data: - - A10: 0 A2: 0 A3: 0 A4: 0 A5: 0 A6: 0 A7: -1 A8: 0 A9: -4 Lhash: '1294854504373152540105668784571' a10: - 0.0 - 0 a2: - 0.0 - 0 a3: - 0.0 - 0 a4: - 0.0 - 0 a5: - 0.0 - 0 a6: - 0.0 - 0 a7: - -0.3779644730092272 - 0 a8: - 0.0 - 0 a9: - -1.3333333333333333 - 0 accuracy: 100 algebraic: true analytic_conductor: 89.57942739416335 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - 1 - - 7 - - 1 - 1 bad_primes: - 2 - 7 central_character: '1404928.1' coefficient_field: 1.1.1.1 conductor: 1404928 conductor_radical: 14 degree: 4 euler_factors: - - 1 - - 1 - 0 - 4 - 0 - 9 - - 1 - 0 - -2 - 0 - 25 - - 1 - 1 - - 1 - -2 - 22 - -22 - 121 - - 1 - 0 - -6 - 0 - 169 - - 1 - 0 - 10 - 0 - 289 - - 1 - 0 - -20 - 0 - 361 - - 1 - -10 - 70 - -230 - 529 - - 1 - 16 - 118 - 464 - 841 - - 1 - 0 - 38 - 0 - 961 - - 1 - -4 - 78 - -148 - 1369 - - 1 - 0 - -38 - 0 - 1681 - - 1 - -10 - 110 - -430 - 1849 - - 1 - 0 - 50 - 0 - 2209 - - 1 - 10 - 130 - 530 - 2809 - - 1 - 0 - 20 - 0 - 3481 - - 1 - 0 - -10 - 0 - 3721 - - 1 - 0 - -10 - 0 - 4489 - - 1 - 0 - 142 - 0 - 5041 - - 1 - 0 - 70 - 0 - 5329 - - 1 - 20 - 222 - 1580 - 6241 - - 1 - 0 - -116 - 0 - 6889 - - 1 - 0 - 102 - 0 - 7921 - - 1 - 0 - -110 - 0 - 9409 - - 1 - 0 - 150 - 0 - 10201 - - 1 - 0 - -90 - 0 - 10609 - - 1 - -4 - 118 - -428 - 11449 - - 1 - -16 - 278 - -1744 - 11881 - - 1 - 0 - -30 - 0 - 12769 gamma_factors: - [] - - 0 - 0 id: 9557092 index: 23 label: 4-112e3-1.1-c1e2-0-23 load_key: Costa motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 - 1 order_of_vanishing: 1 origin: EllipticCurve/2.0.7.1/28672.5/a plot_delta: __RealLiteral__: 0 data: '0.046875' prec: 27 plot_values: - 2.6090367804329066e-75 - 0.19699351334396045 - 0.3923543977354838 - 0.584351760006262 - 0.771065038274683 - 0.9503061283949894 - 1.1195613286627988 - 1.2759587981489768 - 1.4162664083117467 - 1.5369238125919897 - 1.6341112536805544 - 1.7038560714985995 - 1.7421760791208432 - 1.7452569697430245 - 1.7096587580694715 - 1.6325440209582687 - 1.511918486112678 - 1.3468724482342858 - 1.137809712445185 - 0.8866494304953196 - 0.5969854654673833 - 0.27418794717343525 - -0.07456740503562835 - -0.44035471468210047 - -0.8126477210175408 - -1.1795695128907375 - -1.5282429325748559 - -1.8452366581160484 - -2.11709572231784 - -2.3309387421112695 - -2.4750977979144366 - -2.5397711545262616 - -2.5176543177694275 - -2.4045117388796333 - -2.1996502418052293 - -1.9062563164773252 - -1.5315630447778483 - -1.0868187130501568 - -0.5870380502829889 - -0.05052825541664001 - 0.501804921578536 - 1.0473514621213642 - 1.5628574438416292 - 2.0256031031128092 - 2.4146377608358405 - 2.712001055324745 - 2.90385394227862 - 2.981441535335741 - 2.941813695430023 - 2.7882386428704544 - 2.53025969469006 - 2.183365033641945 - 1.7682642733322458 - 1.309792161968279 - 0.835487372928246 - 0.3739210057988549 - -0.04712693234024225 - -0.4025262671244225 - -0.6715623181804756 - -0.8394772600407715 - -0.8986626573064669 - -0.8493953378435574 - -0.7000350647621879 - -0.4666371769942383 - -0.17197449753021496 - 0.15599234702952994 - 