# Properties

 Label 77.2.a.d.1.1 Level $77$ Weight $2$ Character 77.1 Self dual yes Analytic conductor $0.615$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(1,77)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("77.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$77 = 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 77.a (trivial)

## 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: yes Analytic conductor: $$0.614848095564$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$1.61803$$ of defining polynomial Character $$\chi$$ $$=$$ 77.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-2.23607 q^{2} +3.23607 q^{3} +3.00000 q^{4} -2.00000 q^{5} -7.23607 q^{6} +1.00000 q^{7} -2.23607 q^{8} +7.47214 q^{9} +O(q^{10})$$ $$q-2.23607 q^{2} +3.23607 q^{3} +3.00000 q^{4} -2.00000 q^{5} -7.23607 q^{6} +1.00000 q^{7} -2.23607 q^{8} +7.47214 q^{9} +4.47214 q^{10} -1.00000 q^{11} +9.70820 q^{12} -1.23607 q^{13} -2.23607 q^{14} -6.47214 q^{15} -1.00000 q^{16} +1.23607 q^{17} -16.7082 q^{18} -2.47214 q^{19} -6.00000 q^{20} +3.23607 q^{21} +2.23607 q^{22} -6.47214 q^{23} -7.23607 q^{24} -1.00000 q^{25} +2.76393 q^{26} +14.4721 q^{27} +3.00000 q^{28} -0.472136 q^{29} +14.4721 q^{30} -7.23607 q^{31} +6.70820 q^{32} -3.23607 q^{33} -2.76393 q^{34} -2.00000 q^{35} +22.4164 q^{36} +0.472136 q^{37} +5.52786 q^{38} -4.00000 q^{39} +4.47214 q^{40} -6.76393 q^{41} -7.23607 q^{42} +8.00000 q^{43} -3.00000 q^{44} -14.9443 q^{45} +14.4721 q^{46} +7.23607 q^{47} -3.23607 q^{48} +1.00000 q^{49} +2.23607 q^{50} +4.00000 q^{51} -3.70820 q^{52} +8.47214 q^{53} -32.3607 q^{54} +2.00000 q^{55} -2.23607 q^{56} -8.00000 q^{57} +1.05573 q^{58} +3.23607 q^{59} -19.4164 q^{60} -2.76393 q^{61} +16.1803 q^{62} +7.47214 q^{63} -13.0000 q^{64} +2.47214 q^{65} +7.23607 q^{66} +5.52786 q^{67} +3.70820 q^{68} -20.9443 q^{69} +4.47214 q^{70} -1.52786 q^{71} -16.7082 q^{72} -5.23607 q^{73} -1.05573 q^{74} -3.23607 q^{75} -7.41641 q^{76} -1.00000 q^{77} +8.94427 q^{78} +8.94427 q^{79} +2.00000 q^{80} +24.4164 q^{81} +15.1246 q^{82} +15.4164 q^{83} +9.70820 q^{84} -2.47214 q^{85} -17.8885 q^{86} -1.52786 q^{87} +2.23607 q^{88} +2.00000 q^{89} +33.4164 q^{90} -1.23607 q^{91} -19.4164 q^{92} -23.4164 q^{93} -16.1803 q^{94} +4.94427 q^{95} +21.7082 q^{96} -9.41641 q^{97} -2.23607 q^{98} -7.47214 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} + 6 q^{4} - 4 q^{5} - 10 q^{6} + 2 q^{7} + 6 q^{9}+O(q^{10})$$ 2 * q + 2 * q^3 + 6 * q^4 - 4 * q^5 - 10 * q^6 + 2 * q^7 + 6 * q^9 $$2 q + 2 q^{3} + 6 q^{4} - 4 q^{5} - 10 q^{6} + 2 q^{7} + 6 q^{9} - 2 q^{11} + 6 q^{12} + 2 q^{13} - 4 q^{15} - 2 q^{16} - 2 q^{17} - 20 q^{18} + 4 q^{19} - 12 q^{20} + 2 q^{21} - 4 q^{23} - 10 q^{24} - 2 q^{25} + 10 q^{26} + 20 q^{27} + 6 q^{28} + 8 q^{29} + 20 q^{30} - 10 q^{31} - 2 q^{33} - 10 q^{34} - 4 q^{35} + 18 q^{36} - 8 q^{37} + 20 q^{38} - 8 q^{39} - 18 q^{41} - 10 q^{42} + 16 q^{43} - 6 q^{44} - 12 q^{45} + 20 q^{46} + 10 q^{47} - 2 q^{48} + 2 q^{49} + 8 q^{51} + 6 q^{52} + 8 q^{53} - 20 q^{54} + 4 q^{55} - 16 q^{57} + 20 q^{58} + 2 q^{59} - 12 q^{60} - 10 q^{61} + 10 q^{62} + 6 q^{63} - 26 q^{64} - 4 q^{65} + 10 q^{66} + 20 q^{67} - 6 q^{68} - 24 q^{69} - 12 q^{71} - 20 q^{72} - 6 q^{73} - 20 q^{74} - 2 q^{75} + 12 q^{76} - 2 q^{77} + 4 q^{80} + 22 q^{81} - 10 q^{82} + 4 q^{83} + 6 q^{84} + 4 q^{85} - 12 q^{87} + 4 q^{89} + 40 q^{90} + 2 q^{91} - 12 q^{92} - 20 q^{93} - 10 q^{94} - 8 q^{95} + 30 q^{96} + 8 q^{97} - 6 q^{99}+O(q^{100})$$ 2 * q + 2 * q^3 + 6 * q^4 - 4 * q^5 - 10 * q^6 + 2 * q^7 + 6 * q^9 - 2 * q^11 + 6 * q^12 + 2 * q^13 - 4 * q^15 - 2 * q^16 - 2 * q^17 - 20 * q^18 + 4 * q^19 - 12 * q^20 + 2 * q^21 - 4 * q^23 - 10 * q^24 - 2 * q^25 + 10 * q^26 + 20 * q^27 + 6 * q^28 + 8 * q^29 + 20 * q^30 - 10 * q^31 - 2 * q^33 - 10 * q^34 - 4 * q^35 + 18 * q^36 - 8 * q^37 + 20 * q^38 - 8 * q^39 - 18 * q^41 - 10 * q^42 + 16 * q^43 - 6 * q^44 - 12 * q^45 + 20 * q^46 + 10 * q^47 - 2 * q^48 + 2 * q^49 + 8 * q^51 + 6 * q^52 + 8 * q^53 - 20 * q^54 + 4 * q^55 - 16 * q^57 + 20 * q^58 + 2 * q^59 - 12 * q^60 - 10 * q^61 + 10 * q^62 + 6 * q^63 - 26 * q^64 - 4 * q^65 + 10 * q^66 + 20 * q^67 - 6 * q^68 - 24 * q^69 - 12 * q^71 - 20 * q^72 - 6 * q^73 - 20 * q^74 - 2 * q^75 + 12 * q^76 - 2 * q^77 + 4 * q^80 + 22 * q^81 - 10 * q^82 + 4 * q^83 + 6 * q^84 + 4 * q^85 - 12 * q^87 + 4 * q^89 + 40 * q^90 + 2 * q^91 - 12 * q^92 - 20 * q^93 - 10 * q^94 - 8 * q^95 + 30 * q^96 + 8 * q^97 - 6 * q^99

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.23607 −1.58114 −0.790569 0.612372i $$-0.790215\pi$$
−0.790569 + 0.612372i $$0.790215\pi$$
$$3$$ 3.23607 1.86834 0.934172 0.356822i $$-0.116140\pi$$
0.934172 + 0.356822i $$0.116140\pi$$
$$4$$ 3.00000 1.50000
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ −7.23607 −2.95411
$$7$$ 1.00000 0.377964
$$8$$ −2.23607 −0.790569
$$9$$ 7.47214 2.49071
$$10$$ 4.47214 1.41421
$$11$$ −1.00000 −0.301511
$$12$$ 9.70820 2.80252
$$13$$ −1.23607 −0.342824 −0.171412 0.985199i $$-0.554833\pi$$
−0.171412 + 0.985199i $$0.554833\pi$$
$$14$$ −2.23607 −0.597614
$$15$$ −6.47214 −1.67110
$$16$$ −1.00000 −0.250000
$$17$$ 1.23607 0.299791 0.149895 0.988702i $$-0.452106\pi$$
0.149895 + 0.988702i $$0.452106\pi$$
$$18$$ −16.7082 −3.93816
$$19$$ −2.47214 −0.567147 −0.283573 0.958951i $$-0.591520\pi$$
−0.283573 + 0.958951i $$0.591520\pi$$
$$20$$ −6.00000 −1.34164
$$21$$ 3.23607 0.706168
$$22$$ 2.23607 0.476731
$$23$$ −6.47214 −1.34953 −0.674767 0.738031i $$-0.735756\pi$$
