Properties

Label 950.2.l.l.351.2
Level $950$
Weight $2$
Character 950.351
Analytic conductor $7.586$
Analytic rank $0$
Dimension $30$
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] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 351.2
Character \(\chi\) \(=\) 950.351
Dual form 950.2.l.l.701.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.173648 - 0.984808i) q^{2} +(-1.28288 + 1.07646i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28288 + 1.07646i) q^{6} +(-1.16183 + 2.01234i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.0339381 + 0.192472i) q^{9} +O(q^{10})\) \(q+(-0.173648 - 0.984808i) q^{2} +(-1.28288 + 1.07646i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28288 + 1.07646i) q^{6} +(-1.16183 + 2.01234i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.0339381 + 0.192472i) q^{9} +(1.54750 + 2.68035i) q^{11} +(0.837341 - 1.45032i) q^{12} +(-5.18492 - 4.35067i) q^{13} +(2.18352 + 0.794737i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.818439 + 4.64160i) q^{17} +0.195441 q^{18} +(-0.846315 - 4.27595i) q^{19} +(-0.675731 - 3.83226i) q^{21} +(2.37091 - 1.98943i) q^{22} +(2.99540 - 1.09024i) q^{23} +(-1.57369 - 0.572775i) q^{24} +(-3.38422 + 5.86164i) q^{26} +(-2.67567 - 4.63440i) q^{27} +(0.403498 - 2.28835i) q^{28} +(0.115201 - 0.653337i) q^{29} +(2.25407 - 3.90416i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-4.87056 - 1.77274i) q^{33} +(4.42896 - 1.61201i) q^{34} +(-0.0339381 - 0.192472i) q^{36} -9.57421 q^{37} +(-4.06403 + 1.57597i) q^{38} +11.3350 q^{39} +(1.86510 - 1.56501i) q^{41} +(-3.65670 + 1.33093i) q^{42} +(-2.05525 - 0.748052i) q^{43} +(-2.37091 - 1.98943i) q^{44} +(-1.59382 - 2.76058i) q^{46} +(1.08992 - 6.18124i) q^{47} +(-0.290805 + 1.64924i) q^{48} +(0.800316 + 1.38619i) q^{49} +(-6.04648 - 5.07360i) q^{51} +(6.36025 + 2.31494i) q^{52} +(-9.43800 + 3.43515i) q^{53} +(-4.09937 + 3.43978i) q^{54} -2.32365 q^{56} +(5.68863 + 4.57451i) q^{57} -0.663415 q^{58} +(-1.77002 - 10.0383i) q^{59} +(-3.49881 + 1.27346i) q^{61} +(-4.23626 - 1.54187i) q^{62} +(-0.347890 - 0.291915i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.900044 + 5.10440i) q^{66} +(0.920817 - 5.22221i) q^{67} +(-2.35660 - 4.08175i) q^{68} +(-2.66914 + 4.62309i) q^{69} +(-11.0982 - 4.03942i) q^{71} +(-0.183655 + 0.0668449i) q^{72} +(1.96449 - 1.64840i) q^{73} +(1.66254 + 9.42875i) q^{74} +(2.25774 + 3.72862i) q^{76} -7.19172 q^{77} +(-1.96830 - 11.1628i) q^{78} +(-12.6337 + 10.6009i) q^{79} +(7.87038 + 2.86458i) q^{81} +(-1.86510 - 1.56501i) q^{82} +(3.21477 - 5.56814i) q^{83} +(1.94569 + 3.37003i) q^{84} +(-0.379796 + 2.15393i) q^{86} +(0.555505 + 0.962162i) q^{87} +(-1.54750 + 2.68035i) q^{88} +(-6.47935 - 5.43682i) q^{89} +(14.7790 - 5.37912i) q^{91} +(-2.44187 + 2.04898i) q^{92} +(1.31099 + 7.43499i) q^{93} -6.27659 q^{94} +1.67468 q^{96} +(0.923151 + 5.23545i) q^{97} +(1.22615 - 1.02887i) q^{98} +(-0.568413 + 0.206885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 0.984808i −0.122788 0.696364i
\(3\) −1.28288 + 1.07646i −0.740671 + 0.621497i −0.933018 0.359830i \(-0.882835\pi\)
0.192346 + 0.981327i \(0.438390\pi\)
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) 0 0
\(6\) 1.28288 + 1.07646i 0.523734 + 0.439465i
\(7\) −1.16183 + 2.01234i −0.439129 + 0.760594i −0.997623 0.0689147i \(-0.978046\pi\)
0.558493 + 0.829509i \(0.311380\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) −0.0339381 + 0.192472i −0.0113127 + 0.0641574i
\(10\) 0 0
\(11\) 1.54750 + 2.68035i 0.466589 + 0.808156i 0.999272 0.0381589i \(-0.0121493\pi\)
−0.532682 + 0.846315i \(0.678816\pi\)
\(12\) 0.837341 1.45032i 0.241719 0.418670i
\(13\) −5.18492 4.35067i −1.43804 1.20666i −0.940763 0.339065i \(-0.889889\pi\)
−0.497275 0.867593i \(-0.665666\pi\)
\(14\) 2.18352 + 0.794737i 0.583570 + 0.212402i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) 0.818439 + 4.64160i 0.198501 + 1.12575i 0.907345 + 0.420388i \(0.138106\pi\)
−0.708844 + 0.705365i \(0.750783\pi\)
\(18\) 0.195441 0.0460660
\(19\) −0.846315 4.27595i −0.194158 0.980970i
\(20\) 0 0
\(21\) −0.675731 3.83226i −0.147457 0.836268i
\(22\) 2.37091 1.98943i 0.505480 0.424148i
\(23\) 2.99540 1.09024i 0.624585 0.227330i −0.0102880 0.999947i \(-0.503275\pi\)
0.634873 + 0.772617i \(0.281053\pi\)
\(24\) −1.57369 0.572775i −0.321227 0.116917i
\(25\) 0 0
\(26\) −3.38422 + 5.86164i −0.663700 + 1.14956i
\(27\) −2.67567 4.63440i −0.514934 0.891891i
\(28\) 0.403498 2.28835i 0.0762540 0.432458i
\(29\) 0.115201 0.653337i 0.0213923 0.121322i −0.972242 0.233979i \(-0.924825\pi\)
0.993634 + 0.112658i \(0.0359363\pi\)
\(30\) 0 0
\(31\) 2.25407 3.90416i 0.404842 0.701207i −0.589461 0.807797i \(-0.700660\pi\)
0.994303 + 0.106590i \(0.0339932\pi\)
\(32\) −0.766044 0.642788i −0.135419 0.113630i
\(33\) −4.87056 1.77274i −0.847856 0.308594i
\(34\) 4.42896 1.61201i 0.759561 0.276458i
\(35\) 0 0
\(36\) −0.0339381 0.192472i −0.00565634 0.0320787i
\(37\) −9.57421 −1.57399 −0.786995 0.616959i \(-0.788364\pi\)
−0.786995 + 0.616959i \(0.788364\pi\)
\(38\) −4.06403 + 1.57597i −0.659272 + 0.255656i
\(39\) 11.3350 1.81505
\(40\) 0 0
\(41\) 1.86510 1.56501i 0.291280 0.244413i −0.485424 0.874279i \(-0.661335\pi\)
0.776704 + 0.629866i \(0.216890\pi\)
\(42\) −3.65670 + 1.33093i −0.564241 + 0.205367i
\(43\) −2.05525 0.748052i −0.313423 0.114077i 0.180519 0.983572i \(-0.442222\pi\)
−0.493942 + 0.869495i \(0.664445\pi\)
\(44\) −2.37091 1.98943i −0.357428 0.299918i
\(45\) 0 0
\(46\) −1.59382 2.76058i −0.234996 0.407025i
\(47\) 1.08992 6.18124i 0.158981 0.901626i −0.796074 0.605199i \(-0.793094\pi\)
0.955055 0.296427i \(-0.0957953\pi\)
\(48\) −0.290805 + 1.64924i −0.0419741 + 0.238047i
\(49\) 0.800316 + 1.38619i 0.114331 + 0.198027i
\(50\) 0 0
\(51\) −6.04648 5.07360i −0.846676 0.710446i
\(52\) 6.36025 + 2.31494i 0.882008 + 0.321025i
\(53\) −9.43800 + 3.43515i −1.29641 + 0.471854i −0.895825 0.444406i \(-0.853415\pi\)
−0.400583 + 0.916260i \(0.631193\pi\)
\(54\) −4.09937 + 3.43978i −0.557854 + 0.468095i
\(55\) 0 0
\(56\) −2.32365 −0.310511
\(57\) 5.68863 + 4.57451i 0.753477 + 0.605908i
\(58\) −0.663415 −0.0871107
\(59\) −1.77002 10.0383i −0.230437 1.30687i −0.852014 0.523519i \(-0.824619\pi\)
0.621577 0.783353i \(-0.286492\pi\)
\(60\) 0 0
\(61\) −3.49881 + 1.27346i −0.447976 + 0.163050i −0.556150 0.831082i \(-0.687722\pi\)
0.108174 + 0.994132i \(0.465500\pi\)
\(62\) −4.23626 1.54187i −0.538005 0.195818i
\(63\) −0.347890 0.291915i −0.0438300 0.0367778i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −0.900044 + 5.10440i −0.110788 + 0.628308i
\(67\) 0.920817 5.22221i 0.112496 0.637995i −0.875464 0.483283i \(-0.839444\pi\)
0.987960 0.154711i \(-0.0494448\pi\)
\(68\) −2.35660 4.08175i −0.285780 0.494985i
\(69\) −2.66914 + 4.62309i −0.321327 + 0.556554i
\(70\) 0 0
\(71\) −11.0982 4.03942i −1.31711 0.479390i −0.414582 0.910012i \(-0.636072\pi\)
