Properties

Label 855.2.bs.c.586.3
Level $855$
Weight $2$
Character 855.586
Analytic conductor $6.827$
Analytic rank $0$
Dimension $18$
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] = [855,2,Mod(226,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.bs (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 586.3
Root \(0.816390 + 1.41403i\) of defining polynomial
Character \(\chi\) \(=\) 855.586
Dual form 855.2.bs.c.766.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.484738 + 0.406743i) q^{2} +(-0.277766 - 1.57529i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(-2.04448 - 3.54114i) q^{7} +(1.13887 - 1.97259i) q^{8} +O(q^{10})\) \(q+(0.484738 + 0.406743i) q^{2} +(-0.277766 - 1.57529i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(-2.04448 - 3.54114i) q^{7} +(1.13887 - 1.97259i) q^{8} +(-0.484738 + 0.406743i) q^{10} +(-2.17413 + 3.76571i) q^{11} +(-1.45826 - 0.530764i) q^{13} +(0.449299 - 2.54810i) q^{14} +(-1.65185 + 0.601224i) q^{16} +(-4.87326 - 4.08915i) q^{17} +(0.708014 + 4.30101i) q^{19} +1.59959 q^{20} +(-2.58556 + 0.941068i) q^{22} +(0.583829 + 3.31106i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(-0.490990 - 0.850420i) q^{26} +(-5.01042 + 4.20424i) q^{28} +(-3.99325 + 3.35074i) q^{29} +(-3.28366 - 5.68747i) q^{31} +(-5.32603 - 1.93852i) q^{32} +(-0.699019 - 3.96434i) q^{34} +(3.84236 - 1.39850i) q^{35} +0.180685 q^{37} +(-1.40621 + 2.37284i) q^{38} +(1.74486 + 1.46411i) q^{40} +(0.0242217 - 0.00881597i) q^{41} +(0.793995 - 4.50297i) q^{43} +(6.53598 + 2.37890i) q^{44} +(-1.06375 + 1.84246i) q^{46} +(1.09575 - 0.919441i) q^{47} +(-4.85976 + 8.41736i) q^{49} +(-0.316390 - 0.548004i) q^{50} +(-0.431051 + 2.44461i) q^{52} +(0.278010 + 1.57667i) q^{53} +(-3.33097 - 2.79501i) q^{55} -9.31361 q^{56} -3.29857 q^{58} +(-7.31281 - 6.13617i) q^{59} +(-1.05793 - 5.99980i) q^{61} +(0.721625 - 4.09254i) q^{62} +(-0.0353865 - 0.0612913i) q^{64} +(0.775925 - 1.34394i) q^{65} +(7.87159 - 6.60505i) q^{67} +(-5.08797 + 8.81262i) q^{68} +(2.43137 + 0.884946i) q^{70} +(1.88710 - 10.7023i) q^{71} +(12.7987 - 4.65836i) q^{73} +(0.0875850 + 0.0734926i) q^{74} +(6.57867 - 2.31000i) q^{76} +17.7799 q^{77} +(-16.2283 + 5.90661i) q^{79} +(-0.305250 - 1.73116i) q^{80} +(0.0153270 + 0.00557858i) q^{82} +(-2.57831 - 4.46577i) q^{83} +(4.87326 - 4.08915i) q^{85} +(2.21643 - 1.85981i) q^{86} +(4.95213 + 8.57735i) q^{88} +(-0.477195 - 0.173685i) q^{89} +(1.10187 + 6.24904i) q^{91} +(5.05370 - 1.83940i) q^{92} +0.905127 q^{94} +(-4.35862 - 0.0496059i) q^{95} +(2.51273 + 2.10843i) q^{97} +(-5.77942 + 2.10354i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.484738 + 0.406743i 0.342761 + 0.287611i 0.797876 0.602822i \(-0.205957\pi\)
−0.455114 + 0.890433i \(0.650402\pi\)
\(3\) 0 0
\(4\) −0.277766 1.57529i −0.138883 0.787644i
\(5\) −0.173648 + 0.984808i −0.0776578 + 0.440419i
\(6\) 0 0
\(7\) −2.04448 3.54114i −0.772739 1.33842i −0.936056 0.351850i \(-0.885553\pi\)
0.163317 0.986574i \(-0.447781\pi\)
\(8\) 1.13887 1.97259i 0.402653 0.697415i
\(9\) 0 0
\(10\) −0.484738 + 0.406743i −0.153288 + 0.128624i
\(11\) −2.17413 + 3.76571i −0.655526 + 1.13540i 0.326235 + 0.945289i \(0.394220\pi\)
−0.981762 + 0.190116i \(0.939114\pi\)
\(12\) 0 0
\(13\) −1.45826 0.530764i −0.404449 0.147207i 0.131782 0.991279i \(-0.457930\pi\)
−0.536231 + 0.844071i \(0.680152\pi\)
\(14\) 0.449299 2.54810i 0.120080 0.681008i
\(15\) 0 0
\(16\) −1.65185 + 0.601224i −0.412963 + 0.150306i
\(17\) −4.87326 4.08915i −1.18194 0.991765i −0.999964 0.00846250i \(-0.997306\pi\)
−0.181976 0.983303i \(-0.558249\pi\)
\(18\) 0 0
\(19\) 0.708014 + 4.30101i 0.162429 + 0.986720i
\(20\) 1.59959 0.357679
\(21\) 0 0
\(22\) −2.58556 + 0.941068i −0.551244 + 0.200636i
\(23\) 0.583829 + 3.31106i 0.121737 + 0.690403i 0.983193 + 0.182571i \(0.0584419\pi\)
−0.861456 + 0.507832i \(0.830447\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) −0.490990 0.850420i −0.0962911 0.166781i
\(27\) 0 0
\(28\) −5.01042 + 4.20424i −0.946881 + 0.794527i
\(29\) −3.99325 + 3.35074i −0.741529 + 0.622216i −0.933248 0.359233i \(-0.883038\pi\)
0.191719 + 0.981450i \(0.438594\pi\)
\(30\) 0 0
\(31\) −3.28366 5.68747i −0.589763 1.02150i −0.994263 0.106961i \(-0.965888\pi\)
0.404500 0.914538i \(-0.367445\pi\)
\(32\) −5.32603 1.93852i −0.941518 0.342684i
\(33\) 0 0
\(34\) −0.699019 3.96434i −0.119881 0.679878i
\(35\) 3.84236 1.39850i 0.649477 0.236390i
\(36\) 0 0
\(37\) 0.180685 0.0297045 0.0148522 0.999890i \(-0.495272\pi\)
0.0148522 + 0.999890i \(0.495272\pi\)
\(38\) −1.40621 + 2.37284i −0.228117 + 0.384926i
\(39\) 0 0
\(40\) 1.74486 + 1.46411i 0.275886 + 0.231496i
\(41\) 0.0242217 0.00881597i 0.00378279 0.00137682i −0.340128 0.940379i \(-0.610470\pi\)
0.343911 + 0.939002i \(0.388248\pi\)
\(42\) 0 0
\(43\) 0.793995 4.50297i 0.121083 0.686696i −0.862474 0.506101i \(-0.831086\pi\)
0.983557 0.180595i \(-0.0578025\pi\)
\(44\) 6.53598 + 2.37890i 0.985336 + 0.358633i
\(45\) 0 0
\(46\) −1.06375 + 1.84246i −0.156841 + 0.271656i
\(47\) 1.09575 0.919441i 0.159831 0.134114i −0.559365 0.828922i \(-0.688955\pi\)
0.719196 + 0.694807i \(0.244510\pi\)
\(48\) 0 0
\(49\) −4.85976 + 8.41736i −0.694252 + 1.20248i
\(50\) −0.316390 0.548004i −0.0447443 0.0774995i
\(51\) 0 0
\(52\) −0.431051 + 2.44461i −0.0597760 + 0.339006i
\(53\) 0.278010 + 1.57667i 0.0381876 + 0.216573i 0.997930 0.0643090i \(-0.0204843\pi\)
−0.959742 + 0.280882i \(0.909373\pi\)
\(54\) 0 0
\(55\) −3.33097 2.79501i −0.449148 0.376880i
\(56\) −9.31361 −1.24458
\(57\) 0 0
\(58\) −3.29857 −0.433124
\(59\) −7.31281 6.13617i −0.952046 0.798862i 0.0275947 0.999619i \(-0.491215\pi\)
−0.979641 + 0.200758i \(0.935660\pi\)
\(60\) 0 0
\(61\) −1.05793 5.99980i −0.135454 0.768195i −0.974543 0.224201i \(-0.928023\pi\)
0.839089 0.543994i \(-0.183088\pi\)
\(62\) 0.721625 4.09254i 0.0916464 0.519753i
\(63\) 0 0
\(64\) −0.0353865 0.0612913i −0.00442332 0.00766141i
\(65\) 0.775925 1.34394i 0.0962416 0.166695i
\(66\) 0 0
\(67\) 7.87159 6.60505i 0.961668 0.806935i −0.0195559 0.999809i \(-0.506225\pi\)
0.981224 + 0.192874i \(0.0617808\pi\)
\(68\) −5.08797 + 8.81262i −0.617007 + 1.06869i
\(69\) 0 0
\(70\) 2.43137 + 0.884946i 0.290604 + 0.105771i
\(71\) 1.88710 10.7023i 0.223957 1.27012i −0.640711 0.767782i \(-0.721360\pi\)
0.864669 0.502343i \(-0.167528\pi\)
\(72\) 0 0
