# lfunc_search downloaded from the LMFDB on 25 May 2026.
# Search link: https://www.lmfdb.org/L/2/675/5.4
# Query "{'degree': 2, 'conductor': 675}" returned 12296 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.



"2-675-15.14-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"15.14"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	0.903546389881432883975382087892	["ModularForm/GL2/Q/holomorphic/675/1/d/a/674/2"]
"2-675-15.14-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"15.14"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	1.84901785243619914988913026027	["ModularForm/GL2/Q/holomorphic/675/1/d/a/674/1"]
"2-675-3.2-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"3.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.25	0	1.38214971959858102173434535003	["ModularForm/GL2/Q/holomorphic/675/1/c/c/26/2", "ArtinRepresentation/2.675.12t11.a.a"]
"2-675-3.2-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"3.2"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.69075851728213846931389449038	["ModularForm/GL2/Q/holomorphic/675/1/c/a/26/1", "ModularForm/GL2/Q/holomorphic/675/1/c/a", "ArtinRepresentation/2.675.3t2.a.a", "ArtinRepresentation/2.675.3t2.a"]
"2-675-3.2-c0-0-2"	0.5804040691856637	0.3368688835272766	2	675	"3.2"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.86024946456028974217947303823	["ModularForm/GL2/Q/holomorphic/675/1/c/b/26/1", "ModularForm/GL2/Q/holomorphic/675/1/c/b", "ArtinRepresentation/2.675.6t3.a.a", "ArtinRepresentation/2.675.6t3.a"]
"2-675-3.2-c0-0-3"	0.5804040691856637	0.3368688835272766	2	675	"3.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.25	0	1.99624806850556960155525512998	["ModularForm/GL2/Q/holomorphic/675/1/c/c/26/1", "ArtinRepresentation/2.675.12t11.a.b"]
"2-675-5.2-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"5.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.21310409558739168	0	1.26363823024206779536863519643	["ModularForm/GL2/Q/holomorphic/675/1/g/a/82/1"]
"2-675-5.2-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"5.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.052919458624852055	0	1.68777958372204334564742477948	["ModularForm/GL2/Q/holomorphic/675/1/g/b/82/2"]
"2-675-5.2-c0-0-2"	0.5804040691856637	0.3368688835272766	2	675	"5.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2868959044126083	0	1.71008018474612900358493498695	["ModularForm/GL2/Q/holomorphic/675/1/g/a/82/2"]
"2-675-5.2-c0-0-3"	0.5804040691856637	0.3368688835272766	2	675	"5.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2708723502003646	0	2.42443957780060486738654765509	["ModularForm/GL2/Q/holomorphic/675/1/g/b/82/1"]
"2-675-5.3-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"5.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2708723502003646	0	0.871844952090844348394648054402	["ModularForm/GL2/Q/holomorphic/675/1/g/b/568/1"]
"2-675-5.3-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"5.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.21310409558739168	0	1.15099970459919358609853587893	["ModularForm/GL2/Q/holomorphic/675/1/g/a/568/1"]
"2-675-5.3-c0-0-2"	0.5804040691856637	0.3368688835272766	2	675	"5.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.052919458624852055	0	1.59296781081227783987814082373	["ModularForm/GL2/Q/holomorphic/675/1/g/b/568/2"]
"2-675-5.3-c0-0-3"	0.5804040691856637	0.3368688835272766	2	675	"5.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2868959044126083	0	2.57668953878948128329649032184	["ModularForm/GL2/Q/holomorphic/675/1/g/a/568/2"]
"2-675-75.11-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"75.11"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.42000000000000004	0	1.10082940758913253780550383607	["ModularForm/GL2/Q/holomorphic/675/1/o/a/161/2"]
"2-675-75.11-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"75.11"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.42000000000000004	0	2.33864225975531369149378517869	["ModularForm/GL2/Q/holomorphic/675/1/o/a/161/1"]
"2-675-75.41-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"75.41"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.42000000000000004	0	0.45157078934495752557546487299	["ModularForm/GL2/Q/holomorphic/675/1/o/a/566/1"]
