Properties

Label 1890.2.t.b.1151.1
Level $1890$
Weight $2$
Character 1890.1151
Analytic conductor $15.092$
Analytic rank $0$
Dimension $28$
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] = [1890,2,Mod(1151,1890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(15.0917259820\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.1
Character \(\chi\) \(=\) 1890.1151
Dual form 1890.2.t.b.1601.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.555567 - 2.58676i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.555567 - 2.58676i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +4.07809i q^{11} +(-5.20173 - 3.00322i) q^{13} +(-0.812247 + 2.51799i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.641724 - 1.11150i) q^{17} +(2.90701 - 1.67836i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.03904 - 3.53173i) q^{22} -2.18864i q^{23} +1.00000 q^{25} +(3.00322 + 5.20173i) q^{26} +(1.96242 - 1.77452i) q^{28} +(-6.21856 + 3.59029i) q^{29} +(-6.79271 + 3.92178i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.11150 + 0.641724i) q^{34} +(-0.555567 - 2.58676i) q^{35} +(-2.90160 - 5.02572i) q^{37} -3.35672 q^{38} -1.00000i q^{40} +(-1.36925 + 2.37162i) q^{41} +(-2.43768 - 4.22219i) q^{43} +(-3.53173 + 2.03904i) q^{44} +(-1.09432 + 1.89542i) q^{46} +(-4.13613 + 7.16398i) q^{47} +(-6.38269 + 2.87424i) q^{49} +(-0.866025 - 0.500000i) q^{50} -6.00644i q^{52} +(7.48689 + 4.32256i) q^{53} +4.07809i q^{55} +(-2.58676 + 0.555567i) q^{56} +7.18058 q^{58} +(0.630579 + 1.09220i) q^{59} +(-2.56956 - 1.48353i) q^{61} +7.84355 q^{62} -1.00000 q^{64} +(-5.20173 - 3.00322i) q^{65} +(4.31098 + 7.46684i) q^{67} +1.28345 q^{68} +(-0.812247 + 2.51799i) q^{70} -14.1375i q^{71} +(-6.02332 - 3.47757i) q^{73} +5.80320i q^{74} +(2.90701 + 1.67836i) q^{76} +(10.5490 - 2.26565i) q^{77} +(6.09277 - 10.5530i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.37162 - 1.36925i) q^{82} +(-6.87948 - 11.9156i) q^{83} +(0.641724 - 1.11150i) q^{85} +4.87537i q^{86} +4.07809 q^{88} +(7.29497 + 12.6353i) q^{89} +(-4.87871 + 15.1241i) q^{91} +(1.89542 - 1.09432i) q^{92} +(7.16398 - 4.13613i) q^{94} +(2.90701 - 1.67836i) q^{95} +(-16.8723 + 9.74120i) q^{97} +(6.96469 + 0.702180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(1081\) \(1541\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.555567 2.58676i −0.209985 0.977705i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) 4.07809i 1.22959i 0.788687 + 0.614795i \(0.210761\pi\)
−0.788687 + 0.614795i \(0.789239\pi\)
\(12\) 0 0
\(13\) −5.20173 3.00322i −1.44270 0.832943i −0.444671 0.895694i \(-0.646679\pi\)
−0.998029 + 0.0627507i \(0.980013\pi\)
\(14\) −0.812247 + 2.51799i −0.217082 + 0.672960i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.641724 1.11150i 0.155641 0.269578i −0.777651 0.628696i \(-0.783589\pi\)
0.933292 + 0.359118i \(0.116922\pi\)
\(18\) 0 0
\(19\) 2.90701 1.67836i 0.666913 0.385043i −0.127993 0.991775i \(-0.540853\pi\)
0.794906 + 0.606733i \(0.207520\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 2.03904 3.53173i 0.434726 0.752967i
\(23\) 2.18864i 0.456363i −0.973619 0.228182i \(-0.926722\pi\)
0.973619 0.228182i \(-0.0732780\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 3.00322 + 5.20173i 0.588980 + 1.02014i
\(27\) 0 0
\(28\) 1.96242 1.77452i 0.370862 0.335352i
\(29\) −6.21856 + 3.59029i −1.15476 + 0.666700i −0.950042 0.312122i \(-0.898960\pi\)
−0.204716 + 0.978821i \(0.565627\pi\)
\(30\) 0 0
\(31\) −6.79271 + 3.92178i −1.22001 + 0.704372i −0.964919 0.262546i \(-0.915438\pi\)
−0.255088 + 0.966918i \(0.582104\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −1.11150 + 0.641724i −0.190621 + 0.110055i
\(35\) −0.555567 2.58676i −0.0939079 0.437243i
\(36\) 0 0
\(37\) −2.90160 5.02572i −0.477020 0.826223i 0.522633 0.852558i \(-0.324950\pi\)
−0.999653 + 0.0263347i \(0.991616\pi\)
\(38\) −3.35672 −0.544532
\(39\) 0 0
\(40\) 1.00000i 0.158114i
\(41\) −1.36925 + 2.37162i −0.213842 + 0.370384i −0.952914 0.303242i \(-0.901931\pi\)
0.739072 + 0.673626i \(0.235264\pi\)
\(42\) 0 0
\(43\) −2.43768 4.22219i −0.371743 0.643878i 0.618091 0.786107i \(-0.287906\pi\)
−0.989834 + 0.142229i \(0.954573\pi\)
\(44\) −3.53173 + 2.03904i −0.532428 + 0.307397i
\(45\) 0 0
\(46\) −1.09432 + 1.89542i −0.161349 + 0.279464i
\(47\) −4.13613 + 7.16398i −0.603316 + 1.04497i 0.388999 + 0.921238i \(0.372821\pi\)
−0.992315 + 0.123736i \(0.960512\pi\)
\(48\) 0 0
\(49\) −6.38269 + 2.87424i −0.911813 + 0.410606i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 0 0
\(52\) 6.00644i 0.832943i
\(53\) 7.48689 + 4.32256i 1.02840 + 0.593749i 0.916527 0.399973i \(-0.130980\pi\)
0.111877 + 0.993722i \(0.464314\pi\)
\(54\) 0 0
\(55\) 4.07809i 0.549889i
\(56\) −2.58676 + 0.555567i −0.345671 + 0.0742407i
\(57\) 0 0
\(58\) 7.18058 0.942856
\(59\) 0.630579 + 1.09220i 0.0820944 + 0.142192i 0.904149 0.427216i \(-0.140506\pi\)
−0.822055 + 0.569408i \(0.807172\pi\)
\(60\) 0 0
\(61\) −2.56956 1.48353i −0.328998 0.189947i 0.326398 0.945232i \(-0.394165\pi\)
−0.655396 + 0.755285i \(0.727498\pi\)
\(62\) 7.84355 0.996132
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −5.20173 3.00322i −0.645195 0.372504i
\(66\) 0 0
\(67\) 4.31098 + 7.46684i 0.526670 + 0.912220i 0.999517 + 0.0310753i \(0.00989316\pi\)
−0.472847 + 0.881145i \(0.656774\pi\)
\(68\) 1.28345 0.155641
\(69\) 0 0
\(70\) −0.812247 + 2.51799i −0.0970821 + 0.300957i
\(71\) 14.1375i 1.67781i −0.544277 0.838906i \(-0.683196\pi\)
0.544277 0.838906i \(-0.316804\pi\)
\(72\) 0 0
\(73\) −6.02332 3.47757i −0.704977 0.407018i 0.104222 0.994554i \(-0.466765\pi\)
−0.809198 + 0.587536i \(0.800098\pi\)
\(74\) 5.80320i 0.674608i
\(75\) 0 0
\(76\) 2.90701 + 1.67836i 0.333457 + 0.192521i
\(77\) 10.5490 2.26565i 1.20218 0.258195i
\(78\) 0 0
\(79\) 6.09277 10.5530i 0.685490 1.18730i −0.287793 0.957693i \(-0.592921\pi\)
