Properties

Label 1110.2.d.i.889.6
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $6$
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] = [1110,2,Mod(889,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.d (of order \(2\), degree \(1\), 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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.6
Root \(1.32001 + 1.32001i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.i.889.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.80487 - 1.32001i) q^{5} -1.00000 q^{6} -3.64002i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.80487 - 1.32001i) q^{5} -1.00000 q^{6} -3.64002i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.32001 + 1.80487i) q^{10} -4.60975 q^{11} -1.00000i q^{12} +2.12489i q^{13} +3.64002 q^{14} +(1.32001 + 1.80487i) q^{15} +1.00000 q^{16} -0.609747i q^{17} -1.00000i q^{18} -3.48486 q^{19} +(-1.80487 + 1.32001i) q^{20} +3.64002 q^{21} -4.60975i q^{22} -8.76491i q^{23} +1.00000 q^{24} +(1.51514 - 4.76491i) q^{25} -2.12489 q^{26} -1.00000i q^{27} +3.64002i q^{28} +8.15516 q^{29} +(-1.80487 + 1.32001i) q^{30} -5.76491 q^{31} +1.00000i q^{32} -4.60975i q^{33} +0.609747 q^{34} +(-4.80487 - 6.56978i) q^{35} +1.00000 q^{36} +1.00000i q^{37} -3.48486i q^{38} -2.12489 q^{39} +(-1.32001 - 1.80487i) q^{40} -11.3747 q^{41} +3.64002i q^{42} -12.0147i q^{43} +4.60975 q^{44} +(-1.80487 + 1.32001i) q^{45} +8.76491 q^{46} -1.60975i q^{47} +1.00000i q^{48} -6.24977 q^{49} +(4.76491 + 1.51514i) q^{50} +0.609747 q^{51} -2.12489i q^{52} -9.24977i q^{53} +1.00000 q^{54} +(-8.32001 + 6.08492i) q^{55} -3.64002 q^{56} -3.48486i q^{57} +8.15516i q^{58} +3.67030 q^{59} +(-1.32001 - 1.80487i) q^{60} +1.45459 q^{61} -5.76491i q^{62} +3.64002i q^{63} -1.00000 q^{64} +(2.80487 + 3.83515i) q^{65} +4.60975 q^{66} +3.75023i q^{67} +0.609747i q^{68} +8.76491 q^{69} +(6.56978 - 4.80487i) q^{70} +14.1698 q^{71} +1.00000i q^{72} +6.76491i q^{73} -1.00000 q^{74} +(4.76491 + 1.51514i) q^{75} +3.48486 q^{76} +16.7796i q^{77} -2.12489i q^{78} +6.64002 q^{79} +(1.80487 - 1.32001i) q^{80} +1.00000 q^{81} -11.3747i q^{82} -2.90539i q^{83} -3.64002 q^{84} +(-0.804874 - 1.10052i) q^{85} +12.0147 q^{86} +8.15516i q^{87} +4.60975i q^{88} -10.3747 q^{89} +(-1.32001 - 1.80487i) q^{90} +7.73463 q^{91} +8.76491i q^{92} -5.76491i q^{93} +1.60975 q^{94} +(-6.28974 + 4.60006i) q^{95} -1.00000 q^{96} +16.5942i q^{97} -6.24977i q^{98} +4.60975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} - 10 q^{11} + 6 q^{14} + 6 q^{16} - 20 q^{19} - 2 q^{20} + 6 q^{21} + 6 q^{24} + 10 q^{25} + 4 q^{26} + 34 q^{29} - 2 q^{30} - 2 q^{31} - 14 q^{34} - 20 q^{35} + 6 q^{36} + 4 q^{39} - 18 q^{41} + 10 q^{44} - 2 q^{45} + 20 q^{46} - 4 q^{49} - 4 q^{50} - 14 q^{51} + 6 q^{54} - 42 q^{55} - 6 q^{56} + 8 q^{59} + 6 q^{61} - 6 q^{64} + 8 q^{65} + 10 q^{66} + 20 q^{69} - 2 q^{70} + 4 q^{71} - 6 q^{74} - 4 q^{75} + 20 q^{76} + 24 q^{79} + 2 q^{80} + 6 q^{81} - 6 q^{84} + 4 q^{85} + 6 q^{86} - 12 q^{89} + 12 q^{91} - 8 q^{94} - 28 q^{95} - 6 q^{96} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.80487 1.32001i 0.807164 0.590327i
\(6\) −1.00000 −0.408248
\(7\) 3.64002i 1.37580i −0.725806 0.687900i \(-0.758533\pi\)
0.725806 0.687900i \(-0.241467\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.32001 + 1.80487i 0.417424 + 0.570751i
\(11\) −4.60975 −1.38989 −0.694946 0.719062i \(-0.744572\pi\)
−0.694946 + 0.719062i \(0.744572\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.12489i 0.589337i 0.955600 + 0.294669i \(0.0952093\pi\)
−0.955600 + 0.294669i \(0.904791\pi\)
\(14\) 3.64002 0.972837
\(15\) 1.32001 + 1.80487i 0.340826 + 0.466016i
\(16\) 1.00000 0.250000
\(17\) 0.609747i 0.147885i −0.997262 0.0739427i \(-0.976442\pi\)
0.997262 0.0739427i \(-0.0235582\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.48486 −0.799482 −0.399741 0.916628i \(-0.630900\pi\)
−0.399741 + 0.916628i \(0.630900\pi\)
\(20\) −1.80487 + 1.32001i −0.403582 + 0.295164i
\(21\) 3.64002 0.794318
\(22\) 4.60975i 0.982801i
\(23\) 8.76491i 1.82761i −0.406153 0.913805i \(-0.633130\pi\)
0.406153 0.913805i \(-0.366870\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.51514 4.76491i 0.303028 0.952982i
\(26\) −2.12489 −0.416724
\(27\) 1.00000i 0.192450i
\(28\) 3.64002i 0.687900i
\(29\) 8.15516 1.51438 0.757188 0.653197i \(-0.226573\pi\)
0.757188 + 0.653197i \(0.226573\pi\)
\(30\) −1.80487 + 1.32001i −0.329523 + 0.241000i
\(31\) −5.76491 −1.03541 −0.517704 0.855560i \(-0.673213\pi\)
−0.517704 + 0.855560i \(0.673213\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.60975i 0.802454i
\(34\) 0.609747 0.104571
\(35\) −4.80487 6.56978i −0.812172 1.11050i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 3.48486i 0.565319i
\(39\) −2.12489 −0.340254
\(40\) −1.32001 1.80487i −0.208712 0.285376i
\(41\) −11.3747 −1.77642 −0.888211 0.459435i \(-0.848052\pi\)
−0.888211 + 0.459435i \(0.848052\pi\)
\(42\) 3.64002i 0.561668i
\(43\) 12.0147i 1.83222i −0.400925 0.916111i \(-0.631311\pi\)
0.400925 0.916111i \(-0.368689\pi\)
\(44\) 4.60975 0.694946
\(45\) −1.80487 + 1.32001i −0.269055 + 0.196776i
\(46\) 8.76491 1.29232
\(47\) 1.60975i 0.234806i −0.993084 0.117403i \(-0.962543\pi\)
0.993084 0.117403i \(-0.0374569\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.24977 −0.892824
\(50\) 4.76491 + 1.51514i 0.673860 + 0.214273i
\(51\) 0.609747 0.0853817
\(52\) 2.12489i 0.294669i
\(53\) 9.24977i 1.27055i −0.772284 0.635277i \(-0.780886\pi\)
0.772284 0.635277i \(-0.219114\pi\)
\(54\) 1.00000 0.136083
\(55\) −8.32001 + 6.08492i −1.12187 + 0.820491i
\(56\) −3.64002 −0.486419
\(57\) 3.48486i 0.461581i
\(58\) 8.15516i 1.07083i
\(59\) 3.67030 0.477832 0.238916 0.971040i \(-0.423208\pi\)
0.238916 + 0.971040i \(0.423208\pi\)
\(60\) −1.32001 1.80487i −0.170413 0.233008i
\(61\) 1.45459 0.186241 0.0931203 0.995655i \(-0.470316\pi\)
