Properties

Label 441.2.s.b.362.1
Level $441$
Weight $2$
Character 441.362
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
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] = [441,2,Mod(362,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.s (of order \(6\), degree \(2\), not 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 362.1
Root \(1.07065 - 1.85442i\) of defining polynomial
Character \(\chi\) \(=\) 441.362
Dual form 441.2.s.b.374.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.24607 + 1.29677i) q^{2} +(-1.61958 + 0.613974i) q^{3} +(2.36322 - 4.09323i) q^{4} -1.25299 q^{5} +(2.84151 - 3.47925i) q^{6} +7.07116i q^{8} +(2.24607 - 1.98876i) q^{9} +O(q^{10})\) \(q+(-2.24607 + 1.29677i) q^{2} +(-1.61958 + 0.613974i) q^{3} +(2.36322 - 4.09323i) q^{4} -1.25299 q^{5} +(2.84151 - 3.47925i) q^{6} +7.07116i q^{8} +(2.24607 - 1.98876i) q^{9} +(2.81429 - 1.62483i) q^{10} -0.616756i q^{11} +(-1.31429 + 8.08026i) q^{12} +(1.06343 - 0.613974i) q^{13} +(2.02931 - 0.769301i) q^{15} +(-4.44321 - 7.69587i) q^{16} +(2.21501 + 3.83652i) q^{17} +(-2.46587 + 7.37953i) q^{18} +(1.64679 + 0.950775i) q^{19} +(-2.96109 + 5.12875i) q^{20} +(0.799790 + 1.38528i) q^{22} +4.74890i q^{23} +(-4.34151 - 11.4523i) q^{24} -3.43003 q^{25} +(-1.59237 + 2.75806i) q^{26} +(-2.41664 + 4.59998i) q^{27} +(-5.07629 - 2.93080i) q^{29} +(-3.56037 + 4.35945i) q^{30} +(2.14851 + 1.24044i) q^{31} +(7.71195 + 4.45249i) q^{32} +(0.378672 + 0.998884i) q^{33} +(-9.95016 - 5.74473i) q^{34} +(-2.83247 - 13.8936i) q^{36} +(1.33217 - 2.30738i) q^{37} -4.93175 q^{38} +(-1.34535 + 1.64730i) q^{39} -8.86005i q^{40} +(-2.09966 - 3.63671i) q^{41} +(-2.24637 + 3.89083i) q^{43} +(-2.52452 - 1.45753i) q^{44} +(-2.81429 + 2.49189i) q^{45} +(-6.15823 - 10.6664i) q^{46} +(-3.80738 - 6.59458i) q^{47} +(11.9212 + 9.73605i) q^{48} +(7.70409 - 4.44796i) q^{50} +(-5.94291 - 4.85358i) q^{51} -5.80384i q^{52} +(2.67782 - 1.54604i) q^{53} +(-0.537165 - 13.4657i) q^{54} +0.772786i q^{55} +(-3.25086 - 0.528768i) q^{57} +15.2023 q^{58} +(-1.78229 + 3.08702i) q^{59} +(1.64679 - 10.1244i) q^{60} +(-12.5136 + 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(-1.33247 + 0.769301i) q^{65} +(-2.14585 - 1.75252i) q^{66} +(-6.80644 + 11.7891i) q^{67} +20.9383 q^{68} +(-2.91570 - 7.69121i) q^{69} +10.4095i q^{71} +(14.0628 + 15.8823i) q^{72} +(-9.95016 + 5.74473i) q^{73} +6.91006i q^{74} +(5.55520 - 2.10595i) q^{75} +(7.78348 - 4.49379i) q^{76} +(0.885586 - 5.44457i) q^{78} +(2.01592 + 3.49168i) q^{79} +(5.56728 + 9.64281i) q^{80} +(1.08967 - 8.93379i) q^{81} +(9.43196 + 5.44554i) q^{82} +(-4.36775 + 7.56516i) q^{83} +(-2.77538 - 4.80710i) q^{85} -11.6521i q^{86} +(10.0209 + 1.62995i) q^{87} +4.36118 q^{88} +(0.811226 - 1.40508i) q^{89} +(3.08970 - 9.24645i) q^{90} +(19.4383 + 11.2227i) q^{92} +(-4.24128 - 0.689866i) q^{93} +(17.1033 + 9.87459i) q^{94} +(-2.06341 - 1.19131i) q^{95} +(-15.2238 - 2.47623i) q^{96} +(8.76527 + 5.06063i) q^{97} +(-1.22658 - 1.38528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{4} + 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{4} + 12 q^{6} + 15 q^{10} - 6 q^{13} - 3 q^{15} - 6 q^{16} + 12 q^{17} - 18 q^{18} - 3 q^{19} + 3 q^{20} + 5 q^{22} - 27 q^{24} - 14 q^{25} - 3 q^{26} - 27 q^{27} - 15 q^{29} + 9 q^{31} + 48 q^{32} + 9 q^{33} - 3 q^{34} - 18 q^{36} + 6 q^{37} - 36 q^{38} + 12 q^{39} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 15 q^{45} - 13 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} - 24 q^{51} - 9 q^{53} - 27 q^{54} - 36 q^{57} - 16 q^{58} + 18 q^{59} - 3 q^{60} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} + 33 q^{66} - 10 q^{67} + 54 q^{68} + 3 q^{69} + 18 q^{72} - 3 q^{73} + 21 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} + 30 q^{80} - 48 q^{81} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 30 q^{87} + 16 q^{88} - 24 q^{89} - 24 q^{90} + 39 q^{92} + 6 q^{93} + 3 q^{94} - 3 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24607 + 1.29677i −1.58821 + 0.916955i −0.594611 + 0.804014i \(0.702694\pi\)
−0.993602 + 0.112941i \(0.963973\pi\)
\(3\) −1.61958 + 0.613974i −0.935064 + 0.354478i
\(4\) 2.36322 4.09323i 1.18161 2.04661i
\(5\) −1.25299 −0.560352 −0.280176 0.959949i \(-0.590393\pi\)
−0.280176 + 0.959949i \(0.590393\pi\)
\(6\) 2.84151 3.47925i 1.16004 1.42040i
\(7\) 0 0
\(8\) 7.07116i 2.50003i
\(9\) 2.24607 1.98876i 0.748690 0.662920i
\(10\) 2.81429 1.62483i 0.889958 0.513817i
\(11\) 0.616756i 0.185959i −0.995668 0.0929794i \(-0.970361\pi\)
0.995668 0.0929794i \(-0.0296391\pi\)
\(12\) −1.31429 + 8.08026i −0.379404 + 2.33257i
\(13\) 1.06343 0.613974i 0.294944 0.170286i −0.345226 0.938520i \(-0.612198\pi\)
0.640169 + 0.768234i \(0.278864\pi\)
\(14\) 0 0
\(15\) 2.02931 0.769301i 0.523965 0.198633i
\(16\) −4.44321 7.69587i −1.11080 1.92397i
\(17\) 2.21501 + 3.83652i 0.537220 + 0.930492i 0.999052 + 0.0435249i \(0.0138588\pi\)
−0.461833 + 0.886967i \(0.652808\pi\)
\(18\) −2.46587 + 7.37953i −0.581212 + 1.73937i
\(19\) 1.64679 + 0.950775i 0.377800 + 0.218123i 0.676861 0.736111i \(-0.263340\pi\)
−0.299061 + 0.954234i \(0.596673\pi\)
\(20\) −2.96109 + 5.12875i −0.662119 + 1.14682i
\(21\) 0 0
\(22\) 0.799790 + 1.38528i 0.170516 + 0.295342i
\(23\) 4.74890i 0.990213i 0.868832 + 0.495107i \(0.164871\pi\)
−0.868832 + 0.495107i \(0.835129\pi\)
\(24\) −4.34151 11.4523i −0.886206 2.33769i
\(25\) −3.43003 −0.686006
\(26\) −1.59237 + 2.75806i −0.312289 + 0.540900i
\(27\) −2.41664 + 4.59998i −0.465083 + 0.885267i
\(28\) 0 0
\(29\) −5.07629 2.93080i −0.942643 0.544235i −0.0518553 0.998655i \(-0.516513\pi\)
−0.890788 + 0.454419i \(0.849847\pi\)
\(30\) −3.56037 + 4.35945i −0.650031 + 0.795923i
\(31\) 2.14851 + 1.24044i 0.385884 + 0.222790i 0.680375 0.732864i \(-0.261817\pi\)
−0.294491 + 0.955654i \(0.595150\pi\)
\(32\) 7.71195 + 4.45249i 1.36329 + 0.787097i
\(33\) 0.378672 + 0.998884i 0.0659183 + 0.173883i
\(34\) −9.95016 5.74473i −1.70644 0.985213i
\(35\) 0 0
\(36\) −2.83247 13.8936i −0.472078 2.31559i
\(37\) 1.33217 2.30738i 0.219007 0.379331i −0.735498 0.677527i \(-0.763052\pi\)
0.954505 + 0.298196i \(0.0963849\pi\)
\(38\) −4.93175 −0.800035
\(39\) −1.34535 + 1.64730i −0.215429 + 0.263779i
\(40\) 8.86005i 1.40090i
\(41\) −2.09966 3.63671i −0.327911 0.567959i 0.654186 0.756334i \(-0.273011\pi\)
−0.982097 + 0.188375i \(0.939678\pi\)
\(42\) 0 0
\(43\) −2.24637 + 3.89083i −0.342568 + 0.593346i −0.984909 0.173073i \(-0.944630\pi\)
0.642340 + 0.766419i \(0.277964\pi\)
\(44\) −2.52452 1.45753i −0.380586 0.219731i
\(45\) −2.81429 + 2.49189i −0.419530 + 0.371468i
\(46\) −6.15823 10.6664i −0.907981 1.57267i
\(47\) −3.80738 6.59458i −0.555364 0.961918i −0.997875 0.0651551i \(-0.979246\pi\)
0.442512 0.896763i \(-0.354088\pi\)
\(48\) 11.9212 + 9.73605i 1.72068 + 1.40528i
\(49\) 0 0
\(50\) 7.70409 4.44796i 1.08952 0.629036i
\(51\) −5.94291 4.85358i −0.832174 0.679637i
\(52\) 5.80384i 0.804847i
\(53\) 2.67782 1.54604i 0.367827 0.212365i −0.304682 0.952454i \(-0.598550\pi\)
0.672509 + 0.740089i \(0.265217\pi\)
\(54\) −0.537165 13.4657i −0.0730990 1.83245i
\(55\) 0.772786i 0.104202i
\(56\) 0 0
