Properties

Label 210.2.r.a.101.4
Level $210$
Weight $2$
Character 210.101
Analytic conductor $1.677$
Analytic rank $0$
Dimension $12$
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] = [210,2,Mod(101,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.r (of order \(6\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} - 864 x^{3} + 891 x^{2} - 972 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.4
Root \(-0.384890 - 1.68874i\) of defining polynomial
Character \(\chi\) \(=\) 210.101
Dual form 210.2.r.a.131.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-1.68874 + 0.384890i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.27005 + 1.17770i) q^{6} +(2.63608 + 0.226058i) q^{7} -1.00000i q^{8} +(2.70372 - 1.29996i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-1.68874 + 0.384890i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.27005 + 1.17770i) q^{6} +(2.63608 + 0.226058i) q^{7} -1.00000i q^{8} +(2.70372 - 1.29996i) q^{9} +(0.866025 + 0.500000i) q^{10} +(4.29143 + 2.47766i) q^{11} +(-0.511048 + 1.65494i) q^{12} -6.37523i q^{13} +(2.39594 - 1.12227i) q^{14} +(-1.17770 - 1.27005i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.81377 + 3.14155i) q^{17} +(1.69151 - 2.47766i) q^{18} +(-3.64345 + 2.10355i) q^{19} +1.00000 q^{20} +(-4.53867 + 0.632846i) q^{21} +4.95532 q^{22} +(-1.65996 + 0.958379i) q^{23} +(0.384890 + 1.68874i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.18762 - 5.52111i) q^{26} +(-4.06555 + 3.23594i) q^{27} +(1.51381 - 2.16988i) q^{28} -0.800269i q^{29} +(-1.65494 - 0.511048i) q^{30} +(4.36166 + 2.51820i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-8.20077 - 2.53241i) q^{33} +3.62755i q^{34} +(1.12227 + 2.39594i) q^{35} +(0.226058 - 2.99147i) q^{36} +(-2.91394 - 5.04710i) q^{37} +(-2.10355 + 3.64345i) q^{38} +(2.45377 + 10.7661i) q^{39} +(0.866025 - 0.500000i) q^{40} -7.45163 q^{41} +(-3.61418 + 2.81739i) q^{42} -4.64827 q^{43} +(4.29143 - 2.47766i) q^{44} +(2.47766 + 1.69151i) q^{45} +(-0.958379 + 1.65996i) q^{46} +(-0.303890 - 0.526352i) q^{47} +(1.17770 + 1.27005i) q^{48} +(6.89780 + 1.19181i) q^{49} +1.00000i q^{50} +(1.85385 - 6.00338i) q^{51} +(-5.52111 - 3.18762i) q^{52} +(-12.3898 - 7.15326i) q^{53} +(-1.90290 + 4.83518i) q^{54} +4.95532i q^{55} +(0.226058 - 2.63608i) q^{56} +(5.34323 - 4.95469i) q^{57} +(-0.400134 - 0.693053i) q^{58} +(0.875658 - 1.51668i) q^{59} +(-1.68874 + 0.384890i) q^{60} +(2.96447 - 1.71154i) q^{61} +5.03641 q^{62} +(7.42108 - 2.81561i) q^{63} -1.00000 q^{64} +(5.52111 - 3.18762i) q^{65} +(-8.36827 + 1.90726i) q^{66} +(-3.99147 + 6.91343i) q^{67} +(1.81377 + 3.14155i) q^{68} +(2.43438 - 2.25736i) q^{69} +(2.16988 + 1.51381i) q^{70} +2.48759i q^{71} +(-1.29996 - 2.70372i) q^{72} +(13.0712 + 7.54666i) q^{73} +(-5.04710 - 2.91394i) q^{74} +(0.511048 - 1.65494i) q^{75} +4.20710i q^{76} +(10.7525 + 7.50142i) q^{77} +(7.50809 + 8.09687i) q^{78} +(-1.33404 - 2.31062i) q^{79} +(0.500000 - 0.866025i) q^{80} +(5.62019 - 7.02947i) q^{81} +(-6.45330 + 3.72581i) q^{82} -7.27215 q^{83} +(-1.72127 + 4.24702i) q^{84} -3.62755 q^{85} +(-4.02552 + 2.32413i) q^{86} +(0.308016 + 1.35145i) q^{87} +(2.47766 - 4.29143i) q^{88} +(-0.942474 - 1.63241i) q^{89} +(2.99147 + 0.226058i) q^{90} +(1.44117 - 16.8056i) q^{91} +1.91676i q^{92} +(-8.33496 - 2.57384i) q^{93} +(-0.526352 - 0.303890i) q^{94} +(-3.64345 - 2.10355i) q^{95} +(1.65494 + 0.511048i) q^{96} -17.6562i q^{97} +(6.56957 - 2.41676i) q^{98} +(14.8237 + 1.12019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −1.68874 + 0.384890i −0.974997 + 0.222217i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −1.27005 + 1.17770i −0.518496 + 0.480793i
\(7\) 2.63608 + 0.226058i 0.996343 + 0.0854419i
\(8\) 1.00000i 0.353553i
\(9\) 2.70372 1.29996i 0.901240 0.433321i
\(10\) 0.866025 + 0.500000i 0.273861 + 0.158114i
\(11\) 4.29143 + 2.47766i 1.29392 + 0.747043i 0.979346 0.202191i \(-0.0648063\pi\)
0.314570 + 0.949234i \(0.398140\pi\)
\(12\) −0.511048 + 1.65494i −0.147527 + 0.477740i
\(13\) 6.37523i 1.76817i −0.467325 0.884086i \(-0.654782\pi\)
0.467325 0.884086i \(-0.345218\pi\)
\(14\) 2.39594 1.12227i 0.640341 0.299938i
\(15\) −1.17770 1.27005i −0.304080 0.327926i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.81377 + 3.14155i −0.439905 + 0.761937i −0.997682 0.0680536i \(-0.978321\pi\)
0.557777 + 0.829991i \(0.311654\pi\)
\(18\) 1.69151 2.47766i 0.398692 0.583990i
\(19\) −3.64345 + 2.10355i −0.835865 + 0.482587i −0.855857 0.517213i \(-0.826969\pi\)
0.0199914 + 0.999800i \(0.493636\pi\)
\(20\) 1.00000 0.223607
\(21\) −4.53867 + 0.632846i −0.990419 + 0.138098i
\(22\) 4.95532 1.05648
\(23\) −1.65996 + 0.958379i −0.346126 + 0.199836i −0.662978 0.748639i \(-0.730708\pi\)
0.316852 + 0.948475i \(0.397374\pi\)
\(24\) 0.384890 + 1.68874i 0.0785654 + 0.344714i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.18762 5.52111i −0.625143 1.08278i
\(27\) −4.06555 + 3.23594i −0.782415 + 0.622757i
\(28\) 1.51381 2.16988i 0.286083 0.410069i
\(29\) 0.800269i 0.148606i −0.997236 0.0743031i \(-0.976327\pi\)
0.997236 0.0743031i \(-0.0236732\pi\)
\(30\) −1.65494 0.511048i −0.302150 0.0933041i
\(31\) 4.36166 + 2.51820i 0.783377 + 0.452283i 0.837626 0.546245i \(-0.183943\pi\)
−0.0542489 + 0.998527i \(0.517276\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −8.20077 2.53241i −1.42757 0.440835i
\(34\) 3.62755i 0.622119i
\(35\) 1.12227 + 2.39594i 0.189698 + 0.404987i
\(36\) 0.226058 2.99147i 0.0376763 0.498578i
\(37\) −2.91394 5.04710i −0.479050 0.829738i 0.520662 0.853763i \(-0.325685\pi\)
−0.999711 + 0.0240249i \(0.992352\pi\)
\(38\) −2.10355 + 3.64345i −0.341241 + 0.591046i
\(39\) 2.45377 + 10.7661i 0.392917 + 1.72396i
\(40\) 0.866025 0.500000i 0.136931 0.0790569i
\(41\) −7.45163 −1.16375 −0.581874 0.813279i \(-0.697680\pi\)
−0.581874 + 0.813279i \(0.697680\pi\)
\(42\) −3.61418 + 2.81739i −0.557680 + 0.434733i
\(43\) −4.64827 −0.708854 −0.354427 0.935084i \(-0.615324\pi\)
−0.354427 + 0.935084i \(0.615324\pi\)
\(44\) 4.29143 2.47766i 0.646958 0.373521i
\(45\) 2.47766 + 1.69151i 0.369348 + 0.252155i
\(46\) −0.958379 + 1.65996i −0.141305 + 0.244748i
\(47\) −0.303890 0.526352i −0.0443269 0.0767764i 0.843011 0.537897i \(-0.180781\pi\)
−0.887338 + 0.461120i \(0.847448\pi\)
\(48\) 1.17770 + 1.27005i 0.169986 + 0.183316i
\(49\) 6.89780 + 1.19181i 0.985399 + 0.170259i
\(50\) 1.00000i 0.141421i
\(51\) 1.85385 6.00338i 0.259591 0.840641i
\(52\) −5.52111 3.18762i −0.765641 0.442043i
\(53\) −12.3898 7.15326i −1.70187 0.982576i −0.943866 0.330329i \(-0.892840\pi\)
−0.758006 0.652247i \(-0.773826\pi\)
\(54\) −1.90290 + 4.83518i −0.258951 + 0.657985i
\(55\) 4.95532i 0.668175i
\(56\) 0.226058 2.63608i 0.0302083 0.352260i
\(57\) 5.34323 4.95469i 0.707727 0.656264i
\(58\) −0.400134 0.693053i −0.0525402 0.0910023i
\(59\) 0.875658 1.51668i 0.114001 0.197456i −0.803379 0.595468i \(-0.796967\pi\)
0.917380 + 0.398013i \(0.130300\pi\)
\(60\) −1.68874 + 0.384890i −0.218016 + 0.0496891i
\(61\) 2.96447 1.71154i 0.379561 0.219140i −0.298066 0.954545i \(-0.596342\pi\)
0.677627 + 0.735405i \(0.263008\pi\)
\(62\) 5.03641 0.639624
\(63\) 7.42108 2.81561i 0.934968 0.354733i
\(64\) −1.00000 −0.125000
\(65\) 5.52111 3.18762i 0.684810 0.395375i
\(66\) −8.36827 + 1.90726i −1.03006 + 0.234767i
\(67\) −3.99147 + 6.91343i −0.487636 + 0.844610i −0.999899 0.0142186i \(-0.995474\pi\)
0.512263 + 0.858829i \(0.328807\pi\)
\(68\) 1.81377 + 3.14155i 0.219952 + 0.380969i
\(69\) 2.43438 2.25736i 0.293065 0.271754i
\(70\) 2.16988 + 1.51381i 0.259350 + 0.180935i
\(71\) 2.48759i 0.295222i 0.989045 + 0.147611i \(0.0471584\pi\)
