Properties

Label 231.2.p.a.10.14
Level $231$
Weight $2$
Character 231.10
Analytic conductor $1.845$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(10,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.p (of order \(6\), degree \(2\), 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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.14
Character \(\chi\) \(=\) 231.10
Dual form 231.2.p.a.208.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.71613 - 0.990810i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.963407 - 1.66867i) q^{4} +(0.315938 - 0.182407i) q^{5} +1.98162 q^{6} +(-0.143176 - 2.64187i) q^{7} +0.145025i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.71613 - 0.990810i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.963407 - 1.66867i) q^{4} +(0.315938 - 0.182407i) q^{5} +1.98162 q^{6} +(-0.143176 - 2.64187i) q^{7} +0.145025i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.361461 - 0.626069i) q^{10} +(-1.16965 + 3.10353i) q^{11} +(1.66867 - 0.963407i) q^{12} -5.43170 q^{13} +(-2.86330 - 4.39195i) q^{14} +0.364814 q^{15} +(2.07051 + 3.58622i) q^{16} +(2.93710 - 5.08721i) q^{17} +(1.71613 + 0.990810i) q^{18} +(1.11224 + 1.92646i) q^{19} -0.702929i q^{20} +(1.19694 - 2.35952i) q^{21} +(1.06774 + 6.48497i) q^{22} +(-1.38495 - 2.39880i) q^{23} +(-0.0725127 + 0.125596i) q^{24} +(-2.43346 + 4.21487i) q^{25} +(-9.32152 + 5.38178i) q^{26} +1.00000i q^{27} +(-4.54636 - 2.30629i) q^{28} -2.01743i q^{29} +(0.626069 - 0.361461i) q^{30} +(-4.99947 - 2.88645i) q^{31} +(6.85534 + 3.95793i) q^{32} +(-2.56471 + 2.10292i) q^{33} -11.6404i q^{34} +(-0.527131 - 0.808553i) q^{35} +1.92681 q^{36} +(4.00554 + 6.93780i) q^{37} +(3.81751 + 2.20404i) q^{38} +(-4.70399 - 2.71585i) q^{39} +(0.0264536 + 0.0458191i) q^{40} -8.88534 q^{41} +(-0.283721 - 5.23519i) q^{42} +5.90706i q^{43} +(4.05193 + 4.94172i) q^{44} +(0.315938 + 0.182407i) q^{45} +(-4.75351 - 2.74444i) q^{46} +(5.45165 - 3.14751i) q^{47} +4.14101i q^{48} +(-6.95900 + 0.756509i) q^{49} +9.64436i q^{50} +(5.08721 - 2.93710i) q^{51} +(-5.23294 + 9.06372i) q^{52} +(6.47002 - 11.2064i) q^{53} +(0.990810 + 1.71613i) q^{54} +(0.196570 + 1.19388i) q^{55} +(0.383139 - 0.0207642i) q^{56} +2.22448i q^{57} +(-1.99888 - 3.46217i) q^{58} +(7.39894 + 4.27178i) q^{59} +(0.351465 - 0.608755i) q^{60} +(-1.35352 - 2.34437i) q^{61} -11.4397 q^{62} +(2.21634 - 1.44493i) q^{63} +7.40420 q^{64} +(-1.71608 + 0.990781i) q^{65} +(-2.31779 + 6.15002i) q^{66} +(7.30735 - 12.6567i) q^{67} +(-5.65925 - 9.80210i) q^{68} -2.76990i q^{69} +(-1.70575 - 0.865297i) q^{70} +2.64558 q^{71} +(-0.125596 + 0.0725127i) q^{72} +(-2.91182 + 5.04342i) q^{73} +(13.7481 + 7.93746i) q^{74} +(-4.21487 + 2.43346i) q^{75} +4.28617 q^{76} +(8.36661 + 2.64571i) q^{77} -10.7636 q^{78} +(1.59178 - 0.919015i) q^{79} +(1.30831 + 0.755350i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-15.2484 + 8.80368i) q^{82} +5.21418 q^{83} +(-2.78412 - 4.27048i) q^{84} -2.14299i q^{85} +(5.85278 + 10.1373i) q^{86} +(1.00871 - 1.74714i) q^{87} +(-0.450091 - 0.169628i) q^{88} +(-0.367796 + 0.212347i) q^{89} +0.722923 q^{90} +(0.777692 + 14.3499i) q^{91} -5.33708 q^{92} +(-2.88645 - 4.99947i) q^{93} +(6.23717 - 10.8031i) q^{94} +(0.702799 + 0.405761i) q^{95} +(3.95793 + 6.85534i) q^{96} -10.0948i q^{97} +(-11.1930 + 8.19331i) q^{98} +(-3.27256 + 0.538824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.71613 0.990810i 1.21349 0.700608i 0.249971 0.968253i \(-0.419579\pi\)
0.963518 + 0.267645i \(0.0862454\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.963407 1.66867i 0.481704 0.834335i
\(5\) 0.315938 0.182407i 0.141292 0.0815749i −0.427688 0.903927i \(-0.640672\pi\)
0.568980 + 0.822352i \(0.307338\pi\)
\(6\) 1.98162 0.808993
\(7\) −0.143176 2.64187i −0.0541156 0.998535i
\(8\) 0.145025i 0.0512742i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0.361461 0.626069i 0.114304 0.197981i
\(11\) −1.16965 + 3.10353i −0.352662 + 0.935751i
\(12\) 1.66867 0.963407i 0.481704 0.278112i
\(13\) −5.43170 −1.50648 −0.753242 0.657744i \(-0.771511\pi\)
−0.753242 + 0.657744i \(0.771511\pi\)
\(14\) −2.86330 4.39195i −0.765250 1.17380i
\(15\) 0.364814 0.0941946
\(16\) 2.07051 + 3.58622i 0.517627 + 0.896556i
\(17\) 2.93710 5.08721i 0.712351 1.23383i −0.251621 0.967826i \(-0.580964\pi\)
0.963972 0.266003i \(-0.0857031\pi\)
\(18\) 1.71613 + 0.990810i 0.404496 + 0.233536i
\(19\) 1.11224 + 1.92646i 0.255166 + 0.441960i 0.964940 0.262469i \(-0.0845367\pi\)
−0.709775 + 0.704429i \(0.751203\pi\)
\(20\) 0.702929i 0.157180i
\(21\) 1.19694 2.35952i 0.261194 0.514889i
\(22\) 1.06774 + 6.48497i 0.227644 + 1.38260i
\(23\) −1.38495 2.39880i −0.288782 0.500185i 0.684737 0.728790i \(-0.259917\pi\)
−0.973519 + 0.228605i \(0.926584\pi\)
\(24\) −0.0725127 + 0.125596i −0.0148016 + 0.0256371i
\(25\) −2.43346 + 4.21487i −0.486691 + 0.842974i
\(26\) −9.32152 + 5.38178i −1.82810 + 1.05545i
\(27\) 1.00000i 0.192450i
\(28\) −4.54636 2.30629i −0.859180 0.435847i
\(29\) 2.01743i 0.374627i −0.982300 0.187313i \(-0.940022\pi\)
0.982300 0.187313i \(-0.0599779\pi\)
\(30\) 0.626069 0.361461i 0.114304 0.0659935i
\(31\) −4.99947 2.88645i −0.897931 0.518421i −0.0214029 0.999771i \(-0.506813\pi\)
−0.876528 + 0.481350i \(0.840147\pi\)
\(32\) 6.85534 + 3.95793i 1.21186 + 0.699670i
\(33\) −2.56471 + 2.10292i −0.446459 + 0.366071i
\(34\) 11.6404i 1.99632i
\(35\) −0.527131 0.808553i −0.0891015 0.136670i
\(36\) 1.92681 0.321136
\(37\) 4.00554 + 6.93780i 0.658507 + 1.14057i 0.981002 + 0.193997i \(0.0621452\pi\)
−0.322495 + 0.946571i \(0.604521\pi\)
\(38\) 3.81751 + 2.20404i 0.619281 + 0.357542i
\(39\) −4.70399 2.71585i −0.753242 0.434884i
\(40\) 0.0264536 + 0.0458191i 0.00418269 + 0.00724463i
\(41\) −8.88534 −1.38766 −0.693829 0.720140i \(-0.744078\pi\)
−0.693829 + 0.720140i \(0.744078\pi\)
\(42\) −0.283721 5.23519i −0.0437791 0.807807i
\(43\) 5.90706i 0.900819i 0.892822 + 0.450409i \(0.148722\pi\)
−0.892822 + 0.450409i \(0.851278\pi\)
\(44\) 4.05193 + 4.94172i 0.610852 + 0.744993i
\(45\) 0.315938 + 0.182407i 0.0470973 + 0.0271916i
\(46\) −4.75351 2.74444i −0.700867 0.404646i
\(47\) 5.45165 3.14751i 0.795205 0.459112i −0.0465868 0.998914i \(-0.514834\pi\)
0.841792 + 0.539802i \(0.181501\pi\)
\(48\) 4.14101i 0.597704i
\(49\) −6.95900 + 0.756509i −0.994143 + 0.108073i
\(50\) 9.64436i 1.36392i
\(51\) 5.08721 2.93710i 0.712351 0.411276i
\(52\) −5.23294 + 9.06372i −0.725679 + 1.25691i
\(53\) 6.47002 11.2064i 0.888725 1.53932i 0.0473417 0.998879i \(-0.484925\pi\)
0.841384 0.540438i \(-0.181742\pi\)
\(54\) 0.990810 + 1.71613i 0.134832 + 0.233536i
\(55\) 0.196570 + 1.19388i 0.0265056 + 0.160982i
\(56\) 0.383139 0.0207642i 0.0511991 0.00277474i
\(57\) 2.22448i 0.294640i
\(58\) −1.99888 3.46217i −0.262466 0.454605i
\(59\) 7.39894 + 4.27178i 0.963260 + 0.556139i 0.897175 0.441675i \(-0.145616\pi\)
0.0660854 + 0.997814i \(0.478949\pi\)
\(60\) 0.351465 0.608755i 0.0453739 0.0785899i
\(61\) −1.35352 2.34437i −0.173301 0.300166i 0.766271 0.642517i \(-0.222110\pi\)
−0.939572 + 0.342352i \(0.888777\pi\)
\(62\) −11.4397 −1.45284
\(63\) 2.21634 1.44493i 0.279233 0.182044i
\(64\) 7.40420 0.925525
\(65\) −1.71608 + 0.990781i −0.212854 + 0.122891i
\(66\) −2.31779 + 6.15002i −0.285301 + 0.757016i
\(67\) 7.30735 12.6567i 0.892735 1.54626i 0.0561520 0.998422i \(-0.482117\pi\)
0.836583 0.547840i \(-0.184550\pi\)
\(68\) −5.65925 9.80210i −0.686285 1.18868i
