Properties

Label 693.2.m.g.631.2
Level $693$
Weight $2$
Character 693.631
Analytic conductor $5.534$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,2,Mod(64,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.m (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 631.2
Root \(-0.762262 - 2.34600i\) of defining polynomial
Character \(\chi\) \(=\) 693.631
Dual form 693.2.m.g.190.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.99563 + 1.44991i) q^{2} +(1.26226 + 3.88484i) q^{4} +(-2.80464 + 2.03769i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-1.58914 + 4.89086i) q^{8} +O(q^{10})\) \(q+(1.99563 + 1.44991i) q^{2} +(1.26226 + 3.88484i) q^{4} +(-2.80464 + 2.03769i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-1.58914 + 4.89086i) q^{8} -8.55150 q^{10} +(-2.91998 + 1.57281i) q^{11} +(0.528896 + 0.384266i) q^{13} +(0.762262 - 2.34600i) q^{14} +(-3.65334 + 2.65431i) q^{16} +(-0.919977 + 0.668402i) q^{17} +(-1.87759 + 5.77864i) q^{19} +(-11.4563 - 8.32350i) q^{20} +(-8.10762 - 1.09495i) q^{22} +6.66708 q^{23} +(2.16875 - 6.67473i) q^{25} +(0.498330 + 1.53370i) q^{26} +(3.30464 - 2.40097i) q^{28} +(1.41331 + 4.34973i) q^{29} +(-2.26226 - 1.64363i) q^{31} -0.854102 q^{32} -2.80505 q^{34} +(2.80464 + 2.03769i) q^{35} +(-0.135893 - 0.418235i) q^{37} +(-12.1255 + 8.80968i) q^{38} +(-5.50911 - 16.9553i) q^{40} +(1.82417 - 5.61423i) q^{41} +8.70820 q^{43} +(-9.79590 - 9.35835i) q^{44} +(13.3050 + 9.66666i) q^{46} +(0.186864 - 0.575107i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(14.0058 - 10.1758i) q^{50} +(-0.825206 + 2.53972i) q^{52} +(7.94654 + 5.77350i) q^{53} +(4.98459 - 10.3612i) q^{55} +5.14256 q^{56} +(-3.48626 + 10.7296i) q^{58} +(-0.523492 - 1.61114i) q^{59} +(-5.54839 + 4.03114i) q^{61} +(-2.13152 - 6.56015i) q^{62} +(5.60222 + 4.07025i) q^{64} -2.26638 q^{65} -6.17828 q^{67} +(-3.75789 - 2.73027i) q^{68} +(2.64256 + 8.13296i) q^{70} +(-4.38234 + 3.18395i) q^{71} +(2.07103 + 6.37396i) q^{73} +(0.335211 - 1.03167i) q^{74} -24.8191 q^{76} +(2.39815 + 2.29104i) q^{77} +(-2.14693 - 1.55984i) q^{79} +(4.83766 - 14.8888i) q^{80} +(11.7805 - 8.55903i) q^{82} +(5.41765 - 3.93615i) q^{83} +(1.21821 - 3.74926i) q^{85} +(17.3783 + 12.6261i) q^{86} +(-3.05216 - 16.7806i) q^{88} +0.698213 q^{89} +(0.202020 - 0.621755i) q^{91} +(8.41560 + 25.9006i) q^{92} +(1.20676 - 0.876765i) q^{94} +(-6.50911 - 20.0330i) q^{95} +(12.0209 + 8.73372i) q^{97} -2.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99563 + 1.44991i 1.41112 + 1.02524i 0.993158 + 0.116777i \(0.0372561\pi\)
0.417964 + 0.908464i \(0.362744\pi\)
\(3\) 0 0
\(4\) 1.26226 + 3.88484i 0.631131 + 1.94242i
\(5\) −2.80464 + 2.03769i −1.25428 + 0.911284i −0.998462 0.0554418i \(-0.982343\pi\)
−0.255813 + 0.966726i \(0.582343\pi\)
\(6\) 0 0
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) −1.58914 + 4.89086i −0.561845 + 1.72918i
\(9\) 0 0
\(10\) −8.55150 −2.70422
\(11\) −2.91998 + 1.57281i −0.880406 + 0.474220i
\(12\) 0 0
\(13\) 0.528896 + 0.384266i 0.146689 + 0.106576i 0.658709 0.752397i \(-0.271103\pi\)
−0.512020 + 0.858973i \(0.671103\pi\)
\(14\) 0.762262 2.34600i 0.203723 0.626995i
\(15\) 0 0
\(16\) −3.65334 + 2.65431i −0.913336 + 0.663577i
\(17\) −0.919977 + 0.668402i −0.223127 + 0.162111i −0.693733 0.720232i \(-0.744035\pi\)
0.470606 + 0.882343i \(0.344035\pi\)
\(18\) 0 0
\(19\) −1.87759 + 5.77864i −0.430750 + 1.32571i 0.466630 + 0.884452i \(0.345468\pi\)
−0.897380 + 0.441259i \(0.854532\pi\)
\(20\) −11.4563 8.32350i −2.56171 1.86119i
\(21\) 0 0
\(22\) −8.10762 1.09495i −1.72855 0.233445i
\(23\) 6.66708 1.39018 0.695091 0.718921i \(-0.255364\pi\)
0.695091 + 0.718921i \(0.255364\pi\)
\(24\) 0 0
\(25\) 2.16875 6.67473i 0.433750 1.33495i
\(26\) 0.498330 + 1.53370i 0.0977306 + 0.300784i
\(27\) 0 0
\(28\) 3.30464 2.40097i 0.624519 0.453740i
\(29\) 1.41331 + 4.34973i 0.262445 + 0.807724i 0.992271 + 0.124090i \(0.0396013\pi\)
−0.729826 + 0.683633i \(0.760399\pi\)
\(30\) 0 0
\(31\) −2.26226 1.64363i −0.406314 0.295205i 0.365794 0.930696i \(-0.380798\pi\)
−0.772108 + 0.635491i \(0.780798\pi\)
\(32\) −0.854102 −0.150985
\(33\) 0 0
\(34\) −2.80505 −0.481063
\(35\) 2.80464 + 2.03769i 0.474072 + 0.344433i
\(36\) 0 0
\(37\) −0.135893 0.418235i −0.0223406 0.0687574i 0.939265 0.343194i \(-0.111509\pi\)
−0.961605 + 0.274436i \(0.911509\pi\)
\(38\) −12.1255 + 8.80968i −1.96701 + 1.42912i
\(39\) 0 0
\(40\) −5.50911 16.9553i −0.871068 2.68087i
\(41\) 1.82417 5.61423i 0.284888 0.876795i −0.701544 0.712626i \(-0.747506\pi\)
0.986432 0.164169i \(-0.0524943\pi\)
\(42\) 0 0
\(43\) 8.70820 1.32799 0.663994 0.747738i \(-0.268860\pi\)
0.663994 + 0.747738i \(0.268860\pi\)
\(44\) −9.79590 9.35835i −1.47679 1.41082i
\(45\) 0 0
\(46\) 13.3050 + 9.66666i 1.96172 + 1.42527i
\(47\) 0.186864 0.575107i 0.0272569 0.0838880i −0.936503 0.350660i \(-0.885957\pi\)
0.963760 + 0.266772i \(0.0859572\pi\)
\(48\) 0 0
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 14.0058 10.1758i 1.98072 1.43907i
\(51\) 0 0
\(52\) −0.825206 + 2.53972i −0.114435 + 0.352196i
\(53\) 7.94654 + 5.77350i 1.09154 + 0.793051i 0.979659 0.200670i \(-0.0643120\pi\)
0.111883 + 0.993721i \(0.464312\pi\)
\(54\) 0 0
\(55\) 4.98459 10.3612i 0.672122 1.39710i
\(56\) 5.14256 0.687203
\(57\) 0 0
\(58\) −3.48626 + 10.7296i −0.457768 + 1.40887i
\(59\) −0.523492 1.61114i −0.0681529 0.209753i 0.911180 0.412009i \(-0.135173\pi\)
−0.979333 + 0.202256i \(0.935173\pi\)
\(60\) 0 0
\(61\) −5.54839 + 4.03114i −0.710398 + 0.516134i −0.883302 0.468804i \(-0.844685\pi\)
0.172904 + 0.984939i \(0.444685\pi\)
\(62\) −2.13152 6.56015i −0.270703 0.833139i
\(63\) 0 0
\(64\) 5.60222 + 4.07025i 0.700277 + 0.508781i
\(65\) −2.26638 −0.281110
\(66\) 0 0
\(67\) −6.17828 −0.754797 −0.377398 0.926051i \(-0.623181\pi\)
−0.377398 + 0.926051i \(0.623181\pi\)
\(68\) −3.75789 2.73027i −0.455711 0.331093i
\(69\) 0 0
\(70\) 2.64256 + 8.13296i 0.315846 + 0.972074i
\(71\) −4.38234 + 3.18395i −0.520088 + 0.377866i −0.816637 0.577152i \(-0.804164\pi\)
0.296549 + 0.955018i \(0.404164\pi\)
\(72\) 0 0
\(73\) 2.07103 + 6.37396i 0.242395 + 0.746016i 0.996054 + 0.0887500i \(0.0282872\pi\)
−0.753659 + 0.657266i \(0.771713\pi\)
