Properties

Label 350.2.m.a.29.2
Level $350$
Weight $2$
Character 350.29
Analytic conductor $2.795$
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] = [350,2,Mod(29,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.m (of order \(10\), 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: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 29.2
Character \(\chi\) \(=\) 350.29
Dual form 350.2.m.a.169.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.310301 - 0.427092i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.73700 + 1.40813i) q^{5} +(-0.427092 + 0.310301i) q^{6} +1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.840930 + 2.58812i) q^{9} +O(q^{10})\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.310301 - 0.427092i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.73700 + 1.40813i) q^{5} +(-0.427092 + 0.310301i) q^{6} +1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.840930 + 2.58812i) q^{9} +(-1.21685 - 1.87597i) q^{10} +(-0.793851 + 2.44322i) q^{11} +(0.502077 - 0.163135i) q^{12} +(-3.01682 + 0.980226i) q^{13} +(0.309017 - 0.951057i) q^{14} +(1.14039 - 0.304915i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.00697007 + 0.00959347i) q^{17} -2.72131i q^{18} +(0.938159 - 0.681613i) q^{19} +(0.577583 + 2.16018i) q^{20} +(0.427092 + 0.310301i) q^{21} +(1.50999 - 2.07833i) q^{22} +(-2.24222 - 0.728540i) q^{23} -0.527915 q^{24} +(1.03433 + 4.89185i) q^{25} +3.17208 q^{26} +(2.87254 + 0.933344i) q^{27} +(-0.587785 + 0.809017i) q^{28} +(1.76399 + 1.28162i) q^{29} +(-1.17880 - 0.0624101i) q^{30} +(2.70035 - 1.96192i) q^{31} -1.00000i q^{32} +(0.797149 + 1.09718i) q^{33} +(-0.00366438 - 0.0112778i) q^{34} +(-1.40813 + 1.73700i) q^{35} +(-0.840930 + 2.58812i) q^{36} +(10.1998 - 3.31412i) q^{37} +(-1.10287 + 0.358345i) q^{38} +(-0.517476 + 1.59263i) q^{39} +(0.118220 - 2.23294i) q^{40} +(2.05670 + 6.32986i) q^{41} +(-0.310301 - 0.427092i) q^{42} -10.8385i q^{43} +(-2.07833 + 1.50999i) q^{44} +(-2.18371 + 5.67969i) q^{45} +(1.90734 + 1.38577i) q^{46} +(5.05571 - 6.95858i) q^{47} +(0.502077 + 0.163135i) q^{48} -1.00000 q^{49} +(0.527956 - 4.97205i) q^{50} +0.00626011 q^{51} +(-3.01682 - 0.980226i) q^{52} +(-6.39017 + 8.79532i) q^{53} +(-2.44353 - 1.77533i) q^{54} +(-4.81930 + 3.12603i) q^{55} +(0.809017 - 0.587785i) q^{56} -0.612185i q^{57} +(-1.28162 - 1.76399i) q^{58} +(2.71379 + 8.35218i) q^{59} +(1.10182 + 0.423626i) q^{60} +(3.61919 - 11.1387i) q^{61} +(-3.17445 + 1.03144i) q^{62} +(-2.58812 + 0.840930i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-6.62051 - 2.54543i) q^{65} +(-0.419086 - 1.28981i) q^{66} +(-4.33622 - 5.96830i) q^{67} +0.0118582i q^{68} +(-1.00692 + 0.731567i) q^{69} +(1.87597 - 1.21685i) q^{70} +(2.26208 + 1.64350i) q^{71} +(1.59954 - 2.20158i) q^{72} +(-6.83196 - 2.21984i) q^{73} -10.7247 q^{74} +(2.41022 + 1.07619i) q^{75} +1.15963 q^{76} +(-2.44322 - 0.793851i) q^{77} +(0.984298 - 1.35477i) q^{78} +(-9.57198 - 6.95445i) q^{79} +(-0.802450 + 2.08712i) q^{80} +(-5.31477 + 3.86141i) q^{81} -6.65561i q^{82} +(-6.48822 - 8.93027i) q^{83} +(0.163135 + 0.502077i) q^{84} +(-0.00140187 + 0.0264786i) q^{85} +(-3.34927 + 10.3080i) q^{86} +(1.09474 - 0.355702i) q^{87} +(2.44322 - 0.793851i) q^{88} +(2.71414 - 8.35325i) q^{89} +(3.83196 - 4.72691i) q^{90} +(-0.980226 - 3.01682i) q^{91} +(-1.38577 - 1.90734i) q^{92} -1.76208i q^{93} +(-6.95858 + 5.05571i) q^{94} +(2.58938 + 0.137091i) q^{95} +(-0.427092 - 0.310301i) q^{96} +(3.17565 - 4.37091i) q^{97} +(0.951057 + 0.309017i) q^{98} -6.99091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 0.309017i −0.672499 0.218508i
\(3\) 0.310301 0.427092i 0.179152 0.246582i −0.709991 0.704211i \(-0.751301\pi\)
0.889143 + 0.457629i \(0.151301\pi\)
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 1.73700 + 1.40813i 0.776810 + 0.629736i
\(6\) −0.427092 + 0.310301i −0.174360 + 0.126680i
\(7\) 1.00000i 0.377964i
\(8\) −0.587785 0.809017i −0.207813 0.286031i
\(9\) 0.840930 + 2.58812i 0.280310 + 0.862705i
\(10\) −1.21685 1.87597i −0.384801 0.593235i
\(11\) −0.793851 + 2.44322i −0.239355 + 0.736659i 0.757159 + 0.653231i \(0.226587\pi\)
−0.996514 + 0.0834282i \(0.973413\pi\)
\(12\) 0.502077 0.163135i 0.144937 0.0470929i
\(13\) −3.01682 + 0.980226i −0.836717 + 0.271866i −0.695872 0.718166i \(-0.744982\pi\)
−0.140845 + 0.990032i \(0.544982\pi\)
\(14\) 0.309017 0.951057i 0.0825883 0.254181i
\(15\) 1.14039 0.304915i 0.294448 0.0787286i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 0.00697007 + 0.00959347i 0.00169049 + 0.00232676i 0.809861 0.586621i \(-0.199542\pi\)
−0.808171 + 0.588948i \(0.799542\pi\)
\(18\) 2.72131i 0.641418i
\(19\) 0.938159 0.681613i 0.215229 0.156373i −0.474948 0.880014i \(-0.657533\pi\)
0.690176 + 0.723641i \(0.257533\pi\)
\(20\) 0.577583 + 2.16018i 0.129151 + 0.483032i
\(21\) 0.427092 + 0.310301i 0.0931992 + 0.0677132i
\(22\) 1.50999 2.07833i 0.321932 0.443101i
\(23\) −2.24222 0.728540i −0.467534 0.151911i 0.0657695 0.997835i \(-0.479050\pi\)
−0.533304 + 0.845924i \(0.679050\pi\)
\(24\) −0.527915 −0.107760
\(25\) 1.03433 + 4.89185i 0.206866 + 0.978369i
\(26\) 3.17208 0.622095
\(27\) 2.87254 + 0.933344i 0.552820 + 0.179622i
\(28\) −0.587785 + 0.809017i −0.111081 + 0.152890i
\(29\) 1.76399 + 1.28162i 0.327566 + 0.237990i 0.739397 0.673270i \(-0.235111\pi\)
−0.411831 + 0.911260i \(0.635111\pi\)
\(30\) −1.17880 0.0624101i −0.215219 0.0113945i
\(31\) 2.70035 1.96192i 0.484997 0.352371i −0.318260 0.948003i \(-0.603098\pi\)
0.803257 + 0.595632i \(0.203098\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.797149 + 1.09718i 0.138766 + 0.190995i
\(34\) −0.00366438 0.0112778i −0.000628436 0.00193413i
\(35\) −1.40813 + 1.73700i −0.238018 + 0.293606i
\(36\) −0.840930 + 2.58812i −0.140155 + 0.431353i
\(37\) 10.1998 3.31412i 1.67684 0.544837i 0.692543 0.721376i \(-0.256490\pi\)
0.984294 + 0.176539i \(0.0564901\pi\)
\(38\) −1.10287 + 0.358345i −0.178910 + 0.0581312i
\(39\) −0.517476 + 1.59263i −0.0828625 + 0.255024i
\(40\) 0.118220 2.23294i 0.0186922 0.353059i
\(41\) 2.05670 + 6.32986i 0.321202 + 0.988558i 0.973126 + 0.230274i \(0.0739621\pi\)
−0.651924 + 0.758284i \(0.726038\pi\)
\(42\) −0.310301 0.427092i −0.0478804 0.0659018i
\(43\) 10.8385i 1.65285i −0.563045 0.826426i \(-0.690370\pi\)
0.563045 0.826426i \(-0.309630\pi\)
\(44\) −2.07833 + 1.50999i −0.313320 + 0.227640i
\(45\) −2.18371 + 5.67969i −0.325529 + 0.846679i
\(46\) 1.90734 + 1.38577i 0.281222 + 0.204320i
\(47\) 5.05571 6.95858i 0.737451 1.01501i −0.261311 0.965255i \(-0.584155\pi\)
0.998761 0.0497589i \(-0.0158453\pi\)
\(48\) 0.502077 + 0.163135i 0.0724686 + 0.0235465i
\(49\) −1.00000 −0.142857
\(50\) 0.527956 4.97205i 0.0746643 0.703154i
\(51\) 0.00626011 0.000876591
\(52\) −3.01682 0.980226i −0.418358 0.135933i
\(53\) −6.39017 + 8.79532i −0.877758 + 1.20813i 0.0992790 + 0.995060i \(0.468346\pi\)
−0.977037 + 0.213070i \(0.931654\pi\)
\(54\) −2.44353 1.77533i −0.332522 0.241591i
\(55\) −4.81930 + 3.12603i −0.649834 + 0.421513i
\(56\) 0.809017 0.587785i 0.108109 0.0785461i
\(57\) 0.612185i 0.0810859i
\(58\) −1.28162 1.76399i −0.168285 0.231624i
\(59\) 2.71379 + 8.35218i 0.353305 + 1.08736i 0.956986 + 0.290135i \(0.0937003\pi\)
−0.603680 + 0.797226i \(0.706300\pi\)
\(60\) 1.10182 + 0.423626i 0.142245 + 0.0546898i
\(61\) 3.61919 11.1387i 0.463390 1.42617i −0.397607 0.917556i \(-0.630159\pi\)
0.860997 0.508611i \(-0.169841\pi\)
\(62\) −3.17445 + 1.03144i −0.403156 + 0.130993i
\(63\) −2.58812 + 0.840930i −0.326072 + 0.105947i
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) −6.62051 2.54543i −0.821173 0.315722i
\(66\) −0.419086 1.28981i −0.0515859 0.158765i
\(67\) −4.33622 5.96830i −0.529754 0.729144i 0.457339 0.889292i \(-0.348803\pi\)