\(57\) −3.25086 0.528768i −0.430587 0.0700371i
\(58\) 15.2023 1.99616
\(59\) −1.78229 + 3.08702i −0.232035 + 0.401896i −0.958407 0.285406i \(-0.907872\pi\)
0.726372 + 0.687302i \(0.241205\pi\)
\(60\) 1.64679 10.1244i 0.212600 1.30706i
\(61\) −12.5136 + 7.22473i −1.60220 + 0.925032i −0.611156 + 0.791510i \(0.709295\pi\)
−0.991046 + 0.133521i \(0.957372\pi\)
\(62\) −6.43428 −0.817154
\(63\) 0 0
\(64\) −5.32259 −0.665324
\(65\) −1.33247 + 0.769301i −0.165272 + 0.0954200i
\(66\) −2.14585 1.75252i −0.264136 0.215720i
\(67\) −6.80644 + 11.7891i −0.831539 + 1.44027i 0.0652791 + 0.997867i \(0.479206\pi\)
−0.896818 + 0.442400i \(0.854127\pi\)
\(68\) 20.9383 2.53914
\(69\) −2.91570 7.69121i −0.351009 0.925913i
\(70\) 0 0
\(71\) 10.4095i 1.23538i 0.786420 + 0.617692i \(0.211932\pi\)
−0.786420 + 0.617692i \(0.788068\pi\)
\(72\) 14.0628 + 15.8823i 1.65732 + 1.87175i
\(73\) −9.95016 + 5.74473i −1.16458 + 0.672369i −0.952397 0.304861i \(-0.901390\pi\)
−0.212181 + 0.977230i \(0.568057\pi\)
\(74\) 6.91006i 0.803278i
\(75\) 5.55520 2.10595i 0.641459 0.243174i
\(76\) 7.78348 4.49379i 0.892826 0.515473i
\(77\) 0 0
\(78\) 0.885586 5.44457i 0.100273 0.616476i
\(79\) 2.01592 + 3.49168i 0.226809 + 0.392845i 0.956861 0.290547i \(-0.0938373\pi\)
−0.730052 + 0.683392i \(0.760504\pi\)
\(80\) 5.56728 + 9.64281i 0.622441 + 1.07810i
\(81\) 1.08967 8.93379i 0.121075 0.992643i
\(82\) 9.43196 + 5.44554i 1.04159 + 0.601360i
\(83\) −4.36775 + 7.56516i −0.479422 + 0.830384i −0.999721 0.0236001i \(-0.992487\pi\)
0.520299 + 0.853984i \(0.325820\pi\)
\(84\) 0 0
\(85\) −2.77538 4.80710i −0.301032 0.521403i
\(86\) 11.6521i 1.25648i
\(87\) 10.0209 + 1.62995i 1.07435 + 0.174749i
\(88\) 4.36118 0.464903
\(89\) 0.811226 1.40508i 0.0859897 0.148939i −0.819823 0.572617i \(-0.805928\pi\)
0.905813 + 0.423679i \(0.139261\pi\)
\(90\) 3.08970 9.24645i 0.325683 0.974661i
\(91\) 0 0
\(92\) 19.4383 + 11.2227i 2.02658 + 1.17005i
\(93\) −4.24128 0.689866i −0.439801 0.0715357i
\(94\) 17.1033 + 9.87459i 1.76407 + 1.01849i
\(95\) −2.06341 1.19131i −0.211701 0.122226i
\(96\) −15.2238 2.47623i −1.55377 0.252729i
\(97\) 8.76527 + 5.06063i 0.889979 + 0.513829i 0.873936 0.486042i \(-0.161560\pi\)
0.0160431 + 0.999871i \(0.494893\pi\)
\(98\) 0 0
\(99\) −1.22658 1.38528i −0.123276 0.139226i
\(100\) −8.10593 + 14.0399i −0.810593 + 1.40399i
\(101\) 1.71322 0.170472 0.0852360 0.996361i \(-0.472836\pi\)
0.0852360 + 0.996361i \(0.472836\pi\)
\(102\) 19.6422 + 3.19490i 1.94487 + 0.316342i
\(103\) 7.40526i 0.729662i 0.931074 + 0.364831i \(0.118873\pi\)
−0.931074 + 0.364831i \(0.881127\pi\)
\(104\) 4.34151 + 7.51971i 0.425720 + 0.737368i
\(105\) 0 0
\(106\) −4.00972 + 6.94503i −0.389458 + 0.674561i
\(107\) −0.131657 0.0760123i −0.0127278 0.00734839i 0.493623 0.869676i \(-0.335672\pi\)
−0.506350 + 0.862328i \(0.669006\pi\)
\(108\) 13.1177 + 20.7627i 1.26225 + 1.99789i
\(109\) 2.70051 + 4.67742i 0.258662 + 0.448016i 0.965884 0.258976i \(-0.0833851\pi\)
−0.707222 + 0.706992i \(0.750052\pi\)
\(110\) −1.00213 1.73573i −0.0955489 0.165496i
\(111\) −0.740877 + 4.55490i −0.0703210 + 0.432332i
\(112\) 0 0
\(113\) −5.60391 + 3.23542i −0.527171 + 0.304362i −0.739864 0.672757i \(-0.765110\pi\)
0.212693 + 0.977119i \(0.431777\pi\)
\(114\) 7.98735 3.02797i 0.748084 0.283595i
\(115\) 5.95030i 0.554868i
\(116\) −23.9928 + 13.8523i −2.22768 + 1.28615i
\(117\) 1.16750 3.49394i 0.107936 0.323015i
\(118\) 9.24490i 0.851062i
\(119\) 0 0
\(120\) 5.43984 + 14.3496i 0.496588 + 1.30993i
\(121\) 10.6196 0.965419
\(122\) 18.7376 32.4545i 1.69642 2.93829i
\(123\) 5.63341 + 4.60081i 0.507947 + 0.414841i
\(124\) 10.1548 5.86289i 0.911930 0.526503i
\(125\) 10.5627 0.944757
\(126\) 0 0
\(127\) −2.93175 −0.260151 −0.130075 0.991504i \(-0.541522\pi\)
−0.130075 + 0.991504i \(0.541522\pi\)
\(128\) −3.46897 + 2.00281i −0.306617 + 0.177025i
\(129\) 1.24931 7.68072i 0.109995 0.676250i
\(130\) 1.99521 3.45581i 0.174992 0.303094i
\(131\) −16.2276 −1.41782 −0.708908 0.705301i \(-0.750812\pi\)
−0.708908 + 0.705301i \(0.750812\pi\)
\(132\) 4.98355 + 0.810598i 0.433762 + 0.0705535i
\(133\) 0 0
\(134\) 35.3055i 3.04993i
\(135\) 3.02802 5.76371i 0.260610 0.496061i
\(136\) −27.1286 + 15.6627i −2.32626 + 1.34307i
\(137\) 17.4026i 1.48680i −0.668845 0.743402i \(-0.733211\pi\)
0.668845 0.743402i \(-0.266789\pi\)
\(138\) 16.5226 + 13.4940i 1.40650 + 1.14869i
\(139\) −5.45273 + 3.14813i −0.462494 + 0.267021i −0.713092 0.701070i \(-0.752706\pi\)
0.250598 + 0.968091i \(0.419373\pi\)
\(140\) 0 0
\(141\) 10.2153 + 8.34280i 0.860279 + 0.702591i
\(142\) −13.4988 23.3805i −1.13279 1.96205i
\(143\) −0.378672 0.655879i −0.0316661 0.0548474i
\(144\) −25.2850 8.44899i −2.10708 0.704083i
\(145\) 6.36052 + 3.67225i 0.528212 + 0.304963i
\(146\) 14.8992 25.8061i 1.23306 2.13573i
\(147\) 0 0
\(148\) −6.29642 10.9057i −0.517563 0.896445i
\(149\) 10.6269i 0.870592i 0.900287 + 0.435296i \(0.143356\pi\)
−0.900287 + 0.435296i \(0.856644\pi\)
\(150\) −9.74645 + 11.9339i −0.795794 + 0.974401i
\(151\) 9.48930 0.772229 0.386114 0.922451i \(-0.373817\pi\)
0.386114 + 0.922451i \(0.373817\pi\)
\(152\) −6.72308 + 11.6447i −0.545314 + 0.944511i
\(153\) 12.6050 + 4.21196i 1.01905 + 0.340517i
\(154\) 0 0
\(155\) −2.69205 1.55426i −0.216231 0.124841i
\(156\) 3.56341 + 9.39977i 0.285301 + 0.752584i
\(157\) −20.6214 11.9058i −1.64577 0.950185i −0.978728 0.205163i \(-0.934228\pi\)
−0.667040 0.745022i \(-0.732439\pi\)
\(158\) −9.05582 5.22838i −0.720442 0.415947i
\(159\) −3.38771 + 4.14805i −0.268663 + 0.328961i
\(160\) −9.66295 5.57891i −0.763924 0.441051i
\(161\) 0 0
\(162\) 9.13759 + 21.4790i 0.717916 + 1.68755i
\(163\) −4.41101 + 7.64009i −0.345497 + 0.598418i −0.985444 0.170001i \(-0.945623\pi\)
0.639947 + 0.768419i \(0.278956\pi\)
\(164\) −19.8478 −1.54986
\(165\) −0.474470 1.25159i −0.0369375 0.0974360i
\(166\) 22.6558i 1.75843i
\(167\) 11.0335 + 19.1106i 0.853800 + 1.47883i 0.877754 + 0.479112i \(0.159041\pi\)
−0.0239535 + 0.999713i \(0.507625\pi\)
\(168\) 0 0
\(169\) −5.74607 + 9.95249i −0.442005 + 0.765576i
\(170\) 12.4674 + 7.19806i 0.956206 + 0.552066i
\(171\) 5.58967 1.13956i 0.427453 0.0871445i
\(172\) 10.6174 + 18.3898i 0.809566 + 1.40221i
\(173\) −2.03375 3.52256i −0.154623 0.267815i 0.778299 0.627894i \(-0.216083\pi\)
−0.932922 + 0.360079i \(0.882750\pi\)
\(174\) −24.6213 + 9.33381i −1.86653 + 0.707594i
\(175\) 0 0
\(176\) −4.74647 + 2.74038i −0.357779 + 0.206564i
\(177\) 0.991213 6.09396i 0.0745041 0.458050i
\(178\) 4.20789i 0.315395i
\(179\) 7.20787 4.16146i 0.538741 0.311042i −0.205827 0.978588i \(-0.565989\pi\)
0.744569 + 0.667546i \(0.232655\pi\)
\(180\) 3.54904 + 17.4084i 0.264530 + 1.29755i
\(181\) 12.6701i 0.941763i −0.882196 0.470881i \(-0.843936\pi\)
0.882196 0.470881i \(-0.156064\pi\)
\(182\) 0 0
\(183\) 15.8310 19.3840i 1.17026 1.43291i
\(184\) −33.5802 −2.47556
\(185\) −1.66919 + 2.89111i −0.122721 + 0.212559i
\(186\) 10.4208 3.95048i 0.764092 0.289663i
\(187\) 2.36619 1.36612i 0.173033 0.0999008i
\(188\) −35.9908 −2.62490
\(189\) 0 0
\(190\) 6.17941 0.448301
\(191\) −3.29133 + 1.90025i −0.238152 + 0.137497i −0.614327 0.789051i \(-0.710573\pi\)
0.376175 + 0.926549i \(0.377239\pi\)