−0.902533 + 0.430621i \(0.858294\pi\)
\(72\) −0.183655 + 0.0668449i −0.0216439 + 0.00787775i
\(73\) 1.96449 1.64840i 0.229926 0.192931i −0.520545 0.853834i \(-0.674271\pi\)
0.750471 + 0.660903i \(0.229827\pi\)
\(74\) 1.66254 + 9.42875i 0.193267 + 1.09607i
\(75\) 0 0
\(76\) 2.25774 + 3.72862i 0.258980 + 0.427702i
\(77\) −7.19172 −0.819572
\(78\) −1.96830 11.1628i −0.222866 1.26393i
\(79\) −12.6337 + 10.6009i −1.42140 + 1.19270i −0.470821 + 0.882229i \(0.656042\pi\)
−0.950583 + 0.310470i \(0.899513\pi\)
\(80\) 0 0
\(81\) 7.87038 + 2.86458i 0.874486 + 0.318287i
\(82\) −1.86510 1.56501i −0.205966 0.172826i
\(83\) 3.21477 5.56814i 0.352866 0.611183i −0.633884 0.773428i \(-0.718540\pi\)
0.986750 + 0.162246i \(0.0518737\pi\)
\(84\) 1.94569 + 3.37003i 0.212292 + 0.367701i
\(85\) 0 0
\(86\) −0.379796 + 2.15393i −0.0409544 + 0.232264i
\(87\) 0.555505 + 0.962162i 0.0595564 + 0.103155i
\(88\) −1.54750 + 2.68035i −0.164964 + 0.285726i
\(89\) −6.47935 5.43682i −0.686810 0.576302i 0.231178 0.972912i \(-0.425742\pi\)
−0.917987 + 0.396610i \(0.870187\pi\)
\(90\) 0 0
\(91\) 14.7790 5.37912i 1.54926 0.563885i
\(92\) −2.44187 + 2.04898i −0.254583 + 0.213620i
\(93\) 1.31099 + 7.43499i 0.135943 + 0.770972i
\(94\) −6.27659 −0.647381
\(95\) 0 0
\(96\) 1.67468 0.170921
\(97\) 0.923151 + 5.23545i 0.0937318 + 0.531579i 0.995129 + 0.0985853i \(0.0314317\pi\)
−0.901397 + 0.432994i \(0.857457\pi\)
\(98\) 1.22615 1.02887i 0.123860 0.103931i
\(99\) −0.568413 + 0.206885i −0.0571276 + 0.0207927i
\(100\) 0 0
\(101\) −9.73383 8.16765i −0.968552 0.812712i 0.0137710 0.999905i \(-0.495616\pi\)
−0.982323 + 0.187193i \(0.940061\pi\)
\(102\) −3.94656 + 6.83564i −0.390767 + 0.676829i
\(103\) 4.56327 + 7.90381i 0.449632 + 0.778785i 0.998362 0.0572143i \(-0.0182218\pi\)
−0.548730 + 0.836000i \(0.684888\pi\)
\(104\) 1.17533 6.66561i 0.115250 0.653616i
\(105\) 0 0
\(106\) 5.02185 + 8.69811i 0.487766 + 0.844835i
\(107\) 4.47737 7.75503i 0.432843 0.749707i −0.564274 0.825588i \(-0.690844\pi\)
0.997117 + 0.0758813i \(0.0241770\pi\)
\(108\) 4.09937 + 3.43978i 0.394462 + 0.330993i
\(109\) 9.01456 + 3.28103i 0.863439 + 0.314266i 0.735507 0.677517i \(-0.236944\pi\)
0.127932 + 0.991783i \(0.459166\pi\)
\(110\) 0 0
\(111\) 12.2826 10.3063i 1.16581 0.978230i
\(112\) 0.403498 + 2.28835i 0.0381270 + 0.216229i
\(113\) −3.77955 −0.355551 −0.177775 0.984071i \(-0.556890\pi\)
−0.177775 + 0.984071i \(0.556890\pi\)
\(114\) 3.51719 6.39656i 0.329415 0.599093i
\(115\) 0 0
\(116\) 0.115201 + 0.653337i 0.0106961 + 0.0606608i
\(117\) 1.01335 0.850300i 0.0936841 0.0786103i
\(118\) −9.57841 + 3.48626i −0.881764 + 0.320936i
\(119\) −10.2914 3.74575i −0.943409 0.343373i
\(120\) 0 0
\(121\) 0.710478 1.23058i 0.0645889 0.111871i
\(122\) 1.86168 + 3.22452i 0.168548 + 0.291934i
\(123\) −0.708029 + 4.01543i −0.0638408 + 0.362059i
\(124\) −0.782829 + 4.43964i −0.0703001 + 0.398692i
\(125\) 0 0
\(126\) −0.227069 + 0.393295i −0.0202289 + 0.0350375i
\(127\) 1.37966 + 1.15767i 0.122425 + 0.102727i 0.701945 0.712231i \(-0.252315\pi\)
−0.579520 + 0.814958i \(0.696760\pi\)
\(128\) 0.939693 + 0.342020i 0.0830579 + 0.0302306i
\(129\) 3.44190 1.25275i 0.303042 0.110298i
\(130\) 0 0
\(131\) 1.39065 + 7.88678i 0.121502 + 0.689072i 0.983324 + 0.181861i \(0.0582122\pi\)
−0.861822 + 0.507210i \(0.830677\pi\)
\(132\) 5.18314 0.451135
\(133\) 9.58795 + 3.26484i 0.831381 + 0.283097i
\(134\) −5.30277 −0.458090
\(135\) 0 0
\(136\) −3.61052 + 3.02959i −0.309600 + 0.259785i
\(137\) 18.0566 6.57208i 1.54268 0.561491i 0.575996 0.817452i \(-0.304614\pi\)
0.966687 + 0.255961i \(0.0823920\pi\)
\(138\) 5.01634 + 1.82580i 0.427020 + 0.155422i
\(139\) −0.826741 0.693718i −0.0701233 0.0588404i 0.607052 0.794662i \(-0.292352\pi\)
−0.677176 + 0.735821i \(0.736796\pi\)
\(140\) 0 0
\(141\) 5.25565 + 9.10305i 0.442605 + 0.766615i
\(142\) −2.05087 + 11.6310i −0.172105 + 0.976055i
\(143\) 3.63764 20.6301i 0.304195 1.72517i
\(144\) 0.0977207 + 0.169257i 0.00814339 + 0.0141048i
\(145\) 0 0
\(146\) −1.96449 1.64840i −0.162582 0.136423i
\(147\) −2.51889 0.916801i −0.207755 0.0756165i
\(148\) 8.99681 3.27457i 0.739533 0.269168i
\(149\) −2.12048 + 1.77929i −0.173716 + 0.145765i −0.725501 0.688222i \(-0.758392\pi\)
0.551784 + 0.833987i \(0.313947\pi\)
\(150\) 0 0
\(151\) −10.2734 −0.836034 −0.418017 0.908439i \(-0.637275\pi\)
−0.418017 + 0.908439i \(0.637275\pi\)
\(152\) 3.27992 2.87091i 0.266037 0.232861i
\(153\) −0.921155 −0.0744710
\(154\) 1.24883 + 7.08246i 0.100633 + 0.570721i
\(155\) 0 0
\(156\) −10.6514 + 3.87679i −0.852794 + 0.310392i
\(157\) −6.55116 2.38443i −0.522840 0.190298i 0.0670986 0.997746i \(-0.478626\pi\)
−0.589938 + 0.807448i \(0.700848\pi\)
\(158\) 12.6337 + 10.6009i 1.00508 + 0.843366i
\(159\) 8.41001 14.5666i 0.666957 1.15520i
\(160\) 0 0
\(161\) −1.28621 + 7.29445i −0.101367 + 0.574883i
\(162\) 1.45439 8.24824i 0.114267 0.648043i
\(163\) 2.51501 + 4.35612i 0.196991 + 0.341198i 0.947551 0.319604i \(-0.103550\pi\)
−0.750561 + 0.660802i \(0.770216\pi\)
\(164\) −1.21736 + 2.10853i −0.0950598 + 0.164648i
\(165\) 0 0
\(166\) −6.04178 2.19903i −0.468933 0.170678i
\(167\) 5.55242 2.02091i 0.429659 0.156383i −0.118133 0.992998i \(-0.537691\pi\)
0.547792 + 0.836615i \(0.315469\pi\)
\(168\) 2.98097 2.50133i 0.229987 0.192982i
\(169\) 5.69769 + 32.3132i 0.438284 + 2.48563i
\(170\) 0 0
\(171\) 0.851724 0.0177748i 0.0651330 0.00135927i
\(172\) 2.18716 0.166769
\(173\) 3.35907 + 19.0502i 0.255386 + 1.44836i 0.795081 + 0.606503i \(0.207428\pi\)
−0.539695 + 0.841860i \(0.681461\pi\)
\(174\) 0.851083 0.714143i 0.0645204 0.0541391i
\(175\) 0 0
\(176\) 2.90835 + 1.05855i 0.219225 + 0.0797915i
\(177\) 13.0766 + 10.9725i 0.982895 + 0.824747i
\(178\) −4.22909 + 7.32501i −0.316984 + 0.549032i
\(179\) 3.95499 + 6.85025i 0.295610 + 0.512012i 0.975127 0.221648i \(-0.0711437\pi\)
−0.679517 + 0.733660i \(0.737810\pi\)
\(180\) 0 0
\(181\) −2.41624 + 13.7032i −0.179597 + 1.01855i 0.753105 + 0.657900i \(0.228555\pi\)
−0.932702 + 0.360647i \(0.882556\pi\)
\(182\) −7.86375 13.6204i −0.582900 1.00961i
\(183\) 3.11772 5.40004i 0.230468 0.399183i
\(184\) 2.44187 + 2.04898i 0.180017 + 0.151052i
\(185\) 0 0
\(186\) 7.09438 2.58214i 0.520185 0.189332i
\(187\) −11.1746 + 9.37659i −0.817166 + 0.685684i
\(188\) 1.08992 + 6.18124i 0.0794905 + 0.450813i
\(189\) 12.4347 0.904490
\(190\) 0 0
\(191\) −20.3770 −1.47442 −0.737212 0.675661i \(-0.763858\pi\)
−0.737212 + 0.675661i \(0.763858\pi\)
\(192\) −0.290805 1.64924i −0.0209871 0.119024i
\(193\) 14.1218 11.8496i 1.01651 0.852955i 0.0273270 0.999627i \(-0.491300\pi\)
0.989185 + 0.146671i \(0.0468560\pi\)
\(194\) 4.99561 1.81825i 0.358664 0.130543i
\(195\) 0 0
\(196\) −1.22615 1.02887i −0.0875825 0.0734904i
\(197\) −4.44834 + 7.70476i −0.316931 + 0.548941i −0.979846 0.199754i \(-0.935986\pi\)
0.662915 + 0.748695i \(0.269319\pi\)
\(198\) 0.302446 + 0.523852i 0.0214939 + 0.0372285i
