Properties

Label 507.2.t.b.205.2
Level $507$
Weight $2$
Character 507.205
Analytic conductor $4.048$
Analytic rank $0$
Dimension $360$
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(4,507)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.t (of order \(78\), 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: \(360\)
Relative dimension: \(15\) over \(\Q(\zeta_{78})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label 205.2
Character \(\chi\) \(=\) 507.205
Dual form 507.2.t.b.277.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.700274 + 2.09758i) q^{2} +(0.632445 - 0.774605i) q^{3} +(-2.31055 - 1.73627i) q^{4} +(-0.365976 - 1.48482i) q^{5} +(1.18191 + 1.86904i) q^{6} +(-0.0438574 - 0.543271i) q^{7} +(1.62011 - 1.11828i) q^{8} +(-0.200026 - 0.979791i) q^{9} +O(q^{10})\) \(q+(-0.700274 + 2.09758i) q^{2} +(0.632445 - 0.774605i) q^{3} +(-2.31055 - 1.73627i) q^{4} +(-0.365976 - 1.48482i) q^{5} +(1.18191 + 1.86904i) q^{6} +(-0.0438574 - 0.543271i) q^{7} +(1.62011 - 1.11828i) q^{8} +(-0.200026 - 0.979791i) q^{9} +(3.37081 + 0.272120i) q^{10} +(-2.12796 - 0.434426i) q^{11} +(-2.80622 + 0.691672i) q^{12} +(-3.52629 - 0.751835i) q^{13} +(1.17026 + 0.288444i) q^{14} +(-1.38161 - 0.655582i) q^{15} +(-0.397050 - 1.37077i) q^{16} +(-8.02433 + 0.647791i) q^{17} +(2.19526 + 0.266553i) q^{18} +(0.698122 + 0.403061i) q^{19} +(-1.73244 + 4.06619i) q^{20} +(-0.448558 - 0.309617i) q^{21} +(2.40139 - 4.15934i) q^{22} +(-0.423373 - 0.733304i) q^{23} +(0.158405 - 1.96220i) q^{24} +(2.35652 - 1.23680i) q^{25} +(4.04640 - 6.87018i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(-0.841930 + 1.33141i) q^{28} +(-6.60079 - 2.20367i) q^{29} +(2.34264 - 2.43894i) q^{30} +(1.68091 - 3.20270i) q^{31} +(7.08732 + 0.285609i) q^{32} +(-1.68233 + 1.37358i) q^{33} +(4.26044 - 17.2853i) q^{34} +(-0.790610 + 0.263944i) q^{35} +(-1.23901 + 2.61116i) q^{36} +(-6.63211 + 0.267265i) q^{37} +(-1.33433 + 1.18211i) q^{38} +(-2.81256 + 2.25599i) q^{39} +(-2.25338 - 1.99632i) q^{40} +(7.85340 + 6.41210i) q^{41} +(0.963559 - 0.724067i) q^{42} +(0.260181 - 6.45631i) q^{43} +(4.16248 + 4.69847i) q^{44} +(-1.38161 + 0.655582i) q^{45} +(1.83464 - 0.374544i) q^{46} +(1.35344 - 0.164337i) q^{47} +(-1.31292 - 0.559383i) q^{48} +(6.61613 - 1.07523i) q^{49} +(0.944068 + 5.80908i) q^{50} +(-4.57317 + 6.62538i) q^{51} +(6.84231 + 7.85975i) q^{52} +(0.922012 + 1.33577i) q^{53} +(1.59485 - 1.53188i) q^{54} +(0.133736 + 3.31863i) q^{55} +(-0.678585 - 0.831116i) q^{56} +(0.753737 - 0.285855i) q^{57} +(9.24471 - 12.3025i) q^{58} +(-8.50884 - 2.46462i) q^{59} +(2.05402 + 3.91361i) q^{60} +(-0.298531 - 0.629140i) q^{61} +(5.54081 + 5.76859i) q^{62} +(-0.523519 + 0.151639i) q^{63} +(-4.55003 + 11.9974i) q^{64} +(0.174197 + 5.51107i) q^{65} +(-1.70309 - 4.49068i) q^{66} +(3.90721 + 5.19955i) q^{67} +(19.6654 + 12.4356i) q^{68} +(-0.835781 - 0.135828i) q^{69} -1.84320i q^{70} +(-1.74319 + 10.7263i) q^{71} +(-1.41975 - 1.36369i) q^{72} +(2.71204 - 3.06126i) q^{73} +(4.08368 - 14.0985i) q^{74} +(0.532342 - 2.60758i) q^{75} +(-0.913227 - 2.14342i) q^{76} +(-0.142684 + 1.17511i) q^{77} +(-2.76255 - 7.47937i) q^{78} +(-1.46207 - 12.0412i) q^{79} +(-1.89004 + 1.09122i) q^{80} +(-0.919979 + 0.391967i) q^{81} +(-18.9494 + 11.9829i) q^{82} +(3.95130 + 1.49853i) q^{83} +(0.498839 + 1.49420i) q^{84} +(3.89856 + 11.6776i) q^{85} +(13.3604 + 5.06693i) q^{86} +(-5.88161 + 3.71930i) q^{87} +(-3.93335 + 1.67584i) q^{88} +(13.9328 - 8.04412i) q^{89} +(-0.407628 - 3.35712i) q^{90} +(-0.253796 + 1.94871i) q^{91} +(-0.294986 + 2.42943i) q^{92} +(-1.41774 - 3.32757i) q^{93} +(-0.603067 + 2.95402i) q^{94} +(0.342978 - 1.18410i) q^{95} +(4.70358 - 5.30924i) q^{96} +(-1.71263 - 1.64501i) q^{97} +(-2.37773 + 14.6308i) q^{98} +2.17185i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{47}{78}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.700274 + 2.09758i −0.495168 + 1.48321i 0.343807 + 0.939040i \(0.388283\pi\)
−0.838975 + 0.544170i \(0.816845\pi\)
\(3\) 0.632445 0.774605i 0.365143 0.447218i
\(4\) −2.31055 1.73627i −1.15528 0.868135i
\(5\) −0.365976 1.48482i −0.163669 0.664032i −0.994245 0.107127i \(-0.965835\pi\)
0.830576 0.556905i \(-0.188011\pi\)
\(6\) 1.18191 + 1.86904i 0.482512 + 0.763031i
\(7\) −0.0438574 0.543271i −0.0165765 0.205337i −0.999744 0.0226300i \(-0.992796\pi\)
0.983167 0.182707i \(-0.0584860\pi\)
\(8\) 1.62011 1.11828i 0.572797 0.395373i
\(9\) −0.200026 0.979791i −0.0666752 0.326597i
\(10\) 3.37081 + 0.272120i 1.06594 + 0.0860518i
\(11\) −2.12796 0.434426i −0.641603 0.130984i −0.131802 0.991276i \(-0.542076\pi\)
−0.509802 + 0.860292i \(0.670281\pi\)
\(12\) −2.80622 + 0.691672i −0.810087 + 0.199668i
\(13\) −3.52629 0.751835i −0.978018 0.208521i
\(14\) 1.17026 + 0.288444i 0.312766 + 0.0770900i
\(15\) −1.38161 0.655582i −0.356730 0.169271i
\(16\) −0.397050 1.37077i −0.0992624 0.342694i
\(17\) −8.02433 + 0.647791i −1.94619 + 0.157112i −0.990523 0.137348i \(-0.956142\pi\)
−0.955664 + 0.294461i \(0.904860\pi\)
\(18\) 2.19526 + 0.266553i 0.517427 + 0.0628270i
\(19\) 0.698122 + 0.403061i 0.160160 + 0.0924685i 0.577938 0.816081i \(-0.303858\pi\)
−0.417778 + 0.908549i \(0.637191\pi\)
\(20\) −1.73244 + 4.06619i −0.387386 + 0.909229i
\(21\) −0.448558 0.309617i −0.0978834 0.0675640i
\(22\) 2.40139 4.15934i 0.511979 0.886773i
\(23\) −0.423373 0.733304i −0.0882794 0.152904i 0.818505 0.574500i \(-0.194803\pi\)
−0.906784 + 0.421596i \(0.861470\pi\)
\(24\) 0.158405 1.96220i 0.0323344 0.400533i
\(25\) 2.35652 1.23680i 0.471305 0.247360i
\(26\) 4.04640 6.87018i 0.793564 1.34735i
\(27\) −0.885456 0.464723i −0.170406 0.0894360i
\(28\) −0.841930 + 1.33141i −0.159110 + 0.251612i
\(29\) −6.60079 2.20367i −1.22574 0.409210i −0.371175 0.928563i \(-0.621045\pi\)
−0.854560 + 0.519352i \(0.826173\pi\)
\(30\) 2.34264 2.43894i 0.427705 0.445288i
\(31\) 1.68091 3.20270i 0.301900 0.575222i −0.686494 0.727135i \(-0.740851\pi\)
0.988394 + 0.151914i \(0.0485436\pi\)
\(32\) 7.08732 + 0.285609i 1.25287 + 0.0504891i
\(33\) −1.68233 + 1.37358i −0.292855 + 0.239109i
\(34\) 4.26044 17.2853i 0.730659 2.96440i
\(35\) −0.790610 + 0.263944i −0.133637 + 0.0446148i
\(36\) −1.23901 + 2.61116i −0.206502 + 0.435193i
\(37\) −6.63211 + 0.267265i −1.09031 + 0.0439381i −0.578901 0.815398i \(-0.696518\pi\)
−0.511411 + 0.859336i \(0.670877\pi\)
\(38\) −1.33433 + 1.18211i −0.216456 + 0.191764i
\(39\) −2.81256 + 2.25599i −0.450370 + 0.361248i
\(40\) −2.25338 1.99632i −0.356290 0.315645i
\(41\) 7.85340 + 6.41210i 1.22649 + 1.00140i 0.999622 + 0.0274772i \(0.00874736\pi\)
0.226872 + 0.973925i \(0.427150\pi\)
\(42\) 0.963559 0.724067i 0.148680 0.111726i
\(43\) 0.260181 6.45631i 0.0396772 0.984578i −0.849661 0.527329i \(-0.823194\pi\)
0.889338 0.457250i \(-0.151165\pi\)
\(44\) 4.16248 + 4.69847i 0.627518 + 0.708321i
\(45\) −1.38161 + 0.655582i −0.205958 + 0.0977284i
\(46\) 1.83464 0.374544i 0.270502 0.0552235i
\(47\) 1.35344 0.164337i 0.197419 0.0239710i −0.0212297 0.999775i \(-0.506758\pi\)
0.218649 + 0.975804i \(0.429835\pi\)
\(48\) −1.31292 0.559383i −0.189504 0.0807400i
\(49\) 6.61613 1.07523i 0.945162 0.153604i
\(50\) 0.944068 + 5.80908i 0.133511 + 0.821528i
\(51\) −4.57317 + 6.62538i −0.640372 + 0.927739i
\(52\) 6.84231 + 7.85975i 0.948857 + 1.08995i
\(53\) 0.922012 + 1.33577i 0.126648 + 0.183482i 0.881179 0.472783i \(-0.156751\pi\)
−0.754530 + 0.656265i \(0.772135\pi\)
\(54\) 1.59485 1.53188i 0.217032 0.208462i
\(55\) 0.133736 + 3.31863i 0.0180330 + 0.447484i
\(56\) −0.678585 0.831116i −0.0906798 0.111063i
\(57\) 0.753737 0.285855i 0.0998349 0.0378624i
\(58\) 9.24471 12.3025i 1.21389 1.61539i
\(59\) −8.50884 2.46462i −1.10776 0.320866i −0.326576 0.945171i \(-0.605895\pi\)
−0.781180 + 0.624305i \(0.785382\pi\)
\(60\) 2.05402 + 3.91361i 0.265173 + 0.505244i
\(61\) −0.298531 0.629140i −0.0382229 0.0805531i 0.883441 0.468543i \(-0.155221\pi\)
−0.921664 + 0.387990i \(0.873170\pi\)
\(62\) 5.54081 + 5.76859i 0.703683 + 0.732612i
\(63\) −0.523519 + 0.151639i −0.0659572 + 0.0191047i
