-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3779291830190514943364702213671', 'a10': [1.961587231845209, -1.0733943971634332], 'a2': [-0.9096319953545183, -0.41541501300188644], 'a3': [0.8800992352489153, -2.997342734443419], 'a4': [0.6548607339452851, 0.7557495743542583], 'a5': [-1.338418360311504, 1.791266672715446], 'a6': [-2.045707594469379, 2.360872417039257], 'a7': [-3.805874168061576, -0.5472020950434318], 'a8': [-0.28173255684142967, -0.9594929736144974], 'a9': [-5.6857282053414835, -3.6539956443582993], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9096319953545183, 0.41541501300188644]]], [5, [[1.0, 0], [1.338418360311504, -1.791266672715446]]], [23, [[1.0, 0], [-4.495871666830206, 1.6694723583795505]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.29', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '680733208673450644678458083416', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [-0.8800992352489153, 2.997342734443419], [-2.5237605984935434, -1.6219224523667928]], [[1.0, 0], [1.338418360311504, -1.791266672715446]], [[1.0, 0], [3.805874168061576, 0.5472020950434318], [6.7164508153014815, 1.9721278978900079]], [[1.0, 0], [1.3479163949099449, 2.951525201298958], [-7.2034680733981356, 8.313245317896842]], [[1.0, 0], [-1.8897639991087603, 0.27170704384497585], [12.473408656988466, -3.662523238938586]], [[1.0, 0], [4.552531150217561, 3.9447906972194606], [2.4193522506458476, 16.826964511975856]], [[1.0, 0], [-2.4213801965901403, -2.794421711465335], [-2.7039819271924177, 18.80660739573772]], [[1.0, 0], [-4.495871666830206, 1.6694723583795505]], [[1.0, 0], [-0.49498914278919653, 0.5712479227746311], [-4.127130309925269, -28.70482181454705]], [[1.0, 0], [-9.293832953136903, 2.7289155759846127], [26.078859517766617, -16.759865341123525]], [[1.0, 0], [-0.6397763298437918, 0.9955114011476947], [-15.370355481069797, -33.65638382811718]], [[1.0, 0], [3.6576984655606757, -2.350660070064329], [17.03201553307734, -37.29491180953525]], [[1.0, 0], [-0.6240913028665267, 2.125459786074296], [-36.17390191174079, -23.247555150590696]], [[1.0, 0], [0, -3.458836889393694], [-47.0, 0]], [[1.0, 0], [10.623362143994294, 1.5274088855542818], [50.85312760156836, 14.931825512595774]], [[1.0, 0], [1.2418873869934528, 8.637516501878029], [-56.61008544325534, 16.622220853644354]], [[1.0, 0], [-3.2956447872835186, 0.9676886208606691], [51.31646550270205, -32.979089864791455]], [[1.0, 0], [-10.22701854648734, -4.670522875356627], [43.8756691743341, 50.63522148173531]], [[1.0, 0], [-2.3749398202573775, 5.20039281184527], [-46.49511211011524, -53.65821977915234]], [[1.0, 0], [-1.37929217706645, 1.1951634748461384], [10.388983193949816, -72.2569652573081]], [[1.0, 0], [0.9260085832169331, 6.44053116424728], [-75.7999449155453, 22.256871990472945]], [[1.0, 0], [0.3614363929872633, -0.5624060053868697], [-34.479446079156574, -75.49945561442503]], [[1.0, 0], [2.318899597913419, 0.680890356411506], [74.87156442197512, 48.11703275354819]], [[1.0, 0], [-0.03743730225660526, -0.05825357939353982], [-40.295256261182985, 88.23430354938829]], [[1.0, 0], [4.868922215679875, 3.1290663088854243], [41.956916313190526, 91.87283153080635]], [[1.0, 0], [8.107523070803568, -3.7025817243360324], [67.45065559636436, -77.84220615848861]], [[1.0, 0], [1.3200394499097188, 4.495641509387915], [-90.01412801293638, 57.84856746774894]], [[1.0, 0], [4.549520777981093, -5.250426866733381], [-15.51231737178808, -107.89053716502167]], [[1.0, 0], [-9.3580376316144, -4.273672588763924], [73.99926293581721, 85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-230-115.29-c1-0-10', '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/230/2/j/a/29/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5864661719150939, 0.7342483635971798, 0.8968921961831173, 1.0782152366211968, 1.2803050395449191, 1.5031817363231705, 1.744636055631469, 2.0001830090125003, 2.263096639291735, 2.5245259890646636, 2.7737157194373827, 2.9983619883088792, 3.185128619533934, 3.320334709338433, 3.390805900126656, 3.3848598330083863, 3.2933736208423707, 3.110859523680911, 2.836456612843231, 2.474733577214294, 2.036193489196368, 1.5373775659936937, 1.000483353880729, 0.45244393969816554, -0.07654196844120019, -0.5549862369264813, -0.9524920660210416, -1.242378349090512, -1.40433366408484, -1.426846427690517, -1.309138838573893, -1.0623399474072848, -0.7096714829265806, -0.28548994135222877, 0.16687274388898712, 0.5984065707620773, 0.9586627726949241, 1.2006084555727137, 1.2856576490047793, 1.188362067316136, 0.9002162929751668, 0.4320635153896508, -0.18531575143568277, -0.9026910580584802, -1.6559949619986338, -2.371869447619154, -2.974706492141174, -3.3945209946677024, -3.5748280645294788, -3.4796148365490587, -3.098520118104638, -2.4494723843406496, -1.5782827610526544, -0.5550240809124201, 0.5325852389288994, 1.58817935808185, 2.5171636013895937, 3.237341316022771, 3.6884279893228586, 3.839192685918247, 3.691204603326378, 3.2785588669252292, 2.663467610868538, 1.9281658227036607, 1.1641185894915687, 0.4599462262430813, -0.11026593341773015, -0.49658691236630753, -0.6793344059220482, -0.6706563646385097, -0.5112584693763307, -0.2626742843721438, 0.003805050149090478, 0.2198390304192504, 0.3323343381968007, 