0.48611175663100387 - 0.7863785595358292 - 1.0264501040511143 - 1.1801541379910256 - 1.2277897359296088 - 1.158025931733656 - 0.9692222949907227 - 0.6700311149992565 - 0.27919040778502524 - -0.17552243014288463 - -0.6591391093070181 - -1.1320449096966472 - -1.5530482049954464 - -1.8827494666300093 - -2.086945027804461 - -2.1397817942251782 - -2.026383129887165 - -1.744694595921657 - -1.3063502706960874 - -0.736433049715402 - -0.07209056177624287 - 0.6399346795656476 - 1.3467046436264598 - 1.993168879854932 - 2.526612682921446 - 2.9011031033876713 - 3.0815472407000524 - 3.0469926289277565 - 2.7928491966478495 - 2.331793662717494 - 1.6932245898147695 - 0.9212611220145029 - 0.07140997265363765 - -0.7938484869419951 - -1.6101953535762754 - -2.3168896903081975 - -2.861984166163357 - -3.2068589321139527 - -3.329639874485749 - -3.227157794316569 - -2.915232075046677 - -2.42721529078221 - -1.8109001146960741 - -1.124051045469752 - -0.42896469581972807 - 0.21343129357607735 - 0.7493714062947224 - 1.1373639455924498 - 1.3521012644129364 - 1.3867566453604616 - 1.253409763504792 - 0.9815280955624848 - 0.6146306547646612 - 0.20545276043692096 - -0.18990427977543578 - -0.5182351936436689 - -0.7352417089442352 - -0.8106390791570565 - -0.7317845712428239 - -0.5053985789105795 - -0.15714459724254717 - 0.2709381580391518 - 0.7249198471428608 - 1.1449346042491673 - 1.4719798987708381 - 1.6548226044618168 - 1.656238623080643 - 1.4578629336031093 - 1.0630597291591553 - 0.49742609093397516 - -0.19320285036274493 - -0.9471009712647904 - -1.6929326453193017 - -2.3573174189885133 - -2.872859296702435 - -3.185742515367735 - -3.262016358539327 - -3.0918137949803306 - -2.6909621666421484 - -2.0997274298754984 - -1.3787562211357012 - -0.602606117713285 - 0.14845406402049038 - 0.7974706085445596 - 1.2796315425980578 - 1.549860635696021 - 1.5882604519450039 - 1.4027126439987936 - 1.0282590074919793 - 0.52325649326654 - -0.03731882367576375 - -0.5706950927747928 - -0.996258800977755 - -1.245481348109057 - -1.2706320891132503 - -1.0512057382029885 - -0.5972380977879542 - 0.05096348330930823 - 0.8267293257208518 - 1.6441938298821104 - 2.4079348050906595 - 3.0239848332508754 - 3.410923489304449 - 3.5097220041455346 - 3.2911363353578356 - 2.7597193238939477 - 1.953917322994829 - 0.9421852148221593 - -0.18446059540463958 - -1.322589125868429 - -2.3679967477687516 - -3.227441126580811 - -3.829039006037575 - -4.130053876869881 - -4.121116972385844 - -3.826368051257859 - -3.2995164200991964 - -2.616342532626034 - -1.864618964230542 - -1.1327658042820816 - -0.4987234145724684 - -0.0205000997363776 - 0.2703664344322353 - 0.37158118391634193 - 0.3087500013026419 - 0.13013467900609568 - -0.10174688112717874 - -0.3204843249942485 - -0.46662488897269816 - -0.49744506679264106 - -0.3942072295151265 - -0.16579535618069555 - 0.1518832158653424 - 0.5007526130159203 - 0.8090935668402139 - 1.002609578580836 - 1.0165050008888592 - 0.806849176119137 - 0.3595404738436258 - -0.3045382086830761 - -1.1290966479588471 - -2.027041669016293 - -2.8897112420099105 - -3.5996810450088104 - -4.045551252421493 - -4.13678922233407 - -3.816626699974974 - -3.0712062690593536 - -1.9336216959434793 - -0.4821452756980722 - 1.1673020929971594 - 2.873608130129498 - 4.486344602023975 - 5.863063985698161 - 6.885795440480962 - 7.47459264734412 - 7.596355402372361 - 7.2677649298204186 - 6.551957734486802 - 5.549407402918353 - 4.384270667491814 - 3.1880719868217566 - 2.0829607620233843 - 1.1668233761858287 - 0.5022585793019023 - 0.11086545827043971 - -0.02647387404138596 - 0.03649927841283934 - 0.22230069646756065 - 0.4436552985849535 - 0.6183650565223509 - 0.68281497389177 - 0.6020563303129789 - 0.3749334427961927 - 0.03348164432983673 - -0.36329177367932397 - -0.7402571757912445 - -1.0199234828209396 - -1.1369136553694192 - -1.0508127277380146 - -0.755260870614281 - -0.2817118559979064 - 0.3029191857799695 - 0.9045540163415496 - 1.4150944819694287 - 1.7285217108012567 - 1.7575473925346399 - 1.448256411961781 - 0.7904137201259659 - -0.17829458642603419 - -1.3749387867260612 positive_zeros: - '1.02146009644930970224782609679153' - '1.83244092276388395722828423857986' - '2.61942115191895265346521724222072' - '3.02489626653297184699187880186572' - '3.49808653690208959590256103111214' - '4.03608431046928950244930672345639' - '4.59760253603988668246969274775496' - '5.18685509698218462461608229093535' - '5.60186678453625226372964075247437' - '5.92419077433525637228473259977377' - '6.36249529789059442871028676113633' - '6.92786456894508405007857583570194' - '7.30938610443441778756699473080159' - '7.63730866217015373707714422513756' prelabel: 4-112e3-1.1-c1e2-0 primitive: true rational: true root_analytic_conductor: 3.076465650952455 root_angle: 1.0 root_number: '-1' self_dual: true spectral_label: c1e2-0 st_group: SU(2) symmetry_type: symplectic trace_hash: 666130974372567318 z1: __RealLiteral__: 0 data: '1.02146009644930970224782609679153' prec: 113 z2: __RealLiteral__: 0 data: '1.83244092276388395722828423857986' prec: 113 z3: __RealLiteral__: 0 data: '2.61942115191895265346521724222072' prec: 113 - - algebraic: true analytic_conductor: 89.57942739416335 bad_primes: - 2 - 7 central_character: '1.1' conductor: 1404928 conductor_radical: 14 degree: 4 dirichlet_coefficients: - 1 - 0 - 0 - 0 - 0 - 0 - -1 - 0 - -4 - 0 - 2 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 10 - 0 - 2 - 0 - 0 - 0 - -16 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 4 - 0 - 0 - 0 - 0 - 0 - 10 - 0 - 0 - 0 - 0 - 0 - 1 - 0 - 0 - 0 - -10 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 4 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - -2 - 0 - -20 - 0 - 7 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - -8 - 0 euler11: - 1 - -2 - 22 - -22 - 121 euler13: - 1 - 0 - -6 - 0 - 169 euler17: - 1 - 0 - 10 - 0 - 289 euler19: - 1 - 0 - -20 - 0 - 361 euler2: - 1 - 0 - 0 - 0 - 0 euler23: - 1 - -10 - 70 - -230 - 529 euler29: - 1 - 16 - 118 - 464 - 841 euler3: - 1 - 0 - 4 - 0 - 9 euler31: - 1 - 0 - 38 - 0 - 961 euler37: - 1 - -4 - 78 - -148 - 1369 euler41: - 1 - 0 - -38 - 0 - 1681 euler43: - 