−0.674767 + 0.738031i $$0.735756\pi$$
$$24$$ −7.23607 −1.47706
$$25$$ −1.00000 −0.200000
$$26$$ 2.76393 0.542052
$$27$$ 14.4721 2.78516
$$28$$ 3.00000 0.566947
$$29$$ −0.472136 −0.0876734 −0.0438367 0.999039i $$-0.513958\pi$$
−0.0438367 + 0.999039i $$0.513958\pi$$
$$30$$ 14.4721 2.64224
$$31$$ −7.23607 −1.29964 −0.649818 0.760090i $$-0.725155\pi$$
−0.649818 + 0.760090i $$0.725155\pi$$
$$32$$ 6.70820 1.18585
$$33$$ −3.23607 −0.563327
$$34$$ −2.76393 −0.474010
$$35$$ −2.00000 −0.338062
$$36$$ 22.4164 3.73607
$$37$$ 0.472136 0.0776187 0.0388093 0.999247i $$-0.487644\pi$$
0.0388093 + 0.999247i $$0.487644\pi$$
$$38$$ 5.52786 0.896738
$$39$$ −4.00000 −0.640513
$$40$$ 4.47214 0.707107
$$41$$ −6.76393 −1.05635 −0.528174 0.849136i $$-0.677123\pi$$
−0.528174 + 0.849136i $$0.677123\pi$$
$$42$$ −7.23607 −1.11655
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ −3.00000 −0.452267
$$45$$ −14.9443 −2.22776
$$46$$ 14.4721 2.13380
$$47$$ 7.23607 1.05549 0.527744 0.849403i $$-0.323038\pi$$
0.527744 + 0.849403i $$0.323038\pi$$
$$48$$ −3.23607 −0.467086
$$49$$ 1.00000 0.142857
$$50$$ 2.23607 0.316228
$$51$$ 4.00000 0.560112
$$52$$ −3.70820 −0.514235
$$53$$ 8.47214 1.16374 0.581869 0.813283i $$-0.302322\pi$$
0.581869 + 0.813283i $$0.302322\pi$$
$$54$$ −32.3607 −4.40373
$$55$$ 2.00000 0.269680
$$56$$ −2.23607 −0.298807
$$57$$ −8.00000 −1.05963
$$58$$ 1.05573 0.138624
$$59$$ 3.23607 0.421300 0.210650 0.977562i $$-0.432442\pi$$
0.210650 + 0.977562i $$0.432442\pi$$
$$60$$ −19.4164 −2.50665
$$61$$ −2.76393 −0.353885 −0.176943 0.984221i $$-0.556621\pi$$
−0.176943 + 0.984221i $$0.556621\pi$$
$$62$$ 16.1803 2.05491
$$63$$ 7.47214 0.941401
$$64$$ −13.0000 −1.62500
$$65$$ 2.47214 0.306631
$$66$$ 7.23607 0.890698
$$67$$ 5.52786 0.675336 0.337668 0.941265i $$-0.390362\pi$$
0.337668 + 0.941265i $$0.390362\pi$$
$$68$$ 3.70820 0.449686
$$69$$ −20.9443 −2.52139
$$70$$ 4.47214 0.534522
$$71$$ −1.52786 −0.181324 −0.0906621 0.995882i $$-0.528898\pi$$
−0.0906621 + 0.995882i $$0.528898\pi$$
$$72$$ −16.7082 −1.96908
$$73$$ −5.23607 −0.612835 −0.306418 0.951897i $$-0.599130\pi$$
−0.306418 + 0.951897i $$0.599130\pi$$
$$74$$ −1.05573 −0.122726
$$75$$ −3.23607 −0.373669
$$76$$ −7.41641 −0.850720
$$77$$ −1.00000 −0.113961
$$78$$ 8.94427 1.01274
$$79$$ 8.94427 1.00631 0.503155 0.864196i $$-0.332173\pi$$
0.503155 + 0.864196i $$0.332173\pi$$
$$80$$ 2.00000 0.223607
$$81$$ 24.4164 2.71293
$$82$$ 15.1246 1.67023
$$83$$ 15.4164 1.69217 0.846085 0.533048i $$-0.178953\pi$$
0.846085 + 0.533048i $$0.178953\pi$$
$$84$$ 9.70820 1.05925
$$85$$ −2.47214 −0.268141
$$86$$ −17.8885 −1.92897
$$87$$ −1.52786 −0.163804
$$88$$ 2.23607 0.238366
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ 33.4164 3.52240
$$91$$ −1.23607 −0.129575
$$92$$ −19.4164 −2.02430
$$93$$ −23.4164 −2.42817
$$94$$ −16.1803 −1.66887
$$95$$ 4.94427 0.507272
$$96$$ 21.7082 2.21558
$$97$$ −9.41641 −0.956091 −0.478046 0.878335i $$-0.658655\pi$$
−0.478046 + 0.878335i $$0.658655\pi$$
$$98$$ −2.23607 −0.225877
$$99$$ −7.47214 −0.750978
$$100$$ −3.00000 −0.300000
$$101$$ −9.23607 −0.919023 −0.459512 0.888172i $$-0.651976\pi$$
−0.459512 + 0.888172i $$0.651976\pi$$
$$102$$ −8.94427 −0.885615
$$103$$ −5.70820 −0.562446 −0.281223 0.959642i $$-0.590740\pi$$
−0.281223 + 0.959642i $$0.590740\pi$$
$$104$$ 2.76393 0.271026
$$105$$ −6.47214 −0.631616
$$106$$ −18.9443 −1.84003
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 43.4164 4.17775
$$109$$ 4.47214 0.428353 0.214176 0.976795i $$-0.431293\pi$$
0.214176 + 0.976795i $$0.431293\pi$$
$$110$$ −4.47214 −0.426401
$$111$$ 1.52786 0.145018
$$112$$ −1.00000 −0.0944911
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 17.8885 1.67542
$$115$$ 12.9443 1.20706
$$116$$ −1.41641 −0.131510
$$117$$ −9.23607 −0.853875
$$118$$ −7.23607 −0.666134
$$119$$ 1.23607 0.113310
$$120$$ 14.4721 1.32112
$$121$$ 1.00000 0.0909091
$$122$$ 6.18034 0.559542
$$123$$ −21.8885 −1.97362
$$124$$ −21.7082 −1.94945
$$125$$ 12.0000 1.07331
$$126$$ −16.7082 −1.48849
$$127$$ 20.9443 1.85850 0.929252 0.369447i $$-0.120453\pi$$
0.929252 + 0.369447i $$0.120453\pi$$
$$128$$ 15.6525 1.38350
$$129$$ 25.8885 2.27936
$$130$$ −5.52786 −0.484826
$$131$$ −13.8885 −1.21345 −0.606724 0.794913i $$-0.707517\pi$$
−0.606724 + 0.794913i $$0.707517\pi$$
$$132$$ −9.70820 −0.844991
$$133$$ −2.47214 −0.214361
$$134$$ −12.3607 −1.06780
$$135$$ −28.9443 −2.49113
$$136$$ −2.76393 −0.237005
$$137$$ 7.52786 0.643149 0.321574 0.946884i $$-0.395788\pi$$
0.321574 + 0.946884i $$0.395788\pi$$
$$138$$ 46.8328 3.98667
$$139$$ −10.4721 −0.888235 −0.444117 0.895969i $$-0.646483\pi$$
−0.444117 + 0.895969i $$0.646483\pi$$
$$140$$ −6.00000 −0.507093
$$141$$ 23.4164 1.97202
$$142$$ 3.41641 0.286699
$$143$$ 1.23607 0.103365
$$144$$ −7.47214 −0.622678
$$145$$ 0.944272 0.0784175
$$146$$ 11.7082 0.968978
$$147$$ 3.23607 0.266906
$$148$$ 1.41641 0.116428
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 7.23607 0.590822
$$151$$ −8.94427 −0.727875 −0.363937 0.931423i $$-0.618568\pi$$
−0.363937 + 0.931423i $$0.618568\pi$$
$$152$$ 5.52786 0.448369
$$153$$ 9.23607 0.746692
$$154$$ 2.23607 0.180187
$$155$$ 14.4721 1.16243
$$156$$ −12.0000 −0.960769
$$157$$ −6.94427 −0.554213 −0.277107 0.960839i $$-0.589376\pi$$
−0.277107 + 0.960839i $$0.589376\pi$$
$$158$$ −20.0000 −1.59111
$$159$$ 27.4164 2.17426
$$160$$ −13.4164 −1.06066
$$161$$ −6.47214 −0.510076
$$162$$ −54.5967 −4.28953
$$163$$ 23.4164 1.83411 0.917057 0.398755i $$-0.130558\pi$$
