Properties

Label 756.2.bj.b.523.11
Level $756$
Weight $2$
Character 756.523
Analytic conductor $6.037$
Analytic rank $0$
Dimension $84$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [756,2,Mod(451,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.451"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bj (of order \(6\), degree \(2\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 523.11
Character \(\chi\) \(=\) 756.523
Dual form 756.2.bj.b.451.12

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.937998 - 1.05838i) q^{2} +(-0.240318 + 1.98551i) q^{4} +(3.41753 - 1.97311i) q^{5} +(0.174185 - 2.64001i) q^{7} +(2.32683 - 1.60806i) q^{8} +(-5.29393 - 1.76626i) q^{10} +(-4.23698 - 2.44622i) q^{11} +(-1.13829 - 0.657191i) q^{13} +(-2.95751 + 2.29197i) q^{14} +(-3.88449 - 0.954307i) q^{16} +(-1.67931 + 0.969547i) q^{17} +(1.49477 - 2.58902i) q^{19} +(3.09634 + 7.25972i) q^{20} +(1.38526 + 6.77887i) q^{22} +(-2.92226 + 1.68717i) q^{23} +(5.28635 - 9.15623i) q^{25} +(0.372157 + 1.82118i) q^{26} +(5.19991 + 0.980288i) q^{28} +(1.32976 + 2.30322i) q^{29} +0.886605 q^{31} +(2.63363 + 5.00639i) q^{32} +(2.60133 + 0.867902i) q^{34} +(-4.61376 - 9.36601i) q^{35} +(0.237205 - 0.410852i) q^{37} +(-4.14225 + 0.846467i) q^{38} +(4.77915 - 10.0867i) q^{40} +(8.79016 + 5.07500i) q^{41} +(-2.31047 + 1.33395i) q^{43} +(5.87522 - 7.82469i) q^{44} +(4.52673 + 1.51029i) q^{46} -2.46166 q^{47} +(-6.93932 - 0.919699i) q^{49} +(-14.6493 + 2.99358i) q^{50} +(1.57841 - 2.10215i) q^{52} +(-6.34427 - 10.9886i) q^{53} -19.3067 q^{55} +(-3.83999 - 6.42296i) q^{56} +(1.19035 - 3.56781i) q^{58} +6.99484 q^{59} +2.37140i q^{61} +(-0.831634 - 0.938361i) q^{62} +(2.82830 - 7.48336i) q^{64} -5.18685 q^{65} +1.39480i q^{67} +(-1.52148 - 3.56728i) q^{68} +(-5.58506 + 13.6684i) q^{70} +2.15535i q^{71} +(3.96915 - 2.29159i) q^{73} +(-0.657333 + 0.134326i) q^{74} +(4.78130 + 3.59007i) q^{76} +(-7.19607 + 10.7596i) q^{77} -10.0544i q^{79} +(-15.1583 + 4.40317i) q^{80} +(-2.87390 - 14.0636i) q^{82} +(-1.29635 - 2.24535i) q^{83} +(-3.82605 + 6.62692i) q^{85} +(3.57904 + 1.19410i) q^{86} +(-13.7924 + 1.12136i) q^{88} +(11.6706 + 6.73801i) q^{89} +(-1.93326 + 2.89062i) q^{91} +(-2.64761 - 6.20762i) q^{92} +(2.30903 + 2.60536i) q^{94} -11.7974i q^{95} +(-1.88401 + 1.08773i) q^{97} +(5.53568 + 8.20708i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.937998 1.05838i −0.663265 0.748385i
\(3\) 0 0
\(4\) −0.240318 + 1.98551i −0.120159 + 0.992755i
\(5\) 3.41753 1.97311i 1.52837 0.882403i 0.528936 0.848662i \(-0.322591\pi\)
0.999431 0.0337413i \(-0.0107422\pi\)
\(6\) 0 0
\(7\) 0.174185 2.64001i 0.0658356 0.997830i
\(8\) 2.32683 1.60806i 0.822660 0.568534i
\(9\) 0 0
\(10\) −5.29393 1.76626i −1.67409 0.558539i
\(11\) −4.23698 2.44622i −1.27750 0.737563i −0.301109 0.953590i \(-0.597357\pi\)
−0.976388 + 0.216026i \(0.930690\pi\)
\(12\) 0 0
\(13\) −1.13829 0.657191i −0.315704 0.182272i 0.333772 0.942654i \(-0.391678\pi\)
−0.649476 + 0.760382i \(0.725012\pi\)
\(14\) −2.95751 + 2.29197i −0.790427 + 0.612556i
\(15\) 0 0
\(16\) −3.88449 0.954307i −0.971124 0.238577i
\(17\) −1.67931 + 0.969547i −0.407291 + 0.235150i −0.689625 0.724166i \(-0.742225\pi\)
0.282334 + 0.959316i \(0.408891\pi\)
\(18\) 0 0
\(19\) 1.49477 2.58902i 0.342924 0.593962i −0.642050 0.766662i \(-0.721916\pi\)
0.984974 + 0.172701i \(0.0552493\pi\)
\(20\) 3.09634 + 7.25972i 0.692363 + 1.62332i
\(21\) 0 0
\(22\) 1.38526 + 6.77887i 0.295338 + 1.44526i
\(23\) −2.92226 + 1.68717i −0.609333 + 0.351798i −0.772704 0.634766i \(-0.781096\pi\)
0.163372 + 0.986565i \(0.447763\pi\)
\(24\) 0 0
\(25\) 5.28635 9.15623i 1.05727 1.83125i
\(26\) 0.372157 + 1.82118i 0.0729861 + 0.357163i
\(27\) 0 0
\(28\) 5.19991 + 0.980288i 0.982690 + 0.185257i
\(29\) 1.32976 + 2.30322i 0.246931 + 0.427697i 0.962673 0.270668i \(-0.0872445\pi\)
−0.715742 + 0.698365i \(0.753911\pi\)
\(30\) 0 0
\(31\) 0.886605 0.159239 0.0796195 0.996825i \(-0.474629\pi\)
0.0796195 + 0.996825i \(0.474629\pi\)
\(32\) 2.63363 + 5.00639i 0.465565 + 0.885014i
\(33\) 0 0
\(34\) 2.60133 + 0.867902i 0.446125 + 0.148844i
\(35\) −4.61376 9.36601i −0.779868 1.58314i
\(36\) 0 0
\(37\) 0.237205 0.410852i 0.0389963 0.0675436i −0.845869 0.533391i \(-0.820917\pi\)
0.884865 + 0.465848i \(0.154251\pi\)
\(38\) −4.14225 + 0.846467i −0.671961 + 0.137315i
\(39\) 0 0
\(40\) 4.77915 10.0867i 0.755649 1.59485i
\(41\) 8.79016 + 5.07500i 1.37279 + 0.792582i 0.991279 0.131781i \(-0.0420696\pi\)
0.381514 + 0.924363i \(0.375403\pi\)
\(42\) 0 0
\(43\) −2.31047 + 1.33395i −0.352344 + 0.203426i −0.665717 0.746204i \(-0.731874\pi\)
0.313373 + 0.949630i \(0.398541\pi\)
\(44\) 5.87522 7.82469i 0.885722 1.17962i
\(45\) 0 0
\(46\) 4.52673 + 1.51029i 0.667430 + 0.222680i
\(47\) −2.46166 −0.359070 −0.179535 0.983752i \(-0.557459\pi\)
−0.179535 + 0.983752i \(0.557459\pi\)
\(48\) 0 0
\(49\) −6.93932 0.919699i −0.991331 0.131386i
\(50\) −14.6493 + 2.99358i −2.07173 + 0.423356i
\(51\) 0 0
\(52\) 1.57841 2.10215i 0.218886 0.291515i
\(53\) −6.34427 10.9886i −0.871453 1.50940i −0.860494 0.509460i \(-0.829845\pi\)
−0.0109585 0.999940i \(-0.503488\pi\)
\(54\) 0 0
\(55\) −19.3067 −2.60331
\(56\) −3.83999 6.42296i −0.513141 0.858305i
\(57\) 0 0
\(58\) 1.19035 3.56781i 0.156301 0.468476i
\(59\) 6.99484 0.910650 0.455325 0.890325i \(-0.349523\pi\)
0.455325 + 0.890325i \(0.349523\pi\)
\(60\) 0 0
\(61\) 2.37140i 0.303626i 0.988409 + 0.151813i \(0.0485112\pi\)
−0.988409 + 0.151813i \(0.951489\pi\)
\(62\) −0.831634 0.938361i −0.105618 0.119172i
\(63\) 0 0
\(64\) 2.82830 7.48336i 0.353538 0.935420i
\(65\) −5.18685 −0.643349
\(66\) 0 0
\(67\) 1.39480i 0.170402i 0.996364 + 0.0852008i \(0.0271532\pi\)
−0.996364 + 0.0852008i \(0.972847\pi\)
\(68\) −1.52148 3.56728i −0.184506 0.432596i
\(69\) 0 0
\(70\) −5.58506 + 13.6684i −0.667542 + 1.63369i
\(71\) 2.15535i 0.255793i 0.991788 + 0.127896i \(0.0408225\pi\)
−0.991788 + 0.127896i \(0.959177\pi\)
\(72\) 0 0
\(73\) 3.96915 2.29159i 0.464554 0.268210i −0.249403 0.968400i \(-0.580234\pi\)
0.713957 + 0.700189i \(0.246901\pi\)
\(74\) −0.657333 + 0.134326i −0.0764135 + 0.0156151i
\(75\) 0 0
\(76\) 4.78130 + 3.59007i 0.548453 + 0.411809i
\(77\) −7.19607 + 10.7596i −0.820068 + 1.22617i
