Properties

Label 350.2.h.a.211.2
Level $350$
Weight $2$
Character 350.211
Analytic conductor $2.795$
Analytic rank $0$
Dimension $8$
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(71,350)]
 
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([6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.h (of order \(5\), 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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 211.2
Root \(0.913545 + 0.406737i\) of defining polynomial
Character \(\chi\) \(=\) 350.211
Dual form 350.2.h.a.141.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.604528 - 1.86055i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(0.604528 + 1.86055i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.669131 - 0.486152i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.604528 - 1.86055i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(0.604528 + 1.86055i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.669131 - 0.486152i) q^{9} +(-0.233733 - 2.22382i) q^{10} +(3.64350 - 2.64716i) q^{11} +(-1.58268 - 1.14988i) q^{12} +(1.94890 + 1.41596i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(2.92705 + 3.25082i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.43540 + 4.41770i) q^{17} +0.827091 q^{18} +(-2.32709 - 7.16205i) q^{19} +(1.49622 + 1.66172i) q^{20} +(0.604528 - 1.86055i) q^{21} +(-1.39169 + 4.28319i) q^{22} +(4.09618 - 2.97605i) q^{23} +1.95630 q^{24} +(-2.50000 - 4.33013i) q^{25} -2.40898 q^{26} +(3.43901 - 2.49859i) q^{27} +(0.309017 - 0.951057i) q^{28} +(0.647278 - 1.99212i) q^{29} +(-4.27882 - 0.909491i) q^{30} +(0.0580002 + 0.178506i) q^{31} +1.00000 q^{32} +(-2.72256 - 8.37919i) q^{33} +(-3.75792 - 2.73029i) q^{34} +(-1.11803 + 1.93649i) q^{35} +(-0.669131 + 0.486152i) q^{36} +(0.232455 + 0.168888i) q^{37} +(6.09240 + 4.42639i) q^{38} +(3.81263 - 2.77004i) q^{39} +(-2.18720 - 0.464905i) q^{40} +(6.66440 + 4.84197i) q^{41} +(0.604528 + 1.86055i) q^{42} -3.73403 q^{43} +(-1.39169 - 4.28319i) q^{44} +(1.68954 - 0.752232i) q^{45} +(-1.56460 + 4.81535i) q^{46} +(-3.85207 + 11.8554i) q^{47} +(-1.58268 + 1.14988i) q^{48} +1.00000 q^{49} +(4.56773 + 2.03368i) q^{50} +9.08708 q^{51} +(1.94890 - 1.41596i) q^{52} +(-2.99856 + 9.22861i) q^{53} +(-1.31359 + 4.04280i) q^{54} +(1.05264 + 10.0152i) q^{55} +(0.309017 + 0.951057i) q^{56} -14.7321 q^{57} +(0.647278 + 1.99212i) q^{58} +(-2.60814 - 1.89493i) q^{59} +(3.99622 - 1.77923i) q^{60} +(-0.184869 + 0.134315i) q^{61} +(-0.151847 - 0.110323i) q^{62} +(-0.669131 - 0.486152i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-4.92094 + 2.19094i) q^{65} +(7.12776 + 5.17862i) q^{66} +(-1.96320 - 6.04210i) q^{67} +4.64505 q^{68} +(-3.06082 - 9.42025i) q^{69} +(-0.233733 - 2.22382i) q^{70} +(2.57120 - 7.91335i) q^{71} +(0.255585 - 0.786610i) q^{72} +(-3.74957 + 2.72422i) q^{73} -0.287330 q^{74} +(-9.56773 + 2.03368i) q^{75} -7.53062 q^{76} +(3.64350 - 2.64716i) q^{77} +(-1.45630 + 4.48202i) q^{78} +(0.224307 - 0.690347i) q^{79} +(2.04275 - 0.909491i) q^{80} +(-3.33652 - 10.2687i) q^{81} -8.23765 q^{82} +(3.67333 + 11.3054i) q^{83} +(-1.58268 - 1.14988i) q^{84} +(-10.1597 - 2.15950i) q^{85} +(3.02090 - 2.19481i) q^{86} +(-3.31513 - 2.40858i) q^{87} +(3.64350 + 2.64716i) q^{88} +(-11.5034 + 8.35774i) q^{89} +(-0.924716 + 1.60165i) q^{90} +(1.94890 + 1.41596i) q^{91} +(-1.56460 - 4.81535i) q^{92} +0.367182 q^{93} +(-3.85207 - 11.8554i) q^{94} +(16.4710 + 3.50102i) q^{95} +(0.604528 - 1.86055i) q^{96} +(4.37080 - 13.4519i) q^{97} +(-0.809017 + 0.587785i) q^{98} -3.72490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} - q^{9} + 5 q^{10} - q^{11} - 2 q^{12} + 11 q^{13} - 2 q^{14} + 10 q^{15} - 2 q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 5 q^{20} + 3 q^{21} + 4 q^{22} + 15 q^{23} - 2 q^{24} - 20 q^{25} - 14 q^{26} - 2 q^{28} - 8 q^{29} - 5 q^{30} - 7 q^{31} + 8 q^{32} - 11 q^{33} - 21 q^{34} - q^{36} + 14 q^{37} + 14 q^{38} - 4 q^{39} - 5 q^{40} + 3 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 10 q^{45} - 10 q^{46} + 2 q^{47} - 2 q^{48} + 8 q^{49} + 5 q^{50} + 14 q^{51} + 11 q^{52} + 4 q^{53} - 5 q^{54} + 20 q^{55} - 2 q^{56} - 36 q^{57} - 8 q^{58} + 11 q^{59} + 15 q^{60} + 13 q^{62} - q^{63} - 2 q^{64} - 20 q^{65} + 24 q^{66} + 14 q^{67} + 14 q^{68} - 5 q^{69} + 5 q^{70} + 23 q^{71} + 4 q^{72} - 5 q^{73} - 36 q^{74} - 45 q^{75} - 16 q^{76} - q^{77} + 6 q^{78} + 2 q^{79} + 5 q^{80} - 7 q^{81} - 12 q^{82} - 27 q^{83} - 2 q^{84} + 15 q^{85} + 4 q^{86} - 28 q^{87} - q^{88} - 15 q^{89} - 5 q^{90} + 11 q^{91} - 10 q^{92} + 38 q^{93} + 2 q^{94} + 20 q^{95} + 3 q^{96} + 40 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0.604528 1.86055i 0.349025 1.07419i −0.610369 0.792117i \(-0.708979\pi\)
0.959394 0.282070i \(-0.0910211\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −1.11803 + 1.93649i −0.500000 + 0.866025i
\(6\) 0.604528 + 1.86055i 0.246798 + 0.759565i
\(7\) 1.00000 0.377964
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) −0.669131 0.486152i −0.223044 0.162051i
\(10\) −0.233733 2.22382i −0.0739128 0.703233i
\(11\) 3.64350 2.64716i 1.09856 0.798148i 0.117733 0.993045i \(-0.462437\pi\)
0.980824 + 0.194897i \(0.0624374\pi\)
\(12\) −1.58268 1.14988i −0.456879 0.331942i
\(13\) 1.94890 + 1.41596i 0.540529 + 0.392717i 0.824281 0.566181i \(-0.191579\pi\)
−0.283753 + 0.958897i \(0.591579\pi\)
\(14\) −0.809017 + 0.587785i −0.216219 + 0.157092i
\(15\) 2.92705 + 3.25082i 0.755761 + 0.839358i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 1.43540 + 4.41770i 0.348135 + 1.07145i 0.959884 + 0.280398i \(0.0904663\pi\)
−0.611749 + 0.791052i \(0.709534\pi\)
\(18\) 0.827091 0.194947
\(19\) −2.32709 7.16205i −0.533871 1.64309i −0.746075 0.665861i \(-0.768064\pi\)
0.212204 0.977225i \(-0.431936\pi\)
\(20\) 1.49622 + 1.66172i 0.334565 + 0.371572i
\(21\) 0.604528 1.86055i 0.131919 0.406005i
\(22\) −1.39169 + 4.28319i −0.296710 + 0.913179i
\(23\) 4.09618 2.97605i 0.854113 0.620549i −0.0721641 0.997393i \(-0.522991\pi\)
0.926277 + 0.376843i \(0.122991\pi\)
\(24\) 1.95630 0.399327
\(25\) −2.50000 4.33013i −0.500000 0.866025i
\(26\) −2.40898 −0.472439
\(27\) 3.43901 2.49859i 0.661838 0.480853i
\(28\) 0.309017 0.951057i 0.0583987 0.179733i
\(29\) 0.647278 1.99212i 0.120197 0.369927i −0.872799 0.488080i \(-0.837697\pi\)
0.992995 + 0.118153i \(0.0376974\pi\)
\(30\) −4.27882 0.909491i −0.781202 0.166050i
\(31\) 0.0580002 + 0.178506i 0.0104172 + 0.0320607i 0.956130 0.292943i \(-0.0946345\pi\)
−0.945713 + 0.325003i \(0.894635\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.72256 8.37919i −0.473937 1.45863i
\(34\) −3.75792 2.73029i −0.644478 0.468241i
\(35\) −1.11803 + 1.93649i −0.188982 + 0.327327i
\(36\) −0.669131 + 0.486152i −0.111522 + 0.0810253i
\(37\) 0.232455 + 0.168888i 0.0382153 + 0.0277650i 0.606729 0.794909i \(-0.292481\pi\)
−0.568514 + 0.822674i \(0.692481\pi\)
\(38\) 6.09240 + 4.42639i 0.988318 + 0.718055i
\(39\) 3.81263 2.77004i 0.610509 0.443561i
\(40\) −2.18720 0.464905i −0.345827 0.0735079i
\(41\) 6.66440 + 4.84197i 1.04080 + 0.756188i 0.970442 0.241333i \(-0.0775847\pi\)
0.0703616 + 0.997522i \(0.477585\pi\)
\(42\) 0.604528 + 1.86055i 0.0932808 + 0.287089i
\(43\) −3.73403 −0.569435 −0.284717 0.958611i \(-0.591900\pi\)
−0.284717 + 0.958611i \(0.591900\pi\)
\(44\) −1.39169 4.28319i −0.209806 0.645715i
\(45\) 1.68954 0.752232i 0.251862 0.112136i
\(46\) −1.56460 + 4.81535i −0.230688 + 0.709985i
\(47\) −3.85207 + 11.8554i −0.561882 + 1.72929i 0.115157 + 0.993347i \(0.463263\pi\)
−0.677039 + 0.735947i \(0.736737\pi\)
\(48\) −1.58268 + 1.14988i −0.228440 + 0.165971i
\(49\) 1.00000 0.142857
\(50\) 4.56773 + 2.03368i 0.645974 + 0.287606i
\(51\) 9.08708 1.27245
\(52\) 1.94890 1.41596i 0.270264 0.196358i
