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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '2805950199904634710558393273500', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [-1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 3]], [13, [1, 5, 13]]], 'bad_primes': [3, 13], 'central_character': '13689.1', 'coefficient_field': '1.1.1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 4], [1, 1, 3], [1, 0, -1, 0, 25], [1, 0, -5, 0, 49], [1, 0, 5, 0, 121], [1, 5, 13], [1, 0, 25, 0, 289], [1, 0, -2, 0, 361], [1, 3, 46, 69, 529], [1, 12, 85, 348, 841], [1, 0, 55, 0, 961], [1, 0, 34, 0, 1369], [1, 0, -37, 0, 1681], [1, 11, 114, 473, 1849], [1, 0, -55, 0, 2209], [1, -12, 133, -636, 2809], [1, 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-4.225198878483024, -2.5484069448046625], 'positive_zeros': ['2.21350441470184917104183116838697', '3.38434697765581707429375510649397', '4.29189245265897939806533711215885', '4.95287287063942728295349208421471', '5.48114874742225891130904665830375', '6.06697710305086175522084812219864', '6.99355924731825873030171106118380', '7.47671691054370486042388375079116', '8.222861338133290193246821662946331', '8.838535630268282341179855629224964', '9.259193378129729411314699302121810', '9.865541943633370090286786133496456', '10.31453851596519414293283116869555', '11.00532084754246167124084101707883'], 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 241838607272646056, 'z1': {'__RealLiteral__': 0, 'data': '2.21350441470184917104183116838697', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.38434697765581707429375510649397', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.29189245265897939806533711215885', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 5, 0, -12, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, -11, 0, 0, 0, 0, 0, 5, 0, 0, 10, 12, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, -7, 0, 1, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2], 'euler11': [1, 0, 5, 0, 121], 'euler13': [1, 5, 13, 0, 0], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, 0, 2, 0, 4], 'euler23': [1, 3, 46, 69, 529], 'euler29': [1, 12, 85, 348, 841], 'euler3': [1, 1, 3, 0, 0], 'euler31': [1, 0, 55, 0, 961], 'euler37': [1, 0, 34, 0, 1369], 'euler41': [1, 0, -37, 0, 1681], 'euler43': [1, 11, 114, 473, 1849], 'euler47': [1, 0, -55, 0, 2209], 'euler5': [1, 0, -1, 0, 25], 'euler53': [1, -12, 133, -636, 2809], 'euler59': [1, 0, 53, 0, 3481], 'euler61': [1, 13, 144, 793, 3721], 'euler67': [1, 0, -89, 0, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, 0, 98, 0, 5041], 'euler73': [1, 0, 34, 0, 5329], 'euler79': [1, 7, 150, 553, 6241], 'euler83': [1, 0, 125, 0, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 0, 157, 0, 9409], 'euler_factors': [[1, 0, 2, 0, 4], [1, 1, 3, 0, 0], [1, 0, -1, 0, 25], [1, 0, -5, 0, 49], [1, 0, 5, 0, 121], [1, 5, 13, 0, 0], [1, 0, 25, 0, 289], [1, 0, -2, 0, 361], [1, 3, 46, 69, 529], [1, 12, 85, 348, 841], [1, 0, 55, 0, 961], [1, 0, 34, 0, 1369], [1, 0, -37, 0, 1681], [1, 11, 114, 473, 1849], [1, 0, -55, 0, 2209], [1, -12, 133, -636, 2809], [1, 0, 53, 0, 3481], [1, 13, 144, 793, 3721], [1, 0, -89, 0, 4489], [1, 0, 98, 0, 5041], [1, 0, 34, 0, 5329], [1, 7, 150, 553, 6241], [1, 0, 125, 0, 6889], [1, 0, -130, 0, 7921], [1, 0, 157, 0, 9409]], 'index': 15, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.13.1/81.5/c', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.5-c', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.4-c', 'EllipticCurve/2.2.13.1/81.4/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-117e2-1.1-c1e2-0-15', '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': '4-117e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 241838607272646056, 'z1': {'__RealLiteral__': 0, 'data': '2.21350441470184917104183116838697', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9530748
{'Lhash': '2805950199904634710558393273500', 'Lhash_array': ['2805950199904634710558393273500'], 'label': '4-117e2-1.1-c1e2-0-15', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/81.4/c'}
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id: 9530620
{'Lhash': '2805950199904634710558393273500', 'Lhash_array': ['2805950199904634710558393273500'], 'label': '4-117e2-1.1-c1e2-0-15', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.4-c'}
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id: 9530317
{'Lhash': '2805950199904634710558393273500', 'Lhash_array': ['2805950199904634710558393273500'], 'label': '4-117e2-1.1-c1e2-0-15', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.5-c'}
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id: 9529959
{'Lhash': '2805950199904634710558393273500', 'Lhash_array': ['2805950199904634710558393273500'], 'label': '4-117e2-1.1-c1e2-0-15', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/81.5/c'}