\(69\) 2.76990i 0.333457i
\(70\) −1.70575 0.865297i −0.203876 0.103423i
\(71\) 2.64558 0.313973 0.156987 0.987601i \(-0.449822\pi\)
0.156987 + 0.987601i \(0.449822\pi\)
\(72\) −0.125596 + 0.0725127i −0.0148016 + 0.00854570i
\(73\) −2.91182 + 5.04342i −0.340802 + 0.590287i −0.984582 0.174924i \(-0.944032\pi\)
0.643779 + 0.765211i \(0.277365\pi\)
\(74\) 13.7481 + 7.93746i 1.59818 + 0.922711i
\(75\) −4.21487 + 2.43346i −0.486691 + 0.280991i
\(76\) 4.28617 0.491657
\(77\) 8.36661 + 2.64571i 0.953464 + 0.301506i
\(78\) −10.7636 −1.21873
\(79\) 1.59178 0.919015i 0.179089 0.103397i −0.407775 0.913082i \(-0.633695\pi\)
0.586865 + 0.809685i \(0.300362\pi\)
\(80\) 1.30831 + 0.755350i 0.146273 + 0.0844507i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −15.2484 + 8.80368i −1.68391 + 0.972204i
\(83\) 5.21418 0.572330 0.286165 0.958180i \(-0.407619\pi\)
0.286165 + 0.958180i \(0.407619\pi\)
\(84\) −2.78412 4.27048i −0.303772 0.465948i
\(85\) 2.14299i 0.232440i
\(86\) 5.85278 + 10.1373i 0.631121 + 1.09313i
\(87\) 1.00871 1.74714i 0.108145 0.187313i
\(88\) −0.450091 0.169628i −0.0479799 0.0180824i
\(89\) −0.367796 + 0.212347i −0.0389863 + 0.0225087i −0.519366 0.854552i \(-0.673832\pi\)
0.480380 + 0.877060i \(0.340499\pi\)
\(90\) 0.722923 0.0762027
\(91\) 0.777692 + 14.3499i 0.0815243 + 1.50428i
\(92\) −5.33708 −0.556429
\(93\) −2.88645 4.99947i −0.299310 0.518421i
\(94\) 6.23717 10.8031i 0.643315 1.11425i
\(95\) 0.702799 + 0.405761i 0.0721057 + 0.0416302i
\(96\) 3.95793 + 6.85534i 0.403955 + 0.699670i
\(97\) 10.0948i 1.02497i −0.858695 0.512487i \(-0.828724\pi\)
0.858695 0.512487i \(-0.171276\pi\)
\(98\) −11.1930 + 8.19331i −1.13066 + 0.827650i
\(99\) −3.27256 + 0.538824i −0.328905 + 0.0541538i
\(100\) 4.68882 + 8.12127i 0.468882 + 0.812127i
\(101\) 7.62305 13.2035i 0.758522 1.31380i −0.185083 0.982723i \(-0.559255\pi\)
0.943604 0.331075i \(-0.107411\pi\)
\(102\) 5.82021 10.0809i 0.576287 0.998159i
\(103\) −4.57538 + 2.64160i −0.450826 + 0.260284i −0.708179 0.706033i \(-0.750483\pi\)
0.257353 + 0.966317i \(0.417150\pi\)
\(104\) 0.787735i 0.0772438i
\(105\) −0.0522328 0.963793i −0.00509740 0.0940566i
\(106\) 25.6422i 2.49059i
\(107\) −3.38728 + 1.95565i −0.327461 + 0.189060i −0.654713 0.755877i \(-0.727211\pi\)
0.327252 + 0.944937i \(0.393877\pi\)
\(108\) 1.66867 + 0.963407i 0.160568 + 0.0927039i
\(109\) −5.50618 3.17899i −0.527396 0.304492i 0.212559 0.977148i \(-0.431820\pi\)
−0.739955 + 0.672656i \(0.765153\pi\)
\(110\) 1.52025 + 1.85409i 0.144950 + 0.176780i
\(111\) 8.01109i 0.760379i
\(112\) 9.17790 5.98348i 0.867230 0.565386i
\(113\) 4.20066 0.395165 0.197582 0.980286i \(-0.436691\pi\)
0.197582 + 0.980286i \(0.436691\pi\)
\(114\) 2.20404 + 3.81751i 0.206427 + 0.357542i
\(115\) −0.875117 0.505249i −0.0816051 0.0471147i
\(116\) −3.36642 1.94360i −0.312564 0.180459i
\(117\) −2.71585 4.70399i −0.251081 0.434884i
\(118\) 16.9301 1.55854
\(119\) −13.8603 7.03108i −1.27057 0.644538i
\(120\) 0.0529073i 0.00482975i
\(121\) −8.26385 7.26008i −0.751259 0.660007i
\(122\) −4.64565 2.68216i −0.420597 0.242832i
\(123\) −7.69493 4.44267i −0.693829 0.400582i
\(124\) −9.63305 + 5.56165i −0.865074 + 0.499451i
\(125\) 3.59959i 0.321957i
\(126\) 2.37188 4.67567i 0.211304 0.416542i
\(127\) 14.3427i 1.27271i 0.771396 + 0.636356i \(0.219559\pi\)
−0.771396 + 0.636356i \(0.780441\pi\)
\(128\) −1.00409 + 0.579713i −0.0887501 + 0.0512399i
\(129\) −2.95353 + 5.11567i −0.260044 + 0.450409i
\(130\) −1.96335 + 3.40062i −0.172197 + 0.298254i
\(131\) 2.55274 + 4.42148i 0.223034 + 0.386307i 0.955728 0.294252i \(-0.0950705\pi\)
−0.732694 + 0.680559i \(0.761737\pi\)
\(132\) 1.03821 + 6.30562i 0.0903649 + 0.548834i
\(133\) 4.93021 3.21423i 0.427504 0.278709i
\(134\) 28.9608i 2.50183i
\(135\) 0.182407 + 0.315938i 0.0156991 + 0.0271916i
\(136\) 0.737774 + 0.425954i 0.0632636 + 0.0365253i
\(137\) 1.19506 2.06991i 0.102101 0.176845i −0.810449 0.585809i \(-0.800777\pi\)
0.912550 + 0.408965i \(0.134110\pi\)
\(138\) −2.74444 4.75351i −0.233622 0.404646i
\(139\) 16.1644 1.37104 0.685522 0.728052i \(-0.259574\pi\)
0.685522 + 0.728052i \(0.259574\pi\)
\(140\) −1.85705 + 0.100643i −0.156949 + 0.00850588i
\(141\) 6.29502 0.530137
\(142\) 4.54017 2.62127i 0.381003 0.219972i
\(143\) 6.35317 16.8575i 0.531279 1.40969i
\(144\) −2.07051 + 3.58622i −0.172542 + 0.298852i
\(145\) −0.367993 0.637382i −0.0305601 0.0529317i
\(146\) 11.5402i 0.955076i
\(147\) −6.40493 2.82434i −0.528269 0.232948i
\(148\) 15.4359 1.26882
\(149\) −15.9785 + 9.22518i −1.30901 + 0.755756i −0.981931 0.189241i \(-0.939397\pi\)
−0.327077 + 0.944998i \(0.606064\pi\)
\(150\) −4.82218 + 8.35226i −0.393729 + 0.681959i
\(151\) 8.36660 + 4.83046i 0.680864 + 0.393097i 0.800180 0.599759i \(-0.204737\pi\)
−0.119317 + 0.992856i \(0.538070\pi\)
\(152\) −0.279385 + 0.161303i −0.0226611 + 0.0130834i
\(153\) 5.87420 0.474901
\(154\) 16.9796 3.74934i 1.36826 0.302130i
\(155\) −2.10603 −0.169161
\(156\) −9.06372 + 5.23294i −0.725679 + 0.418971i
\(157\) −11.4917 6.63471i −0.917134 0.529508i −0.0344145 0.999408i \(-0.510957\pi\)
−0.882720 + 0.469900i \(0.844290\pi\)
\(158\) 1.82114 3.15430i 0.144882 0.250943i
\(159\) 11.2064 6.47002i 0.888725 0.513106i
\(160\) 2.88782 0.228302
\(161\) −6.13904 + 4.00231i −0.483824 + 0.315427i
\(162\) 1.98162i 0.155691i
\(163\) 3.96651 + 6.87020i 0.310681 + 0.538115i 0.978510 0.206199i \(-0.0661096\pi\)
−0.667829 + 0.744315i \(0.732776\pi\)
\(164\) −8.56020 + 14.8267i −0.668440 + 1.15777i
\(165\) −0.426704 + 1.13221i −0.0332188 + 0.0881427i
\(166\) 8.94822 5.16626i 0.694516 0.400979i
\(167\) −0.682227 −0.0527923 −0.0263961 0.999652i \(-0.508403\pi\)
−0.0263961 + 0.999652i \(0.508403\pi\)
\(168\) 0.342190 + 0.173587i 0.0264005 + 0.0133925i
\(169\) 16.5034 1.26949
\(170\) −2.12330 3.67766i −0.162849 0.282063i
\(171\) −1.11224 + 1.92646i −0.0850552 + 0.147320i
\(172\) 9.85694 + 5.69091i 0.751585 + 0.433928i
\(173\) 0.749385 + 1.29797i 0.0569747 + 0.0986831i 0.893106 0.449846i \(-0.148521\pi\)
−0.836131 + 0.548529i \(0.815188\pi\)
\(174\) 3.99777i 0.303070i
\(175\) 11.4836 + 5.82541i 0.868076 + 0.440360i
\(176\) −13.5517 + 2.23128i −1.02150 + 0.168189i
\(177\) 4.27178 + 7.39894i 0.321087 + 0.556139i
\(178\) −0.420791 + 0.728832i −0.0315396 + 0.0546282i
\(179\) 3.10621 5.38012i 0.232169 0.402129i −0.726277 0.687402i \(-0.758751\pi\)
0.958446 + 0.285273i \(0.0920844\pi\)
\(180\) 0.608755 0.351465i 0.0453739 0.0261966i
\(181\) 9.87854i 0.734266i 0.930168 + 0.367133i \(0.119661\pi\)
−0.930168 + 0.367133i \(0.880339\pi\)
\(182\) 15.5526 + 23.8558i 1.15284 + 1.76831i
\(183\) 2.70704i 0.200110i
\(184\) 0.347887 0.200853i 0.0256466 0.0148071i
\(185\) 2.53101 + 1.46128i 0.186083 + 0.107435i
\(186\) −9.90705 5.71984i −0.726420 0.419399i
\(187\) 12.3530 + 15.0656i 0.903337 + 1.10171i
\(188\) 12.1293i 0.884623i
\(189\) 2.64187 0.143176i 0.192168 0.0104146i
\(190\) 1.60813 0.116666
\(191\) −0.439746 0.761663i −0.0318189 0.0551120i 0.849677 0.527303i \(-0.176797\pi\)
−0.881496 + 0.472191i \(0.843463\pi\)
\(192\) 6.41222 + 3.70210i 0.462762 + 0.267176i
\(193\) −19.3467 11.1698i −1.39261 0.804022i −0.399003 0.916950i \(-0.630644\pi\)
−0.993603 + 0.112928i \(0.963977\pi\)
\(194\) −10.0020 17.3240i −0.718105 1.24379i
\(195\) −1.98156 −0.141903
\(196\) −5.44199 + 12.3411i −0.388714 + 0.881508i
\(197\) 1.93301i 0.137721i 0.997626 + 0.0688607i \(0.0219364\pi\)
−0.997626 + 0.0688607i \(0.978064\pi\)
