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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': -2, 'A3': -1, 'A4': 1, 'A5': -2, 'A6': 2, 'A7': 0, 'A8': 2, 'A9': 0, 'Lhash': '315995603033814010', 'a10': [0.041237113402061855, 0.0], 'a2': [-0.020618556701030927, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.020618556701030927, 0.0], 'a6': [0.020618556701030927, 0.0], 'a7': [0.0, 0.0], 'a8': [0.020618556701030927, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.01874569490670271, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 2, 3, 2]], [3, [1, 1, 1, -3]], [7, [1, 0, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '294.1', 'coefficient_field': '1.1.1.1', 'conductor': 294, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 2, 3, 2], [1, 1, 1, -3], [1, 2, 10, 10, 25], [1, 0, -1], [1, -4, 22, -44, 121], [1, 6, 34, 78, 169], [1, 0, -2, 0, 289], [1, -6, 46, -114, 361], [1, 0, 46, 0, 529], [1, 8, 70, 232, 841], [1, 4, 62, 124, 961], [1, -8, 86, -296, 1369], [1, -8, 94, -328, 1681], [1, -4, 54, -172, 1849], [1, 12, 94, 564, 2209], [1, -12, 142, -636, 2809], [1, -6, 46, -354, 3481], [1, -6, 106, -366, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 4, 134, 292, 5329], [1, 8, 30, 632, 6241], [1, 18, 238, 1494, 6889], [1, 20, 262, 1780, 7921], [1, -8, 14, -776, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-294-1.1-c1e2-0-0', 'leading_term': '0.148968979954', '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': 0, 'origin': 'Genus2Curve/Q/294/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.1489689799540566, 0.1558748259653341, 0.1772791868405267, 0.2152395043705907, 0.2731608727711687, 0.355711753230862, 0.4686110080002262, 0.6181975676149059, 0.8106833573694512, 1.050999120743985, 1.341182764279342, 1.678341841905588, 2.052352231876384, 2.443629712858802, 2.821508388247738, 3.143935404999584, 3.359277489302666, 3.410948223956464, 3.245226063633376, 2.821996707223622, 2.127247377620662, 1.185100521509881, 0.06625949599535595, -1.110691912334946, -2.188257881574906, -2.99080805724921, -3.355969729172242, -3.171945405294964, -2.412666021314369, -1.160586139731355, 0.3926346928143209, 1.973522912790339, 3.281175505400511, 4.058684397791071, 4.163567771495293, 3.615155859924075, 2.599691060543205, 1.424478142567778, 0.4288056650208362, -0.1234188990057789, -0.1331148404689188, 0.2977977820362716, 0.90334835725559, 1.356637615310886, 1.403411727692314, 0.9722167005686646, 0.2103228782429203, -0.5782377741334551, -1.073225662907318, -1.097359330393311, -0.7166228553476739, -0.2234007584352632, 0.003090643303061964, -0.3000328185876797, -1.115259513141427, -2.116761597332638, -2.814429548922213, -2.813054354574385, -2.053408848586405, 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3.606334705782567, 7.054313596075744, 9.105524113141335, 7.73927068321811, 2.829951719799401, -3.360011487535396, -7.536612775796635, -7.678551860950729, -4.483467513499765, -0.7304319873121679, 0.9764606446746665, 0.224929317536645, -1.127433236182469, -0.8529108782564796, 1.477544146302499, 4.026399411877617, 4.370606628543131, 1.806016112717293, -1.866908556583748, -3.857408540070066, -2.850934477570301, -0.1592187489266681, 1.525630580753892, 0.6266185436094264, -1.893923086741786, -3.495047668632726, -2.467477497861511, 0.4897779041298824, 2.971295841318751, 3.097002421122648, 1.116750293973709, -1.053076154442473, -1.738336162043319, -0.9141754452557925, 0.1530738646042683, 0.4142925968960102, 0.004722723318009714, -0.2377390550076342, 0.06523246827091538, 0.4355710892673907, 0.3229139824018014, -9.678201151655825e-05, 0.338681469961589, 1.634893299042939, 2.944929367157743, 2.951017806395532, 1.533895304006831, 0.153438896945814, 0.2949171635974614, 1.545857478008647, 