0.0931203 + 0.995655i \(0.470316\pi\)
\(62\) 5.76491i 0.732144i
\(63\) 3.64002i 0.458600i
\(64\) −1.00000 −0.125000
\(65\) 2.80487 + 3.83515i 0.347902 + 0.475692i
\(66\) 4.60975 0.567421
\(67\) 3.75023i 0.458163i 0.973407 + 0.229082i \(0.0735723\pi\)
−0.973407 + 0.229082i \(0.926428\pi\)
\(68\) 0.609747i 0.0739427i
\(69\) 8.76491 1.05517
\(70\) 6.56978 4.80487i 0.785239 0.574292i
\(71\) 14.1698 1.68165 0.840825 0.541306i \(-0.182070\pi\)
0.840825 + 0.541306i \(0.182070\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 6.76491i 0.791773i 0.918300 + 0.395886i \(0.129563\pi\)
−0.918300 + 0.395886i \(0.870437\pi\)
\(74\) −1.00000 −0.116248
\(75\) 4.76491 + 1.51514i 0.550204 + 0.174953i
\(76\) 3.48486 0.399741
\(77\) 16.7796i 1.91221i
\(78\) 2.12489i 0.240596i
\(79\) 6.64002 0.747061 0.373531 0.927618i \(-0.378147\pi\)
0.373531 + 0.927618i \(0.378147\pi\)
\(80\) 1.80487 1.32001i 0.201791 0.147582i
\(81\) 1.00000 0.111111
\(82\) 11.3747i 1.25612i
\(83\) 2.90539i 0.318908i −0.987205 0.159454i \(-0.949027\pi\)
0.987205 0.159454i \(-0.0509734\pi\)
\(84\) −3.64002 −0.397159
\(85\) −0.804874 1.10052i −0.0873008 0.119368i
\(86\) 12.0147 1.29558
\(87\) 8.15516i 0.874325i
\(88\) 4.60975i 0.491401i
\(89\) −10.3747 −1.09971 −0.549856 0.835260i \(-0.685317\pi\)
−0.549856 + 0.835260i \(0.685317\pi\)
\(90\) −1.32001 1.80487i −0.139141 0.190250i
\(91\) 7.73463 0.810810
\(92\) 8.76491i 0.913805i
\(93\) 5.76491i 0.597793i
\(94\) 1.60975 0.166033
\(95\) −6.28974 + 4.60006i −0.645313 + 0.471956i
\(96\) −1.00000 −0.102062
\(97\) 16.5942i 1.68488i 0.538790 + 0.842440i \(0.318882\pi\)
−0.538790 + 0.842440i \(0.681118\pi\)
\(98\) 6.24977i 0.631322i
\(99\) 4.60975 0.463297
\(100\) −1.51514 + 4.76491i −0.151514 + 0.476491i
\(101\) 4.06055 0.404040 0.202020 0.979381i \(-0.435249\pi\)
0.202020 + 0.979381i \(0.435249\pi\)
\(102\) 0.609747i 0.0603740i
\(103\) 3.13957i 0.309351i 0.987965 + 0.154675i \(0.0494331\pi\)
−0.987965 + 0.154675i \(0.950567\pi\)
\(104\) 2.12489 0.208362
\(105\) 6.56978 4.80487i 0.641145 0.468908i
\(106\) 9.24977 0.898417
\(107\) 13.9045i 1.34420i −0.740462 0.672098i \(-0.765393\pi\)
0.740462 0.672098i \(-0.234607\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 6.85952 0.657023 0.328511 0.944500i \(-0.393453\pi\)
0.328511 + 0.944500i \(0.393453\pi\)
\(110\) −6.08492 8.32001i −0.580174 0.793282i
\(111\) −1.00000 −0.0949158
\(112\) 3.64002i 0.343950i
\(113\) 10.9844i 1.03333i −0.856189 0.516663i \(-0.827174\pi\)
0.856189 0.516663i \(-0.172826\pi\)
\(114\) 3.48486 0.326387
\(115\) −11.5698 15.8196i −1.07889 1.47518i
\(116\) −8.15516 −0.757188
\(117\) 2.12489i 0.196446i
\(118\) 3.67030i 0.337878i
\(119\) −2.21949 −0.203461
\(120\) 1.80487 1.32001i 0.164762 0.120500i
\(121\) 10.2498 0.931797
\(122\) 1.45459i 0.131692i
\(123\) 11.3747i 1.02562i
\(124\) 5.76491 0.517704
\(125\) −3.55510 10.6001i −0.317978 0.948098i
\(126\) −3.64002 −0.324279
\(127\) 19.6547i 1.74407i 0.489441 + 0.872036i \(0.337201\pi\)
−0.489441 + 0.872036i \(0.662799\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 12.0147 1.05783
\(130\) −3.83515 + 2.80487i −0.336365 + 0.246004i
\(131\) −1.54920 −0.135354 −0.0676769 0.997707i \(-0.521559\pi\)
−0.0676769 + 0.997707i \(0.521559\pi\)
\(132\) 4.60975i 0.401227i
\(133\) 12.6850i 1.09993i
\(134\) −3.75023 −0.323970
\(135\) −1.32001 1.80487i −0.113609 0.155339i
\(136\) −0.609747 −0.0522854
\(137\) 16.6400i 1.42165i 0.703367 + 0.710827i \(0.251679\pi\)
−0.703367 + 0.710827i \(0.748321\pi\)
\(138\) 8.76491i 0.746119i
\(139\) −3.04496 −0.258270 −0.129135 0.991627i \(-0.541220\pi\)
−0.129135 + 0.991627i \(0.541220\pi\)
\(140\) 4.80487 + 6.56978i 0.406086 + 0.555248i
\(141\) 1.60975 0.135565
\(142\) 14.1698i 1.18911i
\(143\) 9.79518i 0.819115i
\(144\) −1.00000 −0.0833333
\(145\) 14.7190 10.7649i 1.22235 0.893977i
\(146\) −6.76491 −0.559868
\(147\) 6.24977i 0.515472i
\(148\) 1.00000i 0.0821995i
\(149\) −19.8401 −1.62537 −0.812684 0.582705i \(-0.801994\pi\)
−0.812684 + 0.582705i \(0.801994\pi\)
\(150\) −1.51514 + 4.76491i −0.123711 + 0.389053i
\(151\) 6.59507 0.536699 0.268349 0.963322i \(-0.413522\pi\)
0.268349 + 0.963322i \(0.413522\pi\)
\(152\) 3.48486i 0.282660i
\(153\) 0.609747i 0.0492952i
\(154\) −16.7796 −1.35214
\(155\) −10.4049 + 7.60975i −0.835744 + 0.611230i
\(156\) 2.12489 0.170127
\(157\) 10.6741i 0.851884i 0.904750 + 0.425942i \(0.140057\pi\)
−0.904750 + 0.425942i \(0.859943\pi\)
\(158\) 6.64002i 0.528252i
\(159\) 9.24977 0.733555
\(160\) 1.32001 + 1.80487i 0.104356 + 0.142688i
\(161\) −31.9045 −2.51442
\(162\) 1.00000i 0.0785674i
\(163\) 7.00000i 0.548282i −0.961689 0.274141i \(-0.911606\pi\)
0.961689 0.274141i \(-0.0883936\pi\)
\(164\) 11.3747 0.888211
\(165\) −6.08492 8.32001i −0.473710 0.647712i
\(166\) 2.90539 0.225502
\(167\) 3.17454i 0.245653i 0.992428 + 0.122827i \(0.0391959\pi\)
−0.992428 + 0.122827i \(0.960804\pi\)
\(168\) 3.64002i 0.280834i
\(169\) 8.48486 0.652682
\(170\) 1.10052 0.804874i 0.0844058 0.0617310i
\(171\) 3.48486 0.266494
\(172\) 12.0147i 0.916111i
\(173\) 1.96972i 0.149755i 0.997193 + 0.0748777i \(0.0238566\pi\)
−0.997193 + 0.0748777i \(0.976143\pi\)
\(174\) −8.15516 −0.618241
\(175\) −17.3444 5.51514i −1.31111 0.416905i
\(176\) −4.60975 −0.347473
\(177\) 3.67030i 0.275877i
\(178\) 10.3747i 0.777613i
\(179\) −22.7493 −1.70036 −0.850182 0.526489i \(-0.823508\pi\)
−0.850182 + 0.526489i \(0.823508\pi\)
\(180\) 1.80487 1.32001i 0.134527 0.0983879i
\(181\) 11.6703 0.867447 0.433723 0.901046i \(-0.357200\pi\)
0.433723 + 0.901046i \(0.357200\pi\)
\(182\) 7.73463i 0.573329i
\(183\) 1.45459i 0.107526i
\(184\) −8.76491 −0.646158
\(185\) 1.32001 + 1.80487i 0.0970492 + 0.132697i
\(186\) 5.76491 0.422704
\(187\) 2.81078i 0.205545i
\(188\) 1.60975i 0.117403i
\(189\) −3.64002 −0.264773
\(190\) −4.60006 6.28974i −0.333723 0.456305i