\(198\) −5.08228 + 4.16718i −0.361182 + 0.296149i
\(199\) −1.75591 1.01378i −0.124473 0.0718648i 0.436470 0.899719i \(-0.356228\pi\)
−0.560944 + 0.827854i \(0.689562\pi\)
\(200\) −0.611263 0.352913i −0.0432228 0.0249547i
\(201\) 12.6567 7.30735i 0.892735 0.515421i
\(202\) 30.2120i 2.12571i
\(203\) −5.32978 + 0.288848i −0.374078 + 0.0202731i
\(204\) 11.3185i 0.792453i
\(205\) −2.80722 + 1.62075i −0.196065 + 0.113198i
\(206\) −5.23464 + 9.06666i −0.364715 + 0.631704i
\(207\) 1.38495 2.39880i 0.0962606 0.166728i
\(208\) −11.2464 19.4793i −0.779796 1.35065i
\(209\) −7.27976 + 1.19860i −0.503551 + 0.0829092i
\(210\) −1.04457 1.60224i −0.0720824 0.110565i
\(211\) 8.17186i 0.562574i 0.959624 + 0.281287i \(0.0907612\pi\)
−0.959624 + 0.281287i \(0.909239\pi\)
\(212\) −12.4665 21.5927i −0.856204 1.48299i
\(213\) 2.29114 + 1.32279i 0.156987 + 0.0906362i
\(214\) −3.87535 + 6.71230i −0.264913 + 0.458844i
\(215\) 1.07749 + 1.86627i 0.0734842 + 0.127278i
\(216\) −0.145025 −0.00986773
\(217\) −6.90982 + 13.6212i −0.469069 + 0.924670i
\(218\) −12.5991 −0.853319
\(219\) −5.04342 + 2.91182i −0.340802 + 0.196762i
\(220\) 2.18157 + 0.822179i 0.147081 + 0.0554313i
\(221\) −15.9535 + 27.6322i −1.07315 + 1.85874i
\(222\) 7.93746 + 13.7481i 0.532728 + 0.922711i
\(223\) 24.2491i 1.62384i 0.583767 + 0.811921i \(0.301578\pi\)
−0.583767 + 0.811921i \(0.698422\pi\)
\(224\) 9.47483 18.6776i 0.633064 1.24795i
\(225\) −4.86691 −0.324461
\(226\) 7.20889 4.16205i 0.479528 0.276856i
\(227\) −1.68016 + 2.91012i −0.111516 + 0.193151i −0.916382 0.400306i \(-0.868904\pi\)
0.804866 + 0.593457i \(0.202237\pi\)
\(228\) 3.71193 + 2.14308i 0.245828 + 0.141929i
\(229\) −18.9480 + 10.9396i −1.25212 + 0.722910i −0.971530 0.236918i \(-0.923863\pi\)
−0.280587 + 0.959828i \(0.590529\pi\)
\(230\) −2.00242 −0.132036
\(231\) 5.92285 + 6.47456i 0.389695 + 0.425995i
\(232\) 0.292578 0.0192087
\(233\) −6.88201 + 3.97333i −0.450856 + 0.260302i −0.708192 0.706020i \(-0.750489\pi\)
0.257336 + 0.966322i \(0.417155\pi\)
\(234\) −9.32152 5.38178i −0.609367 0.351818i
\(235\) 1.14826 1.98884i 0.0749040 0.129738i
\(236\) 14.2564 8.23093i 0.928012 0.535788i
\(237\) 1.83803 0.119393
\(238\) −30.7526 + 1.66664i −1.99339 + 0.108032i
\(239\) 18.3659i 1.18799i −0.804467 0.593997i \(-0.797549\pi\)
0.804467 0.593997i \(-0.202451\pi\)
\(240\) 0.755350 + 1.30831i 0.0487576 + 0.0844507i
\(241\) −4.58938 + 7.94904i −0.295628 + 0.512043i −0.975131 0.221630i \(-0.928862\pi\)
0.679503 + 0.733673i \(0.262196\pi\)
\(242\) −21.3752 4.27135i −1.37405 0.274573i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −5.21597 −0.333918
\(245\) −2.06062 + 1.50838i −0.131648 + 0.0963669i
\(246\) −17.6074 −1.12260
\(247\) −6.04137 10.4640i −0.384403 0.665805i
\(248\) 0.418608 0.725050i 0.0265816 0.0460407i
\(249\) 4.51561 + 2.60709i 0.286165 + 0.165218i
\(250\) 3.56651 + 6.17737i 0.225566 + 0.390691i
\(251\) 25.7949i 1.62816i 0.580752 + 0.814080i \(0.302758\pi\)
−0.580752 + 0.814080i \(0.697242\pi\)
\(252\) −0.275875 5.09040i −0.0173785 0.320665i
\(253\) 9.06467 1.49249i 0.569891 0.0938318i
\(254\) 14.2109 + 24.6140i 0.891672 + 1.54442i
\(255\) 1.07150 1.85588i 0.0670997 0.116220i
\(256\) −8.55297 + 14.8142i −0.534561 + 0.925886i
\(257\) −5.11786 + 2.95480i −0.319243 + 0.184315i −0.651055 0.759030i \(-0.725673\pi\)
0.331812 + 0.943346i \(0.392340\pi\)
\(258\) 11.7056i 0.728756i
\(259\) 17.7553 11.5755i 1.10326 0.719265i
\(260\) 3.81810i 0.236789i
\(261\) 1.74714 1.00871i 0.108145 0.0624378i
\(262\) 8.76170 + 5.05857i 0.541299 + 0.312519i
\(263\) 16.8128 + 9.70685i 1.03672 + 0.598550i 0.918902 0.394485i \(-0.129077\pi\)
0.117817 + 0.993035i \(0.462410\pi\)
\(264\) −0.304976 0.371948i −0.0187700 0.0228918i
\(265\) 4.72071i 0.289991i
\(266\) 5.27622 10.4009i 0.323506 0.637723i
\(267\) −0.424694 −0.0259909
\(268\) −14.0799 24.3871i −0.860067 1.48968i
\(269\) −24.5994 14.2025i −1.49985 0.865940i −0.499852 0.866111i \(-0.666612\pi\)
−1.00000 0.000170607i \(0.999946\pi\)
\(270\) 0.626069 + 0.361461i 0.0381014 + 0.0219978i
\(271\) −7.89059 13.6669i −0.479319 0.830205i 0.520399 0.853923i \(-0.325783\pi\)
−0.999719 + 0.0237176i \(0.992450\pi\)
\(272\) 24.3251 1.47493
\(273\) −6.50144 + 12.8162i −0.393485 + 0.775672i
\(274\) 4.73633i 0.286132i
\(275\) −10.2347 12.4822i −0.617176 0.752706i
\(276\) −4.62205 2.66854i −0.278215 0.160627i
\(277\) −14.7731 8.52924i −0.887628 0.512472i −0.0144621 0.999895i \(-0.504604\pi\)
−0.873166 + 0.487423i \(0.837937\pi\)
\(278\) 27.7402 16.0158i 1.66375 0.960565i
\(279\) 5.77289i 0.345614i
\(280\) 0.117261 0.0764474i 0.00700767 0.00456861i
\(281\) 26.5761i 1.58540i 0.609612 + 0.792700i \(0.291325\pi\)
−0.609612 + 0.792700i \(0.708675\pi\)
\(282\) 10.8031 6.23717i 0.643315 0.371418i
\(283\) −4.78709 + 8.29148i −0.284563 + 0.492877i −0.972503 0.232890i \(-0.925182\pi\)
0.687940 + 0.725767i \(0.258515\pi\)
\(284\) 2.54878 4.41461i 0.151242 0.261959i
\(285\) 0.405761 + 0.702799i 0.0240352 + 0.0416302i
\(286\) −5.79967 35.2245i −0.342941 2.08287i
\(287\) 1.27217 + 23.4740i 0.0750940 + 1.38562i
\(288\) 7.91586i 0.466447i
\(289\) −8.75312 15.1608i −0.514889 0.891814i
\(290\) −1.26305 0.729221i −0.0741688 0.0428213i
\(291\) 5.04741 8.74237i 0.295884 0.512487i
\(292\) 5.61053 + 9.71773i 0.328332 + 0.568687i
\(293\) 16.8865 0.986518 0.493259 0.869883i \(-0.335806\pi\)
0.493259 + 0.869883i \(0.335806\pi\)
\(294\) −13.7901 + 1.49911i −0.804254 + 0.0874300i
\(295\) 3.11681 0.181468
\(296\) −1.00616 + 0.580905i −0.0584817 + 0.0337644i
\(297\) −3.10353 1.16965i −0.180085 0.0678698i
\(298\) −18.2808 + 31.6633i −1.05898 + 1.83420i
\(299\) 7.52263 + 13.0296i 0.435045 + 0.753520i
\(300\) 9.37764i 0.541418i
\(301\) 15.6057 0.845753i 0.899499 0.0487484i
\(302\) 19.1443 1.10163
\(303\) 13.2035 7.62305i 0.758522 0.437933i
\(304\) −4.60581 + 7.97749i −0.264161 + 0.457541i
\(305\) −0.855259 0.493784i −0.0489720 0.0282740i
\(306\) 10.0809 5.82021i 0.576287 0.332720i
\(307\) 1.57027 0.0896199 0.0448099 0.998996i \(-0.485732\pi\)
0.0448099 + 0.998996i \(0.485732\pi\)
\(308\) 12.4753 11.4122i 0.710844 0.650272i
\(309\) −5.28319 −0.300550
\(310\) −3.61423 + 2.08668i −0.205274 + 0.118515i
\(311\) 20.8470 + 12.0360i 1.18212 + 0.682499i 0.956505 0.291716i \(-0.0942264\pi\)
0.225619 + 0.974216i \(0.427560\pi\)
\(312\) 0.393867 0.682198i 0.0222984 0.0386219i
\(313\) 0.413571 0.238775i 0.0233764 0.0134964i −0.488266 0.872695i \(-0.662371\pi\)
0.511643 + 0.859198i \(0.329037\pi\)
\(314\) −26.2949 −1.48391
\(315\) 0.436662 0.860786i 0.0246031 0.0484998i
\(316\) 3.54154i 0.199227i
\(317\) 4.70710 + 8.15293i 0.264377 + 0.457914i 0.967400 0.253253i \(-0.0815004\pi\)
−0.703023 + 0.711167i \(0.748167\pi\)
\(318\) 12.8211 22.2068i 0.718972 1.24530i
\(319\) 6.26115 + 2.35967i 0.350557 + 0.132116i
\(320\) 2.33927 1.35058i 0.130769 0.0754996i
\(321\) −3.91130 −0.218307
\(322\) −6.56988 + 12.9511i −0.366125 + 0.721738i
\(323\) 13.0671 0.727070
\(324\) 0.963407 + 1.66867i 0.0535226 + 0.0927039i
\(325\) 13.2178 22.8939i 0.733192 1.26993i
\(326\) 13.6141 + 7.86011i 0.754016 + 0.435331i
\(327\) −3.17899 5.50618i −0.175799 0.304492i
\(328\) 1.28860i 0.0711510i
\(329\) −9.09588 13.9519i −0.501472 0.769195i
\(330\) 0.389528 + 2.36581i 0.0214428 + 0.130234i
\(331\) −9.39932 16.2801i −0.516633 0.894835i −0.999813 0.0193142i \(-0.993852\pi\)
0.483180 0.875521i \(-0.339482\pi\)
