# Properties

 Label 1183.2.c.g.337.5 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 337.5 Root $$0.231361i$$ of defining polynomial Character $$\chi$$ $$=$$ 1183.337 Dual form 1183.2.c.g.337.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+0.231361i q^{2} -3.32225 q^{3} +1.94647 q^{4} -2.23136i q^{5} -0.768639i q^{6} +1.00000i q^{7} +0.913059i q^{8} +8.03736 q^{9} +O(q^{10})$$ $$q+0.231361i q^{2} -3.32225 q^{3} +1.94647 q^{4} -2.23136i q^{5} -0.768639i q^{6} +1.00000i q^{7} +0.913059i q^{8} +8.03736 q^{9} +0.516249 q^{10} -3.32225i q^{11} -6.46667 q^{12} -0.231361 q^{14} +7.41314i q^{15} +3.68170 q^{16} +1.37578 q^{17} +1.85953i q^{18} +3.23531i q^{19} -4.34328i q^{20} -3.32225i q^{21} +0.768639 q^{22} -0.838502 q^{23} -3.03341i q^{24} +0.0210289 q^{25} -16.7354 q^{27} +1.94647i q^{28} -0.607142 q^{29} -1.71511 q^{30} +1.71511i q^{31} +2.67792i q^{32} +11.0374i q^{33} +0.318302i q^{34} +2.23136 q^{35} +15.6445 q^{36} -1.55361i q^{37} -0.748524 q^{38} +2.03736 q^{40} -9.17783i q^{41} +0.768639 q^{42} -1.23136 q^{43} -6.46667i q^{44} -17.9343i q^{45} -0.193997i q^{46} +1.62817i q^{47} -12.2315 q^{48} -1.00000 q^{49} +0.00486525i q^{50} -4.57069 q^{51} +8.39607 q^{53} -3.87192i q^{54} -7.41314 q^{55} -0.913059 q^{56} -10.7485i q^{57} -0.140469i q^{58} -8.82234i q^{59} +14.4295i q^{60} +5.46667 q^{61} -0.396810 q^{62} +8.03736i q^{63} +6.74383 q^{64} -2.55361 q^{66} -10.1857i q^{67} +2.67792 q^{68} +2.78572 q^{69} +0.516249i q^{70} -5.21428i q^{71} +7.33859i q^{72} +3.96355i q^{73} +0.359445 q^{74} -0.0698632 q^{75} +6.29744i q^{76} +3.32225 q^{77} +6.45051 q^{79} -8.21520i q^{80} +31.4871 q^{81} +2.12339 q^{82} -4.64055i q^{83} -6.46667i q^{84} -3.06986i q^{85} -0.284889i q^{86} +2.01708 q^{87} +3.03341 q^{88} -9.12826i q^{89} +4.14929 q^{90} -1.63212 q^{92} -5.69803i q^{93} -0.376695 q^{94} +7.21915 q^{95} -8.89672i q^{96} -15.3589i q^{97} -0.231361i q^{98} -26.7022i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 2 q^{3} - 10 q^{4} + 14 q^{9}+O(q^{10})$$ 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.231361i 0.163597i 0.996649 + 0.0817984i $$0.0260664\pi$$
−0.996649 + 0.0817984i $$0.973934\pi$$
$$3$$ −3.32225 −1.91810 −0.959052 0.283231i $$-0.908594\pi$$
−0.959052 + 0.283231i $$0.908594\pi$$
$$4$$ 1.94647 0.973236
$$5$$ − 2.23136i − 0.997895i −0.866632 0.498947i $$-0.833720\pi$$
0.866632 0.498947i $$-0.166280\pi$$
$$6$$ − 0.768639i − 0.313796i
$$7$$ 1.00000i 0.377964i
$$8$$ 0.913059i 0.322815i
$$9$$ 8.03736 2.67912
$$10$$ 0.516249 0.163252
$$11$$ − 3.32225i − 1.00170i −0.865535 0.500848i $$-0.833021\pi$$
0.865535 0.500848i $$-0.166979\pi$$
$$12$$ −6.46667 −1.86677
$$13$$ 0 0
$$14$$ −0.231361 −0.0618338
$$15$$ 7.41314i 1.91407i
$$16$$ 3.68170 0.920425
$$17$$ 1.37578 0.333676 0.166838 0.985984i $$-0.446644\pi$$
0.166838 + 0.985984i $$0.446644\pi$$
$$18$$ 1.85953i 0.438296i
$$19$$ 3.23531i 0.742231i 0.928587 + 0.371116i $$0.121025\pi$$
−0.928587 + 0.371116i $$0.878975\pi$$
$$20$$ − 4.34328i − 0.971187i
$$21$$ − 3.32225i − 0.724975i
$$22$$ 0.768639 0.163874
$$23$$ −0.838502 −0.174840 −0.0874199 0.996172i $$-0.527862\pi$$
−0.0874199 + 0.996172i $$0.527862\pi$$
$$24$$ − 3.03341i − 0.619193i
$$25$$ 0.0210289 0.00420577
$$26$$ 0 0
$$27$$ −16.7354 −3.22073
$$28$$ 1.94647i 0.367849i
$$29$$ −0.607142 −0.112743 −0.0563717 0.998410i $$-0.517953\pi$$
−0.0563717 + 0.998410i $$0.517953\pi$$
$$30$$ −1.71511 −0.313135
$$31$$ 1.71511i 0.308043i 0.988067 + 0.154022i $$0.0492225\pi$$
−0.988067 + 0.154022i $$0.950777\pi$$
$$32$$ 2.67792i 0.473394i
$$33$$ 11.0374i 1.92136i
$$34$$ 0.318302i 0.0545883i
$$35$$ 2.23136 0.377169
$$36$$ 15.6445 2.60742
$$37$$ − 1.55361i − 0.255413i −0.991812 0.127706i $$-0.959239\pi$$
0.991812 0.127706i $$-0.0407615\pi$$
$$38$$ −0.748524 −0.121427
$$39$$ 0 0
$$40$$ 2.03736 0.322136
$$41$$ − 9.17783i − 1.43334i −0.697414 0.716668i $$-0.745666\pi$$
0.697414 0.716668i $$-0.254334\pi$$
$$42$$ 0.768639 0.118604
$$43$$ −1.23136 −0.187781 −0.0938904 0.995583i $$-0.529930\pi$$
−0.0938904 + 0.995583i $$0.529930\pi$$
$$44$$ − 6.46667i − 0.974888i
$$45$$ − 17.9343i − 2.67348i
$$46$$ − 0.193997i − 0.0286032i
$$47$$ 1.62817i 0.237493i 0.992925 + 0.118747i $$0.0378876\pi$$
−0.992925 + 0.118747i $$0.962112\pi$$
$$48$$ −12.2315 −1.76547
$$49$$ −1.00000 −0.142857
$$50$$ 0.00486525i 0 0.000688051i
$$51$$ −4.57069 −0.640025
$$52$$ 0 0
$$53$$ 8.39607 1.15329 0.576644 0.816995i $$-0.304362\pi$$
0.576644 + 0.816995i $$0.304362\pi$$
$$54$$ − 3.87192i − 0.526901i
$$55$$ −7.41314 −0.999588
$$56$$ −0.913059 −0.122013
$$57$$ − 10.7485i − 1.42368i
$$58$$ − 0.140469i − 0.0184445i
$$59$$ − 8.82234i − 1.14857i −0.818655 0.574285i $$-0.805280\pi$$
0.818655 0.574285i $$-0.194720\pi$$
$$60$$ 14.4295i 1.86284i
$$61$$ 5.46667 0.699936 0.349968 0.936762i $$-0.386193\pi$$
0.349968 + 0.936762i $$0.386193\pi$$
$$62$$ −0.396810 −0.0503949
$$63$$ 8.03736i 1.01261i
$$64$$ 6.74383 0.842979
$$65$$ 0 0
$$66$$ −2.55361 −0.314328
$$67$$ − 10.1857i − 1.24439i −0.782864 0.622193i $$-0.786242\pi$$
0.782864 0.622193i $$-0.213758\pi$$
$$68$$ 2.67792 0.324745
$$69$$ 2.78572 0.335361
$$70$$ 0.516249i 0.0617036i
$$71$$ − 5.21428i − 0.618822i −0.950928 0.309411i $$-0.899868\pi$$
0.950928 0.309411i $$-0.100132\pi$$
$$72$$ 7.33859i 0.864861i
$$73$$ 3.96355i 0.463898i 0.972728 + 0.231949i $$0.0745103\pi$$