\(53\) −2.99856 + 9.22861i −0.411883 + 1.26765i 0.503126 + 0.864213i \(0.332183\pi\)
−0.915009 + 0.403434i \(0.867817\pi\)
\(54\) −1.31359 + 4.04280i −0.178756 + 0.550155i
\(55\) 1.05264 + 10.0152i 0.141938 + 1.35045i
\(56\) 0.309017 + 0.951057i 0.0412941 + 0.127090i
\(57\) −14.7321 −1.95132
\(58\) 0.647278 + 1.99212i 0.0849918 + 0.261578i
\(59\) −2.60814 1.89493i −0.339551 0.246698i 0.404921 0.914352i \(-0.367299\pi\)
−0.744472 + 0.667653i \(0.767299\pi\)
\(60\) 3.99622 1.77923i 0.515910 0.229698i
\(61\) −0.184869 + 0.134315i −0.0236701 + 0.0171973i −0.599557 0.800332i \(-0.704657\pi\)
0.575887 + 0.817529i \(0.304657\pi\)
\(62\) −0.151847 0.110323i −0.0192845 0.0140110i
\(63\) −0.669131 0.486152i −0.0843025 0.0612494i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −4.92094 + 2.19094i −0.610367 + 0.271753i
\(66\) 7.12776 + 5.17862i 0.877367 + 0.637444i
\(67\) −1.96320 6.04210i −0.239843 0.738161i −0.996442 0.0842815i \(-0.973141\pi\)
0.756599 0.653879i \(-0.226859\pi\)
\(68\) 4.64505 0.563294
\(69\) −3.06082 9.42025i −0.368480 1.13406i
\(70\) −0.233733 2.22382i −0.0279364 0.265797i
\(71\) 2.57120 7.91335i 0.305146 0.939142i −0.674477 0.738296i \(-0.735631\pi\)
0.979623 0.200846i \(-0.0643692\pi\)
\(72\) 0.255585 0.786610i 0.0301210 0.0927029i
\(73\) −3.74957 + 2.72422i −0.438854 + 0.318846i −0.785180 0.619268i \(-0.787429\pi\)
0.346325 + 0.938115i \(0.387429\pi\)
\(74\) −0.287330 −0.0334014
\(75\) −9.56773 + 2.03368i −1.10479 + 0.234830i
\(76\) −7.53062 −0.863822
\(77\) 3.64350 2.64716i 0.415215 0.301672i
\(78\) −1.45630 + 4.48202i −0.164893 + 0.507488i
\(79\) 0.224307 0.690347i 0.0252366 0.0776701i −0.937645 0.347594i \(-0.886999\pi\)
0.962882 + 0.269924i \(0.0869986\pi\)
\(80\) 2.04275 0.909491i 0.228386 0.101684i
\(81\) −3.33652 10.2687i −0.370724 1.14097i
\(82\) −8.23765 −0.909696
\(83\) 3.67333 + 11.3054i 0.403201 + 1.24092i 0.922388 + 0.386264i \(0.126235\pi\)
−0.519187 + 0.854660i \(0.673765\pi\)
\(84\) −1.58268 1.14988i −0.172684 0.125462i
\(85\) −10.1597 2.15950i −1.10197 0.234231i
\(86\) 3.02090 2.19481i 0.325752 0.236672i
\(87\) −3.31513 2.40858i −0.355419 0.258227i
\(88\) 3.64350 + 2.64716i 0.388398 + 0.282188i
\(89\) −11.5034 + 8.35774i −1.21936 + 0.885919i −0.996047 0.0888270i \(-0.971688\pi\)
−0.223316 + 0.974746i \(0.571688\pi\)
\(90\) −0.924716 + 1.60165i −0.0974736 + 0.168829i
\(91\) 1.94890 + 1.41596i 0.204301 + 0.148433i
\(92\) −1.56460 4.81535i −0.163121 0.502035i
\(93\) 0.367182 0.0380750
\(94\) −3.85207 11.8554i −0.397311 1.22280i
\(95\) 16.4710 + 3.50102i 1.68989 + 0.359197i
\(96\) 0.604528 1.86055i 0.0616994 0.189891i
\(97\) 4.37080 13.4519i 0.443787 1.36584i −0.440021 0.897987i \(-0.645029\pi\)
0.883808 0.467849i \(-0.154971\pi\)
\(98\) −0.809017 + 0.587785i −0.0817231 + 0.0593753i
\(99\) −3.72490 −0.374366
\(100\) −4.89074 + 1.03956i −0.489074 + 0.103956i
\(101\) −6.21937 −0.618851 −0.309425 0.950924i \(-0.600137\pi\)
−0.309425 + 0.950924i \(0.600137\pi\)
\(102\) −7.35160 + 5.34125i −0.727917 + 0.528863i
\(103\) −4.70558 + 14.4823i −0.463655 + 1.42698i 0.397012 + 0.917813i \(0.370047\pi\)
−0.860667 + 0.509169i \(0.829953\pi\)
\(104\) −0.744415 + 2.29107i −0.0729959 + 0.224658i
\(105\) 2.92705 + 3.25082i 0.285651 + 0.317247i
\(106\) −2.99856 9.22861i −0.291246 0.896362i
\(107\) −13.4665 −1.30185 −0.650927 0.759140i \(-0.725620\pi\)
−0.650927 + 0.759140i \(0.725620\pi\)
\(108\) −1.31359 4.04280i −0.126400 0.389019i
\(109\) 2.31592 + 1.68261i 0.221825 + 0.161165i 0.693148 0.720796i \(-0.256223\pi\)
−0.471323 + 0.881961i \(0.656223\pi\)
\(110\) −6.73840 7.48375i −0.642482 0.713548i
\(111\) 0.454750 0.330395i 0.0431629 0.0313597i
\(112\) −0.809017 0.587785i −0.0764449 0.0555405i
\(113\) −14.5729 10.5878i −1.37090 0.996018i −0.997666 0.0682819i \(-0.978248\pi\)
−0.373236 0.927737i \(-0.621752\pi\)
\(114\) 11.9185 8.65933i 1.11627 0.811020i
\(115\) 1.18343 + 11.2595i 0.110355 + 1.04996i
\(116\) −1.69460 1.23120i −0.157339 0.114314i
\(117\) −0.615699 1.89493i −0.0569214 0.175186i
\(118\) 3.22384 0.296779
\(119\) 1.43540 + 4.41770i 0.131583 + 0.404970i
\(120\) −2.18720 + 3.78835i −0.199664 + 0.345827i
\(121\) 2.86846 8.82821i 0.260769 0.802565i
\(122\) 0.0706138 0.217327i 0.00639307 0.0196759i
\(123\) 13.0375 9.47232i 1.17555 0.854090i
\(124\) 0.187693 0.0168553
\(125\) 11.1803 1.00000
\(126\) 0.827091 0.0736831
\(127\) −5.77599 + 4.19651i −0.512537 + 0.372380i −0.813785 0.581166i \(-0.802597\pi\)
0.301248 + 0.953546i \(0.402597\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) −2.25733 + 6.94735i −0.198747 + 0.611680i
\(130\) 2.69332 4.66496i 0.236220 0.409144i
\(131\) −2.78483 8.57082i −0.243312 0.748836i −0.995910 0.0903559i \(-0.971200\pi\)
0.752598 0.658480i \(-0.228800\pi\)
\(132\) −8.81040 −0.766847
\(133\) −2.32709 7.16205i −0.201784 0.621028i
\(134\) 5.13972 + 3.73423i 0.444004 + 0.322588i
\(135\) 0.993563 + 9.45312i 0.0855123 + 0.813595i
\(136\) −3.75792 + 2.73029i −0.322239 + 0.234120i
\(137\) 2.40770 + 1.74930i 0.205704 + 0.149452i 0.685868 0.727726i \(-0.259423\pi\)
−0.480164 + 0.877179i \(0.659423\pi\)
\(138\) 8.01334 + 5.82203i 0.682141 + 0.495604i
\(139\) −16.5922 + 12.0550i −1.40734 + 1.02249i −0.413632 + 0.910444i \(0.635740\pi\)
−0.993703 + 0.112045i \(0.964260\pi\)
\(140\) 1.49622 + 1.66172i 0.126454 + 0.140441i
\(141\) 19.7289 + 14.3339i 1.66148 + 1.20713i
\(142\) 2.57120 + 7.91335i 0.215771 + 0.664074i
\(143\) 10.8491 0.907247
\(144\) 0.255585 + 0.786610i 0.0212988 + 0.0655509i
\(145\) 3.13404 + 3.48070i 0.260268 + 0.289057i
\(146\) 1.43221 4.40789i 0.118531 0.364799i
\(147\) 0.604528 1.86055i 0.0498607 0.153455i
\(148\) 0.232455 0.168888i 0.0191077 0.0138825i
\(149\) 19.7893 1.62120 0.810602 0.585598i \(-0.199140\pi\)
0.810602 + 0.585598i \(0.199140\pi\)
\(150\) 6.54508 7.26905i 0.534404 0.593516i
\(151\) −3.80224 −0.309422 −0.154711 0.987960i \(-0.549445\pi\)
−0.154711 + 0.987960i \(0.549445\pi\)
\(152\) 6.09240 4.42639i 0.494159 0.359028i
\(153\) 1.18720 3.65384i 0.0959798 0.295395i
\(154\) −1.39169 + 4.28319i −0.112146 + 0.345149i
\(155\) −0.410522 0.0872592i −0.0329740 0.00700883i
\(156\) −1.45630 4.48202i −0.116597 0.358848i
\(157\) 8.53123 0.680866 0.340433 0.940269i \(-0.389426\pi\)
0.340433 + 0.940269i \(0.389426\pi\)
\(158\) 0.224307 + 0.690347i 0.0178449 + 0.0549211i
\(159\) 15.3576 + 11.1579i 1.21793 + 0.884880i
\(160\) −1.11803 + 1.93649i −0.0883883 + 0.153093i
\(161\) 4.09618 2.97605i 0.322824 0.234546i
\(162\) 8.73511 + 6.34643i 0.686295 + 0.498623i
\(163\) 11.3954 + 8.27925i 0.892557 + 0.648481i 0.936544 0.350551i \(-0.114006\pi\)
−0.0439862 + 0.999032i \(0.514006\pi\)
\(164\) 6.66440 4.84197i 0.520402 0.378094i
\(165\) 19.2701 + 4.09599i 1.50018 + 0.318873i
\(166\) −9.61691 6.98710i −0.746417 0.542304i
\(167\) −6.08970 18.7422i −0.471235 1.45031i −0.850968 0.525217i \(-0.823984\pi\)
0.379733 0.925096i \(-0.376016\pi\)
\(168\) 1.95630 0.150931
\(169\) −2.22394 6.84459i −0.171073 0.526507i
\(170\) 9.48866 4.22463i 0.727747 0.324014i
\(171\) −1.92472 + 5.92367i −0.147187 + 0.452994i
\(172\) −1.15388 + 3.55128i −0.0879825 + 0.270782i
\(173\) −6.60262 + 4.79708i −0.501988 + 0.364715i −0.809776 0.586740i \(-0.800411\pi\)
0.307788 + 0.951455i \(0.400411\pi\)
\(174\) 4.09773 0.310648
\(175\) −2.50000 4.33013i −0.188982 0.327327i
\(176\) −4.50361 −0.339473
\(177\) −5.10230 + 3.70703i −0.383512 + 0.278638i
\(178\) 4.39393 13.5231i 0.329339 1.01360i
\(179\) −3.75745 + 11.5643i −0.280845 + 0.864353i 0.706768 + 0.707445i \(0.250152\pi\)
−0.987613 + 0.156907i \(0.949848\pi\)
\(180\) −0.193318 1.83930i −0.0144091 0.137093i
\(181\) −1.92337 5.91954i −0.142963 0.439996i 0.853780 0.520634i \(-0.174304\pi\)
−0.996743 + 0.0806379i \(0.974304\pi\)
