Newform orbit 605.2.s.b

• Label: 605.2.s.b
• Level: $605$
• Weight: $2$
• Character orbit: 605.s
• Analytic conductor: $4.831$
• Analytic rank: $0$
• Dimension: $880$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.83094932229\)
Analytic rank:	\(0\)
Dimension:	\(880\)
Relative dimension:	\(22\) over \(\Q(\zeta_{55})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} + O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
16.1	−2.61070	−	0.299550i	−0.194849	−	0.141566i	4.77802	+	1.11108i	−0.564443	+	0.825472i	0.466287	+	0.427954i	3.66250	+	3.76862i	−7.19116	−	2.56580i	−0.909126	−	2.79800i	1.72086	−	1.98598i
16.2	−2.40958	−	0.276474i	−1.30445	−	0.947741i	3.78161	+	0.879377i	−0.564443	+	0.825472i	2.88116	+	2.64430i	−2.42714	−	2.49747i	−4.30030	−	1.53434i	−0.123665	−	0.380602i	1.58829	−	1.83299i
16.3	−2.03821	−	0.233862i	0.653999	+	0.475158i	2.15157	+	0.500325i	−0.564443	+	0.825472i	−1.22186	−	1.12142i	−0.0770600	−	0.0792929i	−0.403791	−	0.144072i	−0.725112	−	2.23166i	1.34350	−	1.55048i
16.4	−1.80070	−	0.206611i	−1.29126	−	0.938155i	1.25182	+	0.291098i	−0.564443	+	0.825472i	2.13134	+	1.95613i	−0.0685099	−	0.0704951i	1.22021	+	0.435369i	−0.139834	−	0.430365i	1.18695	−	1.36981i
16.5	−1.72317	−	0.197715i	−2.49016	−	1.80921i	0.982201	+	0.228401i	−0.564443	+	0.825472i	3.93327	+	3.60992i	−0.450743	−	0.463803i	1.61987	+	0.577969i	2.00063	+	6.15729i	1.13584	−	1.31083i
16.6	−1.56544	−	0.179618i	1.90128	+	1.38136i	0.470322	+	0.109369i	−0.564443	+	0.825472i	−2.72823	−	2.50395i	−2.64879	−	2.72554i	2.25154	+	0.803346i	0.779664	+	2.39956i	1.03187	−	1.19084i
16.7	−1.42148	−	0.163100i	1.67703	+	1.21843i	0.0459846	+	0.0106933i	−0.564443	+	0.825472i	−2.18514	−	2.00550i	2.67320	+	2.75065i	2.63157	+	0.938944i	0.400791	+	1.23351i	0.936980	−	1.08133i
16.8	−0.756073	−	0.0867513i	−0.251034	−	0.182387i	−1.38390	−	0.321813i	−0.564443	+	0.825472i	0.173978	+	0.159675i	−2.99384	−	3.08059i	2.45196	+	0.874859i	−0.897298	−	2.76160i	0.498371	−	0.575151i
16.9	−0.457329	−	0.0524736i	−2.01066	−	1.46083i	−1.74163	−	0.404998i	−0.564443	+	0.825472i	0.842877	+	0.773585i	1.60972	+	1.65636i	1.64236	+	0.585993i	0.981676	+	3.02129i	0.301451	−	0.347893i
16.10	−0.325381	−	0.0373340i	1.10628	+	0.803759i	−1.84355	−	0.428698i	−0.564443	+	0.825472i	−0.329954	−	0.302829i	0.602100	+	0.619546i	1.20079	+	0.428440i	−0.349226	−	1.07481i	0.214477	−	0.247520i
16.11	0.00892359	+	0.00102389i	−0.467498	−	0.339657i	−1.94795	−	0.452975i	−0.564443	+	0.825472i	−0.00382399	−	0.00350963i	1.06012	+	1.09083i	−0.0338384	−	0.0120735i	−0.823864	−	2.53559i	−0.00588205	+	0.00678825i
16.12	0.252480	+	0.0289694i	2.55133	+	1.85365i	−1.88512	−	0.438365i	−0.564443	+	0.825472i	0.590461	+	0.541921i	−0.840226	−	0.864572i	−0.941970	−	0.336094i	2.14622	+	6.60538i	−0.166424	+	0.192064i
16.13	0.742152	+	0.0851540i	0.230756	+	0.167654i	−1.40448	−	0.326599i	−0.564443	+	0.825472i	0.156980	+	0.144075i	0.473372	+	0.487088i	−2.42169	−	0.864056i	−0.901911	−	2.77580i	−0.489195	+	0.564561i
16.14	1.25197	+	0.143650i	0.302448	+	0.219741i	−0.401226	−	0.0933012i	−0.564443	+	0.825472i	0.347090	+	0.318557i	−2.98838	−	3.07497i	−2.86272	−	1.02142i	−0.883862	−	2.72025i	−0.825246	+	0.952385i
16.15	1.27289	+	0.146051i	−1.27498	−	0.926331i	−0.349093	−	0.0811782i	−0.564443	+	0.825472i	−1.48763	−	1.36533i	1.90619	+	1.96142i	−2.84597	−	1.01544i	−0.159553	−	0.491055i	−0.839038	+	0.968301i
16.16	1.46553	+	0.168154i	−2.14433	−	1.55794i	0.171477	+	0.0398753i	−0.564443	+	0.825472i	−2.88060	−	2.64379i	0.537054	+	0.552615i	−2.53411	−	0.904170i	1.24390	+	3.82832i	−0.966014	+	1.11484i
16.17	1.82551	+	0.209458i	2.66801	+	1.93842i	1.34058	+	0.311739i	−0.564443	+	0.825472i	4.46445	+	4.09744i	0.0611421	+	0.0629137i	−1.07930	−	0.385094i	2.43374	+	7.49028i	−1.20330	+	1.38868i
16.18	2.04825	+	0.235014i	1.13699	+	0.826074i	2.19205	+	0.509740i	−0.564443	+	0.825472i	2.13470	+	1.95921i	3.19973	+	3.29244i	0.486498	+	0.173582i	−0.316695	−	0.974688i	−1.35012	+	1.55812i
16.19	2.13889	+	0.245415i	−1.59867	−	1.16150i	2.56661	+	0.596840i	−0.564443	+	0.825472i	−3.13432	−	2.87666i	−2.87657	−	2.95992i	1.28779	+	0.459482i	0.279601	+	0.860523i	−1.40987	+	1.62707i
16.20	2.28990	+	0.262741i	1.65951	+	1.20570i	3.22657	+	0.750306i	−0.564443	+	0.825472i	3.48331	+	3.19696i	−1.38442	−	1.42453i	2.84961	+	1.01674i	0.373196	+	1.14858i	−1.50940	+	1.74194i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
121.g	even	55	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	605.2.s.b	✓	880
121.g	even	55	1	inner	605.2.s.b	✓	880

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