\(64\) −4.55003 + 11.9974i −0.568753 + 1.49968i
\(65\) 0.174197 + 5.51107i 0.0216065 + 0.683564i
\(66\) −1.70309 4.49068i −0.209636 0.552765i
\(67\) 3.90721 + 5.19955i 0.477341 + 0.635226i 0.972313 0.233684i \(-0.0750780\pi\)
−0.494972 + 0.868909i \(0.664822\pi\)
\(68\) 19.6654 + 12.4356i 2.38478 + 1.50804i
\(69\) −0.835781 0.135828i −0.100616 0.0163517i
\(70\) 1.84320i 0.220304i
\(71\) −1.74319 + 10.7263i −0.206878 + 1.27297i 0.650983 + 0.759092i \(0.274357\pi\)
−0.857862 + 0.513881i \(0.828207\pi\)
\(72\) −1.41975 1.36369i −0.167319 0.160712i
\(73\) 2.71204 3.06126i 0.317420 0.358293i −0.568046 0.822996i \(-0.692301\pi\)
0.885466 + 0.464703i \(0.153839\pi\)
\(74\) 4.08368 14.0985i 0.474718 1.63892i
\(75\) 0.532342 2.60758i 0.0614695 0.301098i
\(76\) −0.913227 2.14342i −0.104754 0.245867i
\(77\) −0.142684 + 1.17511i −0.0162604 + 0.133916i
\(78\) −2.76255 7.47937i −0.312797 0.846872i
\(79\) −1.46207 12.0412i −0.164495 1.35474i −0.807948 0.589254i \(-0.799422\pi\)
0.643453 0.765486i \(-0.277501\pi\)
\(80\) −1.89004 + 1.09122i −0.211313 + 0.122002i
\(81\) −0.919979 + 0.391967i −0.102220 + 0.0435518i
\(82\) −18.9494 + 11.9829i −2.09261 + 1.32329i
\(83\) 3.95130 + 1.49853i 0.433711 + 0.164485i 0.561791 0.827279i \(-0.310112\pi\)
−0.128080 + 0.991764i \(0.540882\pi\)
\(84\) 0.498839 + 1.49420i 0.0544278 + 0.163031i
\(85\) 3.89856 + 11.6776i 0.422859 + 1.26662i
\(86\) 13.3604 + 5.06693i 1.44069 + 0.546382i
\(87\) −5.88161 + 3.71930i −0.630574 + 0.398751i
\(88\) −3.93335 + 1.67584i −0.419296 + 0.178645i
\(89\) 13.9328 8.04412i 1.47688 0.852675i 0.477217 0.878785i \(-0.341645\pi\)
0.999659 + 0.0261104i \(0.00831215\pi\)
\(90\) −0.407628 3.35712i −0.0429678 0.353871i
\(91\) −0.253796 + 1.94871i −0.0266051 + 0.204280i
\(92\) −0.294986 + 2.42943i −0.0307544 + 0.253285i
\(93\) −1.41774 3.32757i −0.147013 0.345053i
\(94\) −0.603067 + 2.95402i −0.0622017 + 0.304684i
\(95\) 0.342978 1.18410i 0.0351888 0.121486i
\(96\) 4.70358 5.30924i 0.480057 0.541872i
\(97\) −1.71263 1.64501i −0.173892 0.167025i 0.600726 0.799455i \(-0.294878\pi\)
−0.774618 + 0.632430i \(0.782058\pi\)
\(98\) −2.37773 + 14.6308i −0.240187 + 1.47793i
\(99\) 2.17185i 0.218279i
\(100\) −7.59229 1.23387i −0.759229 0.123387i
\(101\) 4.89095 + 3.09285i 0.486667 + 0.307750i 0.755170 0.655529i \(-0.227554\pi\)
−0.268502 + 0.963279i \(0.586529\pi\)
\(102\) −10.6948 14.2321i −1.05894 1.40919i
\(103\) −2.59924 6.85363i −0.256111 0.675309i −0.999976 0.00697862i \(-0.997779\pi\)
0.743865 0.668330i \(-0.232991\pi\)
\(104\) −6.55376 + 2.72534i −0.642649 + 0.267242i
\(105\) −0.295565 + 0.779341i −0.0288442 + 0.0760559i
\(106\) −3.44753 + 0.998589i −0.334854 + 0.0969916i
\(107\) −8.68817 9.04534i −0.839917 0.874446i 0.153600 0.988133i \(-0.450913\pi\)
−0.993517 + 0.113687i \(0.963734\pi\)
\(108\) 1.23901 + 2.61116i 0.119224 + 0.251259i
\(109\) 6.12594 + 11.6720i 0.586758 + 1.11797i 0.980086 + 0.198576i \(0.0636316\pi\)
−0.393327 + 0.919399i \(0.628676\pi\)
\(110\) −7.05472 2.04343i −0.672642 0.194833i
\(111\) −3.98742 + 5.30629i −0.378469 + 0.503651i
\(112\) −0.727288 + 0.275824i −0.0687223 + 0.0260629i
\(113\) −10.2217 12.5193i −0.961573 1.17771i −0.984037 0.177965i \(-0.943049\pi\)
0.0224643 0.999748i \(-0.492849\pi\)
\(114\) 0.0717798 + 1.78120i 0.00672279 + 0.166824i
\(115\) −0.933881 + 0.897005i −0.0870849 + 0.0836461i
\(116\) 11.4253 + 16.5524i 1.06081 + 1.53685i
\(117\) −0.0312913 + 3.60542i −0.00289288 + 0.333321i
\(118\) 11.1282 16.1220i 1.02444 1.48415i
\(119\) 0.703852 + 4.33098i 0.0645220 + 0.397020i
\(120\) −2.97149 + 0.482915i −0.271259 + 0.0440839i
\(121\) −5.78029 2.46275i −0.525481 0.223887i
\(122\) 1.52872 0.185620i 0.138404 0.0168053i
\(123\) 9.93369 2.02798i 0.895691 0.182857i
\(124\) −9.44457 + 4.48150i −0.848147 + 0.402451i
\(125\) −7.76929 8.76971i −0.694906 0.784387i
\(126\) 0.0485320 1.20431i 0.00432358 0.107288i
\(127\) −16.7817 + 12.6107i −1.48914 + 1.11902i −0.525840 + 0.850584i \(0.676249\pi\)
−0.963299 + 0.268431i \(0.913495\pi\)
\(128\) −10.9906 8.97354i −0.971441 0.793157i
\(129\) −4.83654 4.28480i −0.425834 0.377256i
\(130\) −11.6819 3.49387i −1.02457 0.306432i
\(131\) −12.0404 + 10.6669i −1.05198 + 0.931971i −0.997782 0.0665596i \(-0.978798\pi\)
−0.0541951 + 0.998530i \(0.517259\pi\)
\(132\) 6.27200 0.252753i 0.545908 0.0219993i
\(133\) 0.188354 0.396947i 0.0163323 0.0344196i
\(134\) −13.6426 + 4.55455i −1.17854 + 0.393454i
\(135\) −0.365976 + 1.48482i −0.0314982 + 0.127793i
\(136\) −12.2759 + 10.0230i −1.05265 + 0.859463i
\(137\) −9.78185 0.394195i −0.835720 0.0336784i −0.381284 0.924458i \(-0.624518\pi\)
−0.454436 + 0.890779i \(0.650159\pi\)
\(138\) 0.870184 1.65800i 0.0740750 0.141138i
\(139\) −8.73854 + 9.09778i −0.741193 + 0.771664i −0.979913 0.199425i \(-0.936093\pi\)
0.238720 + 0.971088i \(0.423272\pi\)
\(140\) 2.28503 + 0.762854i 0.193120 + 0.0644729i
\(141\) 0.728679 1.15231i 0.0613659 0.0970424i
\(142\) −21.2784 11.1678i −1.78565 0.937179i
\(143\) 7.17719 + 3.13179i 0.600187 + 0.261893i
\(144\) −1.26365 + 0.663216i −0.105304 + 0.0552680i
\(145\) −0.856324 + 10.6075i −0.0711138 + 0.880903i
\(146\) 4.52205 + 7.83242i 0.374248 + 0.648216i
\(147\) 3.35147 5.80491i 0.276424 0.478781i
\(148\) 15.7879 + 10.8976i 1.29776 + 0.895777i
\(149\) 4.11158 9.65024i 0.336834 0.790578i −0.662311 0.749229i \(-0.730424\pi\)
0.999145 0.0413491i \(-0.0131656\pi\)
\(150\) 5.09681 + 2.94265i 0.416153 + 0.240266i
\(151\) 5.81795 + 0.706427i 0.473458 + 0.0574882i 0.353788 0.935326i \(-0.384893\pi\)
0.119670 + 0.992814i \(0.461816\pi\)
\(152\) 1.58177 0.127694i 0.128299 0.0103573i
\(153\) 2.23977 + 7.73259i 0.181075 + 0.625143i
\(154\) −2.36497 1.12219i −0.190574 0.0904287i
\(155\) −5.37061 1.32374i −0.431378 0.106325i
\(156\) 10.4156 0.329222i 0.833914 0.0263589i
\(157\) 8.69323 2.14269i 0.693795 0.171005i 0.123377 0.992360i \(-0.460627\pi\)
0.570418 + 0.821355i \(0.306781\pi\)
\(158\) 26.2812 + 5.36534i 2.09082 + 0.426843i
\(159\) 1.61781 + 0.130603i 0.128301 + 0.0103575i
\(160\) −2.16971 10.6279i −0.171531 0.840212i
\(161\) −0.379815 + 0.262167i −0.0299336 + 0.0206617i
\(162\) −0.177942 2.20421i −0.0139805 0.173179i
\(163\) 5.55945 + 8.79156i 0.435450 + 0.688608i 0.989606 0.143804i \(-0.0459335\pi\)
−0.554157 + 0.832412i \(0.686959\pi\)
\(164\) −7.01257 28.4511i −0.547590 2.22166i
\(165\) 2.65521 + 1.99526i 0.206708 + 0.155331i
\(166\) −5.91027 + 7.23876i −0.458726 + 0.561837i
\(167\) 6.90176 20.6733i 0.534074 1.59975i −0.242790 0.970079i \(-0.578063\pi\)
0.776864 0.629668i \(-0.216809\pi\)
\(168\) −1.07296 −0.0827803
\(169\) 11.8695 + 5.30238i 0.913038 + 0.407875i
\(170\) −27.2248 −2.08804
\(171\) 0.255273 0.764636i 0.0195212 0.0584732i
\(172\) −11.8111 + 14.4659i −0.900585 + 1.10302i
\(173\) 1.21926 + 0.916214i 0.0926985 + 0.0696584i 0.646081 0.763269i \(-0.276407\pi\)
−0.553383 + 0.832927i \(0.686663\pi\)
\(174\) −3.68278 14.9416i −0.279191 1.13272i
\(175\) −0.775268 1.22599i −0.0586047 0.0926760i
\(176\) 0.249405 + 3.08944i 0.0187996 + 0.232875i
\(177\) −7.29048 + 5.03226i −0.547986 + 0.378247i
\(178\) 7.11636 + 34.8582i 0.533394 + 2.61274i
\(179\) 1.46947 + 0.118628i 0.109833 + 0.00886667i 0.135261 0.990810i \(-0.456813\pi\)
−0.0254277 + 0.999677i \(0.508095\pi\)
\(180\) 4.33055 + 0.884089i 0.322780 + 0.0658961i
\(181\) 5.01652 1.23646i 0.372875 0.0919054i −0.0484250 0.998827i \(-0.515420\pi\)
0.421300 + 0.906921i \(0.361574\pi\)
\(182\) −3.90983 1.89698i −0.289816 0.140614i
\(183\) −0.676139 0.166653i −0.0499816 0.0123194i
\(184\) −1.50595 0.714584i −0.111020 0.0526799i
\(185\) 2.82403 + 9.74968i 0.207627 + 0.716811i
\(186\) 7.97264 0.643618i 0.584582 0.0471924i
\(187\) 17.3569 + 2.10750i 1.26926 + 0.154116i
\(188\) −3.41253 1.97022i −0.248884 0.143693i
\(189\) −0.213637 + 0.501424i −0.0155398 + 0.0364732i
\(190\) 2.24355 + 1.54861i 0.162765 + 0.112348i
\(191\) 6.32622 10.9573i 0.457749 0.792845i −0.541093 0.840963i \(-0.681989\pi\)
0.998842 + 0.0481184i \(0.0153225\pi\)
\(192\) 6.41563 + 11.1122i 0.463008 + 0.801954i
