-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '656884388970383590419868553693', 'a10': [-20.288681862779786, 0.0], 'a2': [-2.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [4.0, 0.0], 'a5': [10.144340931389893, 0.0], 'a6': [6.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [-8.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.99584506554546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [7.0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [-10.144340931389893, 0], [125.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [47.76479841618556, 0], [1331.0, 0]], [[1.0, 0], [77.27419826360422, 0], [2197.0, 0]], [[1.0, 0], [26.230239564387038, 0], [4913.0, 0]], [[1.0, 0], [-54.96704929583411, 0], [6859.0, 0]], [[1.0, 0], [23.0, 0]], [[1.0, 0], [52.91109316749892, 0], [24389.0, 0]], [[1.0, 0], [97.0968629236765, 0], [29791.0, 0]], [[1.0, 0], [-295.4952786834755, 0], [50653.0, 0]], [[1.0, 0], [-365.501483653547, 0], [68921.0, 0]], [[1.0, 0], [-392.2070380604284, 0], [79507.0, 0]], [[1.0, 0], [-79.98615740084418, 0], [103823.0, 0]], [[1.0, 0], [146.137757681886, 0], [148877.0, 0]], [[1.0, 0], [19.028386220099208, 0], [205379.0, 0]], [[1.0, 0], [-89.22838347389515, 0], [226981.0, 0]], [[1.0, 0], [1020.9850854606196, 0], [300763.0, 0]], [[1.0, 0], [121.66756459523197, 0], [357911.0, 0]], [[1.0, 0], [749.763516889342, 0], [389017.0, 0]], [[1.0, 0], [-548.8705910209042, 0], [493039.0, 0]], [[1.0, 0], [-73.08464155459717, 0], [571787.0, 0]], [[1.0, 0], [-1089.2535515557145, 0], [704969.0, 0]], [[1.0, 0], [-724.2735855969523, 0], [912673.0, 0]], [[1.0, 0], [159.52077368943065, 0], [1030301.0, 0]], [[1.0, 0], [184.34134616087883, 0], [1092727.0, 0]], [[1.0, 0], [-488.61628513914786, 0], [1225043.0, 0]], [[1.0, 0], [-786.6228783139996, 0], [1295029.0, 0]], [[1.0, 0], [-986.7142125168788, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-966-1.1-c3-0-4', 'leading_term': '0.78859292514888223209819623076138', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/966/4/a/m/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.7885929251488822, 0.7775529760358966, 0.7445825410720215, 0.6901297112296764, 0.614940722925359, 0.5200587587339514, 0.4068216330276896, 0.2768577674121028, 0.13207974620508744, -0.025325334313577953, -0.19290954262709986, -0.3679826216508323, -0.5476360778745211, -0.7287734887297705, -0.9081475138186572, -1.0824039007266506, -1.2481325443894205, -1.4019253966189105, -1.5404407367876098, -1.6604730141938209, -1.75902716652492, -1.8333960170602615, -1.8812390663231815, -1.900660732671372, -1.8902858717992528, -1.8493302281588448, -1.777663352270221, -1.6758614663630078, -1.5452477851550466, -1.3879179056425845, -1.2067480743828831, -1.0053844253736743, -0.7882116560498028, -0.5603000699025447, -0.3273304553376359, -0.09549688182782415, 0.12861183698696396, 0.3381505542926822, 0.5261738857074785, 0.685807070454295, 0.8104279747713798, 0.8938559610838652, 0.9305427710334362, 0.9157600992078925, 0.845778192666324, 0.7180296223193211, 0.5312523559091572, 0.2856064345297435, -0.017241074085381093, -0.3740675973929779, -0.780087030698918, -1.2289851685543414, -1.7130004606954783, -2.2230506669740433, -2.748904577622523, -3.279396479786279, -3.8026795340156254, -4.3065127256985445, -4.778574629975904, -5.206795929922285, -5.579701511810769, -5.886752080822796, -6.118674643734072, -6.267770933231799, -6.328192934017736, -6.296175135301662, -6.170213986754658, -5.951186270716934, -5.642399703007006, -5.249571003599893, -4.780728887478439, -4.246041851904364, -3.657573203502709, -3.028968390789225, -2.375082291219779, -1.7115565480340031, -1.0543592616211956, -0.41930121624676836, 0.17845572394859027, 0.724881464453778, 1.2075348045074497, 1.6159780904287435, 1.9421335134955715, 2.180566664087639, 2.3286850609829437, 2.38684204204017, 2.3583395541238916, 2.2493269164679925, 2.068596432180948, 1.8272806495113525, 1.5384599775573378, 1.216693083123625, 0.8774858784616872, 0.5367178015821643, 0.21004635221601553, -0.08768764295947733, -0.34303089743263393, -0.5444417710074384, -0.682745905606974, -0.7515037947349557, -0.7472736842439827, -0.669756986934042, -0.5218178426227127, -0.30937340736185803, -0.041156720109283174, 