# Properties

 Label 1183.2.c.g.337.3 Level $1183$ Weight $2$ Character 1183.337 Analytic conductor $9.446$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1183 = 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1183.c (of order $$2$$, degree $$1$$, not 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: $$9.44630255912$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.11667456256.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} + 13x^{6} + 44x^{4} + 21x^{2} + 1$$ x^8 + 13*x^6 + 44*x^4 + 21*x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 337.3 Root $$-0.710287i$$ of defining polynomial Character $$\chi$$ $$=$$ 1183.337 Dual form 1183.2.c.g.337.6

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.710287i q^{2} +2.40788 q^{3} +1.49549 q^{4} -1.28971i q^{5} -1.71029i q^{6} +1.00000i q^{7} -2.48280i q^{8} +2.79790 q^{9} +O(q^{10})$$ $$q-0.710287i q^{2} +2.40788 q^{3} +1.49549 q^{4} -1.28971i q^{5} -1.71029i q^{6} +1.00000i q^{7} -2.48280i q^{8} +2.79790 q^{9} -0.916066 q^{10} +2.40788i q^{11} +3.60097 q^{12} +0.710287 q^{14} -3.10548i q^{15} +1.22748 q^{16} -3.90338 q^{17} -1.98731i q^{18} -5.89068i q^{19} -1.92876i q^{20} +2.40788i q^{21} +1.71029 q^{22} +6.32395 q^{23} -5.97829i q^{24} +3.33664 q^{25} -0.486640 q^{27} +1.49549i q^{28} +5.61366 q^{29} -2.20578 q^{30} +2.20578i q^{31} -5.83747i q^{32} +5.79790i q^{33} +2.77252i q^{34} +1.28971 q^{35} +4.18424 q^{36} +5.11817i q^{37} -4.18407 q^{38} -3.20210 q^{40} -7.78521i q^{41} +1.71029 q^{42} -0.289713 q^{43} +3.60097i q^{44} -3.60849i q^{45} -4.49182i q^{46} -1.27702i q^{47} +2.95564 q^{48} -1.00000 q^{49} -2.36997i q^{50} -9.39887 q^{51} -13.6225 q^{53} +0.345654i q^{54} +3.10548 q^{55} +2.48280 q^{56} -14.1841i q^{57} -3.98731i q^{58} +4.03056i q^{59} -4.64422i q^{60} -4.60097 q^{61} +1.56674 q^{62} +2.79790i q^{63} -1.69131 q^{64} +4.11817 q^{66} +7.57559i q^{67} -5.83747 q^{68} +15.2273 q^{69} -0.916066i q^{70} +7.22732i q^{71} -6.94662i q^{72} +15.0125i q^{73} +3.63537 q^{74} +8.03424 q^{75} -8.80948i q^{76} -2.40788 q^{77} -9.30758 q^{79} -1.58310i q^{80} -9.56546 q^{81} -5.52973 q^{82} -1.36463i q^{83} +3.60097i q^{84} +5.03424i q^{85} +0.205780i q^{86} +13.5170 q^{87} +5.97829 q^{88} +0.899698i q^{89} -2.56306 q^{90} +9.45742 q^{92} +5.31126i q^{93} -0.907052 q^{94} -7.59729 q^{95} -14.0559i q^{96} +15.6658i q^{97} +0.710287i q^{98} +6.73701i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 2 q^{3} - 10 q^{4} + 14 q^{9}+O(q^{10})$$ 8 * q + 2 * q^3 - 10 * q^4 + 14 * q^9 $$8 q + 2 q^{3} - 10 q^{4} + 14 q^{9} + 22 q^{10} - 24 q^{12} + 2 q^{14} + 38 q^{16} + 8 q^{17} + 10 q^{22} + 4 q^{23} - 10 q^{25} - 52 q^{27} + 2 q^{29} + 8 q^{30} + 14 q^{35} + 68 q^{36} + 46 q^{38} - 34 q^{40} + 10 q^{42} - 6 q^{43} + 22 q^{48} - 8 q^{49} - 14 q^{51} + 4 q^{53} - 6 q^{55} - 12 q^{56} + 16 q^{61} + 10 q^{62} - 28 q^{64} + 12 q^{66} - 66 q^{68} + 36 q^{69} + 40 q^{74} + 14 q^{75} - 2 q^{77} - 52 q^{79} + 48 q^{81} + 28 q^{82} + 26 q^{87} - 6 q^{88} - 52 q^{90} + 24 q^{92} + 66 q^{94} - 42 q^{95}+O(q^{100})$$ 8 * q + 2 * q^3 - 10 * q^4 + 14 * q^9 + 22 * q^10 - 24 * q^12 + 2 * q^14 + 38 * q^16 + 8 * q^17 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 52 * q^27 + 2 * q^29 + 8 * q^30 + 14 * q^35 + 68 * q^36 + 46 * q^38 - 34 * q^40 + 10 * q^42 - 6 * q^43 + 22 * q^48 - 8 * q^49 - 14 * q^51 + 4 * q^53 - 6 * q^55 - 12 * q^56 + 16 * q^61 + 10 * q^62 - 28 * q^64 + 12 * q^66 - 66 * q^68 + 36 * q^69 + 40 * q^74 + 14 * q^75 - 2 * q^77 - 52 * q^79 + 48 * q^81 + 28 * q^82 + 26 * q^87 - 6 * q^88 - 52 * q^90 + 24 * q^92 + 66 * q^94 - 42 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$$.

 $$n$$ $$339$$ $$1016$$ $$\chi(n)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ − 0.710287i − 0.502249i −0.967955 0.251124i $$-0.919200\pi$$
0.967955 0.251124i $$-0.0808003\pi$$
$$3$$ 2.40788 1.39019 0.695096 0.718917i $$-0.255362\pi$$
0.695096 + 0.718917i $$0.255362\pi$$
$$4$$ 1.49549 0.747746
$$5$$ − 1.28971i − 0.576777i −0.957513 0.288389i $$-0.906880\pi$$
0.957513 0.288389i $$-0.0931195\pi$$
$$6$$ − 1.71029i − 0.698222i
$$7$$ 1.00000i 0.377964i
$$8$$ − 2.48280i − 0.877803i
$$9$$ 2.79790 0.932632
$$10$$ −0.916066 −0.289686
$$11$$ 2.40788i 0.726004i 0.931788 + 0.363002i $$0.118248\pi$$
−0.931788 + 0.363002i $$0.881752\pi$$
$$12$$ 3.60097 1.03951
$$13$$ 0 0
$$14$$ 0.710287 0.189832
$$15$$ − 3.10548i − 0.801831i
$$16$$ 1.22748 0.306871
$$17$$ −3.90338 −0.946708 −0.473354 0.880872i $$-0.656957\pi$$
−0.473354 + 0.880872i $$0.656957\pi$$
$$18$$ − 1.98731i − 0.468413i
$$19$$ − 5.89068i − 1.35142i −0.737170 0.675708i $$-0.763838\pi$$
0.737170 0.675708i $$-0.236162\pi$$
$$20$$ − 1.92876i − 0.431283i
$$21$$ 2.40788i 0.525443i
$$22$$ 1.71029 0.364634
$$23$$ 6.32395 1.31863 0.659317 0.751865i $$-0.270845\pi$$
0.659317 + 0.751865i $$0.270845\pi$$
$$24$$ − 5.97829i − 1.22031i
$$25$$ 3.33664 0.667328
$$26$$ 0 0
$$27$$ −0.486640 −0.0936539
$$28$$ 1.49549i 0.282622i
$$29$$ 5.61366 1.04243 0.521215 0.853425i $$-0.325479\pi$$
0.521215 + 0.853425i $$0.325479\pi$$
$$30$$ −2.20578 −0.402718
$$31$$ 2.20578i 0.396170i 0.980185 + 0.198085i $$0.0634722\pi$$
−0.980185 + 0.198085i $$0.936528\pi$$
$$32$$ − 5.83747i − 1.03193i
$$33$$ 5.79790i 1.00928i
$$34$$ 2.77252i 0.475482i
$$35$$ 1.28971 0.218001
$$36$$ 4.18424 0.697373
$$37$$ 5.11817i 0.841422i 0.907195 + 0.420711i $$0.138219\pi$$
−0.907195 + 0.420711i $$0.861781\pi$$
$$38$$ −4.18407 −0.678746
$$39$$ 0 0
$$40$$ −3.20210 −0.506297
$$41$$ − 7.78521i − 1.21584i −0.793996 0.607922i $$-0.792003\pi$$
