data: - - A10: 0 A2: 0 A3: 0 A4: 0 A5: 0 A6: 0 A7: 1 A8: 0 A9: 4 Lhash: '1731432809746266405351497856997' 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 - 14 - -22 - 121 - - 1 - 0 - 6 - 0 - 169 - - 1 - 0 - 26 - 0 - 289 - - 1 - 0 - 20 - 0 - 361 - - 1 - 2 - 22 - 46 - 529 - - 1 - 6 - 58 - 174 - 841 - - 1 - 0 - 34 - 0 - 961 - - 1 - 14 - 114 - 518 - 1369 - - 1 - 0 - 50 - 0 - 1681 - - 1 - 6 - 46 - 258 - 1849 - - 1 - 0 - 70 - 0 - 2209 - - 1 - 8 - 118 - 424 - 2809 - - 1 - 0 - -68 - 0 - 3481 - - 1 - 0 - -14 - 0 - 3721 - - 1 - 4 - 134 - 268 - 4489 - - 1 - 4 - 46 - 284 - 5041 - - 1 - 0 - 86 - 0 - 5329 - - 1 - 0 - -98 - 0 - 6241 - - 1 - 0 - 68 - 0 - 6889 - - 1 - 0 - -162 - 0 - 7921 - - 1 - 0 - 106 - 0 - 9409 - - 1 - 0 - 130 - 0 - 10201 - - 1 - 0 - -30 - 0 - 10609 - - 1 - 20 - 310 - 2140 - 11449 - - 1 - -2 - -6 - -218 - 11881 - - 1 - -16 - 226 - -1808 - 12769 gamma_factors: - [] - - 0 - 0 id: 9557108 index: 38 label: 4-112e3-1.1-c1e2-0-38 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/2.0.7.1/28672.8/k plot_delta: __RealLiteral__: 0 data: '0.046875' prec: 27 plot_values: - -2.2407653403597895e-74 - 0.25834076685541313 - 0.5156635904036363 - 0.7708418212706692 - 1.0225381288541988 - 1.2691158079594773 - 1.5085695510515267 - 1.73848130299487 - 1.9560060322153436 - 2.1578912373634065 - 2.340532750283972 - 2.5000678920083415 - 2.6325053000072987 - 2.7338888016609064 - 2.8004906120224105 - 2.8290269585035857 - 2.816887080372841 - 2.762364538858113 - 2.664878044784462 - 2.5251677179249987 - 2.345451991958778 - 2.1295304200268967 - 1.882818547256861 - 1.6123028936226524 - 1.3264069812851313 - 1.0347632334831232 - 0.7478903852618878 - 0.4767816207275781 - 0.2324147483264227 - 0.02520202961600995 - -0.1355965940106874 - -0.24246761082645638 - -0.29021166508194757 - -0.2764482534406148 - -0.20201976701018404 - -0.0712585769740252 - 0.10791527377633986 - 0.3240917071399532 - 0.5626804424642466 - 0.8064385352719301 - 1.036207955408747 - 1.2318412138701764 - 1.3732784223944563 - 1.4417252270010268 - 1.4208688612093823 - 1.2980601943880183 - 1.0653841155193493 - 0.7205397487062978 - 0.26745646028282133 - -0.283418313686217 - -0.9152078007873774 - -1.6050989652514827 - -2.32524302989146 - -3.044039182963445 - -3.7277488521972275 - -4.342360585665738 - -4.8556013811971 - -5.238971375072515 - -5.469667077668443 - -5.532255412101754 - -5.419967731424105 - -5.135500153601806 - -4.691233584903302 - -4.108822504977094 - -3.418143957547377 - -2.6556445016712753 - -1.8621698307556076 - -1.080405706982978 - -0.35209605109678493 - 0.28476904241286016 - 0.7985889010969621 - 1.1664066926796024 - 1.3755959512762401 - 1.4248267127360483 - 1.3242074758829248 - 1.0945594205010254 - 0.7658468046478502 - 0.3748570589053787 - -0.0377099601994681 - -0.43052767397192665 - -0.765046140741526 - -1.0087339198571632 - -1.1378801794415574 - -1.1397037905411247 - -1.0135645856520876 - -0.7711409894793817 - -0.4355229581436804 - -0.039262930816836066 - 0.3784776319506425 - 0.7754611463916161 - 1.1102897767510502 - 1.346359768837269 - 1.4554909489305574 - 1.4208820134765536 - 1.2390894443245342 - 0.9208058354993662 - 0.4903164728967185 - -0.016367227536471574 - -0.5545728678424245 - -1.074985877923292 - -1.5282742126733968 - -1.8698967772782205 - -2.064636311726399 - -2.090403290124381 - -1.9409078953808985 - -1.6268897261047945 - -1.1757226451161165 - -0.6293642373231713 - -0.040781801294913385 - 0.5308560834710367 - 1.0257976645955054 - 1.389611536308033 - 1.5787998806392827 - 1.5655500219508278 - 1.3411151803858865 - 0.9174320672755067 - 0.32674482364338947 - -0.3808027590609076 - -1.141440217479616 - -1.88354598228553 - -2.534396067106879 - -3.027237492450122 - -3.307981588420716 - -3.3408269064923872 - -3.11220856184261 - -2.632624210813516 - -1.9360929583365998 - -1.0772424433683967 - -0.12626691815313257 - 0.8377708969351289 - 1.7346344436002454 - 2.4908225199589342 - 3.0468692756720634 - 3.3632570989609163 - 3.424296010166785 - 3.239528773640486 - 2.8424803344537968 - 2.286856334002757 - 1.6405773151384653 - 0.9782811030051847 - 0.37310698591670055 - -0.11133069721218684 - -0.42787838560627917 - -0.5508964076615209 - -0.4788393595893644 - -0.23404830362834242 - 0.14024338942639977 - 0.5853644715204899 - 1.034500931272851 - 1.42098480459507 - 1.6865971398558652 - 1.7888862754700423 - 1.7066020734192604 - 1.4425565238100126 - 1.0235191671340886 - 0.49710867824615823 - -0.07399141863457685 - -0.619828749792189 - -1.0720618348086248 - -1.3728386247745223 - -1.482561277444822 - -1.3855337257942237 - -1.0927251757576912 - -0.6412213690523337 - -0.0903374026242711 - 0.48521693357631973 - 1.0043475090287588 - 1.389694361270311 - 1.57761989641751 - 1.526807585909984 - 1.224348769511975 - 0.688477239585409 - -0.03249242649614591 - -0.8650028090123949 - -1.7183727713740293 - -2.4952763088303556 - -3.103337606955887 - -3.466425078664166 - -3.534228214452411 - -3.2888818196666354 - -2.7477446157979384 - -1.9619039202222461 - -1.010508938463086 - 0.008434317410020776 - 0.9897116165775413 - 1.8335658242453636 - 2.457796330561322 - 2.807754687545925 - 2.8629427331429724 - 2.639335950549999 - 2.1870930636878176 - 1.583905106086073 - 0.9248068126071983 - 0.30974468187735027 - -0.16949484930282463 - -0.4412911996022514 - -0.4635452967518736 - -0.22913515677319957 - 0.23327270733094452 - 0.8631873546434614 - 1.5765251119199868 - 2.277021426875945 - 2.869295010271616 - 3.271797624669439 - 3.427881902031605 - 3.3134607160043674 - 2.940185999288261 - 2.353683547993615 - 1.6270617602176474 - 0.8505730625016856 - 0.11885453108483844 - -0.4824697057488264 - -0.8889307352492856 - -1.066362555605976 - -1.0157187546743842 - -0.7728207790729646 - -0.40301454168850936 - 0.008557939072025072 - 0.3697231594399079 - 0.5952677278012789 - 0.6201382144869507 - 0.409907521594455 - -0.03307551719509029 - -0.6688422635357321 - -1.424505437667347 - -2.203944512395645 - -2.9011785208043364 - -3.415565515413266 - -3.6666615807407683 - -3.6065737297435203 - -3.2279568117801585 - -2.566395751381866 - -1.6967010428471807 - -0.723517145448018 - 0.2325249601739189 - 1.0512104344730342 - 1.629391835148588 - 1.8955043903971238 - 1.8198287558979134 - 1.4189662283928182 - 0.7538070138188325 - -0.07879358181300472 - -0.9594985581150897 - -1.7632342844385192 - -2.3768015484952447 - -2.7148049183311036 - -2.731574541683414 - -2.4273229705443438 - -1.8476153737068552 - -1.0762138544672644 - -0.22234074652285943 - 0.5957557724426575 - 1.2684856329859544 - 1.7111999709558343 - 1.8766184906440764 - 1.7615152024217 - 1.4066375071392692 positive_zeros: - '1.36585965362579962812780371947418' - '1.66066384870243542860380705787622' - '2.27372078903964464441170712080759' - '3.21241631286068701200752599073277' - '3.65194203381077251607794215943818' - '4.08256113897269383538103799876667' - '4.54542721719265047362564008627232' - '5.06574236903714323014596414504345' - '5.45987015954679960643740917137268' - '6.00609131104675387706915268936031' - '6.59719074620483121754814490160779' - '6.82759137091116655199567209076436' - '7.30643370909968080566606447898859' - '7.69482405895834397367412039493645' 