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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': 1, 'A9': 0, 'Lhash': '1595768217479965950', 'a10': [-0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 365.2197687649324, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [7, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '45738.1', 'coefficient_field': '1.1.1.1', 'conductor': 45738, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 1, 5], [1, 1], [1], [1, -1, 13], [1, 5, 17], [1, -6, 19], [1, -1, 23], [1, -6, 29], [1, -4, 31], [1, -6, 37], [1, 3, 41], [1, 10, 43], [1, -8, 47], [1, -3, 53], [1, -4, 59], [1, -3, 61], [1, -11, 67], [1, -12, 71], [1, 2, 73], [1, 11, 79], [1, 7, 83], [1, 6, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 18, 'label': '2-45738-1.1-c1-0-18', 'leading_term': '3.19035672888', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/45738/ck', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.190356728878092, 2.508820348883533, 0.6994778383070747, -1.410067429110526, -2.501693282906654, -1.601445486891592, 0.8840370836240616, 3.127477652454686, 3.324787586279095, 1.467850373240595, -0.4997857962800084, -0.6600696053293383, 0.7688530244708079, 1.739445422664567, 0.9511337254230846, -0.4689746912080155, -0.5191862833648708, 0.8099848612955992, 1.397966413079125, 0.07445538472636772, -1.421708074560202, -0.8094538622494889, 1.181271645433089, 1.558297371508771, -0.4993418628395455, -2.179849128419632, -1.250730576610518, 0.3417554867904016, -0.4595692388446776, -2.524629212849586, -1.880704978129032, 1.651380440535755, 3.36166145401402, 0.9771154862874567, -1.00744978700965, 1.992304506176239, 6.831895387229814, 6.831029106109703, 2.199594803786332, -0.1193495784465554, 2.570818388049358, 4.679836712081277, 1.798847395157544, -2.210653541291235, -2.051048737505775, 0.4983952800062026, 0.6982104917190898, -0.756405330865432, -0.134757404918999, 1.599199993415085, 0.6434404855711532, -2.035407075639704, -2.227701615212729, -0.2775707176212167, -0.03976490101750051, -1.167245627525792, -0.1272007926965147, 1.986967788330577, 0.845708033624771, -2.513491959111288, -2.955788766010642, -0.5489341768927626, 0.196211300297937, -0.6033267120145148, 0.581942876953566, 1.888800599773218, -0.8790173379489824, -4.191241788831794, -1.664089813714321, 3.088856330834309, 1.667722086741216, -3.37013474420564, -2.623400273690692, 2.580218679212729, 2.681225408975973, -1.97632233017424, -2.195518697303565, 2.482932777613942, 3.86851218319328, 1.017899595835492, 0.01098260114208791, 0.5194776856174655, -2.049177408431986, -4.8943465756544, -2.740898211951517, 0.8966249915672169, 0.3539705120963885, -1.43589940307346, -0.1870234176017665, 0.8777970062758483, -0.9904276832490868, -1.891808577554045, -0.2733298498581553, -0.1876770407013992, -1.546553443871706, -0.1629431937469855, 2.029586674960131, 0.5562535630841571, -1.241469198560427, 0.8506484966786863, 2.297579541657564, 0.09363190782941856, 0.5690534194345195, 5.370185785843687, 5.783817918060962, 0.321117552080186, -1.512980943086264, 1.302823229417643, 0.403528825724994, -2.096593569895844, 2.620443230540211, 9.41140722771028, 7.229627381435236, 0.5396582339574082, -0.4350652408154373, 1.274284847744591, 0.01548029651889846, 0.5838566660648117, 5.022835962776596, 5.699162242354022, 1.384176669577269], 'positive_zeros': ['0.5799060216229686', '1.419131681991518', '2.419387259148884', '2.880567740044131', '3.654932151882838', '4.110325831209126', '4.759834299027249', '5.352161080438297', '5.950140173832819', '6.670863058294193', '6.936705132639505', '7.640357500229011', '8.327949145278224', '8.635449724563715', '9.671763208964625', '9.781812345417496', '10.59626401219334', '11.19275397135855', '11.61093678602861', '12.01774608789698', '12.55914502002332', '13.30195493068186', '13.48999644712579', '14.01351138719613', '14.56318521976812', '15.32685618189953', '15.55893666441713', '15.92709071403367', '16.44778049827161', '17.07590025077737', '17.57809287883707', '18.12266610882952', '18.64274903695680', '19.12333688984404', '19.89339729461182', '19.99541168718602'], 'prelabel': '2-45738-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.110723920483295, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1595768217479965950, 'z1': {'__RealLiteral__': 0, 'data': '0.5799060216229686', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.419131681991518', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.419387259148884', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 365.2197687649324, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 45738, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -1, 0, -1, 1, 0, -1, 0, 0, 1, -1, 0, 1, -5, 0, 6, -1, 0, 0, 1, 0, -4, 1, 0, -1, 6, 0, 4, 1, 0, -5, 1, 0, 6, 6, 0, -1, -3, 0, -10, 0, 0, 1, 8, 0, 1, -4, 0, 1, 3, 0, 0, -1, 0, 6, 4, 0, 3, 4, 0, 1, -1, 0, 11, -5, 0, 1, 12, 0, -2, 6, 0, 6, 0, 0, -11, -1, 0, -3, -7, 0, 5, -10, 0, 0, -6, 0, -1, 1, 0, 8, -6, 0, 1, 1, 0, -4], 'euler11': [1, 0, 0], 'euler13': [1, -1, 13], 'euler17': [1, 5, 17], 'euler19': [1, -6, 19], 'euler2': [1, -1, 0], 'euler23': [1, -1, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 3, 41], 'euler43': [1, 10, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 5], 'euler53': [1, -3, 53], 'euler59': [1, -4, 59], 'euler61': [1, -3, 61], 'euler67': [1, -11, 67], 'euler7': [1, 1, 0], 'euler71': [1, -12, 71], 'euler73': [1, 2, 73], 'euler79': [1, 11, 79], 'euler83': [1, 7, 83], 'euler89': [1, 6, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 1, 5], [1, 1, 0], [1, 0, 0], [1, -1, 13], [1, 5, 17], [1, -6, 19], [1, -1, 23], [1, -6, 29], [1, -4, 31], [1, -6, 37], [1, 3, 41], [1, 10, 43], [1, -8, 47], [1, -3, 53], [1, -4, 59], [1, -3, 61], [1, -11, 67], [1, -12, 71], [1, 2, 73], [1, 11, 79], [1, 7, 83], [1, 6, 89], [1, -1, 97]], 'index': 18, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/45738/ck'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-45738-1.1-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-45738-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.110723920483295, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1595768217479965950, 'z1': {'__RealLiteral__': 0, 'data': '0.5799060216229686', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1595768217479965950', 'Lhash_array': ['1595768217479965950'], 'factors': ['2-45738-1.1-c1-0-18'], 'label': '2-45738-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/45738/ck'}