\(191\) 10.2800 0.743838 0.371919 0.928265i \(-0.378700\pi\)
0.371919 + 0.928265i \(0.378700\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 6.00000i 0.431889i 0.976406 + 0.215945i \(0.0692831\pi\)
−0.976406 + 0.215945i \(0.930717\pi\)
\(194\) −16.5942 −1.19139
\(195\) −3.83515 + 2.80487i −0.274641 + 0.200861i
\(196\) 6.24977 0.446412
\(197\) 22.4839i 1.60191i −0.598721 0.800957i \(-0.704324\pi\)
0.598721 0.800957i \(-0.295676\pi\)
\(198\) 4.60975i 0.327600i
\(199\) −26.5601 −1.88280 −0.941398 0.337299i \(-0.890487\pi\)
−0.941398 + 0.337299i \(0.890487\pi\)
\(200\) −4.76491 1.51514i −0.336930 0.107136i
\(201\) −3.75023 −0.264521
\(202\) 4.06055i 0.285699i
\(203\) 29.6850i 2.08348i
\(204\) −0.609747 −0.0426909
\(205\) −20.5298 + 15.0147i −1.43386 + 1.04867i
\(206\) −3.13957 −0.218744
\(207\) 8.76491i 0.609203i
\(208\) 2.12489i 0.147334i
\(209\) 16.0643 1.11119
\(210\) 4.80487 + 6.56978i 0.331568 + 0.453358i
\(211\) 17.7455 1.22165 0.610826 0.791765i \(-0.290837\pi\)
0.610826 + 0.791765i \(0.290837\pi\)
\(212\) 9.24977i 0.635277i
\(213\) 14.1698i 0.970902i
\(214\) 13.9045 0.950490
\(215\) −15.8595 21.6850i −1.08161 1.47890i
\(216\) −1.00000 −0.0680414
\(217\) 20.9844i 1.42451i
\(218\) 6.85952i 0.464585i
\(219\) −6.76491 −0.457130
\(220\) 8.32001 6.08492i 0.560935 0.410245i
\(221\) 1.29564 0.0871544
\(222\) 1.00000i 0.0671156i
\(223\) 5.20482i 0.348540i 0.984698 + 0.174270i \(0.0557566\pi\)
−0.984698 + 0.174270i \(0.944243\pi\)
\(224\) 3.64002 0.243209
\(225\) −1.51514 + 4.76491i −0.101009 + 0.317661i
\(226\) 10.9844 0.730672
\(227\) 16.3856i 1.08755i −0.839232 0.543774i \(-0.816995\pi\)
0.839232 0.543774i \(-0.183005\pi\)
\(228\) 3.48486i 0.230791i
\(229\) 20.6694 1.36587 0.682936 0.730479i \(-0.260703\pi\)
0.682936 + 0.730479i \(0.260703\pi\)
\(230\) 15.8196 11.5698i 1.04311 0.762889i
\(231\) −16.7796 −1.10402
\(232\) 8.15516i 0.535413i
\(233\) 3.28005i 0.214883i 0.994211 + 0.107442i \(0.0342658\pi\)
−0.994211 + 0.107442i \(0.965734\pi\)
\(234\) 2.12489 0.138908
\(235\) −2.12489 2.90539i −0.138612 0.189527i
\(236\) −3.67030 −0.238916
\(237\) 6.64002i 0.431316i
\(238\) 2.21949i 0.143868i
\(239\) 23.3553 1.51073 0.755364 0.655306i \(-0.227460\pi\)
0.755364 + 0.655306i \(0.227460\pi\)
\(240\) 1.32001 + 1.80487i 0.0852064 + 0.116504i
\(241\) −11.7309 −0.755651 −0.377825 0.925877i \(-0.623328\pi\)
−0.377825 + 0.925877i \(0.623328\pi\)
\(242\) 10.2498i 0.658880i
\(243\) 1.00000i 0.0641500i
\(244\) −1.45459 −0.0931203
\(245\) −11.2800 + 8.24977i −0.720656 + 0.527059i
\(246\) 11.3747 0.725222
\(247\) 7.40493i 0.471165i
\(248\) 5.76491i 0.366072i
\(249\) 2.90539 0.184122
\(250\) 10.6001 3.55510i 0.670407 0.224844i
\(251\) 18.6888 1.17962 0.589812 0.807541i \(-0.299202\pi\)
0.589812 + 0.807541i \(0.299202\pi\)
\(252\) 3.64002i 0.229300i
\(253\) 40.4040i 2.54018i
\(254\) −19.6547 −1.23325
\(255\) 1.10052 0.804874i 0.0689170 0.0504031i
\(256\) 1.00000 0.0625000
\(257\) 30.1542i 1.88097i −0.339835 0.940485i \(-0.610371\pi\)
0.339835 0.940485i \(-0.389629\pi\)
\(258\) 12.0147i 0.748001i
\(259\) 3.64002 0.226180
\(260\) −2.80487 3.83515i −0.173951 0.237846i
\(261\) −8.15516 −0.504792
\(262\) 1.54920i 0.0957096i
\(263\) 15.3141i 0.944308i 0.881516 + 0.472154i \(0.156523\pi\)
−0.881516 + 0.472154i \(0.843477\pi\)
\(264\) −4.60975 −0.283710
\(265\) −12.2098 16.6947i −0.750042 1.02555i
\(266\) −12.6850 −0.777766
\(267\) 10.3747i 0.634919i
\(268\) 3.75023i 0.229082i
\(269\) −7.98440 −0.486818 −0.243409 0.969924i \(-0.578266\pi\)
−0.243409 + 0.969924i \(0.578266\pi\)
\(270\) 1.80487 1.32001i 0.109841 0.0803334i
\(271\) −13.3094 −0.808489 −0.404244 0.914651i \(-0.632465\pi\)
−0.404244 + 0.914651i \(0.632465\pi\)
\(272\) 0.609747i 0.0369714i
\(273\) 7.73463i 0.468121i
\(274\) −16.6400 −1.00526
\(275\) −6.98440 + 21.9650i −0.421175 + 1.32454i
\(276\) −8.76491 −0.527586
\(277\) 0.435208i 0.0261491i −0.999915 0.0130746i \(-0.995838\pi\)
0.999915 0.0130746i \(-0.00416188\pi\)
\(278\) 3.04496i 0.182624i
\(279\) 5.76491 0.345136
\(280\) −6.56978 + 4.80487i −0.392620 + 0.287146i
\(281\) −4.65562 −0.277731 −0.138865 0.990311i \(-0.544346\pi\)
−0.138865 + 0.990311i \(0.544346\pi\)
\(282\) 1.60975i 0.0958591i
\(283\) 10.2947i 0.611958i −0.952038 0.305979i \(-0.901016\pi\)
0.952038 0.305979i \(-0.0989837\pi\)
\(284\) −14.1698 −0.840825
\(285\) −4.60006 6.28974i −0.272484 0.372572i
\(286\) 9.79518 0.579201
\(287\) 41.4040i 2.44400i
\(288\) 1.00000i 0.0589256i
\(289\) 16.6282 0.978130
\(290\) 10.7649 + 14.7190i 0.632137 + 0.864332i
\(291\) −16.5942 −0.972766
\(292\) 6.76491i 0.395886i
\(293\) 11.9092i 0.695741i −0.937543 0.347871i \(-0.886905\pi\)
0.937543 0.347871i \(-0.113095\pi\)
\(294\) 6.24977 0.364494
\(295\) 6.62443 4.84484i 0.385689 0.282077i
\(296\) 1.00000 0.0581238
\(297\) 4.60975i 0.267485i
\(298\) 19.8401i 1.14931i
\(299\) 18.6244 1.07708
\(300\) −4.76491 1.51514i −0.275102 0.0874765i
\(301\) −43.7337 −2.52077
\(302\) 6.59507i 0.379503i
\(303\) 4.06055i 0.233273i
\(304\) −3.48486 −0.199871
\(305\) 2.62534 1.92007i 0.150327 0.109943i
\(306\) −0.609747 −0.0348569
\(307\) 13.8595i 0.791004i 0.918465 + 0.395502i \(0.129429\pi\)
−0.918465 + 0.395502i \(0.870571\pi\)
\(308\) 16.7796i 0.956106i
\(309\) −3.13957 −0.178604
\(310\) −7.60975 10.4049i −0.432205 0.590960i
\(311\) 7.54450 0.427809 0.213905 0.976855i \(-0.431382\pi\)
0.213905 + 0.976855i \(0.431382\pi\)
\(312\) 2.12489i 0.120298i
\(313\) 4.64002i 0.262270i 0.991365 + 0.131135i \(0.0418621\pi\)
−0.991365 + 0.131135i \(0.958138\pi\)
\(314\) −10.6741 −0.602373
\(315\) 4.80487 + 6.56978i 0.270724 + 0.370165i
\(316\) −6.64002 −0.373531
\(317\) 10.5142i 0.590538i 0.955414 + 0.295269i \(0.0954092\pi\)
−0.955414 + 0.295269i \(0.904591\pi\)
\(318\) 9.24977i 0.518701i
\(319\) −37.5932 −2.10482
\(320\) −1.80487 + 1.32001i −0.100896 + 0.0737909i