605.2.s.b	✓	880	1.a	even	1	1	trivial
605.2.s.b	✓	880	121.g	even	55	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(23\!\cdots\!99\)\( T_{2}^{854} + \)\(62\!\cdots\!67\)\( T_{2}^{853} + \)\(34\!\cdots\!64\)\( T_{2}^{852} + 492665180714 T_{2}^{851} - \)\(23\!\cdots\!56\)\( T_{2}^{850} - \)\(68\!\cdots\!42\)\( T_{2}^{849} + \)\(11\!\cdots\!40\)\( T_{2}^{848} + \)\(81\!\cdots\!91\)\( T_{2}^{847} + \)\(60\!\cdots\!64\)\( T_{2}^{846} - \)\(55\!\cdots\!88\)\( T_{2}^{845} - \)\(94\!\cdots\!06\)\( T_{2}^{844} + \)\(22\!\cdots\!79\)\( T_{2}^{843} + \)\(11\!\cdots\!17\)\( T_{2}^{842} + \)\(61\!\cdots\!71\)\( T_{2}^{841} - \)\(93\!\cdots\!50\)\( T_{2}^{840} - \)\(19\!\cdots\!67\)\( T_{2}^{839} + \)\(47\!\cdots\!25\)\( T_{2}^{838} + \)\(17\!\cdots\!73\)\( T_{2}^{837} + \)\(14\!\cdots\!39\)\( T_{2}^{836} - \)\(12\!\cdots\!23\)\( T_{2}^{835} - \)\(27\!\cdots\!73\)\( T_{2}^{834} + \)\(65\!\cdots\!34\)\( T_{2}^{833} + \)\(26\!\cdots\!96\)\( T_{2}^{832} - \)\(80\!\cdots\!96\)\( T_{2}^{831} - \)\(16\!\cdots\!26\)\( T_{2}^{830} - \)\(27\!\cdots\!70\)\( T_{2}^{829} + \)\(69\!\cdots\!81\)\( T_{2}^{828} + \)\(30\!\cdots\!94\)\( T_{2}^{827} + \)\(18\!\cdots\!05\)\( T_{2}^{826} - \)\(21\!\cdots\!04\)\( T_{2}^{825} - \)\(34\!\cdots\!11\)\( T_{2}^{824} + \)\(11\!\cdots\!79\)\( T_{2}^{823} + \)\(32\!\cdots\!68\)\( T_{2}^{822} - \)\(22\!\cdots\!81\)\( T_{2}^{821} - \)\(21\!\cdots\!54\)\( T_{2}^{820} - \)\(34\!\cdots\!70\)\( T_{2}^{819} + \)\(12\!\cdots\!79\)\( T_{2}^{818} + \)\(44\!\cdots\!00\)\( T_{2}^{817} - \)\(51\!\cdots\!92\)\( T_{2}^{816} - \)\(35\!\cdots\!06\)\( T_{2}^{815} + \)\(39\!\cdots\!86\)\( T_{2}^{814} + \)\(21\!\cdots\!34\)\( T_{2}^{813} + \)\(20\!\cdots\!02\)\( T_{2}^{812} - \)\(52\!\cdots\!95\)\( T_{2}^{811} - \)\(36\!\cdots\!61\)\( T_{2}^{810} - \)\(47\!\cdots\!06\)\( T_{2}^{809} + \)\(36\!\cdots\!20\)\( T_{2}^{808} + \)\(76\!\cdots\!78\)\( T_{2}^{807} - \)\(21\!\cdots\!84\)\( T_{2}^{806} - \)\(83\!\cdots\!93\)\( T_{2}^{805} + \)\(56\!\cdots\!99\)\( T_{2}^{804} + \)\(70\!\cdots\!51\)\( T_{2}^{803} + \)\(33\!\cdots\!47\)\( T_{2}^{802} - \)\(33\!\cdots\!86\)\( T_{2}^{801} - \)\(82\!\cdots\!42\)\( T_{2}^{800} + \)\(16\!\cdots\!99\)\( T_{2}^{799} + \)\(92\!\cdots\!76\)\( T_{2}^{798} + \)\(11\!\cdots\!73\)\( T_{2}^{797} - \)\(63\!\cdots\!56\)\( T_{2}^{796} - \)\(13\!\cdots\!87\)\( T_{2}^{795} + \)\(22\!\cdots\!22\)\( T_{2}^{794} + \)\(10\!\cdots\!34\)\( T_{2}^{793} + \)\(60\!\cdots\!42\)\( T_{2}^{792} - \)\(52\!\cdots\!29\)\( T_{2}^{791} - \)\(18\!\cdots\!36\)\( T_{2}^{790} + \)\(15\!\cdots\!08\)\( T_{2}^{789} + \)\(17\!\cdots\!33\)\( T_{2}^{788} + \)\(56\!\cdots\!72\)\( T_{2}^{787} - \)\(10\!\cdots\!43\)\( T_{2}^{786} - \)\(76\!\cdots\!53\)\( T_{2}^{785} + \)\(34\!\cdots\!15\)\( T_{2}^{784} + \)\(78\!\cdots\!17\)\( T_{2}^{783} + \)\(17\!\cdots\!97\)\( T_{2}^{782} - \)\(42\!\cdots\!85\)\( T_{2}^{781} - \)\(12\!\cdots\!78\)\( T_{2}^{780} + \)\(20\!\cdots\!85\)\( T_{2}^{779} + \)\(12\!\cdots\!02\)\( T_{2}^{778} - \)\(12\!\cdots\!79\)\( T_{2}^{777} - \)\(60\!\cdots\!57\)\( T_{2}^{776} + \)\(42\!\cdots\!57\)\( T_{2}^{775} + \)\(15\!\cdots\!76\)\( T_{2}^{774} + \)\(21\!\cdots\!65\)\( T_{2}^{773} - \)\(32\!\cdots\!26\)\( T_{2}^{772} - \)\(32\!\cdots\!38\)\( T_{2}^{771} + \)\(25\!\cdots\!36\)\( T_{2}^{770} + \)\(28\!\cdots\!75\)\( T_{2}^{769} - \)\(26\!\cdots\!98\)\( T_{2}^{768} - \)\(19\!\cdots\!85\)\( T_{2}^{767} + \)\(23\!\cdots\!41\)\( T_{2}^{766} + \)\(53\!\cdots\!59\)\( T_{2}^{765} - \)\(10\!\cdots\!89\)\( T_{2}^{764} + \)\(28\!\cdots\!43\)\( T_{2}^{763} - \)\(21\!\cdots\!99\)\( T_{2}^{762} - \)\(35\!\cdots\!45\)\( T_{2}^{761} + \)\(45\!\cdots\!74\)\( T_{2}^{760} + \)\(21\!\cdots\!74\)\( T_{2}^{759} - \)\(99\!\cdots\!35\)\( T_{2}^{758} - \)\(42\!\cdots\!48\)\( T_{2}^{757} - \)\(18\!\cdots\!22\)\( T_{2}^{756} - \)\(98\!\cdots\!22\)\( T_{2}^{755} + \)\(29\!\cdots\!58\)\( T_{2}^{754} + \)\(96\!\cdots\!06\)\( T_{2}^{753} - \)\(19\!\cdots\!69\)\( T_{2}^{752} - \)\(25\!\cdots\!75\)\( T_{2}^{751} - \)\(34\!\cdots\!47\)\( T_{2}^{750} - \)\(13\!\cdots\!63\)\( T_{2}^{749} + \)\(17\!\cdots\!19\)\( T_{2}^{748} + \)\(20\!\cdots\!87\)\( T_{2}^{747} - \)\(15\!\cdots\!63\)\( T_{2}^{746} - \)\(18\!\cdots\!03\)\( T_{2}^{745} + \)\(80\!\cdots\!54\)\( T_{2}^{744} + \)\(10\!\cdots\!34\)\( T_{2}^{743} - \)\(13\!\cdots\!18\)\( T_{2}^{742} - \)\(34\!\cdots\!93\)\( T_{2}^{741} - \)\(21\!\cdots\!15\)\( T_{2}^{740} + \)\(15\!\cdots\!53\)\( T_{2}^{739} + \)\(26\!\cdots\!56\)\( T_{2}^{738} + \)\(82\!\cdots\!35\)\( T_{2}^{737} - \)\(16\!\cdots\!78\)\( T_{2}^{736} - \)\(10\!