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lfunc_lfunctions • Show schema
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{'A10': 15, 'A2': -3, 'A3': -4, 'A4': 4, 'A5': -5, 'A6': 12, 'A7': -3, 'A8': -3, 'A9': 8, 'Lhash': '1280832247219979546', 'a10': [0.15463917525773196, 0.0], 'a2': [-0.030927835051546393, 0.0], 'a3': [-0.041237113402061855, 0.0], 'a4': [0.041237113402061855, 0.0], 'a5': [-0.05154639175257732, 0.0], 'a6': [0.12371134020618557, 0.0], 'a7': [-0.030927835051546393, 0.0], 'a8': [-0.030927835051546393, 0.0], 'a9': [0.08247422680412371, 0.0], 'algebraic': True, 'analytic_conductor': 0.2116223176712459, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3319, [1, -73, 3245, 3319]]], 'bad_primes': [3319], 'central_character': '3319.1', 'coefficient_field': '1.1.1.1', 'conductor': 3319, 'conductor_radical': 3319, 'degree': 4, 'euler_factors': [[1, 3, 5, 6, 4], [1, 4, 8, 12, 9], [1, 5, 13, 25, 25], [1, 3, 7, 21, 49], [1, 2, 7, 22, 121], [1, 4, 26, 52, 169], [1, 2, 7, 34, 289], [1, 0, 4, 0, 361], [1, 1, 28, 23, 529], [1, 8, 37, 232, 841], [1, -2, 36, -62, 961], [1, 5, 44, 185, 1369], [1, 6, 83, 246, 1681], [1, 7, 34, 301, 1849], [1, -7, 84, -329, 2209], [1, 2, -53, 106, 2809], [1, 11, 65, 649, 3481], [1, 9, 103, 549, 3721], [1, -4, 18, -268, 4489], [1, 1, 4, 71, 5041], [1, -16, 154, -1168, 5329], [1, -7, 117, -553, 6241], [1, 5, -16, 415, 6889], [1, 5, 26, 445, 7921], [1, 32, 447, 3104, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-3319-1.1-c1e2-0-0', 'leading_term': '0.192363162224', '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': 2, 'origin': 'Genus2Curve/Q/3319/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.007041992195487512, 0.03157126428103655, 0.08415921569368595, 0.1834219647811384, 0.3567785053593446, 0.6400306327521151, 1.074366260674215, 1.699329024127578, 2.540791659584651, 3.594279609331594, 4.806193168283786, 6.058254609339238, 7.162984926649039, 7.878783394277088, 7.950657699808031, 7.175814966074016, 5.482689299049231, 3.000365939912797, 0.087840726847596, -2.704930384234343, -4.755652185994028, -5.550011748899816, -4.872115671644398, -2.930737902446942, -0.3513614083500051, 1.996295236231748, 3.298046019854076, 3.115719477977843, 1.587092068628444, -0.6066576365437609, -2.522663223910543, -3.378911437002733, -2.918624695485502, -1.52189474701499, 0.01307163963405391, 0.9160588314482729, 0.8713283053449647, 0.1681119528433164, -0.5281257226919563, -0.6481547165457745, -0.1256006310341058, 0.5503531222761009, 0.6952603015670522, -0.03572753474688111, -1.330055599946154, -2.381502704989781, -2.453709130851, -1.440359504341481, 0.01744657992917957, 0.9821811736314302, 0.9164228932793225, 0.07785762078907908, -0.7195012641252401, -0.7940487651373732, -0.155084433470514, 0.5598075208421281, 0.7171141454733155, 0.3024792966574059, 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-3.001302523949669, -9.722984855147873, -12.70930593902904, -6.182603562558953, 8.397635629296737, 21.89075984671224, 25.03942840275216, 16.88382925904768, 5.232338465175967, -1.29010663736934, -0.9831692259743154, 1.336655858487556, 1.200001738125129, -0.8582342120687666, -1.686274892941014, -0.5744313322187707, 0.09298088894687111, -1.111262215469842, -2.266437199556227, -1.10891867798317, 0.9621892785586229, 0.2636645532490951, -3.507488023617874, -5.22536565145798, 0.1035236262636759, 10.41242266501125, 17.37441788291306, 14.88972584195183, 5.494459327046758, -2.725173535631538, -4.651471652604257, -2.09496847339402, 0.2192262907089177, 0.3538871863120835, -0.2108852086868092, -0.02152926221679642, 0.4554024770126866, 0.3447629842683677, -0.05925294165660552, -0.07494681290919224, 0.1026587845245834, -0.06258021390870162, -0.3285748018637849, -0.1615432696158234, 