# lfunc_search downloaded from the LMFDB on 04 July 2026.
# Search link: https://www.lmfdb.org/L/rational/2/235200
# Query "{'degree': 2, 'conductor': 235200, 'rational': True}" returned 754 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, $\epsilon$, $r$, First zero, Origin]
# For more details, see the definitions at the bottom of the file.



"2-235200-1.1-c1-0-0"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.06429287350478205	["EllipticCurve/Q/235200/jt"]
"2-235200-1.1-c1-0-1"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1123445434239704	["EllipticCurve/Q/235200/fw"]
"2-235200-1.1-c1-0-10"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1560782495567448	["EllipticCurve/Q/235200/to"]
"2-235200-1.1-c1-0-100"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3387621172619059	["EllipticCurve/Q/235200/ut"]
"2-235200-1.1-c1-0-101"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3406558924596935	["EllipticCurve/Q/235200/er"]
"2-235200-1.1-c1-0-102"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3412026533690703	["EllipticCurve/Q/235200/ul"]
"2-235200-1.1-c1-0-103"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3422619988194731	["EllipticCurve/Q/235200/px"]
"2-235200-1.1-c1-0-104"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3426641778389271	["EllipticCurve/Q/235200/lm"]
"2-235200-1.1-c1-0-105"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3432547268693970	["EllipticCurve/Q/235200/sc"]
"2-235200-1.1-c1-0-106"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3465910650064200	["EllipticCurve/Q/235200/fy"]
"2-235200-1.1-c1-0-107"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3489269157994069	["EllipticCurve/Q/235200/if"]
"2-235200-1.1-c1-0-108"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3491808804873169	["EllipticCurve/Q/235200/ni"]
"2-235200-1.1-c1-0-109"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3500099649747385	["EllipticCurve/Q/235200/qa"]
"2-235200-1.1-c1-0-11"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1858501343006179	["EllipticCurve/Q/235200/pj"]
"2-235200-1.1-c1-0-110"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3508086928581905	["EllipticCurve/Q/235200/ve"]
"2-235200-1.1-c1-0-111"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3538777843105362	["EllipticCurve/Q/235200/ui"]
"2-235200-1.1-c1-0-112"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3604775758290259	["EllipticCurve/Q/235200/io"]
"2-235200-1.1-c1-0-113"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3630736253559480	["EllipticCurve/Q/235200/fs"]
"2-235200-1.1-c1-0-114"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3680214757218145	["EllipticCurve/Q/235200/ct"]
"2-235200-1.1-c1-0-115"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3681353169780057	["EllipticCurve/Q/235200/so"]
"2-235200-1.1-c1-0-116"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3681981112272259	["EllipticCurve/Q/235200/c"]
"2-235200-1.1-c1-0-117"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3700565062121567	["EllipticCurve/Q/235200/qr"]
"2-235200-1.1-c1-0-118"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3710186616536824	["EllipticCurve/Q/235200/eh"]
"2-235200-1.1-c1-0-119"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3713048091817743	["EllipticCurve/Q/235200/rq"]
"2-235200-1.1-c1-0-12"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1874536417366054	["EllipticCurve/Q/235200/xk"]
"2-235200-1.1-c1-0-120"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3725913180950696	["EllipticCurve/Q/235200/ew"]
"2-235200-1.1-c1-0-121"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3754124698027119	["EllipticCurve/Q/235200/go"]
"2-235200-1.1-c1-0-122"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3766616417323394	["EllipticCurve/Q/235200/uy"]
"2-235200-1.1-c1-0-123"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3822084945801186	["EllipticCurve/Q/235200/fl"]
"2-235200-1.1-c1-0-124"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3864740626769769	["EllipticCurve/Q/235200/mc"]
"2-235200-1.1-c1-0-125"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3876917263098326	["EllipticCurve/Q/235200/ra"]
"2-235200-1.1-c1-0-126"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3892581876295322	["EllipticCurve/Q/235200/ws"]
"2-235200-1.1-c1-0-127"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3903505719195739	["EllipticCurve/Q/235200/hr"]
"2-235200-1.1-c1-0-128"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3910668553485669	["EllipticCurve/Q/235200/yz"]
"2-235200-1.1-c1-0-129"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3925763485468474	["EllipticCurve/Q/235200/e"]
"2-235200-1.1-c1-0-13"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1894932091341550	["EllipticCurve/Q/235200/gf"]
"2-235200-1.1-c1-0-130"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3927656032582221	["EllipticCurve/Q/235200/zh"]
"2-235200-1.1-c1-0-131"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3942693287602280	["EllipticCurve/Q/235200/eg"]