0.793996 0.607922i $$-0.207997\pi$$
$$42$$ 1.71029 0.263903
$$43$$ −0.289713 −0.0441809 −0.0220904 0.999756i $$-0.507032\pi$$
−0.0220904 + 0.999756i $$0.507032\pi$$
$$44$$ 3.60097i 0.542867i
$$45$$ − 3.60849i − 0.537921i
$$46$$ − 4.49182i − 0.662282i
$$47$$ − 1.27702i − 0.186273i −0.995653 0.0931364i $$-0.970311\pi$$
0.995653 0.0931364i $$-0.0296893\pi$$
$$48$$ 2.95564 0.426610
$$49$$ −1.00000 −0.142857
$$50$$ − 2.36997i − 0.335164i
$$51$$ −9.39887 −1.31610
$$52$$ 0 0
$$53$$ −13.6225 −1.87120 −0.935598 0.353067i $$-0.885139\pi$$
−0.935598 + 0.353067i $$0.885139\pi$$
$$54$$ 0.345654i 0.0470375i
$$55$$ 3.10548 0.418743
$$56$$ 2.48280 0.331778
$$57$$ − 14.1841i − 1.87873i
$$58$$ − 3.98731i − 0.523559i
$$59$$ 4.03056i 0.524734i 0.964968 + 0.262367i $$0.0845031\pi$$
−0.964968 + 0.262367i $$0.915497\pi$$
$$60$$ − 4.64422i − 0.599566i
$$61$$ −4.60097 −0.589094 −0.294547 0.955637i $$-0.595169\pi$$
−0.294547 + 0.955637i $$0.595169\pi$$
$$62$$ 1.56674 0.198976
$$63$$ 2.79790i 0.352502i
$$64$$ −1.69131 −0.211413
$$65$$ 0 0
$$66$$ 4.11817 0.506912
$$67$$ 7.57559i 0.925505i 0.886487 + 0.462753i $$0.153138\pi$$
−0.886487 + 0.462753i $$0.846862\pi$$
$$68$$ −5.83747 −0.707897
$$69$$ 15.2273 1.83315
$$70$$ − 0.916066i − 0.109491i
$$71$$ 7.22732i 0.857726i 0.903370 + 0.428863i $$0.141086\pi$$
−0.903370 + 0.428863i $$0.858914\pi$$
$$72$$ − 6.94662i − 0.818668i
$$73$$ 15.0125i 1.75708i 0.477665 + 0.878542i $$0.341483\pi$$
−0.477665 + 0.878542i $$0.658517\pi$$
$$74$$ 3.63537 0.422603
$$75$$ 8.03424 0.927714
$$76$$ − 8.80948i − 1.01052i
$$77$$ −2.40788 −0.274404
$$78$$ 0 0
$$79$$ −9.30758 −1.04718 −0.523592 0.851969i $$-0.675408\pi$$
−0.523592 + 0.851969i $$0.675408\pi$$
$$80$$ − 1.58310i − 0.176996i
$$81$$ −9.56546 −1.06283
$$82$$ −5.52973 −0.610656
$$83$$ − 1.36463i − 0.149788i −0.997192 0.0748940i $$-0.976138\pi$$
0.997192 0.0748940i $$-0.0238618\pi$$
$$84$$ 3.60097i 0.392898i
$$85$$ 5.03424i 0.546039i
$$86$$ 0.205780i 0.0221898i
$$87$$ 13.5170 1.44918
$$88$$ 5.97829 0.637288
$$89$$ 0.899698i 0.0953678i 0.998862 + 0.0476839i $$0.0151840\pi$$
−0.998862 + 0.0476839i $$0.984816\pi$$
$$90$$ −2.56306 −0.270170
$$91$$ 0 0
$$92$$ 9.45742 0.986004
$$93$$ 5.31126i 0.550752i
$$94$$ −0.907052 −0.0935553
$$95$$ −7.59729 −0.779466
$$96$$ − 14.0559i − 1.43458i
$$97$$ 15.6658i 1.59062i 0.606205 + 0.795309i $$0.292691\pi$$
−0.606205 + 0.795309i $$0.707309\pi$$
$$98$$ 0.710287i 0.0717498i
$$99$$ 6.73701i 0.677095i
$$100$$ 4.98992 0.498992
$$101$$ −0.684905 −0.0681506 −0.0340753 0.999419i $$-0.510849\pi$$
−0.0340753 + 0.999419i $$0.510849\pi$$
$$102$$ 6.67589i 0.661012i
$$103$$ −17.9249 −1.76619 −0.883097 0.469190i $$-0.844546\pi$$
−0.883097 + 0.469190i $$0.844546\pi$$
$$104$$ 0 0
$$105$$ 3.10548 0.303064
$$106$$ 9.67589i 0.939806i
$$107$$ 8.49549 0.821290 0.410645 0.911795i $$-0.365304\pi$$
0.410645 + 0.911795i $$0.365304\pi$$
$$108$$ −0.727766 −0.0700293
$$109$$ 12.0928i 1.15828i 0.815228 + 0.579139i $$0.196611\pi$$
−0.815228 + 0.579139i $$0.803389\pi$$
$$110$$ − 2.20578i − 0.210313i
$$111$$ 12.3239i 1.16974i
$$112$$ 1.22748i 0.115986i
$$113$$ −14.2527 −1.34078 −0.670391 0.742008i $$-0.733874\pi$$
−0.670391 + 0.742008i $$0.733874\pi$$
$$114$$ −10.0748 −0.943588
$$115$$ − 8.15608i − 0.760558i
$$116$$ 8.39519 0.779474
$$117$$ 0 0
$$118$$ 2.86285 0.263547
$$119$$ − 3.90338i − 0.357822i
$$120$$ −7.71029 −0.703850
$$121$$ 5.20210 0.472918
$$122$$ 3.26801i 0.295872i
$$123$$ − 18.7459i − 1.69026i
$$124$$ 3.29873i 0.296234i
$$125$$ − 10.7519i − 0.961677i
$$126$$ 1.98731 0.177044
$$127$$ 8.82462 0.783058 0.391529 0.920166i $$-0.371946\pi$$
0.391529 + 0.920166i $$0.371946\pi$$
$$128$$ − 10.4736i − 0.925747i
$$129$$ −0.697596 −0.0614199
$$130$$ 0 0
$$131$$ −19.4294 −1.69756 −0.848778 0.528749i $$-0.822661\pi$$
−0.848778 + 0.528749i $$0.822661\pi$$
$$132$$ 8.67071i 0.754689i
$$133$$ 5.89068 0.510787
$$134$$ 5.38084 0.464834
$$135$$ 0.627626i 0.0540174i
$$136$$ 9.69131i 0.831023i
$$137$$ − 10.2362i − 0.874536i −0.899331 0.437268i $$-0.855946\pi$$
0.899331 0.437268i $$-0.144054\pi$$
$$138$$ − 10.8158i − 0.920699i
$$139$$ 8.14723 0.691039 0.345519 0.938412i $$-0.387703\pi$$
0.345519 + 0.938412i $$0.387703\pi$$
$$140$$ 1.92876 0.163010
$$141$$ − 3.07492i − 0.258955i
$$142$$ 5.13347 0.430791
$$143$$ 0 0
$$144$$ 3.43438 0.286198
$$145$$ − 7.24001i − 0.601250i
$$146$$ 10.6632 0.882493
$$147$$ −2.40788 −0.198599
$$148$$ 7.65419i 0.629170i
$$149$$ − 9.78888i − 0.801937i −0.916092 0.400968i $$-0.868674\pi$$
0.916092 0.400968i $$-0.131326\pi$$
$$150$$ − 5.70661i − 0.465943i
$$151$$ − 14.7407i − 1.19958i −0.800158 0.599790i $$-0.795251\pi$$
0.800158 0.599790i $$-0.204749\pi$$
$$152$$ −14.6254 −1.18628
$$153$$ −10.9212 −0.882930
$$154$$ 1.71029i 0.137819i
$$155$$ 2.84482 0.228502
$$156$$ 0 0
$$157$$ 20.5844 1.64282 0.821409 0.570340i $$-0.193189\pi$$
0.821409 + 0.570340i $$0.193189\pi$$
$$158$$ 6.61105i 0.525947i
$$159$$ −32.8014 −2.60132
$$160$$ −7.52866 −0.595193
$$161$$ 6.32395i 0.498397i
$$162$$ 6.79422i 0.533804i
$$163$$ 3.98086i 0.311805i 0.987772 + 0.155902i $$0.0498286\pi$$
−0.987772 + 0.155902i $$0.950171\pi$$
$$164$$ − 11.6427i − 0.909144i
$$165$$ 7.47763 0.582132
$$166$$ −0.969281 −0.0752308
$$167$$ − 8.67846i − 0.671559i −0.941941 0.335780i $$-0.891000\pi$$
0.941941 0.335780i $$-0.109000\pi$$
$$168$$ 5.97829 0.461235
$$169$$ 0 0
$$170$$ 3.57575 0.274248
$$171$$ − 16.4815i − 1.26037i
$$172$$ −0.433264 −0.0330361
$$173$$ −0.933934 −0.0710057 −0.0355028 0.999370i $$-0.511303\pi$$