\(199\) 4.19553 23.7940i 0.297413 1.68671i −0.359817 0.933023i \(-0.617161\pi\)
0.657230 0.753690i \(-0.271728\pi\)
\(200\) 0 0
\(201\) 4.44023 + 7.69070i 0.313190 + 0.542460i
\(202\) −6.35330 + 11.0042i −0.447017 + 0.774256i
\(203\) 1.18089 + 0.990888i 0.0828825 + 0.0695467i
\(204\) 7.41710 + 2.69960i 0.519301 + 0.189010i
\(205\) 0 0
\(206\) 6.99133 5.86642i 0.487109 0.408733i
\(207\) 0.108182 + 0.613532i 0.00751919 + 0.0426435i
\(208\) −6.76843 −0.469306
\(209\) 10.1514 8.88546i 0.702185 0.614620i
\(210\) 0 0
\(211\) 0.876981 + 4.97361i 0.0603739 + 0.342397i 1.00000 0.000194382i \(6.18739e-5\pi\)
−0.939626 + 0.342203i \(0.888827\pi\)
\(212\) 7.69393 6.45597i 0.528421 0.443398i
\(213\) 18.5860 6.76474i 1.27349 0.463512i
\(214\) −8.41470 3.06270i −0.575217 0.209362i
\(215\) 0 0
\(216\) 2.67567 4.63440i 0.182057 0.315331i
\(217\) 5.23767 + 9.07191i 0.355556 + 0.615841i
\(218\) 1.66582 9.44736i 0.112824 0.639856i
\(219\) −0.745759 + 4.22941i −0.0503937 + 0.285797i
\(220\) 0 0
\(221\) 15.9505 27.6271i 1.07295 1.85840i
\(222\) −12.2826 10.3063i −0.824352 0.691713i
\(223\) 2.60238 + 0.947189i 0.174268 + 0.0634285i 0.427681 0.903930i \(-0.359331\pi\)
−0.253412 + 0.967358i \(0.581553\pi\)
\(224\) 2.18352 0.794737i 0.145893 0.0531006i
\(225\) 0 0
\(226\) 0.656313 + 3.72213i 0.0436573 + 0.247593i
\(227\) 11.4199 0.757967 0.378984 0.925403i \(-0.376274\pi\)
0.378984 + 0.925403i \(0.376274\pi\)
\(228\) −6.91014 2.35300i −0.457635 0.155831i
\(229\) −15.0259 −0.992937 −0.496469 0.868055i \(-0.665370\pi\)
−0.496469 + 0.868055i \(0.665370\pi\)
\(230\) 0 0
\(231\) 9.22611 7.74163i 0.607034 0.509362i
\(232\) 0.623407 0.226901i 0.0409286 0.0148968i
\(233\) −7.44632 2.71024i −0.487825 0.177554i 0.0863852 0.996262i \(-0.472468\pi\)
−0.574210 + 0.818708i \(0.694691\pi\)
\(234\) −1.01335 0.850300i −0.0662447 0.0555859i
\(235\) 0 0
\(236\) 5.09657 + 8.82751i 0.331758 + 0.574622i
\(237\) 4.79600 27.1995i 0.311534 1.76680i
\(238\) −1.90177 + 10.7855i −0.123273 + 0.699118i
\(239\) −7.40667 12.8287i −0.479097 0.829821i 0.520615 0.853791i \(-0.325703\pi\)
−0.999713 + 0.0239703i \(0.992369\pi\)
\(240\) 0 0
\(241\) −6.26586 5.25768i −0.403620 0.338677i 0.418271 0.908322i \(-0.362636\pi\)
−0.821891 + 0.569645i \(0.807081\pi\)
\(242\) −1.33526 0.485995i −0.0858338 0.0312410i
\(243\) 1.90549 0.693542i 0.122237 0.0444908i
\(244\) 2.85225 2.39333i 0.182597 0.153217i
\(245\) 0 0
\(246\) 4.07738 0.259964
\(247\) −14.2152 + 25.8525i −0.904488 + 1.64496i
\(248\) 4.50813 0.286267
\(249\) 1.86974 + 10.6038i 0.118490 + 0.671991i
\(250\) 0 0
\(251\) −0.806527 + 0.293552i −0.0509075 + 0.0185288i −0.367348 0.930083i \(-0.619734\pi\)
0.316441 + 0.948612i \(0.397512\pi\)
\(252\) 0.426751 + 0.155324i 0.0268828 + 0.00978452i
\(253\) 7.55761 + 6.34159i 0.475143 + 0.398692i
\(254\) 0.900509 1.55973i 0.0565030 0.0978660i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −1.97617 + 11.2074i −0.123270 + 0.699101i 0.859050 + 0.511892i \(0.171055\pi\)
−0.982320 + 0.187209i \(0.940056\pi\)
\(258\) −1.83140 3.17207i −0.114018 0.197484i
\(259\) 11.1236 19.2666i 0.691185 1.19717i
\(260\) 0 0
\(261\) 0.121839 + 0.0443459i 0.00754168 + 0.00274495i
\(262\) 7.52548 2.73905i 0.464926 0.169219i
\(263\) −9.72539 + 8.16057i −0.599693 + 0.503202i −0.891347 0.453322i \(-0.850239\pi\)
0.291654 + 0.956524i \(0.405794\pi\)
\(264\) −0.900044 5.10440i −0.0553939 0.314154i
\(265\) 0 0
\(266\) 1.55031 10.0092i 0.0950554 0.613705i
\(267\) 14.1648 0.866870
\(268\) 0.920817 + 5.22221i 0.0562478 + 0.318997i
\(269\) −16.7636 + 14.0663i −1.02209 + 0.857639i −0.989889 0.141842i \(-0.954698\pi\)
−0.0322055 + 0.999481i \(0.510253\pi\)
\(270\) 0 0
\(271\) 13.2666 + 4.82863i 0.805886 + 0.293319i 0.711924 0.702257i \(-0.247824\pi\)
0.0939629 + 0.995576i \(0.470046\pi\)
\(272\) 3.61052 + 3.02959i 0.218920 + 0.183696i
\(273\) −13.1693 + 22.8099i −0.797041 + 1.38052i
\(274\) −9.60774 16.6411i −0.580425 1.00533i
\(275\) 0 0
\(276\) 0.926983 5.25718i 0.0557978 0.316445i
\(277\) −9.12112 15.7982i −0.548035 0.949225i −0.998409 0.0563847i \(-0.982043\pi\)
0.450374 0.892840i \(-0.351291\pi\)
\(278\) −0.539617 + 0.934644i −0.0323641 + 0.0560562i
\(279\) 0.674943 + 0.566344i 0.0404078 + 0.0339062i
\(280\) 0 0
\(281\) −12.2228 + 4.44872i −0.729149 + 0.265389i −0.679805 0.733393i \(-0.737935\pi\)
−0.0493445 + 0.998782i \(0.515713\pi\)
\(282\) 8.05212 6.75653i 0.479497 0.402346i
\(283\) 0.505725 + 2.86811i 0.0300622 + 0.170491i 0.996142 0.0877507i \(-0.0279679\pi\)
−0.966080 + 0.258242i \(0.916857\pi\)
\(284\) 11.8105 0.700822
\(285\) 0 0
\(286\) −20.9483 −1.23870
\(287\) 0.982405 + 5.57149i 0.0579895 + 0.328875i
\(288\) 0.149717 0.125627i 0.00882215 0.00740266i
\(289\) −4.89983 + 1.78339i −0.288225 + 0.104905i
\(290\) 0 0
\(291\) −6.82007 5.72272i −0.399799 0.335472i
\(292\) −1.28223 + 2.22089i −0.0750368 + 0.129968i
\(293\) −0.680540 1.17873i −0.0397575 0.0688621i 0.845462 0.534036i \(-0.179325\pi\)
−0.885219 + 0.465174i \(0.845992\pi\)
\(294\) −0.465472 + 2.63982i −0.0271469 + 0.153958i
\(295\) 0 0
\(296\) −4.78710 8.29151i −0.278245 0.481934i
\(297\) 8.28122 14.3435i 0.480525 0.832294i
\(298\) 2.12048 + 1.77929i 0.122836 + 0.103072i
\(299\) −20.2742 7.37920i −1.17249 0.426750i
\(300\) 0 0
\(301\) 3.89319 3.26677i 0.224400 0.188294i
\(302\) 1.78395 + 10.1173i 0.102655 + 0.582184i
\(303\) 21.2795 1.22248
\(304\) −3.39684 2.73157i −0.194822 0.156666i
\(305\) 0 0
\(306\) 0.159957 + 0.907161i 0.00914413 + 0.0518589i
\(307\) −1.00946 + 0.847040i −0.0576131 + 0.0483431i −0.671140 0.741331i \(-0.734195\pi\)
0.613526 + 0.789674i \(0.289750\pi\)
\(308\) 6.75800 2.45971i 0.385073 0.140155i
\(309\) −14.3623 5.22745i −0.817042 0.297379i
\(310\) 0 0
\(311\) 2.94243 5.09644i 0.166850 0.288993i −0.770461 0.637487i \(-0.779974\pi\)
0.937311 + 0.348495i \(0.113307\pi\)
\(312\) 5.66749 + 9.81637i 0.320858 + 0.555743i
\(313\) 1.08099 6.13058i 0.0611010 0.346521i −0.938896 0.344200i \(-0.888150\pi\)
0.999997 0.00232080i \(-0.000738735\pi\)
\(314\) −1.21061 + 6.86569i −0.0683185 + 0.387453i
\(315\) 0 0
\(316\) 8.24607 14.2826i 0.463878 0.803460i
\(317\) −16.4488 13.8022i −0.923856 0.775207i 0.0508485 0.998706i \(-0.483807\pi\)
−0.974704 + 0.223500i \(0.928252\pi\)
\(318\) −15.8056 5.75278i −0.886337 0.322600i
\(319\) 1.92945 0.702261i 0.108028 0.0393190i
\(320\) 0 0
\(321\) 2.60408 + 14.7685i 0.145346 + 0.824297i
\(322\) 7.40697 0.412775
\(323\) 19.1546 7.42786i 1.06579 0.413297i
\(324\) −8.37548 −0.465304
\(325\) 0 0
\(326\) 3.85322 3.23323i 0.213410 0.179072i
\(327\) −15.0965 + 5.49469i −0.834840 + 0.303857i
\(328\) 2.28789 + 0.832723i 0.126327 + 0.0459794i
\(329\) 11.1725 + 9.37482i 0.615959 + 0.516851i
\(330\) 0 0
\(331\) −10.2669 17.7827i −0.564318 0.977427i −0.997113 0.0759348i \(-0.975806\pi\)
0.432795 0.901492i \(-0.357527\pi\)
