Properties

Label 819.2.gh.d.262.4
Level $819$
Weight $2$
Character 819.262
Analytic conductor $6.540$
Analytic rank $0$
Dimension $40$
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(19,819)]
 
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, 10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.gh (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: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 262.4
Character \(\chi\) \(=\) 819.262
Dual form 819.2.gh.d.397.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.306419 - 1.14357i) q^{2} +(0.518187 - 0.299176i) q^{4} +(0.424345 - 1.58368i) q^{5} +(1.65856 - 2.06135i) q^{7} +(-2.17522 - 2.17522i) q^{8} +O(q^{10})\) \(q+(-0.306419 - 1.14357i) q^{2} +(0.518187 - 0.299176i) q^{4} +(0.424345 - 1.58368i) q^{5} +(1.65856 - 2.06135i) q^{7} +(-2.17522 - 2.17522i) q^{8} -1.94108 q^{10} +(-2.06227 - 2.06227i) q^{11} +(-2.68202 + 2.40972i) q^{13} +(-2.86552 - 1.26505i) q^{14} +(-1.22264 + 2.11767i) q^{16} +(0.405682 + 0.702662i) q^{17} +(-4.56252 - 4.56252i) q^{19} +(-0.253908 - 0.947596i) q^{20} +(-1.72644 + 2.99028i) q^{22} +(1.58869 + 0.917230i) q^{23} +(2.00216 + 1.15595i) q^{25} +(3.57751 + 2.32870i) q^{26} +(0.242740 - 1.56437i) q^{28} +(2.42827 + 4.20589i) q^{29} +(3.78817 - 1.01504i) q^{31} +(-3.14646 - 0.843090i) q^{32} +(0.679235 - 0.679235i) q^{34} +(-2.56071 - 3.50136i) q^{35} +(3.95665 - 1.06018i) q^{37} +(-3.81952 + 6.61561i) q^{38} +(-4.36789 + 2.52180i) q^{40} +(-0.392080 + 1.46326i) q^{41} +(-2.14648 - 1.23927i) q^{43} +(-1.68563 - 0.451662i) q^{44} +(0.562114 - 2.09784i) q^{46} +(1.21631 + 0.325908i) q^{47} +(-1.49834 - 6.83776i) q^{49} +(0.708408 - 2.64382i) q^{50} +(-0.668861 + 2.05108i) q^{52} +(1.12609 - 1.95045i) q^{53} +(-4.14109 + 2.39086i) q^{55} +(-8.09162 + 0.876152i) q^{56} +(4.06566 - 4.06566i) q^{58} +(-6.46664 - 1.73273i) q^{59} +0.516055i q^{61} +(-2.32154 - 4.02102i) q^{62} +8.74708i q^{64} +(2.67812 + 5.27002i) q^{65} +(9.11247 - 9.11247i) q^{67} +(0.420438 + 0.242740i) q^{68} +(-3.21940 + 4.00124i) q^{70} +(2.21845 + 8.27936i) q^{71} +(-2.64503 - 9.87139i) q^{73} +(-2.42479 - 4.19986i) q^{74} +(-3.72923 - 0.999244i) q^{76} +(-7.67148 + 0.830660i) q^{77} +(-2.17152 - 3.76119i) q^{79} +(2.83489 + 2.83489i) q^{80} +1.79349 q^{82} +(-7.44835 - 7.44835i) q^{83} +(1.28494 - 0.344298i) q^{85} +(-0.759473 + 2.83439i) q^{86} +8.97178i q^{88} +(2.18907 + 8.16973i) q^{89} +(0.518974 + 9.52526i) q^{91} +1.09765 q^{92} -1.49080i q^{94} +(-9.16164 + 5.28948i) q^{95} +(-16.5763 + 4.44161i) q^{97} +(-7.36035 + 3.80868i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.306419 1.14357i −0.216671 0.808627i −0.985572 0.169259i \(-0.945863\pi\)
0.768901 0.639368i \(-0.220804\pi\)
\(3\) 0 0
\(4\) 0.518187 0.299176i 0.259094 0.149588i
\(5\) 0.424345 1.58368i 0.189773 0.708243i −0.803785 0.594920i \(-0.797184\pi\)
0.993558 0.113323i \(-0.0361495\pi\)
\(6\) 0 0
\(7\) 1.65856 2.06135i 0.626878 0.779118i
\(8\) −2.17522 2.17522i −0.769055 0.769055i
\(9\) 0 0
\(10\) −1.94108 −0.613823
\(11\) −2.06227 2.06227i −0.621799 0.621799i 0.324192 0.945991i \(-0.394907\pi\)
−0.945991 + 0.324192i \(0.894907\pi\)
\(12\) 0 0
\(13\) −2.68202 + 2.40972i −0.743860 + 0.668336i
\(14\) −2.86552 1.26505i −0.765842 0.338098i
\(15\) 0 0
\(16\) −1.22264 + 2.11767i −0.305659 + 0.529417i
\(17\) 0.405682 + 0.702662i 0.0983923 + 0.170420i 0.911019 0.412364i \(-0.135297\pi\)
−0.812627 + 0.582784i \(0.801963\pi\)
\(18\) 0 0
\(19\) −4.56252 4.56252i −1.04671 1.04671i −0.998854 0.0478587i \(-0.984760\pi\)
−0.0478587 0.998854i \(-0.515240\pi\)
\(20\) −0.253908 0.947596i −0.0567755 0.211889i
\(21\) 0 0
\(22\) −1.72644 + 2.99028i −0.368078 + 0.637529i
\(23\) 1.58869 + 0.917230i 0.331265 + 0.191256i 0.656402 0.754411i \(-0.272077\pi\)
−0.325138 + 0.945667i \(0.605411\pi\)
\(24\) 0 0
\(25\) 2.00216 + 1.15595i 0.400432 + 0.231189i
\(26\) 3.57751 + 2.32870i 0.701608 + 0.456696i
\(27\) 0 0
\(28\) 0.242740 1.56437i 0.0458736 0.295638i
\(29\) 2.42827 + 4.20589i 0.450918 + 0.781013i 0.998443 0.0557760i \(-0.0177633\pi\)
−0.547525 + 0.836789i \(0.684430\pi\)
\(30\) 0 0
\(31\) 3.78817 1.01504i 0.680376 0.182306i 0.0979517 0.995191i \(-0.468771\pi\)
0.582424 + 0.812885i \(0.302104\pi\)
\(32\) −3.14646 0.843090i −0.556220 0.149039i
\(33\) 0 0
\(34\) 0.679235 0.679235i 0.116488 0.116488i
\(35\) −2.56071 3.50136i −0.432840 0.591837i
\(36\) 0 0
\(37\) 3.95665 1.06018i 0.650470 0.174293i 0.0815285 0.996671i \(-0.474020\pi\)
0.568941 + 0.822378i \(0.307353\pi\)
\(38\) −3.81952 + 6.61561i −0.619608 + 1.07319i
\(39\) 0 0
\(40\) −4.36789 + 2.52180i −0.690624 + 0.398732i
\(41\) −0.392080 + 1.46326i −0.0612326 + 0.228523i −0.989760 0.142740i \(-0.954409\pi\)
0.928528 + 0.371263i \(0.121075\pi\)
\(42\) 0 0
\(43\) −2.14648 1.23927i −0.327335 0.188987i 0.327322 0.944913i \(-0.393854\pi\)
−0.654657 + 0.755926i \(0.727187\pi\)
\(44\) −1.68563 0.451662i −0.254118 0.0680906i
\(45\) 0 0
\(46\) 0.562114 2.09784i 0.0828791 0.309309i
\(47\) 1.21631 + 0.325908i 0.177417 + 0.0475386i 0.346434 0.938075i \(-0.387393\pi\)
−0.169017 + 0.985613i \(0.554059\pi\)
\(48\) 0 0
\(49\) −1.49834 6.83776i −0.214048 0.976823i
\(50\) 0.708408 2.64382i 0.100184 0.373892i
\(51\) 0 0
\(52\) −0.668861 + 2.05108i −0.0927544 + 0.284434i
\(53\) 1.12609 1.95045i 0.154681 0.267915i −0.778262 0.627940i \(-0.783898\pi\)
0.932943 + 0.360025i \(0.117232\pi\)
\(54\) 0 0
\(55\) −4.14109 + 2.39086i −0.558385 + 0.322384i
\(56\) −8.09162 + 0.876152i −1.08129 + 0.117081i
\(57\) 0 0
\(58\) 4.06566 4.06566i 0.533848 0.533848i
\(59\) −6.46664 1.73273i −0.841885 0.225582i −0.187993 0.982170i \(-0.560198\pi\)
−0.653892 + 0.756588i \(0.726865\pi\)
\(60\) 0 0
\(61\) 0.516055i 0.0660741i 0.999454 + 0.0330370i \(0.0105179\pi\)
−0.999454 + 0.0330370i \(0.989482\pi\)
\(62\) −2.32154 4.02102i −0.294836 0.510670i
\(63\) 0 0
\(64\) 8.74708i 1.09339i
\(65\) 2.67812 + 5.27002i 0.332180 + 0.653665i
\(66\) 0 0
\(67\) 9.11247 9.11247i 1.11327 1.11327i 0.120560 0.992706i \(-0.461531\pi\)
0.992706 0.120560i \(-0.0384689\pi\)
\(68\) 0.420438 + 0.242740i 0.0509856 + 0.0294366i
\(69\) 0 0
\(70\) −3.21940 + 4.00124i −0.384792 + 0.478240i