−0.0355028 + 0.999370i $$0.511303\pi$$
$$174$$ − 9.60097i − 0.727848i
$$175$$ 3.33664i 0.252226i
$$176$$ 2.95564i 0.222790i
$$177$$ 9.70511i 0.729481i
$$178$$ 0.639044 0.0478984
$$179$$ −13.5461 −1.01248 −0.506241 0.862392i $$-0.668966\pi$$
−0.506241 + 0.862392i $$0.668966\pi$$
$$180$$ − 5.39646i − 0.402229i
$$181$$ 8.86269 0.658759 0.329379 0.944198i $$-0.393161\pi$$
0.329379 + 0.944198i $$0.393161\pi$$
$$182$$ 0 0
$$183$$ −11.0786 −0.818953
$$184$$ − 15.7011i − 1.15750i
$$185$$ 6.60097 0.485313
$$186$$ 3.77252 0.276614
$$187$$ − 9.39887i − 0.687313i
$$188$$ − 1.90978i − 0.139285i
$$189$$ − 0.486640i − 0.0353978i
$$190$$ 5.39626i 0.391486i
$$191$$ −15.3735 −1.11239 −0.556193 0.831053i $$-0.687739\pi$$
−0.556193 + 0.831053i $$0.687739\pi$$
$$192$$ −4.07247 −0.293905
$$193$$ 24.4953i 1.76321i 0.471986 + 0.881606i $$0.343537\pi$$
−0.471986 + 0.881606i $$0.656463\pi$$
$$194$$ 11.1272 0.798885
$$195$$ 0 0
$$196$$ −1.49549 −0.106821
$$197$$ − 6.71412i − 0.478362i −0.970975 0.239181i $$-0.923121\pi$$
0.970975 0.239181i $$-0.0768789\pi$$
$$198$$ 4.78521 0.340070
$$199$$ 4.87282 0.345425 0.172712 0.984972i $$-0.444747\pi$$
0.172712 + 0.984972i $$0.444747\pi$$
$$200$$ − 8.28421i − 0.585782i
$$201$$ 18.2411i 1.28663i
$$202$$ 0.486479i 0.0342285i
$$203$$ 5.61366i 0.394002i
$$204$$ −14.0559 −0.984113
$$205$$ −10.0407 −0.701272
$$206$$ 12.7318i 0.887069i
$$207$$ 17.6938 1.22980
$$208$$ 0 0
$$209$$ 14.1841 0.981133
$$210$$ − 2.20578i − 0.152213i
$$211$$ 3.68747 0.253856 0.126928 0.991912i $$-0.459488\pi$$
0.126928 + 0.991912i $$0.459488\pi$$
$$212$$ −20.3724 −1.39918
$$213$$ 17.4025i 1.19240i
$$214$$ − 6.03424i − 0.412492i
$$215$$ 0.373647i 0.0254825i
$$216$$ 1.20823i 0.0822096i
$$217$$ −2.20578 −0.149738
$$218$$ 8.58935 0.581744
$$219$$ 36.1484i 2.44268i
$$220$$ 4.64422 0.313113
$$221$$ 0 0
$$222$$ 8.75354 0.587499
$$223$$ 8.81426i 0.590247i 0.955459 + 0.295123i $$0.0953608\pi$$
−0.955459 + 0.295123i $$0.904639\pi$$
$$224$$ 5.83747 0.390032
$$225$$ 9.33557 0.622372
$$226$$ 10.1235i 0.673406i
$$227$$ − 13.4511i − 0.892783i −0.894838 0.446391i $$-0.852709\pi$$
0.894838 0.446391i $$-0.147291\pi$$
$$228$$ − 21.2122i − 1.40481i
$$229$$ − 6.81576i − 0.450398i −0.974313 0.225199i $$-0.927697\pi$$
0.974313 0.225199i $$-0.0723033\pi$$
$$230$$ −5.79316 −0.381989
$$231$$ −5.79790 −0.381474
$$232$$ − 13.9376i − 0.915049i
$$233$$ 25.0672 1.64221 0.821105 0.570777i $$-0.193358\pi$$
0.821105 + 0.570777i $$0.193358\pi$$
$$234$$ 0 0
$$235$$ −1.64699 −0.107438
$$236$$ 6.02767i 0.392368i
$$237$$ −22.4116 −1.45579
$$238$$ −2.77252 −0.179715
$$239$$ − 2.78521i − 0.180160i −0.995935 0.0900800i $$-0.971288\pi$$
0.995935 0.0900800i $$-0.0287123\pi$$
$$240$$ − 3.81193i − 0.246059i
$$241$$ − 6.97829i − 0.449511i −0.974415 0.224756i $$-0.927842\pi$$
0.974415 0.224756i $$-0.0721584\pi$$
$$242$$ − 3.69498i − 0.237523i
$$243$$ −21.5726 −1.38388
$$244$$ −6.88072 −0.440493
$$245$$ 1.28971i 0.0823968i
$$246$$ −13.3149 −0.848929
$$247$$ 0 0
$$248$$ 5.47651 0.347759
$$249$$ − 3.28588i − 0.208234i
$$250$$ −7.63691 −0.483001
$$251$$ 0.783029 0.0494244 0.0247122 0.999695i $$-0.492133\pi$$
0.0247122 + 0.999695i $$0.492133\pi$$
$$252$$ 4.18424i 0.263582i
$$253$$ 15.2273i 0.957334i
$$254$$ − 6.26801i − 0.393290i
$$255$$ 12.1218i 0.759099i
$$256$$ −10.8219 −0.676368
$$257$$ −3.25804 −0.203231 −0.101616 0.994824i $$-0.532401\pi$$
−0.101616 + 0.994824i $$0.532401\pi$$
$$258$$ 0.495493i 0.0308480i
$$259$$ −5.11817 −0.318028
$$260$$ 0 0
$$261$$ 15.7064 0.972205
$$262$$ 13.8005i 0.852595i
$$263$$ 29.5829 1.82416 0.912081 0.410010i $$-0.134475\pi$$
0.912081 + 0.410010i $$0.134475\pi$$
$$264$$ 14.3950 0.885953
$$265$$ 17.5691i 1.07926i
$$266$$ − 4.18407i − 0.256542i
$$267$$ 2.16637i 0.132580i
$$268$$ 11.3292i 0.692043i
$$269$$ 1.23650 0.0753907 0.0376953 0.999289i $$-0.487998\pi$$
0.0376953 + 0.999289i $$0.487998\pi$$
$$270$$ 0.445794 0.0271302
$$271$$ − 25.2071i − 1.53122i −0.643303 0.765612i $$-0.722436\pi$$
0.643303 0.765612i $$-0.277564\pi$$
$$272$$ −4.79133 −0.290517
$$273$$ 0 0
$$274$$ −7.27062 −0.439234
$$275$$ 8.03424i 0.484483i
$$276$$ 22.7724 1.37073
$$277$$ −9.53602 −0.572964 −0.286482 0.958086i $$-0.592486\pi$$
−0.286482 + 0.958086i $$0.592486\pi$$
$$278$$ − 5.78687i − 0.347073i
$$279$$ 6.17154i 0.369481i
$$280$$ − 3.20210i − 0.191362i
$$281$$ − 9.56546i − 0.570628i −0.958434 0.285314i $$-0.907902\pi$$
0.958434 0.285314i $$-0.0920978\pi$$
$$282$$ −2.18407 −0.130060
$$283$$ −11.4320 −0.679564 −0.339782 0.940504i $$-0.610353\pi$$
−0.339782 + 0.940504i $$0.610353\pi$$
$$284$$ 10.8084i 0.641361i
$$285$$ −18.2934 −1.08361
$$286$$ 0 0
$$287$$ 7.78521 0.459546
$$288$$ − 16.3326i − 0.962410i
$$289$$ −1.76366 −0.103745
$$290$$ −5.14249 −0.301977
$$291$$ 37.7213i 2.21126i
$$292$$ 22.4511i 1.31385i
$$293$$ 9.35562i 0.546561i 0.961934 + 0.273281i $$0.0881087\pi$$
−0.961934 + 0.273281i $$0.911891\pi$$
$$294$$ 1.71029i 0.0997459i
$$295$$ 5.19826 0.302655
$$296$$ 12.7074 0.738603
$$297$$ − 1.17177i − 0.0679931i
$$298$$ −6.95291 −0.402771
$$299$$ 0 0
$$300$$ 12.0151 0.693695
$$301$$ − 0.289713i − 0.0166988i
$$302$$ −10.4701 −0.602487
$$303$$ −1.64917 −0.0947423
$$304$$ − 7.23072i − 0.414711i
$$305$$ 5.93393i 0.339776i
$$306$$ 7.75721i 0.443450i
$$307$$ − 8.11449i − 0.463119i −0.972821 0.231559i $$-0.925617\pi$$
0.972821 0.231559i $$-0.0743827\pi$$
$$308$$ −3.60097 −0.205184
$$309$$ −43.1611 −2.45535
$$310$$ − 2.02064i − 0.114765i
$$311$$ 8.64016 0.489938 0.244969 0.969531i $$-0.421222\pi$$
0.244969 + 0.969531i $$0.421222\pi$$
$$312$$ 0 0