\(332\) 5.02338 8.70074i 0.275694 0.477515i
\(333\) −4.00554 + 6.93780i −0.219502 + 0.380189i
\(334\) −1.17079 + 0.675957i −0.0640629 + 0.0369867i
\(335\) 5.33165i 0.291299i
\(336\) 10.9400 0.592896i 0.596828 0.0323451i
\(337\) 5.47186i 0.298071i 0.988832 + 0.149036i \(0.0476169\pi\)
−0.988832 + 0.149036i \(0.952383\pi\)
\(338\) 28.3220 16.3517i 1.54052 0.889417i
\(339\) 3.63788 + 2.10033i 0.197582 + 0.114074i
\(340\) −3.57595 2.06457i −0.193933 0.111967i
\(341\) 14.8058 12.1399i 0.801779 0.657413i
\(342\) 4.40808i 0.238362i
\(343\) 2.99497 + 18.2765i 0.161713 + 0.986838i
\(344\) −0.856674 −0.0461888
\(345\) −0.505249 0.875117i −0.0272017 0.0471147i
\(346\) 2.57209 + 1.48500i 0.138276 + 0.0798339i
\(347\) −15.3867 8.88350i −0.826000 0.476891i 0.0264813 0.999649i \(-0.491570\pi\)
−0.852481 + 0.522758i \(0.824903\pi\)
\(348\) −1.94360 3.36642i −0.104188 0.180459i
\(349\) −30.5643 −1.63607 −0.818035 0.575169i \(-0.804936\pi\)
−0.818035 + 0.575169i \(0.804936\pi\)
\(350\) 25.4792 1.38085i 1.36192 0.0738093i
\(351\) 5.43170i 0.289923i
\(352\) −20.3019 + 16.6464i −1.08209 + 0.887256i
\(353\) 14.2411 + 8.22211i 0.757978 + 0.437619i 0.828569 0.559887i \(-0.189155\pi\)
−0.0705915 + 0.997505i \(0.522489\pi\)
\(354\) 14.6619 + 8.46504i 0.779271 + 0.449912i
\(355\) 0.835841 0.482573i 0.0443619 0.0256123i
\(356\) 0.818307i 0.0433702i
\(357\) −8.48782 13.0192i −0.449223 0.689051i
\(358\) 12.3107i 0.650639i
\(359\) 29.0708 16.7841i 1.53430 0.885828i 0.535143 0.844761i \(-0.320258\pi\)
0.999156 0.0410671i \(-0.0130757\pi\)
\(360\) −0.0264536 + 0.0458191i −0.00139423 + 0.00241488i
\(361\) 7.02584 12.1691i 0.369781 0.640479i
\(362\) 9.78775 + 16.9529i 0.514433 + 0.891024i
\(363\) −3.52667 10.4193i −0.185102 0.546873i
\(364\) 24.6945 + 12.5271i 1.29434 + 0.656597i
\(365\) 2.12454i 0.111204i
\(366\) −2.68216 4.64565i −0.140199 0.242832i
\(367\) 5.26096 + 3.03742i 0.274620 + 0.158552i 0.630985 0.775795i \(-0.282651\pi\)
−0.356365 + 0.934347i \(0.615984\pi\)
\(368\) 5.73509 9.93348i 0.298962 0.517818i
\(369\) −4.44267 7.69493i −0.231276 0.400582i
\(370\) 5.79140 0.301080
\(371\) −30.5323 15.4885i −1.58516 0.804122i
\(372\) −11.1233 −0.576716
\(373\) 30.2576 17.4692i 1.56668 0.904522i 0.570125 0.821558i \(-0.306895\pi\)
0.996553 0.0829641i \(-0.0264387\pi\)
\(374\) 36.1265 + 13.6152i 1.86806 + 0.704025i
\(375\) −1.79979 + 3.11733i −0.0929410 + 0.160978i
\(376\) 0.456469 + 0.790628i 0.0235406 + 0.0407735i
\(377\) 10.9581i 0.564369i
\(378\) 4.39195 2.86330i 0.225897 0.147272i
\(379\) −14.1967 −0.729235 −0.364617 0.931157i \(-0.618800\pi\)
−0.364617 + 0.931157i \(0.618800\pi\)
\(380\) 1.35416 0.781827i 0.0694671 0.0401069i
\(381\) −7.17137 + 12.4212i −0.367400 + 0.636356i
\(382\) −1.50933 0.871409i −0.0772238 0.0445852i
\(383\) 16.3497 9.43952i 0.835432 0.482337i −0.0202770 0.999794i \(-0.506455\pi\)
0.855709 + 0.517458i \(0.173121\pi\)
\(384\) −1.15943 −0.0591667
\(385\) 3.12593 0.690250i 0.159312 0.0351784i
\(386\) −44.2687 −2.25322
\(387\) −5.11567 + 2.95353i −0.260044 + 0.150136i
\(388\) −16.8449 9.72542i −0.855172 0.493734i
\(389\) 1.82144 3.15483i 0.0923508 0.159956i −0.816149 0.577841i \(-0.803895\pi\)
0.908500 + 0.417885i \(0.137229\pi\)
\(390\) −3.40062 + 1.96335i −0.172197 + 0.0994181i
\(391\) −16.2709 −0.822857
\(392\) −0.109713 1.00923i −0.00554134 0.0509739i
\(393\) 5.10549i 0.257538i
\(394\) 1.91525 + 3.31731i 0.0964888 + 0.167123i
\(395\) 0.335270 0.580704i 0.0168692 0.0292184i
\(396\) −2.25369 + 5.97994i −0.113252 + 0.300503i
\(397\) 16.2129 9.36051i 0.813701 0.469790i −0.0345385 0.999403i \(-0.510996\pi\)
0.848239 + 0.529613i \(0.177663\pi\)
\(398\) −4.01784 −0.201396
\(399\) 5.87680 0.318494i 0.294208 0.0159446i
\(400\) −20.1539 −1.00770
\(401\) −9.72588 16.8457i −0.485687 0.841235i 0.514178 0.857684i \(-0.328097\pi\)
−0.999865 + 0.0164490i \(0.994764\pi\)
\(402\) 14.4804 25.0808i 0.722216 1.25091i
\(403\) 27.1556 + 15.6783i 1.35272 + 0.780993i
\(404\) −14.6882 25.4407i −0.730765 1.26572i
\(405\) 0.364814i 0.0181278i
\(406\) −8.86042 + 5.77650i −0.439735 + 0.286683i
\(407\) −26.2168 + 4.31656i −1.29952 + 0.213964i
\(408\) 0.425954 + 0.737774i 0.0210879 + 0.0365253i
\(409\) −2.00889 + 3.47950i −0.0993331 + 0.172050i −0.911409 0.411502i \(-0.865004\pi\)
0.812076 + 0.583552i \(0.198338\pi\)
\(410\) −3.21171 + 5.56284i −0.158615 + 0.274729i
\(411\) 2.06991 1.19506i 0.102101 0.0589482i
\(412\) 10.1797i 0.501519i
\(413\) 10.2262 20.1587i 0.503196 0.991945i
\(414\) 5.48888i 0.269764i
\(415\) 1.64736 0.951103i 0.0808656 0.0466878i
\(416\) −37.2362 21.4983i −1.82565 1.05404i
\(417\) 13.9988 + 8.08218i 0.685522 + 0.395786i
\(418\) −11.3054 + 9.26982i −0.552967 + 0.453402i
\(419\) 18.7760i 0.917268i −0.888625 0.458634i \(-0.848339\pi\)
0.888625 0.458634i \(-0.151661\pi\)
\(420\) −1.65857 0.841366i −0.0809301 0.0410545i
\(421\) 37.7836 1.84146 0.920730 0.390201i \(-0.127594\pi\)
0.920730 + 0.390201i \(0.127594\pi\)
\(422\) 8.09675 + 14.0240i 0.394144 + 0.682677i
\(423\) 5.45165 + 3.14751i 0.265068 + 0.153037i
\(424\) 1.62521 + 0.938317i 0.0789273 + 0.0455687i
\(425\) 14.2946 + 24.7590i 0.693390 + 1.20099i
\(426\) 5.24254 0.254002
\(427\) −5.99974 + 3.91149i −0.290348 + 0.189290i
\(428\) 7.53634i 0.364283i
\(429\) 13.9308 11.4224i 0.672583 0.551480i
\(430\) 3.69823 + 2.13517i 0.178345 + 0.102967i
\(431\) −10.5902 6.11424i −0.510111 0.294512i 0.222769 0.974871i \(-0.428491\pi\)
−0.732879 + 0.680359i \(0.761824\pi\)
\(432\) −3.58622 + 2.07051i −0.172542 + 0.0996173i
\(433\) 15.0598i 0.723726i 0.932231 + 0.361863i \(0.117859\pi\)
−0.932231 + 0.361863i \(0.882141\pi\)
\(434\) 1.63789 + 30.2222i 0.0786213 + 1.45071i
\(435\) 0.735985i 0.0352878i
\(436\) −10.6094 + 6.12533i −0.508097 + 0.293350i
\(437\) 3.08080 5.33609i 0.147374 0.255260i
\(438\) −5.77011 + 9.99413i −0.275707 + 0.477538i
\(439\) −7.66796 13.2813i −0.365972 0.633882i 0.622960 0.782254i \(-0.285930\pi\)
−0.988932 + 0.148372i \(0.952597\pi\)
\(440\) −0.173142 + 0.0285077i −0.00825424 + 0.00135905i
\(441\) −4.13466 5.64842i −0.196888 0.268972i
\(442\) 63.2274i 3.00742i
\(443\) −7.86874 13.6291i −0.373855 0.647536i 0.616300 0.787512i \(-0.288631\pi\)
−0.990155 + 0.139975i \(0.955298\pi\)
\(444\) 13.3679 + 7.71794i 0.634411 + 0.366277i
\(445\) −0.0774672 + 0.134177i −0.00367230 + 0.00636061i
\(446\) 24.0263 + 41.6147i 1.13768 + 1.97051i
\(447\) −18.4504 −0.872672
\(448\) −1.06011 19.5610i −0.0500854 0.924169i
\(449\) −14.0305 −0.662142 −0.331071 0.943606i \(-0.607410\pi\)
−0.331071 + 0.943606i \(0.607410\pi\)
\(450\) −8.35226 + 4.82218i −0.393729 + 0.227320i
\(451\) 10.3927 27.5760i 0.489374 1.29850i
\(452\) 4.04695 7.00951i 0.190352 0.329700i
\(453\) 4.83046 + 8.36660i 0.226955 + 0.393097i
\(454\) 6.65886i 0.312516i
\(455\) 2.86322 + 4.39182i 0.134230 + 0.205892i
\(456\) −0.322606 −0.0151074
\(457\) −28.3403 + 16.3623i −1.32570 + 0.765396i −0.984632 0.174642i \(-0.944123\pi\)
−0.341072 + 0.940037i \(0.610790\pi\)
\(458\) −21.6782 + 37.5477i −1.01295 + 1.75449i
\(459\) 5.08721 + 2.93710i 0.237450 + 0.137092i
\(460\) −1.68619 + 0.973521i −0.0786189 + 0.0453907i
\(461\) 17.3441 0.807795 0.403897 0.914804i \(-0.367655\pi\)
0.403897 + 0.914804i \(0.367655\pi\)
\(462\) 16.5794 + 5.24278i 0.771346 + 0.243916i
\(463\) −28.3707 −1.31850 −0.659250 0.751924i \(-0.729126\pi\)
−0.659250 + 0.751924i \(0.729126\pi\)
\(464\) 7.23494 4.17709i 0.335874 0.193917i
