# Properties

 Label 35.2.a.b.1.2 Level $35$ Weight $2$ Character 35.1 Self dual yes Analytic conductor $0.279$ 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] = [35,2,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, 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("35.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 35.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: $$0.279476407074$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{17})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 4$$ x^2 - x - 4 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-1.56155$$ of defining polynomial Character $$\chi$$ $$=$$ 35.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.56155 q^{2} -2.56155 q^{3} +0.438447 q^{4} +1.00000 q^{5} -4.00000 q^{6} -1.00000 q^{7} -2.43845 q^{8} +3.56155 q^{9} +O(q^{10})$$ $$q+1.56155 q^{2} -2.56155 q^{3} +0.438447 q^{4} +1.00000 q^{5} -4.00000 q^{6} -1.00000 q^{7} -2.43845 q^{8} +3.56155 q^{9} +1.56155 q^{10} +2.56155 q^{11} -1.12311 q^{12} +4.56155 q^{13} -1.56155 q^{14} -2.56155 q^{15} -4.68466 q^{16} -4.56155 q^{17} +5.56155 q^{18} +1.12311 q^{19} +0.438447 q^{20} +2.56155 q^{21} +4.00000 q^{22} -5.12311 q^{23} +6.24621 q^{24} +1.00000 q^{25} +7.12311 q^{26} -1.43845 q^{27} -0.438447 q^{28} -5.68466 q^{29} -4.00000 q^{30} -2.43845 q^{32} -6.56155 q^{33} -7.12311 q^{34} -1.00000 q^{35} +1.56155 q^{36} +6.00000 q^{37} +1.75379 q^{38} -11.6847 q^{39} -2.43845 q^{40} -3.12311 q^{41} +4.00000 q^{42} +9.12311 q^{43} +1.12311 q^{44} +3.56155 q^{45} -8.00000 q^{46} +3.68466 q^{47} +12.0000 q^{48} +1.00000 q^{49} +1.56155 q^{50} +11.6847 q^{51} +2.00000 q^{52} +3.12311 q^{53} -2.24621 q^{54} +2.56155 q^{55} +2.43845 q^{56} -2.87689 q^{57} -8.87689 q^{58} -4.00000 q^{59} -1.12311 q^{60} -9.36932 q^{61} -3.56155 q^{63} +5.56155 q^{64} +4.56155 q^{65} -10.2462 q^{66} -6.24621 q^{67} -2.00000 q^{68} +13.1231 q^{69} -1.56155 q^{70} +8.00000 q^{71} -8.68466 q^{72} +4.24621 q^{73} +9.36932 q^{74} -2.56155 q^{75} +0.492423 q^{76} -2.56155 q^{77} -18.2462 q^{78} -6.56155 q^{79} -4.68466 q^{80} -7.00000 q^{81} -4.87689 q^{82} +4.00000 q^{83} +1.12311 q^{84} -4.56155 q^{85} +14.2462 q^{86} +14.5616 q^{87} -6.24621 q^{88} +7.12311 q^{89} +5.56155 q^{90} -4.56155 q^{91} -2.24621 q^{92} +5.75379 q^{94} +1.12311 q^{95} +6.24621 q^{96} -14.8078 q^{97} +1.56155 q^{98} +9.12311 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{3} + 5 q^{4} + 2 q^{5} - 8 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10})$$ 2 * q - q^2 - q^3 + 5 * q^4 + 2 * q^5 - 8 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 $$2 q - q^{2} - q^{3} + 5 q^{4} + 2 q^{5} - 8 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} - q^{10} + q^{11} + 6 q^{12} + 5 q^{13} + q^{14} - q^{15} + 3 q^{16} - 5 q^{17} + 7 q^{18} - 6 q^{19} + 5 q^{20} + q^{21} + 8 q^{22} - 2 q^{23} - 4 q^{24} + 2 q^{25} + 6 q^{26} - 7 q^{27} - 5 q^{28} + q^{29} - 8 q^{30} - 9 q^{32} - 9 q^{33} - 6 q^{34} - 2 q^{35} - q^{36} + 12 q^{37} + 20 q^{38} - 11 q^{39} - 9 q^{40} + 2 q^{41} + 8 q^{42} + 10 q^{43} - 6 q^{44} + 3 q^{45} - 16 q^{46} - 5 q^{47} + 24 q^{48} + 2 q^{49} - q^{50} + 11 q^{51} + 4 q^{52} - 2 q^{53} + 12 q^{54} + q^{55} + 9 q^{56} - 14 q^{57} - 26 q^{58} - 8 q^{59} + 6 q^{60} + 6 q^{61} - 3 q^{63} + 7 q^{64} + 5 q^{65} - 4 q^{66} + 4 q^{67} - 4 q^{68} + 18 q^{69} + q^{70} + 16 q^{71} - 5 q^{72} - 8 q^{73} - 6 q^{74} - q^{75} - 32 q^{76} - q^{77} - 20 q^{78} - 9 q^{79} + 3 q^{80} - 14 q^{81} - 18 q^{82} + 8 q^{83} - 6 q^{84} - 5 q^{85} + 12 q^{86} + 25 q^{87} + 4 q^{88} + 6 q^{89} + 7 q^{90} - 5 q^{91} + 12 q^{92} + 28 q^{94} - 6 q^{95} - 4 q^{96} - 9 q^{97} - q^{98} + 10 q^{99}+O(q^{100})$$ 2 * q - q^2 - q^3 + 5 * q^4 + 2 * q^5 - 8 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 - q^10 + q^11 + 6 * q^12 + 5 * q^13 + q^14 - q^15 + 3 * q^16 - 5 * q^17 + 7 * q^18 - 6 * q^19 + 5 * q^20 + q^21 + 8 * q^22 - 2 * q^23 - 4 * q^24 + 2 * q^25 + 6 * q^26 - 7 * q^27 - 5 * q^28 + q^29 - 8 * q^30 - 9 * q^32 - 9 * q^33 - 6 * q^34 - 2 * q^35 - q^36 + 12 * q^37 + 20 * q^38 - 11 * q^39 - 9 * q^40 + 2 * q^41 + 8 * q^42 + 10 * q^43 - 6 * q^44 + 3 * q^45 - 16 * q^46 - 5 * q^47 + 24 * q^48 + 2 * q^49 - q^50 + 11 * q^51 + 4 * q^52 - 2 * q^53 + 12 * q^54 + q^55 + 9 * q^56 - 14 * q^57 - 26 * q^58 - 8 * q^59 + 6 * q^60 + 6 * q^61 - 3 * q^63 + 7 * q^64 + 5 * q^65 - 4 * q^66 + 4 * q^67 - 4 * q^68 + 18 * q^69 + q^70 + 16 * q^71 - 5 * q^72 - 8 * q^73 - 6 * q^74 - q^75 - 32 * q^76 - q^77 - 20 * q^78 - 9 * q^79 + 3 * q^80 - 14 * q^81 - 18 * q^82 + 8 * q^83 - 6 * q^84 - 5 * q^85 + 12 * q^86 + 25 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 5 * q^91 + 12 * q^92 + 28 * q^94 - 6 * q^95 - 4 * q^96 - 9 * q^97 - q^98 + 10 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.56155 1.10418 0.552092 0.833783i $$-0.313830\pi$$
0.552092 + 0.833783i $$0.313830\pi$$
$$3$$ −2.56155 −1.47891 −0.739457 0.673204i $$-0.764917\pi$$
−0.739457 + 0.673204i $$0.764917\pi$$
$$4$$ 0.438447 0.219224
$$5$$ 1.00000 0.447214
$$6$$ −4.00000 −1.63299
$$7$$ −1.00000 −0.377964
$$8$$ −2.43845 −0.862121
$$9$$ 3.56155 1.18718
$$10$$ 1.56155 0.493806
$$11$$ 2.56155 0.772337 0.386169 0.922428i $$-0.373798\pi$$
0.386169 + 0.922428i $$0.373798\pi$$
$$12$$ −1.12311 −0.324213
$$13$$ 4.56155 1.26515 0.632574 0.774500i $$-0.281999\pi$$
0.632574 + 0.774500i $$0.281999\pi$$
$$14$$ −1.56155 −0.417343
$$15$$ −2.56155 −0.661390
$$16$$ −4.68466 −1.17116
$$17$$ −4.56155 −1.10634 −0.553170 0.833069i $$-0.686582\pi$$
