Properties

Label 225.2.h.a.46.1
Level $225$
Weight $2$
Character 225.46
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 225.46
Dual form 225.2.h.a.181.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} -4.47214 q^{7} +(-2.42705 + 1.76336i) q^{8} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} -4.47214 q^{7} +(-2.42705 + 1.76336i) q^{8} +(-0.690983 - 2.12663i) q^{10} +(0.381966 - 1.17557i) q^{11} +(1.73607 + 5.34307i) q^{13} +(1.38197 - 4.25325i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(3.11803 - 2.26538i) q^{17} +(-1.00000 + 0.726543i) q^{19} -2.23607 q^{20} +(1.00000 + 0.726543i) q^{22} +(-1.38197 + 4.25325i) q^{23} +(1.54508 - 4.75528i) q^{25} -5.61803 q^{26} +(-3.61803 - 2.62866i) q^{28} +(5.35410 + 3.88998i) q^{29} +(-2.23607 + 1.62460i) q^{31} -5.00000 q^{32} +(1.19098 + 3.66547i) q^{34} +(8.09017 - 5.87785i) q^{35} +(-0.954915 - 2.93893i) q^{37} +(-0.381966 - 1.17557i) q^{38} +(2.07295 - 6.37988i) q^{40} +(1.11803 + 3.44095i) q^{41} +7.70820 q^{43} +(1.00000 - 0.726543i) q^{44} +(-3.61803 - 2.62866i) q^{46} +(-0.618034 - 0.449028i) q^{47} +13.0000 q^{49} +(4.04508 + 2.93893i) q^{50} +(-1.73607 + 5.34307i) q^{52} +(2.92705 + 2.12663i) q^{53} +(0.854102 + 2.62866i) q^{55} +(10.8541 - 7.88597i) q^{56} +(-5.35410 + 3.88998i) q^{58} +(1.23607 + 3.80423i) q^{59} +(0.500000 - 1.53884i) q^{61} +(-0.854102 - 2.62866i) q^{62} +(2.16312 - 6.65740i) q^{64} +(-10.1631 - 7.38394i) q^{65} +(-0.618034 + 0.449028i) q^{67} +3.85410 q^{68} +(3.09017 + 9.51057i) q^{70} +(-4.23607 - 3.07768i) q^{71} +(-2.50000 + 7.69421i) q^{73} +3.09017 q^{74} -1.23607 q^{76} +(-1.70820 + 5.25731i) q^{77} +(1.80902 + 1.31433i) q^{80} -3.61803 q^{82} +(10.0902 - 7.33094i) q^{83} +(-2.66312 + 8.19624i) q^{85} +(-2.38197 + 7.33094i) q^{86} +(1.14590 + 3.52671i) q^{88} +(-1.66312 + 5.11855i) q^{89} +(-7.76393 - 23.8949i) q^{91} +(-3.61803 + 2.62866i) q^{92} +(0.618034 - 0.449028i) q^{94} +(0.854102 - 2.62866i) q^{95} +(-1.73607 - 1.26133i) q^{97} +(-4.01722 + 12.3637i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + 4 q^{22} - 10 q^{23} - 5 q^{25} - 18 q^{26} - 10 q^{28} + 8 q^{29} - 20 q^{32} + 7 q^{34} + 10 q^{35} - 15 q^{37} - 6 q^{38} + 15 q^{40} + 4 q^{43} + 4 q^{44} - 10 q^{46} + 2 q^{47} + 52 q^{49} + 5 q^{50} + 2 q^{52} + 5 q^{53} - 10 q^{55} + 30 q^{56} - 8 q^{58} - 4 q^{59} + 2 q^{61} + 10 q^{62} - 7 q^{64} - 25 q^{65} + 2 q^{67} + 2 q^{68} - 10 q^{70} - 8 q^{71} - 10 q^{73} - 10 q^{74} + 4 q^{76} + 20 q^{77} + 5 q^{80} - 10 q^{82} + 18 q^{83} + 5 q^{85} - 14 q^{86} + 18 q^{88} + 9 q^{89} - 40 q^{91} - 10 q^{92} - 2 q^{94} - 10 q^{95} + 2 q^{97} + 13 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i 0.780378 + 0.625308i \(0.215027\pi\)
−0.998886 + 0.0471903i \(0.984973\pi\)
\(3\) 0 0
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) −1.80902 + 1.31433i −0.809017 + 0.587785i
\(6\) 0 0
\(7\) −4.47214 −1.69031 −0.845154 0.534522i \(-0.820491\pi\)
−0.845154 + 0.534522i \(0.820491\pi\)
\(8\) −2.42705 + 1.76336i −0.858092 + 0.623440i
\(9\) 0 0
\(10\) −0.690983 2.12663i −0.218508 0.672499i
\(11\) 0.381966 1.17557i 0.115167 0.354448i −0.876815 0.480828i \(-0.840336\pi\)
0.991982 + 0.126380i \(0.0403360\pi\)
\(12\) 0 0
\(13\) 1.73607 + 5.34307i 0.481499 + 1.48190i 0.836989 + 0.547220i \(0.184314\pi\)
−0.355490 + 0.934680i \(0.615686\pi\)
\(14\) 1.38197 4.25325i 0.369346 1.13673i
\(15\) 0 0
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) 3.11803 2.26538i 0.756234 0.549436i −0.141519 0.989936i \(-0.545199\pi\)
0.897753 + 0.440499i \(0.145199\pi\)
\(18\) 0 0
\(19\) −1.00000 + 0.726543i −0.229416 + 0.166680i −0.696555 0.717504i \(-0.745285\pi\)
0.467139 + 0.884184i \(0.345285\pi\)
\(20\) −2.23607 −0.500000
\(21\) 0 0
\(22\) 1.00000 + 0.726543i 0.213201 + 0.154899i
\(23\) −1.38197 + 4.25325i −0.288160 + 0.886865i 0.697274 + 0.716805i \(0.254396\pi\)
−0.985434 + 0.170060i \(0.945604\pi\)
\(24\) 0 0
\(25\) 1.54508 4.75528i 0.309017 0.951057i
\(26\) −5.61803 −1.10179
\(27\) 0 0
\(28\) −3.61803 2.62866i −0.683744 0.496769i
\(29\) 5.35410 + 3.88998i 0.994232 + 0.722352i 0.960844 0.277091i \(-0.0893703\pi\)
0.0333880 + 0.999442i \(0.489370\pi\)
\(30\) 0 0
\(31\) −2.23607 + 1.62460i −0.401610 + 0.291787i −0.770196 0.637807i \(-0.779842\pi\)
0.368587 + 0.929593i \(0.379842\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 1.19098 + 3.66547i 0.204252 + 0.628623i
\(35\) 8.09017 5.87785i 1.36749 0.993538i
\(36\) 0 0
\(37\) −0.954915 2.93893i −0.156987 0.483157i 0.841370 0.540460i \(-0.181750\pi\)
−0.998357 + 0.0573034i \(0.981750\pi\)
\(38\) −0.381966 1.17557i −0.0619631 0.190703i
\(39\) 0 0
\(40\) 2.07295 6.37988i 0.327762 1.00875i
\(41\) 1.11803 + 3.44095i 0.174608 + 0.537387i 0.999615 0.0277346i \(-0.00882932\pi\)
