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lfunc_lfunctions • Show schema
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{'Lhash': '1006045175936200137700043607865,1557964292126905249501561875822', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 261.4594053632578, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '2025.1', 'coefficient_field': '1.1.1.1', 'conductor': 4100625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1], [1], [1, 0, -14, 0, 49], [1, -10, 47, -110, 121], [1, 0, -10, 0, 169], [1, 0, -18, 0, 289], [1, -10, 63, -190, 361], [1, 0, -10, 0, 529], [1, -10, 83, -290, 841], [1, 18, 143, 558, 961], [1, 0, 26, 0, 1369], [1, -14, 131, -574, 1681], [1, 0, -82, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -42, 0, 2809], [1, -2, 119, -118, 3481], [1, 4, 126, 244, 3721], [1, 0, -98, 0, 4489], [1, -2, 143, -142, 5041], [1, 0, -82, 0, 5329], [1, 24, 302, 1896, 6241], [1, 0, -130, 0, 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1.968025436419189, 2.736892588722837, 3.551206872693418, 4.36909818692502, 5.131997436308958, 5.783307700127058], 'positive_zeros': ['0.793629708182262923546600713212064', '1.22901712178924335094102592128998', '1.80871195297257303763879179492408', '2.49273549885662812806547616181086', '3.13986918992379447472209950127075', '3.70273475350232943408782369464011', '3.85317928540879815311252466217211', '4.50504761785847529968900571770239', '4.69640535634946212378317671111423', '5.53869196918469484730253253698693', '5.77776791828149324925887121240117', '6.13681259531888009002934379623540', '6.68591512574905174627733785393206', '7.10461552715674291774889312506642', '7.39113424670458149948219062460587', '7.41230652305881932370041170001015', '8.416621609205187749505237078390337', '8.647564499423975792781250859876879', '9.052150047314487167564381113354089', '9.334098062684827383259916935914144'], 'prelabel': '4-45e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.021157346997166, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1524624351996078981, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.793629708182262923546600713212', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.22901712178924335094102592129', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.80871195297257303763879179492', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 261.4594053632578, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 4100625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, -4, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -10, 47, -110, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, -18, 0, 289], 'euler19': [1, -10, 63, -190, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, -10, 83, -290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 18, 143, 558, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, -14, 131, -574, 1681], 'euler43': [1, 0, -82, 0, 1849], 'euler47': [1, 0, -90, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -42, 0, 2809], 'euler59': [1, -2, 119, -118, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -98, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, -2, 143, -142, 5041], 'euler73': [1, 0, -82, 0, 5329], 'euler79': [1, 24, 302, 1896, 6241], 'euler83': [1, 0, -130, 0, 6889], 'euler89': [1, -18, 259, -1602, 7921], 'euler97': [1, 0, 2, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -14, 0, 49], [1, -10, 47, -110, 121], [1, 0, -10, 0, 169], [1, 0, -18, 0, 289], [1, -10, 63, -190, 361], [1, 0, -10, 0, 529], [1, -10, 83, -290, 841], [1, 18, 143, 558, 961], [1, 0, 26, 0, 1369], [1, -14, 131, -574, 1681], [1, 0, -82, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -42, 0, 2809], [1, -2, 119, -118, 3481], [1, 4, 126, 244, 3721], [1, 0, -98, 0, 4489], [1, -2, 143, -142, 5041], [1, 0, -82, 0, 5329], [1, 24, 302, 1896, 6241], [1, 0, -130, 0, 6889], [1, -18, 259, -1602, 7921], [1, 0, 2, 0, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2025/2/b/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': '4-45e4-1.1-c1e2-0-3', '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': '4-45e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.021157346997166, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1524624351996078981, 'z1': {'__RealLiteral__': 0, 'data': '0.793629708182262923546600713212', 'prec': 107}}
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{'Lhash': '1006045175936200137700043607865,1557964292126905249501561875822', 'Lhash_array': ['1006045175936200137700043607865', '1557964292126905249501561875822'], 'label': '4-45e4-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2025/2/b/b'}