−0.987093 + 0.160149i \(0.948803\pi\)
\(68\) 0.0118582i 0.00143802i
\(69\) −1.00692 + 0.731567i −0.121218 + 0.0880703i
\(70\) 1.87597 1.21685i 0.224222 0.145441i
\(71\) 2.26208 + 1.64350i 0.268459 + 0.195047i 0.713868 0.700280i \(-0.246942\pi\)
−0.445409 + 0.895327i \(0.646942\pi\)
\(72\) 1.59954 2.20158i 0.188508 0.259459i
\(73\) −6.83196 2.21984i −0.799621 0.259812i −0.119425 0.992843i \(-0.538105\pi\)
−0.680196 + 0.733031i \(0.738105\pi\)
\(74\) −10.7247 −1.24672
\(75\) 2.41022 + 1.07619i 0.278309 + 0.124268i
\(76\) 1.15963 0.133019
\(77\) −2.44322 0.793851i −0.278431 0.0904677i
\(78\) 0.984298 1.35477i 0.111450 0.153397i
\(79\) −9.57198 6.95445i −1.07693 0.782437i −0.0997867 0.995009i \(-0.531816\pi\)
−0.977145 + 0.212572i \(0.931816\pi\)
\(80\) −0.802450 + 2.08712i −0.0897167 + 0.233347i
\(81\) −5.31477 + 3.86141i −0.590530 + 0.429045i
\(82\) 6.65561i 0.734989i
\(83\) −6.48822 8.93027i −0.712175 0.980224i −0.999748 0.0224656i \(-0.992848\pi\)
0.287573 0.957759i \(-0.407152\pi\)
\(84\) 0.163135 + 0.502077i 0.0177995 + 0.0547811i
\(85\) −0.00140187 + 0.0264786i −0.000152055 + 0.00287201i
\(86\) −3.34927 + 10.3080i −0.361162 + 1.11154i
\(87\) 1.09474 0.355702i 0.117368 0.0381352i
\(88\) 2.44322 0.793851i 0.260448 0.0846248i
\(89\) 2.71414 8.35325i 0.287698 0.885443i −0.697879 0.716215i \(-0.745873\pi\)
0.985577 0.169227i \(-0.0541272\pi\)
\(90\) 3.83196 4.72691i 0.403924 0.498260i
\(91\) −0.980226 3.01682i −0.102756 0.316249i
\(92\) −1.38577 1.90734i −0.144476 0.198854i
\(93\) 1.76208i 0.182720i
\(94\) −6.95858 + 5.05571i −0.717723 + 0.521456i
\(95\) 2.58938 + 0.137091i 0.265665 + 0.0140653i
\(96\) −0.427092 0.310301i −0.0435899 0.0316699i
\(97\) 3.17565 4.37091i 0.322438 0.443798i −0.616771 0.787142i \(-0.711560\pi\)
0.939210 + 0.343344i \(0.111560\pi\)
\(98\) 0.951057 + 0.309017i 0.0960712 + 0.0312154i
\(99\) −6.99091 −0.702613
\(100\) −2.03856 + 4.56555i −0.203856 + 0.456555i
\(101\) 5.01343 0.498855 0.249427 0.968394i \(-0.419758\pi\)
0.249427 + 0.968394i \(0.419758\pi\)
\(102\) −0.00595372 0.00193448i −0.000589506 0.000191542i
\(103\) 1.55705 2.14309i 0.153420 0.211165i −0.725388 0.688341i \(-0.758339\pi\)
0.878808 + 0.477176i \(0.158339\pi\)
\(104\) 2.56626 + 1.86450i 0.251643 + 0.182829i
\(105\) 0.304915 + 1.14039i 0.0297566 + 0.111291i
\(106\) 8.79532 6.39017i 0.854277 0.620669i
\(107\) 4.72706i 0.456982i 0.973546 + 0.228491i \(0.0733792\pi\)
−0.973546 + 0.228491i \(0.926621\pi\)
\(108\) 1.77533 + 2.44353i 0.170831 + 0.235128i
\(109\) 1.11184 + 3.42189i 0.106495 + 0.327758i 0.990078 0.140516i \(-0.0448761\pi\)
−0.883583 + 0.468274i \(0.844876\pi\)
\(110\) 5.54942 1.48378i 0.529116 0.141473i
\(111\) 1.74957 5.38463i 0.166062 0.511086i
\(112\) −0.951057 + 0.309017i −0.0898664 + 0.0291994i
\(113\) −10.9324 + 3.55215i −1.02843 + 0.334158i −0.774170 0.632978i \(-0.781833\pi\)
−0.254262 + 0.967135i \(0.581833\pi\)
\(114\) −0.189176 + 0.582223i −0.0177179 + 0.0545302i
\(115\) −2.86885 4.42281i −0.267521 0.412429i
\(116\) 0.673786 + 2.07370i 0.0625595 + 0.192538i
\(117\) −5.07387 6.98359i −0.469080 0.645633i
\(118\) 8.78201i 0.808449i
\(119\) −0.00959347 + 0.00697007i −0.000879432 + 0.000638945i
\(120\) −0.916988 0.743374i −0.0837092 0.0678604i
\(121\) 3.56005 + 2.58653i 0.323641 + 0.235139i
\(122\) −6.88411 + 9.47516i −0.623258 + 0.857841i
\(123\) 3.34163 + 1.08576i 0.301304 + 0.0978998i
\(124\) 3.33782 0.299745
\(125\) −5.09173 + 9.95361i −0.455418 + 0.890278i
\(126\) 2.72131 0.242433
\(127\) 20.0693 + 6.52090i 1.78086 + 0.578636i 0.998995 0.0448128i \(-0.0142691\pi\)
0.781864 + 0.623449i \(0.214269\pi\)
\(128\) 0.587785 0.809017i 0.0519534 0.0715077i
\(129\) −4.62903 3.36319i −0.407563 0.296112i
\(130\) 5.50989 + 4.46670i 0.483250 + 0.391756i
\(131\) 6.01064 4.36699i 0.525152 0.381545i −0.293389 0.955993i \(-0.594783\pi\)
0.818541 + 0.574448i \(0.194783\pi\)
\(132\) 1.35619i 0.118041i
\(133\) 0.681613 + 0.938159i 0.0591033 + 0.0813487i
\(134\) 2.27969 + 7.01615i 0.196935 + 0.606103i
\(135\) 3.67532 + 5.66613i 0.316321 + 0.487662i
\(136\) 0.00366438 0.0112778i 0.000314218 0.000967064i
\(137\) −4.03872 + 1.31226i −0.345051 + 0.112114i −0.476415 0.879220i \(-0.658064\pi\)
0.131365 + 0.991334i \(0.458064\pi\)
\(138\) 1.18370 0.384607i 0.100763 0.0327400i
\(139\) 3.17407 9.76880i 0.269221 0.828579i −0.721469 0.692447i \(-0.756533\pi\)
0.990691 0.136132i \(-0.0434671\pi\)
\(140\) −2.16018 + 0.577583i −0.182569 + 0.0488147i
\(141\) −1.40317 4.31851i −0.118168 0.363684i
\(142\) −1.64350 2.26208i −0.137919 0.189829i
\(143\) 8.14892i 0.681447i
\(144\) −2.20158 + 1.59954i −0.183465 + 0.133295i
\(145\) 1.25937 + 4.71010i 0.104585 + 0.391153i
\(146\) 5.81161 + 4.22238i 0.480973 + 0.349447i
\(147\) −0.310301 + 0.427092i −0.0255932 + 0.0352260i
\(148\) 10.1998 + 3.31412i 0.838419 + 0.272419i
\(149\) −5.05554 −0.414166 −0.207083 0.978323i \(-0.566397\pi\)
−0.207083 + 0.978323i \(0.566397\pi\)
\(150\) −1.95970 1.76832i −0.160009 0.144382i
\(151\) −20.0482 −1.63150 −0.815748 0.578408i \(-0.803674\pi\)
−0.815748 + 0.578408i \(0.803674\pi\)
\(152\) −1.10287 0.358345i −0.0894548 0.0290656i
\(153\) −0.0189677 + 0.0261068i −0.00153345 + 0.00211061i
\(154\) 2.07833 + 1.50999i 0.167476 + 0.121679i
\(155\) 7.45315 + 0.394597i 0.598651 + 0.0316948i
\(156\) −1.35477 + 0.984298i −0.108468 + 0.0788069i
\(157\) 6.27754i 0.501002i 0.968116 + 0.250501i \(0.0805954\pi\)
−0.968116 + 0.250501i \(0.919405\pi\)
\(158\) 6.95445 + 9.57198i 0.553267 + 0.761506i
\(159\) 1.77354 + 5.45839i 0.140651 + 0.432878i
\(160\) 1.40813 1.73700i 0.111323 0.137322i
\(161\) 0.728540 2.24222i 0.0574170 0.176711i
\(162\) 6.24789 2.03006i 0.490881 0.159497i
\(163\) −0.181385 + 0.0589357i −0.0142072 + 0.00461620i −0.316112 0.948722i \(-0.602378\pi\)
0.301905 + 0.953338i \(0.402378\pi\)
\(164\) −2.05670 + 6.32986i −0.160601 + 0.494279i
\(165\) −0.160329 + 3.02829i −0.0124816 + 0.235752i
\(166\) 3.41106 + 10.4982i 0.264750 + 0.814815i
\(167\) 1.88481 + 2.59422i 0.145851 + 0.200747i 0.875692 0.482871i \(-0.160406\pi\)
−0.729841 + 0.683617i \(0.760406\pi\)
\(168\) 0.527915i 0.0407295i
\(169\) −2.37683 + 1.72687i −0.182833 + 0.132836i
\(170\) 0.00951561 0.0247495i 0.000729814 0.00189820i
\(171\) 2.55302 + 1.85488i 0.195234 + 0.141846i
\(172\) 6.37070 8.76851i 0.485761 0.668593i
\(173\) 16.7682 + 5.44832i 1.27486 + 0.414228i 0.866768 0.498712i \(-0.166193\pi\)
0.408095 + 0.912940i \(0.366193\pi\)
\(174\) −1.15108 −0.0872628
\(175\) −4.89185 + 1.03433i −0.369789 + 0.0781881i
\(176\) −2.56896 −0.193642
\(177\) 4.40924 + 1.43265i 0.331419 + 0.107685i
\(178\) −5.16259 + 7.10570i −0.386953 + 0.532595i
\(179\) −10.8320 7.86994i −0.809625 0.588227i 0.104097 0.994567i \(-0.466805\pi\)
−0.913722 + 0.406340i \(0.866805\pi\)
\(180\) −5.10510 + 3.31141i −0.380512 + 0.246818i
\(181\) 12.8063 9.30431i 0.951883 0.691584i 0.000631630 1.00000i \(-0.499799\pi\)
0.951252 + 0.308416i \(0.0997989\pi\)
\(182\) 3.17208i 0.235130i
\(183\) −3.63422 5.00208i −0.268650 0.369764i
\(184\) 0.728540 + 2.24222i 0.0537087 + 0.165298i
\(185\) 22.3838 + 8.60605i 1.64569 + 0.632729i
\(186\) −0.544514 + 1.67584i −0.0399257 + 0.122879i
\(187\) −0.0289722 + 0.00941363i −0.00211866 + 0.000688393i
\(188\) 8.18031 2.65794i 0.596610 0.193850i
\(189\) −0.933344 + 2.87254i −0.0678908 + 0.208946i
\(190\) −2.42029 0.930545i −0.175586 0.0675088i
\(191\) 0.840195 + 2.58585i 0.0607944 + 0.187106i 0.976841 0.213965i \(-0.0686380\pi\)
−0.916047 + 0.401071i \(0.868638\pi\)
\(192\) 0.310301 + 0.427092i 0.0223940 + 0.0308227i
\(193\) 4.00500i 0.288286i 0.989557 + 0.144143i \(0.0460426\pi\)
−0.989557 + 0.144143i \(0.953957\pi\)