\(71\) 2.21845 + 8.27936i 0.263281 + 0.982580i 0.963294 + 0.268449i \(0.0865111\pi\)
−0.700012 + 0.714131i \(0.746822\pi\)
\(72\) 0 0
\(73\) −2.64503 9.87139i −0.309578 1.15536i −0.928933 0.370248i \(-0.879273\pi\)
0.619355 0.785111i \(-0.287394\pi\)
\(74\) −2.42479 4.19986i −0.281876 0.488223i
\(75\) 0 0
\(76\) −3.72923 0.999244i −0.427772 0.114621i
\(77\) −7.67148 + 0.830660i −0.874246 + 0.0946625i
\(78\) 0 0
\(79\) −2.17152 3.76119i −0.244315 0.423167i 0.717623 0.696431i \(-0.245230\pi\)
−0.961939 + 0.273265i \(0.911897\pi\)
\(80\) 2.83489 + 2.83489i 0.316950 + 0.316950i
\(81\) 0 0
\(82\) 1.79349 0.198058
\(83\) −7.44835 7.44835i −0.817563 0.817563i 0.168191 0.985754i \(-0.446207\pi\)
−0.985754 + 0.168191i \(0.946207\pi\)
\(84\) 0 0
\(85\) 1.28494 0.344298i 0.139371 0.0373444i
\(86\) −0.759473 + 2.83439i −0.0818961 + 0.305640i
\(87\) 0 0
\(88\) 8.97178i 0.956395i
\(89\) 2.18907 + 8.16973i 0.232041 + 0.865989i 0.979460 + 0.201637i \(0.0646260\pi\)
−0.747419 + 0.664353i \(0.768707\pi\)
\(90\) 0 0
\(91\) 0.518974 + 9.52526i 0.0544033 + 0.998519i
\(92\) 1.09765 0.114438
\(93\) 0 0
\(94\) 1.49080i 0.153764i
\(95\) −9.16164 + 5.28948i −0.939964 + 0.542689i
\(96\) 0 0
\(97\) −16.5763 + 4.44161i −1.68307 + 0.450978i −0.968587 0.248674i \(-0.920005\pi\)
−0.714484 + 0.699652i \(0.753339\pi\)
\(98\) −7.36035 + 3.80868i −0.743508 + 0.384735i
\(99\) 0 0
\(100\) 1.38332 0.138332
\(101\) 15.2229 1.51473 0.757365 0.652992i \(-0.226486\pi\)
0.757365 + 0.652992i \(0.226486\pi\)
\(102\) 0 0
\(103\) 8.54491 + 14.8002i 0.841955 + 1.45831i 0.888240 + 0.459380i \(0.151928\pi\)
−0.0462849 + 0.998928i \(0.514738\pi\)
\(104\) 11.0756 + 0.592320i 1.08606 + 0.0580817i
\(105\) 0 0
\(106\) −2.57554 0.690114i −0.250159 0.0670298i
\(107\) 8.82716 15.2891i 0.853354 1.47805i −0.0248100 0.999692i \(-0.507898\pi\)
0.878164 0.478360i \(-0.158769\pi\)
\(108\) 0 0
\(109\) −2.21695 8.27379i −0.212346 0.792485i −0.987084 0.160203i \(-0.948785\pi\)
0.774738 0.632282i \(-0.217882\pi\)
\(110\) 4.00303 + 4.00303i 0.381674 + 0.381674i
\(111\) 0 0
\(112\) 2.33744 + 6.03257i 0.220867 + 0.570024i
\(113\) 0.708253 1.22673i 0.0666268 0.115401i −0.830788 0.556589i \(-0.812110\pi\)
0.897414 + 0.441188i \(0.145443\pi\)
\(114\) 0 0
\(115\) 2.12675 2.12675i 0.198320 0.198320i
\(116\) 2.51660 + 1.45296i 0.233660 + 0.134904i
\(117\) 0 0
\(118\) 7.92601i 0.729649i
\(119\) 2.12128 + 0.329156i 0.194458 + 0.0301736i
\(120\) 0 0
\(121\) 2.49406i 0.226733i
\(122\) 0.590146 0.158129i 0.0534293 0.0143163i
\(123\) 0 0
\(124\) 1.65931 1.65931i 0.149010 0.149010i
\(125\) 8.47692 8.47692i 0.758199 0.758199i
\(126\) 0 0
\(127\) −5.29671 + 3.05806i −0.470007 + 0.271359i −0.716243 0.697851i \(-0.754140\pi\)
0.246236 + 0.969210i \(0.420806\pi\)
\(128\) 3.71001 0.994093i 0.327921 0.0878662i
\(129\) 0 0
\(130\) 5.20602 4.67745i 0.456598 0.410240i
\(131\) 14.8958 8.60009i 1.30145 0.751393i 0.320798 0.947148i \(-0.396049\pi\)
0.980653 + 0.195755i \(0.0627156\pi\)
\(132\) 0 0
\(133\) −16.9722 + 1.83773i −1.47167 + 0.159351i
\(134\) −13.2130 7.62853i −1.14143 0.659005i
\(135\) 0 0
\(136\) 0.645995 2.41089i 0.0553936 0.206732i
\(137\) −4.40600 + 16.4434i −0.376430 + 1.40486i 0.474814 + 0.880086i \(0.342515\pi\)
−0.851244 + 0.524770i \(0.824151\pi\)
\(138\) 0 0
\(139\) 9.74248 + 5.62482i 0.826346 + 0.477091i 0.852600 0.522564i \(-0.175024\pi\)
−0.0262538 + 0.999655i \(0.508358\pi\)
\(140\) −2.37445 1.04825i −0.200678 0.0885937i
\(141\) 0 0
\(142\) 8.78827 5.07391i 0.737495 0.425793i
\(143\) 10.5006 + 0.561565i 0.878101 + 0.0469604i
\(144\) 0 0
\(145\) 7.69120 2.06085i 0.638719 0.171144i
\(146\) −10.4782 + 6.04957i −0.867179 + 0.500666i
\(147\) 0 0
\(148\) 1.73311 1.73311i 0.142461 0.142461i
\(149\) 16.6802 16.6802i 1.36649 1.36649i 0.501107 0.865386i \(-0.332926\pi\)
0.865386 0.501107i \(-0.167074\pi\)
\(150\) 0 0
\(151\) −1.75102 + 0.469184i −0.142496 + 0.0381817i −0.329362 0.944204i \(-0.606834\pi\)
0.186866 + 0.982385i \(0.440167\pi\)
\(152\) 19.8489i 1.60996i
\(153\) 0 0
\(154\) 3.30061 + 8.51836i 0.265970 + 0.686429i
\(155\) 6.42998i 0.516468i
\(156\) 0 0
\(157\) −0.0225395 0.0130132i −0.00179885 0.00103857i 0.499100 0.866544i \(-0.333664\pi\)
−0.500899 + 0.865506i \(0.666997\pi\)
\(158\) −3.63579 + 3.63579i −0.289248 + 0.289248i
\(159\) 0 0
\(160\) −2.67037 + 4.62521i −0.211111 + 0.365655i
\(161\) 4.52567 1.75356i 0.356673 0.138200i
\(162\) 0 0
\(163\) 12.2030 + 12.2030i 0.955814 + 0.955814i 0.999064 0.0432504i \(-0.0137713\pi\)
−0.0432504 + 0.999064i \(0.513771\pi\)
\(164\) 0.234602 + 0.875545i 0.0183193 + 0.0683686i
\(165\) 0 0
\(166\) −6.23541 + 10.8000i −0.483962 + 0.838246i
\(167\) −8.63919 2.31486i −0.668521 0.179130i −0.0914324 0.995811i \(-0.529145\pi\)
−0.577088 + 0.816682i \(0.695811\pi\)
\(168\) 0 0
\(169\) 1.38650 12.9259i 0.106654 0.994296i
\(170\) −0.787460 1.36392i −0.0603954 0.104608i
\(171\) 0 0
\(172\) −1.48304 −0.113081
\(173\) −19.0267 −1.44657 −0.723287 0.690548i \(-0.757369\pi\)
−0.723287 + 0.690548i \(0.757369\pi\)
\(174\) 0 0
\(175\) 5.70352 2.20994i 0.431145 0.167056i
\(176\) 6.88862 1.84580i 0.519249 0.139132i
\(177\) 0 0
\(178\) 8.67189 5.00672i 0.649986 0.375270i
\(179\) 21.5069i 1.60750i −0.594967 0.803750i \(-0.702835\pi\)
0.594967 0.803750i \(-0.297165\pi\)
\(180\) 0 0
\(181\) −6.08778 −0.452501 −0.226250 0.974069i \(-0.572647\pi\)
−0.226250 + 0.974069i \(0.572647\pi\)
\(182\) 10.7338 3.51221i 0.795642 0.260342i
\(183\) 0 0
\(184\) −1.46057 5.45092i −0.107675 0.401847i
\(185\) 6.71595i 0.493767i
\(186\) 0 0
\(187\) 0.612453 2.28571i 0.0447870 0.167147i
\(188\) 0.727779 0.195008i 0.0530787 0.0142224i
\(189\) 0 0
\(190\) 8.85620 + 8.85620i 0.642496 + 0.642496i
\(191\) 26.1213 1.89007 0.945034 0.326971i \(-0.106028\pi\)
0.945034 + 0.326971i \(0.106028\pi\)
\(192\) 0 0
\(193\) 15.2997 + 15.2997i 1.10129 + 1.10129i 0.994255 + 0.107040i \(0.0341371\pi\)
0.107040 + 0.994255i \(0.465863\pi\)
\(194\) 10.1586 + 17.5952i 0.729346 + 1.26326i
\(195\) 0 0
\(196\) −2.82211 3.09497i −0.201579 0.221070i
\(197\) −2.18156 0.584548i −0.155430 0.0416473i 0.180265 0.983618i \(-0.442304\pi\)
−0.335695 + 0.941971i \(0.608971\pi\)
\(198\) 0 0
\(199\) −3.41153 5.90895i −0.241837 0.418874i 0.719400 0.694596i \(-0.244417\pi\)
