Properties

Label 432.2.u.d.337.3
Level $432$
Weight $2$
Character 432.337
Analytic conductor $3.450$
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] = [432,2,Mod(49,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.u (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
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: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 337.3
Root \(0.381933 + 1.68942i\) of defining polynomial
Character \(\chi\) \(=\) 432.337
Dual form 432.2.u.d.241.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73007 - 0.0827666i) q^{3} +(2.26400 + 1.89972i) q^{5} +(-2.50885 - 0.913148i) q^{7} +(2.98630 - 0.286384i) q^{9} +O(q^{10})\) \(q+(1.73007 - 0.0827666i) q^{3} +(2.26400 + 1.89972i) q^{5} +(-2.50885 - 0.913148i) q^{7} +(2.98630 - 0.286384i) q^{9} +(2.22454 - 1.86661i) q^{11} +(0.588684 - 3.33859i) q^{13} +(4.07411 + 3.09927i) q^{15} +(-2.40583 + 4.16701i) q^{17} +(3.13789 + 5.43498i) q^{19} +(-4.41608 - 1.37216i) q^{21} +(-0.841669 + 0.306343i) q^{23} +(0.648507 + 3.67787i) q^{25} +(5.14281 - 0.742631i) q^{27} +(-1.06019 - 6.01265i) q^{29} +(-7.86152 + 2.86136i) q^{31} +(3.69412 - 3.41349i) q^{33} +(-3.94531 - 6.83348i) q^{35} +(-4.71058 + 8.15896i) q^{37} +(0.742142 - 5.82473i) q^{39} +(1.77855 - 10.0866i) q^{41} +(1.13098 - 0.949006i) q^{43} +(7.30502 + 5.02475i) q^{45} +(5.41276 + 1.97008i) q^{47} +(0.0981944 + 0.0823949i) q^{49} +(-3.81737 + 7.40836i) q^{51} -4.51324 q^{53} +8.58238 q^{55} +(5.87861 + 9.14320i) q^{57} +(-8.89034 - 7.45989i) q^{59} +(-0.667734 - 0.243035i) q^{61} +(-7.75370 - 2.00844i) q^{63} +(7.67516 - 6.44023i) q^{65} +(-0.472021 + 2.67696i) q^{67} +(-1.43079 + 0.599657i) q^{69} +(-0.000646382 + 0.00111957i) q^{71} +(0.878080 + 1.52088i) q^{73} +(1.42637 + 6.30930i) q^{75} +(-7.28554 + 2.65172i) q^{77} +(-1.73545 - 9.84220i) q^{79} +(8.83597 - 1.71046i) q^{81} +(0.296685 + 1.68259i) q^{83} +(-13.3629 + 4.86371i) q^{85} +(-2.33186 - 10.3146i) q^{87} +(-6.52283 - 11.2979i) q^{89} +(-4.52555 + 7.83848i) q^{91} +(-13.3642 + 5.60103i) q^{93} +(-3.22077 + 18.2659i) q^{95} +(-2.43956 + 2.04703i) q^{97} +(6.10857 - 6.21133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\)

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 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 −0.178836 0.983879i \(-0.557233\pi\)
−0.769421 + 0.638741i \(0.779455\pi\)
\(8\) 0 0
\(9\) 2.98630 0.286384i 0.995433 0.0954615i
\(10\) 0 0
\(11\) 2.22454 1.86661i 0.670724 0.562804i −0.242556 0.970138i \(-0.577986\pi\)
0.913280 + 0.407333i \(0.133541\pi\)
\(12\) 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 \(0.0891369\pi\)
−0.241166 + 0.970484i \(0.577530\pi\)
\(20\) 0 0
\(21\) −4.41608 1.37216i −0.963667 0.299430i
\(22\) 0 0
\(23\) −0.841669 + 0.306343i −0.175500 + 0.0638769i −0.428276 0.903648i \(-0.640879\pi\)
0.252776 + 0.967525i \(0.418657\pi\)
\(24\) 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 −0.931708 0.363209i \(-0.881681\pi\)
−0.480263 + 0.877124i \(0.659459\pi\)
\(32\) 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 −0.552465 0.833536i \(-0.686313\pi\)
0.724938 + 0.688814i \(0.241868\pi\)
\(44\) 0 0
\(45\) 7.30502 + 5.02475i 1.08897 + 0.749046i
\(46\) 0 0
