −3.50895 + 1.16163i −0.236573 + 0.0783172i
\(221\) 2.85565 8.78880i 0.192092 0.591199i
\(222\) 7.84753 + 2.54982i 0.526692 + 0.171133i
\(223\) −13.3137 18.3248i −0.891553 1.22712i −0.973085 0.230447i \(-0.925981\pi\)
0.0815321 0.996671i \(-0.474019\pi\)
\(224\) 20.1858 1.34872
\(225\) −19.3746 13.7515i −1.29164 0.916768i
\(226\) −2.42026 −0.160993
\(227\) 14.8797 + 20.4801i 0.987599 + 1.35931i 0.932633 + 0.360825i \(0.117505\pi\)
0.0549659 + 0.998488i \(0.482495\pi\)
\(228\) 4.76659 + 1.54876i 0.315675 + 0.102569i
\(229\) 7.95002 24.4676i 0.525352 1.61687i −0.238267 0.971200i \(-0.576579\pi\)
0.763619 0.645667i \(-0.223421\pi\)
\(230\) 5.96077 + 1.90037i 0.393042 + 0.125307i
\(231\) 3.41647 + 10.5148i 0.224787 + 0.691823i
\(232\) 10.4651i 0.687070i
\(233\) 8.25006 2.68061i 0.540479 0.175612i −0.0260400 0.999661i \(-0.508290\pi\)
0.566519 + 0.824049i \(0.308290\pi\)
\(234\) −5.17197 3.75766i −0.338102 0.245646i
\(235\) 7.19717 22.5749i 0.469492 1.47262i
\(236\) −10.2287 + 7.43159i −0.665832 + 0.483755i
\(237\) 17.7447 24.4235i 1.15264 1.58648i
\(238\) −3.48972 + 4.80319i −0.226205 + 0.311345i
\(239\) 0.768449 0.558311i 0.0497068 0.0361141i −0.562654 0.826692i \(-0.690220\pi\)
0.612361 + 0.790578i \(0.290220\pi\)
\(240\) 14.2498 10.4740i 0.919818 0.676094i
\(241\) 1.74154 + 1.26531i 0.112183 + 0.0815055i 0.642462 0.766317i \(-0.277913\pi\)
−0.530279 + 0.847823i \(0.677913\pi\)
\(242\) 4.31864 1.40321i 0.277613 0.0902019i
\(243\) 16.5140i 1.05937i
\(244\) −4.33146 13.3309i −0.277294 0.853422i
\(245\) −0.144759 26.1618i −0.00924834 1.67142i
\(246\) 0.930191 2.86283i 0.0593068 0.182528i
\(247\) 2.86197 + 0.929910i 0.182103 + 0.0591687i
\(248\) 1.48034 + 2.03751i 0.0940016 + 0.129382i
\(249\) −29.4828 −1.86839
\(250\) −3.99455 + 3.00477i −0.252638 + 0.190038i
\(251\) 8.34465 0.526709 0.263355 0.964699i \(-0.415171\pi\)
0.263355 + 0.964699i \(0.415171\pi\)
\(252\) −21.7419 29.9251i −1.36961 1.88510i
\(253\) −5.46552 1.77585i −0.343614 0.111647i
\(254\) 1.20608 3.71193i 0.0756762 0.232907i
\(255\) 0.105785 + 19.1180i 0.00662448 + 1.19722i
\(256\) 0.709652 + 2.18409i 0.0443533 + 0.136505i
\(257\) 21.5289i 1.34294i −0.741034 0.671468i \(-0.765664\pi\)
0.741034 0.671468i \(-0.234336\pi\)
\(258\) 11.4098 3.70727i 0.710344 0.230805i
\(259\) 23.1911 + 16.8493i 1.44102 + 1.04696i
\(260\) 9.75992 7.17384i 0.605285 0.444903i
\(261\) −23.6796 + 17.2043i −1.46573 + 1.06492i
\(262\) 0.530632 0.730353i 0.0327826 0.0451213i
\(263\) 10.3428 14.2356i 0.637764 0.877807i −0.360730 0.932670i \(-0.617472\pi\)
0.998494 + 0.0548634i \(0.0174723\pi\)
\(264\) 3.51409 2.55314i 0.216277 0.157135i
\(265\) 3.50253 10.9861i 0.215159 0.674874i
\(266\) −1.56410 1.13639i −0.0959012 0.0696763i
\(267\) −12.6201 + 4.10053i −0.772339 + 0.250948i
\(268\) 15.2342i 0.930579i
\(269\) 5.46680 + 16.8251i 0.333317 + 1.02584i 0.967545 + 0.252698i \(0.0813179\pi\)
−0.634228 + 0.773146i \(0.718682\pi\)
\(270\) 4.64542 + 1.48102i 0.282711 + 0.0901321i
\(271\) 7.01444 21.5882i 0.426097 1.31139i −0.475843 0.879530i \(-0.657857\pi\)
0.901940 0.431862i \(-0.142143\pi\)
\(272\) −8.29644 2.69568i −0.503045 0.163449i
\(273\) −21.2961 29.3115i −1.28890 1.77401i
\(274\) 8.35746 0.504892
\(275\) 3.68441 2.73968i 0.222178 0.165209i
\(276\) 31.3656 1.88799
\(277\) 12.2108 + 16.8067i 0.733673 + 1.00981i 0.998958 + 0.0456446i \(0.0145342\pi\)
−0.265284 + 0.964170i \(0.585466\pi\)
\(278\) −7.19150 2.33666i −0.431317 0.140143i
\(279\) 2.17669 6.69917i 0.130315 0.401069i
\(280\) −15.5958 + 5.16296i −0.932027 + 0.308546i
\(281\) 0.910488 + 2.80219i 0.0543152 + 0.167165i 0.974534 0.224239i \(-0.0719896\pi\)
−0.920219 + 0.391404i \(0.871990\pi\)
\(282\) 13.1900i 0.785456i
\(283\) −20.1731 + 6.55465i −1.19917 + 0.389633i −0.839455 0.543429i \(-0.817126\pi\)
−0.359713 + 0.933063i \(0.617126\pi\)
\(284\) −17.0768 12.4070i −1.01332 0.736220i
\(285\) −6.22556 + 0.0344475i −0.368770 + 0.00204049i
\(286\) 0.999480 0.726165i 0.0591005 0.0429390i
\(287\) 6.14674 8.46026i 0.362831 0.499394i
\(288\) −13.0376 + 17.9447i −0.768247 + 1.05740i
\(289\) −6.12394 + 4.44931i −0.360232 + 0.261724i
\(290\) 1.93527 + 5.84590i 0.113643 + 0.343283i
\(291\) −1.16921 0.849484i −0.0685405 0.0497976i
\(292\) 22.0052 7.14993i 1.28776 0.418418i
\(293\) 19.8597i 1.16022i −0.814540 0.580108i \(-0.803011\pi\)
0.814540 0.580108i \(-0.196989\pi\)
\(294\) 4.50047 + 13.8510i 0.262473 + 0.807807i
\(295\) 9.16091 12.7568i 0.533369 0.742727i
\(296\) 3.48021 10.7110i 0.202283 0.622564i
\(297\) −4.25946 1.38398i −0.247159 0.0803067i
\(298\) 0.721335 + 0.992832i 0.0417858 + 0.0575132i
\(299\) 18.8326 1.08912
\(300\) −14.5043 + 20.4353i −0.837407 + 1.17983i
\(301\) 41.6782 2.40229
\(302\) 4.39051 + 6.04303i 0.252646 + 0.347737i
\(303\) −39.2548 12.7547i −2.25513 0.732736i
\(304\) 0.877815 2.70164i 0.0503461 0.154949i
\(305\) 10.3120 + 14.0293i 0.590464 + 0.803318i
\(306\) −2.01598 6.20456i −0.115246 0.354691i
\(307\) 22.5851i 1.28900i 0.764605 + 0.644499i \(0.222934\pi\)
−0.764605 + 0.644499i \(0.777066\pi\)
\(308\) 6.79833 2.20891i 0.387371 0.125864i
\(309\) 9.44331 + 6.86097i 0.537211 + 0.390307i
\(310\) −1.20372 0.864415i −0.0683664 0.0490955i
\(311\) 8.53985 6.20456i 0.484250 0.351828i −0.318719 0.947849i \(-0.603252\pi\)
0.802969 + 0.596021i \(0.203252\pi\)
\(312\) −8.36681 + 11.5159i −0.473677 + 0.651961i
\(313\) −16.2695 + 22.3931i −0.919607 + 1.26573i 0.0441712 + 0.999024i \(0.485935\pi\)
−0.963778 + 0.266706i \(0.914065\pi\)
