Properties

Label 52.2.f.b.47.1
Level $52$
Weight $2$
Character 52.47
Analytic conductor $0.415$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [52,2,Mod(31,52)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(52, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("52.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 52.f (of order \(4\), degree \(2\), 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: \(0.415222090511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.1
Root \(0.500000 - 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 52.47
Dual form 52.2.f.b.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37456 - 0.332548i) q^{2} +1.47363i q^{3} +(1.77882 + 0.914214i) q^{4} +(0.707107 + 0.707107i) q^{5} +(0.490051 - 2.02559i) q^{6} +(1.04201 + 1.04201i) q^{7} +(-2.14108 - 1.84818i) q^{8} +0.828427 q^{9} +O(q^{10})\) \(q+(-1.37456 - 0.332548i) q^{2} +1.47363i q^{3} +(1.77882 + 0.914214i) q^{4} +(0.707107 + 0.707107i) q^{5} +(0.490051 - 2.02559i) q^{6} +(1.04201 + 1.04201i) q^{7} +(-2.14108 - 1.84818i) q^{8} +0.828427 q^{9} +(-0.736813 - 1.20711i) q^{10} +(-3.55765 - 3.55765i) q^{11} +(-1.34721 + 2.62132i) q^{12} +(-3.53553 - 0.707107i) q^{13} +(-1.08579 - 1.77882i) q^{14} +(-1.04201 + 1.04201i) q^{15} +(2.32843 + 3.25245i) q^{16} +0.171573i q^{17} +(-1.13872 - 0.275492i) q^{18} +(5.03127 - 5.03127i) q^{19} +(0.611372 + 1.90426i) q^{20} +(-1.53553 + 1.53553i) q^{21} +(3.70711 + 6.07328i) q^{22} +2.08402 q^{23} +(2.72353 - 3.15515i) q^{24} -4.00000i q^{25} +(4.62465 + 2.14769i) q^{26} +5.64167i q^{27} +(0.900933 + 2.80617i) q^{28} -3.41421 q^{29} +(1.77882 - 1.08579i) q^{30} +(-2.08402 + 2.08402i) q^{31} +(-2.11896 - 5.24500i) q^{32} +(5.24264 - 5.24264i) q^{33} +(0.0570562 - 0.235837i) q^{34} +1.47363i q^{35} +(1.47363 + 0.757359i) q^{36} +(-6.12132 + 6.12132i) q^{37} +(-8.58892 + 5.24264i) q^{38} +(1.04201 - 5.21005i) q^{39} +(-0.207107 - 2.82083i) q^{40} +(4.24264 + 4.24264i) q^{41} +(2.62132 - 1.60004i) q^{42} -5.64167 q^{43} +(-3.07598 - 9.58088i) q^{44} +(0.585786 + 0.585786i) q^{45} +(-2.86461 - 0.693037i) q^{46} +(-1.04201 - 1.04201i) q^{47} +(-4.79289 + 3.43123i) q^{48} -4.82843i q^{49} +(-1.33019 + 5.49824i) q^{50} -0.252834 q^{51} +(-5.64264 - 4.49005i) q^{52} +8.24264 q^{53} +(1.87613 - 7.75481i) q^{54} -5.03127i q^{55} +(-0.305198 - 4.15685i) q^{56} +(7.41421 + 7.41421i) q^{57} +(4.69304 + 1.13539i) q^{58} +(7.11529 + 7.11529i) q^{59} +(-2.80617 + 0.900933i) q^{60} -4.82843 q^{61} +(3.55765 - 2.17157i) q^{62} +(0.863230 + 0.863230i) q^{63} +(1.16843 + 7.91421i) q^{64} +(-2.00000 - 3.00000i) q^{65} +(-8.94975 + 5.46289i) q^{66} +(-1.47363 + 1.47363i) q^{67} +(-0.156854 + 0.305198i) q^{68} +3.07107i q^{69} +(0.490051 - 2.02559i) q^{70} +(-9.02054 + 9.02054i) q^{71} +(-1.77373 - 1.53109i) q^{72} +(1.65685 - 1.65685i) q^{73} +(10.4497 - 6.37848i) q^{74} +5.89450 q^{75} +(13.5494 - 4.35009i) q^{76} -7.41421i q^{77} +(-3.16490 + 6.81501i) q^{78} -0.863230i q^{79} +(-0.653382 + 3.94628i) q^{80} -5.82843 q^{81} +(-4.42088 - 7.24264i) q^{82} +(-0.610396 + 0.610396i) q^{83} +(-4.13525 + 1.32764i) q^{84} +(-0.121320 + 0.121320i) q^{85} +(7.75481 + 1.87613i) q^{86} -5.03127i q^{87} +(1.04201 + 14.1924i) q^{88} +(-2.24264 + 2.24264i) q^{89} +(-0.610396 - 1.00000i) q^{90} +(-2.94725 - 4.42088i) q^{91} +(3.70711 + 1.90524i) q^{92} +(-3.07107 - 3.07107i) q^{93} +(1.08579 + 1.77882i) q^{94} +7.11529 q^{95} +(7.72916 - 3.12256i) q^{96} +(-2.41421 - 2.41421i) q^{97} +(-1.60568 + 6.63696i) q^{98} +(-2.94725 - 2.94725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40} + 4 q^{42} - 28 q^{44} + 16 q^{45} - 20 q^{46} - 44 q^{48} - 16 q^{50} + 8 q^{52} + 32 q^{53} - 32 q^{54} + 48 q^{57} + 12 q^{58} - 12 q^{60} - 16 q^{61} - 16 q^{65} - 32 q^{66} + 44 q^{68} + 8 q^{70} + 16 q^{72} - 32 q^{73} + 44 q^{74} + 32 q^{76} + 40 q^{78} + 16 q^{80} - 24 q^{81} - 48 q^{84} + 16 q^{85} + 32 q^{86} + 16 q^{89} + 24 q^{92} + 32 q^{93} + 20 q^{94} - 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37456 0.332548i −0.971960 0.235147i
\(3\) 1.47363i 0.850798i 0.905006 + 0.425399i \(0.139866\pi\)
−0.905006 + 0.425399i \(0.860134\pi\)
\(4\) 1.77882 + 0.914214i 0.889412 + 0.457107i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i 0.847316 0.531089i \(-0.178217\pi\)
−0.531089 + 0.847316i \(0.678217\pi\)
\(6\) 0.490051 2.02559i 0.200063 0.826942i
\(7\) 1.04201 + 1.04201i 0.393843 + 0.393843i 0.876055 0.482212i \(-0.160166\pi\)
−0.482212 + 0.876055i \(0.660166\pi\)
\(8\) −2.14108 1.84818i −0.756985 0.653432i
\(9\) 0.828427 0.276142
\(10\) −0.736813 1.20711i −0.233001 0.381721i
\(11\) −3.55765 3.55765i −1.07267 1.07267i −0.997144 0.0755273i \(-0.975936\pi\)
−0.0755273 0.997144i \(-0.524064\pi\)
\(12\) −1.34721 + 2.62132i −0.388906 + 0.756710i
\(13\) −3.53553 0.707107i −0.980581 0.196116i
\(14\) −1.08579 1.77882i −0.290189 0.475411i
\(15\) −1.04201 + 1.04201i −0.269046 + 0.269046i
\(16\) 2.32843 + 3.25245i 0.582107 + 0.813112i
\(17\) 0.171573i 0.0416125i 0.999784 + 0.0208063i \(0.00662332\pi\)
−0.999784 + 0.0208063i \(0.993377\pi\)
\(18\) −1.13872 0.275492i −0.268399 0.0649340i
\(19\) 5.03127 5.03127i 1.15425 1.15425i 0.168562 0.985691i \(-0.446088\pi\)
0.985691 0.168562i \(-0.0539124\pi\)
\(20\) 0.611372 + 1.90426i 0.136707 + 0.425807i
\(21\) −1.53553 + 1.53553i −0.335081 + 0.335081i
\(22\) 3.70711 + 6.07328i 0.790358 + 1.29483i
\(23\) 2.08402 0.434549 0.217274 0.976111i \(-0.430283\pi\)
0.217274 + 0.976111i \(0.430283\pi\)
\(24\) 2.72353 3.15515i 0.555939 0.644042i
\(25\) 4.00000i 0.800000i
\(26\) 4.62465 + 2.14769i 0.906969 + 0.421198i
\(27\) 5.64167i 1.08574i
\(28\) 0.900933 + 2.80617i 0.170260 + 0.530317i
\(29\) −3.41421 −0.634004 −0.317002 0.948425i \(-0.602676\pi\)
−0.317002 + 0.948425i \(0.602676\pi\)
\(30\) 1.77882 1.08579i 0.324767 0.198237i
\(31\) −2.08402 + 2.08402i −0.374301 + 0.374301i −0.869041 0.494740i \(-0.835263\pi\)
0.494740 + 0.869041i \(0.335263\pi\)
\(32\) −2.11896 5.24500i −0.374584 0.927193i
\(33\) 5.24264 5.24264i 0.912627 0.912627i
\(34\) 0.0570562 0.235837i 0.00978506 0.0404457i
\(35\) 1.47363i 0.249088i
\(36\) 1.47363 + 0.757359i 0.245604 + 0.126227i
\(37\) −6.12132 + 6.12132i −1.00634 + 1.00634i −0.00635908 + 0.999980i \(0.502024\pi\)
−0.999980 + 0.00635908i \(0.997976\pi\)
\(38\) −8.58892 + 5.24264i −1.39331 + 0.850469i
\(39\) 1.04201 5.21005i 0.166855 0.834276i
\(40\) −0.207107 2.82083i −0.0327465 0.446013i
\(41\) 4.24264 + 4.24264i 0.662589 + 0.662589i 0.955990 0.293400i \(-0.0947869\pi\)
−0.293400 + 0.955990i \(0.594787\pi\)
\(42\) 2.62132 1.60004i 0.404479 0.246892i
\(43\) −5.64167 −0.860346 −0.430173 0.902746i \(-0.641548\pi\)
−0.430173 + 0.902746i \(0.641548\pi\)
\(44\) −3.07598 9.58088i −0.463721 1.44437i
\(45\) 0.585786 + 0.585786i 0.0873239 + 0.0873239i
\(46\) −2.86461 0.693037i −0.422364 0.102183i
\(47\) −1.04201 1.04201i −0.151993 0.151993i 0.627015 0.779007i \(-0.284277\pi\)
−0.779007 + 0.627015i \(0.784277\pi\)
\(48\) −4.79289 + 3.43123i −0.691795 + 0.495255i
\(49\) 4.82843i 0.689775i
\(50\) −1.33019 + 5.49824i −0.188118 + 0.777568i
\(51\) −0.252834 −0.0354039
\(52\) −5.64264 4.49005i −0.782494 0.622658i
\(53\) 8.24264 1.13221 0.566107 0.824332i \(-0.308449\pi\)
0.566107 + 0.824332i \(0.308449\pi\)
\(54\) 1.87613 7.75481i 0.255308 1.05530i
\(55\) 5.03127i 0.678417i
\(56\) −0.305198 4.15685i −0.0407838 0.555483i
\(57\) 7.41421 + 7.41421i 0.982037 + 0.982037i
\(58\) 4.69304 + 1.13539i 0.616226 + 0.149084i
\(59\) 7.11529 + 7.11529i 0.926332 + 0.926332i 0.997467 0.0711343i \(-0.0226619\pi\)
−0.0711343 + 0.997467i \(0.522662\pi\)
\(60\) −2.80617 + 0.900933i −0.362275 + 0.116310i
