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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
2-896-112.13-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 112.13 $$ $0.0$ $0$ ✓ ✓ $-0.187$ $0$ $0.937534$ Artin representation 2.896.8t17.d.b Modular form 896.1.l.a.545.1
2-896-112.13-c0-0-1 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 112.13 $$ $0.0$ $0$ ✓ ✓ $0.0625$ $0$ $1.62432$ Artin representation 2.896.8t17.a.b Modular form 896.1.l.b.545.1
2-896-112.69-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 112.69 $$ $0.0$ $0$ ✓ ✓ $-0.0625$ $0$ $1.28183$ Artin representation 2.896.8t17.a.a Modular form 896.1.l.b.97.1
2-896-112.69-c0-0-1 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 112.69 $$ $0.0$ $0$ ✓ ✓ $0.187$ $0$ $2.07047$ Artin representation 2.896.8t17.d.a Modular form 896.1.l.a.97.1
2-896-224.125-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 224.125 $$ $0.0$ $0$ ✓ ✓ $-0.0937$ $0$ $1.17278$ Modular form 896.1.v.a.209.1
2-896-224.13-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 224.13 $$ $0.0$ $0$ ✓ ✓ $0.156$ $0$ $2.00195$ Modular form 896.1.v.a.657.1
2-896-224.181-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 224.181 $$ $0.0$ $0$ ✓ ✓ $0.0937$ $0$ $1.68642$ Modular form 896.1.v.a.433.1
2-896-224.69-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 224.69 $$ $0.0$ $0$ ✓ ✓ $-0.156$ $0$ $1.02917$ Modular form 896.1.v.a.881.1
2-896-56.13-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 56.13 $$ $0.0$ $0$ ✓ ✓ ✓ $0$ $0$ $0.826826$ Artin representation 2.896.8t6.a.b Modular form 896.1.h.a.321.1
2-896-56.13-c0-0-1 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 56.13 $$ $0.0$ $0$ ✓ ✓ ✓ $0$ $0$ $1.35654$ Artin representation 2.896.8t6.b.b Modular form 896.1.h.b.321.1
2-896-56.13-c0-0-2 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 56.13 $$ $0.0$ $0$ ✓ ✓ ✓ $0$ $0$ $1.69662$ Artin representation 2.896.8t6.b.a Modular form 896.1.h.b.321.2
2-896-56.13-c0-0-3 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 56.13 $$ $0.0$ $0$ ✓ ✓ ✓ $0$ $0$ $2.11120$ Artin representation 2.896.8t6.a.a Modular form 896.1.h.a.321.2
2-896-896.125-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.125 $$ $0.0$ $0$ ✓ ✓ $-0.242$ $0$ $0.952617$ Modular form 896.1.bm.a.125.1
2-896-896.13-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.13 $$ $0.0$ $0$ ✓ ✓ $-0.179$ $0$ $0.437125$ Modular form 896.1.bm.a.13.1
2-896-896.181-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.181 $$ $0.0$ $0$ ✓ ✓ $0.242$ $0$ $2.43506$ Modular form 896.1.bm.a.181.1
2-896-896.237-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.237 $$ $0.0$ $0$ ✓ ✓ $0.0703$ $0$ $1.96008$ Modular form 896.1.bm.a.237.1
2-896-896.293-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.293 $$ $0.0$ $0$ ✓ ✓ $-0.0703$ $0$ $1.06235$ Modular form 896.1.bm.a.293.1
2-896-896.349-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.349 $$ $0.0$ $0$ ✓ ✓ $0.257$ $0$ $1.72384$ Modular form 896.1.bm.a.349.1
2-896-896.405-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.405 $$ $0.0$ $0$ ✓ ✓ $-0.257$ $0$ $1.35333$ Modular form 896.1.bm.a.405.1
2-896-896.461-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.461 $$ $0.0$ $0$ ✓ ✓ $-0.179$ $0$ $1.45448$ Modular form 896.1.bm.a.461.1
2-896-896.517-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.517 $$ $0.0$ $0$ ✓ ✓ $0.179$ $0$ $1.50682$ Modular form 896.1.bm.a.517.1
2-896-896.573-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.573 $$ $0.0$ $0$ ✓ ✓ $0.257$ $0$ $2.05441$ Modular form 896.1.bm.a.573.1
