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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': -2, 'A4': 1, 'A5': 2, 'A6': 2, 'A7': 0, 'A8': -1, 'A9': -2, 'Lhash': '312369878683860827', 'a10': [-0.020618556701030927, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [0.020618556701030927, 0.0], 'a6': [0.020618556701030927, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.010309278350515464, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.04998851975120723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1]], [7, [1, 0, -1]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': '1.1.1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, 1], [1, 2, 6, 6, 9], [1, -2, 10, -10, 25], [1, 0, -1], [1, 4, 22, 44, 121], [1, 2, 18, 26, 169], [1, 0, -2, 0, 289], [1, -10, 54, -190, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -4, 30, -124, 961], [1, 0, 70, 0, 1369], [1, -8, 94, -328, 1681], [1, -4, 54, -172, 1849], [1, 20, 190, 940, 2209], [1, -12, 142, -636, 2809], [1, 6, 118, 354, 3481], [1, -2, 74, -122, 3721], [1, 8, 150, 536, 4489], [1, 8, 142, 568, 5041], [1, -12, 166, -876, 5329], [1, -24, 286, -1896, 6241], [1, -2, 118, -166, 6889], [1, 12, 214, 1068, 7921], [1, 16, 254, 1552, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-28e2-1.1-c1e2-0-0', 'leading_term': '0.288796544585', 'load_key': 'G2Q', '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, 'origin': 'Genus2Curve/Q/784/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.2887965445848189, 0.3007539739902801, 0.3371805825804069, 0.3995551383290226, 0.4897085106888263, 0.6088147858753983, 0.7559015811108113, 0.9258929221627089, 1.107324895498646, 1.280073177009214, 1.413681381569853, 1.467123871202436, 1.390979785050231, 1.132908243876345, 0.6468672200698989, -0.09436884068918004, -1.085121877186755, -2.274331963016038, -3.559032356923878, -4.788395265602705, -5.78173948152248, -6.360832570643292, -6.392178984792182, -5.829813144872797, -4.745233625843377, -3.330689040762722, -1.866754825941403, -0.6552270656182126, 0.0682931987092267, 0.2156123565827192, -0.110737847874473, -0.6371843946073483, -1.007464051414113, -0.9176446486836608, -0.250209008569941, 0.8511815128149286, 2.010947018113754, 2.76111443292813, 2.746394283241687, 1.909094135461865, 0.5607629301870944, -0.7140801192731197, -1.301817978245689, -0.8512660880189974, 0.5290278669444413, 2.282650122653576, 3.646476198744625, 4.019219043961812, 3.271560384034962, 1.822174653217468, 0.4180789336043843, -0.2761993439274905, -0.05212458093936963, 0.7333228139561476, 1.393990125448423, 1.364813903430989, 0.5829745539004056, -0.4610110335980225, -1.059539145106016, -0.8010975810294934, 0.09984403705071769, 0.9226717382291378, 0.9722024061718653, 0.1642465120527197, -0.7879734584089736, -0.8010641876184018, 0.7674802448602642, 3.494394145314116, 5.975006132515089, 6.676856843306752, 5.035993150478338, 1.998429169038318, -0.4837887236256574, -0.7602130391492392, 1.293926296766171, 4.065865920420963, 5.262468036047904, 3.551164787486676, -0.402180296714745, -4.309895130427238, -5.833870486506712, -4.212104916169695, -0.7289520581212247, 2.307503439398762, 3.263276361488589, 2.227334877951004, 0.6509752613083128, -0.01257625957834651, 0.5318938507199267, 1.404474693247951, 1.55831916483829, 0.7949288214071015, -0.1576931160927789, -0.4896071358596216, -0.1501326536533955, 0.2064680647087148, 0.1038077049996768, -0.03333825699847594, 0.7935244221246998, 2.983158661168793, 5.528395376703227, 6.59876478061011, 5.184182495022824, 2.257738410019405, 0.1594592556037361, 0.5534983446436411, 2.821462610963491, 4.529931273358471, 3.683233886152824, 0.6553249431654181, -2.129967900022995, -2.545610762225613, -0.8483278475423774, 0.6109281518469046, -0.1905386708101123, -2.844302705412168, -4.914178171677912, -4.459486545234239, -2.046593114469263, -0.1124163377838952, -0.348807317240815, -1.932039736877069, -2.546458964115724, -1.097929641321214, 0.9115655301962783, 0.9724877651840008, -1.554786428837412, -4.498062000101447, -5.051417357444858, -2.775301660462298, -0.09176004279052002, 0.3495670056587559, -1.443923546224873, -2.889263994294142, -1.786579691704037, 1.189153748573417, 3.275417457219437, 