-
lfunc_lfunctions • Show schema
Hide schema
{'A10': -1, 'A2': 1, 'A3': 1, 'A4': -1, 'A5': -1, 'A6': 1, 'A7': -1, 'A8': -1, 'A9': -2, 'Lhash': '1362904070926178778', 'a10': [-0.010309278350515464, 0.0], 'a2': [0.010309278350515464, 0.0], 'a3': [0.010309278350515464, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.010309278350515464, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [-0.010309278350515464, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.20875307865491385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, -1, 2, -2]], [1637, [1, -10, 1646, -1637]]], 'bad_primes': [2, 1637], 'central_character': '3274.1', 'coefficient_field': '1.1.1.1', 'conductor': 3274, 'conductor_radical': 3274, 'degree': 4, 'euler_factors': [[1, -1, 2, -2], [1, -1, 3, -3, 9], [1, 1, 4, 5, 25], [1, 1, -4, 7, 49], [1, -1, -2, -11, 121], [1, -1, 6, -13, 169], [1, 3, 16, 51, 289], [1, 3, 10, 57, 361], [1, -3, 37, -69, 529], [1, 3, -14, 87, 841], [1, 9, 46, 279, 961], [1, -9, 52, -333, 1369], [1, 2, 52, 82, 1681], [1, -9, 58, -387, 1849], [1, -5, 46, -235, 2209], [1, -8, 52, -424, 2809], [1, -5, 67, -295, 3481], [1, -7, 33, -427, 3721], [1, -10, 78, -670, 4489], [1, 19, 187, 1349, 5041], [1, -7, 102, -511, 5329], [1, 10, 86, 790, 6241], [1, -3, 130, -249, 6889], [1, 6, 16, 534, 7921], [1, 20, 294, 1940, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-3274-1.1-c1e2-0-0', 'leading_term': '0.947385575223', '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/3274/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.9473855752226255, 0.9812014415459467, 1.081948762699711, 1.246763075009336, 1.468461478356487, 1.732443217825087, 2.013478624282359, 2.273653539399089, 2.463071170759248, 2.524898325993021, 2.405684673202635, 2.070383976306073, 1.519254949145238, 0.8013712589247789, 0.0178863421220305, -0.6911814033730177, -1.178998154405812, -1.338038000863948, -1.14696159286017, -0.6985829226739029, -0.1896262330295922, 0.1367177338086287, 0.08489489571224153, -0.395170236237628, -1.153459748168049, -1.869546805151255, -2.176753207293434, -1.84281280603233, -0.9253072135386976, 0.1913750568418732, 0.9311867141868667, 0.8026971275311179, -0.3068985256202368, -1.988047392191506, -3.436592877182732, -3.838210128356203, -2.831950303297838, -0.7854998094205107, 1.322752416521629, 2.4081717392551, 1.911562414230023, 0.170050025317166, -1.748361415237976, -2.697558479427849, -2.199010324919111, -0.7680606867574303, 0.4525035558456997, 0.5455568207415681, -0.4409825292909256, -1.457139071052252, -1.228536491007575, 0.6755641993925288, 3.31597657007392, 4.906210608649597, 4.102511055380018, 1.112225269953795, -2.299502124820393, -4.026642297772999, -3.191255422208243, -0.8237023174042366, 0.9470092064200577, 0.5924061374588451, -1.602457842954252, -3.827881640729177, -4.298474449455971, -2.728664561173146, -0.4630427498313642, 0.8047435707501667, 0.5155620540952699, -0.4322453556388677, -0.7479075716090791, -0.08267021322060977, 0.7142698495199961, 0.6295331966703556, -0.3374356798489018, -1.153355262304299, -0.9245588502992643, 0.05144180094678728, 0.6061194866684726, 0.1187020686086318, -0.5890728496566389, -0.07560406316258086, 1.911478953424391, 3.705351768718641, 3.19670847762017, 0.1954592745115151, -2.936599150912773, -3.421430879598259, -0.9731675239513419, 1.685595389890122, 1.553571956704601, -1.390484965965142, -3.988997692201215, -3.233025547275377, 0.3523653471906574, 3.047459978464333, 1.830039710431978, -2.348130609162002, -5.536089952159199, -4.973915451289811, -1.858198158847511, 0.3180543969433332, -0.2168509718892122, -1.821396518944141, -1.850797334601578, -0.01113004622469595, 1.494872916834928, 1.056133001106639, -0.09938634557078453, 0.519898862030162, 3.240784604399753, 5.422575211463588, 4.507708314257225, 1.189324285640938, -1.321309540066627, -1.054371479756667, 0.6312854768808656, 1.128594593994718, -0.04927440695438734, -0.9953632360412215, -0.3227510916529163, 0.8997878926046338, 0.8182190140793996, -0.4485598590587346, -1.010962562750943, -0.1065171600149972, 0.6297371153453742, -0.3478338804386413, -1.723957042182863, -0.6369158404761238, 