−0.825008 + 0.565121i \(0.808829\pi\)
\(42\) 0 0
\(43\) 7.70820 1.17549 0.587745 0.809046i \(-0.300016\pi\)
0.587745 + 0.809046i \(0.300016\pi\)
\(44\) 1.00000 0.726543i 0.150756 0.109530i
\(45\) 0 0
\(46\) −3.61803 2.62866i −0.533450 0.387574i
\(47\) −0.618034 0.449028i −0.0901495 0.0654975i 0.541797 0.840509i \(-0.317744\pi\)
−0.631947 + 0.775012i \(0.717744\pi\)
\(48\) 0 0
\(49\) 13.0000 1.85714
\(50\) 4.04508 + 2.93893i 0.572061 + 0.415627i
\(51\) 0 0
\(52\) −1.73607 + 5.34307i −0.240749 + 0.740950i
\(53\) 2.92705 + 2.12663i 0.402061 + 0.292115i 0.770380 0.637585i \(-0.220066\pi\)
−0.368319 + 0.929700i \(0.620066\pi\)
\(54\) 0 0
\(55\) 0.854102 + 2.62866i 0.115167 + 0.354448i
\(56\) 10.8541 7.88597i 1.45044 1.05381i
\(57\) 0 0
\(58\) −5.35410 + 3.88998i −0.703028 + 0.510780i
\(59\) 1.23607 + 3.80423i 0.160922 + 0.495268i 0.998713 0.0507240i \(-0.0161529\pi\)
−0.837790 + 0.545992i \(0.816153\pi\)
\(60\) 0 0
\(61\) 0.500000 1.53884i 0.0640184 0.197028i −0.913931 0.405869i \(-0.866969\pi\)
0.977950 + 0.208840i \(0.0669689\pi\)
\(62\) −0.854102 2.62866i −0.108471 0.333840i
\(63\) 0 0
\(64\) 2.16312 6.65740i 0.270390 0.832174i
\(65\) −10.1631 7.38394i −1.26058 0.915865i
\(66\) 0 0
\(67\) −0.618034 + 0.449028i −0.0755049 + 0.0548575i −0.624897 0.780707i \(-0.714859\pi\)
0.549392 + 0.835564i \(0.314859\pi\)
\(68\) 3.85410 0.467379
\(69\) 0 0
\(70\) 3.09017 + 9.51057i 0.369346 + 1.13673i
\(71\) −4.23607 3.07768i −0.502729 0.365254i 0.307330 0.951603i \(-0.400565\pi\)
−0.810058 + 0.586349i \(0.800565\pi\)
\(72\) 0 0
\(73\) −2.50000 + 7.69421i −0.292603 + 0.900539i 0.691413 + 0.722460i \(0.256988\pi\)
−0.984016 + 0.178080i \(0.943012\pi\)
\(74\) 3.09017 0.359225
\(75\) 0 0
\(76\) −1.23607 −0.141787
\(77\) −1.70820 + 5.25731i −0.194668 + 0.599126i
\(78\) 0 0
\(79\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) 1.80902 + 1.31433i 0.202254 + 0.146946i
\(81\) 0 0
\(82\) −3.61803 −0.399545
\(83\) 10.0902 7.33094i 1.10754 0.804675i 0.125266 0.992123i \(-0.460022\pi\)
0.982274 + 0.187448i \(0.0600217\pi\)
\(84\) 0 0
\(85\) −2.66312 + 8.19624i −0.288856 + 0.889007i
\(86\) −2.38197 + 7.33094i −0.256854 + 0.790515i
\(87\) 0 0
\(88\) 1.14590 + 3.52671i 0.122153 + 0.375949i
\(89\) −1.66312 + 5.11855i −0.176290 + 0.542566i −0.999690 0.0248961i \(-0.992075\pi\)
0.823400 + 0.567462i \(0.192075\pi\)
\(90\) 0 0
\(91\) −7.76393 23.8949i −0.813881 2.50487i
\(92\) −3.61803 + 2.62866i −0.377206 + 0.274056i
\(93\) 0 0
\(94\) 0.618034 0.449028i 0.0637453 0.0463137i
\(95\) 0.854102 2.62866i 0.0876290 0.269694i
\(96\) 0 0
\(97\) −1.73607 1.26133i −0.176271 0.128068i 0.496151 0.868236i \(-0.334746\pi\)
−0.672422 + 0.740168i \(0.734746\pi\)
\(98\) −4.01722 + 12.3637i −0.405801 + 1.24893i
\(99\) 0 0
\(100\) 4.04508 2.93893i 0.404508 0.293893i
\(101\) −3.56231 −0.354463 −0.177231 0.984169i \(-0.556714\pi\)
−0.177231 + 0.984169i \(0.556714\pi\)
\(102\) 0 0
\(103\) −2.61803 1.90211i −0.257963 0.187421i 0.451286 0.892379i \(-0.350966\pi\)
−0.709248 + 0.704959i \(0.750966\pi\)
\(104\) −13.6353 9.90659i −1.33705 0.971421i
\(105\) 0 0
\(106\) −2.92705 + 2.12663i −0.284300 + 0.206556i
\(107\) −7.52786 −0.727746 −0.363873 0.931449i \(-0.618546\pi\)
−0.363873 + 0.931449i \(0.618546\pi\)
\(108\) 0 0
\(109\) −2.44427 7.52270i −0.234119 0.720544i −0.997237 0.0742847i \(-0.976333\pi\)
0.763118 0.646259i \(-0.223667\pi\)
\(110\) −2.76393 −0.263531
\(111\) 0 0
\(112\) 1.38197 + 4.25325i 0.130584 + 0.401895i
\(113\) −5.66312 17.4293i −0.532741 1.63961i −0.748479 0.663158i \(-0.769216\pi\)
0.215738 0.976451i \(-0.430784\pi\)
\(114\) 0 0
\(115\) −3.09017 9.51057i −0.288160 0.886865i
\(116\) 2.04508 + 6.29412i 0.189881 + 0.584395i
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) −13.9443 + 10.1311i −1.27827 + 0.928717i
\(120\) 0 0
\(121\) 7.66312 + 5.56758i 0.696647 + 0.506144i
\(122\) 1.30902 + 0.951057i 0.118513 + 0.0861046i
\(123\) 0 0
\(124\) −2.76393 −0.248208
\(125\) 3.45492 + 10.6331i 0.309017 + 0.951057i
\(126\) 0 0
\(127\) −1.14590 + 3.52671i −0.101682 + 0.312945i −0.988937 0.148333i \(-0.952609\pi\)
0.887255 + 0.461279i \(0.152609\pi\)
\(128\) −2.42705 1.76336i −0.214523 0.155860i
\(129\) 0 0
\(130\) 10.1631 7.38394i 0.891364 0.647614i
\(131\) −6.61803 + 4.80828i −0.578220 + 0.420102i −0.838082 0.545544i \(-0.816323\pi\)
0.259862 + 0.965646i \(0.416323\pi\)
\(132\) 0 0
\(133\) 4.47214 3.24920i 0.387783 0.281741i
\(134\) −0.236068 0.726543i −0.0203932 0.0627637i
\(135\) 0 0
\(136\) −3.57295 + 10.9964i −0.306378 + 0.942934i
\(137\) 2.35410 + 7.24518i 0.201125 + 0.618998i 0.999850 + 0.0173024i \(0.00550780\pi\)
−0.798726 + 0.601695i \(0.794492\pi\)
\(138\) 0 0
\(139\) −7.09017 + 21.8213i −0.601380 + 1.85086i −0.0813976 + 0.996682i \(0.525938\pi\)
−0.519983 + 0.854177i \(0.674062\pi\)
