# lfunc_search downloaded from the LMFDB on 25 June 2026.
# Search link: https://www.lmfdb.org/L/2/1450/145.144/c1-0
# Query "{'degree': 2, 'conductor': 1450, 'spectral_label': 'c1-0'}" returned 357 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.



"2-1450-1.1-c1-0-0"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.42843226143094794011313825231	["ModularForm/GL2/Q/holomorphic/1450/2/a/q/1/1"]
"2-1450-1.1-c1-0-1"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.54320018563705730371232959243	["ModularForm/GL2/Q/holomorphic/1450/2/a/r/1/2"]
"2-1450-1.1-c1-0-10"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.05515224977993121655757897581	["ModularForm/GL2/Q/holomorphic/1450/2/a/o/1/1"]
"2-1450-1.1-c1-0-11"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.06972222138763499328748791956	["ModularForm/GL2/Q/holomorphic/1450/2/a/u/1/2"]
"2-1450-1.1-c1-0-12"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.18708198345144175297112436366	["ModularForm/GL2/Q/holomorphic/1450/2/a/t/1/2"]
"2-1450-1.1-c1-0-13"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.20961679332076836614305149339	["ModularForm/GL2/Q/holomorphic/1450/2/a/t/1/1"]
"2-1450-1.1-c1-0-14"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.21080665042461353631135414395	["ModularForm/GL2/Q/holomorphic/1450/2/a/s/1/2"]
"2-1450-1.1-c1-0-15"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.23703647210232309480960412774	["EllipticCurve/Q/1450/g", "ModularForm/GL2/Q/holomorphic/1450/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/g"]
"2-1450-1.1-c1-0-16"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.26228509726072334939018720444	["ModularForm/GL2/Q/holomorphic/1450/2/a/u/1/3"]
"2-1450-1.1-c1-0-17"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.26442527499546901267205251222	["ModularForm/GL2/Q/holomorphic/1450/2/a/k/1/2"]
"2-1450-1.1-c1-0-18"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.28610088248889993556666124540	["ModularForm/GL2/Q/holomorphic/1450/2/a/p/1/2"]
"2-1450-1.1-c1-0-19"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.29944131853051590179279684701	["ModularForm/GL2/Q/holomorphic/1450/2/a/p/1/1"]
"2-1450-1.1-c1-0-2"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.67492365452187855793059790386	["ModularForm/GL2/Q/holomorphic/1450/2/a/j/1/1"]
"2-1450-1.1-c1-0-20"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.33411306635085223504095250984	["ModularForm/GL2/Q/holomorphic/1450/2/a/q/1/3"]
"2-1450-1.1-c1-0-21"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.36305420618944472633869877336	["ModularForm/GL2/Q/holomorphic/1450/2/a/n/1/2"]
"2-1450-1.1-c1-0-22"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.38132525966072170317473643714	["ModularForm/GL2/Q/holomorphic/1450/2/a/r/1/3"]
"2-1450-1.1-c1-0-23"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.49224604013497417637561469512	["ModularForm/GL2/Q/holomorphic/1450/2/a/s/1/3"]
"2-1450-1.1-c1-0-24"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.53956994707840171168269220470	["ModularForm/GL2/Q/holomorphic/1450/2/a/o/1/2"]
"2-1450-1.1-c1-0-25"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.55650428064789173643083965606	["ModularForm/GL2/Q/holomorphic/1450/2/a/t/1/3"]
"2-1450-1.1-c1-0-26"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.58132477886192592368656951147	["ModularForm/GL2/Q/holomorphic/1450/2/a/u/1/5"]
"2-1450-1.1-c1-0-27"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.59467675660403654560302602943	["EllipticCurve/Q/1450/a", "ModularForm/GL2/Q/holomorphic/1450/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/a"]
"2-1450-1.1-c1-0-28"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.60699227236898800973358051930	["EllipticCurve/Q/1450/b", "ModularForm/GL2/Q/holomorphic/1450/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/b"]