\(465\) −1.82388 1.05302i −0.0845803 0.0488325i
\(466\) −7.87363 + 13.6375i −0.364739 + 0.631746i
\(467\) −30.8759 + 17.8262i −1.42877 + 0.824899i −0.997024 0.0770966i \(-0.975435\pi\)
−0.431744 + 0.901996i \(0.642102\pi\)
\(468\) −10.4659 −0.483786
\(469\) −34.4837 17.4930i −1.59231 0.807750i
\(470\) 4.55082i 0.209913i
\(471\) −6.63471 11.4917i −0.305711 0.529508i
\(472\) −0.619517 + 1.07303i −0.0285156 + 0.0493904i
\(473\) −18.3328 6.90918i −0.842942 0.317684i
\(474\) 3.15430 1.82114i 0.144882 0.0836476i
\(475\) −10.8264 −0.496747
\(476\) −25.0857 + 16.3545i −1.14980 + 0.749605i
\(477\) 12.9400 0.592483
\(478\) −18.1972 31.5184i −0.832318 1.44162i
\(479\) −13.1341 + 22.7489i −0.600111 + 1.03942i 0.392693 + 0.919670i \(0.371544\pi\)
−0.992804 + 0.119753i \(0.961790\pi\)
\(480\) 2.50092 + 1.44391i 0.114151 + 0.0659051i
\(481\) −21.7569 37.6841i −0.992031 1.71825i
\(482\) 18.1888i 0.828478i
\(483\) −7.31772 + 0.396584i −0.332968 + 0.0180452i
\(484\) −20.0761 + 6.79524i −0.912552 + 0.308874i
\(485\) −1.84137 3.18934i −0.0836121 0.144820i
\(486\) −0.990810 + 1.71613i −0.0449440 + 0.0778454i
\(487\) 13.2119 22.8836i 0.598687 1.03696i −0.394328 0.918970i \(-0.629023\pi\)
0.993015 0.117987i \(-0.0376441\pi\)
\(488\) 0.339993 0.196295i 0.0153908 0.00888586i
\(489\) 7.93302i 0.358744i
\(490\) −2.04178 + 4.63027i −0.0922383 + 0.209174i
\(491\) 16.9030i 0.762823i −0.924405 0.381412i \(-0.875438\pi\)
0.924405 0.381412i \(-0.124562\pi\)
\(492\) −14.8267 + 8.56020i −0.668440 + 0.385924i
\(493\) −10.2631 5.92538i −0.462225 0.266866i
\(494\) −20.7356 11.9717i −0.932937 0.538632i
\(495\) −0.935643 + 0.767174i −0.0420540 + 0.0344819i
\(496\) 23.9056i 1.07339i
\(497\) −0.378785 6.98930i −0.0169909 0.313513i
\(498\) 10.3325 0.463011
\(499\) 12.8090 + 22.1859i 0.573411 + 0.993178i 0.996212 + 0.0869550i \(0.0277136\pi\)
−0.422801 + 0.906223i \(0.638953\pi\)
\(500\) 6.00653 + 3.46787i 0.268620 + 0.155088i
\(501\) −0.590826 0.341113i −0.0263961 0.0152398i
\(502\) 25.5579 + 44.2675i 1.14070 + 1.97576i
\(503\) −11.1759 −0.498307 −0.249153 0.968464i \(-0.580152\pi\)
−0.249153 + 0.968464i \(0.580152\pi\)
\(504\) 0.209552 + 0.321426i 0.00933418 + 0.0143174i
\(505\) 5.56199i 0.247505i
\(506\) 14.0774 11.5427i 0.625817 0.513134i
\(507\) 14.2924 + 8.25171i 0.634747 + 0.366471i
\(508\) 23.9333 + 13.8179i 1.06187 + 0.613070i
\(509\) −14.0836 + 8.13115i −0.624243 + 0.360407i −0.778519 0.627621i \(-0.784029\pi\)
0.154276 + 0.988028i \(0.450695\pi\)
\(510\) 4.24659i 0.188042i
\(511\) 13.7410 + 6.97056i 0.607865 + 0.308359i
\(512\) 31.5786i 1.39559i
\(513\) −1.92646 + 1.11224i −0.0850552 + 0.0491066i
\(514\) −5.85528 + 10.1416i −0.258265 + 0.447329i
\(515\) −0.963692 + 1.66916i −0.0424653 + 0.0735521i
\(516\) 5.69091 + 9.85694i 0.250528 + 0.433928i
\(517\) 3.39191 + 20.6009i 0.149176 + 0.906025i
\(518\) 19.0014 37.4572i 0.834872 1.64577i
\(519\) 1.49877i 0.0657887i
\(520\) −0.143688 0.248876i −0.00630115 0.0109139i
\(521\) −34.1873 19.7380i −1.49777 0.864739i −0.497775 0.867306i \(-0.665849\pi\)
−0.999997 + 0.00256769i \(0.999183\pi\)
\(522\) 1.99888 3.46217i 0.0874888 0.151535i
\(523\) 2.70950 + 4.69299i 0.118478 + 0.205210i 0.919165 0.393873i \(-0.128865\pi\)
−0.800687 + 0.599083i \(0.795532\pi\)
\(524\) 9.83733 0.429746
\(525\) 7.03235 + 10.7867i 0.306917 + 0.470772i
\(526\) 38.4706 1.67740
\(527\) −29.3679 + 16.9556i −1.27929 + 0.738596i
\(528\) −12.8518 4.84352i −0.559302 0.210787i
\(529\) 7.66383 13.2741i 0.333210 0.577137i
\(530\) −4.67732 8.10136i −0.203170 0.351901i
\(531\) 8.54356i 0.370759i
\(532\) −0.613678 11.3235i −0.0266063 0.490936i
\(533\) 48.2626 2.09048
\(534\) −0.728832 + 0.420791i −0.0315396 + 0.0182094i
\(535\) −0.713448 + 1.23573i −0.0308450 + 0.0534252i
\(536\) 1.83554 + 1.05975i 0.0792834 + 0.0457743i
\(537\) 5.38012 3.10621i 0.232169 0.134043i
\(538\) −56.2878 −2.42674
\(539\) 5.79172 22.4823i 0.249467 0.968383i
\(540\) 0.702929 0.0302493
\(541\) 34.5920 19.9717i 1.48723 0.858651i 0.487334 0.873216i \(-0.337970\pi\)
0.999894 + 0.0145646i \(0.00463623\pi\)
\(542\) −27.0826 15.6361i −1.16330 0.671630i
\(543\) −4.93927 + 8.55507i −0.211964 + 0.367133i
\(544\) 40.2696 23.2497i 1.72655 0.996822i
\(545\) −2.31948 −0.0993557
\(546\) 1.54109 + 28.4360i 0.0659526 + 1.21695i
\(547\) 16.5342i 0.706952i −0.935444 0.353476i \(-0.885000\pi\)
0.935444 0.353476i \(-0.115000\pi\)
\(548\) −2.30267 3.98834i −0.0983651 0.170373i
\(549\) 1.35352 2.34437i 0.0577669 0.100055i
\(550\) −29.9316 11.2805i −1.27629 0.481002i
\(551\) 3.88649 2.24386i 0.165570 0.0955918i
\(552\) 0.401706 0.0170977
\(553\) −2.65583 4.07370i −0.112937 0.173232i
\(554\) −33.8034 −1.43617
\(555\) 1.46128 + 2.53101i 0.0620278 + 0.107435i
\(556\) 15.5729 26.9730i 0.660437 1.14391i
\(557\) 17.1555 + 9.90471i 0.726900 + 0.419676i 0.817287 0.576231i \(-0.195477\pi\)
−0.0903867 + 0.995907i \(0.528810\pi\)
\(558\) −5.71984 9.90705i −0.242140 0.419399i
\(559\) 32.0854i 1.35707i
\(560\) 1.80822 3.56453i 0.0764113 0.150629i
\(561\) 3.16516 + 19.2237i 0.133633 + 0.811625i
\(562\) 26.3319 + 45.6082i 1.11074 + 1.92386i
\(563\) −2.13380 + 3.69585i −0.0899289 + 0.155761i −0.907481 0.420093i \(-0.861997\pi\)
0.817552 + 0.575855i \(0.195331\pi\)
\(564\) 6.06467 10.5043i 0.255369 0.442312i
\(565\) 1.32715 0.766230i 0.0558336 0.0322355i
\(566\) 18.9724i 0.797468i
\(567\) 2.35952 + 1.19694i 0.0990905 + 0.0502669i
\(568\) 0.383677i 0.0160987i
\(569\) 10.1806 5.87778i 0.426793 0.246409i −0.271186 0.962527i \(-0.587416\pi\)
0.697980 + 0.716118i \(0.254083\pi\)
\(570\) 1.39268 + 0.804064i 0.0583330 + 0.0336785i
\(571\) 17.2181 + 9.94087i 0.720554 + 0.416012i 0.814957 0.579522i \(-0.196761\pi\)
−0.0944023 + 0.995534i \(0.530094\pi\)
\(572\) −22.0089 26.8420i −0.920238 1.12232i
\(573\) 0.879492i 0.0367413i
\(574\) 25.4414 + 39.0239i 1.06191 + 1.62883i
\(575\) 13.4808 0.562190
\(576\) 3.70210 + 6.41222i 0.154254 + 0.267176i
\(577\) −0.243841 0.140782i −0.0101513 0.00586083i 0.494916 0.868941i \(-0.335199\pi\)
−0.505067 + 0.863080i \(0.668532\pi\)
\(578\) −30.0430 17.3453i −1.24962 0.721471i
\(579\) −11.1698 19.3467i −0.464202 0.804022i
\(580\) −1.41811 −0.0588837
\(581\) −0.746548 13.7752i −0.0309720 0.571492i
\(582\) 20.0041i 0.829196i
\(583\) 27.2118 + 33.1874i 1.12700 + 1.37448i
\(584\) −0.731423 0.422287i −0.0302665 0.0174744i
\(585\) −1.71608 0.990781i −0.0709513 0.0409638i
\(586\) 28.9794 16.7313i 1.19713 0.691163i
\(587\) 2.55977i 0.105653i −0.998604 0.0528265i \(-0.983177\pi\)
0.998604 0.0528265i \(-0.0168230\pi\)
\(588\) −10.8835 + 7.96672i −0.448826 + 0.328542i
\(589\) 12.8417i 0.529133i
\(590\) 5.34886 3.08817i 0.220209 0.127138i
\(591\) −0.966506 + 1.67404i −0.0397568 + 0.0688607i
\(592\) −16.5870 + 28.7296i −0.681722 + 1.18078i
\(593\) 8.67463 + 15.0249i 0.356224 + 0.616998i 0.987327 0.158701i \(-0.0507306\pi\)
−0.631102 + 0.775699i \(0.717397\pi\)
\(594\) −6.48497 + 1.06774i −0.266082 + 0.0438100i
\(595\) −5.66151 + 0.306826i −0.232099 + 0.0125786i
\(596\) 35.5504i 1.45620i
\(597\) −1.01378 1.75591i −0.0414911 0.0718648i
\(598\) 25.8197 + 14.9070i 1.05585 + 0.609592i
\(599\) −3.42921 + 5.93957i −0.140114 + 0.242684i −0.927539 0.373726i \(-0.878080\pi\)
0.787426 + 0.616410i \(0.211414\pi\)
\(600\) −0.352913 0.611263i −0.0144076 0.0249547i
\(601\) 1.68577 0.0687641 0.0343821 0.999409i \(-0.489054\pi\)
0.0343821 + 0.999409i \(0.489054\pi\)
\(602\) 25.9435 16.9137i 1.05738 0.689352i