0.973283 0.229610i \(-0.0737452\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 2.37162 1.36925i 0.261901 0.151209i
\(83\) −6.87948 11.9156i −0.755121 1.30791i −0.945314 0.326161i \(-0.894245\pi\)
0.190194 0.981747i \(-0.439088\pi\)
\(84\) 0 0
\(85\) 0.641724 1.11150i 0.0696048 0.120559i
\(86\) 4.87537i 0.525724i
\(87\) 0 0
\(88\) 4.07809 0.434726
\(89\) 7.29497 + 12.6353i 0.773265 + 1.33933i 0.935764 + 0.352626i \(0.114711\pi\)
−0.162499 + 0.986709i \(0.551955\pi\)
\(90\) 0 0
\(91\) −4.87871 + 15.1241i −0.511428 + 1.58544i
\(92\) 1.89542 1.09432i 0.197611 0.114091i
\(93\) 0 0
\(94\) 7.16398 4.13613i 0.738908 0.426609i
\(95\) 2.90701 1.67836i 0.298253 0.172196i
\(96\) 0 0
\(97\) −16.8723 + 9.74120i −1.71312 + 0.989069i −0.782832 + 0.622233i \(0.786226\pi\)
−0.930285 + 0.366837i \(0.880441\pi\)
\(98\) 6.96469 + 0.702180i 0.703540 + 0.0709309i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −8.53717 −0.849480 −0.424740 0.905315i \(-0.639635\pi\)
−0.424740 + 0.905315i \(0.639635\pi\)
\(102\) 0 0
\(103\) 3.61248i 0.355948i 0.984035 + 0.177974i \(0.0569543\pi\)
−0.984035 + 0.177974i \(0.943046\pi\)
\(104\) −3.00322 + 5.20173i −0.294490 + 0.510072i
\(105\) 0 0
\(106\) −4.32256 7.48689i −0.419844 0.727191i
\(107\) −11.5596 + 6.67392i −1.11751 + 0.645192i −0.940763 0.339065i \(-0.889889\pi\)
−0.176743 + 0.984257i \(0.556556\pi\)
\(108\) 0 0
\(109\) 5.38583 9.32854i 0.515869 0.893512i −0.483961 0.875090i \(-0.660802\pi\)
0.999830 0.0184222i \(-0.00586429\pi\)
\(110\) 2.03904 3.53173i 0.194415 0.336737i
\(111\) 0 0
\(112\) 2.51799 + 0.812247i 0.237927 + 0.0767501i
\(113\) 2.45659 + 1.41832i 0.231097 + 0.133424i 0.611078 0.791570i \(-0.290736\pi\)
−0.379981 + 0.924994i \(0.624070\pi\)
\(114\) 0 0
\(115\) 2.18864i 0.204092i
\(116\) −6.21856 3.59029i −0.577379 0.333350i
\(117\) 0 0
\(118\) 1.26116i 0.116099i
\(119\) −3.23171 1.04248i −0.296250 0.0955637i
\(120\) 0 0
\(121\) −5.63079 −0.511890
\(122\) 1.48353 + 2.56956i 0.134313 + 0.232637i
\(123\) 0 0
\(124\) −6.79271 3.92178i −0.610004 0.352186i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −10.9625 −0.972768 −0.486384 0.873745i \(-0.661684\pi\)
−0.486384 + 0.873745i \(0.661684\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 3.00322 + 5.20173i 0.263400 + 0.456222i
\(131\) −20.7312 −1.81129 −0.905647 0.424032i \(-0.860614\pi\)
−0.905647 + 0.424032i \(0.860614\pi\)
\(132\) 0 0
\(133\) −5.95656 6.58730i −0.516499 0.571191i
\(134\) 8.62197i 0.744825i
\(135\) 0 0
\(136\) −1.11150 0.641724i −0.0953103 0.0550274i
\(137\) 9.67432i 0.826533i −0.910610 0.413267i \(-0.864388\pi\)
0.910610 0.413267i \(-0.135612\pi\)
\(138\) 0 0
\(139\) −4.57137 2.63928i −0.387739 0.223861i 0.293441 0.955977i \(-0.405200\pi\)
−0.681180 + 0.732116i \(0.738533\pi\)
\(140\) 1.96242 1.77452i 0.165855 0.149974i
\(141\) 0 0
\(142\) −7.06874 + 12.2434i −0.593196 + 1.02745i
\(143\) 12.2474 21.2131i 1.02418 1.77393i
\(144\) 0 0
\(145\) −6.21856 + 3.59029i −0.516423 + 0.298157i
\(146\) 3.47757 + 6.02332i 0.287806 + 0.498494i
\(147\) 0 0
\(148\) 2.90160 5.02572i 0.238510 0.413112i
\(149\) 4.37779i 0.358642i 0.983791 + 0.179321i \(0.0573901\pi\)
−0.983791 + 0.179321i \(0.942610\pi\)
\(150\) 0 0
\(151\) −5.57316 −0.453538 −0.226769 0.973949i \(-0.572816\pi\)
−0.226769 + 0.973949i \(0.572816\pi\)
\(152\) −1.67836 2.90701i −0.136133 0.235789i
\(153\) 0 0
\(154\) −10.2686 3.31241i −0.827465 0.266922i
\(155\) −6.79271 + 3.92178i −0.545604 + 0.315005i
\(156\) 0 0
\(157\) −0.243649 + 0.140671i −0.0194453 + 0.0112267i −0.509691 0.860357i \(-0.670240\pi\)
0.490246 + 0.871584i \(0.336907\pi\)
\(158\) −10.5530 + 6.09277i −0.839550 + 0.484714i
\(159\) 0 0
\(160\) 0.866025 0.500000i 0.0684653 0.0395285i
\(161\) −5.66149 + 1.21594i −0.446188 + 0.0958292i
\(162\) 0 0
\(163\) −3.76577 6.52251i −0.294958 0.510882i 0.680017 0.733196i \(-0.261972\pi\)
−0.974975 + 0.222314i \(0.928639\pi\)
\(164\) −2.73851 −0.213842
\(165\) 0 0
\(166\) 13.7590i 1.06790i
\(167\) 4.87241 8.43926i 0.377039 0.653050i −0.613591 0.789624i \(-0.710276\pi\)
0.990630 + 0.136574i \(0.0436091\pi\)
\(168\) 0 0
\(169\) 11.5387 + 19.9855i 0.887589 + 1.53735i
\(170\) −1.11150 + 0.641724i −0.0852481 + 0.0492180i
\(171\) 0 0
\(172\) 2.43768 4.22219i 0.185872 0.321939i
\(173\) −7.13345 + 12.3555i −0.542346 + 0.939370i 0.456423 + 0.889763i \(0.349130\pi\)
−0.998769 + 0.0496076i \(0.984203\pi\)
\(174\) 0 0
\(175\) −0.555567 2.58676i −0.0419969 0.195541i
\(176\) −3.53173 2.03904i −0.266214 0.153699i
\(177\) 0 0
\(178\) 14.5899i 1.09356i
\(179\) −7.42444 4.28650i −0.554928 0.320388i 0.196179 0.980568i \(-0.437147\pi\)
−0.751107 + 0.660180i \(0.770480\pi\)
\(180\) 0 0
\(181\) 1.70947i 0.127064i 0.997980 + 0.0635319i \(0.0202365\pi\)
−0.997980 + 0.0635319i \(0.979764\pi\)
\(182\) 11.7872 10.6585i 0.873722 0.790063i
\(183\) 0 0
\(184\) −2.18864 −0.161349
\(185\) −2.90160 5.02572i −0.213330 0.369498i
\(186\) 0 0
\(187\) 4.53279 + 2.61701i 0.331470 + 0.191375i
\(188\) −8.27225 −0.603316
\(189\) 0 0
\(190\) −3.35672 −0.243522
\(191\) 8.02069 + 4.63075i 0.580357 + 0.335069i 0.761275 0.648429i \(-0.224574\pi\)
−0.180918 + 0.983498i \(0.557907\pi\)
\(192\) 0 0
\(193\) 12.1247 + 21.0006i 0.872756 + 1.51166i 0.859134 + 0.511751i \(0.171003\pi\)
0.0136221 + 0.999907i \(0.495664\pi\)
\(194\) 19.4824 1.39875
\(195\) 0 0
\(196\) −5.68051 4.09045i −0.405751 0.292175i
\(197\) 18.8947i 1.34619i 0.739554 + 0.673097i \(0.235036\pi\)
−0.739554 + 0.673097i \(0.764964\pi\)
\(198\) 0 0
\(199\) 2.25502 + 1.30194i 0.159854 + 0.0922919i 0.577793 0.816183i \(-0.303914\pi\)
−0.417939 + 0.908475i \(0.637247\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 7.39341 + 4.26859i 0.520198 + 0.300337i
\(203\) 12.7421 + 14.0913i 0.894317 + 0.989016i
\(204\) 0 0
\(205\) −1.36925 + 2.37162i −0.0956329 + 0.165641i
\(206\) 1.80624 3.12850i 0.125847 0.217973i
\(207\) 0 0