\(314\) −0.872741 + 0.634084i −0.0492516 + 0.0357834i
\(315\) 37.3211 + 26.8012i 2.10281 + 1.51007i
\(316\) −15.7910 11.4728i −0.888311 0.645396i
\(317\) −24.1290 + 7.83999i −1.35522 + 0.440338i −0.894445 0.447179i \(-0.852429\pi\)
−0.460776 + 0.887517i \(0.652429\pi\)
\(318\) 6.41898i 0.359959i
\(319\) −1.74790 5.37950i −0.0978639 0.301194i
\(320\) −4.76013 6.47610i −0.266099 0.362025i
\(321\) −2.01737 + 6.20883i −0.112599 + 0.346543i
\(322\) −11.5071 3.73888i −0.641266 0.208360i
\(323\) 1.80503 + 2.48441i 0.100434 + 0.138236i
\(324\) −1.21697 −0.0676094
\(325\) −8.70872 + 12.2698i −0.483073 + 0.680606i
\(326\) 6.82733 0.378131
\(327\) −13.0190 17.9190i −0.719950 0.990926i
\(328\) −3.90745 1.26961i −0.215753 0.0701023i
\(329\) −14.1601 + 43.5802i −0.780670 + 2.40265i
\(330\) −1.49085 + 2.07604i −0.0820688 + 0.114282i
\(331\) −1.04782 3.22485i −0.0575932 0.177254i 0.918121 0.396299i \(-0.129706\pi\)
−0.975715 + 0.219045i \(0.929706\pi\)
\(332\) 19.0620i 1.04617i
\(333\) −29.9573 + 9.73370i −1.64165 + 0.533404i
\(334\) −8.28258 6.01765i −0.453203 0.329271i
\(335\) 5.94722 + 17.9648i 0.324931 + 0.981523i
\(336\) −27.6694 + 20.1030i −1.50949 + 1.09671i
\(337\) 5.92137 8.15007i 0.322558 0.443963i −0.616688 0.787207i \(-0.711526\pi\)
0.939246 + 0.343245i \(0.111526\pi\)
\(338\) 1.03654 1.42667i 0.0563803 0.0776008i
\(339\) 12.1937 8.85921i 0.662268 0.481166i
\(340\) 12.3607 0.0683948i 0.670355 0.00370923i
\(341\) 1.10126 + 0.800113i 0.0596366 + 0.0433286i
\(342\) 2.02044 0.656481i 0.109253 0.0354984i
\(343\) 20.3249i 1.09744i
\(344\) −5.06001 15.5731i −0.272818 0.839646i
\(345\) −36.9876 + 12.2447i −1.99134 + 0.659231i
\(346\) 0.978591 3.01179i 0.0526094 0.161915i
\(347\) 11.3207 + 3.67832i 0.607727 + 0.197463i 0.596684 0.802476i \(-0.296485\pi\)
0.0110436 + 0.999939i \(0.496485\pi\)
\(348\) 18.1461 + 24.9759i 0.972732 + 1.33885i
\(349\) 9.35956 0.501006 0.250503 0.968116i \(-0.419404\pi\)
0.250503 + 0.968116i \(0.419404\pi\)
\(350\) 7.75715 5.76813i 0.414637 0.308319i
\(351\) 14.6769 0.783394
\(352\) −2.51950 3.46780i −0.134290 0.184834i
\(353\) −5.18894 1.68599i −0.276179 0.0897361i 0.167653 0.985846i \(-0.446381\pi\)
−0.443832 + 0.896110i \(0.646381\pi\)
\(354\) −2.70165 + 8.31483i −0.143591 + 0.441928i
\(355\) 24.9811 + 7.96430i 1.32586 + 0.422701i
\(356\) 2.65119 + 8.15952i 0.140513 + 0.432454i
\(357\) 36.9732i 1.95683i
\(358\) −0.298913 + 0.0971226i −0.0157980 + 0.00513309i
\(359\) −23.0491 16.7461i −1.21648 0.883828i −0.220681 0.975346i \(-0.570828\pi\)
−0.995803 + 0.0915182i \(0.970828\pi\)
\(360\) 5.48325 17.1990i 0.288993 0.906464i
\(361\) −0.809017 + 0.587785i −0.0425798 + 0.0309361i
\(362\) 1.90310 2.61939i 0.100024 0.137672i
\(363\) −16.6217 + 22.8778i −0.872411 + 1.20077i
\(364\) −18.9513 + 13.7689i −0.993319 + 0.721688i
\(365\) −23.1582 + 17.0220i −1.21215 + 0.890971i
\(366\) −7.84141 5.69712i −0.409877 0.297793i
\(367\) 22.9990 7.47283i 1.20054 0.390078i 0.360579 0.932729i \(-0.382579\pi\)
0.839959 + 0.542650i \(0.182579\pi\)
\(368\) 17.7776i 0.926721i
\(369\) 3.55092 + 10.9286i 0.184854 + 0.568921i
\(370\) 0.0366677 + 6.62681i 0.00190626 + 0.344512i
\(371\) −6.89104 + 21.2084i −0.357765 + 1.10109i
\(372\) −7.06591 2.29585i −0.366350 0.119034i
\(373\) 2.97740 + 4.09804i 0.154164 + 0.212188i 0.879112 0.476615i \(-0.158136\pi\)
−0.724948 + 0.688803i \(0.758136\pi\)
\(374\) 1.26073 0.0651909
\(375\) 9.12644 29.7603i 0.471287 1.53682i
\(376\) 18.0029 0.928431
\(377\) 10.8953 + 14.9961i 0.561137 + 0.772339i
\(378\) −8.96786 2.91383i −0.461257 0.149871i
\(379\) 8.59922 26.4657i 0.441712 1.35945i −0.444337 0.895860i \(-0.646561\pi\)
0.886049 0.463591i \(-0.153439\pi\)
\(380\) 0.0222720 + 4.02513i 0.00114253 + 0.206485i
\(381\) 7.51088 + 23.1161i 0.384794 + 1.18427i
\(382\) 0.225540i 0.0115396i
\(383\) 9.24435 3.00367i 0.472364 0.153480i −0.0631546 0.998004i \(-0.520116\pi\)
0.535519 + 0.844523i \(0.320116\pi\)
\(384\) 24.6483 + 17.9081i 1.25783 + 0.913867i
\(385\) −7.15453 + 5.25880i −0.364629 + 0.268013i
\(386\) −8.43448 + 6.12801i −0.429304 + 0.311907i
\(387\) −26.9191 + 37.0509i −1.36837 + 1.88340i
\(388\) −0.549232 + 0.755953i −0.0278830 + 0.0383777i
\(389\) 3.64753 2.65008i 0.184937 0.134365i −0.491465 0.870897i \(-0.663538\pi\)
0.676402 + 0.736533i \(0.263538\pi\)
\(390\) 2.54416 7.98011i 0.128829 0.404088i
\(391\) 15.5480 + 11.2963i 0.786297 + 0.571278i
\(392\) 18.9051 6.14263i 0.954851 0.310250i
\(393\) 5.62199i 0.283592i
\(394\) −1.09809 3.37957i −0.0553210 0.170260i
\(395\) 23.1001 + 7.36463i 1.16229 + 0.370555i
\(396\) −2.42723 + 7.47025i −0.121973 + 0.375394i
\(397\) 19.7046 + 6.40241i 0.988945 + 0.321328i 0.758440 0.651743i \(-0.225962\pi\)
0.230505 + 0.973071i \(0.425962\pi\)
\(398\) −1.19964 1.65116i −0.0601324 0.0827651i
\(399\) 12.0399 0.602748
\(400\) 11.5824 + 8.22085i 0.579121 + 0.411042i
\(401\) −7.91289 −0.395151 −0.197575 0.980288i \(-0.563307\pi\)
−0.197575 + 0.980288i \(0.563307\pi\)
\(402\) −6.19190 8.52242i −0.308824 0.425059i
\(403\) −4.24253 1.37848i −0.211335 0.0686670i
\(404\) −8.24651 + 25.3801i −0.410279 + 1.26271i
\(405\) 1.43510 0.475087i 0.0713106 0.0236072i
\(406\) −3.68004 11.3260i −0.182637 0.562100i
\(407\) 6.08715i 0.301729i
\(408\) −13.8151 + 4.48880i −0.683949 + 0.222229i
\(409\) −26.5157 19.2648i −1.31112 0.952583i −0.999998 0.00221288i \(-0.999296\pi\)
−0.311121 0.950370i \(-0.600704\pi\)
\(410\) 2.41751 0.0133766i 0.119392 0.000660625i
\(411\) −42.1063 + 30.5920i −2.07695 + 1.50899i