"2-675-75.41-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"75.41"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.42000000000000004	0	2.99529557305337859936780823234	["ModularForm/GL2/Q/holomorphic/675/1/o/a/566/2"]
"2-675-75.56-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"75.56"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.060000000000000005	0	1.15042548397837421120614910556	["ModularForm/GL2/Q/holomorphic/675/1/o/a/431/1"]
"2-675-75.56-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"75.56"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.060000000000000005	0	1.50814893227143101926670875839	["ModularForm/GL2/Q/holomorphic/675/1/o/a/431/2"]
"2-675-75.71-c0-0-0"	0.5804040691856637	0.3368688835272766	2	675	"75.71"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.060000000000000005	0	1.21768196221950467882785111316	["ModularForm/GL2/Q/holomorphic/675/1/o/a/296/1"]
"2-675-75.71-c0-0-1"	0.5804040691856637	0.3368688835272766	2	675	"75.71"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.060000000000000005	0	2.06740151735685846216634824003	["ModularForm/GL2/Q/holomorphic/675/1/o/a/296/2"]
"2-675-1.1-c1-0-0"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.73148826163501750075410840339	["ModularForm/GL2/Q/holomorphic/675/2/a/p/1/1"]
"2-675-1.1-c1-0-1"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.74637271727844988252325148508	["ModularForm/GL2/Q/holomorphic/675/2/a/n/1/1"]
"2-675-1.1-c1-0-10"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.41968084240141269635968831838	["ModularForm/GL2/Q/holomorphic/675/2/a/m/1/2"]
"2-675-1.1-c1-0-11"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.63478332918835121438091684468	["EllipticCurve/Q/675/i", "ModularForm/GL2/Q/holomorphic/675/2/a/i/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/i"]
"2-675-1.1-c1-0-12"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.66344828877219173145922126766	["ModularForm/GL2/Q/holomorphic/675/2/a/l/1/1"]
"2-675-1.1-c1-0-13"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.69513718397245009221846235026	["ModularForm/GL2/Q/holomorphic/675/2/a/j/1/1"]
"2-675-1.1-c1-0-14"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.74952470977637072478622222235	["ModularForm/GL2/Q/holomorphic/675/2/a/k/1/1"]
"2-675-1.1-c1-0-15"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.76125584480235740498550240381	["EllipticCurve/Q/675/b", "ModularForm/GL2/Q/holomorphic/675/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/b"]
"2-675-1.1-c1-0-16"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.80480433633238358010960385504	["ModularForm/GL2/Q/holomorphic/675/2/a/p/1/2"]
"2-675-1.1-c1-0-17"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.87220090675730271137255508551	["ModularForm/GL2/Q/holomorphic/675/2/a/n/1/2"]
"2-675-1.1-c1-0-18"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.87757341903363932694788708409	["ModularForm/GL2/Q/holomorphic/675/2/a/j/1/2"]
"2-675-1.1-c1-0-19"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.92860018740434397351518724248	["ModularForm/GL2/Q/holomorphic/675/2/a/q/1/2"]
"2-675-1.1-c1-0-2"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.895025331879932514186462794519	["EllipticCurve/Q/675/d", "ModularForm/GL2/Q/holomorphic/675/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/d"]
"2-675-1.1-c1-0-20"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.99536449833225922120154017244	["EllipticCurve/Q/675/e", "ModularForm/GL2/Q/holomorphic/675/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/e"]
"2-675-1.1-c1-0-21"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.04797652867607365880276607097	["ModularForm/GL2/Q/holomorphic/675/2/a/o/1/2"]
"2-675-1.1-c1-0-22"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.40058573044279568120832059087	["EllipticCurve/Q/675/g", "ModularForm/GL2/Q/holomorphic/675/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/g"]
"2-675-1.1-c1-0-23"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.48120253506961143226195840223	["ModularForm/GL2/Q/holomorphic/675/2/a/k/1/2"]
"2-675-1.1-c1-0-24"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.66331458192668103061953617832	["ModularForm/GL2/Q/holomorphic/675/2/a/l/1/2"]
