Properties

Label 483.2.i.g.415.8
Level $483$
Weight $2$
Character 483.415
Analytic conductor $3.857$
Analytic rank $0$
Dimension $16$
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] = [483,2,Mod(277,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (of order \(3\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} - 158 x^{7} + 8993 x^{6} + 265 x^{5} + 15176 x^{4} + 383 x^{3} + 12649 x^{2} + \cdots + 6400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.8
Root \(-1.27611 - 2.21029i\) of defining polynomial
Character \(\chi\) \(=\) 483.415
Dual form 483.2.i.g.277.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.27611 - 2.21029i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.25692 - 3.90910i) q^{4} +(-0.324080 + 0.561322i) q^{5} -2.55222 q^{6} +(-2.38478 - 1.14579i) q^{7} -6.41586 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.27611 - 2.21029i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.25692 - 3.90910i) q^{4} +(-0.324080 + 0.561322i) q^{5} -2.55222 q^{6} +(-2.38478 - 1.14579i) q^{7} -6.41586 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.827123 + 1.43262i) q^{10} +(1.49007 + 2.58088i) q^{11} +(-2.25692 + 3.90910i) q^{12} -3.87158 q^{13} +(-5.57576 + 3.80890i) q^{14} +0.648159 q^{15} +(-3.67352 + 6.36272i) q^{16} +(-3.36610 - 5.83026i) q^{17} +(1.27611 + 2.21029i) q^{18} +(3.48863 - 6.04248i) q^{19} +2.92568 q^{20} +(0.200110 + 2.63817i) q^{21} +7.60600 q^{22} +(0.500000 - 0.866025i) q^{23} +(3.20793 + 5.55630i) q^{24} +(2.28994 + 3.96630i) q^{25} +(-4.94057 + 8.55732i) q^{26} +1.00000 q^{27} +(0.903263 + 11.9083i) q^{28} +4.40182 q^{29} +(0.827123 - 1.43262i) q^{30} +(-1.10823 - 1.91951i) q^{31} +(2.95976 + 5.12646i) q^{32} +(1.49007 - 2.58088i) q^{33} -17.1821 q^{34} +(1.41601 - 0.967304i) q^{35} +4.51383 q^{36} +(2.20547 - 3.81998i) q^{37} +(-8.90375 - 15.4217i) q^{38} +(1.93579 + 3.35289i) q^{39} +(2.07925 - 3.60137i) q^{40} -0.194472 q^{41} +(6.08649 + 2.92430i) q^{42} -1.37588 q^{43} +(6.72595 - 11.6497i) q^{44} +(-0.324080 - 0.561322i) q^{45} +(-1.27611 - 2.21029i) q^{46} +(1.24416 - 2.15495i) q^{47} +7.34703 q^{48} +(4.37435 + 5.46489i) q^{49} +11.6889 q^{50} +(-3.36610 + 5.83026i) q^{51} +(8.73784 + 15.1344i) q^{52} +(-4.73464 - 8.20065i) q^{53} +(1.27611 - 2.21029i) q^{54} -1.93161 q^{55} +(15.3004 + 7.35120i) q^{56} -6.97725 q^{57} +(5.61721 - 9.72929i) q^{58} +(-3.40017 - 5.88927i) q^{59} +(-1.46284 - 2.53372i) q^{60} +(-4.36166 + 7.55461i) q^{61} -5.65689 q^{62} +(2.18467 - 1.49239i) q^{63} +0.413880 q^{64} +(1.25470 - 2.17321i) q^{65} +(-3.80300 - 6.58699i) q^{66} +(0.446927 + 0.774100i) q^{67} +(-15.1940 + 26.3168i) q^{68} -1.00000 q^{69} +(-0.331031 - 4.36419i) q^{70} +15.2489 q^{71} +(3.20793 - 5.55630i) q^{72} +(-0.471714 - 0.817032i) q^{73} +(-5.62884 - 9.74943i) q^{74} +(2.28994 - 3.96630i) q^{75} -31.4942 q^{76} +(-0.596357 - 7.86215i) q^{77} +9.88114 q^{78} +(-7.07474 + 12.2538i) q^{79} +(-2.38102 - 4.12405i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.248168 + 0.429839i) q^{82} +14.6280 q^{83} +(9.86124 - 6.73639i) q^{84} +4.36354 q^{85} +(-1.75577 + 3.04108i) q^{86} +(-2.20091 - 3.81209i) q^{87} +(-9.56011 - 16.5586i) q^{88} +(7.87304 - 13.6365i) q^{89} -1.65425 q^{90} +(9.23287 + 4.43601i) q^{91} -4.51383 q^{92} +(-1.10823 + 1.91951i) q^{93} +(-3.17537 - 5.49991i) q^{94} +(2.26119 + 3.91649i) q^{95} +(2.95976 - 5.12646i) q^{96} +3.23421 q^{97} +(17.6611 - 2.69476i) q^{98} -2.98015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27611 2.21029i 0.902347 1.56291i 0.0779065 0.996961i \(-0.475176\pi\)
0.824440 0.565949i \(-0.191490\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −2.25692 3.90910i −1.12846 1.95455i
\(5\) −0.324080 + 0.561322i −0.144933 + 0.251031i −0.929348 0.369205i \(-0.879630\pi\)
0.784415 + 0.620236i \(0.212963\pi\)
\(6\) −2.55222 −1.04194
\(7\) −2.38478 1.14579i −0.901362 0.433066i
\(8\) −6.41586 −2.26835
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.827123 + 1.43262i 0.261559 + 0.453034i
\(11\) 1.49007 + 2.58088i 0.449274 + 0.778166i 0.998339 0.0576140i \(-0.0183493\pi\)
−0.549065 + 0.835780i \(0.685016\pi\)
\(12\) −2.25692 + 3.90910i −0.651516 + 1.12846i
\(13\) −3.87158 −1.07378 −0.536892 0.843651i \(-0.680402\pi\)
−0.536892 + 0.843651i \(0.680402\pi\)
\(14\) −5.57576 + 3.80890i −1.49018 + 1.01797i
\(15\) 0.648159 0.167354
\(16\) −3.67352 + 6.36272i −0.918379 + 1.59068i
\(17\) −3.36610 5.83026i −0.816400 1.41405i −0.908318 0.418280i \(-0.862633\pi\)
0.0919178 0.995767i \(-0.470700\pi\)
\(18\) 1.27611 + 2.21029i 0.300782 + 0.520970i
\(19\) 3.48863 6.04248i 0.800346 1.38624i −0.119043 0.992889i \(-0.537982\pi\)
0.919389 0.393351i \(-0.128684\pi\)
\(20\) 2.92568 0.654203
\(21\) 0.200110 + 2.63817i 0.0436676 + 0.575697i
\(22\) 7.60600 1.62160
\(23\) 0.500000 0.866025i 0.104257 0.180579i
\(24\) 3.20793 + 5.55630i 0.654816 + 1.13417i
\(25\) 2.28994 + 3.96630i 0.457989 + 0.793260i
\(26\) −4.94057 + 8.55732i −0.968925 + 1.67823i
\(27\) 1.00000 0.192450
\(28\) 0.903263 + 11.9083i 0.170701 + 2.25045i
\(29\) 4.40182 0.817397 0.408699 0.912669i \(-0.365983\pi\)
0.408699 + 0.912669i \(0.365983\pi\)
\(30\) 0.827123 1.43262i 0.151011 0.261559i
\(31\) −1.10823 1.91951i −0.199044 0.344754i 0.749175 0.662372i \(-0.230450\pi\)
−0.948219 + 0.317618i \(0.897117\pi\)
\(32\) 2.95976 + 5.12646i 0.523217 + 0.906239i
\(33\) 1.49007 2.58088i 0.259389 0.449274i
\(34\) −17.1821 −2.94670
\(35\) 1.41601 0.967304i 0.239350 0.163504i
\(36\) 4.51383 0.752306
\(37\) 2.20547 3.81998i 0.362576 0.628001i −0.625808 0.779977i \(-0.715231\pi\)
0.988384 + 0.151977i \(0.0485639\pi\)
\(38\) −8.90375 15.4217i −1.44438 2.50174i
\(39\) 1.93579 + 3.35289i 0.309975 + 0.536892i
\(40\) 2.07925 3.60137i 0.328758 0.569426i
\(41\) −0.194472 −0.0303714 −0.0151857 0.999885i \(-0.504834\pi\)
−0.0151857 + 0.999885i \(0.504834\pi\)
\(42\) 6.08649 + 2.92430i 0.939165 + 0.451229i
\(43\) −1.37588 −0.209819 −0.104910 0.994482i \(-0.533455\pi\)
−0.104910 + 0.994482i \(0.533455\pi\)
\(44\) 6.72595 11.6497i 1.01397 1.75626i
\(45\) −0.324080 0.561322i −0.0483109 0.0836770i
\(46\) −1.27611 2.21029i −0.188152 0.325889i
\(47\) 1.24416 2.15495i 0.181479 0.314332i −0.760905 0.648863i \(-0.775245\pi\)
0.942385 + 0.334532i \(0.108578\pi\)
\(48\) 7.34703 1.06045
\(49\) 4.37435 + 5.46489i 0.624907 + 0.780699i
\(50\) 11.6889 1.65306
\(51\) −3.36610 + 5.83026i −0.471349 + 0.816400i
\(52\) 8.73784 + 15.1344i 1.21172 + 2.09876i
\(53\) −4.73464 8.20065i −0.650353 1.12645i −0.983037 0.183407i \(-0.941287\pi\)
0.332684 0.943039i \(-0.392046\pi\)
\(54\) 1.27611 2.21029i 0.173657 0.300782i
\(55\) −1.93161 −0.260458
\(56\) 15.3004 + 7.35120i 2.04460 + 0.982346i
\(57\) −6.97725 −0.924160
\(58\) 5.61721 9.72929i 0.737575 1.27752i
\(59\) −3.40017 5.88927i −0.442664 0.766717i 0.555222 0.831702i \(-0.312633\pi\)
−0.997886 + 0.0649851i \(0.979300\pi\)
\(60\) −1.46284 2.53372i −0.188852 0.327101i
\(61\) −4.36166 + 7.55461i −0.558453 + 0.967269i 0.439173 + 0.898403i \(0.355272\pi\)
−0.997626 + 0.0688665i \(0.978062\pi\)
\(62\) −5.65689 −0.718426
\(63\) 2.18467 1.49239i 0.275243 0.188023i
\(64\) 0.413880 0.0517349
\(65\) 1.25470 2.17321i 0.155627 0.269553i
