Properties

Label 819.2.fm.f.496.8
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
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] = [819,2,Mod(370,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.370");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.8
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.f.748.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.16866 + 0.581092i) q^{2} +(2.63339 + 1.52039i) q^{4} +(1.87790 + 1.87790i) q^{5} +(2.25300 + 1.38707i) q^{7} +(1.65230 + 1.65230i) q^{8} +O(q^{10})\) \(q+(2.16866 + 0.581092i) q^{2} +(2.63339 + 1.52039i) q^{4} +(1.87790 + 1.87790i) q^{5} +(2.25300 + 1.38707i) q^{7} +(1.65230 + 1.65230i) q^{8} +(2.98130 + 5.16377i) q^{10} +(1.20979 - 4.51499i) q^{11} +(-1.52548 - 3.26694i) q^{13} +(4.07999 + 4.31730i) q^{14} +(-0.417624 - 0.723346i) q^{16} +(-2.18729 + 3.78849i) q^{17} +(-0.194491 + 0.0521138i) q^{19} +(2.09010 + 7.80037i) q^{20} +(5.24724 - 9.08849i) q^{22} +(-7.20237 + 4.15829i) q^{23} +2.05302i q^{25} +(-1.40986 - 7.97134i) q^{26} +(3.82414 + 7.07814i) q^{28} +(5.20380 + 9.01325i) q^{29} +(-6.75799 - 6.75799i) q^{31} +(-1.69492 - 6.32554i) q^{32} +(-6.94495 + 6.94495i) q^{34} +(1.62613 + 6.83570i) q^{35} +(1.22755 - 4.58128i) q^{37} -0.452070 q^{38} +6.20572i q^{40} +(-0.136339 + 0.508825i) q^{41} +(2.49507 + 1.44053i) q^{43} +(10.0504 - 10.0504i) q^{44} +(-18.0359 + 4.83270i) q^{46} +(-0.928461 + 0.928461i) q^{47} +(3.15206 + 6.25016i) q^{49} +(-1.19299 + 4.45231i) q^{50} +(0.949833 - 10.9224i) q^{52} -1.95082 q^{53} +(10.7506 - 6.20683i) q^{55} +(1.43078 + 6.01451i) q^{56} +(6.04777 + 22.5706i) q^{58} +(-1.76081 - 6.57142i) q^{59} +(2.13306 + 1.23152i) q^{61} +(-10.7288 - 18.5828i) q^{62} -13.0324i q^{64} +(3.27029 - 8.99969i) q^{65} +(-1.40878 - 0.377482i) q^{67} +(-11.5199 + 6.65104i) q^{68} +(-0.445637 + 15.7693i) q^{70} +(1.44014 + 5.37468i) q^{71} +(8.75032 - 8.75032i) q^{73} +(5.32429 - 9.22194i) q^{74} +(-0.591404 - 0.158466i) q^{76} +(8.98827 - 8.49422i) q^{77} -4.46495 q^{79} +(0.574115 - 2.14263i) q^{80} +(-0.591348 + 1.02425i) q^{82} +(5.42187 + 5.42187i) q^{83} +(-11.2219 + 3.00690i) q^{85} +(4.57389 + 4.57389i) q^{86} +(9.45905 - 5.46119i) q^{88} +(-15.0461 - 4.03159i) q^{89} +(1.09457 - 9.47639i) q^{91} -25.2888 q^{92} +(-2.55304 + 1.47400i) q^{94} +(-0.463100 - 0.267371i) q^{95} +(-2.84925 + 0.763454i) q^{97} +(3.20383 + 15.3861i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.16866 + 0.581092i 1.53348 + 0.410894i 0.924152 0.382026i \(-0.124774\pi\)
0.609326 + 0.792920i \(0.291440\pi\)
\(3\) 0 0
\(4\) 2.63339 + 1.52039i 1.31669 + 0.760193i
\(5\) 1.87790 + 1.87790i 0.839823 + 0.839823i 0.988835 0.149013i \(-0.0476095\pi\)
−0.149013 + 0.988835i \(0.547610\pi\)
\(6\) 0 0
\(7\) 2.25300 + 1.38707i 0.851556 + 0.524264i
\(8\) 1.65230 + 1.65230i 0.584177 + 0.584177i
\(9\) 0 0
\(10\) 2.98130 + 5.16377i 0.942771 + 1.63293i
\(11\) 1.20979 4.51499i 0.364764 1.36132i −0.502975 0.864301i \(-0.667761\pi\)
0.867740 0.497019i \(-0.165572\pi\)
\(12\) 0 0
\(13\) −1.52548 3.26694i −0.423092 0.906087i
\(14\) 4.07999 + 4.31730i 1.09042 + 1.15385i
\(15\) 0 0
\(16\) −0.417624 0.723346i −0.104406 0.180836i
\(17\) −2.18729 + 3.78849i −0.530495 + 0.918845i 0.468872 + 0.883266i \(0.344661\pi\)
−0.999367 + 0.0355783i \(0.988673\pi\)
\(18\) 0 0
\(19\) −0.194491 + 0.0521138i −0.0446194 + 0.0119557i −0.281060 0.959690i \(-0.590686\pi\)
0.236440 + 0.971646i \(0.424019\pi\)
\(20\) 2.09010 + 7.80037i 0.467361 + 1.74422i
\(21\) 0 0
\(22\) 5.24724 9.08849i 1.11872 1.93767i
\(23\) −7.20237 + 4.15829i −1.50180 + 0.867064i −0.501801 + 0.864983i \(0.667329\pi\)
−0.999998 + 0.00208060i \(0.999338\pi\)
\(24\) 0 0
\(25\) 2.05302i 0.410604i
\(26\) −1.40986 7.97134i −0.276497 1.56331i
\(27\) 0 0
\(28\) 3.82414 + 7.07814i 0.722695 + 1.33764i
\(29\) 5.20380 + 9.01325i 0.966322 + 1.67372i 0.706022 + 0.708190i \(0.250488\pi\)
0.260300 + 0.965528i \(0.416179\pi\)
\(30\) 0 0
\(31\) −6.75799 6.75799i −1.21377 1.21377i −0.969777 0.243995i \(-0.921542\pi\)
−0.243995 0.969777i \(-0.578458\pi\)
\(32\) −1.69492 6.32554i −0.299623 1.11821i
\(33\) 0 0
\(34\) −6.94495 + 6.94495i −1.19105 + 1.19105i
\(35\) 1.62613 + 6.83570i 0.274866 + 1.15544i
\(36\) 0 0
\(37\) 1.22755 4.58128i 0.201808 0.753158i −0.788591 0.614919i \(-0.789189\pi\)
0.990399 0.138240i \(-0.0441444\pi\)
\(38\) −0.452070 −0.0733354
\(39\) 0 0
\(40\) 6.20572i 0.981210i
\(41\) −0.136339 + 0.508825i −0.0212926 + 0.0794651i −0.975755 0.218867i \(-0.929764\pi\)
0.954462 + 0.298333i \(0.0964304\pi\)
\(42\) 0 0
\(43\) 2.49507 + 1.44053i 0.380494 + 0.219678i 0.678033 0.735031i \(-0.262832\pi\)
−0.297539 + 0.954710i \(0.596166\pi\)
\(44\) 10.0504 10.0504i 1.51515 1.51515i
\(45\) 0 0
\(46\) −18.0359 + 4.83270i −2.65925 + 0.712543i
\(47\) −0.928461 + 0.928461i −0.135430 + 0.135430i −0.771572 0.636142i \(-0.780529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(48\) 0 0
\(49\) 3.15206 + 6.25016i 0.450294 + 0.892881i
\(50\) −1.19299 + 4.45231i −0.168715 + 0.629651i
\(51\) 0 0
\(52\) 0.949833 10.9224i 0.131718 1.51467i
\(53\) −1.95082 −0.267966 −0.133983 0.990984i \(-0.542777\pi\)
−0.133983 + 0.990984i \(0.542777\pi\)
\(54\) 0 0
\(55\) 10.7506 6.20683i 1.44960 0.836929i
\(56\) 1.43078 + 6.01451i 0.191196 + 0.803722i
\(57\) 0 0
\(58\) 6.04777 + 22.5706i 0.794111 + 2.96366i
\(59\) −1.76081 6.57142i −0.229237 0.855526i −0.980662 0.195707i \(-0.937300\pi\)
0.751425 0.659819i \(-0.229367\pi\)
\(60\) 0 0
\(61\) 2.13306 + 1.23152i 0.273111 + 0.157681i 0.630300 0.776351i \(-0.282932\pi\)
−0.357190 + 0.934032i \(0.616265\pi\)
\(62\) −10.7288 18.5828i −1.36256 2.36002i
\(63\) 0 0
\(64\) 13.0324i 1.62905i
\(65\) 3.27029 8.99969i 0.405630 1.11627i
\(66\) 0 0
\(67\) −1.40878 0.377482i −0.172110 0.0461168i 0.171735 0.985143i \(-0.445063\pi\)
−0.343845 + 0.939026i \(0.611729\pi\)
\(68\) −11.5199 + 6.65104i −1.39700 + 0.806558i
\(69\) 0 0
\(70\) −0.445637 + 15.7693i −0.0532638 + 1.88479i
\(71\) 1.44014 + 5.37468i 0.170913 + 0.637857i 0.997212 + 0.0746244i \(0.0237758\pi\)
−0.826299 + 0.563232i \(0.809558\pi\)
\(72\) 0 0
\(73\) 8.75032 8.75032i 1.02415 1.02415i 0.0244465 0.999701i \(-0.492218\pi\)
