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lfunc_lfunctions • Show schema
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{'Lhash': '860419806263847685978726555206', 'a10': [0.4112070629269773, -0.1377160501859268], 'a2': [0.16795399328975946, -0.09696828323731523], 'a3': [-0.8660254037844386, -0.5], 'a4': [-0.9811943040920156, 1.6994783867845582], 'a5': [2.191303040620266, 0.4451864600011754], 'a6': [-0.19393656647463045, 4.038164941406777e-62], 'a7': [0.0, 0.0], 'a8': [0.0, 0.7684520417094008], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 0.5]]], [5, [[1.0, 0], [-2.191303040620266, -0.4451864600011754]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.214', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '2105229344911874237066295633345', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.16795399328975946, 0.09696828323731523], [1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-735-35.4-c1-0-10', '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/735/2/q/e/214/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.238791503624275, 1.0588463370367351, 0.8621999136358095, 0.6436380235795888, 0.3987006019572193, 0.12563249182917055, -0.17308956935032965, -0.4897879634153184, -0.8112124533755203, -1.118782119201668, -1.389460768519229, -1.5972759368402687, -1.7154526777125638, -1.7190665581570468, -1.5880360564334723, -1.310187377830071, -0.8840506560793053, -0.3210017369927457, 0.35363731356021255, 1.1008725800987327, 1.8699091412393765, 2.601672955931375, 3.233829483343333, 3.7069165997609956, 3.9709924679321906, 3.9920283946501858, 3.7571872569416804, 3.278148650392645, 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'7.42094311338360886288594896542837', '8.896235275701272264161262754719397', '9.370758151663862177415798125218507', '10.16199609312863869803924213818674'], 'prelabel': '2-735-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.4765461797955144, 'root_number': '0.0736156960152974 - 0.9972866836071679*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.238273089898', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67875154723938648913771673678', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18666793887950695988208025001', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86975992356494657428738607309', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '35.4', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/q/e/214/4'], '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': '2-735-35.4-c1-0-10', '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': '2-735-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.2382730898977572, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67875154723938648913771673678', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '860419806263847685978726555206', 'Lhash_array': ['860419806263847685978726555206'], 'label': '2-735-35.4-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/q/e/214/4'}