Properties

Label 38.3.f.a.21.2
Level $38$
Weight $3$
Character 38.21
Analytic conductor $1.035$
Analytic rank $0$
Dimension $24$
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] = [38,3,Mod(3,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 38.f (of order \(18\), degree \(6\), 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: \(1.03542500457\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 21.2
Character \(\chi\) \(=\) 38.21
Dual form 38.3.f.a.29.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39273 - 0.245576i) q^{2} +(0.272417 - 0.324654i) q^{3} +(1.87939 + 0.684040i) q^{4} +(7.98876 - 2.90767i) q^{5} +(-0.459130 + 0.385256i) q^{6} +(-2.58545 - 4.47813i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(1.53164 + 8.68639i) q^{9} +O(q^{10})\) \(q+(-1.39273 - 0.245576i) q^{2} +(0.272417 - 0.324654i) q^{3} +(1.87939 + 0.684040i) q^{4} +(7.98876 - 2.90767i) q^{5} +(-0.459130 + 0.385256i) q^{6} +(-2.58545 - 4.47813i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(1.53164 + 8.68639i) q^{9} +(-11.8402 + 2.08775i) q^{10} +(-4.81869 + 8.34622i) q^{11} +(0.734053 - 0.423806i) q^{12} +(-8.78112 - 10.4649i) q^{13} +(2.50111 + 6.87174i) q^{14} +(1.23229 - 3.38568i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-3.08077 + 17.4719i) q^{17} -12.4739i q^{18} +(-17.6183 - 7.11298i) q^{19} +17.0029 q^{20} +(-2.15816 - 0.380542i) q^{21} +(8.76075 - 10.4407i) q^{22} +(14.1083 + 5.13501i) q^{23} +(-1.12641 + 0.409981i) q^{24} +(36.2147 - 30.3877i) q^{25} +(9.65978 + 16.7312i) q^{26} +(6.54055 + 3.77619i) q^{27} +(-1.79583 - 10.1847i) q^{28} +(11.5878 - 2.04324i) q^{29} +(-2.54768 + 4.41272i) q^{30} +(-44.1349 + 25.4813i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(1.39694 + 3.83806i) q^{33} +(8.58135 - 23.5771i) q^{34} +(-33.6755 - 28.2571i) q^{35} +(-3.06329 + 17.3728i) q^{36} +17.8330i q^{37} +(22.7908 + 14.2331i) q^{38} -5.78961 q^{39} +(-23.6805 - 4.17550i) q^{40} +(-15.8487 + 18.8877i) q^{41} +(2.91228 + 1.05998i) q^{42} +(14.2358 - 5.18140i) q^{43} +(-14.7653 + 12.3896i) q^{44} +(37.4931 + 64.9400i) q^{45} +(-18.3880 - 10.6163i) q^{46} +(-13.4551 - 76.3075i) q^{47} +(1.66947 - 0.294372i) q^{48} +(11.1309 - 19.2793i) q^{49} +(-57.8997 + 33.4284i) q^{50} +(4.83307 + 5.75983i) q^{51} +(-9.34467 - 25.6743i) q^{52} +(21.5316 - 59.1576i) q^{53} +(-8.18187 - 6.86541i) q^{54} +(-14.2273 + 80.6871i) q^{55} +14.6255i q^{56} +(-7.10879 + 3.78216i) q^{57} -16.6404 q^{58} +(52.2374 + 9.21086i) q^{59} +(4.63189 - 5.52007i) q^{60} +(46.5312 + 16.9360i) q^{61} +(67.7255 - 24.6501i) q^{62} +(34.9388 - 29.3171i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-100.579 - 58.0692i) q^{65} +(-1.00302 - 5.68843i) q^{66} +(9.95299 - 1.75498i) q^{67} +(-17.7414 + 30.7291i) q^{68} +(5.51045 - 3.18146i) q^{69} +(39.9616 + 47.6243i) q^{70} +(38.9935 + 107.134i) q^{71} +(8.53266 - 23.4433i) q^{72} +(-85.5417 - 71.7780i) q^{73} +(4.37934 - 24.8365i) q^{74} -20.0354i q^{75} +(-28.2461 - 25.4197i) q^{76} +49.8339 q^{77} +(8.06335 + 1.42179i) q^{78} +(97.8772 - 116.645i) q^{79} +(31.9550 + 11.6307i) q^{80} +(-71.5884 + 26.0560i) q^{81} +(26.7112 - 22.4134i) q^{82} +(26.5522 + 45.9897i) q^{83} +(-3.79571 - 2.19146i) q^{84} +(26.1910 + 148.537i) q^{85} +(-21.0990 + 3.72032i) q^{86} +(2.49337 - 4.31864i) q^{87} +(23.6067 - 13.6293i) q^{88} +(-71.6292 - 85.3643i) q^{89} +(-36.2700 - 99.6511i) q^{90} +(-24.1602 + 66.3796i) q^{91} +(23.0024 + 19.3013i) q^{92} +(-3.75049 + 21.2701i) q^{93} +109.580i q^{94} +(-161.431 - 5.59555i) q^{95} -2.39741 q^{96} +(-84.8296 - 14.9577i) q^{97} +(-20.2368 + 24.1173i) q^{98} +(-79.8790 - 29.0736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39273 0.245576i −0.696364 0.122788i
\(3\) 0.272417 0.324654i 0.0908057 0.108218i −0.718728 0.695291i \(-0.755275\pi\)
0.809534 + 0.587073i \(0.199720\pi\)
\(4\) 1.87939 + 0.684040i 0.469846 + 0.171010i
\(5\) 7.98876 2.90767i 1.59775 0.581534i 0.618787 0.785559i \(-0.287625\pi\)
0.978966 + 0.204025i \(0.0654023\pi\)
\(6\) −0.459130 + 0.385256i −0.0765217 + 0.0642093i
\(7\) −2.58545 4.47813i −0.369350 0.639733i 0.620114 0.784512i \(-0.287086\pi\)
−0.989464 + 0.144779i \(0.953753\pi\)
\(8\) −2.44949 1.41421i −0.306186 0.176777i
\(9\) 1.53164 + 8.68639i 0.170183 + 0.965154i
\(10\) −11.8402 + 2.08775i −1.18402 + 0.208775i
\(11\) −4.81869 + 8.34622i −0.438063 + 0.758747i −0.997540 0.0700987i \(-0.977669\pi\)
0.559477 + 0.828846i \(0.311002\pi\)
\(12\) 0.734053 0.423806i 0.0611711 0.0353171i
\(13\) −8.78112 10.4649i −0.675471 0.804995i 0.314047 0.949407i \(-0.398315\pi\)
−0.989518 + 0.144413i \(0.953871\pi\)
\(14\) 2.50111 + 6.87174i 0.178651 + 0.490839i
\(15\) 1.23229 3.38568i 0.0821525 0.225712i
\(16\) 3.06418 + 2.57115i 0.191511 + 0.160697i
\(17\) −3.08077 + 17.4719i −0.181222 + 1.02776i 0.749493 + 0.662012i \(0.230297\pi\)
−0.930715 + 0.365747i \(0.880814\pi\)
\(18\) 12.4739i 0.692995i
\(19\) −17.6183 7.11298i −0.927281 0.374367i
\(20\) 17.0029 0.850146
\(21\) −2.15816 0.380542i −0.102770 0.0181211i
\(22\) 8.76075 10.4407i 0.398216 0.474576i
\(23\) 14.1083 + 5.13501i 0.613406 + 0.223261i 0.629993 0.776601i \(-0.283058\pi\)
−0.0165870 + 0.999862i \(0.505280\pi\)
\(24\) −1.12641 + 0.409981i −0.0469339 + 0.0170825i
\(25\) 36.2147 30.3877i 1.44859 1.21551i
\(26\) 9.65978 + 16.7312i 0.371530 + 0.643509i
\(27\) 6.54055 + 3.77619i 0.242243 + 0.139859i
\(28\) −1.79583 10.1847i −0.0641370 0.363739i
\(29\) 11.5878 2.04324i 0.399579 0.0704566i 0.0297524 0.999557i \(-0.490528\pi\)
0.369827 + 0.929101i \(0.379417\pi\)
\(30\) −2.54768 + 4.41272i −0.0849227 + 0.147091i
\(31\) −44.1349 + 25.4813i −1.42371 + 0.821977i −0.996613 0.0822315i \(-0.973795\pi\)
−0.427092 + 0.904208i \(0.640462\pi\)
\(32\) −3.63616 4.33340i −0.113630 0.135419i
\(33\) 1.39694 + 3.83806i 0.0423315 + 0.116305i
\(34\) 8.58135 23.5771i 0.252393 0.693443i
\(35\) −33.6755 28.2571i −0.962157 0.807345i
\(36\) −3.06329 + 17.3728i −0.0850914 + 0.482577i
\(37\) 17.8330i 0.481972i 0.970529 + 0.240986i \(0.0774708\pi\)
−0.970529 + 0.240986i \(0.922529\pi\)
\(38\) 22.7908 + 14.2331i 0.599757 + 0.374555i
\(39\) −5.78961 −0.148451
\(40\) −23.6805 4.17550i −0.592011 0.104388i
\(41\) −15.8487 + 18.8877i −0.386553 + 0.460676i −0.923871 0.382704i \(-0.874993\pi\)
0.537318 + 0.843380i \(0.319437\pi\)
\(42\) 2.91228 + 1.05998i 0.0693401 + 0.0252377i
\(43\) 14.2358 5.18140i 0.331065 0.120498i −0.171139 0.985247i \(-0.554745\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(44\) −14.7653 + 12.3896i −0.335576 + 0.281581i
\(45\) 37.4931 + 64.9400i 0.833180 + 1.44311i
\(46\) −18.3880 10.6163i −0.399740 0.230790i
\(47\) −13.4551 76.3075i −0.286278 1.62356i −0.700684 0.713472i \(-0.747122\pi\)
0.414406 0.910092i \(-0.363989\pi\)
\(48\) 1.66947 0.294372i 0.0347806 0.00613276i
\(49\) 11.1309 19.2793i 0.227161 0.393455i
\(50\) −57.8997 + 33.4284i −1.15799 + 0.668568i
\(51\) 4.83307 + 5.75983i 0.0947660 + 0.112938i
\(52\) −9.34467 25.6743i −0.179705 0.493736i
\(53\) 21.5316 59.1576i 0.406257 1.11618i −0.552885 0.833257i \(-0.686473\pi\)
0.959142 0.282924i \(-0.0913045\pi\)
\(54\) −8.18187 6.86541i −0.151516 0.127137i
\(55\) −14.2273 + 80.6871i −0.258678 + 1.46704i
\(56\) 14.6255i 0.261170i
\(57\) −7.10879 + 3.78216i −0.124716 + 0.0663538i
\(58\) −16.6404 −0.286904
\(59\) 52.2374 + 9.21086i 0.885379 + 0.156116i 0.597805 0.801642i \(-0.296040\pi\)
0.287575 + 0.957758i \(0.407151\pi\)
\(60\) 4.63189 5.52007i 0.0771981 0.0920011i
\(61\) 46.5312 + 16.9360i 0.762807 + 0.277639i 0.693984 0.719990i \(-0.255854\pi\)
0.0688223 + 0.997629i \(0.478076\pi\)
\(62\) 67.7255 24.6501i 1.09235 0.397581i
\(63\) 34.9388 29.3171i 0.554584 0.465351i
\(64\) 4.00000 + 6.92820i 0.0625000 + 0.108253i
\(65\) −100.579 58.0692i −1.54737 0.893373i
\(66\) −1.00302 5.68843i −0.0151973 0.0861883i