\(208\) 5.20173 3.00322i 0.360675 0.208236i
\(209\) 6.84450 + 11.8550i 0.473444 + 0.820029i
\(210\) 0 0
\(211\) −3.12513 + 5.41288i −0.215143 + 0.372638i −0.953317 0.301972i \(-0.902355\pi\)
0.738174 + 0.674610i \(0.235688\pi\)
\(212\) 8.64512i 0.593749i
\(213\) 0 0
\(214\) 13.3478 0.912440
\(215\) −2.43768 4.22219i −0.166249 0.287951i
\(216\) 0 0
\(217\) 13.9185 + 15.3923i 0.944850 + 1.04490i
\(218\) −9.32854 + 5.38583i −0.631808 + 0.364775i
\(219\) 0 0
\(220\) −3.53173 + 2.03904i −0.238109 + 0.137472i
\(221\) −6.67615 + 3.85448i −0.449087 + 0.259280i
\(222\) 0 0
\(223\) 4.24320 2.44981i 0.284145 0.164051i −0.351153 0.936318i \(-0.614210\pi\)
0.635299 + 0.772267i \(0.280877\pi\)
\(224\) −1.77452 1.96242i −0.118565 0.131120i
\(225\) 0 0
\(226\) −1.41832 2.45659i −0.0943449 0.163410i
\(227\) −17.4808 −1.16024 −0.580121 0.814531i \(-0.696995\pi\)
−0.580121 + 0.814531i \(0.696995\pi\)
\(228\) 0 0
\(229\) 14.5924i 0.964292i −0.876091 0.482146i \(-0.839857\pi\)
0.876091 0.482146i \(-0.160143\pi\)
\(230\) −1.09432 + 1.89542i −0.0721573 + 0.124980i
\(231\) 0 0
\(232\) 3.59029 + 6.21856i 0.235714 + 0.408269i
\(233\) −3.42360 + 1.97662i −0.224288 + 0.129493i −0.607934 0.793988i \(-0.708002\pi\)
0.383646 + 0.923480i \(0.374668\pi\)
\(234\) 0 0
\(235\) −4.13613 + 7.16398i −0.269811 + 0.467327i
\(236\) −0.630579 + 1.09220i −0.0410472 + 0.0710959i
\(237\) 0 0
\(238\) 2.27750 + 2.51866i 0.147628 + 0.163261i
\(239\) −16.0317 9.25590i −1.03700 0.598714i −0.118021 0.993011i \(-0.537655\pi\)
−0.918983 + 0.394297i \(0.870988\pi\)
\(240\) 0 0
\(241\) 21.9366i 1.41306i −0.707681 0.706532i \(-0.750259\pi\)
0.707681 0.706532i \(-0.249741\pi\)
\(242\) 4.87641 + 2.81540i 0.313468 + 0.180981i
\(243\) 0 0
\(244\) 2.96707i 0.189947i
\(245\) −6.38269 + 2.87424i −0.407775 + 0.183628i
\(246\) 0 0
\(247\) −20.1620 −1.28287
\(248\) 3.92178 + 6.79271i 0.249033 + 0.431338i
\(249\) 0 0
\(250\) −0.866025 0.500000i −0.0547723 0.0316228i
\(251\) −15.6773 −0.989540 −0.494770 0.869024i \(-0.664748\pi\)
−0.494770 + 0.869024i \(0.664748\pi\)
\(252\) 0 0
\(253\) 8.92547 0.561139
\(254\) 9.49383 + 5.48127i 0.595696 + 0.343925i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.5872 0.660411 0.330206 0.943909i \(-0.392882\pi\)
0.330206 + 0.943909i \(0.392882\pi\)
\(258\) 0 0
\(259\) −11.3883 + 10.2979i −0.707635 + 0.639879i
\(260\) 6.00644i 0.372504i
\(261\) 0 0
\(262\) 17.9538 + 10.3656i 1.10919 + 0.640389i
\(263\) 24.2649i 1.49624i −0.663564 0.748120i \(-0.730957\pi\)
0.663564 0.748120i \(-0.269043\pi\)
\(264\) 0 0
\(265\) 7.48689 + 4.32256i 0.459916 + 0.265533i
\(266\) 1.86488 + 8.68305i 0.114343 + 0.532392i
\(267\) 0 0
\(268\) −4.31098 + 7.46684i −0.263335 + 0.456110i
\(269\) 9.04616 15.6684i 0.551554 0.955320i −0.446608 0.894730i \(-0.647368\pi\)
0.998163 0.0605906i \(-0.0192984\pi\)
\(270\) 0 0
\(271\) −3.07389 + 1.77471i −0.186725 + 0.107806i −0.590449 0.807075i \(-0.701049\pi\)
0.403723 + 0.914881i \(0.367716\pi\)
\(272\) 0.641724 + 1.11150i 0.0389102 + 0.0673945i
\(273\) 0 0
\(274\) −4.83716 + 8.37821i −0.292224 + 0.506146i
\(275\) 4.07809i 0.245918i
\(276\) 0 0
\(277\) 2.30895 0.138732 0.0693658 0.997591i \(-0.477902\pi\)
0.0693658 + 0.997591i \(0.477902\pi\)
\(278\) 2.63928 + 4.57137i 0.158294 + 0.274173i
\(279\) 0 0
\(280\) −2.58676 + 0.555567i −0.154589 + 0.0332015i
\(281\) 0.186637 0.107755i 0.0111338 0.00642812i −0.494423 0.869222i \(-0.664621\pi\)
0.505557 + 0.862793i \(0.331287\pi\)
\(282\) 0 0
\(283\) 13.3787 7.72421i 0.795283 0.459157i −0.0465363 0.998917i \(-0.514818\pi\)
0.841819 + 0.539760i \(0.181485\pi\)
\(284\) 12.2434 7.06874i 0.726514 0.419453i
\(285\) 0 0
\(286\) −21.2131 + 12.2474i −1.25436 + 0.724203i
\(287\) 6.89553 + 2.22434i 0.407030 + 0.131299i
\(288\) 0 0
\(289\) 7.67638 + 13.2959i 0.451552 + 0.782111i
\(290\) 7.18058 0.421658
\(291\) 0 0
\(292\) 6.95513i 0.407018i
\(293\) −0.347292 + 0.601528i −0.0202890 + 0.0351417i −0.875992 0.482326i \(-0.839792\pi\)
0.855703 + 0.517468i \(0.173125\pi\)
\(294\) 0 0
\(295\) 0.630579 + 1.09220i 0.0367137 + 0.0635901i
\(296\) −5.02572 + 2.90160i −0.292114 + 0.168652i
\(297\) 0 0
\(298\) 2.18889 3.79127i 0.126799 0.219623i
\(299\) −6.57297 + 11.3847i −0.380125 + 0.658395i
\(300\) 0 0
\(301\) −9.56751 + 8.65142i −0.551462 + 0.498659i
\(302\) 4.82650 + 2.78658i 0.277734 + 0.160350i
\(303\) 0 0
\(304\) 3.35672i 0.192521i
\(305\) −2.56956 1.48353i −0.147132 0.0849469i
\(306\) 0 0
\(307\) 34.0796i 1.94502i −0.232853 0.972512i \(-0.574806\pi\)
0.232853 0.972512i \(-0.425194\pi\)
\(308\) 7.23663 + 8.00292i 0.412345 + 0.456009i
\(309\) 0 0
\(310\) 7.84355 0.445484
\(311\) 4.24381 + 7.35049i 0.240644 + 0.416808i 0.960898 0.276903i \(-0.0893080\pi\)
−0.720254 + 0.693711i \(0.755975\pi\)
\(312\) 0 0
\(313\) 23.6250 + 13.6399i 1.33536 + 0.770973i 0.986116 0.166057i \(-0.0531037\pi\)
0.349248 + 0.937030i \(0.386437\pi\)
\(314\) 0.281341 0.0158770
\(315\) 0 0
\(316\) 12.1855 0.685490
\(317\) −0.0390775 0.0225614i −0.00219481 0.00126717i 0.498902 0.866658i \(-0.333737\pi\)
−0.501097 + 0.865391i \(0.667070\pi\)
\(318\) 0 0
\(319\) −14.6415 25.3598i −0.819767 1.41988i
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 5.51097 + 1.77772i 0.307114 + 0.0990682i
\(323\) 4.30818i 0.239714i
\(324\) 0 0
\(325\) −5.20173 3.00322i −0.288540 0.166589i
\(326\) 7.53154i 0.417134i
\(327\) 0 0
\(328\) 2.37162 + 1.36925i 0.130951 + 0.0756044i
\(329\) 20.8294 + 6.71911i 1.14836 + 0.370437i
\(330\) 0 0
\(331\) −9.23258 + 15.9913i −0.507468 + 0.878961i 0.492494 + 0.870316i \(0.336085\pi\)
−0.999963 + 0.00864533i \(0.997248\pi\)
\(332\) 6.87948 11.9156i 0.377560 0.653954i
\(333\) 0 0
\(334\) −8.43926 + 4.87241i −0.461776 + 0.266607i
\(335\) 4.31098 + 7.46684i 0.235534 + 0.407957i
\(336\) 0 0
\(337\) 11.5293 19.9693i 0.628041 1.08780i −0.359903 0.932990i \(-0.617190\pi\)
0.987944 0.154810i \(-0.0494764\pi\)