0.917057 + 0.398755i $$0.130558\pi$$
$$164$$ −20.2918 −1.58452
$$165$$ 6.47214 0.503855
$$166$$ −34.4721 −2.67556
$$167$$ −12.9443 −1.00166 −0.500829 0.865546i $$-0.666971\pi$$
−0.500829 + 0.865546i $$0.666971\pi$$
$$168$$ −7.23607 −0.558275
$$169$$ −11.4721 −0.882472
$$170$$ 5.52786 0.423968
$$171$$ −18.4721 −1.41260
$$172$$ 24.0000 1.82998
$$173$$ −17.2361 −1.31043 −0.655217 0.755441i $$-0.727423\pi$$
−0.655217 + 0.755441i $$0.727423\pi$$
$$174$$ 3.41641 0.258997
$$175$$ −1.00000 −0.0755929
$$176$$ 1.00000 0.0753778
$$177$$ 10.4721 0.787134
$$178$$ −4.47214 −0.335201
$$179$$ 8.94427 0.668526 0.334263 0.942480i $$-0.391513\pi$$
0.334263 + 0.942480i $$0.391513\pi$$
$$180$$ −44.8328 −3.34164
$$181$$ 1.41641 0.105281 0.0526404 0.998614i $$-0.483236\pi$$
0.0526404 + 0.998614i $$0.483236\pi$$
$$182$$ 2.76393 0.204876
$$183$$ −8.94427 −0.661180
$$184$$ 14.4721 1.06690
$$185$$ −0.944272 −0.0694243
$$186$$ 52.3607 3.83927
$$187$$ −1.23607 −0.0903902
$$188$$ 21.7082 1.58323
$$189$$ 14.4721 1.05269
$$190$$ −11.0557 −0.802067
$$191$$ −20.9443 −1.51547 −0.757737 0.652560i $$-0.773695\pi$$
−0.757737 + 0.652560i $$0.773695\pi$$
$$192$$ −42.0689 −3.03606
$$193$$ −23.8885 −1.71954 −0.859768 0.510686i $$-0.829392\pi$$
−0.859768 + 0.510686i $$0.829392\pi$$
$$194$$ 21.0557 1.51171
$$195$$ 8.00000 0.572892
$$196$$ 3.00000 0.214286
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 16.7082 1.18740
$$199$$ 20.1803 1.43055 0.715273 0.698845i $$-0.246302\pi$$
0.715273 + 0.698845i $$0.246302\pi$$
$$200$$ 2.23607 0.158114
$$201$$ 17.8885 1.26176
$$202$$ 20.6525 1.45310
$$203$$ −0.472136 −0.0331374
$$204$$ 12.0000 0.840168
$$205$$ 13.5279 0.944827
$$206$$ 12.7639 0.889305
$$207$$ −48.3607 −3.36130
$$208$$ 1.23607 0.0857059
$$209$$ 2.47214 0.171001
$$210$$ 14.4721 0.998672
$$211$$ 21.8885 1.50687 0.753435 0.657523i $$-0.228396\pi$$
0.753435 + 0.657523i $$0.228396\pi$$
$$212$$ 25.4164 1.74561
$$213$$ −4.94427 −0.338776
$$214$$ 8.94427 0.611418
$$215$$ −16.0000 −1.09119
$$216$$ −32.3607 −2.20187
$$217$$ −7.23607 −0.491216
$$218$$ −10.0000 −0.677285
$$219$$ −16.9443 −1.14499
$$220$$ 6.00000 0.404520
$$221$$ −1.52786 −0.102775
$$222$$ −3.41641 −0.229294
$$223$$ 12.1803 0.815656 0.407828 0.913059i $$-0.366286\pi$$
0.407828 + 0.913059i $$0.366286\pi$$
$$224$$ 6.70820 0.448211
$$225$$ −7.47214 −0.498142
$$226$$ −4.47214 −0.297482
$$227$$ −29.8885 −1.98377 −0.991886 0.127129i $$-0.959424\pi$$
−0.991886 + 0.127129i $$0.959424\pi$$
$$228$$ −24.0000 −1.58944
$$229$$ 4.47214 0.295527 0.147764 0.989023i $$-0.452793\pi$$
0.147764 + 0.989023i $$0.452793\pi$$
$$230$$ −28.9443 −1.90853
$$231$$ −3.23607 −0.212918
$$232$$ 1.05573 0.0693119
$$233$$ −17.4164 −1.14099 −0.570493 0.821302i $$-0.693248\pi$$
−0.570493 + 0.821302i $$0.693248\pi$$
$$234$$ 20.6525 1.35009
$$235$$ −14.4721 −0.944058
$$236$$ 9.70820 0.631950
$$237$$ 28.9443 1.88013
$$238$$ −2.76393 −0.179159
$$239$$ 25.8885 1.67459 0.837295 0.546751i $$-0.184136\pi$$
0.837295 + 0.546751i $$0.184136\pi$$
$$240$$ 6.47214 0.417775
$$241$$ 27.1246 1.74725 0.873625 0.486600i $$-0.161763\pi$$
0.873625 + 0.486600i $$0.161763\pi$$
$$242$$ −2.23607 −0.143740
$$243$$ 35.5967 2.28353
$$244$$ −8.29180 −0.530828
$$245$$ −2.00000 −0.127775
$$246$$ 48.9443 3.12057
$$247$$ 3.05573 0.194431
$$248$$ 16.1803 1.02745
$$249$$ 49.8885 3.16156
$$250$$ −26.8328 −1.69706
$$251$$ 17.7082 1.11773 0.558866 0.829258i $$-0.311237\pi$$
0.558866 + 0.829258i $$0.311237\pi$$
$$252$$ 22.4164 1.41210
$$253$$ 6.47214 0.406900
$$254$$ −46.8328 −2.93855
$$255$$ −8.00000 −0.500979
$$256$$ −9.00000 −0.562500
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ −57.8885 −3.60398
$$259$$ 0.472136 0.0293371
$$260$$ 7.41641 0.459946
$$261$$ −3.52786 −0.218369
$$262$$ 31.0557 1.91863
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 7.23607 0.445349
$$265$$ −16.9443 −1.04088
$$266$$ 5.52786 0.338935
$$267$$ 6.47214 0.396088
$$268$$ 16.5836 1.01300
$$269$$ −13.4164 −0.818013 −0.409006 0.912532i $$-0.634125\pi$$
−0.409006 + 0.912532i $$0.634125\pi$$
$$270$$ 64.7214 3.93882
$$271$$ −1.52786 −0.0928111 −0.0464056 0.998923i $$-0.514777\pi$$
−0.0464056 + 0.998923i $$0.514777\pi$$
$$272$$ −1.23607 −0.0749476
$$273$$ −4.00000 −0.242091
$$274$$ −16.8328 −1.01691
$$275$$ 1.00000 0.0603023
$$276$$ −62.8328 −3.78209
$$277$$ 15.8885 0.954650 0.477325 0.878727i $$-0.341606\pi$$
0.477325 + 0.878727i $$0.341606\pi$$
$$278$$ 23.4164 1.40442
$$279$$ −54.0689 −3.23702
$$280$$ 4.47214 0.267261
$$281$$ −12.4721 −0.744025 −0.372013 0.928228i $$-0.621332\pi$$
−0.372013 + 0.928228i $$0.621332\pi$$
$$282$$ −52.3607 −3.11803
$$283$$ −5.88854 −0.350038 −0.175019 0.984565i $$-0.555999\pi$$
−0.175019 + 0.984565i $$0.555999\pi$$
$$284$$ −4.58359 −0.271986
$$285$$ 16.0000 0.947758
$$286$$ −2.76393 −0.163435
$$287$$ −6.76393 −0.399262
$$288$$ 50.1246 2.95362
$$289$$ −15.4721 −0.910126
$$290$$ −2.11146 −0.123989
$$291$$ −30.4721 −1.78631
$$292$$ −15.7082 −0.919253
$$293$$ 15.1246 0.883589 0.441795 0.897116i $$-0.354342\pi$$
0.441795 + 0.897116i $$0.354342\pi$$
$$294$$ −7.23607 −0.422016
$$295$$ −6.47214 −0.376822
$$296$$ −1.05573 −0.0613629
$$297$$ −14.4721 −0.839759
$$298$$ −31.3050 −1.81345
$$299$$ 8.00000 0.462652
$$300$$ −9.70820 −0.560503
$$301$$ 8.00000 0.461112
$$302$$ 20.0000 1.15087
$$303$$ −29.8885 −1.71705
$$304$$ 2.47214 0.141787
$$305$$ 5.52786 0.316525
$$306$$ −20.6525 −1.18062
$$307$$ 8.94427 0.510477 0.255238 0.966878i $$-0.417846\pi$$