$$313$$ −5.22732 −0.295466 −0.147733 0.989027i $$-0.547198\pi$$
−0.147733 + 0.989027i $$0.547198\pi$$
$$314$$ − 14.6209i − 0.825103i
$$315$$ 3.60849 0.203315
$$316$$ −13.9194 −0.783029
$$317$$ 11.1929i 0.628657i 0.949314 + 0.314329i $$0.101779\pi$$
−0.949314 + 0.314329i $$0.898221\pi$$
$$318$$ 23.2984i 1.30651i
$$319$$ 13.5170i 0.756809i
$$320$$ 2.18130i 0.121938i
$$321$$ 20.4561 1.14175
$$322$$ 4.49182 0.250319
$$323$$ 22.9936i 1.27940i
$$324$$ −14.3051 −0.794727
$$325$$ 0 0
$$326$$ 2.82755 0.156604
$$327$$ 29.1180i 1.61023i
$$328$$ −19.3291 −1.06727
$$329$$ 1.27702 0.0704045
$$330$$ − 5.31126i − 0.292375i
$$331$$ 20.0468i 1.10187i 0.834548 + 0.550935i $$0.185729\pi$$
−0.834548 + 0.550935i $$0.814271\pi$$
$$332$$ − 2.04080i − 0.112003i
$$333$$ 14.3201i 0.784737i
$$334$$ −6.16419 −0.337290
$$335$$ 9.77034 0.533811
$$336$$ 2.95564i 0.161243i
$$337$$ −18.5866 −1.01248 −0.506239 0.862393i $$-0.668965\pi$$
−0.506239 + 0.862393i $$0.668965\pi$$
$$338$$ 0 0
$$339$$ −34.3188 −1.86394
$$340$$ 7.52866i 0.408299i
$$341$$ −5.31126 −0.287621
$$342$$ −11.7066 −0.633021
$$343$$ − 1.00000i − 0.0539949i
$$344$$ 0.719301i 0.0387821i
$$345$$ − 19.6389i − 1.05732i
$$346$$ 0.663361i 0.0356625i
$$347$$ 22.3417 1.19936 0.599681 0.800239i $$-0.295294\pi$$
0.599681 + 0.800239i $$0.295294\pi$$
$$348$$ 20.2146 1.08362
$$349$$ − 8.78632i − 0.470321i −0.971957 0.235160i $$-0.924438\pi$$
0.971957 0.235160i $$-0.0755615\pi$$
$$350$$ 2.36997 0.126680
$$351$$ 0 0
$$352$$ 14.0559 0.749184
$$353$$ 7.71898i 0.410840i 0.978674 + 0.205420i $$0.0658560\pi$$
−0.978674 + 0.205420i $$0.934144\pi$$
$$354$$ 6.89341 0.366381
$$355$$ 9.32118 0.494717
$$356$$ 1.34549i 0.0713110i
$$357$$ − 9.39887i − 0.497441i
$$358$$ 9.62161i 0.508518i
$$359$$ 10.5956i 0.559216i 0.960114 + 0.279608i $$0.0902045\pi$$
−0.960114 + 0.279608i $$0.909795\pi$$
$$360$$ −8.95915 −0.472189
$$361$$ −15.7002 −0.826324
$$362$$ − 6.29505i − 0.330861i
$$363$$ 12.5261 0.657447
$$364$$ 0 0
$$365$$ 19.3619 1.01345
$$366$$ 7.86898i 0.411318i
$$367$$ 5.82067 0.303836 0.151918 0.988393i $$-0.451455\pi$$
0.151918 + 0.988393i $$0.451455\pi$$
$$368$$ 7.76255 0.404651
$$369$$ − 21.7822i − 1.13394i
$$370$$ − 4.68858i − 0.243748i
$$371$$ − 13.6225i − 0.707246i
$$372$$ 7.94295i 0.411823i
$$373$$ 26.0569 1.34917 0.674587 0.738195i $$-0.264322\pi$$
0.674587 + 0.738195i $$0.264322\pi$$
$$374$$ −6.67589 −0.345202
$$375$$ − 25.8893i − 1.33692i
$$376$$ −3.17059 −0.163511
$$377$$ 0 0
$$378$$ −0.345654 −0.0177785
$$379$$ 15.6532i 0.804053i 0.915628 + 0.402026i $$0.131694\pi$$
−0.915628 + 0.402026i $$0.868306\pi$$
$$380$$ −11.3617 −0.582843
$$381$$ 21.2486 1.08860
$$382$$ 10.9196i 0.558694i
$$383$$ − 12.5588i − 0.641724i −0.947126 0.320862i $$-0.896027\pi$$
0.947126 0.320862i $$-0.103973\pi$$
$$384$$ − 25.2193i − 1.28696i
$$385$$ 3.10548i 0.158270i
$$386$$ 17.3987 0.885571
$$387$$ −0.810588 −0.0412045
$$388$$ 23.4280i 1.18938i
$$389$$ 0.503007 0.0255035 0.0127517 0.999919i $$-0.495941\pi$$
0.0127517 + 0.999919i $$0.495941\pi$$
$$390$$ 0 0
$$391$$ −24.6847 −1.24836
$$392$$ 2.48280i 0.125400i
$$393$$ −46.7838 −2.35993
$$394$$ −4.76895 −0.240256
$$395$$ 12.0041i 0.603992i
$$396$$ 10.0751i 0.506295i
$$397$$ 2.35044i 0.117965i 0.998259 + 0.0589827i $$0.0187857\pi$$
−0.998259 + 0.0589827i $$0.981214\pi$$
$$398$$ − 3.46110i − 0.173489i
$$399$$ 14.1841 0.710092
$$400$$ 4.09567 0.204784
$$401$$ 34.6046i 1.72807i 0.503429 + 0.864037i $$0.332072\pi$$
−0.503429 + 0.864037i $$0.667928\pi$$
$$402$$ 12.9564 0.646208
$$403$$ 0 0
$$404$$ −1.02427 −0.0509593
$$405$$ 12.3367i 0.613016i
$$406$$ 3.98731 0.197887
$$407$$ −12.3239 −0.610875
$$408$$ 23.3355i 1.15528i
$$409$$ − 8.02411i − 0.396767i −0.980125 0.198383i $$-0.936431\pi$$
0.980125 0.198383i $$-0.0635691\pi$$
$$410$$ 7.13176i 0.352213i
$$411$$ − 24.6475i − 1.21577i
$$412$$ −26.8066 −1.32067
$$413$$ −4.03056 −0.198331
$$414$$ − 12.5676i − 0.617666i
$$415$$ −1.75999 −0.0863943
$$416$$ 0 0
$$417$$ 19.6176 0.960676
$$418$$ − 10.0748i − 0.492773i
$$419$$ −11.6694 −0.570090 −0.285045 0.958514i $$-0.592008\pi$$
−0.285045 + 0.958514i $$0.592008\pi$$
$$420$$ 4.64422 0.226615
$$421$$ − 18.3381i − 0.893746i −0.894597 0.446873i $$-0.852538\pi$$
0.894597 0.446873i $$-0.147462\pi$$
$$422$$ − 2.61916i − 0.127499i
$$423$$ − 3.57298i − 0.173724i
$$424$$ 33.8220i 1.64254i
$$425$$ −13.0242 −0.631764
$$426$$ 12.3608 0.598882
$$427$$ − 4.60097i − 0.222657i
$$428$$ 12.7049 0.614117
$$429$$ 0 0
$$430$$ 0.265397 0.0127986
$$431$$ − 31.2435i − 1.50495i −0.658622 0.752474i $$-0.728860\pi$$
0.658622 0.752474i $$-0.271140\pi$$
$$432$$ −0.597343 −0.0287397
$$433$$ 30.5513 1.46820 0.734100 0.679041i $$-0.237604\pi$$
0.734100 + 0.679041i $$0.237604\pi$$
$$434$$ 1.56674i 0.0752057i
$$435$$ − 17.4331i − 0.835853i
$$436$$ 18.0847i 0.866099i
$$437$$ − 37.2524i − 1.78202i
$$438$$ 25.6757 1.22683
$$439$$ 12.1472 0.579756 0.289878 0.957064i $$-0.406385\pi$$
0.289878 + 0.957064i $$0.406385\pi$$
$$440$$ − 7.71029i − 0.367573i
$$441$$ −2.79790 −0.133233
$$442$$ 0 0
$$443$$ −8.46532 −0.402200 −0.201100 0.979571i $$-0.564452\pi$$
−0.201100 + 0.979571i $$0.564452\pi$$
$$444$$ 18.4304i 0.874667i
$$445$$ 1.16035 0.0550060
$$446$$ 6.26065 0.296451
$$447$$ − 23.5705i − 1.11485i
$$448$$ − 1.69131i − 0.0799068i
$$449$$ 23.3264i 1.10084i 0.834888 + 0.550420i $$0.185533\pi$$
−0.834888 + 0.550420i $$0.814467\pi$$
$$450$$ − 6.63093i − 0.312585i
$$451$$ 18.7459 0.882708
$$452$$ −21.3148 −1.00256
$$453$$ − 35.4938i − 1.66765i
$$454$$ −9.55416 −0.448399
$$455$$ 0 0
$$456$$ −35.2162 −1.64915
