Properties

Label 1386.2.ba.b.989.14
Level $1386$
Weight $2$
Character 1386.989
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1386,2,Mod(989,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.989");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), 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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 989.14
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.b.1187.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.34835 + 1.35582i) q^{5} +(0.222226 + 2.63640i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.34835 + 1.35582i) q^{5} +(0.222226 + 2.63640i) q^{7} -1.00000 q^{8} +(2.34835 - 1.35582i) q^{10} +(-2.77145 + 1.82183i) q^{11} +2.18074i q^{13} +(2.39430 + 1.12575i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.0281751 - 0.0488007i) q^{17} +(-2.38555 - 1.37730i) q^{19} -2.71165i q^{20} +(0.192032 + 3.31106i) q^{22} +(6.02718 + 3.47980i) q^{23} +(1.17651 + 2.03778i) q^{25} +(1.88857 + 1.09037i) q^{26} +(2.17208 - 1.51065i) q^{28} -6.43297 q^{29} +(3.65147 + 6.32453i) q^{31} +(0.500000 + 0.866025i) q^{32} -0.0563502 q^{34} +(-3.05263 + 6.49251i) q^{35} +(-1.62140 + 2.80836i) q^{37} +(-2.38555 + 1.37730i) q^{38} +(-2.34835 - 1.35582i) q^{40} -2.71397 q^{41} +10.6345i q^{43} +(2.96348 + 1.48923i) q^{44} +(6.02718 - 3.47980i) q^{46} +(-2.58268 - 1.49111i) q^{47} +(-6.90123 + 1.17175i) q^{49} +2.35302 q^{50} +(1.88857 - 1.09037i) q^{52} +(10.1931 - 5.88497i) q^{53} +(-8.97843 + 0.520722i) q^{55} +(-0.222226 - 2.63640i) q^{56} +(-3.21649 + 5.57112i) q^{58} +(12.2489 - 7.07189i) q^{59} +(-10.2720 - 5.93056i) q^{61} +7.30294 q^{62} +1.00000 q^{64} +(-2.95669 + 5.12114i) q^{65} +(0.749028 + 1.29735i) q^{67} +(-0.0281751 + 0.0488007i) q^{68} +(4.09636 + 5.88991i) q^{70} -1.82248i q^{71} +(-6.82420 + 3.93995i) q^{73} +(1.62140 + 2.80836i) q^{74} +2.75460i q^{76} +(-5.41898 - 6.90179i) q^{77} +(7.82062 + 4.51524i) q^{79} +(-2.34835 + 1.35582i) q^{80} +(-1.35699 + 2.35037i) q^{82} +17.2299 q^{83} -0.152802i q^{85} +(9.20975 + 5.31725i) q^{86} +(2.77145 - 1.82183i) q^{88} +(7.43764 + 4.29412i) q^{89} +(-5.74929 + 0.484616i) q^{91} -6.95959i q^{92} +(-2.58268 + 1.49111i) q^{94} +(-3.73475 - 6.46878i) q^{95} +6.25716 q^{97} +(-2.43585 + 6.56252i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 2 q^{11} - 16 q^{16} + 4 q^{17} + 4 q^{22} + 4 q^{25} + 16 q^{29} + 4 q^{31} + 16 q^{32} + 8 q^{34} + 16 q^{35} + 4 q^{37} - 32 q^{41} + 2 q^{44} + 20 q^{49} + 8 q^{50} - 12 q^{55} + 8 q^{58} + 8 q^{62} + 32 q^{64} - 8 q^{67} + 4 q^{68} - 4 q^{70} - 4 q^{74} + 14 q^{77} - 16 q^{82} + 88 q^{83} - 2 q^{88} - 24 q^{95} - 32 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.34835 + 1.35582i 1.05022 + 0.606343i 0.922710 0.385495i \(-0.125969\pi\)
0.127506 + 0.991838i \(0.459303\pi\)
\(6\) 0 0
\(7\) 0.222226 + 2.63640i 0.0839935 + 0.996466i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 2.34835 1.35582i 0.742615 0.428749i
\(11\) −2.77145 + 1.82183i −0.835623 + 0.549304i
\(12\) 0 0
\(13\) 2.18074i 0.604827i 0.953177 + 0.302414i \(0.0977924\pi\)
−0.953177 + 0.302414i \(0.902208\pi\)
\(14\) 2.39430 + 1.12575i 0.639905 + 0.300869i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.0281751 0.0488007i −0.00683347 0.0118359i 0.862588 0.505906i \(-0.168842\pi\)
−0.869422 + 0.494070i \(0.835509\pi\)
\(18\) 0 0
\(19\) −2.38555 1.37730i −0.547284 0.315974i 0.200742 0.979644i \(-0.435665\pi\)
−0.748026 + 0.663670i \(0.768998\pi\)
\(20\) 2.71165i 0.606343i
\(21\) 0 0
\(22\) 0.192032 + 3.31106i 0.0409413 + 0.705921i
\(23\) 6.02718 + 3.47980i 1.25675 + 0.725587i 0.972442 0.233144i \(-0.0749014\pi\)
0.284312 + 0.958732i \(0.408235\pi\)
\(24\) 0 0
\(25\) 1.17651 + 2.03778i 0.235302 + 0.407556i
\(26\) 1.88857 + 1.09037i 0.370379 + 0.213839i
\(27\) 0 0
\(28\) 2.17208 1.51065i 0.410484 0.285487i
\(29\) −6.43297 −1.19457 −0.597286 0.802028i \(-0.703754\pi\)
−0.597286 + 0.802028i \(0.703754\pi\)
\(30\) 0 0
\(31\) 3.65147 + 6.32453i 0.655823 + 1.13592i 0.981687 + 0.190502i \(0.0610116\pi\)
−0.325864 + 0.945417i \(0.605655\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −0.0563502 −0.00966399
\(35\) −3.05263 + 6.49251i −0.515989 + 1.09743i
\(36\) 0 0
\(37\) −1.62140 + 2.80836i −0.266557 + 0.461691i −0.967970 0.251064i \(-0.919219\pi\)
0.701413 + 0.712755i \(0.252553\pi\)
\(38\) −2.38555 + 1.37730i −0.386988 + 0.223428i
\(39\) 0 0
\(40\) −2.34835 1.35582i −0.371307 0.214374i
\(41\) −2.71397 −0.423852 −0.211926 0.977286i \(-0.567974\pi\)
−0.211926 + 0.977286i \(0.567974\pi\)
\(42\) 0 0
\(43\) 10.6345i 1.62175i 0.585221 + 0.810874i \(0.301008\pi\)
−0.585221 + 0.810874i \(0.698992\pi\)
\(44\) 2.96348 + 1.48923i 0.446761 + 0.224509i
\(45\) 0 0
\(46\) 6.02718 3.47980i 0.888660 0.513068i
\(47\) −2.58268 1.49111i −0.376723 0.217501i 0.299669 0.954043i \(-0.403124\pi\)
−0.676391 + 0.736542i \(0.736457\pi\)
\(48\) 0 0
\(49\) −6.90123 + 1.17175i −0.985890 + 0.167393i
\(50\) 2.35302 0.332768
\(51\) 0 0
\(52\) 1.88857 1.09037i 0.261898 0.151207i
\(53\) 10.1931 5.88497i 1.40012 0.808362i 0.405719 0.913998i \(-0.367021\pi\)
0.994405 + 0.105636i \(0.0336877\pi\)
\(54\) 0 0
\(55\) −8.97843 + 0.520722i −1.21065 + 0.0702142i
\(56\) −0.222226 2.63640i −0.0296962 0.352304i
\(57\) 0 0
\(58\) −3.21649 + 5.57112i −0.422345 + 0.731524i
\(59\) 12.2489 7.07189i 1.59467 0.920681i 0.602175 0.798364i \(-0.294301\pi\)
0.992491 0.122317i \(-0.0390326\pi\)
\(60\) 0 0
\(61\) −10.2720 5.93056i −1.31520 0.759331i −0.332247 0.943192i \(-0.607807\pi\)
−0.982952 + 0.183861i \(0.941140\pi\)
\(62\) 7.30294 0.927474
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.95669 + 5.12114i −0.366732 + 0.635199i
\(66\) 0 0
\(67\) 0.749028 + 1.29735i 0.0915083 + 0.158497i 0.908146 0.418654i \(-0.137498\pi\)
−0.816638 + 0.577151i \(0.804165\pi\)
\(68\) −0.0281751 + 0.0488007i −0.00341674 + 0.00591796i
\(69\) 0 0
\(70\) 4.09636 + 5.88991i 0.489609 + 0.703979i
\(71\) 1.82248i 0.216288i −0.994135 0.108144i \(-0.965509\pi\)