\(603\) 14.6147 0.595157
\(604\) 16.1209 9.30740i 0.655949 0.378713i
\(605\) −3.93516 0.786351i −0.159987 0.0319697i
\(606\) 15.1060 26.1643i 0.613638 1.06285i
\(607\) −8.25751 14.3024i −0.335162 0.580518i 0.648354 0.761339i \(-0.275458\pi\)
−0.983516 + 0.180821i \(0.942124\pi\)
\(608\) 17.6087i 0.714127i
\(609\) −4.76015 2.41474i −0.192891 0.0978503i
\(610\) −1.95698 −0.0792359
\(611\) −29.6118 + 17.0964i −1.19796 + 0.691644i
\(612\) 5.65925 9.80210i 0.228762 0.396227i
\(613\) 19.5034 + 11.2603i 0.787733 + 0.454798i 0.839164 0.543879i \(-0.183045\pi\)
−0.0514307 + 0.998677i \(0.516378\pi\)
\(614\) 2.69479 1.55584i 0.108753 0.0627884i
\(615\) −3.24150 −0.130710
\(616\) −0.383694 + 1.21337i −0.0154595 + 0.0488881i
\(617\) 28.3379 1.14084 0.570421 0.821353i \(-0.306780\pi\)
0.570421 + 0.821353i \(0.306780\pi\)
\(618\) −9.06666 + 5.23464i −0.364715 + 0.210568i
\(619\) −14.5332 8.39077i −0.584140 0.337253i 0.178637 0.983915i \(-0.442831\pi\)
−0.762777 + 0.646662i \(0.776165\pi\)
\(620\) −2.02897 + 3.51427i −0.0814853 + 0.141137i
\(621\) 2.39880 1.38495i 0.0962606 0.0555761i
\(622\) 47.7016 1.91266
\(623\) 0.613654 + 0.941268i 0.0245855 + 0.0377111i
\(624\) 22.4928i 0.900431i
\(625\) −11.5107 19.9371i −0.460427 0.797484i
\(626\) 0.473161 0.819539i 0.0189113 0.0327554i
\(627\) −6.90376 2.60186i −0.275710 0.103908i
\(628\) −22.1423 + 12.7839i −0.883574 + 0.510132i
\(629\) 47.0587 1.87635
\(630\) −0.103506 1.90987i −0.00412376 0.0760911i
\(631\) −11.8060 −0.469991 −0.234995 0.971997i \(-0.575507\pi\)
−0.234995 + 0.971997i \(0.575507\pi\)
\(632\) 0.133281 + 0.230849i 0.00530161 + 0.00918266i
\(633\) −4.08593 + 7.07703i −0.162401 + 0.281287i
\(634\) 16.1560 + 9.32768i 0.641637 + 0.370449i
\(635\) 2.61622 + 4.53142i 0.103821 + 0.179824i
\(636\) 24.9330i 0.988660i
\(637\) 37.7992 4.10913i 1.49766 0.162810i
\(638\) 13.0830 2.15409i 0.517959 0.0852813i
\(639\) 1.32279 + 2.29114i 0.0523288 + 0.0906362i
\(640\) −0.211488 + 0.366307i −0.00835978 + 0.0144796i
\(641\) −8.90108 + 15.4171i −0.351572 + 0.608940i −0.986525 0.163610i \(-0.947686\pi\)
0.634953 + 0.772550i \(0.281019\pi\)
\(642\) −6.71230 + 3.87535i −0.264913 + 0.152948i
\(643\) 35.8544i 1.41396i 0.707233 + 0.706980i \(0.249943\pi\)
−0.707233 + 0.706980i \(0.750057\pi\)
\(644\) 0.764145 + 14.0999i 0.0301115 + 0.555614i
\(645\) 2.15498i 0.0848523i
\(646\) 22.4248 12.9470i 0.882292 0.509391i
\(647\) 34.7363 + 20.0550i 1.36563 + 0.788444i 0.990366 0.138475i \(-0.0442201\pi\)
0.375260 + 0.926920i \(0.377553\pi\)
\(648\) −0.125596 0.0725127i −0.00493386 0.00284857i
\(649\) −21.9118 + 17.9664i −0.860112 + 0.705243i
\(650\) 52.3853i 2.05472i
\(651\) −12.7947 + 8.34143i −0.501464 + 0.326927i
\(652\) 15.2855 0.598625
\(653\) −4.30668 7.45939i −0.168533 0.291908i 0.769371 0.638802i \(-0.220570\pi\)
−0.937904 + 0.346894i \(0.887236\pi\)
\(654\) −10.9111 6.29955i −0.426660 0.246332i
\(655\) 1.61302 + 0.931277i 0.0630259 + 0.0363880i
\(656\) −18.3972 31.8648i −0.718289 1.24411i
\(657\) −5.82364 −0.227202
\(658\) −29.4334 14.9311i −1.14743 0.582074i
\(659\) 16.0122i 0.623745i −0.950124 0.311873i \(-0.899044\pi\)
0.950124 0.311873i \(-0.100956\pi\)
\(660\) 1.47820 + 1.80281i 0.0575389 + 0.0701743i
\(661\) −29.2549 16.8903i −1.13788 0.656958i −0.191979 0.981399i \(-0.561491\pi\)
−0.945906 + 0.324441i \(0.894824\pi\)
\(662\) −32.2610 18.6259i −1.25386 0.723915i
\(663\) −27.6322 + 15.9535i −1.07315 + 0.619581i
\(664\) 0.756188i 0.0293458i
\(665\) 0.971346 1.91480i 0.0376672 0.0742529i
\(666\) 15.8749i 0.615141i
\(667\) −4.83941 + 2.79403i −0.187383 + 0.108185i
\(668\) −0.657262 + 1.13841i −0.0254302 + 0.0440465i
\(669\) −12.1246 + 21.0004i −0.468763 + 0.811921i
\(670\) −5.28265 9.14982i −0.204087 0.353488i
\(671\) 8.85897 1.45862i 0.341997 0.0563094i
\(672\) 17.5443 11.4379i 0.676785 0.441226i
\(673\) 39.0078i 1.50364i −0.659368 0.751820i \(-0.729176\pi\)
0.659368 0.751820i \(-0.270824\pi\)
\(674\) 5.42157 + 9.39043i 0.208831 + 0.361706i
\(675\) −4.21487 2.43346i −0.162230 0.0936637i
\(676\) 15.8995 27.5388i 0.611520 1.05918i
\(677\) −11.4527 19.8367i −0.440164 0.762387i 0.557537 0.830152i \(-0.311747\pi\)
−0.997701 + 0.0677650i \(0.978413\pi\)
\(678\) 8.32411 0.319685
\(679\) −26.6692 + 1.44534i −1.02347 + 0.0554671i
\(680\) 0.310788 0.0119182
\(681\) −2.91012 + 1.68016i −0.111516 + 0.0643838i
\(682\) 13.3804 35.5034i 0.512361 1.35950i
\(683\) 16.3370 28.2966i 0.625120 1.08274i −0.363398 0.931634i \(-0.618384\pi\)
0.988518 0.151105i \(-0.0482831\pi\)
\(684\) 2.14308 + 3.71193i 0.0819428 + 0.141929i
\(685\) 0.871953i 0.0333156i
\(686\) 23.2483 + 28.3974i 0.887624 + 1.08422i
\(687\) −21.8792 −0.834745
\(688\) −21.1841 + 12.2306i −0.807634 + 0.466288i
\(689\) −35.1432 + 60.8698i −1.33885 + 2.31896i
\(690\) −1.73415 1.00121i −0.0660179 0.0381155i
\(691\) 20.2148 11.6710i 0.769007 0.443986i −0.0635132 0.997981i \(-0.520230\pi\)
0.832520 + 0.553995i \(0.186897\pi\)
\(692\) 2.88785 0.109780
\(693\) 1.89206 + 8.56855i 0.0718734 + 0.325492i
\(694\) −35.2074 −1.33646
\(695\) 5.10694 2.94849i 0.193717 0.111843i
\(696\) 0.253380 + 0.146289i 0.00960434 + 0.00554507i
\(697\) −26.0971 + 45.2016i −0.988500 + 1.71213i
\(698\) −52.4524 + 30.2834i −1.98535 + 1.14624i
\(699\) −7.94667 −0.300570
\(700\) 20.7840 13.5500i 0.785563 0.512143i
\(701\) 41.9176i 1.58321i −0.611036 0.791603i \(-0.709247\pi\)
0.611036 0.791603i \(-0.290753\pi\)
\(702\) −5.38178 9.32152i −0.203122 0.351818i
\(703\) −8.91026 + 15.4330i −0.336057 + 0.582068i
\(704\) −8.66029 + 22.9792i −0.326397 + 0.866061i
\(705\) 1.98884 1.14826i 0.0749040 0.0432459i
\(706\) 32.5862 1.22640
\(707\) −35.9734 18.2487i −1.35292 0.686313i
\(708\) 16.4619 0.618675
\(709\) 15.6972 + 27.1883i 0.589519 + 1.02108i 0.994295 + 0.106662i \(0.0340162\pi\)
−0.404776 + 0.914416i \(0.632650\pi\)
\(710\) 0.956276 1.65632i 0.0358884 0.0621606i
\(711\) 1.59178 + 0.919015i 0.0596965 + 0.0344658i
\(712\) −0.0307957 0.0533397i −0.00115412 0.00199899i
\(713\) 15.9903i 0.598842i
\(714\) −27.4658 13.9329i −1.02788 0.521427i
\(715\) −1.06771 6.48479i −0.0399302 0.242517i
\(716\) −5.98510 10.3665i −0.223674 0.387414i
\(717\) 9.18297 15.9054i 0.342944 0.593997i
\(718\) 33.2596 57.6073i 1.24124 2.14989i
\(719\) 0.570677 0.329481i 0.0212827 0.0122876i −0.489321 0.872104i \(-0.662755\pi\)
0.510604 + 0.859816i \(0.329422\pi\)
\(720\) 1.51070i 0.0563005i
\(721\) 7.63385 + 11.7094i 0.284300 + 0.436079i
\(722\) 27.8451i 1.03629i
\(723\) −7.94904 + 4.58938i −0.295628 + 0.170681i
\(724\) 16.4840 + 9.51706i 0.612624 + 0.353699i
\(725\) 8.50318 + 4.90931i 0.315800 + 0.182327i
\(726\) −16.3758 14.3867i −0.607763 0.533941i
\(727\) 3.90800i 0.144940i 0.997371 + 0.0724698i \(0.0230881\pi\)
−0.997371 + 0.0724698i \(0.976912\pi\)
\(728\) −2.08110 + 0.112785i −0.0771306 + 0.00418009i
\(729\) −1.00000 −0.0370370
\(730\) 2.10502 + 3.64600i 0.0779102 + 0.134945i
\(731\) 30.0505 + 17.3496i 1.11146 + 0.641700i
\(732\) −4.51716 2.60799i −0.166959 0.0963939i
\(733\) 16.0679 + 27.8304i 0.593482 + 1.02794i 0.993759 + 0.111546i \(0.0355804\pi\)
−0.400278 + 0.916394i \(0.631086\pi\)
\(734\) 12.0380 0.444331
\(735\) −2.53874 + 0.275985i −0.0936429 + 0.0101799i
\(736\) 21.9261i 0.808208i
\(737\) 30.7335 + 37.4825i 1.13208 + 1.38069i
\(738\) −15.2484 8.80368i −0.561302 0.324068i
\(739\) −8.70546 5.02610i −0.320235 0.184888i 0.331262 0.943539i \(-0.392526\pi\)
−0.651498 + 0.758651i \(0.725859\pi\)
