Properties

Label 1638.2.bj.h.127.3
Level $1638$
Weight $2$
Character 1638.127
Analytic conductor $13.079$
Analytic rank $0$
Dimension $16$
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] = [1638,2,Mod(127,1638)]
 
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([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.127");
 
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.bj (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: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + 6655 x^{8} + 478 x^{7} + 1106 x^{6} + 11266 x^{5} + 55249 x^{4} + 8856 x^{3} + \cdots + 97344 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.3
Root \(2.24849 - 2.24849i\) of defining polynomial
Character \(\chi\) \(=\) 1638.127
Dual form 1638.2.bj.h.1135.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.24768i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.24768i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.623842 - 1.08053i) q^{10} +(1.41441 - 0.816612i) q^{11} +(3.60364 + 0.117447i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.78174 + 4.81811i) q^{17} +(-4.23947 - 2.44766i) q^{19} +(1.08053 + 0.623842i) q^{20} +(-0.816612 + 1.41441i) q^{22} +(2.83571 + 4.91159i) q^{23} +3.44329 q^{25} +(-3.17957 + 1.70011i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.59985 - 2.77102i) q^{29} +3.53063i q^{31} +(0.866025 + 0.500000i) q^{32} -5.56348i q^{34} +(-0.623842 + 1.08053i) q^{35} +(6.12562 - 3.53663i) q^{37} +4.89532 q^{38} -1.24768 q^{40} +(3.46229 - 1.99895i) q^{41} +(2.69078 - 4.66057i) q^{43} -1.63322i q^{44} +(-4.91159 - 2.83571i) q^{46} +11.4980i q^{47} +(0.500000 + 0.866025i) q^{49} +(-2.98197 + 1.72164i) q^{50} +(1.90353 - 3.06212i) q^{52} -4.82030 q^{53} +(1.01887 + 1.76474i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(2.77102 + 1.59985i) q^{58} +(-4.48259 - 2.58803i) q^{59} +(-2.97263 + 5.14874i) q^{61} +(-1.76532 - 3.05762i) q^{62} -1.00000 q^{64} +(-0.146537 + 4.49620i) q^{65} +(-5.48962 + 3.16943i) q^{67} +(2.78174 + 4.81811i) q^{68} -1.24768i q^{70} +(11.3538 + 6.55514i) q^{71} -6.62310i q^{73} +(-3.53663 + 6.12562i) q^{74} +(-4.23947 + 2.44766i) q^{76} +1.63322 q^{77} -8.21115 q^{79} +(1.08053 - 0.623842i) q^{80} +(-1.99895 + 3.46229i) q^{82} +11.1721i q^{83} +(-6.01148 - 3.47073i) q^{85} +5.38157i q^{86} +(0.816612 + 1.41441i) q^{88} +(2.16375 - 1.24924i) q^{89} +(3.06212 + 1.90353i) q^{91} +5.67142 q^{92} +(-5.74902 - 9.95759i) q^{94} +(3.05390 - 5.28951i) q^{95} +(9.02271 + 5.20926i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.24768i 0.557981i 0.960294 + 0.278991i \(0.0899998\pi\)
−0.960294 + 0.278991i \(0.910000\pi\)
\(6\) 0 0
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.623842 1.08053i −0.197276 0.341692i
\(11\) 1.41441 0.816612i 0.426461 0.246218i −0.271377 0.962473i \(-0.587479\pi\)
0.697838 + 0.716256i \(0.254146\pi\)
\(12\) 0 0
\(13\) 3.60364 + 0.117447i 0.999469 + 0.0325741i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.78174 + 4.81811i −0.674671 + 1.16856i 0.301894 + 0.953341i \(0.402381\pi\)
−0.976565 + 0.215223i \(0.930952\pi\)
\(18\) 0 0
\(19\) −4.23947 2.44766i −0.972601 0.561531i −0.0725725 0.997363i \(-0.523121\pi\)
−0.900028 + 0.435832i \(0.856454\pi\)
\(20\) 1.08053 + 0.623842i 0.241613 + 0.139495i
\(21\) 0 0
\(22\) −0.816612 + 1.41441i −0.174102 + 0.301554i
\(23\) 2.83571 + 4.91159i 0.591286 + 1.02414i 0.994059 + 0.108838i \(0.0347131\pi\)
−0.402773 + 0.915300i \(0.631954\pi\)
\(24\) 0 0
\(25\) 3.44329 0.688657
\(26\) −3.17957 + 1.70011i −0.623564 + 0.333418i
\(27\) 0 0
\(28\) 0.866025 0.500000i 0.163663 0.0944911i
\(29\) −1.59985 2.77102i −0.297085 0.514566i 0.678383 0.734708i \(-0.262681\pi\)
−0.975468 + 0.220143i \(0.929348\pi\)
\(30\) 0 0
\(31\) 3.53063i 0.634121i 0.948405 + 0.317060i \(0.102696\pi\)
−0.948405 + 0.317060i \(0.897304\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.56348i 0.954129i
\(35\) −0.623842 + 1.08053i −0.105449 + 0.182642i
\(36\) 0 0
\(37\) 6.12562 3.53663i 1.00705 0.581418i 0.0967201 0.995312i \(-0.469165\pi\)
0.910325 + 0.413894i \(0.135832\pi\)
\(38\) 4.89532 0.794125
\(39\) 0 0
\(40\) −1.24768 −0.197276
\(41\) 3.46229 1.99895i 0.540718 0.312184i −0.204652 0.978835i \(-0.565606\pi\)
0.745370 + 0.666651i \(0.232273\pi\)
\(42\) 0 0
\(43\) 2.69078 4.66057i 0.410341 0.710731i −0.584586 0.811332i \(-0.698743\pi\)
0.994927 + 0.100601i \(0.0320765\pi\)
\(44\) 1.63322i 0.246218i
\(45\) 0 0
\(46\) −4.91159 2.83571i −0.724175 0.418103i
\(47\) 11.4980i 1.67716i 0.544778 + 0.838580i \(0.316614\pi\)
−0.544778 + 0.838580i \(0.683386\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −2.98197 + 1.72164i −0.421715 + 0.243477i
\(51\) 0 0
\(52\) 1.90353 3.06212i 0.263972 0.424639i
\(53\) −4.82030 −0.662120 −0.331060 0.943610i \(-0.607406\pi\)
−0.331060 + 0.943610i \(0.607406\pi\)
\(54\) 0 0
\(55\) 1.01887 + 1.76474i 0.137385 + 0.237957i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 2.77102 + 1.59985i 0.363853 + 0.210071i
\(59\) −4.48259 2.58803i −0.583584 0.336932i 0.178972 0.983854i \(-0.442723\pi\)
−0.762556 + 0.646922i \(0.776056\pi\)
\(60\) 0 0
\(61\) −2.97263 + 5.14874i −0.380606 + 0.659229i −0.991149 0.132754i \(-0.957618\pi\)
0.610543 + 0.791983i \(0.290951\pi\)
\(62\) −1.76532 3.05762i −0.224196 0.388318i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.146537 + 4.49620i −0.0181757 + 0.557685i
\(66\) 0 0
\(67\) −5.48962 + 3.16943i −0.670664 + 0.387208i −0.796328 0.604865i \(-0.793227\pi\)
0.125664 + 0.992073i \(0.459894\pi\)
\(68\) 2.78174 + 4.81811i 0.337335 + 0.584282i
\(69\) 0 0
\(70\) 1.24768i 0.149127i
\(71\) 11.3538 + 6.55514i 1.34745 + 0.777952i 0.987888 0.155168i \(-0.0495919\pi\)
0.359565 + 0.933120i \(0.382925\pi\)
\(72\) 0 0
\(73\) 6.62310i 0.775175i −0.921833 0.387588i \(-0.873308\pi\)