\(338\) 23.0773i 1.25524i
\(339\) 0 0
\(340\) 1.28345 0.0696048
\(341\) −15.9933 27.7013i −0.866088 1.50011i
\(342\) 0 0
\(343\) 10.9810 + 14.9137i 0.592918 + 0.805263i
\(344\) −4.22219 + 2.43768i −0.227645 + 0.131431i
\(345\) 0 0
\(346\) 12.3555 7.13345i 0.664235 0.383496i
\(347\) 19.3393 11.1655i 1.03819 0.599398i 0.118868 0.992910i \(-0.462073\pi\)
0.919319 + 0.393512i \(0.128740\pi\)
\(348\) 0 0
\(349\) −8.01876 + 4.62963i −0.429235 + 0.247819i −0.699020 0.715102i \(-0.746380\pi\)
0.269786 + 0.962920i \(0.413047\pi\)
\(350\) −0.812247 + 2.51799i −0.0434164 + 0.134592i
\(351\) 0 0
\(352\) 2.03904 + 3.53173i 0.108681 + 0.188242i
\(353\) −13.1868 −0.701860 −0.350930 0.936402i \(-0.614135\pi\)
−0.350930 + 0.936402i \(0.614135\pi\)
\(354\) 0 0
\(355\) 14.1375i 0.750340i
\(356\) −7.29497 + 12.6353i −0.386633 + 0.669667i
\(357\) 0 0
\(358\) 4.28650 + 7.42444i 0.226549 + 0.392394i
\(359\) −9.81294 + 5.66550i −0.517907 + 0.299014i −0.736078 0.676897i \(-0.763324\pi\)
0.218171 + 0.975911i \(0.429991\pi\)
\(360\) 0 0
\(361\) −3.86621 + 6.69647i −0.203485 + 0.352446i
\(362\) 0.854734 1.48044i 0.0449238 0.0778104i
\(363\) 0 0
\(364\) −15.5372 + 3.33698i −0.814373 + 0.174905i
\(365\) −6.02332 3.47757i −0.315275 0.182024i
\(366\) 0 0
\(367\) 24.3474i 1.27092i −0.772133 0.635461i \(-0.780810\pi\)
0.772133 0.635461i \(-0.219190\pi\)
\(368\) 1.89542 + 1.09432i 0.0988055 + 0.0570454i
\(369\) 0 0
\(370\) 5.80320i 0.301694i
\(371\) 7.02197 21.7683i 0.364563 1.13015i
\(372\) 0 0
\(373\) −27.4626 −1.42196 −0.710979 0.703214i \(-0.751748\pi\)
−0.710979 + 0.703214i \(0.751748\pi\)
\(374\) −2.61701 4.53279i −0.135322 0.234385i
\(375\) 0 0
\(376\) 7.16398 + 4.13613i 0.369454 + 0.213304i
\(377\) 43.1297 2.22129
\(378\) 0 0
\(379\) 32.0033 1.64390 0.821948 0.569562i \(-0.192887\pi\)
0.821948 + 0.569562i \(0.192887\pi\)
\(380\) 2.90701 + 1.67836i 0.149126 + 0.0860981i
\(381\) 0 0
\(382\) −4.63075 8.02069i −0.236930 0.410374i
\(383\) −14.2705 −0.729191 −0.364595 0.931166i \(-0.618793\pi\)
−0.364595 + 0.931166i \(0.618793\pi\)
\(384\) 0 0
\(385\) 10.5490 2.26565i 0.537629 0.115468i
\(386\) 24.2494i 1.23426i
\(387\) 0 0
\(388\) −16.8723 9.74120i −0.856559 0.494535i
\(389\) 10.7610i 0.545604i −0.962070 0.272802i \(-0.912050\pi\)
0.962070 0.272802i \(-0.0879504\pi\)
\(390\) 0 0
\(391\) −2.43267 1.40450i −0.123025 0.0710288i
\(392\) 2.87424 + 6.38269i 0.145171 + 0.322375i
\(393\) 0 0
\(394\) 9.44736 16.3633i 0.475951 0.824372i
\(395\) 6.09277 10.5530i 0.306560 0.530978i
\(396\) 0 0
\(397\) 19.3500 11.1717i 0.971150 0.560694i 0.0715634 0.997436i \(-0.477201\pi\)
0.899587 + 0.436742i \(0.143868\pi\)
\(398\) −1.30194 2.25502i −0.0652602 0.113034i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 18.9839i 0.948009i 0.880522 + 0.474005i \(0.157192\pi\)
−0.880522 + 0.474005i \(0.842808\pi\)
\(402\) 0 0
\(403\) 47.1118 2.34681
\(404\) −4.26859 7.39341i −0.212370 0.367836i
\(405\) 0 0
\(406\) −3.98929 18.5745i −0.197985 0.921835i
\(407\) 20.4953 11.8330i 1.01592 0.586539i
\(408\) 0 0
\(409\) 22.5328 13.0093i 1.11418 0.643270i 0.174269 0.984698i \(-0.444244\pi\)
0.939908 + 0.341428i \(0.110910\pi\)
\(410\) 2.37162 1.36925i 0.117126 0.0676226i
\(411\) 0 0
\(412\) −3.12850 + 1.80624i −0.154130 + 0.0889869i
\(413\) 2.47492 2.23795i 0.121783 0.110122i
\(414\) 0 0
\(415\) −6.87948 11.9156i −0.337700 0.584914i
\(416\) −6.00644 −0.294490
\(417\) 0 0
\(418\) 13.6890i 0.669551i
\(419\) −3.75114 + 6.49717i −0.183255 + 0.317407i −0.942987 0.332829i \(-0.891997\pi\)
0.759732 + 0.650236i \(0.225330\pi\)
\(420\) 0 0
\(421\) −7.94926 13.7685i −0.387423 0.671037i 0.604679 0.796469i \(-0.293301\pi\)
−0.992102 + 0.125433i \(0.959968\pi\)
\(422\) 5.41288 3.12513i 0.263495 0.152129i
\(423\) 0 0
\(424\) 4.32256 7.48689i 0.209922 0.363596i
\(425\) 0.641724 1.11150i 0.0311282 0.0539156i
\(426\) 0 0
\(427\) −2.40999 + 7.47104i −0.116628 + 0.361549i
\(428\) −11.5596 6.67392i −0.558753 0.322596i
\(429\) 0 0
\(430\) 4.87537i 0.235111i
\(431\) 19.4232 + 11.2140i 0.935581 + 0.540158i 0.888572 0.458737i \(-0.151698\pi\)
0.0470087 + 0.998894i \(0.485031\pi\)
\(432\) 0 0
\(433\) 1.97195i 0.0947659i 0.998877 + 0.0473830i \(0.0150881\pi\)
−0.998877 + 0.0473830i \(0.984912\pi\)
\(434\) −4.35762 20.2894i −0.209172 0.973923i
\(435\) 0 0
\(436\) 10.7717 0.515869
\(437\) −3.67333 6.36239i −0.175719 0.304355i
\(438\) 0 0
\(439\) 9.15130 + 5.28351i 0.436768 + 0.252168i 0.702226 0.711954i \(-0.252190\pi\)
−0.265458 + 0.964122i \(0.585523\pi\)
\(440\) 4.07809 0.194415
\(441\) 0 0
\(442\) 7.70896 0.366678
\(443\) 5.85561 + 3.38074i 0.278208 + 0.160624i 0.632612 0.774469i \(-0.281983\pi\)
−0.354404 + 0.935093i \(0.615316\pi\)
\(444\) 0 0
\(445\) 7.29497 + 12.6353i 0.345815 + 0.598969i
\(446\) −4.89962 −0.232004
\(447\) 0 0
\(448\) 0.555567 + 2.58676i 0.0262481 + 0.122213i
\(449\) 3.97534i 0.187608i 0.995591 + 0.0938039i \(0.0299027\pi\)
−0.995591 + 0.0938039i \(0.970097\pi\)
\(450\) 0 0
\(451\) −9.67166 5.58394i −0.455421 0.262937i
\(452\) 2.83663i 0.133424i
\(453\) 0 0
\(454\) 15.1388 + 8.74040i 0.710500 + 0.410207i
\(455\) −4.87871 + 15.1241i −0.228717 + 0.709030i
\(456\) 0 0
\(457\) 3.26014 5.64673i 0.152503 0.264143i −0.779644 0.626223i \(-0.784600\pi\)
0.932147 + 0.362080i \(0.117933\pi\)
\(458\) −7.29619 + 12.6374i −0.340929 + 0.590506i
\(459\) 0 0
\(460\) 1.89542 1.09432i 0.0883743 0.0510229i
\(461\) −4.69303 8.12857i −0.218576 0.378585i 0.735797 0.677203i \(-0.236808\pi\)
−0.954373 + 0.298617i \(0.903475\pi\)
\(462\) 0 0
\(463\) 16.8709 29.2212i 0.784056 1.35803i −0.145505 0.989357i \(-0.546481\pi\)
0.929561 0.368668i \(-0.120186\pi\)
\(464\) 7.18058i 0.333350i
\(465\) 0 0
\(466\) 3.95324 0.183130
\(467\) −17.9147 31.0293i −0.828996 1.43586i −0.898827 0.438304i \(-0.855579\pi\)
0.0698312 0.997559i \(-0.477754\pi\)
\(468\) 0 0
\(469\) 16.9199 15.2998i 0.781289 0.706480i
