Properties

Label 684.2.ce.a.575.10
Level $684$
Weight $2$
Character 684.575
Analytic conductor $5.462$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(35,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.ce (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.46176749826\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(40\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 575.10
Character \(\chi\) \(=\) 684.575
Dual form 684.2.ce.a.251.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965713 + 1.03315i) q^{2} +(-0.134799 - 1.99545i) q^{4} +(-1.43514 + 1.71034i) q^{5} +(-4.02185 + 2.32202i) q^{7} +(2.19178 + 1.78777i) q^{8} +O(q^{10})\) \(q+(-0.965713 + 1.03315i) q^{2} +(-0.134799 - 1.99545i) q^{4} +(-1.43514 + 1.71034i) q^{5} +(-4.02185 + 2.32202i) q^{7} +(2.19178 + 1.78777i) q^{8} +(-0.381099 - 3.13441i) q^{10} +(0.536161 - 0.928658i) q^{11} +(-1.05836 - 6.00224i) q^{13} +(1.48496 - 6.39757i) q^{14} +(-3.96366 + 0.537968i) q^{16} +(1.77847 + 4.88630i) q^{17} +(0.0924188 - 4.35792i) q^{19} +(3.60635 + 2.63321i) q^{20} +(0.441666 + 1.45075i) q^{22} +(-1.58786 + 1.33238i) q^{23} +(0.00262386 + 0.0148807i) q^{25} +(7.22328 + 4.70300i) q^{26} +(5.17561 + 7.71240i) q^{28} +(2.09106 - 5.74513i) q^{29} +(7.31415 - 4.22283i) q^{31} +(3.27195 - 4.61458i) q^{32} +(-6.76576 - 2.88133i) q^{34} +(1.80050 - 10.2111i) q^{35} -0.855354 q^{37} +(4.41313 + 4.30398i) q^{38} +(-6.20320 + 1.18298i) q^{40} +(-3.14767 - 0.555019i) q^{41} +(0.281613 - 0.335613i) q^{43} +(-1.92537 - 0.944702i) q^{44} +(0.156876 - 2.92719i) q^{46} +(-7.05503 - 2.56782i) q^{47} +(7.28352 - 12.6154i) q^{49} +(-0.0179078 - 0.0116596i) q^{50} +(-11.8345 + 2.92099i) q^{52} +(-8.37829 - 9.98486i) q^{53} +(0.818851 + 2.24977i) q^{55} +(-12.9662 - 2.10078i) q^{56} +(3.91623 + 7.70853i) q^{58} +(11.3491 - 4.13074i) q^{59} +(0.109574 - 0.0919436i) q^{61} +(-2.70055 + 11.6347i) q^{62} +(1.60779 + 7.83677i) q^{64} +(11.7847 + 6.80392i) q^{65} +(-0.0969723 + 0.266429i) q^{67} +(9.51063 - 4.20751i) q^{68} +(8.81088 + 11.7212i) q^{70} +(-3.16455 - 2.65538i) q^{71} +(2.33242 - 13.2278i) q^{73} +(0.826026 - 0.883709i) q^{74} +(-8.70848 + 0.403024i) q^{76} +4.97990i q^{77} +(5.33062 + 0.939933i) q^{79} +(4.76831 - 7.55125i) q^{80} +(3.61316 - 2.71603i) q^{82} +(6.42814 + 11.1339i) q^{83} +(-10.9096 - 3.97076i) q^{85} +(0.0747817 + 0.615054i) q^{86} +(2.83537 - 1.07688i) q^{88} +(-13.2855 + 2.34260i) q^{89} +(18.1938 + 21.6826i) q^{91} +(2.87273 + 2.98890i) q^{92} +(9.46607 - 4.80913i) q^{94} +(7.32088 + 6.41231i) q^{95} +(-4.04180 + 1.47109i) q^{97} +(5.99984 + 19.7078i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965713 + 1.03315i −0.682862 + 0.730547i
\(3\) 0 0
\(4\) −0.134799 1.99545i −0.0673993 0.997726i
\(5\) −1.43514 + 1.71034i −0.641816 + 0.764886i −0.984656 0.174508i \(-0.944167\pi\)
0.342840 + 0.939394i \(0.388611\pi\)
\(6\) 0 0
\(7\) −4.02185 + 2.32202i −1.52012 + 0.877640i −0.520397 + 0.853924i \(0.674216\pi\)
−0.999719 + 0.0237154i \(0.992450\pi\)
\(8\) 2.19178 + 1.78777i 0.774911 + 0.632071i
\(9\) 0 0
\(10\) −0.381099 3.13441i −0.120514 0.991188i
\(11\) 0.536161 0.928658i 0.161659 0.280001i −0.773805 0.633424i \(-0.781649\pi\)
0.935464 + 0.353423i \(0.114982\pi\)
\(12\) 0 0
\(13\) −1.05836 6.00224i −0.293535 1.66472i −0.673097 0.739555i \(-0.735036\pi\)
0.379561 0.925167i \(-0.376075\pi\)
\(14\) 1.48496 6.39757i 0.396872 1.70982i
\(15\) 0 0
\(16\) −3.96366 + 0.537968i −0.990915 + 0.134492i
\(17\) 1.77847 + 4.88630i 0.431341 + 1.18510i 0.944990 + 0.327100i \(0.106071\pi\)
−0.513648 + 0.858001i \(0.671706\pi\)
\(18\) 0 0
\(19\) 0.0924188 4.35792i 0.0212023 0.999775i
\(20\) 3.60635 + 2.63321i 0.806405 + 0.588803i
\(21\) 0 0
\(22\) 0.441666 + 1.45075i 0.0941635 + 0.309301i
\(23\) −1.58786 + 1.33238i −0.331092 + 0.277819i −0.793145 0.609033i \(-0.791558\pi\)
0.462052 + 0.886853i \(0.347113\pi\)
\(24\) 0 0
\(25\) 0.00262386 + 0.0148807i 0.000524772 + 0.00297613i
\(26\) 7.22328 + 4.70300i 1.41660 + 0.922333i
\(27\) 0 0
\(28\) 5.17561 + 7.71240i 0.978099 + 1.45751i
\(29\) 2.09106 5.74513i 0.388300 1.06684i −0.579467 0.814996i \(-0.696739\pi\)
0.967767 0.251849i \(-0.0810386\pi\)
\(30\) 0 0
\(31\) 7.31415 4.22283i 1.31366 0.758442i 0.330960 0.943645i \(-0.392627\pi\)
0.982700 + 0.185202i \(0.0592941\pi\)
\(32\) 3.27195 4.61458i 0.578405 0.815750i
\(33\) 0 0
\(34\) −6.76576 2.88133i −1.16032 0.494145i
\(35\) 1.80050 10.2111i 0.304340 1.72600i
\(36\) 0 0
\(37\) −0.855354 −0.140619 −0.0703097 0.997525i \(-0.522399\pi\)
−0.0703097 + 0.997525i \(0.522399\pi\)
\(38\) 4.41313 + 4.30398i 0.715905 + 0.698198i
\(39\) 0 0
\(40\) −6.20320 + 1.18298i −0.980812 + 0.187046i
\(41\) −3.14767 0.555019i −0.491583 0.0866794i −0.0776389 0.996982i \(-0.524738\pi\)
−0.413944 + 0.910302i \(0.635849\pi\)
\(42\) 0 0
\(43\) 0.281613 0.335613i 0.0429455 0.0511805i −0.744144 0.668019i \(-0.767142\pi\)
0.787090 + 0.616839i \(0.211587\pi\)
\(44\) −1.92537 0.944702i −0.290260 0.142419i
\(45\) 0 0
\(46\) 0.156876 2.92719i 0.0231300 0.431591i
\(47\) −7.05503 2.56782i −1.02908 0.374555i −0.228351 0.973579i \(-0.573333\pi\)
−0.800731 + 0.599024i \(0.795555\pi\)
\(48\) 0 0
\(49\) 7.28352 12.6154i 1.04050 1.80220i
\(50\) −0.0179078 0.0116596i −0.00253255 0.00164891i
\(51\) 0 0
\(52\) −11.8345 + 2.92099i −1.64115 + 0.405069i
\(53\) −8.37829 9.98486i −1.15085 1.37153i −0.916823 0.399295i \(-0.869255\pi\)
−0.234024 0.972231i \(-0.575189\pi\)
\(54\) 0 0
\(55\) 0.818851 + 2.24977i 0.110414 + 0.303359i
\(56\) −12.9662 2.10078i −1.73268 0.280729i
\(57\) 0 0
\(58\) 3.91623 + 7.70853i 0.514226 + 1.01218i
\(59\) 11.3491 4.13074i 1.47753 0.537777i 0.527396 0.849620i \(-0.323168\pi\)
0.950134 + 0.311843i \(0.100946\pi\)
\(60\) 0 0
\(61\) 0.109574 0.0919436i 0.0140295 0.0117722i −0.635746 0.771898i \(-0.719307\pi\)
0.649775 + 0.760126i \(0.274863\pi\)
\(62\) −2.70055 + 11.6347i −0.342971 + 1.47760i
\(63\) 0 0
\(64\) 1.60779 + 7.83677i 0.200973 + 0.979597i
\(65\) 11.7847 + 6.80392i 1.46172 + 0.843923i
\(66\) 0 0
\(67\) −0.0969723 + 0.266429i −0.0118471 + 0.0325495i −0.945475 0.325694i \(-0.894402\pi\)
0.933628 + 0.358244i \(0.116624\pi\)
\(68\) 9.51063 4.20751i 1.15333 0.510235i
\(69\) 0 0
\(70\) 8.81088 + 11.7212i 1.05310 + 1.40095i
\(71\) −3.16455 2.65538i −0.375563 0.315135i 0.435394 0.900240i \(-0.356609\pi\)
−0.810958 + 0.585105i \(0.801053\pi\)
\(72\) 0 0