−0.989045 + 0.147611i \(0.952842\pi\)
\(72\) −1.29996 2.70372i −0.153202 0.318636i
\(73\) 13.0712 + 7.54666i 1.52987 + 0.883270i 0.999367 + 0.0355852i \(0.0113295\pi\)
0.530501 + 0.847684i \(0.322004\pi\)
\(74\) −5.04710 2.91394i −0.586713 0.338739i
\(75\) 0.511048 1.65494i 0.0590107 0.191096i
\(76\) 4.20710i 0.482587i
\(77\) 10.7525 + 7.50142i 1.22536 + 0.854866i
\(78\) 7.50809 + 8.09687i 0.850124 + 0.916790i
\(79\) −1.33404 2.31062i −0.150091 0.259965i 0.781170 0.624319i \(-0.214623\pi\)
−0.931261 + 0.364354i \(0.881290\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 5.62019 7.02947i 0.624466 0.781052i
\(82\) −6.45330 + 3.72581i −0.712648 + 0.411447i
\(83\) −7.27215 −0.798222 −0.399111 0.916903i \(-0.630681\pi\)
−0.399111 + 0.916903i \(0.630681\pi\)
\(84\) −1.72127 + 4.24702i −0.187806 + 0.463388i
\(85\) −3.62755 −0.393463
\(86\) −4.02552 + 2.32413i −0.434083 + 0.250618i
\(87\) 0.308016 + 1.35145i 0.0330227 + 0.144891i
\(88\) 2.47766 4.29143i 0.264120 0.457468i
\(89\) −0.942474 1.63241i −0.0999021 0.173035i 0.811742 0.584016i \(-0.198520\pi\)
−0.911644 + 0.410981i \(0.865186\pi\)
\(90\) 2.99147 + 0.226058i 0.315329 + 0.0238286i
\(91\) 1.44117 16.8056i 0.151076 1.76171i
\(92\) 1.91676i 0.199836i
\(93\) −8.33496 2.57384i −0.864295 0.266895i
\(94\) −0.526352 0.303890i −0.0542891 0.0313438i
\(95\) −3.64345 2.10355i −0.373810 0.215819i
\(96\) 1.65494 + 0.511048i 0.168907 + 0.0521586i
\(97\) 17.6562i 1.79271i −0.443334 0.896356i \(-0.646205\pi\)
0.443334 0.896356i \(-0.353795\pi\)
\(98\) 6.56957 2.41676i 0.663627 0.244129i
\(99\) 14.8237 + 1.12019i 1.48984 + 0.112583i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −0.574210 + 0.994562i −0.0571361 + 0.0989626i −0.893179 0.449702i \(-0.851530\pi\)
0.836043 + 0.548664i \(0.184864\pi\)
\(102\) −1.39621 6.12600i −0.138245 0.606565i
\(103\) −6.30781 + 3.64182i −0.621527 + 0.358839i −0.777463 0.628928i \(-0.783494\pi\)
0.155936 + 0.987767i \(0.450161\pi\)
\(104\) −6.37523 −0.625143
\(105\) −2.81739 3.61418i −0.274950 0.352708i
\(106\) −14.3065 −1.38957
\(107\) 2.32646 1.34318i 0.224908 0.129850i −0.383313 0.923618i \(-0.625217\pi\)
0.608221 + 0.793768i \(0.291884\pi\)
\(108\) 0.769634 + 5.13884i 0.0740581 + 0.494485i
\(109\) −4.51172 + 7.81452i −0.432144 + 0.748495i −0.997058 0.0766547i \(-0.975576\pi\)
0.564914 + 0.825150i \(0.308909\pi\)
\(110\) 2.47766 + 4.29143i 0.236236 + 0.409172i
\(111\) 6.86349 + 7.40171i 0.651454 + 0.702540i
\(112\) −1.12227 2.39594i −0.106044 0.226395i
\(113\) 12.4267i 1.16901i 0.811391 + 0.584504i \(0.198711\pi\)
−0.811391 + 0.584504i \(0.801289\pi\)
\(114\) 2.15003 6.96250i 0.201368 0.652098i
\(115\) −1.65996 0.958379i −0.154792 0.0893693i
\(116\) −0.693053 0.400134i −0.0643483 0.0371515i
\(117\) −8.28757 17.2368i −0.766186 1.59355i
\(118\) 1.75132i 0.161222i
\(119\) −5.49142 + 7.87134i −0.503397 + 0.721565i
\(120\) −1.27005 + 1.17770i −0.115939 + 0.107509i
\(121\) 6.77761 + 11.7392i 0.616146 + 1.06720i
\(122\) 1.71154 2.96447i 0.154955 0.268390i
\(123\) 12.5839 2.86806i 1.13465 0.258604i
\(124\) 4.36166 2.51820i 0.391688 0.226141i
\(125\) −1.00000 −0.0894427
\(126\) 5.01904 6.14892i 0.447131 0.547790i
\(127\) 8.06679 0.715812 0.357906 0.933758i \(-0.383491\pi\)
0.357906 + 0.933758i \(0.383491\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 7.84974 1.78907i 0.691131 0.157519i
\(130\) 3.18762 5.52111i 0.279572 0.484234i
\(131\) −1.69151 2.92978i −0.147788 0.255976i 0.782622 0.622497i \(-0.213882\pi\)
−0.930410 + 0.366522i \(0.880549\pi\)
\(132\) −6.29351 + 5.83587i −0.547780 + 0.507947i
\(133\) −10.0799 + 4.72148i −0.874042 + 0.409404i
\(134\) 7.98294i 0.689621i
\(135\) −4.83518 1.90290i −0.416146 0.163775i
\(136\) 3.14155 + 1.81377i 0.269386 + 0.155530i
\(137\) 12.8409 + 7.41370i 1.09707 + 0.633395i 0.935451 0.353458i \(-0.114994\pi\)
0.161622 + 0.986853i \(0.448327\pi\)
\(138\) 0.979554 3.17212i 0.0833852 0.270029i
\(139\) 7.24669i 0.614656i −0.951604 0.307328i \(-0.900565\pi\)
0.951604 0.307328i \(-0.0994349\pi\)
\(140\) 2.63608 + 0.226058i 0.222789 + 0.0191054i
\(141\) 0.715780 + 0.771911i 0.0602796 + 0.0650066i
\(142\) 1.24379 + 2.15432i 0.104377 + 0.180786i
\(143\) 15.7957 27.3589i 1.32090 2.28787i
\(144\) −2.47766 1.69151i −0.206472 0.140959i
\(145\) 0.693053 0.400134i 0.0575549 0.0332293i
\(146\) 15.0933 1.24913
\(147\) −12.1073 + 0.642228i −0.998596 + 0.0529701i
\(148\) −5.82789 −0.479050
\(149\) 5.70973 3.29651i 0.467759 0.270061i −0.247542 0.968877i \(-0.579623\pi\)
0.715301 + 0.698816i \(0.246289\pi\)
\(150\) −0.384890 1.68874i −0.0314262 0.137885i
\(151\) −5.88717 + 10.1969i −0.479091 + 0.829811i −0.999713 0.0239772i \(-0.992367\pi\)
0.520621 + 0.853788i \(0.325700\pi\)
\(152\) 2.10355 + 3.64345i 0.170620 + 0.295523i
\(153\) −0.820036 + 10.8517i −0.0662960 + 0.877308i
\(154\) 13.0626 + 1.12019i 1.05261 + 0.0902675i
\(155\) 5.03641i 0.404534i
\(156\) 10.5506 + 3.25805i 0.844727 + 0.260853i
\(157\) 1.33783 + 0.772397i 0.106770 + 0.0616440i 0.552434 0.833556i \(-0.313699\pi\)
−0.445664 + 0.895200i \(0.647032\pi\)
\(158\) −2.31062 1.33404i −0.183823 0.106130i
\(159\) 23.6765 + 7.31132i 1.87767 + 0.579825i
\(160\) 1.00000i 0.0790569i
\(161\) −4.59243 + 2.15111i −0.361934 + 0.169531i
\(162\) 1.35249 8.89780i 0.106262 0.699077i
\(163\) 1.68880 + 2.92508i 0.132277 + 0.229110i 0.924554 0.381051i \(-0.124438\pi\)
−0.792277 + 0.610161i \(0.791105\pi\)
\(164\) −3.72581 + 6.45330i −0.290937 + 0.503918i
\(165\) −1.90726 8.36827i −0.148480 0.651469i
\(166\) −6.29787 + 3.63608i −0.488809 + 0.282214i
\(167\) 12.7685 0.988053 0.494027 0.869447i \(-0.335525\pi\)
0.494027 + 0.869447i \(0.335525\pi\)
\(168\) 0.632846 + 4.53867i 0.0488251 + 0.350166i
\(169\) −27.6436 −2.12643
\(170\) −3.14155 + 1.81377i −0.240946 + 0.139110i
\(171\) −7.11633 + 10.4238i −0.544200 + 0.797125i
\(172\) −2.32413 + 4.02552i −0.177214 + 0.306943i
\(173\) 0.123778 + 0.214390i 0.00941068 + 0.0162998i 0.870692 0.491828i \(-0.163671\pi\)
−0.861282 + 0.508128i \(0.830338\pi\)
\(174\) 0.942474 + 1.01638i 0.0714488 + 0.0770517i
\(175\) −1.51381 + 2.16988i −0.114433 + 0.164028i
\(176\) 4.95532i 0.373521i
\(177\) −0.895006 + 2.89833i −0.0672728 + 0.217852i
\(178\) −1.63241 0.942474i −0.122355 0.0706414i
\(179\) −16.9709 9.79815i −1.26846 0.732348i −0.293767 0.955877i \(-0.594909\pi\)
−0.974697 + 0.223528i \(0.928242\pi\)
\(180\) 2.70372 1.29996i 0.201523 0.0968936i
\(181\) 14.8103i 1.10084i 0.834887 + 0.550422i \(0.185533\pi\)
−0.834887 + 0.550422i \(0.814467\pi\)
\(182\) −7.15471 15.2747i −0.530342 1.13223i
\(183\) −4.34748 + 4.03134i −0.321375 + 0.298005i
\(184\) 0.958379 + 1.65996i 0.0706526 + 0.122374i
\(185\) 2.91394 5.04710i 0.214237 0.371070i
\(186\) −8.50521 + 1.93847i −0.623632 + 0.142135i
\(187\) −15.5674 + 8.98783i −1.13840 + 0.657255i
\(188\) −0.607779 −0.0443269
\(189\) −11.4486 + 7.61114i −0.832763 + 0.553629i
\(190\) −4.20710 −0.305215
\(191\) −0.463759 + 0.267752i −0.0335564 + 0.0193738i −0.516684 0.856176i \(-0.672834\pi\)
0.483128 + 0.875550i \(0.339501\pi\)
\(192\) 1.68874 0.384890i 0.121875 0.0277771i
\(193\) 2.76772 4.79383i 0.199225 0.345068i −0.749052 0.662511i \(-0.769491\pi\)
0.948277 + 0.317443i \(0.102824\pi\)
\(194\) −8.82809 15.2907i −0.633820 1.09781i
\(195\) −8.09687 + 7.50809i −0.579829 + 0.537666i
\(196\) 4.48104 5.37776i 0.320074 0.384126i
\(197\) 0.666454i 0.0474829i −0.999718 0.0237414i \(-0.992442\pi\)
0.999718 0.0237414i \(-0.00755785\pi\)
\(198\) 13.3978 6.44174i 0.952140 0.457794i
\(199\) −7.81326 4.51099i −0.553867 0.319775i 0.196813 0.980441i \(-0.436941\pi\)
−0.750680 + 0.660666i \(0.770274\pi\)
\(200\) 0.866025 + 0.500000i 0.0612372 + 0.0353553i