\(321\) 13.9045 0.776072
\(322\) 31.9045i 1.77797i
\(323\) 2.12489i 0.118232i
\(324\) −1.00000 −0.0555556
\(325\) 10.1249 + 3.21949i 0.561628 + 0.178585i
\(326\) 7.00000 0.387694
\(327\) 6.85952i 0.379332i
\(328\) 11.3747i 0.628060i
\(329\) −5.85952 −0.323046
\(330\) 8.32001 6.08492i 0.458002 0.334964i
\(331\) −1.34060 −0.0736860 −0.0368430 0.999321i \(-0.511730\pi\)
−0.0368430 + 0.999321i \(0.511730\pi\)
\(332\) 2.90539i 0.159454i
\(333\) 1.00000i 0.0547997i
\(334\) −3.17454 −0.173703
\(335\) 4.95035 + 6.76869i 0.270466 + 0.369813i
\(336\) 3.64002 0.198580
\(337\) 20.1055i 1.09522i −0.836735 0.547608i \(-0.815538\pi\)
0.836735 0.547608i \(-0.184462\pi\)
\(338\) 8.48486i 0.461516i
\(339\) 10.9844 0.596591
\(340\) 0.804874 + 1.10052i 0.0436504 + 0.0596839i
\(341\) 26.5748 1.43910
\(342\) 3.48486i 0.188440i
\(343\) 2.73085i 0.147452i
\(344\) −12.0147 −0.647788
\(345\) 15.8196 11.5698i 0.851696 0.622896i
\(346\) −1.96972 −0.105893
\(347\) 4.70058i 0.252340i 0.992009 + 0.126170i \(0.0402685\pi\)
−0.992009 + 0.126170i \(0.959731\pi\)
\(348\) 8.15516i 0.437163i
\(349\) 9.54920 0.511157 0.255578 0.966788i \(-0.417734\pi\)
0.255578 + 0.966788i \(0.417734\pi\)
\(350\) 5.51514 17.3444i 0.294797 0.927096i
\(351\) 2.12489 0.113418
\(352\) 4.60975i 0.245700i
\(353\) 14.4537i 0.769291i 0.923064 + 0.384646i \(0.125676\pi\)
−0.923064 + 0.384646i \(0.874324\pi\)
\(354\) −3.67030 −0.195074
\(355\) 25.5748 18.7044i 1.35737 0.992724i
\(356\) 10.3747 0.549856
\(357\) 2.21949i 0.117468i
\(358\) 22.7493i 1.20234i
\(359\) 11.0790 0.584728 0.292364 0.956307i \(-0.405558\pi\)
0.292364 + 0.956307i \(0.405558\pi\)
\(360\) 1.32001 + 1.80487i 0.0695707 + 0.0951252i
\(361\) −6.85574 −0.360828
\(362\) 11.6703i 0.613377i
\(363\) 10.2498i 0.537973i
\(364\) −7.73463 −0.405405
\(365\) 8.92976 + 12.2098i 0.467405 + 0.639090i
\(366\) −1.45459 −0.0760324
\(367\) 10.9201i 0.570023i 0.958524 + 0.285012i \(0.0919974\pi\)
−0.958524 + 0.285012i \(0.908003\pi\)
\(368\) 8.76491i 0.456902i
\(369\) 11.3747 0.592141
\(370\) −1.80487 + 1.32001i −0.0938309 + 0.0686241i
\(371\) −33.6694 −1.74803
\(372\) 5.76491i 0.298897i
\(373\) 5.92007i 0.306530i −0.988185 0.153265i \(-0.951021\pi\)
0.988185 0.153265i \(-0.0489787\pi\)
\(374\) −2.81078 −0.145342
\(375\) 10.6001 3.55510i 0.547385 0.183585i
\(376\) −1.60975 −0.0830164
\(377\) 17.3288i 0.892478i
\(378\) 3.64002i 0.187223i
\(379\) −22.5189 −1.15672 −0.578360 0.815782i \(-0.696307\pi\)
−0.578360 + 0.815782i \(0.696307\pi\)
\(380\) 6.28974 4.60006i 0.322657 0.235978i
\(381\) −19.6547 −1.00694
\(382\) 10.2800i 0.525973i
\(383\) 27.2039i 1.39005i −0.718984 0.695027i \(-0.755392\pi\)
0.718984 0.695027i \(-0.244608\pi\)
\(384\) 1.00000 0.0510310
\(385\) 22.1493 + 30.2850i 1.12883 + 1.54347i
\(386\) −6.00000 −0.305392
\(387\) 12.0147i 0.610740i
\(388\) 16.5942i 0.842440i
\(389\) 0.295643 0.0149897 0.00749486 0.999972i \(-0.497614\pi\)
0.00749486 + 0.999972i \(0.497614\pi\)
\(390\) −2.80487 3.83515i −0.142030 0.194200i
\(391\) −5.34438 −0.270277
\(392\) 6.24977i 0.315661i
\(393\) 1.54920i 0.0781466i
\(394\) 22.4839 1.13272
\(395\) 11.9844 8.76491i 0.603001 0.441010i
\(396\) −4.60975 −0.231649
\(397\) 14.1287i 0.709097i −0.935038 0.354549i \(-0.884635\pi\)
0.935038 0.354549i \(-0.115365\pi\)
\(398\) 26.5601i 1.33134i
\(399\) −12.6850 −0.635043
\(400\) 1.51514 4.76491i 0.0757569 0.238245i
\(401\) 17.2838 0.863113 0.431557 0.902086i \(-0.357965\pi\)
0.431557 + 0.902086i \(0.357965\pi\)
\(402\) 3.75023i 0.187044i
\(403\) 12.2498i 0.610205i
\(404\) −4.06055 −0.202020
\(405\) 1.80487 1.32001i 0.0896849 0.0655919i
\(406\) 29.6850 1.47324
\(407\) 4.60975i 0.228497i
\(408\) 0.609747i 0.0301870i
\(409\) −5.73085 −0.283372 −0.141686 0.989912i \(-0.545252\pi\)
−0.141686 + 0.989912i \(0.545252\pi\)
\(410\) −15.0147 20.5298i −0.741522 1.01390i
\(411\) −16.6400 −0.820792
\(412\) 3.13957i 0.154675i
\(413\) 13.3600i 0.657401i
\(414\) −8.76491 −0.430772
\(415\) −3.83515 5.24386i −0.188260 0.257411i
\(416\) −2.12489 −0.104181
\(417\) 3.04496i 0.149112i
\(418\) 16.0643i 0.785732i
\(419\) −4.06433 −0.198556 −0.0992778 0.995060i \(-0.531653\pi\)
−0.0992778 + 0.995060i \(0.531653\pi\)
\(420\) −6.56978 + 4.80487i −0.320573 + 0.234454i
\(421\) 34.7493 1.69358 0.846789 0.531929i \(-0.178533\pi\)
0.846789 + 0.531929i \(0.178533\pi\)
\(422\) 17.7455i 0.863839i
\(423\) 1.60975i 0.0782686i
\(424\) −9.24977 −0.449209
\(425\) −2.90539 0.923851i −0.140932 0.0448134i
\(426\) −14.1698 −0.686531
\(427\) 5.29473i 0.256230i
\(428\) 13.9045i 0.672098i
\(429\) 9.79518 0.472916
\(430\) 21.6850 15.8595i 1.04574 0.764814i
\(431\) −9.68120 −0.466327 −0.233163 0.972438i \(-0.574908\pi\)
−0.233163 + 0.972438i \(0.574908\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 23.7346i 1.14061i −0.821432 0.570307i \(-0.806824\pi\)
0.821432 0.570307i \(-0.193176\pi\)
\(434\) −20.9844 −1.00728
\(435\) 10.7649 + 14.7190i 0.516138 + 0.705724i
\(436\) −6.85952 −0.328511
\(437\) 30.5445i 1.46114i
\(438\) 6.76491i 0.323240i
\(439\) −7.49576 −0.357753 −0.178877 0.983872i \(-0.557246\pi\)
−0.178877 + 0.983872i \(0.557246\pi\)
\(440\) 6.08492 + 8.32001i 0.290087 + 0.396641i
\(441\) 6.24977 0.297608
\(442\) 1.29564i 0.0616275i
\(443\) 27.1202i 1.28852i 0.764807 + 0.644260i \(0.222834\pi\)
−0.764807 + 0.644260i \(0.777166\pi\)
\(444\) 1.00000 0.0474579
\(445\) −18.7249 + 13.6947i −0.887647 + 0.649190i
\(446\) −5.20482 −0.246455
\(447\) 19.8401i 0.938406i
\(448\) 3.64002i 0.171975i
\(449\) 33.2489 1.56911 0.784555 0.620059i \(-0.212891\pi\)
0.784555 + 0.620059i \(0.212891\pi\)
\(450\) −4.76491 1.51514i −0.224620 0.0714243i
\(451\) 52.4343 2.46903
\(452\) 10.9844i 0.516663i
\(453\) 6.59507i 0.309863i
\(454\) 16.3856 0.769012
\(455\) 13.9600 10.2098i 0.654457 0.478643i
\(456\) −3.48486 −0.163194
\(457\) 37.2635i 1.74311i 0.490294 + 0.871557i \(0.336890\pi\)
