Properties

Label 243.2.e.d.28.1
Level $243$
Weight $2$
Character 243.28
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
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] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.e (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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 28.1
Root \(0.500000 - 2.22827i\) of defining polynomial
Character \(\chi\) \(=\) 243.28
Dual form 243.2.e.d.217.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.367548 - 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(-2.05537 - 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(0.508086 + 0.880031i) q^{8} +O(q^{10})\) \(q+(-0.367548 - 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(-2.05537 - 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(0.508086 + 0.880031i) q^{8} +(-2.83955 + 4.91825i) q^{10} +(-0.242761 + 0.203701i) q^{11} +(-0.262909 + 1.49103i) q^{13} +(-0.357379 + 2.02679i) q^{14} +(-2.15207 + 1.80580i) q^{16} +(-0.587342 + 1.01731i) q^{17} +(-3.11040 - 5.38737i) q^{19} +(6.25302 + 2.27591i) q^{20} +(0.513834 + 0.431158i) q^{22} +(-2.03231 + 0.739701i) q^{23} +(0.381855 + 2.16561i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(-0.764905 - 4.33799i) q^{29} +(8.15017 - 2.96642i) q^{31} +(6.11199 + 5.12857i) q^{32} +(2.33642 + 0.850386i) q^{34} +(1.30443 + 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(-10.0866 + 8.46364i) q^{38} +(0.473450 - 2.68507i) q^{40} +(1.01501 - 5.75638i) q^{41} +(4.28295 - 3.59382i) q^{43} +(0.392973 - 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(2.32674 + 0.846865i) q^{47} +(-4.63807 - 3.89180i) q^{49} +(4.37378 - 1.59193i) q^{50} +(-0.652037 - 3.69789i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(-0.171574 - 0.973047i) q^{56} +(-8.76126 + 3.18884i) q^{58} +(-1.32082 - 1.10830i) q^{59} +(-0.953579 - 0.347074i) q^{61} +(-9.17898 - 15.8985i) q^{62} +(5.63455 - 9.75933i) q^{64} +(3.11190 - 2.61119i) q^{65} +(0.148739 - 0.843538i) q^{67} +(0.505893 - 2.86906i) q^{68} +(4.23008 - 3.54946i) q^{70} +(4.79788 - 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(-8.88405 - 3.23353i) q^{74} +(11.8187 + 9.91703i) q^{76} +(0.289552 - 0.105388i) q^{77} +(-1.94725 - 11.0434i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(0.813530 + 4.61376i) q^{83} +(2.96172 - 1.07798i) q^{85} +(-9.06538 - 7.60676i) q^{86} +(-0.302607 - 0.110140i) q^{88} +(7.74976 + 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(4.10891 - 3.44778i) q^{92} +(0.910073 - 5.16128i) q^{94} +(-2.89837 + 16.4375i) q^{95} +(-4.25115 + 3.56714i) q^{97} +(-6.40762 + 11.0983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} + 3 q^{13} - 21 q^{14} + 9 q^{16} + 9 q^{17} - 3 q^{19} + 24 q^{20} + 12 q^{22} - 12 q^{23} + 12 q^{25} - 30 q^{26} - 12 q^{28} - 24 q^{29} + 12 q^{31} + 27 q^{32} + 12 q^{35} - 3 q^{37} - 30 q^{38} - 15 q^{40} + 6 q^{41} - 15 q^{43} + 3 q^{44} - 3 q^{46} + 12 q^{47} - 33 q^{49} + 21 q^{50} - 45 q^{52} - 18 q^{53} - 12 q^{55} + 30 q^{56} - 51 q^{58} - 3 q^{59} - 33 q^{61} - 12 q^{62} + 12 q^{64} + 21 q^{65} - 6 q^{67} + 9 q^{68} - 15 q^{70} + 27 q^{71} + 6 q^{73} - 21 q^{74} + 6 q^{76} - 12 q^{77} + 21 q^{79} + 42 q^{80} - 12 q^{82} - 6 q^{83} + 36 q^{85} - 21 q^{86} + 42 q^{88} + 9 q^{89} + 6 q^{91} - 3 q^{92} + 48 q^{94} + 3 q^{95} + 39 q^{97} - 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.367548 2.08447i −0.259895 1.47394i −0.783187 0.621786i \(-0.786407\pi\)
0.523291 0.852154i \(-0.324704\pi\)
\(3\) 0 0
\(4\) −2.33052 + 0.848241i −1.16526 + 0.424121i
\(5\) −2.05537 1.72466i −0.919190 0.771292i 0.0546547 0.998505i \(-0.482594\pi\)
−0.973845 + 0.227213i \(0.927039\pi\)
\(6\) 0 0
\(7\) −0.913694 0.332557i −0.345344 0.125695i 0.163524 0.986539i \(-0.447714\pi\)
−0.508868 + 0.860844i \(0.669936\pi\)
\(8\) 0.508086 + 0.880031i 0.179636 + 0.311138i
\(9\) 0 0
\(10\) −2.83955 + 4.91825i −0.897945 + 1.55529i
\(11\) −0.242761 + 0.203701i −0.0731952 + 0.0614181i −0.678651 0.734461i \(-0.737435\pi\)
0.605456 + 0.795879i \(0.292991\pi\)
\(12\) 0 0
\(13\) −0.262909 + 1.49103i −0.0729177 + 0.413537i 0.926398 + 0.376546i \(0.122888\pi\)
−0.999316 + 0.0369909i \(0.988223\pi\)
\(14\) −0.357379 + 2.02679i −0.0955135 + 0.541684i
\(15\) 0 0
\(16\) −2.15207 + 1.80580i −0.538018 + 0.451451i
\(17\) −0.587342 + 1.01731i −0.142451 + 0.246733i −0.928419 0.371534i \(-0.878832\pi\)
0.785968 + 0.618267i \(0.212165\pi\)
\(18\) 0 0
\(19\) −3.11040 5.38737i −0.713575 1.23595i −0.963507 0.267685i \(-0.913741\pi\)
0.249931 0.968264i \(-0.419592\pi\)
\(20\) 6.25302 + 2.27591i 1.39822 + 0.508910i
\(21\) 0 0
\(22\) 0.513834 + 0.431158i 0.109550 + 0.0919231i
\(23\) −2.03231 + 0.739701i −0.423766 + 0.154238i −0.545095 0.838374i \(-0.683507\pi\)
0.121329 + 0.992612i \(0.461284\pi\)
\(24\) 0 0
\(25\) 0.381855 + 2.16561i 0.0763710 + 0.433121i
\(26\) 3.20463 0.628480
\(27\) 0 0
\(28\) 2.41147 0.455726
\(29\) −0.764905 4.33799i −0.142039 0.805545i −0.969697 0.244311i \(-0.921438\pi\)
0.827658 0.561233i \(-0.189673\pi\)
\(30\) 0 0
\(31\) 8.15017 2.96642i 1.46381 0.532784i 0.517400 0.855743i \(-0.326900\pi\)
0.946413 + 0.322959i \(0.104678\pi\)
\(32\) 6.11199 + 5.12857i 1.08046 + 0.906611i
\(33\) 0 0
\(34\) 2.33642 + 0.850386i 0.400692 + 0.145840i
\(35\) 1.30443 + 2.25934i 0.220489 + 0.381899i
\(36\) 0 0
\(37\) 2.23332 3.86823i 0.367156 0.635933i −0.621964 0.783046i \(-0.713665\pi\)
0.989120 + 0.147113i \(0.0469982\pi\)
\(38\) −10.0866 + 8.46364i −1.63626 + 1.37298i
\(39\) 0 0
\(40\) 0.473450 2.68507i 0.0748590 0.424547i
\(41\) 1.01501 5.75638i 0.158517 0.898996i −0.796982 0.604003i \(-0.793572\pi\)
0.955499 0.294993i \(-0.0953174\pi\)
\(42\) 0 0
\(43\) 4.28295 3.59382i 0.653143 0.548052i −0.254880 0.966973i \(-0.582036\pi\)
0.908023 + 0.418920i \(0.137591\pi\)
\(44\) 0.392973 0.680649i 0.0592429 0.102612i
\(45\) 0 0
\(46\) 2.28885 + 3.96441i 0.337473 + 0.584521i
\(47\) 2.32674 + 0.846865i 0.339390 + 0.123528i 0.506092 0.862479i \(-0.331090\pi\)
−0.166702 + 0.986007i \(0.553312\pi\)
\(48\) 0 0
\(49\) −4.63807 3.89180i −0.662581 0.555972i
\(50\) 4.37378 1.59193i 0.618546 0.225132i
\(51\) 0 0
\(52\) −0.652037 3.69789i −0.0904213 0.512805i
\(53\) −10.8920 −1.49613 −0.748063 0.663628i \(-0.769016\pi\)
−0.748063 + 0.663628i \(0.769016\pi\)
\(54\) 0 0
\(55\) 0.850279 0.114652
\(56\) −0.171574 0.973047i −0.0229276 0.130029i
\(57\) 0 0
\(58\) −8.76126 + 3.18884i −1.15041 + 0.418715i