\(67\) 9.95299 1.75498i 0.148552 0.0261937i −0.0988775 0.995100i \(-0.531525\pi\)
0.247430 + 0.968906i \(0.420414\pi\)
\(68\) −17.7414 + 30.7291i −0.260903 + 0.451898i
\(69\) 5.51045 3.18146i 0.0798616 0.0461081i
\(70\) 39.9616 + 47.6243i 0.570879 + 0.680347i
\(71\) 38.9935 + 107.134i 0.549205 + 1.50893i 0.834787 + 0.550573i \(0.185591\pi\)
−0.285582 + 0.958354i \(0.592187\pi\)
\(72\) 8.53266 23.4433i 0.118509 0.325601i
\(73\) −85.5417 71.7780i −1.17180 0.983260i −0.171806 0.985131i \(-0.554960\pi\)
−0.999998 + 0.00187066i \(0.999405\pi\)
\(74\) 4.37934 24.8365i 0.0591803 0.335628i
\(75\) 20.0354i 0.267138i
\(76\) −28.2461 25.4197i −0.371659 0.334469i
\(77\) 49.8339 0.647194
\(78\) 8.06335 + 1.42179i 0.103376 + 0.0182280i
\(79\) 97.8772 116.645i 1.23895 1.47652i 0.415043 0.909802i \(-0.363766\pi\)
0.823908 0.566723i \(-0.191789\pi\)
\(80\) 31.9550 + 11.6307i 0.399438 + 0.145384i
\(81\) −71.5884 + 26.0560i −0.883807 + 0.321679i
\(82\) 26.7112 22.4134i 0.325747 0.273334i
\(83\) 26.5522 + 45.9897i 0.319906 + 0.554093i 0.980468 0.196678i \(-0.0630154\pi\)
−0.660562 + 0.750771i \(0.729682\pi\)
\(84\) −3.79571 2.19146i −0.0451871 0.0260888i
\(85\) 26.1910 + 148.537i 0.308130 + 1.74749i
\(86\) −21.0990 + 3.72032i −0.245337 + 0.0432596i
\(87\) 2.49337 4.31864i 0.0286594 0.0496395i
\(88\) 23.6067 13.6293i 0.268258 0.154879i
\(89\) −71.6292 85.3643i −0.804822 0.959150i 0.194943 0.980815i \(-0.437548\pi\)
−0.999765 + 0.0216646i \(0.993103\pi\)
\(90\) −36.2700 99.6511i −0.403000 1.10723i
\(91\) −24.1602 + 66.3796i −0.265497 + 0.729446i
\(92\) 23.0024 + 19.3013i 0.250027 + 0.209797i
\(93\) −3.75049 + 21.2701i −0.0403279 + 0.228711i
\(94\) 109.580i 1.16574i
\(95\) −161.431 5.59555i −1.69927 0.0589006i
\(96\) −2.39741 −0.0249730
\(97\) −84.8296 14.9577i −0.874531 0.154203i −0.281673 0.959510i \(-0.590889\pi\)
−0.592858 + 0.805307i \(0.702001\pi\)
\(98\) −20.2368 + 24.1173i −0.206498 + 0.246095i
\(99\) −79.8790 29.0736i −0.806859 0.293672i
\(100\) 88.8477 32.3379i 0.888477 0.323379i
\(101\) −46.6818 + 39.1707i −0.462196 + 0.387828i −0.843938 0.536440i \(-0.819769\pi\)
0.381742 + 0.924269i \(0.375324\pi\)
\(102\) −5.31668 9.20876i −0.0521243 0.0902819i
\(103\) 14.3917 + 8.30906i 0.139725 + 0.0806705i 0.568233 0.822868i \(-0.307627\pi\)
−0.428508 + 0.903538i \(0.640961\pi\)
\(104\) 6.70961 + 38.0521i 0.0645155 + 0.365886i
\(105\) −18.3475 + 3.23517i −0.174739 + 0.0308111i
\(106\) −44.5154 + 77.1029i −0.419956 + 0.727385i
\(107\) 27.8456 16.0766i 0.260239 0.150249i −0.364205 0.931319i \(-0.618659\pi\)
0.624444 + 0.781070i \(0.285326\pi\)
\(108\) 9.70915 + 11.5709i 0.0898996 + 0.107138i
\(109\) 16.1872 + 44.4741i 0.148507 + 0.408019i 0.991533 0.129853i \(-0.0414505\pi\)
−0.843026 + 0.537872i \(0.819228\pi\)
\(110\) 39.6296 108.881i 0.360269 0.989830i
\(111\) 5.78954 + 4.85800i 0.0521580 + 0.0437658i
\(112\) 3.59167 20.3694i 0.0320685 0.181869i
\(113\) 45.7668i 0.405016i 0.979281 + 0.202508i \(0.0649092\pi\)
−0.979281 + 0.202508i \(0.935091\pi\)
\(114\) 10.8294 3.52178i 0.0949949 0.0308928i
\(115\) 127.639 1.10990
\(116\) 23.1756 + 4.08648i 0.199790 + 0.0352283i
\(117\) 77.4529 92.3047i 0.661990 0.788929i
\(118\) −70.4905 25.6565i −0.597377 0.217428i
\(119\) 86.2066 31.3767i 0.724426 0.263669i
\(120\) −7.80655 + 6.55047i −0.0650546 + 0.0545873i
\(121\) 14.0604 + 24.3534i 0.116202 + 0.201268i
\(122\) −60.6463 35.0141i −0.497101 0.287001i
\(123\) 1.81452 + 10.2907i 0.0147522 + 0.0836639i
\(124\) −100.377 + 17.6991i −0.809489 + 0.142735i
\(125\) 94.6845 163.998i 0.757476 1.31199i
\(126\) −55.8598 + 32.2507i −0.443332 + 0.255958i
\(127\) 38.9964 + 46.4741i 0.307058 + 0.365938i 0.897402 0.441214i \(-0.145452\pi\)
−0.590343 + 0.807152i \(0.701008\pi\)
\(128\) −3.86952 10.6314i −0.0302306 0.0830579i
\(129\) 2.19591 6.03320i 0.0170225 0.0467690i
\(130\) 125.819 + 105.574i 0.967836 + 0.812111i
\(131\) 21.6520 122.795i 0.165283 0.937364i −0.783490 0.621405i \(-0.786562\pi\)
0.948773 0.315960i \(-0.102327\pi\)
\(132\) 8.16875i 0.0618845i
\(133\) 13.6985 + 97.2874i 0.102996 + 0.731485i
\(134\) −14.2928 −0.106663
\(135\) 63.2308 + 11.1493i 0.468377 + 0.0825874i
\(136\) 32.2553 38.4404i 0.237171 0.282650i
\(137\) 55.7673 + 20.2976i 0.407060 + 0.148158i 0.537431 0.843307i \(-0.319395\pi\)
−0.130371 + 0.991465i \(0.541617\pi\)
\(138\) −8.45585 + 3.07768i −0.0612743 + 0.0223020i
\(139\) 32.9531 27.6509i 0.237072 0.198927i −0.516509 0.856282i \(-0.672769\pi\)
0.753582 + 0.657354i \(0.228324\pi\)
\(140\) −43.9602 76.1413i −0.314002 0.543867i
\(141\) −28.4389 16.4192i −0.201694 0.116448i
\(142\) −27.9979 158.784i −0.197169 1.11820i
\(143\) 129.656 22.8619i 0.906686 0.159873i
\(144\) −17.6408 + 30.5547i −0.122505 + 0.212186i
\(145\) 86.6311 50.0165i 0.597456 0.344941i
\(146\) 101.509 + 120.974i 0.695270 + 0.828590i
\(147\) −3.22685 8.86569i −0.0219513 0.0603108i
\(148\) −12.1985 + 33.5150i −0.0824220 + 0.226453i
\(149\) −30.0869 25.2459i −0.201925 0.169435i 0.536218 0.844080i \(-0.319853\pi\)
−0.738143 + 0.674644i \(0.764297\pi\)
\(150\) −4.92019 + 27.9038i −0.0328013 + 0.186025i
\(151\) 30.0563i 0.199048i −0.995035 0.0995242i \(-0.968268\pi\)
0.995035 0.0995242i \(-0.0317321\pi\)
\(152\) 33.0967 + 42.3392i 0.217741 + 0.278548i
\(153\) −156.486 −1.02279
\(154\) −69.4051 12.2380i −0.450683 0.0794675i
\(155\) −278.492 + 331.894i −1.79672 + 2.14125i
\(156\) −10.8809 3.96032i −0.0697494 0.0253867i
\(157\) −217.146 + 79.0346i −1.38309 + 0.503405i −0.923115 0.384525i \(-0.874365\pi\)
−0.459979 + 0.887930i \(0.652143\pi\)
\(158\) −164.962 + 138.419i −1.04406 + 0.876071i
\(159\) −13.3402 23.1059i −0.0839005 0.145320i
\(160\) −41.6485 24.0458i −0.260303 0.150286i
\(161\) −13.4811 76.4553i −0.0837337 0.474878i
\(162\) 106.102 18.7086i 0.654950 0.115485i
\(163\) 25.1151 43.5007i 0.154080 0.266875i −0.778643 0.627467i \(-0.784092\pi\)
0.932724 + 0.360592i \(0.117425\pi\)
\(164\) −42.7057 + 24.6561i −0.260401 + 0.150342i
\(165\) 22.3196 + 26.5995i 0.135270 + 0.161209i
\(166\) −25.6860 70.5718i −0.154735 0.425131i
\(167\) −50.6145 + 139.062i −0.303081 + 0.832708i 0.690880 + 0.722970i \(0.257223\pi\)
−0.993961 + 0.109738i \(0.964999\pi\)
\(168\) 4.74823 + 3.98424i 0.0282633 + 0.0237157i
\(169\) −3.06017 + 17.3551i −0.0181075 + 0.102693i
\(170\) 213.303i 1.25472i
\(171\) 34.8010 163.934i 0.203515 0.958679i
\(172\) 30.2988 0.176156
\(173\) 111.686 + 19.6933i 0.645584 + 0.113834i 0.486847 0.873487i \(-0.338147\pi\)
0.158737 + 0.987321i \(0.449258\pi\)
\(174\) −4.53313 + 5.40238i −0.0260525 + 0.0310482i
\(175\) −229.711 83.6081i −1.31264 0.477760i
\(176\) −36.2247 + 13.1847i −0.205822 + 0.0749131i
\(177\) 17.2207 14.4499i 0.0972920 0.0816377i
\(178\) 78.7966 + 136.480i 0.442678 + 0.766740i
\(179\) 215.541 + 124.443i 1.20414 + 0.695210i 0.961473 0.274900i \(-0.0886448\pi\)
0.242666 + 0.970110i \(0.421978\pi\)
\(180\) 26.0424 + 147.694i 0.144680 + 0.820522i
\(181\) 176.042 31.0409i 0.972605 0.171497i 0.335303 0.942110i \(-0.391161\pi\)
0.637302 + 0.770614i \(0.280050\pi\)
\(182\) 49.9498 86.5155i 0.274449 0.475360i
\(183\) 18.1742 10.4929i 0.0993127 0.0573382i
\(184\) −27.2962 32.5304i −0.148349 0.176795i
\(185\) 51.8524 + 142.463i 0.280283 + 0.770072i
\(186\) 10.4468 28.7024i 0.0561657 0.154314i
\(187\) −130.979 109.904i −0.700423 0.587724i
\(188\) 26.9101 152.615i 0.143139 0.811782i
\(189\) 39.0526i 0.206628i
\(190\) 223.455 + 47.4366i 1.17608 + 0.249666i
\(191\) −299.431 −1.56770 −0.783850 0.620950i \(-0.786747\pi\)
−0.783850 + 0.620950i \(0.786747\pi\)
\(192\) 3.33894 + 0.588744i 0.0173903 + 0.00306638i
\(193\) 2.36990 2.82434i 0.0122793 0.0146339i −0.759870 0.650075i \(-0.774737\pi\)
0.772149 + 0.635441i \(0.219182\pi\)
\(194\) 114.471 + 41.6641i 0.590058 + 0.214764i
\(195\) −46.2518 + 16.8343i −0.237189 + 0.0863296i