\(78\) 0 0
\(79\) 10.0544i 1.13121i −0.824675 0.565607i \(-0.808642\pi\)
0.824675 0.565607i \(-0.191358\pi\)
\(80\) −15.1583 + 4.40317i −1.69475 + 0.492289i
\(81\) 0 0
\(82\) −2.87390 14.0636i −0.317369 1.55307i
\(83\) −1.29635 2.24535i −0.142293 0.246459i 0.786067 0.618142i \(-0.212114\pi\)
−0.928360 + 0.371683i \(0.878781\pi\)
\(84\) 0 0
\(85\) −3.82605 + 6.62692i −0.414994 + 0.718790i
\(86\) 3.57904 + 1.19410i 0.385938 + 0.128763i
\(87\) 0 0
\(88\) −13.7924 + 1.12136i −1.47028 + 0.119537i
\(89\) 11.6706 + 6.73801i 1.23708 + 0.714227i 0.968496 0.249029i \(-0.0801115\pi\)
0.268582 + 0.963257i \(0.413445\pi\)
\(90\) 0 0
\(91\) −1.93326 + 2.89062i −0.202661 + 0.303019i
\(92\) −2.64761 6.20762i −0.276033 0.647190i
\(93\) 0 0
\(94\) 2.30903 + 2.60536i 0.238158 + 0.268722i
\(95\) 11.7974i 1.21039i
\(96\) 0 0
\(97\) −1.88401 + 1.08773i −0.191292 + 0.110442i −0.592587 0.805506i \(-0.701893\pi\)
0.401295 + 0.915949i \(0.368560\pi\)
\(98\) 5.53568 + 8.20708i 0.559188 + 0.829041i
\(99\) 0 0
\(100\) 16.9094 + 12.6965i 1.69094 + 1.26965i
\(101\) 0.618126 + 0.356875i 0.0615058 + 0.0355104i 0.530438 0.847724i \(-0.322028\pi\)
−0.468932 + 0.883234i \(0.655361\pi\)
\(102\) 0 0
\(103\) −0.582342 1.00865i −0.0573798 0.0993848i 0.835909 0.548869i \(-0.184941\pi\)
−0.893288 + 0.449484i \(0.851608\pi\)
\(104\) −3.70541 + 0.301260i −0.363345 + 0.0295409i
\(105\) 0 0
\(106\) −5.67915 + 17.0219i −0.551608 + 1.65331i
\(107\) 10.5529 + 6.09270i 1.02018 + 0.589004i 0.914157 0.405360i \(-0.132854\pi\)
0.106027 + 0.994363i \(0.466187\pi\)
\(108\) 0 0
\(109\) −4.74875 8.22508i −0.454848 0.787820i 0.543832 0.839194i \(-0.316973\pi\)
−0.998679 + 0.0513747i \(0.983640\pi\)
\(110\) 18.1096 + 20.4337i 1.72669 + 1.94828i
\(111\) 0 0
\(112\) −3.19600 + 10.0889i −0.301994 + 0.953310i
\(113\) 6.24802 10.8219i 0.587764 1.01804i −0.406761 0.913535i \(-0.633342\pi\)
0.994525 0.104502i \(-0.0333250\pi\)
\(114\) 0 0
\(115\) −6.65794 + 11.5319i −0.620856 + 1.07535i
\(116\) −4.89263 + 2.08675i −0.454269 + 0.193750i
\(117\) 0 0
\(118\) −6.56115 7.40317i −0.604003 0.681517i
\(119\) 2.26711 + 4.60227i 0.207825 + 0.421889i
\(120\) 0 0
\(121\) 6.46799 + 11.2029i 0.587999 + 1.01844i
\(122\) 2.50983 2.22437i 0.227229 0.201385i
\(123\) 0 0
\(124\) −0.213067 + 1.76036i −0.0191340 + 0.158085i
\(125\) 21.9911i 1.96695i
\(126\) 0 0
\(127\) 6.01418i 0.533672i 0.963742 + 0.266836i \(0.0859782\pi\)
−0.963742 + 0.266836i \(0.914022\pi\)
\(128\) −10.5732 + 4.02598i −0.934543 + 0.355850i
\(129\) 0 0
\(130\) 4.86525 + 5.48963i 0.426711 + 0.481473i
\(131\) −0.999291 1.73082i −0.0873085 0.151223i 0.819064 0.573702i \(-0.194493\pi\)
−0.906373 + 0.422479i \(0.861160\pi\)
\(132\) 0 0
\(133\) −6.57467 4.39718i −0.570097 0.381284i
\(134\) 1.47622 1.30832i 0.127526 0.113021i
\(135\) 0 0
\(136\) −2.34837 + 4.95639i −0.201371 + 0.425007i
\(137\) 5.03081 8.71362i 0.429811 0.744455i −0.567045 0.823687i \(-0.691913\pi\)
0.996856 + 0.0792320i \(0.0252468\pi\)
\(138\) 0 0
\(139\) 8.02010 13.8912i 0.680256 1.17824i −0.294647 0.955606i \(-0.595202\pi\)
0.974903 0.222631i \(-0.0714646\pi\)
\(140\) 19.7051 6.90984i 1.66538 0.583988i
\(141\) 0 0
\(142\) 2.28117 2.02171i 0.191431 0.169658i
\(143\) 3.21527 + 5.56901i 0.268874 + 0.465704i
\(144\) 0 0
\(145\) 9.08903 + 5.24755i 0.754803 + 0.435785i
\(146\) −6.14842 2.05135i −0.508847 0.169771i
\(147\) 0 0
\(148\) 0.758745 + 0.569708i 0.0623684 + 0.0468297i
\(149\) 4.84527 + 8.39226i 0.396940 + 0.687521i 0.993347 0.115162i \(-0.0367387\pi\)
−0.596406 + 0.802683i \(0.703405\pi\)
\(150\) 0 0
\(151\) 14.3307 + 8.27382i 1.16621 + 0.673314i 0.952785 0.303645i \(-0.0982037\pi\)
0.213428 + 0.976959i \(0.431537\pi\)
\(152\) −0.685211 8.42789i −0.0555779 0.683592i
\(153\) 0 0
\(154\) 18.1376 2.47632i 1.46157 0.199548i
\(155\) 3.03000 1.74937i 0.243375 0.140513i
\(156\) 0 0
\(157\) 13.0987i 1.04539i −0.852519 0.522696i \(-0.824926\pi\)
0.852519 0.522696i \(-0.175074\pi\)
\(158\) −10.6414 + 9.43106i −0.846583 + 0.750295i
\(159\) 0 0
\(160\) 18.8787 + 11.9131i 1.49249 + 0.941809i
\(161\) 3.94512 + 8.00867i 0.310919 + 0.631172i
\(162\) 0 0
\(163\) 6.95666 + 4.01643i 0.544888 + 0.314591i 0.747057 0.664759i \(-0.231466\pi\)
−0.202170 + 0.979350i \(0.564799\pi\)
\(164\) −12.1889 + 16.2333i −0.951793 + 1.26761i
\(165\) 0 0
\(166\) −1.16044 + 3.47816i −0.0900680 + 0.269957i
\(167\) 4.83680 8.37758i 0.374283 0.648277i −0.615937 0.787796i \(-0.711222\pi\)
0.990219 + 0.139519i \(0.0445556\pi\)
\(168\) 0 0
\(169\) −5.63620 9.76219i −0.433554 0.750937i
\(170\) 10.6026 2.16664i 0.813182 0.166173i
\(171\) 0 0
\(172\) −2.09333 4.90804i −0.159615 0.374234i
\(173\) 16.3879i 1.24595i −0.782242 0.622974i \(-0.785924\pi\)
0.782242 0.622974i \(-0.214076\pi\)
\(174\) 0 0
\(175\) −23.2517 15.5509i −1.75767 1.17554i
\(176\) 14.1241 + 13.5457i 1.06464 + 1.02105i
\(177\) 0 0
\(178\) −3.81563 18.6721i −0.285994 1.39953i
\(179\) −16.0572 + 9.27065i −1.20017 + 0.692921i −0.960594 0.277955i \(-0.910343\pi\)
−0.239581 + 0.970876i \(0.577010\pi\)
\(180\) 0 0
\(181\) 23.0045i 1.70991i 0.518700 + 0.854956i \(0.326416\pi\)
−0.518700 + 0.854956i \(0.673584\pi\)
\(182\) 4.87276 0.665278i 0.361193 0.0493137i
\(183\) 0 0
\(184\) −4.08654 + 8.62491i −0.301264 + 0.635837i
\(185\) 1.87213i 0.137642i
\(186\) 0 0
\(187\) 9.48691 0.693751
\(188\) 0.591581 4.88764i 0.0431455 0.356468i
\(189\) 0 0
\(190\) −12.4861 + 11.0660i −0.905836 + 0.802808i
\(191\) 3.94412i 0.285386i −0.989767 0.142693i \(-0.954424\pi\)
0.989767 0.142693i \(-0.0455762\pi\)
\(192\) 0 0
\(193\) 5.75001 0.413895 0.206947 0.978352i \(-0.433647\pi\)
0.206947 + 0.978352i \(0.433647\pi\)
\(194\) 2.91842 + 0.973695i 0.209530 + 0.0699073i
\(195\) 0 0
\(196\) 3.49371 13.5571i 0.249551 0.968362i
\(197\) 16.6012 1.18279 0.591393 0.806384i \(-0.298578\pi\)
0.591393 + 0.806384i \(0.298578\pi\)
\(198\) 0 0
\(199\) 6.23391 + 10.7974i 0.441910 + 0.765411i 0.997831 0.0658244i \(-0.0209677\pi\)
−0.555921 + 0.831235i \(0.687634\pi\)
\(200\) −2.42329 29.8058i −0.171352 2.10759i
\(201\) 0 0
\(202\) −0.202093 0.988957i −0.0142192 0.0695828i
\(203\) 6.31215 3.10941i 0.443026 0.218238i
\(204\) 0 0
\(205\) 40.0542 2.79751
\(206\) −0.521290 + 1.56244i −0.0363200 + 0.108861i