\(740\) 4.87679 2.81561i 0.179274 0.103504i
\(741\) 12.0827i 0.443870i
\(742\) −67.7435 + 3.67136i −2.48694 + 0.134780i
\(743\) 1.22246i 0.0448476i 0.999749 + 0.0224238i \(0.00713831\pi\)
−0.999749 + 0.0224238i \(0.992862\pi\)
\(744\) 0.725050 0.418608i 0.0265816 0.0153469i
\(745\) −3.36548 + 5.82917i −0.123301 + 0.213564i
\(746\) 34.6173 59.9590i 1.26743 2.19525i
\(747\) 2.60709 + 4.51561i 0.0953884 + 0.165218i
\(748\) 37.0405 6.09867i 1.35433 0.222990i
\(749\) 5.65156 + 8.66877i 0.206503 + 0.316750i
\(750\) 7.13301i 0.260461i
\(751\) −3.77946 6.54621i −0.137914 0.238875i 0.788793 0.614659i \(-0.210707\pi\)
−0.926707 + 0.375785i \(0.877373\pi\)
\(752\) 22.5754 + 13.0339i 0.823239 + 0.475297i
\(753\) −12.8975 + 22.3391i −0.470009 + 0.814080i
\(754\) 10.8573 + 18.8055i 0.395401 + 0.684855i
\(755\) 3.52444 0.128267
\(756\) 2.30629 4.54636i 0.0838788 0.165349i
\(757\) −12.3734 −0.449721 −0.224860 0.974391i \(-0.572193\pi\)
−0.224860 + 0.974391i \(0.572193\pi\)
\(758\) −24.3634 + 14.0662i −0.884918 + 0.510908i
\(759\) 8.59648 + 3.23980i 0.312032 + 0.117597i
\(760\) −0.0588457 + 0.101924i −0.00213456 + 0.00369716i
\(761\) 26.9061 + 46.6027i 0.975346 + 1.68935i 0.678790 + 0.734332i \(0.262505\pi\)
0.296555 + 0.955016i \(0.404162\pi\)
\(762\) 28.4218i 1.02961i
\(763\) −7.61015 + 15.0018i −0.275506 + 0.543101i
\(764\) −1.69462 −0.0613091
\(765\) 1.85588 1.07150i 0.0670997 0.0387400i
\(766\) 18.7055 32.3989i 0.675858 1.17062i
\(767\) −40.1889 23.2031i −1.45114 0.837814i
\(768\) −14.8142 + 8.55297i −0.534561 + 0.308629i
\(769\) 22.8557 0.824199 0.412099 0.911139i \(-0.364796\pi\)
0.412099 + 0.911139i \(0.364796\pi\)
\(770\) 4.68060 4.28176i 0.168677 0.154304i
\(771\) −5.90959 −0.212829
\(772\) −37.2775 + 21.5222i −1.34165 + 0.774600i
\(773\) 10.1111 + 5.83765i 0.363671 + 0.209966i 0.670690 0.741738i \(-0.265998\pi\)
−0.307019 + 0.951703i \(0.599331\pi\)
\(774\) −5.85278 + 10.1373i −0.210374 + 0.364378i
\(775\) 24.3320 14.0481i 0.874030 0.504622i
\(776\) 1.46400 0.0525547
\(777\) 21.1643 1.14700i 0.759265 0.0411484i
\(778\) 7.21881i 0.258807i
\(779\) −9.88264 17.1172i −0.354082 0.613289i
\(780\) −1.90905 + 3.30657i −0.0683550 + 0.118394i
\(781\) −3.09440 + 8.21066i −0.110726 + 0.293801i
\(782\) −27.9231 + 16.1214i −0.998528 + 0.576500i
\(783\) 2.01743 0.0720969
\(784\) −17.1217 23.3902i −0.611488 0.835363i
\(785\) −4.84087 −0.172778
\(786\) 5.05857 + 8.76170i 0.180433 + 0.312519i
\(787\) 6.06595 10.5065i 0.216228 0.374518i −0.737424 0.675430i \(-0.763958\pi\)
0.953652 + 0.300913i \(0.0972913\pi\)
\(788\) 3.22556 + 1.86228i 0.114906 + 0.0663409i
\(789\) 9.70685 + 16.8128i 0.345573 + 0.598550i
\(790\) 1.32875i 0.0472749i
\(791\) −0.601436 11.0976i −0.0213846 0.394586i
\(792\) −0.0781431 0.474605i −0.00277669 0.0168643i
\(793\) 7.35193 + 12.7339i 0.261075 + 0.452195i
\(794\) 18.5490 32.1277i 0.658278 1.14017i
\(795\) 2.36035 4.08825i 0.0837131 0.144995i
\(796\) −3.38332 + 1.95336i −0.119919 + 0.0692350i
\(797\) 1.57399i 0.0557537i 0.999611 + 0.0278769i \(0.00887463\pi\)
−0.999611 + 0.0278769i \(0.991125\pi\)
\(798\) 9.76981 6.36937i 0.345847 0.225473i
\(799\) 36.9782i 1.30820i
\(800\) −33.3643 + 19.2629i −1.17961 + 0.681046i
\(801\) −0.367796 0.212347i −0.0129954 0.00750292i
\(802\) −33.3818 19.2730i −1.17875 0.680553i
\(803\) −12.2466 14.9359i −0.432174 0.527078i
\(804\) 28.1598i 0.993120i
\(805\) −1.20951 + 2.38429i −0.0426296 + 0.0840351i
\(806\) 62.1369 2.18868
\(807\) −14.2025 24.5994i −0.499951 0.865940i
\(808\) 1.91484 + 1.10554i 0.0673639 + 0.0388926i
\(809\) 42.3484 + 24.4499i 1.48889 + 0.859612i 0.999920 0.0126872i \(-0.00403857\pi\)
0.488972 + 0.872299i \(0.337372\pi\)
\(810\) 0.361461 + 0.626069i 0.0127005 + 0.0219978i
\(811\) 46.4357 1.63058 0.815290 0.579053i \(-0.196578\pi\)
0.815290 + 0.579053i \(0.196578\pi\)
\(812\) −4.65276 + 9.17193i −0.163280 + 0.321872i
\(813\) 15.7812i 0.553470i
\(814\) −40.7146 + 33.3836i −1.42705 + 1.17010i
\(815\) 2.50634 + 1.44704i 0.0877934 + 0.0506876i
\(816\) 21.0662 + 12.1626i 0.737464 + 0.425775i
\(817\) −11.3797 + 6.57008i −0.398126 + 0.229858i
\(818\) 7.96170i 0.278374i
\(819\) −12.0385 + 7.84844i −0.420660 + 0.274247i
\(820\) 6.24577i 0.218112i
\(821\) −17.1993 + 9.93003i −0.600260 + 0.346560i −0.769144 0.639076i \(-0.779317\pi\)
0.168884 + 0.985636i \(0.445984\pi\)
\(822\) 2.36816 4.10178i 0.0825992 0.143066i
\(823\) 9.53005 16.5065i 0.332197 0.575381i −0.650746 0.759296i \(-0.725544\pi\)
0.982942 + 0.183914i \(0.0588769\pi\)
\(824\) −0.383098 0.663546i −0.0133459 0.0231157i
\(825\) −2.62241 15.9273i −0.0913005 0.554516i
\(826\) −2.42399 44.7272i −0.0843414 1.55626i
\(827\) 37.0755i 1.28924i 0.764502 + 0.644621i \(0.222985\pi\)
−0.764502 + 0.644621i \(0.777015\pi\)
\(828\) −2.66854 4.62205i −0.0927382 0.160627i
\(829\) −5.02798 2.90291i −0.174629 0.100822i 0.410138 0.912024i \(-0.365481\pi\)
−0.584767 + 0.811201i \(0.698814\pi\)
\(830\) 1.88472 3.26444i 0.0654197 0.113310i
\(831\) −8.52924 14.7731i −0.295876 0.512472i
\(832\) −40.2174 −1.39429
\(833\) −16.5908 + 37.6238i −0.574836 + 1.30359i
\(834\) 32.0316 1.10916
\(835\) −0.215542 + 0.124443i −0.00745912 + 0.00430653i
\(836\) −5.01330 + 13.3023i −0.173389 + 0.460068i
\(837\) 2.88645 4.99947i 0.0997702 0.172807i
\(838\) −18.6035 32.2221i −0.642646 1.11310i
\(839\) 11.3409i 0.391530i −0.980651 0.195765i \(-0.937281\pi\)
0.980651 0.195765i \(-0.0627190\pi\)
\(840\) 0.139774 0.00757508i 0.00482268 0.000261365i
\(841\) 24.9300 0.859655
\(842\) 64.8416 37.4363i 2.23459 1.29014i
\(843\) −13.2881 + 23.0156i −0.457665 + 0.792700i
\(844\) 13.6361 + 7.87283i 0.469375 + 0.270994i
\(845\) 5.21406 3.01034i 0.179369 0.103559i
\(846\) 12.4743 0.428877
\(847\) −17.9970 + 22.8715i −0.618385 + 0.785875i
\(848\) 53.5849 1.84011
\(849\) −8.29148 + 4.78709i −0.284563 + 0.164292i
\(850\) 49.0629 + 28.3265i 1.68284 + 0.971590i
\(851\) 11.0949 19.2170i 0.380330 0.658751i
\(852\) 4.41461 2.54878i 0.151242 0.0873196i
\(853\) −13.7963 −0.472377 −0.236189 0.971707i \(-0.575898\pi\)
−0.236189 + 0.971707i \(0.575898\pi\)
\(854\) −6.42080 + 12.6572i −0.219715 + 0.433122i
\(855\) 0.811523i 0.0277535i
\(856\) −0.283619 0.491242i −0.00969388 0.0167903i
\(857\) 15.2865 26.4770i 0.522177 0.904438i −0.477490 0.878637i \(-0.658453\pi\)
0.999667 0.0258003i \(-0.00821339\pi\)
\(858\) 12.5896 33.4051i 0.429801 1.14043i
\(859\) −35.1496 + 20.2936i −1.19929 + 0.692410i −0.960397 0.278637i \(-0.910117\pi\)
−0.238892 + 0.971046i \(0.576784\pi\)
\(860\) 4.15225 0.141590
\(861\) −10.6352 + 20.9651i −0.362448 + 0.714490i
\(862\) −24.2322 −0.825351
\(863\) −14.6033 25.2937i −0.497103 0.861008i 0.502891 0.864350i \(-0.332270\pi\)
−0.999994 + 0.00334172i \(0.998936\pi\)
\(864\) −3.95793 + 6.85534i −0.134652 + 0.233223i
\(865\) 0.473519 + 0.273386i 0.0161001 + 0.00929541i
\(866\) 14.9214 + 25.8446i 0.507049 + 0.878234i
\(867\) 17.5062i 0.594543i
\(868\) 16.0724 + 24.6530i 0.545533 + 0.836778i
\(869\) 0.990374 + 6.01507i 0.0335961 + 0.204047i
\(870\) −0.729221 1.26305i −0.0247229 0.0428213i
\(871\) −39.6914 + 68.7475i −1.34489 + 2.32942i
\(872\) 0.461035 0.798535i 0.0156126 0.0270418i
\(873\) 8.74237 5.04741i 0.295884 0.170829i
\(874\) 12.2099i 0.413007i
\(875\) 9.50966 0.515376i 0.321485 0.0174229i
\(876\) 11.2211i 0.379125i
\(877\) 11.6589 6.73125i 0.393692 0.227298i −0.290067 0.957006i \(-0.593677\pi\)
0.683759 + 0.729708i \(0.260344\pi\)