\(201\) 4.07966 13.2113i 0.287757 0.931853i
\(202\) 1.14842i 0.0808026i
\(203\) 0.180907 2.10957i 0.0126972 0.148063i
\(204\) −4.27215 4.60717i −0.299110 0.322566i
\(205\) −3.72581 6.45330i −0.260222 0.450718i
\(206\) −3.64182 + 6.30781i −0.253737 + 0.439486i
\(207\) −3.24221 + 4.74908i −0.225349 + 0.330084i
\(208\) −5.52111 + 3.18762i −0.382820 + 0.221021i
\(209\) −20.8475 −1.44205
\(210\) −4.24702 1.72127i −0.293073 0.118779i
\(211\) 11.4386 0.787467 0.393733 0.919225i \(-0.371183\pi\)
0.393733 + 0.919225i \(0.371183\pi\)
\(212\) −12.3898 + 7.15326i −0.850936 + 0.491288i
\(213\) −0.957449 4.20090i −0.0656033 0.287841i
\(214\) 1.34318 2.32646i 0.0918181 0.159034i
\(215\) −2.32413 4.02552i −0.158505 0.274538i
\(216\) 3.23594 + 4.06555i 0.220178 + 0.276625i
\(217\) 10.9284 + 7.62417i 0.741868 + 0.517562i
\(218\) 9.02343i 0.611144i
\(219\) −24.9786 7.71340i −1.68789 0.521223i
\(220\) 4.29143 + 2.47766i 0.289328 + 0.167044i
\(221\) 20.0281 + 11.5632i 1.34724 + 0.777827i
\(222\) 9.64481 + 2.97833i 0.647317 + 0.199892i
\(223\) 5.23397i 0.350493i −0.984525 0.175246i \(-0.943928\pi\)
0.984525 0.175246i \(-0.0560722\pi\)
\(224\) −2.16988 1.51381i −0.144981 0.101146i
\(225\) −0.226058 + 2.99147i −0.0150705 + 0.199431i
\(226\) 6.21336 + 10.7619i 0.413306 + 0.715868i
\(227\) −6.73117 + 11.6587i −0.446763 + 0.773817i −0.998173 0.0604178i \(-0.980757\pi\)
0.551410 + 0.834234i \(0.314090\pi\)
\(228\) −1.61927 7.10471i −0.107239 0.470521i
\(229\) 14.3082 8.26082i 0.945509 0.545890i 0.0538263 0.998550i \(-0.482858\pi\)
0.891683 + 0.452660i \(0.149525\pi\)
\(230\) −1.91676 −0.126387
\(231\) −21.0454 8.52946i −1.38468 0.561197i
\(232\) −0.800269 −0.0525402
\(233\) −16.1392 + 9.31796i −1.05731 + 0.610440i −0.924688 0.380727i \(-0.875674\pi\)
−0.132625 + 0.991166i \(0.542341\pi\)
\(234\) −15.7957 10.7838i −1.03259 0.704956i
\(235\) 0.303890 0.526352i 0.0198236 0.0343354i
\(236\) −0.875658 1.51668i −0.0570005 0.0987278i
\(237\) 3.14218 + 3.38859i 0.204107 + 0.220113i
\(238\) −0.820036 + 9.56249i −0.0531551 + 0.619844i
\(239\) 24.8065i 1.60460i −0.596922 0.802299i \(-0.703610\pi\)
0.596922 0.802299i \(-0.296390\pi\)
\(240\) −0.511048 + 1.65494i −0.0329880 + 0.106826i
\(241\) −19.3439 11.1682i −1.24605 0.719408i −0.275731 0.961235i \(-0.588920\pi\)
−0.970319 + 0.241827i \(0.922253\pi\)
\(242\) 11.7392 + 6.77761i 0.754622 + 0.435681i
\(243\) −6.78549 + 14.0341i −0.435290 + 0.900291i
\(244\) 3.42307i 0.219140i
\(245\) 2.41676 + 6.56957i 0.154401 + 0.419715i
\(246\) 9.46395 8.77576i 0.603399 0.559522i
\(247\) 13.4106 + 23.2279i 0.853297 + 1.47795i
\(248\) 2.51820 4.36166i 0.159906 0.276966i
\(249\) 12.2808 2.79898i 0.778265 0.177378i
\(250\) −0.866025 + 0.500000i −0.0547723 + 0.0316228i
\(251\) 2.72107 0.171752 0.0858762 0.996306i \(-0.472631\pi\)
0.0858762 + 0.996306i \(0.472631\pi\)
\(252\) 1.27215 7.83464i 0.0801381 0.493536i
\(253\) −9.49815 −0.597144
\(254\) 6.98605 4.03340i 0.438344 0.253078i
\(255\) 6.12600 1.39621i 0.383625 0.0874339i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.75189 + 9.96256i 0.358793 + 0.621448i 0.987759 0.155985i \(-0.0498551\pi\)
−0.628966 + 0.777432i \(0.716522\pi\)
\(258\) 5.90354 5.47425i 0.367538 0.340812i
\(259\) −6.54044 13.9633i −0.406403 0.867635i
\(260\) 6.37523i 0.395375i
\(261\) −1.04032 2.16370i −0.0643942 0.133930i
\(262\) −2.92978 1.69151i −0.181002 0.104502i
\(263\) 11.0726 + 6.39277i 0.682766 + 0.394195i 0.800896 0.598803i \(-0.204357\pi\)
−0.118130 + 0.992998i \(0.537690\pi\)
\(264\) −2.53241 + 8.20077i −0.155859 + 0.504722i
\(265\) 14.3065i 0.878843i
\(266\) −6.36874 + 9.12889i −0.390493 + 0.559728i
\(267\) 2.21990 + 2.39398i 0.135856 + 0.146509i
\(268\) 3.99147 + 6.91343i 0.243818 + 0.422305i
\(269\) −5.84575 + 10.1251i −0.356422 + 0.617341i −0.987360 0.158492i \(-0.949337\pi\)
0.630938 + 0.775833i \(0.282670\pi\)
\(270\) −5.13884 + 0.769634i −0.312740 + 0.0468384i
\(271\) 19.1130 11.0349i 1.16103 0.670323i 0.209482 0.977812i \(-0.432822\pi\)
0.951552 + 0.307489i \(0.0994888\pi\)
\(272\) 3.62755 0.219952
\(273\) 4.03454 + 28.9351i 0.244181 + 1.75123i
\(274\) 14.8274 0.895756
\(275\) −4.29143 + 2.47766i −0.258783 + 0.149409i
\(276\) −0.737742 3.23691i −0.0444068 0.194839i
\(277\) 3.90328 6.76068i 0.234525 0.406210i −0.724609 0.689160i \(-0.757980\pi\)
0.959135 + 0.282950i \(0.0913131\pi\)
\(278\) −3.62334 6.27582i −0.217314 0.376398i
\(279\) 15.0663 + 1.13852i 0.901994 + 0.0681615i
\(280\) 2.39594 1.12227i 0.143185 0.0670682i
\(281\) 23.0892i 1.37738i −0.725054 0.688692i \(-0.758185\pi\)
0.725054 0.688692i \(-0.241815\pi\)
\(282\) 1.00584 + 0.310604i 0.0598968 + 0.0184962i
\(283\) 21.4345 + 12.3752i 1.27415 + 0.735631i 0.975766 0.218815i \(-0.0702190\pi\)
0.298384 + 0.954446i \(0.403552\pi\)
\(284\) 2.15432 + 1.24379i 0.127835 + 0.0738056i
\(285\) 6.96250 + 2.15003i 0.412423 + 0.127357i
\(286\) 31.5913i 1.86803i
\(287\) −19.6431 1.68450i −1.15949 0.0994329i
\(288\) −2.99147 0.226058i −0.176274 0.0133206i
\(289\) 1.92045 + 3.32632i 0.112968 + 0.195666i
\(290\) 0.400134 0.693053i 0.0234967 0.0406975i
\(291\) 6.79569 + 29.8168i 0.398370 + 1.74789i
\(292\) 13.0712 7.54666i 0.764934 0.441635i
\(293\) 25.3384 1.48029 0.740143 0.672449i \(-0.234758\pi\)
0.740143 + 0.672449i \(0.234758\pi\)
\(294\) −10.1641 + 6.60985i −0.592785 + 0.385494i
\(295\) 1.75132 0.101966
\(296\) −5.04710 + 2.91394i −0.293357 + 0.169370i
\(297\) −25.4646 + 3.81378i −1.47761 + 0.221298i
\(298\) 3.29651 5.70973i 0.190962 0.330756i
\(299\) 6.10989 + 10.5826i 0.353344 + 0.612010i
\(300\) −1.17770 1.27005i −0.0679944 0.0733264i
\(301\) −12.2532 1.05078i −0.706262 0.0605659i
\(302\) 11.7743i 0.677538i
\(303\) 0.586898 1.90057i 0.0337164 0.109185i
\(304\) 3.64345 + 2.10355i 0.208966 + 0.120647i
\(305\) 2.96447 + 1.71154i 0.169745 + 0.0980023i
\(306\) 4.71568 + 9.80787i 0.269577 + 0.560678i
\(307\) 13.1396i 0.749919i −0.927041 0.374960i \(-0.877657\pi\)
0.927041 0.374960i \(-0.122343\pi\)
\(308\) 11.8726 5.56119i 0.676507 0.316878i
\(309\) 9.25059 8.57792i 0.526248 0.487981i
\(310\) 2.51820 + 4.36166i 0.143024 + 0.247725i
\(311\) 3.80332 6.58755i 0.215667 0.373545i −0.737812 0.675006i \(-0.764141\pi\)
0.953479 + 0.301461i \(0.0974742\pi\)
\(312\) 10.7661 2.45377i 0.609513 0.138917i
\(313\) 10.7608 6.21272i 0.608234 0.351164i −0.164040 0.986454i \(-0.552453\pi\)
0.772274 + 0.635290i \(0.219119\pi\)
\(314\) 1.54479 0.0871777
\(315\) 6.14892 + 5.01904i 0.346453 + 0.282791i
\(316\) −2.66807 −0.150091
\(317\) 24.0199 13.8679i 1.34909 0.778898i 0.360971 0.932577i \(-0.382445\pi\)
0.988121 + 0.153679i \(0.0491121\pi\)
\(318\) 24.1601 5.50644i 1.35483 0.308786i
\(319\) 1.98279 3.43430i 0.111015 0.192284i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −3.41182 + 3.16373i −0.190429 + 0.176582i
\(322\) −2.90161 + 4.15913i −0.161700 + 0.231779i
\(323\) 15.2614i 0.849169i
\(324\) −3.27761 8.38196i −0.182089 0.465665i
\(325\) 5.52111 + 3.18762i 0.306256 + 0.176817i
\(326\) 2.92508 + 1.68880i 0.162005 + 0.0935337i
\(327\) 4.61140 14.9332i 0.255011 0.825810i
\(328\) 7.45163i 0.411447i
\(329\) −0.682090 1.45620i −0.0376048 0.0802830i
\(330\) −5.83587 6.29351i −0.321254 0.346446i
\(331\) −5.89462 10.2098i −0.323997 0.561180i 0.657312 0.753619i \(-0.271694\pi\)
−0.981309 + 0.192439i \(0.938360\pi\)
\(332\) −3.63608 + 6.29787i −0.199556 + 0.345640i
\(333\) −14.4395 9.85792i −0.791281 0.540211i
\(334\) 11.0578 6.38423i 0.605056 0.349329i
\(335\) −7.98294 −0.436155
\(336\) 2.81739 + 3.61418i 0.153701 + 0.197170i
\(337\) −5.58238 −0.304092 −0.152046 0.988373i \(-0.548586\pi\)
−0.152046 + 0.988373i \(0.548586\pi\)