"2-1450-1.1-c1-0-29"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.66121967923646700510412427159	["ModularForm/GL2/Q/holomorphic/1450/2/a/l/1/1"]
"2-1450-1.1-c1-0-3"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.75173783562438084876241770075	["ModularForm/GL2/Q/holomorphic/1450/2/a/n/1/1"]
"2-1450-1.1-c1-0-30"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.69465286739611247746851171454	["ModularForm/GL2/Q/holomorphic/1450/2/a/m/1/1"]
"2-1450-1.1-c1-0-31"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.70220586222286324033390168785	["ModularForm/GL2/Q/holomorphic/1450/2/a/t/1/4"]
"2-1450-1.1-c1-0-32"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.72442631092141105461475033401	["EllipticCurve/Q/1450/i", "ModularForm/GL2/Q/holomorphic/1450/2/a/i/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/i"]
"2-1450-1.1-c1-0-33"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.80291580566443065403518737055	["EllipticCurve/Q/1450/e", "ModularForm/GL2/Q/holomorphic/1450/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/e"]
"2-1450-1.1-c1-0-34"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.82349081547964929363993815727	["ModularForm/GL2/Q/holomorphic/1450/2/a/u/1/4"]
"2-1450-1.1-c1-0-35"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.85066707974485418871903777358	["ModularForm/GL2/Q/holomorphic/1450/2/a/p/1/3"]
"2-1450-1.1-c1-0-36"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.89442567285374802225669499718	["EllipticCurve/Q/1450/c", "ModularForm/GL2/Q/holomorphic/1450/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/c"]
"2-1450-1.1-c1-0-37"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.89656967211782839762177545446	["EllipticCurve/Q/1450/d", "ModularForm/GL2/Q/holomorphic/1450/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/d"]
"2-1450-1.1-c1-0-38"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.00166666035664867117236592387	["ModularForm/GL2/Q/holomorphic/1450/2/a/l/1/2"]
"2-1450-1.1-c1-0-39"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.23801014953161754739500105156	["EllipticCurve/Q/1450/f", "ModularForm/GL2/Q/holomorphic/1450/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/f"]
"2-1450-1.1-c1-0-4"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.78364951582886345058469964768	["ModularForm/GL2/Q/holomorphic/1450/2/a/s/1/1"]
"2-1450-1.1-c1-0-40"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.23955397953840556301918311516	["ModularForm/GL2/Q/holomorphic/1450/2/a/t/1/5"]
"2-1450-1.1-c1-0-41"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.33003810453632801774037550607	["EllipticCurve/Q/1450/h", "ModularForm/GL2/Q/holomorphic/1450/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/1450/2/a/h"]
"2-1450-1.1-c1-0-42"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.50474533305269970826657323526	["ModularForm/GL2/Q/holomorphic/1450/2/a/m/1/2"]
"2-1450-1.1-c1-0-5"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.817830881536822859916775847018	["ModularForm/GL2/Q/holomorphic/1450/2/a/q/1/2"]
"2-1450-1.1-c1-0-6"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.893087285673127174109390224422	["ModularForm/GL2/Q/holomorphic/1450/2/a/r/1/1"]
"2-1450-1.1-c1-0-7"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.949892798736348240233440998415	["ModularForm/GL2/Q/holomorphic/1450/2/a/u/1/1"]
"2-1450-1.1-c1-0-8"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.991612327571351067344683468349	["ModularForm/GL2/Q/holomorphic/1450/2/a/k/1/1"]
"2-1450-1.1-c1-0-9"	3.4026913308564533	11.57830829308566	2	1450	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.04877331184732252688522458754	["ModularForm/GL2/Q/holomorphic/1450/2/a/j/1/2"]
"2-1450-145.12-c1-0-0"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16491020631084854	0	0.02128709348361537053402276572	["ModularForm/GL2/Q/holomorphic/1450/2/j/j/157/3"]
