Properties

Label 13.3.f.a.11.1
Level $13$
Weight $3$
Character 13.11
Analytic conductor $0.354$
Analytic rank $0$
Dimension $4$
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] = [13,3,Mod(2,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.354224343668\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 13.11
Dual form 13.3.f.a.6.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 1.86603i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-4.36603 - 4.36603i) q^{5} +(5.09808 - 1.36603i) q^{6} +(2.26795 + 8.46410i) q^{7} +(-5.83013 + 5.83013i) q^{8} +(0.767949 - 1.33013i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 1.86603i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-4.36603 - 4.36603i) q^{5} +(5.09808 - 1.36603i) q^{6} +(2.26795 + 8.46410i) q^{7} +(-5.83013 + 5.83013i) q^{8} +(0.767949 - 1.33013i) q^{9} +(10.3301 - 5.96410i) q^{10} +(6.19615 + 1.66025i) q^{11} -0.732051i q^{12} +(-6.50000 - 11.2583i) q^{13} -16.9282 q^{14} +(-4.36603 + 16.2942i) q^{15} +(-7.42820 - 12.8660i) q^{16} +(9.99038 + 5.76795i) q^{17} +(2.09808 + 2.09808i) q^{18} +(3.36603 - 0.901924i) q^{19} +(-0.428203 - 1.59808i) q^{20} +(16.9282 - 16.9282i) q^{21} +(-6.19615 + 10.7321i) q^{22} +(-8.49038 + 4.90192i) q^{23} +(21.7583 + 5.83013i) q^{24} +13.1244i q^{25} +(24.2583 - 6.50000i) q^{26} -28.7846 q^{27} +(-0.607695 + 2.26795i) q^{28} +(5.69615 + 9.86603i) q^{29} +(-28.2224 - 16.2942i) q^{30} +(1.92820 + 1.92820i) q^{31} +(-4.13397 + 1.10770i) q^{32} +(-4.53590 - 16.9282i) q^{33} +(-15.7583 + 15.7583i) q^{34} +(27.0526 - 46.8564i) q^{35} +(0.356406 - 0.205771i) q^{36} +(-42.1147 - 11.2846i) q^{37} +6.73205i q^{38} +(-17.7583 + 30.7583i) q^{39} +50.9090 q^{40} +(5.08142 - 18.9641i) q^{41} +(23.1244 + 40.0526i) q^{42} +(45.0000 + 25.9808i) q^{43} +(1.21539 + 1.21539i) q^{44} +(-9.16025 + 2.45448i) q^{45} +(-4.90192 - 18.2942i) q^{46} +(0.320508 - 0.320508i) q^{47} +(-20.2942 + 35.1506i) q^{48} +(-24.0622 + 13.8923i) q^{49} +(-24.4904 - 6.56218i) q^{50} -31.5167i q^{51} -3.48334i q^{52} +78.7654 q^{53} +(14.3923 - 53.7128i) q^{54} +(-19.8038 - 34.3013i) q^{55} +(-62.5692 - 36.1244i) q^{56} +(-6.73205 - 6.73205i) q^{57} +(-21.2583 + 5.69615i) q^{58} +(10.9615 + 40.9090i) q^{59} +(-3.19615 + 3.19615i) q^{60} +(-49.1865 + 85.1936i) q^{61} +(-4.56218 + 2.63397i) q^{62} +(13.0000 + 3.48334i) q^{63} -67.6936i q^{64} +(-20.7750 + 77.5333i) q^{65} +33.8564 q^{66} +(19.9737 - 74.5429i) q^{67} +(1.54552 + 2.67691i) q^{68} +(23.1962 + 13.3923i) q^{69} +(73.9090 + 73.9090i) q^{70} +(-31.0263 + 8.31347i) q^{71} +(3.27757 + 12.2321i) q^{72} +(48.2750 - 48.2750i) q^{73} +(42.1147 - 72.9449i) q^{74} +(31.0526 - 17.9282i) q^{75} +(0.901924 + 0.241670i) q^{76} +56.2102i q^{77} +(-48.5167 - 48.5167i) q^{78} -82.7461 q^{79} +(-23.7417 + 88.6051i) q^{80} +(32.4090 + 56.1340i) q^{81} +(32.8468 + 18.9641i) q^{82} +(-69.5167 - 69.5167i) q^{83} +(6.19615 - 1.66025i) q^{84} +(-18.4352 - 68.8013i) q^{85} +(-70.9808 + 70.9808i) q^{86} +(15.5622 - 26.9545i) q^{87} +(-45.8038 + 26.4449i) q^{88} +(-31.8301 - 8.52886i) q^{89} -18.3205i q^{90} +(80.5500 - 80.5500i) q^{91} -2.62693 q^{92} +(1.92820 - 7.19615i) q^{93} +(0.437822 + 0.758330i) q^{94} +(-18.6340 - 10.7583i) q^{95} +(8.26795 + 8.26795i) q^{96} +(74.8109 - 20.0455i) q^{97} +(-13.8923 - 51.8468i) q^{98} +(6.96668 - 6.96668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 14 q^{5} + 10 q^{6} + 16 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 14 q^{5} + 10 q^{6} + 16 q^{7} - 6 q^{8} + 10 q^{9} + 24 q^{10} + 4 q^{11} - 26 q^{13} - 40 q^{14} - 14 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} + 10 q^{19} + 26 q^{20} + 40 q^{21} - 4 q^{22} + 18 q^{23} + 42 q^{24} + 52 q^{26} - 32 q^{27} - 44 q^{28} + 2 q^{29} - 54 q^{30} - 20 q^{31} - 20 q^{32} - 32 q^{33} - 18 q^{34} + 32 q^{35} - 54 q^{36} - 68 q^{37} - 26 q^{39} + 72 q^{40} + 100 q^{41} + 44 q^{42} + 180 q^{43} + 88 q^{44} - 2 q^{45} - 30 q^{46} - 68 q^{47} - 50 q^{48} - 72 q^{49} - 46 q^{50} + 128 q^{53} + 16 q^{54} - 100 q^{55} - 84 q^{56} - 20 q^{57} - 40 q^{58} - 164 q^{59} + 8 q^{60} - 124 q^{61} + 6 q^{62} + 52 q^{63} + 52 q^{65} + 80 q^{66} + 118 q^{67} + 72 q^{68} + 72 q^{69} + 164 q^{70} - 86 q^{71} + 72 q^{72} + 58 q^{73} + 68 q^{74} + 48 q^{75} + 14 q^{76} - 104 q^{78} - 40 q^{79} - 140 q^{80} - 2 q^{81} + 24 q^{82} - 188 q^{83} + 4 q^{84} + 96 q^{85} - 180 q^{86} + 38 q^{87} - 204 q^{88} - 110 q^{89} + 52 q^{91} - 156 q^{92} - 20 q^{93} + 26 q^{94} - 78 q^{95} + 40 q^{96} + 178 q^{97} - 14 q^{98} + 208 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 1.86603i −0.250000 + 0.933013i 0.720804 + 0.693139i \(0.243773\pi\)
−0.970804 + 0.239874i \(0.922894\pi\)
\(3\) −1.36603 2.36603i −0.455342 0.788675i 0.543366 0.839496i \(-0.317150\pi\)
−0.998708 + 0.0508208i \(0.983816\pi\)
\(4\) 0.232051 + 0.133975i 0.0580127 + 0.0334936i
\(5\) −4.36603 4.36603i −0.873205 0.873205i 0.119615 0.992820i \(-0.461834\pi\)
−0.992820 + 0.119615i \(0.961834\pi\)
\(6\) 5.09808 1.36603i 0.849679 0.227671i
\(7\) 2.26795 + 8.46410i 0.323993 + 1.20916i 0.915321 + 0.402726i \(0.131937\pi\)
−0.591328 + 0.806431i \(0.701396\pi\)
\(8\) −5.83013 + 5.83013i −0.728766 + 0.728766i
\(9\) 0.767949 1.33013i 0.0853277 0.147792i
\(10\) 10.3301 5.96410i 1.03301 0.596410i
\(11\) 6.19615 + 1.66025i 0.563287 + 0.150932i 0.529216 0.848487i \(-0.322486\pi\)
0.0340707 + 0.999419i \(0.489153\pi\)
\(12\) 0.732051i 0.0610042i
\(13\) −6.50000 11.2583i −0.500000 0.866025i
\(14\) −16.9282 −1.20916
\(15\) −4.36603 + 16.2942i −0.291068 + 1.08628i
\(16\) −7.42820 12.8660i −0.464263 0.804127i
\(17\) 9.99038 + 5.76795i 0.587669 + 0.339291i 0.764175 0.645008i \(-0.223146\pi\)
−0.176506 + 0.984300i \(0.556479\pi\)
\(18\) 2.09808 + 2.09808i 0.116560 + 0.116560i
\(19\) 3.36603 0.901924i 0.177159 0.0474697i −0.169149 0.985591i \(-0.554102\pi\)
0.346308 + 0.938121i \(0.387435\pi\)
\(20\) −0.428203 1.59808i −0.0214102 0.0799038i
\(21\) 16.9282 16.9282i 0.806105 0.806105i
\(22\) −6.19615 + 10.7321i −0.281643 + 0.487820i
\(23\) −8.49038 + 4.90192i −0.369147 + 0.213127i −0.673086 0.739564i \(-0.735032\pi\)
0.303939 + 0.952692i \(0.401698\pi\)
\(24\) 21.7583 + 5.83013i 0.906597 + 0.242922i
\(25\) 13.1244i 0.524974i
\(26\) 24.2583 6.50000i 0.933013 0.250000i
\(27\) −28.7846 −1.06610
\(28\) −0.607695 + 2.26795i −0.0217034 + 0.0809982i
\(29\) 5.69615 + 9.86603i 0.196419 + 0.340208i 0.947365 0.320156i \(-0.103735\pi\)
−0.750946 + 0.660364i \(0.770402\pi\)
\(30\) −28.2224 16.2942i −0.940748 0.543141i
\(31\) 1.92820 + 1.92820i 0.0622001 + 0.0622001i 0.737523 0.675322i \(-0.235996\pi\)
−0.675322 + 0.737523i \(0.735996\pi\)
\(32\) −4.13397 + 1.10770i −0.129187 + 0.0346155i
\(33\) −4.53590 16.9282i −0.137451 0.512976i
\(34\) −15.7583 + 15.7583i −0.463480 + 0.463480i
\(35\) 27.0526 46.8564i 0.772930 1.33875i
\(36\) 0.356406 0.205771i 0.00990018 0.00571587i
\(37\) −42.1147 11.2846i −1.13824 0.304989i −0.359995 0.932954i \(-0.617221\pi\)
−0.778242 + 0.627965i \(0.783888\pi\)
\(38\) 6.73205i 0.177159i
\(39\) −17.7583 + 30.7583i −0.455342 + 0.788675i
\(40\) 50.9090 1.27272
\(41\) 5.08142 18.9641i 0.123937 0.462539i −0.875863 0.482561i \(-0.839707\pi\)
0.999800 + 0.0200215i \(0.00637348\pi\)
\(42\) 23.1244 + 40.0526i 0.550580 + 0.953632i
\(43\) 45.0000 + 25.9808i 1.04651 + 0.604204i 0.921671 0.387973i \(-0.126825\pi\)
0.124841 + 0.992177i \(0.460158\pi\)
\(44\) 1.21539 + 1.21539i 0.0276225 + 0.0276225i
\(45\) −9.16025 + 2.45448i −0.203561 + 0.0545441i
\(46\) −4.90192 18.2942i −0.106564 0.397701i
\(47\) 0.320508 0.320508i 0.00681932 0.00681932i −0.703689 0.710508i \(-0.748465\pi\)
0.710508 + 0.703689i \(0.248465\pi\)
\(48\) −20.2942 + 35.1506i −0.422796 + 0.732305i
\(49\) −24.0622 + 13.8923i −0.491065 + 0.283516i
\(50\) −24.4904 6.56218i −0.489808 0.131244i
\(51\) 31.5167i 0.617974i
\(52\) 3.48334i 0.0669873i