\(193\) −0.445255 + 5.51548i −0.0320502 + 0.397013i 0.960766 + 0.277361i \(0.0894598\pi\)
−0.992816 + 0.119652i \(0.961822\pi\)
\(194\) 4.64984 2.44042i 0.333839 0.175212i
\(195\) 4.37907 + 3.35052i 0.313592 + 0.239936i
\(196\) −17.1538 9.00302i −1.22527 0.643073i
\(197\) −6.65764 + 10.5282i −0.474337 + 0.750104i −0.994587 0.103910i \(-0.966865\pi\)
0.520249 + 0.854014i \(0.325839\pi\)
\(198\) −4.55562 1.52089i −0.323754 0.108085i
\(199\) −5.49232 + 5.71811i −0.389340 + 0.405346i −0.886809 0.462136i \(-0.847083\pi\)
0.497469 + 0.867482i \(0.334263\pi\)
\(200\) 2.43474 4.63902i 0.172162 0.328028i
\(201\) 6.49869 + 0.261888i 0.458382 + 0.0184722i
\(202\) −9.91248 + 8.09329i −0.697440 + 0.569442i
\(203\) −0.907695 + 3.68266i −0.0637077 + 0.258472i
\(204\) 22.0700 7.36805i 1.54521 0.515867i
\(205\) 6.64667 14.0076i 0.464224 0.978331i
\(206\) 16.1962 0.652684i 1.12844 0.0454747i
\(207\) −0.633799 + 0.561497i −0.0440521 + 0.0390267i
\(208\) 0.369518 + 5.13227i 0.0256214 + 0.355859i
\(209\) −1.31047 1.16098i −0.0906474 0.0803066i
\(210\) −1.42775 1.16572i −0.0985241 0.0804425i
\(211\) 9.17732 6.89631i 0.631793 0.474762i −0.235956 0.971764i \(-0.575822\pi\)
0.867749 + 0.497002i \(0.165566\pi\)
\(212\) 0.188889 4.68722i 0.0129729 0.321920i
\(213\) 7.20614 + 8.13405i 0.493757 + 0.557336i
\(214\) 25.0574 11.8899i 1.71289 0.812775i
\(215\) −9.68169 + 1.97653i −0.660286 + 0.134798i
\(216\) −1.95423 + 0.237287i −0.132969 + 0.0161453i
\(217\) −1.81365 0.772726i −0.123119 0.0524560i
\(218\) −28.7727 + 4.67602i −1.94873 + 0.316700i
\(219\) −0.656050 4.03684i −0.0443317 0.272784i
\(220\) 5.45303 7.90007i 0.367643 0.532623i
\(221\) 28.7832 + 3.74867i 1.93617 + 0.252163i
\(222\) −8.33806 12.0798i −0.559614 0.810741i
\(223\) −3.80298 + 3.65281i −0.254667 + 0.244611i −0.809175 0.587567i \(-0.800086\pi\)
0.554509 + 0.832178i \(0.312906\pi\)
\(224\) −0.155668 3.86286i −0.0104010 0.258099i
\(225\) −1.68317 2.06151i −0.112211 0.137434i
\(226\) 33.4180 12.6738i 2.22294 0.843048i
\(227\) −8.80889 + 11.7225i −0.584667 + 0.778050i −0.990737 0.135792i \(-0.956642\pi\)
0.406071 + 0.913842i \(0.366899\pi\)
\(228\) −2.23787 0.648207i −0.148207 0.0429286i
\(229\) −5.72133 10.9011i −0.378076 0.720363i 0.619851 0.784719i \(-0.287193\pi\)
−0.997927 + 0.0643561i \(0.979501\pi\)
\(230\) −1.22756 2.58704i −0.0809431 0.170584i
\(231\) 0.820007 + 0.853717i 0.0539525 + 0.0561705i
\(232\) −13.1584 + 3.81136i −0.863888 + 0.250228i
\(233\) 8.88517 23.4283i 0.582087 1.53484i −0.243115 0.969998i \(-0.578169\pi\)
0.825201 0.564839i \(-0.191062\pi\)
\(234\) −7.54072 2.59041i −0.492952 0.169341i
\(235\) −0.739337 1.94947i −0.0482290 0.127169i
\(236\) 15.3809 + 20.4683i 1.00121 + 1.33237i
\(237\) −10.2518 6.48287i −0.665929 0.421108i
\(238\) −9.57744 1.55649i −0.620813 0.100892i
\(239\) 3.97021i 0.256812i 0.991722 + 0.128406i \(0.0409860\pi\)
−0.991722 + 0.128406i \(0.959014\pi\)
\(240\) −0.350087 + 2.15417i −0.0225980 + 0.139051i
\(241\) 3.90573 + 3.75151i 0.251591 + 0.241656i 0.807901 0.589319i \(-0.200604\pi\)
−0.556310 + 0.830975i \(0.687783\pi\)
\(242\) 9.21360 10.4000i 0.592273 0.668538i
\(243\) −0.278217 + 0.960518i −0.0178477 + 0.0616173i
\(244\) −0.402585 + 1.97199i −0.0257729 + 0.126244i
\(245\) −4.01786 9.43027i −0.256692 0.602478i
\(246\) −2.70247 + 22.2568i −0.172303 + 1.41904i
\(247\) −2.15875 1.94618i −0.137358 0.123833i
\(248\) −0.858267 7.06847i −0.0545000 0.448848i
\(249\) 3.65975 2.11296i 0.231927 0.133903i
\(250\) 23.8358 10.1555i 1.50751 0.642288i
\(251\) 1.06765 0.675138i 0.0673892 0.0426143i −0.500346 0.865825i \(-0.666794\pi\)
0.567736 + 0.823211i \(0.307820\pi\)
\(252\) 1.47291 + 0.558600i 0.0927844 + 0.0351885i
\(253\) 0.582354 + 1.74436i 0.0366123 + 0.109667i
\(254\) −14.7000 44.0319i −0.922360 2.76281i
\(255\) 11.5112 + 4.36561i 0.720858 + 0.273385i
\(256\) 4.82941 3.05393i 0.301838 0.190871i
\(257\) 7.45339 3.17559i 0.464930 0.198088i −0.146782 0.989169i \(-0.546892\pi\)
0.611712 + 0.791081i \(0.290481\pi\)
\(258\) 12.3746 7.14448i 0.770409 0.444796i
\(259\) 0.436064 + 3.59131i 0.0270957 + 0.223153i
\(260\) 9.16621 13.0361i 0.568464 0.808464i
\(261\) −0.838805 + 6.90818i −0.0519207 + 0.427605i
\(262\) −13.9430 32.7255i −0.861402 2.02179i
\(263\) −0.276174 + 1.35279i −0.0170296 + 0.0834166i −0.987417 0.158136i \(-0.949452\pi\)
0.970388 + 0.241553i \(0.0776567\pi\)
\(264\) −1.18951 + 4.10667i −0.0732093 + 0.252748i
\(265\) 1.64594 1.85788i 0.101109 0.114129i
\(266\) 0.700727 + 0.673057i 0.0429643 + 0.0412678i
\(267\) 2.58073 15.8799i 0.157938 0.971834i
\(268\) 18.7978i 1.14826i
\(269\) −4.86402 0.790480i −0.296564 0.0481964i 0.0103087 0.999947i \(-0.496719\pi\)
−0.306873 + 0.951750i \(0.599283\pi\)
\(270\) −2.85824 1.80744i −0.173947 0.109997i
\(271\) −9.74755 12.9716i −0.592121 0.787970i 0.399557 0.916708i \(-0.369164\pi\)
−0.991679 + 0.128738i \(0.958907\pi\)
\(272\) 4.07403 + 10.7423i 0.247025 + 0.651350i
\(273\) 1.34897 + 1.42904i 0.0816431 + 0.0864896i
\(274\) 7.67683 20.2421i 0.463774 1.22287i
\(275\) −5.55188 + 1.60812i −0.334791 + 0.0969733i
\(276\) 1.69528 + 1.76498i 0.102044 + 0.106239i
\(277\) 3.21418 + 6.77374i 0.193121 + 0.406995i 0.976794 0.214179i \(-0.0687075\pi\)
−0.783673 + 0.621173i \(0.786656\pi\)
\(278\) −12.9639 24.7007i −0.777524 1.48145i
\(279\) −3.47420 1.00631i −0.207995 0.0602464i
\(280\) −0.985714 + 1.31175i −0.0589077 + 0.0783919i
\(281\) 12.5192 4.74792i 0.746835 0.283237i 0.0483193 0.998832i \(-0.484614\pi\)
0.698516 + 0.715595i \(0.253844\pi\)
\(282\) 1.90679 + 2.33540i 0.113548 + 0.139071i
\(283\) 0.140545 + 3.48758i 0.00835452 + 0.207315i 0.997975 + 0.0636090i \(0.0202611\pi\)
−0.989620 + 0.143706i \(0.954098\pi\)
\(284\) 22.6514 21.7570i 1.34411 1.29104i
\(285\) −0.700293 1.01455i −0.0414818 0.0600967i
\(286\) −11.5952 + 12.8616i −0.685636 + 0.760522i
\(287\) 3.13908 4.54774i 0.185294 0.268445i
\(288\) −1.13781 7.00122i −0.0670461 0.412551i
\(289\) 47.1904 7.66919i 2.77591 0.451129i
\(290\) −21.6503 9.22434i −1.27135 0.541672i
\(291\) −2.35738 + 0.286238i −0.138192 + 0.0167795i
\(292\) −11.5815 + 2.36438i −0.677755 + 0.138365i
\(293\) 4.84119 2.29717i 0.282825 0.134202i −0.281996 0.959416i \(-0.590996\pi\)
0.564821 + 0.825213i \(0.308945\pi\)
\(294\) 9.82929 + 11.0950i 0.573256 + 0.647072i
\(295\) −0.545486 + 13.5361i −0.0317594 + 0.788102i
\(296\) −10.4459 + 7.84958i −0.607155 + 0.456248i
\(297\) 1.68233 + 1.37358i 0.0976184 + 0.0797030i
\(298\) 17.3629 + 15.3822i 1.00580 + 0.891065i
\(299\) 0.941615 + 2.90415i 0.0544550 + 0.167951i
\(300\) −5.75747 + 5.10067i −0.332408 + 0.294487i
\(301\) −3.51894 + 0.141808i −0.202828 + 0.00817370i
\(302\) −5.55594 + 11.7089i −0.319708 + 0.673771i
\(303\) 5.48899 1.83249i 0.315334 0.105274i
\(304\) 0.275316 1.11700i 0.0157905 0.0640645i
\(305\) −0.824906 + 0.673515i −0.0472340 + 0.0385653i
\(306\) −17.7881 0.716838i −1.01688 0.0409789i
\(307\) −8.52822 + 16.2492i −0.486731 + 0.927388i 0.510969 + 0.859599i \(0.329287\pi\)
−0.997700 + 0.0677891i \(0.978406\pi\)
\(308\) 2.36999 2.46742i 0.135043 0.140594i
\(309\) −6.95274 2.32116i −0.395527 0.132046i
\(310\) 6.53753 10.3383i 0.371307 0.587175i
\(311\) 9.88550 + 5.18831i 0.560555 + 0.294202i 0.721105 0.692826i \(-0.243634\pi\)
−0.160550 + 0.987028i \(0.551327\pi\)
\(312\) −2.03384 + 6.80021i −0.115143 + 0.384986i
\(313\) −11.3672 + 5.96599i −0.642514 + 0.337218i −0.754315 0.656513i \(-0.772031\pi\)
0.111800 + 0.993731i \(0.464338\pi\)
\(314\) −1.59319 + 19.7352i −0.0899088 + 1.11372i
\(315\) 0.416753 + 0.721837i 0.0234813 + 0.0406709i
\(316\) −17.5286 + 30.3604i −0.986059 + 1.70790i
\(317\) −20.0401 13.8327i −1.12557 0.776921i −0.148300 0.988942i \(-0.547380\pi\)
−0.977265 + 0.212021i \(0.931995\pi\)
\(318\) −1.40686 + 3.30203i −0.0788929 + 0.185169i
\(319\) 13.0889 + 7.55686i 0.732836 + 0.423103i
\(320\) 19.4793 + 2.36521i 1.08892 + 0.132219i
\(321\) −12.5014 + 1.00921i −0.697758 + 0.0563288i
\(322\) −0.283941 0.980279i −0.0158234 0.0546288i
\(323\) −5.86306 2.78206i −0.326229 0.154798i