\(207\) 0 0
\(208\) 3.79451 + 3.63913i 0.263102 + 0.252328i
\(209\) −12.6666 + 7.31308i −0.876169 + 0.505856i
\(210\) 0 0
\(211\) 19.4166 + 11.2102i 1.33669 + 0.771739i 0.986315 0.164870i \(-0.0527205\pi\)
0.350376 + 0.936609i \(0.386054\pi\)
\(212\) 23.3426 9.95585i 1.60318 0.683771i
\(213\) 0 0
\(214\) −3.45021 16.8838i −0.235851 1.15416i
\(215\) −5.26408 + 9.11765i −0.359007 + 0.621819i
\(216\) 0 0
\(217\) 0.154433 2.34065i 0.0104836 0.158893i
\(218\) −4.25090 + 12.7411i −0.287907 + 0.862934i
\(219\) 0 0
\(220\) 4.63974 38.3336i 0.312811 2.58445i
\(221\) 2.54871 0.171445
\(222\) 0 0
\(223\) 4.48502 + 7.76829i 0.300339 + 0.520203i 0.976213 0.216815i \(-0.0695668\pi\)
−0.675873 + 0.737018i \(0.736233\pi\)
\(224\) 13.6757 6.08079i 0.913744 0.406290i
\(225\) 0 0
\(226\) −17.3142 + 3.53816i −1.15173 + 0.235355i
\(227\) 3.89688 6.74960i 0.258645 0.447987i −0.707234 0.706980i \(-0.750057\pi\)
0.965879 + 0.258993i \(0.0833906\pi\)
\(228\) 0 0
\(229\) −5.88977 + 3.40046i −0.389207 + 0.224709i −0.681816 0.731523i \(-0.738810\pi\)
0.292610 + 0.956232i \(0.405476\pi\)
\(230\) 18.4502 3.77029i 1.21657 0.248606i
\(231\) 0 0
\(232\) 6.79785 + 3.22087i 0.446301 + 0.211460i
\(233\) −8.45700 + 14.6480i −0.554037 + 0.959619i 0.443941 + 0.896056i \(0.353580\pi\)
−0.997978 + 0.0635635i \(0.979753\pi\)
\(234\) 0 0
\(235\) −8.41279 + 4.85713i −0.548790 + 0.316844i
\(236\) −1.68099 + 13.8883i −0.109423 + 0.904052i
\(237\) 0 0
\(238\) 2.74438 6.71637i 0.177892 0.435357i
\(239\) 16.8495 + 9.72804i 1.08990 + 0.629254i 0.933550 0.358447i \(-0.116694\pi\)
0.156351 + 0.987702i \(0.450027\pi\)
\(240\) 0 0
\(241\) −20.4013 11.7787i −1.31417 0.758734i −0.331382 0.943497i \(-0.607515\pi\)
−0.982783 + 0.184763i \(0.940848\pi\)
\(242\) 5.78990 17.3539i 0.372189 1.11555i
\(243\) 0 0
\(244\) −4.70843 0.569889i −0.301426 0.0364834i
\(245\) −25.5300 + 10.5490i −1.63105 + 0.673948i
\(246\) 0 0
\(247\) −3.40296 + 1.96470i −0.216525 + 0.125011i
\(248\) 2.06298 1.42571i 0.130999 0.0905328i
\(249\) 0 0
\(250\) −23.2749 + 20.6276i −1.47203 + 1.30461i
\(251\) 4.53190 0.286051 0.143026 0.989719i \(-0.454317\pi\)
0.143026 + 0.989719i \(0.454317\pi\)
\(252\) 0 0
\(253\) 16.5087 1.03789
\(254\) 6.36526 5.64129i 0.399392 0.353966i
\(255\) 0 0
\(256\) 14.1786 + 7.41400i 0.886162 + 0.463375i
\(257\) −20.6842 + 11.9420i −1.29025 + 0.744924i −0.978698 0.205306i \(-0.934181\pi\)
−0.311549 + 0.950230i \(0.600848\pi\)
\(258\) 0 0
\(259\) −1.04334 0.697789i −0.0648297 0.0433585i
\(260\) 1.24649 10.2985i 0.0773042 0.638688i
\(261\) 0 0
\(262\) −0.894528 + 2.68113i −0.0552641 + 0.165641i
\(263\) 23.5572 + 13.6008i 1.45260 + 0.838660i 0.998628 0.0523561i \(-0.0166731\pi\)
0.453972 + 0.891016i \(0.350006\pi\)
\(264\) 0 0
\(265\) −43.3635 25.0359i −2.66380 1.53794i
\(266\) 1.51317 + 11.0830i 0.0927781 + 0.679544i
\(267\) 0 0
\(268\) −2.76938 0.335195i −0.169167 0.0204753i
\(269\) −15.8637 + 9.15891i −0.967227 + 0.558429i −0.898390 0.439199i \(-0.855262\pi\)
−0.0688372 + 0.997628i \(0.521929\pi\)
\(270\) 0 0
\(271\) 0.772505 1.33802i 0.0469264 0.0812788i −0.841608 0.540089i \(-0.818391\pi\)
0.888535 + 0.458810i \(0.151724\pi\)
\(272\) 7.44850 2.16363i 0.451632 0.131189i
\(273\) 0 0
\(274\) −13.9412 + 2.84887i −0.842217 + 0.172107i
\(275\) −44.7963 + 25.8632i −2.70132 + 1.55961i
\(276\) 0 0
\(277\) −0.243046 + 0.420968i −0.0146032 + 0.0252935i −0.873235 0.487300i \(-0.837982\pi\)
0.858631 + 0.512593i \(0.171315\pi\)
\(278\) −22.2250 + 4.54166i −1.33296 + 0.272391i
\(279\) 0 0
\(280\) −25.7965 14.3739i −1.54164 0.859007i
\(281\) 13.1672 + 22.8062i 0.785489 + 1.36051i 0.928707 + 0.370815i \(0.120922\pi\)
−0.143218 + 0.989691i \(0.545745\pi\)
\(282\) 0 0
\(283\) −17.1770 −1.02107 −0.510533 0.859858i \(-0.670552\pi\)
−0.510533 + 0.859858i \(0.670552\pi\)
\(284\) −4.27947 0.517969i −0.253940 0.0307358i
\(285\) 0 0
\(286\) 2.87818 8.62668i 0.170191 0.510106i
\(287\) 14.9292 22.3221i 0.881241 1.31763i
\(288\) 0 0
\(289\) −6.61996 + 11.4661i −0.389409 + 0.674476i
\(290\) −2.97161 14.5418i −0.174499 0.853924i
\(291\) 0 0
\(292\) 3.59612 + 8.43150i 0.210447 + 0.493416i
\(293\) −21.5170 12.4229i −1.25704 0.725751i −0.284540 0.958664i \(-0.591841\pi\)
−0.972498 + 0.232913i \(0.925174\pi\)
\(294\) 0 0
\(295\) 23.9051 13.8016i 1.39181 0.803561i
\(296\) −0.108736 1.33742i −0.00632016 0.0777361i
\(297\) 0 0
\(298\) 4.33730 13.0000i 0.251253 0.753072i
\(299\) 4.43516 0.256492
\(300\) 0 0
\(301\) 3.11920 + 6.33203i 0.179788 + 0.364972i
\(302\) −4.68534 22.9281i −0.269611 1.31936i
\(303\) 0 0
\(304\) −8.27715 + 8.63056i −0.474727 + 0.494997i
\(305\) 4.67903 + 8.10432i 0.267921 + 0.464052i
\(306\) 0 0
\(307\) 32.0881 1.83136 0.915682 0.401904i \(-0.131652\pi\)
0.915682 + 0.401904i \(0.131652\pi\)
\(308\) −19.6339 16.8736i −1.11874 0.961461i
\(309\) 0 0
\(310\) −4.69363 1.56597i −0.266580 0.0889412i
\(311\) −13.0485 −0.739915 −0.369957 0.929049i \(-0.620628\pi\)
−0.369957 + 0.929049i \(0.620628\pi\)
\(312\) 0 0
\(313\) 13.3212i 0.752960i 0.926425 + 0.376480i \(0.122866\pi\)
−0.926425 + 0.376480i \(0.877134\pi\)
\(314\) −13.8634 + 12.2866i −0.782355 + 0.693371i
\(315\) 0 0
\(316\) 19.9632 + 2.41627i 1.12302 + 0.135926i
\(317\) 19.6535 1.10385 0.551927 0.833893i \(-0.313893\pi\)
0.551927 + 0.833893i \(0.313893\pi\)
\(318\) 0 0
\(319\) 13.0116i 0.728509i
\(320\) −5.09971 31.1552i −0.285083 1.74163i
\(321\) 0 0
\(322\) 4.77566 11.6875i 0.266137 0.651321i
\(323\) 5.79701i 0.322554i
\(324\) 0 0
\(325\) −12.0348 + 6.94828i −0.667569 + 0.385421i
\(326\) −2.27444 11.1302i −0.125970 0.616443i
\(327\) 0 0
\(328\) 28.6141 2.32641i 1.57995 0.128454i
\(329\) −0.428783 + 6.49880i −0.0236396 + 0.358291i
\(330\) 0 0
\(331\) 14.4064i 0.791847i 0.918283 + 0.395924i \(0.129575\pi\)
−0.918283 + 0.395924i \(0.870425\pi\)
\(332\) 4.76969 2.03432i 0.261771 0.111648i
\(333\) 0 0
\(334\) −13.4035 + 2.73901i −0.733409 + 0.149872i
\(335\) 2.75209 + 4.76677i 0.150363 + 0.260436i
\(336\) 0 0
\(337\) −0.489878 + 0.848494i −0.0266854 + 0.0462204i −0.879060 0.476712i \(-0.841829\pi\)
0.852374 + 0.522932i \(0.175162\pi\)
\(338\) −5.04531 + 15.1221i −0.274429 + 0.822536i
\(339\) 0 0
\(340\) −12.2383 9.18923i −0.663717 0.498356i
