Properties

Label 108.2.i.a.13.1
Level $108$
Weight $2$
Character 108.13
Analytic conductor $0.862$
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] = [108,2,Mod(13,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.i (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: \(0.862384341830\)
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: \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + 2700 x^{10} - 4941 x^{9} + 8100 x^{8} - 12150 x^{7} + 17577 x^{6} - 25515 x^{5} + \cdots + 19683 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.1
Root \(0.381933 + 1.68942i\) of defining polynomial
Character \(\chi\) \(=\) 108.13
Dual form 108.2.i.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73007 + 0.0827666i) q^{3} +(2.26400 + 1.89972i) q^{5} +(2.50885 + 0.913148i) q^{7} +(2.98630 - 0.286384i) q^{9} +O(q^{10})\) \(q+(-1.73007 + 0.0827666i) q^{3} +(2.26400 + 1.89972i) q^{5} +(2.50885 + 0.913148i) q^{7} +(2.98630 - 0.286384i) q^{9} +(-2.22454 + 1.86661i) q^{11} +(0.588684 - 3.33859i) q^{13} +(-4.07411 - 3.09927i) q^{15} +(-2.40583 + 4.16701i) q^{17} +(-3.13789 - 5.43498i) q^{19} +(-4.41608 - 1.37216i) q^{21} +(0.841669 - 0.306343i) q^{23} +(0.648507 + 3.67787i) q^{25} +(-5.14281 + 0.742631i) q^{27} +(-1.06019 - 6.01265i) q^{29} +(7.86152 - 2.86136i) q^{31} +(3.69412 - 3.41349i) q^{33} +(3.94531 + 6.83348i) q^{35} +(-4.71058 + 8.15896i) q^{37} +(-0.742142 + 5.82473i) q^{39} +(1.77855 - 10.0866i) q^{41} +(-1.13098 + 0.949006i) q^{43} +(7.30502 + 5.02475i) q^{45} +(-5.41276 - 1.97008i) q^{47} +(0.0981944 + 0.0823949i) q^{49} +(3.81737 - 7.40836i) q^{51} -4.51324 q^{53} -8.58238 q^{55} +(5.87861 + 9.14320i) q^{57} +(8.89034 + 7.45989i) q^{59} +(-0.667734 - 0.243035i) q^{61} +(7.75370 + 2.00844i) q^{63} +(7.67516 - 6.44023i) q^{65} +(0.472021 - 2.67696i) q^{67} +(-1.43079 + 0.599657i) q^{69} +(0.000646382 - 0.00111957i) q^{71} +(0.878080 + 1.52088i) q^{73} +(-1.42637 - 6.30930i) q^{75} +(-7.28554 + 2.65172i) q^{77} +(1.73545 + 9.84220i) q^{79} +(8.83597 - 1.71046i) q^{81} +(-0.296685 - 1.68259i) q^{83} +(-13.3629 + 4.86371i) q^{85} +(2.33186 + 10.3146i) q^{87} +(-6.52283 - 11.2979i) q^{89} +(4.52555 - 7.83848i) q^{91} +(-13.3642 + 5.60103i) q^{93} +(3.22077 - 18.2659i) q^{95} +(-2.43956 + 2.04703i) q^{97} +(-6.10857 + 6.21133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.73007 + 0.0827666i −0.998858 + 0.0477853i
\(4\) 0 0
\(5\) 2.26400 + 1.89972i 1.01249 + 0.849580i 0.988665 0.150136i \(-0.0479713\pi\)
0.0238244 + 0.999716i \(0.492416\pi\)
\(6\) 0 0
\(7\) 2.50885 + 0.913148i 0.948257 + 0.345137i 0.769421 0.638741i \(-0.220545\pi\)
0.178836 + 0.983879i \(0.442767\pi\)
\(8\) 0 0
\(9\) 2.98630 0.286384i 0.995433 0.0954615i
\(10\) 0 0
\(11\) −2.22454 + 1.86661i −0.670724 + 0.562804i −0.913280 0.407333i \(-0.866459\pi\)
0.242556 + 0.970138i \(0.422014\pi\)
\(12\) 0 0
\(13\) 0.588684 3.33859i 0.163272 0.925959i −0.787557 0.616242i \(-0.788654\pi\)
0.950829 0.309717i \(-0.100234\pi\)
\(14\) 0 0
\(15\) −4.07411 3.09927i −1.05193 0.800227i
\(16\) 0 0
\(17\) −2.40583 + 4.16701i −0.583499 + 1.01065i 0.411562 + 0.911382i \(0.364983\pi\)
−0.995061 + 0.0992678i \(0.968350\pi\)
\(18\) 0 0
\(19\) −3.13789 5.43498i −0.719881 1.24687i −0.961047 0.276386i \(-0.910863\pi\)
0.241166 0.970484i \(-0.422470\pi\)
\(20\) 0 0
\(21\) −4.41608 1.37216i −0.963667 0.299430i
\(22\) 0 0
\(23\) 0.841669 0.306343i 0.175500 0.0638769i −0.252776 0.967525i \(-0.581343\pi\)
0.428276 + 0.903648i \(0.359121\pi\)
\(24\) 0 0
\(25\) 0.648507 + 3.67787i 0.129701 + 0.735574i
\(26\) 0 0
\(27\) −5.14281 + 0.742631i −0.989734 + 0.142919i
\(28\) 0 0
\(29\) −1.06019 6.01265i −0.196873 1.11652i −0.909726 0.415208i \(-0.863709\pi\)
0.712854 0.701313i \(-0.247402\pi\)
\(30\) 0 0
\(31\) 7.86152 2.86136i 1.41197 0.513916i 0.480263 0.877124i \(-0.340541\pi\)
0.931708 + 0.363209i \(0.118319\pi\)
\(32\) 0 0
\(33\) 3.69412 3.41349i 0.643064 0.594212i
\(34\) 0 0
\(35\) 3.94531 + 6.83348i 0.666879 + 1.15507i
\(36\) 0 0
\(37\) −4.71058 + 8.15896i −0.774414 + 1.34132i 0.160709 + 0.987002i \(0.448622\pi\)
−0.935123 + 0.354323i \(0.884711\pi\)
\(38\) 0 0
\(39\) −0.742142 + 5.82473i −0.118838 + 0.932703i
\(40\) 0 0
\(41\) 1.77855 10.0866i 0.277762 1.57527i −0.452286 0.891873i \(-0.649391\pi\)
0.730048 0.683396i \(-0.239498\pi\)
\(42\) 0 0
\(43\) −1.13098 + 0.949006i −0.172473 + 0.144722i −0.724938 0.688814i \(-0.758132\pi\)
0.552465 + 0.833536i \(0.313687\pi\)
\(44\) 0 0
\(45\) 7.30502 + 5.02475i 1.08897 + 0.749046i
\(46\) 0 0
\(47\) −5.41276 1.97008i −0.789532 0.287366i −0.0843906 0.996433i \(-0.526894\pi\)
−0.705142 + 0.709067i \(0.749117\pi\)
\(48\) 0 0
\(49\) 0.0981944 + 0.0823949i 0.0140278 + 0.0117707i
\(50\) 0 0
\(51\) 3.81737 7.40836i 0.534538 1.03738i
\(52\) 0 0
\(53\) −4.51324 −0.619942 −0.309971 0.950746i \(-0.600319\pi\)
−0.309971 + 0.950746i \(0.600319\pi\)
\(54\) 0 0
\(55\) −8.58238 −1.15725
\(56\) 0 0
\(57\) 5.87861 + 9.14320i 0.778641 + 1.21105i
\(58\) 0 0
\(59\) 8.89034 + 7.45989i 1.15742 + 0.971194i 0.999867 0.0163155i \(-0.00519361\pi\)
0.157557 + 0.987510i \(0.449638\pi\)
\(60\) 0 0
\(61\) −0.667734 0.243035i −0.0854946 0.0311175i 0.298919 0.954279i \(-0.403374\pi\)
−0.384413 + 0.923161i \(0.625596\pi\)
\(62\) 0 0
\(63\) 7.75370 + 2.00844i 0.976874 + 0.253039i
\(64\) 0 0
\(65\) 7.67516 6.44023i 0.951987 0.798812i
\(66\) 0 0
\(67\) 0.472021 2.67696i 0.0576665 0.327043i −0.942304 0.334759i \(-0.891345\pi\)
0.999970 + 0.00771610i \(0.00245614\pi\)
\(68\) 0 0
\(69\) −1.43079 + 0.599657i −0.172247 + 0.0721902i
\(70\) 0 0
\(71\) 0.000646382 0.00111957i 7.67115e−5 0.000132868i −0.865987 0.500066i \(-0.833309\pi\)