\(53\) 78.7654 1.48614 0.743070 0.669214i \(-0.233369\pi\)
0.743070 + 0.669214i \(0.233369\pi\)
\(54\) 14.3923 53.7128i 0.266524 0.994682i
\(55\) −19.8038 34.3013i −0.360070 0.623659i
\(56\) −62.5692 36.1244i −1.11731 0.645078i
\(57\) −6.73205 6.73205i −0.118106 0.118106i
\(58\) −21.2583 + 5.69615i −0.366523 + 0.0982095i
\(59\) 10.9615 + 40.9090i 0.185789 + 0.693372i 0.994460 + 0.105112i \(0.0335202\pi\)
−0.808672 + 0.588260i \(0.799813\pi\)
\(60\) −3.19615 + 3.19615i −0.0532692 + 0.0532692i
\(61\) −49.1865 + 85.1936i −0.806337 + 1.39662i 0.109048 + 0.994036i \(0.465220\pi\)
−0.915385 + 0.402580i \(0.868114\pi\)
\(62\) −4.56218 + 2.63397i −0.0735835 + 0.0424835i
\(63\) 13.0000 + 3.48334i 0.206349 + 0.0552911i
\(64\) 67.6936i 1.05771i
\(65\) −20.7750 + 77.5333i −0.319615 + 1.19282i
\(66\) 33.8564 0.512976
\(67\) 19.9737 74.5429i 0.298115 1.11258i −0.640596 0.767878i \(-0.721313\pi\)
0.938712 0.344703i \(-0.112021\pi\)
\(68\) 1.54552 + 2.67691i 0.0227282 + 0.0393664i
\(69\) 23.1962 + 13.3923i 0.336176 + 0.194091i
\(70\) 73.9090 + 73.9090i 1.05584 + 1.05584i
\(71\) −31.0263 + 8.31347i −0.436990 + 0.117091i −0.470605 0.882344i \(-0.655964\pi\)
0.0336156 + 0.999435i \(0.489298\pi\)
\(72\) 3.27757 + 12.2321i 0.0455218 + 0.169890i
\(73\) 48.2750 48.2750i 0.661301 0.661301i −0.294386 0.955687i \(-0.595115\pi\)
0.955687 + 0.294386i \(0.0951150\pi\)
\(74\) 42.1147 72.9449i 0.569118 0.985741i
\(75\) 31.0526 17.9282i 0.414034 0.239043i
\(76\) 0.901924 + 0.241670i 0.0118674 + 0.00317987i
\(77\) 56.2102i 0.730003i
\(78\) −48.5167 48.5167i −0.622008 0.622008i
\(79\) −82.7461 −1.04742 −0.523710 0.851897i \(-0.675452\pi\)
−0.523710 + 0.851897i \(0.675452\pi\)
\(80\) −23.7417 + 88.6051i −0.296771 + 1.10756i
\(81\) 32.4090 + 56.1340i 0.400111 + 0.693012i
\(82\) 32.8468 + 18.9641i 0.400571 + 0.231270i
\(83\) −69.5167 69.5167i −0.837550 0.837550i 0.150986 0.988536i \(-0.451755\pi\)
−0.988536 + 0.150986i \(0.951755\pi\)
\(84\) 6.19615 1.66025i 0.0737637 0.0197649i
\(85\) −18.4352 68.8013i −0.216885 0.809427i
\(86\) −70.9808 + 70.9808i −0.825358 + 0.825358i
\(87\) 15.5622 26.9545i 0.178876 0.309822i
\(88\) −45.8038 + 26.4449i −0.520498 + 0.300510i
\(89\) −31.8301 8.52886i −0.357642 0.0958299i 0.0755242 0.997144i \(-0.475937\pi\)
−0.433166 + 0.901314i \(0.642604\pi\)
\(90\) 18.3205i 0.203561i
\(91\) 80.5500 80.5500i 0.885165 0.885165i
\(92\) −2.62693 −0.0285536
\(93\) 1.92820 7.19615i 0.0207334 0.0773780i
\(94\) 0.437822 + 0.758330i 0.00465768 + 0.00806734i
\(95\) −18.6340 10.7583i −0.196147 0.113246i
\(96\) 8.26795 + 8.26795i 0.0861245 + 0.0861245i
\(97\) 74.8109 20.0455i 0.771246 0.206655i 0.148324 0.988939i \(-0.452612\pi\)
0.622922 + 0.782284i \(0.285945\pi\)
\(98\) −13.8923 51.8468i −0.141758 0.529049i
\(99\) 6.96668 6.96668i 0.0703705 0.0703705i
\(100\) −1.75833 + 3.04552i −0.0175833 + 0.0304552i
\(101\) 29.4404 16.9974i 0.291489 0.168291i −0.347124 0.937819i \(-0.612842\pi\)
0.638613 + 0.769528i \(0.279508\pi\)
\(102\) 58.8109 + 15.7583i 0.576577 + 0.154493i
\(103\) 179.229i 1.74009i 0.492971 + 0.870046i \(0.335911\pi\)
−0.492971 + 0.870046i \(0.664089\pi\)
\(104\) 103.533 + 27.7417i 0.995513 + 0.266747i
\(105\) −147.818 −1.40779
\(106\) −39.3827 + 146.978i −0.371535 + 1.38659i
\(107\) −40.6673 70.4378i −0.380068 0.658297i 0.611003 0.791628i \(-0.290766\pi\)
−0.991072 + 0.133331i \(0.957433\pi\)
\(108\) −6.67949 3.85641i −0.0618471 0.0357075i
\(109\) −0.0192379 0.0192379i −0.000176494 0.000176494i 0.707019 0.707195i \(-0.250040\pi\)
−0.707195 + 0.707019i \(0.750040\pi\)
\(110\) 73.9090 19.8038i 0.671900 0.180035i
\(111\) 30.8301 + 115.060i 0.277749 + 1.03657i
\(112\) 92.0526 92.0526i 0.821898 0.821898i
\(113\) 46.0096 79.6910i 0.407165 0.705230i −0.587406 0.809292i \(-0.699851\pi\)
0.994571 + 0.104062i \(0.0331841\pi\)
\(114\) 15.9282 9.19615i 0.139721 0.0806680i
\(115\) 58.4711 + 15.6673i 0.508445 + 0.136237i
\(116\) 3.05256i 0.0263152i
\(117\) −19.9667 −0.170655
\(118\) −81.8179 −0.693372
\(119\) −26.1628 + 97.6410i −0.219856 + 0.820513i
\(120\) −69.5429 120.452i −0.579524 1.00377i
\(121\) −69.1532 39.9256i −0.571514 0.329964i
\(122\) −134.380 134.380i −1.10148 1.10148i
\(123\) −51.8109 + 13.8827i −0.421227 + 0.112867i
\(124\) 0.189111 + 0.705771i 0.00152509 + 0.00569170i
\(125\) −51.8494 + 51.8494i −0.414795 + 0.414795i
\(126\) −13.0000 + 22.5167i −0.103175 + 0.178704i
\(127\) 63.6673 36.7583i 0.501317 0.289436i −0.227940 0.973675i \(-0.573199\pi\)
0.729257 + 0.684239i \(0.239866\pi\)
\(128\) 109.782 + 29.4160i 0.857672 + 0.229813i
\(129\) 141.962i 1.10048i
\(130\) −134.292 77.5333i −1.03301 0.596410i
\(131\) 48.9808 0.373899 0.186949 0.982370i \(-0.440140\pi\)
0.186949 + 0.982370i \(0.440140\pi\)
\(132\) 1.21539 4.53590i 0.00920750 0.0343629i
\(133\) 15.2679 + 26.4449i 0.114797 + 0.198834i
\(134\) 129.112 + 74.5429i 0.963524 + 0.556291i
\(135\) 125.674 + 125.674i 0.930921 + 0.930921i
\(136\) −91.8731 + 24.6173i −0.675537 + 0.181010i
\(137\) 18.3949 + 68.6506i 0.134269 + 0.501100i 1.00000 0.000589281i \(0.000187574\pi\)
−0.865731 + 0.500510i \(0.833146\pi\)
\(138\) −36.5885 + 36.5885i −0.265134 + 0.265134i
\(139\) −57.7846 + 100.086i −0.415717 + 0.720042i −0.995503 0.0947259i \(-0.969803\pi\)
0.579787 + 0.814768i \(0.303136\pi\)
\(140\) 12.5551 7.24871i 0.0896795 0.0517765i
\(141\) −1.19615 0.320508i −0.00848335 0.00227311i
\(142\) 62.0526i 0.436990i
\(143\) −21.5833 80.5500i −0.150932 0.563287i
\(144\) −22.8179 −0.158458
\(145\) 18.2058 67.9449i 0.125557 0.468585i
\(146\) 65.9449 + 114.220i 0.451677 + 0.782328i
\(147\) 65.7391 + 37.9545i 0.447205 + 0.258194i
\(148\) −8.26091 8.26091i −0.0558169 0.0558169i
\(149\) 263.090 70.4948i 1.76571 0.473120i 0.777845 0.628456i \(-0.216313\pi\)
0.987862 + 0.155336i \(0.0496460\pi\)
\(150\) 17.9282 + 66.9090i 0.119521 + 0.446060i
\(151\) −65.9948 + 65.9948i −0.437052 + 0.437052i −0.891019 0.453967i \(-0.850009\pi\)
0.453967 + 0.891019i \(0.350009\pi\)
\(152\) −14.3660 + 24.8827i −0.0945133 + 0.163702i
\(153\) 15.3442 8.85898i 0.100289 0.0579019i
\(154\) −104.890 28.1051i −0.681102 0.182501i
\(155\) 16.8372i 0.108627i
\(156\) −8.24167 + 4.75833i −0.0528312 + 0.0305021i
\(157\) 47.7461 0.304116 0.152058 0.988372i \(-0.451410\pi\)
0.152058 + 0.988372i \(0.451410\pi\)
\(158\) 41.3731 154.406i 0.261855 0.977256i
\(159\) −107.595 186.361i −0.676701 1.17208i
\(160\) 22.8853 + 13.2128i 0.143033 + 0.0825801i
\(161\) −60.7461 60.7461i −0.377305 0.377305i
\(162\) −120.952 + 32.4090i −0.746617 + 0.200055i
\(163\) 16.2820 + 60.7654i 0.0998898 + 0.372794i 0.997715 0.0675575i \(-0.0215206\pi\)
−0.897826 + 0.440351i \(0.854854\pi\)
\(164\) 3.71985 3.71985i 0.0226820 0.0226820i
\(165\) −54.1051 + 93.7128i −0.327910 + 0.567956i
\(166\) 164.478 94.9615i 0.990832 0.572057i
\(167\) −176.406 47.2679i −1.05633 0.283042i −0.311462 0.950259i \(-0.600819\pi\)
−0.744863 + 0.667217i \(0.767485\pi\)
\(168\) 197.387i 1.17492i
\(169\) −84.5000 + 146.358i −0.500000 + 0.866025i
\(170\) 137.603 0.809427
\(171\) 1.38526 5.16987i 0.00810095 0.0302332i
\(172\) 6.96152 + 12.0577i 0.0404740 + 0.0701030i
\(173\) −244.865 141.373i −1.41541 0.817185i −0.419516 0.907748i \(-0.637800\pi\)
−0.995891 + 0.0905627i \(0.971133\pi\)
\(174\) 42.5167 + 42.5167i 0.244349 + 0.244349i
\(175\) −111.086 + 29.7654i −0.634776 + 0.170088i
\(176\) −24.6654 92.0526i −0.140144 0.523026i
\(177\) 81.8179 81.8179i 0.462248 0.462248i
\(178\) 31.8301 55.1314i 0.178821 0.309727i
\(179\) −258.904 + 149.478i −1.44639 + 0.835074i −0.998264 0.0588968i \(-0.981242\pi\)
−0.448126 + 0.893970i \(0.647908\pi\)
\(180\) −2.45448 0.657677i −0.0136360 0.00365376i
\(181\) 299.081i 1.65238i −0.563392 0.826190i \(-0.690504\pi\)
0.563392 0.826190i \(-0.309496\pi\)
\(182\) 110.033 + 190.583i 0.604579 + 1.04716i
\(183\) 268.760 1.46864
\(184\) 20.9212 78.0788i 0.113702 0.424342i