\(324\) 2.80622 + 0.691672i 0.155901 + 0.0384262i
\(325\) −9.23966 + 2.58960i −0.512524 + 0.143645i
\(326\) −22.3341 + 5.50486i −1.23697 + 0.304886i
\(327\) 12.9155 + 2.63672i 0.714229 + 0.145811i
\(328\) 19.8940 + 1.60601i 1.09846 + 0.0886768i
\(329\) −0.148638 0.728076i −0.00819467 0.0401402i
\(330\) −6.04458 + 4.17227i −0.332743 + 0.229676i
\(331\) −1.60475 19.8784i −0.0882052 1.09262i −0.877812 0.479004i \(-0.840998\pi\)
0.789607 0.613612i \(-0.210284\pi\)
\(332\) −6.52784 10.3229i −0.358262 0.566545i
\(333\) 1.58846 + 6.44462i 0.0870468 + 0.353163i
\(334\) 38.5307 + 28.9539i 2.10830 + 1.58429i
\(335\) 6.29046 7.70441i 0.343684 0.420937i
\(336\) −0.246315 + 0.737805i −0.0134376 + 0.0402506i
\(337\) 30.9774 1.68744 0.843722 0.536780i \(-0.180360\pi\)
0.843722 + 0.536780i \(0.180360\pi\)
\(338\) −19.4340 + 21.1840i −1.05707 + 1.15226i
\(339\) −16.1621 −0.877806
\(340\) 11.2677 33.7508i 0.611075 1.83039i
\(341\) −4.96823 + 6.08498i −0.269045 + 0.329520i
\(342\) 1.42512 + 1.07091i 0.0770617 + 0.0579081i
\(343\) −1.78736 7.25160i −0.0965083 0.391550i
\(344\) −6.79847 10.7509i −0.366549 0.579651i
\(345\) 0.104196 + 1.29070i 0.00560971 + 0.0694887i
\(346\) −2.77564 + 1.91589i −0.149219 + 0.102999i
\(347\) 3.85800 + 18.8977i 0.207108 + 1.01448i 0.941824 + 0.336107i \(0.109110\pi\)
−0.734716 + 0.678375i \(0.762684\pi\)
\(348\) 20.0475 + 1.61840i 1.07466 + 0.0867554i
\(349\) −14.5193 2.96414i −0.777200 0.158667i −0.204980 0.978766i \(-0.565713\pi\)
−0.572221 + 0.820100i \(0.693918\pi\)
\(350\) 3.11450 0.767656i 0.166477 0.0410329i
\(351\) 2.77298 + 2.30447i 0.148011 + 0.123003i
\(352\) −14.9575 3.68668i −0.797235 0.196501i
\(353\) −9.53796 4.52582i −0.507654 0.240885i 0.157598 0.987503i \(-0.449625\pi\)
−0.665253 + 0.746618i \(0.731676\pi\)
\(354\) −5.45020 18.8163i −0.289675 1.00007i
\(355\) 16.5645 1.33723i 0.879155 0.0709727i
\(356\) −46.1593 5.60475i −2.44644 0.297051i
\(357\) 3.79994 + 2.19390i 0.201114 + 0.116113i
\(358\) −1.27786 + 2.99925i −0.0675371 + 0.158515i
\(359\) 5.90429 + 4.07544i 0.311617 + 0.215093i 0.713600 0.700554i \(-0.247064\pi\)
−0.401983 + 0.915647i \(0.631679\pi\)
\(360\) −1.50524 + 2.60715i −0.0793331 + 0.137409i
\(361\) −9.17508 15.8917i −0.482899 0.836406i
\(362\) −0.919365 + 11.3884i −0.0483208 + 0.598560i
\(363\) −5.56338 + 2.91989i −0.292002 + 0.153254i
\(364\) 3.96989 4.06194i 0.208079 0.212903i
\(365\) −5.53796 2.90655i −0.289870 0.152136i
\(366\) 0.823050 1.30155i 0.0430215 0.0680331i
\(367\) −29.4453 9.83029i −1.53703 0.513137i −0.582906 0.812540i \(-0.698084\pi\)
−0.954127 + 0.299403i \(0.903212\pi\)
\(368\) −0.837094 + 0.871507i −0.0436365 + 0.0454304i
\(369\) 4.71163 8.97727i 0.245278 0.467338i
\(370\) −22.4283 0.903829i −1.16599 0.0469878i
\(371\) 0.685246 0.559486i 0.0355762 0.0290471i
\(372\) −2.50178 + 10.1501i −0.129711 + 0.526259i
\(373\) −2.31463 + 0.772735i −0.119847 + 0.0400107i −0.375959 0.926636i \(-0.622687\pi\)
0.256112 + 0.966647i \(0.417558\pi\)
\(374\) −16.5752 + 34.9315i −0.857083 + 1.80626i
\(375\) −11.7067 + 0.471764i −0.604532 + 0.0243618i
\(376\) 2.00895 1.77977i 0.103604 0.0917848i
\(377\) 21.6195 + 12.7335i 1.11346 + 0.655807i
\(378\) −0.902171 0.799254i −0.0464027 0.0411092i
\(379\) −14.3203 11.6922i −0.735587 0.600588i 0.188813 0.982013i \(-0.439536\pi\)
−0.924400 + 0.381425i \(0.875433\pi\)
\(380\) −2.84838 + 2.14042i −0.146119 + 0.109801i
\(381\) −0.845254 + 20.9748i −0.0433037 + 1.07457i
\(382\) 18.5537 + 20.9429i 0.949292 + 1.07153i
\(383\) −9.61786 + 4.56373i −0.491450 + 0.233196i −0.658256 0.752794i \(-0.728706\pi\)
0.166807 + 0.985990i \(0.446654\pi\)
\(384\) −13.9019 + 2.83809i −0.709428 + 0.144831i
\(385\) 1.79705 0.218201i 0.0915861 0.0111206i
\(386\) −11.2573 4.79630i −0.572983 0.244125i
\(387\) −6.37788 + 1.03651i −0.324206 + 0.0526886i
\(388\) 1.10096 + 6.77447i 0.0558927 + 0.343922i
\(389\) 21.2565 30.7954i 1.07775 1.56139i 0.278456 0.960449i \(-0.410177\pi\)
0.799294 0.600941i \(-0.205207\pi\)
\(390\) −10.0945 + 6.83916i −0.511155 + 0.346314i
\(391\) 3.87231 + 5.61002i 0.195831 + 0.283711i
\(392\) 9.51648 9.14070i 0.480655 0.461675i
\(393\) 0.647712 + 16.0728i 0.0326727 + 0.810766i
\(394\) −17.4216 21.3375i −0.877685 1.07497i
\(395\) −17.3439 + 6.57769i −0.872668 + 0.330959i
\(396\) 3.77092 5.01818i 0.189496 0.252173i
\(397\) −7.93675 2.29891i −0.398334 0.115379i 0.0730037 0.997332i \(-0.476742\pi\)
−0.471338 + 0.881953i \(0.656229\pi\)
\(398\) −8.14804 15.5248i −0.408425 0.778188i
\(399\) −0.188354 0.396947i −0.00942947 0.0198722i
\(400\) −2.63103 2.73919i −0.131551 0.136959i
\(401\) 33.9554 9.83530i 1.69565 0.491151i 0.717068 0.697003i \(-0.245484\pi\)
0.978583 + 0.205852i \(0.0659966\pi\)
\(402\) −5.10019 + 13.4481i −0.254374 + 0.670730i
\(403\) −8.33527 + 10.0299i −0.415209 + 0.499624i
\(404\) −5.93078 15.6382i −0.295068 0.778029i
\(405\) 0.918691 + 1.22256i 0.0456501 + 0.0607493i
\(406\) −7.08903 4.48283i −0.351823 0.222479i
\(407\) 14.2289 + 2.31243i 0.705303 + 0.114623i
\(408\) 15.8480i 0.784592i
\(409\) −4.16185 + 25.6089i −0.205790 + 1.26628i 0.654339 + 0.756202i \(0.272947\pi\)
−0.860129 + 0.510077i \(0.829617\pi\)
\(410\) 24.7274 + 23.7510i 1.22120 + 1.17298i
\(411\) −6.49183 + 7.32777i −0.320219 + 0.361452i
\(412\) −5.89407 + 20.3487i −0.290380 + 1.00251i
\(413\) −0.965779 + 4.73070i −0.0475229 + 0.232782i
\(414\) −0.733949 1.72264i −0.0360716 0.0846632i
\(415\) 0.778970 6.41540i 0.0382381 0.314919i
\(416\) −24.7773 6.33564i −1.21480 0.310630i
\(417\) 1.52054 + 12.5228i 0.0744611 + 0.613242i
\(418\) 3.35293 1.93582i 0.163997 0.0946838i
\(419\) −10.4586 + 4.45598i −0.510934 + 0.217689i −0.632018 0.774954i \(-0.717773\pi\)
0.121084 + 0.992642i \(0.461363\pi\)
\(420\) 2.03606 1.28753i 0.0993498 0.0628250i
\(421\) −6.35693 2.41087i −0.309818 0.117498i 0.194795 0.980844i \(-0.437596\pi\)
−0.504613 + 0.863345i \(0.668365\pi\)
\(422\) 8.03889 + 24.0794i 0.391327 + 1.17217i
\(423\) −0.431738 1.29321i −0.0209918 0.0628782i
\(424\) 2.98753 + 1.13302i 0.145087 + 0.0550244i
\(425\) −18.1083 + 11.4510i −0.878383 + 0.555456i
\(426\) −22.1081 + 9.41937i −1.07114 + 0.456370i
\(427\) −0.328701 + 0.189775i −0.0159069 + 0.00918388i
\(428\) 4.36934 + 35.9848i 0.211200 + 1.73939i
\(429\) 6.96508 3.57880i 0.336277 0.172786i
\(430\) 2.63391 21.6922i 0.127018 1.04609i
\(431\) −8.08820 18.9837i −0.389595 0.914413i −0.993123 0.117072i \(-0.962649\pi\)
0.603529 0.797341i \(-0.293761\pi\)
\(432\) −0.285461 + 1.39828i −0.0137342 + 0.0672747i
\(433\) 0.970380 3.35014i 0.0466335 0.160997i −0.933822 0.357737i \(-0.883548\pi\)
0.980456 + 0.196740i \(0.0630355\pi\)
\(434\) 2.89090 3.26316i 0.138768 0.156636i
\(435\) 7.67503 + 7.37196i 0.367989 + 0.353459i
\(436\) 6.11142 37.6051i 0.292684 1.80096i
\(437\) 0.682580i 0.0326523i
\(438\) 8.92698 + 1.45078i 0.426548 + 0.0693207i
\(439\) −25.7301 16.2707i −1.22803 0.776560i −0.246739 0.969082i \(-0.579359\pi\)
−0.981293 + 0.192522i \(0.938333\pi\)
\(440\) 3.92784 + 5.22700i 0.187252 + 0.249187i
\(441\) −2.37689 6.26735i −0.113185 0.298445i
\(442\) −28.0192 + 57.7498i −1.33274 + 2.74688i
\(443\) −6.63565 + 17.4968i −0.315269 + 0.831297i 0.679916 + 0.733290i \(0.262016\pi\)
−0.995186 + 0.0980071i \(0.968753\pi\)
\(444\) 18.4263 5.33724i 0.874474 0.253294i
\(445\) −17.0432 17.7438i −0.807923 0.841137i
\(446\) −4.99893 10.5350i −0.236706 0.498847i
\(447\) −4.87477 9.28810i −0.230569 0.439312i
\(448\) 6.71741 + 1.94572i 0.317368 + 0.0919267i
\(449\) 16.6917 22.2126i 0.787731 1.04828i −0.209779 0.977749i \(-0.567274\pi\)
0.997510 0.0705302i \(-0.0224691\pi\)
\(450\) 5.50285 2.08695i 0.259407 0.0983800i
\(451\) −13.9261 17.0564i −0.655755 0.803154i
\(452\) 1.88090 + 46.6740i 0.0884699 + 2.19536i
\(453\) 4.22674 4.05983i 0.198589 0.190748i
\(454\) −18.4202 26.6863i −0.864503 1.25245i
\(455\) 2.98637 0.336337i 0.140003 0.0157677i
\(456\) 0.901473 1.30601i 0.0422153 0.0611595i
\(457\) 3.36682 + 20.7169i 0.157493 + 0.969094i 0.938678 + 0.344795i \(0.112051\pi\)
−0.781185 + 0.624300i \(0.785384\pi\)