"2-235200-1.1-c1-0-132"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3950529222383350	["EllipticCurve/Q/235200/wi"]
"2-235200-1.1-c1-0-133"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3956763459096629	["EllipticCurve/Q/235200/oi"]
"2-235200-1.1-c1-0-134"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3962187358128352	["EllipticCurve/Q/235200/qk"]
"2-235200-1.1-c1-0-135"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3963165568605302	["EllipticCurve/Q/235200/fx"]
"2-235200-1.1-c1-0-136"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3973140617134347	["EllipticCurve/Q/235200/xe"]
"2-235200-1.1-c1-0-137"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4002440459687445	["EllipticCurve/Q/235200/pc"]
"2-235200-1.1-c1-0-138"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4017510241208635	["EllipticCurve/Q/235200/cv"]
"2-235200-1.1-c1-0-139"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4031750036718643	["EllipticCurve/Q/235200/vy"]
"2-235200-1.1-c1-0-14"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1931880912315833	["EllipticCurve/Q/235200/od"]
"2-235200-1.1-c1-0-140"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4032896840366720	["EllipticCurve/Q/235200/r"]
"2-235200-1.1-c1-0-141"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4033479067001509	["EllipticCurve/Q/235200/mq"]
"2-235200-1.1-c1-0-142"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4035169062109337	["EllipticCurve/Q/235200/bv"]
"2-235200-1.1-c1-0-143"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4045968329144705	["EllipticCurve/Q/235200/qu"]
"2-235200-1.1-c1-0-144"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4053318939485940	["EllipticCurve/Q/235200/cd"]
"2-235200-1.1-c1-0-145"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4059889516279286	["EllipticCurve/Q/235200/ta"]
"2-235200-1.1-c1-0-146"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4065945487296269	["EllipticCurve/Q/235200/xb"]
"2-235200-1.1-c1-0-147"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4074840173870012	["EllipticCurve/Q/235200/os"]
"2-235200-1.1-c1-0-148"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4081779457903998	["EllipticCurve/Q/235200/hj"]
"2-235200-1.1-c1-0-149"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4082005529925504	["EllipticCurve/Q/235200/et"]
"2-235200-1.1-c1-0-15"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1938439575774539	["EllipticCurve/Q/235200/k"]
"2-235200-1.1-c1-0-150"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4095054770270216	["EllipticCurve/Q/235200/rc"]
"2-235200-1.1-c1-0-151"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4100828175298242	["EllipticCurve/Q/235200/w"]
"2-235200-1.1-c1-0-152"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4126341327416696	["EllipticCurve/Q/235200/b"]
"2-235200-1.1-c1-0-153"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4156261201675667	["EllipticCurve/Q/235200/qj"]
"2-235200-1.1-c1-0-154"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4179201602341433	["EllipticCurve/Q/235200/jf"]
"2-235200-1.1-c1-0-155"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4202214737113480	["EllipticCurve/Q/235200/ig"]
"2-235200-1.1-c1-0-156"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4219739845461152	["EllipticCurve/Q/235200/ru"]
"2-235200-1.1-c1-0-157"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4239070772309044	["EllipticCurve/Q/235200/lr"]
"2-235200-1.1-c1-0-158"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4240604676756367	["EllipticCurve/Q/235200/lj"]
"2-235200-1.1-c1-0-159"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4264064451635623	["EllipticCurve/Q/235200/tf"]
"2-235200-1.1-c1-0-16"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1947060599293297	["EllipticCurve/Q/235200/qf"]
"2-235200-1.1-c1-0-160"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4287061589469266	["EllipticCurve/Q/235200/or"]
"2-235200-1.1-c1-0-161"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4290567474239716	["EllipticCurve/Q/235200/ir"]
"2-235200-1.1-c1-0-162"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4290572236938969	["EllipticCurve/Q/235200/uv"]
"2-235200-1.1-c1-0-163"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4305476426662777	["EllipticCurve/Q/235200/im"]
"2-235200-1.1-c1-0-164"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4310613661429045	["EllipticCurve/Q/235200/wq"]
"2-235200-1.1-c1-0-165"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4328360139347785	["EllipticCurve/Q/235200/vb"]
"2-235200-1.1-c1-0-166"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4332300176607275	["EllipticCurve/Q/235200/gw"]
"2-235200-1.1-c1-0-167"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4348947647075705	["EllipticCurve/Q/235200/xc"]
"2-235200-1.1-c1-0-168"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	0.4353887830318852	["EllipticCurve/Q/235200/bf"]
