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Lowest zero Conductor Analytic conductor Central character Analytic rank
Degree Bad \(p\) Root analytic conductor Motivic weight Spectral label
Root angle Primitive Origin Exclude origin Self-dual
Arithmetic
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Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim arith $\mathbb{Q}$ self-dual $\operatorname{Arg}(\epsilon)$ $r$ First zero Origin
2-211-211.210-c0-0-0 $0.324$ $0.105$ $2$ $211$ 211.210 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $2.29906$ Artin representation 2.211.3t2.a Artin representation 2.211.3t2.a.a Modular form 211.1.b.a Modular form 211.1.b.a.210.1
2-211-1.1-c1-0-0 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.747640$ Modular form 211.2.a.d.1.4
2-211-1.1-c1-0-1 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.04320$ Modular form 211.2.a.d.1.1
2-211-1.1-c1-0-10 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.45169$ Modular form 211.2.a.c.1.1
2-211-1.1-c1-0-11 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.56333$ Modular form 211.2.a.d.1.7
2-211-1.1-c1-0-12 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.65431$ Modular form 211.2.a.a.1.2
2-211-1.1-c1-0-13 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.83809$ Modular form 211.2.a.c.1.2
2-211-1.1-c1-0-14 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.90375$ Modular form 211.2.a.b.1.2
2-211-1.1-c1-0-15 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.47373$ Modular form 211.2.a.c.1.3
2-211-1.1-c1-0-16 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.57692$ Modular form 211.2.a.b.1.3
2-211-1.1-c1-0-2 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.36933$ Modular form 211.2.a.d.1.3
2-211-1.1-c1-0-3 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.45157$ Modular form 211.2.a.d.1.6
2-211-1.1-c1-0-4 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.58038$ Modular form 211.2.a.a.1.1
2-211-1.1-c1-0-5 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.90919$ Modular form 211.2.a.b.1.1
2-211-1.1-c1-0-6 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.93015$ Modular form 211.2.a.d.1.5
2-211-1.1-c1-0-7 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.11562$ Modular form 211.2.a.d.1.2
2-211-1.1-c1-0-8 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.24816$ Modular form 211.2.a.d.1.8
2-211-1.1-c1-0-9 $1.29$ $1.68$ $2$ $211$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.38593$ Modular form 211.2.a.d.1.9
2-211-211.100-c1-0-0 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.148$ $0$ $1.14098$ Modular form 211.2.i.a.100.5
2-211-211.100-c1-0-1 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.0368$ $0$ $1.16737$ Modular form 211.2.i.a.100.4
2-211-211.100-c1-0-10 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.128$ $0$ $2.15838$ Modular form 211.2.i.a.100.9
2-211-211.100-c1-0-11 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.00582$ $0$ $2.37604$ Modular form 211.2.i.a.100.15
2-211-211.100-c1-0-12 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.134$ $0$ $2.56937$ Modular form 211.2.i.a.100.12
2-211-211.100-c1-0-13 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.434$ $0$ $2.89537$ Modular form 211.2.i.a.100.7
2-211-211.100-c1-0-14 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.210$ $0$ $3.18046$ Modular form 211.2.i.a.100.13
2-211-211.100-c1-0-15 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.319$ $0$ $3.34813$ Modular form 211.2.i.a.100.3
2-211-211.100-c1-0-16 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.411$ $0$ $3.36264$ Modular form 211.2.i.a.100.8
2-211-211.100-c1-0-2 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.232$ $0$ $1.33370$ Modular form 211.2.i.a.100.1
2-211-211.100-c1-0-3 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.399$ $0$ $1.42023$ Modular form 211.2.i.a.100.14
2-211-211.100-c1-0-4 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.218$ $0$ $1.65922$ Modular form 211.2.i.a.100.10
2-211-211.100-c1-0-5 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.325$ $0$ $1.70320$ Modular form 211.2.i.a.100.16
2-211-211.100-c1-0-6 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.0811$ $0$ $1.79890$ Modular form 211.2.i.a.100.11
2-211-211.100-c1-0-7 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.472$ $0$ $1.92010$ Modular form 211.2.i.a.100.2
2-211-211.100-c1-0-8 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $0.185$ $0$ $1.95464$ Modular form 211.2.i.a.100.6
2-211-211.100-c1-0-9 $1.29$ $1.68$ $2$ $211$ 211.100 $1.0$ $1$ ✓ ✓ $-0.174$ $0$ $1.97066$ Modular form 211.2.i.a.100.17
2-211-211.101-c1-0-0 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.440$ $0$ $0.154673$ Modular form 211.2.j.a.101.4
2-211-211.101-c1-0-1 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.323$ $0$ $0.745981$ Modular form 211.2.j.a.101.3
2-211-211.101-c1-0-10 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.114$ $0$ $2.09910$ Modular form 211.2.j.a.101.5
2-211-211.101-c1-0-11 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.167$ $0$ $2.23407$ Modular form 211.2.j.a.101.10
2-211-211.101-c1-0-12 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.464$ $0$ $2.47406$ Modular form 211.2.j.a.101.2
2-211-211.101-c1-0-13 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.236$ $0$ $2.65588$ Modular form 211.2.j.a.101.16
2-211-211.101-c1-0-14 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.115$ $0$ $2.83063$ Modular form 211.2.j.a.101.15
2-211-211.101-c1-0-15 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.104$ $0$ $2.86751$ Modular form 211.2.j.a.101.12
2-211-211.101-c1-0-16 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $0.114$ $0$ $3.00027$ Modular form 211.2.j.a.101.17
2-211-211.101-c1-0-2 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.292$ $0$ $0.776227$ Modular form 211.2.j.a.101.8
2-211-211.101-c1-0-3 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.270$ $0$ $0.776408$ Modular form 211.2.j.a.101.11
2-211-211.101-c1-0-4 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.240$ $0$ $0.867418$ Modular form 211.2.j.a.101.14
2-211-211.101-c1-0-5 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.0343$ $0$ $0.979839$ Modular form 211.2.j.a.101.7
2-211-211.101-c1-0-6 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.230$ $0$ $1.08769$ Modular form 211.2.j.a.101.1
2-211-211.101-c1-0-7 $1.29$ $1.68$ $2$ $211$ 211.101 $1.0$ $1$ ✓ ✓ $-0.192$ $0$ $1.13683$ Modular form 211.2.j.a.101.6
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