\(74\) 0.335211 1.03167i 0.0389675 0.119930i
\(75\) 0 0
\(76\) −24.8191 −2.84695
\(77\) 2.39815 + 2.29104i 0.273295 + 0.261088i
\(78\) 0 0
\(79\) −2.14693 1.55984i −0.241549 0.175495i 0.460424 0.887699i \(-0.347697\pi\)
−0.701973 + 0.712204i \(0.747697\pi\)
\(80\) 4.83766 14.8888i 0.540867 1.66462i
\(81\) 0 0
\(82\) 11.7805 8.55903i 1.30094 0.945187i
\(83\) 5.41765 3.93615i 0.594664 0.432049i −0.249317 0.968422i \(-0.580206\pi\)
0.843981 + 0.536373i \(0.180206\pi\)
\(84\) 0 0
\(85\) 1.21821 3.74926i 0.132133 0.406665i
\(86\) 17.3783 + 12.6261i 1.87395 + 1.36151i
\(87\) 0 0
\(88\) −3.05216 16.7806i −0.325361 1.78882i
\(89\) 0.698213 0.0740105 0.0370052 0.999315i \(-0.488218\pi\)
0.0370052 + 0.999315i \(0.488218\pi\)
\(90\) 0 0
\(91\) 0.202020 0.621755i 0.0211775 0.0651776i
\(92\) 8.41560 + 25.9006i 0.877387 + 2.70032i
\(93\) 0 0
\(94\) 1.20676 0.876765i 0.124468 0.0904314i
\(95\) −6.50911 20.0330i −0.667821 2.05534i
\(96\) 0 0
\(97\) 12.0209 + 8.73372i 1.22054 + 0.886775i 0.996145 0.0877234i \(-0.0279592\pi\)
0.224396 + 0.974498i \(0.427959\pi\)
\(98\) −2.46673 −0.249178
\(99\) 0 0
\(100\) 28.6678 2.86678
\(101\) 6.97340 + 5.06647i 0.693879 + 0.504133i 0.877933 0.478784i \(-0.158922\pi\)
−0.184054 + 0.982916i \(0.558922\pi\)
\(102\) 0 0
\(103\) −0.288300 0.887296i −0.0284070 0.0874279i 0.935848 0.352404i \(-0.114636\pi\)
−0.964255 + 0.264976i \(0.914636\pi\)
\(104\) −2.71988 + 1.97611i −0.266706 + 0.193773i
\(105\) 0 0
\(106\) 7.48729 + 23.0435i 0.727230 + 2.23818i
\(107\) −2.04635 + 6.29801i −0.197828 + 0.608851i 0.802104 + 0.597184i \(0.203714\pi\)
−0.999932 + 0.0116671i \(0.996286\pi\)
\(108\) 0 0
\(109\) −4.12507 −0.395110 −0.197555 0.980292i \(-0.563300\pi\)
−0.197555 + 0.980292i \(0.563300\pi\)
\(110\) 24.9702 13.4499i 2.38081 1.28240i
\(111\) 0 0
\(112\) 3.65334 + 2.65431i 0.345208 + 0.250809i
\(113\) 5.81749 17.9044i 0.547264 1.68430i −0.168282 0.985739i \(-0.553822\pi\)
0.715546 0.698566i \(-0.246178\pi\)
\(114\) 0 0
\(115\) −18.6988 + 13.5855i −1.74367 + 1.26685i
\(116\) −15.1140 + 10.9810i −1.40330 + 1.01956i
\(117\) 0 0
\(118\) 1.29131 3.97426i 0.118875 0.365860i
\(119\) 0.919977 + 0.668402i 0.0843341 + 0.0612723i
\(120\) 0 0
\(121\) 6.05253 9.18514i 0.550230 0.835013i
\(122\) −16.9173 −1.53162
\(123\) 0 0
\(124\) 3.52968 10.8632i 0.316974 0.975546i
\(125\) 2.16209 + 6.65422i 0.193383 + 0.595171i
\(126\) 0 0
\(127\) 6.44491 4.68250i 0.571893 0.415505i −0.263899 0.964550i \(-0.585009\pi\)
0.835792 + 0.549045i \(0.185009\pi\)
\(128\) 5.80631 + 17.8700i 0.513211 + 1.57950i
\(129\) 0 0
\(130\) −4.52285 3.28605i −0.396681 0.288205i
\(131\) 4.80505 0.419819 0.209910 0.977721i \(-0.432683\pi\)
0.209910 + 0.977721i \(0.432683\pi\)
\(132\) 0 0
\(133\) 6.07602 0.526858
\(134\) −12.3295 8.95793i −1.06511 0.773848i
\(135\) 0 0
\(136\) −1.80709 5.56166i −0.154957 0.476909i
\(137\) −17.6995 + 12.8594i −1.51217 + 1.09865i −0.546962 + 0.837157i \(0.684216\pi\)
−0.965204 + 0.261496i \(0.915784\pi\)
\(138\) 0 0
\(139\) −6.12278 18.8440i −0.519327 1.59832i −0.775268 0.631632i \(-0.782385\pi\)
0.255941 0.966692i \(-0.417615\pi\)
\(140\) −4.37592 + 13.4677i −0.369833 + 1.13823i
\(141\) 0 0
\(142\) −13.3620 −1.12131
\(143\) −2.14874 0.290193i −0.179687 0.0242671i
\(144\) 0 0
\(145\) −12.8272 9.31954i −1.06524 0.773946i
\(146\) −5.10867 + 15.7229i −0.422796 + 1.30123i
\(147\) 0 0
\(148\) 1.45325 1.05584i 0.119456 0.0867899i
\(149\) 2.55820 1.85864i 0.209576 0.152266i −0.478046 0.878335i \(-0.658655\pi\)
0.687622 + 0.726069i \(0.258655\pi\)
\(150\) 0 0
\(151\) 2.75892 8.49109i 0.224518 0.690995i −0.773822 0.633403i \(-0.781658\pi\)
0.998340 0.0575923i \(-0.0183423\pi\)
\(152\) −25.2788 18.3661i −2.05038 1.48969i
\(153\) 0 0
\(154\) 1.46403 + 8.04916i 0.117975 + 0.648620i
\(155\) 9.69406 0.778645
\(156\) 0 0
\(157\) 0.352179 1.08390i 0.0281070 0.0865044i −0.936019 0.351949i \(-0.885519\pi\)
0.964126 + 0.265445i \(0.0855189\pi\)
\(158\) −2.02285 6.22570i −0.160930 0.495290i
\(159\) 0 0
\(160\) 2.39545 1.74040i 0.189377 0.137591i
\(161\) −2.06024 6.34077i −0.162370 0.499723i
\(162\) 0 0
\(163\) 4.09951 + 2.97847i 0.321099 + 0.233292i 0.736644 0.676281i \(-0.236409\pi\)
−0.415545 + 0.909572i \(0.636409\pi\)
\(164\) 24.1130 1.88291
\(165\) 0 0
\(166\) 16.5187 1.28210
\(167\) −15.9432 11.5834i −1.23372 0.896351i −0.236558 0.971617i \(-0.576019\pi\)
−0.997164 + 0.0752658i \(0.976019\pi\)
\(168\) 0 0
\(169\) −3.88515 11.9573i −0.298858 0.919789i
\(170\) 7.86718 5.71584i 0.603385 0.438385i
\(171\) 0 0
\(172\) 10.9920 + 33.8300i 0.838135 + 2.57951i
\(173\) 4.44824 13.6903i 0.338193 1.04085i −0.626935 0.779072i \(-0.715691\pi\)
0.965128 0.261779i \(-0.0843093\pi\)
\(174\) 0 0
\(175\) −7.01823 −0.530528
\(176\) 6.49295 13.4965i 0.489424 1.01734i
\(177\) 0 0
\(178\) 1.39337 + 1.01235i 0.104438 + 0.0758785i
\(179\) 1.44132 4.43592i 0.107729 0.331556i −0.882632 0.470064i \(-0.844231\pi\)
0.990361 + 0.138508i \(0.0442307\pi\)
\(180\) 0 0
\(181\) −8.01578 + 5.82381i −0.595808 + 0.432880i −0.844389 0.535731i \(-0.820036\pi\)
0.248580 + 0.968611i \(0.420036\pi\)
\(182\) 1.30464 0.947880i 0.0967067 0.0702615i
\(183\) 0 0
\(184\) −10.5949 + 32.6078i −0.781067 + 2.40388i
\(185\) 1.23337 + 0.896093i 0.0906789 + 0.0658821i
\(186\) 0 0
\(187\) 1.63504 3.39867i 0.119566 0.248535i
\(188\) 2.47007 0.180148
\(189\) 0 0
\(190\) 16.0562 49.4160i 1.16484 3.58502i
\(191\) −3.07254 9.45631i −0.222321 0.684234i −0.998552 0.0537861i \(-0.982871\pi\)
0.776231 0.630448i \(-0.217129\pi\)
\(192\) 0 0
\(193\) −2.99874 + 2.17871i −0.215854 + 0.156827i −0.690458 0.723372i \(-0.742591\pi\)
0.474604 + 0.880199i \(0.342591\pi\)
\(194\) 11.3262 + 34.8585i 0.813175 + 2.50269i
\(195\) 0 0
\(196\) −3.30464 2.40097i −0.236046 0.171498i
\(197\) −5.91982 −0.421770 −0.210885 0.977511i \(-0.567635\pi\)
−0.210885 + 0.977511i \(0.567635\pi\)
\(198\) 0 0
\(199\) 11.4842 0.814095 0.407047 0.913407i \(-0.366558\pi\)
0.407047 + 0.913407i \(0.366558\pi\)
\(200\) 29.1988 + 21.2141i 2.06466 + 1.50007i
\(201\) 0 0
\(202\) 6.57039 + 20.2216i 0.462291 + 1.42279i
\(203\) 3.70010 2.68828i 0.259696 0.188680i
\(204\) 0 0
\(205\) 6.32392 + 19.4630i 0.441682 + 1.35936i
\(206\) 0.711159 2.18872i 0.0495488 0.152495i
