Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1815}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.df
\(\chi_{5445}(53,\cdot)\) \(\chi_{5445}(152,\cdot)\) \(\chi_{5445}(278,\cdot)\) \(\chi_{5445}(368,\cdot)\) \(\chi_{5445}(377,\cdot)\) \(\chi_{5445}(422,\cdot)\) \(\chi_{5445}(467,\cdot)\) \(\chi_{5445}(548,\cdot)\) \(\chi_{5445}(647,\cdot)\) \(\chi_{5445}(773,\cdot)\) \(\chi_{5445}(818,\cdot)\) \(\chi_{5445}(863,\cdot)\) \(\chi_{5445}(872,\cdot)\) \(\chi_{5445}(917,\cdot)\) \(\chi_{5445}(962,\cdot)\) \(\chi_{5445}(1043,\cdot)\) \(\chi_{5445}(1142,\cdot)\) \(\chi_{5445}(1268,\cdot)\) \(\chi_{5445}(1313,\cdot)\) \(\chi_{5445}(1367,\cdot)\) \(\chi_{5445}(1457,\cdot)\) \(\chi_{5445}(1538,\cdot)\) \(\chi_{5445}(1637,\cdot)\) \(\chi_{5445}(1763,\cdot)\) \(\chi_{5445}(1808,\cdot)\) \(\chi_{5445}(1853,\cdot)\) \(\chi_{5445}(1862,\cdot)\) \(\chi_{5445}(1907,\cdot)\) \(\chi_{5445}(1952,\cdot)\) \(\chi_{5445}(2033,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((-1,-i,e\left(\frac{53}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{103}{220}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{9}{44}\right)\) |