0.999701 0.0244465i \(-0.00778234\pi\)
\(74\) 5.32429 9.22194i 0.618936 1.07203i
\(75\) 0 0
\(76\) −0.591404 0.158466i −0.0678387 0.0181773i
\(77\) 8.98827 8.49422i 1.02431 0.968006i
\(78\) 0 0
\(79\) −4.46495 −0.502346 −0.251173 0.967942i \(-0.580816\pi\)
−0.251173 + 0.967942i \(0.580816\pi\)
\(80\) 0.574115 2.14263i 0.0641880 0.239553i
\(81\) 0 0
\(82\) −0.591348 + 1.02425i −0.0653035 + 0.113109i
\(83\) 5.42187 + 5.42187i 0.595128 + 0.595128i 0.939012 0.343884i \(-0.111743\pi\)
−0.343884 + 0.939012i \(0.611743\pi\)
\(84\) 0 0
\(85\) −11.2219 + 3.00690i −1.21719 + 0.326145i
\(86\) 4.57389 + 4.57389i 0.493215 + 0.493215i
\(87\) 0 0
\(88\) 9.45905 5.46119i 1.00834 0.582164i
\(89\) −15.0461 4.03159i −1.59488 0.427347i −0.651390 0.758743i \(-0.725814\pi\)
−0.943492 + 0.331396i \(0.892480\pi\)
\(90\) 0 0
\(91\) 1.09457 9.47639i 0.114742 0.993395i
\(92\) −25.2888 −2.63654
\(93\) 0 0
\(94\) −2.55304 + 1.47400i −0.263326 + 0.152031i
\(95\) −0.463100 0.267371i −0.0475131 0.0274317i
\(96\) 0 0
\(97\) −2.84925 + 0.763454i −0.289297 + 0.0775170i −0.400549 0.916275i \(-0.631181\pi\)
0.111252 + 0.993792i \(0.464514\pi\)
\(98\) 3.20383 + 15.3861i 0.323636 + 1.55423i
\(99\) 0 0
\(100\) −3.12138 + 5.40639i −0.312138 + 0.540639i
\(101\) −0.316767 0.548657i −0.0315195 0.0545934i 0.849835 0.527048i \(-0.176701\pi\)
−0.881355 + 0.472455i \(0.843368\pi\)
\(102\) 0 0
\(103\) 1.95716 0.192845 0.0964223 0.995341i \(-0.469260\pi\)
0.0964223 + 0.995341i \(0.469260\pi\)
\(104\) 2.87742 7.91853i 0.282154 0.776475i
\(105\) 0 0
\(106\) −4.23068 1.13361i −0.410920 0.110106i
\(107\) 3.59988 + 6.23517i 0.348013 + 0.602777i 0.985896 0.167357i \(-0.0535231\pi\)
−0.637883 + 0.770133i \(0.720190\pi\)
\(108\) 0 0
\(109\) −2.42207 + 2.42207i −0.231992 + 0.231992i −0.813524 0.581531i \(-0.802454\pi\)
0.581531 + 0.813524i \(0.302454\pi\)
\(110\) 26.9211 7.21348i 2.56682 0.687778i
\(111\) 0 0
\(112\) 0.0624252 2.20898i 0.00589863 0.208729i
\(113\) −0.379755 + 0.657754i −0.0357243 + 0.0618763i −0.883335 0.468743i \(-0.844707\pi\)
0.847610 + 0.530619i \(0.178040\pi\)
\(114\) 0 0
\(115\) −21.3342 5.71648i −1.98942 0.533065i
\(116\) 31.6471i 2.93836i
\(117\) 0 0
\(118\) 15.2744i 1.40612i
\(119\) −10.1829 + 5.50156i −0.933464 + 0.504327i
\(120\) 0 0
\(121\) −9.39523 5.42434i −0.854112 0.493122i
\(122\) 3.91027 + 3.91027i 0.354019 + 0.354019i
\(123\) 0 0
\(124\) −7.52164 28.0712i −0.675464 2.52086i
\(125\) 5.53414 5.53414i 0.494988 0.494988i
\(126\) 0 0
\(127\) −1.04032 + 0.600626i −0.0923131 + 0.0532970i −0.545446 0.838146i \(-0.683640\pi\)
0.453133 + 0.891443i \(0.350306\pi\)
\(128\) 4.18317 15.6118i 0.369743 1.37990i
\(129\) 0 0
\(130\) 12.3218 17.6170i 1.08069 1.54511i
\(131\) 3.03417i 0.265097i −0.991177 0.132548i \(-0.957684\pi\)
0.991177 0.132548i \(-0.0423160\pi\)
\(132\) 0 0
\(133\) −0.510476 0.152361i −0.0442639 0.0132114i
\(134\) −2.83582 1.63726i −0.244978 0.141438i
\(135\) 0 0
\(136\) −9.87379 + 2.64567i −0.846671 + 0.226865i
\(137\) 11.2793 3.02227i 0.963654 0.258210i 0.257508 0.966276i \(-0.417099\pi\)
0.706146 + 0.708066i \(0.250432\pi\)
\(138\) 0 0
\(139\) 5.80746 + 3.35294i 0.492582 + 0.284393i 0.725645 0.688069i \(-0.241541\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(140\) −6.11067 + 20.4734i −0.516446 + 1.73032i
\(141\) 0 0
\(142\) 12.4927i 1.04837i
\(143\) −16.5957 + 2.93522i −1.38780 + 0.245455i
\(144\) 0 0
\(145\) −7.15376 + 26.6982i −0.594087 + 2.21716i
\(146\) 24.0612 13.8918i 1.99132 1.14969i
\(147\) 0 0
\(148\) 10.1979 10.1979i 0.838265 0.838265i
\(149\) 1.23932 + 4.62521i 0.101529 + 0.378912i 0.997928 0.0643356i \(-0.0204928\pi\)
−0.896399 + 0.443248i \(0.853826\pi\)
\(150\) 0 0
\(151\) −7.66300 7.66300i −0.623606 0.623606i 0.322845 0.946452i \(-0.395361\pi\)
−0.946452 + 0.322845i \(0.895361\pi\)
\(152\) −0.407466 0.235251i −0.0330499 0.0190814i
\(153\) 0 0
\(154\) 24.4285 13.1981i 1.96850 1.06353i
\(155\) 25.3817i 2.03870i
\(156\) 0 0
\(157\) 8.00601i 0.638949i 0.947595 + 0.319475i \(0.103506\pi\)
−0.947595 + 0.319475i \(0.896494\pi\)
\(158\) −9.68297 2.59455i −0.770336 0.206411i
\(159\) 0 0
\(160\) 8.69584 15.0616i 0.687467 1.19073i
\(161\) −21.9948 0.621570i −1.73344 0.0489865i
\(162\) 0 0
\(163\) 18.3794 4.92475i 1.43959 0.385736i 0.547199 0.837003i \(-0.315694\pi\)
0.892389 + 0.451266i \(0.149028\pi\)
\(164\) −1.13264 + 1.13264i −0.0884447 + 0.0884447i
\(165\) 0 0
\(166\) 8.60761 + 14.9088i 0.668080 + 1.15715i
\(167\) −10.5127 2.81688i −0.813500 0.217977i −0.171997 0.985097i \(-0.555022\pi\)
−0.641503 + 0.767121i \(0.721689\pi\)
\(168\) 0 0
\(169\) −8.34582 + 9.96731i −0.641986 + 0.766716i
\(170\) −26.0839 −2.00054
\(171\) 0 0
\(172\) 4.38032 + 7.58693i 0.333996 + 0.578498i
\(173\) −4.07283 + 7.05435i −0.309651 + 0.536332i −0.978286 0.207259i \(-0.933546\pi\)
0.668635 + 0.743591i \(0.266879\pi\)
\(174\) 0 0
\(175\) −2.84769 + 4.62546i −0.215265 + 0.349652i
\(176\) −3.77113 + 1.01047i −0.284260 + 0.0761672i
\(177\) 0 0
\(178\) −30.2872 17.4863i −2.27012 1.31065i
\(179\) −10.2340 + 5.90863i −0.764928 + 0.441631i −0.831062 0.556179i \(-0.812267\pi\)
0.0661342 + 0.997811i \(0.478933\pi\)
\(180\) 0 0
\(181\) −10.4995 −0.780423 −0.390212 0.920725i \(-0.627598\pi\)
−0.390212 + 0.920725i \(0.627598\pi\)
\(182\) 7.88041 19.9151i 0.584135 1.47620i
\(183\) 0 0
\(184\) −18.7712 5.02974i −1.38383 0.370797i
\(185\) 10.9084 6.29797i 0.802002 0.463036i
\(186\) 0 0
\(187\) 14.4588 + 14.4588i 1.05734 + 1.05734i
\(188\) −3.85661 + 1.03338i −0.281272 + 0.0753667i
\(189\) 0 0
\(190\) −0.848942 0.848942i −0.0615887 0.0615887i
\(191\) 6.67464 11.5608i 0.482960 0.836511i −0.516849 0.856077i \(-0.672895\pi\)
0.999809 + 0.0195655i \(0.00622830\pi\)
\(192\) 0 0
\(193\) −2.08783 + 7.79189i −0.150285 + 0.560872i 0.849178 + 0.528107i \(0.177098\pi\)
−0.999463 + 0.0327652i \(0.989569\pi\)
\(194\) −6.62270 −0.475482
\(195\) 0 0
\(196\) −1.20208 + 21.2514i −0.0858631 + 1.51796i
\(197\) 12.2629 + 3.28585i 0.873699 + 0.234107i 0.667686 0.744443i \(-0.267285\pi\)
0.206012 + 0.978549i \(0.433951\pi\)
\(198\) 0 0
\(199\) 10.8366 18.7696i 0.768188 1.33054i −0.170356 0.985383i \(-0.554492\pi\)
0.938544 0.345158i \(-0.112175\pi\)
