Properties

Label 675.2.l.c.601.2
Level $675$
Weight $2$
Character 675.601
Analytic conductor $5.390$
Analytic rank $0$
Dimension $12$
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] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 601.2
Root \(0.500000 + 1.27297i\) of defining polynomial
Character \(\chi\) \(=\) 675.601
Dual form 675.2.l.c.301.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.57954 - 0.574906i) q^{2} +(-1.45446 - 0.940501i) q^{3} +(0.632343 - 0.530599i) q^{4} +(-2.83808 - 0.649381i) q^{6} +(2.99441 + 2.51261i) q^{7} +(-0.987144 + 1.70978i) q^{8} +(1.23092 + 2.73584i) q^{9} +O(q^{10})\) \(q+(1.57954 - 0.574906i) q^{2} +(-1.45446 - 0.940501i) q^{3} +(0.632343 - 0.530599i) q^{4} +(-2.83808 - 0.649381i) q^{6} +(2.99441 + 2.51261i) q^{7} +(-0.987144 + 1.70978i) q^{8} +(1.23092 + 2.73584i) q^{9} +(-0.324801 + 1.84204i) q^{11} +(-1.41875 + 0.177016i) q^{12} +(-0.688417 - 0.250563i) q^{13} +(6.17430 + 2.24726i) q^{14} +(-0.862951 + 4.89404i) q^{16} +(0.944822 + 1.63648i) q^{17} +(3.51713 + 3.61372i) q^{18} +(-1.37143 + 2.37538i) q^{19} +(-1.99214 - 6.47073i) q^{21} +(0.545962 + 3.09631i) q^{22} +(4.46428 - 3.74597i) q^{23} +(3.04382 - 1.55840i) q^{24} -1.23143 q^{26} +(0.782746 - 5.13686i) q^{27} +3.22668 q^{28} +(4.99910 - 1.81953i) q^{29} +(1.02696 - 0.861722i) q^{31} +(0.764882 + 4.33786i) q^{32} +(2.20485 - 2.37370i) q^{33} +(2.43321 + 2.04170i) q^{34} +(2.23000 + 1.07687i) q^{36} +(1.69806 + 2.94112i) q^{37} +(-0.800605 + 4.54046i) q^{38} +(0.765621 + 1.01189i) q^{39} +(-1.68800 - 0.614382i) q^{41} +(-6.86673 - 9.07549i) q^{42} +(-0.873477 + 4.95373i) q^{43} +(0.771999 + 1.33714i) q^{44} +(4.89793 - 8.48346i) q^{46} +(-1.30892 - 1.09832i) q^{47} +(5.85798 - 6.30658i) q^{48} +(1.43775 + 8.15389i) q^{49} +(0.164904 - 3.26880i) q^{51} +(-0.568265 + 0.206831i) q^{52} -2.84494 q^{53} +(-1.71683 - 8.56388i) q^{54} +(-7.25193 + 2.63949i) q^{56} +(4.22874 - 2.16507i) q^{57} +(6.85023 - 5.74803i) q^{58} +(-1.95529 - 11.0890i) q^{59} +(4.00710 + 3.36235i) q^{61} +(1.12672 - 1.95153i) q^{62} +(-3.18824 + 11.2850i) q^{63} +(-1.26751 - 2.19540i) q^{64} +(2.11800 - 5.01694i) q^{66} +(-1.77511 - 0.646086i) q^{67} +(1.46577 + 0.533495i) q^{68} +(-10.0162 + 1.24972i) q^{69} +(6.09193 + 10.5515i) q^{71} +(-5.89280 - 0.596074i) q^{72} +(4.94384 - 8.56298i) q^{73} +(4.37302 + 3.66940i) q^{74} +(0.393163 + 2.22974i) q^{76} +(-5.60091 + 4.69972i) q^{77} +(1.79107 + 1.15816i) q^{78} +(-11.6079 + 4.22493i) q^{79} +(-5.96969 + 6.73519i) q^{81} -3.01948 q^{82} +(-10.9786 + 3.99588i) q^{83} +(-4.69308 - 3.03470i) q^{84} +(1.46824 + 8.32679i) q^{86} +(-8.98227 - 2.05523i) q^{87} +(-2.82886 - 2.37370i) q^{88} +(2.86437 - 4.96123i) q^{89} +(-1.43183 - 2.48001i) q^{91} +(0.835346 - 4.73748i) q^{92} +(-2.30412 + 0.287484i) q^{93} +(-2.69893 - 0.982329i) q^{94} +(2.96727 - 7.02862i) q^{96} +(0.0596270 - 0.338162i) q^{97} +(6.95870 + 12.0528i) q^{98} +(-5.43934 + 1.37879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57954 0.574906i 1.11690 0.406520i 0.283383 0.959007i \(-0.408543\pi\)
0.833521 + 0.552487i \(0.186321\pi\)
\(3\) −1.45446 0.940501i −0.839734 0.542999i
\(4\) 0.632343 0.530599i 0.316172 0.265300i
\(5\) 0 0
\(6\) −2.83808 0.649381i −1.15864 0.265109i
\(7\) 2.99441 + 2.51261i 1.13178 + 0.949676i 0.999139 0.0414879i \(-0.0132098\pi\)
0.132641 + 0.991164i \(0.457654\pi\)
\(8\) −0.987144 + 1.70978i −0.349008 + 0.604500i
\(9\) 1.23092 + 2.73584i 0.410305 + 0.911948i
\(10\) 0 0
\(11\) −0.324801 + 1.84204i −0.0979313 + 0.555396i 0.895878 + 0.444299i \(0.146547\pi\)
−0.993810 + 0.111096i \(0.964564\pi\)
\(12\) −1.41875 + 0.177016i −0.409557 + 0.0511002i
\(13\) −0.688417 0.250563i −0.190932 0.0694937i 0.244784 0.969578i \(-0.421283\pi\)
−0.435717 + 0.900084i \(0.643505\pi\)
\(14\) 6.17430 + 2.24726i 1.65015 + 0.600606i
\(15\) 0 0
\(16\) −0.862951 + 4.89404i −0.215738 + 1.22351i
\(17\) 0.944822 + 1.63648i 0.229153 + 0.396905i 0.957557 0.288243i \(-0.0930711\pi\)
−0.728404 + 0.685147i \(0.759738\pi\)
\(18\) 3.51713 + 3.61372i 0.828997 + 0.851761i
\(19\) −1.37143 + 2.37538i −0.314627 + 0.544950i −0.979358 0.202133i \(-0.935213\pi\)
0.664731 + 0.747083i \(0.268546\pi\)
\(20\) 0 0
\(21\) −1.99214 6.47073i −0.434721 1.41203i
\(22\) 0.545962 + 3.09631i 0.116400 + 0.660135i
\(23\) 4.46428 3.74597i 0.930866 0.781089i −0.0451066 0.998982i \(-0.514363\pi\)
0.975973 + 0.217893i \(0.0699183\pi\)
\(24\) 3.04382 1.55840i 0.621317 0.318108i
\(25\) 0 0
\(26\) −1.23143 −0.241504
\(27\) 0.782746 5.13686i 0.150640 0.988589i
\(28\) 3.22668 0.609786
\(29\) 4.99910 1.81953i 0.928310 0.337877i 0.166771 0.985996i \(-0.446666\pi\)
0.761540 + 0.648118i \(0.224444\pi\)
\(30\) 0 0
\(31\) 1.02696 0.861722i 0.184447 0.154770i −0.545889 0.837858i \(-0.683808\pi\)
0.730336 + 0.683088i \(0.239363\pi\)
\(32\) 0.764882 + 4.33786i 0.135213 + 0.766833i
\(33\) 2.20485 2.37370i 0.383815 0.413208i
\(34\) 2.43321 + 2.04170i 0.417291 + 0.350149i
\(35\) 0 0
\(36\) 2.23000 + 1.07687i 0.371666 + 0.179478i
\(37\) 1.69806 + 2.94112i 0.279159 + 0.483517i 0.971176 0.238364i \(-0.0766111\pi\)
−0.692017 + 0.721881i \(0.743278\pi\)
\(38\) −0.800605 + 4.54046i −0.129875 + 0.736559i
\(39\) 0.765621 + 1.01189i 0.122597 + 0.162032i
\(40\) 0 0
\(41\) −1.68800 0.614382i −0.263621 0.0959503i 0.206828 0.978377i \(-0.433686\pi\)
−0.470449 + 0.882427i \(0.655908\pi\)
\(42\) −6.86673 9.07549i −1.05956 1.40038i
\(43\) −0.873477 + 4.95373i −0.133204 + 0.755437i 0.842890 + 0.538087i \(0.180853\pi\)
−0.976094 + 0.217351i \(0.930258\pi\)
\(44\) 0.771999 + 1.33714i 0.116383 + 0.201582i
\(45\) 0 0
\(46\) 4.89793 8.48346i 0.722160 1.25082i
\(47\) −1.30892 1.09832i −0.190926 0.160206i 0.542314 0.840176i \(-0.317548\pi\)
−0.733240 + 0.679970i \(0.761993\pi\)
\(48\) 5.85798 6.30658i 0.845526 0.910277i
\(49\) 1.43775 + 8.15389i 0.205393 + 1.16484i
\(50\) 0 0
\(51\) 0.164904 3.26880i 0.0230912 0.457724i
\(52\) −0.568265 + 0.206831i −0.0788041 + 0.0286824i
\(53\) −2.84494 −0.390783 −0.195391 0.980725i \(-0.562598\pi\)
−0.195391 + 0.980725i \(0.562598\pi\)
\(54\) −1.71683 8.56388i −0.233631 1.16540i
\(55\) 0 0
\(56\) −7.25193 + 2.63949i −0.969080 + 0.352716i
\(57\) 4.22874 2.16507i 0.560110 0.286771i
\(58\) 6.85023 5.74803i 0.899480 0.754753i
\(59\) −1.95529 11.0890i −0.254557 1.44366i −0.797208 0.603704i \(-0.793691\pi\)
0.542652 0.839958i \(-0.317420\pi\)
\(60\) 0 0
\(61\) 4.00710 + 3.36235i 0.513056 + 0.430505i 0.862203 0.506563i \(-0.169084\pi\)
−0.349147 + 0.937068i \(0.613529\pi\)
\(62\) 1.12672 1.95153i 0.143093 0.247844i
\(63\) −3.18824 + 11.2850i −0.401680 + 1.42178i
\(64\) −1.26751 2.19540i −0.158439 0.274425i
\(65\) 0 0
\(66\) 2.11800 5.01694i 0.260708 0.617542i
\(67\) −1.77511 0.646086i −0.216864 0.0789319i 0.231304 0.972882i \(-0.425701\pi\)
−0.448167 + 0.893950i \(0.647923\pi\)
\(68\) 1.46577 + 0.533495i 0.177750 + 0.0646958i
\(69\) −10.0162 + 1.24972i −1.20581 + 0.150448i
\(70\) 0 0
\(71\) 6.09193 + 10.5515i 0.722980 + 1.25224i 0.959800 + 0.280684i \(0.0905613\pi\)
−0.236821 + 0.971553i \(0.576105\pi\)