\(458\) 26.8723 4.36718i 1.25566 0.204065i
\(459\) 7.40624 + 3.15550i 0.345694 + 0.147286i
\(460\) 3.71523 0.451110i 0.173223 0.0210331i
\(461\) −4.41192 + 0.900701i −0.205484 + 0.0419498i −0.301665 0.953414i \(-0.597542\pi\)
0.0961810 + 0.995364i \(0.469337\pi\)
\(462\) −2.36497 + 1.12219i −0.110028 + 0.0522090i
\(463\) −19.3289 21.8178i −0.898289 1.01396i −0.999817 0.0191257i \(-0.993912\pi\)
0.101528 0.994833i \(-0.467627\pi\)
\(464\) −0.399889 + 9.92315i −0.0185644 + 0.460671i
\(465\) −4.42199 + 3.32291i −0.205065 + 0.154096i
\(466\) 42.9205 + 35.0435i 1.98825 + 1.62336i
\(467\) 2.24027 + 1.98471i 0.103667 + 0.0918414i 0.713364 0.700793i \(-0.247170\pi\)
−0.609697 + 0.792635i \(0.708709\pi\)
\(468\) 6.33227 8.27618i 0.292709 0.382567i
\(469\) 2.65340 2.35071i 0.122523 0.108546i
\(470\) 4.60690 0.185652i 0.212500 0.00856348i
\(471\) 3.83826 8.08895i 0.176857 0.372719i
\(472\) −16.5414 + 5.52234i −0.761381 + 0.254186i
\(473\) −3.35844 + 13.6257i −0.154421 + 0.626512i
\(474\) 20.7774 16.9642i 0.954338 0.779193i
\(475\) 2.14364 + 0.0863859i 0.0983572 + 0.00396366i
\(476\) 5.89345 11.2290i 0.270126 0.514682i
\(477\) 1.12434 1.17057i 0.0514802 0.0535966i
\(478\) −8.32782 2.78024i −0.380906 0.127165i
\(479\) −16.5406 + 26.1568i −0.755758 + 1.19514i 0.219832 + 0.975538i \(0.429449\pi\)
−0.975590 + 0.219598i \(0.929525\pi\)
\(480\) −9.60468 5.04092i −0.438392 0.230086i
\(481\) 23.5877 + 4.04379i 1.07551 + 0.184381i
\(482\) −10.6042 + 5.56549i −0.483006 + 0.253501i
\(483\) −0.0371361 + 0.460013i −0.00168975 + 0.0209313i
\(484\) 9.07968 + 15.7265i 0.412713 + 0.714840i
\(485\) −1.81576 + 3.14499i −0.0824494 + 0.142807i
\(486\) −1.81993 1.25621i −0.0825537 0.0569827i
\(487\) 13.4791 31.6367i 0.610798 1.43360i −0.271284 0.962499i \(-0.587448\pi\)
0.882082 0.471096i \(-0.156142\pi\)
\(488\) −1.18721 0.685437i −0.0537425 0.0310283i
\(489\) 10.3260 + 1.25381i 0.466960 + 0.0566992i
\(490\) 22.5943 1.82400i 1.02071 0.0824000i
\(491\) −11.9638 41.3037i −0.539917 1.86401i −0.502257 0.864718i \(-0.667497\pi\)
−0.0376592 0.999291i \(-0.511990\pi\)
\(492\) −26.4734 12.5618i −1.19352 0.566330i
\(493\) 54.3944 + 13.4070i 2.44980 + 0.603822i
\(494\) 5.59398 3.16527i 0.251685 0.142412i
\(495\) 3.22481 0.794844i 0.144944 0.0357256i
\(496\) −5.05758 1.03251i −0.227092 0.0463612i
\(497\) 5.90372 + 0.476597i 0.264818 + 0.0213783i
\(498\) 1.86926 + 9.15624i 0.0837636 + 0.410301i
\(499\) 7.03928 4.85886i 0.315121 0.217513i −0.399996 0.916517i \(-0.630989\pi\)
0.715118 + 0.699004i \(0.246373\pi\)
\(500\) 2.72478 + 33.7525i 0.121856 + 1.50946i
\(501\) −11.6486 18.4209i −0.520423 0.822983i
\(502\) 0.668509 + 2.71225i 0.0298370 + 0.121054i
\(503\) −26.9207 20.2296i −1.20034 0.901994i −0.203315 0.979113i \(-0.565171\pi\)
−0.997022 + 0.0771190i \(0.975428\pi\)
\(504\) −0.678585 + 0.831116i −0.0302266 + 0.0370209i
\(505\) 2.80236 8.39409i 0.124703 0.373532i
\(506\) −4.06674 −0.180789
\(507\) 11.6141 5.84070i 0.515798 0.259395i
\(508\) 60.6706 2.69182
\(509\) 13.2461 39.6769i 0.587122 1.75865i −0.0621251 0.998068i \(-0.519788\pi\)
0.649247 0.760577i \(-0.275084\pi\)
\(510\) −17.2182 + 21.0884i −0.762434 + 0.933812i
\(511\) −1.78204 1.33911i −0.0788326 0.0592389i
\(512\) −3.76718 15.2841i −0.166488 0.675467i
\(513\) −0.430844 0.681326i −0.0190222 0.0300813i
\(514\) 1.44163 + 17.8578i 0.0635878 + 0.787676i
\(515\) −9.22517 + 6.36767i −0.406509 + 0.280593i
\(516\) 3.73552 + 18.2978i 0.164447 + 0.805516i
\(517\) −2.95145 0.238266i −0.129805 0.0104789i
\(518\) −7.83841 1.60022i −0.344400 0.0703097i
\(519\) 1.48082 0.364989i 0.0650007 0.0160212i
\(520\) 6.44516 + 8.73376i 0.282639 + 0.383001i
\(521\) 27.8543 + 6.86546i 1.22032 + 0.300781i 0.796316 0.604880i \(-0.206779\pi\)
0.424001 + 0.905662i \(0.360625\pi\)
\(522\) −13.9030 6.59707i −0.608519 0.288746i
\(523\) −1.76115 6.08018i −0.0770095 0.265868i 0.912770 0.408474i \(-0.133939\pi\)
−0.989780 + 0.142606i \(0.954452\pi\)
\(524\) 46.3407 3.74101i 2.02440 0.163427i
\(525\) −1.43997 0.174844i −0.0628455 0.00763082i
\(526\) −2.64418 1.52662i −0.115292 0.0665637i
\(527\) −11.4135 + 26.7884i −0.497178 + 1.16692i
\(528\) 2.55083 + 1.76071i 0.111011 + 0.0766251i
\(529\) 11.1415 19.2977i 0.484413 0.839029i
\(530\) 2.74444 + 4.75351i 0.119211 + 0.206479i
\(531\) −0.712821 + 8.82987i −0.0309338 + 0.383184i
\(532\) −1.12441 + 0.590134i −0.0487492 + 0.0255856i
\(533\) −22.8725 28.5154i −0.990720 1.23514i
\(534\) 31.5021 + 16.5336i 1.36323 + 0.715477i
\(535\) −10.2511 + 16.2108i −0.443192 + 0.700852i
\(536\) 12.1447 + 4.05449i 0.524571 + 0.175127i
\(537\) 1.02125 1.06323i 0.0440702 0.0458819i
\(538\) 5.06423 9.64909i 0.218335 0.416002i
\(539\) −14.5460 0.586182i −0.626539 0.0252486i
\(540\) 3.42366 2.79533i 0.147331 0.120292i
\(541\) −10.5371 + 42.7507i −0.453026 + 1.83800i 0.0868077 + 0.996225i \(0.472333\pi\)
−0.539833 + 0.841772i \(0.681513\pi\)
\(542\) 34.0349 11.3625i 1.46192 0.488062i
\(543\) 2.21490 4.66781i 0.0950507 0.200315i
\(544\) −57.0561 + 2.29928i −2.44626 + 0.0985808i
\(545\) 15.0889 13.3676i 0.646337 0.572605i
\(546\) −3.94217 + 1.82884i −0.168709 + 0.0782670i
\(547\) 29.8837 + 26.4746i 1.27773 + 1.13197i 0.984397 + 0.175964i \(0.0563043\pi\)
0.293337 + 0.956009i \(0.405234\pi\)
\(548\) 21.9171 + 17.8947i 0.936251 + 0.764425i
\(549\) −0.556712 + 0.418342i −0.0237599 + 0.0178544i
\(550\) 0.514678 12.7716i 0.0219460 0.544583i
\(551\) −3.71994 4.19895i −0.158475 0.178881i
\(552\) −1.50595 + 0.714584i −0.0640977 + 0.0304147i
\(553\) −6.47751 + 1.32239i −0.275452 + 0.0562339i
\(554\) −16.4592 + 1.99851i −0.699286 + 0.0849087i
\(555\) 9.33820 + 3.97863i 0.396384 + 0.168884i
\(556\) 35.9871 5.84847i 1.52619 0.248030i
\(557\) −6.81234 41.9180i −0.288648 1.77612i −0.575153 0.818046i \(-0.695058\pi\)
0.286505 0.958079i \(-0.407506\pi\)
\(558\) 4.54371 6.58270i 0.192351 0.278668i
\(559\) −5.77155 + 22.5712i −0.244111 + 0.954662i
\(560\) 0.675720 + 0.978949i 0.0285544 + 0.0413681i
\(561\) 12.6097 12.1118i 0.532384 0.511362i
\(562\) 1.19223 + 29.5849i 0.0502912 + 1.24796i
\(563\) −16.7398 20.5026i −0.705500 0.864081i 0.290176 0.956973i \(-0.406286\pi\)
−0.995676 + 0.0928926i \(0.970389\pi\)
\(564\) −3.68438 + 1.39730i −0.155140 + 0.0588370i
\(565\) −14.8480 + 19.7591i −0.624659 + 0.831271i
\(566\) −7.41389 2.14746i −0.311629 0.0902645i
\(567\) 0.253292 + 0.482608i 0.0106373 + 0.0202676i
\(568\) 9.17084 + 19.3271i 0.384800 + 0.810949i
\(569\) 8.95674 + 9.32496i 0.375486 + 0.390923i 0.881953 0.471337i \(-0.156228\pi\)
−0.506467 + 0.862259i \(0.669049\pi\)
\(570\) 2.61849 0.758455i 0.109676 0.0317682i
\(571\) 10.3115 27.1892i 0.431524 1.13783i −0.526255 0.850327i \(-0.676404\pi\)
0.957778 0.287507i \(-0.0928266\pi\)
\(572\) −11.1457 19.6977i −0.466024 0.823602i
\(573\) −4.48662 11.8302i −0.187431 0.494215i
\(574\) 7.34102 + 9.76912i 0.306408 + 0.407755i
\(575\) −1.90464 1.20442i −0.0794289 0.0502278i
\(576\) 12.6651 + 2.05828i 0.527712 + 0.0857616i
\(577\) 7.56916i 0.315108i 0.987510 + 0.157554i \(0.0503608\pi\)
−0.987510 + 0.157554i \(0.949639\pi\)
\(578\) −16.9595 + 104.356i −0.705422 + 4.34064i
\(579\) 3.99072 + 3.83313i 0.165848 + 0.159300i
\(580\) 20.3960 23.0223i 0.846899 0.955951i
\(581\) 0.640814 2.21235i 0.0265854 0.0917836i
\(582\) 1.05040 5.14522i 0.0435407 0.213276i
\(583\) −1.38171 3.24300i −0.0572247 0.134311i
\(584\) 0.970455 7.99241i 0.0401577 0.330728i
\(585\) 5.36485 1.27303i 0.221809 0.0526334i
\(586\) 1.42834 + 11.7634i 0.0590041 + 0.485942i
\(587\) 9.07594 5.24000i 0.374604 0.216278i −0.300864 0.953667i \(-0.597275\pi\)
0.675468 + 0.737389i \(0.263942\pi\)
\(588\) −17.8226 + 7.59351i −0.734993 + 0.313151i
\(589\) 2.46436 1.55837i 0.101542 0.0642114i
\(590\) −28.0110 10.6232i −1.15319 0.437349i
\(591\) 3.94461 + 11.8156i 0.162260 + 0.486027i
\(592\) 2.99963 + 8.98500i 0.123284 + 0.369281i
\(593\) 6.90314 + 2.61802i 0.283478 + 0.107509i 0.492246 0.870456i \(-0.336176\pi\)
−0.208768 + 0.977965i \(0.566945\pi\)
\(594\) −4.05927 + 2.56693i −0.166554 + 0.105322i