\(61\) −4.82843 −0.618217 −0.309108 0.951027i \(-0.600031\pi\)
−0.309108 + 0.951027i \(0.600031\pi\)
\(62\) 3.55765 2.17157i 0.451822 0.275790i
\(63\) 0.863230 + 0.863230i 0.108757 + 0.108757i
\(64\) 1.16843 + 7.91421i 0.146053 + 0.989277i
\(65\) −2.00000 3.00000i −0.248069 0.372104i
\(66\) −8.94975 + 5.46289i −1.10164 + 0.672435i
\(67\) −1.47363 + 1.47363i −0.180032 + 0.180032i −0.791370 0.611338i \(-0.790632\pi\)
0.611338 + 0.791370i \(0.290632\pi\)
\(68\) −0.156854 + 0.305198i −0.0190214 + 0.0370107i
\(69\) 3.07107i 0.369713i
\(70\) 0.490051 2.02559i 0.0585723 0.242104i
\(71\) −9.02054 + 9.02054i −1.07054 + 1.07054i −0.0732252 + 0.997315i \(0.523329\pi\)
−0.997315 + 0.0732252i \(0.976671\pi\)
\(72\) −1.77373 1.53109i −0.209036 0.180440i
\(73\) 1.65685 1.65685i 0.193920 0.193920i −0.603467 0.797388i \(-0.706215\pi\)
0.797388 + 0.603467i \(0.206215\pi\)
\(74\) 10.4497 6.37848i 1.21476 0.741483i
\(75\) 5.89450 0.680639
\(76\) 13.5494 4.35009i 1.55422 0.498989i
\(77\) 7.41421i 0.844928i
\(78\) −3.16490 + 6.81501i −0.358354 + 0.771648i
\(79\) 0.863230i 0.0971210i −0.998820 0.0485605i \(-0.984537\pi\)
0.998820 0.0485605i \(-0.0154634\pi\)
\(80\) −0.653382 + 3.94628i −0.0730504 + 0.441207i
\(81\) −5.82843 −0.647603
\(82\) −4.42088 7.24264i −0.488204 0.799816i
\(83\) −0.610396 + 0.610396i −0.0669996 + 0.0669996i −0.739813 0.672813i \(-0.765086\pi\)
0.672813 + 0.739813i \(0.265086\pi\)
\(84\) −4.13525 + 1.32764i −0.451193 + 0.144857i
\(85\) −0.121320 + 0.121320i −0.0131590 + 0.0131590i
\(86\) 7.75481 + 1.87613i 0.836222 + 0.202308i
\(87\) 5.03127i 0.539409i
\(88\) 1.04201 + 14.1924i 0.111079 + 1.51291i
\(89\) −2.24264 + 2.24264i −0.237719 + 0.237719i −0.815905 0.578186i \(-0.803761\pi\)
0.578186 + 0.815905i \(0.303761\pi\)
\(90\) −0.610396 1.00000i −0.0643414 0.105409i
\(91\) −2.94725 4.42088i −0.308956 0.463434i
\(92\) 3.70711 + 1.90524i 0.386493 + 0.198635i
\(93\) −3.07107 3.07107i −0.318455 0.318455i
\(94\) 1.08579 + 1.77882i 0.111990 + 0.183472i
\(95\) 7.11529 0.730014
\(96\) 7.72916 3.12256i 0.788854 0.318695i
\(97\) −2.41421 2.41421i −0.245126 0.245126i 0.573841 0.818967i \(-0.305453\pi\)
−0.818967 + 0.573841i \(0.805453\pi\)
\(98\) −1.60568 + 6.63696i −0.162199 + 0.670434i
\(99\) −2.94725 2.94725i −0.296210 0.296210i
\(100\) 3.65685 7.11529i 0.365685 0.711529i
\(101\) 5.17157i 0.514591i 0.966333 + 0.257295i \(0.0828313\pi\)
−0.966333 + 0.257295i \(0.917169\pi\)
\(102\) 0.347535 + 0.0840795i 0.0344111 + 0.00832511i
\(103\) 15.0938 1.48724 0.743619 0.668603i \(-0.233108\pi\)
0.743619 + 0.668603i \(0.233108\pi\)
\(104\) 6.26299 + 8.04829i 0.614137 + 0.789200i
\(105\) −2.17157 −0.211924
\(106\) −11.3300 2.74107i −1.10047 0.266237i
\(107\) 11.2833i 1.09080i −0.838175 0.545401i \(-0.816377\pi\)
0.838175 0.545401i \(-0.183623\pi\)
\(108\) −5.15769 + 10.0355i −0.496299 + 0.965670i
\(109\) −3.29289 3.29289i −0.315402 0.315402i 0.531596 0.846998i \(-0.321592\pi\)
−0.846998 + 0.531596i \(0.821592\pi\)
\(110\) −1.67314 + 6.91578i −0.159528 + 0.659394i
\(111\) −9.02054 9.02054i −0.856191 0.856191i
\(112\) −0.962841 + 5.81533i −0.0909799 + 0.549497i
\(113\) −7.31371 −0.688016 −0.344008 0.938967i \(-0.611785\pi\)
−0.344008 + 0.938967i \(0.611785\pi\)
\(114\) −7.72569 12.6569i −0.723577 1.18542i
\(115\) 1.47363 + 1.47363i 0.137416 + 0.137416i
\(116\) −6.07328 3.12132i −0.563890 0.289807i
\(117\) −2.92893 0.585786i −0.270780 0.0541560i
\(118\) −7.41421 12.1466i −0.682534 1.11818i
\(119\) −0.178781 + 0.178781i −0.0163888 + 0.0163888i
\(120\) 4.15685 0.305198i 0.379467 0.0278606i
\(121\) 14.3137i 1.30125i
\(122\) 6.63696 + 1.60568i 0.600882 + 0.145372i
\(123\) −6.25206 + 6.25206i −0.563730 + 0.563730i
\(124\) −5.61235 + 1.80187i −0.504004 + 0.161812i
\(125\) 6.36396 6.36396i 0.569210 0.569210i
\(126\) −0.899495 1.47363i −0.0801334 0.131281i
\(127\) −13.8730 −1.23103 −0.615516 0.788124i \(-0.711052\pi\)
−0.615516 + 0.788124i \(0.711052\pi\)
\(128\) 1.02578 11.2671i 0.0906673 0.995881i
\(129\) 8.31371i 0.731981i
\(130\) 1.75147 + 4.78877i 0.153614 + 0.420003i
\(131\) 2.69442i 0.235412i −0.993048 0.117706i \(-0.962446\pi\)
0.993048 0.117706i \(-0.0375541\pi\)
\(132\) 14.1186 4.53284i 1.22887 0.394533i
\(133\) 10.4853 0.909189
\(134\) 2.51564 1.53553i 0.217318 0.132650i
\(135\) −3.98926 + 3.98926i −0.343341 + 0.343341i
\(136\) 0.317098 0.367351i 0.0271910 0.0315001i
\(137\) −2.65685 + 2.65685i −0.226990 + 0.226990i −0.811434 0.584444i \(-0.801313\pi\)
0.584444 + 0.811434i \(0.301313\pi\)
\(138\) 1.02128 4.22136i 0.0869369 0.359346i
\(139\) 3.20009i 0.271428i 0.990748 + 0.135714i \(0.0433328\pi\)
−0.990748 + 0.135714i \(0.956667\pi\)
\(140\) −1.34721 + 2.62132i −0.113860 + 0.221542i
\(141\) 1.53553 1.53553i 0.129315 0.129315i
\(142\) 15.3990 9.39949i 1.29226 0.788788i
\(143\) 10.0625 + 15.0938i 0.841472 + 1.26221i
\(144\) 1.92893 + 2.69442i 0.160744 + 0.224535i
\(145\) −2.41421 2.41421i −0.200490 0.200490i
\(146\) −2.82843 + 1.72646i −0.234082 + 0.142883i
\(147\) 7.11529 0.586860
\(148\) −16.4849 + 5.29256i −1.35505 + 0.435045i
\(149\) 10.4853 + 10.4853i 0.858988 + 0.858988i 0.991219 0.132231i \(-0.0422141\pi\)
−0.132231 + 0.991219i \(0.542214\pi\)
\(150\) −8.10234 1.96021i −0.661553 0.160050i
\(151\) 11.1046 + 11.1046i 0.903676 + 0.903676i 0.995752 0.0920760i \(-0.0293503\pi\)
−0.0920760 + 0.995752i \(0.529350\pi\)
\(152\) −20.0711 + 1.47363i −1.62798 + 0.119527i
\(153\) 0.142136i 0.0114910i
\(154\) −2.46558 + 10.1913i −0.198682 + 0.821236i
\(155\) −2.94725 −0.236729
\(156\) 6.61666 8.31515i 0.529756 0.665745i
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) −0.287065 + 1.18656i −0.0228377 + 0.0943977i
\(159\) 12.1466i 0.963285i
\(160\) 2.21044 5.20711i 0.174751 0.411658i
\(161\) 2.17157 + 2.17157i 0.171144 + 0.171144i
\(162\) 8.01152 + 1.93823i 0.629444 + 0.152282i
\(163\) −2.69442 2.69442i −0.211043 0.211043i 0.593667 0.804710i \(-0.297679\pi\)
−0.804710 + 0.593667i \(0.797679\pi\)
\(164\) 3.66823 + 11.4256i 0.286441 + 0.892189i
\(165\) 7.41421 0.577196
\(166\) 1.04201 0.636039i 0.0808757 0.0493662i
\(167\) −0.863230 0.863230i −0.0667987 0.0667987i 0.672918 0.739717i \(-0.265041\pi\)
−0.739717 + 0.672918i \(0.765041\pi\)
\(168\) 6.12565 0.449747i 0.472604 0.0346988i
\(169\) 12.0000 + 5.00000i 0.923077 + 0.384615i
\(170\) 0.207107 0.126417i 0.0158844 0.00969575i
\(171\) 4.16804 4.16804i 0.318738 0.318738i
\(172\) −10.0355 5.15769i −0.765202 0.393270i
\(173\) 24.3848i 1.85394i −0.375135 0.926970i \(-0.622404\pi\)
0.375135 0.926970i \(-0.377596\pi\)
\(174\) −1.67314 + 6.91578i −0.126840 + 0.524284i
\(175\) 4.16804 4.16804i 0.315074 0.315074i
\(176\) 3.28735 19.8548i 0.247793 1.49661i
\(177\) −10.4853 + 10.4853i −0.788122 + 0.788122i
\(178\) 3.82843 2.33686i 0.286953 0.175155i
\(179\) −12.7570 −0.953500 −0.476750 0.879039i \(-0.658185\pi\)
−0.476750 + 0.879039i \(0.658185\pi\)
\(180\) 0.506477 + 1.57754i 0.0377506 + 0.117583i
\(181\) 8.58579i 0.638176i 0.947725 + 0.319088i \(0.103377\pi\)
−0.947725 + 0.319088i \(0.896623\pi\)
\(182\) 2.58102 + 7.05686i 0.191318 + 0.523089i
\(183\) 7.11529i 0.525978i
\(184\) −4.46205 3.85166i −0.328947 0.283948i
\(185\) −8.65685 −0.636465
\(186\) 3.20009 + 5.24264i 0.234642 + 0.384409i
\(187\) 0.610396 0.610396i 0.0446366 0.0446366i
\(188\) −0.900933 2.80617i −0.0657073 0.204661i
\(189\) −5.87868 + 5.87868i −0.427611 + 0.427611i
\(190\) −9.78039 2.36618i −0.709544 0.171661i
\(191\) 16.8203i 1.21707i −0.793526 0.608536i \(-0.791757\pi\)
0.793526 0.608536i \(-0.208243\pi\)
\(192\) −11.6626 + 1.72183i −0.841675 + 0.124262i
\(193\) 8.07107 8.07107i 0.580968 0.580968i −0.354201 0.935169i \(-0.615247\pi\)
0.935169 + 0.354201i \(0.115247\pi\)
\(194\) 2.51564 + 4.12132i 0.180612 + 0.295894i