0.255238 + 0.966878i $$0.417846\pi$$
$$308$$ −3.00000 −0.170941
$$309$$ −18.4721 −1.05084
$$310$$ −32.3607 −1.83796
$$311$$ −21.7082 −1.23096 −0.615480 0.788153i $$-0.711038\pi$$
−0.615480 + 0.788153i $$0.711038\pi$$
$$312$$ 8.94427 0.506370
$$313$$ −2.94427 −0.166420 −0.0832100 0.996532i $$-0.526517\pi$$
−0.0832100 + 0.996532i $$0.526517\pi$$
$$314$$ 15.5279 0.876288
$$315$$ −14.9443 −0.842014
$$316$$ 26.8328 1.50946
$$317$$ 14.0000 0.786318 0.393159 0.919470i $$-0.371382\pi$$
0.393159 + 0.919470i $$0.371382\pi$$
$$318$$ −61.3050 −3.43781
$$319$$ 0.472136 0.0264345
$$320$$ 26.0000 1.45344
$$321$$ −12.9443 −0.722479
$$322$$ 14.4721 0.806501
$$323$$ −3.05573 −0.170025
$$324$$ 73.2492 4.06940
$$325$$ 1.23607 0.0685647
$$326$$ −52.3607 −2.89999
$$327$$ 14.4721 0.800311
$$328$$ 15.1246 0.835117
$$329$$ 7.23607 0.398937
$$330$$ −14.4721 −0.796665
$$331$$ 21.8885 1.20310 0.601552 0.798834i $$-0.294549\pi$$
0.601552 + 0.798834i $$0.294549\pi$$
$$332$$ 46.2492 2.53826
$$333$$ 3.52786 0.193326
$$334$$ 28.9443 1.58376
$$335$$ −11.0557 −0.604039
$$336$$ −3.23607 −0.176542
$$337$$ −20.4721 −1.11519 −0.557594 0.830114i $$-0.688275\pi$$
−0.557594 + 0.830114i $$0.688275\pi$$
$$338$$ 25.6525 1.39531
$$339$$ 6.47214 0.351518
$$340$$ −7.41641 −0.402211
$$341$$ 7.23607 0.391855
$$342$$ 41.3050 2.23352
$$343$$ 1.00000 0.0539949
$$344$$ −17.8885 −0.964486
$$345$$ 41.8885 2.25520
$$346$$ 38.5410 2.07198
$$347$$ 3.05573 0.164040 0.0820200 0.996631i $$-0.473863\pi$$
0.0820200 + 0.996631i $$0.473863\pi$$
$$348$$ −4.58359 −0.245706
$$349$$ −2.76393 −0.147950 −0.0739749 0.997260i $$-0.523568\pi$$
−0.0739749 + 0.997260i $$0.523568\pi$$
$$350$$ 2.23607 0.119523
$$351$$ −17.8885 −0.954820
$$352$$ −6.70820 −0.357548
$$353$$ −15.8885 −0.845662 −0.422831 0.906209i $$-0.638964\pi$$
−0.422831 + 0.906209i $$0.638964\pi$$
$$354$$ −23.4164 −1.24457
$$355$$ 3.05573 0.162181
$$356$$ 6.00000 0.317999
$$357$$ 4.00000 0.211702
$$358$$ −20.0000 −1.05703
$$359$$ −7.05573 −0.372387 −0.186194 0.982513i $$-0.559615\pi$$
−0.186194 + 0.982513i $$0.559615\pi$$
$$360$$ 33.4164 1.76120
$$361$$ −12.8885 −0.678344
$$362$$ −3.16718 −0.166464
$$363$$ 3.23607 0.169850
$$364$$ −3.70820 −0.194363
$$365$$ 10.4721 0.548137
$$366$$ 20.0000 1.04542
$$367$$ 17.1246 0.893897 0.446949 0.894560i $$-0.352511\pi$$
0.446949 + 0.894560i $$0.352511\pi$$
$$368$$ 6.47214 0.337383
$$369$$ −50.5410 −2.63106
$$370$$ 2.11146 0.109769
$$371$$ 8.47214 0.439851
$$372$$ −70.2492 −3.64225
$$373$$ 6.00000 0.310668 0.155334 0.987862i $$-0.450355\pi$$
0.155334 + 0.987862i $$0.450355\pi$$
$$374$$ 2.76393 0.142920
$$375$$ 38.8328 2.00532
$$376$$ −16.1803 −0.834437
$$377$$ 0.583592 0.0300565
$$378$$ −32.3607 −1.66445
$$379$$ −25.3050 −1.29983 −0.649914 0.760008i $$-0.725195\pi$$
−0.649914 + 0.760008i $$0.725195\pi$$
$$380$$ 14.8328 0.760907
$$381$$ 67.7771 3.47233
$$382$$ 46.8328 2.39618
$$383$$ 26.6525 1.36188 0.680939 0.732340i $$-0.261572\pi$$
0.680939 + 0.732340i $$0.261572\pi$$
$$384$$ 50.6525 2.58485
$$385$$ 2.00000 0.101929
$$386$$ 53.4164 2.71882
$$387$$ 59.7771 3.03864
$$388$$ −28.2492 −1.43414
$$389$$ −19.8885 −1.00839 −0.504195 0.863590i $$-0.668211\pi$$
−0.504195 + 0.863590i $$0.668211\pi$$
$$390$$ −17.8885 −0.905822
$$391$$ −8.00000 −0.404577
$$392$$ −2.23607 −0.112938
$$393$$ −44.9443 −2.26714
$$394$$ 4.47214 0.225303
$$395$$ −17.8885 −0.900070
$$396$$ −22.4164 −1.12647
$$397$$ −0.111456 −0.00559383 −0.00279691 0.999996i $$-0.500890\pi$$
−0.00279691 + 0.999996i $$0.500890\pi$$
$$398$$ −45.1246 −2.26189
$$399$$ −8.00000 −0.400501
$$400$$ 1.00000 0.0500000
$$401$$ 5.05573 0.252471 0.126236 0.992000i $$-0.459710\pi$$
0.126236 + 0.992000i $$0.459710\pi$$
$$402$$ −40.0000 −1.99502
$$403$$ 8.94427 0.445546
$$404$$ −27.7082 −1.37853
$$405$$ −48.8328 −2.42652
$$406$$ 1.05573 0.0523949
$$407$$ −0.472136 −0.0234029
$$408$$ −8.94427 −0.442807
$$409$$ −31.1246 −1.53901 −0.769507 0.638639i $$-0.779498\pi$$
−0.769507 + 0.638639i $$0.779498\pi$$
$$410$$ −30.2492 −1.49390
$$411$$ 24.3607 1.20162
$$412$$ −17.1246 −0.843669
$$413$$ 3.23607 0.159236
$$414$$ 108.138 5.31468
$$415$$ −30.8328 −1.51352
$$416$$ −8.29180 −0.406539
$$417$$ −33.8885 −1.65953
$$418$$ −5.52786 −0.270377
$$419$$ −6.65248 −0.324995 −0.162497 0.986709i $$-0.551955\pi$$
−0.162497 + 0.986709i $$0.551955\pi$$
$$420$$ −19.4164 −0.947424
$$421$$ −22.3607 −1.08979 −0.544896 0.838503i $$-0.683431\pi$$
−0.544896 + 0.838503i $$0.683431\pi$$
$$422$$ −48.9443 −2.38257
$$423$$ 54.0689 2.62892
$$424$$ −18.9443 −0.920015
$$425$$ −1.23607 −0.0599581
$$426$$ 11.0557 0.535652
$$427$$ −2.76393 −0.133756
$$428$$ −12.0000 −0.580042
$$429$$ 4.00000 0.193122
$$430$$ 35.7771 1.72532
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ −14.4721 −0.696291
$$433$$ 0.472136 0.0226894 0.0113447 0.999936i $$-0.496389\pi$$
0.0113447 + 0.999936i $$0.496389\pi$$
$$434$$ 16.1803 0.776681
$$435$$ 3.05573 0.146511
$$436$$ 13.4164 0.642529
$$437$$ 16.0000 0.765384
$$438$$ 37.8885 1.81038
$$439$$ 1.52786 0.0729210 0.0364605 0.999335i $$-0.488392\pi$$
0.0364605 + 0.999335i $$0.488392\pi$$
$$440$$ −4.47214 −0.213201
$$441$$ 7.47214 0.355816
$$442$$ 3.41641 0.162502
$$443$$ −7.05573 −0.335228 −0.167614 0.985853i $$-0.553606\pi$$
−0.167614 + 0.985853i $$0.553606\pi$$
$$444$$ 4.58359 0.217528
$$445$$ −4.00000 −0.189618
$$446$$ −27.2361 −1.28967
$$447$$ 45.3050 2.14285
$$448$$ −13.0000 −0.614192
$$449$$ −19.5279 −0.921577 −0.460788 0.887510i $$-0.652433\pi$$