0.124421724974223, -0.07682165475089829, -0.2821887434276833, 0.3370118839454128, 0.7927287862957342, -0.9883950771425466, -4.225056748511841, -4.49359889269017, 0.2798332001489974], 'positive_zeros': [3.568075918259732, 4.712874155150404, 5.57423781474919, 6.560648733952188, 7.163777496956125, 7.719944649657068, 8.24396548524474, 9.185094014090046, 9.765128586016967, 10.34834857274147, 10.99818258759531, 11.20056912864643, 12.01930090415259, 12.21148373328005, 12.65767556590087, 13.62476064412318, 15.12263190006636, 15.33101984990012, 15.79551239360489, 16.40585737691579, 16.78140479053822, 16.98791563012555, 17.46457048720833, 18.2580273292312, 18.39384796579496, 18.96609997865704, 19.31750641481712, 19.7306486063698], 'prelabel': '4-3319-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6782508810895173, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1280832247219979546, 'z1': {'__RealLiteral__': 0, 'data': '3.56807591826', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.71287415515', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.57423781475', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2116223176712459, 'bad_primes': [3319], 'central_character': '1.1', 'conductor': 3319, 'conductor_radical': 3319, 'degree': 4, 'dirichlet_coefficients': [1, -3, -4, 4, -5, 12, -3, -3, 8, 15, -2, -16, -4, 9, 20, 3, -2, -24, 0, -20, 12, 6, -1, 12, 12, 12, -12, -12, -8, -60, 2, -6, 8, 6, 15, 32, -5, 0, 16, 15, -6, -36, -7, -8, -40, 3, 7, -12, 2, -36, 8, -16, -2, 36, 10, 9, 0, 24, -11, 80, -9, -6, -24, 5, 20, -24, 4, -8, 4, -45, -1, -24, 16, 15, -48, 0, 6, -48, 7, -15, 23, 18, -5, 48, 10, 21, 32, 6, -5, 120, 12, -4, -8, -21, 0, 24, -32, -6, -16, 48], 'euler11': [1, 2, 7, 22, 121], 'euler13': [1, 4, 26, 52, 169], 'euler17': [1, 2, 7, 34, 289], 'euler19': [1, 0, 4, 0, 361], 'euler2': [1, 3, 5, 6, 4], 'euler23': [1, 1, 28, 23, 529], 'euler29': [1, 8, 37, 232, 841], 'euler3': [1, 4, 8, 12, 9], 'euler31': [1, -2, 36, -62, 961], 'euler37': [1, 5, 44, 185, 1369], 'euler41': [1, 6, 83, 246, 1681], 'euler43': [1, 7, 34, 301, 1849], 'euler47': [1, -7, 84, -329, 2209], 'euler5': [1, 5, 13, 25, 25], 'euler53': [1, 2, -53, 106, 2809], 'euler59': [1, 11, 65, 649, 3481], 'euler61': [1, 9, 103, 549, 3721], 'euler67': [1, -4, 18, -268, 4489], 'euler7': [1, 3, 7, 21, 49], 'euler71': [1, 1, 4, 71, 5041], 'euler73': [1, -16, 154, -1168, 5329], 'euler79': [1, -7, 117, -553, 6241], 'euler83': [1, 5, -16, 415, 6889], 'euler89': [1, 5, 26, 445, 7921], 'euler97': [1, 32, 447, 3104, 9409], 'euler_factors': [[1, 3, 5, 6, 4], [1, 4, 8, 12, 9], [1, 5, 13, 25, 25], [1, 3, 7, 21, 49], [1, 2, 7, 22, 121], [1, 4, 26, 52, 169], [1, 2, 7, 34, 289], [1, 0, 4, 0, 361], [1, 1, 28, 23, 529], [1, 8, 37, 232, 841], [1, -2, 36, -62, 961], [1, 5, 44, 185, 1369], [1, 6, 83, 246, 1681], [1, 7, 34, 301, 1849], [1, -7, 84, -329, 2209], [1, 2, -53, 106, 2809], [1, 11, 65, 649, 3481], [1, 9, 103, 549, 3721], [1, -4, 18, -268, 4489], [1, 1, 4, 71, 5041], [1, -16, 154, -1168, 5329], [1, -7, 117, -553, 6241], [1, 5, -16, 415, 6889], [1, 5, 26, 445, 7921], [1, 32, 447, 3104, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/3319/a'], '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': '4-3319-1.1-c1e2-0-0', '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': 2, 'prelabel': '4-3319-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6782508810895173, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1280832247219979546, 'z1': {'__RealLiteral__': 0, 'data': '3.56807591826', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1280832247219979546', 'Lhash_array': ['1280832247219979546'], 'label': '4-3319-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/3319/a'}