0.866064 + 0.499934i \(0.166642\pi\)
\(72\) 0 0
\(73\) 0.878080 + 1.52088i 0.102772 + 0.178005i 0.912826 0.408350i \(-0.133896\pi\)
−0.810054 + 0.586355i \(0.800562\pi\)
\(74\) 0 0
\(75\) −1.42637 6.30930i −0.164703 0.728535i
\(76\) 0 0
\(77\) −7.28554 + 2.65172i −0.830264 + 0.302191i
\(78\) 0 0
\(79\) 1.73545 + 9.84220i 0.195253 + 1.10733i 0.912058 + 0.410061i \(0.134493\pi\)
−0.716805 + 0.697273i \(0.754396\pi\)
\(80\) 0 0
\(81\) 8.83597 1.71046i 0.981774 0.190051i
\(82\) 0 0
\(83\) −0.296685 1.68259i −0.0325654 0.184688i 0.964186 0.265227i \(-0.0854469\pi\)
−0.996751 + 0.0805392i \(0.974336\pi\)
\(84\) 0 0
\(85\) −13.3629 + 4.86371i −1.44941 + 0.527544i
\(86\) 0 0
\(87\) 2.33186 + 10.3146i 0.250001 + 1.10584i
\(88\) 0 0
\(89\) −6.52283 11.2979i −0.691418 1.19757i −0.971373 0.237558i \(-0.923653\pi\)
0.279955 0.960013i \(-0.409680\pi\)
\(90\) 0 0
\(91\) 4.52555 7.83848i 0.474407 0.821696i
\(92\) 0 0
\(93\) −13.3642 + 5.60103i −1.38580 + 0.580800i
\(94\) 0 0
\(95\) 3.22077 18.2659i 0.330444 1.87404i
\(96\) 0 0
\(97\) −2.43956 + 2.04703i −0.247699 + 0.207845i −0.758181 0.652044i \(-0.773912\pi\)
0.510481 + 0.859889i \(0.329467\pi\)
\(98\) 0 0
\(99\) −6.10857 + 6.21133i −0.613935 + 0.624262i
\(100\) 0 0
\(101\) −10.3176 3.75529i −1.02664 0.373666i −0.226838 0.973932i \(-0.572839\pi\)
−0.799800 + 0.600267i \(0.795061\pi\)
\(102\) 0 0
\(103\) −3.45382 2.89810i −0.340315 0.285558i 0.456572 0.889686i \(-0.349077\pi\)
−0.796887 + 0.604128i \(0.793521\pi\)
\(104\) 0 0
\(105\) −7.39125 11.4959i −0.721313 1.12188i
\(106\) 0 0
\(107\) 5.98188 0.578290 0.289145 0.957285i \(-0.406629\pi\)
0.289145 + 0.957285i \(0.406629\pi\)
\(108\) 0 0
\(109\) −4.37994 −0.419522 −0.209761 0.977753i \(-0.567269\pi\)
−0.209761 + 0.977753i \(0.567269\pi\)
\(110\) 0 0
\(111\) 7.47435 14.5055i 0.709434 1.37680i
\(112\) 0 0
\(113\) 10.7510 + 9.02115i 1.01137 + 0.848638i 0.988518 0.151101i \(-0.0482818\pi\)
0.0228490 + 0.999739i \(0.492726\pi\)
\(114\) 0 0
\(115\) 2.48750 + 0.905376i 0.231961 + 0.0844268i
\(116\) 0 0
\(117\) 0.801866 10.1386i 0.0741325 0.937317i
\(118\) 0 0
\(119\) −9.84097 + 8.25755i −0.902120 + 0.756969i
\(120\) 0 0
\(121\) −0.445787 + 2.52818i −0.0405261 + 0.229835i
\(122\) 0 0
\(123\) −2.24218 + 17.5978i −0.202170 + 1.58674i
\(124\) 0 0
\(125\) 1.86990 3.23876i 0.167249 0.289683i
\(126\) 0 0
\(127\) 4.24395 + 7.35074i 0.376590 + 0.652273i 0.990564 0.137054i \(-0.0437633\pi\)
−0.613974 + 0.789326i \(0.710430\pi\)
\(128\) 0 0
\(129\) 1.87813 1.73546i 0.165360 0.152798i
\(130\) 0 0
\(131\) −12.2866 + 4.47197i −1.07349 + 0.390718i −0.817480 0.575956i \(-0.804630\pi\)
−0.256009 + 0.966675i \(0.582408\pi\)
\(132\) 0 0
\(133\) −2.90956 16.5009i −0.252291 1.43081i
\(134\) 0 0
\(135\) −13.0541 8.08858i −1.12352 0.696154i
\(136\) 0 0
\(137\) 3.21248 + 18.2189i 0.274461 + 1.55654i 0.740670 + 0.671869i \(0.234508\pi\)
−0.466209 + 0.884675i \(0.654381\pi\)
\(138\) 0 0
\(139\) 15.5758 5.66914i 1.32112 0.480850i 0.417306 0.908766i \(-0.362974\pi\)
0.903818 + 0.427916i \(0.140752\pi\)
\(140\) 0 0
\(141\) 9.52752 + 2.96039i 0.802362 + 0.249310i
\(142\) 0 0
\(143\) 4.92230 + 8.52568i 0.411624 + 0.712953i
\(144\) 0 0
\(145\) 9.02207 15.6267i 0.749242 1.29772i
\(146\) 0 0
\(147\) −0.176703 0.134422i −0.0145742 0.0110869i
\(148\) 0 0
\(149\) −2.39504 + 13.5830i −0.196209 + 1.11276i 0.714477 + 0.699659i \(0.246665\pi\)
−0.910686 + 0.413099i \(0.864446\pi\)
\(150\) 0 0
\(151\) −0.312333 + 0.262078i −0.0254173 + 0.0213276i −0.655408 0.755275i \(-0.727503\pi\)
0.629991 + 0.776603i \(0.283059\pi\)
\(152\) 0 0
\(153\) −5.99115 + 13.1329i −0.484356 + 1.06174i
\(154\) 0 0
\(155\) 23.2342 + 8.45657i 1.86622 + 0.679248i
\(156\) 0 0
\(157\) 6.54870 + 5.49501i 0.522643 + 0.438550i 0.865552 0.500819i \(-0.166968\pi\)
−0.342909 + 0.939369i \(0.611412\pi\)
\(158\) 0 0
\(159\) 7.80824 0.373546i 0.619234 0.0296241i
\(160\) 0 0
\(161\) 2.39136 0.188466
\(162\) 0 0
\(163\) 8.49244 0.665179 0.332590 0.943072i \(-0.392078\pi\)
0.332590 + 0.943072i \(0.392078\pi\)
\(164\) 0 0
\(165\) 14.8481 0.710335i 1.15593 0.0552995i
\(166\) 0 0
\(167\) −6.42577 5.39186i −0.497241 0.417235i 0.359372 0.933194i \(-0.382991\pi\)
−0.856613 + 0.515960i \(0.827435\pi\)
\(168\) 0 0
\(169\) 1.41635 + 0.515509i 0.108950 + 0.0396545i
\(170\) 0 0
\(171\) −10.9272 15.3318i −0.835621 1.17245i
\(172\) 0 0
\(173\) 10.9442 9.18331i 0.832075 0.698194i −0.123691 0.992321i \(-0.539473\pi\)
0.955766 + 0.294127i \(0.0950287\pi\)
\(174\) 0 0
\(175\) −1.73143 + 9.81941i −0.130884 + 0.742278i
\(176\) 0 0
\(177\) −15.9984 12.1703i −1.20251 0.914777i
\(178\) 0 0
\(179\) −0.850987 + 1.47395i −0.0636058 + 0.110168i −0.896075 0.443903i \(-0.853593\pi\)
0.832469 + 0.554072i \(0.186927\pi\)
\(180\) 0 0
\(181\) 9.85598 + 17.0710i 0.732589 + 1.26888i 0.955773 + 0.294105i \(0.0950215\pi\)
−0.223184 + 0.974776i \(0.571645\pi\)
\(182\) 0 0
\(183\) 1.17534 + 0.365202i 0.0868838 + 0.0269965i
\(184\) 0 0
\(185\) −26.1644 + 9.52308i −1.92365 + 0.700151i
\(186\) 0 0
\(187\) −2.42634 13.7604i −0.177431 1.00626i
\(188\) 0 0
\(189\) −13.5807 2.83299i −0.987850 0.206070i
\(190\) 0 0
\(191\) −0.676006 3.83382i −0.0489141 0.277405i 0.950534 0.310620i \(-0.100537\pi\)
−0.999448 + 0.0332146i \(0.989426\pi\)
\(192\) 0 0
\(193\) −10.7186 + 3.90124i −0.771540 + 0.280818i −0.697640 0.716448i \(-0.745767\pi\)
−0.0738996 + 0.997266i \(0.523544\pi\)
\(194\) 0 0
\(195\) −12.7456 + 11.7773i −0.912728 + 0.843390i
\(196\) 0 0
\(197\) −0.538764 0.933167i −0.0383854 0.0664854i 0.846194 0.532874i \(-0.178888\pi\)
−0.884580 + 0.466389i \(0.845555\pi\)
\(198\) 0 0
\(199\) −4.39347 + 7.60971i −0.311445 + 0.539438i −0.978675 0.205413i \(-0.934146\pi\)
