Basic properties
| Modulus: | \(7569\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{841}(231,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7569.y
\(\chi_{7569}(28,\cdot)\) \(\chi_{7569}(289,\cdot)\) \(\chi_{7569}(550,\cdot)\) \(\chi_{7569}(811,\cdot)\) \(\chi_{7569}(1072,\cdot)\) \(\chi_{7569}(1333,\cdot)\) \(\chi_{7569}(1594,\cdot)\) \(\chi_{7569}(1855,\cdot)\) \(\chi_{7569}(2116,\cdot)\) \(\chi_{7569}(2377,\cdot)\) \(\chi_{7569}(2638,\cdot)\) \(\chi_{7569}(2899,\cdot)\) \(\chi_{7569}(3160,\cdot)\) \(\chi_{7569}(3421,\cdot)\) \(\chi_{7569}(3682,\cdot)\) \(\chi_{7569}(3943,\cdot)\) \(\chi_{7569}(4465,\cdot)\) \(\chi_{7569}(4726,\cdot)\) \(\chi_{7569}(4987,\cdot)\) \(\chi_{7569}(5248,\cdot)\) \(\chi_{7569}(5509,\cdot)\) \(\chi_{7569}(5770,\cdot)\) \(\chi_{7569}(6031,\cdot)\) \(\chi_{7569}(6292,\cdot)\) \(\chi_{7569}(6553,\cdot)\) \(\chi_{7569}(6814,\cdot)\) \(\chi_{7569}(7075,\cdot)\) \(\chi_{7569}(7336,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((5888,1684)\) → \((1,e\left(\frac{13}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 7569 }(1072, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(-1\) | \(e\left(\frac{26}{29}\right)\) |