\(73\) 12.7987 4.65836i 1.49798 0.545220i 0.542443 0.840093i \(-0.317500\pi\)
0.955536 + 0.294873i \(0.0952774\pi\)
\(74\) 0.0875850 + 0.0734926i 0.0101816 + 0.00854334i
\(75\) 0 0
\(76\) 6.57867 2.31000i 0.754625 0.264975i
\(77\) 17.7799 2.02620
\(78\) 0 0
\(79\) −16.2283 + 5.90661i −1.82582 + 0.664545i −0.831839 + 0.555016i \(0.812712\pi\)
−0.993984 + 0.109529i \(0.965066\pi\)
\(80\) −0.305250 1.73116i −0.0341279 0.193549i
\(81\) 0 0
\(82\) 0.0153270 + 0.00557858i 0.00169259 + 0.000616051i
\(83\) −2.57831 4.46577i −0.283007 0.490182i 0.689117 0.724650i \(-0.257999\pi\)
−0.972124 + 0.234468i \(0.924665\pi\)
\(84\) 0 0
\(85\) 4.87326 4.08915i 0.528580 0.443531i
\(86\) 2.21643 1.85981i 0.239004 0.200548i
\(87\) 0 0
\(88\) 4.95213 + 8.57735i 0.527899 + 0.914348i
\(89\) −0.477195 0.173685i −0.0505826 0.0184106i 0.316605 0.948557i \(-0.397457\pi\)
−0.367188 + 0.930147i \(0.619679\pi\)
\(90\) 0 0
\(91\) 1.10187 + 6.24904i 0.115508 + 0.655077i
\(92\) 5.05370 1.83940i 0.526885 0.191770i
\(93\) 0 0
\(94\) 0.905127 0.0933567
\(95\) −4.35862 0.0496059i −0.447185 0.00508946i
\(96\) 0 0
\(97\) 2.51273 + 2.10843i 0.255129 + 0.214079i 0.761377 0.648309i \(-0.224524\pi\)
−0.506248 + 0.862388i \(0.668968\pi\)
\(98\) −5.77942 + 2.10354i −0.583809 + 0.212489i
\(99\) 0 0
\(100\) −0.277766 + 1.57529i −0.0277766 + 0.157529i
\(101\) −3.27996 1.19381i −0.326369 0.118788i 0.173639 0.984809i \(-0.444447\pi\)
−0.500008 + 0.866021i \(0.666670\pi\)
\(102\) 0 0
\(103\) −4.31572 + 7.47504i −0.425240 + 0.736537i −0.996443 0.0842716i \(-0.973144\pi\)
0.571203 + 0.820809i \(0.306477\pi\)
\(104\) −2.70776 + 2.27208i −0.265517 + 0.222796i
\(105\) 0 0
\(106\) −0.506539 + 0.877351i −0.0491994 + 0.0852159i
\(107\) 3.13732 + 5.43399i 0.303296 + 0.525324i 0.976880 0.213786i \(-0.0685796\pi\)
−0.673584 + 0.739110i \(0.735246\pi\)
\(108\) 0 0
\(109\) 1.71297 9.71476i 0.164073 0.930506i −0.785942 0.618301i \(-0.787821\pi\)
0.950015 0.312205i \(-0.101068\pi\)
\(110\) −0.477793 2.70970i −0.0455558 0.258360i
\(111\) 0 0
\(112\) 5.50619 + 4.62024i 0.520286 + 0.436571i
\(113\) 5.24756 0.493649 0.246825 0.969060i \(-0.420613\pi\)
0.246825 + 0.969060i \(0.420613\pi\)
\(114\) 0 0
\(115\) −3.36213 −0.313521
\(116\) 6.38756 + 5.35980i 0.593071 + 0.497645i
\(117\) 0 0
\(118\) −1.04895 5.94887i −0.0965634 0.547638i
\(119\) −4.51698 + 25.6171i −0.414071 + 2.34831i
\(120\) 0 0
\(121\) −3.95372 6.84804i −0.359429 0.622550i
\(122\) 1.92756 3.33863i 0.174513 0.302266i
\(123\) 0 0
\(124\) −8.04731 + 6.75249i −0.722669 + 0.606392i
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) −5.00719 1.82247i −0.444316 0.161718i 0.110167 0.993913i \(-0.464862\pi\)
−0.554482 + 0.832195i \(0.687084\pi\)
\(128\) −1.96064 + 11.1194i −0.173298 + 0.982822i
\(129\) 0 0
\(130\) 0.922760 0.335857i 0.0809314 0.0294566i
\(131\) 1.31194 + 1.10085i 0.114625 + 0.0961816i 0.698298 0.715807i \(-0.253941\pi\)
−0.583674 + 0.811988i \(0.698385\pi\)
\(132\) 0 0
\(133\) 13.7830 11.3005i 1.19513 0.979877i
\(134\) 6.50222 0.561706
\(135\) 0 0
\(136\) −13.6163 + 4.95591i −1.16758 + 0.424966i
\(137\) −0.997739 5.65846i −0.0852426 0.483435i −0.997304 0.0733811i \(-0.976621\pi\)
0.912061 0.410054i \(-0.134490\pi\)
\(138\) 0 0
\(139\) 16.5249 + 6.01458i 1.40162 + 0.510150i 0.928660 0.370932i \(-0.120962\pi\)
0.472965 + 0.881081i \(0.343184\pi\)
\(140\) −3.27032 5.66436i −0.276393 0.478726i
\(141\) 0 0
\(142\) 5.26782 4.42023i 0.442066 0.370937i
\(143\) 5.16916 4.33744i 0.432267 0.362715i
\(144\) 0 0
\(145\) −2.60641 4.51444i −0.216451 0.374904i
\(146\) 8.09879 + 2.94772i 0.670261 + 0.243955i
\(147\) 0 0
\(148\) −0.0501882 0.284631i −0.00412544 0.0233966i
\(149\) 10.3558 3.76921i 0.848381 0.308785i 0.119001 0.992894i \(-0.462031\pi\)
0.729380 + 0.684109i \(0.239809\pi\)
\(150\) 0 0
\(151\) −2.37114 −0.192960 −0.0964802 0.995335i \(-0.530758\pi\)
−0.0964802 + 0.995335i \(0.530758\pi\)
\(152\) 9.29047 + 3.50170i 0.753557 + 0.284025i
\(153\) 0 0
\(154\) 8.61857 + 7.23184i 0.694504 + 0.582758i
\(155\) 6.17126 2.24616i 0.495688 0.180416i
\(156\) 0 0
\(157\) −0.561125 + 3.18230i −0.0447827 + 0.253975i −0.998977 0.0452110i \(-0.985604\pi\)
0.954195 + 0.299186i \(0.0967151\pi\)
\(158\) −10.2689 3.73759i −0.816952 0.297346i
\(159\) 0 0
\(160\) 2.83392 4.90849i 0.224041 0.388050i
\(161\) 10.5313 8.83679i 0.829981 0.696437i
\(162\) 0 0
\(163\) −3.29087 + 5.69996i −0.257761 + 0.446455i −0.965642 0.259877i \(-0.916318\pi\)
0.707881 + 0.706332i \(0.249651\pi\)
\(164\) −0.0206156 0.0357074i −0.00160981 0.00278828i
\(165\) 0 0
\(166\) 0.566616 3.21344i 0.0439780 0.249411i
\(167\) −2.75277 15.6118i −0.213016 1.20807i −0.884316 0.466888i \(-0.845375\pi\)
0.671300 0.741185i \(-0.265736\pi\)
\(168\) 0 0
\(169\) −8.11376 6.80825i −0.624135 0.523712i
\(170\) 4.02549 0.308741
\(171\) 0 0
\(172\) −7.31401 −0.557688
\(173\) 1.45639 + 1.22206i 0.110728 + 0.0929114i 0.696470 0.717585i \(-0.254753\pi\)
−0.585743 + 0.810497i \(0.699197\pi\)
\(174\) 0 0
\(175\) 0.710039 + 4.02683i 0.0536739 + 0.304400i
\(176\) 1.32731 7.52753i 0.100050 0.567409i
\(177\) 0 0
\(178\) −0.160670 0.278288i −0.0120427 0.0208586i
\(179\) −7.14016 + 12.3671i −0.533681 + 0.924362i 0.465545 + 0.885024i \(0.345858\pi\)
−0.999226 + 0.0393383i \(0.987475\pi\)
\(180\) 0 0
\(181\) 11.0202 9.24705i 0.819125 0.687328i −0.133642 0.991030i \(-0.542667\pi\)
0.952767 + 0.303702i \(0.0982227\pi\)
\(182\) −2.00763 + 3.47733i −0.148816 + 0.257756i
\(183\) 0 0
\(184\) 7.19626 + 2.61922i 0.530515 + 0.193092i
\(185\) −0.0313757 + 0.177940i −0.00230679 + 0.0130824i
\(186\) 0 0
\(187\) 25.9937 9.46093i 1.90085 0.691852i
\(188\) −1.75274 1.47073i −0.127832 0.107264i
\(189\) 0 0
\(190\) −2.09261 1.79688i −0.151814 0.130360i
\(191\) −24.1791 −1.74954 −0.874769 0.484540i \(-0.838987\pi\)
−0.874769 + 0.484540i \(0.838987\pi\)
\(192\) 0 0
\(193\) 4.80540 1.74902i 0.345900 0.125897i −0.163227 0.986588i \(-0.552190\pi\)
0.509128 + 0.860691i \(0.329968\pi\)
\(194\) 0.360425 + 2.04407i 0.0258770 + 0.146756i
\(195\) 0 0
\(196\) 14.6096 + 5.31747i 1.04355 + 0.379819i
\(197\) 0.0321431 + 0.0556735i 0.00229010 + 0.00396658i 0.867168 0.498015i \(-0.165938\pi\)
−0.864878 + 0.501982i \(0.832604\pi\)
\(198\) 0 0
\(199\) −4.88735 + 4.10098i −0.346455 + 0.290711i −0.799365 0.600846i \(-0.794831\pi\)
0.452910 + 0.891556i \(0.350386\pi\)