\(195\) 4.42088 2.94725i 0.316586 0.211057i
\(196\) 4.41421 8.58892i 0.315301 0.613494i
\(197\) 2.60660 + 2.60660i 0.185713 + 0.185713i 0.793840 0.608127i \(-0.208079\pi\)
−0.608127 + 0.793840i \(0.708079\pi\)
\(198\) 3.07107 + 5.03127i 0.218251 + 0.357557i
\(199\) −20.4827 −1.45198 −0.725988 0.687707i \(-0.758617\pi\)
−0.725988 + 0.687707i \(0.758617\pi\)
\(200\) −7.39274 + 8.56431i −0.522746 + 0.605588i
\(201\) −2.17157 2.17157i −0.153171 0.153171i
\(202\) 1.71980 7.10863i 0.121004 0.500162i
\(203\) −3.55765 3.55765i −0.249698 0.249698i
\(204\) −0.449747 0.231144i −0.0314886 0.0161833i
\(205\) 6.00000i 0.419058i
\(206\) −20.7473 5.01942i −1.44554 0.349720i
\(207\) 1.72646 0.119997
\(208\) −5.93240 13.1456i −0.411338 0.911483i
\(209\) −35.7990 −2.47627
\(210\) 2.98495 + 0.722152i 0.205981 + 0.0498332i
\(211\) 19.8723i 1.36806i 0.729453 + 0.684031i \(0.239775\pi\)
−0.729453 + 0.684031i \(0.760225\pi\)
\(212\) 14.6622 + 7.53553i 1.00700 + 0.517543i
\(213\) −13.2929 13.2929i −0.910814 0.910814i
\(214\) −3.75225 + 15.5096i −0.256499 + 1.06022i
\(215\) −3.98926 3.98926i −0.272065 0.272065i
\(216\) 10.4268 12.0793i 0.709457 0.821889i
\(217\) −4.34315 −0.294832
\(218\) 3.43123 + 5.62132i 0.232392 + 0.380724i
\(219\) 2.44158 + 2.44158i 0.164987 + 0.164987i
\(220\) 4.59966 8.94975i 0.310109 0.603392i
\(221\) 0.121320 0.606602i 0.00816089 0.0408044i
\(222\) 9.39949 + 15.3990i 0.630853 + 1.03351i
\(223\) 9.37810 9.37810i 0.628004 0.628004i −0.319562 0.947565i \(-0.603536\pi\)
0.947565 + 0.319562i \(0.103536\pi\)
\(224\) 3.25736 7.67333i 0.217641 0.512696i
\(225\) 3.31371i 0.220914i
\(226\) 10.0531 + 2.43216i 0.668724 + 0.161785i
\(227\) 10.9258 10.9258i 0.725169 0.725169i −0.244484 0.969653i \(-0.578619\pi\)
0.969653 + 0.244484i \(0.0786186\pi\)
\(228\) 6.41040 + 19.9668i 0.424539 + 1.32233i
\(229\) 13.2929 13.2929i 0.878419 0.878419i −0.114952 0.993371i \(-0.536671\pi\)
0.993371 + 0.114952i \(0.0366714\pi\)
\(230\) −1.53553 2.51564i −0.101250 0.165876i
\(231\) 10.9258 0.718863
\(232\) 7.31010 + 6.31010i 0.479931 + 0.414278i
\(233\) 21.9706i 1.43934i 0.694317 + 0.719670i \(0.255707\pi\)
−0.694317 + 0.719670i \(0.744293\pi\)
\(234\) 3.83119 + 1.77921i 0.250453 + 0.116310i
\(235\) 1.47363i 0.0961287i
\(236\) 6.15196 + 19.1618i 0.400458 + 1.24732i
\(237\) 1.27208 0.0826303
\(238\) 0.305198 0.186292i 0.0197830 0.0120755i
\(239\) 10.2413 10.2413i 0.662456 0.662456i −0.293502 0.955958i \(-0.594821\pi\)
0.955958 + 0.293502i \(0.0948208\pi\)
\(240\) −5.81533 0.962841i −0.375378 0.0621511i
\(241\) −1.07107 + 1.07107i −0.0689935 + 0.0689935i −0.740762 0.671768i \(-0.765535\pi\)
0.671768 + 0.740762i \(0.265535\pi\)
\(242\) 4.76000 19.6750i 0.305984 1.26476i
\(243\) 8.33609i 0.534760i
\(244\) −8.58892 4.41421i −0.549849 0.282591i
\(245\) 3.41421 3.41421i 0.218126 0.218126i
\(246\) 10.6729 6.51472i 0.680482 0.415363i
\(247\) −21.3459 + 14.2306i −1.35821 + 0.905471i
\(248\) 8.31371 0.610396i 0.527921 0.0387602i
\(249\) −0.899495 0.899495i −0.0570032 0.0570032i
\(250\) −10.8640 + 6.63132i −0.687097 + 0.419401i
\(251\) 15.4514 0.975283 0.487641 0.873044i \(-0.337857\pi\)
0.487641 + 0.873044i \(0.337857\pi\)
\(252\) 0.746357 + 2.32471i 0.0470161 + 0.146443i
\(253\) −7.41421 7.41421i −0.466128 0.466128i
\(254\) 19.0693 + 4.61345i 1.19651 + 0.289473i
\(255\) −0.178781 0.178781i −0.0111957 0.0111957i
\(256\) −5.15685 + 15.1462i −0.322303 + 0.946636i
\(257\) 10.6569i 0.664756i −0.943146 0.332378i \(-0.892149\pi\)
0.943146 0.332378i \(-0.107851\pi\)
\(258\) −2.76471 + 11.4277i −0.172123 + 0.711456i
\(259\) −12.7570 −0.792679
\(260\) −0.815007 7.16490i −0.0505446 0.444348i
\(261\) −2.82843 −0.175075
\(262\) −0.896023 + 3.70363i −0.0553565 + 0.228811i
\(263\) 13.0098i 0.802218i −0.916030 0.401109i \(-0.868625\pi\)
0.916030 0.401109i \(-0.131375\pi\)
\(264\) −20.9143 + 1.53553i −1.28718 + 0.0945056i
\(265\) 5.82843 + 5.82843i 0.358037 + 0.358037i
\(266\) −14.4126 3.48686i −0.883695 0.213793i
\(267\) −3.30481 3.30481i −0.202251 0.202251i
\(268\) −3.96853 + 1.27411i −0.242416 + 0.0778288i
\(269\) 20.1421 1.22809 0.614044 0.789272i \(-0.289542\pi\)
0.614044 + 0.789272i \(0.289542\pi\)
\(270\) 6.81010 4.15685i 0.414449 0.252978i
\(271\) 4.85249 + 4.85249i 0.294768 + 0.294768i 0.838960 0.544192i \(-0.183164\pi\)
−0.544192 + 0.838960i \(0.683164\pi\)
\(272\) −0.558032 + 0.399495i −0.0338357 + 0.0242229i
\(273\) 6.51472 4.34315i 0.394289 0.262859i
\(274\) 4.53553 2.76847i 0.274002 0.167249i
\(275\) −14.2306 + 14.2306i −0.858137 + 0.858137i
\(276\) −2.80761 + 5.46289i −0.168998 + 0.328827i
\(277\) 6.00000i 0.360505i 0.983620 + 0.180253i \(0.0576915\pi\)
−0.983620 + 0.180253i \(0.942309\pi\)
\(278\) 1.06418 4.39871i 0.0638254 0.263817i
\(279\) −1.72646 + 1.72646i −0.103360 + 0.103360i
\(280\) 2.72353 3.15515i 0.162762 0.188556i
\(281\) −16.2426 + 16.2426i −0.968955 + 0.968955i −0.999532 0.0305777i \(-0.990265\pi\)
0.0305777 + 0.999532i \(0.490265\pi\)
\(282\) −2.62132 + 1.60004i −0.156097 + 0.0952812i
\(283\) 24.2931 1.44408 0.722038 0.691853i \(-0.243205\pi\)
0.722038 + 0.691853i \(0.243205\pi\)
\(284\) −24.2926 + 7.79925i −1.44150 + 0.462800i
\(285\) 10.4853i 0.621094i
\(286\) −8.81214 24.0936i −0.521073 1.42469i
\(287\) 8.84175i 0.521912i
\(288\) −1.75541 4.34510i −0.103438 0.256037i
\(289\) 16.9706 0.998268
\(290\) 2.51564 + 4.12132i 0.147723 + 0.242012i
\(291\) 3.55765 3.55765i 0.208553 0.208553i
\(292\) 4.46197 1.43253i 0.261117 0.0838326i
\(293\) −0.807612 + 0.807612i −0.0471812 + 0.0471812i −0.730304 0.683123i \(-0.760621\pi\)
0.683123 + 0.730304i \(0.260621\pi\)
\(294\) −9.78039 2.36618i −0.570404 0.137998i
\(295\) 10.0625i 0.585864i
\(296\) 24.4196 1.79289i 1.41936 0.104210i
\(297\) 20.0711 20.0711i 1.16464 1.16464i
\(298\) −10.9258 17.8995i −0.632913 1.03689i
\(299\) −7.36813 1.47363i −0.426110 0.0852220i
\(300\) 10.4853 + 5.38883i 0.605368 + 0.311125i
\(301\) −5.87868 5.87868i −0.338841 0.338841i
\(302\) −11.5711 18.9567i −0.665840 1.09083i
\(303\) −7.62096 −0.437813
\(304\) 28.0789 + 4.64901i 1.61044 + 0.266639i
\(305\) −3.41421 3.41421i −0.195497 0.195497i
\(306\) 0.0472669 0.195374i 0.00270207 0.0111688i
\(307\) −1.72646 1.72646i −0.0985343 0.0985343i 0.656121 0.754656i \(-0.272196\pi\)
−0.754656 + 0.656121i \(0.772196\pi\)
\(308\) 6.77817 13.1886i 0.386222 0.751489i
\(309\) 22.2426i 1.26534i
\(310\) 4.05117 + 0.980103i 0.230091 + 0.0556661i
\(311\) −29.6820 −1.68311 −0.841555 0.540171i \(-0.818359\pi\)
−0.841555 + 0.540171i \(0.818359\pi\)
\(312\) −11.8602 + 9.22930i −0.671450 + 0.522506i
\(313\) 3.48528 0.197000 0.0984999 0.995137i \(-0.468596\pi\)
0.0984999 + 0.995137i \(0.468596\pi\)
\(314\) −16.4947 3.99058i −0.930850 0.225201i
\(315\) 1.22079i 0.0687838i
\(316\) 0.789177 1.53553i 0.0443946 0.0863805i
\(317\) −15.6569 15.6569i −0.879377 0.879377i 0.114093 0.993470i \(-0.463604\pi\)
−0.993470 + 0.114093i \(0.963604\pi\)
\(318\) 4.03932 16.6962i 0.226514 0.936275i
\(319\) 12.1466 + 12.1466i 0.680077 + 0.680077i
\(320\) −4.76999 + 6.42240i −0.266651 + 0.359023i
\(321\) 16.6274 0.928052
\(322\) −2.26280 3.70711i −0.126101 0.206589i
\(323\) 0.863230 + 0.863230i 0.0480314 + 0.0480314i
\(324\) −10.3677 5.32843i −0.575986 0.296024i
\(325\) −2.82843 + 14.1421i −0.156893 + 0.784465i
\(326\) 2.80761 + 4.59966i 0.155499 + 0.254751i
\(327\) 4.85249 4.85249i 0.268343 0.268343i
\(328\) −1.24264 16.9250i −0.0686134 0.934527i
\(329\) 2.17157i 0.119723i
\(330\) −10.1913 2.46558i −0.561011 0.135726i
\(331\) 4.77844 4.77844i 0.262647 0.262647i −0.563482 0.826129i \(-0.690538\pi\)
0.826129 + 0.563482i \(0.190538\pi\)
\(332\) −1.64382 + 0.527754i −0.0902163 + 0.0289643i