\(194\) −4.37091 + 3.17565i −0.313813 + 0.227998i
\(195\) −3.14148 + 2.03772i −0.224966 + 0.145924i
\(196\) −0.809017 0.587785i −0.0577869 0.0419847i
\(197\) −8.00830 + 11.0225i −0.570568 + 0.785319i −0.992622 0.121252i \(-0.961309\pi\)
0.422054 + 0.906571i \(0.361309\pi\)
\(198\) 6.64875 + 2.16031i 0.472506 + 0.153527i
\(199\) 24.0565 1.70532 0.852659 0.522468i \(-0.174989\pi\)
0.852659 + 0.522468i \(0.174989\pi\)
\(200\) 3.34962 3.71215i 0.236854 0.262488i
\(201\) −3.89455 −0.274700
\(202\) −4.76805 1.54923i −0.335479 0.109004i
\(203\) −1.28162 + 1.76399i −0.0899519 + 0.123808i
\(204\) 0.00506454 + 0.00367960i 0.000354589 + 0.000257624i
\(205\) −5.34080 + 13.8911i −0.373017 + 0.970194i
\(206\) −2.14309 + 1.55705i −0.149316 + 0.108485i
\(207\) 6.41577i 0.445927i
\(208\) −1.86450 2.56626i −0.129280 0.177938i
\(209\) 0.920572 + 2.83323i 0.0636773 + 0.195979i
\(210\) 0.0624101 1.17880i 0.00430671 0.0813451i
\(211\) 1.52748 4.70111i 0.105156 0.323637i −0.884611 0.466330i \(-0.845576\pi\)
0.989767 + 0.142692i \(0.0455760\pi\)
\(212\) −10.3395 + 3.35951i −0.710121 + 0.230732i
\(213\) 1.40385 0.456138i 0.0961902 0.0312541i
\(214\) 1.46074 4.49570i 0.0998543 0.307320i
\(215\) 15.2620 18.8264i 1.04086 1.28395i
\(216\) −0.933344 2.87254i −0.0635060 0.195451i
\(217\) 1.96192 + 2.70035i 0.133184 + 0.183312i
\(218\) 3.59799i 0.243687i
\(219\) −3.06804 + 2.22906i −0.207319 + 0.150626i
\(220\) −5.73633 0.303702i −0.386743 0.0204756i
\(221\) −0.0304312 0.0221096i −0.00204703 0.00148725i
\(222\) −3.32788 + 4.58044i −0.223353 + 0.307419i
\(223\) 12.3425 + 4.01031i 0.826513 + 0.268550i 0.691576 0.722304i \(-0.256917\pi\)
0.134937 + 0.990854i \(0.456917\pi\)
\(224\) 1.00000 0.0668153
\(225\) −11.7909 + 6.79067i −0.786058 + 0.452711i
\(226\) 11.4950 0.764635
\(227\) −5.60413 1.82089i −0.371959 0.120857i 0.117071 0.993123i \(-0.462649\pi\)
−0.489031 + 0.872267i \(0.662649\pi\)
\(228\) 0.359834 0.495268i 0.0238306 0.0328000i
\(229\) −7.40014 5.37652i −0.489015 0.355290i 0.315790 0.948829i \(-0.397730\pi\)
−0.804805 + 0.593539i \(0.797730\pi\)
\(230\) 1.36171 + 5.09286i 0.0897887 + 0.335814i
\(231\) −1.09718 + 0.797149i −0.0721892 + 0.0524485i
\(232\) 2.18042i 0.143151i
\(233\) 6.55585 + 9.02336i 0.429488 + 0.591140i 0.967836 0.251583i \(-0.0809512\pi\)
−0.538347 + 0.842723i \(0.680951\pi\)
\(234\) 2.66749 + 8.20970i 0.174380 + 0.536685i
\(235\) 18.5804 4.96795i 1.21205 0.324073i
\(236\) −2.71379 + 8.35218i −0.176653 + 0.543681i
\(237\) −5.94039 + 1.93015i −0.385870 + 0.125377i
\(238\) 0.0112778 0.00366438i 0.000731031 0.000237527i
\(239\) 5.77221 17.7650i 0.373373 1.14912i −0.571197 0.820813i \(-0.693521\pi\)
0.944570 0.328311i \(-0.106479\pi\)
\(240\) 0.642392 + 0.990355i 0.0414662 + 0.0639272i
\(241\) −5.07425 15.6169i −0.326861 1.00597i −0.970594 0.240724i \(-0.922615\pi\)
0.643733 0.765250i \(-0.277385\pi\)
\(242\) −2.58653 3.56005i −0.166268 0.228849i
\(243\) 12.5292i 0.803748i
\(244\) 9.47516 6.88411i 0.606585 0.440710i
\(245\) −1.73700 1.40813i −0.110973 0.0899622i
\(246\) −2.84256 2.06524i −0.181235 0.131675i
\(247\) −2.16213 + 2.97591i −0.137573 + 0.189353i
\(248\) −3.17445 1.03144i −0.201578 0.0654966i
\(249\) −5.82735 −0.369293
\(250\) 7.91836 7.89301i 0.500801 0.499198i
\(251\) −6.82263 −0.430640 −0.215320 0.976543i \(-0.569080\pi\)
−0.215320 + 0.976543i \(0.569080\pi\)
\(252\) −2.58812 0.840930i −0.163036 0.0529736i
\(253\) 3.55997 4.89988i 0.223813 0.308053i
\(254\) −17.0719 12.4035i −1.07119 0.778264i
\(255\) 0.0108738 + 0.00881507i 0.000680945 + 0.000552021i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 3.25905i 0.203294i 0.994821 + 0.101647i \(0.0324112\pi\)
−0.994821 + 0.101647i \(0.967589\pi\)
\(258\) 3.36319 + 4.62903i 0.209383 + 0.288191i
\(259\) 3.31412 + 10.1998i 0.205929 + 0.633785i
\(260\) −3.85993 5.95074i −0.239383 0.369049i
\(261\) −1.83358 + 5.64317i −0.113496 + 0.349304i
\(262\) −7.06593 + 2.29586i −0.436535 + 0.141839i
\(263\) −19.8171 + 6.43898i −1.22198 + 0.397045i −0.847802 0.530313i \(-0.822074\pi\)
−0.374176 + 0.927358i \(0.622074\pi\)
\(264\) 0.419086 1.28981i 0.0257930 0.0793825i
\(265\) −23.4847 + 6.27926i −1.44265 + 0.385732i
\(266\) −0.358345 1.10287i −0.0219715 0.0676215i
\(267\) −2.72541 3.75121i −0.166792 0.229570i
\(268\) 7.37722i 0.450636i
\(269\) 24.9456 18.1240i 1.52096 1.10504i 0.559947 0.828529i \(-0.310822\pi\)
0.961011 0.276512i \(-0.0891784\pi\)
\(270\) −1.74451 6.52454i −0.106167 0.397071i
\(271\) −16.7335 12.1576i −1.01648 0.738519i −0.0509254 0.998702i \(-0.516217\pi\)
−0.965559 + 0.260183i \(0.916217\pi\)
\(272\) −0.00697007 + 0.00959347i −0.000422622 + 0.000581690i
\(273\) −1.59263 0.517476i −0.0963902 0.0313191i
\(274\) 4.24656 0.256544
\(275\) −12.7730 1.35630i −0.770239 0.0817877i
\(276\) −1.24462 −0.0749171
\(277\) −1.89277 0.614998i −0.113725 0.0369516i 0.251601 0.967831i \(-0.419043\pi\)
−0.365327 + 0.930879i \(0.619043\pi\)
\(278\) −6.03745 + 8.30984i −0.362102 + 0.498391i
\(279\) 7.34848 + 5.33898i 0.439942 + 0.319636i
\(280\) 2.23294 + 0.118220i 0.133444 + 0.00706499i
\(281\) −8.91578 + 6.47769i −0.531871 + 0.386427i −0.821057 0.570846i \(-0.806615\pi\)
0.289186 + 0.957273i \(0.406615\pi\)
\(282\) 4.54075i 0.270398i
\(283\) −15.7850 21.7262i −0.938320 1.29149i −0.956524 0.291653i \(-0.905795\pi\)
0.0182041 0.999834i \(-0.494205\pi\)
\(284\) 0.864037 + 2.65923i 0.0512712 + 0.157796i
\(285\) 0.862038 1.06337i 0.0510627 0.0629883i
\(286\) −2.51816 + 7.75009i −0.148902 + 0.458272i
\(287\) −6.32986 + 2.05670i −0.373640 + 0.121403i
\(288\) 2.58812 0.840930i 0.152506 0.0495523i
\(289\) 5.25325 16.1678i 0.309014 0.951049i
\(290\) 0.257769 4.86874i 0.0151367 0.285902i
\(291\) −0.881374 2.71259i −0.0516671 0.159015i
\(292\) −4.22238 5.81161i −0.247096 0.340099i
\(293\) 31.0610i 1.81460i −0.420482 0.907301i \(-0.638139\pi\)
0.420482 0.907301i \(-0.361861\pi\)
\(294\) 0.427092 0.310301i 0.0249085 0.0180971i
\(295\) −7.04712 + 18.3291i −0.410299 + 1.06716i
\(296\) −8.67647 6.30382i −0.504310 0.366402i
\(297\) −4.56073 + 6.27731i −0.264640 + 0.364246i
\(298\) 4.80810 + 1.56225i 0.278526 + 0.0904985i
\(299\) 7.47851 0.432493
\(300\) 1.31734 + 2.28735i 0.0760569 + 0.132060i
\(301\) 10.8385 0.624720
\(302\) 19.0669 + 6.19522i 1.09718 + 0.356495i
\(303\) 1.55567 2.14120i 0.0893709 0.123009i
\(304\) 0.938159 + 0.681613i 0.0538071 + 0.0390932i
\(305\) 21.9713 14.2516i 1.25807 0.816047i
\(306\) 0.0261068 0.0189677i 0.00149242 0.00108431i
\(307\) 29.8864i 1.70570i 0.522153 + 0.852852i \(0.325129\pi\)
−0.522153 + 0.852852i \(0.674871\pi\)
\(308\) −1.50999 2.07833i −0.0860399 0.118424i
\(309\) −0.432145 1.33000i −0.0245839 0.0756613i
\(310\) −6.96643 2.67843i −0.395666 0.152125i
\(311\) 2.88342 8.87426i 0.163504 0.503213i −0.835419 0.549614i \(-0.814775\pi\)
0.998923 + 0.0464003i \(0.0147750\pi\)
\(312\) 1.59263 0.517476i 0.0901648 0.0292963i
\(313\) −22.9223 + 7.44790i −1.29564 + 0.420980i −0.874064 0.485811i \(-0.838524\pi\)
−0.421580 + 0.906791i \(0.638524\pi\)
\(314\) 1.93987 5.97030i 0.109473 0.336923i
\(315\) −5.67969 2.18371i −0.320014 0.123038i
\(316\) −3.65617 11.2525i −0.205676 0.633005i
\(317\) 3.30582 + 4.55007i 0.185674 + 0.255558i 0.891699 0.452629i \(-0.149514\pi\)
−0.706026 + 0.708186i \(0.749514\pi\)
\(318\) 5.73929i 0.321843i
\(319\) −4.53162 + 3.29242i −0.253722 + 0.184340i
\(320\) −1.87597 + 1.21685i −0.104870 + 0.0680239i
\(321\) 2.01889 + 1.46681i 0.112683 + 0.0818693i
\(322\) −1.38577 + 1.90734i −0.0772257 + 0.106292i
\(323\) 0.0130781 + 0.00424932i 0.000727683 + 0.000236439i
\(324\) −6.56942 −0.364968
\(325\) −7.91551 13.7440i −0.439073 0.762378i
\(326\) 0.190720 0.0105630
\(327\) 1.80647 + 0.586957i 0.0998979 + 0.0324588i