"2-235200-1.1-c1-0-169"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4375174575789118	["EllipticCurve/Q/235200/oo"]
"2-235200-1.1-c1-0-17"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1973472399202529	["EllipticCurve/Q/235200/gs"]
"2-235200-1.1-c1-0-170"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4441827571597634	["EllipticCurve/Q/235200/vf"]
"2-235200-1.1-c1-0-171"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4452588612123305	["EllipticCurve/Q/235200/gl"]
"2-235200-1.1-c1-0-172"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4465847443537713	["EllipticCurve/Q/235200/hc"]
"2-235200-1.1-c1-0-173"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4491472054579820	["EllipticCurve/Q/235200/gx"]
"2-235200-1.1-c1-0-174"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.4500081484673144	["EllipticCurve/Q/235200/iz"]
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"2-235200-1.1-c1-0-709"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.084112310310391	["EllipticCurve/Q/235200/zd"]
"2-235200-1.1-c1-0-71"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3054280502607943	["EllipticCurve/Q/235200/zg"]
"2-235200-1.1-c1-0-710"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.086755610878463	["EllipticCurve/Q/235200/g"]
"2-235200-1.1-c1-0-711"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.089992470514230	["EllipticCurve/Q/235200/bbo"]
"2-235200-1.1-c1-0-712"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.090351930100387	["EllipticCurve/Q/235200/bba"]
"2-235200-1.1-c1-0-713"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.096777124847284	["EllipticCurve/Q/235200/bbl"]
"2-235200-1.1-c1-0-714"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.112722873061404	["EllipticCurve/Q/235200/bbn"]
"2-235200-1.1-c1-0-715"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.118516996890991	["EllipticCurve/Q/235200/cc"]
"2-235200-1.1-c1-0-716"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.125072643738018	["EllipticCurve/Q/235200/bco"]
"2-235200-1.1-c1-0-717"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.128687018043206	["EllipticCurve/Q/235200/wc"]
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"2-235200-1.1-c1-0-719"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.134022744522697	["EllipticCurve/Q/235200/bn"]
"2-235200-1.1-c1-0-72"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3063359232913649	["EllipticCurve/Q/235200/js"]
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"2-235200-1.1-c1-0-723"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	-1	1	1.162331339399484	["EllipticCurve/Q/235200/bct"]
"2-235200-1.1-c1-0-724"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.186686523659574	["EllipticCurve/Q/235200/gm"]
"2-235200-1.1-c1-0-725"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.199655974169430	["EllipticCurve/Q/235200/ma"]
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"2-235200-1.1-c1-0-734"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.265138842055020	["EllipticCurve/Q/235200/oa"]
"2-235200-1.1-c1-0-735"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.267383542415009	["EllipticCurve/Q/235200/rj"]
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"2-235200-1.1-c1-0-749"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	2	1.409835033734528	["EllipticCurve/Q/235200/zx"]
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"2-235200-1.1-c1-0-79"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3179829710364526	["EllipticCurve/Q/235200/fz"]
"2-235200-1.1-c1-0-8"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.1516827508955898	["EllipticCurve/Q/235200/jn"]
"2-235200-1.1-c1-0-80"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3183091829919405	["EllipticCurve/Q/235200/gy"]
"2-235200-1.1-c1-0-81"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3193606898033825	["EllipticCurve/Q/235200/cn"]
"2-235200-1.1-c1-0-82"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3195931041793993	["EllipticCurve/Q/235200/y"]
"2-235200-1.1-c1-0-83"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3208346933473089	["EllipticCurve/Q/235200/cr"]
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"2-235200-1.1-c1-0-85"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3229390137456386	["EllipticCurve/Q/235200/xv"]
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"2-235200-1.1-c1-0-90"	43.336837165862896	1878.0814555405154	2	235200	"1.1"	[]	[[0.5, 0.0]]	1	true	1	0	0.3274367913524304	["EllipticCurve/Q/235200/tz"]
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# 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 $1$.


#$\epsilon$ (root_number) --
#    The **sign** of the functional equation of an analytic L-function, also called the **root number**, is the complex number $\varepsilon$ that appears in the functional equation of $\Lambda(s)=\varepsilon \overline{\Lambda}(1-s)$.  The sign appears as the 4th entry in the quadruple
#    known as the Selberg data.


#$r$ (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).