−0.460788 + 0.887510i $$0.652433\pi$$
$$450$$ 16.7082 0.787632
$$451$$ 6.76393 0.318501
$$452$$ 6.00000 0.282216
$$453$$ −28.9443 −1.35992
$$454$$ 66.8328 3.13662
$$455$$ 2.47214 0.115896
$$456$$ 17.8885 0.837708
$$457$$ 24.8328 1.16163 0.580815 0.814036i $$-0.302734\pi$$
0.580815 + 0.814036i $$0.302734\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 17.8885 0.834966
$$460$$ 38.8328 1.81059
$$461$$ 10.1803 0.474146 0.237073 0.971492i $$-0.423812\pi$$
0.237073 + 0.971492i $$0.423812\pi$$
$$462$$ 7.23607 0.336652
$$463$$ −14.4721 −0.672577 −0.336289 0.941759i $$-0.609172\pi$$
−0.336289 + 0.941759i $$0.609172\pi$$
$$464$$ 0.472136 0.0219184
$$465$$ 46.8328 2.17182
$$466$$ 38.9443 1.80406
$$467$$ −34.0689 −1.57652 −0.788260 0.615342i $$-0.789018\pi$$
−0.788260 + 0.615342i $$0.789018\pi$$
$$468$$ −27.7082 −1.28081
$$469$$ 5.52786 0.255253
$$470$$ 32.3607 1.49269
$$471$$ −22.4721 −1.03546
$$472$$ −7.23607 −0.333067
$$473$$ −8.00000 −0.367840
$$474$$ −64.7214 −2.97275
$$475$$ 2.47214 0.113429
$$476$$ 3.70820 0.169965
$$477$$ 63.3050 2.89853
$$478$$ −57.8885 −2.64776
$$479$$ 22.4721 1.02678 0.513389 0.858156i $$-0.328390\pi$$
0.513389 + 0.858156i $$0.328390\pi$$
$$480$$ −43.4164 −1.98168
$$481$$ −0.583592 −0.0266095
$$482$$ −60.6525 −2.76264
$$483$$ −20.9443 −0.952997
$$484$$ 3.00000 0.136364
$$485$$ 18.8328 0.855154
$$486$$ −79.5967 −3.61058
$$487$$ 8.36068 0.378859 0.189429 0.981894i $$-0.439336\pi$$
0.189429 + 0.981894i $$0.439336\pi$$
$$488$$ 6.18034 0.279771
$$489$$ 75.7771 3.42676
$$490$$ 4.47214 0.202031
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ −65.6656 −2.96044
$$493$$ −0.583592 −0.0262837
$$494$$ −6.83282 −0.307423
$$495$$ 14.9443 0.671695
$$496$$ 7.23607 0.324909
$$497$$ −1.52786 −0.0685341
$$498$$ −111.554 −4.99886
$$499$$ 10.4721 0.468797 0.234399 0.972141i $$-0.424688\pi$$
0.234399 + 0.972141i $$0.424688\pi$$
$$500$$ 36.0000 1.60997
$$501$$ −41.8885 −1.87144
$$502$$ −39.5967 −1.76729
$$503$$ −3.41641 −0.152330 −0.0761650 0.997095i $$-0.524268\pi$$
−0.0761650 + 0.997095i $$0.524268\pi$$
$$504$$ −16.7082 −0.744243
$$505$$ 18.4721 0.821999
$$506$$ −14.4721 −0.643365
$$507$$ −37.1246 −1.64876
$$508$$ 62.8328 2.78776
$$509$$ 31.5279 1.39745 0.698724 0.715391i $$-0.253752\pi$$
0.698724 + 0.715391i $$0.253752\pi$$
$$510$$ 17.8885 0.792118
$$511$$ −5.23607 −0.231630
$$512$$ −11.1803 −0.494106
$$513$$ −35.7771 −1.57960
$$514$$ 13.4164 0.591772
$$515$$ 11.4164 0.503067
$$516$$ 77.6656 3.41904
$$517$$ −7.23607 −0.318242
$$518$$ −1.05573 −0.0463860
$$519$$ −55.7771 −2.44834
$$520$$ −5.52786 −0.242413
$$521$$ −14.3607 −0.629153 −0.314576 0.949232i $$-0.601862\pi$$
−0.314576 + 0.949232i $$0.601862\pi$$
$$522$$ 7.88854 0.345272
$$523$$ 44.0000 1.92399 0.961993 0.273075i $$-0.0880406\pi$$
0.961993 + 0.273075i $$0.0880406\pi$$
$$524$$ −41.6656 −1.82017
$$525$$ −3.23607 −0.141234
$$526$$ 0 0
$$527$$ −8.94427 −0.389619
$$528$$ 3.23607 0.140832
$$529$$ 18.8885 0.821241
$$530$$ 37.8885 1.64577
$$531$$ 24.1803 1.04934
$$532$$ −7.41641 −0.321542
$$533$$ 8.36068 0.362141
$$534$$ −14.4721 −0.626271
$$535$$ 8.00000 0.345870
$$536$$ −12.3607 −0.533900
$$537$$ 28.9443 1.24904
$$538$$ 30.0000 1.29339
$$539$$ −1.00000 −0.0430730
$$540$$ −86.8328 −3.73669
$$541$$ −32.8328 −1.41159 −0.705797 0.708415i $$-0.749411\pi$$
−0.705797 + 0.708415i $$0.749411\pi$$
$$542$$ 3.41641 0.146747
$$543$$ 4.58359 0.196701
$$544$$ 8.29180 0.355508
$$545$$ −8.94427 −0.383131
$$546$$ 8.94427 0.382780
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 22.5836 0.964723
$$549$$ −20.6525 −0.881426
$$550$$ −2.23607 −0.0953463
$$551$$ 1.16718 0.0497237
$$552$$ 46.8328 1.99334
$$553$$ 8.94427 0.380349
$$554$$ −35.5279 −1.50943
$$555$$ −3.05573 −0.129708
$$556$$ −31.4164 −1.33235
$$557$$ −21.0557 −0.892160 −0.446080 0.894993i $$-0.647180\pi$$
−0.446080 + 0.894993i $$0.647180\pi$$
$$558$$ 120.902 5.11818
$$559$$ −9.88854 −0.418241
$$560$$ 2.00000 0.0845154
$$561$$ −4.00000 −0.168880
$$562$$ 27.8885 1.17641
$$563$$ 39.4164 1.66120 0.830602 0.556867i $$-0.187997\pi$$
0.830602 + 0.556867i $$0.187997\pi$$
$$564$$ 70.2492 2.95803
$$565$$ −4.00000 −0.168281
$$566$$ 13.1672 0.553458
$$567$$ 24.4164 1.02539
$$568$$ 3.41641 0.143349
$$569$$ 16.4721 0.690548 0.345274 0.938502i $$-0.387786\pi$$
0.345274 + 0.938502i $$0.387786\pi$$
$$570$$ −35.7771 −1.49854
$$571$$ −32.9443 −1.37867 −0.689337 0.724440i $$-0.742098\pi$$
−0.689337 + 0.724440i $$0.742098\pi$$
$$572$$ 3.70820 0.155048
$$573$$ −67.7771 −2.83143
$$574$$ 15.1246 0.631289
$$575$$ 6.47214 0.269907
$$576$$ −97.1378 −4.04741
$$577$$ −28.4721 −1.18531 −0.592655 0.805456i $$-0.701920\pi$$
−0.592655 + 0.805456i $$0.701920\pi$$
$$578$$ 34.5967 1.43903
$$579$$ −77.3050 −3.21268
$$580$$ 2.83282 0.117626
$$581$$ 15.4164 0.639580
$$582$$ 68.1378 2.82440
$$583$$ −8.47214 −0.350880
$$584$$ 11.7082 0.484489
$$585$$ 18.4721 0.763729
$$586$$ −33.8197 −1.39708
$$587$$ −13.1246 −0.541711 −0.270855 0.962620i $$-0.587307\pi$$
−0.270855 + 0.962620i $$0.587307\pi$$
$$588$$ 9.70820 0.400360
$$589$$ 17.8885 0.737085
$$590$$ 14.4721 0.595808
$$591$$ −6.47214 −0.266228
$$592$$ −0.472136 −0.0194047
$$593$$ −32.2918 −1.32607 −0.663033 0.748591i $$-0.730731\pi$$
−0.663033 + 0.748591i $$0.730731\pi$$
$$594$$ 32.3607 1.32777
$$595$$ −2.47214 −0.101348
$$596$$ 42.0000 1.72039
$$597$$ 65.3050 2.67275
$$598$$ −17.8885 −0.731517
$$599$$ 3.41641 0.139591 0.0697953 0.997561i $$-0.477765\pi$$
0.0697953 + 0.997561i $$0.477765\pi$$