0.921833 0.387588i \(-0.126692\pi\)
\(74\) −3.53663 + 6.12562i −0.411125 + 0.712089i
\(75\) 0 0
\(76\) −4.23947 + 2.44766i −0.486300 + 0.280766i
\(77\) 1.63322 0.186123
\(78\) 0 0
\(79\) −8.21115 −0.923827 −0.461914 0.886925i \(-0.652837\pi\)
−0.461914 + 0.886925i \(0.652837\pi\)
\(80\) 1.08053 0.623842i 0.120806 0.0697476i
\(81\) 0 0
\(82\) −1.99895 + 3.46229i −0.220747 + 0.382346i
\(83\) 11.1721i 1.22630i 0.789968 + 0.613148i \(0.210097\pi\)
−0.789968 + 0.613148i \(0.789903\pi\)
\(84\) 0 0
\(85\) −6.01148 3.47073i −0.652037 0.376453i
\(86\) 5.38157i 0.580309i
\(87\) 0 0
\(88\) 0.816612 + 1.41441i 0.0870511 + 0.150777i
\(89\) 2.16375 1.24924i 0.229357 0.132419i −0.380918 0.924609i \(-0.624392\pi\)
0.610275 + 0.792189i \(0.291059\pi\)
\(90\) 0 0
\(91\) 3.06212 + 1.90353i 0.320997 + 0.199544i
\(92\) 5.67142 0.591286
\(93\) 0 0
\(94\) −5.74902 9.95759i −0.592966 1.02705i
\(95\) 3.05390 5.28951i 0.313324 0.542693i
\(96\) 0 0
\(97\) 9.02271 + 5.20926i 0.916117 + 0.528920i 0.882394 0.470511i \(-0.155930\pi\)
0.0337228 + 0.999431i \(0.489264\pi\)
\(98\) −0.866025 0.500000i −0.0874818 0.0505076i
\(99\) 0 0
\(100\) 1.72164 2.98197i 0.172164 0.298197i
\(101\) −1.78522 3.09210i −0.177636 0.307675i 0.763434 0.645886i \(-0.223512\pi\)
−0.941071 + 0.338210i \(0.890178\pi\)
\(102\) 0 0
\(103\) 9.63810 0.949670 0.474835 0.880075i \(-0.342508\pi\)
0.474835 + 0.880075i \(0.342508\pi\)
\(104\) −0.117447 + 3.60364i −0.0115167 + 0.353366i
\(105\) 0 0
\(106\) 4.17451 2.41015i 0.405464 0.234095i
\(107\) 2.18140 + 3.77830i 0.210884 + 0.365262i 0.951991 0.306125i \(-0.0990324\pi\)
−0.741107 + 0.671387i \(0.765699\pi\)
\(108\) 0 0
\(109\) 19.3037i 1.84896i 0.381230 + 0.924480i \(0.375501\pi\)
−0.381230 + 0.924480i \(0.624499\pi\)
\(110\) −1.76474 1.01887i −0.168261 0.0971457i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 4.73647 8.20380i 0.445569 0.771748i −0.552522 0.833498i \(-0.686335\pi\)
0.998092 + 0.0617495i \(0.0196680\pi\)
\(114\) 0 0
\(115\) −6.12812 + 3.53807i −0.571450 + 0.329927i
\(116\) −3.19970 −0.297085
\(117\) 0 0
\(118\) 5.17605 0.476494
\(119\) −4.81811 + 2.78174i −0.441676 + 0.255002i
\(120\) 0 0
\(121\) −4.16629 + 7.21623i −0.378754 + 0.656021i
\(122\) 5.94526i 0.538258i
\(123\) 0 0
\(124\) 3.05762 + 1.76532i 0.274582 + 0.158530i
\(125\) 10.5345i 0.942239i
\(126\) 0 0
\(127\) 7.47672 + 12.9501i 0.663452 + 1.14913i 0.979703 + 0.200457i \(0.0642425\pi\)
−0.316251 + 0.948676i \(0.602424\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.12119 3.96709i −0.186041 0.347937i
\(131\) −13.3546 −1.16680 −0.583398 0.812187i \(-0.698277\pi\)
−0.583398 + 0.812187i \(0.698277\pi\)
\(132\) 0 0
\(133\) −2.44766 4.23947i −0.212239 0.367608i
\(134\) 3.16943 5.48962i 0.273797 0.474231i
\(135\) 0 0
\(136\) −4.81811 2.78174i −0.413150 0.238532i
\(137\) 6.27707 + 3.62407i 0.536286 + 0.309625i 0.743573 0.668655i \(-0.233130\pi\)
−0.207286 + 0.978280i \(0.566463\pi\)
\(138\) 0 0
\(139\) 7.86534 13.6232i 0.667129 1.15550i −0.311574 0.950222i \(-0.600856\pi\)
0.978703 0.205280i \(-0.0658104\pi\)
\(140\) 0.623842 + 1.08053i 0.0527243 + 0.0913211i
\(141\) 0 0
\(142\) −13.1103 −1.10019
\(143\) 5.19294 2.77665i 0.434255 0.232195i
\(144\) 0 0
\(145\) 3.45736 1.99611i 0.287118 0.165768i
\(146\) 3.31155 + 5.73577i 0.274066 + 0.474696i
\(147\) 0 0
\(148\) 7.07325i 0.581418i
\(149\) −2.20523 1.27319i −0.180659 0.104304i 0.406943 0.913454i \(-0.366595\pi\)
−0.587602 + 0.809150i \(0.699928\pi\)
\(150\) 0 0
\(151\) 9.89437i 0.805192i 0.915378 + 0.402596i \(0.131892\pi\)
−0.915378 + 0.402596i \(0.868108\pi\)
\(152\) 2.44766 4.23947i 0.198531 0.343866i
\(153\) 0 0
\(154\) −1.41441 + 0.816612i −0.113977 + 0.0658044i
\(155\) −4.40511 −0.353827
\(156\) 0 0
\(157\) 8.96414 0.715416 0.357708 0.933833i \(-0.383558\pi\)
0.357708 + 0.933833i \(0.383558\pi\)
\(158\) 7.11107 4.10558i 0.565726 0.326622i
\(159\) 0 0
\(160\) −0.623842 + 1.08053i −0.0493190 + 0.0854231i
\(161\) 5.67142i 0.446971i
\(162\) 0 0
\(163\) 0.371849 + 0.214687i 0.0291254 + 0.0168156i 0.514492 0.857495i \(-0.327981\pi\)
−0.485367 + 0.874311i \(0.661314\pi\)
\(164\) 3.99790i 0.312184i
\(165\) 0 0
\(166\) −5.58604 9.67531i −0.433561 0.750949i
\(167\) −19.5072 + 11.2625i −1.50951 + 0.871516i −0.509572 + 0.860428i \(0.670196\pi\)
−0.999939 + 0.0110885i \(0.996470\pi\)
\(168\) 0 0
\(169\) 12.9724 + 0.846476i 0.997878 + 0.0651136i
\(170\) 6.94146 0.532386
\(171\) 0 0
\(172\) −2.69078 4.66057i −0.205170 0.355365i
\(173\) −5.50562 + 9.53601i −0.418584 + 0.725010i −0.995797 0.0915841i \(-0.970807\pi\)
0.577213 + 0.816594i \(0.304140\pi\)
\(174\) 0 0
\(175\) 2.98197 + 1.72164i 0.225416 + 0.130144i
\(176\) −1.41441 0.816612i −0.106615 0.0615544i
\(177\) 0 0
\(178\) −1.24924 + 2.16375i −0.0936347 + 0.162180i
\(179\) 1.09732 + 1.90062i 0.0820179 + 0.142059i 0.904117 0.427286i \(-0.140530\pi\)
−0.822099 + 0.569345i \(0.807197\pi\)
\(180\) 0 0
\(181\) −4.81625 −0.357989 −0.178995 0.983850i \(-0.557284\pi\)
−0.178995 + 0.983850i \(0.557284\pi\)
\(182\) −3.60364 0.117447i −0.267119 0.00870579i
\(183\) 0 0
\(184\) −4.91159 + 2.83571i −0.362088 + 0.209051i
\(185\) 4.41259 + 7.64283i 0.324420 + 0.561912i
\(186\) 0 0
\(187\) 9.08640i 0.664463i
\(188\) 9.95759 + 5.74902i 0.726232 + 0.419290i
\(189\) 0 0
\(190\) 6.10780i 0.443107i
\(191\) 6.13215 10.6212i 0.443707 0.768523i −0.554254 0.832347i \(-0.686996\pi\)
0.997961 + 0.0638244i \(0.0203298\pi\)
\(192\) 0 0
\(193\) −16.2180 + 9.36349i −1.16740 + 0.673999i −0.953066 0.302762i \(-0.902091\pi\)
−0.214334 + 0.976760i \(0.568758\pi\)
\(194\) −10.4185 −0.748006
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 15.7761 9.10832i 1.12400 0.648941i 0.181580 0.983376i \(-0.441879\pi\)
0.942419 + 0.334435i \(0.108546\pi\)
\(198\) 0 0
\(199\) −4.60392 + 7.97423i −0.326364 + 0.565278i −0.981787 0.189983i \(-0.939157\pi\)