\(412\) 4.43595 6.10556i 0.218543 0.300799i
\(413\) −17.8526 + 24.5720i −0.878471 + 1.20911i
\(414\) 10.7560 7.81468i 0.528628 0.384070i
\(415\) −7.44153 22.4787i −0.365290 1.10344i
\(416\) 11.3642 + 8.25659i 0.557177 + 0.404813i
\(417\) 44.7852 14.5516i 2.19314 0.712594i
\(418\) 0.410542i 0.0200803i
\(419\) 4.01813 + 12.3665i 0.196298 + 0.604145i 0.999959 + 0.00905653i \(0.00288282\pi\)
−0.803661 + 0.595088i \(0.797117\pi\)
\(420\) 28.2683 39.3642i 1.37935 1.92078i
\(421\) 10.7403 33.0553i 0.523452 1.61102i −0.243905 0.969799i \(-0.578429\pi\)
0.767357 0.641220i \(-0.221571\pi\)
\(422\) −5.12137 1.66403i −0.249304 0.0810039i
\(423\) −29.5961 40.7355i −1.43901 1.98063i
\(424\) 8.76119 0.425481
\(425\) −14.5496 + 4.90610i −0.705758 + 0.237981i
\(426\) −14.5959 −0.707176
\(427\) −19.7921 27.2415i −0.957806 1.31831i
\(428\) 4.01431 + 1.30433i 0.194039 + 0.0630471i
\(429\) −2.37746 + 7.31708i −0.114785 + 0.353272i
\(430\) 5.70642 + 7.76352i 0.275188 + 0.374390i
\(431\) −5.31757 16.3658i −0.256138 0.788312i −0.993603 0.112927i \(-0.963977\pi\)
0.737465 0.675385i \(-0.236023\pi\)
\(432\) 13.8547i 0.666582i
\(433\) −29.6654 + 9.63887i −1.42563 + 0.463215i −0.917386 0.397999i \(-0.869705\pi\)
−0.508242 + 0.861214i \(0.669705\pi\)
\(434\) 2.31860 + 1.68456i 0.111296 + 0.0808614i
\(435\) −31.1488 22.3686i −1.49347 1.07249i
\(436\) −11.5855 + 8.41738i −0.554846 + 0.403120i
\(437\) −3.67850 + 5.06302i −0.175967 + 0.242197i
\(438\) 9.40420 12.9438i 0.449350 0.618478i
\(439\) −12.8137 + 9.30970i −0.611565 + 0.444328i −0.849965 0.526839i \(-0.823377\pi\)
0.238400 + 0.971167i \(0.423377\pi\)
\(440\) 2.83357 + 2.03485i 0.135085 + 0.0970076i
\(441\) −44.9782 32.6786i −2.14182 1.55612i
\(442\) −3.92930 + 1.27671i −0.186898 + 0.0607267i
\(443\) 10.5951i 0.503388i 0.967807 + 0.251694i \(0.0809876\pi\)
−0.967807 + 0.251694i \(0.919012\pi\)
\(444\) 10.2666 + 31.5972i 0.487229 + 1.49954i
\(445\) −6.31174 8.58704i −0.299205 0.407065i
\(446\) −3.12931 + 9.63103i −0.148177 + 0.456042i
\(447\) −7.26841 2.36165i −0.343784 0.111702i
\(448\) 9.13624 + 12.5750i 0.431647 + 0.594111i
\(449\) −19.3596 −0.913636 −0.456818 0.889560i \(-0.651011\pi\)
−0.456818 + 0.889560i \(0.651011\pi\)
\(450\) 0.117545 + 10.6214i 0.00554114 + 0.500699i
\(451\) −2.22063 −0.104566
\(452\) −5.72791 7.88379i −0.269418 0.370822i
\(453\) −44.2403 14.3745i −2.07859 0.675375i
\(454\) 3.49738 10.7638i 0.164140 0.505171i
\(455\) 16.9729 23.6352i 0.795704 1.10803i
\(456\) −1.46172 4.49872i −0.0684515 0.210672i
\(457\) 2.56820i 0.120135i −0.998194 0.0600676i \(-0.980868\pi\)
0.998194 0.0600676i \(-0.0191316\pi\)
\(458\) −10.9390 + 3.55429i −0.511145 + 0.166081i
\(459\) 12.1171 + 8.80356i 0.565576 + 0.410915i
\(460\) 7.91677 + 23.9143i 0.369121 + 1.11501i
\(461\) 8.00363 5.81498i 0.372766 0.270831i −0.385591 0.922670i \(-0.626002\pi\)
0.758357 + 0.651839i \(0.226002\pi\)
\(462\) 2.90535 3.99888i 0.135169 0.186045i
\(463\) −17.3898 + 23.9349i −0.808170 + 1.11235i 0.183433 + 0.983032i \(0.441279\pi\)
−0.991603 + 0.129319i \(0.958721\pi\)
\(464\) 14.1560 10.2849i 0.657176 0.477466i
\(465\) 9.22866 0.0510643i 0.427969 0.00236805i
\(466\) −3.13757 2.27958i −0.145345 0.105599i
\(467\) 12.7024 4.12726i 0.587797 0.190987i 6.54700e−6 1.00000i \(-0.499998\pi\)
0.587791 + 0.809013i \(0.299998\pi\)
\(468\) 25.7403i 1.18985i
\(469\) −11.3090 34.8055i −0.522201 1.60717i
\(470\) −10.0566 + 3.32920i −0.463874 + 0.153565i
\(471\) 2.07599 6.38924i 0.0956565 0.294400i
\(472\) 11.3488 + 3.68745i 0.522372 + 0.169729i
\(473\) −5.20209 7.16007i −0.239192 0.329220i
\(474\) −13.4969 −0.619935
\(475\) −1.59761 4.73789i −0.0733035 0.217389i
\(476\) −23.9050 −1.09568
\(477\) −14.4030 19.8241i −0.659469 0.907682i
\(478\) −0.403877 0.131228i −0.0184729 0.00600221i
\(479\) −0.406052 + 1.24970i −0.0185530 + 0.0571003i −0.959904 0.280328i \(-0.909557\pi\)
0.941351 + 0.337428i \(0.109557\pi\)
\(480\) −27.6878 8.82724i −1.26377 0.402907i
\(481\) 6.16427 + 18.9717i 0.281067 + 0.865034i
\(482\) 0.962415i 0.0438368i
\(483\) 71.6607 23.2840i 3.26067 1.05946i
\(484\) 14.7916 + 10.7467i 0.672345 + 0.488487i
\(485\) 0.352563 1.10586i 0.0160091 0.0502146i
\(486\) −5.97304 + 4.33967i −0.270943 + 0.196851i
\(487\) 10.3577 14.2562i 0.469353 0.646010i −0.507062 0.861910i \(-0.669269\pi\)
0.976415 + 0.215900i \(0.0692685\pi\)
\(488\) −7.77593 + 10.7026i −0.352000 + 0.484486i
\(489\) −34.3972 + 24.9910i −1.55550 + 1.13013i
\(490\) −9.42457 + 6.92735i −0.425759 + 0.312946i
\(491\) 27.4410 + 19.9371i 1.23839 + 0.899747i 0.997490 0.0708023i \(-0.0225559\pi\)
0.240905 + 0.970549i \(0.422556\pi\)
\(492\) 11.5269 3.74531i 0.519672 0.168852i
\(493\) 18.9159i 0.851930i
\(494\) −0.415744 1.27953i −0.0187052 0.0575687i
\(495\) −0.0539864 9.75676i −0.00242651 0.438534i
\(496\) −1.30126 + 4.00486i −0.0584281 + 0.179823i
\(497\) −48.2253 15.6693i −2.16320 0.702866i
\(498\) 7.74769 + 10.6638i 0.347182 + 0.477855i
\(499\) −1.30681 −0.0585011 −0.0292505 0.999572i \(-0.509312\pi\)
−0.0292505 + 0.999572i \(0.509312\pi\)
\(500\) −19.2415 5.90069i −0.860506 0.263887i
\(501\) 63.7563 2.84842
\(502\) −2.19286 3.01822i −0.0978724 0.134710i
\(503\) 27.6699 + 8.99049i 1.23374 + 0.400866i 0.852067 0.523432i \(-0.175349\pi\)
0.381671 + 0.924298i \(0.375349\pi\)
\(504\) −10.7880 + 33.2021i −0.480536 + 1.47894i
\(505\) −0.183419 33.1486i −0.00816203 1.47509i
\(506\) 0.793949 + 2.44352i 0.0352954 + 0.108628i
\(507\) 10.9820i 0.487728i
\(508\) 14.9457 4.85615i 0.663108 0.215457i