"2-675-1.1-c1-0-3"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.929391360715818373685365786299	["EllipticCurve/Q/675/c", "ModularForm/GL2/Q/holomorphic/675/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/c"]
"2-675-1.1-c1-0-4"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.991594080094343570012066853212	["ModularForm/GL2/Q/holomorphic/675/2/a/m/1/1"]
"2-675-1.1-c1-0-5"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.05639703435404280964920717849	["ModularForm/GL2/Q/holomorphic/675/2/a/q/1/1"]
"2-675-1.1-c1-0-6"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.06897770472745757504364106971	["EllipticCurve/Q/675/a", "ModularForm/GL2/Q/holomorphic/675/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/a"]
"2-675-1.1-c1-0-7"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.09487630533171000851650484764	["EllipticCurve/Q/675/f", "ModularForm/GL2/Q/holomorphic/675/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/f"]
"2-675-1.1-c1-0-8"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.10101715408560923160360372720	["ModularForm/GL2/Q/holomorphic/675/2/a/o/1/1"]
"2-675-1.1-c1-0-9"	2.321616276742655	5.389902136436429	2	675	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.22726947298899977457345127093	["EllipticCurve/Q/675/h", "ModularForm/GL2/Q/holomorphic/675/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/675/2/a/h"]
"2-675-135.113-c1-0-0"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2517981354126189	0	0.19700216332776654457048217258	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/13"]
"2-675-135.113-c1-0-1"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.33250255644393123	0	0.28258367036834946814043110916	["ModularForm/GL2/Q/holomorphic/675/2/ba/a/518/5"]
"2-675-135.113-c1-0-10"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2067522681789127	0	0.52267022979094782981175291326	["ModularForm/GL2/Q/holomorphic/675/2/ba/b/518/4"]
"2-675-135.113-c1-0-11"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16385164204620972	0	0.52501038106097029793801949215	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/4"]
"2-675-135.113-c1-0-12"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.28845725259189525	0	0.60753266693207607905642412919	["ModularForm/GL2/Q/holomorphic/675/2/ba/a/518/7"]
"2-675-135.113-c1-0-13"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2729663530191927	0	0.64012852341887855037726934363	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/11"]
"2-675-135.113-c1-0-14"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.02180919006247798	0	0.71374878113671116360959835575	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/1"]
"2-675-135.113-c1-0-15"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.089382392829459	0	0.74838078124044680452125738788	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/15"]
"2-675-135.113-c1-0-16"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.16769497762740934	0	0.833903906432005224024446614265	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/5"]
"2-675-135.113-c1-0-17"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2624856028311749	0	1.01586133952158299709972284402	["ModularForm/GL2/Q/holomorphic/675/2/ba/b/518/12"]
"2-675-135.113-c1-0-18"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.01844084088179097	0	1.07768485989707330481403823460	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/6"]
"2-675-135.113-c1-0-19"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.23320882028441778	0	1.08881427685445848459028954185	["ModularForm/GL2/Q/holomorphic/675/2/ba/b/518/6"]
"2-675-135.113-c1-0-2"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3057652594482775	0	0.28841120208746071581239749648	["ModularForm/GL2/Q/holomorphic/675/2/ba/c/518/2"]
"2-675-135.113-c1-0-20"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.009014898201342913	0	1.10509874014072309856766851166	["ModularForm/GL2/Q/holomorphic/675/2/ba/b/518/7"]
"2-675-135.113-c1-0-21"	2.321616276742655	5.389902136436429	2	675	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21154274740810478	0	1.12037495610579000663777122904	["ModularForm/GL2/Q/holomorphic/675/2/ba/a/518/6"]
