Properties

Label 1638.2.cm.a.341.22
Level $1638$
Weight $2$
Character 1638.341
Analytic conductor $13.079$
Analytic rank $0$
Dimension $72$
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] = [1638,2,Mod(269,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.269");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.cm (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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 341.22
Character \(\chi\) \(=\) 1638.341
Dual form 1638.2.cm.a.269.22

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(0.377027 - 0.653029i) q^{5} +(-2.31742 - 1.27655i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(0.377027 - 0.653029i) q^{5} +(-2.31742 - 1.27655i) q^{7} +1.00000i q^{8} +(-0.653029 - 0.377027i) q^{10} +(4.23768 + 2.44663i) q^{11} +(-0.743889 + 3.52798i) q^{13} +(-1.27655 + 2.31742i) q^{14} +1.00000 q^{16} -3.42925 q^{17} +(3.15853 - 1.82358i) q^{19} +(-0.377027 + 0.653029i) q^{20} +(2.44663 - 4.23768i) q^{22} +2.97706i q^{23} +(2.21570 + 3.83771i) q^{25} +(3.52798 + 0.743889i) q^{26} +(2.31742 + 1.27655i) q^{28} +(2.55786 - 1.47678i) q^{29} +(5.86618 - 3.38684i) q^{31} -1.00000i q^{32} +3.42925i q^{34} +(-1.70735 + 1.03205i) q^{35} +8.60752 q^{37} +(-1.82358 - 3.15853i) q^{38} +(0.653029 + 0.377027i) q^{40} +(-1.57286 - 2.72428i) q^{41} +(-1.02223 + 1.77055i) q^{43} +(-4.23768 - 2.44663i) q^{44} +2.97706 q^{46} +(0.0925217 - 0.160252i) q^{47} +(3.74083 + 5.91660i) q^{49} +(3.83771 - 2.21570i) q^{50} +(0.743889 - 3.52798i) q^{52} +(-5.09102 + 2.93930i) q^{53} +(3.19544 - 1.84489i) q^{55} +(1.27655 - 2.31742i) q^{56} +(-1.47678 - 2.55786i) q^{58} -9.86178 q^{59} +(7.49997 - 4.33011i) q^{61} +(-3.38684 - 5.86618i) q^{62} -1.00000 q^{64} +(2.02341 + 1.81592i) q^{65} +(2.34769 - 4.06632i) q^{67} +3.42925 q^{68} +(1.03205 + 1.70735i) q^{70} +(7.33372 + 4.23413i) q^{71} +(4.00551 - 2.31258i) q^{73} -8.60752i q^{74} +(-3.15853 + 1.82358i) q^{76} +(-6.69723 - 11.0795i) q^{77} +(4.83243 - 8.37001i) q^{79} +(0.377027 - 0.653029i) q^{80} +(-2.72428 + 1.57286i) q^{82} +2.66655 q^{83} +(-1.29292 + 2.23940i) q^{85} +(1.77055 + 1.02223i) q^{86} +(-2.44663 + 4.23768i) q^{88} +12.9287 q^{89} +(6.22755 - 7.22618i) q^{91} -2.97706i q^{92} +(-0.160252 - 0.0925217i) q^{94} -2.75015i q^{95} +(-5.57654 - 3.21961i) q^{97} +(5.91660 - 3.74083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0.377027 0.653029i 0.168611 0.292044i −0.769320 0.638863i \(-0.779405\pi\)
0.937932 + 0.346820i \(0.112738\pi\)
\(6\) 0 0
\(7\) −2.31742 1.27655i −0.875901 0.482491i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.653029 0.377027i −0.206506 0.119226i
\(11\) 4.23768 + 2.44663i 1.27771 + 0.737686i 0.976427 0.215849i \(-0.0692519\pi\)
0.301283 + 0.953535i \(0.402585\pi\)
\(12\) 0 0
\(13\) −0.743889 + 3.52798i −0.206318 + 0.978485i
\(14\) −1.27655 + 2.31742i −0.341173 + 0.619355i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.42925 −0.831715 −0.415858 0.909430i \(-0.636519\pi\)
−0.415858 + 0.909430i \(0.636519\pi\)
\(18\) 0 0
\(19\) 3.15853 1.82358i 0.724616 0.418357i −0.0918334 0.995774i \(-0.529273\pi\)
0.816449 + 0.577417i \(0.195939\pi\)
\(20\) −0.377027 + 0.653029i −0.0843057 + 0.146022i
\(21\) 0 0
\(22\) 2.44663 4.23768i 0.521623 0.903477i
\(23\) 2.97706i 0.620759i 0.950613 + 0.310380i \(0.100456\pi\)
−0.950613 + 0.310380i \(0.899544\pi\)
\(24\) 0 0
\(25\) 2.21570 + 3.83771i 0.443140 + 0.767542i
\(26\) 3.52798 + 0.743889i 0.691893 + 0.145889i
\(27\) 0 0
\(28\) 2.31742 + 1.27655i 0.437950 + 0.241246i
\(29\) 2.55786 1.47678i 0.474982 0.274231i −0.243341 0.969941i \(-0.578243\pi\)
0.718323 + 0.695710i \(0.244910\pi\)
\(30\) 0 0
\(31\) 5.86618 3.38684i 1.05360 0.608294i 0.129943 0.991521i \(-0.458521\pi\)
0.923654 + 0.383227i \(0.125187\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 3.42925i 0.588112i
\(35\) −1.70735 + 1.03205i −0.288595 + 0.174448i
\(36\) 0 0
\(37\) 8.60752 1.41507 0.707534 0.706679i \(-0.249808\pi\)
0.707534 + 0.706679i \(0.249808\pi\)
\(38\) −1.82358 3.15853i −0.295823 0.512381i
\(39\) 0 0
\(40\) 0.653029 + 0.377027i 0.103253 + 0.0596131i
\(41\) −1.57286 2.72428i −0.245640 0.425461i 0.716671 0.697411i \(-0.245665\pi\)
−0.962311 + 0.271950i \(0.912331\pi\)
\(42\) 0 0
\(43\) −1.02223 + 1.77055i −0.155889 + 0.270007i −0.933382 0.358884i \(-0.883157\pi\)
0.777494 + 0.628891i \(0.216491\pi\)
\(44\) −4.23768 2.44663i −0.638855 0.368843i
\(45\) 0 0
\(46\) 2.97706 0.438943
\(47\) 0.0925217 0.160252i 0.0134957 0.0233752i −0.859199 0.511642i \(-0.829037\pi\)
0.872694 + 0.488267i \(0.162371\pi\)
\(48\) 0 0
\(49\) 3.74083 + 5.91660i 0.534404 + 0.845229i
\(50\) 3.83771 2.21570i 0.542734 0.313348i
\(51\) 0 0
\(52\) 0.743889 3.52798i 0.103159 0.489243i
\(53\) −5.09102 + 2.93930i −0.699306 + 0.403744i −0.807089 0.590430i \(-0.798958\pi\)
0.107783 + 0.994174i \(0.465625\pi\)
\(54\) 0 0
\(55\) 3.19544 1.84489i 0.430873 0.248765i
\(56\) 1.27655 2.31742i 0.170586 0.309678i
\(57\) 0 0
\(58\) −1.47678 2.55786i −0.193911 0.335863i
\(59\) −9.86178 −1.28389 −0.641947 0.766749i \(-0.721873\pi\)
−0.641947 + 0.766749i \(0.721873\pi\)
\(60\) 0 0
\(61\) 7.49997 4.33011i 0.960273 0.554414i 0.0640159 0.997949i \(-0.479609\pi\)
0.896257 + 0.443535i \(0.146276\pi\)
\(62\) −3.38684 5.86618i −0.430129 0.745006i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.02341 + 1.81592i 0.250973 + 0.225238i
\(66\) 0 0
\(67\) 2.34769 4.06632i 0.286816 0.496780i −0.686232 0.727383i \(-0.740737\pi\)
0.973048 + 0.230603i \(0.0740699\pi\)
\(68\) 3.42925 0.415858
\(69\) 0 0
\(70\) 1.03205 + 1.70735i 0.123353 + 0.204068i
\(71\) 7.33372 + 4.23413i 0.870353 + 0.502498i 0.867465 0.497497i \(-0.165748\pi\)
0.00288731 + 0.999996i \(0.499081\pi\)
\(72\) 0 0
\(73\) 4.00551 2.31258i 0.468809 0.270667i −0.246932 0.969033i \(-0.579422\pi\)
0.715741 + 0.698366i \(0.246089\pi\)
\(74\) 8.60752i 1.00060i
\(75\) 0 0
\(76\) −3.15853 + 1.82358i −0.362308 + 0.209179i