\(200\) −1.74486 + 1.46411i −0.123380 + 0.103528i
\(201\) 0 0
\(202\) −1.10435 1.91279i −0.0777017 0.134583i
\(203\) 20.0295 + 7.29015i 1.40580 + 0.511668i
\(204\) 0 0
\(205\) 0.00447599 + 0.0253846i 0.000312617 + 0.00177294i
\(206\) −5.13241 + 1.86805i −0.357592 + 0.130153i
\(207\) 0 0
\(208\) 2.72794 0.189149
\(209\) −17.7357 6.68481i −1.22680 0.462398i
\(210\) 0 0
\(211\) −4.52874 3.80006i −0.311771 0.261607i 0.473453 0.880819i \(-0.343008\pi\)
−0.785224 + 0.619212i \(0.787452\pi\)
\(212\) 2.40649 0.875891i 0.165278 0.0601564i
\(213\) 0 0
\(214\) −0.689464 + 3.91015i −0.0471308 + 0.267292i
\(215\) 4.29668 + 1.56386i 0.293031 + 0.106655i
\(216\) 0 0
\(217\) −13.4267 + 23.2558i −0.911466 + 1.57870i
\(218\) 4.78176 4.01237i 0.323862 0.271752i
\(219\) 0 0
\(220\) −3.47772 + 6.02359i −0.234468 + 0.406110i
\(221\) 4.93612 + 8.54961i 0.332039 + 0.575109i
\(222\) 0 0
\(223\) −5.09043 + 28.8693i −0.340881 + 1.93323i 0.0179785 + 0.999838i \(0.494277\pi\)
−0.358859 + 0.933392i \(0.616834\pi\)
\(224\) 4.02439 + 22.8234i 0.268891 + 1.52495i
\(225\) 0 0
\(226\) 2.54369 + 2.13441i 0.169204 + 0.141979i
\(227\) −8.00202 −0.531113 −0.265557 0.964095i \(-0.585556\pi\)
−0.265557 + 0.964095i \(0.585556\pi\)
\(228\) 0 0
\(229\) 28.2694 1.86809 0.934047 0.357150i \(-0.116251\pi\)
0.934047 + 0.357150i \(0.116251\pi\)
\(230\) −1.62975 1.36753i −0.107463 0.0901720i
\(231\) 0 0
\(232\) 2.06181 + 11.6931i 0.135365 + 0.767691i
\(233\) 1.18970 6.74715i 0.0779401 0.442020i −0.920718 0.390229i \(-0.872396\pi\)
0.998658 0.0517912i \(-0.0164930\pi\)
\(234\) 0 0
\(235\) 0.715198 + 1.23876i 0.0466544 + 0.0808078i
\(236\) −7.63499 + 13.2242i −0.496996 + 0.860821i
\(237\) 0 0
\(238\) −12.6091 + 10.5803i −0.817328 + 0.685820i
\(239\) −6.69674 + 11.5991i −0.433176 + 0.750283i −0.997145 0.0755132i \(-0.975941\pi\)
0.563969 + 0.825796i \(0.309274\pi\)
\(240\) 0 0
\(241\) 24.1069 + 8.77421i 1.55286 + 0.565196i 0.969087 0.246717i \(-0.0793520\pi\)
0.583777 + 0.811914i \(0.301574\pi\)
\(242\) 0.868879 4.92766i 0.0558536 0.316762i
\(243\) 0 0
\(244\) −9.15755 + 3.33308i −0.586252 + 0.213378i
\(245\) −7.44559 6.24759i −0.475681 0.399144i
\(246\) 0 0
\(247\) 1.25035 6.64779i 0.0795581 0.422989i
\(248\) −14.9587 −0.949879
\(249\) 0 0
\(250\) 0.594619 0.216424i 0.0376070 0.0136878i
\(251\) 1.58376 + 8.98194i 0.0999660 + 0.566935i 0.993112 + 0.117168i \(0.0373817\pi\)
−0.893146 + 0.449767i \(0.851507\pi\)
\(252\) 0 0
\(253\) −13.7378 5.00015i −0.863688 0.314357i
\(254\) −1.68590 2.92006i −0.105783 0.183221i
\(255\) 0 0
\(256\) −5.58156 + 4.68348i −0.348847 + 0.292718i
\(257\) 18.9570 15.9068i 1.18250 0.992237i 0.182543 0.983198i \(-0.441567\pi\)
0.999959 0.00903962i \(-0.00287744\pi\)
\(258\) 0 0
\(259\) −0.369407 0.639831i −0.0229538 0.0397572i
\(260\) −2.33262 0.849004i −0.144663 0.0526530i
\(261\) 0 0
\(262\) 0.188184 + 1.06725i 0.0116261 + 0.0659347i
\(263\) −13.7492 + 5.00428i −0.847809 + 0.308577i −0.729147 0.684357i \(-0.760083\pi\)
−0.118662 + 0.992935i \(0.537861\pi\)
\(264\) 0 0
\(265\) −1.60099 −0.0983483
\(266\) 11.2775 + 0.128351i 0.691469 + 0.00786969i
\(267\) 0 0
\(268\) −12.5913 10.5654i −0.769136 0.645382i
\(269\) 16.1661 5.88396i 0.985662 0.358752i 0.201623 0.979463i \(-0.435378\pi\)
0.784039 + 0.620712i \(0.213156\pi\)
\(270\) 0 0
\(271\) 2.37389 13.4630i 0.144203 0.817819i −0.823800 0.566881i \(-0.808150\pi\)
0.968003 0.250938i \(-0.0807389\pi\)
\(272\) 10.5084 + 3.82475i 0.637165 + 0.231909i
\(273\) 0 0
\(274\) 1.81790 3.14869i 0.109823 0.190220i
\(275\) 3.33097 2.79501i 0.200865 0.168546i
\(276\) 0 0
\(277\) 6.72984 11.6564i 0.404357 0.700367i −0.589889 0.807484i \(-0.700829\pi\)
0.994246 + 0.107117i \(0.0341620\pi\)
\(278\) 5.56386 + 9.63689i 0.333698 + 0.577982i
\(279\) 0 0
\(280\) 1.61729 9.17211i 0.0966516 0.548139i
\(281\) 3.03476 + 17.2110i 0.181039 + 1.02672i 0.930940 + 0.365172i \(0.118990\pi\)
−0.749901 + 0.661550i \(0.769899\pi\)
\(282\) 0 0
\(283\) −16.1126 13.5201i −0.957794 0.803684i 0.0227990 0.999740i \(-0.492742\pi\)
−0.980593 + 0.196056i \(0.937187\pi\)
\(284\) −17.3833 −1.03151
\(285\) 0 0
\(286\) 4.26991 0.252485
\(287\) −0.0807392 0.0677483i −0.00476589 0.00399905i
\(288\) 0 0
\(289\) 4.07550 + 23.1133i 0.239735 + 1.35961i
\(290\) 0.572791 3.24846i 0.0336354 0.190756i
\(291\) 0 0
\(292\) −10.8933 18.8678i −0.637483 1.10415i
\(293\) −5.36574 + 9.29373i −0.313470 + 0.542945i −0.979111 0.203326i \(-0.934825\pi\)
0.665641 + 0.746272i \(0.268158\pi\)
\(294\) 0 0
\(295\) 7.31281 6.13617i 0.425768 0.357262i
\(296\) 0.205778 0.356418i 0.0119606 0.0207164i
\(297\) 0 0
\(298\) 6.55295 + 2.38508i 0.379602 + 0.138164i
\(299\) 0.906014 5.13826i 0.0523962 0.297153i
\(300\) 0 0
\(301\) −17.5689 + 6.39457i −1.01266 + 0.368577i
\(302\) −1.14938 0.964444i −0.0661394 0.0554975i
\(303\) 0 0
\(304\) −3.75541 6.67896i −0.215387 0.383064i
\(305\) 6.09235 0.348847
\(306\) 0 0
\(307\) 2.54584 0.926610i 0.145299 0.0528845i −0.268347 0.963322i \(-0.586477\pi\)
0.413646 + 0.910438i \(0.364255\pi\)
\(308\) −4.93864 28.0084i −0.281405 1.59593i
\(309\) 0 0
\(310\) 3.90505 + 1.42132i 0.221792 + 0.0807257i
\(311\) −3.62852 6.28478i −0.205755 0.356377i 0.744618 0.667491i \(-0.232632\pi\)
−0.950373 + 0.311113i \(0.899298\pi\)
\(312\) 0 0
\(313\) −6.64853 + 5.57878i −0.375797 + 0.315331i −0.811050 0.584977i \(-0.801103\pi\)
0.435253 + 0.900308i \(0.356659\pi\)
\(314\) −1.56638 + 1.31435i −0.0883958 + 0.0741729i
\(315\) 0 0
\(316\) 13.8123 + 23.9235i 0.777000 + 1.34580i
\(317\) −30.0020 10.9198i −1.68508 0.613319i −0.691089 0.722770i \(-0.742869\pi\)
−0.993992 + 0.109451i \(0.965091\pi\)
\(318\) 0 0
\(319\) −3.93604 22.3224i −0.220376 1.24981i
\(320\) 0.0665049 0.0242058i 0.00371774 0.00135315i
\(321\) 0 0
\(322\) 8.69922 0.484788
\(323\) 14.1372 23.8551i 0.786613 1.32734i
\(324\) 0 0
\(325\) 1.18879 + 0.997510i 0.0659420 + 0.0553319i
\(326\) −3.91363 + 1.42445i −0.216756 + 0.0788928i
\(327\) 0 0
\(328\) 0.0101952 0.0578197i 0.000562935 0.00319256i
\(329\) −5.49609 2.00041i −0.303009 0.110286i
\(330\) 0 0
\(331\) −12.1500 + 21.0443i −0.667822 + 1.15670i 0.310690 + 0.950511i \(0.399440\pi\)
−0.978512 + 0.206190i \(0.933893\pi\)
\(332\) −6.31871 + 5.30202i −0.346784 + 0.290986i
\(333\) 0 0
\(334\) 5.01560 8.68728i 0.274442 0.475347i
\(335\) 5.13781 + 8.89896i 0.280709 + 0.486202i
\(336\) 0 0