\(192\) 8.62036 3.26793i 0.622121 0.235843i
\(193\) −3.39448 + 5.87942i −0.244340 + 0.423210i −0.961946 0.273240i \(-0.911905\pi\)
0.717606 + 0.696450i \(0.245238\pi\)
\(194\) −26.2499 −1.88463
\(195\) 1.68571 2.06404i 0.120716 0.147809i
\(196\) 0 0
\(197\) 6.41453i 0.457017i −0.973542 0.228508i \(-0.926615\pi\)
0.973542 0.228508i \(-0.0733848\pi\)
\(198\) 4.55137 + 1.52084i 0.323452 + 0.108082i
\(199\) 13.8921 8.02063i 0.984788 0.568568i 0.0810756 0.996708i \(-0.474164\pi\)
0.903712 + 0.428140i \(0.140831\pi\)
\(200\) 24.2543i 1.71504i
\(201\) 3.78536 23.2723i 0.266999 1.64150i
\(202\) −3.84802 + 2.22166i −0.270746 + 0.156315i
\(203\) 0 0
\(204\) −33.9112 + 12.8556i −2.37426 + 0.900070i
\(205\) 2.63084 + 4.55675i 0.183746 + 0.318257i
\(206\) −9.60292 16.6327i −0.669067 1.15886i
\(207\) 9.44441 + 10.6664i 0.656432 + 0.741363i
\(208\) −9.45013 5.45604i −0.655249 0.378308i
\(209\) 0.586396 1.01567i 0.0405619 0.0702552i
\(210\) 0 0
\(211\) −4.06070 7.03333i −0.279550 0.484194i 0.691723 0.722163i \(-0.256852\pi\)
−0.971273 + 0.237968i \(0.923519\pi\)
\(212\) 14.6146i 1.00373i
\(213\) −6.39118 16.8590i −0.437916 1.15516i
\(214\) 0.394282 0.0269526
\(215\) 2.81467 4.87515i 0.191959 0.332483i
\(216\) −32.5272 17.0885i −2.21319 1.16272i
\(217\) 0 0
\(218\) −12.1311 7.00388i −0.821620 0.474363i
\(219\) 12.5880 15.4132i 0.850615 1.04153i
\(220\) 3.16319 + 1.82627i 0.213262 + 0.123127i
\(221\) 4.71104 + 2.71992i 0.316899 + 0.182962i
\(222\) −4.24260 11.1914i −0.284744 0.751117i
\(223\) 6.96205 + 4.01954i 0.466213 + 0.269168i 0.714653 0.699479i \(-0.246585\pi\)
−0.248440 + 0.968647i \(0.579918\pi\)
\(224\) 0 0
\(225\) −7.70409 + 6.82150i −0.513606 + 0.454767i
\(226\) 8.39118 14.5340i 0.558173 0.966784i
\(227\) 20.8234 1.38210 0.691048 0.722809i \(-0.257149\pi\)
0.691048 + 0.722809i \(0.257149\pi\)
\(228\) −9.84688 + 12.0569i −0.652126 + 0.798488i
\(229\) 6.01918i 0.397759i −0.980024 0.198879i \(-0.936270\pi\)
0.980024 0.198879i \(-0.0637302\pi\)
\(230\) 7.71617 + 13.3648i 0.508789 + 0.881248i
\(231\) 0 0
\(232\) 20.7241 35.8952i 1.36061 2.35664i
\(233\) −18.2156 10.5168i −1.19335 0.688978i −0.234282 0.972169i \(-0.575274\pi\)
−0.959064 + 0.283191i \(0.908607\pi\)
\(234\) 1.90855 + 9.36163i 0.124766 + 0.611989i
\(235\) 4.77059 + 8.26291i 0.311199 + 0.539013i
\(236\) 8.42392 + 14.5907i 0.548350 + 0.949771i
\(237\) −5.40875 4.41733i −0.351336 0.286936i
\(238\) 0 0
\(239\) −7.51079 + 4.33636i −0.485832 + 0.280496i −0.722844 0.691011i \(-0.757165\pi\)
0.237011 + 0.971507i \(0.423832\pi\)
\(240\) −14.9371 12.1991i −0.964185 0.787450i
\(241\) 8.47315i 0.545804i 0.962042 + 0.272902i \(0.0879834\pi\)
−0.962042 + 0.272902i \(0.912017\pi\)
\(242\) −23.8524 + 13.7712i −1.53329 + 0.885246i
\(243\) 3.72030 + 15.1380i 0.238658 + 0.971104i
\(244\) 68.2946i 4.37211i
\(245\) 0 0
\(246\) −18.6192 3.02851i −1.18712 0.193091i
\(247\) 2.33501 0.148573
\(248\) −8.77137 + 15.1925i −0.556982 + 0.964722i
\(249\) 2.42910 14.9341i 0.153938 0.946407i
\(250\) −23.7246 + 13.6974i −1.50047 + 0.866299i
\(251\) −23.4435 −1.47974 −0.739871 0.672749i \(-0.765113\pi\)
−0.739871 + 0.672749i \(0.765113\pi\)
\(252\) 0 0
\(253\) 2.92891 0.184139
\(254\) 6.58492 3.80180i 0.413174 0.238546i
\(255\) 7.44638 + 6.08146i 0.466310 + 0.380836i
\(256\) 10.5170 18.2159i 0.657310 1.13849i
\(257\) 24.5170 1.52933 0.764665 0.644428i \(-0.222904\pi\)
0.764665 + 0.644428i \(0.222904\pi\)
\(258\) 7.15409 + 18.8715i 0.445394 + 1.17489i
\(259\) 0 0
\(260\) 7.27212i 0.450998i
\(261\) −17.2304 + 3.51274i −1.06653 + 0.217433i
\(262\) 36.4484 21.0435i 2.25179 1.30007i
\(263\) 10.5544i 0.650811i 0.945575 + 0.325406i \(0.105501\pi\)
−0.945575 + 0.325406i \(0.894499\pi\)
\(264\) −7.06327 + 2.67765i −0.434714 + 0.164798i
\(265\) −3.35527 + 1.93716i −0.206112 + 0.118999i
\(266\) 0 0
\(267\) −0.451159 + 2.77372i −0.0276105 + 0.169749i
\(268\) 32.1703 + 55.7206i 1.96511 + 3.40367i
\(269\) −1.14451 1.98235i −0.0697821 0.120866i 0.829023 0.559214i \(-0.188897\pi\)
−0.898805 + 0.438348i \(0.855564\pi\)
\(270\) 0.673060 + 16.8723i 0.0409611 + 1.02682i
\(271\) 20.9239 + 12.0804i 1.27103 + 0.733831i 0.975182 0.221403i \(-0.0710635\pi\)
0.295851 + 0.955234i \(0.404397\pi\)
\(272\) 19.6836 34.0929i 1.19349 2.06719i
\(273\) 0 0
\(274\) 22.5672 + 39.0875i 1.36333 + 2.36136i
\(275\) 2.11549i 0.127569i
\(276\) −38.3723 6.24145i −2.30974 0.375691i
\(277\) −11.3710 −0.683219 −0.341609 0.939842i \(-0.610972\pi\)
−0.341609 + 0.939842i \(0.610972\pi\)
\(278\) 8.16481 14.1419i 0.489693 0.848173i
\(279\) 7.29265 1.48675i 0.436600 0.0890092i
\(280\) 0 0
\(281\) 17.6382 + 10.1834i 1.05221 + 0.607492i 0.923267 0.384160i \(-0.125509\pi\)
0.128941 + 0.991652i \(0.458842\pi\)
\(282\) −33.7629 5.49170i −2.01055 0.327026i
\(283\) −10.5318 6.08055i −0.626052 0.361451i 0.153169 0.988200i \(-0.451052\pi\)
−0.779222 + 0.626749i \(0.784385\pi\)
\(284\) 42.6085 + 24.6000i 2.52835 + 1.45974i
\(285\) 4.07328 + 0.662539i 0.241280 + 0.0392454i
\(286\) 1.70105 + 0.982101i 0.100585 + 0.0580729i
\(287\) 0 0
\(288\) 26.1765 5.33658i 1.54247 0.314461i
\(289\) −1.31257 + 2.27345i −0.0772103 + 0.133732i
\(290\) −19.0482 −1.11855
\(291\) −17.3031 2.81444i −1.01433 0.164986i
\(292\) 54.3043i 3.17792i
\(293\) −13.4674 23.3262i −0.786773 1.36273i −0.927934 0.372745i \(-0.878417\pi\)
0.141161 0.989987i \(-0.454917\pi\)
\(294\) 0 0
\(295\) 2.23319 3.86799i 0.130021 0.225203i
\(296\) 16.3159 + 9.41996i 0.948340 + 0.547524i
\(297\) 2.83707 + 1.49048i 0.164623 + 0.0864863i
\(298\) −13.7807 23.8688i −0.798293 1.38268i
\(299\) 2.91570 + 5.05014i 0.168619 + 0.292057i
\(300\) 4.50807 27.7155i 0.260273 1.60016i
\(301\) 0 0
\(302\) −21.3137 + 12.3054i −1.22646 + 0.708099i
\(303\) −2.77470 + 1.05187i −0.159402 + 0.0604286i
\(304\) 16.8980i 0.969166i
\(305\) 15.6793 9.05248i 0.897797 0.518343i
\(306\) −33.7736 + 6.88540i −1.93071 + 0.393612i
\(307\) 21.3700i 1.21965i −0.792536 0.609825i \(-0.791240\pi\)
0.792536 0.609825i \(-0.208760\pi\)
\(308\) 0 0
\(309\) −4.54664 11.9934i −0.258649 0.682281i
\(310\) 8.06206 0.457894
\(311\) −8.11558 + 14.0566i −0.460192 + 0.797076i −0.998970 0.0453714i \(-0.985553\pi\)
0.538778 + 0.842448i \(0.318886\pi\)
\(312\) −11.6483 9.51319i −0.659456 0.538578i
\(313\) −12.1941 + 7.04027i −0.689252 + 0.397940i −0.803332 0.595532i \(-0.796941\pi\)
0.114080 + 0.993472i \(0.463608\pi\)
\(314\) 61.7562 3.48511
\(315\) 0 0
\(316\) 19.0563 1.07200
\(317\) 17.5776 10.1484i 0.987254 0.569991i 0.0828017 0.996566i \(-0.473613\pi\)
0.904452 + 0.426575i \(0.140280\pi\)
\(318\) 2.22998 13.7099i 0.125051 0.768812i
\(319\) −1.80759 + 3.13083i −0.101205 + 0.175293i
\(320\) 6.66913 0.372816
\(321\) 0.259899 + 0.0422738i 0.0145061 + 0.00235950i
\(322\) 0 0
\(323\) 8.42392i 0.468720i
\(324\) −33.9929 25.5728i −1.88849 1.42071i
\(325\) −3.64761 + 2.10595i −0.202333 + 0.116817i
\(326\) 22.8802i 1.26722i
\(327\) −7.24550 5.91741i −0.400677 0.327233i
\(328\) 25.7158 14.8470i 1.41991 0.819788i
\(329\) 0 0
\(330\) 2.68872 + 2.19588i 0.148009 + 0.120879i
\(331\) −13.2341 22.9221i −0.727411 1.25991i −0.957974 0.286856i \(-0.907390\pi\)
