Basic properties
| Modulus: | \(5415\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1805}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5415.bt
\(\chi_{5415}(37,\cdot)\) \(\chi_{5415}(208,\cdot)\) \(\chi_{5415}(322,\cdot)\) \(\chi_{5415}(493,\cdot)\) \(\chi_{5415}(607,\cdot)\) \(\chi_{5415}(778,\cdot)\) \(\chi_{5415}(892,\cdot)\) \(\chi_{5415}(1063,\cdot)\) \(\chi_{5415}(1177,\cdot)\) \(\chi_{5415}(1348,\cdot)\) \(\chi_{5415}(1462,\cdot)\) \(\chi_{5415}(1633,\cdot)\) \(\chi_{5415}(1747,\cdot)\) \(\chi_{5415}(1918,\cdot)\) \(\chi_{5415}(2032,\cdot)\) \(\chi_{5415}(2203,\cdot)\) \(\chi_{5415}(2317,\cdot)\) \(\chi_{5415}(2488,\cdot)\) \(\chi_{5415}(2602,\cdot)\) \(\chi_{5415}(2773,\cdot)\) \(\chi_{5415}(3058,\cdot)\) \(\chi_{5415}(3172,\cdot)\) \(\chi_{5415}(3343,\cdot)\) \(\chi_{5415}(3457,\cdot)\) \(\chi_{5415}(3628,\cdot)\) \(\chi_{5415}(3742,\cdot)\) \(\chi_{5415}(3913,\cdot)\) \(\chi_{5415}(4027,\cdot)\) \(\chi_{5415}(4198,\cdot)\) \(\chi_{5415}(4312,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3611,2167,5056)\) → \((1,i,e\left(\frac{5}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 5415 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{76}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{11}{76}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{61}{76}\right)\) |