\(470\) 7.16398 4.13613i 0.330450 0.190785i
\(471\) 0 0
\(472\) 1.09220 0.630579i 0.0502724 0.0290248i
\(473\) 17.2185 9.94108i 0.791706 0.457092i
\(474\) 0 0
\(475\) 2.90701 1.67836i 0.133383 0.0770085i
\(476\) −0.713041 3.31998i −0.0326822 0.152171i
\(477\) 0 0
\(478\) 9.25590 + 16.0317i 0.423355 + 0.733272i
\(479\) 13.8779 0.634096 0.317048 0.948409i \(-0.397308\pi\)
0.317048 + 0.948409i \(0.397308\pi\)
\(480\) 0 0
\(481\) 34.8566i 1.58932i
\(482\) −10.9683 + 18.9977i −0.499593 + 0.865321i
\(483\) 0 0
\(484\) −2.81540 4.87641i −0.127973 0.221655i
\(485\) −16.8723 + 9.74120i −0.766130 + 0.442325i
\(486\) 0 0
\(487\) 13.8002 23.9026i 0.625345 1.08313i −0.363129 0.931739i \(-0.618292\pi\)
0.988474 0.151390i \(-0.0483750\pi\)
\(488\) −1.48353 + 2.56956i −0.0671564 + 0.116318i
\(489\) 0 0
\(490\) 6.96469 + 0.702180i 0.314633 + 0.0317213i
\(491\) 18.1949 + 10.5048i 0.821122 + 0.474075i 0.850803 0.525484i \(-0.176116\pi\)
−0.0296811 + 0.999559i \(0.509449\pi\)
\(492\) 0 0
\(493\) 9.21590i 0.415063i
\(494\) 17.4608 + 10.0810i 0.785597 + 0.453565i
\(495\) 0 0
\(496\) 7.84355i 0.352186i
\(497\) −36.5703 + 7.85432i −1.64040 + 0.352314i
\(498\) 0 0
\(499\) 0.395326 0.0176972 0.00884862 0.999961i \(-0.497183\pi\)
0.00884862 + 0.999961i \(0.497183\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 13.5769 + 7.83863i 0.605967 + 0.349855i
\(503\) 10.3934 0.463418 0.231709 0.972785i \(-0.425568\pi\)
0.231709 + 0.972785i \(0.425568\pi\)
\(504\) 0 0
\(505\) −8.53717 −0.379899
\(506\) −7.72968 4.46273i −0.343626 0.198393i
\(507\) 0 0
\(508\) −5.48127 9.49383i −0.243192 0.421221i
\(509\) 40.5347 1.79667 0.898334 0.439313i \(-0.144778\pi\)
0.898334 + 0.439313i \(0.144778\pi\)
\(510\) 0 0
\(511\) −5.64928 + 17.5129i −0.249910 + 0.774727i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.16878 5.29360i −0.404417 0.233491i
\(515\) 3.61248i 0.159185i
\(516\) 0 0
\(517\) −29.2153 16.8675i −1.28489 0.741831i
\(518\) 15.0115 3.22407i 0.659568 0.141657i
\(519\) 0 0
\(520\) −3.00322 + 5.20173i −0.131700 + 0.228111i
\(521\) −4.80694 + 8.32586i −0.210596 + 0.364763i −0.951901 0.306405i \(-0.900874\pi\)
0.741305 + 0.671168i \(0.234207\pi\)
\(522\) 0 0
\(523\) −14.2342 + 8.21809i −0.622416 + 0.359352i −0.777809 0.628501i \(-0.783669\pi\)
0.155393 + 0.987853i \(0.450336\pi\)
\(524\) −10.3656 17.9538i −0.452824 0.784313i
\(525\) 0 0
\(526\) −12.1325 + 21.0140i −0.529001 + 0.916256i
\(527\) 10.0668i 0.438516i
\(528\) 0 0
\(529\) 18.2099 0.791733
\(530\) −4.32256 7.48689i −0.187760 0.325210i
\(531\) 0 0
\(532\) 2.72649 8.45218i 0.118208 0.366449i
\(533\) 14.2450 8.22434i 0.617019 0.356236i
\(534\) 0 0
\(535\) −11.5596 + 6.67392i −0.499764 + 0.288539i
\(536\) 7.46684 4.31098i 0.322518 0.186206i
\(537\) 0 0
\(538\) −15.6684 + 9.04616i −0.675513 + 0.390008i
\(539\) −11.7214 26.0292i −0.504877 1.12116i
\(540\) 0 0
\(541\) 16.1578 + 27.9861i 0.694678 + 1.20322i 0.970289 + 0.241948i \(0.0777863\pi\)
−0.275612 + 0.961269i \(0.588880\pi\)
\(542\) 3.54942 0.152461
\(543\) 0 0
\(544\) 1.28345i 0.0550274i
\(545\) 5.38583 9.32854i 0.230704 0.399591i
\(546\) 0 0
\(547\) −3.41985 5.92335i −0.146222 0.253264i 0.783606 0.621258i \(-0.213378\pi\)
−0.929828 + 0.367994i \(0.880045\pi\)
\(548\) 8.37821 4.83716i 0.357899 0.206633i
\(549\) 0 0
\(550\) 2.03904 3.53173i 0.0869451 0.150593i
\(551\) −12.0516 + 20.8740i −0.513416 + 0.889262i
\(552\) 0 0
\(553\) −30.6830 9.89766i −1.30477 0.420891i
\(554\) −1.99961 1.15448i −0.0849554 0.0490490i
\(555\) 0 0
\(556\) 5.27856i 0.223861i
\(557\) 5.91206 + 3.41333i 0.250502 + 0.144627i 0.619994 0.784607i \(-0.287135\pi\)
−0.369492 + 0.929234i \(0.620468\pi\)
\(558\) 0 0
\(559\) 29.2836i 1.23856i
\(560\) 2.51799 + 0.812247i 0.106404 + 0.0343237i
\(561\) 0 0
\(562\) −0.215510 −0.00909074
\(563\) 5.41857 + 9.38524i 0.228366 + 0.395541i 0.957324 0.289017i \(-0.0933285\pi\)
−0.728958 + 0.684558i \(0.759995\pi\)
\(564\) 0 0
\(565\) 2.45659 + 1.41832i 0.103350 + 0.0596690i
\(566\) −15.4484 −0.649346
\(567\) 0 0
\(568\) −14.1375 −0.593196
\(569\) 12.0811 + 6.97501i 0.506465 + 0.292408i 0.731379 0.681971i \(-0.238877\pi\)
−0.224914 + 0.974379i \(0.572210\pi\)
\(570\) 0 0
\(571\) 13.6060 + 23.5662i 0.569393 + 0.986217i 0.996626 + 0.0820756i \(0.0261549\pi\)
−0.427234 + 0.904141i \(0.640512\pi\)
\(572\) 24.4948 1.02418
\(573\) 0 0
\(574\) −4.85953 5.37410i −0.202833 0.224311i
\(575\) 2.18864i 0.0912726i
\(576\) 0 0
\(577\) 13.2438 + 7.64631i 0.551346 + 0.318320i 0.749665 0.661818i \(-0.230215\pi\)
−0.198318 + 0.980138i \(0.563548\pi\)
\(578\) 15.3528i 0.638591i
\(579\) 0 0
\(580\) −6.21856 3.59029i −0.258212 0.149079i
\(581\) −27.0008 + 24.4155i −1.12018 + 1.01293i
\(582\) 0 0
\(583\) −17.6278 + 30.5322i −0.730068 + 1.26451i
\(584\) −3.47757 + 6.02332i −0.143903 + 0.249247i
\(585\) 0 0
\(586\) 0.601528 0.347292i 0.0248489 0.0143465i
\(587\) 7.16231 + 12.4055i 0.295620 + 0.512029i 0.975129 0.221638i \(-0.0711404\pi\)
−0.679509 + 0.733667i \(0.737807\pi\)
\(588\) 0 0
\(589\) −13.1643 + 22.8013i −0.542426 + 0.939509i
\(590\) 1.26116i 0.0519211i
\(591\) 0 0
\(592\) 5.80320 0.238510
\(593\) −0.594674 1.03001i −0.0244203 0.0422973i 0.853557 0.521000i \(-0.174441\pi\)
−0.877977 + 0.478702i \(0.841107\pi\)
\(594\) 0 0
\(595\) −3.23171 1.04248i −0.132487 0.0427374i
\(596\) −3.79127 + 2.18889i −0.155297 + 0.0896606i
\(597\) 0 0
\(598\) 11.3847 6.57297i 0.465556 0.268789i
\(599\) 39.8059 22.9819i 1.62642 0.939016i 0.641276 0.767310i \(-0.278405\pi\)
0.985148 0.171706i \(-0.0549280\pi\)
\(600\) 0 0
\(601\) −14.0543 + 8.11427i −0.573288 + 0.330988i −0.758462 0.651718i \(-0.774049\pi\)
0.185173 + 0.982706i \(0.440715\pi\)
\(602\) 12.6114 2.70859i 0.514003 0.110394i
\(603\) 0 0
\(604\) −2.78658 4.82650i −0.113384 0.196387i
\(605\) −5.63079 −0.228924
\(606\) 0 0
\(607\) 6.95304i 0.282215i −0.989994 0.141108i \(-0.954934\pi\)