0.230563 0.973057i \(-0.425943\pi\)
\(332\) 20.6439 + 35.7563i 1.13298 + 1.96238i
\(333\) −1.59668 7.83190i −0.0874977 0.429186i
\(334\) −49.5642 28.6159i −2.71203 1.56579i
\(335\) 8.52836 14.7716i 0.465954 0.807057i
\(336\) 0 0
\(337\) −1.73659 3.00785i −0.0945979 0.163848i 0.814843 0.579682i \(-0.196823\pi\)
−0.909441 + 0.415834i \(0.863490\pi\)
\(338\) 29.8053i 1.62120i
\(339\) 7.08951 8.68067i 0.385049 0.471469i
\(340\) −26.2354 −1.42281
\(341\) 0.765051 1.32511i 0.0414298 0.0717585i
\(342\) −11.0771 + 9.80806i −0.598979 + 0.530359i
\(343\) 0 0
\(344\) −27.5127 15.8844i −1.48338 0.856432i
\(345\) 3.65333 + 9.63698i 0.196689 + 0.518837i
\(346\) 9.13589 + 5.27461i 0.491149 + 0.283565i
\(347\) 8.14765 + 4.70405i 0.437389 + 0.252527i 0.702489 0.711694i \(-0.252072\pi\)
−0.265101 + 0.964221i \(0.585405\pi\)
\(348\) 30.3533 37.1658i 1.62711 1.99230i
\(349\) 12.3253 + 7.11603i 0.659759 + 0.380912i 0.792185 0.610281i \(-0.208943\pi\)
−0.132426 + 0.991193i \(0.542277\pi\)
\(350\) 0 0
\(351\) 0.254329 + 6.37554i 0.0135751 + 0.340301i
\(352\) 2.74610 4.75639i 0.146368 0.253516i
\(353\) −17.1652 −0.913614 −0.456807 0.889566i \(-0.651007\pi\)
−0.456807 + 0.889566i \(0.651007\pi\)
\(354\) 5.67613 + 14.9728i 0.301683 + 0.795798i
\(355\) 13.0430i 0.692250i
\(356\) −3.83422 6.64106i −0.203213 0.351975i
\(357\) 0 0
\(358\) −10.7929 + 18.6939i −0.570424 + 0.988003i
\(359\) 24.4705 + 14.1281i 1.29150 + 0.745650i 0.978921 0.204241i \(-0.0654725\pi\)
0.312583 + 0.949890i \(0.398806\pi\)
\(360\) −17.6205 19.9003i −0.928682 1.04884i
\(361\) −7.69205 13.3230i −0.404845 0.701212i
\(362\) 16.4302 + 28.4580i 0.863554 + 1.49572i
\(363\) −17.1993 + 6.52017i −0.902729 + 0.342220i
\(364\) 0 0
\(365\) 12.4674 7.19806i 0.652574 0.376764i
\(366\) −10.4208 + 64.0670i −0.544705 + 3.34884i
\(367\) 23.0704i 1.20427i 0.798396 + 0.602133i \(0.205682\pi\)
−0.798396 + 0.602133i \(0.794318\pi\)
\(368\) 36.5469 21.1004i 1.90514 1.09993i
\(369\) −11.9485 3.99260i −0.622015 0.207847i
\(370\) 8.65820i 0.450118i
\(371\) 0 0
\(372\) −12.8469 + 15.7302i −0.666080 + 0.815574i
\(373\) −13.8727 −0.718301 −0.359150 0.933280i \(-0.616933\pi\)
−0.359150 + 0.933280i \(0.616933\pi\)
\(374\) −3.54309 + 6.13682i −0.183209 + 0.317327i
\(375\) −17.1071 + 6.48523i −0.883408 + 0.334896i
\(376\) 46.6313 26.9226i 2.40482 1.38843i
\(377\) −7.19773 −0.370702
\(378\) 0 0
\(379\) 22.7814 1.17020 0.585101 0.810961i \(-0.301055\pi\)
0.585101 + 0.810961i \(0.301055\pi\)
\(380\) −9.75258 + 5.63065i −0.500297 + 0.288846i
\(381\) 4.74820 1.80002i 0.243257 0.0922177i
\(382\) 4.92838 8.53620i 0.252158 0.436750i
\(383\) 15.2320 0.778317 0.389158 0.921171i \(-0.372766\pi\)
0.389158 + 0.921171i \(0.372766\pi\)
\(384\) 4.38860 5.37357i 0.223955 0.274219i
\(385\) 0 0
\(386\) 17.6075i 0.896196i
\(387\) 2.69241 + 13.2066i 0.136863 + 0.671328i
\(388\) 41.4286 23.9188i 2.10322 1.21429i
\(389\) 14.1479i 0.717328i 0.933467 + 0.358664i \(0.116768\pi\)
−0.933467 + 0.358664i \(0.883232\pi\)
\(390\) −1.10963 + 6.82196i −0.0561881 + 0.345443i
\(391\) −18.2192 + 10.5189i −0.921386 + 0.531962i
\(392\) 0 0
\(393\) 26.2819 9.96335i 1.32575 0.502584i
\(394\) 8.31817 + 14.4075i 0.419063 + 0.725839i
\(395\) −2.52592 4.37503i −0.127093 0.220131i
\(396\) −8.56893 + 1.74694i −0.430605 + 0.0877871i
\(397\) −8.40688 4.85371i −0.421929 0.243601i 0.273973 0.961737i \(-0.411662\pi\)
−0.695902 + 0.718136i \(0.744995\pi\)
\(398\) −20.8018 + 36.0298i −1.04270 + 1.80601i
\(399\) 0 0
\(400\) 15.2403 + 26.3970i 0.762017 + 1.31985i
\(401\) 8.73133i 0.436022i 0.975946 + 0.218011i \(0.0699569\pi\)
−0.975946 + 0.218011i \(0.930043\pi\)
\(402\) 21.6767 + 57.1801i 1.08113 + 2.85188i
\(403\) 3.04640 0.151752
\(404\) 4.04873 7.01261i 0.201432 0.348890i
\(405\) −1.36535 + 11.1939i −0.0678446 + 0.556230i
\(406\) 0 0
\(407\) −1.42309 0.821622i −0.0705400 0.0407263i
\(408\) 34.3204 42.0233i 1.69911 2.08046i
\(409\) 12.8967 + 7.44591i 0.637700 + 0.368176i 0.783728 0.621104i \(-0.213316\pi\)
−0.146028 + 0.989280i \(0.546649\pi\)
\(410\) −11.8181 6.82318i −0.583654 0.336973i
\(411\) 10.6847 + 28.1849i 0.527039 + 1.39026i
\(412\) 30.3114 + 17.5003i 1.49334 + 0.862178i
\(413\) 0 0
\(414\) −35.0446 11.7102i −1.72235 0.575524i
\(415\) 5.47272 9.47903i 0.268645 0.465307i
\(416\) 10.9349 0.536126
\(417\) 6.89825 8.44648i 0.337809 0.413626i
\(418\) 3.04168i 0.148774i
\(419\) 2.13859 + 3.70414i 0.104477 + 0.180959i 0.913524 0.406784i \(-0.133350\pi\)
−0.809048 + 0.587743i \(0.800017\pi\)
\(420\) 0 0
\(421\) 5.76681 9.98841i 0.281057 0.486805i −0.690588 0.723248i \(-0.742648\pi\)
0.971645 + 0.236443i \(0.0759816\pi\)
\(422\) 18.2412 + 10.5316i 0.887969 + 0.512669i
\(423\) −21.6667 7.23993i −1.05347 0.352017i
\(424\) 10.9323 + 18.9353i 0.530919 + 0.919578i
\(425\) −7.59756 13.1594i −0.368536 0.638323i
\(426\) 36.2174 + 29.5787i 1.75474 + 1.43309i
\(427\) 0 0
\(428\) −0.622271 + 0.359268i −0.0300786 + 0.0173659i
\(429\) 1.01598 + 0.829753i 0.0490521 + 0.0400609i
\(430\) 14.5999i 0.704071i
\(431\) −14.4497 + 8.34254i −0.696018 + 0.401846i −0.805863 0.592103i \(-0.798298\pi\)
0.109845 + 0.993949i \(0.464965\pi\)
\(432\) 46.1385 1.84053i 2.21984 0.0885524i
\(433\) 12.3503i 0.593516i −0.954953 0.296758i \(-0.904094\pi\)
0.954953 0.296758i \(-0.0959055\pi\)
\(434\) 0 0
\(435\) −12.5560 2.04230i −0.602015 0.0979207i
\(436\) 25.5276 1.22255
\(437\) −4.51513 + 7.82044i −0.215988 + 0.374102i
\(438\) −8.28610 + 50.9428i −0.395925 + 2.43414i
\(439\) 19.1691 11.0673i 0.914892 0.528213i 0.0328902 0.999459i \(-0.489529\pi\)
0.882002 + 0.471246i \(0.156195\pi\)
\(440\) −5.46449 −0.260509
\(441\) 0 0
\(442\) −14.1085 −0.671071
\(443\) −4.22906 + 2.44165i −0.200929 + 0.116006i −0.597089 0.802175i \(-0.703676\pi\)
0.396160 + 0.918182i \(0.370343\pi\)
\(444\) 16.8934 + 13.7968i 0.801724 + 0.654769i
\(445\) −1.01645 + 1.76055i −0.0481845 + 0.0834580i
\(446\) −20.8497 −0.987260
\(447\) −6.52466 17.2111i −0.308606 0.814059i
\(448\) 0 0
\(449\) 12.4409i 0.587121i 0.955941 + 0.293560i \(0.0948401\pi\)
−0.955941 + 0.293560i \(0.905160\pi\)
\(450\) 8.45802 25.3120i 0.398715 1.19322i
\(451\) −2.24296 + 1.29498i −0.105617 + 0.0609780i
\(452\) 30.5841i 1.43855i
\(453\) −15.3687 + 5.82619i −0.722083 + 0.273738i
\(454\) −46.7708 + 27.0031i −2.19506 + 1.26732i
\(455\) 0 0
\(456\) 3.73900 22.9873i 0.175095 1.07648i
\(457\) 5.38774 + 9.33185i 0.252028 + 0.436525i 0.964084 0.265597i \(-0.0855691\pi\)
−0.712056 + 0.702123i \(0.752236\pi\)
\(458\) 7.80549 + 13.5195i 0.364727 + 0.631725i
\(459\) −23.0008 + 0.917533i −1.07359 + 0.0428268i
\(460\) −24.3559 14.0619i −1.13560 0.655639i
\(461\) 0.333303 0.577297i 0.0155235 0.0268874i −0.858159 0.513383i \(-0.828392\pi\)
0.873683 + 0.486496i \(0.161725\pi\)
\(462\) 0 0
\(463\) −20.7892 36.0079i −0.966155 1.67343i −0.706479 0.707734i \(-0.749717\pi\)
−0.259677 0.965696i \(-0.583616\pi\)
\(464\) 52.0886i 2.41815i
\(465\) 5.31426 + 0.864391i 0.246443 + 0.0400852i
\(466\) 54.5515 2.52705
\(467\) −19.6568 + 34.0465i −0.909606 + 1.57548i −0.0949943 + 0.995478i \(0.530283\pi\)
−0.814612 + 0.580006i \(0.803050\pi\)
\(468\) −11.5424 13.0358i −0.533549 0.602581i
\(469\) 0 0