\(66\) −3.80300 6.58699i −0.468117 0.810802i
\(67\) 0.446927 + 0.774100i 0.0546008 + 0.0945714i 0.892034 0.451968i \(-0.149278\pi\)
−0.837433 + 0.546540i \(0.815945\pi\)
\(68\) −15.1940 + 26.3168i −1.84255 + 3.19139i
\(69\) −1.00000 −0.120386
\(70\) −0.331031 4.36419i −0.0395658 0.521620i
\(71\) 15.2489 1.80971 0.904856 0.425718i \(-0.139979\pi\)
0.904856 + 0.425718i \(0.139979\pi\)
\(72\) 3.20793 5.55630i 0.378058 0.654816i
\(73\) −0.471714 0.817032i −0.0552099 0.0956264i 0.837100 0.547051i \(-0.184249\pi\)
−0.892309 + 0.451424i \(0.850916\pi\)
\(74\) −5.62884 9.74943i −0.654339 1.13335i
\(75\) 2.28994 3.96630i 0.264420 0.457989i
\(76\) −31.4942 −3.61263
\(77\) −0.596357 7.86215i −0.0679612 0.895975i
\(78\) 9.88114 1.11882
\(79\) −7.07474 + 12.2538i −0.795971 + 1.37866i 0.126250 + 0.991998i \(0.459706\pi\)
−0.922221 + 0.386663i \(0.873628\pi\)
\(80\) −2.38102 4.12405i −0.266206 0.461083i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.248168 + 0.429839i −0.0274055 + 0.0474678i
\(83\) 14.6280 1.60563 0.802815 0.596228i \(-0.203335\pi\)
0.802815 + 0.596228i \(0.203335\pi\)
\(84\) 9.86124 6.73639i 1.07595 0.735000i
\(85\) 4.36354 0.473293
\(86\) −1.75577 + 3.04108i −0.189330 + 0.327928i
\(87\) −2.20091 3.81209i −0.235962 0.408699i
\(88\) −9.56011 16.5586i −1.01911 1.76515i
\(89\) 7.87304 13.6365i 0.834541 1.44547i −0.0598628 0.998207i \(-0.519066\pi\)
0.894404 0.447261i \(-0.147600\pi\)
\(90\) −1.65425 −0.174373
\(91\) 9.23287 + 4.43601i 0.967868 + 0.465020i
\(92\) −4.51383 −0.470600
\(93\) −1.10823 + 1.91951i −0.114918 + 0.199044i
\(94\) −3.17537 5.49991i −0.327515 0.567272i
\(95\) 2.26119 + 3.91649i 0.231993 + 0.401823i
\(96\) 2.95976 5.12646i 0.302080 0.523217i
\(97\) 3.23421 0.328384 0.164192 0.986428i \(-0.447498\pi\)
0.164192 + 0.986428i \(0.447498\pi\)
\(98\) 17.6611 2.69476i 1.78405 0.272212i
\(99\) −2.98015 −0.299516
\(100\) 10.3364 17.9032i 1.03364 1.79032i
\(101\) −1.50331 2.60382i −0.149585 0.259089i 0.781489 0.623919i \(-0.214461\pi\)
−0.931074 + 0.364830i \(0.881127\pi\)
\(102\) 8.59104 + 14.8801i 0.850640 + 1.47335i
\(103\) −6.97973 + 12.0892i −0.687733 + 1.19119i 0.284837 + 0.958576i \(0.408061\pi\)
−0.972570 + 0.232612i \(0.925273\pi\)
\(104\) 24.8395 2.43572
\(105\) −1.54572 0.742652i −0.150847 0.0724754i
\(106\) −24.1677 −2.34738
\(107\) 0.614369 1.06412i 0.0593933 0.102872i −0.834800 0.550553i \(-0.814417\pi\)
0.894193 + 0.447681i \(0.147750\pi\)
\(108\) −2.25692 3.90910i −0.217172 0.376153i
\(109\) −8.08553 14.0046i −0.774454 1.34139i −0.935101 0.354381i \(-0.884691\pi\)
0.160647 0.987012i \(-0.448642\pi\)
\(110\) −2.46495 + 4.26942i −0.235024 + 0.407073i
\(111\) −4.41093 −0.418667
\(112\) 16.0508 10.9646i 1.51666 1.03606i
\(113\) −4.70467 −0.442578 −0.221289 0.975208i \(-0.571026\pi\)
−0.221289 + 0.975208i \(0.571026\pi\)
\(114\) −8.90375 + 15.4217i −0.833912 + 1.44438i
\(115\) 0.324080 + 0.561322i 0.0302206 + 0.0523436i
\(116\) −9.93454 17.2071i −0.922399 1.59764i
\(117\) 1.93579 3.35289i 0.178964 0.309975i
\(118\) −17.3560 −1.59775
\(119\) 1.34718 + 17.7607i 0.123496 + 1.62812i
\(120\) −4.15850 −0.379617
\(121\) 1.05936 1.83486i 0.0963053 0.166806i
\(122\) 11.1319 + 19.2810i 1.00784 + 1.74562i
\(123\) 0.0972360 + 0.168418i 0.00876747 + 0.0151857i
\(124\) −5.00236 + 8.66435i −0.449226 + 0.778081i
\(125\) −6.20929 −0.555376
\(126\) −0.510725 6.73320i −0.0454990 0.599841i
\(127\) 15.9640 1.41657 0.708287 0.705924i \(-0.249468\pi\)
0.708287 + 0.705924i \(0.249468\pi\)
\(128\) −5.39137 + 9.33813i −0.476534 + 0.825382i
\(129\) 0.687938 + 1.19154i 0.0605696 + 0.104910i
\(130\) −3.20228 5.54650i −0.280858 0.486461i
\(131\) −7.79630 + 13.5036i −0.681166 + 1.17981i 0.293459 + 0.955972i \(0.405194\pi\)
−0.974625 + 0.223843i \(0.928140\pi\)
\(132\) −13.4519 −1.17084
\(133\) −15.2430 + 10.4128i −1.32174 + 0.902901i
\(134\) 2.28131 0.197075
\(135\) −0.324080 + 0.561322i −0.0278923 + 0.0483109i
\(136\) 21.5965 + 37.4062i 1.85188 + 3.20755i
\(137\) −5.36277 9.28859i −0.458173 0.793578i 0.540692 0.841221i \(-0.318162\pi\)
−0.998864 + 0.0476426i \(0.984829\pi\)
\(138\) −1.27611 + 2.21029i −0.108630 + 0.188152i
\(139\) 21.4287 1.81756 0.908781 0.417273i \(-0.137014\pi\)
0.908781 + 0.417273i \(0.137014\pi\)
\(140\) −6.97711 3.35221i −0.589673 0.283313i
\(141\) −2.48832 −0.209554
\(142\) 19.4593 33.7045i 1.63299 2.82842i
\(143\) −5.76895 9.99211i −0.482424 0.835582i
\(144\) −3.67352 6.36272i −0.306126 0.530226i
\(145\) −1.42654 + 2.47084i −0.118468 + 0.205192i
\(146\) −2.40784 −0.199274
\(147\) 2.54556 6.52074i 0.209955 0.537822i
\(148\) −19.9102 −1.63661
\(149\) 5.17626 8.96554i 0.424055 0.734486i −0.572276 0.820061i \(-0.693939\pi\)
0.996332 + 0.0855753i \(0.0272728\pi\)
\(150\) −5.84445 10.1229i −0.477197 0.826530i
\(151\) 4.40288 + 7.62602i 0.358302 + 0.620597i 0.987677 0.156505i \(-0.0500226\pi\)
−0.629376 + 0.777101i \(0.716689\pi\)
\(152\) −22.3825 + 38.7677i −1.81546 + 3.14448i
\(153\) 6.73221 0.544267
\(154\) −18.1386 8.71485i −1.46165 0.702262i
\(155\) 1.43662 0.115392
\(156\) 8.73784 15.1344i 0.699587 1.21172i
\(157\) 4.66548 + 8.08085i 0.372346 + 0.644922i 0.989926 0.141586i \(-0.0452201\pi\)
−0.617580 + 0.786508i \(0.711887\pi\)
\(158\) 18.0563 + 31.2744i 1.43648 + 2.48806i
\(159\) −4.73464 + 8.20065i −0.375482 + 0.650353i
\(160\) −3.83679 −0.303325
\(161\) −2.18467 + 1.49239i −0.172176 + 0.117617i
\(162\) −2.55222 −0.200521
\(163\) −0.231561 + 0.401075i −0.0181373 + 0.0314146i −0.874952 0.484210i \(-0.839107\pi\)
0.856814 + 0.515625i \(0.172440\pi\)
\(164\) 0.438907 + 0.760209i 0.0342729 + 0.0593624i
\(165\) 0.965805 + 1.67282i 0.0751878 + 0.130229i
\(166\) 18.6669 32.3321i 1.44884 2.50946i
\(167\) 2.40385 0.186015 0.0930076 0.995665i \(-0.470352\pi\)
0.0930076 + 0.995665i \(0.470352\pi\)
\(168\) −1.28388 16.9262i −0.0990533 1.30588i
\(169\) 1.98916 0.153012
\(170\) 5.56836 9.64469i 0.427074 0.739714i
\(171\) 3.48863 + 6.04248i 0.266782 + 0.462080i
\(172\) 3.10524 + 5.37843i 0.236772 + 0.410101i
\(173\) −2.57407 + 4.45842i −0.195703 + 0.338967i −0.947131 0.320848i \(-0.896032\pi\)
0.751428 + 0.659815i \(0.229366\pi\)
\(174\) −11.2344 −0.851679
\(175\) −0.916482 12.0825i −0.0692795 0.913354i
\(176\) −21.8952 −1.65042
\(177\) −3.40017 + 5.88927i −0.255572 + 0.442664i
\(178\) −20.0937 34.8034i −1.50609 2.60862i
\(179\) 3.88943 + 6.73668i 0.290709 + 0.503523i 0.973978 0.226644i \(-0.0727754\pi\)
−0.683268 + 0.730167i \(0.739442\pi\)
\(180\) −1.46284 + 2.53372i −0.109034 + 0.188852i
\(181\) −7.61327 −0.565890 −0.282945 0.959136i \(-0.591311\pi\)
−0.282945 + 0.959136i \(0.591311\pi\)
\(182\) 21.5870 14.7465i 1.60014 1.09308i
\(183\) 8.72332 0.644846
\(184\) −3.20793 + 5.55630i −0.236492 + 0.409616i
\(185\) 1.42949 + 2.47595i 0.105098 + 0.182036i
\(186\) 2.82845 + 4.89901i 0.207392 + 0.359213i
\(187\) 10.0315 17.3751i 0.733575 1.27059i
\(188\) −11.2319 −0.819168
\(189\) −2.38478 1.14579i −0.173467 0.0833437i
\(190\) 11.5421 0.837351
\(191\) 0.369439 0.639887i 0.0267317 0.0463006i −0.852350 0.522972i \(-0.824823\pi\)
0.879082 + 0.476671i \(0.158157\pi\)
\(192\) −0.206940 0.358430i −0.0149346 0.0258675i
\(193\) 7.98512 + 13.8306i 0.574781 + 0.995551i 0.996065 + 0.0886218i \(0.0282463\pi\)
