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'19.74589105824024445259505976782201', '20.06374713047679510172826553572134'], 'prelabel': '8-13e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.875799537608138, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e4-0', 'trace_hash': 1934881217355092915, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.58625571942394858965526178874', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.83978155581531791135561886183', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19022483144951431422246083571', 'prec': 103}}
-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.34612876477022675, 'bad_primes': [13], 'central_character': '1.1', 'conductor': 28561, 'conductor_radical': 13, 'degree': 8, 'dirichlet_coefficients': [1, 5, -5, 18, -30, -25, -15, 65, 22, -150, -17, -90, 125, -75, 150, 189, -70, 110, 141, -540, 75, -85, -145, -325, 275, 625, 65, -270, -34, 750, -280, 450, 85, -350, 450, 396, 190, 705, -625, -1950, -538, 375, -455, -306, -660, -725, 120, -945, 738, 1375, 350, 2250, 1090, 325, 510, -975, -705, -170, 809, 2700, -502, -1400, -330, 449, -3750, 425, 475, -1260, 725, 2250, -127, 1430, 1170, 950, -1375, 2538, 255, -3125, 480, -5670, -271, -2690, 520, 1350, 2100, -2275, 170, -1105, -921, -3300, -1875, -2610, 1400, 600, -4230, -2250, 415, 3690, -374, 4950], 'euler11': [1, 17, -1489, -15028, 1005064, -20002268, -2637854329, 40085110747, 3138428376721], 'euler13': [1, -125, 7956, -274625, 4826809, 0, 0, 0, 0], 'euler17': [1, 70, -5063, 9590, 51050100, 47115670, -122208511847, 8301151354790, 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37992516774, -2853915694440, 2738912381376268, -134295656772332040, 116191483108948578241], 'euler5': [1, 30, 625, 9750, 127500, 1218750, 9765625, 58593750, 244140625], 'euler53': [1, -1090, 809633, -441647290, 198460844524, -65751123593330, 17944998193955657, -3596742315064324970, 491258904256726154641], 'euler59': [1, -809, 92959, -121968076, 138709769544, -25049681480804, 3921060226733719, -7008363617291845651, 1779197418239532716881], 'euler61': [1, 502, -94959, -53713498, 11662829084, -12191943489538, -4892323228946199, 5870461338602738782, 2654348974297586158321], 'euler67': [1, -475, -397113, -10075700, 229484582600, -3030397759100, -35922199518278097, -12923103838240099825, 8182718904632857144561], 'euler7': [1, 15, -513, 780, 349820, 267540, -60353937, 605304105, 13841287201], 'euler71': [1, 127, -656869, -5438648, 319053277564, -1946551944328, -84145105398903349, 5822759591243026937, 16409682740640811134241], 'euler73': [1, -1170, 2007993, -1429624170, 1262626895684, 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[1, -125, 7956, -274625, 4826809, 0, 0, 0, 0], [1, 70, -5063, 9590, 51050100, 47115670, -122208511847, 8301151354790, 582622237229761], [1, -141, 1299, -685824, 161881064, -4704066816, 61112599419, -45498965386839, 2213314919066161], [1, 145, -3937, 91060, 219254380, 1107927020, -582817294993, 261167135912135, 21914624432020321], [1, 34, -32611, -510374, 517193284, -12447511486, -19397783321131, 493242963179546, 353814783205469041], [1, 280, 63564, 14496440, 3426022886, 431863444040, 56413283979084, 7403094204987880, 787662783788549761], [1, -190, -66003, -151430, 6030722900, -7670383790, -169345640173227, -24692730561064630, 6582952005840035281], [1, 538, 80941, 38015618, 18774626844, 2620074408178, 384478187370781, 176131480703951018, 22563490300366186081], [1, 455, 36243, 5354440, 6385191800, 425715461080, 229105160984907, 228679638431263565, 39959630797262576401], [1, -120, 254092, -27488280, 37992516774, -2853915694440, 2738912381376268, -134295656772332040, 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753122843193413212, -97208932739121009560, 106890007738661124410161], [1, 921, -707351, 134147334, 1324901569974, 94569711902646, -351540213142554311, 322678247814593877489, 246990403565262140303521], [1, -415, -761343, 370087870, -118607901730, 337769206576510, -634177405148659647, -315495889341644565055, 693842360995438000295041]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/13/4/c/b'], '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': '8-13e4-1.1-c3e4-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '8-13e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.875799537608138, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e4-0', 'trace_hash': 1934881217355092915, 'z1': {'__RealLiteral__': 0, 'data': '3.58625571942394858965526178874', 'prec': 103}}
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{'Lhash': '4546119215299689080503902962460,4867501393974572285882506943821,5311741022678208195551037730562,7160242585993072847561087725692', 'Lhash_array': ['4546119215299689080503902962460', '4867501393974572285882506943821', '5311741022678208195551037730562', '7160242585993072847561087725692'], 'label': '8-13e4-1.1-c3e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/13/4/c/b'}