\(47\) 5.41276 + 1.97008i 0.789532 + 0.287366i 0.705142 0.709067i \(-0.250883\pi\)
0.0843906 + 0.996433i \(0.473106\pi\)
\(48\) 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 −0.157557 0.987510i \(-0.550362\pi\)
−0.999867 + 0.0163155i \(0.994806\pi\)
\(60\) 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 −0.999970 0.00771610i \(-0.997544\pi\)
0.942304 + 0.334759i \(0.108655\pi\)
\(68\) 0 0
\(69\) −1.43079 + 0.599657i −0.172247 + 0.0721902i
\(70\) 0 0
\(71\) −0.000646382 0.00111957i −7.67115e−5 0.000132868i −0.866064 0.499934i \(-0.833358\pi\)
0.865987 + 0.500066i \(0.166691\pi\)
\(72\) 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 \(-0.865507\pi\)
0.716805 0.697273i \(-0.245604\pi\)
\(80\) 0 0
\(81\) 8.83597 1.71046i 0.981774 0.190051i
\(82\) 0 0
\(83\) 0.296685 + 1.68259i 0.0325654 + 0.184688i 0.996751 0.0805392i \(-0.0256642\pi\)
−0.964186 + 0.265227i \(0.914553\pi\)
\(84\) 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 0.796887 0.604128i \(-0.206479\pi\)
−0.456572 + 0.889686i \(0.650923\pi\)
\(104\) 0 0
\(105\) −7.39125 11.4959i −0.721313 1.12188i
\(106\) 0 0
\(107\) −5.98188 −0.578290 −0.289145 0.957285i \(-0.593371\pi\)
−0.289145 + 0.957285i \(0.593371\pi\)
\(108\) 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 0.613974 0.789326i \(-0.289570\pi\)
−0.990564 + 0.137054i \(0.956237\pi\)
\(128\) 0 0
\(129\) 1.87813 1.73546i 0.165360 0.152798i
\(130\) 0 0
\(131\) 12.2866 4.47197i 1.07349 0.390718i 0.256009 0.966675i \(-0.417592\pi\)
0.817480 + 0.575956i \(0.195370\pi\)
\(132\) 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 −0.903818 0.427916i \(-0.859248\pi\)
−0.417306 + 0.908766i \(0.637026\pi\)
\(140\) 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 −0.629991 0.776603i \(-0.716941\pi\)
0.655408 + 0.755275i \(0.272497\pi\)
\(152\) 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 \(-0.607922\pi\)
−0.332590 + 0.943072i \(0.607922\pi\)
\(164\) 0 0
\(165\) 14.8481 0.710335i 1.15593 0.0552995i
\(166\) 0 0
\(167\) 6.42577 + 5.39186i 0.497241 + 0.417235i 0.856613 0.515960i \(-0.172565\pi\)
−0.359372 + 0.933194i \(0.617009\pi\)
\(168\) 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 −0.832469 0.554072i \(-0.813073\pi\)
0.896075 + 0.443903i \(0.146407\pi\)
\(180\) 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 0.999448 0.0332146i \(-0.0105745\pi\)
−0.950534 + 0.310620i \(0.899463\pi\)
\(192\) 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 −0.667231 0.744851i \(-0.732520\pi\)
0.978675 + 0.205413i \(0.0658538\pi\)
\(200\) 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 0.590008 0.807397i \(-0.299125\pi\)
−0.692677 + 0.721248i \(0.743569\pi\)
\(212\) 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 \(0.0177657\pi\)
0.800709 + 0.599054i \(0.204457\pi\)
\(224\) 0 0
\(225\) 2.98992 + 10.7975i 0.199328 + 0.719833i
\(226\) 0 0
\(227\) 14.8265 12.4409i 0.984068 0.825731i −0.000630367 1.00000i \(-0.500201\pi\)
0.984698 + 0.174269i \(0.0557562\pi\)
\(228\) 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 0.417398 0.908724i \(-0.362942\pi\)
0.903862 + 0.427825i \(0.140720\pi\)
\(240\) 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 \(0.0553592\pi\)