\(470\) −21.4302 12.3727i −0.988500 0.570711i
\(471\) 40.7078 + 6.62133i 1.87572 + 0.305095i
\(472\) −21.8288 12.6029i −1.00475 0.580094i
\(473\) 2.39969 + 1.38546i 0.110338 + 0.0637036i
\(474\) 17.8767 + 2.90773i 0.821104 + 0.133557i
\(475\) −5.64854 3.26119i −0.259173 0.149633i
\(476\) 0 0
\(477\) 2.93987 8.79805i 0.134608 0.402835i
\(478\) 11.2465 19.4795i 0.514403 0.890973i
\(479\) 38.1153 1.74153 0.870767 0.491696i \(-0.163623\pi\)
0.870767 + 0.491696i \(0.163623\pi\)
\(480\) 19.0752 + 3.10268i 0.870661 + 0.141617i
\(481\) 3.27167i 0.149175i
\(482\) −10.9877 19.0313i −0.500477 0.866852i
\(483\) 0 0
\(484\) 25.0965 43.4685i 1.14075 1.97584i
\(485\) −10.9828 6.34090i −0.498701 0.287925i
\(486\) −27.9866 29.1767i −1.26950 1.32348i
\(487\) −3.80277 6.58659i −0.172320 0.298467i 0.766911 0.641754i \(-0.221793\pi\)
−0.939231 + 0.343287i \(0.888460\pi\)
\(488\) −51.0872 88.4856i −2.31261 4.00555i
\(489\) 2.45316 15.0820i 0.110936 0.682030i
\(490\) 0 0
\(491\) 3.33297 1.92429i 0.150415 0.0868420i −0.422904 0.906175i \(-0.638989\pi\)
0.573318 + 0.819333i \(0.305656\pi\)
\(492\) 32.1451 12.1861i 1.44921 0.549390i
\(493\) 25.9670i 1.16950i
\(494\) −5.24459 + 3.02797i −0.235965 + 0.136235i
\(495\) 1.53688 + 1.73573i 0.0690778 + 0.0780154i
\(496\) 22.0462i 0.989904i
\(497\) 0 0
\(498\) 13.9101 + 36.6929i 0.623327 + 1.64425i
\(499\) −32.1588 −1.43962 −0.719812 0.694169i \(-0.755772\pi\)
−0.719812 + 0.694169i \(0.755772\pi\)
\(500\) 24.9620 43.2355i 1.11634 1.93355i
\(501\) −29.6031 24.1769i −1.32257 1.08014i
\(502\) 52.6558 30.4009i 2.35014 1.35686i
\(503\) 0.425693 0.0189807 0.00949035 0.999955i \(-0.496979\pi\)
0.00949035 + 0.999955i \(0.496979\pi\)
\(504\) 0 0
\(505\) −2.14664 −0.0955243
\(506\) −6.57854 + 3.79812i −0.292452 + 0.168847i
\(507\) 3.19565 19.6468i 0.141924 0.872544i
\(508\) −6.92838 + 12.0003i −0.307397 + 0.532427i
\(509\) 25.7926 1.14323 0.571617 0.820520i \(-0.306316\pi\)
0.571617 + 0.820520i \(0.306316\pi\)
\(510\) −24.6114 4.00316i −1.08981 0.177263i
\(511\) 0 0
\(512\) 46.5411i 2.05684i
\(513\) −8.35326 + 5.27753i −0.368805 + 0.233008i
\(514\) −55.0670 + 31.7929i −2.42890 + 1.40233i
\(515\) 9.27868i 0.408868i
\(516\) −28.4865 23.2650i −1.25405 1.02418i
\(517\) −4.06724 + 2.34822i −0.178877 + 0.103275i
\(518\) 0 0
\(519\) 5.45658 + 4.45639i 0.239517 + 0.195614i
\(520\) −5.43984 9.42209i −0.238553 0.413186i
\(521\) 9.07174 + 15.7127i 0.397440 + 0.688386i 0.993409 0.114621i \(-0.0365653\pi\)
−0.595969 + 0.803007i \(0.703232\pi\)
\(522\) 34.1454 30.2337i 1.49450 1.32329i
\(523\) −12.0723 6.96997i −0.527887 0.304776i 0.212269 0.977211i \(-0.431915\pi\)
−0.740155 + 0.672436i \(0.765248\pi\)
\(524\) −38.3495 + 66.4234i −1.67531 + 2.90172i
\(525\) 0 0
\(526\) −13.6866 23.7059i −0.596764 1.03363i
\(527\) 10.9904i 0.478749i
\(528\) 6.00476 7.35247i 0.261324 0.319975i
\(529\) 0.447980 0.0194774
\(530\) 5.02411 8.70202i 0.218234 0.377992i
\(531\) 2.13619 + 10.4782i 0.0927026 + 0.454716i
\(532\) 0 0
\(533\) −4.46569 2.57827i −0.193431 0.111677i
\(534\) −2.58354 6.81501i −0.111801 0.294914i
\(535\) 0.164965 + 0.0952423i 0.00713204 + 0.00411769i
\(536\) −83.3625 48.1294i −3.60071 2.07887i
\(537\) −9.11868 + 11.1653i −0.393500 + 0.481817i
\(538\) 5.14131 + 2.96834i 0.221658 + 0.127974i
\(539\) 0 0
\(540\) −16.4363 26.0153i −0.707305 1.11952i
\(541\) −14.8576 + 25.7341i −0.638779 + 1.10640i 0.346922 + 0.937894i \(0.387227\pi\)
−0.985701 + 0.168503i \(0.946107\pi\)
\(542\) −62.6620 −2.69156
\(543\) 7.77913 + 20.5203i 0.333834 + 0.880609i
\(544\) 39.4493i 1.69138i
\(545\) −3.38370 5.86074i −0.144942 0.251046i
\(546\) 0 0
\(547\) −9.13516 + 15.8226i −0.390591 + 0.676524i −0.992528 0.122020i \(-0.961063\pi\)
0.601937 + 0.798544i \(0.294396\pi\)
\(548\) −71.2327 41.1262i −3.04291 1.75683i
\(549\) −13.7382 + 41.1138i −0.586331 + 1.75469i
\(550\) −2.74330 4.75154i −0.116975 0.202606i
\(551\) −5.57306 9.65282i −0.237420 0.411224i
\(552\) 54.3858 20.6174i 2.31481 0.877533i
\(553\) 0 0
\(554\) 25.5401 14.7456i 1.08510 0.626481i
\(555\) 0.928308 5.70723i 0.0394045 0.242258i
\(556\) 29.7590i 1.26206i
\(557\) −0.359456 + 0.207532i −0.0152307 + 0.00879343i −0.507596 0.861595i \(-0.669466\pi\)
0.492365 + 0.870389i \(0.336132\pi\)
\(558\) −14.4519 + 12.7962i −0.611796 + 0.541708i
\(559\) 5.51686i 0.233338i
\(560\) 0 0
\(561\) −2.99347 + 3.66532i −0.126385 + 0.154750i
\(562\) −52.8222 −2.22817
\(563\) −1.82962 + 3.16900i −0.0771095 + 0.133558i −0.902002 0.431733i \(-0.857902\pi\)
0.824892 + 0.565290i \(0.191236\pi\)
\(564\) 58.2899 22.0974i 2.45445 0.930469i
\(565\) 7.02161 4.05393i 0.295401 0.170550i
\(566\) 31.5403 1.32574
\(567\) 0 0
\(568\) −73.6074 −3.08850
\(569\) 30.4692 17.5914i 1.27733 0.737470i 0.300977 0.953631i \(-0.402687\pi\)
0.976358 + 0.216162i \(0.0693538\pi\)
\(570\) −10.0080 + 3.79400i −0.419191 + 0.158913i
\(571\) 5.02680 8.70667i 0.210365 0.364363i −0.741464 0.670993i \(-0.765868\pi\)
0.951829 + 0.306630i \(0.0992014\pi\)
\(572\) −3.57955 −0.149668
\(573\) 4.16387 5.09840i 0.173948 0.212989i
\(574\) 0 0
\(575\) 16.2888i 0.679292i
\(576\) −11.9549 + 10.5854i −0.498122 + 0.441056i
\(577\) −0.0597672 + 0.0345066i −0.00248814 + 0.00143653i −0.501244 0.865306i \(-0.667124\pi\)
0.498755 + 0.866743i \(0.333791\pi\)
\(578\) 6.80843i 0.283193i
\(579\) 1.88782 11.6063i 0.0784552 0.482342i
\(580\) 30.0627 17.3567i 1.24828 0.720697i
\(581\) 0 0
\(582\) 42.5138 16.1168i 1.76225 0.668061i
\(583\) −0.953529 1.65156i −0.0394911 0.0684006i
\(584\) −40.6219 70.3591i −1.68094 2.91148i
\(585\) −1.46286 + 4.37786i −0.0604820 + 0.181002i
\(586\) 60.4974 + 34.9282i 2.49913 + 1.44287i
\(587\) 11.4799 19.8838i 0.473827 0.820693i −0.525724 0.850655i \(-0.676205\pi\)
0.999551 + 0.0299626i \(0.00953881\pi\)
\(588\) 0 0
\(589\) 2.35877 + 4.08550i 0.0971913 + 0.168340i
\(590\) 11.5837i 0.476894i
\(591\) 3.93836 + 10.3888i 0.162002 + 0.427340i
\(592\) −23.6764 −0.973094
\(593\) −14.3970 + 24.9363i −0.591213 + 1.02401i 0.402856 + 0.915263i \(0.368018\pi\)
−0.994069 + 0.108748i \(0.965316\pi\)
\(594\) −8.30506 + 0.331300i −0.340761 + 0.0135934i
\(595\) 0 0
\(596\) 43.4984 + 25.1138i 1.78176 + 1.02870i
\(597\) −17.5750 + 21.5195i −0.719295 + 0.880733i
\(598\) −13.0977 7.56198i −0.535606 0.309233i
\(599\) −33.1588 19.1442i −1.35483 0.782212i −0.365910 0.930650i \(-0.619242\pi\)
−0.988922 + 0.148438i \(0.952575\pi\)
\(600\) 14.8915 + 39.2817i 0.607943 + 1.60367i
\(601\) −26.7618 15.4509i −1.09164 0.630257i −0.157625 0.987499i \(-0.550384\pi\)
−0.934012 + 0.357242i \(0.883717\pi\)
\(602\) 0 0
\(603\) 8.15793 + 40.0155i 0.332216 + 1.62956i
\(604\) 22.4254 38.8419i 0.912475 1.58045i
\(605\) −13.3062 −0.540975
\(606\) 4.86813 5.96073i 0.197754 0.242138i
\(607\) 33.1791i 1.34670i −0.739325 0.673349i \(-0.764855\pi\)
0.739325 0.673349i \(-0.235145\pi\)
\(608\) 8.46664 + 14.6647i 0.343368 + 0.594730i
\(609\) 0 0
\(610\) −23.4780 + 40.6650i −0.950595 + 1.64648i
\(611\) −8.09780 4.67527i −0.327602 0.189141i
\(612\) 47.0289 41.6412i 1.90103 1.68325i
\(613\) −2.01164 3.48426i −0.0812492 0.140728i 0.822538 0.568711i \(-0.192558\pi\)
−0.903787 + 0.427983i \(0.859224\pi\)