\(200\) −3.39221 + 3.39221i −0.239865 + 0.239865i
\(201\) 0 0
\(202\) −0.368142 1.37392i −0.0259024 0.0966689i
\(203\) −0.777849 + 27.5249i −0.0545943 + 1.93187i
\(204\) 0 0
\(205\) −1.21155 + 0.699491i −0.0846186 + 0.0488546i
\(206\) 4.24442 + 1.13729i 0.295723 + 0.0792387i
\(207\) 0 0
\(208\) −1.72605 + 2.46780i −0.119680 + 0.171111i
\(209\) 0.941173i 0.0651023i
\(210\) 0 0
\(211\) 6.50914 + 11.2742i 0.448108 + 0.776145i 0.998263 0.0589170i \(-0.0187647\pi\)
−0.550155 + 0.835062i \(0.685431\pi\)
\(212\) −5.13727 2.96601i −0.352829 0.203706i
\(213\) 0 0
\(214\) 4.18372 + 15.6138i 0.285993 + 1.06734i
\(215\) 1.98032 + 7.39066i 0.135057 + 0.504039i
\(216\) 0 0
\(217\) −5.85195 24.5996i −0.397257 1.66993i
\(218\) −6.66011 + 3.84521i −0.451079 + 0.260431i
\(219\) 0 0
\(220\) 37.7471 2.54491
\(221\) 15.7135 + 1.36647i 1.05700 + 0.0919186i
\(222\) 0 0
\(223\) 4.38178 16.3530i 0.293426 1.09508i −0.649034 0.760759i \(-0.724827\pi\)
0.942460 0.334320i \(-0.108507\pi\)
\(224\) 4.95532 16.6025i 0.331091 1.10930i
\(225\) 0 0
\(226\) −1.20578 + 1.20578i −0.0802070 + 0.0802070i
\(227\) 18.2910 4.90106i 1.21402 0.325295i 0.405679 0.914015i \(-0.367035\pi\)
0.808336 + 0.588721i \(0.200368\pi\)
\(228\) 0 0
\(229\) −0.181433 + 0.181433i −0.0119894 + 0.0119894i −0.713076 0.701087i \(-0.752699\pi\)
0.701087 + 0.713076i \(0.252699\pi\)
\(230\) −42.9449 24.7943i −2.83170 1.63488i
\(231\) 0 0
\(232\) −6.29435 + 23.4909i −0.413245 + 1.54225i
\(233\) 11.3848i 0.745842i 0.927863 + 0.372921i \(0.121644\pi\)
−0.927863 + 0.372921i \(0.878356\pi\)
\(234\) 0 0
\(235\) −3.48711 −0.227474
\(236\) 5.35421 19.9822i 0.348529 1.30073i
\(237\) 0 0
\(238\) −25.2802 + 6.01385i −1.63867 + 0.389820i
\(239\) 12.2181 12.2181i 0.790322 0.790322i −0.191224 0.981546i \(-0.561246\pi\)
0.981546 + 0.191224i \(0.0612458\pi\)
\(240\) 0 0
\(241\) 7.89185 + 29.4528i 0.508359 + 1.89722i 0.436254 + 0.899824i \(0.356305\pi\)
0.0721047 + 0.997397i \(0.477028\pi\)
\(242\) −17.2231 17.2231i −1.10714 1.10714i
\(243\) 0 0
\(244\) 3.74479 + 6.48616i 0.239735 + 0.415234i
\(245\) −5.81794 + 17.6564i −0.371694 + 1.12803i
\(246\) 0 0
\(247\) 0.466946 + 0.555894i 0.0297111 + 0.0353707i
\(248\) 22.3325i 1.41811i
\(249\) 0 0
\(250\) 15.2175 8.78584i 0.962441 0.555666i
\(251\) 5.46171 9.45996i 0.344740 0.597107i −0.640566 0.767903i \(-0.721300\pi\)
0.985307 + 0.170795i \(0.0546337\pi\)
\(252\) 0 0
\(253\) 10.0613 + 37.5493i 0.632548 + 2.36070i
\(254\) −2.60511 + 0.698038i −0.163459 + 0.0437988i
\(255\) 0 0
\(256\) 5.11138 8.85317i 0.319461 0.553323i
\(257\) 14.2035 + 24.6012i 0.885991 + 1.53458i 0.844574 + 0.535439i \(0.179854\pi\)
0.0414174 + 0.999142i \(0.486813\pi\)
\(258\) 0 0
\(259\) 9.12025 8.61895i 0.566705 0.535555i
\(260\) 22.2949 18.7276i 1.38267 1.16143i
\(261\) 0 0
\(262\) 1.76313 6.58009i 0.108927 0.406520i
\(263\) −10.8579 18.8064i −0.669526 1.15965i −0.978037 0.208433i \(-0.933164\pi\)
0.308510 0.951221i \(-0.400170\pi\)
\(264\) 0 0
\(265\) −3.66345 3.66345i −0.225044 0.225044i
\(266\) −1.01851 0.627054i −0.0624491 0.0384471i
\(267\) 0 0
\(268\) −3.13595 3.13595i −0.191559 0.191559i
\(269\) −10.7149 6.18625i −0.653298 0.377182i 0.136420 0.990651i \(-0.456440\pi\)
−0.789719 + 0.613469i \(0.789774\pi\)
\(270\) 0 0
\(271\) −7.64449 2.04834i −0.464370 0.124427i 0.0190456 0.999819i \(-0.493937\pi\)
−0.483415 + 0.875391i \(0.660604\pi\)
\(272\) 3.65385 0.221547
\(273\) 0 0
\(274\) 26.2172 1.58384
\(275\) 9.26935 + 2.48371i 0.558963 + 0.149774i
\(276\) 0 0
\(277\) 9.70888 + 5.60543i 0.583350 + 0.336797i 0.762464 0.647031i \(-0.223990\pi\)
−0.179113 + 0.983828i \(0.557323\pi\)
\(278\) 10.6461 + 10.6461i 0.638509 + 0.638509i
\(279\) 0 0
\(280\) −8.60778 + 13.9815i −0.514413 + 0.835555i
\(281\) 15.1948 + 15.1948i 0.906448 + 0.906448i 0.995984 0.0895355i \(-0.0285383\pi\)
−0.0895355 + 0.995984i \(0.528538\pi\)
\(282\) 0 0
\(283\) 7.64747 + 13.2458i 0.454595 + 0.787382i 0.998665 0.0516583i \(-0.0164507\pi\)
−0.544070 + 0.839040i \(0.683117\pi\)
\(284\) −4.37914 + 16.3432i −0.259854 + 0.969789i
\(285\) 0 0
\(286\) −37.6961 3.27812i −2.22902 0.193839i
\(287\) −1.01295 + 0.957272i −0.0597926 + 0.0565060i
\(288\) 0 0
\(289\) −1.06845 1.85062i −0.0628502 0.108860i
\(290\) −31.0282 + 53.7424i −1.82204 + 3.15586i
\(291\) 0 0
\(292\) 36.3468 9.73911i 2.12704 0.569938i
\(293\) −5.44000 20.3023i −0.317808 1.18608i −0.921347 0.388742i \(-0.872910\pi\)
0.603539 0.797334i \(-0.293757\pi\)
\(294\) 0 0
\(295\) 9.03385 15.6471i 0.525971 0.911009i
\(296\) 9.59795 5.54138i 0.557869 0.322086i
\(297\) 0 0
\(298\) 10.7507i 0.622771i
\(299\) 24.5720 + 17.1863i 1.42103 + 0.993912i
\(300\) 0 0
\(301\) 3.62328 + 6.70636i 0.208842 + 0.386548i
\(302\) −12.1656 21.0714i −0.700050 1.21252i
\(303\) 0 0
\(304\) 0.118921 + 0.118921i 0.00682057 + 0.00682057i
\(305\) 1.69300 + 6.31836i 0.0969409 + 0.361788i
\(306\) 0 0
\(307\) −12.7905 + 12.7905i −0.729995 + 0.729995i −0.970618 0.240624i \(-0.922648\pi\)
0.240624 + 0.970618i \(0.422648\pi\)
\(308\) 36.5841 8.70292i 2.08457 0.495895i
\(309\) 0 0
\(310\) 14.7491 55.0443i 0.837692 3.12631i
\(311\) 19.5517 1.10868 0.554338 0.832292i \(-0.312972\pi\)
0.554338 + 0.832292i \(0.312972\pi\)
\(312\) 0 0
\(313\) 13.2495i 0.748904i 0.927246 + 0.374452i \(0.122169\pi\)
−0.927246 + 0.374452i \(0.877831\pi\)
\(314\) −4.65223 + 17.3624i −0.262540 + 0.979814i
\(315\) 0 0
\(316\) −11.7579 6.78845i −0.661435 0.381880i
\(317\) −17.8861 + 17.8861i −1.00458 + 1.00458i −0.00459262 + 0.999989i \(0.501462\pi\)
−0.999989 + 0.00459262i \(0.998538\pi\)
\(318\) 0 0
\(319\) 46.9902 12.5910i 2.63094 0.704959i
\(320\) 24.4735 24.4735i 1.36811 1.36811i
\(321\) 0 0
\(322\) −47.3382 14.1290i −2.63806 0.787378i
\(323\) 0.227976 0.850818i 0.0126849 0.0473408i
\(324\) 0 0
\(325\) 6.70709 3.13184i 0.372043 0.173723i
\(326\) 42.7206 2.36607
\(327\) 0 0
\(328\) −1.06601 + 0.615459i −0.0588603 + 0.0339830i
\(329\) −3.37967 + 0.803983i −0.186327 + 0.0443250i
\(330\) 0 0
\(331\) −3.51837 13.1307i −0.193387 0.721731i −0.992678 0.120787i \(-0.961458\pi\)
0.799291 0.600944i \(-0.205208\pi\)
\(332\) 6.03454 + 22.5212i 0.331189 + 1.23601i
\(333\) 0 0
