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lfunc_lfunctions • Show schema
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{'Lhash': '1457539614586985941511315181537', 'a10': [2.097887892923008, -6.061448991443403], 'a2': [-1.9214040182938237, 0.9905526174369143], 'a3': [-0.7860530947427875, 0.6181589862206052], 'a4': [1.550485094462134, -2.177351654848832], 'a5': [-2.14746424103355, 2.047603017989426], 'a6': [0.8980065730381176, -1.966360110510562], 'a7': [2.4791432930152735, 0.9240392484615496], 'a8': [-0.20704023904397426, 1.4399964924553401], 'a9': [0.23575893550942723, -0.9718115683235417], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.7860530947427875, -0.6181589862206052]]], [7, [[1.0, 0], [-2.4791432930152735, -0.9240392484615496]]], [23, [[1.0, 0], [-4.723973382348211, 0.8270885580550645]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.163', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '346343073010697741211376408813', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9214040182938237, -0.9905526174369143], [1.1601138191423963, -1.6291519041006715]], [[1.0, 0], [0.7860530947427875, -0.6181589862206052]], [[1.0, 0], [2.14746424103355, -2.047603017989426], [0.2379095791187115, -4.99433669591504]], [[1.0, 0], [-2.4791432930152735, -0.9240392484615496]], [[1.0, 0], [3.811439404626442, 1.964933581125452], [6.38062600528318, 8.960335472553693]], [[1.0, 0], [1.5946472281263984, 1.8403210048053003], [-1.850092897552707, 12.867678744452126]], [[1.0, 0], [2.338240143547187, -0.22327486220414391], [16.692787853466015, -3.2172711541269736]], [[1.0, 0], [5.356265872204093, 0.5114613774147588], [18.656645247991428, 3.595773642847794]], [[1.0, 0], [-4.723973382348211, 0.8270885580550645]], [[1.0, 0], [-2.704300896677898, 5.921592970143713], [-18.990961284413267, -21.91673765627349]], [[1.0, 0], [-3.5369531221418145, 1.4159824312974527], [22.435755181257175, -21.392449355945473]], [[1.0, 0], [0.4259734437284248, -1.755886450366787], [-32.88691160023217, -16.954381303914186]], [[1.0, 0], [-1.7292353035324148, -0.5077492976414351], [34.49139484607843, 22.1662735156795]], [[1.0, 0], [1.064211322904145, 7.401752332249479], [-41.25819786542339, 12.114499944181476]], [[1.0, 0], [-3.9410580443846572, 6.826112768452266], [-23.5, -40.703193977868615]], [[1.0, 0], [-11.442354554424623, -2.205333079555074], [49.20350044985185, 19.69811014999736]], [[1.0, 0], [3.3808308137213636, -9.76826912210233], [-46.37713258982446, -36.471380187015704]], [[1.0, 0], [9.322881043723504, 7.331594688942987], [14.381295066075062, 59.280505667736044]], [[1.0, 0], [-0.588579627602402, 12.355806956120539], [-66.69661881239666, -6.368754901380238]], [[1.0, 0], [-10.702806841219445, -6.878276303021988], [29.494465923133937, 64.58387167017081]], [[1.0, 0], [1.9308580448272163, -2.711510722804561], [-23.87596132217178, -68.9850597661708]], [[1.0, 0], [9.374336650306361, -1.806755298087832], [73.34106670826974, -29.361333997165875]], [[1.0, 0], [-3.59494013459731, 1.0555696640451881], [69.82404322498803, -44.8731878488146]], [[1.0, 0], [9.789847854381694, 3.919263865868034], [64.41232939135125, 61.417032021907964]], [[1.0, 0], [-3.8573830898596135, -1.132629868595239], [81.60159268462458, 52.442159293192965]], [[1.0, 0], [3.5226590547152306, 3.3588486243250073], [4.805773498197972, 100.8856012574838]], [[1.0, 0], [0.49212760828608154, 10.331029890602546], [-102.53360802502772, 9.790772460330814]], [[1.0, 0], [1.7992762760802685, 1.4149665031425285], [25.226206099508712, 103.98383781061897]], [[1.0, 0], [2.226722066195441, -0.21262617694283914], [107.03022800163502, -20.62838563528471]], [[1.0, 0], [17.123701642043454, 11.0047348300146], [46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-483-161.2-c1-0-16', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/483/2/y/b/163/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.23566737003012295, 0.3079288990198518, 0.36098314648522817, 0.3944571078662087, 0.4061438973856878, 0.39265226993879154, 0.3503127570514065, 0.27619944691337395, 0.1691628799794441, 0.030793550482361542, -0.13376250109149151, -0.31522532661135516, -0.49993965561758463, -0.6700699805535139, -0.8043150369415383, -0.8791889958535382, -0.8708627223555503, -0.7574894493858237, -0.5218613249056762, -0.1541653015209405, 0.34546036143332715, 0.9649121429456532, 1.6790030473955908, 2.4495594832984766, 3.226969423282764, 3.953285942636498, 4.566816704331301, 5.00793009962673, 5.225604722504727, 5.184068074686632, 4.868742552273029, 4.2906698061063855, 3.488640136418995, 2.5284224765664547, 1.4987689523215733, 0.5042354113642027, -0.3447215883030756, 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'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.16169760438509634, 'root_number': '0.873724950169033 + 0.48642030328936814*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0808488021925', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14979601975857439272187794865', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41717470122171386282633000286', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44558010747370537565227941709', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.2', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/y/b/163/3'], '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': '2-483-161.2-c1-0-16', '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': '2-483-161.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.08084880219254817, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14979601975857439272187794865', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1457539614586985941511315181537', 'Lhash_array': ['1457539614586985941511315181537'], 'label': '2-483-161.2-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/y/b/163/3'}