\(140\) 10.0000 0.845154
\(141\) 0 0
\(142\) 4.23607 3.07768i 0.355483 0.258273i
\(143\) 6.94427 0.580709
\(144\) 0 0
\(145\) −14.7984 −1.22894
\(146\) −6.54508 4.75528i −0.541675 0.393550i
\(147\) 0 0
\(148\) 0.954915 2.93893i 0.0784935 0.241578i
\(149\) 18.8541 1.54459 0.772294 0.635265i \(-0.219109\pi\)
0.772294 + 0.635265i \(0.219109\pi\)
\(150\) 0 0
\(151\) 7.52786 0.612609 0.306304 0.951934i \(-0.400907\pi\)
0.306304 + 0.951934i \(0.400907\pi\)
\(152\) 1.14590 3.52671i 0.0929446 0.286054i
\(153\) 0 0
\(154\) −4.47214 3.24920i −0.360375 0.261828i
\(155\) 1.90983 5.87785i 0.153401 0.472120i
\(156\) 0 0
\(157\) 10.7984 0.861804 0.430902 0.902399i \(-0.358195\pi\)
0.430902 + 0.902399i \(0.358195\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 9.04508 6.57164i 0.715077 0.519534i
\(161\) 6.18034 19.0211i 0.487079 1.49908i
\(162\) 0 0
\(163\) −4.61803 14.2128i −0.361712 1.11324i −0.952014 0.306054i \(-0.900991\pi\)
0.590302 0.807183i \(-0.299009\pi\)
\(164\) −1.11803 + 3.44095i −0.0873038 + 0.268693i
\(165\) 0 0
\(166\) 3.85410 + 11.8617i 0.299136 + 0.920647i
\(167\) 2.76393 2.00811i 0.213879 0.155393i −0.475688 0.879614i \(-0.657801\pi\)
0.689567 + 0.724222i \(0.257801\pi\)
\(168\) 0 0
\(169\) −15.0172 + 10.9106i −1.15517 + 0.839281i
\(170\) −6.97214 5.06555i −0.534738 0.388510i
\(171\) 0 0
\(172\) 6.23607 + 4.53077i 0.475496 + 0.345468i
\(173\) −6.51722 + 20.0579i −0.495495 + 1.52498i 0.320689 + 0.947185i \(0.396086\pi\)
−0.816184 + 0.577793i \(0.803914\pi\)
\(174\) 0 0
\(175\) −6.90983 + 21.2663i −0.522334 + 1.60758i
\(176\) −1.23607 −0.0931721
\(177\) 0 0
\(178\) −4.35410 3.16344i −0.326354 0.237110i
\(179\) −13.0902 9.51057i −0.978405 0.710853i −0.0210536 0.999778i \(-0.506702\pi\)
−0.957352 + 0.288925i \(0.906702\pi\)
\(180\) 0 0
\(181\) −11.9721 + 8.69827i −0.889882 + 0.646537i −0.935847 0.352406i \(-0.885364\pi\)
0.0459654 + 0.998943i \(0.485364\pi\)
\(182\) 25.1246 1.86236
\(183\) 0 0
\(184\) −4.14590 12.7598i −0.305640 0.940662i
\(185\) 5.59017 + 4.06150i 0.410997 + 0.298607i
\(186\) 0 0
\(187\) −1.47214 4.53077i −0.107653 0.331323i
\(188\) −0.236068 0.726543i −0.0172170 0.0529886i
\(189\) 0 0
\(190\) 2.23607 + 1.62460i 0.162221 + 0.117861i
\(191\) −2.05573 6.32688i −0.148747 0.457797i 0.848727 0.528832i \(-0.177370\pi\)
−0.997474 + 0.0710349i \(0.977370\pi\)
\(192\) 0 0
\(193\) 23.3262 1.67906 0.839530 0.543314i \(-0.182831\pi\)
0.839530 + 0.543314i \(0.182831\pi\)
\(194\) 1.73607 1.26133i 0.124642 0.0905580i
\(195\) 0 0
\(196\) 10.5172 + 7.64121i 0.751230 + 0.545801i
\(197\) 6.16312 + 4.47777i 0.439104 + 0.319028i 0.785279 0.619142i \(-0.212520\pi\)
−0.346175 + 0.938170i \(0.612520\pi\)
\(198\) 0 0
\(199\) 12.6525 0.896910 0.448455 0.893805i \(-0.351974\pi\)
0.448455 + 0.893805i \(0.351974\pi\)
\(200\) 4.63525 + 14.2658i 0.327762 + 1.00875i
\(201\) 0 0
\(202\) 1.10081 3.38795i 0.0774529 0.238376i
\(203\) −23.9443 17.3965i −1.68056 1.22100i
\(204\) 0 0
\(205\) −6.54508 4.75528i −0.457129 0.332123i
\(206\) 2.61803 1.90211i 0.182407 0.132526i
\(207\) 0 0
\(208\) 4.54508 3.30220i 0.315145 0.228966i
\(209\) 0.472136 + 1.45309i 0.0326583 + 0.100512i
\(210\) 0 0
\(211\) 5.52786 17.0130i 0.380554 1.17122i −0.559101 0.829100i \(-0.688854\pi\)
0.939655 0.342125i \(-0.111146\pi\)
\(212\) 1.11803 + 3.44095i 0.0767869 + 0.236326i
\(213\) 0 0
\(214\) 2.32624 7.15942i 0.159018 0.489408i
\(215\) −13.9443 + 10.1311i −0.950991 + 0.690936i
\(216\) 0 0
\(217\) 10.0000 7.26543i 0.678844 0.493209i
\(218\) 7.90983 0.535721
\(219\) 0 0
\(220\) −0.854102 + 2.62866i −0.0575835 + 0.177224i
\(221\) 17.5172 + 12.7270i 1.17834 + 0.856111i
\(222\) 0 0
\(223\) 2.52786 7.77997i 0.169278 0.520985i −0.830048 0.557692i \(-0.811687\pi\)
0.999326 + 0.0367073i \(0.0116869\pi\)
\(224\) 22.3607 1.49404
\(225\) 0 0
\(226\) 18.3262 1.21904
\(227\) 6.18034 19.0211i 0.410204 1.26248i −0.506268 0.862376i \(-0.668975\pi\)
0.916471 0.400100i \(-0.131025\pi\)
\(228\) 0 0
\(229\) −17.7812 12.9188i −1.17501 0.853696i −0.183411 0.983036i \(-0.558714\pi\)
−0.991600 + 0.129340i \(0.958714\pi\)
\(230\) 10.0000 0.659380
\(231\) 0 0
\(232\) −19.8541 −1.30349
\(233\) 10.0172 7.27794i 0.656250 0.476794i −0.209144 0.977885i \(-0.567068\pi\)
0.865394 + 0.501091i \(0.167068\pi\)
\(234\) 0 0
\(235\) 1.70820 0.111431
\(236\) −1.23607 + 3.80423i −0.0804612 + 0.247634i
\(237\) 0 0
\(238\) −5.32624 16.3925i −0.345249 1.06257i
\(239\) 7.70820 23.7234i 0.498602 1.53454i −0.312664 0.949864i \(-0.601222\pi\)
0.811267 0.584676i \(-0.198778\pi\)
\(240\) 0 0
\(241\) 8.66312 + 26.6623i 0.558041 + 1.71747i 0.687775 + 0.725923i \(0.258587\pi\)
−0.129735 + 0.991549i \(0.541413\pi\)
\(242\) −7.66312 + 5.56758i −0.492604 + 0.357898i
\(243\) 0 0
\(244\) 1.30902 0.951057i 0.0838012 0.0608852i
