# lfunc_search downloaded from the LMFDB on 02 May 2026.
# Search link: https://www.lmfdb.org/L/2/87/87.17
# Query "{'degree': 2, 'conductor': 87}" returned 14151 lfunc_searchs, sorted by root analytic conductor.

# Each entry in the following data list has the form:
#    [Label, $\alpha$, $A$, $d$, $N$, $\chi$, $\mu$, $\nu$, $w$, prim, arith, $\mathbb{Q}$, self-dual, $\operatorname{Arg}(\epsilon)$, $r$, First zero, Origin]
# For more details, see the definitions at the bottom of the file.



"2-87-87.86-c0-0-0"	0.20837143781975304	0.04341865609907121	2	87	"87.86"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	2.68368590772453422884570720998	["ModularForm/GL2/Q/holomorphic/87/1/d/a/86/1", "ModularForm/GL2/Q/holomorphic/87/1/d/a", "ArtinRepresentation/2.87.3t2.a.a", "ArtinRepresentation/2.87.3t2.a"]
"2-87-87.86-c0-0-1"	0.20837143781975304	0.04341865609907121	2	87	"87.86"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	3.53215773738360323132247593606	["ModularForm/GL2/Q/holomorphic/87/1/d/b/86/1", "ModularForm/GL2/Q/holomorphic/87/1/d/b", "ArtinRepresentation/2.87.6t3.b.a", "ArtinRepresentation/2.87.6t3.b"]
"2-87-1.1-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.52848030486985068602653439662	["ModularForm/GL2/Q/holomorphic/87/2/a/b/1/1"]
"2-87-1.1-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.20009654735353763797367045973	["ModularForm/GL2/Q/holomorphic/87/2/a/a/1/1"]
"2-87-1.1-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.73387108539709217330115468964	["ModularForm/GL2/Q/holomorphic/87/2/a/b/1/2"]
"2-87-1.1-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	3.30630143514452427642507298744	["ModularForm/GL2/Q/holomorphic/87/2/a/b/1/3"]
"2-87-1.1-c1-0-4"	0.8334857512790124	0.6946984975851397	2	87	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	3.33284344106940796359913592368	["ModularForm/GL2/Q/holomorphic/87/2/a/a/1/2"]
"2-87-29.13-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2415196836075747	0	1.80689044405937911001205286325	["ModularForm/GL2/Q/holomorphic/87/2/i/a/13/1"]
"2-87-29.13-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.02431099297058303	0	2.30387443474146191356411231388	["ModularForm/GL2/Q/holomorphic/87/2/i/a/13/2"]
"2-87-29.13-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1848901509510199	0	3.30280658399391151816377016859	["ModularForm/GL2/Q/holomorphic/87/2/i/a/13/3"]
"2-87-29.13-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.30344383944481546	0	4.03184616537391272655102077259	["ModularForm/GL2/Q/holomorphic/87/2/i/a/13/4"]
"2-87-29.16-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.31947766185930704	0	0.33663499338349850951616216263	["ModularForm/GL2/Q/holomorphic/87/2/g/b/16/1"]
"2-87-29.16-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.16182342771676841	0	1.91455088683630914974446783842	["ModularForm/GL2/Q/holomorphic/87/2/g/a/16/1"]
"2-87-29.16-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.048361618425384875	0	1.93482905611807858650630086516	["ModularForm/GL2/Q/holomorphic/87/2/g/b/16/2"]
"2-87-29.16-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1376339710411093	0	2.54215679615060119698579005786	["ModularForm/GL2/Q/holomorphic/87/2/g/b/16/3"]
"2-87-29.16-c1-0-4"	0.8334857512790124	0.6946984975851397	2	87	"29.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03182533609900125	0	2.93429556732389874933229058579	["ModularForm/GL2/Q/holomorphic/87/2/g/a/16/3"]
"2-87-29.16-c1-0-5"	0.8334857512790124	0.6946984975851397	2	87	"29.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3209402221396724	0	3.33691846232215542560157743956	["ModularForm/GL2/Q/holomorphic/87/2/g/a/16/2"]
"2-87-29.20-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3209402221396724	0	1.03469816379415901820362250377	["ModularForm/GL2/Q/holomorphic/87/2/g/a/49/2"]
"2-87-29.20-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16182342771676841	0	1.71581533436500632589262428423	["ModularForm/GL2/Q/holomorphic/87/2/g/a/49/1"]
"2-87-29.20-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.048361618425384875	0	1.80351932704876151773841839122	["ModularForm/GL2/Q/holomorphic/87/2/g/b/49/2"]
"2-87-29.20-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03182533609900125	0	2.38999204025373528884186425916	["ModularForm/GL2/Q/holomorphic/87/2/g/a/49/3"]
"2-87-29.20-c1-0-4"	0.8334857512790124	0.6946984975851397	2	87	"29.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.31947766185930704	0	2.69930477157737553204957959417	["ModularForm/GL2/Q/holomorphic/87/2/g/b/49/1"]
"2-87-29.20-c1-0-5"	0.8334857512790124	0.6946984975851397	2	87	"29.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1376339710411093	0	3.66740160253107730561586249301	["ModularForm/GL2/Q/holomorphic/87/2/g/b/49/3"]