\(185\) 134.605 + 233.143i 0.727595 + 1.26023i
\(186\) 12.4641 + 7.19615i 0.0670113 + 0.0386890i
\(187\) 52.3257 + 52.3257i 0.279816 + 0.279816i
\(188\) 0.117314 0.0314342i 0.000624011 0.000167203i
\(189\) −65.2820 243.636i −0.345408 1.28908i
\(190\) 29.3923 29.3923i 0.154696 0.154696i
\(191\) 118.002 204.385i 0.617811 1.07008i −0.372073 0.928203i \(-0.621353\pi\)
0.989884 0.141877i \(-0.0453136\pi\)
\(192\) −160.165 + 92.4711i −0.834191 + 0.481621i
\(193\) 312.449 + 83.7205i 1.61891 + 0.433785i 0.950681 0.310172i \(-0.100386\pi\)
0.668228 + 0.743957i \(0.267053\pi\)
\(194\) 149.622i 0.771246i
\(195\) 211.825 56.7583i 1.08628 0.291068i
\(196\) −7.44486 −0.0379840
\(197\) −62.1122 + 231.806i −0.315290 + 1.17668i 0.608429 + 0.793608i \(0.291800\pi\)
−0.923719 + 0.383071i \(0.874867\pi\)
\(198\) 9.51666 + 16.4833i 0.0480639 + 0.0832492i
\(199\) 44.5481 + 25.7199i 0.223860 + 0.129245i 0.607736 0.794139i \(-0.292078\pi\)
−0.383876 + 0.923384i \(0.625411\pi\)
\(200\) −76.5167 76.5167i −0.382583 0.382583i
\(201\) −203.655 + 54.5692i −1.01321 + 0.271489i
\(202\) 16.9974 + 63.4352i 0.0841457 + 0.314036i
\(203\) −70.5885 + 70.5885i −0.347726 + 0.347726i
\(204\) 4.22243 7.31347i 0.0206982 0.0358503i
\(205\) −104.983 + 60.6122i −0.512114 + 0.295669i
\(206\) −334.447 89.6147i −1.62353 0.435023i
\(207\) 15.0577i 0.0727426i
\(208\) −96.5666 + 167.258i −0.464263 + 0.804127i
\(209\) 22.3538 0.106956
\(210\) 73.9090 275.832i 0.351947 1.31349i
\(211\) 103.648 + 179.524i 0.491223 + 0.850823i 0.999949 0.0101053i \(-0.00321667\pi\)
−0.508726 + 0.860929i \(0.669883\pi\)
\(212\) 18.2776 + 10.5526i 0.0862149 + 0.0497762i
\(213\) 62.0526 + 62.0526i 0.291327 + 0.291327i
\(214\) 151.772 40.6673i 0.709217 0.190034i
\(215\) −83.0385 309.904i −0.386225 1.44141i
\(216\) 167.818 167.818i 0.776935 0.776935i
\(217\) −11.9474 + 20.6936i −0.0550573 + 0.0953621i
\(218\) 0.0455173 0.0262794i 0.000208795 0.000120548i
\(219\) −180.165 48.2750i −0.822670 0.220434i
\(220\) 10.6128i 0.0482402i
\(221\) 149.967i 0.678582i
\(222\) −230.119 −1.03657
\(223\) 84.5326 315.480i 0.379070 1.41471i −0.468236 0.883604i \(-0.655110\pi\)
0.847306 0.531105i \(-0.178223\pi\)
\(224\) −18.7513 32.4782i −0.0837111 0.144992i
\(225\) 17.4571 + 10.0788i 0.0775869 + 0.0447948i
\(226\) 125.701 + 125.701i 0.556197 + 0.556197i
\(227\) −234.720 + 62.8930i −1.03401 + 0.277062i −0.735628 0.677386i \(-0.763113\pi\)
−0.298380 + 0.954447i \(0.596446\pi\)
\(228\) −0.660254 2.46410i −0.00289585 0.0108075i
\(229\) −75.7321 + 75.7321i −0.330708 + 0.330708i −0.852855 0.522148i \(-0.825131\pi\)
0.522148 + 0.852855i \(0.325131\pi\)
\(230\) −58.4711 + 101.275i −0.254222 + 0.440326i
\(231\) 132.995 76.7846i 0.575735 0.332401i
\(232\) −90.7295 24.3109i −0.391075 0.104788i
\(233\) 304.592i 1.30726i 0.756813 + 0.653631i \(0.226755\pi\)
−0.756813 + 0.653631i \(0.773245\pi\)
\(234\) 9.98334 37.2583i 0.0426638 0.159224i
\(235\) −2.79869 −0.0119093
\(236\) −2.93713 + 10.9615i −0.0124455 + 0.0464471i
\(237\) 113.033 + 195.779i 0.476934 + 0.826074i
\(238\) −169.119 97.6410i −0.710585 0.410256i
\(239\) 250.655 + 250.655i 1.04877 + 1.04877i 0.998748 + 0.0500178i \(0.0159278\pi\)
0.0500178 + 0.998748i \(0.484072\pi\)
\(240\) 242.074 64.8634i 1.00864 0.270264i
\(241\) 11.6487 + 43.4737i 0.0483351 + 0.180389i 0.985873 0.167494i \(-0.0535674\pi\)
−0.937538 + 0.347883i \(0.886901\pi\)
\(242\) 109.079 109.079i 0.450739 0.450739i
\(243\) −40.9878 + 70.9930i −0.168674 + 0.292152i
\(244\) −22.8275 + 13.1795i −0.0935555 + 0.0540143i
\(245\) 165.710 + 44.4019i 0.676368 + 0.181232i
\(246\) 103.622i 0.421227i
\(247\) −32.0333 32.0333i −0.129690 0.129690i
\(248\) −22.4833 −0.0906586
\(249\) −69.5167 + 259.440i −0.279183 + 1.04193i
\(250\) −70.8275 122.677i −0.283310 0.490708i
\(251\) 116.375 + 67.1891i 0.463645 + 0.267686i 0.713576 0.700578i \(-0.247074\pi\)
−0.249931 + 0.968264i \(0.580408\pi\)
\(252\) 2.54998 + 2.54998i 0.0101190 + 0.0101190i
\(253\) −60.7461 + 16.2769i −0.240103 + 0.0643355i
\(254\) 36.7583 + 137.184i 0.144718 + 0.540094i
\(255\) −137.603 + 137.603i −0.539618 + 0.539618i
\(256\) 25.6051 44.3494i 0.100020 0.173240i
\(257\) 283.227 163.521i 1.10205 0.636269i 0.165291 0.986245i \(-0.447144\pi\)
0.936759 + 0.349976i \(0.113810\pi\)
\(258\) 264.904 + 70.9808i 1.02676 + 0.275119i
\(259\) 382.056i 1.47512i
\(260\) −15.2083 + 15.2083i −0.0584936 + 0.0584936i
\(261\) 17.4974 0.0670399
\(262\) −24.4904 + 91.3993i −0.0934747 + 0.348852i
\(263\) −225.669 390.870i −0.858058 1.48620i −0.873779 0.486323i \(-0.838338\pi\)
0.0157213 0.999876i \(-0.494996\pi\)
\(264\) 125.138 + 72.2487i 0.474009 + 0.273669i
\(265\) −343.892 343.892i −1.29770 1.29770i
\(266\) −56.9808 + 15.2679i −0.214213 + 0.0573983i
\(267\) 23.3013 + 86.9615i 0.0872707 + 0.325699i
\(268\) 14.6218 14.6218i 0.0545589 0.0545589i
\(269\) −78.3538 + 135.713i −0.291278 + 0.504509i −0.974112 0.226065i \(-0.927414\pi\)
0.682834 + 0.730573i \(0.260747\pi\)
\(270\) −297.349 + 171.674i −1.10129 + 0.635831i
\(271\) 247.133 + 66.2192i 0.911931 + 0.244351i 0.684133 0.729357i \(-0.260181\pi\)
0.227798 + 0.973708i \(0.426847\pi\)
\(272\) 171.382i 0.630081i
\(273\) −300.617 80.5500i −1.10116 0.295055i
\(274\) −137.301 −0.501100
\(275\) −21.7898 + 81.3205i −0.0792355 + 0.295711i
\(276\) 3.58846 + 6.21539i 0.0130017 + 0.0225195i
\(277\) −57.8904 33.4230i −0.208991 0.120661i 0.391852 0.920028i \(-0.371835\pi\)
−0.600842 + 0.799368i \(0.705168\pi\)
\(278\) −157.870 157.870i −0.567879 0.567879i
\(279\) 4.04552 1.08399i 0.0145001 0.00388528i
\(280\) 115.459 + 430.899i 0.412353 + 1.53892i
\(281\) 111.026 111.026i 0.395111 0.395111i −0.481393 0.876505i \(-0.659869\pi\)
0.876505 + 0.481393i \(0.159869\pi\)
\(282\) 1.19615 2.07180i 0.00424168 0.00734680i
\(283\) −41.1962 + 23.7846i −0.145569 + 0.0840446i −0.571016 0.820939i \(-0.693450\pi\)
0.425446 + 0.904984i \(0.360117\pi\)
\(284\) −8.31347 2.22759i −0.0292728 0.00784361i
\(285\) 58.7846i 0.206262i
\(286\) 161.100 0.563287
\(287\) 172.038 0.599437
\(288\) −1.70131 + 6.34936i −0.00590732 + 0.0220464i
\(289\) −77.9615 135.033i −0.269763 0.467243i
\(290\) 117.684 + 67.9449i 0.405807 + 0.234293i
\(291\) −149.622 149.622i −0.514164 0.514164i
\(292\) 17.6699 4.73463i 0.0605133 0.0162145i
\(293\) 2.24236 + 8.36860i 0.00765311 + 0.0285618i 0.969647 0.244510i \(-0.0786271\pi\)
−0.961994 + 0.273072i \(0.911960\pi\)
\(294\) −103.694 + 103.694i −0.352699 + 0.352699i
\(295\) 130.751 226.468i 0.443225 0.767688i
\(296\) 311.325 179.744i 1.05177 0.607242i
\(297\) −178.354 47.7898i −0.600518 0.160908i
\(298\) 526.181i 1.76571i
\(299\) 110.375 + 63.7250i 0.369147 + 0.213127i
\(300\) 9.60770 0.0320257
\(301\) −117.846 + 439.808i −0.391515 + 1.46115i
\(302\) −90.1506 156.145i −0.298512 0.517038i
\(303\) −80.4327 46.4378i −0.265454 0.153260i
\(304\) −36.6077 36.6077i −0.120420 0.120420i
\(305\) 586.707 157.208i 1.92363 0.515435i
\(306\) 8.85898 + 33.0622i 0.0289509 + 0.108046i
\(307\) −228.219 + 228.219i −0.743385 + 0.743385i −0.973228 0.229843i \(-0.926179\pi\)
0.229843 + 0.973228i \(0.426179\pi\)
\(308\) −7.53074 + 13.0436i −0.0244505 + 0.0423494i
\(309\) 424.061 244.832i 1.37237 0.792337i
\(310\) 31.4186 + 8.41858i 0.101350 + 0.0271567i
\(311\) 77.4782i 0.249126i −0.992212 0.124563i \(-0.960247\pi\)
0.992212 0.124563i \(-0.0397529\pi\)
\(312\) −75.7917 282.858i −0.242922 0.906597i
\(313\) −165.685 −0.529344 −0.264672 0.964339i \(-0.585264\pi\)
−0.264672 + 0.964339i \(0.585264\pi\)
\(314\) −23.8731 + 89.0955i −0.0760289 + 0.283744i
\(315\) −41.5500 71.9667i −0.131905 0.228466i
\(316\) −19.2013 11.0859i −0.0607636 0.0350819i
\(317\) 97.0544 + 97.0544i 0.306165 + 0.306165i 0.843420 0.537255i \(-0.180539\pi\)
−0.537255 + 0.843420i \(0.680539\pi\)
\(318\) 401.552 107.595i 1.26274 0.338351i
\(319\) 18.9141 + 70.5885i 0.0592919 + 0.221280i
\(320\) −295.552 + 295.552i −0.923600 + 0.923600i