\(77\) −6.69723 11.0795i −0.763220 1.26262i
\(78\) 0 0
\(79\) 4.83243 8.37001i 0.543691 0.941700i −0.454998 0.890493i \(-0.650360\pi\)
0.998688 0.0512070i \(-0.0163068\pi\)
\(80\) 0.377027 0.653029i 0.0421529 0.0730109i
\(81\) 0 0
\(82\) −2.72428 + 1.57286i −0.300846 + 0.173694i
\(83\) 2.66655 0.292692 0.146346 0.989233i \(-0.453249\pi\)
0.146346 + 0.989233i \(0.453249\pi\)
\(84\) 0 0
\(85\) −1.29292 + 2.23940i −0.140237 + 0.242897i
\(86\) 1.77055 + 1.02223i 0.190924 + 0.110230i
\(87\) 0 0
\(88\) −2.44663 + 4.23768i −0.260811 + 0.451739i
\(89\) 12.9287 1.37044 0.685221 0.728335i \(-0.259705\pi\)
0.685221 + 0.728335i \(0.259705\pi\)
\(90\) 0 0
\(91\) 6.22755 7.22618i 0.652824 0.757509i
\(92\) 2.97706i 0.310380i
\(93\) 0 0
\(94\) −0.160252 0.0925217i −0.0165288 0.00954289i
\(95\) 2.75015i 0.282159i
\(96\) 0 0
\(97\) −5.57654 3.21961i −0.566211 0.326902i 0.189423 0.981896i \(-0.439338\pi\)
−0.755635 + 0.654993i \(0.772671\pi\)
\(98\) 5.91660 3.74083i 0.597667 0.377881i
\(99\) 0 0
\(100\) −2.21570 3.83771i −0.221570 0.383771i
\(101\) 1.53036 2.65067i 0.152277 0.263751i −0.779787 0.626044i \(-0.784673\pi\)
0.932064 + 0.362293i \(0.118006\pi\)
\(102\) 0 0
\(103\) 5.42602 + 3.13272i 0.534642 + 0.308676i 0.742905 0.669397i \(-0.233448\pi\)
−0.208263 + 0.978073i \(0.566781\pi\)
\(104\) −3.52798 0.743889i −0.345947 0.0729443i
\(105\) 0 0
\(106\) 2.93930 + 5.09102i 0.285490 + 0.494484i
\(107\) 5.83707i 0.564291i 0.959372 + 0.282145i \(0.0910461\pi\)
−0.959372 + 0.282145i \(0.908954\pi\)
\(108\) 0 0
\(109\) −2.00167 3.46699i −0.191725 0.332077i 0.754097 0.656763i \(-0.228075\pi\)
−0.945822 + 0.324686i \(0.894741\pi\)
\(110\) −1.84489 3.19544i −0.175903 0.304673i
\(111\) 0 0
\(112\) −2.31742 1.27655i −0.218975 0.120623i
\(113\) −4.32172 2.49515i −0.406554 0.234724i 0.282754 0.959192i \(-0.408752\pi\)
−0.689308 + 0.724469i \(0.742085\pi\)
\(114\) 0 0
\(115\) 1.94411 + 1.12243i 0.181289 + 0.104667i
\(116\) −2.55786 + 1.47678i −0.237491 + 0.137115i
\(117\) 0 0
\(118\) 9.86178i 0.907850i
\(119\) 7.94700 + 4.37762i 0.728500 + 0.401295i
\(120\) 0 0
\(121\) 6.47197 + 11.2098i 0.588361 + 1.01907i
\(122\) −4.33011 7.49997i −0.392030 0.679016i
\(123\) 0 0
\(124\) −5.86618 + 3.38684i −0.526798 + 0.304147i
\(125\) 7.11178 0.636097
\(126\) 0 0
\(127\) 10.3407 + 17.9106i 0.917590 + 1.58931i 0.803065 + 0.595892i \(0.203201\pi\)
0.114525 + 0.993420i \(0.463465\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 1.81592 2.02341i 0.159267 0.177465i
\(131\) −3.65280 + 6.32683i −0.319146 + 0.552778i −0.980310 0.197464i \(-0.936730\pi\)
0.661164 + 0.750242i \(0.270063\pi\)
\(132\) 0 0
\(133\) −9.64751 + 0.193960i −0.836545 + 0.0168185i
\(134\) −4.06632 2.34769i −0.351276 0.202809i
\(135\) 0 0
\(136\) 3.42925i 0.294056i
\(137\) 14.7307i 1.25853i −0.777192 0.629263i \(-0.783357\pi\)
0.777192 0.629263i \(-0.216643\pi\)
\(138\) 0 0
\(139\) 6.99518 + 4.03867i 0.593323 + 0.342555i 0.766410 0.642351i \(-0.222041\pi\)
−0.173087 + 0.984906i \(0.555374\pi\)
\(140\) 1.70735 1.03205i 0.144298 0.0872238i
\(141\) 0 0
\(142\) 4.23413 7.33372i 0.355320 0.615432i
\(143\) −11.7840 + 13.1304i −0.985429 + 1.09802i
\(144\) 0 0
\(145\) 2.22714i 0.184954i
\(146\) −2.31258 4.00551i −0.191390 0.331498i
\(147\) 0 0
\(148\) −8.60752 −0.707534
\(149\) −8.07815 + 4.66392i −0.661788 + 0.382083i −0.792958 0.609277i \(-0.791460\pi\)
0.131170 + 0.991360i \(0.458127\pi\)
\(150\) 0 0
\(151\) 6.63758 + 11.4966i 0.540159 + 0.935583i 0.998894 + 0.0470097i \(0.0149692\pi\)
−0.458736 + 0.888573i \(0.651697\pi\)
\(152\) 1.82358 + 3.15853i 0.147912 + 0.256190i
\(153\) 0 0
\(154\) −11.0795 + 6.69723i −0.892810 + 0.539678i
\(155\) 5.10772i 0.410262i
\(156\) 0 0
\(157\) 7.74046 4.46895i 0.617756 0.356661i −0.158239 0.987401i \(-0.550582\pi\)
0.775995 + 0.630739i \(0.217248\pi\)
\(158\) −8.37001 4.83243i −0.665882 0.384447i
\(159\) 0 0
\(160\) −0.653029 0.377027i −0.0516265 0.0298066i
\(161\) 3.80037 6.89908i 0.299511 0.543724i
\(162\) 0 0
\(163\) 1.41328 + 2.44787i 0.110696 + 0.191732i 0.916051 0.401061i \(-0.131359\pi\)
−0.805355 + 0.592793i \(0.798025\pi\)
\(164\) 1.57286 + 2.72428i 0.122820 + 0.212731i
\(165\) 0 0
\(166\) 2.66655i 0.206965i
\(167\) 7.61244 + 13.1851i 0.589068 + 1.02030i 0.994355 + 0.106106i \(0.0338383\pi\)
−0.405287 + 0.914190i \(0.632828\pi\)
\(168\) 0 0
\(169\) −11.8933 5.24885i −0.914866 0.403757i
\(170\) 2.23940 + 1.29292i 0.171754 + 0.0991623i
\(171\) 0 0
\(172\) 1.02223 1.77055i 0.0779443 0.135004i
\(173\) 0.569456 + 0.986326i 0.0432949 + 0.0749890i 0.886861 0.462037i \(-0.152881\pi\)
−0.843566 + 0.537026i \(0.819548\pi\)
\(174\) 0 0
\(175\) −0.235668 11.7220i −0.0178148 0.886102i
\(176\) 4.23768 + 2.44663i 0.319427 + 0.184421i
\(177\) 0 0
\(178\) 12.9287i 0.969049i
\(179\) −5.18256 2.99215i −0.387363 0.223644i 0.293654 0.955912i \(-0.405129\pi\)
−0.681017 + 0.732268i \(0.738462\pi\)
\(180\) 0 0
\(181\) 18.8486i 1.40101i −0.713648 0.700505i \(-0.752958\pi\)
0.713648 0.700505i \(-0.247042\pi\)
\(182\) −7.22618 6.22755i −0.535640 0.461616i
\(183\) 0 0
\(184\) −2.97706 −0.219472
\(185\) 3.24526 5.62096i 0.238597 0.413261i
\(186\) 0 0
\(187\) −14.5321 8.39010i −1.06269 0.613545i
\(188\) −0.0925217 + 0.160252i −0.00674784 + 0.0116876i
\(189\) 0 0
\(190\) −2.75015 −0.199517
\(191\) 20.3390 11.7427i 1.47168 0.849673i 0.472184 0.881500i \(-0.343466\pi\)
0.999493 + 0.0318268i \(0.0101325\pi\)
\(192\) 0 0
\(193\) −1.78214 + 3.08676i −0.128281 + 0.222190i −0.923011 0.384774i \(-0.874279\pi\)
0.794729 + 0.606964i \(0.207613\pi\)
\(194\) −3.21961 + 5.57654i −0.231155 + 0.400372i
\(195\) 0 0
\(196\) −3.74083 5.91660i −0.267202 0.422615i
\(197\) −21.8018 + 12.5873i −1.55331 + 0.896806i −0.555444 + 0.831554i \(0.687452\pi\)
−0.997869 + 0.0652521i \(0.979215\pi\)
\(198\) 0 0
\(199\) 12.4959i 0.885808i 0.896569 + 0.442904i \(0.146052\pi\)
−0.896569 + 0.442904i \(0.853948\pi\)
\(200\) −3.83771 + 2.21570i −0.271367 + 0.156674i
\(201\) 0 0