"2-87-29.22-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.198663737519503	0	1.39822617267249514659316740078	["ModularForm/GL2/Q/holomorphic/87/2/i/a/22/2"]
"2-87-29.22-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20676675792586038	0	2.72446716534536972901693521289	["ModularForm/GL2/Q/holomorphic/87/2/i/a/22/1"]
"2-87-29.22-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.011614895392857313	0	2.99387542425803434543901231548	["ModularForm/GL2/Q/holomorphic/87/2/i/a/22/4"]
"2-87-29.22-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07413984105064705	0	3.21812271479302537499477625860	["ModularForm/GL2/Q/holomorphic/87/2/i/a/22/3"]
"2-87-29.23-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.23"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4217620479497884	0	0.840602669496891280351210769258	["ModularForm/GL2/Q/holomorphic/87/2/g/b/52/1"]
"2-87-29.23-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.23"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2890881962645032	0	1.40518222025409769858113908078	["ModularForm/GL2/Q/holomorphic/87/2/g/a/52/1"]
"2-87-29.23-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.23"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17126020523539132	0	1.59293336240047390911440003872	["ModularForm/GL2/Q/holomorphic/87/2/g/a/52/2"]
"2-87-29.23-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.23"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.01642868544374206	0	2.42845099258208896765894669285	["ModularForm/GL2/Q/holomorphic/87/2/g/b/52/2"]
"2-87-29.23-c1-0-4"	0.8334857512790124	0.6946984975851397	2	87	"29.23"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20302886285088081	0	3.64903650112333742707224865203	["ModularForm/GL2/Q/holomorphic/87/2/g/b/52/3"]
"2-87-29.23-c1-0-5"	0.8334857512790124	0.6946984975851397	2	87	"29.23"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2116522871623411	0	3.75731764435968774470892816384	["ModularForm/GL2/Q/holomorphic/87/2/g/a/52/3"]
"2-87-29.24-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.01642868544374206	0	2.32574764180977286338758692199	["ModularForm/GL2/Q/holomorphic/87/2/g/b/82/2"]
"2-87-29.24-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.20302886285088081	0	2.42521494632738723457307893262	["ModularForm/GL2/Q/holomorphic/87/2/g/b/82/3"]
"2-87-29.24-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2116522871623411	0	2.54866113577040171331492330518	["ModularForm/GL2/Q/holomorphic/87/2/g/a/82/3"]
"2-87-29.24-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2890881962645032	0	3.11329208469633293741539300682	["ModularForm/GL2/Q/holomorphic/87/2/g/a/82/1"]
"2-87-29.24-c1-0-4"	0.8334857512790124	0.6946984975851397	2	87	"29.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4217620479497884	0	3.18949509739808649516602472934	["ModularForm/GL2/Q/holomorphic/87/2/g/b/82/1"]
"2-87-29.24-c1-0-5"	0.8334857512790124	0.6946984975851397	2	87	"29.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17126020523539132	0	3.60024090728967690911123052478	["ModularForm/GL2/Q/holomorphic/87/2/g/a/82/2"]
"2-87-29.25-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.47790902555928166	0	0.938251382334138438353262608340	["ModularForm/GL2/Q/holomorphic/87/2/g/a/25/1"]
"2-87-29.25-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.24406311696228292	0	1.91113329301265944928779355277	["ModularForm/GL2/Q/holomorphic/87/2/g/b/25/1"]
"2-87-29.25-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07373465139043911	0	1.92334256256028243820663637251	["ModularForm/GL2/Q/holomorphic/87/2/g/a/25/2"]
"2-87-29.25-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10912698461971578	0	2.86944808053454088208169353824	["ModularForm/GL2/Q/holomorphic/87/2/g/b/25/2"]
"2-87-29.25-c1-0-4"	0.8334857512790124	0.6946984975851397	2	87	"29.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3325405255381621	0	3.66412296839382104671714134181	["ModularForm/GL2/Q/holomorphic/87/2/g/a/25/3"]
"2-87-29.25-c1-0-5"	0.8334857512790124	0.6946984975851397	2	87	"29.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3413816471624331	0	4.27790468720207800230934456506	["ModularForm/GL2/Q/holomorphic/87/2/g/b/25/3"]
"2-87-29.28-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.15595968107605412	0	2.00718633194260351255256283593	["ModularForm/GL2/Q/holomorphic/87/2/c/a/28/3"]
"2-87-29.28-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.15595968107605412	0	2.28633013347696907907297447780	["ModularForm/GL2/Q/holomorphic/87/2/c/a/28/4"]