\(509\) 33.7617 + 24.5293i 1.49646 + 1.08724i 0.971764 + 0.235957i \(0.0758223\pi\)
0.524699 + 0.851288i \(0.324178\pi\)
\(510\) 6.88711 5.06224i 0.304966 0.224160i
\(511\) 44.9674 32.6707i 1.98924 1.44527i
\(512\) 13.4676 18.5365i 0.595187 0.819205i
\(513\) −2.86678 + 3.94578i −0.126571 + 0.174210i
\(514\) −7.78690 + 5.65752i −0.343466 + 0.249542i
\(515\) −2.84753 + 8.93164i −0.125477 + 0.393575i
\(516\) 39.0792 + 28.3927i 1.72037 + 1.24992i
\(517\) 9.25422 3.00688i 0.407000 0.132242i
\(518\) 12.8159i 0.563097i
\(519\) 6.09419 + 18.7560i 0.267505 + 0.823297i
\(520\) −10.8920 3.47250i −0.477644 0.152279i
\(521\) −2.29698 + 7.06938i −0.100633 + 0.309715i −0.988681 0.150036i \(-0.952061\pi\)
0.888048 + 0.459751i \(0.152061\pi\)
\(522\) 12.4454 + 4.04376i 0.544720 + 0.176990i
\(523\) −9.24536 12.7251i −0.404271 0.556432i 0.557538 0.830151i \(-0.311746\pi\)
−0.961810 + 0.273720i \(0.911746\pi\)
\(524\) 3.63489 0.158791
\(525\) −17.9679 + 57.4554i −0.784185 + 2.50756i
\(526\) −7.86692 −0.343014
\(527\) −2.67574 3.68284i −0.116557 0.160427i
\(528\) 6.90716 + 2.24427i 0.300596 + 0.0976695i
\(529\) −4.99544 + 15.3744i −0.217193 + 0.668452i
\(530\) −4.89406 + 1.62017i −0.212584 + 0.0703756i
\(531\) −10.3133 31.7411i −0.447560 1.37745i
\(532\) 7.78437i 0.337495i
\(533\) 6.92100 2.24877i 0.299782 0.0974051i
\(534\) 4.79955 + 3.48708i 0.207697 + 0.150901i
\(535\) −5.24302 + 0.0290109i −0.226676 + 0.00125425i
\(536\) −11.6321 + 8.45125i −0.502432 + 0.365038i
\(537\) 1.15046 1.58347i 0.0496460 0.0683319i
\(538\) 4.64895 6.39873i 0.200431 0.275869i
\(539\) 8.69201 6.31511i 0.374391 0.272011i
\(540\) 6.16979 + 18.6372i 0.265506 + 0.802015i
\(541\) −7.76452 5.64125i −0.333823 0.242536i 0.408228 0.912880i \(-0.366147\pi\)
−0.742051 + 0.670344i \(0.766147\pi\)
\(542\) −9.65167 + 3.13602i −0.414575 + 0.134704i
\(543\) 20.1631i 0.865280i
\(544\) 4.42966 + 13.6331i 0.189920 + 0.584514i
\(545\) 10.3761 14.4489i 0.444463 0.618924i
\(546\) −5.00551 + 15.4054i −0.214216 + 0.659289i
\(547\) 14.4631 + 4.69934i 0.618396 + 0.200929i 0.601428 0.798927i \(-0.294599\pi\)
0.0169681 + 0.999856i \(0.494599\pi\)
\(548\) 19.7792 + 27.2237i 0.844926 + 1.16294i
\(549\) 37.0003 1.57914
\(550\) −1.95915 0.612680i −0.0835382 0.0261248i
\(551\) −6.15974 −0.262414
\(552\) −17.4002 23.9493i −0.740601 1.01935i
\(553\) −44.5942 14.4895i −1.89634 0.616157i
\(554\) 2.87006 8.83315i 0.121937 0.375285i
\(555\) −24.4418 33.2528i −1.03750 1.41150i
\(556\) −9.40830 28.9558i −0.399001 1.22800i
\(557\) 36.8412i 1.56101i −0.625149 0.780506i \(-0.714962\pi\)
0.625149 0.780506i \(-0.285038\pi\)
\(558\) −2.99506 + 0.973156i −0.126791 + 0.0411970i
\(559\) 23.4640 + 17.0476i 0.992423 + 0.721038i
\(560\) −22.3111 16.0221i −0.942816 0.677057i
\(561\) −6.35178 + 4.61484i −0.268172 + 0.194839i
\(562\) 0.774276 1.06570i 0.0326609 0.0449538i
\(563\) 23.6267 32.5193i 0.995746 1.37053i 0.0678467 0.997696i \(-0.478387\pi\)
0.927899 0.372831i \(-0.121613\pi\)
\(564\) −42.9655 + 31.2163i −1.80917 + 1.31444i
\(565\) 9.83228 + 7.06078i 0.413647 + 0.297049i
\(566\) 7.67202 + 5.57405i 0.322479 + 0.234295i
\(567\) −2.78040 + 0.903406i −0.116766 + 0.0379395i
\(568\) 19.9218i 0.835901i
\(569\) −6.47592 19.9308i −0.271485 0.835544i −0.990128 0.140165i \(-0.955237\pi\)
0.718643 0.695379i \(-0.244763\pi\)
\(570\) 1.64846 + 2.24270i 0.0690463 + 0.0939366i
\(571\) 9.46988 29.1453i 0.396302 1.21969i −0.531641 0.846970i \(-0.678424\pi\)
0.927943 0.372723i \(-0.121576\pi\)
\(572\) 4.73085 + 1.53715i 0.197807 + 0.0642713i
\(573\) −0.825575 1.13631i −0.0344889 0.0474699i
\(574\) −4.67532 −0.195144
\(575\) −18.6715 25.1100i −0.778656 1.04716i
\(576\) −17.0797 −0.711656
\(577\) −14.8081 20.3817i −0.616471 0.848499i 0.380619 0.924732i \(-0.375711\pi\)
−0.997090 + 0.0762324i \(0.975711\pi\)
\(578\) 3.21859 + 1.04578i 0.133876 + 0.0434988i
\(579\) 20.0631 61.7479i 0.833794 2.56615i
\(580\) −14.4624 + 20.1392i −0.600519 + 0.836235i
\(581\) 14.1505 + 43.5508i 0.587063 + 1.80679i
\(582\) 0.646133i 0.0267831i
\(583\) 4.50360 1.46331i 0.186520 0.0606040i
\(584\) −17.6668 12.8357i −0.731058 0.531144i
\(585\) 10.0486 + 30.3540i 0.415460 + 1.25498i
\(586\) −7.18316 + 5.21887i −0.296733 + 0.215589i
\(587\) −27.7123 + 38.1427i −1.14381 + 1.57432i −0.385113 + 0.922869i \(0.625838\pi\)
−0.758694 + 0.651447i \(0.774162\pi\)
\(588\) −34.4675 + 47.4404i −1.42142 + 1.95641i
\(589\) 1.19927 0.871322i 0.0494151 0.0359022i
\(590\) −7.02143 + 0.0388512i −0.289068 + 0.00159948i
\(591\) 17.9031 + 13.0074i 0.736435 + 0.535051i
\(592\) 17.9089 5.81894i 0.736050 0.239157i
\(593\) 4.27977i 0.175749i 0.996132 + 0.0878746i \(0.0280075\pi\)
−0.996132 + 0.0878746i \(0.971993\pi\)
\(594\) 0.618750 + 1.90432i 0.0253876 + 0.0781351i
\(595\) 28.1897 9.33214i 1.15566 0.382580i
\(596\) −1.52692 + 4.69938i −0.0625451 + 0.192494i
\(597\) 12.0879 + 3.92761i 0.494726 + 0.160746i
\(598\) −4.94897 6.81167i −0.202378 0.278550i
\(599\) −39.6614 −1.62052 −0.810260 0.586071i \(-0.800674\pi\)
−0.810260 + 0.586071i \(0.800674\pi\)
\(600\) 23.6497 0.261727i 0.965496 0.0106850i
\(601\) −26.2384 −1.07029 −0.535143 0.844762i \(-0.679742\pi\)
−0.535143 + 0.844762i \(0.679742\pi\)
\(602\) −10.9525 15.0748i −0.446390 0.614403i
\(603\) 38.2455 + 12.4267i 1.55748 + 0.506055i
\(604\) −9.29384 + 28.6035i −0.378161 + 1.16386i
\(605\) −21.6382 6.89853i −0.879717 0.280465i
\(606\) 5.70236 + 17.5501i 0.231642 + 0.712922i
\(607\) 16.7230i 0.678767i 0.940648 + 0.339383i \(0.110218\pi\)
−0.940648 + 0.339383i \(0.889782\pi\)