\(73\) 2.33242 13.2278i 0.272989 1.54820i −0.472289 0.881444i \(-0.656572\pi\)
0.745278 0.666754i \(-0.232317\pi\)
\(74\) 0.826026 0.883709i 0.0960236 0.102729i
\(75\) 0 0
\(76\) −8.70848 + 0.403024i −0.998931 + 0.0462300i
\(77\) 4.97990i 0.567512i
\(78\) 0 0
\(79\) 5.33062 + 0.939933i 0.599742 + 0.105751i 0.465273 0.885167i \(-0.345956\pi\)
0.134469 + 0.990918i \(0.457067\pi\)
\(80\) 4.76831 7.55125i 0.533113 0.844256i
\(81\) 0 0
\(82\) 3.61316 2.71603i 0.399007 0.299935i
\(83\) 6.42814 + 11.1339i 0.705580 + 1.22210i 0.966482 + 0.256734i \(0.0826466\pi\)
−0.260902 + 0.965365i \(0.584020\pi\)
\(84\) 0 0
\(85\) −10.9096 3.97076i −1.18331 0.430689i
\(86\) 0.0747817 + 0.615054i 0.00806392 + 0.0663230i
\(87\) 0 0
\(88\) 2.83537 1.07688i 0.302251 0.114796i
\(89\) −13.2855 + 2.34260i −1.40826 + 0.248315i −0.825535 0.564352i \(-0.809126\pi\)
−0.582729 + 0.812667i \(0.698015\pi\)
\(90\) 0 0
\(91\) 18.1938 + 21.6826i 1.90723 + 2.27295i
\(92\) 2.87273 + 2.98890i 0.299503 + 0.311615i
\(93\) 0 0
\(94\) 9.46607 4.80913i 0.976351 0.496024i
\(95\) 7.32088 + 6.41231i 0.751106 + 0.657889i
\(96\) 0 0
\(97\) −4.04180 + 1.47109i −0.410382 + 0.149367i −0.538958 0.842333i \(-0.681182\pi\)
0.128576 + 0.991700i \(0.458960\pi\)
\(98\) 5.99984 + 19.7078i 0.606075 + 1.99079i
\(99\) 0 0
\(100\) 0.0293399 0.00724168i 0.00293399 0.000724168i
\(101\) −4.83726 + 0.852939i −0.481325 + 0.0848706i −0.409046 0.912514i \(-0.634138\pi\)
−0.0722793 + 0.997384i \(0.523027\pi\)
\(102\) 0 0
\(103\) −10.3746 5.98981i −1.02224 0.590193i −0.107491 0.994206i \(-0.534282\pi\)
−0.914753 + 0.404013i \(0.867615\pi\)
\(104\) 8.41091 15.0477i 0.824758 1.47555i
\(105\) 0 0
\(106\) 18.4069 + 0.986470i 1.78783 + 0.0958144i
\(107\) 2.03872 + 3.53116i 0.197090 + 0.341370i 0.947584 0.319507i \(-0.103517\pi\)
−0.750493 + 0.660878i \(0.770184\pi\)
\(108\) 0 0
\(109\) −7.78890 6.53566i −0.746041 0.626003i 0.188412 0.982090i \(-0.439666\pi\)
−0.934453 + 0.356087i \(0.884111\pi\)
\(110\) −3.11513 1.32664i −0.297016 0.126490i
\(111\) 0 0
\(112\) 14.6921 11.3673i 1.38827 1.07411i
\(113\) 4.51368i 0.424612i 0.977203 + 0.212306i \(0.0680973\pi\)
−0.977203 + 0.212306i \(0.931903\pi\)
\(114\) 0 0
\(115\) 4.62793i 0.431557i
\(116\) −11.7460 3.39817i −1.09059 0.315512i
\(117\) 0 0
\(118\) −6.69231 + 15.7145i −0.616077 + 1.44663i
\(119\) −18.4988 15.5223i −1.69578 1.42293i
\(120\) 0 0
\(121\) 4.92506 + 8.53046i 0.447733 + 0.775496i
\(122\) −0.0108256 + 0.201998i −0.000980099 + 0.0182880i
\(123\) 0 0
\(124\) −9.41239 14.0258i −0.845257 1.25955i
\(125\) −9.69703 5.59858i −0.867329 0.500753i
\(126\) 0 0
\(127\) −0.174744 + 0.0308120i −0.0155060 + 0.00273413i −0.181396 0.983410i \(-0.558062\pi\)
0.165890 + 0.986144i \(0.446950\pi\)
\(128\) −9.64922 5.90699i −0.852879 0.522109i
\(129\) 0 0
\(130\) −18.4102 + 5.60477i −1.61468 + 0.491571i
\(131\) −0.901495 + 0.328117i −0.0787640 + 0.0286677i −0.381102 0.924533i \(-0.624455\pi\)
0.302338 + 0.953201i \(0.402233\pi\)
\(132\) 0 0
\(133\) 9.74746 + 17.7415i 0.845212 + 1.53838i
\(134\) −0.181614 0.357481i −0.0156891 0.0308817i
\(135\) 0 0
\(136\) −4.83755 + 13.8892i −0.414816 + 1.19099i
\(137\) −5.71328 6.80882i −0.488118 0.581716i 0.464620 0.885510i \(-0.346191\pi\)
−0.952738 + 0.303794i \(0.901747\pi\)
\(138\) 0 0
\(139\) −1.13792 + 0.200646i −0.0965172 + 0.0170186i −0.221698 0.975115i \(-0.571160\pi\)
0.125181 + 0.992134i \(0.460049\pi\)
\(140\) −20.6186 2.21636i −1.74259 0.187317i
\(141\) 0 0
\(142\) 5.79945 0.705129i 0.486679 0.0591731i
\(143\) −6.14148 2.23531i −0.513576 0.186926i
\(144\) 0 0
\(145\) 6.82515 + 11.8215i 0.566798 + 0.981723i
\(146\) 11.4139 + 15.1840i 0.944618 + 1.25664i
\(147\) 0 0
\(148\) 0.115300 + 1.70682i 0.00947764 + 0.140300i
\(149\) −11.7692 2.07523i −0.964173 0.170010i −0.330667 0.943748i \(-0.607274\pi\)
−0.633506 + 0.773738i \(0.718385\pi\)
\(150\) 0 0
\(151\) 2.10738i 0.171496i 0.996317 + 0.0857480i \(0.0273280\pi\)
−0.996317 + 0.0857480i \(0.972672\pi\)
\(152\) 7.99350 9.38637i 0.648359 0.761335i
\(153\) 0 0
\(154\) −5.14498 4.80915i −0.414594 0.387532i
\(155\) −3.27440 + 18.5700i −0.263006 + 1.49158i
\(156\) 0 0
\(157\) 9.68593 + 8.12746i 0.773021 + 0.648642i 0.941481 0.337067i \(-0.109435\pi\)
−0.168459 + 0.985709i \(0.553879\pi\)
\(158\) −6.11894 + 4.59963i −0.486797 + 0.365927i
\(159\) 0 0
\(160\) 3.19676 + 12.2187i 0.252726 + 0.965975i
\(161\) 3.29235 9.04566i 0.259474 0.712898i
\(162\) 0 0
\(163\) −15.0618 8.69594i −1.17973 0.681118i −0.223779 0.974640i \(-0.571839\pi\)
−0.955952 + 0.293522i \(0.905173\pi\)
\(164\) −0.683213 + 6.35584i −0.0533499 + 0.496308i
\(165\) 0 0
\(166\) −17.7107 4.11088i −1.37462 0.319066i
\(167\) 4.13627 3.47074i 0.320074 0.268574i −0.468567 0.883428i \(-0.655230\pi\)
0.788641 + 0.614854i \(0.210785\pi\)
\(168\) 0 0
\(169\) −22.6907 + 8.25875i −1.74544 + 0.635289i
\(170\) 14.6379 7.43661i 1.12268 0.570362i
\(171\) 0 0
\(172\) −0.707661 0.516705i −0.0539586 0.0393984i
\(173\) 4.02831 + 11.0677i 0.306267 + 0.841461i 0.993376 + 0.114907i \(0.0366571\pi\)
−0.687109 + 0.726554i \(0.741121\pi\)
\(174\) 0 0
\(175\) −0.0451059 0.0537551i −0.00340968 0.00406350i
\(176\) −1.62557 + 3.96932i −0.122532 + 0.299199i
\(177\) 0 0
\(178\) 10.4097 15.9882i 0.780244 1.19837i
\(179\) 0.475394 0.823406i 0.0355326 0.0615443i −0.847712 0.530456i \(-0.822021\pi\)
0.883245 + 0.468912i \(0.155354\pi\)
\(180\) 0 0
\(181\) 6.88127 + 2.50458i 0.511481 + 0.186164i 0.584851 0.811141i \(-0.301153\pi\)
−0.0733698 + 0.997305i \(0.523375\pi\)
\(182\) −39.9714 2.14217i −2.96288 0.158788i
\(183\) 0 0
\(184\) −5.86222 + 0.0815438i −0.432169 + 0.00601149i
\(185\) 1.22756 1.46294i 0.0902517 0.107558i
\(186\) 0 0
\(187\) 5.49124 + 0.968254i 0.401559 + 0.0708057i
\(188\) −4.17296 + 14.4241i −0.304344 + 1.05199i
\(189\) 0 0
\(190\) −13.6947 + 1.37112i −0.993521 + 0.0994716i
\(191\) −12.1950 −0.882396 −0.441198 0.897410i \(-0.645446\pi\)
−0.441198 + 0.897410i \(0.645446\pi\)
\(192\) 0 0
\(193\) 4.15567 23.5680i 0.299131 1.69646i −0.350788 0.936455i \(-0.614086\pi\)
0.649919 0.760003i \(-0.274803\pi\)
\(194\) 2.38335 5.59644i 0.171115 0.401801i
\(195\) 0 0
\(196\) −26.1553 12.8334i −1.86823 0.916669i
\(197\) 0.412356 0.238074i 0.0293791 0.0169620i −0.485239 0.874382i \(-0.661267\pi\)
0.514618 + 0.857420i \(0.327934\pi\)
\(198\) 0 0
\(199\) 6.07508 16.6911i 0.430651 1.18320i −0.514763 0.857332i \(-0.672120\pi\)