\(245\) −23.5172 + 17.0863i −1.50246 + 1.09160i
\(246\) 0 0
\(247\) −5.61803 4.08174i −0.357467 0.259715i
\(248\) 2.56231 7.88597i 0.162707 0.500759i
\(249\) 0 0
\(250\) −11.1803 −0.707107
\(251\) 9.05573 0.571592 0.285796 0.958290i \(-0.407742\pi\)
0.285796 + 0.958290i \(0.407742\pi\)
\(252\) 0 0
\(253\) 4.47214 + 3.24920i 0.281161 + 0.204275i
\(254\) −3.00000 2.17963i −0.188237 0.136762i
\(255\) 0 0
\(256\) 13.7533 9.99235i 0.859581 0.624522i
\(257\) −11.7984 −0.735962 −0.367981 0.929833i \(-0.619951\pi\)
−0.367981 + 0.929833i \(0.619951\pi\)
\(258\) 0 0
\(259\) 4.27051 + 13.1433i 0.265357 + 0.816684i
\(260\) −3.88197 11.9475i −0.240749 0.740950i
\(261\) 0 0
\(262\) −2.52786 7.77997i −0.156172 0.480648i
\(263\) 7.38197 + 22.7194i 0.455192 + 1.40094i 0.870910 + 0.491442i \(0.163530\pi\)
−0.415719 + 0.909493i \(0.636470\pi\)
\(264\) 0 0
\(265\) −8.09017 −0.496975
\(266\) 1.70820 + 5.25731i 0.104737 + 0.322346i
\(267\) 0 0
\(268\) −0.763932 −0.0466646
\(269\) −5.54508 + 4.02874i −0.338090 + 0.245637i −0.743855 0.668341i \(-0.767005\pi\)
0.405766 + 0.913977i \(0.367005\pi\)
\(270\) 0 0
\(271\) 0.145898 + 0.106001i 0.00886267 + 0.00643911i 0.592208 0.805785i \(-0.298256\pi\)
−0.583345 + 0.812224i \(0.698256\pi\)
\(272\) −3.11803 2.26538i −0.189059 0.137359i
\(273\) 0 0
\(274\) −7.61803 −0.460222
\(275\) −5.00000 3.63271i −0.301511 0.219061i
\(276\) 0 0
\(277\) 5.80902 17.8783i 0.349030 1.07420i −0.610361 0.792124i \(-0.708976\pi\)
0.959391 0.282080i \(-0.0910245\pi\)
\(278\) −18.5623 13.4863i −1.11329 0.808855i
\(279\) 0 0
\(280\) −9.27051 + 28.5317i −0.554019 + 1.70509i
\(281\) −15.8713 + 11.5312i −0.946804 + 0.687893i −0.950049 0.312102i \(-0.898967\pi\)
0.00324500 + 0.999995i \(0.498967\pi\)
\(282\) 0 0
\(283\) −11.0902 + 8.05748i −0.659242 + 0.478967i −0.866407 0.499339i \(-0.833576\pi\)
0.207165 + 0.978306i \(0.433576\pi\)
\(284\) −1.61803 4.97980i −0.0960127 0.295497i
\(285\) 0 0
\(286\) −2.14590 + 6.60440i −0.126890 + 0.390526i
\(287\) −5.00000 15.3884i −0.295141 0.908350i
\(288\) 0 0
\(289\) −0.663119 + 2.04087i −0.0390070 + 0.120051i
\(290\) 4.57295 14.0741i 0.268533 0.826459i
\(291\) 0 0
\(292\) −6.54508 + 4.75528i −0.383022 + 0.278282i
\(293\) 20.7984 1.21505 0.607527 0.794299i \(-0.292162\pi\)
0.607527 + 0.794299i \(0.292162\pi\)
\(294\) 0 0
\(295\) −7.23607 5.25731i −0.421300 0.306092i
\(296\) 7.50000 + 5.44907i 0.435929 + 0.316721i
\(297\) 0 0
\(298\) −5.82624 + 17.9313i −0.337505 + 1.03873i
\(299\) −25.1246 −1.45299
\(300\) 0 0
\(301\) −34.4721 −1.98694
\(302\) −2.32624 + 7.15942i −0.133860 + 0.411979i
\(303\) 0 0
\(304\) 1.00000 + 0.726543i 0.0573539 + 0.0416701i
\(305\) 1.11803 + 3.44095i 0.0640184 + 0.197028i
\(306\) 0 0
\(307\) 32.6525 1.86358 0.931788 0.363004i \(-0.118249\pi\)
0.931788 + 0.363004i \(0.118249\pi\)
\(308\) −4.47214 + 3.24920i −0.254824 + 0.185140i
\(309\) 0 0
\(310\) 5.00000 + 3.63271i 0.283981 + 0.206324i
\(311\) −5.47214 + 16.8415i −0.310296 + 0.954994i 0.667351 + 0.744743i \(0.267428\pi\)
−0.977647 + 0.210251i \(0.932572\pi\)
\(312\) 0 0
\(313\) −0.145898 0.449028i −0.00824664 0.0253806i 0.946849 0.321680i \(-0.104247\pi\)
−0.955095 + 0.296299i \(0.904247\pi\)
\(314\) −3.33688 + 10.2699i −0.188311 + 0.579562i
\(315\) 0 0
\(316\) 0 0
\(317\) 23.3262 16.9475i 1.31013 0.951867i 0.310133 0.950693i \(-0.399627\pi\)
0.999999 0.00117338i \(-0.000373499\pi\)
\(318\) 0 0
\(319\) 6.61803 4.80828i 0.370539 0.269212i
\(320\) 4.83688 + 14.8864i 0.270390 + 0.832174i
\(321\) 0 0
\(322\) 16.1803 + 11.7557i 0.901695 + 0.655120i
\(323\) −1.47214 + 4.53077i −0.0819118 + 0.252099i
\(324\) 0 0
\(325\) 28.0902 1.55816
\(326\) 14.9443 0.827687
\(327\) 0 0
\(328\) −8.78115 6.37988i −0.484858 0.352270i
\(329\) 2.76393 + 2.00811i 0.152381 + 0.110711i
\(330\) 0 0
\(331\) 5.61803 4.08174i 0.308795 0.224353i −0.422584 0.906324i \(-0.638877\pi\)
0.731379 + 0.681971i \(0.238877\pi\)
\(332\) 12.4721 0.684497
\(333\) 0 0
\(334\) 1.05573 + 3.24920i 0.0577669 + 0.177788i
\(335\) 0.527864 1.62460i 0.0288403 0.0887613i
\(336\) 0 0
\(337\) 0.909830 + 2.80017i 0.0495616 + 0.152535i 0.972774 0.231754i \(-0.0744465\pi\)
−0.923213 + 0.384289i \(0.874447\pi\)
\(338\) −5.73607 17.6538i −0.312001 0.960240i
\(339\) 0 0
\(340\) −6.97214 + 5.06555i −0.378117 + 0.274718i
\(341\) 1.05573 + 3.24920i 0.0571709 + 0.175954i
\(342\) 0 0
\(343\) −26.8328 −1.44884
\(344\) −18.7082 + 13.5923i −1.00868 + 0.732848i
\(345\) 0 0
\(346\) −17.0623 12.3965i −0.917275 0.666439i
\(347\) −16.4164 11.9272i −0.881279 0.640287i 0.0523106 0.998631i \(-0.483341\pi\)
−0.933590 + 0.358344i \(0.883341\pi\)
\(348\) 0 0
\(349\) −4.03444 −0.215959 −0.107979 0.994153i \(-0.534438\pi\)
−0.107979 + 0.994153i \(0.534438\pi\)
\(350\) −18.0902 13.1433i −0.966960 0.702538i
\(351\) 0 0