−0.490294 + 0.871557i \(0.663110\pi\)
\(458\) 20.6694i 0.965817i
\(459\) −0.609747 −0.0284606
\(460\) 11.5698 + 15.8196i 0.539444 + 0.737590i
\(461\) −23.5151 −1.09521 −0.547605 0.836737i \(-0.684460\pi\)
−0.547605 + 0.836737i \(0.684460\pi\)
\(462\) 16.7796i 0.780657i
\(463\) 32.4196i 1.50667i −0.657639 0.753334i \(-0.728445\pi\)
0.657639 0.753334i \(-0.271555\pi\)
\(464\) 8.15516 0.378594
\(465\) −7.60975 10.4049i −0.352894 0.482517i
\(466\) −3.28005 −0.151945
\(467\) 33.6244i 1.55595i 0.628293 + 0.777976i \(0.283754\pi\)
−0.628293 + 0.777976i \(0.716246\pi\)
\(468\) 2.12489i 0.0982229i
\(469\) 13.6509 0.630341
\(470\) 2.90539 2.12489i 0.134016 0.0980137i
\(471\) −10.6741 −0.491836
\(472\) 3.67030i 0.168939i
\(473\) 55.3846i 2.54659i
\(474\) −6.64002 −0.304986
\(475\) −5.28005 + 16.6050i −0.242265 + 0.761892i
\(476\) 2.21949 0.101730
\(477\) 9.24977i 0.423518i
\(478\) 23.3553i 1.06825i
\(479\) −13.7952 −0.630318 −0.315159 0.949039i \(-0.602058\pi\)
−0.315159 + 0.949039i \(0.602058\pi\)
\(480\) −1.80487 + 1.32001i −0.0823808 + 0.0602500i
\(481\) −2.12489 −0.0968864
\(482\) 11.7309i 0.534326i
\(483\) 31.9045i 1.45170i
\(484\) −10.2498 −0.465899
\(485\) 21.9045 + 29.9503i 0.994631 + 1.35998i
\(486\) −1.00000 −0.0453609
\(487\) 9.03028i 0.409201i 0.978846 + 0.204600i \(0.0655895\pi\)
−0.978846 + 0.204600i \(0.934411\pi\)
\(488\) 1.45459i 0.0658460i
\(489\) 7.00000 0.316551
\(490\) −8.24977 11.2800i −0.372687 0.509581i
\(491\) −27.3737 −1.23536 −0.617680 0.786430i \(-0.711927\pi\)
−0.617680 + 0.786430i \(0.711927\pi\)
\(492\) 11.3747i 0.512809i
\(493\) 4.97259i 0.223954i
\(494\) 7.40493 0.333164
\(495\) 8.32001 6.08492i 0.373957 0.273497i
\(496\) −5.76491 −0.258852
\(497\) 51.5786i 2.31361i
\(498\) 2.90539i 0.130194i
\(499\) −0.333481 −0.0149287 −0.00746434 0.999972i \(-0.502376\pi\)
−0.00746434 + 0.999972i \(0.502376\pi\)
\(500\) 3.55510 + 10.6001i 0.158989 + 0.474049i
\(501\) −3.17454 −0.141828
\(502\) 18.6888i 0.834120i
\(503\) 12.4390i 0.554627i −0.960779 0.277314i \(-0.910556\pi\)
0.960779 0.277314i \(-0.0894441\pi\)
\(504\) 3.64002 0.162140
\(505\) 7.32878 5.35998i 0.326127 0.238516i
\(506\) −40.4040 −1.79618
\(507\) 8.48486i 0.376826i
\(508\) 19.6547i 0.872036i
\(509\) 36.4234 1.61444 0.807219 0.590252i \(-0.200972\pi\)
0.807219 + 0.590252i \(0.200972\pi\)
\(510\) 0.804874 + 1.10052i 0.0356404 + 0.0487317i
\(511\) 24.6244 1.08932
\(512\) 1.00000i 0.0441942i
\(513\) 3.48486i 0.153860i
\(514\) 30.1542 1.33005
\(515\) 4.14426 + 5.66652i 0.182618 + 0.249697i
\(516\) −12.0147 −0.528917
\(517\) 7.42053i 0.326354i
\(518\) 3.64002i 0.159933i
\(519\) −1.96972 −0.0864613
\(520\) 3.83515 2.80487i 0.168182 0.123002i
\(521\) 40.8733 1.79069 0.895345 0.445372i \(-0.146929\pi\)
0.895345 + 0.445372i \(0.146929\pi\)
\(522\) 8.15516i 0.356942i
\(523\) 19.4693i 0.851332i 0.904880 + 0.425666i \(0.139960\pi\)
−0.904880 + 0.425666i \(0.860040\pi\)
\(524\) 1.54920 0.0676769
\(525\) 5.51514 17.3444i 0.240700 0.756971i
\(526\) −15.3141 −0.667727
\(527\) 3.51514i 0.153122i
\(528\) 4.60975i 0.200614i
\(529\) −53.8236 −2.34016
\(530\) 16.6947 12.2098i 0.725170 0.530360i
\(531\) −3.67030 −0.159277
\(532\) 12.6850i 0.549964i
\(533\) 24.1698i 1.04691i
\(534\) 10.3747 0.448955
\(535\) −18.3541 25.0958i −0.793516 1.08499i
\(536\) 3.75023 0.161985
\(537\) 22.7493i 0.981705i
\(538\) 7.98440i 0.344232i
\(539\) 28.8099 1.24093
\(540\) 1.32001 + 1.80487i 0.0568043 + 0.0776694i
\(541\) 1.15516 0.0496643 0.0248321 0.999692i \(-0.492095\pi\)
0.0248321 + 0.999692i \(0.492095\pi\)
\(542\) 13.3094i 0.571688i
\(543\) 11.6703i 0.500820i
\(544\) 0.609747 0.0261427
\(545\) 12.3806 9.05464i 0.530325 0.387858i
\(546\) −7.73463 −0.331012
\(547\) 7.59885i 0.324903i −0.986717 0.162452i \(-0.948060\pi\)
0.986717 0.162452i \(-0.0519402\pi\)
\(548\) 16.6400i 0.710827i
\(549\) −1.45459 −0.0620802
\(550\) −21.9650 6.98440i −0.936592 0.297816i
\(551\) −28.4196 −1.21072
\(552\) 8.76491i 0.373059i
\(553\) 24.1698i 1.02781i
\(554\) 0.435208 0.0184902
\(555\) −1.80487 + 1.32001i −0.0766126 + 0.0560314i
\(556\) 3.04496 0.129135
\(557\) 3.73841i 0.158402i −0.996859 0.0792008i \(-0.974763\pi\)
0.996859 0.0792008i \(-0.0252368\pi\)
\(558\) 5.76491i 0.244048i
\(559\) 25.5298 1.07980
\(560\) −4.80487 6.56978i −0.203043 0.277624i
\(561\) −2.81078 −0.118671
\(562\) 4.65562i 0.196385i
\(563\) 23.5033i 0.990547i −0.868737 0.495273i \(-0.835068\pi\)
0.868737 0.495273i \(-0.164932\pi\)
\(564\) −1.60975 −0.0677826
\(565\) −14.4995 19.8255i −0.610000 0.834063i
\(566\) 10.2947 0.432720
\(567\) 3.64002i 0.152867i
\(568\) 14.1698i 0.594553i
\(569\) 45.2526 1.89709 0.948545 0.316644i \(-0.102556\pi\)
0.948545 + 0.316644i \(0.102556\pi\)
\(570\) 6.28974 4.60006i 0.263448 0.192675i
\(571\) 20.4655 0.856454 0.428227 0.903671i \(-0.359138\pi\)
0.428227 + 0.903671i \(0.359138\pi\)
\(572\) 9.79518i 0.409557i
\(573\) 10.2800i 0.429455i
\(574\) −41.4040 −1.72817
\(575\) −41.7640 13.2800i −1.74168 0.553816i
\(576\) 1.00000 0.0416667
\(577\) 23.7796i 0.989957i −0.868905 0.494979i \(-0.835176\pi\)
0.868905 0.494979i \(-0.164824\pi\)
\(578\) 16.6282i 0.691642i
\(579\) −6.00000 −0.249351
\(580\) −14.7190 + 10.7649i −0.611175 + 0.446989i
\(581\) −10.5757 −0.438754
\(582\) 16.5942i 0.687850i
\(583\) 42.6391i 1.76593i
\(584\) 6.76491 0.279934
\(585\) −2.80487 3.83515i −0.115967 0.158564i
\(586\) 11.9092 0.491963
\(587\) 10.8633i 0.448376i 0.974546 + 0.224188i \(0.0719730\pi\)
−0.974546 + 0.224188i \(0.928027\pi\)
\(588\) 6.24977i 0.257736i
\(589\) 20.0899 0.827790
\(590\) 4.84484 + 6.62443i 0.199459 + 0.272723i
\(591\) 22.4839 0.924866
\(592\) 1.00000i 0.0410997i
\(593\) 11.5005i 0.472267i 0.971721 + 0.236134i \(0.0758803\pi\)
−0.971721 + 0.236134i \(0.924120\pi\)
\(594\) −4.60975 −0.189140
\(595\) −4.00591 + 2.92976i −0.164226 + 0.120108i