\(341\) −3.75652 2.16883i −0.203427 0.117449i
\(342\) 0 0
\(343\) −3.63674 + 18.1597i −0.196365 + 0.980531i
\(344\) −3.23101 + 6.81926i −0.174204 + 0.367670i
\(345\) 0 0
\(346\) −17.3445 + 15.3718i −0.932448 + 0.826394i
\(347\) 27.4334i 1.47270i 0.676600 + 0.736351i \(0.263453\pi\)
−0.676600 + 0.736351i \(0.736547\pi\)
\(348\) 0 0
\(349\) 13.0352 7.52589i 0.697760 0.402852i −0.108753 0.994069i \(-0.534686\pi\)
0.806512 + 0.591217i \(0.201352\pi\)
\(350\) 5.35140 + 39.1958i 0.286045 + 2.09510i
\(351\) 0 0
\(352\) 1.08809 27.6544i 0.0579955 1.47399i
\(353\) −16.0275 9.25348i −0.853058 0.492513i 0.00862373 0.999963i \(-0.497255\pi\)
−0.861681 + 0.507450i \(0.830588\pi\)
\(354\) 0 0
\(355\) 4.25275 + 7.36598i 0.225712 + 0.390945i
\(356\) −16.1830 + 21.5528i −0.857699 + 1.14229i
\(357\) 0 0
\(358\) 24.8735 + 8.29874i 1.31461 + 0.438602i
\(359\) 5.04854 + 2.91478i 0.266452 + 0.153836i 0.627274 0.778799i \(-0.284171\pi\)
−0.360822 + 0.932635i \(0.617504\pi\)
\(360\) 0 0
\(361\) 5.03132 + 8.71450i 0.264806 + 0.458658i
\(362\) 24.3474 21.5782i 1.27967 1.13413i
\(363\) 0 0
\(364\) −5.27475 4.53318i −0.276472 0.237603i
\(365\) 9.04313 15.6632i 0.473339 0.819848i
\(366\) 0 0
\(367\) 0.903984 1.56575i 0.0471876 0.0817313i −0.841467 0.540309i \(-0.818307\pi\)
0.888654 + 0.458577i \(0.151641\pi\)
\(368\) 12.9616 3.76505i 0.675668 0.196267i
\(369\) 0 0
\(370\) −1.98142 + 1.75606i −0.103009 + 0.0912930i
\(371\) −30.1151 + 14.8349i −1.56350 + 0.770190i
\(372\) 0 0
\(373\) 2.97957 + 5.16077i 0.154276 + 0.267214i 0.932795 0.360407i \(-0.117362\pi\)
−0.778519 + 0.627621i \(0.784029\pi\)
\(374\) −8.89870 10.0407i −0.460141 0.519193i
\(375\) 0 0
\(376\) −5.72787 + 3.95849i −0.295392 + 0.204143i
\(377\) 3.49564i 0.180034i
\(378\) 0 0
\(379\) 16.5311i 0.849146i −0.905394 0.424573i \(-0.860424\pi\)
0.905394 0.424573i \(-0.139576\pi\)
\(380\) 23.4239 + 2.83513i 1.20162 + 0.145439i
\(381\) 0 0
\(382\) −4.17436 + 3.69957i −0.213579 + 0.189287i
\(383\) −1.64900 2.85616i −0.0842601 0.145943i 0.820816 0.571193i \(-0.193519\pi\)
−0.905076 + 0.425250i \(0.860186\pi\)
\(384\) 0 0
\(385\) −3.36293 + 50.9698i −0.171391 + 2.59766i
\(386\) −5.39350 6.08567i −0.274522 0.309753i
\(387\) 0 0
\(388\) −1.70694 4.00211i −0.0866567 0.203176i
\(389\) 4.82441 8.35612i 0.244607 0.423672i −0.717414 0.696647i \(-0.754674\pi\)
0.962021 + 0.272975i \(0.0880076\pi\)
\(390\) 0 0
\(391\) 3.27157 5.66653i 0.165451 0.286569i
\(392\) −17.6256 + 9.01884i −0.890225 + 0.455520i
\(393\) 0 0
\(394\) −15.5719 17.5703i −0.784500 0.885178i
\(395\) −19.8386 34.3614i −0.998186 1.72891i
\(396\) 0 0
\(397\) −3.22184 1.86013i −0.161700 0.0933573i 0.416967 0.908922i \(-0.363093\pi\)
−0.578666 + 0.815565i \(0.696427\pi\)
\(398\) 5.58036 16.7258i 0.279718 0.838389i
\(399\) 0 0
\(400\) −29.2727 + 30.5225i −1.46363 + 1.52613i
\(401\) −11.9860 20.7604i −0.598553 1.03672i −0.993035 0.117821i \(-0.962409\pi\)
0.394482 0.918904i \(-0.370924\pi\)
\(402\) 0 0
\(403\) −1.00921 0.582668i −0.0502724 0.0290248i
\(404\) −0.857125 + 1.14153i −0.0426436 + 0.0567933i
\(405\) 0 0
\(406\) −9.21171 3.76401i −0.457169 0.186805i
\(407\) −2.01007 + 1.16051i −0.0996353 + 0.0575245i
\(408\) 0 0
\(409\) 22.1550i 1.09549i 0.836644 + 0.547747i \(0.184514\pi\)
−0.836644 + 0.547747i \(0.815486\pi\)
\(410\) −37.5708 42.3924i −1.85549 2.09361i
\(411\) 0 0
\(412\) 2.14262 0.913849i 0.105559 0.0450221i
\(413\) 1.21839 18.4665i 0.0599532 0.908675i
\(414\) 0 0
\(415\) −8.86064 5.11570i −0.434952 0.251120i
\(416\) 0.292322 7.42952i 0.0143323 0.364262i
\(417\) 0 0
\(418\) 19.6213 + 6.54639i 0.959707 + 0.320194i
\(419\) 17.6835 30.6287i 0.863895 1.49631i −0.00424524 0.999991i \(-0.501351\pi\)
0.868140 0.496319i \(-0.165315\pi\)
\(420\) 0 0
\(421\) −15.4856 26.8219i −0.754723 1.30722i −0.945512 0.325588i \(-0.894438\pi\)
0.190788 0.981631i \(-0.438896\pi\)
\(422\) −6.34815 31.0651i −0.309023 1.51223i
\(423\) 0 0
\(424\) −32.4324 15.3667i −1.57505 0.746272i
\(425\) 20.5015i 0.994467i
\(426\) 0 0
\(427\) 6.26051 + 0.413061i 0.302967 + 0.0199894i
\(428\) −14.6332 + 19.4886i −0.707321 + 0.942019i
\(429\) 0 0
\(430\) 14.5876 2.98097i 0.703476 0.143755i
\(431\) −4.22345 + 2.43841i −0.203437 + 0.117454i −0.598257 0.801304i \(-0.704140\pi\)
0.394821 + 0.918758i \(0.370807\pi\)
\(432\) 0 0
\(433\) 13.0744i 0.628314i 0.949371 + 0.314157i \(0.101722\pi\)
−0.949371 + 0.314157i \(0.898278\pi\)
\(434\) −2.62214 + 2.03207i −0.125867 + 0.0975427i
\(435\) 0 0
\(436\) 17.4722 7.45206i 0.836766 0.356889i
\(437\) 10.0877i 0.482560i
\(438\) 0 0
\(439\) 1.91733 0.0915094 0.0457547 0.998953i \(-0.485431\pi\)
0.0457547 + 0.998953i \(0.485431\pi\)
\(440\) −44.9234 + 31.0463i −2.14164 + 1.48007i
\(441\) 0 0
\(442\) −2.39069 2.69749i −0.113713 0.128307i
\(443\) 21.2905i 1.01154i −0.862668 0.505770i \(-0.831208\pi\)
0.862668 0.505770i \(-0.168792\pi\)
\(444\) 0 0
\(445\) 53.1794 2.52095
\(446\) 4.01482 12.0335i 0.190107 0.569802i
\(447\) 0 0
\(448\) −19.2635 8.77023i −0.910116 0.414355i
\(449\) −5.99969 −0.283143 −0.141572 0.989928i \(-0.545216\pi\)
−0.141572 + 0.989928i \(0.545216\pi\)
\(450\) 0 0
\(451\) −24.8291 43.0053i −1.16916 2.02504i
\(452\) 19.9854 + 15.0062i 0.940036 + 0.705832i
\(453\) 0 0
\(454\) −10.7989 + 2.20675i −0.506817 + 0.103568i
\(455\) −0.903469 + 13.6933i −0.0423553 + 0.641953i
\(456\) 0 0
\(457\) −25.3351 −1.18513 −0.592563 0.805524i \(-0.701884\pi\)
−0.592563 + 0.805524i \(0.701884\pi\)
\(458\) 9.12356 + 3.04396i 0.426316 + 0.142235i
\(459\) 0 0
\(460\) −21.2966 15.9907i −0.992961 0.745571i
\(461\) 17.3693 10.0282i 0.808970 0.467059i −0.0376278 0.999292i \(-0.511980\pi\)
0.846598 + 0.532233i \(0.178647\pi\)
\(462\) 0 0
\(463\) −33.2880 19.2188i −1.54702 0.893175i −0.998367 0.0571279i \(-0.981806\pi\)
−0.548658 0.836047i \(-0.684861\pi\)
\(464\) −2.96748 10.2158i −0.137762 0.474259i
\(465\) 0 0
\(466\) 23.4357 4.78907i 1.08564 0.221850i
\(467\) 16.3595 28.3355i 0.757028 1.31121i −0.187332 0.982297i \(-0.559984\pi\)
0.944360 0.328914i \(-0.106683\pi\)
\(468\) 0 0
\(469\) 3.68228 + 0.242952i 0.170032 + 0.0112185i
\(470\) 13.0319 + 4.34792i 0.601115 + 0.200554i
\(471\) 0 0
\(472\) 16.2758 11.2481i 0.749155 0.517736i
\(473\) 13.0526 0.600158
\(474\) 0 0
