Properties

Label 507.2.q.b.55.3
Level $507$
Weight $2$
Character 507.55
Analytic conductor $4.048$
Analytic rank $0$
Dimension $384$
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] = [507,2,Mod(16,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.q (of order \(39\), degree \(24\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(384\)
Relative dimension: \(16\) over \(\Q(\zeta_{39})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label 55.3
Character \(\chi\) \(=\) 507.55
Dual form 507.2.q.b.295.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.21429 + 1.48724i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-0.337321 - 1.65231i) q^{4} +(-0.0596193 - 0.491009i) q^{5} +(1.33003 - 1.38471i) q^{6} +(0.351566 - 0.222317i) q^{7} +(-0.533160 - 0.279824i) q^{8} +(0.987050 + 0.160411i) q^{9} +O(q^{10})\) \(q+(-1.21429 + 1.48724i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-0.337321 - 1.65231i) q^{4} +(-0.0596193 - 0.491009i) q^{5} +(1.33003 - 1.38471i) q^{6} +(0.351566 - 0.222317i) q^{7} +(-0.533160 - 0.279824i) q^{8} +(0.987050 + 0.160411i) q^{9} +(0.802643 + 0.507561i) q^{10} +(-0.655329 + 0.106501i) q^{11} +(0.203272 + 1.67409i) q^{12} +(3.60021 - 0.196167i) q^{13} +(-0.0962657 + 0.792820i) q^{14} +(0.0199161 + 0.494214i) q^{15} +(4.16647 - 1.77517i) q^{16} +(1.53745 - 0.972226i) q^{17} +(-1.43714 + 1.27319i) q^{18} +(-3.32336 + 5.75624i) q^{19} +(-0.791188 + 0.264137i) q^{20} +(-0.368315 + 0.193306i) q^{21} +(0.637369 - 1.10396i) q^{22} +(1.79357 + 3.10655i) q^{23} +(0.508915 + 0.321818i) q^{24} +(4.61717 - 1.13803i) q^{25} +(-4.07996 + 5.59258i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.485926 - 0.505903i) q^{28} +(-3.20355 + 3.92364i) q^{29} +(-0.759199 - 0.570501i) q^{30} +(9.76630 + 2.40718i) q^{31} +(-2.08417 + 7.19539i) q^{32} +(0.661774 - 0.0534239i) q^{33} +(-0.420986 + 3.46713i) q^{34} +(-0.130119 - 0.159367i) q^{35} +(-0.0679041 - 1.68502i) q^{36} +(-1.40651 - 4.85582i) q^{37} +(-4.52536 - 11.9324i) q^{38} +(-3.60432 - 0.0941653i) q^{39} +(-0.105609 + 0.278469i) q^{40} +(-11.9008 - 0.960731i) q^{41} +(0.159749 - 0.782503i) q^{42} +(-2.78040 + 9.59906i) q^{43} +(0.397030 + 1.04688i) q^{44} +(0.0199161 - 0.494214i) q^{45} +(-6.79810 - 1.10480i) q^{46} +(7.97158 + 7.06221i) q^{47} +(-4.29580 + 1.43415i) q^{48} +(-2.92667 + 6.16784i) q^{49} +(-3.91408 + 8.24875i) q^{50} +(-1.61070 + 0.845360i) q^{51} +(-1.53856 - 5.88249i) q^{52} +(7.81874 + 4.10359i) q^{53} +(1.53493 - 1.15342i) q^{54} +(0.0913634 + 0.315423i) q^{55} +(-0.249650 + 0.0201538i) q^{56} +(3.77577 - 5.47015i) q^{57} +(-1.94534 - 9.52890i) q^{58} +(-5.70977 - 2.43271i) q^{59} +(0.809876 - 0.199617i) q^{60} +(0.350414 - 8.69542i) q^{61} +(-15.4392 + 11.6018i) q^{62} +(0.382675 - 0.163043i) q^{63} +(-3.02509 - 4.38260i) q^{64} +(-0.310962 - 1.75604i) q^{65} +(-0.724134 + 1.04909i) q^{66} +(0.0907319 - 0.444434i) q^{67} +(-2.12503 - 2.21240i) q^{68} +(-1.53778 - 3.24080i) q^{69} +0.395021 q^{70} +(-0.299260 - 0.630677i) q^{71} +(-0.481369 - 0.361725i) q^{72} +(1.99522 - 5.26095i) q^{73} +(8.92968 + 3.80458i) q^{74} +(-4.69378 + 0.762813i) q^{75} +(10.6321 + 3.54952i) q^{76} +(-0.206714 + 0.183133i) q^{77} +(4.51675 - 5.24614i) q^{78} +(4.53713 + 4.01954i) q^{79} +(-1.12002 - 1.93994i) q^{80} +(0.948536 + 0.316668i) q^{81} +(15.8799 - 16.5327i) q^{82} +(4.76899 + 6.90907i) q^{83} +(0.443642 + 0.543363i) q^{84} +(-0.569034 - 0.696940i) q^{85} +(-10.8999 - 15.7912i) q^{86} +(3.50889 - 3.65314i) q^{87} +(0.379197 + 0.126595i) q^{88} +(2.35043 + 4.07107i) q^{89} +(0.710831 + 0.629741i) q^{90} +(1.22210 - 0.869352i) q^{91} +(4.52797 - 4.01143i) q^{92} +(-9.54093 - 3.18523i) q^{93} +(-20.1830 + 3.28006i) q^{94} +(3.02450 + 1.28862i) q^{95} +(2.65640 - 7.00435i) q^{96} +(10.4127 + 7.82461i) q^{97} +(-5.61921 - 11.8422i) q^{98} -0.663927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{28}{39}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21429 + 1.48724i −0.858635 + 1.05164i 0.139477 + 0.990225i \(0.455458\pi\)
−0.998113 + 0.0614119i \(0.980440\pi\)
\(3\) −0.996757 0.0804666i −0.575478 0.0464574i
\(4\) −0.337321 1.65231i −0.168661 0.826155i
\(5\) −0.0596193 0.491009i −0.0266626 0.219586i 0.973287 0.229590i \(-0.0737386\pi\)
−0.999950 + 0.0100043i \(0.996815\pi\)
\(6\) 1.33003 1.38471i 0.542982 0.565304i
\(7\) 0.351566 0.222317i 0.132879 0.0840278i −0.466372 0.884589i \(-0.654439\pi\)
0.599252 + 0.800561i \(0.295465\pi\)
\(8\) −0.533160 0.279824i −0.188501 0.0989327i
\(9\) 0.987050 + 0.160411i 0.329017 + 0.0534704i
\(10\) 0.802643 + 0.507561i 0.253818 + 0.160505i
\(11\) −0.655329 + 0.106501i −0.197589 + 0.0321114i −0.258400 0.966038i \(-0.583195\pi\)
0.0608112 + 0.998149i \(0.480631\pi\)
\(12\) 0.203272 + 1.67409i 0.0586795 + 0.483269i
\(13\) 3.60021 0.196167i 0.998519 0.0544071i
\(14\) −0.0962657 + 0.792820i −0.0257281 + 0.211890i
\(15\) 0.0199161 + 0.494214i 0.00514233 + 0.127606i
\(16\) 4.16647 1.77517i 1.04162 0.443791i
\(17\) 1.53745 0.972226i 0.372887 0.235800i −0.334856 0.942269i \(-0.608688\pi\)
0.707743 + 0.706470i \(0.249713\pi\)
\(18\) −1.43714 + 1.27319i −0.338737 + 0.300095i
\(19\) −3.32336 + 5.75624i −0.762432 + 1.32057i 0.179161 + 0.983820i \(0.442662\pi\)
−0.941594 + 0.336751i \(0.890672\pi\)
\(20\) −0.791188 + 0.264137i −0.176915 + 0.0590629i
\(21\) −0.368315 + 0.193306i −0.0803728 + 0.0421829i
\(22\) 0.637369 1.10396i 0.135887 0.235364i
\(23\) 1.79357 + 3.10655i 0.373985 + 0.647761i 0.990175 0.139837i \(-0.0446579\pi\)
−0.616190 + 0.787598i \(0.711325\pi\)
\(24\) 0.508915 + 0.321818i 0.103882 + 0.0656909i
\(25\) 4.61717 1.13803i 0.923435 0.227606i
\(26\) −4.07996 + 5.59258i −0.800147 + 1.09680i
\(27\) −0.970942 0.239316i −0.186858 0.0460563i
\(28\) −0.485926 0.505903i −0.0918314 0.0956066i
\(29\) −3.20355 + 3.92364i −0.594885 + 0.728602i −0.981034 0.193834i \(-0.937908\pi\)
0.386149 + 0.922436i \(0.373805\pi\)
\(30\) −0.759199 0.570501i −0.138610 0.104159i
\(31\) 9.76630 + 2.40718i 1.75408 + 0.432342i 0.979715 0.200398i \(-0.0642236\pi\)
0.774364 + 0.632740i \(0.218070\pi\)
\(32\) −2.08417 + 7.19539i −0.368433 + 1.27198i
\(33\) 0.661774 0.0534239i 0.115200 0.00929991i
\(34\) −0.420986 + 3.46713i −0.0721985 + 0.594608i
\(35\) −0.130119 0.159367i −0.0219942 0.0269380i
\(36\) −0.0679041 1.68502i −0.0113173 0.280837i
\(37\) −1.40651 4.85582i −0.231228 0.798292i −0.989272 0.146088i \(-0.953332\pi\)
0.758044 0.652204i \(-0.226155\pi\)
\(38\) −4.52536 11.9324i −0.734111 1.93569i
\(39\) −3.60432 0.0941653i −0.577153 0.0150785i
\(40\) −0.105609 + 0.278469i −0.0166983 + 0.0440299i
\(41\) −11.9008 0.960731i −1.85859 0.150041i −0.900196 0.435485i \(-0.856577\pi\)
−0.958395 + 0.285444i \(0.907859\pi\)
\(42\) 0.159749 0.782503i 0.0246498 0.120743i
\(43\) −2.78040 + 9.59906i −0.424007 + 1.46384i 0.409998 + 0.912086i \(0.365529\pi\)
−0.834005 + 0.551756i \(0.813958\pi\)
\(44\) 0.397030 + 1.04688i 0.0598545 + 0.157823i
\(45\) 0.0199161 0.494214i 0.00296892 0.0736731i
\(46\) −6.79810 1.10480i −1.00233 0.162894i
\(47\) 7.97158 + 7.06221i 1.16277 + 1.03013i 0.999048 + 0.0436230i \(0.0138900\pi\)
0.163727 + 0.986506i \(0.447648\pi\)
\(48\) −4.29580 + 1.43415i −0.620045 + 0.207001i
\(49\) −2.92667 + 6.16784i −0.418096 + 0.881119i
\(50\) −3.91408 + 8.24875i −0.553534 + 1.16655i
\(51\) −1.61070 + 0.845360i −0.225543 + 0.118374i
\(52\) −1.53856 5.88249i −0.213359 0.815755i
\(53\) 7.81874 + 4.10359i 1.07399 + 0.563672i 0.906502 0.422203i \(-0.138743\pi\)
0.167486 + 0.985875i \(0.446435\pi\)
\(54\) 1.53493 1.15342i 0.208877 0.156961i
\(55\) 0.0913634 + 0.315423i 0.0123194 + 0.0425316i
\(56\) −0.249650 + 0.0201538i −0.0333609 + 0.00269317i
\(57\) 3.77577 5.47015i 0.500113 0.724539i
\(58\) −1.94534 9.52890i −0.255436 1.25121i
\(59\) −5.70977 2.43271i −0.743349 0.316712i −0.0131203 0.999914i \(-0.504176\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(60\) 0.809876 0.199617i 0.104555 0.0257704i
\(61\) 0.350414 8.69542i 0.0448659 1.11334i −0.807326 0.590106i \(-0.799086\pi\)
0.852192 0.523229i \(-0.175273\pi\)
\(62\) −15.4392 + 11.6018i −1.96078 + 1.47343i