\(608\) −4.43946 + 1.44247i −0.180044 + 0.0584998i
\(609\) 59.9988 + 43.5917i 2.43127 + 1.76642i
\(610\) 2.36449 7.41654i 0.0957354 0.300287i
\(611\) −25.7975 + 18.7430i −1.04365 + 0.758259i
\(612\) 15.4397 21.2509i 0.624114 0.859019i
\(613\) 6.23766 8.58540i 0.251937 0.346761i −0.664252 0.747509i \(-0.731250\pi\)
0.916188 + 0.400748i \(0.131250\pi\)
\(614\) 8.16892 5.93507i 0.329671 0.239520i
\(615\) −12.1308 + 8.91654i −0.489163 + 0.359550i
\(616\) −5.45802 3.96548i −0.219910 0.159774i
\(617\) 46.5002 15.1088i 1.87203 0.608258i 0.881269 0.472615i \(-0.156690\pi\)
0.990758 0.135643i \(-0.0433101\pi\)
\(618\) 5.21858i 0.209922i
\(619\) 0.894829 + 2.75400i 0.0359662 + 0.110693i 0.967428 0.253147i \(-0.0814656\pi\)
−0.931462 + 0.363840i \(0.881466\pi\)
\(620\) −0.0330155 5.96677i −0.00132594 0.239631i
\(621\) −9.43213 + 29.0291i −0.378498 + 1.16490i
\(622\) −4.48832 1.45834i −0.179965 0.0584743i
\(623\) 12.1143 + 16.6739i 0.485349 + 0.668025i
\(624\) −23.8001 −0.952767
\(625\) 24.9939 0.553272i 0.999755 0.0221309i
\(626\) 12.3749 0.494600
\(627\) −1.50277 2.06838i −0.0600147 0.0826032i
\(628\) −4.13095 1.34223i −0.164843 0.0535607i
\(629\) −6.29054 + 19.3603i −0.250820 + 0.771946i
\(630\) −0.113663 20.5419i −0.00452844 0.818408i
\(631\) 7.18553 + 22.1148i 0.286051 + 0.880376i 0.986082 + 0.166262i \(0.0531699\pi\)
−0.700030 + 0.714113i \(0.746830\pi\)
\(632\) 18.4218i 0.732780i
\(633\) 31.8934 10.3628i 1.26765 0.411884i
\(634\) 9.17648 + 6.66710i 0.364445 + 0.264785i
\(635\) −15.7288 + 11.5611i −0.624177 + 0.458790i
\(636\) −20.9093 + 15.1915i −0.829108 + 0.602382i
\(637\) −20.6951 + 28.4843i −0.819968 + 1.12859i
\(638\) −1.48641 + 2.04587i −0.0588476 + 0.0809968i
\(639\) 45.0774 32.7506i 1.78323 1.29560i
\(640\) −7.43243 + 23.3128i −0.293793 + 0.921519i
\(641\) −35.8071 26.0153i −1.41429 1.02754i −0.992681 0.120769i \(-0.961464\pi\)
−0.421613 0.906776i \(-0.638536\pi\)
\(642\) 2.77585 0.901927i 0.109554 0.0355962i
\(643\) 15.2181i 0.600143i 0.953917 + 0.300072i \(0.0970105\pi\)
−0.953917 + 0.300072i \(0.902989\pi\)
\(644\) −15.0542 46.3321i −0.593219 1.82574i
\(645\) −57.1678 18.2259i −2.25098 0.717643i
\(646\) 0.424260 1.30574i 0.0166923 0.0513736i
\(647\) 14.3779 + 4.67165i 0.565252 + 0.183661i 0.577683 0.816261i \(-0.303957\pi\)
−0.0124310 + 0.999923i \(0.503957\pi\)
\(648\) 0.675118 + 0.929220i 0.0265211 + 0.0365032i
\(649\) 6.44962 0.253170
\(650\) 6.72647 0.0744405i 0.263834 0.00291980i
\(651\) −17.8477 −0.699506
\(652\) 16.1579 + 22.2395i 0.632793 + 0.870965i
\(653\) −29.9088 9.71794i −1.17042 0.380293i −0.341620 0.939838i \(-0.610976\pi\)
−0.828800 + 0.559545i \(0.810976\pi\)
\(654\) −3.06003 + 9.41779i −0.119656 + 0.368265i
\(655\) −4.28640 + 1.41901i −0.167484 + 0.0554451i
\(656\) −2.12279 6.53328i −0.0828811 0.255082i
\(657\) 61.0763i 2.38281i
\(658\) 19.4838 6.33068i 0.759559 0.246796i
\(659\) 8.16136 + 5.92957i 0.317921 + 0.230983i 0.735288 0.677755i \(-0.237047\pi\)
−0.417367 + 0.908738i \(0.637047\pi\)
\(660\) −10.2909 + 0.0569418i −0.400572 + 0.00221646i
\(661\) −13.9774 + 10.1552i −0.543660 + 0.394992i −0.825442 0.564486i \(-0.809074\pi\)
0.281783 + 0.959478i \(0.409074\pi\)
\(662\) −0.891061 + 1.22644i −0.0346321 + 0.0476669i
\(663\) 15.1231 20.8152i 0.587334 0.808396i
\(664\) 14.5549 10.5747i 0.564838 0.410379i
\(665\) 3.03890 + 9.17963i 0.117843 + 0.355971i
\(666\) 11.3930 + 8.27751i 0.441470 + 0.320747i
\(667\) −36.6624 + 11.9123i −1.41958 + 0.461248i
\(668\) 41.2215i 1.59491i
\(669\) −19.4878 59.9774i −0.753443 2.31886i
\(670\) 4.93494 6.87200i 0.190653 0.265489i
\(671\) −2.20956 + 6.80033i −0.0852992 + 0.262524i
\(672\) 53.4505 + 17.3671i 2.06190 + 0.669952i
\(673\) −18.4091 25.3380i −0.709619 0.976707i −0.999805 0.0197365i \(-0.993717\pi\)
0.290186 0.956970i \(-0.406283\pi\)
\(674\) −4.50390 −0.173484
\(675\) −14.5513 19.5691i −0.560081 0.753214i
\(676\) 7.10040 0.273092
\(677\) −19.6780 27.0844i −0.756285 1.04094i −0.997514 0.0704693i \(-0.977550\pi\)
0.241228 0.970468i \(-0.422450\pi\)
\(678\) −6.40867 2.08230i −0.246123 0.0799704i
\(679\) −0.693650 + 2.13484i −0.0266198 + 0.0819275i
\(680\) −6.90938 9.40013i −0.264963 0.360479i
\(681\) 21.7800 + 67.0319i 0.834611 + 2.56867i
\(682\) 0.608581i 0.0233038i
\(683\) 5.31100 1.72565i 0.203220 0.0660302i −0.205638 0.978628i \(-0.565927\pi\)
0.408858 + 0.912598i \(0.365927\pi\)
\(684\) 6.92012 + 5.02776i 0.264597 + 0.192241i
\(685\) −33.9521 24.3818i −1.29724 0.931580i
\(686\) 7.35144 5.34113i 0.280679 0.203925i
\(687\) 42.1022 57.9487i 1.60630 2.21088i
\(688\) 16.0926 22.1495i 0.613524 0.844444i
\(689\) −12.5544 + 9.12132i −0.478285 + 0.347495i
\(690\) 14.1487 + 10.1605i 0.538632 + 0.386803i
\(691\) −7.70620 5.59888i −0.293158 0.212992i 0.431478 0.902123i \(-0.357992\pi\)
−0.724636 + 0.689132i \(0.757992\pi\)
\(692\) 12.1267 3.94019i 0.460986 0.149784i
\(693\) 18.8690i 0.716775i
\(694\) −1.64450 5.06126i −0.0624245 0.192123i
\(695\) 22.3985 + 30.4729i 0.849625 + 1.15590i
\(696\) 9.00384 27.7110i 0.341290 1.05038i
\(697\) 7.06278 + 2.29483i 0.267522 + 0.0869231i
\(698\) −2.45957 3.38531i −0.0930961 0.128136i
\(699\) 24.1519 0.913508
\(700\) 37.1477 + 11.6171i 1.40405 + 0.439087i
\(701\) −9.07800 −0.342871 −0.171436 0.985195i \(-0.554841\pi\)
−0.171436 + 0.985195i \(0.554841\pi\)
\(702\) −3.85689 5.30856i −0.145569 0.200359i
\(703\) −6.30445 2.04844i −0.237777 0.0772584i
\(704\) 1.01996 3.13910i 0.0384411 0.118309i
\(705\) 38.4802 53.5845i 1.44925 2.01811i