−0.342600 + 0.939482i \(0.611307\pi\)
\(252\) 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 0.463275 0.886214i \(-0.346674\pi\)
−0.214758 + 0.976667i \(0.568896\pi\)
\(264\) 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 \(-0.521137\pi\)
−0.0663558 + 0.997796i \(0.521137\pi\)
\(272\) 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 −0.986796 0.161970i \(-0.948215\pi\)
0.982682 + 0.185302i \(0.0593263\pi\)
\(284\) 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 −0.677569 0.735459i \(-0.736967\pi\)
0.975711 + 0.219063i \(0.0702999\pi\)
\(308\) 0 0
\(309\) 6.21522 + 4.72805i 0.353571 + 0.268970i
\(310\) 0 0
\(311\) −0.545372 + 3.09296i −0.0309252 + 0.175386i −0.996358 0.0852656i \(-0.972826\pi\)
0.965433 + 0.260651i \(0.0839372\pi\)
\(312\) 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 −0.371510 0.928429i \(-0.621160\pi\)
−0.881376 + 0.472416i \(0.843382\pi\)
\(332\) 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 −0.845951 0.533261i \(-0.820966\pi\)
−0.305262 + 0.952268i \(0.598744\pi\)
\(348\) 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 0.980477 0.196636i \(-0.0630017\pi\)
−0.660530 + 0.750800i \(0.729668\pi\)
\(360\) 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 −0.700864 0.713295i \(-0.747202\pi\)
0.580755 + 0.814078i \(0.302757\pi\)
\(368\) 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 \(-0.420590\pi\)
0.246893 + 0.969043i \(0.420590\pi\)
\(380\) 0 0
\(381\) −7.95074 12.3661i −0.407329 0.633532i
\(382\) 0 0
\(383\) −0.551178 0.462493i −0.0281639 0.0236323i 0.628597 0.777731i \(-0.283629\pi\)
−0.656761 + 0.754099i \(0.728074\pi\)
\(384\) 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 \(-0.784719\pi\)
0.946927 0.321448i \(-0.104170\pi\)
\(420\) 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 \(-0.409373\pi\)
0.280882 + 0.959742i \(0.409373\pi\)
\(432\) 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 −0.145684 0.989331i \(-0.546538\pi\)
−0.747531 + 0.664227i \(0.768761\pi\)
\(440\) 0 0
\(441\) 0.316835 + 0.217935i 0.0150874 + 0.0103778i
\(442\) 0 0
\(443\) 12.6039 10.5759i 0.598830 0.502478i −0.292240 0.956345i \(-0.594400\pi\)
0.891069 + 0.453867i \(0.149956\pi\)
\(444\) 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 −0.576720 0.816942i \(-0.695667\pi\)
0.0833274 + 0.996522i \(0.473445\pi\)
\(464\) 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 \(-0.957860\pi\)
0.381308 0.924448i \(-0.375474\pi\)
\(468\) 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 −0.0352661 0.999378i \(-0.511228\pi\)
−0.669403 + 0.742899i \(0.733450\pi\)
\(480\) 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 \(-0.400699\pi\)
0.306926 + 0.951733i \(0.400699\pi\)
\(488\) 0 0
\(489\) −14.6925 + 0.702890i −0.664419 + 0.0317858i
\(490\) 0 0
\(491\) −7.54691 6.33261i −0.340587 0.285787i 0.456410 0.889770i \(-0.349135\pi\)
−0.796997 + 0.603983i \(0.793579\pi\)
\(492\) 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 \(0.343214\pi\)
−0.745725 + 0.666254i \(0.767897\pi\)
\(500\) 0 0
\(501\) 11.5633 + 8.79646i 0.516610 + 0.392997i
\(502\) 0 0
\(503\) 6.77729 11.7386i 0.302185 0.523399i −0.674446 0.738324i \(-0.735617\pi\)
0.976631 + 0.214925i \(0.0689508\pi\)