\(196\) 34.1070 28.6192i 0.174016 0.146016i
\(197\) −72.8974 126.262i −0.370038 0.640924i 0.619533 0.784970i \(-0.287322\pi\)
−0.989571 + 0.144046i \(0.953989\pi\)
\(198\) 104.110 + 60.1079i 0.525808 + 0.303575i
\(199\) −8.31426 47.1525i −0.0417802 0.236947i 0.956765 0.290861i \(-0.0939416\pi\)
−0.998546 + 0.0539134i \(0.982831\pi\)
\(200\) −131.682 + 23.2191i −0.658411 + 0.116096i
\(201\) 2.14160 3.70936i 0.0106547 0.0184545i
\(202\) 74.6344 43.0902i 0.369477 0.213318i
\(203\) −39.1096 46.6090i −0.192658 0.229601i
\(204\) 5.14324 + 14.1309i 0.0252120 + 0.0692693i
\(205\) −71.6920 + 196.972i −0.349717 + 0.960839i
\(206\) −18.0032 15.1065i −0.0873944 0.0733326i
\(207\) −22.9958 + 130.415i −0.111091 + 0.630026i
\(208\) 54.6440i 0.262711i
\(209\) 144.264 112.771i 0.690257 0.539575i
\(210\) 26.3476 0.125465
\(211\) 10.7276 + 1.89157i 0.0508419 + 0.00896479i 0.199011 0.979997i \(-0.436227\pi\)
−0.148169 + 0.988962i \(0.547338\pi\)
\(212\) 80.9324 96.4515i 0.381757 0.454960i
\(213\) 45.4039 + 16.5257i 0.213164 + 0.0775853i
\(214\) −42.7294 + 15.5522i −0.199670 + 0.0726739i
\(215\) 98.6604 82.7859i 0.458886 0.385051i
\(216\) −10.6807 18.4995i −0.0494476 0.0856457i
\(217\) 228.217 + 131.761i 1.05169 + 0.607194i
\(218\) −11.6227 65.9155i −0.0533151 0.302365i
\(219\) −46.6060 + 8.21790i −0.212813 + 0.0375246i
\(220\) −81.9318 + 141.910i −0.372417 + 0.645046i
\(221\) 209.895 121.183i 0.949750 0.548339i
\(222\) −6.87025 8.18764i −0.0309471 0.0368813i
\(223\) −104.550 287.248i −0.468832 1.28811i −0.918681 0.395001i \(-0.870744\pi\)
0.449849 0.893105i \(-0.351478\pi\)
\(224\) −10.0044 + 27.4870i −0.0446627 + 0.122710i
\(225\) 319.427 + 268.031i 1.41968 + 1.19125i
\(226\) 11.2392 63.7407i 0.0497310 0.282038i
\(227\) 227.790i 1.00348i 0.865019 + 0.501740i \(0.167306\pi\)
−0.865019 + 0.501740i \(0.832694\pi\)
\(228\) −15.9473 + 2.24545i −0.0699443 + 0.00984845i
\(229\) 103.650 0.452620 0.226310 0.974055i \(-0.427334\pi\)
0.226310 + 0.974055i \(0.427334\pi\)
\(230\) −177.767 31.3450i −0.772898 0.136283i
\(231\) 13.5756 16.1788i 0.0587689 0.0700380i
\(232\) −31.2738 11.3827i −0.134801 0.0490635i
\(233\) −129.992 + 47.3131i −0.557904 + 0.203060i −0.605555 0.795804i \(-0.707049\pi\)
0.0476508 + 0.998864i \(0.484827\pi\)
\(234\) −130.539 + 109.535i −0.557857 + 0.468098i
\(235\) −329.366 570.479i −1.40156 2.42757i
\(236\) 91.8736 + 53.0432i 0.389295 + 0.224759i
\(237\) −11.2060 63.5524i −0.0472827 0.268154i
\(238\) −127.768 + 22.5289i −0.536839 + 0.0946593i
\(239\) −124.786 + 216.135i −0.522116 + 0.904331i 0.477553 + 0.878603i \(0.341524\pi\)
−0.999669 + 0.0257281i \(0.991810\pi\)
\(240\) 12.4810 7.20593i 0.0520044 0.0300247i
\(241\) −90.9129 108.346i −0.377232 0.449567i 0.543707 0.839275i \(-0.317020\pi\)
−0.920939 + 0.389708i \(0.872576\pi\)
\(242\) −13.6018 37.3706i −0.0562057 0.154424i
\(243\) −34.2903 + 94.2118i −0.141112 + 0.387703i
\(244\) 75.8652 + 63.6584i 0.310923 + 0.260895i
\(245\) 32.8643 186.383i 0.134140 0.760745i
\(246\) 14.7777i 0.0600719i
\(247\) 80.2719 + 246.834i 0.324987 + 0.999330i
\(248\) 144.144 0.581225
\(249\) 22.1640 + 3.90811i 0.0890121 + 0.0156952i
\(250\) −172.144 + 205.153i −0.688575 + 0.820612i
\(251\) 334.402 + 121.713i 1.33228 + 0.484910i 0.907373 0.420326i \(-0.138084\pi\)
0.424907 + 0.905237i \(0.360307\pi\)
\(252\) 85.7175 31.1986i 0.340149 0.123804i
\(253\) −110.842 + 93.0072i −0.438109 + 0.367617i
\(254\) −42.8985 74.3024i −0.168892 0.292529i
\(255\) 55.3579 + 31.9609i 0.217090 + 0.125337i
\(256\) 2.77837 + 15.7569i 0.0108530 + 0.0615505i
\(257\) −500.070 + 88.1758i −1.94580 + 0.343097i −0.945975 + 0.324238i \(0.894892\pi\)
−0.999822 + 0.0188584i \(0.993997\pi\)
\(258\) −4.53991 + 7.86335i −0.0175965 + 0.0304781i
\(259\) 79.8583 46.1062i 0.308333 0.178016i
\(260\) −149.305 177.934i −0.574249 0.684363i
\(261\) 35.4968 + 97.5266i 0.136003 + 0.373665i
\(262\) −60.3108 + 165.703i −0.230194 + 0.632452i
\(263\) 157.860 + 132.460i 0.600227 + 0.503651i 0.891519 0.452984i \(-0.149640\pi\)
−0.291291 + 0.956634i \(0.594085\pi\)
\(264\) 2.00605 11.3769i 0.00759866 0.0430941i
\(265\) 535.203i 2.01963i
\(266\) 4.81316 138.859i 0.0180946 0.522026i
\(267\) −47.2269 −0.176880
\(268\) 19.9060 + 3.50996i 0.0742760 + 0.0130969i
\(269\) −11.1613 + 13.3015i −0.0414918 + 0.0494480i −0.786391 0.617729i \(-0.788053\pi\)
0.744899 + 0.667177i \(0.232497\pi\)
\(270\) −85.3254 31.0559i −0.316020 0.115022i
\(271\) 79.0847 28.7845i 0.291826 0.106216i −0.191959 0.981403i \(-0.561484\pi\)
0.483785 + 0.875187i \(0.339262\pi\)
\(272\) −54.3629 + 45.6159i −0.199864 + 0.167705i
\(273\) 14.9687 + 25.9266i 0.0548305 + 0.0949693i
\(274\) −72.6840 41.9642i −0.265270 0.153154i
\(275\) 79.1151 + 448.684i 0.287691 + 1.63158i
\(276\) 12.5325 2.20982i 0.0454076 0.00800659i
\(277\) −87.0326 + 150.745i −0.314197 + 0.544206i −0.979267 0.202576i \(-0.935069\pi\)
0.665069 + 0.746782i \(0.268402\pi\)
\(278\) −52.6850 + 30.4177i −0.189515 + 0.109416i
\(279\) −288.939 344.344i −1.03562 1.23421i
\(280\) 42.5262 + 116.840i 0.151879 + 0.417285i
\(281\) 15.8834 43.6394i 0.0565247 0.155300i −0.908217 0.418501i \(-0.862556\pi\)
0.964741 + 0.263200i \(0.0847780\pi\)
\(282\) 35.5755 + 29.8514i 0.126154 + 0.105856i
\(283\) 27.2953 154.800i 0.0964500 0.546995i −0.897843 0.440315i \(-0.854867\pi\)
0.994293 0.106680i \(-0.0340221\pi\)
\(284\) 228.019i 0.802884i
\(285\) −45.7931 + 50.8848i −0.160678 + 0.178543i
\(286\) −186.190 −0.651014
\(287\) 125.558 + 22.1392i 0.437483 + 0.0771400i
\(288\) 32.0723 38.2223i 0.111362 0.132716i
\(289\) −24.2050 8.80992i −0.0837545 0.0304841i
\(290\) −132.936 + 48.3849i −0.458401 + 0.166844i
\(291\) −27.9651 + 23.4655i −0.0961000 + 0.0806375i
\(292\) −111.667 193.412i −0.382420 0.662371i
\(293\) 235.642 + 136.048i 0.804238 + 0.464327i 0.844951 0.534844i \(-0.179630\pi\)
−0.0407129 + 0.999171i \(0.512963\pi\)
\(294\) 2.31692 + 13.1399i 0.00788070 + 0.0446936i
\(295\) 444.094 78.3058i 1.50540 0.265443i
\(296\) 25.2196 43.6816i 0.0852014 0.147573i
\(297\) −63.0338 + 36.3926i −0.212235 + 0.122534i
\(298\) 35.7031 + 42.5492i 0.119809 + 0.142783i
\(299\) −70.1494 192.734i −0.234613 0.644595i
\(300\) 13.7050 37.6541i 0.0456833 0.125514i
\(301\) −60.0089 50.3534i −0.199365 0.167287i
\(302\) −7.38110 + 41.8603i −0.0244407 + 0.138610i
\(303\) 25.8262i 0.0852349i
\(304\) −35.6972 67.0948i −0.117425 0.220707i
\(305\) 420.971 1.38023
\(306\) 217.943 + 38.4292i 0.712232 + 0.125586i
\(307\) −170.891 + 203.660i −0.556649 + 0.663388i −0.968834 0.247712i \(-0.920321\pi\)
0.412185 + 0.911100i \(0.364766\pi\)
\(308\) 93.6572 + 34.0884i 0.304082 + 0.110677i
\(309\) 6.61812 2.40880i 0.0214179 0.00779546i
\(310\) 469.368 393.847i 1.51409 1.27047i
\(311\) 79.8596 + 138.321i 0.256783 + 0.444762i 0.965378 0.260854i \(-0.0840040\pi\)
−0.708595 + 0.705615i \(0.750671\pi\)
\(312\) 14.1816 + 8.18774i 0.0454538 + 0.0262428i
\(313\) −32.6715 185.290i −0.104382 0.591979i −0.991465 0.130370i \(-0.958383\pi\)
0.887083 0.461609i \(-0.152728\pi\)
\(314\) 321.834 56.7480i 1.02495 0.180726i
\(315\) 193.873 335.798i 0.615470 1.06603i
\(316\) 263.739 152.270i 0.834617 0.481867i
\(317\) 109.932 + 131.012i 0.346788 + 0.413285i 0.911041 0.412316i \(-0.135280\pi\)
−0.564253 + 0.825602i \(0.690836\pi\)
\(318\) 12.9050 + 35.4562i 0.0405818 + 0.111498i
\(319\) −38.7847 + 106.560i −0.121582 + 0.334044i
\(320\) 52.1000 + 43.7171i 0.162812 + 0.136616i
\(321\) 2.36626 13.4197i 0.00737153 0.0418060i
\(322\) 109.792i 0.340969i
\(323\) 178.555 285.912i 0.552802 0.885177i
\(324\) −152.366 −0.470264
\(325\) −636.010 112.146i −1.95695 0.345064i
\(326\) −45.6612 + 54.4169i −0.140065 + 0.166923i
\(327\) 18.8484 + 6.86024i 0.0576403 + 0.0209793i
\(328\) 65.5324 23.8518i 0.199794 0.0727190i
\(329\) −306.928 + 257.543i −0.932911 + 0.782805i