\(334\) −21.1617 12.2177i −1.15792 0.668524i
\(335\) −1.93668 3.35443i −0.105812 0.183272i
\(336\) 0 0
\(337\) 1.75678i 0.0956980i 0.998855 + 0.0478490i \(0.0152366\pi\)
−0.998855 + 0.0478490i \(0.984763\pi\)
\(338\) −23.8912 + 16.7661i −1.29951 + 0.911954i
\(339\) 0 0
\(340\) −34.1233 9.14331i −1.85060 0.495866i
\(341\) −38.6880 + 22.3365i −2.09507 + 1.20959i
\(342\) 0 0
\(343\) −1.56784 + 18.4538i −0.0846554 + 0.996410i
\(344\) 1.74242 + 6.50279i 0.0939449 + 0.350607i
\(345\) 0 0
\(346\) −12.9318 + 12.9318i −0.695219 + 0.695219i
\(347\) −5.43920 + 9.42098i −0.291992 + 0.505744i −0.974281 0.225338i \(-0.927651\pi\)
0.682289 + 0.731083i \(0.260985\pi\)
\(348\) 0 0
\(349\) −11.9450 3.20064i −0.639399 0.171326i −0.0754676 0.997148i \(-0.524045\pi\)
−0.563931 + 0.825822i \(0.690712\pi\)
\(350\) −8.86349 + 8.37630i −0.473774 + 0.447732i
\(351\) 0 0
\(352\) −30.6102 −1.63153
\(353\) −4.55715 + 17.0075i −0.242552 + 0.905218i 0.732045 + 0.681256i \(0.238566\pi\)
−0.974598 + 0.223962i \(0.928101\pi\)
\(354\) 0 0
\(355\) −7.38867 + 12.7975i −0.392150 + 0.679223i
\(356\) −33.4926 33.4926i −1.77510 1.77510i
\(357\) 0 0
\(358\) −25.6277 + 6.86691i −1.35446 + 0.362927i
\(359\) −11.4993 11.4993i −0.606911 0.606911i 0.335227 0.942137i \(-0.391187\pi\)
−0.942137 + 0.335227i \(0.891187\pi\)
\(360\) 0 0
\(361\) −16.4194 + 9.47973i −0.864177 + 0.498933i
\(362\) −22.7699 6.10119i −1.19676 0.320671i
\(363\) 0 0
\(364\) 17.2902 23.2908i 0.906253 1.22077i
\(365\) 32.8645 1.72020
\(366\) 0 0
\(367\) −11.3884 + 6.57510i −0.594470 + 0.343217i −0.766863 0.641811i \(-0.778183\pi\)
0.172393 + 0.985028i \(0.444850\pi\)
\(368\) 6.01577 + 3.47320i 0.313594 + 0.181053i
\(369\) 0 0
\(370\) 27.3164 7.31940i 1.42011 0.380518i
\(371\) −4.39522 2.70594i −0.228188 0.140485i
\(372\) 0 0
\(373\) 4.81532 8.34037i 0.249328 0.431848i −0.714012 0.700134i \(-0.753124\pi\)
0.963339 + 0.268286i \(0.0864571\pi\)
\(374\) 22.9545 + 39.7583i 1.18695 + 2.05585i
\(375\) 0 0
\(376\) −3.06819 −0.158230
\(377\) 21.5075 30.7500i 1.10769 1.58371i
\(378\) 0 0
\(379\) −32.1516 8.61500i −1.65152 0.442523i −0.691481 0.722395i \(-0.743041\pi\)
−0.960037 + 0.279872i \(0.909708\pi\)
\(380\) −0.813014 1.40818i −0.0417068 0.0722382i
\(381\) 0 0
\(382\) 21.1930 21.1930i 1.08433 1.08433i
\(383\) 3.73221 1.00004i 0.190707 0.0510998i −0.162201 0.986758i \(-0.551859\pi\)
0.352908 + 0.935658i \(0.385193\pi\)
\(384\) 0 0
\(385\) 32.8304 + 0.927780i 1.67319 + 0.0472840i
\(386\) −9.05560 + 15.6848i −0.460918 + 0.798334i
\(387\) 0 0
\(388\) −8.66392 2.32149i −0.439844 0.117856i
\(389\) 12.5816i 0.637911i 0.947770 + 0.318955i \(0.103332\pi\)
−0.947770 + 0.318955i \(0.896668\pi\)
\(390\) 0 0
\(391\) 36.3815i 1.83989i
\(392\) −5.11901 + 15.5353i −0.258549 + 0.784651i
\(393\) 0 0
\(394\) 24.6848 + 14.2518i 1.24360 + 0.717995i
\(395\) −8.38473 8.38473i −0.421881 0.421881i
\(396\) 0 0
\(397\) −6.87160 25.6452i −0.344876 1.28709i −0.892757 0.450538i \(-0.851232\pi\)
0.547882 0.836556i \(-0.315434\pi\)
\(398\) 34.4079 34.4079i 1.72471 1.72471i
\(399\) 0 0
\(400\) 1.48504 0.857390i 0.0742521 0.0428695i
\(401\) 3.89519 14.5370i 0.194517 0.725946i −0.797875 0.602823i \(-0.794043\pi\)
0.992391 0.123123i \(-0.0392908\pi\)
\(402\) 0 0
\(403\) −11.7688 + 32.3872i −0.586245 + 1.61332i
\(404\) 1.92643i 0.0958437i
\(405\) 0 0
\(406\) −17.6814 + 59.2403i −0.877514 + 2.94005i
\(407\) −19.1994 11.0848i −0.951676 0.549451i
\(408\) 0 0
\(409\) 23.9970 6.42996i 1.18657 0.317941i 0.389042 0.921220i \(-0.372806\pi\)
0.797531 + 0.603279i \(0.206139\pi\)
\(410\) −3.03392 + 0.812937i −0.149835 + 0.0401481i
\(411\) 0 0
\(412\) 5.15395 + 2.97564i 0.253917 + 0.146599i
\(413\) 5.14793 17.2478i 0.253313 0.848709i
\(414\) 0 0
\(415\) 20.3635i 0.999603i
\(416\) −18.0796 + 15.1867i −0.886426 + 0.744590i
\(417\) 0 0
\(418\) −0.546908 + 2.04109i −0.0267501 + 0.0998329i
\(419\) −15.5289 + 8.96562i −0.758637 + 0.437999i −0.828806 0.559536i \(-0.810979\pi\)
0.0701691 + 0.997535i \(0.477646\pi\)
\(420\) 0 0
\(421\) 0.833811 0.833811i 0.0406375 0.0406375i −0.686496 0.727134i \(-0.740852\pi\)
0.727134 + 0.686496i \(0.240852\pi\)
\(422\) 7.56482 + 28.2323i 0.368250 + 1.37433i
\(423\) 0 0
\(424\) −3.22335 3.22335i −0.156540 0.156540i
\(425\) −7.77785 4.49054i −0.377281 0.217823i
\(426\) 0 0
\(427\) 3.09758 + 5.73334i 0.149903 + 0.277456i
\(428\) 21.8928i 1.05823i
\(429\) 0 0
\(430\) 17.1786i 0.828426i
\(431\) −13.4572 3.60584i −0.648209 0.173687i −0.0802899 0.996772i \(-0.525585\pi\)
−0.567919 + 0.823085i \(0.692251\pi\)
\(432\) 0 0
\(433\) −0.380141 + 0.658423i −0.0182684 + 0.0316418i −0.875015 0.484096i \(-0.839149\pi\)
0.856747 + 0.515737i \(0.172482\pi\)
\(434\) 1.60371 56.7488i 0.0769806 2.72403i
\(435\) 0 0
\(436\) −10.0607 + 2.69577i −0.481822 + 0.129104i
\(437\) 1.18410 1.18410i 0.0566430 0.0566430i
\(438\) 0 0
\(439\) 15.9560 + 27.6366i 0.761539 + 1.31902i 0.942057 + 0.335453i \(0.108889\pi\)
−0.180518 + 0.983572i \(0.557777\pi\)
\(440\) 28.0187 + 7.50759i 1.33574 + 0.357910i
\(441\) 0 0
\(442\) 33.2832 + 12.0944i 1.58312 + 0.575270i
\(443\) −13.9082 −0.660799 −0.330399 0.943841i \(-0.607183\pi\)
−0.330399 + 0.943841i \(0.607183\pi\)
\(444\) 0 0
\(445\) −20.6841 35.8260i −0.980522 1.69831i
\(446\) 19.0052 32.9180i 0.899923 1.55871i
\(447\) 0 0
\(448\) 18.0769 29.3620i 0.854052 1.38723i
\(449\) −37.3413 + 10.0056i −1.76224 + 0.472192i −0.987169 0.159677i \(-0.948955\pi\)
−0.775075 + 0.631869i \(0.782288\pi\)
\(450\) 0 0
\(451\) 2.13240 + 1.23114i 0.100411 + 0.0579721i
\(452\) −2.00008 + 1.15475i −0.0940759 + 0.0543148i
\(453\) 0 0
\(454\) 42.5150 1.99533
\(455\) 19.8512 15.7402i 0.930639 0.737912i
\(456\) 0 0
\(457\) −11.2913 3.02549i −0.528183 0.141526i −0.0151341 0.999885i \(-0.504818\pi\)
−0.513049 + 0.858359i \(0.671484\pi\)
\(458\) −0.498897 + 0.288038i −0.0233119 + 0.0134591i
\(459\) 0 0
\(460\) −47.4899 47.4899i −2.21423 2.21423i
\(461\) −33.0727 + 8.86180i −1.54035 + 0.412735i −0.926379 0.376594i \(-0.877095\pi\)
−0.613971 + 0.789329i \(0.710429\pi\)
\(462\) 0 0
\(463\) −18.1263 18.1263i −0.842399 0.842399i 0.146772 0.989170i \(-0.453112\pi\)
−0.989170 + 0.146772i \(0.953112\pi\)
\(464\) 4.34646 7.52830i 0.201780 0.349492i