\(338\) −23.9401 + 13.8218i −1.30217 + 0.751807i
\(339\) −4.78292 20.9856i −0.259773 1.13978i
\(340\) −1.81377 + 3.14155i −0.0983657 + 0.170374i
\(341\) 12.4785 + 21.6134i 0.675749 + 1.17043i
\(342\) −0.951048 + 12.5854i −0.0514268 + 0.680541i
\(343\) 17.9137 + 4.70101i 0.967249 + 0.253831i
\(344\) 4.64827i 0.250618i
\(345\) 3.17212 + 0.979554i 0.170781 + 0.0527374i
\(346\) 0.214390 + 0.123778i 0.0115257 + 0.00665435i
\(347\) −27.6342 15.9546i −1.48348 0.856489i −0.483659 0.875257i \(-0.660692\pi\)
−0.999824 + 0.0187674i \(0.994026\pi\)
\(348\) 1.32440 + 0.408975i 0.0709951 + 0.0219234i
\(349\) 1.64353i 0.0879759i 0.999032 + 0.0439879i \(0.0140063\pi\)
−0.999032 + 0.0439879i \(0.985994\pi\)
\(350\) −0.226058 + 2.63608i −0.0120833 + 0.140904i
\(351\) 20.6299 + 25.9188i 1.10114 + 1.38344i
\(352\) −2.47766 4.29143i −0.132060 0.228734i
\(353\) 7.30038 12.6446i 0.388560 0.673006i −0.603696 0.797215i \(-0.706306\pi\)
0.992256 + 0.124209i \(0.0396392\pi\)
\(354\) 0.674065 + 2.95753i 0.0358261 + 0.157191i
\(355\) −2.15432 + 1.24379i −0.114339 + 0.0660138i
\(356\) −1.88495 −0.0999021
\(357\) 6.24400 15.4063i 0.330468 0.815387i
\(358\) −19.5963 −1.03570
\(359\) 0.438209 0.253000i 0.0231278 0.0133528i −0.488392 0.872625i \(-0.662416\pi\)
0.511519 + 0.859272i \(0.329083\pi\)
\(360\) 1.69151 2.47766i 0.0891503 0.130584i
\(361\) −0.650173 + 1.12613i −0.0342196 + 0.0592701i
\(362\) 7.40517 + 12.8261i 0.389207 + 0.674127i
\(363\) −15.9639 17.2158i −0.837889 0.903595i
\(364\) −13.8335 9.65089i −0.725072 0.505844i
\(365\) 15.0933i 0.790020i
\(366\) −1.74935 + 5.66498i −0.0914401 + 0.296113i
\(367\) −1.17547 0.678660i −0.0613592 0.0354258i 0.469007 0.883195i \(-0.344612\pi\)
−0.530366 + 0.847769i \(0.677945\pi\)
\(368\) 1.65996 + 0.958379i 0.0865314 + 0.0499590i
\(369\) −20.1471 + 9.68684i −1.04882 + 0.504277i
\(370\) 5.82789i 0.302978i
\(371\) −31.0434 21.6574i −1.61170 1.12439i
\(372\) −6.39649 + 5.93136i −0.331643 + 0.307527i
\(373\) 17.0548 + 29.5397i 0.883062 + 1.52951i 0.847919 + 0.530125i \(0.177855\pi\)
0.0351422 + 0.999382i \(0.488812\pi\)
\(374\) −8.98783 + 15.5674i −0.464750 + 0.804970i
\(375\) 1.68874 0.384890i 0.0872064 0.0198757i
\(376\) −0.526352 + 0.303890i −0.0271445 + 0.0156719i
\(377\) −5.10190 −0.262761
\(378\) −6.10921 + 12.3157i −0.314224 + 0.633453i
\(379\) −1.53951 −0.0790795 −0.0395398 0.999218i \(-0.512589\pi\)
−0.0395398 + 0.999218i \(0.512589\pi\)
\(380\) −3.64345 + 2.10355i −0.186905 + 0.107910i
\(381\) −13.6228 + 3.10483i −0.697915 + 0.159065i
\(382\) −0.267752 + 0.463759i −0.0136994 + 0.0237280i
\(383\) 16.2631 + 28.1685i 0.831004 + 1.43934i 0.897243 + 0.441537i \(0.145567\pi\)
−0.0662394 + 0.997804i \(0.521100\pi\)
\(384\) 1.27005 1.17770i 0.0648120 0.0600991i
\(385\) −1.12019 + 13.0626i −0.0570902 + 0.665732i
\(386\) 5.53544i 0.281747i
\(387\) −12.5676 + 6.04258i −0.638848 + 0.307162i
\(388\) −15.2907 8.82809i −0.776267 0.448178i
\(389\) −6.15025 3.55085i −0.311830 0.180035i 0.335915 0.941892i \(-0.390954\pi\)
−0.647745 + 0.761857i \(0.724288\pi\)
\(390\) −3.25805 + 10.5506i −0.164978 + 0.534252i
\(391\) 6.95313i 0.351635i
\(392\) 1.19181 6.89780i 0.0601956 0.348391i
\(393\) 3.98417 + 4.29660i 0.200975 + 0.216735i
\(394\) −0.333227 0.577166i −0.0167877 0.0290772i
\(395\) 1.33404 2.31062i 0.0671227 0.116260i
\(396\) 8.38196 12.2776i 0.421209 0.616973i
\(397\) 11.2790 6.51194i 0.566077 0.326825i −0.189504 0.981880i \(-0.560688\pi\)
0.755581 + 0.655055i \(0.227355\pi\)
\(398\) −9.02198 −0.452231
\(399\) 15.2052 11.8530i 0.761212 0.593395i
\(400\) 1.00000 0.0500000
\(401\) 20.2676 11.7015i 1.01211 0.584345i 0.100305 0.994957i \(-0.468018\pi\)
0.911810 + 0.410612i \(0.134685\pi\)
\(402\) −3.07256 13.4812i −0.153245 0.672379i
\(403\) 16.0541 27.8066i 0.799714 1.38514i
\(404\) 0.574210 + 0.994562i 0.0285680 + 0.0494813i
\(405\) 8.89780 + 1.35249i 0.442135 + 0.0672059i
\(406\) −0.898114 1.91739i −0.0445727 0.0951587i
\(407\) 28.8791i 1.43148i
\(408\) −6.00338 1.85385i −0.297211 0.0917792i
\(409\) 11.4311 + 6.59972i 0.565229 + 0.326335i 0.755242 0.655447i \(-0.227520\pi\)
−0.190013 + 0.981782i \(0.560853\pi\)
\(410\) −6.45330 3.72581i −0.318706 0.184005i
\(411\) −24.5385 7.57751i −1.21039 0.373771i
\(412\) 7.28364i 0.358839i
\(413\) 2.65116 3.80015i 0.130455 0.186993i
\(414\) −0.433299 + 5.73392i −0.0212955 + 0.281807i
\(415\) −3.63608 6.29787i −0.178488 0.309150i
\(416\) −3.18762 + 5.52111i −0.156286 + 0.270695i
\(417\) 2.78918 + 12.2378i 0.136587 + 0.599288i
\(418\) −18.0545 + 10.4238i −0.883073 + 0.509843i
\(419\) 27.9492 1.36541 0.682704 0.730695i \(-0.260804\pi\)
0.682704 + 0.730695i \(0.260804\pi\)
\(420\) −4.53867 + 0.632846i −0.221464 + 0.0308797i
\(421\) 24.6795 1.20281 0.601403 0.798946i \(-0.294609\pi\)
0.601403 + 0.798946i \(0.294609\pi\)
\(422\) 9.90613 5.71931i 0.482223 0.278412i
\(423\) −1.50587 1.02806i −0.0732179 0.0499861i
\(424\) −7.15326 + 12.3898i −0.347393 + 0.601703i
\(425\) −1.81377 3.14155i −0.0879809 0.152387i
\(426\) −2.92963 3.15936i −0.141941 0.153072i
\(427\) 8.20147 3.84160i 0.396897 0.185908i
\(428\) 2.68637i 0.129850i
\(429\) −16.1447 + 52.2818i −0.779472 + 2.52419i
\(430\) −4.02552 2.32413i −0.194128 0.112080i
\(431\) 2.89638 + 1.67223i 0.139514 + 0.0805483i 0.568132 0.822937i \(-0.307666\pi\)
−0.428619 + 0.903486i \(0.641000\pi\)
\(432\) 4.83518 + 1.90290i 0.232633 + 0.0915532i
\(433\) 14.6756i 0.705264i −0.935762 0.352632i \(-0.885287\pi\)
0.935762 0.352632i \(-0.114713\pi\)
\(434\) 13.2764 + 1.13852i 0.637285 + 0.0546507i
\(435\) −1.01638 + 0.942474i −0.0487318 + 0.0451882i
\(436\) 4.51172 + 7.81452i 0.216072 + 0.374248i
\(437\) 4.03199 6.98361i 0.192876 0.334072i
\(438\) −25.4888 + 5.80927i −1.21790 + 0.277578i
\(439\) −5.70453 + 3.29351i −0.272262 + 0.157191i −0.629915 0.776664i \(-0.716910\pi\)
0.357653 + 0.933855i \(0.383577\pi\)
\(440\) 4.95532 0.236236
\(441\) 20.1990 5.74456i 0.961858 0.273550i
\(442\) 23.1265 1.10001
\(443\) −35.2654 + 20.3605i −1.67551 + 0.967357i −0.711047 + 0.703144i \(0.751779\pi\)
−0.964464 + 0.264213i \(0.914888\pi\)
\(444\) 9.84182 2.24310i 0.467072 0.106453i
\(445\) 0.942474 1.63241i 0.0446776 0.0773838i
\(446\) −2.61699 4.53275i −0.123918 0.214632i
\(447\) −8.37348 + 7.76459i −0.396052 + 0.367253i
\(448\) −2.63608 0.226058i −0.124543 0.0106802i
\(449\) 18.3485i 0.865919i 0.901413 + 0.432960i \(0.142531\pi\)
−0.901413 + 0.432960i \(0.857469\pi\)
\(450\) 1.29996 + 2.70372i 0.0612809 + 0.127455i
\(451\) −31.9782 18.4626i −1.50579 0.869370i
\(452\) 10.7619 + 6.21336i 0.506195 + 0.292252i
\(453\) 6.01725 19.4859i 0.282715 0.915525i
\(454\) 13.4623i 0.631819i
\(455\) 15.2747 7.15471i 0.716087 0.335418i
\(456\) −4.95469 5.34323i −0.232024 0.250219i
\(457\) 4.32166 + 7.48533i 0.202159 + 0.350149i 0.949224 0.314602i \(-0.101871\pi\)
−0.747065 + 0.664751i \(0.768538\pi\)
\(458\) 8.26082 14.3082i 0.386003 0.668576i
\(459\) −2.79188 18.6414i −0.130314 0.870105i
\(460\) −1.65996 + 0.958379i −0.0773961 + 0.0446846i
\(461\) −24.7864 −1.15442 −0.577210 0.816596i \(-0.695859\pi\)
−0.577210 + 0.816596i \(0.695859\pi\)
\(462\) −22.4906 + 3.13596i −1.04636 + 0.145898i
\(463\) −17.9797 −0.835589 −0.417794 0.908542i \(-0.637197\pi\)
−0.417794 + 0.908542i \(0.637197\pi\)
\(464\) −0.693053 + 0.400134i −0.0321742 + 0.0185758i
\(465\) −1.93847 8.50521i −0.0898942 0.394420i
\(466\) −9.31796 + 16.1392i −0.431646 + 0.747633i
\(467\) −0.636712 1.10282i −0.0294635 0.0510323i 0.850918 0.525299i \(-0.176047\pi\)
−0.880381 + 0.474267i \(0.842713\pi\)
\(468\) −19.0713 1.44117i −0.881572 0.0666182i
\(469\) −12.0847 + 17.3220i −0.558018 + 0.799857i