−0.972728 + 0.231949i $$0.925490\pi$$
$$74$$ 0.359445 0.0417847
$$75$$ −0.0698632 −0.00806711
$$76$$ 6.29744i 0.722366i
$$77$$ 3.32225 0.378606
$$78$$ 0 0
$$79$$ 6.45051 0.725739 0.362869 0.931840i $$-0.381797\pi$$
0.362869 + 0.931840i $$0.381797\pi$$
$$80$$ − 8.21520i − 0.918487i
$$81$$ 31.4871 3.49857
$$82$$ 2.12339 0.234489
$$83$$ − 4.64055i − 0.509367i −0.967024 0.254684i $$-0.918029\pi$$
0.967024 0.254684i $$-0.0819713\pi$$
$$84$$ − 6.46667i − 0.705572i
$$85$$ − 3.06986i − 0.332973i
$$86$$ − 0.284889i − 0.0307203i
$$87$$ 2.01708 0.216253
$$88$$ 3.03341 0.323363
$$89$$ − 9.12826i − 0.967593i −0.875180 0.483797i $$-0.839257\pi$$
0.875180 0.483797i $$-0.160743\pi$$
$$90$$ 4.14929 0.437373
$$91$$ 0 0
$$92$$ −1.63212 −0.170160
$$93$$ − 5.69803i − 0.590859i
$$94$$ −0.376695 −0.0388531
$$95$$ 7.21915 0.740669
$$96$$ − 8.89672i − 0.908018i
$$97$$ − 15.3589i − 1.55946i −0.626117 0.779729i $$-0.715357\pi$$
0.626117 0.779729i $$-0.284643\pi$$
$$98$$ − 0.231361i − 0.0233710i
$$99$$ − 26.7022i − 2.68367i
$$100$$ 0.0409321 0.00409321
$$101$$ 7.95042 0.791097 0.395548 0.918445i $$-0.370555\pi$$
0.395548 + 0.918445i $$0.370555\pi$$
$$102$$ − 1.05748i − 0.104706i
$$103$$ −0.694825 −0.0684631 −0.0342316 0.999414i $$-0.510898\pi$$
−0.0342316 + 0.999414i $$0.510898\pi$$
$$104$$ 0 0
$$105$$ −7.41314 −0.723449
$$106$$ 1.94252i 0.188674i
$$107$$ 8.94647 0.864888 0.432444 0.901661i $$-0.357651\pi$$
0.432444 + 0.901661i $$0.357651\pi$$
$$108$$ −32.5750 −3.13453
$$109$$ − 2.27268i − 0.217683i −0.994059 0.108841i $$-0.965286\pi$$
0.994059 0.108841i $$-0.0347141\pi$$
$$110$$ − 1.71511i − 0.163529i
$$111$$ 5.16150i 0.489908i
$$112$$ 3.68170i 0.347888i
$$113$$ −9.50478 −0.894134 −0.447067 0.894500i $$-0.647532\pi$$
−0.447067 + 0.894500i $$0.647532\pi$$
$$114$$ 2.48679 0.232909
$$115$$ 1.87100i 0.174472i
$$116$$ −1.18178 −0.109726
$$117$$ 0 0
$$118$$ 2.04114 0.187902
$$119$$ 1.37578i 0.126118i
$$120$$ −6.76864 −0.617889
$$121$$ −0.0373642 −0.00339675
$$122$$ 1.26477i 0.114507i
$$123$$ 30.4911i 2.74929i
$$124$$ 3.33842i 0.299799i
$$125$$ − 11.2037i − 1.00209i
$$126$$ −1.85953 −0.165660
$$127$$ −18.4334 −1.63570 −0.817851 0.575430i $$-0.804835\pi$$
−0.817851 + 0.575430i $$0.804835\pi$$
$$128$$ 6.91610i 0.611302i
$$129$$ 4.09089 0.360183
$$130$$ 0 0
$$131$$ −1.74835 −0.152754 −0.0763771 0.997079i $$-0.524335\pi$$
−0.0763771 + 0.997079i $$0.524335\pi$$
$$132$$ 21.4839i 1.86994i
$$133$$ −3.23531 −0.280537
$$134$$ 2.35658 0.203578
$$135$$ 37.3427i 3.21395i
$$136$$ 1.25617i 0.107716i
$$137$$ 18.0032i 1.53812i 0.639178 + 0.769059i $$0.279275\pi$$
−0.639178 + 0.769059i $$0.720725\pi$$
$$138$$ 0.644506i 0.0548640i
$$139$$ 13.9179 1.18050 0.590251 0.807219i $$-0.299029\pi$$
0.590251 + 0.807219i $$0.299029\pi$$
$$140$$ 4.34328 0.367074
$$141$$ − 5.40919i − 0.455536i
$$142$$ 1.20638 0.101237
$$143$$ 0 0
$$144$$ 29.5911 2.46593
$$145$$ 1.35475i 0.112506i
$$146$$ −0.917010 −0.0758923
$$147$$ 3.32225 0.274015
$$148$$ − 3.02407i − 0.248577i
$$149$$ − 15.9303i − 1.30506i −0.757762 0.652531i $$-0.773707\pi$$
0.757762 0.652531i $$-0.226293\pi$$
$$150$$ − 0.0161636i − 0.00131975i
$$151$$ 13.9497i 1.13521i 0.823301 + 0.567604i $$0.192130\pi$$
−0.823301 + 0.567604i $$0.807870\pi$$
$$152$$ −2.95403 −0.239604
$$153$$ 11.0577 0.893958
$$154$$ 0.768639i 0.0619387i
$$155$$ 3.82703 0.307395
$$156$$ 0 0
$$157$$ −12.9747 −1.03549 −0.517745 0.855535i $$-0.673229\pi$$
−0.517745 + 0.855535i $$0.673229\pi$$
$$158$$ 1.49240i 0.118729i
$$159$$ −27.8939 −2.21213
$$160$$ 5.97540 0.472397
$$161$$ − 0.838502i − 0.0660832i
$$162$$ 7.28489i 0.572355i
$$163$$ − 18.4085i − 1.44186i −0.693007 0.720931i $$-0.743715\pi$$
0.693007 0.720931i $$-0.256285\pi$$
$$164$$ − 17.8644i − 1.39498i
$$165$$ 24.6283 1.91731
$$166$$ 1.07364 0.0833308
$$167$$ 18.4993i 1.43152i 0.698345 + 0.715761i $$0.253920\pi$$
−0.698345 + 0.715761i $$0.746080\pi$$
$$168$$ 3.03341 0.234033
$$169$$ 0 0
$$170$$ 0.710246 0.0544734
$$171$$ 26.0034i 1.98853i
$$172$$ −2.39681 −0.182755
$$173$$ 17.1981 1.30755 0.653774 0.756690i $$-0.273185\pi$$
0.653774 + 0.756690i $$0.273185\pi$$
$$174$$ 0.466673i 0.0353784i
$$175$$ 0.0210289i 0.00158963i
$$176$$ − 12.2315i − 0.921986i
$$177$$ 29.3100i 2.20308i
$$178$$ 2.11192 0.158295
$$179$$ −14.4886 −1.08293 −0.541465 0.840723i $$-0.682130\pi$$
−0.541465 + 0.840723i $$0.682130\pi$$
$$180$$ − 34.9085i − 2.60193i
$$181$$ −6.85484 −0.509516 −0.254758 0.967005i $$-0.581996\pi$$
−0.254758 + 0.967005i $$0.581996\pi$$
$$182$$ 0 0
$$183$$ −18.1617 −1.34255
$$184$$ − 0.765602i − 0.0564409i
$$185$$ −3.46667 −0.254875
$$186$$ 1.31830 0.0966626
$$187$$ − 4.57069i − 0.334242i
$$188$$ 3.16919i 0.231137i
$$189$$ − 16.7354i − 1.21732i
$$190$$ 1.67023i 0.121171i
$$191$$ −2.85163 −0.206337 −0.103168 0.994664i $$-0.532898\pi$$
−0.103168 + 0.994664i $$0.532898\pi$$
$$192$$ −22.4047 −1.61692
$$193$$ 10.0505i 0.723450i 0.932285 + 0.361725i $$0.117812\pi$$
−0.932285 + 0.361725i $$0.882188\pi$$
$$194$$ 3.55344 0.255122
$$195$$ 0 0
$$196$$ −1.94647 −0.139034
$$197$$ − 25.4171i − 1.81089i −0.424460 0.905447i $$-0.639536\pi$$
0.424460 0.905447i $$-0.360464\pi$$
$$198$$ 6.17783 0.439039
$$199$$ 12.4466 0.882313 0.441157 0.897430i $$-0.354568\pi$$
0.441157 + 0.897430i $$0.354568\pi$$
$$200$$ 0.0192006i 0.00135769i
$$201$$ 33.8396i 2.38686i
$$202$$ 1.83942i 0.129421i
$$203$$ − 0.607142i − 0.0426130i