\(333\) −5.07107 + 5.07107i −0.277893 + 0.277893i
\(334\) 0.899495 + 1.47363i 0.0492182 + 0.0806332i
\(335\) −2.08402 −0.113862
\(336\) −8.56963 1.41887i −0.467511 0.0774056i
\(337\) 13.8284i 0.753282i 0.926359 + 0.376641i \(0.122921\pi\)
−0.926359 + 0.376641i \(0.877079\pi\)
\(338\) −14.8320 10.8634i −0.806753 0.590889i
\(339\) 10.7777i 0.585363i
\(340\) −0.326720 + 0.104895i −0.0177189 + 0.00568872i
\(341\) 14.8284 0.803004
\(342\) −7.11529 + 4.34315i −0.384751 + 0.234850i
\(343\) 12.3253 12.3253i 0.665506 0.665506i
\(344\) 12.0793 + 10.4268i 0.651270 + 0.562178i
\(345\) −2.17157 + 2.17157i −0.116914 + 0.116914i
\(346\) −8.10911 + 33.5183i −0.435948 + 1.80196i
\(347\) 21.5987i 1.15948i 0.814802 + 0.579740i \(0.196846\pi\)
−0.814802 + 0.579740i \(0.803154\pi\)
\(348\) 4.59966 8.94975i 0.246568 0.479757i
\(349\) −7.53553 + 7.53553i −0.403368 + 0.403368i −0.879418 0.476050i \(-0.842068\pi\)
0.476050 + 0.879418i \(0.342068\pi\)
\(350\) −7.11529 + 4.34315i −0.380328 + 0.232151i
\(351\) 3.98926 19.9463i 0.212931 1.06466i
\(352\) −11.1213 + 26.1984i −0.592768 + 1.39638i
\(353\) −1.58579 1.58579i −0.0844029 0.0844029i 0.663645 0.748048i \(-0.269009\pi\)
−0.748048 + 0.663645i \(0.769009\pi\)
\(354\) 17.8995 10.9258i 0.951347 0.580698i
\(355\) −12.7570 −0.677069
\(356\) −6.03951 + 1.93901i −0.320094 + 0.102767i
\(357\) −0.263456 0.263456i −0.0139436 0.0139436i
\(358\) 17.5352 + 4.24230i 0.926764 + 0.224213i
\(359\) −2.08402 2.08402i −0.109990 0.109990i 0.649970 0.759960i \(-0.274782\pi\)
−0.759960 + 0.649970i \(0.774782\pi\)
\(360\) −0.171573 2.33686i −0.00904268 0.123163i
\(361\) 31.6274i 1.66460i
\(362\) 2.85519 11.8017i 0.150065 0.620282i
\(363\) −21.0930 −1.10710
\(364\) −1.20101 10.5584i −0.0629503 0.553409i
\(365\) 2.34315 0.122646
\(366\) −2.36618 + 9.78039i −0.123682 + 0.511229i
\(367\) 3.81048i 0.198906i −0.995042 0.0994528i \(-0.968291\pi\)
0.995042 0.0994528i \(-0.0317092\pi\)
\(368\) 4.85249 + 6.77817i 0.252954 + 0.353337i
\(369\) 3.51472 + 3.51472i 0.182969 + 0.182969i
\(370\) 11.8994 + 2.87882i 0.618618 + 0.149663i
\(371\) 8.58892 + 8.58892i 0.445915 + 0.445915i
\(372\) −2.65528 8.27050i −0.137670 0.428805i
\(373\) −14.6274 −0.757379 −0.378689 0.925524i \(-0.623625\pi\)
−0.378689 + 0.925524i \(0.623625\pi\)
\(374\) −1.04201 + 0.636039i −0.0538811 + 0.0328888i
\(375\) 9.37810 + 9.37810i 0.484283 + 0.484283i
\(376\) 0.305198 + 4.15685i 0.0157394 + 0.214373i
\(377\) 12.0711 + 2.41421i 0.621692 + 0.124338i
\(378\) 10.0355 6.12565i 0.516172 0.315069i
\(379\) 7.36813 7.36813i 0.378475 0.378475i −0.492077 0.870552i \(-0.663762\pi\)
0.870552 + 0.492077i \(0.163762\pi\)
\(380\) 12.6569 + 6.50490i 0.649283 + 0.333694i
\(381\) 20.4437i 1.04736i
\(382\) −5.59355 + 23.1205i −0.286191 + 1.18295i
\(383\) −0.178781 + 0.178781i −0.00913527 + 0.00913527i −0.711660 0.702524i \(-0.752056\pi\)
0.702524 + 0.711660i \(0.252056\pi\)
\(384\) 16.6035 + 1.51162i 0.847294 + 0.0771396i
\(385\) 5.24264 5.24264i 0.267190 0.267190i
\(386\) −13.7782 + 8.41014i −0.701291 + 0.428065i
\(387\) −4.67371 −0.237578
\(388\) −2.08735 6.50157i −0.105969 0.330067i
\(389\) 6.14214i 0.311419i 0.987803 + 0.155709i \(0.0497663\pi\)
−0.987803 + 0.155709i \(0.950234\pi\)
\(390\) −7.05686 + 2.58102i −0.357338 + 0.130695i
\(391\) 0.357562i 0.0180827i
\(392\) −8.92382 + 10.3380i −0.450721 + 0.522150i
\(393\) 3.97056 0.200288
\(394\) −2.71611 4.44975i −0.136835 0.224175i
\(395\) 0.610396 0.610396i 0.0307123 0.0307123i
\(396\) −2.54822 7.93706i −0.128053 0.398852i
\(397\) −18.4853 + 18.4853i −0.927750 + 0.927750i −0.997560 0.0698106i \(-0.977761\pi\)
0.0698106 + 0.997560i \(0.477761\pi\)
\(398\) 28.1546 + 6.81147i 1.41126 + 0.341428i
\(399\) 15.4514i 0.773537i
\(400\) 13.0098 9.31371i 0.650490 0.465685i
\(401\) 2.51472 2.51472i 0.125579 0.125579i −0.641524 0.767103i \(-0.721698\pi\)
0.767103 + 0.641524i \(0.221698\pi\)
\(402\) 2.26280 + 3.70711i 0.112858 + 0.184894i
\(403\) 8.84175 5.89450i 0.440439 0.293626i
\(404\) −4.72792 + 9.19932i −0.235223 + 0.457683i
\(405\) −4.12132 4.12132i −0.204790 0.204790i
\(406\) 3.70711 + 6.07328i 0.183981 + 0.301412i
\(407\) 43.5550 2.15894
\(408\) 0.541338 + 0.467284i 0.0268002 + 0.0231340i
\(409\) −23.1421 23.1421i −1.14430 1.14430i −0.987654 0.156651i \(-0.949930\pi\)
−0.156651 0.987654i \(-0.550070\pi\)
\(410\) 1.99529 8.24735i 0.0985403 0.407308i
\(411\) −3.91521 3.91521i −0.193123 0.193123i
\(412\) 26.8492 + 13.7990i 1.32277 + 0.679827i
\(413\) 14.8284i 0.729659i
\(414\) −2.37312 0.574131i −0.116633 0.0282170i
\(415\) −0.863230 −0.0423743
\(416\) 3.78290 + 20.0422i 0.185472 + 0.982650i
\(417\) −4.71573 −0.230930
\(418\) 49.2078 + 11.9049i 2.40683 + 0.582287i
\(419\) 5.64167i 0.275614i −0.990459 0.137807i \(-0.955995\pi\)
0.990459 0.137807i \(-0.0440053\pi\)
\(420\) −3.86285 1.98528i −0.188488 0.0968718i
\(421\) −24.0208 24.0208i −1.17070 1.17070i −0.982042 0.188661i \(-0.939585\pi\)
−0.188661 0.982042i \(-0.560415\pi\)
\(422\) 6.60848 27.3156i 0.321696 1.32970i
\(423\) −0.863230 0.863230i −0.0419717 0.0419717i
\(424\) −17.6481 15.2339i −0.857069 0.739825i
\(425\) 0.686292 0.0332900
\(426\) 13.8513 + 22.6924i 0.671100 + 1.09945i
\(427\) −5.03127 5.03127i −0.243480 0.243480i
\(428\) 10.3154 20.0711i 0.498613 0.970172i
\(429\) −22.2426 + 14.8284i −1.07388 + 0.715923i
\(430\) 4.15685 + 6.81010i 0.200461 + 0.328412i
\(431\) −15.7783 + 15.7783i −0.760012 + 0.760012i −0.976324 0.216312i \(-0.930597\pi\)
0.216312 + 0.976324i \(0.430597\pi\)
\(432\) −18.3492 + 13.1362i −0.882828 + 0.632016i
\(433\) 32.3137i 1.55290i 0.630180 + 0.776449i \(0.282981\pi\)
−0.630180 + 0.776449i \(0.717019\pi\)
\(434\) 5.96991 + 1.44430i 0.286565 + 0.0693288i
\(435\) 3.55765 3.55765i 0.170576 0.170576i
\(436\) −2.84707 8.86788i −0.136350 0.424695i
\(437\) 10.4853 10.4853i 0.501579 0.501579i
\(438\) −2.54416 4.16804i −0.121564 0.199157i
\(439\) −12.5041 −0.596790 −0.298395 0.954443i \(-0.596451\pi\)
−0.298395 + 0.954443i \(0.596451\pi\)
\(440\) −9.29872 + 10.7723i −0.443299 + 0.513551i
\(441\) 4.00000i 0.190476i
\(442\) −0.368486 + 0.793465i −0.0175271 + 0.0377413i
\(443\) 6.14734i 0.292069i −0.989280 0.146034i \(-0.953349\pi\)
0.989280 0.146034i \(-0.0466510\pi\)
\(444\) −7.79925 24.2926i −0.370136 1.15288i
\(445\) −3.17157 −0.150347
\(446\) −16.0094 + 9.77208i −0.758068 + 0.462721i
\(447\) −15.4514 + 15.4514i −0.730825 + 0.730825i
\(448\) −7.02918 + 9.46421i −0.332098 + 0.447142i
\(449\) 25.7279 25.7279i 1.21418 1.21418i 0.244535 0.969640i \(-0.421365\pi\)
0.969640 0.244535i \(-0.0786354\pi\)
\(450\) −1.10197 + 4.55489i −0.0519472 + 0.214719i
\(451\) 30.1876i 1.42148i
\(452\) −13.0098 6.68629i −0.611929 0.314497i
\(453\) −16.3640 + 16.3640i −0.768846 + 0.768846i
\(454\) −18.6515 + 11.3848i −0.875357 + 0.534314i
\(455\) 1.04201 5.21005i 0.0488502 0.244251i
\(456\) −2.17157 29.5772i −0.101693 1.38508i
\(457\) 0.585786 + 0.585786i 0.0274019 + 0.0274019i 0.720675 0.693273i \(-0.243832\pi\)
−0.693273 + 0.720675i \(0.743832\pi\)
\(458\) −22.6924 + 13.8513i −1.06035 + 0.647231i
\(459\) −0.967957 −0.0451804
\(460\) 1.27411 + 3.96853i 0.0594058 + 0.185034i
\(461\) 6.46447 + 6.46447i 0.301080 + 0.301080i 0.841436 0.540356i \(-0.181710\pi\)
−0.540356 + 0.841436i \(0.681710\pi\)
\(462\) −15.0181 3.63335i −0.698706 0.169039i
\(463\) −20.9883 20.9883i −0.975410 0.975410i 0.0242948 0.999705i \(-0.492266\pi\)
−0.999705 + 0.0242948i \(0.992266\pi\)
\(464\) −7.94975 11.1046i −0.369058 0.515516i
\(465\) 4.34315i 0.201409i
\(466\) 7.30627 30.1998i 0.338456 1.39898i
\(467\) 21.3459 0.987770 0.493885 0.869527i \(-0.335576\pi\)
0.493885 + 0.869527i \(0.335576\pi\)
\(468\) −4.67452 3.71968i −0.216080 0.171942i
\(469\) −3.07107 −0.141809