\cdots\!35\)\( T_{2}^{735} + \)\(47\!\cdots\!19\)\( T_{2}^{734} + \)\(60\!\cdots\!33\)\( T_{2}^{733} + \)\(17\!\cdots\!53\)\( T_{2}^{732} - \)\(24\!\cdots\!67\)\( T_{2}^{731} - \)\(36\!\cdots\!98\)\( T_{2}^{730} + \)\(18\!\cdots\!09\)\( T_{2}^{729} + \)\(25\!\cdots\!83\)\( T_{2}^{728} - \)\(14\!\cdots\!83\)\( T_{2}^{727} - \)\(76\!\cdots\!18\)\( T_{2}^{726} + \)\(48\!\cdots\!70\)\( T_{2}^{725} - \)\(21\!\cdots\!02\)\( T_{2}^{724} + \)\(35\!\cdots\!56\)\( T_{2}^{723} + \)\(42\!\cdots\!62\)\( T_{2}^{722} - \)\(13\!\cdots\!37\)\( T_{2}^{721} - \)\(31\!\cdots\!54\)\( T_{2}^{720} + \)\(13\!\cdots\!50\)\( T_{2}^{719} + \)\(12\!\cdots\!41\)\( T_{2}^{718} - \)\(84\!\cdots\!62\)\( T_{2}^{717} + \)\(61\!\cdots\!96\)\( T_{2}^{716} + \)\(23\!\cdots\!61\)\( T_{2}^{715} - \)\(45\!\cdots\!30\)\( T_{2}^{714} - \)\(25\!\cdots\!91\)\( T_{2}^{713} + \)\(37\!\cdots\!77\)\( T_{2}^{712} - \)\(32\!\cdots\!95\)\( T_{2}^{711} - \)\(18\!\cdots\!24\)\( T_{2}^{710} + \)\(43\!\cdots\!83\)\( T_{2}^{709} + \)\(25\!\cdots\!48\)\( T_{2}^{708} - \)\(77\!\cdots\!06\)\( T_{2}^{707} + \)\(41\!\cdots\!61\)\( T_{2}^{706} - \)\(29\!\cdots\!65\)\( T_{2}^{705} - \)\(40\!\cdots\!83\)\( T_{2}^{704} + \)\(25\!\cdots\!41\)\( T_{2}^{703} + \)\(20\!\cdots\!78\)\( T_{2}^{702} - \)\(80\!\cdots\!58\)\( T_{2}^{701} - \)\(58\!\cdots\!33\)\( T_{2}^{700} + \)\(35\!\cdots\!21\)\( T_{2}^{699} - \)\(11\!\cdots\!73\)\( T_{2}^{698} + \)\(17\!\cdots\!30\)\( T_{2}^{697} + \)\(30\!\cdots\!87\)\( T_{2}^{696} - \)\(22\!\cdots\!44\)\( T_{2}^{695} - \)\(21\!\cdots\!59\)\( T_{2}^{694} + \)\(15\!\cdots\!03\)\( T_{2}^{693} + \)\(87\!\cdots\!41\)\( T_{2}^{692} - \)\(59\!\cdots\!45\)\( T_{2}^{691} - \)\(14\!\cdots\!38\)\( T_{2}^{690} + \)\(17\!\cdots\!61\)\( T_{2}^{689} - \)\(13\!\cdots\!29\)\( T_{2}^{688} + \)\(33\!\cdots\!88\)\( T_{2}^{687} + \)\(14\!\cdots\!23\)\( T_{2}^{686} - \)\(56\!\cdots\!94\)\( T_{2}^{685} - \)\(70\!\cdots\!29\)\( T_{2}^{684} + \)\(14\!\cdots\!70\)\( T_{2}^{683} + \)\(16\!\cdots\!50\)\( T_{2}^{682} + \)\(16\!\cdots\!92\)\( T_{2}^{681} + \)\(83\!\cdots\!60\)\( T_{2}^{680} - \)\(90\!\cdots\!12\)\( T_{2}^{679} - \)\(50\!\cdots\!37\)\( T_{2}^{678} - \)\(48\!\cdots\!00\)\( T_{2}^{677} + \)\(42\!\cdots\!44\)\( T_{2}^{676} + \)\(16\!\cdots\!89\)\( T_{2}^{675} - \)\(14\!\cdots\!40\)\( T_{2}^{674} - \)\(20\!\cdots\!66\)\( T_{2}^{673} - \)\(23\!\cdots\!91\)\( T_{2}^{672} + \)\(21\!\cdots\!01\)\( T_{2}^{671} + \)\(49\!\cdots\!68\)\( T_{2}^{670} - \)\(11\!\cdots\!07\)\( T_{2}^{669} - \)\(31\!\cdots\!24\)\( T_{2}^{668} + \)\(36\!\cdots\!55\)\( T_{2}^{667} + \)\(14\!\cdots\!56\)\( T_{2}^{666} - \)\(39\!\cdots\!49\)\( T_{2}^{665} - \)\(28\!\cdots\!56\)\( T_{2}^{664} - \)\(55\!\cdots\!68\)\( T_{2}^{663} - \)\(18\!\cdots\!85\)\( T_{2}^{662} + \)\(56\!\cdots\!08\)\( T_{2}^{661} + \)\(20\!\cdots\!19\)\( T_{2}^{660} - \)\(18\!\cdots\!27\)\( T_{2}^{659} - \)\(14\!\cdots\!03\)\( T_{2}^{658} + \)\(49\!\cdots\!97\)\( T_{2}^{657} + \)\(88\!\cdots\!97\)\( T_{2}^{656} - \)\(96\!\cdots\!22\)\( T_{2}^{655} - \)\(33\!\cdots\!53\)\( T_{2}^{654} + \)\(17\!\cdots\!02\)\( T_{2}^{653} + \)\(33\!\cdots\!59\)\( T_{2}^{652} - \)\(79\!\cdots\!71\)\( T_{2}^{651} + \)\(28\!\cdots\!67\)\( T_{2}^{650} + \)\(68\!\cdots\!01\)\( T_{2}^{649} - \)\(26\!\cdots\!31\)\( T_{2}^{648} - \)\(65\!\cdots\!81\)\( T_{2}^{647} + \)\(20\!\cdots\!94\)\( T_{2}^{646} + \)\(31\!\cdots\!13\)\( T_{2}^{645} - \)\(10\!\cdots\!54\)\( T_{2}^{644} - \)\(60\!\cdots\!21\)\( T_{2}^{643} + \)\(30\!\cdots\!67\)\( T_{2}^{642} - \)\(15\!\cdots\!87\)\( T_{2}^{641} - \)\(35\!\cdots\!92\)\( T_{2}^{640} + \)\(29\!\cdots\!59\)\( T_{2}^{639} - \)\(25\!\cdots\!08\)\( T_{2}^{638} - \)\(24\!\cdots\!67\)\( T_{2}^{637} + \)\(32\!\cdots\!26\)\( T_{2}^{636} + \)\(11\!\cdots\!84\)\( T_{2}^{635} - \)\(16\!\cdots\!94\)\( T_{2}^{634} - \)\(43\!\cdots\!15\)\( T_{2}^{633} + \)\(41\!\cdots\!27\)\( T_{2}^{632} + \)\(16\!\cdots\!10\)\( T_{2}^{631} - \)\(10\!\cdots\!84\)\( T_{2}^{630} - \)\(32\!\cdots\!80\)\( T_{2}^{629} + \)\(43\!\cdots\!90\)\( T_{2}^{628} - \)\(21\!\cdots\!70\)\( T_{2}^{627} + \)\(19\!\cdots\!34\)\( T_{2}^{626} + \)\(17\!\cdots\!14\)\( T_{2}^{625} - \)\(22\!\cdots\!15\)\( T_{2}^{624} - \)\(66\!\cdots\!67\)\( T_{2}^{623} + \)\(32\!\cdots\!74\)\( T_{2}^{622} + \)\(35\!\cdots\!09\)\( T_{2}^{621} + \)\(71\!\cdots\!63\)\( T_{2}^{620} - \)\(21\!\cdots\!47\)\( T_{2}^{619} + \)\(10\!\cdots\!90\)\( T_{2}^{618} + \)\(66\!\cdots\!61\)\( T_{2}^{617} - \)\(75\!\cdots\!41\)\( T_{2}^{616} - \)\(80\!\cdots\!31\)\( T_{2}^{615} + \)\(58\!\cdots\!31\)\( T_{2}^{614} + \)\(43\!\cdots\!08\)\( T_{2}^{613} - \)\(86\!