\(72\) −5.89280 0.596074i −0.694473 0.0702480i
\(73\) 4.94384 8.56298i 0.578633 1.00222i −0.417004 0.908905i \(-0.636920\pi\)
0.995637 0.0933164i \(-0.0297468\pi\)
\(74\) 4.37302 + 3.66940i 0.508353 + 0.426559i
\(75\) 0 0
\(76\) 0.393163 + 2.22974i 0.0450989 + 0.255768i
\(77\) −5.60091 + 4.69972i −0.638283 + 0.535583i
\(78\) 1.79107 + 1.15816i 0.202799 + 0.131136i
\(79\) −11.6079 + 4.22493i −1.30599 + 0.475342i −0.898943 0.438065i \(-0.855664\pi\)
−0.407048 + 0.913407i \(0.633442\pi\)
\(80\) 0 0
\(81\) −5.96969 + 6.73519i −0.663299 + 0.748354i
\(82\) −3.01948 −0.333445
\(83\) −10.9786 + 3.99588i −1.20506 + 0.438605i −0.864986 0.501796i \(-0.832673\pi\)
−0.340070 + 0.940400i \(0.610451\pi\)
\(84\) −4.69308 3.03470i −0.512057 0.331113i
\(85\) 0 0
\(86\) 1.46824 + 8.32679i 0.158324 + 0.897901i
\(87\) −8.98227 2.05523i −0.963000 0.220344i
\(88\) −2.82886 2.37370i −0.301558 0.253037i
\(89\) 2.86437 4.96123i 0.303622 0.525889i −0.673331 0.739341i \(-0.735137\pi\)
0.976954 + 0.213452i \(0.0684706\pi\)
\(90\) 0 0
\(91\) −1.43183 2.48001i −0.150097 0.259976i
\(92\) 0.835346 4.73748i 0.0870908 0.493917i
\(93\) −2.30412 + 0.287484i −0.238926 + 0.0298107i
\(94\) −2.69893 0.982329i −0.278373 0.101319i
\(95\) 0 0
\(96\) 2.96727 7.02862i 0.302846 0.717356i
\(97\) 0.0596270 0.338162i 0.00605421 0.0343351i −0.981631 0.190789i \(-0.938895\pi\)
0.987685 + 0.156454i \(0.0500064\pi\)
\(98\) 6.95870 + 12.0528i 0.702935 + 1.21752i
\(99\) −5.43934 + 1.37879i −0.546674 + 0.138574i
\(100\) 0 0
\(101\) −13.3309 11.1860i −1.32647 1.11304i −0.984888 0.173194i \(-0.944591\pi\)
−0.341586 0.939850i \(-0.610964\pi\)
\(102\) −1.61878 5.25801i −0.160283 0.520621i
\(103\) 2.74590 + 15.5728i 0.270561 + 1.53443i 0.752717 + 0.658345i \(0.228743\pi\)
−0.482155 + 0.876086i \(0.660146\pi\)
\(104\) 1.10798 0.929702i 0.108646 0.0911648i
\(105\) 0 0
\(106\) −4.49370 + 1.63557i −0.436467 + 0.158861i
\(107\) 16.5298 1.59800 0.798999 0.601332i \(-0.205363\pi\)
0.798999 + 0.601332i \(0.205363\pi\)
\(108\) −2.23065 3.66358i −0.214644 0.352528i
\(109\) −4.71844 −0.451945 −0.225972 0.974134i \(-0.572556\pi\)
−0.225972 + 0.974134i \(0.572556\pi\)
\(110\) 0 0
\(111\) 0.296369 5.87477i 0.0281301 0.557608i
\(112\) −14.8808 + 12.4865i −1.40611 + 1.17986i
\(113\) −3.46338 19.6418i −0.325807 1.84775i −0.503939 0.863739i \(-0.668116\pi\)
0.178132 0.984007i \(-0.442995\pi\)
\(114\) 5.43475 5.85095i 0.509011 0.547992i
\(115\) 0 0
\(116\) 2.19571 3.80308i 0.203867 0.353108i
\(117\) −0.161881 2.19182i −0.0149659 0.202634i
\(118\) −9.46357 16.3914i −0.871193 1.50895i
\(119\) −1.28265 + 7.27425i −0.117580 + 0.666830i
\(120\) 0 0
\(121\) 7.04901 + 2.56563i 0.640819 + 0.233239i
\(122\) 8.26241 + 3.00727i 0.748043 + 0.272266i
\(123\) 1.87730 + 2.48116i 0.169271 + 0.223719i
\(124\) 0.192163 1.08981i 0.0172567 0.0978676i
\(125\) 0 0
\(126\) 1.45188 + 19.6581i 0.129344 + 1.75128i
\(127\) 0.534728 0.926176i 0.0474495 0.0821849i −0.841325 0.540529i \(-0.818224\pi\)
0.888775 + 0.458344i \(0.151557\pi\)
\(128\) −10.0128 8.40170i −0.885011 0.742612i
\(129\) 5.92943 6.38351i 0.522057 0.562037i
\(130\) 0 0
\(131\) 5.85281 4.91109i 0.511362 0.429084i −0.350246 0.936658i \(-0.613902\pi\)
0.861608 + 0.507574i \(0.169458\pi\)
\(132\) 0.134740 2.67089i 0.0117276 0.232471i
\(133\) −10.0750 + 3.66701i −0.873615 + 0.317970i
\(134\) −3.17529 −0.274303
\(135\) 0 0
\(136\) −3.73070 −0.319905
\(137\) 14.7067 5.35279i 1.25647 0.457319i 0.373890 0.927473i \(-0.378024\pi\)
0.882585 + 0.470154i \(0.155801\pi\)
\(138\) −15.1025 + 7.73235i −1.28561 + 0.658222i
\(139\) 6.63160 5.56457i 0.562485 0.471981i −0.316658 0.948540i \(-0.602561\pi\)
0.879142 + 0.476559i \(0.158116\pi\)
\(140\) 0 0
\(141\) 0.870810 + 2.82850i 0.0733354 + 0.238203i
\(142\) 15.6886 + 13.1643i 1.31656 + 1.10472i
\(143\) 0.685146 1.18671i 0.0572948 0.0992375i
\(144\) −14.4516 + 3.66325i −1.20430 + 0.305271i
\(145\) 0 0
\(146\) 2.88609 16.3678i 0.238854 1.35461i
\(147\) 5.57759 13.2117i 0.460032 1.08968i
\(148\) 2.63431 + 0.958811i 0.216539 + 0.0788137i
\(149\) 2.31524 + 0.842677i 0.189672 + 0.0690348i 0.435110 0.900377i \(-0.356710\pi\)
−0.245438 + 0.969412i \(0.578932\pi\)
\(150\) 0 0
\(151\) −1.82563 + 10.3537i −0.148568 + 0.842571i 0.815865 + 0.578243i \(0.196261\pi\)
−0.964433 + 0.264328i \(0.914850\pi\)
\(152\) −2.70760 4.68969i −0.219615 0.380384i
\(153\) −3.31416 + 4.59925i −0.267934 + 0.371828i
\(154\) −6.14497 + 10.6434i −0.495176 + 0.857669i
\(155\) 0 0
\(156\) 1.02104 + 0.233625i 0.0817489 + 0.0187050i
\(157\) −0.0625044 0.354480i −0.00498840 0.0282906i 0.982212 0.187776i \(-0.0601278\pi\)
−0.987200 + 0.159485i \(0.949017\pi\)
\(158\) −15.9062 + 13.3469i −1.26543 + 1.06182i
\(159\) 4.13786 + 2.67567i 0.328154 + 0.212195i
\(160\) 0 0
\(161\) 22.7800 1.79532
\(162\) −5.55728 + 14.0705i −0.436621 + 1.10548i
\(163\) −14.6186 −1.14502 −0.572508 0.819899i \(-0.694029\pi\)
−0.572508 + 0.819899i \(0.694029\pi\)
\(164\) −1.39339 + 0.507151i −0.108805 + 0.0396019i
\(165\) 0 0
\(166\) −15.0439 + 12.6233i −1.16763 + 0.979758i
\(167\) −0.377832 2.14279i −0.0292375 0.165814i 0.966693 0.255939i \(-0.0823846\pi\)
−0.995930 + 0.0901247i \(0.971273\pi\)
\(168\) 13.0301 + 2.98142i 1.00529 + 0.230021i
\(169\) −9.54744 8.01125i −0.734419 0.616250i
\(170\) 0 0
\(171\) −8.18679 0.828119i −0.626060 0.0633278i
\(172\) 2.07611 + 3.59593i 0.158302 + 0.274187i
\(173\) 3.05048 17.3001i 0.231924 1.31531i −0.617072 0.786906i \(-0.711681\pi\)
0.848996 0.528399i \(-0.177207\pi\)
\(174\) −15.3694 + 1.91763i −1.16515 + 0.145375i
\(175\) 0 0
\(176\) −8.73473 3.17918i −0.658405 0.239640i
\(177\) −7.58531 + 17.9674i −0.570147 + 1.35052i
\(178\) 1.67214 9.48320i 0.125333 0.710796i
\(179\) −0.502236 0.869898i −0.0375388 0.0650192i 0.846646 0.532157i \(-0.178618\pi\)
−0.884184 + 0.467138i \(0.845285\pi\)
\(180\) 0 0
\(181\) 10.5866 18.3366i 0.786898 1.36295i −0.140961 0.990015i \(-0.545019\pi\)
0.927859 0.372932i \(-0.121647\pi\)
\(182\) −3.68741 3.09411i −0.273329 0.229350i
\(183\) −2.66587 8.65909i −0.197067 0.640099i
\(184\) 1.99792 + 11.3308i 0.147289 + 0.835315i
\(185\) 0 0
\(186\) −3.47418 + 1.77875i −0.254739 + 0.130424i
\(187\) −3.32134 + 1.20887i −0.242880 + 0.0884012i
\(188\) −1.41045 −0.102868
\(189\) 15.2508 13.4151i 1.10933 0.975806i
\(190\) 0 0
\(191\) 9.23566 3.36150i 0.668269 0.243230i 0.0144664 0.999895i \(-0.495395\pi\)
0.653802 + 0.756665i \(0.273173\pi\)
\(192\) −0.221225 + 4.38522i −0.0159655 + 0.316476i
\(193\) 8.54606 7.17099i 0.615159 0.516179i −0.281119 0.959673i \(-0.590706\pi\)
0.896278 + 0.443494i \(0.146261\pi\)
\(194\) −0.100228 0.568420i −0.00719594 0.0408102i
\(195\) 0 0
\(196\) 5.23560 + 4.39319i 0.373971 + 0.313799i
\(197\) 4.54497 7.87212i 0.323816 0.560865i −0.657456 0.753493i \(-0.728368\pi\)
0.981272 + 0.192628i \(0.0617009\pi\)
\(198\) −7.79898 + 5.30496i −0.554249 + 0.377007i
\(199\) 7.34694 + 12.7253i 0.520811 + 0.902071i 0.999707 + 0.0241994i \(0.00770367\pi\)
−0.478896 + 0.877872i \(0.658963\pi\)
\(200\) 0 0
\(201\) 1.97418 + 2.60920i 0.139248 + 0.184038i
\(202\) −27.4876 10.0047i −1.93402 0.703925i