\(352\) −1.90983 + 5.87785i −0.101794 + 0.313291i
\(353\) 11.6180 + 8.44100i 0.618366 + 0.449269i 0.852350 0.522971i \(-0.175177\pi\)
−0.233985 + 0.972240i \(0.575177\pi\)
\(354\) 0 0
\(355\) 11.7082 0.621407
\(356\) −4.35410 + 3.16344i −0.230767 + 0.167662i
\(357\) 0 0
\(358\) 13.0902 9.51057i 0.691837 0.502649i
\(359\) 11.5623 + 35.5851i 0.610235 + 1.87811i 0.455728 + 0.890119i \(0.349379\pi\)
0.154507 + 0.987992i \(0.450621\pi\)
\(360\) 0 0
\(361\) −5.39919 + 16.6170i −0.284168 + 0.874578i
\(362\) −4.57295 14.0741i −0.240349 0.739718i
\(363\) 0 0
\(364\) 7.76393 23.8949i 0.406941 1.25243i
\(365\) −5.59017 17.2048i −0.292603 0.900539i
\(366\) 0 0
\(367\) 4.85410 3.52671i 0.253382 0.184093i −0.453842 0.891082i \(-0.649947\pi\)
0.707224 + 0.706989i \(0.249947\pi\)
\(368\) 4.47214 0.233126
\(369\) 0 0
\(370\) −5.59017 + 4.06150i −0.290619 + 0.211147i
\(371\) −13.0902 9.51057i −0.679608 0.493764i
\(372\) 0 0
\(373\) 0.798374 2.45714i 0.0413382 0.127226i −0.928258 0.371938i \(-0.878693\pi\)
0.969596 + 0.244712i \(0.0786934\pi\)
\(374\) 4.76393 0.246337
\(375\) 0 0
\(376\) 2.29180 0.118190
\(377\) −11.4894 + 35.3606i −0.591732 + 1.82116i
\(378\) 0 0
\(379\) 2.76393 + 2.00811i 0.141974 + 0.103150i 0.656505 0.754322i \(-0.272034\pi\)
−0.514531 + 0.857472i \(0.672034\pi\)
\(380\) 2.23607 1.62460i 0.114708 0.0833401i
\(381\) 0 0
\(382\) 6.65248 0.340370
\(383\) −26.5623 + 19.2986i −1.35727 + 0.986115i −0.358657 + 0.933469i \(0.616765\pi\)
−0.998613 + 0.0526453i \(0.983235\pi\)
\(384\) 0 0
\(385\) −3.81966 11.7557i −0.194668 0.599126i
\(386\) −7.20820 + 22.1846i −0.366888 + 1.12916i
\(387\) 0 0
\(388\) −0.663119 2.04087i −0.0336648 0.103609i
\(389\) 8.00658 24.6417i 0.405950 1.24938i −0.514150 0.857700i \(-0.671893\pi\)
0.920100 0.391684i \(-0.128107\pi\)
\(390\) 0 0
\(391\) 5.32624 + 16.3925i 0.269359 + 0.829003i
\(392\) −31.5517 + 22.9236i −1.59360 + 1.15782i
\(393\) 0 0
\(394\) −6.16312 + 4.47777i −0.310493 + 0.225587i
\(395\) 0 0
\(396\) 0 0
\(397\) 5.61803 + 4.08174i 0.281961 + 0.204857i 0.719772 0.694210i \(-0.244246\pi\)
−0.437811 + 0.899067i \(0.644246\pi\)
\(398\) −3.90983 + 12.0332i −0.195982 + 0.603171i
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 22.4508 1.12114 0.560571 0.828106i \(-0.310582\pi\)
0.560571 + 0.828106i \(0.310582\pi\)
\(402\) 0 0
\(403\) −12.5623 9.12705i −0.625773 0.454651i
\(404\) −2.88197 2.09387i −0.143383 0.104174i
\(405\) 0 0
\(406\) 23.9443 17.3965i 1.18833 0.863375i
\(407\) −3.81966 −0.189334
\(408\) 0 0
\(409\) 0.371323 + 1.14281i 0.0183607 + 0.0565085i 0.959817 0.280626i \(-0.0905422\pi\)
−0.941456 + 0.337135i \(0.890542\pi\)
\(410\) 6.54508 4.75528i 0.323239 0.234847i
\(411\) 0 0
\(412\) −1.00000 3.07768i −0.0492665 0.151627i
\(413\) −5.52786 17.0130i −0.272008 0.837156i
\(414\) 0 0
\(415\) −8.61803 + 26.5236i −0.423043 + 1.30199i
\(416\) −8.68034 26.7153i −0.425589 1.30983i
\(417\) 0 0
\(418\) −1.52786 −0.0747303
\(419\) 12.1803 8.84953i 0.595049 0.432328i −0.249069 0.968486i \(-0.580125\pi\)
0.844118 + 0.536158i \(0.180125\pi\)
\(420\) 0 0
\(421\) −24.1525 17.5478i −1.17712 0.855227i −0.185276 0.982687i \(-0.559318\pi\)
−0.991844 + 0.127459i \(0.959318\pi\)
\(422\) 14.4721 + 10.5146i 0.704493 + 0.511844i
\(423\) 0 0
\(424\) −10.8541 −0.527122
\(425\) −5.95492 18.3273i −0.288856 0.889007i
\(426\) 0 0
\(427\) −2.23607 + 6.88191i −0.108211 + 0.333039i
\(428\) −6.09017 4.42477i −0.294379 0.213879i
\(429\) 0 0
\(430\) −5.32624 16.3925i −0.256854 0.790515i
\(431\) 16.7082 12.1392i 0.804806 0.584726i −0.107514 0.994204i \(-0.534289\pi\)
0.912320 + 0.409478i \(0.134289\pi\)
\(432\) 0 0
\(433\) 17.7812 12.9188i 0.854508 0.620836i −0.0718775 0.997413i \(-0.522899\pi\)
0.926385 + 0.376577i \(0.122899\pi\)
\(434\) 3.81966 + 11.7557i 0.183350 + 0.564292i
\(435\) 0 0
\(436\) 2.44427 7.52270i 0.117059 0.360272i
\(437\) −1.70820 5.25731i −0.0817145 0.251491i
\(438\) 0 0
\(439\) 5.00000 15.3884i 0.238637 0.734449i −0.757981 0.652276i \(-0.773814\pi\)
0.996618 0.0821726i \(-0.0261859\pi\)
\(440\) −6.70820 4.87380i −0.319801 0.232349i
\(441\) 0 0
\(442\) −17.5172 + 12.7270i −0.833209 + 0.605362i
\(443\) 35.2361 1.67412 0.837058 0.547114i \(-0.184274\pi\)
0.837058 + 0.547114i \(0.184274\pi\)
\(444\) 0 0
\(445\) −3.71885 11.4454i −0.176290 0.542566i
\(446\) 6.61803 + 4.80828i 0.313373 + 0.227679i
\(447\) 0 0
\(448\) −9.67376 + 29.7728i −0.457042 + 1.40663i
\(449\) −16.7984 −0.792764 −0.396382 0.918086i \(-0.629734\pi\)
−0.396382 + 0.918086i \(0.629734\pi\)
\(450\) 0 0
\(451\) 4.47214 0.210585
\(452\) 5.66312 17.4293i 0.266371 0.819805i
\(453\) 0 0
\(454\) 16.1803 + 11.7557i 0.759381 + 0.551723i
\(455\) 45.4508 + 33.0220i 2.13077 + 1.54809i
\(456\) 0 0
\(457\) −22.3607 −1.04599 −0.522994 0.852336i \(-0.675185\pi\)
