Basic properties
| Modulus: | \(2300\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2300.bv
\(\chi_{2300}(13,\cdot)\) \(\chi_{2300}(73,\cdot)\) \(\chi_{2300}(77,\cdot)\) \(\chi_{2300}(117,\cdot)\) \(\chi_{2300}(133,\cdot)\) \(\chi_{2300}(173,\cdot)\) \(\chi_{2300}(177,\cdot)\) \(\chi_{2300}(197,\cdot)\) \(\chi_{2300}(213,\cdot)\) \(\chi_{2300}(233,\cdot)\) \(\chi_{2300}(317,\cdot)\) \(\chi_{2300}(353,\cdot)\) \(\chi_{2300}(377,\cdot)\) \(\chi_{2300}(397,\cdot)\) \(\chi_{2300}(417,\cdot)\) \(\chi_{2300}(453,\cdot)\) \(\chi_{2300}(473,\cdot)\) \(\chi_{2300}(533,\cdot)\) \(\chi_{2300}(537,\cdot)\) \(\chi_{2300}(577,\cdot)\) \(\chi_{2300}(633,\cdot)\) \(\chi_{2300}(637,\cdot)\) \(\chi_{2300}(653,\cdot)\) \(\chi_{2300}(673,\cdot)\) \(\chi_{2300}(717,\cdot)\) \(\chi_{2300}(777,\cdot)\) \(\chi_{2300}(813,\cdot)\) \(\chi_{2300}(817,\cdot)\) \(\chi_{2300}(837,\cdot)\) \(\chi_{2300}(853,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{93}{220}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{41}{110}\right)\) |