\(328\) 3.91207 5.38450i 0.216008 0.297309i
\(329\) 6.95858 + 5.05571i 0.383639 + 0.278730i
\(330\) 1.08828 2.83053i 0.0599076 0.155816i
\(331\) −11.0911 + 8.05812i −0.609620 + 0.442915i −0.849280 0.527942i \(-0.822964\pi\)
0.239661 + 0.970857i \(0.422964\pi\)
\(332\) 11.0384i 0.605812i
\(333\) 17.1546 + 23.6113i 0.940068 + 1.29389i
\(334\) −0.990903 3.04969i −0.0542198 0.166871i
\(335\) 0.872135 16.4729i 0.0476498 0.900011i
\(336\) −0.163135 + 0.502077i −0.00889973 + 0.0273905i
\(337\) −26.1267 + 8.48908i −1.42321 + 0.462430i −0.916621 0.399757i \(-0.869095\pi\)
−0.506591 + 0.862187i \(0.669095\pi\)
\(338\) 2.79414 0.907870i 0.151981 0.0493816i
\(339\) −1.87523 + 5.77137i −0.101849 + 0.313458i
\(340\) −0.0166979 + 0.0205977i −0.000905570 + 0.00111706i
\(341\) 2.64973 + 8.15503i 0.143491 + 0.441619i
\(342\) −1.85488 2.55302i −0.100300 0.138051i
\(343\) 1.00000i 0.0539949i
\(344\) −8.76851 + 6.37070i −0.472767 + 0.343485i
\(345\) −2.77915 0.147138i −0.149625 0.00792167i
\(346\) −14.2639 10.3633i −0.766831 0.557135i
\(347\) 10.9969 15.1359i 0.590345 0.812540i −0.404437 0.914566i \(-0.632532\pi\)
0.994782 + 0.102026i \(0.0325325\pi\)
\(348\) 1.09474 + 0.355702i 0.0586841 + 0.0190676i
\(349\) 11.3924 0.609823 0.304911 0.952381i \(-0.401373\pi\)
0.304911 + 0.952381i \(0.401373\pi\)
\(350\) 4.97205 + 0.527956i 0.265767 + 0.0282205i
\(351\) −9.58083 −0.511387
\(352\) 2.44322 + 0.793851i 0.130224 + 0.0423124i
\(353\) −10.3784 + 14.2846i −0.552386 + 0.760295i −0.990334 0.138706i \(-0.955706\pi\)
0.437947 + 0.899001i \(0.355706\pi\)
\(354\) −3.75073 2.72506i −0.199349 0.144835i
\(355\) 1.61497 + 6.04006i 0.0857137 + 0.320573i
\(356\) 7.10570 5.16259i 0.376601 0.273617i
\(357\) 0.00626011i 0.000331320i
\(358\) 7.86994 + 10.8320i 0.415939 + 0.572491i
\(359\) −2.76992 8.52494i −0.146191 0.449929i 0.850971 0.525212i \(-0.176014\pi\)
−0.997162 + 0.0752830i \(0.976014\pi\)
\(360\) 5.87852 1.57178i 0.309825 0.0828400i
\(361\) −5.45578 + 16.7912i −0.287146 + 0.883745i
\(362\) −15.0547 + 4.89156i −0.791257 + 0.257095i
\(363\) 2.20937 0.717869i 0.115962 0.0376784i
\(364\) 0.980226 3.01682i 0.0513778 0.158125i
\(365\) −8.74129 13.4762i −0.457540 0.705374i
\(366\) 1.91062 + 5.88030i 0.0998699 + 0.307368i
\(367\) 9.76022 + 13.4338i 0.509479 + 0.701238i 0.983831 0.179097i \(-0.0573176\pi\)
−0.474352 + 0.880335i \(0.657318\pi\)
\(368\) 2.35761i 0.122899i
\(369\) −14.6529 + 10.6459i −0.762798 + 0.554205i
\(370\) −18.6288 15.1018i −0.968465 0.785105i
\(371\) −8.79532 6.39017i −0.456630 0.331761i
\(372\) 1.03573 1.42556i 0.0536999 0.0739116i
\(373\) 32.0924 + 10.4274i 1.66168 + 0.539913i 0.981223 0.192876i \(-0.0617815\pi\)
0.680457 + 0.732788i \(0.261781\pi\)
\(374\) 0.0304631 0.00157521
\(375\) 2.67114 + 5.26325i 0.137937 + 0.271793i
\(376\) −8.60128 −0.443577
\(377\) −6.57794 2.13730i −0.338781 0.110077i
\(378\) 1.77533 2.44353i 0.0913129 0.125681i
\(379\) 18.4613 + 13.4129i 0.948293 + 0.688975i 0.950403 0.311023i \(-0.100671\pi\)
−0.00210957 + 0.999998i \(0.500671\pi\)
\(380\) 2.01427 + 1.63291i 0.103330 + 0.0837665i
\(381\) 9.01253 6.54799i 0.461726 0.335464i
\(382\) 2.71893i 0.139112i
\(383\) 12.3353 + 16.9780i 0.630302 + 0.867537i 0.998052 0.0623882i \(-0.0198717\pi\)
−0.367750 + 0.929925i \(0.619872\pi\)
\(384\) −0.163135 0.502077i −0.00832493 0.0256215i
\(385\) −3.12603 4.81930i −0.159317 0.245614i
\(386\) 1.23761 3.80898i 0.0629928 0.193872i
\(387\) 28.0512 9.11440i 1.42592 0.463311i
\(388\) 5.13831 1.66954i 0.260858 0.0847580i
\(389\) 9.89540 30.4549i 0.501717 1.54413i −0.304504 0.952511i \(-0.598491\pi\)
0.806221 0.591615i \(-0.201509\pi\)
\(390\) 3.61742 0.967213i 0.183175 0.0489767i
\(391\) −0.00863917 0.0265886i −0.000436901 0.00134464i
\(392\) 0.587785 + 0.809017i 0.0296876 + 0.0408615i
\(393\) 3.92218i 0.197848i
\(394\) 11.0225 8.00830i 0.555304 0.403452i
\(395\) −6.83374 25.5585i −0.343843 1.28599i
\(396\) −5.65577 4.10916i −0.284213 0.206493i
\(397\) 7.14778 9.83807i 0.358737 0.493759i −0.591060 0.806628i \(-0.701290\pi\)
0.949796 + 0.312869i \(0.101290\pi\)
\(398\) −22.8791 7.43386i −1.14682 0.372626i
\(399\) 0.612185 0.0306476
\(400\) −4.33280 + 2.49537i −0.216640 + 0.124769i
\(401\) 9.88154 0.493461 0.246730 0.969084i \(-0.420644\pi\)
0.246730 + 0.969084i \(0.420644\pi\)
\(402\) 3.70393 + 1.20348i 0.184735 + 0.0600242i
\(403\) −6.22336 + 8.56572i −0.310008 + 0.426689i
\(404\) 4.05595 + 2.94682i 0.201791 + 0.146610i
\(405\) −14.6691 0.776637i −0.728915 0.0385914i
\(406\) 1.76399 1.28162i 0.0875456 0.0636056i
\(407\) 27.5513i 1.36567i
\(408\) −0.00367960 0.00506454i −0.000182167 0.000250732i
\(409\) 8.23964 + 25.3590i 0.407424 + 1.25392i 0.918854 + 0.394597i \(0.129116\pi\)
−0.511430 + 0.859325i \(0.670884\pi\)
\(410\) 9.37197 11.5608i 0.462849 0.570946i
\(411\) −0.692761 + 2.13210i −0.0341714 + 0.105169i
\(412\) 2.51935 0.818588i 0.124120 0.0403289i
\(413\) −8.35218 + 2.71379i −0.410984 + 0.133537i
\(414\) −1.98258 + 6.10176i −0.0974385 + 0.299885i
\(415\) 1.30496 24.6481i 0.0640580 1.20993i
\(416\) 0.980226 + 3.01682i 0.0480595 + 0.147912i
\(417\) −3.18726 4.38689i −0.156081 0.214827i
\(418\) 2.97903i 0.145709i
\(419\) −8.23681 + 5.98439i −0.402394 + 0.292357i −0.770516 0.637421i \(-0.780001\pi\)
0.368121 + 0.929778i \(0.380001\pi\)
\(420\) −0.423626 + 1.10182i −0.0206708 + 0.0537634i
\(421\) 10.4319 + 7.57920i 0.508419 + 0.369388i 0.812223 0.583347i \(-0.198257\pi\)
−0.303805 + 0.952734i \(0.598257\pi\)
\(422\) −2.90544 + 3.99900i −0.141435 + 0.194668i
\(423\) 22.2611 + 7.23307i 1.08237 + 0.351684i
\(424\) 10.8716 0.527972
\(425\) −0.0397204 + 0.0440193i −0.00192672 + 0.00213525i
\(426\) −1.47609 −0.0715170
\(427\) 11.1387 + 3.61919i 0.539040 + 0.175145i
\(428\) −2.77850 + 3.82427i −0.134304 + 0.184853i
\(429\) −3.48034 2.52862i −0.168033 0.122083i
\(430\) −20.3327 + 13.1888i −0.980531 + 0.636019i
\(431\) −25.8040 + 18.7477i −1.24293 + 0.903043i −0.997790 0.0664437i \(-0.978835\pi\)
−0.245142 + 0.969487i \(0.578835\pi\)
\(432\) 3.02036i 0.145317i
\(433\) 6.99719 + 9.63081i 0.336264 + 0.462827i 0.943345 0.331812i \(-0.107660\pi\)
−0.607082 + 0.794639i \(0.707660\pi\)
\(434\) −1.03144 3.17445i −0.0495108 0.152379i
\(435\) 2.40243 + 0.923681i 0.115188 + 0.0442871i
\(436\) −1.11184 + 3.42189i −0.0532475 + 0.163879i
\(437\) −2.60014 + 0.844836i −0.124382 + 0.0404140i
\(438\) 3.60670 1.17189i 0.172335 0.0559949i
\(439\) −7.22295 + 22.2300i −0.344733 + 1.06098i 0.616994 + 0.786968i \(0.288350\pi\)
−0.961727 + 0.274011i \(0.911650\pi\)
\(440\) 5.36172 + 2.06146i 0.255610 + 0.0982762i
\(441\) −0.840930 2.58812i −0.0400443 0.123244i
\(442\) 0.0221096 + 0.0304312i 0.00105165 + 0.00144747i
\(443\) 2.11986i 0.100718i −0.998731 0.0503589i \(-0.983963\pi\)
0.998731 0.0503589i \(-0.0160365\pi\)
\(444\) 4.58044 3.32788i 0.217378 0.157934i
\(445\) 16.4769 10.6877i 0.781081 0.506647i
\(446\) −10.4991 7.62806i −0.497148 0.361199i
\(447\) −1.56874 + 2.15918i −0.0741987 + 0.102126i
\(448\) −0.951057 0.309017i −0.0449332 0.0145997i
\(449\) 15.0557 0.710525 0.355262 0.934767i \(-0.384392\pi\)
0.355262 + 0.934767i \(0.384392\pi\)
\(450\) 13.3122 2.81473i 0.627544 0.132688i
\(451\) −17.0980 −0.805111
\(452\) −10.9324 3.55215i −0.514216 0.167079i
\(453\) −6.22096 + 8.56241i −0.292286 + 0.402297i
\(454\) 4.76716 + 3.46354i 0.223734 + 0.162552i
\(455\) 2.54543 6.62051i 0.119332 0.310374i
\(456\) −0.495268 + 0.359834i −0.0231931 + 0.0168508i
\(457\) 27.2587i 1.27511i −0.770405 0.637554i \(-0.779946\pi\)
0.770405 0.637554i \(-0.220054\pi\)
\(458\) 5.37652 + 7.40014i 0.251228 + 0.345786i
\(459\) 0.0110678 + 0.0340631i 0.000516599 + 0.00158993i
\(460\) 0.278716 5.26439i 0.0129952 0.245454i