0.655424 + 0.755261i \(0.272490\pi\)
\(200\) 3.44329i 0.243477i
\(201\) 0 0
\(202\) 3.09210 + 1.78522i 0.217559 + 0.125608i
\(203\) 3.19970i 0.224575i
\(204\) 0 0
\(205\) 2.49406 + 4.31984i 0.174193 + 0.301711i
\(206\) −8.34684 + 4.81905i −0.581552 + 0.335759i
\(207\) 0 0
\(208\) −1.70011 3.17957i −0.117881 0.220463i
\(209\) −7.99514 −0.553036
\(210\) 0 0
\(211\) −2.17384 3.76520i −0.149653 0.259207i 0.781446 0.623973i \(-0.214482\pi\)
−0.931099 + 0.364766i \(0.881149\pi\)
\(212\) −2.41015 + 4.17451i −0.165530 + 0.286706i
\(213\) 0 0
\(214\) −3.77830 2.18140i −0.258279 0.149118i
\(215\) 5.81492 + 3.35725i 0.396574 + 0.228962i
\(216\) 0 0
\(217\) −1.76532 + 3.05762i −0.119838 + 0.207565i
\(218\) −9.65186 16.7175i −0.653706 1.13225i
\(219\) 0 0
\(220\) 2.03775 0.137385
\(221\) −10.5903 + 17.0360i −0.712378 + 1.14597i
\(222\) 0 0
\(223\) −4.15095 + 2.39655i −0.277968 + 0.160485i −0.632503 0.774558i \(-0.717973\pi\)
0.354535 + 0.935043i \(0.384639\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 9.47293i 0.630130i
\(227\) −4.71526 2.72236i −0.312963 0.180689i 0.335289 0.942115i \(-0.391166\pi\)
−0.648252 + 0.761426i \(0.724500\pi\)
\(228\) 0 0
\(229\) 15.0809i 0.996573i 0.867012 + 0.498287i \(0.166037\pi\)
−0.867012 + 0.498287i \(0.833963\pi\)
\(230\) 3.53807 6.12812i 0.233293 0.404076i
\(231\) 0 0
\(232\) 2.77102 1.59985i 0.181927 0.105035i
\(233\) 5.27514 0.345586 0.172793 0.984958i \(-0.444721\pi\)
0.172793 + 0.984958i \(0.444721\pi\)
\(234\) 0 0
\(235\) −14.3459 −0.935824
\(236\) −4.48259 + 2.58803i −0.291792 + 0.168466i
\(237\) 0 0
\(238\) 2.78174 4.81811i 0.180313 0.312312i
\(239\) 29.0721i 1.88052i −0.340461 0.940259i \(-0.610583\pi\)
0.340461 0.940259i \(-0.389417\pi\)
\(240\) 0 0
\(241\) 25.5375 + 14.7441i 1.64502 + 0.949751i 0.979012 + 0.203805i \(0.0653307\pi\)
0.666006 + 0.745947i \(0.268003\pi\)
\(242\) 8.33258i 0.535639i
\(243\) 0 0
\(244\) 2.97263 + 5.14874i 0.190303 + 0.329615i
\(245\) −1.08053 + 0.623842i −0.0690323 + 0.0398558i
\(246\) 0 0
\(247\) −14.9900 9.31839i −0.953793 0.592915i
\(248\) −3.53063 −0.224196
\(249\) 0 0
\(250\) −5.26727 9.12319i −0.333132 0.577001i
\(251\) 1.04396 1.80819i 0.0658941 0.114132i −0.831196 0.555979i \(-0.812343\pi\)
0.897090 + 0.441847i \(0.145677\pi\)
\(252\) 0 0
\(253\) 8.02173 + 4.63135i 0.504322 + 0.291170i
\(254\) −12.9501 7.47672i −0.812559 0.469131i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.1891 24.5763i −0.885094 1.53303i −0.845606 0.533808i \(-0.820760\pi\)
−0.0394885 0.999220i \(-0.512573\pi\)
\(258\) 0 0
\(259\) 7.07325 0.439511
\(260\) 3.82055 + 2.37500i 0.236941 + 0.147292i
\(261\) 0 0
\(262\) 11.5654 6.67729i 0.714513 0.412524i
\(263\) −12.2799 21.2695i −0.757214 1.31153i −0.944266 0.329183i \(-0.893227\pi\)
0.187053 0.982350i \(-0.440106\pi\)
\(264\) 0 0
\(265\) 6.01421i 0.369450i
\(266\) 4.23947 + 2.44766i 0.259938 + 0.150076i
\(267\) 0 0
\(268\) 6.33887i 0.387208i
\(269\) 13.3076 23.0494i 0.811379 1.40535i −0.100521 0.994935i \(-0.532051\pi\)
0.911899 0.410414i \(-0.134616\pi\)
\(270\) 0 0
\(271\) −16.9931 + 9.81095i −1.03225 + 0.595973i −0.917630 0.397436i \(-0.869900\pi\)
−0.114625 + 0.993409i \(0.536567\pi\)
\(272\) 5.56348 0.337335
\(273\) 0 0
\(274\) −7.24814 −0.437876
\(275\) 4.87023 2.81183i 0.293686 0.169560i
\(276\) 0 0
\(277\) 11.6675 20.2087i 0.701034 1.21423i −0.267070 0.963677i \(-0.586056\pi\)
0.968104 0.250549i \(-0.0806110\pi\)
\(278\) 15.7307i 0.943463i
\(279\) 0 0
\(280\) −1.08053 0.623842i −0.0645738 0.0372817i
\(281\) 21.2604i 1.26829i −0.773215 0.634143i \(-0.781353\pi\)
0.773215 0.634143i \(-0.218647\pi\)
\(282\) 0 0
\(283\) −9.32039 16.1434i −0.554039 0.959625i −0.997978 0.0635671i \(-0.979752\pi\)
0.443938 0.896057i \(-0.353581\pi\)
\(284\) 11.3538 6.55514i 0.673726 0.388976i
\(285\) 0 0
\(286\) −3.10889 + 5.00112i −0.183833 + 0.295723i
\(287\) 3.99790 0.235989
\(288\) 0 0
\(289\) −6.97614 12.0830i −0.410361 0.710767i
\(290\) −1.99611 + 3.45736i −0.117215 + 0.203023i
\(291\) 0 0
\(292\) −5.73577 3.31155i −0.335661 0.193794i
\(293\) −10.0804 5.81994i −0.588905 0.340004i 0.175760 0.984433i \(-0.443762\pi\)
−0.764664 + 0.644429i \(0.777095\pi\)
\(294\) 0 0
\(295\) 3.22904 5.59286i 0.188002 0.325629i
\(296\) 3.53663 + 6.12562i 0.205562 + 0.356044i
\(297\) 0 0
\(298\) 2.54638 0.147508
\(299\) 9.64202 + 18.0327i 0.557612 + 1.04286i
\(300\) 0 0
\(301\) 4.66057 2.69078i 0.268631 0.155094i
\(302\) −4.94718 8.56877i −0.284678 0.493077i
\(303\) 0 0
\(304\) 4.89532i 0.280766i
\(305\) −6.42400 3.70890i −0.367837 0.212371i
\(306\) 0 0
\(307\) 0.802209i 0.0457845i −0.999738 0.0228922i \(-0.992713\pi\)
0.999738 0.0228922i \(-0.00728747\pi\)
\(308\) 0.816612 1.41441i 0.0465308 0.0805936i
\(309\) 0 0
\(310\) 3.81494 2.20256i 0.216674 0.125097i
\(311\) −10.2961 −0.583838 −0.291919 0.956443i \(-0.594294\pi\)
−0.291919 + 0.956443i \(0.594294\pi\)
\(312\) 0 0
\(313\) −12.2030 −0.689752 −0.344876 0.938648i \(-0.612079\pi\)
−0.344876 + 0.938648i \(0.612079\pi\)
\(314\) −7.76317 + 4.48207i −0.438101 + 0.252938i
\(315\) 0 0
\(316\) −4.10558 + 7.11107i −0.230957 + 0.400029i
\(317\) 8.53952i 0.479627i 0.970819 + 0.239814i \(0.0770863\pi\)
−0.970819 + 0.239814i \(0.922914\pi\)
\(318\) 0 0
\(319\) −4.52570 2.61291i −0.253390 0.146295i
\(320\) 1.24768i 0.0697476i
\(321\) 0 0
\(322\) −2.83571 4.91159i −0.158028 0.273712i
\(323\) 23.5862 13.6175i 1.31237 0.757697i
\(324\) 0 0
\(325\) 12.4084 + 0.404405i 0.688292 + 0.0224324i
\(326\) −0.429374 −0.0237808
\(327\) 0 0
\(328\) 1.99895 + 3.46229i 0.110374 + 0.191173i
\(329\) −5.74902 + 9.95759i −0.316954 + 0.548980i
\(330\) 0 0
\(331\) 23.3998 + 13.5099i 1.28617 + 0.742571i 0.977969 0.208750i \(-0.0669396\pi\)
0.308202 + 0.951321i \(0.400273\pi\)
\(332\) 9.67531 + 5.58604i 0.531001 + 0.306574i
\(333\) 0 0