0.2716406399682263, 0.6158336534031328, 0.9767993828178086, 1.3391012817875603, 1.6871571431054126, 2.0059230014046454, 2.281563887571087, 2.502082138869261, 2.6578750522906165, 2.742196027193528, 2.7514969171587254, 2.685633983051108, 2.5479254379415437, 2.345054879182196, 2.0868216520257366, 1.785746090709868, 1.4565443266924578, 1.1154936250913807, 0.7797147048938599, 0.4664019366237201, 0.19203545253807122, -0.028389139112408677, -0.18207769762697837, -0.2590670295472768, -0.2527360384866978, -0.16017247098137766, 0.01762466761987047, 0.2757197002206854, 0.6053964964008683, 0.9944924766081401, 1.4278980483884502, 1.8882009887846343, 2.3564479362594044, 2.812988966466614, 3.2383665345011714, 3.6142071443916532, 3.9240731480592763, 4.154233182739799, 4.294312930050394, 4.337793020063805, 4.282327806500099, 4.129867105805895, 3.886572441500896, 3.562529417128438, 3.171268061936388, 2.729112836499405, 2.254392938235497, 1.76655112711524, 1.285195074414773, 0.829138877449402, 0.4154836375947295, 0.058784741845894245, -0.22965027800672, -0.44229557538928566, -0.5757430268433289, -0.6308209762319804, -0.6124874050845639, -0.529501145580286, -0.393886705655779, -0.2202196451544888, -0.024769600877873936, 0.17545357283121307, 0.3636990021909343, 0.5244643849130639, 0.6444205618029968, 0.7132182259791099, 0.7241294693336408, 0.6744851548491495, 0.5658797533202427, 0.40412776661688177, 0.19896953232379191, -0.03646166334172568, -0.2863854230347666, -0.5332945706695099, -0.7590006533763216, -0.9457469256024931, -1.077325815628536, -1.1401359989795863, -1.124115968310554, -1.0234963999494953, -0.8373224715145491, -0.5697091792641442, -0.229807049165473, 0.16852831464811308, 0.607352513339258, 1.065507355387946, 1.5197117503699602, 1.9458119569842551, 2.3201237873899654, 2.620792069825885, 2.8290894590203695, 2.9305778672584077, 2.9160614324321914, 2.782269851760915, 2.5322246473166543, 2.1752578132518567, 1.7266714428055217, 1.2070473055343365, 0.6412357986389273, 0.05707304797782774, -0.5161079703404524, -1.049092636499453, -1.5144370023090434, -1.888063319261266, -2.1507055119096097, -2.289117380061328, -2.296967590032474, -2.1753615103949264, -1.932949863131975, -1.5856069463803792, -1.1556855913427613, -0.6708806644795089, -0.16275638478341237, 0.33498640713876127, 0.7884099046147852, 1.1653007800996362, 1.4370820811875735, 1.5805643548091723, 1.5794313667904698, 1.4253686232908698, 1.1187613909176175, 0.6689121061296738, 0.09375371291817425, -0.5809359132485316, -1.322784344000157, -2.0944780755250068, -2.8557328235202912, -3.5654743038962287, -4.184108922296017, -4.675756315986459, -5.010315556270204, -5.165244181089641, -5.126943794470519, -4.891667013967694, -4.465886939476454, -3.8661005846670986, -3.118070123733644, -2.2555384684841835, -1.3184866625830418, -0.35102798774002997, 0.6009441688912753, 1.4922221356851255, 2.280723086751303, 2.9297615154173116, 3.4100238171981303, 3.701130371469844, 3.7926941095391884, 3.684813776911073, 3.387973223841211, 2.922353114402139, 2.316596311903614, 1.6061007468339479], 'positive_zeros': ['0.51819041370872802208889147313581', '2.07540100124240468021451588113427', '2.80943022359566815360018308202818', '4.55234591994062507145449997258984', '5.54837728029661330739861253223174', '6.10190723556114739509246801492233', '7.37423084546189453805903575484769', '7.67099565151689244810104949897131', '9.151464891674154761364474722142684', '9.675191772094885954077502829777027'], 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51819041370872802208889147314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07540100124240468021451588113', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80943022359566815360018308203', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 56.99584506554546, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/4/a/m/1/4'], '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': '2-966-1.1-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51819041370872802208889147314', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '656884388970383590419868553693', 'Lhash_array': ['656884388970383590419868553693'], 'label': '2-966-1.1-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/4/a/m/1/4'}