−0.553170 + 0.833069i $$0.686582\pi$$
$$18$$ 5.56155 1.31087
$$19$$ 1.12311 0.257658 0.128829 0.991667i $$-0.458878\pi$$
0.128829 + 0.991667i $$0.458878\pi$$
$$20$$ 0.438447 0.0980398
$$21$$ 2.56155 0.558977
$$22$$ 4.00000 0.852803
$$23$$ −5.12311 −1.06824 −0.534121 0.845408i $$-0.679357\pi$$
−0.534121 + 0.845408i $$0.679357\pi$$
$$24$$ 6.24621 1.27500
$$25$$ 1.00000 0.200000
$$26$$ 7.12311 1.39696
$$27$$ −1.43845 −0.276829
$$28$$ −0.438447 −0.0828587
$$29$$ −5.68466 −1.05561 −0.527807 0.849364i $$-0.676986\pi$$
−0.527807 + 0.849364i $$0.676986\pi$$
$$30$$ −4.00000 −0.730297
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −2.43845 −0.431061
$$33$$ −6.56155 −1.14222
$$34$$ −7.12311 −1.22160
$$35$$ −1.00000 −0.169031
$$36$$ 1.56155 0.260259
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 1.75379 0.284502
$$39$$ −11.6847 −1.87104
$$40$$ −2.43845 −0.385552
$$41$$ −3.12311 −0.487747 −0.243874 0.969807i $$-0.578418\pi$$
−0.243874 + 0.969807i $$0.578418\pi$$
$$42$$ 4.00000 0.617213
$$43$$ 9.12311 1.39126 0.695630 0.718400i $$-0.255125\pi$$
0.695630 + 0.718400i $$0.255125\pi$$
$$44$$ 1.12311 0.169315
$$45$$ 3.56155 0.530925
$$46$$ −8.00000 −1.17954
$$47$$ 3.68466 0.537463 0.268731 0.963215i $$-0.413396\pi$$
0.268731 + 0.963215i $$0.413396\pi$$
$$48$$ 12.0000 1.73205
$$49$$ 1.00000 0.142857
$$50$$ 1.56155 0.220837
$$51$$ 11.6847 1.63618
$$52$$ 2.00000 0.277350
$$53$$ 3.12311 0.428992 0.214496 0.976725i $$-0.431189\pi$$
0.214496 + 0.976725i $$0.431189\pi$$
$$54$$ −2.24621 −0.305671
$$55$$ 2.56155 0.345400
$$56$$ 2.43845 0.325851
$$57$$ −2.87689 −0.381054
$$58$$ −8.87689 −1.16559
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ −1.12311 −0.144992
$$61$$ −9.36932 −1.19962 −0.599809 0.800143i $$-0.704757\pi$$
−0.599809 + 0.800143i $$0.704757\pi$$
$$62$$ 0 0
$$63$$ −3.56155 −0.448713
$$64$$ 5.56155 0.695194
$$65$$ 4.56155 0.565791
$$66$$ −10.2462 −1.26122
$$67$$ −6.24621 −0.763096 −0.381548 0.924349i $$-0.624609\pi$$
−0.381548 + 0.924349i $$0.624609\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ 13.1231 1.57984
$$70$$ −1.56155 −0.186641
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ −8.68466 −1.02350
$$73$$ 4.24621 0.496981 0.248491 0.968634i $$-0.420065\pi$$
0.248491 + 0.968634i $$0.420065\pi$$
$$74$$ 9.36932 1.08916
$$75$$ −2.56155 −0.295783
$$76$$ 0.492423 0.0564847
$$77$$ −2.56155 −0.291916
$$78$$ −18.2462 −2.06598
$$79$$ −6.56155 −0.738232 −0.369116 0.929383i $$-0.620340\pi$$
−0.369116 + 0.929383i $$0.620340\pi$$
$$80$$ −4.68466 −0.523761
$$81$$ −7.00000 −0.777778
$$82$$ −4.87689 −0.538563
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 1.12311 0.122541
$$85$$ −4.56155 −0.494770
$$86$$ 14.2462 1.53621
$$87$$ 14.5616 1.56116
$$88$$ −6.24621 −0.665848
$$89$$ 7.12311 0.755048 0.377524 0.926000i $$-0.376776\pi$$
0.377524 + 0.926000i $$0.376776\pi$$
$$90$$ 5.56155 0.586239
$$91$$ −4.56155 −0.478181
$$92$$ −2.24621 −0.234184
$$93$$ 0 0
$$94$$ 5.75379 0.593458
$$95$$ 1.12311 0.115228
$$96$$ 6.24621 0.637501
$$97$$ −14.8078 −1.50350 −0.751750 0.659448i $$-0.770790\pi$$
−0.751750 + 0.659448i $$0.770790\pi$$
$$98$$ 1.56155 0.157741
$$99$$ 9.12311 0.916907
$$100$$ 0.438447 0.0438447
$$101$$ 0.246211 0.0244989 0.0122495 0.999925i $$-0.496101\pi$$
0.0122495 + 0.999925i $$0.496101\pi$$
$$102$$ 18.2462 1.80664
$$103$$ 1.43845 0.141734 0.0708672 0.997486i $$-0.477423\pi$$
0.0708672 + 0.997486i $$0.477423\pi$$
$$104$$ −11.1231 −1.09071
$$105$$ 2.56155 0.249982
$$106$$ 4.87689 0.473686
$$107$$ −11.3693 −1.09911 −0.549557 0.835456i $$-0.685203\pi$$
−0.549557 + 0.835456i $$0.685203\pi$$
$$108$$ −0.630683 −0.0606875
$$109$$ 17.6847 1.69388 0.846942 0.531686i $$-0.178441\pi$$
0.846942 + 0.531686i $$0.178441\pi$$
$$110$$ 4.00000 0.381385
$$111$$ −15.3693 −1.45879
$$112$$ 4.68466 0.442659
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ −4.49242 −0.420754
$$115$$ −5.12311 −0.477732
$$116$$ −2.49242 −0.231416
$$117$$ 16.2462 1.50196
$$118$$ −6.24621 −0.575010
$$119$$ 4.56155 0.418157
$$120$$ 6.24621 0.570198
$$121$$ −4.43845 −0.403495
$$122$$ −14.6307 −1.32460
$$123$$ 8.00000 0.721336
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ −5.56155 −0.495463
$$127$$ 10.2462 0.909204 0.454602 0.890695i $$-0.349781\pi$$
0.454602 + 0.890695i $$0.349781\pi$$
$$128$$ 13.5616 1.19868
$$129$$ −23.3693 −2.05755
$$130$$ 7.12311 0.624738
$$131$$ −9.12311 −0.797089 −0.398545 0.917149i $$-0.630485\pi$$
−0.398545 + 0.917149i $$0.630485\pi$$
$$132$$ −2.87689 −0.250402
$$133$$ −1.12311 −0.0973856
$$134$$ −9.75379 −0.842599
$$135$$ −1.43845 −0.123802
$$136$$ 11.1231 0.953798
$$137$$ −8.87689 −0.758404 −0.379202 0.925314i $$-0.623801\pi$$
−0.379202 + 0.925314i $$0.623801\pi$$
$$138$$ 20.4924 1.74443
$$139$$ −6.87689 −0.583291 −0.291645 0.956527i $$-0.594203\pi$$
−0.291645 + 0.956527i $$0.594203\pi$$
$$140$$ −0.438447 −0.0370556
$$141$$ −9.43845 −0.794861
$$142$$ 12.4924 1.04834
$$143$$ 11.6847 0.977120
$$144$$ −16.6847 −1.39039
$$145$$ −5.68466 −0.472085
$$146$$ 6.63068 0.548759
$$147$$ −2.56155 −0.211273
$$148$$ 2.63068 0.216241
$$149$$ −4.24621 −0.347863 −0.173932 0.984758i $$-0.555647\pi$$
−0.173932 + 0.984758i $$0.555647\pi$$
$$150$$ −4.00000 −0.326599
$$151$$ 21.9309 1.78471 0.892354 0.451335i $$-0.149052\pi$$
0.892354 + 0.451335i $$0.149052\pi$$
$$152$$ −2.73863 −0.222133
$$153$$ −16.2462 −1.31343
$$154$$ −4.00000 −0.322329
$$155$$ 0 0
$$156$$ −5.12311 −0.410177
$$157$$ 3.75379 0.299585 0.149792 0.988717i $$-0.452139\pi$$
0.149792 + 0.988717i $$0.452139\pi$$