\(59\) −1.32082 1.10830i −0.171956 0.144289i 0.552748 0.833348i \(-0.313579\pi\)
−0.724704 + 0.689060i \(0.758024\pi\)
\(60\) 0 0
\(61\) −0.953579 0.347074i −0.122093 0.0444383i 0.280251 0.959927i \(-0.409582\pi\)
−0.402344 + 0.915488i \(0.631805\pi\)
\(62\) −9.17898 15.8985i −1.16573 2.01911i
\(63\) 0 0
\(64\) 5.63455 9.75933i 0.704319 1.21992i
\(65\) 3.11190 2.61119i 0.385983 0.323878i
\(66\) 0 0
\(67\) 0.148739 0.843538i 0.0181713 0.103055i −0.974373 0.224938i \(-0.927782\pi\)
0.992544 + 0.121883i \(0.0388933\pi\)
\(68\) 0.505893 2.86906i 0.0613486 0.347925i
\(69\) 0 0
\(70\) 4.23008 3.54946i 0.505592 0.424242i
\(71\) 4.79788 8.31018i 0.569404 0.986237i −0.427221 0.904147i \(-0.640507\pi\)
0.996625 0.0820894i \(-0.0261593\pi\)
\(72\) 0 0
\(73\) 7.62091 + 13.1998i 0.891960 + 1.54492i 0.837522 + 0.546404i \(0.184004\pi\)
0.0544385 + 0.998517i \(0.482663\pi\)
\(74\) −8.88405 3.23353i −1.03275 0.375890i
\(75\) 0 0
\(76\) 11.8187 + 9.91703i 1.35569 + 1.13756i
\(77\) 0.289552 0.105388i 0.0329975 0.0120101i
\(78\) 0 0
\(79\) −1.94725 11.0434i −0.219083 1.24248i −0.873680 0.486502i \(-0.838273\pi\)
0.654597 0.755978i \(-0.272838\pi\)
\(80\) 7.53771 0.842741
\(81\) 0 0
\(82\) −12.3721 −1.36626
\(83\) 0.813530 + 4.61376i 0.0892965 + 0.506425i 0.996347 + 0.0854026i \(0.0272177\pi\)
−0.907050 + 0.421023i \(0.861671\pi\)
\(84\) 0 0
\(85\) 2.96172 1.07798i 0.321243 0.116923i
\(86\) −9.06538 7.60676i −0.977546 0.820258i
\(87\) 0 0
\(88\) −0.302607 0.110140i −0.0322580 0.0117409i
\(89\) 7.74976 + 13.4230i 0.821473 + 1.42283i 0.904586 + 0.426292i \(0.140180\pi\)
−0.0831130 + 0.996540i \(0.526486\pi\)
\(90\) 0 0
\(91\) 0.736071 1.27491i 0.0771612 0.133647i
\(92\) 4.10891 3.44778i 0.428383 0.359456i
\(93\) 0 0
\(94\) 0.910073 5.16128i 0.0938669 0.532346i
\(95\) −2.89837 + 16.4375i −0.297366 + 1.68645i
\(96\) 0 0
\(97\) −4.25115 + 3.56714i −0.431639 + 0.362188i −0.832570 0.553920i \(-0.813131\pi\)
0.400931 + 0.916108i \(0.368687\pi\)
\(98\) −6.40762 + 11.0983i −0.647267 + 1.12110i
\(99\) 0 0
\(100\) −2.72688 4.72309i −0.272688 0.472309i
\(101\) 9.52759 + 3.46776i 0.948030 + 0.345055i 0.769332 0.638849i \(-0.220589\pi\)
0.178698 + 0.983904i \(0.442811\pi\)
\(102\) 0 0
\(103\) −7.54806 6.33357i −0.743732 0.624065i 0.190105 0.981764i \(-0.439117\pi\)
−0.933837 + 0.357698i \(0.883562\pi\)
\(104\) −1.44573 + 0.526203i −0.141766 + 0.0515985i
\(105\) 0 0
\(106\) 4.00331 + 22.7039i 0.388836 + 2.20520i
\(107\) 5.17080 0.499880 0.249940 0.968261i \(-0.419589\pi\)
0.249940 + 0.968261i \(0.419589\pi\)
\(108\) 0 0
\(109\) −7.31065 −0.700234 −0.350117 0.936706i \(-0.613858\pi\)
−0.350117 + 0.936706i \(0.613858\pi\)
\(110\) −0.312518 1.77238i −0.0297974 0.168990i
\(111\) 0 0
\(112\) 2.56687 0.934263i 0.242546 0.0882796i
\(113\) 7.94820 + 6.66933i 0.747704 + 0.627398i 0.934895 0.354925i \(-0.115494\pi\)
−0.187191 + 0.982324i \(0.559938\pi\)
\(114\) 0 0
\(115\) 5.45289 + 1.98469i 0.508485 + 0.185073i
\(116\) 5.46229 + 9.46096i 0.507161 + 0.878428i
\(117\) 0 0
\(118\) −1.82475 + 3.16056i −0.167982 + 0.290953i
\(119\) 0.874964 0.734182i 0.0802078 0.0673023i
\(120\) 0 0
\(121\) −1.89269 + 10.7340i −0.172063 + 0.975817i
\(122\) −0.372979 + 2.11527i −0.0337680 + 0.191508i
\(123\) 0 0
\(124\) −16.4779 + 13.8266i −1.47976 + 1.24167i
\(125\) −3.75766 + 6.50846i −0.336095 + 0.582134i
\(126\) 0 0
\(127\) −2.61372 4.52709i −0.231930 0.401714i 0.726446 0.687223i \(-0.241171\pi\)
−0.958376 + 0.285509i \(0.907837\pi\)
\(128\) −7.41903 2.70031i −0.655756 0.238676i
\(129\) 0 0
\(130\) −6.58671 5.52691i −0.577693 0.484742i
\(131\) 6.79802 2.47428i 0.593946 0.216179i −0.0275183 0.999621i \(-0.508760\pi\)
0.621464 + 0.783443i \(0.286538\pi\)
\(132\) 0 0
\(133\) 1.05034 + 5.95680i 0.0910764 + 0.516520i
\(134\) −1.81300 −0.156619
\(135\) 0 0
\(136\) −1.19368 −0.102357
\(137\) 1.95342 + 11.0784i 0.166892 + 0.946493i 0.947092 + 0.320962i \(0.104006\pi\)
−0.780200 + 0.625531i \(0.784883\pi\)
\(138\) 0 0
\(139\) −8.81447 + 3.20820i −0.747634 + 0.272116i −0.687610 0.726081i \(-0.741340\pi\)
−0.0600240 + 0.998197i \(0.519118\pi\)
\(140\) −4.95648 4.15898i −0.418899 0.351498i
\(141\) 0 0
\(142\) −19.0857 6.94664i −1.60164 0.582949i
\(143\) −0.239900 0.415518i −0.0200614 0.0347474i
\(144\) 0 0
\(145\) −5.90940 + 10.2354i −0.490749 + 0.850003i
\(146\) 24.7135 20.7371i 2.04530 1.71621i
\(147\) 0 0
\(148\) −1.92362 + 10.9094i −0.158121 + 0.896747i
\(149\) 3.30821 18.7618i 0.271019 1.53703i −0.480309 0.877099i \(-0.659475\pi\)
0.751328 0.659928i \(-0.229413\pi\)
\(150\) 0 0
\(151\) 3.07490 2.58015i 0.250232 0.209970i −0.509040 0.860743i \(-0.670000\pi\)
0.759272 + 0.650773i \(0.225555\pi\)
\(152\) 3.16070 5.47450i 0.256367 0.444041i
\(153\) 0 0
\(154\) −0.326102 0.564825i −0.0262780 0.0455149i
\(155\) −21.8677 7.95919i −1.75646 0.639298i
\(156\) 0 0
\(157\) 5.57368 + 4.67687i 0.444828 + 0.373255i 0.837512 0.546418i \(-0.184009\pi\)
−0.392685 + 0.919673i \(0.628454\pi\)
\(158\) −22.3039 + 8.11795i −1.77440 + 0.645830i
\(159\) 0 0
\(160\) −3.71737 21.0822i −0.293884 1.66670i
\(161\) 2.10290 0.165732
\(162\) 0 0
\(163\) 12.4492 0.975094 0.487547 0.873097i \(-0.337892\pi\)
0.487547 + 0.873097i \(0.337892\pi\)
\(164\) 2.51731 + 14.2764i 0.196569 + 1.11480i
\(165\) 0 0
\(166\) 9.31821 3.39155i 0.723233 0.263235i
\(167\) −1.78633 1.49891i −0.138230 0.115989i 0.571051 0.820915i \(-0.306536\pi\)
−0.709281 + 0.704926i \(0.750980\pi\)
\(168\) 0 0
\(169\) 10.0620 + 3.66225i 0.773997 + 0.281712i
\(170\) −3.33558 5.77739i −0.255827 0.443106i
\(171\) 0 0
\(172\) −6.93308 + 12.0085i −0.528643 + 0.915636i
\(173\) −2.74418 + 2.30264i −0.208636 + 0.175066i −0.741118 0.671375i \(-0.765704\pi\)
0.532482 + 0.846442i \(0.321260\pi\)
\(174\) 0 0
\(175\) 0.371290 2.10569i 0.0280669 0.159175i
\(176\) 0.154596 0.876757i 0.0116531 0.0660880i
\(177\) 0 0
\(178\) 25.1313 21.0877i 1.88367 1.58059i
\(179\) 9.99785 17.3168i 0.747275 1.29432i −0.201850 0.979416i \(-0.564695\pi\)
0.949124 0.314901i \(-0.101971\pi\)
\(180\) 0 0
\(181\) −4.86616 8.42844i −0.361699 0.626481i 0.626542 0.779388i \(-0.284470\pi\)
−0.988241 + 0.152907i \(0.951136\pi\)
\(182\) −2.92805 1.06572i −0.217042 0.0789967i
\(183\) 0 0
\(184\) −1.68355 1.41267i −0.124113 0.104143i
\(185\) −11.2617 + 4.09892i −0.827976 + 0.301359i
\(186\) 0 0
\(187\) −0.0646422 0.366604i −0.00472711 0.0268088i
\(188\) −6.14088 −0.447869
\(189\) 0 0
\(190\) 35.3286 2.56301
\(191\) −3.08339 17.4868i −0.223106 1.26530i −0.866273 0.499571i \(-0.833491\pi\)
0.643167 0.765726i \(-0.277620\pi\)