\(465\) 0 0
\(466\) −6.61561 + 24.6898i −0.306462 + 1.14373i
\(467\) 20.4427 0.945975 0.472988 0.881069i \(-0.343176\pi\)
0.472988 + 0.881069i \(0.343176\pi\)
\(468\) 0 0
\(469\) −2.65040 2.80455i −0.122384 0.129502i
\(470\) −7.56238 2.02633i −0.348826 0.0934678i
\(471\) 0 0
\(472\) 7.94858 13.7673i 0.365863 0.633694i
\(473\) 9.52246 9.52246i 0.437843 0.437843i
\(474\) 0 0
\(475\) −0.106991 0.399295i −0.00490907 0.0183209i
\(476\) −35.1800 0.994179i −1.61247 0.0455681i
\(477\) 0 0
\(478\) 33.5967 19.3971i 1.53668 0.887202i
\(479\) 11.4241 + 3.06108i 0.521980 + 0.139864i 0.510182 0.860066i \(-0.329578\pi\)
0.0117979 + 0.999930i \(0.496245\pi\)
\(480\) 0 0
\(481\) −16.8394 + 2.97832i −0.767810 + 0.135800i
\(482\) 68.4591i 3.11823i
\(483\) 0 0
\(484\) −16.4942 28.5688i −0.749736 1.29858i
\(485\) −6.78430 3.91692i −0.308059 0.177858i
\(486\) 0 0
\(487\) 0.0483236 + 0.180346i 0.00218975 + 0.00817226i 0.967012 0.254731i \(-0.0819868\pi\)
−0.964822 + 0.262903i \(0.915320\pi\)
\(488\) 1.48961 + 5.55931i 0.0674316 + 0.251658i
\(489\) 0 0
\(490\) −22.8772 + 34.9101i −1.03348 + 1.57708i
\(491\) 2.43785 1.40749i 0.110019 0.0635193i −0.443981 0.896036i \(-0.646434\pi\)
0.554000 + 0.832517i \(0.313101\pi\)
\(492\) 0 0
\(493\) −45.5288 −2.05052
\(494\) 0.689624 + 1.47689i 0.0310276 + 0.0664482i
\(495\) 0 0
\(496\) −2.06607 + 7.71067i −0.0927691 + 0.346219i
\(497\) −4.21043 + 14.1067i −0.188864 + 0.632774i
\(498\) 0 0
\(499\) 1.80207 1.80207i 0.0806719 0.0806719i −0.665619 0.746291i \(-0.731833\pi\)
0.746291 + 0.665619i \(0.231833\pi\)
\(500\) 22.9875 6.15949i 1.02803 0.275461i
\(501\) 0 0
\(502\) 17.3417 17.3417i 0.773999 0.773999i
\(503\) −6.33177 3.65565i −0.282320 0.162997i 0.352153 0.935942i \(-0.385450\pi\)
−0.634473 + 0.772945i \(0.718783\pi\)
\(504\) 0 0
\(505\) 0.435466 1.62518i 0.0193780 0.0723196i
\(506\) 87.2783i 3.87999i
\(507\) 0 0
\(508\) −3.65274 −0.162064
\(509\) −6.75398 + 25.2062i −0.299365 + 1.11724i 0.638324 + 0.769768i \(0.279628\pi\)
−0.937689 + 0.347477i \(0.887039\pi\)
\(510\) 0 0
\(511\) 31.8518 7.57717i 1.40904 0.335194i
\(512\) −6.62788 + 6.62788i −0.292914 + 0.292914i
\(513\) 0 0
\(514\) 16.5071 + 61.6053i 0.728097 + 2.71729i
\(515\) 3.67535 + 3.67535i 0.161955 + 0.161955i
\(516\) 0 0
\(517\) 3.06875 + 5.31523i 0.134963 + 0.233763i
\(518\) 24.7872 13.3919i 1.08909 0.588406i
\(519\) 0 0
\(520\) 20.2737 9.46670i 0.889061 0.415142i
\(521\) 5.50223i 0.241057i 0.992710 + 0.120529i \(0.0384589\pi\)
−0.992710 + 0.120529i \(0.961541\pi\)
\(522\) 0 0
\(523\) −35.0507 + 20.2365i −1.53266 + 0.884882i −0.533423 + 0.845849i \(0.679095\pi\)
−0.999238 + 0.0390336i \(0.987572\pi\)
\(524\) 4.61311 7.99014i 0.201525 0.349051i
\(525\) 0 0
\(526\) −12.6189 47.0943i −0.550209 2.05341i
\(527\) 40.3843 10.8209i 1.75917 0.471367i
\(528\) 0 0
\(529\) 23.0828 39.9806i 1.00360 1.73829i
\(530\) −5.81600 10.0736i −0.252631 0.437569i
\(531\) 0 0
\(532\) −1.11263 1.17735i −0.0482387 0.0510444i
\(533\) 1.87028 0.330790i 0.0810110 0.0143281i
\(534\) 0 0
\(535\) −4.94882 + 18.4692i −0.213956 + 0.798495i
\(536\) −1.70402 2.95145i −0.0736024 0.127483i
\(537\) 0 0
\(538\) −19.6422 19.6422i −0.846836 0.846836i
\(539\) 32.0327 6.67012i 1.37975 0.287302i
\(540\) 0 0
\(541\) 25.7367 + 25.7367i 1.10651 + 1.10651i 0.993606 + 0.112900i \(0.0360139\pi\)
0.112900 + 0.993606i \(0.463986\pi\)
\(542\) −15.3881 8.88430i −0.660974 0.381613i
\(543\) 0 0
\(544\) 27.6716 + 7.41457i 1.18641 + 0.317897i
\(545\) −9.09682 −0.389665
\(546\) 0 0
\(547\) 31.3852 1.34193 0.670967 0.741487i \(-0.265879\pi\)
0.670967 + 0.741487i \(0.265879\pi\)
\(548\) 34.2977 + 9.19005i 1.46513 + 0.392579i
\(549\) 0 0
\(550\) 18.6588 + 10.7727i 0.795616 + 0.459349i
\(551\) −1.48181 1.48181i −0.0631272 0.0631272i
\(552\) 0 0
\(553\) −10.0595 6.19321i −0.427775 0.263362i
\(554\) 17.7980 + 17.7980i 0.756166 + 0.756166i
\(555\) 0 0
\(556\) 10.1955 + 17.6592i 0.432387 + 0.748916i
\(557\) 0.169733 0.633453i 0.00719183 0.0268403i −0.962237 0.272214i \(-0.912244\pi\)
0.969429 + 0.245374i \(0.0789107\pi\)
\(558\) 0 0
\(559\) 0.899944 10.3487i 0.0380636 0.437705i
\(560\) 4.26547 4.03101i 0.180249 0.170341i
\(561\) 0 0
\(562\) 24.1229 + 41.7821i 1.01756 + 1.76247i
\(563\) 12.5830 21.7944i 0.530309 0.918523i −0.469065 0.883164i \(-0.655409\pi\)
0.999375 0.0353593i \(-0.0112576\pi\)
\(564\) 0 0
\(565\) −1.94834 + 0.522056i −0.0819672 + 0.0219630i
\(566\) 8.88777 + 33.1696i 0.373581 + 1.39422i
\(567\) 0 0
\(568\) −6.50104 + 11.2601i −0.272778 + 0.472465i
\(569\) 3.46005 1.99766i 0.145053 0.0837463i −0.425717 0.904856i \(-0.639978\pi\)
0.570770 + 0.821110i \(0.306645\pi\)
\(570\) 0 0
\(571\) 17.9370i 0.750640i 0.926895 + 0.375320i \(0.122467\pi\)
−0.926895 + 0.375320i \(0.877533\pi\)
\(572\) −48.1656 17.5023i −2.01390 0.731808i
\(573\) 0 0
\(574\) −2.75301 + 1.48739i −0.114909 + 0.0620823i
\(575\) −8.53705 14.7866i −0.356020 0.616644i
\(576\) 0 0
\(577\) 29.6210 + 29.6210i 1.23314 + 1.23314i 0.962751 + 0.270389i \(0.0871524\pi\)
0.270389 + 0.962751i \(0.412848\pi\)
\(578\) −1.24174 4.63424i −0.0516496 0.192759i
\(579\) 0 0
\(580\) −59.4302 + 59.4302i −2.46770 + 2.46770i
\(581\) 4.69497 + 19.7360i 0.194780 + 0.818789i
\(582\) 0 0
\(583\) −2.36008 + 8.80794i −0.0977446 + 0.364788i
\(584\) 28.9163 1.19657
\(585\) 0 0
\(586\) 47.1901i 1.94941i
\(587\) 0.571868 2.13424i 0.0236035 0.0880895i −0.953119 0.302595i \(-0.902147\pi\)
0.976723 + 0.214505i \(0.0688138\pi\)
\(588\) 0 0
\(589\) 1.66656 + 0.962187i 0.0686693 + 0.0396462i
\(590\) 28.6838 28.6838i 1.18089 1.18089i
\(591\) 0 0
\(592\) −3.82651 + 1.02531i −0.157268 + 0.0421400i
\(593\) −1.48928 + 1.48928i −0.0611573 + 0.0611573i −0.737024 0.675867i \(-0.763770\pi\)
0.675867 + 0.737024i \(0.263770\pi\)
\(594\) 0 0
\(595\) −29.4538 8.79106i −1.20749 0.360398i
\(596\) −3.76850 + 14.0642i −0.154364 + 0.576093i
\(597\) 0 0
\(598\) 43.3015 + 51.5500i 1.77073 + 2.10804i
\(599\) −13.9002 −0.567945 −0.283973 0.958832i \(-0.591653\pi\)
−0.283973 + 0.958832i \(0.591653\pi\)
\(600\) 0 0
\(601\) −8.59776 + 4.96392i −0.350710 + 0.202482i −0.664998 0.746845i \(-0.731568\pi\)
0.314288 + 0.949328i \(0.398234\pi\)