\(203\) 19.5411 + 7.11238i 1.37152 + 0.499191i
\(204\) −1.63015 2.15450i −0.114133 0.150845i
\(205\) 0 0
\(206\) 13.2901 + 23.0192i 0.925968 + 1.60382i
\(207\) 15.7435 + 7.60259i 1.09425 + 0.528417i
\(208\) 1.82034 3.15292i 0.126218 0.218615i
\(209\) −3.93011 3.29775i −0.271851 0.228110i
\(210\) 0 0
\(211\) 1.36458 + 7.73891i 0.0939415 + 0.532769i 0.995067 + 0.0992096i \(0.0316314\pi\)
−0.901125 + 0.433559i \(0.857257\pi\)
\(212\) −1.79898 + 1.50952i −0.123555 + 0.103675i
\(213\) 1.06325 21.0763i 0.0728528 1.44412i
\(214\) 26.1095 9.50309i 1.78481 0.649618i
\(215\) 0 0
\(216\) 8.01024 + 6.40915i 0.545028 + 0.436087i
\(217\) 5.24030 0.355735
\(218\) −7.45297 + 2.71266i −0.504779 + 0.183724i
\(219\) −15.2441 + 7.80484i −1.03010 + 0.527402i
\(220\) 0 0
\(221\) −0.240390 1.36332i −0.0161704 0.0917067i
\(222\) −2.90931 9.44982i −0.195260 0.634231i
\(223\) 6.69591 + 5.61853i 0.448391 + 0.376245i 0.838838 0.544380i \(-0.183235\pi\)
−0.390447 + 0.920625i \(0.627680\pi\)
\(224\) −8.60897 + 14.9112i −0.575211 + 0.996295i
\(225\) 0 0
\(226\) −16.7627 29.0339i −1.11504 1.93131i
\(227\) −0.706473 + 4.00661i −0.0468903 + 0.265928i −0.999236 0.0390942i \(-0.987553\pi\)
0.952345 + 0.305022i \(0.0986639\pi\)
\(228\) 1.52523 3.61284i 0.101011 0.239266i
\(229\) −15.1816 5.52563i −1.00323 0.365144i −0.212398 0.977183i \(-0.568127\pi\)
−0.790827 + 0.612039i \(0.790349\pi\)
\(230\) 0 0
\(231\) 12.5664 1.56790i 0.826808 0.103160i
\(232\) −1.82384 + 10.3435i −0.119741 + 0.679086i
\(233\) 8.60658 + 14.9070i 0.563836 + 0.976592i 0.997157 + 0.0753527i \(0.0240083\pi\)
−0.433321 + 0.901240i \(0.642658\pi\)
\(234\) −1.51579 3.36901i −0.0990903 0.220239i
\(235\) 0 0
\(236\) −7.12022 5.97457i −0.463487 0.388911i
\(237\) 20.8568 + 4.77225i 1.35479 + 0.309991i
\(238\) 2.15602 + 12.2274i 0.139754 + 0.792583i
\(239\) −1.17621 + 0.986962i −0.0760830 + 0.0638412i −0.680036 0.733179i \(-0.738036\pi\)
0.603953 + 0.797020i \(0.293591\pi\)
\(240\) 0 0
\(241\) 5.18868 1.88852i 0.334232 0.121650i −0.169452 0.985538i \(-0.554200\pi\)
0.503684 + 0.863888i \(0.331978\pi\)
\(242\) 12.6092 0.810549
\(243\) 15.0171 4.18157i 0.963350 0.268248i
\(244\) 4.31792 0.276427
\(245\) 0 0
\(246\) 4.39171 + 2.83982i 0.280005 + 0.181060i
\(247\) 1.53930 1.29162i 0.0979432 0.0821841i
\(248\) 0.459600 + 2.60652i 0.0291847 + 0.165514i
\(249\) 19.7261 + 4.51352i 1.25009 + 0.286033i
\(250\) 0 0
\(251\) 10.7204 18.5683i 0.676668 1.17202i −0.299310 0.954156i \(-0.596756\pi\)
0.975978 0.217868i \(-0.0699102\pi\)
\(252\) 3.97177 + 8.82770i 0.250198 + 0.556093i
\(253\) 5.45023 + 9.44007i 0.342653 + 0.593492i
\(254\) 0.312161 1.77035i 0.0195867 0.111082i
\(255\) 0 0
\(256\) −15.8814 5.78037i −0.992590 0.361273i
\(257\) −13.8947 5.05727i −0.866730 0.315464i −0.129888 0.991529i \(-0.541462\pi\)
−0.736842 + 0.676065i \(0.763684\pi\)
\(258\) 5.69586 13.4919i 0.354609 0.839967i
\(259\) −2.30520 + 13.0735i −0.143238 + 0.812346i
\(260\) 0 0
\(261\) 11.1314 + 11.4371i 0.689017 + 0.707938i
\(262\) 6.42133 11.1221i 0.396711 0.687124i
\(263\) −2.14704 1.80158i −0.132392 0.111090i 0.574187 0.818724i \(-0.305318\pi\)
−0.706579 + 0.707634i \(0.749763\pi\)
\(264\) 1.88201 + 6.11300i 0.115830 + 0.376229i
\(265\) 0 0
\(266\) −13.8057 + 11.5844i −0.846483 + 0.710284i
\(267\) −8.83215 + 4.52197i −0.540519 + 0.276740i
\(268\) −1.46529 + 0.533322i −0.0895068 + 0.0325778i
\(269\) −0.356528 −0.0217379 −0.0108689 0.999941i \(-0.503460\pi\)
−0.0108689 + 0.999941i \(0.503460\pi\)
\(270\) 0 0
\(271\) −12.1467 −0.737857 −0.368928 0.929458i \(-0.620275\pi\)
−0.368928 + 0.929458i \(0.620275\pi\)
\(272\) −8.82433 + 3.21179i −0.535054 + 0.194744i
\(273\) −0.249904 + 4.95372i −0.0151249 + 0.299813i
\(274\) 20.1524 16.9099i 1.21745 1.02156i
\(275\) 0 0
\(276\) −5.67059 + 6.10484i −0.341329 + 0.367468i
\(277\) −19.1434 16.0632i −1.15022 0.965146i −0.150492 0.988611i \(-0.548086\pi\)
−0.999725 + 0.0234648i \(0.992530\pi\)
\(278\) 7.27577 12.6020i 0.436372 0.755818i
\(279\) 3.62164 + 1.74890i 0.216822 + 0.104704i
\(280\) 0 0
\(281\) 1.27160 7.21162i 0.0758575 0.430209i −0.923100 0.384560i \(-0.874353\pi\)
0.998958 0.0456492i \(-0.0145356\pi\)
\(282\) 3.00160 + 3.96710i 0.178743 + 0.236237i
\(283\) −13.5204 4.92102i −0.803703 0.292524i −0.0926830 0.995696i \(-0.529544\pi\)
−0.711020 + 0.703172i \(0.751767\pi\)
\(284\) 9.45083 + 3.43982i 0.560804 + 0.204116i
\(285\) 0 0
\(286\) 0.399971 2.26835i 0.0236508 0.134130i
\(287\) −3.51086 6.08099i −0.207240 0.358950i
\(288\) −10.9262 + 7.43214i −0.643833 + 0.437943i
\(289\) 6.71462 11.6301i 0.394978 0.684122i
\(290\) 0 0
\(291\) −0.404767 + 0.435764i −0.0237278 + 0.0255449i
\(292\) −1.41731 8.03794i −0.0829416 0.470385i
\(293\) 11.0429 9.26611i 0.645134 0.541332i −0.260456 0.965486i \(-0.583873\pi\)
0.905590 + 0.424154i \(0.139428\pi\)
\(294\) 1.21453 24.0750i 0.0708330 1.40409i
\(295\) 0 0
\(296\) −6.70491 −0.389715
\(297\) 9.20806 + 3.11031i 0.534306 + 0.180478i
\(298\) 4.14147 0.239909
\(299\) −4.01189 + 1.46021i −0.232013 + 0.0844460i
\(300\) 0 0
\(301\) −15.0623 + 12.6388i −0.868178 + 0.728488i
\(302\) 3.06873 + 17.4036i 0.176586 + 1.00147i
\(303\) 8.86888 + 28.8073i 0.509504 + 1.65493i
\(304\) −10.4417 8.76166i −0.598875 0.502516i
\(305\) 0 0
\(306\) −2.59071 + 9.17004i −0.148101 + 0.524216i
\(307\) −15.2163 26.3554i −0.868440 1.50418i −0.863591 0.504193i \(-0.831790\pi\)
−0.00484869 0.999988i \(-0.501543\pi\)
\(308\) −1.04803 + 5.94367i −0.0597171 + 0.338672i
\(309\) 10.6524 25.2325i 0.605994 1.43543i
\(310\) 0 0
\(311\) 13.1516 + 4.78678i 0.745757 + 0.271433i 0.686819 0.726828i \(-0.259006\pi\)
0.0589378 + 0.998262i \(0.481229\pi\)
\(312\) −2.48589 + 0.310163i −0.140736 + 0.0175595i
\(313\) −3.83547 + 21.7520i −0.216793 + 1.22950i 0.660974 + 0.750409i \(0.270143\pi\)
−0.877767 + 0.479087i \(0.840968\pi\)
\(314\) −0.302521 0.523982i −0.0170722 0.0295700i
\(315\) 0 0
\(316\) −5.09844 + 8.83075i −0.286810 + 0.496769i
\(317\) −13.3205 11.1773i −0.748156 0.627777i 0.186859 0.982387i \(-0.440169\pi\)
−0.935014 + 0.354610i \(0.884614\pi\)
\(318\) 8.07418 + 1.84745i 0.452777 + 0.103600i
\(319\) 1.72792 + 9.79953i 0.0967450 + 0.548668i
\(320\) 0 0
\(321\) −24.0420 15.5463i −1.34189 0.867711i
\(322\) 35.9820 13.0964i 2.00520 0.729832i
\(323\) −5.18302 −0.288391
\(324\) −0.201212 + 7.42647i −0.0111784 + 0.412581i
\(325\) 0 0
\(326\) −23.0906 + 8.40430i −1.27887 + 0.465471i
\(327\) 6.86279 + 4.43770i 0.379513 + 0.245405i
\(328\) 2.71676 2.27963i 0.150008 0.125872i
\(329\) −1.15981 6.57762i −0.0639425 0.362636i
\(330\) 0 0
\(331\) 0.661975 + 0.555463i 0.0363855 + 0.0305310i 0.660799 0.750563i \(-0.270218\pi\)
−0.624414 + 0.781094i \(0.714662\pi\)
\(332\) −4.82203 + 8.35199i −0.264643 + 0.458375i
\(333\) −5.95628 + 8.26589i −0.326402 + 0.452968i
\(334\) −1.82870 3.16741i −0.100062 0.173313i
\(335\) 0 0
\(336\) 33.3871 4.16569i 1.82142 0.227257i
\(337\) 0.393289 + 0.143145i 0.0214238 + 0.00779762i 0.352710 0.935733i \(-0.385260\pi\)
−0.331286 + 0.943530i \(0.607483\pi\)
\(338\) −19.6863 7.16522i −1.07079 0.389737i