\(337\) 4.92922 27.9550i 0.268512 1.52280i −0.490334 0.871534i \(-0.663125\pi\)
0.758846 0.651270i \(-0.225764\pi\)
\(338\) −1.16384 6.60044i −0.0633043 0.359016i
\(339\) 0 0
\(340\) −7.79522 6.54097i −0.422755 0.354734i
\(341\) 28.5565 1.54642
\(342\) 0 0
\(343\) 11.1200 0.600424
\(344\) −7.97824 6.69454i −0.430158 0.360945i
\(345\) 0 0
\(346\) 0.208905 + 1.18476i 0.0112308 + 0.0636929i
\(347\) 5.40071 30.6289i 0.289925 1.64425i −0.397217 0.917725i \(-0.630024\pi\)
0.687142 0.726523i \(-0.258865\pi\)
\(348\) 0 0
\(349\) −8.73989 15.1379i −0.467836 0.810315i 0.531489 0.847065i \(-0.321633\pi\)
−0.999324 + 0.0367503i \(0.988299\pi\)
\(350\) −1.29370 + 2.24076i −0.0691514 + 0.119774i
\(351\) 0 0
\(352\) 18.8794 15.8417i 1.00627 0.844365i
\(353\) −4.41270 + 7.64303i −0.234865 + 0.406797i −0.959233 0.282615i \(-0.908798\pi\)
0.724369 + 0.689413i \(0.242131\pi\)
\(354\) 0 0
\(355\) 10.2120 + 3.71686i 0.541996 + 0.197270i
\(356\) −0.141055 + 0.799964i −0.00747591 + 0.0423980i
\(357\) 0 0
\(358\) −8.49136 + 3.09060i −0.448782 + 0.163343i
\(359\) −15.2610 12.8055i −0.805443 0.675847i 0.144073 0.989567i \(-0.453980\pi\)
−0.949515 + 0.313720i \(0.898425\pi\)
\(360\) 0 0
\(361\) −17.9974 + 6.09035i −0.947233 + 0.320545i
\(362\) 9.10309 0.478448
\(363\) 0 0
\(364\) 9.53797 3.47154i 0.499925 0.181958i
\(365\) 2.36511 + 13.4132i 0.123796 + 0.702080i
\(366\) 0 0
\(367\) −7.94641 2.89226i −0.414799 0.150975i 0.126186 0.992007i \(-0.459726\pi\)
−0.540985 + 0.841032i \(0.681949\pi\)
\(368\) −2.95509 5.11836i −0.154044 0.266813i
\(369\) 0 0
\(370\) −0.0875850 + 0.0734926i −0.00455333 + 0.00382070i
\(371\) 5.01483 4.20794i 0.260357 0.218465i
\(372\) 0 0
\(373\) 3.56895 + 6.18160i 0.184793 + 0.320071i 0.943507 0.331353i \(-0.107505\pi\)
−0.758714 + 0.651424i \(0.774172\pi\)
\(374\) 16.4483 + 5.98669i 0.850522 + 0.309565i
\(375\) 0 0
\(376\) −0.565760 3.20859i −0.0291769 0.165470i
\(377\) 7.60166 2.76678i 0.391505 0.142496i
\(378\) 0 0
\(379\) 6.11358 0.314033 0.157017 0.987596i \(-0.449812\pi\)
0.157017 + 0.987596i \(0.449812\pi\)
\(380\) 1.13253 + 6.87985i 0.0580976 + 0.352929i
\(381\) 0 0
\(382\) −11.7205 9.83469i −0.599674 0.503186i
\(383\) 0.492206 0.179148i 0.0251505 0.00915404i −0.329414 0.944185i \(-0.606851\pi\)
0.354565 + 0.935031i \(0.384629\pi\)
\(384\) 0 0
\(385\) −3.08744 + 17.5097i −0.157351 + 0.892379i
\(386\) 3.04076 + 1.10675i 0.154771 + 0.0563319i
\(387\) 0 0
\(388\) 2.62343 4.54392i 0.133185 0.230683i
\(389\) 1.91233 1.60464i 0.0969590 0.0813583i −0.593020 0.805188i \(-0.702064\pi\)
0.689979 + 0.723830i \(0.257620\pi\)
\(390\) 0 0
\(391\) 10.6943 18.5230i 0.540832 0.936749i
\(392\) 11.0693 + 19.1726i 0.559085 + 0.968364i
\(393\) 0 0
\(394\) −0.00706385 + 0.0400611i −0.000355872 + 0.00201825i
\(395\) −2.99886 17.0074i −0.150889 0.855735i
\(396\) 0 0
\(397\) −2.21214 1.85621i −0.111024 0.0931604i 0.585586 0.810611i \(-0.300865\pi\)
−0.696610 + 0.717450i \(0.745309\pi\)
\(398\) −4.03713 −0.202363
\(399\) 0 0
\(400\) 1.75786 0.0878931
\(401\) 13.2096 + 11.0842i 0.659658 + 0.553519i 0.909984 0.414643i \(-0.136093\pi\)
−0.250326 + 0.968162i \(0.580538\pi\)
\(402\) 0 0
\(403\) 1.76973 + 10.0367i 0.0881567 + 0.499962i
\(404\) −0.969531 + 5.49848i −0.0482360 + 0.273560i
\(405\) 0 0
\(406\) 6.74385 + 11.6807i 0.334692 + 0.579703i
\(407\) −0.392834 + 0.680409i −0.0194721 + 0.0337266i
\(408\) 0 0
\(409\) −20.0017 + 16.7834i −0.989019 + 0.829886i −0.985425 0.170108i \(-0.945588\pi\)
−0.00359375 + 0.999994i \(0.501144\pi\)
\(410\) −0.00815533 + 0.0141255i −0.000402763 + 0.000697606i
\(411\) 0 0
\(412\) 12.9741 + 4.72218i 0.639188 + 0.232645i
\(413\) −6.77817 + 38.4409i −0.333532 + 1.89155i
\(414\) 0 0
\(415\) 4.84565 1.76367i 0.237863 0.0865752i
\(416\) 6.73785 + 5.65373i 0.330350 + 0.277197i
\(417\) 0 0
\(418\) −5.87816 10.4543i −0.287510 0.511334i
\(419\) 0.112702 0.00550586 0.00275293 0.999996i \(-0.499124\pi\)
0.00275293 + 0.999996i \(0.499124\pi\)
\(420\) 0 0
\(421\) −18.9996 + 6.91529i −0.925985 + 0.337031i −0.760617 0.649201i \(-0.775103\pi\)
−0.165368 + 0.986232i \(0.552881\pi\)
\(422\) −0.649600 3.68407i −0.0316221 0.179338i
\(423\) 0 0
\(424\) 3.42674 + 1.24723i 0.166417 + 0.0605710i
\(425\) 3.18080 + 5.50930i 0.154291 + 0.267240i
\(426\) 0 0
\(427\) −19.0832 + 16.0127i −0.923500 + 0.774909i
\(428\) 7.68866 6.45156i 0.371646 0.311848i
\(429\) 0 0
\(430\) 1.44667 + 2.50571i 0.0697648 + 0.120836i
\(431\) −38.1011 13.8677i −1.83526 0.667982i −0.991306 0.131573i \(-0.957997\pi\)
−0.843958 0.536409i \(-0.819781\pi\)
\(432\) 0 0
\(433\) −3.95457 22.4275i −0.190044 1.07779i −0.919301 0.393555i \(-0.871245\pi\)
0.729257 0.684240i \(-0.239866\pi\)
\(434\) −15.9676 + 5.81172i −0.766468 + 0.278972i
\(435\) 0 0
\(436\) −15.7794 −0.755694
\(437\) −13.8275 + 4.85533i −0.661461 + 0.232262i
\(438\) 0 0
\(439\) −25.0285 21.0014i −1.19455 1.00234i −0.999769 0.0214950i \(-0.993157\pi\)
−0.194777 0.980848i \(-0.562398\pi\)
\(440\) −9.30697 + 3.38746i −0.443692 + 0.161491i
\(441\) 0 0
\(442\) −1.08477 + 6.15205i −0.0515974 + 0.292623i
\(443\) −13.0384 4.74560i −0.619475 0.225470i 0.0131689 0.999913i \(-0.495808\pi\)
−0.632644 + 0.774443i \(0.718030\pi\)
\(444\) 0 0
\(445\) 0.253910 0.439786i 0.0120365 0.0208478i
\(446\) −14.2099 + 11.9235i −0.672859 + 0.564596i
\(447\) 0 0
\(448\) −0.144694 + 0.250617i −0.00683614 + 0.0118405i
\(449\) −3.00375 5.20265i −0.141756 0.245528i 0.786402 0.617715i \(-0.211941\pi\)
−0.928158 + 0.372187i \(0.878608\pi\)
\(450\) 0 0
\(451\) −0.0194628 + 0.110379i −0.000916467 + 0.00519754i
\(452\) −1.45759 8.26642i −0.0685594 0.388820i
\(453\) 0 0
\(454\) −3.87889 3.25477i −0.182045 0.152754i
\(455\) −6.34544 −0.297479
\(456\) 0 0
\(457\) −23.9751 −1.12151 −0.560754 0.827982i \(-0.689489\pi\)
−0.560754 + 0.827982i \(0.689489\pi\)
\(458\) 13.7032 + 11.4984i 0.640311 + 0.537285i
\(459\) 0 0
\(460\) 0.933886 + 5.29633i 0.0435426 + 0.246943i
\(461\) 6.26625 35.5376i 0.291848 1.65515i −0.387896 0.921703i \(-0.626798\pi\)
0.679744 0.733450i \(-0.262091\pi\)
\(462\) 0 0
\(463\) −3.52141 6.09926i −0.163654 0.283457i 0.772523 0.634987i \(-0.218995\pi\)
−0.936176 + 0.351531i \(0.885661\pi\)
\(464\) 4.58171 7.93576i 0.212701 0.368408i
\(465\) 0 0
\(466\) 3.32105 2.78669i 0.153845 0.129091i
\(467\) 19.8650 34.4072i 0.919244 1.59218i 0.118678 0.992933i \(-0.462134\pi\)