$$600$$ 7.23607 0.295411
$$601$$ 3.12461 0.127456 0.0637278 0.997967i $$-0.479701\pi$$
0.0637278 + 0.997967i $$0.479701\pi$$
$$602$$ −17.8885 −0.729083
$$603$$ 41.3050 1.68207
$$604$$ −26.8328 −1.09181
$$605$$ −2.00000 −0.0813116
$$606$$ 66.8328 2.71490
$$607$$ −4.94427 −0.200682 −0.100341 0.994953i $$-0.531993\pi$$
−0.100341 + 0.994953i $$0.531993\pi$$
$$608$$ −16.5836 −0.672553
$$609$$ −1.52786 −0.0619122
$$610$$ −12.3607 −0.500469
$$611$$ −8.94427 −0.361847
$$612$$ 27.7082 1.12004
$$613$$ −47.3050 −1.91063 −0.955315 0.295591i $$-0.904483\pi$$
−0.955315 + 0.295591i $$0.904483\pi$$
$$614$$ −20.0000 −0.807134
$$615$$ 43.7771 1.76526
$$616$$ 2.23607 0.0900937
$$617$$ 33.4164 1.34529 0.672647 0.739964i $$-0.265157\pi$$
0.672647 + 0.739964i $$0.265157\pi$$
$$618$$ 41.3050 1.66153
$$619$$ −29.1246 −1.17062 −0.585308 0.810811i $$-0.699027\pi$$
−0.585308 + 0.810811i $$0.699027\pi$$
$$620$$ 43.4164 1.74364
$$621$$ −93.6656 −3.75867
$$622$$ 48.5410 1.94632
$$623$$ 2.00000 0.0801283
$$624$$ 4.00000 0.160128
$$625$$ −19.0000 −0.760000
$$626$$ 6.58359 0.263133
$$627$$ 8.00000 0.319489
$$628$$ −20.8328 −0.831320
$$629$$ 0.583592 0.0232693
$$630$$ 33.4164 1.33134
$$631$$ −24.0000 −0.955425 −0.477712 0.878516i $$-0.658534\pi$$
−0.477712 + 0.878516i $$0.658534\pi$$
$$632$$ −20.0000 −0.795557
$$633$$ 70.8328 2.81535
$$634$$ −31.3050 −1.24328
$$635$$ −41.8885 −1.66230
$$636$$ 82.2492 3.26139
$$637$$ −1.23607 −0.0489748
$$638$$ −1.05573 −0.0417967
$$639$$ −11.4164 −0.451626
$$640$$ −31.3050 −1.23744
$$641$$ −24.4721 −0.966591 −0.483296 0.875457i $$-0.660560\pi$$
−0.483296 + 0.875457i $$0.660560\pi$$
$$642$$ 28.9443 1.14234
$$643$$ −29.1246 −1.14856 −0.574281 0.818658i $$-0.694718\pi$$
−0.574281 + 0.818658i $$0.694718\pi$$
$$644$$ −19.4164 −0.765114
$$645$$ −51.7771 −2.03872
$$646$$ 6.83282 0.268834
$$647$$ −22.0689 −0.867617 −0.433809 0.901005i $$-0.642831\pi$$
−0.433809 + 0.901005i $$0.642831\pi$$
$$648$$ −54.5967 −2.14476
$$649$$ −3.23607 −0.127027
$$650$$ −2.76393 −0.108410
$$651$$ −23.4164 −0.917761
$$652$$ 70.2492 2.75117
$$653$$ 42.9443 1.68054 0.840270 0.542169i $$-0.182397\pi$$
0.840270 + 0.542169i $$0.182397\pi$$
$$654$$ −32.3607 −1.26540
$$655$$ 27.7771 1.08534
$$656$$ 6.76393 0.264087
$$657$$ −39.1246 −1.52640
$$658$$ −16.1803 −0.630775
$$659$$ 17.8885 0.696839 0.348419 0.937339i $$-0.386719\pi$$
0.348419 + 0.937339i $$0.386719\pi$$
$$660$$ 19.4164 0.755783
$$661$$ 12.8328 0.499139 0.249569 0.968357i $$-0.419711\pi$$
0.249569 + 0.968357i $$0.419711\pi$$
$$662$$ −48.9443 −1.90227
$$663$$ −4.94427 −0.192020
$$664$$ −34.4721 −1.33778
$$665$$ 4.94427 0.191731
$$666$$ −7.88854 −0.305675
$$667$$ 3.05573 0.118318
$$668$$ −38.8328 −1.50249
$$669$$ 39.4164 1.52393
$$670$$ 24.7214 0.955069
$$671$$ 2.76393 0.106700
$$672$$ 21.7082 0.837412
$$673$$ 5.41641 0.208787 0.104394 0.994536i $$-0.466710\pi$$
0.104394 + 0.994536i $$0.466710\pi$$
$$674$$ 45.7771 1.76327
$$675$$ −14.4721 −0.557033
$$676$$ −34.4164 −1.32371
$$677$$ 3.70820 0.142518 0.0712589 0.997458i $$-0.477298\pi$$
0.0712589 + 0.997458i $$0.477298\pi$$
$$678$$ −14.4721 −0.555799
$$679$$ −9.41641 −0.361369
$$680$$ 5.52786 0.211984
$$681$$ −96.7214 −3.70637
$$682$$ −16.1803 −0.619577
$$683$$ 29.8885 1.14365 0.571827 0.820374i $$-0.306235\pi$$
0.571827 + 0.820374i $$0.306235\pi$$
$$684$$ −55.4164 −2.11890
$$685$$ −15.0557 −0.575250
$$686$$ −2.23607 −0.0853735
$$687$$ 14.4721 0.552146
$$688$$ −8.00000 −0.304997
$$689$$ −10.4721 −0.398957
$$690$$ −93.6656 −3.56579
$$691$$ −48.5410 −1.84659 −0.923294 0.384095i $$-0.874514\pi$$
−0.923294 + 0.384095i $$0.874514\pi$$
$$692$$ −51.7082 −1.96565
$$693$$ −7.47214 −0.283843
$$694$$ −6.83282 −0.259370
$$695$$ 20.9443 0.794462
$$696$$ 3.41641 0.129499
$$697$$ −8.36068 −0.316683
$$698$$ 6.18034 0.233929
$$699$$ −56.3607 −2.13176
$$700$$ −3.00000 −0.113389
$$701$$ −24.4721 −0.924300 −0.462150 0.886802i $$-0.652922\pi$$
−0.462150 + 0.886802i $$0.652922\pi$$
$$702$$ 40.0000 1.50970
$$703$$ −1.16718 −0.0440212
$$704$$ 13.0000 0.489956
$$705$$ −46.8328 −1.76383
$$706$$ 35.5279 1.33711
$$707$$ −9.23607 −0.347358
$$708$$ 31.4164 1.18070
$$709$$ 2.94427 0.110574 0.0552872 0.998470i $$-0.482393\pi$$
0.0552872 + 0.998470i $$0.482393\pi$$
$$710$$ −6.83282 −0.256431
$$711$$ 66.8328 2.50643
$$712$$ −4.47214 −0.167600
$$713$$ 46.8328 1.75390
$$714$$ −8.94427 −0.334731
$$715$$ −2.47214 −0.0924526
$$716$$ 26.8328 1.00279
$$717$$ 83.7771 3.12871
$$718$$ 15.7771 0.588796
$$719$$ 33.4853 1.24879 0.624395 0.781108i $$-0.285345\pi$$
0.624395 + 0.781108i $$0.285345\pi$$
$$720$$ 14.9443 0.556940
$$721$$ −5.70820 −0.212585
$$722$$ 28.8197 1.07256
$$723$$ 87.7771 3.26447
$$724$$ 4.24922 0.157921
$$725$$ 0.472136 0.0175347
$$726$$ −7.23607 −0.268556
$$727$$ −51.0132 −1.89197 −0.945987 0.324206i $$-0.894903\pi$$
−0.945987 + 0.324206i $$0.894903\pi$$
$$728$$ 2.76393 0.102438
$$729$$ 41.9443 1.55349
$$730$$ −23.4164 −0.866680
$$731$$ 9.88854 0.365741
$$732$$ −26.8328 −0.991769
$$733$$ 13.2361 0.488885 0.244443 0.969664i $$-0.421395\pi$$
0.244443 + 0.969664i $$0.421395\pi$$
$$734$$ −38.2918 −1.41338
$$735$$ −6.47214 −0.238728
$$736$$ −43.4164 −1.60035
$$737$$ −5.52786 −0.203621
$$738$$ 113.013 4.16007
$$739$$ 7.05573 0.259549 0.129775 0.991544i $$-0.458575\pi$$
0.129775 + 0.991544i $$0.458575\pi$$
$$740$$ −2.83282 −0.104136
$$741$$ 9.88854 0.363265
$$742$$ −18.9443 −0.695466
$$743$$ −33.8885 −1.24325 −0.621625 0.783315i $$-0.713527\pi$$
−0.621625 + 0.783315i $$0.713527\pi$$