−0.522994 + 0.852336i \(0.675185\pi\)
\(458\) 17.7812 12.9188i 0.830859 0.603654i
\(459\) 0 0
\(460\) 3.09017 9.51057i 0.144080 0.443432i
\(461\) 10.1353 31.1931i 0.472046 1.45281i −0.377855 0.925865i \(-0.623338\pi\)
0.849901 0.526943i \(-0.176662\pi\)
\(462\) 0 0
\(463\) 5.79837 + 17.8456i 0.269473 + 0.829353i 0.990629 + 0.136580i \(0.0436112\pi\)
−0.721156 + 0.692773i \(0.756389\pi\)
\(464\) 2.04508 6.29412i 0.0949407 0.292197i
\(465\) 0 0
\(466\) 3.82624 + 11.7759i 0.177247 + 0.545510i
\(467\) 22.7984 16.5640i 1.05498 0.766490i 0.0818293 0.996646i \(-0.473924\pi\)
0.973154 + 0.230156i \(0.0739238\pi\)
\(468\) 0 0
\(469\) 2.76393 2.00811i 0.127627 0.0927261i
\(470\) −0.527864 + 1.62460i −0.0243486 + 0.0749371i
\(471\) 0 0
\(472\) −9.70820 7.05342i −0.446856 0.324660i
\(473\) 2.94427 9.06154i 0.135378 0.416650i
\(474\) 0 0
\(475\) 1.90983 + 5.87785i 0.0876290 + 0.269694i
\(476\) −17.2361 −0.790014
\(477\) 0 0
\(478\) 20.1803 + 14.6619i 0.923027 + 0.670619i
\(479\) 15.3262 + 11.1352i 0.700274 + 0.508779i 0.880021 0.474934i \(-0.157528\pi\)
−0.179748 + 0.983713i \(0.557528\pi\)
\(480\) 0 0
\(481\) 14.0451 10.2044i 0.640401 0.465278i
\(482\) −28.0344 −1.27693
\(483\) 0 0
\(484\) 2.92705 + 9.00854i 0.133048 + 0.409479i
\(485\) 4.79837 0.217883
\(486\) 0 0
\(487\) 3.00000 + 9.23305i 0.135943 + 0.418389i 0.995736 0.0922541i \(-0.0294072\pi\)
−0.859793 + 0.510644i \(0.829407\pi\)
\(488\) 1.50000 + 4.61653i 0.0679018 + 0.208980i
\(489\) 0 0
\(490\) −8.98278 27.6462i −0.405801 1.24893i
\(491\) −1.81966 5.60034i −0.0821201 0.252740i 0.901563 0.432647i \(-0.142420\pi\)
−0.983684 + 0.179907i \(0.942420\pi\)
\(492\) 0 0
\(493\) 25.5066 1.14876
\(494\) 5.61803 4.08174i 0.252767 0.183646i
\(495\) 0 0
\(496\) 2.23607 + 1.62460i 0.100402 + 0.0729466i
\(497\) 18.9443 + 13.7638i 0.849767 + 0.617392i
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) −3.45492 + 10.6331i −0.154508 + 0.475528i
\(501\) 0 0
\(502\) −2.79837 + 8.61251i −0.124898 + 0.384395i
\(503\) 6.94427 + 5.04531i 0.309630 + 0.224959i 0.731738 0.681586i \(-0.238710\pi\)
−0.422108 + 0.906546i \(0.638710\pi\)
\(504\) 0 0
\(505\) 6.44427 4.68204i 0.286766 0.208348i
\(506\) −4.47214 + 3.24920i −0.198811 + 0.144444i
\(507\) 0 0
\(508\) −3.00000 + 2.17963i −0.133103 + 0.0967053i
\(509\) −6.22542 19.1599i −0.275937 0.849247i −0.988970 0.148116i \(-0.952679\pi\)
0.713033 0.701131i \(-0.247321\pi\)
\(510\) 0 0
\(511\) 11.1803 34.4095i 0.494589 1.52219i
\(512\) 3.39919 + 10.4616i 0.150224 + 0.462343i
\(513\) 0 0
\(514\) 3.64590 11.2209i 0.160814 0.494934i
\(515\) 7.23607 0.318859
\(516\) 0 0
\(517\) −0.763932 + 0.555029i −0.0335977 + 0.0244102i
\(518\) −13.8197 −0.607201
\(519\) 0 0
\(520\) 37.6869 1.65268
\(521\) −21.8713 15.8904i −0.958200 0.696173i −0.00546804 0.999985i \(-0.501741\pi\)
−0.952732 + 0.303812i \(0.901741\pi\)
\(522\) 0 0
\(523\) −7.94427 + 24.4500i −0.347379 + 1.06912i 0.612919 + 0.790146i \(0.289995\pi\)
−0.960298 + 0.278976i \(0.910005\pi\)
\(524\) −8.18034 −0.357360
\(525\) 0 0
\(526\) −23.8885 −1.04159
\(527\) −3.29180 + 10.1311i −0.143393 + 0.441318i
\(528\) 0 0
\(529\) 2.42705 + 1.76336i 0.105524 + 0.0766676i
\(530\) 2.50000 7.69421i 0.108593 0.334215i
\(531\) 0 0
\(532\) 5.52786 0.239663
\(533\) −16.4443 + 11.9475i −0.712280 + 0.517502i
\(534\) 0 0
\(535\) 13.6180 9.89408i 0.588759 0.427758i
\(536\) 0.708204 2.17963i 0.0305898 0.0941456i
\(537\) 0 0
\(538\) −2.11803 6.51864i −0.0913149 0.281038i
\(539\) 4.96556 15.2824i 0.213882 0.658260i
\(540\) 0 0
\(541\) −6.07953 18.7109i −0.261379 0.804443i −0.992505 0.122200i \(-0.961005\pi\)
0.731126 0.682242i \(-0.238995\pi\)
\(542\) −0.145898 + 0.106001i −0.00626686 + 0.00455314i
\(543\) 0 0
\(544\) −15.5902 + 11.3269i −0.668423 + 0.485638i
\(545\) 14.3090 + 10.3961i 0.612931 + 0.445320i
\(546\) 0 0
\(547\) −34.2705 24.8990i −1.46530 1.06460i −0.981942 0.189181i \(-0.939417\pi\)
−0.483359 0.875422i \(-0.660583\pi\)
\(548\) −2.35410 + 7.24518i −0.100562 + 0.309499i
\(549\) 0 0
\(550\) 5.00000 3.63271i 0.213201 0.154899i
\(551\) −8.18034 −0.348494
\(552\) 0 0
\(553\) 0 0
\(554\) 15.2082 + 11.0494i 0.646135 + 0.469444i
\(555\) 0 0
\(556\) −18.5623 + 13.4863i −0.787217 + 0.571947i
\(557\) 11.2705 0.477547 0.238773 0.971075i \(-0.423255\pi\)
0.238773 + 0.971075i \(0.423255\pi\)
\(558\) 0 0
\(559\) 13.3820 + 41.1855i 0.565997 + 1.74196i
\(560\) −8.09017 5.87785i −0.341872 0.248385i
\(561\) 0 0
\(562\) −6.06231 18.6579i −0.255723 0.787034i
\(563\) 8.18034 + 25.1765i 0.344760 + 1.06106i 0.961712 + 0.274062i \(0.0883673\pi\)
−0.616952 + 0.787001i \(0.711633\pi\)
\(564\) 0 0
\(565\) 33.1525 + 24.0867i 1.39474 + 1.01333i
\(566\) −4.23607 13.0373i −0.178055 0.547998i
\(567\) 0 0
\(568\) 15.7082 0.659102
\(569\) 2.64590 1.92236i 0.110922 0.0805894i −0.530942 0.847408i \(-0.678162\pi\)
