-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2827969201099922775417249562817', 'a10': [0.45961028648577645, 1.2627688838687408], 'a2': [-0.7885681894097494, 0.6616872768918562], 'a3': [-0.8977941127834199, -1.4812041490123609], 'a4': [-0.16328661838545028, 0.9260444302362589], 'a5': [0.4464825118374191, -1.22670061945469], 'a6': [1.688065817861262, 0.5739715322356849], 'a7': [-0.9475452866630604, -1.641196578972837], 'a8': [-1.5133918468998893, -2.621271570591108], 'a9': [-1.3879314621028638, 2.659632729627346], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8977941127834199, 1.4812041490123609]]], [19, [[1.0, 0], [1.2887523365546942, 4.164026586733665]]]], 'bad_primes': [3, 19], 'central_character': '171.110', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '852986329092705480130622907040', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7885681894097494, -0.6616872768918562], [0.3472963553338607, -1.969615506024416]], [[1.0, 0], [0.8977941127834199, 1.4812041490123609]], [[1.0, 0], [-0.4464825118374191, 1.22670061945469], [-3.83022221559489, -3.2139380484326967]], [[1.0, 0], [0.9475452866630604, 1.641196578972837], [-3.5, 6.06217782649107]], [[1.0, 0], [0, 5.092405724777867], [-11.0, 0]], [[1.0, 0], [-0.18894414946872315, -0.5191197842033759], [-9.958577760546714, 8.35623892592501]], [[1.0, 0], [-1.7963937197478945, 4.935551181457435], [-13.022755533022627, -10.927389364671168]], [[1.0, 0], [1.2887523365546942, 4.164026586733665]], [[1.0, 0], [4.43591458160607, 0.782171424855252], [21.612930278075893, 7.866463296490381]], [[1.0, 0], [0.7443539707959281, -4.221441141935199], [-27.251086002791343, -9.918584156444393]], [[1.0, 0], [0, -9.561535386555231], [-31.0, 0]], [[1.0, 0], [0, 0.8224390941607628], [-37.0, 0]], [[1.0, 0], [4.692260080254057, -3.9372737027290534], [7.119575284344144, -40.37711787350053]], [[1.0, 0], [0.6202722192982794, 3.517738560520261], [-40.406782693794064, 14.706866163003756]], [[1.0, 0], [-6.740357259351123, -1.1885068444377673], [44.16555317693769, 16.07494673630643]], [[1.0, 0], [3.872850913008253, 3.2497077727098174], [9.203353416347309, 52.194810909647025]], [[1.0, 0], [-1.1403421027572338, -6.467201435511729], [-55.44186462636859, 20.179188456214455]], [[1.0, 0], [-2.204208361158804, 0.8022662335824919], [46.728711030257664, -39.2100441908789]], [[1.0, 0], [-10.001201161703719, 11.918967414717793], [-11.634427903684333, -65.98211945181794]], [[1.0, 0], [-0.27693496718670396, 0.23237602882645544], [12.329020614352055, -69.92135046386677]], [[1.0, 0], [-0.9205199211166634, -5.220527893224861], [-68.59756131737132, 24.967470462773818]], [[1.0, 0], [-4.775467683718056, 13.120489628350628], [-60.51751100639927, -50.780221165236604]], [[1.0, 0], [-6.968721178103758, 4.023393048085651], [41.5, -71.88010851410841]], [[1.0, 0], [0.45707620792104847, -2.5922079881624462], [-83.63264324994584, -30.439792755984517]], [[1.0, 0], [-1.4787861060117329, -1.762348654517885], [-16.843873233692243, 95.52635204218419]], [[1.0, 0], [-5.317007295357287, 6.336562546091671], [-17.538465944359967, -99.46558305423301]], [[1.0, 0], [12.126695198762947, 7.001350737386329], [51.5, 89.20061658979718]], [[1.0, 0], [1.2666273150114253, -2.193862863854338], [-53.5, -92.66471820493493]], [[1.0, 0], [-7.359923045409197, -8.77121473058333], [-18.927651365695407, 107.34404507833068]], [[1.0, 0], [-3.0432509783116313, -5.271065314619437], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-171-171.110-c1-0-11', '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/171/2/x/a/110/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.566542589004691, 0.6519630237497341, 0.740577947958802, 0.8335719737074225, 0.9303888158837329, 1.0287854050008978, 1.1249956200728284, 1.2139468102009676, 1.2895061499235094, 1.344762025140046, 1.3723577602120518, 1.3648935367211776, 1.3154030997670996, 1.2178992107901292, 1.0679682651854838, 0.8633814017265627, 0.6046777710497772, 0.29566639838440406, -0.05621262032255808, -0.4397278551227291, -0.839952739077175, -1.238662499829292, -1.6150580330901774, -1.9468183853125876, -2.2114536069085555, -2.3878964008006, -2.4582369609427803, -2.409474081031674, -2.2351308558178196, -1.9365690212391766, -1.5238357591420368, -1.0158933627628322, -0.4401169247749523, 0.1690021904698071, 0.7719413317352876, 1.3269354831120526, 1.7933027863013369, 2.135060828797238, 2.3245230505169245, 2.345522900780381, 2.1959030851407824, 1.8889344475306478, 1.4533964180913055, 0.9321569140722895, 0.37922770237473813, -0.1445696851516682, -0.5770277293436568, -0.8606147022715644, -0.9486029436924859, -0.810622681967426, -0.4369959584883387, 0.1587257076317176, 0.9394529723813873, 1.84670362088133, 2.8051676922129367, 3.7293804261691332, 4.531921196890865, 5.1323311689890465, 5.465793645142178, 5.490575331761334, 5.193299891044272, 4.59131917857827, 3.7317487801348737, 2.687113545792436, 1.5479631498403095, 0.41321578729489744, -0.6206842014472254, -1.4705012284759684, -2.0754919432228833, -2.4040192198756105, -2.456576424297956, -2.264742682396729, -1.8861221397619161, -1.3958746437462264, -0.8759439504227678, -0.40345649840815995, -0.039936557880114604, 0.1770761644646804, 