\(475\) −15.8038 27.3729i −0.725126 1.25596i
\(476\) −9.68267 + 3.39535i −0.443804 + 0.155626i
\(477\) 0 0
\(478\) −5.50884 26.9579i −0.251969 1.23303i
\(479\) −18.3983 + 31.8668i −0.840639 + 1.45603i 0.0487157 + 0.998813i \(0.484487\pi\)
−0.889355 + 0.457217i \(0.848846\pi\)
\(480\) 0 0
\(481\) −0.540016 + 0.311778i −0.0246226 + 0.0142159i
\(482\) 6.67011 + 32.6407i 0.303815 + 1.48674i
\(483\) 0 0
\(484\) −23.7978 + 10.1500i −1.08172 + 0.461363i
\(485\) −4.29243 + 7.43471i −0.194909 + 0.337593i
\(486\) 0 0
\(487\) −3.93075 + 2.26942i −0.178119 + 0.102837i −0.586409 0.810015i \(-0.699459\pi\)
0.408289 + 0.912853i \(0.366125\pi\)
\(488\) 3.81334 + 5.51784i 0.172622 + 0.249781i
\(489\) 0 0
\(490\) 35.1119 + 17.1254i 1.58619 + 0.773648i
\(491\) 10.6660 + 6.15804i 0.481351 + 0.277908i 0.720980 0.692956i \(-0.243692\pi\)
−0.239628 + 0.970865i \(0.577025\pi\)
\(492\) 0 0
\(493\) −4.46616 2.57854i −0.201146 0.116132i
\(494\) 5.27136 + 1.75872i 0.237170 + 0.0791288i
\(495\) 0 0
\(496\) −3.44401 0.846093i −0.154641 0.0379907i
\(497\) 5.69015 + 0.375429i 0.255238 + 0.0168403i
\(498\) 0 0
\(499\) −11.2164 + 6.47580i −0.502115 + 0.289896i −0.729587 0.683888i \(-0.760288\pi\)
0.227471 + 0.973785i \(0.426954\pi\)
\(500\) 43.6636 + 5.28487i 1.95270 + 0.236346i
\(501\) 0 0
\(502\) −4.25092 4.79645i −0.189728 0.214076i
\(503\) −20.4872 −0.913480 −0.456740 0.889600i \(-0.650983\pi\)
−0.456740 + 0.889600i \(0.650983\pi\)
\(504\) 0 0
\(505\) 2.81662 0.125338
\(506\) −15.4852 17.4724i −0.688399 0.776744i
\(507\) 0 0
\(508\) −11.9412 1.44532i −0.529806 0.0641255i
\(509\) 24.6392 14.2255i 1.09211 0.630533i 0.157976 0.987443i \(-0.449503\pi\)
0.934139 + 0.356910i \(0.116170\pi\)
\(510\) 0 0
\(511\) −5.35846 10.8778i −0.237044 0.481204i
\(512\) −5.45270 21.9606i −0.240977 0.970531i
\(513\) 0 0
\(514\) 32.0409 + 10.6901i 1.41327 + 0.471519i
\(515\) −3.98034 2.29805i −0.175395 0.101264i
\(516\) 0 0
\(517\) 10.4300 + 6.02176i 0.458710 + 0.264837i
\(518\) 0.240124 + 1.75877i 0.0105505 + 0.0772757i
\(519\) 0 0
\(520\) −12.0689 + 8.34075i −0.529257 + 0.365766i
\(521\) −32.0751 + 18.5186i −1.40524 + 0.811314i −0.994924 0.100630i \(-0.967914\pi\)
−0.410314 + 0.911944i \(0.634581\pi\)
\(522\) 0 0
\(523\) 2.33168 4.03859i 0.101957 0.176595i −0.810534 0.585692i \(-0.800823\pi\)
0.912491 + 0.409097i \(0.134156\pi\)
\(524\) 3.67671 1.56815i 0.160618 0.0685051i
\(525\) 0 0
\(526\) −7.70192 37.6899i −0.335820 1.64336i
\(527\) −1.48888 + 0.859605i −0.0648566 + 0.0374450i
\(528\) 0 0
\(529\) −5.80694 + 10.0579i −0.252476 + 0.437301i
\(530\) 14.1775 + 69.3785i 0.615830 + 3.01361i
\(531\) 0 0
\(532\) 10.3107 11.9974i 0.447024 0.520151i
\(533\) −6.67049 11.5536i −0.288931 0.500443i
\(534\) 0 0
\(535\) 48.0864 2.07895
\(536\) 2.24292 + 3.24546i 0.0968792 + 0.140183i
\(537\) 0 0
\(538\) 24.5737 + 8.19871i 1.05945 + 0.353472i
\(539\) 27.1520 + 20.8718i 1.16952 + 0.899014i
\(540\) 0 0
\(541\) 11.6836 20.2366i 0.502318 0.870040i −0.497678 0.867362i \(-0.665814\pi\)
0.999996 0.00267870i \(-0.000852658\pi\)
\(542\) −2.14074 + 0.437458i −0.0919524 + 0.0187904i
\(543\) 0 0
\(544\) −9.27661 5.85383i −0.397731 0.250981i
\(545\) −32.4580 18.7396i −1.39035 0.802718i
\(546\) 0 0
\(547\) 21.8092 12.5915i 0.932493 0.538375i 0.0448939 0.998992i \(-0.485705\pi\)
0.887599 + 0.460617i \(0.152372\pi\)
\(548\) 16.0920 + 12.0828i 0.687415 + 0.516150i
\(549\) 0 0
\(550\) 69.3918 + 23.1517i 2.95888 + 0.987192i
\(551\) 7.95077 0.338714
\(552\) 0 0
\(553\) −26.5439 1.75133i −1.12876 0.0744742i
\(554\) 0.673520 0.137633i 0.0286151 0.00584749i
\(555\) 0 0
\(556\) 25.6538 + 19.2623i 1.08796 + 0.816903i
\(557\) 3.17042 + 5.49134i 0.134335 + 0.232675i 0.925343 0.379130i \(-0.123777\pi\)
−0.791008 + 0.611806i \(0.790443\pi\)
\(558\) 0 0
\(559\) 3.50664 0.148315
\(560\) 8.98407 + 40.7852i 0.379646 + 1.72349i
\(561\) 0 0
\(562\) 11.7868 35.3280i 0.497195 1.49022i
\(563\) −1.28515 −0.0541628 −0.0270814 0.999633i \(-0.508621\pi\)
−0.0270814 + 0.999633i \(0.508621\pi\)
\(564\) 0 0
\(565\) 49.3122i 2.07458i
\(566\) 16.1120 + 18.1797i 0.677237 + 0.764149i
\(567\) 0 0
\(568\) 3.46593 + 5.01514i 0.145427 + 0.210430i
\(569\) 19.8770 0.833286 0.416643 0.909070i \(-0.363207\pi\)
0.416643 + 0.909070i \(0.363207\pi\)
\(570\) 0 0
\(571\) 14.3467i 0.600391i 0.953878 + 0.300196i \(0.0970519\pi\)
−0.953878 + 0.300196i \(0.902948\pi\)
\(572\) −11.8300 + 5.04561i −0.494637 + 0.210968i
\(573\) 0 0
\(574\) −37.6287 + 5.13745i −1.57059 + 0.214433i
\(575\) 35.6758i 1.48778i
\(576\) 0 0
\(577\) 10.9881 6.34398i 0.457440 0.264103i −0.253527 0.967328i \(-0.581591\pi\)
0.710967 + 0.703225i \(0.248257\pi\)
\(578\) 18.3449 3.74878i 0.763049 0.155929i
\(579\) 0 0
\(580\) −12.6033 + 16.7853i −0.523324 + 0.696970i
\(581\) −6.15354 + 3.03128i −0.255292 + 0.125759i
\(582\) 0 0
\(583\) 62.0779i 2.57101i
\(584\) 5.55054 11.7148i 0.229683 0.484761i
\(585\) 0 0
\(586\) 7.03488 + 34.4257i 0.290608 + 1.42211i
\(587\) 12.4489 + 21.5622i 0.513823 + 0.889967i 0.999871 + 0.0160352i \(0.00510440\pi\)
−0.486049 + 0.873932i \(0.661562\pi\)
\(588\) 0 0
\(589\) 1.32527 2.29544i 0.0546068 0.0945818i
\(590\) −37.0302 12.3547i −1.52451 0.508634i
\(591\) 0 0
\(592\) −1.31350 + 1.36958i −0.0539846 + 0.0562896i
\(593\) 22.9565 + 13.2540i 0.942712 + 0.544275i 0.890809 0.454377i \(-0.150138\pi\)
0.0519027 + 0.998652i \(0.483471\pi\)
\(594\) 0 0
\(595\) 16.8287 + 11.2551i 0.689909 + 0.461415i
\(596\) −17.8273 + 7.60352i −0.730235 + 0.311452i
\(597\) 0 0
\(598\) −4.16017 4.69406i −0.170122 0.191955i
\(599\) 24.6495i 1.00715i −0.863951 0.503576i \(-0.832017\pi\)
0.863951 0.503576i \(-0.167983\pi\)
\(600\) 0 0
\(601\) 0.673377 0.388774i 0.0274676 0.0158584i −0.486203 0.873846i \(-0.661619\pi\)
0.513671 + 0.857987i \(0.328285\pi\)
\(602\) 3.77586 9.24072i 0.153893 0.376624i
\(603\) 0 0
\(604\) −19.8717 + 26.4653i −0.808566 + 1.07686i
\(605\) 44.2091 + 25.5241i 1.79736 + 1.03770i
\(606\) 0 0
\(607\) 21.0843 + 36.5192i 0.855787 + 1.48227i 0.875913 + 0.482469i \(0.160260\pi\)
−0.0201256 + 0.999797i \(0.506407\pi\)
\(608\) 16.8983 + 0.664883i 0.685318 + 0.0269646i
\(609\) 0 0
\(610\) 4.18849 12.5540i 0.169587 0.508297i
\(611\) 2.80208 + 1.61778i 0.113360 + 0.0654483i
