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lfunc_lfunctions • Show schema
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{'Lhash': '2046250895784511096014423325068', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.13077997952679463, 0.2265175691532259], 'a4': [0, 0], 'a5': [9.75047307107071, -16.888314756926615], 'a6': [0, 0], 'a7': [-7.512033030124299, -16.92835962975508], 'a8': [0, 0], 'a9': [13.465793193909942, -23.323437976067208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.43285568257181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [7.512033030124299, 16.92835962975508]]]], 'bad_primes': [2, 7], 'central_character': '448.65', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '1113297456338565718226842042040', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.13077997952679463, -0.2265175691532259], [-13.5, 23.382685902179844]], [[1.0, 0], [-9.75047307107071, 16.888314756926615], [-62.5, -108.25317547305482]], [[1.0, 0], [7.512033030124299, 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[-72.65649085115847, 125.84473365386977], [-113490.5, -196571.31217639567]], [[1.0, 0], [238.0471438636276, 412.3097477684609], [-150381.5, 260468.39851841913]], [[1.0, 0], [131.7631239660797, 0], [357911.0, 0]], [[1.0, 0], [174.80405391633107, 302.76950275209475], [-194508.5, 336898.604504011]], [[1.0, 0], [403.4531001841728, -698.8012679901636], [-246519.5, -426984.29905647587]], [[1.0, 0], [233.6479368822569, 0], [571787.0, 0]], [[1.0, 0], [-267.74131715699946, 463.7415646013358], [-352484.5, -610521.062880512]], [[1.0, 0], [-80.72211484620084, 0], [912673.0, 0]], [[1.0, 0], [86.73586843223632, 150.2309309632428], [-515150.5, 892266.8395445109]], [[1.0, 0], [97.87563765729155, -169.52557724563064], [-546363.5, -946329.3414011582]], [[1.0, 0], [1024.459823328334, -1774.4164643177105], [-612521.5, -1060918.3587283]], [[1.0, 0], [-778.9706063437035, -1349.2166677900295], [-647514.5, 1121528.0126375577]], [[1.0, 0], [652.9816982915153, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-448-7.2-c3-0-34', 'leading_term': '2.470993985350141722225718131663655311097596452215264845', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/448/4/i/m/65/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.470993985350142, 2.6035461636674126, 2.721211320103588, 2.822670521402787, 2.9066985674775934, 2.9721704300944416, 3.01807069033766, 3.0435060210195712, 3.0477205896564397, 3.0301140886130895, 2.9902619371076686, 2.9279370500152515, 2.8431324352392746, 2.7360837685966226, 2.607291005813356, 2.4575380279082992, 2.287909281008033, 2.099802366115868, 1.8949355597875395, 1.6753493039048362, 1.443400792230617, 1.2017509031423812, 0.9533428812738434, 0.7013723544621404, 0.4492484843267156, 0.20054628602165425, 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'7.01586165893913500529852594301059', '8.253380106162851329644057892527076', '9.173274255986217784234823297784139', '10.13745336871710890965554334426934', '10.89724492900073472352301875981790'], 'prelabel': '2-448-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.141289301583, 'root_angle': 0.5135522555494859, 'root_number': '-0.0425628049107364140987250072298067119350695469270738013 + 0.99909379321369552395317486914450886772147934986763557258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25677612777474296', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61420733395787571298718151117', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83027704761139693017030658908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70762801442455127485315694133', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.43285568257181, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/4/i/m/65/2'], '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': '2-448-7.2-c3-0-34', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-448-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.141289301583, 'root_angle': 0.25677612777474296, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61420733395787571298718151117', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2046250895784511096014423325068', 'Lhash_array': ['2046250895784511096014423325068'], 'label': '2-448-7.2-c3-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/4/i/m/65/2'}