\(504\) 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 −0.995377 0.0960487i \(-0.969380\pi\)
0.580869 + 0.813997i \(0.302713\pi\)
\(524\) 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 0.172634 0.984986i \(-0.444772\pi\)
−0.500892 + 0.865510i \(0.666995\pi\)
\(548\) 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 −0.999851 0.0172875i \(-0.994497\pi\)
−0.754818 + 0.655935i \(0.772275\pi\)
\(564\) 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 0.345769 0.938320i \(-0.387618\pi\)
0.868014 + 0.496539i \(0.165396\pi\)
\(572\) 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 −0.103121 0.994669i \(-0.532883\pi\)
−0.718356 + 0.695676i \(0.755105\pi\)
\(588\) 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 0.864932 0.501889i \(-0.167361\pi\)
−0.344070 + 0.938944i \(0.611806\pi\)
\(600\) 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 \(0.306990\pi\)
−0.816559 + 0.577263i \(0.804121\pi\)
\(608\) 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 \(-0.854134\pi\)
0.691439 0.722435i \(-0.256977\pi\)
\(620\) 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 −0.855389 0.517986i \(-0.826682\pi\)
0.876284 + 0.481796i \(0.160015\pi\)
\(632\) 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 0.925580 0.378552i \(-0.123578\pi\)
−0.212076 + 0.977253i \(0.568022\pi\)
\(644\) 0 0
\(645\) 7.54896 0.361142i 0.297240 0.0142200i
\(646\) 0 0
\(647\) 43.5704 1.71293 0.856465 0.516205i \(-0.172656\pi\)
0.856465 + 0.516205i \(0.172656\pi\)
\(648\) 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 −0.838585 0.544771i \(-0.816616\pi\)
0.390876 + 0.920443i \(0.372172\pi\)
\(660\) 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 0.999913 0.0131986i \(-0.00420138\pi\)
−0.511387 + 0.859351i \(0.670868\pi\)
\(684\) 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 −0.510188 0.860063i \(-0.670424\pi\)
0.758403 + 0.651785i \(0.225980\pi\)
\(692\) 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 −0.944576 0.328293i \(-0.893527\pi\)
0.756598 + 0.653880i \(0.226860\pi\)
\(720\) 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 \(0.293901\pi\)
−0.294004 + 0.955804i \(0.594988\pi\)
\(728\) 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 −0.749037 0.662528i \(-0.769483\pi\)
0.948285 + 0.317421i \(0.102817\pi\)
\(740\) 0 0
\(741\) 33.9861 14.2438i 1.24851 0.523260i
\(742\) 0 0
\(743\) −1.12864 + 6.40081i −0.0414056 + 0.234823i −0.998486 0.0549982i \(-0.982485\pi\)
0.957081 + 0.289821i \(0.0935958\pi\)
\(744\) 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 0.885312 0.464998i \(-0.153945\pi\)
−0.304200 + 0.952608i \(0.598389\pi\)
\(752\) 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 −0.594599 0.804022i \(-0.702689\pi\)
0.0613265 + 0.998118i \(0.480467\pi\)
\(788\) 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 \(-0.859785\pi\)
−0.904539 + 0.426391i \(0.859785\pi\)
\(812\) 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 \(-0.818133\pi\)
0.975396 0.220461i \(-0.0707561\pi\)
\(824\) 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 \(0.402309\pi\)
−0.976613 + 0.215003i \(0.931024\pi\)
\(828\) 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 \(-0.636383\pi\)