\(330\) −24.5530 42.5270i −0.0744030 0.128870i
\(331\) −301.436 174.034i −0.910683 0.525783i −0.0300322 0.999549i \(-0.509561\pi\)
−0.880651 + 0.473766i \(0.842894\pi\)
\(332\) 18.4430 + 104.595i 0.0555511 + 0.315046i
\(333\) −154.904 + 27.3138i −0.465177 + 0.0820233i
\(334\) 104.643 181.246i 0.313301 0.542654i
\(335\) 74.4091 42.9601i 0.222117 0.128239i
\(336\) −5.63456 6.71501i −0.0167695 0.0199852i
\(337\) 113.696 + 312.377i 0.337377 + 0.926935i 0.986136 + 0.165941i \(0.0530662\pi\)
−0.648759 + 0.760994i \(0.724712\pi\)
\(338\) 8.52396 23.4194i 0.0252188 0.0692881i
\(339\) 14.8584 + 12.4676i 0.0438300 + 0.0367777i
\(340\) −52.3821 + 297.073i −0.154065 + 0.873745i
\(341\) 491.146i 1.44031i
\(342\) −88.7266 + 219.770i −0.259435 + 0.642601i
\(343\) −368.488 −1.07431
\(344\) −42.1980 7.44064i −0.122669 0.0216298i
\(345\) 34.7710 41.4385i 0.100786 0.120112i
\(346\) −150.712 54.8548i −0.435584 0.158540i
\(347\) −423.794 + 154.248i −1.22131 + 0.444520i −0.870612 0.491970i \(-0.836277\pi\)
−0.350696 + 0.936489i \(0.614055\pi\)
\(348\) 7.64012 6.41082i 0.0219544 0.0184219i
\(349\) 204.775 + 354.680i 0.586747 + 1.01628i 0.994655 + 0.103253i \(0.0329252\pi\)
−0.407908 + 0.913023i \(0.633742\pi\)
\(350\) 299.393 + 172.855i 0.855410 + 0.493871i
\(351\) −17.9158 101.606i −0.0510422 0.289475i
\(352\) 53.6890 9.46682i 0.152526 0.0268944i
\(353\) 32.9614 57.0908i 0.0933750 0.161730i −0.815554 0.578681i \(-0.803568\pi\)
0.908929 + 0.416950i \(0.136901\pi\)
\(354\) −27.5323 + 15.8958i −0.0777748 + 0.0449033i
\(355\) 623.020 + 742.486i 1.75499 + 2.09151i
\(356\) −76.2262 209.430i −0.214119 0.588286i
\(357\) 13.2976 36.5349i 0.0372482 0.102339i
\(358\) −269.630 226.246i −0.753156 0.631973i
\(359\) −21.5577 + 122.260i −0.0600494 + 0.340557i −1.00000 0.000754240i \(-0.999760\pi\)
0.939950 + 0.341311i \(0.110871\pi\)
\(360\) 212.093i 0.589147i
\(361\) 259.811 + 250.638i 0.719698 + 0.694287i
\(362\) −252.801 −0.698345
\(363\) 11.7367 + 2.06950i 0.0323326 + 0.00570111i
\(364\) −90.8126 + 108.226i −0.249485 + 0.297325i
\(365\) −892.079 324.690i −2.44405 0.889562i
\(366\) −27.8886 + 10.1506i −0.0761982 + 0.0277339i
\(367\) 245.165 205.718i 0.668023 0.560538i −0.244456 0.969660i \(-0.578609\pi\)
0.912480 + 0.409122i \(0.134165\pi\)
\(368\) 30.0276 + 52.0092i 0.0815966 + 0.141329i
\(369\) −188.340 108.738i −0.510408 0.294684i
\(370\) −37.2308 211.146i −0.100624 0.570666i
\(371\) −320.584 + 56.5277i −0.864109 + 0.152366i
\(372\) −21.5982 + 37.4092i −0.0580597 + 0.100562i
\(373\) −433.118 + 250.061i −1.16117 + 0.670404i −0.951585 0.307386i \(-0.900546\pi\)
−0.209588 + 0.977790i \(0.567212\pi\)
\(374\) 155.428 + 185.232i 0.415584 + 0.495274i
\(375\) −27.4490 75.4156i −0.0731974 0.201108i
\(376\) −74.9570 + 205.943i −0.199354 + 0.547720i
\(377\) −123.136 103.324i −0.326621 0.274068i
\(378\) −9.59037 + 54.3897i −0.0253713 + 0.143888i
\(379\) 715.542i 1.88797i 0.329982 + 0.943987i \(0.392957\pi\)
−0.329982 + 0.943987i \(0.607043\pi\)
\(380\) −299.563 120.941i −0.788324 0.318267i
\(381\) 25.7113 0.0674837
\(382\) 417.026 + 73.5329i 1.09169 + 0.192495i
\(383\) 111.458 132.831i 0.291014 0.346817i −0.600652 0.799510i \(-0.705092\pi\)
0.891666 + 0.452693i \(0.149537\pi\)
\(384\) −4.50565 1.63992i −0.0117335 0.00427063i
\(385\) 398.111 144.901i 1.03406 0.376366i
\(386\) −3.99422 + 3.35155i −0.0103477 + 0.00868278i
\(387\) 66.8118 + 115.721i 0.172640 + 0.299022i
\(388\) −149.196 86.1382i −0.384525 0.222006i
\(389\) −37.0880 210.336i −0.0953419 0.540711i −0.994642 0.103379i \(-0.967035\pi\)
0.899300 0.437332i \(-0.144076\pi\)
\(390\) 68.5503 12.0873i 0.175770 0.0309930i
\(391\) −133.183 + 230.680i −0.340621 + 0.589974i
\(392\) −54.5300 + 31.4829i −0.139107 + 0.0803136i
\(393\) −33.9674 40.4808i −0.0864311 0.103005i
\(394\) 70.5195 + 193.751i 0.178983 + 0.491753i
\(395\) 442.751 1216.45i 1.12089 3.07961i
\(396\) −130.236 109.281i −0.328879 0.275962i
\(397\) 60.3300 342.149i 0.151965 0.861836i −0.809544 0.587060i \(-0.800285\pi\)
0.961508 0.274776i \(-0.0886036\pi\)
\(398\) 67.7124i 0.170132i
\(399\) 35.3164 + 22.0555i 0.0885124 + 0.0552769i
\(400\) 189.099 0.472749
\(401\) 98.1719 + 17.3104i 0.244818 + 0.0431680i 0.294710 0.955587i \(-0.404777\pi\)
−0.0498926 + 0.998755i \(0.515888\pi\)
\(402\) −3.89360 + 4.64021i −0.00968557 + 0.0115428i
\(403\) 654.213 + 238.114i 1.62336 + 0.590854i
\(404\) −114.527 + 41.6846i −0.283484 + 0.103180i
\(405\) −496.140 + 416.311i −1.22504 + 1.02793i
\(406\) 43.0230 + 74.5180i 0.105968 + 0.183542i
\(407\) −148.838 85.9315i −0.365695 0.211134i
\(408\) −3.69293 20.9436i −0.00905129 0.0513324i
\(409\) 487.607 85.9782i 1.19219 0.210216i 0.457872 0.889018i \(-0.348612\pi\)
0.734321 + 0.678802i \(0.237501\pi\)
\(410\) 148.219 256.723i 0.361510 0.626153i
\(411\) 21.7816 12.5756i 0.0529967 0.0305977i
\(412\) 21.3638 + 25.4604i 0.0518540 + 0.0617972i
\(413\) −93.8097 257.740i −0.227142 0.624068i
\(414\) 64.0537 175.986i 0.154719 0.425087i
\(415\) 345.842 + 290.196i 0.833354 + 0.699267i
\(416\) −13.4192 + 76.1042i −0.0322578 + 0.182943i
\(417\) 18.2309i 0.0437192i
\(418\) −228.614 + 121.632i −0.546924 + 0.290986i
\(419\) 61.5336 0.146858 0.0734291 0.997300i \(-0.476606\pi\)
0.0734291 + 0.997300i \(0.476606\pi\)
\(420\) −36.6951 6.47033i −0.0873693 0.0154056i
\(421\) 394.068 469.631i 0.936027 1.11551i −0.0570875 0.998369i \(-0.518181\pi\)
0.993115 0.117145i \(-0.0373741\pi\)
\(422\) −14.4762 5.26889i −0.0343037 0.0124855i
\(423\) 642.228 233.752i 1.51827 0.552605i
\(424\) −136.403 + 114.456i −0.321705 + 0.269943i
\(425\) 419.362 + 726.356i 0.986734 + 1.70907i
\(426\) −59.1770 34.1659i −0.138913 0.0802016i
\(427\) −44.4626 252.160i −0.104128 0.590539i
\(428\) 63.3296 11.1667i 0.147966 0.0260905i
\(429\) 27.8983 48.3213i 0.0650310 0.112637i
\(430\) −157.737 + 91.0697i −0.366831 + 0.211790i
\(431\) −30.0869 35.8562i −0.0698073 0.0831931i 0.730011 0.683436i \(-0.239515\pi\)
−0.799818 + 0.600243i \(0.795071\pi\)
\(432\) 10.3323 + 28.3877i 0.0239173 + 0.0657122i
\(433\) −245.011 + 673.161i −0.565845 + 1.55465i 0.245085 + 0.969502i \(0.421184\pi\)
−0.810930 + 0.585144i \(0.801038\pi\)
\(434\) −285.487 239.552i −0.657804 0.551963i
\(435\) 7.36173 41.7504i 0.0169235 0.0959780i
\(436\) 94.6567i 0.217102i
\(437\) −212.040 190.823i −0.485218 0.436665i
\(438\) 66.9276 0.152803
\(439\) 30.4549 + 5.37002i 0.0693734 + 0.0122324i 0.208227 0.978080i \(-0.433231\pi\)
−0.138854 + 0.990313i \(0.544342\pi\)
\(440\) 148.958 177.522i 0.338542 0.403459i
\(441\) 184.516 + 67.1583i 0.418403 + 0.152286i
\(442\) −322.086 + 117.230i −0.728701 + 0.265226i
\(443\) 242.766 203.705i 0.548005 0.459831i −0.326260 0.945280i \(-0.605788\pi\)
0.874265 + 0.485449i \(0.161344\pi\)
\(444\) 7.55771 + 13.0903i 0.0170219 + 0.0294827i
\(445\) −820.440 473.681i −1.84369 1.06445i
\(446\) 75.0682 + 425.733i 0.168314 + 0.954558i
\(447\) −16.3923 + 2.89041i −0.0366719 + 0.00646625i
\(448\) 20.6836 35.8250i 0.0461688 0.0799666i
\(449\) −223.046 + 128.776i −0.496762 + 0.286805i −0.727375 0.686240i \(-0.759260\pi\)
0.230614 + 0.973045i \(0.425927\pi\)
\(450\) −379.054 451.738i −0.842341 1.00386i
\(451\) −81.2710 223.290i −0.180202 0.495101i
\(452\) −31.3063 + 86.0134i −0.0692618 + 0.190295i
\(453\) −9.75790 8.18785i −0.0215406 0.0180747i
\(454\) 55.9396 317.249i 0.123215 0.698787i
\(455\) 600.540i 1.31987i
\(456\) 22.7617 + 0.788971i 0.0499160 + 0.00173020i
\(457\) 780.810 1.70856 0.854278 0.519816i \(-0.174000\pi\)
0.854278 + 0.519816i \(0.174000\pi\)
\(458\) −144.356 25.4539i −0.315189 0.0555762i
\(459\) −86.1271 + 102.642i −0.187641 + 0.223622i
\(460\) 239.883 + 87.3103i 0.521485 + 0.189805i
\(461\) 398.212 144.937i 0.863801 0.314398i 0.128147 0.991755i \(-0.459097\pi\)
0.735654 + 0.677357i \(0.236875\pi\)