\(595\) 6.17314 2.63013i 0.253074 0.107825i
\(596\) −26.2554 + 15.1586i −1.07546 + 0.620920i
\(597\) 0.955685 + 7.87077i 0.0391136 + 0.322129i
\(598\) −6.75106 0.0585923i −0.276072 0.00239602i
\(599\) 2.05747 16.9448i 0.0840660 0.692346i −0.888362 0.459143i \(-0.848156\pi\)
0.972428 0.233202i \(-0.0749205\pi\)
\(600\) −2.05356 4.81989i −0.0838364 0.196771i
\(601\) −2.36515 + 11.5853i −0.0964766 + 0.472573i 0.902634 + 0.430409i \(0.141631\pi\)
−0.999111 + 0.0421647i \(0.986575\pi\)
\(602\) 2.16677 7.48055i 0.0883108 0.304884i
\(603\) 4.31293 4.86829i 0.175636 0.198252i
\(604\) −12.2161 11.7338i −0.497068 0.477440i
\(605\) −1.54130 + 9.48402i −0.0626629 + 0.385580i
\(606\) 12.7968i 0.519835i
\(607\) 18.3151 + 2.97650i 0.743389 + 0.120812i 0.520297 0.853985i \(-0.325821\pi\)
0.223091 + 0.974798i \(0.428385\pi\)
\(608\) 4.83270 + 3.05601i 0.195992 + 0.123938i
\(609\) 2.27854 + 3.03219i 0.0923312 + 0.122870i
\(610\) −0.835088 2.20195i −0.0338117 0.0891542i
\(611\) −4.89617 0.438061i −0.198078 0.0177220i
\(612\) 8.25074 21.7554i 0.333517 0.879411i
\(613\) −19.0937 + 5.53055i −0.771186 + 0.223377i −0.640408 0.768035i \(-0.721235\pi\)
−0.130778 + 0.991412i \(0.541748\pi\)
\(614\) −28.1118 29.2674i −1.13450 1.18114i
\(615\) −6.64667 14.0076i −0.268020 0.564840i
\(616\) 1.08294 + 2.06338i 0.0436330 + 0.0831358i
\(617\) 19.5148 + 5.65254i 0.785638 + 0.227563i 0.646706 0.762739i \(-0.276146\pi\)
0.138931 + 0.990302i \(0.455633\pi\)
\(618\) 9.73764 12.9584i 0.391705 0.521265i
\(619\) 2.47883 0.940097i 0.0996327 0.0377857i −0.304285 0.952581i \(-0.598417\pi\)
0.403918 + 0.914795i \(0.367648\pi\)
\(620\) 10.1107 + 12.3834i 0.406056 + 0.497329i
\(621\) 0.0340950 + 0.846060i 0.00136819 + 0.0339512i
\(622\) −17.8054 + 17.1023i −0.713933 + 0.685742i
\(623\) −4.98119 7.21651i −0.199567 0.289123i
\(624\) 4.20918 + 2.95965i 0.168502 + 0.118481i
\(625\) −2.61895 + 3.79420i −0.104758 + 0.151768i
\(626\) −4.55393 28.0215i −0.182012 1.11996i
\(627\) −1.72810 + 0.280844i −0.0690138 + 0.0112158i
\(628\) −23.8065 10.1430i −0.949981 0.404749i
\(629\) 53.0451 6.44084i 2.11505 0.256813i
\(630\) −1.80595 + 0.368687i −0.0719507 + 0.0146888i
\(631\) −6.33098 + 3.00409i −0.252032 + 0.119591i −0.550518 0.834823i \(-0.685570\pi\)
0.298486 + 0.954414i \(0.403519\pi\)
\(632\) −15.8342 17.8731i −0.629850 0.710954i
\(633\) 0.462239 11.4703i 0.0183723 0.455905i
\(634\) 43.0487 32.3490i 1.70968 1.28474i
\(635\) 24.8663 + 20.3027i 0.986789 + 0.805688i
\(636\) −3.51128 3.11073i −0.139231 0.123348i
\(637\) −24.1388 1.18267i −0.956415 0.0468593i
\(638\) −25.0169 + 22.1630i −0.990427 + 0.877442i
\(639\) 10.8582 0.437569i 0.429543 0.0173100i
\(640\) −9.30182 + 19.6032i −0.367687 + 0.774884i
\(641\) 13.4718 4.49755i 0.532105 0.177643i −0.0379038 0.999281i \(-0.512068\pi\)
0.570009 + 0.821639i \(0.306940\pi\)
\(642\) 6.63747 26.9293i 0.261960 1.06281i
\(643\) −15.5729 + 12.7148i −0.614134 + 0.501425i −0.887696 0.460430i \(-0.847695\pi\)
0.273563 + 0.961854i \(0.411798\pi\)
\(644\) 1.33278 + 0.0537090i 0.0525187 + 0.00211643i
\(645\) −4.59211 + 8.74954i −0.180814 + 0.344513i
\(646\) 9.94132 10.3500i 0.391136 0.407216i
\(647\) −36.9494 12.3355i −1.45263 0.484959i −0.522643 0.852552i \(-0.675054\pi\)
−0.929987 + 0.367593i \(0.880182\pi\)
\(648\) −1.05214 + 1.66383i −0.0413320 + 0.0653614i
\(649\) 17.0358 + 8.94106i 0.668712 + 0.350967i
\(650\) 1.03841 21.1943i 0.0407298 0.831309i
\(651\) −1.74559 + 0.916158i −0.0684152 + 0.0359071i
\(652\) 2.41911 29.9661i 0.0947398 1.17356i
\(653\) 0.0769017 + 0.133198i 0.00300940 + 0.00521243i 0.867526 0.497392i \(-0.165709\pi\)
−0.864517 + 0.502604i \(0.832375\pi\)
\(654\) −14.5751 + 25.2448i −0.569932 + 0.987151i
\(655\) 20.2449 + 13.9741i 0.791035 + 0.546012i
\(656\) 5.67135 13.3112i 0.221429 0.519713i
\(657\) −3.54187 2.04490i −0.138181 0.0797791i
\(658\) 1.63128 + 0.198074i 0.0635940 + 0.00772171i
\(659\) −0.293297 + 0.0236774i −0.0114252 + 0.000922340i −0.0861779 0.996280i \(-0.527465\pi\)
0.0747526 + 0.997202i \(0.476183\pi\)
\(660\) −2.67069 9.22031i −0.103957 0.358900i
\(661\) −22.2348 10.5506i −0.864834 0.410369i −0.0560175 0.998430i \(-0.517840\pi\)
−0.808817 + 0.588061i \(0.799892\pi\)
\(662\) 42.8203 + 10.5542i 1.66426 + 0.410202i
\(663\) 21.1075 19.9248i 0.819748 0.773814i
\(664\) 8.07733 1.99088i 0.313461 0.0772613i
\(665\) −0.658328 0.134399i −0.0255289 0.00521175i
\(666\) −14.6304 1.18109i −0.566917 0.0457663i
\(667\) 1.17864 + 5.77335i 0.0456371 + 0.223545i
\(668\) −51.8413 + 35.7835i −2.00580 + 1.38450i
\(669\) 0.424309 + 5.25602i 0.0164047 + 0.203209i
\(670\) 11.7555 + 18.5899i 0.454156 + 0.718191i
\(671\) 0.361946 + 1.46847i 0.0139728 + 0.0566898i
\(672\) −3.09065 2.32247i −0.119224 0.0895912i
\(673\) −21.7158 + 26.5971i −0.837084 + 1.02524i 0.162176 + 0.986762i \(0.448149\pi\)
−0.999259 + 0.0384793i \(0.987749\pi\)
\(674\) −21.6926 + 64.9773i −0.835569 + 2.50283i
\(675\) −2.66137 −0.102436
\(676\) −18.2187 32.8601i −0.700721 1.26385i
\(677\) 32.8693 1.26327 0.631635 0.775266i \(-0.282384\pi\)
0.631635 + 0.775266i \(0.282384\pi\)
\(678\) 11.3179 33.9013i 0.434661 1.30197i
\(679\) −0.818573 + 1.00257i −0.0314140 + 0.0384751i
\(680\) 19.3750 + 14.5594i 0.742998 + 0.558327i
\(681\) 3.50917 + 14.2373i 0.134472 + 0.545573i
\(682\) −9.28458 14.6824i −0.355525 0.562218i
\(683\) 0.617522 + 7.64938i 0.0236288 + 0.292695i 0.997770 + 0.0667532i \(0.0212640\pi\)
−0.974141 + 0.225942i \(0.927454\pi\)
\(684\) −1.91744 + 1.32351i −0.0733150 + 0.0506057i
\(685\) 2.99461 + 14.6686i 0.114418 + 0.560457i
\(686\) 16.4624 + 1.32898i 0.628538 + 0.0507409i
\(687\) −12.0625 2.46257i −0.460211 0.0939528i
\(688\) −8.95345 + 2.20683i −0.341347 + 0.0841345i
\(689\) −2.24701 5.40350i −0.0856043 0.205857i
\(690\) −2.78030 0.685282i −0.105844 0.0260882i
\(691\) −26.4807 12.5652i −1.00737 0.478004i −0.147799 0.989017i \(-0.547219\pi\)
−0.859573 + 0.511014i \(0.829270\pi\)
\(692\) −1.22637 4.23392i −0.0466196 0.160950i
\(693\) 1.17990 0.0952516i 0.0448208 0.00361831i
\(694\) −42.3410 5.14113i −1.60724 0.195155i
\(695\) 16.7067 + 9.64560i 0.633720 + 0.365879i
\(696\) −5.36964 + 12.6030i −0.203536 + 0.477716i
\(697\) −67.1720 46.3655i −2.54432 1.75622i
\(698\) 16.3850 28.3796i 0.620181 1.07418i
\(699\) −12.5283 21.6996i −0.473862 0.820754i
\(700\) −0.337346 + 4.17879i −0.0127505 + 0.157943i
\(701\) −36.3304 + 19.0677i −1.37218 + 0.720177i −0.979866 0.199654i \(-0.936018\pi\)
−0.392316 + 0.919831i \(0.628326\pi\)
\(702\) −6.77564 + 4.20278i −0.255730 + 0.158624i
\(703\) −4.73774 2.48656i −0.178687 0.0937823i
\(704\) 14.8943 23.5534i 0.561348 0.887702i
\(705\) −1.97766 0.660240i −0.0744830 0.0248661i
\(706\) 16.1724 16.8373i 0.608657 0.633680i
\(707\) 1.46575 2.79275i 0.0551252 0.105032i
\(708\) 25.5824 + 1.03094i 0.961446 + 0.0387449i
\(709\) 2.29345 1.87254i 0.0861323 0.0703249i −0.588401 0.808569i \(-0.700242\pi\)
0.674533 + 0.738244i \(0.264345\pi\)
\(710\) −8.79478 + 35.6818i −0.330062 + 1.33911i
\(711\) −11.5054 + 3.84106i −0.431486 + 0.144051i
\(712\) 13.5772 28.6132i 0.508825 1.07233i
\(713\) −3.06020 + 0.123322i −0.114605 + 0.00461844i
\(714\) −7.26287 + 6.43434i −0.271806 + 0.240799i
\(715\) 2.02347 11.8030i 0.0756734 0.441407i
\(716\) −3.18932 2.82549i −0.119191 0.105594i
\(717\) 3.07535 + 2.51094i 0.114851 + 0.0937729i
\(718\) −12.6832 + 9.53078i −0.473331 + 0.355685i
\(719\) 1.23071 30.5398i 0.0458978 1.13894i −0.798076 0.602557i \(-0.794149\pi\)
0.843974 0.536385i \(-0.180210\pi\)
\(720\) 1.44722 + 1.63358i 0.0539348 + 0.0608798i
\(721\) −3.60939 + 1.71267i −0.134421 + 0.0637833i
\(722\) 39.7591 8.11689i 1.47968 0.302079i
\(723\) 5.37610 0.652777i 0.199939 0.0242770i
\(724\) −13.7378 5.85311i −0.510560 0.217529i
\(725\) −18.2804 + 2.97085i −0.678917 + 0.110335i
\(726\) −2.22880 13.7143i −0.0827184 0.508987i
\(727\) −18.2176 + 26.3927i −0.675653 + 0.978852i 0.323812 + 0.946122i \(0.395036\pi\)
−0.999464 + 0.0327301i \(0.989580\pi\)
\(728\) 1.76803 + 3.44094i 0.0655275 + 0.127530i
\(729\) 0.568065 + 0.822984i 0.0210394 + 0.0304809i