\(182\) −2.40898 −0.178565
\(183\) 0.138141 + 0.425156i 0.0102117 + 0.0314284i
\(184\) 4.09618 + 2.97605i 0.301975 + 0.219397i
\(185\) −0.586943 + 0.261324i −0.0431529 + 0.0192129i
\(186\) −0.297057 + 0.215824i −0.0217813 + 0.0158250i
\(187\) 16.9242 + 12.2962i 1.23762 + 0.899185i
\(188\) 10.0848 + 7.32707i 0.735513 + 0.534381i
\(189\) 3.43901 2.49859i 0.250151 0.181746i
\(190\) −15.3832 + 6.84903i −1.11601 + 0.496881i
\(191\) 2.90063 + 2.10743i 0.209882 + 0.152488i 0.687760 0.725938i \(-0.258594\pi\)
−0.477878 + 0.878426i \(0.658594\pi\)
\(192\) 0.604528 + 1.86055i 0.0436281 + 0.134273i
\(193\) 1.52319 0.109642 0.0548209 0.998496i \(-0.482541\pi\)
0.0548209 + 0.998496i \(0.482541\pi\)
\(194\) 4.37080 + 13.4519i 0.313805 + 0.965792i
\(195\) 1.10151 + 10.4801i 0.0788804 + 0.750497i
\(196\) 0.309017 0.951057i 0.0220726 0.0679326i
\(197\) 7.41289 22.8145i 0.528147 1.62547i −0.229861 0.973223i \(-0.573827\pi\)
0.758008 0.652245i \(-0.226173\pi\)
\(198\) 3.01351 2.18944i 0.214161 0.155597i
\(199\) −13.7108 −0.971930 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(200\) 3.34565 3.71572i 0.236573 0.262741i
\(201\) −12.4284 −0.876634
\(202\) 5.03158 3.65566i 0.354021 0.257211i
\(203\) 0.647278 1.99212i 0.0454300 0.139819i
\(204\) 2.80806 8.64233i 0.196604 0.605084i
\(205\) −16.8275 + 7.49206i −1.17528 + 0.523269i
\(206\) −4.70558 14.4823i −0.327853 1.00903i
\(207\) −4.18769 −0.291065
\(208\) −0.744415 2.29107i −0.0516159 0.158857i
\(209\) −27.4378 19.9347i −1.89791 1.37892i
\(210\) −4.27882 0.909491i −0.295266 0.0627608i
\(211\) 12.5320 9.10503i 0.862739 0.626816i −0.0658899 0.997827i \(-0.520989\pi\)
0.928629 + 0.371010i \(0.120989\pi\)
\(212\) 7.85032 + 5.70359i 0.539162 + 0.391724i
\(213\) −13.1688 9.56769i −0.902311 0.655568i
\(214\) 10.8946 7.91540i 0.744741 0.541086i
\(215\) 4.17478 7.23093i 0.284717 0.493145i
\(216\) 3.43901 + 2.49859i 0.233995 + 0.170007i
\(217\) 0.0580002 + 0.178506i 0.00393731 + 0.0121178i
\(218\) −2.86264 −0.193882
\(219\) 2.80182 + 8.62313i 0.189330 + 0.582697i
\(220\) 9.85032 + 2.09375i 0.664109 + 0.141161i
\(221\) −3.45784 + 10.6421i −0.232600 + 0.715868i
\(222\) −0.173699 + 0.534591i −0.0116579 + 0.0358794i
\(223\) −6.12977 + 4.45354i −0.410480 + 0.298231i −0.773796 0.633435i \(-0.781644\pi\)
0.363316 + 0.931666i \(0.381644\pi\)
\(224\) 1.00000 0.0668153
\(225\) −0.432273 + 4.11280i −0.0288182 + 0.274187i
\(226\) 18.0131 1.19821
\(227\) 12.9209 9.38756i 0.857589 0.623075i −0.0696393 0.997572i \(-0.522185\pi\)
0.927228 + 0.374498i \(0.122185\pi\)
\(228\) −4.55248 + 14.0111i −0.301495 + 0.927907i
\(229\) 2.04082 6.28099i 0.134861 0.415060i −0.860707 0.509100i \(-0.829978\pi\)
0.995568 + 0.0940404i \(0.0299783\pi\)
\(230\) −7.57561 8.41356i −0.499521 0.554774i
\(231\) −2.72256 8.37919i −0.179131 0.551310i
\(232\) 2.09464 0.137520
\(233\) 3.28332 + 10.1050i 0.215098 + 0.662002i 0.999147 + 0.0413035i \(0.0131511\pi\)
−0.784049 + 0.620699i \(0.786849\pi\)
\(234\) 1.61192 + 1.17113i 0.105375 + 0.0765591i
\(235\) −18.6512 20.7143i −1.21667 1.35125i
\(236\) −2.60814 + 1.89493i −0.169776 + 0.123349i
\(237\) −1.14882 0.834669i −0.0746241 0.0542176i
\(238\) −3.75792 2.73029i −0.243590 0.176978i
\(239\) −16.5083 + 11.9940i −1.06784 + 0.775828i −0.975522 0.219902i \(-0.929426\pi\)
−0.0923137 + 0.995730i \(0.529426\pi\)
\(240\) −0.457250 4.35045i −0.0295154 0.280820i
\(241\) 15.8138 + 11.4894i 1.01866 + 0.740099i 0.966008 0.258514i \(-0.0832327\pi\)
0.0526517 + 0.998613i \(0.483233\pi\)
\(242\) 2.86846 + 8.82821i 0.184392 + 0.567499i
\(243\) −8.36994 −0.536932
\(244\) 0.0706138 + 0.217327i 0.00452058 + 0.0139129i
\(245\) −1.11803 + 1.93649i −0.0714286 + 0.123718i
\(246\) −4.97989 + 15.3265i −0.317506 + 0.977184i
\(247\) 5.60591 17.2532i 0.356695 1.09780i
\(248\) −0.151847 + 0.110323i −0.00964227 + 0.00700552i
\(249\) 23.2548 1.47371
\(250\) −9.04508 + 6.57164i −0.572061 + 0.415627i
\(251\) −7.53314 −0.475487 −0.237744 0.971328i \(-0.576408\pi\)
−0.237744 + 0.971328i \(0.576408\pi\)
\(252\) −0.669131 + 0.486152i −0.0421513 + 0.0306247i
\(253\) 7.04636 21.6865i 0.443001 1.36342i
\(254\) 2.20623 6.79009i 0.138431 0.426048i
\(255\) −10.1597 + 17.5971i −0.636223 + 1.10197i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −25.2517 −1.57516 −0.787579 0.616214i \(-0.788666\pi\)
−0.787579 + 0.616214i \(0.788666\pi\)
\(258\) −2.25733 6.94735i −0.140535 0.432523i
\(259\) 0.232455 + 0.168888i 0.0144440 + 0.0104942i
\(260\) 0.563057 + 5.35713i 0.0349193 + 0.332235i
\(261\) −1.40159 + 1.01831i −0.0867559 + 0.0630319i
\(262\) 7.29078 + 5.29706i 0.450426 + 0.327253i
\(263\) 25.6109 + 18.6074i 1.57924 + 1.14738i 0.917564 + 0.397589i \(0.130153\pi\)
0.661672 + 0.749793i \(0.269847\pi\)
\(264\) 7.12776 5.17862i 0.438683 0.318722i
\(265\) −14.5186 16.1246i −0.891873 0.990525i
\(266\) 6.09240 + 4.42639i 0.373549 + 0.271399i
\(267\) 8.59582 + 26.4552i 0.526055 + 1.61903i
\(268\) −6.35304 −0.388074
\(269\) 0.503676 + 1.55016i 0.0307097 + 0.0945147i 0.965237 0.261378i \(-0.0841769\pi\)
−0.934527 + 0.355893i \(0.884177\pi\)
\(270\) −6.36022 7.06374i −0.387070 0.429885i
\(271\) −1.58422 + 4.87573i −0.0962346 + 0.296180i −0.987573 0.157158i \(-0.949767\pi\)
0.891339 + 0.453338i \(0.149767\pi\)
\(272\) 1.43540 4.41770i 0.0870338 0.267862i
\(273\) 3.81263 2.77004i 0.230751 0.167650i
\(274\) −2.97608 −0.179792
\(275\) −20.5713 9.15892i −1.24049 0.552304i
\(276\) −9.90503 −0.596213
\(277\) −10.8931 + 7.91431i −0.654503 + 0.475525i −0.864802 0.502113i \(-0.832556\pi\)
0.210299 + 0.977637i \(0.432556\pi\)
\(278\) 6.33767 19.5053i 0.380108 1.16985i
\(279\) 0.0479715 0.147641i 0.00287198 0.00883904i
\(280\) −2.18720 0.464905i −0.130710 0.0277834i
\(281\) 8.84811 + 27.2317i 0.527834 + 1.62451i 0.758643 + 0.651507i \(0.225863\pi\)
−0.230808 + 0.972999i \(0.574137\pi\)
\(282\) −24.3863 −1.45218
\(283\) −8.55556 26.3313i −0.508575 1.56523i −0.794675 0.607034i \(-0.792359\pi\)
0.286100 0.958200i \(-0.407641\pi\)
\(284\) −6.73150 4.89072i −0.399441 0.290211i
\(285\) 16.4710 28.5286i 0.975659 1.68989i
\(286\) −8.77711 + 6.37694i −0.519001 + 0.377076i
\(287\) 6.66440 + 4.84197i 0.393387 + 0.285812i
\(288\) −0.669131 0.486152i −0.0394289 0.0286468i
\(289\) −3.70242 + 2.68997i −0.217789 + 0.158233i
\(290\) −4.58140 0.973806i −0.269029 0.0571839i
\(291\) −22.3857 16.2641i −1.31227 0.953421i
\(292\) 1.43221 + 4.40789i 0.0838137 + 0.257952i
\(293\) −12.8726 −0.752027 −0.376013 0.926614i \(-0.622705\pi\)
−0.376013 + 0.926614i \(0.622705\pi\)
\(294\) 0.604528 + 1.86055i 0.0352568 + 0.108509i
\(295\) 6.58550 2.93205i 0.383423 0.170711i
\(296\) −0.0887898 + 0.273267i −0.00516080 + 0.0158833i
\(297\) 5.91588 18.2072i 0.343274 1.05649i
\(298\) −16.0099 + 11.6319i −0.927428 + 0.673816i
\(299\) 12.1970 0.705373
\(300\) −1.02244 + 9.72789i −0.0590308 + 0.561640i
\(301\) −3.73403 −0.215226
\(302\) 3.07607 2.23490i 0.177008 0.128604i
\(303\) −3.75979 + 11.5714i −0.215994 + 0.664762i
\(304\) −2.32709 + 7.16205i −0.133468 + 0.410772i
\(305\) −0.0534105 0.508167i −0.00305828 0.0290976i
\(306\) 1.18720 + 3.65384i 0.0678680 + 0.208876i
\(307\) 14.3288 0.817787 0.408894 0.912582i \(-0.365915\pi\)
0.408894 + 0.912582i \(0.365915\pi\)
\(308\) −1.39169 4.28319i −0.0792991 0.244057i
\(309\) 24.1003 + 17.5099i 1.37102 + 0.996104i
\(310\) 0.383409 0.170705i 0.0217762 0.00969538i
\(311\) −15.3439 + 11.1480i −0.870072 + 0.632144i −0.930606 0.366022i \(-0.880719\pi\)
0.0605346 + 0.998166i \(0.480719\pi\)
\(312\) 3.81263 + 2.77004i 0.215848 + 0.156823i
\(313\) −18.4094 13.3752i −1.04056 0.756013i −0.0701675 0.997535i \(-0.522353\pi\)
−0.970395 + 0.241522i \(0.922353\pi\)
\(314\) −6.90191 + 5.01453i −0.389497 + 0.282986i
\(315\) 1.68954 0.752232i 0.0951948 0.0423834i