\(334\) 11.2625 19.5072i 0.616255 1.06739i
\(335\) −3.95445 6.84931i −0.216055 0.374218i
\(336\) 0 0
\(337\) 3.48883 0.190048 0.0950242 0.995475i \(-0.469707\pi\)
0.0950242 + 0.995475i \(0.469707\pi\)
\(338\) −11.6577 + 5.75314i −0.634094 + 0.312929i
\(339\) 0 0
\(340\) −6.01148 + 3.47073i −0.326018 + 0.188227i
\(341\) 2.88316 + 4.99377i 0.156132 + 0.270428i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 4.66057 + 2.69078i 0.251281 + 0.145077i
\(345\) 0 0
\(346\) 11.0112i 0.591968i
\(347\) 10.8293 18.7569i 0.581347 1.00692i −0.413973 0.910289i \(-0.635859\pi\)
0.995320 0.0966337i \(-0.0308075\pi\)
\(348\) 0 0
\(349\) 26.8664 15.5113i 1.43813 0.830303i 0.440407 0.897798i \(-0.354834\pi\)
0.997720 + 0.0674949i \(0.0215007\pi\)
\(350\) −3.44329 −0.184051
\(351\) 0 0
\(352\) 1.63322 0.0870511
\(353\) 25.8321 14.9142i 1.37491 0.793802i 0.383365 0.923597i \(-0.374765\pi\)
0.991541 + 0.129795i \(0.0414318\pi\)
\(354\) 0 0
\(355\) −8.17874 + 14.1660i −0.434083 + 0.751853i
\(356\) 2.49848i 0.132419i
\(357\) 0 0
\(358\) −1.90062 1.09732i −0.100451 0.0579954i
\(359\) 21.5254i 1.13607i 0.823006 + 0.568033i \(0.192295\pi\)
−0.823006 + 0.568033i \(0.807705\pi\)
\(360\) 0 0
\(361\) 2.48206 + 4.29905i 0.130635 + 0.226266i
\(362\) 4.17100 2.40813i 0.219223 0.126568i
\(363\) 0 0
\(364\) 3.17957 1.70011i 0.166655 0.0891098i
\(365\) 8.26353 0.432533
\(366\) 0 0
\(367\) −2.21213 3.83153i −0.115472 0.200004i 0.802496 0.596657i \(-0.203505\pi\)
−0.917969 + 0.396653i \(0.870172\pi\)
\(368\) 2.83571 4.91159i 0.147822 0.256035i
\(369\) 0 0
\(370\) −7.64283 4.41259i −0.397332 0.229400i
\(371\) −4.17451 2.41015i −0.216730 0.125129i
\(372\) 0 0
\(373\) 13.3688 23.1554i 0.692209 1.19894i −0.278903 0.960319i \(-0.589971\pi\)
0.971112 0.238622i \(-0.0766958\pi\)
\(374\) −4.54320 7.86905i −0.234923 0.406899i
\(375\) 0 0
\(376\) −11.4980 −0.592966
\(377\) −5.43983 10.1737i −0.280166 0.523970i
\(378\) 0 0
\(379\) −14.0198 + 8.09436i −0.720151 + 0.415780i −0.814808 0.579730i \(-0.803158\pi\)
0.0946571 + 0.995510i \(0.469825\pi\)
\(380\) −3.05390 5.28951i −0.156662 0.271346i
\(381\) 0 0
\(382\) 12.2643i 0.627496i
\(383\) 0.351106 + 0.202711i 0.0179407 + 0.0103580i 0.508944 0.860800i \(-0.330036\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(384\) 0 0
\(385\) 2.03775i 0.103853i
\(386\) 9.36349 16.2180i 0.476589 0.825477i
\(387\) 0 0
\(388\) 9.02271 5.20926i 0.458058 0.264460i
\(389\) 2.18998 0.111037 0.0555183 0.998458i \(-0.482319\pi\)
0.0555183 + 0.998458i \(0.482319\pi\)
\(390\) 0 0
\(391\) −31.5528 −1.59569
\(392\) −0.866025 + 0.500000i −0.0437409 + 0.0252538i
\(393\) 0 0
\(394\) −9.10832 + 15.7761i −0.458871 + 0.794787i
\(395\) 10.2449i 0.515478i
\(396\) 0 0
\(397\) −6.24673 3.60655i −0.313515 0.181008i 0.334984 0.942224i \(-0.391269\pi\)
−0.648498 + 0.761216i \(0.724603\pi\)
\(398\) 9.20785i 0.461548i
\(399\) 0 0
\(400\) −1.72164 2.98197i −0.0860821 0.149099i
\(401\) 2.39085 1.38036i 0.119393 0.0689318i −0.439114 0.898431i \(-0.644708\pi\)
0.558507 + 0.829500i \(0.311374\pi\)
\(402\) 0 0
\(403\) −0.414664 + 12.7231i −0.0206559 + 0.633784i
\(404\) −3.57045 −0.177636
\(405\) 0 0
\(406\) 1.59985 + 2.77102i 0.0793992 + 0.137524i
\(407\) 5.77610 10.0045i 0.286311 0.495905i
\(408\) 0 0
\(409\) 8.60545 + 4.96836i 0.425512 + 0.245670i 0.697433 0.716650i \(-0.254325\pi\)
−0.271921 + 0.962320i \(0.587659\pi\)
\(410\) −4.31984 2.49406i −0.213342 0.123173i
\(411\) 0 0
\(412\) 4.81905 8.34684i 0.237418 0.411219i
\(413\) −2.58803 4.48259i −0.127348 0.220574i
\(414\) 0 0
\(415\) −13.9392 −0.684249
\(416\) 3.06212 + 1.90353i 0.150133 + 0.0933283i
\(417\) 0 0
\(418\) 6.92400 3.99757i 0.338664 0.195528i
\(419\) 9.01445 + 15.6135i 0.440385 + 0.762769i 0.997718 0.0675201i \(-0.0215087\pi\)
−0.557333 + 0.830289i \(0.688175\pi\)
\(420\) 0 0
\(421\) 3.61265i 0.176070i −0.996117 0.0880348i \(-0.971941\pi\)
0.996117 0.0880348i \(-0.0280587\pi\)
\(422\) 3.76520 + 2.17384i 0.183287 + 0.105821i
\(423\) 0 0
\(424\) 4.82030i 0.234095i
\(425\) −9.57832 + 16.5901i −0.464617 + 0.804740i
\(426\) 0 0
\(427\) −5.14874 + 2.97263i −0.249165 + 0.143856i
\(428\) 4.36280 0.210884
\(429\) 0 0
\(430\) −6.71449 −0.323802
\(431\) 24.7893 14.3121i 1.19406 0.689389i 0.234833 0.972036i \(-0.424546\pi\)
0.959224 + 0.282646i \(0.0912122\pi\)
\(432\) 0 0
\(433\) 12.3338 21.3627i 0.592723 1.02663i −0.401141 0.916016i \(-0.631386\pi\)
0.993864 0.110610i \(-0.0352804\pi\)
\(434\) 3.53063i 0.169476i
\(435\) 0 0
\(436\) 16.7175 + 9.65186i 0.800623 + 0.462240i
\(437\) 27.7634i 1.32810i
\(438\) 0 0
\(439\) 7.13469 + 12.3576i 0.340520 + 0.589798i 0.984529 0.175219i \(-0.0560635\pi\)
−0.644009 + 0.765018i \(0.722730\pi\)
\(440\) −1.76474 + 1.01887i −0.0841306 + 0.0485729i
\(441\) 0 0
\(442\) 0.653416 20.0488i 0.0310799 0.953622i
\(443\) −32.2838 −1.53385 −0.766925 0.641736i \(-0.778214\pi\)
−0.766925 + 0.641736i \(0.778214\pi\)
\(444\) 0 0
\(445\) 1.55866 + 2.69968i 0.0738875 + 0.127977i
\(446\) 2.39655 4.15095i 0.113480 0.196553i
\(447\) 0 0
\(448\) −0.866025 0.500000i −0.0409159 0.0236228i
\(449\) −18.8020 10.8554i −0.887323 0.512296i −0.0142572 0.999898i \(-0.504538\pi\)
−0.873066 + 0.487602i \(0.837872\pi\)
\(450\) 0 0
\(451\) 3.26473 5.65469i 0.153730 0.266269i
\(452\) −4.73647 8.20380i −0.222785 0.385874i
\(453\) 0 0
\(454\) 5.44472 0.255533
\(455\) −2.37500 + 3.82055i −0.111342 + 0.179110i
\(456\) 0 0
\(457\) 2.41901 1.39662i 0.113156 0.0653309i −0.442354 0.896841i \(-0.645856\pi\)
0.555510 + 0.831510i \(0.312523\pi\)
\(458\) −7.54045 13.0604i −0.352342 0.610274i
\(459\) 0 0
\(460\) 7.07614i 0.329927i
\(461\) 12.4200 + 7.17070i 0.578458 + 0.333973i 0.760520 0.649314i \(-0.224944\pi\)
−0.182062 + 0.983287i \(0.558277\pi\)
\(462\) 0 0
\(463\) 38.1760i 1.77419i −0.461588 0.887095i \(-0.652720\pi\)
0.461588 0.887095i \(-0.347280\pi\)