\(192\) 0 0
\(193\) −9.94602 + 3.62006i −0.715930 + 0.260577i −0.674197 0.738551i \(-0.735510\pi\)
−0.0417333 + 0.999129i \(0.513288\pi\)
\(194\) 8.99809 + 7.55029i 0.646025 + 0.542079i
\(195\) 0 0
\(196\) 14.1103 + 5.13574i 1.00788 + 0.366838i
\(197\) −7.07945 12.2620i −0.504390 0.873628i −0.999987 0.00507615i \(-0.998384\pi\)
0.495597 0.868552i \(-0.334949\pi\)
\(198\) 0 0
\(199\) −3.77010 + 6.53000i −0.267255 + 0.462899i −0.968152 0.250363i \(-0.919450\pi\)
0.700897 + 0.713263i \(0.252783\pi\)
\(200\) −1.71179 + 1.43636i −0.121042 + 0.101566i
\(201\) 0 0
\(202\) 3.72658 21.1345i 0.262201 1.48702i
\(203\) −0.743742 + 4.21797i −0.0522004 + 0.296043i
\(204\) 0 0
\(205\) −12.0140 + 10.0810i −0.839096 + 0.704085i
\(206\) −10.4278 + 18.0616i −0.726543 + 1.25841i
\(207\) 0 0
\(208\) −2.12670 3.68356i −0.147460 0.255409i
\(209\) 1.85250 + 0.674254i 0.128140 + 0.0466391i
\(210\) 0 0
\(211\) 3.99388 + 3.35126i 0.274950 + 0.230710i 0.769827 0.638253i \(-0.220342\pi\)
−0.494877 + 0.868963i \(0.664787\pi\)
\(212\) 25.3840 9.23901i 1.74338 0.634538i
\(213\) 0 0
\(214\) −1.90052 10.7784i −0.129917 0.736794i
\(215\) −15.0012 −1.02307
\(216\) 0 0
\(217\) −8.43326 −0.572487
\(218\) 2.68701 + 15.2388i 0.181988 + 1.03210i
\(219\) 0 0
\(220\) −1.98160 + 0.721242i −0.133599 + 0.0486261i
\(221\) −1.36242 1.14320i −0.0916460 0.0769001i
\(222\) 0 0
\(223\) −16.6267 6.05164i −1.11341 0.405248i −0.281166 0.959659i \(-0.590721\pi\)
−0.832243 + 0.554412i \(0.812943\pi\)
\(224\) −3.87894 6.71853i −0.259173 0.448901i
\(225\) 0 0
\(226\) 10.9807 19.0191i 0.730423 1.26513i
\(227\) −12.0820 + 10.1380i −0.801913 + 0.672885i −0.948663 0.316289i \(-0.897563\pi\)
0.146750 + 0.989174i \(0.453119\pi\)
\(228\) 0 0
\(229\) −0.306813 + 1.74002i −0.0202748 + 0.114984i −0.993266 0.115860i \(-0.963038\pi\)
0.972991 + 0.230844i \(0.0741487\pi\)
\(230\) 2.13282 12.0958i 0.140634 0.797576i
\(231\) 0 0
\(232\) 3.42893 2.87721i 0.225120 0.188898i
\(233\) 6.94920 12.0364i 0.455257 0.788529i −0.543446 0.839444i \(-0.682881\pi\)
0.998703 + 0.0509157i \(0.0162140\pi\)
\(234\) 0 0
\(235\) −3.32177 5.75347i −0.216688 0.375315i
\(236\) 4.01831 + 1.46255i 0.261570 + 0.0952037i
\(237\) 0 0
\(238\) −1.85197 1.55399i −0.120045 0.100730i
\(239\) 18.6366 6.78318i 1.20550 0.438767i 0.340362 0.940295i \(-0.389451\pi\)
0.865142 + 0.501527i \(0.167228\pi\)
\(240\) 0 0
\(241\) 3.36438 + 19.0804i 0.216719 + 1.22907i 0.877899 + 0.478846i \(0.158945\pi\)
−0.661180 + 0.750227i \(0.729944\pi\)
\(242\) 23.0703 1.48301
\(243\) 0 0
\(244\) 2.51674 0.161118
\(245\) 2.82091 + 15.9982i 0.180222 + 1.02209i
\(246\) 0 0
\(247\) 8.85048 3.22131i 0.563143 0.204967i
\(248\) 6.75153 + 5.66521i 0.428723 + 0.359741i
\(249\) 0 0
\(250\) 14.9478 + 5.44055i 0.945381 + 0.344090i
\(251\) 2.73786 + 4.74212i 0.172812 + 0.299320i 0.939402 0.342818i \(-0.111381\pi\)
−0.766590 + 0.642137i \(0.778048\pi\)
\(252\) 0 0
\(253\) 0.342689 0.593554i 0.0215447 0.0373164i
\(254\) −8.47590 + 7.11212i −0.531825 + 0.446254i
\(255\) 0 0
\(256\) 1.01187 5.73859i 0.0632418 0.358662i
\(257\) −2.00827 + 11.3895i −0.125272 + 0.710455i 0.855873 + 0.517186i \(0.173020\pi\)
−0.981146 + 0.193270i \(0.938091\pi\)
\(258\) 0 0
\(259\) −3.32698 + 2.79167i −0.206729 + 0.173466i
\(260\) −5.03743 + 8.72508i −0.312408 + 0.541107i
\(261\) 0 0
\(262\) −7.65614 13.2608i −0.472998 0.819257i
\(263\) −6.08727 2.21558i −0.375357 0.136619i 0.147451 0.989069i \(-0.452893\pi\)
−0.522808 + 0.852451i \(0.675115\pi\)
\(264\) 0 0
\(265\) 22.3870 + 18.7849i 1.37522 + 1.15395i
\(266\) 12.0307 4.37881i 0.737649 0.268482i
\(267\) 0 0
\(268\) 0.368885 + 2.09205i 0.0225332 + 0.127792i
\(269\) −13.8387 −0.843758 −0.421879 0.906652i \(-0.638629\pi\)
−0.421879 + 0.906652i \(0.638629\pi\)
\(270\) 0 0
\(271\) 1.94536 0.118172 0.0590860 0.998253i \(-0.481181\pi\)
0.0590860 + 0.998253i \(0.481181\pi\)
\(272\) −0.573052 3.24994i −0.0347464 0.197057i
\(273\) 0 0
\(274\) 22.3746 8.14369i 1.35170 0.491978i
\(275\) −0.533835 0.447941i −0.0321915 0.0270118i
\(276\) 0 0
\(277\) −11.7205 4.26591i −0.704216 0.256314i −0.0350062 0.999387i \(-0.511145\pi\)
−0.669210 + 0.743073i \(0.733367\pi\)
\(278\) 9.92713 + 17.1943i 0.595390 + 1.03125i
\(279\) 0 0
\(280\) −1.32553 + 2.29588i −0.0792154 + 0.137205i
\(281\) 7.47343 6.27095i 0.445827 0.374094i −0.392057 0.919941i \(-0.628237\pi\)
0.837885 + 0.545847i \(0.183792\pi\)
\(282\) 0 0
\(283\) 4.61405 26.1676i 0.274277 1.55550i −0.466974 0.884271i \(-0.654656\pi\)
0.741250 0.671229i \(-0.234233\pi\)
\(284\) −4.13255 + 23.4368i −0.245221 + 1.39072i
\(285\) 0 0
\(286\) −0.777960 + 0.652786i −0.0460017 + 0.0386000i
\(287\) −2.84173 + 4.92202i −0.167742 + 0.290538i
\(288\) 0 0
\(289\) 7.81006 + 13.5274i 0.459415 + 0.795730i
\(290\) 23.5073 + 8.55596i 1.38040 + 0.502423i
\(291\) 0 0
\(292\) −28.9573 24.2981i −1.69460 1.42194i
\(293\) −11.5182 + 4.19230i −0.672903 + 0.244917i −0.655797 0.754937i \(-0.727667\pi\)
−0.0171059 + 0.999854i \(0.505445\pi\)
\(294\) 0 0
\(295\) 0.803336 + 4.55594i 0.0467720 + 0.265257i
\(296\) 4.53888 0.263817
\(297\) 0 0
\(298\) −40.3243 −2.33592
\(299\) −0.568603 3.22471i −0.0328832 0.186490i
\(300\) 0 0
\(301\) −5.10845 + 1.85933i −0.294446 + 0.107170i
\(302\) −6.50841 5.46121i −0.374517 0.314257i
\(303\) 0 0
\(304\) 16.4223 + 5.97724i 0.941886 + 0.342818i
\(305\) 1.36137 + 2.35797i 0.0779521 + 0.135017i
\(306\) 0 0
\(307\) 13.2370 22.9271i 0.755475 1.30852i −0.189663 0.981849i \(-0.560740\pi\)
0.945138 0.326671i \(-0.105927\pi\)
\(308\) −0.585412 + 0.491219i −0.0333569 + 0.0279898i
\(309\) 0 0
\(310\) −8.55325 + 48.5079i −0.485792 + 2.75506i
\(311\) −3.06654 + 17.3912i −0.173887 + 0.986164i 0.765533 + 0.643397i \(0.222475\pi\)
−0.939420 + 0.342768i \(0.888636\pi\)
\(312\) 0 0
\(313\) 7.39019 6.20111i 0.417718 0.350507i −0.409576 0.912276i \(-0.634323\pi\)
0.827294 + 0.561769i \(0.189879\pi\)
\(314\) 7.70019 13.3371i 0.434547 0.752657i
\(315\) 0 0
\(316\) 13.9056 + 24.0852i 0.782250 + 1.35490i
\(317\) 3.48672 + 1.26906i 0.195834 + 0.0712777i 0.438075 0.898938i \(-0.355660\pi\)
−0.242241 + 0.970216i \(0.577883\pi\)
\(318\) 0 0
\(319\) 1.06934 + 0.897284i 0.0598716 + 0.0502382i
\(320\) −28.4126 + 10.3414i −1.58831 + 0.578099i
\(321\) 0 0
\(322\) −0.772918 4.38343i −0.0430730 0.244279i
\(323\) 7.30748 0.406599
\(324\) 0 0
\(325\) −3.32937 −0.184680
\(326\) −4.57566 25.9499i −0.253422 1.43723i
\(327\) 0 0
\(328\) 5.58151 2.03150i 0.308187 0.112171i
\(329\) −1.84430 1.54755i −0.101680 0.0853193i