$$204$$ −8.89672 −0.622895
$$205$$ −20.4791 −1.43032
$$206$$ − 0.160755i − 0.0112003i
$$207$$ −6.73935 −0.468417
$$208$$ 0 0
$$209$$ 10.7485 0.743491
$$210$$ − 1.71511i − 0.118354i
$$211$$ −24.3923 −1.67923 −0.839617 0.543179i $$-0.817221\pi$$
−0.839617 + 0.543179i $$0.817221\pi$$
$$212$$ 16.3427 1.12242
$$213$$ 17.3232i 1.18696i
$$214$$ 2.06986i 0.141493i
$$215$$ 2.74761i 0.187385i
$$216$$ − 15.2804i − 1.03970i
$$217$$ −1.71511 −0.116429
$$218$$ 0.525808 0.0356122
$$219$$ − 13.1679i − 0.889805i
$$220$$ −14.4295 −0.972835
$$221$$ 0 0
$$222$$ −1.19417 −0.0801473
$$223$$ 22.6494i 1.51671i 0.651839 + 0.758357i $$0.273998\pi$$
−0.651839 + 0.758357i $$0.726002\pi$$
$$224$$ −2.67792 −0.178926
$$225$$ 0.169017 0.0112678
$$226$$ − 2.19903i − 0.146278i
$$227$$ 1.28506i 0.0852925i 0.999090 + 0.0426462i $$0.0135788\pi$$
−0.999090 + 0.0426462i $$0.986421\pi$$
$$228$$ − 20.9217i − 1.38557i
$$229$$ 4.64451i 0.306918i 0.988155 + 0.153459i $$0.0490412\pi$$
−0.988155 + 0.153459i $$0.950959\pi$$
$$230$$ −0.432876 −0.0285430
$$231$$ −11.0374 −0.726205
$$232$$ − 0.554356i − 0.0363953i
$$233$$ −11.8877 −0.778790 −0.389395 0.921071i $$-0.627316\pi$$
−0.389395 + 0.921071i $$0.627316\pi$$
$$234$$ 0 0
$$235$$ 3.63304 0.236993
$$236$$ − 17.1724i − 1.11783i
$$237$$ −21.4302 −1.39204
$$238$$ −0.318302 −0.0206324
$$239$$ − 4.17783i − 0.270242i −0.990829 0.135121i $$-0.956858\pi$$
0.990829 0.135121i $$-0.0431422\pi$$
$$240$$ 27.2930i 1.76175i
$$241$$ − 4.03341i − 0.259815i −0.991526 0.129907i $$-0.958532\pi$$
0.991526 0.129907i $$-0.0414680\pi$$
$$242$$ − 0.00864462i 0 0.000555697i
$$243$$ −54.4020 −3.48989
$$244$$ 10.6407 0.681203
$$245$$ 2.23136i 0.142556i
$$246$$ −7.05444 −0.449775
$$247$$ 0 0
$$248$$ −1.56600 −0.0994410
$$249$$ 15.4171i 0.977019i
$$250$$ 2.59210 0.163939
$$251$$ −27.8685 −1.75905 −0.879523 0.475857i $$-0.842138\pi$$
−0.879523 + 0.475857i $$0.842138\pi$$
$$252$$ 15.6445i 0.985511i
$$253$$ 2.78572i 0.175137i
$$254$$ − 4.26477i − 0.267596i
$$255$$ 10.1989i 0.638678i
$$256$$ 11.8875 0.742972
$$257$$ 7.14064 0.445421 0.222710 0.974885i $$-0.428510\pi$$
0.222710 + 0.974885i $$0.428510\pi$$
$$258$$ 0.946472i 0.0589248i
$$259$$ 1.55361 0.0965369
$$260$$ 0 0
$$261$$ −4.87982 −0.302053
$$262$$ − 0.404500i − 0.0249901i
$$263$$ 21.3192 1.31460 0.657300 0.753629i $$-0.271699\pi$$
0.657300 + 0.753629i $$0.271699\pi$$
$$264$$ −10.0778 −0.620244
$$265$$ − 18.7347i − 1.15086i
$$266$$ − 0.748524i − 0.0458950i
$$267$$ 30.3264i 1.85594i
$$268$$ − 19.8263i − 1.21108i
$$269$$ 2.78875 0.170033 0.0850167 0.996380i $$-0.472906\pi$$
0.0850167 + 0.996380i $$0.472906\pi$$
$$270$$ −8.63964 −0.525792
$$271$$ 15.4747i 0.940024i 0.882660 + 0.470012i $$0.155750\pi$$
−0.882660 + 0.470012i $$0.844250\pi$$
$$272$$ 5.06521 0.307123
$$273$$ 0 0
$$274$$ −4.16524 −0.251631
$$275$$ − 0.0698632i − 0.00421291i
$$276$$ 5.42232 0.326385
$$277$$ −5.52955 −0.332238 −0.166119 0.986106i $$-0.553124\pi$$
−0.166119 + 0.986106i $$0.553124\pi$$
$$278$$ 3.22006i 0.193127i
$$279$$ 13.7850i 0.825285i
$$280$$ 2.03736i 0.121756i
$$281$$ 31.4871i 1.87836i 0.343419 + 0.939182i $$0.388415\pi$$
−0.343419 + 0.939182i $$0.611585\pi$$
$$282$$ 1.25148 0.0745243
$$283$$ 7.35118 0.436983 0.218491 0.975839i $$-0.429886\pi$$
0.218491 + 0.975839i $$0.429886\pi$$
$$284$$ − 10.1495i − 0.602259i
$$285$$ −23.9838 −1.42068
$$286$$ 0 0
$$287$$ 9.17783 0.541750
$$288$$ 21.5234i 1.26828i
$$289$$ −15.1072 −0.888660
$$290$$ −0.313437 −0.0184056
$$291$$ 51.0261i 2.99120i
$$292$$ 7.71494i 0.451483i
$$293$$ 13.5335i 0.790635i 0.918544 + 0.395318i $$0.129366\pi$$
−0.918544 + 0.395318i $$0.870634\pi$$
$$294$$ 0.768639i 0.0448279i
$$295$$ −19.6858 −1.14615
$$296$$ 1.41854 0.0824510
$$297$$ 55.5992i 3.22619i
$$298$$ 3.68565 0.213504
$$299$$ 0 0
$$300$$ −0.135987 −0.00785120
$$301$$ − 1.23136i − 0.0709745i
$$302$$ −3.22741 −0.185717
$$303$$ −26.4133 −1.51741
$$304$$ 11.9114i 0.683168i
$$305$$ − 12.1981i − 0.698462i
$$306$$ 2.55831i 0.146249i
$$307$$ 3.30609i 0.188688i 0.995540 + 0.0943442i $$0.0300754\pi$$
−0.995540 + 0.0943442i $$0.969925\pi$$
$$308$$ 6.46667 0.368473
$$309$$ 2.30838 0.131319
$$310$$ 0.885425i 0.0502888i
$$311$$ 34.3063 1.94533 0.972665 0.232214i $$-0.0745969\pi$$
0.972665 + 0.232214i $$0.0745969\pi$$
$$312$$ 0 0
$$313$$ 7.21428 0.407775 0.203888 0.978994i $$-0.434642\pi$$
0.203888 + 0.978994i $$0.434642\pi$$
$$314$$ − 3.00183i − 0.169403i
$$315$$ 17.9343 1.01048
$$316$$ 12.5557 0.706315
$$317$$ − 8.04040i − 0.451594i −0.974174 0.225797i $$-0.927501\pi$$
0.974174 0.225797i $$-0.0724986\pi$$
$$318$$ − 6.45355i − 0.361897i
$$319$$ 2.01708i 0.112935i
$$320$$ − 15.0479i − 0.841204i
$$321$$ −29.7224 −1.65894
$$322$$ 0.193997 0.0108110
$$323$$ 4.45108i 0.247665i
$$324$$ 61.2888 3.40493
$$325$$ 0 0
$$326$$ 4.25899 0.235884
$$327$$ 7.55040i 0.417538i
$$328$$ 8.37990 0.462703
$$329$$ −1.62817 −0.0897639
$$330$$ 5.69803i 0.313666i
$$331$$ 0.893687i 0.0491215i 0.999698 + 0.0245607i $$0.00781871\pi$$
−0.999698 + 0.0245607i $$0.992181\pi$$
$$332$$ − 9.03271i − 0.495734i
$$333$$ − 12.4870i − 0.684281i
$$334$$ −4.28002 −0.234192
$$335$$ −22.7281 −1.24177
$$336$$ − 12.2315i − 0.667285i
$$337$$ −15.0717 −0.821007 −0.410504 0.911859i $$-0.634647\pi$$
−0.410504 + 0.911859i $$0.634647\pi$$
$$338$$ 0 0
$$339$$ 31.5773 1.71504
$$340$$ − 5.97540i − 0.324062i
