LMFDB - L-function search results

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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

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Results (1-50 of at least 1000)

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	$\nu$	$w$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
2-768-48.29-c0-0-2	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.29	$$	$0.0$	$0$	✓	✓			$-0.0625$	$0$	$1.66274$	Modular form 768.1.i.b.65.2
2-768-48.5-c0-0-2	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.5	$$	$0.0$	$0$	✓	✓			$0.0625$	$0$	$1.73880$	Modular form 768.1.i.b.449.2
2-768-3.2-c0-0-2	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	3.2	$$	$0.0$	$0$	✓	✓	✓	✓	$0$	$0$	$1.80861$	Artin representation 2.768.4t3.c Artin representation 2.768.4t3.c.a Modular form 768.1.e.b Modular form 768.1.e.b.257.1
2-768-48.29-c0-0-1	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.29	$$	$0.0$	$0$	✓	✓			$-0.187$	$0$	$1.30094$	Modular form 768.1.i.a.65.2
2-768-48.5-c0-0-1	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.5	$$	$0.0$	$0$	✓	✓			$0.0625$	$0$	$1.63729$	Modular form 768.1.i.b.449.1
2-768-48.5-c0-0-3	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.5	$$	$0.0$	$0$	✓	✓			$0.187$	$0$	$2.36187$	Modular form 768.1.i.a.449.2
2-768-3.2-c0-0-0	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	3.2	$$	$0.0$	$0$	✓	✓			$-0.250$	$0$	$1.02777$	Artin representation 2.768.8t11.c.b Modular form 768.1.e.c.257.2
2-768-3.2-c0-0-1	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	3.2	$$	$0.0$	$0$	✓	✓	✓	✓	$0$	$0$	$1.24462$	Artin representation 2.768.4t3.d Artin representation 2.768.4t3.d.a Modular form 768.1.e.a Modular form 768.1.e.a.257.1
2-768-3.2-c0-0-3	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	3.2	$$	$0.0$	$0$	✓	✓			$0.250$	$0$	$2.11411$	Artin representation 2.768.8t11.c.a Modular form 768.1.e.c.257.1
2-768-48.29-c0-0-0	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.29	$$	$0.0$	$0$	✓	✓			$-0.0625$	$0$	$1.02178$	Modular form 768.1.i.b.65.1
2-768-48.29-c0-0-3	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.29	$$	$0.0$	$0$	✓	✓			$0.312$	$0$	$2.10110$	Modular form 768.1.i.a.65.1
2-768-48.5-c0-0-0	$0.619$	$0.383$	$2$	$2^{8} \cdot 3$	48.5	$$	$0.0$	$0$	✓	✓			$-0.312$	$0$	$0.751370$	Modular form 768.1.i.a.449.1
2-768-256.157-c1-0-21	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$-0.151$	$0$	$1.09584$	Modular form 768.2.z.a.157.33
2-768-256.149-c1-0-6	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.149	$$	$1.0$	$1$	✓	✓			$-0.228$	$0$	$0.164971$	Modular form 768.2.z.a.661.9
2-768-256.157-c1-0-22	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$-0.222$	$0$	$1.10904$	Modular form 768.2.z.a.157.64
2-768-256.173-c1-0-19	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.173	$$	$1.0$	$1$	✓	✓			$0.0966$	$0$	$0.748412$	Modular form 768.2.z.a.685.28
2-768-256.165-c1-0-34	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$-0.198$	$0$	$1.37322$	Modular form 768.2.z.a.421.34
2-768-256.173-c1-0-2	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.173	$$	$1.0$	$1$	✓	✓			$-0.331$	$0$	$0.0738235$	Modular form 768.2.z.a.685.55
2-768-256.173-c1-0-20	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.173	$$	$1.0$	$1$	✓	✓			$0.0220$	$0$	$0.786886$	Modular form 768.2.z.a.685.5
2-768-256.165-c1-0-10	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$-0.198$	$0$	$0.359889$	Modular form 768.2.z.a.421.31
2-768-256.157-c1-0-54	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$0.220$	$0$	$2.19801$	Modular form 768.2.z.a.157.63
2-768-256.165-c1-0-11	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$-0.0573$	$0$	$0.371375$	Modular form 768.2.z.a.421.43
2-768-256.165-c1-0-20	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$-0.0742$	$0$	$0.616296$	Modular form 768.2.z.a.421.7