\(321\) −111.105 + 192.440i −0.346122 + 0.599501i
\(322\) 143.727 82.9808i 0.446357 0.257704i
\(323\) 38.8301 + 10.4045i 0.120217 + 0.0322121i
\(324\) 17.3679i 0.0536047i
\(325\) 147.758 85.3083i 0.454641 0.262487i
\(326\) −121.531 −0.372794
\(327\) −0.0192379 + 0.0717968i −5.88315e−5 + 0.000219562i
\(328\) 80.9378 + 140.188i 0.246762 + 0.427404i
\(329\) 3.43971 + 1.98592i 0.0104550 + 0.00603622i
\(330\) −147.818 147.818i −0.447933 0.447933i
\(331\) −292.603 + 78.4026i −0.883996 + 0.236866i −0.672130 0.740433i \(-0.734621\pi\)
−0.211865 + 0.977299i \(0.567954\pi\)
\(332\) −6.81793 25.4449i −0.0205359 0.0766412i
\(333\) −47.3519 + 47.3519i −0.142198 + 0.142198i
\(334\) 176.406 305.545i 0.528163 0.914805i
\(335\) −412.662 + 238.251i −1.23183 + 0.711196i
\(336\) −343.545 92.0526i −1.02245 0.273966i
\(337\) 90.7795i 0.269375i 0.990888 + 0.134688i \(0.0430031\pi\)
−0.990888 + 0.134688i \(0.956997\pi\)
\(338\) −230.858 230.858i −0.683013 0.683013i
\(339\) −251.401 −0.741597
\(340\) 4.93971 18.4352i 0.0145286 0.0542213i
\(341\) 8.74613 + 15.1487i 0.0256485 + 0.0444245i
\(342\) 8.95448 + 5.16987i 0.0261827 + 0.0151166i
\(343\) 131.454 + 131.454i 0.383247 + 0.383247i
\(344\) −413.827 + 110.885i −1.20299 + 0.322339i
\(345\) −42.8038 159.746i −0.124069 0.463032i
\(346\) 386.238 386.238i 1.11630 1.11630i
\(347\) 52.5903 91.0891i 0.151557 0.262505i −0.780243 0.625477i \(-0.784905\pi\)
0.931800 + 0.362972i \(0.118238\pi\)
\(348\) 7.22243 4.16987i 0.0207541 0.0119824i
\(349\) 158.040 + 42.3468i 0.452838 + 0.121338i 0.478027 0.878345i \(-0.341352\pi\)
−0.0251892 + 0.999683i \(0.508019\pi\)
\(350\) 222.172i 0.634776i
\(351\) 187.100 + 324.067i 0.533048 + 0.923267i
\(352\) −27.4538 −0.0779937
\(353\) 77.1692 287.999i 0.218610 0.815862i −0.766255 0.642537i \(-0.777882\pi\)
0.984865 0.173325i \(-0.0554513\pi\)
\(354\) 111.765 + 193.583i 0.315721 + 0.546845i
\(355\) 171.758 + 99.1647i 0.483826 + 0.279337i
\(356\) −6.24356 6.24356i −0.0175381 0.0175381i
\(357\) 266.760 71.4782i 0.747227 0.200219i
\(358\) −149.478 557.860i −0.417537 1.55827i
\(359\) 299.923 299.923i 0.835440 0.835440i −0.152815 0.988255i \(-0.548834\pi\)
0.988255 + 0.152815i \(0.0488337\pi\)
\(360\) 39.0955 67.7154i 0.108599 0.188098i
\(361\) −302.119 + 174.428i −0.836893 + 0.483181i
\(362\) 558.092 + 149.540i 1.54169 + 0.413095i
\(363\) 218.158i 0.600985i
\(364\) 29.4833 7.90004i 0.0809982 0.0217034i
\(365\) −421.540 −1.15490
\(366\) −134.380 + 501.513i −0.367159 + 1.37026i
\(367\) 61.2750 + 106.131i 0.166962 + 0.289186i 0.937350 0.348388i \(-0.113271\pi\)
−0.770388 + 0.637575i \(0.779938\pi\)
\(368\) 126.137 + 72.8250i 0.342762 + 0.197894i
\(369\) −21.3224 21.3224i −0.0577843 0.0577843i
\(370\) −502.353 + 134.605i −1.35771 + 0.363798i
\(371\) 178.636 + 666.678i 0.481498 + 1.79698i
\(372\) 1.41154 1.41154i 0.00379447 0.00379447i
\(373\) −10.6384 + 18.4263i −0.0285213 + 0.0494003i −0.879934 0.475096i \(-0.842413\pi\)
0.851412 + 0.524497i \(0.175747\pi\)
\(374\) −123.804 + 71.4782i −0.331026 + 0.191118i
\(375\) 193.504 + 51.8494i 0.516012 + 0.138265i
\(376\) 3.73721i 0.00993938i
\(377\) 74.0500 128.258i 0.196419 0.340208i
\(378\) 487.272 1.28908
\(379\) 87.1417 325.217i 0.229925 0.858093i −0.750446 0.660932i \(-0.770161\pi\)
0.980371 0.197161i \(-0.0631722\pi\)
\(380\) −2.88269 4.99296i −0.00758602 0.0131394i
\(381\) −173.942 100.426i −0.456541 0.263584i
\(382\) 322.387 + 322.387i 0.843945 + 0.843945i
\(383\) −183.061 + 49.0512i −0.477967 + 0.128071i −0.489756 0.871860i \(-0.662914\pi\)
0.0117887 + 0.999931i \(0.496247\pi\)
\(384\) −80.3660 299.930i −0.209287 0.781068i
\(385\) 245.415 245.415i 0.637442 0.637442i
\(386\) −312.449 + 541.178i −0.809454 + 1.40202i
\(387\) 69.1154 39.9038i 0.178593 0.103111i
\(388\) 20.0455 + 5.37118i 0.0516637 + 0.0138432i
\(389\) 195.522i 0.502627i −0.967906 0.251313i \(-0.919138\pi\)
0.967906 0.251313i \(-0.0808625\pi\)
\(390\) 423.650i 1.08628i
\(391\) −113.096 −0.289249
\(392\) 59.2917 221.279i 0.151254 0.564488i
\(393\) −66.9090 115.890i −0.170252 0.294885i
\(394\) −401.499 231.806i −1.01903 0.588339i
\(395\) 361.272 + 361.272i 0.914612 + 0.914612i
\(396\) 2.54998 0.683265i 0.00643935 0.00172542i
\(397\) −108.578 405.217i −0.273495 1.02070i −0.956843 0.290605i \(-0.906143\pi\)
0.683348 0.730093i \(-0.260523\pi\)
\(398\) −70.2679 + 70.2679i −0.176553 + 0.176553i
\(399\) 41.7128 72.2487i 0.104543 0.181074i
\(400\) 168.858 97.4904i 0.422146 0.243726i
\(401\) −753.833 201.989i −1.87988 0.503713i −0.999570 0.0293204i \(-0.990666\pi\)
−0.880313 0.474393i \(-0.842668\pi\)
\(402\) 407.310i 1.01321i
\(403\) 9.17503 34.2417i 0.0227668 0.0849669i
\(404\) 9.10889 0.0225468
\(405\) 103.584 386.581i 0.255763 0.954520i
\(406\) −96.4256 167.014i −0.237502 0.411365i
\(407\) −242.214 139.842i −0.595120 0.343593i
\(408\) 183.746 + 183.746i 0.450358 + 0.450358i
\(409\) 353.679 94.7679i 0.864740 0.231706i 0.200928 0.979606i \(-0.435604\pi\)
0.663812 + 0.747899i \(0.268937\pi\)
\(410\) −60.6122 226.208i −0.147835 0.551726i
\(411\) 137.301 137.301i 0.334066 0.334066i
\(412\) −24.0122 + 41.5903i −0.0582820 + 0.100947i
\(413\) −321.397 + 185.559i −0.778202 + 0.449295i
\(414\) −28.0981 7.52886i −0.0678697 0.0181856i
\(415\) 607.023i 1.46271i
\(416\) 39.3416 + 39.3416i 0.0945712 + 0.0945712i
\(417\) 315.741 0.757173
\(418\) −11.1769 + 41.7128i −0.0267390 + 0.0997914i
\(419\) 275.279 + 476.797i 0.656990 + 1.13794i 0.981391 + 0.192020i \(0.0615039\pi\)
−0.324401 + 0.945920i \(0.605163\pi\)
\(420\) −34.3013 19.8038i −0.0816697 0.0471520i
\(421\) −233.619 233.619i −0.554913 0.554913i 0.372942 0.927855i \(-0.378349\pi\)
−0.927855 + 0.372942i \(0.878349\pi\)
\(422\) −386.820 + 103.648i −0.916635 + 0.245612i
\(423\) −0.180183 0.672450i −0.000425963 0.00158972i
\(424\) −459.212 + 459.212i −1.08305 + 1.08305i
\(425\) −75.7006 + 131.117i −0.178119 + 0.308511i
\(426\) −146.818 + 84.7654i −0.344643 + 0.198980i
\(427\) −832.640 223.105i −1.94998 0.522494i
\(428\) 21.7935i 0.0509195i
\(429\) −161.100 + 161.100i −0.375524 + 0.375524i
\(430\) 619.808 1.44141
\(431\) 188.301 702.750i 0.436894 1.63051i −0.299599 0.954065i \(-0.596853\pi\)
0.736493 0.676445i \(-0.236480\pi\)
\(432\) 213.818 + 370.344i 0.494949 + 0.857277i
\(433\) 576.108 + 332.616i 1.33050 + 0.768166i 0.985377 0.170390i \(-0.0545028\pi\)
0.345126 + 0.938556i \(0.387836\pi\)
\(434\) −32.6410 32.6410i −0.0752097 0.0752097i
\(435\) −185.629 + 49.7391i −0.426733 + 0.114343i
\(436\) −0.00188678 0.00704156i −4.32747e−6 1.61504e-5i
\(437\) −24.1577 + 24.1577i −0.0552807 + 0.0552807i
\(438\) 180.165 312.054i 0.411335 0.712453i
\(439\) 233.942 135.067i 0.532898 0.307669i −0.209298 0.977852i \(-0.567118\pi\)
0.742196 + 0.670183i \(0.233784\pi\)
\(440\) 315.440 + 84.5218i 0.716908 + 0.192095i
\(441\) 42.6743i 0.0967672i
\(442\) 279.842 + 74.9833i 0.633126 + 0.169646i
\(443\) 309.723 0.699149 0.349575 0.936909i \(-0.386326\pi\)
0.349575 + 0.936909i \(0.386326\pi\)
\(444\) −8.26091 + 30.8301i −0.0186056 + 0.0694372i
\(445\) 101.734 + 176.208i 0.228616 + 0.395974i
\(446\) 546.428 + 315.480i 1.22517 + 0.707354i
\(447\) −526.181 526.181i −1.17714 1.17714i
\(448\) 572.965 153.526i 1.27894 0.342691i
\(449\) 114.399 + 426.944i 0.254787 + 0.950878i 0.968209 + 0.250143i \(0.0804777\pi\)
−0.713422 + 0.700735i \(0.752856\pi\)
\(450\) −27.5359 + 27.5359i −0.0611909 + 0.0611909i
\(451\) 62.9705 109.068i 0.139624 0.241836i
\(452\) 21.3531 12.3282i 0.0472415 0.0272749i
\(453\) 246.296 + 65.9948i 0.543700 + 0.145684i
\(454\) 469.440i 1.03401i
\(455\) −703.367 −1.54586
\(456\) 78.4974 0.172143
\(457\) −46.6980 + 174.279i −0.102184 + 0.381355i −0.998010 0.0630483i \(-0.979918\pi\)
0.895827 + 0.444404i \(0.146584\pi\)
\(458\) −103.452 179.184i −0.225878 0.391231i
\(459\) −287.569 166.028i −0.626512 0.361717i
\(460\) 11.4693 + 11.4693i 0.0249332 + 0.0249332i