−0.961238 + 0.275721i \(0.911083\pi\)
\(200\) −1.84069 6.86956i −0.130157 0.485751i
\(201\) 0 0
\(202\) −4.66457 17.4084i −0.328198 1.22485i
\(203\) 12.6972 + 1.97021i 0.891172 + 0.138282i
\(204\) 0 0
\(205\) 2.15096 + 1.24186i 0.150230 + 0.0867351i
\(206\) 14.3068 14.3068i 0.996801 0.996801i
\(207\) 0 0
\(208\) −1.82385 8.62585i −0.126461 0.598095i
\(209\) 18.8183i 1.30169i
\(210\) 0 0
\(211\) −0.270154 0.467920i −0.0185982 0.0322130i 0.856577 0.516020i \(-0.172587\pi\)
−0.875175 + 0.483807i \(0.839254\pi\)
\(212\) 1.34760i 0.0925536i
\(213\) 0 0
\(214\) −20.1890 5.40962i −1.38009 0.369794i
\(215\) −2.87346 + 2.87346i −0.195968 + 0.195968i
\(216\) 0 0
\(217\) 4.19057 9.49226i 0.284475 0.644377i
\(218\) −8.78235 + 5.07049i −0.594816 + 0.343417i
\(219\) 0 0
\(220\) −1.43057 + 2.47783i −0.0964493 + 0.167055i
\(221\) −2.78127 0.906975i −0.187088 0.0610098i
\(222\) 0 0
\(223\) 1.64421 6.13628i 0.110105 0.410916i −0.888770 0.458354i \(-0.848439\pi\)
0.998874 + 0.0474384i \(0.0151058\pi\)
\(224\) −6.95650 + 5.08763i −0.464801 + 0.339932i
\(225\) 0 0
\(226\) −1.61988 0.434044i −0.107753 0.0288722i
\(227\) −5.68899 + 21.2316i −0.377592 + 1.40919i 0.471929 + 0.881636i \(0.343558\pi\)
−0.849521 + 0.527555i \(0.823109\pi\)
\(228\) 0 0
\(229\) 25.8801 + 6.93454i 1.71020 + 0.458247i 0.975474 0.220115i \(-0.0706431\pi\)
0.734728 + 0.678362i \(0.237310\pi\)
\(230\) −3.08377 1.78041i −0.203338 0.117397i
\(231\) 0 0
\(232\) 3.86670 14.4307i 0.253861 0.947423i
\(233\) 9.35685 5.40218i 0.612988 0.353909i −0.161146 0.986931i \(-0.551519\pi\)
0.774134 + 0.633022i \(0.218186\pi\)
\(234\) 0 0
\(235\) 1.03227 1.78794i 0.0673378 0.116632i
\(236\) −3.86932 + 1.03678i −0.251872 + 0.0674888i
\(237\) 0 0
\(238\) −0.273588 2.52670i −0.0177341 0.163781i
\(239\) 20.4504 20.4504i 1.32282 1.32282i 0.411345 0.911480i \(-0.365059\pi\)
0.911480 0.411345i \(-0.134941\pi\)
\(240\) 0 0
\(241\) −7.71785 2.06799i −0.497150 0.133211i 0.00152691 0.999999i \(-0.499514\pi\)
−0.498677 + 0.866788i \(0.666181\pi\)
\(242\) −2.85214 + 0.764227i −0.183342 + 0.0491264i
\(243\) 0 0
\(244\) 0.154391 + 0.267413i 0.00988388 + 0.0171194i
\(245\) −11.4646 0.528686i −0.732448 0.0337765i
\(246\) 0 0
\(247\) 23.2312 + 1.24239i 1.47816 + 0.0790514i
\(248\) −10.4480 6.03217i −0.663450 0.383043i
\(249\) 0 0
\(250\) −12.2915 7.09648i −0.777380 0.448821i
\(251\) −3.59872 + 6.23316i −0.227149 + 0.393434i −0.956962 0.290213i \(-0.906274\pi\)
0.729813 + 0.683647i \(0.239607\pi\)
\(252\) 0 0
\(253\) −1.38473 5.16789i −0.0870573 0.324902i
\(254\) 5.12012 + 5.12012i 0.321265 + 0.321265i
\(255\) 0 0
\(256\) 6.47345 + 11.2123i 0.404591 + 0.700772i
\(257\) −9.95744 + 17.2468i −0.621128 + 1.07583i 0.368148 + 0.929767i \(0.379992\pi\)
−0.989276 + 0.146058i \(0.953341\pi\)
\(258\) 0 0
\(259\) 4.37695 9.91443i 0.271970 0.616053i
\(260\) 2.96443 + 1.92963i 0.183846 + 0.119670i
\(261\) 0 0
\(262\) −14.3992 14.3992i −0.889584 0.889584i
\(263\) −13.6905 −0.844194 −0.422097 0.906551i \(-0.638706\pi\)
−0.422097 + 0.906551i \(0.638706\pi\)
\(264\) 0 0
\(265\) −2.61104 2.61104i −0.160395 0.160395i
\(266\) 7.30217 + 18.8458i 0.447725 + 1.15551i
\(267\) 0 0
\(268\) 1.99574 7.44820i 0.121909 0.454971i
\(269\) 1.73392 1.00108i 0.105719 0.0610368i −0.446208 0.894929i \(-0.647226\pi\)
0.551927 + 0.833892i \(0.313893\pi\)
\(270\) 0 0
\(271\) 5.53795 + 20.6679i 0.336407 + 1.25549i 0.902336 + 0.431033i \(0.141851\pi\)
−0.565930 + 0.824454i \(0.691483\pi\)
\(272\) −1.98401 −0.120298
\(273\) 0 0
\(274\) 20.1543 1.21757
\(275\) −1.74512 6.51287i −0.105235 0.392741i
\(276\) 0 0
\(277\) −15.3585 + 8.86722i −0.922801 + 0.532780i −0.884528 0.466488i \(-0.845519\pi\)
−0.0382736 + 0.999267i \(0.512186\pi\)
\(278\) 3.44711 12.8648i 0.206744 0.771578i
\(279\) 0 0
\(280\) −2.04610 + 13.1863i −0.122278 + 0.788033i
\(281\) 20.0393 + 20.0393i 1.19545 + 1.19545i 0.975515 + 0.219932i \(0.0705834\pi\)
0.219932 + 0.975515i \(0.429417\pi\)
\(282\) 0 0
\(283\) 7.43296 0.441843 0.220922 0.975292i \(-0.429093\pi\)
0.220922 + 0.975292i \(0.429093\pi\)
\(284\) 3.62656 + 3.62656i 0.215196 + 0.215196i
\(285\) 0 0
\(286\) −2.57538 12.1802i −0.152286 0.720232i
\(287\) 2.36601 + 3.23513i 0.139661 + 0.190964i
\(288\) 0 0
\(289\) 8.17084 14.1523i 0.480638 0.832489i
\(290\) −4.71346 8.16395i −0.276784 0.479404i
\(291\) 0 0
\(292\) −4.32390 4.32390i −0.253037 0.253037i
\(293\) 1.93278 + 7.21323i 0.112914 + 0.421401i 0.999122 0.0418859i \(-0.0133366\pi\)
−0.886208 + 0.463287i \(0.846670\pi\)
\(294\) 0 0
\(295\) −5.48818 + 9.50581i −0.319534 + 0.553450i
\(296\) −10.9127 6.30045i −0.634288 0.366206i
\(297\) 0 0
\(298\) −24.1861 13.9638i −1.40106 0.808904i
\(299\) −6.47117 + 1.36826i −0.374237 + 0.0791287i
\(300\) 0 0
\(301\) −6.11465 + 2.36924i −0.352442 + 0.136561i
\(302\) 1.07309 + 1.85865i 0.0617495 + 0.106953i
\(303\) 0 0
\(304\) 15.2402 4.08360i 0.874085 0.234210i
\(305\) 0.817265 + 0.218986i 0.0467965 + 0.0125391i
\(306\) 0 0
\(307\) 14.3746 14.3746i 0.820400 0.820400i −0.165765 0.986165i \(-0.553009\pi\)
0.986165 + 0.165765i \(0.0530094\pi\)
\(308\) −3.72675 + 2.72556i −0.212351 + 0.155303i
\(309\) 0 0
\(310\) −7.35314 + 1.97027i −0.417630 + 0.111904i
\(311\) −2.05346 + 3.55670i −0.116441 + 0.201682i −0.918355 0.395758i \(-0.870482\pi\)
0.801914 + 0.597440i \(0.203815\pi\)
\(312\) 0 0
\(313\) −20.5196 + 11.8470i −1.15984 + 0.669632i −0.951265 0.308375i \(-0.900215\pi\)
−0.208572 + 0.978007i \(0.566882\pi\)
\(314\) −0.00797499 + 0.0297631i −0.000450055 + 0.00167963i
\(315\) 0 0
\(316\) −2.25051 1.29933i −0.126601 0.0730932i
\(317\) 10.7209 + 2.87265i 0.602144 + 0.161344i 0.546998 0.837134i \(-0.315771\pi\)
0.0551466 + 0.998478i \(0.482437\pi\)
\(318\) 0 0
\(319\) 3.66593 13.6814i 0.205253 0.766013i
\(320\) 13.8526 + 3.71178i 0.774382 + 0.207495i
\(321\) 0 0
\(322\) −3.39208 4.63811i −0.189033 0.258472i
\(323\) 1.35497 5.05683i 0.0753928 0.281370i
\(324\) 0 0
\(325\) −8.15534 + 1.72436i −0.452377 + 0.0956505i
\(326\) 10.2158 17.6943i 0.565800 0.979994i
\(327\) 0 0
\(328\) 4.03577 2.33005i 0.222838 0.128656i
\(329\) 2.68913 1.96670i 0.148257 0.108427i
\(330\) 0 0
\(331\) −10.2743 + 10.2743i −0.564729 + 0.564729i −0.930647 0.365918i \(-0.880755\pi\)
