Basic properties
| Modulus: | \(2075\) | |
| Conductor: | \(2075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(205\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2075.s
\(\chi_{2075}(11,\cdot)\) \(\chi_{2075}(16,\cdot)\) \(\chi_{2075}(21,\cdot)\) \(\chi_{2075}(31,\cdot)\) \(\chi_{2075}(36,\cdot)\) \(\chi_{2075}(41,\cdot)\) \(\chi_{2075}(61,\cdot)\) \(\chi_{2075}(81,\cdot)\) \(\chi_{2075}(86,\cdot)\) \(\chi_{2075}(106,\cdot)\) \(\chi_{2075}(111,\cdot)\) \(\chi_{2075}(116,\cdot)\) \(\chi_{2075}(121,\cdot)\) \(\chi_{2075}(131,\cdot)\) \(\chi_{2075}(146,\cdot)\) \(\chi_{2075}(161,\cdot)\) \(\chi_{2075}(191,\cdot)\) \(\chi_{2075}(196,\cdot)\) \(\chi_{2075}(206,\cdot)\) \(\chi_{2075}(231,\cdot)\) \(\chi_{2075}(236,\cdot)\) \(\chi_{2075}(241,\cdot)\) \(\chi_{2075}(256,\cdot)\) \(\chi_{2075}(261,\cdot)\) \(\chi_{2075}(266,\cdot)\) \(\chi_{2075}(286,\cdot)\) \(\chi_{2075}(336,\cdot)\) \(\chi_{2075}(341,\cdot)\) \(\chi_{2075}(361,\cdot)\) \(\chi_{2075}(381,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{205})$ |
| Fixed field: | Number field defined by a degree 205 polynomial (not computed) |
Values on generators
\((1827,251)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{12}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2075 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{205}\right)\) | \(e\left(\frac{138}{205}\right)\) | \(e\left(\frac{38}{205}\right)\) | \(e\left(\frac{157}{205}\right)\) | \(e\left(\frac{14}{41}\right)\) | \(e\left(\frac{57}{205}\right)\) | \(e\left(\frac{71}{205}\right)\) | \(e\left(\frac{169}{205}\right)\) | \(e\left(\frac{176}{205}\right)\) | \(e\left(\frac{151}{205}\right)\) |