\(596\) 19.8401 0.812684
\(597\) 26.5601i 1.08703i
\(598\) 18.6244i 0.761609i
\(599\) −32.7905 −1.33978 −0.669891 0.742459i \(-0.733659\pi\)
−0.669891 + 0.742459i \(0.733659\pi\)
\(600\) 1.51514 4.76491i 0.0618553 0.194527i
\(601\) −13.4390 −0.548188 −0.274094 0.961703i \(-0.588378\pi\)
−0.274094 + 0.961703i \(0.588378\pi\)
\(602\) 43.7337i 1.78245i
\(603\) 3.75023i 0.152721i
\(604\) −6.59507 −0.268349
\(605\) 18.4995 13.5298i 0.752113 0.550065i
\(606\) −4.06055 −0.164949
\(607\) 27.9007i 1.13245i 0.824249 + 0.566227i \(0.191597\pi\)
−0.824249 + 0.566227i \(0.808403\pi\)
\(608\) 3.48486i 0.141330i
\(609\) 29.6850 1.20290
\(610\) 1.92007 + 2.62534i 0.0777414 + 0.106297i
\(611\) 3.42053 0.138380
\(612\) 0.609747i 0.0246476i
\(613\) 27.3553i 1.10487i −0.833556 0.552435i \(-0.813699\pi\)
0.833556 0.552435i \(-0.186301\pi\)
\(614\) −13.8595 −0.559325
\(615\) −15.0147 20.5298i −0.605450 0.827842i
\(616\) 16.7796 0.676069
\(617\) 38.2985i 1.54184i −0.636932 0.770920i \(-0.719797\pi\)
0.636932 0.770920i \(-0.280203\pi\)
\(618\) 3.13957i 0.126292i
\(619\) 26.4948 1.06492 0.532459 0.846456i \(-0.321268\pi\)
0.532459 + 0.846456i \(0.321268\pi\)
\(620\) 10.4049 7.60975i 0.417872 0.305615i
\(621\) −8.76491 −0.351724
\(622\) 7.54450i 0.302507i
\(623\) 37.7640i 1.51298i
\(624\) −2.12489 −0.0850635
\(625\) −20.4087 14.4390i −0.816349 0.577560i
\(626\) −4.64002 −0.185453
\(627\) 16.0643i 0.641548i
\(628\) 10.6741i 0.425942i
\(629\) 0.609747 0.0243122
\(630\) −6.56978 + 4.80487i −0.261746 + 0.191431i
\(631\) 0.666519 0.0265337 0.0132668 0.999912i \(-0.495777\pi\)
0.0132668 + 0.999912i \(0.495777\pi\)
\(632\) 6.64002i 0.264126i
\(633\) 17.7455i 0.705322i
\(634\) −10.5142 −0.417573
\(635\) 25.9444 + 35.4743i 1.02957 + 1.40775i
\(636\) −9.24977 −0.366777
\(637\) 13.2800i 0.526175i
\(638\) 37.5932i 1.48833i
\(639\) −14.1698 −0.560550
\(640\) −1.32001 1.80487i −0.0521780 0.0713439i
\(641\) 22.5436 0.890418 0.445209 0.895427i \(-0.353129\pi\)
0.445209 + 0.895427i \(0.353129\pi\)
\(642\) 13.9045i 0.548766i
\(643\) 6.52982i 0.257511i 0.991676 + 0.128755i \(0.0410982\pi\)
−0.991676 + 0.128755i \(0.958902\pi\)
\(644\) 31.9045 1.25721
\(645\) 21.6850 15.8595i 0.853845 0.624468i
\(646\) −2.12489 −0.0836025
\(647\) 0.294727i 0.0115869i 0.999983 + 0.00579345i \(0.00184412\pi\)
−0.999983 + 0.00579345i \(0.998156\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −16.9192 −0.664135
\(650\) −3.21949 + 10.1249i −0.126279 + 0.397131i
\(651\) −20.9844 −0.822444
\(652\) 7.00000i 0.274141i
\(653\) 7.68968i 0.300920i −0.988616 0.150460i \(-0.951924\pi\)
0.988616 0.150460i \(-0.0480755\pi\)
\(654\) −6.85952 −0.268228
\(655\) −2.79610 + 2.04496i −0.109253 + 0.0799030i
\(656\) −11.3747 −0.444106
\(657\) 6.76491i 0.263924i
\(658\) 5.85952i 0.228428i
\(659\) 2.22041 0.0864949 0.0432475 0.999064i \(-0.486230\pi\)
0.0432475 + 0.999064i \(0.486230\pi\)
\(660\) 6.08492 + 8.32001i 0.236855 + 0.323856i
\(661\) 7.76869 0.302167 0.151084 0.988521i \(-0.451724\pi\)
0.151084 + 0.988521i \(0.451724\pi\)
\(662\) 1.34060i 0.0521039i
\(663\) 1.29564i 0.0503186i
\(664\) −2.90539 −0.112751
\(665\) 16.7443 + 22.8948i 0.649317 + 0.887822i
\(666\) 1.00000 0.0387492
\(667\) 71.4792i 2.76769i
\(668\) 3.17454i 0.122827i
\(669\) −5.20482 −0.201230
\(670\) −6.76869 + 4.95035i −0.261497 + 0.191249i
\(671\) −6.70527 −0.258854
\(672\) 3.64002i 0.140417i
\(673\) 10.9853i 0.423453i −0.977329 0.211726i \(-0.932091\pi\)
0.977329 0.211726i \(-0.0679086\pi\)
\(674\) 20.1055 0.774435
\(675\) −4.76491 1.51514i −0.183401 0.0583177i
\(676\) −8.48486 −0.326341
\(677\) 32.9229i 1.26533i −0.774425 0.632666i \(-0.781961\pi\)
0.774425 0.632666i \(-0.218039\pi\)
\(678\) 10.9844i 0.421853i
\(679\) 60.4031 2.31806
\(680\) −1.10052 + 0.804874i −0.0422029 + 0.0308655i
\(681\) 16.3856 0.627896
\(682\) 26.5748i 1.01760i
\(683\) 34.4343i 1.31759i −0.752322 0.658796i \(-0.771066\pi\)
0.752322 0.658796i \(-0.228934\pi\)
\(684\) −3.48486 −0.133247
\(685\) 21.9650 + 30.0331i 0.839241 + 1.14751i
\(686\) 2.73085 0.104264
\(687\) 20.6694i 0.788586i
\(688\) 12.0147i 0.458055i
\(689\) 19.6547 0.748785
\(690\) 11.5698 + 15.8196i 0.440454 + 0.602240i
\(691\) 7.02558 0.267266 0.133633 0.991031i \(-0.457336\pi\)
0.133633 + 0.991031i \(0.457336\pi\)
\(692\) 1.96972i 0.0748777i
\(693\) 16.7796i 0.637404i
\(694\) −4.70058 −0.178431
\(695\) −5.49576 + 4.01938i −0.208466 + 0.152464i
\(696\) 8.15516 0.309121
\(697\) 6.93567i 0.262707i
\(698\) 9.54920i 0.361442i
\(699\) −3.28005 −0.124063
\(700\) 17.3444 + 5.51514i 0.655556 + 0.208453i
\(701\) 19.6509 0.742205 0.371103 0.928592i \(-0.378980\pi\)
0.371103 + 0.928592i \(0.378980\pi\)
\(702\) 2.12489i 0.0801986i
\(703\) 3.48486i 0.131434i
\(704\) 4.60975 0.173736
\(705\) 2.90539 2.12489i 0.109423 0.0800278i
\(706\) −14.4537 −0.543971
\(707\) 14.7805i 0.555878i
\(708\) 3.67030i 0.137938i
\(709\) 28.7990 1.08157 0.540784 0.841162i \(-0.318128\pi\)
0.540784 + 0.841162i \(0.318128\pi\)
\(710\) 18.7044 + 25.5748i 0.701962 + 0.959804i
\(711\) −6.64002 −0.249020
\(712\) 10.3747i 0.388807i
\(713\) 50.5289i 1.89232i
\(714\) 2.21949 0.0830625
\(715\) −12.9298 17.6791i −0.483546 0.661160i
\(716\) 22.7493 0.850182
\(717\) 23.3553i 0.872219i
\(718\) 11.0790i 0.413465i
\(719\) 52.2598 1.94896 0.974480 0.224475i \(-0.0720666\pi\)
0.974480 + 0.224475i \(0.0720666\pi\)
\(720\) −1.80487 + 1.32001i −0.0672637 + 0.0491939i
\(721\) 11.4281 0.425604
\(722\) 6.85574i 0.255144i
\(723\) 11.7309i 0.436275i
\(724\) −11.6703 −0.433723
\(725\) 12.3562 38.8586i 0.458898 1.44317i
\(726\) −10.2498 −0.380405
\(727\) 20.3591i 0.755076i −0.925994 0.377538i \(-0.876771\pi\)
0.925994 0.377538i \(-0.123229\pi\)
\(728\) 7.73463i 0.286665i
\(729\) −1.00000 −0.0370370
\(730\) −12.2098 + 8.92976i −0.451905 + 0.330505i
\(731\) −7.32592 −0.270959
\(732\) 1.45459i 0.0537630i