0.945414 0.325871i \(-0.105658\pi\)
\(200\) −0.0208522 + 0.0373059i −0.00147447 + 0.00263793i
\(201\) 0 0
\(202\) 3.79019 5.82131i 0.266677 0.409586i
\(203\) 4.93037 + 27.9615i 0.346044 + 1.96252i
\(204\) 0 0
\(205\) 5.46663 4.58704i 0.381806 0.320373i
\(206\) 16.2073 4.93414i 1.12922 0.343778i
\(207\) 0 0
\(208\) 7.42398 + 23.2215i 0.514760 + 1.61012i
\(209\) −3.99747 2.42237i −0.276510 0.167559i
\(210\) 0 0
\(211\) −3.19568 8.78005i −0.219999 0.604443i 0.779767 0.626070i \(-0.215338\pi\)
−0.999766 + 0.0216268i \(0.993115\pi\)
\(212\) −18.7949 + 18.0644i −1.29084 + 1.24067i
\(213\) 0 0
\(214\) −5.61704 1.30379i −0.383973 0.0891250i
\(215\) 0.169857 + 0.963306i 0.0115841 + 0.0656969i
\(216\) 0 0
\(217\) −19.6109 + 33.9672i −1.33128 + 2.30584i
\(218\) 14.2742 1.73553i 0.966768 0.117545i
\(219\) 0 0
\(220\) 4.37894 1.93724i 0.295228 0.130609i
\(221\) 27.4465 15.8462i 1.84625 1.06593i
\(222\) 0 0
\(223\) −2.33724 + 2.78541i −0.156513 + 0.186525i −0.838603 0.544744i \(-0.816627\pi\)
0.682090 + 0.731269i \(0.261071\pi\)
\(224\) −2.44418 + 26.1567i −0.163309 + 1.74767i
\(225\) 0 0
\(226\) −4.66331 4.35892i −0.310199 0.289951i
\(227\) −12.1355 −0.805461 −0.402731 0.915319i \(-0.631939\pi\)
−0.402731 + 0.915319i \(0.631939\pi\)
\(228\) 0 0
\(229\) −17.0403 −1.12606 −0.563028 0.826438i \(-0.690364\pi\)
−0.563028 + 0.826438i \(0.690364\pi\)
\(230\) 4.78135 + 4.46925i 0.315273 + 0.294694i
\(231\) 0 0
\(232\) 14.8541 8.85374i 0.975219 0.581276i
\(233\) 5.73459 6.83422i 0.375686 0.447725i −0.544762 0.838591i \(-0.683380\pi\)
0.920448 + 0.390866i \(0.127824\pi\)
\(234\) 0 0
\(235\) 14.5168 8.38129i 0.946973 0.546735i
\(236\) −9.77254 22.0898i −0.636138 1.43792i
\(237\) 0 0
\(238\) 33.9014 4.12192i 2.19750 0.267184i
\(239\) 3.06867 5.31509i 0.198496 0.343805i −0.749545 0.661953i \(-0.769728\pi\)
0.948041 + 0.318149i \(0.103061\pi\)
\(240\) 0 0
\(241\) −0.381152 2.16162i −0.0245521 0.139242i 0.970068 0.242835i \(-0.0780773\pi\)
−0.994620 + 0.103593i \(0.966966\pi\)
\(242\) −13.5694 3.14964i −0.872277 0.202467i
\(243\) 0 0
\(244\) −0.198239 0.206256i −0.0126910 0.0132042i
\(245\) 11.1237 + 30.5622i 0.710669 + 1.95255i
\(246\) 0 0
\(247\) −26.2551 + 4.05751i −1.67057 + 0.258173i
\(248\) 23.5804 + 3.82049i 1.49736 + 0.242601i
\(249\) 0 0
\(250\) 15.1487 4.61187i 0.958090 0.291680i
\(251\) 17.2346 14.4615i 1.08784 0.912803i 0.0912887 0.995824i \(-0.470901\pi\)
0.996548 + 0.0830212i \(0.0264569\pi\)
\(252\) 0 0
\(253\) 0.385971 + 2.18895i 0.0242658 + 0.137618i
\(254\) 0.136919 0.210292i 0.00859104 0.0131949i
\(255\) 0 0
\(256\) 15.4212 4.26464i 0.963824 0.266540i
\(257\) −1.47246 + 4.04556i −0.0918497 + 0.252355i −0.977108 0.212745i \(-0.931760\pi\)
0.885258 + 0.465100i \(0.153982\pi\)
\(258\) 0 0
\(259\) 3.44010 1.98615i 0.213758 0.123413i
\(260\) 11.9883 24.4331i 0.743485 1.51527i
\(261\) 0 0
\(262\) 0.531590 1.24825i 0.0328418 0.0771169i
\(263\) −3.29418 + 18.6822i −0.203128 + 1.15200i 0.697230 + 0.716847i \(0.254416\pi\)
−0.900358 + 0.435149i \(0.856696\pi\)
\(264\) 0 0
\(265\) 29.1015 1.78769
\(266\) −27.7429 7.06259i −1.70102 0.433035i
\(267\) 0 0
\(268\) 0.544719 + 0.157589i 0.0332740 + 0.00962630i
\(269\) 16.4491 + 2.90041i 1.00292 + 0.176841i 0.650909 0.759156i \(-0.274388\pi\)
0.352008 + 0.935997i \(0.385499\pi\)
\(270\) 0 0
\(271\) −18.6418 + 22.2165i −1.13241 + 1.34955i −0.203577 + 0.979059i \(0.565257\pi\)
−0.928834 + 0.370496i \(0.879188\pi\)
\(272\) −9.67790 18.4108i −0.586809 1.11632i
\(273\) 0 0
\(274\) 12.5519 + 0.672688i 0.758289 + 0.0406386i
\(275\) 0.0152258 + 0.00554176i 0.000918153 + 0.000334180i
\(276\) 0 0
\(277\) 2.51576 4.35742i 0.151157 0.261812i −0.780496 0.625161i \(-0.785033\pi\)
0.931653 + 0.363349i \(0.118367\pi\)
\(278\) 0.891607 1.36941i 0.0534751 0.0821318i
\(279\) 0 0
\(280\) 22.2014 19.1617i 1.32679 1.14513i
\(281\) −0.803979 0.958145i −0.0479614 0.0571581i 0.741530 0.670919i \(-0.234100\pi\)
−0.789492 + 0.613761i \(0.789656\pi\)
\(282\) 0 0
\(283\) 2.56938 + 7.05932i 0.152734 + 0.419633i 0.992336 0.123569i \(-0.0394340\pi\)
−0.839602 + 0.543202i \(0.817212\pi\)
\(284\) −4.87210 + 6.67266i −0.289106 + 0.395949i
\(285\) 0 0
\(286\) 8.24032 4.18640i 0.487260 0.247547i
\(287\) 13.9482 5.07674i 0.823337 0.299670i
\(288\) 0 0
\(289\) −7.69018 + 6.45283i −0.452364 + 0.379578i
\(290\) −18.8045 4.36477i −1.10424 0.256308i
\(291\) 0 0
\(292\) −26.7099 2.87114i −1.56308 0.168021i
\(293\) −4.47923 2.58608i −0.261679 0.151081i 0.363421 0.931625i \(-0.381609\pi\)
−0.625100 + 0.780544i \(0.714942\pi\)
\(294\) 0 0
\(295\) −9.22265 + 25.3390i −0.536964 + 1.47530i
\(296\) −1.87475 1.52917i −0.108967 0.0888813i
\(297\) 0 0
\(298\) 13.5097 10.1553i 0.782597 0.588281i
\(299\) 9.67776 + 8.12060i 0.559679 + 0.469627i
\(300\) 0 0
\(301\) −0.353305 + 2.00369i −0.0203642 + 0.115491i
\(302\) −2.17724 2.03512i −0.125286 0.117108i
\(303\) 0 0
\(304\) 1.97811 + 17.3230i 0.113452 + 0.993543i
\(305\) 0.319361i 0.0182866i
\(306\) 0 0
\(307\) 5.05324 + 0.891023i 0.288404 + 0.0508534i 0.315978 0.948766i \(-0.397667\pi\)
−0.0275747 + 0.999620i \(0.508778\pi\)
\(308\) 9.93715 0.671283i 0.566221 0.0382499i
\(309\) 0 0
\(310\) −16.0235 21.3163i −0.910074 1.21068i
\(311\) −7.97132 13.8067i −0.452012 0.782908i 0.546499 0.837460i \(-0.315960\pi\)
−0.998511 + 0.0545521i \(0.982627\pi\)
\(312\) 0 0
\(313\) 7.81385 + 2.84401i 0.441665 + 0.160753i 0.553274 0.832999i \(-0.313378\pi\)
−0.111609 + 0.993752i \(0.535600\pi\)
\(314\) −17.7507 + 2.15823i −1.00173 + 0.121796i
\(315\) 0 0
\(316\) 1.15703 10.7637i 0.0650880 0.605506i
\(317\) 17.8892 3.15435i 1.00476 0.177166i 0.353025 0.935614i \(-0.385153\pi\)
0.651734 + 0.758448i \(0.274042\pi\)
\(318\) 0 0
\(319\) −4.21412 5.02219i −0.235946 0.281189i
\(320\) −15.7109 8.49704i −0.878268 0.474999i
\(321\) 0 0
\(322\) 6.16606 + 12.1370i 0.343621 + 0.676368i
\(323\) 21.4584 7.29883i 1.19398 0.406118i
\(324\) 0 0
\(325\) 0.0865402 0.0314981i 0.00480039 0.00174720i
\(326\) 23.5296 7.16333i 1.30318 0.396740i
\(327\) 0 0
\(328\) −5.90675 6.84377i −0.326146 0.377884i
\(329\) 34.3368 6.05450i 1.89305 0.333795i
\(330\) 0 0
\(331\) −10.0663 5.81180i −0.553296 0.319445i 0.197154 0.980372i \(-0.436830\pi\)
−0.750450 + 0.660927i \(0.770163\pi\)
\(332\) 21.3506 14.3279i 1.17177 0.786344i
\(333\) 0 0
\(334\) −0.408649 + 7.62512i −0.0223603 + 0.417228i