\(602\) 3.96067 + 16.6493i 0.161425 + 0.678575i
\(603\) 0 0
\(604\) −8.52892 31.8304i −0.347037 1.29516i
\(605\) −7.45694 27.8297i −0.303168 1.13144i
\(606\) 0 0
\(607\) 26.6015 + 15.3584i 1.07972 + 0.623378i 0.930821 0.365475i \(-0.119093\pi\)
0.148900 + 0.988852i \(0.452427\pi\)
\(608\) 0.659297 + 1.14194i 0.0267380 + 0.0463116i
\(609\) 0 0
\(610\) 14.6862i 0.594626i
\(611\) 4.44958 + 1.61688i 0.180011 + 0.0654119i
\(612\) 0 0
\(613\) 9.42794 + 2.52621i 0.380791 + 0.102033i 0.444137 0.895959i \(-0.353510\pi\)
−0.0633459 + 0.997992i \(0.520177\pi\)
\(614\) −35.1709 + 20.3059i −1.41938 + 0.819480i
\(615\) 0 0
\(616\) 28.8863 + 0.816322i 1.16386 + 0.0328906i
\(617\) −6.69956 25.0031i −0.269714 1.00659i −0.959301 0.282384i \(-0.908875\pi\)
0.689587 0.724203i \(-0.257792\pi\)
\(618\) 0 0
\(619\) 25.5525 25.5525i 1.02704 1.02704i 0.0274172 0.999624i \(-0.491272\pi\)
0.999624 0.0274172i \(-0.00872826\pi\)
\(620\) 38.5899 66.8397i 1.54981 2.68435i
\(621\) 0 0
\(622\) 42.4011 + 11.3613i 1.70013 + 0.455548i
\(623\) −28.3068 29.9532i −1.13409 1.20005i
\(624\) 0 0
\(625\) 31.0502 1.24201
\(626\) −7.69915 + 28.7336i −0.307720 + 1.14843i
\(627\) 0 0
\(628\) −12.1722 + 21.0829i −0.485725 + 0.841300i
\(629\) 14.6712 + 14.6712i 0.584977 + 0.584977i
\(630\) 0 0
\(631\) 9.92759 2.66009i 0.395211 0.105897i −0.0557396 0.998445i \(-0.517752\pi\)
0.450951 + 0.892549i \(0.351085\pi\)
\(632\) −7.37744 7.37744i −0.293459 0.293459i
\(633\) 0 0
\(634\) −49.1823 + 28.3954i −1.95328 + 1.12773i
\(635\) −3.08153 0.825692i −0.122287 0.0327666i
\(636\) 0 0
\(637\) 15.6105 19.8321i 0.618511 0.785776i
\(638\) 109.222 4.32416
\(639\) 0 0
\(640\) 37.1730 21.4618i 1.46939 0.848353i
\(641\) 26.2509 + 15.1559i 1.03685 + 0.598624i 0.918939 0.394401i \(-0.129048\pi\)
0.117908 + 0.993025i \(0.462381\pi\)
\(642\) 0 0
\(643\) 35.0393 9.38876i 1.38182 0.370256i 0.510035 0.860153i \(-0.329632\pi\)
0.871780 + 0.489897i \(0.162966\pi\)
\(644\) −56.9759 35.0775i −2.24516 1.38225i
\(645\) 0 0
\(646\) 0.988806 1.71266i 0.0389041 0.0673838i
\(647\) 9.62979 + 16.6793i 0.378586 + 0.655730i 0.990857 0.134918i \(-0.0430771\pi\)
−0.612271 + 0.790648i \(0.709744\pi\)
\(648\) 0 0
\(649\) −31.8001 −1.24826
\(650\) 16.3653 2.89447i 0.641901 0.113531i
\(651\) 0 0
\(652\) 55.8877 + 14.9751i 2.18873 + 0.586468i
\(653\) 0.0312823 + 0.0541825i 0.00122417 + 0.00212033i 0.866637 0.498939i \(-0.166277\pi\)
−0.865413 + 0.501060i \(0.832944\pi\)
\(654\) 0 0
\(655\) 5.69787 5.69787i 0.222634 0.222634i
\(656\) 0.424995 0.113877i 0.0165933 0.00444615i
\(657\) 0 0
\(658\) −7.79655 0.220329i −0.303941 0.00858932i
\(659\) −3.09067 + 5.35320i −0.120395 + 0.208531i −0.919924 0.392098i \(-0.871750\pi\)
0.799528 + 0.600628i \(0.205083\pi\)
\(660\) 0 0
\(661\) −6.90812 1.85103i −0.268695 0.0719965i 0.121956 0.992536i \(-0.461083\pi\)
−0.390651 + 0.920539i \(0.627750\pi\)
\(662\) 30.5207i 1.18622i
\(663\) 0 0
\(664\) 17.9171i 0.695320i
\(665\) −0.672503 1.24474i −0.0260786 0.0482690i
\(666\) 0 0
\(667\) −74.9594 43.2778i −2.90244 1.67572i
\(668\) −23.4013 23.4013i −0.905425 0.905425i
\(669\) 0 0
\(670\) −2.25078 8.40001i −0.0869551 0.324521i
\(671\) 8.14087 8.14087i 0.314275 0.314275i
\(672\) 0 0
\(673\) −4.05354 + 2.34031i −0.156253 + 0.0902125i −0.576088 0.817388i \(-0.695421\pi\)
0.419835 + 0.907600i \(0.362088\pi\)
\(674\) −1.02085 + 3.80987i −0.0393217 + 0.146751i
\(675\) 0 0
\(676\) −37.1319 + 13.5589i −1.42815 + 0.521497i
\(677\) 31.1590i 1.19754i −0.800922 0.598769i \(-0.795657\pi\)
0.800922 0.598769i \(-0.204343\pi\)
\(678\) 0 0
\(679\) −7.47834 2.23205i −0.286992 0.0856583i
\(680\) −23.5103 13.5737i −0.901579 0.520527i
\(681\) 0 0
\(682\) −96.8808 + 25.9591i −3.70976 + 0.994026i
\(683\) −41.3109 + 11.0692i −1.58072 + 0.423552i −0.939148 0.343512i \(-0.888383\pi\)
−0.641570 + 0.767064i \(0.721717\pi\)
\(684\) 0 0
\(685\) 26.8569 + 15.5058i 1.02615 + 0.592447i
\(686\) −14.1235 + 39.1090i −0.539236 + 1.49319i
\(687\) 0 0
\(688\) 2.40640i 0.0917430i
\(689\) 2.97595 + 6.37323i 0.113374 + 0.242801i
\(690\) 0 0
\(691\) 4.65384 17.3684i 0.177040 0.660724i −0.819155 0.573573i \(-0.805557\pi\)
0.996195 0.0871512i \(-0.0277763\pi\)
\(692\) −21.4507 + 12.3845i −0.815432 + 0.470790i
\(693\) 0 0
\(694\) −17.2703 + 17.2703i −0.655570 + 0.655570i
\(695\) 4.60935 + 17.2023i 0.174843 + 0.652521i
\(696\) 0 0
\(697\) −1.62947 1.62947i −0.0617205 0.0617205i
\(698\) −24.0447 13.8822i −0.910106 0.525450i
\(699\) 0 0
\(700\) −14.5315 + 7.85104i −0.549241 + 0.296741i
\(701\) 34.0110i 1.28458i −0.766462 0.642290i \(-0.777985\pi\)
0.766462 0.642290i \(-0.222015\pi\)
\(702\) 0 0
\(703\) 0.954993i 0.0360182i
\(704\) −58.8411 15.7664i −2.21766 0.594219i
\(705\) 0 0
\(706\) −19.7658 + 34.2354i −0.743897 + 1.28847i
\(707\) 0.0473495 1.67551i 0.00178076 0.0630139i
\(708\) 0 0
\(709\) −2.70932 + 0.725960i −0.101751 + 0.0272640i −0.309335 0.950953i \(-0.600106\pi\)
0.207584 + 0.978217i \(0.433440\pi\)
\(710\) −23.4601 + 23.4601i −0.880441 + 0.880441i
\(711\) 0 0
\(712\) −18.1993 31.5221i −0.682047 1.18134i
\(713\) 76.7753 + 20.5719i 2.87526 + 0.770423i
\(714\) 0 0
\(715\) −36.6771 25.6530i −1.37165 0.959369i
\(716\) −35.9336 −1.34290
\(717\) 0 0
\(718\) −18.2560 31.6203i −0.681308 1.18006i
\(719\) 10.7719 18.6575i 0.401725 0.695809i −0.592209 0.805784i \(-0.701744\pi\)
0.993934 + 0.109976i \(0.0350773\pi\)
\(720\) 0 0
\(721\) 4.40949 + 2.71472i 0.164218 + 0.101102i
\(722\) −41.1167 + 11.0172i −1.53021 + 0.410017i
\(723\) 0 0
\(724\) −27.6493 15.9633i −1.02758 0.593272i
\(725\) −18.5044 + 10.6835i −0.687235 + 0.396775i
\(726\) 0 0
\(727\) 25.2656 0.937048 0.468524 0.883451i \(-0.344786\pi\)
0.468524 + 0.883451i \(0.344786\pi\)
\(728\) 17.4664 13.8493i 0.647348 0.513289i
\(729\) 0 0
\(730\) 71.2720 + 19.0973i 2.63789 + 0.706822i
\(731\) −10.9149 + 6.30170i −0.403701 + 0.233077i
\(732\) 0 0
\(733\) −22.8545 22.8545i −0.844152 0.844152i 0.145244 0.989396i \(-0.453603\pi\)
−0.989396 + 0.145244i \(0.953603\pi\)
\(734\) −28.5184 + 7.64147i −1.05263 + 0.282052i
\(735\) 0 0
\(736\) 38.5109 + 38.5109i 1.41953 + 1.41953i
\(737\) −3.40865 + 5.90396i −0.125559 + 0.217475i
\(738\) 0 0
