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lfunc_lfunctions • Show schema
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{'Lhash': '2176693684426466518604183861514', 'a10': [-4.403673748451237, 7.627386672274831], 'a2': [-2.341036478426952, -1.3515980410025343], 'a3': [-0.1729745867612707, 0.29960077268875174], 'a4': [2.653634528883777, 4.596229828745804], 'a5': [0.0, -3.258123802239944], 'a6': [0.8098796348979249, -0.4675842252195128], 'a7': [0.0, 0.0], 'a8': [0.0, -8.94019675909385], 'a9': [1.4401595846695352, 2.4944295716549276], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.6055030607763165, -0.01864614524806625]]]], 'bad_primes': [7, 13], 'central_character': '637.589', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '307485060193981597220976280126', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.341036478426952, 1.3515980410025343], [1.0, 1.7320508075688772]], [[1.0, 0], [0.1729745867612707, 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[0]], 'group': 'GL2', 'index': 29, 'label': '2-637-13.4-c1-0-29', '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/637/2/q/h/589/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.2603667325994483, 0.40218594315237133, 0.5497850585456738, 0.701881566300751, 0.8545220427119277, 1.0004895458138965, 1.1292100760406016, 1.227145531340801, 1.278645865293162, 1.2672374757904075, 1.1773155382608829, 0.9961738937452853, 0.7162515632109184, 0.33741089833853605, -0.13099856368079518, -0.6685816588621315, -1.2431532860214392, -1.8110969466231694, -2.3190504687776397, -2.7070325144153946, -2.912970697245028, -2.8784088249267863, -2.5549756149111102, -1.9110149861770738, -0.9376371615399997, 0.3466210542288595, 1.893314941889536, 3.6244442551938665, 5.436048695308031, 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'9.546740400207982405016672387512492', '9.938619361701919234115014695010781', '10.69119104332016837387309183957511'], 'prelabel': '2-637-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.8390613862837125, 'root_number': '-0.874882305056211 - 0.48433557818885337*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.419530693142', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71710855028552178484169654058', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09388419833914978482892697174', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12627087211969657961939697512', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '13.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/h/589/1'], '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': '2-637-13.4-c1-0-29', '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': '2-637-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.41953069314185626, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71710855028552178484169654058', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2176693684426466518604183861514', 'Lhash_array': ['2176693684426466518604183861514'], 'label': '2-637-13.4-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/h/589/1'}