0.994135 0.108144i \(-0.0344908\pi\)
\(72\) 0 0
\(73\) −6.82420 + 3.93995i −0.798712 + 0.461137i −0.843021 0.537881i \(-0.819225\pi\)
0.0443085 + 0.999018i \(0.485892\pi\)
\(74\) 1.62140 + 2.80836i 0.188484 + 0.326465i
\(75\) 0 0
\(76\) 2.75460i 0.315974i
\(77\) −5.41898 6.90179i −0.617550 0.786532i
\(78\) 0 0
\(79\) 7.82062 + 4.51524i 0.879889 + 0.508004i 0.870622 0.491953i \(-0.163717\pi\)
0.00926708 + 0.999957i \(0.497050\pi\)
\(80\) −2.34835 + 1.35582i −0.262554 + 0.151586i
\(81\) 0 0
\(82\) −1.35699 + 2.35037i −0.149854 + 0.259555i
\(83\) 17.2299 1.89123 0.945615 0.325288i \(-0.105461\pi\)
0.945615 + 0.325288i \(0.105461\pi\)
\(84\) 0 0
\(85\) 0.152802i 0.0165737i
\(86\) 9.20975 + 5.31725i 0.993113 + 0.573374i
\(87\) 0 0
\(88\) 2.77145 1.82183i 0.295437 0.194208i
\(89\) 7.43764 + 4.29412i 0.788388 + 0.455176i 0.839395 0.543522i \(-0.182910\pi\)
−0.0510066 + 0.998698i \(0.516243\pi\)
\(90\) 0 0
\(91\) −5.74929 + 0.484616i −0.602690 + 0.0508015i
\(92\) 6.95959i 0.725587i
\(93\) 0 0
\(94\) −2.58268 + 1.49111i −0.266383 + 0.153796i
\(95\) −3.73475 6.46878i −0.383177 0.663683i
\(96\) 0 0
\(97\) 6.25716 0.635319 0.317659 0.948205i \(-0.397103\pi\)
0.317659 + 0.948205i \(0.397103\pi\)
\(98\) −2.43585 + 6.56252i −0.246058 + 0.662914i
\(99\) 0 0
\(100\) 1.17651 2.03778i 0.117651 0.203778i
\(101\) −7.86795 13.6277i −0.782891 1.35601i −0.930251 0.366924i \(-0.880411\pi\)
0.147360 0.989083i \(-0.452922\pi\)
\(102\) 0 0
\(103\) −4.13406 + 7.16040i −0.407341 + 0.705535i −0.994591 0.103870i \(-0.966877\pi\)
0.587250 + 0.809406i \(0.300211\pi\)
\(104\) 2.18074i 0.213839i
\(105\) 0 0
\(106\) 11.7699i 1.14320i
\(107\) 5.86711 10.1621i 0.567195 0.982410i −0.429647 0.902997i \(-0.641362\pi\)
0.996842 0.0794132i \(-0.0253046\pi\)
\(108\) 0 0
\(109\) 5.76234 3.32689i 0.551932 0.318658i −0.197969 0.980208i \(-0.563434\pi\)
0.749901 + 0.661550i \(0.230101\pi\)
\(110\) −4.03825 + 8.03591i −0.385032 + 0.766194i
\(111\) 0 0
\(112\) −2.39430 1.12575i −0.226240 0.106373i
\(113\) 12.8006i 1.20418i 0.798428 + 0.602090i \(0.205665\pi\)
−0.798428 + 0.602090i \(0.794335\pi\)
\(114\) 0 0
\(115\) 9.43597 + 16.3436i 0.879909 + 1.52405i
\(116\) 3.21649 + 5.57112i 0.298643 + 0.517265i
\(117\) 0 0
\(118\) 14.1438i 1.30204i
\(119\) 0.122397 0.0851257i 0.0112201 0.00780346i
\(120\) 0 0
\(121\) 4.36184 10.0982i 0.396531 0.918022i
\(122\) −10.2720 + 5.93056i −0.929987 + 0.536928i
\(123\) 0 0
\(124\) 3.65147 6.32453i 0.327911 0.567959i
\(125\) 7.17766i 0.641989i
\(126\) 0 0
\(127\) 5.80675i 0.515265i 0.966243 + 0.257633i \(0.0829424\pi\)
−0.966243 + 0.257633i \(0.917058\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.95669 + 5.12114i 0.259319 + 0.449154i
\(131\) −0.981044 + 1.69922i −0.0857142 + 0.148461i −0.905695 0.423929i \(-0.860651\pi\)
0.819981 + 0.572391i \(0.193984\pi\)
\(132\) 0 0
\(133\) 3.10098 6.59535i 0.268889 0.571889i
\(134\) 1.49806 0.129412
\(135\) 0 0
\(136\) 0.0281751 + 0.0488007i 0.00241600 + 0.00418463i
\(137\) 5.51740 3.18547i 0.471383 0.272153i −0.245435 0.969413i \(-0.578931\pi\)
0.716819 + 0.697260i \(0.245598\pi\)
\(138\) 0 0
\(139\) 11.2048i 0.950382i 0.879883 + 0.475191i \(0.157621\pi\)
−0.879883 + 0.475191i \(0.842379\pi\)
\(140\) 7.14899 0.602598i 0.604200 0.0509288i
\(141\) 0 0
\(142\) −1.57831 0.911240i −0.132449 0.0764695i
\(143\) −3.97294 6.04379i −0.332234 0.505407i
\(144\) 0 0
\(145\) −15.1069 8.72197i −1.25456 0.724320i
\(146\) 7.87991i 0.652146i
\(147\) 0 0
\(148\) 3.24281 0.266557
\(149\) 8.08008 13.9951i 0.661946 1.14652i −0.318157 0.948038i \(-0.603064\pi\)
0.980104 0.198487i \(-0.0636027\pi\)
\(150\) 0 0
\(151\) 11.4616 6.61738i 0.932734 0.538514i 0.0450590 0.998984i \(-0.485652\pi\)
0.887675 + 0.460470i \(0.152319\pi\)
\(152\) 2.38555 + 1.37730i 0.193494 + 0.111714i
\(153\) 0 0
\(154\) −8.68661 + 1.24208i −0.699987 + 0.100089i
\(155\) 19.8030i 1.59061i
\(156\) 0 0
\(157\) −0.671466 1.16301i −0.0535888 0.0928185i 0.837987 0.545691i \(-0.183733\pi\)
−0.891575 + 0.452872i \(0.850399\pi\)
\(158\) 7.82062 4.51524i 0.622175 0.359213i
\(159\) 0 0
\(160\) 2.71165i 0.214374i
\(161\) −7.83474 + 16.6634i −0.617464 + 1.31326i
\(162\) 0 0
\(163\) 9.16486 15.8740i 0.717847 1.24335i −0.244004 0.969774i \(-0.578461\pi\)
0.961851 0.273574i \(-0.0882057\pi\)
\(164\) 1.35699 + 2.35037i 0.105963 + 0.183533i
\(165\) 0 0
\(166\) 8.61496 14.9216i 0.668651 1.15814i
\(167\) 5.04452 0.390357 0.195178 0.980768i \(-0.437471\pi\)
0.195178 + 0.980768i \(0.437471\pi\)
\(168\) 0 0
\(169\) 8.24439 0.634184
\(170\) −0.132330 0.0764010i −0.0101493 0.00585969i
\(171\) 0 0
\(172\) 9.20975 5.31725i 0.702237 0.405437i
\(173\) −0.459832 + 0.796453i −0.0349604 + 0.0605532i −0.882976 0.469418i \(-0.844464\pi\)
0.848016 + 0.529971i \(0.177797\pi\)
\(174\) 0 0
\(175\) −5.11095 + 3.55461i −0.386352 + 0.268703i
\(176\) −0.192032 3.31106i −0.0144749 0.249581i
\(177\) 0 0
\(178\) 7.43764 4.29412i 0.557475 0.321858i
\(179\) −14.9660 + 8.64063i −1.11861 + 0.645831i −0.941046 0.338278i \(-0.890156\pi\)
−0.177566 + 0.984109i \(0.556822\pi\)
\(180\) 0 0
\(181\) −9.68621 −0.719970 −0.359985 0.932958i \(-0.617218\pi\)
−0.359985 + 0.932958i \(0.617218\pi\)
\(182\) −2.45496 + 5.22134i −0.181974 + 0.387032i
\(183\) 0 0
\(184\) −6.02718 3.47980i −0.444330 0.256534i
\(185\) −7.61527 + 4.39668i −0.559885 + 0.323250i
\(186\) 0 0
\(187\) 0.166993 + 0.0839183i 0.0122117 + 0.00613671i
\(188\) 2.98222i 0.217501i
\(189\) 0 0
\(190\) −7.46950 −0.541895
\(191\) −10.5752 6.10561i −0.765197 0.441787i 0.0659616 0.997822i \(-0.478989\pi\)
−0.831159 + 0.556035i \(0.812322\pi\)
\(192\) 0 0
\(193\) −6.93577 + 4.00437i −0.499248 + 0.288241i −0.728403 0.685149i \(-0.759737\pi\)
0.229155 + 0.973390i \(0.426404\pi\)
\(194\) 3.12858 5.41886i 0.224619 0.389052i
\(195\) 0 0
\(196\) 4.46538 + 5.39076i 0.318956 + 0.385055i
\(197\) 6.14148 0.437562 0.218781 0.975774i \(-0.429792\pi\)
0.218781 + 0.975774i \(0.429792\pi\)
\(198\) 0 0
\(199\) −5.93851 10.2858i −0.420970 0.729141i 0.575065 0.818108i \(-0.304977\pi\)