\(335\) −0.316515 0.548220i −0.0172930 0.0299524i
\(336\) 0 0
\(337\) −2.06068 1.72912i −0.112252 0.0941909i 0.584934 0.811081i \(-0.301120\pi\)
−0.697186 + 0.716890i \(0.745565\pi\)
\(338\) 13.3802 31.4185i 0.727787 1.70894i
\(339\) 0 0
\(340\) −6.45286 + 22.3048i −0.349956 + 1.20965i
\(341\) 9.05646i 0.490435i
\(342\) 0 0
\(343\) 35.1415i 1.89746i
\(344\) 1.21723 0.232132i 0.0656287 0.0125157i
\(345\) 0 0
\(346\) −15.3248 6.52636i −0.823865 0.350859i
\(347\) −23.5669 19.7750i −1.26514 1.06158i −0.995115 0.0987232i \(-0.968524\pi\)
−0.270023 0.962854i \(-0.587031\pi\)
\(348\) 0 0
\(349\) 8.73087 + 15.1223i 0.467353 + 0.809479i 0.999304 0.0372962i \(-0.0118745\pi\)
−0.531952 + 0.846775i \(0.678541\pi\)
\(350\) 0.0990964 + 0.00531082i 0.00529693 + 0.000283875i
\(351\) 0 0
\(352\) −2.53107 5.51268i −0.134907 0.293827i
\(353\) 14.5026 + 8.37305i 0.771893 + 0.445653i 0.833549 0.552445i \(-0.186305\pi\)
−0.0616565 + 0.998097i \(0.519638\pi\)
\(354\) 0 0
\(355\) 9.08318 1.60161i 0.482085 0.0850046i
\(356\) 6.46541 + 26.1949i 0.342666 + 1.38833i
\(357\) 0 0
\(358\) 0.391609 + 1.28633i 0.0206972 + 0.0679845i
\(359\) −12.5043 + 4.55120i −0.659953 + 0.240203i −0.650216 0.759749i \(-0.725322\pi\)
−0.00973709 + 0.999953i \(0.503099\pi\)
\(360\) 0 0
\(361\) −18.9829 0.805507i −0.999101 0.0423951i
\(362\) −9.23293 + 4.69068i −0.485272 + 0.246537i
\(363\) 0 0
\(364\) 40.8140 39.2277i 2.13924 2.05609i
\(365\) 19.2767 + 22.9730i 1.00899 + 1.20246i
\(366\) 0 0
\(367\) 33.6177 5.92771i 1.75483 0.309424i 0.798562 0.601913i \(-0.205595\pi\)
0.956269 + 0.292489i \(0.0944834\pi\)
\(368\) 5.57697 6.13530i 0.290720 0.319825i
\(369\) 0 0
\(370\) 0.325975 + 2.68103i 0.0169466 + 0.139380i
\(371\) 56.8812 + 20.7031i 2.95313 + 1.07485i
\(372\) 0 0
\(373\) 5.84474 + 10.1234i 0.302629 + 0.524169i 0.976731 0.214469i \(-0.0688023\pi\)
−0.674101 + 0.738639i \(0.735469\pi\)
\(374\) −6.30331 + 4.73822i −0.325937 + 0.245008i
\(375\) 0 0
\(376\) −10.8724 18.2408i −0.560701 0.940699i
\(377\) −36.6967 6.47063i −1.88998 0.333254i
\(378\) 0 0
\(379\) 35.9517i 1.84672i −0.383941 0.923358i \(-0.625433\pi\)
0.383941 0.923358i \(-0.374567\pi\)
\(380\) 11.8086 15.4728i 0.605769 0.793739i
\(381\) 0 0
\(382\) 11.7768 12.5992i 0.602555 0.644632i
\(383\) 4.36295 24.7435i 0.222936 1.26433i −0.643656 0.765315i \(-0.722583\pi\)
0.866592 0.499018i \(-0.166306\pi\)
\(384\) 0 0
\(385\) −8.51730 7.14687i −0.434082 0.364238i
\(386\) 20.3361 + 27.0533i 1.03508 + 1.37698i
\(387\) 0 0
\(388\) 3.48032 + 7.86691i 0.176687 + 0.399382i
\(389\) 7.50992 20.6333i 0.380768 1.04615i −0.590266 0.807209i \(-0.700977\pi\)
0.971034 0.238942i \(-0.0768007\pi\)
\(390\) 0 0
\(391\) −9.33434 5.38918i −0.472058 0.272543i
\(392\) 38.5173 14.6290i 1.94542 0.738875i
\(393\) 0 0
\(394\) −0.152251 + 0.655936i −0.00767030 + 0.0330456i
\(395\) −9.25781 + 7.76823i −0.465811 + 0.390862i
\(396\) 0 0
\(397\) −4.71404 + 1.71577i −0.236591 + 0.0861120i −0.457595 0.889161i \(-0.651289\pi\)
0.221004 + 0.975273i \(0.429067\pi\)
\(398\) 11.3777 + 22.3953i 0.570311 + 1.12258i
\(399\) 0 0
\(400\) −0.0184054 0.0575703i −0.000920270 0.00287851i
\(401\) −4.37597 12.0229i −0.218525 0.600394i 0.781189 0.624295i \(-0.214614\pi\)
−0.999714 + 0.0239011i \(0.992391\pi\)
\(402\) 0 0
\(403\) −33.0874 39.4320i −1.64820 1.96425i
\(404\) 2.35405 + 9.53754i 0.117119 + 0.474511i
\(405\) 0 0
\(406\) −33.6498 21.9090i −1.67001 1.08732i
\(407\) −0.458607 + 0.794331i −0.0227323 + 0.0393735i
\(408\) 0 0
\(409\) 26.4036 + 9.61011i 1.30557 + 0.475189i 0.898807 0.438344i \(-0.144435\pi\)
0.406765 + 0.913533i \(0.366657\pi\)
\(410\) −0.540084 + 10.0776i −0.0266729 + 0.497698i
\(411\) 0 0
\(412\) −10.5539 + 21.5095i −0.519952 + 1.05970i
\(413\) −36.0528 + 42.9661i −1.77404 + 2.11422i
\(414\) 0 0
\(415\) −28.2679 4.98440i −1.38762 0.244675i
\(416\) −31.1607 14.7552i −1.52778 0.723432i
\(417\) 0 0
\(418\) 6.36308 1.79067i 0.311228 0.0875844i
\(419\) −17.3920 −0.849655 −0.424828 0.905274i \(-0.639665\pi\)
−0.424828 + 0.905274i \(0.639665\pi\)
\(420\) 0 0
\(421\) 2.07309 11.7571i 0.101036 0.573006i −0.891693 0.452640i \(-0.850482\pi\)
0.992730 0.120366i \(-0.0384067\pi\)
\(422\) 12.1572 + 5.17739i 0.591804 + 0.252031i
\(423\) 0 0
\(424\) −0.512767 36.8630i −0.0249022 1.79023i
\(425\) −0.0680448 + 0.0392857i −0.00330066 + 0.00190564i
\(426\) 0 0
\(427\) −0.227196 + 0.624216i −0.0109948 + 0.0302079i
\(428\) 6.77145 4.54416i 0.327310 0.219650i
\(429\) 0 0
\(430\) −1.15927 0.754789i −0.0559051 0.0363991i
\(431\) −3.64832 20.6906i −0.175733 0.996633i −0.937294 0.348539i \(-0.886678\pi\)
0.761561 0.648093i \(-0.224433\pi\)
\(432\) 0 0
\(433\) −22.9278 + 19.2387i −1.10184 + 0.924554i −0.997547 0.0699929i \(-0.977702\pi\)
−0.104293 + 0.994547i \(0.533258\pi\)
\(434\) −16.1546 53.0636i −0.775447 2.54713i
\(435\) 0 0
\(436\) −11.9917 + 16.4234i −0.574297 + 0.786537i
\(437\) 5.65964 + 7.04292i 0.270737 + 0.336908i
\(438\) 0 0
\(439\) 4.79704 + 13.1798i 0.228950 + 0.629036i 0.999970 0.00777581i \(-0.00247514\pi\)
−0.771019 + 0.636812i \(0.780253\pi\)
\(440\) −2.22733 + 6.39492i −0.106184 + 0.304866i
\(441\) 0 0
\(442\) −10.1339 + 43.6592i −0.482019 + 2.07666i
\(443\) −2.91096 16.5089i −0.138304 0.784360i −0.972502 0.232895i \(-0.925180\pi\)
0.834198 0.551465i \(-0.185931\pi\)
\(444\) 0 0
\(445\) 15.0600 26.0847i 0.713913 1.23653i
\(446\) −0.620648 5.10462i −0.0293885 0.241711i
\(447\) 0 0
\(448\) −24.6634 27.7850i −1.16524 1.31272i
\(449\) −2.94406 + 1.69975i −0.138939 + 0.0802162i −0.567858 0.823127i \(-0.692228\pi\)
0.428919 + 0.903343i \(0.358894\pi\)
\(450\) 0 0
\(451\) −2.20308 + 2.62553i −0.103739 + 0.123631i
\(452\) 9.00684 0.608438i 0.423646 0.0286185i
\(453\) 0 0
\(454\) 11.7194 12.5378i 0.550019 0.588428i
\(455\) −63.1953 −2.96264
\(456\) 0 0
\(457\) 1.68657 0.0788945 0.0394472 0.999222i \(-0.487440\pi\)
0.0394472 + 0.999222i \(0.487440\pi\)
\(458\) 16.4561 17.6052i 0.768941 0.822638i
\(459\) 0 0
\(460\) −9.23482 + 0.623838i −0.430575 + 0.0290866i
\(461\) 13.2389 15.7775i 0.616598 0.734832i −0.363884 0.931444i \(-0.618549\pi\)
0.980481 + 0.196612i \(0.0629939\pi\)
\(462\) 0 0
\(463\) 3.60533 2.08154i 0.167554 0.0967374i −0.413878 0.910332i \(-0.635826\pi\)
0.581432 + 0.813595i \(0.302493\pi\)
\(464\) −5.19754 + 23.8967i −0.241290 + 1.10938i
\(465\) 0 0
\(466\) 1.52281 + 12.5246i 0.0705427 + 0.580190i
