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lfunc_lfunctions • Show schema
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{'Lhash': '388110116231792397857784734662', 'a10': [0, 0], 'a2': [1.7320508075688772, -1.0], 'a3': [-2.6646360424328104, -1.538428336390962], 'a4': [2.0, -3.4641016151377544], 'a5': [0, 0], 'a6': [-6.153713345563848, 0], 'a7': [11.047160246000292, 14.864731766809342], 'a8': [0, -8.0], 'a9': [-8.766476507578673, -15.183982714485232], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.650668502009225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.7320508075688772, 1.0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-11.047160246000292, -14.864731766809342]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.249', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'conjugate': '2146728378481045639046583495906', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, 1.0]], [[1.0, 0], [2.6646360424328104, 1.538428336390962], [13.5, 23.382685902179844]], [[1.0, 0], [0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-350-35.4-c3-0-4', 'leading_term': '1.067988261177031731187447418271640726827574452229683353', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/350/4/j/j/249/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0679882611770317, 0.870748108554958, 0.6616660136108122, 0.44192777584635823, 0.21279940469635844, -0.02436419000995731, -0.2681104241275226, -0.5168808802730022, -0.769004469181187, -1.0226926011651774, -1.2760370207064915, -1.5270109005102772, -1.7734737165828878, -2.0131803350303503, -2.243794636423994, -2.462907886826343, -2.668061937985109, -2.8567772048438758, -3.0265852284776766, -3.1750654890319545, -3.2998859885851917, -3.3988469806606756, -3.469927084248847, -3.511330888830431, 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'6.80368721571556215893975541101016', '8.080454489385349347855403746140007', '8.552449248232460125443234386854770', '10.42919905799239251542503726836676', '10.86312231234827084162391080450676'], 'prelabel': '2-350-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.544300661488985, 'root_angle': -0.4975160294997359, 'root_number': '0.007803544273327371168084658390821983687074605226525686 - 0.999969551884843251496022606591015626582914257177575725*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24875801474986795', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30616489761604385823315638464', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46868731518455627730339693384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92971350904434226546844642926', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.650668502009225, 'bad_primes': [2, 5, 7], 'central_character': '35.4', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/4/j/j/249/6'], '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': '2-350-35.4-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-350-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.544300661488985, 'root_angle': -0.24875801474986795, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.30616489761604385823315638464', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '388110116231792397857784734662', 'Lhash_array': ['388110116231792397857784734662'], 'label': '2-350-35.4-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/4/j/j/249/6'}