0.989994 0.141108i \(-0.0450664\pi\)
\(608\) 1.67836 2.90701i 0.0680665 0.117895i
\(609\) 0 0
\(610\) 1.48353 + 2.56956i 0.0600665 + 0.104038i
\(611\) 43.0300 24.8434i 1.74081 1.00506i
\(612\) 0 0
\(613\) −20.0114 + 34.6608i −0.808253 + 1.39993i 0.105821 + 0.994385i \(0.466253\pi\)
−0.914073 + 0.405549i \(0.867080\pi\)
\(614\) −17.0398 + 29.5138i −0.687670 + 1.19108i
\(615\) 0 0
\(616\) −2.26565 10.5490i −0.0912856 0.425033i
\(617\) −7.94775 4.58864i −0.319964 0.184732i 0.331412 0.943486i \(-0.392475\pi\)
−0.651377 + 0.758754i \(0.725808\pi\)
\(618\) 0 0
\(619\) 38.3260i 1.54045i −0.637770 0.770227i \(-0.720143\pi\)
0.637770 0.770227i \(-0.279857\pi\)
\(620\) −6.79271 3.92178i −0.272802 0.157502i
\(621\) 0 0
\(622\) 8.48761i 0.340322i
\(623\) 28.6316 25.8901i 1.14710 1.03726i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −13.6399 23.6250i −0.545160 0.944245i
\(627\) 0 0
\(628\) −0.243649 0.140671i −0.00972264 0.00561337i
\(629\) −7.44811 −0.296976
\(630\) 0 0
\(631\) −21.4220 −0.852797 −0.426399 0.904535i \(-0.640218\pi\)
−0.426399 + 0.904535i \(0.640218\pi\)
\(632\) −10.5530 6.09277i −0.419775 0.242357i
\(633\) 0 0
\(634\) 0.0225614 + 0.0390775i 0.000896027 + 0.00155196i
\(635\) −10.9625 −0.435035
\(636\) 0 0
\(637\) 41.8330 + 4.21760i 1.65748 + 0.167108i
\(638\) 29.2830i 1.15933i
\(639\) 0 0
\(640\) 0.866025 + 0.500000i 0.0342327 + 0.0197642i
\(641\) 23.8349i 0.941421i −0.882288 0.470710i \(-0.843998\pi\)
0.882288 0.470710i \(-0.156002\pi\)
\(642\) 0 0
\(643\) 10.6419 + 6.14411i 0.419676 + 0.242300i 0.694939 0.719069i \(-0.255432\pi\)
−0.275263 + 0.961369i \(0.588765\pi\)
\(644\) −3.88378 4.29503i −0.153042 0.169248i
\(645\) 0 0
\(646\) −2.15409 + 3.73099i −0.0847516 + 0.146794i
\(647\) −8.50175 + 14.7255i −0.334238 + 0.578917i −0.983338 0.181786i \(-0.941812\pi\)
0.649100 + 0.760703i \(0.275146\pi\)
\(648\) 0 0
\(649\) −4.45407 + 2.57156i −0.174837 + 0.100942i
\(650\) 3.00322 + 5.20173i 0.117796 + 0.204029i
\(651\) 0 0
\(652\) 3.76577 6.52251i 0.147479 0.255441i
\(653\) 11.0926i 0.434087i −0.976162 0.217044i \(-0.930359\pi\)
0.976162 0.217044i \(-0.0696414\pi\)
\(654\) 0 0
\(655\) −20.7312 −0.810035
\(656\) −1.36925 2.37162i −0.0534604 0.0925961i
\(657\) 0 0
\(658\) −14.6793 16.2336i −0.572257 0.632853i
\(659\) 39.7712 22.9619i 1.54927 0.894470i 0.551069 0.834459i \(-0.314220\pi\)
0.998198 0.0600103i \(-0.0191133\pi\)
\(660\) 0 0
\(661\) −18.0299 + 10.4096i −0.701281 + 0.404885i −0.807824 0.589423i \(-0.799355\pi\)
0.106543 + 0.994308i \(0.466022\pi\)
\(662\) 15.9913 9.23258i 0.621519 0.358834i
\(663\) 0 0
\(664\) −11.9156 + 6.87948i −0.462415 + 0.266975i
\(665\) −5.95656 6.58730i −0.230986 0.255444i
\(666\) 0 0
\(667\) 7.85785 + 13.6102i 0.304257 + 0.526989i
\(668\) 9.74482 0.377039
\(669\) 0 0
\(670\) 8.62197i 0.333096i
\(671\) 6.04998 10.4789i 0.233557 0.404532i
\(672\) 0 0
\(673\) 14.6307 + 25.3410i 0.563970 + 0.976825i 0.997145 + 0.0755149i \(0.0240600\pi\)
−0.433175 + 0.901310i \(0.642607\pi\)
\(674\) −19.9693 + 11.5293i −0.769190 + 0.444092i
\(675\) 0 0
\(676\) −11.5387 + 19.9855i −0.443795 + 0.768675i
\(677\) −12.3058 + 21.3142i −0.472949 + 0.819172i −0.999521 0.0309588i \(-0.990144\pi\)
0.526571 + 0.850131i \(0.323477\pi\)
\(678\) 0 0
\(679\) 34.5718 + 38.2326i 1.32675 + 1.46723i
\(680\) −1.11150 0.641724i −0.0426240 0.0246090i
\(681\) 0 0
\(682\) 31.9867i 1.22483i
\(683\) 4.84830 + 2.79917i 0.185515 + 0.107107i 0.589881 0.807490i \(-0.299175\pi\)
−0.404366 + 0.914597i \(0.632508\pi\)
\(684\) 0 0
\(685\) 9.67432i 0.369637i
\(686\) −2.05298 18.4061i −0.0783831 0.702749i
\(687\) 0 0
\(688\) 4.87537 0.185872
\(689\) −25.9632 44.9696i −0.989119 1.71320i
\(690\) 0 0
\(691\) −28.6519 16.5422i −1.08997 0.629294i −0.156401 0.987694i \(-0.549989\pi\)
−0.933568 + 0.358399i \(0.883323\pi\)
\(692\) −14.2669 −0.542346
\(693\) 0 0
\(694\) −22.3311 −0.847677
\(695\) −4.57137 2.63928i −0.173402 0.100114i
\(696\) 0 0
\(697\) 1.75737 + 3.04385i 0.0665650 + 0.115294i
\(698\) 9.25927 0.350469
\(699\) 0 0
\(700\) 1.96242 1.77452i 0.0741725 0.0670704i
\(701\) 3.12417i 0.117998i −0.998258 0.0589992i \(-0.981209\pi\)
0.998258 0.0589992i \(-0.0187909\pi\)
\(702\) 0 0
\(703\) −16.8699 9.73987i −0.636262 0.367346i
\(704\) 4.07809i 0.153699i
\(705\) 0 0
\(706\) 11.4201 + 6.59338i 0.429800 + 0.248145i
\(707\) 4.74297 + 22.0836i 0.178378 + 0.830541i
\(708\) 0 0
\(709\) 21.7411 37.6567i 0.816504 1.41423i −0.0917396 0.995783i \(-0.529243\pi\)
0.908243 0.418443i \(-0.137424\pi\)
\(710\) −7.06874 + 12.2434i −0.265285 + 0.459487i
\(711\) 0 0
\(712\) 12.6353 7.29497i 0.473526 0.273391i
\(713\) 8.58336 + 14.8668i 0.321449 + 0.556766i
\(714\) 0 0
\(715\) 12.2474 21.2131i 0.458026 0.793325i
\(716\) 8.57300i 0.320388i
\(717\) 0 0
\(718\) 11.3310 0.422869
\(719\) 2.21764 + 3.84106i 0.0827039 + 0.143247i 0.904411 0.426663i \(-0.140311\pi\)
−0.821707 + 0.569911i \(0.806978\pi\)
\(720\) 0 0
\(721\) 9.34462 2.00697i 0.348012 0.0747435i
\(722\) 6.69647 3.86621i 0.249217 0.143885i
\(723\) 0 0
\(724\) −1.48044 + 0.854734i −0.0550202 + 0.0317659i
\(725\) −6.21856 + 3.59029i −0.230952 + 0.133340i
\(726\) 0 0
\(727\) 36.5068 21.0772i 1.35396 0.781711i 0.365162 0.930944i \(-0.381014\pi\)
0.988802 + 0.149233i \(0.0476803\pi\)
\(728\) 15.1241 + 4.87871i 0.560538 + 0.180817i
\(729\) 0 0
\(730\) 3.47757 + 6.02332i 0.128711 + 0.222933i
\(731\) −6.25728 −0.231434
\(732\) 0 0
\(733\) 46.2254i 1.70738i −0.520785 0.853688i \(-0.674361\pi\)
0.520785 0.853688i \(-0.325639\pi\)
\(734\) −12.1737 + 21.0854i −0.449339 + 0.778278i
\(735\) 0 0
\(736\) −1.09432 1.89542i −0.0403372 0.0698660i
\(737\) −30.4504 + 17.5806i −1.12166 + 0.647589i
\(738\) 0 0
\(739\) −14.2820 + 24.7371i −0.525371 + 0.909969i 0.474193 + 0.880421i \(0.342740\pi\)
−0.999563 + 0.0295478i \(0.990593\pi\)
\(740\) 2.90160 5.02572i 0.106665 0.184749i