$$158$$ −10.2462 −0.815145
$$159$$ −8.00000 −0.634441
$$160$$ −2.43845 −0.192776
$$161$$ 5.12311 0.403757
$$162$$ −10.9309 −0.858810
$$163$$ 1.12311 0.0879684 0.0439842 0.999032i $$-0.485995\pi$$
0.0439842 + 0.999032i $$0.485995\pi$$
$$164$$ −1.36932 −0.106926
$$165$$ −6.56155 −0.510816
$$166$$ 6.24621 0.484800
$$167$$ 21.9309 1.69706 0.848531 0.529146i $$-0.177488\pi$$
0.848531 + 0.529146i $$0.177488\pi$$
$$168$$ −6.24621 −0.481906
$$169$$ 7.80776 0.600597
$$170$$ −7.12311 −0.546317
$$171$$ 4.00000 0.305888
$$172$$ 4.00000 0.304997
$$173$$ −8.56155 −0.650923 −0.325461 0.945555i $$-0.605520\pi$$
−0.325461 + 0.945555i $$0.605520\pi$$
$$174$$ 22.7386 1.72381
$$175$$ −1.00000 −0.0755929
$$176$$ −12.0000 −0.904534
$$177$$ 10.2462 0.770152
$$178$$ 11.1231 0.833712
$$179$$ 20.0000 1.49487 0.747435 0.664335i $$-0.231285\pi$$
0.747435 + 0.664335i $$0.231285\pi$$
$$180$$ 1.56155 0.116391
$$181$$ 23.6155 1.75533 0.877664 0.479276i $$-0.159101\pi$$
0.877664 + 0.479276i $$0.159101\pi$$
$$182$$ −7.12311 −0.528000
$$183$$ 24.0000 1.77413
$$184$$ 12.4924 0.920954
$$185$$ 6.00000 0.441129
$$186$$ 0 0
$$187$$ −11.6847 −0.854467
$$188$$ 1.61553 0.117824
$$189$$ 1.43845 0.104632
$$190$$ 1.75379 0.127233
$$191$$ −9.43845 −0.682942 −0.341471 0.939892i $$-0.610925\pi$$
−0.341471 + 0.939892i $$0.610925\pi$$
$$192$$ −14.2462 −1.02813
$$193$$ −5.36932 −0.386492 −0.193246 0.981150i $$-0.561902\pi$$
−0.193246 + 0.981150i $$0.561902\pi$$
$$194$$ −23.1231 −1.66014
$$195$$ −11.6847 −0.836756
$$196$$ 0.438447 0.0313177
$$197$$ −7.12311 −0.507500 −0.253750 0.967270i $$-0.581664\pi$$
−0.253750 + 0.967270i $$0.581664\pi$$
$$198$$ 14.2462 1.01243
$$199$$ −18.2462 −1.29344 −0.646720 0.762728i $$-0.723860\pi$$
−0.646720 + 0.762728i $$0.723860\pi$$
$$200$$ −2.43845 −0.172424
$$201$$ 16.0000 1.12855
$$202$$ 0.384472 0.0270513
$$203$$ 5.68466 0.398985
$$204$$ 5.12311 0.358689
$$205$$ −3.12311 −0.218127
$$206$$ 2.24621 0.156501
$$207$$ −18.2462 −1.26820
$$208$$ −21.3693 −1.48170
$$209$$ 2.87689 0.198999
$$210$$ 4.00000 0.276026
$$211$$ −23.0540 −1.58710 −0.793551 0.608504i $$-0.791770\pi$$
−0.793551 + 0.608504i $$0.791770\pi$$
$$212$$ 1.36932 0.0940451
$$213$$ −20.4924 −1.40412
$$214$$ −17.7538 −1.21362
$$215$$ 9.12311 0.622191
$$216$$ 3.50758 0.238660
$$217$$ 0 0
$$218$$ 27.6155 1.87036
$$219$$ −10.8769 −0.734992
$$220$$ 1.12311 0.0757198
$$221$$ −20.8078 −1.39968
$$222$$ −24.0000 −1.61077
$$223$$ −6.56155 −0.439394 −0.219697 0.975568i $$-0.570507\pi$$
−0.219697 + 0.975568i $$0.570507\pi$$
$$224$$ 2.43845 0.162926
$$225$$ 3.56155 0.237437
$$226$$ −21.8617 −1.45422
$$227$$ 23.6847 1.57201 0.786003 0.618223i $$-0.212147\pi$$
0.786003 + 0.618223i $$0.212147\pi$$
$$228$$ −1.26137 −0.0835360
$$229$$ 19.1231 1.26369 0.631845 0.775095i $$-0.282298\pi$$
0.631845 + 0.775095i $$0.282298\pi$$
$$230$$ −8.00000 −0.527504
$$231$$ 6.56155 0.431718
$$232$$ 13.8617 0.910068
$$233$$ −3.12311 −0.204601 −0.102301 0.994754i $$-0.532620\pi$$
−0.102301 + 0.994754i $$0.532620\pi$$
$$234$$ 25.3693 1.65844
$$235$$ 3.68466 0.240361
$$236$$ −1.75379 −0.114162
$$237$$ 16.8078 1.09178
$$238$$ 7.12311 0.461722
$$239$$ −0.807764 −0.0522499 −0.0261250 0.999659i $$-0.508317\pi$$
−0.0261250 + 0.999659i $$0.508317\pi$$
$$240$$ 12.0000 0.774597
$$241$$ 12.2462 0.788848 0.394424 0.918929i $$-0.370944\pi$$
0.394424 + 0.918929i $$0.370944\pi$$
$$242$$ −6.93087 −0.445533
$$243$$ 22.2462 1.42710
$$244$$ −4.10795 −0.262985
$$245$$ 1.00000 0.0638877
$$246$$ 12.4924 0.796488
$$247$$ 5.12311 0.325975
$$248$$ 0 0
$$249$$ −10.2462 −0.649327
$$250$$ 1.56155 0.0987613
$$251$$ −17.1231 −1.08080 −0.540400 0.841408i $$-0.681727\pi$$
−0.540400 + 0.841408i $$0.681727\pi$$
$$252$$ −1.56155 −0.0983686
$$253$$ −13.1231 −0.825043
$$254$$ 16.0000 1.00393
$$255$$ 11.6847 0.731722
$$256$$ 10.0540 0.628373
$$257$$ 22.4924 1.40304 0.701519 0.712650i $$-0.252505\pi$$
0.701519 + 0.712650i $$0.252505\pi$$
$$258$$ −36.4924 −2.27192
$$259$$ −6.00000 −0.372822
$$260$$ 2.00000 0.124035
$$261$$ −20.2462 −1.25321
$$262$$ −14.2462 −0.880134
$$263$$ −21.1231 −1.30251 −0.651253 0.758860i $$-0.725756\pi$$
−0.651253 + 0.758860i $$0.725756\pi$$
$$264$$ 16.0000 0.984732
$$265$$ 3.12311 0.191851
$$266$$ −1.75379 −0.107532
$$267$$ −18.2462 −1.11665
$$268$$ −2.73863 −0.167289
$$269$$ 28.7386 1.75223 0.876113 0.482106i $$-0.160128\pi$$
0.876113 + 0.482106i $$0.160128\pi$$
$$270$$ −2.24621 −0.136700
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 21.3693 1.29571
$$273$$ 11.6847 0.707188
$$274$$ −13.8617 −0.837418
$$275$$ 2.56155 0.154467
$$276$$ 5.75379 0.346337
$$277$$ 16.2462 0.976140 0.488070 0.872804i $$-0.337701\pi$$
0.488070 + 0.872804i $$0.337701\pi$$
$$278$$ −10.7386 −0.644060
$$279$$ 0 0
$$280$$ 2.43845 0.145725
$$281$$ 16.5616 0.987979 0.493990 0.869468i $$-0.335538\pi$$
0.493990 + 0.869468i $$0.335538\pi$$
$$282$$ −14.7386 −0.877673
$$283$$ −23.6847 −1.40791 −0.703953 0.710246i $$-0.748584\pi$$
−0.703953 + 0.710246i $$0.748584\pi$$
$$284$$ 3.50758 0.208136
$$285$$ −2.87689 −0.170413
$$286$$ 18.2462 1.07892
$$287$$ 3.12311 0.184351
$$288$$ −8.68466 −0.511748
$$289$$ 3.80776 0.223986
$$290$$ −8.87689 −0.521269
$$291$$ 37.9309 2.22355
$$292$$ 1.86174 0.108950
$$293$$ 9.68466 0.565784 0.282892 0.959152i $$-0.408706\pi$$
0.282892 + 0.959152i $$0.408706\pi$$
$$294$$ −4.00000 −0.233285
$$295$$ −4.00000 −0.232889
$$296$$ −14.6307 −0.850391
$$297$$ −3.68466 −0.213806
$$298$$ −6.63068 −0.384105
$$299$$ −23.3693 −1.35148
$$300$$ −1.12311 −0.0648425