\(63\) 0.382675 0.163043i 0.0482125 0.0205414i
\(64\) −3.02509 4.38260i −0.378137 0.547825i
\(65\) −0.310962 1.75604i −0.0385701 0.217810i
\(66\) −0.724134 + 1.04909i −0.0891347 + 0.129134i
\(67\) 0.0907319 0.444434i 0.0110847 0.0542963i −0.973872 0.227097i \(-0.927077\pi\)
0.984957 + 0.172801i \(0.0552817\pi\)
\(68\) −2.12503 2.21240i −0.257698 0.268292i
\(69\) −1.53778 3.24080i −0.185127 0.390146i
\(70\) 0.395021 0.0472140
\(71\) −0.299260 0.630677i −0.0355156 0.0748476i 0.884917 0.465748i \(-0.154215\pi\)
−0.920433 + 0.390901i \(0.872164\pi\)
\(72\) −0.481369 0.361725i −0.0567299 0.0426297i
\(73\) 1.99522 5.26095i 0.233522 0.615748i −0.766114 0.642704i \(-0.777812\pi\)
0.999637 + 0.0269567i \(0.00858163\pi\)
\(74\) 8.92968 + 3.80458i 1.03805 + 0.442273i
\(75\) −4.69378 + 0.762813i −0.541990 + 0.0880820i
\(76\) 10.6321 + 3.54952i 1.21959 + 0.407158i
\(77\) −0.206714 + 0.183133i −0.0235573 + 0.0208699i
\(78\) 4.51675 5.24614i 0.511421 0.594009i
\(79\) 4.53713 + 4.01954i 0.510467 + 0.452234i 0.878613 0.477534i \(-0.158469\pi\)
−0.368147 + 0.929768i \(0.620008\pi\)
\(80\) −1.12002 1.93994i −0.125222 0.216892i
\(81\) 0.948536 + 0.316668i 0.105393 + 0.0351853i
\(82\) 15.8799 16.5327i 1.75364 1.82573i
\(83\) 4.76899 + 6.90907i 0.523465 + 0.758369i 0.992158 0.124992i \(-0.0398904\pi\)
−0.468693 + 0.883361i \(0.655275\pi\)
\(84\) 0.443642 + 0.543363i 0.0484053 + 0.0592858i
\(85\) −0.569034 0.696940i −0.0617204 0.0755937i
\(86\) −10.8999 15.7912i −1.17536 1.70281i
\(87\) 3.50889 3.65314i 0.376192 0.391658i
\(88\) 0.379197 + 0.126595i 0.0404225 + 0.0134950i
\(89\) 2.35043 + 4.07107i 0.249145 + 0.431533i 0.963289 0.268467i \(-0.0865169\pi\)
−0.714143 + 0.699999i \(0.753184\pi\)
\(90\) 0.710831 + 0.629741i 0.0749281 + 0.0663805i
\(91\) 1.22210 0.869352i 0.128111 0.0911329i
\(92\) 4.52797 4.01143i 0.472074 0.418221i
\(93\) −9.54093 3.18523i −0.989349 0.330293i
\(94\) −20.1830 + 3.28006i −2.08172 + 0.338313i
\(95\) 3.02450 + 1.28862i 0.310307 + 0.132210i
\(96\) 2.65640 7.00435i 0.271118 0.714879i
\(97\) 10.4127 + 7.82461i 1.05725 + 0.794469i 0.979285 0.202487i \(-0.0649025\pi\)
0.0779614 + 0.996956i \(0.475159\pi\)
\(98\) −5.61921 11.8422i −0.567626 1.19625i
\(99\) −0.663927 −0.0667272
\(100\) −3.43785 7.24512i −0.343785 0.724512i
\(101\) 13.3002 + 13.8469i 1.32341 + 1.37782i 0.875098 + 0.483946i \(0.160797\pi\)
0.448317 + 0.893875i \(0.352024\pi\)
\(102\) 0.698609 3.42201i 0.0691726 0.338830i
\(103\) 4.78244 6.92856i 0.471228 0.682691i −0.513243 0.858244i \(-0.671556\pi\)
0.984470 + 0.175553i \(0.0561712\pi\)
\(104\) −1.97438 0.902837i −0.193604 0.0885304i
\(105\) 0.116874 + 0.169321i 0.0114057 + 0.0165240i
\(106\) −15.5973 + 6.64538i −1.51494 + 0.645456i
\(107\) 13.9280 10.4662i 1.34647 1.01181i 0.349271 0.937022i \(-0.386429\pi\)
0.997200 0.0747848i \(-0.0238270\pi\)
\(108\) −0.0679041 + 1.68502i −0.00653407 + 0.162141i
\(109\) −6.89701 + 1.69996i −0.660614 + 0.162827i −0.555349 0.831618i \(-0.687415\pi\)
−0.105265 + 0.994444i \(0.533569\pi\)
\(110\) −0.580051 0.247137i −0.0553057 0.0235636i
\(111\) 1.01121 + 4.95325i 0.0959801 + 0.470142i
\(112\) 1.07014 1.55036i 0.101118 0.146495i
\(113\) 13.9210 1.12382i 1.30958 0.105720i 0.594121 0.804376i \(-0.297500\pi\)
0.715458 + 0.698656i \(0.246218\pi\)
\(114\) 3.55053 + 12.2578i 0.332537 + 1.14805i
\(115\) 1.41841 1.06587i 0.132268 0.0993927i
\(116\) 7.56370 + 3.96973i 0.702272 + 0.368581i
\(117\) 3.58506 + 0.383887i 0.331439 + 0.0354904i
\(118\) 10.5514 5.53778i 0.971332 0.509794i
\(119\) 0.324373 0.683603i 0.0297353 0.0626657i
\(120\) 0.127674 0.269068i 0.0116550 0.0245625i
\(121\) −10.0158 + 3.34376i −0.910526 + 0.303978i
\(122\) 12.5067 + 11.0799i 1.13230 + 1.00313i
\(123\) 11.7849 + 1.91523i 1.06261 + 0.172691i
\(124\) 0.683019 16.9489i 0.0613369 1.52206i
\(125\) −1.71102 4.51159i −0.153038 0.403529i
\(126\) −0.222196 + 0.767111i −0.0197948 + 0.0683397i
\(127\) 1.24788 6.11252i 0.110731 0.542398i −0.886144 0.463410i \(-0.846626\pi\)
0.996876 0.0789885i \(-0.0251691\pi\)
\(128\) −4.74240 0.382846i −0.419173 0.0338391i
\(129\) 3.54379 9.34420i 0.312013 0.822711i
\(130\) 2.98925 + 1.66987i 0.262175 + 0.146458i
\(131\) −3.54498 9.34734i −0.309726 0.816681i −0.996001 0.0893387i \(-0.971525\pi\)
0.686275 0.727342i \(-0.259245\pi\)
\(132\) −0.311503 1.07543i −0.0271129 0.0936045i
\(133\) 0.111326 + 2.76253i 0.00965321 + 0.239542i
\(134\) 0.550805 + 0.674614i 0.0475823 + 0.0582778i
\(135\) −0.0596193 + 0.491009i −0.00513121 + 0.0422593i
\(136\) −1.09176 + 0.0881361i −0.0936177 + 0.00755760i
\(137\) 3.72955 12.8759i 0.318637 1.10006i −0.628120 0.778116i \(-0.716175\pi\)
0.946758 0.321947i \(-0.104337\pi\)
\(138\) 6.68716 + 1.64824i 0.569249 + 0.140307i
\(139\) 5.97012 + 4.48625i 0.506379 + 0.380519i 0.823007 0.568031i \(-0.192294\pi\)
−0.316629 + 0.948550i \(0.602551\pi\)
\(140\) −0.219432 + 0.268756i −0.0185454 + 0.0227140i
\(141\) −7.37746 7.68075i −0.621294 0.646836i
\(142\) 1.30136 + 0.320756i 0.109207 + 0.0269172i
\(143\) −2.33843 + 0.511982i −0.195549 + 0.0428140i
\(144\) 4.39727 1.08383i 0.366439 0.0903191i
\(145\) 2.11754 + 1.33905i 0.175852 + 0.111202i
\(146\) 5.40152 + 9.35570i 0.447033 + 0.774283i
\(147\) 3.41349 5.91234i 0.281540 0.487641i
\(148\) −7.54887 + 3.96195i −0.620513 + 0.325671i
\(149\) −3.43766 + 1.14766i −0.281624 + 0.0940199i −0.453971 0.891016i \(-0.649993\pi\)
0.172347 + 0.985036i \(0.444865\pi\)
\(150\) 4.56514 7.90705i 0.372742 0.645608i
\(151\) −3.88156 + 3.43876i −0.315877 + 0.279842i −0.806131 0.591737i \(-0.798442\pi\)
0.490254 + 0.871579i \(0.336904\pi\)
\(152\) 3.38262 2.13904i 0.274367 0.173499i
\(153\) 1.67350 0.713012i 0.135294 0.0576436i
\(154\) −0.0213506 0.529810i −0.00172048 0.0426933i
\(155\) 0.599685 4.93885i 0.0481679 0.396698i
\(156\) 1.06022 + 5.98722i 0.0848859 + 0.479361i
\(157\) 1.64318 + 13.5328i 0.131140 + 1.08003i 0.898548 + 0.438875i \(0.144623\pi\)
−0.767409 + 0.641158i \(0.778454\pi\)
\(158\) −11.4874 + 1.86689i −0.913891 + 0.148522i
\(159\) −7.46319 4.71943i −0.591869 0.374276i
\(160\) 3.65726 + 0.594362i 0.289132 + 0.0469885i
\(161\) 1.32119 + 0.693416i 0.104125 + 0.0546489i
\(162\) −1.62276 + 1.02617i −0.127496 + 0.0806238i
\(163\) −10.4847 + 10.9157i −0.821225 + 0.854985i −0.991459 0.130418i \(-0.958368\pi\)
0.170234 + 0.985404i \(0.445547\pi\)
\(164\) 2.42697 + 19.9879i 0.189514 + 1.56079i
\(165\) −0.0656861 0.321752i −0.00511366 0.0250483i
\(166\) −16.0664 1.29701i −1.24699 0.100668i
\(167\) −3.58604 + 4.39210i −0.277496 + 0.339871i −0.894483 0.447103i \(-0.852456\pi\)
0.616987 + 0.786974i \(0.288353\pi\)
\(168\) 0.250462 0.0193236
\(169\) 12.9230 1.41249i 0.994080 0.108653i
\(170\) 1.72749 0.132492
\(171\) −4.20369 + 5.14859i −0.321464 + 0.393722i
\(172\) 16.7985 + 1.35612i 1.28087 + 0.103403i
\(173\) −5.11164 25.0385i −0.388631 1.90364i −0.426754 0.904368i \(-0.640343\pi\)
0.0381224 0.999273i \(-0.487862\pi\)
\(174\) 1.17227 + 9.65454i 0.0888698 + 0.731909i
\(175\) 1.37024 1.42657i 0.103580 0.107838i
\(176\) −2.54135 + 1.60705i −0.191561 + 0.121136i
\(177\) 5.49551 + 2.88427i 0.413068 + 0.216795i
\(178\) −8.90877 1.44782i −0.667741 0.108518i
\(179\) −6.26436 3.96134i −0.468220 0.296084i 0.279444 0.960162i \(-0.409850\pi\)
−0.747664 + 0.664078i \(0.768824\pi\)
\(180\) −0.823313 + 0.133801i −0.0613661 + 0.00997296i
\(181\) −2.76209 22.7478i −0.205304 1.69083i −0.622981 0.782237i \(-0.714079\pi\)
0.417677 0.908596i \(-0.362844\pi\)
\(182\) −0.191052 + 2.87320i −0.0141617 + 0.212976i
\(183\) −1.04897 + 8.63903i −0.0775420 + 0.638616i
\(184\) −0.0869714 2.15817i −0.00641161 0.159103i
\(185\) −2.30040 + 0.980107i −0.169128 + 0.0720589i
\(186\) 16.3227 10.3218i 1.19684 0.756834i
\(187\) −0.903994 + 0.800869i −0.0661066 + 0.0585654i
\(188\) 8.97996 15.5538i 0.654931 1.13437i
\(189\) −0.394554 + 0.131721i −0.0286995 + 0.00958132i
\(190\) −5.58912 + 2.93339i −0.405477 + 0.212811i
\(191\) 2.76415 4.78764i 0.200007 0.346422i −0.748524 0.663108i \(-0.769237\pi\)
0.948530 + 0.316686i \(0.102570\pi\)
\(192\) 2.66263 + 4.61181i 0.192159 + 0.332829i