$$457$$ 15.4866i 0.724434i 0.932094 + 0.362217i $$0.117980\pi$$
−0.932094 + 0.362217i $$0.882020\pi$$
$$458$$ −4.84115 −0.226212
$$459$$ 1.89954 0.0886628
$$460$$ − 12.1974i − 0.568705i
$$461$$ − 9.28204i − 0.432308i −0.976359 0.216154i $$-0.930649\pi$$
0.976359 0.216154i $$-0.0693513\pi$$
$$462$$ 4.11817i 0.191595i
$$463$$ − 28.8283i − 1.33976i −0.742467 0.669882i $$-0.766345\pi$$
0.742467 0.669882i $$-0.233655\pi$$
$$464$$ 6.89068 0.319892
$$465$$ 6.85000 0.317661
$$466$$ − 17.8049i − 0.824797i
$$467$$ 2.87393 0.132990 0.0664948 0.997787i $$-0.478818\pi$$
0.0664948 + 0.997787i $$0.478818\pi$$
$$468$$ 0 0
$$469$$ −7.57559 −0.349808
$$470$$ 1.16984i 0.0539606i
$$471$$ 49.5649 2.28383
$$472$$ 10.0071 0.460613
$$473$$ − 0.697596i − 0.0320755i
$$474$$ 15.9186i 0.731167i
$$475$$ − 19.6551i − 0.901837i
$$476$$ − 5.83747i − 0.267560i
$$477$$ −38.1144 −1.74514
$$478$$ −1.97829 −0.0904851
$$479$$ 22.6082i 1.03299i 0.856289 + 0.516497i $$0.172764\pi$$
−0.856289 + 0.516497i $$0.827236\pi$$
$$480$$ −18.1281 −0.827432
$$481$$ 0 0
$$482$$ −4.95659 −0.225766
$$483$$ 15.2273i 0.692867i
$$484$$ 7.77971 0.353623
$$485$$ 20.2043 0.917432
$$486$$ 15.3227i 0.695053i
$$487$$ 2.86803i 0.129963i 0.997886 + 0.0649814i $$0.0206988\pi$$
−0.997886 + 0.0649814i $$0.979301\pi$$
$$488$$ 11.4233i 0.517108i
$$489$$ 9.58544i 0.433469i
$$490$$ 0.916066 0.0413837
$$491$$ 22.7201 1.02534 0.512672 0.858585i $$-0.328656\pi$$
0.512672 + 0.858585i $$0.328656\pi$$
$$492$$ − 28.0343i − 1.26388i
$$493$$ −21.9122 −0.986877
$$494$$ 0 0
$$495$$ 8.68881 0.390533
$$496$$ 2.70756i 0.121573i
$$497$$ −7.22732 −0.324190
$$498$$ −2.33391 −0.104585
$$499$$ − 18.0151i − 0.806466i −0.915097 0.403233i $$-0.867886\pi$$
0.915097 0.403233i $$-0.132114\pi$$
$$500$$ − 16.0794i − 0.719091i
$$501$$ − 20.8967i − 0.933596i
$$502$$ − 0.556175i − 0.0248233i
$$503$$ −31.1496 −1.38889 −0.694447 0.719544i $$-0.744351\pi$$
−0.694447 + 0.719544i $$0.744351\pi$$
$$504$$ 6.94662 0.309427
$$505$$ 0.883331i 0.0393077i
$$506$$ 10.8158 0.480819
$$507$$ 0 0
$$508$$ 13.1972 0.585529
$$509$$ − 39.5018i − 1.75089i −0.483319 0.875444i $$-0.660569\pi$$
0.483319 0.875444i $$-0.339431\pi$$
$$510$$ 8.60999 0.381257
$$511$$ −15.0125 −0.664115
$$512$$ − 13.2606i − 0.586042i
$$513$$ 2.86664i 0.126565i
$$514$$ 2.31414i 0.102073i
$$515$$ 23.1180i 1.01870i
$$516$$ −1.04325 −0.0459265
$$517$$ 3.07492 0.135235
$$518$$ 3.63537i 0.159729i
$$519$$ −2.24880 −0.0987115
$$520$$ 0 0
$$521$$ −17.7672 −0.778394 −0.389197 0.921155i $$-0.627247\pi$$
−0.389197 + 0.921155i $$0.627247\pi$$
$$522$$ − 11.1561i − 0.488288i
$$523$$ −1.78904 −0.0782294 −0.0391147 0.999235i $$-0.512454\pi$$
−0.0391147 + 0.999235i $$0.512454\pi$$
$$524$$ −29.0566 −1.26934
$$525$$ 8.03424i 0.350643i
$$526$$ − 21.0124i − 0.916183i
$$527$$ − 8.60999i − 0.375057i
$$528$$ 7.11683i 0.309720i
$$529$$ 16.9923 0.738797
$$530$$ 12.4791 0.542059
$$531$$ 11.2771i 0.489384i
$$532$$ 8.80948 0.381939
$$533$$ 0 0
$$534$$ 1.53874 0.0665879
$$535$$ − 10.9568i − 0.473702i
$$536$$ 18.8087 0.812412
$$537$$ −32.6174 −1.40754
$$538$$ − 0.878269i − 0.0378649i
$$539$$ − 2.40788i − 0.103715i
$$540$$ 0.938610i 0.0403913i
$$541$$ − 15.4027i − 0.662214i −0.943593 0.331107i $$-0.892578\pi$$
0.943593 0.331107i $$-0.107422\pi$$
$$542$$ −17.9043 −0.769055
$$543$$ 21.3403 0.915801
$$544$$ 22.7858i 0.976935i
$$545$$ 15.5962 0.668069
$$546$$ 0 0
$$547$$ −3.96944 −0.169721 −0.0848605 0.996393i $$-0.527044\pi$$
−0.0848605 + 0.996393i $$0.527044\pi$$
$$548$$ − 15.3081i − 0.653931i
$$549$$ −12.8730 −0.549408
$$550$$ 5.70661 0.243331
$$551$$ − 33.0683i − 1.40876i
$$552$$ − 37.8064i − 1.60915i
$$553$$ − 9.30758i − 0.395799i
$$554$$ 6.77331i 0.287770i
$$555$$ 15.8944 0.674678
$$556$$ 12.1841 0.516722
$$557$$ − 18.6901i − 0.791924i −0.918267 0.395962i $$-0.870411\pi$$
0.918267 0.395962i $$-0.129589\pi$$
$$558$$ 4.38357 0.185571
$$559$$ 0 0
$$560$$ 1.58310 0.0668983
$$561$$ − 22.6314i − 0.955497i
$$562$$ −6.79422 −0.286597
$$563$$ −36.3059 −1.53011 −0.765056 0.643964i $$-0.777289\pi$$
−0.765056 + 0.643964i $$0.777289\pi$$
$$564$$ − 4.59852i − 0.193633i
$$565$$ 18.3819i 0.773333i
$$566$$ 8.12002i 0.341310i
$$567$$ − 9.56546i − 0.401712i
$$568$$ 17.9440 0.752914
$$569$$ −10.9760 −0.460136 −0.230068 0.973175i $$-0.573895\pi$$
−0.230068 + 0.973175i $$0.573895\pi$$
$$570$$ 12.9936i 0.544240i
$$571$$ −31.3363 −1.31138 −0.655692 0.755028i $$-0.727623\pi$$
−0.655692 + 0.755028i $$0.727623\pi$$
$$572$$ 0 0
$$573$$ −37.0175 −1.54643
$$574$$ − 5.52973i − 0.230806i
$$575$$ 21.1007 0.879962
$$576$$ −4.73210 −0.197171
$$577$$ − 42.7876i − 1.78127i −0.454717 0.890636i $$-0.650260\pi$$
0.454717 0.890636i $$-0.349740\pi$$
$$578$$ 1.25271i 0.0521057i
$$579$$ 58.9819i 2.45120i
$$580$$ − 10.8274i − 0.449583i
$$581$$ 1.36463 0.0566145
$$582$$ 26.7929 1.11060
$$583$$ − 32.8014i − 1.35850i
$$584$$ 37.2731 1.54237
$$585$$ 0 0
$$586$$ 6.64517 0.274509
$$587$$ − 38.7886i − 1.60098i −0.599349 0.800488i $$-0.704574\pi$$
0.599349 0.800488i $$-0.295426\pi$$
$$588$$ −3.60097 −0.148502
$$589$$ 12.9936 0.535390
$$590$$ − 3.69226i − 0.152008i
$$591$$ − 16.1668i − 0.665014i
$$592$$ 6.28247i 0.258208i
$$593$$ 29.9564i 1.23016i 0.788464 + 0.615081i $$0.210877\pi$$
−0.788464 + 0.615081i $$0.789123\pi$$
$$594$$ −0.832293 −0.0341494
$$595$$ −5.03424 −0.206384
$$596$$ − 14.6392i − 0.599645i
$$597$$ 11.7332 0.480207
$$598$$ 0 0
$$599$$ 41.2539 1.68559 0.842794 0.538236i $$-0.180909\pi$$
0.842794 + 0.538236i $$0.180909\pi$$
$$600$$ − 19.9474i − 0.814350i