\(741\) 0 0
\(742\) −16.9654 + 15.3409i −0.622818 + 0.563183i
\(743\) −3.36454 1.94252i −0.123433 0.0712640i 0.437012 0.899456i \(-0.356037\pi\)
−0.560445 + 0.828192i \(0.689370\pi\)
\(744\) 0 0
\(745\) 4.37779i 0.160390i
\(746\) 23.7833 + 13.7313i 0.870767 + 0.502738i
\(747\) 0 0
\(748\) 5.23401i 0.191375i
\(749\) 23.6860 + 26.1941i 0.865467 + 0.957111i
\(750\) 0 0
\(751\) 21.2885 0.776829 0.388415 0.921485i \(-0.373023\pi\)
0.388415 + 0.921485i \(0.373023\pi\)
\(752\) −4.13613 7.16398i −0.150829 0.261244i
\(753\) 0 0
\(754\) −37.3514 21.5649i −1.36026 0.785346i
\(755\) −5.57316 −0.202828
\(756\) 0 0
\(757\) −42.1251 −1.53106 −0.765531 0.643399i \(-0.777524\pi\)
−0.765531 + 0.643399i \(0.777524\pi\)
\(758\) −27.7156 16.0016i −1.00668 0.581205i
\(759\) 0 0
\(760\) −1.67836 2.90701i −0.0608806 0.105448i
\(761\) −48.8379 −1.77037 −0.885187 0.465236i \(-0.845970\pi\)
−0.885187 + 0.465236i \(0.845970\pi\)
\(762\) 0 0
\(763\) −27.1229 8.74925i −0.981915 0.316744i
\(764\) 9.26150i 0.335069i
\(765\) 0 0
\(766\) 12.3587 + 7.13527i 0.446536 + 0.257808i
\(767\) 7.57507i 0.273520i
\(768\) 0 0
\(769\) −41.1583 23.7627i −1.48420 0.856906i −0.484366 0.874866i \(-0.660950\pi\)
−0.999839 + 0.0179596i \(0.994283\pi\)
\(770\) −10.2686 3.31241i −0.370053 0.119371i
\(771\) 0 0
\(772\) −12.1247 + 21.0006i −0.436378 + 0.755829i
\(773\) −2.07497 + 3.59395i −0.0746314 + 0.129265i −0.900926 0.433973i \(-0.857111\pi\)
0.826295 + 0.563238i \(0.190445\pi\)
\(774\) 0 0
\(775\) −6.79271 + 3.92178i −0.244001 + 0.140874i
\(776\) 9.74120 + 16.8723i 0.349689 + 0.605679i
\(777\) 0 0
\(778\) −5.38049 + 9.31929i −0.192900 + 0.334113i
\(779\) 9.19241i 0.329352i
\(780\) 0 0
\(781\) 57.6539 2.06302
\(782\) 1.40450 + 2.43267i 0.0502249 + 0.0869922i
\(783\) 0 0
\(784\) 0.702180 6.96469i 0.0250779 0.248739i
\(785\) −0.243649 + 0.140671i −0.00869619 + 0.00502075i
\(786\) 0 0
\(787\) 23.6630 13.6618i 0.843495 0.486992i −0.0149557 0.999888i \(-0.504761\pi\)
0.858451 + 0.512896i \(0.171427\pi\)
\(788\) −16.3633 + 9.44736i −0.582919 + 0.336548i
\(789\) 0 0
\(790\) −10.5530 + 6.09277i −0.375458 + 0.216771i
\(791\) 2.30404 7.14260i 0.0819224 0.253961i
\(792\) 0 0
\(793\) 8.91076 + 15.4339i 0.316430 + 0.548073i
\(794\) −22.3435 −0.792941
\(795\) 0 0
\(796\) 2.60387i 0.0922919i
\(797\) −14.7404 + 25.5311i −0.522132 + 0.904359i 0.477536 + 0.878612i \(0.341530\pi\)
−0.999668 + 0.0257473i \(0.991803\pi\)
\(798\) 0 0
\(799\) 5.30850 + 9.19460i 0.187801 + 0.325282i
\(800\) 0.866025 0.500000i 0.0306186 0.0176777i
\(801\) 0 0
\(802\) 9.49194 16.4405i 0.335172 0.580535i
\(803\) 14.1818 24.5636i 0.500466 0.866832i
\(804\) 0 0
\(805\) −5.66149 + 1.21594i −0.199541 + 0.0428561i
\(806\) −40.8000 23.5559i −1.43712 0.829721i
\(807\) 0 0
\(808\) 8.53717i 0.300337i
\(809\) −1.53294 0.885046i −0.0538955 0.0311166i 0.472810 0.881164i \(-0.343240\pi\)
−0.526706 + 0.850048i \(0.676573\pi\)
\(810\) 0 0
\(811\) 21.7821i 0.764872i 0.923982 + 0.382436i \(0.124915\pi\)
−0.923982 + 0.382436i \(0.875085\pi\)
\(812\) −5.83240 + 18.0806i −0.204677 + 0.634504i
\(813\) 0 0
\(814\) −23.6660 −0.829491
\(815\) −3.76577 6.52251i −0.131909 0.228473i
\(816\) 0 0
\(817\) −14.1727 8.18263i −0.495841 0.286274i
\(818\) −26.0187 −0.909722
\(819\) 0 0
\(820\) −2.73851 −0.0956329
\(821\) 21.5112 + 12.4195i 0.750746 + 0.433443i 0.825963 0.563724i \(-0.190632\pi\)
−0.0752177 + 0.997167i \(0.523965\pi\)
\(822\) 0 0
\(823\) −22.3540 38.7182i −0.779210 1.34963i −0.932398 0.361434i \(-0.882287\pi\)
0.153187 0.988197i \(-0.451046\pi\)
\(824\) 3.61248 0.125847
\(825\) 0 0
\(826\) −3.26232 + 0.700658i −0.113511 + 0.0243790i
\(827\) 43.9883i 1.52962i 0.644255 + 0.764811i \(0.277168\pi\)
−0.644255 + 0.764811i \(0.722832\pi\)
\(828\) 0 0
\(829\) 23.3072 + 13.4564i 0.809492 + 0.467360i 0.846779 0.531944i \(-0.178538\pi\)
−0.0372876 + 0.999305i \(0.511872\pi\)
\(830\) 13.7590i 0.477580i
\(831\) 0 0
\(832\) 5.20173 + 3.00322i 0.180338 + 0.104118i
\(833\) −0.901212 + 8.93882i −0.0312252 + 0.309712i
\(834\) 0 0
\(835\) 4.87241 8.43926i 0.168617 0.292053i
\(836\) −6.84450 + 11.8550i −0.236722 + 0.410015i
\(837\) 0 0
\(838\) 6.49717 3.75114i 0.224441 0.129581i
\(839\) −7.52241 13.0292i −0.259702 0.449818i 0.706460 0.707753i \(-0.250291\pi\)
−0.966162 + 0.257935i \(0.916958\pi\)
\(840\) 0 0
\(841\) 11.2803 19.5381i 0.388977 0.673728i
\(842\) 15.8985i 0.547899i
\(843\) 0 0
\(844\) −6.25025 −0.215143
\(845\) 11.5387 + 19.9855i 0.396942 + 0.687524i
\(846\) 0 0
\(847\) 3.12828 + 14.5655i 0.107489 + 0.500478i
\(848\) −7.48689 + 4.32256i −0.257101 + 0.148437i
\(849\) 0 0
\(850\) −1.11150 + 0.641724i −0.0381241 + 0.0220110i
\(851\) −10.9995 + 6.35056i −0.377058 + 0.217694i
\(852\) 0 0
\(853\) 11.0905 6.40312i 0.379732 0.219239i −0.297970 0.954575i \(-0.596309\pi\)
0.677702 + 0.735337i \(0.262976\pi\)
\(854\) 5.82263 5.26511i 0.199246 0.180168i
\(855\) 0 0
\(856\) 6.67392 + 11.5596i 0.228110 + 0.395098i
\(857\) 42.5215 1.45251 0.726254 0.687426i \(-0.241260\pi\)
0.726254 + 0.687426i \(0.241260\pi\)
\(858\) 0 0
\(859\) 7.34964i 0.250767i −0.992108 0.125383i \(-0.959984\pi\)
0.992108 0.125383i \(-0.0400161\pi\)
\(860\) 2.43768 4.22219i 0.0831243 0.143976i
\(861\) 0 0
\(862\) −11.2140 19.4232i −0.381949 0.661556i
\(863\) −3.64790 + 2.10612i −0.124176 + 0.0716930i −0.560801 0.827950i \(-0.689507\pi\)
0.436625 + 0.899643i \(0.356174\pi\)
\(864\) 0 0
\(865\) −7.13345 + 12.3555i −0.242544 + 0.420099i
\(866\) 0.985975 1.70776i 0.0335048 0.0580320i
\(867\) 0 0
\(868\) −6.37090 + 19.7500i −0.216242 + 0.670357i
\(869\) 43.0360 + 24.8468i 1.45990 + 0.842871i
\(870\) 0 0
\(871\) 51.7873i 1.75475i
\(872\) −9.32854 5.38583i −0.315904 0.182387i
\(873\) 0 0
\(874\) 7.34666i 0.248504i
\(875\) −0.555567 2.58676i −0.0187816 0.0874486i
\(876\) 0 0
\(877\) −26.7236 −0.902390 −0.451195 0.892425i \(-0.649002\pi\)