−0.996035 + 0.0889669i \(0.971643\pi\)
\(200\) −1.17651 2.03778i −0.0831920 0.144093i
\(201\) 0 0
\(202\) −15.7359 −1.10717
\(203\) −1.42957 16.9599i −0.100336 1.19035i
\(204\) 0 0
\(205\) −6.37337 3.67967i −0.445136 0.256999i
\(206\) 4.13406 + 7.16040i 0.288034 + 0.498889i
\(207\) 0 0
\(208\) −1.88857 1.09037i −0.130949 0.0756034i
\(209\) 9.12065 0.528971i 0.630888 0.0365897i
\(210\) 0 0
\(211\) 19.9499i 1.37341i −0.726936 0.686706i \(-0.759056\pi\)
0.726936 0.686706i \(-0.240944\pi\)
\(212\) −10.1931 5.88497i −0.700062 0.404181i
\(213\) 0 0
\(214\) −5.86711 10.1621i −0.401067 0.694669i
\(215\) −14.4185 + 24.9736i −0.983334 + 1.70318i
\(216\) 0 0
\(217\) −15.8625 + 11.0322i −1.07682 + 0.748915i
\(218\) 6.65378i 0.450651i
\(219\) 0 0
\(220\) 4.94017 + 7.51518i 0.333066 + 0.506674i
\(221\) 0.106421 0.0614425i 0.00715868 0.00413307i
\(222\) 0 0
\(223\) −13.6887 −0.916665 −0.458333 0.888781i \(-0.651553\pi\)
−0.458333 + 0.888781i \(0.651553\pi\)
\(224\) −2.17208 + 1.51065i −0.145128 + 0.100935i
\(225\) 0 0
\(226\) 11.0856 + 6.40030i 0.737406 + 0.425742i
\(227\) 3.18180 + 5.51104i 0.211184 + 0.365781i 0.952085 0.305833i \(-0.0989349\pi\)
−0.740902 + 0.671614i \(0.765602\pi\)
\(228\) 0 0
\(229\) −5.17077 + 8.95604i −0.341694 + 0.591832i −0.984747 0.173990i \(-0.944334\pi\)
0.643053 + 0.765822i \(0.277667\pi\)
\(230\) 18.8719 1.24438
\(231\) 0 0
\(232\) 6.43297 0.422345
\(233\) 4.45228 7.71157i 0.291678 0.505202i −0.682528 0.730859i \(-0.739120\pi\)
0.974207 + 0.225657i \(0.0724529\pi\)
\(234\) 0 0
\(235\) −4.04336 7.00331i −0.263760 0.456846i
\(236\) −12.2489 7.07189i −0.797333 0.460341i
\(237\) 0 0
\(238\) −0.0125225 0.148562i −0.000811712 0.00962984i
\(239\) −22.6090 −1.46246 −0.731228 0.682133i \(-0.761053\pi\)
−0.731228 + 0.682133i \(0.761053\pi\)
\(240\) 0 0
\(241\) −8.06528 + 4.65649i −0.519530 + 0.299951i −0.736742 0.676173i \(-0.763637\pi\)
0.217212 + 0.976124i \(0.430304\pi\)
\(242\) −6.56441 8.82658i −0.421976 0.567394i
\(243\) 0 0
\(244\) 11.8611i 0.759331i
\(245\) −17.7952 6.60516i −1.13690 0.421988i
\(246\) 0 0
\(247\) 3.00353 5.20226i 0.191110 0.331012i
\(248\) −3.65147 6.32453i −0.231868 0.401608i
\(249\) 0 0
\(250\) −6.21604 3.58883i −0.393137 0.226978i
\(251\) 4.12748i 0.260524i −0.991480 0.130262i \(-0.958418\pi\)
0.991480 0.130262i \(-0.0415819\pi\)
\(252\) 0 0
\(253\) −23.0436 + 1.33646i −1.44874 + 0.0840227i
\(254\) 5.02879 + 2.90337i 0.315534 + 0.182174i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −13.1583 7.59695i −0.820792 0.473885i 0.0298973 0.999553i \(-0.490482\pi\)
−0.850690 + 0.525668i \(0.823815\pi\)
\(258\) 0 0
\(259\) −7.76427 3.65058i −0.482448 0.226836i
\(260\) 5.91338 0.366732
\(261\) 0 0
\(262\) 0.981044 + 1.69922i 0.0606091 + 0.104978i
\(263\) −8.24623 14.2829i −0.508484 0.880720i −0.999952 0.00982443i \(-0.996873\pi\)
0.491468 0.870896i \(-0.336461\pi\)
\(264\) 0 0
\(265\) 31.9159 1.96058
\(266\) −4.16125 5.98321i −0.255143 0.366854i
\(267\) 0 0
\(268\) 0.749028 1.29735i 0.0457541 0.0792485i
\(269\) −12.6371 + 7.29606i −0.770500 + 0.444848i −0.833053 0.553193i \(-0.813409\pi\)
0.0625529 + 0.998042i \(0.480076\pi\)
\(270\) 0 0
\(271\) 21.0688 + 12.1641i 1.27984 + 0.738914i 0.976818 0.214071i \(-0.0686723\pi\)
0.303018 + 0.952985i \(0.402006\pi\)
\(272\) 0.0563502 0.00341674
\(273\) 0 0
\(274\) 6.37094i 0.384883i
\(275\) −6.97314 3.50419i −0.420496 0.211310i
\(276\) 0 0
\(277\) −2.92994 + 1.69160i −0.176043 + 0.101638i −0.585432 0.810721i \(-0.699075\pi\)
0.409389 + 0.912360i \(0.365742\pi\)
\(278\) 9.70368 + 5.60242i 0.581988 + 0.336011i
\(279\) 0 0
\(280\) 3.05263 6.49251i 0.182430 0.388001i
\(281\) 7.92539 0.472789 0.236395 0.971657i \(-0.424034\pi\)
0.236395 + 0.971657i \(0.424034\pi\)
\(282\) 0 0
\(283\) 20.8485 12.0369i 1.23931 0.715518i 0.270360 0.962759i \(-0.412857\pi\)
0.968954 + 0.247241i \(0.0795240\pi\)
\(284\) −1.57831 + 0.911240i −0.0936557 + 0.0540721i
\(285\) 0 0
\(286\) −7.22055 + 0.418770i −0.426960 + 0.0247624i
\(287\) −0.603115 7.15513i −0.0356008 0.422354i
\(288\) 0 0
\(289\) 8.49841 14.7197i 0.499907 0.865864i
\(290\) −15.1069 + 8.72197i −0.887108 + 0.512172i
\(291\) 0 0
\(292\) 6.82420 + 3.93995i 0.399356 + 0.230568i
\(293\) 16.6528 0.972864 0.486432 0.873718i \(-0.338298\pi\)
0.486432 + 0.873718i \(0.338298\pi\)
\(294\) 0 0
\(295\) 38.3529 2.23299
\(296\) 1.62140 2.80836i 0.0942422 0.163232i
\(297\) 0 0
\(298\) −8.08008 13.9951i −0.468067 0.810715i
\(299\) −7.58851 + 13.1437i −0.438855 + 0.760119i
\(300\) 0 0
\(301\) −28.0368 + 2.36326i −1.61602 + 0.136216i
\(302\) 13.2348i 0.761574i
\(303\) 0 0
\(304\) 2.38555 1.37730i 0.136821 0.0789936i
\(305\) −16.0816 27.8541i −0.920829 1.59492i
\(306\) 0 0
\(307\) 29.4599i 1.68137i 0.541528 + 0.840683i \(0.317846\pi\)
−0.541528 + 0.840683i \(0.682154\pi\)
\(308\) −3.26764 + 8.14387i −0.186191 + 0.464040i
\(309\) 0 0
\(310\) 17.1499 + 9.90149i 0.974048 + 0.562367i
\(311\) 0.466034 0.269065i 0.0264263 0.0152573i −0.486729 0.873553i \(-0.661810\pi\)
0.513155 + 0.858296i \(0.328477\pi\)
\(312\) 0 0
\(313\) −6.81418 + 11.8025i −0.385160 + 0.667117i −0.991791 0.127866i \(-0.959187\pi\)
0.606631 + 0.794984i \(0.292521\pi\)
\(314\) −1.34293 −0.0757860
\(315\) 0 0
\(316\) 9.03048i 0.508004i
\(317\) 0.730381 + 0.421686i 0.0410223 + 0.0236842i 0.520371 0.853940i \(-0.325794\pi\)
−0.479349 + 0.877625i \(0.659127\pi\)
\(318\) 0 0
\(319\) 17.8286 11.7198i 0.998212 0.656184i
\(320\) 2.34835 + 1.35582i 0.131277 + 0.0757928i
\(321\) 0 0
\(322\) 10.5135 + 15.1168i 0.585896 + 0.842425i
\(323\) 0.155222i 0.00863681i
\(324\) 0 0
\(325\) −4.44386 + 2.56566i −0.246501 + 0.142317i
\(326\) −9.16486 15.8740i −0.507595 0.879180i
\(327\) 0 0
\(328\) 2.71397 0.149854
\(329\) 3.35723 7.14034i 0.185090 0.393660i
\(330\) 0 0
\(331\) 5.79849 10.0433i 0.318714 0.552028i −0.661506 0.749940i \(-0.730082\pi\)
0.980220 + 0.197911i \(0.0634158\pi\)
\(332\) −8.61496 14.9216i −0.472808 0.818927i
\(333\) 0 0