$$744$$ 52.3607 1.91964
$$745$$ −28.0000 −1.02584
$$746$$ −13.4164 −0.491210
$$747$$ 115.193 4.21471
$$748$$ −3.70820 −0.135585
$$749$$ −4.00000 −0.146157
$$750$$ −86.8328 −3.17069
$$751$$ 38.4721 1.40387 0.701934 0.712242i $$-0.252320\pi$$
0.701934 + 0.712242i $$0.252320\pi$$
$$752$$ −7.23607 −0.263872
$$753$$ 57.3050 2.08831
$$754$$ −1.30495 −0.0475235
$$755$$ 17.8885 0.651031
$$756$$ 43.4164 1.57904
$$757$$ −19.8885 −0.722861 −0.361431 0.932399i $$-0.617712\pi$$
−0.361431 + 0.932399i $$0.617712\pi$$
$$758$$ 56.5836 2.05521
$$759$$ 20.9443 0.760229
$$760$$ −11.0557 −0.401033
$$761$$ 17.5967 0.637882 0.318941 0.947775i $$-0.396673\pi$$
0.318941 + 0.947775i $$0.396673\pi$$
$$762$$ −151.554 −5.49023
$$763$$ 4.47214 0.161902
$$764$$ −62.8328 −2.27321
$$765$$ −18.4721 −0.667861
$$766$$ −59.5967 −2.15332
$$767$$ −4.00000 −0.144432
$$768$$ −29.1246 −1.05094
$$769$$ 31.7082 1.14343 0.571714 0.820453i $$-0.306279\pi$$
0.571714 + 0.820453i $$0.306279\pi$$
$$770$$ −4.47214 −0.161165
$$771$$ −19.4164 −0.699265
$$772$$ −71.6656 −2.57930
$$773$$ 6.36068 0.228778 0.114389 0.993436i $$-0.463509\pi$$
0.114389 + 0.993436i $$0.463509\pi$$
$$774$$ −133.666 −4.80451
$$775$$ 7.23607 0.259927
$$776$$ 21.0557 0.755857
$$777$$ 1.52786 0.0548118
$$778$$ 44.4721 1.59440
$$779$$ 16.7214 0.599105
$$780$$ 24.0000 0.859338
$$781$$ 1.52786 0.0546713
$$782$$ 17.8885 0.639693
$$783$$ −6.83282 −0.244185
$$784$$ −1.00000 −0.0357143
$$785$$ 13.8885 0.495703
$$786$$ 100.498 3.58466
$$787$$ −16.5836 −0.591141 −0.295571 0.955321i $$-0.595510\pi$$
−0.295571 + 0.955321i $$0.595510\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ 40.0000 1.42314
$$791$$ 2.00000 0.0711118
$$792$$ 16.7082 0.593700
$$793$$ 3.41641 0.121320
$$794$$ 0.249224 0.00884461
$$795$$ −54.8328 −1.94472
$$796$$ 60.5410 2.14582
$$797$$ 2.94427 0.104291 0.0521457 0.998639i $$-0.483394\pi$$
0.0521457 + 0.998639i $$0.483394\pi$$
$$798$$ 17.8885 0.633248
$$799$$ 8.94427 0.316426
$$800$$ −6.70820 −0.237171
$$801$$ 14.9443 0.528030
$$802$$ −11.3050 −0.399192
$$803$$ 5.23607 0.184777
$$804$$ 53.6656 1.89264
$$805$$ 12.9443 0.456226
$$806$$ −20.0000 −0.704470
$$807$$ −43.4164 −1.52833
$$808$$ 20.6525 0.726552
$$809$$ 38.9443 1.36921 0.684604 0.728915i $$-0.259975\pi$$
0.684604 + 0.728915i $$0.259975\pi$$
$$810$$ 109.193 3.83667
$$811$$ 18.8328 0.661310 0.330655 0.943752i $$-0.392730\pi$$
0.330655 + 0.943752i $$0.392730\pi$$
$$812$$ −1.41641 −0.0497062
$$813$$ −4.94427 −0.173403
$$814$$ 1.05573 0.0370033
$$815$$ −46.8328 −1.64048
$$816$$ −4.00000 −0.140028
$$817$$ −19.7771 −0.691913
$$818$$ 69.5967 2.43339
$$819$$ −9.23607 −0.322734
$$820$$ 40.5836 1.41724
$$821$$ −8.83282 −0.308267 −0.154134 0.988050i $$-0.549259\pi$$
−0.154134 + 0.988050i $$0.549259\pi$$
$$822$$ −54.4721 −1.89993
$$823$$ −49.8885 −1.73901 −0.869503 0.493928i $$-0.835561\pi$$
−0.869503 + 0.493928i $$0.835561\pi$$
$$824$$ 12.7639 0.444653
$$825$$ 3.23607 0.112665
$$826$$ −7.23607 −0.251775
$$827$$ 4.94427 0.171929 0.0859646 0.996298i $$-0.472603\pi$$
0.0859646 + 0.996298i $$0.472603\pi$$
$$828$$ −145.082 −5.04195
$$829$$ −16.8328 −0.584628 −0.292314 0.956322i $$-0.594425\pi$$
−0.292314 + 0.956322i $$0.594425\pi$$
$$830$$ 68.9443 2.39309
$$831$$ 51.4164 1.78362
$$832$$ 16.0689 0.557088
$$833$$ 1.23607 0.0428272
$$834$$ 75.7771 2.62395
$$835$$ 25.8885 0.895910
$$836$$ 7.41641 0.256502
$$837$$ −104.721 −3.61970
$$838$$ 14.8754 0.513862
$$839$$ −14.0689 −0.485712 −0.242856 0.970062i $$-0.578084\pi$$
−0.242856 + 0.970062i $$0.578084\pi$$
$$840$$ 14.4721 0.499336
$$841$$ −28.7771 −0.992313
$$842$$ 50.0000 1.72311
$$843$$ −40.3607 −1.39010
$$844$$ 65.6656 2.26030
$$845$$ 22.9443 0.789307
$$846$$ −120.902 −4.15669
$$847$$ 1.00000 0.0343604
$$848$$ −8.47214 −0.290934
$$849$$ −19.0557 −0.653991
$$850$$ 2.76393 0.0948021
$$851$$ −3.05573 −0.104749
$$852$$ −14.8328 −0.508164
$$853$$ 0.652476 0.0223403 0.0111702 0.999938i $$-0.496444\pi$$
0.0111702 + 0.999938i $$0.496444\pi$$
$$854$$ 6.18034 0.211487
$$855$$ 36.9443 1.26347
$$856$$ 8.94427 0.305709
$$857$$ 10.7639 0.367689 0.183844 0.982955i $$-0.441146\pi$$
0.183844 + 0.982955i $$0.441146\pi$$
$$858$$ −8.94427 −0.305352
$$859$$ 40.5410 1.38324 0.691621 0.722261i $$-0.256897\pi$$
0.691621 + 0.722261i $$0.256897\pi$$
$$860$$ −48.0000 −1.63679
$$861$$ −21.8885 −0.745960
$$862$$ −26.8328 −0.913929
$$863$$ −20.9443 −0.712951 −0.356476 0.934305i $$-0.616022\pi$$
−0.356476 + 0.934305i $$0.616022\pi$$
$$864$$ 97.0820 3.30280
$$865$$ 34.4721 1.17209
$$866$$ −1.05573 −0.0358751
$$867$$ −50.0689 −1.70043
$$868$$ −21.7082 −0.736824
$$869$$ −8.94427 −0.303414
$$870$$ −6.83282 −0.231654
$$871$$ −6.83282 −0.231521
$$872$$ −10.0000 −0.338643
$$873$$ −70.3607 −2.38135
$$874$$ −35.7771 −1.21018
$$875$$ 12.0000 0.405674
$$876$$ −50.8328 −1.71748
$$877$$ 41.4164 1.39853 0.699266 0.714861i $$-0.253510\pi$$
0.699266 + 0.714861i $$0.253510\pi$$
$$878$$ −3.41641 −0.115298
$$879$$ 48.9443 1.65085
$$880$$ −2.00000 −0.0674200
$$881$$ 29.4164 0.991064 0.495532 0.868590i $$-0.334973\pi$$
0.495532 + 0.868590i $$0.334973\pi$$
$$882$$ −16.7082 −0.562594
$$883$$ 8.94427 0.300999 0.150499 0.988610i $$-0.451912\pi$$
0.150499 + 0.988610i $$0.451912\pi$$
$$884$$ −4.58359 −0.154163
$$885$$ −20.9443 −0.704034
$$886$$ 15.7771 0.530042
$$887$$ 40.3607 1.35518 0.677589 0.735440i $$-0.263025\pi$$
0.677589 + 0.735440i $$0.263025\pi$$
$$888$$ −3.41641 −0.114647
$$889$$ 20.9443 0.702448
$$890$$ 8.94427 0.299813