2.740668663793792, 0.7191932576655647, -0.3132031924742298, 0.4620409445331491, 1.331184141606932, 0.3157960169548477, -2.199617775653704, -3.712002696316312, -2.477965406360794, 0.4127713021723662, 2.243287097129741, 1.67816262997087, -0.001068769008903905, -0.7250442512958118, -0.07459880205701898, 0.6452574013398837, 0.4429325554689183, -0.1366250702070796, -0.1580132024712978, 0.1019017747325565, -0.2889954109344805, -0.8094659527080645, 0.8350067480691856, 5.881070695335607], 'positive_zeros': [2.791838006127257, 5.223164094353384, 5.579286817429504, 6.42262084813564, 7.575711000888679, 8.188420417684288, 9.457349313423189, 9.765547119459919, 10.602242446058, 11.23136141438461, 11.84146297682029, 12.30526099005271, 13.45094853660694, 13.77746713200327, 14.6077730656713, 15.41323382474483, 16.28523153907899, 16.33708100139527, 17.21285321618276, 17.68571678800724, 18.07433600423375, 18.21205413166163, 19.55018827324056, 19.58002701984274], 'prelabel': '4-28e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.47284365879176726, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 312369878683860827, 'z1': {'__RealLiteral__': 0, 'data': '2.79183800613', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.22316409435', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.57928681743', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04998851975120723, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, 1, 2, 2, 0, -1, -2, -2, -4, -2, -2, 0, -4, 1, 0, 2, 10, 2, 0, 4, 0, 2, -6, 2, 10, 0, 0, 4, 4, -1, 8, 0, 0, -2, 0, -10, 4, -2, 8, 0, 4, -4, -4, 0, -20, -2, 1, 6, 0, -2, 12, -10, -8, 0, -20, 0, -6, -4, 2, -4, 0, 1, -4, -8, -8, 0, 0, 0, -8, 2, 12, 0, 12, 10, 0, -4, 24, 2, -5, -8, 2, 0, 0, -4, 0, 4, -12, 4, 0, 0, -8, 20, 20, 2, -16, -1, 8, -6], 'euler11': [1, 4, 22, 44, 121], 'euler13': [1, 2, 18, 26, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, -10, 54, -190, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 2, 6, 6, 9], 'euler31': [1, -4, 30, -124, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, -8, 94, -328, 1681], 'euler43': [1, -4, 54, -172, 1849], 'euler47': [1, 20, 190, 940, 2209], 'euler5': [1, -2, 10, -10, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 6, 118, 354, 3481], 'euler61': [1, -2, 74, -122, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 8, 142, 568, 5041], 'euler73': [1, -12, 166, -876, 5329], 'euler79': [1, -24, 286, -1896, 6241], 'euler83': [1, -2, 118, -166, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 16, 254, 1552, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 2, 6, 6, 9], [1, -2, 10, -10, 25], [1, 0, -1, 0, 0], [1, 4, 22, 44, 121], [1, 2, 18, 26, 169], [1, 0, -2, 0, 289], [1, -10, 54, -190, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -4, 30, -124, 961], [1, 0, 70, 0, 1369], [1, -8, 94, -328, 1681], [1, -4, 54, -172, 1849], [1, 20, 190, 940, 2209], [1, -12, 142, -636, 2809], [1, 6, 118, 354, 3481], [1, -2, 74, -122, 3721], [1, 8, 150, 536, 4489], [1, 8, 142, 568, 5041], [1, -12, 166, -876, 5329], [1, -24, 286, -1896, 6241], [1, -2, 118, -166, 6889], [1, 12, 214, 1068, 7921], [1, 16, 254, 1552, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/784/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-28e2-1.1-c1e2-0-0', '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': '4-28e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.47284365879176726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 312369878683860827, 'z1': {'__RealLiteral__': 0, 'data': '2.79183800613', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9953282
{'Lhash': '312369878683860827', 'Lhash_array': ['312369878683860827'], 'label': '4-28e2-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/14/a|EllipticCurve/Q/56/a'}
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id: 9952870
{'Lhash': '312369878683860827', 'Lhash_array': ['312369878683860827'], 'label': '4-28e2-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/14/a|EllipticCurve/Q/56/a'}
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id: 1221844
{'Lhash': '312369878683860827', 'Lhash_array': ['312369878683860827'], 'label': '4-28e2-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/784/a'}