\(461\) −201.397 + 53.9641i −0.436869 + 0.117059i −0.470549 0.882374i \(-0.655944\pi\)
0.0336796 + 0.999433i \(0.489277\pi\)
\(462\) 76.7846 + 286.564i 0.166200 + 0.620269i
\(463\) −316.809 + 316.809i −0.684253 + 0.684253i −0.960956 0.276703i \(-0.910758\pi\)
0.276703 + 0.960956i \(0.410758\pi\)
\(464\) 84.6244 146.574i 0.182380 0.315892i
\(465\) −39.8372 + 23.0000i −0.0856713 + 0.0494624i
\(466\) −568.377 152.296i −1.21969 0.326816i
\(467\) 357.415i 0.765343i −0.923884 0.382672i \(-0.875004\pi\)
0.923884 0.382672i \(-0.124996\pi\)
\(468\) −4.63328 2.67503i −0.00990018 0.00571587i
\(469\) 676.238 1.44187
\(470\) 1.39935 5.22243i 0.00297733 0.0111116i
\(471\) −65.2224 112.969i −0.138477 0.239848i
\(472\) −302.412 174.597i −0.640702 0.369910i
\(473\) 235.692 + 235.692i 0.498292 + 0.498292i
\(474\) −421.846 + 113.033i −0.889971 + 0.238467i
\(475\) 11.8372 + 44.1769i 0.0249204 + 0.0930040i
\(476\) −19.1525 + 19.1525i −0.0402364 + 0.0402364i
\(477\) 60.4878 104.768i 0.126809 0.219639i
\(478\) −593.056 + 342.401i −1.24070 + 0.716321i
\(479\) 417.217 + 111.793i 0.871017 + 0.233388i 0.666528 0.745480i \(-0.267780\pi\)
0.204490 + 0.978869i \(0.434447\pi\)
\(480\) 72.1962i 0.150409i
\(481\) 146.700 + 547.492i 0.304989 + 1.13824i
\(482\) −86.9474 −0.180389
\(483\) −60.7461 + 226.708i −0.125768 + 0.469374i
\(484\) −10.6980 18.5295i −0.0221034 0.0382842i
\(485\) −414.145 239.107i −0.853908 0.493004i
\(486\) −111.981 111.981i −0.230413 0.230413i
\(487\) 286.937 76.8846i 0.589193 0.157874i 0.0481088 0.998842i \(-0.484681\pi\)
0.541084 + 0.840968i \(0.318014\pi\)
\(488\) −209.926 783.453i −0.430175 1.60544i
\(489\) 121.531 121.531i 0.248529 0.248529i
\(490\) −165.710 + 287.019i −0.338184 + 0.585752i
\(491\) 685.319 395.669i 1.39576 0.805844i 0.401817 0.915720i \(-0.368379\pi\)
0.993945 + 0.109877i \(0.0350456\pi\)
\(492\) −13.8827 3.71985i −0.0282168 0.00756068i
\(493\) 131.420i 0.266573i
\(494\) 75.7917 43.7583i 0.153424 0.0885796i
\(495\) −60.8334 −0.122896
\(496\) 10.4852 39.1314i 0.0211396 0.0788939i
\(497\) −140.732 243.755i −0.283163 0.490453i
\(498\) −449.363 259.440i −0.902335 0.520963i
\(499\) −307.603 307.603i −0.616438 0.616438i 0.328178 0.944616i \(-0.393565\pi\)
−0.944616 + 0.328178i \(0.893565\pi\)
\(500\) −18.9782 + 5.08519i −0.0379564 + 0.0101704i
\(501\) 129.138 + 481.951i 0.257761 + 0.961978i
\(502\) −183.564 + 183.564i −0.365665 + 0.365665i
\(503\) −142.200 + 246.297i −0.282704 + 0.489657i −0.972050 0.234775i \(-0.924565\pi\)
0.689346 + 0.724432i \(0.257898\pi\)
\(504\) −96.1000 + 55.4833i −0.190675 + 0.110086i
\(505\) −202.749 54.3264i −0.401483 0.107577i
\(506\) 121.492i 0.240103i
\(507\) 461.717 0.910684
\(508\) 19.6987 0.0387770
\(509\) 3.39488 12.6699i 0.00666971 0.0248917i −0.962511 0.271243i \(-0.912565\pi\)
0.969180 + 0.246352i \(0.0792318\pi\)
\(510\) −187.969 325.571i −0.368566 0.638375i
\(511\) 518.090 + 299.119i 1.01387 + 0.585360i
\(512\) 391.419 + 391.419i 0.764489 + 0.764489i
\(513\) −96.8897 + 25.9615i −0.188869 + 0.0506073i
\(514\) 163.521 + 610.269i 0.318134 + 1.18729i
\(515\) 782.520 782.520i 1.51946 1.51946i
\(516\) 19.0192 32.9423i 0.0368590 0.0638416i
\(517\) 2.51804 1.45379i 0.00487049 0.00281198i
\(518\) 712.927 + 191.028i 1.37631 + 0.368780i
\(519\) 772.477i 1.48839i
\(520\) −330.908 573.150i −0.636362 1.10221i
\(521\) −913.011 −1.75242 −0.876210 0.481929i \(-0.839936\pi\)
−0.876210 + 0.481929i \(0.839936\pi\)
\(522\) −8.74871 + 32.6506i −0.0167600 + 0.0625491i
\(523\) −375.827 650.951i −0.718598 1.24465i −0.961555 0.274612i \(-0.911451\pi\)
0.242957 0.970037i \(-0.421883\pi\)
\(524\) 11.3660 + 6.56218i 0.0216909 + 0.0125232i
\(525\) 222.172 + 222.172i 0.423184 + 0.423184i
\(526\) 842.209 225.669i 1.60116 0.429029i
\(527\) 8.14171 + 30.3853i 0.0154492 + 0.0576570i
\(528\) −184.105 + 184.105i −0.348684 + 0.348684i
\(529\) −216.442 + 374.889i −0.409154 + 0.708675i
\(530\) 813.656 469.765i 1.53520 0.886348i
\(531\) 62.8320 + 16.8358i 0.118328 + 0.0317058i
\(532\) 8.18207i 0.0153798i
\(533\) −246.533 + 66.0584i −0.462539 + 0.123937i
\(534\) −173.923 −0.325699
\(535\) −129.979 + 485.088i −0.242951 + 0.906706i
\(536\) 318.145 + 551.044i 0.593555 + 1.02807i
\(537\) 707.338 + 408.382i 1.31720 + 0.760488i
\(538\) −214.067 214.067i −0.397893 0.397893i
\(539\) −172.158 + 46.1295i −0.319402 + 0.0855835i
\(540\) 12.3257 + 46.0000i 0.0228253 + 0.0851852i
\(541\) 125.371 125.371i 0.231740 0.231740i −0.581679 0.813419i \(-0.697604\pi\)
0.813419 + 0.581679i \(0.197604\pi\)
\(542\) −247.133 + 428.047i −0.455965 + 0.789755i
\(543\) −707.633 + 408.552i −1.30319 + 0.752398i
\(544\) −47.6891 12.7783i −0.0876638 0.0234894i
\(545\) 0.167986i 0.000308232i
\(546\) 300.617 520.683i 0.550580 0.953632i
\(547\) −465.096 −0.850267 −0.425134 0.905131i \(-0.639773\pi\)
−0.425134 + 0.905131i \(0.639773\pi\)
\(548\) −4.92889 + 18.3949i −0.00899433 + 0.0335673i
\(549\) 75.5455 + 130.849i 0.137606 + 0.238340i
\(550\) −140.851 81.3205i −0.256093 0.147855i
\(551\) 28.0718 + 28.0718i 0.0509470 + 0.0509470i
\(552\) −213.315 + 57.1577i −0.386441 + 0.103547i
\(553\) −187.664 700.372i −0.339356 1.26649i
\(554\) 91.3135 91.3135i 0.164826 0.164826i
\(555\) 367.748 636.958i 0.662609 1.14767i
\(556\) −26.8179 + 15.4833i −0.0482337 + 0.0278477i
\(557\) 246.064 + 65.9327i 0.441767 + 0.118371i 0.472844 0.881146i \(-0.343227\pi\)
−0.0310777 + 0.999517i \(0.509894\pi\)
\(558\) 8.09103i 0.0145001i
\(559\) 675.500i 1.20841i
\(560\) −803.808 −1.43537
\(561\) 52.3257 195.282i 0.0932721 0.348096i
\(562\) 151.665 + 262.691i 0.269866 + 0.467422i
\(563\) 306.888 + 177.182i 0.545095 + 0.314711i 0.747141 0.664665i \(-0.231426\pi\)
−0.202046 + 0.979376i \(0.564759\pi\)
\(564\) −0.234628 0.234628i −0.000416007 0.000416007i
\(565\) −548.812 + 147.054i −0.971349 + 0.260272i
\(566\) −23.7846 88.7654i −0.0420223 0.156829i
\(567\) −401.622 + 401.622i −0.708328 + 0.708328i
\(568\) 132.419 229.356i 0.233131 0.403795i
\(569\) −152.685 + 88.1525i −0.268339 + 0.154925i −0.628132 0.778106i \(-0.716180\pi\)
0.359794 + 0.933032i \(0.382847\pi\)
\(570\) −109.694 29.3923i −0.192445 0.0515654i
\(571\) 569.751i 0.997813i −0.866656 0.498907i \(-0.833735\pi\)
0.866656 0.498907i \(-0.166265\pi\)
\(572\) 5.78323 21.5833i 0.0101105 0.0377330i
\(573\) −644.774 −1.12526
\(574\) −86.0192 + 321.028i −0.149859 + 0.559283i
\(575\) −64.3346 111.431i −0.111886 0.193793i
\(576\) −90.0411 51.9852i −0.156321 0.0902521i
\(577\) −94.7635 94.7635i −0.164235 0.164235i 0.620205 0.784440i \(-0.287049\pi\)
−0.784440 + 0.620205i \(0.787049\pi\)
\(578\) 290.956 77.9615i 0.503385 0.134882i
\(579\) −228.729 853.627i −0.395041 1.47431i
\(580\) 13.3275 13.3275i 0.0229785 0.0229785i
\(581\) 430.736 746.056i 0.741370 1.28409i
\(582\) 354.009 204.387i 0.608263 0.351181i
\(583\) 488.042 + 130.771i 0.837122 + 0.224306i
\(584\) 562.899i 0.963868i
\(585\) 87.1750 + 87.1750i 0.149017 + 0.149017i
\(586\) −16.7372 −0.0285618
\(587\) −283.123 + 1056.63i −0.482322 + 1.80005i 0.109507 + 0.993986i \(0.465073\pi\)
−0.591829 + 0.806064i \(0.701594\pi\)
\(588\) 10.1699 + 17.6147i 0.0172957 + 0.0299570i
\(589\) 8.22947 + 4.75129i 0.0139719 + 0.00806670i
\(590\) 357.219 + 357.219i 0.605456 + 0.605456i
\(591\) 633.305 169.694i 1.07158 0.287130i
\(592\) 167.649 + 625.674i 0.283190 + 1.05688i
\(593\) −228.671 + 228.671i −0.385617 + 0.385617i −0.873121 0.487504i \(-0.837908\pi\)
0.487504 + 0.873121i \(0.337908\pi\)
\(594\) 178.354 308.918i 0.300259 0.520064i
\(595\) 540.531 312.076i 0.908455 0.524497i
\(596\) 70.4948 + 18.8890i 0.118280 + 0.0316930i
\(597\) 140.536i 0.235404i
\(598\) −174.100 + 174.100i −0.291137 + 0.291137i
\(599\) −282.596 −0.471780 −0.235890 0.971780i \(-0.575800\pi\)
−0.235890 + 0.971780i \(0.575800\pi\)
\(600\) −76.5167 + 285.564i −0.127528 + 0.475940i
\(601\) 70.6558 + 122.379i 0.117564 + 0.203626i 0.918802 0.394720i \(-0.129158\pi\)
