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{'Lhash': '1542452905071320603581777206098,1803627477071312848371630957377,1836184959095754920790435385664,2100560073732333534350488814978', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1721078.2314673786, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 4, 6, 4, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '4536.1', 'coefficient_field': '1.1.1.1', 'conductor': 423342805487616, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1], [1, -3, 12, -36, 68, -180, 300, -375, 625], [1, 4, 6, 4, 1], [1, 7, 51, 219, 865, 2409, 6171, 9317, 14641], [1, 3, 41, 90, 738, 1170, 6929, 6591, 28561], [1, -3, 41, -189, 807, -3213, 11849, -14739, 83521], [1, 4, 49, 193, 1297, 3667, 17689, 27436, 130321], [1, 2, 63, 159, 1876, 3657, 33327, 24334, 279841], [1, -9, 68, -270, 1290, -7830, 57188, -219501, 707281], [1, 3, 50, 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'6.37781716570781289276013940096043', '6.39232508827344027075461123047357', '6.41867421112928465019927174616518', '6.79360645655882936291171243639737', '7.02043759957227283311262444046758', '7.14473707995022313585256268374108', '7.37061322928917174719079438191473', '7.45080814084445531261889576531158', '7.73439826387826853511744134818466', '7.964182051883071715338498347837268', '7.981919670703891916581722344945399', '8.144555280204902737548081645347969'], 'prelabel': '8-4536e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.0183172363089, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1182526496060219329, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21678079495534136219904515026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.42281120424396556810230449314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.44849452898548376135255993536', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1721078.2314673786, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 423342805487616, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -4, 0, 0, 0, -7, 0, -3, 0, 0, 0, 3, 0, -4, 0, 0, 0, -2, 0, -3, 0, 0, 0, 9, 0, -3, 0, 0, 0, -12, 0, 3, 0, 0, 0, -9, 0, -8, 0, 0, 0, -3, 0, 10, 0, 0, 0, 6, 0, -21, 0, 0, 0, -10, 0, -20, 0, 0, 0, -9, 0, -11, 0, 0, 0, -3, 0, -24, 0, 0, 0, 28, 0, -21, 0, 0, 0, -8, 0, 9, 0, 0, 0, 6, 0, 12, 0, 0, 0, -12, 0, -16, 0, 0, 0], 'euler11': [1, 7, 51, 219, 865, 2409, 6171, 9317, 14641], 'euler13': [1, 3, 41, 90, 738, 1170, 6929, 6591, 28561], 'euler17': [1, -3, 41, -189, 807, -3213, 11849, -14739, 83521], 'euler19': [1, 4, 49, 193, 1297, 3667, 17689, 27436, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 2, 63, 159, 1876, 3657, 33327, 24334, 279841], 'euler29': [1, -9, 68, -270, 1290, -7830, 57188, -219501, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 3, 50, 252, 1872, 7812, 48050, 89373, 923521], 'euler37': [1, -3, 140, -324, 7620, -11988, 191660, -151959, 1874161], 'euler41': [1, 9, 117, 717, 6341, 29397, 196677, 620289, 2825761], 'euler43': [1, 8, 137, 1005, 8087, 43215, 253313, 636056, 3418801], 'euler47': [1, 3, 150, 468, 9674, 21996, 331350, 311469, 4879681], 'euler5': [1, -3, 12, -36, 68, -180, 300, -375, 625], 'euler53': [1, -6, 59, -621, 4704, -32913, 165731, -893262, 7890481], 'euler59': [1, 10, 171, 1623, 13357, 95757, 595251, 2053790, 12117361], 'euler61': [1, 20, 239, 2109, 15872, 128649, 889319, 4539620, 13845841], 'euler67': [1, 11, 203, 1461, 17099, 97887, 911267, 3308393, 20151121], 'euler7': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler71': [1, 3, 276, 630, 29126, 44730, 1391316, 1073733, 25411681], 'euler73': [1, 24, 425, 4923, 48495, 359379, 2264825, 9336408, 28398241], 'euler79': [1, 21, 308, 3360, 34200, 265440, 1922228, 10353819, 38950081], 'euler83': [1, 8, 323, 1865, 39832, 154795, 2225147, 4574296, 47458321], 'euler89': [1, -6, 263, -1377, 32646, -122553, 2083223, -4229814, 62742241], 'euler97': [1, 16, 431, 4491, 64415, 435627, 4055279, 14602768, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 12, -36, 68, -180, 300, -375, 625], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 7, 51, 219, 865, 2409, 6171, 9317, 14641], [1, 3, 41, 90, 738, 1170, 6929, 6591, 28561], [1, -3, 41, -189, 807, -3213, 11849, -14739, 83521], [1, 4, 49, 193, 1297, 3667, 17689, 27436, 130321], [1, 2, 63, 159, 1876, 3657, 33327, 24334, 279841], [1, -9, 68, -270, 1290, -7830, 57188, -219501, 707281], [1, 3, 50, 252, 1872, 7812, 48050, 89373, 923521], [1, -3, 140, -324, 7620, -11988, 191660, -151959, 1874161], [1, 9, 117, 717, 6341, 29397, 196677, 620289, 2825761], [1, 8, 137, 1005, 8087, 43215, 253313, 636056, 3418801], [1, 3, 150, 468, 9674, 21996, 331350, 311469, 4879681], [1, -6, 59, -621, 4704, -32913, 165731, -893262, 7890481], [1, 10, 171, 1623, 13357, 95757, 595251, 2053790, 12117361], [1, 20, 239, 2109, 15872, 128649, 889319, 4539620, 13845841], [1, 11, 203, 1461, 17099, 97887, 911267, 3308393, 20151121], [1, 3, 276, 630, 29126, 44730, 1391316, 1073733, 25411681], [1, 24, 425, 4923, 48495, 359379, 2264825, 9336408, 28398241], [1, 21, 308, 3360, 34200, 265440, 1922228, 10353819, 38950081], [1, 8, 323, 1865, 39832, 154795, 2225147, 4574296, 47458321], [1, -6, 263, -1377, 32646, -122553, 2083223, -4229814, 62742241], [1, 16, 431, 4491, 64415, 435627, 4055279, 14602768, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4536/2/a/z'], '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': '8-4536e4-1.1-c1e4-0-4', 'motivic_weight': 1, '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': [1, 1, 1, 1], 'order_of_vanishing': 4, 'prelabel': '8-4536e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.0183172363089, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1182526496060219329, 'z1': {'__RealLiteral__': 0, 'data': '1.21678079495534136219904515026', 'prec': 103}}
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{'Lhash': '1542452905071320603581777206098,1803627477071312848371630957377,1836184959095754920790435385664,2100560073732333534350488814978', 'Lhash_array': ['1542452905071320603581777206098', '1803627477071312848371630957377', '1836184959095754920790435385664', '2100560073732333534350488814978'], 'label': '8-4536e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4536/2/a/z'}