\(706\) 0.753772 + 2.31987i 0.0283686 + 0.0873095i
\(707\) 64.1074i 2.41101i
\(708\) −33.4788 + 10.8779i −1.25821 + 0.408817i
\(709\) 20.2899 + 14.7415i 0.762005 + 0.553629i 0.899525 0.436870i \(-0.143913\pi\)
−0.137520 + 0.990499i \(0.543913\pi\)
\(710\) −3.68406 11.1285i −0.138260 0.417644i
\(711\) 41.6833 30.2847i 1.56325 1.13576i
\(712\) 4.75947 6.55085i 0.178369 0.245503i
\(713\) 5.45294 7.50533i 0.204214 0.281077i
\(714\) −13.3730 + 9.71608i −0.500473 + 0.363615i
\(715\) −6.17888 + 0.0341892i −0.231077 + 0.00127860i
\(716\) −1.02379 0.743828i −0.0382609 0.0277982i
\(717\) 2.51515 0.817222i 0.0939300 0.0305197i
\(718\) 12.7374i 0.475356i
\(719\) −4.95854 15.2608i −0.184922 0.569133i 0.815025 0.579426i \(-0.196723\pi\)
−0.999947 + 0.0102936i \(0.996723\pi\)
\(720\) 28.6535 9.48570i 1.06785 0.353511i
\(721\) 5.60236 17.2423i 0.208643 0.642136i
\(722\) 0.425198 + 0.138155i 0.0158242 + 0.00514161i
\(723\) 3.52286 + 4.84881i 0.131017 + 0.180329i
\(724\) 13.0364 0.484494
\(725\) 9.19260 29.3948i 0.341405 1.09170i
\(726\) 12.6427 0.469216
\(727\) −7.74716 10.6631i −0.287326 0.395471i 0.640817 0.767694i \(-0.278596\pi\)
−0.928143 + 0.372223i \(0.878596\pi\)
\(728\) 21.0266 + 6.83196i 0.779298 + 0.253209i
\(729\) 13.5813 41.7991i 0.503012 1.54811i
\(730\) 12.2424 + 3.90305i 0.453113 + 0.144458i
\(731\) 9.14605 + 28.1487i 0.338279 + 1.04112i
\(732\) 39.0259i 1.44244i
\(733\) −45.3997 + 14.7513i −1.67688 + 0.544850i −0.984301 0.176496i \(-0.943524\pi\)
−0.692575 + 0.721346i \(0.743524\pi\)
\(734\) −8.74673 6.35487i −0.322848 0.234563i
\(735\) 22.1254 69.3992i 0.816107 2.55983i
\(736\) −23.6338 + 17.1710i −0.871154 + 0.632930i
\(737\) −4.56784 + 6.28709i −0.168259 + 0.231588i
\(738\) 3.01969 4.15625i 0.111156 0.152994i
\(739\) 5.32735 3.87054i 0.195970 0.142380i −0.485473 0.874251i \(-0.661353\pi\)
0.681443 + 0.731871i \(0.261353\pi\)
\(740\) −21.4995 + 15.8028i −0.790338 + 0.580923i
\(741\) 6.77823 + 4.92467i 0.249004 + 0.180912i
\(742\) 9.48188 3.08085i 0.348091 0.113101i
\(743\) 32.4303i 1.18975i 0.803818 + 0.594876i \(0.202799\pi\)
−0.803818 + 0.594876i \(0.797201\pi\)
\(744\) 2.16683 + 6.66882i 0.0794399 + 0.244491i
\(745\) −0.0339617 6.13778i −0.00124426 0.224871i
\(746\) 0.699819 2.15382i 0.0256222 0.0788570i
\(747\) −47.8552 15.5491i −1.75093 0.568912i
\(748\) 2.98372 + 4.10673i 0.109095 + 0.150157i
\(749\) 10.1397 0.370497
\(750\) −13.1625 + 4.51964i −0.480626 + 0.165034i
\(751\) −14.7647 −0.538773 −0.269387 0.963032i \(-0.586821\pi\)
−0.269387 + 0.963032i \(0.586821\pi\)
\(752\) 17.6929 + 24.3522i 0.645195 + 0.888035i
\(753\) 22.0960 + 7.17944i 0.805224 + 0.261633i
\(754\) 2.56088 7.88157i 0.0932617 0.287030i
\(755\) −0.206713 37.3585i −0.00752307 1.35962i
\(756\) −11.7322 36.1081i −0.426697 1.31324i
\(757\) 35.6208i 1.29466i 0.762210 + 0.647330i \(0.224114\pi\)
−0.762210 + 0.647330i \(0.775886\pi\)
\(758\) −11.8323 + 3.84454i −0.429768 + 0.139640i
\(759\) −12.9444 9.40468i −0.469853 0.341368i
\(760\) 3.06104 2.24996i 0.111036 0.0816146i
\(761\) −0.488874 + 0.355188i −0.0177217 + 0.0128756i −0.596611 0.802531i \(-0.703486\pi\)
0.578889 + 0.815406i \(0.303486\pi\)
\(762\) 6.38723 8.79127i 0.231385 0.318474i
\(763\) −20.2208 + 27.8315i −0.732041 + 1.00757i
\(764\) −0.734677 + 0.533774i −0.0265797 + 0.0193113i
\(765\) −9.91107 + 31.0874i −0.358336 + 1.12397i
\(766\) −3.51571 2.55431i −0.127028 0.0922910i
\(767\) −20.1014 + 6.53134i −0.725820 + 0.235833i
\(768\) 6.39387i 0.230719i
\(769\) −2.90165 8.93035i −0.104636 0.322037i 0.885009 0.465574i \(-0.154152\pi\)
−0.989645 + 0.143538i \(0.954152\pi\)
\(770\) 3.78220 + 1.20582i 0.136301 + 0.0434546i
\(771\) 18.5227 57.0070i 0.667079 2.05306i
\(772\) −39.9230 12.9718i −1.43686 0.466864i
\(773\) −4.06806 5.59921i −0.146318 0.201390i 0.729567 0.683909i \(-0.239722\pi\)
−0.875885 + 0.482520i \(0.839722\pi\)
\(774\) 20.4751 0.735963
\(775\) 2.36827 + 7.02337i 0.0850708 + 0.252287i
\(776\) 0.881899 0.0316583
\(777\) 46.9118 + 64.5685i 1.68295 + 2.31638i
\(778\) −1.91705 0.622886i −0.0687294 0.0223315i
\(779\) −0.747286 + 2.29991i −0.0267743 + 0.0824028i
\(780\) 32.0157 10.5987i 1.14635 0.379496i
\(781\) 3.32737 + 10.2406i 0.119063 + 0.366438i
\(782\) 8.59216i 0.307255i
\(783\) −28.5722 + 9.28368i −1.02109 + 0.331772i
\(784\) 26.8886 + 19.5357i 0.960306 + 0.697703i
\(785\) 5.39536 0.0298538i 0.192569 0.00106553i
\(786\) 2.03345 1.47739i 0.0725307 0.0526966i
\(787\) 16.7936 23.1144i 0.598628 0.823941i −0.396954 0.917839i \(-0.629933\pi\)
0.995582 + 0.0938978i \(0.0299327\pi\)
\(788\) 8.40989 11.5752i 0.299590 0.412350i
\(789\) 39.6348 28.7964i 1.41104 1.02518i
\(790\) −3.40666 10.2905i −0.121204 0.366121i
\(791\) −18.9389 13.7599i −0.673391 0.489247i
\(792\) 7.05044 2.29083i 0.250526 0.0814010i
\(793\) 23.4320i 0.832095i
\(794\) −2.86239 8.80953i −0.101582 0.312638i
\(795\) 18.7265 26.0771i 0.664162 0.924859i
\(796\) 2.53939 7.81544i 0.0900063 0.277011i
\(797\) −25.5813 8.31187i −0.906136 0.294422i −0.181369 0.983415i \(-0.558053\pi\)
−0.724767 + 0.688994i \(0.758053\pi\)
\(798\) −3.16393 4.35477i −0.112002 0.154157i
\(799\) −32.5406 −1.15120
\(800\) −0.258279 23.3382i −0.00913154 0.825129i
\(801\) −22.6471 −0.800194
\(802\) 2.07940 + 2.86206i 0.0734263 + 0.101063i
\(803\) −11.2253 3.64731i −0.396131 0.128711i
\(804\) 13.1070 40.3392i 0.462248 1.42265i
\(805\) 35.8399 + 48.7597i 1.26319 + 1.71855i
\(806\) 0.616291 + 1.89675i 0.0217079 + 0.0668102i
\(807\) 49.2551i 1.73386i