\(470\) −0.490051 + 2.02559i −0.0226044 + 0.0934333i
\(471\) 17.6835i 0.814813i
\(472\) −2.08402 28.3848i −0.0959249 1.30652i
\(473\) 20.0711 + 20.0711i 0.922869 + 0.922869i
\(474\) −1.74855 0.423027i −0.0803134 0.0194303i
\(475\) −20.1251 20.1251i −0.923403 0.923403i
\(476\) −0.481463 + 0.154576i −0.0220678 + 0.00708496i
\(477\) 6.82843 0.312652
\(478\) −17.4830 + 10.6716i −0.799656 + 0.488106i
\(479\) −1.90524 1.90524i −0.0870527 0.0870527i 0.662240 0.749292i \(-0.269606\pi\)
−0.749292 + 0.662240i \(0.769606\pi\)
\(480\) 7.67333 + 3.25736i 0.350238 + 0.148677i
\(481\) 25.9706 17.3137i 1.18416 0.789437i
\(482\) 1.82843 1.11606i 0.0832826 0.0508353i
\(483\) −3.20009 + 3.20009i −0.145609 + 0.145609i
\(484\) −13.0858 + 25.4616i −0.594808 + 1.15734i
\(485\) 3.41421i 0.155031i
\(486\) 2.77215 11.4584i 0.125747 0.519765i
\(487\) 9.19932 9.19932i 0.416861 0.416861i −0.467259 0.884120i \(-0.654759\pi\)
0.884120 + 0.467259i \(0.154759\pi\)
\(488\) 10.3380 + 8.92382i 0.467981 + 0.403963i
\(489\) 3.97056 3.97056i 0.179555 0.179555i
\(490\) −5.82843 + 3.55765i −0.263301 + 0.160718i
\(491\) 1.47363 0.0665038 0.0332519 0.999447i \(-0.489414\pi\)
0.0332519 + 0.999447i \(0.489414\pi\)
\(492\) −16.8370 + 5.40560i −0.759073 + 0.243703i
\(493\) 0.585786i 0.0263825i
\(494\) 34.0735 12.4623i 1.53304 0.560703i
\(495\) 4.16804i 0.187340i
\(496\) −11.6307 1.92568i −0.522232 0.0864657i
\(497\) −18.7990 −0.843250
\(498\) 0.937283 + 1.53553i 0.0420007 + 0.0688089i
\(499\) 2.08402 2.08402i 0.0932936 0.0932936i −0.658920 0.752213i \(-0.728986\pi\)
0.752213 + 0.658920i \(0.228986\pi\)
\(500\) 17.1384 5.50234i 0.766452 0.246072i
\(501\) 1.27208 1.27208i 0.0568323 0.0568323i
\(502\) −21.2388 5.13833i −0.947935 0.229335i
\(503\) 28.9668i 1.29157i 0.763520 + 0.645784i \(0.223469\pi\)
−0.763520 + 0.645784i \(0.776531\pi\)
\(504\) −0.252834 3.44365i −0.0112621 0.153392i
\(505\) −3.65685 + 3.65685i −0.162728 + 0.162728i
\(506\) 7.72569 + 12.6569i 0.343449 + 0.562666i
\(507\) −7.36813 + 17.6835i −0.327230 + 0.785352i
\(508\) −24.6777 12.6829i −1.09489 0.562713i
\(509\) 19.6569 + 19.6569i 0.871275 + 0.871275i 0.992611 0.121337i \(-0.0387181\pi\)
−0.121337 + 0.992611i \(0.538718\pi\)
\(510\) 0.186292 + 0.305198i 0.00824913 + 0.0135144i
\(511\) 3.45292 0.152748
\(512\) 12.1252 19.1044i 0.535865 0.844304i
\(513\) 28.3848 + 28.3848i 1.25322 + 1.25322i
\(514\) −3.54392 + 14.6485i −0.156315 + 0.646116i
\(515\) 10.6729 + 10.6729i 0.470306 + 0.470306i
\(516\) 7.60051 14.7886i 0.334594 0.651033i
\(517\) 7.41421i 0.326077i
\(518\) 17.5352 + 4.24230i 0.770452 + 0.186396i
\(519\) 35.9340 1.57733
\(520\) −1.26240 + 10.1196i −0.0553598 + 0.443774i
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) 3.88784 + 0.940588i 0.170166 + 0.0411684i
\(523\) 25.5139i 1.11565i 0.829960 + 0.557823i \(0.188363\pi\)
−0.829960 + 0.557823i \(0.811637\pi\)
\(524\) 2.46327 4.79289i 0.107609 0.209379i
\(525\) 6.14214 + 6.14214i 0.268065 + 0.268065i
\(526\) −4.32638 + 17.8827i −0.188639 + 0.779724i
\(527\) −0.357562 0.357562i −0.0155756 0.0155756i
\(528\) 29.2585 + 4.84432i 1.27331 + 0.210822i
\(529\) −18.6569 −0.811168
\(530\) −6.07328 9.94975i −0.263807 0.432189i
\(531\) 5.89450 + 5.89450i 0.255800 + 0.255800i
\(532\) 18.6515 + 9.58579i 0.808644 + 0.415597i
\(533\) −12.0000 18.0000i −0.519778 0.779667i
\(534\) 3.44365 + 5.64167i 0.149021 + 0.244139i
\(535\) 7.97852 7.97852i 0.344942 0.344942i
\(536\) 5.87868 0.431615i 0.253920 0.0186429i
\(537\) 18.7990i 0.811236i
\(538\) −27.6865 6.69823i −1.19365 0.288781i
\(539\) −17.1778 + 17.1778i −0.739902 + 0.739902i
\(540\) −10.7432 + 3.44916i −0.462315 + 0.148428i
\(541\) 11.8787 11.8787i 0.510704 0.510704i −0.404038 0.914742i \(-0.632394\pi\)
0.914742 + 0.404038i \(0.132394\pi\)
\(542\) −5.05635 8.28372i −0.217189 0.355816i
\(543\) −12.6522 −0.542959
\(544\) 0.899899 0.363557i 0.0385829 0.0155874i
\(545\) 4.65685i 0.199478i
\(546\) −10.3992 + 3.80345i −0.445043 + 0.162773i
\(547\) 34.1028i 1.45813i 0.684443 + 0.729066i \(0.260045\pi\)
−0.684443 + 0.729066i \(0.739955\pi\)
\(548\) −7.15501 + 2.29714i −0.305647 + 0.0981291i
\(549\) −4.00000 −0.170716
\(550\) 24.2931 14.8284i 1.03586 0.632286i
\(551\) −17.1778 + 17.1778i −0.731801 + 0.731801i
\(552\) 5.67590 6.57539i 0.241582 0.279867i
\(553\) 0.899495 0.899495i 0.0382504 0.0382504i
\(554\) 1.99529 8.24735i 0.0847717 0.350396i
\(555\) 12.7570i 0.541503i
\(556\) −2.92556 + 5.69239i −0.124071 + 0.241411i
\(557\) 4.36396 4.36396i 0.184907 0.184907i −0.608583 0.793490i \(-0.708262\pi\)
0.793490 + 0.608583i \(0.208262\pi\)
\(558\) 2.94725 1.79899i 0.124767 0.0761573i
\(559\) 19.9463 + 3.98926i 0.843639 + 0.168728i
\(560\) −4.79289 + 3.43123i −0.202537 + 0.144996i
\(561\) 0.899495 + 0.899495i 0.0379767 + 0.0379767i
\(562\) 27.7279 16.9250i 1.16963 0.713938i
\(563\) −23.3252 −0.983039 −0.491520 0.870867i \(-0.663558\pi\)
−0.491520 + 0.870867i \(0.663558\pi\)
\(564\) 4.13525 1.32764i 0.174125 0.0559036i
\(565\) −5.17157 5.17157i −0.217570 0.217570i
\(566\) −33.3923 8.07863i −1.40358 0.339570i
\(567\) −6.07328 6.07328i −0.255054 0.255054i
\(568\) 35.9853 2.64205i 1.50991 0.110858i
\(569\) 12.5147i 0.524644i −0.964980 0.262322i \(-0.915512\pi\)
0.964980 0.262322i \(-0.0844883\pi\)
\(570\) 3.48686 14.4126i 0.146048 0.603679i
\(571\) 14.4834 0.606112 0.303056 0.952973i \(-0.401993\pi\)
0.303056 + 0.952973i \(0.401993\pi\)
\(572\) 4.10052 + 36.0486i 0.171451 + 1.50727i
\(573\) 24.7868 1.03548
\(574\) 2.94031 12.1535i 0.122726 0.507278i
\(575\) 8.33609i 0.347639i
\(576\) 0.967957 + 6.55635i 0.0403316 + 0.273181i
\(577\) 16.4853 + 16.4853i 0.686291 + 0.686291i 0.961410 0.275119i \(-0.0887172\pi\)
−0.275119 + 0.961410i \(0.588717\pi\)
\(578\) −23.3270 5.64353i −0.970277 0.234740i
\(579\) 11.8937 + 11.8937i 0.494287 + 0.494287i
\(580\) −2.08735 6.50157i −0.0866726 0.269963i
\(581\) −1.27208 −0.0527747
\(582\) −6.07328 + 3.70711i −0.251746 + 0.153665i
\(583\) −29.3244 29.3244i −1.21449 1.21449i
\(584\) −6.60963 + 0.485281i −0.273508 + 0.0200811i
\(585\) −1.65685 2.48528i −0.0685025 0.102754i
\(586\) 1.37868 0.841540i 0.0569527 0.0347637i
\(587\) 13.2626 13.2626i 0.547407 0.547407i −0.378283 0.925690i \(-0.623485\pi\)
0.925690 + 0.378283i \(0.123485\pi\)
\(588\) 12.6569 + 6.50490i 0.521960 + 0.268258i
\(589\) 20.9706i 0.864077i
\(590\) 3.34628 13.8316i 0.137764 0.569436i
\(591\) −3.84116 + 3.84116i −0.158004 + 0.158004i
\(592\) −34.1623 5.65624i −1.40406 0.232470i
\(593\) −32.5563 + 32.5563i −1.33693 + 1.33693i −0.437910 + 0.899019i \(0.644281\pi\)
−0.899019 + 0.437910i \(0.855719\pi\)
\(594\) −34.2635 + 20.9143i −1.40585 + 0.858123i
\(595\) −0.252834 −0.0103652
\(596\) 9.06568 + 28.2373i 0.371345 + 1.15664i
\(597\) 30.1838i 1.23534i
\(598\) 9.63787 + 4.47584i 0.394122 + 0.183031i
\(599\) 42.6918i 1.74434i −0.489204 0.872169i \(-0.662713\pi\)
0.489204 0.872169i \(-0.337287\pi\)
\(600\) −12.6206 10.8941i −0.515233 0.444751i
\(601\) −17.9706 −0.733035 −0.366517 0.930411i \(-0.619450\pi\)
−0.366517 + 0.930411i \(0.619450\pi\)
\(602\) 6.12565 + 10.0355i 0.249663 + 0.409018i
\(603\) −1.22079 + 1.22079i −0.0497145 + 0.0497145i
\(604\) 9.60111 + 29.9050i 0.390664 + 1.21682i
\(605\) −10.1213 + 10.1213i −0.411490 + 0.411490i
\(606\) 10.4755 + 2.53434i 0.425537 + 0.102950i
\(607\) 36.7973i 1.49355i −0.665074 0.746777i \(-0.731600\pi\)
0.665074 0.746777i \(-0.268400\pi\)
\(608\) −37.0501 15.7279i −1.50258 0.637851i
\(609\) 5.24264 5.24264i 0.212443 0.212443i
\(610\) 3.55765 + 5.82843i 0.144045 + 0.235986i
\(611\) 2.94725 + 4.42088i 0.119233 + 0.178850i
\(612\) −0.129942 + 0.252834i −0.00525261 + 0.0102202i
\(613\) −22.8701 22.8701i −0.923713 0.923713i 0.0735766 0.997290i \(-0.476559\pi\)