\(464\) −1.59985 + 2.77102i −0.0742712 + 0.128641i
\(465\) 0 0
\(466\) −4.56841 + 2.63757i −0.211627 + 0.122183i
\(467\) −13.0228 −0.602622 −0.301311 0.953526i \(-0.597424\pi\)
−0.301311 + 0.953526i \(0.597424\pi\)
\(468\) 0 0
\(469\) −6.33887 −0.292702
\(470\) 12.4239 7.17295i 0.573073 0.330864i
\(471\) 0 0
\(472\) 2.58803 4.48259i 0.119124 0.206328i
\(473\) 8.78930i 0.404132i
\(474\) 0 0
\(475\) −14.5977 8.42799i −0.669788 0.386702i
\(476\) 5.56348i 0.255002i
\(477\) 0 0
\(478\) 14.5360 + 25.1772i 0.664863 + 1.15158i
\(479\) 17.5949 10.1584i 0.803932 0.464150i −0.0409123 0.999163i \(-0.513026\pi\)
0.844844 + 0.535012i \(0.179693\pi\)
\(480\) 0 0
\(481\) 22.4899 12.0253i 1.02545 0.548306i
\(482\) −29.4882 −1.34315
\(483\) 0 0
\(484\) 4.16629 + 7.21623i 0.189377 + 0.328010i
\(485\) −6.49951 + 11.2575i −0.295128 + 0.511176i
\(486\) 0 0
\(487\) −4.36922 2.52257i −0.197988 0.114309i 0.397728 0.917503i \(-0.369799\pi\)
−0.595717 + 0.803195i \(0.703132\pi\)
\(488\) −5.14874 2.97263i −0.233073 0.134565i
\(489\) 0 0
\(490\) 0.623842 1.08053i 0.0281823 0.0488132i
\(491\) −17.9099 31.0208i −0.808261 1.39995i −0.914067 0.405562i \(-0.867076\pi\)
0.105807 0.994387i \(-0.466258\pi\)
\(492\) 0 0
\(493\) 17.8015 0.801738
\(494\) 17.6409 + 0.574942i 0.793704 + 0.0258679i
\(495\) 0 0
\(496\) 3.05762 1.76532i 0.137291 0.0792651i
\(497\) 6.55514 + 11.3538i 0.294038 + 0.509289i
\(498\) 0 0
\(499\) 33.0174i 1.47806i −0.673670 0.739032i \(-0.735283\pi\)
0.673670 0.739032i \(-0.264717\pi\)
\(500\) 9.12319 + 5.26727i 0.408001 + 0.235560i
\(501\) 0 0
\(502\) 2.08792i 0.0931883i
\(503\) −3.46368 + 5.99927i −0.154438 + 0.267494i −0.932854 0.360254i \(-0.882690\pi\)
0.778416 + 0.627748i \(0.216023\pi\)
\(504\) 0 0
\(505\) 3.85796 2.22740i 0.171677 0.0991178i
\(506\) −9.26269 −0.411777
\(507\) 0 0
\(508\) 14.9534 0.663452
\(509\) 4.11620 2.37649i 0.182447 0.105336i −0.405995 0.913875i \(-0.633075\pi\)
0.588442 + 0.808539i \(0.299742\pi\)
\(510\) 0 0
\(511\) 3.31155 5.73577i 0.146494 0.253736i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 24.5763 + 14.1891i 1.08401 + 0.625856i
\(515\) 12.0253i 0.529898i
\(516\) 0 0
\(517\) 9.38943 + 16.2630i 0.412946 + 0.715244i
\(518\) −6.12562 + 3.53663i −0.269144 + 0.155390i
\(519\) 0 0
\(520\) −4.49620 0.146537i −0.197171 0.00642609i
\(521\) −0.0344780 −0.00151051 −0.000755255 1.00000i \(-0.500240\pi\)
−0.000755255 1.00000i \(0.500240\pi\)
\(522\) 0 0
\(523\) −1.60834 2.78573i −0.0703278 0.121811i 0.828717 0.559668i \(-0.189071\pi\)
−0.899045 + 0.437856i \(0.855738\pi\)
\(524\) −6.67729 + 11.5654i −0.291699 + 0.505237i
\(525\) 0 0
\(526\) 21.2695 + 12.2799i 0.927393 + 0.535431i
\(527\) −17.0110 9.82130i −0.741011 0.427823i
\(528\) 0 0
\(529\) −4.58250 + 7.93713i −0.199239 + 0.345093i
\(530\) 3.00711 + 5.20846i 0.130620 + 0.226241i
\(531\) 0 0
\(532\) −4.89532 −0.212239
\(533\) 12.7116 6.79686i 0.550600 0.294405i
\(534\) 0 0
\(535\) −4.71412 + 2.72170i −0.203809 + 0.117669i
\(536\) −3.16943 5.48962i −0.136899 0.237115i
\(537\) 0 0
\(538\) 26.6152i 1.14746i
\(539\) 1.41441 + 0.816612i 0.0609231 + 0.0351739i
\(540\) 0 0
\(541\) 41.4438i 1.78181i −0.454190 0.890905i \(-0.650071\pi\)
0.454190 0.890905i \(-0.349929\pi\)
\(542\) 9.81095 16.9931i 0.421416 0.729915i
\(543\) 0 0
\(544\) −4.81811 + 2.78174i −0.206575 + 0.119266i
\(545\) −24.0849 −1.03168
\(546\) 0 0
\(547\) −28.9393 −1.23736 −0.618678 0.785645i \(-0.712331\pi\)
−0.618678 + 0.785645i \(0.712331\pi\)
\(548\) 6.27707 3.62407i 0.268143 0.154813i
\(549\) 0 0
\(550\) −2.81183 + 4.87023i −0.119897 + 0.207667i
\(551\) 15.6635i 0.667289i
\(552\) 0 0
\(553\) −7.11107 4.10558i −0.302393 0.174587i
\(554\) 23.3350i 0.991411i
\(555\) 0 0
\(556\) −7.86534 13.6232i −0.333565 0.577751i
\(557\) 27.8019 16.0514i 1.17800 0.680121i 0.222453 0.974944i \(-0.428594\pi\)
0.955552 + 0.294822i \(0.0952604\pi\)
\(558\) 0 0
\(559\) 10.2440 16.4790i 0.433274 0.696987i
\(560\) 1.24768 0.0527243
\(561\) 0 0
\(562\) 10.6302 + 18.4120i 0.448407 + 0.776664i
\(563\) −1.79857 + 3.11521i −0.0758006 + 0.131291i −0.901434 0.432916i \(-0.857485\pi\)
0.825634 + 0.564207i \(0.190818\pi\)
\(564\) 0 0
\(565\) 10.2357 + 5.90961i 0.430621 + 0.248619i
\(566\) 16.1434 + 9.32039i 0.678557 + 0.391765i
\(567\) 0 0
\(568\) −6.55514 + 11.3538i −0.275048 + 0.476396i
\(569\) −18.3294 31.7474i −0.768407 1.33092i −0.938426 0.345480i \(-0.887716\pi\)
0.170019 0.985441i \(-0.445617\pi\)
\(570\) 0 0
\(571\) −47.5969 −1.99187 −0.995934 0.0900902i \(-0.971284\pi\)
−0.995934 + 0.0900902i \(0.971284\pi\)
\(572\) 0.191818 5.88554i 0.00802031 0.246087i
\(573\) 0 0
\(574\) −3.46229 + 1.99895i −0.144513 + 0.0834346i
\(575\) 9.76416 + 16.9120i 0.407194 + 0.705280i
\(576\) 0 0
\(577\) 25.7012i 1.06996i 0.844866 + 0.534978i \(0.179680\pi\)
−0.844866 + 0.534978i \(0.820320\pi\)
\(578\) 12.0830 + 6.97614i 0.502588 + 0.290169i
\(579\) 0 0
\(580\) 3.99221i 0.165768i
\(581\) −5.58604 + 9.67531i −0.231748 + 0.401399i
\(582\) 0 0
\(583\) −6.81790 + 3.93632i −0.282368 + 0.163026i
\(584\) 6.62310 0.274066
\(585\) 0 0
\(586\) 11.6399 0.480839
\(587\) 25.7531 14.8686i 1.06294 0.613691i 0.136699 0.990613i \(-0.456351\pi\)
0.926245 + 0.376921i \(0.123017\pi\)
\(588\) 0 0
\(589\) 8.64179 14.9680i 0.356079 0.616746i
\(590\) 6.45808i 0.265875i
\(591\) 0 0
\(592\) −6.12562 3.53663i −0.251761 0.145354i
\(593\) 38.5870i 1.58458i 0.610146 + 0.792289i \(0.291111\pi\)
−0.610146 + 0.792289i \(0.708889\pi\)
\(594\) 0 0
\(595\) −3.47073 6.01148i −0.142286 0.246447i
\(596\) −2.20523 + 1.27319i −0.0903297 + 0.0521519i
\(597\) 0 0
\(598\) −17.3666 10.7957i −0.710171 0.441470i
\(599\) −24.8717 −1.01623 −0.508114 0.861290i \(-0.669657\pi\)
−0.508114 + 0.861290i \(0.669657\pi\)
\(600\) 0 0
\(601\) −1.82588 3.16252i −0.0744792 0.129002i 0.826380 0.563112i \(-0.190396\pi\)