\cdots\!21\)\( T_{2}^{612} - \)\(37\!\cdots\!38\)\( T_{2}^{611} + \)\(59\!\cdots\!90\)\( T_{2}^{610} + \)\(99\!\cdots\!78\)\( T_{2}^{609} - \)\(27\!\cdots\!46\)\( T_{2}^{608} - \)\(88\!\cdots\!37\)\( T_{2}^{607} + \)\(51\!\cdots\!73\)\( T_{2}^{606} + \)\(15\!\cdots\!21\)\( T_{2}^{605} + \)\(22\!\cdots\!11\)\( T_{2}^{604} - \)\(13\!\cdots\!00\)\( T_{2}^{603} - \)\(23\!\cdots\!84\)\( T_{2}^{602} + \)\(37\!\cdots\!90\)\( T_{2}^{601} - \)\(21\!\cdots\!64\)\( T_{2}^{600} + \)\(50\!\cdots\!91\)\( T_{2}^{599} - \)\(28\!\cdots\!51\)\( T_{2}^{598} - \)\(71\!\cdots\!36\)\( T_{2}^{597} + \)\(27\!\cdots\!47\)\( T_{2}^{596} + \)\(24\!\cdots\!38\)\( T_{2}^{595} - \)\(12\!\cdots\!01\)\( T_{2}^{594} - \)\(88\!\cdots\!48\)\( T_{2}^{593} + \)\(35\!\cdots\!69\)\( T_{2}^{592} + \)\(66\!\cdots\!71\)\( T_{2}^{591} - \)\(15\!\cdots\!39\)\( T_{2}^{590} - \)\(33\!\cdots\!98\)\( T_{2}^{589} + \)\(85\!\cdots\!17\)\( T_{2}^{588} + \)\(61\!\cdots\!14\)\( T_{2}^{587} - \)\(23\!\cdots\!56\)\( T_{2}^{586} + \)\(17\!\cdots\!47\)\( T_{2}^{585} + \)\(14\!\cdots\!27\)\( T_{2}^{584} + \)\(60\!\cdots\!68\)\( T_{2}^{583} + \)\(13\!\cdots\!43\)\( T_{2}^{582} - \)\(65\!\cdots\!67\)\( T_{2}^{581} - \)\(30\!\cdots\!41\)\( T_{2}^{580} + \)\(23\!\cdots\!96\)\( T_{2}^{579} + \)\(12\!\cdots\!98\)\( T_{2}^{578} - \)\(69\!\cdots\!62\)\( T_{2}^{577} - \)\(73\!\cdots\!27\)\( T_{2}^{576} + \)\(27\!\cdots\!92\)\( T_{2}^{575} + \)\(44\!\cdots\!32\)\( T_{2}^{574} - \)\(86\!\cdots\!81\)\( T_{2}^{573} - \)\(27\!\cdots\!09\)\( T_{2}^{572} + \)\(11\!\cdots\!86\)\( T_{2}^{571} + \)\(12\!\cdots\!01\)\( T_{2}^{570} + \)\(28\!\cdots\!73\)\( T_{2}^{569} - \)\(50\!\cdots\!43\)\( T_{2}^{568} - \)\(47\!\cdots\!71\)\( T_{2}^{567} + \)\(25\!\cdots\!05\)\( T_{2}^{566} + \)\(33\!\cdots\!03\)\( T_{2}^{565} - \)\(96\!\cdots\!65\)\( T_{2}^{564} - \)\(14\!\cdots\!31\)\( T_{2}^{563} + \)\(20\!\cdots\!13\)\( T_{2}^{562} + \)\(68\!\cdots\!79\)\( T_{2}^{561} - \)\(65\!\cdots\!51\)\( T_{2}^{560} - \)\(33\!\cdots\!67\)\( T_{2}^{559} + \)\(44\!\cdots\!22\)\( T_{2}^{558} + \)\(83\!\cdots\!71\)\( T_{2}^{557} - \)\(17\!\cdots\!38\)\( T_{2}^{556} + \)\(16\!\cdots\!69\)\( T_{2}^{555} + \)\(24\!\cdots\!04\)\( T_{2}^{554} - \)\(20\!\cdots\!51\)\( T_{2}^{553} + \)\(16\!\cdots\!61\)\( T_{2}^{552} + \)\(76\!\cdots\!08\)\( T_{2}^{551} - \)\(18\!\cdots\!65\)\( T_{2}^{550} - \)\(16\!\cdots\!36\)\( T_{2}^{549} + \)\(90\!\cdots\!48\)\( T_{2}^{548} - \)\(55\!\cdots\!79\)\( T_{2}^{547} - \)\(25\!\cdots\!57\)\( T_{2}^{546} + \)\(28\!\cdots\!29\)\( T_{2}^{545} + \)\(59\!\cdots\!30\)\( T_{2}^{544} - \)\(13\!\cdots\!03\)\( T_{2}^{543} - \)\(14\!\cdots\!73\)\( T_{2}^{542} + \)\(36\!\cdots\!10\)\( T_{2}^{541} + \)\(61\!\cdots\!14\)\( T_{2}^{540} - \)\(93\!\cdots\!64\)\( T_{2}^{539} + \)\(70\!\cdots\!91\)\( T_{2}^{538} + \)\(26\!\cdots\!40\)\( T_{2}^{537} + \)\(65\!\cdots\!09\)\( T_{2}^{536} - \)\(28\!\cdots\!12\)\( T_{2}^{535} + \)\(38\!\cdots\!53\)\( T_{2}^{534} - \)\(35\!\cdots\!18\)\( T_{2}^{533} - \)\(12\!\cdots\!48\)\( T_{2}^{532} + \)\(45\!\cdots\!59\)\( T_{2}^{531} + \)\(61\!\cdots\!97\)\( T_{2}^{530} - \)\(86\!\cdots\!50\)\( T_{2}^{529} - \)\(16\!\cdots\!58\)\( T_{2}^{528} + \)\(58\!\cdots\!49\)\( T_{2}^{527} + \)\(35\!\cdots\!10\)\( T_{2}^{526} - \)\(18\!\cdots\!85\)\( T_{2}^{525} + \)\(30\!\cdots\!03\)\( T_{2}^{524} + \)\(30\!\cdots\!90\)\( T_{2}^{523} - \)\(64\!\cdots\!28\)\( T_{2}^{522} + \)\(20\!\cdots\!46\)\( T_{2}^{521} + \)\(14\!\cdots\!24\)\( T_{2}^{520} - \)\(48\!\cdots\!66\)\( T_{2}^{519} + \)\(33\!\cdots\!99\)\( T_{2}^{518} + \)\(22\!\cdots\!71\)\( T_{2}^{517} - \)\(28\!\cdots\!11\)\( T_{2}^{516} - \)\(46\!\cdots\!41\)\( T_{2}^{515} + \)\(12\!\cdots\!95\)\( T_{2}^{514} - \)\(35\!\cdots\!70\)\( T_{2}^{513} - \)\(35\!\cdots\!94\)\( T_{2}^{512} + \)\(62\!\cdots\!49\)\( T_{2}^{511} - \)\(10\!\cdots\!96\)\( T_{2}^{510} - \)\(25\!\cdots\!97\)\( T_{2}^{509} + \)\(49\!\cdots\!03\)\( T_{2}^{508} + \)\(48\!\cdots\!99\)\( T_{2}^{507} - \)\(21\!\cdots\!13\)\( T_{2}^{506} + \)\(78\!\cdots\!60\)\( T_{2}^{505} + \)\(64\!\cdots\!54\)\( T_{2}^{504} - \)\(83\!\cdots\!93\)\( T_{2}^{503} - \)\(13\!\cdots\!06\)\( T_{2}^{502} + \)\(31\!\cdots\!50\)\( T_{2}^{501} - \)\(36\!\cdots\!43\)\( T_{2}^{500} - \)\(77\!\cdots\!64\)\( T_{2}^{499} + \)\(11\!\cdots\!00\)\( T_{2}^{498} + \)\(28\!\cdots\!94\)\( T_{2}^{497} - \)\(38\!\cdots\!66\)\( T_{2}^{496} + \)\(87\!\cdots\!95\)\( T_{2}^{495} + \)\(69\!\cdots\!14\)\( T_{2}^{494} - \)\(49\!\cdots\!59\)\( T_{2}^{493} + \)\(67\!\cdots\!93\)\( T_{2}^{492} + \)\(16\!\cdots\!96\)\( T_{2}^{491} - \)\(10\!