\(334\) 2.52226 4.36868i 0.138012 0.239044i
\(335\) 4.06220i 0.221941i
\(336\) 0 0
\(337\) 0.863660i 0.0470466i −0.999723 0.0235233i \(-0.992512\pi\)
0.999723 0.0235233i \(-0.00748838\pi\)
\(338\) 4.12220 7.13986i 0.224218 0.388357i
\(339\) 0 0
\(340\) −0.132330 + 0.0764010i −0.00717662 + 0.00414342i
\(341\) −21.6421 10.8757i −1.17199 0.588953i
\(342\) 0 0
\(343\) −4.62285 17.9340i −0.249610 0.968346i
\(344\) 10.6345i 0.573374i
\(345\) 0 0
\(346\) 0.459832 + 0.796453i 0.0247207 + 0.0428176i
\(347\) 3.69571 + 6.40116i 0.198396 + 0.343632i 0.948009 0.318245i \(-0.103093\pi\)
−0.749612 + 0.661877i \(0.769760\pi\)
\(348\) 0 0
\(349\) 31.5777i 1.69032i 0.534515 + 0.845159i \(0.320494\pi\)
−0.534515 + 0.845159i \(0.679506\pi\)
\(350\) 0.522903 + 6.20352i 0.0279503 + 0.331592i
\(351\) 0 0
\(352\) −2.96348 1.48923i −0.157954 0.0793760i
\(353\) −3.85186 + 2.22387i −0.205014 + 0.118365i −0.598992 0.800755i \(-0.704432\pi\)
0.393978 + 0.919120i \(0.371099\pi\)
\(354\) 0 0
\(355\) 2.47096 4.27983i 0.131145 0.227150i
\(356\) 8.58825i 0.455176i
\(357\) 0 0
\(358\) 17.2813i 0.913343i
\(359\) −10.0548 + 17.4154i −0.530673 + 0.919152i 0.468687 + 0.883364i \(0.344727\pi\)
−0.999359 + 0.0357874i \(0.988606\pi\)
\(360\) 0 0
\(361\) −5.70609 9.88324i −0.300320 0.520170i
\(362\) −4.84310 + 8.38850i −0.254548 + 0.440890i
\(363\) 0 0
\(364\) 3.29434 + 4.73673i 0.172670 + 0.248272i
\(365\) −21.3675 −1.11843
\(366\) 0 0
\(367\) −6.39813 11.0819i −0.333980 0.578470i 0.649309 0.760525i \(-0.275058\pi\)
−0.983288 + 0.182055i \(0.941725\pi\)
\(368\) −6.02718 + 3.47980i −0.314189 + 0.181397i
\(369\) 0 0
\(370\) 8.79335i 0.457145i
\(371\) 17.7803 + 25.5652i 0.923107 + 1.32728i
\(372\) 0 0
\(373\) −6.97826 4.02890i −0.361321 0.208609i 0.308339 0.951276i \(-0.400227\pi\)
−0.669660 + 0.742668i \(0.733560\pi\)
\(374\) 0.156172 0.102661i 0.00807545 0.00530847i
\(375\) 0 0
\(376\) 2.58268 + 1.49111i 0.133192 + 0.0768982i
\(377\) 14.0286i 0.722510i
\(378\) 0 0
\(379\) −30.6120 −1.57244 −0.786218 0.617950i \(-0.787964\pi\)
−0.786218 + 0.617950i \(0.787964\pi\)
\(380\) −3.73475 + 6.46878i −0.191589 + 0.331841i
\(381\) 0 0
\(382\) −10.5752 + 6.10561i −0.541076 + 0.312390i
\(383\) 0.763632 + 0.440883i 0.0390198 + 0.0225281i 0.519383 0.854542i \(-0.326162\pi\)
−0.480363 + 0.877070i \(0.659495\pi\)
\(384\) 0 0
\(385\) −3.36807 23.5550i −0.171653 1.20048i
\(386\) 8.00874i 0.407634i
\(387\) 0 0
\(388\) −3.12858 5.41886i −0.158830 0.275101i
\(389\) 5.35275 3.09041i 0.271395 0.156690i −0.358126 0.933673i \(-0.616584\pi\)
0.629522 + 0.776983i \(0.283251\pi\)
\(390\) 0 0
\(391\) 0.392175i 0.0198331i
\(392\) 6.90123 1.17175i 0.348565 0.0591825i
\(393\) 0 0
\(394\) 3.07074 5.31868i 0.154702 0.267951i
\(395\) 12.2437 + 21.2068i 0.616049 + 1.06703i
\(396\) 0 0
\(397\) 13.4710 23.3325i 0.676091 1.17102i −0.300058 0.953921i \(-0.597006\pi\)
0.976149 0.217103i \(-0.0696608\pi\)
\(398\) −11.8770 −0.595341
\(399\) 0 0
\(400\) −2.35302 −0.117651
\(401\) 3.85186 + 2.22387i 0.192353 + 0.111055i 0.593083 0.805141i \(-0.297910\pi\)
−0.400731 + 0.916196i \(0.631244\pi\)
\(402\) 0 0
\(403\) −13.7921 + 7.96288i −0.687034 + 0.396659i
\(404\) −7.86795 + 13.6277i −0.391445 + 0.678003i
\(405\) 0 0
\(406\) −15.4025 7.24190i −0.764413 0.359410i
\(407\) −0.622722 10.7371i −0.0308672 0.532220i
\(408\) 0 0
\(409\) −1.50956 + 0.871544i −0.0746428 + 0.0430951i −0.536857 0.843673i \(-0.680388\pi\)
0.462214 + 0.886768i \(0.347055\pi\)
\(410\) −6.37337 + 3.67967i −0.314758 + 0.181726i
\(411\) 0 0
\(412\) 8.26812 0.407341
\(413\) 21.3663 + 30.7214i 1.05137 + 1.51170i
\(414\) 0 0
\(415\) 40.4620 + 23.3607i 1.98620 + 1.14673i
\(416\) −1.88857 + 1.09037i −0.0925949 + 0.0534597i
\(417\) 0 0
\(418\) 4.10222 8.16320i 0.200646 0.399275i
\(419\) 22.8877i 1.11814i 0.829121 + 0.559069i \(0.188841\pi\)
−0.829121 + 0.559069i \(0.811159\pi\)
\(420\) 0 0
\(421\) 29.7817 1.45147 0.725735 0.687975i \(-0.241500\pi\)
0.725735 + 0.687975i \(0.241500\pi\)
\(422\) −17.2772 9.97497i −0.841039 0.485574i
\(423\) 0 0
\(424\) −10.1931 + 5.88497i −0.495019 + 0.285799i
\(425\) 0.0662968 0.114829i 0.00321587 0.00557004i
\(426\) 0 0
\(427\) 13.3526 28.3991i 0.646179 1.37433i
\(428\) −11.7342 −0.567195
\(429\) 0 0
\(430\) 14.4185 + 24.9736i 0.695322 + 1.20433i
\(431\) −5.29786 9.17616i −0.255189 0.442000i 0.709758 0.704446i \(-0.248804\pi\)
−0.964947 + 0.262446i \(0.915471\pi\)
\(432\) 0 0
\(433\) −23.5494 −1.13171 −0.565856 0.824504i \(-0.691454\pi\)
−0.565856 + 0.824504i \(0.691454\pi\)
\(434\) 1.62290 + 19.2535i 0.0779018 + 0.924196i
\(435\) 0 0
\(436\) −5.76234 3.32689i −0.275966 0.159329i
\(437\) −9.58544 16.6025i −0.458534 0.794204i
\(438\) 0 0
\(439\) −10.0258 5.78842i −0.478507 0.276266i 0.241287 0.970454i \(-0.422430\pi\)
−0.719794 + 0.694188i \(0.755764\pi\)
\(440\) 8.97843 0.520722i 0.428030 0.0248245i
\(441\) 0 0
\(442\) 0.122885i 0.00584504i
\(443\) 32.4006 + 18.7065i 1.53940 + 0.888771i 0.998874 + 0.0474425i \(0.0151071\pi\)
0.540523 + 0.841329i \(0.318226\pi\)
\(444\) 0 0
\(445\) 11.6441 + 20.1682i 0.551985 + 0.956067i
\(446\) −6.84437 + 11.8548i −0.324090 + 0.561340i
\(447\) 0 0
\(448\) 0.222226 + 2.63640i 0.0104992 + 0.124558i
\(449\) 19.4749i 0.919075i 0.888158 + 0.459538i \(0.151985\pi\)
−0.888158 + 0.459538i \(0.848015\pi\)
\(450\) 0 0
\(451\) 7.52164 4.94441i 0.354180 0.232823i
\(452\) 11.0856 6.40030i 0.521425 0.301045i
\(453\) 0 0
\(454\) 6.36360 0.298659
\(455\) −14.1584 6.65698i −0.663758 0.312084i
\(456\) 0 0
\(457\) 23.7421 + 13.7075i 1.11061 + 0.641212i 0.938988 0.343951i \(-0.111765\pi\)
0.171623 + 0.985163i \(0.445099\pi\)
\(458\) 5.17077 + 8.95604i 0.241614 + 0.418488i
\(459\) 0 0
\(460\) 9.43597 16.3436i 0.439955 0.762024i
\(461\) 38.6594 1.80055 0.900273 0.435325i \(-0.143366\pi\)
0.900273 + 0.435325i \(0.143366\pi\)
\(462\) 0 0
\(463\) 35.4956 1.64962 0.824810 0.565409i \(-0.191282\pi\)
0.824810 + 0.565409i \(0.191282\pi\)
\(464\) 3.21649 5.57112i 0.149322 0.258633i
\(465\) 0 0