\(330\) 0 0
\(331\) 1.32759 + 0.483205i 0.0729712 + 0.0265593i 0.378248 0.925704i \(-0.376527\pi\)
−0.305277 + 0.952264i \(0.598749\pi\)
\(332\) −5.80953 10.0624i −0.318839 0.552246i
\(333\) 0 0
\(334\) −2.46786 + 4.27446i −0.135035 + 0.233888i
\(335\) −1.76053 + 1.47726i −0.0961881 + 0.0807114i
\(336\) 0 0
\(337\) −2.25570 + 12.7927i −0.122876 + 0.696864i 0.859671 + 0.510848i \(0.170669\pi\)
−0.982547 + 0.186016i \(0.940442\pi\)
\(338\) 3.93559 22.3199i 0.214068 1.21404i
\(339\) 0 0
\(340\) −5.98797 + 5.02450i −0.324743 + 0.272492i
\(341\) −1.37428 + 2.38033i −0.0744215 + 0.128902i
\(342\) 0 0
\(343\) 6.34669 + 10.9928i 0.342689 + 0.593555i
\(344\) 5.33878 + 1.94316i 0.287848 + 0.104768i
\(345\) 0 0
\(346\) 5.80839 + 4.87382i 0.312261 + 0.262018i
\(347\) 4.51096 1.64185i 0.242161 0.0881394i −0.218089 0.975929i \(-0.569982\pi\)
0.460250 + 0.887790i \(0.347760\pi\)
\(348\) 0 0
\(349\) −3.92055 22.2346i −0.209862 1.19019i −0.889602 0.456736i \(-0.849018\pi\)
0.679740 0.733453i \(-0.262093\pi\)
\(350\) −4.52571 −0.241909
\(351\) 0 0
\(352\) −2.52845 −0.134767
\(353\) −5.15849 29.2553i −0.274559 1.55710i −0.740360 0.672211i \(-0.765345\pi\)
0.465801 0.884889i \(-0.345766\pi\)
\(354\) 0 0
\(355\) −24.1937 + 8.80578i −1.28407 + 0.467362i
\(356\) −29.4469 24.7089i −1.56068 1.30957i
\(357\) 0 0
\(358\) −39.7710 14.4754i −2.10196 0.765051i
\(359\) −6.70991 11.6219i −0.354136 0.613381i 0.632834 0.774288i \(-0.281892\pi\)
−0.986970 + 0.160906i \(0.948558\pi\)
\(360\) 0 0
\(361\) −9.84920 + 17.0593i −0.518379 + 0.897858i
\(362\) −15.7802 + 13.2412i −0.829392 + 0.695942i
\(363\) 0 0
\(364\) −0.633997 + 3.59558i −0.0332305 + 0.188459i
\(365\) 7.10140 40.2740i 0.371704 2.10804i
\(366\) 0 0
\(367\) −6.09004 + 5.11015i −0.317897 + 0.266748i −0.787747 0.615999i \(-0.788753\pi\)
0.469850 + 0.882746i \(0.344308\pi\)
\(368\) 3.03793 5.26184i 0.158363 0.274293i
\(369\) 0 0
\(370\) 12.6833 + 21.9681i 0.659372 + 1.14207i
\(371\) 9.95192 + 3.62220i 0.516678 + 0.188055i
\(372\) 0 0
\(373\) −8.74862 7.34096i −0.452986 0.380101i 0.387556 0.921846i \(-0.373319\pi\)
−0.840543 + 0.541745i \(0.817764\pi\)
\(374\) −0.740415 + 0.269489i −0.0382860 + 0.0139350i
\(375\) 0 0
\(376\) 0.436918 + 2.47789i 0.0225323 + 0.127787i
\(377\) 6.66917 0.343480
\(378\) 0 0
\(379\) −24.1705 −1.24155 −0.620777 0.783987i \(-0.713183\pi\)
−0.620777 + 0.783987i \(0.713183\pi\)
\(380\) −7.18821 40.7664i −0.368748 2.09127i
\(381\) 0 0
\(382\) −35.3173 + 12.8544i −1.80699 + 0.657690i
\(383\) 7.23397 + 6.07003i 0.369639 + 0.310164i 0.808619 0.588333i \(-0.200216\pi\)
−0.438980 + 0.898497i \(0.644660\pi\)
\(384\) 0 0
\(385\) −0.776895 0.282767i −0.0395942 0.0144111i
\(386\) 11.2015 + 19.4016i 0.570143 + 0.987516i
\(387\) 0 0
\(388\) 6.88162 11.9193i 0.349361 0.605111i
\(389\) −1.95166 + 1.63763i −0.0989529 + 0.0830314i −0.690922 0.722929i \(-0.742795\pi\)
0.591969 + 0.805961i \(0.298351\pi\)
\(390\) 0 0
\(391\) 0.441160 2.50194i 0.0223104 0.126529i
\(392\) 1.06837 6.05902i 0.0539607 0.306027i
\(393\) 0 0
\(394\) −22.9576 + 19.2637i −1.15659 + 0.970492i
\(395\) −15.0438 + 26.0567i −0.756937 + 1.31105i
\(396\) 0 0
\(397\) −1.83759 3.18279i −0.0922258 0.159740i 0.816222 0.577739i \(-0.196065\pi\)
−0.908447 + 0.417999i \(0.862731\pi\)
\(398\) 14.9973 + 5.45855i 0.751744 + 0.273613i
\(399\) 0 0
\(400\) −4.73244 3.97098i −0.236622 0.198549i
\(401\) −15.1748 + 5.52319i −0.757795 + 0.275815i −0.691882 0.722010i \(-0.743218\pi\)
−0.0659131 + 0.997825i \(0.520996\pi\)
\(402\) 0 0
\(403\) 2.28027 + 12.9320i 0.113588 + 0.644190i
\(404\) −25.1458 −1.25105
\(405\) 0 0
\(406\) 9.06558 0.449917
\(407\) 0.245797 + 1.39399i 0.0121837 + 0.0690973i
\(408\) 0 0
\(409\) −8.62823 + 3.14042i −0.426639 + 0.155284i −0.546410 0.837518i \(-0.684006\pi\)
0.119772 + 0.992801i \(0.461784\pi\)
\(410\) 25.4292 + 21.3376i 1.25586 + 1.05379i
\(411\) 0 0
\(412\) 22.9633 + 8.35797i 1.13132 + 0.411767i
\(413\) 0.838253 + 1.45190i 0.0412477 + 0.0714432i
\(414\) 0 0
\(415\) 6.28506 10.8860i 0.308522 0.534375i
\(416\) −9.25374 + 7.76481i −0.453702 + 0.380701i
\(417\) 0 0
\(418\) 0.724578 4.10929i 0.0354403 0.200992i
\(419\) −1.21187 + 6.87285i −0.0592037 + 0.335761i −0.999995 0.00322608i \(-0.998973\pi\)
0.940791 + 0.338987i \(0.110084\pi\)
\(420\) 0 0
\(421\) 23.6023 19.8047i 1.15031 0.965221i 0.150579 0.988598i \(-0.451886\pi\)
0.999727 + 0.0233767i \(0.00744170\pi\)
\(422\) 5.51765 9.55686i 0.268595 0.465221i
\(423\) 0 0
\(424\) −5.53405 9.58526i −0.268757 0.465502i
\(425\) −2.42736 0.883488i −0.117744 0.0428555i
\(426\) 0 0
\(427\) 0.755857 + 0.634240i 0.0365785 + 0.0306930i
\(428\) −12.0507 + 4.38609i −0.582491 + 0.212010i
\(429\) 0 0
\(430\) 5.51365 + 31.2694i 0.265892 + 1.50795i
\(431\) 27.8971 1.34376 0.671879 0.740661i \(-0.265487\pi\)
0.671879 + 0.740661i \(0.265487\pi\)
\(432\) 0 0
\(433\) 19.1706 0.921278 0.460639 0.887588i \(-0.347620\pi\)
0.460639 + 0.887588i \(0.347620\pi\)
\(434\) 3.09963 + 17.5789i 0.148787 + 0.843812i
\(435\) 0 0
\(436\) 17.0377 6.20120i 0.815956 0.296984i
\(437\) 10.3064 + 8.64806i 0.493020 + 0.413693i
\(438\) 0 0
\(439\) 22.3167 + 8.12263i 1.06512 + 0.387672i 0.814350 0.580375i \(-0.197094\pi\)
0.250770 + 0.968047i \(0.419316\pi\)
\(440\) 0.432015 + 0.748272i 0.0205955 + 0.0356725i
\(441\) 0 0
\(442\) −1.88221 + 3.26009i −0.0895278 + 0.155067i
\(443\) 17.8935 15.0144i 0.850144 0.713356i −0.109677 0.993967i \(-0.534982\pi\)
0.959821 + 0.280612i \(0.0905373\pi\)
\(444\) 0 0
\(445\) 7.22146 40.9549i 0.342330 1.94145i
\(446\) −6.50332 + 36.8821i −0.307941 + 1.74642i
\(447\) 0 0
\(448\) −8.39379 + 7.04323i −0.396569 + 0.332761i
\(449\) −2.40953 + 4.17343i −0.113713 + 0.196956i −0.917264 0.398279i \(-0.869608\pi\)
0.803552 + 0.595235i \(0.202941\pi\)
\(450\) 0 0
\(451\) 0.926176 + 1.60418i 0.0436119 + 0.0755380i
\(452\) −24.1807 8.80105i −1.13736 0.413966i
\(453\) 0 0
\(454\) 25.5731 + 21.4584i 1.20021 + 1.00709i
\(455\) −3.71169 + 1.35095i −0.174007 + 0.0633333i
\(456\) 0 0
\(457\) −0.849765 4.81926i −0.0397503 0.225435i 0.958461 0.285225i \(-0.0920682\pi\)
−0.998211 + 0.0597894i \(0.980957\pi\)
\(458\) 3.73978 0.174749
\(459\) 0 0
\(460\) −14.3916 −0.671012
\(461\) 4.86049 + 27.5652i 0.226376 + 1.28384i 0.860038 + 0.510230i \(0.170440\pi\)
−0.633662 + 0.773610i \(0.718449\pi\)
\(462\) 0 0
\(463\) 25.8184 9.39712i 1.19988 0.436721i 0.336699 0.941612i \(-0.390690\pi\)
0.863183 + 0.504891i \(0.168467\pi\)
\(464\) 9.47968 + 7.95440i 0.440083 + 0.369274i