0.3132459040086631, 0.16510600396965514, -0.07887149973319338, -0.36040505997523536, -0.6068017578430898, -0.7450576049143808, -0.7170880086341789, -0.49340557958636966, -0.08263124184005208, 0.4652452775312129, 1.0630024516295173, 1.5976541196063403, 1.947877271830157, 2.0048611944633907, 1.6932172909286585, 0.9882883528395324, -0.07348848788354462, -1.3935851949239622, -2.8207508404369905, -4.170035264970851, -5.249045097211098, -5.8875878844024445, -5.96600362118742, -5.437381569265744, -4.339583594189794, -2.7944706337362155, -0.993744343722383, 0.8269511050967228, 2.421953531213916, 3.5722911334678282, 4.119242938970111, 3.989133962081476, 3.2050569519104006, 1.8833255731390368, 0.21503321522737942, -1.5643298545696473, -3.212128928917726, -4.5163769432128005, -5.327596835255673, -5.57932002874396, -5.293832617299135, -4.572475028741944, -3.5726458549724596, -2.476114478130764, -1.4548293179335963, -0.6407964209666595, -0.10570237435087157, 0.1460729864333833, 0.17017249761536057, 0.0627719501482967, -0.0665224945797237, -0.12322260717519573, -0.05151090876762341, 0.15253341347389512, 0.44108107971547944, 0.7281210846108397, 0.913426954629314, 0.911418472731985, 0.6780985636463778, 0.2294207318665199, -0.35387076255431626, -0.9370031913853955, -1.3561301419213978, -1.4527338516766217, -1.1102982382373685, -0.2851329421716798, 0.9759438921154838, 2.5358592919642406, 4.186581726667916, 5.684450826085818, 6.794885773552452, 7.337472942670972, 7.221966933613789, 6.467333036656135, 5.199341592450037, 3.62671171357009, 2.0004339494390426, 0.5646495597202452, -0.49054003703991433, -1.0642194206865152, -1.1601700601127742, -0.8794356747665681, -0.3917442125478798, 0.10761381743993306, 0.44547889665615603, 0.5119854757294049, 0.28552253553634654, -0.1644567067741619, -0.697523366872467, -1.1405180014907914, -1.3347292198379725, -1.1804081246181028, -0.6673856469687546, 0.11633784503466689, 1.000981012515538, 1.773224041793365, 2.227655552878886, 2.2191612706199875, 1.703242881911672, 0.753663383385993, -0.44808323216787627, -1.6503212408886452, -2.587948333168868, -3.04555006993055, -2.9119051261299402, -2.2123325280321398, -1.1100862861286063, 0.12493412187576952, 1.1741411298510012, 1.7422833296448252, 1.6271426655311925, 0.770513934708377, -0.7220100005532498, -2.597930129645841, -4.508421358318716, -6.081663861637733, -7.002487517557036, -7.080205995351177, -6.2891153217355695, -4.772444224845672, -2.8090845441454135, -0.7511483341938915, 1.0528230938002952, 2.330991401740765, 2.9408815799015953, 2.8900203535531084, 2.321012057086139, 1.4662532826554915, 0.5847638760214435, -0.10239909727470956, -0.4619512613491127, -0.4716309123068346, -0.21245071692606918, 0.16616833330246958, 0.4974187971850468, 0.649352234741154, 0.5635905579067725, 0.2699765354967003, -0.12627046681220022, -0.48035617292320576, -0.655519012891597, -0.5679078187149107, -0.21502316503977043, 0.32113566441559477, 0.8975503049953265, 1.3535536531824375, 1.5610878206909533, 1.4662708726404086, 1.1086940958876845, 0.6110404493401065, 0.14032058877201964, -0.1491707527174765, -0.174745557620422, 0.03223709601229648, 0.31527514016534613, 0.41985867625459505, 0.055126730952963804, -1.0239866256069492, -2.9352563713330904, -5.611153056907934, -8.78261804111161, -12.01307206227454, -14.778307974733478, -16.575520475772727, -17.036098076017737, -16.01444084342053, -13.629869073072523, -10.249648156375693, -6.415575189018977, -2.7307428037603985, 0.2667269928688958, 2.212759211010546, 2.9833167238490375, 2.7024210015280246, 1.6921423397672235, 0.37920943811984464, -0.816433729204603, -1.5819845232031167, -1.7759306880125918, -1.4415328531428162, -0.7694748249855662, -0.02343752071303435], 'positive_zeros': ['2.98133557425846405120690433787381', '4.20395919521475240799641572007191', '5.21501163083716019160679032161906', '6.68902562834005090299009317257401', '8.222667892494493357686239953089169', '8.998113673008705769607556601147971', '9.588129830508823892718951100775947', '10.39556568165037607971699723271379', '11.36737124899249209804726574673880', '12.69230737443861204763140784305991'], 'prelabel': '2-230-115.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.9921979020436844, 'root_number': '-0.9996996201448216 + 0.02450855936809213*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.496098951022', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.98133557425846405120690433787', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20395919521475240799641572007', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.21501163083716019160679032162', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.29', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/29/6'], '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': '2-230-115.29-c1-0-10', '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': '2-230-115.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.4960989510218422, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.98133557425846405120690433787', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3779291830190514943364702213671', 'Lhash_array': ['3779291830190514943364702213671'], 'label': '2-230-115.29-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/29/6'}