\(466\) −4.45228 7.71157i −0.206248 0.357232i
\(467\) −9.49408 5.48141i −0.439334 0.253649i 0.263981 0.964528i \(-0.414964\pi\)
−0.703315 + 0.710878i \(0.748298\pi\)
\(468\) 0 0
\(469\) −3.25389 + 2.26304i −0.150251 + 0.104498i
\(470\) −8.08673 −0.373013
\(471\) 0 0
\(472\) −12.2489 + 7.07189i −0.563800 + 0.325510i
\(473\) −19.3743 29.4730i −0.890832 1.35517i
\(474\) 0 0
\(475\) 6.48164i 0.297398i
\(476\) −0.134920 0.0634362i −0.00618403 0.00290759i
\(477\) 0 0
\(478\) −11.3045 + 19.5800i −0.517057 + 0.895568i
\(479\) −6.08034 10.5315i −0.277818 0.481195i 0.693024 0.720914i \(-0.256278\pi\)
−0.970842 + 0.239719i \(0.922945\pi\)
\(480\) 0 0
\(481\) −6.12428 3.53585i −0.279243 0.161221i
\(482\) 9.31298i 0.424195i
\(483\) 0 0
\(484\) −10.9262 + 1.27166i −0.496648 + 0.0578026i
\(485\) 14.6940 + 8.48360i 0.667222 + 0.385221i
\(486\) 0 0
\(487\) −1.22436 2.12066i −0.0554813 0.0960964i 0.836951 0.547278i \(-0.184336\pi\)
−0.892432 + 0.451182i \(0.851003\pi\)
\(488\) 10.2720 + 5.93056i 0.464993 + 0.268464i
\(489\) 0 0
\(490\) −14.6178 + 12.1085i −0.660367 + 0.547008i
\(491\) −0.134894 −0.00608767 −0.00304383 0.999995i \(-0.500969\pi\)
−0.00304383 + 0.999995i \(0.500969\pi\)
\(492\) 0 0
\(493\) 0.181250 + 0.313934i 0.00816308 + 0.0141389i
\(494\) −3.00353 5.20226i −0.135135 0.234061i
\(495\) 0 0
\(496\) −7.30294 −0.327911
\(497\) 4.80479 0.405002i 0.215524 0.0181668i
\(498\) 0 0
\(499\) −18.6333 + 32.2738i −0.834140 + 1.44477i 0.0605888 + 0.998163i \(0.480702\pi\)
−0.894729 + 0.446610i \(0.852631\pi\)
\(500\) −6.21604 + 3.58883i −0.277990 + 0.160497i
\(501\) 0 0
\(502\) −3.57450 2.06374i −0.159538 0.0921092i
\(503\) −22.4935 −1.00294 −0.501469 0.865176i \(-0.667207\pi\)
−0.501469 + 0.865176i \(0.667207\pi\)
\(504\) 0 0
\(505\) 42.6702i 1.89880i
\(506\) −10.3644 + 20.6246i −0.460754 + 0.916875i
\(507\) 0 0
\(508\) 5.02879 2.90337i 0.223116 0.128816i
\(509\) −20.3512 11.7498i −0.902053 0.520801i −0.0241874 0.999707i \(-0.507700\pi\)
−0.877866 + 0.478907i \(0.841033\pi\)
\(510\) 0 0
\(511\) −11.9038 17.1158i −0.526594 0.757157i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −13.1583 + 7.59695i −0.580388 + 0.335087i
\(515\) −19.4165 + 11.2101i −0.855592 + 0.493976i
\(516\) 0 0
\(517\) 9.87432 0.572681i 0.434272 0.0251865i
\(518\) −7.04363 + 4.89876i −0.309480 + 0.215239i
\(519\) 0 0
\(520\) 2.95669 5.12114i 0.129659 0.224577i
\(521\) −4.95557 + 2.86110i −0.217107 + 0.125347i −0.604610 0.796522i \(-0.706671\pi\)
0.387503 + 0.921869i \(0.373338\pi\)
\(522\) 0 0
\(523\) −1.75580 1.01371i −0.0767758 0.0443265i 0.461121 0.887337i \(-0.347448\pi\)
−0.537896 + 0.843011i \(0.680781\pi\)
\(524\) 1.96209 0.0857142
\(525\) 0 0
\(526\) −16.4925 −0.719105
\(527\) 0.205761 0.356389i 0.00896309 0.0155245i
\(528\) 0 0
\(529\) 12.7179 + 22.0281i 0.552954 + 0.957745i
\(530\) 15.9579 27.6400i 0.693169 1.20060i
\(531\) 0 0
\(532\) −7.26223 + 0.612144i −0.314858 + 0.0265398i
\(533\) 5.91846i 0.256357i
\(534\) 0 0
\(535\) 27.5561 15.9095i 1.19135 0.687829i
\(536\) −0.749028 1.29735i −0.0323531 0.0560371i
\(537\) 0 0
\(538\) 14.5921i 0.629111i
\(539\) 16.9917 15.8204i 0.731882 0.681431i
\(540\) 0 0
\(541\) −12.1688 7.02567i −0.523179 0.302057i 0.215056 0.976602i \(-0.431007\pi\)
−0.738234 + 0.674544i \(0.764340\pi\)
\(542\) 21.0688 12.1641i 0.904981 0.522491i
\(543\) 0 0
\(544\) 0.0281751 0.0488007i 0.00120800 0.00209231i
\(545\) 18.0427 0.772864
\(546\) 0 0
\(547\) 14.9517i 0.639290i −0.947537 0.319645i \(-0.896436\pi\)
0.947537 0.319645i \(-0.103564\pi\)
\(548\) −5.51740 3.18547i −0.235692 0.136077i
\(549\) 0 0
\(550\) −6.52128 + 4.28682i −0.278068 + 0.182791i
\(551\) 15.3462 + 8.86013i 0.653770 + 0.377454i
\(552\) 0 0
\(553\) −10.1660 + 21.6217i −0.432304 + 0.919449i
\(554\) 3.38320i 0.143738i
\(555\) 0 0
\(556\) 9.70368 5.60242i 0.411528 0.237596i
\(557\) −8.41830 14.5809i −0.356695 0.617813i 0.630712 0.776017i \(-0.282763\pi\)
−0.987406 + 0.158204i \(0.949430\pi\)
\(558\) 0 0
\(559\) −23.1910 −0.980876
\(560\) −4.09636 5.88991i −0.173103 0.248894i
\(561\) 0 0
\(562\) 3.96270 6.86359i 0.167156 0.289523i
\(563\) 17.2551 + 29.8868i 0.727218 + 1.25958i 0.958055 + 0.286585i \(0.0925202\pi\)
−0.230837 + 0.972992i \(0.574146\pi\)
\(564\) 0 0
\(565\) −17.3554 + 30.0604i −0.730145 + 1.26465i
\(566\) 24.0738i 1.01190i
\(567\) 0 0
\(568\) 1.82248i 0.0764695i
\(569\) 21.8150 37.7846i 0.914531 1.58401i 0.106944 0.994265i \(-0.465894\pi\)
0.807587 0.589748i \(-0.200773\pi\)
\(570\) 0 0
\(571\) 33.1381 19.1323i 1.38678 0.800660i 0.393833 0.919182i \(-0.371149\pi\)
0.992951 + 0.118522i \(0.0378155\pi\)
\(572\) −3.24761 + 6.46256i −0.135789 + 0.270213i
\(573\) 0 0
\(574\) −6.49808 3.05525i −0.271225 0.127524i
\(575\) 16.3761i 0.682930i
\(576\) 0 0
\(577\) −18.5319 32.0982i −0.771492 1.33626i −0.936745 0.350013i \(-0.886177\pi\)
0.165253 0.986251i \(-0.447156\pi\)
\(578\) −8.49841 14.7197i −0.353487 0.612258i
\(579\) 0 0
\(580\) 17.4439i 0.724320i
\(581\) 3.82894 + 45.4250i 0.158851 + 1.88455i
\(582\) 0 0
\(583\) −17.5281 + 34.8799i −0.725939 + 1.44458i
\(584\) 6.82420 3.93995i 0.282387 0.163036i
\(585\) 0 0
\(586\) 8.32638 14.4217i 0.343960 0.595755i
\(587\) 40.7527i 1.68204i −0.541002 0.841021i \(-0.681955\pi\)
0.541002 0.841021i \(-0.318045\pi\)
\(588\) 0 0
\(589\) 20.1167i 0.828893i
\(590\) 19.1765 33.2146i 0.789482 1.36742i
\(591\) 0 0
\(592\) −1.62140 2.80836i −0.0666393 0.115423i
\(593\) 2.07883 3.60063i 0.0853672 0.147860i −0.820180 0.572105i \(-0.806127\pi\)
0.905548 + 0.424245i \(0.139460\pi\)
\(594\) 0 0
\(595\) 0.402847 0.0339565i 0.0165151 0.00139208i
\(596\) −16.1602 −0.661946
\(597\) 0 0
\(598\) 7.58851 + 13.1437i 0.310317 + 0.537485i
\(599\) 1.70659 0.985302i 0.0697295 0.0402584i −0.464730 0.885452i \(-0.653849\pi\)
0.534459 + 0.845194i \(0.320515\pi\)
\(600\) 0 0
\(601\) 1.40392i 0.0572672i −0.999590 0.0286336i \(-0.990884\pi\)
0.999590 0.0286336i \(-0.00911560\pi\)
\(602\) −11.9718 + 25.4622i −0.487933 + 1.03776i
\(603\) 0 0
\(604\) −11.4616 6.61738i −0.466367 0.269257i