\(339\) −13.4358 + 31.8256i −0.729732 + 1.72853i
\(340\) 0 0
\(341\) 1.25377 + 2.17159i 0.0678953 + 0.117598i
\(342\) −13.4075 + 3.39859i −0.724992 + 0.183775i
\(343\) −2.50108 + 4.33199i −0.135046 + 0.233906i
\(344\) −7.60757 6.38351i −0.410173 0.344176i
\(345\) 0 0
\(346\) −5.12759 29.0800i −0.275661 1.56335i
\(347\) −17.9329 + 15.0475i −0.962689 + 0.807792i −0.981388 0.192033i \(-0.938492\pi\)
0.0186996 + 0.999825i \(0.494047\pi\)
\(348\) −6.77038 + 3.46637i −0.362931 + 0.185817i
\(349\) −19.8993 + 7.24276i −1.06519 + 0.387696i −0.814374 0.580340i \(-0.802920\pi\)
−0.250811 + 0.968036i \(0.580697\pi\)
\(350\) 0 0
\(351\) −1.82596 + 3.34017i −0.0974627 + 0.178285i
\(352\) −8.23894 −0.439137
\(353\) 22.1246 8.05268i 1.17757 0.428601i 0.322228 0.946662i \(-0.395568\pi\)
0.855344 + 0.518061i \(0.173346\pi\)
\(354\) −1.65172 + 32.7411i −0.0877878 + 1.74017i
\(355\) 0 0
\(356\) −0.821160 4.65703i −0.0435214 0.246822i
\(357\) 8.70700 9.37379i 0.460823 0.496114i
\(358\) −1.29341 1.08530i −0.0683589 0.0573599i
\(359\) 5.23047 9.05943i 0.276053 0.478139i −0.694347 0.719640i \(-0.744307\pi\)
0.970400 + 0.241502i \(0.0776400\pi\)
\(360\) 0 0
\(361\) 5.73837 + 9.93915i 0.302019 + 0.523113i
\(362\) 6.18020 35.0497i 0.324824 1.84217i
\(363\) −7.83953 10.3612i −0.411469 0.543822i
\(364\) −2.22130 0.808488i −0.116428 0.0423763i
\(365\) 0 0
\(366\) −9.18901 12.1448i −0.480317 0.634817i
\(367\) −3.69146 + 20.9353i −0.192693 + 1.09281i 0.722974 + 0.690875i \(0.242775\pi\)
−0.915666 + 0.401939i \(0.868336\pi\)
\(368\) 14.4805 + 25.0809i 0.754848 + 1.30743i
\(369\) −0.396932 5.37436i −0.0206635 0.279778i
\(370\) 0 0
\(371\) −8.51892 7.14822i −0.442280 0.371117i
\(372\) −1.30446 + 1.40435i −0.0676330 + 0.0728124i
\(373\) −0.401142 2.27499i −0.0207704 0.117795i 0.972660 0.232235i \(-0.0746037\pi\)
−0.993430 + 0.114440i \(0.963493\pi\)
\(374\) −4.55120 + 3.81891i −0.235337 + 0.197471i
\(375\) 0 0
\(376\) 3.16998 1.15378i 0.163479 0.0595016i
\(377\) −3.89737 −0.200725
\(378\) 16.3768 29.9575i 0.842331 1.54085i
\(379\) 12.5539 0.644850 0.322425 0.946595i \(-0.395502\pi\)
0.322425 + 0.946595i \(0.395502\pi\)
\(380\) 0 0
\(381\) −1.64881 + 0.844175i −0.0844712 + 0.0432484i
\(382\) 12.6555 10.6193i 0.647514 0.543329i
\(383\) 3.41297 + 19.3559i 0.174395 + 0.989042i 0.938840 + 0.344353i \(0.111902\pi\)
−0.764445 + 0.644689i \(0.776987\pi\)
\(384\) 6.66136 + 21.6369i 0.339936 + 1.10416i
\(385\) 0 0
\(386\) 9.37620 16.2401i 0.477236 0.826597i
\(387\) −14.6278 + 3.70793i −0.743574 + 0.188485i
\(388\) −0.141724 0.245472i −0.00719492 0.0124620i
\(389\) −3.27198 + 18.5563i −0.165896 + 0.940843i 0.782240 + 0.622978i \(0.214077\pi\)
−0.948136 + 0.317866i \(0.897034\pi\)
\(390\) 0 0
\(391\) 10.3482 + 3.76642i 0.523329 + 0.190476i
\(392\) −15.3607 5.59082i −0.775831 0.282379i
\(393\) −13.1316 + 1.63842i −0.662400 + 0.0826472i
\(394\) 2.65324 15.0473i 0.133668 0.758070i
\(395\) 0 0
\(396\) −2.70794 + 3.75798i −0.136079 + 0.188845i
\(397\) 10.0589 17.4225i 0.504841 0.874410i −0.495143 0.868811i \(-0.664884\pi\)
0.999984 0.00559897i \(-0.00178222\pi\)
\(398\) 18.9206 + 15.8763i 0.948405 + 0.795807i
\(399\) 18.1026 + 4.14205i 0.906261 + 0.207362i
\(400\) 0 0
\(401\) −23.5985 + 19.8015i −1.17845 + 0.988840i −0.178466 + 0.983946i \(0.557113\pi\)
−0.999988 + 0.00489430i \(0.998442\pi\)
\(402\) 4.61834 + 2.98636i 0.230342 + 0.148946i
\(403\) −0.922892 + 0.335905i −0.0459725 + 0.0167326i
\(404\) −14.3650 −0.714684
\(405\) 0 0
\(406\) 34.9549 1.73478
\(407\) −5.96919 + 2.17261i −0.295882 + 0.107692i
\(408\) 5.42616 + 3.50873i 0.268635 + 0.173708i
\(409\) 30.4059 25.5136i 1.50347 1.26156i 0.628086 0.778144i \(-0.283839\pi\)
0.875388 0.483421i \(-0.160606\pi\)
\(410\) 0 0
\(411\) −26.4246 6.04621i −1.30343 0.298237i
\(412\) 9.99925 + 8.39037i 0.492628 + 0.413364i
\(413\) 22.0073 38.1178i 1.08291 1.87565i
\(414\) 29.2384 + 2.95755i 1.43699 + 0.145355i
\(415\) 0 0
\(416\) 0.560351 3.17791i 0.0274735 0.155810i
\(417\) −14.8789 + 1.85643i −0.728622 + 0.0909097i
\(418\) −8.10366 2.94949i −0.396363 0.144264i
\(419\) −14.5099 5.28118i −0.708856 0.258002i −0.0376687 0.999290i \(-0.511993\pi\)
−0.671187 + 0.741288i \(0.734215\pi\)
\(420\) 0 0
\(421\) −3.14193 + 17.8188i −0.153128 + 0.868433i 0.807349 + 0.590074i \(0.200902\pi\)
−0.960477 + 0.278359i \(0.910210\pi\)
\(422\) 6.60456 + 11.4394i 0.321505 + 0.556863i
\(423\) 1.39365 4.93294i 0.0677616 0.239848i
\(424\) 2.80837 4.86424i 0.136386 0.236228i
\(425\) 0 0
\(426\) −10.4374 33.9021i −0.505695 1.64256i
\(427\) 3.55061 + 20.1365i 0.171826 + 0.974475i
\(428\) 10.4525 8.77071i 0.505242 0.423948i
\(429\) −2.11262 + 1.08164i −0.101998 + 0.0522221i
\(430\) 0 0
\(431\) −28.9683 −1.39535 −0.697677 0.716412i \(-0.745783\pi\)
−0.697677 + 0.716412i \(0.745783\pi\)
\(432\) 24.4645 + 8.26365i 1.17705 + 0.397585i
\(433\) 37.5902 1.80647 0.903235 0.429146i \(-0.141185\pi\)
0.903235 + 0.429146i \(0.141185\pi\)
\(434\) 8.27727 3.01268i 0.397322 0.144613i
\(435\) 0 0
\(436\) −2.98367 + 2.50360i −0.142892 + 0.119901i
\(437\) 2.77569 + 15.7417i 0.132779 + 0.753028i
\(438\) −19.5917 + 21.0920i −0.936126 + 1.00781i
\(439\) 7.86232 + 6.59727i 0.375248 + 0.314871i 0.810834 0.585277i \(-0.199014\pi\)
−0.435585 + 0.900147i \(0.643459\pi\)
\(440\) 0 0
\(441\) −20.5380 + 13.9702i −0.978001 + 0.665248i
\(442\) −1.16348 2.01521i −0.0553413 0.0958540i
\(443\) −3.80437 + 21.5757i −0.180751 + 1.02509i 0.750543 + 0.660822i \(0.229792\pi\)
−0.931294 + 0.364269i \(0.881319\pi\)
\(444\) −2.92974 3.87212i −0.139039 0.183763i
\(445\) 0 0
\(446\) 13.8066 + 5.02519i 0.653761 + 0.237949i
\(447\) −2.57488 3.40312i −0.121788 0.160962i
\(448\) 1.72072 9.75869i 0.0812964 0.461055i
\(449\) −4.98565 8.63540i −0.235287 0.407530i 0.724069 0.689728i \(-0.242270\pi\)
−0.959356 + 0.282198i \(0.908936\pi\)
\(450\) 0 0
\(451\) 1.67998 2.90981i 0.0791072 0.137018i
\(452\) −12.6120 10.5827i −0.593217 0.497768i
\(453\) 12.3930 13.3420i 0.582272 0.626863i
\(454\) 1.18752 + 6.73475i 0.0557330 + 0.316078i
\(455\) 0 0
\(456\) −0.472568 + 9.36747i −0.0221300 + 0.438672i
\(457\) −7.15867 + 2.60554i −0.334869 + 0.121882i −0.503981 0.863715i \(-0.668132\pi\)
0.169113 + 0.985597i \(0.445910\pi\)
\(458\) −27.1566 −1.26894
\(459\) 9.14592 3.57247i 0.426895 0.166748i
\(460\) 0 0
\(461\) 21.4255 7.79824i 0.997885 0.363200i 0.209116 0.977891i \(-0.432941\pi\)
0.788768 + 0.614690i \(0.210719\pi\)
\(462\) 18.9477 9.70106i 0.881529 0.451334i
\(463\) 6.73792 5.65379i 0.313138 0.262754i −0.472650 0.881250i \(-0.656702\pi\)
0.785787 + 0.618497i \(0.212258\pi\)
\(464\) 4.59084 + 26.0360i 0.213125 + 1.20869i
\(465\) 0 0
\(466\) 22.1646 + 18.5983i 1.02675 + 0.861549i
\(467\) −5.49878 + 9.52416i −0.254453 + 0.440726i −0.964747 0.263180i \(-0.915229\pi\)
0.710294 + 0.703905i \(0.248562\pi\)
\(468\) −1.26534 1.30009i −0.0584906 0.0600968i
\(469\) −3.69203 6.39479i −0.170482 0.295284i
\(470\) 0 0
\(471\) −0.242479 + 0.574363i −0.0111728 + 0.0264653i
\(472\) 20.8899 + 7.60331i 0.961536 + 0.349971i
\(473\) −8.84127 3.21796i −0.406522 0.147962i