$$891$$ −24.4164 −0.817980
$$892$$ 36.5410 1.22348
$$893$$ −17.8885 −0.598617
$$894$$ −101.305 −3.38814
$$895$$ −17.8885 −0.597948
$$896$$ 15.6525 0.522913
$$897$$ 25.8885 0.864393
$$898$$ 43.6656 1.45714
$$899$$ 3.41641 0.113944
$$900$$ −22.4164 −0.747214
$$901$$ 10.4721 0.348877
$$902$$ −15.1246 −0.503594
$$903$$ 25.8885 0.861517
$$904$$ −4.47214 −0.148741
$$905$$ −2.83282 −0.0941660
$$906$$ 64.7214 2.15022
$$907$$ 13.5279 0.449185 0.224593 0.974453i $$-0.427895\pi$$
0.224593 + 0.974453i $$0.427895\pi$$
$$908$$ −89.6656 −2.97566
$$909$$ −69.0132 −2.28902
$$910$$ −5.52786 −0.183247
$$911$$ 33.5279 1.11083 0.555414 0.831574i $$-0.312560\pi$$
0.555414 + 0.831574i $$0.312560\pi$$
$$912$$ 8.00000 0.264906
$$913$$ −15.4164 −0.510209
$$914$$ −55.5279 −1.83670
$$915$$ 17.8885 0.591377
$$916$$ 13.4164 0.443291
$$917$$ −13.8885 −0.458640
$$918$$ −40.0000 −1.32020
$$919$$ 6.11146 0.201598 0.100799 0.994907i $$-0.467860\pi$$
0.100799 + 0.994907i $$0.467860\pi$$
$$920$$ −28.9443 −0.954264
$$921$$ 28.9443 0.953746
$$922$$ −22.7639 −0.749690
$$923$$ 1.88854 0.0621622
$$924$$ −9.70820 −0.319376
$$925$$ −0.472136 −0.0155237
$$926$$ 32.3607 1.06344
$$927$$ −42.6525 −1.40089
$$928$$ −3.16718 −0.103968
$$929$$ 28.2492 0.926827 0.463413 0.886142i $$-0.346624\pi$$
0.463413 + 0.886142i $$0.346624\pi$$
$$930$$ −104.721 −3.43395
$$931$$ −2.47214 −0.0810210
$$932$$ −52.2492 −1.71148
$$933$$ −70.2492 −2.29986
$$934$$ 76.1803 2.49270
$$935$$ 2.47214 0.0808475
$$936$$ 20.6525 0.675047
$$937$$ 20.6525 0.674687 0.337343 0.941382i $$-0.390472\pi$$
0.337343 + 0.941382i $$0.390472\pi$$
$$938$$ −12.3607 −0.403591
$$939$$ −9.52786 −0.310930
$$940$$ −43.4164 −1.41609
$$941$$ −41.5967 −1.35602 −0.678008 0.735055i $$-0.737156\pi$$
−0.678008 + 0.735055i $$0.737156\pi$$
$$942$$ 50.2492 1.63721
$$943$$ 43.7771 1.42558
$$944$$ −3.23607 −0.105325
$$945$$ −28.9443 −0.941557
$$946$$ 17.8885 0.581607
$$947$$ −58.8328 −1.91181 −0.955905 0.293677i $$-0.905121\pi$$
−0.955905 + 0.293677i $$0.905121\pi$$
$$948$$ 86.8328 2.82020
$$949$$ 6.47214 0.210094
$$950$$ −5.52786 −0.179348
$$951$$ 45.3050 1.46911
$$952$$ −2.76393 −0.0895796
$$953$$ 5.05573 0.163771 0.0818855 0.996642i $$-0.473906\pi$$
0.0818855 + 0.996642i $$0.473906\pi$$
$$954$$ −141.554 −4.58299
$$955$$ 41.8885 1.35548
$$956$$ 77.6656 2.51189
$$957$$ 1.52786 0.0493888
$$958$$ −50.2492 −1.62348
$$959$$ 7.52786 0.243087
$$960$$ 84.1378 2.71553
$$961$$ 21.3607 0.689054
$$962$$ 1.30495 0.0420733
$$963$$ −29.8885 −0.963145
$$964$$ 81.3738 2.62087
$$965$$ 47.7771 1.53800
$$966$$ 46.8328 1.50682
$$967$$ 21.8885 0.703888 0.351944 0.936021i $$-0.385521\pi$$
0.351944 + 0.936021i $$0.385521\pi$$
$$968$$ −2.23607 −0.0718699
$$969$$ −9.88854 −0.317666
$$970$$ −42.1115 −1.35212
$$971$$ −29.1246 −0.934653 −0.467327 0.884085i $$-0.654783\pi$$
−0.467327 + 0.884085i $$0.654783\pi$$
$$972$$ 106.790 3.42530
$$973$$ −10.4721 −0.335721
$$974$$ −18.6950 −0.599028
$$975$$ 4.00000 0.128103
$$976$$ 2.76393 0.0884713
$$977$$ 5.05573 0.161747 0.0808735 0.996724i $$-0.474229\pi$$
0.0808735 + 0.996724i $$0.474229\pi$$
$$978$$ −169.443 −5.41818
$$979$$ −2.00000 −0.0639203
$$980$$ −6.00000 −0.191663
$$981$$ 33.4164 1.06690
$$982$$ 0 0
$$983$$ 44.1803 1.40913 0.704567 0.709637i $$-0.251141\pi$$
0.704567 + 0.709637i $$0.251141\pi$$
$$984$$ 48.9443 1.56029
$$985$$ 4.00000 0.127451
$$986$$ 1.30495 0.0415581
$$987$$ 23.4164 0.745352
$$988$$ 9.16718 0.291647
$$989$$ −51.7771 −1.64642
$$990$$ −33.4164 −1.06204
$$991$$ −26.2492 −0.833834 −0.416917 0.908945i $$-0.636889\pi$$
−0.416917 + 0.908945i $$0.636889\pi$$
$$992$$ −48.5410 −1.54118
$$993$$ 70.8328 2.24781
$$994$$ 3.41641 0.108362
$$995$$ −40.3607 −1.27952
$$996$$ 149.666 4.74234
$$997$$ 32.6525 1.03411 0.517057 0.855951i $$-0.327027\pi$$
0.517057 + 0.855951i $$0.327027\pi$$
$$998$$ −23.4164 −0.741233
$$999$$ 6.83282 0.216181
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 77.2.a.d.1.1 2
3.2 odd 2 693.2.a.h.1.2 2
4.3 odd 2 1232.2.a.m.1.1 2
5.2 odd 4 1925.2.b.h.1849.1 4
5.3 odd 4 1925.2.b.h.1849.4 4
5.4 even 2 1925.2.a.r.1.2 2
7.2 even 3 539.2.e.i.67.2 4
7.3 odd 6 539.2.e.j.177.2 4
7.4 even 3 539.2.e.i.177.2 4
7.5 odd 6 539.2.e.j.67.2 4
7.6 odd 2 539.2.a.f.1.1 2
8.3 odd 2 4928.2.a.bv.1.2 2
8.5 even 2 4928.2.a.bm.1.1 2
11.2 odd 10 847.2.f.b.323.1 4
11.3 even 5 847.2.f.a.372.1 4
11.4 even 5 847.2.f.a.148.1 4
11.5 even 5 847.2.f.n.729.1 4
11.6 odd 10 847.2.f.b.729.1 4
11.7 odd 10 847.2.f.m.148.1 4
11.8 odd 10 847.2.f.m.372.1 4
11.9 even 5 847.2.f.n.323.1 4
11.10 odd 2 847.2.a.f.1.2 2
21.20 even 2 4851.2.a.y.1.2 2
28.27 even 2 8624.2.a.ce.1.2 2
33.32 even 2 7623.2.a.bl.1.1 2
77.76 even 2 5929.2.a.m.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.a.d.1.1 2 1.1 even 1 trivial
539.2.a.f.1.1 2 7.6 odd 2
539.2.e.i.67.2 4 7.2 even 3
539.2.e.i.177.2 4 7.4 even 3
539.2.e.j.67.2 4 7.5 odd 6
539.2.e.j.177.2 4 7.3 odd 6
693.2.a.h.1.2 2 3.2 odd 2
847.2.a.f.1.2 2 11.10 odd 2
847.2.f.a.148.1 4 11.4 even 5
847.2.f.a.372.1 4 11.3 even 5
847.2.f.b.323.1 4 11.2 odd 10
847.2.f.b.729.1 4 11.6 odd 10
847.2.f.m.148.1 4 11.7 odd 10
847.2.f.m.372.1 4 11.8 odd 10
847.2.f.n.323.1 4 11.9 even 5
847.2.f.n.729.1 4 11.5 even 5
1232.2.a.m.1.1 2 4.3 odd 2
1925.2.a.r.1.2 2 5.4 even 2
1925.2.b.h.1849.1 4 5.2 odd 4
1925.2.b.h.1849.4 4 5.3 odd 4
4851.2.a.y.1.2 2 21.20 even 2
4928.2.a.bm.1.1 2 8.5 even 2
4928.2.a.bv.1.2 2 8.3 odd 2
5929.2.a.m.1.2 2 77.76 even 2
7623.2.a.bl.1.1 2 33.32 even 2
8624.2.a.ce.1.2 2 28.27 even 2