−0.997290 + 0.0735766i \(0.976559\pi\)
\(614\) 1.79899 + 2.94725i 0.0726013 + 0.118941i
\(615\) −8.84175 −0.356534
\(616\) −13.7028 + 15.8744i −0.552103 + 0.639598i
\(617\) −7.51472 7.51472i −0.302531 0.302531i 0.539472 0.842003i \(-0.318624\pi\)
−0.842003 + 0.539472i \(0.818624\pi\)
\(618\) 7.39675 30.5738i 0.297541 1.22986i
\(619\) 34.7132 + 34.7132i 1.39524 + 1.39524i 0.813052 + 0.582191i \(0.197804\pi\)
0.582191 + 0.813052i \(0.302196\pi\)
\(620\) −5.24264 2.69442i −0.210550 0.108210i
\(621\) 11.7574i 0.471807i
\(622\) 40.7996 + 9.87068i 1.63592 + 0.395778i
\(623\) −4.67371 −0.187248
\(624\) 19.3717 8.74214i 0.775488 0.349966i
\(625\) −11.0000 −0.440000
\(626\) −4.79072 1.15902i −0.191476 0.0463239i
\(627\) 52.7543i 2.10680i
\(628\) 21.3459 + 10.9706i 0.851793 + 0.437773i
\(629\) −1.05025 1.05025i −0.0418763 0.0418763i
\(630\) 0.405972 1.67805i 0.0161743 0.0668551i
\(631\) −1.04201 1.04201i −0.0414818 0.0414818i 0.686062 0.727543i \(-0.259338\pi\)
−0.727543 + 0.686062i \(0.759338\pi\)
\(632\) −1.59541 + 1.84824i −0.0634619 + 0.0735191i
\(633\) −29.2843 −1.16395
\(634\) 16.3146 + 26.7279i 0.647936 + 1.06150i
\(635\) −9.80971 9.80971i −0.389287 0.389287i
\(636\) −11.1046 + 21.6066i −0.440324 + 0.856757i
\(637\) −3.41421 + 17.0711i −0.135276 + 0.676380i
\(638\) −12.6569 20.7355i −0.501090 0.820926i
\(639\) −7.47286 + 7.47286i −0.295622 + 0.295622i
\(640\) 8.69239 7.24171i 0.343597 0.286254i
\(641\) 9.85786i 0.389362i 0.980867 + 0.194681i \(0.0623672\pi\)
−0.980867 + 0.194681i \(0.937633\pi\)
\(642\) −22.8554 5.52941i −0.902029 0.218229i
\(643\) −17.4307 + 17.4307i −0.687399 + 0.687399i −0.961656 0.274258i \(-0.911568\pi\)
0.274258 + 0.961656i \(0.411568\pi\)
\(644\) 1.87756 + 5.84813i 0.0739864 + 0.230448i
\(645\) 5.87868 5.87868i 0.231473 0.231473i
\(646\) −0.899495 1.47363i −0.0353902 0.0579790i
\(647\) 17.6835 0.695210 0.347605 0.937641i \(-0.386995\pi\)
0.347605 + 0.937641i \(0.386995\pi\)
\(648\) 12.4791 + 10.7720i 0.490226 + 0.423164i
\(649\) 50.6274i 1.98730i
\(650\) 8.59078 18.4986i 0.336958 0.725575i
\(651\) 6.40017i 0.250842i
\(652\) −2.32962 7.25617i −0.0912350 0.284173i
\(653\) −9.17157 −0.358911 −0.179456 0.983766i \(-0.557434\pi\)
−0.179456 + 0.983766i \(0.557434\pi\)
\(654\) −8.28372 + 5.05635i −0.323919 + 0.197719i
\(655\) 1.90524 1.90524i 0.0744439 0.0744439i
\(656\) −3.92029 + 23.6777i −0.153062 + 0.924457i
\(657\) 1.37258 1.37258i 0.0535496 0.0535496i
\(658\) −0.722152 + 2.98495i −0.0281524 + 0.116366i
\(659\) 34.8613i 1.35801i −0.734136 0.679003i \(-0.762412\pi\)
0.734136 0.679003i \(-0.237588\pi\)
\(660\) 13.1886 + 6.77817i 0.513365 + 0.263840i
\(661\) −16.9289 + 16.9289i −0.658459 + 0.658459i −0.955015 0.296556i \(-0.904162\pi\)
0.296556 + 0.955015i \(0.404162\pi\)
\(662\) −8.15731 + 4.97918i −0.317043 + 0.193522i
\(663\) 0.893904 + 0.178781i 0.0347164 + 0.00694327i
\(664\) 2.43503 0.178781i 0.0944974 0.00693804i
\(665\) 7.41421 + 7.41421i 0.287511 + 0.287511i
\(666\) 8.65685 5.28411i 0.335446 0.204755i
\(667\) −7.11529 −0.275505
\(668\) −0.746357 2.32471i −0.0288774 0.0899457i
\(669\) 13.8198 + 13.8198i 0.534305 + 0.534305i
\(670\) 2.86461 + 0.693037i 0.110670 + 0.0267744i
\(671\) 17.1778 + 17.1778i 0.663143 + 0.663143i
\(672\) 11.3076 + 4.80013i 0.436201 + 0.185169i
\(673\) 3.20101i 0.123390i −0.998095 0.0616949i \(-0.980349\pi\)
0.998095 0.0616949i \(-0.0196506\pi\)
\(674\) 4.59862 19.0080i 0.177132 0.732160i
\(675\) 22.5667 0.868592
\(676\) 16.7748 + 19.8647i 0.645185 + 0.764026i
\(677\) 11.2132 0.430958 0.215479 0.976508i \(-0.430869\pi\)
0.215479 + 0.976508i \(0.430869\pi\)
\(678\) −3.58409 + 14.8145i −0.137646 + 0.568949i
\(679\) 5.03127i 0.193083i
\(680\) 0.483979 0.0355339i 0.0185597 0.00136266i
\(681\) 16.1005 + 16.1005i 0.616973 + 0.616973i
\(682\) −20.3825 4.93116i −0.780488 0.188824i
\(683\) −4.06332 4.06332i −0.155478 0.155478i 0.625081 0.780560i \(-0.285066\pi\)
−0.780560 + 0.625081i \(0.785066\pi\)
\(684\) 11.2247 3.60373i 0.429187 0.137792i
\(685\) −3.75736 −0.143561
\(686\) −21.0407 + 12.8431i −0.803337 + 0.490354i
\(687\) 19.5887 + 19.5887i 0.747357 + 0.747357i
\(688\) −13.1362 18.3492i −0.500813 0.699558i
\(689\) −29.1421 5.82843i −1.11023 0.222045i
\(690\) 3.70711 2.26280i 0.141127 0.0861434i
\(691\) 7.11529 7.11529i 0.270679 0.270679i −0.558695 0.829373i \(-0.688698\pi\)
0.829373 + 0.558695i \(0.188698\pi\)
\(692\) 22.2929 43.3762i 0.847449 1.64892i
\(693\) 6.14214i 0.233320i
\(694\) 7.18261 29.6887i 0.272648 1.12697i
\(695\) −2.26280 + 2.26280i −0.0858330 + 0.0858330i
\(696\) −9.29872 + 10.7723i −0.352467 + 0.408325i
\(697\) −0.727922 + 0.727922i −0.0275720 + 0.0275720i
\(698\) 12.8640 7.85211i 0.486908 0.297207i
\(699\) −32.3764 −1.22459
\(700\) 11.2247 3.60373i 0.424254 0.136208i
\(701\) 39.3553i 1.48643i −0.669052 0.743215i \(-0.733300\pi\)
0.669052 0.743215i \(-0.266700\pi\)
\(702\) −12.1166 + 26.0908i −0.457311 + 0.984732i
\(703\) 61.5961i 2.32314i
\(704\) 23.9991 32.3128i 0.904501 1.21784i
\(705\) 2.17157 0.0817862
\(706\) 1.65241 + 2.70711i 0.0621891 + 0.101883i
\(707\) −5.38883 + 5.38883i −0.202668 + 0.202668i
\(708\) −28.2373 + 9.06568i −1.06122 + 0.340709i
\(709\) 30.9706 30.9706i 1.16312 1.16312i 0.179336 0.983788i \(-0.442605\pi\)
0.983788 0.179336i \(-0.0573949\pi\)
\(710\) 17.5352 + 4.24230i 0.658084 + 0.159211i
\(711\) 0.715123i 0.0268192i
\(712\) 8.94648 0.656854i 0.335284 0.0246167i
\(713\) −4.34315 + 4.34315i −0.162652 + 0.162652i
\(714\) 0.274524 + 0.449747i 0.0102738 + 0.0168314i
\(715\) −3.55765 + 17.7882i −0.133048 + 0.665242i
\(716\) −22.6924 11.6626i −0.848054 0.435851i
\(717\) 15.0919 + 15.0919i 0.563617 + 0.563617i
\(718\) 2.17157 + 3.55765i 0.0810424 + 0.132770i
\(719\) −38.1662 −1.42336 −0.711679 0.702505i \(-0.752065\pi\)
−0.711679 + 0.702505i \(0.752065\pi\)
\(720\) −0.541280 + 3.26920i −0.0201723 + 0.121836i
\(721\) 15.7279 + 15.7279i 0.585738 + 0.585738i
\(722\) −10.5176 + 43.4737i −0.391426 + 1.61793i
\(723\) −1.57835 1.57835i −0.0586996 0.0586996i
\(724\) −7.84924 + 15.2726i −0.291715 + 0.567602i
\(725\) 13.6569i 0.507203i
\(726\) 28.9936 + 7.01445i 1.07605 + 0.260331i
\(727\) −18.5467 −0.687860 −0.343930 0.938995i \(-0.611758\pi\)
−0.343930 + 0.938995i \(0.611758\pi\)
\(728\) −1.86030 + 14.9125i −0.0689474 + 0.552694i
\(729\) −29.7696 −1.10258
\(730\) −3.22079 0.779208i −0.119207 0.0288398i
\(731\) 0.967957i 0.0358012i
\(732\) 6.50490 12.6569i 0.240428 0.467811i
\(733\) 14.8492 + 14.8492i 0.548469 + 0.548469i 0.925998 0.377529i \(-0.123226\pi\)
−0.377529 + 0.925998i \(0.623226\pi\)
\(734\) −1.26717 + 5.23773i −0.0467720 + 0.193328i
\(735\) 5.03127 + 5.03127i 0.185581 + 0.185581i
\(736\) −4.41597 10.9307i −0.162775 0.402910i
\(737\) 10.4853 0.386230
\(738\) −3.66237 6.00000i −0.134814 0.220863i
\(739\) 15.5995 + 15.5995i 0.573836 + 0.573836i 0.933198 0.359362i \(-0.117006\pi\)
−0.359362 + 0.933198i \(0.617006\pi\)
\(740\) −15.3990 7.91421i −0.566079 0.290932i
\(741\) −20.9706 31.4558i −0.770373 1.15556i
\(742\) −8.94975 14.6622i −0.328556 0.538266i
\(743\) −6.93651 + 6.93651i −0.254476 + 0.254476i −0.822803 0.568327i \(-0.807591\pi\)
0.568327 + 0.822803i \(0.307591\pi\)
\(744\) 0.899495 + 12.2513i 0.0329771 + 0.449154i
\(745\) 14.8284i 0.543272i
\(746\) 20.1062 + 4.86432i 0.736142 + 0.178095i
\(747\) −0.505668 + 0.505668i −0.0185014 + 0.0185014i
\(748\) 1.64382 0.527754i 0.0601040 0.0192966i
\(749\) 11.7574 11.7574i 0.429605 0.429605i
\(750\) −9.77208 16.0094i −0.356826 0.584581i
\(751\) 45.6390 1.66539 0.832696 0.553731i \(-0.186796\pi\)
0.832696 + 0.553731i \(0.186796\pi\)
\(752\) 0.962841 5.81533i 0.0351112 0.212063i
\(753\) 22.7696i 0.829769i