\(332\) −1.11648 + 6.33185i −0.0612746 + 0.347506i
\(333\) 0.324930 1.84277i 0.0178061 0.100983i
\(334\) −2.95438 5.11713i −0.161656 0.279997i
\(335\) 0 0
\(336\) −2.98097 2.50133i −0.162625 0.136459i
\(337\) −30.5745 11.1282i −1.66550 0.606192i −0.674287 0.738469i \(-0.735549\pi\)
−0.991213 + 0.132277i \(0.957771\pi\)
\(338\) 30.8329 11.2223i 1.67709 0.610411i
\(339\) 4.84872 4.06856i 0.263346 0.220974i
\(340\) 0 0
\(341\) 13.9527 0.755580
\(342\) −0.165405 0.835698i −0.00894408 0.0451894i
\(343\) −19.9849 −1.07908
\(344\) −0.379796 2.15393i −0.0204772 0.116132i
\(345\) 0 0
\(346\) 18.1775 6.61608i 0.977230 0.355683i
\(347\) 0.243254 + 0.0885371i 0.0130585 + 0.00475292i 0.348541 0.937293i \(-0.386677\pi\)
−0.335483 + 0.942046i \(0.608899\pi\)
\(348\) −0.851083 0.714143i −0.0456228 0.0382821i
\(349\) 15.5129 26.8692i 0.830387 1.43827i −0.0673443 0.997730i \(-0.521453\pi\)
0.897732 0.440543i \(-0.145214\pi\)
\(350\) 0 0
\(351\) −6.28958 + 35.6700i −0.335713 + 1.90392i
\(352\) 0.537442 3.04798i 0.0286457 0.162458i
\(353\) −5.19728 9.00195i −0.276623 0.479125i 0.693920 0.720052i \(-0.255882\pi\)
−0.970543 + 0.240927i \(0.922549\pi\)
\(354\) 8.53513 14.7833i 0.453637 0.785722i
\(355\) 0 0
\(356\) 7.94810 + 2.89287i 0.421248 + 0.153322i
\(357\) 17.2348 6.27295i 0.912161 0.332000i
\(358\) 6.05940 5.08444i 0.320249 0.268721i
\(359\) 4.15028 + 23.5374i 0.219044 + 1.24226i 0.873750 + 0.486375i \(0.161681\pi\)
−0.654707 + 0.755883i \(0.727208\pi\)
\(360\) 0 0
\(361\) −17.5675 + 7.23760i −0.924605 + 0.380926i
\(362\) 13.9145 0.731332
\(363\) 0.413222 + 2.34350i 0.0216885 + 0.123002i
\(364\) −12.0480 + 10.1094i −0.631485 + 0.529879i
\(365\) 0 0
\(366\) −5.85939 2.13264i −0.306275 0.111475i
\(367\) 28.5180 + 23.9294i 1.48863 + 1.24911i 0.896331 + 0.443385i \(0.146222\pi\)
0.592295 + 0.805721i \(0.298222\pi\)
\(368\) 1.59382 2.76058i 0.0830836 0.143905i
\(369\) 0.237922 + 0.412094i 0.0123857 + 0.0214527i
\(370\) 0 0
\(371\) 4.05262 22.9835i 0.210402 1.19325i
\(372\) −3.77484 6.53822i −0.195716 0.338991i
\(373\) −3.31321 + 5.73866i −0.171552 + 0.297136i −0.938963 0.344019i \(-0.888211\pi\)
0.767411 + 0.641156i \(0.221545\pi\)
\(374\) 11.1746 + 9.37659i 0.577824 + 0.484852i
\(375\) 0 0
\(376\) 5.89807 2.14672i 0.304170 0.110709i
\(377\) −3.43976 + 2.88630i −0.177156 + 0.148652i
\(378\) −2.15926 12.2458i −0.111060 0.629854i
\(379\) 24.9336 1.28075 0.640377 0.768060i \(-0.278778\pi\)
0.640377 + 0.768060i \(0.278778\pi\)
\(380\) 0 0
\(381\) −3.01613 −0.154521
\(382\) 3.53842 + 20.0674i 0.181041 + 1.02674i
\(383\) −13.1589 + 11.0417i −0.672390 + 0.564203i −0.913772 0.406228i \(-0.866844\pi\)
0.241381 + 0.970430i \(0.422400\pi\)
\(384\) −1.57369 + 0.572775i −0.0803068 + 0.0292293i
\(385\) 0 0
\(386\) −14.1218 11.8496i −0.718783 0.603130i
\(387\) 0.213731 0.370192i 0.0108645 0.0188179i
\(388\) −2.65811 4.60398i −0.134945 0.233731i
\(389\) −3.89323 + 22.0796i −0.197394 + 1.11948i 0.711573 + 0.702612i \(0.247983\pi\)
−0.908967 + 0.416867i \(0.863128\pi\)
\(390\) 0 0
\(391\) 7.51200 + 13.0112i 0.379898 + 0.658003i
\(392\) −0.800316 + 1.38619i −0.0404220 + 0.0700130i
\(393\) −10.2739 8.62081i −0.518249 0.434862i
\(394\) 8.36015 + 3.04285i 0.421178 + 0.153296i
\(395\) 0 0
\(396\) 0.463374 0.388817i 0.0232854 0.0195388i
\(397\) 6.53610 + 37.0681i 0.328038 + 1.86039i 0.487408 + 0.873175i \(0.337943\pi\)
−0.159370 + 0.987219i \(0.550946\pi\)
\(398\) −24.1611 −1.21108
\(399\) −15.8147 + 6.13269i −0.791724 + 0.307019i
\(400\) 0 0
\(401\) 3.13998 + 17.8077i 0.156803 + 0.889273i 0.957119 + 0.289695i \(0.0935539\pi\)
−0.800316 + 0.599578i \(0.795335\pi\)
\(402\) 6.80282 5.70825i 0.339294 0.284702i
\(403\) −28.6728 + 10.4361i −1.42830 + 0.519857i
\(404\) 11.9403 + 4.34592i 0.594053 + 0.216217i
\(405\) 0 0
\(406\) 0.770774 1.33502i 0.0382529 0.0662559i
\(407\) −14.8161 25.6622i −0.734407 1.27203i
\(408\) 1.37063 7.77320i 0.0678561 0.384831i
\(409\) −2.43421 + 13.8051i −0.120364 + 0.682618i 0.863590 + 0.504195i \(0.168211\pi\)
−0.983954 + 0.178423i \(0.942900\pi\)
\(410\) 0 0
\(411\) −16.0899 + 27.8685i −0.793657 + 1.37465i
\(412\) −6.99133 5.86642i −0.344438 0.289018i
\(413\) 22.2569 + 8.10085i 1.09519 + 0.398617i
\(414\) 0.585426 0.213078i 0.0287721 0.0104722i
\(415\) 0 0
\(416\) 1.17533 + 6.66561i 0.0576251 + 0.326808i
\(417\) 1.80737 0.0885075
\(418\) −10.5132 8.45421i −0.514219 0.413509i
\(419\) −24.5099 −1.19739 −0.598693 0.800978i \(-0.704313\pi\)
−0.598693 + 0.800978i \(0.704313\pi\)
\(420\) 0 0
\(421\) −28.5396 + 23.9475i −1.39093 + 1.16713i −0.425974 + 0.904736i \(0.640068\pi\)
−0.964960 + 0.262396i \(0.915487\pi\)
\(422\) 4.74576 1.72732i 0.231020 0.0840844i
\(423\) 1.15273 + 0.419558i 0.0560475 + 0.0203996i
\(424\) −7.69393 6.45597i −0.373650 0.313530i
\(425\) 0 0
\(426\) −9.88938 17.1289i −0.479142 0.829899i
\(427\) 1.50237 8.52035i 0.0727046 0.412328i
\(428\) −1.55497 + 8.81869i −0.0751625 + 0.426267i
\(429\) 17.5409 + 30.3817i 0.846882 + 1.46684i
\(430\) 0 0
\(431\) −3.57632 3.00089i −0.172265 0.144548i 0.552579 0.833461i \(-0.313644\pi\)
−0.724844 + 0.688913i \(0.758088\pi\)
\(432\) −5.02862 1.83027i −0.241940 0.0880588i
\(433\) −25.9265 + 9.43648i −1.24595 + 0.453488i −0.879031 0.476765i \(-0.841809\pi\)
−0.366918 + 0.930253i \(0.619587\pi\)
\(434\) 8.02457 6.73342i 0.385192 0.323214i
\(435\) 0 0
\(436\) −9.59310 −0.459426
\(437\) −7.19685 11.8855i −0.344272 0.568561i
\(438\) 4.29465 0.205206
\(439\) 1.01404 + 5.75093i 0.0483977 + 0.274477i 0.999397 0.0347154i \(-0.0110525\pi\)
−0.951000 + 0.309192i \(0.899941\pi\)
\(440\) 0 0
\(441\) −0.293964 + 0.106994i −0.0139983 + 0.00509496i
\(442\) −29.9771 10.9108i −1.42587 0.518973i
\(443\) −28.0241 23.5150i −1.33146 1.11723i −0.983733 0.179635i \(-0.942508\pi\)
−0.347730 0.937595i \(-0.613047\pi\)
\(444\) −8.01688 + 13.8856i −0.380464 + 0.658983i
\(445\) 0 0
\(446\) 0.480901 2.72732i 0.0227713 0.129143i
\(447\) 0.804975 4.56524i 0.0380740 0.215929i
\(448\) −1.16183 2.01234i −0.0548912 0.0950743i
\(449\) −8.87052 + 15.3642i −0.418626 + 0.725081i −0.995802 0.0915387i \(-0.970821\pi\)
0.577176 + 0.816620i \(0.304155\pi\)
\(450\) 0 0
\(451\) 7.08102 + 2.57728i 0.333432 + 0.121359i
\(452\) 3.55162 1.29268i 0.167054 0.0608027i
\(453\) 13.1795 11.0589i 0.619227 0.519593i
\(454\) −1.98305 11.2464i −0.0930692 0.527821i
\(455\) 0 0
\(456\) −1.11732 + 7.21375i −0.0523234 + 0.337815i
\(457\) −35.9758 −1.68288 −0.841438 0.540354i \(-0.818290\pi\)
−0.841438 + 0.540354i \(0.818290\pi\)
\(458\) 2.60921 + 14.7976i 0.121921 + 0.691446i
\(459\) 19.3212 16.2124i 0.901835 0.756729i
\(460\) 0 0
\(461\) −35.7175 13.0001i −1.66353 0.605476i −0.672620 0.739988i \(-0.734831\pi\)
−0.990912 + 0.134512i \(0.957053\pi\)
\(462\) −9.22611 7.74163i −0.429238 0.360173i
\(463\) −10.1192 + 17.5270i −0.470281 + 0.814551i −0.999422 0.0339831i \(-0.989181\pi\)
0.529141 + 0.848534i \(0.322514\pi\)