"2-1450-145.12-c1-0-1"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.31110721727478735	0	0.03572234111187658924741191233	["ModularForm/GL2/Q/holomorphic/1450/2/j/g/157/4"]
"2-1450-145.12-c1-0-10"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.41609021814863617	0	0.58454857285756605840454134500	["ModularForm/GL2/Q/holomorphic/1450/2/j/e/157/2"]
"2-1450-145.12-c1-0-11"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3828630978863611	0	0.60051968199864698114877574691	["ModularForm/GL2/Q/holomorphic/1450/2/j/i/157/8"]
"2-1450-145.12-c1-0-12"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35969561414419887	0	0.66051560061058800049222990064	["ModularForm/GL2/Q/holomorphic/1450/2/j/i/157/5"]
"2-1450-145.12-c1-0-13"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21930505975340864	0	0.68473916334256611110191689870	["ModularForm/GL2/Q/holomorphic/1450/2/j/h/157/1"]
"2-1450-145.12-c1-0-14"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24568586249984067	0	0.76969279810885630732773059615	["ModularForm/GL2/Q/holomorphic/1450/2/j/g/157/1"]
"2-1450-145.12-c1-0-15"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09942210202426607	0	0.822486720350440221909435559728	["ModularForm/GL2/Q/holomorphic/1450/2/j/g/157/2"]
"2-1450-145.12-c1-0-16"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03955586567528641	0	0.858898089222250141502714429851	["ModularForm/GL2/Q/holomorphic/1450/2/j/j/157/7"]
"2-1450-145.12-c1-0-17"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06012798220621151	0	0.891850119131331367578258437500	["ModularForm/GL2/Q/holomorphic/1450/2/j/i/157/6"]
"2-1450-145.12-c1-0-18"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03441688580351431	0	0.948968304635949432730755680873	["ModularForm/GL2/Q/holomorphic/1450/2/j/i/157/1"]
"2-1450-145.12-c1-0-19"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.006130236426374581	0	1.01269795421174874476227650011	["ModularForm/GL2/Q/holomorphic/1450/2/j/f/157/3"]
"2-1450-145.12-c1-0-2"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2780808737817241	0	0.20749629221631450976913532410	["ModularForm/GL2/Q/holomorphic/1450/2/j/j/157/5"]
"2-1450-145.12-c1-0-20"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.14867402193333917	0	1.03999093383918903166549917810	["ModularForm/GL2/Q/holomorphic/1450/2/j/h/157/4"]
"2-1450-145.12-c1-0-21"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.25431413750015935	0	1.04454571122472518988732939593	["ModularForm/GL2/Q/holomorphic/1450/2/j/f/157/5"]
"2-1450-145.12-c1-0-22"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3534805035753282	0	1.07659036571164248410154985140	["ModularForm/GL2/Q/holomorphic/1450/2/j/j/157/2"]
"2-1450-145.12-c1-0-23"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.22703550979030315	0	1.09357019922522702853621584485	["ModularForm/GL2/Q/holomorphic/1450/2/j/i/157/10"]
"2-1450-145.12-c1-0-24"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2805550175076228	0	1.11907273236633721528759515011	["ModularForm/GL2/Q/holomorphic/1450/2/j/h/157/3"]
"2-1450-145.12-c1-0-25"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07314156854923311	0	1.14049161001351785224833178492	["ModularForm/GL2/Q/holomorphic/1450/2/j/j/157/9"]
"2-1450-145.12-c1-0-26"	3.4026913308564533	11.57830829308566	2	1450	"145.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.29109446012474566	0	1.20052554965313075416675894772	["ModularForm/GL2/Q/holomorphic/1450/2/j/i/157/2"]
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"2-1450-29.28-c1-0-7"	3.4026913308564533	11.57830829308566	2	1450	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.26447405896465476	0	0.46815423324071915231852133463	["ModularForm/GL2/Q/holomorphic/1450/2/c/e/1101/7"]