0.800566 0.599245i \(-0.204532\pi\)
\(468\) 0 0
\(469\) −39.4826 14.3705i −1.82314 0.663568i
\(470\) −0.157174 + 0.891376i −0.00724988 + 0.0411161i
\(471\) 0 0
\(472\) −20.4325 + 7.43683i −0.940483 + 0.342308i
\(473\) 15.2306 + 12.7800i 0.700305 + 0.587626i
\(474\) 0 0
\(475\) 0.805718 4.28379i 0.0369689 0.196554i
\(476\) 41.6089 1.90714
\(477\) 0 0
\(478\) −7.96402 + 2.89867i −0.364266 + 0.132582i
\(479\) 6.30401 + 35.7518i 0.288038 + 1.63354i 0.694229 + 0.719754i \(0.255745\pi\)
−0.406192 + 0.913788i \(0.633143\pi\)
\(480\) 0 0
\(481\) −0.263486 0.0959012i −0.0120139 0.00437272i
\(482\) 8.11670 + 14.0585i 0.369705 + 0.640349i
\(483\) 0 0
\(484\) −9.68943 + 8.13040i −0.440429 + 0.369564i
\(485\) −2.51273 + 2.10843i −0.114097 + 0.0957389i
\(486\) 0 0
\(487\) 1.26752 + 2.19541i 0.0574368 + 0.0994835i 0.893314 0.449433i \(-0.148374\pi\)
−0.835877 + 0.548916i \(0.815041\pi\)
\(488\) −13.0400 4.74616i −0.590292 0.214849i
\(489\) 0 0
\(490\) −1.06799 6.05689i −0.0482470 0.273622i
\(491\) −34.1243 + 12.4202i −1.54001 + 0.560516i −0.966047 0.258367i \(-0.916815\pi\)
−0.573959 + 0.818884i \(0.694593\pi\)
\(492\) 0 0
\(493\) 33.1619 1.49354
\(494\) 3.31004 2.71386i 0.148926 0.122102i
\(495\) 0 0
\(496\) 8.84356 + 7.42063i 0.397088 + 0.333196i
\(497\) −41.7563 + 15.1980i −1.87303 + 0.681725i
\(498\) 0 0
\(499\) −3.11167 + 17.6471i −0.139297 + 0.789994i 0.832473 + 0.554066i \(0.186924\pi\)
−0.971770 + 0.235929i \(0.924187\pi\)
\(500\) −1.50312 0.547092i −0.0672217 0.0244667i
\(501\) 0 0
\(502\) −2.88564 + 4.99807i −0.128792 + 0.223075i
\(503\) 15.7096 13.1819i 0.700457 0.587753i −0.221447 0.975173i \(-0.571078\pi\)
0.921904 + 0.387419i \(0.126633\pi\)
\(504\) 0 0
\(505\) 1.74523 3.02283i 0.0776618 0.134514i
\(506\) −4.62546 8.01153i −0.205627 0.356156i
\(507\) 0 0
\(508\) −1.48008 + 8.39397i −0.0656681 + 0.372422i
\(509\) 2.67442 + 15.1674i 0.118542 + 0.672283i 0.984936 + 0.172922i \(0.0553207\pi\)
−0.866394 + 0.499361i \(0.833568\pi\)
\(510\) 0 0
\(511\) −42.6626 35.7982i −1.88728 1.58362i
\(512\) 17.9712 0.794223
\(513\) 0 0
\(514\) 15.6591 0.690695
\(515\) −6.61206 5.54818i −0.291362 0.244482i
\(516\) 0 0
\(517\) 1.08005 + 6.12526i 0.0475004 + 0.269388i
\(518\) 0.0811817 0.460404i 0.00356692 0.0202290i
\(519\) 0 0
\(520\) −1.76736 3.06116i −0.0775040 0.134241i
\(521\) −1.17999 + 2.04381i −0.0516965 + 0.0895409i −0.890716 0.454561i \(-0.849796\pi\)
0.839019 + 0.544102i \(0.183130\pi\)
\(522\) 0 0
\(523\) 14.5909 12.2432i 0.638014 0.535358i −0.265393 0.964140i \(-0.585502\pi\)
0.903408 + 0.428783i \(0.141057\pi\)
\(524\) 1.36974 2.37246i 0.0598374 0.103641i
\(525\) 0 0
\(526\) −8.70019 3.16661i −0.379346 0.138071i
\(527\) −7.25478 + 41.1439i −0.316023 + 1.79226i
\(528\) 0 0
\(529\) 10.9907 4.00028i 0.477856 0.173925i
\(530\) −0.776063 0.651194i −0.0337100 0.0282861i
\(531\) 0 0
\(532\) −21.6300 18.5732i −0.937777 0.805252i
\(533\) −0.0400008 −0.00173263
\(534\) 0 0
\(535\) −5.89623 + 2.14605i −0.254916 + 0.0927819i
\(536\) −4.06429 23.0497i −0.175551 0.995597i
\(537\) 0 0
\(538\) 10.2296 + 3.72326i 0.441028 + 0.160521i
\(539\) −21.1316 36.6009i −0.910200 1.57651i
\(540\) 0 0
\(541\) −3.83099 + 3.21458i −0.164707 + 0.138206i −0.721416 0.692502i \(-0.756508\pi\)
0.556709 + 0.830708i \(0.312064\pi\)
\(542\) 6.62670 5.56046i 0.284641 0.238842i
\(543\) 0 0
\(544\) 18.0282 + 31.2258i 0.772955 + 1.33880i
\(545\) 9.26972 + 3.37390i 0.397071 + 0.144522i
\(546\) 0 0
\(547\) −0.426450 2.41852i −0.0182337 0.103408i 0.974333 0.225113i \(-0.0722751\pi\)
−0.992566 + 0.121705i \(0.961164\pi\)
\(548\) −8.63656 + 3.14345i −0.368936 + 0.134282i
\(549\) 0 0
\(550\) 2.75150 0.117324
\(551\) −17.2388 14.8027i −0.734400 0.630615i
\(552\) 0 0
\(553\) 54.0944 + 45.3906i 2.30033 + 1.93020i
\(554\) 8.00339 2.91299i 0.340031 0.123761i
\(555\) 0 0
\(556\) 4.88463 27.7021i 0.207155 1.17483i
\(557\) −4.38265 1.59515i −0.185699 0.0675889i 0.247497 0.968889i \(-0.420392\pi\)
−0.433196 + 0.901300i \(0.642614\pi\)
\(558\) 0 0
\(559\) −3.54786 + 6.14508i −0.150059 + 0.259909i
\(560\) −5.50619 + 4.62024i −0.232679 + 0.195241i
\(561\) 0 0
\(562\) −5.52939 + 9.57719i −0.233243 + 0.403989i
\(563\) 17.3165 + 29.9930i 0.729803 + 1.26406i 0.956966 + 0.290199i \(0.0937215\pi\)
−0.227163 + 0.973857i \(0.572945\pi\)
\(564\) 0 0
\(565\) −0.911229 + 5.16784i −0.0383357 + 0.217413i
\(566\) −2.31118 13.1074i −0.0971463 0.550944i
\(567\) 0 0
\(568\) −18.9620 15.9110i −0.795628 0.667611i
\(569\) 20.6116 0.864081 0.432041 0.901854i \(-0.357794\pi\)
0.432041 + 0.901854i \(0.357794\pi\)
\(570\) 0 0
\(571\) 11.1132 0.465071 0.232536 0.972588i \(-0.425298\pi\)
0.232536 + 0.972588i \(0.425298\pi\)
\(572\) −8.26853 6.93812i −0.345725 0.290097i
\(573\) 0 0
\(574\) −0.0115812 0.0656803i −0.000483390 0.00274144i
\(575\) 0.583829 3.31106i 0.0243473 0.138081i
\(576\) 0 0
\(577\) 14.3527 + 24.8596i 0.597510 + 1.03492i 0.993187 + 0.116528i \(0.0371765\pi\)
−0.395677 + 0.918390i \(0.629490\pi\)
\(578\) −7.42564 + 12.8616i −0.308866 + 0.534971i
\(579\) 0 0
\(580\) −6.38756 + 5.35980i −0.265229 + 0.222554i
\(581\) −10.5426 + 18.2603i −0.437381 + 0.757566i
\(582\) 0 0
\(583\) −6.54172 2.38099i −0.270930 0.0986106i
\(584\) 5.38713 30.5519i 0.222921 1.26425i
\(585\) 0 0
\(586\) −6.38114 + 2.32254i −0.263602 + 0.0959434i
\(587\) −1.37306 1.15213i −0.0566723 0.0475537i 0.614012 0.789297i \(-0.289555\pi\)
−0.670684 + 0.741743i \(0.733999\pi\)
\(588\) 0 0
\(589\) 22.1370 18.1499i 0.912139 0.747852i
\(590\) 6.04064 0.248689
\(591\) 0 0
\(592\) −0.298465 + 0.108632i −0.0122668 + 0.00446476i
\(593\) −0.291962 1.65580i −0.0119894 0.0679955i 0.978226 0.207542i \(-0.0665465\pi\)
−0.990215 + 0.139547i \(0.955435\pi\)
\(594\) 0 0
\(595\) −24.4435 8.89671i −1.00209 0.364730i
\(596\) −8.81407 15.2664i −0.361039 0.625337i
\(597\) 0 0
\(598\) 2.52913 2.12220i 0.103424 0.0867830i
\(599\) 1.65586 1.38943i 0.0676568 0.0567708i −0.608332 0.793683i \(-0.708161\pi\)
0.675989 + 0.736912i \(0.263717\pi\)
\(600\) 0 0
\(601\) −2.21602 3.83826i −0.0903934 0.156566i 0.817283 0.576236i \(-0.195479\pi\)
−0.907677 + 0.419670i \(0.862146\pi\)
\(602\) −11.1173 4.04636i −0.453106 0.164917i
\(603\) 0 0
\(604\) 0.658620 + 3.73522i 0.0267989 + 0.151984i
\(605\) 7.43056 2.70450i 0.302095 0.109954i
\(606\) 0 0