\(464\) −0.331708 0.574535i −0.0153991 0.0266721i
\(465\) 0 0
\(466\) −1.37602 + 7.80382i −0.0637431 + 0.361505i
\(467\) 9.70916 + 16.8168i 0.449286 + 0.778186i 0.998340 0.0576007i \(-0.0183450\pi\)
−0.549054 + 0.835787i \(0.685012\pi\)
\(468\) −0.661416 + 1.14561i −0.0305740 + 0.0529557i
\(469\) 9.43905 + 7.92031i 0.435855 + 0.365726i
\(470\) 0 0
\(471\) 10.9711 3.99316i 0.505522 0.183995i
\(472\) 7.80839 6.55202i 0.359410 0.301581i
\(473\) −1.17547 6.66642i −0.0540481 0.306522i
\(474\) −27.6191 −1.26859
\(475\) 0 0
\(476\) 10.9519 0.501977
\(477\) −0.340864 1.93314i −0.0156071 0.0885122i
\(478\) −11.3477 + 9.52183i −0.519030 + 0.435518i
\(479\) 6.88996 2.50774i 0.314810 0.114582i −0.179782 0.983706i \(-0.557539\pi\)
0.494593 + 0.869125i \(0.335317\pi\)
\(480\) 0 0
\(481\) 49.6415 + 41.6542i 2.26346 + 1.89927i
\(482\) −4.08975 + 7.08366i −0.186283 + 0.322652i
\(483\) −6.20216 10.7425i −0.282208 0.488799i
\(484\) −0.246746 + 1.39937i −0.0112157 + 0.0636076i
\(485\) 0 0
\(486\) −1.01389 1.75611i −0.0459910 0.0796588i
\(487\) −11.5058 + 19.9286i −0.521376 + 0.903049i 0.478315 + 0.878188i \(0.341248\pi\)
−0.999691 + 0.0248610i \(0.992086\pi\)
\(488\) −2.85225 2.39333i −0.129115 0.108341i
\(489\) −7.91567 2.88107i −0.357959 0.130286i
\(490\) 0 0
\(491\) 16.1944 13.5887i 0.730842 0.613249i −0.199519 0.979894i \(-0.563938\pi\)
0.930361 + 0.366645i \(0.119494\pi\)
\(492\) −0.708029 4.01543i −0.0319204 0.181030i
\(493\) 3.12681 0.140825
\(494\) 27.9282 + 9.50995i 1.25655 + 0.427873i
\(495\) 0 0
\(496\) −0.782829 4.43964i −0.0351500 0.199346i
\(497\) 21.0229 17.6403i 0.943005 0.791275i
\(498\) 10.1181 3.68267i 0.453401 0.165025i
\(499\) −12.7827 4.65252i −0.572232 0.208275i 0.0396647 0.999213i \(-0.487371\pi\)
−0.611897 + 0.790938i \(0.709593\pi\)
\(500\) 0 0
\(501\) −4.94764 + 8.56957i −0.221044 + 0.382860i
\(502\) 0.429144 + 0.743299i 0.0191536 + 0.0331751i
\(503\) 1.42656 8.09040i 0.0636070 0.360733i −0.936346 0.351078i \(-0.885815\pi\)
0.999953 0.00965567i \(-0.00307354\pi\)
\(504\) 0.0788603 0.447239i 0.00351272 0.0199216i
\(505\) 0 0
\(506\) 4.93288 8.54400i 0.219293 0.379827i
\(507\) −42.0935 35.3206i −1.86944 1.56864i
\(508\) −1.69240 0.615985i −0.0750883 0.0273299i
\(509\) 5.81193 2.11537i 0.257609 0.0937621i −0.209987 0.977704i \(-0.567342\pi\)
0.467597 + 0.883942i \(0.345120\pi\)
\(510\) 0 0
\(511\) 1.03476 + 5.86839i 0.0457749 + 0.259602i
\(512\) −1.00000 −0.0441942
\(513\) −17.5520 + 15.3632i −0.774940 + 0.678302i
\(514\) 11.3803 0.501965
\(515\) 0 0
\(516\) −2.80586 + 2.35440i −0.123521 + 0.103647i
\(517\) 18.2545 6.64411i 0.802834 0.292208i
\(518\) −20.9055 7.60897i −0.918534 0.334319i
\(519\) −24.8162 20.8233i −1.08931 0.914040i
\(520\) 0 0
\(521\) 8.76833 + 15.1872i 0.384148 + 0.665363i 0.991651 0.128954i \(-0.0411620\pi\)
−0.607503 + 0.794317i \(0.707829\pi\)
\(522\) 0.0225150 0.127689i 0.000985456 0.00558880i
\(523\) −0.0595191 + 0.337550i −0.00260259 + 0.0147600i −0.986081 0.166263i \(-0.946830\pi\)
0.983479 + 0.181023i \(0.0579409\pi\)
\(524\) −4.00423 6.93552i −0.174925 0.302980i
\(525\) 0 0
\(526\) 9.72539 + 8.16057i 0.424047 + 0.355818i
\(527\) 19.9663 + 7.26715i 0.869747 + 0.316562i
\(528\) −4.87056 + 1.77274i −0.211964 + 0.0771486i
\(529\) −9.83521 + 8.25272i −0.427618 + 0.358814i
\(530\) 0 0
\(531\) 1.99216 0.0864524
\(532\) −10.1264 + 0.211329i −0.439034 + 0.00916227i
\(533\) −16.4792 −0.713795
\(534\) −2.45969 13.9496i −0.106441 0.603657i
\(535\) 0 0
\(536\) 4.98298 1.81366i 0.215232 0.0783380i
\(537\) −12.4478 4.53064i −0.537164 0.195512i
\(538\) 16.7636 + 14.0663i 0.722730 + 0.606443i
\(539\) −2.47698 + 4.29025i −0.106691 + 0.184794i
\(540\) 0 0
\(541\) 5.40498 30.6532i 0.232378 1.31788i −0.615687 0.787991i \(-0.711121\pi\)
0.848065 0.529892i \(-0.177767\pi\)
\(542\) 2.45156 13.9035i 0.105304 0.597206i
\(543\) −11.6512 20.1805i −0.500002 0.866028i
\(544\) 2.35660 4.08175i 0.101038 0.175004i
\(545\) 0 0
\(546\) 24.7501 + 9.00832i 1.05921 + 0.385520i
\(547\) 20.5259 7.47082i 0.877625 0.319429i 0.136374 0.990657i \(-0.456455\pi\)
0.741251 + 0.671228i \(0.234233\pi\)
\(548\) −14.7199 + 12.3515i −0.628804 + 0.527629i
\(549\) −0.126363 0.716642i −0.00539306 0.0305855i
\(550\) 0 0
\(551\) −2.89113 + 0.0603355i −0.123166 + 0.00257038i
\(552\) −5.33828 −0.227212
\(553\) −6.65455 37.7398i −0.282980 1.60486i
\(554\) −13.9744 + 11.7259i −0.593714 + 0.498185i
\(555\) 0 0
\(556\) 1.01415 + 0.369120i 0.0430095 + 0.0156542i
\(557\) 5.09607 + 4.27611i 0.215928 + 0.181185i 0.744335 0.667806i \(-0.232766\pi\)
−0.528408 + 0.848991i \(0.677211\pi\)
\(558\) 0.440538 0.763034i 0.0186495 0.0323018i
\(559\) 7.40181 + 12.8203i 0.313063 + 0.542242i
\(560\) 0 0
\(561\) 4.24209 24.0581i 0.179101 1.01573i
\(562\) 6.50360 + 11.2646i 0.274338 + 0.475167i
\(563\) 3.63425 6.29471i 0.153165 0.265290i −0.779224 0.626745i \(-0.784387\pi\)
0.932390 + 0.361455i \(0.117720\pi\)
\(564\) −8.05212 6.75653i −0.339055 0.284501i
\(565\) 0 0
\(566\) 2.73672 0.996084i 0.115033 0.0418685i
\(567\) −14.9085 + 12.5097i −0.626100 + 0.525360i
\(568\) −2.05087 11.6310i −0.0860524 0.488027i
\(569\) −17.9593 −0.752892 −0.376446 0.926438i \(-0.622854\pi\)
−0.376446 + 0.926438i \(0.622854\pi\)
\(570\) 0 0
\(571\) −0.175164 −0.00733040 −0.00366520 0.999993i \(-0.501167\pi\)
−0.00366520 + 0.999993i \(0.501167\pi\)
\(572\) 3.63764 + 20.6301i 0.152097 + 0.862587i
\(573\) 26.1412 21.9351i 1.09206 0.916351i
\(574\) 5.31626 1.93496i 0.221896 0.0807636i
\(575\) 0 0
\(576\) −0.149717 0.125627i −0.00623820 0.00523447i
\(577\) −21.4197 + 37.0999i −0.891712 + 1.54449i −0.0538907 + 0.998547i \(0.517162\pi\)
−0.837822 + 0.545944i \(0.816171\pi\)
\(578\) 2.60714 + 4.51570i 0.108443 + 0.187829i
\(579\) −5.36093 + 30.4033i −0.222792 + 1.26352i
\(580\) 0 0
\(581\) 7.47001 + 12.9384i 0.309908 + 0.536776i
\(582\) −4.45148 + 7.71019i −0.184520 + 0.319598i
\(583\) −23.8127 19.9813i −0.986223 0.827539i
\(584\) 2.40980 + 0.877097i 0.0997184 + 0.0362945i
\(585\) 0 0
\(586\) −1.04265 + 0.874885i −0.0430714 + 0.0361412i
\(587\) −6.74126 38.2316i −0.278242 1.57799i −0.728472 0.685075i \(-0.759769\pi\)
0.450231 0.892912i \(-0.351342\pi\)
\(588\) 2.68055 0.110544
\(589\) −18.6016 6.33412i −0.766467 0.260993i
\(590\) 0 0
\(591\) −2.58721 14.6728i −0.106423 0.603557i
\(592\) −7.33427 + 6.15418i −0.301437 + 0.252935i
\(593\) 35.1745 12.8025i 1.44444 0.525735i 0.503411 0.864047i \(-0.332078\pi\)
0.941034 + 0.338312i \(0.109856\pi\)
\(594\) −15.5636 5.66469i −0.638582 0.232425i
\(595\) 0 0
\(596\) 1.38404 2.39724i 0.0566927 0.0981946i
\(597\) 20.2310 + 35.0412i 0.828002 + 1.43414i
\(598\) −3.74652 + 21.2476i −0.153206 + 0.868877i
\(599\) 7.72566 43.8144i 0.315662 1.79021i −0.252822 0.967513i \(-0.581359\pi\)
0.568484 0.822694i \(-0.307530\pi\)
\(600\) 0 0
\(601\) −2.34958 + 4.06960i −0.0958415 + 0.166002i −0.909959 0.414697i \(-0.863888\pi\)