\(739\) 3.35655 12.5268i 0.123473 0.460806i −0.876308 0.481751i \(-0.840001\pi\)
0.999781 + 0.0209450i \(0.00666750\pi\)
\(740\) 38.3014 1.40799
\(741\) 0 0
\(742\) −7.95935 8.42229i −0.292197 0.309192i
\(743\) −31.0606 8.32266i −1.13950 0.305329i −0.360751 0.932662i \(-0.617480\pi\)
−0.778751 + 0.627333i \(0.784146\pi\)
\(744\) 0 0
\(745\) −6.35837 + 11.0130i −0.232953 + 0.403486i
\(746\) 15.2893 15.2893i 0.559782 0.559782i
\(747\) 0 0
\(748\) 16.0927 + 60.0587i 0.588407 + 2.19596i
\(749\) −0.538099 + 19.0412i −0.0196617 + 0.695749i
\(750\) 0 0
\(751\) −13.1305 + 7.58091i −0.479140 + 0.276631i −0.720058 0.693914i \(-0.755885\pi\)
0.240918 + 0.970545i \(0.422551\pi\)
\(752\) 1.05935 + 0.283851i 0.0386304 + 0.0103510i
\(753\) 0 0
\(754\) 64.5111 54.1887i 2.34935 1.97344i
\(755\) 28.7807i 1.04744i
\(756\) 0 0
\(757\) −17.8529 30.9221i −0.648875 1.12388i −0.983392 0.181494i \(-0.941907\pi\)
0.334517 0.942390i \(-0.391427\pi\)
\(758\) −64.7200 37.3661i −2.35074 1.35720i
\(759\) 0 0
\(760\) −0.323404 1.20696i −0.0117311 0.0437810i
\(761\) 0.802382 + 2.99453i 0.0290863 + 0.108552i 0.978943 0.204134i \(-0.0654379\pi\)
−0.949857 + 0.312686i \(0.898771\pi\)
\(762\) 0 0
\(763\) −8.81653 + 2.09735i −0.319180 + 0.0759291i
\(764\) 35.1538 20.2961i 1.27182 0.734286i
\(765\) 0 0
\(766\) 8.67503 0.313442
\(767\) −18.7824 + 15.7770i −0.678192 + 0.569675i
\(768\) 0 0
\(769\) 8.07284 30.1282i 0.291114 1.08645i −0.653141 0.757237i \(-0.726549\pi\)
0.944255 0.329216i \(-0.106784\pi\)
\(770\) 70.6589 + 21.0895i 2.54637 + 0.760013i
\(771\) 0 0
\(772\) −17.3447 + 17.3447i −0.624251 + 0.624251i
\(773\) −5.18000 + 1.38798i −0.186312 + 0.0499220i −0.350768 0.936462i \(-0.614080\pi\)
0.164457 + 0.986384i \(0.447413\pi\)
\(774\) 0 0
\(775\) 13.8743 13.8743i 0.498379 0.498379i
\(776\) −5.96928 3.44636i −0.214284 0.123717i
\(777\) 0 0
\(778\) −7.31105 + 27.2852i −0.262114 + 0.978222i
\(779\) 0.106067i 0.00380026i
\(780\) 0 0
\(781\) 26.0089 0.930670
\(782\) 21.1410 78.8993i 0.756001 2.82143i
\(783\) 0 0
\(784\) 3.20466 4.89024i 0.114452 0.174652i
\(785\) −15.0345 + 15.0345i −0.536604 + 0.536604i
\(786\) 0 0
\(787\) −3.63938 13.5824i −0.129730 0.484159i 0.870234 0.492638i \(-0.163967\pi\)
−0.999964 + 0.00847973i \(0.997301\pi\)
\(788\) 27.2973 + 27.2973i 0.972426 + 0.972426i
\(789\) 0 0
\(790\) −13.3114 23.0560i −0.473597 0.820294i
\(791\) −1.76794 + 0.955176i −0.0628608 + 0.0339621i
\(792\) 0 0
\(793\) 0.769372 8.84726i 0.0273212 0.314175i
\(794\) 59.6088i 2.11544i
\(795\) 0 0
\(796\) 57.0740 32.9517i 2.02294 1.16794i
\(797\) −14.0098 + 24.2657i −0.496252 + 0.859534i −0.999991 0.00432247i \(-0.998624\pi\)
0.503739 + 0.863856i \(0.331957\pi\)
\(798\) 0 0
\(799\) −1.48666 5.54828i −0.0525941 0.196284i
\(800\) 12.9865 3.47971i 0.459141 0.123026i
\(801\) 0 0
\(802\) 16.8947 29.2625i 0.596573 1.03330i
\(803\) −28.9216 50.0936i −1.02062 1.76776i
\(804\) 0 0
\(805\) −40.1369 42.4713i −1.41464 1.49692i
\(806\) −44.3424 + 63.3981i −1.56190 + 2.23310i
\(807\) 0 0
\(808\) 0.383152 1.42994i 0.0134792 0.0503052i
\(809\) −22.8429 39.5651i −0.803115 1.39104i −0.917556 0.397606i \(-0.869841\pi\)
0.114441 0.993430i \(-0.463492\pi\)
\(810\) 0 0
\(811\) −7.85623 7.85623i −0.275870 0.275870i 0.555588 0.831458i \(-0.312493\pi\)
−0.831458 + 0.555588i \(0.812493\pi\)
\(812\) −43.8969 + 71.3012i −1.54048 + 2.50218i
\(813\) 0 0
\(814\) −35.1957 35.1957i −1.23361 1.23361i
\(815\) 43.7629 + 25.2665i 1.53295 + 0.885048i
\(816\) 0 0
\(817\) −0.560341 0.150143i −0.0196038 0.00525284i
\(818\) 55.7777 1.95022
\(819\) 0 0
\(820\) −4.25399 −0.148556
\(821\) −25.7120 6.88952i −0.897356 0.240446i −0.219476 0.975618i \(-0.570435\pi\)
−0.677881 + 0.735172i \(0.737101\pi\)
\(822\) 0 0
\(823\) 38.5488 + 22.2561i 1.34373 + 0.775800i 0.987352 0.158543i \(-0.0506798\pi\)
0.356373 + 0.934344i \(0.384013\pi\)
\(824\) 3.23382 + 3.23382i 0.112655 + 0.112655i
\(825\) 0 0
\(826\) 21.1867 34.4133i 0.737179 1.19739i
\(827\) 10.7544 + 10.7544i 0.373966 + 0.373966i 0.868920 0.494953i \(-0.164815\pi\)
−0.494953 + 0.868920i \(0.664815\pi\)
\(828\) 0 0
\(829\) −22.8384 39.5572i −0.793209 1.37388i −0.923970 0.382464i \(-0.875076\pi\)
0.130761 0.991414i \(-0.458258\pi\)
\(830\) −11.8330 + 44.1615i −0.410731 + 1.53287i
\(831\) 0 0
\(832\) −42.5761 + 19.8807i −1.47606 + 0.689238i
\(833\) −30.5732 1.72936i −1.05930 0.0599189i
\(834\) 0 0
\(835\) −14.4521 25.0317i −0.500134 0.866257i
\(836\) −1.43095 + 2.47847i −0.0494903 + 0.0857197i
\(837\) 0 0
\(838\) −38.8869 + 10.4197i −1.34332 + 0.359943i
\(839\) 0.546041 + 2.03785i 0.0188514 + 0.0703546i 0.974711 0.223470i \(-0.0717385\pi\)
−0.955859 + 0.293825i \(0.905072\pi\)
\(840\) 0 0
\(841\) −39.6591 + 68.6916i −1.36755 + 2.36867i
\(842\) 2.29278 1.32374i 0.0790144 0.0456190i
\(843\) 0 0
\(844\) 39.5856i 1.36259i
\(845\) −34.3902 + 3.04501i −1.18306 + 0.104751i
\(846\) 0 0
\(847\) −13.6435 25.2529i −0.468798 0.867701i
\(848\) 0.814711 + 1.41112i 0.0279773 + 0.0484581i
\(849\) 0 0
\(850\) −14.2581 14.2581i −0.489050 0.489050i
\(851\) 10.2090 + 38.1006i 0.349961 + 1.30607i
\(852\) 0 0
\(853\) 31.7998 31.7998i 1.08881 1.08881i 0.0931541 0.995652i \(-0.470305\pi\)
0.995652 0.0931541i \(-0.0296949\pi\)
\(854\) 3.38602 + 14.2337i 0.115867 + 0.487066i
\(855\) 0 0
\(856\) −4.35430 + 16.2505i −0.148827 + 0.555429i
\(857\) 0.314991 0.0107599 0.00537994 0.999986i \(-0.498288\pi\)
0.00537994 + 0.999986i \(0.498288\pi\)
\(858\) 0 0
\(859\) 11.6151i 0.396303i 0.980171 + 0.198151i \(0.0634938\pi\)
−0.980171 + 0.198151i \(0.936506\pi\)
\(860\) −6.02170 + 22.4733i −0.205338 + 0.766333i
\(861\) 0 0
\(862\) −27.0887 15.6397i −0.922646 0.532690i
\(863\) 10.5474 10.5474i 0.359038 0.359038i −0.504420 0.863458i \(-0.668294\pi\)
0.863458 + 0.504420i \(0.168294\pi\)
\(864\) 0 0
\(865\) −20.8957 + 5.59899i −0.710476 + 0.190371i
\(866\) −1.20700 + 1.20700i −0.0410156 + 0.0410156i
\(867\) 0 0
\(868\) 21.9905 73.6775i 0.746405 2.50078i
\(869\) −5.40164 + 20.1592i −0.183238 + 0.683853i
\(870\) 0 0
\(871\) 0.915858 + 5.17825i 0.0310327 + 0.175458i
\(872\) −8.00399 −0.271049
\(873\) 0 0
\(874\) 3.25597 1.87984i 0.110135 0.0635865i
\(875\) 20.1447 4.79218i 0.681015 0.162005i