\(193\) −16.6004 10.4974i −1.19492 0.755622i −0.219422 0.975630i \(-0.570417\pi\)
−0.975498 + 0.220008i \(0.929391\pi\)
\(194\) −24.2811 + 5.98476i −1.74328 + 0.429680i
\(195\) 0.168651 + 1.77537i 0.0120774 + 0.127137i
\(196\) 11.1784 + 2.75523i 0.798457 + 0.196802i
\(197\) 4.58084 + 4.76916i 0.326372 + 0.339789i 0.864092 0.503335i \(-0.167894\pi\)
−0.537720 + 0.843123i \(0.680714\pi\)
\(198\) 0.806202 0.987418i 0.0572943 0.0701728i
\(199\) 6.07252 + 4.56320i 0.430470 + 0.323477i 0.793795 0.608185i \(-0.208102\pi\)
−0.363325 + 0.931662i \(0.618359\pi\)
\(200\) −2.78014 0.685243i −0.196586 0.0484540i
\(201\) −0.126200 + 0.435692i −0.00890145 + 0.0307314i
\(202\) −36.7440 + 2.96628i −2.58530 + 0.208707i
\(203\) −0.253969 + 2.09162i −0.0178251 + 0.146803i
\(204\) 1.94012 + 2.37622i 0.135836 + 0.166368i
\(205\) 0.237789 + 5.90067i 0.0166079 + 0.412121i
\(206\) 4.49714 + 15.5259i 0.313331 + 1.08174i
\(207\) 1.27202 + 3.35403i 0.0884112 + 0.233121i
\(208\) 14.6519 7.20829i 1.01593 0.499805i
\(209\) 1.56485 4.12617i 0.108243 0.285413i
\(210\) −0.393740 0.0317860i −0.0271706 0.00219344i
\(211\) −1.00324 + 4.91421i −0.0690661 + 0.338308i −0.999612 0.0278681i \(-0.991128\pi\)
0.930545 + 0.366176i \(0.119333\pi\)
\(212\) 4.14298 14.3032i 0.284541 0.982349i
\(213\) 0.247541 + 0.652712i 0.0169612 + 0.0447231i
\(214\) −1.34691 + 33.4233i −0.0920731 + 2.28477i
\(215\) 4.87899 + 0.792913i 0.332744 + 0.0540762i
\(216\) 0.450701 + 0.399286i 0.0306663 + 0.0271680i
\(217\) 3.96865 1.32493i 0.269409 0.0899421i
\(218\) 5.84674 12.3218i 0.395992 0.834534i
\(219\) −2.41208 + 5.08334i −0.162993 + 0.343500i
\(220\) 0.490357 0.257359i 0.0330599 0.0173512i
\(221\) 5.34444 3.80182i 0.359506 0.255738i
\(222\) −8.59458 4.51078i −0.576830 0.302744i
\(223\) −18.0174 + 13.5392i −1.20653 + 0.906652i −0.997459 0.0712473i \(-0.977302\pi\)
−0.209076 + 0.977899i \(0.567046\pi\)
\(224\) 0.866932 + 2.99300i 0.0579243 + 0.199978i
\(225\) 4.73994 0.382647i 0.315996 0.0255098i
\(226\) −15.2328 + 22.0685i −1.01327 + 1.46798i
\(227\) 1.93863 + 9.49606i 0.128672 + 0.630276i 0.992063 + 0.125741i \(0.0401308\pi\)
−0.863391 + 0.504535i \(0.831664\pi\)
\(228\) −10.3120 4.39354i −0.682931 0.290970i
\(229\) −14.8137 + 3.65124i −0.978916 + 0.241281i −0.696141 0.717905i \(-0.745101\pi\)
−0.282775 + 0.959186i \(0.591255\pi\)
\(230\) −0.137168 + 3.40380i −0.00904461 + 0.224440i
\(231\) 0.220780 0.165905i 0.0145262 0.0109158i
\(232\) 2.80594 1.19550i 0.184219 0.0784883i
\(233\) −11.1883 16.2090i −0.732970 1.06189i −0.995293 0.0969101i \(-0.969104\pi\)
0.262323 0.964980i \(-0.415511\pi\)
\(234\) −4.92424 + 4.86569i −0.321908 + 0.318080i
\(235\) 2.99235 4.33516i 0.195199 0.282795i
\(236\) −2.09356 + 10.2549i −0.136279 + 0.667538i
\(237\) −4.19898 4.37160i −0.272753 0.283966i
\(238\) 0.622796 + 1.31252i 0.0403699 + 0.0850777i
\(239\) −12.3006 −0.795661 −0.397830 0.917459i \(-0.630237\pi\)
−0.397830 + 0.917459i \(0.630237\pi\)
\(240\) 0.960292 + 2.02377i 0.0619866 + 0.130634i
\(241\) −16.0551 12.0646i −1.03420 0.777149i −0.0589490 0.998261i \(-0.518775\pi\)
−0.975248 + 0.221112i \(0.929031\pi\)
\(242\) 7.18913 18.9562i 0.462135 1.21855i
\(243\) −0.919979 0.391967i −0.0590167 0.0251447i
\(244\) −14.4857 + 2.35416i −0.927354 + 0.150710i
\(245\) 3.20295 + 1.06930i 0.204629 + 0.0683152i
\(246\) −17.1587 + 15.2013i −1.09400 + 0.969200i
\(247\) −10.8356 + 21.3756i −0.689454 + 1.36010i
\(248\) −4.53341 4.01625i −0.287872 0.255032i
\(249\) −4.19758 7.27041i −0.266011 0.460744i
\(250\) 8.78750 + 2.93370i 0.555770 + 0.185543i
\(251\) −15.5808 + 16.2213i −0.983451 + 1.02388i 0.0162603 + 0.999868i \(0.494824\pi\)
−0.999712 + 0.0240135i \(0.992356\pi\)
\(252\) −0.398481 0.577300i −0.0251019 0.0363665i
\(253\) −1.50623 1.84480i −0.0946958 0.115981i
\(254\) 7.57549 + 9.27829i 0.475328 + 0.582171i
\(255\) 0.511108 + 0.740468i 0.0320068 + 0.0463699i
\(256\) 13.7059 14.2694i 0.856620 0.891836i
\(257\) −0.574721 0.191870i −0.0358501 0.0119685i 0.298686 0.954351i \(-0.403452\pi\)
−0.334536 + 0.942383i \(0.608580\pi\)
\(258\) 9.59387 + 16.6171i 0.597288 + 1.03453i
\(259\) −1.57401 1.39445i −0.0978041 0.0866469i
\(260\) −2.79663 + 1.10616i −0.173439 + 0.0686008i
\(261\) −3.79147 + 3.35895i −0.234686 + 0.207913i
\(262\) 18.2064 + 6.07818i 1.12479 + 0.375511i
\(263\) 13.1323 2.13420i 0.809770 0.131600i 0.258591 0.965987i \(-0.416742\pi\)
0.551180 + 0.834387i \(0.314178\pi\)
\(264\) −0.367781 0.156697i −0.0226353 0.00964402i
\(265\) 1.54875 4.08373i 0.0951392 0.250861i
\(266\) −4.24373 3.18896i −0.260200 0.195528i
\(267\) −2.01523 4.24700i −0.123330 0.259912i
\(268\) −0.764949 −0.0467267
\(269\) 9.00991 + 18.9880i 0.549344 + 1.15772i 0.968318 + 0.249720i \(0.0803385\pi\)
−0.418974 + 0.907998i \(0.637610\pi\)
\(270\) −0.657853 0.684897i −0.0400356 0.0416815i
\(271\) 2.40547 11.7828i 0.146122 0.715753i −0.839032 0.544081i \(-0.816878\pi\)
0.985154 0.171671i \(-0.0549166\pi\)
\(272\) 4.67988 6.77998i 0.283760 0.411097i
\(273\) −1.28809 + 0.768195i −0.0779587 + 0.0464933i
\(274\) 14.6208 + 21.1819i 0.883275 + 1.27964i
\(275\) −2.90457 + 1.23752i −0.175152 + 0.0746253i
\(276\) −4.83608 + 3.63408i −0.291098 + 0.218746i
\(277\) 0.593061 14.7167i 0.0356336 0.884238i −0.878235 0.478229i \(-0.841279\pi\)
0.913869 0.406009i \(-0.133080\pi\)
\(278\) −13.9216 + 3.43137i −0.834963 + 0.205800i
\(279\) 9.25369 + 3.94263i 0.554004 + 0.236039i
\(280\) 0.0247797 + 0.121379i 0.00148087 + 0.00725378i
\(281\) 9.11527 13.2058i 0.543772 0.787789i −0.450713 0.892669i \(-0.648830\pi\)
0.994485 + 0.104880i \(0.0334457\pi\)
\(282\) 20.3815 1.64537i 1.21370 0.0979802i
\(283\) 2.73534 + 9.44348i 0.162599 + 0.561357i 0.999893 + 0.0146044i \(0.00464888\pi\)
−0.837294 + 0.546752i \(0.815864\pi\)
\(284\) −0.941126 + 0.707210i −0.0558456 + 0.0419652i
\(285\) −2.91100 1.52781i −0.172433 0.0904997i
\(286\) 2.07810 4.09950i 0.122881 0.242409i
\(287\) −4.39749 + 2.30798i −0.259576 + 0.136236i
\(288\) −3.21140 + 6.76789i −0.189234 + 0.398802i
\(289\) −5.86924 + 12.3692i −0.345249 + 0.727597i
\(290\) −4.56280 + 1.52329i −0.267937 + 0.0894504i
\(291\) −9.74928 8.63711i −0.571513 0.506316i
\(292\) −9.36574 1.52208i −0.548089 0.0890731i
\(293\) −0.420547 + 10.4358i −0.0245686 + 0.609664i 0.939270 + 0.343178i \(0.111504\pi\)
−0.963839 + 0.266486i \(0.914138\pi\)
\(294\) 4.64808 + 12.2560i 0.271082 + 0.714784i
\(295\) −0.854069 + 2.94859i −0.0497258 + 0.171673i
\(296\) −0.608882 + 2.98250i −0.0353906 + 0.173354i
\(297\) 0.661774 + 0.0534239i 0.0384000 + 0.00309997i
\(298\) 2.46748 6.50622i 0.142937 0.376895i
\(299\) 7.06663 + 10.8324i 0.408674 + 0.626454i
\(300\) 2.84371 + 7.49825i 0.164182 + 0.432912i
\(301\) 1.15654 + 3.99283i 0.0666617 + 0.230143i
\(302\) −0.400910 9.94847i −0.0230698 0.572470i
\(303\) −12.1428 14.8722i −0.697586 0.854388i
\(304\) −3.62841 + 29.8827i −0.208104 + 1.71389i
\(305\) −4.29042 + 0.346359i −0.245669 + 0.0198324i
\(306\) −0.971701 + 3.35470i −0.0555484 + 0.191775i
\(307\) −20.7077 5.10399i −1.18185 0.291300i −0.401035 0.916063i \(-0.631350\pi\)
−0.780815 + 0.624763i \(0.785196\pi\)
\(308\) 0.372321 + 0.279781i 0.0212150 + 0.0159420i
\(309\) −5.32445 + 6.52126i −0.302897 + 0.370982i
\(310\) 6.61706 + 6.88909i 0.375824 + 0.391274i
\(311\) −2.28669 0.563618i −0.129666 0.0319599i 0.173948 0.984755i \(-0.444347\pi\)
−0.303615 + 0.952795i \(0.598194\pi\)
\(312\) 1.89533 + 1.05878i 0.107302 + 0.0599417i
\(313\) 1.68587 0.415531i 0.0952913 0.0234872i −0.191382 0.981516i \(-0.561297\pi\)
0.286673 + 0.958028i \(0.407451\pi\)
\(314\) −22.1218 13.9890i −1.24840 0.789443i
\(315\) −0.102870 0.178176i −0.00579608 0.0100391i
\(316\) 5.11106 8.85261i 0.287520 0.497998i
\(317\) 17.9935 9.44373i 1.01062 0.530413i 0.123689 0.992321i \(-0.460527\pi\)
0.886928 + 0.461908i \(0.152835\pi\)
\(318\) 16.0814 5.36877i 0.901802 0.301066i
\(319\) 1.68151 2.91246i 0.0941464 0.163066i
\(320\) −1.97154 + 1.74664i −0.110213 + 0.0976399i
\(321\) −14.7250 + 9.31153i −0.821870 + 0.519719i
\(322\) −2.63559 + 1.12292i −0.146876 + 0.0625780i