0.667231 + 0.744851i \(0.267480\pi\)
\(200\) 0 0
\(201\) −0.595067 + 4.67041i −0.0419728 + 0.329425i
\(202\) 0 0
\(203\) 2.83057 16.0530i 0.198667 1.12670i
\(204\) 0 0
\(205\) 23.1884 19.4574i 1.61955 1.35896i
\(206\) 0 0
\(207\) 2.42575 1.15587i 0.168601 0.0803386i
\(208\) 0 0
\(209\) 17.1254 + 6.23312i 1.18459 + 0.431154i
\(210\) 0 0
\(211\) 1.49136 + 1.25140i 0.102669 + 0.0861498i 0.692677 0.721248i \(-0.256431\pi\)
−0.590008 + 0.807397i \(0.700875\pi\)
\(212\) 0 0
\(213\) −0.00102563 + 0.00199043i −7.02747e−5 + 0.000136382i
\(214\) 0 0
\(215\) −4.36338 −0.297580
\(216\) 0 0
\(217\) 22.3363 1.51628
\(218\) 0 0
\(219\) −1.64502 2.55856i −0.111160 0.172891i
\(220\) 0 0
\(221\) 12.4957 + 10.4851i 0.840551 + 0.705306i
\(222\) 0 0
\(223\) −26.8671 9.77881i −1.79915 0.654838i −0.998443 0.0557835i \(-0.982234\pi\)
−0.800709 0.599054i \(-0.795543\pi\)
\(224\) 0 0
\(225\) 2.98992 + 10.7975i 0.199328 + 0.719833i
\(226\) 0 0
\(227\) −14.8265 + 12.4409i −0.984068 + 0.825731i −0.984698 0.174269i \(-0.944244\pi\)
0.000630367 1.00000i \(0.499799\pi\)
\(228\) 0 0
\(229\) −1.27846 + 7.25052i −0.0844832 + 0.479128i 0.912984 + 0.407996i \(0.133772\pi\)
−0.997467 + 0.0711320i \(0.977339\pi\)
\(230\) 0 0
\(231\) 12.3850 5.19066i 0.814875 0.341521i
\(232\) 0 0
\(233\) 8.53698 14.7865i 0.559276 0.968695i −0.438281 0.898838i \(-0.644412\pi\)
0.997557 0.0698569i \(-0.0222543\pi\)
\(234\) 0 0
\(235\) −8.51186 14.7430i −0.555253 0.961726i
\(236\) 0 0
\(237\) −3.81705 16.8841i −0.247944 1.09674i
\(238\) 0 0
\(239\) −20.4262 + 7.43452i −1.32126 + 0.480899i −0.903862 0.427825i \(-0.859280\pi\)
−0.417398 + 0.908724i \(0.637058\pi\)
\(240\) 0 0
\(241\) −1.59919 9.06945i −0.103013 0.584214i −0.991995 0.126274i \(-0.959698\pi\)
0.888983 0.457941i \(-0.151413\pi\)
\(242\) 0 0
\(243\) −15.1453 + 3.69054i −0.971571 + 0.236748i
\(244\) 0 0
\(245\) 0.0657847 + 0.373084i 0.00420283 + 0.0238354i
\(246\) 0 0
\(247\) −19.9924 + 7.27664i −1.27209 + 0.463002i
\(248\) 0 0
\(249\) 0.652549 + 2.88644i 0.0413536 + 0.182921i
\(250\) 0 0
\(251\) −10.1762 17.6257i −0.642315 1.11252i −0.984915 0.173041i \(-0.944641\pi\)
0.342600 0.939482i \(-0.388693\pi\)
\(252\) 0 0
\(253\) −1.30051 + 2.25254i −0.0817621 + 0.141616i
\(254\) 0 0
\(255\) 22.7163 9.52058i 1.42255 0.596202i
\(256\) 0 0
\(257\) −0.478088 + 2.71137i −0.0298223 + 0.169131i −0.996081 0.0884415i \(-0.971811\pi\)
0.966259 + 0.257572i \(0.0829225\pi\)
\(258\) 0 0
\(259\) −19.2685 + 16.1682i −1.19729 + 1.00464i
\(260\) 0 0
\(261\) −4.88798 17.6519i −0.302558 1.09263i
\(262\) 0 0
\(263\) −4.03027 1.46690i −0.248517 0.0904528i 0.214758 0.976667i \(-0.431104\pi\)
−0.463275 + 0.886214i \(0.653326\pi\)
\(264\) 0 0
\(265\) −10.2180 8.57389i −0.627685 0.526690i
\(266\) 0 0
\(267\) 12.2200 + 19.0063i 0.747855 + 1.16316i
\(268\) 0 0
\(269\) −4.91806 −0.299859 −0.149930 0.988697i \(-0.547905\pi\)
−0.149930 + 0.988697i \(0.547905\pi\)
\(270\) 0 0
\(271\) 2.18471 0.132712 0.0663558 0.997796i \(-0.478863\pi\)
0.0663558 + 0.997796i \(0.478863\pi\)
\(272\) 0 0
\(273\) −7.18077 + 13.9357i −0.434600 + 0.843427i
\(274\) 0 0
\(275\) −8.30778 6.97105i −0.500978 0.420370i
\(276\) 0 0
\(277\) 1.57230 + 0.572270i 0.0944703 + 0.0343844i 0.388823 0.921313i \(-0.372882\pi\)
−0.294353 + 0.955697i \(0.595104\pi\)
\(278\) 0 0
\(279\) 22.6574 10.7963i 1.35646 0.646357i
\(280\) 0 0
\(281\) 0.411839 0.345574i 0.0245683 0.0206152i −0.630421 0.776254i \(-0.717118\pi\)
0.654989 + 0.755638i \(0.272673\pi\)
\(282\) 0 0
\(283\) 0.0692086 0.392502i 0.00411403 0.0233318i −0.982682 0.185302i \(-0.940674\pi\)
0.986796 + 0.161970i \(0.0517848\pi\)
\(284\) 0 0
\(285\) −4.06035 + 31.8679i −0.240515 + 1.88769i
\(286\) 0 0
\(287\) 13.6727 23.6818i 0.807074 1.39789i
\(288\) 0 0
\(289\) −3.07601 5.32780i −0.180942 0.313400i
\(290\) 0 0
\(291\) 4.05118 3.74343i 0.237485 0.219443i
\(292\) 0 0
\(293\) 27.0188 9.83404i 1.57845 0.574511i 0.603588 0.797297i \(-0.293737\pi\)
0.974867 + 0.222786i \(0.0715151\pi\)
\(294\) 0 0
\(295\) 5.95603 + 33.7783i 0.346773 + 1.96665i
\(296\) 0 0
\(297\) 10.0542 11.2516i 0.583403 0.652886i
\(298\) 0 0
\(299\) −0.527276 2.99033i −0.0304932 0.172935i
\(300\) 0 0
\(301\) −3.70405 + 1.34816i −0.213498 + 0.0777068i
\(302\) 0 0
\(303\) 18.1610 + 5.64298i 1.04332 + 0.324181i
\(304\) 0 0
\(305\) −1.05005 1.81874i −0.0601256 0.104141i
\(306\) 0 0
\(307\) −5.22386 + 9.04800i −0.298142 + 0.516397i −0.975711 0.219063i \(-0.929700\pi\)
0.677569 + 0.735459i \(0.263033\pi\)
\(308\) 0 0
\(309\) 6.21522 + 4.72805i 0.353571 + 0.268970i
\(310\) 0 0
\(311\) 0.545372 3.09296i 0.0309252 0.175386i −0.965433 0.260651i \(-0.916063\pi\)
0.996358 + 0.0852656i \(0.0271739\pi\)
\(312\) 0 0
\(313\) −4.77097 + 4.00332i −0.269671 + 0.226281i −0.767588 0.640944i \(-0.778543\pi\)
0.497916 + 0.867225i \(0.334099\pi\)
\(314\) 0 0
\(315\) 13.7389 + 19.2769i 0.774098 + 1.08613i
\(316\) 0 0
\(317\) −10.2045 3.71413i −0.573141 0.208606i 0.0391571 0.999233i \(-0.487533\pi\)
−0.612299 + 0.790627i \(0.709755\pi\)
\(318\) 0 0
\(319\) 13.5817 + 11.3964i 0.760430 + 0.638077i
\(320\) 0 0
\(321\) −10.3491 + 0.495099i −0.577629 + 0.0276338i
\(322\) 0 0
\(323\) 30.1969 1.68020
\(324\) 0 0
\(325\) 12.6607 0.702288
\(326\) 0 0
\(327\) 7.57761 0.362513i 0.419043 0.0200470i
\(328\) 0 0
\(329\) −11.7808 9.88530i −0.649499 0.544994i
\(330\) 0 0
\(331\) 22.7943 + 8.29643i 1.25289 + 0.456013i 0.881376 0.472416i \(-0.156618\pi\)
0.371510 + 0.928429i \(0.378840\pi\)
\(332\) 0 0
\(333\) −11.7306 + 25.7141i −0.642833 + 1.40913i
\(334\) 0 0
\(335\) 6.15413 5.16393i 0.336236 0.282135i
\(336\) 0 0