\(465\) 0 0
\(466\) −27.6436 10.0614i −1.28056 0.466087i
\(467\) 10.6232 + 18.4000i 0.491585 + 0.851450i 0.999953 0.00968963i \(-0.00308435\pi\)
−0.508368 + 0.861140i \(0.669751\pi\)
\(468\) 0 0
\(469\) −0.416426 + 0.721272i −0.0192288 + 0.0333052i
\(470\) −10.7720 + 9.03879i −0.496876 + 0.416928i
\(471\) 0 0
\(472\) 0.304248 1.72548i 0.0140042 0.0794215i
\(473\) −0.307669 + 1.74488i −0.0141466 + 0.0802296i
\(474\) 0 0
\(475\) 10.4792 8.79310i 0.480819 0.403455i
\(476\) −1.41636 + 2.45321i −0.0649188 + 0.112443i
\(477\) 0 0
\(478\) −20.9892 36.3543i −0.960022 1.66281i
\(479\) 39.1653 + 14.2550i 1.78951 + 0.651328i 0.999257 + 0.0385448i \(0.0122722\pi\)
0.790251 + 0.612783i \(0.209950\pi\)
\(480\) 0 0
\(481\) 5.18048 + 4.34694i 0.236210 + 0.198203i
\(482\) 38.5358 14.0259i 1.75526 0.638861i
\(483\) 0 0
\(484\) −4.69405 26.6213i −0.213366 1.21006i
\(485\) 14.8898 0.676112
\(486\) 0 0
\(487\) 4.02801 0.182527 0.0912634 0.995827i \(-0.470909\pi\)
0.0912634 + 0.995827i \(0.470909\pi\)
\(488\) −0.179064 1.01552i −0.00810585 0.0459706i
\(489\) 0 0
\(490\) 32.3109 11.7602i 1.45966 0.531272i
\(491\) −29.5857 24.8253i −1.33518 1.12035i −0.982836 0.184482i \(-0.940939\pi\)
−0.352347 0.935869i \(-0.614616\pi\)
\(492\) 0 0
\(493\) 4.86233 + 1.76974i 0.218988 + 0.0797052i
\(494\) −9.96769 17.2645i −0.448468 0.776769i
\(495\) 0 0
\(496\) −12.1830 + 21.1015i −0.547032 + 0.947487i
\(497\) −7.14741 + 5.99739i −0.320605 + 0.269020i
\(498\) 0 0
\(499\) −0.707071 + 4.01000i −0.0316528 + 0.179512i −0.996535 0.0831694i \(-0.973496\pi\)
0.964883 + 0.262682i \(0.0846069\pi\)
\(500\) 3.23657 18.3555i 0.144744 0.820884i
\(501\) 0 0
\(502\) 8.87849 7.44994i 0.396266 0.332507i
\(503\) 1.71297 2.96695i 0.0763775 0.132290i −0.825307 0.564684i \(-0.808998\pi\)
0.901684 + 0.432395i \(0.142331\pi\)
\(504\) 0 0
\(505\) −13.6020 23.5594i −0.605282 1.04838i
\(506\) −1.36320 0.496164i −0.0606016 0.0220572i
\(507\) 0 0
\(508\) 9.93139 + 8.33343i 0.440634 + 0.369736i
\(509\) 11.5238 4.19434i 0.510785 0.185911i −0.0737534 0.997277i \(-0.523498\pi\)
0.584539 + 0.811366i \(0.301276\pi\)
\(510\) 0 0
\(511\) −2.57349 14.5950i −0.113844 0.645644i
\(512\) −28.1241 −1.24292
\(513\) 0 0
\(514\) 24.4791 1.07973
\(515\) 4.59080 + 26.0357i 0.202295 + 1.14727i
\(516\) 0 0
\(517\) −0.737350 + 0.268373i −0.0324286 + 0.0118030i
\(518\) 7.04196 + 5.90891i 0.309406 + 0.259623i
\(519\) 0 0
\(520\) 3.87904 + 1.41186i 0.170107 + 0.0619140i
\(521\) −7.04117 12.1957i −0.308479 0.534302i 0.669551 0.742766i \(-0.266487\pi\)
−0.978030 + 0.208465i \(0.933153\pi\)
\(522\) 0 0
\(523\) −4.88956 + 8.46897i −0.213806 + 0.370322i −0.952902 0.303277i \(-0.901919\pi\)
0.739097 + 0.673599i \(0.235253\pi\)
\(524\) −13.7442 + 11.5327i −0.600416 + 0.503809i
\(525\) 0 0
\(526\) −2.38095 + 13.5030i −0.103814 + 0.588761i
\(527\) −1.76918 + 10.0335i −0.0770667 + 0.437067i
\(528\) 0 0
\(529\) −14.0359 + 11.7775i −0.610256 + 0.512065i
\(530\) 30.9283 53.5694i 1.34344 2.32691i
\(531\) 0 0
\(532\) −7.50065 12.9915i −0.325195 0.563254i
\(533\) 8.31608 + 3.02681i 0.360209 + 0.131105i
\(534\) 0 0
\(535\) −10.6279 8.91789i −0.459485 0.385554i
\(536\) 0.817912 0.297696i 0.0353284 0.0128585i
\(537\) 0 0
\(538\) 5.08637 + 28.8462i 0.219289 + 1.24365i
\(539\) 1.91871 0.0826445
\(540\) 0 0
\(541\) 40.9454 1.76038 0.880189 0.474623i \(-0.157416\pi\)
0.880189 + 0.474623i \(0.157416\pi\)
\(542\) −0.715012 4.05503i −0.0307124 0.174179i
\(543\) 0 0
\(544\) −8.80715 + 3.20554i −0.377604 + 0.137436i
\(545\) 15.0261 + 12.6084i 0.643648 + 0.540085i
\(546\) 0 0
\(547\) −1.04332 0.379737i −0.0446091 0.0162364i 0.319619 0.947546i \(-0.396445\pi\)
−0.364228 + 0.931310i \(0.618667\pi\)
\(548\) −13.9497 24.1615i −0.595900 1.03213i
\(549\) 0 0
\(550\) −0.737508 + 1.27740i −0.0314474 + 0.0544686i
\(551\) −20.9912 + 17.6137i −0.894256 + 0.750370i
\(552\) 0 0
\(553\) −1.89338 + 10.7379i −0.0805145 + 0.456620i
\(554\) −4.58431 + 25.9989i −0.194769 + 1.10459i
\(555\) 0 0
\(556\) 17.8210 14.9536i 0.755779 0.634174i
\(557\) −17.5201 + 30.3458i −0.742352 + 1.28579i 0.209070 + 0.977901i \(0.432956\pi\)
−0.951422 + 0.307890i \(0.900377\pi\)
\(558\) 0 0
\(559\) 4.23247 + 7.33084i 0.179014 + 0.310062i
\(560\) −6.88716 2.50672i −0.291035 0.105928i
\(561\) 0 0
\(562\) −15.8184 13.2732i −0.667260 0.559898i
\(563\) 36.4330 13.2605i 1.53547 0.558865i 0.570515 0.821287i \(-0.306744\pi\)
0.964953 + 0.262423i \(0.0845215\pi\)
\(564\) 0 0
\(565\) −4.83417 27.4159i −0.203375 1.15340i
\(566\) −56.2413 −2.36400
\(567\) 0 0
\(568\) 9.75095 0.409141
\(569\) −5.89854 33.4523i −0.247280 1.40239i −0.815138 0.579266i \(-0.803339\pi\)
0.567859 0.823126i \(-0.307772\pi\)
\(570\) 0 0
\(571\) −9.48043 + 3.45060i −0.396744 + 0.144403i −0.532684 0.846314i \(-0.678817\pi\)
0.135940 + 0.990717i \(0.456594\pi\)
\(572\) 0.911552 + 0.764883i 0.0381139 + 0.0319814i
\(573\) 0 0
\(574\) 11.3043 + 4.11442i 0.471831 + 0.171732i
\(575\) −2.37795 4.11873i −0.0991674 0.171763i
\(576\) 0 0
\(577\) 6.06615 10.5069i 0.252537 0.437407i −0.711687 0.702497i \(-0.752068\pi\)
0.964224 + 0.265090i \(0.0854017\pi\)
\(578\) 25.3269 21.2518i 1.05346 0.883957i
\(579\) 0 0
\(580\) 5.08993 28.8664i 0.211348 1.19861i
\(581\) 0.791021 4.48611i 0.0328171 0.186115i
\(582\) 0 0
\(583\) 2.64414 2.21870i 0.109509 0.0918892i
\(584\) −7.74416 + 13.4133i −0.320456 + 0.555046i
\(585\) 0 0
\(586\) 12.9722 + 22.4685i 0.535877 + 0.928167i
\(587\) −29.8345 10.8589i −1.23140 0.448193i −0.357324 0.933981i \(-0.616311\pi\)
−0.874077 + 0.485787i \(0.838533\pi\)
\(588\) 0 0
\(589\) −41.3315 34.6812i −1.70303 1.42902i
\(590\) 9.20145 3.34905i 0.378818 0.137878i
\(591\) 0 0
\(592\) 2.17899 + 12.3576i 0.0895558 + 0.507896i
\(593\) 13.4906 0.553993 0.276996 0.960871i \(-0.410661\pi\)
0.276996 + 0.960871i \(0.410661\pi\)
\(594\) 0 0
\(595\) −3.06459 −0.125636
\(596\) 8.20467 + 46.5310i 0.336077 + 1.90598i
\(597\) 0 0
\(598\) −6.51281 + 2.37047i −0.266329 + 0.0969357i
\(599\) −32.5036 27.2737i −1.32806 1.11437i −0.984527 0.175233i \(-0.943932\pi\)
−0.343532 0.939141i \(-0.611623\pi\)
\(600\) 0 0
\(601\) 18.6104 + 6.77362i 0.759133 + 0.276302i 0.692444 0.721472i \(-0.256534\pi\)
0.0666892 + 0.997774i \(0.478756\pi\)
\(602\) 5.75330 + 9.96501i 0.234487 + 0.406144i
\(603\) 0 0
\(604\) −4.97755 + 8.62136i −0.202533 + 0.350798i
\(605\) 22.4027 18.7981i 0.910798 0.764251i
\(606\) 0 0
\(607\) −6.25117 + 35.4521i −0.253727 + 1.43896i 0.545592 + 0.838051i \(0.316305\pi\)