\(202\) −2.65067 1.53036i −0.186500 0.107676i
\(203\) −7.81280 + 0.157074i −0.548351 + 0.0110244i
\(204\) 0 0
\(205\) −2.37205 −0.165671
\(206\) 3.13272 5.42602i 0.218267 0.378049i
\(207\) 0 0
\(208\) −0.743889 + 3.52798i −0.0515794 + 0.244621i
\(209\) 17.8465 1.23446
\(210\) 0 0
\(211\) 2.63458 + 4.56323i 0.181372 + 0.314145i 0.942348 0.334635i \(-0.108613\pi\)
−0.760976 + 0.648780i \(0.775280\pi\)
\(212\) 5.09102 2.93930i 0.349653 0.201872i
\(213\) 0 0
\(214\) 5.83707 0.399014
\(215\) 0.770816 + 1.33509i 0.0525692 + 0.0910526i
\(216\) 0 0
\(217\) −17.9179 + 0.360233i −1.21634 + 0.0244542i
\(218\) −3.46699 + 2.00167i −0.234814 + 0.135570i
\(219\) 0 0
\(220\) −3.19544 + 1.84489i −0.215436 + 0.124382i
\(221\) 2.55098 12.0983i 0.171598 0.813821i
\(222\) 0 0
\(223\) 8.40211 4.85096i 0.562647 0.324844i −0.191560 0.981481i \(-0.561355\pi\)
0.754207 + 0.656636i \(0.228021\pi\)
\(224\) −1.27655 + 2.31742i −0.0852932 + 0.154839i
\(225\) 0 0
\(226\) −2.49515 + 4.32172i −0.165975 + 0.287477i
\(227\) 5.62699 0.373477 0.186738 0.982410i \(-0.440208\pi\)
0.186738 + 0.982410i \(0.440208\pi\)
\(228\) 0 0
\(229\) −7.13664 4.12034i −0.471603 0.272280i 0.245308 0.969445i \(-0.421111\pi\)
−0.716910 + 0.697165i \(0.754444\pi\)
\(230\) 1.12243 1.94411i 0.0740109 0.128191i
\(231\) 0 0
\(232\) 1.47678 + 2.55786i 0.0969553 + 0.167931i
\(233\) −16.7363 9.66269i −1.09643 0.633024i −0.161149 0.986930i \(-0.551520\pi\)
−0.935281 + 0.353906i \(0.884853\pi\)
\(234\) 0 0
\(235\) −0.0697663 0.120839i −0.00455105 0.00788265i
\(236\) 9.86178 0.641947
\(237\) 0 0
\(238\) 4.37762 7.94700i 0.283759 0.515127i
\(239\) 26.1899i 1.69408i 0.531526 + 0.847042i \(0.321619\pi\)
−0.531526 + 0.847042i \(0.678381\pi\)
\(240\) 0 0
\(241\) 16.3956i 1.05614i −0.849202 0.528068i \(-0.822917\pi\)
0.849202 0.528068i \(-0.177083\pi\)
\(242\) 11.2098 6.47197i 0.720592 0.416034i
\(243\) 0 0
\(244\) −7.49997 + 4.33011i −0.480136 + 0.277207i
\(245\) 5.27411 0.212154i 0.336950 0.0135541i
\(246\) 0 0
\(247\) 4.08395 + 12.4998i 0.259855 + 0.795340i
\(248\) 3.38684 + 5.86618i 0.215065 + 0.372503i
\(249\) 0 0
\(250\) 7.11178i 0.449789i
\(251\) 5.92653 10.2650i 0.374079 0.647924i −0.616110 0.787660i \(-0.711292\pi\)
0.990189 + 0.139736i \(0.0446255\pi\)
\(252\) 0 0
\(253\) −7.28375 + 12.6158i −0.457926 + 0.793150i
\(254\) 17.9106 10.3407i 1.12381 0.648834i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.78334 0.423133 0.211567 0.977364i \(-0.432143\pi\)
0.211567 + 0.977364i \(0.432143\pi\)
\(258\) 0 0
\(259\) −19.9472 10.9879i −1.23946 0.682758i
\(260\) −2.02341 1.81592i −0.125486 0.112619i
\(261\) 0 0
\(262\) 6.32683 + 3.65280i 0.390873 + 0.225671i
\(263\) −11.7706 6.79576i −0.725806 0.419044i 0.0910797 0.995844i \(-0.470968\pi\)
−0.816886 + 0.576799i \(0.804302\pi\)
\(264\) 0 0
\(265\) 4.43278i 0.272304i
\(266\) 0.193960 + 9.64751i 0.0118925 + 0.591527i
\(267\) 0 0
\(268\) −2.34769 + 4.06632i −0.143408 + 0.248390i
\(269\) −16.7602 −1.02189 −0.510944 0.859614i \(-0.670704\pi\)
−0.510944 + 0.859614i \(0.670704\pi\)
\(270\) 0 0
\(271\) 26.2139i 1.59238i 0.605048 + 0.796189i \(0.293154\pi\)
−0.605048 + 0.796189i \(0.706846\pi\)
\(272\) −3.42925 −0.207929
\(273\) 0 0
\(274\) −14.7307 −0.889912
\(275\) 21.6840i 1.30759i
\(276\) 0 0
\(277\) 28.5686 1.71652 0.858261 0.513213i \(-0.171545\pi\)
0.858261 + 0.513213i \(0.171545\pi\)
\(278\) 4.03867 6.99518i 0.242223 0.419543i
\(279\) 0 0
\(280\) −1.03205 1.70735i −0.0616766 0.102034i
\(281\) 19.1103i 1.14002i 0.821637 + 0.570012i \(0.193061\pi\)
−0.821637 + 0.570012i \(0.806939\pi\)
\(282\) 0 0
\(283\) −24.1452 13.9403i −1.43529 0.828662i −0.437768 0.899088i \(-0.644231\pi\)
−0.997517 + 0.0704252i \(0.977564\pi\)
\(284\) −7.33372 4.23413i −0.435176 0.251249i
\(285\) 0 0
\(286\) 13.1304 + 11.7840i 0.776419 + 0.696803i
\(287\) 0.167294 + 8.32113i 0.00987505 + 0.491181i
\(288\) 0 0
\(289\) −5.24024 −0.308250
\(290\) −2.22714 −0.130782
\(291\) 0 0
\(292\) −4.00551 + 2.31258i −0.234405 + 0.135334i
\(293\) −16.8908 + 29.2557i −0.986771 + 1.70914i −0.352988 + 0.935628i \(0.614834\pi\)
−0.633784 + 0.773510i \(0.718499\pi\)
\(294\) 0 0
\(295\) −3.71815 + 6.44003i −0.216479 + 0.374953i
\(296\) 8.60752i 0.500302i
\(297\) 0 0
\(298\) 4.66392 + 8.07815i 0.270174 + 0.467954i
\(299\) −10.5030 2.21460i −0.607404 0.128074i
\(300\) 0 0
\(301\) 4.62914 2.79818i 0.266819 0.161284i
\(302\) 11.4966 6.63758i 0.661557 0.381950i
\(303\) 0 0
\(304\) 3.15853 1.82358i 0.181154 0.104589i
\(305\) 6.53027i 0.373922i
\(306\) 0 0
\(307\) 12.4632i 0.711312i 0.934617 + 0.355656i \(0.115742\pi\)
−0.934617 + 0.355656i \(0.884258\pi\)
\(308\) 6.69723 + 11.0795i 0.381610 + 0.631312i
\(309\) 0 0
\(310\) −5.10772 −0.290099
\(311\) 0.922899 + 1.59851i 0.0523328 + 0.0906430i 0.891005 0.453993i \(-0.150001\pi\)
−0.838672 + 0.544636i \(0.816668\pi\)
\(312\) 0 0
\(313\) −26.7492 15.4436i −1.51195 0.872926i −0.999902 0.0139696i \(-0.995553\pi\)
−0.512049 0.858956i \(-0.671113\pi\)
\(314\) −4.46895 7.74046i −0.252198 0.436819i
\(315\) 0 0
\(316\) −4.83243 + 8.37001i −0.271845 + 0.470850i
\(317\) −6.78164 3.91538i −0.380895 0.219910i 0.297313 0.954780i \(-0.403910\pi\)
−0.678207 + 0.734871i \(0.737243\pi\)
\(318\) 0 0
\(319\) 14.4525 0.809185
\(320\) −0.377027 + 0.653029i −0.0210764 + 0.0365054i
\(321\) 0 0
\(322\) −6.89908 3.80037i −0.384471 0.211786i
\(323\) −10.8314 + 6.25350i −0.602674 + 0.347954i
\(324\) 0 0
\(325\) −15.1876 + 4.96212i −0.842456 + 0.275249i
\(326\) 2.44787 1.41328i 0.135575 0.0782741i
\(327\) 0 0
\(328\) 2.72428 1.57286i 0.150423 0.0868469i
\(329\) −0.418982 + 0.253262i −0.0230992 + 0.0139628i
\(330\) 0 0
\(331\) −2.06308 3.57337i −0.113397 0.196410i 0.803741 0.594980i \(-0.202840\pi\)
−0.917138 + 0.398570i \(0.869507\pi\)
\(332\) −2.66655 −0.146346
\(333\) 0 0
\(334\) 13.1851 7.61244i 0.721458 0.416534i
\(335\) −1.77028 3.06622i −0.0967209 0.167525i
\(336\) 0 0
\(337\) −33.0546 −1.80060 −0.900300 0.435270i \(-0.856653\pi\)
