Basic properties
| Modulus: | \(4600\) | |
| 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 \(\chi_{575}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4600.dk
\(\chi_{4600}(17,\cdot)\) \(\chi_{4600}(33,\cdot)\) \(\chi_{4600}(97,\cdot)\) \(\chi_{4600}(113,\cdot)\) \(\chi_{4600}(153,\cdot)\) \(\chi_{4600}(217,\cdot)\) \(\chi_{4600}(273,\cdot)\) \(\chi_{4600}(297,\cdot)\) \(\chi_{4600}(313,\cdot)\) \(\chi_{4600}(337,\cdot)\) \(\chi_{4600}(433,\cdot)\) \(\chi_{4600}(497,\cdot)\) \(\chi_{4600}(513,\cdot)\) \(\chi_{4600}(617,\cdot)\) \(\chi_{4600}(697,\cdot)\) \(\chi_{4600}(753,\cdot)\) \(\chi_{4600}(833,\cdot)\) \(\chi_{4600}(937,\cdot)\) \(\chi_{4600}(953,\cdot)\) \(\chi_{4600}(977,\cdot)\) \(\chi_{4600}(1017,\cdot)\) \(\chi_{4600}(1033,\cdot)\) \(\chi_{4600}(1073,\cdot)\) \(\chi_{4600}(1137,\cdot)\) \(\chi_{4600}(1217,\cdot)\) \(\chi_{4600}(1233,\cdot)\) \(\chi_{4600}(1353,\cdot)\) \(\chi_{4600}(1377,\cdot)\) \(\chi_{4600}(1417,\cdot)\) \(\chi_{4600}(1433,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((1,1,e\left(\frac{13}{20}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{149}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{3}{110}\right)\) |