\(207\) 0 0
\(208\) −2.95220 −0.204698
\(209\) −3.60618 19.8266i −0.249445 1.37143i
\(210\) 0 0
\(211\) −7.05857 5.12835i −0.485932 0.353050i 0.317686 0.948196i \(-0.397094\pi\)
−0.803618 + 0.595146i \(0.797094\pi\)
\(212\) −12.3985 + 38.1587i −0.851534 + 2.62075i
\(213\) 0 0
\(214\) −13.2153 + 9.60146i −0.903378 + 0.656342i
\(215\) −24.4234 + 17.7447i −1.66566 + 1.21018i
\(216\) 0 0
\(217\) −0.864107 + 2.65945i −0.0586594 + 0.180535i
\(218\) −8.23210 5.98097i −0.557548 0.405083i
\(219\) 0 0
\(220\) 46.5435 + 6.28581i 3.13796 + 0.423789i
\(221\) −0.743416 −0.0500076
\(222\) 0 0
\(223\) 3.19302 9.82712i 0.213821 0.658072i −0.785415 0.618970i \(-0.787550\pi\)
0.999235 0.0391023i \(-0.0124498\pi\)
\(224\) 0.263932 + 0.812299i 0.0176347 + 0.0542740i
\(225\) 0 0
\(226\) 37.5693 27.2957i 2.49907 1.81568i
\(227\) 4.10033 + 12.6195i 0.272149 + 0.837587i 0.989960 + 0.141349i \(0.0451441\pi\)
−0.717811 + 0.696238i \(0.754856\pi\)
\(228\) 0 0
\(229\) 2.01949 + 1.46725i 0.133452 + 0.0969583i 0.652508 0.757781i \(-0.273717\pi\)
−0.519057 + 0.854740i \(0.673717\pi\)
\(230\) −57.0135 −3.75936
\(231\) 0 0
\(232\) −23.5199 −1.54415
\(233\) −7.76971 5.64502i −0.509010 0.369818i 0.303438 0.952851i \(-0.401866\pi\)
−0.812448 + 0.583034i \(0.801866\pi\)
\(234\) 0 0
\(235\) 0.647806 + 1.99374i 0.0422582 + 0.130057i
\(236\) 5.59825 4.06737i 0.364415 0.264763i
\(237\) 0 0
\(238\) 0.866809 + 2.66776i 0.0561869 + 0.172925i
\(239\) −1.71914 + 5.29098i −0.111202 + 0.342245i −0.991136 0.132851i \(-0.957587\pi\)
0.879934 + 0.475096i \(0.157587\pi\)
\(240\) 0 0
\(241\) 15.0208 0.967572 0.483786 0.875186i \(-0.339261\pi\)
0.483786 + 0.875186i \(0.339261\pi\)
\(242\) 25.3962 9.55452i 1.63253 0.614188i
\(243\) 0 0
\(244\) −22.6639 16.4663i −1.45090 1.05414i
\(245\) 1.07128 3.29706i 0.0684415 0.210641i
\(246\) 0 0
\(247\) −3.21358 + 2.33481i −0.204475 + 0.148560i
\(248\) 11.6338 8.45246i 0.738748 0.536732i
\(249\) 0 0
\(250\) −5.33329 + 16.4142i −0.337307 + 1.03812i
\(251\) 22.3394 + 16.2305i 1.41005 + 1.02446i 0.993315 + 0.115436i \(0.0368266\pi\)
0.416738 + 0.909027i \(0.363173\pi\)
\(252\) 0 0
\(253\) −19.4677 + 10.4861i −1.22393 + 0.659253i
\(254\) 19.6508 1.23300
\(255\) 0 0
\(256\) −10.0429 + 30.9089i −0.627682 + 1.93181i
\(257\) 8.79709 + 27.0747i 0.548747 + 1.68887i 0.711909 + 0.702271i \(0.247831\pi\)
−0.163162 + 0.986599i \(0.552169\pi\)
\(258\) 0 0
\(259\) −0.355772 + 0.258483i −0.0221066 + 0.0160614i
\(260\) −2.86077 8.80454i −0.177417 0.546034i
\(261\) 0 0
\(262\) 9.58910 + 6.96689i 0.592417 + 0.430416i
\(263\) −14.1803 −0.874397 −0.437199 0.899365i \(-0.644029\pi\)
−0.437199 + 0.899365i \(0.644029\pi\)
\(264\) 0 0
\(265\) −34.0519 −2.09179
\(266\) 12.1255 + 8.80968i 0.743461 + 0.540156i
\(267\) 0 0
\(268\) −7.79860 24.0016i −0.476375 1.46613i
\(269\) −19.5731 + 14.2207i −1.19339 + 0.867050i −0.993619 0.112792i \(-0.964021\pi\)
−0.199774 + 0.979842i \(0.564021\pi\)
\(270\) 0 0
\(271\) 2.30210 + 7.08513i 0.139843 + 0.430391i 0.996312 0.0858070i \(-0.0273468\pi\)
−0.856469 + 0.516198i \(0.827347\pi\)
\(272\) 1.58684 4.88381i 0.0962166 0.296124i
\(273\) 0 0
\(274\) −53.9665 −3.26024
\(275\) 4.16539 + 22.9011i 0.251182 + 1.38099i
\(276\) 0 0
\(277\) 15.5242 + 11.2790i 0.932761 + 0.677690i 0.946667 0.322213i \(-0.104427\pi\)
−0.0139064 + 0.999903i \(0.504427\pi\)
\(278\) 15.1032 46.4830i 0.905833 2.78787i
\(279\) 0 0
\(280\) −14.4230 + 10.4790i −0.861942 + 0.626238i
\(281\) −1.53764 + 1.11716i −0.0917279 + 0.0666442i −0.632704 0.774394i \(-0.718055\pi\)
0.540976 + 0.841038i \(0.318055\pi\)
\(282\) 0 0
\(283\) 2.24092 6.89685i 0.133209 0.409975i −0.862098 0.506741i \(-0.830850\pi\)
0.995307 + 0.0967663i \(0.0308499\pi\)
\(284\) −17.9008 13.0057i −1.06222 0.771747i
\(285\) 0 0
\(286\) −3.86734 3.69460i −0.228680 0.218466i
\(287\) −5.90315 −0.348452
\(288\) 0 0
\(289\) −4.85369 + 14.9381i −0.285511 + 0.878714i
\(290\) −12.0859 37.1967i −0.709710 2.18426i
\(291\) 0 0
\(292\) −22.1477 + 16.0912i −1.29609 + 0.941668i
\(293\) 1.01078 + 3.11088i 0.0590507 + 0.181739i 0.976231 0.216734i \(-0.0695403\pi\)
−0.917180 + 0.398473i \(0.869540\pi\)
\(294\) 0 0
\(295\) 4.75122 + 3.45197i 0.276627 + 0.200981i
\(296\) 2.26148 0.131446
\(297\) 0 0
\(298\) 7.80008 0.451846
\(299\) 3.52619 + 2.56193i 0.203925 + 0.148160i
\(300\) 0 0
\(301\) −2.69098 8.28199i −0.155106 0.477366i
\(302\) 17.8171 12.9449i 1.02526 0.744894i
\(303\) 0 0
\(304\) −8.47880 26.0951i −0.486293 1.49665i
\(305\) 7.34703 22.6118i 0.420690 1.29475i
\(306\) 0 0
\(307\) 31.6121 1.80420 0.902099 0.431530i \(-0.142026\pi\)
0.902099 + 0.431530i \(0.142026\pi\)
\(308\) −5.87322 + 12.2083i −0.334658 + 0.695635i
\(309\) 0 0
\(310\) 19.3457 + 14.0555i 1.09876 + 0.798298i
\(311\) 2.79298 8.59592i 0.158376 0.487430i −0.840112 0.542414i \(-0.817511\pi\)
0.998487 + 0.0549835i \(0.0175106\pi\)
\(312\) 0 0
\(313\) −11.7300 + 8.52232i −0.663017 + 0.481710i −0.867680 0.497122i \(-0.834390\pi\)
0.204664 + 0.978832i \(0.434390\pi\)
\(314\) 2.27437 1.65243i 0.128350 0.0932518i
\(315\) 0 0
\(316\) 3.34973 10.3094i 0.188437 0.579950i
\(317\) −14.9000 10.8255i −0.836865 0.608018i 0.0846278 0.996413i \(-0.473030\pi\)
−0.921493 + 0.388394i \(0.873030\pi\)
\(318\) 0 0
\(319\) −10.9681 10.4782i −0.614098 0.586668i
\(320\) −24.0061 −1.34198
\(321\) 0 0
\(322\) 5.08206 15.6410i 0.283212 0.871638i
\(323\) −2.13511 6.57120i −0.118801 0.365632i
\(324\) 0 0
\(325\) 3.71191 2.69686i 0.205900 0.149595i
\(326\) 3.86259 + 11.8878i 0.213929 + 0.658407i
\(327\) 0 0
\(328\) 24.5596 + 17.8436i 1.35608 + 0.985246i
\(329\) −0.604703 −0.0333384
\(330\) 0 0
\(331\) −6.47653 −0.355982 −0.177991 0.984032i \(-0.556960\pi\)
−0.177991 + 0.984032i \(0.556960\pi\)
\(332\) 22.1298 + 16.0782i 1.21453 + 0.882409i
\(333\) 0 0
\(334\) −15.0218 46.2324i −0.821957 2.52972i
\(335\) 17.3279 12.5894i 0.946723 0.687834i
\(336\) 0 0
\(337\) 1.93346 + 5.95059i 0.105322 + 0.324149i 0.989806 0.142422i \(-0.0454891\pi\)
−0.884484 + 0.466571i \(0.845489\pi\)
\(338\) 9.58362 29.4954i 0.521280 1.60434i
\(339\) 0 0
\(340\) 16.1030 0.873308
\(341\) 9.19087 + 1.24125i 0.497714 + 0.0672174i
\(342\) 0 0
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) −13.8385 + 42.5906i −0.746124 + 2.29633i