−0.799319 + 0.600906i \(0.794806\pi\)
\(608\) 8.61877 48.8795i 0.349537 1.98232i
\(609\) 0 0
\(610\) 4.41474 3.70441i 0.178748 0.149987i
\(611\) −1.87442 + 3.24659i −0.0758310 + 0.131343i
\(612\) 0 0
\(613\) −13.2314 22.9175i −0.534411 0.925627i −0.999192 0.0402013i \(-0.987200\pi\)
0.464780 0.885426i \(-0.346133\pi\)
\(614\) −52.6561 19.1652i −2.12503 0.773446i
\(615\) 0 0
\(616\) 0.239862 + 0.201268i 0.00966431 + 0.00810932i
\(617\) −46.1546 + 16.7989i −1.85812 + 0.676299i −0.877747 + 0.479124i \(0.840955\pi\)
−0.980368 + 0.197175i \(0.936823\pi\)
\(618\) 0 0
\(619\) −4.20336 23.8385i −0.168947 0.958149i −0.944900 0.327358i \(-0.893842\pi\)
0.775953 0.630791i \(-0.217269\pi\)
\(620\) 57.7145 2.31787
\(621\) 0 0
\(622\) 37.3785 1.49874
\(623\) −2.61700 14.8417i −0.104848 0.594621i
\(624\) 0 0
\(625\) 29.2803 10.6571i 1.17121 0.426286i
\(626\) −15.6422 13.1254i −0.625190 0.524597i
\(627\) 0 0
\(628\) −16.9567 6.17173i −0.676646 0.246279i
\(629\) 2.62345 + 4.54395i 0.104604 + 0.181179i
\(630\) 0 0
\(631\) −8.84842 + 15.3259i −0.352250 + 0.610115i −0.986643 0.162895i \(-0.947917\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(632\) 8.72917 7.32464i 0.347228 0.291359i
\(633\) 0 0
\(634\) 1.36378 7.73439i 0.0541627 0.307172i
\(635\) −2.43554 + 13.8126i −0.0966514 + 0.548137i
\(636\) 0 0
\(637\) 7.02218 5.89231i 0.278229 0.233462i
\(638\) 1.47732 2.55880i 0.0584878 0.101304i
\(639\) 0 0
\(640\) 10.5917 + 18.3454i 0.418676 + 0.725167i
\(641\) −35.7557 13.0140i −1.41226 0.514022i −0.480471 0.877011i \(-0.659534\pi\)
−0.931794 + 0.362988i \(0.881757\pi\)
\(642\) 0 0
\(643\) 35.9600 + 30.1741i 1.41813 + 1.18995i 0.952335 + 0.305053i \(0.0986743\pi\)
0.465790 + 0.884895i \(0.345770\pi\)
\(644\) −4.90087 + 1.78377i −0.193121 + 0.0702904i
\(645\) 0 0
\(646\) −2.68585 15.2322i −0.105673 0.599303i
\(647\) −28.2333 −1.10997 −0.554983 0.831862i \(-0.687275\pi\)
−0.554983 + 0.831862i \(0.687275\pi\)
\(648\) 0 0
\(649\) 0.546406 0.0214483
\(650\) 1.22370 + 6.93997i 0.0479976 + 0.272208i
\(651\) 0 0
\(652\) −29.0131 + 10.5599i −1.13624 + 0.413557i
\(653\) 27.0469 + 22.6950i 1.05843 + 0.888125i 0.993954 0.109794i \(-0.0350192\pi\)
0.0644721 + 0.997920i \(0.479464\pi\)
\(654\) 0 0
\(655\) −18.2398 6.63873i −0.712686 0.259397i
\(656\) 8.21052 + 14.2210i 0.320567 + 0.555239i
\(657\) 0 0
\(658\) −2.54795 + 4.41318i −0.0993295 + 0.172044i
\(659\) 31.9392 26.8002i 1.24418 1.04399i 0.246990 0.969018i \(-0.420558\pi\)
0.997186 0.0749700i \(-0.0238861\pi\)
\(660\) 0 0
\(661\) 0.221213 1.25456i 0.00860418 0.0487967i −0.980203 0.197993i \(-0.936558\pi\)
0.988808 + 0.149197i \(0.0476687\pi\)
\(662\) 0.519270 2.94493i 0.0201820 0.114458i
\(663\) 0 0
\(664\) −3.64691 + 3.06012i −0.141527 + 0.118756i
\(665\) 8.11461 14.0549i 0.314671 0.545027i
\(666\) 0 0
\(667\) 4.76334 + 8.25035i 0.184437 + 0.319455i
\(668\) 5.43452 + 1.97800i 0.210268 + 0.0765312i
\(669\) 0 0
\(670\) 3.72638 + 3.12680i 0.143963 + 0.120799i
\(671\) 0.302191 0.109989i 0.0116660 0.00424606i
\(672\) 0 0
\(673\) 6.18756 + 35.0914i 0.238513 + 1.35267i 0.835088 + 0.550117i \(0.185417\pi\)
−0.596575 + 0.802558i \(0.703472\pi\)
\(674\) 27.4951 1.05907
\(675\) 0 0
\(676\) −26.5561 −1.02139
\(677\) 3.12600 + 17.7284i 0.120142 + 0.681358i 0.984075 + 0.177752i \(0.0568825\pi\)
−0.863934 + 0.503606i \(0.832006\pi\)
\(678\) 0 0
\(679\) 5.07053 1.84552i 0.194589 0.0708246i
\(680\) 2.45346 + 2.05870i 0.0940859 + 0.0789474i
\(681\) 0 0
\(682\) 5.46682 + 1.98976i 0.209336 + 0.0761919i
\(683\) −19.8807 34.4344i −0.760715 1.31760i −0.942483 0.334255i \(-0.891515\pi\)
0.181768 0.983341i \(-0.441818\pi\)
\(684\) 0 0
\(685\) 15.0915 26.1393i 0.576617 0.998730i
\(686\) 20.5814 17.2698i 0.785801 0.659366i
\(687\) 0 0
\(688\) −2.72748 + 15.4683i −0.103984 + 0.589724i
\(689\) 2.86359 16.2402i 0.109094 0.618703i
\(690\) 0 0
\(691\) −12.9007 + 10.8250i −0.490767 + 0.411802i −0.854301 0.519779i \(-0.826014\pi\)
0.363534 + 0.931581i \(0.381570\pi\)
\(692\) 4.44218 7.69408i 0.168866 0.292485i
\(693\) 0 0
\(694\) −5.08038 8.79948i −0.192849 0.334024i
\(695\) 23.6501 + 8.60793i 0.897099 + 0.326517i
\(696\) 0 0
\(697\) 5.25985 + 4.41354i 0.199231 + 0.167175i
\(698\) −44.9062 + 16.3445i −1.69973 + 0.618649i
\(699\) 0 0
\(700\) 0.920833 + 5.22230i 0.0348042 + 0.197385i
\(701\) −8.96921 −0.338762 −0.169381 0.985551i \(-0.554177\pi\)
−0.169381 + 0.985551i \(0.554177\pi\)
\(702\) 0 0
\(703\) −27.7861 −1.04797
\(704\) 0.620133 + 3.51695i 0.0233721 + 0.132550i
\(705\) 0 0
\(706\) −59.0856 + 21.5054i −2.22372 + 0.809366i
\(707\) −7.55207 6.33694i −0.284025 0.238325i
\(708\) 0 0
\(709\) −17.0476 6.20480i −0.640235 0.233026i 0.00144523 0.999999i \(-0.499540\pi\)
−0.641680 + 0.766973i \(0.721762\pi\)
\(710\) 27.2477 + 47.1944i 1.02259 + 1.77117i
\(711\) 0 0
\(712\) −7.87509 + 13.6401i −0.295131 + 0.511183i
\(713\) −14.3694 + 12.0574i −0.538139 + 0.451552i
\(714\) 0 0
\(715\) −0.223546 + 1.26779i −0.00836014 + 0.0474127i
\(716\) −8.61142 + 48.8378i −0.321824 + 1.82515i
\(717\) 0 0
\(718\) −21.7593 + 18.2582i −0.812049 + 0.681390i
\(719\) −15.7860 + 27.3421i −0.588718 + 1.01969i 0.405683 + 0.914014i \(0.367034\pi\)
−0.994401 + 0.105675i \(0.966300\pi\)
\(720\) 0 0
\(721\) 4.79034 + 8.29711i 0.178402 + 0.309001i
\(722\) 39.1796 + 14.2602i 1.45811 + 0.530710i
\(723\) 0 0
\(724\) 18.4901 + 15.5150i 0.687177 + 0.576610i
\(725\) 9.10230 3.31296i 0.338051 0.123040i
\(726\) 0 0
\(727\) 6.66970 + 37.8257i 0.247365 + 1.40288i 0.814934 + 0.579553i \(0.196773\pi\)
−0.567569 + 0.823326i \(0.692116\pi\)
\(728\) 1.49595 0.0554436
\(729\) 0 0
\(730\) −86.5599 −3.20373
\(731\) 1.14046 + 6.46787i 0.0421814 + 0.239223i
\(732\) 0 0
\(733\) 28.5012 10.3736i 1.05271 0.383157i 0.243028 0.970019i \(-0.421859\pi\)
0.809686 + 0.586863i \(0.199637\pi\)
\(734\) 12.8903 + 10.8163i 0.475790 + 0.399235i
\(735\) 0 0
\(736\) −16.2151 5.90181i −0.597696 0.217543i
\(737\) 0.135721 + 0.235076i 0.00499936 + 0.00865915i
\(738\) 0 0
\(739\) −5.00127 + 8.66245i −0.183975 + 0.318653i −0.943230 0.332139i \(-0.892230\pi\)
0.759256 + 0.650792i \(0.225563\pi\)
\(740\) 22.7688 19.1053i 0.836997 0.702324i
\(741\) 0 0
\(742\) 3.89255 22.0758i 0.142900 0.810427i
\(743\) 6.29888 35.7227i 0.231083 1.31054i −0.619624 0.784899i \(-0.712715\pi\)
0.850707 0.525640i \(-0.176174\pi\)
\(744\) 0 0
\(745\) −39.1574 + 32.8570i −1.43462 + 1.20379i
\(746\) −12.0865 + 20.9344i −0.442517 + 0.766461i
\(747\) 0 0
\(748\) 0.461619 + 0.799548i 0.0168785 + 0.0292344i