"2-87-29.28-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.15595968107605412	0	2.65736448253604769807169716639	["ModularForm/GL2/Q/holomorphic/87/2/c/a/28/1"]
"2-87-29.28-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.15595968107605412	0	2.97038936806824430773598937284	["ModularForm/GL2/Q/holomorphic/87/2/c/a/28/2"]
"2-87-29.4-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.20676675792586038	0	1.08084547614026677837850972094	["ModularForm/GL2/Q/holomorphic/87/2/i/a/4/1"]
"2-87-29.4-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07413984105064705	0	2.59533023758488096287048152454	["ModularForm/GL2/Q/holomorphic/87/2/i/a/4/3"]
"2-87-29.4-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.198663737519503	0	3.11036998320454956327061987260	["ModularForm/GL2/Q/holomorphic/87/2/i/a/4/2"]
"2-87-29.4-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.011614895392857313	0	3.18677978205172165909607287098	["ModularForm/GL2/Q/holomorphic/87/2/i/a/4/4"]
"2-87-29.5-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21767486006710626	0	1.31335840720314956086786272610	["ModularForm/GL2/Q/holomorphic/87/2/i/a/34/3"]
"2-87-29.5-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.24440938373554014	0	1.53171059161865618191000690707	["ModularForm/GL2/Q/holomorphic/87/2/i/a/34/2"]
"2-87-29.5-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1708266266282152	0	2.32208091884222823149020789333	["ModularForm/GL2/Q/holomorphic/87/2/i/a/34/1"]
"2-87-29.5-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1139900742654492	0	3.36303401425244278562343086529	["ModularForm/GL2/Q/holomorphic/87/2/i/a/34/4"]
"2-87-29.6-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1708266266282152	0	0.50178101746188341919141276171	["ModularForm/GL2/Q/holomorphic/87/2/i/a/64/1"]
"2-87-29.6-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24440938373554014	0	2.48671069793583341086589471620	["ModularForm/GL2/Q/holomorphic/87/2/i/a/64/2"]
"2-87-29.6-c1-0-2"	0.8334857512790124	0.6946984975851397	2	87	"29.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1139900742654492	0	2.52909503681193402078837800486	["ModularForm/GL2/Q/holomorphic/87/2/i/a/64/4"]
"2-87-29.6-c1-0-3"	0.8334857512790124	0.6946984975851397	2	87	"29.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21767486006710626	0	2.99194967560821617722478232466	["ModularForm/GL2/Q/holomorphic/87/2/i/a/64/3"]
"2-87-29.7-c1-0-0"	0.8334857512790124	0.6946984975851397	2	87	"29.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3325405255381621	0	1.62846935687453105587633689092	["ModularForm/GL2/Q/holomorphic/87/2/g/a/7/3"]
"2-87-29.7-c1-0-1"	0.8334857512790124	0.6946984975851397	2	87	"29.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3413816471624331	0	2.09730961705240444748345141327	["ModularForm/GL2/Q/holomorphic/87/2/g/b/7/3"]
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"2-87-29.28-c19-0-64"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.2772920279688801	0	0.817333207195693836207697339547	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/5"]
"2-87-29.28-c19-0-65"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.015202506744574008	0	0.825982046447304741205506125237	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/74"]
"2-87-29.28-c19-0-66"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.26361835865729655	0	0.905004958716120023382090208249	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/26"]
"2-87-29.28-c19-0-67"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.09767868721674997	0	0.917436813505766492498710758145	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/51"]
"2-87-29.28-c19-0-68"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.038312604976053946	0	0.950612928184454367082354091213	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/67"]
"2-87-29.28-c19-0-69"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.09381269165614063	0	1.02461555167487392586857367343	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/78"]
"2-87-29.28-c19-0-7"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.46856997901905273	0	0.091424059920228434609625039960	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/43"]
"2-87-29.28-c19-0-70"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.4700212092116673	0	1.03948642709837968012011036759	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/12"]
"2-87-29.28-c19-0-71"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.3763041766920374	0	1.11012271555435283599928508162	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/35"]
"2-87-29.28-c19-0-72"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.3308513803665633	0	1.12162026827564073336538918657	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/58"]