$$301$$ −9.12311 −0.525847
$$302$$ 34.2462 1.97065
$$303$$ −0.630683 −0.0362318
$$304$$ −5.26137 −0.301760
$$305$$ −9.36932 −0.536486
$$306$$ −25.3693 −1.45027
$$307$$ −31.6847 −1.80834 −0.904169 0.427174i $$-0.859509\pi$$
−0.904169 + 0.427174i $$0.859509\pi$$
$$308$$ −1.12311 −0.0639949
$$309$$ −3.68466 −0.209613
$$310$$ 0 0
$$311$$ −9.61553 −0.545247 −0.272623 0.962121i $$-0.587891\pi$$
−0.272623 + 0.962121i $$0.587891\pi$$
$$312$$ 28.4924 1.61307
$$313$$ 31.3002 1.76919 0.884596 0.466359i $$-0.154434\pi$$
0.884596 + 0.466359i $$0.154434\pi$$
$$314$$ 5.86174 0.330797
$$315$$ −3.56155 −0.200671
$$316$$ −2.87689 −0.161838
$$317$$ −22.4924 −1.26330 −0.631650 0.775254i $$-0.717622\pi$$
−0.631650 + 0.775254i $$0.717622\pi$$
$$318$$ −12.4924 −0.700540
$$319$$ −14.5616 −0.815290
$$320$$ 5.56155 0.310900
$$321$$ 29.1231 1.62549
$$322$$ 8.00000 0.445823
$$323$$ −5.12311 −0.285057
$$324$$ −3.06913 −0.170507
$$325$$ 4.56155 0.253029
$$326$$ 1.75379 0.0971334
$$327$$ −45.3002 −2.50511
$$328$$ 7.61553 0.420497
$$329$$ −3.68466 −0.203142
$$330$$ −10.2462 −0.564035
$$331$$ 12.0000 0.659580 0.329790 0.944054i $$-0.393022\pi$$
0.329790 + 0.944054i $$0.393022\pi$$
$$332$$ 1.75379 0.0962517
$$333$$ 21.3693 1.17103
$$334$$ 34.2462 1.87387
$$335$$ −6.24621 −0.341267
$$336$$ −12.0000 −0.654654
$$337$$ −34.4924 −1.87892 −0.939461 0.342656i $$-0.888674\pi$$
−0.939461 + 0.342656i $$0.888674\pi$$
$$338$$ 12.1922 0.663170
$$339$$ 35.8617 1.94774
$$340$$ −2.00000 −0.108465
$$341$$ 0 0
$$342$$ 6.24621 0.337756
$$343$$ −1.00000 −0.0539949
$$344$$ −22.2462 −1.19944
$$345$$ 13.1231 0.706524
$$346$$ −13.3693 −0.718739
$$347$$ −1.12311 −0.0602915 −0.0301457 0.999546i $$-0.509597\pi$$
−0.0301457 + 0.999546i $$0.509597\pi$$
$$348$$ 6.38447 0.342244
$$349$$ −22.4924 −1.20399 −0.601996 0.798499i $$-0.705628\pi$$
−0.601996 + 0.798499i $$0.705628\pi$$
$$350$$ −1.56155 −0.0834685
$$351$$ −6.56155 −0.350230
$$352$$ −6.24621 −0.332924
$$353$$ −14.8078 −0.788138 −0.394069 0.919081i $$-0.628933\pi$$
−0.394069 + 0.919081i $$0.628933\pi$$
$$354$$ 16.0000 0.850390
$$355$$ 8.00000 0.424596
$$356$$ 3.12311 0.165524
$$357$$ −11.6847 −0.618418
$$358$$ 31.2311 1.65061
$$359$$ 8.00000 0.422224 0.211112 0.977462i $$-0.432292\pi$$
0.211112 + 0.977462i $$0.432292\pi$$
$$360$$ −8.68466 −0.457722
$$361$$ −17.7386 −0.933612
$$362$$ 36.8769 1.93821
$$363$$ 11.3693 0.596734
$$364$$ −2.00000 −0.104828
$$365$$ 4.24621 0.222257
$$366$$ 37.4773 1.95897
$$367$$ 3.68466 0.192338 0.0961688 0.995365i $$-0.469341\pi$$
0.0961688 + 0.995365i $$0.469341\pi$$
$$368$$ 24.0000 1.25109
$$369$$ −11.1231 −0.579046
$$370$$ 9.36932 0.487088
$$371$$ −3.12311 −0.162144
$$372$$ 0 0
$$373$$ 29.3693 1.52069 0.760343 0.649522i $$-0.225031\pi$$
0.760343 + 0.649522i $$0.225031\pi$$
$$374$$ −18.2462 −0.943489
$$375$$ −2.56155 −0.132278
$$376$$ −8.98485 −0.463358
$$377$$ −25.9309 −1.33551
$$378$$ 2.24621 0.115533
$$379$$ 16.4924 0.847159 0.423579 0.905859i $$-0.360773\pi$$
0.423579 + 0.905859i $$0.360773\pi$$
$$380$$ 0.492423 0.0252607
$$381$$ −26.2462 −1.34463
$$382$$ −14.7386 −0.754094
$$383$$ −10.2462 −0.523557 −0.261778 0.965128i $$-0.584309\pi$$
−0.261778 + 0.965128i $$0.584309\pi$$
$$384$$ −34.7386 −1.77275
$$385$$ −2.56155 −0.130549
$$386$$ −8.38447 −0.426758
$$387$$ 32.4924 1.65168
$$388$$ −6.49242 −0.329603
$$389$$ 3.93087 0.199303 0.0996515 0.995022i $$-0.468227\pi$$
0.0996515 + 0.995022i $$0.468227\pi$$
$$390$$ −18.2462 −0.923933
$$391$$ 23.3693 1.18184
$$392$$ −2.43845 −0.123160
$$393$$ 23.3693 1.17883
$$394$$ −11.1231 −0.560374
$$395$$ −6.56155 −0.330148
$$396$$ 4.00000 0.201008
$$397$$ 23.4384 1.17634 0.588171 0.808737i $$-0.299848\pi$$
0.588171 + 0.808737i $$0.299848\pi$$
$$398$$ −28.4924 −1.42820
$$399$$ 2.87689 0.144025
$$400$$ −4.68466 −0.234233
$$401$$ 27.4384 1.37021 0.685105 0.728444i $$-0.259756\pi$$
0.685105 + 0.728444i $$0.259756\pi$$
$$402$$ 24.9848 1.24613
$$403$$ 0 0
$$404$$ 0.107951 0.00537074
$$405$$ −7.00000 −0.347833
$$406$$ 8.87689 0.440553
$$407$$ 15.3693 0.761829
$$408$$ −28.4924 −1.41059
$$409$$ −26.4924 −1.30997 −0.654983 0.755644i $$-0.727324\pi$$
−0.654983 + 0.755644i $$0.727324\pi$$
$$410$$ −4.87689 −0.240853
$$411$$ 22.7386 1.12161
$$412$$ 0.630683 0.0310715
$$413$$ 4.00000 0.196827
$$414$$ −28.4924 −1.40033
$$415$$ 4.00000 0.196352
$$416$$ −11.1231 −0.545355
$$417$$ 17.6155 0.862636
$$418$$ 4.49242 0.219732
$$419$$ 9.75379 0.476504 0.238252 0.971203i $$-0.423426\pi$$
0.238252 + 0.971203i $$0.423426\pi$$
$$420$$ 1.12311 0.0548019
$$421$$ 9.68466 0.472001 0.236001 0.971753i $$-0.424163\pi$$
0.236001 + 0.971753i $$0.424163\pi$$
$$422$$ −36.0000 −1.75245
$$423$$ 13.1231 0.638067
$$424$$ −7.61553 −0.369843
$$425$$ −4.56155 −0.221268
$$426$$ −32.0000 −1.55041
$$427$$ 9.36932 0.453413
$$428$$ −4.98485 −0.240952
$$429$$ −29.9309 −1.44508
$$430$$ 14.2462 0.687013
$$431$$ 0.807764 0.0389086 0.0194543 0.999811i $$-0.493807\pi$$
0.0194543 + 0.999811i $$0.493807\pi$$
$$432$$ 6.73863 0.324213
$$433$$ −8.24621 −0.396288 −0.198144 0.980173i $$-0.563491\pi$$
−0.198144 + 0.980173i $$0.563491\pi$$
$$434$$ 0 0
$$435$$ 14.5616 0.698173
$$436$$ 7.75379 0.371339
$$437$$ −5.75379 −0.275241
$$438$$ −16.9848 −0.811567
$$439$$ −15.3693 −0.733537 −0.366769 0.930312i $$-0.619536\pi$$
−0.366769 + 0.930312i $$0.619536\pi$$
$$440$$ −6.24621 −0.297776
$$441$$ 3.56155 0.169598
$$442$$ −32.4924 −1.54551
$$443$$ −27.3693 −1.30036 −0.650178 0.759782i $$-0.725306\pi$$
−0.650178 + 0.759782i $$0.725306\pi$$
$$444$$ −6.73863 −0.319801