\(733\) 22.1433i 0.817883i 0.912561 + 0.408942i \(0.134102\pi\)
−0.912561 + 0.408942i \(0.865898\pi\)
\(734\) −10.9201 −0.403067
\(735\) −8.24977 11.2800i −0.304297 0.416071i
\(736\) 8.76491 0.323079
\(737\) 17.2876i 0.636797i
\(738\) 11.3747i 0.418707i
\(739\) −34.6429 −1.27436 −0.637180 0.770715i \(-0.719899\pi\)
−0.637180 + 0.770715i \(0.719899\pi\)
\(740\) −1.32001 1.80487i −0.0485246 0.0663485i
\(741\) 7.40493 0.272027
\(742\) 33.6694i 1.23604i
\(743\) 46.4049i 1.70243i 0.524816 + 0.851216i \(0.324134\pi\)
−0.524816 + 0.851216i \(0.675866\pi\)
\(744\) −5.76491 −0.211352
\(745\) −35.8089 + 26.1892i −1.31194 + 0.959499i
\(746\) 5.92007 0.216749
\(747\) 2.90539i 0.106303i
\(748\) 2.81078i 0.102772i
\(749\) −50.6126 −1.84934
\(750\) 3.55510 + 10.6001i 0.129814 + 0.387059i
\(751\) −25.6585 −0.936291 −0.468146 0.883651i \(-0.655078\pi\)
−0.468146 + 0.883651i \(0.655078\pi\)
\(752\) 1.60975i 0.0587014i
\(753\) 18.6888i 0.681056i
\(754\) −17.3288 −0.631077
\(755\) 11.9033 8.70557i 0.433204 0.316828i
\(756\) 3.64002 0.132386
\(757\) 21.2157i 0.771098i 0.922687 + 0.385549i \(0.125988\pi\)
−0.922687 + 0.385549i \(0.874012\pi\)
\(758\) 22.5189i 0.817924i
\(759\) −40.4040 −1.46657
\(760\) 4.60006 + 6.28974i 0.166862 + 0.228153i
\(761\) −41.2654 −1.49587 −0.747934 0.663773i \(-0.768954\pi\)
−0.747934 + 0.663773i \(0.768954\pi\)
\(762\) 19.6547i 0.712015i
\(763\) 24.9688i 0.903932i
\(764\) −10.2800 −0.371919
\(765\) 0.804874 + 1.10052i 0.0291003 + 0.0397893i
\(766\) 27.2039 0.982917
\(767\) 7.79897i 0.281604i
\(768\) 1.00000i 0.0360844i
\(769\) −15.2607 −0.550314 −0.275157 0.961399i \(-0.588730\pi\)
−0.275157 + 0.961399i \(0.588730\pi\)
\(770\) −30.2850 + 22.1493i −1.09140 + 0.798204i
\(771\) 30.1542 1.08598
\(772\) 6.00000i 0.215945i
\(773\) 26.4693i 0.952033i −0.879436 0.476017i \(-0.842080\pi\)
0.879436 0.476017i \(-0.157920\pi\)
\(774\) −12.0147 −0.431859
\(775\) −8.73463 + 27.4693i −0.313757 + 0.986725i
\(776\) 16.5942 0.595695
\(777\) 3.64002i 0.130585i
\(778\) 0.295643i 0.0105993i
\(779\) 39.6391 1.42022
\(780\) 3.83515 2.80487i 0.137320 0.100431i
\(781\) −65.3194 −2.33731
\(782\) 5.34438i 0.191115i
\(783\) 8.15516i 0.291442i
\(784\) −6.24977 −0.223206
\(785\) 14.0899 + 19.2654i 0.502891 + 0.687610i
\(786\) 1.54920 0.0552580
\(787\) 37.7190i 1.34454i 0.740307 + 0.672269i \(0.234680\pi\)
−0.740307 + 0.672269i \(0.765320\pi\)
\(788\) 22.4839i 0.800957i
\(789\) −15.3141 −0.545197
\(790\) 8.76491 + 11.9844i 0.311841 + 0.426386i
\(791\) −39.9835 −1.42165
\(792\) 4.60975i 0.163800i
\(793\) 3.09083i 0.109759i
\(794\) 14.1287 0.501408
\(795\) 16.6947 12.2098i 0.592099 0.433037i
\(796\) 26.5601 0.941398
\(797\) 26.6013i 0.942265i −0.882062 0.471133i \(-0.843845\pi\)
0.882062 0.471133i \(-0.156155\pi\)
\(798\) 12.6850i 0.449043i
\(799\) −0.981539 −0.0347244
\(800\) 4.76491 + 1.51514i 0.168465 + 0.0535682i
\(801\) 10.3747 0.366570
\(802\) 17.2838i 0.610313i
\(803\) 31.1845i 1.10048i
\(804\) 3.75023 0.132260
\(805\) −57.5835 + 42.1143i −2.02955 + 1.48433i
\(806\) 12.2498 0.431480
\(807\) 7.98440i 0.281064i
\(808\) 4.06055i 0.142850i
\(809\) 39.7834 1.39871 0.699354 0.714775i \(-0.253471\pi\)
0.699354 + 0.714775i \(0.253471\pi\)
\(810\) 1.32001 + 1.80487i 0.0463805 + 0.0634168i
\(811\) −3.62156 −0.127170 −0.0635851 0.997976i \(-0.520253\pi\)
−0.0635851 + 0.997976i \(0.520253\pi\)
\(812\) 29.6850i 1.04174i
\(813\) 13.3094i 0.466781i
\(814\) 4.60975 0.161572
\(815\) −9.24008 12.6341i −0.323666 0.442554i
\(816\) 0.609747 0.0213454
\(817\) 41.8695i 1.46483i
\(818\) 5.73085i 0.200375i
\(819\) −7.73463 −0.270270
\(820\) 20.5298 15.0147i 0.716932 0.524335i
\(821\) 29.4537 1.02794 0.513970 0.857808i \(-0.328174\pi\)
0.513970 + 0.857808i \(0.328174\pi\)
\(822\) 16.6400i 0.580387i
\(823\) 31.6159i 1.10206i −0.834485 0.551031i \(-0.814234\pi\)
0.834485 0.551031i \(-0.185766\pi\)
\(824\) 3.13957 0.109372
\(825\) −21.9650 6.98440i −0.764724 0.243166i
\(826\) 13.3600 0.464853
\(827\) 27.3359i 0.950562i 0.879834 + 0.475281i \(0.157654\pi\)
−0.879834 + 0.475281i \(0.842346\pi\)
\(828\) 8.76491i 0.304602i
\(829\) −14.6391 −0.508437 −0.254219 0.967147i \(-0.581818\pi\)
−0.254219 + 0.967147i \(0.581818\pi\)
\(830\) 5.24386 3.83515i 0.182017 0.133120i
\(831\) 0.435208 0.0150972
\(832\) 2.12489i 0.0736671i
\(833\) 3.81078i 0.132036i
\(834\) 3.04496 0.105438
\(835\) 4.19043 + 5.72964i 0.145016 + 0.198282i
\(836\) −16.0643 −0.555597
\(837\) 5.76491i 0.199264i
\(838\) 4.06433i 0.140400i
\(839\) −16.1386 −0.557168 −0.278584 0.960412i \(-0.589865\pi\)
−0.278584 + 0.960412i \(0.589865\pi\)
\(840\) −4.80487 6.56978i −0.165784 0.226679i
\(841\) 37.5067 1.29333
\(842\) 34.7493i 1.19754i
\(843\) 4.65562i 0.160348i
\(844\) −17.7455 −0.610826
\(845\) 15.3141 11.2001i 0.526821 0.385296i
\(846\) −1.60975 −0.0553443
\(847\) 37.3094i 1.28197i
\(848\) 9.24977i 0.317638i
\(849\) 10.2947 0.353314
\(850\) 0.923851 2.90539i 0.0316878 0.0996541i
\(851\) 8.76491 0.300457
\(852\) 14.1698i 0.485451i
\(853\) 9.44369i 0.323346i 0.986844 + 0.161673i \(0.0516889\pi\)
−0.986844 + 0.161673i \(0.948311\pi\)
\(854\) 5.29473 0.181182
\(855\) 6.28974 4.60006i 0.215104 0.157319i
\(856\) −13.9045 −0.475245
\(857\) 40.0091i 1.36668i 0.730099 + 0.683342i \(0.239474\pi\)
−0.730099 + 0.683342i \(0.760526\pi\)
\(858\) 9.79518i 0.334402i
\(859\) −24.5739 −0.838449 −0.419225 0.907883i \(-0.637698\pi\)
−0.419225 + 0.907883i \(0.637698\pi\)
\(860\) 15.8595 + 21.6850i 0.540805 + 0.739452i
\(861\) −41.4040 −1.41105
\(862\) 9.68120i 0.329743i
\(863\) 2.43613i 0.0829267i −0.999140 0.0414633i \(-0.986798\pi\)
0.999140 0.0414633i \(-0.0132020\pi\)
\(864\) 1.00000 0.0340207
\(865\) 2.60006 + 3.55510i 0.0884046 + 0.120877i
\(866\) 23.7346 0.806536
\(867\) 16.6282i 0.564724i
\(868\) 20.9844i 0.712257i
\(869\) −30.6088 −1.03833
\(870\) −14.7190 + 10.7649i −0.499022 + 0.364965i