\(461\) 12.9938 39.9908i 0.605182 1.86256i 0.109645 0.993971i \(-0.465029\pi\)
0.495537 0.868587i \(-0.334971\pi\)
\(462\) 1.28981 0.419086i 0.0600076 0.0194976i
\(463\) −25.7164 + 8.35577i −1.19514 + 0.388326i −0.837972 0.545713i \(-0.816259\pi\)
−0.357171 + 0.934039i \(0.616259\pi\)
\(464\) −0.673786 + 2.07370i −0.0312797 + 0.0962691i
\(465\) 2.48125 3.06074i 0.115065 0.141938i
\(466\) −3.44662 10.6076i −0.159661 0.491387i
\(467\) 7.52839 + 10.3619i 0.348372 + 0.479493i 0.946863 0.321636i \(-0.104233\pi\)
−0.598491 + 0.801129i \(0.704233\pi\)
\(468\) 8.63219i 0.399023i
\(469\) 5.96830 4.33622i 0.275590 0.200228i
\(470\) −19.2062 1.01684i −0.885914 0.0469035i
\(471\) 2.68109 + 1.94793i 0.123538 + 0.0897557i
\(472\) 5.16193 7.10479i 0.237597 0.327025i
\(473\) 26.4808 + 8.60414i 1.21759 + 0.395619i
\(474\) 6.24609 0.286892
\(475\) 4.30471 + 3.88432i 0.197514 + 0.178225i
\(476\) −0.0118582 −0.000543519
\(477\) −28.1370 9.14226i −1.28830 0.418595i
\(478\) −10.9794 + 15.1118i −0.502186 + 0.691199i
\(479\) −5.39304 3.91827i −0.246414 0.179030i 0.457722 0.889095i \(-0.348666\pi\)
−0.704136 + 0.710065i \(0.748666\pi\)
\(480\) −0.304915 1.14039i −0.0139174 0.0520516i
\(481\) −27.5224 + 19.9962i −1.25491 + 0.911749i
\(482\) 16.4206i 0.747938i
\(483\) −0.731567 1.00692i −0.0332874 0.0458162i
\(484\) 1.35982 + 4.18509i 0.0618100 + 0.190232i
\(485\) 11.6709 3.12053i 0.529949 0.141696i
\(486\) 3.87173 11.9160i 0.175625 0.540519i
\(487\) 5.04993 1.64082i 0.228834 0.0743527i −0.192356 0.981325i \(-0.561613\pi\)
0.421190 + 0.906973i \(0.361613\pi\)
\(488\) −11.1387 + 3.61919i −0.504226 + 0.163833i
\(489\) −0.0311130 + 0.0957561i −0.00140698 + 0.00433024i
\(490\) 1.21685 + 1.87597i 0.0549716 + 0.0847479i
\(491\) 9.94345 + 30.6028i 0.448742 + 1.38109i 0.878328 + 0.478059i \(0.158660\pi\)
−0.429586 + 0.903026i \(0.641340\pi\)
\(492\) 2.06524 + 2.84256i 0.0931082 + 0.128152i
\(493\) 0.0258558i 0.00116449i
\(494\) 2.97591 2.16213i 0.133893 0.0972787i
\(495\) −12.1432 9.84413i −0.545797 0.442461i
\(496\) 2.70035 + 1.96192i 0.121249 + 0.0880928i
\(497\) −1.64350 + 2.26208i −0.0737209 + 0.101468i
\(498\) 5.54214 + 1.80075i 0.248349 + 0.0806935i
\(499\) 7.97008 0.356790 0.178395 0.983959i \(-0.442910\pi\)
0.178395 + 0.983959i \(0.442910\pi\)
\(500\) −9.96988 + 5.05979i −0.445867 + 0.226281i
\(501\) 1.69283 0.0756300
\(502\) 6.48870 + 2.10831i 0.289605 + 0.0940984i
\(503\) −7.89399 + 10.8651i −0.351975 + 0.484453i −0.947891 0.318594i \(-0.896789\pi\)
0.595916 + 0.803047i \(0.296789\pi\)
\(504\) 2.20158 + 1.59954i 0.0980663 + 0.0712493i
\(505\) 8.70832 + 7.05957i 0.387515 + 0.314147i
\(506\) −4.89988 + 3.55997i −0.217826 + 0.158260i
\(507\) 1.55098i 0.0688813i
\(508\) 12.4035 + 17.0719i 0.550316 + 0.757445i
\(509\) −5.54765 17.0739i −0.245895 0.756787i −0.995488 0.0948881i \(-0.969751\pi\)
0.749593 0.661899i \(-0.230249\pi\)
\(510\) −0.00761761 0.0117438i −0.000337313 0.000520025i
\(511\) 2.21984 6.83196i 0.0981999 0.302228i
\(512\) 0.951057 0.309017i 0.0420312 0.0136568i
\(513\) 3.33108 1.08233i 0.147071 0.0477861i
\(514\) 1.00710 3.09954i 0.0444214 0.136715i
\(515\) 5.72234 1.53002i 0.252156 0.0674207i
\(516\) −1.76813 5.44175i −0.0778377 0.239560i
\(517\) 12.9879 + 17.8763i 0.571207 + 0.786198i
\(518\) 10.7247i 0.471217i
\(519\) 7.53012 5.47095i 0.330536 0.240148i
\(520\) 1.83214 + 6.85227i 0.0803445 + 0.300492i
\(521\) 20.3401 + 14.7780i 0.891117 + 0.647435i 0.936169 0.351550i \(-0.114345\pi\)
−0.0450517 + 0.998985i \(0.514345\pi\)
\(522\) 3.48767 4.80037i 0.152651 0.210106i
\(523\) 23.7957 + 7.73170i 1.04051 + 0.338083i 0.778939 0.627100i \(-0.215758\pi\)
0.261575 + 0.965183i \(0.415758\pi\)
\(524\) 7.42956 0.324562
\(525\) −1.07619 + 2.41022i −0.0469687 + 0.105191i
\(526\) 20.8370 0.908536
\(527\) 0.0376432 + 0.0122310i 0.00163977 + 0.000532792i
\(528\) −0.797149 + 1.09718i −0.0346914 + 0.0477487i
\(529\) −14.1106 10.2520i −0.613506 0.445738i
\(530\) 24.2757 + 1.28524i 1.05447 + 0.0558273i
\(531\) −19.3343 + 14.0472i −0.839038 + 0.609596i
\(532\) 1.15963i 0.0502763i
\(533\) −12.4094 17.0800i −0.537510 0.739819i
\(534\) 1.43283 + 4.40981i 0.0620047 + 0.190831i
\(535\) −6.65632 + 8.21090i −0.287778 + 0.354988i
\(536\) −2.27969 + 7.01615i −0.0984675 + 0.303052i
\(537\) −6.72238 + 2.18423i −0.290092 + 0.0942567i
\(538\) −29.3253 + 9.52835i −1.26430 + 0.410797i
\(539\) 0.793851 2.44322i 0.0341936 0.105237i
\(540\) −0.357067 + 6.74429i −0.0153657 + 0.290228i
\(541\) −7.10983 21.8818i −0.305675 0.940772i −0.979424 0.201812i \(-0.935317\pi\)
0.673749 0.738960i \(-0.264683\pi\)
\(542\) 12.1576 + 16.7335i 0.522212 + 0.718763i
\(543\) 8.35659i 0.358616i
\(544\) 0.00959347 0.00697007i 0.000411317 0.000298839i
\(545\) −2.88721 + 7.50944i −0.123674 + 0.321669i
\(546\) 1.35477 + 0.984298i 0.0579788 + 0.0421241i
\(547\) −8.99749 + 12.3840i −0.384705 + 0.529501i −0.956823 0.290670i \(-0.906122\pi\)
0.572118 + 0.820171i \(0.306122\pi\)
\(548\) −4.03872 1.31226i −0.172525 0.0560569i
\(549\) 31.8718 1.36025
\(550\) 11.7287 + 5.23698i 0.500113 + 0.223306i
\(551\) 2.52847 0.107717
\(552\) 1.18370 + 0.384607i 0.0503816 + 0.0163700i
\(553\) 6.95445 9.57198i 0.295733 0.407042i
\(554\) 1.61008 + 1.16979i 0.0684059 + 0.0496998i
\(555\) 10.6213 6.88947i 0.450848 0.292442i
\(556\) 8.30984 6.03745i 0.352416 0.256045i
\(557\) 34.8071i 1.47483i −0.675442 0.737413i \(-0.736047\pi\)
0.675442 0.737413i \(-0.263953\pi\)
\(558\) −5.33898 7.34848i −0.226017 0.311086i
\(559\) 10.6242 + 32.6978i 0.449354 + 1.38297i
\(560\) −2.08712 0.802450i −0.0881970 0.0339097i
\(561\) −0.00496960 + 0.0152948i −0.000209817 + 0.000645749i
\(562\) 10.4811 3.40553i 0.442120 0.143653i
\(563\) 3.84472 1.24923i 0.162036 0.0526486i −0.226876 0.973924i \(-0.572851\pi\)
0.388912 + 0.921275i \(0.372851\pi\)
\(564\) 1.40317 4.31851i 0.0590840 0.181842i
\(565\) −23.9914 9.22416i −1.00933 0.388063i
\(566\) 8.29866 + 25.5406i 0.348819 + 1.07355i
\(567\) −3.86141 5.31477i −0.162164 0.223200i
\(568\) 2.79608i 0.117321i
\(569\) 0.336115 0.244202i 0.0140907 0.0102375i −0.580718 0.814105i \(-0.697228\pi\)
0.594808 + 0.803868i \(0.297228\pi\)
\(570\) −1.14844 + 0.744936i −0.0481031 + 0.0312020i
\(571\) 13.5904 + 9.87402i 0.568742 + 0.413215i 0.834648 0.550784i \(-0.185671\pi\)
−0.265906 + 0.963999i \(0.585671\pi\)
\(572\) 4.78982 6.59262i 0.200272 0.275651i
\(573\) 1.36511 + 0.443552i 0.0570284 + 0.0185296i
\(574\) 6.65561 0.277800
\(575\) 1.24471 11.7221i 0.0519081 0.488847i
\(576\) −2.72131 −0.113388
\(577\) −17.1932 5.58640i −0.715761 0.232565i −0.0715765 0.997435i \(-0.522803\pi\)
−0.644184 + 0.764870i \(0.722803\pi\)
\(578\) −9.99227 + 13.7532i −0.415623 + 0.572057i
\(579\) 1.71050 + 1.24275i 0.0710861 + 0.0516471i
\(580\) −1.74968 + 4.55079i −0.0726514 + 0.188961i
\(581\) 8.93027 6.48822i 0.370490 0.269177i
\(582\) 2.85219i 0.118227i
\(583\) −16.4161 22.5948i −0.679884 0.935780i
\(584\) 2.21984 + 6.83196i 0.0918576 + 0.282709i
\(585\) 1.02050 19.2752i 0.0421924 0.796930i
\(586\) −9.59837 + 29.5407i −0.396505 + 1.22032i
\(587\) −7.81203 + 2.53828i −0.322437 + 0.104766i −0.465763 0.884909i \(-0.654220\pi\)
0.143326 + 0.989676i \(0.454220\pi\)
\(588\) −0.502077 + 0.163135i −0.0207053 + 0.00672756i
\(589\) 1.19609 3.68119i 0.0492840 0.151681i
\(590\) 12.3662 15.2543i 0.509109 0.628011i
\(591\) 2.22263 + 6.84056i 0.0914269 + 0.281383i
\(592\) 6.30382 + 8.67647i 0.259086 + 0.356601i
\(593\) 32.2906i 1.32602i 0.748613 + 0.663008i \(0.230720\pi\)
−0.748613 + 0.663008i \(0.769280\pi\)
\(594\) 6.27731 4.56073i 0.257561 0.187129i
\(595\) −0.0264786 0.00140187i −0.00108552 5.74712e-5i
\(596\) −4.09001 2.97157i −0.167534 0.121720i
\(597\) 7.46474 10.2743i 0.305511 0.420500i