"2-1450-29.28-c1-0-8"	3.4026913308564533	11.57830829308566	2	1450	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.36049898243046286	0	0.49396020269499589632159789597	["ModularForm/GL2/Q/holomorphic/1450/2/c/f/1101/5"]
"2-1450-29.28-c1-0-9"	3.4026913308564533	11.57830829308566	2	1450	"29.28"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.15595968107605412	0	0.50554558264701842514551978090	["ModularForm/GL2/Q/holomorphic/1450/2/c/d/1101/1"]
"2-1450-5.4-c1-0-0"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	0.084140855267864550246695129046	["ModularForm/GL2/Q/holomorphic/1450/2/b/j/349/1"]
"2-1450-5.4-c1-0-1"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42620819117478337	0	0.22309634533403511021705049936	["ModularForm/GL2/Q/holomorphic/1450/2/b/g/349/2"]
"2-1450-5.4-c1-0-10"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17620819117478337	0	0.61108539328174925184052725970	["ModularForm/GL2/Q/holomorphic/1450/2/b/e/349/1"]
"2-1450-5.4-c1-0-11"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	0.61445261276570403090813048055	["ModularForm/GL2/Q/holomorphic/1450/2/b/j/349/2"]
"2-1450-5.4-c1-0-12"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	0.68223598987335013418230784781	["ModularForm/GL2/Q/holomorphic/1450/2/b/f/349/2"]
"2-1450-5.4-c1-0-13"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.32379180882521663	0	0.853153442287446562542221416101	["ModularForm/GL2/Q/holomorphic/1450/2/b/k/349/6"]
"2-1450-5.4-c1-0-14"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	0.882389806037690548075944819292	["ModularForm/GL2/Q/holomorphic/1450/2/b/d/349/1"]
"2-1450-5.4-c1-0-15"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42620819117478337	0	0.886800886204523991175676590830	["ModularForm/GL2/Q/holomorphic/1450/2/b/l/349/6"]
"2-1450-5.4-c1-0-16"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.32379180882521663	0	0.899860982485450110058481782859	["ModularForm/GL2/Q/holomorphic/1450/2/b/k/349/5"]
"2-1450-5.4-c1-0-17"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17620819117478337	0	0.912206623876116998074364764163	["ModularForm/GL2/Q/holomorphic/1450/2/b/c/349/2"]
"2-1450-5.4-c1-0-18"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	0.930832256054411639963939567755	["ModularForm/GL2/Q/holomorphic/1450/2/b/j/349/3"]
"2-1450-5.4-c1-0-19"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	0.968309749179320741965891951673	["ModularForm/GL2/Q/holomorphic/1450/2/b/h/349/3"]
"2-1450-5.4-c1-0-2"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42620819117478337	0	0.26659252343118219712424611478	["ModularForm/GL2/Q/holomorphic/1450/2/b/l/349/3"]
"2-1450-5.4-c1-0-20"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17620819117478337	0	1.06542709336287273711984559794	["ModularForm/GL2/Q/holomorphic/1450/2/b/c/349/1"]
"2-1450-5.4-c1-0-21"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	1.07662233890556900058323718633	["ModularForm/GL2/Q/holomorphic/1450/2/b/h/349/2"]
"2-1450-5.4-c1-0-22"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	1.12289180430134975203737351371	["ModularForm/GL2/Q/holomorphic/1450/2/b/f/349/1"]
"2-1450-5.4-c1-0-23"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32379180882521663	0	1.12722578318187148976148965090	["ModularForm/GL2/Q/holomorphic/1450/2/b/k/349/1"]
"2-1450-5.4-c1-0-24"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	1.19489318023799982831494508720	["ModularForm/GL2/Q/holomorphic/1450/2/b/j/349/4"]
"2-1450-5.4-c1-0-25"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	1.19532162781379419160640371541	["ModularForm/GL2/Q/holomorphic/1450/2/b/d/349/2"]
"2-1450-5.4-c1-0-26"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07379180882521663	0	1.22269177486588105291891970859	["ModularForm/GL2/Q/holomorphic/1450/2/b/h/349/4"]
"2-1450-5.4-c1-0-27"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	1.25250922116294137712448783863	["ModularForm/GL2/Q/holomorphic/1450/2/b/j/349/5"]