\(345\) 0 0
\(346\) 28.7266 20.8711i 1.54435 1.12204i
\(347\) 18.3773 13.3519i 0.986547 0.716768i 0.0273845 0.999625i \(-0.491282\pi\)
0.959162 + 0.282857i \(0.0912822\pi\)
\(348\) 0 0
\(349\) 9.17597 28.2407i 0.491178 1.51169i −0.331651 0.943402i \(-0.607606\pi\)
0.822829 0.568289i \(-0.192394\pi\)
\(350\) −14.0058 10.1758i −0.748640 0.543919i
\(351\) 0 0
\(352\) 2.49396 1.34334i 0.132928 0.0716003i
\(353\) 6.82506 0.363262 0.181631 0.983367i \(-0.441862\pi\)
0.181631 + 0.983367i \(0.441862\pi\)
\(354\) 0 0
\(355\) 5.80297 17.8597i 0.307990 0.947896i
\(356\) 0.881328 + 2.71245i 0.0467103 + 0.143760i
\(357\) 0 0
\(358\) 9.30801 6.76266i 0.491944 0.357418i
\(359\) 2.24337 + 6.90439i 0.118401 + 0.364400i 0.992641 0.121094i \(-0.0386401\pi\)
−0.874241 + 0.485493i \(0.838640\pi\)
\(360\) 0 0
\(361\) −14.4960 10.5320i −0.762947 0.554314i
\(362\) −24.4405 −1.28456
\(363\) 0 0
\(364\) 2.67042 0.139968
\(365\) −18.7967 13.6566i −0.983863 0.714818i
\(366\) 0 0
\(367\) −11.2286 34.5582i −0.586130 1.80392i −0.594686 0.803958i \(-0.702723\pi\)
0.00855584 0.999963i \(-0.497277\pi\)
\(368\) −24.3571 + 17.6965i −1.26970 + 0.922494i
\(369\) 0 0
\(370\) 1.16209 + 3.57654i 0.0604140 + 0.185935i
\(371\) 3.03531 9.34172i 0.157585 0.484998i
\(372\) 0 0
\(373\) −14.2913 −0.739977 −0.369989 0.929036i \(-0.620638\pi\)
−0.369989 + 0.929036i \(0.620638\pi\)
\(374\) 8.19069 4.41182i 0.423531 0.228130i
\(375\) 0 0
\(376\) 2.51582 + 1.82785i 0.129743 + 0.0942641i
\(377\) −0.923955 + 2.84364i −0.0475861 + 0.146455i
\(378\) 0 0
\(379\) 2.05917 1.49608i 0.105773 0.0768482i −0.533642 0.845711i \(-0.679177\pi\)
0.639414 + 0.768862i \(0.279177\pi\)
\(380\) 69.6088 50.5738i 3.57086 2.59438i
\(381\) 0 0
\(382\) 7.57913 23.3262i 0.387782 1.19347i
\(383\) −18.7180 13.5994i −0.956444 0.694897i −0.00412192 0.999992i \(-0.501312\pi\)
−0.952322 + 0.305094i \(0.901312\pi\)
\(384\) 0 0
\(385\) −11.3944 1.53884i −0.580713 0.0784266i
\(386\) −9.14330 −0.465382
\(387\) 0 0
\(388\) −18.7556 + 57.7237i −0.952169 + 2.93048i
\(389\) −9.35130 28.7804i −0.474130 1.45922i −0.847128 0.531390i \(-0.821670\pi\)
0.372998 0.927832i \(-0.378330\pi\)
\(390\) 0 0
\(391\) −6.13356 + 4.45629i −0.310188 + 0.225364i
\(392\) −1.58914 4.89086i −0.0802636 0.247026i
\(393\) 0 0
\(394\) −11.8138 8.58320i −0.595169 0.432415i
\(395\) 9.19985 0.462894
\(396\) 0 0
\(397\) −22.6740 −1.13798 −0.568989 0.822345i \(-0.692665\pi\)
−0.568989 + 0.822345i \(0.692665\pi\)
\(398\) 22.9182 + 16.6511i 1.14879 + 0.834643i
\(399\) 0 0
\(400\) 9.79361 + 30.1416i 0.489680 + 1.50708i
\(401\) −13.1211 + 9.53304i −0.655237 + 0.476057i −0.865051 0.501684i \(-0.832714\pi\)
0.209814 + 0.977741i \(0.432714\pi\)
\(402\) 0 0
\(403\) −0.564911 1.73862i −0.0281402 0.0866068i
\(404\) −10.8802 + 33.4858i −0.541309 + 1.66598i
\(405\) 0 0
\(406\) 11.2818 0.559905
\(407\) 1.05461 + 1.00750i 0.0522750 + 0.0499401i
\(408\) 0 0
\(409\) 28.3653 + 20.6086i 1.40257 + 1.01903i 0.994351 + 0.106146i \(0.0338512\pi\)
0.408222 + 0.912883i \(0.366149\pi\)
\(410\) −15.5994 + 48.0101i −0.770400 + 2.37105i
\(411\) 0 0
\(412\) 3.08310 2.24000i 0.151893 0.110357i
\(413\) −1.37052 + 0.995741i −0.0674389 + 0.0489972i
\(414\) 0 0
\(415\) −7.17390 + 22.0790i −0.352153 + 1.08382i
\(416\) −0.451731 0.328202i −0.0221479 0.0160914i
\(417\) 0 0
\(418\) 21.5502 44.7951i 1.05405 2.19100i
\(419\) −28.2633 −1.38075 −0.690376 0.723451i \(-0.742555\pi\)
−0.690376 + 0.723451i \(0.742555\pi\)
\(420\) 0 0
\(421\) −4.26279 + 13.1195i −0.207756 + 0.639406i 0.791833 + 0.610737i \(0.209127\pi\)
−0.999589 + 0.0286688i \(0.990873\pi\)
\(422\) −6.65064 20.4686i −0.323748 0.996394i
\(423\) 0 0
\(424\) −40.8656 + 29.6906i −1.98461 + 1.44190i
\(425\) 2.46621 + 7.59020i 0.119629 + 0.368179i
\(426\) 0 0
\(427\) 5.54839 + 4.03114i 0.268505 + 0.195080i
\(428\) −27.0498 −1.30750
\(429\) 0 0
\(430\) −74.4682 −3.59117
\(431\) 22.7900 + 16.5579i 1.09776 + 0.797568i 0.980692 0.195557i \(-0.0626514\pi\)
0.117065 + 0.993124i \(0.462651\pi\)
\(432\) 0 0
\(433\) 4.38165 + 13.4853i 0.210569 + 0.648064i 0.999439 + 0.0335038i \(0.0106666\pi\)
−0.788870 + 0.614560i \(0.789333\pi\)
\(434\) −5.58039 + 4.05439i −0.267867 + 0.194617i
\(435\) 0 0
\(436\) −5.20692 16.0252i −0.249366 0.767470i
\(437\) −12.5181 + 38.5267i −0.598821 + 1.84298i
\(438\) 0 0
\(439\) 28.0185 1.33725 0.668625 0.743599i \(-0.266883\pi\)
0.668625 + 0.743599i \(0.266883\pi\)
\(440\) 42.7540 + 40.8443i 2.03822 + 1.94718i
\(441\) 0 0
\(442\) −1.48358 1.07789i −0.0705668 0.0512698i
\(443\) −5.35743 + 16.4885i −0.254539 + 0.783391i 0.739381 + 0.673287i \(0.235118\pi\)
−0.993920 + 0.110103i \(0.964882\pi\)
\(444\) 0 0
\(445\) −1.95824 + 1.42274i −0.0928295 + 0.0674446i
\(446\) 20.6205 14.9817i 0.976409 0.709403i
\(447\) 0 0
\(448\) 2.13986 6.58580i 0.101099 0.311150i
\(449\) −23.8834 17.3523i −1.12713 0.818906i −0.141853 0.989888i \(-0.545306\pi\)
−0.985274 + 0.170982i \(0.945306\pi\)
\(450\) 0 0
\(451\) 3.50358 + 19.2625i 0.164977 + 0.907036i
\(452\) 76.8990 3.61702
\(453\) 0 0
\(454\) −10.1144 + 31.1290i −0.474693 + 1.46096i
\(455\) 0.700350 + 2.15546i 0.0328329 + 0.101049i
\(456\) 0 0
\(457\) −7.84524 + 5.69990i −0.366985 + 0.266630i −0.755960 0.654618i \(-0.772829\pi\)
0.388975 + 0.921248i \(0.372829\pi\)
\(458\) 1.90278 + 5.85615i 0.0889110 + 0.273640i
\(459\) 0 0
\(460\) −76.3802 55.4935i −3.56125 2.58740i
\(461\) 19.2216 0.895240 0.447620 0.894224i \(-0.352272\pi\)
0.447620 + 0.894224i \(0.352272\pi\)
\(462\) 0 0
\(463\) 20.5327 0.954235 0.477117 0.878840i \(-0.341682\pi\)
0.477117 + 0.878840i \(0.341682\pi\)
\(464\) −16.7088 12.1397i −0.775688 0.563570i
\(465\) 0 0
\(466\) −7.32068 22.5307i −0.339124 1.04372i
\(467\) 27.2408 19.7916i 1.26055 0.915845i 0.261768 0.965131i \(-0.415695\pi\)
0.998785 + 0.0492858i \(0.0156945\pi\)
\(468\) 0 0
\(469\) 1.90919 + 5.87589i 0.0881583 + 0.271323i
\(470\) −1.59796 + 4.91803i −0.0737086 + 0.226852i
\(471\) 0 0
\(472\) 8.71178 0.400992
\(473\) −25.4278 + 13.6964i −1.16917 + 0.629759i
\(474\) 0 0
\(475\) 34.4988 + 25.0649i 1.58292 + 1.15006i
\(476\) −1.43539 + 4.41766i −0.0657908 + 0.202483i
\(477\) 0 0
\(478\) −11.1022 + 8.06623i −0.507804 + 0.368941i