\(614\) 27.7120 + 47.9985i 1.11836 + 1.93706i
\(615\) −7.05857 5.76474i −0.284629 0.232457i
\(616\) 0 0
\(617\) 27.1191 15.6572i 1.09177 0.630336i 0.157726 0.987483i \(-0.449584\pi\)
0.934048 + 0.357147i \(0.116251\pi\)
\(618\) 25.7648 + 21.0421i 1.03641 + 0.846437i
\(619\) 13.9310i 0.559934i 0.960010 + 0.279967i \(0.0903235\pi\)
−0.960010 + 0.279967i \(0.909676\pi\)
\(620\) −12.7238 + 7.34612i −0.511002 + 0.295027i
\(621\) −21.8448 11.4764i −0.876603 0.460532i
\(622\) 42.0962i 1.68790i
\(623\) 0 0
\(624\) 18.6551 + 3.03434i 0.746802 + 0.121471i
\(625\) 3.91523 0.156609
\(626\) 18.2592 31.6259i 0.729786 1.26403i
\(627\) −0.326121 + 2.00499i −0.0130240 + 0.0800714i
\(628\) −97.4661 + 56.2721i −3.88932 + 2.24550i
\(629\) 11.8031 0.470620
\(630\) 0 0
\(631\) −4.61815 −0.183846 −0.0919229 0.995766i \(-0.529301\pi\)
−0.0919229 + 0.995766i \(0.529301\pi\)
\(632\) −24.6902 + 14.2549i −0.982124 + 0.567030i
\(633\) 10.8949 + 8.89787i 0.433033 + 0.353659i
\(634\) −26.3203 + 45.5881i −1.04531 + 1.81053i
\(635\) 3.67344 0.145776
\(636\) 8.97296 + 23.6694i 0.355801 + 0.938554i
\(637\) 0 0
\(638\) 9.37609i 0.371203i
\(639\) 20.7020 + 23.3805i 0.818960 + 0.924920i
\(640\) 4.34657 2.50949i 0.171813 0.0991964i
\(641\) 42.4724i 1.67756i 0.544473 + 0.838779i \(0.316730\pi\)
−0.544473 + 0.838779i \(0.683270\pi\)
\(642\) −0.638571 + 0.242079i −0.0252024 + 0.00955410i
\(643\) 3.13514 1.81008i 0.123638 0.0713825i −0.436905 0.899507i \(-0.643926\pi\)
0.560544 + 0.828125i \(0.310592\pi\)
\(644\) 0 0
\(645\) −1.56536 + 9.62383i −0.0616361 + 0.378938i
\(646\) −10.9239 18.9207i −0.429795 0.744426i
\(647\) −6.00617 10.4030i −0.236127 0.408984i 0.723473 0.690353i \(-0.242545\pi\)
−0.959600 + 0.281369i \(0.909211\pi\)
\(648\) 63.1722 + 7.70525i 2.48164 + 0.302691i
\(649\) 1.90394 + 1.09924i 0.0747361 + 0.0431489i
\(650\) 5.46186 9.46022i 0.214232 0.371060i
\(651\) 0 0
\(652\) 20.8484 + 36.1105i 0.816486 + 1.41420i
\(653\) 46.1822i 1.80725i −0.428324 0.903625i \(-0.640896\pi\)
0.428324 0.903625i \(-0.359104\pi\)
\(654\) 23.9474 + 3.89517i 0.936419 + 0.152313i
\(655\) 20.3330 0.794476
\(656\) −18.6584 + 32.3174i −0.728490 + 1.26178i
\(657\) −10.9239 + 32.6915i −0.426182 + 1.27542i
\(658\) 0 0
\(659\) −16.3479 9.43847i −0.636824 0.367671i 0.146566 0.989201i \(-0.453178\pi\)
−0.783390 + 0.621530i \(0.786511\pi\)
\(660\) −6.24431 1.01567i −0.243059 0.0395348i
\(661\) −2.88202 1.66393i −0.112097 0.0647195i 0.442903 0.896570i \(-0.353949\pi\)
−0.555000 + 0.831850i \(0.687282\pi\)
\(662\) 59.4494 + 34.3231i 2.31057 + 1.33401i
\(663\) −9.29987 1.51267i −0.361177 0.0587472i
\(664\) −53.4944 30.8850i −2.07599 1.19857i
\(665\) 0 0
\(666\) 13.7424 + 15.5205i 0.532509 + 0.601407i
\(667\) 13.9181 24.1068i 0.538909 0.933418i
\(668\) 104.299 4.03544
\(669\) −13.7435 2.23544i −0.531353 0.0864273i
\(670\) 44.2373i 1.70904i
\(671\) 4.45589 + 7.71783i 0.172018 + 0.297944i
\(672\) 0 0
\(673\) −16.3678 + 28.3499i −0.630934 + 1.09281i 0.356427 + 0.934323i \(0.383995\pi\)
−0.987361 + 0.158487i \(0.949339\pi\)
\(674\) 7.80099 + 4.50390i 0.300483 + 0.173484i
\(675\) 8.28915 15.7781i 0.319050 0.607298i
\(676\) 27.1585 + 47.0399i 1.04456 + 1.80923i
\(677\) 16.9228 + 29.3111i 0.650396 + 1.12652i 0.983027 + 0.183461i \(0.0587302\pi\)
−0.332631 + 0.943057i \(0.607937\pi\)
\(678\) −4.66671 + 28.6909i −0.179224 + 1.10187i
\(679\) 0 0
\(680\) 33.9917 19.6251i 1.30352 0.752590i
\(681\) −33.7251 + 12.7850i −1.29235 + 0.489923i
\(682\) 3.96838i 0.151957i
\(683\) 4.79617 2.76907i 0.183520 0.105956i −0.405425 0.914128i \(-0.632877\pi\)
0.588946 + 0.808173i \(0.299543\pi\)
\(684\) 8.54517 25.5728i 0.326733 0.977802i
\(685\) 21.8052i 0.833133i
\(686\) 0 0
\(687\) 3.69562 + 9.74854i 0.140997 + 0.371930i
\(688\) 39.9244 1.52210
\(689\) 1.89846 3.28822i 0.0723254 0.125271i
\(690\) −20.7026 16.9078i −0.788134 0.643669i
\(691\) −12.3417 + 7.12550i −0.469502 + 0.271067i −0.716031 0.698068i \(-0.754043\pi\)
0.246530 + 0.969135i \(0.420710\pi\)
\(692\) −19.2248 −0.730818
\(693\) 0 0
\(694\) −24.4003 −0.926222
\(695\) 6.83219 3.94456i 0.259160 0.149626i
\(696\) −11.5256 + 70.8592i −0.436877 + 2.68591i
\(697\) 9.30154 16.1107i 0.352321 0.610238i
\(698\) −36.9114 −1.39712
\(699\) 35.9587 + 5.84886i 1.36008 + 0.221224i
\(700\) 0 0
\(701\) 18.6105i 0.702908i 0.936205 + 0.351454i \(0.114313\pi\)
−0.936205 + 0.351454i \(0.885687\pi\)
\(702\) −8.83884 13.9901i −0.333601 0.528022i
\(703\) 4.38760 2.53318i 0.165482 0.0955408i
\(704\) 3.28274i 0.123723i
\(705\) −12.7996 10.4534i −0.482059 0.393698i
\(706\) 38.5544 22.2594i 1.45101 0.837743i
\(707\) 0 0
\(708\) −22.6015 18.4587i −0.849416 0.693719i
\(709\) 6.74733 + 11.6867i 0.253401 + 0.438904i 0.964460 0.264229i \(-0.0851174\pi\)
−0.711059 + 0.703133i \(0.751784\pi\)
\(710\) 16.9137 + 29.2955i 0.634762 + 1.09944i
\(711\) 11.4720 + 3.83338i 0.430234 + 0.143763i
\(712\) 9.93557 + 5.73630i 0.372351 + 0.214977i
\(713\) −5.89074 + 10.2031i −0.220610 + 0.382107i
\(714\) 0 0
\(715\) 0.474470 + 0.821807i 0.0177442 + 0.0307338i
\(716\) 39.3379i 1.47013i
\(717\) 9.50190 11.6345i 0.354855 0.434498i
\(718\) −73.2833 −2.73491
\(719\) 18.8692 32.6824i 0.703702 1.21885i −0.263456 0.964671i \(-0.584863\pi\)
0.967158 0.254176i \(-0.0818042\pi\)
\(720\) 31.6817 + 10.5865i 1.18071 + 0.394534i
\(721\) 0 0
\(722\) 34.5538 + 19.9496i 1.28596 + 0.742449i
\(723\) −5.20230 13.7229i −0.193476 0.510362i
\(724\) −51.8617 29.9424i −1.92742 1.11280i
\(725\) 17.4118 + 10.0527i 0.646659 + 0.373348i
\(726\) 30.1757 36.9483i 1.11993 1.37128i
\(727\) −1.98480 1.14592i −0.0736121 0.0424999i 0.462742 0.886493i \(-0.346866\pi\)
−0.536354 + 0.843993i \(0.680199\pi\)
\(728\) 0 0
\(729\) −15.3197 22.2330i −0.567395 0.823446i
\(730\) −18.6685 + 32.3347i −0.690950 + 1.19676i
\(731\) −19.9030 −0.736138
\(732\) −41.9311 110.609i −1.54982 4.08821i
\(733\) 24.7888i 0.915596i 0.889056 + 0.457798i \(0.151362\pi\)
−0.889056 + 0.457798i \(0.848638\pi\)
\(734\) −29.9170 51.8178i −1.10426 1.91263i
\(735\) 0 0
\(736\) −21.1444 + 36.6232i −0.779394 + 1.34995i
\(737\) 7.27099 + 4.19791i 0.267830 + 0.154632i
\(738\) 32.0147 6.52681i 1.17848 0.240255i
\(739\) 8.10081 + 14.0310i 0.297993 + 0.516139i 0.975677 0.219214i \(-0.0703494\pi\)
−0.677684 + 0.735354i \(0.737016\pi\)
\(740\) 7.88932 + 13.6647i 0.290017 + 0.502325i
\(741\) −3.78173 + 1.43363i −0.138925 + 0.0526658i
\(742\) 0 0
\(743\) −18.8312 + 10.8722i −0.690848 + 0.398862i −0.803930 0.594724i \(-0.797261\pi\)
0.113081 + 0.993586i \(0.463928\pi\)
\(744\) 4.87815 29.9908i 0.178842 1.09952i
\(745\) 13.3154i 0.487838i
\(746\) 31.1591 17.9897i 1.14081 0.658649i
\(747\) 5.23501 + 25.6783i 0.191539 + 0.939519i
\(748\) 12.9138i 0.472176i
\(749\) 0 0
\(750\) 30.0140 36.7503i 1.09596 1.34193i
\(751\) −7.57995 −0.276596 −0.138298 0.990391i \(-0.544163\pi\)
−0.138298 + 0.990391i \(0.544163\pi\)
\(752\) −33.8340 + 58.6022i −1.23380 + 2.13700i
\(753\) 37.9686 14.3937i 1.38365 0.524536i
\(754\) 16.1666 9.33381i 0.588754 0.339917i
\(755\) −11.8900 −0.432720
\(756\) 0 0
\(757\) 10.3436 0.375944 0.187972 0.982174i \(-0.439809\pi\)
0.187972 + 0.982174i \(0.439809\pi\)