−0.801238 + 0.598346i \(0.795825\pi\)
\(602\) −761.769 439.808i −1.26540 0.730577i
\(603\) −83.8128 83.8128i −0.138993 0.138993i
\(604\) −24.1558 + 6.47252i −0.0399930 + 0.0107161i
\(605\) 127.608 + 476.241i 0.210923 + 0.787175i
\(606\) 126.870 126.870i 0.209357 0.209357i
\(607\) −344.398 + 596.515i −0.567377 + 0.982726i 0.429447 + 0.903092i \(0.358709\pi\)
−0.996824 + 0.0796341i \(0.974625\pi\)
\(608\) −12.9160 + 7.45706i −0.0212434 + 0.0122649i
\(609\) 263.440 + 70.5885i 0.432578 + 0.115909i
\(610\) 1173.41i 1.92363i
\(611\) −5.69169 1.52508i −0.00931537 0.00249604i
\(612\) 4.74752 0.00775738
\(613\) 33.1608 123.758i 0.0540959 0.201888i −0.933589 0.358346i \(-0.883341\pi\)
0.987685 + 0.156458i \(0.0500075\pi\)
\(614\) −311.753 539.972i −0.507741 0.879434i
\(615\) 286.820 + 165.595i 0.466374 + 0.269261i
\(616\) −327.713 327.713i −0.532001 0.532001i
\(617\) −103.088 + 27.6225i −0.167080 + 0.0447690i −0.341389 0.939922i \(-0.610897\pi\)
0.174309 + 0.984691i \(0.444231\pi\)
\(618\) 244.832 + 913.726i 0.396168 + 1.47852i
\(619\) 251.517 251.517i 0.406327 0.406327i −0.474128 0.880456i \(-0.657237\pi\)
0.880456 + 0.474128i \(0.157237\pi\)
\(620\) 2.25575 3.90708i 0.00363831 0.00630174i
\(621\) 244.392 141.100i 0.393546 0.227214i
\(622\) 144.576 + 38.7391i 0.232438 + 0.0622815i
\(623\) 288.756i 0.463493i
\(624\) 527.650 0.845593
\(625\) 780.860 1.24938
\(626\) 82.8423 309.172i 0.132336 0.493885i
\(627\) −30.5359 52.8897i −0.0487016 0.0843536i
\(628\) 11.0795 + 6.39677i 0.0176426 + 0.0101859i
\(629\) −355.653 355.653i −0.565426 0.565426i
\(630\) 155.067 41.5500i 0.246138 0.0659524i
\(631\) −103.187 385.100i −0.163530 0.610301i −0.998223 0.0595863i \(-0.981022\pi\)
0.834693 0.550715i \(-0.185645\pi\)
\(632\) 482.420 482.420i 0.763324 0.763324i
\(633\) 283.172 490.468i 0.447349 0.774831i
\(634\) −229.633 + 132.579i −0.362198 + 0.209115i
\(635\) −438.461 117.485i −0.690490 0.185016i
\(636\) 57.6603i 0.0906608i
\(637\) 312.808 + 180.600i 0.491065 + 0.283516i
\(638\) −141.177 −0.221280
\(639\) −12.7686 + 47.6532i −0.0199822 + 0.0745747i
\(640\) −350.880 607.742i −0.548250 0.949597i
\(641\) −248.283 143.346i −0.387337 0.223629i 0.293669 0.955907i \(-0.405124\pi\)
−0.681005 + 0.732278i \(0.738457\pi\)
\(642\) −303.545 303.545i −0.472811 0.472811i
\(643\) 837.927 224.522i 1.30315 0.349179i 0.460511 0.887654i \(-0.347666\pi\)
0.842641 + 0.538475i \(0.181000\pi\)
\(644\) −5.95775 22.2346i −0.00925117 0.0345258i
\(645\) −619.808 + 619.808i −0.960942 + 0.960942i
\(646\) −38.8301 + 67.2558i −0.0601086 + 0.104111i
\(647\) −856.944 + 494.757i −1.32449 + 0.764694i −0.984441 0.175714i \(-0.943776\pi\)
−0.340047 + 0.940408i \(0.610443\pi\)
\(648\) −516.217 138.320i −0.796631 0.213457i
\(649\) 271.677i 0.418609i
\(650\) 85.3083 + 318.375i 0.131244 + 0.489808i
\(651\) 65.2820 0.100280
\(652\) −4.36276 + 16.2820i −0.00669135 + 0.0249724i
\(653\) 67.5692 + 117.033i 0.103475 + 0.179224i 0.913114 0.407704i \(-0.133670\pi\)
−0.809639 + 0.586928i \(0.800337\pi\)
\(654\) −0.124356 0.0717968i −0.000190146 0.000109781i
\(655\) −213.851 213.851i −0.326490 0.326490i
\(656\) −281.738 + 75.4916i −0.429479 + 0.115079i
\(657\) −27.1391 101.285i −0.0413077 0.154162i
\(658\) −5.42563 + 5.42563i −0.00824563 + 0.00824563i
\(659\) −618.512 + 1071.29i −0.938561 + 1.62563i −0.170403 + 0.985375i \(0.554507\pi\)
−0.768158 + 0.640260i \(0.778826\pi\)
\(660\) −25.1103 + 14.4974i −0.0380459 + 0.0219658i
\(661\) −89.8083 24.0641i −0.135867 0.0364055i 0.190244 0.981737i \(-0.439072\pi\)
−0.326112 + 0.945331i \(0.605739\pi\)
\(662\) 585.205i 0.883996i
\(663\) −354.825 + 204.858i −0.535181 + 0.308987i
\(664\) 810.582 1.22076
\(665\) 48.7987 182.119i 0.0733815 0.273863i
\(666\) −64.6840 112.036i −0.0971231 0.168222i
\(667\) −96.7250 55.8442i −0.145015 0.0837245i
\(668\) −34.6025 34.6025i −0.0518002 0.0518002i
\(669\) −861.908 + 230.947i −1.28835 + 0.345213i
\(670\) −238.251 889.163i −0.355598 1.32711i
\(671\) −446.210 + 446.210i −0.664993 + 0.664993i
\(672\) −51.2295 + 88.7321i −0.0762343 + 0.132042i
\(673\) 242.210 139.840i 0.359895 0.207786i −0.309140 0.951017i \(-0.600041\pi\)
0.669035 + 0.743231i \(0.266708\pi\)
\(674\) −169.397 45.3897i −0.251331 0.0673438i
\(675\) 377.779i 0.559673i
\(676\) −39.2166 + 22.6417i −0.0580127 + 0.0334936i
\(677\) 1115.38 1.64754 0.823770 0.566924i \(-0.191867\pi\)
0.823770 + 0.566924i \(0.191867\pi\)
\(678\) 125.701 469.121i 0.185399 0.691919i
\(679\) 339.335 + 587.745i 0.499756 + 0.865603i
\(680\) 508.600 + 293.640i 0.747941 + 0.431824i
\(681\) 469.440 + 469.440i 0.689339 + 0.689339i
\(682\) −32.6410 + 8.74613i −0.0478607 + 0.0128242i
\(683\) 220.046 + 821.221i 0.322175 + 1.20237i 0.917121 + 0.398608i \(0.130507\pi\)
−0.594946 + 0.803765i \(0.702827\pi\)
\(684\) 1.01408 1.01408i 0.00148258 0.00148258i
\(685\) 219.418 380.043i 0.320318 0.554807i
\(686\) −311.023 + 179.569i −0.453386 + 0.261763i
\(687\) 282.636 + 75.7321i 0.411406 + 0.110236i
\(688\) 771.962i 1.12204i
\(689\) −511.975 886.767i −0.743070 1.28703i
\(690\) 319.492 0.463032
\(691\) −142.754 + 532.764i −0.206590 + 0.771004i 0.782369 + 0.622815i \(0.214011\pi\)
−0.988959 + 0.148189i \(0.952656\pi\)
\(692\) −37.8808 65.6115i −0.0547410 0.0948143i
\(693\) 74.7668 + 43.1666i 0.107889 + 0.0622895i
\(694\) 143.679 + 143.679i 0.207031 + 0.207031i
\(695\) 689.267 184.688i 0.991750 0.265739i
\(696\) 66.4186 + 247.878i 0.0954290 + 0.356146i
\(697\) 160.149 160.149i 0.229769 0.229769i
\(698\) −158.040 + 273.734i −0.226419 + 0.392169i
\(699\) 720.673 416.081i 1.03101 0.595251i
\(700\) −29.7654 7.97561i −0.0425220 0.0113937i
\(701\) 650.323i 0.927707i −0.885912 0.463854i \(-0.846466\pi\)
0.885912 0.463854i \(-0.153534\pi\)
\(702\) −698.267 + 187.100i −0.994682 + 0.266524i
\(703\) −151.937 −0.216127
\(704\) 112.389 419.440i 0.159643 0.595795i
\(705\) 3.82309 + 6.62178i 0.00542282 + 0.00939259i
\(706\) 498.829 + 287.999i 0.706557 + 0.407931i
\(707\) 210.637 + 210.637i 0.297931 + 0.297931i
\(708\) 29.9474 8.02439i 0.0422986 0.0113339i
\(709\) 135.185 + 504.518i 0.190670 + 0.711591i 0.993345 + 0.115174i \(0.0367426\pi\)
−0.802675 + 0.596416i \(0.796591\pi\)
\(710\) −270.923 + 270.923i −0.381582 + 0.381582i
\(711\) −63.5448 + 110.063i −0.0893739 + 0.154800i
\(712\) 235.298 135.849i 0.330475 0.190800i
\(713\) −25.8231 6.91927i −0.0362175 0.00970445i
\(714\) 533.520i 0.747227i
\(715\) −257.450 + 445.917i −0.360070 + 0.623659i
\(716\) −80.1051 −0.111879
\(717\) 250.655 935.458i 0.349589 1.30468i
\(718\) 409.703 + 709.626i 0.570616 + 0.988336i
\(719\) −74.3806 42.9437i −0.103450 0.0597269i 0.447382 0.894343i \(-0.352356\pi\)
−0.550832 + 0.834616i \(0.685690\pi\)
\(720\) 99.6237 + 99.6237i 0.138366 + 0.138366i
\(721\) −1517.02 + 406.483i −2.10405 + 0.563777i
\(722\) −174.428 650.975i −0.241590 0.901627i
\(723\) 86.9474 86.9474i 0.120259 0.120259i
\(724\) 40.0692 69.4019i 0.0553442 0.0958590i
\(725\) −129.485 + 74.7583i −0.178600 + 0.103115i
\(726\) −407.088 109.079i −0.560727 0.150246i
\(727\) 460.974i 0.634077i 0.948413 + 0.317039i \(0.102689\pi\)
−0.948413 + 0.317039i \(0.897311\pi\)
\(728\) 939.233i 1.29016i
\(729\) 807.323 1.10744
\(730\) 210.770 786.604i 0.288726 1.07754i
\(731\) 299.711 + 519.115i 0.410002 + 0.710144i
\(732\) 62.3660 + 36.0070i 0.0851995 + 0.0491899i
\(733\) 631.319 + 631.319i 0.861281 + 0.861281i 0.991487 0.130206i \(-0.0415640\pi\)
−0.130206 + 0.991487i \(0.541564\pi\)
\(734\) −228.681 + 61.2750i −0.311555 + 0.0834809i
\(735\) −121.308 452.729i −0.165045 0.615958i
\(736\) 29.6692 29.6692i 0.0403114 0.0403114i
\(737\) 247.520 428.718i 0.335849 0.581707i
\(738\) 50.4493 29.1269i 0.0683595 0.0394674i
\(739\) −794.424 212.865i −1.07500 0.288045i −0.322453 0.946585i \(-0.604508\pi\)
−0.752546 + 0.658540i \(0.771174\pi\)
\(740\) 72.1347i 0.0974793i
\(741\) −32.0333 + 119.550i −0.0432299 + 0.161336i
