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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 1, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1221962300074229217', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.041237113402061855, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.010309278350515464, 0.0], 'algebraic': True, 'analytic_conductor': 0.04310234611201031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 0, -1]], [13, [1, 0, -1]]], 'bad_primes': [2, 13], 'central_character': '676.1', 'coefficient_field': '1.1.1.1', 'conductor': 676, 'conductor_radical': 26, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 2, 3, 6, 9], [1, 4, 13, 20, 25], [1, 0, 13, 0, 49], [1, -4, 10, -44, 121], [1, 0, -1], [1, 6, 43, 102, 289], [1, -8, 50, -152, 361], [1, 4, 46, 92, 529], [1, -8, 70, -232, 841], [1, 0, 46, 0, 961], [1, 4, 53, 148, 1369], [1, 0, 82, 0, 1681], [1, 6, 91, 258, 1849], [1, -16, 133, -752, 2209], [1, -12, 106, -636, 2809], [1, 16, 178, 944, 3481], [1, 0, 58, 0, 3721], [1, -12, 106, -804, 4489], [1, 8, 157, 568, 5041], [1, 8, 126, 584, 5329], [1, -4, 126, -316, 6241], [1, -12, 166, -996, 6889], [1, 0, 142, 0, 7921], [1, -4, 54, -388, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 2, 'label': '4-26e2-1.1-c1e2-0-2', 'leading_term': '0.32015523548', 'load_key': 'G2Q', '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': 0, 'origin': 'Genus2Curve/Q/676/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.3201552354797366, 0.3340411490319237, 0.3766558505268181, 0.4507449263728869, 0.5604421435489074, 0.7105280461478766, 0.9052647227562866, 1.146748321513525, 1.432803131149497, 1.754590880883143, 2.094320758422117, 2.423687909023496, 2.703874825805183, 2.888020491802799, 2.926876501456895, 2.777824183627337, 2.416490026473322, 1.84897113023225, 1.121451941259569, 0.3232196427862649, -0.4206800363614872, -0.9692054152543, -1.196289148084307, -1.027461044235817, -0.4723573234518956, 0.358965450167102, 1.26661107504112, 2.002900961933926, 2.340222130190883, 2.14726263416636, 1.447571124762959, 0.433732338944843, -0.5789807497540645, -1.254696799751392, -1.364862134338937, -0.8931184817534431, -0.06651308567458394, 0.7160098176433894, 1.045583529755978, 0.6974662033166763, -0.2301828800617555, -1.312273480211535, -1.956521350714634, -1.678476176261346, -0.3733953044143204, 1.556286237085959, 3.311185417498724, 4.027820780221029, 3.197318876939214, 0.9637647072371687, -1.871564214008386, -4.179002822439021, -5.02390788552437, -4.12283626029817, -1.982231250418194, 0.3719918904919296, 1.93687167825704, 2.243394138472214, 1.539654200450084, 0.5433910242299606, -0.06725308281539619, -0.08064518025334048, 0.197678526097349, 0.3028599544520894, 0.1038157496193437, 0.03034044541956399, 0.8011904487204338, 2.795236384100994, 5.527811079708475, 7.698921727761657, 7.913051889833011, 5.658171766313854, 1.852010849306956, -1.527024639306898, -2.595455365375651, -0.778883021443714, 2.767300160758719, 5.880066236711628, 6.794578174160323, 5.254346194038732, 2.538378589234526, 0.4171398555950422, -0.1420841409068759, 0.4753600342096734, 1.103049713770594, 0.9361568326032799, 0.2331757232799863, -0.02723341072580681, 0.8067976917186743, 2.306409483911444, 3.254284984877787, 2.770480210125606, 1.232070315095588, 0.05509072162412044, 0.4263081525019734, 2.10480984917659, 3.464446759256042, 2.872844234658421, 0.2299745685367565, -2.77144911533685, -4.007578595949743, -2.742653479475937, -0.2427811276484493, 1.412447590245182, 1.21946803923084, 0.03433506661473441, -0.5154803735443573, 0.09622656384002459, 0.5739543746343575, -0.9126090789803138, -4.618950197368121, -8.450569209614383, -9.504254394487193, -6.63045959919345, -1.592602996730248, 2.361655238209855, 3.227285230891683, 1.715227211406804, 0.1718618712049099, 0.1693300360312754, 1.220044888175141, 1.757902107718993, 1.098747434205725, 0.1486378498836965, 0.1581234954502427, 1.088935267310299, 1.592140526470531, 0.6732137155174073, -0.9588193107284407, -1.609247126110931, -0.6962081985201837, 0.2903295433839677, -0.5949667578985792, -3.142246090075609, -4.476464362425085, -1.722471700361437, 4.680651375600186, 10.67641598029574, 12.03476253065133, 8.24461800583737, 2.872486274911882, 0.02274074017929051, 