"2-87-29.28-c19-0-73"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.1503793328401689	0	1.13134600491573230265611471796	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/66"]
"2-87-29.28-c19-0-74"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.13085588103845047	0	1.14671094643725769421125103196	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/44"]
"2-87-29.28-c19-0-75"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.2892901291742672	0	1.16267275212658910750066214049	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/9"]
"2-87-29.28-c19-0-76"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.07866257412111063	0	1.17152948705638631505937614151	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/95"]
"2-87-29.28-c19-0-77"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.3108065902005091	0	1.19044814196046970906968096224	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/68"]
"2-87-29.28-c19-0-78"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.17885511910148955	0	1.20278703007477008465411316650	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/60"]
"2-87-29.28-c19-0-79"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.3245407647615733	0	1.23062456658138208868040997771	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/65"]
"2-87-29.28-c19-0-8"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.08615008474468337	0	0.093699848058577926058451999384	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/13"]
"2-87-29.28-c19-0-80"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.48318391920257714	0	1.24116645354851252937421825282	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/28"]
"2-87-29.28-c19-0-81"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.038463485039454695	0	1.24680415055414234854221520536	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/82"]
"2-87-29.28-c19-0-82"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.13256116713811503	0	1.28274001767834173203188877971	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/21"]
"2-87-29.28-c19-0-83"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.2502474769715855	0	1.30164416883403404873106462719	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/34"]
"2-87-29.28-c19-0-84"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.3623152111564419	0	1.32197384968072207637912454891	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/33"]
"2-87-29.28-c19-0-85"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.40586625785336006	0	1.33980832259557831499028987735	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/41"]
"2-87-29.28-c19-0-86"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.19962202651356664	0	1.38258696774826586979219455874	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/25"]
"2-87-29.28-c19-0-87"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.4801134420460349	0	1.38871902309399749421910590036	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/42"]
"2-87-29.28-c19-0-88"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.23330029315255285	0	1.41246637376077632838496160880	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/48"]
"2-87-29.28-c19-0-89"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.35293960498655663	0	1.45318807684971791806939759742	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/90"]
"2-87-29.28-c19-0-9"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.1768631337884862	0	0.10047917360941663680209151524	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/38"]
"2-87-29.28-c19-0-90"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.3183033588082336	0	1.46484543531561146650042238589	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/47"]
"2-87-29.28-c19-0-91"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.46856997901905273	0	1.55297514449424182268741208968	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/54"]
"2-87-29.28-c19-0-92"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.4151036147801052	0	1.55388576922069379320399280711	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/20"]
"2-87-29.28-c19-0-93"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.22530058191780192	0	1.65447591119280365983250854604	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/14"]
"2-87-29.28-c19-0-94"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	-0.07993356212912152	0	1.80741723724756171744752933603	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/22"]
"2-87-29.28-c19-0-95"	14.109235486164772	199.07052600405126	2	87	"29.28"	[]	[[9.5, 0.0]]	19	true	true	false	false	0.12085895322783488	0	1.86182646617296198735107617896	["ModularForm/GL2/Q/holomorphic/87/20/c/a/28/16"]