\(754\) −15.7896 7.33269i −0.575022 0.267041i
\(755\) 15.7042i 0.571535i
\(756\) −15.8315 + 5.08277i −0.575786 + 0.184858i
\(757\) 19.2721 0.700456 0.350228 0.936665i \(-0.386104\pi\)
0.350228 + 0.936665i \(0.386104\pi\)
\(758\) −12.5782 + 7.67767i −0.456860 + 0.278866i
\(759\) 10.9258 10.9258i 0.396581 0.396581i
\(760\) −15.2344 13.1504i −0.552610 0.477014i
\(761\) −11.6569 + 11.6569i −0.422561 + 0.422561i −0.886084 0.463524i \(-0.846585\pi\)
0.463524 + 0.886084i \(0.346585\pi\)
\(762\) −6.79850 + 28.1010i −0.246284 + 1.01799i
\(763\) 6.86246i 0.248438i
\(764\) 15.3773 29.9203i 0.556332 1.08248i
\(765\) −0.100505 + 0.100505i −0.00363377 + 0.00363377i
\(766\) 0.305198 0.186292i 0.0110272 0.00673099i
\(767\) −20.1251 30.1876i −0.726675 1.09001i
\(768\) −22.3198 7.59927i −0.805397 0.274215i
\(769\) 9.65685 + 9.65685i 0.348235 + 0.348235i 0.859452 0.511217i \(-0.170805\pi\)
−0.511217 + 0.859452i \(0.670805\pi\)
\(770\) −8.94975 + 5.46289i −0.322527 + 0.196869i
\(771\) 15.7042 0.565573
\(772\) 21.7357 6.97833i 0.782284 0.251155i
\(773\) 27.8787 + 27.8787i 1.00273 + 1.00273i 0.999996 + 0.00273014i \(0.000869031\pi\)
0.00273014 + 0.999996i \(0.499131\pi\)
\(774\) 6.42429 + 1.55423i 0.230916 + 0.0558658i
\(775\) 8.33609 + 8.33609i 0.299441 + 0.299441i
\(776\) 0.707107 + 9.63093i 0.0253837 + 0.345730i
\(777\) 18.7990i 0.674410i
\(778\) 2.04255 8.44273i 0.0732291 0.302686i
\(779\) 42.6918 1.52959
\(780\) 10.5584 1.20101i 0.378051 0.0430032i
\(781\) 64.1838 2.29668
\(782\) 0.118906 0.491489i 0.00425208 0.0175756i
\(783\) 19.2619i 0.688363i
\(784\) 15.7042 11.2426i 0.560865 0.401523i
\(785\) 8.48528 + 8.48528i 0.302853 + 0.302853i
\(786\) −5.45777 1.32040i −0.194672 0.0470972i
\(787\) −13.8730 13.8730i −0.494520 0.494520i 0.415207 0.909727i \(-0.363709\pi\)
−0.909727 + 0.415207i \(0.863709\pi\)
\(788\) 2.25369 + 7.01968i 0.0802845 + 0.250066i
\(789\) 19.1716 0.682526
\(790\) −1.04201 + 0.636039i −0.0370731 + 0.0226293i
\(791\) −7.62096 7.62096i −0.270970 0.270970i
\(792\) 0.863230 + 11.7574i 0.0306735 + 0.417780i
\(793\) 17.0711 + 3.41421i 0.606211 + 0.121242i
\(794\) 31.5563 19.2619i 1.11989 0.683578i
\(795\) −8.58892 + 8.58892i −0.304618 + 0.304618i
\(796\) −36.4350 18.7255i −1.29141 0.663708i
\(797\) 36.8284i 1.30453i −0.757991 0.652265i \(-0.773819\pi\)
0.757991 0.652265i \(-0.226181\pi\)
\(798\) 5.13833 21.2388i 0.181895 0.751846i
\(799\) 0.178781 0.178781i 0.00632481 0.00632481i
\(800\) −20.9800 + 8.47586i −0.741755 + 0.299667i
\(801\) −1.85786 + 1.85786i −0.0656444 + 0.0656444i
\(802\) −4.29289 + 2.62036i −0.151587 + 0.0925283i
\(803\) −11.7890 −0.416025
\(804\) −1.87756 5.84813i −0.0662166 0.206248i
\(805\) 3.07107i 0.108241i
\(806\) −14.1137 + 5.16203i −0.497134 + 0.181825i
\(807\) 29.6820i 1.04485i
\(808\) 9.55802 11.0727i 0.336250 0.389538i
\(809\) −35.1421 −1.23553 −0.617766 0.786362i \(-0.711962\pi\)
−0.617766 + 0.786362i \(0.711962\pi\)
\(810\) 4.29446 + 7.03553i 0.150892 + 0.247203i
\(811\) −20.1251 + 20.1251i −0.706688 + 0.706688i −0.965837 0.259150i \(-0.916558\pi\)
0.259150 + 0.965837i \(0.416558\pi\)
\(812\) −3.07598 9.58088i −0.107946 0.336223i
\(813\) −7.15076 + 7.15076i −0.250788 + 0.250788i
\(814\) −59.8689 14.4841i −2.09840 0.507668i
\(815\) 3.81048i 0.133475i
\(816\) −0.588706 0.822330i −0.0206088 0.0287873i
\(817\) −28.3848 + 28.3848i −0.993058 + 0.993058i
\(818\) 24.1144 + 39.5061i 0.843139 + 1.38130i
\(819\) −2.44158 3.66237i −0.0853158 0.127974i
\(820\) −5.48528 + 10.6729i −0.191554 + 0.372715i
\(821\) −17.7782 17.7782i −0.620463 0.620463i 0.325187 0.945650i \(-0.394573\pi\)
−0.945650 + 0.325187i \(0.894573\pi\)
\(822\) 4.07969 + 6.68368i 0.142296 + 0.233120i
\(823\) −4.88317 −0.170216 −0.0851082 0.996372i \(-0.527124\pi\)
−0.0851082 + 0.996372i \(0.527124\pi\)
\(824\) −32.3170 27.8962i −1.12582 0.971809i
\(825\) −20.9706 20.9706i −0.730101 0.730101i
\(826\) 4.93116 20.3825i 0.171577 0.709199i
\(827\) −28.8187 28.8187i −1.00213 1.00213i −0.999998 0.00212804i \(-0.999323\pi\)
−0.00212804 0.999998i \(-0.500677\pi\)
\(828\) 3.07107 + 1.57835i 0.106727 + 0.0548516i
\(829\) 14.3848i 0.499604i 0.968297 + 0.249802i \(0.0803655\pi\)
−0.968297 + 0.249802i \(0.919634\pi\)
\(830\) 1.18656 + 0.287065i 0.0411861 + 0.00996419i
\(831\) −8.84175 −0.306717
\(832\) 1.46518 28.8072i 0.0507959 0.998709i
\(833\) 0.828427 0.0287033
\(834\) 6.48205 + 1.56821i 0.224455 + 0.0543025i
\(835\) 1.22079i 0.0422472i
\(836\) −63.6801 32.7279i −2.20242 1.13192i
\(837\) −11.7574 11.7574i −0.406394 0.406394i
\(838\) −1.87613 + 7.75481i −0.0648097 + 0.267885i
\(839\) 16.8203 + 16.8203i 0.580701 + 0.580701i 0.935096 0.354395i \(-0.115313\pi\)
−0.354395 + 0.935096i \(0.615313\pi\)
\(840\) 4.64951 + 4.01347i 0.160423 + 0.138478i
\(841\) −17.3431 −0.598040
\(842\) 25.0299 + 41.0061i 0.862589 + 1.41316i
\(843\) −23.9356 23.9356i −0.824385 0.824385i
\(844\) −18.1675 + 35.3492i −0.625351 + 1.21677i
\(845\) 4.94975 + 12.0208i 0.170276 + 0.413529i
\(846\) 0.899495 + 1.47363i 0.0309253 + 0.0506643i
\(847\) −14.9150 + 14.9150i −0.512487 + 0.512487i
\(848\) 19.1924 + 26.8088i 0.659069 + 0.920617i
\(849\) 35.7990i 1.22862i
\(850\) −0.943348 0.228225i −0.0323566 0.00782805i
\(851\) −12.7570 + 12.7570i −0.437303 + 0.437303i
\(852\) −11.4932 35.7983i −0.393749 1.22643i
\(853\) 15.5772 15.5772i 0.533352 0.533352i −0.388216 0.921568i \(-0.626909\pi\)
0.921568 + 0.388216i \(0.126909\pi\)
\(854\) 5.24264 + 8.58892i 0.179399 + 0.293907i
\(855\) 5.89450 0.201588
\(856\) −20.8537 + 24.1585i −0.712764 + 0.825721i
\(857\) 1.85786i 0.0634634i 0.999496 + 0.0317317i \(0.0101022\pi\)
−0.999496 + 0.0317317i \(0.989898\pi\)
\(858\) 35.5050 12.9858i 1.21212 0.443328i
\(859\) 48.0806i 1.64049i −0.572013 0.820244i \(-0.693837\pi\)
0.572013 0.820244i \(-0.306163\pi\)
\(860\) −3.44916 10.7432i −0.117615 0.366341i
\(861\) −13.0294 −0.444042
\(862\) 26.9352 16.4411i 0.917416 0.559987i
\(863\) 27.9248 27.9248i 0.950572 0.950572i −0.0482622 0.998835i \(-0.515368\pi\)
0.998835 + 0.0482622i \(0.0153683\pi\)
\(864\) 29.5905 11.9545i 1.00669 0.406700i
\(865\) 17.2426 17.2426i 0.586267 0.586267i
\(866\) 10.7459 44.4171i 0.365159 1.50935i
\(867\) 25.0083i 0.849325i
\(868\) −7.72569 3.97056i −0.262227 0.134770i
\(869\) −3.07107 + 3.07107i −0.104179 + 0.104179i
\(870\) −6.07328 + 3.70711i −0.205904 + 0.125683i
\(871\) 6.25206 4.16804i 0.211843 0.141229i
\(872\) 0.964466 + 13.1362i 0.0326609 + 0.444848i
\(873\) −2.00000 2.00000i −0.0676897 0.0676897i
\(874\) −17.8995 + 10.9258i −0.605459 + 0.369570i
\(875\) 13.2626 0.448359
\(876\) 2.11102 + 6.57527i 0.0713247 + 0.222158i
\(877\) −18.2635 18.2635i −0.616713 0.616713i 0.327974 0.944687i \(-0.393634\pi\)
−0.944687 + 0.327974i \(0.893634\pi\)
\(878\) 17.1877 + 4.15822i 0.580055 + 0.140333i
\(879\) −1.19012 1.19012i −0.0401417 0.0401417i
\(880\) 16.3640 11.7150i 0.551629 0.394911i
\(881\) 10.3137i 0.347478i 0.984792 + 0.173739i \(0.0555849\pi\)
−0.984792 + 0.173739i \(0.944415\pi\)
\(882\) −1.33019 + 5.49824i −0.0447899 + 0.185135i
\(883\) −15.1985 −0.511472 −0.255736 0.966747i \(-0.582318\pi\)
−0.255736 + 0.966747i \(0.582318\pi\)
\(884\) 0.770371 0.968125i 0.0259104 0.0325616i
\(885\) −14.8284 −0.498452
\(886\) −2.04428 + 8.44988i −0.0686791 + 0.283879i
\(887\) 42.1861i 1.41647i 0.705976 + 0.708235i \(0.250508\pi\)
−0.705976 + 0.708235i \(0.749492\pi\)
\(888\) 2.64205 + 35.9853i 0.0886615 + 1.20759i
\(889\) −14.4558 14.4558i −0.484833 0.484833i
\(890\) 4.35951 + 1.05470i 0.146131 + 0.0353536i
\(891\) 20.7355 + 20.7355i 0.694665 + 0.694665i
\(892\) 25.2556 8.10840i 0.845619 0.271489i
\(893\) −10.4853 −0.350877
\(894\) 26.3772 16.1005i 0.882184 0.538481i
\(895\) −9.02054 9.02054i −0.301523 0.301523i