$$445$$ 7.12311 0.337668
$$446$$ −10.2462 −0.485172
$$447$$ 10.8769 0.514459
$$448$$ −5.56155 −0.262759
$$449$$ 18.8078 0.887593 0.443797 0.896128i $$-0.353631\pi$$
0.443797 + 0.896128i $$0.353631\pi$$
$$450$$ 5.56155 0.262174
$$451$$ −8.00000 −0.376705
$$452$$ −6.13826 −0.288719
$$453$$ −56.1771 −2.63943
$$454$$ 36.9848 1.73578
$$455$$ −4.56155 −0.213849
$$456$$ 7.01515 0.328515
$$457$$ −8.87689 −0.415244 −0.207622 0.978209i $$-0.566572\pi$$
−0.207622 + 0.978209i $$0.566572\pi$$
$$458$$ 29.8617 1.39535
$$459$$ 6.56155 0.306267
$$460$$ −2.24621 −0.104730
$$461$$ −4.87689 −0.227140 −0.113570 0.993530i $$-0.536229\pi$$
−0.113570 + 0.993530i $$0.536229\pi$$
$$462$$ 10.2462 0.476697
$$463$$ −20.4924 −0.952364 −0.476182 0.879347i $$-0.657980\pi$$
−0.476182 + 0.879347i $$0.657980\pi$$
$$464$$ 26.6307 1.23630
$$465$$ 0 0
$$466$$ −4.87689 −0.225918
$$467$$ 26.5616 1.22912 0.614561 0.788869i $$-0.289333\pi$$
0.614561 + 0.788869i $$0.289333\pi$$
$$468$$ 7.12311 0.329266
$$469$$ 6.24621 0.288423
$$470$$ 5.75379 0.265402
$$471$$ −9.61553 −0.443060
$$472$$ 9.75379 0.448955
$$473$$ 23.3693 1.07452
$$474$$ 26.2462 1.20553
$$475$$ 1.12311 0.0515316
$$476$$ 2.00000 0.0916698
$$477$$ 11.1231 0.509292
$$478$$ −1.26137 −0.0576935
$$479$$ 13.1231 0.599610 0.299805 0.954001i $$-0.403078\pi$$
0.299805 + 0.954001i $$0.403078\pi$$
$$480$$ 6.24621 0.285099
$$481$$ 27.3693 1.24793
$$482$$ 19.1231 0.871034
$$483$$ −13.1231 −0.597122
$$484$$ −1.94602 −0.0884557
$$485$$ −14.8078 −0.672386
$$486$$ 34.7386 1.57578
$$487$$ 5.12311 0.232150 0.116075 0.993240i $$-0.462969\pi$$
0.116075 + 0.993240i $$0.462969\pi$$
$$488$$ 22.8466 1.03422
$$489$$ −2.87689 −0.130098
$$490$$ 1.56155 0.0705438
$$491$$ 4.17708 0.188509 0.0942545 0.995548i $$-0.469953\pi$$
0.0942545 + 0.995548i $$0.469953\pi$$
$$492$$ 3.50758 0.158134
$$493$$ 25.9309 1.16787
$$494$$ 8.00000 0.359937
$$495$$ 9.12311 0.410053
$$496$$ 0 0
$$497$$ −8.00000 −0.358849
$$498$$ −16.0000 −0.716977
$$499$$ −4.17708 −0.186992 −0.0934959 0.995620i $$-0.529804\pi$$
−0.0934959 + 0.995620i $$0.529804\pi$$
$$500$$ 0.438447 0.0196080
$$501$$ −56.1771 −2.50981
$$502$$ −26.7386 −1.19340
$$503$$ 10.0691 0.448960 0.224480 0.974479i $$-0.427932\pi$$
0.224480 + 0.974479i $$0.427932\pi$$
$$504$$ 8.68466 0.386845
$$505$$ 0.246211 0.0109563
$$506$$ −20.4924 −0.910999
$$507$$ −20.0000 −0.888231
$$508$$ 4.49242 0.199319
$$509$$ −28.2462 −1.25199 −0.625996 0.779827i $$-0.715307\pi$$
−0.625996 + 0.779827i $$0.715307\pi$$
$$510$$ 18.2462 0.807956
$$511$$ −4.24621 −0.187841
$$512$$ −11.4233 −0.504843
$$513$$ −1.61553 −0.0713273
$$514$$ 35.1231 1.54921
$$515$$ 1.43845 0.0633856
$$516$$ −10.2462 −0.451064
$$517$$ 9.43845 0.415102
$$518$$ −9.36932 −0.411664
$$519$$ 21.9309 0.962658
$$520$$ −11.1231 −0.487780
$$521$$ 10.0000 0.438108 0.219054 0.975713i $$-0.429703\pi$$
0.219054 + 0.975713i $$0.429703\pi$$
$$522$$ −31.6155 −1.38377
$$523$$ 7.50758 0.328283 0.164142 0.986437i $$-0.447515\pi$$
0.164142 + 0.986437i $$0.447515\pi$$
$$524$$ −4.00000 −0.174741
$$525$$ 2.56155 0.111795
$$526$$ −32.9848 −1.43821
$$527$$ 0 0
$$528$$ 30.7386 1.33773
$$529$$ 3.24621 0.141140
$$530$$ 4.87689 0.211839
$$531$$ −14.2462 −0.618233
$$532$$ −0.492423 −0.0213492
$$533$$ −14.2462 −0.617072
$$534$$ −28.4924 −1.23299
$$535$$ −11.3693 −0.491538
$$536$$ 15.2311 0.657881
$$537$$ −51.2311 −2.21078
$$538$$ 44.8769 1.93478
$$539$$ 2.56155 0.110334
$$540$$ −0.630683 −0.0271403
$$541$$ −17.1922 −0.739152 −0.369576 0.929201i $$-0.620497\pi$$
−0.369576 + 0.929201i $$0.620497\pi$$
$$542$$ −24.9848 −1.07319
$$543$$ −60.4924 −2.59598
$$544$$ 11.1231 0.476899
$$545$$ 17.6847 0.757528
$$546$$ 18.2462 0.780866
$$547$$ 14.2462 0.609124 0.304562 0.952493i $$-0.401490\pi$$
0.304562 + 0.952493i $$0.401490\pi$$
$$548$$ −3.89205 −0.166260
$$549$$ −33.3693 −1.42417
$$550$$ 4.00000 0.170561
$$551$$ −6.38447 −0.271988
$$552$$ −32.0000 −1.36201
$$553$$ 6.56155 0.279026
$$554$$ 25.3693 1.07784
$$555$$ −15.3693 −0.652391
$$556$$ −3.01515 −0.127871
$$557$$ −4.87689 −0.206641 −0.103320 0.994648i $$-0.532947\pi$$
−0.103320 + 0.994648i $$0.532947\pi$$
$$558$$ 0 0
$$559$$ 41.6155 1.76015
$$560$$ 4.68466 0.197963
$$561$$ 29.9309 1.26368
$$562$$ 25.8617 1.09091
$$563$$ −28.0000 −1.18006 −0.590030 0.807382i $$-0.700884\pi$$
−0.590030 + 0.807382i $$0.700884\pi$$
$$564$$ −4.13826 −0.174252
$$565$$ −14.0000 −0.588984
$$566$$ −36.9848 −1.55459
$$567$$ 7.00000 0.293972
$$568$$ −19.5076 −0.818520
$$569$$ 34.9848 1.46664 0.733320 0.679883i $$-0.237969\pi$$
0.733320 + 0.679883i $$0.237969\pi$$
$$570$$ −4.49242 −0.188167
$$571$$ 7.50758 0.314182 0.157091 0.987584i $$-0.449788\pi$$
0.157091 + 0.987584i $$0.449788\pi$$
$$572$$ 5.12311 0.214208
$$573$$ 24.1771 1.01001
$$574$$ 4.87689 0.203558
$$575$$ −5.12311 −0.213648
$$576$$ 19.8078 0.825324
$$577$$ 13.0540 0.543444 0.271722 0.962376i $$-0.412407\pi$$
0.271722 + 0.962376i $$0.412407\pi$$
$$578$$ 5.94602 0.247322
$$579$$ 13.7538 0.571588
$$580$$ −2.49242 −0.103492
$$581$$ −4.00000 −0.165948
$$582$$ 59.2311 2.45521
$$583$$ 8.00000 0.331326
$$584$$ −10.3542 −0.428458
$$585$$ 16.2462 0.671698
$$586$$ 15.1231 0.624730
$$587$$ −9.75379 −0.402582 −0.201291 0.979531i $$-0.564514\pi$$
−0.201291 + 0.979531i $$0.564514\pi$$
$$588$$ −1.12311 −0.0463161
$$589$$ 0 0
$$590$$ −6.24621 −0.257152
$$591$$ 18.2462 0.750549
$$592$$ −28.1080 −1.15523
$$593$$ −23.4384 −0.962502 −0.481251 0.876583i $$-0.659817\pi$$
−0.481251 + 0.876583i $$0.659817\pi$$
$$594$$ −5.75379 −0.236081
$$595$$ 4.56155 0.187005