\(749\) −4.72453 1.71959i −0.172631 0.0628324i
\(750\) 0 0
\(751\) −11.1493 9.35536i −0.406843 0.341382i 0.416288 0.909233i \(-0.363331\pi\)
−0.823132 + 0.567851i \(0.807775\pi\)
\(752\) −6.53659 + 2.37912i −0.238365 + 0.0867577i
\(753\) 0 0
\(754\) −2.45124 13.9017i −0.0892688 0.506268i
\(755\) −10.7700 −0.391959
\(756\) 0 0
\(757\) −45.5754 −1.65646 −0.828232 0.560385i \(-0.810653\pi\)
−0.828232 + 0.560385i \(0.810653\pi\)
\(758\) 8.88380 + 50.3826i 0.322674 + 1.82998i
\(759\) 0 0
\(760\) −15.9381 + 5.80099i −0.578135 + 0.210424i
\(761\) 17.0411 + 14.2992i 0.617739 + 0.518344i 0.897092 0.441844i \(-0.145676\pi\)
−0.279353 + 0.960188i \(0.590120\pi\)
\(762\) 0 0
\(763\) 6.67970 + 2.43121i 0.241821 + 0.0880158i
\(764\) 22.0189 + 38.1379i 0.796616 + 1.37978i
\(765\) 0 0
\(766\) 9.99393 17.3100i 0.361096 0.625436i
\(767\) 1.99976 1.67800i 0.0722073 0.0605891i
\(768\) 0 0
\(769\) 2.37289 13.4573i 0.0855686 0.485284i −0.911664 0.410937i \(-0.865202\pi\)
0.997232 0.0743470i \(-0.0236872\pi\)
\(770\) −0.303872 + 1.72334i −0.0109508 + 0.0621049i
\(771\) 0 0
\(772\) 20.1088 16.8733i 0.723730 0.607282i
\(773\) 10.3270 17.8869i 0.371436 0.643345i −0.618351 0.785902i \(-0.712199\pi\)
0.989787 + 0.142557i \(0.0455323\pi\)
\(774\) 0 0
\(775\) 9.53628 + 16.5173i 0.342553 + 0.593319i
\(776\) −5.29915 1.92873i −0.190228 0.0692374i
\(777\) 0 0
\(778\) 4.13092 + 3.46625i 0.148101 + 0.124271i
\(779\) −34.1689 + 12.4364i −1.22423 + 0.445582i
\(780\) 0 0
\(781\) 0.528050 + 2.99472i 0.0188951 + 0.107160i
\(782\) −5.37736 −0.192294
\(783\) 0 0
\(784\) 17.0093 0.607474
\(785\) −3.38996 19.2254i −0.120993 0.686185i
\(786\) 0 0
\(787\) 23.2136 8.44905i 0.827475 0.301176i 0.106653 0.994296i \(-0.465987\pi\)
0.720822 + 0.693120i \(0.243764\pi\)
\(788\) 26.8999 + 22.5717i 0.958270 + 0.804084i
\(789\) 0 0
\(790\) 59.8435 + 21.7813i 2.12914 + 0.774943i
\(791\) −5.04429 8.73696i −0.179354 0.310651i
\(792\) 0 0
\(793\) 0.768202 1.33057i 0.0272797 0.0472498i
\(794\) −5.95902 + 5.00022i −0.211478 + 0.177451i
\(795\) 0 0
\(796\) 3.24728 18.4163i 0.115097 0.652747i
\(797\) −5.30769 + 30.1014i −0.188008 + 1.06625i 0.734021 + 0.679127i \(0.237641\pi\)
−0.922029 + 0.387120i \(0.873470\pi\)
\(798\) 0 0
\(799\) −2.22812 + 1.86961i −0.0788251 + 0.0661421i
\(800\) −8.77257 + 15.1945i −0.310157 + 0.537208i
\(801\) 0 0
\(802\) 17.0904 + 29.6014i 0.603482 + 1.04526i
\(803\) −4.53887 1.65201i −0.160173 0.0582983i
\(804\) 0 0
\(805\) −4.32225 3.62680i −0.152339 0.127828i
\(806\) 26.1183 9.50628i 0.919977 0.334844i
\(807\) 0 0
\(808\) 1.78910 + 10.1465i 0.0629403 + 0.356952i
\(809\) 46.8599 1.64751 0.823753 0.566949i \(-0.191876\pi\)
0.823753 + 0.566949i \(0.191876\pi\)
\(810\) 0 0
\(811\) 10.9984 0.386206 0.193103 0.981178i \(-0.438145\pi\)
0.193103 + 0.981178i \(0.438145\pi\)
\(812\) −1.84455 10.4610i −0.0647309 0.367107i
\(813\) 0 0
\(814\) 2.81537 1.02471i 0.0986788 0.0359161i
\(815\) −25.5877 21.4706i −0.896297 0.752082i
\(816\) 0 0
\(817\) −32.6829 11.8956i −1.14343 0.416175i
\(818\) 9.71738 + 16.8310i 0.339760 + 0.588482i
\(819\) 0 0
\(820\) 19.4479 33.6847i 0.679150 1.17632i
\(821\) −27.5648 + 23.1296i −0.962019 + 0.807230i −0.981280 0.192585i \(-0.938313\pi\)
0.0192613 + 0.999814i \(0.493869\pi\)
\(822\) 0 0
\(823\) −8.50644 + 48.2424i −0.296516 + 1.68163i 0.364461 + 0.931219i \(0.381253\pi\)
−0.660977 + 0.750406i \(0.729858\pi\)
\(824\) 1.73868 9.86053i 0.0605697 0.343508i
\(825\) 0 0
\(826\) 2.71833 2.28095i 0.0945829 0.0793645i
\(827\) 7.80533 13.5192i 0.271418 0.470109i −0.697807 0.716286i \(-0.745841\pi\)
0.969225 + 0.246176i \(0.0791742\pi\)
\(828\) 0 0
\(829\) −5.73541 9.93401i −0.199199 0.345023i 0.749070 0.662491i \(-0.230501\pi\)
−0.948269 + 0.317468i \(0.897167\pi\)
\(830\) −25.0017 9.09986i −0.867820 0.315861i
\(831\) 0 0
\(832\) 13.0701 + 10.9671i 0.453123 + 0.380215i
\(833\) 6.68329 2.43252i 0.231562 0.0842817i
\(834\) 0 0
\(835\) 1.08646 + 6.16163i 0.0375986 + 0.213232i
\(836\) −4.88922 −0.169097
\(837\) 0 0
\(838\) 14.7716 0.510278
\(839\) −0.117269 0.665065i −0.00404857 0.0229606i 0.982717 0.185117i \(-0.0592663\pi\)
−0.986765 + 0.162156i \(0.948155\pi\)
\(840\) 0 0
\(841\) 9.01801 3.28229i 0.310966 0.113182i
\(842\) −49.9572 41.9190i −1.72164 1.44463i
\(843\) 0 0
\(844\) −12.1505 4.42242i −0.418238 0.152226i
\(845\) −14.3649 24.8808i −0.494168 0.855925i
\(846\) 0 0
\(847\) 5.29901 9.17815i 0.182076 0.315365i
\(848\) 23.4403 19.6687i 0.804942 0.675427i
\(849\) 0 0
\(850\) −0.949430 + 5.38448i −0.0325652 + 0.184686i
\(851\) −1.67748 + 9.51344i −0.0575032 + 0.326117i
\(852\) 0 0
\(853\) 30.1483 25.2974i 1.03226 0.866166i 0.0411388 0.999153i \(-0.486901\pi\)
0.991118 + 0.132987i \(0.0424570\pi\)
\(854\) 1.04424 1.80867i 0.0357331 0.0618915i
\(855\) 0 0
\(856\) 2.62721 + 4.55047i 0.0897963 + 0.155532i
\(857\) −30.6923 11.1711i −1.04843 0.381598i −0.240360 0.970684i \(-0.577266\pi\)
−0.808070 + 0.589086i \(0.799488\pi\)
\(858\) 0 0
\(859\) −25.4301 21.3384i −0.867664 0.728056i 0.0959411 0.995387i \(-0.469414\pi\)
−0.963605 + 0.267331i \(0.913858\pi\)
\(860\) 34.9606 12.7246i 1.19215 0.433906i
\(861\) 0 0
\(862\) −10.2535 58.1507i −0.349237 1.98062i
\(863\) 22.6796 0.772024 0.386012 0.922494i \(-0.373852\pi\)
0.386012 + 0.922494i \(0.373852\pi\)
\(864\) 0 0
\(865\) 9.61158 0.326804
\(866\) −7.04609 39.9604i −0.239436 1.35791i
\(867\) 0 0
\(868\) 19.6539 7.15344i 0.667097 0.242804i
\(869\) 2.72227 + 2.28425i 0.0923466 + 0.0774880i
\(870\) 0 0
\(871\) 1.21863 + 0.443547i 0.0412919 + 0.0150290i
\(872\) −3.71444 6.43360i −0.125787 0.217869i
\(873\) 0 0
\(874\) 14.2385 24.6618i 0.481625 0.834199i
\(875\) 5.59779 4.69710i 0.189240 0.158791i
\(876\) 0 0
\(877\) 1.60516 9.10333i 0.0542025 0.307398i −0.945639 0.325219i \(-0.894562\pi\)
0.999841 + 0.0178215i \(0.00567306\pi\)
\(878\) 8.72888 49.5040i 0.294586 1.67068i
\(879\) 0 0
\(880\) −1.82986 + 1.53544i −0.0616846 + 0.0517595i
\(881\) −3.89378 + 6.74422i −0.131185 + 0.227219i −0.924134 0.382070i \(-0.875211\pi\)
0.792949 + 0.609288i \(0.208545\pi\)
\(882\) 0 0
\(883\) 16.2309 + 28.1127i 0.546213 + 0.946068i 0.998530 + 0.0542106i \(0.0172642\pi\)
−0.452317 + 0.891857i \(0.649402\pi\)
\(884\) 4.14485 + 1.50860i 0.139407 + 0.0507398i
\(885\) 0 0
\(886\) −37.8737 31.7798i −1.27239 1.06766i
\(887\) 31.8064 11.5766i 1.06795 0.388704i 0.252543 0.967586i \(-0.418733\pi\)
0.815411 + 0.578882i \(0.196511\pi\)
\(888\) 0 0
\(889\) 0.882619 + 5.00558i 0.0296021 + 0.167882i
\(890\) −88.0234 −2.95055