\cdots\!89\)\( T_{2}^{490} - \)\(35\!\cdots\!39\)\( T_{2}^{489} + \)\(33\!\cdots\!86\)\( T_{2}^{488} + \)\(30\!\cdots\!43\)\( T_{2}^{487} - \)\(92\!\cdots\!72\)\( T_{2}^{486} + \)\(14\!\cdots\!86\)\( T_{2}^{485} - \)\(34\!\cdots\!38\)\( T_{2}^{484} - \)\(88\!\cdots\!91\)\( T_{2}^{483} + \)\(22\!\cdots\!46\)\( T_{2}^{482} + \)\(27\!\cdots\!49\)\( T_{2}^{481} - \)\(86\!\cdots\!99\)\( T_{2}^{480} - \)\(53\!\cdots\!32\)\( T_{2}^{479} + \)\(21\!\cdots\!82\)\( T_{2}^{478} + \)\(34\!\cdots\!35\)\( T_{2}^{477} - \)\(23\!\cdots\!80\)\( T_{2}^{476} + \)\(17\!\cdots\!78\)\( T_{2}^{475} - \)\(68\!\cdots\!13\)\( T_{2}^{474} - \)\(63\!\cdots\!73\)\( T_{2}^{473} + \)\(54\!\cdots\!32\)\( T_{2}^{472} + \)\(48\!\cdots\!53\)\( T_{2}^{471} - \)\(21\!\cdots\!99\)\( T_{2}^{470} + \)\(47\!\cdots\!73\)\( T_{2}^{469} + \)\(58\!\cdots\!85\)\( T_{2}^{468} - \)\(25\!\cdots\!89\)\( T_{2}^{467} - \)\(12\!\cdots\!16\)\( T_{2}^{466} + \)\(66\!\cdots\!08\)\( T_{2}^{465} + \)\(15\!\cdots\!48\)\( T_{2}^{464} - \)\(52\!\cdots\!47\)\( T_{2}^{463} + \)\(63\!\cdots\!51\)\( T_{2}^{462} - \)\(38\!\cdots\!50\)\( T_{2}^{461} - \)\(99\!\cdots\!07\)\( T_{2}^{460} + \)\(22\!\cdots\!54\)\( T_{2}^{459} + \)\(27\!\cdots\!40\)\( T_{2}^{458} - \)\(70\!\cdots\!01\)\( T_{2}^{457} - \)\(41\!\cdots\!31\)\( T_{2}^{456} + \)\(14\!\cdots\!16\)\( T_{2}^{455} - \)\(64\!\cdots\!00\)\( T_{2}^{454} - \)\(94\!\cdots\!92\)\( T_{2}^{453} + \)\(30\!\cdots\!05\)\( T_{2}^{452} - \)\(65\!\cdots\!71\)\( T_{2}^{451} - \)\(11\!\cdots\!33\)\( T_{2}^{450} + \)\(34\!\cdots\!93\)\( T_{2}^{449} + \)\(23\!\cdots\!52\)\( T_{2}^{448} - \)\(98\!\cdots\!57\)\( T_{2}^{447} - \)\(27\!\cdots\!70\)\( T_{2}^{446} + \)\(17\!\cdots\!22\)\( T_{2}^{445} - \)\(33\!\cdots\!29\)\( T_{2}^{444} - \)\(11\!\cdots\!56\)\( T_{2}^{443} + \)\(30\!\cdots\!51\)\( T_{2}^{442} - \)\(51\!\cdots\!56\)\( T_{2}^{441} - \)\(90\!\cdots\!84\)\( T_{2}^{440} + \)\(23\!\cdots\!73\)\( T_{2}^{439} + \)\(16\!\cdots\!87\)\( T_{2}^{438} - \)\(50\!\cdots\!45\)\( T_{2}^{437} - \)\(28\!\cdots\!36\)\( T_{2}^{436} + \)\(53\!\cdots\!97\)\( T_{2}^{435} + \)\(45\!\cdots\!83\)\( T_{2}^{434} + \)\(82\!\cdots\!07\)\( T_{2}^{433} - \)\(39\!\cdots\!48\)\( T_{2}^{432} - \)\(60\!\cdots\!61\)\( T_{2}^{431} + \)\(36\!\cdots\!27\)\( T_{2}^{430} + \)\(15\!\cdots\!03\)\( T_{2}^{429} + \)\(32\!\cdots\!48\)\( T_{2}^{428} - \)\(18\!\cdots\!01\)\( T_{2}^{427} - \)\(15\!\cdots\!45\)\( T_{2}^{426} - \)\(21\!\cdots\!96\)\( T_{2}^{425} + \)\(73\!\cdots\!39\)\( T_{2}^{424} + \)\(17\!\cdots\!58\)\( T_{2}^{423} - \)\(21\!\cdots\!82\)\( T_{2}^{422} - \)\(53\!\cdots\!70\)\( T_{2}^{421} + \)\(54\!\cdots\!67\)\( T_{2}^{420} + \)\(10\!\cdots\!06\)\( T_{2}^{419} - \)\(89\!\cdots\!41\)\( T_{2}^{418} - \)\(14\!\cdots\!30\)\( T_{2}^{417} + \)\(73\!\cdots\!06\)\( T_{2}^{416} + \)\(16\!\cdots\!37\)\( T_{2}^{415} + \)\(31\!\cdots\!96\)\( T_{2}^{414} - \)\(24\!\cdots\!00\)\( T_{2}^{413} - \)\(81\!\cdots\!29\)\( T_{2}^{412} + \)\(89\!\cdots\!83\)\( T_{2}^{411} + \)\(13\!\cdots\!47\)\( T_{2}^{410} + \)\(11\!\cdots\!05\)\( T_{2}^{409} - \)\(14\!\cdots\!20\)\( T_{2}^{408} - \)\(55\!\cdots\!33\)\( T_{2}^{407} + \)\(56\!\cdots\!01\)\( T_{2}^{406} + \)\(21\!\cdots\!97\)\( T_{2}^{405} - \)\(79\!\cdots\!76\)\( T_{2}^{404} - \)\(51\!\cdots\!19\)\( T_{2}^{403} + \)\(45\!\cdots\!41\)\( T_{2}^{402} + \)\(49\!\cdots\!70\)\( T_{2}^{401} - \)\(97\!\cdots\!27\)\( T_{2}^{400} + \)\(73\!\cdots\!24\)\( T_{2}^{399} + \)\(95\!\cdots\!88\)\( T_{2}^{398} - \)\(39\!\cdots\!46\)\( T_{2}^{397} + \)\(57\!\cdots\!46\)\( T_{2}^{396} + \)\(89\!\cdots\!26\)\( T_{2}^{395} - \)\(77\!\cdots\!91\)\( T_{2}^{394} - \)\(59\!\cdots\!30\)\( T_{2}^{393} + \)\(24\!\cdots\!87\)\( T_{2}^{392} - \)\(37\!\cdots\!16\)\( T_{2}^{391} - \)\(42\!\cdots\!26\)\( T_{2}^{390} + \)\(14\!\cdots\!38\)\( T_{2}^{389} + \)\(80\!\cdots\!87\)\( T_{2}^{388} - \)\(26\!\cdots\!81\)\( T_{2}^{387} - \)\(27\!\cdots\!45\)\( T_{2}^{386} + \)\(21\!\cdots\!86\)\( T_{2}^{385} + \)\(73\!\cdots\!63\)\( T_{2}^{384} + \)\(79\!\cdots\!26\)\( T_{2}^{383} - \)\(13\!\cdots\!62\)\( T_{2}^{382} - \)\(45\!\cdots\!08\)\( T_{2}^{381} + \)\(13\!\cdots\!61\)\( T_{2}^{380} + \)\(12\!\cdots\!76\)\( T_{2}^{379} + \)\(33\!\cdots\!23\)\( T_{2}^{378} - \)\(20\!\cdots\!49\)\( T_{2}^{377} - \)\(23\!\cdots\!31\)\( T_{2}^{376} + \)\(21\!\cdots\!15\)\( T_{2}^{375} + \)\(65\!\cdots\!31\)\( T_{2}^{374} + \)\(21\!\cdots\!49\)\( T_{2}^{373} - \)\(12\!\cdots\!46\)\( T_{2}^{372} - \)\(16\!\cdots\!87\)\( T_{2}^{371} + \)\(14\!\cdots\!62\)\( T_{2}^{370} + \)\(44\!\cdots\!86\)\( T_{2}^{369} + \)\(75\!\cdots\!83\)\( T_{2}^{368} - \)\(74\!