\(474\) 35.6878 4.45274i 1.63919 0.204521i
\(475\) 0 0
\(476\) 3.04864 + 5.28040i 0.139734 + 0.242027i
\(477\) −3.50188 7.78332i −0.160340 0.356374i
\(478\) −1.29047 + 2.23516i −0.0590247 + 0.102234i
\(479\) 19.6816 + 16.5148i 0.899276 + 0.754582i 0.970049 0.242911i \(-0.0781021\pi\)
−0.0707730 + 0.997492i \(0.522547\pi\)
\(480\) 0 0
\(481\) −0.432034 2.45019i −0.0196991 0.111719i
\(482\) 7.11000 5.96600i 0.323852 0.271744i
\(483\) −33.1327 21.4246i −1.50759 0.974855i
\(484\) 5.81871 2.11784i 0.264487 0.0962654i
\(485\) 0 0
\(486\) 21.3162 15.2384i 0.966921 0.691228i
\(487\) 30.3800 1.37665 0.688325 0.725402i \(-0.258346\pi\)
0.688325 + 0.725402i \(0.258346\pi\)
\(488\) −9.70448 + 3.53214i −0.439301 + 0.159893i
\(489\) 21.2621 + 13.7488i 0.961508 + 0.621742i
\(490\) 0 0
\(491\) 1.51218 + 8.57597i 0.0682435 + 0.387028i 0.999730 + 0.0232514i \(0.00740183\pi\)
−0.931486 + 0.363777i \(0.881487\pi\)
\(492\) 2.50360 + 0.572850i 0.112871 + 0.0258261i
\(493\) 7.70088 + 6.46180i 0.346830 + 0.291025i
\(494\) 1.68882 2.92512i 0.0759837 0.131608i
\(495\) 0 0
\(496\) 3.33108 + 5.76961i 0.149570 + 0.259063i
\(497\) −8.27013 + 46.9023i −0.370966 + 2.10385i
\(498\) 33.7530 4.21133i 1.51251 0.188714i
\(499\) −10.9338 3.97957i −0.489463 0.178150i 0.0854858 0.996339i \(-0.472756\pi\)
−0.574949 + 0.818189i \(0.694978\pi\)
\(500\) 0 0
\(501\) −1.46576 + 3.47196i −0.0654851 + 0.155116i
\(502\) 6.25832 35.4927i 0.279323 1.58412i
\(503\) −18.8996 32.7350i −0.842689 1.45958i −0.887613 0.460590i \(-0.847638\pi\)
0.0449234 0.998990i \(-0.485696\pi\)
\(504\) −16.1477 16.5912i −0.719277 0.739029i
\(505\) 0 0
\(506\) 14.0360 + 11.7776i 0.623977 + 0.523579i
\(507\) 6.35179 + 20.6314i 0.282093 + 0.916274i
\(508\) −0.153297 0.869388i −0.00680143 0.0385729i
\(509\) 18.0585 15.1528i 0.800427 0.671638i −0.147875 0.989006i \(-0.547243\pi\)
0.948302 + 0.317368i \(0.102799\pi\)
\(510\) 0 0
\(511\) 36.3193 13.2191i 1.60667 0.584780i
\(512\) −2.26711 −0.100193
\(513\) 11.1285 + 8.90415i 0.491336 + 0.393128i
\(514\) −24.8548 −1.09630
\(515\) 0 0
\(516\) 0.362352 7.18272i 0.0159517 0.316202i
\(517\) 2.44828 2.05435i 0.107675 0.0903503i
\(518\) 3.87485 + 21.9753i 0.170251 + 0.965541i
\(519\) −20.7076 + 22.2934i −0.908963 + 0.978572i
\(520\) 0 0
\(521\) −3.93474 + 6.81517i −0.172384 + 0.298578i −0.939253 0.343226i \(-0.888480\pi\)
0.766869 + 0.641804i \(0.221814\pi\)
\(522\) 24.1578 + 11.6658i 1.05736 + 0.510600i
\(523\) 16.6467 + 28.8330i 0.727911 + 1.26078i 0.957765 + 0.287554i \(0.0928419\pi\)
−0.229854 + 0.973225i \(0.573825\pi\)
\(524\) 1.09517 6.21099i 0.0478425 0.271328i
\(525\) 0 0
\(526\) −4.42707 1.61132i −0.193029 0.0702570i
\(527\) 2.38048 + 0.866425i 0.103695 + 0.0377421i
\(528\) 9.71430 + 12.8390i 0.422761 + 0.558746i
\(529\) 1.90355 10.7955i 0.0827628 0.469371i
\(530\) 0 0
\(531\) 27.9309 18.9990i 1.21210 0.824485i
\(532\) −4.42516 + 7.66461i −0.191855 + 0.332303i
\(533\) 1.00811 + 0.845902i 0.0436659 + 0.0366401i
\(534\) −11.3510 + 12.2203i −0.491207 + 0.528824i
\(535\) 0 0
\(536\) 2.85695 2.39727i 0.123402 0.103546i
\(537\) −0.0876573 + 1.73759i −0.00378269 + 0.0749823i
\(538\) −0.563150 + 0.204970i −0.0242791 + 0.00883687i
\(539\) −15.4868 −0.667062
\(540\) 0 0
\(541\) 22.4283 0.964266 0.482133 0.876098i \(-0.339862\pi\)
0.482133 + 0.876098i \(0.339862\pi\)
\(542\) −19.1861 + 6.98318i −0.824115 + 0.299953i
\(543\) −32.6434 + 16.7131i −1.40086 + 0.717228i
\(544\) −6.37614 + 5.35022i −0.273375 + 0.229389i
\(545\) 0 0
\(546\) 2.45319 + 7.96827i 0.104987 + 0.341011i
\(547\) 16.0036 + 13.4286i 0.684262 + 0.574164i 0.917248 0.398316i \(-0.130405\pi\)
−0.232986 + 0.972480i \(0.574850\pi\)
\(548\) 6.45948 11.1881i 0.275935 0.477934i
\(549\) −4.26648 + 15.1016i −0.182089 + 0.644519i
\(550\) 0 0
\(551\) −2.53384 + 14.3701i −0.107945 + 0.612188i
\(552\) 7.75070 18.3592i 0.329892 0.781420i
\(553\) −45.3744 16.5149i −1.92952 0.702286i
\(554\) −39.4727 14.3669i −1.67703 0.610390i
\(555\) 0 0
\(556\) 1.24089 7.03744i 0.0526255 0.298454i
\(557\) 4.28920 + 7.42911i 0.181739 + 0.314782i 0.942473 0.334283i \(-0.108494\pi\)
−0.760734 + 0.649064i \(0.775161\pi\)
\(558\) 6.72597 + 0.680352i 0.284733 + 0.0288016i
\(559\) 1.84254 3.19137i 0.0779311 0.134981i
\(560\) 0 0
\(561\) 5.96770 + 1.36547i 0.251957 + 0.0576502i
\(562\) −2.13745 12.1221i −0.0901630 0.511340i
\(563\) 12.0383 10.1013i 0.507354 0.425720i −0.352843 0.935682i \(-0.614785\pi\)
0.860197 + 0.509962i \(0.170341\pi\)
\(564\) 2.05145 + 1.32653i 0.0863817 + 0.0558572i
\(565\) 0 0
\(566\) −24.1851 −1.01658
\(567\) −34.7986 + 5.16841i −1.46140 + 0.217053i
\(568\) −24.0545 −1.00930
\(569\) −11.9085 + 4.33435i −0.499231 + 0.181705i −0.579348 0.815080i \(-0.696693\pi\)
0.0801169 + 0.996785i \(0.474471\pi\)
\(570\) 0 0
\(571\) −20.1644 + 16.9199i −0.843852 + 0.708076i −0.958427 0.285339i \(-0.907894\pi\)
0.114575 + 0.993415i \(0.463449\pi\)
\(572\) −0.196419 1.11394i −0.00821267 0.0465764i
\(573\) −16.5944 3.79697i −0.693241 0.158621i
\(574\) −9.04155 7.58676i −0.377387 0.316665i
\(575\) 0 0
\(576\) 4.44607 6.17008i 0.185253 0.257087i
\(577\) −11.0577 19.1525i −0.460338 0.797329i 0.538640 0.842536i \(-0.318938\pi\)
−0.998978 + 0.0452074i \(0.985605\pi\)
\(578\) 3.91983 22.2304i 0.163043 0.924665i
\(579\) −19.1742 + 2.39236i −0.796854 + 0.0994230i
\(580\) 0 0
\(581\) −42.9144 15.6196i −1.78039 0.648009i
\(582\) −0.388822 + 0.921009i −0.0161172 + 0.0381771i
\(583\) 0.924041 5.24050i 0.0382699 0.217039i
\(584\) 9.76057 + 16.9058i 0.403895 + 0.699567i
\(585\) 0 0
\(586\) 12.1156 20.9848i 0.500491 0.866876i
\(587\) −10.9568 9.19388i −0.452237 0.379472i 0.388028 0.921647i \(-0.373156\pi\)
−0.840265 + 0.542176i \(0.817601\pi\)
\(588\) −3.48318 11.3138i −0.143644 0.466574i
\(589\) 0.638517 + 3.62121i 0.0263097 + 0.149209i
\(590\) 0 0
\(591\) −14.0142 + 7.17514i −0.576468 + 0.295146i
\(592\) −15.8593 + 5.77231i −0.651813 + 0.237241i
\(593\) −47.7300 −1.96004 −0.980018 0.198908i \(-0.936260\pi\)
−0.980018 + 0.198908i \(0.936260\pi\)
\(594\) 16.3326 0.380910i 0.670136 0.0156289i
\(595\) 0 0
\(596\) 1.91115 0.695601i 0.0782837 0.0284929i
\(597\) 1.28229 25.4182i 0.0524808 1.04030i
\(598\) −5.49746 + 4.61291i −0.224808 + 0.188636i
\(599\) −0.0867493 0.491980i −0.00354448 0.0201018i 0.982984 0.183690i \(-0.0588043\pi\)
−0.986529 + 0.163588i \(0.947693\pi\)
\(600\) 0 0
\(601\) −12.9669 10.8805i −0.528931 0.443826i 0.338801 0.940858i \(-0.389979\pi\)
−0.867732 + 0.497032i \(0.834423\pi\)
\(602\) −16.5254 + 28.6229i −0.673527 + 1.16658i
\(603\) −0.417415 5.65169i −0.0169985 0.230155i
\(604\) 4.33923 + 7.51577i 0.176561 + 0.305812i
\(605\) 0 0
\(606\) 30.5702 + 40.4035i 1.24183 + 1.64128i
\(607\) 0.652741 + 0.237578i 0.0264939 + 0.00964301i 0.355233 0.934778i \(-0.384401\pi\)
−0.328739 + 0.944421i \(0.606624\pi\)
\(608\) −11.3531 4.13218i −0.460427 0.167582i
\(609\) −21.7326 28.7231i −0.880649 1.16392i
\(610\) 0 0
\(611\) 0.625887 + 1.08407i 0.0253207 + 0.0438567i
\(612\) 0.344674 + 4.66680i 0.0139326 + 0.188644i
\(613\) −16.3317 + 28.2873i −0.659630 + 1.14251i 0.321081 + 0.947052i \(0.395954\pi\)