\(612\) 0 0
\(613\) 4.18716 + 7.25237i 0.169118 + 0.292921i 0.938110 0.346338i \(-0.112575\pi\)
−0.768992 + 0.639258i \(0.779241\pi\)
\(614\) −30.0986 33.9612i −1.21468 1.37056i
\(615\) 0 0
\(616\) 0.557978 + 36.6074i 0.0224816 + 1.47496i
\(617\) 8.84616 15.3220i 0.356133 0.616840i −0.631178 0.775638i \(-0.717428\pi\)
0.987311 + 0.158797i \(0.0507617\pi\)
\(618\) 0 0
\(619\) −14.1334 + 24.4797i −0.568068 + 0.983922i 0.428689 + 0.903452i \(0.358975\pi\)
−0.996757 + 0.0804700i \(0.974358\pi\)
\(620\) 2.74523 + 6.43650i 0.110251 + 0.258496i
\(621\) 0 0
\(622\) 12.2395 + 13.8103i 0.490760 + 0.553741i
\(623\) 19.8213 29.6368i 0.794122 1.18737i
\(624\) 0 0
\(625\) −16.9592 29.3743i −0.678369 1.17497i
\(626\) 14.0989 12.4953i 0.563504 0.499412i
\(627\) 0 0
\(628\) 26.0076 + 3.14786i 1.03782 + 0.125613i
\(629\) 0.919927i 0.0366799i
\(630\) 0 0
\(631\) 21.2515i 0.846007i 0.906128 + 0.423004i \(0.139024\pi\)
−0.906128 + 0.423004i \(0.860976\pi\)
\(632\) −16.1681 23.3950i −0.643134 0.930604i
\(633\) 0 0
\(634\) −18.4350 20.8008i −0.732147 0.826107i
\(635\) 11.8667 + 20.5537i 0.470914 + 0.815647i
\(636\) 0 0
\(637\) 7.29452 + 5.60734i 0.289020 + 0.222171i
\(638\) −13.7711 + 12.2049i −0.545205 + 0.483195i
\(639\) 0 0
\(640\) −28.1904 + 34.6209i −1.11432 + 1.36851i
\(641\) −17.2510 + 29.8796i −0.681373 + 1.18017i 0.293189 + 0.956055i \(0.405284\pi\)
−0.974562 + 0.224119i \(0.928050\pi\)
\(642\) 0 0
\(643\) 3.50574 6.07213i 0.138253 0.239461i −0.788582 0.614929i \(-0.789185\pi\)
0.926835 + 0.375468i \(0.122518\pi\)
\(644\) −16.8494 + 5.90845i −0.663958 + 0.232826i
\(645\) 0 0
\(646\) 6.13541 5.43758i 0.241394 0.213939i
\(647\) 0.330066 + 0.571691i 0.0129762 + 0.0224755i 0.872441 0.488720i \(-0.162536\pi\)
−0.859464 + 0.511196i \(0.829203\pi\)
\(648\) 0 0
\(649\) −29.6370 17.1109i −1.16335 0.671662i
\(650\) 18.6425 + 6.21984i 0.731219 + 0.243962i
\(651\) 0 0
\(652\) −9.64647 + 12.8473i −0.377785 + 0.503139i
\(653\) 1.19024 + 2.06155i 0.0465776 + 0.0806748i 0.888374 0.459120i \(-0.151835\pi\)
−0.841797 + 0.539795i \(0.818502\pi\)
\(654\) 0 0
\(655\) −6.83022 3.94343i −0.266879 0.154083i
\(656\) −29.3022 28.1023i −1.14406 1.09721i
\(657\) 0 0
\(658\) 7.28037 5.64205i 0.283819 0.219950i
\(659\) 4.53599 2.61885i 0.176697 0.102016i −0.409043 0.912515i \(-0.634137\pi\)
0.585740 + 0.810499i \(0.300804\pi\)
\(660\) 0 0
\(661\) 7.34107i 0.285535i 0.989756 + 0.142767i \(0.0456001\pi\)
−0.989756 + 0.142767i \(0.954400\pi\)
\(662\) 15.2474 13.5132i 0.592606 0.525204i
\(663\) 0 0
\(664\) −6.62704 3.13994i −0.257179 0.121853i
\(665\) −31.1453 2.05493i −1.20776 0.0796867i
\(666\) 0 0
\(667\) −7.77183 4.48707i −0.300926 0.173740i
\(668\) 15.4714 + 11.6168i 0.598606 + 0.449467i
\(669\) 0 0
\(670\) 2.46357 7.38397i 0.0951760 0.285268i
\(671\) 5.80096 10.0476i 0.223943 0.387881i
\(672\) 0 0
\(673\) 6.21172 + 10.7590i 0.239444 + 0.414730i 0.960555 0.278090i \(-0.0897014\pi\)
−0.721111 + 0.692820i \(0.756368\pi\)
\(674\) 1.35753 0.277411i 0.0522901 0.0106855i
\(675\) 0 0
\(676\) 20.7374 8.84470i 0.797592 0.340181i
\(677\) 29.8294i 1.14644i −0.819403 0.573218i \(-0.805695\pi\)
0.819403 0.573218i \(-0.194305\pi\)
\(678\) 0 0
\(679\) 2.54346 + 5.16326i 0.0976089 + 0.198148i
\(680\) 1.75388 + 21.5722i 0.0672583 + 0.827258i
\(681\) 0 0
\(682\) 1.22818 + 6.01017i 0.0470293 + 0.230141i
\(683\) −9.32990 + 5.38662i −0.356999 + 0.206113i −0.667763 0.744374i \(-0.732748\pi\)
0.310765 + 0.950487i \(0.399415\pi\)
\(684\) 0 0
\(685\) 39.7054i 1.51707i
\(686\) 22.6310 13.1847i 0.864056 0.503395i
\(687\) 0 0
\(688\) 10.2480 2.97683i 0.390702 0.113491i
\(689\) 16.6776i 0.635365i
\(690\) 0 0
\(691\) −47.3937 −1.80294 −0.901471 0.432840i \(-0.857512\pi\)
−0.901471 + 0.432840i \(0.857512\pi\)
\(692\) 32.5383 + 3.93831i 1.23692 + 0.149712i
\(693\) 0 0
\(694\) 29.0348 25.7325i 1.10215 0.976791i
\(695\) 63.2982i 2.40104i
\(696\) 0 0
\(697\) −19.6818 −0.745502
\(698\) −20.1922 6.73689i −0.764287 0.254995i
\(699\) 0 0
\(700\) 36.4643 42.4294i 1.37822 1.60368i
\(701\) 39.5982 1.49560 0.747801 0.663923i \(-0.231110\pi\)
0.747801 + 0.663923i \(0.231110\pi\)
\(702\) 0 0
\(703\) −0.709135 1.22826i −0.0267455 0.0463246i
\(704\) −30.2894 + 24.7882i −1.14157 + 0.934240i
\(705\) 0 0
\(706\) 5.24011 + 25.6429i 0.197214 + 0.965082i
\(707\) 1.04982 1.56970i 0.0394826 0.0590345i
\(708\) 0 0
\(709\) 27.4992 1.03276 0.516378 0.856361i \(-0.327280\pi\)
0.516378 + 0.856361i \(0.327280\pi\)
\(710\) 3.80690 11.4103i 0.142870 0.428220i
\(711\) 0 0
\(712\) 37.9906 3.08874i 1.42376 0.115755i
\(713\) −2.59089 + 1.49585i −0.0970295 + 0.0560200i
\(714\) 0 0
\(715\) 21.9766 + 12.6882i 0.821877 + 0.474511i
\(716\) −14.5481 34.1097i −0.543689 1.27474i
\(717\) 0 0
\(718\) −1.65060 8.07731i −0.0615997 0.301443i
\(719\) −26.4956 + 45.8917i −0.988118 + 1.71147i −0.360954 + 0.932584i \(0.617549\pi\)
−0.627164 + 0.778887i \(0.715784\pi\)
\(720\) 0 0
\(721\) −2.76427 + 1.36170i −0.102947 + 0.0507123i
\(722\) 4.50385 13.4992i 0.167616 0.502389i
\(723\) 0 0
\(724\) −45.6757 5.52840i −1.69752 0.205461i
\(725\) 28.1184 1.04429
\(726\) 0 0
\(727\) −15.2977 26.4963i −0.567359 0.982694i −0.996826 0.0796118i \(-0.974632\pi\)
0.429467 0.903082i \(-0.358701\pi\)
\(728\) 0.149904 + 9.83479i 0.00555580 + 0.364502i
\(729\) 0 0
\(730\) −25.0600 + 5.12099i −0.927511 + 0.189536i
\(731\) 2.58666 4.48023i 0.0956711 0.165707i
\(732\) 0 0
\(733\) −0.610768 + 0.352627i −0.0225592 + 0.0130246i −0.511237 0.859440i \(-0.670813\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(734\) −2.50508 + 0.511913i −0.0924643 + 0.0188950i
\(735\) 0 0
\(736\) −16.1428 10.1866i −0.595030 0.375483i
\(737\) 3.41198 5.90973i 0.125682 0.217688i
\(738\) 0 0
\(739\) −29.5374 + 17.0534i −1.08655 + 0.627321i −0.932656 0.360766i \(-0.882515\pi\)
−0.153896 + 0.988087i \(0.549182\pi\)
\(740\) 3.71713 + 0.449907i 0.136645 + 0.0165389i
\(741\) 0 0
\(742\) 43.9488 + 17.9580i 1.61341 + 0.659258i
\(743\) −32.7970 18.9353i −1.20320 0.694670i −0.241938 0.970292i \(-0.577783\pi\)
−0.961266 + 0.275621i \(0.911116\pi\)
\(744\) 0 0
\(745\) 33.1178 + 19.1205i 1.21334 + 0.700523i
\(746\) 2.66720 7.99429i 0.0976530 0.292692i
\(747\) 0 0
\(748\) −2.27987 + 18.8363i −0.0833605 + 0.688725i