$$341$$ 5.69803 0.308566
$$342$$ −6.01616 −0.325317
$$343$$ − 1.00000i − 0.0539949i
$$344$$ − 1.12431i − 0.0606185i
$$345$$ − 6.21594i − 0.334655i
$$346$$ 3.97897i 0.213911i
$$347$$ −16.4164 −0.881276 −0.440638 0.897685i $$-0.645248\pi$$
−0.440638 + 0.897685i $$0.645248\pi$$
$$348$$ 3.92619 0.210466
$$349$$ − 34.3722i − 1.83990i −0.392035 0.919950i $$-0.628229\pi$$
0.392035 0.919950i $$-0.371771\pi$$
$$350$$ −0.00486525 −0.000260059 0
$$351$$ 0 0
$$352$$ 8.89672 0.474197
$$353$$ − 23.9163i − 1.27293i −0.771304 0.636467i $$-0.780395\pi$$
0.771304 0.636467i $$-0.219605\pi$$
$$354$$ −6.78120 −0.360416
$$355$$ −11.6349 −0.617519
$$356$$ − 17.7679i − 0.941697i
$$357$$ − 4.57069i − 0.241907i
$$358$$ − 3.35210i − 0.177164i
$$359$$ 6.17875i 0.326102i 0.986618 + 0.163051i $$0.0521335\pi$$
−0.986618 + 0.163051i $$0.947867\pi$$
$$360$$ 16.3750 0.863040
$$361$$ 8.53276 0.449092
$$362$$ − 1.58594i − 0.0833552i
$$363$$ 0.124133 0.00651531
$$364$$ 0 0
$$365$$ 8.84411 0.462922
$$366$$ − 4.20190i − 0.219637i
$$367$$ 19.8560 1.03647 0.518236 0.855237i $$-0.326589\pi$$
0.518236 + 0.855237i $$0.326589\pi$$
$$368$$ −3.08711 −0.160927
$$369$$ − 73.7656i − 3.84008i
$$370$$ − 0.802052i − 0.0416967i
$$371$$ 8.39607i 0.435902i
$$372$$ − 11.0911i − 0.575045i
$$373$$ 30.1951 1.56344 0.781721 0.623628i $$-0.214342\pi$$
0.781721 + 0.623628i $$0.214342\pi$$
$$374$$ 1.05748 0.0546809
$$375$$ 37.2216i 1.92212i
$$376$$ −1.48662 −0.0766664
$$377$$ 0 0
$$378$$ 3.87192 0.199150
$$379$$ − 4.32242i − 0.222028i −0.993819 0.111014i $$-0.964590\pi$$
0.993819 0.111014i $$-0.0354098\pi$$
$$380$$ 14.0519 0.720846
$$381$$ 61.2405 3.13745
$$382$$ − 0.659755i − 0.0337560i
$$383$$ − 17.3481i − 0.886449i −0.896411 0.443224i $$-0.853834\pi$$
0.896411 0.443224i $$-0.146166\pi$$
$$384$$ − 22.9770i − 1.17254i
$$385$$ − 7.41314i − 0.377809i
$$386$$ −2.32529 −0.118354
$$387$$ −9.89690 −0.503087
$$388$$ − 29.8956i − 1.51772i
$$389$$ 25.3474 1.28516 0.642582 0.766217i $$-0.277863\pi$$
0.642582 + 0.766217i $$0.277863\pi$$
$$390$$ 0 0
$$391$$ −1.15360 −0.0583398
$$392$$ − 0.913059i − 0.0461164i
$$393$$ 5.80847 0.292999
$$394$$ 5.88052 0.296256
$$395$$ − 14.3934i − 0.724211i
$$396$$ − 51.9750i − 2.61184i
$$397$$ 27.0749i 1.35885i 0.733745 + 0.679425i $$0.237771\pi$$
−0.733745 + 0.679425i $$0.762229\pi$$
$$398$$ 2.87965i 0.144344i
$$399$$ 10.7485 0.538099
$$400$$ 0.0774219 0.00387110
$$401$$ 29.2858i 1.46246i 0.682129 + 0.731232i $$0.261054\pi$$
−0.682129 + 0.731232i $$0.738946\pi$$
$$402$$ −7.82916 −0.390483
$$403$$ 0 0
$$404$$ 15.4753 0.769924
$$405$$ − 70.2592i − 3.49121i
$$406$$ 0.140469 0.00697135
$$407$$ −5.16150 −0.255846
$$408$$ − 4.17331i − 0.206610i
$$409$$ 23.3713i 1.15563i 0.816166 + 0.577817i $$0.196095\pi$$
−0.816166 + 0.577817i $$0.803905\pi$$
$$410$$ − 4.73805i − 0.233996i
$$411$$ − 59.8112i − 2.95027i
$$412$$ −1.35246 −0.0666308
$$413$$ 8.82234 0.434119
$$414$$ − 1.55922i − 0.0766315i
$$415$$ −10.3548 −0.508295
$$416$$ 0 0
$$417$$ −46.2389 −2.26433
$$418$$ 2.48679i 0.121633i
$$419$$ 14.6064 0.713569 0.356785 0.934187i $$-0.383873\pi$$
0.356785 + 0.934187i $$0.383873\pi$$
$$420$$ −14.4295 −0.704087
$$421$$ 10.2728i 0.500668i 0.968160 + 0.250334i $$0.0805404\pi$$
−0.968160 + 0.250334i $$0.919460\pi$$
$$422$$ − 5.64342i − 0.274717i
$$423$$ 13.0862i 0.636273i
$$424$$ 7.66611i 0.372299i
$$425$$ 0.0289311 0.00140336
$$426$$ −4.00790 −0.194183
$$427$$ 5.46667i 0.264551i
$$428$$ 17.4141 0.841740
$$429$$ 0 0
$$430$$ −0.635689 −0.0306557
$$431$$ − 12.5017i − 0.602188i −0.953595 0.301094i $$-0.902648\pi$$
0.953595 0.301094i $$-0.0973518\pi$$
$$432$$ −61.6147 −2.96444
$$433$$ 10.9472 0.526090 0.263045 0.964784i $$-0.415273\pi$$
0.263045 + 0.964784i $$0.415273\pi$$
$$434$$ − 0.396810i − 0.0190475i
$$435$$ − 4.50083i − 0.215798i
$$436$$ − 4.42370i − 0.211857i
$$437$$ − 2.71282i − 0.129772i
$$438$$ 3.04654 0.145569
$$439$$ 17.9179 0.855176 0.427588 0.903974i $$-0.359363\pi$$
0.427588 + 0.903974i $$0.359363\pi$$
$$440$$ − 6.76864i − 0.322682i
$$441$$ −8.03736 −0.382732
$$442$$ 0 0
$$443$$ 27.7194 1.31699 0.658494 0.752586i $$-0.271194\pi$$
0.658494 + 0.752586i $$0.271194\pi$$
$$444$$ 10.0467i 0.476796i
$$445$$ −20.3684 −0.965556
$$446$$ −5.24018 −0.248130
$$447$$ 52.9245i 2.50324i
$$448$$ 6.74383i 0.318616i
$$449$$ 0.165980i 0.00783306i 0.999992 + 0.00391653i $$0.00124667\pi$$
−0.999992 + 0.00391653i $$0.998753\pi$$
$$450$$ 0.0391038i 0.00184337i
$$451$$ −30.4911 −1.43577
$$452$$ −18.5008 −0.870204
$$453$$ − 46.3444i − 2.17745i
$$454$$ −0.297313 −0.0139536
$$455$$ 0 0
$$456$$ 9.81404 0.459584
$$457$$ 31.7354i 1.48452i 0.670112 + 0.742260i $$0.266246\pi$$
−0.670112 + 0.742260i $$0.733754\pi$$
$$458$$ −1.07456 −0.0502107
$$459$$ −23.0242 −1.07468
$$460$$ 3.64185i 0.169802i
$$461$$ 29.0656i 1.35372i 0.736113 + 0.676859i $$0.236659\pi$$
−0.736113 + 0.676859i $$0.763341\pi$$
$$462$$ − 2.55361i − 0.118805i
$$463$$ − 6.31904i − 0.293671i −0.989161 0.146835i $$-0.953091\pi$$
0.989161 0.146835i $$-0.0469088\pi$$
$$464$$ −2.23531 −0.103772
$$465$$ −12.7144 −0.589615
$$466$$ − 2.75035i − 0.127408i
$$467$$ 34.6409 1.60299 0.801495 0.598002i $$-0.204038\pi$$
0.801495 + 0.598002i $$0.204038\pi$$
$$468$$ 0 0
$$469$$ 10.1857 0.470334
$$470$$ 0.840542i 0.0387713i
$$471$$ 43.1051 1.98618
$$472$$ 8.05532 0.370776
$$473$$ 4.09089i 0.188099i
$$474$$ − 4.95811i − 0.227734i