\(470\) 0.607779i 0.0280348i
\(471\) −2.55654 0.789463i −0.117799 0.0363765i
\(472\) −1.51668 0.875658i −0.0698111 0.0403054i
\(473\) −19.9477 11.5168i −0.917198 0.529545i
\(474\) 4.41551 + 1.36351i 0.202811 + 0.0626282i
\(475\) 4.20710i 0.193035i
\(476\) 4.07107 + 8.69138i 0.186597 + 0.398369i
\(477\) −42.7976 3.23411i −1.95957 0.148080i
\(478\) −12.4032 21.4831i −0.567311 0.982612i
\(479\) 7.11334 12.3207i 0.325017 0.562945i −0.656499 0.754327i \(-0.727963\pi\)
0.981516 + 0.191381i \(0.0612967\pi\)
\(480\) 0.384890 + 1.68874i 0.0175678 + 0.0770803i
\(481\) −32.1764 + 18.5771i −1.46712 + 0.847042i
\(482\) −22.3364 −1.01740
\(483\) 6.92751 5.40026i 0.315212 0.245720i
\(484\) 13.5552 0.616146
\(485\) 15.2907 8.82809i 0.694315 0.400863i
\(486\) 1.14066 + 15.5467i 0.0517415 + 0.705211i
\(487\) −19.9476 + 34.5502i −0.903910 + 1.56562i −0.0815361 + 0.996670i \(0.525983\pi\)
−0.822374 + 0.568947i \(0.807351\pi\)
\(488\) −1.71154 2.96447i −0.0774776 0.134195i
\(489\) −3.97778 4.28971i −0.179881 0.193988i
\(490\) 5.37776 + 4.48104i 0.242942 + 0.202433i
\(491\) 15.9778i 0.721069i −0.932746 0.360535i \(-0.882594\pi\)
0.932746 0.360535i \(-0.117406\pi\)
\(492\) 3.80814 12.3320i 0.171684 0.555970i
\(493\) 2.51408 + 1.45151i 0.113229 + 0.0653725i
\(494\) 23.2279 + 13.4106i 1.04507 + 0.603372i
\(495\) 6.44174 + 13.3978i 0.289535 + 0.602186i
\(496\) 5.03641i 0.226141i
\(497\) −0.562340 + 6.55747i −0.0252244 + 0.294143i
\(498\) 9.23600 8.56439i 0.413875 0.383780i
\(499\) 6.90313 + 11.9566i 0.309027 + 0.535250i 0.978150 0.207902i \(-0.0666634\pi\)
−0.669123 + 0.743152i \(0.733330\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −21.5627 + 4.91446i −0.963349 + 0.219562i
\(502\) 2.35652 1.36054i 0.105176 0.0607237i
\(503\) 2.11183 0.0941620 0.0470810 0.998891i \(-0.485008\pi\)
0.0470810 + 0.998891i \(0.485008\pi\)
\(504\) −2.81561 7.42108i −0.125417 0.330561i
\(505\) −1.14842 −0.0511041
\(506\) −8.22564 + 4.74908i −0.365674 + 0.211122i
\(507\) 46.6830 10.6398i 2.07326 0.472528i
\(508\) 4.03340 6.98605i 0.178953 0.309956i
\(509\) −8.09556 14.0219i −0.358830 0.621511i 0.628936 0.777457i \(-0.283491\pi\)
−0.987766 + 0.155946i \(0.950157\pi\)
\(510\) 4.60717 4.27215i 0.204009 0.189174i
\(511\) 32.7507 + 22.8484i 1.44880 + 1.01075i
\(512\) 1.00000i 0.0441942i
\(513\) 8.00567 20.3421i 0.353459 0.898124i
\(514\) 9.96256 + 5.75189i 0.439430 + 0.253705i
\(515\) −6.30781 3.64182i −0.277955 0.160478i
\(516\) 2.37549 7.69261i 0.104575 0.338648i
\(517\) 3.01174i 0.132456i
\(518\) −12.6458 8.82232i −0.555625 0.387630i
\(519\) −0.291546 0.314409i −0.0127975 0.0138010i
\(520\) −3.18762 5.52111i −0.139786 0.242117i
\(521\) −12.4676 + 21.5945i −0.546216 + 0.946073i 0.452314 + 0.891859i \(0.350599\pi\)
−0.998529 + 0.0542143i \(0.982735\pi\)
\(522\) −1.98279 1.35366i −0.0867845 0.0592481i
\(523\) 17.0768 9.85929i 0.746716 0.431116i −0.0777903 0.996970i \(-0.524786\pi\)
0.824506 + 0.565853i \(0.191453\pi\)
\(524\) −3.38301 −0.147788
\(525\) 1.72127 4.24702i 0.0751225 0.185355i
\(526\) 12.7855 0.557476
\(527\) −15.8221 + 9.13490i −0.689222 + 0.397923i
\(528\) 1.90726 + 8.36827i 0.0830026 + 0.364182i
\(529\) −9.66302 + 16.7368i −0.420131 + 0.727689i
\(530\) −7.15326 12.3898i −0.310718 0.538179i
\(531\) 0.395899 5.23901i 0.0171806 0.227354i
\(532\) −0.951048 + 11.0902i −0.0412332 + 0.480822i
\(533\) 47.5059i 2.05771i
\(534\) 3.11948 + 0.963298i 0.134993 + 0.0416860i
\(535\) 2.32646 + 1.34318i 0.100582 + 0.0580709i
\(536\) 6.91343 + 3.99147i 0.298615 + 0.172405i
\(537\) 32.4307 + 10.0146i 1.39949 + 0.432164i
\(538\) 11.6915i 0.504057i
\(539\) 26.6485 + 22.2050i 1.14783 + 0.956436i
\(540\) −4.06555 + 3.23594i −0.174953 + 0.139253i
\(541\) 4.27923 + 7.41184i 0.183978 + 0.318660i 0.943232 0.332135i \(-0.107769\pi\)
−0.759253 + 0.650795i \(0.774436\pi\)
\(542\) 11.0349 19.1130i 0.473990 0.820975i
\(543\) −5.70036 25.0109i −0.244626 1.07332i
\(544\) 3.14155 1.81377i 0.134693 0.0777649i
\(545\) −9.02343 −0.386521
\(546\) 17.9615 + 23.0412i 0.768683 + 0.986074i
\(547\) −33.5472 −1.43437 −0.717187 0.696881i \(-0.754570\pi\)
−0.717187 + 0.696881i \(0.754570\pi\)
\(548\) 12.8409 7.41370i 0.548536 0.316698i
\(549\) 5.79015 8.48121i 0.247118 0.361969i
\(550\) −2.47766 + 4.29143i −0.105648 + 0.182987i
\(551\) 1.68340 + 2.91574i 0.0717154 + 0.124215i
\(552\) −2.25736 2.43438i −0.0960796 0.103614i
\(553\) −2.99429 6.39254i −0.127330 0.271838i
\(554\) 7.80656i 0.331669i
\(555\) −2.97833 + 9.64481i −0.126423 + 0.409400i
\(556\) −6.27582 3.62334i −0.266154 0.153664i
\(557\) 4.63348 + 2.67514i 0.196327 + 0.113349i 0.594941 0.803769i \(-0.297175\pi\)
−0.398614 + 0.917119i \(0.630509\pi\)
\(558\) 13.6170 6.54715i 0.576455 0.277163i
\(559\) 29.6338i 1.25338i
\(560\) 1.51381 2.16988i 0.0639702 0.0916942i
\(561\) 22.8300 21.1699i 0.963883 0.893793i
\(562\) −11.5446 19.9958i −0.486979 0.843472i
\(563\) −14.6685 + 25.4066i −0.618205 + 1.07076i 0.371609 + 0.928390i \(0.378806\pi\)
−0.989813 + 0.142372i \(0.954527\pi\)
\(564\) 1.02638 0.233928i 0.0432186 0.00985016i
\(565\) −10.7619 + 6.21336i −0.452755 + 0.261398i
\(566\) 24.7505 1.04034
\(567\) 16.4043 17.2597i 0.688917 0.724841i
\(568\) 2.48759 0.104377
\(569\) 36.5568 21.1061i 1.53254 0.884812i 0.533295 0.845929i \(-0.320954\pi\)
0.999244 0.0388825i \(-0.0123798\pi\)
\(570\) 7.10471 1.61927i 0.297584 0.0678238i
\(571\) 15.6790 27.1568i 0.656145 1.13648i −0.325461 0.945556i \(-0.605519\pi\)
0.981605 0.190921i \(-0.0611473\pi\)
\(572\) −15.7957 27.3589i −0.660450 1.14393i
\(573\) 0.680116 0.630661i 0.0284123 0.0263462i
\(574\) −17.8536 + 8.36271i −0.745196 + 0.349053i
\(575\) 1.91676i 0.0799343i
\(576\) −2.70372 + 1.29996i −0.112655 + 0.0541651i
\(577\) −27.7794 16.0385i −1.15647 0.667689i −0.206016 0.978549i \(-0.566050\pi\)
−0.950456 + 0.310859i \(0.899383\pi\)
\(578\) 3.32632 + 1.92045i 0.138357 + 0.0798802i
\(579\) −2.82887 + 9.16083i −0.117564 + 0.380711i
\(580\) 0.800269i 0.0332293i
\(581\) −19.1699 1.64393i −0.795303 0.0682017i
\(582\) 20.7936 + 22.4242i 0.861924 + 0.929515i
\(583\) −35.4467 61.3955i −1.46805 2.54274i
\(584\) 7.54666 13.0712i 0.312283 0.540890i
\(585\) 10.7838 15.7957i 0.445853 0.653070i
\(586\) 21.9437 12.6692i 0.906487 0.523360i
\(587\) −1.93731 −0.0799612 −0.0399806 0.999200i \(-0.512730\pi\)
−0.0399806 + 0.999200i \(0.512730\pi\)
\(588\) −5.49748 + 10.8064i −0.226712 + 0.445647i
\(589\) −21.1887 −0.873063
\(590\) 1.51668 0.875658i 0.0624409 0.0360503i
\(591\) 0.256512 + 1.12547i 0.0105515 + 0.0462957i
\(592\) −2.91394 + 5.04710i −0.119762 + 0.207435i
\(593\) 5.63074 + 9.75274i 0.231227 + 0.400497i 0.958169 0.286201i \(-0.0923927\pi\)
−0.726942 + 0.686698i \(0.759059\pi\)
\(594\) −20.1461 + 16.0351i −0.826604 + 0.657929i
\(595\) −9.56249 0.820036i −0.392024 0.0336182i
\(596\) 6.59303i 0.270061i
\(597\) 14.9308 + 4.61066i 0.611079 + 0.188702i
\(598\) 10.5826 + 6.10989i 0.432756 + 0.249852i
\(599\) 38.4047 + 22.1730i 1.56917 + 0.905963i 0.996265 + 0.0863446i \(0.0275186\pi\)
0.572909 + 0.819619i \(0.305815\pi\)
\(600\) −1.65494 0.511048i −0.0675627 0.0208634i
\(601\) 17.7126i 0.722514i 0.932466 + 0.361257i \(0.117652\pi\)
−0.932466 + 0.361257i \(0.882348\pi\)
\(602\) −11.1370 + 5.21659i −0.453909 + 0.212613i
\(603\) −1.80461 + 23.8807i −0.0734893 + 0.972499i
\(604\) 5.88717 + 10.1969i 0.239546 + 0.414905i
\(605\) −6.77761 + 11.7392i −0.275549 + 0.477265i
\(606\) −0.442016 1.93939i −0.0179557 0.0787823i
\(607\) −15.8915 + 9.17497i −0.645016 + 0.372400i −0.786544 0.617534i \(-0.788132\pi\)
0.141528 + 0.989934i \(0.454799\pi\)
\(608\) 4.20710 0.170620
\(609\) 0.506447 + 3.63215i 0.0205223 + 0.147182i