−0.451195 + 0.892425i \(0.649002\pi\)
\(878\) −5.28351 9.15130i −0.178310 0.308842i
\(879\) 0 0
\(880\) −3.53173 2.03904i −0.119054 0.0687361i
\(881\) −5.40270 −0.182022 −0.0910109 0.995850i \(-0.529010\pi\)
−0.0910109 + 0.995850i \(0.529010\pi\)
\(882\) 0 0
\(883\) −27.9671 −0.941169 −0.470584 0.882355i \(-0.655957\pi\)
−0.470584 + 0.882355i \(0.655957\pi\)
\(884\) −6.67615 3.85448i −0.224543 0.129640i
\(885\) 0 0
\(886\) −3.38074 5.85561i −0.113578 0.196723i
\(887\) −21.4552 −0.720395 −0.360198 0.932876i \(-0.617291\pi\)
−0.360198 + 0.932876i \(0.617291\pi\)
\(888\) 0 0
\(889\) 6.09042 + 28.3575i 0.204266 + 0.951079i
\(890\) 14.5899i 0.489056i
\(891\) 0 0
\(892\) 4.24320 + 2.44981i 0.142073 + 0.0820257i
\(893\) 27.7677i 0.929209i
\(894\) 0 0
\(895\) −7.42444 4.28650i −0.248172 0.143282i
\(896\) 0.812247 2.51799i 0.0271353 0.0841200i
\(897\) 0 0
\(898\) 1.98767 3.44275i 0.0663294 0.114886i
\(899\) 28.1606 48.7756i 0.939209 1.62676i
\(900\) 0 0
\(901\) 9.60904 5.54778i 0.320124 0.184823i
\(902\) 5.58394 + 9.67166i 0.185925 + 0.322031i
\(903\) 0 0
\(904\) 1.41832 2.45659i 0.0471725 0.0817051i
\(905\) 1.70947i 0.0568247i
\(906\) 0 0
\(907\) −21.1006 −0.700634 −0.350317 0.936631i \(-0.613926\pi\)
−0.350317 + 0.936631i \(0.613926\pi\)
\(908\) −8.74040 15.1388i −0.290060 0.502399i
\(909\) 0 0
\(910\) 11.7872 10.6585i 0.390740 0.353327i
\(911\) −18.9423 + 10.9363i −0.627585 + 0.362337i −0.779816 0.626008i \(-0.784688\pi\)
0.152231 + 0.988345i \(0.451354\pi\)
\(912\) 0 0
\(913\) 48.5929 28.0551i 1.60819 0.928488i
\(914\) −5.64673 + 3.26014i −0.186777 + 0.107836i
\(915\) 0 0
\(916\) 12.6374 7.29619i 0.417551 0.241073i
\(917\) 11.5176 + 53.6267i 0.380344 + 1.77091i
\(918\) 0 0
\(919\) −10.9564 18.9770i −0.361418 0.625994i 0.626777 0.779199i \(-0.284374\pi\)
−0.988194 + 0.153205i \(0.951040\pi\)
\(920\) −2.18864 −0.0721573
\(921\) 0 0
\(922\) 9.38607i 0.309114i
\(923\) −42.4580 + 73.5394i −1.39752 + 2.42058i
\(924\) 0 0
\(925\) −2.90160 5.02572i −0.0954040 0.165245i
\(926\) −29.2212 + 16.8709i −0.960269 + 0.554411i
\(927\) 0 0
\(928\) −3.59029 + 6.21856i −0.117857 + 0.204134i
\(929\) −12.1080 + 20.9717i −0.397251 + 0.688059i −0.993386 0.114826i \(-0.963369\pi\)
0.596135 + 0.802884i \(0.296702\pi\)
\(930\) 0 0
\(931\) −13.7305 + 19.0679i −0.449999 + 0.624925i
\(932\) −3.42360 1.97662i −0.112144 0.0647463i
\(933\) 0 0
\(934\) 35.8295i 1.17238i
\(935\) 4.53279 + 2.61701i 0.148238 + 0.0855853i
\(936\) 0 0
\(937\) 38.1815i 1.24733i −0.781690 0.623667i \(-0.785642\pi\)
0.781690 0.623667i \(-0.214358\pi\)
\(938\) −22.3030 + 4.79008i −0.728218 + 0.156402i
\(939\) 0 0
\(940\) −8.27225 −0.269811
\(941\) −3.96611 6.86950i −0.129291 0.223939i 0.794111 0.607773i \(-0.207937\pi\)
−0.923402 + 0.383834i \(0.874604\pi\)
\(942\) 0 0
\(943\) 5.19062 + 2.99680i 0.169030 + 0.0975894i
\(944\) −1.26116 −0.0410472
\(945\) 0 0
\(946\) −19.8822 −0.646425
\(947\) 2.86322 + 1.65308i 0.0930421 + 0.0537179i 0.545799 0.837916i \(-0.316226\pi\)
−0.452757 + 0.891634i \(0.649560\pi\)
\(948\) 0 0
\(949\) 20.8878 + 36.1787i 0.678047 + 1.17441i
\(950\) −3.35672 −0.108906
\(951\) 0 0
\(952\) −1.04248 + 3.23171i −0.0337869 + 0.104740i
\(953\) 53.6699i 1.73854i 0.494339 + 0.869269i \(0.335410\pi\)
−0.494339 + 0.869269i \(0.664590\pi\)
\(954\) 0 0
\(955\) 8.02069 + 4.63075i 0.259543 + 0.149847i
\(956\) 18.5118i 0.598714i
\(957\) 0 0
\(958\) −12.0186 6.93894i −0.388303 0.224187i
\(959\) −25.0252 + 5.37473i −0.808105 + 0.173559i
\(960\) 0 0
\(961\) 15.2606 26.4322i 0.492279 0.852652i
\(962\) 17.4283 30.1867i 0.561910 0.973257i
\(963\) 0 0
\(964\) 18.9977 10.9683i 0.611874 0.353266i
\(965\) 12.1247 + 21.0006i 0.390308 + 0.676034i
\(966\) 0 0
\(967\) 8.76620 15.1835i 0.281902 0.488268i −0.689951 0.723856i \(-0.742368\pi\)
0.971853 + 0.235587i \(0.0757014\pi\)
\(968\) 5.63079i 0.180981i
\(969\) 0 0
\(970\) 19.4824 0.625542
\(971\) −1.13150 1.95981i −0.0363115 0.0628933i 0.847299 0.531117i \(-0.178228\pi\)
−0.883610 + 0.468224i \(0.844894\pi\)
\(972\) 0 0
\(973\) −4.28750 + 13.2914i −0.137451 + 0.426101i
\(974\) −23.9026 + 13.8002i −0.765888 + 0.442186i
\(975\) 0 0
\(976\) 2.56956 1.48353i 0.0822495 0.0474868i
\(977\) −39.2275 + 22.6480i −1.25500 + 0.724574i −0.972098 0.234575i \(-0.924630\pi\)
−0.282901 + 0.959149i \(0.591297\pi\)
\(978\) 0 0
\(979\) −51.5277 + 29.7495i −1.64683 + 0.950799i
\(980\) −5.68051 4.09045i −0.181457 0.130665i
\(981\) 0 0
\(982\) −10.5048 18.1949i −0.335222 0.580621i
\(983\) −27.1875 −0.867145 −0.433572 0.901119i \(-0.642747\pi\)
−0.433572 + 0.901119i \(0.642747\pi\)
\(984\) 0 0
\(985\) 18.8947i 0.602036i
\(986\) 4.60795 7.98120i 0.146747 0.254173i
\(987\) 0 0
\(988\) −10.0810 17.4608i −0.320719 0.555501i
\(989\) −9.24086 + 5.33521i −0.293842 + 0.169650i
\(990\) 0 0
\(991\) −13.1793 + 22.8272i −0.418654 + 0.725130i −0.995804 0.0915077i \(-0.970831\pi\)
0.577150 + 0.816638i \(0.304165\pi\)
\(992\) −3.92178 + 6.79271i −0.124516 + 0.215669i
\(993\) 0 0
\(994\) 35.5980 + 11.4831i 1.12910 + 0.364223i
\(995\) 2.25502 + 1.30194i 0.0714890 + 0.0412742i
\(996\) 0 0
\(997\) 51.3611i 1.62662i −0.581828 0.813312i \(-0.697662\pi\)
0.581828 0.813312i \(-0.302338\pi\)
\(998\) −0.342363 0.197663i −0.0108373 0.00625692i
\(999\) 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 1890.2.t.b.1151.1 28
3.2 odd 2 630.2.t.b.311.9 28
7.5 odd 6 1890.2.bk.b.341.13 28
9.2 odd 6 1890.2.bk.b.521.13 28
9.7 even 3 630.2.bk.b.101.12 yes 28
21.5 even 6 630.2.bk.b.131.5 yes 28
63.47 even 6 inner 1890.2.t.b.1601.1 28
63.61 odd 6 630.2.t.b.551.9 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.t.b.311.9 28 3.2 odd 2
630.2.t.b.551.9 yes 28 63.61 odd 6
630.2.bk.b.101.12 yes 28 9.7 even 3
630.2.bk.b.131.5 yes 28 21.5 even 6
1890.2.t.b.1151.1 28 1.1 even 1 trivial
1890.2.t.b.1601.1 28 63.47 even 6 inner
1890.2.bk.b.341.13 28 7.5 odd 6
1890.2.bk.b.521.13 28 9.2 odd 6