\(337\) −1.27520 + 7.23200i −0.0694644 + 0.393952i 0.930175 + 0.367115i \(0.119655\pi\)
−0.999640 + 0.0268369i \(0.991457\pi\)
\(338\) 0 0
\(339\) −19.3466 14.7174i −1.05076 0.799340i
\(340\) 0 0
\(341\) −12.1472 + 21.0396i −0.657809 + 1.13936i
\(342\) 0 0
\(343\) −9.17341 15.8888i −0.495318 0.857916i
\(344\) 0 0
\(345\) −4.37849 1.36048i −0.235730 0.0732460i
\(346\) 0 0
\(347\) 21.4447 7.80524i 1.15121 0.419007i 0.305262 0.952268i \(-0.401256\pi\)
0.845951 + 0.533261i \(0.179034\pi\)
\(348\) 0 0
\(349\) −1.69320 9.60262i −0.0906349 0.514016i −0.995998 0.0893775i \(-0.971512\pi\)
0.905363 0.424639i \(-0.139599\pi\)
\(350\) 0 0
\(351\) −0.548146 + 17.6069i −0.0292579 + 0.939788i
\(352\) 0 0
\(353\) 2.81438 + 15.9611i 0.149794 + 0.849526i 0.963392 + 0.268098i \(0.0863950\pi\)
−0.813597 + 0.581429i \(0.802494\pi\)
\(354\) 0 0
\(355\) 0.00359027 0.00130675i 0.000190552 6.93551e-5i
\(356\) 0 0
\(357\) 16.3421 15.1007i 0.864918 0.799212i
\(358\) 0 0
\(359\) −6.06212 10.4999i −0.319947 0.554164i 0.660530 0.750800i \(-0.270332\pi\)
−0.980477 + 0.196636i \(0.936998\pi\)
\(360\) 0 0
\(361\) −10.1927 + 17.6542i −0.536457 + 0.929170i
\(362\) 0 0
\(363\) 0.561995 4.41084i 0.0294971 0.231509i
\(364\) 0 0
\(365\) −0.901272 + 5.11137i −0.0471748 + 0.267541i
\(366\) 0 0
\(367\) 2.30095 1.93072i 0.120109 0.100783i −0.580755 0.814078i \(-0.697243\pi\)
0.700864 + 0.713295i \(0.252798\pi\)
\(368\) 0 0
\(369\) 2.42262 30.6311i 0.126116 1.59459i
\(370\) 0 0
\(371\) −11.3231 4.12126i −0.587864 0.213965i
\(372\) 0 0
\(373\) −17.6639 14.8217i −0.914601 0.767441i 0.0583881 0.998294i \(-0.481404\pi\)
−0.972989 + 0.230853i \(0.925848\pi\)
\(374\) 0 0
\(375\) −2.96700 + 5.75805i −0.153215 + 0.297344i
\(376\) 0 0
\(377\) −20.6979 −1.06600
\(378\) 0 0
\(379\) −9.61297 −0.493785 −0.246893 0.969043i \(-0.579410\pi\)
−0.246893 + 0.969043i \(0.579410\pi\)
\(380\) 0 0
\(381\) −7.95074 12.3661i −0.407329 0.633532i
\(382\) 0 0
\(383\) 0.551178 + 0.462493i 0.0281639 + 0.0236323i 0.656761 0.754099i \(-0.271926\pi\)
−0.628597 + 0.777731i \(0.716371\pi\)
\(384\) 0 0
\(385\) −21.5319 7.83699i −1.09737 0.399410i
\(386\) 0 0
\(387\) −3.10567 + 3.15791i −0.157870 + 0.160526i
\(388\) 0 0
\(389\) 24.1482 20.2627i 1.22436 1.02736i 0.225775 0.974179i \(-0.427509\pi\)
0.998585 0.0531804i \(-0.0169358\pi\)
\(390\) 0 0
\(391\) −0.748377 + 4.24426i −0.0378471 + 0.214641i
\(392\) 0 0
\(393\) 20.8866 8.75376i 1.05359 0.441569i
\(394\) 0 0
\(395\) −14.7684 + 25.5796i −0.743077 + 1.28705i
\(396\) 0 0
\(397\) 1.11075 + 1.92388i 0.0557472 + 0.0965569i 0.892552 0.450944i \(-0.148913\pi\)
−0.836805 + 0.547501i \(0.815579\pi\)
\(398\) 0 0
\(399\) 6.39947 + 28.3070i 0.320374 + 1.41712i
\(400\) 0 0
\(401\) −15.3280 + 5.57893i −0.765443 + 0.278598i −0.695089 0.718924i \(-0.744635\pi\)
−0.0703539 + 0.997522i \(0.522413\pi\)
\(402\) 0 0
\(403\) −4.92496 27.9309i −0.245330 1.39134i
\(404\) 0 0
\(405\) 23.2540 + 12.9134i 1.15550 + 0.641671i
\(406\) 0 0
\(407\) −4.75073 26.9427i −0.235485 1.33550i
\(408\) 0 0
\(409\) 35.3919 12.8816i 1.75002 0.636954i 0.750307 0.661089i \(-0.229906\pi\)
0.999709 + 0.0241357i \(0.00768337\pi\)
\(410\) 0 0
\(411\) −7.06574 31.2541i −0.348527 1.54165i
\(412\) 0 0
\(413\) 15.4926 + 26.8340i 0.762341 + 1.32041i
\(414\) 0 0
\(415\) 2.52474 4.37299i 0.123935 0.214661i
\(416\) 0 0
\(417\) −26.4781 + 11.0972i −1.29664 + 0.543431i
\(418\) 0 0
\(419\) −3.41940 + 19.3924i −0.167048 + 0.947379i 0.779879 + 0.625931i \(0.215281\pi\)
−0.946927 + 0.321448i \(0.895830\pi\)
\(420\) 0 0
\(421\) −5.06082 + 4.24653i −0.246649 + 0.206963i −0.757728 0.652571i \(-0.773691\pi\)
0.511079 + 0.859534i \(0.329246\pi\)
\(422\) 0 0
\(423\) −16.7283 4.33313i −0.813359 0.210684i
\(424\) 0 0
\(425\) −16.8859 6.14598i −0.819088 0.298124i
\(426\) 0 0
\(427\) −1.45332 1.21948i −0.0703310 0.0590147i
\(428\) 0 0
\(429\) −9.22158 14.3426i −0.445222 0.692469i
\(430\) 0 0
\(431\) −11.6625 −0.561765 −0.280882 0.959742i \(-0.590627\pi\)
−0.280882 + 0.959742i \(0.590627\pi\)
\(432\) 0 0
\(433\) −33.1187 −1.59158 −0.795791 0.605571i \(-0.792945\pi\)
−0.795791 + 0.605571i \(0.792945\pi\)
\(434\) 0 0
\(435\) −14.3155 + 27.7820i −0.686374 + 1.33205i
\(436\) 0 0
\(437\) −4.30603 3.61319i −0.205985 0.172842i
\(438\) 0 0
\(439\) 18.7149 + 6.81168i 0.893215 + 0.325104i 0.747531 0.664227i \(-0.231239\pi\)
0.145684 + 0.989331i \(0.453462\pi\)
\(440\) 0 0
\(441\) 0.316835 + 0.217935i 0.0150874 + 0.0103778i
\(442\) 0 0
\(443\) −12.6039 + 10.5759i −0.598830 + 0.502478i −0.891069 0.453867i \(-0.850044\pi\)
0.292240 + 0.956345i \(0.405600\pi\)
\(444\) 0 0
\(445\) 6.69511 37.9699i 0.317379 1.79994i
\(446\) 0 0
\(447\) 3.01938 23.6977i 0.142812 1.12086i
\(448\) 0 0
\(449\) 1.40137 2.42724i 0.0661347 0.114549i −0.831062 0.556180i \(-0.812267\pi\)
0.897197 + 0.441631i \(0.145600\pi\)
\(450\) 0 0
\(451\) 14.8714 + 25.7580i 0.700266 + 1.21290i
\(452\) 0 0
\(453\) 0.518667 0.479265i 0.0243691 0.0225178i
\(454\) 0 0
\(455\) 25.1367 9.14902i 1.17843 0.428913i
\(456\) 0 0
\(457\) 5.54631 + 31.4547i 0.259445 + 1.47139i 0.784399 + 0.620256i \(0.212971\pi\)
−0.524954 + 0.851131i \(0.675917\pi\)
\(458\) 0 0
\(459\) 9.27816 23.2168i 0.433067 1.08367i
\(460\) 0 0
\(461\) 2.08832 + 11.8434i 0.0972627 + 0.551604i 0.994030 + 0.109103i \(0.0347977\pi\)
−0.896768 + 0.442501i \(0.854091\pi\)
\(462\) 0 0
\(463\) 10.6165 3.86410i 0.493392 0.179580i −0.0833274 0.996522i \(-0.526555\pi\)
0.576720 + 0.816942i \(0.304333\pi\)
\(464\) 0 0
\(465\) −40.8968 12.7075i −1.89654 0.589294i
\(466\) 0 0
\(467\) 13.1810 + 22.8301i 0.609942 + 1.05645i 0.991249 + 0.132002i \(0.0421405\pi\)
−0.381308 + 0.924448i \(0.624526\pi\)
\(468\) 0 0
\(469\) 3.62869 6.28508i 0.167558 0.290218i