0.365918 + 0.930647i \(0.380755\pi\)
\(332\) −6.08801 1.63128i −0.334123 0.0895280i
\(333\) 0 0
\(334\) 10.5889i 0.579396i
\(335\) −10.5644 18.2981i −0.577194 0.999730i
\(336\) 0 0
\(337\) 8.20930i 0.447189i 0.974682 + 0.223594i \(0.0717791\pi\)
−0.974682 + 0.223594i \(0.928221\pi\)
\(338\) −15.2065 + 2.37516i −0.827124 + 0.129192i
\(339\) 0 0
\(340\) 0.562834 0.562834i 0.0305239 0.0305239i
\(341\) −9.90553 5.71896i −0.536415 0.309699i
\(342\) 0 0
\(343\) −16.5801 8.25225i −0.895242 0.445580i
\(344\) 1.97338 + 7.36475i 0.106397 + 0.397080i
\(345\) 0 0
\(346\) 5.83014 + 21.7584i 0.313430 + 1.16974i
\(347\) −6.17589 10.6970i −0.331539 0.574243i 0.651275 0.758842i \(-0.274235\pi\)
−0.982814 + 0.184599i \(0.940901\pi\)
\(348\) 0 0
\(349\) −3.95084 1.05862i −0.211483 0.0566668i 0.151522 0.988454i \(-0.451583\pi\)
−0.363005 + 0.931787i \(0.618249\pi\)
\(350\) −4.27489 5.84521i −0.228503 0.312440i
\(351\) 0 0
\(352\) 4.75017 + 8.22753i 0.253185 + 0.438529i
\(353\) −17.6691 17.6691i −0.940431 0.940431i 0.0578922 0.998323i \(-0.481562\pi\)
−0.998323 + 0.0578922i \(0.981562\pi\)
\(354\) 0 0
\(355\) 14.0532 0.745869
\(356\) 3.57853 + 3.57853i 0.189662 + 0.189662i
\(357\) 0 0
\(358\) −24.5947 + 6.59012i −1.29987 + 0.348299i
\(359\) −5.24373 + 19.5699i −0.276753 + 1.03286i 0.677904 + 0.735151i \(0.262889\pi\)
−0.954657 + 0.297707i \(0.903778\pi\)
\(360\) 0 0
\(361\) 22.6331i 1.19122i
\(362\) 1.86541 + 6.96181i 0.0980438 + 0.365905i
\(363\) 0 0
\(364\) 3.11865 + 4.78061i 0.163462 + 0.250572i
\(365\) −16.7555 −0.877024
\(366\) 0 0
\(367\) 22.6562i 1.18265i 0.806435 + 0.591323i \(0.201394\pi\)
−0.806435 + 0.591323i \(0.798606\pi\)
\(368\) −3.88478 + 2.24288i −0.202508 + 0.116918i
\(369\) 0 0
\(370\) −7.68017 + 2.05790i −0.399273 + 0.106985i
\(371\) −2.15287 5.55623i −0.111771 0.288465i
\(372\) 0 0
\(373\) −15.2022 −0.787140 −0.393570 0.919295i \(-0.628760\pi\)
−0.393570 + 0.919295i \(0.628760\pi\)
\(374\) −2.80154 −0.144864
\(375\) 0 0
\(376\) −1.93681 3.35465i −0.0998833 0.173003i
\(377\) −16.6477 5.42884i −0.857399 0.279599i
\(378\) 0 0
\(379\) 29.1074 + 7.79931i 1.49515 + 0.400623i 0.911471 0.411364i \(-0.134947\pi\)
0.583676 + 0.811987i \(0.301614\pi\)
\(380\) −3.16496 + 5.48188i −0.162359 + 0.281214i
\(381\) 0 0
\(382\) −8.00406 29.8715i −0.409523 1.52836i
\(383\) −2.01992 2.01992i −0.103213 0.103213i 0.653614 0.756828i \(-0.273252\pi\)
−0.756828 + 0.653614i \(0.773252\pi\)
\(384\) 0 0
\(385\) −1.93986 + 12.5016i −0.0988643 + 0.637143i
\(386\) 12.8082 22.1844i 0.651918 1.12916i
\(387\) 0 0
\(388\) −7.26082 + 7.26082i −0.368612 + 0.368612i
\(389\) 8.56918 + 4.94742i 0.434474 + 0.250844i 0.701251 0.712914i \(-0.252625\pi\)
−0.266777 + 0.963758i \(0.585959\pi\)
\(390\) 0 0
\(391\) 1.48841i 0.0752723i
\(392\) −11.6144 + 18.1328i −0.586616 + 0.915846i
\(393\) 0 0
\(394\) 2.67389i 0.134709i
\(395\) −6.87799 + 1.84295i −0.346069 + 0.0927290i
\(396\) 0 0
\(397\) −8.23489 + 8.23489i −0.413297 + 0.413297i −0.882886 0.469588i \(-0.844402\pi\)
0.469588 + 0.882886i \(0.344402\pi\)
\(398\) −5.71195 + 5.71195i −0.286314 + 0.286314i
\(399\) 0 0
\(400\) −4.89582 + 2.82661i −0.244791 + 0.141330i
\(401\) −8.23517 + 2.20661i −0.411245 + 0.110193i −0.458509 0.888690i \(-0.651616\pi\)
0.0472642 + 0.998882i \(0.484950\pi\)
\(402\) 0 0
\(403\) −7.71401 + 11.8508i −0.384262 + 0.590330i
\(404\) 7.88829 4.55431i 0.392457 0.226585i
\(405\) 0 0
\(406\) −1.63760 15.1239i −0.0812728 0.750587i
\(407\) −10.3461 5.97332i −0.512836 0.296086i
\(408\) 0 0
\(409\) −7.67045 + 28.6265i −0.379280 + 1.41549i 0.467710 + 0.883882i \(0.345079\pi\)
−0.846990 + 0.531609i \(0.821588\pi\)
\(410\) 0.761058 2.84031i 0.0375860 0.140273i
\(411\) 0 0
\(412\) 8.85573 + 5.11286i 0.436290 + 0.251892i
\(413\) −14.2971 + 10.4562i −0.703514 + 0.514515i
\(414\) 0 0
\(415\) −14.9565 + 8.63512i −0.734184 + 0.423882i
\(416\) 10.4705 5.32089i 0.513358 0.260878i
\(417\) 0 0
\(418\) 21.5201 5.76629i 1.05258 0.282038i
\(419\) −5.87227 + 3.39035i −0.286879 + 0.165630i −0.636533 0.771249i \(-0.719632\pi\)
0.349655 + 0.936879i \(0.386299\pi\)
\(420\) 0 0
\(421\) −0.568530 + 0.568530i −0.0277084 + 0.0277084i −0.720825 0.693117i \(-0.756237\pi\)
0.693117 + 0.720825i \(0.256237\pi\)
\(422\) −0.452320 + 0.452320i −0.0220186 + 0.0220186i
\(423\) 0 0
\(424\) −6.69216 + 1.79316i −0.325000 + 0.0870835i
\(425\) 1.87579i 0.0909890i
\(426\) 0 0
\(427\) 1.06377 + 0.855910i 0.0514795 + 0.0414204i
\(428\) 10.5635i 0.510605i
\(429\) 0 0
\(430\) 4.16649 + 2.40552i 0.200926 + 0.116005i
\(431\) 27.9494 27.9494i 1.34628 1.34628i 0.456609 0.889668i \(-0.349064\pi\)
0.889668 0.456609i \(-0.150936\pi\)
\(432\) 0 0
\(433\) −6.52576 + 11.3030i −0.313608 + 0.543185i −0.979141 0.203184i \(-0.934871\pi\)
0.665533 + 0.746369i \(0.268204\pi\)
\(434\) −12.1392 1.88361i −0.582698 0.0904162i
\(435\) 0 0
\(436\) −3.62411 3.62411i −0.173564 0.173564i
\(437\) −3.06354 11.4333i −0.146549 0.546929i
\(438\) 0 0
\(439\) 6.52378 11.2995i 0.311363 0.539297i −0.667295 0.744794i \(-0.732548\pi\)
0.978658 + 0.205497i \(0.0658811\pi\)
\(440\) 14.2084 + 3.80713i 0.677360 + 0.181498i
\(441\) 0 0
\(442\) −0.184958 + 3.45849i −0.00879757 + 0.164504i
\(443\) −6.21784 10.7696i −0.295418 0.511680i 0.679664 0.733524i \(-0.262126\pi\)
−0.975082 + 0.221844i \(0.928792\pi\)
\(444\) 0 0
\(445\) 13.8671 0.657366
\(446\) −7.52110 −0.356134
\(447\) 0 0
\(448\) 18.0308 + 14.5076i 0.851876 + 0.685419i
\(449\) −34.8689 + 9.34311i −1.64557 + 0.440928i −0.958367 0.285539i \(-0.907827\pi\)
−0.687200 + 0.726468i \(0.741161\pi\)
\(450\) 0 0
\(451\) 3.82622 2.20907i 0.180170 0.104021i
\(452\) 0.847568i 0.0398662i
\(453\) 0 0
\(454\) 26.0231 1.22132
\(455\) 15.3052 + 3.22011i 0.717518 + 0.150961i
\(456\) 0 0
\(457\) 7.53955 + 28.1380i 0.352685 + 1.31624i 0.883372 + 0.468672i \(0.155267\pi\)
−0.530687 + 0.847568i \(0.678066\pi\)
\(458\) 31.7206i 1.48220i
\(459\) 0 0
\(460\) 0.465783 1.73833i 0.0217173 0.0810499i
\(461\) −9.16537 + 2.45585i −0.426874 + 0.114381i −0.465858 0.884859i \(-0.654254\pi\)
0.0389845 + 0.999240i \(0.487588\pi\)
\(462\) 0 0
\(463\) −20.6084 20.6084i −0.957754 0.957754i 0.0413889 0.999143i \(-0.486822\pi\)
−0.999143 + 0.0413889i \(0.986822\pi\)
\(464\) −11.8756 −0.551309