−0.900860 + 0.434110i \(0.857063\pi\)
\(602\) −2.69078 + 4.66057i −0.109668 + 0.189951i
\(603\) 0 0
\(604\) 8.56877 + 4.94718i 0.348658 + 0.201298i
\(605\) −9.00357 5.19821i −0.366047 0.211337i
\(606\) 0 0
\(607\) −8.01855 + 13.8885i −0.325463 + 0.563718i −0.981606 0.190918i \(-0.938853\pi\)
0.656143 + 0.754636i \(0.272187\pi\)
\(608\) −2.44766 4.23947i −0.0992656 0.171933i
\(609\) 0 0
\(610\) 7.41780 0.300338
\(611\) −1.35041 + 41.4347i −0.0546319 + 1.67627i
\(612\) 0 0
\(613\) 16.1663 9.33363i 0.652952 0.376982i −0.136635 0.990622i \(-0.543629\pi\)
0.789586 + 0.613640i \(0.210295\pi\)
\(614\) 0.401105 + 0.694734i 0.0161873 + 0.0280372i
\(615\) 0 0
\(616\) 1.63322i 0.0658044i
\(617\) −15.3613 8.86883i −0.618422 0.357046i 0.157833 0.987466i \(-0.449549\pi\)
−0.776254 + 0.630420i \(0.782883\pi\)
\(618\) 0 0
\(619\) 25.3244i 1.01787i 0.860804 + 0.508937i \(0.169961\pi\)
−0.860804 + 0.508937i \(0.830039\pi\)
\(620\) −2.20256 + 3.81494i −0.0884568 + 0.153212i
\(621\) 0 0
\(622\) 8.91668 5.14805i 0.357526 0.206418i
\(623\) 2.49848 0.100100
\(624\) 0 0
\(625\) 4.07265 0.162906
\(626\) 10.5681 6.10148i 0.422385 0.243864i
\(627\) 0 0
\(628\) 4.48207 7.76317i 0.178854 0.309784i
\(629\) 39.3519i 1.56906i
\(630\) 0 0
\(631\) −3.68116 2.12532i −0.146545 0.0846075i 0.424935 0.905224i \(-0.360297\pi\)
−0.571479 + 0.820616i \(0.693630\pi\)
\(632\) 8.21115i 0.326622i
\(633\) 0 0
\(634\) −4.26976 7.39544i −0.169574 0.293710i
\(635\) −16.1576 + 9.32858i −0.641194 + 0.370194i
\(636\) 0 0
\(637\) 1.70011 + 3.17957i 0.0673607 + 0.125979i
\(638\) 5.22582 0.206892
\(639\) 0 0
\(640\) 0.623842 + 1.08053i 0.0246595 + 0.0427115i
\(641\) −17.2678 + 29.9086i −0.682036 + 1.18132i 0.292323 + 0.956320i \(0.405572\pi\)
−0.974359 + 0.225001i \(0.927762\pi\)
\(642\) 0 0
\(643\) −8.67586 5.00901i −0.342143 0.197536i 0.319077 0.947729i \(-0.396627\pi\)
−0.661219 + 0.750193i \(0.729961\pi\)
\(644\) 4.91159 + 2.83571i 0.193544 + 0.111743i
\(645\) 0 0
\(646\) −13.6175 + 23.5862i −0.535773 + 0.927986i
\(647\) −7.91081 13.7019i −0.311006 0.538678i 0.667574 0.744543i \(-0.267333\pi\)
−0.978580 + 0.205865i \(0.933999\pi\)
\(648\) 0 0
\(649\) −8.45365 −0.331835
\(650\) −10.9482 + 5.85395i −0.429422 + 0.229611i
\(651\) 0 0
\(652\) 0.371849 0.214687i 0.0145627 0.00840779i
\(653\) 5.37123 + 9.30325i 0.210193 + 0.364064i 0.951775 0.306798i \(-0.0992576\pi\)
−0.741582 + 0.670862i \(0.765924\pi\)
\(654\) 0 0
\(655\) 16.6623i 0.651050i
\(656\) −3.46229 1.99895i −0.135180 0.0780460i
\(657\) 0 0
\(658\) 11.4980i 0.448240i
\(659\) 8.19715 14.1979i 0.319315 0.553071i −0.661030 0.750360i \(-0.729880\pi\)
0.980345 + 0.197289i \(0.0632137\pi\)
\(660\) 0 0
\(661\) −16.7580 + 9.67522i −0.651809 + 0.376322i −0.789149 0.614202i \(-0.789478\pi\)
0.137340 + 0.990524i \(0.456145\pi\)
\(662\) −27.0198 −1.05015
\(663\) 0 0
\(664\) −11.1721 −0.433561
\(665\) 5.28951 3.05390i 0.205119 0.118425i
\(666\) 0 0
\(667\) 9.07342 15.7156i 0.351324 0.608512i
\(668\) 22.5249i 0.871516i
\(669\) 0 0
\(670\) 6.84931 + 3.95445i 0.264612 + 0.152774i
\(671\) 9.70993i 0.374848i
\(672\) 0 0
\(673\) 11.4635 + 19.8553i 0.441884 + 0.765366i 0.997829 0.0658530i \(-0.0209768\pi\)
−0.555945 + 0.831219i \(0.687643\pi\)
\(674\) −3.02141 + 1.74441i −0.116380 + 0.0671923i
\(675\) 0 0
\(676\) 7.21928 10.8112i 0.277664 0.415815i
\(677\) 22.8391 0.877776 0.438888 0.898542i \(-0.355372\pi\)
0.438888 + 0.898542i \(0.355372\pi\)
\(678\) 0 0
\(679\) 5.20926 + 9.02271i 0.199913 + 0.346260i
\(680\) 3.47073 6.01148i 0.133096 0.230530i
\(681\) 0 0
\(682\) −4.99377 2.88316i −0.191222 0.110402i
\(683\) 6.52984 + 3.77001i 0.249857 + 0.144255i 0.619699 0.784840i \(-0.287255\pi\)
−0.369842 + 0.929095i \(0.620588\pi\)
\(684\) 0 0
\(685\) −4.52169 + 7.83180i −0.172765 + 0.299238i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −5.38157 −0.205170
\(689\) −17.3706 0.566133i −0.661768 0.0215679i
\(690\) 0 0
\(691\) 22.6929 13.1017i 0.863278 0.498414i −0.00183036 0.999998i \(-0.500583\pi\)
0.865109 + 0.501584i \(0.167249\pi\)
\(692\) 5.50562 + 9.53601i 0.209292 + 0.362505i
\(693\) 0 0
\(694\) 21.6586i 0.822149i
\(695\) 16.9974 + 9.81345i 0.644748 + 0.372245i
\(696\) 0 0
\(697\) 22.2422i 0.842485i
\(698\) −15.5113 + 26.8664i −0.587113 + 1.01691i
\(699\) 0 0
\(700\) 2.98197 1.72164i 0.112708 0.0650720i
\(701\) 37.4467 1.41434 0.707171 0.707043i \(-0.249971\pi\)
0.707171 + 0.707043i \(0.249971\pi\)
\(702\) 0 0
\(703\) −34.6258 −1.30594
\(704\) −1.41441 + 0.816612i −0.0533077 + 0.0307772i
\(705\) 0 0
\(706\) −14.9142 + 25.8321i −0.561303 + 0.972205i
\(707\) 3.57045i 0.134281i
\(708\) 0 0
\(709\) −29.1468 16.8279i −1.09463 0.631986i −0.159826 0.987145i \(-0.551093\pi\)
−0.934806 + 0.355159i \(0.884427\pi\)
\(710\) 16.3575i 0.613885i
\(711\) 0 0
\(712\) 1.24924 + 2.16375i 0.0468173 + 0.0810900i
\(713\) −17.3410 + 10.0119i −0.649427 + 0.374947i
\(714\) 0 0
\(715\) 3.46438 + 6.47915i 0.129561 + 0.242306i
\(716\) 2.19465 0.0820179
\(717\) 0 0
\(718\) −10.7627 18.6415i −0.401660 0.695695i
\(719\) −10.7899 + 18.6887i −0.402396 + 0.696971i −0.994015 0.109247i \(-0.965156\pi\)
0.591618 + 0.806218i \(0.298489\pi\)
\(720\) 0 0
\(721\) 8.34684 + 4.81905i 0.310853 + 0.179471i
\(722\) −4.29905 2.48206i −0.159994 0.0923726i
\(723\) 0 0
\(724\) −2.40813 + 4.17100i −0.0894973 + 0.155014i
\(725\) −5.50874 9.54142i −0.204590 0.354359i
\(726\) 0 0
\(727\) 26.5309 0.983978 0.491989 0.870601i \(-0.336270\pi\)
0.491989 + 0.870601i \(0.336270\pi\)
\(728\) −1.90353 + 3.06212i −0.0705496 + 0.113490i
\(729\) 0 0
\(730\) −7.15643 + 4.13177i −0.264871 + 0.152924i
\(731\) 14.9701 + 25.9290i 0.553690 + 0.959019i
\(732\) 0 0
\(733\) 15.0423i 0.555599i −0.960639 0.277799i \(-0.910395\pi\)
0.960639 0.277799i \(-0.0896050\pi\)
\(734\) 3.83153 + 2.21213i 0.141424 + 0.0816514i
\(735\) 0 0