\(323\) 0.486848 + 12.0810i 0.0270889 + 0.672205i
\(324\) 0.203272 1.67409i 0.0112929 0.0930052i
\(325\) 16.3996 5.00289i 0.909684 0.277510i
\(326\) −3.50280 28.8481i −0.194002 1.59775i
\(327\) 7.01143 1.13947i 0.387733 0.0630128i
\(328\) 6.07619 + 3.84235i 0.335501 + 0.212158i
\(329\) 4.37258 + 0.710613i 0.241068 + 0.0391774i
\(330\) 0.558284 + 0.293010i 0.0307325 + 0.0161297i
\(331\) 15.5191 9.81366i 0.853004 0.539407i −0.0349234 0.999390i \(-0.511119\pi\)
0.887928 + 0.459983i \(0.152144\pi\)
\(332\) 9.80724 10.2104i 0.538242 0.560370i
\(333\) −0.609363 5.01856i −0.0333929 0.275015i
\(334\) −2.17760 10.6666i −0.119153 0.583650i
\(335\) −0.223631 0.0180533i −0.0122182 0.000986359i
\(336\) −1.19142 + 1.45922i −0.0649973 + 0.0796072i
\(337\) 20.9130 1.13921 0.569603 0.821920i \(-0.307097\pi\)
0.569603 + 0.821920i \(0.307097\pi\)
\(338\) −13.5917 + 20.9348i −0.739288 + 1.13870i
\(339\) −13.9663 −0.758546
\(340\) −0.959613 + 1.17531i −0.0520423 + 0.0637403i
\(341\) −6.65651 0.537369i −0.360470 0.0291002i
\(342\) −2.55267 12.5038i −0.138032 0.676128i
\(343\) 0.693264 + 5.70954i 0.0374327 + 0.308286i
\(344\) 4.16845 4.33981i 0.224748 0.233987i
\(345\) −1.49958 + 0.948277i −0.0807347 + 0.0510535i
\(346\) 43.4453 + 22.8018i 2.33563 + 1.22583i
\(347\) −6.70618 1.08986i −0.360007 0.0585068i −0.0222820 0.999752i \(-0.507093\pi\)
−0.337725 + 0.941245i \(0.609657\pi\)
\(348\) −7.21974 4.56549i −0.387019 0.244736i
\(349\) −0.582664 + 0.0946920i −0.0311893 + 0.00506875i −0.175986 0.984393i \(-0.556311\pi\)
0.144797 + 0.989461i \(0.453747\pi\)
\(350\) 0.457778 + 3.77014i 0.0244693 + 0.201522i
\(351\) −3.54254 0.671120i −0.189087 0.0358217i
\(352\) 0.599499 4.93732i 0.0319534 0.263160i
\(353\) −0.930146 23.0813i −0.0495067 1.22850i −0.812839 0.582489i \(-0.802079\pi\)
0.763332 0.646006i \(-0.223562\pi\)
\(354\) −10.9628 + 4.67079i −0.582664 + 0.248250i
\(355\) −0.291826 + 0.184540i −0.0154885 + 0.00979435i
\(356\) 5.93382 5.25690i 0.314492 0.278615i
\(357\) −0.378329 + 0.655285i −0.0200233 + 0.0346813i
\(358\) 13.4982 4.50637i 0.713403 0.238169i
\(359\) 18.8550 9.89586i 0.995128 0.522284i 0.113152 0.993578i \(-0.463905\pi\)
0.881976 + 0.471294i \(0.156213\pi\)
\(360\) −0.148911 + 0.257922i −0.00784832 + 0.0135937i
\(361\) −12.5895 21.8057i −0.662605 1.14767i
\(362\) 37.1854 + 23.5146i 1.95442 + 1.23590i
\(363\) 10.2524 2.52698i 0.538110 0.132632i
\(364\) −1.84868 1.72603i −0.0968971 0.0904688i
\(365\) −2.70213 0.666014i −0.141436 0.0348608i
\(366\) −11.5746 12.0504i −0.605012 0.629884i
\(367\) −19.7000 + 24.1282i −1.02833 + 1.25948i −0.0631235 + 0.998006i \(0.520106\pi\)
−0.965210 + 0.261475i \(0.915791\pi\)
\(368\) 12.9875 + 9.75946i 0.677019 + 0.508747i
\(369\) −11.5926 2.85731i −0.603485 0.148746i
\(370\) 1.33570 4.61138i 0.0694398 0.239734i
\(371\) 3.66110 0.295554i 0.190075 0.0153444i
\(372\) −2.04463 + 16.8390i −0.106009 + 0.873062i
\(373\) −16.9473 20.7567i −0.877498 1.07474i −0.996644 0.0818628i \(-0.973913\pi\)
0.119146 0.992877i \(-0.461984\pi\)
\(374\) −0.0933697 2.31695i −0.00482803 0.119806i
\(375\) 1.34244 + 4.63464i 0.0693233 + 0.239332i
\(376\) −2.27396 5.99593i −0.117270 0.309216i
\(377\) −10.7638 + 14.7544i −0.554363 + 0.759889i
\(378\) 0.283203 0.746744i 0.0145664 0.0384084i
\(379\) 8.13466 + 0.656697i 0.417849 + 0.0337323i 0.287604 0.957750i \(-0.407141\pi\)
0.130245 + 0.991482i \(0.458423\pi\)
\(380\) 1.10897 5.43209i 0.0568889 0.278660i
\(381\) −1.73569 + 5.99228i −0.0889219 + 0.306994i
\(382\) 3.76389 + 9.92455i 0.192577 + 0.507784i
\(383\) 0.381416 9.46474i 0.0194894 0.483626i −0.959742 0.280882i \(-0.909373\pi\)
0.979232 0.202744i \(-0.0649859\pi\)
\(384\) 4.69621 + 0.763209i 0.239653 + 0.0389473i
\(385\) 0.102244 + 0.0905802i 0.00521083 + 0.00461640i
\(386\) 35.7699 11.9417i 1.82064 0.607819i
\(387\) −4.28419 + 9.02875i −0.217778 + 0.458957i
\(388\) 9.41626 19.8444i 0.478038 1.00744i
\(389\) −2.11342 + 1.10921i −0.107155 + 0.0562391i −0.517449 0.855714i \(-0.673118\pi\)
0.410294 + 0.911953i \(0.365426\pi\)
\(390\) −2.84519 1.90499i −0.144072 0.0964631i
\(391\) 5.77780 + 3.03242i 0.292196 + 0.153356i
\(392\) 3.28629 2.46949i 0.165983 0.124728i
\(393\) 2.78133 + 9.60228i 0.140300 + 0.484371i
\(394\) −12.6554 + 1.02165i −0.637568 + 0.0514698i
\(395\) 1.70313 2.46741i 0.0856939 0.124149i
\(396\) 0.223957 + 1.09701i 0.0112542 + 0.0551269i
\(397\) −17.6541 7.52173i −0.886036 0.377505i −0.0994915 0.995038i \(-0.531722\pi\)
−0.786544 + 0.617534i \(0.788132\pi\)
\(398\) −14.1604 + 3.49022i −0.709797 + 0.174949i
\(399\) 0.111326 2.76253i 0.00557328 0.138300i
\(400\) 17.2171 12.9378i 0.860855 0.646891i
\(401\) −13.1002 + 5.58148i −0.654193 + 0.278726i −0.693451 0.720503i \(-0.743911\pi\)
0.0392582 + 0.999229i \(0.487501\pi\)
\(402\) −0.494735 0.716748i −0.0246751 0.0357481i
\(403\) 35.6329 + 6.75051i 1.77500 + 0.336267i
\(404\) 18.3930 26.6468i 0.915085 1.32573i
\(405\) 0.0989358 0.484619i 0.00491616 0.0240809i
\(406\) −2.80235 2.91755i −0.139078 0.144796i
\(407\) 1.43888 + 3.03237i 0.0713224 + 0.150309i
\(408\) 1.09531 0.0542261
\(409\) −0.253218 0.533646i −0.0125208 0.0263871i 0.897094 0.441840i \(-0.145674\pi\)
−0.909615 + 0.415453i \(0.863623\pi\)
\(410\) −9.06446 6.81150i −0.447662 0.336396i
\(411\) −4.75354 + 12.5341i −0.234475 + 0.618260i
\(412\) −13.0613 5.56491i −0.643486 0.274164i
\(413\) −2.54819 + 0.414121i −0.125388 + 0.0203776i
\(414\) −6.53285 2.18098i −0.321072 0.107190i
\(415\) 3.10809 2.75353i 0.152570 0.135165i
\(416\) −6.09195 + 26.3138i −0.298682 + 1.29014i
\(417\) −5.58977 4.95210i −0.273732 0.242505i
\(418\) 4.23642 + 7.33769i 0.207210 + 0.358898i
\(419\) 17.2167 + 5.74776i 0.841089 + 0.280797i 0.704387 0.709816i \(-0.251222\pi\)
0.136701 + 0.990612i \(0.456350\pi\)
\(420\) 0.240347 0.250227i 0.0117277 0.0122098i
\(421\) −0.434846 0.629983i −0.0211931 0.0307035i 0.812244 0.583318i \(-0.198246\pi\)
−0.833437 + 0.552614i \(0.813630\pi\)
\(422\) −6.09038 7.45936i −0.296475 0.363116i
\(423\) 6.73550 + 8.24948i 0.327491 + 0.401104i
\(424\) −3.02036 4.37575i −0.146682 0.212505i
\(425\) 5.99226 6.23861i 0.290668 0.302617i
\(426\) −1.27133 0.424431i −0.0615960 0.0205638i
\(427\) −1.80994 3.13491i −0.0875893 0.151709i
\(428\) −21.9916 19.4829i −1.06301 0.941741i
\(429\) 2.37205 0.322156i 0.114523 0.0155538i
\(430\) −7.10378 + 6.29340i −0.342574 + 0.303495i
\(431\) 9.76314 + 3.25942i 0.470274 + 0.157001i 0.541921 0.840429i \(-0.317697\pi\)
−0.0716468 + 0.997430i \(0.522825\pi\)
\(432\) −4.47022 + 0.726482i −0.215074 + 0.0349529i
\(433\) 19.0985 + 8.13710i 0.917814 + 0.391044i 0.798626 0.601828i \(-0.205561\pi\)
0.119188 + 0.992872i \(0.461971\pi\)
\(434\) −2.84862 + 7.51118i −0.136738 + 0.360548i
\(435\) −2.00292 1.50510i −0.0960327 0.0721639i
\(436\) 5.13537 + 10.8226i 0.245939 + 0.518306i
\(437\) −23.8427 −1.14055
\(438\) −4.63118 9.76000i −0.221286 0.466351i
\(439\) −17.2706 17.9806i −0.824281 0.858168i 0.167532 0.985867i \(-0.446420\pi\)
−0.991813 + 0.127699i \(0.959241\pi\)
\(440\) 0.0395516 0.193737i 0.00188555 0.00923603i
\(441\) −3.87816 + 5.61849i −0.184675 + 0.267547i
\(442\) −0.835499 + 12.5650i −0.0397407 + 0.597655i
\(443\) 5.83416 + 8.45224i 0.277189 + 0.401578i 0.936709 0.350109i \(-0.113856\pi\)
−0.659519 + 0.751687i \(0.729240\pi\)
\(444\) 7.84320 3.34167i 0.372222 0.158589i
\(445\) 1.85880 1.39680i 0.0881156 0.0662146i
\(446\) 1.74238 43.2368i 0.0825042 2.04732i
\(447\) 3.51886 0.867321i 0.166436 0.0410229i
\(448\) −2.03784 0.868244i −0.0962791 0.0410207i
\(449\) 4.33495 + 21.2340i 0.204579 + 1.00209i 0.944276 + 0.329154i \(0.106764\pi\)
−0.739697 + 0.672940i \(0.765031\pi\)
\(450\) −5.18658 + 7.51407i −0.244498 + 0.354216i
\(451\) 7.90125 0.637855i 0.372055 0.0300354i
\(452\) −6.55275 22.6227i −0.308216 1.06408i
\(453\) 4.14568 3.11527i 0.194781 0.146368i
\(454\) −16.4770 8.64779i −0.773303 0.405861i
\(455\) −0.499720 0.548231i −0.0234273 0.0257015i
\(456\) −3.54377 + 1.85991i −0.165952 + 0.0870985i
\(457\) 7.46723 15.7369i 0.349302 0.736139i −0.650423 0.759572i \(-0.725408\pi\)
0.999725 + 0.0234331i \(0.00745965\pi\)