\(876\) 0 0
\(877\) 13.5647 + 50.6241i 0.458047 + 1.70945i 0.678972 + 0.734164i \(0.262426\pi\)
−0.220925 + 0.975291i \(0.570908\pi\)
\(878\) 18.5438 + 69.2065i 0.625824 + 2.33561i
\(879\) 0 0
\(880\) −8.97938 5.18425i −0.302695 0.174761i
\(881\) 2.13878 + 3.70447i 0.0720572 + 0.124807i 0.899803 0.436297i \(-0.143710\pi\)
−0.827746 + 0.561104i \(0.810377\pi\)
\(882\) 0 0
\(883\) 33.8768i 1.14004i −0.821630 0.570022i \(-0.806935\pi\)
0.821630 0.570022i \(-0.193065\pi\)
\(884\) 39.3020 + 27.4890i 1.32187 + 0.924554i
\(885\) 0 0
\(886\) −30.1622 8.08195i −1.01332 0.271518i
\(887\) −3.88879 + 2.24520i −0.130573 + 0.0753863i −0.563864 0.825868i \(-0.690686\pi\)
0.433291 + 0.901254i \(0.357352\pi\)
\(888\) 0 0
\(889\) −3.17695 0.0897799i −0.106551 0.00301112i
\(890\) −24.0388 89.7139i −0.805781 3.00722i
\(891\) 0 0
\(892\) 36.4018 36.4018i 1.21882 1.21882i
\(893\) 0.132192 0.228963i 0.00442364 0.00766197i
\(894\) 0 0
\(895\) −30.3143 8.12270i −1.01330 0.271512i
\(896\) 31.0794 29.3711i 1.03829 0.981219i
\(897\) 0 0
\(898\) −86.7949 −2.89638
\(899\) 25.7442 96.0787i 0.858617 3.20440i
\(900\) 0 0
\(901\) 4.26701 7.39069i 0.142155 0.246219i
\(902\) 3.90905 + 3.90905i 0.130157 + 0.130157i
\(903\) 0 0
\(904\) −1.71428 + 0.459339i −0.0570160 + 0.0152774i
\(905\) −19.7171 19.7171i −0.655417 0.655417i
\(906\) 0 0
\(907\) 13.2542 7.65232i 0.440099 0.254091i −0.263541 0.964648i \(-0.584890\pi\)
0.703640 + 0.710557i \(0.251557\pi\)
\(908\) 55.6187 + 14.9030i 1.84577 + 0.494573i
\(909\) 0 0
\(910\) 52.1971 22.5999i 1.73032 0.749178i
\(911\) −15.6790 −0.519470 −0.259735 0.965680i \(-0.583635\pi\)
−0.259735 + 0.965680i \(0.583635\pi\)
\(912\) 0 0
\(913\) 31.0390 17.9204i 1.02724 0.593077i
\(914\) −22.7289 13.1225i −0.751805 0.434055i
\(915\) 0 0
\(916\) −0.753632 + 0.201935i −0.0249007 + 0.00667212i
\(917\) 4.20861 6.83600i 0.138981 0.225744i
\(918\) 0 0
\(919\) −26.1402 + 45.2762i −0.862287 + 1.49352i 0.00742976 + 0.999972i \(0.497635\pi\)
−0.869716 + 0.493552i \(0.835698\pi\)
\(920\) −25.8052 44.6959i −0.850771 1.47358i
\(921\) 0 0
\(922\) −76.8731 −2.53168
\(923\) 15.3619 12.9038i 0.505641 0.424734i
\(924\) 0 0
\(925\) 9.40546 + 2.52019i 0.309250 + 0.0828632i
\(926\) −28.7768 49.8428i −0.945663 1.63794i
\(927\) 0 0
\(928\) 48.1936 48.1936i 1.58203 1.58203i
\(929\) 19.0687 5.10945i 0.625625 0.167636i 0.0679414 0.997689i \(-0.478357\pi\)
0.557684 + 0.830054i \(0.311690\pi\)
\(930\) 0 0
\(931\) −0.938768 1.05134i −0.0307669 0.0344562i
\(932\) −17.3093 + 29.9806i −0.566984 + 0.982046i
\(933\) 0 0
\(934\) 44.3333 + 11.8791i 1.45063 + 0.388696i
\(935\) 54.3045i 1.77595i
\(936\) 0 0
\(937\) 32.0301i 1.04638i −0.852217 0.523189i \(-0.824742\pi\)
0.852217 0.523189i \(-0.175258\pi\)
\(938\) −4.11812 7.62226i −0.134461 0.248875i
\(939\) 0 0
\(940\) −9.18291 5.30176i −0.299514 0.172924i
\(941\) −16.4141 16.4141i −0.535083 0.535083i 0.386998 0.922081i \(-0.373512\pi\)
−0.922081 + 0.386998i \(0.873512\pi\)
\(942\) 0 0
\(943\) −1.13388 4.23169i −0.0369241 0.137803i
\(944\) −4.01805 + 4.01805i −0.130777 + 0.130777i
\(945\) 0 0
\(946\) 26.1845 15.1176i 0.851330 0.491516i
\(947\) 11.1001 41.4261i 0.360704 1.34617i −0.512447 0.858719i \(-0.671261\pi\)
0.873152 0.487449i \(-0.162072\pi\)
\(948\) 0 0
\(949\) −41.9352 15.2383i −1.36128 0.494658i
\(950\) 0.928107i 0.0301118i
\(951\) 0 0
\(952\) −25.9154 7.73496i −0.839924 0.250691i
\(953\) 10.3745 + 5.98973i 0.336064 + 0.194026i 0.658530 0.752554i \(-0.271179\pi\)
−0.322466 + 0.946581i \(0.604512\pi\)
\(954\) 0 0
\(955\) 34.2444 9.17575i 1.10812 0.296920i
\(956\) 50.7511 13.5987i 1.64141 0.439814i
\(957\) 0 0
\(958\) 22.9963 + 13.2769i 0.742976 + 0.428957i
\(959\) 29.6044 + 8.83599i 0.955975 + 0.285329i
\(960\) 0 0
\(961\) 60.3409i 1.94648i
\(962\) −38.2497 3.32625i −1.23322 0.107243i
\(963\) 0 0
\(964\) −23.9973 + 89.5592i −0.772902 + 2.88451i
\(965\) −18.5531 + 10.7117i −0.597246 + 0.344820i
\(966\) 0 0
\(967\) 3.08553 3.08553i 0.0992241 0.0992241i −0.655752 0.754976i \(-0.727648\pi\)
0.754976 + 0.655752i \(0.227648\pi\)
\(968\) −6.56111 24.4864i −0.210882 0.787023i
\(969\) 0 0
\(970\) −12.4368 12.4368i −0.399321 0.399321i
\(971\) 25.8972 + 14.9518i 0.831081 + 0.479825i 0.854223 0.519907i \(-0.174033\pi\)
−0.0231414 + 0.999732i \(0.507367\pi\)
\(972\) 0 0
\(973\) 8.43346 + 15.6096i 0.270364 + 0.500420i
\(974\) 0.419190i 0.0134317i
\(975\) 0 0
\(976\) 2.05726i 0.0658512i
\(977\) 9.78075 + 2.62074i 0.312914 + 0.0838450i 0.411858 0.911248i \(-0.364880\pi\)
−0.0989443 + 0.995093i \(0.531547\pi\)
\(978\) 0 0
\(979\) −36.4051 + 63.0555i −1.16351 + 2.01526i
\(980\) −42.1655 + 37.6507i −1.34693 + 1.20271i
\(981\) 0 0
\(982\) 6.10476 1.63577i 0.194811 0.0521994i
\(983\) −5.97019 + 5.97019i −0.190419 + 0.190419i −0.795877 0.605458i \(-0.792990\pi\)
0.605458 + 0.795877i \(0.292990\pi\)
\(984\) 0 0
\(985\) 16.8581 + 29.1991i 0.537144 + 0.930360i
\(986\) −98.7368 26.4564i −3.14442 0.842545i
\(987\) 0 0
\(988\) 0.384476 + 2.17382i 0.0122318 + 0.0691585i
\(989\) −23.9605 −0.761901
\(990\) 0 0
\(991\) −27.8012 48.1532i −0.883136 1.52964i −0.847836 0.530259i \(-0.822095\pi\)
−0.0353002 0.999377i \(-0.511239\pi\)
\(992\) −31.2937 + 54.2023i −0.993576 + 1.72092i
\(993\) 0 0
\(994\) −17.3283 + 28.1462i −0.549621 + 0.892742i
\(995\) 55.5975 14.8973i 1.76256 0.472277i
\(996\) 0 0
\(997\) −9.66852 5.58213i −0.306205 0.176788i 0.339022 0.940778i \(-0.389904\pi\)
−0.645227 + 0.763991i \(0.723237\pi\)
\(998\) 4.95526 2.86092i 0.156856 0.0905609i
\(999\) 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 819.2.fm.f.496.8 32
3.2 odd 2 273.2.by.c.223.1 yes 32
7.6 odd 2 819.2.fm.e.496.8 32
13.7 odd 12 819.2.fm.e.748.8 32
21.20 even 2 273.2.by.d.223.1 yes 32
39.20 even 12 273.2.by.d.202.1 yes 32
91.20 even 12 inner 819.2.fm.f.748.8 32
273.20 odd 12 273.2.by.c.202.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.by.c.202.1 32 273.20 odd 12
273.2.by.c.223.1 yes 32 3.2 odd 2
273.2.by.d.202.1 yes 32 39.20 even 12
273.2.by.d.223.1 yes 32 21.20 even 2
819.2.fm.e.496.8 32 7.6 odd 2
819.2.fm.e.748.8 32 13.7 odd 12
819.2.fm.f.496.8 32 1.1 even 1 trivial
819.2.fm.f.748.8 32 91.20 even 12 inner