−0.421284 + 0.906929i \(0.638420\pi\)
\(194\) 4.12720 7.14853i 0.296316 0.513234i
\(195\) −2.50940 −0.179702
\(196\) 11.4903 29.4336i 0.820732 2.10240i
\(197\) −9.50195 −0.676986 −0.338493 0.940969i \(-0.609917\pi\)
−0.338493 + 0.940969i \(0.609917\pi\)
\(198\) −3.80300 + 6.58699i −0.270267 + 0.468117i
\(199\) 8.32964 + 14.4274i 0.590473 + 1.02273i 0.994169 + 0.107836i \(0.0343921\pi\)
−0.403696 + 0.914893i \(0.632275\pi\)
\(200\) −14.6920 25.4472i −1.03888 1.79939i
\(201\) 0.446927 0.774100i 0.0315238 0.0546008i
\(202\) −7.67358 −0.539911
\(203\) −10.4974 5.04354i −0.736771 0.353987i
\(204\) 30.3881 2.12759
\(205\) 0.0630244 0.109161i 0.00440181 0.00762417i
\(206\) 17.8138 + 30.8544i 1.24115 + 2.14973i
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) 14.2223 24.6338i 0.986141 1.70805i
\(209\) 20.7933 1.43830
\(210\) −3.61398 + 2.46877i −0.249388 + 0.170362i
\(211\) 19.6449 1.35241 0.676207 0.736712i \(-0.263623\pi\)
0.676207 + 0.736712i \(0.263623\pi\)
\(212\) −21.3714 + 37.0164i −1.46779 + 2.54229i
\(213\) −7.62445 13.2059i −0.522419 0.904856i
\(214\) −1.56800 2.71586i −0.107187 0.185653i
\(215\) 0.445893 0.772310i 0.0304097 0.0526711i
\(216\) −6.41586 −0.436544
\(217\) 0.443535 + 5.84740i 0.0301092 + 0.396947i
\(218\) −41.2721 −2.79530
\(219\) −0.471714 + 0.817032i −0.0318755 + 0.0552099i
\(220\) 4.35948 + 7.55085i 0.293916 + 0.509078i
\(221\) 13.0322 + 22.5724i 0.876638 + 1.51838i
\(222\) −5.62884 + 9.74943i −0.377783 + 0.654339i
\(223\) −17.5246 −1.17353 −0.586766 0.809757i \(-0.699599\pi\)
−0.586766 + 0.809757i \(0.699599\pi\)
\(224\) −1.18456 15.6167i −0.0791465 1.04344i
\(225\) −4.57989 −0.305326
\(226\) −6.00368 + 10.3987i −0.399359 + 0.691710i
\(227\) 5.34607 + 9.25966i 0.354831 + 0.614585i 0.987089 0.160172i \(-0.0512050\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(228\) 15.7471 + 27.2747i 1.04288 + 1.80631i
\(229\) −4.65000 + 8.05404i −0.307281 + 0.532226i −0.977767 0.209697i \(-0.932752\pi\)
0.670486 + 0.741922i \(0.266086\pi\)
\(230\) 1.65425 0.109078
\(231\) −6.51064 + 4.44753i −0.428369 + 0.292626i
\(232\) −28.2415 −1.85414
\(233\) 11.8630 20.5474i 0.777172 1.34610i −0.156393 0.987695i \(-0.549987\pi\)
0.933565 0.358407i \(-0.116680\pi\)
\(234\) −4.94057 8.55732i −0.322975 0.559409i
\(235\) 0.806414 + 1.39675i 0.0526047 + 0.0911139i
\(236\) −15.3478 + 26.5832i −0.999057 + 1.73042i
\(237\) 14.1495 0.919108
\(238\) 40.9755 + 19.6870i 2.65605 + 1.27612i
\(239\) 26.6326 1.72272 0.861360 0.507994i \(-0.169613\pi\)
0.861360 + 0.507994i \(0.169613\pi\)
\(240\) −2.38102 + 4.12405i −0.153694 + 0.266206i
\(241\) −5.84295 10.1203i −0.376377 0.651905i 0.614155 0.789186i \(-0.289497\pi\)
−0.990532 + 0.137281i \(0.956164\pi\)
\(242\) −2.70372 4.68297i −0.173801 0.301033i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 39.3756 2.52076
\(245\) −4.48520 + 0.684358i −0.286549 + 0.0437221i
\(246\) 0.496336 0.0316452
\(247\) −13.5065 + 23.3940i −0.859399 + 1.48852i
\(248\) 7.11025 + 12.3153i 0.451501 + 0.782023i
\(249\) −7.31399 12.6682i −0.463506 0.802815i
\(250\) −7.92375 + 13.7243i −0.501142 + 0.868003i
\(251\) −12.0271 −0.759142 −0.379571 0.925163i \(-0.623928\pi\)
−0.379571 + 0.925163i \(0.623928\pi\)
\(252\) −10.7645 5.17189i −0.678100 0.325798i
\(253\) 2.98015 0.187360
\(254\) 20.3718 35.2850i 1.27824 2.21398i
\(255\) −2.18177 3.77894i −0.136628 0.236646i
\(256\) 14.1738 + 24.5498i 0.885866 + 1.53436i
\(257\) 5.09201 8.81961i 0.317631 0.550152i −0.662363 0.749183i \(-0.730446\pi\)
0.979993 + 0.199031i \(0.0637795\pi\)
\(258\) 3.51154 0.218619
\(259\) −9.63643 + 6.58281i −0.598778 + 0.409036i
\(260\) −11.3270 −0.702472
\(261\) −2.20091 + 3.81209i −0.136233 + 0.235962i
\(262\) 19.8979 + 34.4642i 1.22930 + 2.12920i
\(263\) −10.4282 18.0622i −0.643033 1.11377i −0.984752 0.173964i \(-0.944342\pi\)
0.341719 0.939802i \(-0.388991\pi\)
\(264\) −9.56011 + 16.5586i −0.588384 + 1.01911i
\(265\) 6.13761 0.377030
\(266\) 3.56346 + 46.9793i 0.218490 + 2.88048i
\(267\) −15.7461 −0.963645
\(268\) 2.01735 3.49416i 0.123230 0.213440i
\(269\) 10.2355 + 17.7284i 0.624071 + 1.08092i 0.988720 + 0.149777i \(0.0478557\pi\)
−0.364649 + 0.931145i \(0.618811\pi\)
\(270\) 0.827123 + 1.43262i 0.0503371 + 0.0871864i
\(271\) 9.42784 16.3295i 0.572700 0.991946i −0.423587 0.905855i \(-0.639229\pi\)
0.996287 0.0860907i \(-0.0274375\pi\)
\(272\) 49.4617 2.99906
\(273\) −0.774742 10.2139i −0.0468895 0.618174i
\(274\) −27.3740 −1.65372
\(275\) −6.82438 + 11.8202i −0.411525 + 0.712783i
\(276\) 2.25692 + 3.90910i 0.135850 + 0.235300i
\(277\) 2.48103 + 4.29727i 0.149070 + 0.258198i 0.930884 0.365314i \(-0.119039\pi\)
−0.781814 + 0.623512i \(0.785705\pi\)
\(278\) 27.3454 47.3637i 1.64007 2.84069i
\(279\) 2.21646 0.132696
\(280\) −9.08495 + 6.20609i −0.542929 + 0.370885i
\(281\) 9.56605 0.570663 0.285331 0.958429i \(-0.407896\pi\)
0.285331 + 0.958429i \(0.407896\pi\)
\(282\) −3.17537 + 5.49991i −0.189091 + 0.327515i
\(283\) −3.70917 6.42447i −0.220487 0.381895i 0.734469 0.678642i \(-0.237431\pi\)
−0.954956 + 0.296748i \(0.904098\pi\)
\(284\) −34.4155 59.6094i −2.04218 3.53717i
\(285\) 2.26119 3.91649i 0.133941 0.231993i
\(286\) −29.4473 −1.74125
\(287\) 0.463773 + 0.222823i 0.0273756 + 0.0131528i
\(288\) −5.91953 −0.348811
\(289\) −14.1613 + 24.5281i −0.833019 + 1.44283i
\(290\) 3.64084 + 6.30613i 0.213798 + 0.370309i
\(291\) −1.61710 2.80090i −0.0947963 0.164192i
\(292\) −2.12924 + 3.68795i −0.124604 + 0.215821i
\(293\) 9.37108 0.547464 0.273732 0.961806i \(-0.411742\pi\)
0.273732 + 0.961806i \(0.411742\pi\)
\(294\) −11.1643 13.9476i −0.651116 0.813442i
\(295\) 4.40770 0.256626
\(296\) −14.1500 + 24.5085i −0.822450 + 1.42452i
\(297\) 1.49007 + 2.58088i 0.0864629 + 0.149758i
\(298\) −13.2110 22.8820i −0.765290 1.32552i
\(299\) −1.93579 + 3.35289i −0.111950 + 0.193903i
\(300\) −20.6729 −1.19355
\(301\) 3.28116 + 1.57646i 0.189123 + 0.0908656i
\(302\) 22.4743 1.29325
\(303\) −1.50331 + 2.60382i −0.0863631 + 0.149585i
\(304\) 25.6310 + 44.3943i 1.47004 + 2.54619i
\(305\) −2.82705 4.89659i −0.161876 0.280378i
\(306\) 8.59104 14.8801i 0.491117 0.850640i
\(307\) −0.0388797 −0.00221898 −0.00110949 0.999999i \(-0.500353\pi\)
−0.00110949 + 0.999999i \(0.500353\pi\)
\(308\) −29.3879 + 20.0754i −1.67453 + 1.14390i
\(309\) 13.9595 0.794125
\(310\) 1.83328 3.17534i 0.104124 0.180347i
\(311\) −4.56923 7.91415i −0.259098 0.448770i 0.706903 0.707311i \(-0.250092\pi\)
−0.966000 + 0.258541i \(0.916758\pi\)
\(312\) −12.4198 21.5117i −0.703131 1.21786i
\(313\) 6.43808 11.1511i 0.363902 0.630296i −0.624698 0.780867i \(-0.714778\pi\)
0.988599 + 0.150571i \(0.0481111\pi\)
\(314\) 23.8147 1.34394
\(315\) 0.129703 + 1.70996i 0.00730794 + 0.0963451i
\(316\) 63.8684 3.59288
\(317\) −5.39355 + 9.34191i −0.302932 + 0.524694i −0.976799 0.214159i \(-0.931299\pi\)
0.673867 + 0.738853i \(0.264632\pi\)
\(318\) 12.0839 + 20.9299i 0.677629 + 1.17369i
\(319\) 6.55904 + 11.3606i 0.367235 + 0.636071i
\(320\) −0.134130 + 0.232320i −0.00749809 + 0.0129871i
\(321\) −1.22874 −0.0685814
\(322\) 0.510725 + 6.73320i 0.0284616 + 0.375227i
\(323\) −46.9723 −2.61361
\(324\) −2.25692 + 3.90910i −0.125384 + 0.217172i
\(325\) −8.86571 15.3559i −0.491781 0.851790i