\(610\) 3.42307 0.138596
\(611\) −3.35562 + 1.93737i −0.135754 + 0.0783775i
\(612\) 8.98783 + 6.13602i 0.363312 + 0.248034i
\(613\) −0.315836 + 0.547045i −0.0127565 + 0.0220949i −0.872333 0.488912i \(-0.837394\pi\)
0.859577 + 0.511007i \(0.170727\pi\)
\(614\) −6.56982 11.3793i −0.265136 0.459230i
\(615\) 8.77576 + 9.46395i 0.353873 + 0.381623i
\(616\) 7.50142 10.7525i 0.302241 0.433229i
\(617\) 15.5902i 0.627638i −0.949483 0.313819i \(-0.898392\pi\)
0.949483 0.313819i \(-0.101608\pi\)
\(618\) 3.72228 12.0540i 0.149732 0.484883i
\(619\) 10.9863 + 6.34296i 0.441578 + 0.254945i 0.704267 0.709936i \(-0.251276\pi\)
−0.262689 + 0.964881i \(0.584609\pi\)
\(620\) 4.36166 + 2.51820i 0.175168 + 0.101134i
\(621\) 3.64739 9.26787i 0.146365 0.371907i
\(622\) 7.60664i 0.304999i
\(623\) −2.11541 4.51622i −0.0847522 0.180938i
\(624\) 8.09687 7.50809i 0.324134 0.300564i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 6.21272 10.7608i 0.248310 0.430086i
\(627\) 35.2061 8.02401i 1.40600 0.320448i
\(628\) 1.33783 0.772397i 0.0533852 0.0308220i
\(629\) 21.1409 0.842945
\(630\) 7.83464 + 1.27215i 0.312140 + 0.0506838i
\(631\) −5.96052 −0.237284 −0.118642 0.992937i \(-0.537854\pi\)
−0.118642 + 0.992937i \(0.537854\pi\)
\(632\) −2.31062 + 1.33404i −0.0919115 + 0.0530651i
\(633\) −19.3169 + 4.40261i −0.767778 + 0.174988i
\(634\) 13.8679 24.0199i 0.550764 0.953952i
\(635\) 4.03340 + 6.98605i 0.160060 + 0.277233i
\(636\) 18.1700 16.8488i 0.720488 0.668097i
\(637\) 7.59808 43.9751i 0.301047 1.74235i
\(638\) 3.96559i 0.156999i
\(639\) 3.23377 + 6.72574i 0.127926 + 0.266066i
\(640\) −0.866025 0.500000i −0.0342327 0.0197642i
\(641\) −11.2070 6.47036i −0.442649 0.255564i 0.262071 0.965048i \(-0.415594\pi\)
−0.704721 + 0.709485i \(0.748928\pi\)
\(642\) −1.37286 + 4.44578i −0.0541825 + 0.175461i
\(643\) 27.7420i 1.09404i 0.837120 + 0.547019i \(0.184237\pi\)
−0.837120 + 0.547019i \(0.815763\pi\)
\(644\) −0.433299 + 5.05272i −0.0170744 + 0.199105i
\(645\) 5.47425 + 5.90354i 0.215549 + 0.232452i
\(646\) −7.63072 13.2168i −0.300227 0.520008i
\(647\) −23.3856 + 40.5050i −0.919382 + 1.59242i −0.119027 + 0.992891i \(0.537977\pi\)
−0.800356 + 0.599526i \(0.795356\pi\)
\(648\) −7.02947 5.62019i −0.276144 0.220782i
\(649\) 7.51566 4.33917i 0.295015 0.170327i
\(650\) 6.37523 0.250057
\(651\) −21.3897 8.66903i −0.838330 0.339766i
\(652\) 3.37759 0.132277
\(653\) 27.3651 15.7992i 1.07088 0.618271i 0.142456 0.989801i \(-0.454500\pi\)
0.928421 + 0.371530i \(0.121167\pi\)
\(654\) −3.47303 15.2383i −0.135806 0.595864i
\(655\) 1.69151 2.92978i 0.0660927 0.114476i
\(656\) 3.72581 + 6.45330i 0.145469 + 0.251959i
\(657\) 45.1512 + 3.41197i 1.76152 + 0.133113i
\(658\) −1.31881 0.920062i −0.0514125 0.0358678i
\(659\) 29.8627i 1.16329i 0.813444 + 0.581643i \(0.197590\pi\)
−0.813444 + 0.581643i \(0.802410\pi\)
\(660\) −8.20077 2.53241i −0.319214 0.0985737i
\(661\) −12.0007 6.92861i −0.466773 0.269492i 0.248115 0.968731i \(-0.420189\pi\)
−0.714888 + 0.699239i \(0.753522\pi\)
\(662\) −10.2098 5.89462i −0.396814 0.229101i
\(663\) −38.2729 11.8187i −1.48640 0.459001i
\(664\) 7.27215i 0.282214i
\(665\) −9.12889 6.36874i −0.354003 0.246969i
\(666\) −17.4340 1.31744i −0.675552 0.0510498i
\(667\) 0.766960 + 1.32841i 0.0296968 + 0.0514364i
\(668\) 6.38423 11.0578i 0.247013 0.427840i
\(669\) 2.01450 + 8.83884i 0.0778853 + 0.341729i
\(670\) −6.91343 + 3.99147i −0.267089 + 0.154204i
\(671\) 16.9624 0.654827
\(672\) 4.24702 + 1.72127i 0.163833 + 0.0663996i
\(673\) 21.1836 0.816568 0.408284 0.912855i \(-0.366127\pi\)
0.408284 + 0.912855i \(0.366127\pi\)
\(674\) −4.83448 + 2.79119i −0.186217 + 0.107513i
\(675\) −0.769634 5.13884i −0.0296232 0.197794i
\(676\) −13.8218 + 23.9401i −0.531608 + 0.920771i
\(677\) −24.1682 41.8606i −0.928860 1.60883i −0.785232 0.619202i \(-0.787456\pi\)
−0.143628 0.989632i \(-0.545877\pi\)
\(678\) −14.6349 15.7826i −0.562050 0.606126i
\(679\) 3.99132 46.5430i 0.153173 1.78616i
\(680\) 3.62755i 0.139110i
\(681\) 6.87989 22.2794i 0.263638 0.853747i
\(682\) 21.6134 + 12.4785i 0.827620 + 0.477827i
\(683\) −22.8004 13.1638i −0.872433 0.503699i −0.00427708 0.999991i \(-0.501361\pi\)
−0.868156 + 0.496291i \(0.834695\pi\)
\(684\) 5.46907 + 11.3748i 0.209115 + 0.434926i
\(685\) 14.8274i 0.566526i
\(686\) 17.8642 4.88565i 0.682059 0.186535i
\(687\) −20.9833 + 19.4575i −0.800563 + 0.742349i
\(688\) 2.32413 + 4.02552i 0.0886068 + 0.153471i
\(689\) −45.6037 + 78.9880i −1.73736 + 3.00920i
\(690\) 3.23691 0.737742i 0.123227 0.0280853i
\(691\) −16.5539 + 9.55742i −0.629741 + 0.363581i −0.780652 0.624966i \(-0.785113\pi\)
0.150911 + 0.988547i \(0.451779\pi\)
\(692\) 0.247556 0.00941068
\(693\) 38.8232 + 6.30392i 1.47477 + 0.239466i
\(694\) −31.9093 −1.21126
\(695\) 6.27582 3.62334i 0.238055 0.137441i
\(696\) 1.35145 0.308016i 0.0512266 0.0116753i
\(697\) 13.5156 23.4096i 0.511939 0.886704i
\(698\) 0.821763 + 1.42333i 0.0311042 + 0.0538740i
\(699\) 23.6686 21.9475i 0.895227 0.830130i
\(700\) 1.12227 + 2.39594i 0.0424177 + 0.0905579i
\(701\) 36.3536i 1.37306i 0.727103 + 0.686528i \(0.240866\pi\)
−0.727103 + 0.686528i \(0.759134\pi\)
\(702\) 30.8254 + 12.1314i 1.16343 + 0.457871i
\(703\) 21.2336 + 12.2592i 0.800842 + 0.462366i
\(704\) −4.29143 2.47766i −0.161740 0.0933804i
\(705\) −0.310604 + 1.00584i −0.0116980 + 0.0378821i
\(706\) 14.6008i 0.549507i
\(707\) −1.73849 + 2.49194i −0.0653827 + 0.0937189i
\(708\) 2.06252 + 2.22426i 0.0775143 + 0.0835928i
\(709\) −2.54606 4.40991i −0.0956193 0.165618i 0.814248 0.580518i \(-0.197150\pi\)
−0.909867 + 0.414900i \(0.863816\pi\)
\(710\) −1.24379 + 2.15432i −0.0466788 + 0.0808500i
\(711\) −6.61058 4.51307i −0.247916 0.169253i
\(712\) −1.63241 + 0.942474i −0.0611773 + 0.0353207i
\(713\) −9.65357 −0.361529
\(714\) −2.29568 16.4642i −0.0859136 0.616158i
\(715\) 31.5913 1.18145
\(716\) −16.9709 + 9.79815i −0.634232 + 0.366174i
\(717\) 9.54778 + 41.8918i 0.356568 + 1.56448i
\(718\) 0.253000 0.438209i 0.00944189 0.0163538i
\(719\) −20.5822 35.6494i −0.767587 1.32950i −0.938868 0.344278i \(-0.888124\pi\)
0.171281 0.985222i \(-0.445209\pi\)
\(720\) 0.226058 2.99147i 0.00842469 0.111486i
\(721\) −17.4511 + 8.17418i −0.649914 + 0.304422i
\(722\) 1.30035i 0.0483938i
\(723\) 36.9655 + 11.4150i 1.37476 + 0.424528i
\(724\) 12.8261 + 7.40517i 0.476679 + 0.275211i
\(725\) 0.693053 + 0.400134i 0.0257393 + 0.0148606i
\(726\) −22.4331 6.92736i −0.832570 0.257098i
\(727\) 46.1288i 1.71082i 0.517948 + 0.855412i \(0.326696\pi\)
−0.517948 + 0.855412i \(0.673304\pi\)
\(728\) −16.8056 1.44117i −0.622857 0.0534134i
\(729\) 6.05736 26.3118i 0.224347 0.974509i
\(730\) 7.54666 + 13.0712i 0.279314 + 0.483787i
\(731\) 8.43091 14.6028i 0.311828 0.540103i
\(732\) 1.31751 + 5.78070i 0.0486965 + 0.213661i
\(733\) −8.65789 + 4.99864i −0.319787 + 0.184629i −0.651297 0.758823i \(-0.725775\pi\)
0.331511 + 0.943451i \(0.392442\pi\)
\(734\) −1.35732 −0.0500996
\(735\) −6.60985 10.1641i −0.243808 0.374910i
\(736\) 1.91676 0.0706526
\(737\) −34.2583 + 19.7790i −1.26192 + 0.728570i
\(738\) −12.6045 + 18.4626i −0.463977 + 0.679618i
\(739\) −0.418026 + 0.724042i −0.0153773 + 0.0266343i −0.873612 0.486624i \(-0.838228\pi\)
0.858234 + 0.513258i \(0.171562\pi\)
\(740\) −2.91394 5.04710i −0.107119 0.185535i
\(741\) −31.5873 34.0643i −1.16039 1.25138i
\(742\) −37.7131 3.23411i −1.38449 0.118728i
\(743\) 53.3336i 1.95662i −0.207146 0.978310i \(-0.566418\pi\)
0.207146 0.978310i \(-0.433582\pi\)
\(744\) −2.57384 + 8.33496i −0.0943617 + 0.305574i
\(745\) 5.70973 + 3.29651i 0.209188 + 0.120775i
\(746\) 29.5397 + 17.0548i 1.08153 + 0.624419i