\(316\) −0.587244 0.426658i −0.0330351 0.0240014i
\(317\) 1.46950 + 4.52265i 0.0825353 + 0.254017i 0.983805 0.179240i \(-0.0573640\pi\)
−0.901270 + 0.433258i \(0.857364\pi\)
\(318\) −18.9830 −1.06451
\(319\) −2.91509 8.97173i −0.163214 0.502320i
\(320\) −0.233733 2.22382i −0.0130661 0.124315i
\(321\) −8.14088 + 25.0550i −0.454379 + 1.39844i
\(322\) −1.56460 + 4.81535i −0.0871919 + 0.268349i
\(323\) 28.2995 20.5608i 1.57463 1.14403i
\(324\) −10.7972 −0.599844
\(325\) 1.25903 11.9789i 0.0698386 0.664470i
\(326\) −14.0855 −0.780124
\(327\) 4.53062 3.29169i 0.250544 0.182031i
\(328\) −2.54557 + 7.83447i −0.140556 + 0.432586i
\(329\) −3.85207 + 11.8554i −0.212371 + 0.653612i
\(330\) −17.9974 + 8.01298i −0.990726 + 0.441100i
\(331\) −5.29803 16.3057i −0.291206 0.896241i −0.984469 0.175556i \(-0.943828\pi\)
0.693263 0.720685i \(-0.256172\pi\)
\(332\) 11.8872 0.652393
\(333\) −0.0734372 0.226016i −0.00402433 0.0123856i
\(334\) 15.9430 + 11.5833i 0.872365 + 0.633810i
\(335\) 13.8954 + 2.95356i 0.759187 + 0.161370i
\(336\) −1.58268 + 1.14988i −0.0863421 + 0.0627312i
\(337\) 9.29561 + 6.75366i 0.506364 + 0.367895i 0.811443 0.584432i \(-0.198683\pi\)
−0.305078 + 0.952327i \(0.598683\pi\)
\(338\) 5.82236 + 4.23019i 0.316694 + 0.230092i
\(339\) −28.5089 + 20.7129i −1.54839 + 1.12497i
\(340\) −5.19332 + 8.99509i −0.281647 + 0.487827i
\(341\) 0.683858 + 0.496852i 0.0370330 + 0.0269061i
\(342\) −1.92472 5.92367i −0.104077 0.320315i
\(343\) 1.00000 0.0539949
\(344\) −1.15388 3.55128i −0.0622130 0.191472i
\(345\) 21.6643 + 4.60490i 1.16637 + 0.247919i
\(346\) 2.52198 7.76184i 0.135582 0.417279i
\(347\) 9.34306 28.7550i 0.501561 1.54365i −0.304914 0.952380i \(-0.598628\pi\)
0.806475 0.591268i \(-0.201372\pi\)
\(348\) −3.31513 + 2.40858i −0.177710 + 0.129114i
\(349\) 14.7758 0.790932 0.395466 0.918481i \(-0.370583\pi\)
0.395466 + 0.918481i \(0.370583\pi\)
\(350\) 4.56773 + 2.03368i 0.244155 + 0.108705i
\(351\) 10.2402 0.546582
\(352\) 3.64350 2.64716i 0.194199 0.141094i
\(353\) −5.38940 + 16.5869i −0.286849 + 0.882829i 0.698990 + 0.715132i \(0.253633\pi\)
−0.985838 + 0.167698i \(0.946367\pi\)
\(354\) 1.94890 5.99811i 0.103583 0.318796i
\(355\) 12.4494 + 13.8265i 0.660748 + 0.733835i
\(356\) 4.39393 + 13.5231i 0.232878 + 0.716724i
\(357\) 9.08708 0.480939
\(358\) −3.75745 11.5643i −0.198588 0.611190i
\(359\) −18.1138 13.1604i −0.956008 0.694580i −0.00378757 0.999993i \(-0.501206\pi\)
−0.952220 + 0.305413i \(0.901206\pi\)
\(360\) 1.23751 + 1.37440i 0.0652226 + 0.0724370i
\(361\) −30.5083 + 22.1656i −1.60570 + 1.16661i
\(362\) 5.03546 + 3.65848i 0.264658 + 0.192285i
\(363\) −14.6912 10.6738i −0.771090 0.560230i
\(364\) 1.94890 1.41596i 0.102150 0.0742165i
\(365\) −1.08329 10.3068i −0.0567019 0.539482i
\(366\) −0.361659 0.262761i −0.0189042 0.0137347i
\(367\) 8.15438 + 25.0966i 0.425655 + 1.31003i 0.902365 + 0.430972i \(0.141829\pi\)
−0.476710 + 0.879061i \(0.658171\pi\)
\(368\) −5.06316 −0.263935
\(369\) −2.10542 6.47982i −0.109604 0.337326i
\(370\) 0.321244 0.556412i 0.0167007 0.0289265i
\(371\) −2.99856 + 9.22861i −0.155677 + 0.479125i
\(372\) 0.113466 0.349211i 0.00588292 0.0181058i
\(373\) −0.826301 + 0.600343i −0.0427842 + 0.0310846i −0.608972 0.793192i \(-0.708418\pi\)
0.566188 + 0.824276i \(0.308418\pi\)
\(374\) −20.9195 −1.08172
\(375\) 6.75883 20.8016i 0.349025 1.07419i
\(376\) −12.4656 −0.642862
\(377\) 4.08224 2.96592i 0.210246 0.152753i
\(378\) −1.31359 + 4.04280i −0.0675635 + 0.207939i
\(379\) 5.89964 18.1572i 0.303044 0.932673i −0.677356 0.735655i \(-0.736874\pi\)
0.980400 0.197018i \(-0.0631257\pi\)
\(380\) 8.41949 14.5830i 0.431911 0.748092i
\(381\) 4.31604 + 13.2834i 0.221118 + 0.680530i
\(382\) −3.58538 −0.183444
\(383\) 2.40735 + 7.40905i 0.123010 + 0.378585i 0.993533 0.113542i \(-0.0362196\pi\)
−0.870524 + 0.492127i \(0.836220\pi\)
\(384\) −1.58268 1.14988i −0.0807656 0.0586796i
\(385\) 1.05264 + 10.0152i 0.0536476 + 0.510423i
\(386\) −1.23229 + 0.895311i −0.0627219 + 0.0455701i
\(387\) 2.49856 + 1.81531i 0.127009 + 0.0922773i
\(388\) −11.4429 8.31375i −0.580925 0.422067i
\(389\) −2.65307 + 1.92757i −0.134516 + 0.0977315i −0.653008 0.757351i \(-0.726493\pi\)
0.518493 + 0.855082i \(0.326493\pi\)
\(390\) −7.05120 7.83115i −0.357051 0.396546i
\(391\) 19.0269 + 13.8239i 0.962234 + 0.699104i
\(392\) 0.309017 + 0.951057i 0.0156077 + 0.0480356i
\(393\) −17.6299 −0.889312
\(394\) 7.41289 + 22.8145i 0.373456 + 1.14938i
\(395\) 1.08607 + 1.20620i 0.0546460 + 0.0606906i
\(396\) −1.15106 + 3.54259i −0.0578428 + 0.178022i
\(397\) −3.52602 + 10.8520i −0.176966 + 0.544644i −0.999718 0.0237559i \(-0.992438\pi\)
0.822752 + 0.568400i \(0.192438\pi\)
\(398\) 11.0922 8.05898i 0.556004 0.403960i
\(399\) −14.7321 −0.737529
\(400\) −0.522642 + 4.97261i −0.0261321 + 0.248630i
\(401\) −14.8579 −0.741966 −0.370983 0.928640i \(-0.620979\pi\)
−0.370983 + 0.928640i \(0.620979\pi\)
\(402\) 10.0548 7.30525i 0.501488 0.364353i
\(403\) −0.139721 + 0.430018i −0.00696001 + 0.0214207i
\(404\) −1.92189 + 5.91498i −0.0956177 + 0.294281i
\(405\) 23.6157 + 5.01967i 1.17347 + 0.249429i
\(406\) 0.647278 + 1.99212i 0.0321239 + 0.0988671i
\(407\) 1.29402 0.0641423
\(408\) 2.80806 + 8.64233i 0.139020 + 0.427859i
\(409\) 16.8588 + 12.2486i 0.833614 + 0.605656i 0.920579 0.390556i \(-0.127717\pi\)
−0.0869657 + 0.996211i \(0.527717\pi\)
\(410\) 9.20997 15.9521i 0.454848 0.787820i
\(411\) 4.71017 3.42214i 0.232336 0.168802i
\(412\) 12.3194 + 8.95055i 0.606932 + 0.440962i
\(413\) −2.60814 1.89493i −0.128338 0.0932432i
\(414\) 3.38791 2.46146i 0.166507 0.120974i
\(415\) −25.9996 5.52640i −1.27627 0.271280i
\(416\) 1.94890 + 1.41596i 0.0955528 + 0.0694232i
\(417\) 12.3984 + 38.1582i 0.607150 + 1.86862i
\(418\) 33.9150 1.65884
\(419\) −2.16186 6.65353i −0.105614 0.325046i 0.884260 0.466995i \(-0.154663\pi\)
−0.989874 + 0.141949i \(0.954663\pi\)
\(420\) 3.99622 1.77923i 0.194996 0.0868177i
\(421\) −1.22190 + 3.76061i −0.0595516 + 0.183281i −0.976407 0.215939i \(-0.930719\pi\)
0.916855 + 0.399220i \(0.130719\pi\)
\(422\) −4.78680 + 14.7323i −0.233018 + 0.717155i
\(423\) 8.34108 6.06015i 0.405557 0.294655i
\(424\) −9.70353 −0.471245
\(425\) 15.5407 17.2597i 0.753835 0.837219i
\(426\) 16.2775 0.788649
\(427\) −0.184869 + 0.134315i −0.00894645 + 0.00649998i
\(428\) −4.16137 + 12.8074i −0.201148 + 0.619069i
\(429\) 6.55859 20.1853i 0.316652 0.974554i
\(430\) 0.872766 + 8.30382i 0.0420885 + 0.400446i
\(431\) −9.16302 28.2009i −0.441367 1.35839i −0.886419 0.462883i \(-0.846815\pi\)
0.445052 0.895505i \(-0.353185\pi\)
\(432\) −4.25085 −0.204519
\(433\) 0.467670 + 1.43934i 0.0224748 + 0.0691702i 0.961665 0.274227i \(-0.0884221\pi\)
−0.939190 + 0.343398i \(0.888422\pi\)
\(434\) −0.151847 0.110323i −0.00728887 0.00529567i
\(435\) 8.37063 3.72684i 0.401341 0.178689i
\(436\) 2.31592 1.68261i 0.110912 0.0805826i
\(437\) −30.8468 22.4115i −1.47560 1.07209i
\(438\) −7.33527 5.32939i −0.350493 0.254648i
\(439\) 17.0512 12.3884i 0.813809 0.591267i −0.101123 0.994874i \(-0.532244\pi\)
0.914932 + 0.403607i \(0.132244\pi\)
\(440\) −9.19975 + 4.09599i −0.438581 + 0.195269i
\(441\) −0.669131 0.486152i −0.0318634 0.0231501i
\(442\) −3.45784 10.6421i −0.164473 0.506195i
\(443\) −28.7328 −1.36514 −0.682568 0.730822i \(-0.739137\pi\)
−0.682568 + 0.730822i \(0.739137\pi\)
\(444\) −0.173699 0.534591i −0.00824339 0.0253705i
\(445\) −3.32346 31.6206i −0.157547 1.49896i
\(446\) 2.34137 7.20598i 0.110867 0.341213i
\(447\) 11.9632 36.8189i 0.565840 1.74148i
\(448\) −0.809017 + 0.587785i −0.0382225 + 0.0277702i
\(449\) −30.2457 −1.42738 −0.713692 0.700460i \(-0.752978\pi\)
−0.713692 + 0.700460i \(0.752978\pi\)
\(450\) −2.06773 3.58141i −0.0974736 0.168829i
\(451\) 37.0992 1.74693