\(749\) 17.9229 26.7984i 0.654890 0.979194i
\(750\) 0 0
\(751\) −15.6928 + 9.06026i −0.572639 + 0.330613i −0.758203 0.652019i \(-0.773922\pi\)
0.185563 + 0.982632i \(0.440589\pi\)
\(752\) 9.56230 + 2.34918i 0.348701 + 0.0856657i
\(753\) 0 0
\(754\) −3.69970 + 3.27890i −0.134735 + 0.119411i
\(755\) 65.3007 2.37654
\(756\) 0 0
\(757\) −30.0755 −1.09311 −0.546555 0.837423i \(-0.684061\pi\)
−0.546555 + 0.837423i \(0.684061\pi\)
\(758\) −17.4961 + 15.5061i −0.635488 + 0.563209i
\(759\) 0 0
\(760\) −18.9709 27.4506i −0.688147 0.995738i
\(761\) −19.2695 + 11.1252i −0.698518 + 0.403290i −0.806795 0.590831i \(-0.798800\pi\)
0.108277 + 0.994121i \(0.465467\pi\)
\(762\) 0 0
\(763\) −22.5415 + 11.1041i −0.816056 + 0.401995i
\(764\) 7.83108 + 0.947842i 0.283318 + 0.0342917i
\(765\) 0 0
\(766\) −1.47613 + 4.42434i −0.0533346 + 0.159858i
\(767\) −7.96214 4.59694i −0.287496 0.165986i
\(768\) 0 0
\(769\) 9.46235 + 5.46309i 0.341221 + 0.197004i 0.660812 0.750552i \(-0.270212\pi\)
−0.319591 + 0.947556i \(0.603545\pi\)
\(770\) 57.0997 44.2504i 2.05773 1.59467i
\(771\) 0 0
\(772\) −1.38183 + 11.4167i −0.0497332 + 0.410896i
\(773\) 10.6286 6.13643i 0.382284 0.220712i −0.296527 0.955024i \(-0.595829\pi\)
0.678812 + 0.734312i \(0.262495\pi\)
\(774\) 0 0
\(775\) 4.68690 8.11795i 0.168359 0.291605i
\(776\) −2.63463 + 5.56056i −0.0945777 + 0.199612i
\(777\) 0 0
\(778\) −13.3692 + 2.73199i −0.479309 + 0.0979467i
\(779\) 26.2786 15.1719i 0.941527 0.543591i
\(780\) 0 0
\(781\) 5.27246 9.13217i 0.188663 0.326775i
\(782\) −9.06605 + 1.85264i −0.324201 + 0.0662504i
\(783\) 0 0
\(784\) 26.0781 + 10.1948i 0.931360 + 0.364100i
\(785\) −25.8452 44.7653i −0.922456 1.59774i
\(786\) 0 0
\(787\) 2.27050 0.0809345 0.0404672 0.999181i \(-0.487115\pi\)
0.0404672 + 0.999181i \(0.487115\pi\)
\(788\) −3.98956 + 32.9618i −0.142122 + 1.17422i
\(789\) 0 0
\(790\) −17.7587 + 53.2276i −0.631827 + 1.89375i
\(791\) −27.4816 18.3798i −0.977133 0.653512i
\(792\) 0 0
\(793\) 1.55846 2.69933i 0.0553425 0.0958560i
\(794\) 1.05336 + 5.15472i 0.0373825 + 0.182934i
\(795\) 0 0
\(796\) −22.9365 + 9.78266i −0.812964 + 0.346737i
\(797\) −4.92030 2.84074i −0.174286 0.100624i 0.410319 0.911942i \(-0.365417\pi\)
−0.584605 + 0.811318i \(0.698751\pi\)
\(798\) 0 0
\(799\) 4.13388 2.38669i 0.146246 0.0844352i
\(800\) 59.7620 + 2.35140i 2.11290 + 0.0831345i
\(801\) 0 0
\(802\) −10.7294 + 32.1589i −0.378869 + 1.13557i
\(803\) −22.4229 −0.791289
\(804\) 0 0
\(805\) 29.2846 + 19.5857i 1.03215 + 0.690306i
\(806\) 0.329957 + 1.61467i 0.0116222 + 0.0568742i
\(807\) 0 0
\(808\) 2.01215 0.163593i 0.0707872 0.00575519i
\(809\) 8.28527 + 14.3505i 0.291295 + 0.504537i 0.974116 0.226048i \(-0.0725806\pi\)
−0.682821 + 0.730585i \(0.739247\pi\)
\(810\) 0 0
\(811\) 10.2931 0.361438 0.180719 0.983535i \(-0.442158\pi\)
0.180719 + 0.983535i \(0.442158\pi\)
\(812\) 4.65683 + 13.2801i 0.163423 + 0.466040i
\(813\) 0 0
\(814\) 3.11370 + 1.03885i 0.109135 + 0.0364116i
\(815\) 31.6995 1.11038
\(816\) 0 0
\(817\) 7.97581i 0.279038i
\(818\) 23.4483 20.7814i 0.819851 0.726603i
\(819\) 0 0
\(820\) −9.62575 + 79.5280i −0.336146 + 2.77724i
\(821\) 0.101592 0.00354560 0.00177280 0.999998i \(-0.499436\pi\)
0.00177280 + 0.999998i \(0.499436\pi\)
\(822\) 0 0
\(823\) 55.1859i 1.92366i −0.273650 0.961829i \(-0.588231\pi\)
0.273650 0.961829i \(-0.411769\pi\)
\(824\) −2.97697 1.41051i −0.103708 0.0491374i
\(825\) 0 0
\(826\) −20.6873 + 16.0320i −0.719803 + 0.557824i
\(827\) 37.1634i 1.29230i −0.763211 0.646149i \(-0.776378\pi\)
0.763211 0.646149i \(-0.223622\pi\)
\(828\) 0 0
\(829\) 33.4823 19.3310i 1.16289 0.671393i 0.210893 0.977509i \(-0.432363\pi\)
0.951994 + 0.306116i \(0.0990295\pi\)
\(830\) 2.89694 + 14.1764i 0.100554 + 0.492070i
\(831\) 0 0
\(832\) −8.13742 + 6.65949i −0.282114 + 0.230876i
\(833\) 12.5449 5.18354i 0.434656 0.179599i
\(834\) 0 0
\(835\) 38.1742i 1.32107i
\(836\) −11.4762 26.9072i −0.396912 0.930604i
\(837\) 0 0
\(838\) −49.0038 + 10.0139i −1.69281 + 0.345924i
\(839\) 2.58403 + 4.47567i 0.0892106 + 0.154517i 0.907178 0.420748i \(-0.138232\pi\)
−0.817967 + 0.575265i \(0.804899\pi\)
\(840\) 0 0
\(841\) 10.9635 18.9893i 0.378050 0.654802i
\(842\) −13.8621 + 41.5485i −0.477721 + 1.43186i
\(843\) 0 0
\(844\) −26.9240 + 35.8578i −0.926763 + 1.23427i
\(845\) −38.5238 22.2417i −1.32526 0.765138i
\(846\) 0 0
\(847\) 30.7024 15.1242i 1.05495 0.519673i
\(848\) 14.1578 + 48.7395i 0.486180 + 1.67372i
\(849\) 0 0
\(850\) 21.6983 19.2303i 0.744244 0.659595i
\(851\) 1.60082i 0.0548754i
\(852\) 0 0
\(853\) −30.1332 + 17.3974i −1.03174 + 0.595675i −0.917483 0.397776i \(-0.869782\pi\)
−0.114257 + 0.993451i \(0.536449\pi\)
\(854\) −5.43518 7.01342i −0.185988 0.239994i
\(855\) 0 0
\(856\) 34.3522 2.79293i 1.17413 0.0954602i
\(857\) −37.1025 21.4212i −1.26740 0.731733i −0.292903 0.956142i \(-0.594621\pi\)
−0.974495 + 0.224409i \(0.927955\pi\)
\(858\) 0 0
\(859\) −15.9716 27.6637i −0.544945 0.943873i −0.998610 0.0527008i \(-0.983217\pi\)
0.453665 0.891172i \(-0.350116\pi\)
\(860\) −16.8381 12.6430i −0.574175 0.431123i
\(861\) 0 0
\(862\) 6.54235 + 2.18277i 0.222833 + 0.0743455i
\(863\) −30.0490 17.3488i −1.02288 0.590560i −0.107943 0.994157i \(-0.534426\pi\)
−0.914937 + 0.403597i \(0.867760\pi\)
\(864\) 0 0
\(865\) −32.3352 56.0061i −1.09943 1.90427i
\(866\) 13.8376 12.2637i 0.470221 0.416739i
\(867\) 0 0
\(868\) 4.61026 + 0.869128i 0.156482 + 0.0295001i
\(869\) −24.5954 + 42.6005i −0.834342 + 1.44512i
\(870\) 0 0
\(871\) 0.916648 1.58768i 0.0310594 0.0537965i
\(872\) −24.2760 11.5021i −0.822088 0.389511i
\(873\) 0 0
\(874\) 10.6766 9.46225i 0.361141 0.320065i
\(875\) −58.0568 3.83052i −1.96268 0.129495i
\(876\) 0 0
\(877\) 11.1213 + 19.2627i 0.375540 + 0.650455i 0.990408 0.138175i \(-0.0441238\pi\)
−0.614867 + 0.788631i \(0.710790\pi\)
\(878\) −1.79846 2.02926i −0.0606950 0.0684842i
\(879\) 0 0
\(880\) 74.9967 + 18.4245i 2.52814 + 0.621090i
\(881\) 20.4228i 0.688061i 0.938958 + 0.344031i \(0.111792\pi\)
−0.938958 + 0.344031i \(0.888208\pi\)
\(882\) 0 0
\(883\) 11.6027i 0.390461i 0.980757 + 0.195231i \(0.0625456\pi\)
−0.980757 + 0.195231i \(0.937454\pi\)
\(884\) −0.612501 + 5.06049i −0.0206006 + 0.170203i
\(885\) 0 0