\(326\) 0.590995 + 1.02363i 0.0327322 + 0.0566938i
\(327\) −8.08553 + 14.0046i −0.447131 + 0.774454i
\(328\) 1.24771 0.0688930
\(329\) −5.43616 + 3.71354i −0.299705 + 0.204734i
\(330\) 4.92990 0.271382
\(331\) −11.2883 + 19.5519i −0.620461 + 1.07467i 0.368939 + 0.929454i \(0.379721\pi\)
−0.989400 + 0.145216i \(0.953612\pi\)
\(332\) −33.0142 57.1822i −1.81189 3.13828i
\(333\) 2.20547 + 3.81998i 0.120859 + 0.209334i
\(334\) 3.06757 5.31319i 0.167850 0.290725i
\(335\) −0.579360 −0.0316538
\(336\) −17.5210 8.41813i −0.955852 0.459246i
\(337\) −6.39947 −0.348601 −0.174301 0.984693i \(-0.555766\pi\)
−0.174301 + 0.984693i \(0.555766\pi\)
\(338\) 2.53839 4.39662i 0.138070 0.239144i
\(339\) 2.35234 + 4.07437i 0.127761 + 0.221289i
\(340\) −9.84815 17.0575i −0.534091 0.925073i
\(341\) 3.30269 5.72042i 0.178851 0.309778i
\(342\) 17.8075 0.962919
\(343\) −4.17026 18.0446i −0.225173 0.974319i
\(344\) 8.82743 0.475943
\(345\) 0.324080 0.561322i 0.0174479 0.0302206i
\(346\) 6.56960 + 11.3789i 0.353184 + 0.611732i
\(347\) −16.6599 28.8558i −0.894351 1.54906i −0.834606 0.550848i \(-0.814305\pi\)
−0.0597451 0.998214i \(-0.519029\pi\)
\(348\) −9.93454 + 17.2071i −0.532547 + 0.922399i
\(349\) −28.5439 −1.52792 −0.763961 0.645262i \(-0.776748\pi\)
−0.763961 + 0.645262i \(0.776748\pi\)
\(350\) −27.8754 13.3930i −1.49000 0.715884i
\(351\) −3.87158 −0.206650
\(352\) −8.82053 + 15.2776i −0.470136 + 0.814299i
\(353\) 0.0765559 + 0.132599i 0.00407466 + 0.00705752i 0.868056 0.496467i \(-0.165370\pi\)
−0.863981 + 0.503525i \(0.832036\pi\)
\(354\) 8.67798 + 15.0307i 0.461230 + 0.798873i
\(355\) −4.94186 + 8.55955i −0.262287 + 0.454294i
\(356\) −71.0752 −3.76698
\(357\) 14.7077 10.0471i 0.778412 0.531747i
\(358\) 19.8534 1.04928
\(359\) −10.8426 + 18.7799i −0.572250 + 0.991166i 0.424084 + 0.905623i \(0.360596\pi\)
−0.996334 + 0.0855436i \(0.972737\pi\)
\(360\) 2.07925 + 3.60137i 0.109586 + 0.189809i
\(361\) −14.8410 25.7054i −0.781107 1.35292i
\(362\) −9.71537 + 16.8275i −0.510629 + 0.884435i
\(363\) −2.11872 −0.111204
\(364\) −3.49706 46.1039i −0.183296 2.41650i
\(365\) 0.611491 0.0320069
\(366\) 11.1319 19.2810i 0.581875 1.00784i
\(367\) −1.52104 2.63451i −0.0793974 0.137520i 0.823593 0.567182i \(-0.191966\pi\)
−0.902990 + 0.429661i \(0.858633\pi\)
\(368\) 3.67352 + 6.36272i 0.191495 + 0.331679i
\(369\) 0.0972360 0.168418i 0.00506190 0.00876747i
\(370\) 7.29676 0.379341
\(371\) 1.89490 + 24.9816i 0.0983783 + 1.29698i
\(372\) 10.0047 0.518721
\(373\) −13.8069 + 23.9142i −0.714892 + 1.23823i 0.248109 + 0.968732i \(0.420191\pi\)
−0.963001 + 0.269497i \(0.913142\pi\)
\(374\) −25.6026 44.3450i −1.32388 2.29302i
\(375\) 3.10465 + 5.37741i 0.160323 + 0.277688i
\(376\) −7.98236 + 13.8259i −0.411659 + 0.713014i
\(377\) −17.0420 −0.877708
\(378\) −5.57576 + 3.80890i −0.286786 + 0.195909i
\(379\) 24.0119 1.23341 0.616705 0.787194i \(-0.288467\pi\)
0.616705 + 0.787194i \(0.288467\pi\)
\(380\) 10.2066 17.6784i 0.523588 0.906882i
\(381\) −7.98199 13.8252i −0.408930 0.708287i
\(382\) −0.942890 1.63313i −0.0482424 0.0835583i
\(383\) 5.50591 9.53651i 0.281339 0.487293i −0.690376 0.723451i \(-0.742555\pi\)
0.971715 + 0.236158i \(0.0758882\pi\)
\(384\) 10.7827 0.550254
\(385\) 4.60647 + 2.21321i 0.234767 + 0.112796i
\(386\) 40.7596 2.07461
\(387\) 0.687938 1.19154i 0.0349699 0.0605696i
\(388\) −7.29933 12.6428i −0.370568 0.641842i
\(389\) −17.5477 30.3935i −0.889704 1.54101i −0.840226 0.542237i \(-0.817577\pi\)
−0.0494782 0.998775i \(-0.515756\pi\)
\(390\) −3.20228 + 5.54650i −0.162154 + 0.280858i
\(391\) −6.73221 −0.340462
\(392\) −28.0652 35.0620i −1.41751 1.77090i
\(393\) 15.5926 0.786543
\(394\) −12.1255 + 21.0020i −0.610876 + 1.05807i
\(395\) −4.58556 7.94242i −0.230725 0.399627i
\(396\) 6.72595 + 11.6497i 0.337992 + 0.585419i
\(397\) −7.61416 + 13.1881i −0.382144 + 0.661892i −0.991368 0.131106i \(-0.958147\pi\)
0.609225 + 0.792997i \(0.291481\pi\)
\(398\) 42.5182 2.13124
\(399\) 16.6392 + 7.99444i 0.833003 + 0.400223i
\(400\) −33.6486 −1.68243
\(401\) 9.49301 16.4424i 0.474058 0.821093i −0.525501 0.850793i \(-0.676122\pi\)
0.999559 + 0.0297003i \(0.00945529\pi\)
\(402\) −1.14066 1.97567i −0.0568908 0.0985377i
\(403\) 4.29060 + 7.43154i 0.213730 + 0.370191i
\(404\) −6.78571 + 11.7532i −0.337602 + 0.584743i
\(405\) 0.648159 0.0322073
\(406\) −24.5435 + 16.7661i −1.21807 + 0.832087i
\(407\) 13.1452 0.651585
\(408\) 21.5965 37.4062i 1.06918 1.85188i
\(409\) −3.72738 6.45601i −0.184307 0.319229i 0.759036 0.651049i \(-0.225671\pi\)
−0.943343 + 0.331820i \(0.892337\pi\)
\(410\) −0.160852 0.278604i −0.00794392 0.0137593i
\(411\) −5.36277 + 9.28859i −0.264526 + 0.458173i
\(412\) 63.0106 3.10431
\(413\) 1.36082 + 17.9405i 0.0669614 + 0.882793i
\(414\) 2.55222 0.125435
\(415\) −4.74063 + 8.21102i −0.232708 + 0.403063i
\(416\) −11.4590 19.8475i −0.561822 0.973105i
\(417\) −10.7144 18.5578i −0.524685 0.908781i
\(418\) 26.5345 45.9591i 1.29784 2.24793i
\(419\) 3.17379 0.155050 0.0775248 0.996990i \(-0.475298\pi\)
0.0775248 + 0.996990i \(0.475298\pi\)
\(420\) 0.585458 + 7.71846i 0.0285674 + 0.376622i
\(421\) 15.1064 0.736239 0.368120 0.929778i \(-0.380002\pi\)
0.368120 + 0.929778i \(0.380002\pi\)
\(422\) 25.0691 43.4210i 1.22035 2.11370i
\(423\) 1.24416 + 2.15495i 0.0604932 + 0.104777i
\(424\) 30.3768 + 52.6142i 1.47523 + 2.55517i
\(425\) 15.4164 26.7020i 0.747805 1.29524i
\(426\) −38.9186 −1.88561
\(427\) 19.0576 13.0186i 0.922260 0.630012i
\(428\) −5.54632 −0.268091
\(429\) −5.76895 + 9.99211i −0.278527 + 0.482424i
\(430\) −1.13802 1.97111i −0.0548801 0.0950552i
\(431\) −12.5136 21.6742i −0.602760 1.04401i −0.992401 0.123044i \(-0.960734\pi\)
0.389641 0.920967i \(-0.372599\pi\)
\(432\) −3.67352 + 6.36272i −0.176742 + 0.306126i
\(433\) −27.5871 −1.32575 −0.662876 0.748729i \(-0.730664\pi\)
−0.662876 + 0.748729i \(0.730664\pi\)
\(434\) 13.4904 + 6.48159i 0.647562 + 0.311126i
\(435\) 2.85308 0.136795
\(436\) −36.4968 + 63.2142i −1.74788 + 3.02741i
\(437\) −3.48863 6.04248i −0.166884 0.289051i
\(438\) 1.20392 + 2.08525i 0.0575254 + 0.0996370i
\(439\) 10.1933 17.6554i 0.486501 0.842645i −0.513378 0.858162i \(-0.671606\pi\)
0.999880 + 0.0155176i \(0.00493960\pi\)
\(440\) 12.3929 0.590810
\(441\) −6.91991 + 1.05585i −0.329520 + 0.0502785i
\(442\) 66.5219 3.16412
\(443\) −13.9371 + 24.1398i −0.662173 + 1.14692i 0.317871 + 0.948134i \(0.397032\pi\)
−0.980044 + 0.198783i \(0.936301\pi\)
\(444\) 9.95511 + 17.2427i 0.472448 + 0.818305i
\(445\) 5.10298 + 8.83863i 0.241905 + 0.418991i
\(446\) −22.3633 + 38.7343i −1.05893 + 1.83412i
\(447\) −10.3525 −0.489657
\(448\) −0.987012 0.474217i −0.0466319 0.0224047i
\(449\) −12.5841 −0.593882 −0.296941 0.954896i \(-0.595966\pi\)
−0.296941 + 0.954896i \(0.595966\pi\)
\(450\) −5.84445 + 10.1229i −0.275510 + 0.477197i
\(451\) −0.289778 0.501910i −0.0136451 0.0236340i
\(452\) 10.6181 + 18.3910i 0.499431 + 0.865041i
\(453\) 4.40288 7.62602i 0.206866 0.358302i
\(454\) 27.2887 1.28072
\(455\) −5.48222 + 3.74500i −0.257010 + 0.175568i
\(456\) 44.7651 2.09632
\(457\) 10.6464 18.4401i 0.498019 0.862594i −0.501979 0.864880i \(-0.667394\pi\)
0.999997 + 0.00228642i \(0.000727790\pi\)
\(458\) 11.8678 + 20.5557i 0.554547 + 0.960504i