\(742\) −1333.36 −1.79698
\(743\) 209.252 780.941i 0.281632 1.05106i −0.669634 0.742692i \(-0.733549\pi\)
0.951266 0.308373i \(-0.0997845\pi\)
\(744\) 30.7128 + 53.1962i 0.0412807 + 0.0715002i
\(745\) −1456.44 840.877i −1.95495 1.12869i
\(746\) −29.0648 29.0648i −0.0389608 0.0389608i
\(747\) −145.851 + 39.0807i −0.195249 + 0.0523169i
\(748\) 5.13190 + 19.1525i 0.00686083 + 0.0256050i
\(749\) 503.962 503.962i 0.672846 0.672846i
\(750\) −193.504 + 335.160i −0.258006 + 0.446879i
\(751\) −407.585 + 235.319i −0.542723 + 0.313341i −0.746182 0.665742i \(-0.768115\pi\)
0.203459 + 0.979083i \(0.434782\pi\)
\(752\) −6.50446 1.74287i −0.00864955 0.00231764i
\(753\) 367.128i 0.487554i
\(754\) 202.308 + 202.308i 0.268313 + 0.268313i
\(755\) 576.270 0.763272
\(756\) 17.4923 65.2820i 0.0231379 0.0863519i
\(757\) −310.415 537.655i −0.410060 0.710245i 0.584836 0.811152i \(-0.301159\pi\)
−0.994896 + 0.100907i \(0.967826\pi\)
\(758\) 563.293 + 325.217i 0.743130 + 0.429047i
\(759\) 121.492 + 121.492i 0.160069 + 0.160069i
\(760\) 171.361 45.9160i 0.225475 0.0604158i
\(761\) −50.9559 190.170i −0.0669591 0.249895i 0.924331 0.381592i \(-0.124624\pi\)
−0.991290 + 0.131697i \(0.957957\pi\)
\(762\) 274.368 274.368i 0.360063 0.360063i
\(763\) 0.119201 0.206462i 0.000156227 0.000270592i
\(764\) 54.7649 31.6185i 0.0716818 0.0413855i
\(765\) −105.672 28.3147i −0.138133 0.0370126i
\(766\) 366.123i 0.477967i
\(767\) 389.317 389.317i 0.507584 0.507584i
\(768\) −139.909 −0.182173
\(769\) 112.701 420.604i 0.146555 0.546950i −0.853127 0.521704i \(-0.825297\pi\)
0.999681 0.0252457i \(-0.00803682\pi\)
\(770\) 335.244 + 580.659i 0.435381 + 0.754102i
\(771\) −773.790 446.748i −1.00362 0.579440i
\(772\) 61.2877 + 61.2877i 0.0793882 + 0.0793882i
\(773\) −8.31862 + 2.22897i −0.0107615 + 0.00288353i −0.264196 0.964469i \(-0.585107\pi\)
0.253434 + 0.967353i \(0.418440\pi\)
\(774\) 39.9038 + 148.923i 0.0515553 + 0.192407i
\(775\) −25.3064 + 25.3064i −0.0326535 + 0.0326535i
\(776\) −319.289 + 553.025i −0.411455 + 0.712661i
\(777\) −903.955 + 521.899i −1.16339 + 0.671684i
\(778\) 364.849 + 97.7609i 0.468957 + 0.125657i
\(779\) 68.4167i 0.0878263i
\(780\) 56.7583 + 15.2083i 0.0727671 + 0.0194979i
\(781\) −206.046 −0.263823
\(782\) 56.5481 211.040i 0.0723121 0.269873i
\(783\) −163.962 283.990i −0.209402 0.362694i
\(784\) 357.477 + 206.390i 0.455966 + 0.263252i
\(785\) −208.461 208.461i −0.265555 0.265555i
\(786\) 249.708 66.9090i 0.317694 0.0851259i
\(787\) −115.617 431.489i −0.146909 0.548271i −0.999663 0.0259585i \(-0.991736\pi\)
0.852754 0.522312i \(-0.174930\pi\)
\(788\) −45.4693 + 45.4693i −0.0577021 + 0.0577021i
\(789\) −616.540 + 1067.88i −0.781419 + 1.35346i
\(790\) −854.778 + 493.506i −1.08200 + 0.624692i
\(791\) 778.860 + 208.695i 0.984653 + 0.263837i
\(792\) 81.2332i 0.102567i
\(793\) 1278.85 1.61267
\(794\) 810.435 1.02070
\(795\) −343.892 + 1283.42i −0.432568 + 1.61437i
\(796\) 6.89161 + 11.9366i 0.00865781 + 0.0149958i
\(797\) 352.061 + 203.263i 0.441733 + 0.255035i 0.704333 0.709870i \(-0.251246\pi\)
−0.262599 + 0.964905i \(0.584580\pi\)
\(798\) 113.962 + 113.962i 0.142809 + 0.142809i
\(799\) 5.05067 1.35332i 0.00632124 0.00169377i
\(800\) −14.5378 54.2558i −0.0181722 0.0678197i
\(801\) −35.7884 + 35.7884i −0.0446796 + 0.0446796i
\(802\) 753.833 1305.68i 0.939942 1.62803i
\(803\) 379.268 218.970i 0.472314 0.272690i
\(804\) −54.5692 14.6218i −0.0678722 0.0181863i
\(805\) 530.438i 0.658930i
\(806\) 59.3083 + 34.2417i 0.0735835 + 0.0424835i
\(807\) 428.133 0.530525
\(808\) −72.5441 + 270.738i −0.0897823 + 0.335072i
\(809\) −17.4634 30.2475i −0.0215864 0.0373888i 0.855030 0.518578i \(-0.173538\pi\)
−0.876617 + 0.481189i \(0.840205\pi\)
\(810\) 669.577 + 386.581i 0.826639 + 0.477260i
\(811\) 755.708 + 755.708i 0.931822 + 0.931822i 0.997820 0.0659978i \(-0.0210230\pi\)
−0.0659978 + 0.997820i \(0.521023\pi\)
\(812\) −25.8372 + 6.92305i −0.0318192 + 0.00852592i
\(813\) −180.914 675.181i −0.222527 0.830481i
\(814\) 382.056 382.056i 0.469357 0.469357i
\(815\) 194.215 336.391i 0.238301 0.412750i
\(816\) −405.494 + 234.112i −0.496929 + 0.286902i
\(817\) 174.904 + 46.8653i 0.214081 + 0.0573627i
\(818\) 707.358i 0.864740i
\(819\) −45.2834 169.000i −0.0552911 0.206349i
\(820\) −32.4820 −0.0396121
\(821\) −254.210 + 948.724i −0.309634 + 1.15557i 0.619248 + 0.785196i \(0.287438\pi\)
−0.928882 + 0.370375i \(0.879229\pi\)
\(822\) 187.557 + 324.858i 0.228172 + 0.395205i
\(823\) −1146.14 661.726i −1.39264 0.804041i −0.399033 0.916937i \(-0.630654\pi\)
−0.993607 + 0.112896i \(0.963987\pi\)
\(824\) −1044.93 1044.93i −1.26812 1.26812i
\(825\) 222.172 59.5307i 0.269299 0.0721585i
\(826\) −185.559 692.515i −0.224648 0.838396i
\(827\) 51.7691 51.7691i 0.0625987 0.0625987i −0.675114 0.737713i \(-0.735906\pi\)
0.737713 + 0.675114i \(0.235906\pi\)
\(828\) −2.01735 + 3.49415i −0.00243641 + 0.00421999i
\(829\) −21.9059 + 12.6474i −0.0264245 + 0.0152562i −0.513154 0.858297i \(-0.671523\pi\)
0.486730 + 0.873553i \(0.338190\pi\)
\(830\) −1132.72 303.512i −1.36472 0.365677i
\(831\) 182.627i 0.219768i
\(832\) −762.117 + 440.008i −0.916006 + 0.528856i
\(833\) −320.520 −0.384778
\(834\) −157.870 + 589.181i −0.189293 + 0.706452i
\(835\) 563.822 + 976.568i 0.675236 + 1.16954i
\(836\) 5.18722 + 2.99485i 0.00620481 + 0.00358235i
\(837\) −55.5026 55.5026i −0.0663113 0.0663113i
\(838\) −1027.35 + 275.279i −1.22596 + 0.328495i
\(839\) −232.757 868.661i −0.277422 1.03535i −0.954201 0.299166i \(-0.903291\pi\)
0.676779 0.736186i \(-0.263375\pi\)
\(840\) 861.797 861.797i 1.02595 1.02595i
\(841\) 355.608 615.931i 0.422839 0.732379i
\(842\) 552.747 319.129i 0.656470 0.379013i
\(843\) −414.356 111.026i −0.491525 0.131704i
\(844\) 55.5448i 0.0658114i
\(845\) 1007.93 270.075i 1.19282 0.319615i
\(846\) 1.34490 0.00158972
\(847\) 181.099 675.869i 0.213812 0.797956i
\(848\) −585.085 1013.40i −0.689959 1.19504i
\(849\) 112.550 + 64.9808i 0.132568 + 0.0765380i
\(850\) −206.818 206.818i −0.243315 0.243315i
\(851\) 412.886 110.633i 0.485178 0.130003i
\(852\) 6.08588 + 22.7128i 0.00714305 + 0.0266582i
\(853\) −702.043 + 702.043i −0.823028 + 0.823028i −0.986541 0.163513i \(-0.947717\pi\)
0.163513 + 0.986541i \(0.447717\pi\)
\(854\) 832.640 1442.17i 0.974988 1.68873i
\(855\) −28.6199 + 16.5237i −0.0334736 + 0.0193260i
\(856\) 647.757 + 173.566i 0.756725 + 0.202764i
\(857\) 959.663i 1.11979i 0.828563 + 0.559897i \(0.189159\pi\)
−0.828563 + 0.559897i \(0.810841\pi\)
\(858\) −220.067 381.167i −0.256488 0.444250i
\(859\) −1526.98 −1.77763 −0.888813 0.458270i \(-0.848469\pi\)
−0.888813 + 0.458270i \(0.848469\pi\)
\(860\) 22.2501 83.0385i 0.0258722 0.0965564i
\(861\) −235.009 407.047i −0.272949 0.472761i
\(862\) 1217.20 + 702.750i 1.41206 + 0.815255i
\(863\) −149.604 149.604i −0.173353 0.173353i 0.615098 0.788451i \(-0.289117\pi\)
−0.788451 + 0.615098i \(0.789117\pi\)
\(864\) 118.995 31.8846i 0.137726 0.0369034i
\(865\) 451.850 + 1686.33i 0.522370 + 1.94951i
\(866\) −908.724 + 908.724i −1.04933 + 1.04933i
\(867\) −212.995 + 368.918i −0.245669 + 0.425511i
\(868\) −5.54483 + 3.20131i −0.00638805 + 0.00368814i
\(869\) −512.708 137.380i −0.589997 0.158089i
\(870\) 371.258i 0.426733i
\(871\) −969.058 + 259.658i −1.11258 + 0.298115i
\(872\) 0.224319 0.000257246
\(873\) 30.7879 114.902i 0.0352668 0.131617i
\(874\) −33.0000 57.1577i −0.0377574 0.0653978i
\(875\) −556.450 321.267i −0.635943 0.367162i
\(876\) −35.3397 35.3397i −0.0403422 0.0403422i
\(877\) 1180.45 316.301i 1.34601 0.360662i 0.487349 0.873207i \(-0.337964\pi\)
0.858660 + 0.512545i \(0.171297\pi\)
\(878\) 135.067 + 504.076i 0.153834 + 0.574118i
\(879\) 16.7372 16.7372i 0.0190412 0.0190412i
\(880\) −294.214 + 509.594i −0.334334 + 0.579084i
\(881\) 321.323 185.516i 0.364725 0.210574i −0.306426 0.951894i \(-0.599133\pi\)
0.671152 + 0.741320i \(0.265800\pi\)