\(891\) 0 0
\(892\) 43.8822 1.46929
\(893\) −2.67473 15.1691i −0.0895063 0.507616i
\(894\) 0 0
\(895\) −50.4149 + 18.3495i −1.68518 + 0.613357i
\(896\) 5.88071 + 4.93450i 0.196461 + 0.164850i
\(897\) 0 0
\(898\) 9.58500 + 3.48865i 0.319855 + 0.116418i
\(899\) −19.1024 33.0863i −0.637101 1.10349i
\(900\) 0 0
\(901\) 6.39731 11.0805i 0.213125 0.369144i
\(902\) 3.00345 2.52020i 0.100004 0.0839133i
\(903\) 0 0
\(904\) −1.83085 + 10.3833i −0.0608931 + 0.345342i
\(905\) −4.53444 + 25.7161i −0.150730 + 0.854831i
\(906\) 0 0
\(907\) −8.47233 + 7.10913i −0.281319 + 0.236055i −0.772518 0.634992i \(-0.781003\pi\)
0.491199 + 0.871047i \(0.336559\pi\)
\(908\) 19.5580 33.8754i 0.649054 1.12420i
\(909\) 0 0
\(910\) 4.18022 + 7.24036i 0.138573 + 0.240016i
\(911\) −11.7886 4.29070i −0.390574 0.142157i 0.139266 0.990255i \(-0.455526\pi\)
−0.529840 + 0.848098i \(0.677748\pi\)
\(912\) 0 0
\(913\) −1.13732 0.954324i −0.0376398 0.0315835i
\(914\) −9.73325 + 3.54261i −0.321947 + 0.117179i
\(915\) 0 0
\(916\) −0.760923 4.31541i −0.0251416 0.142585i
\(917\) −7.03415 −0.232288
\(918\) 0 0
\(919\) −5.92909 −0.195583 −0.0977913 0.995207i \(-0.531178\pi\)
−0.0977913 + 0.995207i \(0.531178\pi\)
\(920\) 1.02395 + 5.80711i 0.0337586 + 0.191455i
\(921\) 0 0
\(922\) 55.6723 20.2631i 1.83347 0.667328i
\(923\) 11.1293 + 9.33860i 0.366326 + 0.307384i
\(924\) 0 0
\(925\) 9.22987 + 3.35940i 0.303476 + 0.110456i
\(926\) −29.0775 50.3636i −0.955545 1.65505i
\(927\) 0 0
\(928\) 17.5726 30.4366i 0.576848 0.999131i
\(929\) −7.68555 + 6.44894i −0.252155 + 0.211583i −0.760100 0.649807i \(-0.774850\pi\)
0.507945 + 0.861390i \(0.330405\pi\)
\(930\) 0 0
\(931\) −6.54033 + 37.0921i −0.214351 + 1.21564i
\(932\) −5.98553 + 33.9456i −0.196063 + 1.11193i
\(933\) 0 0
\(934\) 34.4496 28.9067i 1.12723 0.945855i
\(935\) −0.499405 + 0.864995i −0.0163323 + 0.0282883i
\(936\) 0 0
\(937\) 11.7671 + 20.3811i 0.384413 + 0.665823i 0.991688 0.128669i \(-0.0410705\pi\)
−0.607274 + 0.794492i \(0.707737\pi\)
\(938\) 1.65652 + 0.602925i 0.0540874 + 0.0196862i
\(939\) 0 0
\(940\) 12.6218 + 10.5909i 0.411677 + 0.345438i
\(941\) 27.5326 10.0210i 0.897536 0.326676i 0.148271 0.988947i \(-0.452629\pi\)
0.749265 + 0.662270i \(0.230407\pi\)
\(942\) 0 0
\(943\) 2.19520 + 12.4496i 0.0714854 + 0.405414i
\(944\) 4.84388 0.157655
\(945\) 0 0
\(946\) 3.75023 0.121930
\(947\) 9.31829 + 52.8467i 0.302804 + 1.71729i 0.633666 + 0.773607i \(0.281549\pi\)
−0.330862 + 0.943679i \(0.607340\pi\)
\(948\) 0 0
\(949\) −21.6849 + 7.89266i −0.703922 + 0.256207i
\(950\) −22.1805 18.6117i −0.719631 0.603842i
\(951\) 0 0
\(952\) 1.09066 + 0.396968i 0.0353485 + 0.0128658i
\(953\) 2.44828 + 4.24055i 0.0793076 + 0.137365i 0.902951 0.429743i \(-0.141396\pi\)
−0.823644 + 0.567108i \(0.808062\pi\)
\(954\) 0 0
\(955\) −23.8212 + 41.2596i −0.770837 + 1.33513i
\(956\) −37.6793 + 31.6167i −1.21864 + 1.02256i
\(957\) 0 0
\(958\) 15.3190 86.8781i 0.494933 2.80691i
\(959\) 1.89938 10.7719i 0.0613341 0.347843i
\(960\) 0 0
\(961\) 33.8782 28.4272i 1.09285 0.917007i
\(962\) 7.15698 12.3962i 0.230750 0.399671i
\(963\) 0 0
\(964\) −24.0255 41.6134i −0.773810 1.34028i
\(965\) 26.6862 + 9.71297i 0.859058 + 0.312671i
\(966\) 0 0
\(967\) 13.0175 + 10.9230i 0.418615 + 0.351259i 0.827636 0.561266i \(-0.189685\pi\)
−0.409021 + 0.912525i \(0.634130\pi\)
\(968\) −10.4079 + 3.78816i −0.334522 + 0.121756i
\(969\) 0 0
\(970\) −5.47272 31.0373i −0.175718 0.996548i
\(971\) −2.68374 −0.0861253 −0.0430627 0.999072i \(-0.513712\pi\)
−0.0430627 + 0.999072i \(0.513712\pi\)
\(972\) 0 0
\(973\) 9.12064 0.292394
\(974\) −1.48049 8.39626i −0.0474379 0.269034i
\(975\) 0 0
\(976\) 2.67892 0.975047i 0.0857501 0.0312105i
\(977\) 8.42115 + 7.06619i 0.269417 + 0.226067i 0.767479 0.641074i \(-0.221511\pi\)
−0.498063 + 0.867141i \(0.665955\pi\)
\(978\) 0 0
\(979\) −4.61561 1.67994i −0.147515 0.0536912i
\(980\) −20.1445 34.8914i −0.643494 1.11456i
\(981\) 0 0
\(982\) −40.8734 + 70.7948i −1.30432 + 2.25915i
\(983\) −36.5983 + 30.7096i −1.16730 + 0.979484i −0.999979 0.00641835i \(-0.997957\pi\)
−0.167324 + 0.985902i \(0.553513\pi\)
\(984\) 0 0
\(985\) −6.59684 + 37.4125i −0.210193 + 1.19206i
\(986\) 1.90183 10.7858i 0.0605666 0.343490i
\(987\) 0 0
\(988\) −17.8938 + 15.0147i −0.569278 + 0.477681i
\(989\) −6.04594 + 10.4719i −0.192250 + 0.332986i
\(990\) 0 0
\(991\) −27.7503 48.0649i −0.881517 1.52683i −0.849654 0.527340i \(-0.823189\pi\)
−0.0318627 0.999492i \(-0.510144\pi\)
\(992\) 65.0272 + 23.6680i 2.06462 + 0.751459i
\(993\) 0 0
\(994\) 15.1284 + 12.6942i 0.479843 + 0.402636i
\(995\) 19.0110 6.91944i 0.602689 0.219361i
\(996\) 0 0
\(997\) −7.82228 44.3624i −0.247734 1.40497i −0.814056 0.580786i \(-0.802745\pi\)
0.566322 0.824184i \(-0.308366\pi\)
\(998\) 8.61859 0.272817
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 243.2.e.d.28.1 12
3.2 odd 2 243.2.e.a.28.2 12
9.2 odd 6 81.2.e.a.37.2 12
9.4 even 3 243.2.e.c.190.2 12
9.5 odd 6 243.2.e.b.190.1 12
9.7 even 3 27.2.e.a.22.1 yes 12
27.2 odd 18 243.2.e.a.217.2 12
27.4 even 9 729.2.c.e.487.5 12
27.5 odd 18 729.2.a.d.1.5 6
27.7 even 9 27.2.e.a.16.1 12
27.11 odd 18 243.2.e.b.55.1 12
27.13 even 9 729.2.c.e.244.5 12
27.14 odd 18 729.2.c.b.244.2 12
27.16 even 9 243.2.e.c.55.2 12
27.20 odd 18 81.2.e.a.46.2 12
27.22 even 9 729.2.a.a.1.2 6
27.23 odd 18 729.2.c.b.487.2 12
27.25 even 9 inner 243.2.e.d.217.1 12
36.7 odd 6 432.2.u.c.49.2 12
45.7 odd 12 675.2.u.b.49.1 24
45.34 even 6 675.2.l.c.76.2 12
45.43 odd 12 675.2.u.b.49.4 24
108.7 odd 18 432.2.u.c.97.2 12
135.7 odd 36 675.2.u.b.124.4 24
135.34 even 18 675.2.l.c.151.2 12
135.88 odd 36 675.2.u.b.124.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.1 12 27.7 even 9
27.2.e.a.22.1 yes 12 9.7 even 3
81.2.e.a.37.2 12 9.2 odd 6
81.2.e.a.46.2 12 27.20 odd 18
243.2.e.a.28.2 12 3.2 odd 2
243.2.e.a.217.2 12 27.2 odd 18
243.2.e.b.55.1 12 27.11 odd 18
243.2.e.b.190.1 12 9.5 odd 6
243.2.e.c.55.2 12 27.16 even 9
243.2.e.c.190.2 12 9.4 even 3
243.2.e.d.28.1 12 1.1 even 1 trivial
243.2.e.d.217.1 12 27.25 even 9 inner
432.2.u.c.49.2 12 36.7 odd 6
432.2.u.c.97.2 12 108.7 odd 18
675.2.l.c.76.2 12 45.34 even 6
675.2.l.c.151.2 12 135.34 even 18
675.2.u.b.49.1 24 45.7 odd 12
675.2.u.b.49.4 24 45.43 odd 12
675.2.u.b.124.1 24 135.88 odd 36
675.2.u.b.124.4 24 135.7 odd 36
729.2.a.a.1.2 6 27.22 even 9
729.2.a.d.1.5 6 27.5 odd 18
729.2.c.b.244.2 12 27.14 odd 18
729.2.c.b.487.2 12 27.23 odd 18
729.2.c.e.244.5 12 27.13 even 9
729.2.c.e.487.5 12 27.4 even 9