\(808\) 23.9539 7.78308i 0.842694 0.273808i
\(809\) 1.22311 + 0.888640i 0.0430022 + 0.0312429i 0.609079 0.793110i \(-0.291539\pi\)
−0.566077 + 0.824353i \(0.691539\pi\)
\(810\) −0.548962 0.394222i −0.0192886 0.0138515i
\(811\) −1.46105 + 1.06152i −0.0513045 + 0.0372749i −0.613142 0.789973i \(-0.710095\pi\)
0.561837 + 0.827248i \(0.310095\pi\)
\(812\) 28.1841 38.7921i 0.989069 1.36134i
\(813\) 37.1475 51.1292i 1.30282 1.79318i
\(814\) −2.20169 + 1.59962i −0.0771693 + 0.0560668i
\(815\) −27.7360 19.9179i −0.971550 0.697692i
\(816\) −19.6491 14.2759i −0.687857 0.499757i
\(817\) −9.16628 + 2.97830i −0.320687 + 0.104198i
\(818\) 14.6532i 0.512336i
\(819\) −19.1081 58.8087i −0.667691 2.05494i
\(820\) 5.76498 + 7.84318i 0.201322 + 0.273896i
\(821\) −7.54485 + 23.2207i −0.263317 + 0.810407i 0.728759 + 0.684770i \(0.240097\pi\)
−0.992076 + 0.125637i \(0.959903\pi\)
\(822\) 22.1300 + 7.19046i 0.771871 + 0.250796i
\(823\) 22.4939 + 30.9601i 0.784086 + 1.07920i 0.994819 + 0.101659i \(0.0324150\pi\)
−0.210733 + 0.977544i \(0.567585\pi\)
\(824\) −7.12277 −0.248133
\(825\) 12.1132 4.08455i 0.421727 0.142206i
\(826\) 13.5790 0.472475
\(827\) 7.03287 + 9.67991i 0.244557 + 0.336604i 0.913596 0.406624i \(-0.133294\pi\)
−0.669039 + 0.743227i \(0.733294\pi\)
\(828\) 50.9114 + 16.5421i 1.76929 + 0.574878i
\(829\) −4.90284 + 15.0894i −0.170283 + 0.524076i −0.999387 0.0350181i \(-0.988851\pi\)
0.829104 + 0.559094i \(0.188851\pi\)
\(830\) −6.17490 + 8.59868i −0.214334 + 0.298465i
\(831\) 17.8734 + 55.0086i 0.620020 + 1.90823i
\(832\) 10.8165i 0.374993i
\(833\) −34.1712 + 11.1029i −1.18396 + 0.384693i
\(834\) −17.0322 12.3746i −0.589777 0.428498i
\(835\) 16.0923 + 48.6100i 0.556896 + 1.68222i
\(836\) −1.33731 + 0.971612i −0.0462518 + 0.0336039i
\(837\) 4.24966 5.84915i 0.146890 0.202176i
\(838\) 3.41700 4.70310i 0.118038 0.162466i
\(839\) 4.50180 3.27075i 0.155419 0.112919i −0.507358 0.861736i \(-0.669378\pi\)
0.662777 + 0.748817i \(0.269378\pi\)
\(840\) −45.7386 + 0.253082i −1.57813 + 0.00873217i
\(841\) −7.23459 5.25623i −0.249468 0.181249i
\(842\) −14.7784 + 4.80179i −0.509297 + 0.165481i
\(843\) 8.20337i 0.282539i
\(844\) −6.70005 20.6206i −0.230625 0.709792i
\(845\) −8.37307 + 2.77189i −0.288042 + 0.0953559i
\(846\) −6.95638 + 21.4095i −0.239165 + 0.736075i
\(847\) 41.7719 + 13.5725i 1.43530 + 0.466357i
\(848\) 8.61033 + 11.8511i 0.295680 + 0.406969i
\(849\) −59.0564 −2.02681
\(850\) 5.59795 + 3.97325i 0.192008 + 0.136281i
\(851\) −41.4852 −1.42210
\(852\) −34.5435 47.5451i −1.18344 1.62887i
\(853\) −10.6450 3.45877i −0.364478 0.118426i 0.121052 0.992646i \(-0.461373\pi\)
−0.485530 + 0.874220i \(0.661373\pi\)
\(854\) −4.65201 + 14.3174i −0.159189 + 0.489932i
\(855\) −10.1232 3.22742i −0.346207 0.110376i
\(856\) −1.23103 3.78872i −0.0420757 0.129496i
\(857\) 34.7124i 1.18575i 0.805294 + 0.592876i \(0.202008\pi\)
−0.805294 + 0.592876i \(0.797992\pi\)
\(858\) 3.27132 1.06292i 0.111681 0.0362874i
\(859\) 44.2128 + 32.1224i 1.50852 + 1.09600i 0.966829 + 0.255426i \(0.0822157\pi\)
0.541691 + 0.840578i \(0.317784\pi\)
\(860\) −11.7839 + 36.9618i −0.401828 + 1.26039i
\(861\) 23.5551 17.1137i 0.802754 0.583235i
\(862\) −4.52204 + 6.22406i −0.154021 + 0.211992i
\(863\) −15.3092 + 21.0713i −0.521132 + 0.717276i −0.985747 0.168236i \(-0.946193\pi\)
0.464615 + 0.885513i \(0.346193\pi\)
\(864\) −18.4186 + 13.3819i −0.626613 + 0.455261i
\(865\) −12.7620 + 9.38049i −0.433922 + 0.318946i
\(866\) 11.2820 + 8.19687i 0.383379 + 0.278541i
\(867\) −20.0438 + 6.51263i −0.680723 + 0.221180i
\(868\) 11.5394i 0.391673i
\(869\) 3.07684 + 9.46954i 0.104375 + 0.321232i
\(870\) 0.0948649 + 17.1446i 0.00321622 + 0.581255i
\(871\) 7.86974 24.2206i 0.266656 0.820683i
\(872\) 12.8542 + 4.17659i 0.435299 + 0.141437i
\(873\) −1.44980 1.99548i −0.0490684 0.0675369i
\(874\) 2.79794 0.0946416
\(875\) −48.3412 + 0.802514i −1.63423 + 0.0271299i
\(876\) 64.4198 2.17654
\(877\) 13.4941 + 18.5730i 0.455663 + 0.627167i 0.973602 0.228251i \(-0.0733006\pi\)
−0.517939 + 0.855417i \(0.673301\pi\)
\(878\) 6.73455 + 2.18819i 0.227280 + 0.0738478i
\(879\) 17.0866 52.5871i 0.576316 1.77372i
\(880\) 0.0322738 + 5.83273i 0.00108795 + 0.196621i
\(881\) 1.66227 + 5.11593i 0.0560032 + 0.172360i 0.975145 0.221566i \(-0.0711167\pi\)
−0.919142 + 0.393926i \(0.871117\pi\)
\(882\) 24.8559i 0.836942i
\(883\) −31.9303 + 10.3748i −1.07454 + 0.349139i −0.792254 0.610192i \(-0.791092\pi\)
−0.282285 + 0.959331i \(0.591092\pi\)
\(884\) −13.4581 9.77785i −0.452643 0.328865i
\(885\) 35.2329 25.8973i 1.18434 0.870527i
\(886\) 3.83219 2.78425i 0.128745 0.0935388i
\(887\) −30.6492 + 42.1850i −1.02910 + 1.41644i −0.123479 + 0.992347i \(0.539405\pi\)
−0.905621 + 0.424088i \(0.860595\pi\)
\(888\) 18.4307 25.3677i 0.618495 0.851285i
\(889\) 30.5413 22.1896i 1.02432 0.744215i
\(890\) −1.44725 + 4.53949i −0.0485119 + 0.152164i
\(891\) 0.502237 + 0.364897i 0.0168256 + 0.0122245i
\(892\) −38.7783 + 12.5998i −1.29839 + 0.421873i
\(893\) 10.5965i 0.354597i
\(894\) 1.05585 + 3.24956i 0.0353128 + 0.108682i
\(895\) 1.49768 + 0.477479i 0.0500618 + 0.0159604i
\(896\) 14.6229 45.0047i 0.488517 1.50350i
\(897\) 49.8675 + 16.2029i 1.66503 + 0.541000i
\(898\) 5.08745 + 7.00228i 0.169771 + 0.233669i
\(899\) 9.13109 0.304539
\(900\) −34.3203 + 25.5202i −1.14401 + 0.850672i
\(901\) −15.8360 −0.527574
\(902\) 0.583554 + 0.803193i 0.0194302 + 0.0267434i
\(903\) 110.361 + 35.8584i 3.67258 + 1.19329i
\(904\) −2.84211 + 8.74712i −0.0945272 + 0.290925i