−0.980711 + 0.195461i \(0.937380\pi\)
\(614\) −39.1866 32.8815i −1.58144 1.32699i
\(615\) 0 0
\(616\) −2.50660 14.2157i −0.100994 0.572765i
\(617\) −17.5305 + 14.7098i −0.705751 + 0.592195i −0.923403 0.383831i \(-0.874605\pi\)
0.217652 + 0.976026i \(0.430160\pi\)
\(618\) 2.31958 45.9799i 0.0933074 1.84958i
\(619\) −7.97398 + 2.90229i −0.320501 + 0.116653i −0.497261 0.867601i \(-0.665661\pi\)
0.176759 + 0.984254i \(0.443439\pi\)
\(620\) 0 0
\(621\) −15.7481 25.8645i −0.631951 1.03791i
\(622\) 23.5254 0.943282
\(623\) 21.0427 7.65892i 0.843058 0.306848i
\(624\) −5.61293 + 2.87377i −0.224697 + 0.115043i
\(625\) 0 0
\(626\) 6.44708 + 36.5632i 0.257677 + 1.46136i
\(627\) 2.61465 + 8.49272i 0.104419 + 0.339167i
\(628\) −0.227611 0.190988i −0.00908267 0.00762127i
\(629\) −3.20872 + 5.55767i −0.127940 + 0.221599i
\(630\) 0 0
\(631\) −0.795865 1.37848i −0.0316829 0.0548763i 0.849749 0.527187i \(-0.176753\pi\)
−0.881432 + 0.472311i \(0.843420\pi\)
\(632\) 4.23496 24.0176i 0.168458 0.955370i
\(633\) 5.29373 12.5393i 0.210407 0.498394i
\(634\) −27.4662 9.99688i −1.09082 0.397027i
\(635\) 0 0
\(636\) 4.03626 0.503601i 0.160048 0.0199691i
\(637\) 1.05329 5.97352i 0.0417330 0.236680i
\(638\) 8.36313 + 14.4854i 0.331099 + 0.573481i
\(639\) −21.3687 + 29.6546i −0.845333 + 1.17312i
\(640\) 0 0
\(641\) 16.6038 + 13.9322i 0.655809 + 0.550289i 0.908827 0.417173i \(-0.136979\pi\)
−0.253019 + 0.967461i \(0.581423\pi\)
\(642\) −46.9130 10.7342i −1.85151 0.423644i
\(643\) 1.19853 + 6.79720i 0.0472654 + 0.268056i 0.999278 0.0380047i \(-0.0121002\pi\)
−0.952012 + 0.306060i \(0.900989\pi\)
\(644\) 14.4048 12.0871i 0.567629 0.476297i
\(645\) 0 0
\(646\) −8.18679 + 2.97975i −0.322105 + 0.117237i
\(647\) 6.18972 0.243343 0.121671 0.992570i \(-0.461175\pi\)
0.121671 + 0.992570i \(0.461175\pi\)
\(648\) −5.62277 16.8555i −0.220883 0.662146i
\(649\) 21.0614 0.826733
\(650\) 0 0
\(651\) −7.62182 4.92851i −0.298723 0.193164i
\(652\) −9.24396 + 7.75660i −0.362021 + 0.303772i
\(653\) 4.72574 + 26.8010i 0.184933 + 1.04881i 0.926042 + 0.377421i \(0.123189\pi\)
−0.741109 + 0.671384i \(0.765700\pi\)
\(654\) 13.3913 + 3.06407i 0.523642 + 0.119815i
\(655\) 0 0
\(656\) 4.46347 7.73096i 0.174269 0.301843i
\(657\) 29.5124 + 2.98527i 1.15139 + 0.116467i
\(658\) −5.61348 9.72283i −0.218836 0.379035i
\(659\) 0.917209 5.20175i 0.0357294 0.202631i −0.961718 0.274043i \(-0.911639\pi\)
0.997447 + 0.0714110i \(0.0227502\pi\)
\(660\) 0 0
\(661\) −10.9616 3.98968i −0.426355 0.155181i 0.119925 0.992783i \(-0.461734\pi\)
−0.546280 + 0.837602i \(0.683957\pi\)
\(662\) 1.36496 + 0.496803i 0.0530505 + 0.0193088i
\(663\) −0.932564 + 2.20898i −0.0362178 + 0.0857897i
\(664\) 4.00536 22.7155i 0.155438 0.881533i
\(665\) 0 0
\(666\) −4.65609 + 16.4806i −0.180420 + 0.638611i
\(667\) 15.5015 26.8494i 0.600220 1.03961i
\(668\) −1.37588 1.15450i −0.0532345 0.0446690i
\(669\) −4.45470 14.4694i −0.172229 0.559421i
\(670\) 0 0
\(671\) −7.49510 + 6.28913i −0.289345 + 0.242789i
\(672\) 26.5454 13.5910i 1.02401 0.524283i
\(673\) 46.1412 16.7940i 1.77861 0.647362i 0.778814 0.627255i \(-0.215822\pi\)
0.999798 0.0201071i \(-0.00640071\pi\)
\(674\) 0.703510 0.0270982
\(675\) 0 0
\(676\) −10.2880 −0.395693
\(677\) −21.2550 + 7.73617i −0.816894 + 0.297325i −0.716469 0.697619i \(-0.754243\pi\)
−0.100426 + 0.994945i \(0.532020\pi\)
\(678\) −2.92567 + 57.9941i −0.112360 + 2.22725i
\(679\) 1.02822 0.862775i 0.0394593 0.0331103i
\(680\) 0 0
\(681\) 4.79576 5.16302i 0.183774 0.197847i
\(682\) 3.22884 + 2.70931i 0.123639 + 0.103745i
\(683\) −8.56931 + 14.8425i −0.327896 + 0.567932i −0.982094 0.188391i \(-0.939673\pi\)
0.654198 + 0.756323i \(0.273006\pi\)
\(684\) −5.61626 + 3.82025i −0.214743 + 0.146071i
\(685\) 0 0
\(686\) −1.46007 + 8.28045i −0.0557456 + 0.316149i
\(687\) 16.8841 + 22.3151i 0.644169 + 0.851374i
\(688\) −23.4900 8.54966i −0.895548 0.325953i
\(689\) 1.95851 + 0.712838i 0.0746132 + 0.0271570i
\(690\) 0 0
\(691\) 3.17011 17.9786i 0.120597 0.683937i −0.863230 0.504811i \(-0.831562\pi\)
0.983826 0.179126i \(-0.0573268\pi\)
\(692\) −7.25049 12.5582i −0.275622 0.477392i
\(693\) −19.7520 9.53826i −0.750315 0.362328i
\(694\) −19.6749 + 34.0779i −0.746848 + 1.29358i
\(695\) 0 0
\(696\) 12.3808 13.3289i 0.469293 0.505232i
\(697\) −0.589436 3.34286i −0.0223265 0.126620i
\(698\) −27.2679 + 22.8805i −1.03210 + 0.866038i
\(699\) 1.50214 29.7762i 0.0568163 1.12624i
\(700\) 0 0
\(701\) −2.92075 −0.110315 −0.0551575 0.998478i \(-0.517566\pi\)
−0.0551575 + 0.998478i \(0.517566\pi\)
\(702\) −0.963899 + 6.32570i −0.0363800 + 0.238748i
\(703\) −9.31505 −0.351324
\(704\) 4.45570 1.62174i 0.167931 0.0611218i
\(705\) 0 0
\(706\) 30.3171 25.4391i 1.14100 0.957412i
\(707\) −11.8123 66.9906i −0.444246 2.51944i
\(708\) 4.73699 + 15.3864i 0.178027 + 0.578255i
\(709\) 23.0023 + 19.3012i 0.863868 + 0.724872i 0.962798 0.270223i \(-0.0870974\pi\)
−0.0989295 + 0.995094i \(0.531542\pi\)
\(710\) 0 0
\(711\) −25.8471 26.5569i −0.969342 0.995961i
\(712\) 5.65509 + 9.79490i 0.211933 + 0.367079i
\(713\) 1.35665 7.69393i 0.0508068 0.288140i
\(714\) 8.36402 19.8120i 0.313016 0.741445i
\(715\) 0 0
\(716\) −0.779152 0.283588i −0.0291183 0.0105982i
\(717\) 2.63900 0.329266i 0.0985552 0.0122967i
\(718\) 3.05341 17.3168i 0.113952 0.646256i
\(719\) −20.0285 34.6903i −0.746936 1.29373i −0.949285 0.314418i \(-0.898191\pi\)
0.202349 0.979314i \(-0.435143\pi\)
\(720\) 0 0
\(721\) −30.9059 + 53.5306i −1.15100 + 1.99358i
\(722\) 14.7781 + 12.4003i 0.549983 + 0.461490i
\(723\) −9.32289 2.13317i −0.346722 0.0793335i
\(724\) −3.03499 17.2123i −0.112794 0.639689i
\(725\) 0 0
\(726\) −18.3396 11.8590i −0.680645 0.440127i
\(727\) −1.44598 + 0.526294i −0.0536285 + 0.0195192i −0.368695 0.929550i \(-0.620195\pi\)
0.315067 + 0.949070i \(0.397973\pi\)
\(728\) 5.65371 0.209540
\(729\) −25.7746 8.04171i −0.954615 0.297841i
\(730\) 0 0
\(731\) −8.93196 + 3.25097i −0.330361 + 0.120241i
\(732\) −6.28025 4.06101i −0.232125 0.150099i
\(733\) 1.15818 0.971827i 0.0427783 0.0358952i −0.621148 0.783693i \(-0.713333\pi\)
0.663926 + 0.747798i \(0.268889\pi\)
\(734\) 6.20502 + 35.1904i 0.229031 + 1.29890i
\(735\) 0 0
\(736\) 19.6642 + 16.5002i 0.724830 + 0.608205i
\(737\) 1.76667 3.05997i 0.0650762 0.112715i
\(738\) −3.71672 8.26082i −0.136814 0.304085i
\(739\) −10.6779 18.4946i −0.392792 0.680336i 0.600024 0.799982i \(-0.295157\pi\)
−0.992817 + 0.119646i \(0.961824\pi\)
\(740\) 0 0
\(741\) −3.45362 + 0.430906i −0.126872 + 0.0158297i
\(742\) −17.5655 6.39333i −0.644851 0.234707i
\(743\) −19.1028 6.95284i −0.700812 0.255075i −0.0330547 0.999454i \(-0.510524\pi\)
−0.667758 + 0.744379i \(0.732746\pi\)
\(744\) 1.78297 4.22334i 0.0653667 0.154835i
\(745\) 0 0
\(746\) −1.94153 3.36282i −0.0710843 0.123122i
\(747\) −24.4458 25.1171i −0.894425 0.918987i
\(748\) −1.45880 + 2.52672i −0.0533391 + 0.0923860i
\(749\) 49.4970 + 41.5329i 1.80858 + 1.51758i
\(750\) 0 0
\(751\) 0.740289 + 4.19839i 0.0270135 + 0.153201i 0.995331 0.0965214i \(-0.0307716\pi\)
−0.968317 + 0.249723i \(0.919661\pi\)
\(752\) 6.50474 5.45813i 0.237204 0.199037i