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"2-675-1.1-c5-0-50"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.821641920376072622259761366679	["ModularForm/GL2/Q/holomorphic/675/6/a/ba/1/6"]
"2-675-1.1-c5-0-51"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.0	0	0.843097843074319443764515977568	["ModularForm/GL2/Q/holomorphic/675/6/a/c/1/1", "ModularForm/GL2/Q/holomorphic/675/6/a/c"]
"2-675-1.1-c5-0-52"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.879598246509887990720727681450	["ModularForm/GL2/Q/holomorphic/675/6/a/s/1/1"]
"2-675-1.1-c5-0-53"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.879808760893520422497749562922	["ModularForm/GL2/Q/holomorphic/675/6/a/j/1/1"]
"2-675-1.1-c5-0-54"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.890450395319697279130281963355	["ModularForm/GL2/Q/holomorphic/675/6/a/bc/1/1"]
"2-675-1.1-c5-0-55"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.892321594387123528895436956008	["ModularForm/GL2/Q/holomorphic/675/6/a/y/1/1"]
"2-675-1.1-c5-0-56"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.903832445542918091758835865057	["ModularForm/GL2/Q/holomorphic/675/6/a/bd/1/5"]
"2-675-1.1-c5-0-57"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.921963426590431733914526414169	["ModularForm/GL2/Q/holomorphic/675/6/a/bd/1/9"]
"2-675-1.1-c5-0-58"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.934786466757824121086081503216	["ModularForm/GL2/Q/holomorphic/675/6/a/w/1/3"]
"2-675-1.1-c5-0-59"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.935623297233826059606270844344	["ModularForm/GL2/Q/holomorphic/675/6/a/y/1/3"]
"2-675-1.1-c5-0-6"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.19332510770816830293407231263	["ModularForm/GL2/Q/holomorphic/675/6/a/bd/1/4"]
"2-675-1.1-c5-0-60"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.954523705915611645058941328628	["ModularForm/GL2/Q/holomorphic/675/6/a/bc/1/5"]
"2-675-1.1-c5-0-61"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.970565989179909657421023631823	["ModularForm/GL2/Q/holomorphic/675/6/a/bb/1/6"]
"2-675-1.1-c5-0-62"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.979920740474402611087503820194	["ModularForm/GL2/Q/holomorphic/675/6/a/x/1/3"]
"2-675-1.1-c5-0-63"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.986743644549489868149310520479	["ModularForm/GL2/Q/holomorphic/675/6/a/v/1/2"]
"2-675-1.1-c5-0-64"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.991714738727098136541455004346	["ModularForm/GL2/Q/holomorphic/675/6/a/q/1/2"]
"2-675-1.1-c5-0-65"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.5	1	0.992121322448337735939863647066	["ModularForm/GL2/Q/holomorphic/675/6/a/b/1/1", "ModularForm/GL2/Q/holomorphic/675/6/a/b"]
"2-675-1.1-c5-0-66"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.994470500311715688515723759483	["ModularForm/GL2/Q/holomorphic/675/6/a/bb/1/7"]
"2-675-1.1-c5-0-67"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.01856816054968560824076330992	["ModularForm/GL2/Q/holomorphic/675/6/a/v/1/4"]
"2-675-1.1-c5-0-68"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.03528420140094694400972238818	["ModularForm/GL2/Q/holomorphic/675/6/a/p/1/4"]
"2-675-1.1-c5-0-69"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.03604999795944904961593514011	["ModularForm/GL2/Q/holomorphic/675/6/a/r/1/1"]
"2-675-1.1-c5-0-7"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.26606777794054089950025895887	["ModularForm/GL2/Q/holomorphic/675/6/a/u/1/5"]
"2-675-1.1-c5-0-70"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.05775218951206121475334801915	["ModularForm/GL2/Q/holomorphic/675/6/a/z/1/8"]
"2-675-1.1-c5-0-71"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.05795430390577628419266796355	["ModularForm/GL2/Q/holomorphic/675/6/a/t/1/4"]
"2-675-1.1-c5-0-72"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.06517438709029059153817581420	["ModularForm/GL2/Q/holomorphic/675/6/a/z/1/7"]
"2-675-1.1-c5-0-73"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.07183599102881256391834826677	["ModularForm/GL2/Q/holomorphic/675/6/a/bb/1/8"]
"2-675-1.1-c5-0-74"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.07622746204318544070228871571	["ModularForm/GL2/Q/holomorphic/675/6/a/w/1/1"]