$$596$$ −1.86174 −0.0762598
$$597$$ 46.7386 1.91288
$$598$$ −36.4924 −1.49229
$$599$$ 8.80776 0.359875 0.179938 0.983678i $$-0.442410\pi$$
0.179938 + 0.983678i $$0.442410\pi$$
$$600$$ 6.24621 0.255001
$$601$$ −26.4924 −1.08065 −0.540324 0.841457i $$-0.681698\pi$$
−0.540324 + 0.841457i $$0.681698\pi$$
$$602$$ −14.2462 −0.580632
$$603$$ −22.2462 −0.905936
$$604$$ 9.61553 0.391250
$$605$$ −4.43845 −0.180449
$$606$$ −0.984845 −0.0400066
$$607$$ −4.94602 −0.200753 −0.100376 0.994950i $$-0.532005\pi$$
−0.100376 + 0.994950i $$0.532005\pi$$
$$608$$ −2.73863 −0.111066
$$609$$ −14.5616 −0.590064
$$610$$ −14.6307 −0.592379
$$611$$ 16.8078 0.679969
$$612$$ −7.12311 −0.287934
$$613$$ −8.73863 −0.352950 −0.176475 0.984305i $$-0.556469\pi$$
−0.176475 + 0.984305i $$0.556469\pi$$
$$614$$ −49.4773 −1.99674
$$615$$ 8.00000 0.322591
$$616$$ 6.24621 0.251667
$$617$$ 15.7538 0.634224 0.317112 0.948388i $$-0.397287\pi$$
0.317112 + 0.948388i $$0.397287\pi$$
$$618$$ −5.75379 −0.231451
$$619$$ −42.1080 −1.69246 −0.846231 0.532817i $$-0.821134\pi$$
−0.846231 + 0.532817i $$0.821134\pi$$
$$620$$ 0 0
$$621$$ 7.36932 0.295720
$$622$$ −15.0152 −0.602053
$$623$$ −7.12311 −0.285381
$$624$$ 54.7386 2.19130
$$625$$ 1.00000 0.0400000
$$626$$ 48.8769 1.95351
$$627$$ −7.36932 −0.294302
$$628$$ 1.64584 0.0656761
$$629$$ −27.3693 −1.09129
$$630$$ −5.56155 −0.221578
$$631$$ 8.80776 0.350632 0.175316 0.984512i $$-0.443905\pi$$
0.175316 + 0.984512i $$0.443905\pi$$
$$632$$ 16.0000 0.636446
$$633$$ 59.0540 2.34718
$$634$$ −35.1231 −1.39492
$$635$$ 10.2462 0.406608
$$636$$ −3.50758 −0.139084
$$637$$ 4.56155 0.180735
$$638$$ −22.7386 −0.900231
$$639$$ 28.4924 1.12714
$$640$$ 13.5616 0.536067
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 45.4773 1.79484
$$643$$ −2.56155 −0.101018 −0.0505089 0.998724i $$-0.516084\pi$$
−0.0505089 + 0.998724i $$0.516084\pi$$
$$644$$ 2.24621 0.0885131
$$645$$ −23.3693 −0.920166
$$646$$ −8.00000 −0.314756
$$647$$ 3.50758 0.137897 0.0689486 0.997620i $$-0.478036\pi$$
0.0689486 + 0.997620i $$0.478036\pi$$
$$648$$ 17.0691 0.670539
$$649$$ −10.2462 −0.402199
$$650$$ 7.12311 0.279391
$$651$$ 0 0
$$652$$ 0.492423 0.0192848
$$653$$ 49.2311 1.92656 0.963280 0.268499i $$-0.0865275\pi$$
0.963280 + 0.268499i $$0.0865275\pi$$
$$654$$ −70.7386 −2.76610
$$655$$ −9.12311 −0.356469
$$656$$ 14.6307 0.571232
$$657$$ 15.1231 0.590009
$$658$$ −5.75379 −0.224306
$$659$$ −36.1771 −1.40926 −0.704629 0.709575i $$-0.748887\pi$$
−0.704629 + 0.709575i $$0.748887\pi$$
$$660$$ −2.87689 −0.111983
$$661$$ 3.12311 0.121475 0.0607374 0.998154i $$-0.480655\pi$$
0.0607374 + 0.998154i $$0.480655\pi$$
$$662$$ 18.7386 0.728298
$$663$$ 53.3002 2.07001
$$664$$ −9.75379 −0.378520
$$665$$ −1.12311 −0.0435522
$$666$$ 33.3693 1.29303
$$667$$ 29.1231 1.12765
$$668$$ 9.61553 0.372036
$$669$$ 16.8078 0.649826
$$670$$ −9.75379 −0.376822
$$671$$ −24.0000 −0.926510
$$672$$ −6.24621 −0.240953
$$673$$ −25.8617 −0.996897 −0.498448 0.866919i $$-0.666097\pi$$
−0.498448 + 0.866919i $$0.666097\pi$$
$$674$$ −53.8617 −2.07468
$$675$$ −1.43845 −0.0553659
$$676$$ 3.42329 0.131665
$$677$$ −23.9309 −0.919738 −0.459869 0.887987i $$-0.652104\pi$$
−0.459869 + 0.887987i $$0.652104\pi$$
$$678$$ 56.0000 2.15067
$$679$$ 14.8078 0.568270
$$680$$ 11.1231 0.426552
$$681$$ −60.6695 −2.32486
$$682$$ 0 0
$$683$$ 42.7386 1.63535 0.817674 0.575681i $$-0.195263\pi$$
0.817674 + 0.575681i $$0.195263\pi$$
$$684$$ 1.75379 0.0670578
$$685$$ −8.87689 −0.339169
$$686$$ −1.56155 −0.0596204
$$687$$ −48.9848 −1.86889
$$688$$ −42.7386 −1.62940
$$689$$ 14.2462 0.542737
$$690$$ 20.4924 0.780133
$$691$$ 8.49242 0.323067 0.161533 0.986867i $$-0.448356\pi$$
0.161533 + 0.986867i $$0.448356\pi$$
$$692$$ −3.75379 −0.142698
$$693$$ −9.12311 −0.346558
$$694$$ −1.75379 −0.0665729
$$695$$ −6.87689 −0.260855
$$696$$ −35.5076 −1.34591
$$697$$ 14.2462 0.539614
$$698$$ −35.1231 −1.32943
$$699$$ 8.00000 0.302588
$$700$$ −0.438447 −0.0165717
$$701$$ 0.0691303 0.00261102 0.00130551 0.999999i $$-0.499584\pi$$
0.00130551 + 0.999999i $$0.499584\pi$$
$$702$$ −10.2462 −0.386718
$$703$$ 6.73863 0.254152
$$704$$ 14.2462 0.536924
$$705$$ −9.43845 −0.355472
$$706$$ −23.1231 −0.870250
$$707$$ −0.246211 −0.00925973
$$708$$ 4.49242 0.168836
$$709$$ −18.1771 −0.682655 −0.341327 0.939945i $$-0.610876\pi$$
−0.341327 + 0.939945i $$0.610876\pi$$
$$710$$ 12.4924 0.468832
$$711$$ −23.3693 −0.876418
$$712$$ −17.3693 −0.650943
$$713$$ 0 0
$$714$$ −18.2462 −0.682847
$$715$$ 11.6847 0.436981
$$716$$ 8.76894 0.327711
$$717$$ 2.06913 0.0772731
$$718$$ 12.4924 0.466213
$$719$$ 49.6155 1.85035 0.925173 0.379544i $$-0.123919\pi$$
0.925173 + 0.379544i $$0.123919\pi$$
$$720$$ −16.6847 −0.621801
$$721$$ −1.43845 −0.0535706
$$722$$ −27.6998 −1.03088
$$723$$ −31.3693 −1.16664
$$724$$ 10.3542 0.384809
$$725$$ −5.68466 −0.211123
$$726$$ 17.7538 0.658905
$$727$$ 19.5076 0.723496 0.361748 0.932276i $$-0.382180\pi$$
0.361748 + 0.932276i $$0.382180\pi$$
$$728$$ 11.1231 0.412250
$$729$$ −35.9848 −1.33277
$$730$$ 6.63068 0.245413
$$731$$ −41.6155 −1.53921
$$732$$ 10.5227 0.388931
$$733$$ −5.68466 −0.209968 −0.104984 0.994474i $$-0.533479\pi$$
−0.104984 + 0.994474i $$0.533479\pi$$
$$734$$ 5.75379 0.212376
$$735$$ −2.56155 −0.0944843
$$736$$ 12.4924 0.460477
$$737$$ −16.0000 −0.589368
$$738$$ −17.3693 −0.639373
$$739$$ 6.06913 0.223257 0.111628 0.993750i $$-0.464393\pi$$
0.111628 + 0.993750i $$0.464393\pi$$
$$740$$ 2.63068 0.0967058
$$741$$ −13.1231 −0.482089
$$742$$ −4.87689 −0.179036