\(452\) −14.5729 + 10.5878i −0.685451 + 0.498009i
\(453\) −2.29856 + 7.07424i −0.107996 + 0.332377i
\(454\) −4.93533 + 15.1894i −0.231627 + 0.712874i
\(455\) −4.92094 + 2.19094i −0.230697 + 0.102713i
\(456\) −4.55248 14.0111i −0.213189 0.656129i
\(457\) 3.24578 0.151831 0.0759156 0.997114i \(-0.475812\pi\)
0.0759156 + 0.997114i \(0.475812\pi\)
\(458\) 2.04082 + 6.28099i 0.0953612 + 0.293492i
\(459\) 15.9744 + 11.6061i 0.745619 + 0.541724i
\(460\) 11.0742 + 2.35389i 0.516336 + 0.109751i
\(461\) 20.9773 15.2409i 0.977010 0.709839i 0.0199716 0.999801i \(-0.493642\pi\)
0.957038 + 0.289961i \(0.0936424\pi\)
\(462\) 7.12776 + 5.17862i 0.331613 + 0.240931i
\(463\) 5.13089 + 3.72781i 0.238453 + 0.173246i 0.700594 0.713561i \(-0.252919\pi\)
−0.462141 + 0.886806i \(0.652919\pi\)
\(464\) −1.69460 + 1.23120i −0.0786697 + 0.0571569i
\(465\) −0.410522 + 0.711046i −0.0190375 + 0.0329740i
\(466\) −8.59585 6.24525i −0.398195 0.289306i
\(467\) 2.13617 + 6.57446i 0.0988502 + 0.304230i 0.988238 0.152924i \(-0.0488690\pi\)
−0.889388 + 0.457154i \(0.848869\pi\)
\(468\) −1.99244 −0.0921007
\(469\) −1.96320 6.04210i −0.0906521 0.278998i
\(470\) 27.2647 + 5.79529i 1.25763 + 0.267317i
\(471\) 5.15737 15.8728i 0.237639 0.731378i
\(472\) 0.996222 3.06605i 0.0458548 0.141127i
\(473\) −13.6050 + 9.88458i −0.625556 + 0.454493i
\(474\) 1.42002 0.0652239
\(475\) −25.1949 + 27.9817i −1.15602 + 1.28389i
\(476\) 4.64505 0.212905
\(477\) 6.49293 4.71739i 0.297291 0.215994i
\(478\) 6.30562 19.4067i 0.288413 0.887643i
\(479\) −8.14439 + 25.0659i −0.372127 + 1.14529i 0.573270 + 0.819367i \(0.305675\pi\)
−0.945397 + 0.325922i \(0.894325\pi\)
\(480\) 2.92705 + 3.25082i 0.133601 + 0.148379i
\(481\) 0.213893 + 0.658293i 0.00975266 + 0.0300156i
\(482\) −19.5470 −0.890341
\(483\) −3.06082 9.42025i −0.139272 0.428636i
\(484\) −7.50973 5.45614i −0.341351 0.248006i
\(485\) 21.1628 + 23.5037i 0.960955 + 1.06725i
\(486\) 6.77143 4.91973i 0.307158 0.223163i
\(487\) −9.85511 7.16016i −0.446578 0.324458i 0.341665 0.939822i \(-0.389009\pi\)
−0.788243 + 0.615364i \(0.789009\pi\)
\(488\) −0.184869 0.134315i −0.00836864 0.00608017i
\(489\) 22.2928 16.1967i 1.00811 0.732438i
\(490\) −0.233733 2.22382i −0.0105590 0.100462i
\(491\) −7.29429 5.29961i −0.329187 0.239168i 0.410899 0.911681i \(-0.365215\pi\)
−0.740085 + 0.672513i \(0.765215\pi\)
\(492\) −4.97989 15.3265i −0.224511 0.690973i
\(493\) 9.72968 0.438203
\(494\) 5.60591 + 17.2532i 0.252222 + 0.776259i
\(495\) 4.16456 7.21323i 0.187183 0.324211i
\(496\) 0.0580002 0.178506i 0.00260429 0.00801517i
\(497\) 2.57120 7.91335i 0.115334 0.354962i
\(498\) −18.8135 + 13.6688i −0.843054 + 0.612515i
\(499\) 29.3922 1.31578 0.657888 0.753115i \(-0.271450\pi\)
0.657888 + 0.753115i \(0.271450\pi\)
\(500\) 3.45492 10.6331i 0.154508 0.475528i
\(501\) −38.5521 −1.72238
\(502\) 6.09444 4.42787i 0.272008 0.197625i
\(503\) 6.94020 21.3598i 0.309448 0.952384i −0.668531 0.743684i \(-0.733077\pi\)
0.977980 0.208700i \(-0.0669233\pi\)
\(504\) 0.255585 0.786610i 0.0113847 0.0350384i
\(505\) 6.95347 12.0438i 0.309425 0.535941i
\(506\) 7.04636 + 21.6865i 0.313249 + 0.964081i
\(507\) −14.0791 −0.625276
\(508\) 2.20623 + 6.79009i 0.0978858 + 0.301261i
\(509\) −11.9281 8.66629i −0.528705 0.384127i 0.291168 0.956672i \(-0.405956\pi\)
−0.819873 + 0.572545i \(0.805956\pi\)
\(510\) −2.12395 20.2080i −0.0940500 0.894826i
\(511\) −3.74957 + 2.72422i −0.165871 + 0.120513i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) −25.8979 18.8159i −1.14342 0.830743i
\(514\) 20.4291 14.8426i 0.901087 0.654678i
\(515\) −22.7838 25.3040i −1.00398 1.11503i
\(516\) 5.90977 + 4.29370i 0.260163 + 0.189019i
\(517\) 17.3482 + 53.3924i 0.762974 + 2.34819i
\(518\) −0.287330 −0.0126245
\(519\) 4.93373 + 15.1845i 0.216567 + 0.666524i
\(520\) −3.60436 4.00305i −0.158062 0.175545i
\(521\) −5.56559 + 17.1291i −0.243833 + 0.750441i 0.751993 + 0.659171i \(0.229093\pi\)
−0.995826 + 0.0912699i \(0.970907\pi\)
\(522\) 0.535358 1.64766i 0.0234320 0.0721162i
\(523\) −6.41620 + 4.66164i −0.280561 + 0.203839i −0.719162 0.694842i \(-0.755474\pi\)
0.438601 + 0.898682i \(0.355474\pi\)
\(524\) −9.01190 −0.393687
\(525\) −9.56773 + 2.03368i −0.417570 + 0.0887572i
\(526\) −31.6568 −1.38030
\(527\) −0.705334 + 0.512455i −0.0307248 + 0.0223229i
\(528\) −2.72256 + 8.37919i −0.118484 + 0.364657i
\(529\) 0.814438 2.50658i 0.0354104 0.108982i
\(530\) 21.2236 + 4.51122i 0.921895 + 0.195955i
\(531\) 0.823966 + 2.53591i 0.0357571 + 0.110049i
\(532\) −7.53062 −0.326494
\(533\) 6.13223 + 18.8731i 0.265616 + 0.817483i
\(534\) −22.5041 16.3502i −0.973849 0.707543i
\(535\) 15.0560 26.0777i 0.650927 1.12744i
\(536\) 5.13972 3.73423i 0.222002 0.161294i
\(537\) 19.2444 + 13.9818i 0.830455 + 0.603361i
\(538\) −1.31864 0.958049i −0.0568507 0.0413044i
\(539\) 3.64350 2.64716i 0.156937 0.114021i
\(540\) 9.29748 + 1.97624i 0.400100 + 0.0850439i
\(541\) 16.9688 + 12.3285i 0.729545 + 0.530045i 0.889419 0.457092i \(-0.151109\pi\)
−0.159875 + 0.987137i \(0.551109\pi\)
\(542\) −1.58422 4.87573i −0.0680481 0.209431i
\(543\) −12.1763 −0.522536
\(544\) 1.43540 + 4.41770i 0.0615422 + 0.189407i
\(545\) −5.84765 + 2.60354i −0.250486 + 0.111523i
\(546\) −1.45630 + 4.48202i −0.0623237 + 0.191813i
\(547\) −0.814074 + 2.50546i −0.0348073 + 0.107126i −0.966951 0.254964i \(-0.917936\pi\)
0.932143 + 0.362089i \(0.117936\pi\)
\(548\) 2.40770 1.74930i 0.102852 0.0747262i
\(549\) 0.188999 0.00806630
\(550\) 22.0260 4.68177i 0.939191 0.199631i
\(551\) −15.7739 −0.671992
\(552\) 8.01334 5.82203i 0.341070 0.247802i
\(553\) 0.224307 0.690347i 0.00953852 0.0293566i
\(554\) 4.16080 12.8056i 0.176775 0.544058i
\(555\) 0.131382 + 1.25001i 0.00557684 + 0.0530601i
\(556\) 6.33767 + 19.5053i 0.268777 + 0.827211i
\(557\) −24.7613 −1.04917 −0.524585 0.851358i \(-0.675780\pi\)
−0.524585 + 0.851358i \(0.675780\pi\)
\(558\) 0.0479715 + 0.147641i 0.00203079 + 0.00625014i
\(559\) −7.27727 5.28725i −0.307796 0.223627i
\(560\) 2.04275 0.909491i 0.0863219 0.0384330i
\(561\) 33.1088 24.0549i 1.39785 1.01560i
\(562\) −23.1647 16.8301i −0.977142 0.709935i
\(563\) −17.8374 12.9596i −0.751757 0.546184i 0.144614 0.989488i \(-0.453806\pi\)
−0.896371 + 0.443305i \(0.853806\pi\)
\(564\) 19.7289 14.3339i 0.830738 0.603567i
\(565\) 36.7962 16.3827i 1.54803 0.689227i
\(566\) 22.3988 + 16.2736i 0.941490 + 0.684032i
\(567\) −3.33652 10.2687i −0.140121 0.431247i
\(568\) 8.32059 0.349124
\(569\) 8.24923 + 25.3885i 0.345826 + 1.06434i 0.961140 + 0.276060i \(0.0890290\pi\)
−0.615315 + 0.788282i \(0.710971\pi\)
\(570\) 3.44338 + 32.7616i 0.144227 + 1.37223i
\(571\) 3.91494 12.0489i 0.163835 0.504233i −0.835113 0.550078i \(-0.814598\pi\)
0.998949 + 0.0458452i \(0.0145981\pi\)
\(572\) 3.35256 10.3181i 0.140177 0.431422i
\(573\) 5.67449 4.12276i 0.237055 0.172231i
\(574\) −8.23765 −0.343833
\(575\) −23.1271 10.2969i −0.964468 0.429409i
\(576\) 0.827091 0.0344621
\(577\) 2.53168 1.83937i 0.105395 0.0765742i −0.533839 0.845586i \(-0.679251\pi\)
0.639235 + 0.769012i \(0.279251\pi\)
\(578\) 1.41420 4.35246i 0.0588229 0.181038i
\(579\) 0.920814 2.83397i 0.0382677 0.117776i
\(580\) 4.27882 1.90505i 0.177668 0.0791030i
\(581\) 3.67333 + 11.3054i 0.152396 + 0.469025i
\(582\) 27.6702 1.14697
\(583\) 13.5043 + 41.5621i 0.559293 + 1.72133i
\(584\) −3.74957 2.72422i −0.155158 0.112729i
\(585\) 4.35788 + 0.926296i 0.180176 + 0.0382976i
\(586\) 10.4142 7.56634i 0.430205 0.312563i
\(587\) 17.1991 + 12.4959i 0.709884 + 0.515761i 0.883136 0.469117i \(-0.155428\pi\)
−0.173252 + 0.984877i \(0.555428\pi\)
\(588\) −1.58268 1.14988i −0.0652685 0.0474203i
\(589\) 1.14350 0.830801i 0.0471171 0.0342326i
\(590\) −3.60436 + 6.24294i −0.148389 + 0.257018i
\(591\) −37.9662 27.5841i −1.56172 1.13466i