\(882\) −79.6314 21.3372i −0.0902850 0.0241918i
\(883\) 1407.20i 1.59365i −0.604208 0.796827i \(-0.706510\pi\)
0.604208 0.796827i \(-0.293490\pi\)
\(884\) 20.0917 34.7999i 0.0227282 0.0393664i
\(885\) −714.438 −0.807275
\(886\) −154.862 + 577.951i −0.174787 + 0.652315i
\(887\) 258.623 + 447.948i 0.291571 + 0.505015i 0.974181 0.225767i \(-0.0724888\pi\)
−0.682611 + 0.730782i \(0.739155\pi\)
\(888\) −850.556 491.069i −0.957833 0.553005i
\(889\) 455.520 + 455.520i 0.512396 + 0.512396i
\(890\) −379.676 + 101.734i −0.426602 + 0.114308i
\(891\) 107.614 + 401.622i 0.120779 + 0.450754i
\(892\) 61.8822 61.8822i 0.0693746 0.0693746i
\(893\) 0.789764 1.36791i 0.000884395 0.00153182i
\(894\) 1244.96 718.776i 1.39257 0.804000i
\(895\) 1783.01 + 477.755i 1.99219 + 0.533805i
\(896\) 995.920i 1.11152i
\(897\) 348.200i 0.388183i
\(898\) −853.888 −0.950878
\(899\) −8.04036 + 30.0070i −0.00894367 + 0.0333782i
\(900\) 2.70062 + 4.67761i 0.00300069 + 0.00519734i
\(901\) 786.896 + 454.315i 0.873359 + 0.504234i
\(902\) 172.038 + 172.038i 0.190730 + 0.190730i
\(903\) 1201.58 321.962i 1.33065 0.356547i
\(904\) 196.367 + 732.851i 0.217220 + 0.810675i
\(905\) −1305.79 + 1305.79i −1.44287 + 1.44287i
\(906\) −246.296 + 426.597i −0.271850 + 0.470858i
\(907\) 1299.20 750.093i 1.43241 0.827005i 0.435110 0.900377i \(-0.356710\pi\)
0.997305 + 0.0733725i \(0.0233762\pi\)
\(908\) −62.8930 16.8521i −0.0692654 0.0185596i
\(909\) 52.2126i 0.0574396i
\(910\) 351.683 1312.50i 0.386465 1.44231i
\(911\) 663.346 0.728151 0.364076 0.931369i \(-0.381385\pi\)
0.364076 + 0.931369i \(0.381385\pi\)
\(912\) −36.6077 + 136.622i −0.0401400 + 0.149805i
\(913\) −315.321 546.151i −0.345367 0.598194i
\(914\) −301.861 174.279i −0.330264 0.190678i
\(915\) −1173.41 1173.41i −1.28242 1.28242i
\(916\) −27.7199 + 7.42751i −0.0302618 + 0.00810864i
\(917\) 111.086 + 414.578i 0.121141 + 0.452103i
\(918\) 453.597 453.597i 0.494115 0.494115i
\(919\) −51.1596 + 88.6110i −0.0556687 + 0.0964211i −0.892517 0.451014i \(-0.851062\pi\)
0.836848 + 0.547435i \(0.184396\pi\)
\(920\) −432.237 + 249.552i −0.469822 + 0.271252i
\(921\) 851.726 + 228.219i 0.924783 + 0.247795i
\(922\) 402.794i 0.436869i
\(923\) 295.267 + 295.267i 0.319899 + 0.319899i
\(924\) 41.1487 0.0445333
\(925\) 148.103 552.729i 0.160112 0.597545i
\(926\) −432.769 749.578i −0.467353 0.809480i
\(927\) 238.398 + 137.639i 0.257171 + 0.148478i
\(928\) −34.4763 34.4763i −0.0371512 0.0371512i
\(929\) −31.5737 + 8.46014i −0.0339867 + 0.00910672i −0.275772 0.961223i \(-0.588934\pi\)
0.241786 + 0.970330i \(0.422267\pi\)
\(930\) −23.0000 85.8372i −0.0247312 0.0922980i
\(931\) −68.4641 + 68.4641i −0.0735382 + 0.0735382i
\(932\) −40.8076 + 70.6809i −0.0437850 + 0.0758378i
\(933\) −183.315 + 105.837i −0.196479 + 0.113437i
\(934\) 666.946 + 178.708i 0.714075 + 0.191336i
\(935\) 456.910i 0.488674i
\(936\) 116.408 116.408i 0.124368 0.124368i
\(937\) −196.615 −0.209835 −0.104917 0.994481i \(-0.533458\pi\)
−0.104917 + 0.994481i \(0.533458\pi\)
\(938\) −338.119 + 1261.88i −0.360468 + 1.34529i
\(939\) 226.329 + 392.014i 0.241032 + 0.417480i
\(940\) −0.649439 0.374954i −0.000690892 0.000398887i
\(941\) 269.659 + 269.659i 0.286566 + 0.286566i 0.835721 0.549155i \(-0.185050\pi\)
−0.549155 + 0.835721i \(0.685050\pi\)
\(942\) 243.413 65.2224i 0.258401 0.0692383i
\(943\) 49.8174 + 185.921i 0.0528287 + 0.197159i
\(944\) 444.911 444.911i 0.471304 0.471304i
\(945\) −778.697 + 1348.74i −0.824018 + 1.42724i
\(946\) −557.654 + 321.962i −0.589486 + 0.340340i
\(947\) −1237.89 331.692i −1.30717 0.350255i −0.463013 0.886351i \(-0.653232\pi\)
−0.844157 + 0.536096i \(0.819898\pi\)
\(948\) 60.5744i 0.0638970i
\(949\) −857.283 229.708i −0.903354 0.242053i
\(950\) −88.3538 −0.0930040
\(951\) 97.0544 362.212i 0.102055 0.380875i
\(952\) −416.727 721.792i −0.437738 0.758185i
\(953\) 1142.09 + 659.387i 1.19842 + 0.691907i 0.960202 0.279306i \(-0.0901042\pi\)
0.238215 + 0.971212i \(0.423438\pi\)
\(954\) 165.256 + 165.256i 0.173224 + 0.173224i
\(955\) −1407.55 + 377.152i −1.47387 + 0.394924i
\(956\) 24.5833 + 91.7461i 0.0257148 + 0.0959688i
\(957\) 141.177 141.177i 0.147520 0.147520i
\(958\) −417.217 + 722.642i −0.435509 + 0.754323i
\(959\) −539.347 + 311.392i −0.562406 + 0.324705i
\(960\) 1103.01 + 295.552i 1.14897 + 0.307867i
\(961\) 953.564i 0.992262i
\(962\) −1094.98 −1.13824
\(963\) −124.922 −0.129721
\(964\) −3.12127 + 11.6487i −0.00323783 + 0.0120838i
\(965\) −998.636 1729.69i −1.03486 1.79242i
\(966\) −392.669 226.708i −0.406490 0.234687i
\(967\) −879.683 879.683i −0.909703 0.909703i 0.0865445 0.996248i \(-0.472418\pi\)
−0.996248 + 0.0865445i \(0.972418\pi\)
\(968\) 635.943 170.401i 0.656966 0.176034i
\(969\) −28.4256 106.086i −0.0293350 0.109480i
\(970\) 653.252 653.252i 0.673456 0.673456i
\(971\) 23.1366 40.0737i 0.0238276 0.0412705i −0.853866 0.520493i \(-0.825748\pi\)
0.877693 + 0.479223i \(0.159081\pi\)
\(972\) −19.0225 + 10.9826i −0.0195705 + 0.0112990i
\(973\) −978.190 262.105i −1.00533 0.269378i
\(974\) 573.874i 0.589193i
\(975\) −403.683 233.067i −0.414034 0.239043i
\(976\) 1461.47 1.49741
\(977\) −411.992 + 1537.57i −0.421691 + 1.57377i 0.349355 + 0.936991i \(0.386401\pi\)
−0.771045 + 0.636780i \(0.780266\pi\)
\(978\) 166.014 + 287.545i 0.169749 + 0.294013i
\(979\) −183.064 105.692i −0.186991 0.107959i
\(980\) 32.5045 + 32.5045i 0.0331678 + 0.0331678i
\(981\) −0.0403626 + 0.0108151i −4.11443e−5 + 1.10246e-5i
\(982\) 395.669 + 1476.66i 0.402922 + 1.50372i
\(983\) 632.213 632.213i 0.643146 0.643146i −0.308181 0.951328i \(-0.599720\pi\)
0.951328 + 0.308181i \(0.0997204\pi\)
\(984\) 221.126 383.002i 0.224722 0.389230i
\(985\) 1283.25 740.886i 1.30279 0.752169i
\(986\) −245.234 65.7102i −0.248716 0.0666432i
\(987\) 10.8513i 0.0109942i
\(988\) −3.14171 11.7250i −0.00317987 0.0118674i
\(989\) −509.423 −0.515089
\(990\) 30.4167 113.517i 0.0307239 0.114663i
\(991\) −600.733 1040.50i −0.606188 1.04995i −0.991862 0.127314i \(-0.959364\pi\)
0.385674 0.922635i \(-0.373969\pi\)
\(992\) −10.1070 5.83528i −0.0101885 0.00588234i
\(993\) 585.205 + 585.205i 0.589330 + 0.589330i
\(994\) 525.219 140.732i 0.528390 0.141582i
\(995\) −82.2046 306.792i −0.0826177 0.308333i
\(996\) −50.8897 + 50.8897i −0.0510941 + 0.0510941i
\(997\) 242.817 420.572i 0.243548 0.421837i −0.718174 0.695863i \(-0.755022\pi\)
0.961722 + 0.274026i \(0.0883554\pi\)
\(998\) 727.795 420.193i 0.729254 0.421035i
\(999\) 1212.26 + 324.823i 1.21347 + 0.325148i
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 13.3.f.a.11.1 yes 4
3.2 odd 2 117.3.bd.b.37.1 4
4.3 odd 2 208.3.bd.d.193.1 4
5.2 odd 4 325.3.w.a.24.1 4
5.3 odd 4 325.3.w.b.24.1 4
5.4 even 2 325.3.t.a.76.1 4
13.2 odd 12 169.3.d.a.70.1 4
13.3 even 3 169.3.d.a.99.1 4
13.4 even 6 169.3.f.a.150.1 4
13.5 odd 4 169.3.f.c.80.1 4
13.6 odd 12 inner 13.3.f.a.6.1 4
13.7 odd 12 169.3.f.b.19.1 4
13.8 odd 4 169.3.f.a.80.1 4
13.9 even 3 169.3.f.c.150.1 4
13.10 even 6 169.3.d.c.99.2 4
13.11 odd 12 169.3.d.c.70.2 4
13.12 even 2 169.3.f.b.89.1 4
39.32 even 12 117.3.bd.b.19.1 4
52.19 even 12 208.3.bd.d.97.1 4
65.19 odd 12 325.3.t.a.201.1 4
65.32 even 12 325.3.w.b.149.1 4
65.58 even 12 325.3.w.a.149.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.3.f.a.6.1 4 13.6 odd 12 inner
13.3.f.a.11.1 yes 4 1.1 even 1 trivial
117.3.bd.b.19.1 4 39.32 even 12
117.3.bd.b.37.1 4 3.2 odd 2
169.3.d.a.70.1 4 13.2 odd 12
169.3.d.a.99.1 4 13.3 even 3
169.3.d.c.70.2 4 13.11 odd 12
169.3.d.c.99.2 4 13.10 even 6
169.3.f.a.80.1 4 13.8 odd 4
169.3.f.a.150.1 4 13.4 even 6
169.3.f.b.19.1 4 13.7 odd 12
169.3.f.b.89.1 4 13.12 even 2
169.3.f.c.80.1 4 13.5 odd 4
169.3.f.c.150.1 4 13.9 even 3
208.3.bd.d.97.1 4 52.19 even 12
208.3.bd.d.193.1 4 4.3 odd 2
325.3.t.a.76.1 4 5.4 even 2
325.3.t.a.201.1 4 65.19 odd 12
325.3.w.a.24.1 4 5.2 odd 4
325.3.w.a.149.1 4 65.58 even 12
325.3.w.b.24.1 4 5.3 odd 4
325.3.w.b.149.1 4 65.32 even 12