\(753\) −33.0560 + 16.9244i −1.20463 + 0.616758i
\(754\) −6.15606 + 2.24062i −0.224191 + 0.0815987i
\(755\) 0 0
\(756\) 2.52567 16.5750i 0.0918578 0.602827i
\(757\) −54.3419 −1.97509 −0.987546 0.157332i \(-0.949711\pi\)
−0.987546 + 0.157332i \(0.949711\pi\)
\(758\) 19.8294 7.21730i 0.720235 0.262144i
\(759\) 0.951252 18.8562i 0.0345282 0.684435i
\(760\) 0 0
\(761\) 3.15364 + 17.8852i 0.114319 + 0.648338i 0.987085 + 0.160198i \(0.0512133\pi\)
−0.872765 + 0.488140i \(0.837676\pi\)
\(762\) −2.11904 + 2.28132i −0.0767649 + 0.0826435i
\(763\) −14.1289 11.8556i −0.511502 0.429201i
\(764\) 4.05650 7.02606i 0.146759 0.254194i
\(765\) 0 0
\(766\) 16.5188 + 28.6113i 0.596847 + 1.03377i
\(767\) −1.43244 + 8.12376i −0.0517224 + 0.293332i
\(768\) 17.6625 + 23.3438i 0.637340 + 0.842348i
\(769\) −23.3558 8.50082i −0.842232 0.306547i −0.115363 0.993323i \(-0.536803\pi\)
−0.726869 + 0.686776i \(0.759025\pi\)
\(770\) 0 0
\(771\) 15.4530 + 20.4236i 0.556526 + 0.735539i
\(772\) 1.59912 9.06906i 0.0575536 0.326403i
\(773\) 19.2416 + 33.3274i 0.692071 + 1.19870i 0.971158 + 0.238437i \(0.0766350\pi\)
−0.279087 + 0.960266i \(0.590032\pi\)
\(774\) −20.9735 + 14.2664i −0.753878 + 0.512797i
\(775\) 0 0
\(776\) 0.519323 + 0.435764i 0.0186426 + 0.0156430i
\(777\) 15.6484 16.8468i 0.561385 0.604376i
\(778\) 5.49991 + 31.1916i 0.197181 + 1.11827i
\(779\) 3.77436 3.16707i 0.135231 0.113472i
\(780\) 0 0
\(781\) −21.4150 + 7.79443i −0.766290 + 0.278907i
\(782\) 18.5107 0.661940
\(783\) −5.43361 27.1039i −0.194181 0.968615i
\(784\) −41.1462 −1.46951
\(785\) 0 0
\(786\) −19.7999 + 10.1374i −0.706239 + 0.361588i
\(787\) 0.821566 0.689376i 0.0292857 0.0245736i −0.628027 0.778191i \(-0.716137\pi\)
0.657313 + 0.753618i \(0.271693\pi\)
\(788\) −1.30296 7.38944i −0.0464159 0.263238i
\(789\) 1.42840 + 4.63962i 0.0508523 + 0.165175i
\(790\) 0 0
\(791\) 38.9814 67.5177i 1.38602 2.40065i
\(792\) 3.01198 10.6612i 0.107026 0.378828i
\(793\) −1.91607 3.31873i −0.0680417 0.117852i
\(794\) 5.87212 33.3025i 0.208394 1.18186i
\(795\) 0 0
\(796\) 11.3978 + 4.14846i 0.403985 + 0.147038i
\(797\) 23.7246 + 8.63505i 0.840369 + 0.305869i 0.726107 0.687581i \(-0.241328\pi\)
0.114262 + 0.993451i \(0.463550\pi\)
\(798\) 30.9750 3.86473i 1.09650 0.136810i
\(799\) 0.560674 3.17974i 0.0198352 0.112491i
\(800\) 0 0
\(801\) 17.0989 + 1.72961i 0.604161 + 0.0611127i
\(802\) −25.8908 + 44.8442i −0.914237 + 1.58350i
\(803\) 14.1676 + 11.8880i 0.499963 + 0.419519i
\(804\) 2.63280 + 0.602410i 0.0928515 + 0.0212454i
\(805\) 0 0
\(806\) −1.26463 + 1.06115i −0.0445448 + 0.0373775i
\(807\) 0.518556 + 0.335315i 0.0182540 + 0.0118036i
\(808\) 32.2851 11.7508i 1.13579 0.413392i
\(809\) −11.7337 −0.412536 −0.206268 0.978495i \(-0.566132\pi\)
−0.206268 + 0.978495i \(0.566132\pi\)
\(810\) 0 0
\(811\) −38.4085 −1.34871 −0.674353 0.738409i \(-0.735577\pi\)
−0.674353 + 0.738409i \(0.735577\pi\)
\(812\) 16.1305 5.87103i 0.566070 0.206033i
\(813\) 17.6668 + 11.4239i 0.619603 + 0.400655i
\(814\) −8.17953 + 6.86344i −0.286693 + 0.240564i
\(815\) 0 0
\(816\) 15.8553 + 3.62786i 0.555048 + 0.127001i
\(817\) −10.5691 8.86853i −0.369766 0.310271i
\(818\) 33.3594 57.7802i 1.16639 2.02024i
\(819\) 5.02246 6.96996i 0.175499 0.243550i
\(820\) 0 0
\(821\) 4.64197 26.3259i 0.162006 0.918781i −0.790092 0.612988i \(-0.789967\pi\)
0.952098 0.305793i \(-0.0989216\pi\)
\(822\) −45.2147 + 5.64141i −1.57704 + 0.196767i
\(823\) 4.10107 + 1.49267i 0.142954 + 0.0520311i 0.412506 0.910955i \(-0.364653\pi\)
−0.269552 + 0.962986i \(0.586876\pi\)
\(824\) −29.3367 10.6777i −1.02199 0.371974i
\(825\) 0 0
\(826\) 12.8473 72.8608i 0.447015 2.53515i
\(827\) −19.5727 33.9009i −0.680610 1.17885i −0.974795 0.223102i \(-0.928382\pi\)
0.294185 0.955748i \(-0.404952\pi\)
\(828\) 13.9893 3.54606i 0.486160 0.123234i
\(829\) 16.4433 28.4807i 0.571101 0.989176i −0.425352 0.905028i \(-0.639850\pi\)
0.996453 0.0841481i \(-0.0268169\pi\)
\(830\) 0 0
\(831\) 12.7359 + 41.3678i 0.441803 + 1.43503i
\(832\) 0.322492 + 1.82894i 0.0111804 + 0.0634072i
\(833\) −11.9853 + 10.0568i −0.415264 + 0.348448i
\(834\) −22.4345 + 11.4863i −0.776844 + 0.397737i
\(835\) 0 0
\(836\) −4.23496 −0.146469
\(837\) −3.62269 5.94986i −0.125219 0.205657i
\(838\) −25.9552 −0.896607
\(839\) −29.7322 + 10.8216i −1.02647 + 0.373604i −0.799735 0.600353i \(-0.795027\pi\)
−0.226734 + 0.973957i \(0.572805\pi\)
\(840\) 0 0
\(841\) −0.534920 + 0.448851i −0.0184455 + 0.0154776i
\(842\) 5.28131 + 29.9518i 0.182006 + 1.03221i
\(843\) −8.63203 + 9.29308i −0.297303 + 0.320071i
\(844\) 4.96914 + 4.16961i 0.171045 + 0.143524i
\(845\) 0 0
\(846\) −0.634651 8.59300i −0.0218197 0.295434i
\(847\) 14.6612 + 25.3939i 0.503764 + 0.872545i
\(848\) 2.45505 13.9233i 0.0843066 0.478127i
\(849\) 15.0366 + 19.8734i 0.516056 + 0.682052i
\(850\) 0 0
\(851\) 18.5980 + 6.76910i 0.637530 + 0.232042i
\(852\) −10.5107 13.8916i −0.360091 0.475919i
\(853\) 0.982440 5.57169i 0.0336381 0.190771i −0.963358 0.268217i \(-0.913565\pi\)
0.996997 + 0.0774461i \(0.0246766\pi\)
\(854\) 17.1849 + 29.7652i 0.588057 + 1.01854i
\(855\) 0 0
\(856\) −16.3173 + 28.2624i −0.557715 + 0.965990i
\(857\) 31.5690 + 26.4895i 1.07838 + 0.904864i 0.995785 0.0917193i \(-0.0292362\pi\)
0.0825904 + 0.996584i \(0.473681\pi\)
\(858\) −2.71513 + 2.92305i −0.0926929 + 0.0997913i
\(859\) 6.22605 + 35.3097i 0.212430 + 1.20475i 0.885311 + 0.465000i \(0.153946\pi\)
−0.672880 + 0.739751i \(0.734943\pi\)
\(860\) 0 0
\(861\) −0.612766 + 12.1465i −0.0208830 + 0.413953i
\(862\) −45.7566 + 16.6541i −1.55848 + 0.567239i
\(863\) −20.9694 −0.713806 −0.356903 0.934142i \(-0.616167\pi\)
−0.356903 + 0.934142i \(0.616167\pi\)
\(864\) 22.8817 0.533646i 0.778451 0.0181550i
\(865\) 0 0
\(866\) 59.3753 21.6108i 2.01765 0.734366i
\(867\) −20.7043 + 10.6004i −0.703153 + 0.360008i
\(868\) 3.31367 2.78050i 0.112473 0.0943764i
\(869\) −4.01223 22.7545i −0.136106 0.771893i
\(870\) 0 0
\(871\) 1.06013 + 0.889553i 0.0359210 + 0.0301413i
\(872\) 4.65778 8.06751i 0.157732 0.273201i
\(873\) 0.998554 0.253118i 0.0337959 0.00856675i
\(874\) 13.4343 + 23.2689i 0.454422 + 0.787082i
\(875\) 0 0
\(876\) −5.49828 + 13.0239i −0.185770 + 0.440035i
\(877\) 19.2735 + 7.01498i 0.650819 + 0.236879i 0.646268 0.763111i \(-0.276329\pi\)
0.00455171 + 0.999990i \(0.498551\pi\)
\(878\) 16.2117 + 5.90057i 0.547117 + 0.199134i
\(879\) −24.7763 + 3.09132i −0.835684 + 0.104268i
\(880\) 0 0
\(881\) 19.1438 + 33.1581i 0.644972 + 1.11712i 0.984308 + 0.176459i \(0.0564644\pi\)
−0.339336 + 0.940665i \(0.610202\pi\)
\(882\) −24.4091 + 33.8740i −0.821897 + 1.14060i
\(883\) −8.72326 + 15.1091i −0.293561 + 0.508463i −0.974649 0.223739i \(-0.928174\pi\)
0.681088 + 0.732201i \(0.261507\pi\)
\(884\) −0.875384 0.734534i −0.0294423 0.0247051i
\(885\) 0 0
\(886\) 6.39481 + 36.2668i 0.214838 + 1.21841i
\(887\) 41.5325 34.8499i 1.39453 1.17015i 0.431058 0.902324i \(-0.358140\pi\)
0.963468 0.267823i \(-0.0863041\pi\)
\(888\) 9.75203 + 6.30597i 0.327257 + 0.211615i
\(889\) 3.92831 1.42979i 0.131751 0.0479536i
\(890\) 0 0
\(891\) −10.4675 13.1840i −0.350675 0.441681i