\(467\) −3.71104 + 6.42771i −0.171726 + 0.297439i −0.939024 0.343853i \(-0.888268\pi\)
0.767297 + 0.641292i \(0.221601\pi\)
\(468\) 0 0
\(469\) −0.228645 1.29671i −0.0105578 0.0598765i
\(470\) −5.35994 + 23.0920i −0.247236 + 1.06515i
\(471\) 0 0
\(472\) 32.2596 + 11.2359i 1.48487 + 0.517174i
\(473\) −0.160680 0.441465i −0.00738807 0.0202986i
\(474\) 0 0
\(475\) 0.0650912 0.0100593i 0.00298659 0.000461553i
\(476\) −28.4804 + 39.0058i −1.30540 + 1.78783i
\(477\) 0 0
\(478\) 2.52784 + 8.30325i 0.115621 + 0.379782i
\(479\) −28.0546 + 23.5406i −1.28185 + 1.07560i −0.288861 + 0.957371i \(0.593277\pi\)
−0.992987 + 0.118227i \(0.962279\pi\)
\(480\) 0 0
\(481\) 0.905269 + 5.13404i 0.0412767 + 0.234092i
\(482\) 2.60136 + 1.69372i 0.118489 + 0.0771466i
\(483\) 0 0
\(484\) 16.3582 10.9776i 0.743556 0.498983i
\(485\) 3.28449 9.02406i 0.149141 0.409762i
\(486\) 0 0
\(487\) 9.52219 5.49764i 0.431492 0.249122i −0.268490 0.963282i \(-0.586525\pi\)
0.699982 + 0.714161i \(0.253191\pi\)
\(488\) 0.404536 0.00562712i 0.0183125 0.000254728i
\(489\) 0 0
\(490\) −42.3177 18.0218i −1.91172 0.814143i
\(491\) −0.102881 + 0.583469i −0.00464297 + 0.0263316i −0.987041 0.160467i \(-0.948700\pi\)
0.982398 + 0.186798i \(0.0598111\pi\)
\(492\) 0 0
\(493\) 31.7913 1.43181
\(494\) 21.1628 31.0438i 0.952161 1.39673i
\(495\) 0 0
\(496\) −26.7191 + 20.6726i −1.19972 + 0.928228i
\(497\) 18.8932 + 3.33138i 0.847475 + 0.149433i
\(498\) 0 0
\(499\) 10.6271 12.6649i 0.475736 0.566960i −0.473794 0.880636i \(-0.657116\pi\)
0.949530 + 0.313676i \(0.101560\pi\)
\(500\) −9.86456 + 20.1046i −0.441157 + 0.899107i
\(501\) 0 0
\(502\) −1.70272 + 31.7716i −0.0759960 + 1.41803i
\(503\) 37.5778 + 13.6772i 1.67551 + 0.609836i 0.992683 0.120746i \(-0.0385286\pi\)
0.682826 + 0.730581i \(0.260751\pi\)
\(504\) 0 0
\(505\) 5.48335 9.49743i 0.244006 0.422630i
\(506\) −2.63425 1.71513i −0.117107 0.0762468i
\(507\) 0 0
\(508\) 0.0850391 + 0.344539i 0.00377300 + 0.0152865i
\(509\) 10.7436 + 12.8037i 0.476201 + 0.567514i 0.949652 0.313306i \(-0.101436\pi\)
−0.473451 + 0.880820i \(0.656992\pi\)
\(510\) 0 0
\(511\) 21.3345 + 58.6162i 0.943785 + 2.59303i
\(512\) −10.4864 + 20.0508i −0.463438 + 0.886129i
\(513\) 0 0
\(514\) −2.75769 5.42812i −0.121637 0.239424i
\(515\) 25.1337 9.14792i 1.10752 0.403105i
\(516\) 0 0
\(517\) −6.16726 + 5.17494i −0.271236 + 0.227594i
\(518\) −1.27017 + 5.47219i −0.0558079 + 0.240434i
\(519\) 0 0
\(520\) 13.6657 + 35.9811i 0.599282 + 1.57787i
\(521\) −16.0840 9.28610i −0.704653 0.406831i 0.104425 0.994533i \(-0.466700\pi\)
−0.809078 + 0.587701i \(0.800033\pi\)
\(522\) 0 0
\(523\) −0.157921 + 0.433885i −0.00690542 + 0.0189725i −0.943097 0.332516i \(-0.892102\pi\)
0.936192 + 0.351489i \(0.114325\pi\)
\(524\) 0.776262 + 1.75466i 0.0339112 + 0.0766527i
\(525\) 0 0
\(526\) −16.1203 21.4451i −0.702880 0.935049i
\(527\) 33.6420 + 28.2290i 1.46547 + 1.22967i
\(528\) 0 0
\(529\) −3.24782 + 18.4193i −0.141210 + 0.800840i
\(530\) −28.1037 + 30.0662i −1.22075 + 1.30599i
\(531\) 0 0
\(532\) 34.0884 21.8421i 1.47792 0.946976i
\(533\) 19.4805i 0.843793i
\(534\) 0 0
\(535\) −8.96533 1.58083i −0.387605 0.0683452i
\(536\) −0.688855 + 0.410590i −0.0297540 + 0.0177348i
\(537\) 0 0
\(538\) −18.8816 + 14.1934i −0.814045 + 0.611921i
\(539\) −7.81027 13.5278i −0.336412 0.582683i
\(540\) 0 0
\(541\) 13.0840 + 4.76218i 0.562524 + 0.204742i 0.607602 0.794241i \(-0.292131\pi\)
−0.0450782 + 0.998983i \(0.514354\pi\)
\(542\) −4.95030 40.7145i −0.212634 1.74884i
\(543\) 0 0
\(544\) 28.3672 + 7.78086i 1.21624 + 0.333602i
\(545\) 22.3564 3.94203i 0.957642 0.168858i
\(546\) 0 0
\(547\) −18.6217 22.1924i −0.796204 0.948879i 0.203339 0.979108i \(-0.434821\pi\)
−0.999543 + 0.0302290i \(0.990376\pi\)
\(548\) −12.8165 + 12.3184i −0.547495 + 0.526215i
\(549\) 0 0
\(550\) −0.0204293 + 0.0103788i −0.000871106 + 0.000442555i
\(551\) −24.8436 9.64362i −1.05837 0.410832i
\(552\) 0 0
\(553\) −23.6215 + 8.59752i −1.00449 + 0.365604i
\(554\) 2.07237 + 6.80717i 0.0880466 + 0.289209i
\(555\) 0 0
\(556\) 0.553770 + 2.24362i 0.0234851 + 0.0951507i
\(557\) −21.6378 + 3.81533i −0.916823 + 0.161661i −0.612100 0.790780i \(-0.709675\pi\)
−0.304723 + 0.952441i \(0.598564\pi\)
\(558\) 0 0
\(559\) −2.31248 1.33511i −0.0978073 0.0564691i
\(560\) −1.64330 + 41.4421i −0.0694420 + 1.75125i
\(561\) 0 0
\(562\) 1.76632 + 0.0946614i 0.0745077 + 0.00399305i
\(563\) 18.9942 + 32.8989i 0.800509 + 1.38652i 0.919282 + 0.393601i \(0.128771\pi\)
−0.118773 + 0.992921i \(0.537896\pi\)
\(564\) 0 0
\(565\) −7.71992 6.47778i −0.324779 0.272522i
\(566\) −9.77462 4.16272i −0.410858 0.174972i
\(567\) 0 0
\(568\) −2.18881 11.4775i −0.0918404 0.481584i
\(569\) 17.0920i 0.716536i 0.933619 + 0.358268i \(0.116633\pi\)
−0.933619 + 0.358268i \(0.883367\pi\)
\(570\) 0 0
\(571\) 1.83122i 0.0766342i 0.999266 + 0.0383171i \(0.0121997\pi\)
−0.999266 + 0.0383171i \(0.987800\pi\)
\(572\) −3.63260 + 12.5563i −0.151887 + 0.525007i
\(573\) 0 0
\(574\) −8.22494 + 19.3133i −0.343302 + 0.806120i
\(575\) −0.0239929 0.0201325i −0.00100057 0.000839582i
\(576\) 0 0
\(577\) −20.5459 35.5866i −0.855339 1.48149i −0.876331 0.481710i \(-0.840016\pi\)
0.0209919 0.999780i \(-0.493318\pi\)
\(578\) 0.759764 14.1767i 0.0316020 0.589673i
\(579\) 0 0
\(580\) 22.6692 15.2128i 0.941288 0.631676i
\(581\) −51.7060 29.8525i −2.14513 1.23849i
\(582\) 0 0
\(583\) −13.7646 + 2.42708i −0.570073 + 0.100519i
\(584\) 28.7604 24.8226i 1.19011 1.02717i
\(585\) 0 0
\(586\) 6.99746 2.13030i 0.289062 0.0880020i
\(587\) 5.64357 2.05409i 0.232935 0.0847814i −0.222915 0.974838i \(-0.571557\pi\)
0.455850 + 0.890056i \(0.349335\pi\)
\(588\) 0 0
\(589\) −17.7268 32.2648i −0.730419 1.32945i
\(590\) −17.2726 33.9986i −0.711101 1.39970i
\(591\) 0 0
\(592\) 3.39033 0.460153i 0.139342 0.0189122i
\(593\) −22.6436 26.9856i −0.929860 1.10816i −0.993907 0.110218i \(-0.964845\pi\)
0.0640470 0.997947i \(-0.479599\pi\)
\(594\) 0 0
\(595\) 53.0968 9.36240i 2.17676 0.383821i
\(596\) −2.55455 + 23.7647i −0.104639 + 0.973439i
\(597\) 0 0
\(598\) −17.7357 + 2.15641i −0.725268 + 0.0881821i
\(599\) −21.6993 7.89790i −0.886610 0.322700i −0.141736 0.989905i \(-0.545268\pi\)
−0.744874 + 0.667205i \(0.767490\pi\)
\(600\) 0 0
\(601\) −11.7588 20.3669i −0.479653 0.830784i 0.520074 0.854121i \(-0.325904\pi\)
−0.999728 + 0.0233369i \(0.992571\pi\)
\(602\) −1.72893 2.30001i −0.0704658 0.0937414i
\(603\) 0 0