\(905\) −15.3730 + 5.08922i −0.511017 + 0.169171i
\(906\) 6.42657 + 19.7790i 0.213509 + 0.657112i
\(907\) 24.4809i 0.812876i −0.913678 0.406438i \(-0.866771\pi\)
0.913678 0.406438i \(-0.133229\pi\)
\(908\) 43.3394 14.0818i 1.43827 0.467321i
\(909\) −56.9900 41.4057i −1.89024 1.37334i
\(910\) −13.0090 + 0.0719818i −0.431244 + 0.00238618i
\(911\) 27.6130 20.0620i 0.914859 0.664684i −0.0273802 0.999625i \(-0.508716\pi\)
0.942239 + 0.334941i \(0.108716\pi\)
\(912\) 4.64878 6.39850i 0.153937 0.211876i
\(913\) 5.71557 7.86681i 0.189158 0.260353i
\(914\) −0.928905 + 0.674889i −0.0307255 + 0.0223234i
\(915\) 15.2351 + 46.0208i 0.503657 + 1.52140i
\(916\) −37.4666 27.2211i −1.23793 0.899410i
\(917\) 8.30459 2.69832i 0.274242 0.0891065i
\(918\) 6.69615i 0.221006i
\(919\) 5.76755 + 17.7507i 0.190254 + 0.585542i 0.999999 0.00124006i \(-0.000394722\pi\)
−0.809745 + 0.586782i \(0.800395\pi\)
\(920\) 13.8679 19.3114i 0.457212 0.636677i
\(921\) −19.4314 + 59.8037i −0.640286 + 1.97060i
\(922\) −4.20650 1.36678i −0.138534 0.0450124i
\(923\) −20.7407 28.5471i −0.682689 0.939641i
\(924\) 19.9020 0.654727
\(925\) 19.1839 27.0284i 0.630763 0.888688i
\(926\) 13.2270 0.434665
\(927\) 11.7095 + 16.1168i 0.384592 + 0.529345i
\(928\) −27.3459 8.88523i −0.897674 0.291672i
\(929\) −4.49659 + 13.8391i −0.147528 + 0.454046i −0.997327 0.0730609i \(-0.976723\pi\)
0.849799 + 0.527107i \(0.176723\pi\)
\(930\) −2.44364 3.32454i −0.0801302 0.109016i
\(931\) −3.61553 11.1275i −0.118494 0.364688i
\(932\) 15.6154i 0.511498i
\(933\) 27.9511 9.08186i 0.915078 0.297327i
\(934\) −4.83084 3.50981i −0.158070 0.114844i
\(935\) −5.12172 3.67802i −0.167498 0.120284i
\(936\) −19.6541 + 14.2795i −0.642415 + 0.466741i
\(937\) 6.08778 8.37911i 0.198879 0.273734i −0.697916 0.716180i \(-0.745889\pi\)
0.896795 + 0.442446i \(0.145889\pi\)
\(938\) −9.61713 + 13.2368i −0.314010 + 0.432198i
\(939\) −62.3467 + 45.2975i −2.03461 + 1.47823i
\(940\) −34.6450 24.8793i −1.13000 0.811475i
\(941\) −38.1340 27.7059i −1.24313 0.903188i −0.245328 0.969440i \(-0.578896\pi\)
−0.997803 + 0.0662523i \(0.978896\pi\)
\(942\) −2.85650 + 0.928133i −0.0930698 + 0.0302402i
\(943\) 15.1341i 0.492834i
\(944\) 6.16545 + 18.9753i 0.200668 + 0.617593i
\(945\) 27.9312 + 38.0000i 0.908601 + 1.23614i
\(946\) −1.22272 + 3.76315i −0.0397541 + 0.122350i
\(947\) −26.8778 8.73311i −0.873410 0.283788i −0.162191 0.986759i \(-0.551856\pi\)
−0.711218 + 0.702971i \(0.751856\pi\)
\(948\) −31.9426 43.9652i −1.03745 1.42792i
\(949\) 38.6791 1.25558
\(950\) −1.29384 + 1.82291i −0.0419778 + 0.0591429i
\(951\) −70.6372 −2.29057
\(952\) 13.2614 + 18.2527i 0.429803 + 0.591573i
\(953\) −8.77435 2.85096i −0.284229 0.0923516i 0.163433 0.986554i \(-0.447743\pi\)
−0.447662 + 0.894203i \(0.647743\pi\)
\(954\) −3.38534 + 10.4190i −0.109605 + 0.337328i
\(955\) 0.657983 0.916255i 0.0212918 0.0296493i
\(956\) −0.528374 1.62617i −0.0170888 0.0525940i
\(957\) 15.7484i 0.509072i
\(958\) 0.558716 0.181538i 0.0180513 0.00586523i
\(959\) 65.3986 + 47.5149i 2.11183 + 1.53433i
\(960\) −7.03268 21.2437i −0.226979 0.685637i
\(961\) 23.3017 16.9297i 0.751669 0.546120i
\(962\) 5.24208 7.21510i 0.169011 0.232624i
\(963\) −6.54903 + 9.01396i −0.211039 + 0.290471i
\(964\) 3.13499 2.27770i 0.100971 0.0733599i
\(965\) 52.1427 0.288518i 1.67853 0.00928772i
\(966\) −27.2532 19.8006i −0.876857 0.637074i
\(967\) 3.67980 1.19564i 0.118334 0.0384492i −0.249251 0.968439i \(-0.580184\pi\)
0.367586 + 0.929990i \(0.380184\pi\)
\(968\) 17.2559i 0.554626i
\(969\) 2.64209 + 8.13151i 0.0848761 + 0.261222i
\(970\) −0.492634 + 0.163086i −0.0158175 + 0.00523636i
\(971\) −5.90240 + 18.1657i −0.189417 + 0.582966i −0.999996 0.00266296i \(-0.999152\pi\)
0.810579 + 0.585629i \(0.199152\pi\)
\(972\) −28.2722 9.18621i −0.906832 0.294648i
\(973\) −42.9901 59.1708i −1.37820 1.89693i
\(974\) −7.87827 −0.252436
\(975\) −33.6166 + 24.9969i −1.07659 + 0.800541i
\(976\) −22.1193 −0.708022
\(977\) −18.6283 25.6396i −0.595971 0.820284i 0.399361 0.916794i \(-0.369232\pi\)
−0.995332 + 0.0965099i \(0.969232\pi\)
\(978\) 18.0783 + 5.87399i 0.578080 + 0.187830i
\(979\) 1.35242 4.16233i 0.0432236 0.133029i
\(980\) −44.8700 14.3051i −1.43332 0.456961i
\(981\) −11.6814 35.9516i −0.372958 1.14785i
\(982\) 15.1645i 0.483918i
\(983\) 29.8725 9.70615i 0.952783 0.309578i 0.208937 0.977929i \(-0.433000\pi\)
0.743846 + 0.668351i \(0.233000\pi\)
\(984\) −9.25432 6.72366i −0.295017 0.214342i
\(985\) −5.39848 + 16.9330i −0.172010 + 0.539532i
\(986\) 6.84180 4.97086i 0.217887 0.158304i
\(987\) −74.9897 + 103.214i −2.38695 + 3.28535i
\(988\) 3.18404 4.38245i 0.101298 0.139424i
\(989\) −48.7974 + 35.4534i −1.55167 + 1.12735i
\(990\) −3.51479 + 2.58348i −0.111707 + 0.0821083i
\(991\) −34.6265 25.1576i −1.09995 0.799158i −0.118895 0.992907i \(-0.537935\pi\)
−0.981051 + 0.193749i \(0.937935\pi\)
\(992\) 6.58097 2.13829i 0.208946 0.0678907i
\(993\) 9.44068i 0.299591i
\(994\) 7.00545 + 21.5606i 0.222199 + 0.683860i
\(995\) 0.0564811 + 10.2076i 0.00179057 + 0.323603i
\(996\) −16.4003 + 50.4749i −0.519664 + 1.59936i
\(997\) 42.7807 + 13.9003i 1.35488 + 0.440227i 0.894330 0.447408i \(-0.147653\pi\)
0.460549 + 0.887634i \(0.347653\pi\)
\(998\) 0.343414 + 0.472669i 0.0108706 + 0.0149621i
\(999\) −32.3308 −1.02290
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 475.2.n.b.39.10 96
25.9 even 10 inner 475.2.n.b.134.10 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.n.b.39.10 96 1.1 even 1 trivial
475.2.n.b.134.10 yes 96 25.9 even 10 inner