\(592\) −0.0887898 0.273267i −0.00364924 0.0112312i
\(593\) 20.9829 0.861666 0.430833 0.902432i \(-0.358220\pi\)
0.430833 + 0.902432i \(0.358220\pi\)
\(594\) 5.91588 + 18.2072i 0.242732 + 0.747051i
\(595\) −10.1597 2.15950i −0.416506 0.0885310i
\(596\) 6.11523 18.8207i 0.250490 0.770928i
\(597\) −8.28854 + 25.5095i −0.339228 + 1.04404i
\(598\) −9.86761 + 7.16924i −0.403516 + 0.293172i
\(599\) 39.6199 1.61883 0.809413 0.587240i \(-0.199786\pi\)
0.809413 + 0.587240i \(0.199786\pi\)
\(600\) −4.89074 8.47101i −0.199664 0.345827i
\(601\) 5.63944 0.230038 0.115019 0.993363i \(-0.463307\pi\)
0.115019 + 0.993363i \(0.463307\pi\)
\(602\) 3.02090 2.19481i 0.123123 0.0894538i
\(603\) −1.62374 + 4.99737i −0.0661240 + 0.203509i
\(604\) −1.17496 + 3.61614i −0.0478083 + 0.147139i
\(605\) 13.8887 + 15.4250i 0.564657 + 0.627115i
\(606\) −3.75979 11.5714i −0.152731 0.470058i
\(607\) 26.2204 1.06425 0.532127 0.846665i \(-0.321393\pi\)
0.532127 + 0.846665i \(0.321393\pi\)
\(608\) −2.32709 7.16205i −0.0943760 0.290459i
\(609\) −3.31513 2.40858i −0.134336 0.0976007i
\(610\) 0.341903 + 0.379722i 0.0138433 + 0.0153745i
\(611\) −24.2942 + 17.6507i −0.982837 + 0.714073i
\(612\) −3.10814 2.25820i −0.125639 0.0912822i
\(613\) 24.2758 + 17.6374i 0.980490 + 0.712368i 0.957818 0.287375i \(-0.0927827\pi\)
0.0226718 + 0.999743i \(0.492783\pi\)
\(614\) −11.5922 + 8.42225i −0.467825 + 0.339895i
\(615\) 3.76667 + 35.8374i 0.151887 + 1.44510i
\(616\) 3.64350 + 2.64716i 0.146801 + 0.106657i
\(617\) −7.57277 23.3066i −0.304868 0.938288i −0.979726 0.200340i \(-0.935795\pi\)
0.674858 0.737948i \(-0.264205\pi\)
\(618\) −29.7896 −1.19831
\(619\) 12.4770 + 38.4003i 0.501493 + 1.54344i 0.806587 + 0.591115i \(0.201312\pi\)
−0.305094 + 0.952322i \(0.598688\pi\)
\(620\) −0.209847 + 0.363465i −0.00842765 + 0.0145971i
\(621\) 6.65089 20.4693i 0.266891 0.821406i
\(622\) 5.86084 18.0378i 0.234998 0.723250i
\(623\) −11.5034 + 8.35774i −0.460876 + 0.334846i
\(624\) −4.71267 −0.188658
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 22.7553 0.909485
\(627\) −53.6765 + 38.9983i −2.14363 + 1.55744i
\(628\) 2.63629 8.11368i 0.105200 0.323771i
\(629\) −0.412432 + 1.26934i −0.0164448 + 0.0506118i
\(630\) −0.924716 + 1.60165i −0.0368416 + 0.0638114i
\(631\) −2.71493 8.35570i −0.108080 0.332635i 0.882361 0.470573i \(-0.155953\pi\)
−0.990441 + 0.137938i \(0.955953\pi\)
\(632\) 0.725874 0.0288737
\(633\) −9.36439 28.8206i −0.372201 1.14552i
\(634\) −3.84720 2.79515i −0.152792 0.111010i
\(635\) −1.66874 15.8770i −0.0662219 0.630060i
\(636\) 15.3576 11.1579i 0.608966 0.442440i
\(637\) 1.94890 + 1.41596i 0.0772184 + 0.0561024i
\(638\) 7.63181 + 5.54483i 0.302146 + 0.219522i
\(639\) −5.56756 + 4.04507i −0.220249 + 0.160021i
\(640\) 1.49622 + 1.66172i 0.0591433 + 0.0656853i
\(641\) 31.6947 + 23.0275i 1.25187 + 0.909533i 0.998329 0.0577927i \(-0.0184062\pi\)
0.253536 + 0.967326i \(0.418406\pi\)
\(642\) −8.14088 25.0550i −0.321295 0.988844i
\(643\) −24.8946 −0.981747 −0.490873 0.871231i \(-0.663322\pi\)
−0.490873 + 0.871231i \(0.663322\pi\)
\(644\) −1.56460 4.81535i −0.0616540 0.189751i
\(645\) −10.9297 12.1387i −0.430357 0.477960i
\(646\) −10.8094 + 33.2680i −0.425292 + 1.30891i
\(647\) 9.26911 28.5274i 0.364406 1.12153i −0.585946 0.810350i \(-0.699277\pi\)
0.950352 0.311177i \(-0.100723\pi\)
\(648\) 8.73511 6.34643i 0.343148 0.249311i
\(649\) −14.5189 −0.569918
\(650\) 6.02244 + 10.4312i 0.236220 + 0.409144i
\(651\) 0.367182 0.0143910
\(652\) 11.3954 8.27925i 0.446279 0.324240i
\(653\) −2.43208 + 7.48518i −0.0951748 + 0.292918i −0.987299 0.158872i \(-0.949214\pi\)
0.892124 + 0.451790i \(0.149214\pi\)
\(654\) −1.73054 + 5.32607i −0.0676696 + 0.208266i
\(655\) 19.7109 + 4.18967i 0.770167 + 0.163704i
\(656\) −2.54557 7.83447i −0.0993879 0.305885i
\(657\) 3.83334 0.149553
\(658\) −3.85207 11.8554i −0.150169 0.462173i
\(659\) 28.4892 + 20.6986i 1.10978 + 0.806303i 0.982629 0.185580i \(-0.0594163\pi\)
0.127152 + 0.991883i \(0.459416\pi\)
\(660\) 9.85032 17.0613i 0.383423 0.664109i
\(661\) 22.5235 16.3643i 0.876064 0.636498i −0.0561435 0.998423i \(-0.517880\pi\)
0.932207 + 0.361925i \(0.117880\pi\)
\(662\) 13.8704 + 10.0775i 0.539090 + 0.391672i
\(663\) 17.7098 + 12.8670i 0.687793 + 0.499711i
\(664\) −9.61691 + 6.98710i −0.373209 + 0.271152i
\(665\) 16.4710 + 3.50102i 0.638719 + 0.135764i
\(666\) 0.192261 + 0.139686i 0.00744997 + 0.00541272i
\(667\) −3.27727 10.0864i −0.126896 0.390547i
\(668\) −19.7067 −0.762475
\(669\) 4.58040 + 14.0970i 0.177089 + 0.545022i
\(670\) −12.9777 + 5.77804i −0.501372 + 0.223225i
\(671\) −0.318017 + 0.978756i −0.0122769 + 0.0377845i
\(672\) 0.604528 1.86055i 0.0233202 0.0717722i
\(673\) −6.95703 + 5.05458i −0.268174 + 0.194840i −0.713743 0.700408i \(-0.753001\pi\)
0.445569 + 0.895248i \(0.353001\pi\)
\(674\) −11.4900 −0.442579
\(675\) −19.4167 8.64489i −0.747350 0.332742i
\(676\) −7.19683 −0.276801
\(677\) −10.7175 + 7.78672i −0.411907 + 0.299268i −0.774373 0.632729i \(-0.781935\pi\)
0.362466 + 0.931997i \(0.381935\pi\)
\(678\) 10.8894 33.5142i 0.418206 1.28710i
\(679\) 4.37080 13.4519i 0.167736 0.516238i
\(680\) −1.08570 10.3297i −0.0416347 0.396127i
\(681\) −9.65497 29.7149i −0.369979 1.13868i
\(682\) −0.845295 −0.0323680
\(683\) 5.42174 + 16.6864i 0.207457 + 0.638487i 0.999604 + 0.0281563i \(0.00896361\pi\)
−0.792146 + 0.610331i \(0.791036\pi\)
\(684\) 5.03897 + 3.66103i 0.192670 + 0.139983i
\(685\) −6.07939 + 2.70672i −0.232281 + 0.103418i
\(686\) −0.809017 + 0.587785i −0.0308884 + 0.0224417i
\(687\) −10.4524 7.59408i −0.398782 0.289732i
\(688\) 3.02090 + 2.19481i 0.115171 + 0.0836764i
\(689\) −18.9112 + 13.7398i −0.720461 + 0.523446i
\(690\) −20.2335 + 9.00854i −0.770276 + 0.342949i
\(691\) 12.8205 + 9.31463i 0.487714 + 0.354345i 0.804305 0.594217i \(-0.202538\pi\)
−0.316590 + 0.948562i \(0.602538\pi\)
\(692\) 2.52198 + 7.76184i 0.0958711 + 0.295061i
\(693\) −3.72490 −0.141497
\(694\) 9.34306 + 28.7550i 0.354658 + 1.09152i
\(695\) −4.79366 45.6086i −0.181834 1.73003i
\(696\) 1.26627 3.89717i 0.0479977 0.147722i
\(697\) −11.8243 + 36.3915i −0.447877 + 1.37842i
\(698\) −11.9539 + 8.68501i −0.452462 + 0.328733i
\(699\) 20.7857 0.786189
\(700\) −4.89074 + 1.03956i −0.184853 + 0.0392916i
\(701\) −9.44203 −0.356621 −0.178310 0.983974i \(-0.557063\pi\)
−0.178310 + 0.983974i \(0.557063\pi\)
\(702\) −8.28450 + 6.01904i −0.312678 + 0.227174i
\(703\) 0.668642 2.05787i 0.0252183 0.0776140i
\(704\) −1.39169 + 4.28319i −0.0524514 + 0.161429i
\(705\) −49.8151 + 22.1791i −1.87615 + 0.835314i
\(706\) −5.38940 16.5869i −0.202833 0.624255i
\(707\) −6.21937 −0.233904
\(708\) 1.94890 + 5.99811i 0.0732443 + 0.225423i
\(709\) 2.61377 + 1.89901i 0.0981621 + 0.0713189i 0.635784 0.771867i \(-0.280677\pi\)
−0.537622 + 0.843186i \(0.680677\pi\)
\(710\) −18.1988 3.86828i −0.682990 0.145174i
\(711\) −0.485705 + 0.352885i −0.0182153 + 0.0132342i
\(712\) −11.5034 8.35774i −0.431110 0.313220i
\(713\) 0.768823 + 0.558583i 0.0287927 + 0.0209191i
\(714\) −7.35160 + 5.34125i −0.275127 + 0.199891i
\(715\) −12.1297 + 21.0092i −0.453624 + 0.785699i
\(716\) 9.83714 + 7.14710i 0.367631 + 0.267100i
\(717\) 12.3357 + 37.9653i 0.460684 + 1.41784i
\(718\) 22.3898 0.835581
\(719\) −8.90964 27.4211i −0.332274 1.02263i −0.968049 0.250759i \(-0.919320\pi\)
0.635776 0.771874i \(-0.280680\pi\)
\(720\) −1.80902 0.384518i −0.0674181 0.0143302i
\(721\) −4.70558 + 14.4823i −0.175245 + 0.539349i
\(722\) 11.6531 35.8646i 0.433684 1.33474i
\(723\) 30.9365 22.4767i 1.15054 0.835918i
\(724\) −6.22417 −0.231319
\(725\) −10.2443 + 2.17750i −0.380464 + 0.0808702i
\(726\) 18.1594 0.673958
\(727\) −12.7469 + 9.26115i −0.472755 + 0.343477i −0.798514 0.601976i \(-0.794380\pi\)