"2-675-1.1-c5-0-75"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.08177467067838628902053584406	["ModularForm/GL2/Q/holomorphic/675/6/a/l/1/1"]
"2-675-1.1-c5-0-76"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.08326629402201504548832269644	["ModularForm/GL2/Q/holomorphic/675/6/a/m/1/1"]
"2-675-1.1-c5-0-77"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.08592791721993770334005684987	["ModularForm/GL2/Q/holomorphic/675/6/a/k/1/1"]
"2-675-1.1-c5-0-78"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.08703407478075750136897047209	["ModularForm/GL2/Q/holomorphic/675/6/a/bc/1/6"]
"2-675-1.1-c5-0-79"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.09418536120618886486442588855	["ModularForm/GL2/Q/holomorphic/675/6/a/u/1/7"]
"2-675-1.1-c5-0-8"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.31332977167430542517228190309	["ModularForm/GL2/Q/holomorphic/675/6/a/ba/1/2"]
"2-675-1.1-c5-0-80"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.11906982945195332691506512004	["ModularForm/GL2/Q/holomorphic/675/6/a/bc/1/2"]
"2-675-1.1-c5-0-81"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.5	1	1.12490980589120367866702008003	["ModularForm/GL2/Q/holomorphic/675/6/a/a/1/1", "ModularForm/GL2/Q/holomorphic/675/6/a/a"]
"2-675-1.1-c5-0-82"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.13037518128083253459388925083	["ModularForm/GL2/Q/holomorphic/675/6/a/v/1/1"]
"2-675-1.1-c5-0-83"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.13558305685319214610340579476	["ModularForm/GL2/Q/holomorphic/675/6/a/bc/1/3"]
"2-675-1.1-c5-0-84"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.14266320708318418921831849172	["ModularForm/GL2/Q/holomorphic/675/6/a/f/1/2"]
"2-675-1.1-c5-0-85"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.14831327930057273872544419532	["ModularForm/GL2/Q/holomorphic/675/6/a/q/1/1"]
"2-675-1.1-c5-0-86"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.15616290527122271024395982079	["ModularForm/GL2/Q/holomorphic/675/6/a/y/1/5"]
"2-675-1.1-c5-0-87"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.16605772346857976694100870328	["ModularForm/GL2/Q/holomorphic/675/6/a/r/1/2"]
"2-675-1.1-c5-0-88"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.17889754995724882684283837841	["ModularForm/GL2/Q/holomorphic/675/6/a/g/1/2"]
"2-675-1.1-c5-0-89"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.18941490694214439408465998956	["ModularForm/GL2/Q/holomorphic/675/6/a/w/1/2"]
"2-675-1.1-c5-0-9"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.31405573475872198186589209267	["ModularForm/GL2/Q/holomorphic/675/6/a/p/1/3"]
"2-675-1.1-c5-0-90"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.20460041817472263440962598687	["ModularForm/GL2/Q/holomorphic/675/6/a/w/1/4"]
"2-675-1.1-c5-0-91"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.21340943803582186386139610845	["ModularForm/GL2/Q/holomorphic/675/6/a/bc/1/4"]
"2-675-1.1-c5-0-92"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.21362303404207582555528735365	["ModularForm/GL2/Q/holomorphic/675/6/a/s/1/3"]
"2-675-1.1-c5-0-93"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.23695793210133591918037258532	["ModularForm/GL2/Q/holomorphic/675/6/a/f/1/1"]
"2-675-1.1-c5-0-94"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.23782182449531078327462115416	["ModularForm/GL2/Q/holomorphic/675/6/a/v/1/3"]
"2-675-1.1-c5-0-95"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.24003509255690971711817221589	["ModularForm/GL2/Q/holomorphic/675/6/a/y/1/4"]
"2-675-1.1-c5-0-96"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.25327508396706215304724902927	["ModularForm/GL2/Q/holomorphic/675/6/a/y/1/6"]
"2-675-1.1-c5-0-97"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.27443154276969184391227604204	["ModularForm/GL2/Q/holomorphic/675/6/a/q/1/3"]
"2-675-1.1-c5-0-98"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.27509466448643293165773904491	["ModularForm/GL2/Q/holomorphic/675/6/a/bd/1/10"]
"2-675-1.1-c5-0-99"	10.404762292996509	108.25907837376195	2	675	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.5	1	1.27918832143648619495957630417	["ModularForm/GL2/Q/holomorphic/675/6/a/d/1/1", "ModularForm/GL2/Q/holomorphic/675/6/a/d"]


# 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).