0.814118 + 0.580699i \(0.197221\pi\)
\(602\) −3.89319 3.26677i −0.158674 0.133144i
\(603\) 0.973880 + 0.354463i 0.0396595 + 0.0144349i
\(604\) 9.65380 3.51370i 0.392808 0.142970i
\(605\) 0 0
\(606\) −3.69515 20.9562i −0.150105 0.851289i
\(607\) 35.6234 1.44591 0.722954 0.690896i \(-0.242784\pi\)
0.722954 + 0.690896i \(0.242784\pi\)
\(608\) −2.10021 + 3.81957i −0.0851749 + 0.154904i
\(609\) −2.58160 −0.104612
\(610\) 0 0
\(611\) −32.5436 + 27.3074i −1.31657 + 1.10474i
\(612\) 0.865603 0.315054i 0.0349899 0.0127353i
\(613\) −7.63724 2.77973i −0.308465 0.112272i 0.183149 0.983085i \(-0.441371\pi\)
−0.491615 + 0.870813i \(0.663593\pi\)
\(614\) 1.00946 + 0.847040i 0.0407386 + 0.0341837i
\(615\) 0 0
\(616\) −3.59586 6.22821i −0.144881 0.250942i
\(617\) 7.17684 40.7019i 0.288929 1.63860i −0.401975 0.915651i \(-0.631676\pi\)
0.690904 0.722946i \(-0.257213\pi\)
\(618\) −2.65404 + 15.0518i −0.106761 + 0.605474i
\(619\) 17.2816 + 29.9327i 0.694608 + 1.20310i 0.970313 + 0.241854i \(0.0777555\pi\)
−0.275705 + 0.961242i \(0.588911\pi\)
\(620\) 0 0
\(621\) −13.0673 10.9648i −0.524373 0.440001i
\(622\) −5.52996 2.01274i −0.221731 0.0807036i
\(623\) 18.4686 6.72203i 0.739930 0.269313i
\(624\) 8.68309 7.28598i 0.347602 0.291673i
\(625\) 0 0
\(626\) −6.22515 −0.248807
\(627\) −3.45812 + 22.3266i −0.138104 + 0.891638i
\(628\) 6.97160 0.278197
\(629\) −7.83591 44.4396i −0.312438 1.77192i
\(630\) 0 0
\(631\) 0.914627 0.332897i 0.0364107 0.0132524i −0.323751 0.946142i \(-0.604944\pi\)
0.360161 + 0.932890i \(0.382722\pi\)
\(632\) −15.4975 5.64064i −0.616459 0.224373i
\(633\) −6.47897 5.43650i −0.257516 0.216082i
\(634\) −10.7362 + 18.5956i −0.426388 + 0.738526i
\(635\) 0 0
\(636\) −2.92077 + 16.5645i −0.115816 + 0.656824i
\(637\) 1.88126 10.6692i 0.0745384 0.422728i
\(638\) −1.02664 1.77819i −0.0406449 0.0703991i
\(639\) 1.15413 1.99901i 0.0456566 0.0790795i
\(640\) 0 0
\(641\) 30.0851 + 10.9501i 1.18829 + 0.432502i 0.859123 0.511770i \(-0.171010\pi\)
0.329167 + 0.944272i \(0.393232\pi\)
\(642\) 14.0919 5.12905i 0.556164 0.202427i
\(643\) −15.2535 + 12.7992i −0.601540 + 0.504752i −0.891940 0.452153i \(-0.850656\pi\)
0.290400 + 0.956905i \(0.406212\pi\)
\(644\) −1.28621 7.29445i −0.0506837 0.287441i
\(645\) 0 0
\(646\) −10.6412 17.5738i −0.418671 0.691430i
\(647\) −30.2057 −1.18751 −0.593753 0.804647i \(-0.702355\pi\)
−0.593753 + 0.804647i \(0.702355\pi\)
\(648\) 1.45439 + 8.24824i 0.0571337 + 0.324021i
\(649\) 24.1670 20.2785i 0.948638 0.796001i
\(650\) 0 0
\(651\) −16.4849 6.00001i −0.646094 0.235159i
\(652\) −3.85322 3.23323i −0.150904 0.126623i
\(653\) −3.44070 + 5.95947i −0.134645 + 0.233212i −0.925462 0.378841i \(-0.876323\pi\)
0.790817 + 0.612053i \(0.209656\pi\)
\(654\) 8.03269 + 13.9130i 0.314103 + 0.544043i
\(655\) 0 0
\(656\) 0.422784 2.39773i 0.0165070 0.0936156i
\(657\) 0.250601 + 0.434053i 0.00977687 + 0.0169340i
\(658\) 7.29232 12.6307i 0.284284 0.492395i
\(659\) −26.2163 21.9981i −1.02124 0.856925i −0.0314603 0.999505i \(-0.510016\pi\)
−0.989783 + 0.142580i \(0.954460\pi\)
\(660\) 0 0
\(661\) 15.7427 5.72986i 0.612319 0.222866i −0.0171986 0.999852i \(-0.505475\pi\)
0.629518 + 0.776986i \(0.283253\pi\)
\(662\) −15.7297 + 13.1988i −0.611354 + 0.512987i
\(663\) 9.27698 + 52.6124i 0.360288 + 2.04330i
\(664\) 6.42953 0.249514
\(665\) 0 0
\(666\) −1.87120 −0.0725074
\(667\) −0.367219 2.08260i −0.0142188 0.0806387i
\(668\) −4.52637 + 3.79808i −0.175131 + 0.146952i
\(669\) −4.35816 + 1.58624i −0.168496 + 0.0613276i
\(670\) 0 0
\(671\) −8.82774 7.40735i −0.340791 0.285958i
\(672\) −1.94569 + 3.37003i −0.0750566 + 0.130002i
\(673\) 4.89013 + 8.46996i 0.188501 + 0.326493i 0.944751 0.327790i \(-0.106304\pi\)
−0.756250 + 0.654283i \(0.772971\pi\)
\(674\) −5.64994 + 32.0424i −0.217628 + 1.23423i
\(675\) 0 0
\(676\) −16.4058 28.4158i −0.630994 1.09291i
\(677\) −2.90819 + 5.03714i −0.111771 + 0.193593i −0.916484 0.400071i \(-0.868986\pi\)
0.804713 + 0.593663i \(0.202319\pi\)
\(678\) −4.84872 4.06856i −0.186214 0.156252i
\(679\) −11.6081 4.22499i −0.445477 0.162140i
\(680\) 0 0
\(681\) −14.6504 + 12.2932i −0.561405 + 0.471075i
\(682\) −2.42286 13.7407i −0.0927760 0.526159i
\(683\) 28.5207 1.09131 0.545657 0.838008i \(-0.316280\pi\)
0.545657 + 0.838008i \(0.316280\pi\)
\(684\) −0.794280 + 0.308010i −0.0303700 + 0.0117770i
\(685\) 0 0
\(686\) 3.47034 + 19.6813i 0.132498 + 0.751435i
\(687\) 19.2764 16.1748i 0.735440 0.617108i
\(688\) −2.05525 + 0.748052i −0.0783559 + 0.0285192i
\(689\) 63.8805 + 23.2506i 2.43365 + 0.885777i
\(690\) 0 0
\(691\) 16.1503 27.9731i 0.614385 1.06415i −0.376107 0.926576i \(-0.622738\pi\)
0.990492 0.137570i \(-0.0439291\pi\)
\(692\) −9.67206 16.7525i −0.367677 0.636835i
\(693\) 0.244073 1.38421i 0.00927156 0.0525816i
\(694\) 0.0449515 0.254933i 0.00170633 0.00967711i
\(695\) 0 0
\(696\) −0.555505 + 0.962162i −0.0210564 + 0.0364707i
\(697\) 8.79061 + 7.37619i 0.332968 + 0.279393i
\(698\) −29.1547 10.6115i −1.10352 0.401650i
\(699\) 12.4702 4.53879i 0.471667 0.171673i
\(700\) 0 0
\(701\) 1.97675 + 11.2107i 0.0746609 + 0.423423i 0.999112 + 0.0421235i \(0.0134123\pi\)
−0.924451 + 0.381300i \(0.875477\pi\)
\(702\) 36.2202 1.36704
\(703\) 8.10280 + 40.9388i 0.305603 + 1.54404i
\(704\) −3.09500 −0.116647
\(705\) 0 0
\(706\) −7.96269 + 6.68149i −0.299680 + 0.251461i
\(707\) 27.7451 10.0984i 1.04346 0.379790i
\(708\) −16.0408 5.83837i −0.602850 0.219419i
\(709\) 26.4481 + 22.1926i 0.993278 + 0.833459i 0.986039 0.166515i \(-0.0532513\pi\)
0.00723886 + 0.999974i \(0.497696\pi\)
\(710\) 0 0
\(711\) −1.61162 2.79141i −0.0604406 0.104686i
\(712\) 1.46875 8.32969i 0.0550437 0.312168i
\(713\) 2.49538 14.1520i 0.0934526 0.529996i
\(714\) −9.17043 15.8837i −0.343195 0.594431i
\(715\) 0 0
\(716\) −6.05940 5.08444i −0.226450 0.190015i
\(717\) 23.3115 + 8.48470i 0.870585 + 0.316867i
\(718\) 22.4592 8.17446i 0.838168 0.305068i
\(719\) 19.8549 16.6603i 0.740464 0.621323i −0.192498 0.981297i \(-0.561659\pi\)
0.932962 + 0.359974i \(0.117215\pi\)
\(720\) 0 0
\(721\) −21.2069 −0.789786
\(722\) 10.1782 + 16.0438i 0.378794 + 0.597089i
\(723\) 13.6981 0.509437
\(724\) −2.41624 13.7032i −0.0897987 0.509274i
\(725\) 0 0
\(726\) 2.23614 0.813887i 0.0829908 0.0302062i
\(727\) −9.38104 3.41442i −0.347923 0.126634i 0.162147 0.986767i \(-0.448158\pi\)
−0.510070 + 0.860133i \(0.670380\pi\)
\(728\) 12.0480 + 10.1094i 0.446527 + 0.374681i
\(729\) −14.2612 + 24.7011i −0.528191 + 0.914854i
\(730\) 0 0
\(731\) 1.79005 10.1519i 0.0662076 0.375482i
\(732\) −1.08277 + 6.14070i −0.0400204 + 0.226967i
\(733\) 1.03498 + 1.79264i 0.0382279 + 0.0662126i 0.884506 0.466528i \(-0.154495\pi\)
−0.846278 + 0.532741i \(0.821162\pi\)
\(734\) 18.6138 32.2400i 0.687048 1.19000i
\(735\) 0 0
\(736\) −2.99540 1.09024i −0.110412 0.0401867i
\(737\) 15.4223 5.61327i 0.568089 0.206767i
\(738\) 0.364518 0.305867i 0.0134181 0.0112591i