−0.900300 + 0.435270i \(0.856653\pi\)
\(338\) −5.24885 + 11.8933i −0.285500 + 0.646908i
\(339\) 0 0
\(340\) 1.29292 2.23940i 0.0701184 0.121449i
\(341\) 33.1453 1.79492
\(342\) 0 0
\(343\) −1.11621 18.4866i −0.0602694 0.998182i
\(344\) −1.77055 1.02223i −0.0954619 0.0551150i
\(345\) 0 0
\(346\) 0.986326 0.569456i 0.0530252 0.0306141i
\(347\) 5.94972i 0.319398i 0.987166 + 0.159699i \(0.0510523\pi\)
−0.987166 + 0.159699i \(0.948948\pi\)
\(348\) 0 0
\(349\) −9.95079 + 5.74509i −0.532654 + 0.307528i −0.742096 0.670293i \(-0.766168\pi\)
0.209443 + 0.977821i \(0.432835\pi\)
\(350\) −11.7220 + 0.235668i −0.626568 + 0.0125970i
\(351\) 0 0
\(352\) 2.44663 4.23768i 0.130406 0.225869i
\(353\) 1.43456 2.48472i 0.0763537 0.132249i −0.825320 0.564665i \(-0.809006\pi\)
0.901674 + 0.432416i \(0.142339\pi\)
\(354\) 0 0
\(355\) 5.53002 3.19276i 0.293503 0.169454i
\(356\) −12.9287 −0.685221
\(357\) 0 0
\(358\) −2.99215 + 5.18256i −0.158140 + 0.273907i
\(359\) −7.07807 4.08652i −0.373566 0.215678i 0.301449 0.953482i \(-0.402530\pi\)
−0.675015 + 0.737804i \(0.735863\pi\)
\(360\) 0 0
\(361\) −2.84914 + 4.93485i −0.149955 + 0.259729i
\(362\) −18.8486 −0.990663
\(363\) 0 0
\(364\) −6.22755 + 7.22618i −0.326412 + 0.378755i
\(365\) 3.48762i 0.182550i
\(366\) 0 0
\(367\) −7.44645 4.29921i −0.388702 0.224417i 0.292896 0.956144i \(-0.405381\pi\)
−0.681597 + 0.731727i \(0.738714\pi\)
\(368\) 2.97706i 0.155190i
\(369\) 0 0
\(370\) −5.62096 3.24526i −0.292220 0.168713i
\(371\) 15.5502 0.312632i 0.807326 0.0162310i
\(372\) 0 0
\(373\) 16.5491 + 28.6639i 0.856882 + 1.48416i 0.874888 + 0.484325i \(0.160935\pi\)
−0.0180066 + 0.999838i \(0.505732\pi\)
\(374\) −8.39010 + 14.5321i −0.433842 + 0.751436i
\(375\) 0 0
\(376\) 0.160252 + 0.0925217i 0.00826438 + 0.00477144i
\(377\) 3.30728 + 10.1226i 0.170334 + 0.521341i
\(378\) 0 0
\(379\) 7.55693 + 13.0890i 0.388173 + 0.672336i 0.992204 0.124625i \(-0.0397728\pi\)
−0.604030 + 0.796961i \(0.706439\pi\)
\(380\) 2.75015i 0.141080i
\(381\) 0 0
\(382\) −11.7427 20.3390i −0.600810 1.04063i
\(383\) 15.2962 + 26.4938i 0.781599 + 1.35377i 0.931010 + 0.364994i \(0.118929\pi\)
−0.149410 + 0.988775i \(0.547738\pi\)
\(384\) 0 0
\(385\) −9.76026 + 0.196227i −0.497429 + 0.0100007i
\(386\) 3.08676 + 1.78214i 0.157112 + 0.0907087i
\(387\) 0 0
\(388\) 5.57654 + 3.21961i 0.283106 + 0.163451i
\(389\) −4.27808 + 2.46995i −0.216907 + 0.125231i −0.604517 0.796592i \(-0.706634\pi\)
0.387610 + 0.921823i \(0.373301\pi\)
\(390\) 0 0
\(391\) 10.2091i 0.516295i
\(392\) −5.91660 + 3.74083i −0.298834 + 0.188940i
\(393\) 0 0
\(394\) 12.5873 + 21.8018i 0.634137 + 1.09836i
\(395\) −3.64391 6.31143i −0.183345 0.317563i
\(396\) 0 0
\(397\) −3.01277 + 1.73942i −0.151207 + 0.0872992i −0.573694 0.819069i \(-0.694490\pi\)
0.422488 + 0.906369i \(0.361157\pi\)
\(398\) 12.4959 0.626361
\(399\) 0 0
\(400\) 2.21570 + 3.83771i 0.110785 + 0.191885i
\(401\) 11.4337i 0.570972i 0.958383 + 0.285486i \(0.0921550\pi\)
−0.958383 + 0.285486i \(0.907845\pi\)
\(402\) 0 0
\(403\) 7.58491 + 23.2152i 0.377831 + 1.15643i
\(404\) −1.53036 + 2.65067i −0.0761384 + 0.131876i
\(405\) 0 0
\(406\) 0.157074 + 7.81280i 0.00779545 + 0.387743i
\(407\) 36.4759 + 21.0594i 1.80805 + 1.04388i
\(408\) 0 0
\(409\) 37.3528i 1.84698i −0.383623 0.923490i \(-0.625324\pi\)
0.383623 0.923490i \(-0.374676\pi\)
\(410\) 2.37205i 0.117147i
\(411\) 0 0
\(412\) −5.42602 3.13272i −0.267321 0.154338i
\(413\) 22.8538 + 12.5891i 1.12456 + 0.619468i
\(414\) 0 0
\(415\) 1.00536 1.74134i 0.0493512 0.0854788i
\(416\) 3.52798 + 0.743889i 0.172973 + 0.0364721i
\(417\) 0 0
\(418\) 17.8465i 0.872898i
\(419\) −19.1641 33.1933i −0.936230 1.62160i −0.772426 0.635105i \(-0.780957\pi\)
−0.163804 0.986493i \(-0.552376\pi\)
\(420\) 0 0
\(421\) 1.61871 0.0788909 0.0394454 0.999222i \(-0.487441\pi\)
0.0394454 + 0.999222i \(0.487441\pi\)
\(422\) 4.56323 2.63458i 0.222134 0.128249i
\(423\) 0 0
\(424\) −2.93930 5.09102i −0.142745 0.247242i
\(425\) −7.59820 13.1605i −0.368567 0.638376i
\(426\) 0 0
\(427\) −22.9082 + 0.460562i −1.10860 + 0.0222881i
\(428\) 5.83707i 0.282145i
\(429\) 0 0
\(430\) 1.33509 0.770816i 0.0643839 0.0371720i
\(431\) −16.4937 9.52265i −0.794474 0.458690i 0.0470613 0.998892i \(-0.485014\pi\)
−0.841535 + 0.540202i \(0.818348\pi\)
\(432\) 0 0
\(433\) 21.2102 + 12.2457i 1.01930 + 0.588490i 0.913900 0.405940i \(-0.133056\pi\)
0.105395 + 0.994430i \(0.466389\pi\)
\(434\) 0.360233 + 17.9179i 0.0172917 + 0.860085i
\(435\) 0 0
\(436\) 2.00167 + 3.46699i 0.0958625 + 0.166039i
\(437\) 5.42889 + 9.40312i 0.259699 + 0.449812i
\(438\) 0 0
\(439\) 34.3635i 1.64008i −0.572306 0.820040i \(-0.693951\pi\)
0.572306 0.820040i \(-0.306049\pi\)
\(440\) 1.84489 + 3.19544i 0.0879516 + 0.152337i
\(441\) 0 0
\(442\) −12.0983 2.55098i −0.575458 0.121338i
\(443\) 23.4324 + 13.5287i 1.11331 + 0.642768i 0.939684 0.342044i \(-0.111119\pi\)
0.173623 + 0.984812i \(0.444453\pi\)
\(444\) 0 0
\(445\) 4.87448 8.44284i 0.231072 0.400229i
\(446\) −4.85096 8.40211i −0.229700 0.397852i
\(447\) 0 0
\(448\) 2.31742 + 1.27655i 0.109488 + 0.0603114i
\(449\) 29.5863 + 17.0817i 1.39626 + 0.806133i 0.993999 0.109390i \(-0.0348897\pi\)
0.402265 + 0.915523i \(0.368223\pi\)
\(450\) 0 0
\(451\) 15.3929i 0.724821i
\(452\) 4.32172 + 2.49515i 0.203277 + 0.117362i
\(453\) 0 0
\(454\) 5.62699i 0.264088i
\(455\) −2.37096 6.79123i −0.111152 0.318378i
\(456\) 0 0
\(457\) 18.2315 0.852833 0.426417 0.904527i \(-0.359776\pi\)
0.426417 + 0.904527i \(0.359776\pi\)
\(458\) −4.12034 + 7.13664i −0.192531 + 0.333473i
\(459\) 0 0
\(460\) −1.94411 1.12243i −0.0906444 0.0523336i
\(461\) 13.8708 24.0250i 0.646029 1.11896i −0.338033 0.941134i \(-0.609762\pi\)
0.984063 0.177822i \(-0.0569050\pi\)
\(462\) 0 0
\(463\) 36.9055 1.71514 0.857572 0.514363i \(-0.171972\pi\)
0.857572 + 0.514363i \(0.171972\pi\)
\(464\) 2.55786 1.47678i 0.118745 0.0685577i
\(465\) 0 0
\(466\) −9.66269 + 16.7363i −0.447616 + 0.775293i