3.193387522447129, 6.262327538233498, 5.25676687251163, 1.270870232299086, -1.499434096779795, -1.056061227609864, 0.2039909089887433, -0.6863071557919128, -2.907401763270244, -3.211984337189888, -0.9963976876726713, 0.4603585076919711, -1.304723406677794, -4.056785231663236, -3.76990012268625, -0.4592270489500996, 1.607918010970369, 0.01281590360960806, -2.133929005342095, -0.6048450647481628, 3.522831308924986, 4.912455509383508, 1.418238990222341, -2.662077507943578, -2.469039073240032, 0.6180734141070258, 1.028092582303034, -2.96023908762551, -6.643152076268609, -5.348017348277879, -0.6473629574987024], 'positive_zeros': [2.62935160096447, 3.83770946753802, 4.173193020462643, 5.403621680313003, 5.959924228182673, 7.002691875153491, 7.703070708270212, 8.53998450265782, 8.93049891948409, 9.509703359141893, 10.37024396787304, 11.13066420301203, 11.49960837552334, 12.42222919220884, 12.85012916528708, 13.32900044112997, 13.81776569258003, 14.42764176581647, 14.83844945233338, 15.19745149144907, 15.94766280510699, 16.55819788873433, 16.98552805235423, 17.60804060675933, 18.08905799602201, 18.88825826798788, 19.09717234577891, 19.68848724769953], 'prelabel': '4-3274-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6759401165636226, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1362904070926178778, 'z1': {'__RealLiteral__': 0, 'data': '2.62935160096', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.83770946754', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.17319302046', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.20875307865491385, 'bad_primes': [2, 1637], 'central_character': '1.1', 'conductor': 3274, 'conductor_radical': 3274, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, -1, -1, 1, -1, -1, -2, -1, 1, -1, 1, -1, -1, 3, -3, -2, -3, 1, -1, 1, 3, -1, -3, 1, -2, 1, -3, -1, -9, 3, 1, -3, 1, 2, 9, -3, 1, 1, -2, -1, 9, -1, 2, 3, 5, 3, 5, -3, -3, -1, 8, -2, -1, 1, -3, -3, 5, 1, 7, -9, 2, -5, -1, 1, 10, 3, 3, 1, -19, 2, 7, 9, -3, 3, -1, 1, -10, -3, -2, -2, 3, 1, 3, 9, -3, -1, -6, 2, -1, -3, -9, 5, 3, 3, -20, 5, -2, 3], 'euler11': [1, -1, -2, -11, 121], 'euler13': [1, -1, 6, -13, 169], 'euler17': [1, 3, 16, 51, 289], 'euler19': [1, 3, 10, 57, 361], 'euler2': [1, -1, 2, -2, 0], 'euler23': [1, -3, 37, -69, 529], 'euler29': [1, 3, -14, 87, 841], 'euler3': [1, -1, 3, -3, 9], 'euler31': [1, 9, 46, 279, 961], 'euler37': [1, -9, 52, -333, 1369], 'euler41': [1, 2, 52, 82, 1681], 'euler43': [1, -9, 58, -387, 1849], 'euler47': [1, -5, 46, -235, 2209], 'euler5': [1, 1, 4, 5, 25], 'euler53': [1, -8, 52, -424, 2809], 'euler59': [1, -5, 67, -295, 3481], 'euler61': [1, -7, 33, -427, 3721], 'euler67': [1, -10, 78, -670, 4489], 'euler7': [1, 1, -4, 7, 49], 'euler71': [1, 19, 187, 1349, 5041], 'euler73': [1, -7, 102, -511, 5329], 'euler79': [1, 10, 86, 790, 6241], 'euler83': [1, -3, 130, -249, 6889], 'euler89': [1, 6, 16, 534, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, -1, 2, -2, 0], [1, -1, 3, -3, 9], [1, 1, 4, 5, 25], [1, 1, -4, 7, 49], [1, -1, -2, -11, 121], [1, -1, 6, -13, 169], [1, 3, 16, 51, 289], [1, 3, 10, 57, 361], [1, -3, 37, -69, 529], [1, 3, -14, 87, 841], [1, 9, 46, 279, 961], [1, -9, 52, -333, 1369], [1, 2, 52, 82, 1681], [1, -9, 58, -387, 1849], [1, -5, 46, -235, 2209], [1, -8, 52, -424, 2809], [1, -5, 67, -295, 3481], [1, -7, 33, -427, 3721], [1, -10, 78, -670, 4489], [1, 19, 187, 1349, 5041], [1, -7, 102, -511, 5329], [1, 10, 86, 790, 6241], [1, -3, 130, -249, 6889], [1, 6, 16, 534, 7921], [1, 20, 294, 1940, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/3274/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': '4-3274-1.1-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': '4-3274-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6759401165636226, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1362904070926178778, 'z1': {'__RealLiteral__': 0, 'data': '2.62935160096', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1362904070926178778', 'Lhash_array': ['1362904070926178778'], 'label': '4-3274-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/3274/a'}