\(747\) −19.6619 + 9.45353i −0.719390 + 0.345887i
\(748\) 17.9757i 0.657255i
\(749\) 6.43637 3.01482i 0.235180 0.110159i
\(750\) 1.27005 1.17770i 0.0463757 0.0430034i
\(751\) −16.8660 29.2127i −0.615448 1.06599i −0.990306 0.138905i \(-0.955642\pi\)
0.374858 0.927082i \(-0.377691\pi\)
\(752\) −0.303890 + 0.526352i −0.0110817 + 0.0191941i
\(753\) −4.59519 + 1.04731i −0.167458 + 0.0381662i
\(754\) −4.41837 + 2.55095i −0.160908 + 0.0929001i
\(755\) −11.7743 −0.428512
\(756\) 0.867138 + 13.7204i 0.0315375 + 0.499004i
\(757\) 37.1033 1.34854 0.674272 0.738483i \(-0.264458\pi\)
0.674272 + 0.738483i \(0.264458\pi\)
\(758\) −1.33326 + 0.769757i −0.0484261 + 0.0279588i
\(759\) 16.0400 3.65575i 0.582213 0.132695i
\(760\) −2.10355 + 3.64345i −0.0763037 + 0.132162i
\(761\) −8.95519 15.5108i −0.324625 0.562268i 0.656811 0.754055i \(-0.271905\pi\)
−0.981436 + 0.191787i \(0.938572\pi\)
\(762\) −10.2452 + 9.50024i −0.371146 + 0.344157i
\(763\) −13.6598 + 19.5798i −0.494517 + 0.708835i
\(764\) 0.535503i 0.0193738i
\(765\) −9.80787 + 4.71568i −0.354604 + 0.170496i
\(766\) 28.1685 + 16.2631i 1.01777 + 0.587608i
\(767\) −9.66922 5.58252i −0.349135 0.201573i
\(768\) 0.511048 1.65494i 0.0184408 0.0597175i
\(769\) 0.619084i 0.0223247i 0.999938 + 0.0111624i \(0.00355317\pi\)
−0.999938 + 0.0111624i \(0.996447\pi\)
\(770\) 5.56119 + 11.8726i 0.200411 + 0.427860i
\(771\) −13.5480 14.6104i −0.487918 0.526180i
\(772\) −2.76772 4.79383i −0.0996125 0.172534i
\(773\) 24.4683 42.3803i 0.880062 1.52431i 0.0287914 0.999585i \(-0.490834\pi\)
0.851271 0.524727i \(-0.175833\pi\)
\(774\) −7.86258 + 11.5168i −0.282615 + 0.413964i
\(775\) −4.36166 + 2.51820i −0.156675 + 0.0904566i
\(776\) −17.6562 −0.633820
\(777\) 16.4195 + 21.0630i 0.589045 + 0.755632i
\(778\) −7.10169 −0.254608
\(779\) 27.1496 15.6749i 0.972737 0.561610i
\(780\) 2.45377 + 10.7661i 0.0878589 + 0.385490i
\(781\) −6.16340 + 10.6753i −0.220544 + 0.381993i
\(782\) −3.47656 6.02159i −0.124322 0.215331i
\(783\) 2.58962 + 3.25353i 0.0925456 + 0.116272i
\(784\) −2.41676 6.56957i −0.0863128 0.234628i
\(785\) 1.54479i 0.0551360i
\(786\) 5.59869 + 1.72888i 0.199699 + 0.0616672i
\(787\) −0.0582062 0.0336053i −0.00207483 0.00119790i 0.498962 0.866624i \(-0.333715\pi\)
−0.501037 + 0.865426i \(0.667048\pi\)
\(788\) −0.577166 0.333227i −0.0205607 0.0118707i
\(789\) −21.1593 6.53402i −0.753292 0.232617i
\(790\) 2.66807i 0.0949258i
\(791\) −2.80916 + 32.7578i −0.0998822 + 1.16473i
\(792\) 1.12019 14.8237i 0.0398042 0.526737i
\(793\) −10.9114 18.8992i −0.387477 0.671129i
\(794\) 6.51194 11.2790i 0.231100 0.400277i
\(795\) 5.50644 + 24.1601i 0.195293 + 0.856870i
\(796\) −7.81326 + 4.51099i −0.276934 + 0.159888i
\(797\) 7.61311 0.269670 0.134835 0.990868i \(-0.456950\pi\)
0.134835 + 0.990868i \(0.456950\pi\)
\(798\) 7.24156 17.8676i 0.256348 0.632508i
\(799\) 2.20475 0.0779984
\(800\) 0.866025 0.500000i 0.0306186 0.0176777i
\(801\) −4.67026 3.18840i −0.165016 0.112657i
\(802\) 11.7015 20.2676i 0.413194 0.715673i
\(803\) 37.3961 + 64.7720i 1.31968 + 2.28575i
\(804\) −9.40149 10.1387i −0.331565 0.357566i
\(805\) −4.15913 2.90161i −0.146590 0.102268i
\(806\) 32.1083i 1.13097i
\(807\) 5.97492 19.3488i 0.210327 0.681108i
\(808\) 0.994562 + 0.574210i 0.0349886 + 0.0202007i
\(809\) −16.9690 9.79703i −0.596597 0.344445i 0.171105 0.985253i \(-0.445266\pi\)
−0.767702 + 0.640807i \(0.778600\pi\)
\(810\) 8.38196 3.27761i 0.294512 0.115163i
\(811\) 38.1099i 1.33822i 0.743164 + 0.669110i \(0.233324\pi\)
−0.743164 + 0.669110i \(0.766676\pi\)
\(812\) −1.73649 1.21145i −0.0609387 0.0425137i
\(813\) −28.0298 + 25.9916i −0.983048 + 0.911564i
\(814\) −14.4395 25.0100i −0.506105 0.876600i
\(815\) −1.68880 + 2.92508i −0.0591559 + 0.102461i
\(816\) −6.12600 + 1.39621i −0.214453 + 0.0488771i
\(817\) 16.9357 9.77786i 0.592507 0.342084i
\(818\) 13.1994 0.461508
\(819\) −17.9501 47.3111i −0.627229 1.65318i
\(820\) −7.45163 −0.260222
\(821\) 32.4054 18.7093i 1.13096 0.652958i 0.186781 0.982402i \(-0.440195\pi\)
0.944175 + 0.329444i \(0.106861\pi\)
\(822\) −25.0397 + 5.70692i −0.873360 + 0.199052i
\(823\) −17.1932 + 29.7795i −0.599318 + 1.03805i 0.393604 + 0.919280i \(0.371228\pi\)
−0.992922 + 0.118768i \(0.962105\pi\)
\(824\) 3.64182 + 6.30781i 0.126869 + 0.219743i
\(825\) 6.29351 5.83587i 0.219112 0.203179i
\(826\) 0.395899 4.61660i 0.0137751 0.160632i
\(827\) 4.15552i 0.144502i −0.997386 0.0722508i \(-0.976982\pi\)
0.997386 0.0722508i \(-0.0230182\pi\)
\(828\) 2.49171 + 5.18237i 0.0865931 + 0.180100i
\(829\) −24.3399 14.0526i −0.845359 0.488068i 0.0137231 0.999906i \(-0.495632\pi\)
−0.859082 + 0.511837i \(0.828965\pi\)
\(830\) −6.29787 3.63608i −0.218602 0.126210i
\(831\) −3.98952 + 12.9194i −0.138395 + 0.448169i
\(832\) 6.37523i 0.221021i
\(833\) −16.2552 + 19.5081i −0.563208 + 0.675915i
\(834\) 8.53440 + 9.20366i 0.295522 + 0.318697i
\(835\) 6.38423 + 11.0578i 0.220935 + 0.382671i
\(836\) −10.4238 + 18.0545i −0.360513 + 0.624427i
\(837\) −25.8813 + 3.87619i −0.894588 + 0.133981i
\(838\) 24.2047 13.9746i 0.836138 0.482745i
\(839\) −23.6646 −0.816992 −0.408496 0.912760i \(-0.633947\pi\)
−0.408496 + 0.912760i \(0.633947\pi\)
\(840\) −3.61418 + 2.81739i −0.124701 + 0.0972094i
\(841\) 28.3596 0.977916
\(842\) 21.3731 12.3398i 0.736565 0.425256i
\(843\) 8.88680 + 38.9917i 0.306078 + 1.34295i
\(844\) 5.71931 9.90613i 0.196867 0.340983i
\(845\) −13.8218 23.9401i −0.475484 0.823563i
\(846\) −1.81815 0.137393i −0.0625094 0.00472368i
\(847\) 15.2126 + 32.4774i 0.522709 + 1.11594i
\(848\) 14.3065i 0.491288i
\(849\) −40.9606 12.6487i −1.40576 0.434101i
\(850\) −3.14155 1.81377i −0.107754 0.0622119i
\(851\) 9.67407 + 5.58533i 0.331623 + 0.191462i
\(852\) −4.11681 1.27128i −0.141040 0.0435532i
\(853\) 23.7742i 0.814012i 0.913426 + 0.407006i \(0.133427\pi\)
−0.913426 + 0.407006i \(0.866573\pi\)
\(854\) 5.18188 7.42766i 0.177320 0.254169i
\(855\) −12.5854 0.951048i −0.430412 0.0325252i
\(856\) −1.34318 2.32646i −0.0459091 0.0795168i
\(857\) 11.1811 19.3662i 0.381938 0.661535i −0.609402 0.792862i \(-0.708590\pi\)
0.991339 + 0.131326i \(0.0419236\pi\)
\(858\) 12.1592 + 53.3497i 0.415108 + 1.82133i
\(859\) −37.1729 + 21.4618i −1.26832 + 0.732267i −0.974671 0.223645i \(-0.928204\pi\)
−0.293653 + 0.955912i \(0.594871\pi\)
\(860\) −4.64827 −0.158505
\(861\) 33.8205 4.71573i 1.15260 0.160712i
\(862\) 3.34445 0.113912
\(863\) 20.3687 11.7599i 0.693360 0.400312i −0.111510 0.993763i \(-0.535569\pi\)
0.804870 + 0.593452i \(0.202235\pi\)
\(864\) 5.13884 0.769634i 0.174827 0.0261835i
\(865\) −0.123778 + 0.214390i −0.00420858 + 0.00728948i
\(866\) −7.33780 12.7094i −0.249348 0.431884i
\(867\) −4.52342 4.87814i −0.153623 0.165670i
\(868\) 12.0669 5.65219i 0.409578 0.191848i
\(869\) 13.2212i 0.448497i
\(870\) −0.408975 + 1.32440i −0.0138656 + 0.0449013i
\(871\) 44.0747 + 25.4466i 1.49342 + 0.862224i
\(872\) 7.81452 + 4.51172i 0.264633 + 0.152786i
\(873\) −22.9524 47.7373i −0.776820 1.61566i
\(874\) 8.06398i 0.272768i
\(875\) −2.63608 0.226058i −0.0891156 0.00764216i
\(876\) −19.1693 + 17.7754i −0.647670 + 0.600574i
\(877\) −4.09356 7.09026i −0.138230 0.239421i 0.788597 0.614911i \(-0.210808\pi\)
−0.926827 + 0.375490i \(0.877475\pi\)
\(878\) −3.29351 + 5.70453i −0.111151 + 0.192518i
\(879\) −42.7901 + 9.75251i −1.44328 + 0.328944i
\(880\) 4.29143 2.47766i 0.144664 0.0835219i
\(881\) −26.6496 −0.897847 −0.448923 0.893570i \(-0.648192\pi\)
−0.448923 + 0.893570i \(0.648192\pi\)
\(882\) 14.6206 15.0744i 0.492301 0.507583i
\(883\) −5.41249 −0.182145 −0.0910724 0.995844i \(-0.529029\pi\)
−0.0910724 + 0.995844i \(0.529029\pi\)
\(884\) 20.0281 11.5632i 0.673618 0.388913i