\(465\) 0 0
\(466\) −9.04490 9.04490i −0.418997 0.418997i
\(467\) 16.5197 + 28.6129i 0.764440 + 1.32405i 0.940542 + 0.339677i \(0.110318\pi\)
−0.176102 + 0.984372i \(0.556349\pi\)
\(468\) 0 0
\(469\) −3.67040 33.8976i −0.169483 1.56525i
\(470\) −2.36095 0.632614i −0.108902 0.0291803i
\(471\) 0 0
\(472\) 10.2973 + 17.8354i 0.473971 + 0.820942i
\(473\) 1.87091 + 6.98235i 0.0860247 + 0.321049i
\(474\) 0 0
\(475\) −3.86085 14.4089i −0.177148 0.661126i
\(476\) 1.19770 0.464071i 0.0548963 0.0212707i
\(477\) 0 0
\(478\) −29.6529 17.1201i −1.35629 0.783054i
\(479\) −18.1414 + 18.1414i −0.828903 + 0.828903i −0.987365 0.158462i \(-0.949346\pi\)
0.158462 + 0.987365i \(0.449346\pi\)
\(480\) 0 0
\(481\) −8.05710 + 12.3779i −0.367372 + 0.564382i
\(482\) 9.45958i 0.430872i
\(483\) 0 0
\(484\) −0.746162 1.29239i −0.0339164 0.0587450i
\(485\) 28.1364i 1.27761i
\(486\) 0 0
\(487\) −6.15499 1.64923i −0.278909 0.0747336i 0.116653 0.993173i \(-0.462784\pi\)
−0.395562 + 0.918439i \(0.629450\pi\)
\(488\) 1.12253 1.12253i 0.0508146 0.0508146i
\(489\) 0 0
\(490\) 2.90839 + 13.2726i 0.131388 + 0.599596i
\(491\) −23.9297 + 13.8158i −1.07993 + 0.623500i −0.930878 0.365329i \(-0.880956\pi\)
−0.149055 + 0.988829i \(0.547623\pi\)
\(492\) 0 0
\(493\) −1.97021 + 3.41250i −0.0887338 + 0.153691i
\(494\) −5.69771 26.9472i −0.256352 1.21241i
\(495\) 0 0
\(496\) −2.48205 + 9.26312i −0.111447 + 0.415926i
\(497\) 20.7461 + 9.15884i 0.930590 + 0.410830i
\(498\) 0 0
\(499\) 1.78545 + 0.478410i 0.0799278 + 0.0214166i 0.298561 0.954390i \(-0.403493\pi\)
−0.218634 + 0.975807i \(0.570160\pi\)
\(500\) 1.85654 6.92872i 0.0830272 0.309862i
\(501\) 0 0
\(502\) 8.23078 + 2.20543i 0.367358 + 0.0984332i
\(503\) −1.57204 0.907615i −0.0700936 0.0404686i 0.464544 0.885550i \(-0.346218\pi\)
−0.534637 + 0.845082i \(0.679552\pi\)
\(504\) 0 0
\(505\) 6.45975 24.1081i 0.287455 1.07280i
\(506\) −5.48554 + 3.16708i −0.243862 + 0.140794i
\(507\) 0 0
\(508\) −1.82979 + 3.16929i −0.0811838 + 0.140615i
\(509\) 17.3620 4.65215i 0.769559 0.206203i 0.147382 0.989080i \(-0.452915\pi\)
0.622177 + 0.782877i \(0.286249\pi\)
\(510\) 0 0
\(511\) −24.7354 10.9200i −1.09423 0.483072i
\(512\) 16.2704 16.2704i 0.719055 0.719055i
\(513\) 0 0
\(514\) 22.7741 + 6.10230i 1.00452 + 0.269161i
\(515\) 27.0648 7.25199i 1.19262 0.319561i
\(516\) 0 0
\(517\) −1.83624 3.18047i −0.0807580 0.139877i
\(518\) −12.6790 1.96739i −0.557085 0.0864420i
\(519\) 0 0
\(520\) 5.63794 17.2889i 0.247240 0.758169i
\(521\) 13.2345 + 7.64094i 0.579814 + 0.334756i 0.761059 0.648682i \(-0.224680\pi\)
−0.181245 + 0.983438i \(0.558013\pi\)
\(522\) 0 0
\(523\) −27.9830 16.1560i −1.22361 0.706452i −0.257925 0.966165i \(-0.583039\pi\)
−0.965686 + 0.259713i \(0.916372\pi\)
\(524\) 5.14587 8.91291i 0.224798 0.389362i
\(525\) 0 0
\(526\) 4.19504 + 15.6561i 0.182912 + 0.682638i
\(527\) 2.25002 + 2.25002i 0.0980125 + 0.0980125i
\(528\) 0 0
\(529\) −9.81738 17.0042i −0.426843 0.739313i
\(530\) −2.18584 + 3.78598i −0.0949467 + 0.164453i
\(531\) 0 0
\(532\) −8.24496 + 6.02995i −0.357464 + 0.261431i
\(533\) −2.47449 4.86931i −0.107182 0.210913i
\(534\) 0 0
\(535\) −20.4672 20.4672i −0.884876 0.884876i
\(536\) −39.6432 −1.71233
\(537\) 0 0
\(538\) −1.67611 1.67611i −0.0722622 0.0722622i
\(539\) −11.0113 + 17.1913i −0.474292 + 0.740482i
\(540\) 0 0
\(541\) 4.91231 18.3330i 0.211197 0.788197i −0.776274 0.630396i \(-0.782893\pi\)
0.987471 0.157802i \(-0.0504407\pi\)
\(542\) 21.9383 12.6661i 0.942331 0.544055i
\(543\) 0 0
\(544\) −0.684053 2.55292i −0.0293285 0.109456i
\(545\) −14.0438 −0.601569
\(546\) 0 0
\(547\) −8.64107 −0.369465 −0.184733 0.982789i \(-0.559142\pi\)
−0.184733 + 0.982789i \(0.559142\pi\)
\(548\) 2.63633 + 9.83894i 0.112619 + 0.420299i
\(549\) 0 0
\(550\) −6.91320 + 3.99134i −0.294780 + 0.170191i
\(551\) 8.11040 30.2684i 0.345515 1.28948i
\(552\) 0 0
\(553\) −11.3547 1.76190i −0.482853 0.0749234i
\(554\) 14.8464 + 14.8464i 0.630764 + 0.630764i
\(555\) 0 0
\(556\) 6.73124 0.285468
\(557\) 12.8552 + 12.8552i 0.544694 + 0.544694i 0.924901 0.380207i \(-0.124147\pi\)
−0.380207 + 0.924901i \(0.624147\pi\)
\(558\) 0 0
\(559\) 8.74321 1.84866i 0.369798 0.0781901i
\(560\) 10.5455 1.14186i 0.445630 0.0482524i
\(561\) 0 0
\(562\) 16.7760 29.0569i 0.707652 1.22569i
\(563\) −7.38562 12.7923i −0.311267 0.539130i 0.667370 0.744726i \(-0.267420\pi\)
−0.978637 + 0.205596i \(0.934087\pi\)
\(564\) 0 0
\(565\) −1.64220 1.64220i −0.0690880 0.0690880i
\(566\) −2.27760 8.50012i −0.0957347 0.357287i
\(567\) 0 0
\(568\) 13.1838 22.8350i 0.553180 0.958136i
\(569\) 23.1049 + 13.3396i 0.968607 + 0.559226i 0.898811 0.438335i \(-0.144432\pi\)
0.0697961 + 0.997561i \(0.477765\pi\)
\(570\) 0 0
\(571\) 17.3259 + 10.0031i 0.725067 + 0.418618i 0.816615 0.577183i \(-0.195848\pi\)
−0.0915476 + 0.995801i \(0.529181\pi\)
\(572\) 5.60927 2.85052i 0.234535 0.119186i
\(573\) 0 0
\(574\) 2.97461 3.69701i 0.124158 0.154310i
\(575\) 2.12054 + 3.67288i 0.0884325 + 0.153170i
\(576\) 0 0
\(577\) 41.8386 11.2106i 1.74177 0.466705i 0.758928 0.651175i \(-0.225724\pi\)
0.982838 + 0.184470i \(0.0590569\pi\)
\(578\) −18.6879 5.00741i −0.777314 0.208281i
\(579\) 0 0
\(580\) 3.36892 3.36892i 0.139887 0.139887i
\(581\) −27.7072 + 3.00011i −1.14949 + 0.124466i
\(582\) 0 0
\(583\) −6.34468 + 1.70005i −0.262770 + 0.0704090i
\(584\) −15.7189 + 27.2259i −0.650453 + 1.12662i
\(585\) 0 0
\(586\) 7.65660 4.42054i 0.316291 0.182611i
\(587\) 9.76067 36.4273i 0.402866 1.50352i −0.405091 0.914276i \(-0.632760\pi\)
0.807958 0.589241i \(-0.200573\pi\)
\(588\) 0 0
\(589\) −21.9147 12.6525i −0.902980 0.521336i
\(590\) 12.5523 + 3.36337i 0.516768 + 0.138468i
\(591\) 0 0
\(592\) −2.59244 + 9.67510i −0.106548 + 0.397644i
\(593\) −10.7514 2.88084i −0.441508 0.118302i 0.0312150 0.999513i \(-0.490062\pi\)
−0.472723 + 0.881211i \(0.656729\pi\)
\(594\) 0 0
\(595\) 1.42143 3.21975i 0.0582731 0.131997i
\(596\) 3.65315 13.6337i 0.149639 0.558460i
\(597\) 0 0
\(598\) 3.54760 + 6.98098i 0.145072 + 0.285474i
\(599\) −10.6818 + 18.5015i −0.436447 + 0.755949i −0.997413 0.0718904i \(-0.977097\pi\)
0.560965 + 0.827839i \(0.310430\pi\)
\(600\) 0 0
\(601\) 13.0625 7.54164i 0.532830 0.307630i −0.209338 0.977843i \(-0.567131\pi\)