0.325759 + 0.945453i \(0.394380\pi\)
\(728\) −0.744415 + 2.29107i −0.0275898 + 0.0849128i
\(729\) 4.94968 15.2335i 0.183321 0.564206i
\(730\) 6.93458 + 7.70163i 0.256660 + 0.285050i
\(731\) −5.35983 16.4958i −0.198240 0.610121i
\(732\) 0.447035 0.0165229
\(733\) 0.710114 + 2.18551i 0.0262287 + 0.0807235i 0.963314 0.268377i \(-0.0864872\pi\)
−0.937085 + 0.349100i \(0.886487\pi\)
\(734\) −21.3484 15.5106i −0.787986 0.572505i
\(735\) 2.92705 + 3.25082i 0.107966 + 0.119908i
\(736\) 4.09618 2.97605i 0.150987 0.109699i
\(737\) −23.1473 16.8175i −0.852642 0.619481i
\(738\) 5.51206 + 4.00475i 0.202902 + 0.147417i
\(739\) 15.6174 11.3467i 0.574495 0.417395i −0.262241 0.965003i \(-0.584461\pi\)
0.836735 + 0.547608i \(0.184461\pi\)
\(740\) 0.0671584 + 0.638969i 0.00246879 + 0.0234890i
\(741\) −28.7115 20.8601i −1.05474 0.766316i
\(742\) −2.99856 9.22861i −0.110080 0.338793i
\(743\) 40.2545 1.47679 0.738397 0.674366i \(-0.235583\pi\)
0.738397 + 0.674366i \(0.235583\pi\)
\(744\) 0.113466 + 0.349211i 0.00415985 + 0.0128027i
\(745\) −22.1251 + 38.3218i −0.810602 + 1.40400i
\(746\) 0.315619 0.971375i 0.0115556 0.0355646i
\(747\) 3.03818 9.35056i 0.111161 0.342119i
\(748\) 16.9242 12.2962i 0.618811 0.449592i
\(749\) −13.4665 −0.492055
\(750\) 6.75883 + 20.8016i 0.246798 + 0.759565i
\(751\) −52.5270 −1.91674 −0.958369 0.285533i \(-0.907829\pi\)
−0.958369 + 0.285533i \(0.907829\pi\)
\(752\) 10.0848 7.32707i 0.367756 0.267191i
\(753\) −4.55400 + 14.0158i −0.165957 + 0.510763i
\(754\) −1.55928 + 4.79897i −0.0567856 + 0.174768i
\(755\) 4.25103 7.36300i 0.154711 0.267967i
\(756\) −1.31359 4.04280i −0.0477746 0.147035i
\(757\) −27.5793 −1.00239 −0.501194 0.865335i \(-0.667106\pi\)
−0.501194 + 0.865335i \(0.667106\pi\)
\(758\) 5.89964 + 18.1572i 0.214284 + 0.659500i
\(759\) −36.0890 26.2202i −1.30995 0.951732i
\(760\) 1.76015 + 16.7467i 0.0638475 + 0.607468i
\(761\) 0.0751263 0.0545825i 0.00272333 0.00197861i −0.586423 0.810005i \(-0.699464\pi\)
0.589146 + 0.808027i \(0.299464\pi\)
\(762\) −11.2995 8.20960i −0.409340 0.297403i
\(763\) 2.31592 + 1.68261i 0.0838420 + 0.0609147i
\(764\) 2.90063 2.10743i 0.104941 0.0762442i
\(765\) 5.74830 + 6.38413i 0.207830 + 0.230819i
\(766\) −6.30252 4.57905i −0.227719 0.165448i
\(767\) −2.39987 7.38606i −0.0866545 0.266695i
\(768\) 1.95630 0.0705917
\(769\) −11.5265 35.4748i −0.415655 1.27925i −0.911664 0.410937i \(-0.865202\pi\)
0.496009 0.868317i \(-0.334798\pi\)
\(770\) −6.73840 7.48375i −0.242835 0.269696i
\(771\) −15.2654 + 46.9820i −0.549769 + 1.69201i
\(772\) 0.470693 1.44864i 0.0169406 0.0521378i
\(773\) 3.85348 2.79972i 0.138600 0.100699i −0.516325 0.856393i \(-0.672700\pi\)
0.654925 + 0.755694i \(0.272700\pi\)
\(774\) −3.08839 −0.111010
\(775\) 0.627955 0.697414i 0.0225568 0.0250519i
\(776\) 14.1442 0.507747
\(777\) 0.454750 0.330395i 0.0163141 0.0118529i
\(778\) 1.01338 3.11887i 0.0363315 0.111817i
\(779\) 19.1698 58.9984i 0.686828 2.11384i
\(780\) 10.3076 + 2.19094i 0.369070 + 0.0784483i
\(781\) −11.5797 35.6387i −0.414355 1.27525i
\(782\) −23.5186 −0.841023
\(783\) −2.75148 8.46820i −0.0983300 0.302629i
\(784\) −0.809017 0.587785i −0.0288935 0.0209923i
\(785\) −9.53820 + 16.5207i −0.340433 + 0.589647i
\(786\) 14.2629 10.3626i 0.508741 0.369622i
\(787\) 8.86766 + 6.44273i 0.316098 + 0.229659i 0.734509 0.678599i \(-0.237413\pi\)
−0.418411 + 0.908258i \(0.637413\pi\)
\(788\) −19.4072 14.1002i −0.691353 0.502297i
\(789\) 50.1025 36.4016i 1.78370 1.29593i
\(790\) −1.58764 0.337462i −0.0564855 0.0120064i
\(791\) −14.5729 10.5878i −0.518152 0.376460i
\(792\) −1.15106 3.54259i −0.0409010 0.125880i
\(793\) −0.550478 −0.0195480
\(794\) −3.52602 10.8520i −0.125134 0.385122i
\(795\) −38.7775 + 17.2648i −1.37530 + 0.612321i
\(796\) −4.23686 + 13.0397i −0.150171 + 0.462180i
\(797\) −4.32360 + 13.3067i −0.153150 + 0.471347i −0.997969 0.0637057i \(-0.979708\pi\)
0.844819 + 0.535052i \(0.179708\pi\)
\(798\) 11.9185 8.65933i 0.421912 0.306537i
\(799\) −57.9031 −2.04846
\(800\) −2.50000 4.33013i −0.0883883 0.153093i
\(801\) 11.7604 0.415535
\(802\) 12.0203 8.73323i 0.424450 0.308381i
\(803\) −6.45012 + 19.8514i −0.227620 + 0.700542i
\(804\) −3.84060 + 11.8201i −0.135447 + 0.416864i
\(805\) 1.18343 + 11.2595i 0.0417103 + 0.396847i
\(806\) −0.139721 0.430018i −0.00492147 0.0151467i
\(807\) 3.18863 0.112245
\(808\) −1.92189 5.91498i −0.0676119 0.208088i
\(809\) 35.7437 + 25.9693i 1.25668 + 0.913032i 0.998590 0.0530881i \(-0.0169064\pi\)
0.258091 + 0.966120i \(0.416906\pi\)
\(810\) −22.0560 + 9.81995i −0.774968 + 0.345038i
\(811\) 42.0941 30.5831i 1.47812 1.07392i 0.499968 0.866044i \(-0.333345\pi\)
0.978155 0.207875i \(-0.0666548\pi\)
\(812\) −1.69460 1.23120i −0.0594687 0.0432065i
\(813\) 8.11382 + 5.89504i 0.284564 + 0.206748i
\(814\) −1.04689 + 0.760607i −0.0366933 + 0.0266593i
\(815\) −28.7732 + 12.8106i −1.00788 + 0.448737i
\(816\) −7.35160 5.34125i −0.257358 0.186981i
\(817\) 8.68944 + 26.7433i 0.304005 + 0.935631i
\(818\) −20.8386 −0.728605
\(819\) −0.615699 1.89493i −0.0215143 0.0662141i
\(820\) 1.92541 + 18.3190i 0.0672382 + 0.639728i
\(821\) −15.3414 + 47.2159i −0.535417 + 1.64784i 0.207329 + 0.978271i \(0.433523\pi\)
−0.742746 + 0.669573i \(0.766477\pi\)
\(822\) −1.79912 + 5.53714i −0.0627517 + 0.193130i
\(823\) −28.3695 + 20.6117i −0.988899 + 0.718477i −0.959680 0.281096i \(-0.909302\pi\)
−0.0292191 + 0.999573i \(0.509302\pi\)
\(824\) −15.2276 −0.530478
\(825\) −29.4765 + 32.7370i −1.02624 + 1.13976i
\(826\) 3.22384 0.112172
\(827\) −24.5230 + 17.8170i −0.852747 + 0.619557i −0.925902 0.377763i \(-0.876693\pi\)
0.0731549 + 0.997321i \(0.476693\pi\)
\(828\) −1.29407 + 3.98273i −0.0449720 + 0.138410i
\(829\) 14.5270 44.7094i 0.504542 1.55282i −0.296996 0.954879i \(-0.595985\pi\)
0.801538 0.597943i \(-0.204015\pi\)
\(830\) 24.2825 10.8113i 0.842858 0.375264i
\(831\) 8.13975 + 25.0516i 0.282365 + 0.869029i
\(832\) −2.40898 −0.0835163
\(833\) 1.43540 + 4.41770i 0.0497336 + 0.153064i
\(834\) −32.4593 23.5831i −1.12397 0.816615i
\(835\) 43.1026 + 9.16173i 1.49163 + 0.317055i
\(836\) −27.4378 + 19.9347i −0.948957 + 0.689458i
\(837\) 0.645477 + 0.468967i 0.0223110 + 0.0162099i
\(838\) 5.65983 + 4.11211i 0.195516 + 0.142050i
\(839\) −25.8348 + 18.7701i −0.891916 + 0.648015i −0.936377 0.350996i \(-0.885843\pi\)
0.0444609 + 0.999011i \(0.485843\pi\)
\(840\) −2.18720 + 3.78835i −0.0754657 + 0.130710i
\(841\) 19.9119 + 14.4669i 0.686618 + 0.498857i
\(842\) −1.22190 3.76061i −0.0421093 0.129599i
\(843\) 56.0148 1.92925
\(844\) −4.78680 14.7323i −0.164768 0.507105i
\(845\) 15.7409 + 3.34584i 0.541505 + 0.115100i
\(846\) −3.18601 + 9.80553i −0.109537 + 0.337121i
\(847\) 2.86846 8.82821i 0.0985615 0.303341i
\(848\) 7.85032 5.70359i 0.269581 0.195862i
\(849\) −54.1627 −1.85886
\(850\) −2.42770 + 23.0980i −0.0832693 + 0.792255i
\(851\) 1.45480 0.0498698
\(852\) −13.1688 + 9.56769i −0.451156 + 0.327784i
\(853\) 12.2775 37.7864i 0.420375 1.29378i −0.486979 0.873414i \(-0.661901\pi\)
0.907354 0.420367i \(-0.138099\pi\)
\(854\) 0.0706138 0.217327i 0.00241635 0.00743677i
\(855\) −9.31923 10.3501i −0.318711 0.353964i
\(856\) −4.16137 12.8074i −0.142233 0.437748i
\(857\) 6.35093 0.216944 0.108472 0.994100i \(-0.465404\pi\)
0.108472 + 0.994100i \(0.465404\pi\)
\(858\) 6.55859 + 20.1853i 0.223907 + 0.689114i
\(859\) 23.5308 + 17.0961i 0.802862 + 0.583313i 0.911752 0.410741i \(-0.134730\pi\)
−0.108891 + 0.994054i \(0.534730\pi\)
\(860\) −5.58694 6.20493i −0.190513 0.211586i
\(861\) 13.0375 9.47232i 0.444318 0.322816i
\(862\) 23.9891 + 17.4291i 0.817072 + 0.593637i
\(863\) 22.9718 + 16.6900i 0.781969 + 0.568134i 0.905569 0.424198i \(-0.139444\pi\)
−0.123600 + 0.992332i \(0.539444\pi\)
\(864\) 3.43901 2.49859i 0.116998 0.0850037i