\(605\) 23.9346 17.8004i 0.973078 0.723688i
\(606\) 0 0
\(607\) 11.4032 + 6.58367i 0.462843 + 0.267223i 0.713239 0.700921i \(-0.247227\pi\)
−0.250396 + 0.968144i \(0.580561\pi\)
\(608\) 2.75460i 0.111714i
\(609\) 0 0
\(610\) −32.1632 −1.30225
\(611\) 3.25172 5.63214i 0.131550 0.227852i
\(612\) 0 0
\(613\) −0.364197 + 0.210269i −0.0147098 + 0.00849270i −0.507337 0.861748i \(-0.669370\pi\)
0.492627 + 0.870241i \(0.336037\pi\)
\(614\) 25.5130 + 14.7300i 1.02962 + 0.594453i
\(615\) 0 0
\(616\) 5.41898 + 6.90179i 0.218337 + 0.278081i
\(617\) 2.85323i 0.114867i −0.998349 0.0574333i \(-0.981708\pi\)
0.998349 0.0574333i \(-0.0182917\pi\)
\(618\) 0 0
\(619\) 12.6081 + 21.8380i 0.506764 + 0.877741i 0.999969 + 0.00782835i \(0.00249187\pi\)
−0.493205 + 0.869913i \(0.664175\pi\)
\(620\) 17.1499 9.90149i 0.688756 0.397653i
\(621\) 0 0
\(622\) 0.538129i 0.0215770i
\(623\) −9.66820 + 20.5629i −0.387348 + 0.823834i
\(624\) 0 0
\(625\) 15.6142 27.0446i 0.624568 1.08178i
\(626\) 6.81418 + 11.8025i 0.272350 + 0.471723i
\(627\) 0 0
\(628\) −0.671466 + 1.16301i −0.0267944 + 0.0464092i
\(629\) 0.182733 0.00728605
\(630\) 0 0
\(631\) −1.15543 −0.0459968 −0.0229984 0.999736i \(-0.507321\pi\)
−0.0229984 + 0.999736i \(0.507321\pi\)
\(632\) −7.82062 4.51524i −0.311088 0.179607i
\(633\) 0 0
\(634\) 0.730381 0.421686i 0.0290071 0.0167473i
\(635\) −7.87292 + 13.6363i −0.312427 + 0.541140i
\(636\) 0 0
\(637\) −2.55528 15.0498i −0.101244 0.596293i
\(638\) −1.23534 21.3000i −0.0489074 0.843274i
\(639\) 0 0
\(640\) 2.34835 1.35582i 0.0928269 0.0535936i
\(641\) 43.5123 25.1218i 1.71863 0.992252i 0.797197 0.603720i \(-0.206315\pi\)
0.921435 0.388533i \(-0.127018\pi\)
\(642\) 0 0
\(643\) 14.5727 0.574690 0.287345 0.957827i \(-0.407227\pi\)
0.287345 + 0.957827i \(0.407227\pi\)
\(644\) 18.3483 1.54660i 0.723023 0.0609446i
\(645\) 0 0
\(646\) 0.134427 + 0.0776112i 0.00528894 + 0.00305357i
\(647\) −3.51582 + 2.02986i −0.138221 + 0.0798020i −0.567516 0.823362i \(-0.692095\pi\)
0.429295 + 0.903164i \(0.358762\pi\)
\(648\) 0 0
\(649\) −21.0633 + 41.9148i −0.826806 + 1.64530i
\(650\) 5.13132i 0.201267i
\(651\) 0 0
\(652\) −18.3297 −0.717847
\(653\) 1.95036 + 1.12604i 0.0763236 + 0.0440654i 0.537676 0.843151i \(-0.319302\pi\)
−0.461353 + 0.887217i \(0.652636\pi\)
\(654\) 0 0
\(655\) −4.60768 + 2.66024i −0.180037 + 0.103944i
\(656\) 1.35699 2.35037i 0.0529814 0.0917666i
\(657\) 0 0
\(658\) −4.50511 6.47762i −0.175627 0.252524i
\(659\) 33.8978 1.32047 0.660236 0.751058i \(-0.270456\pi\)
0.660236 + 0.751058i \(0.270456\pi\)
\(660\) 0 0
\(661\) −0.411025 0.711916i −0.0159870 0.0276903i 0.857921 0.513781i \(-0.171756\pi\)
−0.873908 + 0.486091i \(0.838422\pi\)
\(662\) −5.79849 10.0433i −0.225365 0.390343i
\(663\) 0 0
\(664\) −17.2299 −0.668651
\(665\) 16.2243 11.2838i 0.629153 0.437568i
\(666\) 0 0
\(667\) −38.7727 22.3854i −1.50128 0.866767i
\(668\) −2.52226 4.36868i −0.0975892 0.169029i
\(669\) 0 0
\(670\) 3.51796 + 2.03110i 0.135911 + 0.0784682i
\(671\) 39.2729 2.27771i 1.51611 0.0879302i
\(672\) 0 0
\(673\) 22.8706i 0.881596i 0.897606 + 0.440798i \(0.145304\pi\)
−0.897606 + 0.440798i \(0.854696\pi\)
\(674\) −0.747952 0.431830i −0.0288100 0.0166335i
\(675\) 0 0
\(676\) −4.12220 7.13986i −0.158546 0.274610i
\(677\) 7.34072 12.7145i 0.282127 0.488658i −0.689782 0.724018i \(-0.742293\pi\)
0.971908 + 0.235360i \(0.0756268\pi\)
\(678\) 0 0
\(679\) 1.39050 + 16.4964i 0.0533626 + 0.633074i
\(680\) 0.152802i 0.00585969i
\(681\) 0 0
\(682\) −20.2397 + 13.3047i −0.775018 + 0.509465i
\(683\) −34.3893 + 19.8546i −1.31587 + 0.759717i −0.983061 0.183278i \(-0.941329\pi\)
−0.332807 + 0.942995i \(0.607996\pi\)
\(684\) 0 0
\(685\) 17.2757 0.660072
\(686\) −17.8427 4.96351i −0.681239 0.189508i
\(687\) 0 0
\(688\) −9.20975 5.31725i −0.351119 0.202718i
\(689\) 12.8335 + 22.2284i 0.488919 + 0.846833i
\(690\) 0 0
\(691\) −12.6830 + 21.9677i −0.482486 + 0.835690i −0.999798 0.0201070i \(-0.993599\pi\)
0.517312 + 0.855797i \(0.326933\pi\)
\(692\) 0.919665 0.0349604
\(693\) 0 0
\(694\) 7.39142 0.280574
\(695\) −15.1918 + 26.3129i −0.576257 + 0.998107i
\(696\) 0 0
\(697\) 0.0764666 + 0.132444i 0.00289638 + 0.00501667i
\(698\) 27.3471 + 15.7889i 1.03510 + 0.597617i
\(699\) 0 0
\(700\) 5.63386 + 2.64891i 0.212940 + 0.100119i
\(701\) 36.3036 1.37117 0.685584 0.727994i \(-0.259547\pi\)
0.685584 + 0.727994i \(0.259547\pi\)
\(702\) 0 0
\(703\) 7.73590 4.46632i 0.291765 0.168451i
\(704\) −2.77145 + 1.82183i −0.104453 + 0.0686630i
\(705\) 0 0
\(706\) 4.44774i 0.167393i
\(707\) 34.1796 23.7715i 1.28546 0.894020i
\(708\) 0 0
\(709\) −2.73371 + 4.73492i −0.102667 + 0.177824i −0.912782 0.408446i \(-0.866071\pi\)
0.810116 + 0.586270i \(0.199404\pi\)
\(710\) −2.47096 4.27983i −0.0927335 0.160619i
\(711\) 0 0
\(712\) −7.43764 4.29412i −0.278737 0.160929i
\(713\) 50.8254i 1.90343i
\(714\) 0 0
\(715\) −1.13556 19.5796i −0.0424674 0.732234i
\(716\) 14.9660 + 8.64063i 0.559306 + 0.322915i
\(717\) 0 0
\(718\) 10.0548 + 17.4154i 0.375242 + 0.649938i
\(719\) 13.3827 + 7.72650i 0.499090 + 0.288150i 0.728338 0.685218i \(-0.240293\pi\)
−0.229248 + 0.973368i \(0.573627\pi\)
\(720\) 0 0
\(721\) −19.7964 9.30782i −0.737256 0.346641i
\(722\) −11.4122 −0.424717
\(723\) 0 0
\(724\) 4.84310 + 8.38850i 0.179993 + 0.311756i
\(725\) −7.56847 13.1090i −0.281086 0.486855i
\(726\) 0 0
\(727\) 39.4347 1.46255 0.731276 0.682082i \(-0.238925\pi\)
0.731276 + 0.682082i \(0.238925\pi\)
\(728\) 5.74929 0.484616i 0.213083 0.0179611i
\(729\) 0 0
\(730\) −10.6838 + 18.5048i −0.395424 + 0.684894i
\(731\) 0.518972 0.299629i 0.0191949 0.0110822i
\(732\) 0 0
\(733\) −29.2219 16.8713i −1.07934 0.623156i −0.148620 0.988894i \(-0.547483\pi\)
−0.930717 + 0.365739i \(0.880816\pi\)
\(734\) −12.7963 −0.472319
\(735\) 0 0
\(736\) 6.95959i 0.256534i
\(737\) −4.43945 2.23094i −0.163529 0.0821778i
\(738\) 0 0
\(739\) 43.6352 25.1928i 1.60515 0.926732i 0.614713 0.788751i \(-0.289272\pi\)
0.990435 0.137981i \(-0.0440614\pi\)