\(739\) −4.32655 24.5371i −0.159155 0.902612i −0.954888 0.296965i \(-0.904025\pi\)
0.795733 0.605647i \(-0.207086\pi\)
\(740\) 0 0
\(741\) −9.59296 48.4678i −0.352406 1.78051i
\(742\) −23.3381 −0.856769
\(743\) 0.202822 + 1.15026i 0.00744080 + 0.0421989i 0.988302 0.152509i \(-0.0487353\pi\)
−0.980861 + 0.194708i \(0.937624\pi\)
\(744\) −5.78339 + 4.85284i −0.212029 + 0.177914i
\(745\) 0 0
\(746\) 6.22681 + 2.26637i 0.227980 + 0.0829778i
\(747\) 0.962609 + 0.807725i 0.0352200 + 0.0295531i
\(748\) 7.29369 12.6330i 0.266684 0.461910i
\(749\) 10.4039 + 18.0200i 0.380148 + 0.658436i
\(750\) 0 0
\(751\) 2.41878 13.7176i 0.0882625 0.500562i −0.908342 0.418228i \(-0.862651\pi\)
0.996605 0.0823341i \(-0.0262374\pi\)
\(752\) −3.13830 5.43569i −0.114442 0.198219i
\(753\) 0.718680 1.24479i 0.0261901 0.0453627i
\(754\) 3.43976 + 2.88630i 0.125269 + 0.105113i
\(755\) 0 0
\(756\) −11.6848 + 4.25291i −0.424971 + 0.154677i
\(757\) −6.79067 + 5.69805i −0.246811 + 0.207099i −0.757798 0.652490i \(-0.773725\pi\)
0.510987 + 0.859589i \(0.329280\pi\)
\(758\) −4.32968 24.5548i −0.157261 0.891872i
\(759\) −16.5220 −0.599711
\(760\) 0 0
\(761\) 8.72950 0.316444 0.158222 0.987404i \(-0.449424\pi\)
0.158222 + 0.987404i \(0.449424\pi\)
\(762\) 0.523746 + 2.97031i 0.0189733 + 0.107603i
\(763\) −17.0759 + 14.3284i −0.618190 + 0.518723i
\(764\) 19.1481 6.96933i 0.692753 0.252141i
\(765\) 0 0
\(766\) 13.1589 + 11.0417i 0.475452 + 0.398951i
\(767\) −34.4958 + 59.7484i −1.24557 + 2.15739i
\(768\) 0.837341 + 1.45032i 0.0302149 + 0.0523338i
\(769\) 3.03165 17.1933i 0.109324 0.620008i −0.880081 0.474824i \(-0.842512\pi\)
0.989405 0.145183i \(-0.0463772\pi\)
\(770\) 0 0
\(771\) −9.52921 16.5051i −0.343186 0.594416i
\(772\) −9.21738 + 15.9650i −0.331741 + 0.574592i
\(773\) −10.3498 8.68454i −0.372258 0.312361i 0.437396 0.899269i \(-0.355901\pi\)
−0.809654 + 0.586908i \(0.800345\pi\)
\(774\) −0.401682 0.146200i −0.0144382 0.00525506i
\(775\) 0 0
\(776\) −4.07246 + 3.41720i −0.146193 + 0.122670i
\(777\) 6.46959 + 36.6909i 0.232095 + 1.31628i
\(778\) 22.4202 0.803803
\(779\) −8.27035 6.65059i −0.296316 0.238282i
\(780\) 0 0
\(781\) −6.34743 35.9981i −0.227129 1.28811i
\(782\) 11.5090 9.65724i 0.411563 0.345342i
\(783\) −3.33606 + 1.21423i −0.119221 + 0.0433930i
\(784\) 1.50410 + 0.547448i 0.0537179 + 0.0195517i
\(785\) 0 0
\(786\) −6.70580 + 11.6148i −0.239188 + 0.414286i
\(787\) −17.6119 30.5047i −0.627797 1.08738i −0.987993 0.154500i \(-0.950623\pi\)
0.360196 0.932877i \(-0.382710\pi\)
\(788\) 1.54489 8.76153i 0.0550346 0.312117i
\(789\) 3.69195 20.9381i 0.131437 0.745415i
\(790\) 0 0
\(791\) 4.39119 7.60576i 0.156133 0.270430i
\(792\) −0.463374 0.388817i −0.0164653 0.0138160i
\(793\) 23.6814 + 8.61934i 0.840953 + 0.306082i
\(794\) 35.3699 12.8736i 1.25523 0.456867i
\(795\) 0 0
\(796\) 4.19553 + 23.7940i 0.148706 + 0.843356i
\(797\) 19.1074 0.676818 0.338409 0.940999i \(-0.390111\pi\)
0.338409 + 0.940999i \(0.390111\pi\)
\(798\) 8.78572 + 14.5095i 0.311011 + 0.513630i
\(799\) 29.5829 1.04657
\(800\) 0 0
\(801\) 1.26633 1.06258i 0.0447437 0.0375444i
\(802\) 16.9919 6.18454i 0.600005 0.218384i
\(803\) 7.45835 + 2.71462i 0.263199 + 0.0957968i
\(804\) −6.80282 5.70825i −0.239917 0.201314i
\(805\) 0 0
\(806\) 15.2565 + 26.4250i 0.537387 + 0.930782i
\(807\) 6.36379 36.0908i 0.224016 1.27046i
\(808\) 2.20648 12.5136i 0.0776237 0.440226i
\(809\) −5.22079 9.04268i −0.183553 0.317924i 0.759535 0.650467i \(-0.225427\pi\)
−0.943088 + 0.332543i \(0.892093\pi\)
\(810\) 0 0
\(811\) 7.03037 + 5.89918i 0.246870 + 0.207148i 0.757823 0.652460i \(-0.226263\pi\)
−0.510953 + 0.859609i \(0.670707\pi\)
\(812\) −1.44858 0.527240i −0.0508352 0.0185025i
\(813\) −22.2173 + 8.08643i −0.779194 + 0.283603i
\(814\) −22.6996 + 19.0472i −0.795620 + 0.667604i
\(815\) 0 0
\(816\) −7.89312 −0.276314
\(817\) −1.45924 + 9.42125i −0.0510523 + 0.329608i
\(818\) 14.0181 0.490130
\(819\) 0.533761 + 3.02711i 0.0186511 + 0.105776i
\(820\) 0 0
\(821\) −8.43841 + 3.07133i −0.294503 + 0.107190i −0.485046 0.874489i \(-0.661197\pi\)
0.190544 + 0.981679i \(0.438975\pi\)
\(822\) 30.2391 + 11.0061i 1.05471 + 0.383883i
\(823\) 27.6581 + 23.2079i 0.964101 + 0.808977i 0.981615 0.190870i \(-0.0611309\pi\)
−0.0175145 + 0.999847i \(0.505575\pi\)
\(824\) −4.56327 + 7.90381i −0.158969 + 0.275342i
\(825\) 0 0
\(826\) 4.11291 23.3255i 0.143106 0.811597i
\(827\) 0.988578 5.60650i 0.0343762 0.194957i −0.962783 0.270274i \(-0.912886\pi\)
0.997160 + 0.0753168i \(0.0239968\pi\)
\(828\) −0.311499 0.539531i −0.0108253 0.0187500i
\(829\) −6.25554 + 10.8349i −0.217264 + 0.376312i −0.953970 0.299901i \(-0.903047\pi\)
0.736707 + 0.676212i \(0.236380\pi\)
\(830\) 0 0
\(831\) 28.7076 + 10.4487i 0.995854 + 0.362461i
\(832\) 6.36025 2.31494i 0.220502 0.0802561i
\(833\) −5.77912 + 4.84925i −0.200234 + 0.168017i
\(834\) −0.313847 1.77992i −0.0108676 0.0616334i
\(835\) 0 0
\(836\) −6.50017 + 11.8216i −0.224813 + 0.408858i
\(837\) −24.1246 −0.833867
\(838\) 4.25610 + 24.1375i 0.147025 + 0.833817i
\(839\) 25.8961 21.7294i 0.894033 0.750183i −0.0749821 0.997185i \(-0.523890\pi\)
0.969015 + 0.247002i \(0.0794455\pi\)
\(840\) 0 0
\(841\) 26.8375 + 9.76805i 0.925431 + 0.336829i
\(842\) 28.5396 + 23.9475i 0.983539 + 0.825287i
\(843\) 10.8915 18.8646i 0.375122 0.649730i
\(844\) −2.52517 4.37372i −0.0869198 0.150550i
\(845\) 0 0
\(846\) 0.213015 1.20807i 0.00732362 0.0415343i
\(847\) 1.65090 + 2.85945i 0.0567257 + 0.0982519i
\(848\) −5.02185 + 8.69811i −0.172451 + 0.298694i
\(849\) −3.73620 3.13505i −0.128226 0.107594i
\(850\) 0 0
\(851\) −28.6786 + 10.4382i −0.983090 + 0.357815i
\(852\) −15.1514 + 12.7135i −0.519079 + 0.435559i
\(853\) −1.99098 11.2914i −0.0681697 0.386610i −0.999735 0.0230347i \(-0.992667\pi\)
0.931565 0.363575i \(-0.118444\pi\)
\(854\) −8.65179 −0.296058
\(855\) 0 0
\(856\) 8.95473 0.306066
\(857\) −2.49949 14.1753i −0.0853810 0.484220i −0.997274 0.0737912i \(-0.976490\pi\)
0.911893 0.410429i \(-0.134621\pi\)
\(858\) 26.8742 22.5501i 0.917470 0.769849i
\(859\) −32.3900 + 11.7890i −1.10513 + 0.402236i −0.829206 0.558943i \(-0.811207\pi\)
−0.275927 + 0.961179i \(0.588985\pi\)
\(860\) 0 0
\(861\) −7.25782 6.09004i −0.247346 0.207548i
\(862\) −2.33428 + 4.04309i −0.0795059 + 0.137708i
\(863\) 13.3344 + 23.0958i 0.453907 + 0.786191i 0.998625 0.0524291i \(-0.0166964\pi\)
−0.544717 + 0.838620i \(0.683363\pi\)
\(864\) −0.929252 + 5.27005i −0.0316138 + 0.179291i
\(865\) 0 0
\(866\) 13.7952 + 23.8940i 0.468780 + 0.811951i
\(867\) 4.36613 7.56237i 0.148282 0.256831i
\(868\) −8.02457 6.73342i −0.272372 0.228547i
\(869\) −47.9649 17.4578i −1.62710 0.592216i
\(870\) 0 0
\(871\) −27.4945 + 23.0706i −0.931614 + 0.781717i
\(872\) 1.66582 + 9.44736i 0.0564119 + 0.319928i
\(873\) −1.03901 −0.0351651
\(874\) −10.4552 + 9.15141i −0.353653 + 0.309551i
\(875\) 0 0
\(876\) −0.745759 4.22941i −0.0251969 0.142898i