0.742168 + 0.670214i \(0.233798\pi\)
\(602\) 4.58304 + 6.26656i 0.186791 + 0.255406i
\(603\) 0 0
\(604\) −0.766987 + 0.766987i −0.0312083 + 0.0312083i
\(605\) −3.94979 1.05834i −0.160582 0.0430277i
\(606\) 0 0
\(607\) 44.7577i 1.81666i −0.418254 0.908330i \(-0.637358\pi\)
0.418254 0.908330i \(-0.362642\pi\)
\(608\) 10.5091 + 18.2024i 0.426202 + 0.738203i
\(609\) 0 0
\(610\) 1.00170i 0.0405578i
\(611\) −4.04751 + 2.05686i −0.163745 + 0.0832118i
\(612\) 0 0
\(613\) −32.0127 + 32.0127i −1.29298 + 1.29298i −0.360044 + 0.932935i \(0.617238\pi\)
−0.932935 + 0.360044i \(0.882762\pi\)
\(614\) −20.8430 12.0337i −0.841155 0.485641i
\(615\) 0 0
\(616\) 18.4940 + 14.8803i 0.745144 + 0.599543i
\(617\) −6.09471 22.7458i −0.245364 0.915710i −0.973200 0.229959i \(-0.926141\pi\)
0.727837 0.685751i \(-0.240526\pi\)
\(618\) 0 0
\(619\) −0.944826 3.52614i −0.0379758 0.141727i 0.944335 0.328985i \(-0.106707\pi\)
−0.982311 + 0.187258i \(0.940040\pi\)
\(620\) −1.92369 3.33193i −0.0772573 0.133814i
\(621\) 0 0
\(622\) 4.69656 + 1.25844i 0.188315 + 0.0504588i
\(623\) 20.4714 + 9.03756i 0.820169 + 0.362082i
\(624\) 0 0
\(625\) −4.04784 7.01107i −0.161914 0.280443i
\(626\) 19.8355 + 19.8355i 0.792786 + 0.792786i
\(627\) 0 0
\(628\) −0.0155729 −0.000621427
\(629\) 2.35009 + 2.35009i 0.0937043 + 0.0937043i
\(630\) 0 0
\(631\) −9.03886 + 2.42196i −0.359831 + 0.0964165i −0.434205 0.900814i \(-0.642971\pi\)
0.0743741 + 0.997230i \(0.476304\pi\)
\(632\) −3.45787 + 12.9049i −0.137547 + 0.513331i
\(633\) 0 0
\(634\) 13.1403i 0.521869i
\(635\) 2.59534 + 9.68595i 0.102993 + 0.384375i
\(636\) 0 0
\(637\) 20.4957 + 14.7285i 0.812068 + 0.583563i
\(638\) −16.7690 −0.663892
\(639\) 0 0
\(640\) 6.29729i 0.248922i
\(641\) −7.59400 + 4.38440i −0.299945 + 0.173173i −0.642418 0.766354i \(-0.722069\pi\)
0.342473 + 0.939528i \(0.388735\pi\)
\(642\) 0 0
\(643\) 46.4077 12.4349i 1.83014 0.490384i 0.832196 0.554481i \(-0.187083\pi\)
0.997944 + 0.0640969i \(0.0204167\pi\)
\(644\) 1.82052 2.26264i 0.0717387 0.0891607i
\(645\) 0 0
\(646\) −6.19804 −0.243859
\(647\) 13.7843 0.541918 0.270959 0.962591i \(-0.412659\pi\)
0.270959 + 0.962591i \(0.412659\pi\)
\(648\) 0 0
\(649\) 9.76262 + 16.9094i 0.383216 + 0.663750i
\(650\) 4.47089 + 8.79784i 0.175363 + 0.345080i
\(651\) 0 0
\(652\) 9.97429 + 2.67260i 0.390623 + 0.104667i
\(653\) 20.3999 35.3337i 0.798311 1.38271i −0.122405 0.992480i \(-0.539061\pi\)
0.920716 0.390234i \(-0.127606\pi\)
\(654\) 0 0
\(655\) −7.29881 27.2395i −0.285188 1.06434i
\(656\) −2.61934 2.61934i −0.102268 0.102268i
\(657\) 0 0
\(658\) −3.07306 2.47258i −0.119800 0.0963913i
\(659\) 10.0428 17.3947i 0.391213 0.677601i −0.601396 0.798951i \(-0.705389\pi\)
0.992610 + 0.121349i \(0.0387221\pi\)
\(660\) 0 0
\(661\) −6.18282 + 6.18282i −0.240484 + 0.240484i −0.817050 0.576566i \(-0.804392\pi\)
0.576566 + 0.817050i \(0.304392\pi\)
\(662\) 14.8977 + 8.60119i 0.579016 + 0.334295i
\(663\) 0 0
\(664\) 32.4036i 1.25750i
\(665\) −4.29169 + 27.6583i −0.166425 + 1.07254i
\(666\) 0 0
\(667\) 8.90912i 0.344963i
\(668\) −5.16927 + 1.38510i −0.200005 + 0.0535912i
\(669\) 0 0
\(670\) −17.6880 + 17.6880i −0.683348 + 0.683348i
\(671\) 1.06425 1.06425i 0.0410848 0.0410848i
\(672\) 0 0
\(673\) 21.9793 12.6898i 0.847240 0.489154i −0.0124786 0.999922i \(-0.503972\pi\)
0.859719 + 0.510768i \(0.170639\pi\)
\(674\) 9.38792 2.51549i 0.361609 0.0968929i
\(675\) 0 0
\(676\) −3.14863 7.11282i −0.121101 0.273570i
\(677\) −21.5441 + 12.4385i −0.828009 + 0.478051i −0.853170 0.521632i \(-0.825323\pi\)
0.0251616 + 0.999683i \(0.491990\pi\)
\(678\) 0 0
\(679\) −18.3372 + 41.5363i −0.703716 + 1.59402i
\(680\) −3.54394 2.04610i −0.135904 0.0784643i
\(681\) 0 0
\(682\) −3.50480 + 13.0801i −0.134206 + 0.500862i
\(683\) −10.9521 + 40.8739i −0.419072 + 1.56400i 0.357467 + 0.933926i \(0.383641\pi\)
−0.776538 + 0.630070i \(0.783026\pi\)
\(684\) 0 0
\(685\) 24.1714 + 13.9554i 0.923542 + 0.533207i
\(686\) −4.35658 + 21.4892i −0.166335 + 0.820462i
\(687\) 0 0
\(688\) 5.24873 3.03036i 0.200106 0.115531i
\(689\) 1.67983 + 7.94474i 0.0639966 + 0.302670i
\(690\) 0 0
\(691\) −11.9598 + 3.20461i −0.454971 + 0.121909i −0.479024 0.877802i \(-0.659009\pi\)
0.0240536 + 0.999711i \(0.492343\pi\)
\(692\) −9.85939 + 5.69232i −0.374798 + 0.216390i
\(693\) 0 0
\(694\) −10.3403 + 10.3403i −0.392514 + 0.392514i
\(695\) 13.0421 13.0421i 0.494714 0.494714i
\(696\) 0 0
\(697\) −1.18724 + 0.318120i −0.0449699 + 0.0120496i
\(698\) 4.84245i 0.183289i
\(699\) 0 0
\(700\) 2.29433 2.85152i 0.0867175 0.107777i
\(701\) 42.4269i 1.60244i 0.598369 + 0.801220i \(0.295816\pi\)
−0.598369 + 0.801220i \(0.704184\pi\)
\(702\) 0 0
\(703\) −22.8894 13.2152i −0.863290 0.498421i
\(704\) 18.0389 18.0389i 0.679866 0.679866i
\(705\) 0 0
\(706\) −14.7917 + 25.6200i −0.556694 + 0.964222i
\(707\) 25.2481 31.3796i 0.949551 1.18015i
\(708\) 0 0
\(709\) −0.897457 0.897457i −0.0337047 0.0337047i 0.690054 0.723758i \(-0.257587\pi\)
−0.723758 + 0.690054i \(0.757587\pi\)
\(710\) −4.30618 16.0709i −0.161608 0.603130i
\(711\) 0 0
\(712\) 13.0092 22.5326i 0.487541 0.844446i
\(713\) 6.94925 + 1.86205i 0.260251 + 0.0697342i
\(714\) 0 0
\(715\) 5.34520 16.3912i 0.199899 0.612997i
\(716\) −6.43433 11.1446i −0.240462 0.416493i
\(717\) 0 0
\(718\) 23.9863 0.895162
\(719\) −5.80365 −0.216439 −0.108220 0.994127i \(-0.534515\pi\)
−0.108220 + 0.994127i \(0.534515\pi\)
\(720\) 0 0
\(721\) 44.6807 + 6.93303i 1.66400 + 0.258199i
\(722\) 25.8826 6.93521i 0.963249 0.258102i
\(723\) 0 0
\(724\) −3.15461 + 1.82131i −0.117240 + 0.0676886i
\(725\) 11.2278i 0.416990i
\(726\) 0 0
\(727\) 0.625577 0.0232014 0.0116007 0.999933i \(-0.496307\pi\)
0.0116007 + 0.999933i \(0.496307\pi\)
\(728\) 19.5906 21.8484i 0.726077 0.809755i
\(729\) 0 0
\(730\) 5.13421 + 19.1611i 0.190026 + 0.709186i
\(731\) 2.01100i 0.0743795i
\(732\) 0 0
\(733\) 2.44991 9.14319i 0.0904895 0.337711i −0.905808 0.423689i \(-0.860735\pi\)
0.996297 + 0.0859780i \(0.0274015\pi\)
\(734\) 25.9090 6.94230i 0.956319 0.256245i
\(735\) 0 0
\(736\) −4.22543 4.22543i −0.155751 0.155751i
\(737\) −37.5848 −1.38445
\(738\) 0 0
\(739\) −8.82186 8.82186i −0.324517 0.324517i 0.525980 0.850497i \(-0.323699\pi\)