0.23871888672915073, 0.16502830059814988, 0.0005668737673948511, -0.19396566253462416, -0.35289818559648056, -0.41779600507194925, -0.3487245928355021, -0.13263645111221406, 0.21268228673199044, 0.6400213810990378, 1.0795881913135899, 1.4504494174221985, 1.6749087025464027, 1.6935431423469196, 1.4783459987003487, 1.0415549792304049, 0.4382934834008018, -0.23794465048100993, -0.8668033317531008, -1.3182123169301576, -1.4727724760534961, -1.2422527323418493, -0.5868231317356956, 0.474052774289396, 1.8593074325046146, 3.4335137600789865, 5.023142760324848, 6.439771599105626, 7.5069108024097595, 8.086334601111322, 8.09966111676491, 7.541500640898033, 6.481713105064714, 5.056015610408588, 3.446089859071384, 1.852138040671999, 0.46220658534749165, -0.5767188095055074, -1.1809970895499855, -1.3421455184034745, -1.1260402018093683, -0.6594979406050221, -0.10643779998807822, 0.36230150819030577, 0.6002109799206451, 0.5118660153755801, 0.07034075786458252, -0.6779474180655474, -1.6219461018401273, -2.6067321608935172, -3.4625792532954676, -4.036972128431652, -4.2235815673546995, -3.982703936285732, -3.3492156130266264, -2.4264256880111943, -1.3668999445652616, -0.34386177475201146, 0.4813472592568358, 0.9894279391360942, 1.1249802429535403, 0.9057088365733297, 0.41710241107553164, -0.20639445167563084, -0.8099585530241045, -1.2509304481928814, -1.428656964564139, -1.3054414642985477, -0.9141711182530771, -0.3509078091593441, 0.24614017101635036, 0.7269500717353902, 0.9629547330484294, 0.8761397106252232, 0.4576092134640476, -0.2286056154937321, -1.057629532447318, -1.8694339336252275, -2.5028400452596395, -2.8305958458847984, -2.787868475555811, -2.3877363337911857, -1.7199493471852738, -0.9328082993698956, -0.2017346916385675, 0.30885560682101104, 0.48209419199954184, 0.27545888185778833, -0.2683853563641228, -1.0295258533784315, -1.8362147619353266, -2.502482031563199, -2.869773689121285, -2.843292477869732, -2.4146458949288787, -1.6652732326317987, -0.7493456717040909, 0.14050181088798744, 0.817190669382615, 1.143056909745677, 1.0633257414351251, 0.6210197875944589, -0.05087632567384963, -0.7590445968517414, -1.2951934858759342, -1.48717119322958, -1.2440863887310492, -0.5845643774774, 0.3593121388999387, 1.3645465456785957, 2.162424535156773, 2.497165134402896, 2.1853535002251645, 1.1627667234098655, -0.49248875013635046, -2.5667022556604246, -4.7468495268336, -6.67954526971775, -8.040515782784597, -8.59981073274183, -8.268599388581428, -7.117217983208983, -5.360342958672913, -3.3123832827416004, -1.322778008039549, 0.2946652189390348, 1.322990964365118, 1.680710738752093, 1.4298773553481006, 0.7527034395100352, -0.0970231549841025, -0.8558385153131813, -1.3111478139119033, -1.3464663271168853, -0.9614253560494521, -0.2629351462232802, 0.5690328875774063, 1.3315025012828978, 1.8512456460762392, 2.026840619518729, 1.8497733803891858, 1.4000050996167246, 0.8181959703429739, 0.2628720617689742, -0.13533479231846976, -0.3096586574206568, -0.27349756081894067, -0.11265826257732303, 0.04410892255686208, 0.06780357880379821, -0.12726247301878488, -0.5519092860970277, -1.132349663224482, -1.7261751190052246, -2.160770563397416, -2.2842899217888806, -2.015216429859651, -1.376113164998159, -0.5007148930192106, 0.3897676623961969, 1.0370453334715695, 1.2112086167158005, 0.774778162310222, -0.27179245469382246, -1.7764411848019253, -3.459350325650666, -4.970569852732482, -5.968724886275036, -6.202090409519432, -5.571878942508874, -4.1612925102290195, -2.221958241725522, -0.11984704105278703, 1.746976477751122, 3.0390686156439886, 3.552597024584332, 3.263560507243041, 2.328261880013356, 1.040050481691698], 'positive_zeros': ['2.23087434391682665482962086252303', '4.09054965423608022739485485804920', '5.58890798683969788481860365222489', '6.34555671912650103874906495121217', '8.172920636619565381165068252555367', '9.517598909129448263426753367335529', '10.00037201035597733253376745113913', '10.67795812463845114854827108824817', '11.83123267506606903612976569655540', '12.57444394384049873267902669081685'], 'prelabel': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.48477517322807695, 'root_number': '0.04781196893875364 + 0.9988563538498414*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.242387586614', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23087434391682665482962086252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.09054965423608022739485485805', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.58890798683969788481860365222', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.110', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/x/a/110/7'], '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': '2-171-171.110-c1-0-11', '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': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.24238758661403847, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23087434391682665482962086252', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2827969201099922775417249562817', 'Lhash_array': ['2827969201099922775417249562817'], 'label': '2-171-171.110-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/x/a/110/7'}