\(730\) 9.97479 9.58091i 0.369183 0.354606i
\(731\) 2.09457 + 51.9761i 0.0774704 + 1.92241i
\(732\) 1.27290 + 1.55902i 0.0470478 + 0.0576231i
\(733\) −9.55885 + 3.62519i −0.353064 + 0.133900i −0.524759 0.851251i \(-0.675845\pi\)
0.171695 + 0.985150i \(0.445076\pi\)
\(734\) 41.2395 54.8799i 1.52218 2.02565i
\(735\) −9.84581 2.85187i −0.363168 0.105193i
\(736\) −2.79114 5.31808i −0.102883 0.196027i
\(737\) −6.05555 12.7618i −0.223059 0.470087i
\(738\) 15.5311 + 16.1696i 0.571706 + 0.595210i
\(739\) 43.9612 12.7335i 1.61714 0.468410i 0.658393 0.752674i \(-0.271237\pi\)
0.958746 + 0.284264i \(0.0917493\pi\)
\(740\) 10.4030 27.4305i 0.382422 1.00836i
\(741\) −2.87281 + 0.441322i −0.105535 + 0.0162124i
\(742\) 0.693704 + 1.82915i 0.0254667 + 0.0671501i
\(743\) 14.5176 + 19.3194i 0.532598 + 0.708759i 0.982905 0.184115i \(-0.0589418\pi\)
−0.450307 + 0.892874i \(0.648685\pi\)
\(744\) −6.01808 3.80560i −0.220633 0.139520i
\(745\) −15.8336 2.57321i −0.580099 0.0942753i
\(746\) 5.39623i 0.197570i
\(747\) 0.677884 4.17119i 0.0248025 0.152616i
\(748\) −36.4448 35.0057i −1.33255 1.27993i
\(749\) −4.53303 + 5.11674i −0.165633 + 0.186961i
\(750\) 7.20834 24.8861i 0.263211 0.908711i
\(751\) 9.25748 45.3461i 0.337810 1.65470i −0.355955 0.934503i \(-0.615844\pi\)
0.693765 0.720201i \(-0.255950\pi\)
\(752\) −0.762651 1.79001i −0.0278110 0.0652749i
\(753\) 0.152262 1.25399i 0.00554874 0.0456980i
\(754\) −41.8490 + 36.4316i −1.52405 + 1.32676i
\(755\) −1.08031 8.89715i −0.0393165 0.323800i
\(756\) 1.36423 0.787637i 0.0496165 0.0286461i
\(757\) −19.9321 + 8.49226i −0.724444 + 0.308657i −0.722528 0.691342i \(-0.757020\pi\)
−0.00191552 + 0.999998i \(0.500610\pi\)
\(758\) 34.5534 21.8503i 1.25504 0.793637i
\(759\) 1.71950 + 0.652120i 0.0624139 + 0.0236705i
\(760\) −0.768494 2.30192i −0.0278762 0.0834994i
\(761\) 4.79704 + 14.3689i 0.173892 + 0.520871i 0.999029 0.0440622i \(-0.0140300\pi\)
−0.825136 + 0.564934i \(0.808902\pi\)
\(762\) −43.4043 16.4611i −1.57237 0.596321i
\(763\) 6.07239 3.83995i 0.219835 0.139015i
\(764\) −33.6419 + 14.3335i −1.21712 + 0.518568i
\(765\) 10.6618 6.15560i 0.385479 0.222556i
\(766\) −2.83764 23.3701i −0.102528 0.844394i
\(767\) 28.1517 + 15.0882i 1.01650 + 0.544803i
\(768\) 0.688745 5.67233i 0.0248530 0.204683i
\(769\) 4.10210 + 9.62798i 0.147925 + 0.347194i 0.977415 0.211328i \(-0.0677789\pi\)
−0.829490 + 0.558522i \(0.811369\pi\)
\(770\) −0.800732 + 3.92225i −0.0288564 + 0.141348i
\(771\) 2.25403 7.78183i 0.0811770 0.280256i
\(772\) 10.6051 11.9707i 0.381687 0.430836i
\(773\) 18.6767 + 17.9392i 0.671754 + 0.645228i 0.948892 0.315602i \(-0.102206\pi\)
−0.277138 + 0.960830i \(0.589386\pi\)
\(774\) 2.29211 14.1039i 0.0823882 0.506955i
\(775\) 9.62617i 0.345782i
\(776\) −4.61425 0.749888i −0.165642 0.0269194i
\(777\) 3.05763 + 1.93353i 0.109692 + 0.0693650i
\(778\) 49.7103 + 66.1524i 1.78220 + 2.37168i
\(779\) 2.89816 + 7.64182i 0.103837 + 0.273797i
\(780\) −4.30069 15.3448i −0.153989 0.549432i
\(781\) 8.36919 22.0677i 0.299473 0.789646i
\(782\) −14.4791 + 4.19393i −0.517772 + 0.149974i
\(783\) 4.82061 + 5.01879i 0.172275 + 0.179357i
\(784\) −4.10082 8.64230i −0.146458 0.308654i
\(785\) −6.36302 12.1237i −0.227106 0.432714i
\(786\) −34.1675 9.89674i −1.21871 0.353005i
\(787\) −26.3067 + 35.0078i −0.937731 + 1.24789i 0.0309337 + 0.999521i \(0.490152\pi\)
−0.968665 + 0.248372i \(0.920104\pi\)
\(788\) 33.6627 12.7666i 1.19918 0.454790i
\(789\) 0.873212 + 1.06949i 0.0310872 + 0.0380749i
\(790\) −1.65170 40.9864i −0.0587647 1.45823i
\(791\) −6.35306 + 6.10219i −0.225889 + 0.216969i
\(792\) 2.42874 + 3.51864i 0.0863017 + 0.125030i
\(793\) 0.579697 + 2.44298i 0.0205857 + 0.0867527i
\(794\) 10.3800 15.0381i 0.368373 0.533681i
\(795\) −0.398158 2.44996i −0.0141212 0.0868912i
\(796\) 22.6185 3.67586i 0.801691 0.130287i
\(797\) 29.3783 + 12.5169i 1.04063 + 0.443372i 0.843570 0.537019i \(-0.180450\pi\)
0.197062 + 0.980391i \(0.436860\pi\)
\(798\) 0.964525 0.117114i 0.0341438 0.00414581i
\(799\) −10.7540 + 2.19544i −0.380449 + 0.0776691i
\(800\) 17.0547 8.09255i 0.602974 0.286115i
\(801\) −10.6685 12.0422i −0.376952 0.425491i
\(802\) −3.14778 + 78.1114i −0.111152 + 2.75821i
\(803\) −7.10099 + 5.33605i −0.250588 + 0.188305i
\(804\) −14.5609 11.8886i −0.513522 0.419278i
\(805\) 0.528275 + 0.468010i 0.0186192 + 0.0164952i
\(806\) −15.2015 24.5075i −0.535449 0.863240i
\(807\) −3.68853 + 3.26776i −0.129843 + 0.115030i
\(808\) 11.3826 0.458702i 0.400438 0.0161371i
\(809\) −14.8230 + 31.2388i −0.521149 + 1.09830i 0.456822 + 0.889558i \(0.348988\pi\)
−0.977971 + 0.208741i \(0.933063\pi\)
\(810\) −3.20774 + 1.07090i −0.112708 + 0.0376276i
\(811\) −6.91568 + 28.0580i −0.242843 + 0.985251i 0.715268 + 0.698851i \(0.246305\pi\)
−0.958110 + 0.286400i \(0.907541\pi\)
\(812\) 8.49137 6.93299i 0.297989 0.243300i
\(813\) −16.2127 0.653349i −0.568603 0.0229139i
\(814\) −14.8147 + 28.2270i −0.519253 + 0.989355i
\(815\) 11.0193 11.4723i 0.385989 0.401857i
\(816\) 10.8977 + 3.63818i 0.381495 + 0.127362i
\(817\) 2.78392 4.40242i 0.0973972 0.154021i
\(818\) −50.8022 26.6630i −1.77626 0.932251i
\(819\) 1.96009 0.141124i 0.0684911 0.00493129i
\(820\) −39.6784 + 20.8248i −1.38563 + 0.727235i
\(821\) −1.03104 + 12.7718i −0.0359837 + 0.445738i 0.953530 + 0.301298i \(0.0974200\pi\)
−0.989514 + 0.144440i \(0.953862\pi\)
\(822\) −10.8245 18.7486i −0.377547 0.653931i
\(823\) 2.13798 3.70310i 0.0745255 0.129082i −0.826354 0.563150i \(-0.809589\pi\)
0.900880 + 0.434069i \(0.142922\pi\)
\(824\) −11.8754 8.19698i −0.413698 0.285555i
\(825\) −2.26560 + 5.31756i −0.0788781 + 0.185134i
\(826\) −9.24669 5.33858i −0.321733 0.185753i
\(827\) 3.27513 + 0.397672i 0.113887 + 0.0138284i 0.177282 0.984160i \(-0.443270\pi\)
−0.0633946 + 0.997989i \(0.520193\pi\)
\(828\) 2.43934 0.196924i 0.0847728 0.00684357i
\(829\) −6.09509 21.0427i −0.211691 0.730843i −0.994137 0.108125i \(-0.965515\pi\)
0.782446 0.622718i \(-0.213972\pi\)
\(830\) 12.9113 + 6.12648i 0.448157 + 0.212653i
\(831\) 7.27977 + 1.79430i 0.252532 + 0.0622436i
\(832\) 25.0648 38.8856i 0.868966 1.34812i
\(833\) −52.3935 + 12.9138i −1.81533 + 0.447438i
\(834\) −27.3322 5.57992i −0.946438 0.193217i
\(835\) −33.2220 2.68196i −1.14970 0.0928130i
\(836\) 1.01215 + 4.95784i 0.0350059 + 0.171470i
\(837\) −2.97674 + 2.05469i −0.102891 + 0.0710206i
\(838\) −2.02289 25.0580i −0.0698797 0.865615i
\(839\) 6.50498 + 10.2868i 0.224577 + 0.355140i 0.938615 0.344967i \(-0.112110\pi\)
−0.714038 + 0.700107i \(0.753136\pi\)
\(840\) 0.392675 + 1.59315i 0.0135486 + 0.0549688i
\(841\) 15.5304 + 11.6703i 0.535530 + 0.402425i
\(842\) 9.50856 11.6459i 0.327687 0.401343i
\(843\) 4.23997 12.7003i 0.146032 0.437420i
\(844\) −33.1786 −1.14205
\(845\) 3.52914 19.5646i 0.121406 0.673043i
\(846\) 3.01495 0.103656
\(847\) −1.08443 + 3.24828i −0.0372616 + 0.111612i
\(848\) 1.46495 1.79424i 0.0503065 0.0616143i
\(849\) 2.79039 + 2.09684i 0.0957658 + 0.0719634i
\(850\) −11.3386 46.0024i −0.388910 1.57787i
\(851\) 3.00384 + 4.75020i 0.102970 + 0.162835i
\(852\) −2.52728 31.3060i −0.0865832 1.07253i
\(853\) −35.7785 + 24.6961i −1.22503 + 0.845580i −0.991919 0.126870i \(-0.959507\pi\)
−0.233114 + 0.972449i \(0.574892\pi\)
\(854\) −0.167888 0.822369i −0.00574501 0.0281409i
\(855\) −1.22877 0.0991967i −0.0420231 0.00339246i
\(856\) −24.1911 4.93865i −0.826834 0.168799i
\(857\) 47.3741 11.6767i 1.61827 0.398867i 0.676853 0.736118i \(-0.263343\pi\)
0.941415 + 0.337251i \(0.109497\pi\)
\(858\) 2.62935 + 17.1159i 0.0897645 + 0.584328i
\(859\) 50.2064 + 12.3748i 1.71302 + 0.422222i 0.969223 0.246184i \(-0.0791767\pi\)
0.743797 + 0.668405i \(0.233023\pi\)
\(860\) 25.8019 + 12.2431i 0.879837 + 0.417488i
\(861\) −1.53741 5.30774i −0.0523947 0.180887i
\(862\) 45.4837 3.67182i 1.54918 0.125063i
\(863\) −21.0198 2.55226i −0.715521 0.0868800i −0.245324 0.969441i \(-0.578894\pi\)
−0.470197 + 0.882561i \(0.655817\pi\)
\(864\) −6.14278 3.54654i −0.208982 0.120656i
\(865\) 0.914195 2.14569i 0.0310836 0.0729558i