\(604\) 4.20517 0.284072i 0.171106 0.0115587i
\(605\) −21.6581 3.81891i −0.880528 0.155261i
\(606\) 0 0
\(607\) 3.79848i 0.154176i 0.997024 + 0.0770879i \(0.0245622\pi\)
−0.997024 + 0.0770879i \(0.975438\pi\)
\(608\) −19.8076 14.6854i −0.803303 0.595571i
\(609\) 0 0
\(610\) −0.329948 0.308411i −0.0133592 0.0124872i
\(611\) −7.94593 + 45.0636i −0.321458 + 1.82308i
\(612\) 0 0
\(613\) 27.6028 + 23.1615i 1.11487 + 0.935484i 0.998334 0.0577034i \(-0.0183778\pi\)
0.116532 + 0.993187i \(0.462822\pi\)
\(614\) −5.80054 + 4.36029i −0.234091 + 0.175967i
\(615\) 0 0
\(616\) −8.90289 + 10.9148i −0.358708 + 0.439771i
\(617\) −1.04474 + 2.87040i −0.0420597 + 0.115558i −0.958944 0.283594i \(-0.908473\pi\)
0.916885 + 0.399152i \(0.130695\pi\)
\(618\) 0 0
\(619\) 9.43204 + 5.44559i 0.379106 + 0.218877i 0.677429 0.735588i \(-0.263094\pi\)
−0.298323 + 0.954465i \(0.596427\pi\)
\(620\) 37.4970 + 4.03069i 1.50592 + 0.161876i
\(621\) 0 0
\(622\) 21.9624 + 5.09776i 0.880613 + 0.204402i
\(623\) 47.9929 40.2708i 1.92279 1.61342i
\(624\) 0 0
\(625\) 23.4211 8.52459i 0.936844 0.340983i
\(626\) −10.4842 + 5.32639i −0.419034 + 0.212885i
\(627\) 0 0
\(628\) 14.9123 20.4234i 0.595066 0.814982i
\(629\) −1.52122 4.17951i −0.0606549 0.166648i
\(630\) 0 0
\(631\) 17.2566 + 20.5657i 0.686976 + 0.818706i 0.990986 0.133963i \(-0.0427703\pi\)
−0.304011 + 0.952669i \(0.598326\pi\)
\(632\) 10.0032 + 11.5900i 0.397905 + 0.461027i
\(633\) 0 0
\(634\) −14.0169 + 21.5285i −0.556684 + 0.855005i
\(635\) 0.198083 0.343090i 0.00786069 0.0136151i
\(636\) 0 0
\(637\) −83.4293 30.3658i −3.30559 1.20314i
\(638\) 9.25831 + 0.496176i 0.366540 + 0.0196438i
\(639\) 0 0
\(640\) 23.9510 8.02605i 0.946745 0.317258i
\(641\) 29.2902 34.9067i 1.15689 1.37873i 0.244383 0.969679i \(-0.421415\pi\)
0.912511 0.409053i \(-0.134141\pi\)
\(642\) 0 0
\(643\) −31.0354 5.47238i −1.22392 0.215810i −0.475906 0.879496i \(-0.657880\pi\)
−0.748011 + 0.663686i \(0.768991\pi\)
\(644\) −18.4940 5.35039i −0.728765 0.210835i
\(645\) 0 0
\(646\) −13.1819 + 29.2184i −0.518635 + 1.14958i
\(647\) −29.0580 −1.14239 −0.571193 0.820815i \(-0.693519\pi\)
−0.571193 + 0.820815i \(0.693519\pi\)
\(648\) 0 0
\(649\) 2.24891 12.7542i 0.0882774 0.500646i
\(650\) −0.0510307 + 0.119827i −0.00200159 + 0.00470001i
\(651\) 0 0
\(652\) −15.3220 + 31.2273i −0.600056 + 1.22296i
\(653\) −0.791559 + 0.457007i −0.0309761 + 0.0178841i −0.515408 0.856945i \(-0.672360\pi\)
0.484432 + 0.874829i \(0.339026\pi\)
\(654\) 0 0
\(655\) 0.732583 2.01276i 0.0286244 0.0786449i
\(656\) 12.7749 + 0.506560i 0.498775 + 0.0197778i
\(657\) 0 0
\(658\) −26.9043 + 41.3220i −1.04884 + 1.61090i
\(659\) 5.27629 + 29.9233i 0.205535 + 1.16565i 0.896595 + 0.442851i \(0.146033\pi\)
−0.691060 + 0.722797i \(0.742856\pi\)
\(660\) 0 0
\(661\) −29.8311 + 25.0312i −1.16029 + 0.973602i −0.999910 0.0134522i \(-0.995718\pi\)
−0.160385 + 0.987055i \(0.551273\pi\)
\(662\) 15.7256 4.78751i 0.611195 0.186072i
\(663\) 0 0
\(664\) −5.81568 + 35.8950i −0.225692 + 1.39299i
\(665\) −44.3329 8.79014i −1.71916 0.340867i
\(666\) 0 0
\(667\) 4.33436 + 11.9086i 0.167827 + 0.461101i
\(668\) −7.48326 7.78587i −0.289536 0.301244i
\(669\) 0 0
\(670\) 0.872055 + 0.202415i 0.0336904 + 0.00781998i
\(671\) −0.0266348 0.151053i −0.00102822 0.00583135i
\(672\) 0 0
\(673\) 2.92044 5.05835i 0.112575 0.194985i −0.804233 0.594314i \(-0.797424\pi\)
0.916808 + 0.399329i \(0.130757\pi\)
\(674\) 3.77646 0.459163i 0.145464 0.0176863i
\(675\) 0 0
\(676\) 19.5386 + 44.1650i 0.751485 + 1.69865i
\(677\) 18.8051 10.8571i 0.722738 0.417273i −0.0930215 0.995664i \(-0.529653\pi\)
0.815760 + 0.578391i \(0.196319\pi\)
\(678\) 0 0
\(679\) 12.8396 15.3016i 0.492738 0.587223i
\(680\) −16.8126 28.2068i −0.644732 1.08168i
\(681\) 0 0
\(682\) 9.35668 + 8.74594i 0.358286 + 0.334899i
\(683\) −8.14029 −0.311479 −0.155740 0.987798i \(-0.549776\pi\)
−0.155740 + 0.987798i \(0.549776\pi\)
\(684\) 0 0
\(685\) 19.8447 0.758229
\(686\) −36.3065 33.9366i −1.38619 1.29571i
\(687\) 0 0
\(688\) −0.935668 + 1.48175i −0.0356720 + 0.0564914i
\(689\) −51.0643 + 60.8560i −1.94539 + 2.31843i
\(690\) 0 0
\(691\) 29.2640 16.8956i 1.11325 0.642738i 0.173584 0.984819i \(-0.444465\pi\)
0.939670 + 0.342081i \(0.111132\pi\)
\(692\) 21.5420 9.53021i 0.818906 0.362284i
\(693\) 0 0
\(694\) 43.1894 5.25121i 1.63945 0.199333i
\(695\) 1.28991 2.23419i 0.0489290 0.0847475i
\(696\) 0 0
\(697\) −2.88604 16.3675i −0.109316 0.619964i
\(698\) −24.0551 5.58350i −0.910500 0.211339i
\(699\) 0 0
\(700\) −0.101186 + 0.0972527i −0.00382445 + 0.00367581i
\(701\) −8.85715 24.3348i −0.334530 0.919114i −0.986917 0.161228i \(-0.948455\pi\)
0.652387 0.757886i \(-0.273768\pi\)
\(702\) 0 0
\(703\) −0.0790508 + 3.72756i −0.00298146 + 0.140588i
\(704\) 8.13971 + 2.70869i 0.306777 + 0.102088i
\(705\) 0 0
\(706\) −22.6559 + 6.89735i −0.852667 + 0.259585i
\(707\) 17.4742 14.6626i 0.657184 0.551443i
\(708\) 0 0
\(709\) −0.481137 2.72867i −0.0180695 0.102477i 0.974439 0.224652i \(-0.0721244\pi\)
−0.992509 + 0.122174i \(0.961013\pi\)
\(710\) −7.11703 + 10.9310i −0.267098 + 0.410232i
\(711\) 0 0
\(712\) −33.3070 18.6170i −1.24823 0.697700i
\(713\) −5.98748 + 16.4505i −0.224233 + 0.616075i
\(714\) 0 0
\(715\) 12.6370 7.29600i 0.472598 0.272855i
\(716\) −1.70715 0.837632i −0.0637992 0.0313038i
\(717\) 0 0
\(718\) 7.37351 17.3140i 0.275177 0.646153i
\(719\) 6.44777 36.5671i 0.240461 1.36372i −0.590341 0.807154i \(-0.701007\pi\)
0.830802 0.556569i \(-0.187882\pi\)
\(720\) 0 0
\(721\) 55.6337 2.07191
\(722\) 19.1643 18.8343i 0.713220 0.700941i
\(723\) 0 0
\(724\) 4.07018 14.0689i 0.151267 0.522865i
\(725\) 0.0909780 + 0.0160419i 0.00337884 + 0.000595780i
\(726\) 0 0
\(727\) 20.8894 24.8951i 0.774747 0.923307i −0.223937 0.974604i \(-0.571891\pi\)
0.998683 + 0.0512965i \(0.0163353\pi\)
\(728\) 1.11350 + 80.0497i 0.0412689 + 2.96684i
\(729\) 0 0
\(730\) −42.3503 2.26966i −1.56745 0.0840038i
\(731\) 2.14074 + 0.779167i 0.0791782 + 0.0288185i
\(732\) 0 0
\(733\) −7.33776 + 12.7094i −0.271026 + 0.469432i −0.969125 0.246570i \(-0.920696\pi\)
0.698098 + 0.716002i \(0.254030\pi\)
\(734\) −26.3408 + 40.4566i −0.972258 + 1.49328i
\(735\) 0 0
\(736\) 0.952936 + 11.6868i 0.0351257 + 0.430781i
\(737\) 0.195429 + 0.232903i 0.00719872 + 0.00857910i
\(738\) 0 0
\(739\) 16.5851 + 45.5672i 0.610093 + 1.67622i 0.730012 + 0.683434i \(0.239514\pi\)
−0.119919 + 0.992784i \(0.538263\pi\)