2-896-896.629-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.629 $$ $0.0$ $0$ ✓ ✓ $-0.257$ $0$ $0.848078$ Modular form 896.1.bm.a.629.1
2-896-896.685-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.685 $$ $0.0$ $0$ ✓ ✓ $0.0703$ $0$ $1.59719$ Modular form 896.1.bm.a.685.1
2-896-896.69-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.69 $$ $0.0$ $0$ ✓ ✓ $0.179$ $0$ $2.11760$ Modular form 896.1.bm.a.69.1
2-896-896.741-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.741 $$ $0.0$ $0$ ✓ ✓ $-0.0703$ $0$ $1.71186$ Modular form 896.1.bm.a.741.1
2-896-896.797-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.797 $$ $0.0$ $0$ ✓ ✓ $-0.242$ $0$ $1.27951$ Modular form 896.1.bm.a.797.1
2-896-896.853-c0-0-0 $0.668$ $0.447$ $2$ $2^{7} \cdot 7$ 896.853 $$ $0.0$ $0$ ✓ ✓ $0.242$ $0$ $1.51033$ Modular form 896.1.bm.a.853.1
2-896-1.1-c1-0-0 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.567328$ Modular form 896.2.a.k.1.1
2-896-1.1-c1-0-1 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.613647$ Modular form 896.2.a.f.1.1
2-896-1.1-c1-0-10 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.36211$ Modular form 896.2.a.i.1.1
2-896-1.1-c1-0-11 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.40257$ Modular form 896.2.a.k.1.3
2-896-1.1-c1-0-12 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.51656$ Modular form 896.2.a.h.1.2
2-896-1.1-c1-0-13 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.54957$ Modular form 896.2.a.k.1.2
2-896-1.1-c1-0-14 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.56225$ Modular form 896.2.a.g.1.2
2-896-1.1-c1-0-15 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.61290$ Modular form 896.2.a.e.1.1
2-896-1.1-c1-0-16 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.67776$ Modular form 896.2.a.l.1.3
2-896-1.1-c1-0-17 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.74631$ Modular form 896.2.a.j.1.3
2-896-1.1-c1-0-18 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.01559$ Elliptic curve 896.a Modular form 896.2.a.a Modular form 896.2.a.a.1.1
2-896-1.1-c1-0-19 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.01625$ Modular form 896.2.a.e.1.2
2-896-1.1-c1-0-2 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.663715$ Modular form 896.2.a.j.1.2
2-896-1.1-c1-0-20 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.02232$ Elliptic curve 896.b Modular form 896.2.a.b Modular form 896.2.a.b.1.1
2-896-1.1-c1-0-21 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.08487$ Elliptic curve 896.c Modular form 896.2.a.c Modular form 896.2.a.c.1.1
2-896-1.1-c1-0-22 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.12887$ Modular form 896.2.a.i.1.2
2-896-1.1-c1-0-23 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.34139$ Modular form 896.2.a.i.1.3
2-896-1.1-c1-0-3 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.731340$ Modular form 896.2.a.g.1.1
2-896-1.1-c1-0-4 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.972986$ Modular form 896.2.a.j.1.1
2-896-1.1-c1-0-5 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.992501$ Modular form 896.2.a.l.1.2
2-896-1.1-c1-0-6 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.02221$ Modular form 896.2.a.l.1.1
2-896-1.1-c1-0-7 $2.67$ $7.15$ $2$ $2^{7} \cdot 7$ 1.1 $$ $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.10812$ Elliptic curve 896.d Modular form 896.2.a.d Modular form 896.2.a.d.1.1
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