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 \(\chi_{575}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2300.bs
\(\chi_{2300}(17,\cdot)\) \(\chi_{2300}(33,\cdot)\) \(\chi_{2300}(37,\cdot)\) \(\chi_{2300}(53,\cdot)\) \(\chi_{2300}(97,\cdot)\) \(\chi_{2300}(113,\cdot)\) \(\chi_{2300}(153,\cdot)\) \(\chi_{2300}(217,\cdot)\) \(\chi_{2300}(237,\cdot)\) \(\chi_{2300}(273,\cdot)\) \(\chi_{2300}(297,\cdot)\) \(\chi_{2300}(313,\cdot)\) \(\chi_{2300}(333,\cdot)\) \(\chi_{2300}(337,\cdot)\) \(\chi_{2300}(373,\cdot)\) \(\chi_{2300}(433,\cdot)\) \(\chi_{2300}(477,\cdot)\) \(\chi_{2300}(497,\cdot)\) \(\chi_{2300}(513,\cdot)\) \(\chi_{2300}(517,\cdot)\) \(\chi_{2300}(573,\cdot)\) \(\chi_{2300}(613,\cdot)\) \(\chi_{2300}(617,\cdot)\) \(\chi_{2300}(677,\cdot)\) \(\chi_{2300}(697,\cdot)\) \(\chi_{2300}(733,\cdot)\) \(\chi_{2300}(753,\cdot)\) \(\chi_{2300}(773,\cdot)\) \(\chi_{2300}(797,\cdot)\) \(\chi_{2300}(833,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{3}{20}\right),e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{199}{220}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{83}{110}\right)\) |