\(467\) −16.7749 + 29.0550i −0.776252 + 1.34451i 0.157837 + 0.987465i \(0.449548\pi\)
−0.934088 + 0.357042i \(0.883785\pi\)
\(468\) 0 0
\(469\) −10.6314 + 6.42640i −0.490914 + 0.296744i
\(470\) −0.120839 + 0.0697663i −0.00557388 + 0.00321808i
\(471\) 0 0
\(472\) 9.86178i 0.453925i
\(473\) −8.66378 + 5.00203i −0.398361 + 0.229994i
\(474\) 0 0
\(475\) 13.9967 + 8.08100i 0.642213 + 0.370782i
\(476\) −7.94700 4.37762i −0.364250 0.200648i
\(477\) 0 0
\(478\) 26.1899 1.19790
\(479\) −19.0433 + 32.9840i −0.870110 + 1.50708i −0.00822834 + 0.999966i \(0.502619\pi\)
−0.861882 + 0.507109i \(0.830714\pi\)
\(480\) 0 0
\(481\) −6.40304 + 30.3671i −0.291953 + 1.38462i
\(482\) −16.3956 −0.746801
\(483\) 0 0
\(484\) −6.47197 11.2098i −0.294181 0.509536i
\(485\) −4.20500 + 2.42776i −0.190939 + 0.110239i
\(486\) 0 0
\(487\) 0.531844 0.0241001 0.0120501 0.999927i \(-0.496164\pi\)
0.0120501 + 0.999927i \(0.496164\pi\)
\(488\) 4.33011 + 7.49997i 0.196015 + 0.339508i
\(489\) 0 0
\(490\) −0.212154 5.27411i −0.00958416 0.238260i
\(491\) 4.26515 2.46249i 0.192484 0.111130i −0.400661 0.916226i \(-0.631220\pi\)
0.593145 + 0.805096i \(0.297886\pi\)
\(492\) 0 0
\(493\) −8.77153 + 5.06424i −0.395050 + 0.228082i
\(494\) 12.4998 4.08395i 0.562390 0.183745i
\(495\) 0 0
\(496\) 5.86618 3.38684i 0.263399 0.152074i
\(497\) −11.5902 19.1741i −0.519892 0.860076i
\(498\) 0 0
\(499\) 3.27332 5.66956i 0.146534 0.253804i −0.783410 0.621505i \(-0.786522\pi\)
0.929944 + 0.367701i \(0.119855\pi\)
\(500\) −7.11178 −0.318049
\(501\) 0 0
\(502\) −10.2650 5.92653i −0.458152 0.264514i
\(503\) 15.4926 26.8339i 0.690780 1.19647i −0.280803 0.959765i \(-0.590601\pi\)
0.971583 0.236700i \(-0.0760659\pi\)
\(504\) 0 0
\(505\) −1.15397 1.99874i −0.0513512 0.0889429i
\(506\) 12.6158 + 7.28375i 0.560842 + 0.323802i
\(507\) 0 0
\(508\) −10.3407 17.9106i −0.458795 0.794656i
\(509\) −7.42736 −0.329212 −0.164606 0.986359i \(-0.552635\pi\)
−0.164606 + 0.986359i \(0.552635\pi\)
\(510\) 0 0
\(511\) −12.2346 + 0.245972i −0.541225 + 0.0108812i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 6.78334i 0.299200i
\(515\) 4.09151 2.36224i 0.180294 0.104093i
\(516\) 0 0
\(517\) 0.784156 0.452732i 0.0344871 0.0199112i
\(518\) −10.9879 + 19.9472i −0.482783 + 0.876430i
\(519\) 0 0
\(520\) −1.81592 + 2.02341i −0.0796335 + 0.0887323i
\(521\) −17.4165 30.1662i −0.763029 1.32161i −0.941282 0.337621i \(-0.890378\pi\)
0.178253 0.983985i \(-0.442955\pi\)
\(522\) 0 0
\(523\) 8.07534i 0.353110i −0.984291 0.176555i \(-0.943505\pi\)
0.984291 0.176555i \(-0.0564953\pi\)
\(524\) 3.65280 6.32683i 0.159573 0.276389i
\(525\) 0 0
\(526\) −6.79576 + 11.7706i −0.296309 + 0.513223i
\(527\) −20.1166 + 11.6143i −0.876293 + 0.505928i
\(528\) 0 0
\(529\) 14.1371 0.614658
\(530\) 4.43278 0.192548
\(531\) 0 0
\(532\) 9.64751 0.193960i 0.418273 0.00840925i
\(533\) 10.7812 3.52247i 0.466987 0.152575i
\(534\) 0 0
\(535\) 3.81178 + 2.20073i 0.164798 + 0.0951459i
\(536\) 4.06632 + 2.34769i 0.175638 + 0.101405i
\(537\) 0 0
\(538\) 16.7602i 0.722584i
\(539\) 1.37673 + 34.2251i 0.0592999 + 1.47418i
\(540\) 0 0
\(541\) −17.7730 + 30.7838i −0.764121 + 1.32350i 0.176589 + 0.984285i \(0.443494\pi\)
−0.940710 + 0.339212i \(0.889840\pi\)
\(542\) 26.2139 1.12598
\(543\) 0 0
\(544\) 3.42925i 0.147028i
\(545\) −3.01873 −0.129308
\(546\) 0 0
\(547\) −6.78283 −0.290013 −0.145006 0.989431i \(-0.546320\pi\)
−0.145006 + 0.989431i \(0.546320\pi\)
\(548\) 14.7307i 0.629263i
\(549\) 0 0
\(550\) 21.6840 0.924608
\(551\) 5.38604 9.32889i 0.229453 0.397424i
\(552\) 0 0
\(553\) −21.8835 + 13.2279i −0.930581 + 0.562509i
\(554\) 28.5686i 1.21376i
\(555\) 0 0
\(556\) −6.99518 4.03867i −0.296662 0.171278i
\(557\) 13.3165 + 7.68831i 0.564240 + 0.325764i 0.754845 0.655903i \(-0.227712\pi\)
−0.190606 + 0.981667i \(0.561045\pi\)
\(558\) 0 0
\(559\) −5.48605 4.92350i −0.232035 0.208242i
\(560\) −1.70735 + 1.03205i −0.0721488 + 0.0436119i
\(561\) 0 0
\(562\) 19.1103 0.806118
\(563\) −32.6174 −1.37466 −0.687329 0.726346i \(-0.741217\pi\)
−0.687329 + 0.726346i \(0.741217\pi\)
\(564\) 0 0
\(565\) −3.25881 + 1.88147i −0.137099 + 0.0791542i
\(566\) −13.9403 + 24.1452i −0.585953 + 1.01490i
\(567\) 0 0
\(568\) −4.23413 + 7.33372i −0.177660 + 0.307716i
\(569\) 17.3290i 0.726467i −0.931698 0.363234i \(-0.881673\pi\)
0.931698 0.363234i \(-0.118327\pi\)
\(570\) 0 0
\(571\) 6.55505 + 11.3537i 0.274320 + 0.475137i 0.969963 0.243251i \(-0.0782138\pi\)
−0.695643 + 0.718388i \(0.744880\pi\)
\(572\) 11.7840 13.1304i 0.492714 0.549011i
\(573\) 0 0
\(574\) 8.32113 0.167294i 0.347317 0.00698271i
\(575\) −11.4251 + 6.59627i −0.476459 + 0.275084i
\(576\) 0 0
\(577\) −0.169426 + 0.0978179i −0.00705328 + 0.00407221i −0.503522 0.863982i \(-0.667963\pi\)
0.496469 + 0.868054i \(0.334630\pi\)
\(578\) 5.24024i 0.217965i
\(579\) 0 0
\(580\) 2.22714i 0.0924770i
\(581\) −6.17951 3.40399i −0.256369 0.141221i
\(582\) 0 0
\(583\) −28.7655 −1.19135
\(584\) 2.31258 + 4.00551i 0.0956952 + 0.165749i
\(585\) 0 0
\(586\) 29.2557 + 16.8908i 1.20854 + 0.697753i
\(587\) −6.25620 10.8361i −0.258221 0.447252i 0.707544 0.706669i \(-0.249803\pi\)
−0.965765 + 0.259417i \(0.916470\pi\)
\(588\) 0 0
\(589\) 12.3523 21.3949i 0.508969 0.881560i
\(590\) 6.44003 + 3.71815i 0.265132 + 0.153074i
\(591\) 0 0
\(592\) 8.60752 0.353767
\(593\) 4.26760 7.39170i 0.175249 0.303541i −0.764998 0.644032i \(-0.777260\pi\)
0.940248 + 0.340492i \(0.110594\pi\)
\(594\) 0 0
\(595\) 5.85494 3.53914i 0.240029 0.145091i
\(596\) 8.07815 4.66392i 0.330894 0.191042i
\(597\) 0 0
\(598\) −2.21460 + 10.5030i −0.0905617 + 0.429499i
\(599\) −3.65068 + 2.10772i −0.149163 + 0.0861192i −0.572724 0.819748i \(-0.694113\pi\)
0.423561 + 0.905868i \(0.360780\pi\)
\(600\) 0 0
\(601\) −1.89940 + 1.09662i −0.0774783 + 0.0447321i −0.538239 0.842792i \(-0.680910\pi\)
0.460760 + 0.887525i \(0.347577\pi\)
\(602\) −2.79818 4.62914i −0.114045 0.188670i
\(603\) 0 0
\(604\) −6.63758 11.4966i −0.270079 0.467791i
\(605\) 9.76042 0.396818