\(598\) −7.11248 2.31099i −0.290851 0.0945032i
\(599\) −37.8942 −1.54831 −0.774157 0.632994i \(-0.781826\pi\)
−0.774157 + 0.632994i \(0.781826\pi\)
\(600\) −0.546039 2.58248i −0.0222919 0.105429i
\(601\) −35.7744 −1.45927 −0.729635 0.683837i \(-0.760310\pi\)
−0.729635 + 0.683837i \(0.760310\pi\)
\(602\) −10.3080 3.34927i −0.420123 0.136506i
\(603\) 11.8002 16.2416i 0.480541 0.661408i
\(604\) −16.2193 11.7840i −0.659954 0.479485i
\(605\) 2.54163 + 9.50582i 0.103332 + 0.386467i
\(606\) −2.14120 + 1.55567i −0.0869801 + 0.0631948i
\(607\) 4.87158i 0.197731i −0.995101 0.0988657i \(-0.968479\pi\)
0.995101 0.0988657i \(-0.0315214\pi\)
\(608\) −0.681613 0.938159i −0.0276430 0.0380474i
\(609\) 0.355702 + 1.09474i 0.0144138 + 0.0443610i
\(610\) −25.3000 + 6.76462i −1.02437 + 0.273891i
\(611\) −8.43120 + 25.9486i −0.341090 + 1.04977i
\(612\) −0.0306904 + 0.00997190i −0.00124058 + 0.000403090i
\(613\) 16.5210 5.36800i 0.667277 0.216811i 0.0442604 0.999020i \(-0.485907\pi\)
0.623017 + 0.782209i \(0.285907\pi\)
\(614\) 9.23539 28.4236i 0.372710 1.14708i
\(615\) 4.27551 + 6.59142i 0.172405 + 0.265792i
\(616\) 0.793851 + 2.44322i 0.0319852 + 0.0984402i
\(617\) −6.31500 8.69185i −0.254232 0.349921i 0.662756 0.748836i \(-0.269387\pi\)
−0.916988 + 0.398915i \(0.869387\pi\)
\(618\) 1.39845i 0.0562539i
\(619\) −31.6807 + 23.0174i −1.27336 + 0.925148i −0.999331 0.0365748i \(-0.988355\pi\)
−0.274026 + 0.961722i \(0.588355\pi\)
\(620\) 5.79778 + 4.70008i 0.232845 + 0.188760i
\(621\) −5.76087 4.18552i −0.231176 0.167959i
\(622\) −5.48460 + 7.54890i −0.219912 + 0.302683i
\(623\) 8.35325 + 2.71414i 0.334666 + 0.108740i
\(624\) −1.67459 −0.0670371
\(625\) −22.8603 + 10.1196i −0.914413 + 0.404783i
\(626\) 24.1019 0.963306
\(627\) 1.49570 + 0.485984i 0.0597327 + 0.0194083i
\(628\) −3.68985 + 5.07864i −0.147241 + 0.202660i
\(629\) 0.102887 + 0.0747519i 0.00410238 + 0.00298055i
\(630\) 4.72691 + 3.83196i 0.188324 + 0.152669i
\(631\) 3.95073 2.87037i 0.157276 0.114268i −0.506364 0.862320i \(-0.669011\pi\)
0.663640 + 0.748052i \(0.269011\pi\)
\(632\) 11.8316i 0.470637i
\(633\) −1.53383 2.11113i −0.0609642 0.0839100i
\(634\) −1.73797 5.34893i −0.0690238 0.212433i
\(635\) 25.6780 + 39.5870i 1.01900 + 1.57096i
\(636\) −1.77354 + 5.45839i −0.0703253 + 0.216439i
\(637\) 3.01682 0.980226i 0.119531 0.0388380i
\(638\) 5.32724 1.73093i 0.210908 0.0685280i
\(639\) −2.35131 + 7.23659i −0.0930164 + 0.286275i
\(640\) 2.16018 0.577583i 0.0853888 0.0228310i
\(641\) 11.0360 + 33.9652i 0.435895 + 1.34155i 0.892167 + 0.451706i \(0.149184\pi\)
−0.456272 + 0.889840i \(0.650816\pi\)
\(642\) −1.46681 2.01889i −0.0578904 0.0796793i
\(643\) 28.4443i 1.12173i −0.827907 0.560866i \(-0.810468\pi\)
0.827907 0.560866i \(-0.189532\pi\)
\(644\) 1.90734 1.38577i 0.0751599 0.0546068i
\(645\) −3.30481 12.3601i −0.130127 0.486680i
\(646\) −0.0111249 0.00808269i −0.000437702 0.000318009i
\(647\) −13.1387 + 18.0838i −0.516534 + 0.710948i −0.985004 0.172532i \(-0.944805\pi\)
0.468470 + 0.883479i \(0.344805\pi\)
\(648\) 6.24789 + 2.03006i 0.245440 + 0.0797484i
\(649\) −22.5606 −0.885580
\(650\) 3.28098 + 15.5173i 0.128691 + 0.608639i
\(651\) 1.76208 0.0690615
\(652\) −0.181385 0.0589357i −0.00710360 0.00230810i
\(653\) 18.4528 25.3981i 0.722115 0.993906i −0.277336 0.960773i \(-0.589451\pi\)
0.999451 0.0331331i \(-0.0105485\pi\)
\(654\) −1.53667 1.11646i −0.0600887 0.0436570i
\(655\) 16.5898 + 0.878322i 0.648216 + 0.0343189i
\(656\) −5.38450 + 3.91207i −0.210229 + 0.152741i
\(657\) 19.5486i 0.762665i
\(658\) −5.05571 6.95858i −0.197092 0.271274i
\(659\) −4.64428 14.2936i −0.180915 0.556800i 0.818939 0.573881i \(-0.194563\pi\)
−0.999854 + 0.0170807i \(0.994563\pi\)
\(660\) −1.90969 + 2.35570i −0.0743347 + 0.0916955i
\(661\) 12.1062 37.2592i 0.470879 1.44922i −0.380558 0.924757i \(-0.624268\pi\)
0.851436 0.524458i \(-0.175732\pi\)
\(662\) 13.0383 4.23641i 0.506749 0.164653i
\(663\) −0.0188857 + 0.00613633i −0.000733459 + 0.000238315i
\(664\) −3.41106 + 10.4982i −0.132375 + 0.407408i
\(665\) −0.137091 + 2.58938i −0.00531617 + 0.100412i
\(666\) −9.01872 27.7568i −0.349468 1.07555i
\(667\) −3.02155 4.15880i −0.116995 0.161030i
\(668\) 3.20663i 0.124068i
\(669\) 5.54265 4.02697i 0.214291 0.155692i
\(670\) −5.91985 + 15.3972i −0.228704 + 0.594844i
\(671\) 24.3413 + 17.6850i 0.939684 + 0.682720i
\(672\) 0.310301 0.427092i 0.0119701 0.0164754i
\(673\) 19.5960 + 6.36711i 0.755369 + 0.245434i 0.661290 0.750130i \(-0.270009\pi\)
0.0940791 + 0.995565i \(0.470009\pi\)
\(674\) 27.4712 1.05815
\(675\) −1.59462 + 15.0174i −0.0613770 + 0.578020i
\(676\) −2.93793 −0.112997
\(677\) −29.7915 9.67986i −1.14498 0.372027i −0.325731 0.945462i \(-0.605610\pi\)
−0.819251 + 0.573435i \(0.805610\pi\)
\(678\) 3.56690 4.90942i 0.136986 0.188545i
\(679\) 4.37091 + 3.17565i 0.167740 + 0.121870i
\(680\) 0.0222457 0.0144296i 0.000853082 0.000553350i
\(681\) −2.51665 + 1.82846i −0.0964384 + 0.0700666i
\(682\) 8.57470i 0.328342i
\(683\) 0.177271 + 0.243992i 0.00678307 + 0.00933610i 0.812395 0.583107i \(-0.198163\pi\)
−0.805612 + 0.592444i \(0.798163\pi\)
\(684\) 0.975166 + 3.00125i 0.0372864 + 0.114756i
\(685\) −8.86308 3.40765i −0.338641 0.130200i
\(686\) −0.309017 + 0.951057i −0.0117983 + 0.0363115i
\(687\) −4.59254 + 1.49221i −0.175216 + 0.0569312i
\(688\) 10.3080 3.34927i 0.392989 0.127690i
\(689\) 10.6566 32.7977i 0.405985 1.24949i
\(690\) 2.59766 + 0.998742i 0.0988914 + 0.0380215i
\(691\) −4.49290 13.8277i −0.170918 0.526031i 0.828506 0.559981i \(-0.189191\pi\)
−0.999424 + 0.0339495i \(0.989191\pi\)
\(692\) 10.3633 + 14.2639i 0.393954 + 0.542232i
\(693\) 6.99091i 0.265563i
\(694\) −15.1359 + 10.9969i −0.574552 + 0.417437i
\(695\) 19.2691 12.4989i 0.730919 0.474109i
\(696\) −0.931239 0.676585i −0.0352985 0.0256459i
\(697\) −0.0463900 + 0.0638504i −0.00175715 + 0.00241851i
\(698\) −10.8348 3.52045i −0.410105 0.133251i
\(699\) 5.88809 0.222708
\(700\) −4.56555 2.03856i −0.172562 0.0770505i
\(701\) 46.9864 1.77465 0.887326 0.461143i \(-0.152560\pi\)
0.887326 + 0.461143i \(0.152560\pi\)
\(702\) 9.11191 + 2.96064i 0.343907 + 0.111742i
\(703\) 7.31010 10.0615i 0.275706 0.379476i
\(704\) −2.07833 1.50999i −0.0783300 0.0569100i
\(705\) 3.64372 9.47709i 0.137231 0.356928i
\(706\) 14.2846 10.3784i 0.537609 0.390596i
\(707\) 5.01343i 0.188549i
\(708\) 2.72506 + 3.75073i 0.102414 + 0.140961i
\(709\) 4.86461 + 14.9717i 0.182694 + 0.562275i 0.999901 0.0140698i \(-0.00447869\pi\)
−0.817207 + 0.576344i \(0.804479\pi\)
\(710\) 0.330553 6.24349i 0.0124054 0.234314i
\(711\) 9.94956 30.6216i 0.373138 1.14840i
\(712\) −8.35325 + 2.71414i −0.313051 + 0.101717i
\(713\) −7.48411 + 2.43173i −0.280282 + 0.0910691i
\(714\) 0.00193448 0.00595372i 7.23962e−5 0.000222812i
\(715\) 11.4748 14.1547i 0.429132 0.529355i
\(716\) −4.13747 12.7338i −0.154625 0.475886i
\(717\) −5.79618 7.97776i −0.216462 0.297935i
\(718\) 8.96365i 0.334520i
\(719\) −39.4619 + 28.6707i −1.47168 + 1.06924i −0.491558 + 0.870845i \(0.663572\pi\)
−0.980122 + 0.198393i \(0.936428\pi\)
\(720\) −6.07651 0.321713i −0.226458 0.0119895i
\(721\) 2.14309 + 1.55705i 0.0798129 + 0.0579874i
\(722\) 10.3775 14.2834i 0.386211 0.531573i
\(723\) −8.24441 2.67877i −0.306613 0.0996246i
\(724\) 15.8294 0.588296
\(725\) −4.44492 + 9.95481i −0.165080 + 0.369712i
\(726\) −2.32307 −0.0862173
\(727\) 29.7220 + 9.65727i 1.10233 + 0.358168i 0.802998 0.595981i \(-0.203237\pi\)
0.299331 + 0.954149i \(0.403237\pi\)
\(728\) −1.86450 + 2.56626i −0.0691030 + 0.0951121i
\(729\) −10.5932 7.69641i −0.392341 0.285052i
\(730\) 4.14909 + 15.5178i 0.153565 + 0.574339i
\(731\) 0.103979 0.0755449i 0.00384579 0.00279413i
\(732\) 6.18291i 0.228527i