\(462\) −22.8803 + 19.1988i −0.0495244 + 0.0415559i
\(463\) −341.060 590.733i −0.736630 1.27588i −0.954004 0.299792i \(-0.903083\pi\)
0.217374 0.976088i \(-0.430251\pi\)
\(464\) 40.7605 + 23.5331i 0.0878460 + 0.0507179i
\(465\) 31.8847 + 180.827i 0.0685691 + 0.388875i
\(466\) 192.662 33.9715i 0.413438 0.0729002i
\(467\) −238.816 + 413.642i −0.511384 + 0.885743i 0.488529 + 0.872548i \(0.337534\pi\)
−0.999913 + 0.0131953i \(0.995800\pi\)
\(468\) 208.704 120.495i 0.445949 0.257469i
\(469\) −33.5920 40.0334i −0.0716247 0.0853590i
\(470\) 318.622 + 875.407i 0.677920 + 1.86257i
\(471\) −33.4953 + 92.0275i −0.0711153 + 0.195388i
\(472\) −114.929 96.4367i −0.243493 0.204315i
\(473\) −25.3527 + 143.782i −0.0535998 + 0.303980i
\(474\) 91.2632i 0.192538i
\(475\) −854.189 + 277.787i −1.79829 + 0.584814i
\(476\) 183.478 0.385459
\(477\) 546.845 + 96.4235i 1.14643 + 0.202146i
\(478\) 226.870 270.373i 0.474623 0.565634i
\(479\) −566.558 206.210i −1.18279 0.430502i −0.325606 0.945505i \(-0.605568\pi\)
−0.857188 + 0.515004i \(0.827791\pi\)
\(480\) −19.1523 + 6.97087i −0.0399006 + 0.0145226i
\(481\) 186.621 156.593i 0.387985 0.325558i
\(482\) 100.010 + 173.222i 0.207489 + 0.359382i
\(483\) −28.4940 16.4510i −0.0589938 0.0340601i
\(484\) 9.76628 + 55.3873i 0.0201783 + 0.114437i
\(485\) −721.175 + 127.163i −1.48696 + 0.262191i
\(486\) 70.8932 122.791i 0.145871 0.252656i
\(487\) −235.880 + 136.185i −0.484352 + 0.279641i −0.722229 0.691654i \(-0.756882\pi\)
0.237876 + 0.971296i \(0.423549\pi\)
\(488\) −90.0266 107.290i −0.184481 0.219856i
\(489\) −7.28087 20.0040i −0.0148893 0.0409080i
\(490\) −91.5420 + 251.510i −0.186820 + 0.513285i
\(491\) −454.615 381.468i −0.925897 0.776920i 0.0491792 0.998790i \(-0.484339\pi\)
−0.975076 + 0.221870i \(0.928784\pi\)
\(492\) −3.62904 + 20.5813i −0.00737610 + 0.0418320i
\(493\) 208.756i 0.423439i
\(494\) −51.1804 363.486i −0.103604 0.735802i
\(495\) −722.671 −1.45994
\(496\) −200.753 35.3982i −0.404744 0.0713674i
\(497\) 378.944 451.607i 0.762462 0.908667i
\(498\) −29.9087 10.8859i −0.0600576 0.0218592i
\(499\) 219.524 79.9000i 0.439927 0.160120i −0.112554 0.993646i \(-0.535903\pi\)
0.552481 + 0.833525i \(0.313681\pi\)
\(500\) 290.130 243.448i 0.580260 0.486896i
\(501\) 31.3588 + 54.3151i 0.0625925 + 0.108413i
\(502\) −435.842 251.634i −0.868211 0.501262i
\(503\) 75.1416 + 426.149i 0.149387 + 0.847215i 0.963740 + 0.266845i \(0.0859811\pi\)
−0.814353 + 0.580370i \(0.802908\pi\)
\(504\) −127.043 + 22.4011i −0.252069 + 0.0444466i
\(505\) −259.034 + 448.661i −0.512939 + 0.888437i
\(506\) 177.213 102.314i 0.350223 0.202201i
\(507\) 4.80075 + 5.72131i 0.00946893 + 0.0112846i
\(508\) 41.4991 + 114.018i 0.0816912 + 0.224445i
\(509\) 141.593 389.024i 0.278179 0.764291i −0.719390 0.694606i \(-0.755579\pi\)
0.997569 0.0696845i \(-0.0221993\pi\)
\(510\) −69.2497 58.1074i −0.135784 0.113936i
\(511\) −100.268 + 568.645i −0.196218 + 1.11281i
\(512\) 22.6274i 0.0441942i
\(513\) −88.3737 113.053i −0.172268 0.220376i
\(514\) 718.116 1.39711
\(515\) 139.132 + 24.5327i 0.270159 + 0.0476364i
\(516\) 8.25391 9.83662i 0.0159959 0.0190632i
\(517\) 701.715 + 255.403i 1.35728 + 0.494010i
\(518\) −122.544 + 44.6022i −0.236571 + 0.0861046i
\(519\) 36.8187 30.8945i 0.0709416 0.0595271i
\(520\) 164.245 + 284.480i 0.315855 + 0.547077i
\(521\) 246.294 + 142.198i 0.472733 + 0.272933i 0.717383 0.696679i \(-0.245340\pi\)
−0.244650 + 0.969611i \(0.578673\pi\)
\(522\) −25.4872 144.545i −0.0488261 0.276906i
\(523\) −401.387 + 70.7754i −0.767470 + 0.135326i −0.543658 0.839307i \(-0.682961\pi\)
−0.223812 + 0.974632i \(0.571850\pi\)
\(524\) 124.689 215.968i 0.237956 0.412152i
\(525\) −89.7209 + 51.8004i −0.170897 + 0.0986674i
\(526\) −187.327 223.248i −0.356135 0.424425i
\(527\) −309.237 849.622i −0.586788 1.61219i
\(528\) −5.58775 + 15.3522i −0.0105829 + 0.0290762i
\(529\) −232.561 195.142i −0.439623 0.368888i
\(530\) −131.433 + 745.392i −0.247986 + 1.40640i
\(531\) 467.862i 0.881096i
\(532\) −40.8038 + 192.211i −0.0766989 + 0.361299i
\(533\) 336.827 0.631946
\(534\) 65.7742 + 11.5978i 0.123173 + 0.0217187i
\(535\) 175.706 209.398i 0.328423 0.391399i
\(536\) −26.8617 9.77684i −0.0501150 0.0182404i
\(537\) 99.1177 36.0759i 0.184577 0.0671804i
\(538\) 18.8112 15.7844i 0.0349650 0.0293391i
\(539\) 107.273 + 185.802i 0.199022 + 0.344716i
\(540\) 111.209 + 64.2063i 0.205942 + 0.118901i
\(541\) −6.31951 35.8397i −0.0116812 0.0662471i 0.978410 0.206673i \(-0.0662638\pi\)
−0.990091 + 0.140426i \(0.955153\pi\)
\(542\) −117.212 + 20.6677i −0.216259 + 0.0381323i
\(543\) 37.8792 65.6086i 0.0697590 0.120826i
\(544\) 86.9149 50.1804i 0.159770 0.0922433i
\(545\) 258.632 + 308.226i 0.474554 + 0.565552i
\(546\) −14.4804 39.7847i −0.0265210 0.0728657i
\(547\) 363.049 997.469i 0.663710 1.82353i 0.104458 0.994529i \(-0.466689\pi\)
0.559252 0.828998i \(-0.311089\pi\)
\(548\) 90.9238 + 76.2941i 0.165919 + 0.139223i
\(549\) −75.8432 + 430.128i −0.138148 + 0.783475i
\(550\) 644.324i 1.17150i
\(551\) −218.691 46.4252i −0.396899 0.0842563i
\(552\) −17.9971 −0.0326034
\(553\) −775.410 136.726i −1.40219 0.247244i
\(554\) 158.232 188.574i 0.285618 0.340386i
\(555\) 60.3767 + 21.9753i 0.108787 + 0.0395952i
\(556\) 80.8458 29.4255i 0.145406 0.0529235i
\(557\) −136.150 + 114.244i −0.244435 + 0.205105i −0.756771 0.653680i \(-0.773224\pi\)
0.512337 + 0.858785i \(0.328780\pi\)
\(558\) 317.851 + 550.534i 0.569626 + 0.986621i
\(559\) −179.229 103.478i −0.320624 0.185113i
\(560\) −30.5344 173.169i −0.0545258 0.309231i
\(561\) −71.3618 + 12.5830i −0.127205 + 0.0224296i
\(562\) −32.8381 + 56.8772i −0.0584308 + 0.101205i
\(563\) −264.174 + 152.521i −0.469226 + 0.270907i −0.715915 0.698187i \(-0.753990\pi\)
0.246690 + 0.969094i \(0.420657\pi\)
\(564\) −42.2163 50.3114i −0.0748515 0.0892046i
\(565\) 133.075 + 365.620i 0.235531 + 0.647115i
\(566\) −76.0300 + 208.891i −0.134329 + 0.369065i
\(567\) 301.771 + 253.216i 0.532223 + 0.446588i
\(568\) 55.9959 317.568i 0.0985843 0.559099i
\(569\) 232.210i 0.408103i −0.978960 0.204051i \(-0.934589\pi\)
0.978960 0.204051i \(-0.0654110\pi\)
\(570\) 76.2735 59.6231i 0.133813 0.104602i
\(571\) −153.252 −0.268392 −0.134196 0.990955i \(-0.542845\pi\)
−0.134196 + 0.990955i \(0.542845\pi\)
\(572\) 259.312 + 45.7237i 0.453343 + 0.0799366i
\(573\) −81.5700 + 97.2114i −0.142356 + 0.169653i
\(574\) −169.431 61.6677i −0.295175 0.107435i
\(575\) 666.970 242.757i 1.15995 0.422186i
\(576\) −54.0545 + 45.3571i −0.0938446 + 0.0787450i
\(577\) −158.150 273.925i −0.274091 0.474739i 0.695815 0.718222i \(-0.255044\pi\)
−0.969905 + 0.243482i \(0.921710\pi\)
\(578\) 31.5476 + 18.2140i 0.0545806 + 0.0315121i
\(579\) −0.271332 1.53880i −0.000468621 0.00265768i
\(580\) 197.026 34.7411i 0.339701 0.0598984i
\(581\) 137.299 237.808i 0.236314 0.409309i
\(582\) 44.7103 25.8135i 0.0768219 0.0443531i
\(583\) 389.988 + 464.770i 0.668933 + 0.797204i
\(584\) 108.024 + 296.794i 0.184973 + 0.508208i
\(585\) 350.361 962.608i 0.598907 1.64548i
\(586\) −294.775 247.346i −0.503029 0.422091i
\(587\) −41.1017 + 233.099i −0.0700199 + 0.397103i 0.929575 + 0.368634i \(0.120174\pi\)
−0.999595 + 0.0284689i \(0.990937\pi\)
\(588\) 18.8693i 0.0320907i
\(589\) 958.830 135.007i 1.62790 0.229214i
\(590\) −637.733 −1.08090
\(591\) −60.8500 10.7295i −0.102961 0.0181548i
\(592\) −45.8512 + 54.6434i −0.0774514 + 0.0923030i
\(593\) 413.201 + 150.393i 0.696797 + 0.253613i 0.666043 0.745913i \(-0.267987\pi\)
0.0307545 + 0.999527i \(0.490209\pi\)
\(594\) 96.7261 35.2054i 0.162839 0.0592684i
\(595\) 597.451 501.321i 1.00412 0.842557i
\(596\) −39.2756 68.0273i −0.0658987 0.114140i
\(597\) −17.5732 10.1459i −0.0294358 0.0169948i
\(598\) 50.3683 + 285.653i 0.0842280 + 0.477681i
\(599\) 1114.55 196.525i 1.86068 0.328089i 0.873392 0.487017i \(-0.161915\pi\)