\(606\) 0 0
\(607\) −7.27710 + 4.20144i −0.295369 + 0.170531i −0.640360 0.768075i \(-0.721215\pi\)
0.344992 + 0.938606i \(0.387882\pi\)
\(608\) −1.82358 3.15853i −0.0739558 0.128095i
\(609\) 0 0
\(610\) −6.53027 −0.264403
\(611\) 0.496541 + 0.445625i 0.0200879 + 0.0180280i
\(612\) 0 0
\(613\) 22.9839 39.8092i 0.928309 1.60788i 0.142159 0.989844i \(-0.454596\pi\)
0.786150 0.618035i \(-0.212071\pi\)
\(614\) 12.4632 0.502973
\(615\) 0 0
\(616\) 11.0795 6.69723i 0.446405 0.269839i
\(617\) −9.53772 5.50660i −0.383974 0.221688i 0.295572 0.955321i \(-0.404490\pi\)
−0.679546 + 0.733633i \(0.737823\pi\)
\(618\) 0 0
\(619\) 39.1787 22.6198i 1.57473 0.909168i 0.579148 0.815222i \(-0.303385\pi\)
0.995577 0.0939460i \(-0.0299481\pi\)
\(620\) 5.10772i 0.205131i
\(621\) 0 0
\(622\) 1.59851 0.922899i 0.0640943 0.0370049i
\(623\) −29.9612 16.5042i −1.20037 0.661227i
\(624\) 0 0
\(625\) −8.39718 + 14.5443i −0.335887 + 0.581774i
\(626\) −15.4436 + 26.7492i −0.617252 + 1.06911i
\(627\) 0 0
\(628\) −7.74046 + 4.46895i −0.308878 + 0.178331i
\(629\) −29.5173 −1.17693
\(630\) 0 0
\(631\) −1.81894 + 3.15050i −0.0724109 + 0.125419i −0.899957 0.435978i \(-0.856403\pi\)
0.827547 + 0.561397i \(0.189736\pi\)
\(632\) 8.37001 + 4.83243i 0.332941 + 0.192224i
\(633\) 0 0
\(634\) −3.91538 + 6.78164i −0.155500 + 0.269333i
\(635\) 15.5949 0.618865
\(636\) 0 0
\(637\) −23.6564 + 8.79627i −0.937301 + 0.348521i
\(638\) 14.4525i 0.572180i
\(639\) 0 0
\(640\) 0.653029 + 0.377027i 0.0258133 + 0.0149033i
\(641\) 44.0507i 1.73990i −0.493142 0.869949i \(-0.664152\pi\)
0.493142 0.869949i \(-0.335848\pi\)
\(642\) 0 0
\(643\) −40.9439 23.6390i −1.61467 0.932231i −0.988268 0.152733i \(-0.951193\pi\)
−0.626404 0.779499i \(-0.715474\pi\)
\(644\) −3.80037 + 6.89908i −0.149756 + 0.271862i
\(645\) 0 0
\(646\) 6.25350 + 10.8314i 0.246041 + 0.426155i
\(647\) 5.78761 10.0244i 0.227535 0.394101i −0.729542 0.683936i \(-0.760267\pi\)
0.957077 + 0.289834i \(0.0936002\pi\)
\(648\) 0 0
\(649\) −41.7911 24.1281i −1.64044 0.947111i
\(650\) 4.96212 + 15.1876i 0.194630 + 0.595706i
\(651\) 0 0
\(652\) −1.41328 2.44787i −0.0553482 0.0958658i
\(653\) 28.9682i 1.13361i −0.823851 0.566806i \(-0.808179\pi\)
0.823851 0.566806i \(-0.191821\pi\)
\(654\) 0 0
\(655\) 2.75440 + 4.77077i 0.107623 + 0.186409i
\(656\) −1.57286 2.72428i −0.0614100 0.106365i
\(657\) 0 0
\(658\) 0.253262 + 0.418982i 0.00987320 + 0.0163336i
\(659\) 10.7730 + 6.21981i 0.419658 + 0.242289i 0.694931 0.719077i \(-0.255435\pi\)
−0.275273 + 0.961366i \(0.588768\pi\)
\(660\) 0 0
\(661\) −28.7002 16.5700i −1.11631 0.644500i −0.175851 0.984417i \(-0.556268\pi\)
−0.940456 + 0.339917i \(0.889601\pi\)
\(662\) −3.57337 + 2.06308i −0.138883 + 0.0801840i
\(663\) 0 0
\(664\) 2.66655i 0.103482i
\(665\) −3.51071 + 6.37324i −0.136139 + 0.247143i
\(666\) 0 0
\(667\) 4.39646 + 7.61489i 0.170231 + 0.294850i
\(668\) −7.61244 13.1851i −0.294534 0.510148i
\(669\) 0 0
\(670\) −3.06622 + 1.77028i −0.118458 + 0.0683920i
\(671\) 42.3767 1.63593
\(672\) 0 0
\(673\) 9.10484 + 15.7701i 0.350966 + 0.607891i 0.986419 0.164249i \(-0.0525200\pi\)
−0.635453 + 0.772140i \(0.719187\pi\)
\(674\) 33.0546i 1.27322i
\(675\) 0 0
\(676\) 11.8933 + 5.24885i 0.457433 + 0.201879i
\(677\) −18.2468 + 31.6044i −0.701282 + 1.21466i 0.266735 + 0.963770i \(0.414055\pi\)
−0.968017 + 0.250886i \(0.919278\pi\)
\(678\) 0 0
\(679\) 8.81314 + 14.5799i 0.338217 + 0.559526i
\(680\) −2.23940 1.29292i −0.0858771 0.0495812i
\(681\) 0 0
\(682\) 33.1453i 1.26920i
\(683\) 40.0572i 1.53274i −0.642397 0.766372i \(-0.722060\pi\)
0.642397 0.766372i \(-0.277940\pi\)
\(684\) 0 0
\(685\) −9.61956 5.55386i −0.367544 0.212202i
\(686\) −18.4866 + 1.11621i −0.705821 + 0.0426169i
\(687\) 0 0
\(688\) −1.02223 + 1.77055i −0.0389722 + 0.0675018i
\(689\) −6.58264 20.1475i −0.250779 0.767560i
\(690\) 0 0
\(691\) 36.1396i 1.37481i 0.726273 + 0.687407i \(0.241251\pi\)
−0.726273 + 0.687407i \(0.758749\pi\)
\(692\) −0.569456 0.986326i −0.0216475 0.0374945i
\(693\) 0 0
\(694\) 5.94972 0.225848
\(695\) 5.27474 3.04537i 0.200082 0.115517i
\(696\) 0 0
\(697\) 5.39375 + 9.34224i 0.204303 + 0.353863i
\(698\) 5.74509 + 9.95079i 0.217455 + 0.376643i
\(699\) 0 0
\(700\) 0.235668 + 11.7220i 0.00890740 + 0.443051i
\(701\) 43.7394i 1.65201i −0.563659 0.826007i \(-0.690607\pi\)
0.563659 0.826007i \(-0.309393\pi\)
\(702\) 0 0
\(703\) 27.1871 15.6965i 1.02538 0.592004i
\(704\) −4.23768 2.44663i −0.159714 0.0922107i
\(705\) 0 0
\(706\) −2.48472 1.43456i −0.0935138 0.0539902i
\(707\) −6.93020 + 4.18911i −0.260637 + 0.157548i
\(708\) 0 0
\(709\) −13.2922 23.0228i −0.499199 0.864638i 0.500800 0.865563i \(-0.333039\pi\)
−1.00000 0.000924526i \(0.999706\pi\)
\(710\) −3.19276 5.53002i −0.119822 0.207538i
\(711\) 0 0
\(712\) 12.9287i 0.484525i
\(713\) 10.0828 + 17.4640i 0.377605 + 0.654030i
\(714\) 0 0
\(715\) 4.13167 + 12.6458i 0.154516 + 0.472927i
\(716\) 5.18256 + 2.99215i 0.193681 + 0.111822i
\(717\) 0 0
\(718\) −4.08652 + 7.07807i −0.152508 + 0.264151i
\(719\) −6.00910 10.4081i −0.224102 0.388155i 0.731948 0.681361i \(-0.238611\pi\)
−0.956050 + 0.293205i \(0.905278\pi\)
\(720\) 0 0
\(721\) −8.57528 14.1864i −0.319360 0.528329i
\(722\) 4.93485 + 2.84914i 0.183656 + 0.106034i
\(723\) 0 0
\(724\) 18.8486i 0.700505i
\(725\) 11.3349 + 6.54420i 0.420967 + 0.243046i
\(726\) 0 0
\(727\) 47.0077i 1.74342i −0.490024 0.871709i \(-0.663012\pi\)
0.490024 0.871709i \(-0.336988\pi\)
\(728\) 7.22618 + 6.22755i 0.267820 + 0.230808i
\(729\) 0 0
\(730\) −3.48762 −0.129083
\(731\) 3.50548 6.07167i 0.129655 0.224569i
\(732\) 0 0
\(733\) 32.2548 + 18.6223i 1.19136 + 0.687831i 0.958615 0.284707i \(-0.0918964\pi\)
0.232744 + 0.972538i \(0.425230\pi\)
\(734\) −4.29921 + 7.44645i −0.158687 + 0.274854i
\(735\) 0 0
\(736\) 2.97706 0.109736
\(737\) 19.8975 11.4878i 0.732935 0.423160i
\(738\) 0 0
\(739\) −5.58593 + 9.67512i −0.205482 + 0.355905i −0.950286 0.311378i \(-0.899209\pi\)
0.744804 + 0.667283i \(0.232543\pi\)