\(607\) 29.9817 1.21692 0.608460 0.793585i \(-0.291788\pi\)
0.608460 + 0.793585i \(0.291788\pi\)
\(608\) 4.56668 24.2798i 0.185203 0.984676i
\(609\) 0 0
\(610\) 2.95319 + 2.47802i 0.119571 + 0.100332i
\(611\) −2.08589 + 0.759203i −0.0843862 + 0.0307141i
\(612\) 0 0
\(613\) 3.44456 19.5351i 0.139124 0.789013i −0.832774 0.553613i \(-0.813249\pi\)
0.971898 0.235400i \(-0.0756402\pi\)
\(614\) 1.61096 + 0.586341i 0.0650130 + 0.0236628i
\(615\) 0 0
\(616\) 20.2490 35.0724i 0.815857 1.41311i
\(617\) −16.1011 + 13.5104i −0.648206 + 0.543909i −0.906526 0.422150i \(-0.861275\pi\)
0.258320 + 0.966059i \(0.416831\pi\)
\(618\) 0 0
\(619\) −10.1316 + 17.5484i −0.407223 + 0.705331i −0.994577 0.103999i \(-0.966836\pi\)
0.587354 + 0.809330i \(0.300169\pi\)
\(620\) −5.25251 9.09761i −0.210946 0.365369i
\(621\) 0 0
\(622\) 0.797413 4.52235i 0.0319733 0.181330i
\(623\) 0.360573 + 2.04491i 0.0144460 + 0.0819275i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) −5.49193 −0.219501
\(627\) 0 0
\(628\) 5.16890 0.206261
\(629\) −0.880527 0.738850i −0.0351089 0.0294599i
\(630\) 0 0
\(631\) 6.98027 + 39.5871i 0.277880 + 1.57594i 0.729661 + 0.683809i \(0.239678\pi\)
−0.451781 + 0.892129i \(0.649211\pi\)
\(632\) −6.83066 + 38.7386i −0.271709 + 1.54094i
\(633\) 0 0
\(634\) −10.1015 17.4964i −0.401183 0.694870i
\(635\) 2.66427 4.61465i 0.105728 0.183127i
\(636\) 0 0
\(637\) 11.5544 9.69532i 0.457803 0.384143i
\(638\) 7.17154 12.4215i 0.283924 0.491771i
\(639\) 0 0
\(640\) −10.6100 3.86171i −0.419396 0.152648i
\(641\) −0.606201 + 3.43794i −0.0239435 + 0.135790i −0.994436 0.105340i \(-0.966407\pi\)
0.970493 + 0.241130i \(0.0775181\pi\)
\(642\) 0 0
\(643\) −34.0072 + 12.3776i −1.34111 + 0.488125i −0.910162 0.414252i \(-0.864043\pi\)
−0.430949 + 0.902376i \(0.641821\pi\)
\(644\) −16.8457 14.1352i −0.663814 0.557006i
\(645\) 0 0
\(646\) 16.5557 5.81330i 0.651377 0.228721i
\(647\) 21.1005 0.829545 0.414772 0.909925i \(-0.363861\pi\)
0.414772 + 0.909925i \(0.363861\pi\)
\(648\) 0 0
\(649\) 39.0061 14.1971i 1.53112 0.557283i
\(650\) 0.170519 + 0.967062i 0.00668831 + 0.0379313i
\(651\) 0 0
\(652\) 9.89317 + 3.60082i 0.387446 + 0.141019i
\(653\) −8.38024 14.5150i −0.327944 0.568016i 0.654160 0.756356i \(-0.273022\pi\)
−0.982104 + 0.188341i \(0.939689\pi\)
\(654\) 0 0
\(655\) −1.31194 + 1.10085i −0.0512617 + 0.0430137i
\(656\) −0.0347102 + 0.0291253i −0.00135521 + 0.00113715i
\(657\) 0 0
\(658\) −1.85051 3.20518i −0.0721404 0.124951i
\(659\) 34.8179 + 12.6727i 1.35631 + 0.493658i 0.914913 0.403652i \(-0.132259\pi\)
0.441401 + 0.897310i \(0.354482\pi\)
\(660\) 0 0
\(661\) 3.76649 + 21.3608i 0.146500 + 0.830841i 0.966151 + 0.257978i \(0.0830561\pi\)
−0.819651 + 0.572863i \(0.805833\pi\)
\(662\) −14.4492 + 5.25908i −0.561584 + 0.204400i
\(663\) 0 0
\(664\) −11.7455 −0.455814
\(665\) 8.73543 + 15.5359i 0.338745 + 0.602455i
\(666\) 0 0
\(667\) −13.4259 11.2656i −0.519851 0.436207i
\(668\) −23.8284 + 8.67282i −0.921948 + 0.335561i
\(669\) 0 0
\(670\) −1.12910 + 6.40343i −0.0436209 + 0.247386i
\(671\) 24.8936 + 9.06052i 0.961006 + 0.349777i
\(672\) 0 0
\(673\) 2.69790 4.67290i 0.103996 0.180127i −0.809331 0.587352i \(-0.800170\pi\)
0.913328 + 0.407225i \(0.133504\pi\)
\(674\) 13.7599 11.5459i 0.530011 0.444732i
\(675\) 0 0
\(676\) −8.47123 + 14.6726i −0.325817 + 0.564331i
\(677\) −15.4611 26.7794i −0.594217 1.02921i −0.993657 0.112455i \(-0.964129\pi\)
0.399440 0.916759i \(-0.369205\pi\)
\(678\) 0 0
\(679\) 2.32902 13.2086i 0.0893798 0.506898i
\(680\) −2.51618 14.2700i −0.0964912 0.547229i
\(681\) 0 0
\(682\) 13.8424 + 11.6152i 0.530053 + 0.444767i
\(683\) 21.3136 0.815542 0.407771 0.913084i \(-0.366306\pi\)
0.407771 + 0.913084i \(0.366306\pi\)
\(684\) 0 0
\(685\) 5.74575 0.219534
\(686\) 5.39029 + 4.52299i 0.205802 + 0.172689i
\(687\) 0 0
\(688\) 1.39573 + 7.91560i 0.0532118 + 0.301779i
\(689\) 0.431429 2.44676i 0.0164362 0.0932141i
\(690\) 0 0
\(691\) 3.81597 + 6.60946i 0.145166 + 0.251436i 0.929435 0.368986i \(-0.120295\pi\)
−0.784269 + 0.620421i \(0.786962\pi\)
\(692\) 1.52056 2.63368i 0.0578029 0.100118i
\(693\) 0 0
\(694\) 15.0760 12.6503i 0.572279 0.480199i
\(695\) −8.79272 + 15.2294i −0.333527 + 0.577686i
\(696\) 0 0
\(697\) −0.154089 0.0560837i −0.00583652 0.00212432i
\(698\) 1.92070 10.8928i 0.0726995 0.412299i
\(699\) 0 0
\(700\) 6.14619 2.23703i 0.232304 0.0845518i
\(701\) −12.1942 10.2321i −0.460568 0.386463i 0.382772 0.923843i \(-0.374970\pi\)
−0.843340 + 0.537380i \(0.819414\pi\)
\(702\) 0 0
\(703\) 0.127928 + 0.777130i 0.00482488 + 0.0293100i
\(704\) 0.307740 0.0115984
\(705\) 0 0
\(706\) −5.24776 + 1.91003i −0.197502 + 0.0718848i
\(707\) 2.47837 + 14.0555i 0.0932085 + 0.528612i
\(708\) 0 0
\(709\) 37.3356 + 13.5890i 1.40217 + 0.510347i 0.928821 0.370530i \(-0.120824\pi\)
0.473346 + 0.880877i \(0.343046\pi\)
\(710\) 3.43833 + 5.95536i 0.129038 + 0.223501i
\(711\) 0 0
\(712\) −0.886075 + 0.743505i −0.0332071 + 0.0278640i
\(713\) 16.9144 14.1929i 0.633450 0.531528i
\(714\) 0 0
\(715\) 3.37393 + 5.84382i 0.126178 + 0.218546i
\(716\) 21.4651 + 7.81265i 0.802187 + 0.291972i
\(717\) 0 0
\(718\) −2.18903 12.4146i −0.0816938 0.463308i
\(719\) −7.66940 + 2.79143i −0.286020 + 0.104103i −0.481046 0.876695i \(-0.659743\pi\)
0.195026 + 0.980798i \(0.437521\pi\)
\(720\) 0 0
\(721\) 35.2935 1.31440
\(722\) −11.2012 4.36811i −0.416867 0.162564i
\(723\) 0 0
\(724\) −17.6278 14.7915i −0.655132 0.549721i
\(725\) 4.89845 1.78289i 0.181924 0.0662149i
\(726\) 0 0
\(727\) −0.272620 + 1.54611i −0.0101109 + 0.0573419i −0.989446 0.144904i \(-0.953713\pi\)
0.979335 + 0.202246i \(0.0648239\pi\)
\(728\) 13.5817 + 4.94333i 0.503370 + 0.183212i
\(729\) 0 0
\(730\) −4.30928 + 7.46389i −0.159493 + 0.276251i
\(731\) −22.2827 + 18.6974i −0.824154 + 0.691548i
\(732\) 0 0
\(733\) −2.20731 + 3.82317i −0.0815288 + 0.141212i −0.903907 0.427729i \(-0.859314\pi\)
0.822378 + 0.568941i \(0.192647\pi\)
\(734\) −2.67552 4.63414i −0.0987553 0.171049i
\(735\) 0 0
\(736\) 3.30905 18.7665i 0.121973 0.691744i
\(737\) 7.75881 + 44.0024i 0.285799 + 1.62085i
\(738\) 0 0
\(739\) −7.78848 6.53531i −0.286504 0.240405i 0.488197 0.872734i \(-0.337655\pi\)
−0.774700 + 0.632328i \(0.782099\pi\)
\(740\) 0.289022 0.0106247
\(741\) 0 0
\(742\) 4.14243 0.152073
\(743\) −5.39641 4.52813i −0.197975 0.166121i 0.538411 0.842682i \(-0.319025\pi\)