\(459\) −3.36610 5.83026i −0.157116 0.272133i
\(460\) 1.46284 2.53372i 0.0682053 0.118135i
\(461\) −3.83733 −0.178722 −0.0893612 0.995999i \(-0.528483\pi\)
−0.0893612 + 0.995999i \(0.528483\pi\)
\(462\) 1.52204 + 20.0659i 0.0708115 + 0.933552i
\(463\) −40.4632 −1.88048 −0.940242 0.340508i \(-0.889401\pi\)
−0.940242 + 0.340508i \(0.889401\pi\)
\(464\) −16.1701 + 28.0075i −0.750680 + 1.30022i
\(465\) −0.718309 1.24415i −0.0333108 0.0576960i
\(466\) −30.2771 52.4414i −1.40256 2.42930i
\(467\) 0.886015 1.53462i 0.0409999 0.0710139i −0.844797 0.535087i \(-0.820279\pi\)
0.885797 + 0.464073i \(0.153612\pi\)
\(468\) −17.4757 −0.807814
\(469\) −0.178869 2.35814i −0.00825941 0.108889i
\(470\) 4.11629 0.189870
\(471\) 4.66548 8.08085i 0.214974 0.372346i
\(472\) 21.8150 + 37.7847i 1.00412 + 1.73918i
\(473\) −2.05016 3.55098i −0.0942663 0.163274i
\(474\) 18.0563 31.2744i 0.829354 1.43648i
\(475\) 31.9551 1.46620
\(476\) 66.3879 45.3508i 3.04288 2.07865i
\(477\) 9.46929 0.433569
\(478\) 33.9862 58.8658i 1.55449 2.69246i
\(479\) 7.00989 + 12.1415i 0.320290 + 0.554759i 0.980548 0.196280i \(-0.0628863\pi\)
−0.660258 + 0.751039i \(0.729553\pi\)
\(480\) 1.91840 + 3.32276i 0.0875625 + 0.151663i
\(481\) −8.53864 + 14.7894i −0.389329 + 0.674337i
\(482\) −29.8250 −1.35849
\(483\) 2.38478 + 1.14579i 0.108511 + 0.0521351i
\(484\) −9.56353 −0.434706
\(485\) −1.04814 + 1.81543i −0.0475936 + 0.0824345i
\(486\) 1.27611 + 2.21029i 0.0578856 + 0.100261i
\(487\) 13.3895 + 23.1913i 0.606736 + 1.05090i 0.991775 + 0.127997i \(0.0408549\pi\)
−0.385038 + 0.922901i \(0.625812\pi\)
\(488\) 27.9838 48.4693i 1.26677 2.19410i
\(489\) 0.463122 0.0209431
\(490\) −4.21099 + 10.7869i −0.190233 + 0.487303i
\(491\) 36.1444 1.63117 0.815587 0.578635i \(-0.196414\pi\)
0.815587 + 0.578635i \(0.196414\pi\)
\(492\) 0.438907 0.760209i 0.0197875 0.0342729i
\(493\) −14.8170 25.6638i −0.667323 1.15584i
\(494\) 34.4716 + 59.7066i 1.55095 + 2.68633i
\(495\) 0.965805 1.67282i 0.0434097 0.0751878i
\(496\) 16.2844 0.731191
\(497\) −36.3653 17.4720i −1.63121 0.783725i
\(498\) −37.3339 −1.67297
\(499\) −19.0160 + 32.9367i −0.851274 + 1.47445i 0.0287847 + 0.999586i \(0.490836\pi\)
−0.880059 + 0.474865i \(0.842497\pi\)
\(500\) 14.0139 + 24.2727i 0.626719 + 1.08551i
\(501\) −1.20192 2.08179i −0.0536980 0.0930076i
\(502\) −15.3479 + 26.5833i −0.685009 + 1.18647i
\(503\) −13.8143 −0.615947 −0.307974 0.951395i \(-0.599651\pi\)
−0.307974 + 0.951395i \(0.599651\pi\)
\(504\) −14.0165 + 9.57495i −0.624346 + 0.426502i
\(505\) 1.94877 0.0867193
\(506\) 3.80300 6.58699i 0.169064 0.292827i
\(507\) −0.994580 1.72266i −0.0441708 0.0765061i
\(508\) −36.0294 62.4047i −1.59855 2.76876i
\(509\) −4.19047 + 7.25811i −0.185739 + 0.321710i −0.943825 0.330445i \(-0.892801\pi\)
0.758086 + 0.652154i \(0.226135\pi\)
\(510\) −11.1367 −0.493143
\(511\) 0.188789 + 2.48892i 0.00835154 + 0.110104i
\(512\) 50.7841 2.24436
\(513\) 3.48863 6.04248i 0.154027 0.266782i
\(514\) −12.9959 22.5096i −0.573226 0.992856i
\(515\) −4.52397 7.83575i −0.199350 0.345284i
\(516\) 3.10524 5.37843i 0.136700 0.236772i
\(517\) 7.41557 0.326136
\(518\) 2.25277 + 29.6997i 0.0989811 + 1.30493i
\(519\) 5.14814 0.225978
\(520\) −8.04999 + 13.9430i −0.353015 + 0.611441i
\(521\) 0.175171 + 0.303404i 0.00767436 + 0.0132924i 0.869837 0.493339i \(-0.164224\pi\)
−0.862163 + 0.506631i \(0.830890\pi\)
\(522\) 5.61721 + 9.72929i 0.245858 + 0.425839i
\(523\) 19.6404 34.0181i 0.858813 1.48751i −0.0142487 0.999898i \(-0.504536\pi\)
0.873062 0.487609i \(-0.162131\pi\)
\(524\) 70.3824 3.07467
\(525\) −10.0055 + 6.83497i −0.436678 + 0.298302i
\(526\) −53.2304 −2.32095
\(527\) −7.46083 + 12.9225i −0.324999 + 0.562915i
\(528\) 10.9476 + 18.9618i 0.476434 + 0.825208i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) 7.83227 13.5659i 0.340212 0.589264i
\(531\) 6.80034 0.295110
\(532\) 75.1067 + 36.0856i 3.25629 + 1.56451i
\(533\) 0.752915 0.0326123
\(534\) −20.0937 + 34.8034i −0.869542 + 1.50609i
\(535\) 0.398209 + 0.689718i 0.0172161 + 0.0298191i
\(536\) −2.86742 4.96652i −0.123854 0.214521i
\(537\) 3.88943 6.73668i 0.167841 0.290709i
\(538\) 52.2466 2.25251
\(539\) −7.58616 + 19.4328i −0.326759 + 0.837029i
\(540\) 2.92568 0.125901
\(541\) 9.54946 16.5401i 0.410563 0.711116i −0.584388 0.811474i \(-0.698665\pi\)
0.994951 + 0.100358i \(0.0319988\pi\)
\(542\) −24.0619 41.6765i −1.03355 1.79016i
\(543\) 3.80663 + 6.59328i 0.163358 + 0.282945i
\(544\) 19.9257 34.5124i 0.854309 1.47971i
\(545\) 10.4814 0.448975
\(546\) −23.5643 11.3217i −1.00846 0.484523i
\(547\) −14.2276 −0.608330 −0.304165 0.952619i \(-0.598377\pi\)
−0.304165 + 0.952619i \(0.598377\pi\)
\(548\) −24.2067 + 41.9272i −1.03406 + 1.79104i
\(549\) −4.36166 7.55461i −0.186151 0.322423i
\(550\) 17.4173 + 30.1677i 0.742677 + 1.28635i
\(551\) 15.3563 26.5979i 0.654200 1.13311i
\(552\) 6.41586 0.273077
\(553\) 30.9120 21.1165i 1.31451 0.897965i
\(554\) 12.6643 0.538053
\(555\) 1.42949 2.47595i 0.0606786 0.105098i
\(556\) −48.3629 83.7670i −2.05104 3.55251i
\(557\) 6.88024 + 11.9169i 0.291525 + 0.504936i 0.974171 0.225813i \(-0.0725040\pi\)
−0.682645 + 0.730750i \(0.739171\pi\)
\(558\) 2.82845 4.89901i 0.119738 0.207392i
\(559\) 5.32682 0.225300
\(560\) 0.952933 + 12.5631i 0.0402688 + 0.530888i
\(561\) −20.0630 −0.847060
\(562\) 12.2073 21.1437i 0.514935 0.891894i
\(563\) 11.7109 + 20.2839i 0.493555 + 0.854863i 0.999972 0.00742562i \(-0.00236367\pi\)
−0.506417 + 0.862289i \(0.669030\pi\)
\(564\) 5.61593 + 9.72708i 0.236473 + 0.409584i
\(565\) 1.52469 2.64084i 0.0641441 0.111101i
\(566\) −18.9332 −0.795823
\(567\) 0.200110 + 2.63817i 0.00840383 + 0.110793i
\(568\) −97.8348 −4.10506
\(569\) −8.47391 + 14.6773i −0.355245 + 0.615302i −0.987160 0.159735i \(-0.948936\pi\)
0.631915 + 0.775038i \(0.282269\pi\)
\(570\) −5.77105 9.99575i −0.241723 0.418676i
\(571\) −11.6928 20.2526i −0.489330 0.847545i 0.510594 0.859822i \(-0.329425\pi\)
−0.999925 + 0.0122769i \(0.996092\pi\)
\(572\) −26.0401 + 45.1027i −1.08879 + 1.88584i
\(573\) −0.738878 −0.0308671
\(574\) 1.08433 0.740725i 0.0452590 0.0309172i
\(575\) 4.57989 0.190995
\(576\) −0.206940 + 0.358430i −0.00862249 + 0.0149346i
\(577\) 9.33006 + 16.1601i 0.388415 + 0.672755i 0.992237 0.124365i \(-0.0396892\pi\)
−0.603821 + 0.797120i \(0.706356\pi\)
\(578\) 36.1428 + 62.6012i 1.50334 + 2.60387i
\(579\) 7.98512 13.8306i 0.331850 0.574781i
\(580\) 12.8783 0.534743
\(581\) −34.8845 16.7605i −1.44725 0.695345i
\(582\) −8.25441 −0.342156
\(583\) 14.1099 24.4391i 0.584374 1.01217i
\(584\) 3.02645 + 5.24197i 0.125235 + 0.216914i
\(585\) 1.25470 + 2.17321i 0.0518755 + 0.0898510i
\(586\) 11.9585 20.7128i 0.494003 0.855638i
\(587\) 36.1742 1.49307 0.746535 0.665346i \(-0.231716\pi\)
0.746535 + 0.665346i \(0.231716\pi\)
\(588\) −31.2353 + 4.76593i −1.28812 + 0.196544i
\(589\) −15.4648 −0.637216
\(590\) 5.62472 9.74229i 0.231566 0.401084i
\(591\) 4.75097 + 8.22893i 0.195429 + 0.338493i
\(592\) 16.2036 + 28.0655i 0.665965 + 1.15348i
\(593\) −14.5370 + 25.1788i −0.596961 + 1.03397i 0.396305 + 0.918119i \(0.370292\pi\)
−0.993267 + 0.115849i \(0.963041\pi\)
\(594\) 7.60600 0.312078
\(595\) −10.4061 4.99969i −0.426608 0.204967i
\(596\) −46.7295 −1.91412