\(740\) −3.24526 + 5.62096i −0.119298 + 0.206631i
\(741\) 0 0
\(742\) −0.312632 15.5502i −0.0114771 0.570865i
\(743\) 12.6809 7.32130i 0.465216 0.268592i −0.249019 0.968499i \(-0.580108\pi\)
0.714235 + 0.699906i \(0.246775\pi\)
\(744\) 0 0
\(745\) 7.03369i 0.257694i
\(746\) 28.6639 16.5491i 1.04946 0.605907i
\(747\) 0 0
\(748\) 14.5321 + 8.39010i 0.531345 + 0.306772i
\(749\) 7.45132 13.5269i 0.272265 0.494263i
\(750\) 0 0
\(751\) −45.2981 −1.65295 −0.826475 0.562973i \(-0.809658\pi\)
−0.826475 + 0.562973i \(0.809658\pi\)
\(752\) 0.0925217 0.160252i 0.00337392 0.00584380i
\(753\) 0 0
\(754\) 10.1226 3.30728i 0.368644 0.120444i
\(755\) 10.0102 0.364308
\(756\) 0 0
\(757\) −0.217479 0.376684i −0.00790440 0.0136908i 0.862046 0.506830i \(-0.169183\pi\)
−0.869951 + 0.493139i \(0.835849\pi\)
\(758\) 13.0890 7.55693i 0.475413 0.274480i
\(759\) 0 0
\(760\) 2.75015 0.0997583
\(761\) −26.2848 45.5265i −0.952822 1.65034i −0.739275 0.673403i \(-0.764832\pi\)
−0.213547 0.976933i \(-0.568502\pi\)
\(762\) 0 0
\(763\) 0.212902 + 10.5897i 0.00770759 + 0.383372i
\(764\) −20.3390 + 11.7427i −0.735839 + 0.424837i
\(765\) 0 0
\(766\) 26.4938 15.2962i 0.957260 0.552674i
\(767\) 7.33607 34.7921i 0.264890 1.25627i
\(768\) 0 0
\(769\) −13.8078 + 7.97196i −0.497924 + 0.287476i −0.727856 0.685730i \(-0.759483\pi\)
0.229932 + 0.973207i \(0.426150\pi\)
\(770\) 0.196227 + 9.76026i 0.00707153 + 0.351735i
\(771\) 0 0
\(772\) 1.78214 3.08676i 0.0641407 0.111095i
\(773\) 0.442280 0.0159077 0.00795385 0.999968i \(-0.497468\pi\)
0.00795385 + 0.999968i \(0.497468\pi\)
\(774\) 0 0
\(775\) 25.9954 + 15.0085i 0.933783 + 0.539120i
\(776\) 3.21961 5.57654i 0.115577 0.200186i
\(777\) 0 0
\(778\) 2.46995 + 4.27808i 0.0885520 + 0.153377i
\(779\) −9.93587 5.73648i −0.355989 0.205531i
\(780\) 0 0
\(781\) 20.7187 + 35.8858i 0.741372 + 1.28409i
\(782\) −10.2091 −0.365076
\(783\) 0 0
\(784\) 3.74083 + 5.91660i 0.133601 + 0.211307i
\(785\) 6.73966i 0.240549i
\(786\) 0 0
\(787\) 11.1465i 0.397330i 0.980067 + 0.198665i \(0.0636606\pi\)
−0.980067 + 0.198665i \(0.936339\pi\)
\(788\) 21.8018 12.5873i 0.776657 0.448403i
\(789\) 0 0
\(790\) −6.31143 + 3.64391i −0.224551 + 0.129644i
\(791\) 6.83004 + 11.2992i 0.242848 + 0.401753i
\(792\) 0 0
\(793\) 9.69739 + 29.6809i 0.344364 + 1.05400i
\(794\) 1.73942 + 3.01277i 0.0617299 + 0.106919i
\(795\) 0 0
\(796\) 12.4959i 0.442904i
\(797\) 14.5054 25.1240i 0.513806 0.889939i −0.486065 0.873922i \(-0.661568\pi\)
0.999872 0.0160163i \(-0.00509838\pi\)
\(798\) 0 0
\(799\) −0.317280 + 0.549545i −0.0112246 + 0.0194415i
\(800\) 3.83771 2.21570i 0.135683 0.0783369i
\(801\) 0 0
\(802\) 11.4337 0.403738
\(803\) 22.6321 0.798669
\(804\) 0 0
\(805\) −3.07246 5.08289i −0.108290 0.179148i
\(806\) 23.2152 7.58491i 0.817720 0.267167i
\(807\) 0 0
\(808\) 2.65067 + 1.53036i 0.0932501 + 0.0538380i
\(809\) −15.0227 8.67337i −0.528170 0.304939i 0.212101 0.977248i \(-0.431970\pi\)
−0.740271 + 0.672309i \(0.765303\pi\)
\(810\) 0 0
\(811\) 29.7180i 1.04354i −0.853086 0.521770i \(-0.825272\pi\)
0.853086 0.521770i \(-0.174728\pi\)
\(812\) 7.81280 0.157074i 0.274176 0.00551222i
\(813\) 0 0
\(814\) 21.0594 36.4759i 0.738131 1.27848i
\(815\) 2.13137 0.0746587
\(816\) 0 0
\(817\) 7.45646i 0.260869i
\(818\) −37.3528 −1.30601
\(819\) 0 0
\(820\) 2.37205 0.0828355
\(821\) 41.5883i 1.45144i −0.687988 0.725722i \(-0.741506\pi\)
0.687988 0.725722i \(-0.258494\pi\)
\(822\) 0 0
\(823\) 26.4928 0.923482 0.461741 0.887015i \(-0.347225\pi\)
0.461741 + 0.887015i \(0.347225\pi\)
\(824\) −3.13272 + 5.42602i −0.109133 + 0.189025i
\(825\) 0 0
\(826\) 12.5891 22.8538i 0.438030 0.795187i
\(827\) 43.5660i 1.51494i 0.652872 + 0.757468i \(0.273564\pi\)
−0.652872 + 0.757468i \(0.726436\pi\)
\(828\) 0 0
\(829\) −0.951475 0.549334i −0.0330461 0.0190792i 0.483386 0.875407i \(-0.339407\pi\)
−0.516432 + 0.856328i \(0.672740\pi\)
\(830\) −1.74134 1.00536i −0.0604427 0.0348966i
\(831\) 0 0
\(832\) 0.743889 3.52798i 0.0257897 0.122311i
\(833\) −12.8282 20.2895i −0.444472 0.702990i
\(834\) 0 0
\(835\) 11.4804 0.397294
\(836\) −17.8465 −0.617232
\(837\) 0 0
\(838\) −33.1933 + 19.1641i −1.14664 + 0.662015i
\(839\) 8.15758 14.1293i 0.281631 0.487799i −0.690156 0.723661i \(-0.742458\pi\)
0.971787 + 0.235862i \(0.0757913\pi\)
\(840\) 0 0
\(841\) −10.1382 + 17.5600i −0.349595 + 0.605516i
\(842\) 1.61871i 0.0557843i
\(843\) 0 0
\(844\) −2.63458 4.56323i −0.0906860 0.157073i
\(845\) −7.91173 + 5.78769i −0.272172 + 0.199103i
\(846\) 0 0
\(847\) −0.688376 34.2395i −0.0236529 1.17648i
\(848\) −5.09102 + 2.93930i −0.174826 + 0.100936i
\(849\) 0 0
\(850\) −13.1605 + 7.59820i −0.451400 + 0.260616i
\(851\) 25.6251i 0.878417i
\(852\) 0 0
\(853\) 5.34078i 0.182865i 0.995811 + 0.0914324i \(0.0291445\pi\)
−0.995811 + 0.0914324i \(0.970855\pi\)
\(854\) 0.460562 + 22.9082i 0.0157601 + 0.783901i
\(855\) 0 0
\(856\) −5.83707 −0.199507
\(857\) −16.1046 27.8940i −0.550122 0.952840i −0.998265 0.0588780i \(-0.981248\pi\)
0.448143 0.893962i \(-0.352086\pi\)
\(858\) 0 0
\(859\) 26.4379 + 15.2639i 0.902050 + 0.520799i 0.877865 0.478909i \(-0.158967\pi\)
0.0241854 + 0.999707i \(0.492301\pi\)
\(860\) −0.770816 1.33509i −0.0262846 0.0455263i
\(861\) 0 0
\(862\) −9.52265 + 16.4937i −0.324343 + 0.561778i
\(863\) −42.8644 24.7478i −1.45912 0.842424i −0.460154 0.887839i \(-0.652206\pi\)
−0.998968 + 0.0454148i \(0.985539\pi\)
\(864\) 0 0
\(865\) 0.858800 0.0292001
\(866\) 12.2457 21.2102i 0.416126 0.720751i
\(867\) 0 0
\(868\) 17.9179 0.360233i 0.608172 0.0122271i
\(869\) 40.9566 23.6463i 1.38936 0.802146i
\(870\) 0 0
\(871\) 12.5995 + 11.3075i 0.426916 + 0.383139i
\(872\) 3.46699 2.00167i 0.117407 0.0677850i
\(873\) 0 0
\(874\) 9.40312 5.42889i 0.318065 0.183635i
\(875\) −16.4810 9.07856i −0.557158 0.306911i
\(876\) 0 0
\(877\) 1.19794 + 2.07489i 0.0404514 + 0.0700640i 0.885542 0.464559i \(-0.153787\pi\)
−0.845091 + 0.534623i \(0.820454\pi\)
\(878\) −34.3635 −1.15971
\(879\) 0 0