\(758\) −51.1686 + 29.5422i −1.85853 + 1.07302i
\(759\) −4.74360 + 1.79827i −0.172182 + 0.0652732i
\(760\) 8.42392 14.5907i 0.305568 0.529259i
\(761\) 34.4339 1.24823 0.624114 0.781333i \(-0.285460\pi\)
0.624114 + 0.781333i \(0.285460\pi\)
\(762\) −8.33058 + 10.2003i −0.301785 + 0.369517i
\(763\) 0 0
\(764\) 17.9629i 0.649874i
\(765\) −15.7939 5.27753i −0.571028 0.190809i
\(766\) −34.2121 + 19.7523i −1.23613 + 0.713681i
\(767\) 4.37713i 0.158049i
\(768\) −5.84895 + 35.9593i −0.211056 + 1.29757i
\(769\) 12.9344 7.46765i 0.466425 0.269290i −0.248317 0.968679i \(-0.579877\pi\)
0.714742 + 0.699388i \(0.246544\pi\)
\(770\) 0 0
\(771\) −39.7073 + 15.0528i −1.43002 + 0.542114i
\(772\) 16.0439 + 27.7888i 0.577431 + 1.00014i
\(773\) −19.9924 34.6278i −0.719076 1.24548i −0.961366 0.275272i \(-0.911232\pi\)
0.242290 0.970204i \(-0.422101\pi\)
\(774\) −23.1732 26.1715i −0.832945 0.940714i
\(775\) −7.36945 4.25476i −0.264719 0.152835i
\(776\) −35.7845 + 61.9806i −1.28459 + 2.22497i
\(777\) 0 0
\(778\) −18.3466 31.7772i −0.657758 1.13927i
\(779\) 7.98521i 0.286100i
\(780\) −4.46489 11.7778i −0.159869 0.421712i
\(781\) 6.42013 0.229730
\(782\) 27.2811 47.2523i 0.975571 1.68974i
\(783\) 25.7492 16.2681i 0.920201 0.581376i
\(784\) 0 0
\(785\) 25.8383 + 14.9178i 0.922209 + 0.532438i
\(786\) −46.1109 + 56.4600i −1.64472 + 2.01386i
\(787\) 1.94091 + 1.12059i 0.0691860 + 0.0399446i 0.534194 0.845362i \(-0.320615\pi\)
−0.465008 + 0.885307i \(0.653949\pi\)
\(788\) −26.2561 15.1590i −0.935336 0.540016i
\(789\) −6.48012 17.0937i −0.230698 0.608550i
\(790\) 11.3468 + 6.55108i 0.403701 + 0.233077i
\(791\) 0 0
\(792\) 9.79551 8.67333i 0.348068 0.308193i
\(793\) −8.87159 + 15.3660i −0.315039 + 0.545664i
\(794\) 25.1766 0.893484
\(795\) 4.24475 5.19744i 0.150546 0.184334i
\(796\) 75.8182i 2.68731i
\(797\) 22.1077 + 38.2916i 0.783094 + 1.35636i 0.930131 + 0.367227i \(0.119693\pi\)
−0.147037 + 0.989131i \(0.546974\pi\)
\(798\) 0 0
\(799\) 16.8668 29.2142i 0.596705 1.03352i
\(800\) −26.4522 15.2722i −0.935226 0.539953i
\(801\) −0.972303 4.76925i −0.0343546 0.168513i
\(802\) −11.3225 19.6112i −0.399812 0.692495i
\(803\) 3.54309 + 6.13682i 0.125033 + 0.216564i
\(804\) −86.3133 70.4921i −3.04404 2.48607i
\(805\) 0 0
\(806\) −6.84243 + 3.95048i −0.241014 + 0.139150i
\(807\) 3.07074 + 2.50788i 0.108095 + 0.0882814i
\(808\) 12.1145i 0.426185i
\(809\) 4.31478 2.49114i 0.151699 0.0875837i −0.422229 0.906489i \(-0.638752\pi\)
0.573928 + 0.818906i \(0.305419\pi\)
\(810\) −11.4493 26.9129i −0.402286 0.945621i
\(811\) 36.5749i 1.28432i 0.766571 + 0.642160i \(0.221961\pi\)
−0.766571 + 0.642160i \(0.778039\pi\)
\(812\) 0 0
\(813\) −41.3049 6.71844i −1.44863 0.235626i
\(814\) 4.26182 0.149377
\(815\) 5.52693 9.57292i 0.193600 0.335325i
\(816\) −10.9469 + 67.3014i −0.383218 + 2.35602i
\(817\) −7.39861 + 4.27159i −0.258845 + 0.149444i
\(818\) −38.6225 −1.35040
\(819\) 0 0
\(820\) 24.8690 0.868465
\(821\) 34.8397 20.1147i 1.21591 0.702008i 0.251872 0.967761i \(-0.418954\pi\)
0.964041 + 0.265753i \(0.0856205\pi\)
\(822\) −60.5480 49.4496i −2.11185 1.72475i
\(823\) 17.9016 31.0065i 0.624011 1.08082i −0.364720 0.931117i \(-0.618835\pi\)
0.988731 0.149701i \(-0.0478313\pi\)
\(824\) −52.3638 −1.82418
\(825\) −1.29886 3.42620i −0.0452204 0.119285i
\(826\) 0 0
\(827\) 32.0733i 1.11530i −0.830077 0.557648i \(-0.811704\pi\)
0.830077 0.557648i \(-0.188296\pi\)
\(828\) 65.9791 13.4511i 2.29293 0.467458i
\(829\) 14.0640 8.11986i 0.488463 0.282014i −0.235474 0.971881i \(-0.575664\pi\)
0.723937 + 0.689866i \(0.242331\pi\)
\(830\) 28.3874i 0.985343i
\(831\) 18.4163 6.98152i 0.638854 0.242186i
\(832\) −5.66023 + 3.26793i −0.196233 + 0.113295i
\(833\) 0 0
\(834\) −4.54081 + 27.9169i −0.157236 + 0.966682i
\(835\) −13.8248 23.9453i −0.478429 0.828663i
\(836\) −2.77157 4.80050i −0.0958568 0.166029i
\(837\) −10.8982 + 6.88540i −0.376697 + 0.237994i
\(838\) −9.60684 5.54651i −0.331863 0.191601i
\(839\) 1.35145 2.34077i 0.0466571 0.0808125i −0.841754 0.539862i \(-0.818477\pi\)
0.888411 + 0.459049i \(0.151810\pi\)
\(840\) 0 0
\(841\) 2.67914 + 4.64041i 0.0923842 + 0.160014i
\(842\) 29.9129i 1.03087i
\(843\) −34.8188 5.66346i −1.19922 0.195060i
\(844\) −38.3853 −1.32128
\(845\) 7.19974 12.4703i 0.247679 0.428992i
\(846\) 58.0534 11.8353i 1.99592 0.406906i
\(847\) 0 0
\(848\) −23.7962 13.7388i −0.817166 0.471791i
\(849\) 20.7904 + 3.38167i 0.713526 + 0.116058i
\(850\) 34.1293 + 19.7046i 1.17063 + 0.675861i
\(851\) 10.9575 + 6.32632i 0.375619 + 0.216864i
\(852\) −84.1117 13.6812i −2.88162 0.468710i
\(853\) 41.3187 + 23.8554i 1.41473 + 0.816793i 0.995829 0.0912411i \(-0.0290834\pi\)
0.418897 + 0.908034i \(0.362417\pi\)
\(854\) 0 0
\(855\) −7.00378 + 1.42785i −0.239524 + 0.0488316i
\(856\) 0.537495 0.930969i 0.0183712 0.0318199i
\(857\) −17.8795 −0.610751 −0.305375 0.952232i \(-0.598782\pi\)
−0.305375 + 0.952232i \(0.598782\pi\)
\(858\) −3.35797 0.546190i −0.114639 0.0186466i
\(859\) 33.7058i 1.15003i −0.818144 0.575014i \(-0.804997\pi\)
0.818144 0.575014i \(-0.195003\pi\)
\(860\) −13.3034 23.0422i −0.453642 0.785731i
\(861\) 0 0
\(862\) 21.6367 37.4759i 0.736950 1.27643i
\(863\) −16.4318 9.48693i −0.559347 0.322939i 0.193537 0.981093i \(-0.438004\pi\)
−0.752883 + 0.658154i \(0.771338\pi\)
\(864\) −39.1184 + 24.7147i −1.33084 + 0.840812i
\(865\) 2.54826 + 4.41371i 0.0866434 + 0.150071i
\(866\) 16.0155 + 27.7396i 0.544228 + 0.942630i
\(867\) 0.729981 4.48791i 0.0247915 0.152417i
\(868\) 0 0
\(869\) 2.15351 1.24333i 0.0730530 0.0421772i
\(870\) 30.8501 11.6951i 1.04592 0.396502i
\(871\) 16.7159i 0.566397i
\(872\) −33.0748 + 19.0957i −1.12005 + 0.646663i
\(873\) 29.7518 6.06547i 1.00695 0.205285i
\(874\) 23.4204i 0.792206i
\(875\) 0 0
\(876\) −33.3415 87.9501i −1.12650 2.97156i
\(877\) 37.2376 1.25742 0.628712 0.777638i \(-0.283582\pi\)
0.628712 + 0.777638i \(0.283582\pi\)
\(878\) −28.7035 + 49.7159i −0.968695 + 1.67783i
\(879\) 36.1332 + 29.5100i 1.21874 + 0.995347i
\(880\) 5.94726 3.43365i 0.200482 0.115748i
\(881\) 4.71527 0.158862 0.0794308 0.996840i \(-0.474690\pi\)
0.0794308 + 0.996840i \(0.474690\pi\)
\(882\) 0 0
\(883\) 30.1766 1.01552 0.507762 0.861497i \(-0.330473\pi\)
0.507762 + 0.861497i \(0.330473\pi\)
\(884\) 22.2665 12.8556i 0.748904 0.432380i
\(885\) −1.24197 + 7.63564i −0.0417485 + 0.256669i
\(886\) 6.33251 10.9682i 0.212745 0.368485i
\(887\) −38.4434 −1.29080 −0.645402 0.763843i \(-0.723310\pi\)
−0.645402 + 0.763843i \(0.723310\pi\)
\(888\) −32.2084 5.23886i −1.08084 0.175805i
\(889\) 0 0
\(890\) 5.27243i 0.176732i
\(891\) −5.50997 0.672063i −0.184591 0.0225149i
\(892\) 32.9058 18.9981i 1.10177 0.636105i
\(893\) 14.4799i 0.484550i
\(894\) 36.9737 + 30.1965i 1.23659 + 1.00992i
\(895\) −9.03135 + 5.21425i −0.301885 + 0.174293i
\(896\) 0 0
\(897\) −7.82286 6.38894i −0.261198 0.213320i
\(898\) −16.1329 27.9431i −0.538363 0.932472i
\(899\) −7.27098 12.5937i −0.242501 0.420023i
\(900\) 9.71544 + 47.6553i 0.323848 + 1.58851i
\(901\) 11.8628 + 6.84900i 0.395208 + 0.228173i
\(902\) 3.35857 5.81721i 0.111828 0.193692i
\(903\) 0 0
\(904\) −22.8781 39.6261i −0.760916 1.31794i
\(905\) 15.8755i 0.527719i