\(458\) 12.5579 26.4652i 0.586791 1.23664i
\(459\) −1.72545 + 0.576039i −0.0805369 + 0.0268872i
\(460\) −2.23960 1.98412i −0.104422 0.0925099i
\(461\) 12.9220 + 2.10003i 0.601839 + 0.0978083i 0.453694 0.891157i \(-0.350106\pi\)
0.148145 + 0.988966i \(0.452670\pi\)
\(462\) −0.0213506 + 0.529810i −0.000993321 + 0.0246490i
\(463\) 1.62065 + 4.27331i 0.0753181 + 0.198597i 0.967388 0.253301i \(-0.0815162\pi\)
−0.892069 + 0.451898i \(0.850747\pi\)
\(464\) −6.38239 + 22.0346i −0.296295 + 1.02293i
\(465\) −0.995153 + 4.87458i −0.0461491 + 0.226053i
\(466\) 37.6926 + 3.04286i 1.74608 + 0.140958i
\(467\) 8.66325 22.8431i 0.400887 1.05705i −0.570864 0.821045i \(-0.693392\pi\)
0.971751 0.236008i \(-0.0758392\pi\)
\(468\) −0.575016 6.05311i −0.0265801 0.279805i
\(469\) −0.0669069 0.176419i −0.00308947 0.00814627i
\(470\) 2.81384 + 9.71449i 0.129793 + 0.448096i
\(471\) −0.548912 13.6211i −0.0252925 0.627628i
\(472\) 2.36349 + 2.89475i 0.108789 + 0.133242i
\(473\) 0.799765 6.58666i 0.0367732 0.302855i
\(474\) 11.6004 0.936481i 0.532824 0.0430140i
\(475\) −8.79378 + 30.3596i −0.403486 + 1.39300i
\(476\) −1.23894 0.305372i −0.0567868 0.0139967i
\(477\) 7.05923 + 5.30467i 0.323220 + 0.242884i
\(478\) 14.9366 18.2940i 0.683182 0.836746i
\(479\) −8.06476 8.39631i −0.368488 0.383637i 0.510981 0.859592i \(-0.329282\pi\)
−0.879470 + 0.475955i \(0.842103\pi\)
\(480\) −3.59757 0.886722i −0.164206 0.0404731i
\(481\) −6.01627 17.2061i −0.274318 0.784529i
\(482\) 37.4385 9.22776i 1.70528 0.420313i
\(483\) −1.26111 0.797480i −0.0573826 0.0362866i
\(484\) 8.90347 + 15.4213i 0.404703 + 0.700966i
\(485\) 3.22116 5.57921i 0.146265 0.253339i
\(486\) 1.70007 0.892267i 0.0771169 0.0404741i
\(487\) 29.2512 9.76547i 1.32550 0.442516i 0.436201 0.899849i \(-0.356324\pi\)
0.889295 + 0.457333i \(0.151195\pi\)
\(488\) −2.62002 + 4.53800i −0.118603 + 0.205426i
\(489\) 11.3290 10.0367i 0.512317 0.453873i
\(490\) −5.47963 + 3.46511i −0.247544 + 0.156538i
\(491\) −27.8705 + 11.8745i −1.25778 + 0.535889i −0.914972 0.403517i \(-0.867787\pi\)
−0.342806 + 0.939406i \(0.611377\pi\)
\(492\) −0.810741 20.1183i −0.0365510 0.907004i
\(493\) −1.11065 + 9.14700i −0.0500210 + 0.411960i
\(494\) −18.6330 42.0714i −0.838339 1.89288i
\(495\) 0.0395828 + 0.325994i 0.00177912 + 0.0146523i
\(496\) 44.9641 7.30738i 2.01895 0.328111i
\(497\) −0.245419 0.155194i −0.0110086 0.00696139i
\(498\) 15.9099 + 2.58562i 0.712941 + 0.115864i
\(499\) −31.3031 16.4292i −1.40132 0.735470i −0.416515 0.909129i \(-0.636749\pi\)
−0.984806 + 0.173659i \(0.944441\pi\)
\(500\) −6.87738 + 4.34899i −0.307566 + 0.194493i
\(501\) 3.92783 4.08930i 0.175482 0.182696i
\(502\) −5.20534 42.8698i −0.232326 1.91337i
\(503\) 0.514512 + 2.52025i 0.0229409 + 0.112372i 0.989649 0.143510i \(-0.0458391\pi\)
−0.966708 + 0.255883i \(0.917634\pi\)
\(504\) −0.249650 0.0201538i −0.0111203 0.000897724i
\(505\) 6.00602 7.35604i 0.267264 0.327339i
\(506\) 4.57266 0.203279
\(507\) −12.9948 + 0.368036i −0.577119 + 0.0163450i
\(508\) −10.5207 −0.466781
\(509\) −18.3132 + 22.4295i −0.811716 + 0.994172i 0.188211 + 0.982129i \(0.439731\pi\)
−0.999927 + 0.0120436i \(0.996166\pi\)
\(510\) −1.72189 0.139005i −0.0762465 0.00615525i
\(511\) −0.468147 2.29314i −0.0207096 0.101442i
\(512\) 3.43198 + 28.2649i 0.151674 + 1.24914i
\(513\) 4.60435 4.79364i 0.203287 0.211644i
\(514\) 0.983236 0.621761i 0.0433687 0.0274247i
\(515\) −3.68711 1.93514i −0.162473 0.0852726i
\(516\) −16.6349 2.70344i −0.732311 0.119012i
\(517\) −5.97615 3.77909i −0.262831 0.166204i
\(518\) 3.98519 0.647656i 0.175099 0.0284564i
\(519\) 3.08031 + 25.3686i 0.135210 + 1.11356i
\(520\) −0.325590 + 1.02327i −0.0142781 + 0.0448731i
\(521\) 0.646577 5.32504i 0.0283270 0.233294i −0.971668 0.236349i \(-0.924049\pi\)
0.999995 + 0.00305459i \(0.000972309\pi\)
\(522\) −0.391604 9.71756i −0.0171401 0.425326i
\(523\) −0.160485 + 0.0683763i −0.00701752 + 0.00298988i −0.395473 0.918478i \(-0.629419\pi\)
0.388455 + 0.921468i \(0.373009\pi\)
\(524\) −14.2489 + 9.01045i −0.622466 + 0.393624i
\(525\) −1.48058 + 1.31168i −0.0646180 + 0.0572465i
\(526\) −12.7724 + 22.1224i −0.556901 + 0.964581i
\(527\) 17.3555 5.79413i 0.756019 0.252396i
\(528\) 2.66242 1.39735i 0.115867 0.0608117i
\(529\) 5.06623 8.77497i 0.220271 0.381520i
\(530\) 4.19284 + 7.26221i 0.182125 + 0.315450i
\(531\) −5.24560 3.31712i −0.227640 0.143951i
\(532\) 4.52701 1.11581i 0.196271 0.0483764i
\(533\) −43.0338 1.12429i −1.86400 0.0486983i
\(534\) 8.76338 + 2.15998i 0.379229 + 0.0934715i
\(535\) −5.96938 6.21478i −0.258079 0.268688i
\(536\) −0.172738 + 0.211566i −0.00746115 + 0.00913825i
\(537\) 5.92529 + 4.45257i 0.255695 + 0.192142i
\(538\) −39.1804 9.65709i −1.68919 0.416347i
\(539\) 1.26105 4.35366i 0.0543174 0.187525i
\(540\) 0.831409 0.0671183i 0.0357782 0.00288831i
\(541\) −3.51887 + 28.9805i −0.151288 + 1.24597i 0.697247 + 0.716830i \(0.254408\pi\)
−0.848536 + 0.529138i \(0.822515\pi\)
\(542\) 14.6029 + 17.8853i 0.627247 + 0.768238i
\(543\) 0.922690 + 22.8963i 0.0395964 + 0.982575i
\(544\) 3.79123 + 13.0889i 0.162548 + 0.561180i
\(545\) 1.24589 + 3.28514i 0.0533681 + 0.140720i
\(546\) 0.421629 2.84851i 0.0180440 0.121905i
\(547\) 8.28160 21.8368i 0.354096 0.933673i −0.633087 0.774080i \(-0.718213\pi\)
0.987183 0.159593i \(-0.0510182\pi\)
\(548\) −22.5331 1.81906i −0.962564 0.0777062i
\(549\) 1.74072 8.52661i 0.0742921 0.363907i
\(550\) 1.68651 5.82250i 0.0719129 0.248272i
\(551\) −11.9388 31.4801i −0.508611 1.34110i
\(552\) −0.0869714 + 2.15817i −0.00370175 + 0.0918579i
\(553\) 2.48871 + 0.404455i 0.105831 + 0.0171992i
\(554\) 21.1670 + 18.7524i 0.899301 + 0.796711i
\(555\) 2.37180 0.791824i 0.100677 0.0336111i
\(556\) 5.39883 11.3778i 0.228961 0.482526i
\(557\) 2.07839 4.38011i 0.0880640 0.185591i −0.854640 0.519221i \(-0.826222\pi\)
0.942704 + 0.333630i \(0.108274\pi\)
\(558\) −17.1003 + 8.97494i −0.723915 + 0.379940i
\(559\) −8.12701 + 35.1041i −0.343736 + 1.48474i
\(560\) −0.825042 0.433015i −0.0348644 0.0182982i
\(561\) 0.965506 0.725531i 0.0407637 0.0306319i
\(562\) 8.57150 + 29.5922i 0.361567 + 1.24827i
\(563\) −40.4368 + 3.26439i −1.70421 + 0.137578i −0.893852 0.448362i \(-0.852008\pi\)
−0.810355 + 0.585940i \(0.800726\pi\)
\(564\) −10.2024 + 14.7807i −0.429599 + 0.622381i
\(565\) −1.38177 6.76834i −0.0581314 0.284746i
\(566\) −17.3662 7.39905i −0.729957 0.311005i
\(567\) 0.403873 0.0995458i 0.0169611 0.00418053i
\(568\) −0.0169251 + 0.419992i −0.000710161 + 0.0176225i
\(569\) 17.1975 12.9231i 0.720956 0.541763i −0.175726 0.984439i \(-0.556227\pi\)
0.896682 + 0.442676i \(0.145971\pi\)
\(570\) 5.80703 2.47414i 0.243230 0.103631i
\(571\) 3.23171 + 4.68195i 0.135243 + 0.195933i 0.884754 0.466059i \(-0.154327\pi\)
−0.749511 + 0.661992i \(0.769711\pi\)
\(572\) 1.63475 + 3.69111i 0.0683525 + 0.154333i
\(573\) −3.14043 + 4.54970i −0.131193 + 0.190066i
\(574\) 1.90732 9.34269i 0.0796102 0.389957i
\(575\) 11.8166 + 12.3023i 0.492785 + 0.513043i
\(576\) −2.28290 4.81111i −0.0951208 0.200463i
\(577\) −15.7138 −0.654174 −0.327087 0.944994i \(-0.606067\pi\)
−0.327087 + 0.944994i \(0.606067\pi\)
\(578\) −11.2689 23.7487i −0.468725 0.987817i
\(579\) 15.7018 + 11.7992i 0.652546 + 0.490357i
\(580\) 1.49823 3.95051i 0.0622107 0.164036i
\(581\) 3.21261 + 1.36877i 0.133282 + 0.0567860i
\(582\) 24.6839 4.01153i 1.02318 0.166283i
\(583\) −5.56089 1.85650i −0.230309 0.0768883i
\(584\) −2.53591 + 2.24662i −0.104937 + 0.0929658i
\(585\) −0.0252464 1.78318i −0.00104381 0.0737255i
\(586\) −15.0098 13.2975i −0.620050 0.549316i
\(587\) −7.10107 12.2994i −0.293093 0.507651i 0.681447 0.731868i \(-0.261351\pi\)
−0.974539 + 0.224216i \(0.928018\pi\)
\(588\) −10.9204 3.64578i −0.450352 0.150349i
\(589\) −46.3132 + 48.2172i −1.90830 + 1.98675i
\(590\) −3.34816 4.85065i −0.137842 0.199698i
\(591\) −4.18223 5.12230i −0.172034 0.210703i
\(592\) −14.4800 17.7348i −0.595126 0.728897i
\(593\) 22.8797 + 33.1470i 0.939556 + 1.36118i 0.932486 + 0.361207i \(0.117635\pi\)
0.00707066 + 0.999975i \(0.497749\pi\)
\(594\) −0.883042 + 0.919344i −0.0362316 + 0.0377211i