0.987290 + 0.158928i \(0.0508039\pi\)
\(600\) −28.3343 + 49.0764i −0.0472238 + 0.0817940i
\(601\) −332.710 + 192.090i −0.553594 + 0.319618i −0.750570 0.660791i \(-0.770221\pi\)
0.196976 + 0.980408i \(0.436888\pi\)
\(602\) 71.2105 + 84.8654i 0.118290 + 0.140972i
\(603\) 30.4889 + 83.7675i 0.0505620 + 0.138918i
\(604\) 20.5597 56.4874i 0.0340393 0.0935222i
\(605\) 183.137 + 153.670i 0.302706 + 0.254001i
\(606\) 6.34228 35.9689i 0.0104658 0.0593545i
\(607\) 725.336i 1.19495i −0.801887 0.597476i \(-0.796170\pi\)
0.801887 0.597476i \(-0.203830\pi\)
\(608\) 33.2396 + 102.211i 0.0546704 + 0.168111i
\(609\) −25.7859 −0.0423414
\(610\) −586.298 103.380i −0.961145 0.169476i
\(611\) −680.402 + 810.872i −1.11359 + 1.32712i
\(612\) −294.098 107.043i −0.480552 0.174907i
\(613\) −323.685 + 117.812i −0.528034 + 0.192189i −0.592260 0.805747i \(-0.701764\pi\)
0.0642263 + 0.997935i \(0.479542\pi\)
\(614\) 288.019 241.677i 0.469086 0.393610i
\(615\) 44.4176 + 76.9336i 0.0722238 + 0.125095i
\(616\) −122.068 70.4758i −0.198162 0.114409i
\(617\) −94.6496 536.785i −0.153403 0.869991i −0.960231 0.279206i \(-0.909929\pi\)
0.806828 0.590786i \(-0.201182\pi\)
\(618\) −9.80878 + 1.72955i −0.0158718 + 0.00279863i
\(619\) −492.260 + 852.619i −0.795250 + 1.37741i 0.127431 + 0.991847i \(0.459327\pi\)
−0.922680 + 0.385566i \(0.874006\pi\)
\(620\) −750.422 + 433.256i −1.21036 + 0.698800i
\(621\) 72.8855 + 86.8616i 0.117368 + 0.139874i
\(622\) −77.2545 212.255i −0.124203 0.341246i
\(623\) −197.079 + 541.470i −0.316339 + 0.869134i
\(624\) −17.7404 14.8859i −0.0284301 0.0238557i
\(625\) 74.3286 421.539i 0.118926 0.674462i
\(626\) 266.081i 0.425050i
\(627\) 2.68828 77.5566i 0.00428753 0.123695i
\(628\) −462.163 −0.735929
\(629\) −311.576 54.9392i −0.495351 0.0873437i
\(630\) −352.476 + 420.065i −0.559486 + 0.666770i
\(631\) −499.596 181.838i −0.791752 0.288174i −0.0856881 0.996322i \(-0.527309\pi\)
−0.706064 + 0.708148i \(0.749531\pi\)
\(632\) −404.711 + 147.303i −0.640365 + 0.233074i
\(633\) 3.53650 2.96747i 0.00558688 0.00468795i
\(634\) −120.932 209.460i −0.190744 0.330379i
\(635\) 446.665 + 257.882i 0.703409 + 0.406113i
\(636\) −9.26599 52.5500i −0.0145692 0.0826258i
\(637\) −299.498 + 52.8096i −0.470169 + 0.0829036i
\(638\) 80.1851 138.885i 0.125682 0.217687i
\(639\) −870.882 + 502.804i −1.36288 + 0.786861i
\(640\) −61.8253 73.6805i −0.0966020 0.115126i
\(641\) 81.2045 + 223.108i 0.126684 + 0.348062i 0.986779 0.162073i \(-0.0518179\pi\)
−0.860095 + 0.510134i \(0.829596\pi\)
\(642\) −6.59111 + 18.1089i −0.0102665 + 0.0282071i
\(643\) −206.587 173.347i −0.321286 0.269591i 0.467852 0.883807i \(-0.345028\pi\)
−0.789138 + 0.614216i \(0.789472\pi\)
\(644\) 26.9623 152.911i 0.0418669 0.237439i
\(645\) 54.5828i 0.0846245i
\(646\) −318.892 + 354.349i −0.493641 + 0.548529i
\(647\) −172.930 −0.267280 −0.133640 0.991030i \(-0.542667\pi\)
−0.133640 + 0.991030i \(0.542667\pi\)
\(648\) 212.204 + 37.4173i 0.327475 + 0.0577427i
\(649\) −328.592 + 391.600i −0.506305 + 0.603390i
\(650\) 858.249 + 312.377i 1.32038 + 0.480580i
\(651\) 104.947 38.1976i 0.161209 0.0586752i
\(652\) 76.9572 64.5747i 0.118032 0.0990410i
\(653\) 566.373 + 980.986i 0.867339 + 1.50228i 0.864705 + 0.502279i \(0.167505\pi\)
0.00263396 + 0.999997i \(0.499162\pi\)
\(654\) −24.5659 14.1832i −0.0375626 0.0216868i
\(655\) −184.074 1043.93i −0.281029 1.59379i
\(656\) −97.1262 + 17.1260i −0.148058 + 0.0261067i
\(657\) 492.472 852.987i 0.749577 1.29831i
\(658\) 490.713 283.313i 0.745764 0.430567i
\(659\) −727.538 867.046i −1.10400 1.31570i −0.944503 0.328502i \(-0.893456\pi\)
−0.159500 0.987198i \(-0.550988\pi\)
\(660\) 23.7520 + 65.2582i 0.0359879 + 0.0988761i
\(661\) −200.912 + 552.002i −0.303952 + 0.835101i 0.689852 + 0.723951i \(0.257676\pi\)
−0.993804 + 0.111150i \(0.964547\pi\)
\(662\) 377.080 + 316.408i 0.569607 + 0.477957i
\(663\) 17.8364 101.155i 0.0269026 0.152572i
\(664\) 150.202i 0.226208i
\(665\) 392.314 + 737.376i 0.589946 + 1.10884i
\(666\) 222.447 0.334004
\(667\) 173.977 + 30.6768i 0.260834 + 0.0459922i
\(668\) −190.248 + 226.729i −0.284803 + 0.339415i
\(669\) −121.737 44.3087i −0.181969 0.0662312i
\(670\) −114.182 + 41.5587i −0.170420 + 0.0620280i
\(671\) −365.571 + 306.750i −0.544815 + 0.457154i
\(672\) 6.19837 + 10.7359i 0.00922377 + 0.0159760i
\(673\) −818.808 472.739i −1.21665 0.702435i −0.252453 0.967609i \(-0.581237\pi\)
−0.964201 + 0.265174i \(0.914571\pi\)
\(674\) −81.6354 462.978i −0.121121 0.686910i
\(675\) 351.614 61.9990i 0.520909 0.0918503i
\(676\) −17.6228 + 30.5236i −0.0260692 + 0.0451532i
\(677\) 503.136 290.485i 0.743184 0.429077i −0.0800419 0.996792i \(-0.525505\pi\)
0.823226 + 0.567714i \(0.192172\pi\)
\(678\) −17.6319 21.0129i −0.0260058 0.0309925i
\(679\) 152.340 + 418.550i 0.224359 + 0.616422i
\(680\) 145.908 400.879i 0.214571 0.589528i
\(681\) 73.9528 + 62.0538i 0.108594 + 0.0911216i
\(682\) −120.613 + 684.032i −0.176852 + 1.00298i
\(683\) 270.340i 0.395813i −0.980221 0.197906i \(-0.936586\pi\)
0.980221 0.197906i \(-0.0634142\pi\)
\(684\) 177.542 284.290i 0.259565 0.415629i
\(685\) 504.530 0.736540
\(686\) 513.203 + 90.4916i 0.748110 + 0.131912i
\(687\) 28.2360 33.6504i 0.0411005 0.0489816i
\(688\) 56.9431 + 20.7256i 0.0827661 + 0.0301244i
\(689\) −808.152 + 294.143i −1.17293 + 0.426913i
\(690\) −58.6029 + 49.1737i −0.0849318 + 0.0712662i
\(691\) 29.8337 + 51.6734i 0.0431746 + 0.0747806i 0.886805 0.462143i \(-0.152919\pi\)
−0.843631 + 0.536924i \(0.819586\pi\)
\(692\) 196.430 + 113.409i 0.283859 + 0.163886i
\(693\) 76.3279 + 432.877i 0.110141 + 0.624642i
\(694\) 628.109 110.753i 0.905057 0.159586i
\(695\) 182.854 316.713i 0.263100 0.455702i
\(696\) −12.2149 + 7.05230i −0.0175502 + 0.0101326i
\(697\) −281.178 335.095i −0.403412 0.480767i
\(698\) −198.095 544.261i −0.283804 0.779744i
\(699\) −20.0515 + 55.0912i −0.0286860 + 0.0788143i
\(700\) −374.525 314.264i −0.535035 0.448948i
\(701\) −61.8014 + 350.493i −0.0881618 + 0.499991i 0.908468 + 0.417955i \(0.137253\pi\)
−0.996629 + 0.0820353i \(0.973858\pi\)
\(702\) 145.909i 0.207847i
\(703\) 126.845 314.187i 0.180434 0.446923i
\(704\) −77.0990 −0.109516
\(705\) −274.933 48.4782i −0.389976 0.0687634i
\(706\) −59.9264 + 71.4175i −0.0848815 + 0.101158i
\(707\) 296.105 + 107.773i 0.418819 + 0.152438i
\(708\) 42.2486 15.3772i 0.0596732 0.0217193i
\(709\) 698.190 585.851i 0.984754 0.826306i −4.60524e−5 1.00000i \(-0.500015\pi\)
0.984800 + 0.173694i \(0.0555702\pi\)
\(710\) −685.361 1187.08i −0.965298 1.67194i
\(711\) 1163.14 + 671.540i 1.63592 + 0.944500i
\(712\) 54.7316 + 310.398i 0.0768702 + 0.435952i
\(713\) −753.516 + 132.865i −1.05682 + 0.186347i
\(714\) −27.4920 + 47.6176i −0.0385042 + 0.0666913i
\(715\) 969.317 559.635i 1.35569 0.782707i
\(716\) 319.960 + 381.314i 0.446872 + 0.532561i
\(717\) 36.1754 + 99.3910i 0.0504538 + 0.138621i
\(718\) 60.0481 164.981i 0.0836325 0.229778i
\(719\) 131.934 + 110.706i 0.183496 + 0.153972i 0.729909 0.683545i \(-0.239563\pi\)
−0.546413 + 0.837516i \(0.684007\pi\)
\(720\) −52.0849 + 295.388i −0.0723401 + 0.410261i
\(721\) 85.9306i 0.119183i
\(722\) −300.296 412.873i −0.415922 0.571847i
\(723\) −59.9411 −0.0829061
\(724\) 352.083 + 62.0817i 0.486303 + 0.0857483i
\(725\) 357.559 426.122i 0.493184 0.587754i
\(726\) −15.8379 5.76451i −0.0218152 0.00794009i
\(727\) −101.193 + 36.8313i −0.139193 + 0.0506620i −0.410677 0.911781i \(-0.634708\pi\)
0.271485 + 0.962443i \(0.412485\pi\)
\(728\) 153.055 128.428i 0.210240 0.176413i
\(729\) −321.577 556.988i −0.441121 0.764045i
\(730\) 1162.69 + 671.278i 1.59272 + 0.919559i
\(731\) 46.6718 + 264.689i 0.0638465 + 0.362091i
\(732\) 41.3339 7.28829i 0.0564671 0.00995667i
\(733\) 43.4420 75.2438i 0.0592661 0.102652i −0.834870 0.550447i \(-0.814457\pi\)
0.894136 + 0.447795i \(0.147791\pi\)
\(734\) −391.967 + 226.302i −0.534015 + 0.308314i
