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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
2-344-344.107-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.107 $0.0$ 0 ✓ ✓ $-0.249$ $0$ $0.651044$ Modular form 344.1.s.a.107.1
2-344-344.11-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.11 $0.0$ 0 ✓ ✓ $-0.261$ $0$ $1.57917$ Modular form 344.1.s.a.11.1
2-344-344.139-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.139 $0.0$ 0 ✓ ✓ $0.00699$ $0$ $1.85878$ Modular form 344.1.be.a.139.1
2-344-344.187-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.187 $0.0$ 0 ✓ ✓ $0.155$ $0$ $2.37009$ Modular form 344.1.be.a.187.1
2-344-344.195-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.195 $0.0$ 0 ✓ ✓ $-0.155$ $0$ $1.81894$ Modular form 344.1.be.a.195.1
2-344-344.203-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.203 $0.0$ 0 ✓ ✓ $0.0343$ $0$ $2.12113$ Modular form 344.1.be.a.203.1
2-344-344.219-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.219 $0.0$ 0 ✓ ✓ $0.261$ $0$ $2.82949$ Modular form 344.1.s.a.219.1
2-344-344.251-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.251 $0.0$ 0 ✓ ✓ $-0.368$ $0$ $1.38417$ Modular form 344.1.l.b.251.2
2-344-344.251-c0-0-1 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.251 $0.0$ 0 ✓ ✓ $0.131$ $0$ $2.16208$ Modular form 344.1.l.b.251.1
2-344-344.251-c0-0-2 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.251 $0.0$ 0 ✓ ✓ $0.215$ $0$ $3.02806$ Artin representation 2.344.6t5.a.b Modular form 344.1.l.a.251.1
2-344-344.267-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.267 $0.0$ 0 ✓ ✓ $-0.191$ $0$ $1.98239$ Modular form 344.1.be.a.267.1
2-344-344.275-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.275 $0.0$ 0 ✓ ✓ $0.0224$ $0$ $1.02944$ Modular form 344.1.be.a.275.1
2-344-344.283-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.283 $0.0$ 0 ✓ ✓ $-0.0343$ $0$ $1.76980$ Modular form 344.1.be.a.283.1
2-344-344.299-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.299 $0.0$ 0 ✓ ✓ $0.249$ $0$ $2.03497$ Modular form 344.1.s.a.299.1
2-344-344.307-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.307 $0.0$ 0 ✓ ✓ $-0.215$ $0$ $1.65410$ Artin representation 2.344.6t5.a.a Modular form 344.1.l.a.307.1
2-344-344.307-c0-0-1 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.307 $0.0$ 0 ✓ ✓ $-0.131$ $0$ $1.86415$ Modular form 344.1.l.b.307.2
2-344-344.307-c0-0-2 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.307 $0.0$ 0 ✓ ✓ $0.368$ $0$ $3.02678$ Modular form 344.1.l.b.307.1
2-344-344.315-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.315 $0.0$ 0 ✓ ✓ $-0.278$ $0$ $1.28930$ Modular form 344.1.be.a.315.1
2-344-344.339-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.339 $0.0$ 0 ✓ ✓ $-0.0224$ $0$ $1.45210$ Modular form 344.1.be.a.339.1
2-344-344.35-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.35 $0.0$ 0 ✓ ✓ $-0.423$ $0$ $1.37756$ Modular form 344.1.s.a.35.1
2-344-344.59-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.59 $0.0$ 0 ✓ ✓ $0.423$ $0$ $3.18072$ Modular form 344.1.s.a.59.1
2-344-344.67-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.67 $0.0$ 0 ✓ ✓ $0.191$ $0$ $2.83840$ Modular form 344.1.be.a.67.1
2-344-344.83-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.83 $0.0$ 0 ✓ ✓ $0.278$ $0$ $2.22998$ Modular form 344.1.be.a.83.1
2-344-344.85-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.85 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.62399$ Modular form 344.1.h.a.85.1
2-344-344.85-c0-0-1 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.85 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.94894$ Artin representation 2.344.5t2.a.b Modular form 344.1.h.b.85.1
2-344-344.85-c0-0-2 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.85 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.04525$ Modular form 344.1.h.a.85.2
2-344-344.85-c0-0-3 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.85 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.52699$ Artin representation 2.344.5t2.a.a Modular form 344.1.h.b.85.2
2-344-344.99-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 344.99 $0.0$ 0 ✓ ✓ $-0.00699$ $0$ $2.60738$ Modular form 344.1.be.a.99.1
2-344-43.42-c0-0-0 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 43.42 $0.0$ 0 ✓ ✓ $-0.250$ $0$ $1.42520$ Artin representation 2.344.24t22.a.b Modular form 344.1.b.a.257.2
2-344-43.42-c0-0-1 $0.414$ $0.171$ $2$ $2^{3} \cdot 43$ 43.42 $0.0$ 0 ✓ ✓ $0.250$ $0$ $2.88505$ Artin representation 2.344.24t22.a.a Modular form 344.1.b.a.257.1
2-344-1.1-c1-0-0 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.799854$ Modular form 344.2.a.d.1.1
2-344-1.1-c1-0-1 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.13129$ Modular form 344.2.a.d.1.2
2-344-1.1-c1-0-10 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.82403$ Modular form 344.2.a.b.1.2
2-344-1.1-c1-0-2 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.21205$ Modular form 344.2.a.c.1.1
2-344-1.1-c1-0-3 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.63526$ Modular form 344.2.a.d.1.3
2-344-1.1-c1-0-4 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.66850$ Modular form 344.2.a.d.1.4
2-344-1.1-c1-0-5 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.88331$ Modular form 344.2.a.c.1.2
2-344-1.1-c1-0-6 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.94138$ Modular form 344.2.a.c.1.3
2-344-1.1-c1-0-7 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.94321$ Modular form 344.2.a.d.1.5
2-344-1.1-c1-0-8 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.13386$ Modular form 344.2.a.b.1.1
2-344-1.1-c1-0-9 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.60425$ Elliptic curve 344.a Modular form 344.2.a.a Modular form 344.2.a.a.1.1
2-344-344.101-c1-0-0 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $0.358$ $0$ $0.0388021$ Modular form 344.2.z.a.101.30
2-344-344.101-c1-0-1 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $-0.263$ $0$ $0.0476637$ Modular form 344.2.z.a.101.33
2-344-344.101-c1-0-10 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $-0.358$ $0$ $0.953920$ Modular form 344.2.z.a.101.31
2-344-344.101-c1-0-11 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $-0.137$ $0$ $0.986779$ Modular form 344.2.z.a.101.36
2-344-344.101-c1-0-12 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $-0.402$ $0$ $1.08581$ Modular form 344.2.z.a.101.25
2-344-344.101-c1-0-13 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $-0.125$ $0$ $1.19598$ Modular form 344.2.z.a.101.4
2-344-344.101-c1-0-14 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $0.240$ $0$ $1.21929$ Modular form 344.2.z.a.101.14
2-344-344.101-c1-0-15 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $-0.165$ $0$ $1.50564$ Modular form 344.2.z.a.101.6
2-344-344.101-c1-0-16 $1.65$ $2.74$ $2$ $2^{3} \cdot 43$ 344.101 $1.0$ $1$ ✓ ✓ $0.0349$ $0$ $1.53679$ Modular form 344.2.z.a.101.9
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