$$475$$ 0.0680349i 0.00312166i
$$476$$ 2.67792i 0.122742i
$$477$$ 67.4823 3.08980
$$478$$ 0.966587 0.0442107
$$479$$ 7.14230i 0.326340i 0.986598 + 0.163170i $$0.0521719\pi$$
−0.986598 + 0.163170i $$0.947828\pi$$
$$480$$ −19.8518 −0.906107
$$481$$ 0 0
$$482$$ 0.933174 0.0425049
$$483$$ 2.78572i 0.126755i
$$484$$ −0.0727284 −0.00330584
$$485$$ −34.2712 −1.55617
$$486$$ − 12.5865i − 0.570935i
$$487$$ − 18.5003i − 0.838327i −0.907911 0.419163i $$-0.862323\pi$$
0.907911 0.419163i $$-0.137677\pi$$
$$488$$ 4.99140i 0.225950i
$$489$$ 61.1575i 2.76564i
$$490$$ −0.516249 −0.0233218
$$491$$ 15.2781 0.689490 0.344745 0.938696i $$-0.387965\pi$$
0.344745 + 0.938696i $$0.387965\pi$$
$$492$$ 59.3500i 2.67571i
$$493$$ −0.835294 −0.0376197
$$494$$ 0 0
$$495$$ −59.5821 −2.67802
$$496$$ 6.31452i 0.283530i
$$497$$ 5.21428 0.233893
$$498$$ −3.56691 −0.159837
$$499$$ 12.4783i 0.558606i 0.960203 + 0.279303i $$0.0901034\pi$$
−0.960203 + 0.279303i $$0.909897\pi$$
$$500$$ − 21.8077i − 0.975272i
$$501$$ − 61.4595i − 2.74581i
$$502$$ − 6.44768i − 0.287774i
$$503$$ −2.58008 −0.115040 −0.0575200 0.998344i $$-0.518319\pi$$
−0.0575200 + 0.998344i $$0.518319\pi$$
$$504$$ −7.33859 −0.326887
$$505$$ − 17.7403i − 0.789431i
$$506$$ −0.644506 −0.0286518
$$507$$ 0 0
$$508$$ −35.8802 −1.59192
$$509$$ 35.6808i 1.58152i 0.612125 + 0.790761i $$0.290315\pi$$
−0.612125 + 0.790761i $$0.709685\pi$$
$$510$$ −2.35962 −0.104486
$$511$$ −3.96355 −0.175337
$$512$$ 16.5825i 0.732850i
$$513$$ − 54.1442i − 2.39053i
$$514$$ 1.65206i 0.0728694i
$$515$$ 1.55040i 0.0683190i
$$516$$ 7.96281 0.350543
$$517$$ 5.40919 0.237896
$$518$$ 0.359445i 0.0157931i
$$519$$ −57.1365 −2.50801
$$520$$ 0 0
$$521$$ −20.9637 −0.918437 −0.459219 0.888323i $$-0.651871\pi$$
−0.459219 + 0.888323i $$0.651871\pi$$
$$522$$ − 1.12900i − 0.0494149i
$$523$$ −22.8263 −0.998124 −0.499062 0.866566i $$-0.666322\pi$$
−0.499062 + 0.866566i $$0.666322\pi$$
$$524$$ −3.40312 −0.148666
$$525$$ − 0.0698632i − 0.00304908i
$$526$$ 4.93243i 0.215064i
$$527$$ 2.35962i 0.102787i
$$528$$ 40.6362i 1.76847i
$$529$$ −22.2969 −0.969431
$$530$$ 4.33447 0.188277
$$531$$ − 70.9083i − 3.07716i
$$532$$ −6.29744 −0.273029
$$533$$ 0 0
$$534$$ −7.01634 −0.303627
$$535$$ − 19.9628i − 0.863067i
$$536$$ 9.30018 0.401707
$$537$$ 48.1348 2.07717
$$538$$ 0.645208i 0.0278169i
$$539$$ 3.32225i 0.143100i
$$540$$ 72.6865i 3.12793i
$$541$$ − 30.2191i − 1.29922i −0.760266 0.649611i $$-0.774932\pi$$
0.760266 0.649611i $$-0.225068\pi$$
$$542$$ −3.58025 −0.153785
$$543$$ 22.7735 0.977305
$$544$$ 3.68423i 0.157960i
$$545$$ −5.07116 −0.217225
$$546$$ 0 0
$$547$$ −16.8223 −0.719271 −0.359636 0.933093i $$-0.617099\pi$$
−0.359636 + 0.933093i $$0.617099\pi$$
$$548$$ 35.0427i 1.49695i
$$549$$ 43.9376 1.87521
$$550$$ 0.0161636 0.000689219 0
$$551$$ − 1.96429i − 0.0836817i
$$552$$ 2.54352i 0.108260i
$$553$$ 6.45051i 0.274304i
$$554$$ − 1.27932i − 0.0543531i
$$555$$ 11.5172 0.488876
$$556$$ 27.0909 1.14891
$$557$$ 10.4918i 0.444553i 0.974984 + 0.222276i $$0.0713487\pi$$
−0.974984 + 0.222276i $$0.928651\pi$$
$$558$$ −3.18930 −0.135014
$$559$$ 0 0
$$560$$ 8.21520 0.347155
$$561$$ 15.1850i 0.641111i
$$562$$ −7.28489 −0.307294
$$563$$ −30.9474 −1.30428 −0.652138 0.758100i $$-0.726128\pi$$
−0.652138 + 0.758100i $$0.726128\pi$$
$$564$$ − 10.5288i − 0.443344i
$$565$$ 21.2086i 0.892252i
$$566$$ 1.70078i 0.0714889i
$$567$$ 31.4871i 1.32234i
$$568$$ 4.76095 0.199765
$$569$$ 36.9089 1.54730 0.773651 0.633612i $$-0.218428\pi$$
0.773651 + 0.633612i $$0.218428\pi$$
$$570$$ − 5.54892i − 0.232419i
$$571$$ 1.77093 0.0741113 0.0370556 0.999313i $$-0.488202\pi$$
0.0370556 + 0.999313i $$0.488202\pi$$
$$572$$ 0 0
$$573$$ 9.47383 0.395775
$$574$$ 2.12339i 0.0886286i
$$575$$ −0.0176328 −0.000735337 0
$$576$$ 54.2026 2.25844
$$577$$ − 9.83999i − 0.409644i −0.978799 0.204822i $$-0.934338\pi$$
0.978799 0.204822i $$-0.0656616\pi$$
$$578$$ − 3.49522i − 0.145382i
$$579$$ − 33.3903i − 1.38765i
$$580$$ 2.63699i 0.109495i
$$581$$ 4.64055 0.192523
$$582$$ −11.8054 −0.489351
$$583$$ − 27.8939i − 1.15525i
$$584$$ −3.61896 −0.149753
$$585$$ 0 0
$$586$$ −3.13112 −0.129345
$$587$$ − 15.1383i − 0.624826i −0.949946 0.312413i $$-0.898863\pi$$
0.949946 0.312413i $$-0.101137\pi$$
$$588$$ 6.46667 0.266681
$$589$$ −5.54892 −0.228639
$$590$$ − 4.55453i − 0.187507i
$$591$$ 84.4420i 3.47348i
$$592$$ − 5.71994i − 0.235088i
$$593$$ − 9.17148i − 0.376628i −0.982109 0.188314i $$-0.939698\pi$$
0.982109 0.188314i $$-0.0603022\pi$$
$$594$$ −12.8635 −0.527795
$$595$$ 3.06986 0.125852
$$596$$ − 31.0079i − 1.27013i
$$597$$ −41.3506 −1.69237
$$598$$ 0 0
$$599$$ −18.5811 −0.759202 −0.379601 0.925150i $$-0.623939\pi$$
−0.379601 + 0.925150i $$0.623939\pi$$
$$600$$ − 0.0637892i − 0.00260418i
$$601$$ −13.4036 −0.546744 −0.273372 0.961908i $$-0.588139\pi$$
−0.273372 + 0.961908i $$0.588139\pi$$
$$602$$ 0.284889 0.0116112
$$603$$ − 81.8665i − 3.33386i
$$604$$ 27.1527i 1.10483i
$$605$$ 0.0833731i 0.00338960i
$$606$$ − 6.11101i − 0.248243i
$$607$$ 12.6362 0.512889 0.256445 0.966559i $$-0.417449\pi$$
0.256445 + 0.966559i $$0.417449\pi$$
$$608$$ −8.66390 −0.351368
$$609$$ 2.01708i 0.0817361i
$$610$$ 2.82217 0.114266
$$611$$ 0 0
$$612$$ 21.5234 0.870032
$$613$$ 25.7079i 1.03833i 0.854673 + 0.519167i $$0.173758\pi$$
−0.854673 + 0.519167i $$0.826242\pi$$
$$614$$ −0.764900 −0.0308688