\(736\) 5.67142i 0.209051i
\(737\) −5.17639 + 8.96577i −0.190675 + 0.330258i
\(738\) 0 0
\(739\) −13.1481 + 7.59105i −0.483660 + 0.279241i −0.721941 0.691955i \(-0.756750\pi\)
0.238280 + 0.971196i \(0.423416\pi\)
\(740\) 8.82518 0.324420
\(741\) 0 0
\(742\) 4.82030 0.176959
\(743\) 31.1626 17.9917i 1.14324 0.660052i 0.196012 0.980602i \(-0.437201\pi\)
0.947232 + 0.320550i \(0.103868\pi\)
\(744\) 0 0
\(745\) 1.58854 2.75143i 0.0581995 0.100804i
\(746\) 26.7376i 0.978932i
\(747\) 0 0
\(748\) 7.86905 + 4.54320i 0.287721 + 0.166116i
\(749\) 4.36280i 0.159413i
\(750\) 0 0
\(751\) 8.91824 + 15.4468i 0.325431 + 0.563663i 0.981599 0.190951i \(-0.0611573\pi\)
−0.656168 + 0.754614i \(0.727824\pi\)
\(752\) 9.95759 5.74902i 0.363116 0.209645i
\(753\) 0 0
\(754\) 9.79786 + 6.09073i 0.356817 + 0.221811i
\(755\) −12.3450 −0.449282
\(756\) 0 0
\(757\) 0.850916 + 1.47383i 0.0309271 + 0.0535673i 0.881075 0.472977i \(-0.156821\pi\)
−0.850148 + 0.526544i \(0.823487\pi\)
\(758\) 8.09436 14.0198i 0.294001 0.509224i
\(759\) 0 0
\(760\) 5.28951 + 3.05390i 0.191871 + 0.110777i
\(761\) 13.2906 + 7.67330i 0.481782 + 0.278157i 0.721159 0.692770i \(-0.243610\pi\)
−0.239377 + 0.970927i \(0.576943\pi\)
\(762\) 0 0
\(763\) −9.65186 + 16.7175i −0.349421 + 0.605214i
\(764\) −6.13215 10.6212i −0.221854 0.384262i
\(765\) 0 0
\(766\) −0.405422 −0.0146485
\(767\) −15.8497 9.85278i −0.572299 0.355763i
\(768\) 0 0
\(769\) −19.5852 + 11.3075i −0.706259 + 0.407759i −0.809674 0.586880i \(-0.800356\pi\)
0.103415 + 0.994638i \(0.467023\pi\)
\(770\) −1.01887 1.76474i −0.0367176 0.0635968i
\(771\) 0 0
\(772\) 18.7270i 0.673999i
\(773\) 37.9606 + 21.9166i 1.36535 + 0.788285i 0.990330 0.138732i \(-0.0443028\pi\)
0.375019 + 0.927017i \(0.377636\pi\)
\(774\) 0 0
\(775\) 12.1570i 0.436692i
\(776\) −5.20926 + 9.02271i −0.187002 + 0.323896i
\(777\) 0 0
\(778\) −1.89658 + 1.09499i −0.0679957 + 0.0392573i
\(779\) −19.5710 −0.701204
\(780\) 0 0
\(781\) 21.4120 0.766182
\(782\) 27.3255 15.7764i 0.977159 0.564163i
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.0178571 0.0309295i
\(785\) 11.1844i 0.399189i
\(786\) 0 0
\(787\) 0.630664 + 0.364114i 0.0224808 + 0.0129793i 0.511198 0.859463i \(-0.329202\pi\)
−0.488718 + 0.872442i \(0.662535\pi\)
\(788\) 18.2166i 0.648941i
\(789\) 0 0
\(790\) 5.12246 + 8.87236i 0.182249 + 0.315665i
\(791\) 8.20380 4.73647i 0.291694 0.168409i
\(792\) 0 0
\(793\) −11.3170 + 18.2051i −0.401878 + 0.646481i
\(794\) 7.21311 0.255984
\(795\) 0 0
\(796\) 4.60392 + 7.97423i 0.163182 + 0.282639i
\(797\) −19.4943 + 33.7652i −0.690525 + 1.19602i 0.281142 + 0.959666i \(0.409287\pi\)
−0.971666 + 0.236357i \(0.924046\pi\)
\(798\) 0 0
\(799\) −55.3988 31.9845i −1.95987 1.13153i
\(800\) 2.98197 + 1.72164i 0.105429 + 0.0608693i
\(801\) 0 0
\(802\) −1.38036 + 2.39085i −0.0487421 + 0.0844238i
\(803\) −5.40850 9.36780i −0.190862 0.330582i
\(804\) 0 0
\(805\) −7.07614 −0.249401
\(806\) −6.00245 11.2259i −0.211427 0.395415i
\(807\) 0 0
\(808\) 3.09210 1.78522i 0.108780 0.0628040i
\(809\) 13.9625 + 24.1838i 0.490895 + 0.850256i 0.999945 0.0104813i \(-0.00333635\pi\)
−0.509050 + 0.860737i \(0.670003\pi\)
\(810\) 0 0
\(811\) 16.8777i 0.592655i 0.955086 + 0.296327i \(0.0957619\pi\)
−0.955086 + 0.296327i \(0.904238\pi\)
\(812\) −2.77102 1.59985i −0.0972438 0.0561437i
\(813\) 0 0
\(814\) 11.5522i 0.404904i
\(815\) −0.267861 + 0.463950i −0.00938278 + 0.0162514i
\(816\) 0 0
\(817\) −22.8150 + 13.1722i −0.798195 + 0.460838i
\(818\) −9.93672 −0.347429
\(819\) 0 0
\(820\) 4.98812 0.174193
\(821\) −37.6774 + 21.7531i −1.31495 + 0.759187i −0.982912 0.184078i \(-0.941070\pi\)
−0.332039 + 0.943266i \(0.607737\pi\)
\(822\) 0 0
\(823\) 12.0681 20.9025i 0.420667 0.728617i −0.575338 0.817916i \(-0.695129\pi\)
0.996005 + 0.0892992i \(0.0284627\pi\)
\(824\) 9.63810i 0.335759i
\(825\) 0 0
\(826\) 4.48259 + 2.58803i 0.155969 + 0.0900490i
\(827\) 23.2109i 0.807121i −0.914953 0.403560i \(-0.867773\pi\)
0.914953 0.403560i \(-0.132227\pi\)
\(828\) 0 0
\(829\) 0.0392158 + 0.0679238i 0.00136202 + 0.00235909i 0.866706 0.498820i \(-0.166233\pi\)
−0.865344 + 0.501179i \(0.832900\pi\)
\(830\) 12.0717 6.96961i 0.419016 0.241919i
\(831\) 0 0
\(832\) −3.60364 0.117447i −0.124934 0.00407176i
\(833\) −5.56348 −0.192763
\(834\) 0 0
\(835\) −14.0520 24.3388i −0.486290 0.842278i
\(836\) −3.99757 + 6.92400i −0.138259 + 0.239471i
\(837\) 0 0
\(838\) −15.6135 9.01445i −0.539359 0.311399i
\(839\) −41.7182 24.0860i −1.44027 0.831541i −0.442404 0.896816i \(-0.645874\pi\)
−0.997867 + 0.0652750i \(0.979208\pi\)
\(840\) 0 0
\(841\) 9.38096 16.2483i 0.323481 0.560286i
\(842\) 1.80632 + 3.12864i 0.0622500 + 0.107820i
\(843\) 0 0
\(844\) −4.34768 −0.149653
\(845\) −1.05613 + 16.1855i −0.0363321 + 0.556797i
\(846\) 0 0
\(847\) −7.21623 + 4.16629i −0.247953 + 0.143155i
\(848\) 2.41015 + 4.17451i 0.0827649 + 0.143353i
\(849\) 0 0
\(850\) 19.1566i 0.657067i
\(851\) 34.7410 + 20.0577i 1.19090 + 0.687569i
\(852\) 0 0
\(853\) 38.8560i 1.33040i −0.746664 0.665201i \(-0.768346\pi\)
0.746664 0.665201i \(-0.231654\pi\)
\(854\) 2.97263 5.14874i 0.101721 0.176186i
\(855\) 0 0
\(856\) −3.77830 + 2.18140i −0.129140 + 0.0745588i
\(857\) −27.1368 −0.926974 −0.463487 0.886104i \(-0.653402\pi\)
−0.463487 + 0.886104i \(0.653402\pi\)
\(858\) 0 0
\(859\) −13.1359 −0.448191 −0.224096 0.974567i \(-0.571943\pi\)
−0.224096 + 0.974567i \(0.571943\pi\)
\(860\) 5.81492 3.35725i 0.198287 0.114481i
\(861\) 0 0
\(862\) −14.3121 + 24.7893i −0.487472 + 0.844326i
\(863\) 5.98646i 0.203781i −0.994796 0.101891i \(-0.967511\pi\)
0.994796 0.101891i \(-0.0324892\pi\)
\(864\) 0 0
\(865\) −11.8979 6.86927i −0.404542 0.233562i
\(866\) 24.6675i 0.838237i
\(867\) 0 0
\(868\) 1.76532 + 3.05762i 0.0599188 + 0.103782i
\(869\) −11.6140 + 6.70532i −0.393977 + 0.227463i
\(870\) 0 0