\(740\) 7.61527 + 4.39668i 0.279943 + 0.161625i
\(741\) 0 0
\(742\) 31.0303 2.61558i 1.13916 0.0960211i
\(743\) −52.0125 −1.90815 −0.954077 0.299560i \(-0.903160\pi\)
−0.954077 + 0.299560i \(0.903160\pi\)
\(744\) 0 0
\(745\) 37.9498 21.9103i 1.39037 0.802732i
\(746\) −6.97826 + 4.02890i −0.255492 + 0.147509i
\(747\) 0 0
\(748\) −0.0108210 0.186579i −0.000395656 0.00682201i
\(749\) 28.0953 + 13.2098i 1.02658 + 0.482674i
\(750\) 0 0
\(751\) −12.9264 + 22.3892i −0.471691 + 0.816993i −0.999475 0.0323857i \(-0.989689\pi\)
0.527785 + 0.849378i \(0.323023\pi\)
\(752\) 2.58268 1.49111i 0.0941806 0.0543752i
\(753\) 0 0
\(754\) −12.1491 7.01430i −0.442445 0.255446i
\(755\) 35.8880 1.30610
\(756\) 0 0
\(757\) 17.3219 0.629576 0.314788 0.949162i \(-0.398067\pi\)
0.314788 + 0.949162i \(0.398067\pi\)
\(758\) −15.3060 + 26.5108i −0.555940 + 0.962916i
\(759\) 0 0
\(760\) 3.73475 + 6.46878i 0.135474 + 0.234647i
\(761\) −20.4262 + 35.3793i −0.740450 + 1.28250i 0.211840 + 0.977304i \(0.432054\pi\)
−0.952290 + 0.305193i \(0.901279\pi\)
\(762\) 0 0
\(763\) 10.0516 + 14.4525i 0.363891 + 0.523217i
\(764\) 12.2112i 0.441787i
\(765\) 0 0
\(766\) 0.763632 0.440883i 0.0275912 0.0159298i
\(767\) 15.4219 + 26.7115i 0.556853 + 0.964497i
\(768\) 0 0
\(769\) 41.5890i 1.49974i 0.661586 + 0.749869i \(0.269884\pi\)
−0.661586 + 0.749869i \(0.730116\pi\)
\(770\) −22.0833 8.86067i −0.795826 0.319317i
\(771\) 0 0
\(772\) 6.93577 + 4.00437i 0.249624 + 0.144120i
\(773\) 42.1450 24.3325i 1.51585 0.875178i 0.516025 0.856574i \(-0.327411\pi\)
0.999827 0.0186040i \(-0.00592219\pi\)
\(774\) 0 0
\(775\) −8.59199 + 14.8818i −0.308634 + 0.534569i
\(776\) −6.25716 −0.224619
\(777\) 0 0
\(778\) 6.18083i 0.221593i
\(779\) 6.47433 + 3.73796i 0.231967 + 0.133926i
\(780\) 0 0
\(781\) 3.32026 + 5.05090i 0.118808 + 0.180736i
\(782\) −0.339633 0.196087i −0.0121453 0.00701207i
\(783\) 0 0
\(784\) 2.43585 6.56252i 0.0869945 0.234376i
\(785\) 3.64155i 0.129973i
\(786\) 0 0
\(787\) −37.6497 + 21.7371i −1.34207 + 0.774842i −0.987110 0.160041i \(-0.948837\pi\)
−0.354956 + 0.934883i \(0.615504\pi\)
\(788\) −3.07074 5.31868i −0.109391 0.189470i
\(789\) 0 0
\(790\) 24.4875 0.871225
\(791\) −33.7475 + 2.84463i −1.19992 + 0.101143i
\(792\) 0 0
\(793\) 12.9330 22.4006i 0.459264 0.795468i
\(794\) −13.4710 23.3325i −0.478069 0.828039i
\(795\) 0 0
\(796\) −5.93851 + 10.2858i −0.210485 + 0.364570i
\(797\) 0.736909i 0.0261026i −0.999915 0.0130513i \(-0.995846\pi\)
0.999915 0.0130513i \(-0.00415448\pi\)
\(798\) 0 0
\(799\) 0.168049i 0.00594514i
\(800\) −1.17651 + 2.03778i −0.0415960 + 0.0720464i
\(801\) 0 0
\(802\) 3.85186 2.22387i 0.136014 0.0785277i
\(803\) 11.7350 23.3519i 0.414118 0.824072i
\(804\) 0 0
\(805\) −40.9913 + 28.5090i −1.44475 + 1.00481i
\(806\) 15.9258i 0.560961i
\(807\) 0 0
\(808\) 7.86795 + 13.6277i 0.276794 + 0.479421i
\(809\) 18.6491 + 32.3012i 0.655668 + 1.13565i 0.981726 + 0.190301i \(0.0609464\pi\)
−0.326057 + 0.945350i \(0.605720\pi\)
\(810\) 0 0
\(811\) 53.0883i 1.86418i −0.362223 0.932091i \(-0.617982\pi\)
0.362223 0.932091i \(-0.382018\pi\)
\(812\) −13.9729 + 9.71800i −0.490353 + 0.341035i
\(813\) 0 0
\(814\) −9.61000 4.82928i −0.336830 0.169266i
\(815\) 43.0447 24.8519i 1.50779 0.870523i
\(816\) 0 0
\(817\) 14.6469 25.3692i 0.512430 0.887556i
\(818\) 1.74309i 0.0609456i
\(819\) 0 0
\(820\) 7.35934i 0.256999i
\(821\) 11.8592 20.5407i 0.413888 0.716875i −0.581423 0.813601i \(-0.697504\pi\)
0.995311 + 0.0967264i \(0.0308372\pi\)
\(822\) 0 0
\(823\) 12.9977 + 22.5127i 0.453072 + 0.784744i 0.998575 0.0533647i \(-0.0169946\pi\)
−0.545503 + 0.838109i \(0.683661\pi\)
\(824\) 4.13406 7.16040i 0.144017 0.249444i
\(825\) 0 0
\(826\) 37.2887 3.14311i 1.29744 0.109363i
\(827\) −4.74683 −0.165064 −0.0825318 0.996588i \(-0.526301\pi\)
−0.0825318 + 0.996588i \(0.526301\pi\)
\(828\) 0 0
\(829\) −25.4414 44.0659i −0.883618 1.53047i −0.847289 0.531131i \(-0.821767\pi\)
−0.0363286 0.999340i \(-0.511566\pi\)
\(830\) 40.4620 23.3607i 1.40446 0.810863i
\(831\) 0 0
\(832\) 2.18074i 0.0756034i
\(833\) 0.251625 + 0.303771i 0.00871831 + 0.0105250i
\(834\) 0 0
\(835\) 11.8463 + 6.83948i 0.409959 + 0.236690i
\(836\) −5.01843 7.63423i −0.173566 0.264035i
\(837\) 0 0
\(838\) 19.8214 + 11.4439i 0.684717 + 0.395322i
\(839\) 44.2410i 1.52737i 0.645589 + 0.763685i \(0.276612\pi\)
−0.645589 + 0.763685i \(0.723388\pi\)
\(840\) 0 0
\(841\) 12.3831 0.427005
\(842\) 14.8908 25.7917i 0.513172 0.888840i
\(843\) 0 0
\(844\) −17.2772 + 9.97497i −0.594704 + 0.343353i
\(845\) 19.3608 + 11.1779i 0.666030 + 0.384533i
\(846\) 0 0
\(847\) 27.5923 + 9.25546i 0.948084 + 0.318021i
\(848\) 11.7699i 0.404181i
\(849\) 0 0
\(850\) −0.0662968 0.114829i −0.00227396 0.00393861i
\(851\) −19.5450 + 11.2843i −0.669994 + 0.386821i
\(852\) 0 0
\(853\) 33.7537i 1.15570i −0.816142 0.577852i \(-0.803891\pi\)
0.816142 0.577852i \(-0.196109\pi\)
\(854\) −17.9181 25.7633i −0.613144 0.881602i
\(855\) 0 0
\(856\) −5.86711 + 10.1621i −0.200534 + 0.347334i
\(857\) −8.96910 15.5349i −0.306379 0.530664i 0.671189 0.741287i \(-0.265784\pi\)
−0.977567 + 0.210623i \(0.932451\pi\)
\(858\) 0 0
\(859\) −2.69866 + 4.67422i −0.0920771 + 0.159482i −0.908385 0.418135i \(-0.862684\pi\)
0.816308 + 0.577617i \(0.196017\pi\)
\(860\) 28.8370 0.983334
\(861\) 0 0
\(862\) −10.5957 −0.360892
\(863\) 14.4176 + 8.32401i 0.490781 + 0.283353i 0.724899 0.688856i \(-0.241887\pi\)
−0.234117 + 0.972208i \(0.575220\pi\)
\(864\) 0 0
\(865\) −2.15970 + 1.24690i −0.0734320 + 0.0423960i
\(866\) −11.7747 + 20.3944i −0.400121 + 0.693029i
\(867\) 0 0
\(868\) 17.4854 + 8.22126i 0.593495 + 0.279048i
\(869\) −29.9005 + 1.73414i −1.01430 + 0.0588266i
\(870\) 0 0
\(871\) −2.82918 + 1.63343i −0.0958633 + 0.0553467i
\(872\) −5.76234 + 3.32689i −0.195138 + 0.112663i
\(873\) 0 0
\(874\) −19.1709 −0.648465
\(875\) 18.9232 1.59506i 0.639721 0.0539229i
\(876\) 0 0
\(877\) −8.41495 4.85837i −0.284153 0.164056i 0.351149 0.936320i \(-0.385791\pi\)
−0.635302 + 0.772264i \(0.719124\pi\)