\(735\) −51.5570 61.4433i −0.0701456 0.0835963i
\(736\) −29.0480 79.8088i −0.0394674 0.108436i
\(737\) −33.3129 + 91.5265i −0.0452007 + 0.124188i
\(738\) 235.604 + 197.695i 0.319246 + 0.267879i
\(739\) 120.006 680.590i 0.162390 0.920961i −0.789324 0.613977i \(-0.789569\pi\)
0.951715 0.306984i \(-0.0993200\pi\)
\(740\) 303.212i 0.409747i
\(741\) 102.003 + 41.1813i 0.137656 + 0.0555753i
\(742\) 460.369 0.620443
\(743\) 837.812 + 147.729i 1.12761 + 0.198827i 0.706178 0.708034i \(-0.250418\pi\)
0.421428 + 0.906862i \(0.361529\pi\)
\(744\) 39.2672 46.7969i 0.0527785 0.0628990i
\(745\) −313.763 114.201i −0.421159 0.153289i
\(746\) 664.624 241.903i 0.890917 0.324267i
\(747\) −358.816 + 301.082i −0.480343 + 0.403055i
\(748\) −170.981 296.148i −0.228584 0.395919i
\(749\) −143.987 83.1308i −0.192239 0.110989i
\(750\) 19.7088 + 111.774i 0.0262784 + 0.149032i
\(751\) −1004.82 + 177.177i −1.33797 + 0.235921i −0.796420 0.604744i \(-0.793275\pi\)
−0.541555 + 0.840665i \(0.682164\pi\)
\(752\) 154.969 268.415i 0.206076 0.356934i
\(753\) 130.611 75.4085i 0.173455 0.100144i
\(754\) 146.122 + 174.141i 0.193795 + 0.230956i
\(755\) −87.3939 240.113i −0.115753 0.318030i
\(756\) 26.7136 73.3949i 0.0353354 0.0970832i
\(757\) 506.858 + 425.305i 0.669562 + 0.561829i 0.912936 0.408103i \(-0.133810\pi\)
−0.243374 + 0.969933i \(0.578254\pi\)
\(758\) 175.720 996.556i 0.231820 1.31472i
\(759\) 61.3219i 0.0807930i
\(760\) 387.510 + 242.004i 0.509881 + 0.318426i
\(761\) −723.005 −0.950072 −0.475036 0.879966i \(-0.657565\pi\)
−0.475036 + 0.879966i \(0.657565\pi\)
\(762\) −35.8089 6.31407i −0.0469932 0.00828618i
\(763\) 157.309 187.474i 0.206172 0.245707i
\(764\) −562.746 204.823i −0.736578 0.268093i
\(765\) −1250.13 + 455.011i −1.63416 + 0.594785i
\(766\) −187.851 + 157.626i −0.245237 + 0.205778i
\(767\) −362.312 627.542i −0.472375 0.818178i
\(768\) 5.87242 + 3.39044i 0.00764638 + 0.00441464i
\(769\) 210.668 + 1194.76i 0.273951 + 1.55365i 0.742276 + 0.670095i \(0.233747\pi\)
−0.468325 + 0.883556i \(0.655142\pi\)
\(770\) −590.045 + 104.041i −0.766293 + 0.135118i
\(771\) −107.601 + 186.370i −0.139560 + 0.241725i
\(772\) 6.38593 3.68692i 0.00827193 0.00477580i
\(773\) −633.445 754.910i −0.819463 0.976598i 0.180513 0.983573i \(-0.442224\pi\)
−0.999976 + 0.00697460i \(0.997780\pi\)
\(774\) −64.6323 177.576i −0.0835043 0.229426i
\(775\) −824.011 + 2263.95i −1.06324 + 2.92123i
\(776\) 186.636 + 156.606i 0.240510 + 0.201812i
\(777\) 6.78620 38.4864i 0.00873384 0.0495321i
\(778\) 302.049i 0.388238i
\(779\) 413.575 220.039i 0.530905 0.282463i
\(780\) −98.4402 −0.126205
\(781\) −1082.06 190.796i −1.38548 0.244298i
\(782\) 242.137 288.568i 0.309638 0.369012i
\(783\) 83.5063 + 30.3938i 0.106649 + 0.0388171i
\(784\) 83.6770 30.4559i 0.106731 0.0388468i
\(785\) −1504.92 + 1262.78i −1.91709 + 1.60863i
\(786\) 37.3663 + 64.7203i 0.0475398 + 0.0823414i
\(787\) 421.297 + 243.236i 0.535320 + 0.309067i 0.743180 0.669091i \(-0.233316\pi\)
−0.207860 + 0.978159i \(0.566650\pi\)
\(788\) −50.6340 287.160i −0.0642564 0.364416i
\(789\) 86.0074 15.1654i 0.109008 0.0192211i
\(790\) −915.361 + 1585.45i −1.15869 + 2.00690i
\(791\) 204.950 118.328i 0.259102 0.149593i
\(792\) 154.547 + 184.181i 0.195135 + 0.232552i
\(793\) −231.362 635.663i −0.291756 0.801592i
\(794\) −168.047 + 461.705i −0.211646 + 0.581492i
\(795\) −173.756 145.798i −0.218561 0.183394i
\(796\) 16.6285 94.3050i 0.0208901 0.118474i
\(797\) 1186.46i 1.48865i −0.667817 0.744326i \(-0.732771\pi\)
0.667817 0.744326i \(-0.267229\pi\)
\(798\) −43.7699 39.3902i −0.0548495 0.0493611i
\(799\) 1374.69 1.72051
\(800\) −263.364 46.4382i −0.329205 0.0580478i
\(801\) 631.797 752.947i 0.788761 0.940008i
\(802\) −132.476 48.2173i −0.165182 0.0601213i
\(803\) 1011.27 368.073i 1.25937 0.458373i
\(804\) 6.56225 5.50638i 0.00816200 0.00684873i
\(805\) −330.004 571.584i −0.409943 0.710043i
\(806\) −852.666 492.287i −1.05790 0.610778i
\(807\) 1.27786 + 7.24711i 0.00158347 + 0.00898031i
\(808\) 169.742 29.9301i 0.210077 0.0370423i
\(809\) −346.462 + 600.089i −0.428259 + 0.741766i −0.996719 0.0809449i \(-0.974206\pi\)
0.568460 + 0.822711i \(0.307540\pi\)
\(810\) 793.224 457.968i 0.979289 0.565393i
\(811\) 572.213 + 681.937i 0.705565 + 0.840860i 0.993144 0.116897i \(-0.0372948\pi\)
−0.287579 + 0.957757i \(0.592850\pi\)
\(812\) −41.6195 114.349i −0.0512556 0.140824i
\(813\) 12.1990 33.5165i 0.0150050 0.0412258i
\(814\) 186.188 + 156.230i 0.228732 + 0.191929i
\(815\) 74.1531 420.543i 0.0909853 0.516004i
\(816\) 30.0757i 0.0368574i
\(817\) −287.666 9.97114i −0.352100 0.0122046i
\(818\) −700.218 −0.856012
\(819\) −613.603 108.195i −0.749210 0.132106i
\(820\) −269.474 + 321.146i −0.328626 + 0.391642i
\(821\) 605.463 + 220.370i 0.737470 + 0.268417i 0.683323 0.730116i \(-0.260534\pi\)
0.0541466 + 0.998533i \(0.482756\pi\)
\(822\) −33.4242 + 12.1654i −0.0406620 + 0.0147998i
\(823\) 253.156 212.423i 0.307602 0.258109i −0.475898 0.879500i \(-0.657877\pi\)
0.783500 + 0.621392i \(0.213432\pi\)
\(824\) −23.5016 40.7059i −0.0285213 0.0494004i
\(825\) 167.219 + 96.5442i 0.202690 + 0.117023i
\(826\) 67.3568 + 381.999i 0.0815457 + 0.462469i
\(827\) 641.165 113.055i 0.775290 0.136705i 0.228015 0.973658i \(-0.426776\pi\)
0.547275 + 0.836953i \(0.315665\pi\)
\(828\) −132.427 + 229.371i −0.159936 + 0.277018i
\(829\) 1274.18 735.648i 1.53701 0.887392i 0.537995 0.842948i \(-0.319182\pi\)
0.999012 0.0444438i \(-0.0141516\pi\)
\(830\) −410.399 489.095i −0.494457 0.589271i
\(831\) 25.2308 + 69.3210i 0.0303619 + 0.0834187i
\(832\) 37.3787 102.697i 0.0449263 0.123434i
\(833\) 302.554 + 253.873i 0.363210 + 0.304769i
\(834\) −4.47707 + 25.3907i −0.00536819 + 0.0304445i
\(835\) 1258.11i 1.50671i
\(836\) 348.267 113.258i 0.416587 0.135476i
\(837\) −384.889 −0.459843
\(838\) −85.6995 15.1111i −0.102267 0.0180324i
\(839\) −397.880 + 474.175i −0.474231 + 0.565167i −0.949134 0.314871i \(-0.898039\pi\)
0.474903 + 0.880038i \(0.342483\pi\)
\(840\) 49.5173 + 18.0228i 0.0589492 + 0.0214558i
\(841\) −660.179 + 240.286i −0.784993 + 0.285714i
\(842\) −664.159 + 557.296i −0.788787 + 0.661871i
\(843\) −9.84078 17.0447i −0.0116735 0.0202191i
\(844\) 18.8674 + 10.8931i 0.0223548 + 0.0129065i
\(845\) 26.0159 + 147.543i 0.0307880 + 0.174608i
\(846\) −951.853 + 167.837i −1.12512 + 0.198389i
\(847\) 72.7051 125.929i 0.0858384 0.148677i
\(848\) 218.080 125.908i 0.257170 0.148477i
\(849\) −42.8206 51.0316i −0.0504365 0.0601079i
\(850\) −405.682 1114.60i −0.477273 1.31130i
\(851\) −91.5725 + 251.593i −0.107606 + 0.295644i
\(852\) 74.0272 + 62.1162i 0.0868864 + 0.0729064i
\(853\) 159.925 906.980i 0.187485 1.06328i −0.735235 0.677812i \(-0.762928\pi\)
0.922720 0.385470i \(-0.125961\pi\)
\(854\) 362.109i 0.424016i
\(855\) −198.650 1410.82i −0.232339 1.65008i
\(856\) −90.9433 −0.106242
\(857\) 1231.45 + 217.138i 1.43693 + 0.253370i 0.837230 0.546852i \(-0.184174\pi\)
0.599704 + 0.800222i \(0.295285\pi\)
\(858\) −50.7213 + 60.4473i −0.0591158 + 0.0704514i
\(859\) −703.340 255.995i −0.818789 0.298015i −0.101540 0.994831i \(-0.532377\pi\)
−0.717249 + 0.696817i \(0.754599\pi\)
\(860\) 242.050 88.0989i 0.281453 0.102441i
\(861\) 41.3916 34.7317i 0.0480738 0.0403387i
\(862\) 33.0975 + 57.3266i 0.0383962 + 0.0665042i
\(863\) 66.6518 + 38.4815i 0.0772327 + 0.0445903i 0.538119 0.842869i \(-0.319135\pi\)
−0.460886 + 0.887459i \(0.652468\pi\)
\(864\) −7.41872 42.0737i −0.00858648 0.0486964i
\(865\) 949.495 167.422i 1.09768 0.193551i
\(866\) 506.545 877.362i 0.584925 1.01312i
\(867\) −9.45404 + 5.45829i −0.0109043 + 0.00629561i
\(868\) 338.778 + 403.740i 0.390297 + 0.465138i
\(869\) 501.909 + 1378.98i 0.577570 + 1.58686i
\(870\) −20.5058 + 56.3392i −0.0235699 + 0.0647577i
\(871\) −105.764 88.7466i −0.121428 0.101891i