\cdots\!23\)\( T_{2}^{367} - \)\(62\!\cdots\!64\)\( T_{2}^{366} + \)\(86\!\cdots\!59\)\( T_{2}^{365} + \)\(17\!\cdots\!19\)\( T_{2}^{364} - \)\(81\!\cdots\!55\)\( T_{2}^{363} - \)\(29\!\cdots\!93\)\( T_{2}^{362} - \)\(25\!\cdots\!69\)\( T_{2}^{361} + \)\(37\!\cdots\!94\)\( T_{2}^{360} + \)\(67\!\cdots\!27\)\( T_{2}^{359} - \)\(18\!\cdots\!99\)\( T_{2}^{358} - \)\(11\!\cdots\!99\)\( T_{2}^{357} - \)\(53\!\cdots\!19\)\( T_{2}^{356} + \)\(13\!\cdots\!86\)\( T_{2}^{355} + \)\(16\!\cdots\!03\)\( T_{2}^{354} - \)\(87\!\cdots\!41\)\( T_{2}^{353} - \)\(29\!\cdots\!57\)\( T_{2}^{352} - \)\(79\!\cdots\!46\)\( T_{2}^{351} + \)\(45\!\cdots\!47\)\( T_{2}^{350} + \)\(25\!\cdots\!95\)\( T_{2}^{349} - \)\(44\!\cdots\!05\)\( T_{2}^{348} - \)\(55\!\cdots\!87\)\( T_{2}^{347} + \)\(24\!\cdots\!77\)\( T_{2}^{346} + \)\(12\!\cdots\!73\)\( T_{2}^{345} - \)\(17\!\cdots\!42\)\( T_{2}^{344} - \)\(16\!\cdots\!60\)\( T_{2}^{343} - \)\(73\!\cdots\!12\)\( T_{2}^{342} + \)\(18\!\cdots\!10\)\( T_{2}^{341} + \)\(34\!\cdots\!88\)\( T_{2}^{340} - \)\(27\!\cdots\!54\)\( T_{2}^{339} - \)\(56\!\cdots\!08\)\( T_{2}^{338} - \)\(95\!\cdots\!26\)\( T_{2}^{337} + \)\(76\!\cdots\!73\)\( T_{2}^{336} + \)\(89\!\cdots\!59\)\( T_{2}^{335} - \)\(94\!\cdots\!36\)\( T_{2}^{334} - \)\(15\!\cdots\!76\)\( T_{2}^{333} - \)\(37\!\cdots\!80\)\( T_{2}^{332} + \)\(23\!\cdots\!70\)\( T_{2}^{331} + \)\(29\!\cdots\!31\)\( T_{2}^{330} - \)\(23\!\cdots\!87\)\( T_{2}^{329} - \)\(42\!\cdots\!77\)\( T_{2}^{328} - \)\(28\!\cdots\!22\)\( T_{2}^{327} + \)\(62\!\cdots\!16\)\( T_{2}^{326} + \)\(91\!\cdots\!24\)\( T_{2}^{325} - \)\(46\!\cdots\!87\)\( T_{2}^{324} - \)\(93\!\cdots\!18\)\( T_{2}^{323} - \)\(12\!\cdots\!36\)\( T_{2}^{322} + \)\(13\!\cdots\!05\)\( T_{2}^{321} + \)\(27\!\cdots\!81\)\( T_{2}^{320} - \)\(82\!\cdots\!92\)\( T_{2}^{319} - \)\(21\!\cdots\!37\)\( T_{2}^{318} - \)\(39\!\cdots\!81\)\( T_{2}^{317} + \)\(31\!\cdots\!56\)\( T_{2}^{316} + \)\(69\!\cdots\!91\)\( T_{2}^{315} - \)\(23\!\cdots\!10\)\( T_{2}^{314} - \)\(39\!\cdots\!36\)\( T_{2}^{313} - \)\(82\!\cdots\!28\)\( T_{2}^{312} + \)\(53\!\cdots\!95\)\( T_{2}^{311} + \)\(14\!\cdots\!59\)\( T_{2}^{310} - \)\(51\!\cdots\!04\)\( T_{2}^{309} - \)\(69\!\cdots\!38\)\( T_{2}^{308} - \)\(15\!\cdots\!69\)\( T_{2}^{307} + \)\(98\!\cdots\!43\)\( T_{2}^{306} + \)\(27\!\cdots\!94\)\( T_{2}^{305} - \)\(12\!\cdots\!35\)\( T_{2}^{304} - \)\(12\!\cdots\!51\)\( T_{2}^{303} - \)\(20\!\cdots\!85\)\( T_{2}^{302} + \)\(10\!\cdots\!14\)\( T_{2}^{301} + \)\(46\!\cdots\!53\)\( T_{2}^{300} - \)\(18\!\cdots\!70\)\( T_{2}^{299} - \)\(19\!\cdots\!30\)\( T_{2}^{298} - \)\(25\!\cdots\!28\)\( T_{2}^{297} + \)\(47\!\cdots\!10\)\( T_{2}^{296} + \)\(68\!\cdots\!17\)\( T_{2}^{295} - \)\(22\!\cdots\!39\)\( T_{2}^{294} - \)\(14\!\cdots\!70\)\( T_{2}^{293} - \)\(31\!\cdots\!08\)\( T_{2}^{292} - \)\(23\!\cdots\!15\)\( T_{2}^{291} + \)\(84\!\cdots\!67\)\( T_{2}^{290} - \)\(34\!\cdots\!98\)\( T_{2}^{289} - \)\(13\!\cdots\!40\)\( T_{2}^{288} - \)\(34\!\cdots\!73\)\( T_{2}^{287} - \)\(57\!\cdots\!12\)\( T_{2}^{286} + \)\(10\!\cdots\!30\)\( T_{2}^{285} + \)\(19\!\cdots\!54\)\( T_{2}^{284} - \)\(91\!\cdots\!51\)\( T_{2}^{283} - \)\(57\!\cdots\!15\)\( T_{2}^{282} - \)\(14\!\cdots\!53\)\( T_{2}^{281} + \)\(13\!\cdots\!58\)\( T_{2}^{280} + \)\(96\!\cdots\!53\)\( T_{2}^{279} + \)\(61\!\cdots\!92\)\( T_{2}^{278} - \)\(53\!\cdots\!49\)\( T_{2}^{277} - \)\(23\!\cdots\!45\)\( T_{2}^{276} + \)\(50\!\cdots\!23\)\( T_{2}^{275} + \)\(66\!\cdots\!22\)\( T_{2}^{274} + \)\(49\!\cdots\!11\)\( T_{2}^{273} + \)\(71\!\cdots\!41\)\( T_{2}^{272} - \)\(14\!\cdots\!79\)\( T_{2}^{271} + \)\(11\!\cdots\!29\)\( T_{2}^{270} + \)\(65\!\cdots\!71\)\( T_{2}^{269} - \)\(12\!\cdots\!82\)\( T_{2}^{268} - \)\(76\!\cdots\!05\)\( T_{2}^{267} - \)\(23\!\cdots\!47\)\( T_{2}^{266} + \)\(22\!\cdots\!57\)\( T_{2}^{265} + \)\(31\!\cdots\!12\)\( T_{2}^{264} + \)\(29\!\cdots\!11\)\( T_{2}^{263} - \)\(70\!\cdots\!15\)\( T_{2}^{262} - \)\(37\!\cdots\!68\)\( T_{2}^{261} - \)\(13\!\cdots\!14\)\( T_{2}^{260} + \)\(24\!\cdots\!30\)\( T_{2}^{259} + \)\(13\!\cdots\!73\)\( T_{2}^{258} + \)\(17\!\cdots\!60\)\( T_{2}^{257} - \)\(12\!\cdots\!11\)\( T_{2}^{256} - \)\(19\!\cdots\!74\)\( T_{2}^{255} + \)\(43\!\cdots\!15\)\( T_{2}^{254} - \)\(40\!\cdots\!27\)\( T_{2}^{253} + \)\(11\!\cdots\!05\)\( T_{2}^{252} + \)\(25\!\cdots\!33\)\( T_{2}^{251} - \)\(59\!\cdots\!29\)\( T_{2}^{250} + \)\(45\!\cdots\!79\)\( T_{2}^{249} - \)\(61\!\cdots\!93\)\( T_{2}^{248} - \)\(99\!\cdots\!37\)\( T_{2}^{247} + \)\(85\!\cdots\!21\)\( T_{2}^{246} - \)\(48\!