\(479\) 11.4644 8.32937i 0.523822 0.380579i −0.294220 0.955738i \(-0.595060\pi\)
0.818042 + 0.575159i \(0.195060\pi\)
\(480\) 0 0
\(481\) 0.0888401 0.273422i 0.00405076 0.0124670i
\(482\) 29.9758 + 21.7787i 1.36536 + 0.991993i
\(483\) 0 0
\(484\) 43.3227 + 11.9191i 1.96921 + 0.541776i
\(485\) −51.5111 −2.33900
\(486\) 0 0
\(487\) 8.57259 26.3837i 0.388461 1.19556i −0.545477 0.838126i \(-0.683652\pi\)
0.933938 0.357434i \(-0.116348\pi\)
\(488\) −10.8986 33.5424i −0.493356 1.51839i
\(489\) 0 0
\(490\) 6.91831 5.02644i 0.312537 0.227072i
\(491\) 1.06393 + 3.27444i 0.0480145 + 0.147774i 0.972189 0.234196i \(-0.0752458\pi\)
−0.924175 + 0.381970i \(0.875246\pi\)
\(492\) 0 0
\(493\) −4.20758 3.05699i −0.189500 0.137680i
\(494\) −9.79837 −0.440850
\(495\) 0 0
\(496\) 12.6275 0.566992
\(497\) 4.38234 + 3.18395i 0.196575 + 0.142820i
\(498\) 0 0
\(499\) −0.800117 2.46251i −0.0358181 0.110237i 0.931549 0.363616i \(-0.118458\pi\)
−0.967367 + 0.253379i \(0.918458\pi\)
\(500\) −23.1215 + 16.7987i −1.03402 + 0.751262i
\(501\) 0 0
\(502\) 21.0484 + 64.7803i 0.939435 + 2.89129i
\(503\) 7.07731 21.7817i 0.315561 0.971198i −0.659961 0.751300i \(-0.729427\pi\)
0.975523 0.219899i \(-0.0705727\pi\)
\(504\) 0 0
\(505\) −29.8818 −1.32972
\(506\) −54.0542 7.30014i −2.40300 0.324531i
\(507\) 0 0
\(508\) 26.3259 + 19.1269i 1.16803 + 0.848620i
\(509\) 7.44685 22.9191i 0.330076 1.01587i −0.639021 0.769189i \(-0.720660\pi\)
0.969097 0.246680i \(-0.0793397\pi\)
\(510\) 0 0
\(511\) 5.42202 3.93933i 0.239856 0.174266i
\(512\) −34.4547 + 25.0328i −1.52270 + 1.10631i
\(513\) 0 0
\(514\) −21.7001 + 66.7859i −0.957149 + 2.94580i
\(515\) 2.61662 + 1.90108i 0.115302 + 0.0837717i
\(516\) 0 0
\(517\) 0.358897 + 1.97320i 0.0157843 + 0.0867813i
\(518\) −1.08477 −0.0476619
\(519\) 0 0
\(520\) 3.60159 11.0846i 0.157940 0.486090i
\(521\) 10.3538 + 31.8658i 0.453610 + 1.39607i 0.872760 + 0.488150i \(0.162328\pi\)
−0.419150 + 0.907917i \(0.637672\pi\)
\(522\) 0 0
\(523\) 25.2068 18.3138i 1.10222 0.800808i 0.120798 0.992677i \(-0.461455\pi\)
0.981421 + 0.191869i \(0.0614548\pi\)
\(524\) 6.06524 + 18.6669i 0.264961 + 0.815466i
\(525\) 0 0
\(526\) −28.2987 20.5602i −1.23388 0.896467i
\(527\) 3.17983 0.138516
\(528\) 0 0
\(529\) 21.4500 0.932608
\(530\) −67.9548 49.3721i −2.95177 2.14459i
\(531\) 0 0
\(532\) 7.66953 + 23.6044i 0.332516 + 1.02338i
\(533\) 3.12215 2.26838i 0.135235 0.0982543i
\(534\) 0 0
\(535\) −7.09413 21.8335i −0.306706 0.943944i
\(536\) 9.81813 30.2171i 0.424079 1.30518i
\(537\) 0 0
\(538\) −59.6793 −2.57296
\(539\) 1.43784 2.98875i 0.0619320 0.128735i
\(540\) 0 0
\(541\) −18.2896 13.2881i −0.786330 0.571302i 0.120542 0.992708i \(-0.461537\pi\)
−0.906872 + 0.421406i \(0.861537\pi\)
\(542\) −5.67866 + 17.4771i −0.243919 + 0.750707i
\(543\) 0 0
\(544\) 0.785754 0.570884i 0.0336889 0.0244764i
\(545\) 11.5694 8.40563i 0.495577 0.360058i
\(546\) 0 0
\(547\) −8.48072 + 26.1010i −0.362610 + 1.11600i 0.588855 + 0.808239i \(0.299579\pi\)
−0.951464 + 0.307759i \(0.900421\pi\)
\(548\) −72.2981 52.5277i −3.08842 2.24387i
\(549\) 0 0
\(550\) −24.8919 + 51.7415i −1.06140 + 2.20627i
\(551\) −27.7891 −1.18386
\(552\) 0 0
\(553\) −0.820054 + 2.52387i −0.0348723 + 0.107326i
\(554\) 14.6271 + 45.0174i 0.621444 + 1.91261i
\(555\) 0 0
\(556\) 65.4773 47.5721i 2.77686 2.01750i
\(557\) 9.34788 + 28.7698i 0.396082 + 1.21902i 0.928115 + 0.372293i \(0.121428\pi\)
−0.532033 + 0.846724i \(0.678572\pi\)
\(558\) 0 0
\(559\) 4.60574 + 3.34626i 0.194802 + 0.141532i
\(560\) −15.6550 −0.661544
\(561\) 0 0
\(562\) −4.68834 −0.197766
\(563\) 6.03716 + 4.38625i 0.254436 + 0.184858i 0.707690 0.706523i \(-0.249737\pi\)
−0.453255 + 0.891381i \(0.649737\pi\)
\(564\) 0 0
\(565\) 20.1677 + 62.0698i 0.848461 + 2.61129i
\(566\) 14.4718 10.5144i 0.608297 0.441954i
\(567\) 0 0
\(568\) −8.60815 26.4932i −0.361190 1.11163i
\(569\) −11.0159 + 33.9036i −0.461812 + 1.42131i 0.401136 + 0.916019i \(0.368616\pi\)
−0.862948 + 0.505293i \(0.831384\pi\)
\(570\) 0 0
\(571\) 25.8902 1.08347 0.541737 0.840548i \(-0.317767\pi\)
0.541737 + 0.840548i \(0.317767\pi\)
\(572\) −1.58492 8.71382i −0.0662689 0.364343i
\(573\) 0 0
\(574\) −11.7805 8.55903i −0.491708 0.357247i
\(575\) 14.4592 44.5010i 0.602992 1.85582i
\(576\) 0 0
\(577\) −6.60467 + 4.79857i −0.274956 + 0.199767i −0.716714 0.697367i \(-0.754355\pi\)
0.441758 + 0.897134i \(0.354355\pi\)
\(578\) −31.3451 + 22.7735i −1.30378 + 0.947254i
\(579\) 0 0
\(580\) 20.0136 61.5955i 0.831020 2.55762i
\(581\) −5.41765 3.93615i −0.224762 0.163299i
\(582\) 0 0
\(583\) −32.2843 4.36008i −1.33708 0.180576i
\(584\) −34.4653 −1.42619
\(585\) 0 0
\(586\) −2.49333 + 7.67370i −0.102999 + 0.316997i
\(587\) 3.85140 + 11.8534i 0.158964 + 0.489242i 0.998541 0.0539994i \(-0.0171969\pi\)
−0.839577 + 0.543241i \(0.817197\pi\)
\(588\) 0 0
\(589\) 13.7456 9.98673i 0.566376 0.411496i
\(590\) 4.47664 + 13.7777i 0.184300 + 0.567218i
\(591\) 0 0
\(592\) 1.60659 + 1.16725i 0.0660304 + 0.0479739i
\(593\) 23.6707 0.972037 0.486019 0.873948i \(-0.338449\pi\)
0.486019 + 0.873948i \(0.338449\pi\)
\(594\) 0 0
\(595\) −3.94221 −0.161615
\(596\) 10.4497 + 7.59212i 0.428034 + 0.310985i
\(597\) 0 0
\(598\) 3.32241 + 10.2253i 0.135863 + 0.418144i
\(599\) 31.5362 22.9124i 1.28853 0.936175i 0.288759 0.957402i \(-0.406757\pi\)
0.999775 + 0.0212271i \(0.00675731\pi\)
\(600\) 0 0
\(601\) 9.44078 + 29.0557i 0.385097 + 1.18521i 0.936410 + 0.350909i \(0.114127\pi\)
−0.551312 + 0.834299i \(0.685873\pi\)
\(602\) 6.63793 20.4295i 0.270542 0.832643i
\(603\) 0 0
\(604\) 36.4690 1.48390
\(605\) 1.74132 + 38.0943i 0.0707946 + 1.54875i
\(606\) 0 0
\(607\) −30.4330 22.1109i −1.23524 0.897454i −0.237967 0.971273i \(-0.576481\pi\)
−0.997272 + 0.0738195i \(0.976481\pi\)
\(608\) 1.60366 4.93555i 0.0650369 0.200163i
\(609\) 0 0
\(610\) 47.4470 34.4723i 1.92107 1.39574i
\(611\) 0.319825 0.232367i 0.0129387 0.00940055i
\(612\) 0 0
\(613\) 5.44711 16.7645i 0.220007 0.677111i −0.778754 0.627330i \(-0.784148\pi\)
0.998760 0.0497807i \(-0.0158522\pi\)
\(614\) 63.0860 + 45.8346i 2.54594 + 1.84974i
\(615\) 0 0
\(616\) −15.0162 + 8.08827i −0.605018 + 0.325886i
\(617\) 44.4849 1.79089 0.895447 0.445168i \(-0.146856\pi\)