\(872\) 23.2454 131.831i 0.0266575 0.151182i
\(873\) 759.772i 0.870300i
\(874\) 248.453 + 317.836i 0.284271 + 0.363657i
\(875\) −979.208 −1.11910
\(876\) −93.2120 16.4358i −0.106406 0.0187623i
\(877\) −509.911 + 607.688i −0.581426 + 0.692917i −0.973934 0.226832i \(-0.927163\pi\)
0.392508 + 0.919749i \(0.371608\pi\)
\(878\) −41.0967 14.9580i −0.0468072 0.0170364i
\(879\) 108.361 39.4403i 0.123278 0.0448695i
\(880\) −251.054 + 210.659i −0.285288 + 0.239385i
\(881\) −309.941 536.834i −0.351806 0.609346i 0.634760 0.772710i \(-0.281099\pi\)
−0.986566 + 0.163363i \(0.947766\pi\)
\(882\) −240.488 138.846i −0.272662 0.157422i
\(883\) −45.1234 255.907i −0.0511024 0.289816i 0.948537 0.316666i \(-0.102563\pi\)
−0.999639 + 0.0268501i \(0.991452\pi\)
\(884\) 477.367 84.1727i 0.540008 0.0952180i
\(885\) 95.5565 165.509i 0.107973 0.187016i
\(886\) −388.132 + 224.088i −0.438073 + 0.252921i
\(887\) 75.1189 + 89.5233i 0.0846888 + 0.100928i 0.806725 0.590927i \(-0.201238\pi\)
−0.722036 + 0.691855i \(0.756794\pi\)
\(888\) −7.31117 20.0873i −0.00823330 0.0226208i
\(889\) 107.294 294.788i 0.120691 0.331595i
\(890\) 1026.33 + 861.189i 1.15317 + 0.967629i
\(891\) 127.493 723.048i 0.143090 0.811502i
\(892\) 611.365i 0.685387i
\(893\) −305.718 + 1440.12i −0.342349 + 1.61267i
\(894\) 23.5399 0.0263310
\(895\) 2083.74 + 367.420i 2.32820 + 0.410525i
\(896\) −37.6044 + 44.8152i −0.0419692 + 0.0500169i
\(897\) −81.6817 29.7297i −0.0910610 0.0331435i
\(898\) 342.267 124.575i 0.381143 0.138725i
\(899\) −459.361 + 385.450i −0.510969 + 0.428754i
\(900\) 416.983 + 722.235i 0.463314 + 0.802484i
\(901\) 967.262 + 558.449i 1.07354 + 0.619810i
\(902\) 58.3538 + 330.941i 0.0646938 + 0.366897i
\(903\) −32.6949 + 5.76499i −0.0362069 + 0.00638426i
\(904\) 64.7240 112.105i 0.0715973 0.124010i
\(905\) 1316.10 759.849i 1.45425 0.839612i
\(906\) 11.5794 + 13.7998i 0.0127808 + 0.0152315i
\(907\) 191.542 + 526.257i 0.211182 + 0.580217i 0.999380 0.0352042i \(-0.0112082\pi\)
−0.788198 + 0.615421i \(0.788986\pi\)
\(908\) −155.817 + 428.105i −0.171605 + 0.471481i
\(909\) −411.752 345.501i −0.452972 0.380089i
\(910\) 147.478 836.390i 0.162064 0.919109i
\(911\) 749.720i 0.822964i −0.911418 0.411482i \(-0.865011\pi\)
0.911418 0.411482i \(-0.134989\pi\)
\(912\) −31.5071 6.68854i −0.0345473 0.00733392i
\(913\) −511.787 −0.560555
\(914\) −1087.46 191.748i −1.18978 0.209790i
\(915\) 114.680 136.670i 0.125333 0.149366i
\(916\) 194.798 + 70.9008i 0.212662 + 0.0774026i
\(917\) −605.871 + 220.519i −0.660710 + 0.240479i
\(918\) 145.158 121.802i 0.158124 0.132682i
\(919\) −657.952 1139.61i −0.715944 1.24005i −0.962594 0.270946i \(-0.912663\pi\)
0.246651 0.969104i \(-0.420670\pi\)
\(920\) −312.651 180.509i −0.339838 0.196205i
\(921\) 19.5654 + 110.961i 0.0212437 + 0.120479i
\(922\) −590.195 + 104.067i −0.640125 + 0.112871i
\(923\) 778.741 1348.82i 0.843707 1.46134i
\(924\) 36.5807 21.1199i 0.0395895 0.0228570i
\(925\) 541.903 + 645.814i 0.585841 + 0.698178i
\(926\) 329.934 + 906.486i 0.356300 + 0.978927i
\(927\) −50.1327 + 137.739i −0.0540806 + 0.148585i
\(928\) −50.9892 42.7850i −0.0549453 0.0461046i
\(929\) −3.86617 + 21.9261i −0.00416164 + 0.0236019i −0.986818 0.161835i \(-0.948259\pi\)
0.982656 + 0.185437i \(0.0593699\pi\)
\(930\) 259.673i 0.279218i
\(931\) −333.241 + 260.495i −0.357939 + 0.279801i
\(932\) −276.668 −0.296854
\(933\) 66.6615 + 11.7542i 0.0714486 + 0.0125983i
\(934\) 434.187 517.443i 0.464868 0.554008i
\(935\) −1365.93 497.156i −1.46088 0.531718i
\(936\) −320.259 + 116.565i −0.342157 + 0.124535i
\(937\) 280.376 235.263i 0.299227 0.251081i −0.480796 0.876833i \(-0.659652\pi\)
0.780022 + 0.625752i \(0.215208\pi\)
\(938\) 36.9533 + 64.0050i 0.0393958 + 0.0682356i
\(939\) −69.0553 39.8691i −0.0735413 0.0424591i
\(940\) −228.776 1297.45i −0.243378 1.38027i
\(941\) 1353.51 238.661i 1.43838 0.253625i 0.600563 0.799578i \(-0.294943\pi\)
0.837816 + 0.545953i \(0.183832\pi\)
\(942\) 69.2496 119.944i 0.0735133 0.127329i
\(943\) −320.587 + 185.091i −0.339965 + 0.196279i
\(944\) 136.382 + 162.534i 0.144473 + 0.172176i
\(945\) −113.552 311.982i −0.120161 0.330140i
\(946\) 70.6189 194.024i 0.0746500 0.205099i
\(947\) 481.476 + 404.007i 0.508423 + 0.426617i 0.860574 0.509326i \(-0.170105\pi\)
−0.352151 + 0.935943i \(0.614550\pi\)
\(948\) 22.4120 127.105i 0.0236414 0.134077i
\(949\) 1525.48i 1.60746i
\(950\) 1257.87 177.113i 1.32407 0.186435i
\(951\) 72.4807 0.0762152
\(952\) −255.536 45.0578i −0.268420 0.0473296i
\(953\) −1194.00 + 1422.96i −1.25289 + 1.49314i −0.454807 + 0.890590i \(0.650292\pi\)
−0.798084 + 0.602547i \(0.794153\pi\)
\(954\) −737.927 268.583i −0.773508 0.281534i
\(955\) −2392.08 + 870.646i −2.50480 + 0.911672i
\(956\) −382.365 + 320.843i −0.399964 + 0.335609i
\(957\) 24.0295 + 41.6203i 0.0251092 + 0.0434904i
\(958\) 738.422 + 426.328i 0.770795 + 0.445019i
\(959\) −53.2881 302.212i −0.0555663 0.315132i
\(960\) 28.3858 5.00519i 0.0295686 0.00521374i
\(961\) 818.091 1416.97i 0.851291 1.47448i
\(962\) −298.367 + 172.262i −0.310153 + 0.179067i
\(963\) 182.298 + 217.254i 0.189302 + 0.225601i
\(964\) −96.7475 265.811i −0.100360 0.275738i
\(965\) 10.7203 29.4539i 0.0111092 0.0305222i
\(966\) 35.6444 + 29.9092i 0.0368990 + 0.0309619i
\(967\) −249.595 + 1415.53i −0.258113 + 1.46383i 0.529841 + 0.848097i \(0.322252\pi\)
−0.787954 + 0.615735i \(0.788859\pi\)
\(968\) 79.5379i 0.0821672i
\(969\) −44.1811 135.856i −0.0455945 0.140202i
\(970\) 1035.63 1.06766
\(971\) −449.774 79.3073i −0.463207 0.0816759i −0.0628256 0.998025i \(-0.520011\pi\)
−0.400381 + 0.916349i \(0.631122\pi\)
\(972\) −128.889 + 153.604i −0.132602 + 0.158029i
\(973\) −209.023 76.0781i −0.214823 0.0781892i
\(974\) 361.960 131.743i 0.371622 0.135259i
\(975\) −209.669 + 175.933i −0.215045 + 0.180444i
\(976\) 99.0350 + 171.534i 0.101470 + 0.175752i
\(977\) −13.1868 7.61342i −0.0134973 0.00779265i 0.493236 0.869895i \(-0.335814\pi\)
−0.506733 + 0.862103i \(0.669147\pi\)
\(978\) 5.22778 + 29.6482i 0.00534537 + 0.0303151i
\(979\) 1057.63 186.488i 1.08031 0.190489i
\(980\) 189.258 327.804i 0.193120 0.334494i
\(981\) −361.526 + 208.727i −0.368528 + 0.212770i
\(982\) 539.477 + 642.923i 0.549365 + 0.654708i
\(983\) −313.799 862.154i −0.319225 0.877064i −0.990703 0.136040i \(-0.956562\pi\)
0.671478 0.741024i \(-0.265660\pi\)
\(984\) 10.1085 27.7730i 0.0102729 0.0282246i
\(985\) −949.489 796.716i −0.963948 0.808849i
\(986\) 51.2653 290.740i 0.0519932 0.294868i
\(987\) 169.804i 0.172041i
\(988\) −17.9830 + 518.806i −0.0182014 + 0.525108i
\(989\) 227.450 0.229979
\(990\) 1006.48 + 177.470i 1.01665 + 0.179263i
\(991\) −618.738 + 737.383i −0.624357 + 0.744079i −0.981813 0.189850i \(-0.939200\pi\)
0.357456 + 0.933930i \(0.383644\pi\)
\(992\) 270.902 + 98.6002i 0.273087 + 0.0993954i
\(993\) −138.617 + 50.4525i −0.139594 + 0.0508082i
\(994\) −638.669 + 535.907i −0.642524 + 0.539142i
\(995\) −203.525 352.515i −0.204547 0.354286i
\(996\) 38.9814 + 22.5059i 0.0391380 + 0.0225963i
\(997\) −102.940 583.803i −0.103250 0.585559i −0.991905 0.126983i \(-0.959471\pi\)
0.888655 0.458576i \(-0.151640\pi\)
\(998\) −325.358 + 57.3694i −0.326010 + 0.0574844i
\(999\) −67.3406 + 116.637i −0.0674080 + 0.116754i
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 38.3.f.a.21.2 24
3.2 odd 2 342.3.z.b.325.3 24
4.3 odd 2 304.3.z.c.97.2 24
19.3 odd 18 722.3.b.f.721.20 24
19.10 odd 18 inner 38.3.f.a.29.2 yes 24
19.16 even 9 722.3.b.f.721.5 24
57.29 even 18 342.3.z.b.181.3 24
76.67 even 18 304.3.z.c.257.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.3.f.a.21.2 24 1.1 even 1 trivial
38.3.f.a.29.2 yes 24 19.10 odd 18 inner
304.3.z.c.97.2 24 4.3 odd 2
304.3.z.c.257.2 24 76.67 even 18
342.3.z.b.181.3 24 57.29 even 18
342.3.z.b.325.3 24 3.2 odd 2
722.3.b.f.721.5 24 19.16 even 9
722.3.b.f.721.20 24 19.3 odd 18