\(885\) −2.95753 + 0.674065i −0.0994162 + 0.0226584i
\(886\) −20.3605 + 35.2654i −0.684025 + 1.18477i
\(887\) 12.0499 + 20.8711i 0.404597 + 0.700782i 0.994274 0.106856i \(-0.0340785\pi\)
−0.589678 + 0.807639i \(0.700745\pi\)
\(888\) 7.40171 6.86349i 0.248385 0.230324i
\(889\) 21.2647 + 1.82356i 0.713195 + 0.0611604i
\(890\) 1.88495i 0.0631836i
\(891\) 41.5353 16.2416i 1.39149 0.544114i
\(892\) −4.53275 2.61699i −0.151768 0.0876231i
\(893\) 2.21441 + 1.27849i 0.0741026 + 0.0427831i
\(894\) −3.36935 + 10.9111i −0.112688 + 0.364921i
\(895\) 19.5963i 0.655032i
\(896\) −2.39594 + 1.12227i −0.0800427 + 0.0374923i
\(897\) −14.3912 15.5197i −0.480508 0.518189i
\(898\) 9.17425 + 15.8903i 0.306149 + 0.530265i
\(899\) 2.01524 3.49050i 0.0672120 0.116415i
\(900\) 2.47766 + 1.69151i 0.0825887 + 0.0563836i
\(901\) 44.9446 25.9488i 1.49732 0.864480i
\(902\) −36.9252 −1.22948
\(903\) 21.0969 2.94164i 0.702062 0.0978916i
\(904\) 12.4267 0.413306
\(905\) −12.8261 + 7.40517i −0.426355 + 0.246156i
\(906\) −4.53183 19.8839i −0.150560 0.660597i
\(907\) 10.8290 18.7564i 0.359572 0.622797i −0.628317 0.777957i \(-0.716256\pi\)
0.987889 + 0.155160i \(0.0495893\pi\)
\(908\) 6.73117 + 11.6587i 0.223382 + 0.386908i
\(909\) −0.259610 + 3.43547i −0.00861071 + 0.113947i
\(910\) 9.65089 13.8335i 0.319924 0.458576i
\(911\) 47.4302i 1.57143i 0.618587 + 0.785716i \(0.287705\pi\)
−0.618587 + 0.785716i \(0.712295\pi\)
\(912\) −6.96250 2.15003i −0.230551 0.0711945i
\(913\) −31.2080 18.0179i −1.03283 0.596306i
\(914\) 7.48533 + 4.32166i 0.247593 + 0.142948i
\(915\) −5.66498 1.74935i −0.187279 0.0578318i
\(916\) 16.5216i 0.545890i
\(917\) −3.79664 8.10549i −0.125376 0.267667i
\(918\) −11.7385 14.7480i −0.387429 0.486755i
\(919\) −5.32208 9.21812i −0.175559 0.304078i 0.764795 0.644273i \(-0.222840\pi\)
−0.940355 + 0.340196i \(0.889507\pi\)
\(920\) −0.958379 + 1.65996i −0.0315968 + 0.0547273i
\(921\) 5.05732 + 22.1895i 0.166644 + 0.731169i
\(922\) −21.4657 + 12.3932i −0.706935 + 0.408149i
\(923\) 15.8590 0.522004
\(924\) −17.9094 + 13.9611i −0.589177 + 0.459286i
\(925\) 5.82789 0.191620
\(926\) −15.5709 + 8.98986i −0.511691 + 0.295425i
\(927\) −12.3203 + 18.0464i −0.404653 + 0.592721i
\(928\) −0.400134 + 0.693053i −0.0131351 + 0.0227506i
\(929\) −17.1983 29.7883i −0.564257 0.977322i −0.997118 0.0758612i \(-0.975829\pi\)
0.432861 0.901460i \(-0.357504\pi\)
\(930\) −5.93136 6.39649i −0.194497 0.209749i
\(931\) −27.6388 + 10.1675i −0.905826 + 0.333227i
\(932\) 18.6359i 0.610440i
\(933\) −3.88736 + 12.5885i −0.127266 + 0.412131i
\(934\) −1.10282 0.636712i −0.0360853 0.0208339i
\(935\) −15.5674 8.98783i −0.509108 0.293933i
\(936\) −17.2368 + 8.28757i −0.563404 + 0.270888i
\(937\) 40.0917i 1.30974i −0.755742 0.654870i \(-0.772723\pi\)
0.755742 0.654870i \(-0.227277\pi\)
\(938\) −1.80461 + 21.0436i −0.0589226 + 0.687099i
\(939\) −15.7809 + 14.6334i −0.514992 + 0.477543i
\(940\) −0.303890 0.526352i −0.00991179 0.0171677i
\(941\) 13.6315 23.6104i 0.444374 0.769678i −0.553635 0.832760i \(-0.686760\pi\)
0.998008 + 0.0630819i \(0.0200929\pi\)
\(942\) −2.60876 + 0.594576i −0.0849980 + 0.0193723i
\(943\) 12.3694 7.14148i 0.402803 0.232559i
\(944\) −1.75132 −0.0570005
\(945\) −12.3157 6.10921i −0.400631 0.198733i
\(946\) −23.0337 −0.748889
\(947\) −19.6642 + 11.3531i −0.638999 + 0.368926i −0.784229 0.620472i \(-0.786941\pi\)
0.145230 + 0.989398i \(0.453608\pi\)
\(948\) 4.50570 1.02692i 0.146338 0.0333527i
\(949\) 48.1117 83.3319i 1.56177 2.70507i
\(950\) −2.10355 3.64345i −0.0682481 0.118209i
\(951\) −35.2258 + 32.6644i −1.14228 + 1.05921i
\(952\) 7.87134 + 5.49142i 0.255112 + 0.177978i
\(953\) 38.7288i 1.25455i −0.778799 0.627274i \(-0.784171\pi\)
0.778799 0.627274i \(-0.215829\pi\)
\(954\) −38.6808 + 18.5980i −1.25234 + 0.602131i
\(955\) −0.463759 0.267752i −0.0150069 0.00866424i
\(956\) −21.4831 12.4032i −0.694812 0.401150i
\(957\) −2.02660 + 6.56281i −0.0655108 + 0.212146i
\(958\) 14.2267i 0.459643i
\(959\) 32.1737 + 22.4459i 1.03894 + 0.724815i
\(960\) 1.17770 + 1.27005i 0.0380100 + 0.0409907i
\(961\) −2.81730 4.87970i −0.0908805 0.157410i
\(962\) −18.5771 + 32.1764i −0.598949 + 1.03741i
\(963\) 4.54401 6.65590i 0.146429 0.214484i
\(964\) −19.3439 + 11.1682i −0.623025 + 0.359704i
\(965\) 5.53544 0.178192
\(966\) 3.29926 8.14052i 0.106152 0.261917i
\(967\) 39.1631 1.25940 0.629700 0.776838i \(-0.283178\pi\)
0.629700 + 0.776838i \(0.283178\pi\)
\(968\) 11.7392 6.77761i 0.377311 0.217840i
\(969\) 5.87398 + 25.7727i 0.188699 + 0.827938i
\(970\) 8.82809 15.2907i 0.283453 0.490955i
\(971\) 13.4005 + 23.2104i 0.430044 + 0.744858i 0.996877 0.0789753i \(-0.0251648\pi\)
−0.566833 + 0.823833i \(0.691831\pi\)
\(972\) 8.76118 + 12.8935i 0.281015 + 0.413559i
\(973\) 1.63817 19.1028i 0.0525174 0.612408i
\(974\) 39.8951i 1.27832i
\(975\) −10.5506 3.25805i −0.337891 0.104341i
\(976\) −2.96447 1.71154i −0.0948903 0.0547849i
\(977\) −24.1424 13.9386i −0.772383 0.445936i 0.0613410 0.998117i \(-0.480462\pi\)
−0.833724 + 0.552181i \(0.813796\pi\)
\(978\) −5.58972 1.72611i −0.178739 0.0551949i
\(979\) 9.34052i 0.298524i
\(980\) 6.89780 + 1.19181i 0.220342 + 0.0380711i
\(981\) −2.03982 + 26.9933i −0.0651264 + 0.861831i
\(982\) −7.98891 13.8372i −0.254936 0.441563i
\(983\) −10.9212 + 18.9161i −0.348332 + 0.603329i −0.985953 0.167021i \(-0.946585\pi\)
0.637621 + 0.770350i \(0.279919\pi\)
\(984\) −2.86806 12.5839i −0.0914304 0.401160i
\(985\) 0.577166 0.333227i 0.0183900 0.0106175i
\(986\) 2.90301 0.0924507
\(987\) 1.71235 + 2.19662i 0.0545048 + 0.0699193i
\(988\) 26.8212 0.853297
\(989\) 7.71594 4.45480i 0.245353 0.141654i
\(990\) 12.2776 + 8.38196i 0.390208 + 0.266396i
\(991\) 29.4300 50.9743i 0.934875 1.61925i 0.160019 0.987114i \(-0.448845\pi\)
0.774856 0.632137i \(-0.217822\pi\)
\(992\) −2.51820 4.36166i −0.0799531 0.138483i
\(993\) 13.8841 + 14.9729i 0.440600 + 0.475151i
\(994\) 2.79174 + 5.96011i 0.0885485 + 0.189043i
\(995\) 9.02198i 0.286016i
\(996\) 3.71642 12.0350i 0.117759 0.381343i
\(997\) −10.4327 6.02334i −0.330408 0.190761i 0.325614 0.945503i \(-0.394429\pi\)
−0.656022 + 0.754742i \(0.727762\pi\)
\(998\) 11.9566 + 6.90313i 0.378479 + 0.218515i
\(999\) 28.1789 + 11.0899i 0.891541 + 0.350868i
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 210.2.r.a.101.4 12
3.2 odd 2 210.2.r.b.101.2 yes 12
5.2 odd 4 1050.2.u.g.899.5 12
5.3 odd 4 1050.2.u.f.899.2 12
5.4 even 2 1050.2.s.g.101.3 12
7.3 odd 6 1470.2.b.a.881.8 12
7.4 even 3 1470.2.b.b.881.11 12
7.5 odd 6 210.2.r.b.131.2 yes 12
15.2 even 4 1050.2.u.e.899.1 12
15.8 even 4 1050.2.u.h.899.6 12
15.14 odd 2 1050.2.s.f.101.5 12
21.5 even 6 inner 210.2.r.a.131.4 yes 12
21.11 odd 6 1470.2.b.a.881.2 12
21.17 even 6 1470.2.b.b.881.5 12
35.12 even 12 1050.2.u.h.299.6 12
35.19 odd 6 1050.2.s.f.551.5 12
35.33 even 12 1050.2.u.e.299.1 12
105.47 odd 12 1050.2.u.f.299.2 12
105.68 odd 12 1050.2.u.g.299.5 12
105.89 even 6 1050.2.s.g.551.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.r.a.101.4 12 1.1 even 1 trivial
210.2.r.a.131.4 yes 12 21.5 even 6 inner
210.2.r.b.101.2 yes 12 3.2 odd 2
210.2.r.b.131.2 yes 12 7.5 odd 6
1050.2.s.f.101.5 12 15.14 odd 2
1050.2.s.f.551.5 12 35.19 odd 6
1050.2.s.g.101.3 12 5.4 even 2
1050.2.s.g.551.3 12 105.89 even 6
1050.2.u.e.299.1 12 35.33 even 12
1050.2.u.e.899.1 12 15.2 even 4
1050.2.u.f.299.2 12 105.47 odd 12
1050.2.u.f.899.2 12 5.3 odd 4
1050.2.u.g.299.5 12 105.68 odd 12
1050.2.u.g.899.5 12 5.2 odd 4
1050.2.u.h.299.6 12 35.12 even 12
1050.2.u.h.899.6 12 15.8 even 4
1470.2.b.a.881.2 12 21.11 odd 6
1470.2.b.a.881.8 12 7.3 odd 6
1470.2.b.b.881.5 12 21.17 even 6
1470.2.b.b.881.11 12 7.4 even 3