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lfunc_lfunctions • Show schema
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{'Lhash': '2259112593080444392264221273178', 'a10': [-0.5578132754342126, -0.3584848246680184], 'a2': [-0.052882645176933, -0.3678068761810587], 'a3': [0.9096319953545183, 0.41541501300188644], 'a4': [1.7865006232238356, -0.5245639126294213], 'a5': [1.1685516382100314, -1.348580480414008], 'a6': [0.10468875219901914, -0.3565371474194384], 'a7': [-2.0679462124396473, 1.6503328338418641], 'a8': [-0.5961404888753862, -1.3053655872684435], 'a9': [0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9096319953545183, -0.41541501300188644]]], [7, [[1.0, 0], [2.0679462124396473, -1.6503328338418641]]], [23, [[1.0, 0], [-2.2443178510569957, 4.238282362399526]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.181', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1934327461512703421524576276005', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.052882645176933, 0.3678068761810587], [-1.9189859472289947, 0.5634651136828593]], [[1.0, 0], [-0.9096319953545183, -0.41541501300188644]], [[1.0, 0], [-1.1685516382100314, 1.348580480414008], [-0.7115741913664257, -4.949107209404664]], [[1.0, 0], [2.0679462124396473, -1.6503328338418641]], [[1.0, 0], [-2.5276427096184864, -0.3634201566177777], [10.554422709759471, 3.0990581252557265]], [[1.0, 0], [-1.2997945657108827, 2.0225198228745573], [-5.400395169024524, -11.82521593960874]], [[1.0, 0], [-2.4193813602089302, -0.7103944638786035], [14.30131005813008, 9.190893896745159]], [[1.0, 0], [4.985997391174455, -1.4640209277704008], [15.983817123792441, -10.272175531656353]], [[1.0, 0], [-2.2443178510569957, 4.238282362399526]], [[1.0, 0], [0.5403204371581646, 0.15865239502567702], [24.396352452104253, 15.67858370621233]], [[1.0, 0], [6.425220958793994, -2.9343000925304272], [20.300682752303835, 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[-32.817786027149026, -71.86092763300695]], [[1.0, 0], [10.705535458117007, 12.354846528914562], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [2.9941093506766205, -6.556184966173161], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [-0.026185302453129215, 0.030219449964675044], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-8.113348859620004, 7.030256806303367], [14.373798665601798, -99.9719656299742]], [[1.0, 0], [-0.3007406976832789, 2.0916974970769453], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [13.114419694490346, -5.9891547963587595], [70.07009853214551, -80.86520445590564]], [[1.0, 0], [5.415517563015127, -18.44355905634123], [-91.69663507859875, -58.929849102660135]], [[1.0, 0], [9.676590371684586, -1.3912836553289945], [108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-483-161.20-c1-0-23', '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/483/2/r/a/181/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.09088256213036, 2.1379725588818044, 2.1853907400271484, 2.228003314993288, 2.2573559126577734, 2.2628611590693204, 2.23316802869829, 2.157536018035985, 2.0271373248074247, 1.8362561834370486, 1.583348440448632, 1.2718942312370312, 0.9109469783898139, 0.5152670311007103, 0.10493427168595976, -0.29563743028937434, -0.659311074056634, -0.9584220124746766, -1.167437695522251, -1.2658783141005767, -1.2412194081860919, -1.091441345380692, -0.8268657984399987, -0.47093614657893096, -0.05966362954609741, 0.3604248177943568, 0.7358435581393203, 1.0110287173229904, 1.134162822640675, 1.0633819661461987, 0.772665475658923, 0.25664099188741574, -0.4664360868082421, -1.3541385865594224, -2.3421338130266176, -3.3493134885311293, -4.285465938798784, 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'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.1635268537132967, 'root_number': '0.8709151992024026 + 0.49143332792784766*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0817634268566', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78212560517362665390880930478', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01756260012489939252642541524', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92329802657789462765493853314', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.20', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/181/16'], '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': '2-483-161.20-c1-0-23', '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': '2-483-161.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.08176342685664835, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78212560517362665390880930478', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2259112593080444392264221273178', 'Lhash_array': ['2259112593080444392264221273178'], 'label': '2-483-161.20-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/181/16'}