0.895447 + 0.445168i \(0.146856\pi\)
\(618\) 0 0
\(619\) −1.91722 + 5.90058i −0.0770594 + 0.237164i −0.982165 0.188023i \(-0.939792\pi\)
0.905105 + 0.425188i \(0.139792\pi\)
\(620\) 12.2364 + 37.6599i 0.491427 + 1.51246i
\(621\) 0 0
\(622\) 18.0371 13.1047i 0.723220 0.525450i
\(623\) −0.215760 0.664040i −0.00864423 0.0266042i
\(624\) 0 0
\(625\) 8.76619 + 6.36901i 0.350647 + 0.254760i
\(626\) −35.7652 −1.42947
\(627\) 0 0
\(628\) 4.65531 0.185767
\(629\) 0.404567 + 0.293935i 0.0161312 + 0.0117200i
\(630\) 0 0
\(631\) 13.8457 + 42.6128i 0.551190 + 1.69639i 0.705799 + 0.708412i \(0.250588\pi\)
−0.154609 + 0.987976i \(0.549412\pi\)
\(632\) 11.0407 8.02155i 0.439176 0.319080i
\(633\) 0 0
\(634\) −14.0389 43.2072i −0.557554 1.71598i
\(635\) −8.53418 + 26.2655i −0.338669 + 1.04231i
\(636\) 0 0
\(637\) −0.653752 −0.0259026
\(638\) −6.69585 36.8134i −0.265091 1.45746i
\(639\) 0 0
\(640\) −52.6982 38.2875i −2.08308 1.51345i
\(641\) 3.17534 9.77271i 0.125419 0.385999i −0.868559 0.495587i \(-0.834953\pi\)
0.993977 + 0.109588i \(0.0349531\pi\)
\(642\) 0 0
\(643\) 13.3039 9.66588i 0.524656 0.381185i −0.293699 0.955898i \(-0.594886\pi\)
0.818355 + 0.574713i \(0.194886\pi\)
\(644\) 22.0323 16.0074i 0.868196 0.630781i
\(645\) 0 0
\(646\) 5.26675 16.2094i 0.207218 0.637750i
\(647\) −21.8181 15.8518i −0.857758 0.623197i 0.0695163 0.997581i \(-0.477854\pi\)
−0.927274 + 0.374383i \(0.877854\pi\)
\(648\) 0 0
\(649\) 4.06261 + 3.88115i 0.159471 + 0.152348i
\(650\) 11.3178 0.443921
\(651\) 0 0
\(652\) −6.39623 + 19.6856i −0.250496 + 0.770947i
\(653\) −2.19588 6.75823i −0.0859315 0.264470i 0.898853 0.438250i \(-0.144402\pi\)
−0.984784 + 0.173780i \(0.944402\pi\)
\(654\) 0 0
\(655\) −13.4765 + 9.79123i −0.526569 + 0.382575i
\(656\) 8.23757 + 25.3526i 0.321623 + 0.989854i
\(657\) 0 0
\(658\) −1.20676 0.876765i −0.0470445 0.0341798i
\(659\) 32.6279 1.27100 0.635502 0.772099i \(-0.280793\pi\)
0.635502 + 0.772099i \(0.280793\pi\)
\(660\) 0 0
\(661\) −33.8165 −1.31531 −0.657654 0.753320i \(-0.728451\pi\)
−0.657654 + 0.753320i \(0.728451\pi\)
\(662\) −12.9247 9.39038i −0.502334 0.364967i
\(663\) 0 0
\(664\) 10.6418 + 32.7520i 0.412981 + 1.27103i
\(665\) −17.0411 + 12.3811i −0.660825 + 0.480117i
\(666\) 0 0
\(667\) 9.42266 + 29.0000i 0.364847 + 1.12288i
\(668\) 24.8752 76.5581i 0.962452 2.96212i
\(669\) 0 0
\(670\) 52.8335 2.04114
\(671\) 9.86094 20.4974i 0.380677 0.791293i
\(672\) 0 0
\(673\) −19.2138 13.9596i −0.740638 0.538105i 0.152273 0.988338i \(-0.451341\pi\)
−0.892911 + 0.450234i \(0.851341\pi\)
\(674\) −4.76934 + 14.6785i −0.183708 + 0.565395i
\(675\) 0 0
\(676\) 41.5480 30.1864i 1.59800 1.16102i
\(677\) −36.9164 + 26.8213i −1.41881 + 1.03083i −0.426845 + 0.904325i \(0.640375\pi\)
−0.991966 + 0.126502i \(0.959625\pi\)
\(678\) 0 0
\(679\) 4.59159 14.1315i 0.176209 0.542315i
\(680\) 16.4012 + 11.9162i 0.628958 + 0.456965i
\(681\) 0 0
\(682\) 16.5419 + 15.8030i 0.633421 + 0.605128i
\(683\) 28.8727 1.10478 0.552392 0.833585i \(-0.313715\pi\)
0.552392 + 0.833585i \(0.313715\pi\)
\(684\) 0 0
\(685\) 23.4372 72.1322i 0.895488 2.75603i
\(686\) 0.762262 + 2.34600i 0.0291033 + 0.0895707i
\(687\) 0 0
\(688\) −31.8141 + 23.1143i −1.21290 + 0.881223i
\(689\) 1.98434 + 6.10716i 0.0755973 + 0.232664i
\(690\) 0 0
\(691\) 21.8948 + 15.9075i 0.832918 + 0.605150i 0.920383 0.391017i \(-0.127877\pi\)
−0.0874654 + 0.996168i \(0.527877\pi\)
\(692\) 58.7994 2.23522
\(693\) 0 0
\(694\) 56.0334 2.12700
\(695\) 55.5705 + 40.3743i 2.10791 + 1.53148i
\(696\) 0 0
\(697\) 2.07437 + 6.38424i 0.0785722 + 0.241820i
\(698\) 59.2583 43.0537i 2.24296 1.62961i
\(699\) 0 0
\(700\) −8.85884 27.2647i −0.334833 1.03051i
\(701\) −11.9020 + 36.6305i −0.449531 + 1.38352i 0.427905 + 0.903823i \(0.359252\pi\)
−0.877437 + 0.479692i \(0.840748\pi\)
\(702\) 0 0
\(703\) 2.67198 0.100776
\(704\) −22.7601 3.07380i −0.857802 0.115848i
\(705\) 0 0
\(706\) 13.6203 + 9.89572i 0.512606 + 0.372430i
\(707\) 2.66360 8.19772i 0.100175 0.308307i
\(708\) 0 0
\(709\) 1.53280 1.11364i 0.0575654 0.0418237i −0.558630 0.829417i \(-0.688673\pi\)
0.616196 + 0.787593i \(0.288673\pi\)
\(710\) 37.4755 27.2276i 1.40643 1.02183i
\(711\) 0 0
\(712\) −1.10956 + 3.41487i −0.0415824 + 0.127978i
\(713\) −15.0827 10.9582i −0.564851 0.410388i
\(714\) 0 0
\(715\) 6.61778 3.56459i 0.247491 0.133308i
\(716\) 19.0522 0.712013
\(717\) 0 0
\(718\) −5.53379 + 17.0313i −0.206519 + 0.635601i
\(719\) −4.50461 13.8638i −0.167994 0.517031i 0.831251 0.555898i \(-0.187625\pi\)
−0.999244 + 0.0388664i \(0.987625\pi\)
\(720\) 0 0
\(721\) −0.754779 + 0.548379i −0.0281094 + 0.0204227i
\(722\) −13.6582 42.0357i −0.508307 1.56441i
\(723\) 0 0
\(724\) −32.7426 23.7889i −1.21687 0.884107i
\(725\) 32.0984 1.19210
\(726\) 0 0
\(727\) 4.04780 0.150125 0.0750623 0.997179i \(-0.476084\pi\)
0.0750623 + 0.997179i \(0.476084\pi\)
\(728\) 2.71988 + 1.97611i 0.100805 + 0.0732394i
\(729\) 0 0
\(730\) −17.7104 54.5069i −0.655490 2.01739i
\(731\) −8.01135 + 5.82058i −0.296310 + 0.215282i
\(732\) 0 0
\(733\) −7.26226 22.3509i −0.268238 0.825551i −0.990930 0.134381i \(-0.957095\pi\)
0.722692 0.691170i \(-0.242905\pi\)
\(734\) 27.6980 85.2457i 1.02235 3.14648i
\(735\) 0 0
\(736\) −5.69437 −0.209897
\(737\) 18.0404 9.71726i 0.664527 0.357940i
\(738\) 0 0
\(739\) 26.4376 + 19.2080i 0.972522 + 0.706578i 0.956025 0.293286i \(-0.0947487\pi\)
0.0164968 + 0.999864i \(0.494749\pi\)
\(740\) −1.92435 + 5.92254i −0.0707405 + 0.217717i
\(741\) 0 0
\(742\) 19.6020 14.2417i 0.719612 0.522828i
\(743\) −14.6479 + 10.6423i −0.537379 + 0.390429i −0.823111 0.567881i \(-0.807763\pi\)
0.285731 + 0.958310i \(0.407763\pi\)
\(744\) 0 0
\(745\) −3.38750 + 10.4257i −0.124108 + 0.381967i
\(746\) −28.5202 20.7211i −1.04420 0.758655i
\(747\) 0 0
\(748\) 15.2671 + 2.06186i 0.558222 + 0.0753892i
\(749\) 6.62212 0.241967
\(750\) 0 0
\(751\) 2.82552 8.69605i 0.103105 0.317323i −0.886176 0.463348i \(-0.846648\pi\)
0.989281 + 0.146025i \(0.0466479\pi\)
\(752\) 0.843835 + 2.59706i 0.0307715 + 0.0947049i
\(753\) 0 0
\(754\) −5.96689 + 4.33520i −0.217301 + 0.157879i
\(755\) 9.56444 + 29.4363i 0.348086 + 1.07130i
\(756\) 0 0
\(757\) −38.3077 27.8322i −1.39232 1.01158i −0.995607 0.0936338i \(-0.970152\pi\)