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: 2173993193089532017 z1: __RealLiteral__: 0 data: '1.36585965362579962812780371947418' prec: 113 z2: __RealLiteral__: 0 data: '1.66066384870243542860380705787622' prec: 113 z3: __RealLiteral__: 0 data: '2.27372078903964464441170712080759' 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 - -2 - 0 - -2 - 0 - 0 - 0 - -6 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - -14 - 0 - 0 - 0 - 0 - 0 - -6 - 0 - 0 - 0 - 0 - 0 - 1 - 0 - 0 - 0 - -8 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 4 - 0 - 0 - 0 - -4 - 0 - 0 - 0 - -4 - 0 - 0 - 0 - 0 - 0 - 2 - 0 - 0 - 0 - 7 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 8 - 0 euler11: - 1 - -2 - 14 - -22 - 121 euler13: - 1 - 0 - 6 - 0 - 169 euler17: - 1 - 0 - 26 - 0 - 289 euler19: - 1 - 0 - 20 - 0 - 361 euler2: - 1 - 0 - 0 - 0 - 0 euler23: - 1 - 2 - 22 - 46 - 529 euler29: - 1 - 6 - 58 - 174 - 841 euler3: - 1 - 0 - -4 - 0 - 9 euler31: - 1 - 0 - 34 - 0 - 961 euler37: - 1 - 14 - 114 - 518 - 1369 euler41: - 1 - 0 - 50 - 0 - 1681 euler43: - 1 - 6 - 46 - 258 - 1849 euler47: - 1 - 0 - 70 - 0 - 2209 euler5: - 1 - 0 - 2 - 0 - 25 euler53: - 1 - 8 - 118 - 424 - 2809 euler59: - 1 - 0 - -68 - 0 - 3481 euler61: - 1 - 0 - -14 - 0 - 3721 euler67: - 1 - 4 - 134 - 268 - 4489 euler7: - 1 - -1 - 0 - 0 - 0 euler71: - 1 - 4 - 46 - 284 - 5041 euler73: - 1 - 0 - 86 - 0 - 5329 euler79: - 1 - 0 - -98 - 0 - 6241 euler83: - 1 - 0 - 68 - 0 - 6889 euler89: - 1 - 0 - -162 - 0 - 7921 euler97: - 1 - 0 - 106 - 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 - 14 - -22 - 121 - - 1 - 0 - 6 - 0 - 169 - - 1 - 0 - 26 - 0 - 289 - - 1 - 0 - 20 - 0 - 361 - - 1 - 2 - 22 - 46 - 529 - - 1 - 6 - 58 - 174 - 841 - - 1 - 0 - 34 - 0 - 961 - - 1 - 14 - 114 - 518 - 1369 - - 1 - 0 - 50 - 0 - 1681 - - 1 - 6 - 46 - 258 - 1849 - - 1 - 0 - 70 - 0 - 2209 - - 1 - 8 - 118 - 424 - 2809 - - 1 - 0 - -68 - 0 - 3481 - - 1 - 0 - -14 - 0 - 3721 - - 1 - 4 - 134 - 268 - 4489 - - 1 - 4 - 46 - 284 - 5041 - - 1 - 0 - 86 - 0 - 5329 - - 1 - 0 - -98 - 0 - 6241 - - 1 - 0 - 68 - 0 - 6889 - - 1 - 0 - -162 - 0 - 7921 - - 1 - 0 - 106 - 0 - 9409 id: 9557108 index: 38 instance_types: - ECNF - BMF - ECNF - BMF instance_urls: - EllipticCurve/2.0.7.1/28672.6/l - ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/l - EllipticCurve/2.0.7.1/28672.8/k - ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/k 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-c1e2-0-38 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: 2173993193089532017 z1: __RealLiteral__: 0 data: '1.36585965362579962812780371947418' prec: 113 - - Lhash: '1731432809746266405351497856997' Lhash_array: - '1731432809746266405351497856997' id: 9621317 label: 4-112e3-1.1-c1e2-0-38 type: BMF url: ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/k - Lhash: '1731432809746266405351497856997' Lhash_array: - '1731432809746266405351497856997' id: 9620935 label: 4-112e3-1.1-c1e2-0-38 type: ECNF url: EllipticCurve/2.0.7.1/28672.8/k - Lhash: '1731432809746266405351497856997' Lhash_array: - '1731432809746266405351497856997' id: 9620440 label: 4-112e3-1.1-c1e2-0-38 type: BMF url: ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/l - Lhash: '1731432809746266405351497856997' Lhash_array: - '1731432809746266405351497856997' id: 9620150 label: 4-112e3-1.1-c1e2-0-38 type: ECNF url: EllipticCurve/2.0.7.1/28672.6/l label_cols: - label - label - label labels: - 4-112e3-1.1-c1e2-0-38 - 4-112e3-1.1-c1e2-0-38 - 4-112e3-1.1-c1e2-0-38 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-20T01:27:00.181030'