\(470\) 0 0
\(471\) −11.7845 8.96476i −0.543002 0.413074i
\(472\) 0 0
\(473\) 0.744488 4.22220i 0.0342316 0.194137i
\(474\) 0 0
\(475\) 17.9542 15.0654i 0.823795 0.691246i
\(476\) 0 0
\(477\) −13.4779 + 1.29252i −0.617111 + 0.0591805i
\(478\) 0 0
\(479\) 15.4224 + 5.61331i 0.704669 + 0.256479i 0.669403 0.742899i \(-0.266550\pi\)
0.0352661 + 0.999378i \(0.488772\pi\)
\(480\) 0 0
\(481\) 24.4664 + 20.5297i 1.11557 + 0.936076i
\(482\) 0 0
\(483\) −4.13723 + 0.197925i −0.188250 + 0.00900589i
\(484\) 0 0
\(485\) −9.41193 −0.427374
\(486\) 0 0
\(487\) −13.5466 −0.613853 −0.306926 0.951733i \(-0.599301\pi\)
−0.306926 + 0.951733i \(0.599301\pi\)
\(488\) 0 0
\(489\) −14.6925 + 0.702890i −0.664419 + 0.0317858i
\(490\) 0 0
\(491\) 7.54691 + 6.33261i 0.340587 + 0.285787i 0.796997 0.603983i \(-0.206421\pi\)
−0.456410 + 0.889770i \(0.650865\pi\)
\(492\) 0 0
\(493\) 27.6054 + 10.0476i 1.24329 + 0.452519i
\(494\) 0 0
\(495\) −25.6296 + 2.45786i −1.15196 + 0.110473i
\(496\) 0 0
\(497\) 0.00264401 0.00221859i 0.000118600 9.95172e-5i
\(498\) 0 0
\(499\) 6.09489 34.5659i 0.272845 1.54738i −0.472880 0.881127i \(-0.656786\pi\)
0.745725 0.666254i \(-0.232103\pi\)
\(500\) 0 0
\(501\) 11.5633 + 8.79646i 0.516610 + 0.392997i
\(502\) 0 0
\(503\) −6.77729 + 11.7386i −0.302185 + 0.523399i −0.976631 0.214925i \(-0.931049\pi\)
0.674446 + 0.738324i \(0.264383\pi\)
\(504\) 0 0
\(505\) −16.2250 28.1025i −0.722002 1.25054i
\(506\) 0 0
\(507\) −2.49305 0.774641i −0.110720 0.0344030i
\(508\) 0 0
\(509\) 37.5176 13.6553i 1.66294 0.605260i 0.672117 0.740445i \(-0.265385\pi\)
0.990820 + 0.135185i \(0.0431629\pi\)
\(510\) 0 0
\(511\) 0.814186 + 4.61748i 0.0360175 + 0.204265i
\(512\) 0 0
\(513\) 20.1737 + 25.6208i 0.890693 + 1.13119i
\(514\) 0 0
\(515\) −2.31386 13.1226i −0.101961 0.578249i
\(516\) 0 0
\(517\) 15.7183 5.72099i 0.691289 0.251609i
\(518\) 0 0
\(519\) −18.1743 + 16.7936i −0.797761 + 0.737158i
\(520\) 0 0
\(521\) 9.26497 + 16.0474i 0.405906 + 0.703049i 0.994426 0.105433i \(-0.0336228\pi\)
−0.588521 + 0.808482i \(0.700289\pi\)
\(522\) 0 0
\(523\) 9.47946 16.4189i 0.414508 0.717948i −0.580869 0.813997i \(-0.697287\pi\)
0.995377 + 0.0960487i \(0.0306205\pi\)
\(524\) 0 0
\(525\) 2.18278 17.1316i 0.0952641 0.747684i
\(526\) 0 0
\(527\) −6.99013 + 39.6430i −0.304495 + 1.72688i
\(528\) 0 0
\(529\) −17.0045 + 14.2684i −0.739324 + 0.620367i
\(530\) 0 0
\(531\) 28.6856 + 19.7314i 1.24485 + 0.856270i
\(532\) 0 0
\(533\) −32.6282 11.8757i −1.41328 0.514393i
\(534\) 0 0
\(535\) 13.5429 + 11.3639i 0.585512 + 0.491303i
\(536\) 0 0
\(537\) 1.35028 2.62048i 0.0582687 0.113082i
\(538\) 0 0
\(539\) −0.372237 −0.0160334
\(540\) 0 0
\(541\) 7.63965 0.328454 0.164227 0.986423i \(-0.447487\pi\)
0.164227 + 0.986423i \(0.447487\pi\)
\(542\) 0 0
\(543\) −18.4645 28.7184i −0.792386 1.23242i
\(544\) 0 0
\(545\) −9.91617 8.32065i −0.424762 0.356418i
\(546\) 0 0
\(547\) 7.67732 + 2.79431i 0.328258 + 0.119476i 0.500892 0.865510i \(-0.333005\pi\)
−0.172634 + 0.984986i \(0.555228\pi\)
\(548\) 0 0
\(549\) −2.06365 0.534547i −0.0880746 0.0228139i
\(550\) 0 0
\(551\) −29.3519 + 24.6291i −1.25043 + 1.04924i
\(552\) 0 0
\(553\) −4.63341 + 26.2774i −0.197033 + 1.11743i
\(554\) 0 0
\(555\) 44.4782 18.6412i 1.88799 0.791273i
\(556\) 0 0
\(557\) −5.87975 + 10.1840i −0.249133 + 0.431511i −0.963286 0.268479i \(-0.913479\pi\)
0.714152 + 0.699990i \(0.246812\pi\)
\(558\) 0 0
\(559\) 2.50255 + 4.33455i 0.105847 + 0.183332i
\(560\) 0 0
\(561\) 5.33664 + 23.6057i 0.225313 + 0.996635i
\(562\) 0 0
\(563\) 41.6341 15.1536i 1.75467 0.638647i 0.754818 0.655935i \(-0.227725\pi\)
0.999851 + 0.0172875i \(0.00550305\pi\)
\(564\) 0 0
\(565\) 7.20255 + 40.8477i 0.303013 + 1.71847i
\(566\) 0 0
\(567\) 23.7300 + 3.77726i 0.996568 + 0.158630i
\(568\) 0 0
\(569\) 1.86387 + 10.5705i 0.0781374 + 0.443139i 0.998628 + 0.0523735i \(0.0166786\pi\)
−0.920490 + 0.390766i \(0.872210\pi\)
\(570\) 0 0
\(571\) −29.0041 + 10.5566i −1.21378 + 0.441781i −0.868014 0.496539i \(-0.834604\pi\)
−0.345769 + 0.938320i \(0.612382\pi\)
\(572\) 0 0
\(573\) 1.48685 + 6.57683i 0.0621141 + 0.274751i
\(574\) 0 0
\(575\) 1.67252 + 2.89688i 0.0697488 + 0.120808i
\(576\) 0 0
\(577\) 17.6690 30.6037i 0.735572 1.27405i −0.218900 0.975747i \(-0.570247\pi\)
0.954472 0.298301i \(-0.0964198\pi\)
\(578\) 0 0
\(579\) 18.2210 7.63657i 0.757240 0.317365i
\(580\) 0 0
\(581\) 0.792110 4.49228i 0.0328623 0.186371i
\(582\) 0 0
\(583\) 10.0399 8.42447i 0.415810 0.348906i
\(584\) 0 0
\(585\) 21.0760 21.4305i 0.871384 0.886042i
\(586\) 0 0
\(587\) 19.9028 + 7.24403i 0.821477 + 0.298993i 0.718356 0.695676i \(-0.244895\pi\)
0.103121 + 0.994669i \(0.467117\pi\)
\(588\) 0 0
\(589\) −40.2200 33.7486i −1.65724 1.39059i
\(590\) 0 0
\(591\) 1.00934 + 1.56985i 0.0415185 + 0.0645752i
\(592\) 0 0
\(593\) 39.4642 1.62060 0.810299 0.586016i \(-0.199305\pi\)
0.810299 + 0.586016i \(0.199305\pi\)
\(594\) 0 0
\(595\) −37.9669 −1.55649
\(596\) 0 0
\(597\) 6.97119 13.5290i 0.285312 0.553704i
\(598\) 0 0
\(599\) −12.7478 10.6967i −0.520862 0.437055i 0.344070 0.938944i \(-0.388194\pi\)
−0.864932 + 0.501889i \(0.832639\pi\)
\(600\) 0 0
\(601\) −4.95551 1.80366i −0.202140 0.0735728i 0.238966 0.971028i \(-0.423191\pi\)
−0.441106 + 0.897455i \(0.645414\pi\)
\(602\) 0 0
\(603\) 0.642955 8.12939i 0.0261832 0.331054i
\(604\) 0 0
\(605\) −5.81210 + 4.87693i −0.236295 + 0.198275i
\(606\) 0 0
\(607\) 6.07754 34.4675i 0.246680 1.39899i −0.569879 0.821729i \(-0.693010\pi\)
0.816559 0.577263i \(-0.195879\pi\)
\(608\) 0 0
\(609\) −3.56844 + 28.0071i −0.144601 + 1.13490i
\(610\) 0 0
\(611\) −9.76371 + 16.9112i −0.394998 + 0.684156i
\(612\) 0 0