−0.396710 0.917944i \(-0.629848\pi\)
\(758\) 6.27851 0.228046
\(759\) 0 0
\(760\) 108.323 3.92927
\(761\) 2.78972 + 2.02685i 0.101127 + 0.0734732i 0.637200 0.770699i \(-0.280093\pi\)
−0.536073 + 0.844172i \(0.680093\pi\)
\(762\) 0 0
\(763\) 1.27472 + 3.92317i 0.0461478 + 0.142028i
\(764\) 32.8579 23.8727i 1.18876 0.863683i
\(765\) 0 0
\(766\) −17.6362 54.2787i −0.637223 1.96117i
\(767\) 0.342234 1.05329i 0.0123573 0.0380320i
\(768\) 0 0
\(769\) 34.9787 1.26137 0.630683 0.776041i \(-0.282775\pi\)
0.630683 + 0.776041i \(0.282775\pi\)
\(770\) −20.5078 19.5918i −0.739050 0.706040i
\(771\) 0 0
\(772\) −12.2491 8.89953i −0.440856 0.320301i
\(773\) −7.84266 + 24.1372i −0.282081 + 0.868155i 0.705178 + 0.709031i \(0.250867\pi\)
−0.987258 + 0.159125i \(0.949133\pi\)
\(774\) 0 0
\(775\) −15.8771 + 11.5354i −0.570321 + 0.414363i
\(776\) −61.8183 + 44.9137i −2.21915 + 1.61231i
\(777\) 0 0
\(778\) 23.0672 70.9934i 0.826998 2.54524i
\(779\) 29.0176 + 21.0825i 1.03966 + 0.755358i
\(780\) 0 0
\(781\) 7.78856 16.1897i 0.278697 0.579312i
\(782\) −18.7015 −0.668765
\(783\) 0 0
\(784\) 1.39545 4.29476i 0.0498376 0.153384i
\(785\) 1.22091 + 3.75758i 0.0435762 + 0.134114i
\(786\) 0 0
\(787\) −24.0725 + 17.4897i −0.858090 + 0.623439i −0.927365 0.374159i \(-0.877932\pi\)
0.0692745 + 0.997598i \(0.477932\pi\)
\(788\) −7.47236 22.9976i −0.266192 0.819255i
\(789\) 0 0
\(790\) 18.3595 + 13.3389i 0.653201 + 0.474578i
\(791\) −18.8258 −0.669369
\(792\) 0 0
\(793\) −4.48355 −0.159215
\(794\) −45.2490 32.8753i −1.60583 1.16670i
\(795\) 0 0
\(796\) 14.4961 + 44.6144i 0.513800 + 1.58132i
\(797\) −5.05094 + 3.66972i −0.178913 + 0.129988i −0.673638 0.739062i \(-0.735269\pi\)
0.494724 + 0.869050i \(0.335269\pi\)
\(798\) 0 0
\(799\) 0.212493 + 0.653985i 0.00751745 + 0.0231363i
\(800\) −1.85234 + 5.70090i −0.0654899 + 0.201557i
\(801\) 0 0
\(802\) −40.0069 −1.41269
\(803\) −16.0724 15.3545i −0.567182 0.541848i
\(804\) 0 0
\(805\) 18.6988 + 13.5855i 0.659046 + 0.478825i
\(806\) 1.39349 4.28871i 0.0490834 0.151063i
\(807\) 0 0
\(808\) −35.8611 + 26.0546i −1.26159 + 0.916598i
\(809\) 31.7022 23.0330i 1.11459 0.809796i 0.131209 0.991355i \(-0.458114\pi\)
0.983380 + 0.181559i \(0.0581142\pi\)
\(810\) 0 0
\(811\) −3.82591 + 11.7749i −0.134346 + 0.413474i −0.995488 0.0948906i \(-0.969750\pi\)
0.861142 + 0.508365i \(0.169750\pi\)
\(812\) 15.1140 + 10.9810i 0.530399 + 0.385357i
\(813\) 0 0
\(814\) 0.643819 + 3.53969i 0.0225659 + 0.124066i
\(815\) −17.5669 −0.615341
\(816\) 0 0
\(817\) −16.3505 + 50.3216i −0.572031 + 1.76053i
\(818\) 26.7260 + 82.2541i 0.934452 + 2.87595i
\(819\) 0 0
\(820\) −67.6284 + 49.1349i −2.36168 + 1.71586i
\(821\) −14.7397 45.3642i −0.514420 1.58322i −0.784335 0.620337i \(-0.786996\pi\)
0.269916 0.962884i \(-0.413004\pi\)
\(822\) 0 0
\(823\) 11.7475 + 8.53507i 0.409493 + 0.297514i 0.773396 0.633923i \(-0.218556\pi\)
−0.363904 + 0.931437i \(0.618556\pi\)
\(824\) 4.79779 0.167139
\(825\) 0 0
\(826\) −4.17878 −0.145398
\(827\) −25.0287 18.1844i −0.870335 0.632335i 0.0603420 0.998178i \(-0.480781\pi\)
−0.930677 + 0.365843i \(0.880781\pi\)
\(828\) 0 0
\(829\) 0.0265154 + 0.0816061i 0.000920918 + 0.00283430i 0.951516 0.307600i \(-0.0995257\pi\)
−0.950595 + 0.310434i \(0.899526\pi\)
\(830\) −46.3290 + 33.6600i −1.60810 + 1.16835i
\(831\) 0 0
\(832\) 1.39893 + 4.30548i 0.0484993 + 0.149266i
\(833\) 0.351400 1.08150i 0.0121753 0.0374717i
\(834\) 0 0
\(835\) 68.3185 2.36426
\(836\) 72.4713 39.0358i 2.50647 1.35008i
\(837\) 0 0
\(838\) −56.4030 40.9792i −1.94841 1.41560i
\(839\) −3.30355 + 10.1673i −0.114051 + 0.351014i −0.991748 0.128203i \(-0.959079\pi\)
0.877697 + 0.479217i \(0.159079\pi\)
\(840\) 0 0
\(841\) 6.53883 4.75074i 0.225477 0.163819i
\(842\) −27.5290 + 20.0010i −0.948713 + 0.689281i
\(843\) 0 0
\(844\) 11.0131 33.8948i 0.379086 1.16671i
\(845\) 35.2617 + 25.6191i 1.21304 + 0.881325i
\(846\) 0 0
\(847\) −10.6059 2.91793i −0.364424 0.100261i
\(848\) −44.3561 −1.52319
\(849\) 0 0
\(850\) −6.08347 + 18.7230i −0.208661 + 0.642193i
\(851\) −0.906008 2.78841i −0.0310576 0.0955854i
\(852\) 0 0
\(853\) −17.1514 + 12.4612i −0.587252 + 0.426664i −0.841331 0.540520i \(-0.818228\pi\)
0.254079 + 0.967183i \(0.418228\pi\)
\(854\) 5.22773 + 16.0893i 0.178889 + 0.550565i
\(855\) 0 0
\(856\) −27.5508 20.0168i −0.941666 0.684160i
\(857\) 9.45359 0.322929 0.161464 0.986879i \(-0.448378\pi\)
0.161464 + 0.986879i \(0.448378\pi\)
\(858\) 0 0
\(859\) −38.8261 −1.32473 −0.662365 0.749181i \(-0.730447\pi\)
−0.662365 + 0.749181i \(0.730447\pi\)
\(860\) −99.7640 72.4828i −3.40192 2.47164i
\(861\) 0 0
\(862\) 21.4730 + 66.0869i 0.731372 + 2.25093i
\(863\) −30.4228 + 22.1034i −1.03560 + 0.752410i −0.969423 0.245398i \(-0.921081\pi\)
−0.0661810 + 0.997808i \(0.521081\pi\)
\(864\) 0 0
\(865\) 15.4208 + 47.4605i 0.524324 + 1.61370i
\(866\) −10.8084 + 33.2647i −0.367283 + 1.13038i
\(867\) 0 0
\(868\) −11.4223 −0.387697
\(869\) 8.72231 + 1.17797i 0.295884 + 0.0399599i
\(870\) 0 0
\(871\) −3.26767 2.37410i −0.110721 0.0804433i
\(872\) 6.55530 20.1752i 0.221991 0.683217i
\(873\) 0 0
\(874\) −80.8416 + 58.7348i −2.73451 + 1.98674i
\(875\) 5.66042 4.11253i 0.191357 0.139029i
\(876\) 0 0
\(877\) 6.80103 20.9314i 0.229654 0.706804i −0.768131 0.640293i \(-0.778813\pi\)
0.997786 0.0665113i \(-0.0211869\pi\)
\(878\) 55.9145 + 40.6243i 1.88702 + 1.37100i
\(879\) 0 0
\(880\) 9.29140 + 51.0836i 0.313213 + 1.72203i
\(881\) 6.92969 0.233467 0.116734 0.993163i \(-0.462758\pi\)
0.116734 + 0.993163i \(0.462758\pi\)
\(882\) 0 0
\(883\) 13.0834 40.2666i 0.440292 1.35508i −0.447274 0.894397i \(-0.647605\pi\)
0.887566 0.460681i \(-0.152395\pi\)
\(884\) −0.938386 2.88806i −0.0315613 0.0971358i
\(885\) 0 0
\(886\) −34.5982 + 25.1371i −1.16235 + 0.844496i
\(887\) −2.48959 7.66216i −0.0835921 0.257270i 0.900521 0.434812i \(-0.143185\pi\)
−0.984113 + 0.177542i \(0.943185\pi\)
\(888\) 0 0
\(889\) −6.44491 4.68250i −0.216155 0.157046i
\(890\) −5.97077 −0.200141
\(891\) 0 0
\(892\) 42.2072 1.41320
\(893\) 2.97248 + 2.15964i 0.0994703 + 0.0722694i
\(894\) 0 0
\(895\) 4.99666 + 15.3781i 0.167020 + 0.514034i
\(896\) 15.2011 11.0443i 0.507834 0.368963i
\(897\) 0 0