$$601$$ 6.61089 0.269664 0.134832 0.990868i $$-0.456951\pi$$
0.134832 + 0.990868i $$0.456951\pi$$
$$602$$ −0.205780 −0.00838695
$$603$$ 21.1957i 0.863156i
$$604$$ − 22.0446i − 0.896982i
$$605$$ − 6.70922i − 0.272769i
$$606$$ 1.17138i 0.0475842i
$$607$$ −20.8832 −0.847622 −0.423811 0.905751i $$-0.639308\pi$$
−0.423811 + 0.905751i $$0.639308\pi$$
$$608$$ −34.3867 −1.39456
$$609$$ 13.5170i 0.547738i
$$610$$ 4.21479 0.170652
$$611$$ 0 0
$$612$$ −16.3326 −0.660208
$$613$$ − 4.29655i − 0.173536i −0.996229 0.0867680i $$-0.972346\pi$$
0.996229 0.0867680i $$-0.0276539\pi$$
$$614$$ −5.76362 −0.232601
$$615$$ −24.1768 −0.974902
$$616$$ 5.97829i 0.240872i
$$617$$ − 30.7380i − 1.23746i −0.785602 0.618732i $$-0.787647\pi$$
0.785602 0.618732i $$-0.212353\pi$$
$$618$$ 30.6568i 1.23320i
$$619$$ 20.6417i 0.829658i 0.909899 + 0.414829i $$0.136159\pi$$
−0.909899 + 0.414829i $$0.863841\pi$$
$$620$$ 4.25441 0.170861
$$621$$ −3.07748 −0.123495
$$622$$ − 6.13699i − 0.246071i
$$623$$ −0.899698 −0.0360457
$$624$$ 0 0
$$625$$ 2.81636 0.112654
$$626$$ 3.71290i 0.148397i
$$627$$ 34.1536 1.36396
$$628$$ 30.7839 1.22841
$$629$$ − 19.9781i − 0.796580i
$$630$$ − 2.56306i − 0.102115i
$$631$$ − 29.3366i − 1.16787i −0.811799 0.583937i $$-0.801512\pi$$
0.811799 0.583937i $$-0.198488\pi$$
$$632$$ 23.1089i 0.919222i
$$633$$ 8.87899 0.352908
$$634$$ 7.95019 0.315742
$$635$$ − 11.3812i − 0.451650i
$$636$$ −49.0543 −1.94513
$$637$$ 0 0
$$638$$ 9.60097 0.380106
$$639$$ 20.2213i 0.799943i
$$640$$ −13.5080 −0.533950
$$641$$ 4.01680 0.158654 0.0793271 0.996849i $$-0.474723\pi$$
0.0793271 + 0.996849i $$0.474723\pi$$
$$642$$ − 14.5297i − 0.573443i
$$643$$ − 6.87282i − 0.271037i −0.990775 0.135519i $$-0.956730\pi$$
0.990775 0.135519i $$-0.0432701\pi$$
$$644$$ 9.45742i 0.372675i
$$645$$ 0.899698i 0.0354256i
$$646$$ 16.3320 0.642574
$$647$$ 33.7431 1.32658 0.663289 0.748363i $$-0.269160\pi$$
0.663289 + 0.748363i $$0.269160\pi$$
$$648$$ 23.7491i 0.932955i
$$649$$ −9.70511 −0.380959
$$650$$ 0 0
$$651$$ −5.31126 −0.208165
$$652$$ 5.95335i 0.233151i
$$653$$ 32.4002 1.26792 0.633958 0.773367i $$-0.281429\pi$$
0.633958 + 0.773367i $$0.281429\pi$$
$$654$$ 20.6821 0.808735
$$655$$ 25.0584i 0.979112i
$$656$$ − 9.55622i − 0.373108i
$$657$$ 42.0035i 1.63871i
$$658$$ − 0.907052i − 0.0353606i
$$659$$ 4.01035 0.156221 0.0781106 0.996945i $$-0.475111\pi$$
0.0781106 + 0.996945i $$0.475111\pi$$
$$660$$ 11.1827 0.435287
$$661$$ 1.81794i 0.0707097i 0.999375 + 0.0353549i $$0.0112561\pi$$
−0.999375 + 0.0353549i $$0.988744\pi$$
$$662$$ 14.2389 0.553412
$$663$$ 0 0
$$664$$ −3.38811 −0.131484
$$665$$ − 7.59729i − 0.294610i
$$666$$ 10.1714 0.394133
$$667$$ 35.5005 1.37459
$$668$$ − 12.9786i − 0.502156i
$$669$$ 21.2237i 0.820556i
$$670$$ − 6.93974i − 0.268106i
$$671$$ − 11.0786i − 0.427684i
$$672$$ 14.0559 0.542220
$$673$$ 22.9743 0.885594 0.442797 0.896622i $$-0.353986\pi$$
0.442797 + 0.896622i $$0.353986\pi$$
$$674$$ 13.2018i 0.508515i
$$675$$ −1.62374 −0.0624978
$$676$$ 0 0
$$677$$ 38.0276 1.46152 0.730760 0.682634i $$-0.239166\pi$$
0.730760 + 0.682634i $$0.239166\pi$$
$$678$$ 24.3762i 0.936163i
$$679$$ −15.6658 −0.601197
$$680$$ 12.4990 0.479315
$$681$$ − 32.3887i − 1.24114i
$$682$$ 3.77252i 0.144457i
$$683$$ 40.7786i 1.56035i 0.625560 + 0.780176i $$0.284870\pi$$
−0.625560 + 0.780176i $$0.715130\pi$$
$$684$$ − 24.6480i − 0.942440i
$$685$$ −13.2017 −0.504412
$$686$$ −0.710287 −0.0271189
$$687$$ − 16.4116i − 0.626140i
$$688$$ −0.355619 −0.0135578
$$689$$ 0 0
$$690$$ −13.9492 −0.531038
$$691$$ − 3.12868i − 0.119021i −0.998228 0.0595104i $$-0.981046\pi$$
0.998228 0.0595104i $$-0.0189539\pi$$
$$692$$ −1.39669 −0.0530942
$$693$$ −6.73701 −0.255918
$$694$$ − 15.8690i − 0.602378i
$$695$$ − 10.5076i − 0.398576i
$$696$$ − 33.5601i − 1.27209i
$$697$$ 30.3886i 1.15105i
$$698$$ −6.24080 −0.236218
$$699$$ 60.3590 2.28299
$$700$$ 4.98992i 0.188601i
$$701$$ −9.61382 −0.363109 −0.181555 0.983381i $$-0.558113\pi$$
−0.181555 + 0.983381i $$0.558113\pi$$
$$702$$ 0 0
$$703$$ 30.1495 1.13711
$$704$$ − 4.07247i − 0.153487i
$$705$$ −3.96576 −0.149359
$$706$$ 5.48269 0.206344
$$707$$ − 0.684905i − 0.0257585i
$$708$$ 14.5139i 0.545467i
$$709$$ − 28.1294i − 1.05642i −0.849113 0.528211i $$-0.822863\pi$$
0.849113 0.528211i $$-0.177137\pi$$
$$710$$ − 6.62071i − 0.248471i
$$711$$ −26.0417 −0.976638
$$712$$ 2.23377 0.0837142
$$713$$ 13.9492i 0.522403i
$$714$$ −6.67589 −0.249839
$$715$$ 0 0
$$716$$ −20.2581 −0.757080
$$717$$ − 6.70645i − 0.250457i
$$718$$ 7.52594 0.280865
$$719$$ −24.9044 −0.928779 −0.464389 0.885631i $$-0.653726\pi$$
−0.464389 + 0.885631i $$0.653726\pi$$
$$720$$ − 4.42936i − 0.165073i
$$721$$ − 17.9249i − 0.667559i
$$722$$ 11.1516i 0.415020i
$$723$$ − 16.8029i − 0.624907i
$$724$$ 13.2541 0.492584
$$725$$ 18.7308 0.695643
$$726$$ − 8.89709i − 0.330202i
$$727$$ 24.2120 0.897974 0.448987 0.893538i $$-0.351785\pi$$
0.448987 + 0.893538i $$0.351785\pi$$
$$728$$ 0 0
$$729$$ −23.2479 −0.861032
$$730$$ − 13.7525i − 0.509002i
$$731$$ 1.13086 0.0418264
$$732$$ −16.5680 −0.612369
$$733$$ − 12.3989i − 0.457963i −0.973431 0.228981i $$-0.926461\pi$$
0.973431 0.228981i $$-0.0735395\pi$$
$$734$$ − 4.13434i − 0.152601i
$$735$$ 3.10548i 0.114547i
$$736$$ − 36.9159i − 1.36074i
$$737$$ −18.2411 −0.671921
$$738$$ −15.4716 −0.569518
$$739$$ 10.9604i 0.403184i 0.979470 + 0.201592i $$0.0646115\pi$$
−0.979470 + 0.201592i $$0.935388\pi$$
$$740$$ 9.87170 0.362891
$$741$$ 0 0
$$742$$ −9.67589 −0.355213
$$743$$ 40.6925i 1.49286i 0.665463 + 0.746431i $$0.268234\pi$$
−0.665463 + 0.746431i $$0.731766\pi$$