\(613\) 13.4980 + 23.3791i 0.545177 + 0.944275i 0.998596 + 0.0529768i \(0.0168709\pi\)
−0.453419 + 0.891298i \(0.649796\pi\)
\(614\) 0 0
\(615\) −38.5072 + 35.5819i −1.55276 + 1.43480i
\(616\) 0 0
\(617\) 16.8274 6.12466i 0.677444 0.246569i 0.0196943 0.999806i \(-0.493731\pi\)
0.657750 + 0.753237i \(0.271508\pi\)
\(618\) 0 0
\(619\) 5.11001 + 28.9803i 0.205388 + 1.16482i 0.896827 + 0.442381i \(0.145866\pi\)
−0.691439 + 0.722435i \(0.743023\pi\)
\(620\) 0 0
\(621\) −4.10105 + 2.20051i −0.164569 + 0.0883035i
\(622\) 0 0
\(623\) −6.04819 34.3010i −0.242316 1.37424i
\(624\) 0 0
\(625\) 27.9331 10.1668i 1.11732 0.406672i
\(626\) 0 0
\(627\) −30.1440 9.36634i −1.20383 0.374055i
\(628\) 0 0
\(629\) −22.6657 39.2581i −0.903739 1.56532i
\(630\) 0 0
\(631\) −0.524861 + 0.909086i −0.0208944 + 0.0361902i −0.876284 0.481796i \(-0.839985\pi\)
0.855389 + 0.517986i \(0.173318\pi\)
\(632\) 0 0
\(633\) −2.68373 2.04157i −0.106669 0.0811453i
\(634\) 0 0
\(635\) −4.35605 + 24.7044i −0.172864 + 0.980363i
\(636\) 0 0
\(637\) 0.332889 0.279327i 0.0131895 0.0110673i
\(638\) 0 0
\(639\) 0.00160966 0.00352848i 6.36774e−5 0.000139584i
\(640\) 0 0
\(641\) −31.4725 11.4550i −1.24309 0.452447i −0.365028 0.930997i \(-0.618940\pi\)
−0.878061 + 0.478550i \(0.841163\pi\)
\(642\) 0 0
\(643\) −18.0926 15.1815i −0.713504 0.598701i 0.212076 0.977253i \(-0.431978\pi\)
−0.925580 + 0.378552i \(0.876422\pi\)
\(644\) 0 0
\(645\) 7.54896 0.361142i 0.297240 0.0142200i
\(646\) 0 0
\(647\) −43.5704 −1.71293 −0.856465 0.516205i \(-0.827344\pi\)
−0.856465 + 0.516205i \(0.827344\pi\)
\(648\) 0 0
\(649\) −33.7016 −1.32290
\(650\) 0 0
\(651\) −38.6433 + 1.84870i −1.51455 + 0.0724561i
\(652\) 0 0
\(653\) −15.8475 13.2976i −0.620160 0.520376i 0.277694 0.960670i \(-0.410430\pi\)
−0.897854 + 0.440294i \(0.854874\pi\)
\(654\) 0 0
\(655\) −36.3124 13.2166i −1.41884 0.516416i
\(656\) 0 0
\(657\) 3.05777 + 4.29033i 0.119295 + 0.167382i
\(658\) 0 0
\(659\) 11.4931 9.64387i 0.447708 0.375672i −0.390876 0.920443i \(-0.627828\pi\)
0.838585 + 0.544771i \(0.183384\pi\)
\(660\) 0 0
\(661\) −7.43517 + 42.1670i −0.289195 + 1.64010i 0.400710 + 0.916205i \(0.368763\pi\)
−0.689905 + 0.723900i \(0.742348\pi\)
\(662\) 0 0
\(663\) −22.4863 17.1058i −0.873294 0.664335i
\(664\) 0 0
\(665\) 24.7599 42.8854i 0.960147 1.66302i
\(666\) 0 0
\(667\) −2.73426 4.73588i −0.105871 0.183374i
\(668\) 0 0
\(669\) 47.2913 + 14.6944i 1.82839 + 0.568117i
\(670\) 0 0
\(671\) 1.93905 0.705758i 0.0748563 0.0272455i
\(672\) 0 0
\(673\) −6.50198 36.8746i −0.250633 1.42141i −0.807039 0.590499i \(-0.798931\pi\)
0.556406 0.830911i \(-0.312180\pi\)
\(674\) 0 0
\(675\) −6.06645 18.4330i −0.233498 0.709486i
\(676\) 0 0
\(677\) −4.63351 26.2780i −0.178080 1.00994i −0.934528 0.355890i \(-0.884178\pi\)
0.756448 0.654054i \(-0.226933\pi\)
\(678\) 0 0
\(679\) −7.98973 + 2.90802i −0.306618 + 0.111600i
\(680\) 0 0
\(681\) 24.6212 22.7508i 0.943486 0.871812i
\(682\) 0 0
\(683\) −12.7673 22.1136i −0.488526 0.846152i 0.511387 0.859351i \(-0.329132\pi\)
−0.999913 + 0.0131986i \(0.995799\pi\)
\(684\) 0 0
\(685\) −27.3377 + 47.3503i −1.04452 + 1.80916i
\(686\) 0 0
\(687\) 1.61173 12.6497i 0.0614914 0.482618i
\(688\) 0 0
\(689\) −2.65688 + 15.0679i −0.101219 + 0.574041i
\(690\) 0 0
\(691\) −6.52481 + 5.47497i −0.248215 + 0.208278i −0.758403 0.651785i \(-0.774020\pi\)
0.510188 + 0.860063i \(0.329576\pi\)
\(692\) 0 0
\(693\) −20.9974 + 10.0053i −0.797625 + 0.380069i
\(694\) 0 0
\(695\) 46.0334 + 16.7548i 1.74615 + 0.635545i
\(696\) 0 0
\(697\) 37.7523 + 31.6779i 1.42997 + 1.19989i
\(698\) 0 0
\(699\) −13.5458 + 26.2883i −0.512348 + 0.994314i
\(700\) 0 0
\(701\) 8.06432 0.304585 0.152293 0.988335i \(-0.451334\pi\)
0.152293 + 0.988335i \(0.451334\pi\)
\(702\) 0 0
\(703\) 59.1251 2.22994
\(704\) 0 0
\(705\) 15.9464 + 24.8019i 0.600575 + 0.934094i
\(706\) 0 0
\(707\) −22.4562 18.8430i −0.844551 0.708663i
\(708\) 0 0
\(709\) 13.5612 + 4.93586i 0.509300 + 0.185370i 0.583872 0.811846i \(-0.301537\pi\)
−0.0745721 + 0.997216i \(0.523759\pi\)
\(710\) 0 0
\(711\) 8.00121 + 28.8948i 0.300069 + 1.08364i
\(712\) 0 0
\(713\) 5.74025 4.81664i 0.214974 0.180385i
\(714\) 0 0
\(715\) −5.05231 + 28.6531i −0.188946 + 1.07156i
\(716\) 0 0
\(717\) 34.7234 14.5529i 1.29677 0.543487i
\(718\) 0 0
\(719\) 5.04046 8.73033i 0.187977 0.325586i −0.756598 0.653880i \(-0.773140\pi\)
0.944576 + 0.328293i \(0.106473\pi\)
\(720\) 0 0
\(721\) −6.01873 10.4247i −0.224149 0.388238i
\(722\) 0 0
\(723\) 3.51736 + 15.5584i 0.130812 + 0.578625i
\(724\) 0 0
\(725\) 21.4262 7.79849i 0.795749 0.289629i
\(726\) 0 0
\(727\) −8.33623 47.2771i −0.309174 1.75341i −0.603178 0.797607i \(-0.706099\pi\)
0.294004 0.955804i \(-0.405012\pi\)
\(728\) 0 0
\(729\) 25.8970 7.63843i 0.959148 0.282905i
\(730\) 0 0
\(731\) −1.23358 6.99596i −0.0456255 0.258755i
\(732\) 0 0
\(733\) −43.3735 + 15.7867i −1.60204 + 0.583094i −0.979843 0.199768i \(-0.935981\pi\)
−0.622195 + 0.782862i \(0.713759\pi\)
\(734\) 0 0
\(735\) −0.144691 0.640017i −0.00533701 0.0236074i
\(736\) 0 0
\(737\) 3.94682 + 6.83609i 0.145383 + 0.251811i
\(738\) 0 0
\(739\) −5.41647 + 9.38160i −0.199248 + 0.345108i −0.948285 0.317421i \(-0.897183\pi\)
0.749037 + 0.662528i \(0.230517\pi\)
\(740\) 0 0
\(741\) 33.9861 14.2438i 1.24851 0.523260i
\(742\) 0 0
\(743\) 1.12864 6.40081i 0.0414056 0.234823i −0.957081 0.289821i \(-0.906404\pi\)
0.998486 + 0.0549982i \(0.0175153\pi\)
\(744\) 0 0
\(745\) −31.2261 + 26.2018i −1.14404 + 0.959961i
\(746\) 0 0
\(747\) −1.36786 4.93974i −0.0500473 0.180736i
\(748\) 0 0
\(749\) 15.0076 + 5.46234i 0.548367 + 0.199589i
\(750\) 0 0
\(751\) −15.9250 13.3627i −0.581112 0.487610i 0.304200 0.952608i \(-0.401611\pi\)