\(866\) 6.34764 + 4.38146i 0.215702 + 0.148888i
\(867\) 23.9048 41.4043i 0.811849 1.40616i
\(868\) 2.84889 + 4.93442i 0.0966975 + 0.167485i
\(869\) −2.11979 + 26.2583i −0.0719089 + 0.890752i
\(870\) −20.8379 + 10.9366i −0.706470 + 0.370784i
\(871\) −9.86875 21.2727i −0.334390 0.720798i
\(872\) 22.9773 + 12.0594i 0.778110 + 0.408384i
\(873\) −1.26919 + 2.00707i −0.0429556 + 0.0679289i
\(874\) 1.43176 + 0.477993i 0.0484301 + 0.0161684i
\(875\) −4.42359 + 4.60545i −0.149545 + 0.155693i
\(876\) −5.49319 + 10.4664i −0.185598 + 0.353627i
\(877\) 56.5459 + 2.27872i 1.90942 + 0.0769470i 0.966590 0.256326i \(-0.0825120\pi\)
0.942830 + 0.333273i \(0.108153\pi\)
\(878\) 52.1472 42.5769i 1.75988 1.43690i
\(879\) 1.28239 5.20285i 0.0432538 0.175488i
\(880\) 4.49599 1.50098i 0.151560 0.0505981i
\(881\) −9.46552 + 19.9482i −0.318902 + 0.672071i −0.998082 0.0619001i \(-0.980284\pi\)
0.679181 + 0.733971i \(0.262335\pi\)
\(882\) 14.8107 0.596852i 0.498703 0.0200970i
\(883\) 8.40444 7.44568i 0.282832 0.250567i −0.509764 0.860314i \(-0.670267\pi\)
0.792596 + 0.609747i \(0.208729\pi\)
\(884\) −59.9964 58.6369i −2.01790 1.97217i
\(885\) 10.1401 + 8.98338i 0.340857 + 0.301973i
\(886\) −32.0540 26.1713i −1.07688 0.879242i
\(887\) 23.2717 17.4876i 0.781389 0.587176i −0.133422 0.991059i \(-0.542596\pi\)
0.914810 + 0.403884i \(0.132340\pi\)
\(888\) −0.526134 + 13.0559i −0.0176559 + 0.438126i
\(889\) 7.58701 + 8.56396i 0.254460 + 0.287226i
\(890\) 49.1539 23.3238i 1.64764 0.781815i
\(891\) 2.12796 0.434426i 0.0712893 0.0145538i
\(892\) 15.1293 1.83703i 0.506565 0.0615082i
\(893\) 1.01110 + 0.430791i 0.0338353 + 0.0144159i
\(894\) 22.8962 3.72099i 0.765762 0.124448i
\(895\) −0.361649 2.22532i −0.0120886 0.0743841i
\(896\) −4.39305 + 6.36443i −0.146761 + 0.212621i
\(897\) 2.84509 + 1.10734i 0.0949948 + 0.0369729i
\(898\) 34.9039 + 50.5670i 1.16476 + 1.68744i
\(899\) −18.1530 + 17.4362i −0.605436 + 0.581529i
\(900\) 0.309721 + 7.68566i 0.0103240 + 0.256189i
\(901\) −8.26383 10.1214i −0.275308 0.337191i
\(902\) 45.5292 17.2669i 1.51596 0.574926i
\(903\) −2.11569 + 2.81547i −0.0704058 + 0.0936931i
\(904\) −30.5603 8.85191i −1.01642 0.294410i
\(905\) −3.67185 6.99612i −0.122056 0.232559i
\(906\) 5.55594 + 11.7089i 0.184584 + 0.389002i
\(907\) 9.29429 + 9.67638i 0.308612 + 0.321299i 0.857388 0.514670i \(-0.172086\pi\)
−0.548776 + 0.835969i \(0.684906\pi\)
\(908\) 40.7069 11.7909i 1.35090 0.391294i
\(909\) 2.05203 5.41075i 0.0680615 0.179463i
\(910\) −1.38578 + 6.49966i −0.0459382 + 0.215461i
\(911\) 20.5051 + 54.0674i 0.679363 + 1.79133i 0.608079 + 0.793877i \(0.291940\pi\)
0.0712840 + 0.997456i \(0.477290\pi\)
\(912\) −0.691113 0.919704i −0.0228850 0.0304545i
\(913\) −7.75719 4.90535i −0.256726 0.162343i
\(914\) −45.8129 7.44532i −1.51536 0.246269i
\(915\) 1.06494i 0.0352057i
\(916\) −5.70777 + 35.1213i −0.188590 + 1.16044i
\(917\) 6.32308 + 6.07340i 0.208806 + 0.200561i
\(918\) −11.8053 + 13.3254i −0.389633 + 0.439805i
\(919\) 7.67703 26.5042i 0.253242 0.874292i −0.728656 0.684880i \(-0.759855\pi\)
0.981898 0.189412i \(-0.0606583\pi\)
\(920\) −0.509888 + 2.49760i −0.0168105 + 0.0823433i
\(921\) 7.19305 + 16.8827i 0.237019 + 0.556304i
\(922\) 1.20027 9.88508i 0.0395287 0.325548i
\(923\) 14.2114 36.5133i 0.467773 1.20185i
\(924\) −0.412387 3.39631i −0.0135665 0.111730i
\(925\) −15.2982 + 8.83239i −0.503000 + 0.290407i
\(926\) 59.2999 25.2653i 1.94872 0.830271i
\(927\) −6.19521 + 3.91761i −0.203477 + 0.128671i
\(928\) −46.1525 17.5033i −1.51503 0.574575i
\(929\) 5.82665 + 17.4530i 0.191166 + 0.572613i 0.999878 0.0155917i \(-0.00496321\pi\)
−0.808712 + 0.588205i \(0.799835\pi\)
\(930\) −3.87345 11.6024i −0.127015 0.380458i
\(931\) 5.05225 + 1.91606i 0.165581 + 0.0627965i
\(932\) −61.2074 + 38.7052i −2.00492 + 1.26783i
\(933\) 10.2709 4.37603i 0.336255 0.143265i
\(934\) −5.73188 + 3.30930i −0.187553 + 0.108284i
\(935\) −3.22292 26.5431i −0.105401 0.868053i
\(936\) 3.98118 + 5.87618i 0.130129 + 0.192069i
\(937\) −2.24563 + 18.4944i −0.0733616 + 0.604187i 0.908946 + 0.416913i \(0.136888\pi\)
−0.982308 + 0.187274i \(0.940035\pi\)
\(938\) 3.07268 + 7.21185i 0.100327 + 0.235475i
\(939\) −2.56787 + 12.5783i −0.0837994 + 0.410477i
\(940\) −1.67653 + 5.78805i −0.0546823 + 0.188785i
\(941\) 18.0433 20.3667i 0.588196 0.663936i −0.376771 0.926306i \(-0.622966\pi\)
0.964967 + 0.262370i \(0.0845042\pi\)
\(942\) 14.2794 + 13.7155i 0.465247 + 0.446875i
\(943\) 1.37710 8.47364i 0.0448445 0.275940i
\(944\) 12.6423i 0.411471i
\(945\) 0.822712 + 0.133704i 0.0267628 + 0.00434938i
\(946\) −26.2292 16.5863i −0.852784 0.539268i
\(947\) −18.3744 24.4519i −0.597089 0.794581i 0.395191 0.918599i \(-0.370678\pi\)
−0.992280 + 0.124018i \(0.960422\pi\)
\(948\) 12.4314 + 32.7790i 0.403754 + 1.06461i
\(949\) −11.8650 + 8.75589i −0.385154 + 0.284228i
\(950\) −1.68234 + 4.43596i −0.0545823 + 0.143922i
\(951\) −23.3892 + 6.77475i −0.758445 + 0.219686i
\(952\) 5.98359 + 6.22957i 0.193929 + 0.201902i
\(953\) −8.93679 18.8339i −0.289491 0.610089i 0.705649 0.708562i \(-0.250656\pi\)
−0.995140 + 0.0984725i \(0.968604\pi\)
\(954\) 1.66800 + 3.17811i 0.0540036 + 0.102895i
\(955\) −18.5849 5.38319i −0.601394 0.174196i
\(956\) 6.89336 9.17340i 0.222947 0.296689i
\(957\) 14.1316 5.35940i 0.456809 0.173245i
\(958\) −43.2830 53.0120i −1.39841 1.71274i
\(959\) 0.214852 + 5.33149i 0.00693792 + 0.172163i
\(960\) 14.1517 13.5929i 0.456743 0.438708i
\(961\) 10.1782 + 14.7456i 0.328328 + 0.475666i
\(962\) −25.0000 + 46.6452i −0.806032 + 1.50390i
\(963\) −7.12468 + 10.3219i −0.229590 + 0.332618i
\(964\) −2.51078 15.4495i −0.0808669 0.497594i
\(965\) 8.35245 1.35741i 0.268875 0.0436964i
\(966\) −0.938906 0.400031i −0.0302088 0.0128708i
\(967\) 13.7560 1.67028i 0.442364 0.0537127i 0.103675 0.994611i \(-0.466940\pi\)
0.338689 + 0.940898i \(0.390017\pi\)
\(968\) −12.1188 + 2.47407i −0.389513 + 0.0795196i
\(969\) −5.86306 + 2.78206i −0.188349 + 0.0893725i
\(970\) −5.32532 6.01105i −0.170986 0.193003i
\(971\) −1.75154 + 43.4639i −0.0562094 + 1.39482i 0.687434 + 0.726247i \(0.258737\pi\)
−0.743644 + 0.668576i \(0.766904\pi\)
\(972\) 2.31055 1.73627i 0.0741111 0.0556909i
\(973\) 5.32581 + 4.34839i 0.170738 + 0.139403i
\(974\) 56.9213 + 50.4279i 1.82388 + 1.61581i
\(975\) −3.83766 + 8.79486i −0.122904 + 0.281661i
\(976\) −0.743877 + 0.659018i −0.0238109 + 0.0210946i
\(977\) 15.9779 0.643887i 0.511178 0.0205998i 0.216663 0.976247i \(-0.430483\pi\)
0.294515 + 0.955647i \(0.404842\pi\)
\(978\) −9.86101 + 20.7816i −0.315320 + 0.664523i
\(979\) −33.1430 + 11.0648i −1.05926 + 0.353632i
\(980\) −7.09000 + 28.7652i −0.226482 + 0.918872i
\(981\) 10.2108 8.33683i 0.326005 0.266175i
\(982\) 95.0155 + 3.82899i 3.03207 + 0.122188i
\(983\) −27.2558 + 51.9317i −0.869326 + 1.65636i −0.121377 + 0.992606i \(0.538731\pi\)
−0.747949 + 0.663756i \(0.768961\pi\)
\(984\) 13.8259 14.3942i 0.440752 0.458872i
\(985\) 18.0691 + 6.03234i 0.575728 + 0.192206i
\(986\) −66.2132 + 104.708i −2.10866 + 3.33458i
\(987\) −0.657977 0.345333i −0.0209436 0.0109921i
\(988\) 1.60881 + 8.24493i 0.0511829 + 0.262306i
\(989\) −4.84459 + 2.54264i −0.154049 + 0.0808512i
\(990\) −0.591003 + 7.32089i −0.0187833 + 0.232673i
\(991\) 19.2113 + 33.2749i 0.610267 + 1.05701i 0.991195 + 0.132409i \(0.0422712\pi\)
−0.380928 + 0.924605i \(0.624395\pi\)
\(992\) 12.8278 22.2185i 0.407284 0.705437i
\(993\) −16.4128 11.3290i −0.520846 0.359514i
\(994\) −5.13392 + 12.0497i −0.162838 + 0.382195i
\(995\) 10.5004 + 6.06243i 0.332886 + 0.192192i
\(996\) −12.1247 1.47221i −0.384186 0.0466486i
\(997\) 26.5415 2.14265i 0.840577 0.0678584i 0.347325 0.937745i \(-0.387090\pi\)
0.493252 + 0.869887i \(0.335808\pi\)
\(998\) 5.26241 + 18.1680i 0.166579 + 0.575097i
\(999\) 5.99664 + 2.84544i 0.189725 + 0.0900258i
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.t.b.205.2 360
169.108 even 78 inner 507.2.t.b.277.2 yes 360
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.t.b.205.2 360 1.1 even 1 trivial
507.2.t.b.277.2 yes 360 169.108 even 78 inner