$$743$$ 32.9848 1.21010 0.605048 0.796189i $$-0.293154\pi$$
0.605048 + 0.796189i $$0.293154\pi$$
$$744$$ 0 0
$$745$$ −4.24621 −0.155569
$$746$$ 45.8617 1.67912
$$747$$ 14.2462 0.521242
$$748$$ −5.12311 −0.187319
$$749$$ 11.3693 0.415426
$$750$$ −4.00000 −0.146059
$$751$$ 45.9309 1.67604 0.838021 0.545639i $$-0.183713\pi$$
0.838021 + 0.545639i $$0.183713\pi$$
$$752$$ −17.2614 −0.629457
$$753$$ 43.8617 1.59841
$$754$$ −40.4924 −1.47465
$$755$$ 21.9309 0.798146
$$756$$ 0.630683 0.0229377
$$757$$ 14.6307 0.531761 0.265881 0.964006i $$-0.414337\pi$$
0.265881 + 0.964006i $$0.414337\pi$$
$$758$$ 25.7538 0.935420
$$759$$ 33.6155 1.22017
$$760$$ −2.73863 −0.0993407
$$761$$ 31.7538 1.15107 0.575537 0.817776i $$-0.304793\pi$$
0.575537 + 0.817776i $$0.304793\pi$$
$$762$$ −40.9848 −1.48472
$$763$$ −17.6847 −0.640228
$$764$$ −4.13826 −0.149717
$$765$$ −16.2462 −0.587383
$$766$$ −16.0000 −0.578103
$$767$$ −18.2462 −0.658833
$$768$$ −25.7538 −0.929310
$$769$$ −9.50758 −0.342852 −0.171426 0.985197i $$-0.554837\pi$$
−0.171426 + 0.985197i $$0.554837\pi$$
$$770$$ −4.00000 −0.144150
$$771$$ −57.6155 −2.07497
$$772$$ −2.35416 −0.0847281
$$773$$ 8.06913 0.290226 0.145113 0.989415i $$-0.453645\pi$$
0.145113 + 0.989415i $$0.453645\pi$$
$$774$$ 50.7386 1.82376
$$775$$ 0 0
$$776$$ 36.1080 1.29620
$$777$$ 15.3693 0.551371
$$778$$ 6.13826 0.220067
$$779$$ −3.50758 −0.125672
$$780$$ −5.12311 −0.183437
$$781$$ 20.4924 0.733277
$$782$$ 36.4924 1.30497
$$783$$ 8.17708 0.292225
$$784$$ −4.68466 −0.167309
$$785$$ 3.75379 0.133978
$$786$$ 36.4924 1.30164
$$787$$ −3.82292 −0.136272 −0.0681362 0.997676i $$-0.521705\pi$$
−0.0681362 + 0.997676i $$0.521705\pi$$
$$788$$ −3.12311 −0.111256
$$789$$ 54.1080 1.92629
$$790$$ −10.2462 −0.364544
$$791$$ 14.0000 0.497783
$$792$$ −22.2462 −0.790485
$$793$$ −42.7386 −1.51769
$$794$$ 36.6004 1.29890
$$795$$ −8.00000 −0.283731
$$796$$ −8.00000 −0.283552
$$797$$ −13.0540 −0.462396 −0.231198 0.972907i $$-0.574264\pi$$
−0.231198 + 0.972907i $$0.574264\pi$$
$$798$$ 4.49242 0.159030
$$799$$ −16.8078 −0.594616
$$800$$ −2.43845 −0.0862121
$$801$$ 25.3693 0.896381
$$802$$ 42.8466 1.51297
$$803$$ 10.8769 0.383837
$$804$$ 7.01515 0.247405
$$805$$ 5.12311 0.180566
$$806$$ 0 0
$$807$$ −73.6155 −2.59139
$$808$$ −0.600373 −0.0211211
$$809$$ −53.5464 −1.88259 −0.941296 0.337584i $$-0.890390\pi$$
−0.941296 + 0.337584i $$0.890390\pi$$
$$810$$ −10.9309 −0.384072
$$811$$ −21.6155 −0.759024 −0.379512 0.925187i $$-0.623908\pi$$
−0.379512 + 0.925187i $$0.623908\pi$$
$$812$$ 2.49242 0.0874669
$$813$$ 40.9848 1.43740
$$814$$ 24.0000 0.841200
$$815$$ 1.12311 0.0393407
$$816$$ −54.7386 −1.91624
$$817$$ 10.2462 0.358470
$$818$$ −41.3693 −1.44644
$$819$$ −16.2462 −0.567689
$$820$$ −1.36932 −0.0478186
$$821$$ 40.4233 1.41078 0.705391 0.708818i $$-0.250771\pi$$
0.705391 + 0.708818i $$0.250771\pi$$
$$822$$ 35.5076 1.23847
$$823$$ −3.50758 −0.122266 −0.0611332 0.998130i $$-0.519471\pi$$
−0.0611332 + 0.998130i $$0.519471\pi$$
$$824$$ −3.50758 −0.122192
$$825$$ −6.56155 −0.228444
$$826$$ 6.24621 0.217333
$$827$$ 19.3693 0.673537 0.336769 0.941587i $$-0.390666\pi$$
0.336769 + 0.941587i $$0.390666\pi$$
$$828$$ −8.00000 −0.278019
$$829$$ 43.1231 1.49773 0.748864 0.662724i $$-0.230600\pi$$
0.748864 + 0.662724i $$0.230600\pi$$
$$830$$ 6.24621 0.216809
$$831$$ −41.6155 −1.44363
$$832$$ 25.3693 0.879523
$$833$$ −4.56155 −0.158048
$$834$$ 27.5076 0.952510
$$835$$ 21.9309 0.758949
$$836$$ 1.26137 0.0436253
$$837$$ 0 0
$$838$$ 15.2311 0.526148
$$839$$ −37.1231 −1.28163 −0.640816 0.767695i $$-0.721404\pi$$
−0.640816 + 0.767695i $$0.721404\pi$$
$$840$$ −6.24621 −0.215515
$$841$$ 3.31534 0.114322
$$842$$ 15.1231 0.521177
$$843$$ −42.4233 −1.46114
$$844$$ −10.1080 −0.347930
$$845$$ 7.80776 0.268595
$$846$$ 20.4924 0.704544
$$847$$ 4.43845 0.152507
$$848$$ −14.6307 −0.502420
$$849$$ 60.6695 2.08217
$$850$$ −7.12311 −0.244321
$$851$$ −30.7386 −1.05371
$$852$$ −8.98485 −0.307816
$$853$$ −56.7386 −1.94269 −0.971347 0.237666i $$-0.923618\pi$$
−0.971347 + 0.237666i $$0.923618\pi$$
$$854$$ 14.6307 0.500652
$$855$$ 4.00000 0.136797
$$856$$ 27.7235 0.947569
$$857$$ −32.2462 −1.10151 −0.550755 0.834667i $$-0.685660\pi$$
−0.550755 + 0.834667i $$0.685660\pi$$
$$858$$ −46.7386 −1.59563
$$859$$ 16.4924 0.562714 0.281357 0.959603i $$-0.409215\pi$$
0.281357 + 0.959603i $$0.409215\pi$$
$$860$$ 4.00000 0.136399
$$861$$ −8.00000 −0.272639
$$862$$ 1.26137 0.0429623
$$863$$ −42.2462 −1.43808 −0.719039 0.694970i $$-0.755418\pi$$
−0.719039 + 0.694970i $$0.755418\pi$$
$$864$$ 3.50758 0.119330
$$865$$ −8.56155 −0.291102
$$866$$ −12.8769 −0.437575
$$867$$ −9.75379 −0.331256
$$868$$ 0 0
$$869$$ −16.8078 −0.570164
$$870$$ 22.7386 0.770912
$$871$$ −28.4924 −0.965429
$$872$$ −43.1231 −1.46033
$$873$$ −52.7386 −1.78493
$$874$$ −8.98485 −0.303917
$$875$$ −1.00000 −0.0338062
$$876$$ −4.76894 −0.161128
$$877$$ −23.7538 −0.802108 −0.401054 0.916054i $$-0.631356\pi$$
−0.401054 + 0.916054i $$0.631356\pi$$
$$878$$ −24.0000 −0.809961
$$879$$ −24.8078 −0.836745
$$880$$ −12.0000 −0.404520
$$881$$ 45.8617 1.54512 0.772561 0.634941i $$-0.218976\pi$$
0.772561 + 0.634941i $$0.218976\pi$$
$$882$$ 5.56155 0.187267
$$883$$ 24.4924 0.824236 0.412118 0.911131i $$-0.364789\pi$$
0.412118 + 0.911131i $$0.364789\pi$$
$$884$$ −9.12311 −0.306843
$$885$$ 10.2462 0.344423
$$886$$ −42.7386 −1.43583
$$887$$ −12.4924 −0.419454 −0.209727 0.977760i $$-0.567258\pi$$
−0.209727 + 0.977760i $$0.567258\pi$$
$$888$$ 37.4773 1.25765
$$889$$ −10.2462 −0.343647
$$890$$ 11.1231 0.372847