"2-1450-5.4-c1-0-28"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32379180882521663	0	1.39737108339364922699609699868	["ModularForm/GL2/Q/holomorphic/1450/2/b/k/349/2"]
"2-1450-5.4-c1-0-29"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17620819117478337	0	1.40673923246889987950456218687	["ModularForm/GL2/Q/holomorphic/1450/2/b/e/349/2"]
"2-1450-5.4-c1-0-3"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42620819117478337	0	0.31823205749069058925732344679	["ModularForm/GL2/Q/holomorphic/1450/2/b/l/349/5"]
"2-1450-5.4-c1-0-30"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42620819117478337	0	1.43337419471930793188795317925	["ModularForm/GL2/Q/holomorphic/1450/2/b/b/349/1"]
"2-1450-5.4-c1-0-31"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32379180882521663	0	1.44703607625611833275518825717	["ModularForm/GL2/Q/holomorphic/1450/2/b/k/349/3"]
"2-1450-5.4-c1-0-32"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17620819117478337	1	1.47852189572173631258395816757	["ModularForm/GL2/Q/holomorphic/1450/2/b/a/349/2"]
"2-1450-5.4-c1-0-33"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42620819117478337	0	1.50288029230666707008313457400	["ModularForm/GL2/Q/holomorphic/1450/2/b/l/349/1"]
"2-1450-5.4-c1-0-34"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	1.53314618546455915126020148881	["ModularForm/GL2/Q/holomorphic/1450/2/b/j/349/6"]
"2-1450-5.4-c1-0-35"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32379180882521663	0	1.62013578213626474716980281381	["ModularForm/GL2/Q/holomorphic/1450/2/b/i/349/3"]
"2-1450-5.4-c1-0-36"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42620819117478337	0	1.72043373027174672904428374783	["ModularForm/GL2/Q/holomorphic/1450/2/b/l/349/2"]
"2-1450-5.4-c1-0-37"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42620819117478337	0	1.76028422211911830902300797787	["ModularForm/GL2/Q/holomorphic/1450/2/b/g/349/1"]
"2-1450-5.4-c1-0-38"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42620819117478337	0	2.00474466670968750336781631909	["ModularForm/GL2/Q/holomorphic/1450/2/b/g/349/3"]
"2-1450-5.4-c1-0-39"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.32379180882521663	0	2.16217307240048436926906082695	["ModularForm/GL2/Q/holomorphic/1450/2/b/i/349/1"]
"2-1450-5.4-c1-0-4"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.32379180882521663	0	0.38654334699099946757716324355	["ModularForm/GL2/Q/holomorphic/1450/2/b/k/349/4"]
"2-1450-5.4-c1-0-40"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42620819117478337	0	2.40646029926149221049358069514	["ModularForm/GL2/Q/holomorphic/1450/2/b/l/349/4"]
"2-1450-5.4-c1-0-41"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17620819117478337	1	2.45875730195634571050949491854	["ModularForm/GL2/Q/holomorphic/1450/2/b/a/349/1"]
"2-1450-5.4-c1-0-5"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.32379180882521663	0	0.49700477550509189015436159945	["ModularForm/GL2/Q/holomorphic/1450/2/b/i/349/2"]
"2-1450-5.4-c1-0-6"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42620819117478337	0	0.50934430537415501617057669376	["ModularForm/GL2/Q/holomorphic/1450/2/b/b/349/2"]
"2-1450-5.4-c1-0-7"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32379180882521663	0	0.51444890166230282369496532720	["ModularForm/GL2/Q/holomorphic/1450/2/b/i/349/4"]
"2-1450-5.4-c1-0-8"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42620819117478337	0	0.54303561979431377975275011123	["ModularForm/GL2/Q/holomorphic/1450/2/b/g/349/4"]
"2-1450-5.4-c1-0-9"	3.4026913308564533	11.57830829308566	2	1450	"5.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07379180882521663	0	0.58035298103125132904273288199	["ModularForm/GL2/Q/holomorphic/1450/2/b/h/349/1"]


# 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).