\(595\) −0.354994 0.118514i −0.0145533 0.00485862i
\(596\) 3.05588 + 5.29294i 0.125174 + 0.216807i
\(597\) −5.68564 5.03704i −0.232698 0.206152i
\(598\) −24.6913 2.64394i −1.00970 0.108119i
\(599\) −15.6732 + 13.8852i −0.640389 + 0.567335i −0.919581 0.392900i \(-0.871472\pi\)
0.279192 + 0.960235i \(0.409933\pi\)
\(600\) 2.71599 + 0.906730i 0.110880 + 0.0370171i
\(601\) 29.1163 4.73186i 1.18768 0.193017i 0.465707 0.884939i \(-0.345800\pi\)
0.721972 + 0.691922i \(0.243236\pi\)
\(602\) −7.34267 3.12842i −0.299265 0.127505i
\(603\) 0.160849 0.424125i 0.00655029 0.0172717i
\(604\) 6.99123 + 5.25357i 0.284469 + 0.213765i
\(605\) 2.23895 + 4.71849i 0.0910263 + 0.191834i
\(606\) 36.8635 1.49748
\(607\) −15.6478 32.9771i −0.635125 1.33850i −0.924463 0.381271i \(-0.875486\pi\)
0.289338 0.957227i \(-0.406565\pi\)
\(608\) −34.4919 35.9099i −1.39883 1.45634i
\(609\) 0.421451 2.06440i 0.0170780 0.0836538i
\(610\) 4.69471 6.80147i 0.190083 0.275383i
\(611\) 30.0848 + 23.8617i 1.21710 + 0.965340i
\(612\) −1.74262 2.52462i −0.0704413 0.102052i
\(613\) 12.1072 5.15842i 0.489007 0.208346i −0.133366 0.991067i \(-0.542579\pi\)
0.622374 + 0.782720i \(0.286168\pi\)
\(614\) 32.7361 24.5995i 1.32112 0.992757i
\(615\) 0.237789 5.90067i 0.00958858 0.237938i
\(616\) 0.161457 0.0397955i 0.00650527 0.00160341i
\(617\) 33.2718 + 14.1758i 1.33947 + 0.570696i 0.938464 0.345378i \(-0.112249\pi\)
0.401009 + 0.916074i \(0.368660\pi\)
\(618\) −3.23324 15.8375i −0.130060 0.637076i
\(619\) −20.4513 + 29.6288i −0.822008 + 1.19088i 0.157108 + 0.987581i \(0.449783\pi\)
−0.979116 + 0.203302i \(0.934833\pi\)
\(620\) −8.36280 + 0.675115i −0.335858 + 0.0271133i
\(621\) −0.998004 3.44551i −0.0400485 0.138263i
\(622\) 3.61495 2.71646i 0.144946 0.108920i
\(623\) 1.73140 + 0.908708i 0.0693670 + 0.0364066i
\(624\) −15.1844 + 6.00593i −0.607864 + 0.240430i
\(625\) 18.9401 9.94052i 0.757603 0.397621i
\(626\) −1.42915 + 3.01188i −0.0571204 + 0.120379i
\(627\) −1.89180 + 3.98687i −0.0755510 + 0.159220i
\(628\) 21.8060 7.27993i 0.870156 0.290501i
\(629\) −6.88339 6.09815i −0.274459 0.243149i
\(630\) 0.389905 + 0.0633658i 0.0155342 + 0.00252455i
\(631\) −0.313634 + 7.78274i −0.0124856 + 0.309826i 0.980864 + 0.194692i \(0.0623708\pi\)
−0.993350 + 0.115134i \(0.963270\pi\)
\(632\) −1.29425 3.41266i −0.0514825 0.135748i
\(633\) 1.39542 4.81755i 0.0554630 0.191480i
\(634\) −7.80433 + 38.2281i −0.309950 + 1.51823i
\(635\) −3.07570 0.248296i −0.122055 0.00985333i
\(636\) −5.28047 + 13.9235i −0.209384 + 0.552101i
\(637\) −9.32672 + 22.7796i −0.369538 + 0.902562i
\(638\) 2.28968 + 6.03739i 0.0906493 + 0.239022i
\(639\) −0.194217 0.670514i −0.00768310 0.0265251i
\(640\) 0.0947575 + 2.35138i 0.00374562 + 0.0929466i
\(641\) 5.93002 + 7.26296i 0.234222 + 0.286870i 0.878320 0.478073i \(-0.158665\pi\)
−0.644098 + 0.764943i \(0.722767\pi\)
\(642\) 4.03201 33.2066i 0.159131 1.31056i
\(643\) −38.2449 + 3.08744i −1.50823 + 0.121757i −0.806733 0.590916i \(-0.798767\pi\)
−0.701497 + 0.712672i \(0.747485\pi\)
\(644\) 0.700071 2.41693i 0.0275867 0.0952402i
\(645\) −4.79936 1.18294i −0.188975 0.0465781i
\(646\) −18.5585 13.9458i −0.730175 0.548691i
\(647\) 7.36308 9.01814i 0.289473 0.354540i −0.609312 0.792931i \(-0.708554\pi\)
0.898784 + 0.438391i \(0.144452\pi\)
\(648\) −0.417110 0.434258i −0.0163856 0.0170593i
\(649\) 4.00087 + 0.986125i 0.157048 + 0.0387088i
\(650\) −12.4734 + 30.4650i −0.489246 + 1.19494i
\(651\) −4.06239 + 1.00129i −0.159218 + 0.0392436i
\(652\) 21.5729 + 13.6418i 0.844858 + 0.534256i
\(653\) −2.00524 3.47317i −0.0784710 0.135916i 0.824119 0.566416i \(-0.191670\pi\)
−0.902590 + 0.430500i \(0.858337\pi\)
\(654\) −6.81927 + 11.8113i −0.266655 + 0.461860i
\(655\) −4.37828 + 2.29790i −0.171073 + 0.0897863i
\(656\) −51.2897 + 17.1230i −2.00253 + 0.668541i
\(657\) 2.81329 4.87277i 0.109757 0.190105i
\(658\) −6.36645 + 5.64018i −0.248190 + 0.219877i
\(659\) −0.860334 + 0.544042i −0.0335139 + 0.0211929i −0.551118 0.834428i \(-0.685798\pi\)
0.517604 + 0.855620i \(0.326824\pi\)
\(660\) −0.509476 + 0.217067i −0.0198313 + 0.00844934i
\(661\) −2.02555 50.2635i −0.0787848 1.95503i −0.246389 0.969171i \(-0.579244\pi\)
0.167604 0.985854i \(-0.446397\pi\)
\(662\) −4.24943 + 34.9972i −0.165159 + 1.36021i
\(663\) −5.63303 + 3.35944i −0.218769 + 0.130470i
\(664\) −0.609310 5.01812i −0.0236458 0.194741i
\(665\) 1.34979 0.219362i 0.0523427 0.00850651i
\(666\) 8.20374 + 5.18773i 0.317889 + 0.201021i
\(667\) −17.9348 2.91469i −0.694438 0.112857i
\(668\) 8.46675 + 4.44369i 0.327589 + 0.171932i
\(669\) 19.0484 12.0455i 0.736455 0.465706i
\(670\) 0.298403 0.310670i 0.0115283 0.0120022i
\(671\) 0.696438 + 5.73568i 0.0268857 + 0.221424i
\(672\) −0.623285 3.05305i −0.0240437 0.117774i
\(673\) 12.0987 + 0.976708i 0.466370 + 0.0376493i 0.311419 0.950273i \(-0.399196\pi\)
0.154952 + 0.987922i \(0.450478\pi\)
\(674\) −25.3946 + 31.1027i −0.978162 + 1.19803i
\(675\) −4.75536 −0.183034
\(676\) −6.69308 20.8764i −0.257426 0.802938i
\(677\) −38.5403 −1.48123 −0.740613 0.671932i \(-0.765465\pi\)
−0.740613 + 0.671932i \(0.765465\pi\)
\(678\) 16.9592 20.7712i 0.651314 0.797715i
\(679\) 5.40028 + 0.435955i 0.207244 + 0.0167304i
\(680\) 0.108366 + 0.530810i 0.00415563 + 0.0203556i
\(681\) −1.16823 9.62126i −0.0447668 0.368688i
\(682\) 8.88215 9.24730i 0.340115 0.354097i
\(683\) 19.6156 12.4042i 0.750571 0.474632i −0.103604 0.994619i \(-0.533037\pi\)
0.854175 + 0.519986i \(0.174063\pi\)
\(684\) 9.92506 + 5.20907i 0.379494 + 0.199174i
\(685\) −6.54454 1.06359i −0.250054 0.0406378i
\(686\) −9.33328 5.90201i −0.356346 0.225340i
\(687\) 15.0594 2.44740i 0.574554 0.0933741i
\(688\) 5.45547 + 44.9298i 0.207988 + 1.71293i
\(689\) 28.9541 + 13.2400i 1.10306 + 0.504405i
\(690\) 0.410615 3.38172i 0.0156319 0.128740i
\(691\) −1.04630 25.9637i −0.0398032 0.987707i −0.888514 0.458850i \(-0.848262\pi\)
0.848711 0.528857i \(-0.177379\pi\)
\(692\) −39.6471 + 16.8920i −1.50715 + 0.642139i
\(693\) −0.233414 + 0.147602i −0.00886666 + 0.00560693i
\(694\) 9.76416 8.65029i 0.370642 0.328360i
\(695\) 1.84686 3.19885i 0.0700553 0.121339i
\(696\) −2.89304 + 0.965837i −0.109660 + 0.0366100i
\(697\) −19.2310 + 10.0932i −0.728424 + 0.382307i
\(698\) 0.566695 0.981544i 0.0214497 0.0371520i
\(699\) 9.84773 + 17.0568i 0.372475 + 0.645146i
\(700\) −2.81934 1.78284i −0.106561 0.0673851i
\(701\) −6.85011 + 1.68840i −0.258725 + 0.0637700i −0.366545 0.930400i \(-0.619459\pi\)
0.107819 + 0.994170i \(0.465613\pi\)
\(702\) 5.29980 4.45367i 0.200028 0.168093i
\(703\) 32.6256 + 8.04148i 1.23050 + 0.303290i
\(704\) 2.44918 + 2.54987i 0.0923071 + 0.0961019i
\(705\) −3.33148 + 4.08032i −0.125471 + 0.153674i
\(706\) 35.4569 + 26.6442i 1.33444 + 1.00277i
\(707\) 7.75428 + 1.91126i 0.291630 + 0.0718802i
\(708\) 2.91195 10.0532i 0.109438 0.377822i
\(709\) −0.745219 + 0.0601603i −0.0279873 + 0.00225937i −0.0944523 0.995529i \(-0.530110\pi\)
0.0664650 + 0.997789i \(0.478828\pi\)
\(710\) 0.0799079 0.658101i 0.00299889 0.0246981i
\(711\) 3.83359 + 4.69530i 0.143771 + 0.176087i
\(712\) −0.113974 2.82824i −0.00427136 0.105993i
\(713\) 10.0385 + 34.6569i 0.375945 + 1.29791i
\(714\) −0.515163 1.35837i −0.0192795 0.0508358i
\(715\) 0.390803 + 1.11767i 0.0146152 + 0.0417984i
\(716\) −4.43226 + 11.6869i −0.165641 + 0.436760i
\(717\) 12.2607 + 0.989788i 0.457885 + 0.0369643i
\(718\) −8.17797 + 40.0584i −0.305199 + 1.49496i
\(719\) 5.19809 17.9459i 0.193856 0.669268i −0.803414 0.595421i \(-0.796985\pi\)
0.997270 0.0738470i \(-0.0235276\pi\)
\(720\) −0.794332 2.09448i −0.0296030 0.0780567i
\(721\) 0.141007 3.49906i 0.00525138 0.130312i
\(722\) 47.7176 + 7.75486i 1.77586 + 0.288606i
\(723\) 15.0322 + 13.3174i 0.559054 + 0.495278i
\(724\) −36.6547 + 12.2371i −1.36226 + 0.454790i
\(725\) −10.3261 + 21.7619i −0.383503 + 0.808216i
\(726\) −8.69116 + 18.3162i −0.322559 + 0.679779i
\(727\) −25.0618 + 13.1535i −0.929492 + 0.487835i −0.860311 0.509769i \(-0.829731\pi\)
−0.0691805 + 0.997604i \(0.522038\pi\)
\(728\) −0.894840 + 0.121531i −0.0331650 + 0.00450425i
\(729\) 0.885456 + 0.464723i 0.0327947 + 0.0172120i