\(597\) 8.32964 14.4274i 0.340910 0.590473i
\(598\) 4.94057 + 8.55732i 0.202035 + 0.349935i
\(599\) −19.6546 34.0428i −0.803066 1.39095i −0.917589 0.397531i \(-0.869867\pi\)
0.114522 0.993421i \(-0.463466\pi\)
\(600\) −14.6920 + 25.4472i −0.599797 + 1.03888i
\(601\) 45.2577 1.84610 0.923049 0.384682i \(-0.125689\pi\)
0.923049 + 0.384682i \(0.125689\pi\)
\(602\) 7.67155 5.24058i 0.312669 0.213590i
\(603\) −0.893854 −0.0364005
\(604\) 19.8739 34.4226i 0.808657 1.40063i
\(605\) 0.686632 + 1.18928i 0.0279156 + 0.0483512i
\(606\) 3.83679 + 6.64551i 0.155859 + 0.269956i
\(607\) 22.7764 39.4499i 0.924466 1.60122i 0.132047 0.991243i \(-0.457845\pi\)
0.792418 0.609978i \(-0.208822\pi\)
\(608\) 41.3020 1.67502
\(609\) 0.880848 + 11.6128i 0.0356937 + 0.470573i
\(610\) −14.4305 −0.584274
\(611\) −4.81687 + 8.34307i −0.194870 + 0.337524i
\(612\) −15.1940 26.3168i −0.614183 1.06380i
\(613\) −2.97103 5.14597i −0.119999 0.207844i 0.799768 0.600309i \(-0.204956\pi\)
−0.919767 + 0.392465i \(0.871622\pi\)
\(614\) −0.0496148 + 0.0859354i −0.00200229 + 0.00346807i
\(615\) −0.126049 −0.00508278
\(616\) 3.82615 + 50.4424i 0.154160 + 2.03238i
\(617\) 7.63295 0.307291 0.153646 0.988126i \(-0.450899\pi\)
0.153646 + 0.988126i \(0.450899\pi\)
\(618\) 17.8138 30.8544i 0.716576 1.24115i
\(619\) −6.38206 11.0541i −0.256517 0.444300i 0.708790 0.705420i \(-0.249242\pi\)
−0.965306 + 0.261120i \(0.915908\pi\)
\(620\) −3.24233 5.61588i −0.130215 0.225539i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) −23.3234 −0.935183
\(623\) −34.4000 + 23.4993i −1.37821 + 0.941478i
\(624\) −28.4446 −1.13870
\(625\) −9.43742 + 16.3461i −0.377497 + 0.653844i
\(626\) −16.4314 28.4600i −0.656731 1.13749i
\(627\) −10.3966 18.0075i −0.415201 0.719150i
\(628\) 21.0592 36.4756i 0.840354 1.45554i
\(629\) −29.6953 −1.18403
\(630\) 3.94501 + 1.89541i 0.157173 + 0.0755150i
\(631\) −23.8685 −0.950192 −0.475096 0.879934i \(-0.657587\pi\)
−0.475096 + 0.879934i \(0.657587\pi\)
\(632\) 45.3906 78.6188i 1.80554 3.12729i
\(633\) −9.82247 17.0130i −0.390408 0.676207i
\(634\) 13.7655 + 23.8426i 0.546699 + 0.946911i
\(635\) −5.17360 + 8.96094i −0.205308 + 0.355604i
\(636\) 42.7428 1.69486
\(637\) −16.9357 21.1578i −0.671015 0.838302i
\(638\) 33.4802 1.32549
\(639\) −7.62445 + 13.2059i −0.301619 + 0.522419i
\(640\) −3.49447 6.05259i −0.138131 0.239250i
\(641\) −12.3957 21.4700i −0.489601 0.848014i 0.510327 0.859980i \(-0.329524\pi\)
−0.999928 + 0.0119663i \(0.996191\pi\)
\(642\) −1.56800 + 2.71586i −0.0618842 + 0.107187i
\(643\) 40.8527 1.61107 0.805537 0.592546i \(-0.201877\pi\)
0.805537 + 0.592546i \(0.201877\pi\)
\(644\) 10.7645 + 5.17189i 0.424181 + 0.203801i
\(645\) −0.891787 −0.0351141
\(646\) −59.9419 + 103.822i −2.35838 + 4.08484i
\(647\) 14.3158 + 24.7957i 0.562811 + 0.974818i 0.997250 + 0.0741161i \(0.0236135\pi\)
−0.434438 + 0.900702i \(0.643053\pi\)
\(648\) 3.20793 + 5.55630i 0.126019 + 0.218272i
\(649\) 10.1330 17.5509i 0.397755 0.688933i
\(650\) −45.2545 −1.77503
\(651\) 4.84223 3.30781i 0.189782 0.129643i
\(652\) 2.09046 0.0818686
\(653\) 10.4627 18.1219i 0.409437 0.709166i −0.585390 0.810752i \(-0.699059\pi\)
0.994827 + 0.101586i \(0.0323919\pi\)
\(654\) 20.6361 + 35.7427i 0.806934 + 1.39765i
\(655\) −5.05325 8.75248i −0.197447 0.341988i
\(656\) 0.714396 1.23737i 0.0278925 0.0483112i
\(657\) 0.943428 0.0368066
\(658\) 1.27085 + 16.7544i 0.0495428 + 0.653153i
\(659\) −12.2792 −0.478329 −0.239165 0.970979i \(-0.576874\pi\)
−0.239165 + 0.970979i \(0.576874\pi\)
\(660\) 4.35948 7.55085i 0.169693 0.293916i
\(661\) −13.6631 23.6652i −0.531432 0.920468i −0.999327 0.0366836i \(-0.988321\pi\)
0.467895 0.883784i \(-0.345013\pi\)
\(662\) 28.8102 + 49.9008i 1.11974 + 1.93945i
\(663\) 13.0322 22.5724i 0.506127 0.876638i
\(664\) −93.8512 −3.64213
\(665\) −0.904971 11.9308i −0.0350933 0.462656i
\(666\) 11.2577 0.436226
\(667\) 2.20091 3.81209i 0.0852195 0.147605i
\(668\) −5.42528 9.39686i −0.209910 0.363576i
\(669\) 8.76228 + 15.1767i 0.338769 + 0.586766i
\(670\) −0.739327 + 1.28055i −0.0285627 + 0.0494720i
\(671\) −25.9968 −1.00359
\(672\) −12.9322 + 8.83422i −0.498871 + 0.340788i
\(673\) 9.75358 0.375973 0.187986 0.982172i \(-0.439804\pi\)
0.187986 + 0.982172i \(0.439804\pi\)
\(674\) −8.16643 + 14.1447i −0.314559 + 0.544832i
\(675\) 2.28994 + 3.96630i 0.0881400 + 0.152663i
\(676\) −4.48937 7.77581i −0.172668 0.299070i
\(677\) −1.63166 + 2.82612i −0.0627097 + 0.108616i −0.895676 0.444708i \(-0.853308\pi\)
0.832966 + 0.553324i \(0.186641\pi\)
\(678\) 12.0074 0.461140
\(679\) −7.71287 3.70571i −0.295993 0.142212i
\(680\) −27.9959 −1.07359
\(681\) 5.34607 9.25966i 0.204862 0.354831i
\(682\) −8.42919 14.5998i −0.322770 0.559055i
\(683\) 14.2770 + 24.7285i 0.546294 + 0.946209i 0.998524 + 0.0543076i \(0.0172951\pi\)
−0.452230 + 0.891901i \(0.649372\pi\)
\(684\) 15.7471 27.2747i 0.602105 1.04288i
\(685\) 6.95186 0.265617
\(686\) −45.2056 13.8095i −1.72596 0.527249i
\(687\) 9.30000 0.354817
\(688\) 5.05430 8.75431i 0.192693 0.333755i
\(689\) 18.3306 + 31.7495i 0.698339 + 1.20956i
\(690\) −0.827123 1.43262i −0.0314880 0.0545389i
\(691\) −23.1058 + 40.0204i −0.878985 + 1.52245i −0.0265298 + 0.999648i \(0.508446\pi\)
−0.852456 + 0.522800i \(0.824888\pi\)
\(692\) 23.2379 0.883371
\(693\) 7.10700 + 3.41461i 0.269973 + 0.129710i
\(694\) −85.0396 −3.22806
\(695\) −6.94462 + 12.0284i −0.263424 + 0.456264i
\(696\) 14.1207 + 24.4578i 0.535245 + 0.927071i
\(697\) 0.654613 + 1.13382i 0.0247952 + 0.0429466i
\(698\) −36.4252 + 63.0903i −1.37872 + 2.38800i
\(699\) −23.7260 −0.897401
\(700\) −45.1634 + 30.8519i −1.70702 + 1.16609i
\(701\) 29.0091 1.09566 0.547830 0.836590i \(-0.315454\pi\)
0.547830 + 0.836590i \(0.315454\pi\)
\(702\) −4.94057 + 8.55732i −0.186470 + 0.322975i
\(703\) −15.3881 26.6530i −0.580373 1.00524i
\(704\) 0.616711 + 1.06818i 0.0232432 + 0.0402584i
\(705\) 0.806414 1.39675i 0.0303713 0.0526047i
\(706\) 0.390775 0.0147070
\(707\) 0.601656 + 7.93200i 0.0226276 + 0.298314i
\(708\) 30.6956 1.15361
\(709\) −24.6074 + 42.6213i −0.924150 + 1.60067i −0.131228 + 0.991352i \(0.541892\pi\)
−0.792923 + 0.609322i \(0.791441\pi\)
\(710\) 12.6127 + 21.8459i 0.473347 + 0.819861i
\(711\) −7.07474 12.2538i −0.265324 0.459554i
\(712\) −50.5124 + 87.4900i −1.89303 + 3.27883i
\(713\) −2.21646 −0.0830070
\(714\) −3.43831 45.3293i −0.128675 1.69641i
\(715\) 7.47839 0.279676
\(716\) 17.5562 30.4083i 0.656107 1.13641i
\(717\) −13.3163 23.0645i −0.497307 0.861360i
\(718\) 27.6727 + 47.9305i 1.03274 + 1.78875i
\(719\) −9.55428 + 16.5485i −0.356314 + 0.617155i −0.987342 0.158606i \(-0.949300\pi\)
0.631028 + 0.775760i \(0.282633\pi\)
\(720\) 4.76204 0.177471
\(721\) 30.4968 20.8329i 1.13576 0.775858i
\(722\) −75.7552 −2.81932
\(723\) −5.84295 + 10.1203i −0.217302 + 0.376377i
\(724\) 17.1825 + 29.7610i 0.638583 + 1.10606i
\(725\) 10.0799 + 17.4589i 0.374359 + 0.648409i
\(726\) −2.70372 + 4.68297i −0.100344 + 0.173801i
\(727\) 3.03289 0.112483 0.0562417 0.998417i \(-0.482088\pi\)
0.0562417 + 0.998417i \(0.482088\pi\)
\(728\) −59.2368 28.4608i −2.19546 1.05483i
\(729\) 1.00000 0.0370370
\(730\) 0.780330 1.35157i 0.0288813 0.0500239i
\(731\) 4.63134 + 8.02172i 0.171296 + 0.296694i