\(865\) −1.90756 18.1492i −0.0648590 0.617092i
\(866\) −1.22437 0.889560i −0.0416060 0.0302285i
\(867\) 2.76659 + 8.51469i 0.0939583 + 0.289174i
\(868\) 0.187693 0.00637071
\(869\) −1.01019 3.10906i −0.0342685 0.105468i
\(870\) −4.58140 + 7.93521i −0.155324 + 0.269029i
\(871\) 4.72930 14.5553i 0.160246 0.493187i
\(872\) −0.884603 + 2.72253i −0.0299564 + 0.0921964i
\(873\) −9.46431 + 6.87623i −0.320318 + 0.232725i
\(874\) 38.1287 1.28972
\(875\) 11.1803 0.377964
\(876\) 9.06690 0.306342
\(877\) 41.4774 30.1351i 1.40059 1.01759i 0.405983 0.913880i \(-0.366929\pi\)
0.994608 0.103709i \(-0.0330710\pi\)
\(878\) −6.51298 + 20.0449i −0.219802 + 0.676482i
\(879\) −7.78187 + 23.9501i −0.262476 + 0.807818i
\(880\) 5.03519 8.72121i 0.169736 0.293992i
\(881\) 11.3071 + 34.7996i 0.380945 + 1.17243i 0.939380 + 0.342879i \(0.111402\pi\)
−0.558435 + 0.829548i \(0.688598\pi\)
\(882\) 0.827091 0.0278496
\(883\) −0.435313 1.33976i −0.0146495 0.0450864i 0.943465 0.331473i \(-0.107546\pi\)
−0.958114 + 0.286387i \(0.907546\pi\)
\(884\) 9.05274 + 6.57720i 0.304477 + 0.221215i
\(885\) −1.47410 14.0251i −0.0495514 0.471450i
\(886\) 23.2453 16.8887i 0.780941 0.567387i
\(887\) −24.5534 17.8391i −0.824422 0.598978i 0.0935535 0.995614i \(-0.470177\pi\)
−0.917976 + 0.396636i \(0.870177\pi\)
\(888\) 0.454750 + 0.330395i 0.0152604 + 0.0110873i
\(889\) −5.77599 + 4.19651i −0.193721 + 0.140746i
\(890\) 21.2748 + 23.6281i 0.713134 + 0.792016i
\(891\) −39.3396 28.5819i −1.31793 0.957529i
\(892\) 2.34137 + 7.20598i 0.0783947 + 0.241274i
\(893\) 93.8734 3.14135
\(894\) 11.9632 + 36.8189i 0.400109 + 1.23141i
\(895\) −18.1931 20.2055i −0.608129 0.675396i
\(896\) 0.309017 0.951057i 0.0103235 0.0317726i
\(897\) 7.37345 22.6932i 0.246192 0.757702i
\(898\) 24.4693 17.7780i 0.816551 0.593259i
\(899\) 0.393148 0.0131122
\(900\) 3.77793 + 1.68204i 0.125931 + 0.0560680i
\(901\) −45.0734 −1.50161
\(902\) −30.0139 + 21.8064i −0.999352 + 0.726072i
\(903\) −2.25733 + 6.94735i −0.0751192 + 0.231193i
\(904\) 5.56635 17.1315i 0.185134 0.569784i
\(905\) 13.6135 + 2.89365i 0.452529 + 0.0961881i
\(906\) −2.29856 7.07424i −0.0763646 0.235026i
\(907\) −4.00572 −0.133008 −0.0665038 0.997786i \(-0.521184\pi\)
−0.0665038 + 0.997786i \(0.521184\pi\)
\(908\) −4.93533 15.1894i −0.163785 0.504078i
\(909\) 4.16157 + 3.02356i 0.138031 + 0.100285i
\(910\) 2.69332 4.66496i 0.0892826 0.154642i
\(911\) −31.0976 + 22.5937i −1.03031 + 0.748564i −0.968371 0.249516i \(-0.919728\pi\)
−0.0619389 + 0.998080i \(0.519728\pi\)
\(912\) 11.9185 + 8.65933i 0.394662 + 0.286739i
\(913\) 43.3109 + 31.4672i 1.43338 + 1.04141i
\(914\) −2.62589 + 1.90782i −0.0868568 + 0.0631052i
\(915\) −0.977757 0.207829i −0.0323236 0.00687060i
\(916\) −5.34293 3.88187i −0.176535 0.128260i
\(917\) −2.78483 8.57082i −0.0919632 0.283034i
\(918\) −19.7454 −0.651695
\(919\) −5.92683 18.2409i −0.195508 0.601712i −0.999970 0.00770792i \(-0.997546\pi\)
0.804462 0.594004i \(-0.202454\pi\)
\(920\) −10.3428 + 4.60490i −0.340991 + 0.151819i
\(921\) 8.66216 26.6594i 0.285428 0.878457i
\(922\) −8.01261 + 24.6603i −0.263881 + 0.812143i
\(923\) 16.2160 11.7816i 0.533757 0.387797i
\(924\) −8.81040 −0.289841
\(925\) 0.150171 1.42878i 0.00493758 0.0469779i
\(926\) −6.34212 −0.208415
\(927\) 10.1892 7.40291i 0.334658 0.243144i
\(928\) 0.647278 1.99212i 0.0212479 0.0653945i
\(929\) 6.79315 20.9072i 0.222876 0.685942i −0.775624 0.631195i \(-0.782565\pi\)
0.998500 0.0547471i \(-0.0174352\pi\)
\(930\) −0.0858225 0.816547i −0.00281423 0.0267756i
\(931\) −2.32709 7.16205i −0.0762673 0.234727i
\(932\) 10.6251 0.348035
\(933\) 11.4655 + 35.2873i 0.375365 + 1.15525i
\(934\) −5.59257 4.06324i −0.182994 0.132953i
\(935\) −42.7333 + 19.0261i −1.39753 + 0.622219i
\(936\) 1.61192 1.17113i 0.0526873 0.0382795i
\(937\) −32.9163 23.9151i −1.07533 0.781273i −0.0984674 0.995140i \(-0.531394\pi\)
−0.976863 + 0.213867i \(0.931394\pi\)
\(938\) 5.13972 + 3.73423i 0.167818 + 0.121927i
\(939\) −36.0143 + 26.1659i −1.17528 + 0.853892i
\(940\) −25.4640 + 11.3373i −0.830544 + 0.369782i
\(941\) 3.54607 + 2.57637i 0.115599 + 0.0839874i 0.644083 0.764956i \(-0.277239\pi\)
−0.528484 + 0.848943i \(0.677239\pi\)
\(942\) 5.15737 + 15.8728i 0.168036 + 0.517162i
\(943\) 41.7085 1.35822
\(944\) 0.996222 + 3.06605i 0.0324242 + 0.0997916i
\(945\) 0.993563 + 9.45312i 0.0323206 + 0.307510i
\(946\) 5.19663 15.9936i 0.168957 0.519996i
\(947\) −4.99793 + 15.3820i −0.162411 + 0.499849i −0.998836 0.0482317i \(-0.984641\pi\)
0.836425 + 0.548081i \(0.184641\pi\)
\(948\) −1.14882 + 0.834669i −0.0373121 + 0.0271088i
\(949\) −11.1650 −0.362430
\(950\) 3.93582 37.4469i 0.127695 1.21494i
\(951\) 9.30296 0.301669
\(952\) −3.75792 + 2.73029i −0.121795 + 0.0884892i
\(953\) 17.8737 55.0095i 0.578985 1.78193i −0.0432036 0.999066i \(-0.513756\pi\)
0.622189 0.782867i \(-0.286244\pi\)
\(954\) −2.48008 + 7.63290i −0.0802955 + 0.247124i
\(955\) −7.32403 + 3.26087i −0.237000 + 0.105519i
\(956\) 6.30562 + 19.4067i 0.203938 + 0.627658i
\(957\) −18.4546 −0.596552
\(958\) −8.14439 25.0659i −0.263133 0.809841i
\(959\) 2.40770 + 1.74930i 0.0777487 + 0.0564877i
\(960\) −4.27882 0.909491i −0.138098 0.0293537i
\(961\) 25.0510 18.2006i 0.808098 0.587117i
\(962\) −0.559978 0.406848i −0.0180544 0.0131173i
\(963\) 9.01084 + 6.54676i 0.290370 + 0.210966i
\(964\) 15.8138 11.4894i 0.509330 0.370050i
\(965\) −1.70298 + 2.94965i −0.0548209 + 0.0949526i
\(966\) 8.01334 + 5.82203i 0.257825 + 0.187321i
\(967\) −7.85115 24.1634i −0.252476 0.777041i −0.994316 0.106465i \(-0.966047\pi\)
0.741840 0.670576i \(-0.233953\pi\)
\(968\) 9.28253 0.298352
\(969\) −21.1465 65.0821i −0.679322 2.09074i
\(970\) −30.9362 6.57570i −0.993303 0.211133i
\(971\) 1.34111 4.12751i 0.0430382 0.132458i −0.927229 0.374496i \(-0.877816\pi\)
0.970267 + 0.242038i \(0.0778158\pi\)
\(972\) −2.58645 + 7.96029i −0.0829606 + 0.255326i
\(973\) −16.5922 + 12.0550i −0.531923 + 0.386464i
\(974\) 12.1816 0.390323
\(975\) −21.5262 9.58408i −0.689390 0.306936i
\(976\) 0.228511 0.00731446
\(977\) −13.9717 + 10.1510i −0.446995 + 0.324761i −0.788408 0.615153i \(-0.789094\pi\)
0.341413 + 0.939913i \(0.389094\pi\)
\(978\) −8.51509 + 26.2067i −0.272282 + 0.837999i
\(979\) −19.7885 + 60.9029i −0.632445 + 1.94646i
\(980\) 1.49622 + 1.66172i 0.0477950 + 0.0530818i
\(981\) −0.731647 2.25178i −0.0233597 0.0718937i
\(982\) 9.01624 0.287720
\(983\) −12.2692 37.7608i −0.391328 1.20438i −0.931785 0.363011i \(-0.881749\pi\)
0.540457 0.841371i \(-0.318251\pi\)
\(984\) 13.0375 + 9.47232i 0.415621 + 0.301966i
\(985\) 35.8923 + 39.8624i 1.14362 + 1.27012i
\(986\) −7.87148 + 5.71896i −0.250679 + 0.182129i
\(987\) 19.7289 + 14.3339i 0.627979 + 0.456253i
\(988\) −14.6765 10.6631i −0.466920 0.339238i
\(989\) −15.2953 + 11.1127i −0.486362 + 0.353362i
\(990\) 0.870631 + 8.28350i 0.0276705 + 0.263267i
\(991\) 25.6675 + 18.6485i 0.815355 + 0.592390i 0.915378 0.402595i \(-0.131892\pi\)
−0.100023 + 0.994985i \(0.531892\pi\)
\(992\) 0.0580002 + 0.178506i 0.00184151 + 0.00566758i
\(993\) −33.5403 −1.06437
\(994\) 2.57120 + 7.91335i 0.0815536 + 0.250996i
\(995\) 15.3291 26.5508i 0.485965 0.841716i
\(996\) 7.18613 22.1166i 0.227701 0.700792i
\(997\) −10.2160 + 31.4417i −0.323545 + 0.995768i 0.648549 + 0.761173i \(0.275376\pi\)
−0.972093 + 0.234595i \(0.924624\pi\)
\(998\) −23.7788 + 17.2763i −0.752705 + 0.546872i
\(999\) 1.22140 0.0386433
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.h.a.211.2 yes 8
25.4 even 10 8750.2.a.e.1.1 4
25.16 even 5 inner 350.2.h.a.141.2 8
25.21 even 5 8750.2.a.j.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.h.a.141.2 8 25.16 even 5 inner
350.2.h.a.211.2 yes 8 1.1 even 1 trivial
8750.2.a.e.1.1 4 25.4 even 10
8750.2.a.j.1.4 4 25.21 even 5