\(906\) 26.9639 33.0157i 0.895816 1.09687i
\(907\) 43.5902 1.44739 0.723695 0.690120i \(-0.242442\pi\)
0.723695 + 0.690120i \(0.242442\pi\)
\(908\) 49.2103 85.2348i 1.63310 2.82862i
\(909\) 3.84802 3.40719i 0.127631 0.113009i
\(910\) 0 0
\(911\) −1.67736 0.968423i −0.0555734 0.0320853i 0.471956 0.881622i \(-0.343548\pi\)
−0.527529 + 0.849537i \(0.676881\pi\)
\(912\) 10.3749 + 27.3676i 0.343548 + 0.906233i
\(913\) 4.66585 + 2.69383i 0.154417 + 0.0891528i
\(914\) −24.2025 13.9733i −0.800548 0.462197i
\(915\) −19.8360 + 24.2879i −0.655756 + 0.802934i
\(916\) −24.6379 14.2247i −0.814058 0.469997i
\(917\) 0 0
\(918\) 50.4716 31.8876i 1.66581 1.05245i
\(919\) 4.61421 7.99205i 0.152209 0.263634i −0.779830 0.625991i \(-0.784695\pi\)
0.932039 + 0.362357i \(0.118028\pi\)
\(920\) 42.0755 1.38719
\(921\) 13.1206 + 34.6104i 0.432339 + 1.14045i
\(922\) 1.72887i 0.0569372i
\(923\) 6.39118 + 11.0698i 0.210368 + 0.364368i
\(924\) 0 0
\(925\) −4.56937 + 7.91438i −0.150240 + 0.260223i
\(926\) 93.3880 + 53.9176i 3.06892 + 1.77184i
\(927\) 14.7273 + 16.6327i 0.483707 + 0.546291i
\(928\) −26.0987 45.2043i −0.856732 1.48390i
\(929\) −26.6849 46.2197i −0.875504 1.51642i −0.856225 0.516603i \(-0.827196\pi\)
−0.0192794 0.999814i \(-0.506137\pi\)
\(930\) −13.0571 + 4.94989i −0.428160 + 0.162313i
\(931\) 0 0
\(932\) −86.0952 + 49.7071i −2.82014 + 1.62821i
\(933\) 4.51343 27.7485i 0.147763 0.908446i
\(934\) 101.961i 3.33627i
\(935\) −2.96481 + 1.71173i −0.0969595 + 0.0559796i
\(936\) 24.7062 + 8.25560i 0.807548 + 0.269843i
\(937\) 28.6378i 0.935555i −0.883846 0.467778i \(-0.845055\pi\)
0.883846 0.467778i \(-0.154945\pi\)
\(938\) 0 0
\(939\) 15.4268 18.8891i 0.503434 0.616424i
\(940\) 45.0959 1.47087
\(941\) 0.688308 1.19218i 0.0224382 0.0388641i −0.854588 0.519306i \(-0.826190\pi\)
0.877026 + 0.480442i \(0.159524\pi\)
\(942\) −100.019 + 37.9167i −3.25880 + 1.23539i
\(943\) 17.2704 9.97105i 0.562401 0.324702i
\(944\) 31.6764 1.03098
\(945\) 0 0
\(946\) −7.18651 −0.233653
\(947\) −47.0080 + 27.1401i −1.52755 + 0.881933i −0.528090 + 0.849188i \(0.677092\pi\)
−0.999464 + 0.0327450i \(0.989575\pi\)
\(948\) −30.8632 + 11.7001i −1.00239 + 0.380001i
\(949\) −7.05423 + 12.2183i −0.228990 + 0.396622i
\(950\) 16.9160 0.548829
\(951\) −22.2374 + 27.2283i −0.721097 + 0.882939i
\(952\) 0 0
\(953\) 11.2998i 0.366036i 0.983110 + 0.183018i \(0.0585867\pi\)
−0.983110 + 0.183018i \(0.941413\pi\)
\(954\) 4.80589 + 23.5734i 0.155596 + 0.763217i
\(955\) 4.12399 2.38099i 0.133449 0.0770469i
\(956\) 40.9911i 1.32575i
\(957\) 1.00528 6.18044i 0.0324960 0.199785i
\(958\) −85.6097 + 49.4268i −2.76592 + 1.59691i
\(959\) 0 0
\(960\) −10.8012 + 4.09467i −0.348607 + 0.132155i
\(961\) −12.4226 21.5166i −0.400729 0.694083i
\(962\) 4.24260 + 7.34839i 0.136787 + 0.236922i
\(963\) −0.446882 + 0.0911054i −0.0144006 + 0.00293583i
\(964\) 34.6825 + 20.0240i 1.11705 + 0.644928i
\(965\) 4.25324 7.36682i 0.136917 0.237146i
\(966\) 0 0
\(967\) 5.93412 + 10.2782i 0.190829 + 0.330525i 0.945525 0.325549i \(-0.105549\pi\)
−0.754696 + 0.656074i \(0.772216\pi\)
\(968\) 75.0929i 2.41358i
\(969\) −5.17207 13.6432i −0.166151 0.438283i
\(970\) 32.8907 1.05606
\(971\) −28.0837 + 48.6424i −0.901249 + 1.56101i −0.0753736 + 0.997155i \(0.524015\pi\)
−0.825875 + 0.563853i \(0.809318\pi\)
\(972\) 70.7552 + 20.5465i 2.26947 + 0.659029i
\(973\) 0 0
\(974\) 17.0826 + 9.86263i 0.547361 + 0.316019i
\(975\) 4.61459 5.65029i 0.147785 0.180954i
\(976\) 111.201 + 64.2020i 3.55946 + 2.05506i
\(977\) 18.7626 + 10.8326i 0.600268 + 0.346565i 0.769147 0.639072i \(-0.220681\pi\)
−0.168879 + 0.985637i \(0.554015\pi\)
\(978\) 14.0479 + 37.0564i 0.449202 + 1.18493i
\(979\) −0.866594 0.500328i −0.0276964 0.0159906i
\(980\) 0 0
\(981\) 15.3678 + 5.13516i 0.490656 + 0.163953i
\(982\) −4.99072 + 8.64419i −0.159260 + 0.275847i
\(983\) 19.4001 0.618768 0.309384 0.950937i \(-0.399877\pi\)
0.309384 + 0.950937i \(0.399877\pi\)
\(984\) −32.5330 + 39.8347i −1.03711 + 1.26988i
\(985\) 8.03731i 0.256090i
\(986\) 33.6733 + 58.3238i 1.07238 + 1.85741i
\(987\) 0 0
\(988\) 5.51814 9.55771i 0.175556 0.304071i
\(989\) −18.4771 10.6678i −0.587539 0.339216i
\(990\) −5.70280 1.90559i −0.181247 0.0605637i
\(991\) −12.6630 21.9330i −0.402254 0.696725i 0.591743 0.806126i \(-0.298440\pi\)
−0.993998 + 0.109402i \(0.965107\pi\)
\(992\) 11.0461 + 19.1325i 0.350715 + 0.607456i
\(993\) 35.5072 + 28.9988i 1.12679 + 0.920248i
\(994\) 0 0
\(995\) −17.4066 + 10.0497i −0.551828 + 0.318598i
\(996\) −55.3879 45.2354i −1.75503 1.43334i
\(997\) 5.56584i 0.176272i 0.996108 + 0.0881360i \(0.0280910\pi\)
−0.996108 + 0.0881360i \(0.971909\pi\)
\(998\) 72.2309 41.7025i 2.28643 1.32007i
\(999\) 7.39454 + 11.7041i 0.233953 + 0.370300i
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 441.2.s.b.362.1 10
3.2 odd 2 1323.2.s.b.656.5 10
7.2 even 3 441.2.o.d.146.5 10
7.3 odd 6 441.2.i.b.227.1 10
7.4 even 3 63.2.i.b.38.1 yes 10
7.5 odd 6 441.2.o.c.146.5 10
7.6 odd 2 63.2.s.b.47.1 yes 10
9.4 even 3 1323.2.i.b.1097.1 10
9.5 odd 6 441.2.i.b.68.5 10
21.2 odd 6 1323.2.o.c.440.1 10
21.5 even 6 1323.2.o.d.440.1 10
21.11 odd 6 189.2.i.b.143.5 10
21.17 even 6 1323.2.i.b.521.5 10
21.20 even 2 189.2.s.b.89.5 10
28.11 odd 6 1008.2.ca.b.353.1 10
28.27 even 2 1008.2.df.b.929.1 10
63.4 even 3 189.2.s.b.17.5 10
63.5 even 6 441.2.o.d.293.5 10
63.11 odd 6 567.2.p.c.80.5 10
63.13 odd 6 189.2.i.b.152.1 10
63.20 even 6 567.2.p.d.404.1 10
63.23 odd 6 441.2.o.c.293.5 10
63.25 even 3 567.2.p.d.80.1 10
63.31 odd 6 1323.2.s.b.962.5 10
63.32 odd 6 63.2.s.b.59.1 yes 10
63.34 odd 6 567.2.p.c.404.5 10
63.40 odd 6 1323.2.o.c.881.1 10
63.41 even 6 63.2.i.b.5.5 10
63.58 even 3 1323.2.o.d.881.1 10
63.59 even 6 inner 441.2.s.b.374.1 10
84.11 even 6 3024.2.ca.b.2033.2 10
84.83 odd 2 3024.2.df.b.1601.2 10
252.67 odd 6 3024.2.df.b.17.2 10
252.95 even 6 1008.2.df.b.689.1 10
252.139 even 6 3024.2.ca.b.2609.2 10
252.167 odd 6 1008.2.ca.b.257.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.5 10 63.41 even 6
63.2.i.b.38.1 yes 10 7.4 even 3
63.2.s.b.47.1 yes 10 7.6 odd 2
63.2.s.b.59.1 yes 10 63.32 odd 6
189.2.i.b.143.5 10 21.11 odd 6
189.2.i.b.152.1 10 63.13 odd 6
189.2.s.b.17.5 10 63.4 even 3
189.2.s.b.89.5 10 21.20 even 2
441.2.i.b.68.5 10 9.5 odd 6
441.2.i.b.227.1 10 7.3 odd 6
441.2.o.c.146.5 10 7.5 odd 6
441.2.o.c.293.5 10 63.23 odd 6
441.2.o.d.146.5 10 7.2 even 3
441.2.o.d.293.5 10 63.5 even 6
441.2.s.b.362.1 10 1.1 even 1 trivial
441.2.s.b.374.1 10 63.59 even 6 inner
567.2.p.c.80.5 10 63.11 odd 6
567.2.p.c.404.5 10 63.34 odd 6
567.2.p.d.80.1 10 63.25 even 3
567.2.p.d.404.1 10 63.20 even 6
1008.2.ca.b.257.1 10 252.167 odd 6
1008.2.ca.b.353.1 10 28.11 odd 6
1008.2.df.b.689.1 10 252.95 even 6
1008.2.df.b.929.1 10 28.27 even 2
1323.2.i.b.521.5 10 21.17 even 6
1323.2.i.b.1097.1 10 9.4 even 3
1323.2.o.c.440.1 10 21.2 odd 6
1323.2.o.c.881.1 10 63.40 odd 6
1323.2.o.d.440.1 10 21.5 even 6
1323.2.o.d.881.1 10 63.58 even 3
1323.2.s.b.656.5 10 3.2 odd 2
1323.2.s.b.962.5 10 63.31 odd 6
3024.2.ca.b.2033.2 10 84.11 even 6
3024.2.ca.b.2609.2 10 252.139 even 6
3024.2.df.b.17.2 10 252.67 odd 6
3024.2.df.b.1601.2 10 84.83 odd 2