1 - -10 - 110 - -430 - 1849 euler47: - 1 - 0 - 50 - 0 - 2209 euler5: - 1 - 0 - -2 - 0 - 25 euler53: - 1 - 10 - 130 - 530 - 2809 euler59: - 1 - 0 - 20 - 0 - 3481 euler61: - 1 - 0 - -10 - 0 - 3721 euler67: - 1 - 0 - -10 - 0 - 4489 euler7: - 1 - 1 - 0 - 0 - 0 euler71: - 1 - 0 - 142 - 0 - 5041 euler73: - 1 - 0 - 70 - 0 - 5329 euler79: - 1 - 20 - 222 - 1580 - 6241 euler83: - 1 - 0 - -116 - 0 - 6889 euler89: - 1 - 0 - 102 - 0 - 7921 euler97: - 1 - 0 - -110 - 0 - 9409 euler_factors: - - 1 - 0 - 0 - 0 - 0 - - 1 - 0 - 4 - 0 - 9 - - 1 - 0 - -2 - 0 - 25 - - 1 - 1 - 0 - 0 - 0 - - 1 - -2 - 22 - -22 - 121 - - 1 - 0 - -6 - 0 - 169 - - 1 - 0 - 10 - 0 - 289 - - 1 - 0 - -20 - 0 - 361 - - 1 - -10 - 70 - -230 - 529 - - 1 - 16 - 118 - 464 - 841 - - 1 - 0 - 38 - 0 - 961 - - 1 - -4 - 78 - -148 - 1369 - - 1 - 0 - -38 - 0 - 1681 - - 1 - -10 - 110 - -430 - 1849 - - 1 - 0 - 50 - 0 - 2209 - - 1 - 10 - 130 - 530 - 2809 - - 1 - 0 - 20 - 0 - 3481 - - 1 - 0 - -10 - 0 - 3721 - - 1 - 0 - -10 - 0 - 4489 - - 1 - 0 - 142 - 0 - 5041 - - 1 - 0 - 70 - 0 - 5329 - - 1 - 20 - 222 - 1580 - 6241 - - 1 - 0 - -116 - 0 - 6889 - - 1 - 0 - 102 - 0 - 7921 - - 1 - 0 - -110 - 0 - 9409 id: 9557092 index: 23 instance_types: - ECNF - BMF - BMF - ECNF instance_urls: - EllipticCurve/2.0.7.1/28672.5/a - ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.5/a - ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.9/a - EllipticCurve/2.0.7.1/28672.9/a is_instance_Artin: false is_instance_BMF: true is_instance_CMF: false is_instance_DIR: false is_instance_ECNF: true is_instance_ECQ: false is_instance_G2Q: false is_instance_HMF: false is_instance_MaassGL3: false is_instance_MaassGL4: false is_instance_MaassGSp4: false is_instance_NF: false label: 4-112e3-1.1-c1e2-0-23 motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 - 1 order_of_vanishing: 1 prelabel: 4-112e3-1.1-c1e2-0 primitive: true rational: true root_analytic_conductor: 3.076465650952455 root_angle: 0.5 self_dual: true spectral_label: c1e2-0 trace_hash: 666130974372567318 z1: __RealLiteral__: 0 data: '1.02146009644930970224782609679153' prec: 113 - - Lhash: '1294854504373152540105668784571' Lhash_array: - '1294854504373152540105668784571' id: 9620869 label: 4-112e3-1.1-c1e2-0-23 type: ECNF url: EllipticCurve/2.0.7.1/28672.9/a - Lhash: '1294854504373152540105668784571' Lhash_array: - '1294854504373152540105668784571' id: 9620546 label: 4-112e3-1.1-c1e2-0-23 type: BMF url: ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.9/a - Lhash: '1294854504373152540105668784571' Lhash_array: - '1294854504373152540105668784571' id: 9619781 label: 4-112e3-1.1-c1e2-0-23 type: BMF url: ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.5/a - Lhash: '1294854504373152540105668784571' Lhash_array: - '1294854504373152540105668784571' id: 9619644 label: 4-112e3-1.1-c1e2-0-23 type: ECNF url: EllipticCurve/2.0.7.1/28672.5/a label_cols: - label - label - label labels: - 4-112e3-1.1-c1e2-0-23 - 4-112e3-1.1-c1e2-0-23 - 4-112e3-1.1-c1e2-0-23 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-20T01:15:50.993559'