\(740\) −3.08471 2.25233i −0.113396 0.0827971i
\(741\) 0 0
\(742\) −76.3203 + 38.7736i −2.80181 + 1.42342i
\(743\) −19.4456 + 7.07760i −0.713388 + 0.259652i −0.673116 0.739537i \(-0.735045\pi\)
−0.0402720 + 0.999189i \(0.512822\pi\)
\(744\) 0 0
\(745\) 20.4399 17.1511i 0.748859 0.628367i
\(746\) −16.1033 3.73779i −0.589585 0.136850i
\(747\) 0 0
\(748\) 1.19189 11.0880i 0.0435799 0.405418i
\(749\) −16.3988 9.46787i −0.599200 0.345948i
\(750\) 0 0
\(751\) −14.9409 + 41.0498i −0.545201 + 1.49793i 0.294916 + 0.955523i \(0.404708\pi\)
−0.840117 + 0.542405i \(0.817514\pi\)
\(752\) 29.3451 + 6.38258i 1.07011 + 0.232749i
\(753\) 0 0
\(754\) 42.1236 31.6645i 1.53405 1.15315i
\(755\) −3.60433 3.02439i −0.131175 0.110069i
\(756\) 0 0
\(757\) 0.947800 5.37524i 0.0344484 0.195366i −0.962727 0.270475i \(-0.912819\pi\)
0.997175 + 0.0751086i \(0.0239304\pi\)
\(758\) 37.1435 + 34.7190i 1.34911 + 1.26105i
\(759\) 0 0
\(760\) 4.58204 + 27.1424i 0.166208 + 0.984557i
\(761\) 0.810479i 0.0293798i −0.999892 0.0146899i \(-0.995324\pi\)
0.999892 0.0146899i \(-0.00467611\pi\)
\(762\) 0 0
\(763\) 46.5017 + 8.19950i 1.68347 + 0.296842i
\(764\) 1.64386 + 24.3345i 0.0594729 + 0.880390i
\(765\) 0 0
\(766\) 21.3504 + 28.4027i 0.771421 + 1.02623i
\(767\) −36.8051 63.7483i −1.32896 2.30182i
\(768\) 0 0
\(769\) 33.5209 + 12.2006i 1.20880 + 0.439966i 0.866286 0.499548i \(-0.166501\pi\)
0.342510 + 0.939514i \(0.388723\pi\)
\(770\) 15.6091 1.89784i 0.562511 0.0683932i
\(771\) 0 0
\(772\) −47.5889 5.11551i −1.71276 0.184111i
\(773\) −39.6694 + 6.99478i −1.42681 + 0.251585i −0.833112 0.553105i \(-0.813443\pi\)
−0.593696 + 0.804689i \(0.702332\pi\)
\(774\) 0 0
\(775\) 0.0820297 + 0.0977592i 0.00294660 + 0.00351162i
\(776\) −11.4887 4.00147i −0.412420 0.143645i
\(777\) 0 0
\(778\) 14.0649 + 27.6847i 0.504251 + 0.992546i
\(779\) −2.70963 + 13.6660i −0.0970826 + 0.489635i
\(780\) 0 0
\(781\) −4.16265 + 1.51508i −0.148951 + 0.0542138i
\(782\) 14.5821 4.43937i 0.521456 0.158752i
\(783\) 0 0
\(784\) −22.0827 + 53.9215i −0.788667 + 1.92577i
\(785\) −27.8014 + 4.90214i −0.992274 + 0.174965i
\(786\) 0 0
\(787\) 18.6980 + 10.7953i 0.666511 + 0.384810i 0.794753 0.606933i \(-0.207600\pi\)
−0.128243 + 0.991743i \(0.540934\pi\)
\(788\) −0.530649 0.790744i −0.0189036 0.0281691i
\(789\) 0 0
\(790\) 0.914640 17.0666i 0.0325414 0.607202i
\(791\) −10.4808 18.1534i −0.372656 0.645459i
\(792\) 0 0
\(793\) −0.667836 0.560381i −0.0237155 0.0198997i
\(794\) 2.77976 6.52725i 0.0986499 0.231643i
\(795\) 0 0
\(796\) −34.1253 9.87258i −1.20954 0.349924i
\(797\) 14.4296i 0.511123i −0.966793 0.255561i \(-0.917740\pi\)
0.966793 0.255561i \(-0.0822603\pi\)
\(798\) 0 0
\(799\) 39.0397i 1.38113i
\(800\) 0.0772531 + 0.0365808i 0.00273131 + 0.00129333i
\(801\) 0 0
\(802\) 16.6474 + 7.08961i 0.587839 + 0.250343i
\(803\) −11.0336 9.25825i −0.389366 0.326717i
\(804\) 0 0
\(805\) 10.7461 + 18.6128i 0.378751 + 0.656017i
\(806\) 72.6921 + 3.89575i 2.56047 + 0.137222i
\(807\) 0 0
\(808\) −12.1271 6.77843i −0.426628 0.238464i
\(809\) 30.6208 + 17.6789i 1.07657 + 0.621558i 0.929969 0.367638i \(-0.119834\pi\)
0.146600 + 0.989196i \(0.453167\pi\)
\(810\) 0 0
\(811\) −34.2209 + 6.03406i −1.20166 + 0.211885i −0.738414 0.674347i \(-0.764425\pi\)
−0.463242 + 0.886232i \(0.653314\pi\)
\(812\) 55.1313 13.6075i 1.93473 0.477530i
\(813\) 0 0
\(814\) −0.377781 1.24091i −0.0132412 0.0434937i
\(815\) 36.4888 13.2808i 1.27815 0.465208i
\(816\) 0 0
\(817\) −1.43655 1.25826i −0.0502585 0.0440210i
\(818\) −35.4269 + 17.9982i −1.23867 + 0.629294i
\(819\) 0 0
\(820\) −9.89012 10.2901i −0.345378 0.359345i
\(821\) −28.5075 33.9739i −0.994917 1.18570i −0.982593 0.185772i \(-0.940521\pi\)
−0.0123243 0.999924i \(-0.503923\pi\)
\(822\) 0 0
\(823\) 41.7966 7.36987i 1.45694 0.256898i 0.611616 0.791154i \(-0.290520\pi\)
0.845322 + 0.534257i \(0.179409\pi\)
\(824\) −12.0306 31.6758i −0.419104 1.10348i
\(825\) 0 0
\(826\) −9.57375 78.7408i −0.333113 2.73974i
\(827\) −18.9620 6.90159i −0.659372 0.239992i −0.00940667 0.999956i \(-0.502994\pi\)
−0.649965 + 0.759964i \(0.725217\pi\)
\(828\) 0 0
\(829\) −1.27182 2.20286i −0.0441721 0.0765084i 0.843094 0.537766i \(-0.180732\pi\)
−0.887266 + 0.461258i \(0.847398\pi\)
\(830\) 32.4483 24.3915i 1.12630 0.846643i
\(831\) 0 0
\(832\) 45.3366 17.9444i 1.57176 0.622110i
\(833\) 74.5961 + 13.1533i 2.58460 + 0.455735i
\(834\) 0 0
\(835\) 12.0554i 0.417195i
\(836\) −4.29487 + 8.30328i −0.148541 + 0.287175i
\(837\) 0 0
\(838\) 16.7957 17.9686i 0.580197 0.620714i
\(839\) −8.72120 + 49.4604i −0.301089 + 1.70756i 0.340276 + 0.940326i \(0.389480\pi\)
−0.641365 + 0.767236i \(0.721632\pi\)
\(840\) 0 0
\(841\) −6.41876 5.38598i −0.221336 0.185723i
\(842\) 10.1448 + 13.4958i 0.349614 + 0.465096i
\(843\) 0 0
\(844\) −17.0894 + 7.56036i −0.588241 + 0.260238i
\(845\) 18.4392 50.6613i 0.634328 1.74280i
\(846\) 0 0
\(847\) −39.6157 22.8721i −1.36121 0.785896i
\(848\) 38.5802 + 35.0693i 1.32485 + 1.20429i
\(849\) 0 0
\(850\) 0.0251237 0.108239i 0.000861736 0.00371257i
\(851\) 1.35818 1.13965i 0.0465580 0.0390668i
\(852\) 0 0
\(853\) 17.3907 6.32971i 0.595448 0.216725i −0.0266760 0.999644i \(-0.508492\pi\)
0.622124 + 0.782919i \(0.286270\pi\)
\(854\) −0.425503 0.837541i −0.0145604 0.0286601i
\(855\) 0 0
\(856\) −1.84448 + 11.3843i −0.0630429 + 0.389107i
\(857\) 17.2475 + 47.3871i 0.589164 + 1.61871i 0.772037 + 0.635578i \(0.219238\pi\)
−0.182873 + 0.983136i \(0.558540\pi\)
\(858\) 0 0
\(859\) 6.27338 + 7.47632i 0.214045 + 0.255089i 0.862374 0.506271i \(-0.168976\pi\)
−0.648329 + 0.761360i \(0.724532\pi\)
\(860\) 1.89933 0.468793i 0.0647667 0.0159857i
\(861\) 0 0
\(862\) 24.8998 + 16.2119i 0.848089 + 0.552181i
\(863\) 17.3489 30.0491i 0.590562 1.02288i −0.403595 0.914938i \(-0.632239\pi\)
0.994157 0.107946i \(-0.0344272\pi\)
\(864\) 0 0
\(865\) −24.7107 8.99396i −0.840189 0.305804i
\(866\) 2.26519 42.2669i 0.0769743 1.43629i
\(867\) 0 0
\(868\) 70.4234 + 34.5540i 2.39032 + 1.17284i
\(869\) 3.73095 4.44637i 0.126564 0.150833i
\(870\) 0 0
\(871\) 1.70180 + 0.300074i 0.0576634 + 0.0101676i
\(872\) −5.38731 28.2494i −0.182437 0.956647i
\(873\) 0 0
\(874\) −12.7420 0.954178i −0.431004 0.0322756i
\(875\) 52.0000 1.75792
\(876\) 0 0
\(877\) −1.59817 + 9.06369i −0.0539665 + 0.306059i −0.999829 0.0185094i \(-0.994108\pi\)
0.945862 + 0.324568i \(0.105219\pi\)
