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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '2023574274520409034', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.010309278350515464, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 6.3985305281545255, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [7, [1, 0, 7]]], 'bad_primes': [2, 7], 'central_character': '100352.1', 'coefficient_field': '1.1.1.1', 'conductor': 100352, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, -1, 4, -3, 9], [1, 1, 4, 5, 25], [1, 0, 7], [1, 1, 20, 11, 121], [1, 0, 6, 0, 169], [1, 1, 32, 17, 289], [1, 1, -16, 19, 361], [1, 1, 6, 23, 529], [1, 4, 46, 116, 841], [1, 1, 2, 31, 961], [1, -1, 40, -37, 1369], [1, 8, 62, 328, 1681], [1, -2, 30, -86, 1849], [1, -9, 58, -423, 2209], [1, 7, 40, 371, 2809], [1, 11, 112, 649, 3481], [1, 1, -4, 61, 3721], [1, -11, 96, -737, 4489], [1, 4, 46, 284, 5041], [1, 5, 56, 365, 5329], [1, -7, 2, -553, 6241], [1, 2, 30, 166, 6889], [1, 1, 80, 89, 7921], [1, 12, 166, 1164, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 26, 'label': '4-100352-1.1-c1e2-0-26', 'leading_term': '2.64945198376', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'Genus2Curve/Q/100352/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.5048927655907642, 1.051282438553733, 1.645896141113396, 2.233362275371382, 2.687434176991118, 2.834371010556288, 2.516192067048931, 1.682716255536962, 0.4738761515506497, -0.7659144303334704, -1.588560311278421, -1.650316892447514, -0.935994974445582, 0.1502744459805448, 0.94648577503393, 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4.443535788717595, 5.206594200523773, 5.681589597029162, 6.273072494148154, 6.838852422667585, 7.504561706176946, 7.974929702036455, 8.256863201717277, 8.791808112889226, 9.345981257533179, 9.57262362257116, 10.3666716942177, 10.76400909793106, 11.20032370933667, 11.65800677514229, 12.00930423934675, 12.57979176235041, 12.97671811169825, 13.51421710803076, 13.86139882543553, 14.29944570889214, 14.59377083698234, 15.20762502649907, 15.40047886918368, 15.81986371517488, 16.34503488770289, 16.80633326964494, 17.11961384547948, 17.55057575707176, 17.90856339636016, 18.53233264857636, 18.77987475455594, 19.16961636926574, 19.7218207314215, 19.83195909449123], 'prelabel': '4-100352-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5904501506137905, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 2023574274520409034, 'z1': {'__RealLiteral__': 0, 'data': '1.75620021521', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.59878121834', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.19973068379', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.3985305281545255, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 100352, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, -3, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -3, 0, -4, 0, -4, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -8, 0, 2, 0, 3, 0, 9, 0, -7, 0, -1, 0, -7, 0, 1, 0, -1, 0, -11, 0, -1, 0, 0, 0, 0, 0, 11, 0, -1, 0, -4, 0, -5, 0, -3, 0, 0, 0, 7, 0, 2, 0, -2, 0, 1, 0, -4, 0, -1, 0, 0, 0, -1, 0, 1, 0, -12, 0, 3, 0], 'euler11': [1, 1, 20, 11, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, 1, 32, 17, 289], 'euler19': [1, 1, -16, 19, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 1, 6, 23, 529], 'euler29': [1, 4, 46, 116, 841], 'euler3': [1, -1, 4, -3, 9], 'euler31': [1, 1, 2, 31, 961], 'euler37': [1, -1, 40, -37, 1369], 'euler41': [1, 8, 62, 328, 1681], 'euler43': [1, -2, 30, -86, 1849], 'euler47': [1, -9, 58, -423, 2209], 'euler5': [1, 1, 4, 5, 25], 'euler53': [1, 7, 40, 371, 2809], 'euler59': [1, 11, 112, 649, 3481], 'euler61': [1, 1, -4, 61, 3721], 'euler67': [1, -11, 96, -737, 4489], 'euler7': [1, 0, 7, 0, 0], 'euler71': [1, 4, 46, 284, 5041], 'euler73': [1, 5, 56, 365, 5329], 'euler79': [1, -7, 2, -553, 6241], 'euler83': [1, 2, 30, 166, 6889], 'euler89': [1, 1, 80, 89, 7921], 'euler97': [1, 12, 166, 1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 4, -3, 9], [1, 1, 4, 5, 25], [1, 0, 7, 0, 0], [1, 1, 20, 11, 121], [1, 0, 6, 0, 169], [1, 1, 32, 17, 289], [1, 1, -16, 19, 361], [1, 1, 6, 23, 529], [1, 4, 46, 116, 841], [1, 1, 2, 31, 961], [1, -1, 40, -37, 1369], [1, 8, 62, 328, 1681], [1, -2, 30, -86, 1849], [1, -9, 58, -423, 2209], [1, 7, 40, 371, 2809], [1, 11, 112, 649, 3481], [1, 1, -4, 61, 3721], [1, -11, 96, -737, 4489], [1, 4, 46, 284, 5041], [1, 5, 56, 365, 5329], [1, -7, 2, -553, 6241], [1, 2, 30, 166, 6889], [1, 1, 80, 89, 7921], [1, 12, 166, 1164, 9409]], 'index': 26, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/100352/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-100352-1.1-c1e2-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-100352-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5904501506137905, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2023574274520409034, 'z1': {'__RealLiteral__': 0, 'data': '1.75620021521', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '2023574274520409034', 'Lhash_array': ['2023574274520409034'], 'label': '4-100352-1.1-c1e2-0-26', 'type': 'G2Q', 'url': 'Genus2Curve/Q/100352/c'}