$$891$$ −17.9309 −0.600707
$$892$$ −2.87689 −0.0963255
$$893$$ 4.13826 0.138482
$$894$$ 16.9848 0.568058
$$895$$ 20.0000 0.668526
$$896$$ −13.5616 −0.453060
$$897$$ 59.8617 1.99873
$$898$$ 29.3693 0.980067
$$899$$ 0 0
$$900$$ 1.56155 0.0520518
$$901$$ −14.2462 −0.474610
$$902$$ −12.4924 −0.415952
$$903$$ 23.3693 0.777682
$$904$$ 34.1383 1.13542
$$905$$ 23.6155 0.785007
$$906$$ −87.7235 −2.91442
$$907$$ 50.1080 1.66381 0.831904 0.554920i $$-0.187251\pi$$
0.831904 + 0.554920i $$0.187251\pi$$
$$908$$ 10.3845 0.344621
$$909$$ 0.876894 0.0290848
$$910$$ −7.12311 −0.236129
$$911$$ 4.49242 0.148841 0.0744203 0.997227i $$-0.476289\pi$$
0.0744203 + 0.997227i $$0.476289\pi$$
$$912$$ 13.4773 0.446277
$$913$$ 10.2462 0.339100
$$914$$ −13.8617 −0.458506
$$915$$ 24.0000 0.793416
$$916$$ 8.38447 0.277031
$$917$$ 9.12311 0.301271
$$918$$ 10.2462 0.338175
$$919$$ −13.3002 −0.438733 −0.219366 0.975643i $$-0.570399\pi$$
−0.219366 + 0.975643i $$0.570399\pi$$
$$920$$ 12.4924 0.411863
$$921$$ 81.1619 2.67438
$$922$$ −7.61553 −0.250804
$$923$$ 36.4924 1.20116
$$924$$ 2.87689 0.0946429
$$925$$ 6.00000 0.197279
$$926$$ −32.0000 −1.05159
$$927$$ 5.12311 0.168265
$$928$$ 13.8617 0.455034
$$929$$ −52.1080 −1.70961 −0.854803 0.518952i $$-0.826322\pi$$
−0.854803 + 0.518952i $$0.826322\pi$$
$$930$$ 0 0
$$931$$ 1.12311 0.0368083
$$932$$ −1.36932 −0.0448535
$$933$$ 24.6307 0.806372
$$934$$ 41.4773 1.35718
$$935$$ −11.6847 −0.382129
$$936$$ −39.6155 −1.29487
$$937$$ 22.6695 0.740580 0.370290 0.928916i $$-0.379258\pi$$
0.370290 + 0.928916i $$0.379258\pi$$
$$938$$ 9.75379 0.318472
$$939$$ −80.1771 −2.61648
$$940$$ 1.61553 0.0526927
$$941$$ −13.8617 −0.451880 −0.225940 0.974141i $$-0.572545\pi$$
−0.225940 + 0.974141i $$0.572545\pi$$
$$942$$ −15.0152 −0.489220
$$943$$ 16.0000 0.521032
$$944$$ 18.7386 0.609891
$$945$$ 1.43845 0.0467927
$$946$$ 36.4924 1.18647
$$947$$ 4.00000 0.129983 0.0649913 0.997886i $$-0.479298\pi$$
0.0649913 + 0.997886i $$0.479298\pi$$
$$948$$ 7.36932 0.239344
$$949$$ 19.3693 0.628755
$$950$$ 1.75379 0.0569004
$$951$$ 57.6155 1.86831
$$952$$ −11.1231 −0.360502
$$953$$ −24.8769 −0.805842 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$954$$ 17.3693 0.562352
$$955$$ −9.43845 −0.305421
$$956$$ −0.354162 −0.0114544
$$957$$ 37.3002 1.20574
$$958$$ 20.4924 0.662080
$$959$$ 8.87689 0.286650
$$960$$ −14.2462 −0.459794
$$961$$ −31.0000 −1.00000
$$962$$ 42.7386 1.37795
$$963$$ −40.4924 −1.30485
$$964$$ 5.36932 0.172934
$$965$$ −5.36932 −0.172844
$$966$$ −20.4924 −0.659333
$$967$$ −26.8769 −0.864303 −0.432151 0.901801i $$-0.642245\pi$$
−0.432151 + 0.901801i $$0.642245\pi$$
$$968$$ 10.8229 0.347862
$$969$$ 13.1231 0.421575
$$970$$ −23.1231 −0.742438
$$971$$ −49.4773 −1.58780 −0.793901 0.608048i $$-0.791953\pi$$
−0.793901 + 0.608048i $$0.791953\pi$$
$$972$$ 9.75379 0.312853
$$973$$ 6.87689 0.220463
$$974$$ 8.00000 0.256337
$$975$$ −11.6847 −0.374209
$$976$$ 43.8920 1.40495
$$977$$ −49.2311 −1.57504 −0.787521 0.616288i $$-0.788636\pi$$
−0.787521 + 0.616288i $$0.788636\pi$$
$$978$$ −4.49242 −0.143652
$$979$$ 18.2462 0.583151
$$980$$ 0.438447 0.0140057
$$981$$ 62.9848 2.01095
$$982$$ 6.52273 0.208149
$$983$$ −10.4233 −0.332451 −0.166226 0.986088i $$-0.553158\pi$$
−0.166226 + 0.986088i $$0.553158\pi$$
$$984$$ −19.5076 −0.621879
$$985$$ −7.12311 −0.226961
$$986$$ 40.4924 1.28954
$$987$$ 9.43845 0.300429
$$988$$ 2.24621 0.0714615
$$989$$ −46.7386 −1.48620
$$990$$ 14.2462 0.452774
$$991$$ −20.4924 −0.650963 −0.325482 0.945548i $$-0.605526\pi$$
−0.325482 + 0.945548i $$0.605526\pi$$
$$992$$ 0 0
$$993$$ −30.7386 −0.975461
$$994$$ −12.4924 −0.396236
$$995$$ −18.2462 −0.578444
$$996$$ −4.49242 −0.142348
$$997$$ 9.68466 0.306716 0.153358 0.988171i $$-0.450991\pi$$
0.153358 + 0.988171i $$0.450991\pi$$
$$998$$ −6.52273 −0.206473
$$999$$ −8.63068 −0.273063
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 35.2.a.b.1.2 2
3.2 odd 2 315.2.a.e.1.1 2
4.3 odd 2 560.2.a.i.1.2 2
5.2 odd 4 175.2.b.b.99.3 4
5.3 odd 4 175.2.b.b.99.2 4
5.4 even 2 175.2.a.f.1.1 2
7.2 even 3 245.2.e.i.116.1 4
7.3 odd 6 245.2.e.h.226.1 4
7.4 even 3 245.2.e.i.226.1 4
7.5 odd 6 245.2.e.h.116.1 4
7.6 odd 2 245.2.a.d.1.2 2
8.3 odd 2 2240.2.a.bd.1.1 2
8.5 even 2 2240.2.a.bh.1.2 2
11.10 odd 2 4235.2.a.m.1.1 2
12.11 even 2 5040.2.a.bt.1.2 2
13.12 even 2 5915.2.a.l.1.1 2
15.2 even 4 1575.2.d.e.1324.2 4
15.8 even 4 1575.2.d.e.1324.3 4
15.14 odd 2 1575.2.a.p.1.2 2
20.3 even 4 2800.2.g.t.449.4 4
20.7 even 4 2800.2.g.t.449.1 4
20.19 odd 2 2800.2.a.bi.1.1 2
21.20 even 2 2205.2.a.x.1.1 2
28.27 even 2 3920.2.a.bs.1.1 2
35.13 even 4 1225.2.b.f.99.2 4
35.27 even 4 1225.2.b.f.99.3 4
35.34 odd 2 1225.2.a.s.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.a.b.1.2 2 1.1 even 1 trivial
175.2.a.f.1.1 2 5.4 even 2
175.2.b.b.99.2 4 5.3 odd 4
175.2.b.b.99.3 4 5.2 odd 4
245.2.a.d.1.2 2 7.6 odd 2
245.2.e.h.116.1 4 7.5 odd 6
245.2.e.h.226.1 4 7.3 odd 6
245.2.e.i.116.1 4 7.2 even 3
245.2.e.i.226.1 4 7.4 even 3
315.2.a.e.1.1 2 3.2 odd 2
560.2.a.i.1.2 2 4.3 odd 2
1225.2.a.s.1.1 2 35.34 odd 2
1225.2.b.f.99.2 4 35.13 even 4
1225.2.b.f.99.3 4 35.27 even 4
1575.2.a.p.1.2 2 15.14 odd 2
1575.2.d.e.1324.2 4 15.2 even 4
1575.2.d.e.1324.3 4 15.8 even 4
2205.2.a.x.1.1 2 21.20 even 2
2240.2.a.bd.1.1 2 8.3 odd 2
2240.2.a.bh.1.2 2 8.5 even 2
2800.2.a.bi.1.1 2 20.19 odd 2
2800.2.g.t.449.1 4 20.7 even 4
2800.2.g.t.449.4 4 20.3 even 4
3920.2.a.bs.1.1 2 28.27 even 2
4235.2.a.m.1.1 2 11.10 odd 2
5040.2.a.bt.1.2 2 12.11 even 2
5915.2.a.l.1.1 2 13.12 even 2