\cdots\!09\)\( T_{2}^{245} + \)\(13\!\cdots\!13\)\( T_{2}^{244} + \)\(33\!\cdots\!52\)\( T_{2}^{243} + \)\(14\!\cdots\!39\)\( T_{2}^{242} - \)\(99\!\cdots\!28\)\( T_{2}^{241} - \)\(23\!\cdots\!97\)\( T_{2}^{240} - \)\(57\!\cdots\!69\)\( T_{2}^{239} - \)\(69\!\cdots\!21\)\( T_{2}^{238} + \)\(32\!\cdots\!30\)\( T_{2}^{237} - \)\(38\!\cdots\!04\)\( T_{2}^{236} + \)\(24\!\cdots\!64\)\( T_{2}^{235} - \)\(11\!\cdots\!15\)\( T_{2}^{234} - \)\(52\!\cdots\!41\)\( T_{2}^{233} + \)\(41\!\cdots\!49\)\( T_{2}^{232} + \)\(99\!\cdots\!92\)\( T_{2}^{231} + \)\(35\!\cdots\!51\)\( T_{2}^{230} + \)\(87\!\cdots\!70\)\( T_{2}^{229} - \)\(21\!\cdots\!28\)\( T_{2}^{228} - \)\(11\!\cdots\!23\)\( T_{2}^{227} - \)\(10\!\cdots\!10\)\( T_{2}^{226} - \)\(63\!\cdots\!52\)\( T_{2}^{225} + \)\(13\!\cdots\!99\)\( T_{2}^{224} - \)\(11\!\cdots\!56\)\( T_{2}^{223} + \)\(17\!\cdots\!98\)\( T_{2}^{222} - \)\(22\!\cdots\!30\)\( T_{2}^{221} + \)\(18\!\cdots\!61\)\( T_{2}^{220} - \)\(12\!\cdots\!28\)\( T_{2}^{219} + \)\(45\!\cdots\!10\)\( T_{2}^{218} + \)\(15\!\cdots\!45\)\( T_{2}^{217} - \)\(26\!\cdots\!99\)\( T_{2}^{216} - \)\(10\!\cdots\!97\)\( T_{2}^{215} + \)\(20\!\cdots\!70\)\( T_{2}^{214} - \)\(25\!\cdots\!41\)\( T_{2}^{213} + \)\(27\!\cdots\!73\)\( T_{2}^{212} - \)\(25\!\cdots\!29\)\( T_{2}^{211} + \)\(17\!\cdots\!96\)\( T_{2}^{210} - \)\(79\!\cdots\!89\)\( T_{2}^{209} - \)\(46\!\cdots\!84\)\( T_{2}^{208} + \)\(14\!\cdots\!18\)\( T_{2}^{207} - \)\(14\!\cdots\!41\)\( T_{2}^{206} + \)\(67\!\cdots\!41\)\( T_{2}^{205} + \)\(64\!\cdots\!86\)\( T_{2}^{204} - \)\(37\!\cdots\!27\)\( T_{2}^{203} + \)\(42\!\cdots\!64\)\( T_{2}^{202} - \)\(27\!\cdots\!53\)\( T_{2}^{201} + \)\(10\!\cdots\!72\)\( T_{2}^{200} + \)\(13\!\cdots\!08\)\( T_{2}^{199} - \)\(80\!\cdots\!85\)\( T_{2}^{198} + \)\(77\!\cdots\!70\)\( T_{2}^{197} - \)\(10\!\cdots\!47\)\( T_{2}^{196} - \)\(51\!\cdots\!89\)\( T_{2}^{195} + \)\(65\!\cdots\!62\)\( T_{2}^{194} - \)\(43\!\cdots\!55\)\( T_{2}^{193} + \)\(12\!\cdots\!05\)\( T_{2}^{192} + \)\(79\!\cdots\!61\)\( T_{2}^{191} - \)\(12\!\cdots\!66\)\( T_{2}^{190} + \)\(73\!\cdots\!57\)\( T_{2}^{189} - \)\(32\!\cdots\!62\)\( T_{2}^{188} + \)\(22\!\cdots\!74\)\( T_{2}^{187} - \)\(17\!\cdots\!47\)\( T_{2}^{186} + \)\(72\!\cdots\!73\)\( T_{2}^{185} + \)\(27\!\cdots\!67\)\( T_{2}^{184} - \)\(87\!\cdots\!37\)\( T_{2}^{183} + \)\(10\!\cdots\!64\)\( T_{2}^{182} - \)\(92\!\cdots\!15\)\( T_{2}^{181} + \)\(82\!\cdots\!59\)\( T_{2}^{180} - \)\(62\!\cdots\!46\)\( T_{2}^{179} + \)\(24\!\cdots\!33\)\( T_{2}^{178} + \)\(11\!\cdots\!27\)\( T_{2}^{177} - \)\(22\!\cdots\!86\)\( T_{2}^{176} + \)\(13\!\cdots\!49\)\( T_{2}^{175} - \)\(22\!\cdots\!11\)\( T_{2}^{174} - \)\(23\!\cdots\!42\)\( T_{2}^{173} + \)\(17\!\cdots\!51\)\( T_{2}^{172} - \)\(59\!\cdots\!54\)\( T_{2}^{171} + \)\(40\!\cdots\!61\)\( T_{2}^{170} - \)\(47\!\cdots\!71\)\( T_{2}^{169} + \)\(49\!\cdots\!60\)\( T_{2}^{168} + \)\(49\!\cdots\!65\)\( T_{2}^{167} - \)\(61\!\cdots\!50\)\( T_{2}^{166} + \)\(37\!\cdots\!89\)\( T_{2}^{165} - \)\(11\!\cdots\!91\)\( T_{2}^{164} - \)\(18\!\cdots\!97\)\( T_{2}^{163} + \)\(79\!\cdots\!69\)\( T_{2}^{162} - \)\(12\!\cdots\!61\)\( T_{2}^{161} + \)\(13\!\cdots\!86\)\( T_{2}^{160} - \)\(96\!\cdots\!48\)\( T_{2}^{159} + \)\(35\!\cdots\!27\)\( T_{2}^{158} + \)\(12\!\cdots\!23\)\( T_{2}^{157} - \)\(28\!\cdots\!30\)\( T_{2}^{156} + \)\(22\!\cdots\!65\)\( T_{2}^{155} - \)\(12\!\cdots\!91\)\( T_{2}^{154} + \)\(42\!\cdots\!51\)\( T_{2}^{153} + \)\(13\!\cdots\!93\)\( T_{2}^{152} - \)\(19\!\cdots\!75\)\( T_{2}^{151} + \)\(18\!\cdots\!09\)\( T_{2}^{150} - \)\(99\!\cdots\!49\)\( T_{2}^{149} + \)\(24\!\cdots\!66\)\( T_{2}^{148} + \)\(37\!\cdots\!88\)\( T_{2}^{147} - \)\(50\!\cdots\!15\)\( T_{2}^{146} + \)\(37\!\cdots\!29\)\( T_{2}^{145} - \)\(44\!\cdots\!05\)\( T_{2}^{144} + \)\(35\!\cdots\!92\)\( T_{2}^{143} - \)\(90\!\cdots\!99\)\( T_{2}^{142} - \)\(93\!\cdots\!48\)\( T_{2}^{141} + \)\(98\!\cdots\!00\)\( T_{2}^{140} - \)\(25\!\cdots\!16\)\( T_{2}^{139} - \)\(20\!\cdots\!55\)\( T_{2}^{138} + \)\(20\!\cdots\!48\)\( T_{2}^{137} - \)\(40\!\cdots\!62\)\( T_{2}^{136} - \)\(46\!\cdots\!83\)\( T_{2}^{135} + \)\(40\!\cdots\!63\)\( T_{2}^{134} - \)\(65\!\cdots\!26\)\( T_{2}^{133} - \)\(96\!\cdots\!45\)\( T_{2}^{132} + \)\(73\!\cdots\!62\)\( T_{2}^{131} - \)\(82\!\cdots\!67\)\( T_{2}^{130} - \)\(18\!\cdots\!08\)\( T_{2}^{129} + \)\(11\!\cdots\!40\)\( T_{2}^{128} - \)\(64\!\cdots\!80\)\( T_{2}^{127} - \)\(29\!\cdots\!63\)\( T_{2}^{126} + \)\(15\!\cdots\!03\)\( T_{2}^{125} + \)\(75\!\cdots\!59\)\( T_{2}^{124} - \)\(38\!