\(878\) −26.3185 15.1950i −0.888205 0.512806i
\(879\) 14.6241 + 8.44323i 0.493259 + 0.284783i
\(880\) −3.87451 + 3.17688i −0.130610 + 0.107093i
\(881\) 47.1355i 1.58803i −0.607896 0.794017i \(-0.707986\pi\)
0.607896 0.794017i \(-0.292014\pi\)
\(882\) −12.6921 5.59678i −0.427366 0.188453i
\(883\) 6.67601 0.224666 0.112333 0.993671i \(-0.464168\pi\)
0.112333 + 0.993671i \(0.464168\pi\)
\(884\) 30.7394 + 53.2421i 1.03388 + 1.79073i
\(885\) 2.69924 + 1.55841i 0.0907339 + 0.0523853i
\(886\) −27.0076 15.5929i −0.907339 0.523852i
\(887\) −3.21635 5.57089i −0.107995 0.187052i 0.806963 0.590602i \(-0.201110\pi\)
−0.914958 + 0.403550i \(0.867776\pi\)
\(888\) −1.16181 −0.0389878
\(889\) 37.8917 2.05354i 1.27085 0.0688736i
\(890\) 0.307021i 0.0102914i
\(891\) −2.10292 2.56471i −0.0704504 0.0859210i
\(892\) 40.4638 + 23.3618i 1.35483 + 0.782211i
\(893\) 12.1271 + 7.00158i 0.405818 + 0.234299i
\(894\) −31.6633 + 18.2808i −1.05898 + 0.611401i
\(895\) 2.26638i 0.0757567i
\(896\) 1.67529 + 2.56968i 0.0559676 + 0.0858471i
\(897\) 15.0453i 0.502347i
\(898\) −24.0783 + 13.9016i −0.803502 + 0.463902i
\(899\) −5.82319 + 10.0861i −0.194214 + 0.336389i
\(900\) −4.68882 + 8.12127i −0.156294 + 0.270709i
\(901\) −38.0062 65.8286i −1.26617 2.19307i
\(902\) −9.48727 57.6212i −0.315891 1.91858i
\(903\) 13.9378 + 7.07042i 0.463822 + 0.235289i
\(904\) 0.609202i 0.0202618i
\(905\) 1.80192 + 3.12101i 0.0598977 + 0.103746i
\(906\) 16.5794 + 9.57213i 0.550814 + 0.318013i
\(907\) 20.6838 35.8254i 0.686795 1.18956i −0.286074 0.958208i \(-0.592350\pi\)
0.972869 0.231356i \(-0.0743163\pi\)
\(908\) 3.23735 + 5.60726i 0.107435 + 0.186083i
\(909\) 15.2461 0.505681
\(910\) 9.26513 + 4.70004i 0.307136 + 0.155805i
\(911\) −42.9021 −1.42141 −0.710705 0.703490i \(-0.751624\pi\)
−0.710705 + 0.703490i \(0.751624\pi\)
\(912\) −7.97749 + 4.60581i −0.264161 + 0.152514i
\(913\) −6.09874 + 16.1824i −0.201839 + 0.535559i
\(914\) −32.4238 + 56.1597i −1.07248 + 1.85760i
\(915\) −0.493784 0.855259i −0.0163240 0.0282740i
\(916\) 42.1572i 1.39291i
\(917\) 11.3155 7.37708i 0.373671 0.243613i
\(918\) 11.6404 0.384191
\(919\) −21.0723 + 12.1661i −0.695113 + 0.401323i −0.805524 0.592562i \(-0.798116\pi\)
0.110412 + 0.993886i \(0.464783\pi\)
\(920\) 0.0732739 0.126914i 0.00241577 0.00418424i
\(921\) 1.35989 + 0.785133i 0.0448099 + 0.0258710i
\(922\) 29.7648 17.1847i 0.980250 0.565948i
\(923\) −14.3700 −0.472995
\(924\) 16.5100 3.64565i 0.543140 0.119933i
\(925\) −38.9892 −1.28196
\(926\) −48.6879 + 28.1100i −1.59998 + 0.923751i
\(927\) −4.57538 2.64160i −0.150275 0.0867614i
\(928\) 7.98483 13.8301i 0.262115 0.453996i
\(929\) 32.9012 18.9955i 1.07945 0.623224i 0.148706 0.988882i \(-0.452489\pi\)
0.930749 + 0.365658i \(0.119156\pi\)
\(930\) −4.17335 −0.136850
\(931\) −9.19747 12.5648i −0.301435 0.411795i
\(932\) 15.3118i 0.501553i
\(933\) 12.0360 + 20.8470i 0.394041 + 0.682499i
\(934\) −35.3248 + 61.1843i −1.15586 + 2.00201i
\(935\) 6.65085 + 2.50654i 0.217506 + 0.0819727i
\(936\) 0.682198 0.393867i 0.0222984 0.0128740i
\(937\) −31.8024 −1.03894 −0.519469 0.854489i \(-0.673870\pi\)
−0.519469 + 0.854489i \(0.673870\pi\)
\(938\) −76.5107 + 4.14650i −2.49816 + 0.135388i
\(939\) 0.477550 0.0155843
\(940\) −2.21248 3.83212i −0.0721631 0.124990i
\(941\) 2.53829 4.39645i 0.0827460 0.143320i −0.821683 0.569945i \(-0.806964\pi\)
0.904428 + 0.426625i \(0.140298\pi\)
\(942\) −22.7721 13.1475i −0.741955 0.428368i
\(943\) 12.3057 + 21.3142i 0.400730 + 0.694085i
\(944\) 35.3790i 1.15149i
\(945\) 0.808553 0.527131i 0.0263022 0.0171476i
\(946\) −38.3072 + 6.30723i −1.24547 + 0.205066i
\(947\) 20.5441 + 35.5835i 0.667595 + 1.15631i 0.978575 + 0.205892i \(0.0660095\pi\)
−0.310980 + 0.950417i \(0.600657\pi\)
\(948\) 1.77077 3.06707i 0.0575120 0.0996137i
\(949\) 15.8161 27.3943i 0.513413 0.889258i
\(950\) −18.5795 + 10.7269i −0.602797 + 0.348025i
\(951\) 9.41420i 0.305276i
\(952\) 1.01969 2.01009i 0.0330482 0.0651475i
\(953\) 1.56947i 0.0508402i 0.999677 + 0.0254201i \(0.00809234\pi\)
−0.999677 + 0.0254201i \(0.991908\pi\)
\(954\) 22.2068 12.8211i 0.718972 0.415099i
\(955\) −0.277865 0.160426i −0.00899151 0.00519125i
\(956\) −30.6467 17.6939i −0.991185 0.572261i
\(957\) 4.24248 + 5.17411i 0.137140 + 0.167255i
\(958\) 52.0535i 1.68177i
\(959\) −5.63955 2.86085i −0.182111 0.0923816i
\(960\) 2.70116 0.0871794
\(961\) 1.16314 + 2.01461i 0.0375205 + 0.0649874i
\(962\) −74.6755 43.1139i −2.40764 1.39005i
\(963\) −3.38728 1.95565i −0.109154 0.0630199i
\(964\) 8.84289 + 15.3163i 0.284810 + 0.493306i
\(965\) −8.14982 −0.262352
\(966\) −12.1652 + 7.93106i −0.391410 + 0.255178i
\(967\) 45.6739i 1.46877i 0.678732 + 0.734386i \(0.262530\pi\)
−0.678732 + 0.734386i \(0.737470\pi\)
\(968\) 1.05290 1.19847i 0.0338413 0.0385202i
\(969\) 11.3164 + 6.53353i 0.363535 + 0.209887i
\(970\) −6.32006 3.64889i −0.202925 0.117159i
\(971\) −4.86828 + 2.81070i −0.156231 + 0.0901998i −0.576077 0.817395i \(-0.695417\pi\)
0.419847 + 0.907595i \(0.362084\pi\)
\(972\) 1.92681i 0.0618026i
\(973\) −2.31436 42.7042i −0.0741949 1.36903i
\(974\) 52.3618i 1.67778i
\(975\) 22.8939 13.2178i 0.733192 0.423309i
\(976\) 5.60495 9.70806i 0.179410 0.310748i
\(977\) −1.98615 + 3.44011i −0.0635426 + 0.110059i −0.896047 0.443960i \(-0.853573\pi\)
0.832504 + 0.554019i \(0.186907\pi\)
\(978\) 7.86011 + 13.6141i 0.251339 + 0.435331i
\(979\) −0.228835 1.38984i −0.00731361 0.0444194i
\(980\) 0.531772 + 4.89168i 0.0169868 + 0.156259i
\(981\) 6.35799i 0.202995i
\(982\) −16.7477 29.0079i −0.534440 0.925678i
\(983\) −31.0712 17.9390i −0.991019 0.572165i −0.0854402 0.996343i \(-0.527230\pi\)
−0.905579 + 0.424178i \(0.860563\pi\)
\(984\) 0.644300 1.11596i 0.0205395 0.0355755i
\(985\) 0.352595 + 0.610713i 0.0112346 + 0.0194589i
\(986\) −23.4837 −0.747873
\(987\) −0.901299 16.6307i −0.0286887 0.529360i
\(988\) −23.2812 −0.740673
\(989\) 14.1699 8.18098i 0.450576 0.260140i
\(990\) −0.845564 + 2.24362i −0.0268738 + 0.0713068i
\(991\) 8.82827 15.2910i 0.280439 0.485735i −0.691054 0.722803i \(-0.742853\pi\)
0.971493 + 0.237068i \(0.0761865\pi\)
\(992\) −22.8487 39.5751i −0.725447 1.25651i
\(993\) 18.7986i 0.596557i
\(994\) −7.57511 11.6193i −0.240268 0.368541i
\(995\) −0.739680 −0.0234494
\(996\) 8.70074 5.02338i 0.275694 0.159172i
\(997\) 19.6519 34.0381i 0.622382 1.07800i −0.366659 0.930356i \(-0.619498\pi\)
0.989041 0.147642i \(-0.0471684\pi\)
\(998\) 43.9640 + 25.3826i 1.39166 + 0.803473i
\(999\) −6.93780 + 4.00554i −0.219502 + 0.126730i
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 231.2.p.a.10.14 yes 32
3.2 odd 2 693.2.bg.b.10.3 32
7.3 odd 6 1617.2.c.a.538.28 32
7.4 even 3 1617.2.c.a.538.27 32
7.5 odd 6 inner 231.2.p.a.208.3 yes 32
11.10 odd 2 inner 231.2.p.a.10.3 32
21.5 even 6 693.2.bg.b.208.14 32
33.32 even 2 693.2.bg.b.10.14 32
77.10 even 6 1617.2.c.a.538.6 32
77.32 odd 6 1617.2.c.a.538.5 32
77.54 even 6 inner 231.2.p.a.208.14 yes 32
231.131 odd 6 693.2.bg.b.208.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.p.a.10.3 32 11.10 odd 2 inner
231.2.p.a.10.14 yes 32 1.1 even 1 trivial
231.2.p.a.208.3 yes 32 7.5 odd 6 inner
231.2.p.a.208.14 yes 32 77.54 even 6 inner
693.2.bg.b.10.3 32 3.2 odd 2
693.2.bg.b.10.14 32 33.32 even 2
693.2.bg.b.208.3 32 231.131 odd 6
693.2.bg.b.208.14 32 21.5 even 6
1617.2.c.a.538.5 32 77.32 odd 6
1617.2.c.a.538.6 32 77.10 even 6
1617.2.c.a.538.27 32 7.4 even 3
1617.2.c.a.538.28 32 7.3 odd 6