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lfunc_lfunctions • Show schema
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{'Lhash': '1232293412707434226392101628854', 'a10': [5.0, -5.0], 'a2': [-0.7071067811865476, 1.224744871391589], 'a3': [0, 0], 'a4': [-1.0, -1.7320508075688772], 'a5': [-4.8296291314453415, -1.294095225512604], 'a6': [0, 0], 'a7': [4.330127018922194, 2.5], 'a8': [2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.07090141318405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -1.224744871391589]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [4.8296291314453415, 1.294095225512604]]]], 'bad_primes': [2, 3, 5], 'central_character': '810.269', 'coefficient_field': 'CDF', 'conductor': 810, 'conductor_radical': 30, 'conjugate': '604445165926461198248801269668', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.8296291314453415, 1.294095225512604]], [[1.0, 0], [-4.330127018922194, -2.5], [24.5, 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65.5], [2244.5, -3887.5880375883453]], [[1.0, 0], [0, 89.09545442950498], [-5041.0, 0]], [[1.0, 0], [0, -17.0], [-5329.0, 0]], [[1.0, 0], [-58.5, 101.32497224277932], [-3120.5, -5404.864545018681]], [[1.0, 0], [28.991378028648448, -50.214539727055154], [-3444.5, -5966.049006670998]], [[1.0, 0], [0, -147.07821048680188], [-7921.0, 0]], [[1.0, 0], [35.50704155516198, 20.5], [4704.5, 8148.433024207783]], [[1.0, 0], [-78.38367176906169, -45.254833995939045], [5100.5, 8834.325144005059]], [[1.0, 0], [-11.258330249197702, 6.5], [5304.5, -9187.66350874911]], [[1.0, 0], [-123.03657992645927, 0], [11449.0, 0]], [[1.0, 0], [-8.0, 0], [11881.0, 0]], [[1.0, 0], [19.091883092036785, 33.0681115275729], [-6384.5, 11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-810-45.29-c2-0-24', 'leading_term': '0.969992227654483360878673195473402016474704294669441244', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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4.69796779609908, 'root_angle': 0.1388888888888889, 'root_number': '0.9063077870366499632425526567543169832677126251758646809 + 0.422618261740699436186978489647730181563129301194864624*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06944444444444445', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.972108097046276455999098549905', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48704269522586107617181502057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59069449348584302374247285746', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.07090141318405, 'bad_primes': [2, 3, 5], 'central_character': '45.29', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/3/j/e/269/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-810-45.29-c2-0-24', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-810-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.69796779609908, 'root_angle': 0.06944444444444445, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.972108097046276455999098549905', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1232293412707434226392101628854', 'Lhash_array': ['1232293412707434226392101628854'], 'label': '2-810-45.29-c2-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/3/j/e/269/1'}