\(896\) 12.8093 10.6716i 0.427930 0.356512i
\(897\) 2.17157 10.8579i 0.0725067 0.362534i
\(898\) −43.9203 + 26.8088i −1.46564 + 0.894620i
\(899\) 7.11529 7.11529i 0.237308 0.237308i
\(900\) 3.02944 5.89450i 0.100981 0.196483i
\(901\) 1.41421i 0.0471143i
\(902\) −10.0388 + 41.4947i −0.334257 + 1.38162i
\(903\) 8.66297 8.66297i 0.288286 0.288286i
\(904\) 15.6592 + 13.5171i 0.520818 + 0.449571i
\(905\) −6.07107 + 6.07107i −0.201809 + 0.201809i
\(906\) 27.9350 17.0514i 0.928079 0.566496i
\(907\) −0.252834 −0.00839522 −0.00419761 0.999991i \(-0.501336\pi\)
−0.00419761 + 0.999991i \(0.501336\pi\)
\(908\) 29.4235 9.44654i 0.976454 0.313494i
\(909\) 4.28427i 0.142100i
\(910\) −3.16490 + 6.81501i −0.104915 + 0.225915i
\(911\) 15.0938i 0.500081i −0.968235 0.250040i \(-0.919556\pi\)
0.968235 0.250040i \(-0.0804439\pi\)
\(912\) −6.85090 + 41.3778i −0.226856 + 1.37016i
\(913\) 4.34315 0.143737
\(914\) −0.610396 1.00000i −0.0201901 0.0330771i
\(915\) 5.03127 5.03127i 0.166329 0.166329i
\(916\) 35.7983 11.4932i 1.18281 0.379745i
\(917\) 2.80761 2.80761i 0.0927155 0.0927155i
\(918\) 1.33051 + 0.321892i 0.0439135 + 0.0106240i
\(919\) 21.8516i 0.720816i 0.932795 + 0.360408i \(0.117363\pi\)
−0.932795 + 0.360408i \(0.882637\pi\)
\(920\) −0.431615 5.87868i −0.0142299 0.193814i
\(921\) 2.54416 2.54416i 0.0838328 0.0838328i
\(922\) −6.73604 11.0355i −0.221840 0.363436i
\(923\) 38.2709 25.5139i 1.25970 0.839801i
\(924\) 19.4350 + 9.98849i 0.639366 + 0.328597i
\(925\) 24.4853 + 24.4853i 0.805071 + 0.805071i
\(926\) 21.8701 + 35.8293i 0.718695 + 1.17742i
\(927\) 12.5041 0.410689
\(928\) 7.23460 + 17.9075i 0.237487 + 0.587844i
\(929\) −24.6274 24.6274i −0.807999 0.807999i 0.176331 0.984331i \(-0.443577\pi\)
−0.984331 + 0.176331i \(0.943577\pi\)
\(930\) −1.44430 + 5.96991i −0.0473606 + 0.195761i
\(931\) −24.2931 24.2931i −0.796175 0.796175i
\(932\) −20.0858 + 39.0818i −0.657932 + 1.28017i
\(933\) 43.7401i 1.43199i
\(934\) −29.3412 7.09853i −0.960072 0.232271i
\(935\) 0.863230 0.0282306
\(936\) 5.18843 + 6.66742i 0.169589 + 0.217931i
\(937\) 24.9706 0.815753 0.407876 0.913037i \(-0.366269\pi\)
0.407876 + 0.913037i \(0.366269\pi\)
\(938\) 4.22136 + 1.02128i 0.137832 + 0.0333459i
\(939\) 5.13600i 0.167607i
\(940\) 1.34721 2.62132i 0.0439411 0.0854980i
\(941\) 1.73654 + 1.73654i 0.0566097 + 0.0566097i 0.734845 0.678235i \(-0.237255\pi\)
−0.678235 + 0.734845i \(0.737255\pi\)
\(942\) 5.88062 24.3070i 0.191601 0.791966i
\(943\) 8.84175 + 8.84175i 0.287927 + 0.287927i
\(944\) −6.57469 + 39.7096i −0.213988 + 1.29244i
\(945\) −8.31371 −0.270445
\(946\) −20.9143 34.2635i −0.679982 1.11400i
\(947\) 30.7980 + 30.7980i 1.00080 + 1.00080i 1.00000 0.000801955i \(0.000255270\pi\)
0.000801955 1.00000i \(0.499745\pi\)
\(948\) 2.26280 + 1.16295i 0.0734924 + 0.0377709i
\(949\) −7.02944 + 4.68629i −0.228185 + 0.152123i
\(950\) 20.9706 + 34.3557i 0.680375 + 1.11465i
\(951\) 23.0723 23.0723i 0.748172 0.748172i
\(952\) 0.713203 0.0523637i 0.0231151 0.00169712i
\(953\) 22.8579i 0.740439i −0.928944 0.370219i \(-0.879282\pi\)
0.928944 0.370219i \(-0.120718\pi\)
\(954\) −9.38607 2.27078i −0.303885 0.0735192i
\(955\) 11.8937 11.8937i 0.384872 0.384872i
\(956\) 27.5803 8.85475i 0.892010 0.286383i
\(957\) −17.8995 + 17.8995i −0.578608 + 0.578608i
\(958\) 1.98528 + 3.25245i 0.0641415 + 0.105082i
\(959\) −5.53694 −0.178797
\(960\) −9.46421 7.02918i −0.305456 0.226866i
\(961\) 22.3137i 0.719797i
\(962\) −41.4557 + 15.1623i −1.33659 + 0.488851i
\(963\) 9.34742i 0.301216i
\(964\) −2.88443 + 0.926056i −0.0929011 + 0.0298263i
\(965\) 11.4142 0.367437
\(966\) 5.46289 3.33452i 0.175766 0.107287i
\(967\) −31.2296 + 31.2296i −1.00428 + 1.00428i −0.00428700 + 0.999991i \(0.501365\pi\)
−0.999991 + 0.00428700i \(0.998635\pi\)
\(968\) 26.4544 30.6468i 0.850276 0.985024i
\(969\) −1.27208 + 1.27208i −0.0408650 + 0.0408650i
\(970\) −1.13539 + 4.69304i −0.0364552 + 0.150684i
\(971\) 32.8821i 1.05524i 0.849482 + 0.527618i \(0.176915\pi\)
−0.849482 + 0.527618i \(0.823085\pi\)
\(972\) −7.62096 + 14.8284i −0.244443 + 0.475622i
\(973\) −3.33452 + 3.33452i −0.106900 + 0.106900i
\(974\) −15.7042 + 9.58579i −0.503196 + 0.307148i
\(975\) −20.8402 4.16804i −0.667421 0.133484i
\(976\) −11.2426 15.7042i −0.359868 0.502680i
\(977\) −9.62742 9.62742i −0.308008 0.308008i 0.536128 0.844137i \(-0.319886\pi\)
−0.844137 + 0.536128i \(0.819886\pi\)
\(978\) −6.77817 + 4.13737i −0.216742 + 0.132298i
\(979\) 15.9570 0.509990
\(980\) 9.19460 2.95196i 0.293711 0.0942970i
\(981\) −2.72792 2.72792i −0.0870958 0.0870958i
\(982\) −2.02559 0.490051i −0.0646390 0.0156382i
\(983\) −10.5989 10.5989i −0.338052 0.338052i 0.517582 0.855634i \(-0.326832\pi\)
−0.855634 + 0.517582i \(0.826832\pi\)
\(984\) 24.9411 1.83119i 0.795094 0.0583761i
\(985\) 3.68629i 0.117455i
\(986\) −0.194802 + 0.805198i −0.00620376 + 0.0256427i
\(987\) 3.20009 0.101860
\(988\) −50.9804 + 5.79901i −1.62190 + 0.184491i
\(989\) −11.7574 −0.373862
\(990\) −1.38607 + 5.72922i −0.0440523 + 0.182087i
\(991\) 5.38883i 0.171182i −0.996330 0.0855910i \(-0.972722\pi\)
0.996330 0.0855910i \(-0.0272778\pi\)
\(992\) 15.3467 + 6.51472i 0.487257 + 0.206843i
\(993\) 7.04163 + 7.04163i 0.223459 + 0.223459i
\(994\) 25.8403 + 6.25157i 0.819605 + 0.198288i
\(995\) −14.4834 14.4834i −0.459155 0.459155i
\(996\) −0.777712 2.42237i −0.0246428 0.0767558i
\(997\) −2.92893 −0.0927602 −0.0463801 0.998924i \(-0.514769\pi\)
−0.0463801 + 0.998924i \(0.514769\pi\)
\(998\) −3.55765 + 2.17157i −0.112615 + 0.0687399i
\(999\) −34.5345 34.5345i −1.09262 1.09262i
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 52.2.f.b.47.1 yes 8
3.2 odd 2 468.2.n.i.307.4 8
4.3 odd 2 inner 52.2.f.b.47.3 yes 8
8.3 odd 2 832.2.k.h.255.3 8
8.5 even 2 832.2.k.h.255.2 8
12.11 even 2 468.2.n.i.307.2 8
13.2 odd 12 676.2.l.l.19.2 16
13.3 even 3 676.2.l.l.319.3 16
13.4 even 6 676.2.l.h.427.2 16
13.5 odd 4 inner 52.2.f.b.31.3 yes 8
13.6 odd 12 676.2.l.l.587.4 16
13.7 odd 12 676.2.l.h.587.1 16
13.8 odd 4 676.2.f.g.239.2 8
13.9 even 3 676.2.l.l.427.3 16
13.10 even 6 676.2.l.h.319.2 16
13.11 odd 12 676.2.l.h.19.3 16
13.12 even 2 676.2.f.g.99.4 8
39.5 even 4 468.2.n.i.343.2 8
52.3 odd 6 676.2.l.l.319.4 16
52.7 even 12 676.2.l.h.587.2 16
52.11 even 12 676.2.l.h.19.2 16
52.15 even 12 676.2.l.l.19.3 16
52.19 even 12 676.2.l.l.587.3 16
52.23 odd 6 676.2.l.h.319.1 16
52.31 even 4 inner 52.2.f.b.31.1 8
52.35 odd 6 676.2.l.l.427.2 16
52.43 odd 6 676.2.l.h.427.3 16
52.47 even 4 676.2.f.g.239.4 8
52.51 odd 2 676.2.f.g.99.2 8
104.5 odd 4 832.2.k.h.447.2 8
104.83 even 4 832.2.k.h.447.3 8
156.83 odd 4 468.2.n.i.343.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.2.f.b.31.1 8 52.31 even 4 inner
52.2.f.b.31.3 yes 8 13.5 odd 4 inner
52.2.f.b.47.1 yes 8 1.1 even 1 trivial
52.2.f.b.47.3 yes 8 4.3 odd 2 inner
468.2.n.i.307.2 8 12.11 even 2
468.2.n.i.307.4 8 3.2 odd 2
468.2.n.i.343.2 8 39.5 even 4
468.2.n.i.343.4 8 156.83 odd 4
676.2.f.g.99.2 8 52.51 odd 2
676.2.f.g.99.4 8 13.12 even 2
676.2.f.g.239.2 8 13.8 odd 4
676.2.f.g.239.4 8 52.47 even 4
676.2.l.h.19.2 16 52.11 even 12
676.2.l.h.19.3 16 13.11 odd 12
676.2.l.h.319.1 16 52.23 odd 6
676.2.l.h.319.2 16 13.10 even 6
676.2.l.h.427.2 16 13.4 even 6
676.2.l.h.427.3 16 52.43 odd 6
676.2.l.h.587.1 16 13.7 odd 12
676.2.l.h.587.2 16 52.7 even 12
676.2.l.l.19.2 16 13.2 odd 12
676.2.l.l.19.3 16 52.15 even 12
676.2.l.l.319.3 16 13.3 even 3
676.2.l.l.319.4 16 52.3 odd 6
676.2.l.l.427.2 16 52.35 odd 6
676.2.l.l.427.3 16 13.9 even 3
676.2.l.l.587.3 16 52.19 even 12
676.2.l.l.587.4 16 13.6 odd 12
832.2.k.h.255.2 8 8.5 even 2
832.2.k.h.255.3 8 8.3 odd 2
832.2.k.h.447.2 8 104.5 odd 4
832.2.k.h.447.3 8 104.83 even 4