\(898\) −22.5031 69.2575i −0.750939 2.31115i
\(899\) 3.95206 12.1632i 0.131808 0.405665i
\(900\) 0 0
\(901\) −11.1697 −0.372115
\(902\) −20.9370 + 43.5207i −0.697127 + 1.44908i
\(903\) 0 0
\(904\) 78.3232 + 56.9051i 2.60499 + 1.89264i
\(905\) 10.6143 32.6674i 0.352831 1.08590i
\(906\) 0 0
\(907\) −2.34153 + 1.70122i −0.0777492 + 0.0564881i −0.625981 0.779838i \(-0.715301\pi\)
0.548232 + 0.836327i \(0.315301\pi\)
\(908\) −43.8492 + 31.8583i −1.45519 + 1.05725i
\(909\) 0 0
\(910\) −1.72758 + 5.31693i −0.0572686 + 0.176255i
\(911\) −16.3826 11.9026i −0.542779 0.394352i 0.282337 0.959315i \(-0.408890\pi\)
−0.825116 + 0.564963i \(0.808890\pi\)
\(912\) 0 0
\(913\) −9.62858 + 20.0144i −0.318659 + 0.662380i
\(914\) −23.9205 −0.791220
\(915\) 0 0
\(916\) −3.15089 + 9.69745i −0.104108 + 0.320413i
\(917\) −1.48484 4.56988i −0.0490338 0.150911i
\(918\) 0 0
\(919\) −15.1498 + 11.0069i −0.499744 + 0.363085i −0.808919 0.587920i \(-0.799947\pi\)
0.309175 + 0.951005i \(0.399947\pi\)
\(920\) −36.7297 113.042i −1.21094 3.72690i
\(921\) 0 0
\(922\) 38.3592 + 27.8696i 1.26329 + 0.917836i
\(923\) −3.54128 −0.116563
\(924\) 0 0
\(925\) −3.08632 −0.101478
\(926\) 40.9756 + 29.7705i 1.34654 + 0.978320i
\(927\) 0 0
\(928\) −1.20711 3.71511i −0.0396254 0.121954i
\(929\) −36.6243 + 26.6091i −1.20160 + 0.873016i −0.994441 0.105291i \(-0.966423\pi\)
−0.207162 + 0.978307i \(0.566423\pi\)
\(930\) 0 0
\(931\) −1.87759 5.77864i −0.0615357 0.189387i
\(932\) 12.1226 37.3096i 0.397090 1.22212i
\(933\) 0 0
\(934\) 83.0584 2.71775
\(935\) 2.33974 + 12.8638i 0.0765177 + 0.420690i
\(936\) 0 0
\(937\) −23.8336 17.3161i −0.778609 0.565692i 0.125952 0.992036i \(-0.459801\pi\)
−0.904561 + 0.426344i \(0.859801\pi\)
\(938\) −4.70947 + 14.4942i −0.153769 + 0.473254i
\(939\) 0 0
\(940\) −6.92767 + 5.03325i −0.225956 + 0.164167i
\(941\) 47.1128 34.2294i 1.53583 1.11585i 0.582950 0.812508i \(-0.301898\pi\)
0.952882 0.303340i \(-0.0981017\pi\)
\(942\) 0 0
\(943\) 12.1619 37.4305i 0.396046 1.21891i
\(944\) 6.18897 + 4.49655i 0.201434 + 0.146350i
\(945\) 0 0
\(946\) −70.6028 9.53508i −2.29550 0.310012i
\(947\) −45.3642 −1.47414 −0.737069 0.675818i \(-0.763791\pi\)
−0.737069 + 0.675818i \(0.763791\pi\)
\(948\) 0 0
\(949\) −1.35394 + 4.16699i −0.0439506 + 0.135266i
\(950\) 32.5051 + 100.040i 1.05460 + 3.24574i
\(951\) 0 0
\(952\) −4.73103 + 3.43730i −0.153334 + 0.111403i
\(953\) 12.7740 + 39.3143i 0.413790 + 1.27352i 0.913328 + 0.407224i \(0.133503\pi\)
−0.499538 + 0.866292i \(0.666497\pi\)
\(954\) 0 0
\(955\) 27.8864 + 20.2607i 0.902384 + 0.655620i
\(956\) −22.7247 −0.734968
\(957\) 0 0
\(958\) 34.9555 1.12936
\(959\) 17.6995 + 12.8594i 0.571545 + 0.415252i
\(960\) 0 0
\(961\) −7.16322 22.0461i −0.231071 0.711165i
\(962\) 0.573728 0.416838i 0.0184977 0.0134394i
\(963\) 0 0
\(964\) 18.9601 + 58.3533i 0.610665 + 1.87943i
\(965\) 3.97085 12.2210i 0.127826 0.393409i
\(966\) 0 0
\(967\) −6.52818 −0.209932 −0.104966 0.994476i \(-0.533473\pi\)
−0.104966 + 0.994476i \(0.533473\pi\)
\(968\) 35.3050 + 44.1986i 1.13475 + 1.42060i
\(969\) 0 0
\(970\) −102.797 74.6864i −3.30061 2.39803i
\(971\) −8.91783 + 27.4462i −0.286187 + 0.880792i 0.699854 + 0.714286i \(0.253248\pi\)
−0.986040 + 0.166506i \(0.946752\pi\)
\(972\) 0 0
\(973\) −16.0296 + 11.6462i −0.513887 + 0.373360i
\(974\) 55.3617 40.2226i 1.77390 1.28882i
\(975\) 0 0
\(976\) 9.57027 29.4543i 0.306337 0.942808i
\(977\) −7.26864 5.28097i −0.232544 0.168953i 0.465411 0.885095i \(-0.345907\pi\)
−0.697955 + 0.716141i \(0.745907\pi\)
\(978\) 0 0
\(979\) −2.03877 + 1.09816i −0.0651593 + 0.0350973i
\(980\) 14.1608 0.452350
\(981\) 0 0
\(982\) −2.62443 + 8.07717i −0.0837490 + 0.257753i
\(983\) −11.3971 35.0768i −0.363512 1.11877i −0.950908 0.309475i \(-0.899847\pi\)
0.587396 0.809300i \(-0.300153\pi\)
\(984\) 0 0
\(985\) 16.6030 12.0628i 0.529015 0.384352i
\(986\) −3.96441 12.2012i −0.126253 0.388566i
\(987\) 0 0
\(988\) −13.1267 9.53713i −0.417617 0.303417i
\(989\) 58.0583 1.84615
\(990\) 0 0
\(991\) −2.98352 −0.0947746 −0.0473873 0.998877i \(-0.515089\pi\)
−0.0473873 + 0.998877i \(0.515089\pi\)
\(992\) 1.93220 + 1.40383i 0.0613475 + 0.0445716i
\(993\) 0 0
\(994\) 4.12907 + 12.7080i 0.130966 + 0.403072i
\(995\) −32.2092 + 23.4013i −1.02110 + 0.741872i
\(996\) 0 0
\(997\) 19.4234 + 59.7790i 0.615144 + 1.89322i 0.399437 + 0.916760i \(0.369205\pi\)
0.215707 + 0.976458i \(0.430795\pi\)
\(998\) 1.97367 6.07434i 0.0624755 0.192280i
\(999\) 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 693.2.m.g.631.2 8
3.2 odd 2 77.2.f.a.15.1 8
11.3 even 5 inner 693.2.m.g.190.2 8
11.5 even 5 7623.2.a.ch.1.1 4
11.6 odd 10 7623.2.a.co.1.4 4
21.2 odd 6 539.2.q.c.312.1 16
21.5 even 6 539.2.q.b.312.1 16
21.11 odd 6 539.2.q.c.422.2 16
21.17 even 6 539.2.q.b.422.2 16
21.20 even 2 539.2.f.d.246.1 8
33.2 even 10 847.2.f.s.148.1 8
33.5 odd 10 847.2.a.l.1.4 4
33.8 even 10 847.2.f.q.729.2 8
33.14 odd 10 77.2.f.a.36.1 yes 8
33.17 even 10 847.2.a.k.1.1 4
33.20 odd 10 847.2.f.p.148.2 8
33.26 odd 10 847.2.f.p.372.2 8
33.29 even 10 847.2.f.s.372.1 8
33.32 even 2 847.2.f.q.323.2 8
231.47 even 30 539.2.q.b.410.2 16
231.80 even 30 539.2.q.b.520.1 16
231.83 odd 10 5929.2.a.bb.1.1 4
231.104 even 10 5929.2.a.bi.1.4 4
231.146 even 10 539.2.f.d.344.1 8
231.179 odd 30 539.2.q.c.520.1 16
231.212 odd 30 539.2.q.c.410.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.15.1 8 3.2 odd 2
77.2.f.a.36.1 yes 8 33.14 odd 10
539.2.f.d.246.1 8 21.20 even 2
539.2.f.d.344.1 8 231.146 even 10
539.2.q.b.312.1 16 21.5 even 6
539.2.q.b.410.2 16 231.47 even 30
539.2.q.b.422.2 16 21.17 even 6
539.2.q.b.520.1 16 231.80 even 30
539.2.q.c.312.1 16 21.2 odd 6
539.2.q.c.410.2 16 231.212 odd 30
539.2.q.c.422.2 16 21.11 odd 6
539.2.q.c.520.1 16 231.179 odd 30
693.2.m.g.190.2 8 11.3 even 5 inner
693.2.m.g.631.2 8 1.1 even 1 trivial
847.2.a.k.1.1 4 33.17 even 10
847.2.a.l.1.4 4 33.5 odd 10
847.2.f.p.148.2 8 33.20 odd 10
847.2.f.p.372.2 8 33.26 odd 10
847.2.f.q.323.2 8 33.32 even 2
847.2.f.q.729.2 8 33.8 even 10
847.2.f.s.148.1 8 33.2 even 10
847.2.f.s.372.1 8 33.29 even 10
5929.2.a.bb.1.1 4 231.83 odd 10
5929.2.a.bi.1.4 4 231.104 even 10
7623.2.a.ch.1.1 4 11.5 even 5
7623.2.a.co.1.4 4 11.6 odd 10