\(877\) −3.91536 + 3.28538i −0.132212 + 0.110939i −0.706496 0.707717i \(-0.749725\pi\)
0.574284 + 0.818656i \(0.305281\pi\)
\(878\) 5.48747 1.99728i 0.185193 0.0674048i
\(879\) 2.14191 + 0.779592i 0.0722449 + 0.0262950i
\(880\) 0 0
\(881\) 9.23774 16.0002i 0.311227 0.539062i −0.667401 0.744699i \(-0.732593\pi\)
0.978628 + 0.205637i \(0.0659266\pi\)
\(882\) 0.156415 + 0.270918i 0.00526676 + 0.00912230i
\(883\) 3.77236 21.3941i 0.126950 0.719969i −0.853181 0.521616i \(-0.825329\pi\)
0.980131 0.198354i \(-0.0635594\pi\)
\(884\) −5.53955 + 31.4164i −0.186315 + 1.05665i
\(885\) 0 0
\(886\) −18.2914 + 31.6816i −0.614512 + 1.06437i
\(887\) −29.7825 24.9905i −1.00000 0.839099i −0.0130151 0.999915i \(-0.504143\pi\)
−0.986984 + 0.160816i \(0.948587\pi\)
\(888\) 15.0668 + 5.48387i 0.505609 + 0.184026i
\(889\) −3.93256 + 1.43134i −0.131894 + 0.0480054i
\(890\) 0 0
\(891\) 4.50133 + 25.5283i 0.150800 + 0.855231i
\(892\) −2.76940 −0.0927263
\(893\) −27.3531 + 0.570836i −0.915336 + 0.0191023i
\(894\) −4.63567 −0.155040
\(895\) 0 0
\(896\) −1.78002 + 1.49362i −0.0594664 + 0.0498982i
\(897\) 33.9528 12.3578i 1.13365 0.412615i
\(898\) 16.6711 + 6.06780i 0.556323 + 0.202485i
\(899\) −2.29106 1.92243i −0.0764110 0.0641165i
\(900\) 0 0
\(901\) −23.6690 40.9959i −0.788529 1.36577i
\(902\) 1.30852 7.42098i 0.0435689 0.247092i
\(903\) −1.47793 + 8.38176i −0.0491824 + 0.278927i
\(904\) −1.88978 3.27319i −0.0628530 0.108865i
\(905\) 0 0
\(906\) −13.1795 11.0589i −0.437859 0.367408i
\(907\) −1.45333 0.528970i −0.0482572 0.0175642i 0.317779 0.948165i \(-0.397063\pi\)
−0.366036 + 0.930601i \(0.619285\pi\)
\(908\) −10.7312 + 3.90585i −0.356128 + 0.129620i
\(909\) 1.90239 1.59630i 0.0630984 0.0529459i
\(910\) 0 0
\(911\) 34.1846 1.13259 0.566294 0.824204i \(-0.308377\pi\)
0.566294 + 0.824204i \(0.308377\pi\)
\(912\) 7.29818 0.152307i 0.241667 0.00504339i
\(913\) 19.8994 0.658575
\(914\) 6.24713 + 35.4292i 0.206637 + 1.17189i
\(915\) 0 0
\(916\) 14.1197 5.13915i 0.466528 0.169802i
\(917\) −17.4866 6.36461i −0.577459 0.210178i
\(918\) −19.3212 16.2124i −0.637693 0.535088i
\(919\) −1.47826 + 2.56043i −0.0487634 + 0.0844606i −0.889377 0.457175i \(-0.848861\pi\)
0.840613 + 0.541635i \(0.182195\pi\)
\(920\) 0 0
\(921\) 0.383212 2.17330i 0.0126273 0.0716127i
\(922\) −6.60033 + 37.4324i −0.217370 + 1.23277i
\(923\) 39.9692 + 69.2286i 1.31560 + 2.27869i
\(924\) −6.02192 + 10.4303i −0.198107 + 0.343131i
\(925\) 0 0
\(926\) 19.0180 + 6.92197i 0.624969 + 0.227470i
\(927\) −1.67613 + 0.610062i −0.0550514 + 0.0200371i
\(928\) −0.508206 + 0.426435i −0.0166827 + 0.0139984i
\(929\) −5.79901 32.8878i −0.190259 1.07901i −0.919010 0.394235i \(-0.871010\pi\)
0.728750 0.684779i \(-0.240101\pi\)
\(930\) 0 0
\(931\) 5.24995 4.59526i 0.172060 0.150604i
\(932\) 7.92421 0.259566
\(933\) 1.71135 + 9.70555i 0.0560271 + 0.317745i
\(934\) 14.8753 12.4818i 0.486734 0.408419i
\(935\) 0 0
\(936\) 1.24306 + 0.452435i 0.0406306 + 0.0147883i
\(937\) −30.6304 25.7020i −1.00065 0.839647i −0.0135779 0.999908i \(-0.504322\pi\)
−0.987075 + 0.160261i \(0.948767\pi\)
\(938\) 6.16091 10.6710i 0.201161 0.348421i
\(939\) 5.21258 + 9.02845i 0.170106 + 0.294632i
\(940\) 0 0
\(941\) −6.18958 + 35.1028i −0.201774 + 1.14432i 0.700661 + 0.713494i \(0.252889\pi\)
−0.902435 + 0.430825i \(0.858223\pi\)
\(942\) −5.83761 10.1110i −0.190200 0.329435i
\(943\) 3.88050 6.72123i 0.126367 0.218873i
\(944\) −7.80839 6.55202i −0.254142 0.213250i
\(945\) 0 0
\(946\) −6.36102 + 2.31522i −0.206815 + 0.0752744i
\(947\) −12.9277 + 10.8476i −0.420094 + 0.352500i −0.828199 0.560435i \(-0.810634\pi\)
0.408105 + 0.912935i \(0.366190\pi\)
\(948\) 4.79600 + 27.1995i 0.155767 + 0.883398i
\(949\) −17.3574 −0.563444
\(950\) 0 0
\(951\) 35.9594 1.16606
\(952\) −1.90177 10.7855i −0.0616367 0.349559i
\(953\) 18.1350 15.2171i 0.587450 0.492929i −0.299934 0.953960i \(-0.596965\pi\)
0.887384 + 0.461031i \(0.152520\pi\)
\(954\) −1.84458 + 0.671371i −0.0597204 + 0.0217364i
\(955\) 0 0
\(956\) 11.3477 + 9.52183i 0.367010 + 0.307958i
\(957\) −1.71929 + 2.97790i −0.0555767 + 0.0962617i
\(958\) −3.66607 6.34982i −0.118445 0.205154i
\(959\) −7.75341 + 43.9718i −0.250371 + 1.41992i
\(960\) 0 0
\(961\) 5.33838 + 9.24635i 0.172206 + 0.298269i
\(962\) 32.4012 56.1205i 1.04466 1.80940i
\(963\) 1.34067 + 1.12496i 0.0432026 + 0.0362513i
\(964\) 7.68622 + 2.79756i 0.247556 + 0.0901032i
\(965\) 0 0
\(966\) −9.50226 + 7.97335i −0.305730 + 0.256538i
\(967\) −0.149858 0.849889i −0.00481912 0.0273306i 0.982303 0.187297i \(-0.0599726\pi\)
−0.987122 + 0.159966i \(0.948861\pi\)
\(968\) 1.42096 0.0456712
\(969\) −16.5772 + 30.1483i −0.532537 + 0.968503i
\(970\) 0 0
\(971\) 7.54276 + 42.7771i 0.242059 + 1.37278i 0.827226 + 0.561870i \(0.189918\pi\)
−0.585167 + 0.810913i \(0.698971\pi\)
\(972\) −1.55337 + 1.30343i −0.0498244 + 0.0418076i
\(973\) 2.35653 0.857707i 0.0755469 0.0274968i
\(974\) 21.6238 + 7.87040i 0.692870 + 0.252184i
\(975\) 0 0
\(976\) −1.86168 + 3.22452i −0.0595908 + 0.103214i
\(977\) 22.2280 + 38.5001i 0.711138 + 1.23173i 0.964430 + 0.264338i \(0.0851533\pi\)
−0.253292 + 0.967390i \(0.581513\pi\)
\(978\) −1.46276 + 8.29570i −0.0467738 + 0.265267i
\(979\) 4.54578 25.7804i 0.145284 0.823946i
\(980\) 0 0
\(981\) −0.937445 + 1.62370i −0.0299303 + 0.0518408i
\(982\) −16.1944 13.5887i −0.516783 0.433633i
\(983\) −12.2338 4.45274i −0.390198 0.142020i 0.139469 0.990226i \(-0.455461\pi\)
−0.529666 + 0.848206i \(0.677683\pi\)
\(984\) −3.83148 + 1.39455i −0.122143 + 0.0444565i
\(985\) 0 0
\(986\) −0.542965 3.07931i −0.0172915 0.0980652i
\(987\) −24.4246 −0.777444
\(988\) 4.51580 29.1553i 0.143667 0.927553i
\(989\) −6.97187 −0.221693
\(990\) 0 0
\(991\) 20.8851 17.5247i 0.663436 0.556689i −0.247678 0.968842i \(-0.579668\pi\)
0.911115 + 0.412153i \(0.135223\pi\)
\(992\) −4.23626 + 1.54187i −0.134501 + 0.0489545i
\(993\) 32.3136 + 11.7612i 1.02544 + 0.373230i
\(994\) −21.0229 17.6403i −0.666806 0.559516i
\(995\) 0 0
\(996\) −5.38371 9.32486i −0.170589 0.295469i
\(997\) −3.46311 + 19.6403i −0.109678 + 0.622014i 0.879570 + 0.475769i \(0.157830\pi\)
−0.989248 + 0.146246i \(0.953281\pi\)
\(998\) −2.36215 + 13.3964i −0.0747725 + 0.424056i
\(999\) 25.6175 + 44.3707i 0.810500 + 1.40383i
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 950.2.l.l.351.2 30
5.2 odd 4 190.2.p.a.9.9 yes 60
5.3 odd 4 190.2.p.a.9.2 60
5.4 even 2 950.2.l.m.351.4 30
19.17 even 9 inner 950.2.l.l.701.2 30
95.17 odd 36 190.2.p.a.169.2 yes 60
95.74 even 18 950.2.l.m.701.4 30
95.93 odd 36 190.2.p.a.169.9 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.p.a.9.2 60 5.3 odd 4
190.2.p.a.9.9 yes 60 5.2 odd 4
190.2.p.a.169.2 yes 60 95.17 odd 36
190.2.p.a.169.9 yes 60 95.93 odd 36
950.2.l.l.351.2 30 1.1 even 1 trivial
950.2.l.l.701.2 30 19.17 even 9 inner
950.2.l.m.351.4 30 5.4 even 2
950.2.l.m.701.4 30 95.74 even 18