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lfunc_lfunctions • Show schema
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{'Lhash': '1076232725390288019891842613921,1451213216086312742851249831610', 'a10': 75, 'a2': -5, 'a3': 0, 'a4': 7, 'a5': -15, 'a6': 0, 'a7': -15, 'a8': 15, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8053.60953433941, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 5, 18, 40, 64], [1], [1, 15, 200, 1875, 15625], [1, 15, 738, 5145, 117649], [1, -17, 1778, -22627, 1771561], [1], [1, 70, 9963, 343910, 24137569], [1, -141, 18582, -967119, 47045881], [1, 145, 24962, 1764215, 148035889], [1, 34, 33767, 829226, 594823321], [1, -140, 21982, -4170740, 887503681], [1, -190, 102103, -9624070, 2565726409], [1, -538, 208503, -37079498, 4750104241], [1, -455, 170782, -36175685, 6321363049], [1, -60, 125246, -6229380, 10779215329], [1, 545, 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2462207, 1341894210, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 4, 'label': '4-39e4-1.1-c3e2-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [3.4304578075665834e-122, 0.004178776629487711, 0.016598261728184238, 0.036910418138711626, 0.06454399019249919, 0.09871694526225336, 0.13845465584782907, 0.18261150334479526, 0.22989816230224433, 0.2789107171475502, 0.32816628755746785, 0.3761359101501084, 0.4212886423974942, 0.4621232296844044, 0.4972197054516164, 0.5252666361240376, 0.5451150808779072, 0.5558021745968744, 0.5565984938217621, 0.5470300045327037, 0.5269113559310213, 0.4963639574765133, 0.4558342133148848, 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'6.45576384966031824968973947886047', '7.38098639561304497483699160588907', '7.40662131209223513604549297312507', '7.895243051377449855482698446460623', '8.040624311993847007093685666135311', '8.492553806430241363141624930796162', '9.028846860301285114815939076465282'], 'prelabel': '4-39e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 244685614245012549, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.848997921979859223264229607217', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.14480537131054448136326617302', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03329052862266446654586087612', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8053.60953433941, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, -5, 0, 7, -15, 0, -15, 15, 0, 75, 17, 0, 0, 75, 0, -65, -70, 0, 141, -105, 0, -85, -145, 0, 25, 0, 0, -105, -34, 0, 140, 95, 0, 350, 225, 0, 190, -705, 0, -225, 538, 0, 455, 119, 0, 725, 60, 0, -513, -125, 0, 0, -545, 0, -255, -225, 0, 170, -809, 0, 502, -700, 0, -353, 0, 0, 475, -490, 0, -1125, 127, 0, -585, -950, 0, 987, -255, 0, 240, 975, 0, -2690, 260, 0, 1050, -2275, 0, 255, 921, 0, 0, -1015, 0, -300, -2115, 0, 415, 2565, 0, 175], 'euler11': [1, -17, 1778, -22627, 1771561], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 70, 9963, 343910, 24137569], 'euler19': [1, -141, 18582, -967119, 47045881], 'euler2': [1, 5, 18, 40, 64], 'euler23': [1, 145, 24962, 1764215, 148035889], 'euler29': [1, 34, 33767, 829226, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -140, 21982, -4170740, 887503681], 'euler37': [1, -190, 102103, -9624070, 2565726409], 'euler41': [1, -538, 208503, -37079498, 4750104241], 'euler43': [1, -455, 170782, -36175685, 6321363049], 'euler47': [1, -60, 125246, -6229380, 10779215329], 'euler5': [1, 15, 200, 1875, 15625], 'euler53': [1, 545, 256304, 81137965, 22164361129], 'euler59': [1, 809, 561522, 166151611, 42180533641], 'euler61': [1, -502, 346963, -113944462, 51520374361], 'euler67': [1, -475, 622738, -142862425, 90458382169], 'euler7': [1, 15, 738, 5145, 117649], 'euler71': [1, -127, 672998, -45454697, 128100283921], 'euler73': [1, 585, 832884, 227574945, 151334226289], 'euler79': [1, -240, 993678, -118329360, 243087455521], 'euler83': [1, -260, 1117974, -148664620, 326940373369], 'euler89': [1, -921, 1555592, -649276449, 496981290961], 'euler97': [1, -415, 933568, -378759295, 832972004929], 'euler_factors': [[1, 5, 18, 40, 64], [1, 0, 0, 0, 0], [1, 15, 200, 1875, 15625], [1, 15, 738, 5145, 117649], [1, -17, 1778, -22627, 1771561], [1, 0, 0, 0, 0], [1, 70, 9963, 343910, 24137569], [1, -141, 18582, -967119, 47045881], [1, 145, 24962, 1764215, 148035889], [1, 34, 33767, 829226, 594823321], [1, -140, 21982, -4170740, 887503681], [1, -190, 102103, -9624070, 2565726409], [1, -538, 208503, -37079498, 4750104241], [1, -455, 170782, -36175685, 6321363049], [1, -60, 125246, -6229380, 10779215329], [1, 545, 256304, 81137965, 22164361129], [1, 809, 561522, 166151611, 42180533641], [1, -502, 346963, -113944462, 51520374361], [1, -475, 622738, -142862425, 90458382169], [1, -127, 672998, -45454697, 128100283921], [1, 585, 832884, 227574945, 151334226289], [1, -240, 993678, -118329360, 243087455521], [1, -260, 1117974, -148664620, 326940373369], [1, -921, 1555592, -649276449, 496981290961], [1, -415, 933568, -378759295, 832972004929]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/l'], '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': '4-39e4-1.1-c3e2-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-39e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 244685614245012549, 'z1': {'__RealLiteral__': 0, 'data': '0.848997921979859223264229607217', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1076232725390288019891842613921,1451213216086312742851249831610', 'Lhash_array': ['1076232725390288019891842613921', '1451213216086312742851249831610'], 'label': '4-39e4-1.1-c3e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/l'}