$$615$$ 68.0366 2.74350
$$616$$ 3.03341i 0.122220i
$$617$$ − 6.59620i − 0.265553i −0.991146 0.132777i $$-0.957611\pi$$
0.991146 0.132777i $$-0.0423893\pi$$
$$618$$ 0.534070i 0.0214834i
$$619$$ 21.0124i 0.844559i 0.906466 + 0.422280i $$0.138770\pi$$
−0.906466 + 0.422280i $$0.861230\pi$$
$$620$$ 7.44921 0.299168
$$621$$ 14.0327 0.563112
$$622$$ 7.93712i 0.318250i
$$623$$ 9.12826 0.365716
$$624$$ 0 0
$$625$$ −24.8944 −0.995777
$$626$$ 1.66910i 0.0667108i
$$627$$ −35.7093 −1.42609
$$628$$ −25.2548 −1.00778
$$629$$ − 2.13743i − 0.0852250i
$$630$$ 4.14929i 0.165311i
$$631$$ − 26.0210i − 1.03588i −0.855417 0.517940i $$-0.826699\pi$$
0.855417 0.517940i $$-0.173301\pi$$
$$632$$ 5.88970i 0.234280i
$$633$$ 81.0373 3.22095
$$634$$ 1.86023 0.0738793
$$635$$ 41.1316i 1.63226i
$$636$$ −54.2946 −2.15292
$$637$$ 0 0
$$638$$ −0.466673 −0.0184758
$$639$$ − 41.9091i − 1.65790i
$$640$$ 15.4323 0.610015
$$641$$ −18.5339 −0.732044 −0.366022 0.930606i $$-0.619281\pi$$
−0.366022 + 0.930606i $$0.619281\pi$$
$$642$$ − 6.87661i − 0.271398i
$$643$$ − 14.4466i − 0.569717i −0.958570 0.284858i $$-0.908053\pi$$
0.958570 0.284858i $$-0.0919466\pi$$
$$644$$ − 1.63212i − 0.0643146i
$$645$$ − 9.12826i − 0.359425i
$$646$$ −1.02981 −0.0405172
$$647$$ −29.2875 −1.15141 −0.575706 0.817657i $$-0.695273\pi$$
−0.575706 + 0.817657i $$0.695273\pi$$
$$648$$ 28.7496i 1.12939i
$$649$$ −29.3100 −1.15052
$$650$$ 0 0
$$651$$ 5.69803 0.223324
$$652$$ − 35.8315i − 1.40327i
$$653$$ −30.9615 −1.21162 −0.605808 0.795611i $$-0.707150\pi$$
−0.605808 + 0.795611i $$0.707150\pi$$
$$654$$ −1.74687 −0.0683079
$$655$$ 3.90121i 0.152433i
$$656$$ − 33.7900i − 1.31928i
$$657$$ 31.8565i 1.24284i
$$658$$ − 0.376695i − 0.0146851i
$$659$$ −37.0828 −1.44454 −0.722270 0.691611i $$-0.756901\pi$$
−0.722270 + 0.691611i $$0.756901\pi$$
$$660$$ 47.9384 1.86600
$$661$$ 20.4018i 0.793540i 0.917918 + 0.396770i $$0.129869\pi$$
−0.917918 + 0.396770i $$0.870131\pi$$
$$662$$ −0.206764 −0.00803611
$$663$$ 0 0
$$664$$ 4.23710 0.164431
$$665$$ 7.21915i 0.279947i
$$666$$ 2.88899 0.111946
$$667$$ 0.509090 0.0197120
$$668$$ 36.0085i 1.39321i
$$669$$ − 75.2469i − 2.90921i
$$670$$ − 5.25838i − 0.203149i
$$671$$ − 18.1617i − 0.701123i
$$672$$ 8.89672 0.343199
$$673$$ −14.5110 −0.559359 −0.279679 0.960093i $$-0.590228\pi$$
−0.279679 + 0.960093i $$0.590228\pi$$
$$674$$ − 3.48700i − 0.134314i
$$675$$ −0.351926 −0.0135457
$$676$$ 0 0
$$677$$ −3.51476 −0.135083 −0.0675417 0.997716i $$-0.521516\pi$$
−0.0675417 + 0.997716i $$0.521516\pi$$
$$678$$ 7.30575i 0.280575i
$$679$$ 15.3589 0.589420
$$680$$ 2.80297 0.107489
$$681$$ − 4.26930i − 0.163600i
$$682$$ 1.31830i 0.0504804i
$$683$$ 27.0753i 1.03601i 0.855379 + 0.518003i $$0.173324\pi$$
−0.855379 + 0.518003i $$0.826676\pi$$
$$684$$ 50.6149i 1.93531i
$$685$$ 40.1717 1.53488
$$686$$ 0.231361 0.00883340
$$687$$ − 15.4302i − 0.588700i
$$688$$ −4.53350 −0.172838
$$689$$ 0 0
$$690$$ 1.43812 0.0547485
$$691$$ 29.7404i 1.13138i 0.824618 + 0.565690i $$0.191390\pi$$
−0.824618 + 0.565690i $$0.808610\pi$$
$$692$$ 33.4757 1.27255
$$693$$ 26.7022 1.01433
$$694$$ − 3.79810i − 0.144174i
$$695$$ − 31.0559i − 1.17802i
$$696$$ 1.84171i 0.0698099i
$$697$$ − 12.6267i − 0.478270i
$$698$$ 7.95237 0.301002
$$699$$ 39.4940 1.49380
$$700$$ 0.0409321i 0.00154709i
$$701$$ −18.2888 −0.690760 −0.345380 0.938463i $$-0.612250\pi$$
−0.345380 + 0.938463i $$0.612250\pi$$
$$702$$ 0 0
$$703$$ 5.02642 0.189575
$$704$$ − 22.4047i − 0.844409i
$$705$$ −12.0699 −0.454577
$$706$$ 5.53329 0.208248
$$707$$ 7.95042i 0.299006i
$$708$$ 57.0512i 2.14411i
$$709$$ 28.6804i 1.07711i 0.842589 + 0.538557i $$0.181030\pi$$
−0.842589 + 0.538557i $$0.818970\pi$$
$$710$$ − 2.69187i − 0.101024i
$$711$$ 51.8451 1.94434
$$712$$ 8.33464 0.312354
$$713$$ − 1.43812i − 0.0538582i
$$714$$ 1.05748 0.0395752
$$715$$ 0 0
$$716$$ −28.2017 −1.05395
$$717$$ 13.8798i 0.518351i
$$718$$ −1.42952 −0.0533492
$$719$$ −25.4762 −0.950103 −0.475052 0.879958i $$-0.657571\pi$$
−0.475052 + 0.879958i $$0.657571\pi$$
$$720$$ − 66.0285i − 2.46074i
$$721$$ − 0.694825i − 0.0258766i
$$722$$ 1.97415i 0.0734701i
$$723$$ 13.4000i 0.498352i
$$724$$ −13.3428 −0.495879
$$725$$ −0.0127675 −0.000474173 0
$$726$$ 0.0287196i 0.00106588i
$$727$$ 9.02572 0.334746 0.167373 0.985894i $$-0.446472\pi$$
0.167373 + 0.985894i $$0.446472\pi$$
$$728$$ 0 0
$$729$$ 86.2759 3.19540
$$730$$ 2.04618i 0.0757325i
$$731$$ −1.69408 −0.0626579
$$732$$ −35.3512 −1.30662
$$733$$ − 7.57069i − 0.279630i −0.990178 0.139815i $$-0.955349\pi$$
0.990178 0.139815i $$-0.0446508\pi$$
$$734$$ 4.59389i 0.169564i
$$735$$ − 7.41314i − 0.273438i
$$736$$ − 2.24544i − 0.0827681i
$$737$$ −33.8396 −1.24650
$$738$$ 17.0665 0.628225
$$739$$ 6.37296i 0.234433i 0.993106 + 0.117216i $$0.0373971\pi$$
−0.993106 + 0.117216i $$0.962603\pi$$
$$740$$ −6.74778 −0.248053
$$741$$ 0 0
$$742$$ −1.94252 −0.0713122
$$743$$ − 22.8297i − 0.837539i −0.908092 0.418770i $$-0.862461\pi$$
0.908092 0.418770i $$-0.137539\pi$$
$$744$$ 5.20264 0.190738
$$745$$ −35.5463 −1.30231
$$746$$ 6.98596i 0.255774i
$$747$$ − 37.2978i − 1.36466i
$$748$$ − 8.89672i − 0.325296i
$$749$$ 8.94647i 0.326897i
$$750$$ −8.61162 −0.314452
$$751$$ −39.3695 −1.43661 −0.718307 0.695726i $$-0.755083\pi$$
−0.718307 + 0.695726i $$0.755083\pi$$
$$752$$ 5.99443i 0.218594i
$$753$$ 92.5863 3.37403
$$754$$ 0 0
$$755$$ 31.1268 1.13282