0.0793095 0.996850i \(-0.474728\pi\)
\(840\) 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 −0.0486084 0.998818i \(-0.515479\pi\)
−0.992084 + 0.125573i \(0.959923\pi\)
\(860\) 0 0
\(861\) −21.6947 + 42.1029i −0.739354 + 1.43486i
\(862\) 0 0
\(863\) −6.52665 −0.222170 −0.111085 0.993811i \(-0.535433\pi\)
−0.111085 + 0.993811i \(0.535433\pi\)
\(864\) 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 0.580562 0.814216i \(-0.302833\pi\)
−0.995413 + 0.0956737i \(0.969499\pi\)
\(884\) 0 0
\(885\) −13.1001 57.9459i −0.440354 1.94783i
\(886\) 0 0
\(887\) −22.9576 + 8.35590i −0.770842 + 0.280564i −0.697349 0.716732i \(-0.745637\pi\)
−0.0734936 + 0.997296i \(0.523415\pi\)
\(888\) 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 −0.156374 0.987698i \(-0.549980\pi\)
0.945539 + 0.325510i \(0.105536\pi\)
\(908\) 0 0
\(909\) −31.8869 8.25964i −1.05762 0.273955i
\(910\) 0 0
\(911\) −25.6832 9.34792i −0.850922 0.309710i −0.120506 0.992713i \(-0.538452\pi\)
−0.730416 + 0.683002i \(0.760674\pi\)
\(912\) 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 \(-0.572739\pi\)
−0.226532 + 0.974004i \(0.572739\pi\)
\(920\) 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 0.952812 0.303560i \(-0.0981754\pi\)
−0.999174 + 0.0406276i \(0.987064\pi\)
\(948\) 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 \(0.0426189\pi\)
0.303558 + 0.952813i \(0.401826\pi\)
\(968\) 0 0
\(969\) −52.2428 + 2.49929i −1.67828 + 0.0802888i
\(970\) 0 0
\(971\) 20.8321 0.668535 0.334267 0.942478i \(-0.391511\pi\)
0.334267 + 0.942478i \(0.391511\pi\)
\(972\) 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 \(-0.441716\pi\)
0.999963 0.00857126i \(-0.00272835\pi\)
\(984\) 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 \(0.0774415\pi\)
−0.276653 + 0.960970i \(0.589225\pi\)
\(992\) 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 432.2.u.d.337.3 18
4.3 odd 2 108.2.i.a.13.1 18
12.11 even 2 324.2.i.a.253.1 18
27.25 even 9 inner 432.2.u.d.241.3 18
36.7 odd 6 972.2.i.a.109.1 18
36.11 even 6 972.2.i.d.109.3 18
36.23 even 6 972.2.i.b.433.1 18
36.31 odd 6 972.2.i.c.433.3 18
108.7 odd 18 972.2.i.a.865.1 18
108.11 even 18 972.2.i.b.541.1 18
108.23 even 18 2916.2.e.d.1945.7 18
108.31 odd 18 2916.2.e.c.1945.3 18
108.43 odd 18 972.2.i.c.541.3 18
108.47 even 18 972.2.i.d.865.3 18
108.59 even 18 2916.2.a.c.1.3 9
108.67 odd 18 2916.2.e.c.973.3 18
108.79 odd 18 108.2.i.a.25.1 yes 18
108.83 even 18 324.2.i.a.73.1 18
108.95 even 18 2916.2.e.d.973.7 18
108.103 odd 18 2916.2.a.d.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.i.a.13.1 18 4.3 odd 2
108.2.i.a.25.1 yes 18 108.79 odd 18
324.2.i.a.73.1 18 108.83 even 18
324.2.i.a.253.1 18 12.11 even 2
432.2.u.d.241.3 18 27.25 even 9 inner
432.2.u.d.337.3 18 1.1 even 1 trivial
972.2.i.a.109.1 18 36.7 odd 6
972.2.i.a.865.1 18 108.7 odd 18
972.2.i.b.433.1 18 36.23 even 6
972.2.i.b.541.1 18 108.11 even 18
972.2.i.c.433.3 18 36.31 odd 6
972.2.i.c.541.3 18 108.43 odd 18
972.2.i.d.109.3 18 36.11 even 6
972.2.i.d.865.3 18 108.47 even 18
2916.2.a.c.1.3 9 108.59 even 18
2916.2.a.d.1.7 9 108.103 odd 18
2916.2.e.c.973.3 18 108.67 odd 18
2916.2.e.c.1945.3 18 108.31 odd 18
2916.2.e.d.973.7 18 108.95 even 18
2916.2.e.d.1945.7 18 108.23 even 18