\(733\) −15.3681 21.1523i −0.567633 0.781280i 0.424639 0.905363i \(-0.360401\pi\)
−0.992272 + 0.124083i \(0.960401\pi\)
\(734\) −5.13125 15.7924i −0.189398 0.582907i
\(735\) −1.14039 + 0.304915i −0.0420641 + 0.0112469i
\(736\) −0.728540 + 2.24222i −0.0268544 + 0.0826492i
\(737\) 18.0242 5.85641i 0.663930 0.215724i
\(738\) 17.2255 5.59690i 0.634079 0.206025i
\(739\) −8.99849 + 27.6945i −0.331015 + 1.01876i 0.637637 + 0.770337i \(0.279912\pi\)
−0.968652 + 0.248422i \(0.920088\pi\)
\(740\) 13.0503 + 20.1193i 0.479740 + 0.739599i
\(741\) 0.600080 + 1.84686i 0.0220445 + 0.0678460i
\(742\) 6.39017 + 8.79532i 0.234591 + 0.322886i
\(743\) 32.9708i 1.20958i −0.796384 0.604791i \(-0.793257\pi\)
0.796384 0.604791i \(-0.206743\pi\)
\(744\) −1.42556 + 1.03573i −0.0522634 + 0.0379716i
\(745\) −8.78146 7.11886i −0.321728 0.260815i
\(746\) −27.2994 19.8342i −0.999502 0.726181i
\(747\) 17.6564 24.3020i 0.646015 0.889163i
\(748\) −0.0289722 0.00941363i −0.00105933 0.000344196i
\(749\) −4.72706 −0.172723
\(750\) −0.913972 5.83108i −0.0333735 0.212921i
\(751\) −23.9671 −0.874571 −0.437286 0.899323i \(-0.644060\pi\)
−0.437286 + 0.899323i \(0.644060\pi\)
\(752\) 8.18031 + 2.65794i 0.298305 + 0.0969252i
\(753\) −2.11707 + 2.91389i −0.0771502 + 0.106188i
\(754\) 5.59553 + 4.06539i 0.203777 + 0.148053i
\(755\) −34.8236 28.2304i −1.26736 1.02741i
\(756\) −2.44353 + 1.77533i −0.0888702 + 0.0645679i
\(757\) 0.237093i 0.00861730i 0.999991 + 0.00430865i \(0.00137149\pi\)
−0.999991 + 0.00430865i \(0.998629\pi\)
\(758\) −13.4129 18.4613i −0.487179 0.670544i
\(759\) −0.988039 3.04087i −0.0358636 0.110377i
\(760\) −1.41109 2.17543i −0.0511857 0.0789113i
\(761\) −2.04162 + 6.28346i −0.0740087 + 0.227775i −0.981217 0.192906i \(-0.938209\pi\)
0.907209 + 0.420681i \(0.138209\pi\)
\(762\) −10.5949 + 3.44248i −0.383812 + 0.124708i
\(763\) −3.42189 + 1.11184i −0.123881 + 0.0402513i
\(764\) −0.840195 + 2.58585i −0.0303972 + 0.0935529i
\(765\) −0.0697086 + 0.0186384i −0.00252032 + 0.000673875i
\(766\) −6.48503 19.9589i −0.234314 0.721143i
\(767\) −16.3740 22.5369i −0.591233 0.813762i
\(768\) 0.527915i 0.0190495i
\(769\) −25.0919 + 18.2304i −0.904838 + 0.657403i −0.939704 0.341989i \(-0.888900\pi\)
0.0348661 + 0.999392i \(0.488900\pi\)
\(770\) 1.48378 + 5.54942i 0.0534719 + 0.199987i
\(771\) 1.39192 + 1.01129i 0.0501286 + 0.0364206i
\(772\) −2.35408 + 3.24011i −0.0847252 + 0.116614i
\(773\) −48.8552 15.8740i −1.75720 0.570949i −0.760297 0.649576i \(-0.774946\pi\)
−0.996904 + 0.0786271i \(0.974946\pi\)
\(774\) −29.4948 −1.06017
\(775\) 12.3905 + 11.1804i 0.445079 + 0.401613i
\(776\) −5.40274 −0.193947
\(777\) 5.38463 + 1.74957i 0.193172 + 0.0627655i
\(778\) −18.8222 + 25.9065i −0.674808 + 0.928793i
\(779\) 6.24402 + 4.53655i 0.223715 + 0.162539i
\(780\) −3.73925 0.197970i −0.133887 0.00708845i
\(781\) −5.81118 + 4.22207i −0.207940 + 0.151077i
\(782\) 0.0279569i 0.000999738i
\(783\) 3.87095 + 5.32791i 0.138336 + 0.190404i
\(784\) −0.309017 0.951057i −0.0110363 0.0339663i
\(785\) −8.83961 + 10.9041i −0.315499 + 0.389184i
\(786\) −1.21202 + 3.73021i −0.0432313 + 0.133052i
\(787\) −38.0935 + 12.3773i −1.35789 + 0.441204i −0.895337 0.445390i \(-0.853065\pi\)
−0.462549 + 0.886594i \(0.653065\pi\)
\(788\) −12.9577 + 4.21021i −0.461599 + 0.149983i
\(789\) −3.39924 + 10.4618i −0.121016 + 0.372449i
\(790\) −1.39873 + 26.4193i −0.0497647 + 0.939957i
\(791\) −3.55215 10.9324i −0.126300 0.388711i
\(792\) 4.10916 + 5.65577i 0.146012 + 0.200969i
\(793\) 37.1512i 1.31928i
\(794\) −9.83807 + 7.14778i −0.349140 + 0.253665i
\(795\) −4.60549 + 11.9786i −0.163340 + 0.424837i
\(796\) 19.4621 + 14.1400i 0.689816 + 0.501180i
\(797\) −15.4441 + 21.2570i −0.547059 + 0.752962i −0.989609 0.143781i \(-0.954074\pi\)
0.442550 + 0.896744i \(0.354074\pi\)
\(798\) −0.582223 0.189176i −0.0206105 0.00669675i
\(799\) 0.101996 0.00360834
\(800\) 4.89185 1.03433i 0.172953 0.0365691i
\(801\) 23.9016 0.844521
\(802\) −9.39791 3.05356i −0.331852 0.107825i
\(803\) 10.8471 14.9298i 0.382786 0.526860i
\(804\) −3.15075 2.28916i −0.111119 0.0807323i
\(805\) 4.42281 2.86885i 0.155884 0.101114i
\(806\) 8.56572 6.22336i 0.301715 0.219208i
\(807\) 16.2779i 0.573011i
\(808\) −2.94682 4.05595i −0.103669 0.142688i
\(809\) −14.2098 43.7334i −0.499591 1.53758i −0.809678 0.586875i \(-0.800358\pi\)
0.310087 0.950708i \(-0.399642\pi\)
\(810\) 13.7112 + 5.27164i 0.481762 + 0.185226i
\(811\) 13.6999 42.1638i 0.481067 1.48057i −0.356530 0.934284i \(-0.616040\pi\)
0.837597 0.546289i \(-0.183960\pi\)
\(812\) −2.07370 + 0.673786i −0.0727726 + 0.0236453i
\(813\) −10.3848 + 3.37423i −0.364211 + 0.118339i
\(814\) 8.51382 26.2028i 0.298409 0.918409i
\(815\) −0.398055 0.153043i −0.0139433 0.00536087i
\(816\) 0.00193448 + 0.00595372i 6.77204e−5 + 0.000208422i
\(817\) −7.38764 10.1682i −0.258461 0.355741i
\(818\) 26.6640i 0.932286i
\(819\) 6.98359 5.07387i 0.244026 0.177296i
\(820\) −12.4858 + 8.09886i −0.436021 + 0.282824i
\(821\) 6.47903 + 4.70729i 0.226120 + 0.164285i 0.695077 0.718935i \(-0.255370\pi\)
−0.468957 + 0.883221i \(0.655370\pi\)
\(822\) 1.31771 1.81367i 0.0459604 0.0632591i
\(823\) 23.0929 + 7.50333i 0.804967 + 0.261550i 0.682465 0.730918i \(-0.260908\pi\)
0.122502 + 0.992468i \(0.460908\pi\)
\(824\) −2.64901 −0.0922825
\(825\) −4.54272 + 5.03438i −0.158157 + 0.175275i
\(826\) 8.78201 0.305565
\(827\) −25.0911 8.15259i −0.872503 0.283493i −0.161662 0.986846i \(-0.551685\pi\)
−0.710841 + 0.703353i \(0.751685\pi\)
\(828\) 3.77109 5.19046i 0.131055 0.180381i
\(829\) −29.8939 21.7192i −1.03826 0.754338i −0.0683130 0.997664i \(-0.521762\pi\)
−0.969945 + 0.243326i \(0.921762\pi\)
\(830\) −8.85778 + 23.0385i −0.307458 + 0.799678i
\(831\) −0.849988 + 0.617552i −0.0294858 + 0.0214227i
\(832\) 3.17208i 0.109972i
\(833\) −0.00697007 0.00959347i −0.000241498 0.000332394i
\(834\) 1.67564 + 5.15710i 0.0580227 + 0.178576i
\(835\) −0.379088 + 7.16021i −0.0131189 + 0.247789i
\(836\) −0.920572 + 2.83323i −0.0318387 + 0.0979893i
\(837\) 9.58800 3.11533i 0.331410 0.107682i
\(838\) 9.68295 3.14618i 0.334492 0.108683i
\(839\) −7.74947 + 23.8504i −0.267541 + 0.823408i 0.723556 + 0.690266i \(0.242507\pi\)
−0.991097 + 0.133142i \(0.957493\pi\)
\(840\) 0.743374 0.916988i 0.0256488 0.0316391i
\(841\) −7.49236 23.0591i −0.258357 0.795142i
\(842\) −7.57920 10.4319i −0.261197 0.359506i
\(843\) 5.81789i 0.200379i
\(844\) 3.99900 2.90544i 0.137651 0.100009i
\(845\) −6.56022 0.347322i −0.225678 0.0119482i
\(846\) −18.9364 13.7581i −0.651048 0.473014i
\(847\) −2.58653 + 3.56005i −0.0888742 + 0.122325i
\(848\) −10.3395 3.35951i −0.355061 0.115366i
\(849\) −14.1772 −0.486559
\(850\) 0.0513791 0.0295906i 0.00176229 0.00101495i
\(851\) −25.2846 −0.866746
\(852\) 1.40385 + 0.456138i 0.0480951 + 0.0156270i
\(853\) −17.2936 + 23.8026i −0.592122 + 0.814986i −0.994959 0.100286i \(-0.968024\pi\)
0.402836 + 0.915272i \(0.368024\pi\)
\(854\) −9.47516 6.88411i −0.324233 0.235569i
\(855\) 1.82268 + 6.81690i 0.0623344 + 0.233133i
\(856\) 3.82427 2.77850i 0.130711 0.0949670i
\(857\) 11.5565i 0.394763i 0.980327 + 0.197382i \(0.0632438\pi\)
−0.980327 + 0.197382i \(0.936756\pi\)
\(858\) 2.52862 + 3.48034i 0.0863256 + 0.118817i
\(859\) −3.00812 9.25805i −0.102636 0.315881i 0.886532 0.462666i \(-0.153107\pi\)
−0.989168 + 0.146786i \(0.953107\pi\)
\(860\) 23.4131 6.26012i 0.798381 0.213468i
\(861\) −1.08576 + 3.34163i −0.0370026 + 0.113882i
\(862\) 30.3344 9.85623i 1.03319 0.335705i
\(863\) −25.7942 + 8.38104i −0.878045 + 0.285294i −0.713145 0.701016i \(-0.752730\pi\)
−0.164900 + 0.986310i \(0.552730\pi\)
\(864\) 0.933344 2.87254i 0.0317530 0.0977257i
\(865\) 21.4544 + 33.0756i 0.729471 + 1.12460i
\(866\) −3.67864 11.3217i −0.125005 0.384727i