\(730\) 4.27170 3.20997i 0.158103 0.118806i
\(731\) 5.05772 + 17.4613i 0.187067 + 0.645829i
\(732\) 14.6282 1.18091i 0.540673 0.0436477i
\(733\) 5.87740 8.51489i 0.217087 0.314505i −0.699277 0.714851i \(-0.746495\pi\)
0.916364 + 0.400346i \(0.131110\pi\)
\(734\) −11.9627 58.5974i −0.441553 2.16287i
\(735\) −3.10652 1.32356i −0.114586 0.0488204i
\(736\) −26.0909 + 6.43084i −0.961725 + 0.237044i
\(737\) −0.0121264 + 0.300914i −0.000446682 + 0.0110843i
\(738\) 18.3263 13.7713i 0.674600 0.506929i
\(739\) 22.8734 9.74545i 0.841412 0.358492i 0.0721253 0.997396i \(-0.477022\pi\)
0.769287 + 0.638903i \(0.220612\pi\)
\(740\) 2.39541 + 3.47035i 0.0880571 + 0.127573i
\(741\) 12.5205 20.4344i 0.459952 0.750676i
\(742\) −4.00609 + 5.80382i −0.147068 + 0.213065i
\(743\) 2.50947 12.2922i 0.0920635 0.450957i −0.907461 0.420135i \(-0.861983\pi\)
0.999525 0.0308213i \(-0.00981227\pi\)
\(744\) 4.19554 + 4.36802i 0.153816 + 0.160139i
\(745\) 0.768461 + 1.61950i 0.0281543 + 0.0593338i
\(746\) 51.4491 1.88369
\(747\) 3.59894 + 7.58460i 0.131678 + 0.277506i
\(748\) 1.62822 + 1.22353i 0.0595336 + 0.0447366i
\(749\) 2.56979 6.77598i 0.0938981 0.247589i
\(750\) −8.52294 3.63128i −0.311214 0.132596i
\(751\) −5.47064 + 0.889065i −0.199626 + 0.0324424i −0.259402 0.965769i \(-0.583526\pi\)
0.0597758 + 0.998212i \(0.480961\pi\)
\(752\) 45.7499 + 15.2736i 1.66833 + 0.556970i
\(753\) 16.8356 14.9150i 0.613522 0.543533i
\(754\) −8.87289 33.9245i −0.323132 1.23546i
\(755\) 1.91988 + 1.70086i 0.0698715 + 0.0619007i
\(756\) 0.350736 + 0.607492i 0.0127561 + 0.0220943i
\(757\) −23.8817 7.97290i −0.867997 0.289780i −0.152421 0.988316i \(-0.548707\pi\)
−0.715575 + 0.698536i \(0.753835\pi\)
\(758\) −10.8545 + 11.3008i −0.394254 + 0.410462i
\(759\) 1.35290 + 1.96001i 0.0491072 + 0.0711440i
\(760\) −1.25196 1.53337i −0.0454132 0.0556211i
\(761\) 31.5985 + 38.7011i 1.14544 + 1.40291i 0.901312 + 0.433171i \(0.142605\pi\)
0.244131 + 0.969742i \(0.421497\pi\)
\(762\) −6.80433 9.85777i −0.246495 0.357109i
\(763\) −2.04682 + 2.13097i −0.0740999 + 0.0771462i
\(764\) −8.84307 2.95225i −0.319931 0.106809i
\(765\) −0.449868 0.779194i −0.0162650 0.0281718i
\(766\) 13.6132 + 12.0602i 0.491864 + 0.435754i
\(767\) −21.0336 7.63819i −0.759480 0.275799i
\(768\) −14.8097 + 13.1202i −0.534398 + 0.473436i
\(769\) 22.8181 + 7.61781i 0.822842 + 0.274705i 0.696751 0.717313i \(-0.254628\pi\)
0.126092 + 0.992019i \(0.459757\pi\)
\(770\) −0.258869 + 0.0420703i −0.00932898 + 0.00151611i
\(771\) 0.557418 + 0.237494i 0.0200749 + 0.00855312i
\(772\) −11.7453 + 30.9699i −0.422724 + 1.11463i
\(773\) 36.3622 + 27.3244i 1.30786 + 0.982791i 0.999503 + 0.0315194i \(0.0100346\pi\)
0.308354 + 0.951272i \(0.400222\pi\)
\(774\) −8.22564 17.3352i −0.295665 0.623100i
\(775\) 47.8321 1.71818
\(776\) −3.36210 7.08549i −0.120693 0.254354i
\(777\) 1.45670 + 1.51658i 0.0522587 + 0.0544071i
\(778\) 0.916654 4.49007i 0.0328636 0.160977i
\(779\) 45.0809 65.3109i 1.61519 2.34001i
\(780\) 2.87657 0.877533i 0.102998 0.0314207i
\(781\) 0.263282 + 0.381429i 0.00942096 + 0.0136486i
\(782\) −11.5259 + 4.91072i −0.412165 + 0.175607i
\(783\) 4.04945 3.04297i 0.144716 0.108747i
\(784\) −1.24496 + 30.8934i −0.0444629 + 1.10334i
\(785\) 6.54675 1.61363i 0.233663 0.0575929i
\(786\) −17.6582 7.52347i −0.629849 0.268353i
\(787\) 2.69493 + 13.2007i 0.0960640 + 0.470553i 0.999155 + 0.0411033i \(0.0130873\pi\)
−0.903091 + 0.429450i \(0.858708\pi\)
\(788\) 6.33491 9.17771i 0.225672 0.326942i
\(789\) −13.2614 + 1.07057i −0.472119 + 0.0381134i
\(790\) 1.60153 + 5.52913i 0.0569799 + 0.196718i
\(791\) 4.64431 3.48997i 0.165133 0.124089i
\(792\) 0.353979 + 0.185783i 0.0125781 + 0.00660150i
\(793\) −0.444197 31.3741i −0.0157739 1.11413i
\(794\) 32.6239 17.1224i 1.15778 0.607650i
\(795\) −1.87233 + 3.94586i −0.0664049 + 0.139945i
\(796\) 5.49143 11.5729i 0.194639 0.410192i
\(797\) −42.0494 + 14.0382i −1.48947 + 0.497257i −0.940852 0.338819i \(-0.889973\pi\)
−0.548614 + 0.836076i \(0.684844\pi\)
\(798\) 3.97337 + 3.52009i 0.140656 + 0.124610i
\(799\) 19.1220 + 3.10763i 0.676488 + 0.109940i
\(800\) −1.43440 + 35.5942i −0.0507136 + 1.25845i
\(801\) 1.66695 + 4.39539i 0.0588988 + 0.155303i
\(802\) 7.60650 26.2607i 0.268595 0.927297i
\(803\) −0.747224 + 3.66015i −0.0263690 + 0.129164i
\(804\) 0.762468 + 0.0615528i 0.0268902 + 0.00217080i
\(805\) 0.261705 0.690059i 0.00922389 0.0243214i
\(806\) −53.3085 + 44.7976i −1.87771 + 1.57793i
\(807\) −7.45280 19.6514i −0.262351 0.691762i
\(808\) −3.21641 11.1043i −0.113153 0.390649i
\(809\) 0.0358769 + 0.890275i 0.00126136 + 0.0313004i 0.999697 0.0246108i \(-0.00783465\pi\)
−0.998436 + 0.0559112i \(0.982194\pi\)
\(810\) 0.600608 + 0.735611i 0.0211032 + 0.0258467i
\(811\) 3.32652 27.3964i 0.116810 0.962016i −0.809986 0.586450i \(-0.800525\pi\)
0.926796 0.375566i \(-0.122552\pi\)
\(812\) 3.54167 0.285913i 0.124288 0.0100336i
\(813\) −3.34579 + 11.5510i −0.117342 + 0.405111i
\(814\) −6.25707 1.54223i −0.219310 0.0540551i
\(815\) 5.98481 + 4.49729i 0.209639 + 0.157533i
\(816\) −5.21027 + 6.38142i −0.182396 + 0.223394i
\(817\) −46.0142 47.9058i −1.60983 1.67601i
\(818\) 1.10114 + 0.271407i 0.0385005 + 0.00948952i
\(819\) 1.34573 0.662056i 0.0470235 0.0231341i
\(820\) 9.66952 2.38332i 0.337674 0.0832293i
\(821\) 22.4383 + 14.1891i 0.783101 + 0.495203i 0.865204 0.501421i \(-0.167189\pi\)
−0.0821025 + 0.996624i \(0.526163\pi\)
\(822\) −12.8690 22.2897i −0.448856 0.777442i
\(823\) −3.82139 + 6.61884i −0.133205 + 0.230718i −0.924910 0.380185i \(-0.875860\pi\)
0.791705 + 0.610903i \(0.209194\pi\)
\(824\) −4.48858 + 2.35579i −0.156367 + 0.0820678i
\(825\) 2.99473 0.999787i 0.104263 0.0348081i
\(826\) 2.47835 4.29264i 0.0862330 0.149360i
\(827\) −33.5643 + 29.7354i −1.16714 + 1.03400i −0.168310 + 0.985734i \(0.553831\pi\)
−0.998835 + 0.0482657i \(0.984631\pi\)
\(828\) 5.11282 3.23315i 0.177683 0.112360i
\(829\) 23.2924 9.92398i 0.808980 0.344674i 0.0524420 0.998624i \(-0.483300\pi\)
0.756538 + 0.653950i \(0.226889\pi\)
\(830\) 0.321022 + 7.96607i 0.0111428 + 0.276506i
\(831\) −1.77534 + 14.6212i −0.0615857 + 0.507204i
\(832\) −11.7507 15.1849i −0.407382 0.526441i
\(833\) 1.49691 + 12.3281i 0.0518648 + 0.427145i
\(834\) 14.1526 2.30002i 0.490064 0.0796431i
\(835\) 2.37036 + 1.49892i 0.0820296 + 0.0518724i
\(836\) −7.34557 1.19377i −0.254052 0.0412874i
\(837\) −8.90643 4.67446i −0.307851 0.161573i
\(838\) −29.4544 + 18.6258i −1.01748 + 0.643418i
\(839\) −2.88026 + 2.99867i −0.0994378 + 0.103526i −0.769061 0.639175i \(-0.779276\pi\)
0.669624 + 0.742701i \(0.266455\pi\)
\(840\) −0.0149324 0.122979i −0.000515216 0.00424319i
\(841\) 0.668541 + 3.27473i 0.0230532 + 0.112922i
\(842\) 1.46497 + 0.118264i 0.0504861 + 0.00407566i
\(843\) −10.1483 + 12.4295i −0.349527 + 0.428093i
\(844\) 8.45821 0.291144
\(845\) −1.46401 6.26111i −0.0503634 0.215389i
\(846\) −20.4478 −0.703011
\(847\) −2.77783 + 3.40223i −0.0954474 + 0.116902i
\(848\) 39.8611 + 3.21792i 1.36884 + 0.110504i
\(849\) −1.96658 9.63296i −0.0674930 0.330602i
\(850\) 2.00194 + 16.4874i 0.0686659 + 0.565514i
\(851\) 12.5622 13.0786i 0.430626 0.448329i
\(852\) 0.994981 0.629188i 0.0340875 0.0215556i
\(853\) −1.90376 0.999169i −0.0651834 0.0342109i 0.431817 0.901961i \(-0.357873\pi\)
−0.497000 + 0.867751i \(0.665565\pi\)
\(854\) 6.86017 + 1.11489i 0.234750 + 0.0381506i
\(855\) 2.77862 + 1.75710i 0.0950269 + 0.0600914i
\(856\) −10.3545 + 1.68278i −0.353911 + 0.0575162i
\(857\) 5.03170 + 41.4398i 0.171880 + 1.41556i 0.782015 + 0.623259i \(0.214192\pi\)
−0.610136 + 0.792297i \(0.708885\pi\)
\(858\) −2.40124 + 3.91899i −0.0819769 + 0.133792i
\(859\) −4.20683 + 34.6464i −0.143535 + 1.18212i 0.725803 + 0.687903i \(0.241468\pi\)
−0.869338 + 0.494217i \(0.835455\pi\)
\(860\) −0.335650 8.32906i −0.0114456 0.284019i
\(861\) 4.56895 1.94665i 0.155709 0.0663416i
\(862\) −16.7029 + 10.5622i −0.568902 + 0.359752i
\(863\) 16.8957 14.9683i 0.575137 0.509527i −0.324663 0.945830i \(-0.605251\pi\)
0.899800 + 0.436303i \(0.143712\pi\)
\(864\) 3.74558 6.48753i 0.127427 0.220710i
\(865\) −11.9894 + 4.00264i −0.407651 + 0.136094i