\(871\) −20.1548 + 10.7767i −0.682921 + 0.365156i
\(872\) −19.3037 −0.653706
\(873\) 0 0
\(874\) 13.8817 + 24.0438i 0.469555 + 0.813294i
\(875\) −5.26727 + 9.12319i −0.178066 + 0.308420i
\(876\) 0 0
\(877\) −2.51170 1.45013i −0.0848142 0.0489675i 0.456993 0.889470i \(-0.348926\pi\)
−0.541807 + 0.840503i \(0.682260\pi\)
\(878\) −12.3576 7.13469i −0.417050 0.240784i
\(879\) 0 0
\(880\) 1.01887 1.76474i 0.0343462 0.0594894i
\(881\) 28.6722 + 49.6617i 0.965991 + 1.67315i 0.706928 + 0.707285i \(0.250080\pi\)
0.259063 + 0.965860i \(0.416586\pi\)
\(882\) 0 0
\(883\) −31.5545 −1.06189 −0.530947 0.847405i \(-0.678164\pi\)
−0.530947 + 0.847405i \(0.678164\pi\)
\(884\) 9.45850 + 17.6894i 0.318124 + 0.594960i
\(885\) 0 0
\(886\) 27.9586 16.1419i 0.939288 0.542298i
\(887\) −5.63687 9.76335i −0.189268 0.327821i 0.755739 0.654873i \(-0.227278\pi\)
−0.945006 + 0.327052i \(0.893945\pi\)
\(888\) 0 0
\(889\) 14.9534i 0.501522i
\(890\) −2.69968 1.55866i −0.0904934 0.0522464i
\(891\) 0 0
\(892\) 4.79311i 0.160485i
\(893\) 28.1432 48.7455i 0.941778 1.63121i
\(894\) 0 0
\(895\) −2.37137 + 1.36911i −0.0792663 + 0.0457644i
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 21.7107 0.724496
\(899\) 9.78347 5.64849i 0.326297 0.188388i
\(900\) 0 0
\(901\) 13.4088 23.2248i 0.446713 0.773729i
\(902\) 6.52947i 0.217408i
\(903\) 0 0
\(904\) 8.20380 + 4.73647i 0.272854 + 0.157532i
\(905\) 6.00916i 0.199751i
\(906\) 0 0
\(907\) 23.5237 + 40.7443i 0.781092 + 1.35289i 0.931306 + 0.364238i \(0.118670\pi\)
−0.150214 + 0.988654i \(0.547996\pi\)
\(908\) −4.71526 + 2.72236i −0.156481 + 0.0903446i
\(909\) 0 0
\(910\) 0.146537 4.49620i 0.00485766 0.149048i
\(911\) 8.82281 0.292313 0.146156 0.989261i \(-0.453310\pi\)
0.146156 + 0.989261i \(0.453310\pi\)
\(912\) 0 0
\(913\) 9.12325 + 15.8019i 0.301936 + 0.522968i
\(914\) −1.39662 + 2.41901i −0.0461959 + 0.0800137i
\(915\) 0 0
\(916\) 13.0604 + 7.54045i 0.431529 + 0.249143i
\(917\) −11.5654 6.67729i −0.381923 0.220504i
\(918\) 0 0
\(919\) 13.6953 23.7209i 0.451765 0.782481i −0.546730 0.837309i \(-0.684128\pi\)
0.998496 + 0.0548280i \(0.0174611\pi\)
\(920\) −3.53807 6.12812i −0.116647 0.202038i
\(921\) 0 0
\(922\) −14.3414 −0.472309
\(923\) 40.1452 + 24.9558i 1.32140 + 0.821431i
\(924\) 0 0
\(925\) 21.0923 12.1776i 0.693509 0.400398i
\(926\) 19.0880 + 33.0614i 0.627271 + 1.08646i
\(927\) 0 0
\(928\) 3.19970i 0.105035i
\(929\) −5.78441 3.33963i −0.189780 0.109570i 0.402099 0.915596i \(-0.368281\pi\)
−0.591880 + 0.806026i \(0.701614\pi\)
\(930\) 0 0
\(931\) 4.89532i 0.160437i
\(932\) 2.63757 4.56841i 0.0863966 0.149643i
\(933\) 0 0
\(934\) 11.2780 6.51138i 0.369029 0.213059i
\(935\) −11.3370 −0.370758
\(936\) 0 0
\(937\) −29.8852 −0.976307 −0.488153 0.872758i \(-0.662329\pi\)
−0.488153 + 0.872758i \(0.662329\pi\)
\(938\) 5.48962 3.16943i 0.179242 0.103486i
\(939\) 0 0
\(940\) −7.17295 + 12.4239i −0.233956 + 0.405224i
\(941\) 50.3008i 1.63976i 0.572537 + 0.819879i \(0.305959\pi\)
−0.572537 + 0.819879i \(0.694041\pi\)
\(942\) 0 0
\(943\) 19.6361 + 11.3369i 0.639439 + 0.369180i
\(944\) 5.17605i 0.168466i
\(945\) 0 0
\(946\) 4.39465 + 7.61176i 0.142882 + 0.247480i
\(947\) 18.6830 10.7866i 0.607116 0.350519i −0.164720 0.986340i \(-0.552672\pi\)
0.771836 + 0.635822i \(0.219339\pi\)
\(948\) 0 0
\(949\) 0.777866 23.8673i 0.0252506 0.774764i
\(950\) 16.8560 0.546880
\(951\) 0 0
\(952\) −2.78174 4.81811i −0.0901567 0.156156i
\(953\) 5.75014 9.95953i 0.186265 0.322621i −0.757737 0.652560i \(-0.773695\pi\)
0.944002 + 0.329939i \(0.107028\pi\)
\(954\) 0 0
\(955\) 13.2519 + 7.65099i 0.428821 + 0.247580i
\(956\) −25.1772 14.5360i −0.814288 0.470129i
\(957\) 0 0
\(958\) −10.1584 + 17.5949i −0.328204 + 0.568466i
\(959\) 3.62407 + 6.27707i 0.117027 + 0.202697i
\(960\) 0 0
\(961\) 18.5346 0.597891
\(962\) −13.4642 + 21.6591i −0.434102 + 0.698319i
\(963\) 0 0
\(964\) 25.5375 14.7441i 0.822509 0.474876i
\(965\) −11.6827 20.2350i −0.376079 0.651387i
\(966\) 0 0
\(967\) 3.86045i 0.124144i −0.998072 0.0620719i \(-0.980229\pi\)
0.998072 0.0620719i \(-0.0197708\pi\)
\(968\) −7.21623 4.16629i −0.231938 0.133910i
\(969\) 0 0
\(970\) 12.9990i 0.417373i
\(971\) 1.67410 2.89962i 0.0537243 0.0930532i −0.837913 0.545805i \(-0.816224\pi\)
0.891637 + 0.452751i \(0.149557\pi\)
\(972\) 0 0
\(973\) 13.6232 7.86534i 0.436739 0.252151i
\(974\) 5.04515 0.161657
\(975\) 0 0
\(976\) 5.94526 0.190303
\(977\) 40.4030 23.3267i 1.29261 0.746287i 0.313492 0.949591i \(-0.398501\pi\)
0.979116 + 0.203304i \(0.0651679\pi\)
\(978\) 0 0
\(979\) 2.04029 3.53389i 0.0652080 0.112944i
\(980\) 1.24768i 0.0398558i
\(981\) 0 0
\(982\) 31.0208 + 17.9099i 0.989913 + 0.571527i
\(983\) 35.4073i 1.12932i 0.825324 + 0.564659i \(0.190992\pi\)
−0.825324 + 0.564659i \(0.809008\pi\)
\(984\) 0 0
\(985\) 11.3643 + 19.6835i 0.362097 + 0.627170i
\(986\) −15.4165 + 8.90073i −0.490962 + 0.283457i
\(987\) 0 0
\(988\) −15.5650 + 8.32256i −0.495188 + 0.264776i
\(989\) 30.5211 0.970516
\(990\) 0 0
\(991\) 3.95560 + 6.85131i 0.125654 + 0.217639i 0.921988 0.387218i \(-0.126564\pi\)
−0.796334 + 0.604857i \(0.793230\pi\)
\(992\) −1.76532 + 3.05762i −0.0560489 + 0.0970795i
\(993\) 0 0
\(994\) −11.3538 6.55514i −0.360122 0.207916i
\(995\) −9.94932 5.74424i −0.315415 0.182105i
\(996\) 0 0
\(997\) 24.5503 42.5223i 0.777515 1.34669i −0.155855 0.987780i \(-0.549813\pi\)
0.933370 0.358915i \(-0.116853\pi\)
\(998\) 16.5087 + 28.5939i 0.522574 + 0.905125i
\(999\) 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.bj.h.127.3 16
3.2 odd 2 1638.2.bj.i.127.6 yes 16
13.4 even 6 inner 1638.2.bj.h.1135.2 yes 16
39.17 odd 6 1638.2.bj.i.1135.7 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1638.2.bj.h.127.3 16 1.1 even 1 trivial
1638.2.bj.h.1135.2 yes 16 13.4 even 6 inner
1638.2.bj.i.127.6 yes 16 3.2 odd 2
1638.2.bj.i.1135.7 yes 16 39.17 odd 6