\(871\) −7.96881 −0.270013
\(872\) 6.85952i 0.232293i
\(873\) 16.5942i 0.561627i
\(874\) −30.5445 −1.03318
\(875\) −38.5845 + 12.9407i −1.30439 + 0.437474i
\(876\) 6.76491 0.228565
\(877\) 13.0861i 0.441887i −0.975287 0.220944i \(-0.929086\pi\)
0.975287 0.220944i \(-0.0709137\pi\)
\(878\) 7.49576i 0.252970i
\(879\) 11.9092 0.401686
\(880\) −8.32001 + 6.08492i −0.280468 + 0.205123i
\(881\) −38.8539 −1.30902 −0.654511 0.756053i \(-0.727125\pi\)
−0.654511 + 0.756053i \(0.727125\pi\)
\(882\) 6.24977i 0.210441i
\(883\) 9.40023i 0.316343i 0.987412 + 0.158172i \(0.0505599\pi\)
−0.987412 + 0.158172i \(0.949440\pi\)
\(884\) −1.29564 −0.0435772
\(885\) 4.84484 + 6.62443i 0.162857 + 0.222678i
\(886\) −27.1202 −0.911121
\(887\) 23.0156i 0.772788i −0.922334 0.386394i \(-0.873720\pi\)
0.922334 0.386394i \(-0.126280\pi\)
\(888\) 1.00000i 0.0335578i
\(889\) 71.5436 2.39949
\(890\) −13.6947 18.7249i −0.459046 0.627662i
\(891\) −4.60975 −0.154432
\(892\) 5.20482i 0.174270i
\(893\) 5.60975i 0.187723i
\(894\) 19.8401 0.663554
\(895\) −41.0596 + 30.0294i −1.37247 + 1.00377i
\(896\) −3.64002 −0.121605
\(897\) 18.6244i 0.621852i
\(898\) 33.2489i 1.10953i
\(899\) −47.0138 −1.56800
\(900\) 1.51514 4.76491i 0.0505046 0.158830i
\(901\) −5.64002 −0.187896
\(902\) 52.4343i 1.74587i
\(903\) 43.7337i 1.45537i
\(904\) −10.9844 −0.365336
\(905\) 21.0634 15.4049i 0.700172 0.512077i
\(906\) −6.59507 −0.219106
\(907\) 24.8860i 0.826327i −0.910657 0.413163i \(-0.864424\pi\)
0.910657 0.413163i \(-0.135576\pi\)
\(908\) 16.3856i 0.543774i
\(909\) −4.06055 −0.134680
\(910\) 10.2098 + 13.9600i 0.338452 + 0.462771i
\(911\) −5.49863 −0.182178 −0.0910888 0.995843i \(-0.529035\pi\)
−0.0910888 + 0.995843i \(0.529035\pi\)
\(912\) 3.48486i 0.115395i
\(913\) 13.3931i 0.443247i
\(914\) −37.2635 −1.23257
\(915\) 1.92007 + 2.62534i 0.0634756 + 0.0867912i
\(916\) −20.6694 −0.682936
\(917\) 5.63911i 0.186220i
\(918\) 0.609747i 0.0201247i
\(919\) 29.0790 0.959228 0.479614 0.877480i \(-0.340777\pi\)
0.479614 + 0.877480i \(0.340777\pi\)
\(920\) −15.8196 + 11.5698i −0.521555 + 0.381444i
\(921\) −13.8595 −0.456687
\(922\) 23.5151i 0.774430i
\(923\) 30.1093i 0.991059i
\(924\) 16.7796 0.552008
\(925\) 4.76491 + 1.51514i 0.156669 + 0.0498174i
\(926\) 32.4196 1.06537
\(927\) 3.13957i 0.103117i
\(928\) 8.15516i 0.267706i
\(929\) 48.3931 1.58773 0.793863 0.608096i \(-0.208067\pi\)
0.793863 + 0.608096i \(0.208067\pi\)
\(930\) 10.4049 7.60975i 0.341191 0.249533i
\(931\) 21.7796 0.713797
\(932\) 3.28005i 0.107442i
\(933\) 7.54450i 0.246996i
\(934\) −33.6244 −1.10022
\(935\) 3.71026 + 5.07311i 0.121339 + 0.165908i
\(936\) −2.12489 −0.0694541
\(937\) 13.4399i 0.439063i −0.975605 0.219531i \(-0.929547\pi\)
0.975605 0.219531i \(-0.0704528\pi\)
\(938\) 13.6509i 0.445718i
\(939\) −4.64002 −0.151421
\(940\) 2.12489 + 2.90539i 0.0693061 + 0.0947634i
\(941\) −29.3482 −0.956723 −0.478361 0.878163i \(-0.658769\pi\)
−0.478361 + 0.878163i \(0.658769\pi\)
\(942\) 10.6741i 0.347780i
\(943\) 99.6978i 3.24661i
\(944\) 3.67030 0.119458
\(945\) −6.56978 + 4.80487i −0.213715 + 0.156303i
\(946\) −55.3846 −1.80071
\(947\) 21.3435i 0.693569i −0.937945 0.346785i \(-0.887273\pi\)
0.937945 0.346785i \(-0.112727\pi\)
\(948\) 6.64002i 0.215658i
\(949\) −14.3747 −0.466621
\(950\) −16.6050 5.28005i −0.538739 0.171307i
\(951\) −10.5142 −0.340947
\(952\) 2.21949i 0.0719342i
\(953\) 19.2389i 0.623208i −0.950212 0.311604i \(-0.899134\pi\)
0.950212 0.311604i \(-0.100866\pi\)
\(954\) −9.24977 −0.299472
\(955\) 18.5542 13.5698i 0.600399 0.439108i
\(956\) −23.3553 −0.755364
\(957\) 37.5932i 1.21522i
\(958\) 13.7952i 0.445702i
\(959\) 60.5701 1.95591
\(960\) −1.32001 1.80487i −0.0426032 0.0582520i
\(961\) 2.23417 0.0720701
\(962\) 2.12489i 0.0685091i
\(963\) 13.9045i 0.448065i
\(964\) 11.7309 0.377825
\(965\) 7.92007 + 10.8292i 0.254956 + 0.348606i
\(966\) 31.9045 1.02651
\(967\) 21.8813i 0.703656i −0.936065 0.351828i \(-0.885560\pi\)
0.936065 0.351828i \(-0.114440\pi\)
\(968\) 10.2498i 0.329440i
\(969\) −2.12489 −0.0682612
\(970\) −29.9503 + 21.9045i −0.961648 + 0.703310i
\(971\) −49.8236 −1.59892 −0.799458 0.600722i \(-0.794880\pi\)
−0.799458 + 0.600722i \(0.794880\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 11.0837i 0.355327i
\(974\) −9.03028 −0.289349
\(975\) −3.21949 + 10.1249i −0.103106 + 0.324256i
\(976\) 1.45459 0.0465602
\(977\) 1.98910i 0.0636370i 0.999494 + 0.0318185i \(0.0101299\pi\)
−0.999494 + 0.0318185i \(0.989870\pi\)
\(978\) 7.00000i 0.223835i
\(979\) 47.8245 1.52848
\(980\) 11.2800 8.24977i 0.360328 0.263529i
\(981\) −6.85952 −0.219008
\(982\) 27.3737i 0.873531i
\(983\) 35.6950i 1.13849i −0.822167 0.569246i \(-0.807235\pi\)
0.822167 0.569246i \(-0.192765\pi\)
\(984\) −11.3747 −0.362611
\(985\) −29.6791 40.5807i −0.945654 1.29301i
\(986\) 4.97259 0.158359
\(987\) 5.85952i 0.186511i
\(988\) 7.40493i 0.235582i
\(989\) −105.308 −3.34859
\(990\) 6.08492 + 8.32001i 0.193391 + 0.264427i
\(991\) 50.2333 1.59571 0.797856 0.602848i \(-0.205967\pi\)
0.797856 + 0.602848i \(0.205967\pi\)
\(992\) 5.76491i 0.183036i
\(993\) 1.34060i 0.0425426i
\(994\) 51.5786 1.63597
\(995\) −47.9376 + 35.0596i −1.51972 + 1.11147i
\(996\) −2.90539 −0.0920608
\(997\) 36.9036i 1.16875i 0.811485 + 0.584374i \(0.198660\pi\)
−0.811485 + 0.584374i \(0.801340\pi\)
\(998\) 0.333481i 0.0105562i
\(999\) 1.00000 0.0316386
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 1110.2.d.i.889.6 yes 6
3.2 odd 2 3330.2.d.n.1999.1 6
5.2 odd 4 5550.2.a.cf.1.3 3
5.3 odd 4 5550.2.a.cg.1.1 3
5.4 even 2 inner 1110.2.d.i.889.3 6
15.14 odd 2 3330.2.d.n.1999.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.d.i.889.3 6 5.4 even 2 inner
1110.2.d.i.889.6 yes 6 1.1 even 1 trivial
3330.2.d.n.1999.1 6 3.2 odd 2
3330.2.d.n.1999.4 6 15.14 odd 2
5550.2.a.cf.1.3 3 5.2 odd 4
5550.2.a.cg.1.1 3 5.3 odd 4