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lfunc_lfunctions • Show schema
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{'Lhash': '2861245218931146174296695118759', 'a10': [0, 0], 'a2': [1.0, -1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, -3.4641016151377544], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -10.392304845413264], 'a8': [-8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.523223792426723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.451', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '345606434955939453428898686925', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 10.392304845413264], [-49.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-121.0, 0]], [[1.0, 0], [18.0, 0], [169.0, 0]], [[1.0, 0], [-10.0, 0], [289.0, 0]], [[1.0, 0], [0, -13.856406460551018], 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'GL2', 'index': 91, 'label': '2-30e2-4.3-c2-0-91', 'leading_term': '1.005180289707699733063400904955435375468210684005589008', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/900/3/c/j/451/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0051802897076998, 1.2654105191890168, 1.5338500526065924, 1.8089793399039844, 2.08913970712457, 2.3724995302508938, 2.657024503616706, 2.940454290086713, 3.2202875852124087, 3.4937772962469036, 3.75793715290333, 4.009560651465501, 4.245252804406451, 4.4614747361338, 4.654600739390994, 4.82098699040286, 4.9570507165306505, 5.059358220299766, 5.124719791596501, 5.150289190961645, 5.133665068919787, 5.072991409119493, 4.96705385853214, 4.815368649098056, 4.618260735463275, 4.376927785788016, 4.093486778604219, 3.7710001876418247, 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'8.740590340222497032252455340999111', '9.387976789205114897970052659483969', '10.23089801128313510943441740398532'], 'prelabel': '2-30e2-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9520928699315325, 'root_angle': -0.6666666666666667, 'root_number': '-0.50000000000000000000000000000000000000000000000000000000 - 0.86602540378443864676372317075293618347140262690519031403*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.33333333333333337', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25712449346531607530462782551', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14069843552697171708698947382', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75263145445140604838458051010', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.523223792426723, 'bad_primes': [2, 3, 5], 'central_character': '4.3', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 91, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/3/c/j/451/1'], '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': '2-30e2-4.3-c2-0-91', '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': '2-30e2-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9520928699315325, 'root_angle': -0.33333333333333337, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25712449346531607530462782551', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2861245218931146174296695118759', 'Lhash_array': ['2861245218931146174296695118759'], 'label': '2-30e2-4.3-c2-0-91', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/3/c/j/451/1'}