\(732\) −19.6878 34.1003i −0.727682 1.26038i
\(733\) 0.412163 0.713887i 0.0152236 0.0263680i −0.858313 0.513126i \(-0.828487\pi\)
0.873537 + 0.486758i \(0.161821\pi\)
\(734\) −7.76404 −0.286576
\(735\) 2.83527 + 3.54212i 0.104581 + 0.130653i
\(736\) 5.91953 0.218197
\(737\) −1.33191 + 2.30693i −0.0490615 + 0.0849770i
\(738\) −0.248168 0.429839i −0.00913518 0.0158226i
\(739\) 5.10966 + 8.85019i 0.187962 + 0.325560i 0.944571 0.328308i \(-0.106479\pi\)
−0.756609 + 0.653868i \(0.773145\pi\)
\(740\) 6.45249 11.1760i 0.237198 0.410840i
\(741\) 27.0130 0.992348
\(742\) 57.6347 + 27.6910i 2.11584 + 1.01657i
\(743\) 10.5624 0.387496 0.193748 0.981051i \(-0.437936\pi\)
0.193748 + 0.981051i \(0.437936\pi\)
\(744\) 7.11025 12.3153i 0.260674 0.451501i
\(745\) 3.35504 + 5.81110i 0.122919 + 0.212902i
\(746\) 35.2382 + 61.0343i 1.29016 + 2.23462i
\(747\) −7.31399 + 12.6682i −0.267605 + 0.463506i
\(748\) −90.5610 −3.31124
\(749\) −2.68439 + 1.83375i −0.0980853 + 0.0670038i
\(750\) 15.8475 0.578669
\(751\) 20.5518 35.5967i 0.749944 1.29894i −0.197905 0.980221i \(-0.563414\pi\)
0.947849 0.318720i \(-0.103253\pi\)
\(752\) 9.14089 + 15.8325i 0.333334 + 0.577351i
\(753\) 6.01353 + 10.4157i 0.219145 + 0.379571i
\(754\) −21.7475 + 37.6678i −0.791997 + 1.37178i
\(755\) −5.70754 −0.207719
\(756\) 0.903263 + 11.9083i 0.0328514 + 0.433100i
\(757\) −34.3157 −1.24723 −0.623613 0.781733i \(-0.714336\pi\)
−0.623613 + 0.781733i \(0.714336\pi\)
\(758\) 30.6419 53.0733i 1.11296 1.92771i
\(759\) −1.49007 2.58088i −0.0540863 0.0936802i
\(760\) −14.5075 25.1276i −0.526241 0.911476i
\(761\) 2.89620 5.01637i 0.104987 0.181843i −0.808746 0.588158i \(-0.799853\pi\)
0.913733 + 0.406315i \(0.133186\pi\)
\(762\) −40.7436 −1.47599
\(763\) 3.23599 + 42.6621i 0.117151 + 1.54447i
\(764\) −3.33517 −0.120662
\(765\) −2.18177 + 3.77894i −0.0788821 + 0.136628i
\(766\) −14.0523 24.3393i −0.507730 0.879414i
\(767\) 13.1640 + 22.8008i 0.475326 + 0.823289i
\(768\) 14.1738 24.5498i 0.511455 0.885866i
\(769\) −27.9852 −1.00917 −0.504586 0.863361i \(-0.668355\pi\)
−0.504586 + 0.863361i \(0.668355\pi\)
\(770\) 10.7702 7.35731i 0.388131 0.265139i
\(771\) −10.1840 −0.366768
\(772\) 36.0435 62.4292i 1.29723 2.24688i
\(773\) 17.6635 + 30.5941i 0.635313 + 1.10039i 0.986449 + 0.164069i \(0.0524621\pi\)
−0.351136 + 0.936324i \(0.614205\pi\)
\(774\) −1.75577 3.04108i −0.0631098 0.109309i
\(775\) 5.07557 8.79114i 0.182320 0.315787i
\(776\) −20.7502 −0.744889
\(777\) 10.5191 + 5.05398i 0.377371 + 0.181311i
\(778\) −89.5712 −3.21128
\(779\) −0.678440 + 1.17509i −0.0243076 + 0.0421021i
\(780\) 5.66351 + 9.80949i 0.202786 + 0.351236i
\(781\) 22.7220 + 39.3556i 0.813057 + 1.40826i
\(782\) −8.59104 + 14.8801i −0.307215 + 0.532112i
\(783\) 4.40182 0.157308
\(784\) −50.8408 + 7.75736i −1.81574 + 0.277048i
\(785\) −6.04795 −0.215861
\(786\) 19.8979 34.4642i 0.709734 1.22930i
\(787\) 17.1994 + 29.7903i 0.613094 + 1.06191i 0.990716 + 0.135950i \(0.0434085\pi\)
−0.377622 + 0.925960i \(0.623258\pi\)
\(788\) 21.4451 + 37.1440i 0.763950 + 1.32320i
\(789\) −10.4282 + 18.0622i −0.371255 + 0.643033i
\(790\) −23.4067 −0.832774
\(791\) 11.2196 + 5.39055i 0.398923 + 0.191666i
\(792\) 19.1202 0.679407
\(793\) 16.8865 29.2483i 0.599658 1.03864i
\(794\) 19.4330 + 33.6590i 0.689652 + 1.19451i
\(795\) −3.06880 5.31532i −0.108839 0.188515i
\(796\) 37.5986 65.1227i 1.33265 2.30821i
\(797\) −22.2714 −0.788894 −0.394447 0.918919i \(-0.629064\pi\)
−0.394447 + 0.918919i \(0.629064\pi\)
\(798\) 38.9035 26.5757i 1.37717 0.940769i
\(799\) −16.7519 −0.592640
\(800\) −13.5554 + 23.4786i −0.479255 + 0.830095i
\(801\) 7.87304 + 13.6365i 0.278180 + 0.481822i
\(802\) −24.2283 41.9646i −0.855530 1.48182i
\(803\) 1.40578 2.43488i 0.0496088 0.0859250i
\(804\) −4.03471 −0.142293
\(805\) −0.129703 1.70996i −0.00457143 0.0602680i
\(806\) 21.9011 0.771435
\(807\) 10.2355 17.7284i 0.360307 0.624071i
\(808\) 9.64505 + 16.7057i 0.339312 + 0.587705i
\(809\) 17.1349 + 29.6785i 0.602431 + 1.04344i 0.992452 + 0.122635i \(0.0391346\pi\)
−0.390021 + 0.920806i \(0.627532\pi\)
\(810\) 0.827123 1.43262i 0.0290621 0.0503371i
\(811\) −52.1588 −1.83154 −0.915772 0.401698i \(-0.868420\pi\)
−0.915772 + 0.401698i \(0.868420\pi\)
\(812\) 3.97600 + 52.4181i 0.139530 + 1.83951i
\(813\) −18.8557 −0.661297
\(814\) 16.7748 29.0547i 0.587955 1.01837i
\(815\) −0.150088 0.259961i −0.00525737 0.00910602i
\(816\) −24.7309 42.8351i −0.865754 1.49953i
\(817\) −4.79992 + 8.31370i −0.167928 + 0.290860i
\(818\) −19.0262 −0.665235
\(819\) −8.45813 + 5.77790i −0.295551 + 0.201896i
\(820\) −0.568963 −0.0198691
\(821\) 8.86817 15.3601i 0.309501 0.536072i −0.668752 0.743486i \(-0.733171\pi\)
0.978253 + 0.207413i \(0.0665045\pi\)
\(822\) 13.6870 + 23.7065i 0.477388 + 0.826861i
\(823\) 0.295059 + 0.511057i 0.0102851 + 0.0178143i 0.871122 0.491066i \(-0.163393\pi\)
−0.860837 + 0.508881i \(0.830059\pi\)
\(824\) 44.7810 77.5629i 1.56002 2.70203i
\(825\) 13.6488 0.475189
\(826\) 41.3902 + 19.8862i 1.44015 + 0.691930i
\(827\) 50.4841 1.75550 0.877752 0.479114i \(-0.159042\pi\)
0.877752 + 0.479114i \(0.159042\pi\)
\(828\) 2.25692 3.90910i 0.0784333 0.135850i
\(829\) 14.0542 + 24.3427i 0.488124 + 0.845456i 0.999907 0.0136592i \(-0.00434798\pi\)
−0.511783 + 0.859115i \(0.671015\pi\)
\(830\) 12.0991 + 20.9563i 0.419967 + 0.727405i
\(831\) 2.48103 4.29727i 0.0860659 0.149070i
\(832\) −1.60237 −0.0555522
\(833\) 17.1373 43.8990i 0.593771 1.52101i
\(834\) −54.6909 −1.89379
\(835\) −0.779037 + 1.34933i −0.0269597 + 0.0466956i
\(836\) −46.9286 81.2828i −1.62306 2.81122i
\(837\) −1.10823 1.91951i −0.0383060 0.0663480i
\(838\) 4.05011 7.01499i 0.139909 0.242329i
\(839\) −22.3730 −0.772401 −0.386200 0.922415i \(-0.626213\pi\)
−0.386200 + 0.922415i \(0.626213\pi\)
\(840\) 9.91710 + 4.76475i 0.342173 + 0.164400i
\(841\) −9.62400 −0.331862
\(842\) 19.2774 33.3894i 0.664343 1.15068i
\(843\) −4.78302 8.28444i −0.164736 0.285331i
\(844\) −44.3370 76.7939i −1.52614 2.64336i
\(845\) −0.644646 + 1.11656i −0.0221765 + 0.0384108i
\(846\) 6.35075 0.218343
\(847\) −4.62869 + 3.16194i −0.159044 + 0.108646i
\(848\) 69.5712 2.38908
\(849\) −3.70917 + 6.42447i −0.127298 + 0.220487i
\(850\) −39.3460 68.1493i −1.34956 2.33750i
\(851\) −2.20547 3.81998i −0.0756024 0.130947i
\(852\) −34.4155 + 59.6094i −1.17906 + 2.04218i
\(853\) 39.3664 1.34788 0.673940 0.738786i \(-0.264601\pi\)
0.673940 + 0.738786i \(0.264601\pi\)
\(854\) −4.45521 58.7358i −0.152454 2.00990i
\(855\) −4.52237 −0.154662
\(856\) −3.94170 + 6.82723i −0.134725 + 0.233350i
\(857\) −11.9660 20.7257i −0.408751 0.707977i 0.585999 0.810311i \(-0.300702\pi\)
−0.994750 + 0.102335i \(0.967369\pi\)
\(858\) 14.7236 + 25.5021i 0.502656 + 0.870626i
\(859\) −13.0940 + 22.6794i −0.446761 + 0.773812i −0.998173 0.0604207i \(-0.980756\pi\)
0.551412 + 0.834233i \(0.314089\pi\)
\(860\) −4.02538 −0.137264
\(861\) −0.0389158 0.513051i −0.00132625 0.0174847i
\(862\) −63.8751 −2.17559
\(863\) 8.87506 15.3721i 0.302111 0.523271i −0.674503 0.738272i \(-0.735642\pi\)
0.976614 + 0.215001i \(0.0689755\pi\)
\(864\) 2.95976 + 5.12646i 0.100693 + 0.174406i
\(865\) −1.66841 2.88977i −0.0567276 0.0982550i
\(866\) −35.2042 + 60.9755i −1.19629 + 2.07203i
