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lfunc_lfunctions • Show schema
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{'Lhash': '872257276540017807108189191991', 'a10': [-2.074331742790855, -1.1976159900888856], 'a2': [0.9659258262890683, 0.25881904510252074], 'a3': [-1.4508951956999694, -0.9459931982285853], 'a4': [0.8660254037844386, 0.5], 'a5': [-2.3136164296072153, -0.6199316539086307], 'a6': [-1.1566160845263302, -1.2892785707576857], 'a7': [-1.7291348201956256, 2.0025216037753606], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [1.210193737810505, 2.7450739729494065], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [3, [[1.0, 0], [1.4508951956999694, 0.9459931982285853]]], [7, [[1.0, 0], [1.7291348201956256, -2.0025216037753606]]], [13, [[1.0, 0], [-2.938288451529021, -2.0896078521127333]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.515', 'coefficient_field': 'CDF', 'conductor': 546, 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[-50.5, -87.4685657822283]], [[1.0, 0], [-16.194363467048827, 9.349820107055283], [51.5, -89.20061658979718]], [[1.0, 0], [-0.182798533777278, 0.10553878268378035], [53.5, -92.66471820493493]], [[1.0, 0], [13.637207680051025, -3.6540787848851766], [94.39676901250381, -54.5]], [[1.0, 0], [0, -7.741174133238627], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-546-273.242-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/546/2/bv/a/515/22', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2265084131813175, 1.0734337616355436, 0.8986722086398342, 0.6943669978998909, 0.4520037981577986, 0.16417759964245676, -0.17384917375715614, -0.5629083305967448, -0.9990354628998235, -1.4729425675841152, -1.9698900443255556, -2.470013396307, 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2.0223319837451803, 0.8193805567250548], 'positive_zeros': ['0.68808966475697287150310828621365', '3.16302691943311956948496497299576', '4.10104233636530657796372820992524', '4.59380069347033626111426086424138', '6.20392851693893920503232207234305', '6.65390624106891454932665123844117', '7.67483507081267450732580100002025', '9.140464754658409399632347668546013', '9.990621940996557947987070186228237', '11.06540860610339275170571179030384'], 'prelabel': '2-546-273.242-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.36216780343871224, 'root_number': '0.41960727145158205 - 0.9077057550467322*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.181083901719', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68808966475697287150310828621', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16302691943311956948496497300', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10104233636530657796372820993', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.242', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bv/a/515/22'], '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': '2-546-273.242-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-546-273.242-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.18108390171935612, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68808966475697287150310828621', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '872257276540017807108189191991', 'Lhash_array': ['872257276540017807108189191991'], 'label': '2-546-273.242-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bv/a/515/22'}