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lfunc_lfunctions • Show schema
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{'Lhash': '577286566539401672952765488760,1494069370879008559060183422685,2327449163215431820414834838683', 'a10': 0, 'a2': 0, 'a3': 5, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 35, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5770.57331751276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, 57, 1083, 6859]]], 'bad_primes': [2, 19], 'central_character': '304.1', 'coefficient_field': '1.1.1.1', 'conductor': 28094464, 'conductor_radical': 38, 'degree': 6, 'euler_factors': [[1], [1, -5, 29, -298, 783, -3645, 19683], [1, -2, 96, 1016, 12000, -31250, 1953125], [1, -35, 1148, -23983, 393764, -4117715, 40353607], [1, -28, 4182, -74894, 5566242, -49603708, 2357947691], [1, 109, 6999, 365490, 15376803, 526122181, 10604499373], [1, 123, 17610, 1215235, 86517930, 2968920987, 118587876497], [1, 57, 1083, 6859], [1, -193, 39933, -4449614, 485864811, -28570926577, 1801152661463], [1, 297, 71131, 13319430, 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'6.68603890120793934962496917906176', '7.45115180981913637410561665473137', '7.53842227156571053093163280714383', '7.54733890620872877843504723655275', '8.182660064137815763193007904729160', '8.541089446182544506429539718246298', '8.654542548338446332885722090903569', '9.176985651202488577271883588222229', '9.388831197020595096584902351697364', '9.480228984253261288386880547317943', '9.846223777462568546314360223323515', '10.63484033483080936923115039351912', '10.66335839591820873809749102252102', '11.04770699643242291530244288962353', '11.28166930163943009361881601872131', '11.38706949386912544181039078755115'], 'prelabel': '6-304e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.235160049129803, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e3-0', 'trace_hash': 730905079542002297, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45539880345220226819484374287', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17861291637460230647129740104', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.83603365375001199738450358149', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5770.57331751276, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 28094464, 'conductor_radical': 38, 'degree': 6, 'dirichlet_coefficients': [1, 0, 5, 0, 2, 0, 35, 0, -4, 0, 28, 0, -109, 0, 10, 0, -123, 0, -57, 0, 175, 0, 193, 0, -92, 0, 133, 0, -297, 0, 140, 0, 140, 0, 70, 0, 38, 0, -545, 0, 736, 0, 514, 0, -8, 0, -134, 0, 77, 0, -615, 0, 311, 0, 56, 0, -285, 0, -199, 0, 56, 0, -140, 0, -218, 0, 509, 0, 965, 0, 874, 0, 203, 0, -460, 0, 980, 0, -242, 0, 1488, 0, 62, 0, -246, 0, -1485, 0, 1764, 0, -3815, 0, 700, 0, -114, 0, -2178, 0, -112, 0], 'euler11': [1, -28, 4182, -74894, 5566242, -49603708, 2357947691], 'euler13': [1, 109, 6999, 365490, 15376803, 526122181, 10604499373], 'euler17': [1, 123, 17610, 1215235, 86517930, 2968920987, 118587876497], 'euler19': [1, 57, 1083, 6859, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -193, 39933, -4449614, 485864811, -28570926577, 1801152661463], 'euler29': [1, 297, 71131, 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[1, 297, 71131, 13319430, 1734813959, 176662526337, 14507145975869], [1, -140, 62189, -4673384, 1852672499, -124250515340, 26439622160671], [1, -38, 100099, -7279012, 5070314647, -97497603542, 129961739795077], [1, -736, 354551, -108718336, 24436009471, -3496076721376, 327381934393961], [1, -514, 224130, -56635248, 17819903910, -3249180607186, 502592611936843], [1, 134, 8542, -31064212, 886856066, 1444414854086, 1119130473102767], [1, -311, 285651, -106221286, 42526863927, -6893116311119, 3299763591802133], [1, 199, 35145, -35868602, 7218044955, 8393926194559, 8662995818654939], [1, -56, 192812, 95078710, 43764660572, -2885140964216, 11694146092834141], [1, -509, 553245, -128354670, 166395625935, -46043316524021, 27206534396294947], [1, -874, 862737, -513398212, 308783062407, -111959648146954, 45848500718449031], [1, -203, 1104798, -157466799, 429785203566, -30720847936667, 58871586708267913], [1, 242, 502613, 37031420, 247807810907, 58827164236082, 119851595982618319], [1, -62, 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'6-304e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.235160049129803, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 730905079542002297, 'z1': {'__RealLiteral__': 0, 'data': '0.45539880345220226819484374287', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '577286566539401672952765488760,1494069370879008559060183422685,2327449163215431820414834838683', 'Lhash_array': ['577286566539401672952765488760', '1494069370879008559060183422685', '2327449163215431820414834838683'], 'factors': ['2-304-1.1-c3-0-1', '2-304-1.1-c3-0-8', '2-304-1.1-c3-0-18'], 'label': '6-304e3-1.1-c3e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/304/4/a/j'}