2-768-256.165-c1-0-33	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$-0.00728$	$0$	$1.32703$	Modular form 768.2.z.a.421.2
2-768-256.165-c1-0-62	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$0.169$	$0$	$1.99467$	Modular form 768.2.z.a.421.52
2-768-256.173-c1-0-17	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.173	$$	$1.0$	$1$	✓	✓			$-0.443$	$0$	$0.657315$	Modular form 768.2.z.a.685.53
2-768-256.149-c1-0-5	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.149	$$	$1.0$	$1$	✓	✓			$-0.411$	$0$	$0.159153$	Modular form 768.2.z.a.661.26
2-768-256.149-c1-0-59	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.149	$$	$1.0$	$1$	✓	✓			$0.150$	$0$	$1.83789$	Modular form 768.2.z.a.661.56
2-768-256.157-c1-0-10	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$-0.475$	$0$	$0.393329$	Modular form 768.2.z.a.157.5
2-768-256.157-c1-0-20	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$-0.200$	$0$	$1.02262$	Modular form 768.2.z.a.157.26
2-768-256.13-c1-0-23	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.13	$$	$1.0$	$1$	✓	✓			$0.103$	$0$	$0.921078$	Modular form 768.2.z.a.13.30
2-768-256.125-c1-0-7	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.125	$$	$1.0$	$1$	✓	✓			$0.487$	$0$	$0.492256$	Modular form 768.2.z.a.637.50
2-768-256.13-c1-0-24	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.13	$$	$1.0$	$1$	✓	✓			$-0.301$	$0$	$0.941110$	Modular form 768.2.z.a.13.51
2-768-256.165-c1-0-12	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$0.480$	$0$	$0.375620$	Modular form 768.2.z.a.421.24
2-768-256.125-c1-0-47	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.125	$$	$1.0$	$1$	✓	✓			$0.314$	$0$	$1.89505$	Modular form 768.2.z.a.637.54
2-768-256.125-c1-0-41	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.125	$$	$1.0$	$1$	✓	✓			$0.313$	$0$	$1.75007$	Modular form 768.2.z.a.637.45
2-768-256.125-c1-0-48	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.125	$$	$1.0$	$1$	✓	✓			$0.220$	$0$	$1.91972$	Modular form 768.2.z.a.637.49
2-768-256.157-c1-0-49	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$0.203$	$0$	$1.69879$	Modular form 768.2.z.a.157.54
2-768-256.125-c1-0-55	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.125	$$	$1.0$	$1$	✓	✓			$0.355$	$0$	$2.19267$	Modular form 768.2.z.a.637.52
2-768-256.125-c1-0-63	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.125	$$	$1.0$	$1$	✓	✓			$-0.287$	$0$	$3.02204$	Modular form 768.2.z.a.637.44
2-768-256.13-c1-0-13	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.13	$$	$1.0$	$1$	✓	✓			$-0.226$	$0$	$0.653622$	Modular form 768.2.z.a.13.56
2-768-256.13-c1-0-22	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.13	$$	$1.0$	$1$	✓	✓			$-0.157$	$0$	$0.915405$	Modular form 768.2.z.a.13.15
2-768-256.13-c1-0-35	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.13	$$	$1.0$	$1$	✓	✓			$0.237$	$0$	$1.36642$	Modular form 768.2.z.a.13.32
2-768-256.157-c1-0-53	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$0.478$	$0$	$2.14065$	Modular form 768.2.z.a.157.2
2-768-256.157-c1-0-60	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.157	$$	$1.0$	$1$	✓	✓			$0.404$	$0$	$2.50668$	Modular form 768.2.z.a.157.58
2-768-256.165-c1-0-1	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$-0.210$	$0$	$0.114397$	Modular form 768.2.z.a.421.39
2-768-256.165-c1-0-17	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$0.194$	$0$	$0.551027$	Modular form 768.2.z.a.421.14
2-768-256.165-c1-0-2	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$0.472$	$0$	$0.146634$	Modular form 768.2.z.a.421.6
2-768-256.141-c1-0-3	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.141	$$	$1.0$	$1$	✓	✓			$-0.474$	$0$	$0.0771679$	Modular form 768.2.z.a.397.56
2-768-256.165-c1-0-32	$2.47$	$6.13$	$2$	$2^{8} \cdot 3$	256.165	$$	$1.0$	$1$	✓	✓			$0.152$	$0$	$1.32503$	Modular form 768.2.z.a.421.21

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.