\(886\) −22.5333 + 19.9704i −0.757021 + 0.670919i
\(887\) −26.5399 45.9684i −0.891123 1.54347i −0.838531 0.544853i \(-0.816585\pi\)
−0.0525911 0.998616i \(-0.516748\pi\)
\(888\) 0 0
\(889\) 15.8775 + 1.04758i 0.532514 + 0.0351346i
\(890\) −49.8822 56.2838i −1.67206 1.88664i
\(891\) 0 0
\(892\) −16.5018 + 7.03819i −0.552522 + 0.235656i
\(893\) −3.67962 + 6.37328i −0.123134 + 0.213274i
\(894\) 0 0
\(895\) −36.5841 + 63.3655i −1.22287 + 2.11808i
\(896\) 8.78695 + 28.6145i 0.293551 + 0.955943i
\(897\) 0 0
\(898\) 5.62770 + 6.34993i 0.187799 + 0.211900i
\(899\) 1.17898 + 2.04205i 0.0393210 + 0.0681060i
\(900\) 0 0
\(901\) 21.3079 + 12.3021i 0.709870 + 0.409844i
\(902\) −22.2261 + 66.6175i −0.740049 + 2.21812i
\(903\) 0 0
\(904\) −2.86412 35.2279i −0.0952593 1.17166i
\(905\) 45.3905 + 78.6187i 1.50883 + 2.61337i
\(906\) 0 0
\(907\) 47.3583 + 27.3424i 1.57251 + 0.907888i 0.995860 + 0.0908948i \(0.0289727\pi\)
0.576647 + 0.816993i \(0.304361\pi\)
\(908\) 12.4649 + 9.35935i 0.413662 + 0.310601i
\(909\) 0 0
\(910\) 15.3401 11.8881i 0.508521 0.394087i
\(911\) 1.27865 0.738229i 0.0423636 0.0244586i −0.478669 0.877996i \(-0.658880\pi\)
0.521032 + 0.853537i \(0.325547\pi\)
\(912\) 0 0
\(913\) 12.6846i 0.419800i
\(914\) 23.7643 + 26.8141i 0.786053 + 0.886930i
\(915\) 0 0
\(916\) −5.33623 12.5114i −0.176314 0.413388i
\(917\) −4.74345 + 2.33666i −0.156643 + 0.0771632i
\(918\) 0 0
\(919\) 16.9505 + 9.78639i 0.559146 + 0.322823i 0.752803 0.658246i \(-0.228701\pi\)
−0.193657 + 0.981069i \(0.562035\pi\)
\(920\) 3.05203 + 37.5391i 0.100623 + 1.23763i
\(921\) 0 0
\(922\) −26.9060 8.97685i −0.886102 0.295637i
\(923\) 1.41648 2.45341i 0.0466239 0.0807549i
\(924\) 0 0
\(925\) −2.50790 4.34381i −0.0824592 0.142824i
\(926\) 10.8833 + 53.2584i 0.357649 + 1.75018i
\(927\) 0 0
\(928\) −8.02871 + 12.7232i −0.263555 + 0.417658i
\(929\) 14.4455i 0.473942i 0.971517 + 0.236971i \(0.0761546\pi\)
−0.971517 + 0.236971i \(0.923845\pi\)
\(930\) 0 0
\(931\) −12.7538 + 16.5913i −0.417989 + 0.543758i
\(932\) −27.0513 20.3116i −0.886094 0.665329i
\(933\) 0 0
\(934\) −45.3348 + 9.26415i −1.48340 + 0.303132i
\(935\) 32.4218 18.7187i 1.06031 0.612168i
\(936\) 0 0
\(937\) 31.4809i 1.02844i 0.857659 + 0.514218i \(0.171918\pi\)
−0.857659 + 0.514218i \(0.828082\pi\)
\(938\) −3.19684 4.12513i −0.104381 0.134690i
\(939\) 0 0
\(940\) −7.62213 17.8709i −0.248606 0.582886i
\(941\) 40.3346i 1.31487i −0.753511 0.657435i \(-0.771641\pi\)
0.753511 0.657435i \(-0.228359\pi\)
\(942\) 0 0
\(943\) −34.2495 −1.11532
\(944\) −27.1714 6.67523i −0.884354 0.217260i
\(945\) 0 0
\(946\) −12.2433 13.8145i −0.398064 0.449149i
\(947\) 14.8597i 0.482876i 0.970416 + 0.241438i \(0.0776190\pi\)
−0.970416 + 0.241438i \(0.922381\pi\)
\(948\) 0 0
\(949\) −6.02405 −0.195549
\(950\) −14.1469 + 42.4021i −0.458987 + 1.37571i
\(951\) 0 0
\(952\) 12.6759 + 7.06306i 0.410828 + 0.228915i
\(953\) 11.8041 0.382371 0.191185 0.981554i \(-0.438767\pi\)
0.191185 + 0.981554i \(0.438767\pi\)
\(954\) 0 0
\(955\) −7.78219 13.4791i −0.251826 0.436175i
\(956\) −23.3643 + 31.1169i −0.755657 + 1.00639i
\(957\) 0 0
\(958\) 50.9846 10.4187i 1.64724 0.336612i
\(959\) −22.1278 14.7992i −0.714543 0.477890i
\(960\) 0 0
\(961\) −30.2139 −0.974643
\(962\) 0.836512 + 0.279092i 0.0269702 + 0.00899829i
\(963\) 0 0
\(964\) 28.2895 37.6764i 0.911145 1.21347i
\(965\) 19.6508 11.3454i 0.632583 0.365222i
\(966\) 0 0
\(967\) 2.41663 + 1.39524i 0.0777137 + 0.0448680i 0.538353 0.842719i \(-0.319047\pi\)
−0.460640 + 0.887587i \(0.652380\pi\)
\(968\) 33.0648 + 15.6663i 1.06274 + 0.503535i
\(969\) 0 0
\(970\) 11.8950 2.43074i 0.381926 0.0780464i
\(971\) −26.2483 + 45.4633i −0.842347 + 1.45899i 0.0455582 + 0.998962i \(0.485493\pi\)
−0.887905 + 0.460026i \(0.847840\pi\)
\(972\) 0 0
\(973\) −35.2760 23.5928i −1.13090 0.756350i
\(974\) 6.08894 + 2.03150i 0.195102 + 0.0650935i
\(975\) 0 0
\(976\) 2.26304 9.21167i 0.0724382 0.294858i
\(977\) 10.2879 0.329140 0.164570 0.986365i \(-0.447376\pi\)
0.164570 + 0.986365i \(0.447376\pi\)
\(978\) 0 0
\(979\) −32.9653 57.0976i −1.05358 1.82485i
\(980\) −14.8097 53.2252i −0.473080 1.70022i
\(981\) 0 0
\(982\) −3.48721 17.0649i −0.111281 0.544563i
\(983\) −16.4524 + 28.4963i −0.524749 + 0.908891i 0.474836 + 0.880074i \(0.342507\pi\)
−0.999585 + 0.0288169i \(0.990826\pi\)
\(984\) 0 0
\(985\) 56.7351 32.7560i 1.80773 1.04369i
\(986\) 1.46019 + 7.14554i 0.0465019 + 0.227560i
\(987\) 0 0
\(988\) −3.08314 7.22876i −0.0980876 0.229978i
\(989\) 4.50120 7.79630i 0.143130 0.247908i
\(990\) 0 0
\(991\) 48.3716 27.9273i 1.53657 0.887141i 0.537537 0.843240i \(-0.319355\pi\)
0.999036 0.0439007i \(-0.0139785\pi\)
\(992\) 2.33499 + 4.43869i 0.0741361 + 0.140929i
\(993\) 0 0
\(994\) −4.94000 6.37446i −0.156687 0.202186i
\(995\) 42.6092 + 24.6004i 1.35080 + 0.779885i
\(996\) 0 0
\(997\) 0.219422 + 0.126684i 0.00694917 + 0.00401211i 0.503471 0.864012i \(-0.332056\pi\)
−0.496521 + 0.868024i \(0.665390\pi\)
\(998\) 17.3748 + 5.79689i 0.549990 + 0.183497i
\(999\) 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 756.2.bj.b.523.11 84
3.2 odd 2 252.2.bj.b.103.32 yes 84
4.3 odd 2 inner 756.2.bj.b.523.12 84
7.3 odd 6 756.2.n.b.199.39 84
9.2 odd 6 252.2.n.b.187.25 yes 84
9.7 even 3 756.2.n.b.19.18 84
12.11 even 2 252.2.bj.b.103.31 yes 84
21.17 even 6 252.2.n.b.31.4 84
28.3 even 6 756.2.n.b.199.18 84
36.7 odd 6 756.2.n.b.19.39 84
36.11 even 6 252.2.n.b.187.4 yes 84
63.38 even 6 252.2.bj.b.115.32 yes 84
63.52 odd 6 inner 756.2.bj.b.451.11 84
84.59 odd 6 252.2.n.b.31.25 yes 84
252.115 even 6 inner 756.2.bj.b.451.12 84
252.227 odd 6 252.2.bj.b.115.31 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.4 84 21.17 even 6
252.2.n.b.31.25 yes 84 84.59 odd 6
252.2.n.b.187.4 yes 84 36.11 even 6
252.2.n.b.187.25 yes 84 9.2 odd 6
252.2.bj.b.103.31 yes 84 12.11 even 2
252.2.bj.b.103.32 yes 84 3.2 odd 2
252.2.bj.b.115.31 yes 84 252.227 odd 6
252.2.bj.b.115.32 yes 84 63.38 even 6
756.2.n.b.19.18 84 9.7 even 3
756.2.n.b.19.39 84 36.7 odd 6
756.2.n.b.199.18 84 28.3 even 6
756.2.n.b.199.39 84 7.3 odd 6
756.2.bj.b.451.11 84 63.52 odd 6 inner
756.2.bj.b.451.12 84 252.115 even 6 inner
756.2.bj.b.523.11 84 1.1 even 1 trivial
756.2.bj.b.523.12 84 4.3 odd 2 inner