\(892\) 7.21530 0.241586
\(893\) 4.40402 1.60293i 0.147375 0.0536400i
\(894\) −6.02361 3.89506i −0.201460 0.130270i
\(895\) 0 0
\(896\) −8.87211 50.3162i −0.296396 1.68095i
\(897\) 7.20846 + 1.64937i 0.240683 + 0.0550708i
\(898\) −12.8396 10.7737i −0.428462 0.359523i
\(899\) 3.56595 6.17641i 0.118931 0.205995i
\(900\) 0 0
\(901\) −2.68796 4.65569i −0.0895491 0.155104i
\(902\) 0.980730 5.56200i 0.0326547 0.185194i
\(903\) 33.7944 4.21650i 1.12461 0.140316i
\(904\) 37.0021 + 13.4677i 1.23067 + 0.447928i
\(905\) 0 0
\(906\) 11.9048 28.1991i 0.395510 0.936851i
\(907\) −4.98078 + 28.2474i −0.165384 + 0.937939i 0.783284 + 0.621665i \(0.213543\pi\)
−0.948668 + 0.316275i \(0.897568\pi\)
\(908\) 1.67917 + 2.90841i 0.0557252 + 0.0965188i
\(909\) 14.1938 50.2402i 0.470779 1.66636i
\(910\) 0 0
\(911\) −21.7416 18.2433i −0.720330 0.604429i 0.207146 0.978310i \(-0.433582\pi\)
−0.927477 + 0.373881i \(0.878027\pi\)
\(912\) 6.94676 + 22.5640i 0.230030 + 0.747168i
\(913\) −3.79471 21.5208i −0.125586 0.712236i
\(914\) −9.80947 + 8.23112i −0.324468 + 0.272261i
\(915\) 0 0
\(916\) −12.5319 + 4.56122i −0.414064 + 0.150707i
\(917\) 29.8653 0.986240
\(918\) 12.3925 10.9009i 0.409014 0.359783i
\(919\) 37.7786 1.24620 0.623101 0.782141i \(-0.285873\pi\)
0.623101 + 0.782141i \(0.285873\pi\)
\(920\) 0 0
\(921\) −2.65576 + 52.6438i −0.0875104 + 1.73467i
\(922\) 29.3592 24.6353i 0.966893 0.811320i
\(923\) −1.54996 8.79027i −0.0510176 0.289335i
\(924\) 7.11435 7.65917i 0.234045 0.251968i
\(925\) 0 0
\(926\) 7.39243 12.8041i 0.242930 0.420768i
\(927\) −39.2247 + 26.6811i −1.28831 + 0.876323i
\(928\) 11.7166 + 20.2937i 0.384615 + 0.666173i
\(929\) −6.00421 + 34.0516i −0.196992 + 1.11720i 0.712562 + 0.701609i \(0.247535\pi\)
−0.909554 + 0.415586i \(0.863576\pi\)
\(930\) 0 0
\(931\) −21.3404 7.76726i −0.699403 0.254562i
\(932\) 13.3520 + 4.85972i 0.437358 + 0.159185i
\(933\) −14.6265 19.3312i −0.478849 0.632877i
\(934\) −3.21005 + 18.2051i −0.105036 + 0.595688i
\(935\) 0 0
\(936\) 3.90735 + 1.88687i 0.127716 + 0.0616741i
\(937\) −9.71839 + 16.8328i −0.317486 + 0.549902i −0.979963 0.199180i \(-0.936172\pi\)
0.662477 + 0.749082i \(0.269505\pi\)
\(938\) −9.50812 7.97826i −0.310451 0.260499i
\(939\) 26.0363 28.0302i 0.849663 0.914731i
\(940\) 0 0
\(941\) 7.61330 6.38832i 0.248187 0.208253i −0.510204 0.860053i \(-0.670430\pi\)
0.758391 + 0.651800i \(0.225986\pi\)
\(942\) −0.0528003 + 1.04663i −0.00172033 + 0.0341011i
\(943\) −9.83716 + 3.58043i −0.320342 + 0.116595i
\(944\) 55.9572 1.82125
\(945\) 0 0
\(946\) −15.8152 −0.514195
\(947\) 15.8909 5.78380i 0.516384 0.187948i −0.0706647 0.997500i \(-0.522512\pi\)
0.587048 + 0.809552i \(0.300290\pi\)
\(948\) 15.7208 8.04890i 0.510588 0.261416i
\(949\) −5.54899 + 4.65616i −0.180128 + 0.151145i
\(950\) 0 0
\(951\) 8.86198 + 28.7849i 0.287369 + 0.933413i
\(952\) −11.1712 9.37379i −0.362062 0.303806i
\(953\) 8.67866 15.0319i 0.281129 0.486930i −0.690534 0.723300i \(-0.742624\pi\)
0.971663 + 0.236370i \(0.0759577\pi\)
\(954\) −10.0060 10.2808i −0.323958 0.332854i
\(955\) 0 0
\(956\) −0.220091 + 1.24820i −0.00711825 + 0.0403696i
\(957\) 6.70327 15.8782i 0.216686 0.513268i
\(958\) 40.5824 + 14.7708i 1.31116 + 0.477222i
\(959\) 57.4872 + 20.9236i 1.85636 + 0.675659i
\(960\) 0 0
\(961\) −5.07101 + 28.7591i −0.163581 + 0.927714i
\(962\) −2.09104 3.62179i −0.0674179 0.116771i
\(963\) 20.3468 + 45.2230i 0.655667 + 1.45729i
\(964\) 2.27898 3.94730i 0.0734009 0.127134i
\(965\) 0 0
\(966\) −64.6515 14.7929i −2.08013 0.475955i
\(967\) 2.91440 + 16.5284i 0.0937207 + 0.531517i 0.995132 + 0.0985525i \(0.0314212\pi\)
−0.901411 + 0.432964i \(0.857468\pi\)
\(968\) −11.3451 + 9.51963i −0.364644 + 0.305973i
\(969\) 7.53850 + 4.87464i 0.242172 + 0.156596i
\(970\) 0 0
\(971\) −33.4811 −1.07446 −0.537230 0.843436i \(-0.680529\pi\)
−0.537230 + 0.843436i \(0.680529\pi\)
\(972\) 7.27725 10.6123i 0.233418 0.340389i
\(973\) 33.8393 1.08484
\(974\) 47.9865 17.4657i 1.53759 0.559636i
\(975\) 0 0
\(976\) −19.9134 + 16.7093i −0.637413 + 0.534853i
\(977\) −3.94786 22.3894i −0.126303 0.716302i −0.980525 0.196393i \(-0.937077\pi\)
0.854222 0.519909i \(-0.174034\pi\)
\(978\) 41.4887 + 9.49303i 1.32666 + 0.303554i
\(979\) 8.20843 + 6.88769i 0.262342 + 0.220131i
\(980\) 0 0
\(981\) −5.80800 12.9089i −0.185435 0.412150i
\(982\) 7.31892 + 12.6767i 0.233556 + 0.404531i
\(983\) −8.18917 + 46.4431i −0.261194 + 1.48131i 0.518464 + 0.855100i \(0.326504\pi\)
−0.779658 + 0.626206i \(0.784607\pi\)
\(984\) −6.09542 + 0.760522i −0.194315 + 0.0242445i
\(985\) 0 0
\(986\) 15.8788 + 5.77940i 0.505683 + 0.184054i
\(987\) −4.49936 + 10.6577i −0.143216 + 0.339238i
\(988\) 0.288030 1.63350i 0.00916346 0.0519686i
\(989\) 14.6571 + 25.3869i 0.466069 + 0.807255i
\(990\) 0 0
\(991\) 2.18837 3.79036i 0.0695158 0.120405i −0.829172 0.558993i \(-0.811188\pi\)
0.898688 + 0.438588i \(0.144521\pi\)
\(992\) 4.52353 + 3.79569i 0.143622 + 0.120513i
\(993\) −0.440404 1.43049i −0.0139758 0.0453952i
\(994\) 13.9014 + 78.8386i 0.440925 + 2.50061i
\(995\) 0 0
\(996\) 14.8685 7.61253i 0.471127 0.241212i
\(997\) −2.01517 + 0.733462i −0.0638211 + 0.0232290i −0.373733 0.927536i \(-0.621923\pi\)
0.309912 + 0.950765i \(0.399700\pi\)
\(998\) −19.5582 −0.619104
\(999\) 16.4373 6.42052i 0.520052 0.203136i
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 675.2.l.c.601.2 12
5.2 odd 4 675.2.u.b.574.4 24
5.3 odd 4 675.2.u.b.574.1 24
5.4 even 2 27.2.e.a.7.1 yes 12
15.14 odd 2 81.2.e.a.19.2 12
20.19 odd 2 432.2.u.c.385.1 12
27.4 even 9 inner 675.2.l.c.301.2 12
45.4 even 6 243.2.e.c.217.2 12
45.14 odd 6 243.2.e.b.217.1 12
45.29 odd 6 243.2.e.a.136.1 12
45.34 even 6 243.2.e.d.136.2 12
135.4 even 18 27.2.e.a.4.1 12
135.14 odd 18 243.2.e.a.109.1 12
135.29 odd 18 729.2.a.d.1.1 6
135.34 even 18 729.2.c.e.487.1 12
135.49 even 18 243.2.e.c.28.2 12
135.58 odd 36 675.2.u.b.274.4 24
135.59 odd 18 243.2.e.b.28.1 12
135.74 odd 18 729.2.c.b.487.6 12
135.79 even 18 729.2.a.a.1.6 6
135.94 even 18 243.2.e.d.109.2 12
135.104 odd 18 81.2.e.a.64.2 12
135.112 odd 36 675.2.u.b.274.1 24
135.119 odd 18 729.2.c.b.244.6 12
135.124 even 18 729.2.c.e.244.1 12
540.139 odd 18 432.2.u.c.193.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.4.1 12 135.4 even 18
27.2.e.a.7.1 yes 12 5.4 even 2
81.2.e.a.19.2 12 15.14 odd 2
81.2.e.a.64.2 12 135.104 odd 18
243.2.e.a.109.1 12 135.14 odd 18
243.2.e.a.136.1 12 45.29 odd 6
243.2.e.b.28.1 12 135.59 odd 18
243.2.e.b.217.1 12 45.14 odd 6
243.2.e.c.28.2 12 135.49 even 18
243.2.e.c.217.2 12 45.4 even 6
243.2.e.d.109.2 12 135.94 even 18
243.2.e.d.136.2 12 45.34 even 6
432.2.u.c.193.1 12 540.139 odd 18
432.2.u.c.385.1 12 20.19 odd 2
675.2.l.c.301.2 12 27.4 even 9 inner
675.2.l.c.601.2 12 1.1 even 1 trivial
675.2.u.b.274.1 24 135.112 odd 36
675.2.u.b.274.4 24 135.58 odd 36
675.2.u.b.574.1 24 5.3 odd 4
675.2.u.b.574.4 24 5.2 odd 4
729.2.a.a.1.6 6 135.79 even 18
729.2.a.d.1.1 6 135.29 odd 18
729.2.c.b.244.6 12 135.119 odd 18
729.2.c.b.487.6 12 135.74 odd 18
729.2.c.e.244.1 12 135.124 even 18
729.2.c.e.487.1 12 135.34 even 18