$$744$$ 13.1868 0.483452
$$745$$ −12.6249 −0.462539
$$746$$ − 18.5079i − 0.677621i
$$747$$ − 3.81810i − 0.139697i
$$748$$ − 14.0559i − 0.513936i
$$749$$ 8.49549i 0.310419i
$$750$$ −18.3888 −0.671464
$$751$$ −9.40472 −0.343183 −0.171592 0.985168i $$-0.554891\pi$$
−0.171592 + 0.985168i $$0.554891\pi$$
$$752$$ − 1.56753i − 0.0571618i
$$753$$ 1.88544 0.0687093
$$754$$ 0 0
$$755$$ −19.0113 −0.691890
$$756$$ − 0.727766i − 0.0264686i
$$757$$ −29.5808 −1.07513 −0.537566 0.843222i $$-0.680656\pi$$
−0.537566 + 0.843222i $$0.680656\pi$$
$$758$$ 11.1183 0.403834
$$759$$ 36.6656i 1.33088i
$$760$$ 18.8626i 0.684218i
$$761$$ − 16.9417i − 0.614137i −0.951687 0.307068i $$-0.900652\pi$$
0.951687 0.307068i $$-0.0993481\pi$$
$$762$$ − 15.0926i − 0.546748i
$$763$$ −12.0928 −0.437788
$$764$$ −22.9909 −0.831783
$$765$$ 14.0853i 0.509254i
$$766$$ −8.92034 −0.322305
$$767$$ 0 0
$$768$$ −26.0578 −0.940281
$$769$$ 7.36574i 0.265616i 0.991142 + 0.132808i $$0.0423993\pi$$
−0.991142 + 0.132808i $$0.957601\pi$$
$$770$$ 2.20578 0.0794908
$$771$$ −7.84498 −0.282530
$$772$$ 36.6326i 1.31844i
$$773$$ − 44.7734i − 1.61039i −0.593012 0.805194i $$-0.702061\pi$$
0.593012 0.805194i $$-0.297939\pi$$
$$774$$ 0.575750i 0.0206949i
$$775$$ 7.35989i 0.264375i
$$776$$ 38.8950 1.39625
$$777$$ −12.3239 −0.442119
$$778$$ − 0.357279i − 0.0128091i
$$779$$ −45.8602 −1.64311
$$780$$ 0 0
$$781$$ −17.4025 −0.622712
$$782$$ 17.5332i 0.626988i
$$783$$ −2.73183 −0.0976277
$$784$$ −1.22748 −0.0438387
$$785$$ − 26.5480i − 0.947540i
$$786$$ 33.2299i 1.18527i
$$787$$ 18.7682i 0.669016i 0.942393 + 0.334508i $$0.108570\pi$$
−0.942393 + 0.334508i $$0.891430\pi$$
$$788$$ − 10.0409i − 0.357693i
$$789$$ 71.2322 2.53594
$$790$$ 8.52636 0.303354
$$791$$ − 14.2527i − 0.506768i
$$792$$ 16.7267 0.594356
$$793$$ 0 0
$$794$$ 1.66949 0.0592479
$$795$$ 42.3044i 1.50038i
$$796$$ 7.28726 0.258290
$$797$$ −7.21697 −0.255638 −0.127819 0.991797i $$-0.540798\pi$$
−0.127819 + 0.991797i $$0.540798\pi$$
$$798$$ − 10.0748i − 0.356643i
$$799$$ 4.98470i 0.176346i
$$800$$ − 19.4775i − 0.688635i
$$801$$ 2.51726i 0.0889431i
$$802$$ 24.5792 0.867922
$$803$$ −36.1484 −1.27565
$$804$$ 27.2795i 0.962073i
$$805$$ 8.15608 0.287464
$$806$$ 0 0
$$807$$ 2.97734 0.104807
$$808$$ 1.70048i 0.0598228i
$$809$$ 14.8318 0.521459 0.260729 0.965412i $$-0.416037\pi$$
0.260729 + 0.965412i $$0.416037\pi$$
$$810$$ 8.76260 0.307886
$$811$$ 18.5831i 0.652541i 0.945276 + 0.326271i $$0.105792\pi$$
−0.945276 + 0.326271i $$0.894208\pi$$
$$812$$ 8.39519i 0.294613i
$$813$$ − 60.6958i − 2.12869i
$$814$$ 8.75354i 0.306811i
$$815$$ 5.13417 0.179842
$$816$$ −11.5370 −0.403875
$$817$$ 1.70661i 0.0597067i
$$818$$ −5.69942 −0.199275
$$819$$ 0 0
$$820$$ −15.0158 −0.524374
$$821$$ − 26.6236i − 0.929169i −0.885529 0.464585i $$-0.846204\pi$$
0.885529 0.464585i $$-0.153796\pi$$
$$822$$ −17.5068 −0.610620
$$823$$ −6.75136 −0.235338 −0.117669 0.993053i $$-0.537542\pi$$
−0.117669 + 0.993053i $$0.537542\pi$$
$$824$$ 44.5040i 1.55037i
$$825$$ 19.3455i 0.673524i
$$826$$ 2.86285i 0.0996114i
$$827$$ 21.7430i 0.756079i 0.925789 + 0.378039i $$0.123402\pi$$
−0.925789 + 0.378039i $$0.876598\pi$$
$$828$$ 26.4609 0.919579
$$829$$ 14.6216 0.507828 0.253914 0.967227i $$-0.418282\pi$$
0.253914 + 0.967227i $$0.418282\pi$$
$$830$$ 1.25009i 0.0433914i
$$831$$ −22.9616 −0.796529
$$832$$ 0 0
$$833$$ 3.90338 0.135244
$$834$$ − 13.9341i − 0.482498i
$$835$$ −11.1927 −0.387340
$$836$$ 21.2122 0.733639
$$837$$ − 1.07342i − 0.0371028i
$$838$$ 8.28865i 0.286327i
$$839$$ 10.7469i 0.371023i 0.982642 + 0.185511i $$0.0593942\pi$$
−0.982642 + 0.185511i $$0.940606\pi$$
$$840$$ − 7.71029i − 0.266030i
$$841$$ 2.51320 0.0866620
$$842$$ −13.0253 −0.448883
$$843$$ − 23.0325i − 0.793282i
$$844$$ 5.51458 0.189820
$$845$$ 0 0
$$846$$ −2.53784 −0.0872527
$$847$$ 5.20210i 0.178746i
$$848$$ −16.7214 −0.574216
$$849$$ −27.5270 −0.944724
$$850$$ 9.25088i 0.317303i
$$851$$ 32.3670i 1.10953i
$$852$$ 26.0254i 0.891615i
$$853$$ 31.7709i 1.08782i 0.839145 + 0.543908i $$0.183056\pi$$
−0.839145 + 0.543908i $$0.816944\pi$$
$$854$$ −3.26801 −0.111829
$$855$$ −21.2564 −0.726955
$$856$$ − 21.0926i − 0.720931i
$$857$$ 0.648105 0.0221388 0.0110694 0.999939i $$-0.496476\pi$$
0.0110694 + 0.999939i $$0.496476\pi$$
$$858$$ 0 0
$$859$$ −43.1902 −1.47363 −0.736815 0.676095i $$-0.763671\pi$$
−0.736815 + 0.676095i $$0.763671\pi$$
$$860$$ 0.558787i 0.0190545i
$$861$$ 18.7459 0.638857
$$862$$ −22.1919 −0.755858
$$863$$ 21.6094i 0.735592i 0.929906 + 0.367796i $$0.119888\pi$$
−0.929906 + 0.367796i $$0.880112\pi$$
$$864$$ 2.84074i 0.0966441i
$$865$$ 1.20451i 0.0409545i
$$866$$ − 21.7002i − 0.737401i
$$867$$ −4.24669 −0.144225
$$868$$ −3.29873 −0.111966
$$869$$ − 22.4116i − 0.760260i
$$870$$ −12.3825 −0.419806
$$871$$ 0 0
$$872$$ 30.0240 1.01674
$$873$$ 43.8312i 1.48346i
$$874$$ −26.4599 −0.895018
$$875$$ 10.7519 0.363480
$$876$$ 54.0597i 1.82651i
$$877$$ − 0.880766i − 0.0297413i −0.999889 0.0148707i $$-0.995266\pi$$
0.999889 0.0148707i $$-0.00473366\pi$$
$$878$$ − 8.62801i − 0.291181i
$$879$$ 22.5272i 0.759825i
$$880$$ 3.81193 0.128500
$$881$$ 0.140035 0.00471791 0.00235895 0.999997i $$-0.499249\pi$$
0.00235895 + 0.999997i $$0.499249\pi$$
$$882$$ 1.98731i 0.0669162i
$$883$$ 18.8253 0.633522 0.316761 0.948505i $$-0.397405\pi$$
0.316761 + 0.948505i $$0.397405\pi$$
$$884$$ 0 0
$$885$$ 12.5168 0.420748
$$886$$ 6.01281i 0.202004i
$$887$$ −33.3010 −1.11814 −0.559069 0.829121i $$-0.688841\pi$$
−0.559069 + 0.829121i $$0.688841\pi$$
$$888$$ 30.5979 1.02680