−0.736386 + 0.676562i \(0.763469\pi\)
\(744\) 0 0
\(745\) 1.91368 + 10.8530i 0.0701117 + 0.397623i
\(746\) −0.784320 + 4.44810i −0.0287160 + 0.162857i
\(747\) 0 0
\(748\) −22.1239 38.3196i −0.808928 1.40110i
\(749\) 12.8283 22.2193i 0.468737 0.811877i
\(750\) 0 0
\(751\) 19.7520 16.5739i 0.720760 0.604789i −0.206835 0.978376i \(-0.566316\pi\)
0.927595 + 0.373586i \(0.121872\pi\)
\(752\) −1.25722 + 2.17757i −0.0458461 + 0.0794078i
\(753\) 0 0
\(754\) 4.81018 + 1.75076i 0.175176 + 0.0637590i
\(755\) 0.411744 2.33511i 0.0149849 0.0849835i
\(756\) 0 0
\(757\) −18.0947 + 6.58595i −0.657665 + 0.239370i −0.649228 0.760594i \(-0.724908\pi\)
−0.00843696 + 0.999964i \(0.502686\pi\)
\(758\) 2.96348 + 2.48666i 0.107639 + 0.0903195i
\(759\) 0 0
\(760\) −5.06177 + 8.54126i −0.183610 + 0.309824i
\(761\) −30.9500 −1.12194 −0.560969 0.827837i \(-0.689571\pi\)
−0.560969 + 0.827837i \(0.689571\pi\)
\(762\) 0 0
\(763\) −37.9034 + 13.7957i −1.37220 + 0.499439i
\(764\) 6.71612 + 38.0890i 0.242981 + 1.37801i
\(765\) 0 0
\(766\) 0.311458 + 0.113361i 0.0112534 + 0.00409592i
\(767\) 7.40713 + 12.8295i 0.267456 + 0.463247i
\(768\) 0 0
\(769\) −22.7690 + 19.1055i −0.821071 + 0.688960i −0.953223 0.302269i \(-0.902256\pi\)
0.132152 + 0.991230i \(0.457811\pi\)
\(770\) −8.61857 + 7.23184i −0.310592 + 0.260617i
\(771\) 0 0
\(772\) −4.08999 7.08407i −0.147202 0.254961i
\(773\) −11.6190 4.22899i −0.417908 0.152106i 0.124503 0.992219i \(-0.460266\pi\)
−0.542411 + 0.840113i \(0.682488\pi\)
\(774\) 0 0
\(775\) 1.14040 + 6.46755i 0.0409645 + 0.232321i
\(776\) 7.02075 2.55534i 0.252030 0.0917315i
\(777\) 0 0
\(778\) 1.57965 0.0566333
\(779\) 0.0550669 + 0.0979360i 0.00197298 + 0.00350892i
\(780\) 0 0
\(781\) 36.1988 + 30.3744i 1.29530 + 1.08688i
\(782\) 12.7180 4.62899i 0.454796 0.165532i
\(783\) 0 0
\(784\) 2.96688 16.8260i 0.105960 0.600929i
\(785\) −3.03651 1.10520i −0.108378 0.0394463i
\(786\) 0 0
\(787\) −21.9353 + 37.9930i −0.781909 + 1.35431i 0.148920 + 0.988849i \(0.452420\pi\)
−0.930829 + 0.365456i \(0.880913\pi\)
\(788\) 0.0787736 0.0660989i 0.00280619 0.00235468i
\(789\) 0 0
\(790\) 5.46398 9.46390i 0.194400 0.336710i
\(791\) −10.7285 18.5823i −0.381462 0.660712i
\(792\) 0 0
\(793\) −1.64174 + 9.31078i −0.0583000 + 0.330636i
\(794\) −0.317309 1.79955i −0.0112609 0.0638636i
\(795\) 0 0
\(796\) 7.81776 + 6.55988i 0.277093 + 0.232509i
\(797\) 5.08657 0.180176 0.0900879 0.995934i \(-0.471285\pi\)
0.0900879 + 0.995934i \(0.471285\pi\)
\(798\) 0 0
\(799\) −9.09960 −0.321921
\(800\) 4.34182 + 3.64322i 0.153506 + 0.128807i
\(801\) 0 0
\(802\) 1.89479 + 10.7459i 0.0669073 + 0.379450i
\(803\) −10.2841 + 58.3242i −0.362919 + 2.05822i
\(804\) 0 0
\(805\) 6.87380 + 11.9058i 0.242270 + 0.419624i
\(806\) −3.22449 + 5.58498i −0.113578 + 0.196722i
\(807\) 0 0
\(808\) −6.09036 + 5.11042i −0.214258 + 0.179784i
\(809\) 15.1064 26.1650i 0.531112 0.919914i −0.468228 0.883608i \(-0.655108\pi\)
0.999341 0.0363062i \(-0.0115591\pi\)
\(810\) 0 0
\(811\) −3.43739 1.25111i −0.120703 0.0439323i 0.280963 0.959719i \(-0.409346\pi\)
−0.401666 + 0.915786i \(0.631569\pi\)
\(812\) 5.92057 33.5772i 0.207771 1.17833i
\(813\) 0 0
\(814\) −0.467173 + 0.170037i −0.0163744 + 0.00595980i
\(815\) −5.04191 4.23067i −0.176610 0.148194i
\(816\) 0 0
\(817\) 19.9295 + 0.226820i 0.697244 + 0.00793541i
\(818\) −16.5221 −0.577682
\(819\) 0 0
\(820\) 0.0387447 0.0141019i 0.00135303 0.000492461i
\(821\) 3.37413 + 19.1357i 0.117758 + 0.667839i 0.985348 + 0.170558i \(0.0545571\pi\)
−0.867589 + 0.497281i \(0.834332\pi\)
\(822\) 0 0
\(823\) 4.92429 + 1.79230i 0.171650 + 0.0624755i 0.426416 0.904527i \(-0.359776\pi\)
−0.254766 + 0.967003i \(0.581998\pi\)
\(824\) 9.83012 + 17.0263i 0.342448 + 0.593138i
\(825\) 0 0
\(826\) −18.9212 + 15.8768i −0.658353 + 0.552424i
\(827\) −43.8018 + 36.7541i −1.52314 + 1.27806i −0.692187 + 0.721718i \(0.743353\pi\)
−0.830950 + 0.556346i \(0.812203\pi\)
\(828\) 0 0
\(829\) 7.34286 + 12.7182i 0.255028 + 0.441722i 0.964903 0.262606i \(-0.0845819\pi\)
−0.709875 + 0.704328i \(0.751249\pi\)
\(830\) 3.06623 + 1.11602i 0.106430 + 0.0387375i
\(831\) 0 0
\(832\) 0.0190716 + 0.108161i 0.000661190 + 0.00374979i
\(833\) 58.1028 21.1477i 2.01314 0.732724i
\(834\) 0 0
\(835\) 15.8526 0.548602
\(836\) −5.60413 + 29.7956i −0.193823 + 1.03050i
\(837\) 0 0
\(838\) 0.0546310 + 0.0458408i 0.00188720 + 0.00158354i
\(839\) 19.6431 7.14950i 0.678155 0.246828i 0.0200999 0.999798i \(-0.493602\pi\)
0.658055 + 0.752970i \(0.271379\pi\)
\(840\) 0 0
\(841\) −0.317165 + 1.79873i −0.0109367 + 0.0620252i
\(842\) −12.0226 4.37586i −0.414326 0.150802i
\(843\) 0 0
\(844\) −4.72826 + 8.18959i −0.162753 + 0.281897i
\(845\) 8.11376 6.80825i 0.279122 0.234211i
\(846\) 0 0
\(847\) −16.1666 + 28.0013i −0.555490 + 0.962137i
\(848\) −1.40716 2.43728i −0.0483222 0.0836965i
\(849\) 0 0
\(850\) −0.699019 + 3.96434i −0.0239762 + 0.135976i
\(851\) 0.105489 + 0.598259i 0.00361612 + 0.0205081i
\(852\) 0 0
\(853\) 16.4723 + 13.8219i 0.564000 + 0.473253i 0.879649 0.475624i \(-0.157778\pi\)
−0.315648 + 0.948876i \(0.602222\pi\)
\(854\) −15.7634 −0.539413
\(855\) 0 0
\(856\) 14.2920 0.488492
\(857\) 38.9182 + 32.6562i 1.32942 + 1.11552i 0.984213 + 0.176990i \(0.0566359\pi\)
0.345208 + 0.938526i \(0.387808\pi\)
\(858\) 0 0
\(859\) −1.25062 7.09262i −0.0426706 0.241997i 0.956011 0.293331i \(-0.0947638\pi\)
−0.998682 + 0.0513340i \(0.983653\pi\)
\(860\) 1.27007 7.20290i 0.0433089 0.245617i
\(861\) 0 0
\(862\) −12.8285 22.2195i −0.436939 0.756801i
\(863\) 9.02344 15.6291i 0.307161 0.532019i −0.670579 0.741838i \(-0.733954\pi\)
0.977740 + 0.209819i \(0.0672875\pi\)
\(864\) 0 0
\(865\) −1.45639 + 1.22206i −0.0495189 + 0.0415512i
\(866\) 7.20529 12.4799i 0.244846 0.424085i
\(867\) 0 0
\(868\) 40.3640 + 14.6913i 1.37004 + 0.498655i
\(869\) 13.0399 73.9527i 0.442347 2.50867i
\(870\) 0 0
\(871\) −14.9846 + 5.45393i −0.507732 + 0.184799i
\(872\) −17.2124 14.4429i −0.582884 0.489098i
\(873\) 0 0
\(874\) −8.67761 3.27070i −0.293524 0.110633i
\(875\) −4.08895 −0.138232
\(876\) 0 0
\(877\) 22.3078 8.11936i 0.753280 0.274171i 0.0632945 0.997995i \(-0.479839\pi\)
0.689985 + 0.723824i \(0.257617\pi\)
\(878\) −3.59008 20.3604i −0.121159 0.687129i
\(879\) 0 0
\(880\) 7.18269 + 2.61429i 0.242128 + 0.0881275i
\(881\) 16.7038 + 28.9318i 0.562765 + 0.974737i 0.997254 + 0.0740599i \(0.0235956\pi\)