0.6103646995112545, 2.210552342308008, 2.244668202719384, 0.7223375471887954, -0.3766059819824214, 0.08934521405950221, 1.025237392533462, 0.708758188227357, -0.8313918062373988, -1.797775162655814, -0.9848669384821652, 0.5975593531668538, 1.055945732113857, 0.246412139642823, 0.1876703447695345, 2.452775266577031, 5.748149594137727, 6.965815475235794, 4.733846341710914], 'positive_zeros': [3.640287616260134, 4.611534534911821, 5.889084509159496, 6.764231323278578, 7.45985560667589, 8.289125051595985, 9.25208611998247, 10.28025762974353, 11.21486999262722, 11.49712673239204, 12.10810868275674, 12.14995362405969, 13.59228638804353, 14.10812305484995, 15.26212233610873, 15.44251689428644, 16.2105519664871, 16.32893427071431, 17.46439533057334, 17.51877200404443, 18.38839909652752, 19.14446932223225, 19.69339975173152], 'prelabel': '4-26e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.45564355065701206, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 1221962300074229217, 'z1': {'__RealLiteral__': 0, 'data': '3.64028761626', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.61153453491', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.88908450916', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04310234611201031, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 676, 'conductor_radical': 26, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 1, -4, 0, 0, 0, 1, 0, 4, -2, 0, 0, 8, 1, -6, 0, 8, -4, 0, 0, -4, 0, 3, 0, -2, 0, 8, 0, 0, 0, -8, 0, 0, 1, -4, 0, 0, 0, 0, 0, -6, 4, -4, 0, 16, -2, -13, 0, 12, 0, 12, 0, -16, 0, -16, 0, -16, 8, 0, 0, 0, 1, 0, 0, 12, -6, 8, 0, -8, 0, -8, 0, -6, 8, 0, 0, 4, -4, 4, 0, 12, 0, 24, 0, -16, 0, 0, 0, 0, -4, 0, 0, -32, 0, 4, 0, 4, 3], 'euler11': [1, -4, 10, -44, 121], 'euler13': [1, 0, -1, 0, 0], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, -8, 50, -152, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 4, 46, 92, 529], 'euler29': [1, -8, 70, -232, 841], 'euler3': [1, 2, 3, 6, 9], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 4, 53, 148, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 6, 91, 258, 1849], 'euler47': [1, -16, 133, -752, 2209], 'euler5': [1, 4, 13, 20, 25], 'euler53': [1, -12, 106, -636, 2809], 'euler59': [1, 16, 178, 944, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, -12, 106, -804, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, 8, 157, 568, 5041], 'euler73': [1, 8, 126, 584, 5329], 'euler79': [1, -4, 126, -316, 6241], 'euler83': [1, -12, 166, -996, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, -4, 54, -388, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 2, 3, 6, 9], [1, 4, 13, 20, 25], [1, 0, 13, 0, 49], [1, -4, 10, -44, 121], [1, 0, -1, 0, 0], [1, 6, 43, 102, 289], [1, -8, 50, -152, 361], [1, 4, 46, 92, 529], [1, -8, 70, -232, 841], [1, 0, 46, 0, 961], [1, 4, 53, 148, 1369], [1, 0, 82, 0, 1681], [1, 6, 91, 258, 1849], [1, -16, 133, -752, 2209], [1, -12, 106, -636, 2809], [1, 16, 178, 944, 3481], [1, 0, 58, 0, 3721], [1, -12, 106, -804, 4489], [1, 8, 157, 568, 5041], [1, 8, 126, 584, 5329], [1, -4, 126, -316, 6241], [1, -12, 166, -996, 6889], [1, 0, 142, 0, 7921], [1, -4, 54, -388, 9409]], 'index': 2, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/676/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-26e2-1.1-c1e2-0-2', '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': 0, 'prelabel': '4-26e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.45564355065701206, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1221962300074229217, 'z1': {'__RealLiteral__': 0, 'data': '3.64028761626', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9953729
{'Lhash': '1221962300074229217', 'Lhash_array': ['1221962300074229217'], 'label': '4-26e2-1.1-c1e2-0-2', 'type': 'ECQP', 'url': 'EllipticCurve/Q/26/a|EllipticCurve/Q/26/b'}
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id: 9952881
{'Lhash': '1221962300074229217', 'Lhash_array': ['1221962300074229217'], 'label': '4-26e2-1.1-c1e2-0-2', 'type': 'ECQP', 'url': 'EllipticCurve/Q/26/a|EllipticCurve/Q/26/b'}
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id: 1222246
{'Lhash': '1221962300074229217', 'Lhash_array': ['1221962300074229217'], 'label': '4-26e2-1.1-c1e2-0-2', 'type': 'G2Q', 'url': 'Genus2Curve/Q/676/a'}