$$756$$ − 32.5750i − 1.18474i
$$757$$ 8.72714 0.317193 0.158597 0.987343i $$-0.449303\pi$$
0.158597 + 0.987343i $$0.449303\pi$$
$$758$$ 1.00004 0.0363231
$$759$$ − 9.25486i − 0.335930i
$$760$$ 6.59151i 0.239099i
$$761$$ 22.8391i 0.827915i 0.910296 + 0.413958i $$0.135854\pi$$
−0.910296 + 0.413958i $$0.864146\pi$$
$$762$$ 14.1687i 0.513276i
$$763$$ 2.27268 0.0822764
$$764$$ −5.55062 −0.200814
$$765$$ − 24.6736i − 0.892076i
$$766$$ 4.01368 0.145020
$$767$$ 0 0
$$768$$ −39.4934 −1.42510
$$769$$ 34.8349i 1.25618i 0.778141 + 0.628089i $$0.216163\pi$$
−0.778141 + 0.628089i $$0.783837\pi$$
$$770$$ 1.71511 0.0618083
$$771$$ −23.7230 −0.854363
$$772$$ 19.5630i 0.704088i
$$773$$ − 33.2743i − 1.19679i −0.801200 0.598397i $$-0.795804\pi$$
0.801200 0.598397i $$-0.204196\pi$$
$$774$$ − 2.28975i − 0.0823035i
$$775$$ 0.0360668i 0.00129556i
$$776$$ 14.0236 0.503416
$$777$$ −5.16150 −0.185168
$$778$$ 5.86440i 0.210249i
$$779$$ 29.6932 1.06387
$$780$$ 0 0
$$781$$ −17.3232 −0.619872
$$782$$ − 0.266897i − 0.00954421i
$$783$$ 10.1608 0.363116
$$784$$ −3.68170 −0.131489
$$785$$ 28.9512i 1.03331i
$$786$$ 1.34385i 0.0479336i
$$787$$ 27.8157i 0.991524i 0.868458 + 0.495762i $$0.165111\pi$$
−0.868458 + 0.495762i $$0.834889\pi$$
$$788$$ − 49.4737i − 1.76243i
$$789$$ −70.8278 −2.52154
$$790$$ 3.33007 0.118479
$$791$$ − 9.50478i − 0.337951i
$$792$$ 24.3806 0.866329
$$793$$ 0 0
$$794$$ −6.26407 −0.222304
$$795$$ 62.2413i 2.20747i
$$796$$ 24.2269 0.858699
$$797$$ −35.8685 −1.27053 −0.635264 0.772295i $$-0.719109\pi$$
−0.635264 + 0.772295i $$0.719109\pi$$
$$798$$ 2.48679i 0.0880313i
$$799$$ 2.24001i 0.0792457i
$$800$$ 0.0563136i 0.00199099i
$$801$$ − 73.3671i − 2.59230i
$$802$$ −6.77559 −0.239254
$$803$$ 13.1679 0.464686
$$804$$ 65.8678i 2.32298i
$$805$$ −1.87100 −0.0659441
$$806$$ 0 0
$$807$$ −9.26495 −0.326142
$$808$$ 7.25921i 0.255378i
$$809$$ −17.8245 −0.626675 −0.313337 0.949642i $$-0.601447\pi$$
−0.313337 + 0.949642i $$0.601447\pi$$
$$810$$ 16.2552 0.571150
$$811$$ 25.2152i 0.885425i 0.896664 + 0.442713i $$0.145984\pi$$
−0.896664 + 0.442713i $$0.854016\pi$$
$$812$$ − 1.18178i − 0.0414725i
$$813$$ − 51.4110i − 1.80306i
$$814$$ − 1.19417i − 0.0418556i
$$815$$ −41.0759 −1.43883
$$816$$ −16.8279 −0.589095
$$817$$ − 3.98384i − 0.139377i
$$818$$ −5.40719 −0.189058
$$819$$ 0 0
$$820$$ −39.8619 −1.39204
$$821$$ − 10.4559i − 0.364915i −0.983214 0.182457i $$-0.941595\pi$$
0.983214 0.182457i $$-0.0584052\pi$$
$$822$$ 13.8380 0.482655
$$823$$ 33.2405 1.15869 0.579346 0.815082i $$-0.303308\pi$$
0.579346 + 0.815082i $$0.303308\pi$$
$$824$$ − 0.634416i − 0.0221009i
$$825$$ 0.232103i 0.00808080i
$$826$$ 2.04114i 0.0710205i
$$827$$ 37.9927i 1.32113i 0.750767 + 0.660567i $$0.229684\pi$$
−0.750767 + 0.660567i $$0.770316\pi$$
$$828$$ −13.1180 −0.455880
$$829$$ −16.6944 −0.579821 −0.289911 0.957054i $$-0.593626\pi$$
−0.289911 + 0.957054i $$0.593626\pi$$
$$830$$ − 2.39568i − 0.0831554i
$$831$$ 18.3706 0.637268
$$832$$ 0 0
$$833$$ −1.37578 −0.0476680
$$834$$ − 10.6979i − 0.370437i
$$835$$ 41.2787 1.42851
$$836$$ 20.9217 0.723592
$$837$$ − 28.7031i − 0.992123i
$$838$$ 3.37935i 0.116738i
$$839$$ 46.6411i 1.61023i 0.593119 + 0.805115i $$0.297896\pi$$
−0.593119 + 0.805115i $$0.702104\pi$$
$$840$$ − 6.76864i − 0.233540i
$$841$$ −28.6314 −0.987289
$$842$$ −2.37673 −0.0819077
$$843$$ − 104.608i − 3.60290i
$$844$$ −47.4789 −1.63429
$$845$$ 0 0
$$846$$ −3.02763 −0.104092
$$847$$ − 0.0373642i − 0.00128385i
$$848$$ 30.9118 1.06152
$$849$$ −24.4225 −0.838178
$$850$$ 0.00669352i 0 0.000229586i
$$851$$ 1.30271i 0.0446563i
$$852$$ 33.7191i 1.15520i
$$853$$ − 39.5640i − 1.35464i −0.735686 0.677322i $$-0.763140\pi$$
0.735686 0.677322i $$-0.236860\pi$$
$$854$$ −1.26477 −0.0432797
$$855$$ 58.0229 1.98434
$$856$$ 8.16866i 0.279199i
$$857$$ 19.5613 0.668201 0.334101 0.942537i $$-0.391567\pi$$
0.334101 + 0.942537i $$0.391567\pi$$
$$858$$ 0 0
$$859$$ −10.1632 −0.346762 −0.173381 0.984855i $$-0.555469\pi$$
−0.173381 + 0.984855i $$0.555469\pi$$
$$860$$ 5.34815i 0.182370i
$$861$$ −30.4911 −1.03913
$$862$$ 2.89241 0.0985160
$$863$$ 26.8903i 0.915356i 0.889118 + 0.457678i $$0.151319\pi$$
−0.889118 + 0.457678i $$0.848681\pi$$
$$864$$ − 44.8160i − 1.52467i
$$865$$ − 38.3752i − 1.30480i
$$866$$ 2.53276i 0.0860666i
$$867$$ 50.1900 1.70454
$$868$$ −3.33842 −0.113313
$$869$$ − 21.4302i − 0.726971i
$$870$$ 1.04132 0.0353039
$$871$$ 0 0
$$872$$ 2.07509 0.0702713
$$873$$ − 123.445i − 4.17798i
$$874$$ 0.627640 0.0212302
$$875$$ 11.2037 0.378755
$$876$$ − 25.6310i − 0.865991i
$$877$$ − 1.70160i − 0.0574590i −0.999587 0.0287295i $$-0.990854\pi$$
0.999587 0.0287295i $$-0.00914614\pi$$
$$878$$ 4.14551i 0.139904i
$$879$$ − 44.9617i − 1.51652i
$$880$$ −27.2930 −0.920046
$$881$$ 11.3090 0.381008 0.190504 0.981686i $$-0.438988\pi$$
0.190504 + 0.981686i $$0.438988\pi$$
$$882$$ − 1.85953i − 0.0626137i
$$883$$ 46.9068 1.57854 0.789270 0.614047i $$-0.210459\pi$$
0.789270 + 0.614047i $$0.210459\pi$$
$$884$$ 0 0
$$885$$ 65.4013 2.19844
$$886$$ 6.41318i 0.215455i
$$887$$ −2.44692 −0.0821594 −0.0410797 0.999156i $$-0.513080\pi$$
−0.0410797 + 0.999156i $$0.513080\pi$$
$$888$$ −4.71275 −0.158150
$$889$$ − 18.4334i − 0.618237i
$$890$$ − 4.71246i − 0.157962i
$$891$$ − 104.608i − 3.50451i
$$892$$ 44.0864i 1.47612i
$$893$$ −5.26764 −0.176275
$$894$$ −12.2447 −0.409523
$$895$$ 32.3293i 1.08065i