0.641863 + 0.766819i \(0.278162\pi\)
\(570\) 0 0
\(571\) 13.5623 + 9.85359i 0.567565 + 0.412360i 0.834220 0.551432i \(-0.185918\pi\)
−0.266655 + 0.963792i \(0.585918\pi\)
\(572\) 5.61803 + 4.08174i 0.234902 + 0.170666i
\(573\) 0 0
\(574\) 16.1803 0.675354
\(575\) 18.0902 + 13.1433i 0.754412 + 0.548113i
\(576\) 0 0
\(577\) −4.03444 + 12.4167i −0.167956 + 0.516915i −0.999242 0.0389296i \(-0.987605\pi\)
0.831286 + 0.555845i \(0.187605\pi\)
\(578\) −1.73607 1.26133i −0.0722109 0.0524643i
\(579\) 0 0
\(580\) −11.9721 8.69827i −0.497116 0.361176i
\(581\) −45.1246 + 32.7849i −1.87208 + 1.36015i
\(582\) 0 0
\(583\) 3.61803 2.62866i 0.149844 0.108868i
\(584\) −7.50000 23.0826i −0.310352 0.955166i
\(585\) 0 0
\(586\) −6.42705 + 19.7804i −0.265499 + 0.817122i
\(587\) 12.7984 + 39.3893i 0.528245 + 1.62577i 0.757807 + 0.652478i \(0.226271\pi\)
−0.229562 + 0.973294i \(0.573729\pi\)
\(588\) 0 0
\(589\) 1.05573 3.24920i 0.0435005 0.133881i
\(590\) 7.23607 5.25731i 0.297904 0.216440i
\(591\) 0 0
\(592\) −2.50000 + 1.81636i −0.102749 + 0.0746518i
\(593\) −9.74265 −0.400083 −0.200041 0.979787i \(-0.564108\pi\)
−0.200041 + 0.979787i \(0.564108\pi\)
\(594\) 0 0
\(595\) 11.9098 36.6547i 0.488255 1.50270i
\(596\) 15.2533 + 11.0822i 0.624799 + 0.453943i
\(597\) 0 0
\(598\) 7.76393 23.8949i 0.317491 0.977136i
\(599\) 3.52786 0.144145 0.0720723 0.997399i \(-0.477039\pi\)
0.0720723 + 0.997399i \(0.477039\pi\)
\(600\) 0 0
\(601\) −8.67376 −0.353810 −0.176905 0.984228i \(-0.556609\pi\)
−0.176905 + 0.984228i \(0.556609\pi\)
\(602\) 10.6525 32.7849i 0.434163 1.33621i
\(603\) 0 0
\(604\) 6.09017 + 4.42477i 0.247806 + 0.180041i
\(605\) −21.1803 −0.861103
\(606\) 0 0
\(607\) −34.7639 −1.41102 −0.705512 0.708698i \(-0.749283\pi\)
−0.705512 + 0.708698i \(0.749283\pi\)
\(608\) 5.00000 3.63271i 0.202777 0.147326i
\(609\) 0 0
\(610\) −3.61803 −0.146490
\(611\) 1.32624 4.08174i 0.0536538 0.165130i
\(612\) 0 0
\(613\) 0.461493 + 1.42033i 0.0186395 + 0.0573665i 0.959944 0.280193i \(-0.0903985\pi\)
−0.941304 + 0.337560i \(0.890399\pi\)
\(614\) −10.0902 + 31.0543i −0.407206 + 1.25325i
\(615\) 0 0
\(616\) −5.12461 15.7719i −0.206476 0.635469i
\(617\) −16.1631 + 11.7432i −0.650703 + 0.472763i −0.863510 0.504331i \(-0.831739\pi\)
0.212808 + 0.977094i \(0.431739\pi\)
\(618\) 0 0
\(619\) 13.2361 9.61657i 0.532002 0.386522i −0.289104 0.957298i \(-0.593357\pi\)
0.821106 + 0.570775i \(0.193357\pi\)
\(620\) 5.00000 3.63271i 0.200805 0.145893i
\(621\) 0 0
\(622\) −14.3262 10.4086i −0.574430 0.417348i
\(623\) 7.43769 22.8909i 0.297985 0.917103i
\(624\) 0 0
\(625\) −20.2254 14.6946i −0.809017 0.587785i
\(626\) 0.472136 0.0188703
\(627\) 0 0
\(628\) 8.73607 + 6.34712i 0.348607 + 0.253278i
\(629\) −9.63525 7.00042i −0.384183 0.279125i
\(630\) 0 0
\(631\) −19.1803 + 13.9353i −0.763557 + 0.554757i −0.899999 0.435891i \(-0.856433\pi\)
0.136442 + 0.990648i \(0.456433\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 8.90983 + 27.4216i 0.353855 + 1.08905i
\(635\) −2.56231 7.88597i −0.101682 0.312945i
\(636\) 0 0
\(637\) 22.5689 + 69.4599i 0.894212 + 2.75210i
\(638\) 2.52786 + 7.77997i 0.100079 + 0.308012i
\(639\) 0 0
\(640\) 6.70820 0.265165
\(641\) −6.50658 20.0252i −0.256994 0.790947i −0.993430 0.114440i \(-0.963493\pi\)
0.736436 0.676507i \(-0.236507\pi\)
\(642\) 0 0
\(643\) −21.8885 −0.863200 −0.431600 0.902065i \(-0.642051\pi\)
−0.431600 + 0.902065i \(0.642051\pi\)
\(644\) 16.1803 11.7557i 0.637595 0.463240i
\(645\) 0 0
\(646\) −3.85410 2.80017i −0.151638 0.110171i
\(647\) −27.7984 20.1967i −1.09287 0.794014i −0.112986 0.993597i \(-0.536041\pi\)
−0.979881 + 0.199582i \(0.936041\pi\)
\(648\) 0 0
\(649\) 4.94427 0.194080
\(650\) −8.68034 + 26.7153i −0.340471 + 1.04786i
\(651\) 0 0
\(652\) 4.61803 14.2128i 0.180856 0.556618i
\(653\) −34.0623 24.7477i −1.33296 0.968453i −0.999672 0.0256283i \(-0.991841\pi\)
−0.333289 0.942825i \(-0.608159\pi\)
\(654\) 0 0
\(655\) 5.65248 17.3965i 0.220861 0.679739i
\(656\) 2.92705 2.12663i 0.114282 0.0830308i
\(657\) 0 0
\(658\) −2.76393 + 2.00811i −0.107749 + 0.0782844i
\(659\) 10.3262 + 31.7809i 0.402253 + 1.23801i 0.923167 + 0.384399i \(0.125591\pi\)
−0.520914 + 0.853609i \(0.674409\pi\)
\(660\) 0 0
\(661\) −0.437694 + 1.34708i −0.0170243 + 0.0523955i −0.959208 0.282702i \(-0.908769\pi\)
0.942183 + 0.335097i \(0.108769\pi\)
\(662\) 2.14590 + 6.60440i 0.0834027 + 0.256687i
\(663\) 0 0
\(664\) −11.5623 + 35.5851i −0.448704 + 1.38097i
\(665\) −3.81966 + 11.7557i −0.148120 + 0.455867i
\(666\) 0 0
\(667\) −23.9443 + 17.3965i −0.927126 + 0.673596i
\(668\) 3.41641 0.132185
\(669\) 0 0
\(670\) 1.38197 + 1.00406i 0.0533900 + 0.0387901i
\(671\) −1.61803 1.17557i −0.0624635 0.0453824i
\(672\) 0 0