−0.434489 + 0.900677i \(0.643071\pi\)
\(882\) 0 0
\(883\) 32.5424 27.3063i 1.09514 0.918931i 0.0980503 0.995181i \(-0.468739\pi\)
0.997089 + 0.0762507i \(0.0242949\pi\)
\(884\) 12.0970 10.1506i 0.406866 0.341401i
\(885\) 0 0
\(886\) −4.38998 7.60367i −0.147484 0.255450i
\(887\) −8.82015 3.21027i −0.296152 0.107790i 0.189671 0.981848i \(-0.439258\pi\)
−0.485823 + 0.874057i \(0.661480\pi\)
\(888\) 0 0
\(889\) 3.78347 + 21.4571i 0.126893 + 0.719648i
\(890\) 0.301960 0.109904i 0.0101217 0.00368401i
\(891\) 0 0
\(892\) 46.8914 1.57004
\(893\) 4.73033 + 4.06185i 0.158295 + 0.135924i
\(894\) 0 0
\(895\) −10.9394 9.17922i −0.365663 0.306827i
\(896\) 43.3837 15.7904i 1.44935 0.527519i
\(897\) 0 0
\(898\) 0.660111 3.74368i 0.0220282 0.124928i
\(899\) 32.1697 + 11.7088i 1.07292 + 0.390511i
\(900\) 0 0
\(901\) 5.09244 8.82036i 0.169654 0.293849i
\(902\) −0.0543303 + 0.0455885i −0.00180900 + 0.00151793i
\(903\) 0 0
\(904\) 5.97631 10.3513i 0.198769 0.344278i
\(905\) 7.19293 + 12.4585i 0.239101 + 0.414135i
\(906\) 0 0
\(907\) −1.34450 + 7.62501i −0.0446432 + 0.253184i −0.998959 0.0456153i \(-0.985475\pi\)
0.954316 + 0.298800i \(0.0965863\pi\)
\(908\) 2.22269 + 12.6055i 0.0737625 + 0.418328i
\(909\) 0 0
\(910\) −3.07587 2.58097i −0.101964 0.0855582i
\(911\) 31.8865 1.05645 0.528223 0.849106i \(-0.322858\pi\)
0.528223 + 0.849106i \(0.322858\pi\)
\(912\) 0 0
\(913\) 22.4224 0.742073
\(914\) −11.6216 9.75172i −0.384410 0.322558i
\(915\) 0 0
\(916\) −7.85227 44.5324i −0.259446 1.47139i
\(917\) 1.21602 6.89642i 0.0401567 0.227740i
\(918\) 0 0
\(919\) 9.68427 + 16.7736i 0.319455 + 0.553311i 0.980374 0.197145i \(-0.0631670\pi\)
−0.660920 + 0.750457i \(0.729834\pi\)
\(920\) −3.82905 + 6.63211i −0.126240 + 0.218654i
\(921\) 0 0
\(922\) 17.4922 14.6777i 0.576075 0.483384i
\(923\) −8.43225 + 14.6051i −0.277551 + 0.480733i
\(924\) 0 0
\(925\) −0.169789 0.0617980i −0.00558262 0.00203191i
\(926\) 0.773873 4.38885i 0.0254311 0.144227i
\(927\) 0 0
\(928\) 27.7636 10.1051i 0.911386 0.331717i
\(929\) −18.6717 15.6674i −0.612600 0.514032i 0.282868 0.959159i \(-0.408714\pi\)
−0.895468 + 0.445127i \(0.853159\pi\)
\(930\) 0 0
\(931\) −39.6439 14.9423i −1.29928 0.489714i
\(932\) −10.9592 −0.358979
\(933\) 0 0
\(934\) 23.6243 8.59853i 0.773009 0.281352i
\(935\) 4.80344 + 27.2417i 0.157089 + 0.890898i
\(936\) 0 0
\(937\) −17.5551 6.38953i −0.573499 0.208737i 0.0389573 0.999241i \(-0.487596\pi\)
−0.612457 + 0.790504i \(0.709819\pi\)
\(938\) −13.2936 23.0252i −0.434052 0.751801i
\(939\) 0 0
\(940\) 1.75274 1.47073i 0.0571682 0.0479698i
\(941\) 17.9348 15.0491i 0.584659 0.490587i −0.301814 0.953367i \(-0.597592\pi\)
0.886473 + 0.462779i \(0.153148\pi\)
\(942\) 0 0
\(943\) 0.0433315 + 0.0750524i 0.00141107 + 0.00244404i
\(944\) 15.7689 + 5.73940i 0.513233 + 0.186802i
\(945\) 0 0
\(946\) 2.18468 + 12.3899i 0.0710299 + 0.402831i
\(947\) 37.3038 13.5775i 1.21221 0.441208i 0.344740 0.938698i \(-0.387967\pi\)
0.867470 + 0.497490i \(0.165745\pi\)
\(948\) 0 0
\(949\) −21.1364 −0.686117
\(950\) 2.13296 1.74879i 0.0692025 0.0567383i
\(951\) 0 0
\(952\) 45.3877 + 38.0848i 1.47102 + 1.23433i
\(953\) −46.8875 + 17.0657i −1.51884 + 0.552811i −0.960857 0.277045i \(-0.910645\pi\)
−0.557978 + 0.829856i \(0.688423\pi\)
\(954\) 0 0
\(955\) 4.19866 23.8118i 0.135865 0.770531i
\(956\) 20.1320 + 7.32746i 0.651116 + 0.236987i
\(957\) 0 0
\(958\) −11.4860 + 19.8944i −0.371097 + 0.642758i
\(959\) −17.9975 + 15.1017i −0.581170 + 0.487660i
\(960\) 0 0
\(961\) −6.06485 + 10.5046i −0.195640 + 0.338859i
\(962\) −0.0887147 0.153658i −0.00286028 0.00495414i
\(963\) 0 0
\(964\) 7.12582 40.4125i 0.229507 1.30160i
\(965\) 0.888002 + 5.03611i 0.0285858 + 0.162118i
\(966\) 0 0
\(967\) −41.2501 34.6130i −1.32651 1.11308i −0.984879 0.173246i \(-0.944575\pi\)
−0.341636 0.939832i \(-0.610981\pi\)
\(968\) −18.0112 −0.578901
\(969\) 0 0
\(970\) −2.07561 −0.0666437
\(971\) 18.3652 + 15.4102i 0.589367 + 0.494537i 0.888008 0.459828i \(-0.152089\pi\)
−0.298641 + 0.954365i \(0.596533\pi\)
\(972\) 0 0
\(973\) −12.4864 70.8136i −0.400294 2.27018i
\(974\) −0.278553 + 1.57975i −0.00892542 + 0.0506186i
\(975\) 0 0
\(976\) 5.35476 + 9.27472i 0.171402 + 0.296876i
\(977\) −26.3233 + 45.5933i −0.842157 + 1.45866i 0.0459104 + 0.998946i \(0.485381\pi\)
−0.888067 + 0.459713i \(0.847952\pi\)
\(978\) 0 0
\(979\) 1.69153 1.41937i 0.0540617 0.0453631i
\(980\) −7.77362 + 13.4643i −0.248319 + 0.430102i
\(981\) 0 0
\(982\) −21.5932 7.85927i −0.689065 0.250799i
\(983\) 7.12467 40.4060i 0.227242 1.28875i −0.631112 0.775692i \(-0.717401\pi\)
0.858353 0.513059i \(-0.171488\pi\)
\(984\) 0 0
\(985\) −0.0604093 + 0.0219872i −0.00192480 + 0.000700570i
\(986\) 16.0748 + 13.4884i 0.511926 + 0.429557i
\(987\) 0 0
\(988\) −10.8195 0.123138i −0.344214 0.00391753i
\(989\) 15.3731 0.488837
\(990\) 0 0
\(991\) −26.7308 + 9.72922i −0.849133 + 0.309059i −0.729687 0.683782i \(-0.760334\pi\)
−0.119446 + 0.992841i \(0.538112\pi\)
\(992\) 6.46362 + 36.6570i 0.205220 + 1.16386i
\(993\) 0 0
\(994\) −26.4226 9.61703i −0.838073 0.305034i
\(995\) −3.18999 5.52523i −0.101130 0.175162i
\(996\) 0 0
\(997\) −26.9547 + 22.6177i −0.853664 + 0.716309i −0.960593 0.277957i \(-0.910343\pi\)
0.106929 + 0.994267i \(0.465898\pi\)
\(998\) −8.68620 + 7.28859i −0.274957 + 0.230716i
\(999\) 0 0
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 855.2.bs.c.586.3 18
3.2 odd 2 95.2.k.a.16.1 yes 18
15.2 even 4 475.2.u.b.149.4 36
15.8 even 4 475.2.u.b.149.3 36
15.14 odd 2 475.2.l.c.301.3 18
19.6 even 9 inner 855.2.bs.c.766.3 18
57.5 odd 18 1805.2.a.v.1.2 9
57.14 even 18 1805.2.a.s.1.8 9
57.44 odd 18 95.2.k.a.6.1 18
285.14 even 18 9025.2.a.cf.1.2 9
285.44 odd 18 475.2.l.c.101.3 18
285.119 odd 18 9025.2.a.cc.1.8 9
285.158 even 36 475.2.u.b.424.4 36
285.272 even 36 475.2.u.b.424.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.6.1 18 57.44 odd 18
95.2.k.a.16.1 yes 18 3.2 odd 2
475.2.l.c.101.3 18 285.44 odd 18
475.2.l.c.301.3 18 15.14 odd 2
475.2.u.b.149.3 36 15.8 even 4
475.2.u.b.149.4 36 15.2 even 4
475.2.u.b.424.3 36 285.272 even 36
475.2.u.b.424.4 36 285.158 even 36
855.2.bs.c.586.3 18 1.1 even 1 trivial
855.2.bs.c.766.3 18 19.6 even 9 inner
1805.2.a.s.1.8 9 57.14 even 18
1805.2.a.v.1.2 9 57.5 odd 18
9025.2.a.cc.1.8 9 285.119 odd 18
9025.2.a.cf.1.2 9 285.14 even 18