−0.850497 + 0.525980i \(0.823699\pi\)
\(740\) −2.00925 3.48012i −0.0738614 0.127932i
\(741\) 0 0
\(742\) −5.69426 + 4.16450i −0.209043 + 0.152883i
\(743\) −28.7095 7.69268i −1.05325 0.282217i −0.309655 0.950849i \(-0.600214\pi\)
−0.743594 + 0.668632i \(0.766880\pi\)
\(744\) 0 0
\(745\) −19.3379 33.4942i −0.708485 1.22713i
\(746\) 4.65825 + 17.3848i 0.170550 + 0.636503i
\(747\) 0 0
\(748\) −0.366462 1.36766i −0.0133992 0.0500064i
\(749\) −16.8758 43.5538i −0.616628 1.59142i
\(750\) 0 0
\(751\) 14.5612 + 8.40693i 0.531347 + 0.306773i 0.741565 0.670881i \(-0.234084\pi\)
−0.210218 + 0.977655i \(0.567417\pi\)
\(752\) −2.17727 + 2.17727i −0.0793968 + 0.0793968i
\(753\) 0 0
\(754\) −1.10710 + 20.7013i −0.0403180 + 0.753897i
\(755\) 2.97215i 0.108168i
\(756\) 0 0
\(757\) 10.9748 + 19.0089i 0.398886 + 0.690890i 0.993589 0.113055i \(-0.0360637\pi\)
−0.594703 + 0.803945i \(0.702730\pi\)
\(758\) 35.6763i 1.29582i
\(759\) 0 0
\(760\) 31.4343 + 8.42280i 1.14024 + 0.305527i
\(761\) 28.1192 28.1192i 1.01932 1.01932i 0.0195119 0.999810i \(-0.493789\pi\)
0.999810 0.0195119i \(-0.00621123\pi\)
\(762\) 0 0
\(763\) −20.7321 9.15267i −0.750554 0.331349i
\(764\) 13.5357 7.81485i 0.489705 0.282731i
\(765\) 0 0
\(766\) −1.69099 + 2.92887i −0.0610978 + 0.105824i
\(767\) 21.5191 10.9356i 0.777009 0.394861i
\(768\) 0 0
\(769\) 2.10710 7.86381i 0.0759840 0.283576i −0.917471 0.397804i \(-0.869773\pi\)
0.993455 + 0.114227i \(0.0364392\pi\)
\(770\) 14.8909 1.61238i 0.536632 0.0581060i
\(771\) 0 0
\(772\) 12.5054 + 3.35081i 0.450079 + 0.120598i
\(773\) −6.23533 + 23.2706i −0.224269 + 0.836985i 0.758427 + 0.651759i \(0.225968\pi\)
−0.982696 + 0.185226i \(0.940698\pi\)
\(774\) 0 0
\(775\) 8.75785 + 2.34666i 0.314591 + 0.0842945i
\(776\) 45.7186 + 26.3956i 1.64120 + 0.947548i
\(777\) 0 0
\(778\) 3.03197 11.3154i 0.108701 0.405679i
\(779\) 8.46503 4.88729i 0.303291 0.175105i
\(780\) 0 0
\(781\) 12.4993 21.6494i 0.447259 0.774675i
\(782\) 1.70211 0.456079i 0.0608673 0.0163093i
\(783\) 0 0
\(784\) 16.3120 + 5.18711i 0.582573 + 0.185254i
\(785\) −0.0301733 + 0.0301733i −0.00107693 + 0.00107693i
\(786\) 0 0
\(787\) 18.8590 + 5.05325i 0.672250 + 0.180129i 0.578768 0.815492i \(-0.303534\pi\)
0.0934820 + 0.995621i \(0.470200\pi\)
\(788\) −1.30534 + 0.349765i −0.0465008 + 0.0124599i
\(789\) 0 0
\(790\) 4.21509 + 7.30076i 0.149966 + 0.259749i
\(791\) −1.35404 3.49457i −0.0481441 0.124252i
\(792\) 0 0
\(793\) −1.24355 1.38407i −0.0441597 0.0491498i
\(794\) 11.9405 + 6.89386i 0.423753 + 0.244654i
\(795\) 0 0
\(796\) −3.53563 2.04130i −0.125317 0.0723518i
\(797\) −3.93665 + 6.81848i −0.139443 + 0.241523i −0.927286 0.374354i \(-0.877865\pi\)
0.787843 + 0.615877i \(0.211198\pi\)
\(798\) 0 0
\(799\) 0.264430 + 0.986867i 0.00935487 + 0.0349129i
\(800\) −5.32514 5.32514i −0.188272 0.188272i
\(801\) 0 0
\(802\) 5.04683 + 8.74136i 0.178210 + 0.308668i
\(803\) −14.9027 + 25.8123i −0.525906 + 0.910896i
\(804\) 0 0
\(805\) −0.856631 7.91133i −0.0301923 0.278838i
\(806\) 15.9159 + 5.19022i 0.560615 + 0.182818i
\(807\) 0 0
\(808\) −33.1130 33.1130i −1.16491 1.16491i
\(809\) −23.9648 −0.842557 −0.421279 0.906931i \(-0.638419\pi\)
−0.421279 + 0.906931i \(0.638419\pi\)
\(810\) 0 0
\(811\) 9.15807 + 9.15807i 0.321583 + 0.321583i 0.849374 0.527791i \(-0.176980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(812\) 7.16899 2.77777i 0.251582 0.0974805i
\(813\) 0 0
\(814\) −3.66068 + 13.6618i −0.128307 + 0.478847i
\(815\) 24.5039 14.1474i 0.858336 0.495560i
\(816\) 0 0
\(817\) 4.13916 + 15.4476i 0.144811 + 0.540441i
\(818\) 35.0869 1.22678
\(819\) 0 0
\(820\) 1.48613 0.0518981
\(821\) 1.96582 + 7.33655i 0.0686077 + 0.256047i 0.991708 0.128512i \(-0.0410201\pi\)
−0.923100 + 0.384559i \(0.874353\pi\)
\(822\) 0 0
\(823\) −1.53409 + 0.885704i −0.0534748 + 0.0308737i −0.526499 0.850176i \(-0.676496\pi\)
0.473024 + 0.881049i \(0.343162\pi\)
\(824\) 13.6066 50.7807i 0.474010 1.76903i
\(825\) 0 0
\(826\) 16.3383 + 13.1458i 0.568482 + 0.457401i
\(827\) 7.08670 + 7.08670i 0.246429 + 0.246429i 0.819503 0.573074i \(-0.194249\pi\)
−0.573074 + 0.819503i \(0.694249\pi\)
\(828\) 0 0
\(829\) −25.9548 −0.901447 −0.450723 0.892664i \(-0.648834\pi\)
−0.450723 + 0.892664i \(0.648834\pi\)
\(830\) 14.4578 + 14.4578i 0.501839 + 0.501839i
\(831\) 0 0
\(832\) −21.0780 23.4599i −0.730749 0.813325i
\(833\) 4.19678 3.82678i 0.145410 0.132590i
\(834\) 0 0
\(835\) −7.33200 + 12.6994i −0.253734 + 0.439481i
\(836\) 5.62998 + 9.75141i 0.194717 + 0.337259i
\(837\) 0 0
\(838\) 5.67649 + 5.67649i 0.196091 + 0.196091i
\(839\) −1.15171 4.29822i −0.0397613 0.148391i 0.943191 0.332250i \(-0.107808\pi\)
−0.982953 + 0.183859i \(0.941141\pi\)
\(840\) 0 0
\(841\) 2.70702 4.68870i 0.0933455 0.161679i
\(842\) 0.824363 + 0.475946i 0.0284094 + 0.0164022i
\(843\) 0 0
\(844\) −0.279981 0.161647i −0.00963733 0.00556412i
\(845\) −19.8820 7.68080i −0.683963 0.264227i
\(846\) 0 0
\(847\) −5.14113 4.13655i −0.176651 0.142134i
\(848\) 2.75361 + 4.76939i 0.0945594 + 0.163782i
\(849\) 0 0
\(850\) 2.14510 0.574777i 0.0735762 0.0197147i
\(851\) 7.25832 + 1.94486i 0.248812 + 0.0666690i
\(852\) 0 0
\(853\) −20.4636 + 20.4636i −0.700660 + 0.700660i −0.964552 0.263892i \(-0.914994\pi\)
0.263892 + 0.964552i \(0.414994\pi\)
\(854\) 0.652834 1.47877i 0.0223395 0.0506023i
\(855\) 0 0
\(856\) −52.4581 + 14.0561i −1.79298 + 0.480427i
\(857\) −13.0829 + 22.6603i −0.446904 + 0.774060i −0.998183 0.0602609i \(-0.980807\pi\)
0.551279 + 0.834321i \(0.314140\pi\)
\(858\) 0 0
\(859\) 29.0690 16.7830i 0.991820 0.572627i 0.0860021 0.996295i \(-0.472591\pi\)
0.905818 + 0.423667i \(0.139257\pi\)
\(860\) −0.629321 + 2.34866i −0.0214597 + 0.0800886i
\(861\) 0 0
\(862\) −40.5264 23.3979i −1.38033 0.796937i
\(863\) 12.6280 + 3.38366i 0.429862 + 0.115181i 0.467261 0.884119i \(-0.345241\pi\)
−0.0373995 + 0.999300i \(0.511907\pi\)
\(864\) 0 0
\(865\) −8.07389 + 30.1322i −0.274521 + 1.02452i
\(866\) 14.9254 + 3.99924i 0.507184 + 0.135900i
\(867\) 0 0
\(868\) −0.668350 6.17249i −0.0226853 0.209508i
\(869\) −3.27832 + 12.2349i −0.111210 + 0.415040i
\(870\) 0 0
\(871\) −2.48136 + 46.3984i −0.0840777 + 1.57215i
\(872\) −13.1749 + 22.8196i −0.446159 + 0.772770i
\(873\) 0 0
