-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3153296074308195461778107154659', 'a10': [-3.3762145019961474, -4.353883038880803], 'a2': [2.4545688267095804, -0.21474694618121656], 'a3': [0.0, 0.0], 'a4': [4.009176368135873, -0.7069259641211277], 'a5': [-1.2110259038625457, -1.8797383488597301], 'a6': [0.0, 0.0], 'a7': [1.0274792560319936, -0.7194487204277064], 'a8': [4.9290131520722875, -1.320725093580152], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.2110259038625457, 1.8797383488597301]]]], 'bad_primes': [3, 5], 'central_character': '405.197', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2199128829195369031532829215067', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.4545688267095804, 0.21474694618121656], [1.969615506024416, -0.3472963553338607]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2110259038625457, 1.8797383488597301]], [[1.0, 0], [-1.0274792560319936, 0.7194487204277064], [2.3941410032796813, -6.5778483455013586]], [[1.0, 0], [0.9551770282730908, 2.6243273167620864], [-8.426488874308758, 7.070663706551932]], [[1.0, 0], [0.5190694350572427, -5.932990791469066], [-12.802500789158705, -2.2574263096700946]], [[1.0, 0], [-5.376279955070704, -1.4405698722448277], [14.722431864335457, 8.5]], [[1.0, 0], [1.7528370923606351, 1.0120009671199737], [9.5, 16.454482671904334]], [[1.0, 0], [2.679776731597361, -3.827117797744669], [-7.866463296490381, -21.612930278075893]], [[1.0, 0], [2.13513804901252, 1.7915935494389825], [5.03579715234098, 28.559424837354033]], [[1.0, 0], [-0.8601312030113203, -4.87804645412401], [-29.13047124436316, 10.602624443095731]], [[1.0, 0], [-0.3545890427289652, 1.3233443232717097], [-32.04293994002423, -18.5]], [[1.0, 0], [-0.2074260697166555, -0.24720076378252126], [-7.119575284344144, 40.37711787350053]], [[1.0, 0], [-3.7937302750358843, 8.135680829361085], [-27.639867216521193, -32.93991105411605]], [[1.0, 0], [-0.2136943861456447, -0.30518721162588225], [-16.07494673630643, 44.16555317693769]], [[1.0, 0], [7.968781497810526, 7.968781497810526], [0, 53.0]], [[1.0, 0], [2.97237829214102, 1.0818572233183414], [45.196622144019706, 37.92446897150582]], [[1.0, 0], [0.02752561502778099, -0.15610552008085035], [-57.32124986794041, -20.863228742865793]], [[1.0, 0], [-8.09208140885945, -0.7079653876040894], [65.98211945181794, 11.634427903684333]], [[1.0, 0], [7.010946748128056, -4.047771992305864], [35.5, -61.48780366869514]], [[1.0, 0], [1.4194882313195716, 5.297602200030724], [-63.21985447626402, 36.5]], [[1.0, 0], [-10.314802195801143, 12.292702573744657], [-13.718206035687498, -77.79981248796443]], [[1.0, 0], [-0.1513753784404715, -1.730228492924881], [-81.73904350001327, 14.412798746355218]], [[1.0, 0], [6.448921563818524, -11.169859802560222], [-44.5, -77.07626093681505]], [[1.0, 0], [3.2145453023117154, 1.498967091954128], [62.35039813959431, 74.30631098254086]], [[1.0, 0], [-9.188335249861106, -1.6201514123451681], [94.90895469937675, 34.544034475892545]], [[1.0, 0], [0.6253227067907147, -0.291592766994723], [66.20712379771355, -78.90257764125474]], [[1.0, 0], [-7.01111029350128, 7.01111029350128], [0, -107.0]], [[1.0, 0], [0, 3.981293901367055], [-109.0, 0]], [[1.0, 0], [5.382796857553006, 11.543445112719526], [-72.63499989457894, 86.56302207244451]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-405-135.92-c1-0-15', '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/405/2/r/a/197/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.3327619921703886, 3.438683304690023, 3.5669762387326562, 3.7128636241937847, 3.8668561110500503, 4.015941747609261, 4.144948562040639, 4.237882646751012, 4.279186405774608, 4.254934129483233, 4.153983883890317, 3.9690693204794463, 3.697772394527111, 3.3432847725990738, 2.914848899104682, 2.4277715562338646, 1.9029235126442587, 1.3656774050260634, 0.8442897363633599, 0.3677973895410801, -0.036432030485480695, -0.34529152355198134, -0.5424109886039853, -0.6202319914513739, -0.5813954162124203, -0.43919375090215734, -0.21691535031387504, 0.053981329212830435, 0.33678858822288277, 0.5933414548135412, 0.7883142048172247, 0.893539794066906, 0.8918038271494015, 0.7795637115188258, 0.5681191696204709, 0.2829134808152973, -0.039134593413999205, -0.3541024896069872, -0.6168952261475092, -0.7877419277007923, -0.8384818903550584, -0.7576910723202666, -0.5537608418302762, -0.2552460758121716, 0.09186231618418075, 0.4298492594530052, 0.6974019170279137, 0.8391302146644325, 0.8151150823105382, 0.6089469890601181, 0.23277302299449407, -0.2718252887008003, -0.8377656350709811, -1.3811426041014823, -1.8137928361004083, -2.0581433768278172, -2.0621627233671815, -1.811947626596642, -1.3395667520899006, -0.7242767245914089, -0.08609363024030021, 0.4281573634217082, 0.6649399524473695, 0.4877124859611236, -0.1991705067423104, -1.4301724751855838, -3.165523700252862, -5.288210274949341, -7.612448848900322, -9.90336411586825, -11.90574772568324, -13.378132794441424, -14.127265480819913, -14.037633009576528, -13.091147318436523, -11.37337552055148, -9.064691421078866, -6.417100089757321, -3.7198714658201344, -1.259092271704262, 0.7225626672579495, 