\(866\) −35.2930 + 18.5232i −1.19930 + 0.629443i
\(867\) 6.84551 11.8568i 0.232486 0.402677i
\(868\) −3.52790 6.11051i −0.119745 0.207404i
\(869\) −3.40140 2.15091i −0.115385 0.0729648i
\(870\) 4.67058 1.15119i 0.158347 0.0390291i
\(871\) 0.239470 1.61786i 0.00811415 0.0548190i
\(872\) 4.15290 + 1.02360i 0.140635 + 0.0346634i
\(873\) 9.02267 + 9.39360i 0.305371 + 0.317925i
\(874\) 28.9521 35.4598i 0.979318 1.19945i
\(875\) −1.60454 1.20573i −0.0542433 0.0407612i
\(876\) 9.21290 + 2.27078i 0.311275 + 0.0767224i
\(877\) −0.432703 + 1.49386i −0.0146113 + 0.0504442i −0.967493 0.252899i \(-0.918616\pi\)
0.952881 + 0.303344i \(0.0981030\pi\)
\(878\) 47.7131 3.85180i 1.61024 0.129992i
\(879\) 1.25891 10.3681i 0.0424621 0.349707i
\(880\) 0.940590 + 1.15201i 0.0317073 + 0.0388344i
\(881\) −0.661051 16.4038i −0.0222714 0.552658i −0.971355 0.237634i \(-0.923628\pi\)
0.949083 0.315025i \(-0.102013\pi\)
\(882\) −3.64681 12.5903i −0.122795 0.423936i
\(883\) −7.16668 18.8970i −0.241178 0.635934i 0.758702 0.651438i \(-0.225834\pi\)
−0.999880 + 0.0155040i \(0.995065\pi\)
\(884\) −8.08457 7.54823i −0.271914 0.253874i
\(885\) 1.08856 2.87030i 0.0365916 0.0964841i
\(886\) −19.6549 1.58671i −0.660319 0.0533065i
\(887\) −2.90249 + 14.2173i −0.0974562 + 0.477372i 0.901545 + 0.432686i \(0.142434\pi\)
−0.999001 + 0.0446863i \(0.985771\pi\)
\(888\) 0.846900 2.92384i 0.0284201 0.0981176i
\(889\) −0.920203 2.42638i −0.0308626 0.0813780i
\(890\) −0.179756 + 4.46061i −0.00602544 + 0.149520i
\(891\) −0.655329 0.106501i −0.0219544 0.00356793i
\(892\) 28.4486 + 25.2033i 0.952530 + 0.843868i
\(893\) −67.1442 + 22.4160i −2.24690 + 0.750124i
\(894\) −2.98301 + 6.28657i −0.0997669 + 0.210254i
\(895\) −1.57158 + 3.31203i −0.0525320 + 0.110709i
\(896\) −1.75238 + 0.919718i −0.0585428 + 0.0307256i
\(897\) −6.17207 11.3659i −0.206079 0.379496i
\(898\) −36.8439 19.3372i −1.22950 0.645290i
\(899\) −40.7318 + 30.6079i −1.35848 + 1.02083i
\(900\) −2.23113 7.70276i −0.0743711 0.256759i
\(901\) 16.0106 1.29251i 0.533390 0.0430597i
\(902\) −8.64580 + 12.5256i −0.287874 + 0.417057i
\(903\) −0.831497 4.07294i −0.0276705 0.135539i
\(904\) −7.73660 3.29626i −0.257316 0.109632i
\(905\) −11.0047 + 2.71242i −0.365809 + 0.0901638i
\(906\) −0.400910 + 9.94847i −0.0133193 + 0.330516i
\(907\) −11.9100 + 8.94977i −0.395464 + 0.297172i −0.779809 0.626017i \(-0.784684\pi\)
0.384345 + 0.923190i \(0.374427\pi\)
\(908\) 15.0365 6.40645i 0.499003 0.212605i
\(909\) 10.9067 + 15.8011i 0.361753 + 0.524090i
\(910\) 1.42216 0.0774902i 0.0471441 0.00256878i
\(911\) 25.7952 37.3708i 0.854632 1.23815i −0.114947 0.993372i \(-0.536670\pi\)
0.969579 0.244777i \(-0.0787147\pi\)
\(912\) 6.02121 29.4938i 0.199382 0.976638i
\(913\) −3.86108 4.01981i −0.127783 0.133036i
\(914\) 14.3371 + 30.2147i 0.474228 + 0.999414i
\(915\) 4.30438 0.142298
\(916\) 11.0300 + 23.2451i 0.364440 + 0.768041i
\(917\) −3.32436 2.49809i −0.109780 0.0824943i
\(918\) 1.23849 3.26563i 0.0408763 0.107782i
\(919\) −8.07998 3.44256i −0.266534 0.113560i 0.254565 0.967056i \(-0.418068\pi\)
−0.521099 + 0.853496i \(0.674478\pi\)
\(920\) −1.05450 + 0.171372i −0.0347657 + 0.00564998i
\(921\) 20.2298 + 6.75371i 0.666596 + 0.222542i
\(922\) −18.8144 + 16.6681i −0.619619 + 0.548934i
\(923\) −1.20112 2.21186i −0.0395352 0.0728044i
\(924\) −0.348601 0.308833i −0.0114681 0.0101599i
\(925\) −12.0202 20.8195i −0.395220 0.684542i
\(926\) −8.32338 2.77875i −0.273523 0.0913155i
\(927\) 5.83192 6.07168i 0.191546 0.199420i
\(928\) −21.5554 31.2284i −0.707590 1.02512i
\(929\) −23.4371 28.7053i −0.768947 0.941789i 0.230564 0.973057i \(-0.425943\pi\)
−0.999511 + 0.0312684i \(0.990045\pi\)
\(930\) −6.04127 7.39921i −0.198101 0.242630i
\(931\) −25.7771 37.3446i −0.844811 1.22392i
\(932\) −23.0083 + 23.9542i −0.753662 + 0.784645i
\(933\) 2.23392 + 0.745793i 0.0731353 + 0.0244162i
\(934\) 23.4534 + 40.6226i 0.767420 + 1.32921i
\(935\) 0.447129 + 0.396122i 0.0146227 + 0.0129546i
\(936\) −1.80399 1.20786i −0.0589652 0.0394801i
\(937\) −28.8912 + 25.5954i −0.943835 + 0.836165i −0.986640 0.162918i \(-0.947909\pi\)
0.0428044 + 0.999083i \(0.486371\pi\)
\(938\) 0.343622 + 0.114718i 0.0112197 + 0.00374567i
\(939\) −1.71384 + 0.278527i −0.0559292 + 0.00908938i
\(940\) −8.17241 3.48194i −0.266555 0.113568i
\(941\) 7.74099 20.4113i 0.252349 0.665390i −0.747650 0.664093i \(-0.768818\pi\)
0.999999 0.00129710i \(-0.000412881\pi\)
\(942\) 20.9244 + 15.7237i 0.681754 + 0.512305i
\(943\) −18.3603 38.6935i −0.597894 1.26003i
\(944\) −28.1080 −0.914839
\(945\) 0.0881993 + 0.185876i 0.00286912 + 0.00604655i
\(946\) 8.82479 + 9.18758i 0.286919 + 0.298714i
\(947\) 10.1850 49.8893i 0.330967 1.62119i −0.384906 0.922956i \(-0.625766\pi\)
0.715874 0.698230i \(-0.246029\pi\)
\(948\) −5.80683 + 8.41264i −0.188597 + 0.273230i
\(949\) 6.15117 19.3319i 0.199675 0.627541i
\(950\) −34.4738 49.9440i −1.11848 1.62040i
\(951\) −18.6951 + 7.96523i −0.606229 + 0.258290i
\(952\) −0.364231 + 0.273702i −0.0118048 + 0.00887074i
\(953\) 0.877332 21.7708i 0.0284196 0.705224i −0.920693 0.390287i \(-0.872376\pi\)
0.949113 0.314937i \(-0.101983\pi\)
\(954\) −16.4613 + 4.05734i −0.532954 + 0.131361i
\(955\) −2.51557 1.07179i −0.0814020 0.0346822i
\(956\) 4.14926 + 20.3244i 0.134197 + 0.657339i
\(957\) −1.91041 + 2.76771i −0.0617549 + 0.0894674i
\(958\) 22.2803 1.79865i 0.719844 0.0581118i
\(959\) −1.55135 5.35587i −0.0500956 0.172950i
\(960\) 2.10570 1.58233i 0.0679611 0.0510694i
\(961\) 62.1369 + 32.6120i 2.00442 + 1.05200i
\(962\) 32.8951 + 11.9456i 1.06058 + 0.385141i
\(963\) 15.4265 8.09647i 0.497113 0.260905i
\(964\) −14.5187 + 30.5976i −0.467617 + 0.985481i
\(965\) −4.16463 + 8.77677i −0.134064 + 0.282534i
\(966\) 2.71740 0.907203i 0.0874311 0.0291888i
\(967\) 28.9473 + 25.6451i 0.930883 + 0.824690i 0.984771 0.173857i \(-0.0556230\pi\)
−0.0538883 + 0.998547i \(0.517161\pi\)
\(968\) 6.27568 + 1.01990i 0.201708 + 0.0327808i
\(969\) 0.486848 12.0810i 0.0156398 0.388098i
\(970\) 4.38619 + 11.5654i 0.140832 + 0.371344i
\(971\) 0.122670 0.423508i 0.00393668 0.0135910i −0.958526 0.285006i \(-0.908004\pi\)
0.962462 + 0.271415i \(0.0874916\pi\)
\(972\) −0.337321 + 1.65231i −0.0108196 + 0.0529978i
\(973\) 3.09626 + 0.249956i 0.0992614 + 0.00801321i
\(974\) −20.9959 + 55.3616i −0.672752 + 1.77390i
\(975\) −16.7489 + 3.66705i −0.536395 + 0.117440i
\(976\) −13.9758 36.8512i −0.447355 1.17958i
\(977\) −10.7777 37.2090i −0.344810 1.19042i −0.926274 0.376850i \(-0.877007\pi\)
0.581464 0.813572i \(-0.302480\pi\)
\(978\) 1.17013 + 29.0365i 0.0374166 + 0.928483i
\(979\) −1.97388 2.41757i −0.0630856 0.0772658i
\(980\) 0.686393 5.65296i 0.0219260 0.180577i
\(981\) −7.08039 + 0.571588i −0.226059 + 0.0182494i
\(982\) 16.1827 55.8692i 0.516411 1.78286i
\(983\) −44.8981 11.0664i −1.43203 0.352963i −0.554377 0.832266i \(-0.687043\pi\)
−0.877650 + 0.479303i \(0.840890\pi\)
\(984\) −5.74731 4.31882i −0.183217 0.137679i
\(985\) 2.06859 2.53357i 0.0659109 0.0807262i
\(986\) −12.2551 12.7589i −0.390283 0.406327i
\(987\) −4.30122 1.06016i −0.136909 0.0337451i
\(988\) 38.9742 + 10.6934i 1.23993 + 0.340201i
\(989\) −34.8068 + 8.57911i −1.10679 + 0.272800i
\(990\) −0.532896 0.336983i −0.0169366 0.0107100i
\(991\) 13.0225 + 22.5557i 0.413675 + 0.716505i 0.995288 0.0969598i \(-0.0309118\pi\)
−0.581614 + 0.813465i \(0.697578\pi\)
\(992\) −37.6752 + 65.2554i −1.19619 + 2.07186i
\(993\) −16.2584 + 8.53307i −0.515945 + 0.270789i
\(994\) 0.528821 0.176547i 0.0167732 0.00559972i
\(995\) 1.87853 3.25372i 0.0595535 0.103150i
\(996\) −10.5970 + 9.38816i −0.335780 + 0.297475i
\(997\) −32.0554 + 20.2706i −1.01521 + 0.641977i −0.934943 0.354797i \(-0.884550\pi\)
−0.0802619 + 0.996774i \(0.525576\pi\)
\(998\) 62.4453 26.6054i 1.97667 0.842181i
\(999\) 0.203561 + 5.05132i 0.00644039 + 0.159817i
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 507.2.q.b.55.3 384
169.126 even 39 inner 507.2.q.b.295.3 yes 384
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.q.b.55.3 384 1.1 even 1 trivial
507.2.q.b.295.3 yes 384 169.126 even 39 inner