1.650384052285792, -1.08157251583305, -5.428422509087016], 'positive_zeros': [4.135590840507737, 5.579286817429504, 7.250477838028384, 7.575711000888679, 8.672365196683145, 9.724661210726174, 9.765547119459919, 11.23136141438461, 11.5559508175456, 12.30526099005271, 13.19379250527464, 14.51353234037879, 14.6077730656713, 15.87345980006495, 16.33708100139527, 17.15982418199832, 17.21285321618276, 18.21205413166163, 18.41922826796405, 19.58002701984274, 19.66784881755091, 19.89701463571632], 'prelabel': '4-294-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.3700201595802149, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 315995603033814010, 'z1': {'__RealLiteral__': 0, 'data': '4.13559084051', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.57928681743', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.25047783803', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.01874569490670271, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 294, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, -2, -1, 1, -2, 2, 0, 2, 0, 4, 4, -1, -6, 0, 2, -3, 0, 0, 6, -2, 0, -8, 0, -2, -6, 12, 4, 0, -8, -4, -4, -2, -4, 0, 0, 0, 8, -12, 6, -4, 8, 0, 4, 4, 0, 0, -12, 3, 1, 12, 0, -6, 12, -8, -8, 0, -6, 16, 6, 2, 6, 8, 0, 9, 12, 8, 0, 0, 0, 0, 0, 0, -4, -16, 6, 6, 0, -12, -8, 6, -7, -16, -18, 0, 0, -8, 8, 8, -20, 0, 0, 0, 4, 24, -12, 2, 8, -2, 0, -6], 'euler11': [1, -4, 22, -44, 121], 'euler13': [1, 6, 34, 78, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, -6, 46, -114, 361], 'euler2': [1, 2, 3, 2, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 8, 70, 232, 841], 'euler3': [1, 1, 1, -3, 0], 'euler31': [1, 4, 62, 124, 961], 'euler37': [1, -8, 86, -296, 1369], 'euler41': [1, -8, 94, -328, 1681], 'euler43': [1, -4, 54, -172, 1849], 'euler47': [1, 12, 94, 564, 2209], 'euler5': [1, 2, 10, 10, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, -6, 46, -354, 3481], 'euler61': [1, -6, 106, -366, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 4, 134, 292, 5329], 'euler79': [1, 8, 30, 632, 6241], 'euler83': [1, 18, 238, 1494, 6889], 'euler89': [1, 20, 262, 1780, 7921], 'euler97': [1, -8, 14, -776, 9409], 'euler_factors': [[1, 2, 3, 2, 0], [1, 1, 1, -3, 0], [1, 2, 10, 10, 25], [1, 0, -1, 0, 0], [1, -4, 22, -44, 121], [1, 6, 34, 78, 169], [1, 0, -2, 0, 289], [1, -6, 46, -114, 361], [1, 0, 46, 0, 529], [1, 8, 70, 232, 841], [1, 4, 62, 124, 961], [1, -8, 86, -296, 1369], [1, -8, 94, -328, 1681], [1, -4, 54, -172, 1849], [1, 12, 94, 564, 2209], [1, -12, 142, -636, 2809], [1, -6, 46, -354, 3481], [1, -6, 106, -366, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 4, 134, 292, 5329], [1, 8, 30, 632, 6241], [1, 18, 238, 1494, 6889], [1, 20, 262, 1780, 7921], [1, -8, 14, -776, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/294/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': '4-294-1.1-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': 0, 'prelabel': '4-294-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.3700201595802149, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 315995603033814010, 'z1': {'__RealLiteral__': 0, 'data': '4.13559084051', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9953361
{'Lhash': '315995603033814010', 'Lhash_array': ['315995603033814010'], 'label': '4-294-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/14/a|EllipticCurve/Q/21/a'}
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id: 9952690
{'Lhash': '315995603033814010', 'Lhash_array': ['315995603033814010'], 'label': '4-294-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/14/a|EllipticCurve/Q/21/a'}
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id: 1221752
{'Lhash': '315995603033814010', 'Lhash_array': ['315995603033814010'], 'label': '4-294-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/294/a'}