\(867\) 28.3226 0.961887
\(868\) 21.8570 14.9309i 0.741876 0.506789i
\(869\) −42.1676 −1.43044
\(870\) 3.64084 6.30613i 0.123436 0.213798i
\(871\) −1.73031 2.99699i −0.0586295 0.101549i
\(872\) 51.8757 + 89.8513i 1.75673 + 3.04275i
\(873\) −1.61710 + 2.80090i −0.0547306 + 0.0947963i
\(874\) −17.8075 −0.602348
\(875\) 14.8078 + 7.11452i 0.500595 + 0.240515i
\(876\) 4.25848 0.143881
\(877\) −0.490644 + 0.849820i −0.0165679 + 0.0286964i −0.874190 0.485583i \(-0.838607\pi\)
0.857623 + 0.514280i \(0.171941\pi\)
\(878\) −26.0156 45.0604i −0.877985 1.52072i
\(879\) −4.68554 8.11559i −0.158039 0.273732i
\(880\) 7.09580 12.2903i 0.239199 0.414305i
\(881\) 52.6379 1.77341 0.886707 0.462331i \(-0.152987\pi\)
0.886707 + 0.462331i \(0.152987\pi\)
\(882\) −6.49684 + 16.6424i −0.218760 + 0.560378i
\(883\) 22.2550 0.748939 0.374469 0.927239i \(-0.377825\pi\)
0.374469 + 0.927239i \(0.377825\pi\)
\(884\) 58.8250 101.888i 1.97850 3.42686i
\(885\) −2.20385 3.81718i −0.0740816 0.128313i
\(886\) 35.5706 + 61.6101i 1.19502 + 2.06983i
\(887\) 16.6489 28.8367i 0.559014 0.968241i −0.438565 0.898700i \(-0.644513\pi\)
0.997579 0.0695415i \(-0.0221536\pi\)
\(888\) 28.2999 0.949683
\(889\) −38.0706 18.2913i −1.27685 0.613471i
\(890\) 26.0479 0.873127
\(891\) 1.49007 2.58088i 0.0499194 0.0864629i
\(892\) 39.5515 + 68.5052i 1.32428 + 2.29372i
\(893\) −8.68082 15.0356i −0.290493 0.503148i
\(894\) −13.2110 + 22.8820i −0.441840 + 0.765290i
\(895\) −5.04193 −0.168533
\(896\) 23.5567 16.0920i 0.786975 0.537597i
\(897\) 3.87158 0.129268
\(898\) −16.0587 + 27.8145i −0.535887 + 0.928183i
\(899\) −4.87822 8.44933i −0.162698 0.281801i
\(900\) 10.3364 + 17.9032i 0.344548 + 0.596774i
\(901\) −31.8746 + 55.2085i −1.06190 + 1.83926i
\(902\) −1.47915 −0.0492504
\(903\) −0.275326 3.62980i −0.00916229 0.120792i
\(904\) 30.1845 1.00392
\(905\) 2.46730 4.27350i 0.0820160 0.142056i
\(906\) −11.2371 19.4633i −0.373329 0.646624i
\(907\) −3.09177 5.35511i −0.102661 0.177814i 0.810119 0.586265i \(-0.199402\pi\)
−0.912780 + 0.408451i \(0.866069\pi\)
\(908\) 24.1313 41.7966i 0.800824 1.38707i
\(909\) 3.00663 0.0997235
\(910\) 1.28161 + 16.8963i 0.0424851 + 0.560107i
\(911\) 15.7337 0.521282 0.260641 0.965436i \(-0.416066\pi\)
0.260641 + 0.965436i \(0.416066\pi\)
\(912\) 25.6310 44.3943i 0.848729 1.47004i
\(913\) 21.7968 + 37.7531i 0.721368 + 1.24945i
\(914\) −27.1720 47.0633i −0.898771 1.55672i
\(915\) −2.82705 + 4.89659i −0.0934593 + 0.161876i
\(916\) 41.9787 1.38701
\(917\) 34.0647 23.2702i 1.12492 0.768450i
\(918\) −17.1821 −0.567093
\(919\) −5.74393 + 9.94877i −0.189475 + 0.328180i −0.945075 0.326853i \(-0.894012\pi\)
0.755601 + 0.655033i \(0.227345\pi\)
\(920\) −2.07925 3.60137i −0.0685508 0.118734i
\(921\) 0.0194399 + 0.0336708i 0.000640565 + 0.00110949i
\(922\) −4.89686 + 8.48161i −0.161270 + 0.279327i
\(923\) −59.0374 −1.94324
\(924\) 32.0798 + 15.4130i 1.05535 + 0.507050i
\(925\) 20.2016 0.664224
\(926\) −51.6355 + 89.4353i −1.69685 + 2.93903i
\(927\) −6.97973 12.0892i −0.229244 0.397063i
\(928\) 13.0283 + 22.5657i 0.427676 + 0.740757i
\(929\) −5.14417 + 8.90996i −0.168775 + 0.292326i −0.937989 0.346664i \(-0.887314\pi\)
0.769215 + 0.638991i \(0.220648\pi\)
\(930\) −3.66657 −0.120231
\(931\) 48.2820 7.36693i 1.58238 0.241441i
\(932\) −107.095 −3.50803
\(933\) −4.56923 + 7.91415i −0.149590 + 0.259098i
\(934\) −2.26131 3.91670i −0.0739922 0.128158i
\(935\) 6.50200 + 11.2618i 0.212638 + 0.368300i
\(936\) −12.4198 + 21.5117i −0.405953 + 0.703131i
\(937\) −5.44863 −0.177999 −0.0889994 0.996032i \(-0.528367\pi\)
−0.0889994 + 0.996032i \(0.528367\pi\)
\(938\) −5.44043 2.61390i −0.177636 0.0853467i
\(939\) −12.8762 −0.420197
\(940\) 3.64002 6.30470i 0.118724 0.205637i
\(941\) 13.9243 + 24.1177i 0.453921 + 0.786214i 0.998625 0.0524143i \(-0.0166916\pi\)
−0.544705 + 0.838628i \(0.683358\pi\)
\(942\) −11.9073 20.6241i −0.387962 0.671970i
\(943\) −0.0972360 + 0.168418i −0.00316644 + 0.00548443i
\(944\) 49.9623 1.62613
\(945\) 1.41601 0.967304i 0.0460629 0.0314664i
\(946\) −10.4649 −0.340244
\(947\) 24.1522 41.8328i 0.784840 1.35938i −0.144255 0.989541i \(-0.546079\pi\)
0.929095 0.369842i \(-0.120588\pi\)
\(948\) −31.9342 55.3117i −1.03718 1.79644i
\(949\) 1.82628 + 3.16321i 0.0592835 + 0.102682i
\(950\) 40.7782 70.6299i 1.32302 2.29154i
\(951\) 10.7871 0.349796
\(952\) −8.64333 113.950i −0.280132 3.69315i
\(953\) −17.0509 −0.552334 −0.276167 0.961110i \(-0.589064\pi\)
−0.276167 + 0.961110i \(0.589064\pi\)
\(954\) 12.0839 20.9299i 0.391229 0.677629i
\(955\) 0.239455 + 0.414748i 0.00774859 + 0.0134209i
\(956\) −60.1076 104.109i −1.94402 3.36714i
\(957\) 6.55904 11.3606i 0.212024 0.367235i
\(958\) 35.7816 1.15605
\(959\) 2.14629 + 28.2958i 0.0693073 + 0.913720i
\(960\) 0.268260 0.00865805
\(961\) 13.0437 22.5923i 0.420763 0.728783i
\(962\) 21.7925 + 37.7457i 0.702619 + 1.21697i
\(963\) 0.614369 + 1.06412i 0.0197978 + 0.0342907i
\(964\) −26.3741 + 45.6813i −0.849452 + 1.47129i
\(965\) −10.3513 −0.333219
\(966\) 5.57576 3.80890i 0.179397 0.122549i
\(967\) 46.1833 1.48515 0.742577 0.669761i \(-0.233603\pi\)
0.742577 + 0.669761i \(0.233603\pi\)
\(968\) −6.79669 + 11.7722i −0.218454 + 0.378373i
\(969\) 23.4862 + 40.6792i 0.754484 + 1.30681i
\(970\) 2.67509 + 4.63338i 0.0858918 + 0.148769i
\(971\) 1.11493 1.93111i 0.0357797 0.0619723i −0.847581 0.530666i \(-0.821942\pi\)
0.883361 + 0.468694i \(0.155275\pi\)
\(972\) 4.51383 0.144781
\(973\) −51.1028 24.5528i −1.63828 0.787125i
\(974\) 68.3459 2.18995
\(975\) −8.86571 + 15.3559i −0.283930 + 0.491781i
\(976\) −32.0452 55.5040i −1.02574 1.77664i
\(977\) 23.9884 + 41.5491i 0.767456 + 1.32927i 0.938938 + 0.344085i \(0.111811\pi\)
−0.171482 + 0.985187i \(0.554856\pi\)
\(978\) 0.590995 1.02363i 0.0188979 0.0327322i
\(979\) 46.9257 1.49975
\(980\) 12.7980 + 15.9885i 0.408816 + 0.510735i
\(981\) 16.1711 0.516302
\(982\) 46.1243 79.8895i 1.47188 2.54938i
\(983\) 28.2299 + 48.8956i 0.900393 + 1.55953i 0.826985 + 0.562224i \(0.190054\pi\)
0.0734081 + 0.997302i \(0.476612\pi\)
\(984\) −0.623853 1.08054i −0.0198877 0.0344465i
\(985\) 3.07939 5.33365i 0.0981174 0.169944i
\(986\) −75.6324 −2.40863
\(987\) 5.93410 + 2.85108i 0.188884 + 0.0907510i
\(988\) 121.932 3.87918
\(989\) −0.687938 + 1.19154i −0.0218752 + 0.0378889i
\(990\) −2.46495 4.26942i −0.0783412 0.135691i
\(991\) −11.6212 20.1286i −0.369161 0.639405i 0.620274 0.784385i \(-0.287021\pi\)
−0.989435 + 0.144980i \(0.953688\pi\)
\(992\) 6.56019 11.3626i 0.208286 0.360762i
\(993\) 22.5766 0.716447
\(994\) −85.0242 + 58.0816i −2.69680 + 1.84224i
\(995\) −10.7979 −0.342316
\(996\) −33.0142 + 57.1822i −1.04609 + 1.81189i
\(997\) 27.8638 + 48.2615i 0.882454 + 1.52846i 0.848604 + 0.529029i \(0.177444\pi\)
0.0338505 + 0.999427i \(0.489223\pi\)
\(998\) 48.5331 + 84.0618i 1.53629 + 2.66093i
\(999\) 2.20547 3.81998i 0.0697778 0.120859i
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 483.2.i.g.415.8 yes 16
7.2 even 3 3381.2.a.bf.1.1 8
7.4 even 3 inner 483.2.i.g.277.8 16
7.5 odd 6 3381.2.a.be.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.i.g.277.8 16 7.4 even 3 inner
483.2.i.g.415.8 yes 16 1.1 even 1 trivial
3381.2.a.be.1.1 8 7.5 odd 6
3381.2.a.bf.1.1 8 7.2 even 3