$$889$$ 8.82462i 0.295968i
$$890$$ − 0.824183i − 0.0276267i
$$891$$ − 23.0325i − 0.771618i
$$892$$ 13.1817i 0.441355i
$$893$$ −7.52254 −0.251732
$$894$$ −16.7418 −0.559929
$$895$$ 17.4706i 0.583977i
$$896$$ 10.4736 0.349899
$$897$$ 0 0
$$898$$ 16.5684 0.552896
$$899$$ 12.3825i 0.412980i
$$900$$ 13.9613 0.465376
$$901$$ 53.1738 1.77148
$$902$$ − 13.3149i − 0.443339i
$$903$$ − 0.697596i − 0.0232145i
$$904$$ 35.3866i 1.17694i
$$905$$ − 11.4303i − 0.379957i
$$906$$ −25.2108 −0.837573
$$907$$ −11.5870 −0.384740 −0.192370 0.981322i $$-0.561617\pi$$
−0.192370 + 0.981322i $$0.561617\pi$$
$$908$$ − 20.1161i − 0.667575i
$$909$$ −1.91629 −0.0635594
$$910$$ 0 0
$$911$$ 52.5489 1.74102 0.870512 0.492147i $$-0.163788\pi$$
0.870512 + 0.492147i $$0.163788\pi$$
$$912$$ − 17.4107i − 0.576527i
$$913$$ 3.28588 0.108747
$$914$$ 11.0000 0.363846
$$915$$ 14.2882i 0.472354i
$$916$$ − 10.1929i − 0.336784i
$$917$$ − 19.4294i − 0.641616i
$$918$$ − 1.34922i − 0.0445308i
$$919$$ −20.0534 −0.661502 −0.330751 0.943718i $$-0.607302\pi$$
−0.330751 + 0.943718i $$0.607302\pi$$
$$920$$ −20.2499 −0.667621
$$921$$ − 19.5387i − 0.643823i
$$922$$ −6.59291 −0.217126
$$923$$ 0 0
$$924$$ −8.67071 −0.285246
$$925$$ 17.0775i 0.561504i
$$926$$ −20.4764 −0.672895
$$927$$ −50.1521 −1.64721
$$928$$ − 32.7696i − 1.07571i
$$929$$ − 15.9085i − 0.521941i −0.965347 0.260971i $$-0.915957\pi$$
0.965347 0.260971i $$-0.0840426\pi$$
$$930$$ − 4.86546i − 0.159545i
$$931$$ 5.89068i 0.193059i
$$932$$ 37.4879 1.22796
$$933$$ 20.8045 0.681108
$$934$$ − 2.04131i − 0.0667938i
$$935$$ −12.1218 −0.396427
$$936$$ 0 0
$$937$$ 26.1978 0.855846 0.427923 0.903815i $$-0.359245\pi$$
0.427923 + 0.903815i $$0.359245\pi$$
$$938$$ 5.38084i 0.175691i
$$939$$ −12.5868 −0.410754
$$940$$ −2.46307 −0.0803364
$$941$$ − 36.3059i − 1.18354i −0.806108 0.591769i $$-0.798430\pi$$
0.806108 0.591769i $$-0.201570\pi$$
$$942$$ − 35.2053i − 1.14705i
$$943$$ − 49.2332i − 1.60325i
$$944$$ 4.94745i 0.161026i
$$945$$ −0.627626 −0.0204167
$$946$$ −0.495493 −0.0161099
$$947$$ 0.918839i 0.0298582i 0.999889 + 0.0149291i $$0.00475226\pi$$
−0.999889 + 0.0149291i $$0.995248\pi$$
$$948$$ −33.5163 −1.08856
$$949$$ 0 0
$$950$$ −13.9607 −0.452946
$$951$$ 26.9513i 0.873954i
$$952$$ −9.69131 −0.314097
$$953$$ 18.3589 0.594702 0.297351 0.954768i $$-0.403897\pi$$
0.297351 + 0.954768i $$0.403897\pi$$
$$954$$ 27.0721i 0.876493i
$$955$$ 19.8274i 0.641599i
$$956$$ − 4.16526i − 0.134714i
$$957$$ 32.5474i 1.05211i
$$958$$ 16.0583 0.518819
$$959$$ 10.2362 0.330543
$$960$$ 5.25232i 0.169518i
$$961$$ 26.1345 0.843050
$$962$$ 0 0
$$963$$ 23.7695 0.765962
$$964$$ − 10.4360i − 0.336121i
$$965$$ 31.5920 1.01698
$$966$$ 10.8158 0.347992
$$967$$ 12.5923i 0.404940i 0.979288 + 0.202470i $$0.0648969\pi$$
−0.979288 + 0.202470i $$0.935103\pi$$
$$968$$ − 12.9158i − 0.415129i
$$969$$ 55.3658i 1.77860i
$$970$$ − 14.3509i − 0.460779i
$$971$$ −21.3308 −0.684537 −0.342269 0.939602i $$-0.611195\pi$$
−0.342269 + 0.939602i $$0.611195\pi$$
$$972$$ −32.2617 −1.03479
$$973$$ 8.14723i 0.261188i
$$974$$ 2.03712 0.0652736
$$975$$ 0 0
$$976$$ −5.64762 −0.180776
$$977$$ − 42.4279i − 1.35739i −0.734420 0.678695i $$-0.762546\pi$$
0.734420 0.678695i $$-0.237454\pi$$
$$978$$ 6.80841 0.217709
$$979$$ −2.16637 −0.0692374
$$980$$ 1.92876i 0.0616119i
$$981$$ 33.8344i 1.08025i
$$982$$ − 16.1378i − 0.514977i
$$983$$ − 2.09758i − 0.0669023i −0.999440 0.0334511i $$-0.989350\pi$$
0.999440 0.0334511i $$-0.0106498\pi$$
$$984$$ −46.5423 −1.48371
$$985$$ −8.65930 −0.275908
$$986$$ 15.5640i 0.495658i
$$987$$ 3.07492 0.0978758
$$988$$ 0 0
$$989$$ −1.83213 −0.0582584
$$990$$ − 6.17154i − 0.196145i
$$991$$ −27.6349 −0.877851 −0.438926 0.898523i $$-0.644641\pi$$
−0.438926 + 0.898523i $$0.644641\pi$$
$$992$$ 12.8762 0.408819
$$993$$ 48.2703i 1.53181i
$$994$$ 5.13347i 0.162824i
$$995$$ − 6.28454i − 0.199233i
$$996$$ − 4.91400i − 0.155706i
$$997$$ −2.02783 −0.0642221 −0.0321110 0.999484i $$-0.510223\pi$$
−0.0321110 + 0.999484i $$0.510223\pi$$
$$998$$ −12.7959 −0.405047
$$999$$ − 2.49070i − 0.0788024i
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 1183.2.c.g.337.3 8
13.2 odd 12 91.2.f.c.22.3 8
13.5 odd 4 1183.2.a.k.1.2 4
13.6 odd 12 91.2.f.c.29.3 yes 8
13.8 odd 4 1183.2.a.l.1.3 4
13.12 even 2 inner 1183.2.c.g.337.6 8
39.2 even 12 819.2.o.h.568.2 8
39.32 even 12 819.2.o.h.757.2 8
52.15 even 12 1456.2.s.q.113.4 8
52.19 even 12 1456.2.s.q.1121.4 8
91.2 odd 12 637.2.h.h.165.2 8
91.6 even 12 637.2.f.i.393.3 8
91.19 even 12 637.2.g.j.263.3 8
91.32 odd 12 637.2.h.h.471.2 8
91.34 even 4 8281.2.a.bt.1.3 4
91.41 even 12 637.2.f.i.295.3 8
91.45 even 12 637.2.h.i.471.2 8
91.54 even 12 637.2.h.i.165.2 8
91.58 odd 12 637.2.g.k.263.3 8
91.67 odd 12 637.2.g.k.373.3 8
91.80 even 12 637.2.g.j.373.3 8
91.83 even 4 8281.2.a.bp.1.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.f.c.22.3 8 13.2 odd 12
91.2.f.c.29.3 yes 8 13.6 odd 12
637.2.f.i.295.3 8 91.41 even 12
637.2.f.i.393.3 8 91.6 even 12
637.2.g.j.263.3 8 91.19 even 12
637.2.g.j.373.3 8 91.80 even 12
637.2.g.k.263.3 8 91.58 odd 12
637.2.g.k.373.3 8 91.67 odd 12
637.2.h.h.165.2 8 91.2 odd 12
637.2.h.h.471.2 8 91.32 odd 12
637.2.h.i.165.2 8 91.54 even 12
637.2.h.i.471.2 8 91.45 even 12
819.2.o.h.568.2 8 39.2 even 12
819.2.o.h.757.2 8 39.32 even 12
1183.2.a.k.1.2 4 13.5 odd 4
1183.2.a.l.1.3 4 13.8 odd 4
1183.2.c.g.337.3 8 1.1 even 1 trivial
1183.2.c.g.337.6 8 13.12 even 2 inner
1456.2.s.q.113.4 8 52.15 even 12
1456.2.s.q.1121.4 8 52.19 even 12
8281.2.a.bp.1.2 4 91.83 even 4
8281.2.a.bt.1.3 4 91.34 even 4