−0.885312 + 0.464998i \(0.846055\pi\)
\(752\) 0 0
\(753\) 19.0643 + 29.6514i 0.694744 + 1.08056i
\(754\) 0 0
\(755\) −1.20499 −0.0438543
\(756\) 0 0
\(757\) −26.9259 −0.978639 −0.489319 0.872105i \(-0.662755\pi\)
−0.489319 + 0.872105i \(0.662755\pi\)
\(758\) 0 0
\(759\) 2.06353 4.00470i 0.0749015 0.145361i
\(760\) 0 0
\(761\) −32.4256 27.2083i −1.17543 0.986302i −0.999998 0.00180962i \(-0.999424\pi\)
−0.175430 0.984492i \(-0.556132\pi\)
\(762\) 0 0
\(763\) −10.9886 3.99953i −0.397815 0.144793i
\(764\) 0 0
\(765\) −38.5128 + 18.3514i −1.39243 + 0.663497i
\(766\) 0 0
\(767\) 30.1391 25.2897i 1.08826 0.913159i
\(768\) 0 0
\(769\) 4.53460 25.7170i 0.163522 0.927378i −0.787054 0.616885i \(-0.788394\pi\)
0.950575 0.310494i \(-0.100494\pi\)
\(770\) 0 0
\(771\) 0.602715 4.73043i 0.0217063 0.170362i
\(772\) 0 0
\(773\) −24.7533 + 42.8740i −0.890316 + 1.54207i −0.0508186 + 0.998708i \(0.516183\pi\)
−0.839497 + 0.543364i \(0.817150\pi\)
\(774\) 0 0
\(775\) 15.6220 + 27.0580i 0.561157 + 0.971953i
\(776\) 0 0
\(777\) 31.9977 29.5669i 1.14791 1.06071i
\(778\) 0 0
\(779\) −60.4016 + 21.9844i −2.16411 + 0.787672i
\(780\) 0 0
\(781\) 0.000651892 0.00369707i 2.33265e−5 0.000132291i
\(782\) 0 0
\(783\) 9.91755 + 30.1346i 0.354424 + 1.07692i
\(784\) 0 0
\(785\) 4.38726 + 24.8814i 0.156588 + 0.888054i
\(786\) 0 0
\(787\) 14.9602 5.44506i 0.533272 0.194095i −0.0613265 0.998118i \(-0.519533\pi\)
0.594599 + 0.804022i \(0.297311\pi\)
\(788\) 0 0
\(789\) 7.09407 + 2.20427i 0.252555 + 0.0784740i
\(790\) 0 0
\(791\) 18.7350 + 32.4500i 0.666140 + 1.15379i
\(792\) 0 0
\(793\) −1.20448 + 2.08622i −0.0427723 + 0.0740839i
\(794\) 0 0
\(795\) 18.3875 + 13.9877i 0.652136 + 0.496094i
\(796\) 0 0
\(797\) 2.69068 15.2596i 0.0953089 0.540524i −0.899343 0.437243i \(-0.855955\pi\)
0.994652 0.103281i \(-0.0329339\pi\)
\(798\) 0 0
\(799\) 21.2315 17.8154i 0.751118 0.630263i
\(800\) 0 0
\(801\) −22.7146 31.8708i −0.802583 1.12610i
\(802\) 0 0
\(803\) −4.79222 1.74422i −0.169114 0.0615523i
\(804\) 0 0
\(805\) 5.41403 + 4.54291i 0.190820 + 0.160117i
\(806\) 0 0
\(807\) 8.50860 0.407051i 0.299517 0.0143289i
\(808\) 0 0
\(809\) 36.9909 1.30053 0.650265 0.759708i \(-0.274658\pi\)
0.650265 + 0.759708i \(0.274658\pi\)
\(810\) 0 0
\(811\) 51.5190 1.80908 0.904539 0.426391i \(-0.140215\pi\)
0.904539 + 0.426391i \(0.140215\pi\)
\(812\) 0 0
\(813\) −3.77970 + 0.180821i −0.132560 + 0.00634167i
\(814\) 0 0
\(815\) 19.2268 + 16.1332i 0.673487 + 0.565123i
\(816\) 0 0
\(817\) 8.70672 + 3.16899i 0.304610 + 0.110869i
\(818\) 0 0
\(819\) 11.2698 24.7041i 0.393800 0.863231i
\(820\) 0 0
\(821\) −14.5504 + 12.2092i −0.507813 + 0.426105i −0.860359 0.509689i \(-0.829760\pi\)
0.352546 + 0.935794i \(0.385316\pi\)
\(822\) 0 0
\(823\) −3.85066 + 21.8382i −0.134226 + 0.761231i 0.841170 + 0.540770i \(0.181867\pi\)
−0.975396 + 0.220461i \(0.929244\pi\)
\(824\) 0 0
\(825\) 14.9500 + 11.3728i 0.520493 + 0.395951i
\(826\) 0 0
\(827\) 19.3971 33.5968i 0.674505 1.16828i −0.302109 0.953273i \(-0.597691\pi\)
0.976613 0.215003i \(-0.0689761\pi\)
\(828\) 0 0
\(829\) −28.4452 49.2685i −0.987942 1.71117i −0.628054 0.778170i \(-0.716148\pi\)
−0.359888 0.932996i \(-0.617185\pi\)
\(830\) 0 0
\(831\) −2.76756 0.859934i −0.0960054 0.0298308i
\(832\) 0 0
\(833\) −0.579580 + 0.210950i −0.0200812 + 0.00730898i
\(834\) 0 0
\(835\) −4.30490 24.4143i −0.148977 0.844891i
\(836\) 0 0
\(837\) −38.3054 + 20.5536i −1.32403 + 0.710438i
\(838\) 0 0
\(839\) 9.73704 + 55.2215i 0.336160 + 1.90646i 0.415469 + 0.909607i \(0.363617\pi\)
−0.0793095 + 0.996850i \(0.525272\pi\)
\(840\) 0 0
\(841\) −7.77685 + 2.83054i −0.268167 + 0.0976049i
\(842\) 0 0
\(843\) −0.683910 + 0.631955i −0.0235551 + 0.0217657i
\(844\) 0 0
\(845\) 2.22729 + 3.85778i 0.0766210 + 0.132711i
\(846\) 0 0
\(847\) −3.42702 + 5.93577i −0.117754 + 0.203956i
\(848\) 0 0
\(849\) −0.0872499 + 0.684785i −0.00299441 + 0.0235017i
\(850\) 0 0
\(851\) −1.46531 + 8.31020i −0.0502303 + 0.284870i
\(852\) 0 0
\(853\) 18.1372 15.2189i 0.621006 0.521086i −0.277114 0.960837i \(-0.589378\pi\)
0.898119 + 0.439751i \(0.144933\pi\)
\(854\) 0 0
\(855\) 4.38711 55.4697i 0.150036 1.89703i
\(856\) 0 0
\(857\) −13.2321 4.81609i −0.452000 0.164514i 0.105981 0.994368i \(-0.466202\pi\)
−0.557981 + 0.829854i \(0.688424\pi\)
\(858\) 0 0
\(859\) 30.5014 + 25.5937i 1.04069 + 0.873245i 0.992084 0.125573i \(-0.0400769\pi\)
0.0486084 + 0.998818i \(0.484521\pi\)
\(860\) 0 0
\(861\) −21.6947 + 42.1029i −0.739354 + 1.43486i
\(862\) 0 0
\(863\) 6.52665 0.222170 0.111085 0.993811i \(-0.464567\pi\)
0.111085 + 0.993811i \(0.464567\pi\)
\(864\) 0 0
\(865\) 42.2234 1.43564
\(866\) 0 0
\(867\) 5.76268 + 8.96289i 0.195711 + 0.304396i
\(868\) 0 0
\(869\) −22.2321 18.6550i −0.754173 0.632827i
\(870\) 0 0
\(871\) −8.65942 3.15177i −0.293413 0.106794i
\(872\) 0 0
\(873\) −6.69901 + 6.81170i −0.226727 + 0.230541i
\(874\) 0 0
\(875\) 7.64876 6.41807i 0.258575 0.216970i
\(876\) 0 0
\(877\) −1.03569 + 5.87369i −0.0349728 + 0.198340i −0.997288 0.0735953i \(-0.976553\pi\)
0.962315 + 0.271936i \(0.0876638\pi\)
\(878\) 0 0
\(879\) −45.9305 + 19.2498i −1.54920 + 0.649281i
\(880\) 0 0
\(881\) 17.6866 30.6340i 0.595876 1.03209i −0.397547 0.917582i \(-0.630138\pi\)
0.993423 0.114505i \(-0.0365283\pi\)
\(882\) 0 0
\(883\) 12.3274 + 21.3517i 0.414851 + 0.718542i 0.995413 0.0956737i \(-0.0305005\pi\)
−0.580562 + 0.814216i \(0.697167\pi\)
\(884\) 0 0
\(885\) −13.1001 57.9459i −0.440354 1.94783i
\(886\) 0 0
\(887\) 22.9576 8.35590i 0.770842 0.280564i 0.0734936 0.997296i \(-0.476585\pi\)
0.697349 + 0.716732i \(0.254363\pi\)
\(888\) 0 0