# Label --
#    Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where

#     * $d$ is the degree of $L$.
#     * $N$ is the conductor of $L$.  When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions.
#     * q.k is the label of the primitive Dirichlet character from which the central character is induced.
#     * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation.
#     * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label.


#$\alpha$ (root_analytic_conductor) --
#    If $d$ is the degree of the L-function $L(s)$, the **root analytic conductor** $\alpha$ of $L$ is the $d$th root of the analytic conductor of $L$.  It plays a role analogous to the root discriminant for number fields.


#$A$ (analytic_conductor) --
#    The **analytic conductor** of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number
#    \[
#    A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N.
#    \]



#$d$ (degree) --
#    The **degree** of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]

#    The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor.



#$N$ (conductor) --
#    The **conductor** of an L-function is the integer $N$  occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]


#    The conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function
#     associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$.

#    In the literature, the word _level_ is sometimes used instead of _conductor_.


#$\chi$ (central_character) --
#    An L-function has an Euler product of the form
#    $L(s) = \prod_p L_p(p^{-s})^{-1}$
#    where $L_p(x) = 1 + a_p x + \ldots + (-1)^d \chi(p) x^d$. The character $\chi$ is a Dirichlet character mod $N$ and is called **central character** of the L-function.
#    Here, $N$ is the conductor of $L$.


#$\mu$ (mus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$\nu$ (nus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$w$ (motivic_weight) --
#    The **motivic weight** (or **arithmetic weight**) of an arithmetic L-function with analytic normalization $L_{an}(s)=\sum_{n=1}^\infty a_nn^{-s}$ is the least nonnegative integer $w$ for which $a_nn^{w/2}$ is an algebraic integer for all $n\ge 1$.

#    If the L-function arises from a motive, then the weight of the motive has the
#    same parity as the motivic weight of the L-function, but the weight of the motive
#    could be larger.  This apparent discrepancy comes from the fact that a Tate twist
#    increases the weight of the motive.  This corresponds to the change of variables
#    $s \mapsto s + j$ in the L-function of the motive.


#prim (primitive) --
#    An L-function is <b>primitive</b> if it cannot be written as a product of nontrivial L-functions.  The "trivial L-function" is the constant function $1$.


#arith (algebraic) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} a_n n^{-s}$  is called **arithmetic** if its Dirichlet coefficients $a_n$ are algebraic numbers.


#$\mathbb{Q}$ (rational) --
#    A **rational** L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes
#    \[
#    L(s)=\prod_pL_p(p^{-s})^{-1}
#    \]
#    with $L_p\in \Z[T]$.


#self-dual (self_dual) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$ is called **self-dual** if its Dirichlet coefficients $a_n$ are real.


#$\operatorname{Arg}(\epsilon)$ (root_angle) --
#    The **root angle** of an L-function is the argument of its root number, as a real number $\alpha$ with $-0.5 < \alpha \le 0.5$.


#$r$ (order_of_vanishing) --
#    The **analytic rank** of an L-function $L(s)$ is its order of vanishing at its central point.

#    When the analytic rank $r$ is positive, the value listed in the LMFDB is typically an upper bound that is believed to be tight (in the sense that there are known to be $r$ zeroes located very near to the central point).


#First zero (z1) --
#    The **zeros** of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$.

#    Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization).

#    The **lowest zero** of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number.


#Origin (instance_urls) --
#    L-functions arise from many different sources. Already in degree 2 we have examples of
#    L-functions associated with holomorphic cusp forms, with Maass forms, with elliptic curves, with characters of number fields (Hecke characters), and with 2-dimensional representations of the Galois group of a number field (Artin L-functions).

#    Sometimes an L-function may arise from more than one source. For example, the L-functions associated with elliptic curves are also associated with weight 2 cusp forms. A goal of the Langlands program ostensibly is to prove that any degree $d$ L-function is associated with an automorphic form on $\mathrm{GL}(d)$. Because of this representation theoretic genesis, one can associate an L-function not only to an automorphic representation but also to symmetric powers, or exterior powers of that representation, or to the tensor product of two representations (the Rankin-Selberg product of two L-functions).