\(867\) −5.27507 7.26051i −0.179151 0.246580i
\(868\) 3.33782i 0.113293i
\(869\) 24.5900 17.8657i 0.834158 0.606052i
\(870\) −1.99942 1.62087i −0.0677866 0.0549525i
\(871\) 18.9319 + 13.7548i 0.641483 + 0.466065i
\(872\) 2.11485 2.91083i 0.0716177 0.0985733i
\(873\) 13.9829 + 4.54332i 0.473250 + 0.153768i
\(874\) 2.73395 0.0924772
\(875\) −9.95361 5.09173i −0.336493 0.172132i
\(876\) −3.79230 −0.128130
\(877\) −9.05284 2.94145i −0.305693 0.0993256i 0.152154 0.988357i \(-0.451379\pi\)
−0.457847 + 0.889031i \(0.651379\pi\)
\(878\) 13.7389 18.9099i 0.463665 0.638180i
\(879\) −13.2659 9.63824i −0.447448 0.325090i
\(880\) −4.46227 3.61743i −0.150423 0.121943i
\(881\) 41.6465 30.2580i 1.40311 1.01942i 0.408827 0.912612i \(-0.365938\pi\)
0.994280 0.106805i \(-0.0340620\pi\)
\(882\) 2.72131i 0.0916311i
\(883\) −0.852643 1.17356i −0.0286937 0.0394935i 0.794429 0.607357i \(-0.207770\pi\)
−0.823123 + 0.567863i \(0.807770\pi\)
\(884\) −0.0116237 0.0357741i −0.000390947 0.00120321i
\(885\) 5.64149 + 8.69731i 0.189637 + 0.292357i
\(886\) −0.655074 + 2.01611i −0.0220076 + 0.0677325i
\(887\) 33.0302 10.7321i 1.10904 0.360350i 0.303467 0.952842i \(-0.401856\pi\)
0.805577 + 0.592492i \(0.201856\pi\)
\(888\) −5.38463 + 1.74957i −0.180696 + 0.0587118i
\(889\) −6.52090 + 20.0693i −0.218704 + 0.673102i
\(890\) −18.9732 + 5.07298i −0.635982 + 0.170047i
\(891\) −5.21514 16.0506i −0.174714 0.537714i
\(892\) 7.62806 + 10.4991i 0.255406 + 0.351537i
\(893\) 9.97429i 0.333777i
\(894\) 2.15918 1.56874i 0.0722138 0.0524664i
\(895\) −7.73334 28.9230i −0.258497 0.966790i
\(896\) 0.809017 + 0.587785i 0.0270274 + 0.0196365i
\(897\) 2.32059 3.19401i 0.0774821 0.106645i
\(898\) −14.3189 4.65248i −0.477827 0.155255i
\(899\) 7.27783 0.242729
\(900\) −13.5305 1.43673i −0.451015 0.0478910i
\(901\) −0.128918 −0.00429487
\(902\) 16.2611 + 5.28356i 0.541436 + 0.175923i
\(903\) 3.36319 4.62903i 0.111920 0.154044i
\(904\) 9.29964 + 6.75658i 0.309301 + 0.224721i
\(905\) 35.3462 + 1.87135i 1.17495 + 0.0622059i
\(906\) 8.56241 6.22096i 0.284467 0.206677i
\(907\) 53.6447i 1.78124i −0.454746 0.890621i \(-0.650270\pi\)
0.454746 0.890621i \(-0.349730\pi\)
\(908\) −3.46354 4.76716i −0.114942 0.158204i
\(909\) 4.21594 + 12.9753i 0.139834 + 0.430365i
\(910\) −4.46670 + 5.50989i −0.148070 + 0.182651i
\(911\) −10.5565 + 32.4896i −0.349753 + 1.07643i 0.609237 + 0.792988i \(0.291476\pi\)
−0.958990 + 0.283440i \(0.908524\pi\)
\(912\) 0.582223 0.189176i 0.0192793 0.00626423i
\(913\) 26.9693 8.76286i 0.892554 0.290008i
\(914\) −8.42340 + 25.9246i −0.278621 + 0.857509i
\(915\) 0.730943 13.8061i 0.0241642 0.456415i
\(916\) −2.82660 8.69939i −0.0933936 0.287436i
\(917\) 4.36699 + 6.01064i 0.144211 + 0.198489i
\(918\) 0.0358160i 0.00118211i
\(919\) −43.2404 + 31.4160i −1.42637 + 1.03632i −0.435689 + 0.900097i \(0.643495\pi\)
−0.990679 + 0.136220i \(0.956505\pi\)
\(920\) −1.89186 + 4.92061i −0.0623728 + 0.162228i
\(921\) 12.7642 + 9.27376i 0.420596 + 0.305581i
\(922\) −24.7157 + 34.0182i −0.813968 + 1.12033i
\(923\) −8.43529 2.74079i −0.277651 0.0902143i
\(924\) −1.35619 −0.0446154
\(925\) 26.7621 + 46.4680i 0.879933 + 1.52786i
\(926\) 27.0398 0.888584
\(927\) 6.85593 + 2.22763i 0.225178 + 0.0731649i
\(928\) 1.28162 1.76399i 0.0420711 0.0579060i
\(929\) −34.9645 25.4032i −1.14715 0.833452i −0.159049 0.987271i \(-0.550843\pi\)
−0.988099 + 0.153819i \(0.950843\pi\)
\(930\) −3.30562 + 2.14419i −0.108396 + 0.0703107i
\(931\) −0.938159 + 0.681613i −0.0307469 + 0.0223390i
\(932\) 11.1535i 0.365345i
\(933\) −2.89540 3.98518i −0.0947912 0.130469i
\(934\) −3.95791 12.1812i −0.129507 0.398581i
\(935\) −0.0635803 0.0244452i −0.00207930 0.000799443i
\(936\) −2.66749 + 8.20970i −0.0871898 + 0.268342i
\(937\) 33.2641 10.8082i 1.08669 0.353087i 0.289724 0.957110i \(-0.406436\pi\)
0.796967 + 0.604023i \(0.206436\pi\)
\(938\) −7.01615 + 2.27969i −0.229086 + 0.0744344i
\(939\) −3.93186 + 12.1010i −0.128311 + 0.394902i
\(940\) 17.9519 + 6.90210i 0.585527 + 0.225122i
\(941\) 17.4731 + 53.7766i 0.569606 + 1.75307i 0.653851 + 0.756623i \(0.273152\pi\)
−0.0842445 + 0.996445i \(0.526848\pi\)
\(942\) −1.94793 2.68109i −0.0634669 0.0873546i
\(943\) 15.6913i 0.510979i
\(944\) −7.10479 + 5.16193i −0.231241 + 0.168007i
\(945\) −5.66613 + 3.67532i −0.184319 + 0.119558i
\(946\) −22.5259 16.3660i −0.732381 0.532106i
\(947\) −21.9461 + 30.2062i −0.713151 + 0.981568i 0.286573 + 0.958058i \(0.407484\pi\)
−0.999724 + 0.0235095i \(0.992516\pi\)
\(948\) −5.94039 1.93015i −0.192935 0.0626883i
\(949\) 22.7868 0.739690
\(950\) −2.89370 5.02444i −0.0938842 0.163014i
\(951\) 2.96910 0.0962797
\(952\) 0.0112778 + 0.00366438i 0.000365516 + 0.000118763i
\(953\) 0.314186 0.432439i 0.0101775 0.0140081i −0.803898 0.594767i \(-0.797244\pi\)
0.814075 + 0.580759i \(0.197244\pi\)
\(954\) 23.9348 + 17.3896i 0.774916 + 0.563010i
\(955\) −2.18181 + 5.67473i −0.0706016 + 0.183630i
\(956\) 15.1118 10.9794i 0.488752 0.355099i
\(957\) 2.95706i 0.0955882i
\(958\) 3.91827 + 5.39304i 0.126594 + 0.174241i
\(959\) −1.31226 4.03872i −0.0423750 0.130417i
\(960\) −0.0624101 + 1.17880i −0.00201428 + 0.0380457i
\(961\) −6.13676 + 18.8870i −0.197960 + 0.609259i
\(962\) 32.3546 10.5126i 1.04315 0.338941i
\(963\) −12.2342 + 3.97512i −0.394241 + 0.128097i
\(964\) 5.07425 15.6169i 0.163430 0.502987i
\(965\) −5.63957 + 6.95668i −0.181544 + 0.223943i
\(966\) 0.384607 + 1.18370i 0.0123745 + 0.0380849i
\(967\) 8.97704 + 12.3558i 0.288682 + 0.397337i 0.928586 0.371118i \(-0.121026\pi\)
−0.639903 + 0.768455i \(0.721026\pi\)
\(968\) 4.40047i 0.141436i
\(969\) 0.00587299 0.00426697i 0.000188667 0.000137075i
\(970\) −12.0640 0.638712i −0.387352 0.0205078i
\(971\) 23.6200 + 17.1609i 0.758001 + 0.550720i 0.898297 0.439390i \(-0.144805\pi\)
−0.140296 + 0.990110i \(0.544805\pi\)
\(972\) −7.36447 + 10.1363i −0.236216 + 0.325123i
\(973\) 9.76880 + 3.17407i 0.313173 + 0.101756i
\(974\) −5.30981 −0.170137
\(975\) −8.32613 0.884109i −0.266649 0.0283141i
\(976\) 11.7119 0.374890
\(977\) 16.8453 + 5.47338i 0.538930 + 0.175109i 0.565819 0.824530i \(-0.308560\pi\)
−0.0268893 + 0.999638i \(0.508560\pi\)
\(978\) 0.0591805 0.0814550i 0.00189238 0.00260464i
\(979\) 18.2542 + 13.2625i 0.583408 + 0.423870i
\(980\) −0.577583 2.16018i −0.0184502 0.0690046i
\(981\) −7.92127 + 5.75514i −0.252907 + 0.183747i
\(982\) 32.1777i 1.02683i
\(983\) −21.9374 30.1942i −0.699694 0.963046i −0.999958 0.00918981i \(-0.997075\pi\)
0.300264 0.953856i \(-0.402925\pi\)
\(984\) −1.08576 3.34163i −0.0346128 0.106527i
\(985\) −29.4315 + 7.86929i −0.937766 + 0.250737i
\(986\) 0.00798988 0.0245903i 0.000254450 0.000783115i
\(987\) 4.31851 1.40317i 0.137460 0.0446633i
\(988\) −3.49840 + 1.13670i −0.111299 + 0.0361632i
\(989\) −7.89627 + 24.3022i −0.251087 + 0.772766i
\(990\) 8.50688 + 13.1148i 0.270366 + 0.416815i
\(991\) 14.0755 + 43.3200i 0.447124 + 1.37611i 0.880138 + 0.474718i \(0.157450\pi\)
−0.433014 + 0.901387i \(0.642550\pi\)
\(992\) −1.96192 2.70035i −0.0622910 0.0857362i
\(993\) 7.23735i 0.229670i
\(994\) 2.26208 1.64350i 0.0717488 0.0521285i
\(995\) 41.7861 + 33.8747i 1.32471 + 1.07390i
\(996\) −4.71442 3.42523i −0.149382 0.108533i
\(997\) 1.11092 1.52905i 0.0351833 0.0484256i −0.791063 0.611735i \(-0.790472\pi\)
0.826246 + 0.563309i \(0.190472\pi\)
\(998\) −7.58000 2.46289i −0.239941 0.0779614i
\(999\) 32.3925 1.02485
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 350.2.m.a.29.2 24
25.12 odd 20 8750.2.a.bb.1.8 12
25.13 odd 20 8750.2.a.z.1.5 12
25.19 even 10 inner 350.2.m.a.169.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.m.a.29.2 24 1.1 even 1 trivial
350.2.m.a.169.2 yes 24 25.19 even 10 inner
8750.2.a.z.1.5 12 25.13 odd 20
8750.2.a.bb.1.8 12 25.12 odd 20