\(673\) 1.60739 4.94704i 0.0619604 0.190694i −0.915285 0.402807i \(-0.868034\pi\)
0.977245 + 0.212113i \(0.0680345\pi\)
\(674\) −2.94427 −0.113409
\(675\) 0 0
\(676\) −18.5623 −0.713935
\(677\) −3.27051 + 10.0656i −0.125696 + 0.386852i −0.994027 0.109132i \(-0.965193\pi\)
0.868331 + 0.495985i \(0.165193\pi\)
\(678\) 0 0
\(679\) 7.76393 + 5.64083i 0.297952 + 0.216475i
\(680\) −7.98936 24.5887i −0.306378 0.942934i
\(681\) 0 0
\(682\) −3.41641 −0.130821
\(683\) −15.7082 + 11.4127i −0.601058 + 0.436694i −0.846254 0.532779i \(-0.821148\pi\)
0.245196 + 0.969473i \(0.421148\pi\)
\(684\) 0 0
\(685\) −13.7812 10.0126i −0.526551 0.382562i
\(686\) 8.29180 25.5195i 0.316582 0.974340i
\(687\) 0 0
\(688\) −2.38197 7.33094i −0.0908116 0.279489i
\(689\) −6.28115 + 19.3314i −0.239293 + 0.736468i
\(690\) 0 0
\(691\) −5.18034 15.9434i −0.197069 0.606517i −0.999946 0.0103723i \(-0.996698\pi\)
0.802877 0.596145i \(-0.203302\pi\)
\(692\) −17.0623 + 12.3965i −0.648612 + 0.471244i
\(693\) 0 0
\(694\) 16.4164 11.9272i 0.623158 0.452751i
\(695\) −15.8541 48.7939i −0.601380 1.85086i
\(696\) 0 0
\(697\) 11.2812 + 8.19624i 0.427304 + 0.310455i
\(698\) 1.24671 3.83698i 0.0471887 0.145232i
\(699\) 0 0
\(700\) −18.0902 + 13.1433i −0.683744 + 0.496769i
\(701\) −20.5623 −0.776628 −0.388314 0.921527i \(-0.626942\pi\)
−0.388314 + 0.921527i \(0.626942\pi\)
\(702\) 0 0
\(703\) 3.09017 + 2.24514i 0.116548 + 0.0846771i
\(704\) −7.00000 5.08580i −0.263822 0.191678i
\(705\) 0 0
\(706\) −11.6180 + 8.44100i −0.437250 + 0.317681i
\(707\) 15.9311 0.599151
\(708\) 0 0
\(709\) −12.4443 38.2995i −0.467354 1.43837i −0.855997 0.516981i \(-0.827056\pi\)
0.388643 0.921389i \(-0.372944\pi\)
\(710\) −3.61803 + 11.1352i −0.135782 + 0.417895i
\(711\) 0 0
\(712\) −4.98936 15.3557i −0.186984 0.575478i
\(713\) −3.81966 11.7557i −0.143047 0.440255i
\(714\) 0 0
\(715\) −12.5623 + 9.12705i −0.469804 + 0.341332i
\(716\) −5.00000 15.3884i −0.186859 0.575092i
\(717\) 0 0
\(718\) −37.4164 −1.39637
\(719\) −0.0901699 + 0.0655123i −0.00336277 + 0.00244320i −0.589465 0.807794i \(-0.700662\pi\)
0.586103 + 0.810237i \(0.300662\pi\)
\(720\) 0 0
\(721\) 11.7082 + 8.50651i 0.436036 + 0.316799i
\(722\) −14.1353 10.2699i −0.526060 0.382205i
\(723\) 0 0
\(724\) −14.7984 −0.549977
\(725\) 26.7705 19.4499i 0.994232 0.722352i
\(726\) 0 0
\(727\) 14.4164 44.3691i 0.534675 1.64556i −0.209675 0.977771i \(-0.567241\pi\)
0.744350 0.667789i \(-0.232759\pi\)
\(728\) 60.9787 + 44.3036i 2.26002 + 1.64200i
\(729\) 0 0
\(730\) 18.0902 0.669547
\(731\) 24.0344 17.4620i 0.888946 0.645857i
\(732\) 0 0
\(733\) −23.7984 + 17.2905i −0.879013 + 0.638640i −0.932990 0.359902i \(-0.882810\pi\)
0.0539772 + 0.998542i \(0.482810\pi\)
\(734\) 1.85410 + 5.70634i 0.0684362 + 0.210625i
\(735\) 0 0
\(736\) 6.90983 21.2663i 0.254700 0.783885i
\(737\) 0.291796 + 0.898056i 0.0107484 + 0.0330803i
\(738\) 0 0
\(739\) 1.32624 4.08174i 0.0487865 0.150149i −0.923696 0.383127i \(-0.874847\pi\)
0.972482 + 0.232978i \(0.0748470\pi\)
\(740\) 2.13525 + 6.57164i 0.0784935 + 0.241578i
\(741\) 0 0
\(742\) 13.0902 9.51057i 0.480555 0.349144i
\(743\) −41.1246 −1.50872 −0.754358 0.656463i \(-0.772052\pi\)
−0.754358 + 0.656463i \(0.772052\pi\)
\(744\) 0 0
\(745\) −34.1074 + 24.7805i −1.24960 + 0.907886i
\(746\) 2.09017 + 1.51860i 0.0765266 + 0.0555998i
\(747\) 0 0
\(748\) 1.47214 4.53077i 0.0538266 0.165661i
\(749\) 33.6656 1.23012
\(750\) 0 0
\(751\) 36.6525 1.33747 0.668734 0.743502i \(-0.266837\pi\)
0.668734 + 0.743502i \(0.266837\pi\)
\(752\) −0.236068 + 0.726543i −0.00860851 + 0.0264943i
\(753\) 0 0
\(754\) −30.0795 21.8541i −1.09543 0.795878i
\(755\) −13.6180 + 9.89408i −0.495611 + 0.360082i
\(756\) 0 0
\(757\) 29.6180 1.07649 0.538243 0.842790i \(-0.319088\pi\)
0.538243 + 0.842790i \(0.319088\pi\)
\(758\) −2.76393 + 2.00811i −0.100391 + 0.0729380i
\(759\) 0 0
\(760\) 2.56231 + 7.88597i 0.0929446 + 0.286054i
\(761\) −10.1180 + 31.1401i −0.366778 + 1.12883i 0.582081 + 0.813130i \(0.302238\pi\)
−0.948860 + 0.315697i \(0.897762\pi\)
\(762\) 0 0
\(763\) 10.9311 + 33.6425i 0.395733 + 1.21794i
\(764\) 2.05573 6.32688i 0.0743736 0.228899i
\(765\) 0 0
\(766\) −10.1459 31.2259i −0.366586 1.12824i
\(767\) −18.1803 + 13.2088i −0.656454 + 0.476942i
\(768\) 0 0
\(769\) 40.7426 29.6013i 1.46922 1.06745i 0.488378 0.872632i \(-0.337589\pi\)
0.980840 0.194817i \(-0.0624112\pi\)
\(770\) 12.3607 0.445448
\(771\) 0 0
\(772\) 18.8713 + 13.7108i 0.679194 + 0.493463i
\(773\) −8.93769 + 27.5074i −0.321467 + 0.989372i 0.651544 + 0.758611i \(0.274122\pi\)
−0.973010 + 0.230761i \(0.925878\pi\)
\(774\) 0 0
\(775\) 4.27051 + 13.1433i 0.153401 + 0.472120i
\(776\) 6.43769 0.231100
\(777\) 0 0
\(778\) 20.9615 + 15.2294i 0.751506 + 0.546001i
\(779\) −3.61803 2.62866i −0.129630 0.0941814i
\(780\) 0 0
\(781\) −5.23607 + 3.80423