\(880\) 3.19544 1.84489i 0.107718 0.0621911i
\(881\) 19.5418 + 33.8473i 0.658379 + 1.14035i 0.981035 + 0.193830i \(0.0620909\pi\)
−0.322656 + 0.946516i \(0.604576\pi\)
\(882\) 0 0
\(883\) 22.4689 0.756140 0.378070 0.925777i \(-0.376588\pi\)
0.378070 + 0.925777i \(0.376588\pi\)
\(884\) −2.55098 + 12.0983i −0.0857988 + 0.406911i
\(885\) 0 0
\(886\) 13.5287 23.4324i 0.454506 0.787227i
\(887\) −11.8745 −0.398706 −0.199353 0.979928i \(-0.563884\pi\)
−0.199353 + 0.979928i \(0.563884\pi\)
\(888\) 0 0
\(889\) −1.09987 54.7069i −0.0368883 1.83481i
\(890\) −8.44284 4.87448i −0.283005 0.163393i
\(891\) 0 0
\(892\) −8.40211 + 4.85096i −0.281324 + 0.162422i
\(893\) 0.674882i 0.0225841i
\(894\) 0 0
\(895\) −3.90793 + 2.25624i −0.130628 + 0.0754179i
\(896\) 1.27655 2.31742i 0.0426466 0.0774194i
\(897\) 0 0
\(898\) 17.0817 29.5863i 0.570022 0.987308i
\(899\) 10.0032 17.3261i 0.333626 0.577858i
\(900\) 0 0
\(901\) 17.4584 10.0796i 0.581623 0.335800i
\(902\) −15.3929 −0.512526
\(903\) 0 0
\(904\) 2.49515 4.32172i 0.0829874 0.143738i
\(905\) −12.3087 7.10644i −0.409156 0.236226i
\(906\) 0 0
\(907\) 5.00952 8.67674i 0.166338 0.288106i −0.770791 0.637088i \(-0.780139\pi\)
0.937130 + 0.348981i \(0.113472\pi\)
\(908\) −5.62699 −0.186738
\(909\) 0 0
\(910\) −6.79123 + 2.37096i −0.225127 + 0.0785964i
\(911\) 29.3842i 0.973541i 0.873530 + 0.486771i \(0.161825\pi\)
−0.873530 + 0.486771i \(0.838175\pi\)
\(912\) 0 0
\(913\) 11.3000 + 6.52406i 0.373975 + 0.215915i
\(914\) 18.2315i 0.603044i
\(915\) 0 0
\(916\) 7.13664 + 4.12034i 0.235801 + 0.136140i
\(917\) 16.5416 9.99891i 0.546251 0.330193i
\(918\) 0 0
\(919\) −9.72015 16.8358i −0.320638 0.555362i 0.659982 0.751282i \(-0.270564\pi\)
−0.980620 + 0.195920i \(0.937231\pi\)
\(920\) −1.12243 + 1.94411i −0.0370054 + 0.0640953i
\(921\) 0 0
\(922\) −24.0250 13.8708i −0.791221 0.456812i
\(923\) −20.3934 + 22.7235i −0.671256 + 0.747953i
\(924\) 0 0
\(925\) 19.0717 + 33.0332i 0.627074 + 1.08612i
\(926\) 36.9055i 1.21279i
\(927\) 0 0
\(928\) −1.47678 2.55786i −0.0484776 0.0839657i
\(929\) −9.71746 16.8311i −0.318819 0.552211i 0.661423 0.750013i \(-0.269953\pi\)
−0.980242 + 0.197802i \(0.936620\pi\)
\(930\) 0 0
\(931\) 22.6049 + 11.8661i 0.740845 + 0.388894i
\(932\) 16.7363 + 9.66269i 0.548215 + 0.316512i
\(933\) 0 0
\(934\) 29.0550 + 16.7749i 0.950710 + 0.548893i
\(935\) −10.9580 + 6.32658i −0.358364 + 0.206901i
\(936\) 0 0
\(937\) 22.6784i 0.740871i −0.928858 0.370435i \(-0.879208\pi\)
0.928858 0.370435i \(-0.120792\pi\)
\(938\) 6.42640 + 10.6314i 0.209829 + 0.347129i
\(939\) 0 0
\(940\) 0.0697663 + 0.120839i 0.00227553 + 0.00394133i
\(941\) −10.1312 17.5478i −0.330268 0.572040i 0.652297 0.757964i \(-0.273806\pi\)
−0.982564 + 0.185923i \(0.940472\pi\)
\(942\) 0 0
\(943\) 8.11034 4.68251i 0.264109 0.152483i
\(944\) −9.86178 −0.320974
\(945\) 0 0
\(946\) 5.00203 + 8.66378i 0.162630 + 0.281684i
\(947\) 30.5079i 0.991372i −0.868502 0.495686i \(-0.834917\pi\)
0.868502 0.495686i \(-0.165083\pi\)
\(948\) 0 0
\(949\) 5.17908 + 15.8516i 0.168120 + 0.514566i
\(950\) 8.08100 13.9967i 0.262182 0.454113i
\(951\) 0 0
\(952\) −4.37762 + 7.94700i −0.141879 + 0.257564i
\(953\) −33.3289 19.2424i −1.07963 0.623323i −0.148832 0.988863i \(-0.547551\pi\)
−0.930796 + 0.365539i \(0.880885\pi\)
\(954\) 0 0
\(955\) 17.7093i 0.573059i
\(956\) 26.1899i 0.847042i
\(957\) 0 0
\(958\) 32.9840 + 19.0433i 1.06566 + 0.615261i
\(959\) −18.8045 + 34.1371i −0.607228 + 1.10234i
\(960\) 0 0
\(961\) 7.44137 12.8888i 0.240044 0.415769i
\(962\) 30.3671 + 6.40304i 0.979076 + 0.206442i
\(963\) 0 0
\(964\) 16.3956i 0.528068i
\(965\) 1.34383 + 2.32758i 0.0432595 + 0.0749276i
\(966\) 0 0
\(967\) 17.5090 0.563051 0.281525 0.959554i \(-0.409160\pi\)
0.281525 + 0.959554i \(0.409160\pi\)
\(968\) −11.2098 + 6.47197i −0.360296 + 0.208017i
\(969\) 0 0
\(970\) 2.42776 + 4.20500i 0.0779507 + 0.135015i
\(971\) −6.82401 11.8195i −0.218993 0.379307i 0.735507 0.677517i \(-0.236944\pi\)
−0.954500 + 0.298210i \(0.903610\pi\)
\(972\) 0 0
\(973\) −11.0552 18.2890i −0.354412 0.586318i
\(974\) 0.531844i 0.0170414i
\(975\) 0 0
\(976\) 7.49997 4.33011i 0.240068 0.138603i
\(977\) 18.5757 + 10.7247i 0.594290 + 0.343113i 0.766792 0.641896i \(-0.221852\pi\)
−0.172502 + 0.985009i \(0.555185\pi\)
\(978\) 0 0
\(979\) 54.7879 + 31.6318i 1.75103 + 1.01096i
\(980\) −5.27411 + 0.212154i −0.168475 + 0.00677703i
\(981\) 0 0
\(982\) −2.46249 4.26515i −0.0785811 0.136107i
\(983\) 7.53173 + 13.0453i 0.240225 + 0.416081i 0.960778 0.277318i \(-0.0894455\pi\)
−0.720553 + 0.693399i \(0.756112\pi\)
\(984\) 0 0
\(985\) 18.9829i 0.604847i
\(986\) 5.06424 + 8.77153i 0.161278 + 0.279342i
\(987\) 0 0
\(988\) −4.08395 12.4998i −0.129928 0.397670i
\(989\) −5.27104 3.04324i −0.167609 0.0967694i
\(990\) 0 0
\(991\) −6.97010 + 12.0726i −0.221412 + 0.383498i −0.955237 0.295841i \(-0.904400\pi\)
0.733825 + 0.679339i \(0.237733\pi\)
\(992\) −3.38684 5.86618i −0.107532 0.186251i
\(993\) 0 0
\(994\) −19.1741 + 11.5902i −0.608166 + 0.367619i
\(995\) 8.16017 + 4.71127i 0.258695 + 0.149357i
\(996\) 0 0
\(997\) 58.7468i 1.86053i −0.366888 0.930265i \(-0.619577\pi\)
0.366888 0.930265i \(-0.380423\pi\)
\(998\) −5.66956 3.27332i −0.179467 0.103615i
\(999\) 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 1638.2.cm.a.341.22 yes 72
3.2 odd 2 inner 1638.2.cm.a.341.15 yes 72
7.3 odd 6 1638.2.bq.a.1277.28 yes 72
13.9 even 3 1638.2.bq.a.971.9 72
21.17 even 6 1638.2.bq.a.1277.9 yes 72
39.35 odd 6 1638.2.bq.a.971.28 yes 72
91.87 odd 6 inner 1638.2.cm.a.269.15 yes 72
273.269 even 6 inner 1638.2.cm.a.269.22 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1638.2.bq.a.971.9 72 13.9 even 3
1638.2.bq.a.971.28 yes 72 39.35 odd 6
1638.2.bq.a.1277.9 yes 72 21.17 even 6
1638.2.bq.a.1277.28 yes 72 7.3 odd 6
1638.2.cm.a.269.15 yes 72 91.87 odd 6 inner
1638.2.cm.a.269.22 yes 72 273.269 even 6 inner
1638.2.cm.a.341.15 yes 72 3.2 odd 2 inner
1638.2.cm.a.341.22 yes 72 1.1 even 1 trivial