$$896$$ −6.91610 −0.231051
$$897$$ 0 0
$$898$$ −0.0384012 −0.00128146
$$899$$ − 1.04132i − 0.0347298i
$$900$$ 0.328986 0.0109662
$$901$$ 11.5511 0.384825
$$902$$ − 7.05444i − 0.234887i
$$903$$ 4.09089i 0.136136i
$$904$$ − 8.67842i − 0.288640i
$$905$$ 15.2956i 0.508443i
$$906$$ 10.7223 0.356224
$$907$$ 41.4165 1.37521 0.687607 0.726083i $$-0.258661\pi$$
0.687607 + 0.726083i $$0.258661\pi$$
$$908$$ 2.50133i 0.0830097i
$$909$$ 63.9004 2.11944
$$910$$ 0 0
$$911$$ −11.9951 −0.397416 −0.198708 0.980059i $$-0.563675\pi$$
−0.198708 + 0.980059i $$0.563675\pi$$
$$912$$ − 39.5728i − 1.31039i
$$913$$ −15.4171 −0.510231
$$914$$ −7.34233 −0.242863
$$915$$ 40.5252i 1.33972i
$$916$$ 9.04040i 0.298703i
$$917$$ − 1.74835i − 0.0577357i
$$918$$ − 5.32691i − 0.175814i
$$919$$ 44.9416 1.48249 0.741243 0.671237i $$-0.234237\pi$$
0.741243 + 0.671237i $$0.234237\pi$$
$$920$$ −1.70833 −0.0563221
$$921$$ − 10.9837i − 0.361924i
$$922$$ −6.72463 −0.221464
$$923$$ 0 0
$$924$$ −21.4839 −0.706769
$$925$$ − 0.0326707i − 0.00107421i
$$926$$ 1.46198 0.0480436
$$927$$ −5.58456 −0.183421
$$928$$ − 1.62588i − 0.0533720i
$$929$$ 28.2595i 0.927164i 0.886054 + 0.463582i $$0.153436\pi$$
−0.886054 + 0.463582i $$0.846564\pi$$
$$930$$ − 2.94161i − 0.0964591i
$$931$$ − 3.23531i − 0.106033i
$$932$$ −23.1391 −0.757947
$$933$$ −113.974 −3.73134
$$934$$ 8.01455i 0.262244i
$$935$$ −10.1989 −0.333538
$$936$$ 0 0
$$937$$ 32.4601 1.06042 0.530212 0.847865i $$-0.322112\pi$$
0.530212 + 0.847865i $$0.322112\pi$$
$$938$$ 2.35658i 0.0769451i
$$939$$ −23.9677 −0.782155
$$940$$ 7.07160 0.230650
$$941$$ − 12.6051i − 0.410913i −0.978666 0.205457i $$-0.934132\pi$$
0.978666 0.205457i $$-0.0658679\pi$$
$$942$$ 9.97283i 0.324932i
$$943$$ 7.69563i 0.250604i
$$944$$ − 32.4812i − 1.05717i
$$945$$ −37.3427 −1.21476
$$946$$ −0.946472 −0.0307725
$$947$$ 13.2802i 0.431548i 0.976443 + 0.215774i $$0.0692275\pi$$
−0.976443 + 0.215774i $$0.930772\pi$$
$$948$$ −41.7133 −1.35479
$$949$$ 0 0
$$950$$ −0.0157406 −0.000510693 0
$$951$$ 26.7122i 0.866204i
$$952$$ −1.25617 −0.0407127
$$953$$ 58.4319 1.89279 0.946397 0.323006i $$-0.104693\pi$$
0.946397 + 0.323006i $$0.104693\pi$$
$$954$$ 15.6127i 0.505481i
$$955$$ 6.36301i 0.205902i
$$956$$ − 8.13204i − 0.263009i
$$957$$ − 6.70124i − 0.216620i
$$958$$ −1.65245 −0.0533882
$$959$$ −18.0032 −0.581354
$$960$$ 49.9930i 1.61352i
$$961$$ 28.0584 0.905109
$$962$$ 0 0
$$963$$ 71.9061 2.31714
$$964$$ − 7.85093i − 0.252861i
$$965$$ 22.4263 0.721927
$$966$$ −0.644506 −0.0207366
$$967$$ 33.2182i 1.06823i 0.845413 + 0.534113i $$0.179354\pi$$
−0.845413 + 0.534113i $$0.820646\pi$$
$$968$$ − 0.0341157i − 0.00109652i
$$969$$ − 14.7876i − 0.475047i
$$970$$ − 7.92901i − 0.254585i
$$971$$ 16.7778 0.538425 0.269213 0.963081i $$-0.413237\pi$$
0.269213 + 0.963081i $$0.413237\pi$$
$$972$$ −105.892 −3.39649
$$973$$ 13.9179i 0.446188i
$$974$$ 4.28023 0.137148
$$975$$ 0 0
$$976$$ 20.1266 0.644238
$$977$$ − 50.0422i − 1.60099i −0.599338 0.800496i $$-0.704569\pi$$
0.599338 0.800496i $$-0.295431\pi$$
$$978$$ −14.1495 −0.452450
$$979$$ −30.3264 −0.969235
$$980$$ 4.34328i 0.138741i
$$981$$ − 18.2663i − 0.583199i
$$982$$ 3.53475i 0.112798i
$$983$$ − 16.6741i − 0.531822i −0.963998 0.265911i $$-0.914327\pi$$
0.963998 0.265911i $$-0.0856728\pi$$
$$984$$ −27.8402 −0.887512
$$985$$ −56.7147 −1.80708
$$986$$ − 0.193254i − 0.00615447i
$$987$$ 5.40919 0.172177
$$988$$ 0 0
$$989$$ 1.03250 0.0328316
$$990$$ − 13.7850i − 0.438115i
$$991$$ 20.3285 0.645756 0.322878 0.946441i $$-0.395350\pi$$
0.322878 + 0.946441i $$0.395350\pi$$
$$992$$ −4.59293 −0.145826
$$993$$ − 2.96905i − 0.0942201i
$$994$$ 1.20638i 0.0382641i
$$995$$ − 27.7728i − 0.880456i
$$996$$ 30.0089i 0.950870i
$$997$$ 6.27646 0.198777 0.0993887 0.995049i $$-0.468311\pi$$
0.0993887 + 0.995049i $$0.468311\pi$$
$$998$$ −2.88699 −0.0913862
$$999$$ 26.0003i 0.822614i
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.337.5 8
13.2 odd 12 91.2.f.c.22.2 8
13.5 odd 4 1183.2.a.k.1.3 4
13.6 odd 12 91.2.f.c.29.2 yes 8
13.8 odd 4 1183.2.a.l.1.2 4
13.12 even 2 inner 1183.2.c.g.337.4 8
39.2 even 12 819.2.o.h.568.3 8
39.32 even 12 819.2.o.h.757.3 8
52.15 even 12 1456.2.s.q.113.1 8
52.19 even 12 1456.2.s.q.1121.1 8
91.2 odd 12 637.2.h.h.165.3 8
91.6 even 12 637.2.f.i.393.2 8
91.19 even 12 637.2.g.j.263.2 8
91.32 odd 12 637.2.h.h.471.3 8
91.34 even 4 8281.2.a.bt.1.2 4
91.41 even 12 637.2.f.i.295.2 8
91.45 even 12 637.2.h.i.471.3 8
91.54 even 12 637.2.h.i.165.3 8
91.58 odd 12 637.2.g.k.263.2 8
91.67 odd 12 637.2.g.k.373.2 8
91.80 even 12 637.2.g.j.373.2 8
91.83 even 4 8281.2.a.bp.1.3 4

By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.f.c.22.2 8 13.2 odd 12
91.2.f.c.29.2 yes 8 13.6 odd 12
637.2.f.i.295.2 8 91.41 even 12
637.2.f.i.393.2 8 91.6 even 12
637.2.g.j.263.2 8 91.19 even 12
637.2.g.j.373.2 8 91.80 even 12
637.2.g.k.263.2 8 91.58 odd 12
637.2.g.k.373.2 8 91.67 odd 12
637.2.h.h.165.3 8 91.2 odd 12
637.2.h.h.471.3 8 91.32 odd 12
637.2.h.i.165.3 8 91.54 even 12
637.2.h.i.471.3 8 91.45 even 12
819.2.o.h.568.3 8 39.2 even 12
819.2.o.h.757.3 8 39.32 even 12
1183.2.a.k.1.3 4 13.5 odd 4
1183.2.a.l.1.2 4 13.8 odd 4
1183.2.c.g.337.4 8 13.12 even 2 inner
1183.2.c.g.337.5 8 1.1 even 1 trivial
1456.2.s.q.113.1 8 52.15 even 12
1456.2.s.q.1121.1 8 52.19 even 12
8281.2.a.bp.1.3 4 91.83 even 4
8281.2.a.bt.1.2 4 91.34 even 4