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lfunc_lfunctions • Show schema
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{'Lhash': '2324060892971339111052227550029', 'a10': [-4.21509248000974, -1.1414293978621161e-60], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.25865202250415276, -0.4479984444576412], 'a4': [-0.5, -0.8660254037844386], 'a5': [2.10754624000487, 3.6503771669891854], 'a6': [0.5173040450083055, 3.067138299739243e-61], 'a7': [0.25865202250415276, 0.4479984444576412], 'a8': [1.0, 0.0], 'a9': [1.3661982625090225, -2.3663248038779496], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [37, [[1.0, 0], [4.1075462400048695, -4.4864310856427805]]]], 'bad_primes': [2, 37], 'central_character': '74.47', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3489835186185114180573191697975', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.25865202250415276, 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[-29.5, -51.09549882328188]], [[1.0, 0], [1.2413479774958471, 2.1500777668956745], [-30.5, 52.827549630850754]], [[1.0, 0], [-0.13380173749097748, -0.2317514074753665], [-33.5, 58.023702053557386]], [[1.0, 0], [-1.7413479774958471, -3.0161031706801134], [-35.5, 61.48780366869514]], [[1.0, 0], [-5.732396525018045, 0], [73.0, 0]], [[1.0, 0], [2.383502307517328, 4.128347096577671], [-39.5, 68.41600689897065]], [[1.0, 0], [5.473744502513893, -9.480803586004889], [-41.5, -71.88010851410841]], [[1.0, 0], [8.063986697510456, -13.96723467164767], [-44.5, -77.07626093681505]], [[1.0, 0], [-0.30221156499856605, 0], [97.0, 0]], [[1.0, 0], [9.24970057002635, 0], [101.0, 0]], [[1.0, 0], [-6.448087864975084, 0], [103.0, 0]], [[1.0, 0], [-6.124850285013175, -10.608551882395538], [-53.5, 92.66471820493493]], [[1.0, 0], [-3.456440457505587, 5.986730485736291], [-54.5, -94.39676901250381]], [[1.0, 0], [-4.866198262509022, 8.42850263036902], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-74-37.10-c1-0-0', '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/74/2/c/c/47/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8268264829893219, 0.8032049076999392, 0.7886510012645742, 0.7804697162616095, 0.7754147334789109, 0.7699124093551715, 0.7602405795965947, 0.7426540493970868, 0.7134750117971116, 0.6691740535905583, 0.6064624363137087, 0.5224073749942685, 0.41457373817028176, 0.2811892545142887, 0.12132569027560233, -0.06491499925710743, -0.2762232305029353, -0.5099288061503038, -0.7618894885692729, -1.026438733848084, -1.2964095942440226, -1.5632498923137692, -1.8172403828139694, -2.0478226612760304, -2.244037080074542, -2.395063064979851, -2.4908453179814254, -2.5227799410907696, -2.484425173252213, 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'12.58667242233411029729913030423638', '12.92533783418393665808034756015777', '14.06850383922288431820899501511166'], 'prelabel': '2-74-37.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.3108483933873932, 'root_number': '0.5598769608075596 - 0.8285757592138998*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.155424196694', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83336077981812360404894545468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.50928289791509269796628937971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52058422804668733797722400848', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.10', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/c/c/47/2'], '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': '2-74-37.10-c1-0-0', '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': '2-74-37.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.1554241966936966, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83336077981812360404894545468', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2324060892971339111052227550029', 'Lhash_array': ['2324060892971339111052227550029'], 'label': '2-74-37.10-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/c/c/47/2'}