\(878\) −18.2492 7.77180i −0.615882 0.262285i
\(879\) 0 0
\(880\) −4.45595 8.47682i −0.150210 0.285753i
\(881\) −20.4252 + 11.7925i −0.688143 + 0.397299i −0.802916 0.596092i \(-0.796719\pi\)
0.114773 + 0.993392i \(0.463386\pi\)
\(882\) 0 0
\(883\) 17.2857 47.4921i 0.581711 1.59824i −0.203544 0.979066i \(-0.565246\pi\)
0.785255 0.619172i \(-0.212532\pi\)
\(884\) −35.3201 52.6320i −1.18794 1.77021i
\(885\) 0 0
\(886\) 19.8673 + 12.9354i 0.667455 + 0.434572i
\(887\) 9.08332 + 51.5141i 0.304988 + 1.72967i 0.623561 + 0.781775i \(0.285685\pi\)
−0.318573 + 0.947898i \(0.603204\pi\)
\(888\) 0 0
\(889\) 0.631247 0.529679i 0.0211713 0.0177649i
\(890\) 12.4058 + 40.7496i 0.415843 + 1.36593i
\(891\) 0 0
\(892\) 5.87321 + 4.28837i 0.196649 + 0.143585i
\(893\) −11.8424 + 30.5079i −0.396290 + 1.02091i
\(894\) 0 0
\(895\) 0.726044 + 1.99479i 0.0242690 + 0.0666785i
\(896\) 52.5238 + 1.35137i 1.75470 + 0.0451459i
\(897\) 0 0
\(898\) 1.08701 4.68312i 0.0362741 0.156278i
\(899\) −8.96640 50.8510i −0.299046 1.69597i
\(900\) 0 0
\(901\) 33.8885 58.6965i 1.12899 1.95546i
\(902\) −0.585023 4.81162i −0.0194791 0.160209i
\(903\) 0 0
\(904\) −8.06941 + 9.89299i −0.268385 + 0.329036i
\(905\) −14.1593 + 8.17487i −0.470670 + 0.271742i
\(906\) 0 0
\(907\) −25.7092 + 30.6390i −0.853659 + 1.01735i 0.145947 + 0.989292i \(0.453377\pi\)
−0.999606 + 0.0280587i \(0.991067\pi\)
\(908\) 1.63585 + 24.2158i 0.0542875 + 0.803630i
\(909\) 0 0
\(910\) 61.0285 65.2902i 2.02307 2.16435i
\(911\) −14.3208 −0.474468 −0.237234 0.971453i \(-0.576241\pi\)
−0.237234 + 0.971453i \(0.576241\pi\)
\(912\) 0 0
\(913\) 13.7861 0.456252
\(914\) −1.62874 + 1.74248i −0.0538740 + 0.0576361i
\(915\) 0 0
\(916\) 2.29701 + 34.0032i 0.0758954 + 1.12350i
\(917\) 2.86378 3.41292i 0.0945704 0.112705i
\(918\) 0 0
\(919\) −34.9172 + 20.1595i −1.15181 + 0.665000i −0.949328 0.314286i \(-0.898235\pi\)
−0.202485 + 0.979285i \(0.564902\pi\)
\(920\) 8.27366 10.1434i 0.272774 0.334418i
\(921\) 0 0
\(922\) 3.51556 + 28.9143i 0.115779 + 0.952243i
\(923\) −12.5890 + 21.8047i −0.414371 + 0.717712i
\(924\) 0 0
\(925\) −0.00224433 0.0127282i −7.37931e−5 0.000418501i
\(926\) −1.33117 + 5.73502i −0.0437450 + 0.188464i
\(927\) 0 0
\(928\) −19.6695 28.4472i −0.645684 0.933824i
\(929\) 2.21580 + 6.08786i 0.0726981 + 0.199736i 0.970720 0.240215i \(-0.0772179\pi\)
−0.898022 + 0.439951i \(0.854996\pi\)
\(930\) 0 0
\(931\) −54.3038 32.9069i −1.77974 1.07848i
\(932\) −14.4104 10.5219i −0.472027 0.344655i
\(933\) 0 0
\(934\) −3.05699 10.0414i −0.100028 0.328564i
\(935\) −9.53676 + 8.00229i −0.311885 + 0.261703i
\(936\) 0 0
\(937\) 1.62835 + 9.23485i 0.0531960 + 0.301689i 0.999785 0.0207544i \(-0.00660680\pi\)
−0.946589 + 0.322444i \(0.895496\pi\)
\(938\) 1.56050 + 1.01602i 0.0509522 + 0.0331744i
\(939\) 0 0
\(940\) −18.6813 27.8378i −0.609317 0.907970i
\(941\) −10.2784 + 28.2397i −0.335066 + 0.920587i 0.651706 + 0.758472i \(0.274054\pi\)
−0.986772 + 0.162115i \(0.948169\pi\)
\(942\) 0 0
\(943\) 5.73756 3.31258i 0.186841 0.107873i
\(944\) −42.7618 + 22.4783i −1.39178 + 0.731607i
\(945\) 0 0
\(946\) 0.611270 + 0.260321i 0.0198741 + 0.00846378i
\(947\) −0.621313 + 3.52364i −0.0201900 + 0.114503i −0.993237 0.116103i \(-0.962960\pi\)
0.973047 + 0.230606i \(0.0740708\pi\)
\(948\) 0 0
\(949\) −81.8650 −2.65745
\(950\) −0.0524666 + 0.0769634i −0.00170224 + 0.00249702i
\(951\) 0 0
\(952\) −12.7949 67.0930i −0.414687 2.17450i
\(953\) 11.3898 + 2.00834i 0.368953 + 0.0650564i 0.355051 0.934847i \(-0.384464\pi\)
0.0139022 + 0.999903i \(0.495575\pi\)
\(954\) 0 0
\(955\) 17.5015 20.8575i 0.566336 0.674932i
\(956\) −11.0197 5.40692i −0.356401 0.174872i
\(957\) 0 0
\(958\) 2.77170 51.7181i 0.0895496 1.67094i
\(959\) 38.7881 + 14.1177i 1.25253 + 0.455885i
\(960\) 0 0
\(961\) 20.1646 34.9260i 0.650469 1.12665i
\(962\) −6.17846 4.02272i −0.199202 0.129698i
\(963\) 0 0
\(964\) −4.26203 + 1.05195i −0.137271 + 0.0338811i
\(965\) 34.3452 + 40.9310i 1.10561 + 1.31761i
\(966\) 0 0
\(967\) 10.0611 + 27.6427i 0.323544 + 0.888928i 0.989705 + 0.143121i \(0.0457138\pi\)
−0.666162 + 0.745807i \(0.732064\pi\)
\(968\) −4.45582 + 27.5017i −0.143215 + 0.883939i
\(969\) 0 0
\(970\) 6.15134 + 12.1080i 0.197508 + 0.388765i
\(971\) 6.79796 2.47426i 0.218157 0.0794027i −0.230630 0.973042i \(-0.574079\pi\)
0.448787 + 0.893639i \(0.351856\pi\)
\(972\) 0 0
\(973\) 4.11065 3.44924i 0.131781 0.110578i
\(974\) −3.51581 + 15.1470i −0.112654 + 0.485341i
\(975\) 0 0
\(976\) −0.384852 + 0.423380i −0.0123188 + 0.0135521i
\(977\) −19.3199 11.1543i −0.618098 0.356859i 0.158030 0.987434i \(-0.449486\pi\)
−0.776128 + 0.630575i \(0.782819\pi\)
\(978\) 0 0
\(979\) −4.94771 + 13.5937i −0.158130 + 0.434457i
\(980\) 59.4860 26.3166i 1.90021 0.840653i
\(981\) 0 0
\(982\) −0.503457 0.669755i −0.0160660 0.0213727i
\(983\) −24.9318 20.9202i −0.795200 0.667252i 0.151826 0.988407i \(-0.451485\pi\)
−0.947027 + 0.321155i \(0.895929\pi\)
\(984\) 0 0
\(985\) −0.184603 + 1.04694i −0.00588195 + 0.0333582i
\(986\) −30.7013 + 32.8452i −0.977727 + 1.04600i
\(987\) 0 0
\(988\) 11.6357 + 51.8438i 0.370182 + 1.64937i
\(989\) 0.908122i 0.0288766i
\(990\) 0 0
\(991\) −33.1761 5.84984i −1.05387 0.185826i −0.380237 0.924889i \(-0.624158\pi\)
−0.673637 + 0.739063i \(0.735269\pi\)
\(992\) 4.44500 47.5686i 0.141129 1.51031i
\(993\) 0 0
\(994\) −21.6872 + 16.3023i −0.687876 + 0.517079i
\(995\) 19.8289 + 34.3446i 0.628617 + 1.08880i
\(996\) 0 0
\(997\) −40.5883 14.7729i −1.28544 0.467863i −0.393215 0.919447i \(-0.628637\pi\)
−0.892229 + 0.451583i \(0.850859\pi\)
\(998\) 2.82201 + 23.2101i 0.0893293 + 0.734703i
\(999\) 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 684.2.ce.a.575.10 yes 240
3.2 odd 2 inner 684.2.ce.a.575.31 yes 240
4.3 odd 2 inner 684.2.ce.a.575.39 yes 240
12.11 even 2 inner 684.2.ce.a.575.2 yes 240
19.4 even 9 inner 684.2.ce.a.251.2 240
57.23 odd 18 inner 684.2.ce.a.251.39 yes 240
76.23 odd 18 inner 684.2.ce.a.251.31 yes 240
228.23 even 18 inner 684.2.ce.a.251.10 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.2.ce.a.251.2 240 19.4 even 9 inner
684.2.ce.a.251.10 yes 240 228.23 even 18 inner
684.2.ce.a.251.31 yes 240 76.23 odd 18 inner
684.2.ce.a.251.39 yes 240 57.23 odd 18 inner
684.2.ce.a.575.2 yes 240 12.11 even 2 inner
684.2.ce.a.575.10 yes 240 1.1 even 1 trivial
684.2.ce.a.575.31 yes 240 3.2 odd 2 inner
684.2.ce.a.575.39 yes 240 4.3 odd 2 inner