\cdots\!02\)\( T_{2}^{123} + \)\(12\!\cdots\!28\)\( T_{2}^{122} + \)\(36\!\cdots\!51\)\( T_{2}^{121} - \)\(39\!\cdots\!60\)\( T_{2}^{120} + \)\(46\!\cdots\!18\)\( T_{2}^{119} + \)\(69\!\cdots\!63\)\( T_{2}^{118} - \)\(30\!\cdots\!96\)\( T_{2}^{117} - \)\(57\!\cdots\!32\)\( T_{2}^{116} + \)\(81\!\cdots\!20\)\( T_{2}^{115} - \)\(12\!\cdots\!41\)\( T_{2}^{114} - \)\(13\!\cdots\!84\)\( T_{2}^{113} + \)\(66\!\cdots\!30\)\( T_{2}^{112} + \)\(68\!\cdots\!89\)\( T_{2}^{111} - \)\(15\!\cdots\!18\)\( T_{2}^{110} + \)\(33\!\cdots\!81\)\( T_{2}^{109} + \)\(20\!\cdots\!23\)\( T_{2}^{108} - \)\(13\!\cdots\!16\)\( T_{2}^{107} + \)\(85\!\cdots\!54\)\( T_{2}^{106} + \)\(21\!\cdots\!72\)\( T_{2}^{105} - \)\(92\!\cdots\!47\)\( T_{2}^{104} + \)\(17\!\cdots\!94\)\( T_{2}^{103} + \)\(11\!\cdots\!02\)\( T_{2}^{102} - \)\(40\!\cdots\!11\)\( T_{2}^{101} + \)\(48\!\cdots\!71\)\( T_{2}^{100} - \)\(38\!\cdots\!50\)\( T_{2}^{99} + \)\(68\!\cdots\!47\)\( T_{2}^{98} + \)\(64\!\cdots\!92\)\( T_{2}^{97} - \)\(61\!\cdots\!31\)\( T_{2}^{96} + \)\(18\!\cdots\!83\)\( T_{2}^{95} + \)\(46\!\cdots\!05\)\( T_{2}^{94} - \)\(63\!\cdots\!75\)\( T_{2}^{93} + \)\(22\!\cdots\!31\)\( T_{2}^{92} + \)\(24\!\cdots\!11\)\( T_{2}^{91} - \)\(34\!\cdots\!82\)\( T_{2}^{90} + \)\(14\!\cdots\!16\)\( T_{2}^{89} - \)\(12\!\cdots\!51\)\( T_{2}^{88} - \)\(12\!\cdots\!06\)\( T_{2}^{87} + \)\(68\!\cdots\!38\)\( T_{2}^{86} - \)\(12\!\cdots\!32\)\( T_{2}^{85} - \)\(24\!\cdots\!03\)\( T_{2}^{84} + \)\(23\!\cdots\!06\)\( T_{2}^{83} - \)\(62\!\cdots\!50\)\( T_{2}^{82} + \)\(12\!\cdots\!97\)\( T_{2}^{81} + \)\(55\!\cdots\!40\)\( T_{2}^{80} - \)\(18\!\cdots\!63\)\( T_{2}^{79} + \)\(10\!\cdots\!84\)\( T_{2}^{78} + \)\(11\!\cdots\!08\)\( T_{2}^{77} - \)\(37\!\cdots\!74\)\( T_{2}^{76} + \)\(10\!\cdots\!05\)\( T_{2}^{75} + \)\(25\!\cdots\!07\)\( T_{2}^{74} - \)\(67\!\cdots\!39\)\( T_{2}^{73} - \)\(33\!\cdots\!72\)\( T_{2}^{72} + \)\(59\!\cdots\!86\)\( T_{2}^{71} - \)\(12\!\cdots\!88\)\( T_{2}^{70} - \)\(11\!\cdots\!63\)\( T_{2}^{69} + \)\(11\!\cdots\!83\)\( T_{2}^{68} - \)\(22\!\cdots\!80\)\( T_{2}^{67} + \)\(52\!\cdots\!22\)\( T_{2}^{66} + \)\(37\!\cdots\!28\)\( T_{2}^{65} + \)\(12\!\cdots\!32\)\( T_{2}^{64} - \)\(10\!\cdots\!30\)\( T_{2}^{63} + \)\(28\!\cdots\!05\)\( T_{2}^{62} - \)\(41\!\cdots\!93\)\( T_{2}^{61} + \)\(31\!\cdots\!79\)\( T_{2}^{60} - \)\(59\!\cdots\!68\)\( T_{2}^{59} + \)\(32\!\cdots\!66\)\( T_{2}^{58} - \)\(10\!\cdots\!25\)\( T_{2}^{57} + \)\(20\!\cdots\!33\)\( T_{2}^{56} - \)\(29\!\cdots\!02\)\( T_{2}^{55} + \)\(33\!\cdots\!54\)\( T_{2}^{54} - \)\(31\!\cdots\!86\)\( T_{2}^{53} - \)\(19\!\cdots\!14\)\( T_{2}^{52} + \)\(21\!\cdots\!28\)\( T_{2}^{51} - \)\(54\!\cdots\!86\)\( T_{2}^{50} + \)\(56\!\cdots\!72\)\( T_{2}^{49} + \)\(68\!\cdots\!15\)\( T_{2}^{48} - \)\(37\!\cdots\!54\)\( T_{2}^{47} + \)\(68\!\cdots\!74\)\( T_{2}^{46} - \)\(52\!\cdots\!46\)\( T_{2}^{45} - \)\(28\!\cdots\!10\)\( T_{2}^{44} + \)\(86\!\cdots\!35\)\( T_{2}^{43} - \)\(31\!\cdots\!53\)\( T_{2}^{42} - \)\(10\!\cdots\!12\)\( T_{2}^{41} + \)\(72\!\cdots\!86\)\( T_{2}^{40} + \)\(50\!\cdots\!46\)\( T_{2}^{39} - \)\(16\!\cdots\!26\)\( T_{2}^{38} + \)\(22\!\cdots\!23\)\( T_{2}^{37} + \)\(15\!\cdots\!87\)\( T_{2}^{36} - \)\(97\!\cdots\!23\)\( T_{2}^{35} + \)\(17\!\cdots\!92\)\( T_{2}^{34} - \)\(23\!\cdots\!50\)\( T_{2}^{33} + \)\(13\!\cdots\!79\)\( T_{2}^{32} + \)\(15\!\cdots\!12\)\( T_{2}^{31} - \)\(40\!\cdots\!71\)\( T_{2}^{30} + \)\(62\!\cdots\!97\)\( T_{2}^{29} - \)\(54\!\cdots\!21\)\( T_{2}^{28} + \)\(10\!\cdots\!61\)\( T_{2}^{27} + \)\(54\!\cdots\!77\)\( T_{2}^{26} - \)\(12\!\cdots\!32\)\( T_{2}^{25} + \)\(18\!\cdots\!40\)\( T_{2}^{24} - \)\(21\!\cdots\!15\)\( T_{2}^{23} + \)\(21\!\cdots\!51\)\( T_{2}^{22} - \)\(17\!\cdots\!29\)\( T_{2}^{21} + \)\(14\!\cdots\!44\)\( T_{2}^{20} - \)\(82\!\cdots\!51\)\( T_{2}^{19} + \)\(49\!\cdots\!72\)\( T_{2}^{18} - \)\(21\!\cdots\!02\)\( T_{2}^{17} + \)\(92\!\cdots\!82\)\( T_{2}^{16} - \)\(24\!\cdots\!31\)\( T_{2}^{15} + \)\(39\!\cdots\!91\)\( T_{2}^{14} - \)\(70\!\cdots\!43\)\( T_{2}^{13} + \)\(10\!\cdots\!81\)\( T_{2}^{12} + \)\(12\!\cdots\!23\)\( T_{2}^{11} - \)\(59\!\cdots\!13\)\( T_{2}^{10} - \)\(95\!\cdots\!08\)\( T_{2}^{9} + \)\(66\!\cdots\!24\)\( T_{2}^{8} - \)\(11\!\cdots\!98\)\( T_{2}^{7} + \)\(89\!\cdots\!09\)\( T_{2}^{6} - \)\(36\!\cdots\!66\)\( T_{2}^{5} + \)\(23\!\cdots\!58\)\( T_{2}^{4} - \)\(22\!\cdots\!66\)\( T_{2}^{3} + \)\(82\!\cdots\!03\)\( T_{2}^{2} - \)\(34\!\cdots\!32\)\( T_{2} + \)\(43\!\cdots\!21\)\( \)">\(T_{2}^{880} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(605, [\chi])\).