2.0593811634473234, 2.6839847291562835, 2.632969587149563, 2.0359037488165197, 1.0896355413643095, 0.022453401398867295, -0.9455510115747727, -1.6388858411257377, -1.9534119736926845, -1.8688522880425829, -1.4451717306204528, -0.8040286924223895, -0.09936323287766126, 0.5167406615196415, 0.9259319195342706, 1.0667845227186807, 0.9447613219516278, 0.6272306780580033, 0.22500554768131908, -0.13524595165007577, -0.34142234969118335, -0.3223687152765143, -0.06427906237398139, 0.38654254538154487, 0.9351077189067587, 1.4606278545578886, 1.8454447460433823, 2.0031360042313024, 1.8990571300836152, 1.5583187985734144, 1.0591704470431476, 0.5132954013123754, 0.03778373549816727, -0.2742664776183254, -0.3770380710912979, -0.283015262840768, -0.058508174162390646, 0.19566210545551133, 0.3737513752997787, 0.3974366659236731, 0.242215524926931, -0.04984950061896696, -0.3756906153867563, -0.5952557303558538, -0.5692643639203399, -0.20191251165333846, 0.5223998757170469, 1.5187712512816465, 2.605203571347421, 3.5316771859382987, 4.030585299054878, 3.878454509934486, 2.955099917172257, 1.2856618056933498, -0.9462397904393125, -3.4201295339629105, -5.733229052832614, -7.4781951793537225, -8.328159539187633, -8.110379258893316, -6.851220954690101, -4.780745507093221, -2.2937535178837942, 0.1260867097204968, 2.0037291355717093, 2.9710655366077448, 2.8443955498266833, 1.6634956650004031, -0.3169634615894843, -2.682247641764168, -4.946693202332492, -6.657277269240014, -7.488386563063087, -7.30660112562202, -6.191358334407959, -4.40775127058569, -2.3389502707462633, -0.39509132161459204, 1.0793304219918618, 1.8777458278246622, 1.96720384795777, 1.4806329666357005, 0.669746554995264, -0.16772109580961478, -0.7668748574014042, -0.9603249110896187, -0.712905693534756, -0.11918907334511444, 0.633342259482906, 1.32357516624513, 1.7611007260174525, 1.8376154169900005, 1.5517882481937624, 1.0020294649240422, 0.35095182392802904, -0.22668671127082174, -0.59639542225764, -0.7010122404944664, -0.5717992840649644, -0.31113198895064675, -0.053139489570020404, 0.08457429776929838, 0.042312280799225964, -0.16080620681373212, -0.4334539994861097, -0.6444180850385133, -0.6703760795873028, -0.44347611563864875, 0.017468112249197417, 0.6036958642368739, 1.1440710833204684, 1.4564763023824232, 1.407740306306262, 0.9629755654601958, 0.20725251873593814, -0.6698199665039614, -1.424862471213601, -1.8336655985609127, -1.7650030175644735, -1.2319567562484979, -0.40246221856032105, 0.4380851028098368, 0.9651078247784005, 0.913793907991898, 0.1704617405425633, -1.1720231817418707, -2.814753731882682, -4.314209690642207, -5.192069838652062, -5.065781209706449, -3.764218516887225, -1.3945520088334766, 1.6618976730822774, 4.828338231989312, 7.468523786526411, 9.046037507279406, 9.264716343744809, 8.15153779899488, 6.0576749680396125, 3.575050725986619, 1.388691130502079, 0.1030504914997421, 0.0881157644067323, 1.3861727900696232, 3.7038539205677488, 6.49096059094428, 9.084042512273813, 10.875441267585558, 11.462319674561295, 10.736756533880092, 8.895267280817814, 6.369011482095642, 3.697796338818113, 1.3855191277244698, -0.2220919856351655, -1.0052608855270493, -1.0689079814671587, -0.6787877375598396, -0.15940715773564243, 0.21226696025278266, 0.2845979686327612, 0.0591773279945237, -0.3351902051844996, -0.7087874327527883, -0.8916868886190227, -0.7998583141058562, -0.46439093021209193, -0.015486236033367521, 0.370854199367166, 0.5425234677145337, 0.43112615270246285, 0.07969705352376544, -0.3719992111996591, -0.7393786474611924, -0.8632748073284137, -0.6726559409584161], 'positive_zeros': ['2.48751199560862597927574099309842', '3.35105866870697096113825759464338', '4.48501486371627899762508645194209', '5.46749121815125087647215079018870', '6.31073677893459854367624477178985', '7.51816353992334769194030274165439', '7.972278849550520433553189262464643', '9.949997294660862029200046482617884', '10.75267166069739683783061521937713', '11.64335555161647091629812082858480'], 'prelabel': '2-405-135.92-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.20571845824518684, 'root_number': '0.7983274122571594 + 0.602223665126826*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.102859229123', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48751199560862597927574099310', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35105866870697096113825759464', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48501486371627899762508645194', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '135.92', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/r/a/197/15'], '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': '2-405-135.92-c1-0-15', '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': '2-405-135.92-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.10285922912259342, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48751199560862597927574099310', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3153296074308195461778107154659', 'Lhash_array': ['3153296074308195461778107154659'], 'label': '2-405-135.92-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/r/a/197/15'}