\(874\) −12.1361 + 7.00676i −0.410508 + 0.237007i
\(875\) −3.41441 31.5334i −0.115428 1.06602i
\(876\) 0 0
\(877\) −0.105858 + 0.105858i −0.00357457 + 0.00357457i −0.708892 0.705317i \(-0.750805\pi\)
0.705317 + 0.708892i \(0.250805\pi\)
\(878\) −14.9208 3.99802i −0.503554 0.134927i
\(879\) 0 0
\(880\) 11.6926i 0.394158i
\(881\) 15.6550 + 27.1152i 0.527429 + 0.913534i 0.999489 + 0.0319677i \(0.0101774\pi\)
−0.472060 + 0.881567i \(0.656489\pi\)
\(882\) 0 0
\(883\) 14.8521i 0.499812i 0.968270 + 0.249906i \(0.0803998\pi\)
−0.968270 + 0.249906i \(0.919600\pi\)
\(884\) −1.71256 + 0.362104i −0.0575997 + 0.0121789i
\(885\) 0 0
\(886\) −10.4106 + 10.4106i −0.349749 + 0.349749i
\(887\) 37.1161 + 21.4290i 1.24624 + 0.719515i 0.970357 0.241677i \(-0.0776976\pi\)
0.275879 + 0.961192i \(0.411031\pi\)
\(888\) 0 0
\(889\) −2.48119 + 15.9904i −0.0832166 + 0.536299i
\(890\) −4.24916 15.8581i −0.142432 0.531564i
\(891\) 0 0
\(892\) −0.983816 3.67165i −0.0329406 0.122936i
\(893\) −4.06246 7.03638i −0.135945 0.235464i
\(894\) 0 0
\(895\) −34.0600 9.12635i −1.13850 0.305060i
\(896\) 4.10410 9.29639i 0.137108 0.310571i
\(897\) 0 0
\(898\) 21.3690 + 37.0122i 0.713094 + 1.23511i
\(899\) 13.4678 + 13.4678i 0.449177 + 0.449177i
\(900\) 0 0
\(901\) 1.82735 0.0608777
\(902\) −3.69866 3.69866i −0.123152 0.123152i
\(903\) 0 0
\(904\) −4.20901 + 1.12780i −0.139989 + 0.0375101i
\(905\) −2.58332 + 9.64108i −0.0858725 + 0.320480i
\(906\) 0 0
\(907\) 22.3951i 0.743619i 0.928309 + 0.371809i \(0.121262\pi\)
−0.928309 + 0.371809i \(0.878738\pi\)
\(908\) 3.40402 + 12.7040i 0.112966 + 0.421596i
\(909\) 0 0
\(910\) −1.00737 18.4893i −0.0333940 0.612914i
\(911\) −27.2540 −0.902965 −0.451483 0.892280i \(-0.649105\pi\)
−0.451483 + 0.892280i \(0.649105\pi\)
\(912\) 0 0
\(913\) 30.7211i 1.01672i
\(914\) 29.8676 17.2440i 0.987931 0.570382i
\(915\) 0 0
\(916\) 15.4854 4.14929i 0.511651 0.137096i
\(917\) 6.97780 44.9692i 0.230427 1.48501i
\(918\) 0 0
\(919\) −27.4376 −0.905083 −0.452541 0.891743i \(-0.649482\pi\)
−0.452541 + 0.891743i \(0.649482\pi\)
\(920\) −9.25228 −0.305039
\(921\) 0 0
\(922\) 5.61689 + 9.72874i 0.184982 + 0.320399i
\(923\) −25.9009 16.8596i −0.852538 0.554941i
\(924\) 0 0
\(925\) 9.14736 + 2.45103i 0.300763 + 0.0805893i
\(926\) −17.2524 + 29.8820i −0.566949 + 0.981984i
\(927\) 0 0
\(928\) −4.09450 15.2809i −0.134409 0.501620i
\(929\) −34.8854 34.8854i −1.14455 1.14455i −0.987607 0.156946i \(-0.949835\pi\)
−0.156946 0.987607i \(-0.550165\pi\)
\(930\) 0 0
\(931\) −24.3612 + 38.0336i −0.798406 + 1.24650i
\(932\) 3.23240 5.59868i 0.105881 0.183391i
\(933\) 0 0
\(934\) 27.6590 27.6590i 0.905030 0.905030i
\(935\) −3.35993 1.93986i −0.109882 0.0634402i
\(936\) 0 0
\(937\) 18.9902i 0.620384i −0.950674 0.310192i \(-0.899607\pi\)
0.950674 0.310192i \(-0.100393\pi\)
\(938\) −37.6397 + 14.5842i −1.22898 + 0.476192i
\(939\) 0 0
\(940\) 1.23532i 0.0402916i
\(941\) −29.3705 + 7.86979i −0.957450 + 0.256548i −0.703521 0.710675i \(-0.748390\pi\)
−0.253929 + 0.967223i \(0.581723\pi\)
\(942\) 0 0
\(943\) −1.96504 + 1.96504i −0.0639906 + 0.0639906i
\(944\) 11.5757 11.5757i 0.376757 0.376757i
\(945\) 0 0
\(946\) 7.41153 4.27905i 0.240970 0.139124i
\(947\) −54.1565 + 14.5112i −1.75985 + 0.471550i −0.986683 0.162653i \(-0.947995\pi\)
−0.773166 + 0.634204i \(0.781328\pi\)
\(948\) 0 0
\(949\) 30.8813 + 20.1015i 1.00245 + 0.652523i
\(950\) −15.2946 + 8.83033i −0.496221 + 0.286494i
\(951\) 0 0
\(952\) −3.89826 5.33023i −0.126343 0.172754i
\(953\) 12.5739 + 7.25952i 0.407307 + 0.235159i 0.689632 0.724160i \(-0.257772\pi\)
−0.282325 + 0.959319i \(0.591106\pi\)
\(954\) 0 0
\(955\) 11.0844 41.3677i 0.358684 1.33863i
\(956\) 4.47887 16.7154i 0.144857 0.540614i
\(957\) 0 0
\(958\) 26.3049 + 15.1871i 0.849873 + 0.490674i
\(959\) 26.5880 + 36.3547i 0.858572 + 1.17396i
\(960\) 0 0
\(961\) −13.5268 + 7.80972i −0.436350 + 0.251927i
\(962\) 16.6238 + 5.42105i 0.535973 + 0.174782i
\(963\) 0 0
\(964\) −4.61798 + 1.23738i −0.148735 + 0.0398535i
\(965\) 30.7221 17.7374i 0.988979 0.570988i
\(966\) 0 0
\(967\) −35.9101 + 35.9101i −1.15479 + 1.15479i −0.169212 + 0.985580i \(0.554122\pi\)
−0.985580 + 0.169212i \(0.945878\pi\)
\(968\) −5.42512 + 5.42512i −0.174370 + 0.174370i
\(969\) 0 0
\(970\) 32.1759 8.62152i 1.03311 0.276820i
\(971\) 4.67903i 0.150157i 0.997178 + 0.0750785i \(0.0239207\pi\)
−0.997178 + 0.0750785i \(0.976079\pi\)
\(972\) 0 0
\(973\) 27.7532 10.7535i 0.889728 0.344743i
\(974\) 7.54403i 0.241726i
\(975\) 0 0
\(976\) −1.09283 0.630948i −0.0349808 0.0201961i
\(977\) −31.2664 + 31.2664i −1.00030 + 1.00030i −0.000299689 1.00000i \(0.500095\pi\)
−1.00000 0.000299689i \(0.999905\pi\)
\(978\) 0 0
\(979\) 12.3337 21.3627i 0.394188 0.682754i
\(980\) −6.09900 + 3.15598i −0.194825 + 0.100814i
\(981\) 0 0
\(982\) 23.1319 + 23.1319i 0.738169 + 0.738169i
\(983\) −3.59836 13.4293i −0.114770 0.428327i 0.884500 0.466541i \(-0.154500\pi\)
−0.999270 + 0.0382139i \(0.987833\pi\)
\(984\) 0 0
\(985\) −1.85147 + 3.20684i −0.0589928 + 0.102178i
\(986\) 4.50615 + 1.20742i 0.143505 + 0.0384521i
\(987\) 0 0
\(988\) 12.4098 6.30640i 0.394808 0.200633i
\(989\) −2.27339 3.93763i −0.0722897 0.125209i
\(990\) 0 0
\(991\) 35.4158 1.12502 0.562510 0.826791i \(-0.309836\pi\)
0.562510 + 0.826791i \(0.309836\pi\)
\(992\) −12.7751 −0.405609
\(993\) 0 0
\(994\) 4.11679 26.5311i 0.130577 0.841516i
\(995\) −10.8055 + 2.89534i −0.342559 + 0.0917884i
\(996\) 0 0
\(997\) −25.2024 + 14.5506i −0.798167 + 0.460822i −0.842830 0.538180i \(-0.819112\pi\)
0.0446626 + 0.999002i \(0.485779\pi\)
\(998\) 2.18839i 0.0692721i
\(999\) 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.gh.d.262.4 40
3.2 odd 2 273.2.cg.b.262.7 yes 40
7.5 odd 6 819.2.et.d.145.4 40
13.7 odd 12 819.2.et.d.514.4 40
21.5 even 6 273.2.bt.b.145.7 40
39.20 even 12 273.2.bt.b.241.7 yes 40
91.33 even 12 inner 819.2.gh.d.397.4 40
273.215 odd 12 273.2.cg.b.124.7 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.b.145.7 40 21.5 even 6
273.2.bt.b.241.7 yes 40 39.20 even 12
273.2.cg.b.124.7 yes 40 273.215 odd 12
273.2.cg.b.262.7 yes 40 3.2 odd 2
819.2.et.d.145.4 40 7.5 odd 6
819.2.et.d.514.4 40 13.7 odd 12
819.2.gh.d.262.4 40 1.1 even 1 trivial
819.2.gh.d.397.4 40 91.33 even 12 inner