\(889\) 3.93514 + 22.3173i 0.131980 + 0.748498i
\(890\) 0 0
\(891\) −16.4632 + 20.2983i −0.551538 + 0.680019i
\(892\) 0 0
\(893\) 6.27727 + 35.6001i 0.210061 + 1.19131i
\(894\) 0 0
\(895\) −4.72673 + 1.72039i −0.157997 + 0.0575062i
\(896\) 0 0
\(897\) 1.15973 + 5.12985i 0.0387221 + 0.171281i
\(898\) 0 0
\(899\) −25.5391 44.2350i −0.851776 1.47532i
\(900\) 0 0
\(901\) 10.8581 18.8068i 0.361735 0.626544i
\(902\) 0 0
\(903\) 6.29669 2.63899i 0.209541 0.0878201i
\(904\) 0 0
\(905\) −10.1163 + 57.3724i −0.336277 + 1.90712i
\(906\) 0 0
\(907\) −23.7668 + 19.9427i −0.789165 + 0.662188i −0.945539 0.325510i \(-0.894464\pi\)
0.156374 + 0.987698i \(0.450020\pi\)
\(908\) 0 0
\(909\) −31.8869 8.25964i −1.05762 0.273955i
\(910\) 0 0
\(911\) 25.6832 + 9.34792i 0.850922 + 0.309710i 0.730416 0.683002i \(-0.239326\pi\)
0.120506 + 0.992713i \(0.461548\pi\)
\(912\) 0 0
\(913\) 3.80072 + 3.18918i 0.125786 + 0.105547i
\(914\) 0 0
\(915\) 1.96719 + 3.05964i 0.0650333 + 0.101148i
\(916\) 0 0
\(917\) −34.9090 −1.15280
\(918\) 0 0
\(919\) 13.7346 0.453064 0.226532 0.974004i \(-0.427261\pi\)
0.226532 + 0.974004i \(0.427261\pi\)
\(920\) 0 0
\(921\) 8.28879 16.0861i 0.273125 0.530053i
\(922\) 0 0
\(923\) −0.00335726 0.00281708i −0.000110506 9.27253e-5i
\(924\) 0 0
\(925\) −33.0624 12.0337i −1.08709 0.395667i
\(926\) 0 0
\(927\) −11.1441 7.66546i −0.366020 0.251767i
\(928\) 0 0
\(929\) 2.68827 2.25572i 0.0881992 0.0740079i −0.597622 0.801778i \(-0.703888\pi\)
0.685821 + 0.727770i \(0.259443\pi\)
\(930\) 0 0
\(931\) 0.139692 0.792231i 0.00457821 0.0259643i
\(932\) 0 0
\(933\) −0.687539 + 5.39618i −0.0225090 + 0.176663i
\(934\) 0 0
\(935\) 20.6477 35.7629i 0.675253 1.16957i
\(936\) 0 0
\(937\) −1.63152 2.82588i −0.0532996 0.0923176i 0.838145 0.545448i \(-0.183640\pi\)
−0.891444 + 0.453131i \(0.850307\pi\)
\(938\) 0 0
\(939\) 7.92279 7.32091i 0.258550 0.238909i
\(940\) 0 0
\(941\) −1.94129 + 0.706570i −0.0632841 + 0.0230335i −0.373468 0.927643i \(-0.621832\pi\)
0.310184 + 0.950677i \(0.399609\pi\)
\(942\) 0 0
\(943\) −1.59302 9.03446i −0.0518759 0.294203i
\(944\) 0 0
\(945\) −25.3647 32.2134i −0.825115 1.04790i
\(946\) 0 0
\(947\) 1.42672 + 8.09132i 0.0463621 + 0.262933i 0.999174 0.0406276i \(-0.0129357\pi\)
−0.952812 + 0.303560i \(0.901825\pi\)
\(948\) 0 0
\(949\) 5.59451 2.03624i 0.181605 0.0660990i
\(950\) 0 0
\(951\) 17.9619 + 5.58113i 0.582455 + 0.180980i
\(952\) 0 0
\(953\) −12.6318 21.8790i −0.409185 0.708729i 0.585614 0.810590i \(-0.300854\pi\)
−0.994799 + 0.101861i \(0.967520\pi\)
\(954\) 0 0
\(955\) 5.75270 9.96397i 0.186153 0.322426i
\(956\) 0 0
\(957\) −24.4406 18.5925i −0.790052 0.601010i
\(958\) 0 0
\(959\) −8.57689 + 48.6420i −0.276962 + 1.57073i
\(960\) 0 0
\(961\) 29.8688 25.0629i 0.963509 0.808480i
\(962\) 0 0
\(963\) 17.8637 1.71312i 0.575649 0.0552044i
\(964\) 0 0
\(965\) −31.6781 11.5299i −1.01975 0.371160i
\(966\) 0 0
\(967\) −40.2579 33.7804i −1.29461 1.08630i −0.991050 0.133492i \(-0.957381\pi\)
−0.303558 0.952813i \(-0.598174\pi\)
\(968\) 0 0
\(969\) −52.2428 + 2.49929i −1.67828 + 0.0802888i
\(970\) 0 0
\(971\) −20.8321 −0.668535 −0.334267 0.942478i \(-0.608489\pi\)
−0.334267 + 0.942478i \(0.608489\pi\)
\(972\) 0 0
\(973\) 44.2542 1.41873
\(974\) 0 0
\(975\) −21.9039 + 1.04788i −0.701485 + 0.0335590i
\(976\) 0 0
\(977\) −1.37625 1.15481i −0.0440301 0.0369457i 0.620507 0.784201i \(-0.286927\pi\)
−0.664537 + 0.747255i \(0.731371\pi\)
\(978\) 0 0
\(979\) 35.5990 + 12.9570i 1.13775 + 0.414107i
\(980\) 0 0
\(981\) −13.0798 + 1.25435i −0.417606 + 0.0400482i
\(982\) 0 0
\(983\) −37.0605 + 31.0974i −1.18205 + 0.991854i −0.182083 + 0.983283i \(0.558284\pi\)
−0.999963 + 0.00857126i \(0.997272\pi\)
\(984\) 0 0
\(985\) 0.552994 3.13619i 0.0176199 0.0999272i
\(986\) 0 0
\(987\) 21.1999 + 16.1272i 0.674800 + 0.513335i
\(988\) 0 0
\(989\) −0.661191 + 1.14522i −0.0210247 + 0.0364158i
\(990\) 0 0
\(991\) −21.8440 37.8349i −0.693898 1.20187i −0.970551 0.240897i \(-0.922559\pi\)
0.276653 0.960970i \(-0.410775\pi\)
\(992\) 0 0
\(993\) −40.1224 12.4668i −1.27325 0.395623i
\(994\) 0 0
\(995\) −24.4031 + 8.88200i −0.773630 + 0.281578i
\(996\) 0 0
\(997\) −4.22483 23.9602i −0.133802 0.758828i −0.975687 0.219170i \(-0.929665\pi\)
0.841885 0.539657i \(-0.181446\pi\)
\(998\) 0 0
\(999\) 18.1665 45.4582i 0.574763 1.43823i
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 108.2.i.a.13.1 18
3.2 odd 2 324.2.i.a.253.1 18
4.3 odd 2 432.2.u.d.337.3 18
9.2 odd 6 972.2.i.d.109.3 18
9.4 even 3 972.2.i.c.433.3 18
9.5 odd 6 972.2.i.b.433.1 18
9.7 even 3 972.2.i.a.109.1 18
27.2 odd 18 324.2.i.a.73.1 18
27.4 even 9 2916.2.e.c.1945.3 18
27.5 odd 18 2916.2.a.c.1.3 9
27.7 even 9 972.2.i.a.865.1 18
27.11 odd 18 972.2.i.b.541.1 18
27.13 even 9 2916.2.e.c.973.3 18
27.14 odd 18 2916.2.e.d.973.7 18
27.16 even 9 972.2.i.c.541.3 18
27.20 odd 18 972.2.i.d.865.3 18
27.22 even 9 2916.2.a.d.1.7 9
27.23 odd 18 2916.2.e.d.1945.7 18
27.25 even 9 inner 108.2.i.a.25.1 yes 18
108.79 odd 18 432.2.u.d.241.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.i.a.13.1 18 1.1 even 1 trivial
108.2.i.a.25.1 yes 18 27.25 even 9 inner
324.2.i.a.73.1 18 27.2 odd 18
324.2.i.a.253.1 18 3.2 odd 2
432.2.u.d.241.3 18 108.79 odd 18
432.2.u.d.337.3 18 4.3 odd 2
972.2.i.a.109.1 18 9.7 even 3
972.2.i.a.865.1 18 27.7 even 9
972.2.i.b.433.1 18 9.5 odd 6
972.2.i.b.541.1 18 27.11 odd 18
972.2.i.c.433.3 18 9.4 even 3
972.2.i.c.541.3 18 27.16 even 9
972.2.i.d.109.3 18 9.2 odd 6
972.2.i.d.865.3 18 27.20 odd 18
2916.2.a.c.1.3 9 27.5 odd 18
2916.2.a.d.1.7 9 27.22 even 9
2916.2.e.c.973.3 18 27.13 even 9
2916.2.e.c.1945.3 18 27.4 even 9
2916.2.e.d.973.7 18 27.14 odd 18
2916.2.e.d.1945.7 18 27.23 odd 18