\(878\) −10.0258 + 5.78842i −0.338356 + 0.195350i
\(879\) 0 0
\(880\) 4.03825 8.03591i 0.136130 0.270890i
\(881\) 18.1403i 0.611162i 0.952166 + 0.305581i \(0.0988507\pi\)
−0.952166 + 0.305581i \(0.901149\pi\)
\(882\) 0 0
\(883\) 20.9584 0.705308 0.352654 0.935754i \(-0.385279\pi\)
0.352654 + 0.935754i \(0.385279\pi\)
\(884\) −0.106421 0.0614425i −0.00357934 0.00206653i
\(885\) 0 0
\(886\) 32.4006 18.7065i 1.08852 0.628456i
\(887\) −25.0314 + 43.3557i −0.840473 + 1.45574i 0.0490221 + 0.998798i \(0.484390\pi\)
−0.889495 + 0.456945i \(0.848944\pi\)
\(888\) 0 0
\(889\) −15.3089 + 1.29041i −0.513445 + 0.0432789i
\(890\) 23.2883 0.780625
\(891\) 0 0
\(892\) 6.84437 + 11.8548i 0.229166 + 0.396928i
\(893\) 4.10741 + 7.11425i 0.137449 + 0.238069i
\(894\) 0 0
\(895\) −46.8606 −1.56638
\(896\) 2.39430 + 1.12575i 0.0799881 + 0.0376086i
\(897\) 0 0
\(898\) 16.8657 + 9.73743i 0.562816 + 0.324942i
\(899\) −23.4898 40.6855i −0.783428 1.35694i
\(900\) 0 0
\(901\) −0.574381 0.331619i −0.0191354 0.0110478i
\(902\) −0.521169 8.98613i −0.0173530 0.299206i
\(903\) 0 0
\(904\) 12.8006i 0.425742i
\(905\) −22.7466 13.1328i −0.756124 0.436548i
\(906\) 0 0
\(907\) 8.12111 + 14.0662i 0.269657 + 0.467060i 0.968773 0.247948i \(-0.0797563\pi\)
−0.699116 + 0.715008i \(0.746423\pi\)
\(908\) 3.18180 5.51104i 0.105592 0.182890i
\(909\) 0 0
\(910\) −12.8443 + 8.93308i −0.425785 + 0.296129i
\(911\) 30.3752i 1.00637i −0.864177 0.503187i \(-0.832161\pi\)
0.864177 0.503187i \(-0.167839\pi\)
\(912\) 0 0
\(913\) −47.7518 + 31.3901i −1.58035 + 1.03886i
\(914\) 23.7421 13.7075i 0.785321 0.453405i
\(915\) 0 0
\(916\) 10.3415 0.341694
\(917\) −4.69784 2.20882i −0.155136 0.0729416i
\(918\) 0 0
\(919\) 36.4118 + 21.0224i 1.20111 + 0.693463i 0.960803 0.277232i \(-0.0894172\pi\)
0.240311 + 0.970696i \(0.422751\pi\)
\(920\) −9.43597 16.3436i −0.311095 0.538832i
\(921\) 0 0
\(922\) 19.3297 33.4800i 0.636589 1.10261i
\(923\) 3.97434 0.130817
\(924\) 0 0
\(925\) −7.63041 −0.250886
\(926\) 17.7478 30.7401i 0.583229 1.01018i
\(927\) 0 0
\(928\) −3.21649 5.57112i −0.105586 0.182881i
\(929\) −27.9603 16.1429i −0.917347 0.529631i −0.0345593 0.999403i \(-0.511003\pi\)
−0.882788 + 0.469772i \(0.844336\pi\)
\(930\) 0 0
\(931\) 18.0771 + 6.70979i 0.592454 + 0.219904i
\(932\) −8.90456 −0.291678
\(933\) 0 0
\(934\) −9.49408 + 5.48141i −0.310656 + 0.179357i
\(935\) 0.278380 + 0.423482i 0.00910400 + 0.0138494i
\(936\) 0 0
\(937\) 8.45199i 0.276114i −0.990424 0.138057i \(-0.955914\pi\)
0.990424 0.138057i \(-0.0440858\pi\)
\(938\) 0.332907 + 3.94948i 0.0108698 + 0.128955i
\(939\) 0 0
\(940\) −4.04336 + 7.00331i −0.131880 + 0.228423i
\(941\) 4.52993 + 7.84606i 0.147671 + 0.255774i 0.930366 0.366631i \(-0.119489\pi\)
−0.782695 + 0.622405i \(0.786156\pi\)
\(942\) 0 0
\(943\) −16.3576 9.44407i −0.532677 0.307541i
\(944\) 14.1438i 0.460341i
\(945\) 0 0
\(946\) −35.2115 + 2.04216i −1.14482 + 0.0663965i
\(947\) −7.82779 4.51938i −0.254369 0.146860i 0.367394 0.930065i \(-0.380250\pi\)
−0.621763 + 0.783205i \(0.713583\pi\)
\(948\) 0 0
\(949\) −8.59199 14.8818i −0.278908 0.483083i
\(950\) −5.61327 3.24082i −0.182118 0.105146i
\(951\) 0 0
\(952\) −0.122397 + 0.0851257i −0.00396691 + 0.00275894i
\(953\) 9.69684 0.314111 0.157056 0.987590i \(-0.449800\pi\)
0.157056 + 0.987590i \(0.449800\pi\)
\(954\) 0 0
\(955\) −16.5563 28.6763i −0.535748 0.927943i
\(956\) 11.3045 + 19.5800i 0.365614 + 0.633262i
\(957\) 0 0
\(958\) −12.1607 −0.392894
\(959\) 9.62429 + 13.8382i 0.310785 + 0.446858i
\(960\) 0 0
\(961\) −11.1664 + 19.3408i −0.360207 + 0.623898i
\(962\) −6.12428 + 3.53585i −0.197455 + 0.114000i
\(963\) 0 0
\(964\) 8.06528 + 4.65649i 0.259765 + 0.149975i
\(965\) −21.7169 −0.699091
\(966\) 0 0
\(967\) 43.0464i 1.38428i 0.721764 + 0.692139i \(0.243332\pi\)
−0.721764 + 0.692139i \(0.756668\pi\)
\(968\) −4.36184 + 10.0982i −0.140195 + 0.324570i
\(969\) 0 0
\(970\) 14.6940 8.48360i 0.471797 0.272392i
\(971\) −3.16229 1.82575i −0.101483 0.0585910i 0.448400 0.893833i \(-0.351994\pi\)
−0.549882 + 0.835242i \(0.685327\pi\)
\(972\) 0 0
\(973\) −29.5405 + 2.49001i −0.947024 + 0.0798259i
\(974\) −2.44873 −0.0784624
\(975\) 0 0
\(976\) 10.2720 5.93056i 0.328800 0.189833i
\(977\) 40.6302 23.4579i 1.29988 0.750483i 0.319493 0.947589i \(-0.396487\pi\)
0.980382 + 0.197105i \(0.0631541\pi\)
\(978\) 0 0
\(979\) −28.4362 + 1.64922i −0.908825 + 0.0527092i
\(980\) 3.17738 + 18.7137i 0.101498 + 0.597787i
\(981\) 0 0
\(982\) −0.0674469 + 0.116821i −0.00215232 + 0.00372792i
\(983\) −27.9845 + 16.1568i −0.892566 + 0.515323i −0.874781 0.484518i \(-0.838995\pi\)
−0.0177852 + 0.999842i \(0.505661\pi\)
\(984\) 0 0
\(985\) 14.4224 + 8.32676i 0.459535 + 0.265313i
\(986\) 0.362500 0.0115443
\(987\) 0 0
\(988\) −6.00705 −0.191110
\(989\) −37.0059 + 64.0961i −1.17672 + 2.03814i
\(990\) 0 0
\(991\) 14.8118 + 25.6549i 0.470514 + 0.814954i 0.999431 0.0337194i \(-0.0107352\pi\)
−0.528918 + 0.848673i \(0.677402\pi\)
\(992\) −3.65147 + 6.32453i −0.115934 + 0.200804i
\(993\) 0 0
\(994\) 2.05165 4.36357i 0.0650744 0.138404i
\(995\) 32.2063i 1.02101i
\(996\) 0 0
\(997\) 11.8813 6.85966i 0.376284 0.217248i −0.299916 0.953965i \(-0.596959\pi\)
0.676200 + 0.736718i \(0.263625\pi\)
\(998\) 18.6333 + 32.2738i 0.589826 + 1.02161i
\(999\) 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 1386.2.ba.b.989.14 yes 32
3.2 odd 2 1386.2.ba.a.989.3 32
7.4 even 3 inner 1386.2.ba.b.1187.3 yes 32
11.10 odd 2 1386.2.ba.a.989.14 yes 32
21.11 odd 6 1386.2.ba.a.1187.14 yes 32
33.32 even 2 inner 1386.2.ba.b.989.3 yes 32
77.32 odd 6 1386.2.ba.a.1187.3 yes 32
231.32 even 6 inner 1386.2.ba.b.1187.14 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.ba.a.989.3 32 3.2 odd 2
1386.2.ba.a.989.14 yes 32 11.10 odd 2
1386.2.ba.a.1187.3 yes 32 77.32 odd 6
1386.2.ba.a.1187.14 yes 32 21.11 odd 6
1386.2.ba.b.989.3 yes 32 33.32 even 2 inner
1386.2.ba.b.989.14 yes 32 1.1 even 1 trivial
1386.2.ba.b.1187.3 yes 32 7.4 even 3 inner
1386.2.ba.b.1187.14 yes 32 231.32 even 6 inner